%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG137+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:37:00 EDT 2023

% Result   : Unsatisfiable 25.73s 4.11s
% Output   : Proof 204.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : ALG137+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.09  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Mon Aug 28 02:41:30 EDT 2023
% 0.09/0.28  % CPUTime  : 
% 0.14/0.47  ________       _____
% 0.14/0.47  ___  __ \_________(_)________________________________
% 0.14/0.47  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.14/0.47  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.14/0.47  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.14/0.47  
% 0.14/0.47  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.47  (2023-06-19)
% 0.14/0.47  
% 0.14/0.47  (c) Philipp Rümmer, 2009-2023
% 0.14/0.47  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.47                Amanda Stjerna.
% 0.14/0.47  Free software under BSD-3-Clause.
% 0.14/0.47  
% 0.14/0.47  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.47  
% 0.14/0.47  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.48  Running up to 7 provers in parallel.
% 0.14/0.49  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.49  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.49  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.49  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.49  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.49  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.49  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.60/1.10  Prover 1: Preprocessing ...
% 3.60/1.10  Prover 4: Preprocessing ...
% 3.60/1.16  Prover 0: Preprocessing ...
% 3.60/1.16  Prover 3: Preprocessing ...
% 3.60/1.16  Prover 5: Preprocessing ...
% 3.60/1.16  Prover 2: Preprocessing ...
% 3.60/1.16  Prover 6: Preprocessing ...
% 6.98/1.57  Prover 3: Constructing countermodel ...
% 6.98/1.57  Prover 2: Constructing countermodel ...
% 7.41/1.64  Prover 1: Constructing countermodel ...
% 7.41/1.66  Prover 4: Constructing countermodel ...
% 7.68/1.68  Prover 0: Constructing countermodel ...
% 7.68/1.71  Prover 6: Constructing countermodel ...
% 9.65/1.94  Prover 5: Constructing countermodel ...
% 25.73/4.11  Prover 3: proved (3619ms)
% 25.73/4.11  
% 25.73/4.11  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.73/4.11  
% 25.73/4.11  Prover 0: stopped
% 25.73/4.11  Prover 5: stopped
% 25.73/4.12  Prover 2: stopped
% 25.73/4.13  Prover 6: stopped
% 25.73/4.14  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.73/4.14  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.73/4.14  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.73/4.14  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.73/4.14  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 28.18/4.41  Prover 8: Preprocessing ...
% 28.26/4.42  Prover 7: Preprocessing ...
% 28.26/4.43  Prover 10: Preprocessing ...
% 28.26/4.45  Prover 13: Preprocessing ...
% 28.26/4.47  Prover 11: Preprocessing ...
% 28.26/4.50  Prover 8: Constructing countermodel ...
% 28.97/4.58  Prover 10: Constructing countermodel ...
% 29.59/4.63  Prover 7: Constructing countermodel ...
% 29.59/4.64  Prover 11: Constructing countermodel ...
% 30.33/4.69  Prover 13: Constructing countermodel ...
% 66.55/9.48  Prover 13: stopped
% 66.55/9.49  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 67.06/9.54  Prover 16: Preprocessing ...
% 68.27/9.68  Prover 16: Constructing countermodel ...
% 110.89/15.32  Prover 16: stopped
% 110.89/15.32  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 110.89/15.38  Prover 19: Preprocessing ...
% 111.87/15.47  Prover 19: Constructing countermodel ...
% 115.13/15.84  Prover 1: stopped
% 137.18/19.10  Prover 19: stopped
% 177.54/26.77  Prover 7: stopped
% 183.15/27.82  Prover 4: stopped
% 187.39/29.04  Prover 8: Found proof (size 1225918)
% 187.39/29.04  Prover 8: proved (24840ms)
% 187.39/29.04  Prover 10: stopped
% 187.39/29.04  Prover 11: stopped
% 187.39/29.04  
% 187.39/29.04  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 187.39/29.04  
% 190.71/30.44  % SZS output start Proof for theBenchmark
% 190.97/30.60  Assumptions after simplification:
% 190.97/30.60  ---------------------------------
% 190.97/30.60  
% 190.97/30.60    (ax1)
% 190.97/30.65    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 190.97/30.65    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 190.97/30.65      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 190.97/30.65      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 190.97/30.65      op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 190.97/30.65      op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 190.97/30.65      op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 190.97/30.65      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 190.97/30.65      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 190.97/30.65      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 190.97/30.65        e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 190.97/30.65        v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 190.97/30.65        = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 190.97/30.65        v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 190.97/30.65        v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 190.97/30.65        v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 190.97/30.65      (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 190.97/30.65        = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 190.97/30.65        = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 190.97/30.65  
% 190.97/30.65    (ax10)
% 190.97/30.65    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.65    (op(v0, e3) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 190.97/30.65      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 190.97/30.65  
% 190.97/30.65    (ax11)
% 190.97/30.65    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e3) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 190.97/30.66  
% 190.97/30.66    (ax12)
% 190.97/30.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 190.97/30.66  
% 190.97/30.66    (ax13)
% 190.97/30.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 190.97/30.66  
% 190.97/30.66    (ax14)
% 190.97/30.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e2) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 190.97/30.66  
% 190.97/30.66    (ax15)
% 190.97/30.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e2) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 190.97/30.66  
% 190.97/30.66    (ax16)
% 190.97/30.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e3) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 190.97/30.66  
% 190.97/30.66    (ax17)
% 190.97/30.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.66    (op(v0, e3) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 190.97/30.66      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 190.97/30.66  
% 190.97/30.66    (ax18)
% 190.97/30.67    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.67    (op(v0, e0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 190.97/30.67      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 190.97/30.67  
% 190.97/30.67    (ax19)
% 190.97/30.67    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.67    (op(v0, e0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 190.97/30.67      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 190.97/30.67  
% 190.97/30.67    (ax2)
% 190.97/30.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 190.97/30.68    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 190.97/30.68      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 190.97/30.68      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 190.97/30.68      op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 &
% 190.97/30.68      op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 190.97/30.68      op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 190.97/30.68      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 190.97/30.68      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 190.97/30.68      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 =
% 190.97/30.68        e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 |
% 190.97/30.68        v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 =
% 190.97/30.68        e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3
% 190.97/30.68        = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0
% 190.97/30.68        | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 =
% 190.97/30.68        e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 =
% 190.97/30.68        e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 190.97/30.68        v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 =
% 190.97/30.68        e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5
% 190.97/30.68        = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 |
% 190.97/30.68        v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0
% 190.97/30.68        | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3)
% 190.97/30.68      & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 |
% 190.97/30.68        v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 |
% 190.97/30.68        v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 |
% 190.97/30.68        v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) &
% 190.97/30.68      (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 190.97/30.68        = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 |
% 190.97/30.68            v1 = e0))))
% 190.97/30.68  
% 190.97/30.68    (ax20)
% 190.97/30.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.68    (op(v0, e1) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 190.97/30.68      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 190.97/30.68  
% 190.97/30.68    (ax21)
% 190.97/30.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.68    (op(v0, e1) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 190.97/30.68      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 190.97/30.68  
% 190.97/30.68    (ax22)
% 190.97/30.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.68    (op(v0, e3) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 190.97/30.68      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 190.97/30.68  
% 190.97/30.68    (ax23)
% 190.97/30.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.68    (op(v0, e3) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 190.97/30.68      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 190.97/30.68  
% 190.97/30.68    (ax24)
% 190.97/30.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.69    (op(v0, e0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 190.97/30.69      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 190.97/30.69  
% 190.97/30.69    (ax25)
% 190.97/30.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 190.97/30.69    (op(v0, e0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 190.97/30.69      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 190.97/30.69  
% 190.97/30.69    (ax26)
% 191.38/30.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.69    (op(v0, e1) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 191.38/30.69      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 191.38/30.69  
% 191.38/30.69    (ax27)
% 191.38/30.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.69    (op(v0, e1) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 191.38/30.69      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 191.38/30.69  
% 191.38/30.69    (ax28)
% 191.38/30.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.69    (op(v0, e2) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 191.38/30.69      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 191.38/30.69  
% 191.38/30.69    (ax29)
% 191.38/30.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.69    (op(v0, e2) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 191.38/30.69      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 191.38/30.69  
% 191.38/30.69    (ax3)
% 191.38/30.70    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 191.38/30.70    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 191.38/30.70      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 191.38/30.70      $i] :  ? [v14: $i] :  ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~
% 191.38/30.70      (v15 = v12) &  ~ (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 =
% 191.38/30.70        v13) &  ~ (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) & 
% 191.38/30.70      ~ (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12 =
% 191.38/30.70        v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 = v9) &  ~
% 191.38/30.70      (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9) &  ~ (v10 = v8) &
% 191.38/30.70       ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~ (v9 = v5) &  ~ (v9 = v1) &
% 191.38/30.70       ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6) &  ~ (v7 = v5) &  ~ (v7 = v4) & 
% 191.38/30.70      ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6 = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~
% 191.38/30.70      (v5 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~
% 191.38/30.70      (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 191.38/30.70      v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 191.38/30.70      v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 191.38/30.70      & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 191.38/30.70      op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 191.38/30.70      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 191.38/30.70      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 191.38/30.70  
% 191.38/30.70    (ax4)
% 191.38/30.70     ~ (e3 = e2) &  ~ (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~
% 191.38/30.70    (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 191.38/30.70  
% 191.38/30.70    (ax5)
% 191.38/30.70    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 191.38/30.70    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 191.38/30.70      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 191.38/30.70      $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18:
% 191.38/30.70      $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23:
% 191.38/30.70      $i] :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 191.38/30.70      $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : (op(v30, v30) = v31 &
% 191.38/30.70      op(v28, v28) = v29 & op(v26, v26) = v27 & op(v24, v24) = v25 & op(v22, v22)
% 191.38/30.70      = v23 & op(v20, v20) = v21 & op(v18, v18) = v19 & op(v16, v16) = v17 &
% 191.38/30.70      op(v14, v14) = v15 & op(v12, v12) = v13 & op(v10, v10) = v11 & op(v8, v8) =
% 191.38/30.70      v9 & op(v6, v6) = v7 & op(v4, v4) = v5 & op(v2, v2) = v3 & op(v0, v0) = v1 &
% 191.38/30.70      op(e3, e3) = v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 &
% 191.38/30.70      op(e2, e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, e0) = v4 &
% 191.38/30.70      op(e1, e3) = v26 & op(e1, e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 &
% 191.38/30.70      op(e0, e3) = v24 & op(e0, e2) = v16 & op(e0, e1) = v8 & op(e0, e0) = v0 &
% 191.38/30.70      $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) &
% 191.38/30.70      $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) &
% 191.38/30.70      $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) &
% 191.38/30.70      $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 191.38/30.70      $i(v2) & $i(v1) & $i(v0) & ((v31 = e3 & v29 = e2 & v27 = e1 & v25 = e0) |
% 191.38/30.70        (v23 = e3 & v21 = e2 & v19 = e1 & v17 = e0) | (v15 = e3 & v13 = e2 & v11 =
% 191.38/30.70          e1 & v9 = e0) | (v7 = e3 & v5 = e2 & v3 = e1 & v1 = e0)))
% 191.38/30.70  
% 191.38/30.70    (ax6)
% 191.38/30.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.71    (op(v0, e1) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 191.38/30.71      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 191.38/30.71  
% 191.38/30.71    (ax7)
% 191.38/30.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.71    (op(v0, e1) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 191.38/30.71      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 191.38/30.71  
% 191.38/30.71    (ax8)
% 191.38/30.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.71    (op(v0, e2) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 191.38/30.71      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 191.38/30.71  
% 191.38/30.71    (ax9)
% 191.38/30.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 191.38/30.71    (op(v0, e2) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 191.38/30.71      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 191.38/30.71  
% 191.38/30.71    (function-axioms)
% 191.38/30.71     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 191.38/30.71          v2) = v1) |  ~ (op(v3, v2) = v0))
% 191.38/30.71  
% 191.38/30.71  Those formulas are unsatisfiable:
% 191.38/30.71  ---------------------------------
% 191.38/30.71  
% 191.38/30.71  Begin of proof
% 191.38/30.71  | 
% 191.38/30.71  | ALPHA: (ax1) implies:
% 191.38/30.72  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 191.38/30.72  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 191.38/30.72  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 191.38/30.72  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 191.38/30.72  |          & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 191.38/30.72  |          = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 191.38/30.72  |            e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 191.38/30.72  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 191.38/30.72  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 191.38/30.72  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 191.38/30.72  |            = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 191.38/30.72  |            = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 191.38/30.72  |            v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 191.38/30.72  |            v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 191.38/30.72  |            | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 191.38/30.72  |            = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 191.38/30.72  |            e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 191.38/30.72  |          (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 191.38/30.72  |            e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 191.38/30.72  |            | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 191.38/30.72  |            = e0))
% 191.38/30.72  | 
% 191.38/30.72  | ALPHA: (ax2) implies:
% 191.38/30.73  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 191.38/30.73  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 191.38/30.73  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 191.38/30.73  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11
% 191.38/30.73  |          & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1)
% 191.38/30.73  |          = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1,
% 191.38/30.73  |            e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 191.38/30.73  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 191.38/30.73  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 191.38/30.73  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14
% 191.38/30.73  |            = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 =
% 191.38/30.73  |            e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13
% 191.38/30.73  |            = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 =
% 191.38/30.73  |            e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 =
% 191.38/30.73  |            e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 =
% 191.38/30.73  |            e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 =
% 191.38/30.73  |            e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1)
% 191.38/30.73  |          & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 191.38/30.73  |            v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) &
% 191.38/30.73  |          (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 |
% 191.38/30.73  |            v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) &
% 191.38/30.73  |          (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7
% 191.38/30.73  |            = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 =
% 191.38/30.73  |            e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 |
% 191.38/30.73  |            v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8
% 191.38/30.73  |            = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3)
% 191.38/30.73  |          & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 =
% 191.38/30.73  |            e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2
% 191.38/30.73  |            | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 191.38/30.73  |            = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 =
% 191.38/30.73  |                e0 | v1 = e0))))
% 191.38/30.73  | 
% 191.38/30.73  | ALPHA: (ax3) implies:
% 191.38/30.74  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 191.38/30.74  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 191.38/30.74  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 191.38/30.74  |         ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~ (v15 = v12) &  ~
% 191.38/30.74  |          (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 = v13) &  ~
% 191.38/30.74  |          (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) &  ~
% 191.38/30.74  |          (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12
% 191.38/30.74  |            = v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 =
% 191.38/30.74  |            v9) &  ~ (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9)
% 191.38/30.74  |          &  ~ (v10 = v8) &  ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~
% 191.38/30.74  |          (v9 = v5) &  ~ (v9 = v1) &  ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6)
% 191.38/30.74  |          &  ~ (v7 = v5) &  ~ (v7 = v4) &  ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6
% 191.38/30.74  |            = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~ (v5 = v1) &  ~ (v4 = v0) &
% 191.38/30.74  |           ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 191.38/30.74  |            v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 191.38/30.74  |            e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 191.38/30.74  |          op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 191.38/30.74  |          v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 191.38/30.74  |            e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 191.38/30.74  |          $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 191.38/30.74  |          $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 191.38/30.74  | 
% 191.38/30.74  | ALPHA: (ax4) implies:
% 191.38/30.74  |   (4)   ~ (e1 = e0)
% 191.38/30.74  |   (5)   ~ (e2 = e0)
% 191.38/30.74  |   (6)   ~ (e2 = e1)
% 191.38/30.74  |   (7)   ~ (e3 = e0)
% 191.38/30.74  |   (8)   ~ (e3 = e1)
% 191.38/30.74  |   (9)   ~ (e3 = e2)
% 191.38/30.74  | 
% 191.38/30.74  | ALPHA: (ax5) implies:
% 191.38/30.74  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 191.38/30.74  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 191.38/30.74  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 191.38/30.74  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ?
% 191.38/30.74  |         [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i]
% 191.38/30.74  |         :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 191.38/30.74  |           $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : (op(v30, v30) =
% 191.38/30.74  |           v31 & op(v28, v28) = v29 & op(v26, v26) = v27 & op(v24, v24) = v25 &
% 191.38/30.74  |           op(v22, v22) = v23 & op(v20, v20) = v21 & op(v18, v18) = v19 &
% 191.38/30.74  |           op(v16, v16) = v17 & op(v14, v14) = v15 & op(v12, v12) = v13 &
% 191.38/30.74  |           op(v10, v10) = v11 & op(v8, v8) = v9 & op(v6, v6) = v7 & op(v4, v4)
% 191.38/30.74  |           = v5 & op(v2, v2) = v3 & op(v0, v0) = v1 & op(e3, e3) = v30 & op(e3,
% 191.38/30.74  |             e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e2, e3) = v28
% 191.38/30.74  |           & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, e0) = v4 & op(e1, e3)
% 191.38/30.74  |           = v26 & op(e1, e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 &
% 191.38/30.74  |           op(e0, e3) = v24 & op(e0, e2) = v16 & op(e0, e1) = v8 & op(e0, e0) =
% 191.38/30.74  |           v0 & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) &
% 191.38/30.74  |           $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19)
% 191.38/30.75  |           & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) &
% 191.38/30.75  |           $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 191.38/30.75  |           $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v31 = e3 &
% 191.38/30.75  |               v29 = e2 & v27 = e1 & v25 = e0) | (v23 = e3 & v21 = e2 & v19 =
% 191.38/30.75  |               e1 & v17 = e0) | (v15 = e3 & v13 = e2 & v11 = e1 & v9 = e0) |
% 191.38/30.75  |             (v7 = e3 & v5 = e2 & v3 = e1 & v1 = e0)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax6) implies:
% 191.38/30.75  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e1) = v1 & op(e1,
% 191.38/30.75  |             v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e3) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax7) implies:
% 191.38/30.75  |   (12)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e1) = v1 & op(e1,
% 191.38/30.75  |             v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e2) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax8) implies:
% 191.38/30.75  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e2) = v1 & op(e2,
% 191.38/30.75  |             v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e3) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax9) implies:
% 191.38/30.75  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e2) = v1 & op(e2,
% 191.38/30.75  |             v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e1) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax10) implies:
% 191.38/30.75  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e3) = v1 & op(e3,
% 191.38/30.75  |             v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e2) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax11) implies:
% 191.38/30.75  |   (16)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e3) = v1 & op(e3,
% 191.38/30.75  |             v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e1) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax12) implies:
% 191.38/30.75  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e0) = v1 & op(e0,
% 191.38/30.75  |             v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e3) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax13) implies:
% 191.38/30.75  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e0) = v1 & op(e0,
% 191.38/30.75  |             v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.75  |               e2) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 191.38/30.75  | 
% 191.38/30.75  | ALPHA: (ax14) implies:
% 191.38/30.75  |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e2) = v1 & op(e2,
% 191.38/30.76  |             v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e3) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax15) implies:
% 191.38/30.76  |   (20)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e2) = v1 & op(e2,
% 191.38/30.76  |             v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e0) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax16) implies:
% 191.38/30.76  |   (21)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e3) = v1 & op(e3,
% 191.38/30.76  |             v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e2) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax17) implies:
% 191.38/30.76  |   (22)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e3) = v1 & op(e3,
% 191.38/30.76  |             v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e0) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax18) implies:
% 191.38/30.76  |   (23)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e0) = v1 & op(e0,
% 191.38/30.76  |             v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e3) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax19) implies:
% 191.38/30.76  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e0) = v1 & op(e0,
% 191.38/30.76  |             v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e1) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax20) implies:
% 191.38/30.76  |   (25)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e1) = v1 & op(e1,
% 191.38/30.76  |             v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e3) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax21) implies:
% 191.38/30.76  |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e1) = v1 & op(e1,
% 191.38/30.76  |             v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e0) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax22) implies:
% 191.38/30.76  |   (27)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e3) = v1 & op(e3,
% 191.38/30.76  |             v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e1) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax23) implies:
% 191.38/30.76  |   (28)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e3) = v1 & op(e3,
% 191.38/30.76  |             v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e0) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax24) implies:
% 191.38/30.76  |   (29)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e0) = v1 & op(e0,
% 191.38/30.76  |             v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e2) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax25) implies:
% 191.38/30.76  |   (30)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e0) = v1 & op(e0,
% 191.38/30.76  |             v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.76  |               e1) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 191.38/30.76  | 
% 191.38/30.76  | ALPHA: (ax26) implies:
% 191.38/30.77  |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e1) = v1 & op(e1,
% 191.38/30.77  |             v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.77  |               e2) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (ax27) implies:
% 191.38/30.77  |   (32)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e1) = v1 & op(e1,
% 191.38/30.77  |             v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.77  |               e0) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (ax28) implies:
% 191.38/30.77  |   (33)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e2) = v1 & op(e2,
% 191.38/30.77  |             v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.77  |               e1) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (ax29) implies:
% 191.38/30.77  |   (34)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v0, e2) = v1 & op(e2,
% 191.38/30.77  |             v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 191.38/30.77  |               e0) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 191.38/30.77  | 
% 191.38/30.77  | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 191.38/30.77  |   (35)  op(all_4_2, e2) = all_4_1 & op(e2, all_4_1) = all_4_0 & op(e2, e2) =
% 191.38/30.77  |         all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~ (all_4_0 = e0)
% 191.38/30.77  |           |  ~ (all_4_1 = e1) |  ~ (all_4_2 = e3))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (35) implies:
% 191.38/30.77  |   (36)  op(e2, e2) = all_4_2
% 191.38/30.77  |   (37)  op(e2, all_4_1) = all_4_0
% 191.38/30.77  |   (38)  op(all_4_2, e2) = all_4_1
% 191.38/30.77  |   (39)   ~ (all_4_0 = e0) |  ~ (all_4_1 = e1) |  ~ (all_4_2 = e3)
% 191.38/30.77  | 
% 191.38/30.77  | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 191.38/30.77  |   (40)  op(all_6_2, e3) = all_6_1 & op(e3, all_6_1) = all_6_0 & op(e3, e3) =
% 191.38/30.77  |         all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~ (all_6_0 = e1)
% 191.38/30.77  |           |  ~ (all_6_1 = e2) |  ~ (all_6_2 = e0))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (40) implies:
% 191.38/30.77  |   (41)  op(e3, e3) = all_6_2
% 191.38/30.77  |   (42)  op(e3, all_6_1) = all_6_0
% 191.38/30.77  |   (43)  op(all_6_2, e3) = all_6_1
% 191.38/30.77  |   (44)   ~ (all_6_0 = e1) |  ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 191.38/30.77  | 
% 191.38/30.77  | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 191.38/30.77  |   (45)  op(all_8_2, e3) = all_8_1 & op(e3, all_8_1) = all_8_0 & op(e3, e3) =
% 191.38/30.77  |         all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~ (all_8_0 = e2)
% 191.38/30.77  |           |  ~ (all_8_1 = e1) |  ~ (all_8_2 = e0))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (45) implies:
% 191.38/30.77  |   (46)  op(e3, e3) = all_8_2
% 191.38/30.77  |   (47)  op(e3, all_8_1) = all_8_0
% 191.38/30.77  |   (48)  op(all_8_2, e3) = all_8_1
% 191.38/30.77  |   (49)   ~ (all_8_0 = e2) |  ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 191.38/30.77  | 
% 191.38/30.77  | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 191.38/30.77  |        gives:
% 191.38/30.77  |   (50)  op(all_10_2, e1) = all_10_1 & op(e1, all_10_1) = all_10_0 & op(e1, e1)
% 191.38/30.77  |         = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & ( ~
% 191.38/30.77  |           (all_10_0 = e3) |  ~ (all_10_1 = e0) |  ~ (all_10_2 = e2))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (50) implies:
% 191.38/30.77  |   (51)  op(e1, e1) = all_10_2
% 191.38/30.77  |   (52)  op(e1, all_10_1) = all_10_0
% 191.38/30.77  |   (53)  op(all_10_2, e1) = all_10_1
% 191.38/30.77  |   (54)   ~ (all_10_0 = e3) |  ~ (all_10_1 = e0) |  ~ (all_10_2 = e2)
% 191.38/30.77  | 
% 191.38/30.77  | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 191.38/30.77  |        gives:
% 191.38/30.77  |   (55)  op(all_12_2, e3) = all_12_1 & op(e3, all_12_1) = all_12_0 & op(e3, e3)
% 191.38/30.77  |         = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & ( ~
% 191.38/30.77  |           (all_12_0 = e0) |  ~ (all_12_1 = e1) |  ~ (all_12_2 = e2))
% 191.38/30.77  | 
% 191.38/30.77  | ALPHA: (55) implies:
% 191.38/30.77  |   (56)  op(e3, e3) = all_12_2
% 191.38/30.77  |   (57)  op(e3, all_12_1) = all_12_0
% 191.38/30.77  |   (58)  op(all_12_2, e3) = all_12_1
% 191.38/30.78  |   (59)   ~ (all_12_0 = e0) |  ~ (all_12_1 = e1) |  ~ (all_12_2 = e2)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (60)  op(all_14_2, e0) = all_14_1 & op(e0, all_14_1) = all_14_0 & op(e0, e0)
% 191.38/30.78  |         = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & ( ~
% 191.38/30.78  |           (all_14_0 = e2) |  ~ (all_14_1 = e3) |  ~ (all_14_2 = e1))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (60) implies:
% 191.38/30.78  |   (61)  op(e0, e0) = all_14_2
% 191.38/30.78  |   (62)  op(e0, all_14_1) = all_14_0
% 191.38/30.78  |   (63)  op(all_14_2, e0) = all_14_1
% 191.38/30.78  |   (64)   ~ (all_14_0 = e2) |  ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (31) with fresh symbols all_16_0, all_16_1, all_16_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (65)  op(all_16_2, e1) = all_16_1 & op(e1, all_16_1) = all_16_0 & op(e1, e1)
% 191.38/30.78  |         = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & ( ~
% 191.38/30.78  |           (all_16_0 = e2) |  ~ (all_16_1 = e3) |  ~ (all_16_2 = e0))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (65) implies:
% 191.38/30.78  |   (66)  op(e1, e1) = all_16_2
% 191.38/30.78  |   (67)  op(e1, all_16_1) = all_16_0
% 191.38/30.78  |   (68)  op(all_16_2, e1) = all_16_1
% 191.38/30.78  |   (69)   ~ (all_16_0 = e2) |  ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (23) with fresh symbols all_18_0, all_18_1, all_18_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (70)  op(all_18_2, e0) = all_18_1 & op(e0, all_18_1) = all_18_0 & op(e0, e0)
% 191.38/30.78  |         = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & ( ~
% 191.38/30.78  |           (all_18_0 = e3) |  ~ (all_18_1 = e2) |  ~ (all_18_2 = e1))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (70) implies:
% 191.38/30.78  |   (71)  op(e0, e0) = all_18_2
% 191.38/30.78  |   (72)  op(e0, all_18_1) = all_18_0
% 191.38/30.78  |   (73)  op(all_18_2, e0) = all_18_1
% 191.38/30.78  |   (74)   ~ (all_18_0 = e3) |  ~ (all_18_1 = e2) |  ~ (all_18_2 = e1)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1, all_20_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (75)  op(all_20_2, e2) = all_20_1 & op(e2, all_20_1) = all_20_0 & op(e2, e2)
% 191.38/30.78  |         = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & ( ~
% 191.38/30.78  |           (all_20_0 = e3) |  ~ (all_20_1 = e0) |  ~ (all_20_2 = e1))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (75) implies:
% 191.38/30.78  |   (76)  op(e2, e2) = all_20_2
% 191.38/30.78  |   (77)  op(e2, all_20_1) = all_20_0
% 191.38/30.78  |   (78)  op(all_20_2, e2) = all_20_1
% 191.38/30.78  |   (79)   ~ (all_20_0 = e3) |  ~ (all_20_1 = e0) |  ~ (all_20_2 = e1)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (80)  op(all_22_2, e3) = all_22_1 & op(e3, all_22_1) = all_22_0 & op(e3, e3)
% 191.38/30.78  |         = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & ( ~
% 191.38/30.78  |           (all_22_0 = e0) |  ~ (all_22_1 = e2) |  ~ (all_22_2 = e1))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (80) implies:
% 191.38/30.78  |   (81)  op(e3, e3) = all_22_2
% 191.38/30.78  |   (82)  op(e3, all_22_1) = all_22_0
% 191.38/30.78  |   (83)  op(all_22_2, e3) = all_22_1
% 191.38/30.78  |   (84)   ~ (all_22_0 = e0) |  ~ (all_22_1 = e2) |  ~ (all_22_2 = e1)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1, all_24_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (85)  op(all_24_2, e0) = all_24_1 & op(e0, all_24_1) = all_24_0 & op(e0, e0)
% 191.38/30.78  |         = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & ( ~
% 191.38/30.78  |           (all_24_0 = e1) |  ~ (all_24_1 = e3) |  ~ (all_24_2 = e2))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (85) implies:
% 191.38/30.78  |   (86)  op(e0, e0) = all_24_2
% 191.38/30.78  |   (87)  op(e0, all_24_1) = all_24_0
% 191.38/30.78  |   (88)  op(all_24_2, e0) = all_24_1
% 191.38/30.78  |   (89)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1, all_26_2
% 191.38/30.78  |        gives:
% 191.38/30.78  |   (90)  op(all_26_2, e1) = all_26_1 & op(e1, all_26_1) = all_26_0 & op(e1, e1)
% 191.38/30.78  |         = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & ( ~
% 191.38/30.78  |           (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3))
% 191.38/30.78  | 
% 191.38/30.78  | ALPHA: (90) implies:
% 191.38/30.78  |   (91)  op(e1, e1) = all_26_2
% 191.38/30.78  |   (92)  op(e1, all_26_1) = all_26_0
% 191.38/30.78  |   (93)  op(all_26_2, e1) = all_26_1
% 191.38/30.78  |   (94)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 191.38/30.78  | 
% 191.38/30.78  | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2
% 191.38/30.78  |        gives:
% 191.86/30.78  |   (95)  op(all_28_2, e2) = all_28_1 & op(e2, all_28_1) = all_28_0 & op(e2, e2)
% 191.86/30.78  |         = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & ( ~
% 191.86/30.78  |           (all_28_0 = e3) |  ~ (all_28_1 = e1) |  ~ (all_28_2 = e0))
% 191.86/30.78  | 
% 191.86/30.78  | ALPHA: (95) implies:
% 191.86/30.78  |   (96)  op(e2, e2) = all_28_2
% 191.86/30.78  |   (97)  op(e2, all_28_1) = all_28_0
% 191.86/30.78  |   (98)  op(all_28_2, e2) = all_28_1
% 191.86/30.78  |   (99)   ~ (all_28_0 = e3) |  ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 191.86/30.78  | 
% 191.86/30.78  | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1, all_30_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (100)  op(all_30_2, e1) = all_30_1 & op(e1, all_30_1) = all_30_0 & op(e1,
% 191.86/30.79  |            e1) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & ( ~
% 191.86/30.79  |            (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (100) implies:
% 191.86/30.79  |   (101)  op(e1, e1) = all_30_2
% 191.86/30.79  |   (102)  op(e1, all_30_1) = all_30_0
% 191.86/30.79  |   (103)  op(all_30_2, e1) = all_30_1
% 191.86/30.79  |   (104)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1, all_32_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (105)  op(all_32_2, e2) = all_32_1 & op(e2, all_32_1) = all_32_0 & op(e2,
% 191.86/30.79  |            e2) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & ( ~
% 191.86/30.79  |            (all_32_0 = e0) |  ~ (all_32_1 = e3) |  ~ (all_32_2 = e1))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (105) implies:
% 191.86/30.79  |   (106)  op(e2, e2) = all_32_2
% 191.86/30.79  |   (107)  op(e2, all_32_1) = all_32_0
% 191.86/30.79  |   (108)  op(all_32_2, e2) = all_32_1
% 191.86/30.79  |   (109)   ~ (all_32_0 = e0) |  ~ (all_32_1 = e3) |  ~ (all_32_2 = e1)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (24) with fresh symbols all_34_0, all_34_1, all_34_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (110)  op(all_34_2, e0) = all_34_1 & op(e0, all_34_1) = all_34_0 & op(e0,
% 191.86/30.79  |            e0) = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & ( ~
% 191.86/30.79  |            (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (110) implies:
% 191.86/30.79  |   (111)  op(e0, e0) = all_34_2
% 191.86/30.79  |   (112)  op(e0, all_34_1) = all_34_0
% 191.86/30.79  |   (113)  op(all_34_2, e0) = all_34_1
% 191.86/30.79  |   (114)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1, all_36_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (115)  op(all_36_2, e1) = all_36_1 & op(e1, all_36_1) = all_36_0 & op(e1,
% 191.86/30.79  |            e1) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) & ( ~
% 191.86/30.79  |            (all_36_0 = e3) |  ~ (all_36_1 = e2) |  ~ (all_36_2 = e0))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (115) implies:
% 191.86/30.79  |   (116)  op(e1, e1) = all_36_2
% 191.86/30.79  |   (117)  op(e1, all_36_1) = all_36_0
% 191.86/30.79  |   (118)  op(all_36_2, e1) = all_36_1
% 191.86/30.79  |   (119)   ~ (all_36_0 = e3) |  ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1, all_38_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (120)  op(all_38_2, e2) = all_38_1 & op(e2, all_38_1) = all_38_0 & op(e2,
% 191.86/30.79  |            e2) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) & ( ~
% 191.86/30.79  |            (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (120) implies:
% 191.86/30.79  |   (121)  op(e2, e2) = all_38_2
% 191.86/30.79  |   (122)  op(e2, all_38_1) = all_38_0
% 191.86/30.79  |   (123)  op(all_38_2, e2) = all_38_1
% 191.86/30.79  |   (124)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (125)  op(all_40_2, e1) = all_40_1 & op(e1, all_40_1) = all_40_0 & op(e1,
% 191.86/30.79  |            e1) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & ( ~
% 191.86/30.79  |            (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (125) implies:
% 191.86/30.79  |   (126)  op(e1, e1) = all_40_2
% 191.86/30.79  |   (127)  op(e1, all_40_1) = all_40_0
% 191.86/30.79  |   (128)  op(all_40_2, e1) = all_40_1
% 191.86/30.79  |   (129)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1, all_42_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (130)  op(all_42_2, e2) = all_42_1 & op(e2, all_42_1) = all_42_0 & op(e2,
% 191.86/30.79  |            e2) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & ( ~
% 191.86/30.79  |            (all_42_0 = e1) |  ~ (all_42_1 = e0) |  ~ (all_42_2 = e3))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (130) implies:
% 191.86/30.79  |   (131)  op(e2, e2) = all_42_2
% 191.86/30.79  |   (132)  op(e2, all_42_1) = all_42_0
% 191.86/30.79  |   (133)  op(all_42_2, e2) = all_42_1
% 191.86/30.79  |   (134)   ~ (all_42_0 = e1) |  ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 191.86/30.79  | 
% 191.86/30.79  | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1, all_44_2
% 191.86/30.79  |        gives:
% 191.86/30.79  |   (135)  op(all_44_2, e3) = all_44_1 & op(e3, all_44_1) = all_44_0 & op(e3,
% 191.86/30.79  |            e3) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & ( ~
% 191.86/30.79  |            (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1))
% 191.86/30.79  | 
% 191.86/30.79  | ALPHA: (135) implies:
% 191.86/30.79  |   (136)  op(e3, e3) = all_44_2
% 191.90/30.79  |   (137)  op(e3, all_44_1) = all_44_0
% 191.90/30.79  |   (138)  op(all_44_2, e3) = all_44_1
% 191.90/30.79  |   (139)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 191.90/30.79  | 
% 191.90/30.79  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 191.90/30.79  |        gives:
% 191.90/30.79  |   (140)  op(all_46_2, e3) = all_46_1 & op(e3, all_46_1) = all_46_0 & op(e3,
% 191.90/30.79  |            e3) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) & ( ~
% 191.90/30.79  |            (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2))
% 191.90/30.79  | 
% 191.90/30.79  | ALPHA: (140) implies:
% 191.90/30.79  |   (141)  op(e3, e3) = all_46_2
% 191.90/30.79  |   (142)  op(e3, all_46_1) = all_46_0
% 191.90/30.80  |   (143)  op(all_46_2, e3) = all_46_1
% 191.90/30.80  |   (144)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 191.90/30.80  | 
% 191.90/30.80  | DELTA: instantiating (17) with fresh symbols all_48_0, all_48_1, all_48_2
% 191.90/30.80  |        gives:
% 191.90/30.80  |   (145)  op(all_48_2, e0) = all_48_1 & op(e0, all_48_1) = all_48_0 & op(e0,
% 191.90/30.80  |            e0) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & ( ~
% 191.90/30.80  |            (all_48_0 = e3) |  ~ (all_48_1 = e1) |  ~ (all_48_2 = e2))
% 191.90/30.80  | 
% 191.90/30.80  | ALPHA: (145) implies:
% 191.90/30.80  |   (146)  op(e0, e0) = all_48_2
% 191.90/30.80  |   (147)  op(e0, all_48_1) = all_48_0
% 191.90/30.80  |   (148)  op(all_48_2, e0) = all_48_1
% 191.90/30.80  | 
% 191.90/30.80  | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1, all_50_2
% 191.90/30.80  |        gives:
% 191.90/30.80  |   (149)  op(all_50_2, e0) = all_50_1 & op(e0, all_50_1) = all_50_0 & op(e0,
% 191.90/30.80  |            e0) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) & ( ~
% 191.90/30.80  |            (all_50_0 = e2) |  ~ (all_50_1 = e1) |  ~ (all_50_2 = e3))
% 191.90/30.80  | 
% 191.90/30.80  | ALPHA: (149) implies:
% 191.90/30.80  |   (150)  op(e0, e0) = all_50_2
% 191.90/30.80  |   (151)  op(e0, all_50_1) = all_50_0
% 191.90/30.80  |   (152)  op(all_50_2, e0) = all_50_1
% 191.90/30.80  |   (153)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 191.90/30.80  | 
% 191.90/30.80  | DELTA: instantiating (10) with fresh symbols all_52_0, all_52_1, all_52_2,
% 191.90/30.80  |        all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 191.90/30.80  |        all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15,
% 191.90/30.80  |        all_52_16, all_52_17, all_52_18, all_52_19, all_52_20, all_52_21,
% 191.90/30.80  |        all_52_22, all_52_23, all_52_24, all_52_25, all_52_26, all_52_27,
% 191.90/30.80  |        all_52_28, all_52_29, all_52_30, all_52_31 gives:
% 191.90/30.80  |   (154)  op(all_52_1, all_52_1) = all_52_0 & op(all_52_3, all_52_3) = all_52_2
% 191.90/30.80  |          & op(all_52_5, all_52_5) = all_52_4 & op(all_52_7, all_52_7) =
% 191.90/30.80  |          all_52_6 & op(all_52_9, all_52_9) = all_52_8 & op(all_52_11,
% 191.90/30.80  |            all_52_11) = all_52_10 & op(all_52_13, all_52_13) = all_52_12 &
% 191.90/30.80  |          op(all_52_15, all_52_15) = all_52_14 & op(all_52_17, all_52_17) =
% 191.90/30.80  |          all_52_16 & op(all_52_19, all_52_19) = all_52_18 & op(all_52_21,
% 191.90/30.80  |            all_52_21) = all_52_20 & op(all_52_23, all_52_23) = all_52_22 &
% 191.90/30.80  |          op(all_52_25, all_52_25) = all_52_24 & op(all_52_27, all_52_27) =
% 191.90/30.80  |          all_52_26 & op(all_52_29, all_52_29) = all_52_28 & op(all_52_31,
% 191.90/30.80  |            all_52_31) = all_52_30 & op(e3, e3) = all_52_1 & op(e3, e2) =
% 191.90/30.80  |          all_52_9 & op(e3, e1) = all_52_17 & op(e3, e0) = all_52_25 & op(e2,
% 191.90/30.80  |            e3) = all_52_3 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_19 &
% 191.90/30.80  |          op(e2, e0) = all_52_27 & op(e1, e3) = all_52_5 & op(e1, e2) =
% 191.90/30.80  |          all_52_13 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_29 & op(e0,
% 191.90/30.80  |            e3) = all_52_7 & op(e0, e2) = all_52_15 & op(e0, e1) = all_52_23 &
% 191.90/30.80  |          op(e0, e0) = all_52_31 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) &
% 191.90/30.80  |          $i(all_52_3) & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) &
% 191.90/30.80  |          $i(all_52_7) & $i(all_52_8) & $i(all_52_9) & $i(all_52_10) &
% 191.90/30.80  |          $i(all_52_11) & $i(all_52_12) & $i(all_52_13) & $i(all_52_14) &
% 191.90/30.80  |          $i(all_52_15) & $i(all_52_16) & $i(all_52_17) & $i(all_52_18) &
% 191.90/30.80  |          $i(all_52_19) & $i(all_52_20) & $i(all_52_21) & $i(all_52_22) &
% 191.90/30.80  |          $i(all_52_23) & $i(all_52_24) & $i(all_52_25) & $i(all_52_26) &
% 191.90/30.80  |          $i(all_52_27) & $i(all_52_28) & $i(all_52_29) & $i(all_52_30) &
% 191.90/30.80  |          $i(all_52_31) & ((all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.90/30.80  |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 191.90/30.80  |              & all_52_14 = e0) | (all_52_16 = e3 & all_52_18 = e2 & all_52_20
% 191.90/30.80  |              = e1 & all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 191.90/30.80  |              all_52_28 = e1 & all_52_30 = e0))
% 191.90/30.80  | 
% 191.90/30.80  | ALPHA: (154) implies:
% 191.90/30.80  |   (155)  op(e0, e0) = all_52_31
% 191.90/30.80  |   (156)  op(e0, e1) = all_52_23
% 191.90/30.80  |   (157)  op(e0, e2) = all_52_15
% 191.90/30.80  |   (158)  op(e0, e3) = all_52_7
% 191.90/30.80  |   (159)  op(e1, e0) = all_52_29
% 191.90/30.80  |   (160)  op(e1, e1) = all_52_21
% 191.90/30.80  |   (161)  op(e1, e2) = all_52_13
% 191.90/30.80  |   (162)  op(e1, e3) = all_52_5
% 191.90/30.80  |   (163)  op(e2, e0) = all_52_27
% 191.90/30.80  |   (164)  op(e2, e1) = all_52_19
% 191.90/30.80  |   (165)  op(e2, e2) = all_52_11
% 191.90/30.80  |   (166)  op(e2, e3) = all_52_3
% 191.90/30.80  |   (167)  op(e3, e0) = all_52_25
% 191.90/30.80  |   (168)  op(e3, e1) = all_52_17
% 191.90/30.80  |   (169)  op(e3, e2) = all_52_9
% 191.90/30.80  |   (170)  op(e3, e3) = all_52_1
% 191.90/30.80  |   (171)  op(all_52_31, all_52_31) = all_52_30
% 191.90/30.80  |   (172)  op(all_52_29, all_52_29) = all_52_28
% 191.90/30.80  |   (173)  op(all_52_27, all_52_27) = all_52_26
% 191.90/30.80  |   (174)  op(all_52_25, all_52_25) = all_52_24
% 191.90/30.80  |   (175)  op(all_52_23, all_52_23) = all_52_22
% 191.90/30.80  |   (176)  op(all_52_21, all_52_21) = all_52_20
% 191.90/30.80  |   (177)  op(all_52_19, all_52_19) = all_52_18
% 191.90/30.80  |   (178)  op(all_52_17, all_52_17) = all_52_16
% 191.90/30.80  |   (179)  op(all_52_15, all_52_15) = all_52_14
% 191.90/30.80  |   (180)  op(all_52_13, all_52_13) = all_52_12
% 191.90/30.80  |   (181)  op(all_52_11, all_52_11) = all_52_10
% 191.90/30.80  |   (182)  op(all_52_9, all_52_9) = all_52_8
% 191.90/30.80  |   (183)  op(all_52_7, all_52_7) = all_52_6
% 191.90/30.80  |   (184)  op(all_52_5, all_52_5) = all_52_4
% 191.90/30.80  |   (185)  op(all_52_3, all_52_3) = all_52_2
% 191.90/30.80  |   (186)  op(all_52_1, all_52_1) = all_52_0
% 191.90/30.80  |   (187)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 191.90/30.80  |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 191.90/30.80  |          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 191.90/30.80  |          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.90/30.80  | 
% 191.90/30.80  | DELTA: instantiating (3) with fresh symbols all_54_0, all_54_1, all_54_2,
% 191.90/30.80  |        all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 191.90/30.80  |        all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 191.96/30.81  |   (188)   ~ (all_54_0 = all_54_1) &  ~ (all_54_0 = all_54_2) &  ~ (all_54_0 =
% 191.96/30.81  |            all_54_3) &  ~ (all_54_0 = all_54_4) &  ~ (all_54_0 = all_54_8) & 
% 191.96/30.81  |          ~ (all_54_0 = all_54_12) &  ~ (all_54_1 = all_54_2) &  ~ (all_54_1 =
% 191.96/30.81  |            all_54_3) &  ~ (all_54_1 = all_54_5) &  ~ (all_54_1 = all_54_9) & 
% 191.96/30.81  |          ~ (all_54_1 = all_54_13) &  ~ (all_54_2 = all_54_3) &  ~ (all_54_2 =
% 191.96/30.81  |            all_54_6) &  ~ (all_54_2 = all_54_10) &  ~ (all_54_2 = all_54_14) &
% 191.96/30.81  |           ~ (all_54_3 = all_54_7) &  ~ (all_54_3 = all_54_11) &  ~ (all_54_3 =
% 191.96/30.81  |            all_54_15) &  ~ (all_54_4 = all_54_5) &  ~ (all_54_4 = all_54_6) & 
% 191.96/30.81  |          ~ (all_54_4 = all_54_7) &  ~ (all_54_4 = all_54_8) &  ~ (all_54_4 =
% 191.96/30.81  |            all_54_12) &  ~ (all_54_5 = all_54_6) &  ~ (all_54_5 = all_54_7) & 
% 191.96/30.81  |          ~ (all_54_5 = all_54_9) &  ~ (all_54_5 = all_54_13) &  ~ (all_54_6 =
% 191.96/30.81  |            all_54_7) &  ~ (all_54_6 = all_54_10) &  ~ (all_54_6 = all_54_14) &
% 191.96/30.81  |           ~ (all_54_7 = all_54_11) &  ~ (all_54_7 = all_54_15) &  ~ (all_54_8
% 191.96/30.81  |            = all_54_9) &  ~ (all_54_8 = all_54_10) &  ~ (all_54_8 = all_54_11)
% 191.96/30.81  |          &  ~ (all_54_8 = all_54_12) &  ~ (all_54_9 = all_54_10) &  ~
% 191.96/30.81  |          (all_54_9 = all_54_11) &  ~ (all_54_9 = all_54_13) &  ~ (all_54_10 =
% 191.96/30.81  |            all_54_11) &  ~ (all_54_10 = all_54_14) &  ~ (all_54_11 =
% 191.96/30.81  |            all_54_15) &  ~ (all_54_12 = all_54_13) &  ~ (all_54_12 =
% 191.96/30.81  |            all_54_14) &  ~ (all_54_12 = all_54_15) &  ~ (all_54_13 =
% 191.96/30.81  |            all_54_14) &  ~ (all_54_13 = all_54_15) &  ~ (all_54_14 =
% 191.96/30.81  |            all_54_15) & op(e3, e3) = all_54_0 & op(e3, e2) = all_54_4 & op(e3,
% 191.96/30.81  |            e1) = all_54_8 & op(e3, e0) = all_54_12 & op(e2, e3) = all_54_1 &
% 191.96/30.81  |          op(e2, e2) = all_54_5 & op(e2, e1) = all_54_9 & op(e2, e0) =
% 191.96/30.81  |          all_54_13 & op(e1, e3) = all_54_2 & op(e1, e2) = all_54_6 & op(e1,
% 191.96/30.81  |            e1) = all_54_10 & op(e1, e0) = all_54_14 & op(e0, e3) = all_54_3 &
% 191.96/30.81  |          op(e0, e2) = all_54_7 & op(e0, e1) = all_54_11 & op(e0, e0) =
% 191.96/30.81  |          all_54_15 & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3)
% 191.96/30.81  |          & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) & $i(all_54_7) &
% 191.96/30.81  |          $i(all_54_8) & $i(all_54_9) & $i(all_54_10) & $i(all_54_11) &
% 191.96/30.81  |          $i(all_54_12) & $i(all_54_13) & $i(all_54_14) & $i(all_54_15)
% 191.96/30.81  | 
% 191.96/30.81  | ALPHA: (188) implies:
% 191.96/30.81  |   (189)   ~ (all_54_14 = all_54_15)
% 191.96/30.81  |   (190)   ~ (all_54_13 = all_54_15)
% 191.96/30.81  |   (191)   ~ (all_54_13 = all_54_14)
% 191.96/30.81  |   (192)   ~ (all_54_12 = all_54_15)
% 191.96/30.81  |   (193)   ~ (all_54_12 = all_54_14)
% 191.96/30.81  |   (194)   ~ (all_54_12 = all_54_13)
% 191.96/30.81  |   (195)   ~ (all_54_11 = all_54_15)
% 191.96/30.81  |   (196)   ~ (all_54_10 = all_54_14)
% 191.96/30.81  |   (197)   ~ (all_54_10 = all_54_11)
% 191.96/30.81  |   (198)   ~ (all_54_9 = all_54_13)
% 191.96/30.81  |   (199)   ~ (all_54_9 = all_54_11)
% 191.96/30.81  |   (200)   ~ (all_54_9 = all_54_10)
% 191.96/30.81  |   (201)   ~ (all_54_8 = all_54_12)
% 191.96/30.81  |   (202)   ~ (all_54_8 = all_54_11)
% 191.96/30.81  |   (203)   ~ (all_54_8 = all_54_10)
% 191.96/30.81  |   (204)   ~ (all_54_8 = all_54_9)
% 191.96/30.81  |   (205)   ~ (all_54_7 = all_54_15)
% 191.96/30.81  |   (206)   ~ (all_54_7 = all_54_11)
% 191.96/30.81  |   (207)   ~ (all_54_6 = all_54_14)
% 191.96/30.81  |   (208)   ~ (all_54_6 = all_54_10)
% 191.96/30.81  |   (209)   ~ (all_54_6 = all_54_7)
% 191.96/30.81  |   (210)   ~ (all_54_5 = all_54_13)
% 191.96/30.81  |   (211)   ~ (all_54_5 = all_54_9)
% 191.96/30.81  |   (212)   ~ (all_54_5 = all_54_7)
% 191.96/30.81  |   (213)   ~ (all_54_5 = all_54_6)
% 191.96/30.81  |   (214)   ~ (all_54_4 = all_54_12)
% 191.96/30.81  |   (215)   ~ (all_54_4 = all_54_8)
% 191.96/30.81  |   (216)   ~ (all_54_4 = all_54_7)
% 191.96/30.81  |   (217)   ~ (all_54_4 = all_54_6)
% 191.96/30.81  |   (218)   ~ (all_54_4 = all_54_5)
% 191.96/30.81  |   (219)   ~ (all_54_3 = all_54_15)
% 191.96/30.81  |   (220)   ~ (all_54_3 = all_54_11)
% 191.96/30.81  |   (221)   ~ (all_54_3 = all_54_7)
% 191.96/30.81  |   (222)   ~ (all_54_2 = all_54_14)
% 191.96/30.81  |   (223)   ~ (all_54_2 = all_54_10)
% 191.96/30.81  |   (224)   ~ (all_54_2 = all_54_6)
% 191.96/30.81  |   (225)   ~ (all_54_2 = all_54_3)
% 191.96/30.81  |   (226)   ~ (all_54_1 = all_54_13)
% 191.96/30.81  |   (227)   ~ (all_54_1 = all_54_9)
% 191.96/30.81  |   (228)   ~ (all_54_1 = all_54_5)
% 191.96/30.81  |   (229)   ~ (all_54_1 = all_54_3)
% 191.96/30.81  |   (230)   ~ (all_54_1 = all_54_2)
% 191.96/30.81  |   (231)   ~ (all_54_0 = all_54_12)
% 191.96/30.81  |   (232)   ~ (all_54_0 = all_54_8)
% 191.96/30.81  |   (233)   ~ (all_54_0 = all_54_4)
% 191.96/30.81  |   (234)   ~ (all_54_0 = all_54_3)
% 191.96/30.81  |   (235)   ~ (all_54_0 = all_54_2)
% 191.96/30.81  |   (236)   ~ (all_54_0 = all_54_1)
% 191.96/30.81  |   (237)  op(e0, e0) = all_54_15
% 191.96/30.81  |   (238)  op(e0, e1) = all_54_11
% 191.96/30.81  |   (239)  op(e0, e2) = all_54_7
% 191.96/30.81  |   (240)  op(e0, e3) = all_54_3
% 191.96/30.81  |   (241)  op(e1, e0) = all_54_14
% 191.96/30.81  |   (242)  op(e1, e1) = all_54_10
% 191.96/30.81  |   (243)  op(e1, e2) = all_54_6
% 191.96/30.81  |   (244)  op(e1, e3) = all_54_2
% 191.96/30.81  |   (245)  op(e2, e0) = all_54_13
% 191.96/30.81  |   (246)  op(e2, e1) = all_54_9
% 191.96/30.81  |   (247)  op(e2, e2) = all_54_5
% 191.96/30.81  |   (248)  op(e2, e3) = all_54_1
% 191.96/30.81  |   (249)  op(e3, e0) = all_54_12
% 191.96/30.81  |   (250)  op(e3, e1) = all_54_8
% 191.96/30.81  |   (251)  op(e3, e2) = all_54_4
% 191.96/30.81  |   (252)  op(e3, e3) = all_54_0
% 191.96/30.81  | 
% 191.96/30.81  | DELTA: instantiating (1) with fresh symbols all_56_0, all_56_1, all_56_2,
% 191.96/30.81  |        all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 191.96/30.81  |        all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 191.96/30.81  |   (253)  op(e3, e3) = all_56_0 & op(e3, e2) = all_56_1 & op(e3, e1) = all_56_2
% 191.96/30.81  |          & op(e3, e0) = all_56_3 & op(e2, e3) = all_56_4 & op(e2, e2) =
% 191.96/30.81  |          all_56_5 & op(e2, e1) = all_56_6 & op(e2, e0) = all_56_7 & op(e1, e3)
% 191.96/30.81  |          = all_56_8 & op(e1, e2) = all_56_9 & op(e1, e1) = all_56_10 & op(e1,
% 191.96/30.81  |            e0) = all_56_11 & op(e0, e3) = all_56_12 & op(e0, e2) = all_56_13 &
% 191.96/30.81  |          op(e0, e1) = all_56_14 & op(e0, e0) = all_56_15 & $i(all_56_0) &
% 191.96/30.81  |          $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) &
% 191.96/30.81  |          $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & $i(all_56_8) &
% 191.96/30.82  |          $i(all_56_9) & $i(all_56_10) & $i(all_56_11) & $i(all_56_12) &
% 191.96/30.82  |          $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & (all_56_0 = e3 |
% 191.96/30.82  |            all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0) & (all_56_1 = e3 |
% 191.96/30.82  |            all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0) & (all_56_2 = e3 |
% 191.96/30.82  |            all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0) & (all_56_3 = e3 |
% 191.96/30.82  |            all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0) & (all_56_4 = e3 |
% 191.96/30.82  |            all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0) & (all_56_5 = e3 |
% 191.96/30.82  |            all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0) & (all_56_6 = e3 |
% 191.96/30.82  |            all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0) & (all_56_7 = e3 |
% 191.96/30.82  |            all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0) & (all_56_8 = e3 |
% 191.96/30.82  |            all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0) & (all_56_9 = e3 |
% 191.96/30.82  |            all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0) & (all_56_10 = e3 |
% 191.96/30.82  |            all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0) & (all_56_11 = e3
% 191.96/30.82  |            | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0) & (all_56_12 =
% 191.96/30.82  |            e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0) & (all_56_13
% 191.96/30.82  |            = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0) &
% 191.96/30.82  |          (all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0) &
% 191.96/30.82  |          (all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0)
% 191.96/30.82  | 
% 191.96/30.82  | ALPHA: (253) implies:
% 191.96/30.82  |   (254)  op(e0, e0) = all_56_15
% 191.96/30.82  |   (255)  op(e0, e1) = all_56_14
% 191.96/30.82  |   (256)  op(e0, e2) = all_56_13
% 191.96/30.82  |   (257)  op(e0, e3) = all_56_12
% 191.96/30.82  |   (258)  op(e1, e0) = all_56_11
% 191.96/30.82  |   (259)  op(e1, e1) = all_56_10
% 191.96/30.82  |   (260)  op(e1, e2) = all_56_9
% 191.96/30.82  |   (261)  op(e1, e3) = all_56_8
% 191.96/30.82  |   (262)  op(e2, e0) = all_56_7
% 191.96/30.82  |   (263)  op(e2, e1) = all_56_6
% 191.96/30.82  |   (264)  op(e2, e2) = all_56_5
% 191.96/30.82  |   (265)  op(e2, e3) = all_56_4
% 191.96/30.82  |   (266)  op(e3, e0) = all_56_3
% 191.96/30.82  |   (267)  op(e3, e1) = all_56_2
% 191.96/30.82  |   (268)  op(e3, e2) = all_56_1
% 191.96/30.82  |   (269)  op(e3, e3) = all_56_0
% 191.96/30.82  |   (270)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 191.96/30.82  |   (271)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 191.96/30.82  |   (272)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 191.96/30.82  |   (273)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 191.96/30.82  |   (274)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 191.96/30.82  |   (275)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 191.96/30.82  |   (276)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 191.96/30.82  |   (277)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 191.96/30.82  |   (278)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 191.96/30.82  |   (279)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 191.96/30.82  |   (280)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 191.96/30.82  |   (281)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 191.96/30.82  |   (282)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 191.96/30.82  |   (283)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 191.96/30.82  |   (284)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 191.96/30.82  |   (285)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 191.96/30.82  | 
% 191.96/30.82  | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 191.96/30.82  |        all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 191.96/30.82  |        all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 191.96/30.82  |   (286)  op(e3, e3) = all_58_0 & op(e3, e2) = all_58_1 & op(e3, e1) = all_58_4
% 191.96/30.82  |          & op(e3, e0) = all_58_9 & op(e2, e3) = all_58_2 & op(e2, e2) =
% 191.96/30.82  |          all_58_3 & op(e2, e1) = all_58_5 & op(e2, e0) = all_58_10 & op(e1,
% 191.96/30.82  |            e3) = all_58_6 & op(e1, e2) = all_58_7 & op(e1, e1) = all_58_8 &
% 191.96/30.82  |          op(e1, e0) = all_58_11 & op(e0, e3) = all_58_12 & op(e0, e2) =
% 191.96/30.82  |          all_58_13 & op(e0, e1) = all_58_14 & op(e0, e0) = all_58_15 &
% 191.96/30.82  |          $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) &
% 191.96/30.82  |          $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) &
% 191.96/30.82  |          $i(all_58_8) & $i(all_58_9) & $i(all_58_10) & $i(all_58_11) &
% 191.96/30.82  |          $i(all_58_12) & $i(all_58_13) & $i(all_58_14) & $i(all_58_15) &
% 191.96/30.82  |          (all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3) &
% 191.96/30.82  |          (all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3) &
% 191.96/30.82  |          (all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2) &
% 191.96/30.82  |          (all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2) &
% 191.96/30.82  |          (all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1) &
% 191.96/30.82  |          (all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1) &
% 191.96/30.82  |          (all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0) &
% 191.96/30.82  |          (all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0) &
% 191.96/30.82  |          (all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3) &
% 191.96/30.82  |          (all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2) &
% 191.96/30.82  |          (all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1) &
% 191.96/30.82  |          (all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0) &
% 191.96/30.82  |          (all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3) &
% 191.96/30.82  |          (all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2) &
% 191.96/30.82  |          (all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1) &
% 191.96/30.82  |          (all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0) &
% 191.96/30.82  |          (all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3) &
% 191.96/30.82  |          (all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2) &
% 191.96/30.82  |          (all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1) &
% 191.96/30.82  |          (all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0) &
% 191.96/30.82  |          (all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3) &
% 191.96/30.82  |          (all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2) &
% 191.96/30.82  |          (all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1) &
% 191.96/30.82  |          (all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0) &
% 191.96/30.82  |          (all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3) &
% 191.96/30.82  |          (all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2) &
% 191.96/30.82  |          (all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1) &
% 191.96/30.82  |          (all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3) &
% 191.96/30.82  |          (all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2) &
% 191.96/30.82  |          (all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1) &
% 191.96/30.82  |          (all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 191.96/30.82  |              & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)))
% 191.96/30.82  | 
% 191.96/30.82  | ALPHA: (286) implies:
% 191.96/30.82  |   (287)  op(e0, e0) = all_58_15
% 191.96/30.82  |   (288)  op(e0, e1) = all_58_14
% 191.96/30.82  |   (289)  op(e0, e2) = all_58_13
% 191.96/30.82  |   (290)  op(e0, e3) = all_58_12
% 191.96/30.82  |   (291)  op(e1, e0) = all_58_11
% 191.96/30.82  |   (292)  op(e1, e1) = all_58_8
% 191.96/30.83  |   (293)  op(e1, e2) = all_58_7
% 191.96/30.83  |   (294)  op(e1, e3) = all_58_6
% 191.96/30.83  |   (295)  op(e2, e0) = all_58_10
% 191.96/30.83  |   (296)  op(e2, e1) = all_58_5
% 191.96/30.83  |   (297)  op(e2, e2) = all_58_3
% 191.96/30.83  |   (298)  op(e2, e3) = all_58_2
% 191.96/30.83  |   (299)  op(e3, e0) = all_58_9
% 191.96/30.83  |   (300)  op(e3, e1) = all_58_4
% 191.96/30.83  |   (301)  op(e3, e2) = all_58_1
% 191.96/30.83  |   (302)  op(e3, e3) = all_58_0
% 191.96/30.83  |   (303)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 191.96/30.83  |            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 191.96/30.83  |   (304)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 191.96/30.83  |   (305)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 191.96/30.83  |   (306)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 191.96/30.83  |   (307)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 191.96/30.83  |   (308)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 191.96/30.83  |   (309)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 191.96/30.83  |   (310)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 191.96/30.83  |   (311)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 191.96/30.83  |   (312)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 191.96/30.83  |   (313)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 191.96/30.83  |   (314)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 191.96/30.83  |   (315)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 191.96/30.83  |   (316)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 191.96/30.83  |   (317)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 191.96/30.83  |   (318)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 191.96/30.83  |   (319)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 191.96/30.83  |   (320)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 191.96/30.83  |   (321)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 191.96/30.83  |   (322)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 191.96/30.83  |   (323)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 191.96/30.83  |   (324)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 191.96/30.83  |   (325)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 191.96/30.83  |   (326)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 191.96/30.83  |   (327)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 191.96/30.83  |   (328)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 191.96/30.83  |   (329)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 191.96/30.83  |   (330)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 191.96/30.83  |   (331)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 191.96/30.83  |   (332)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 191.96/30.83  |   (333)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_50_2, e0, e0,
% 191.96/30.83  |              simplifying with (111), (150) gives:
% 191.96/30.83  |   (334)  all_50_2 = all_34_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_14_2, all_50_2, e0, e0,
% 191.96/30.83  |              simplifying with (61), (150) gives:
% 191.96/30.83  |   (335)  all_50_2 = all_14_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_52_31, all_54_15, e0,
% 191.96/30.83  |              e0, simplifying with (155), (237) gives:
% 191.96/30.83  |   (336)  all_54_15 = all_52_31
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_54_15, e0, e0,
% 191.96/30.83  |              simplifying with (146), (237) gives:
% 191.96/30.83  |   (337)  all_54_15 = all_48_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_56_15, e0, e0,
% 191.96/30.83  |              simplifying with (146), (254) gives:
% 191.96/30.83  |   (338)  all_56_15 = all_48_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_56_15, e0, e0,
% 191.96/30.83  |              simplifying with (111), (254) gives:
% 191.96/30.83  |   (339)  all_56_15 = all_34_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_56_15, e0, e0,
% 191.96/30.83  |              simplifying with (86), (254) gives:
% 191.96/30.83  |   (340)  all_56_15 = all_24_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_54_15, all_58_15, e0,
% 191.96/30.83  |              e0, simplifying with (237), (287) gives:
% 191.96/30.83  |   (341)  all_58_15 = all_54_15
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_58_15, e0, e0,
% 191.96/30.83  |              simplifying with (71), (287) gives:
% 191.96/30.83  |   (342)  all_58_15 = all_18_2
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_52_23, all_56_14, e1,
% 191.96/30.83  |              e0, simplifying with (156), (255) gives:
% 191.96/30.83  |   (343)  all_56_14 = all_52_23
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_56_14, all_58_14, e1,
% 191.96/30.83  |              e0, simplifying with (255), (288) gives:
% 191.96/30.83  |   (344)  all_58_14 = all_56_14
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_54_11, all_58_14, e1,
% 191.96/30.83  |              e0, simplifying with (238), (288) gives:
% 191.96/30.83  |   (345)  all_58_14 = all_54_11
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_52_15, all_56_13, e2,
% 191.96/30.83  |              e0, simplifying with (157), (256) gives:
% 191.96/30.83  |   (346)  all_56_13 = all_52_15
% 191.96/30.83  | 
% 191.96/30.83  | GROUND_INST: instantiating (function-axioms) with all_56_13, all_58_13, e2,
% 191.96/30.83  |              e0, simplifying with (256), (289) gives:
% 191.96/30.83  |   (347)  all_58_13 = all_56_13
% 191.96/30.83  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_7, all_58_13, e2, e0,
% 191.96/30.84  |              simplifying with (239), (289) gives:
% 191.96/30.84  |   (348)  all_58_13 = all_54_7
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_3, all_56_12, e3, e0,
% 191.96/30.84  |              simplifying with (240), (257) gives:
% 191.96/30.84  |   (349)  all_56_12 = all_54_3
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_12, all_58_12, e3,
% 191.96/30.84  |              e0, simplifying with (257), (290) gives:
% 191.96/30.84  |   (350)  all_58_12 = all_56_12
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_7, all_58_12, e3, e0,
% 191.96/30.84  |              simplifying with (158), (290) gives:
% 191.96/30.84  |   (351)  all_58_12 = all_52_7
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_29, all_56_11, e0,
% 191.96/30.84  |              e1, simplifying with (159), (258) gives:
% 191.96/30.84  |   (352)  all_56_11 = all_52_29
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_11, all_58_11, e0,
% 191.96/30.84  |              e1, simplifying with (258), (291) gives:
% 191.96/30.84  |   (353)  all_58_11 = all_56_11
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_14, all_58_11, e0,
% 191.96/30.84  |              e1, simplifying with (241), (291) gives:
% 191.96/30.84  |   (354)  all_58_11 = all_54_14
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_36_2, e1, e1,
% 191.96/30.84  |              simplifying with (101), (116) gives:
% 191.96/30.84  |   (355)  all_36_2 = all_30_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_36_2, all_40_2, e1, e1,
% 191.96/30.84  |              simplifying with (116), (126) gives:
% 191.96/30.84  |   (356)  all_40_2 = all_36_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_40_2, all_52_21, e1, e1,
% 191.96/30.84  |              simplifying with (126), (160) gives:
% 191.96/30.84  |   (357)  all_52_21 = all_40_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_54_10, e1, e1,
% 191.96/30.84  |              simplifying with (101), (242) gives:
% 191.96/30.84  |   (358)  all_54_10 = all_30_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_16_2, all_54_10, e1, e1,
% 191.96/30.84  |              simplifying with (66), (242) gives:
% 191.96/30.84  |   (359)  all_54_10 = all_16_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_56_10, e1, e1,
% 191.96/30.84  |              simplifying with (101), (259) gives:
% 191.96/30.84  |   (360)  all_56_10 = all_30_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_10_2, all_56_10, e1, e1,
% 191.96/30.84  |              simplifying with (51), (259) gives:
% 191.96/30.84  |   (361)  all_56_10 = all_10_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_21, all_58_8, e1, e1,
% 191.96/30.84  |              simplifying with (160), (292) gives:
% 191.96/30.84  |   (362)  all_58_8 = all_52_21
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_26_2, all_58_8, e1, e1,
% 191.96/30.84  |              simplifying with (91), (292) gives:
% 191.96/30.84  |   (363)  all_58_8 = all_26_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_6, all_56_9, e2, e1,
% 191.96/30.84  |              simplifying with (243), (260) gives:
% 191.96/30.84  |   (364)  all_56_9 = all_54_6
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_7, e2, e1,
% 191.96/30.84  |              simplifying with (260), (293) gives:
% 191.96/30.84  |   (365)  all_58_7 = all_56_9
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_13, all_58_7, e2, e1,
% 191.96/30.84  |              simplifying with (161), (293) gives:
% 191.96/30.84  |   (366)  all_58_7 = all_52_13
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_8, e3, e1,
% 191.96/30.84  |              simplifying with (162), (261) gives:
% 191.96/30.84  |   (367)  all_56_8 = all_52_5
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_8, all_58_6, e3, e1,
% 191.96/30.84  |              simplifying with (261), (294) gives:
% 191.96/30.84  |   (368)  all_58_6 = all_56_8
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_2, all_58_6, e3, e1,
% 191.96/30.84  |              simplifying with (244), (294) gives:
% 191.96/30.84  |   (369)  all_58_6 = all_54_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_13, all_56_7, e0, e2,
% 191.96/30.84  |              simplifying with (245), (262) gives:
% 191.96/30.84  |   (370)  all_56_7 = all_54_13
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_10, e0, e2,
% 191.96/30.84  |              simplifying with (262), (295) gives:
% 191.96/30.84  |   (371)  all_58_10 = all_56_7
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_27, all_58_10, e0,
% 191.96/30.84  |              e2, simplifying with (163), (295) gives:
% 191.96/30.84  |   (372)  all_58_10 = all_52_27
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_6, e1, e2,
% 191.96/30.84  |              simplifying with (246), (263) gives:
% 191.96/30.84  |   (373)  all_56_6 = all_54_9
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_6, all_58_5, e1, e2,
% 191.96/30.84  |              simplifying with (263), (296) gives:
% 191.96/30.84  |   (374)  all_58_5 = all_56_6
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_19, all_58_5, e1, e2,
% 191.96/30.84  |              simplifying with (164), (296) gives:
% 191.96/30.84  |   (375)  all_58_5 = all_52_19
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_4_2, all_28_2, e2, e2,
% 191.96/30.84  |              simplifying with (36), (96) gives:
% 191.96/30.84  |   (376)  all_28_2 = all_4_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_5, e2, e2,
% 191.96/30.84  |              simplifying with (165), (247) gives:
% 191.96/30.84  |   (377)  all_54_5 = all_52_11
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_32_2, all_54_5, e2, e2,
% 191.96/30.84  |              simplifying with (106), (247) gives:
% 191.96/30.84  |   (378)  all_54_5 = all_32_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_54_5, e2, e2,
% 191.96/30.84  |              simplifying with (96), (247) gives:
% 191.96/30.84  |   (379)  all_54_5 = all_28_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_54_5, e2, e2,
% 191.96/30.84  |              simplifying with (76), (247) gives:
% 191.96/30.84  |   (380)  all_54_5 = all_20_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_56_5, e2, e2,
% 191.96/30.84  |              simplifying with (165), (264) gives:
% 191.96/30.84  |   (381)  all_56_5 = all_52_11
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_38_2, all_56_5, e2, e2,
% 191.96/30.84  |              simplifying with (121), (264) gives:
% 191.96/30.84  |   (382)  all_56_5 = all_38_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_5, all_58_3, e2, e2,
% 191.96/30.84  |              simplifying with (247), (297) gives:
% 191.96/30.84  |   (383)  all_58_3 = all_54_5
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_42_2, all_58_3, e2, e2,
% 191.96/30.84  |              simplifying with (131), (297) gives:
% 191.96/30.84  |   (384)  all_58_3 = all_42_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_1, all_56_4, e3, e2,
% 191.96/30.84  |              simplifying with (248), (265) gives:
% 191.96/30.84  |   (385)  all_56_4 = all_54_1
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_4, all_58_2, e3, e2,
% 191.96/30.84  |              simplifying with (265), (298) gives:
% 191.96/30.84  |   (386)  all_58_2 = all_56_4
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_3, all_58_2, e3, e2,
% 191.96/30.84  |              simplifying with (166), (298) gives:
% 191.96/30.84  |   (387)  all_58_2 = all_52_3
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_25, all_56_3, e0, e3,
% 191.96/30.84  |              simplifying with (167), (266) gives:
% 191.96/30.84  |   (388)  all_56_3 = all_52_25
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_3, all_58_9, e0, e3,
% 191.96/30.84  |              simplifying with (266), (299) gives:
% 191.96/30.84  |   (389)  all_58_9 = all_56_3
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_12, all_58_9, e0, e3,
% 191.96/30.84  |              simplifying with (249), (299) gives:
% 191.96/30.84  |   (390)  all_58_9 = all_54_12
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_8, all_56_2, e1, e3,
% 191.96/30.84  |              simplifying with (250), (267) gives:
% 191.96/30.84  |   (391)  all_56_2 = all_54_8
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_2, all_58_4, e1, e3,
% 191.96/30.84  |              simplifying with (267), (300) gives:
% 191.96/30.84  |   (392)  all_58_4 = all_56_2
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_17, all_58_4, e1, e3,
% 191.96/30.84  |              simplifying with (168), (300) gives:
% 191.96/30.84  |   (393)  all_58_4 = all_52_17
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_52_9, all_56_1, e2, e3,
% 191.96/30.84  |              simplifying with (169), (268) gives:
% 191.96/30.84  |   (394)  all_56_1 = all_52_9
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_56_1, all_58_1, e2, e3,
% 191.96/30.84  |              simplifying with (268), (301) gives:
% 191.96/30.84  |   (395)  all_58_1 = all_56_1
% 191.96/30.84  | 
% 191.96/30.84  | GROUND_INST: instantiating (function-axioms) with all_54_4, all_58_1, e2, e3,
% 191.96/30.85  |              simplifying with (251), (301) gives:
% 191.96/30.85  |   (396)  all_58_1 = all_54_4
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_22_2, e3, e3,
% 191.96/30.85  |              simplifying with (56), (81) gives:
% 191.96/30.85  |   (397)  all_22_2 = all_12_2
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_44_2, e3, e3,
% 191.96/30.85  |              simplifying with (81), (136) gives:
% 191.96/30.85  |   (398)  all_44_2 = all_22_2
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_44_2, all_46_2, e3, e3,
% 191.96/30.85  |              simplifying with (136), (141) gives:
% 191.96/30.85  |   (399)  all_46_2 = all_44_2
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_52_1, e3, e3,
% 191.96/30.85  |              simplifying with (56), (170) gives:
% 191.96/30.85  |   (400)  all_52_1 = all_12_2
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_54_0, e3, e3,
% 191.96/30.85  |              simplifying with (141), (252) gives:
% 191.96/30.85  |   (401)  all_54_0 = all_46_2
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_0, e3, e3,
% 191.96/30.85  |              simplifying with (252), (269) gives:
% 191.96/30.85  |   (402)  all_56_0 = all_54_0
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_8_2, all_56_0, e3, e3,
% 191.96/30.85  |              simplifying with (46), (269) gives:
% 191.96/30.85  |   (403)  all_56_0 = all_8_2
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_0, e3, e3,
% 191.96/30.85  |              simplifying with (170), (302) gives:
% 191.96/30.85  |   (404)  all_58_0 = all_52_1
% 191.96/30.85  | 
% 191.96/30.85  | GROUND_INST: instantiating (function-axioms) with all_6_2, all_58_0, e3, e3,
% 191.96/30.85  |              simplifying with (41), (302) gives:
% 191.96/30.85  |   (405)  all_58_0 = all_6_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (404), (405) imply:
% 191.96/30.85  |   (406)  all_52_1 = all_6_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (406) implies:
% 191.96/30.85  |   (407)  all_52_1 = all_6_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (395), (396) imply:
% 191.96/30.85  |   (408)  all_56_1 = all_54_4
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (408) implies:
% 191.96/30.85  |   (409)  all_56_1 = all_54_4
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (386), (387) imply:
% 191.96/30.85  |   (410)  all_56_4 = all_52_3
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (410) implies:
% 191.96/30.85  |   (411)  all_56_4 = all_52_3
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (383), (384) imply:
% 191.96/30.85  |   (412)  all_54_5 = all_42_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (412) implies:
% 191.96/30.85  |   (413)  all_54_5 = all_42_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (392), (393) imply:
% 191.96/30.85  |   (414)  all_56_2 = all_52_17
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (414) implies:
% 191.96/30.85  |   (415)  all_56_2 = all_52_17
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (374), (375) imply:
% 191.96/30.85  |   (416)  all_56_6 = all_52_19
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (416) implies:
% 191.96/30.85  |   (417)  all_56_6 = all_52_19
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (368), (369) imply:
% 191.96/30.85  |   (418)  all_56_8 = all_54_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (418) implies:
% 191.96/30.85  |   (419)  all_56_8 = all_54_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (365), (366) imply:
% 191.96/30.85  |   (420)  all_56_9 = all_52_13
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (420) implies:
% 191.96/30.85  |   (421)  all_56_9 = all_52_13
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (362), (363) imply:
% 191.96/30.85  |   (422)  all_52_21 = all_26_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (422) implies:
% 191.96/30.85  |   (423)  all_52_21 = all_26_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (389), (390) imply:
% 191.96/30.85  |   (424)  all_56_3 = all_54_12
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (424) implies:
% 191.96/30.85  |   (425)  all_56_3 = all_54_12
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (371), (372) imply:
% 191.96/30.85  |   (426)  all_56_7 = all_52_27
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (426) implies:
% 191.96/30.85  |   (427)  all_56_7 = all_52_27
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (353), (354) imply:
% 191.96/30.85  |   (428)  all_56_11 = all_54_14
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (428) implies:
% 191.96/30.85  |   (429)  all_56_11 = all_54_14
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (350), (351) imply:
% 191.96/30.85  |   (430)  all_56_12 = all_52_7
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (430) implies:
% 191.96/30.85  |   (431)  all_56_12 = all_52_7
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (347), (348) imply:
% 191.96/30.85  |   (432)  all_56_13 = all_54_7
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (432) implies:
% 191.96/30.85  |   (433)  all_56_13 = all_54_7
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (344), (345) imply:
% 191.96/30.85  |   (434)  all_56_14 = all_54_11
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (434) implies:
% 191.96/30.85  |   (435)  all_56_14 = all_54_11
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (341), (342) imply:
% 191.96/30.85  |   (436)  all_54_15 = all_18_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (436) implies:
% 191.96/30.85  |   (437)  all_54_15 = all_18_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (402), (403) imply:
% 191.96/30.85  |   (438)  all_54_0 = all_8_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (438) implies:
% 191.96/30.85  |   (439)  all_54_0 = all_8_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (394), (409) imply:
% 191.96/30.85  |   (440)  all_54_4 = all_52_9
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (440) implies:
% 191.96/30.85  |   (441)  all_54_4 = all_52_9
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (391), (415) imply:
% 191.96/30.85  |   (442)  all_54_8 = all_52_17
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (442) implies:
% 191.96/30.85  |   (443)  all_54_8 = all_52_17
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (388), (425) imply:
% 191.96/30.85  |   (444)  all_54_12 = all_52_25
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (444) implies:
% 191.96/30.85  |   (445)  all_54_12 = all_52_25
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (385), (411) imply:
% 191.96/30.85  |   (446)  all_54_1 = all_52_3
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (446) implies:
% 191.96/30.85  |   (447)  all_54_1 = all_52_3
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (381), (382) imply:
% 191.96/30.85  |   (448)  all_52_11 = all_38_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (448) implies:
% 191.96/30.85  |   (449)  all_52_11 = all_38_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (373), (417) imply:
% 191.96/30.85  |   (450)  all_54_9 = all_52_19
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (450) implies:
% 191.96/30.85  |   (451)  all_54_9 = all_52_19
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (370), (427) imply:
% 191.96/30.85  |   (452)  all_54_13 = all_52_27
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (452) implies:
% 191.96/30.85  |   (453)  all_54_13 = all_52_27
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (367), (419) imply:
% 191.96/30.85  |   (454)  all_54_2 = all_52_5
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (454) implies:
% 191.96/30.85  |   (455)  all_54_2 = all_52_5
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (364), (421) imply:
% 191.96/30.85  |   (456)  all_54_6 = all_52_13
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (456) implies:
% 191.96/30.85  |   (457)  all_54_6 = all_52_13
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (360), (361) imply:
% 191.96/30.85  |   (458)  all_30_2 = all_10_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (458) implies:
% 191.96/30.85  |   (459)  all_30_2 = all_10_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (352), (429) imply:
% 191.96/30.85  |   (460)  all_54_14 = all_52_29
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (349), (431) imply:
% 191.96/30.85  |   (461)  all_54_3 = all_52_7
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (461) implies:
% 191.96/30.85  |   (462)  all_54_3 = all_52_7
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (346), (433) imply:
% 191.96/30.85  |   (463)  all_54_7 = all_52_15
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (463) implies:
% 191.96/30.85  |   (464)  all_54_7 = all_52_15
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (343), (435) imply:
% 191.96/30.85  |   (465)  all_54_11 = all_52_23
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (465) implies:
% 191.96/30.85  |   (466)  all_54_11 = all_52_23
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (338), (340) imply:
% 191.96/30.85  |   (467)  all_48_2 = all_24_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (467) implies:
% 191.96/30.85  |   (468)  all_48_2 = all_24_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (339), (340) imply:
% 191.96/30.85  |   (469)  all_34_2 = all_24_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (469) implies:
% 191.96/30.85  |   (470)  all_34_2 = all_24_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (401), (439) imply:
% 191.96/30.85  |   (471)  all_46_2 = all_8_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (471) implies:
% 191.96/30.85  |   (472)  all_46_2 = all_8_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (379), (413) imply:
% 191.96/30.85  |   (473)  all_42_2 = all_28_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (378), (413) imply:
% 191.96/30.85  |   (474)  all_42_2 = all_32_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (377), (413) imply:
% 191.96/30.85  |   (475)  all_52_11 = all_42_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (475) implies:
% 191.96/30.85  |   (476)  all_52_11 = all_42_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (380), (413) imply:
% 191.96/30.85  |   (477)  all_42_2 = all_20_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (358), (359) imply:
% 191.96/30.85  |   (478)  all_30_2 = all_16_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (478) implies:
% 191.96/30.85  |   (479)  all_30_2 = all_16_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (336), (437) imply:
% 191.96/30.85  |   (480)  all_52_31 = all_18_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (336), (337) imply:
% 191.96/30.85  |   (481)  all_52_31 = all_48_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (400), (407) imply:
% 191.96/30.85  |   (482)  all_12_2 = all_6_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (482) implies:
% 191.96/30.85  |   (483)  all_12_2 = all_6_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (449), (476) imply:
% 191.96/30.85  |   (484)  all_42_2 = all_38_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (484) implies:
% 191.96/30.85  |   (485)  all_42_2 = all_38_2
% 191.96/30.85  | 
% 191.96/30.85  | COMBINE_EQS: (357), (423) imply:
% 191.96/30.85  |   (486)  all_40_2 = all_26_2
% 191.96/30.85  | 
% 191.96/30.85  | SIMP: (486) implies:
% 191.96/30.86  |   (487)  all_40_2 = all_26_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (480), (481) imply:
% 191.96/30.86  |   (488)  all_48_2 = all_18_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (488) implies:
% 191.96/30.86  |   (489)  all_48_2 = all_18_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (334), (335) imply:
% 191.96/30.86  |   (490)  all_34_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (490) implies:
% 191.96/30.86  |   (491)  all_34_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (468), (489) imply:
% 191.96/30.86  |   (492)  all_24_2 = all_18_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (492) implies:
% 191.96/30.86  |   (493)  all_24_2 = all_18_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (399), (472) imply:
% 191.96/30.86  |   (494)  all_44_2 = all_8_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (494) implies:
% 191.96/30.86  |   (495)  all_44_2 = all_8_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (398), (495) imply:
% 191.96/30.86  |   (496)  all_22_2 = all_8_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (496) implies:
% 191.96/30.86  |   (497)  all_22_2 = all_8_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (473), (485) imply:
% 191.96/30.86  |   (498)  all_38_2 = all_28_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (477), (485) imply:
% 191.96/30.86  |   (499)  all_38_2 = all_20_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (474), (485) imply:
% 191.96/30.86  |   (500)  all_38_2 = all_32_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (356), (487) imply:
% 191.96/30.86  |   (501)  all_36_2 = all_26_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (501) implies:
% 191.96/30.86  |   (502)  all_36_2 = all_26_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (498), (500) imply:
% 191.96/30.86  |   (503)  all_32_2 = all_28_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (499), (500) imply:
% 191.96/30.86  |   (504)  all_32_2 = all_20_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (355), (502) imply:
% 191.96/30.86  |   (505)  all_30_2 = all_26_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (505) implies:
% 191.96/30.86  |   (506)  all_30_2 = all_26_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (470), (491) imply:
% 191.96/30.86  |   (507)  all_24_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (507) implies:
% 191.96/30.86  |   (508)  all_24_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (503), (504) imply:
% 191.96/30.86  |   (509)  all_28_2 = all_20_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (509) implies:
% 191.96/30.86  |   (510)  all_28_2 = all_20_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (479), (506) imply:
% 191.96/30.86  |   (511)  all_26_2 = all_16_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (459), (506) imply:
% 191.96/30.86  |   (512)  all_26_2 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (376), (510) imply:
% 191.96/30.86  |   (513)  all_20_2 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (513) implies:
% 191.96/30.86  |   (514)  all_20_2 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (511), (512) imply:
% 191.96/30.86  |   (515)  all_16_2 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (493), (508) imply:
% 191.96/30.86  |   (516)  all_18_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (516) implies:
% 191.96/30.86  |   (517)  all_18_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (397), (497) imply:
% 191.96/30.86  |   (518)  all_12_2 = all_8_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (518) implies:
% 191.96/30.86  |   (519)  all_12_2 = all_8_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (483), (519) imply:
% 191.96/30.86  |   (520)  all_8_2 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (520) implies:
% 191.96/30.86  |   (521)  all_8_2 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (497), (521) imply:
% 191.96/30.86  |   (522)  all_22_2 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (504), (514) imply:
% 191.96/30.86  |   (523)  all_32_2 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (502), (512) imply:
% 191.96/30.86  |   (524)  all_36_2 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (500), (523) imply:
% 191.96/30.86  |   (525)  all_38_2 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (487), (512) imply:
% 191.96/30.86  |   (526)  all_40_2 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (485), (525) imply:
% 191.96/30.86  |   (527)  all_42_2 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (495), (521) imply:
% 191.96/30.86  |   (528)  all_44_2 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (472), (521) imply:
% 191.96/30.86  |   (529)  all_46_2 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (489), (517) imply:
% 191.96/30.86  |   (530)  all_48_2 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (480), (517) imply:
% 191.96/30.86  |   (531)  all_52_31 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (423), (512) imply:
% 191.96/30.86  |   (532)  all_52_21 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (449), (525) imply:
% 191.96/30.86  |   (533)  all_52_11 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (336), (531) imply:
% 191.96/30.86  |   (534)  all_54_15 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (359), (515) imply:
% 191.96/30.86  |   (535)  all_54_10 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (413), (527) imply:
% 191.96/30.86  |   (536)  all_54_5 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (439), (521) imply:
% 191.96/30.86  |   (537)  all_54_0 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (340), (508) imply:
% 191.96/30.86  |   (538)  all_56_15 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (382), (525) imply:
% 191.96/30.86  |   (539)  all_56_5 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (403), (521) imply:
% 191.96/30.86  |   (540)  all_56_0 = all_6_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (342), (517) imply:
% 191.96/30.86  |   (541)  all_58_15 = all_14_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (345), (466) imply:
% 191.96/30.86  |   (542)  all_58_14 = all_52_23
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (348), (464) imply:
% 191.96/30.86  |   (543)  all_58_13 = all_52_15
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (354), (460) imply:
% 191.96/30.86  |   (544)  all_58_11 = all_52_29
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (390), (445) imply:
% 191.96/30.86  |   (545)  all_58_9 = all_52_25
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (363), (512) imply:
% 191.96/30.86  |   (546)  all_58_8 = all_10_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (369), (455) imply:
% 191.96/30.86  |   (547)  all_58_6 = all_52_5
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (384), (527) imply:
% 191.96/30.86  |   (548)  all_58_3 = all_4_2
% 191.96/30.86  | 
% 191.96/30.86  | COMBINE_EQS: (396), (441) imply:
% 191.96/30.86  |   (549)  all_58_1 = all_52_9
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (236), (447), (537) imply:
% 191.96/30.86  |   (550)   ~ (all_52_3 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (550) implies:
% 191.96/30.86  |   (551)   ~ (all_52_3 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (235), (455), (537) imply:
% 191.96/30.86  |   (552)   ~ (all_52_5 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (552) implies:
% 191.96/30.86  |   (553)   ~ (all_52_5 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (234), (462), (537) imply:
% 191.96/30.86  |   (554)   ~ (all_52_7 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (554) implies:
% 191.96/30.86  |   (555)   ~ (all_52_7 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (233), (441), (537) imply:
% 191.96/30.86  |   (556)   ~ (all_52_9 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (556) implies:
% 191.96/30.86  |   (557)   ~ (all_52_9 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (232), (443), (537) imply:
% 191.96/30.86  |   (558)   ~ (all_52_17 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (558) implies:
% 191.96/30.86  |   (559)   ~ (all_52_17 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (231), (445), (537) imply:
% 191.96/30.86  |   (560)   ~ (all_52_25 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | SIMP: (560) implies:
% 191.96/30.86  |   (561)   ~ (all_52_25 = all_6_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (230), (447), (455) imply:
% 191.96/30.86  |   (562)   ~ (all_52_3 = all_52_5)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (229), (447), (462) imply:
% 191.96/30.86  |   (563)   ~ (all_52_3 = all_52_7)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (228), (447), (536) imply:
% 191.96/30.86  |   (564)   ~ (all_52_3 = all_4_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (227), (447), (451) imply:
% 191.96/30.86  |   (565)   ~ (all_52_3 = all_52_19)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (226), (447), (453) imply:
% 191.96/30.86  |   (566)   ~ (all_52_3 = all_52_27)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (225), (455), (462) imply:
% 191.96/30.86  |   (567)   ~ (all_52_5 = all_52_7)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (224), (455), (457) imply:
% 191.96/30.86  |   (568)   ~ (all_52_5 = all_52_13)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (223), (455), (535) imply:
% 191.96/30.86  |   (569)   ~ (all_52_5 = all_10_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (222), (455), (460) imply:
% 191.96/30.86  |   (570)   ~ (all_52_5 = all_52_29)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (221), (462), (464) imply:
% 191.96/30.86  |   (571)   ~ (all_52_7 = all_52_15)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (220), (462), (466) imply:
% 191.96/30.86  |   (572)   ~ (all_52_7 = all_52_23)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (219), (462), (534) imply:
% 191.96/30.86  |   (573)   ~ (all_52_7 = all_14_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (218), (441), (536) imply:
% 191.96/30.86  |   (574)   ~ (all_52_9 = all_4_2)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (217), (441), (457) imply:
% 191.96/30.86  |   (575)   ~ (all_52_9 = all_52_13)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (216), (441), (464) imply:
% 191.96/30.86  |   (576)   ~ (all_52_9 = all_52_15)
% 191.96/30.86  | 
% 191.96/30.86  | REDUCE: (215), (441), (443) imply:
% 191.96/30.87  |   (577)   ~ (all_52_9 = all_52_17)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (214), (441), (445) imply:
% 191.96/30.87  |   (578)   ~ (all_52_9 = all_52_25)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (213), (457), (536) imply:
% 191.96/30.87  |   (579)   ~ (all_52_13 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | SIMP: (579) implies:
% 191.96/30.87  |   (580)   ~ (all_52_13 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (212), (464), (536) imply:
% 191.96/30.87  |   (581)   ~ (all_52_15 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | SIMP: (581) implies:
% 191.96/30.87  |   (582)   ~ (all_52_15 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (211), (451), (536) imply:
% 191.96/30.87  |   (583)   ~ (all_52_19 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | SIMP: (583) implies:
% 191.96/30.87  |   (584)   ~ (all_52_19 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (210), (453), (536) imply:
% 191.96/30.87  |   (585)   ~ (all_52_27 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | SIMP: (585) implies:
% 191.96/30.87  |   (586)   ~ (all_52_27 = all_4_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (209), (457), (464) imply:
% 191.96/30.87  |   (587)   ~ (all_52_13 = all_52_15)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (208), (457), (535) imply:
% 191.96/30.87  |   (588)   ~ (all_52_13 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (207), (457), (460) imply:
% 191.96/30.87  |   (589)   ~ (all_52_13 = all_52_29)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (206), (464), (466) imply:
% 191.96/30.87  |   (590)   ~ (all_52_15 = all_52_23)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (205), (464), (534) imply:
% 191.96/30.87  |   (591)   ~ (all_52_15 = all_14_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (204), (443), (451) imply:
% 191.96/30.87  |   (592)   ~ (all_52_17 = all_52_19)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (203), (443), (535) imply:
% 191.96/30.87  |   (593)   ~ (all_52_17 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (202), (443), (466) imply:
% 191.96/30.87  |   (594)   ~ (all_52_17 = all_52_23)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (201), (443), (445) imply:
% 191.96/30.87  |   (595)   ~ (all_52_17 = all_52_25)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (200), (451), (535) imply:
% 191.96/30.87  |   (596)   ~ (all_52_19 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (199), (451), (466) imply:
% 191.96/30.87  |   (597)   ~ (all_52_19 = all_52_23)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (198), (451), (453) imply:
% 191.96/30.87  |   (598)   ~ (all_52_19 = all_52_27)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (197), (466), (535) imply:
% 191.96/30.87  |   (599)   ~ (all_52_23 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | SIMP: (599) implies:
% 191.96/30.87  |   (600)   ~ (all_52_23 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (196), (460), (535) imply:
% 191.96/30.87  |   (601)   ~ (all_52_29 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | SIMP: (601) implies:
% 191.96/30.87  |   (602)   ~ (all_52_29 = all_10_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (195), (466), (534) imply:
% 191.96/30.87  |   (603)   ~ (all_52_23 = all_14_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (194), (445), (453) imply:
% 191.96/30.87  |   (604)   ~ (all_52_25 = all_52_27)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (193), (445), (460) imply:
% 191.96/30.87  |   (605)   ~ (all_52_25 = all_52_29)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (192), (445), (534) imply:
% 191.96/30.87  |   (606)   ~ (all_52_25 = all_14_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (191), (453), (460) imply:
% 191.96/30.87  |   (607)   ~ (all_52_27 = all_52_29)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (190), (453), (534) imply:
% 191.96/30.87  |   (608)   ~ (all_52_27 = all_14_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (189), (460), (534) imply:
% 191.96/30.87  |   (609)   ~ (all_52_29 = all_14_2)
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (186), (407) imply:
% 191.96/30.87  |   (610)  op(all_6_2, all_6_2) = all_52_0
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (181), (533) imply:
% 191.96/30.87  |   (611)  op(all_4_2, all_4_2) = all_52_10
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (176), (532) imply:
% 191.96/30.87  |   (612)  op(all_10_2, all_10_2) = all_52_20
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (171), (531) imply:
% 191.96/30.87  |   (613)  op(all_14_2, all_14_2) = all_52_30
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (152), (335) imply:
% 191.96/30.87  |   (614)  op(all_14_2, e0) = all_50_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (148), (530) imply:
% 191.96/30.87  |   (615)  op(all_14_2, e0) = all_48_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (143), (529) imply:
% 191.96/30.87  |   (616)  op(all_6_2, e3) = all_46_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (138), (528) imply:
% 191.96/30.87  |   (617)  op(all_6_2, e3) = all_44_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (133), (527) imply:
% 191.96/30.87  |   (618)  op(all_4_2, e2) = all_42_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (128), (526) imply:
% 191.96/30.87  |   (619)  op(all_10_2, e1) = all_40_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (123), (525) imply:
% 191.96/30.87  |   (620)  op(all_4_2, e2) = all_38_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (118), (524) imply:
% 191.96/30.87  |   (621)  op(all_10_2, e1) = all_36_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (113), (491) imply:
% 191.96/30.87  |   (622)  op(all_14_2, e0) = all_34_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (108), (523) imply:
% 191.96/30.87  |   (623)  op(all_4_2, e2) = all_32_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (103), (459) imply:
% 191.96/30.87  |   (624)  op(all_10_2, e1) = all_30_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (98), (376) imply:
% 191.96/30.87  |   (625)  op(all_4_2, e2) = all_28_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (93), (512) imply:
% 191.96/30.87  |   (626)  op(all_10_2, e1) = all_26_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (88), (508) imply:
% 191.96/30.87  |   (627)  op(all_14_2, e0) = all_24_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (83), (522) imply:
% 191.96/30.87  |   (628)  op(all_6_2, e3) = all_22_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (78), (514) imply:
% 191.96/30.87  |   (629)  op(all_4_2, e2) = all_20_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (73), (517) imply:
% 191.96/30.87  |   (630)  op(all_14_2, e0) = all_18_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (68), (515) imply:
% 191.96/30.87  |   (631)  op(all_10_2, e1) = all_16_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (58), (483) imply:
% 191.96/30.87  |   (632)  op(all_6_2, e3) = all_12_1
% 191.96/30.87  | 
% 191.96/30.87  | REDUCE: (48), (521) imply:
% 191.96/30.87  |   (633)  op(all_6_2, e3) = all_8_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_32_1, all_38_1, e2,
% 191.96/30.87  |              all_4_2, simplifying with (620), (623) gives:
% 191.96/30.87  |   (634)  all_38_1 = all_32_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_28_1, all_38_1, e2,
% 191.96/30.87  |              all_4_2, simplifying with (620), (625) gives:
% 191.96/30.87  |   (635)  all_38_1 = all_28_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_20_1, all_38_1, e2,
% 191.96/30.87  |              all_4_2, simplifying with (620), (629) gives:
% 191.96/30.87  |   (636)  all_38_1 = all_20_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_4_1, all_42_1, e2,
% 191.96/30.87  |              all_4_2, simplifying with (38), (618) gives:
% 191.96/30.87  |   (637)  all_42_1 = all_4_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_32_1, all_42_1, e2,
% 191.96/30.87  |              all_4_2, simplifying with (618), (623) gives:
% 191.96/30.87  |   (638)  all_42_1 = all_32_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_12_1, all_44_1, e3,
% 191.96/30.87  |              all_6_2, simplifying with (617), (632) gives:
% 191.96/30.87  |   (639)  all_44_1 = all_12_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_8_1, all_44_1, e3,
% 191.96/30.87  |              all_6_2, simplifying with (617), (633) gives:
% 191.96/30.87  |   (640)  all_44_1 = all_8_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_6_1, all_46_1, e3,
% 191.96/30.87  |              all_6_2, simplifying with (43), (616) gives:
% 191.96/30.87  |   (641)  all_46_1 = all_6_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_22_1, all_46_1, e3,
% 191.96/30.87  |              all_6_2, simplifying with (616), (628) gives:
% 191.96/30.87  |   (642)  all_46_1 = all_22_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_12_1, all_46_1, e3,
% 191.96/30.87  |              all_6_2, simplifying with (616), (632) gives:
% 191.96/30.87  |   (643)  all_46_1 = all_12_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_16_1, all_26_1, e1,
% 191.96/30.87  |              all_10_2, simplifying with (626), (631) gives:
% 191.96/30.87  |   (644)  all_26_1 = all_16_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_10_1, all_36_1, e1,
% 191.96/30.87  |              all_10_2, simplifying with (53), (621) gives:
% 191.96/30.87  |   (645)  all_36_1 = all_10_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_26_1, all_36_1, e1,
% 191.96/30.87  |              all_10_2, simplifying with (621), (626) gives:
% 191.96/30.87  |   (646)  all_36_1 = all_26_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_36_1, all_40_1, e1,
% 191.96/30.87  |              all_10_2, simplifying with (619), (621) gives:
% 191.96/30.87  |   (647)  all_40_1 = all_36_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_30_1, all_40_1, e1,
% 191.96/30.87  |              all_10_2, simplifying with (619), (624) gives:
% 191.96/30.87  |   (648)  all_40_1 = all_30_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_14_1, all_24_1, e0,
% 191.96/30.87  |              all_14_2, simplifying with (63), (627) gives:
% 191.96/30.87  |   (649)  all_24_1 = all_14_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_24_1, all_34_1, e0,
% 191.96/30.87  |              all_14_2, simplifying with (622), (627) gives:
% 191.96/30.87  |   (650)  all_34_1 = all_24_1
% 191.96/30.87  | 
% 191.96/30.87  | GROUND_INST: instantiating (function-axioms) with all_34_1, all_48_1, e0,
% 191.96/30.87  |              all_14_2, simplifying with (615), (622) gives:
% 191.96/30.88  |   (651)  all_48_1 = all_34_1
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_48_1, all_50_1, e0,
% 191.96/30.88  |              all_14_2, simplifying with (614), (615) gives:
% 191.96/30.88  |   (652)  all_50_1 = all_48_1
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_18_1, all_50_1, e0,
% 191.96/30.88  |              all_14_2, simplifying with (614), (630) gives:
% 191.96/30.88  |   (653)  all_50_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (652), (653) imply:
% 191.96/30.88  |   (654)  all_48_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (654) implies:
% 191.96/30.88  |   (655)  all_48_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (651), (655) imply:
% 191.96/30.88  |   (656)  all_34_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (656) implies:
% 191.96/30.88  |   (657)  all_34_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (641), (642) imply:
% 191.96/30.88  |   (658)  all_22_1 = all_6_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (642), (643) imply:
% 191.96/30.88  |   (659)  all_22_1 = all_12_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (639), (640) imply:
% 191.96/30.88  |   (660)  all_12_1 = all_8_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (660) implies:
% 191.96/30.88  |   (661)  all_12_1 = all_8_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (637), (638) imply:
% 191.96/30.88  |   (662)  all_32_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (662) implies:
% 191.96/30.88  |   (663)  all_32_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (647), (648) imply:
% 191.96/30.88  |   (664)  all_36_1 = all_30_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (664) implies:
% 191.96/30.88  |   (665)  all_36_1 = all_30_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (634), (635) imply:
% 191.96/30.88  |   (666)  all_32_1 = all_28_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (666) implies:
% 191.96/30.88  |   (667)  all_32_1 = all_28_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (635), (636) imply:
% 191.96/30.88  |   (668)  all_28_1 = all_20_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (646), (665) imply:
% 191.96/30.88  |   (669)  all_30_1 = all_26_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (645), (665) imply:
% 191.96/30.88  |   (670)  all_30_1 = all_10_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (650), (657) imply:
% 191.96/30.88  |   (671)  all_24_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (671) implies:
% 191.96/30.88  |   (672)  all_24_1 = all_18_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (663), (667) imply:
% 191.96/30.88  |   (673)  all_28_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (673) implies:
% 191.96/30.88  |   (674)  all_28_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (669), (670) imply:
% 191.96/30.88  |   (675)  all_26_1 = all_10_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (675) implies:
% 191.96/30.88  |   (676)  all_26_1 = all_10_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (668), (674) imply:
% 191.96/30.88  |   (677)  all_20_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (677) implies:
% 191.96/30.88  |   (678)  all_20_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (644), (676) imply:
% 191.96/30.88  |   (679)  all_16_1 = all_10_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (679) implies:
% 191.96/30.88  |   (680)  all_16_1 = all_10_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (649), (672) imply:
% 191.96/30.88  |   (681)  all_18_1 = all_14_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (658), (659) imply:
% 191.96/30.88  |   (682)  all_12_1 = all_6_1
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (682) implies:
% 191.96/30.88  |   (683)  all_12_1 = all_6_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (661), (683) imply:
% 191.96/30.88  |   (684)  all_8_1 = all_6_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (657), (681) imply:
% 191.96/30.88  |   (685)  all_34_1 = all_14_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (635), (674) imply:
% 191.96/30.88  |   (686)  all_38_1 = all_4_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (648), (670) imply:
% 191.96/30.88  |   (687)  all_40_1 = all_10_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (640), (684) imply:
% 191.96/30.88  |   (688)  all_44_1 = all_6_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (655), (681) imply:
% 191.96/30.88  |   (689)  all_48_1 = all_14_1
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (653), (681) imply:
% 191.96/30.88  |   (690)  all_50_1 = all_14_1
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (142), (641) imply:
% 191.96/30.88  |   (691)  op(e3, all_6_1) = all_46_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (137), (688) imply:
% 191.96/30.88  |   (692)  op(e3, all_6_1) = all_44_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (82), (658) imply:
% 191.96/30.88  |   (693)  op(e3, all_6_1) = all_22_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (57), (683) imply:
% 191.96/30.88  |   (694)  op(e3, all_6_1) = all_12_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (47), (684) imply:
% 191.96/30.88  |   (695)  op(e3, all_6_1) = all_8_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (132), (637) imply:
% 191.96/30.88  |   (696)  op(e2, all_4_1) = all_42_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (122), (686) imply:
% 191.96/30.88  |   (697)  op(e2, all_4_1) = all_38_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (107), (663) imply:
% 191.96/30.88  |   (698)  op(e2, all_4_1) = all_32_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (97), (674) imply:
% 191.96/30.88  |   (699)  op(e2, all_4_1) = all_28_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (77), (678) imply:
% 191.96/30.88  |   (700)  op(e2, all_4_1) = all_20_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (127), (687) imply:
% 191.96/30.88  |   (701)  op(e1, all_10_1) = all_40_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (117), (645) imply:
% 191.96/30.88  |   (702)  op(e1, all_10_1) = all_36_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (102), (670) imply:
% 191.96/30.88  |   (703)  op(e1, all_10_1) = all_30_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (92), (676) imply:
% 191.96/30.88  |   (704)  op(e1, all_10_1) = all_26_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (67), (680) imply:
% 191.96/30.88  |   (705)  op(e1, all_10_1) = all_16_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (151), (690) imply:
% 191.96/30.88  |   (706)  op(e0, all_14_1) = all_50_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (147), (689) imply:
% 191.96/30.88  |   (707)  op(e0, all_14_1) = all_48_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (112), (685) imply:
% 191.96/30.88  |   (708)  op(e0, all_14_1) = all_34_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (87), (649) imply:
% 191.96/30.88  |   (709)  op(e0, all_14_1) = all_24_0
% 191.96/30.88  | 
% 191.96/30.88  | REDUCE: (72), (681) imply:
% 191.96/30.88  |   (710)  op(e0, all_14_1) = all_18_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_14_0, all_24_0,
% 191.96/30.88  |              all_14_1, e0, simplifying with (62), (709) gives:
% 191.96/30.88  |   (711)  all_24_0 = all_14_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_48_0, all_50_0,
% 191.96/30.88  |              all_14_1, e0, simplifying with (706), (707) gives:
% 191.96/30.88  |   (712)  all_50_0 = all_48_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_34_0, all_50_0,
% 191.96/30.88  |              all_14_1, e0, simplifying with (706), (708) gives:
% 191.96/30.88  |   (713)  all_50_0 = all_34_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_24_0, all_50_0,
% 191.96/30.88  |              all_14_1, e0, simplifying with (706), (709) gives:
% 191.96/30.88  |   (714)  all_50_0 = all_24_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_18_0, all_50_0,
% 191.96/30.88  |              all_14_1, e0, simplifying with (706), (710) gives:
% 191.96/30.88  |   (715)  all_50_0 = all_18_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_16_0, all_26_0,
% 191.96/30.88  |              all_10_1, e1, simplifying with (704), (705) gives:
% 191.96/30.88  |   (716)  all_26_0 = all_16_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_10_0, all_36_0,
% 191.96/30.88  |              all_10_1, e1, simplifying with (52), (702) gives:
% 191.96/30.88  |   (717)  all_36_0 = all_10_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_36_0, all_40_0,
% 191.96/30.88  |              all_10_1, e1, simplifying with (701), (702) gives:
% 191.96/30.88  |   (718)  all_40_0 = all_36_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_30_0, all_40_0,
% 191.96/30.88  |              all_10_1, e1, simplifying with (701), (703) gives:
% 191.96/30.88  |   (719)  all_40_0 = all_30_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_26_0, all_40_0,
% 191.96/30.88  |              all_10_1, e1, simplifying with (701), (704) gives:
% 191.96/30.88  |   (720)  all_40_0 = all_26_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_4_0, all_32_0, all_4_1,
% 191.96/30.88  |              e2, simplifying with (37), (698) gives:
% 191.96/30.88  |   (721)  all_32_0 = all_4_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_38_0, all_42_0, all_4_1,
% 191.96/30.88  |              e2, simplifying with (696), (697) gives:
% 191.96/30.88  |   (722)  all_42_0 = all_38_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_32_0, all_42_0, all_4_1,
% 191.96/30.88  |              e2, simplifying with (696), (698) gives:
% 191.96/30.88  |   (723)  all_42_0 = all_32_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_28_0, all_42_0, all_4_1,
% 191.96/30.88  |              e2, simplifying with (696), (699) gives:
% 191.96/30.88  |   (724)  all_42_0 = all_28_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_20_0, all_42_0, all_4_1,
% 191.96/30.88  |              e2, simplifying with (696), (700) gives:
% 191.96/30.88  |   (725)  all_42_0 = all_20_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_12_0, all_22_0, all_6_1,
% 191.96/30.88  |              e3, simplifying with (693), (694) gives:
% 191.96/30.88  |   (726)  all_22_0 = all_12_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_6_0, all_44_0, all_6_1,
% 191.96/30.88  |              e3, simplifying with (42), (692) gives:
% 191.96/30.88  |   (727)  all_44_0 = all_6_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_22_0, all_44_0, all_6_1,
% 191.96/30.88  |              e3, simplifying with (692), (693) gives:
% 191.96/30.88  |   (728)  all_44_0 = all_22_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_12_0, all_46_0, all_6_1,
% 191.96/30.88  |              e3, simplifying with (691), (694) gives:
% 191.96/30.88  |   (729)  all_46_0 = all_12_0
% 191.96/30.88  | 
% 191.96/30.88  | GROUND_INST: instantiating (function-axioms) with all_8_0, all_46_0, all_6_1,
% 191.96/30.88  |              e3, simplifying with (691), (695) gives:
% 191.96/30.88  |   (730)  all_46_0 = all_8_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (712), (715) imply:
% 191.96/30.88  |   (731)  all_48_0 = all_18_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (712), (714) imply:
% 191.96/30.88  |   (732)  all_48_0 = all_24_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (712), (713) imply:
% 191.96/30.88  |   (733)  all_48_0 = all_34_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (731), (733) imply:
% 191.96/30.88  |   (734)  all_34_0 = all_18_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (732), (733) imply:
% 191.96/30.88  |   (735)  all_34_0 = all_24_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (729), (730) imply:
% 191.96/30.88  |   (736)  all_12_0 = all_8_0
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (736) implies:
% 191.96/30.88  |   (737)  all_12_0 = all_8_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (727), (728) imply:
% 191.96/30.88  |   (738)  all_22_0 = all_6_0
% 191.96/30.88  | 
% 191.96/30.88  | SIMP: (738) implies:
% 191.96/30.88  |   (739)  all_22_0 = all_6_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (722), (723) imply:
% 191.96/30.88  |   (740)  all_38_0 = all_32_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (722), (724) imply:
% 191.96/30.88  |   (741)  all_38_0 = all_28_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (722), (725) imply:
% 191.96/30.88  |   (742)  all_38_0 = all_20_0
% 191.96/30.88  | 
% 191.96/30.88  | COMBINE_EQS: (718), (719) imply:
% 191.96/30.88  |   (743)  all_36_0 = all_30_0
% 191.96/30.88  | 
% 191.96/30.89  | SIMP: (743) implies:
% 191.96/30.89  |   (744)  all_36_0 = all_30_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (719), (720) imply:
% 191.96/30.89  |   (745)  all_30_0 = all_26_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (740), (741) imply:
% 191.96/30.89  |   (746)  all_32_0 = all_28_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (746) implies:
% 191.96/30.89  |   (747)  all_32_0 = all_28_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (741), (742) imply:
% 191.96/30.89  |   (748)  all_28_0 = all_20_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (717), (744) imply:
% 191.96/30.89  |   (749)  all_30_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (749) implies:
% 191.96/30.89  |   (750)  all_30_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (734), (735) imply:
% 191.96/30.89  |   (751)  all_24_0 = all_18_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (751) implies:
% 191.96/30.89  |   (752)  all_24_0 = all_18_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (721), (747) imply:
% 191.96/30.89  |   (753)  all_28_0 = all_4_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (753) implies:
% 191.96/30.89  |   (754)  all_28_0 = all_4_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (745), (750) imply:
% 191.96/30.89  |   (755)  all_26_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (755) implies:
% 191.96/30.89  |   (756)  all_26_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (748), (754) imply:
% 191.96/30.89  |   (757)  all_20_0 = all_4_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (757) implies:
% 191.96/30.89  |   (758)  all_20_0 = all_4_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (716), (756) imply:
% 191.96/30.89  |   (759)  all_16_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (759) implies:
% 191.96/30.89  |   (760)  all_16_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (711), (752) imply:
% 191.96/30.89  |   (761)  all_18_0 = all_14_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (726), (739) imply:
% 191.96/30.89  |   (762)  all_12_0 = all_6_0
% 191.96/30.89  | 
% 191.96/30.89  | SIMP: (762) implies:
% 191.96/30.89  |   (763)  all_12_0 = all_6_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (737), (763) imply:
% 191.96/30.89  |   (764)  all_8_0 = all_6_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (734), (761) imply:
% 191.96/30.89  |   (765)  all_34_0 = all_14_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (741), (754) imply:
% 191.96/30.89  |   (766)  all_38_0 = all_4_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (719), (750) imply:
% 191.96/30.89  |   (767)  all_40_0 = all_10_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (722), (766) imply:
% 191.96/30.89  |   (768)  all_42_0 = all_4_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (730), (764) imply:
% 191.96/30.89  |   (769)  all_46_0 = all_6_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (733), (765) imply:
% 191.96/30.89  |   (770)  all_48_0 = all_14_0
% 191.96/30.89  | 
% 191.96/30.89  | COMBINE_EQS: (712), (770) imply:
% 191.96/30.89  |   (771)  all_50_0 = all_14_0
% 191.96/30.89  | 
% 191.96/30.89  | BETA: splitting (39) gives:
% 191.96/30.89  | 
% 191.96/30.89  | Case 1:
% 191.96/30.89  | | 
% 191.96/30.89  | |   (772)   ~ (all_4_1 = e1)
% 191.96/30.89  | | 
% 191.96/30.89  | | BETA: splitting (44) gives:
% 191.96/30.89  | | 
% 191.96/30.89  | | Case 1:
% 191.96/30.89  | | | 
% 191.96/30.89  | | |   (773)   ~ (all_6_0 = e1)
% 191.96/30.89  | | | 
% 191.96/30.89  | | | BETA: splitting (49) gives:
% 191.96/30.89  | | | 
% 191.96/30.89  | | | Case 1:
% 191.96/30.89  | | | | 
% 191.96/30.89  | | | |   (774)   ~ (all_8_0 = e2)
% 191.96/30.89  | | | | 
% 191.96/30.89  | | | | REDUCE: (764), (774) imply:
% 191.96/30.89  | | | |   (775)   ~ (all_6_0 = e2)
% 191.96/30.89  | | | | 
% 191.96/30.89  | | | | BETA: splitting (54) gives:
% 191.96/30.89  | | | | 
% 191.96/30.89  | | | | Case 1:
% 191.96/30.89  | | | | | 
% 191.96/30.89  | | | | |   (776)   ~ (all_10_0 = e3)
% 191.96/30.89  | | | | | 
% 191.96/30.89  | | | | | BETA: splitting (59) gives:
% 191.96/30.89  | | | | | 
% 191.96/30.89  | | | | | Case 1:
% 191.96/30.89  | | | | | | 
% 191.96/30.89  | | | | | |   (777)   ~ (all_12_1 = e1)
% 191.96/30.89  | | | | | | 
% 191.96/30.89  | | | | | | REDUCE: (683), (777) imply:
% 191.96/30.89  | | | | | |   (778)   ~ (all_6_1 = e1)
% 191.96/30.89  | | | | | | 
% 191.96/30.89  | | | | | | BETA: splitting (64) gives:
% 191.96/30.89  | | | | | | 
% 191.96/30.89  | | | | | | Case 1:
% 191.96/30.89  | | | | | | | 
% 191.96/30.89  | | | | | | |   (779)   ~ (all_14_0 = e2)
% 191.96/30.89  | | | | | | | 
% 191.96/30.89  | | | | | | | BETA: splitting (69) gives:
% 191.96/30.89  | | | | | | | 
% 191.96/30.89  | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | 
% 191.96/30.89  | | | | | | | |   (780)   ~ (all_16_0 = e2)
% 191.96/30.89  | | | | | | | | 
% 191.96/30.89  | | | | | | | | REDUCE: (760), (780) imply:
% 191.96/30.89  | | | | | | | |   (781)   ~ (all_10_0 = e2)
% 191.96/30.89  | | | | | | | | 
% 191.96/30.89  | | | | | | | | BETA: splitting (74) gives:
% 191.96/30.89  | | | | | | | | 
% 191.96/30.89  | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | 
% 191.96/30.89  | | | | | | | | |   (782)   ~ (all_18_0 = e3)
% 191.96/30.89  | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | REDUCE: (761), (782) imply:
% 191.96/30.89  | | | | | | | | |   (783)   ~ (all_14_0 = e3)
% 191.96/30.89  | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | BETA: splitting (79) gives:
% 191.96/30.89  | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | |   (784)   ~ (all_20_0 = e3)
% 191.96/30.89  | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | REDUCE: (758), (784) imply:
% 191.96/30.89  | | | | | | | | | |   (785)   ~ (all_4_0 = e3)
% 191.96/30.89  | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | BETA: splitting (84) gives:
% 191.96/30.89  | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | |   (786)   ~ (all_22_1 = e2)
% 191.96/30.89  | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | REDUCE: (658), (786) imply:
% 191.96/30.89  | | | | | | | | | | |   (787)   ~ (all_6_1 = e2)
% 191.96/30.89  | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | BETA: splitting (89) gives:
% 191.96/30.89  | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | |   (788)   ~ (all_24_0 = e1)
% 191.96/30.89  | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | REDUCE: (711), (788) imply:
% 191.96/30.89  | | | | | | | | | | | |   (789)   ~ (all_14_0 = e1)
% 191.96/30.89  | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | BETA: splitting (104) gives:
% 191.96/30.89  | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | |   (790)   ~ (all_30_1 = e3)
% 191.96/30.89  | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | REDUCE: (670), (790) imply:
% 191.96/30.89  | | | | | | | | | | | | |   (791)   ~ (all_10_1 = e3)
% 191.96/30.89  | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | BETA: splitting (109) gives:
% 191.96/30.89  | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | |   (792)   ~ (all_32_1 = e3)
% 191.96/30.89  | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | REDUCE: (663), (792) imply:
% 191.96/30.89  | | | | | | | | | | | | | |   (793)   ~ (all_4_1 = e3)
% 191.96/30.89  | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 191.96/30.89  | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | |   (794)   ~ (all_40_1 = e2)
% 191.96/30.89  | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | REDUCE: (687), (794) imply:
% 191.96/30.89  | | | | | | | | | | | | | | |   (795)   ~ (all_10_1 = e2)
% 191.96/30.89  | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 191.96/30.89  | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | |   (796)  all_58_15 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (796) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (797)  all_14_2 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (573), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (798)   ~ (all_52_7 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (591), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (799)   ~ (all_52_15 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (603), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (800)   ~ (all_52_23 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (606), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (801)   ~ (all_52_25 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (608), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (802)   ~ (all_52_27 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (609), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (803)   ~ (all_52_29 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (613), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (804)  op(e0, e0) = all_52_30
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (63), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (805)  op(e0, e0) = all_14_1
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (61), (797) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (806)  op(e0, e0) = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 191.96/30.89  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (804), (805)
% 191.96/30.89  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (807)  all_52_30 = all_14_1
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 191.96/30.89  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (804), (806)
% 191.96/30.89  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (808)  all_52_30 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | COMBINE_EQS: (807), (808) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (809)  all_14_1 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | SIMP: (809) implies:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (810)  all_14_1 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (62), (810) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (811)  op(e0, e0) = all_14_0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 191.96/30.89  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (806), (811) gives:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (812)  all_14_0 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (783), (812) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (813)   ~ (e3 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (779), (812) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (814)   ~ (e2 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | REDUCE: (789), (812) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | |   (815)   ~ (e1 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 191.96/30.89  | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | |   (816)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.89  | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 191.96/30.89  | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 191.96/30.89  | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | BETA: splitting (816) gives:
% 191.96/30.89  | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.89  | | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (817)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.89  | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | | ALPHA: (817) implies:
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (818)  all_52_6 = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (819)  all_52_4 = e1
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (820)  all_52_2 = e2
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (821)  all_52_0 = e3
% 191.96/30.89  | | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | | REDUCE: (185), (820) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (822)  op(all_52_3, all_52_3) = e2
% 191.96/30.89  | | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | | REDUCE: (184), (819) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (823)  op(all_52_5, all_52_5) = e1
% 191.96/30.89  | | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | | REDUCE: (183), (818) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (824)  op(all_52_7, all_52_7) = e0
% 191.96/30.89  | | | | | | | | | | | | | | | | | | 
% 191.96/30.89  | | | | | | | | | | | | | | | | | | REDUCE: (610), (821) imply:
% 191.96/30.89  | | | | | | | | | | | | | | | | | |   (825)  op(all_6_2, all_6_2) = e3
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (51), (53), (61), (156),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (157), (271), (272), (273), (304), (306), (321),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (332), (343), (346), (351), (387), (405), (431),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (542), (543), (547), (555), (564), (569), (571),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (572), (573), (600), (772), (791), (793), (795),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (796), (798), (799), (822), (823), (824), (825),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            #1348.
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (826)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 191.96/30.90  | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | ALPHA: (826) implies:
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (827)  all_52_14 = e0
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (828)  all_52_12 = e1
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (829)  all_52_10 = e2
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (830)  all_52_8 = e3
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | REDUCE: (182), (830) imply:
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (831)  op(all_52_9, all_52_9) = e3
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | REDUCE: (180), (828) imply:
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (832)  op(all_52_13, all_52_13) = e1
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | REDUCE: (179), (827) imply:
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (833)  op(all_52_15, all_52_15) = e0
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | REDUCE: (611), (829) imply:
% 191.96/30.90  | | | | | | | | | | | | | | | | | |   (834)  op(all_4_2, all_4_2) = e2
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (36), (38), (41), (43), (51), (53),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (178), (272), (273), (277), (278), (280), (281),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (282), (283), (284), (304), (305), (306), (309),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (313), (314), (317), (322), (324), (325), (327),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (333), (346), (351), (366), (367), (372), (375),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (427),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (431), (539), (542), (543), (544), (545), (546),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (568),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (571), (572), (574), (575), (577), (578), (580),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (595),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (604), (605), (612), (772), (778), (787), (791),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (796), (798), (799), (801), (806), (831), (832),
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            (833), (834), (function-axioms) are inconsistent
% 191.96/30.90  | | | | | | | | | | | | | | | | | |            by sub-proof #1287.
% 191.96/30.90  | | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | End of split
% 191.96/30.90  | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.90  | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | |   (835)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 191.96/30.90  | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 191.96/30.90  | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.96/30.90  | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (280),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (304), (305), (306),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (317), (318), (321),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (322), (325), (326), (330), (331), (332), (333),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (415), (427), (431), (539), (542), (543), (544),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (576), (577),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (590), (593), (594), (595), (596), (598), (600),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (602), (604), (605), (608), (610), (611), (612),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (773), (775), (778), (787), (793), (796), (798),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (799), (800), (801), (802), (803), (806), (835),
% 191.96/30.90  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.90  | | | | | | | | | | | | | | | | |            #1202.
% 191.96/30.90  | | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | | End of split
% 191.96/30.90  | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | Case 2:
% 191.96/30.90  | | | | | | | | | | | | | | | | 
% 191.96/30.90  | | | | | | | | | | | | | | | |   (836)   ~ (all_58_15 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | |   (837)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | |          & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 191.96/30.91  | | | | | | | | | | | | | | | |            e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | ALPHA: (837) implies:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (838)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | |   (839)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (541), (836) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (840)   ~ (all_14_2 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (62), (63),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (157), (158), (161), (162), (166), (167), (168),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (276),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (307), (308),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (309), (311), (312), (313), (315), (316), (317),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (538),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (590),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (772), (773), (775), (778), (779), (783), (785),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (787), (789), (793), (838), (839), (840),
% 191.96/30.91  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.91  | | | | | | | | | | | | | | | |            #1007.
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | End of split
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | Case 2:
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | |   (841)  all_40_1 = e2
% 191.96/30.91  | | | | | | | | | | | | | | |   (842)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | COMBINE_EQS: (687), (841) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (843)  all_10_1 = e2
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (791), (843) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (844)   ~ (e3 = e2)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (53), (843) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (845)  op(all_10_2, e1) = e2
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (52), (843) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (846)  op(e1, e2) = all_10_0
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 191.96/30.91  | | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (846)
% 191.96/30.91  | | | | | | | | | | | | | | |              gives:
% 191.96/30.91  | | | | | | | | | | | | | | |   (847)  all_52_13 = all_10_0
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | COMBINE_EQS: (421), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (848)  all_56_9 = all_10_0
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | COMBINE_EQS: (366), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (849)  all_58_7 = all_10_0
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (568), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (850)   ~ (all_52_5 = all_10_0)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (587), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (851)   ~ (all_52_15 = all_10_0)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | SIMP: (851) implies:
% 191.96/30.91  | | | | | | | | | | | | | | |   (852)   ~ (all_52_15 = all_10_0)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (589), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (853)   ~ (all_52_29 = all_10_0)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | SIMP: (853) implies:
% 191.96/30.91  | | | | | | | | | | | | | | |   (854)   ~ (all_52_29 = all_10_0)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (588), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (855)   ~ (all_10_0 = all_10_2)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (580), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (856)   ~ (all_10_0 = all_4_2)
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | REDUCE: (180), (847) imply:
% 191.96/30.91  | | | | | | | | | | | | | | |   (857)  op(all_10_0, all_10_0) = all_52_12
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 191.96/30.91  | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | Case 1:
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | |   (858)  all_58_15 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (858) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (859)  all_14_2 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (573), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (860)   ~ (all_52_7 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (591), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (861)   ~ (all_52_15 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (603), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (862)   ~ (all_52_23 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (606), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (863)   ~ (all_52_25 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (608), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (864)   ~ (all_52_27 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (609), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (865)   ~ (all_52_29 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (613), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (866)  op(e0, e0) = all_52_30
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (63), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (867)  op(e0, e0) = all_14_1
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (61), (859) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (868)  op(e0, e0) = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 191.96/30.91  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (866), (867)
% 191.96/30.91  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (869)  all_52_30 = all_14_1
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 191.96/30.91  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (866), (868)
% 191.96/30.91  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (870)  all_52_30 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | COMBINE_EQS: (869), (870) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (871)  all_14_1 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | SIMP: (871) implies:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (872)  all_14_1 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (62), (872) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (873)  op(e0, e0) = all_14_0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 191.96/30.91  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (868), (873) gives:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (874)  all_14_0 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (783), (874) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (875)   ~ (e3 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (779), (874) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (876)   ~ (e2 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | REDUCE: (789), (874) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | |   (877)   ~ (e1 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 191.96/30.91  | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.91  | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | |   (878)  all_56_9 = e3
% 191.96/30.91  | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | REF_CLOSE: (776), (848), (878) are inconsistent by sub-proof
% 191.96/30.91  | | | | | | | | | | | | | | | | |            #1006.
% 191.96/30.91  | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.91  | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | |   (879)   ~ (all_56_9 = e3)
% 191.96/30.91  | | | | | | | | | | | | | | | | |   (880)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 191.96/30.91  | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | |   (881)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.91  | | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 191.96/30.91  | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 191.96/30.91  | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | BETA: splitting (881) gives:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (882)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | ALPHA: (882) implies:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (883)  all_52_6 = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (884)  all_52_4 = e1
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (885)  all_52_2 = e2
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (886)  all_52_0 = e3
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | REDUCE: (185), (885) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (887)  op(all_52_3, all_52_3) = e2
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | REDUCE: (184), (884) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (888)  op(all_52_5, all_52_5) = e1
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (883) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (889)  op(all_52_7, all_52_7) = e0
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | REDUCE: (610), (886) imply:
% 191.96/30.91  | | | | | | | | | | | | | | | | | | |   (890)  op(all_6_2, all_6_2) = e3
% 191.96/30.91  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (273),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (274), (277), (278), (282), (304), (306), (307),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (308), (309), (310), (311), (312), (317), (321),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (325), (332), (351), (352), (367), (372), (375),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (387), (388), (393), (405), (427), (431), (526),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (549), (555), (557), (559), (561), (564), (566),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (573), (586), (590),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (596), (598), (604), (605), (607), (611), (612),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (767), (776), (781), (842), (845), (848), (849),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (850), (854), (856), (858), (860), (863), (865),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (868), (880), (887), (888), (889), (890),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            #994.
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (891)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | ALPHA: (891) implies:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (892)  all_52_14 = e0
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (893)  all_52_12 = e1
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (894)  all_52_10 = e2
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (895)  all_52_8 = e3
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | REDUCE: (182), (895) imply:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (896)  op(all_52_9, all_52_9) = e3
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | REDUCE: (179), (892) imply:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (897)  op(all_52_15, all_52_15) = e0
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | REDUCE: (857), (893) imply:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (898)  op(all_10_0, all_10_0) = e1
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | REDUCE: (611), (894) imply:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |   (899)  op(all_4_2, all_4_2) = e2
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (43), (51), (53), (156), (158), (164), (169),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (172), (173), (174), (178), (183), (184), (271),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (272), (273), (278), (282), (284), (304), (305),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (312), (313), (317),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (325), (333), (343), (346), (351), (366), (372),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (427), (431), (526),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (549), (555), (557), (567), (571), (572), (577),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (578), (582), (586), (589), (590), (596), (604),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (605), (607), (767), (772), (776), (778), (781),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (787), (791), (842), (845), (848), (849), (852),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (855), (858), (860), (861), (863), (865), (868),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (880), (896), (897), (898), (899),
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.92  | | | | | | | | | | | | | | | | | | |            #981.
% 191.96/30.92  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.92  | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.92  | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | |   (900)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.96/30.92  | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (280),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (304), (305), (306),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (317), (318), (321),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (322), (325), (326), (330), (331), (332), (333),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (415), (427), (431), (539), (542), (543), (544),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (576), (577),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (590), (593), (594), (595), (596), (598), (600),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (602), (604), (605), (608), (610), (611), (612),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (773), (775), (778), (787), (793), (858), (860),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (861), (862), (863), (864), (865), (868), (900),
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.92  | | | | | | | | | | | | | | | | | |            #1202.
% 191.96/30.92  | | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | | End of split
% 191.96/30.92  | | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | End of split
% 191.96/30.92  | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | Case 2:
% 191.96/30.92  | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | |   (901)   ~ (all_58_15 = e0)
% 191.96/30.92  | | | | | | | | | | | | | | | |   (902)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 191.96/30.92  | | | | | | | | | | | | | | | |          & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 191.96/30.92  | | | | | | | | | | | | | | | |            e0)
% 191.96/30.92  | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | ALPHA: (902) implies:
% 191.96/30.92  | | | | | | | | | | | | | | | |   (903)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 191.96/30.92  | | | | | | | | | | | | | | | |   (904)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 191.96/30.92  | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | REDUCE: (541), (901) imply:
% 191.96/30.92  | | | | | | | | | | | | | | | |   (905)   ~ (all_14_2 = e0)
% 191.96/30.92  | | | | | | | | | | | | | | | | 
% 191.96/30.92  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (62), (63),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (157), (158), (161), (162), (166), (167), (168),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (276),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (307), (308),
% 191.96/30.92  | | | | | | | | | | | | | | | |            (309), (311), (312), (313), (315), (316), (317),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (538),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (590),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (772), (773), (775), (778), (779), (783), (785),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (787), (789), (793), (903), (904), (905),
% 191.96/30.93  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.93  | | | | | | | | | | | | | | | |            #1007.
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | End of split
% 191.96/30.93  | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | End of split
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | Case 2:
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | |   (906)  all_32_1 = e3
% 191.96/30.93  | | | | | | | | | | | | | |   (907)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | COMBINE_EQS: (663), (906) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (908)  all_4_1 = e3
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | SIMP: (908) implies:
% 191.96/30.93  | | | | | | | | | | | | | |   (909)  all_4_1 = e3
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | COMBINE_EQS: (686), (909) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (910)  all_38_1 = e3
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | REDUCE: (38), (909) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (911)  op(all_4_2, e2) = e3
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | REDUCE: (37), (909) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (912)  op(e2, e3) = all_4_0
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 191.96/30.93  | | | | | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (912)
% 191.96/30.93  | | | | | | | | | | | | | |              gives:
% 191.96/30.93  | | | | | | | | | | | | | |   (913)  all_52_3 = all_4_0
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | COMBINE_EQS: (411), (913) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (914)  all_56_4 = all_4_0
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | COMBINE_EQS: (387), (913) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (915)  all_58_2 = all_4_0
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | REDUCE: (563), (913) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (916)   ~ (all_52_7 = all_4_0)
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | SIMP: (916) implies:
% 191.96/30.93  | | | | | | | | | | | | | |   (917)   ~ (all_52_7 = all_4_0)
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | REDUCE: (551), (913) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (918)   ~ (all_6_2 = all_4_0)
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | SIMP: (918) implies:
% 191.96/30.93  | | | | | | | | | | | | | |   (919)   ~ (all_6_2 = all_4_0)
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | REDUCE: (564), (913) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (920)   ~ (all_4_0 = all_4_2)
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | REDUCE: (185), (913) imply:
% 191.96/30.93  | | | | | | | | | | | | | |   (921)  op(all_4_0, all_4_0) = all_52_2
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 191.96/30.93  | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | Case 1:
% 191.96/30.93  | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | |   (922)   ~ (all_38_0 = e1)
% 191.96/30.93  | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | REDUCE: (766), (922) imply:
% 191.96/30.93  | | | | | | | | | | | | | | |   (923)   ~ (all_4_0 = e1)
% 191.96/30.93  | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 191.96/30.93  | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | Case 1:
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | |   (924)  all_58_15 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (924) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (925)  all_14_2 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (573), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (926)   ~ (all_52_7 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (591), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (927)   ~ (all_52_15 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (603), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (928)   ~ (all_52_23 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (606), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (929)   ~ (all_52_25 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (609), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (930)   ~ (all_52_29 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (613), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (931)  op(e0, e0) = all_52_30
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (63), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (932)  op(e0, e0) = all_14_1
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (61), (925) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (933)  op(e0, e0) = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 191.96/30.93  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (931), (932)
% 191.96/30.93  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (934)  all_52_30 = all_14_1
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 191.96/30.93  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (931), (933)
% 191.96/30.93  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (935)  all_52_30 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (935) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (936)  all_14_1 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | SIMP: (936) implies:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (937)  all_14_1 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (62), (937) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (938)  op(e0, e0) = all_14_0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 191.96/30.93  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (933), (938) gives:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (939)  all_14_0 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (783), (939) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (940)   ~ (e3 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (779), (939) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (941)   ~ (e2 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | REDUCE: (789), (939) imply:
% 191.96/30.93  | | | | | | | | | | | | | | | |   (942)   ~ (e1 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 191.96/30.93  | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.93  | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | |   (943)  all_56_4 = e3
% 191.96/30.93  | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (785), (914), (943) are inconsistent by sub-proof
% 191.96/30.93  | | | | | | | | | | | | | | | | |            #980.
% 191.96/30.93  | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.93  | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | |   (944)   ~ (all_56_4 = e3)
% 191.96/30.93  | | | | | | | | | | | | | | | | |   (945)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 191.96/30.93  | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | |   (946)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.93  | | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 191.96/30.93  | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | BETA: splitting (946) gives:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |   (947)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (611), (721), (907), (911), (914), (915), (920),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (921), (923), (945), (947), (function-axioms) are
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |   (948)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (36), (38), (41), (43), (51), (53),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (178), (179), (180), (182), (272), (273), (277),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (284), (304),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (305), (306), (309), (313), (314), (317), (322),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (324), (325), (327), (333), (346), (351), (366),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (367), (372), (375), (388), (393), (394), (405),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (411), (415), (427), (431), (539), (542), (543),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (564), (567), (568), (571), (572), (574), (575),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (588), (589), (595), (604), (605), (611), (612),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (772), (778), (787), (791), (924), (926), (927),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (929), (933), (948), (function-axioms) are
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | |   (949)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 191.96/30.93  | | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 191.96/30.93  | | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | BETA: splitting (949) gives:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |   (950)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |          all_52_22 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (42), (43),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (51), (158), (162), (167), (169), (172), (173),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (180), (182), (183),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (282), (283), (284), (304), (307), (308), (317),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (319), (321), (323), (325), (326), (328), (330),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (415),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (417), (421), (427), (431), (523), (539), (542),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (570), (571), (572),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (574), (575), (576), (578), (580), (584), (586),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (595), (597), (598),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (600), (604), (605), (607), (610), (611), (612),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (721), (775), (778), (785), (787), (907), (911),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (914), (915), (917), (919), (920), (923), (924),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (926), (927), (928), (929), (930), (933), (945),
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            (950), (function-axioms) are inconsistent by
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |            sub-proof #942.
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |   (951)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 191.96/30.93  | | | | | | | | | | | | | | | | | | |          all_52_30 = e0
% 191.96/30.93  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            (278), (280), (282), (309), (321), (332), (372),
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            (375), (388), (405), (427), (523), (539), (544),
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            (545), (548), (561), (574), (584), (586), (605),
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            (607), (610), (611), (721), (785), (907), (911),
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            (914), (915), (919), (920), (923), (924), (929),
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            (945), (951), (function-axioms) are inconsistent
% 191.96/30.94  | | | | | | | | | | | | | | | | | | |            by sub-proof #940.
% 191.96/30.94  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.94  | | | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | | End of split
% 191.96/30.94  | | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | End of split
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | Case 2:
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | |   (952)   ~ (all_58_15 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | |   (953)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | |          & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 191.96/30.94  | | | | | | | | | | | | | | | |            e0)
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (158), (162), (166),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (275), (276), (277), (279), (280), (281), (282),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (417), (421), (431), (523), (538), (539), (540),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (586), (587), (588), (590), (591), (592), (593),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (602), (603),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (611), (612), (613), (721), (772), (773), (775),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (778), (785), (787), (907), (911), (914), (915),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (919), (920), (921), (923), (952), (953),
% 191.96/30.94  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.94  | | | | | | | | | | | | | | | |            #928.
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | End of split
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | Case 2:
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | |   (954)  all_38_0 = e1
% 191.96/30.94  | | | | | | | | | | | | | | |   (955)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | COMBINE_EQS: (766), (954) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (956)  all_4_0 = e1
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | SIMP: (956) implies:
% 191.96/30.94  | | | | | | | | | | | | | | |   (957)  all_4_0 = e1
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 191.96/30.94  | | | | | | | | | | | | | | |            (910), (911), (920), (955), (957),
% 191.96/30.94  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.94  | | | | | | | | | | | | | | |            #927.
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | End of split
% 191.96/30.94  | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | End of split
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | Case 2:
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | |   (958)  all_30_1 = e3
% 191.96/30.94  | | | | | | | | | | | | |   (959)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | COMBINE_EQS: (670), (958) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (960)  all_10_1 = e3
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (53), (960) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (961)  op(all_10_2, e1) = e3
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (52), (960) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (962)  op(e1, e3) = all_10_0
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 191.96/30.94  | | | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (962)
% 191.96/30.94  | | | | | | | | | | | | |              gives:
% 191.96/30.94  | | | | | | | | | | | | |   (963)  all_52_5 = all_10_0
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | COMBINE_EQS: (367), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (964)  all_56_8 = all_10_0
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | COMBINE_EQS: (547), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (965)  all_58_6 = all_10_0
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (562), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (966)   ~ (all_52_3 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (567), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (967)   ~ (all_52_7 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | SIMP: (967) implies:
% 191.96/30.94  | | | | | | | | | | | | |   (968)   ~ (all_52_7 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (568), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (969)   ~ (all_52_13 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | SIMP: (969) implies:
% 191.96/30.94  | | | | | | | | | | | | |   (970)   ~ (all_52_13 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (570), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (971)   ~ (all_52_29 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | SIMP: (971) implies:
% 191.96/30.94  | | | | | | | | | | | | |   (972)   ~ (all_52_29 = all_10_0)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (569), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (973)   ~ (all_10_0 = all_10_2)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (553), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (974)   ~ (all_10_0 = all_6_2)
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | REDUCE: (184), (963) imply:
% 191.96/30.94  | | | | | | | | | | | | |   (975)  op(all_10_0, all_10_0) = all_52_4
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | BETA: splitting (109) gives:
% 191.96/30.94  | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | Case 1:
% 191.96/30.94  | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | |   (976)   ~ (all_32_1 = e3)
% 191.96/30.94  | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | REDUCE: (663), (976) imply:
% 191.96/30.94  | | | | | | | | | | | | | |   (977)   ~ (all_4_1 = e3)
% 191.96/30.94  | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 191.96/30.94  | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | Case 1:
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | |   (978)  all_58_15 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (978) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (979)  all_14_2 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (573), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (980)   ~ (all_52_7 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (591), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (981)   ~ (all_52_15 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (603), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (982)   ~ (all_52_23 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (606), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (983)   ~ (all_52_25 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (608), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (984)   ~ (all_52_27 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (609), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (985)   ~ (all_52_29 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (613), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (986)  op(e0, e0) = all_52_30
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (63), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (987)  op(e0, e0) = all_14_1
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (61), (979) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (988)  op(e0, e0) = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 191.96/30.94  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (986), (987)
% 191.96/30.94  | | | | | | | | | | | | | | |              gives:
% 191.96/30.94  | | | | | | | | | | | | | | |   (989)  all_52_30 = all_14_1
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 191.96/30.94  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (986), (988)
% 191.96/30.94  | | | | | | | | | | | | | | |              gives:
% 191.96/30.94  | | | | | | | | | | | | | | |   (990)  all_52_30 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | COMBINE_EQS: (989), (990) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (991)  all_14_1 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | SIMP: (991) implies:
% 191.96/30.94  | | | | | | | | | | | | | | |   (992)  all_14_1 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (62), (992) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (993)  op(e0, e0) = all_14_0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 191.96/30.94  | | | | | | | | | | | | | | |              e0, e0, simplifying with (988), (993) gives:
% 191.96/30.94  | | | | | | | | | | | | | | |   (994)  all_14_0 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (783), (994) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (995)   ~ (e3 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (779), (994) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (996)   ~ (e2 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | REDUCE: (789), (994) imply:
% 191.96/30.94  | | | | | | | | | | | | | | |   (997)   ~ (e1 = e0)
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 191.96/30.94  | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | Case 1:
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | |   (998)  all_56_8 = e3
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | REF_CLOSE: (776), (964), (998) are inconsistent by sub-proof
% 191.96/30.94  | | | | | | | | | | | | | | | |            #926.
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | Case 2:
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | |   (999)   ~ (all_56_8 = e3)
% 191.96/30.94  | | | | | | | | | | | | | | | |   (1000)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 191.96/30.94  | | | | | | | | | | | | | | | | 
% 191.96/30.94  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.94  | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | |   (1001)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.95  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 191.96/30.95  | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1002)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.95  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | ALPHA: (1002) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1003)  all_52_6 = e0
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1004)  all_52_2 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1005)  all_52_0 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | REDUCE: (185), (1004) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1006)  op(all_52_3, all_52_3) = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | REDUCE: (183), (1003) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1007)  op(all_52_7, all_52_7) = e0
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | REDUCE: (610), (1005) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | |   (1008)  op(all_6_2, all_6_2) = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1009)  all_56_7 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (1009) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1010)  all_52_27 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | SIMP: (1010) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1011)  all_52_27 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | REDUCE: (598), (1011) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1012)   ~ (all_52_19 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1011) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1013)  op(e3, e3) = all_52_26
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (41), (1013)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1014)  all_52_26 = all_6_2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1015)  all_58_0 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1015) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1016)  all_6_2 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1016) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1017)   ~ (all_52_17 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1016) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1018)  op(e3, e3) = all_6_1
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1016) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1019)  op(e3, e3) = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1018), (1019) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1020)  all_6_1 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1020) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1021)  op(e3, e3) = all_6_0
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1019), (1021) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1022)  all_6_0 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | |   (1023)  all_58_4 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (393), (1017), (1023) are inconsistent by
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1302.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | |   (1024)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1025)  all_58_0 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1015), (1025) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1026)  e3 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1026) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1027)  $false
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1027) is inconsistent.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1028)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1029)  all_56_10 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1029) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1030)  all_10_2 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (593), (961), (1030), (function-axioms) are
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1031)   ~ (all_56_10 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (1031) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1032)   ~ (all_10_2 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1024) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1033)  all_58_5 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (1033) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1034)  all_52_19 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1034) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1035)  $false
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1035) is inconsistent.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1036)  all_58_8 = e3 | all_58_14 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1036) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1037)  all_58_8 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (1037) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1038)  all_10_2 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1032), (1038) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1039)  $false
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1039) is inconsistent.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1040)  all_58_14 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (1040) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1041)  all_52_23 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (157), (272), (304), (305),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (346), (351), (387), (543), (564), (571), (582),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (590), (772), (781), (965), (1006), (1007),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (1028), (1041), (function-axioms) are inconsistent
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #923.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1042)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (61), (306), (351), (387), (564),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |            (573), (776), (965), (1006), (1007), (1008),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |            (1042), (function-axioms) are inconsistent by
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |            sub-proof #920.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1043)   ~ (all_56_7 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1044)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | REDUCE: (427), (1043) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | |   (1045)   ~ (all_52_27 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1046)  all_58_9 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1046) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1047)  all_52_25 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | SIMP: (1047) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1048)  all_52_25 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1048) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1049)   ~ (all_6_2 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | SIMP: (1049) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1050)   ~ (all_6_2 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (61), (306), (332), (351), (387),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |            (405), (564), (573), (776), (965), (1006), (1007),
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |            (1008), (1050), (function-axioms) are inconsistent
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |            by sub-proof #919.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | |   (1051)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1051) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | |   (1052)  all_58_10 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (1045), (1052) are inconsistent by
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | |   (1053)  all_58_11 = e3 | all_58_15 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1053) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1054)  all_58_11 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1054) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1055)  all_52_29 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1055) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1056)  all_52_29 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (1056) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1057)   ~ (all_52_25 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (972), (1056) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1058)   ~ (all_10_0 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (1056) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1059)  op(e3, e3) = all_52_28
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e3, simplifying with (41), (1059)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | |   (1060)  all_52_28 = all_6_2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1061)  all_56_3 = e3
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (1057), (1061) are inconsistent by
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1339.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1062)   ~ (all_56_3 = e3)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | |   (1063)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1064)  all_58_9 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1064) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1065)  all_52_25 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1065) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1066)  all_52_25 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (1066) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1067)   ~ (all_52_27 = e2)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1067) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1068)   ~ (all_52_27 = e2)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1066) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1069)   ~ (all_6_2 = e2)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1069) implies:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1070)   ~ (all_6_2 = e2)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1057), (1066) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1071)   ~ (e3 = e2)
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (1066) imply:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | |   (1072)  op(e2, e2) = all_52_24
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1044) gives:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1073)  all_56_7 = e2
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (1068), (1073) are inconsistent by
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #918.
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (1074)   ~ (all_56_7 = e2)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (1075)  all_56_7 = e1 | all_56_7 = e0
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1076)  all_56_7 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (1076) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1077)  all_52_27 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1077) implies:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1078)  all_52_27 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1068), (1078) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1079)   ~ (e2 = e1)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1078) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1080)  op(e1, e1) = all_52_26
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_26, e1, e1, simplifying with (51), (1080)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1081)  all_52_26 = all_10_2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e2, e2, simplifying with (36), (1072)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1082)  all_52_24 = all_4_2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1083)  all_58_0 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1083) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1084)  all_6_2 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1070), (1084) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1085)  $false
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1085) is inconsistent.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1086)   ~ (all_58_0 = e2)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1088)  all_56_14 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (1088) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  all_52_23 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (157), (272), (304), (305),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (346), (351), (387), (543), (564), (571), (582),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (590), (772), (781), (965), (1006), (1007),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1087), (1089), (function-axioms) are inconsistent
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #923.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1090)   ~ (all_56_14 = e3)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (1090) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1091)   ~ (all_52_23 = e3)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1092)  all_58_0 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1092) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1093)  all_6_2 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1093) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1094)  op(e3, e3) = all_6_1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1093) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1095)  op(e3, e3) = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1096)  all_58_12 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (387), (564), (781), (965), (1006),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1087), (1096), (function-axioms) are inconsistent
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #916.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1097)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1097) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1098)  all_58_13 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1098) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1099)  all_52_15 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (1099) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1100)  op(e3, e3) = all_52_14
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (1099) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1101)  op(e0, e2) = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (1094), (1100)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1102)  all_52_14 = all_6_1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (1095), (1100)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1103)  all_52_14 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1102), (1103) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1104)  all_6_1 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1104) implies:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1105)  all_6_1 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1105) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1106)  op(e3, e3) = all_6_0
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1095), (1106) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1107)  all_6_0 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1108)  all_56_12 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (1108) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1109)  all_52_7 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (1109) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1110)  all_58_12 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (387), (564), (781), (965), (1006),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1087), (1110), (function-axioms) are inconsistent
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #916.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1111)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1112)  all_58_12 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (1112) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1113)  all_52_7 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (361), (459), (593), (750),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (781), (959), (961), (964), (968), (973), (1000),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1113), (function-axioms) are inconsistent by
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #908.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1114)   ~ (all_58_12 = e1)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (1114) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1115)   ~ (all_52_7 = e1)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (431), (977), (980), (1007), (1101),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1111), (1115), (function-axioms) are inconsistent
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1373.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1116)  all_58_14 = e3 | all_58_15 = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (542), (978), (1091), (1116) are inconsistent
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #983.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1117)   ~ (all_58_0 = e3)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (1117) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1118)   ~ (all_6_2 = e3)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (321), (332), (387), (405),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (564), (776), (781), (965), (1006), (1008),
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1087), (1118), (function-axioms) are inconsistent
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #907.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1119)  all_56_7 = e0
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (984), (1119) are inconsistent by sub-proof
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            #906.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | |   (1120)   ~ (all_58_9 = e2)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | |   (1121)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (1120) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | |   (1122)   ~ (all_52_25 = e2)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1063) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (1123)  all_56_3 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (1122), (1123) are inconsistent by
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1259.
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (1124)  all_56_3 = e1 | all_56_3 = e0
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1125)  all_56_3 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (1125) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1126)  all_52_25 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1126) implies:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1127)  all_52_25 = e1
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (1127) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1128)   ~ (all_52_27 = e1)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1128) implies:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1129)   ~ (all_52_27 = e1)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1121) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1130)  all_58_10 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (1130) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1131)  all_52_27 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1131) implies:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1132)  all_52_27 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (1132) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1133)   ~ (all_52_3 = e2)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1045), (1132) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1134)   ~ (e3 = e2)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1132) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1135)  op(e2, e2) = all_52_26
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_26, e2, e2, simplifying with (36), (1135)
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1136)  all_52_26 = all_4_2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1137)  all_58_0 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1137) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1138)  all_6_2 = e2
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1008), (1138) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1139)  op(e2, e2) = e3
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1138) imply:
% 191.96/30.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1140)  op(e2, e3) = all_6_1
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1138) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1141)  op(e3, e3) = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (166), (332), (351), (387), (564),
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (611), (776), (965), (1007), (1137), (1139),
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1140), (1141), (function-axioms) are inconsistent
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #904.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1142)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1142) gives:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1143)  all_58_2 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (1133), (1143) are inconsistent by
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1156.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1144)  all_58_6 = e2 | all_58_12 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1144) gives:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1145)  all_58_6 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (781), (965), (1145) are inconsistent by sub-proof
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #917.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1146)  all_58_12 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (1146) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1147)  all_52_7 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1147) implies:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1148)  all_52_7 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1148) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1149)   ~ (all_52_15 = e2)
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1149) implies:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1150)   ~ (all_52_15 = e2)
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1007), (1148) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1151)  op(e2, e2) = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (1151) gives:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1152)  all_4_2 = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1152) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1153)  op(e0, e2) = all_4_1
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_15,
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_1, e2, e0, simplifying with (157), (1153)
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1154)  all_52_15 = all_4_1
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (1154) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1155)  all_56_13 = all_4_1
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1156)  all_56_13 = e3
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1155), (1156) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1157)  all_4_1 = e3
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1157) implies:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1158)  all_4_1 = e3
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (977), (1158) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1159)  $false
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1159) is inconsistent.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1160)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (157), (304), (346), (543),
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (772), (981), (1146), (1150), (1151), (1160),
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1197.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1161)   ~ (all_58_10 = e2)
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1161) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1162)   ~ (all_52_27 = e2)
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (984), (1044), (1129), (1162) are
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1163)  all_56_3 = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (983), (1163) are inconsistent by sub-proof
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1258.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | |   (1164)  all_58_15 = e3
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (978), (1164) are inconsistent by sub-proof
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | |            #1350.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1165)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 191.96/30.97  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | ALPHA: (1165) implies:
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1166)  all_52_14 = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1167)  all_52_12 = e1
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1168)  all_52_10 = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1169)  all_52_8 = e3
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | REDUCE: (182), (1169) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1170)  op(all_52_9, all_52_9) = e3
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | REDUCE: (180), (1167) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1171)  op(all_52_13, all_52_13) = e1
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | REDUCE: (179), (1166) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1172)  op(all_52_15, all_52_15) = e0
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | REDUCE: (611), (1168) imply:
% 191.96/30.97  | | | | | | | | | | | | | | | | | |   (1173)  op(all_4_2, all_4_2) = e2
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (51), (158), (166), (167), (168), (173), (175),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (183), (185), (272), (273), (274), (275), (276),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (284), (304), (305),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (306), (307), (308), (317), (321), (322), (323),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (325), (328), (330), (346), (351), (352), (361),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (394),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (405), (411), (421), (427), (431), (459), (539),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (548), (549),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (551), (555), (557), (561), (563), (564), (566),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (571), (572), (578), (582), (584), (586), (587),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (588), (589), (593), (595), (596), (602), (604),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (612), (750), (773), (778), (781), (787), (959),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (961), (964), (965), (966), (968), (970), (972),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (973), (974), (975), (978), (980), (981), (983),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (984), (988), (1000), (1170), (1171), (1172),
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            (1173), (function-axioms) are inconsistent by
% 191.96/30.97  | | | | | | | | | | | | | | | | | |            sub-proof #880.
% 191.96/30.97  | | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | End of split
% 191.96/30.97  | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.97  | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | |   (1174)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 191.96/30.97  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 191.96/30.97  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.96/30.97  | | | | | | | | | | | | | | | | | 
% 191.96/30.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (280),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (304), (305), (306),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (317), (318), (321),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (322), (325), (326), (330), (331), (332), (333),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (415), (427), (431), (539), (542), (543), (544),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (576), (577),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (590), (593), (594), (595), (596), (598), (600),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (602), (604), (605), (608), (610), (611), (612),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (773), (775), (778), (787), (977), (978), (980),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (981), (982), (983), (984), (985), (988), (1174),
% 191.96/30.97  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.97  | | | | | | | | | | | | | | | | |            #1202.
% 191.96/30.97  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | End of split
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | End of split
% 191.96/30.98  | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | Case 2:
% 191.96/30.98  | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | |   (1175)   ~ (all_58_15 = e0)
% 191.96/30.98  | | | | | | | | | | | | | | |   (1176)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 191.96/30.98  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 191.96/30.98  | | | | | | | | | | | | | | |             e0)
% 191.96/30.98  | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | ALPHA: (1176) implies:
% 191.96/30.98  | | | | | | | | | | | | | | |   (1177)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 191.96/30.98  | | | | | | | | | | | | | | |   (1178)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 191.96/30.98  | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | REDUCE: (541), (1175) imply:
% 191.96/30.98  | | | | | | | | | | | | | | |   (1179)   ~ (all_14_2 = e0)
% 191.96/30.98  | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | Case 1:
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | |   (1180)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.98  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 191.96/30.98  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | BETA: splitting (1180) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1181)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.98  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | ALPHA: (1181) implies:
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1182)  all_52_6 = e0
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1183)  all_52_2 = e2
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1184)  all_52_0 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | REDUCE: (185), (1183) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1185)  op(all_52_3, all_52_3) = e2
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | REDUCE: (183), (1182) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1186)  op(all_52_7, all_52_7) = e0
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | REDUCE: (610), (1184) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1187)  op(all_6_2, all_6_2) = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1188)  all_58_0 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1188) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1189)  all_6_2 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | REDUCE: (43), (1189) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1190)  op(e3, e3) = all_6_1
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | REDUCE: (41), (1189) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1191)  op(e3, e3) = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 191.96/30.98  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1190), (1191) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1192)  all_6_1 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | REDUCE: (42), (1192) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1193)  op(e3, e3) = all_6_0
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 191.96/30.98  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1191), (1193) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1194)  all_6_0 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | |   (1195)  all_58_0 = e2
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1188), (1195) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | |   (1196)  e3 = e2
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1196) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | |   (1197)  $false
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | CLOSE: (1197) is inconsistent.
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | |   (1198)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |   (1199)  all_56_13 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (1199) imply:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |   (1200)  all_52_15 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | SIMP: (1200) implies:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |   (1201)  all_52_15 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (38), (51), (61), (157), (273),
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            (304), (305), (351), (431), (542), (543), (571),
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            (573), (600), (977), (1177), (1186), (1201),
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            #1168.
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |   (1202)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (157), (304), (305), (346),
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            (351), (387), (543), (564), (571), (582), (772),
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            (781), (965), (1185), (1186), (1198), (1202),
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | |            #924.
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.98  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | |   (1203)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (61), (306), (351), (387), (564),
% 191.96/30.98  | | | | | | | | | | | | | | | | | |            (573), (776), (965), (1185), (1186), (1187),
% 191.96/30.98  | | | | | | | | | | | | | | | | | |            (1203), (function-axioms) are inconsistent by
% 191.96/30.98  | | | | | | | | | | | | | | | | | |            sub-proof #920.
% 191.96/30.98  | | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | End of split
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1204)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 191.96/30.98  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (277), (278), (280), (281), (282), (284), (304),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (306), (309), (313), (317), (319), (321), (323),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (325), (326), (328), (330), (331), (332), (333),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (421), (427), (431), (538), (539), (541), (542),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (570), (571),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (584), (586), (588), (589), (590), (591), (592),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (593), (594), (595), (597), (603), (604), (605),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (613), (772), (773), (775), (778), (787), (977),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (1177), (1178), (1179), (1204), (function-axioms)
% 191.96/30.98  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1091.
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | End of split
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | Case 2:
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | |   (1205)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 191.96/30.98  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 191.96/30.98  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | BETA: splitting (1205) gives:
% 191.96/30.98  | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | |   (1206)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 191.96/30.98  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 191.96/30.98  | | | | | | | | | | | | | | | | | 
% 191.96/30.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 191.96/30.98  | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (787),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (1177), (1178), (1206), (function-axioms) are
% 191.96/30.99  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | |   (1207)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 191.96/30.99  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (775), (778), (787), (1177), (1179), (1207),
% 191.96/30.99  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.99  | | | | | | | | | | | | | | | | |            #1008.
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | End of split
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | End of split
% 191.96/30.99  | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | End of split
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | Case 2:
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | |   (1208)  all_32_1 = e3
% 191.96/30.99  | | | | | | | | | | | | | |   (1209)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | COMBINE_EQS: (663), (1208) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1210)  all_4_1 = e3
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | COMBINE_EQS: (686), (1210) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1211)  all_38_1 = e3
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | REDUCE: (38), (1210) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1212)  op(all_4_2, e2) = e3
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | REDUCE: (37), (1210) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1213)  op(e2, e3) = all_4_0
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 191.96/30.99  | | | | | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (1213)
% 191.96/30.99  | | | | | | | | | | | | | |              gives:
% 191.96/30.99  | | | | | | | | | | | | | |   (1214)  all_52_3 = all_4_0
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | COMBINE_EQS: (411), (1214) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1215)  all_56_4 = all_4_0
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | COMBINE_EQS: (387), (1214) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1216)  all_58_2 = all_4_0
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | REDUCE: (563), (1214) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1217)   ~ (all_52_7 = all_4_0)
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | SIMP: (1217) implies:
% 191.96/30.99  | | | | | | | | | | | | | |   (1218)   ~ (all_52_7 = all_4_0)
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | REDUCE: (551), (1214) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1219)   ~ (all_6_2 = all_4_0)
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | SIMP: (1219) implies:
% 191.96/30.99  | | | | | | | | | | | | | |   (1220)   ~ (all_6_2 = all_4_0)
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | REDUCE: (564), (1214) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1221)   ~ (all_4_0 = all_4_2)
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | REDUCE: (185), (1214) imply:
% 191.96/30.99  | | | | | | | | | | | | | |   (1222)  op(all_4_0, all_4_0) = all_52_2
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 191.96/30.99  | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | |   (1223)   ~ (all_38_0 = e1)
% 191.96/30.99  | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | REDUCE: (766), (1223) imply:
% 191.96/30.99  | | | | | | | | | | | | | | |   (1224)   ~ (all_4_0 = e1)
% 191.96/30.99  | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1225)  all_58_15 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1225) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1226)  all_14_2 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (573), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1227)   ~ (all_52_7 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (591), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1228)   ~ (all_52_15 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (603), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1229)   ~ (all_52_23 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (606), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1230)   ~ (all_52_25 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (608), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1231)   ~ (all_52_27 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (609), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1232)   ~ (all_52_29 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (613), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1233)  op(e0, e0) = all_52_30
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (63), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1234)  op(e0, e0) = all_14_1
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (61), (1226) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1235)  op(e0, e0) = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 191.96/30.99  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1233), (1234)
% 191.96/30.99  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1236)  all_52_30 = all_14_1
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 191.96/30.99  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1233), (1235)
% 191.96/30.99  | | | | | | | | | | | | | | | |              gives:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1237)  all_52_30 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | COMBINE_EQS: (1236), (1237) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1238)  all_14_1 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (62), (1238) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1239)  op(e0, e0) = all_14_0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 191.96/30.99  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1235), (1239) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1240)  all_14_0 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (783), (1240) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1241)   ~ (e3 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (779), (1240) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1242)   ~ (e2 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | REDUCE: (789), (1240) imply:
% 191.96/30.99  | | | | | | | | | | | | | | | |   (1243)   ~ (e1 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | |   (1244)  all_56_8 = e3
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (776), (964), (1244) are inconsistent by sub-proof
% 191.96/30.99  | | | | | | | | | | | | | | | | |            #926.
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | |   (1245)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | |   (1246)  all_56_4 = e3
% 191.96/30.99  | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | REF_CLOSE: (785), (1215), (1246) are inconsistent by
% 191.96/30.99  | | | | | | | | | | | | | | | | | |            sub-proof #980.
% 191.96/30.99  | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | |   (1247)   ~ (all_56_4 = e3)
% 191.96/30.99  | | | | | | | | | | | | | | | | | |   (1248)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | |   (1249)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.99  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 191.96/30.99  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (1249) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |   (1250)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (611), (721), (1209), (1212), (1215), (1216),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (1221), (1222), (1224), (1248), (1250),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            #970.
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |   (1251)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (51), (158), (166), (167), (168), (173), (175),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (185), (272), (273),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (274), (275), (276), (278), (280), (281), (282),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (317),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (321), (322), (323), (325), (328), (330), (346),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (421), (427),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (431), (459), (539), (542), (543), (544), (545),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (546), (548), (549), (551), (555), (557), (561),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (563), (564), (566), (571), (572), (578), (582),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (593), (595),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (596), (602), (604), (611), (612), (750), (773),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (778), (781), (787), (959), (961), (964), (965),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (966), (968), (970), (972), (973), (974), (975),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (1225), (1227), (1228), (1230), (1231), (1235),
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            (1245), (1251), (function-axioms) are inconsistent
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |            by sub-proof #879.
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | End of split
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | |   (1252)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 191.96/30.99  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 191.96/30.99  | | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (1252) gives:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |   (1253)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 191.96/30.99  | | | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (42), (43),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (51), (158), (162), (167), (169), (172), (173),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (180), (182), (183),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (282), (283), (284), (304), (307), (308), (317),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (319), (321), (323), (325), (326), (328), (330),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (415),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (417), (421), (427), (431), (523), (539), (542),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (570), (571), (572),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (574), (575), (576), (578), (580), (584), (586),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (595), (597), (598),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (600), (604), (605), (607), (610), (611), (612),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (721), (775), (778), (785), (787), (1209), (1212),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (1215), (1216), (1218), (1220), (1221), (1224),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (1225), (1227), (1228), (1229), (1230), (1232),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (1235), (1248), (1253), (function-axioms) are
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |   (1254)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (309), (321), (332),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (405), (427), (523), (539),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (544), (545), (548), (561), (574), (584), (586),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (605), (607), (610), (611), (721), (785), (1209),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (1212), (1215), (1216), (1220), (1221), (1224),
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            (1225), (1230), (1254), (function-axioms) are
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | Case 2:
% 191.96/31.00  | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | |   (1255)   ~ (all_58_15 = e0)
% 191.96/31.00  | | | | | | | | | | | | | | | |   (1256)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 191.96/31.00  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 191.96/31.00  | | | | | | | | | | | | | | | |             e0)
% 191.96/31.00  | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (158), (162), (166),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (275), (276), (277), (279), (280), (281), (282),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (417), (421), (431), (523), (538), (539), (540),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (586), (587), (588), (590), (591), (592), (593),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (602), (603),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (611), (612), (613), (721), (772), (773), (775),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (778), (785), (787), (1209), (1212), (1215),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (1216), (1220), (1221), (1222), (1224), (1255),
% 191.96/31.00  | | | | | | | | | | | | | | | |            (1256), (function-axioms) are inconsistent by
% 191.96/31.00  | | | | | | | | | | | | | | | |            sub-proof #928.
% 191.96/31.00  | | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | Case 2:
% 191.96/31.00  | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | |   (1257)  all_38_0 = e1
% 191.96/31.00  | | | | | | | | | | | | | | |   (1258)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 191.96/31.00  | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | COMBINE_EQS: (766), (1257) imply:
% 191.96/31.00  | | | | | | | | | | | | | | |   (1259)  all_4_0 = e1
% 191.96/31.00  | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 191.96/31.00  | | | | | | | | | | | | | | |            (1211), (1212), (1221), (1258), (1259),
% 191.96/31.00  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 191.96/31.00  | | | | | | | | | | | | | | |            #927.
% 191.96/31.00  | | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | Case 2:
% 191.96/31.00  | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | |   (1260)  all_24_0 = e1
% 191.96/31.00  | | | | | | | | | | | |   (1261)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 191.96/31.00  | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (41), (42),
% 191.96/31.00  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (109), (114),
% 191.96/31.00  | | | | | | | | | | | |            (124), (156), (157), (158), (159), (161), (162),
% 191.96/31.00  | | | | | | | | | | | |            (163), (166), (167), (168), (169), (172), (173),
% 191.96/31.00  | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 191.96/31.00  | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 191.96/31.00  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 191.96/31.00  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 191.96/31.00  | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 191.96/31.00  | | | | | | | | | | | |            (311), (313), (315), (316), (317), (319), (320),
% 191.96/31.00  | | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 191.96/31.00  | | | | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 191.96/31.00  | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 191.96/31.00  | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 191.96/31.00  | | | | | | | | | | | |            (417), (421), (427), (431), (491), (508), (525),
% 191.96/31.00  | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 191.96/31.00  | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 191.96/31.00  | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 191.96/31.00  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (570), (571),
% 191.96/31.00  | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 191.96/31.00  | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 191.96/31.00  | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 191.96/31.00  | | | | | | | | | | | |            (597), (598), (600), (602), (603), (604), (605),
% 191.96/31.00  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 191.96/31.00  | | | | | | | | | | | |            (613), (649), (663), (685), (686), (711), (765),
% 191.96/31.00  | | | | | | | | | | | |            (766), (772), (773), (775), (778), (779), (783),
% 191.96/31.00  | | | | | | | | | | | |            (785), (787), (1260), (1261), (function-axioms)
% 191.96/31.00  | | | | | | | | | | | |            are inconsistent by sub-proof #836.
% 191.96/31.00  | | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | End of split
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | Case 2:
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | |   (1262)  all_22_1 = e2
% 191.96/31.00  | | | | | | | | | | |   (1263)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | COMBINE_EQS: (658), (1262) imply:
% 191.96/31.00  | | | | | | | | | | |   (1264)  all_6_1 = e2
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | SIMP: (1264) implies:
% 191.96/31.00  | | | | | | | | | | |   (1265)  all_6_1 = e2
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | REDUCE: (43), (1265) imply:
% 191.96/31.00  | | | | | | | | | | |   (1266)  op(all_6_2, e3) = e2
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | REDUCE: (42), (1265) imply:
% 191.96/31.00  | | | | | | | | | | |   (1267)  op(e3, e2) = all_6_0
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 191.96/31.00  | | | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (1267)
% 191.96/31.00  | | | | | | | | | | |              gives:
% 191.96/31.00  | | | | | | | | | | |   (1268)  all_52_9 = all_6_0
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | COMBINE_EQS: (394), (1268) imply:
% 191.96/31.00  | | | | | | | | | | |   (1269)  all_56_1 = all_6_0
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | COMBINE_EQS: (549), (1268) imply:
% 191.96/31.00  | | | | | | | | | | |   (1270)  all_58_1 = all_6_0
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | REDUCE: (575), (1268) imply:
% 191.96/31.00  | | | | | | | | | | |   (1271)   ~ (all_52_13 = all_6_0)
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | SIMP: (1271) implies:
% 191.96/31.00  | | | | | | | | | | |   (1272)   ~ (all_52_13 = all_6_0)
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.00  | | | | | | | | | | | REDUCE: (576), (1268) imply:
% 191.96/31.00  | | | | | | | | | | |   (1273)   ~ (all_52_15 = all_6_0)
% 191.96/31.00  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | SIMP: (1273) implies:
% 191.96/31.01  | | | | | | | | | | |   (1274)   ~ (all_52_15 = all_6_0)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | REDUCE: (577), (1268) imply:
% 191.96/31.01  | | | | | | | | | | |   (1275)   ~ (all_52_17 = all_6_0)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | SIMP: (1275) implies:
% 191.96/31.01  | | | | | | | | | | |   (1276)   ~ (all_52_17 = all_6_0)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | REDUCE: (578), (1268) imply:
% 191.96/31.01  | | | | | | | | | | |   (1277)   ~ (all_52_25 = all_6_0)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | SIMP: (1277) implies:
% 191.96/31.01  | | | | | | | | | | |   (1278)   ~ (all_52_25 = all_6_0)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | REDUCE: (557), (1268) imply:
% 191.96/31.01  | | | | | | | | | | |   (1279)   ~ (all_6_0 = all_6_2)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | REDUCE: (574), (1268) imply:
% 191.96/31.01  | | | | | | | | | | |   (1280)   ~ (all_6_0 = all_4_2)
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | REDUCE: (182), (1268) imply:
% 191.96/31.01  | | | | | | | | | | |   (1281)  op(all_6_0, all_6_0) = all_52_8
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | BETA: splitting (89) gives:
% 191.96/31.01  | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | Case 1:
% 191.96/31.01  | | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | |   (1282)   ~ (all_24_0 = e1)
% 191.96/31.01  | | | | | | | | | | | | 
% 191.96/31.01  | | | | | | | | | | | | REDUCE: (711), (1282) imply:
% 191.96/31.01  | | | | | | | | | | | |   (1283)   ~ (all_14_0 = e1)
% 191.96/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 192.58/31.01  | | | | | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (104),
% 192.58/31.01  | | | | | | | | | | | |            (129), (157), (158), (161), (162), (166), (167),
% 192.58/31.01  | | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 192.58/31.01  | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 192.58/31.01  | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (278),
% 192.58/31.01  | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 192.58/31.01  | | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 192.58/31.01  | | | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 192.58/31.01  | | | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 192.58/31.01  | | | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 192.58/31.01  | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 192.58/31.01  | | | | | | | | | | | |            (417), (421), (427), (431), (522), (526), (538),
% 192.58/31.01  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 192.58/31.01  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 192.58/31.01  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 192.58/31.01  | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 192.58/31.01  | | | | | | | | | | | |            (573), (574), (575), (577), (578), (580), (582),
% 192.58/31.01  | | | | | | | | | | | |            (584), (586), (588), (590), (591), (592), (593),
% 192.58/31.01  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 192.58/31.01  | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 192.58/31.01  | | | | | | | | | | | |            (610), (611), (612), (613), (670), (687), (739),
% 192.58/31.01  | | | | | | | | | | | |            (767), (773), (775), (776), (779), (781), (783),
% 192.58/31.01  | | | | | | | | | | | |            (785), (1263), (1266), (1269), (1270), (1272),
% 192.58/31.01  | | | | | | | | | | | |            (1274), (1276), (1278), (1279), (1280), (1281),
% 192.58/31.01  | | | | | | | | | | | |            (1283), (function-axioms) are inconsistent by
% 192.58/31.01  | | | | | | | | | | | |            sub-proof #776.
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | Case 2:
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | |   (1284)  all_24_0 = e1
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | COMBINE_EQS: (711), (1284) imply:
% 192.58/31.01  | | | | | | | | | | | |   (1285)  all_14_0 = e1
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | SIMP: (1285) implies:
% 192.58/31.01  | | | | | | | | | | | |   (1286)  all_14_0 = e1
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | REDUCE: (779), (1286) imply:
% 192.58/31.01  | | | | | | | | | | | |   (1287)   ~ (e2 = e1)
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | REDUCE: (62), (1286) imply:
% 192.58/31.01  | | | | | | | | | | | |   (1288)  op(e0, all_14_1) = e1
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 192.58/31.01  | | | | | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (104),
% 192.58/31.01  | | | | | | | | | | | |            (129), (157), (158), (161), (162), (166), (167),
% 192.58/31.01  | | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 192.58/31.01  | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 192.58/31.01  | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (279),
% 192.58/31.01  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 192.58/31.01  | | | | | | | | | | | |            (304), (306), (307), (309), (311), (313), (315),
% 192.58/31.01  | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 192.58/31.01  | | | | | | | | | | | |            (327), (328), (329), (331), (332), (333), (343),
% 192.58/31.01  | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 192.58/31.01  | | | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (417),
% 192.58/31.01  | | | | | | | | | | | |            (421), (431), (522), (526), (538), (539), (540),
% 192.58/31.01  | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 192.58/31.01  | | | | | | | | | | | |            (548), (549), (551), (553), (555), (559), (561),
% 192.58/31.01  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 192.58/31.01  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 192.58/31.01  | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (588),
% 192.58/31.01  | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 192.58/31.01  | | | | | | | | | | | |            (597), (598), (600), (602), (603), (604), (605),
% 192.58/31.01  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 192.58/31.01  | | | | | | | | | | | |            (613), (670), (687), (739), (767), (773), (775),
% 192.58/31.01  | | | | | | | | | | | |            (776), (779), (781), (785), (1263), (1266),
% 192.58/31.01  | | | | | | | | | | | |            (1269), (1270), (1272), (1274), (1276), (1278),
% 192.58/31.01  | | | | | | | | | | | |            (1279), (1280), (1281), (1288), (function-axioms)
% 192.58/31.01  | | | | | | | | | | | |            are inconsistent by sub-proof #771.
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | End of split
% 192.58/31.01  | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | End of split
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | Case 2:
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | |   (1289)  all_20_0 = e3
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | COMBINE_EQS: (758), (1289) imply:
% 192.58/31.01  | | | | | | | | | |   (1290)  all_4_0 = e3
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | SIMP: (1290) implies:
% 192.58/31.01  | | | | | | | | | |   (1291)  all_4_0 = e3
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | REDUCE: (37), (1291) imply:
% 192.58/31.01  | | | | | | | | | |   (1292)  op(e2, all_4_1) = e3
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | BETA: splitting (84) gives:
% 192.58/31.01  | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | |   (1293)   ~ (all_22_1 = e2)
% 192.58/31.01  | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | REDUCE: (658), (1293) imply:
% 192.58/31.01  | | | | | | | | | | |   (1294)   ~ (all_6_1 = e2)
% 192.58/31.01  | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | BETA: splitting (89) gives:
% 192.58/31.01  | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | |   (1295)   ~ (all_24_0 = e1)
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | REDUCE: (711), (1295) imply:
% 192.58/31.01  | | | | | | | | | | | |   (1296)   ~ (all_14_0 = e1)
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | BETA: splitting (104) gives:
% 192.58/31.01  | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | |   (1297)   ~ (all_30_1 = e3)
% 192.58/31.01  | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | REDUCE: (670), (1297) imply:
% 192.58/31.01  | | | | | | | | | | | | |   (1298)   ~ (all_10_1 = e3)
% 192.58/31.01  | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 192.58/31.01  | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | |   (1299)   ~ (all_40_1 = e2)
% 192.58/31.01  | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | REDUCE: (687), (1299) imply:
% 192.58/31.01  | | | | | | | | | | | | | |   (1300)   ~ (all_10_1 = e2)
% 192.58/31.01  | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 192.58/31.01  | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | |   (1301)  all_58_15 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1301) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1302)  all_14_2 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (573), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1303)   ~ (all_52_7 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (591), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1304)   ~ (all_52_15 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (603), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1305)   ~ (all_52_23 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (606), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1306)   ~ (all_52_25 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (608), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1307)   ~ (all_52_27 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (609), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1308)   ~ (all_52_29 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (613), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1309)  op(e0, e0) = all_52_30
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (63), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1310)  op(e0, e0) = all_14_1
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (61), (1302) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1311)  op(e0, e0) = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 192.58/31.01  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1309), (1310)
% 192.58/31.01  | | | | | | | | | | | | | | |              gives:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1312)  all_52_30 = all_14_1
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 192.58/31.01  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1309), (1311)
% 192.58/31.01  | | | | | | | | | | | | | | |              gives:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1313)  all_52_30 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | COMBINE_EQS: (1312), (1313) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1314)  all_14_1 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | SIMP: (1314) implies:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1315)  all_14_1 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (62), (1315) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1316)  op(e0, e0) = all_14_0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 192.58/31.01  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1311), (1316) gives:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1317)  all_14_0 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (783), (1317) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1318)   ~ (e3 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (779), (1317) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1319)   ~ (e2 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | REDUCE: (1296), (1317) imply:
% 192.58/31.01  | | | | | | | | | | | | | | |   (1320)   ~ (e1 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.01  | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | |   (1321)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.01  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.01  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.01  | | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | | BETA: splitting (1321) gives:
% 192.58/31.01  | | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.01  | | | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | | |   (1322)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.01  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | | | ALPHA: (1322) implies:
% 192.58/31.01  | | | | | | | | | | | | | | | | |   (1323)  all_52_6 = e0
% 192.58/31.01  | | | | | | | | | | | | | | | | |   (1324)  all_52_4 = e1
% 192.58/31.01  | | | | | | | | | | | | | | | | |   (1325)  all_52_2 = e2
% 192.58/31.01  | | | | | | | | | | | | | | | | |   (1326)  all_52_0 = e3
% 192.58/31.01  | | | | | | | | | | | | | | | | | 
% 192.58/31.01  | | | | | | | | | | | | | | | | | REDUCE: (185), (1325) imply:
% 192.58/31.01  | | | | | | | | | | | | | | | | |   (1327)  op(all_52_3, all_52_3) = e2
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | | REDUCE: (184), (1324) imply:
% 192.58/31.02  | | | | | | | | | | | | | | | | |   (1328)  op(all_52_5, all_52_5) = e1
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | | REDUCE: (183), (1323) imply:
% 192.58/31.02  | | | | | | | | | | | | | | | | |   (1329)  op(all_52_7, all_52_7) = e0
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | | REDUCE: (610), (1326) imply:
% 192.58/31.02  | | | | | | | | | | | | | | | | |   (1330)  op(all_6_2, all_6_2) = e3
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (38), (41), (51), (53), (61),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (156), (157), (166), (179), (271), (272), (273),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (304), (306), (321), (332), (343), (346), (351),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (387), (405), (431), (542), (543), (547), (555),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (564), (569), (571), (572), (573), (600), (772),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (1292), (1298), (1300), (1301), (1303), (1304),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (1327), (1328), (1329), (1330), (function-axioms)
% 192.58/31.02  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #767.
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | |   (1331)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.02  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (36), (38), (41), (43), (51), (53),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (178), (179), (180), (182), (272), (273), (277),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (284), (304),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (305), (306), (309), (313), (314), (317), (322),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (324), (325), (327), (333), (346), (351), (366),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (367), (372), (375), (388), (393), (394), (405),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (411), (415), (427), (431), (539), (542), (543),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (564), (567), (568), (571), (572), (574), (575),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (588), (589), (595), (604), (605), (611), (612),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (772), (778), (1294), (1298), (1301), (1303),
% 192.58/31.02  | | | | | | | | | | | | | | | | |            (1304), (1306), (1311), (1331), (function-axioms)
% 192.58/31.02  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #969.
% 192.58/31.02  | | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | End of split
% 192.58/31.02  | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.02  | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | |   (1332)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.02  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.02  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.02  | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (279),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (304), (305),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (313), (317), (318),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (321), (322), (325), (326), (330), (331), (332),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (539), (542),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (564), (565), (567), (568), (569), (570), (571),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (572), (576), (577), (578), (580), (582), (584),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (592), (593), (594),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (604),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (605), (608), (610), (611), (612), (773), (775),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (778), (1292), (1294), (1301), (1303), (1304),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (1305), (1306), (1307), (1308), (1311), (1332),
% 192.58/31.02  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.02  | | | | | | | | | | | | | | | |            #763.
% 192.58/31.02  | | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | End of split
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | Case 2:
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | |   (1333)   ~ (all_58_15 = e0)
% 192.58/31.02  | | | | | | | | | | | | | | |   (1334)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 192.58/31.02  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 192.58/31.02  | | | | | | | | | | | | | | |             e0)
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | ALPHA: (1334) implies:
% 192.58/31.02  | | | | | | | | | | | | | | |   (1335)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 192.58/31.02  | | | | | | | | | | | | | | |   (1336)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | REDUCE: (541), (1333) imply:
% 192.58/31.02  | | | | | | | | | | | | | | |   (1337)   ~ (all_14_2 = e0)
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 192.58/31.02  | | | | | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (62), (63),
% 192.58/31.02  | | | | | | | | | | | | | | |            (157), (158), (159), (161), (162), (163), (166),
% 192.58/31.02  | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 192.58/31.02  | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 192.58/31.02  | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 192.58/31.02  | | | | | | | | | | | | | | |            (275), (276), (277), (278), (279), (280), (281),
% 192.58/31.02  | | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (305), (306),
% 192.58/31.02  | | | | | | | | | | | | | | |            (307), (308), (309), (311), (312), (313), (314),
% 192.58/31.02  | | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 192.58/31.02  | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 192.58/31.02  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 192.58/31.02  | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 192.58/31.02  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 192.58/31.02  | | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 192.58/31.02  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 192.58/31.02  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 192.58/31.02  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 192.58/31.02  | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 192.58/31.02  | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 192.58/31.02  | | | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 192.58/31.02  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 192.58/31.02  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 192.58/31.02  | | | | | | | | | | | | | | |            (611), (612), (613), (772), (773), (775), (778),
% 192.58/31.02  | | | | | | | | | | | | | | |            (779), (783), (1292), (1294), (1296), (1335),
% 192.58/31.02  | | | | | | | | | | | | | | |            (1336), (1337), (function-axioms) are inconsistent
% 192.58/31.02  | | | | | | | | | | | | | | |            by sub-proof #730.
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | End of split
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | Case 2:
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | |   (1338)  all_40_1 = e2
% 192.58/31.02  | | | | | | | | | | | | | |   (1339)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | COMBINE_EQS: (687), (1338) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1340)  all_10_1 = e2
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | SIMP: (1340) implies:
% 192.58/31.02  | | | | | | | | | | | | | |   (1341)  all_10_1 = e2
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (1298), (1341) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1342)   ~ (e3 = e2)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (53), (1341) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1343)  op(all_10_2, e1) = e2
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (52), (1341) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1344)  op(e1, e2) = all_10_0
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 192.58/31.02  | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (1344)
% 192.58/31.02  | | | | | | | | | | | | | |              gives:
% 192.58/31.02  | | | | | | | | | | | | | |   (1345)  all_52_13 = all_10_0
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | COMBINE_EQS: (421), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1346)  all_56_9 = all_10_0
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | COMBINE_EQS: (366), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1347)  all_58_7 = all_10_0
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (568), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1348)   ~ (all_52_5 = all_10_0)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (575), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1349)   ~ (all_52_9 = all_10_0)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (587), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1350)   ~ (all_52_15 = all_10_0)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | SIMP: (1350) implies:
% 192.58/31.02  | | | | | | | | | | | | | |   (1351)   ~ (all_52_15 = all_10_0)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (589), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1352)   ~ (all_52_29 = all_10_0)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | SIMP: (1352) implies:
% 192.58/31.02  | | | | | | | | | | | | | |   (1353)   ~ (all_52_29 = all_10_0)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (588), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1354)   ~ (all_10_0 = all_10_2)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (580), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1355)   ~ (all_10_0 = all_4_2)
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | REDUCE: (180), (1345) imply:
% 192.58/31.02  | | | | | | | | | | | | | |   (1356)  op(all_10_0, all_10_0) = all_52_12
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 192.58/31.02  | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | Case 1:
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | |   (1357)  all_58_15 = e0
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1357) imply:
% 192.58/31.02  | | | | | | | | | | | | | | |   (1358)  all_14_2 = e0
% 192.58/31.02  | | | | | | | | | | | | | | | 
% 192.58/31.02  | | | | | | | | | | | | | | | REDUCE: (573), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1359)   ~ (all_52_7 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (591), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1360)   ~ (all_52_15 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (603), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1361)   ~ (all_52_23 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (606), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1362)   ~ (all_52_25 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (608), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1363)   ~ (all_52_27 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (609), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1364)   ~ (all_52_29 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (613), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1365)  op(e0, e0) = all_52_30
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (63), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1366)  op(e0, e0) = all_14_1
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (61), (1358) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1367)  op(e0, e0) = e0
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 192.58/31.03  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1365), (1366)
% 192.58/31.03  | | | | | | | | | | | | | | |              gives:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1368)  all_52_30 = all_14_1
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 192.58/31.03  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1365), (1367)
% 192.58/31.03  | | | | | | | | | | | | | | |              gives:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1369)  all_52_30 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | COMBINE_EQS: (1368), (1369) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1370)  all_14_1 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (62), (1370) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1371)  op(e0, e0) = all_14_0
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 192.58/31.03  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1367), (1371) gives:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1372)  all_14_0 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (783), (1372) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1373)   ~ (e3 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (779), (1372) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1374)   ~ (e2 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (1296), (1372) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1375)   ~ (e1 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | |   (1376)  all_56_9 = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | REF_CLOSE: (776), (1346), (1376) are inconsistent by
% 192.58/31.03  | | | | | | | | | | | | | | | |            sub-proof #1006.
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | |   (1377)   ~ (all_56_9 = e3)
% 192.58/31.03  | | | | | | | | | | | | | | | |   (1378)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | |   (1379)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.03  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.03  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | BETA: splitting (1379) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1380)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.03  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (183),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (184), (185), (273), (274), (277), (278), (282),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (310), (311),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (312), (317), (321), (325), (332), (351), (352),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (427), (431), (526), (542), (543), (544), (545),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (561), (564), (566), (567), (569), (570), (571),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (573), (586), (590), (596), (598), (604), (605),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (607), (610), (611), (612), (767), (776), (781),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1339), (1343), (1346), (1347), (1348), (1353),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1355), (1357), (1359), (1362), (1364), (1367),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1378), (1380), (function-axioms) are inconsistent
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1381)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.03  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | ALPHA: (1381) implies:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1382)  all_52_14 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1383)  all_52_12 = e1
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1384)  all_52_10 = e2
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1385)  all_52_8 = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (182), (1385) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1386)  op(all_52_9, all_52_9) = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (179), (1382) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1387)  op(all_52_15, all_52_15) = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (1356), (1383) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1388)  op(all_10_0, all_10_0) = e1
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (611), (1384) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1389)  op(all_4_2, all_4_2) = e2
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (43), (51), (53), (156), (158), (164), (169),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (172), (173), (174), (178), (183), (184), (271),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (272), (273), (278), (282), (284), (304), (305),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (312), (313), (317),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (325), (333), (343), (346), (351), (366), (372),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (427), (431), (526),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (549), (555), (557), (567), (571), (572), (577),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (578), (582), (586), (589), (590), (596), (604),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (605), (607), (767), (772), (776), (778), (781),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1294), (1298), (1339), (1343), (1346), (1347),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1351), (1354), (1357), (1359), (1360), (1362),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1364), (1367), (1378), (1386), (1387), (1388),
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            (1389), (function-axioms) are inconsistent by
% 192.58/31.03  | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | |   (1390)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.03  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.03  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (279),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (304), (305),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (313), (317), (318),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (321), (322), (325), (326), (330), (331), (332),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (539), (542),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (564), (565), (567), (568), (569), (570), (571),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (572), (576), (577), (578), (580), (582), (584),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (592), (593), (594),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (604),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (605), (608), (610), (611), (612), (773), (775),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (778), (1292), (1294), (1357), (1359), (1360),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (1361), (1362), (1363), (1364), (1367), (1390),
% 192.58/31.03  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.03  | | | | | | | | | | | | | | | | |            #763.
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | End of split
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | End of split
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | Case 2:
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | |   (1391)   ~ (all_58_15 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | |   (1392)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 192.58/31.03  | | | | | | | | | | | | | | |             e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | ALPHA: (1392) implies:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1393)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 192.58/31.03  | | | | | | | | | | | | | | |   (1394)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | REDUCE: (541), (1391) imply:
% 192.58/31.03  | | | | | | | | | | | | | | |   (1395)   ~ (all_14_2 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | |   (1396)  all_56_9 = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | REF_CLOSE: (776), (1346), (1396) are inconsistent by
% 192.58/31.03  | | | | | | | | | | | | | | | |            sub-proof #1006.
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | |   (1397)   ~ (all_56_9 = e3)
% 192.58/31.03  | | | | | | | | | | | | | | | |   (1398)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | |   (1399)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.03  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.03  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | BETA: splitting (1399) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1400)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.03  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | ALPHA: (1400) implies:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1401)  all_52_6 = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1402)  all_52_4 = e1
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1403)  all_52_2 = e2
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1404)  all_52_0 = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (185), (1403) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1405)  op(all_52_3, all_52_3) = e2
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (184), (1402) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1406)  op(all_52_5, all_52_5) = e1
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (183), (1401) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1407)  op(all_52_7, all_52_7) = e0
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | REDUCE: (610), (1404) imply:
% 192.58/31.03  | | | | | | | | | | | | | | | | | |   (1408)  op(all_6_2, all_6_2) = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 192.58/31.03  | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.03  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |   (1409)  all_56_15 = e3
% 192.58/31.03  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (37), (38), (41), (42), (43), (51),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (61), (62), (63), (157), (167), (169), (174),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (177), (180), (182), (271), (272), (273), (276),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (280), (282), (283), (284), (285), (304), (305),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (308), (312), (315), (317), (321), (332), (343),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (346), (351), (366), (375), (387), (388), (393),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (394), (405), (415), (421), (431), (538), (539),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (540), (542), (543), (544), (545), (546), (547),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (557), (559), (564), (569), (571), (572), (573),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (587), (588), (591), (593), (594), (595), (600),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (603), (605), (606), (611), (612), (613), (772),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (775), (779), (783), (1296), (1405), (1406),
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            (1407), (1408), (1409), (function-axioms) are
% 192.58/31.03  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1174.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | |   (1410)   ~ (all_56_15 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | |   (1411)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | REDUCE: (538), (1410) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | |   (1412)   ~ (all_14_2 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1413)  all_56_13 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (1413) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1414)  all_52_15 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | SIMP: (1414) implies:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1415)  all_52_15 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1415) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1416)  all_58_13 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1415) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1417)   ~ (all_52_7 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (1415) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1418)   ~ (all_14_2 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (1351), (1415) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1419)   ~ (all_10_0 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (1415) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1420)   ~ (all_4_2 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | SIMP: (1420) implies:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1421)   ~ (all_4_2 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (1415) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1422)  op(e3, e3) = all_52_14
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (1422)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |              gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1423)  all_52_14 = all_6_2
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1424)  all_58_1 = e2
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (1424) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1425)  all_52_9 = e2
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (1425) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1426)   ~ (all_52_25 = e2)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | SIMP: (1426) implies:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1427)   ~ (all_52_25 = e2)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (1425) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1428)   ~ (all_4_2 = e2)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | SIMP: (1428) implies:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1429)   ~ (all_4_2 = e2)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (1425) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1430)  op(e2, e2) = all_52_8
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |              all_52_8, e2, e2, simplifying with (36), (1430)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |              gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1431)  all_52_8 = all_4_2
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | |   (1432)  all_56_12 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (1417), (1432) are inconsistent by
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | |   (1433)   ~ (all_56_12 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | |   (1434)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1435)  all_56_0 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (1435) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1436)  all_6_2 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1436) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1437)  all_58_0 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (1436) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1438)   ~ (all_52_3 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (1436) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1439)   ~ (all_52_5 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1436) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1440)   ~ (all_52_25 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1436) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1441)  op(e3, e3) = all_6_1
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1436) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1442)  op(e3, e3) = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1441), (1442) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1443)  all_6_1 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1443) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1444)  op(e3, e3) = all_6_0
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1442), (1444) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1445)  all_6_0 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | |   (1446)  all_58_6 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (1439), (1446) are inconsistent by
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | |   (1447)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (1448)  all_58_9 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (1440), (1448) are inconsistent by
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1300.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (1449)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1450)  all_56_4 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (1438), (1450) are inconsistent by
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1451)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1449) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1452)  all_58_10 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (1452) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1453)  all_52_27 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1453) implies:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1454)  all_52_27 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (1454) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1455)   ~ (all_52_29 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1455) implies:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1456)   ~ (all_52_29 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1447) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1457)  all_58_7 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1347), (1457) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1458)  all_10_0 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (776), (1458) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1459)  $false
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1459) is inconsistent.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1460)  all_58_8 = e3 | all_58_11 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (51), (61), (172),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (177), (180), (304), (306), (308), (312), (313),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (319), (320), (321), (330), (332), (351), (366),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (375), (387), (405), (411), (421), (431), (541),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (545), (546), (547), (548), (553),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (567), (569), (573), (580),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (588), (589), (596), (600), (602), (1393), (1398),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1405), (1406), (1407), (1408), (1416), (1417),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1427), (1429), (1434), (1437), (1451), (1452),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1456), (1460), (function-axioms) are inconsistent
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #723.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1461)  all_58_11 = e3 | all_58_15 = e3
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (61), (62), (63), (158), (159),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (304), (305), (351), (431), (538), (541), (542),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (544), (573), (600), (779), (1393), (1395),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1407), (1411), (1412), (1416), (1434), (1461),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #758.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1462)   ~ (all_56_0 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (1462) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |   (1463)   ~ (all_6_2 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (564), (569), (1405), (1406),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |            (1408), (1417), (1463), (function-axioms) are
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1363.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |   (1464)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (38), (548), (611), (781), (1292),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |            (1347), (1416), (1421), (1464), (function-axioms)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #720.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1465)   ~ (all_56_13 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (1465) imply:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |   (1466)   ~ (all_52_15 = e3)
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (53), (61), (62), (63), (158), (163), (169),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (172), (173), (175), (180), (182), (273), (274),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (276), (277), (281), (283), (284), (304), (305),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (306), (309), (311), (312), (313), (314), (319),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (320), (321), (325), (328), (331), (332), (333),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (421), (431),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (538), (541), (542), (543), (544), (545), (546),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (561),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (570),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (586), (588), (589), (590), (593), (594), (595),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (596), (600), (603), (604), (605), (606), (608),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (609), (612), (613), (772), (773), (1292), (1296),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (1394), (1395), (1405), (1406), (1407), (1408),
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            (1411), (1412), (1466), (function-axioms) are
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #742.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | |   (1467)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.04  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.04  | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (38), (41), (43), (51), (158), (169), (179),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (182), (270), (271), (273), (284), (306), (325),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (327), (343), (351), (394), (405), (431), (538),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (541), (542), (543), (548), (549), (555), (557),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (571), (574), (582), (590), (591), (611), (772),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (776), (778), (781), (1294), (1346), (1347),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (1349), (1351), (1354), (1356), (1398), (1467),
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.04  | | | | | | | | | | | | | | | | | |            #714.
% 192.58/31.04  | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.04  | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.04  | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | |   (1468)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.04  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.04  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.04  | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | BETA: splitting (1468) gives:
% 192.58/31.04  | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.04  | | | | | | | | | | | | | | | | | | 
% 192.58/31.04  | | | | | | | | | | | | | | | | | |   (1469)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 192.58/31.04  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 192.58/31.04  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (1294),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (1393), (1394), (1469), (function-axioms) are
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1470)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 192.58/31.05  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (775), (778), (1294), (1393), (1395), (1470),
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.05  | | | | | | | | | | | | | | | | | |            #1008.
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | Case 2:
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | |   (1471)  all_30_1 = e3
% 192.58/31.05  | | | | | | | | | | | | |   (1472)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | COMBINE_EQS: (670), (1471) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1473)  all_10_1 = e3
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | SIMP: (1473) implies:
% 192.58/31.05  | | | | | | | | | | | | |   (1474)  all_10_1 = e3
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (53), (1474) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1475)  op(all_10_2, e1) = e3
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (52), (1474) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1476)  op(e1, e3) = all_10_0
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 192.58/31.05  | | | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (1476)
% 192.58/31.05  | | | | | | | | | | | | |              gives:
% 192.58/31.05  | | | | | | | | | | | | |   (1477)  all_52_5 = all_10_0
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | COMBINE_EQS: (367), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1478)  all_56_8 = all_10_0
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | COMBINE_EQS: (547), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1479)  all_58_6 = all_10_0
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (562), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1480)   ~ (all_52_3 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (567), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1481)   ~ (all_52_7 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | SIMP: (1481) implies:
% 192.58/31.05  | | | | | | | | | | | | |   (1482)   ~ (all_52_7 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (568), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1483)   ~ (all_52_13 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | SIMP: (1483) implies:
% 192.58/31.05  | | | | | | | | | | | | |   (1484)   ~ (all_52_13 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (570), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1485)   ~ (all_52_29 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | SIMP: (1485) implies:
% 192.58/31.05  | | | | | | | | | | | | |   (1486)   ~ (all_52_29 = all_10_0)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (569), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1487)   ~ (all_10_0 = all_10_2)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (553), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1488)   ~ (all_10_0 = all_6_2)
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | REDUCE: (184), (1477) imply:
% 192.58/31.05  | | | | | | | | | | | | |   (1489)  op(all_10_0, all_10_0) = all_52_4
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 192.58/31.05  | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | |   (1490)  all_58_15 = e0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | COMBINE_EQS: (541), (1490) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1491)  all_14_2 = e0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (573), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1492)   ~ (all_52_7 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (591), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1493)   ~ (all_52_15 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (603), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1494)   ~ (all_52_23 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (606), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1495)   ~ (all_52_25 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (608), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1496)   ~ (all_52_27 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (609), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1497)   ~ (all_52_29 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (613), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1498)  op(e0, e0) = all_52_30
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (63), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1499)  op(e0, e0) = all_14_1
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (61), (1491) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1500)  op(e0, e0) = e0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 192.58/31.05  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1498), (1499)
% 192.58/31.05  | | | | | | | | | | | | | |              gives:
% 192.58/31.05  | | | | | | | | | | | | | |   (1501)  all_52_30 = all_14_1
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 192.58/31.05  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1498), (1500)
% 192.58/31.05  | | | | | | | | | | | | | |              gives:
% 192.58/31.05  | | | | | | | | | | | | | |   (1502)  all_52_30 = e0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | COMBINE_EQS: (1501), (1502) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1503)  all_14_1 = e0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (62), (1503) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1504)  op(e0, e0) = all_14_0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 192.58/31.05  | | | | | | | | | | | | | |              e0, e0, simplifying with (1500), (1504) gives:
% 192.58/31.05  | | | | | | | | | | | | | |   (1505)  all_14_0 = e0
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (783), (1505) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1506)   ~ (e3 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (779), (1505) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1507)   ~ (e2 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | REDUCE: (1296), (1505) imply:
% 192.58/31.05  | | | | | | | | | | | | | |   (1508)   ~ (e1 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 192.58/31.05  | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | |   (1509)  all_56_8 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | REF_CLOSE: (776), (1478), (1509) are inconsistent by
% 192.58/31.05  | | | | | | | | | | | | | | |            sub-proof #926.
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | Case 2:
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | |   (1510)   ~ (all_56_8 = e3)
% 192.58/31.05  | | | | | | | | | | | | | | |   (1511)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | |   (1512)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.05  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.05  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.05  | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | BETA: splitting (1512) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1513)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.05  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | ALPHA: (1513) implies:
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1514)  all_52_6 = e0
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1515)  all_52_2 = e2
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1516)  all_52_0 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | REDUCE: (185), (1515) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1517)  op(all_52_3, all_52_3) = e2
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | REDUCE: (183), (1514) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1518)  op(all_52_7, all_52_7) = e0
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | REDUCE: (610), (1516) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | |   (1519)  op(all_6_2, all_6_2) = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1520)  all_56_13 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (1520) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1521)  all_52_15 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | SIMP: (1521) implies:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1522)  all_52_15 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1522) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1523)  all_58_13 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | REDUCE: (571), (1522) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1524)   ~ (all_52_7 = e3)
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | REDUCE: (179), (1522) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1525)  op(e3, e3) = all_52_14
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | REDUCE: (157), (1522) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1526)  op(e0, e2) = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 192.58/31.05  | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (1525)
% 192.58/31.05  | | | | | | | | | | | | | | | | | |              gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1527)  all_52_14 = all_6_2
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1528)  all_56_12 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (1524), (1528) are inconsistent by
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1529)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |   (1530)  all_58_12 = e1
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (1530) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |   (1531)  all_52_7 = e1
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | SIMP: (1531) implies:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |   (1532)  all_52_7 = e1
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (361), (459), (593), (750),
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |            (781), (1472), (1475), (1478), (1482), (1487),
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |            (1511), (1532), (function-axioms) are inconsistent
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |            by sub-proof #908.
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |   (1533)   ~ (all_58_12 = e1)
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |   (1534)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (1533) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |   (1535)   ~ (all_52_7 = e1)
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (36), (38), (41), (166), (431), (555),
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |            (1292), (1490), (1492), (1517), (1518), (1523),
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |            (1526), (1529), (1534), (1535), (function-axioms)
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #768.
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1536)   ~ (all_56_13 = e3)
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | REDUCE: (346), (1536) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | |   (1537)   ~ (all_52_15 = e3)
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1538)  all_58_0 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (1538) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1539)  all_6_2 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1539) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1540)  op(e3, e3) = all_6_1
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1539) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1541)  op(e3, e3) = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1540), (1541) gives:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1542)  all_6_1 = e3
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1542) imply:
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |   (1543)  op(e3, e3) = all_6_0
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.05  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 192.58/31.05  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (1541), (1543) gives:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | |   (1544)  all_6_0 = e3
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | |   (1545)  all_58_0 = e2
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1538), (1545) imply:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | |   (1546)  e3 = e2
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1546) imply:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | |   (1547)  $false
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | CLOSE: (1547) is inconsistent.
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | |   (1548)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |   (1549)  all_56_13 = e3
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (346), (1537), (1549) are inconsistent by
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1201.
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |   (1550)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (157), (304), (305), (346),
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |            (351), (387), (543), (564), (571), (582), (772),
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |            (781), (1479), (1517), (1518), (1548), (1550),
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | |            #924.
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | |   (1551)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (61), (306), (351), (387), (564),
% 192.58/31.06  | | | | | | | | | | | | | | | | | | |            (573), (776), (1479), (1517), (1518), (1519),
% 192.58/31.06  | | | | | | | | | | | | | | | | | | |            (1551), (function-axioms) are inconsistent by
% 192.58/31.06  | | | | | | | | | | | | | | | | | | |            sub-proof #920.
% 192.58/31.06  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | |   (1552)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.06  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.06  | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (51), (158), (166), (167), (168), (173), (175),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (185), (272), (273),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (274), (275), (276), (278), (280), (281), (282),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (317),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (321), (322), (323), (325), (328), (330), (346),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (421), (427),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (431), (459), (539), (542), (543), (544), (545),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (546), (548), (549), (551), (555), (557), (561),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (563), (564), (566), (571), (572), (578), (582),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (593), (595),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (596), (602), (604), (611), (612), (750), (773),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (778), (781), (1294), (1472), (1475), (1478),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (1479), (1480), (1482), (1484), (1486), (1487),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (1488), (1489), (1490), (1492), (1493), (1495),
% 192.58/31.06  | | | | | | | | | | | | | | | | |            (1496), (1500), (1511), (1552), (function-axioms)
% 192.58/31.06  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #879.
% 192.58/31.06  | | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1553)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.06  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.06  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (279),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (304), (305),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (313), (317), (318),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (321), (322), (325), (326), (330), (331), (332),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (539), (542),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (564), (565), (567), (568), (569), (570), (571),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (572), (576), (577), (578), (580), (582), (584),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (592), (593), (594),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (604),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (605), (608), (610), (611), (612), (773), (775),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (778), (1292), (1294), (1490), (1492), (1493),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (1494), (1495), (1496), (1497), (1500), (1553),
% 192.58/31.06  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.06  | | | | | | | | | | | | | | | |            #763.
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | |   (1554)   ~ (all_58_15 = e0)
% 192.58/31.06  | | | | | | | | | | | | | |   (1555)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 192.58/31.06  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 192.58/31.06  | | | | | | | | | | | | | |             e0)
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | ALPHA: (1555) implies:
% 192.58/31.06  | | | | | | | | | | | | | |   (1556)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 192.58/31.06  | | | | | | | | | | | | | |   (1557)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | REDUCE: (541), (1554) imply:
% 192.58/31.06  | | | | | | | | | | | | | |   (1558)   ~ (all_14_2 = e0)
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 192.58/31.06  | | | | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (62), (63),
% 192.58/31.06  | | | | | | | | | | | | | |            (157), (158), (159), (161), (162), (163), (166),
% 192.58/31.06  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 192.58/31.06  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 192.58/31.06  | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 192.58/31.06  | | | | | | | | | | | | | |            (275), (276), (277), (278), (279), (280), (281),
% 192.58/31.06  | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (305), (306),
% 192.58/31.06  | | | | | | | | | | | | | |            (307), (308), (309), (311), (312), (313), (314),
% 192.58/31.06  | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 192.58/31.06  | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 192.58/31.06  | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 192.58/31.06  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 192.58/31.06  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 192.58/31.06  | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 192.58/31.06  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 192.58/31.06  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 192.58/31.06  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 192.58/31.06  | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 192.58/31.06  | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 192.58/31.06  | | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 192.58/31.06  | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 192.58/31.06  | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 192.58/31.06  | | | | | | | | | | | | | |            (611), (612), (613), (772), (773), (775), (778),
% 192.58/31.06  | | | | | | | | | | | | | |            (779), (783), (1292), (1294), (1296), (1556),
% 192.58/31.06  | | | | | | | | | | | | | |            (1557), (1558), (function-axioms) are inconsistent
% 192.58/31.06  | | | | | | | | | | | | | |            by sub-proof #730.
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | End of split
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | |   (1559)  all_24_0 = e1
% 192.58/31.06  | | | | | | | | | | | |   (1560)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | COMBINE_EQS: (711), (1559) imply:
% 192.58/31.06  | | | | | | | | | | | |   (1561)  all_14_0 = e1
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | SIMP: (1561) implies:
% 192.58/31.06  | | | | | | | | | | | |   (1562)  all_14_0 = e1
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | COMBINE_EQS: (765), (1562) imply:
% 192.58/31.06  | | | | | | | | | | | |   (1563)  all_34_0 = e1
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | REDUCE: (783), (1562) imply:
% 192.58/31.06  | | | | | | | | | | | |   (1564)   ~ (e3 = e1)
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | REDUCE: (779), (1562) imply:
% 192.58/31.06  | | | | | | | | | | | |   (1565)   ~ (e2 = e1)
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | REDUCE: (62), (1562) imply:
% 192.58/31.06  | | | | | | | | | | | |   (1566)  op(e0, all_14_1) = e1
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | BETA: splitting (114) gives:
% 192.58/31.06  | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | Case 1:
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | |   (1567)   ~ (all_34_0 = e1)
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | REDUCE: (1563), (1567) imply:
% 192.58/31.06  | | | | | | | | | | | | |   (1568)  $false
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | CLOSE: (1568) is inconsistent.
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | |   (1569)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 192.58/31.06  | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | Case 1:
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | |   (1570)  all_58_15 = e0
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (1566), (1570),
% 192.58/31.06  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.06  | | | | | | | | | | | | | |            #877.
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | Case 2:
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | |   (1571)   ~ (all_58_15 = e0)
% 192.58/31.06  | | | | | | | | | | | | | |   (1572)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 192.58/31.06  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 192.58/31.06  | | | | | | | | | | | | | |             e0)
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | ALPHA: (1572) implies:
% 192.58/31.06  | | | | | | | | | | | | | |   (1573)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 192.58/31.06  | | | | | | | | | | | | | |   (1574)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | REDUCE: (541), (1571) imply:
% 192.58/31.06  | | | | | | | | | | | | | |   (1575)   ~ (all_14_2 = e0)
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.06  | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | Case 1:
% 192.58/31.06  | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | |   (1576)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.06  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.06  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.06  | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | BETA: splitting (1576) gives:
% 192.58/31.06  | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1577)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.06  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | ALPHA: (1577) implies:
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1578)  all_52_6 = e0
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1579)  all_52_4 = e1
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1580)  all_52_2 = e2
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1581)  all_52_0 = e3
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | REDUCE: (185), (1580) imply:
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1582)  op(all_52_3, all_52_3) = e2
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | REDUCE: (184), (1579) imply:
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1583)  op(all_52_5, all_52_5) = e1
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | REDUCE: (183), (1578) imply:
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1584)  op(all_52_7, all_52_7) = e0
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.06  | | | | | | | | | | | | | | | | REDUCE: (610), (1581) imply:
% 192.58/31.06  | | | | | | | | | | | | | | | |   (1585)  op(all_6_2, all_6_2) = e3
% 192.58/31.06  | | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (156), (158),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (159), (163), (167), (168), (169), (173), (174),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (270),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (272), (273), (274), (276), (277), (279), (280),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (304), (305), (306),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (314),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (324), (325), (328), (329), (330), (331), (332),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (333), (346), (351), (352), (366), (367), (372),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (491), (508), (538),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (592), (594), (595), (596), (597), (598), (600),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (609), (612), (613), (649), (685), (772), (773),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (775), (1292), (1560), (1566), (1569), (1573),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (1574), (1575), (1582), (1583), (1584), (1585),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.07  | | | | | | | | | | | | | | | |            #697.
% 192.58/31.07  | | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.07  | | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | | |   (1586)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.07  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.07  | | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (773), (775), (778), (1294), (1573), (1574),
% 192.58/31.07  | | | | | | | | | | | | | | | |            (1575), (1586), (function-axioms) are inconsistent
% 192.58/31.07  | | | | | | | | | | | | | | | |            by sub-proof #731.
% 192.58/31.07  | | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | | End of split
% 192.58/31.07  | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | Case 2:
% 192.58/31.07  | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | |   (1587)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.07  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.07  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.07  | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 192.58/31.07  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (156), (158), (162),
% 192.58/31.07  | | | | | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 192.58/31.07  | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 192.58/31.07  | | | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (275),
% 192.58/31.07  | | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 192.58/31.07  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 192.58/31.07  | | | | | | | | | | | | | | |            (315), (316), (317), (319), (321), (323), (324),
% 192.58/31.07  | | | | | | | | | | | | | | |            (325), (327), (328), (329), (330), (331), (332),
% 192.58/31.07  | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 192.58/31.07  | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 192.58/31.07  | | | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (431), (491),
% 192.58/31.07  | | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 192.58/31.07  | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 192.58/31.07  | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 192.58/31.07  | | | | | | | | | | | | | | |            (565), (566), (567), (569), (570), (571), (572),
% 192.58/31.07  | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 192.58/31.07  | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 192.58/31.07  | | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 192.58/31.07  | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 192.58/31.07  | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (685),
% 192.58/31.07  | | | | | | | | | | | | | | |            (773), (775), (778), (1294), (1566), (1569),
% 192.58/31.07  | | | | | | | | | | | | | | |            (1573), (1574), (1575), (1587), (function-axioms)
% 192.58/31.07  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #838.
% 192.58/31.07  | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | End of split
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | End of split
% 192.58/31.07  | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | End of split
% 192.58/31.07  | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | End of split
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | Case 2:
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | |   (1588)  all_22_1 = e2
% 192.58/31.07  | | | | | | | | | | |   (1589)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | COMBINE_EQS: (658), (1588) imply:
% 192.58/31.07  | | | | | | | | | | |   (1590)  all_6_1 = e2
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (43), (1590) imply:
% 192.58/31.07  | | | | | | | | | | |   (1591)  op(all_6_2, e3) = e2
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (42), (1590) imply:
% 192.58/31.07  | | | | | | | | | | |   (1592)  op(e3, e2) = all_6_0
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 192.58/31.07  | | | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (1592)
% 192.58/31.07  | | | | | | | | | | |              gives:
% 192.58/31.07  | | | | | | | | | | |   (1593)  all_52_9 = all_6_0
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | COMBINE_EQS: (394), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1594)  all_56_1 = all_6_0
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | COMBINE_EQS: (549), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1595)  all_58_1 = all_6_0
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (575), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1596)   ~ (all_52_13 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | SIMP: (1596) implies:
% 192.58/31.07  | | | | | | | | | | |   (1597)   ~ (all_52_13 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (576), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1598)   ~ (all_52_15 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | SIMP: (1598) implies:
% 192.58/31.07  | | | | | | | | | | |   (1599)   ~ (all_52_15 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (577), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1600)   ~ (all_52_17 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | SIMP: (1600) implies:
% 192.58/31.07  | | | | | | | | | | |   (1601)   ~ (all_52_17 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (578), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1602)   ~ (all_52_25 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | SIMP: (1602) implies:
% 192.58/31.07  | | | | | | | | | | |   (1603)   ~ (all_52_25 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (557), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1604)   ~ (all_6_0 = all_6_2)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (574), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1605)   ~ (all_6_0 = all_4_2)
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | REDUCE: (182), (1593) imply:
% 192.58/31.07  | | | | | | | | | | |   (1606)  op(all_6_0, all_6_0) = all_52_8
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | BETA: splitting (89) gives:
% 192.58/31.07  | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | Case 1:
% 192.58/31.07  | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | |   (1607)   ~ (all_24_0 = e1)
% 192.58/31.07  | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | REDUCE: (711), (1607) imply:
% 192.58/31.07  | | | | | | | | | | | |   (1608)   ~ (all_14_0 = e1)
% 192.58/31.07  | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | BETA: splitting (104) gives:
% 192.58/31.07  | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | Case 1:
% 192.58/31.07  | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | |   (1609)   ~ (all_30_1 = e3)
% 192.58/31.07  | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | REDUCE: (670), (1609) imply:
% 192.58/31.07  | | | | | | | | | | | | |   (1610)   ~ (all_10_1 = e3)
% 192.58/31.07  | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 192.58/31.07  | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | Case 1:
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | |   (1611)   ~ (all_40_1 = e2)
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 192.58/31.07  | | | | | | | | | | | | | |            (53), (61), (62), (63), (157), (158), (162),
% 192.58/31.07  | | | | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 192.58/31.07  | | | | | | | | | | | | | |            (177), (178), (180), (182), (183), (184), (185),
% 192.58/31.07  | | | | | | | | | | | | | |            (187), (270), (271), (273), (274), (275), (277),
% 192.58/31.07  | | | | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (284),
% 192.58/31.07  | | | | | | | | | | | | | |            (285), (303), (304), (306), (307), (309), (311),
% 192.58/31.07  | | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 192.58/31.07  | | | | | | | | | | | | | |            (325), (326), (327), (328), (329), (331), (332),
% 192.58/31.07  | | | | | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 192.58/31.07  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 192.58/31.07  | | | | | | | | | | | | | |            (415), (417), (427), (431), (522), (538), (539),
% 192.58/31.07  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 192.58/31.07  | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 192.58/31.07  | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 192.58/31.07  | | | | | | | | | | | | | |            (567), (568), (569), (570), (572), (573), (574),
% 192.58/31.07  | | | | | | | | | | | | | |            (575), (578), (582), (584), (586), (588), (590),
% 192.58/31.07  | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 192.58/31.07  | | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 192.58/31.07  | | | | | | | | | | | | | |            (607), (608), (609), (610), (612), (613), (687),
% 192.58/31.07  | | | | | | | | | | | | | |            (739), (773), (775), (779), (783), (1589), (1591),
% 192.58/31.07  | | | | | | | | | | | | | |            (1594), (1595), (1597), (1599), (1601), (1603),
% 192.58/31.07  | | | | | | | | | | | | | |            (1604), (1605), (1606), (1608), (1611),
% 192.58/31.07  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.07  | | | | | | | | | | | | | |            #792.
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | Case 2:
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | |   (1612)  all_40_1 = e2
% 192.58/31.07  | | | | | | | | | | | | | |   (1613)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | COMBINE_EQS: (687), (1612) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1614)  all_10_1 = e2
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | SIMP: (1614) implies:
% 192.58/31.07  | | | | | | | | | | | | | |   (1615)  all_10_1 = e2
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | REDUCE: (1610), (1615) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1616)   ~ (e3 = e2)
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | REDUCE: (53), (1615) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1617)  op(all_10_2, e1) = e2
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | REDUCE: (52), (1615) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1618)  op(e1, e2) = all_10_0
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 192.58/31.07  | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (1618)
% 192.58/31.07  | | | | | | | | | | | | | |              gives:
% 192.58/31.07  | | | | | | | | | | | | | |   (1619)  all_52_13 = all_10_0
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | COMBINE_EQS: (421), (1619) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1620)  all_56_9 = all_10_0
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | COMBINE_EQS: (366), (1619) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1621)  all_58_7 = all_10_0
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | REDUCE: (568), (1619) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1622)   ~ (all_52_5 = all_10_0)
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | REDUCE: (1597), (1619) imply:
% 192.58/31.07  | | | | | | | | | | | | | |   (1623)   ~ (all_10_0 = all_6_0)
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 192.58/31.07  | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | Case 1:
% 192.58/31.07  | | | | | | | | | | | | | | | 
% 192.58/31.07  | | | | | | | | | | | | | | |   (1624)  all_58_15 = e0
% 192.58/31.07  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (53), (61), (62),
% 192.58/31.08  | | | | | | | | | | | | | | |            (63), (158), (166), (168), (172), (173), (174),
% 192.58/31.08  | | | | | | | | | | | | | | |            (175), (177), (178), (182), (183), (184), (185),
% 192.58/31.08  | | | | | | | | | | | | | | |            (187), (274), (278), (282), (283), (284), (285),
% 192.58/31.08  | | | | | | | | | | | | | | |            (306), (307), (309), (313), (315), (317), (321),
% 192.58/31.08  | | | | | | | | | | | | | | |            (325), (327), (329), (331), (332), (351), (352),
% 192.58/31.08  | | | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (405),
% 192.58/31.08  | | | | | | | | | | | | | | |            (415), (427), (522), (540), (541), (542), (543),
% 192.58/31.08  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 192.58/31.08  | | | | | | | | | | | | | | |            (557), (559), (561), (563), (564), (569), (570),
% 192.58/31.08  | | | | | | | | | | | | | | |            (572), (573), (584), (590), (592), (593), (594),
% 192.58/31.08  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 192.58/31.08  | | | | | | | | | | | | | | |            (604), (605), (606), (609), (610), (612), (613),
% 192.58/31.08  | | | | | | | | | | | | | | |            (739), (773), (775), (779), (783), (1589), (1591),
% 192.58/31.08  | | | | | | | | | | | | | | |            (1594), (1595), (1597), (1599), (1601), (1603),
% 192.58/31.08  | | | | | | | | | | | | | | |            (1604), (1605), (1606), (1608), (1624),
% 192.58/31.08  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.08  | | | | | | | | | | | | | | |            #818.
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | Case 2:
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | |   (1625)   ~ (all_58_15 = e0)
% 192.58/31.08  | | | | | | | | | | | | | | |   (1626)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 192.58/31.08  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 192.58/31.08  | | | | | | | | | | | | | | |             e0)
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | ALPHA: (1626) implies:
% 192.58/31.08  | | | | | | | | | | | | | | |   (1627)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 192.58/31.08  | | | | | | | | | | | | | | |   (1628)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | REDUCE: (541), (1625) imply:
% 192.58/31.08  | | | | | | | | | | | | | | |   (1629)   ~ (all_14_2 = e0)
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1630)  all_56_1 = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (1594), (1630) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1631)  all_6_0 = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (1595), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1632)  all_58_1 = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REDUCE: (1599), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1633)   ~ (all_52_15 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REDUCE: (1601), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1634)   ~ (all_52_17 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REDUCE: (1603), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1635)   ~ (all_52_25 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REDUCE: (1604), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1636)   ~ (all_6_2 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | SIMP: (1636) implies:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1637)   ~ (all_6_2 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REDUCE: (1605), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1638)   ~ (all_4_2 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | SIMP: (1638) implies:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1639)   ~ (all_4_2 = e3)
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REDUCE: (1606), (1631) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1640)  op(e3, e3) = all_52_8
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 192.58/31.08  | | | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (1640)
% 192.58/31.08  | | | | | | | | | | | | | | | |              gives:
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1641)  all_52_8 = all_6_2
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | |   (1642)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.08  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.08  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | BETA: splitting (1642) gives:
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1643)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.08  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | ALPHA: (1643) implies:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1644)  all_52_6 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1645)  all_52_4 = e1
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1646)  all_52_2 = e2
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1647)  all_52_0 = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (185), (1646) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1648)  op(all_52_3, all_52_3) = e2
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (184), (1645) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1649)  op(all_52_5, all_52_5) = e1
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (183), (1644) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1650)  op(all_52_7, all_52_7) = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (610), (1647) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1651)  op(all_6_2, all_6_2) = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (37), (38), (41), (42),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (157), (158),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (159), (163), (167), (169), (172), (173), (174),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (175), (177), (179), (180), (182), (270), (271),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (272), (273), (274), (276), (277), (278), (279),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (305), (306), (308), (309), (311), (312), (313),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (320), (321), (323),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (325), (328), (331), (332), (333), (343), (346),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (421), (427), (431), (538), (539), (540), (541),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (570),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (589), (590), (591), (593), (594), (595), (596),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (608),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (609), (611), (612), (613), (772), (773), (775),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (779), (783), (1292), (1608), (1627), (1628),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1629), (1648), (1649), (1650), (1651),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            #741.
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1652)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.08  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1637), (1641), (1652) are inconsistent by
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            sub-proof #834.
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | |   (1653)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.08  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.08  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | BETA: splitting (1653) gives:
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1654)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 192.58/31.08  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (53),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (61), (158), (166), (168), (173), (175), (177),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (178), (184), (270), (274), (275), (276), (282),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (283), (304), (306), (313), (315), (317), (321),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (327), (329), (332), (351), (352), (361), (372),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (415), (526),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (538), (541), (542), (543), (544), (545), (546),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (547), (548), (551), (555), (559), (561), (562),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (563), (564), (572), (573), (586), (594), (595),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (596), (597), (600), (602), (603), (606), (608),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (609), (612), (613), (767), (776), (781), (1591),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1613), (1617), (1620), (1621), (1627), (1629),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1632), (1633), (1634), (1635), (1637), (1639),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1640), (1654), (function-axioms) are inconsistent
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            by sub-proof #696.
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1655)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 192.58/31.08  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | ALPHA: (1655) implies:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1656)  all_52_30 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1657)  all_52_28 = e1
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1658)  all_52_26 = e2
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1659)  all_52_24 = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (174), (1659) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1660)  op(all_52_25, all_52_25) = e3
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (173), (1658) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1661)  op(all_52_27, all_52_27) = e2
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (172), (1657) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1662)  op(all_52_29, all_52_29) = e1
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REDUCE: (613), (1656) imply:
% 192.58/31.08  | | | | | | | | | | | | | | | | | |   (1663)  op(all_14_2, all_14_2) = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (175), (177), (180), (182), (183), (184), (185),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (270), (271), (273), (274), (276), (277), (280),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (306), (307), (309), (311),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (313), (316), (319), (321), (324), (325), (326),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (327), (332), (333), (343), (351), (352), (366),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (411), (415), (431), (526), (538), (539), (541),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (559), (561), (562),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (569), (570),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (578), (582),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (584), (586), (590), (593), (594), (595), (596),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (607), (608), (609), (610), (767), (776), (781),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1591), (1613), (1620), (1621), (1622), (1627),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1628), (1629), (1632), (1633), (1635), (1637),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (1639), (1660), (1661), (1662), (1663),
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.08  | | | | | | | | | | | | | | | | | |            #695.
% 192.58/31.08  | | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.08  | | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | End of split
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | |   (1664)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 192.58/31.08  | | | | | | | | | | | | | | | |            (610), (739), (773), (775), (1589), (1591),
% 192.58/31.08  | | | | | | | | | | | | | | | |            (1594), (1604), (1664), (function-axioms) are
% 192.58/31.08  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 192.58/31.08  | | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | | End of split
% 192.58/31.08  | | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | | End of split
% 192.58/31.08  | | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | | End of split
% 192.58/31.08  | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | Case 2:
% 192.58/31.08  | | | | | | | | | | | | | 
% 192.58/31.08  | | | | | | | | | | | | |   (1665)  all_30_1 = e3
% 192.58/31.08  | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 192.58/31.09  | | | | | | | | | | | | |            (52), (53), (61), (62), (63), (158), (162), (166),
% 192.58/31.09  | | | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 192.58/31.09  | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 192.58/31.09  | | | | | | | | | | | | |            (271), (273), (274), (275), (277), (278), (280),
% 192.58/31.09  | | | | | | | | | | | | |            (282), (283), (284), (285), (303), (304), (306),
% 192.58/31.09  | | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (317),
% 192.58/31.09  | | | | | | | | | | | | |            (319), (321), (324), (325), (326), (327), (329),
% 192.58/31.09  | | | | | | | | | | | | |            (331), (332), (333), (343), (351), (352), (361),
% 192.58/31.09  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 192.58/31.09  | | | | | | | | | | | | |            (405), (415), (427), (431), (522), (538), (539),
% 192.58/31.09  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 192.58/31.09  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 192.58/31.09  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 192.58/31.09  | | | | | | | | | | | | |            (567), (569), (570), (572), (573), (574), (575),
% 192.58/31.09  | | | | | | | | | | | | |            (577), (578), (582), (584), (586), (590), (592),
% 192.58/31.09  | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 192.58/31.09  | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 192.58/31.09  | | | | | | | | | | | | |            (609), (610), (612), (613), (670), (739), (773),
% 192.58/31.09  | | | | | | | | | | | | |            (775), (776), (779), (783), (1589), (1591),
% 192.58/31.09  | | | | | | | | | | | | |            (1594), (1595), (1597), (1599), (1601), (1603),
% 192.58/31.09  | | | | | | | | | | | | |            (1604), (1605), (1606), (1608), (1665),
% 192.58/31.09  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.09  | | | | | | | | | | | | |            #777.
% 192.58/31.09  | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | End of split
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | Case 2:
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | |   (1666)  all_24_0 = e1
% 192.58/31.09  | | | | | | | | | | | |   (1667)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | COMBINE_EQS: (711), (1666) imply:
% 192.58/31.09  | | | | | | | | | | | |   (1668)  all_14_0 = e1
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | SIMP: (1668) implies:
% 192.58/31.09  | | | | | | | | | | | |   (1669)  all_14_0 = e1
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | COMBINE_EQS: (765), (1669) imply:
% 192.58/31.09  | | | | | | | | | | | |   (1670)  all_34_0 = e1
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | REDUCE: (779), (1669) imply:
% 192.58/31.09  | | | | | | | | | | | |   (1671)   ~ (e2 = e1)
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | REDUCE: (62), (1669) imply:
% 192.58/31.09  | | | | | | | | | | | |   (1672)  op(e0, all_14_1) = e1
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | BETA: splitting (104) gives:
% 192.58/31.09  | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | |   (1673)   ~ (all_30_1 = e3)
% 192.58/31.09  | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | REDUCE: (670), (1673) imply:
% 192.58/31.09  | | | | | | | | | | | | |   (1674)   ~ (all_10_1 = e3)
% 192.58/31.09  | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | BETA: splitting (114) gives:
% 192.58/31.09  | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | |   (1675)   ~ (all_34_0 = e1)
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | REDUCE: (1670), (1675) imply:
% 192.58/31.09  | | | | | | | | | | | | | |   (1676)  $false
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | CLOSE: (1676) is inconsistent.
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | Case 2:
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | |   (1677)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 192.58/31.09  | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | |   (1678)   ~ (all_40_1 = e2)
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 192.58/31.09  | | | | | | | | | | | | | | |            (53), (61), (62), (63), (157), (158), (162),
% 192.58/31.09  | | | | | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 192.58/31.09  | | | | | | | | | | | | | | |            (177), (178), (180), (182), (183), (184), (185),
% 192.58/31.09  | | | | | | | | | | | | | | |            (187), (270), (271), (273), (274), (275), (277),
% 192.58/31.09  | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 192.58/31.09  | | | | | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 192.58/31.09  | | | | | | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 192.58/31.09  | | | | | | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 192.58/31.09  | | | | | | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 192.58/31.09  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 192.58/31.09  | | | | | | | | | | | | | | |            (417), (431), (522), (538), (539), (540), (541),
% 192.58/31.09  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 192.58/31.09  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (559), (561), (562),
% 192.58/31.09  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 192.58/31.09  | | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (578), (582),
% 192.58/31.09  | | | | | | | | | | | | | | |            (584), (586), (588), (590), (591), (592), (593),
% 192.58/31.09  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 192.58/31.09  | | | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 192.58/31.09  | | | | | | | | | | | | | | |            (610), (612), (613), (687), (739), (773), (775),
% 192.58/31.09  | | | | | | | | | | | | | | |            (779), (1589), (1591), (1594), (1595), (1597),
% 192.58/31.09  | | | | | | | | | | | | | | |            (1599), (1601), (1603), (1604), (1605), (1606),
% 192.58/31.09  | | | | | | | | | | | | | | |            (1672), (1678), (function-axioms) are inconsistent
% 192.58/31.09  | | | | | | | | | | | | | | |            by sub-proof #774.
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | Case 2:
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | |   (1679)  all_40_1 = e2
% 192.58/31.09  | | | | | | | | | | | | | | |   (1680)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | COMBINE_EQS: (687), (1679) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1681)  all_10_1 = e2
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | REDUCE: (1674), (1681) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1682)   ~ (e3 = e2)
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | REDUCE: (53), (1681) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1683)  op(all_10_2, e1) = e2
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | REDUCE: (52), (1681) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1684)  op(e1, e2) = all_10_0
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 192.58/31.09  | | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (1684)
% 192.58/31.09  | | | | | | | | | | | | | | |              gives:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1685)  all_52_13 = all_10_0
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | COMBINE_EQS: (421), (1685) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1686)  all_56_9 = all_10_0
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | COMBINE_EQS: (366), (1685) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1687)  all_58_7 = all_10_0
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | REDUCE: (568), (1685) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1688)   ~ (all_52_5 = all_10_0)
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | REDUCE: (1597), (1685) imply:
% 192.58/31.09  | | | | | | | | | | | | | | |   (1689)   ~ (all_10_0 = all_6_0)
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 192.58/31.09  | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | |   (1690)  all_58_15 = e0
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (1672), (1690),
% 192.58/31.09  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.09  | | | | | | | | | | | | | | | |            #877.
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | Case 2:
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | |   (1691)   ~ (all_58_15 = e0)
% 192.58/31.09  | | | | | | | | | | | | | | | |   (1692)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 192.58/31.09  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 192.58/31.09  | | | | | | | | | | | | | | | |             e0)
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | ALPHA: (1692) implies:
% 192.58/31.09  | | | | | | | | | | | | | | | |   (1693)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 192.58/31.09  | | | | | | | | | | | | | | | |   (1694)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | REDUCE: (541), (1691) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | |   (1695)   ~ (all_14_2 = e0)
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 192.58/31.09  | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1696)  all_56_1 = e3
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | COMBINE_EQS: (1594), (1696) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1697)  all_6_0 = e3
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | COMBINE_EQS: (1595), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1698)  all_58_1 = e3
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | REDUCE: (1599), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1699)   ~ (all_52_15 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | REDUCE: (1601), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1700)   ~ (all_52_17 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | REDUCE: (1603), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1701)   ~ (all_52_25 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | REDUCE: (1604), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1702)   ~ (all_6_2 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | SIMP: (1702) implies:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1703)   ~ (all_6_2 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | REDUCE: (1605), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1704)   ~ (all_4_2 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | SIMP: (1704) implies:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1705)   ~ (all_4_2 = e3)
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | REDUCE: (1606), (1697) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1706)  op(e3, e3) = all_52_8
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 192.58/31.09  | | | | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (1706)
% 192.58/31.09  | | | | | | | | | | | | | | | | |              gives:
% 192.58/31.09  | | | | | | | | | | | | | | | | |   (1707)  all_52_8 = all_6_2
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 192.58/31.09  | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | |   (1708)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.09  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 192.58/31.09  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 192.58/31.09  | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | BETA: splitting (1708) gives:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | Case 1:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1709)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | ALPHA: (1709) implies:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1710)  all_52_6 = e0
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1711)  all_52_4 = e1
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1712)  all_52_2 = e2
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1713)  all_52_0 = e3
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | REDUCE: (185), (1712) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1714)  op(all_52_3, all_52_3) = e2
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | REDUCE: (184), (1711) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1715)  op(all_52_5, all_52_5) = e1
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (1710) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1716)  op(all_52_7, all_52_7) = e0
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | REDUCE: (610), (1713) imply:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1717)  op(all_6_2, all_6_2) = e3
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (156), (158),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (159), (163), (167), (168), (169), (173), (174),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (270),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (272), (273), (274), (276), (277), (279), (280),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (304), (305), (306),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (314),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (324), (325), (328), (329), (330), (331), (332),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (333), (346), (351), (352), (366), (367), (372),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (491), (508), (538),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (592), (594), (595), (596), (597), (598), (600),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (609), (612), (613), (649), (685), (772), (773),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (775), (1292), (1667), (1672), (1677), (1693),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (1694), (1695), (1714), (1715), (1716), (1717),
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            #697.
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |   (1718)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1703), (1707), (1718) are inconsistent by
% 192.58/31.09  | | | | | | | | | | | | | | | | | | |            sub-proof #834.
% 192.58/31.09  | | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | | End of split
% 192.58/31.09  | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.09  | | | | | | | | | | | | | | | | | | 
% 192.58/31.09  | | | | | | | | | | | | | | | | | |   (1719)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 192.58/31.09  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 192.58/31.09  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 192.58/31.09  | | | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (280),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (304), (306), (307), (309),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (311), (313), (315), (316), (317), (319), (321),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (329), (332), (333),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (431), (526), (538), (539), (541), (542), (543),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (553), (555), (559), (561), (562), (563), (564),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (565), (566), (567), (569), (570), (571), (572),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (573), (574), (575), (578), (582), (584), (586),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (590), (593), (594), (595), (596), (597), (598),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (608), (609), (610), (612), (613), (767), (776),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (781), (1591), (1680), (1683), (1686), (1687),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (1688), (1693), (1694), (1695), (1698), (1699),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (1700), (1701), (1703), (1705), (1706), (1719),
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 192.58/31.10  | | | | | | | | | | | | | | | | | |            #694.
% 192.58/31.10  | | | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | | | End of split
% 192.58/31.10  | | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | | Case 2:
% 192.58/31.10  | | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | | |   (1720)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 192.58/31.10  | | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 192.58/31.10  | | | | | | | | | | | | | | | | |            (610), (739), (773), (775), (1589), (1591),
% 192.58/31.10  | | | | | | | | | | | | | | | | |            (1594), (1604), (1720), (function-axioms) are
% 192.58/31.10  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 192.58/31.10  | | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | | End of split
% 192.58/31.10  | | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | | End of split
% 192.58/31.10  | | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | | End of split
% 192.58/31.10  | | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | | End of split
% 192.58/31.10  | | | | | | | | | | | | | 
% 192.58/31.10  | | | | | | | | | | | | Case 2:
% 192.58/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | |   (1721)  all_30_1 = e3
% 193.21/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 193.21/31.10  | | | | | | | | | | | | |            (52), (53), (61), (63), (158), (162), (166),
% 193.21/31.10  | | | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 193.21/31.10  | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 193.21/31.10  | | | | | | | | | | | | |            (271), (273), (274), (275), (277), (280), (282),
% 193.21/31.10  | | | | | | | | | | | | |            (283), (284), (285), (303), (304), (306), (307),
% 193.21/31.10  | | | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 193.21/31.10  | | | | | | | | | | | | |            (321), (324), (325), (326), (327), (329), (332),
% 193.21/31.10  | | | | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 193.21/31.10  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 193.21/31.10  | | | | | | | | | | | | |            (431), (522), (538), (539), (540), (541), (542),
% 193.21/31.10  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.21/31.10  | | | | | | | | | | | | |            (551), (553), (555), (559), (561), (562), (563),
% 193.21/31.10  | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (572),
% 193.21/31.10  | | | | | | | | | | | | |            (573), (574), (575), (577), (578), (582), (584),
% 193.21/31.10  | | | | | | | | | | | | |            (586), (590), (593), (594), (595), (596), (597),
% 193.21/31.10  | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 193.21/31.10  | | | | | | | | | | | | |            (607), (608), (609), (610), (612), (613), (670),
% 193.21/31.10  | | | | | | | | | | | | |            (739), (773), (775), (776), (1589), (1591),
% 193.21/31.10  | | | | | | | | | | | | |            (1594), (1595), (1597), (1599), (1601), (1603),
% 193.21/31.10  | | | | | | | | | | | | |            (1604), (1605), (1606), (1672), (1721),
% 193.21/31.10  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.10  | | | | | | | | | | | | |            #772.
% 193.21/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | End of split
% 193.21/31.10  | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | End of split
% 193.21/31.10  | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | End of split
% 193.21/31.10  | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | End of split
% 193.21/31.10  | | | | | | | | | 
% 193.21/31.10  | | | | | | | | Case 2:
% 193.21/31.10  | | | | | | | | | 
% 193.21/31.10  | | | | | | | | |   (1722)  all_18_0 = e3
% 193.21/31.10  | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | COMBINE_EQS: (761), (1722) imply:
% 193.21/31.10  | | | | | | | | |   (1723)  all_14_0 = e3
% 193.21/31.10  | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | REDUCE: (62), (1723) imply:
% 193.21/31.10  | | | | | | | | |   (1724)  op(e0, all_14_1) = e3
% 193.21/31.10  | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | BETA: splitting (79) gives:
% 193.21/31.10  | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | |   (1725)   ~ (all_20_0 = e3)
% 193.21/31.10  | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | REDUCE: (758), (1725) imply:
% 193.21/31.10  | | | | | | | | | |   (1726)   ~ (all_4_0 = e3)
% 193.21/31.10  | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | BETA: splitting (84) gives:
% 193.21/31.10  | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | |   (1727)   ~ (all_22_1 = e2)
% 193.21/31.10  | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | REDUCE: (658), (1727) imply:
% 193.21/31.10  | | | | | | | | | | |   (1728)   ~ (all_6_1 = e2)
% 193.21/31.10  | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | BETA: splitting (104) gives:
% 193.21/31.10  | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | |   (1729)   ~ (all_30_1 = e3)
% 193.21/31.10  | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | REDUCE: (670), (1729) imply:
% 193.21/31.10  | | | | | | | | | | | |   (1730)   ~ (all_10_1 = e3)
% 193.21/31.10  | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | BETA: splitting (109) gives:
% 193.21/31.10  | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | |   (1731)   ~ (all_32_1 = e3)
% 193.21/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | REDUCE: (663), (1731) imply:
% 193.21/31.10  | | | | | | | | | | | | |   (1732)   ~ (all_4_1 = e3)
% 193.21/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 193.21/31.10  | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | |   (1733)   ~ (all_40_1 = e2)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (687), (1733) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1734)   ~ (all_10_1 = e2)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | |   (1735)  all_58_15 = e0
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (1724), (1735),
% 193.21/31.10  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.10  | | | | | | | | | | | | | | |            #693.
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | Case 2:
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | |   (1736)   ~ (all_58_15 = e0)
% 193.21/31.10  | | | | | | | | | | | | | | |   (1737)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.21/31.10  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.21/31.10  | | | | | | | | | | | | | | |             e0)
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | ALPHA: (1737) implies:
% 193.21/31.10  | | | | | | | | | | | | | | |   (1738)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.21/31.10  | | | | | | | | | | | | | | |   (1739)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | REDUCE: (541), (1736) imply:
% 193.21/31.10  | | | | | | | | | | | | | | |   (1740)   ~ (all_14_2 = e0)
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 193.21/31.10  | | | | | | | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (63),
% 193.21/31.10  | | | | | | | | | | | | | | |            (156), (157), (158), (159), (161), (162), (166),
% 193.21/31.10  | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 193.21/31.10  | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 193.21/31.10  | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 193.21/31.10  | | | | | | | | | | | | | | |            (275), (276), (277), (278), (279), (280), (281),
% 193.21/31.10  | | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (305), (306),
% 193.21/31.10  | | | | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (314),
% 193.21/31.10  | | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 193.21/31.10  | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 193.21/31.10  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 193.21/31.10  | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 193.21/31.10  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 193.21/31.10  | | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 193.21/31.10  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.21/31.10  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 193.21/31.10  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 193.21/31.10  | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 193.21/31.10  | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 193.21/31.10  | | | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 193.21/31.10  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 193.21/31.10  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 193.21/31.10  | | | | | | | | | | | | | | |            (611), (612), (613), (772), (773), (775), (776),
% 193.21/31.10  | | | | | | | | | | | | | | |            (778), (781), (1726), (1728), (1730), (1732),
% 193.21/31.10  | | | | | | | | | | | | | | |            (1734), (1738), (1739), (1740), (function-axioms)
% 193.21/31.10  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #680.
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | End of split
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | Case 2:
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | |   (1741)  all_40_1 = e2
% 193.21/31.10  | | | | | | | | | | | | | |   (1742)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | COMBINE_EQS: (687), (1741) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1743)  all_10_1 = e2
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (1730), (1743) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1744)   ~ (e3 = e2)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (53), (1743) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1745)  op(all_10_2, e1) = e2
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (52), (1743) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1746)  op(e1, e2) = all_10_0
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 193.21/31.10  | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (1746)
% 193.21/31.10  | | | | | | | | | | | | | |              gives:
% 193.21/31.10  | | | | | | | | | | | | | |   (1747)  all_52_13 = all_10_0
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | COMBINE_EQS: (421), (1747) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1748)  all_56_9 = all_10_0
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | COMBINE_EQS: (366), (1747) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1749)  all_58_7 = all_10_0
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (575), (1747) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1750)   ~ (all_52_9 = all_10_0)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (587), (1747) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1751)   ~ (all_52_15 = all_10_0)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | SIMP: (1751) implies:
% 193.21/31.10  | | | | | | | | | | | | | |   (1752)   ~ (all_52_15 = all_10_0)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (588), (1747) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1753)   ~ (all_10_0 = all_10_2)
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | REDUCE: (180), (1747) imply:
% 193.21/31.10  | | | | | | | | | | | | | |   (1754)  op(all_10_0, all_10_0) = all_52_12
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.21/31.10  | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | |   (1755)  all_58_15 = e0
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (1724), (1755),
% 193.21/31.10  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.10  | | | | | | | | | | | | | | |            #678.
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | Case 2:
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | |   (1756)   ~ (all_58_15 = e0)
% 193.21/31.10  | | | | | | | | | | | | | | |   (1757)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.21/31.10  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.21/31.10  | | | | | | | | | | | | | | |             e0)
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | ALPHA: (1757) implies:
% 193.21/31.10  | | | | | | | | | | | | | | |   (1758)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.21/31.10  | | | | | | | | | | | | | | |   (1759)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | REDUCE: (541), (1756) imply:
% 193.21/31.10  | | | | | | | | | | | | | | |   (1760)   ~ (all_14_2 = e0)
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 193.21/31.10  | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | Case 1:
% 193.21/31.10  | | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | |   (1761)  all_56_9 = e3
% 193.21/31.10  | | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | | REF_CLOSE: (776), (1748), (1761) are inconsistent by
% 193.21/31.10  | | | | | | | | | | | | | | | |            sub-proof #1006.
% 193.21/31.10  | | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | Case 2:
% 193.21/31.10  | | | | | | | | | | | | | | | | 
% 193.21/31.10  | | | | | | | | | | | | | | | |   (1762)   ~ (all_56_9 = e3)
% 193.21/31.11  | | | | | | | | | | | | | | | |   (1763)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.21/31.11  | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | Case 1:
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | |   (1764)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.21/31.11  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.21/31.11  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | BETA: splitting (1764) gives:
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | Case 1:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1765)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.21/31.11  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | ALPHA: (1765) implies:
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1766)  all_52_6 = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1767)  all_52_4 = e1
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1768)  all_52_2 = e2
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1769)  all_52_0 = e3
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | REDUCE: (185), (1768) imply:
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1770)  op(all_52_3, all_52_3) = e2
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | REDUCE: (184), (1767) imply:
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1771)  op(all_52_5, all_52_5) = e1
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | REDUCE: (183), (1766) imply:
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1772)  op(all_52_7, all_52_7) = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | REDUCE: (610), (1769) imply:
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1773)  op(all_6_2, all_6_2) = e3
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | Case 1:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |   (1774)  all_56_15 = e3
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (63), (156), (167), (168),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (178), (282), (284), (313), (321), (332), (351),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (387), (388), (394), (405), (526), (538), (544),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (546), (547), (553), (557), (564), (567), (569),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (573), (577), (578), (595), (600), (606), (609),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (612), (613), (767), (776), (781), (1724), (1742),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (1745), (1748), (1749), (1750), (1763), (1770),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (1771), (1773), (1774), (function-axioms) are
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #676.
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | Case 2:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |   (1775)   ~ (all_56_15 = e3)
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |   (1776)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | REDUCE: (538), (1775) imply:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |   (1777)   ~ (all_14_2 = e3)
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (51), (61), (157), (161), (169), (175), (180),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (182), (272), (273), (280), (281), (284), (304),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (305), (306), (319), (320), (321), (324), (325),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (330), (332), (346), (351), (366), (387), (394),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (405), (411), (431), (538), (539), (541), (542),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (543), (547), (548), (549), (551), (555), (557),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (562), (563), (564), (569), (571), (572), (573),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (574), (576), (582), (590), (591), (600), (613),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (772), (1726), (1732), (1758), (1760), (1770),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (1771), (1772), (1773), (1776), (1777),
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.11  | | | | | | | | | | | | | | | | | | |            #1145.
% 193.21/31.11  | | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | End of split
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | Case 2:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1778)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.21/31.11  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (38), (41), (43), (51), (158), (169), (179),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (182), (270), (271), (273), (284), (306), (325),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (327), (343), (351), (394), (405), (431), (538),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (541), (542), (543), (548), (549), (555), (557),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (571), (574), (582), (590), (591), (611), (772),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (776), (778), (781), (1728), (1748), (1749),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (1750), (1752), (1753), (1754), (1763), (1778),
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.11  | | | | | | | | | | | | | | | | | |            #714.
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | End of split
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | Case 2:
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | |   (1779)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.21/31.11  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.21/31.11  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | BETA: splitting (1779) gives:
% 193.21/31.11  | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | Case 1:
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.11  | | | | | | | | | | | | | | | | | |   (1780)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 193.21/31.11  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 193.21/31.11  | | | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (1728),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (1758), (1759), (1780), (function-axioms) are
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 193.21/31.17  | | | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | | | Case 2:
% 193.21/31.17  | | | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | | | |   (1781)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 193.21/31.17  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 193.21/31.17  | | | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (775), (778), (1728), (1758), (1760), (1781),
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.17  | | | | | | | | | | | | | | | | | |            #1008.
% 193.21/31.17  | | | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | | | End of split
% 193.21/31.17  | | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | | End of split
% 193.21/31.17  | | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | | End of split
% 193.21/31.17  | | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | | End of split
% 193.21/31.17  | | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | | End of split
% 193.21/31.17  | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | Case 2:
% 193.21/31.17  | | | | | | | | | | | | | 
% 193.21/31.17  | | | | | | | | | | | | |   (1782)  all_32_1 = e3
% 193.21/31.17  | | | | | | | | | | | | |   (1783)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 193.21/31.17  | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 193.21/31.18  | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (124), (158),
% 193.21/31.18  | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 193.21/31.18  | | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 193.21/31.18  | | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 193.21/31.18  | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 193.21/31.18  | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 193.21/31.18  | | | | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (314),
% 193.21/31.18  | | | | | | | | | | | | |            (315), (316), (317), (318), (319), (321), (323),
% 193.21/31.18  | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 193.21/31.18  | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 193.21/31.18  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 193.21/31.18  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 193.21/31.18  | | | | | | | | | | | | |            (431), (523), (525), (538), (539), (540), (541),
% 193.21/31.18  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.21/31.18  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.21/31.18  | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 193.21/31.18  | | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 193.21/31.18  | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 193.21/31.18  | | | | | | | | | | | | |            (587), (588), (590), (591), (592), (593), (594),
% 193.21/31.18  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 193.21/31.18  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 193.21/31.18  | | | | | | | | | | | | |            (611), (612), (613), (663), (686), (721), (766),
% 193.21/31.18  | | | | | | | | | | | | |            (772), (773), (775), (778), (1724), (1726),
% 193.21/31.18  | | | | | | | | | | | | |            (1728), (1782), (1783), (function-axioms) are
% 193.21/31.18  | | | | | | | | | | | | |            inconsistent by sub-proof #668.
% 193.21/31.18  | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | End of split
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | Case 2:
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | |   (1784)  all_30_1 = e3
% 193.21/31.18  | | | | | | | | | | | |   (1785)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | COMBINE_EQS: (670), (1784) imply:
% 193.21/31.18  | | | | | | | | | | | |   (1786)  all_10_1 = e3
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | SIMP: (1786) implies:
% 193.21/31.18  | | | | | | | | | | | |   (1787)  all_10_1 = e3
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.21/31.18  | | | | | | | | | | | |            (42), (43), (51), (52), (53), (61), (63), (158),
% 193.21/31.18  | | | | | | | | | | | |            (161), (162), (166), (167), (168), (169), (172),
% 193.21/31.18  | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.21/31.18  | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 193.21/31.18  | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 193.21/31.18  | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 193.21/31.18  | | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 193.21/31.18  | | | | | | | | | | | |            (314), (315), (316), (317), (319), (321), (323),
% 193.21/31.18  | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 193.21/31.18  | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 193.21/31.18  | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 193.21/31.18  | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 193.21/31.18  | | | | | | | | | | | |            (427), (431), (459), (538), (539), (540), (541),
% 193.21/31.18  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.21/31.18  | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.21/31.18  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 193.21/31.18  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 193.21/31.18  | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 193.21/31.18  | | | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 193.21/31.18  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 193.21/31.18  | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 193.21/31.18  | | | | | | | | | | | |            (610), (611), (612), (613), (750), (772), (773),
% 193.21/31.18  | | | | | | | | | | | |            (775), (776), (778), (781), (1724), (1728),
% 193.21/31.18  | | | | | | | | | | | |            (1785), (1787), (function-axioms) are inconsistent
% 193.21/31.18  | | | | | | | | | | | |            by sub-proof #665.
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | End of split
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | Case 2:
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | |   (1788)  all_22_1 = e2
% 193.21/31.18  | | | | | | | | | | |   (1789)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | COMBINE_EQS: (658), (1788) imply:
% 193.21/31.18  | | | | | | | | | | |   (1790)  all_6_1 = e2
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | SIMP: (1790) implies:
% 193.21/31.18  | | | | | | | | | | |   (1791)  all_6_1 = e2
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 193.21/31.18  | | | | | | | | | | |            (52), (53), (61), (62), (63), (104), (129), (157),
% 193.21/31.18  | | | | | | | | | | |            (158), (161), (162), (166), (167), (168), (169),
% 193.21/31.18  | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (180),
% 193.21/31.18  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 193.21/31.18  | | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 193.21/31.18  | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 193.21/31.18  | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 193.21/31.18  | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 193.21/31.18  | | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 193.21/31.18  | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 193.21/31.18  | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 193.21/31.18  | | | | | | | | | | |            (421), (431), (522), (526), (538), (539), (540),
% 193.21/31.18  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 193.21/31.18  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 193.21/31.18  | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 193.21/31.18  | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 193.21/31.18  | | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 193.21/31.18  | | | | | | | | | | |            (588), (590), (591), (592), (593), (594), (595),
% 193.21/31.18  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 193.21/31.18  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 193.21/31.18  | | | | | | | | | | |            (613), (670), (687), (739), (767), (773), (775),
% 193.21/31.18  | | | | | | | | | | |            (776), (778), (779), (781), (1724), (1789),
% 193.21/31.18  | | | | | | | | | | |            (1791), (function-axioms) are inconsistent by
% 193.21/31.18  | | | | | | | | | | |            sub-proof #662.
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | End of split
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | Case 2:
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | |   (1792)  all_20_0 = e3
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | COMBINE_EQS: (758), (1792) imply:
% 193.21/31.18  | | | | | | | | | |   (1793)  all_4_0 = e3
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | SIMP: (1793) implies:
% 193.21/31.18  | | | | | | | | | |   (1794)  all_4_0 = e3
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | REDUCE: (37), (1794) imply:
% 193.21/31.18  | | | | | | | | | |   (1795)  op(e2, all_4_1) = e3
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | BETA: splitting (84) gives:
% 193.21/31.18  | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | |   (1796)   ~ (all_22_1 = e2)
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | REDUCE: (658), (1796) imply:
% 193.21/31.18  | | | | | | | | | | |   (1797)   ~ (all_6_1 = e2)
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | BETA: splitting (104) gives:
% 193.21/31.18  | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | |   (1798)   ~ (all_30_1 = e3)
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | REDUCE: (670), (1798) imply:
% 193.21/31.18  | | | | | | | | | | | |   (1799)   ~ (all_10_1 = e3)
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | BETA: splitting (129) gives:
% 193.21/31.18  | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | |   (1800)   ~ (all_40_1 = e2)
% 193.21/31.18  | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | REDUCE: (687), (1800) imply:
% 193.21/31.18  | | | | | | | | | | | | |   (1801)   ~ (all_10_1 = e2)
% 193.21/31.18  | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.21/31.18  | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | |   (1802)  all_58_15 = e0
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (1724), (1802),
% 193.21/31.18  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.21/31.18  | | | | | | | | | | | | | |            #678.
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | Case 2:
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | |   (1803)   ~ (all_58_15 = e0)
% 193.21/31.18  | | | | | | | | | | | | | |   (1804)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.21/31.18  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.21/31.18  | | | | | | | | | | | | | |             e0)
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | ALPHA: (1804) implies:
% 193.21/31.18  | | | | | | | | | | | | | |   (1805)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.21/31.18  | | | | | | | | | | | | | |   (1806)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | REDUCE: (541), (1803) imply:
% 193.21/31.18  | | | | | | | | | | | | | |   (1807)   ~ (all_14_2 = e0)
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.21/31.18  | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | |   (1808)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.21/31.18  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.21/31.18  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.21/31.18  | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | BETA: splitting (1808) gives:
% 193.21/31.18  | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1809)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.21/31.18  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | ALPHA: (1809) implies:
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1810)  all_52_6 = e0
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1811)  all_52_4 = e1
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1812)  all_52_2 = e2
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1813)  all_52_0 = e3
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | REDUCE: (185), (1812) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1814)  op(all_52_3, all_52_3) = e2
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | REDUCE: (184), (1811) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1815)  op(all_52_5, all_52_5) = e1
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | REDUCE: (183), (1810) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1816)  op(all_52_7, all_52_7) = e0
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | REDUCE: (610), (1813) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | |   (1817)  op(all_6_2, all_6_2) = e3
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 193.21/31.18  | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | Case 1:
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1818)  all_56_15 = e3
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (1818) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1819)  all_14_2 = e3
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | SIMP: (1819) implies:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1820)  all_14_2 = e3
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (573), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1821)   ~ (all_52_7 = e3)
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (591), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1822)   ~ (all_52_15 = e3)
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (608), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1823)   ~ (all_52_27 = e3)
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (609), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1824)   ~ (all_52_29 = e3)
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (613), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1825)  op(e3, e3) = all_52_30
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (63), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1826)  op(e3, e0) = all_14_1
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.21/31.18  | | | | | | | | | | | | | | | | | REDUCE: (61), (1820) imply:
% 193.21/31.18  | | | | | | | | | | | | | | | | |   (1827)  op(e0, e0) = e3
% 193.21/31.18  | | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (41), (42),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (43), (51), (52), (53), (61), (156), (159), (167),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (168), (169), (172), (177), (178), (271), (272),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (273), (277), (279), (281), (284), (304), (305),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (310), (312), (313), (314), (315), (317), (319),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (320), (321), (327), (328), (329), (330), (331),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (367),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (405), (411),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (417), (431), (542), (543), (544), (545), (546),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (559), (562), (563), (564), (565), (567), (569),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (578), (580), (582), (590), (596), (597), (598),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (600), (602), (611), (612), (772), (773), (775),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (776), (781), (1799), (1801), (1814), (1815),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (1816), (1817), (1821), (1822), (1823), (1824),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (1825), (1826), (1827), (function-axioms) are
% 193.82/31.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #683.
% 193.82/31.19  | | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | |   (1828)   ~ (all_56_15 = e3)
% 193.82/31.19  | | | | | | | | | | | | | | | | |   (1829)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 193.82/31.19  | | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | | REDUCE: (538), (1828) imply:
% 193.82/31.19  | | | | | | | | | | | | | | | | |   (1830)   ~ (all_14_2 = e3)
% 193.82/31.19  | | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (38), (41), (42), (43),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (51), (53), (61), (62), (63), (156), (158), (159),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (169), (175), (179), (182), (271), (272), (273),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (276), (277), (278), (279), (281), (282), (283),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (309), (311), (312),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (313), (314), (319), (320), (321), (323), (325),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (328), (331), (332), (333), (343), (346), (351),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (417), (421), (427),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (431), (538), (541), (542), (543), (544), (545),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (557), (559), (561), (563), (564), (565), (566),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (568), (569), (571), (572), (573), (574), (575),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (584), (586), (588),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (589), (590), (591), (593), (594), (595), (596),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (598), (600), (603), (604), (606), (608), (609),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (612), (613), (772), (773), (779), (1795), (1799),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (1805), (1806), (1807), (1814), (1815), (1816),
% 193.82/31.19  | | | | | | | | | | | | | | | | |            (1817), (1829), (1830), (function-axioms) are
% 193.82/31.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #656.
% 193.82/31.19  | | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | End of split
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | |   (1831)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.19  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (773), (775), (778), (1797), (1805), (1806),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (1807), (1831), (function-axioms) are inconsistent
% 193.82/31.19  | | | | | | | | | | | | | | | |            by sub-proof #731.
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | End of split
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | |   (1832)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.19  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.19  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | BETA: splitting (1832) gives:
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | |   (1833)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 193.82/31.19  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (1797),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (1805), (1806), (1833), (function-axioms) are
% 193.82/31.19  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | |   (1834)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 193.82/31.19  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (775), (778), (1797), (1805), (1807), (1834),
% 193.82/31.19  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.19  | | | | | | | | | | | | | | | |            #1008.
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | End of split
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | End of split
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | End of split
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | |   (1835)  all_40_1 = e2
% 193.82/31.19  | | | | | | | | | | | | |   (1836)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | COMBINE_EQS: (687), (1835) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1837)  all_10_1 = e2
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (1799), (1837) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1838)   ~ (e3 = e2)
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (53), (1837) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1839)  op(all_10_2, e1) = e2
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (52), (1837) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1840)  op(e1, e2) = all_10_0
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 193.82/31.19  | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (1840)
% 193.82/31.19  | | | | | | | | | | | | |              gives:
% 193.82/31.19  | | | | | | | | | | | | |   (1841)  all_52_13 = all_10_0
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | COMBINE_EQS: (421), (1841) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1842)  all_56_9 = all_10_0
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | COMBINE_EQS: (366), (1841) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1843)  all_58_7 = all_10_0
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (575), (1841) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1844)   ~ (all_52_9 = all_10_0)
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (587), (1841) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1845)   ~ (all_52_15 = all_10_0)
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | SIMP: (1845) implies:
% 193.82/31.19  | | | | | | | | | | | | |   (1846)   ~ (all_52_15 = all_10_0)
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (588), (1841) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1847)   ~ (all_10_0 = all_10_2)
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | REDUCE: (180), (1841) imply:
% 193.82/31.19  | | | | | | | | | | | | |   (1848)  op(all_10_0, all_10_0) = all_52_12
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.82/31.19  | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | Case 1:
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | |   (1849)  all_58_15 = e0
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (1724), (1849),
% 193.82/31.19  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.19  | | | | | | | | | | | | | |            #693.
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | |   (1850)   ~ (all_58_15 = e0)
% 193.82/31.19  | | | | | | | | | | | | | |   (1851)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.82/31.19  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.82/31.19  | | | | | | | | | | | | | |             e0)
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | ALPHA: (1851) implies:
% 193.82/31.19  | | | | | | | | | | | | | |   (1852)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.82/31.19  | | | | | | | | | | | | | |   (1853)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | REDUCE: (541), (1850) imply:
% 193.82/31.19  | | | | | | | | | | | | | |   (1854)   ~ (all_14_2 = e0)
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 193.82/31.19  | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | Case 1:
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | |   (1855)  all_56_9 = e3
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | REF_CLOSE: (776), (1842), (1855) are inconsistent by
% 193.82/31.19  | | | | | | | | | | | | | | |            sub-proof #1006.
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | Case 2:
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | |   (1856)   ~ (all_56_9 = e3)
% 193.82/31.19  | | | | | | | | | | | | | | |   (1857)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.19  | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.19  | | | | | | | | | | | | | | | | 
% 193.82/31.19  | | | | | | | | | | | | | | | |   (1858)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.20  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.20  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | BETA: splitting (1858) gives:
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1859)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.20  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | ALPHA: (1859) implies:
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1860)  all_52_6 = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1861)  all_52_4 = e1
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1862)  all_52_2 = e2
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1863)  all_52_0 = e3
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REDUCE: (185), (1862) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1864)  op(all_52_3, all_52_3) = e2
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REDUCE: (184), (1861) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1865)  op(all_52_5, all_52_5) = e1
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REDUCE: (183), (1860) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1866)  op(all_52_7, all_52_7) = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REDUCE: (610), (1863) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1867)  op(all_6_2, all_6_2) = e3
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1868)  all_56_15 = e3
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (1868) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1869)  all_14_2 = e3
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REDUCE: (573), (1869) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1870)   ~ (all_52_7 = e3)
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REDUCE: (606), (1869) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1871)   ~ (all_52_25 = e3)
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REDUCE: (609), (1869) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1872)   ~ (all_52_29 = e3)
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REDUCE: (613), (1869) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1873)  op(e3, e3) = all_52_30
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REDUCE: (63), (1869) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1874)  op(e3, e0) = all_14_1
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (156), (167), (168), (178),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (282), (284), (313), (321), (332), (351), (387),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (388), (394), (405), (526), (544), (546), (547),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (553), (557), (564), (567), (569), (577), (578),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (595), (600), (612), (767), (776), (781), (1724),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (1836), (1839), (1842), (1843), (1844), (1857),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (1864), (1865), (1867), (1870), (1871), (1872),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (1873), (1874), (function-axioms) are inconsistent
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            by sub-proof #677.
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1875)   ~ (all_56_15 = e3)
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1876)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REDUCE: (538), (1875) imply:
% 193.82/31.20  | | | | | | | | | | | | | | | | | |   (1877)   ~ (all_14_2 = e3)
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (38), (41), (42), (43),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (51), (53), (61), (62), (63), (156), (158), (159),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (169), (175), (179), (182), (271), (272), (273),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (276), (277), (278), (279), (281), (282), (283),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (309), (311), (312),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (313), (314), (319), (320), (321), (323), (325),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (328), (331), (332), (333), (343), (346), (351),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (417), (421), (427),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (431), (538), (541), (542), (543), (544), (545),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (557), (559), (561), (563), (564), (565), (566),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (568), (569), (571), (572), (573), (574), (575),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (584), (586), (588),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (589), (590), (591), (593), (594), (595), (596),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (598), (600), (603), (604), (606), (608), (609),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (612), (613), (772), (773), (779), (1795), (1799),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (1852), (1853), (1854), (1864), (1865), (1866),
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            (1867), (1876), (1877), (function-axioms) are
% 193.82/31.20  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #656.
% 193.82/31.20  | | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1878)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.20  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (38), (41), (43), (51), (158), (169), (179),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (182), (270), (271), (273), (284), (306), (325),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (327), (343), (351), (394), (405), (431), (538),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (541), (542), (543), (548), (549), (555), (557),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (571), (574), (582), (590), (591), (611), (772),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (776), (778), (781), (1797), (1842), (1843),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (1844), (1846), (1847), (1848), (1857), (1878),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.20  | | | | | | | | | | | | | | | | |            #714.
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | |   (1879)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.20  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.20  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | BETA: splitting (1879) gives:
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1880)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 193.82/31.20  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (1797),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (1852), (1853), (1880), (function-axioms) are
% 193.82/31.20  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | |   (1881)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 193.82/31.20  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (775), (778), (1797), (1852), (1854), (1881),
% 193.82/31.20  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.20  | | | | | | | | | | | | | | | | |            #1008.
% 193.82/31.20  | | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | Case 2:
% 193.82/31.20  | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | |   (1882)  all_30_1 = e3
% 193.82/31.20  | | | | | | | | | | | |   (1883)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 193.82/31.20  | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | COMBINE_EQS: (670), (1882) imply:
% 193.82/31.20  | | | | | | | | | | | |   (1884)  all_10_1 = e3
% 193.82/31.20  | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.82/31.20  | | | | | | | | | | | |            (42), (43), (51), (52), (53), (61), (63), (158),
% 193.82/31.20  | | | | | | | | | | | |            (161), (162), (166), (167), (168), (169), (172),
% 193.82/31.20  | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.82/31.20  | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 193.82/31.20  | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 193.82/31.20  | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 193.82/31.20  | | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 193.82/31.20  | | | | | | | | | | | |            (314), (315), (316), (317), (319), (321), (323),
% 193.82/31.20  | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 193.82/31.20  | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 193.82/31.20  | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 193.82/31.20  | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 193.82/31.20  | | | | | | | | | | | |            (427), (431), (459), (538), (539), (540), (541),
% 193.82/31.20  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.82/31.20  | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.82/31.20  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 193.82/31.20  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 193.82/31.20  | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 193.82/31.20  | | | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 193.82/31.20  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 193.82/31.20  | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 193.82/31.20  | | | | | | | | | | | |            (610), (611), (612), (613), (750), (772), (773),
% 193.82/31.20  | | | | | | | | | | | |            (775), (776), (778), (781), (1724), (1797),
% 193.82/31.20  | | | | | | | | | | | |            (1883), (1884), (function-axioms) are inconsistent
% 193.82/31.20  | | | | | | | | | | | |            by sub-proof #665.
% 193.82/31.20  | | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | | End of split
% 193.82/31.20  | | | | | | | | | | | 
% 193.82/31.20  | | | | | | | | | | Case 2:
% 193.82/31.20  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | |   (1885)  all_22_1 = e2
% 193.82/31.21  | | | | | | | | | | |   (1886)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | COMBINE_EQS: (658), (1885) imply:
% 193.82/31.21  | | | | | | | | | | |   (1887)  all_6_1 = e2
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | SIMP: (1887) implies:
% 193.82/31.21  | | | | | | | | | | |   (1888)  all_6_1 = e2
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | REDUCE: (43), (1888) imply:
% 193.82/31.21  | | | | | | | | | | |   (1889)  op(all_6_2, e3) = e2
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | REDUCE: (42), (1888) imply:
% 193.82/31.21  | | | | | | | | | | |   (1890)  op(e3, e2) = all_6_0
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 193.82/31.21  | | | | | | | | | | |            (52), (53), (61), (62), (63), (104), (129), (157),
% 193.82/31.21  | | | | | | | | | | |            (158), (161), (162), (166), (167), (168), (169),
% 193.82/31.21  | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (180),
% 193.82/31.21  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 193.82/31.21  | | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 193.82/31.21  | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 193.82/31.21  | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 193.82/31.21  | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 193.82/31.21  | | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 193.82/31.21  | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 193.82/31.21  | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 193.82/31.21  | | | | | | | | | | |            (421), (431), (522), (526), (538), (539), (540),
% 193.82/31.21  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 193.82/31.21  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 193.82/31.21  | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 193.82/31.21  | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 193.82/31.21  | | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 193.82/31.21  | | | | | | | | | | |            (588), (590), (591), (592), (593), (594), (595),
% 193.82/31.21  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 193.82/31.21  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 193.82/31.21  | | | | | | | | | | |            (613), (670), (687), (739), (767), (773), (775),
% 193.82/31.21  | | | | | | | | | | |            (776), (779), (781), (1724), (1886), (1889),
% 193.82/31.21  | | | | | | | | | | |            (1890), (function-axioms) are inconsistent by
% 193.82/31.21  | | | | | | | | | | |            sub-proof #663.
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | End of split
% 193.82/31.21  | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | End of split
% 193.82/31.21  | | | | | | | | | 
% 193.82/31.21  | | | | | | | | End of split
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | Case 2:
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | |   (1891)  all_16_0 = e2
% 193.82/31.21  | | | | | | | |   (1892)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | COMBINE_EQS: (760), (1891) imply:
% 193.82/31.21  | | | | | | | |   (1893)  all_10_0 = e2
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | SIMP: (1893) implies:
% 193.82/31.21  | | | | | | | |   (1894)  all_10_0 = e2
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | COMBINE_EQS: (756), (1894) imply:
% 193.82/31.21  | | | | | | | |   (1895)  all_26_0 = e2
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | REDUCE: (776), (1894) imply:
% 193.82/31.21  | | | | | | | |   (1896)   ~ (e3 = e2)
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | REDUCE: (52), (1894) imply:
% 193.82/31.21  | | | | | | | |   (1897)  op(e1, all_10_1) = e2
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | BETA: splitting (74) gives:
% 193.82/31.21  | | | | | | | | 
% 193.82/31.21  | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | 
% 193.82/31.21  | | | | | | | | |   (1898)   ~ (all_18_0 = e3)
% 193.82/31.21  | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | REDUCE: (761), (1898) imply:
% 193.82/31.21  | | | | | | | | |   (1899)   ~ (all_14_0 = e3)
% 193.82/31.21  | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | BETA: splitting (79) gives:
% 193.82/31.21  | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | |   (1900)   ~ (all_20_0 = e3)
% 193.82/31.21  | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | REDUCE: (758), (1900) imply:
% 193.82/31.21  | | | | | | | | | |   (1901)   ~ (all_4_0 = e3)
% 193.82/31.21  | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | BETA: splitting (84) gives:
% 193.82/31.21  | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | |   (1902)   ~ (all_22_1 = e2)
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | REDUCE: (658), (1902) imply:
% 193.82/31.21  | | | | | | | | | | |   (1903)   ~ (all_6_1 = e2)
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | BETA: splitting (89) gives:
% 193.82/31.21  | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | |   (1904)   ~ (all_24_0 = e1)
% 193.82/31.21  | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | REDUCE: (711), (1904) imply:
% 193.82/31.21  | | | | | | | | | | | |   (1905)   ~ (all_14_0 = e1)
% 193.82/31.21  | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | BETA: splitting (94) gives:
% 193.82/31.21  | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | |   (1906)   ~ (all_26_0 = e2)
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | REDUCE: (1895), (1906) imply:
% 193.82/31.21  | | | | | | | | | | | | |   (1907)  $false
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | CLOSE: (1907) is inconsistent.
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | Case 2:
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | |   (1908)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | BETA: splitting (109) gives:
% 193.82/31.21  | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | |   (1909)   ~ (all_32_1 = e3)
% 193.82/31.21  | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | REDUCE: (663), (1909) imply:
% 193.82/31.21  | | | | | | | | | | | | | |   (1910)   ~ (all_4_1 = e3)
% 193.82/31.21  | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.82/31.21  | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | |   (1911)  all_58_15 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1911) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1912)  all_14_2 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (573), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1913)   ~ (all_52_7 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (591), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1914)   ~ (all_52_15 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (603), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1915)   ~ (all_52_23 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (606), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1916)   ~ (all_52_25 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (608), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1917)   ~ (all_52_27 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (609), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1918)   ~ (all_52_29 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (613), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1919)  op(e0, e0) = all_52_30
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (63), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1920)  op(e0, e0) = all_14_1
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (61), (1912) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1921)  op(e0, e0) = e0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 193.82/31.21  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1919), (1920)
% 193.82/31.21  | | | | | | | | | | | | | | |              gives:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1922)  all_52_30 = all_14_1
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 193.82/31.21  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (1919), (1921)
% 193.82/31.21  | | | | | | | | | | | | | | |              gives:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1923)  all_52_30 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | COMBINE_EQS: (1922), (1923) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1924)  all_14_1 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (62), (1924) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1925)  op(e0, e0) = all_14_0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 193.82/31.21  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1921), (1925) gives:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1926)  all_14_0 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (1899), (1926) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1927)   ~ (e3 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (779), (1926) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1928)   ~ (e2 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | REDUCE: (1905), (1926) imply:
% 193.82/31.21  | | | | | | | | | | | | | | |   (1929)   ~ (e1 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.21  | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | |   (1930)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.21  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.21  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | BETA: splitting (1930) gives:
% 193.82/31.21  | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1931)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.21  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | ALPHA: (1931) implies:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1932)  all_52_6 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1933)  all_52_4 = e1
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1934)  all_52_2 = e2
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1935)  all_52_0 = e3
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (185), (1934) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1936)  op(all_52_3, all_52_3) = e2
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (184), (1933) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1937)  op(all_52_5, all_52_5) = e1
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (183), (1932) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1938)  op(all_52_7, all_52_7) = e0
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (610), (1935) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1939)  op(all_6_2, all_6_2) = e3
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (51), (53),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (61), (156), (157), (161), (179), (272), (273),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (277), (304), (305), (306), (321), (332), (346),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (351), (367), (387), (405), (431), (515), (542),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (543), (547), (555), (564), (567), (568), (569),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (571), (572), (573), (680), (772), (1892), (1897),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (1910), (1911), (1913), (1914), (1936), (1937),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (1938), (1939), (function-axioms) are inconsistent
% 193.82/31.21  | | | | | | | | | | | | | | | | |            by sub-proof #649.
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1940)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.21  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | ALPHA: (1940) implies:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1941)  all_52_14 = e0
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1942)  all_52_12 = e1
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1943)  all_52_10 = e2
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1944)  all_52_8 = e3
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (182), (1944) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1945)  op(all_52_9, all_52_9) = e3
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (180), (1942) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1946)  op(all_52_13, all_52_13) = e1
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (179), (1941) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1947)  op(all_52_15, all_52_15) = e0
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REDUCE: (611), (1943) imply:
% 193.82/31.21  | | | | | | | | | | | | | | | | |   (1948)  op(all_4_2, all_4_2) = e2
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (38), (41), (43), (51), (53),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (178), (272), (273), (277), (278), (280), (281),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (282), (283), (284), (305), (306), (309), (313),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (314), (317), (322), (324), (325), (327), (333),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (346), (351), (366), (367), (372), (375), (388),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (427), (431),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (515), (539), (542), (543), (544), (545), (546),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (568),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (571), (572), (574), (575), (577), (578), (580),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (595),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (604), (605), (612), (680), (772), (778), (1892),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (1903), (1911), (1913), (1914), (1916), (1921),
% 193.82/31.21  | | | | | | | | | | | | | | | | |            (1945), (1946), (1947), (1948), (function-axioms)
% 193.82/31.21  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #647.
% 193.82/31.21  | | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | | End of split
% 193.82/31.21  | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.21  | | | | | | | | | | | | | | | | 
% 193.82/31.21  | | | | | | | | | | | | | | | |   (1949)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.21  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.21  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.21  | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (280),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (304), (305), (306),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (317), (318), (321),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (322), (325), (326), (330), (331), (332), (333),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (415), (427), (431), (539), (542), (543), (544),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (576), (577),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (590), (593), (594), (595), (596), (598), (600),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (602), (604), (605), (608), (610), (611), (612),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (773), (775), (778), (1903), (1910), (1911),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (1913), (1914), (1915), (1916), (1917), (1918),
% 193.82/31.22  | | | | | | | | | | | | | | | |            (1921), (1949), (function-axioms) are inconsistent
% 193.82/31.22  | | | | | | | | | | | | | | | |            by sub-proof #1202.
% 193.82/31.22  | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | End of split
% 193.82/31.22  | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | |   (1950)   ~ (all_58_15 = e0)
% 193.82/31.22  | | | | | | | | | | | | | | |   (1951)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.82/31.22  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.82/31.22  | | | | | | | | | | | | | | |             e0)
% 193.82/31.22  | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | ALPHA: (1951) implies:
% 193.82/31.22  | | | | | | | | | | | | | | |   (1952)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.82/31.22  | | | | | | | | | | | | | | |   (1953)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | REDUCE: (541), (1950) imply:
% 193.82/31.22  | | | | | | | | | | | | | | |   (1954)   ~ (all_14_2 = e0)
% 193.82/31.22  | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | |   (1955)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.22  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.22  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.22  | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | BETA: splitting (1955) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1956)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.22  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | ALPHA: (1956) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1957)  all_52_6 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1958)  all_52_4 = e1
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1959)  all_52_2 = e2
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1960)  all_52_0 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | REDUCE: (185), (1959) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1961)  op(all_52_3, all_52_3) = e2
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | REDUCE: (184), (1958) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1962)  op(all_52_5, all_52_5) = e1
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | REDUCE: (183), (1957) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1963)  op(all_52_7, all_52_7) = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | REDUCE: (610), (1960) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | |   (1964)  op(all_6_2, all_6_2) = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1965)  all_56_15 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (1965) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1966)  all_14_2 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | SIMP: (1966) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1967)  all_14_2 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (573), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1968)   ~ (all_52_7 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (591), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1969)   ~ (all_52_15 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (603), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1970)   ~ (all_52_23 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (606), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1971)   ~ (all_52_25 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (609), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1972)   ~ (all_52_29 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (613), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1973)  op(e3, e3) = all_52_30
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (63), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1974)  op(e3, e0) = all_14_1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (61), (1967) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1975)  op(e0, e0) = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 193.82/31.22  | | | | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (1974)
% 193.82/31.22  | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1976)  all_52_25 = all_14_1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 193.82/31.22  | | | | | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (1973)
% 193.82/31.22  | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1977)  all_52_30 = all_6_2
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1978)  all_56_3 = all_14_1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1979)  all_58_9 = all_14_1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (578), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1980)   ~ (all_52_9 = all_14_1)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (595), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1981)   ~ (all_52_17 = all_14_1)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (605), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1982)   ~ (all_52_29 = all_14_1)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | SIMP: (1982) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1983)   ~ (all_52_29 = all_14_1)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (1971), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1984)   ~ (all_14_1 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | REDUCE: (174), (1976) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | |   (1985)  op(all_14_1, all_14_1) = all_52_24
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | |   (1986)  all_56_13 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (346), (1969), (1986) are inconsistent by
% 193.82/31.22  | | | | | | | | | | | | | | | | | | |            sub-proof #1201.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | |   (1987)   ~ (all_56_13 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | |   (1988)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | |   (1989)  all_56_3 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1978), (1984), (1989) are inconsistent by
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | |            sub-proof #1200.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | |   (1990)   ~ (all_56_3 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | |   (1991)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | |   (1992)  all_56_12 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (1968), (1992) are inconsistent by
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | |   (1993)   ~ (all_56_12 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | |   (1994)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | |   (1995)  all_56_14 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (343), (1970), (1995) are inconsistent by
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1286.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | |   (1996)   ~ (all_56_14 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | |   (1997)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (1998)  all_58_9 = e2
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1979), (1998) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (1999)  all_14_1 = e2
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1999) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2000)  all_14_1 = e2
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1980), (2000) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2001)   ~ (all_52_9 = e2)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1981), (2000) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2002)   ~ (all_52_17 = e2)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1983), (2000) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2003)   ~ (all_52_29 = e2)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1985), (2000) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2004)  op(e2, e2) = all_52_24
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (2000) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2005)  op(e0, e2) = all_14_0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (41), (42), (43), (51), (157),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (169), (177), (180), (182), (276), (280), (283),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (284), (285), (305), (312), (317), (321), (332),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (346), (351), (366), (375), (387), (393), (394),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (405), (415), (421), (431), (539), (540), (542),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (544), (546), (547), (557), (559), (564), (569),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (571), (574), (575), (576), (577), (580), (582),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (587), (588), (593), (611), (612), (772), (775),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (779), (1905), (1961), (1962), (1963), (1964),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (1968), (1970), (1988), (1994), (2001), (2002),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            (2003), (2004), (2005), (function-axioms) are
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1184.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2006)   ~ (all_58_9 = e2)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1979), (2006) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | |   (2007)   ~ (all_14_1 = e2)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2008)  all_56_9 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (2008) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2009)  all_52_13 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2009) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2010)  all_52_13 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (2010) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2011)  all_58_7 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (2010) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2012)   ~ (all_10_2 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2012) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2013)   ~ (all_10_2 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (2010) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2014)  op(e3, e3) = all_52_12
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (2010) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2015)  op(e1, e2) = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e3, e3, simplifying with (41), (2014)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2016)  all_52_12 = all_6_2
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (2017)  all_58_4 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (2017) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (2018)  all_52_17 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (559), (564), (569), (1961), (1962),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (1964), (1968), (2018), (function-axioms) are
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1199.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (2019)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2019) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2020)  all_58_5 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (2020) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2021)  all_52_19 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2021) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2022)  all_52_19 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (2022) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2023)   ~ (all_52_17 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (2022) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2024)   ~ (all_52_23 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2025)  all_56_2 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (2023), (2025) are inconsistent by
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1327.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2026)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2027)  all_58_12 = e1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2027) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2028)  all_52_7 = e1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (2028) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2029)   ~ (all_52_23 = e1)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2029) implies:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2030)   ~ (all_52_23 = e1)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1963), (2028) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2031)  op(e1, e1) = e0
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (62), (315), (343), (393), (415), (593),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (594), (600), (1899), (1975), (1978), (1981),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1985), (1991), (1997), (2007), (2026), (2030),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2031), (function-axioms) are inconsistent by
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1179.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2032)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (61), (62), (157), (305), (307),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (351), (431), (542), (543), (546), (548),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (549), (571), (573), (772), (1899), (1910),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1963), (1970), (1975), (1978), (1979), (1980),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1984), (1985), (1991), (1994), (2007), (2011),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2013), (2015), (2019), (2020), (2032),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #644.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2033)  all_58_8 = e3 | all_58_14 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (546), (1970), (2013), (2033) are
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1304.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2034)   ~ (all_56_9 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (2034) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | |   (2035)   ~ (all_52_13 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (2036)  all_58_1 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2036) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (2037)  all_52_9 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (557), (564), (569), (1961), (1962),
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (1964), (1968), (2037), (function-axioms) are
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1195.
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (2038)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2038) gives:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2039)  all_58_3 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2039) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2040)  all_4_2 = e3
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (2040) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2041)   ~ (all_52_9 = e3)
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (2040) imply:
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2042)  op(e3, e3) = all_52_10
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (2040) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2043)  op(e3, e2) = all_4_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2040) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2044)  op(e2, e2) = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_1, e2, e3, simplifying with (169), (2043)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2045)  all_52_9 = all_4_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e3, e3, simplifying with (41), (2042)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2046)  all_52_10 = all_6_2
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (2045) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2047)  all_56_1 = all_4_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (2045) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2048)   ~ (all_52_13 = all_4_1)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2048) implies:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2049)   ~ (all_52_13 = all_4_1)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (2045) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2050)   ~ (all_52_15 = all_4_1)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2050) implies:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2051)   ~ (all_52_15 = all_4_1)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2045) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2052)   ~ (all_6_2 = all_4_1)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2052) implies:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2053)   ~ (all_6_2 = all_4_1)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2054)  all_56_1 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1910), (2047), (2054) are inconsistent by
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1167.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2055)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2056)  all_58_6 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (2056) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2057)  all_52_5 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2057) implies:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2058)  all_52_5 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (553), (564), (567), (569), (1961),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1962), (1964), (2058), (function-axioms) are
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2059)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2060)  all_58_0 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (2060) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2061)  all_6_2 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (2061) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2062)   ~ (all_52_3 = e3)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2053), (2061) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2063)   ~ (all_4_1 = e3)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (2061) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2064)  op(e3, e3) = all_6_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (2061) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2065)  op(e3, e3) = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2059) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2066)  all_58_7 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (2066) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2067)  all_52_13 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2035), (2067) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2068)  $false
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2068) is inconsistent.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2069)  all_58_8 = e3 | all_58_11 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2069) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2070)  all_58_8 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2070) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2071)  all_10_2 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (512), (2071) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2072)  all_26_2 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (2071) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2073)  op(e3, e3) = all_52_20
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (2071) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2074)  op(e3, e1) = all_10_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1908) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2075)   ~ (all_26_2 = e3)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2072), (2075) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2076)  $false
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2076) is inconsistent.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2077)   ~ (all_26_1 = e0)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (676), (2077) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2078)   ~ (all_10_1 = e0)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (2074)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2079)  all_52_17 = all_10_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (2064), (2073)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2080)  all_52_20 = all_6_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (2065), (2073)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2081)  all_52_20 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2080), (2081) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2082)  all_6_1 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2082) implies:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2083)  all_6_1 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (2079) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2084)  all_58_4 = all_10_1
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2083) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2085)  op(e3, e3) = all_6_0
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (2065), (2085) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2086)  all_6_0 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2087)  all_56_4 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (2062), (2087) are inconsistent by
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2088)   ~ (all_56_4 = e3)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2089)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (61), (172), (304), (305), (310),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (314), (320), (330), (346), (351), (366), (375),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (387), (411), (431), (542), (543), (544), (547),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (563), (565), (567), (571), (573), (590), (772),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1910), (1961), (1963), (1969), (1972), (1975),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1988), (1994), (2044), (2047), (2049), (2051),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2055), (2060), (2062), (2069), (2070), (2078),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2084), (2089), (function-axioms) are inconsistent
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #684.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2090)  all_58_11 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (1972), (2090) are inconsistent by
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1323.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2091)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (351), (387), (547),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (564), (569), (1961), (1962), (1964), (1968),
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2091), (function-axioms) are inconsistent by
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1364.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2092)  all_58_7 = e3 | all_58_13 = e3
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (366), (543), (1969), (2035), (2092) are
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1298.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | |   (2093)   ~ (all_56_15 = e3)
% 193.82/31.23  | | | | | | | | | | | | | | | | | |   (2094)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 193.82/31.23  | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | REDUCE: (538), (2093) imply:
% 193.82/31.23  | | | | | | | | | | | | | | | | | |   (2095)   ~ (all_14_2 = e3)
% 193.82/31.23  | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (51), (61), (157), (161), (169), (175), (180),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (182), (272), (273), (280), (281), (284), (304),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (305), (306), (319), (320), (321), (324), (325),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (330), (332), (346), (351), (366), (387), (394),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (405), (411), (431), (538), (539), (541), (542),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (543), (547), (548), (549), (551), (555), (557),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (569), (571), (572), (573),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (574), (576), (582), (590), (591), (600), (613),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (772), (1901), (1910), (1952), (1954), (1961),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (1962), (1963), (1964), (2094), (2095),
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.23  | | | | | | | | | | | | | | | | | |            #1145.
% 193.82/31.23  | | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | |   (2096)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.23  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.23  | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (277), (278), (280), (281), (282), (284), (304),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (306), (309), (313), (317), (319), (321), (323),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (325), (326), (328), (330), (331), (332), (333),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (421), (427), (431), (538), (539), (541), (542),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (570), (571),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (584), (586), (588), (589), (590), (591), (592),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (593), (594), (595), (597), (603), (604), (605),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (613), (772), (773), (775), (778), (1903), (1910),
% 193.82/31.23  | | | | | | | | | | | | | | | | |            (1952), (1953), (1954), (2096), (function-axioms)
% 193.82/31.23  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1091.
% 193.82/31.23  | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | End of split
% 193.82/31.23  | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.23  | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | |   (2097)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.23  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.23  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.23  | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | BETA: splitting (2097) gives:
% 193.82/31.23  | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.23  | | | | | | | | | | | | | | | | | 
% 193.82/31.23  | | | | | | | | | | | | | | | | |   (2098)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 193.82/31.23  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 193.82/31.23  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (1903),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (1952), (1953), (2098), (function-axioms) are
% 193.82/31.24  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | |   (2099)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 193.82/31.24  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (775), (778), (1903), (1952), (1954), (2099),
% 193.82/31.24  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.24  | | | | | | | | | | | | | | | | |            #1008.
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | End of split
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | End of split
% 193.82/31.24  | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | End of split
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | Case 2:
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | |   (2100)  all_32_1 = e3
% 193.82/31.24  | | | | | | | | | | | | | |   (2101)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | COMBINE_EQS: (663), (2100) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2102)  all_4_1 = e3
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | COMBINE_EQS: (686), (2102) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2103)  all_38_1 = e3
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (38), (2102) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2104)  op(all_4_2, e2) = e3
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (37), (2102) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2105)  op(e2, e3) = all_4_0
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 193.82/31.24  | | | | | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (2105)
% 193.82/31.24  | | | | | | | | | | | | | |              gives:
% 193.82/31.24  | | | | | | | | | | | | | |   (2106)  all_52_3 = all_4_0
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | COMBINE_EQS: (411), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2107)  all_56_4 = all_4_0
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | COMBINE_EQS: (387), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2108)  all_58_2 = all_4_0
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (562), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2109)   ~ (all_52_5 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | SIMP: (2109) implies:
% 193.82/31.24  | | | | | | | | | | | | | |   (2110)   ~ (all_52_5 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (563), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2111)   ~ (all_52_7 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | SIMP: (2111) implies:
% 193.82/31.24  | | | | | | | | | | | | | |   (2112)   ~ (all_52_7 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (566), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2113)   ~ (all_52_27 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | SIMP: (2113) implies:
% 193.82/31.24  | | | | | | | | | | | | | |   (2114)   ~ (all_52_27 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (551), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2115)   ~ (all_6_2 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | SIMP: (2115) implies:
% 193.82/31.24  | | | | | | | | | | | | | |   (2116)   ~ (all_6_2 = all_4_0)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (564), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2117)   ~ (all_4_0 = all_4_2)
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | REDUCE: (185), (2106) imply:
% 193.82/31.24  | | | | | | | | | | | | | |   (2118)  op(all_4_0, all_4_0) = all_52_2
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 193.82/31.24  | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | Case 1:
% 193.82/31.24  | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | |   (2119)   ~ (all_38_0 = e1)
% 193.82/31.24  | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | REDUCE: (766), (2119) imply:
% 193.82/31.24  | | | | | | | | | | | | | | |   (2120)   ~ (all_4_0 = e1)
% 193.82/31.24  | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.82/31.24  | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2121)  all_58_15 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2121) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2122)  all_14_2 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (573), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2123)   ~ (all_52_7 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (591), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2124)   ~ (all_52_15 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (603), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2125)   ~ (all_52_23 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (606), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2126)   ~ (all_52_25 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (608), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2127)   ~ (all_52_27 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (609), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2128)   ~ (all_52_29 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (613), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2129)  op(e0, e0) = all_52_30
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (63), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2130)  op(e0, e0) = all_14_1
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (61), (2122) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2131)  op(e0, e0) = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 193.82/31.24  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (2129), (2130)
% 193.82/31.24  | | | | | | | | | | | | | | | |              gives:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2132)  all_52_30 = all_14_1
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 193.82/31.24  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (2129), (2131)
% 193.82/31.24  | | | | | | | | | | | | | | | |              gives:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2133)  all_52_30 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | COMBINE_EQS: (2132), (2133) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2134)  all_14_1 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | SIMP: (2134) implies:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2135)  all_14_1 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (62), (2135) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2136)  op(e0, e0) = all_14_0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 193.82/31.24  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (2131), (2136) gives:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2137)  all_14_0 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (1899), (2137) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2138)   ~ (e3 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (779), (2137) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2139)   ~ (e2 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | REDUCE: (1905), (2137) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | |   (2140)   ~ (e1 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 193.82/31.24  | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | |   (2141)  all_56_4 = e3
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (1901), (2107), (2141) are inconsistent by
% 193.82/31.24  | | | | | | | | | | | | | | | | |            sub-proof #980.
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | |   (2142)   ~ (all_56_4 = e3)
% 193.82/31.24  | | | | | | | | | | | | | | | | |   (2143)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.24  | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | |   (2144)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.24  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.24  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | BETA: splitting (2144) gives:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2145)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | ALPHA: (2145) implies:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2146)  all_52_6 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2147)  all_52_4 = e1
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2148)  all_52_0 = e3
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REDUCE: (184), (2147) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2149)  op(all_52_5, all_52_5) = e1
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (2146) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2150)  op(all_52_7, all_52_7) = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REDUCE: (610), (2148) imply:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2151)  op(all_6_2, all_6_2) = e3
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (43), (51), (162), (167), (169), (172), (173),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (174), (273), (277), (278), (280), (282), (304),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (312), (326), (328),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (330), (332), (351), (367), (372), (388), (405),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (427), (431), (523), (539), (544), (545), (547),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (555), (561), (567), (569), (570), (574), (604),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (605), (607), (611), (721), (775), (1901), (1903),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2101), (2104), (2107), (2108), (2110), (2112),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2114), (2116), (2117), (2120), (2121), (2123),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2126), (2127), (2128), (2143), (2149), (2150),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2151), (function-axioms) are inconsistent by
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            sub-proof #638.
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2152)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (38), (41), (43), (51), (53),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (178), (179), (180), (182), (272), (273), (277),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (284), (305),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (306), (309), (313), (314), (317), (322), (324),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (325), (327), (333), (346), (351), (366), (367),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (411),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (415), (427), (431), (515), (539), (542), (543),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (564), (567), (568), (571), (572), (574), (575),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (588), (589), (595), (604), (605), (611), (612),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (680), (772), (778), (1892), (1903), (2121),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2123), (2124), (2126), (2131), (2152),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            #637.
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | |   (2153)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.24  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.24  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | BETA: splitting (2153) gives:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2154)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (42), (43),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (51), (158), (162), (167), (169), (172), (173),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (180), (182), (183),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (282), (283), (284), (304), (307), (308), (317),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (319), (321), (323), (325), (326), (328), (330),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (415),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (417), (421), (427), (431), (523), (539), (542),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (570), (571), (572),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (574), (575), (576), (578), (580), (584), (586),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (595), (597), (598),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (600), (604), (605), (607), (610), (611), (612),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (721), (775), (778), (1901), (1903), (2101),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2104), (2107), (2108), (2112), (2116), (2117),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2120), (2121), (2123), (2124), (2125), (2126),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2128), (2131), (2143), (2154), (function-axioms)
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #942.
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |   (2155)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (309), (321), (332),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (405), (427), (523), (539),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (544), (545), (548), (561), (574), (584), (586),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (605), (607), (610), (611), (721), (1901), (2101),
% 193.82/31.24  | | | | | | | | | | | | | | | | | | |            (2104), (2107), (2108), (2116), (2117), (2120),
% 193.82/31.25  | | | | | | | | | | | | | | | | | | |            (2121), (2126), (2155), (function-axioms) are
% 193.82/31.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 193.82/31.25  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.25  | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | |   (2156)   ~ (all_58_15 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | | |   (2157)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.82/31.25  | | | | | | | | | | | | | | | |             e0)
% 193.82/31.25  | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (158), (162), (166),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (275), (276), (277), (279), (280), (281), (282),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (283), (284), (285), (304), (306), (307), (309),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (318), (319), (321), (323), (324), (325), (326),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (411), (415), (417), (421), (431), (523), (538),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (721),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (772), (773), (775), (778), (1901), (1903),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (2101), (2104), (2107), (2108), (2110), (2112),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (2116), (2117), (2118), (2120), (2156), (2157),
% 193.82/31.25  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.25  | | | | | | | | | | | | | | | |            #669.
% 193.82/31.25  | | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | Case 2:
% 193.82/31.25  | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | |   (2158)  all_38_0 = e1
% 193.82/31.25  | | | | | | | | | | | | | | |   (2159)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | COMBINE_EQS: (766), (2158) imply:
% 193.82/31.25  | | | | | | | | | | | | | | |   (2160)  all_4_0 = e1
% 193.82/31.25  | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 193.82/31.25  | | | | | | | | | | | | | | |            (2103), (2104), (2117), (2159), (2160),
% 193.82/31.25  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.25  | | | | | | | | | | | | | | |            #927.
% 193.82/31.25  | | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | Case 2:
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | |   (2161)  all_24_0 = e1
% 193.82/31.25  | | | | | | | | | | | |   (2162)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (41), (42),
% 193.82/31.25  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (109), (114),
% 193.82/31.25  | | | | | | | | | | | |            (124), (156), (157), (158), (159), (161), (162),
% 193.82/31.25  | | | | | | | | | | | |            (163), (166), (167), (168), (169), (172), (173),
% 193.82/31.25  | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 193.82/31.25  | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 193.82/31.25  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 193.82/31.25  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 193.82/31.25  | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 193.82/31.25  | | | | | | | | | | | |            (311), (313), (315), (316), (317), (319), (320),
% 193.82/31.25  | | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 193.82/31.25  | | | | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 193.82/31.25  | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 193.82/31.25  | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 193.82/31.25  | | | | | | | | | | | |            (417), (421), (427), (431), (491), (508), (525),
% 193.82/31.25  | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 193.82/31.25  | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 193.82/31.25  | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 193.82/31.25  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (570), (571),
% 193.82/31.25  | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 193.82/31.25  | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 193.82/31.25  | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 193.82/31.25  | | | | | | | | | | | |            (597), (598), (600), (602), (603), (604), (605),
% 193.82/31.25  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 193.82/31.25  | | | | | | | | | | | |            (613), (649), (663), (685), (686), (711), (765),
% 193.82/31.25  | | | | | | | | | | | |            (766), (772), (773), (775), (778), (779), (1899),
% 193.82/31.25  | | | | | | | | | | | |            (1901), (1903), (2161), (2162), (function-axioms)
% 193.82/31.25  | | | | | | | | | | | |            are inconsistent by sub-proof #836.
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | Case 2:
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | |   (2163)  all_22_1 = e2
% 193.82/31.25  | | | | | | | | | | |   (2164)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | COMBINE_EQS: (658), (2163) imply:
% 193.82/31.25  | | | | | | | | | | |   (2165)  all_6_1 = e2
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | SIMP: (2165) implies:
% 193.82/31.25  | | | | | | | | | | |   (2166)  all_6_1 = e2
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | REDUCE: (43), (2166) imply:
% 193.82/31.25  | | | | | | | | | | |   (2167)  op(all_6_2, e3) = e2
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | REDUCE: (42), (2166) imply:
% 193.82/31.25  | | | | | | | | | | |   (2168)  op(e3, e2) = all_6_0
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 193.82/31.25  | | | | | | | | | | |            (53), (61), (62), (63), (89), (94), (158), (161),
% 193.82/31.25  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 193.82/31.25  | | | | | | | | | | |            (174), (175), (177), (178), (180), (182), (183),
% 193.82/31.25  | | | | | | | | | | |            (184), (185), (187), (270), (271), (273), (274),
% 193.82/31.25  | | | | | | | | | | |            (275), (277), (278), (280), (281), (282), (283),
% 193.82/31.25  | | | | | | | | | | |            (284), (285), (303), (304), (306), (307), (308),
% 193.82/31.25  | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 193.82/31.25  | | | | | | | | | | |            (321), (324), (325), (326), (327), (328), (329),
% 193.82/31.25  | | | | | | | | | | |            (331), (332), (333), (343), (351), (352), (361),
% 193.82/31.25  | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 193.82/31.25  | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (512),
% 193.82/31.25  | | | | | | | | | | |            (522), (538), (539), (540), (541), (542), (543),
% 193.82/31.25  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 193.82/31.25  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 193.82/31.25  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 193.82/31.25  | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 193.82/31.25  | | | | | | | | | | |            (582), (584), (586), (588), (589), (590), (591),
% 193.82/31.25  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 193.82/31.25  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 193.82/31.25  | | | | | | | | | | |            (608), (609), (610), (612), (613), (676), (711),
% 193.82/31.25  | | | | | | | | | | |            (739), (773), (775), (779), (1895), (1897),
% 193.82/31.25  | | | | | | | | | | |            (1899), (2164), (2167), (2168), (function-axioms)
% 193.82/31.25  | | | | | | | | | | |            are inconsistent by sub-proof #628.
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | End of split
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | Case 2:
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | |   (2169)  all_20_0 = e3
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | COMBINE_EQS: (758), (2169) imply:
% 193.82/31.25  | | | | | | | | | |   (2170)  all_4_0 = e3
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | SIMP: (2170) implies:
% 193.82/31.25  | | | | | | | | | |   (2171)  all_4_0 = e3
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | REDUCE: (37), (2171) imply:
% 193.82/31.25  | | | | | | | | | |   (2172)  op(e2, all_4_1) = e3
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | BETA: splitting (84) gives:
% 193.82/31.25  | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | Case 1:
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | |   (2173)   ~ (all_22_1 = e2)
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | REDUCE: (658), (2173) imply:
% 193.82/31.25  | | | | | | | | | | |   (2174)   ~ (all_6_1 = e2)
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | BETA: splitting (94) gives:
% 193.82/31.25  | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | Case 1:
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | |   (2175)   ~ (all_26_0 = e2)
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | REDUCE: (1895), (2175) imply:
% 193.82/31.25  | | | | | | | | | | | |   (2176)  $false
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | CLOSE: (2176) is inconsistent.
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | Case 2:
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | |   (2177)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | BETA: splitting (89) gives:
% 193.82/31.25  | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | Case 1:
% 193.82/31.25  | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | |   (2178)   ~ (all_24_0 = e1)
% 193.82/31.25  | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | REDUCE: (711), (2178) imply:
% 193.82/31.25  | | | | | | | | | | | | |   (2179)   ~ (all_14_0 = e1)
% 193.82/31.25  | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.82/31.25  | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | Case 1:
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | |   (2180)  all_58_15 = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | COMBINE_EQS: (541), (2180) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2181)  all_14_2 = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (573), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2182)   ~ (all_52_7 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (591), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2183)   ~ (all_52_15 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (603), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2184)   ~ (all_52_23 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (606), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2185)   ~ (all_52_25 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (608), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2186)   ~ (all_52_27 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (609), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2187)   ~ (all_52_29 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (613), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2188)  op(e0, e0) = all_52_30
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (63), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2189)  op(e0, e0) = all_14_1
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (61), (2181) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2190)  op(e0, e0) = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 193.82/31.25  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (2188), (2189)
% 193.82/31.25  | | | | | | | | | | | | | |              gives:
% 193.82/31.25  | | | | | | | | | | | | | |   (2191)  all_52_30 = all_14_1
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 193.82/31.25  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (2188), (2190)
% 193.82/31.25  | | | | | | | | | | | | | |              gives:
% 193.82/31.25  | | | | | | | | | | | | | |   (2192)  all_52_30 = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | COMBINE_EQS: (2191), (2192) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2193)  all_14_1 = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | SIMP: (2193) implies:
% 193.82/31.25  | | | | | | | | | | | | | |   (2194)  all_14_1 = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (62), (2194) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2195)  op(e0, e0) = all_14_0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 193.82/31.25  | | | | | | | | | | | | | |              e0, e0, simplifying with (2190), (2195) gives:
% 193.82/31.25  | | | | | | | | | | | | | |   (2196)  all_14_0 = e0
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (1899), (2196) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2197)   ~ (e3 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (779), (2196) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2198)   ~ (e2 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | REDUCE: (2179), (2196) imply:
% 193.82/31.25  | | | | | | | | | | | | | |   (2199)   ~ (e1 = e0)
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.25  | | | | | | | | | | | | | | 
% 193.82/31.25  | | | | | | | | | | | | | | Case 1:
% 193.82/31.25  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | |   (2200)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.26  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.26  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | BETA: splitting (2200) gives:
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2201)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.26  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | ALPHA: (2201) implies:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2202)  all_52_6 = e0
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2203)  all_52_4 = e1
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2204)  all_52_2 = e2
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2205)  all_52_0 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (185), (2204) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2206)  op(all_52_3, all_52_3) = e2
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (184), (2203) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2207)  op(all_52_5, all_52_5) = e1
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (183), (2202) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2208)  op(all_52_7, all_52_7) = e0
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (610), (2205) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2209)  op(all_6_2, all_6_2) = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (51), (53), (61), (156), (157), (161), (166),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (179), (272), (273), (277), (304), (305), (306),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (321), (332), (346), (351), (367), (387), (405),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (431), (515), (542), (543), (547), (555), (564),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (572), (573), (680),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (772), (1892), (1897), (2172), (2180), (2182),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (2183), (2206), (2207), (2208), (2209),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.26  | | | | | | | | | | | | | | | |            #626.
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2210)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.26  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (38), (41), (43), (51), (53),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (178), (179), (180), (182), (272), (273), (277),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (284), (305),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (306), (309), (313), (314), (317), (322), (324),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (325), (327), (333), (346), (351), (366), (367),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (411),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (415), (427), (431), (515), (539), (542), (543),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (564), (567), (568), (571), (572), (574), (575),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (588), (589), (595), (604), (605), (611), (612),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (680), (772), (778), (1892), (2174), (2180),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (2182), (2183), (2185), (2190), (2210),
% 193.82/31.26  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.26  | | | | | | | | | | | | | | | |            #637.
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | End of split
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | Case 2:
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | |   (2211)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.26  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.26  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.82/31.26  | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (157), (158), (162),
% 193.82/31.26  | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 193.82/31.26  | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 193.82/31.26  | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (278), (279),
% 193.82/31.26  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (304), (305),
% 193.82/31.26  | | | | | | | | | | | | | | |            (306), (307), (308), (309), (313), (317), (318),
% 193.82/31.26  | | | | | | | | | | | | | | |            (321), (322), (325), (326), (330), (331), (332),
% 193.82/31.26  | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 193.82/31.26  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 193.82/31.26  | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (539), (542),
% 193.82/31.26  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.82/31.26  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 193.82/31.26  | | | | | | | | | | | | | | |            (564), (565), (567), (568), (569), (570), (571),
% 193.82/31.26  | | | | | | | | | | | | | | |            (572), (576), (577), (578), (580), (582), (584),
% 193.82/31.26  | | | | | | | | | | | | | | |            (587), (588), (589), (590), (592), (593), (594),
% 193.82/31.26  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (604),
% 193.82/31.26  | | | | | | | | | | | | | | |            (605), (608), (610), (611), (612), (773), (775),
% 193.82/31.26  | | | | | | | | | | | | | | |            (778), (2172), (2174), (2180), (2182), (2183),
% 193.82/31.26  | | | | | | | | | | | | | | |            (2184), (2185), (2186), (2187), (2190), (2211),
% 193.82/31.26  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.26  | | | | | | | | | | | | | | |            #763.
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | End of split
% 193.82/31.26  | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | Case 2:
% 193.82/31.26  | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | |   (2212)   ~ (all_58_15 = e0)
% 193.82/31.26  | | | | | | | | | | | | | |   (2213)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.82/31.26  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.82/31.26  | | | | | | | | | | | | | |             e0)
% 193.82/31.26  | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | ALPHA: (2213) implies:
% 193.82/31.26  | | | | | | | | | | | | | |   (2214)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.82/31.26  | | | | | | | | | | | | | |   (2215)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.82/31.26  | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | REDUCE: (541), (2212) imply:
% 193.82/31.26  | | | | | | | | | | | | | |   (2216)   ~ (all_14_2 = e0)
% 193.82/31.26  | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.26  | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | Case 1:
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | |   (2217)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.26  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.26  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | BETA: splitting (2217) gives:
% 193.82/31.26  | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2218)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.26  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | ALPHA: (2218) implies:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2219)  all_52_6 = e0
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2220)  all_52_4 = e1
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2221)  all_52_2 = e2
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2222)  all_52_0 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (185), (2221) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2223)  op(all_52_3, all_52_3) = e2
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (184), (2220) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2224)  op(all_52_5, all_52_5) = e1
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (183), (2219) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2225)  op(all_52_7, all_52_7) = e0
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | REDUCE: (610), (2222) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | |   (2226)  op(all_6_2, all_6_2) = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 193.82/31.26  | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2227)  all_56_15 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2227) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2228)  all_14_2 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | SIMP: (2228) implies:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2229)  all_14_2 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (573), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2230)   ~ (all_52_7 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (591), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2231)   ~ (all_52_15 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (603), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2232)   ~ (all_52_23 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (606), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2233)   ~ (all_52_25 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (613), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2234)  op(e3, e3) = all_52_30
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (63), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2235)  op(e3, e0) = all_14_1
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (61), (2229) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2236)  op(e0, e0) = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (37), (38), (41), (42), (43), (51),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (61), (62), (157), (167), (169), (174), (177),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (180), (182), (271), (272), (273), (276), (280),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (305), (308),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (312), (315), (317), (321), (332), (343), (346),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (351), (366), (375), (387), (388), (393), (394),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (405), (415), (421), (431), (539), (540), (542),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (557), (559),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (564), (569), (571), (572), (573), (574), (575),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (587), (588),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (593), (594), (595), (600), (605), (611), (612),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (772), (775), (779), (1899), (2179), (2223),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (2224), (2225), (2226), (2230), (2231), (2232),
% 193.82/31.26  | | | | | | | | | | | | | | | | |            (2233), (2234), (2235), (2236), (function-axioms)
% 193.82/31.26  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1175.
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2237)   ~ (all_56_15 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2238)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | REDUCE: (538), (2237) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | |   (2239)   ~ (all_14_2 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 193.82/31.26  | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2240)  all_56_13 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (2240) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2241)  all_52_15 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2241) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2242)  all_58_13 = e3
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | REDUCE: (571), (2241) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2243)   ~ (all_52_7 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | REDUCE: (587), (2241) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2244)   ~ (all_52_13 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | REDUCE: (590), (2241) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2245)   ~ (all_52_23 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | SIMP: (2245) implies:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2246)   ~ (all_52_23 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | REDUCE: (591), (2241) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2247)   ~ (all_14_2 = e3)
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | REDUCE: (179), (2241) imply:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2248)  op(e3, e3) = all_52_14
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 193.82/31.26  | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (2248)
% 193.82/31.26  | | | | | | | | | | | | | | | | | |              gives:
% 193.82/31.26  | | | | | | | | | | | | | | | | | |   (2249)  all_52_14 = all_6_2
% 193.82/31.26  | | | | | | | | | | | | | | | | | | 
% 193.82/31.26  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 193.82/31.26  | | | | | | | | | | | | | | | | | |            (53), (61), (62), (63), (158), (159), (161),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (168), (172), (174), (177), (178), (180), (273),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (275), (276), (279), (281), (282), (283), (304),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (305), (306), (308), (309), (312), (313), (317),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (327), (329), (330),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (332), (351), (361), (366), (372), (375), (387),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (431), (512), (538), (541), (542), (544), (545),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (559), (561), (563), (564), (565), (566), (567),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (569), (573), (577), (578), (580), (586), (588),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (589), (595), (596), (598), (600), (602), (604),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (606), (607), (608), (676), (773), (775), (779),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (1897), (2177), (2214), (2215), (2216), (2223),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (2224), (2225), (2226), (2238), (2239), (2242),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (2243), (2244), (2246), (function-axioms) are
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | |   (2250)   ~ (all_56_13 = e3)
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | | REDUCE: (346), (2250) imply:
% 193.82/31.27  | | | | | | | | | | | | | | | | | |   (2251)   ~ (all_52_15 = e3)
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (53), (61), (62), (63), (158), (163), (169),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (172), (173), (175), (180), (182), (273), (274),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (276), (277), (281), (283), (284), (304), (305),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (306), (309), (311), (312), (313), (314), (319),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (320), (321), (325), (328), (331), (332), (333),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (421), (431),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (538), (541), (542), (543), (544), (545), (546),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (561),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (570),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (586), (588), (589), (590), (593), (594), (595),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (596), (600), (603), (604), (605), (606), (608),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (609), (612), (613), (772), (773), (2172), (2179),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (2215), (2216), (2223), (2224), (2225), (2226),
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            (2238), (2239), (2251), (function-axioms) are
% 193.82/31.27  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #742.
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | End of split
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | End of split
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | |   (2252)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.27  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (773), (775), (778), (2174), (2214), (2215),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (2216), (2252), (function-axioms) are inconsistent
% 193.82/31.27  | | | | | | | | | | | | | | | |            by sub-proof #731.
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | End of split
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | |   (2253)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.27  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.27  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | BETA: splitting (2253) gives:
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | |   (2254)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 193.82/31.27  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (2174),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (2214), (2215), (2254), (function-axioms) are
% 193.82/31.27  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | |   (2255)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 193.82/31.27  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (775), (778), (2174), (2214), (2216), (2255),
% 193.82/31.27  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.27  | | | | | | | | | | | | | | | |            #1008.
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | End of split
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | End of split
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | End of split
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | |   (2256)  all_24_0 = e1
% 193.82/31.27  | | | | | | | | | | | | |   (2257)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | COMBINE_EQS: (711), (2256) imply:
% 193.82/31.27  | | | | | | | | | | | | |   (2258)  all_14_0 = e1
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | SIMP: (2258) implies:
% 193.82/31.27  | | | | | | | | | | | | |   (2259)  all_14_0 = e1
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | COMBINE_EQS: (765), (2259) imply:
% 193.82/31.27  | | | | | | | | | | | | |   (2260)  all_34_0 = e1
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | REDUCE: (1899), (2259) imply:
% 193.82/31.27  | | | | | | | | | | | | |   (2261)   ~ (e3 = e1)
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | REDUCE: (779), (2259) imply:
% 193.82/31.27  | | | | | | | | | | | | |   (2262)   ~ (e2 = e1)
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | REDUCE: (62), (2259) imply:
% 193.82/31.27  | | | | | | | | | | | | |   (2263)  op(e0, all_14_1) = e1
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | BETA: splitting (114) gives:
% 193.82/31.27  | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | Case 1:
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | |   (2264)   ~ (all_34_0 = e1)
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | REDUCE: (2260), (2264) imply:
% 193.82/31.27  | | | | | | | | | | | | | |   (2265)  $false
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | CLOSE: (2265) is inconsistent.
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | |   (2266)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 193.82/31.27  | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | Case 1:
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | |   (2267)  all_58_15 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (2263), (2267),
% 193.82/31.27  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.27  | | | | | | | | | | | | | | |            #877.
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | Case 2:
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | |   (2268)   ~ (all_58_15 = e0)
% 193.82/31.27  | | | | | | | | | | | | | | |   (2269)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 193.82/31.27  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 193.82/31.27  | | | | | | | | | | | | | | |             e0)
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | ALPHA: (2269) implies:
% 193.82/31.27  | | | | | | | | | | | | | | |   (2270)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 193.82/31.27  | | | | | | | | | | | | | | |   (2271)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | REDUCE: (541), (2268) imply:
% 193.82/31.27  | | | | | | | | | | | | | | |   (2272)   ~ (all_14_2 = e0)
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 193.82/31.27  | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | Case 1:
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | |   (2273)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.27  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 193.82/31.27  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | BETA: splitting (2273) gives:
% 193.82/31.27  | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2274)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 193.82/31.27  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | ALPHA: (2274) implies:
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2275)  all_52_6 = e0
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2276)  all_52_4 = e1
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2277)  all_52_2 = e2
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2278)  all_52_0 = e3
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | REDUCE: (185), (2277) imply:
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2279)  op(all_52_3, all_52_3) = e2
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | REDUCE: (184), (2276) imply:
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2280)  op(all_52_5, all_52_5) = e1
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | REDUCE: (183), (2275) imply:
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2281)  op(all_52_7, all_52_7) = e0
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | REDUCE: (610), (2278) imply:
% 193.82/31.27  | | | | | | | | | | | | | | | | |   (2282)  op(all_6_2, all_6_2) = e3
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 193.82/31.27  | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | |   (2283)  all_56_15 = e3
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2283) imply:
% 193.82/31.27  | | | | | | | | | | | | | | | | | |   (2284)  all_14_2 = e3
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.27  | | | | | | | | | | | | | | | | | | SIMP: (2284) implies:
% 193.82/31.27  | | | | | | | | | | | | | | | | | |   (2285)  all_14_2 = e3
% 193.82/31.27  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (51), (61), (63), (156),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (167), (174), (175), (180), (282), (306), (307),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (311), (313), (319), (321), (332), (351), (366),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (405), (491), (544),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (553), (562), (564),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (569), (573), (580), (597), (600), (603), (604),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (605), (606), (609), (613), (685), (2263), (2266),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (2279), (2280), (2281), (2282), (2285),
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 193.82/31.28  | | | | | | | | | | | | | | | | | |            #713.
% 193.82/31.28  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.28  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | |   (2286)   ~ (all_56_15 = e3)
% 193.82/31.28  | | | | | | | | | | | | | | | | | |   (2287)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 193.82/31.28  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | REDUCE: (538), (2286) imply:
% 193.82/31.28  | | | | | | | | | | | | | | | | | |   (2288)   ~ (all_14_2 = e3)
% 193.82/31.28  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 193.82/31.28  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | Case 1:
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |   (2289)  all_56_13 = e3
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (53), (61), (62), (63), (158), (159), (161),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (168), (172), (174), (177), (178), (180), (273),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (275), (276), (279), (281), (282), (283), (304),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (305), (306), (308), (309), (312), (313), (317),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (327), (329), (330),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (332), (346), (351), (361), (366), (372), (375),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (417),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (421), (431), (512), (538), (541), (542), (543),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (553), (555), (559), (561), (563), (564), (565),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (566), (567), (569), (571), (573), (577), (578),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (580), (586), (587), (588), (589), (590), (591),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (604), (606),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (607), (608), (676), (773), (775), (779), (1897),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (2177), (2270), (2271), (2272), (2279), (2280),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (2281), (2282), (2287), (2289), (function-axioms)
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #619.
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |   (2290)   ~ (all_56_13 = e3)
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | REDUCE: (346), (2290) imply:
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |   (2291)   ~ (all_52_15 = e3)
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (38), (41), (42), (43), (51),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (53), (61), (63), (163), (169), (175), (178),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (182), (273), (276), (277), (280), (281), (283),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (284), (305), (306), (309), (311), (312), (313),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (314), (316), (319), (320), (321), (324), (325),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (328), (331), (332), (351), (366), (367), (372),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (375), (387), (393), (394), (405), (411), (415),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (421), (431), (508), (538), (539), (541), (542),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (572),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (573), (575), (576), (577), (578), (580), (582),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (586), (588), (589), (590), (592), (594), (595),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (600), (603), (605), (606), (608), (609), (612),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (613), (649), (772), (775), (2172), (2257),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (2270), (2271), (2279), (2280), (2281), (2282),
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            (2287), (2288), (2291), (function-axioms) are
% 193.82/31.28  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #698.
% 193.82/31.28  | | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | Case 2:
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2292)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 193.82/31.28  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | ALPHA: (2292) implies:
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2293)  all_52_14 = e0
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2294)  all_52_12 = e1
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2295)  all_52_10 = e2
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2296)  all_52_8 = e3
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | REDUCE: (182), (2296) imply:
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2297)  op(all_52_9, all_52_9) = e3
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | REDUCE: (180), (2294) imply:
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2298)  op(all_52_13, all_52_13) = e1
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | REDUCE: (179), (2293) imply:
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2299)  op(all_52_15, all_52_15) = e0
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | REDUCE: (611), (2295) imply:
% 193.82/31.28  | | | | | | | | | | | | | | | | |   (2300)  op(all_4_2, all_4_2) = e2
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (42), (43), (51), (61), (63), (158), (161), (162),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (163), (166), (167), (169), (172), (173), (174),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (175), (177), (178), (183), (184), (185), (270),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (284), (304), (306),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (308), (309), (313), (317), (319), (321), (323),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (325), (326), (328), (330), (331), (332), (333),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (417), (421), (427), (431), (538), (539), (541),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (577),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (613), (772), (773), (775), (778), (2174), (2263),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (2270), (2271), (2272), (2297), (2298), (2299),
% 193.82/31.28  | | | | | | | | | | | | | | | | |            (2300), (function-axioms) are inconsistent by
% 193.82/31.28  | | | | | | | | | | | | | | | | |            sub-proof #618.
% 193.82/31.28  | | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | Case 2:
% 193.82/31.28  | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | |   (2301)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 193.82/31.28  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 193.82/31.28  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 193.82/31.28  | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (156), (158), (162),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (275),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (315), (316), (317), (319), (321), (323), (324),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (325), (327), (328), (329), (330), (331), (332),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (431), (491),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (565), (566), (567), (569), (570), (571), (572),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (685),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (773), (775), (778), (2174), (2263), (2266),
% 193.82/31.28  | | | | | | | | | | | | | | | |            (2270), (2271), (2272), (2301), (function-axioms)
% 193.82/31.28  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #838.
% 193.82/31.28  | | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | End of split
% 193.82/31.28  | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | Case 2:
% 193.82/31.28  | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | |   (2302)  all_22_1 = e2
% 193.82/31.28  | | | | | | | | | | |   (2303)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 193.82/31.28  | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | COMBINE_EQS: (658), (2302) imply:
% 193.82/31.28  | | | | | | | | | | |   (2304)  all_6_1 = e2
% 193.82/31.28  | | | | | | | | | | | 
% 193.82/31.28  | | | | | | | | | | | SIMP: (2304) implies:
% 193.82/31.28  | | | | | | | | | | |   (2305)  all_6_1 = e2
% 193.82/31.28  | | | | | | | | | | | 
% 194.21/31.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 194.21/31.28  | | | | | | | | | | |            (53), (61), (62), (63), (89), (94), (158), (161),
% 194.21/31.28  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 194.21/31.28  | | | | | | | | | | |            (174), (175), (177), (178), (180), (182), (183),
% 194.21/31.28  | | | | | | | | | | |            (184), (185), (187), (270), (271), (273), (274),
% 194.21/31.28  | | | | | | | | | | |            (275), (277), (278), (280), (281), (282), (283),
% 194.21/31.28  | | | | | | | | | | |            (284), (285), (303), (304), (306), (307), (308),
% 194.21/31.28  | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 194.21/31.28  | | | | | | | | | | |            (321), (324), (325), (326), (327), (328), (329),
% 194.21/31.28  | | | | | | | | | | |            (331), (332), (333), (343), (351), (352), (361),
% 194.21/31.28  | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 194.21/31.28  | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (512),
% 194.21/31.28  | | | | | | | | | | |            (522), (538), (539), (540), (541), (542), (543),
% 194.21/31.28  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 194.21/31.28  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 194.21/31.28  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 194.21/31.28  | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 194.21/31.28  | | | | | | | | | | |            (582), (584), (586), (588), (589), (590), (591),
% 194.21/31.28  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 194.21/31.28  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 194.21/31.28  | | | | | | | | | | |            (608), (609), (610), (612), (613), (676), (711),
% 194.21/31.28  | | | | | | | | | | |            (739), (773), (775), (778), (779), (1895), (1897),
% 194.21/31.28  | | | | | | | | | | |            (1899), (2303), (2305), (function-axioms) are
% 194.21/31.28  | | | | | | | | | | |            inconsistent by sub-proof #617.
% 194.21/31.28  | | | | | | | | | | | 
% 194.21/31.28  | | | | | | | | | | End of split
% 194.21/31.28  | | | | | | | | | | 
% 194.21/31.28  | | | | | | | | | End of split
% 194.21/31.28  | | | | | | | | | 
% 194.21/31.28  | | | | | | | | Case 2:
% 194.21/31.28  | | | | | | | | | 
% 194.21/31.28  | | | | | | | | |   (2306)  all_18_0 = e3
% 194.21/31.28  | | | | | | | | | 
% 194.21/31.28  | | | | | | | | | COMBINE_EQS: (761), (2306) imply:
% 194.21/31.29  | | | | | | | | |   (2307)  all_14_0 = e3
% 194.21/31.29  | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | SIMP: (2307) implies:
% 194.21/31.29  | | | | | | | | |   (2308)  all_14_0 = e3
% 194.21/31.29  | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | REDUCE: (62), (2308) imply:
% 194.21/31.29  | | | | | | | | |   (2309)  op(e0, all_14_1) = e3
% 194.21/31.29  | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | BETA: splitting (84) gives:
% 194.21/31.29  | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | Case 1:
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | |   (2310)   ~ (all_22_1 = e2)
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | REDUCE: (658), (2310) imply:
% 194.21/31.29  | | | | | | | | | |   (2311)   ~ (all_6_1 = e2)
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | BETA: splitting (94) gives:
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | Case 1:
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | |   (2312)   ~ (all_26_0 = e2)
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | REDUCE: (1895), (2312) imply:
% 194.21/31.29  | | | | | | | | | | |   (2313)  $false
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | CLOSE: (2313) is inconsistent.
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | Case 2:
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | |   (2314)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | BETA: splitting (303) gives:
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | Case 1:
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | |   (2315)  all_58_15 = e0
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (2309), (2315),
% 194.21/31.29  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.21/31.29  | | | | | | | | | | | |            #678.
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | Case 2:
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | |   (2316)   ~ (all_58_15 = e0)
% 194.21/31.29  | | | | | | | | | | | |   (2317)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.21/31.29  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.21/31.29  | | | | | | | | | | | |             e0)
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | ALPHA: (2317) implies:
% 194.21/31.29  | | | | | | | | | | | |   (2318)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.21/31.29  | | | | | | | | | | | |   (2319)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | REDUCE: (541), (2316) imply:
% 194.21/31.29  | | | | | | | | | | | |   (2320)   ~ (all_14_2 = e0)
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | Case 1:
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | |   (2321)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.21/31.29  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.21/31.29  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | BETA: splitting (2321) gives:
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | Case 1:
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | |   (2322)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.21/31.29  | | | | | | | | | | | | | |           all_52_6 = e0
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | ALPHA: (2322) implies:
% 194.21/31.29  | | | | | | | | | | | | | |   (2323)  all_52_6 = e0
% 194.21/31.29  | | | | | | | | | | | | | |   (2324)  all_52_4 = e1
% 194.21/31.29  | | | | | | | | | | | | | |   (2325)  all_52_2 = e2
% 194.21/31.29  | | | | | | | | | | | | | |   (2326)  all_52_0 = e3
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REDUCE: (185), (2325) imply:
% 194.21/31.29  | | | | | | | | | | | | | |   (2327)  op(all_52_3, all_52_3) = e2
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REDUCE: (184), (2324) imply:
% 194.21/31.29  | | | | | | | | | | | | | |   (2328)  op(all_52_5, all_52_5) = e1
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REDUCE: (183), (2323) imply:
% 194.21/31.29  | | | | | | | | | | | | | |   (2329)  op(all_52_7, all_52_7) = e0
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REDUCE: (610), (2326) imply:
% 194.21/31.29  | | | | | | | | | | | | | |   (2330)  op(all_6_2, all_6_2) = e3
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (42), (43),
% 194.21/31.29  | | | | | | | | | | | | | |            (51), (53), (61), (62), (63), (156), (158), (159),
% 194.21/31.29  | | | | | | | | | | | | | |            (161), (168), (172), (174), (177), (178), (180),
% 194.21/31.29  | | | | | | | | | | | | | |            (270), (272), (273), (275), (276), (277), (279),
% 194.21/31.29  | | | | | | | | | | | | | |            (281), (282), (283), (304), (305), (306), (308),
% 194.21/31.29  | | | | | | | | | | | | | |            (309), (310), (312), (313), (317), (319), (320),
% 194.21/31.29  | | | | | | | | | | | | | |            (321), (323), (327), (328), (329), (330), (332),
% 194.21/31.29  | | | | | | | | | | | | | |            (333), (346), (351), (361), (366), (367), (372),
% 194.21/31.29  | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 194.21/31.29  | | | | | | | | | | | | | |            (417), (421), (431), (512), (515), (538), (541),
% 194.21/31.29  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.21/31.29  | | | | | | | | | | | | | |            (549), (551), (553), (555), (559), (561), (562),
% 194.21/31.29  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 194.21/31.29  | | | | | | | | | | | | | |            (571), (572), (573), (577), (578), (580), (582),
% 194.21/31.29  | | | | | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (595),
% 194.21/31.29  | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (604), (606),
% 194.21/31.29  | | | | | | | | | | | | | |            (607), (608), (613), (676), (680), (773), (775),
% 194.21/31.29  | | | | | | | | | | | | | |            (779), (1892), (1897), (2314), (2318), (2319),
% 194.21/31.29  | | | | | | | | | | | | | |            (2320), (2327), (2328), (2329), (2330),
% 194.21/31.29  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.21/31.29  | | | | | | | | | | | | | |            #614.
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | Case 2:
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | |   (2331)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.21/31.29  | | | | | | | | | | | | | |           all_52_14 = e0
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 194.21/31.29  | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 194.21/31.29  | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 194.21/31.29  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 194.21/31.29  | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 194.21/31.29  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 194.21/31.29  | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 194.21/31.29  | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 194.21/31.29  | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 194.21/31.29  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.21/31.29  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.21/31.29  | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 194.21/31.29  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.21/31.29  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 194.21/31.29  | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 194.21/31.29  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 194.21/31.29  | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 194.21/31.29  | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 194.21/31.29  | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 194.21/31.29  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 194.21/31.29  | | | | | | | | | | | | | |            (773), (775), (778), (2311), (2318), (2319),
% 194.21/31.29  | | | | | | | | | | | | | |            (2320), (2331), (function-axioms) are inconsistent
% 194.21/31.29  | | | | | | | | | | | | | |            by sub-proof #731.
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | End of split
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | Case 2:
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | |   (2332)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.21/31.29  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.21/31.29  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | BETA: splitting (2332) gives:
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | Case 1:
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | |   (2333)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.21/31.29  | | | | | | | | | | | | | |           all_52_22 = e0
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.21/31.29  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.21/31.29  | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.21/31.29  | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.21/31.29  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.21/31.29  | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.21/31.29  | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.21/31.29  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.21/31.29  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.21/31.29  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.21/31.29  | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.21/31.29  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.21/31.29  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.21/31.29  | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.21/31.29  | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.21/31.29  | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.21/31.29  | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.21/31.29  | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.21/31.29  | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (2311),
% 194.21/31.29  | | | | | | | | | | | | | |            (2318), (2319), (2333), (function-axioms) are
% 194.21/31.29  | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | Case 2:
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | |   (2334)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.21/31.29  | | | | | | | | | | | | | |           all_52_30 = e0
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.21/31.29  | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.21/31.29  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.21/31.29  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.21/31.29  | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.21/31.29  | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.21/31.29  | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.21/31.29  | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.21/31.29  | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.21/31.29  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.21/31.29  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.21/31.29  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.21/31.29  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.21/31.29  | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.21/31.29  | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.21/31.29  | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.21/31.29  | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.21/31.29  | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.21/31.29  | | | | | | | | | | | | | |            (775), (778), (2311), (2318), (2320), (2334),
% 194.21/31.29  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.21/31.29  | | | | | | | | | | | | | |            #1008.
% 194.21/31.29  | | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | | End of split
% 194.21/31.29  | | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | | End of split
% 194.21/31.29  | | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | | End of split
% 194.21/31.29  | | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | | End of split
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | Case 2:
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.29  | | | | | | | | | |   (2335)  all_22_1 = e2
% 194.21/31.29  | | | | | | | | | |   (2336)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 194.21/31.29  | | | | | | | | | | 
% 194.21/31.30  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 194.21/31.30  | | | | | | | | | |            (53), (61), (63), (94), (158), (161), (162),
% 194.21/31.30  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 194.21/31.30  | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 194.21/31.30  | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 194.21/31.30  | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 194.21/31.30  | | | | | | | | | |            (303), (304), (306), (307), (308), (309), (311),
% 194.21/31.30  | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 194.21/31.30  | | | | | | | | | |            (325), (326), (327), (328), (329), (331), (332),
% 194.21/31.30  | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 194.21/31.30  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 194.21/31.30  | | | | | | | | | |            (411), (415), (431), (512), (522), (538), (539),
% 194.21/31.30  | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 194.21/31.30  | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 194.21/31.30  | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 194.21/31.30  | | | | | | | | | |            (567), (568), (569), (570), (572), (573), (574),
% 194.21/31.30  | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 194.21/31.30  | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 194.21/31.30  | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 194.21/31.30  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 194.21/31.30  | | | | | | | | | |            (612), (613), (658), (676), (739), (773), (775),
% 194.21/31.30  | | | | | | | | | |            (778), (1895), (1897), (2309), (2335), (2336),
% 194.21/31.30  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.21/31.30  | | | | | | | | | |            #613.
% 194.21/31.30  | | | | | | | | | | 
% 194.21/31.30  | | | | | | | | | End of split
% 194.21/31.30  | | | | | | | | | 
% 194.21/31.30  | | | | | | | | End of split
% 194.21/31.30  | | | | | | | | 
% 194.21/31.30  | | | | | | | End of split
% 194.21/31.30  | | | | | | | 
% 194.21/31.30  | | | | | | Case 2:
% 194.21/31.30  | | | | | | | 
% 194.21/31.30  | | | | | | |   (2337)  all_14_0 = e2
% 194.21/31.30  | | | | | | |   (2338)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 194.26/31.30  | | | | | | | 
% 194.26/31.30  | | | | | | | COMBINE_EQS: (771), (2337) imply:
% 194.26/31.30  | | | | | | |   (2339)  all_50_0 = e2
% 194.26/31.30  | | | | | | | 
% 194.26/31.30  | | | | | | | REDUCE: (62), (2337) imply:
% 194.26/31.30  | | | | | | |   (2340)  op(e0, all_14_1) = e2
% 194.26/31.30  | | | | | | | 
% 194.26/31.30  | | | | | | | BETA: splitting (69) gives:
% 194.26/31.30  | | | | | | | 
% 194.26/31.30  | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | 
% 194.26/31.30  | | | | | | | |   (2341)   ~ (all_16_0 = e2)
% 194.26/31.30  | | | | | | | | 
% 194.26/31.30  | | | | | | | | REDUCE: (760), (2341) imply:
% 194.26/31.30  | | | | | | | |   (2342)   ~ (all_10_0 = e2)
% 194.26/31.30  | | | | | | | | 
% 194.26/31.30  | | | | | | | | BETA: splitting (79) gives:
% 194.26/31.30  | | | | | | | | 
% 194.26/31.30  | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | 
% 194.26/31.30  | | | | | | | | |   (2343)   ~ (all_20_0 = e3)
% 194.26/31.30  | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | REDUCE: (758), (2343) imply:
% 194.26/31.30  | | | | | | | | |   (2344)   ~ (all_4_0 = e3)
% 194.26/31.30  | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | BETA: splitting (84) gives:
% 194.26/31.30  | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | |   (2345)   ~ (all_22_1 = e2)
% 194.26/31.30  | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | REDUCE: (658), (2345) imply:
% 194.26/31.30  | | | | | | | | | |   (2346)   ~ (all_6_1 = e2)
% 194.26/31.30  | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | BETA: splitting (104) gives:
% 194.26/31.30  | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | |   (2347)   ~ (all_30_1 = e3)
% 194.26/31.30  | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | REDUCE: (670), (2347) imply:
% 194.26/31.30  | | | | | | | | | | |   (2348)   ~ (all_10_1 = e3)
% 194.26/31.30  | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | BETA: splitting (109) gives:
% 194.26/31.30  | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | |   (2349)   ~ (all_32_1 = e3)
% 194.26/31.30  | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | REDUCE: (663), (2349) imply:
% 194.26/31.30  | | | | | | | | | | | |   (2350)   ~ (all_4_1 = e3)
% 194.26/31.30  | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | BETA: splitting (129) gives:
% 194.26/31.30  | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | |   (2351)   ~ (all_40_1 = e2)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (687), (2351) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2352)   ~ (all_10_1 = e2)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | |   (2353)  all_58_15 = e0
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (2353),
% 194.26/31.30  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.26/31.30  | | | | | | | | | | | | | |            #612.
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | Case 2:
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | |   (2354)   ~ (all_58_15 = e0)
% 194.26/31.30  | | | | | | | | | | | | | |   (2355)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.26/31.30  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.26/31.30  | | | | | | | | | | | | | |             e0)
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | ALPHA: (2355) implies:
% 194.26/31.30  | | | | | | | | | | | | | |   (2356)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.26/31.30  | | | | | | | | | | | | | |   (2357)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | REDUCE: (541), (2354) imply:
% 194.26/31.30  | | | | | | | | | | | | | |   (2358)   ~ (all_14_2 = e0)
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 194.26/31.30  | | | | | | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (63),
% 194.26/31.30  | | | | | | | | | | | | | |            (156), (157), (158), (159), (161), (162), (166),
% 194.26/31.30  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 194.26/31.30  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 194.26/31.30  | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 194.26/31.30  | | | | | | | | | | | | | |            (275), (276), (277), (278), (279), (280), (281),
% 194.26/31.30  | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (305), (306),
% 194.26/31.30  | | | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (314),
% 194.26/31.30  | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 194.26/31.30  | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 194.26/31.30  | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 194.26/31.30  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.26/31.30  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.26/31.30  | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 194.26/31.30  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.26/31.30  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 194.26/31.30  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 194.26/31.30  | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.26/31.30  | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 194.26/31.30  | | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 194.26/31.30  | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 194.26/31.30  | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 194.26/31.30  | | | | | | | | | | | | | |            (611), (612), (613), (772), (773), (775), (776),
% 194.26/31.30  | | | | | | | | | | | | | |            (778), (2342), (2344), (2346), (2348), (2350),
% 194.26/31.30  | | | | | | | | | | | | | |            (2352), (2356), (2357), (2358), (function-axioms)
% 194.26/31.30  | | | | | | | | | | | | | |            are inconsistent by sub-proof #680.
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | End of split
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | Case 2:
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | |   (2359)  all_40_1 = e2
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | COMBINE_EQS: (687), (2359) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2360)  all_10_1 = e2
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | SIMP: (2360) implies:
% 194.26/31.30  | | | | | | | | | | | | |   (2361)  all_10_1 = e2
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (2348), (2361) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2362)   ~ (e3 = e2)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (52), (2361) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2363)  op(e1, e2) = all_10_0
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 194.26/31.30  | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (2363)
% 194.26/31.30  | | | | | | | | | | | | |              gives:
% 194.26/31.30  | | | | | | | | | | | | |   (2364)  all_52_13 = all_10_0
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | COMBINE_EQS: (421), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2365)  all_56_9 = all_10_0
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | COMBINE_EQS: (366), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2366)  all_58_7 = all_10_0
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (575), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2367)   ~ (all_52_9 = all_10_0)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (587), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2368)   ~ (all_52_15 = all_10_0)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | SIMP: (2368) implies:
% 194.26/31.30  | | | | | | | | | | | | |   (2369)   ~ (all_52_15 = all_10_0)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (589), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2370)   ~ (all_52_29 = all_10_0)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | SIMP: (2370) implies:
% 194.26/31.30  | | | | | | | | | | | | |   (2371)   ~ (all_52_29 = all_10_0)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (588), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2372)   ~ (all_10_0 = all_10_2)
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | REDUCE: (180), (2364) imply:
% 194.26/31.30  | | | | | | | | | | | | |   (2373)  op(all_10_0, all_10_0) = all_52_12
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 194.26/31.30  | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | |   (2374)   ~ (all_42_0 = e1)
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | REDUCE: (768), (2374) imply:
% 194.26/31.30  | | | | | | | | | | | | | |   (2375)   ~ (all_4_0 = e1)
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 194.26/31.30  | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | |   (2376)   ~ (all_50_0 = e2)
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | REDUCE: (2339), (2376) imply:
% 194.26/31.30  | | | | | | | | | | | | | | |   (2377)  $false
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | CLOSE: (2377) is inconsistent.
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | Case 2:
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | |   (2378)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.26/31.30  | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | |   (2379)  all_58_15 = e0
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (2379),
% 194.26/31.30  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.26/31.30  | | | | | | | | | | | | | | | |            #612.
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | Case 2:
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | |   (2380)   ~ (all_58_15 = e0)
% 194.26/31.30  | | | | | | | | | | | | | | | |   (2381)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.26/31.30  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.26/31.30  | | | | | | | | | | | | | | | |             e0)
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | ALPHA: (2381) implies:
% 194.26/31.30  | | | | | | | | | | | | | | | |   (2382)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.26/31.30  | | | | | | | | | | | | | | | |   (2383)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | REDUCE: (541), (2380) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | |   (2384)   ~ (all_14_2 = e0)
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | |   (2385)  all_56_9 = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (776), (2365), (2385) are inconsistent by
% 194.26/31.30  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 194.26/31.30  | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.30  | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | |   (2386)   ~ (all_56_9 = e3)
% 194.26/31.30  | | | | | | | | | | | | | | | | |   (2387)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 194.26/31.30  | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | |   (2388)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.26/31.30  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.26/31.30  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | BETA: splitting (2388) gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2389)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | ALPHA: (2389) implies:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2390)  all_52_6 = e0
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2391)  all_52_4 = e1
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2392)  all_52_2 = e2
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2393)  all_52_0 = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | REDUCE: (185), (2392) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2394)  op(all_52_3, all_52_3) = e2
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | REDUCE: (184), (2391) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2395)  op(all_52_5, all_52_5) = e1
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (2390) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2396)  op(all_52_7, all_52_7) = e0
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | REDUCE: (610), (2393) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | |   (2397)  op(all_6_2, all_6_2) = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2398)  all_56_15 = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2398) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2399)  all_14_2 = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | SIMP: (2399) implies:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2400)  all_14_2 = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2401)  all_50_2 = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2402)   ~ (all_52_7 = e3)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2403)   ~ (all_52_15 = e3)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2404)   ~ (all_52_25 = e3)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (609), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2405)   ~ (all_52_29 = e3)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2406)  op(e3, e3) = all_52_30
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2407)  op(e3, e0) = all_14_1
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (2400) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | |   (2408)  op(e0, e0) = e3
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2378) gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2409)   ~ (all_50_1 = e1)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (690), (2409) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2410)   ~ (all_14_1 = e1)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (2407)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2411)  all_52_25 = all_14_1
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (2406)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2412)  all_52_30 = all_6_2
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (2411) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2413)  all_56_3 = all_14_1
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2411) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2414)  all_58_9 = all_14_1
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (2411) imply:
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | |   (2415)   ~ (all_52_9 = all_14_1)
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (2411) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | |   (2416)   ~ (all_52_27 = all_14_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | SIMP: (2416) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | |   (2417)   ~ (all_52_27 = all_14_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (2411) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | |   (2418)   ~ (all_52_29 = all_14_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | SIMP: (2418) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | |   (2419)   ~ (all_52_29 = all_14_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2404), (2411) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | |   (2420)   ~ (all_14_1 = e3)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (2411) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | |   (2421)  op(all_14_1, all_14_1) = all_52_24
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | |   (2422)  all_56_3 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2413), (2420), (2422) are inconsistent by
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1200.
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | |   (2423)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | |   (2424)  all_58_1 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2424) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | |   (2425)  all_52_9 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (557), (564), (569), (2394), (2395),
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | |            (2397), (2402), (2425), (function-axioms) are
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1195.
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | |   (2426)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2426) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2427)  all_58_3 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2427) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2428)  all_4_2 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (2428) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2429)   ~ (all_52_9 = e3)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (2428) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2430)   ~ (all_52_27 = e3)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (2428) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2431)  op(e3, e2) = all_4_1
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |              all_4_1, e2, e3, simplifying with (169), (2431)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2432)  all_52_9 = all_4_1
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (2432) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2433)  all_56_1 = all_4_1
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2432) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2434)  all_58_1 = all_4_1
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (2432) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2435)   ~ (all_52_15 = all_4_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2435) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2436)   ~ (all_52_15 = all_4_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2415), (2432) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2437)   ~ (all_14_1 = all_4_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2437) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2438)   ~ (all_14_1 = all_4_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2367), (2432) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2439)   ~ (all_10_0 = all_4_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2439) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2440)   ~ (all_10_0 = all_4_1)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (2441)  all_56_1 = e3
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2350), (2433), (2441) are inconsistent by
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1167.
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (2442)   ~ (all_56_1 = e3)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (2443)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2444)  all_58_1 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2434), (2444) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2445)  all_4_1 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2438), (2445) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2446)   ~ (all_14_1 = e2)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2340), (2408), (2410), (2413), (2421),
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2423), (2446), (function-axioms) are inconsistent
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #611.
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2447)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2447) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2448)  all_58_3 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2427), (2448) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2449)  e3 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2449) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2450)  $false
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2450) is inconsistent.
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2451)  all_58_7 = e2 | all_58_13 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2451) gives:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2452)  all_58_7 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2366), (2452) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2453)  all_10_0 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2342), (2453) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2454)  $false
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2454) is inconsistent.
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2455)  all_58_13 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2455) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2456)  all_52_15 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2456) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2457)  all_52_15 = e2
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2436), (2457) imply:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2458)   ~ (all_4_1 = e2)
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2458) implies:
% 194.26/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2459)   ~ (all_4_1 = e2)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2460)  all_58_1 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2434), (2460) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2461)  all_4_1 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (772), (2461) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2462)  $false
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2462) is inconsistent.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2463)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2463) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2464)  all_58_3 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2427), (2464) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2465)  e3 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2465) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2466)  $false
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2466) is inconsistent.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2467)  all_58_7 = e1 | all_58_13 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2467) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2468)  all_58_7 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2366), (2468) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2469)  all_10_0 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2371), (2469) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2470)   ~ (all_52_29 = e1)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2440), (2469) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2471)   ~ (all_4_1 = e1)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2443) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2472)  all_56_1 = e2
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2433), (2459), (2472) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1165.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2473)  all_56_1 = e1 | all_56_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2474)  all_58_9 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2410), (2414), (2474) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #610.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2475)   ~ (all_58_9 = e1)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2476)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2476) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2477)  all_58_10 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (2477) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2478)  all_52_27 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2478) implies:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2479)  all_52_27 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (2479) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2480)  op(e2, e0) = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2481)  all_56_1 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (772), (2433), (2481) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #688.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2482)  all_56_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2433), (2482) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2483)  all_4_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2483) implies:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2484)  all_4_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (2484) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2485)  op(e2, e0) = all_4_0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_4_0,
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (2480), (2485) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2486)  all_4_0 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2375), (2486) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2487)  $false
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2487) is inconsistent.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2488)   ~ (all_58_10 = e1)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2488) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2489)   ~ (all_52_27 = e1)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2490)  all_56_1 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (772), (2433), (2490) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #688.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2491)  all_56_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2433), (2491) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2492)  all_4_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2492) implies:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2493)  all_4_1 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2438), (2493) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2494)   ~ (all_14_1 = e0)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2423) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2495)  all_56_3 = e2
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2413), (2495) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2496)  all_14_1 = e2
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2496) implies:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2497)  all_14_1 = e2
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2497) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2498)   ~ (all_52_27 = e2)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2419), (2497) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2499)   ~ (all_52_29 = e2)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2500)  all_56_11 = e3
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (352), (2405), (2500) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1028.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2501)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2501) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2502)  all_56_11 = e2
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (352), (2499), (2502) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1024.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2503)  all_56_11 = e1 | all_56_11 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2504)  all_56_7 = e3
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (2430), (2504) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #609.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2505)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2503) gives:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2506)  all_56_11 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (352), (2470), (2506) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1023.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2507)  all_56_11 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (2507) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2508)  all_52_29 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2508) implies:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2509)  all_52_29 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (2509) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2510)   ~ (all_52_27 = e0)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (2489), (2498), (2505), (2510) are
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2511)  all_56_3 = e1 | all_56_3 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2410), (2413), (2494), (2511) are inconsistent by
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #806.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2512)  all_58_13 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2455), (2512) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2513)  e2 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2513) implies:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2514)  e2 = e1
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2514) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2515)  $false
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2515) is inconsistent.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | |   (2516)  all_58_7 = e3 | all_58_13 = e3
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (776), (2366), (2403), (2516) are
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #717.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | |   (2517)   ~ (all_50_2 = e3)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2401), (2517) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | |   (2518)  $false
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | CLOSE: (2518) is inconsistent.
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | |   (2519)   ~ (all_56_15 = e3)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | |   (2520)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (2519) imply:
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | |   (2521)   ~ (all_14_2 = e3)
% 194.32/31.31  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (51), (61), (157), (161), (169), (175), (180),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (182), (272), (273), (280), (281), (284), (304),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (305), (306), (319), (320), (321), (324), (325),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (330), (332), (346), (351), (366), (387), (394),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (405), (411), (431), (538), (539), (541), (542),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (543), (547), (548), (549), (551), (555), (557),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (562), (563), (564), (569), (571), (572), (573),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (574), (576), (582), (590), (591), (600), (613),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (772), (2344), (2350), (2382), (2384), (2394),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (2395), (2396), (2397), (2520), (2521),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            #1145.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2522)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (38), (41), (43), (51), (158), (169), (179),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (182), (270), (271), (273), (284), (306), (325),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (327), (343), (351), (394), (405), (431), (538),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (541), (542), (543), (548), (549), (555), (557),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (571), (574), (582), (590), (591), (611), (772),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (776), (778), (2342), (2346), (2365), (2366),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (2367), (2369), (2372), (2373), (2387), (2522),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            #714.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2523)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.32/31.32  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.32/31.32  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | BETA: splitting (2523) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2524)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (2346),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (2382), (2383), (2524), (function-axioms) are
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2525)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (775), (778), (2346), (2382), (2384), (2525),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |            #1008.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | |   (2526)  all_42_0 = e1
% 194.32/31.32  | | | | | | | | | | | | | |   (2527)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | COMBINE_EQS: (768), (2526) imply:
% 194.32/31.32  | | | | | | | | | | | | | |   (2528)  all_4_0 = e1
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | SIMP: (2528) implies:
% 194.32/31.32  | | | | | | | | | | | | | |   (2529)  all_4_0 = e1
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | REDUCE: (2344), (2529) imply:
% 194.32/31.32  | | | | | | | | | | | | | |   (2530)   ~ (e3 = e1)
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | REDUCE: (37), (2529) imply:
% 194.32/31.32  | | | | | | | | | | | | | |   (2531)  op(e2, all_4_1) = e1
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.32/31.32  | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | |   (2532)  all_58_15 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (2532),
% 194.32/31.32  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | |            #612.
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | |   (2533)   ~ (all_58_15 = e0)
% 194.32/31.32  | | | | | | | | | | | | | | |   (2534)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.32/31.32  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.32/31.32  | | | | | | | | | | | | | | |             e0)
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | ALPHA: (2534) implies:
% 194.32/31.32  | | | | | | | | | | | | | | |   (2535)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.32/31.32  | | | | | | | | | | | | | | |   (2536)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | REDUCE: (541), (2533) imply:
% 194.32/31.32  | | | | | | | | | | | | | | |   (2537)   ~ (all_14_2 = e0)
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | |   (2538)  all_56_9 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | REF_CLOSE: (776), (2365), (2538) are inconsistent by
% 194.32/31.32  | | | | | | | | | | | | | | | |            sub-proof #1006.
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | |   (2539)   ~ (all_56_9 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | |   (2540)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | |   (2541)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.32  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.32/31.32  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.32/31.32  | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | BETA: splitting (2541) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2542)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.32  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | ALPHA: (2542) implies:
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2543)  all_52_6 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2544)  all_52_4 = e1
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2545)  all_52_2 = e2
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2546)  all_52_0 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | REDUCE: (185), (2545) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2547)  op(all_52_3, all_52_3) = e2
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | REDUCE: (184), (2544) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2548)  op(all_52_5, all_52_5) = e1
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | REDUCE: (183), (2543) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2549)  op(all_52_7, all_52_7) = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | REDUCE: (610), (2546) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | |   (2550)  op(all_6_2, all_6_2) = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2551)  all_56_15 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2551) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2552)  all_14_2 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | SIMP: (2552) implies:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2553)  all_14_2 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | REDUCE: (573), (2553) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2554)   ~ (all_52_7 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | REDUCE: (591), (2553) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2555)   ~ (all_52_15 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2556)  all_58_1 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2556) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2557)  all_52_9 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (405), (547), (557), (564), (569), (2547), (2548),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (2550), (2554), (2557), (function-axioms) are
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1195.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2558)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (169), (182), (284), (394),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (527), (543), (548), (574), (637), (772), (776),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (2366), (2527), (2531), (2555), (2558),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            #607.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2559)   ~ (all_56_15 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | REDUCE: (538), (2559) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | |   (2560)   ~ (all_14_2 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2561)  all_56_13 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (2561) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2562)  all_52_15 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (38), (51), (61), (157), (273),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (304), (305), (351), (431), (542), (543), (571),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (573), (600), (2350), (2535), (2549), (2562),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |            #1168.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2563)   ~ (all_56_13 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (2563) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | |   (2564)   ~ (all_52_15 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |   (2565)  all_58_12 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2565) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |   (2566)  all_52_7 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (555), (564), (569),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |            (573), (2547), (2548), (2549), (2550), (2566),
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |            #1361.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | |   (2567)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2567) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | |   (2568)  all_58_13 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (2564), (2568) are inconsistent by
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | |   (2569)  all_58_14 = e3 | all_58_15 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2569) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |   (2570)  all_58_14 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2570) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |   (2571)  all_52_23 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2571) implies:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |   (2572)  all_52_23 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (2572) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |   (2573)   ~ (all_52_7 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (2572) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |   (2574)  op(e3, e3) = all_52_22
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (2574)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | |   (2575)  all_52_22 = all_6_2
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | |   (2576)  all_56_12 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (2576) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | |   (2577)  all_52_7 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2573), (2577) imply:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | |   (2578)  $false
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2578) is inconsistent.
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | |   (2579)   ~ (all_56_12 = e3)
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | |   (2580)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (2581)  all_56_5 = e3
% 194.32/31.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (169), (182), (284), (325),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (394), (527), (539), (543), (548), (549),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (574), (580), (582), (637), (772), (2527), (2531),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (2581), (function-axioms) are inconsistent by
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #605.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (2582)   ~ (all_56_5 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (2582) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (2583)   ~ (all_4_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (51), (161),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (180), (281), (304), (305), (319), (320), (321),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (325), (330), (332), (351), (366), (387), (405),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (411), (431), (543), (547), (548), (549), (551),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (557), (562), (563), (564), (569), (582), (2350),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (2535), (2547), (2548), (2549), (2550), (2564),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (2570), (2573), (2580), (2583), (function-axioms)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1146.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2584)  all_58_15 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2584) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2585)  all_14_2 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2560), (2585) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2586)  $false
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2586) is inconsistent.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2587)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.32/31.33  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (38), (41), (43), (51), (158), (169), (179),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (182), (270), (271), (273), (284), (306), (325),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (327), (343), (351), (394), (405), (431), (538),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (541), (542), (543), (548), (549), (555), (557),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (571), (574), (582), (590), (591), (611), (772),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (776), (778), (2342), (2346), (2365), (2366),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (2367), (2369), (2372), (2373), (2540), (2587),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            #714.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.33  | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | |   (2588)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.32/31.33  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.32/31.33  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.32/31.33  | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | BETA: splitting (2588) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2589)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.32/31.33  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (2346),
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            (2535), (2536), (2589), (function-axioms) are
% 194.32/31.33  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2590)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.32/31.33  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | ALPHA: (2590) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2591)  all_52_30 = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2592)  all_52_28 = e1
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2593)  all_52_26 = e2
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2594)  all_52_24 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | REDUCE: (174), (2594) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2595)  op(all_52_25, all_52_25) = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | REDUCE: (173), (2593) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2596)  op(all_52_27, all_52_27) = e2
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | REDUCE: (172), (2592) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2597)  op(all_52_29, all_52_29) = e1
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | REDUCE: (613), (2591) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | |   (2598)  op(all_14_2, all_14_2) = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2599)  all_56_15 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2599) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2600)  all_14_2 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | REDUCE: (573), (2600) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2601)   ~ (all_52_7 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | REDUCE: (2598), (2600) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2602)  op(e3, e3) = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (158), (273), (431), (555), (778),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |            (2346), (2601), (2602), (function-axioms) are
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1342.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2603)   ~ (all_56_15 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2604)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | REDUCE: (538), (2603) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | |   (2605)   ~ (all_14_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2606)  all_56_13 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (2606) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2607)  all_52_15 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (2607) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2608)   ~ (all_52_7 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (2607) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2609)   ~ (all_52_9 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (2607) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2610)   ~ (all_52_13 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (2607) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2611)   ~ (all_14_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (2607) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2612)   ~ (all_4_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | SIMP: (2612) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2613)   ~ (all_4_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (2607) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2614)  op(e3, e3) = all_52_14
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (2614)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2615)  all_52_14 = all_6_2
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (61),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (178), (182), (184), (274), (282), (283), (284),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (307), (309), (313), (321), (323), (324), (325),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (332), (333), (351), (352), (366), (372), (375),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (415), (541),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (553), (557), (559), (561), (562), (563), (564),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (566), (569), (570), (578), (586), (592), (593),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (595), (596), (598), (604), (605), (608), (610),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (773), (775), (2595), (2596), (2597), (2605),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (2608), (2609), (2610), (2613), (2614),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |            #1034.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2616)   ~ (all_56_13 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (2616) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | |   (2617)   ~ (all_52_15 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2618)  all_58_12 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2618) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2619)  all_52_7 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | SIMP: (2619) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2620)  all_52_7 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2621)   ~ (all_52_3 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2622)   ~ (all_52_5 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2623)   ~ (all_52_23 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | SIMP: (2623) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2624)   ~ (all_52_23 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2625)   ~ (all_14_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2626)   ~ (all_6_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | SIMP: (2626) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2627)   ~ (all_6_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2628)  op(e3, e3) = all_52_6
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (2620) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2629)  op(e0, e3) = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (42), (43), (51), (53), (61), (162),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (166), (167), (168), (177), (180), (184), (185),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (271), (274), (277), (280), (281), (282), (283),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (284), (285), (307), (309), (311), (313), (316),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (319), (324), (325), (327), (328), (330), (333),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (343), (352), (366), (367), (372), (375), (387),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (538),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (557),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (559), (561), (562), (570), (574), (575), (578),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (582), (584), (590), (593), (594), (595), (596),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (609), (610), (773), (775), (778), (2346), (2535),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (2537), (2595), (2596), (2597), (2598), (2604),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (2605), (2618), (2621), (2622), (2624), (2627),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            (2628), (2629), (function-axioms) are inconsistent
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1014.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | |   (2630)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2630) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | |   (2631)  all_58_13 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (2617), (2631) are inconsistent by
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | |   (2632)  all_58_14 = e3 | all_58_15 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2632) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2633)  all_58_14 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2633) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2634)  all_52_23 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2634) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2635)  all_52_23 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (2635) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2636)   ~ (all_52_7 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (2635) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2637)   ~ (all_52_17 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (2635) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2638)   ~ (all_52_19 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (603), (2635) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2639)   ~ (all_14_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (2635) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2640)  op(e3, e3) = all_52_22
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (2640)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | |   (2641)  all_52_22 = all_6_2
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |   (2642)  all_56_5 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (169), (182), (284), (325),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |            (366), (394), (527), (539), (543), (548), (549),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |            (574), (580), (582), (637), (772), (2527), (2531),
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |            (2642), (function-axioms) are inconsistent by
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #605.
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |   (2643)   ~ (all_56_5 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (2643) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | |   (2644)   ~ (all_4_2 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (2645)  all_58_1 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2645) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (2646)  all_52_9 = e3
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (2646) imply:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (2647)   ~ (all_52_25 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2647) implies:
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (2648)   ~ (all_52_25 = e3)
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.33  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2646) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (2649)   ~ (all_6_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2649) implies:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (2650)   ~ (all_6_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (2646) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (2651)  op(e3, e3) = all_52_8
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (42), (43), (51), (61), (162), (167),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (185), (277), (282), (307), (309),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (321), (325), (332), (333), (351), (367), (372),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (541), (544),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (545), (547), (548), (549), (551), (553), (561),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (566), (569), (570), (578), (586), (593), (595),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (598), (604), (608), (609), (775), (2346), (2595),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (2596), (2597), (2605), (2636), (2648), (2650),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (2651), (function-axioms) are inconsistent by
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1010.
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (2652)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2652) gives:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2653)  all_58_3 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2653) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2654)  all_4_2 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2644), (2654) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2655)  $false
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2655) is inconsistent.
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2656)  all_58_7 = e3 | all_58_13 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (51), (61), (180), (282), (307), (309),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (321), (333), (366), (372), (375), (387), (388),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (393), (405), (543), (545), (548), (549), (551),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (561), (575), (580), (593), (595), (604), (608),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2595), (2596), (2617), (2637), (2638), (2656),
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1012.
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | |   (2657)  all_58_15 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2657) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | |   (2658)  all_14_2 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2605), (2658) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | |   (2659)  $false
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2659) is inconsistent.
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | |   (2660)  all_32_1 = e3
% 194.32/31.34  | | | | | | | | | | | |   (2661)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | COMBINE_EQS: (663), (2660) imply:
% 194.32/31.34  | | | | | | | | | | | |   (2662)  all_4_1 = e3
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 194.32/31.34  | | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (124), (158),
% 194.32/31.34  | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 194.32/31.34  | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 194.32/31.34  | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 194.32/31.34  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 194.32/31.34  | | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 194.32/31.34  | | | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (314),
% 194.32/31.34  | | | | | | | | | | | |            (315), (316), (317), (318), (319), (321), (323),
% 194.32/31.34  | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 194.32/31.34  | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 194.32/31.34  | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.32/31.34  | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.32/31.34  | | | | | | | | | | | |            (431), (523), (525), (538), (539), (540), (541),
% 194.32/31.34  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.34  | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.34  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 194.32/31.34  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 194.32/31.34  | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 194.32/31.34  | | | | | | | | | | | |            (587), (588), (590), (591), (592), (593), (594),
% 194.32/31.34  | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 194.32/31.34  | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 194.32/31.34  | | | | | | | | | | | |            (611), (612), (613), (686), (721), (766), (772),
% 194.32/31.34  | | | | | | | | | | | |            (773), (775), (778), (2340), (2344), (2346),
% 194.32/31.34  | | | | | | | | | | | |            (2661), (2662), (function-axioms) are inconsistent
% 194.32/31.34  | | | | | | | | | | | |            by sub-proof #604.
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | |   (2663)  all_30_1 = e3
% 194.32/31.34  | | | | | | | | | | |   (2664)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 194.32/31.34  | | | | | | | | | | |            (42), (43), (51), (52), (53), (61), (63), (158),
% 194.32/31.34  | | | | | | | | | | |            (161), (162), (166), (167), (168), (169), (172),
% 194.32/31.34  | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.32/31.34  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 194.32/31.34  | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 194.32/31.34  | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 194.32/31.34  | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 194.32/31.34  | | | | | | | | | | |            (314), (315), (316), (317), (319), (321), (323),
% 194.32/31.34  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 194.32/31.34  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 194.32/31.34  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.32/31.34  | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.32/31.34  | | | | | | | | | | |            (427), (431), (459), (538), (539), (540), (541),
% 194.32/31.34  | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.34  | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.34  | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 194.32/31.34  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 194.32/31.34  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 194.32/31.34  | | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 194.32/31.34  | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 194.32/31.34  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 194.32/31.34  | | | | | | | | | | |            (610), (611), (612), (613), (670), (750), (772),
% 194.32/31.34  | | | | | | | | | | |            (773), (775), (776), (778), (2340), (2342),
% 194.32/31.34  | | | | | | | | | | |            (2346), (2663), (2664), (function-axioms) are
% 194.32/31.34  | | | | | | | | | | |            inconsistent by sub-proof #603.
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | End of split
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | |   (2665)  all_22_1 = e2
% 194.32/31.34  | | | | | | | | | |   (2666)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | COMBINE_EQS: (658), (2665) imply:
% 194.32/31.34  | | | | | | | | | |   (2667)  all_6_1 = e2
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (43), (2667) imply:
% 194.32/31.34  | | | | | | | | | |   (2668)  op(all_6_2, e3) = e2
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (42), (2667) imply:
% 194.32/31.34  | | | | | | | | | |   (2669)  op(e3, e2) = all_6_0
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 194.32/31.34  | | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (2669)
% 194.32/31.34  | | | | | | | | | |              gives:
% 194.32/31.34  | | | | | | | | | |   (2670)  all_52_9 = all_6_0
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | COMBINE_EQS: (394), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2671)  all_56_1 = all_6_0
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | COMBINE_EQS: (549), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2672)  all_58_1 = all_6_0
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (575), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2673)   ~ (all_52_13 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | SIMP: (2673) implies:
% 194.32/31.34  | | | | | | | | | |   (2674)   ~ (all_52_13 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (576), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2675)   ~ (all_52_15 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | SIMP: (2675) implies:
% 194.32/31.34  | | | | | | | | | |   (2676)   ~ (all_52_15 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (577), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2677)   ~ (all_52_17 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | SIMP: (2677) implies:
% 194.32/31.34  | | | | | | | | | |   (2678)   ~ (all_52_17 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (578), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2679)   ~ (all_52_25 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | SIMP: (2679) implies:
% 194.32/31.34  | | | | | | | | | |   (2680)   ~ (all_52_25 = all_6_0)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (557), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2681)   ~ (all_6_0 = all_6_2)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (574), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2682)   ~ (all_6_0 = all_4_2)
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | REDUCE: (182), (2670) imply:
% 194.32/31.34  | | | | | | | | | |   (2683)  op(all_6_0, all_6_0) = all_52_8
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | BETA: splitting (104) gives:
% 194.32/31.34  | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | |   (2684)   ~ (all_30_1 = e3)
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | REDUCE: (670), (2684) imply:
% 194.32/31.34  | | | | | | | | | | |   (2685)   ~ (all_10_1 = e3)
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | BETA: splitting (109) gives:
% 194.32/31.34  | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | |   (2686)   ~ (all_32_1 = e3)
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | REDUCE: (663), (2686) imply:
% 194.32/31.34  | | | | | | | | | | | |   (2687)   ~ (all_4_1 = e3)
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | BETA: splitting (129) gives:
% 194.32/31.34  | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | |   (2688)   ~ (all_40_1 = e2)
% 194.32/31.34  | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | REDUCE: (687), (2688) imply:
% 194.32/31.34  | | | | | | | | | | | | |   (2689)   ~ (all_10_1 = e2)
% 194.32/31.34  | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | BETA: splitting (153) gives:
% 194.32/31.34  | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | |   (2690)   ~ (all_50_0 = e2)
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | REDUCE: (2339), (2690) imply:
% 194.32/31.34  | | | | | | | | | | | | | |   (2691)  $false
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | CLOSE: (2691) is inconsistent.
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | |   (2692)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.32/31.34  | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | |   (2693)  all_58_15 = e0
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (2693),
% 194.32/31.34  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.34  | | | | | | | | | | | | | | |            #612.
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | Case 2:
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | |   (2694)   ~ (all_58_15 = e0)
% 194.32/31.34  | | | | | | | | | | | | | | |   (2695)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.32/31.34  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.32/31.34  | | | | | | | | | | | | | | |             e0)
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | ALPHA: (2695) implies:
% 194.32/31.34  | | | | | | | | | | | | | | |   (2696)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.32/31.34  | | | | | | | | | | | | | | |   (2697)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | REDUCE: (541), (2694) imply:
% 194.32/31.34  | | | | | | | | | | | | | | |   (2698)   ~ (all_14_2 = e0)
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 194.32/31.34  | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | Case 1:
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2699)  all_56_1 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (2671), (2699) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2700)  all_6_0 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (2672), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2701)  all_58_1 = e3
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2674), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2702)   ~ (all_52_13 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2676), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2703)   ~ (all_52_15 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2678), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2704)   ~ (all_52_17 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2680), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2705)   ~ (all_52_25 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2681), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2706)   ~ (all_6_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | SIMP: (2706) implies:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2707)   ~ (all_6_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2682), (2700) imply:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2708)   ~ (all_4_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | SIMP: (2708) implies:
% 194.32/31.34  | | | | | | | | | | | | | | | |   (2709)   ~ (all_4_2 = e3)
% 194.32/31.34  | | | | | | | | | | | | | | | | 
% 194.32/31.34  | | | | | | | | | | | | | | | | REDUCE: (2683), (2700) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | |   (2710)  op(e3, e3) = all_52_8
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.35  | | | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (2710)
% 194.32/31.35  | | | | | | | | | | | | | | | |              gives:
% 194.32/31.35  | | | | | | | | | | | | | | | |   (2711)  all_52_8 = all_6_2
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | |   (2712)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.35  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.32/31.35  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives:
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2713)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.35  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | ALPHA: (2713) implies:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2714)  all_52_6 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2715)  all_52_4 = e1
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2716)  all_52_2 = e2
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2717)  all_52_0 = e3
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (185), (2716) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2718)  op(all_52_3, all_52_3) = e2
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (184), (2715) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2719)  op(all_52_5, all_52_5) = e1
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (183), (2714) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2720)  op(all_52_7, all_52_7) = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (610), (2717) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2721)  op(all_6_2, all_6_2) = e3
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (63),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (156), (157), (159), (161), (167), (168), (169),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (172), (175), (177), (178), (180), (182), (270),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (271), (272), (273), (277), (279), (280), (281),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (310), (312), (313),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (320), (321), (324),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (325), (327), (328), (329), (330), (331), (332),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (366), (367), (372),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (375), (387), (393), (394), (405), (411), (417),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (431), (538), (539), (541), (542), (543), (544),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (555), (557), (559), (562), (563), (564), (565),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (567), (569), (571), (572), (573), (574), (575),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (590), (591),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (608), (609),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (611), (612), (613), (772), (773), (775), (776),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2342), (2344), (2685), (2687), (2689), (2696),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2698), (2718), (2719), (2720), (2721),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            #681.
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2722)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.32/31.35  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2707), (2711), (2722) are inconsistent by
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            sub-proof #791.
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | |   (2723)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.32/31.35  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.32/31.35  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | BETA: splitting (2723) gives:
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2724)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.32/31.35  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | ALPHA: (2724) implies:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2725)  all_52_22 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2726)  all_52_20 = e1
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2727)  all_52_18 = e2
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2728)  all_52_16 = e3
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (178), (2728) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2729)  op(all_52_17, all_52_17) = e3
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (177), (2727) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2730)  op(all_52_19, all_52_19) = e2
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (175), (2725) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2731)  op(all_52_23, all_52_23) = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REDUCE: (612), (2726) imply:
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2732)  op(all_10_2, all_10_2) = e1
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (53), (61), (63), (157), (158), (166), (167),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (168), (173), (174), (184), (185), (270), (271),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (275), (279), (282), (283), (304), (306), (313),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (315), (317), (321), (325), (327), (329), (331),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (332), (335), (343), (351), (361), (366), (372),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (415), (417),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (538), (541), (542), (543), (544), (545), (546),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (547), (548), (551), (555), (559), (561), (562),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (563), (564), (572), (573), (582), (586), (588),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (597), (600), (606), (608), (609), (613), (2340),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2668), (2689), (2692), (2696), (2701), (2702),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2703), (2704), (2705), (2707), (2709), (2710),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2729), (2730), (2731), (2732), (function-axioms)
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #601.
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | |   (2733)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.32/31.35  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (270), (271),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (306), (307), (309), (311), (313), (316), (319),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (321), (324), (325), (326), (327), (328), (331),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (415), (431), (538), (539), (541), (542), (543),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (553), (555), (559), (561), (562), (563), (564),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (565), (566), (567), (569), (570), (572), (573),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (574), (575), (578), (582), (584), (586), (588),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (590), (591), (593), (594), (595), (596), (598),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (608), (609), (610), (613), (2668), (2689),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2696), (2697), (2698), (2701), (2702), (2703),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (2704), (2705), (2707), (2709), (2733),
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.35  | | | | | | | | | | | | | | | | | |            #600.
% 194.32/31.35  | | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | |   (2734)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 194.32/31.35  | | | | | | | | | | | | | | | |            (610), (739), (773), (775), (2666), (2668),
% 194.32/31.35  | | | | | | | | | | | | | | | |            (2671), (2681), (2734), (function-axioms) are
% 194.32/31.35  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 194.32/31.35  | | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | |   (2735)  all_40_1 = e2
% 194.32/31.35  | | | | | | | | | | | | |   (2736)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 194.32/31.35  | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (43), (51), (52),
% 194.32/31.35  | | | | | | | | | | | | |            (53), (61), (63), (158), (161), (162), (166),
% 194.32/31.35  | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.32/31.35  | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (187),
% 194.32/31.35  | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (277),
% 194.32/31.35  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 194.32/31.35  | | | | | | | | | | | | |            (304), (306), (307), (309), (311), (313), (315),
% 194.32/31.35  | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 194.32/31.35  | | | | | | | | | | | | |            (327), (329), (332), (333), (343), (351), (352),
% 194.32/31.35  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.32/31.35  | | | | | | | | | | | | |            (393), (405), (411), (415), (421), (431), (522),
% 194.32/31.35  | | | | | | | | | | | | |            (526), (538), (539), (540), (541), (542), (543),
% 194.32/31.35  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 194.32/31.35  | | | | | | | | | | | | |            (553), (555), (559), (561), (562), (563), (564),
% 194.32/31.35  | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (570), (571),
% 194.32/31.35  | | | | | | | | | | | | |            (572), (573), (574), (575), (578), (582), (584),
% 194.32/31.35  | | | | | | | | | | | | |            (586), (590), (593), (594), (595), (596), (597),
% 194.32/31.35  | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 194.32/31.35  | | | | | | | | | | | | |            (607), (608), (609), (610), (612), (613), (687),
% 194.32/31.35  | | | | | | | | | | | | |            (739), (767), (773), (775), (2340), (2342),
% 194.32/31.35  | | | | | | | | | | | | |            (2666), (2668), (2671), (2672), (2674), (2676),
% 194.32/31.35  | | | | | | | | | | | | |            (2678), (2680), (2681), (2682), (2683), (2685),
% 194.32/31.35  | | | | | | | | | | | | |            (2735), (2736), (function-axioms) are inconsistent
% 194.32/31.35  | | | | | | | | | | | | |            by sub-proof #599.
% 194.32/31.35  | | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | |   (2737)  all_32_1 = e3
% 194.32/31.35  | | | | | | | | | | | |   (2738)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 194.32/31.35  | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | COMBINE_EQS: (663), (2737) imply:
% 194.32/31.35  | | | | | | | | | | | |   (2739)  all_4_1 = e3
% 194.32/31.35  | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (36), (37), (38), (41), (51), (61),
% 194.32/31.35  | | | | | | | | | | | |            (124), (158), (162), (166), (169), (173), (174),
% 194.32/31.35  | | | | | | | | | | | |            (175), (177), (182), (183), (184), (187), (270),
% 194.32/31.35  | | | | | | | | | | | |            (280), (281), (282), (284), (285), (306), (307),
% 194.32/31.35  | | | | | | | | | | | |            (309), (313), (321), (325), (328), (330), (332),
% 194.32/31.35  | | | | | | | | | | | |            (333), (351), (366), (372), (375), (387), (388),
% 194.32/31.35  | | | | | | | | | | | |            (393), (405), (411), (522), (523), (525), (538),
% 194.32/31.35  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.32/31.35  | | | | | | | | | | | |            (547), (548), (549), (551), (555), (561), (562),
% 194.32/31.35  | | | | | | | | | | | |            (563), (564), (569), (570), (571), (573), (574),
% 194.32/31.35  | | | | | | | | | | | |            (578), (584), (586), (593), (595), (598), (604),
% 194.32/31.35  | | | | | | | | | | | |            (608), (610), (611), (613), (686), (721), (739),
% 194.32/31.35  | | | | | | | | | | | |            (766), (773), (775), (2344), (2666), (2668),
% 194.32/31.35  | | | | | | | | | | | |            (2671), (2672), (2674), (2676), (2680), (2681),
% 194.32/31.35  | | | | | | | | | | | |            (2682), (2683), (2738), (2739), (function-axioms)
% 194.32/31.35  | | | | | | | | | | | |            are inconsistent by sub-proof #593.
% 194.32/31.35  | | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | End of split
% 194.32/31.35  | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | Case 2:
% 194.32/31.35  | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | |   (2740)  all_30_1 = e3
% 194.32/31.35  | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | COMBINE_EQS: (670), (2740) imply:
% 194.32/31.35  | | | | | | | | | | |   (2741)  all_10_1 = e3
% 194.32/31.35  | | | | | | | | | | | 
% 194.32/31.35  | | | | | | | | | | | SIMP: (2741) implies:
% 194.32/31.35  | | | | | | | | | | |   (2742)  all_10_1 = e3
% 194.32/31.35  | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 194.32/31.36  | | | | | | | | | | |            (52), (53), (61), (63), (158), (162), (166),
% 194.32/31.36  | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 194.32/31.36  | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 194.32/31.36  | | | | | | | | | | |            (271), (273), (274), (275), (277), (280), (282),
% 194.32/31.36  | | | | | | | | | | |            (283), (284), (285), (303), (304), (306), (307),
% 194.32/31.36  | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 194.32/31.36  | | | | | | | | | | |            (321), (324), (325), (326), (327), (329), (332),
% 194.32/31.36  | | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 194.32/31.36  | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 194.32/31.36  | | | | | | | | | | |            (431), (522), (538), (539), (540), (541), (542),
% 194.32/31.36  | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.32/31.36  | | | | | | | | | | |            (551), (553), (555), (559), (561), (562), (563),
% 194.32/31.36  | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (572),
% 194.32/31.36  | | | | | | | | | | |            (573), (574), (575), (577), (578), (582), (584),
% 194.32/31.36  | | | | | | | | | | |            (586), (590), (593), (594), (595), (596), (597),
% 194.32/31.36  | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 194.32/31.36  | | | | | | | | | | |            (607), (608), (609), (610), (612), (613), (739),
% 194.32/31.36  | | | | | | | | | | |            (773), (775), (776), (2340), (2666), (2668),
% 194.32/31.36  | | | | | | | | | | |            (2671), (2672), (2674), (2676), (2678), (2680),
% 194.32/31.36  | | | | | | | | | | |            (2681), (2682), (2683), (2742), (function-axioms)
% 194.32/31.36  | | | | | | | | | | |            are inconsistent by sub-proof #592.
% 194.32/31.36  | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | End of split
% 194.32/31.36  | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | End of split
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | |   (2743)  all_20_0 = e3
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | COMBINE_EQS: (758), (2743) imply:
% 194.32/31.36  | | | | | | | | |   (2744)  all_4_0 = e3
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | SIMP: (2744) implies:
% 194.32/31.36  | | | | | | | | |   (2745)  all_4_0 = e3
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | REDUCE: (37), (2745) imply:
% 194.32/31.36  | | | | | | | | |   (2746)  op(e2, all_4_1) = e3
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | BETA: splitting (84) gives:
% 194.32/31.36  | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | |   (2747)   ~ (all_22_1 = e2)
% 194.32/31.36  | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | REDUCE: (658), (2747) imply:
% 194.32/31.36  | | | | | | | | | |   (2748)   ~ (all_6_1 = e2)
% 194.32/31.36  | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | BETA: splitting (104) gives:
% 194.32/31.36  | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | |   (2749)   ~ (all_30_1 = e3)
% 194.32/31.36  | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | REDUCE: (670), (2749) imply:
% 194.32/31.36  | | | | | | | | | | |   (2750)   ~ (all_10_1 = e3)
% 194.32/31.36  | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | BETA: splitting (129) gives:
% 194.32/31.36  | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | |   (2751)   ~ (all_40_1 = e2)
% 194.32/31.36  | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | REDUCE: (687), (2751) imply:
% 194.32/31.36  | | | | | | | | | | | |   (2752)   ~ (all_10_1 = e2)
% 194.32/31.36  | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.32/31.36  | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | |   (2753)  all_58_15 = e0
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (2753),
% 194.32/31.36  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.36  | | | | | | | | | | | | |            #612.
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | |   (2754)   ~ (all_58_15 = e0)
% 194.32/31.36  | | | | | | | | | | | | |   (2755)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.32/31.36  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.32/31.36  | | | | | | | | | | | | |             e0)
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | ALPHA: (2755) implies:
% 194.32/31.36  | | | | | | | | | | | | |   (2756)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.32/31.36  | | | | | | | | | | | | |   (2757)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | REDUCE: (541), (2754) imply:
% 194.32/31.36  | | | | | | | | | | | | |   (2758)   ~ (all_14_2 = e0)
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.32/31.36  | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | |   (2759)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.36  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.32/31.36  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.32/31.36  | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | BETA: splitting (2759) gives:
% 194.32/31.36  | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | |   (2760)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.36  | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | ALPHA: (2760) implies:
% 194.32/31.36  | | | | | | | | | | | | | | |   (2761)  all_52_6 = e0
% 194.32/31.36  | | | | | | | | | | | | | | |   (2762)  all_52_4 = e1
% 194.32/31.36  | | | | | | | | | | | | | | |   (2763)  all_52_2 = e2
% 194.32/31.36  | | | | | | | | | | | | | | |   (2764)  all_52_0 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | REDUCE: (185), (2763) imply:
% 194.32/31.36  | | | | | | | | | | | | | | |   (2765)  op(all_52_3, all_52_3) = e2
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | REDUCE: (184), (2762) imply:
% 194.32/31.36  | | | | | | | | | | | | | | |   (2766)  op(all_52_5, all_52_5) = e1
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | REDUCE: (183), (2761) imply:
% 194.32/31.36  | | | | | | | | | | | | | | |   (2767)  op(all_52_7, all_52_7) = e0
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | REDUCE: (610), (2764) imply:
% 194.32/31.36  | | | | | | | | | | | | | | |   (2768)  op(all_6_2, all_6_2) = e3
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | |   (2769)  all_56_15 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (38), (41), (42), (43),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (51), (52), (53), (61), (63), (156), (159), (167),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (168), (169), (172), (177), (178), (271), (272),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (273), (277), (279), (281), (284), (304), (305),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (310), (312), (313), (314), (315), (317), (319),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (320), (321), (327), (328), (329), (330), (331),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (367),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (405), (411),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (417), (431), (538), (542), (543), (544), (545),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (557), (559), (562), (563), (564), (565), (567),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (569), (571), (572), (573), (574), (575), (576),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (590), (591), (596),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (597), (598), (600), (602), (608), (609), (611),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (612), (613), (772), (773), (775), (776), (2342),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (2750), (2752), (2758), (2765), (2766), (2767),
% 194.32/31.36  | | | | | | | | | | | | | | | |            (2768), (2769), (function-axioms) are inconsistent
% 194.32/31.36  | | | | | | | | | | | | | | | |            by sub-proof #682.
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | |   (2770)   ~ (all_56_15 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | |   (2771)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | REDUCE: (538), (2770) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | |   (2772)   ~ (all_14_2 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2773)  all_56_13 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (2773) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2774)  all_52_15 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | SIMP: (2774) implies:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2775)  all_52_15 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2775) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2776)  all_58_13 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | REDUCE: (571), (2775) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2777)   ~ (all_52_7 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | REDUCE: (576), (2775) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2778)   ~ (all_52_9 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | REDUCE: (590), (2775) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2779)   ~ (all_52_23 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | SIMP: (2779) implies:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2780)   ~ (all_52_23 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | REDUCE: (591), (2775) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2781)   ~ (all_14_2 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | REDUCE: (179), (2775) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2782)  op(e3, e3) = all_52_14
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.36  | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (2782)
% 194.32/31.36  | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | |   (2783)  all_52_14 = all_6_2
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | |   (2784)  all_56_12 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (2777), (2784) are inconsistent by
% 194.32/31.36  | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 194.32/31.36  | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | |   (2785)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 194.32/31.36  | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2786)  all_56_7 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (2786) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2787)  all_52_27 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | SIMP: (2787) implies:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2788)  all_52_27 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | REDUCE: (598), (2788) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2789)   ~ (all_52_19 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | REDUCE: (604), (2788) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2790)   ~ (all_52_25 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | REDUCE: (173), (2788) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2791)  op(e3, e3) = all_52_26
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (41), (2791)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | |   (2792)  all_52_26 = all_6_2
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |   (2793)  all_58_4 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |            (351), (387), (393), (405), (547), (559), (564),
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |            (569), (573), (2765), (2766), (2767), (2768),
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |            (2793), (function-axioms) are inconsistent by
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #591.
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |   (2794)   ~ (all_58_4 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |   (2795)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (2794) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | |   (2796)   ~ (all_52_17 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2795) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | |   (2797)  all_58_5 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (375), (2789), (2797) are inconsistent by
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | |   (2798)  all_58_8 = e3 | all_58_14 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | |   (2799)  all_58_0 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (2799) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | |   (2800)  all_6_2 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2798) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2801)  all_58_8 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2801) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2802)  all_10_2 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2802) implies:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2803)  all_10_2 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (2803) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2804)   ~ (all_52_5 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (2803) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2805)  op(e3, e1) = all_10_1
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2803) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2806)  op(e1, e1) = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (2805)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2807)  all_52_17 = all_10_1
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (2807) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2808)  all_56_2 = all_10_1
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (2807) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2809)  all_58_4 = all_10_1
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (2807) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2810)   ~ (all_52_23 = all_10_1)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2810) implies:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2811)   ~ (all_52_23 = all_10_1)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (178), (2807) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | |   (2812)  op(all_10_1, all_10_1) = all_52_16
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | |   (2813)  all_56_2 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2750), (2808), (2813) are inconsistent by
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1029.
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | |   (2814)   ~ (all_56_2 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | |   (2815)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (2816)  all_56_8 = e3
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (2804), (2816) are inconsistent by
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (2817)   ~ (all_56_8 = e3)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (2818)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2819)  all_58_6 = e2
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (61), (304), (351), (431), (542),
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (547), (567), (573), (600), (2756), (2767),
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2776), (2785), (2819), (function-axioms) are
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #727.
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2820)   ~ (all_58_6 = e2)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (2820) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2821)   ~ (all_52_5 = e2)
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2822)  all_58_4 = e1
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2809), (2822) imply:
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2823)  all_10_1 = e1
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2812), (2823) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2824)  op(e1, e1) = all_52_16
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (2823) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2825)  op(e1, e1) = all_10_0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (776), (2806), (2824), (2825), (function-axioms)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #689.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2826)   ~ (all_58_4 = e1)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2809), (2826) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2827)   ~ (all_10_1 = e1)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2815) gives:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2828)  all_56_2 = e2
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2752), (2808), (2828) are inconsistent by
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #815.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2829)   ~ (all_56_2 = e2)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2830)  all_56_2 = e1 | all_56_2 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2830) gives:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2831)  all_56_2 = e1
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2808), (2827), (2831) are inconsistent by
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1025.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2832)  all_56_2 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2808), (2832) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2833)  all_10_1 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2833) implies:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2834)  all_10_1 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2811), (2834) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2835)   ~ (all_52_23 = e0)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2750), (2834) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2836)   ~ (e3 = e0)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2837)  all_58_6 = e1
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (2837) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2838)  all_52_5 = e1
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2838) implies:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2839)  all_52_5 = e1
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (2839) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2840)   ~ (all_52_3 = e1)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2804), (2839) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2841)   ~ (e3 = e1)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (51), (53), (156), (271), (304), (328),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (343), (351), (387), (547), (569), (572), (600),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2750), (2752), (2766), (2767), (2799), (2840),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2842)   ~ (all_58_6 = e1)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (2842) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2843)   ~ (all_52_5 = e1)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2756) gives:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2844)  all_58_12 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2844) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2845)  all_52_7 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2845) implies:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2846)  all_52_7 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2767), (2846) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2847)  op(e0, e0) = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (310), (367), (547), (2766), (2818), (2821),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2843), (2847), (function-axioms) are inconsistent
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1003.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2848)  all_58_13 = e0 | all_58_14 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2848) gives:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2849)  all_58_13 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2776), (2849) are inconsistent by sub-proof
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2850)  all_58_14 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2835), (2850) are inconsistent by
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1019.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | |   (2851)  all_58_14 = e3
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2780), (2851) are inconsistent by
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | |   (2852)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (393), (545), (549), (2778), (2790), (2796),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | |            (2852) are inconsistent by sub-proof #744.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | |   (2853)   ~ (all_56_7 = e3)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | REDUCE: (427), (2853) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | |   (2854)   ~ (all_52_27 = e3)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |   (2855)  all_58_9 = e3
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2855) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |   (2856)  all_52_25 = e3
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (561), (564), (569),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (573), (2765), (2766), (2767), (2768), (2856),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            #1000.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |   (2857)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (61), (63), (159), (172), (177), (304), (305),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (306), (317), (321), (332), (333), (351), (372),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (375), (387), (393), (405), (431), (541), (542),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (544), (546), (547), (559), (564), (569), (573),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (596), (597), (600), (602), (773), (2338), (2756),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (2765), (2766), (2767), (2768), (2772), (2776),
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            (2780), (2785), (2854), (2857), (function-axioms)
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #589.
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | |   (2858)   ~ (all_56_13 = e3)
% 194.32/31.37  | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | REDUCE: (346), (2858) imply:
% 194.32/31.37  | | | | | | | | | | | | | | | | |   (2859)   ~ (all_52_15 = e3)
% 194.32/31.37  | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (53), (61), (156), (169), (175), (182), (273),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (276), (277), (281), (283), (284), (304), (305),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (306), (309), (311), (312), (313), (314), (319),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (320), (321), (325), (328), (331), (332), (333),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (393),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (421), (431), (538),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (548), (549), (553), (555), (557), (559), (561),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (572),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (573), (574), (575), (577), (578), (580), (586),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (588), (589), (590), (593), (594), (595), (596),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (600), (603), (606), (608), (609), (612), (613),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (772), (773), (2746), (2750), (2757), (2765),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (2766), (2767), (2768), (2771), (2772), (2859),
% 194.32/31.37  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.37  | | | | | | | | | | | | | | | | |            #657.
% 194.32/31.37  | | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | |   (2860)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.32/31.37  | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 194.32/31.37  | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 194.32/31.37  | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 194.32/31.37  | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 194.32/31.37  | | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 194.32/31.37  | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 194.32/31.37  | | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 194.32/31.37  | | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 194.32/31.37  | | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 194.32/31.37  | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.32/31.37  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.32/31.37  | | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 194.32/31.37  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.32/31.37  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 194.32/31.37  | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 194.32/31.37  | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 194.32/31.37  | | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 194.32/31.37  | | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 194.32/31.37  | | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 194.32/31.37  | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 194.32/31.37  | | | | | | | | | | | | | | |            (773), (775), (778), (2748), (2756), (2757),
% 194.32/31.37  | | | | | | | | | | | | | | |            (2758), (2860), (function-axioms) are inconsistent
% 194.32/31.37  | | | | | | | | | | | | | | |            by sub-proof #731.
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | End of split
% 194.32/31.37  | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | |   (2861)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.32/31.37  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.32/31.37  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.32/31.37  | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | BETA: splitting (2861) gives:
% 194.32/31.37  | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | Case 1:
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | |   (2862)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.32/31.37  | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.32/31.37  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.32/31.37  | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.32/31.37  | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.32/31.37  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.32/31.37  | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.32/31.37  | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.32/31.37  | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.32/31.37  | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.32/31.37  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.32/31.37  | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.32/31.37  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.37  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.37  | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.32/31.37  | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.32/31.37  | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.32/31.37  | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.32/31.37  | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.32/31.37  | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (2748),
% 194.32/31.37  | | | | | | | | | | | | | | |            (2756), (2757), (2862), (function-axioms) are
% 194.32/31.37  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | Case 2:
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.37  | | | | | | | | | | | | | | |   (2863)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.32/31.37  | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.32/31.37  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.32/31.38  | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.32/31.38  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.32/31.38  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.32/31.38  | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.32/31.38  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.32/31.38  | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.32/31.38  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.32/31.38  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.32/31.38  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.32/31.38  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.32/31.38  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.32/31.38  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.32/31.38  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.32/31.38  | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.32/31.38  | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.32/31.38  | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.32/31.38  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.32/31.38  | | | | | | | | | | | | | | |            (775), (778), (2748), (2756), (2758), (2863),
% 194.32/31.38  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.38  | | | | | | | | | | | | | | |            #1008.
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | End of split
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | End of split
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | End of split
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | Case 2:
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | |   (2864)  all_40_1 = e2
% 194.32/31.38  | | | | | | | | | | | |   (2865)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | COMBINE_EQS: (687), (2864) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2866)  all_10_1 = e2
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | SIMP: (2866) implies:
% 194.32/31.38  | | | | | | | | | | | |   (2867)  all_10_1 = e2
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (2750), (2867) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2868)   ~ (e3 = e2)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (53), (2867) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2869)  op(all_10_2, e1) = e2
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (52), (2867) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2870)  op(e1, e2) = all_10_0
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 194.32/31.38  | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (2870)
% 194.32/31.38  | | | | | | | | | | | |              gives:
% 194.32/31.38  | | | | | | | | | | | |   (2871)  all_52_13 = all_10_0
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | COMBINE_EQS: (421), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2872)  all_56_9 = all_10_0
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | COMBINE_EQS: (366), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2873)  all_58_7 = all_10_0
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (575), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2874)   ~ (all_52_9 = all_10_0)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (587), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2875)   ~ (all_52_15 = all_10_0)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | SIMP: (2875) implies:
% 194.32/31.38  | | | | | | | | | | | |   (2876)   ~ (all_52_15 = all_10_0)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (589), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2877)   ~ (all_52_29 = all_10_0)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | SIMP: (2877) implies:
% 194.32/31.38  | | | | | | | | | | | |   (2878)   ~ (all_52_29 = all_10_0)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (588), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2879)   ~ (all_10_0 = all_10_2)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (580), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2880)   ~ (all_10_0 = all_4_2)
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | REDUCE: (180), (2871) imply:
% 194.32/31.38  | | | | | | | | | | | |   (2881)  op(all_10_0, all_10_0) = all_52_12
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | BETA: splitting (153) gives:
% 194.32/31.38  | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | |   (2882)   ~ (all_50_0 = e2)
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | REDUCE: (2339), (2882) imply:
% 194.32/31.38  | | | | | | | | | | | | |   (2883)  $false
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | CLOSE: (2883) is inconsistent.
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | Case 2:
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | |   (2884)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.32/31.38  | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | |   (2885)  all_58_15 = e0
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (2885),
% 194.32/31.38  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.38  | | | | | | | | | | | | | |            #612.
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | Case 2:
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | |   (2886)   ~ (all_58_15 = e0)
% 194.32/31.38  | | | | | | | | | | | | | |   (2887)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.32/31.38  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.32/31.38  | | | | | | | | | | | | | |             e0)
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | ALPHA: (2887) implies:
% 194.32/31.38  | | | | | | | | | | | | | |   (2888)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.32/31.38  | | | | | | | | | | | | | |   (2889)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | REDUCE: (541), (2886) imply:
% 194.32/31.38  | | | | | | | | | | | | | |   (2890)   ~ (all_14_2 = e0)
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 194.32/31.38  | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | |   (2891)  all_56_9 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | REF_CLOSE: (776), (2872), (2891) are inconsistent by
% 194.32/31.38  | | | | | | | | | | | | | | |            sub-proof #1006.
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | Case 2:
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | |   (2892)   ~ (all_56_9 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | |   (2893)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | |   (2894)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.38  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.32/31.38  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.32/31.38  | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | BETA: splitting (2894) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2895)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.32/31.38  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | ALPHA: (2895) implies:
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2896)  all_52_6 = e0
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2897)  all_52_4 = e1
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2898)  all_52_2 = e2
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2899)  all_52_0 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | REDUCE: (185), (2898) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2900)  op(all_52_3, all_52_3) = e2
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | REDUCE: (184), (2897) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2901)  op(all_52_5, all_52_5) = e1
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | REDUCE: (183), (2896) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2902)  op(all_52_7, all_52_7) = e0
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | REDUCE: (610), (2899) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | |   (2903)  op(all_6_2, all_6_2) = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2904)  all_56_15 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2904) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2905)  all_14_2 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | SIMP: (2905) implies:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2906)  all_14_2 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2907)  all_50_2 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2908)  all_58_15 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REDUCE: (606), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2909)   ~ (all_52_25 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REDUCE: (609), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2910)   ~ (all_52_29 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REDUCE: (613), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2911)  op(e3, e3) = all_52_30
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REDUCE: (63), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2912)  op(e3, e0) = all_14_1
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REDUCE: (61), (2906) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2913)  op(e0, e0) = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (167), (168), (174),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (282), (306), (307), (313), (321), (332), (351),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (372), (387), (388), (405), (526), (544), (545),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (546), (547), (553), (564), (569), (573), (593),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (595), (604), (690), (767), (776), (2340), (2342),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (2865), (2869), (2872), (2873), (2878), (2879),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (2884), (2893), (2900), (2901), (2902), (2903),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (2907), (2908), (2909), (2910), (2911), (2912),
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            (2913), (function-axioms) are inconsistent by
% 194.32/31.38  | | | | | | | | | | | | | | | | | |            sub-proof #588.
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2914)   ~ (all_56_15 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2915)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | REDUCE: (538), (2914) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | |   (2916)   ~ (all_14_2 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2917)  all_58_1 = e2
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2917) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2918)  all_52_9 = e2
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2918) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2919)   ~ (all_52_17 = e2)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | SIMP: (2919) implies:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2920)   ~ (all_52_17 = e2)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | REDUCE: (2874), (2918) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2921)   ~ (all_10_0 = e2)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | REDUCE: (182), (2918) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2922)  op(e2, e2) = all_52_8
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |              all_52_8, e2, e2, simplifying with (36), (2922)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | |   (2923)  all_52_8 = all_4_2
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2924)  all_56_13 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (2924) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2925)  all_52_15 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | SIMP: (2925) implies:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2926)  all_52_15 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2926) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2927)  all_58_13 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (2926) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2928)   ~ (all_52_23 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | SIMP: (2928) implies:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2929)   ~ (all_52_23 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (2926) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2930)  op(e3, e3) = all_52_14
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (2930)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | |   (2931)  all_52_14 = all_6_2
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2932)  all_56_0 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (2932) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2933)  all_6_2 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | SIMP: (2933) implies:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2934)  all_6_2 = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (2934) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2935)   ~ (all_52_3 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2934) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2936)   ~ (all_52_7 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (2934) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2937)   ~ (all_52_17 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (2934) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2938)   ~ (all_52_25 = e3)
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (2934) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2939)  op(e3, e3) = all_6_1
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (2934) imply:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2940)  op(e3, e3) = e3
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (2939), (2940) gives:
% 194.32/31.38  | | | | | | | | | | | | | | | | | | | | |   (2941)  all_6_1 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2941) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |   (2942)  op(e3, e3) = all_6_0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (2940), (2942) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |   (2943)  all_6_0 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | |   (2944)  all_56_2 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (2937), (2944) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1327.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | |   (2945)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | |   (2946)  all_58_9 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (2938), (2946) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1300.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | |   (2947)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | |   (2948)  all_56_12 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (2936), (2948) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | |   (2949)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (2950)  all_58_12 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2950) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (2951)  all_52_7 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2951) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (2952)  all_52_7 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2902), (2952) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (2953)  op(e2, e2) = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2888) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2954)  all_58_12 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2950), (2954) are inconsistent by sub-proof
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1153.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2955)  all_58_13 = e0 | all_58_14 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2955) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2956)  all_58_13 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2927), (2956) are inconsistent by sub-proof
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2957)  all_58_14 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2957) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2958)  all_52_23 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2958) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2959)  all_52_23 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (2959) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2960)   ~ (all_52_17 = e0)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2929), (2959) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2961)   ~ (e3 = e0)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2962)  all_58_12 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2950), (2962) are inconsistent by sub-proof
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1198.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2963)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2963) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2964)  all_58_13 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2927), (2964) are inconsistent by sub-proof
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #770.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2965)  all_58_14 = e1 | all_58_15 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2945) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2966)  all_56_2 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (2966) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2967)  all_52_17 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2920), (2967) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2968)  $false
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2968) is inconsistent.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2969)  all_56_2 = e1 | all_56_2 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2969) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2970)  all_56_2 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (2970) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2971)  all_52_17 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (2971) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2972)   ~ (all_52_19 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2972) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2973)   ~ (all_52_19 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (2971) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2974)   ~ (all_10_2 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2974) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2975)   ~ (all_10_2 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (178), (2971) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2976)  op(e1, e1) = all_52_16
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2965) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2977)  all_58_14 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (2927), (2955), (2977) are inconsistent
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #710.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2978)  all_58_15 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2978) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2979)  all_14_2 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (608), (2979) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2980)   ~ (all_52_27 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (609), (2979) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2981)   ~ (all_52_29 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (2979) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2982)  op(e1, e1) = all_52_30
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (2979) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2983)  op(e1, e0) = all_14_1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2338) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2984)   ~ (all_14_1 = e3)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_1, e0, e1, simplifying with (159), (2983)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2985)  all_52_29 = all_14_1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_16, e1, e1, simplifying with (51), (2976)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2986)  all_52_16 = all_10_2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_30,
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_16, e1, e1, simplifying with (2976), (2982)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2987)  all_52_16 = all_52_30
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (2953) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2988)  all_4_2 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2986), (2987) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2989)  all_52_30 = all_10_2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2989) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2990)  all_52_30 = all_10_2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (2985) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2991)  all_58_11 = all_14_1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (2988) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2992)   ~ (all_52_19 = e0)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2880), (2988) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2993)   ~ (all_10_0 = e0)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2994)  all_58_2 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (2994) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2995)  all_52_3 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2995) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2996)  all_52_3 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2935), (2996) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2997)   ~ (e3 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2900), (2996) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2998)  op(e1, e1) = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2947) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2999)  all_58_10 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (2999) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3000)  all_52_27 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (3000) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3001)   ~ (all_52_19 = e3)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3002)  all_56_6 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (3002) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3003)  all_52_19 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3001), (3003) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3004)  $false
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3004) is inconsistent.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3005)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2893) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3006)  all_56_9 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2342), (2872), (3006) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #991.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3007)  all_56_9 = e1 | all_56_9 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3008)  all_56_9 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2872), (3008) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3009)  all_10_0 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3009) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3010)  all_10_0 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2881), (3010) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3011)  op(e1, e1) = all_52_12
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3005) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3012)  all_56_6 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (3012) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3013)  all_52_19 = e2
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (3013) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3014)   ~ (all_10_2 = e2)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3014) implies:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3015)   ~ (all_10_2 = e2)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (2998), (3011), (3015), (function-axioms)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #954.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3016)  all_56_6 = e1 | all_56_6 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (417), (2973), (2992), (3016) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #757.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3017)  all_56_9 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2872), (2993), (3017) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #989.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3018)  all_58_11 = e3 | all_58_15 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3018) gives:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3019)  all_58_11 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2984), (2991), (3019) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #587.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3020)  all_58_15 = e3
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2978), (3020) are inconsistent by sub-proof
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #586.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3021)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (311), (366), (372), (375), (544), (546),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (547), (548), (569), (580), (2901), (2973),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2975), (2980), (2981), (3021), (function-axioms)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #868.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3022)   ~ (all_14_2 = e1)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2979), (3022) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3023)  $false
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3023) is inconsistent.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3024)  all_56_2 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (3024) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3025)  all_52_17 = e0
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2960), (3025) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3026)  $false
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3026) is inconsistent.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (3027)   ~ (all_58_12 = e2)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (3027) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (3028)   ~ (all_52_7 = e2)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (61), (304), (351), (431), (542),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |            (573), (600), (2888), (2902), (2927), (2949),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |            (3028), (function-axioms) are inconsistent by
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1169.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |   (3029)   ~ (all_56_0 = e3)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (3029) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |   (3030)   ~ (all_6_2 = e3)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (564), (569), (573),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |            (2900), (2901), (2902), (2903), (3030),
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | |            #1362.
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | |   (3031)   ~ (all_56_13 = e3)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3031) imply:
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | |   (3032)   ~ (all_52_15 = e3)
% 194.32/31.39  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (53), (61), (156), (169), (175), (182), (273),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (276), (277), (281), (283), (284), (304), (305),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (306), (309), (311), (312), (313), (314), (319),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (320), (321), (325), (328), (331), (332), (333),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (393),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (421), (431), (538),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (548), (549), (553), (555), (557), (559), (561),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (572),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (573), (574), (575), (577), (578), (580), (586),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (588), (589), (590), (593), (594), (595), (596),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (600), (603), (606), (608), (609), (612), (613),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (772), (773), (2746), (2750), (2889), (2900),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (2901), (2902), (2903), (2915), (2916), (3032),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            #657.
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | |   (3033)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3034)  all_58_0 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (3034) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3035)  all_6_2 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (3035) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3036)   ~ (all_52_7 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (3035) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3037)  op(e3, e3) = all_6_1
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (3035) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3038)  op(e3, e3) = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (3037), (3038) gives:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3039)  all_6_1 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (3039) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3040)  op(e3, e3) = all_6_0
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (3038), (3040) gives:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3041)  all_6_0 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | |   (3042)  all_58_12 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (3036), (3042) are inconsistent by
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1367.
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | |   (3043)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3044)  all_56_13 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (3044) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3045)  all_52_15 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3045) implies:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3046)  all_52_15 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3046) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3047)  all_58_13 = e3
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (3046) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3048)   ~ (all_4_2 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3048) implies:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3049)   ~ (all_4_2 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (38), (548), (611), (2342), (2746),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (2873), (3033), (3047), (3049), (function-axioms)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #720.
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3050)   ~ (all_56_13 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3050) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |   (3051)   ~ (all_52_15 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (53), (61), (156), (169), (175), (182), (273),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (276), (277), (281), (283), (284), (304), (305),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (309), (311), (312), (313), (314), (319), (320),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (321), (325), (328), (331), (332), (333), (351),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (393), (394),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (405), (411), (415), (421), (431), (538), (541),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (549), (553), (557), (559), (561), (563), (564),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (565), (566), (568), (569), (572), (573), (574),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (575), (577), (578), (580), (586), (588), (589),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (590), (593), (594), (595), (596), (600), (603),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (606), (608), (609), (612), (613), (772), (773),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (2746), (2750), (2889), (2900), (2901), (2902),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (2903), (2915), (2916), (3043), (3051),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | |            #658.
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3052)   ~ (all_58_0 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (3052) imply:
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |   (3053)   ~ (all_6_2 = e3)
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (564), (569), (573),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (2900), (2901), (2902), (2903), (3053),
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | |            #1362.
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | |   (3054)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.32/31.40  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (38), (41), (43), (51), (158), (169), (179),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (182), (270), (271), (273), (284), (306), (325),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (327), (343), (351), (394), (405), (431), (538),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (541), (542), (543), (548), (549), (555), (557),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (571), (574), (582), (590), (591), (611), (772),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (776), (778), (2342), (2748), (2872), (2873),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (2874), (2876), (2879), (2881), (2893), (3054),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.40  | | | | | | | | | | | | | | | | |            #714.
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | End of split
% 194.32/31.40  | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | |   (3055)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.32/31.40  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.32/31.40  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.32/31.40  | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | BETA: splitting (3055) gives:
% 194.32/31.40  | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | Case 1:
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | |   (3056)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.32/31.40  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (2748),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (2888), (2889), (3056), (function-axioms) are
% 194.32/31.40  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | Case 2:
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | |   (3057)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.32/31.40  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.32/31.40  | | | | | | | | | | | | | | | | | 
% 194.32/31.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (775), (778), (2748), (2888), (2890), (3057),
% 194.32/31.40  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.32/31.40  | | | | | | | | | | | | | | | | |            #1008.
% 194.32/31.41  | | | | | | | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | Case 2:
% 194.32/31.41  | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | |   (3058)  all_30_1 = e3
% 194.32/31.41  | | | | | | | | | | |   (3059)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 194.32/31.41  | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 194.32/31.41  | | | | | | | | | | |            (42), (43), (51), (52), (53), (61), (63), (158),
% 194.32/31.41  | | | | | | | | | | |            (161), (162), (166), (167), (168), (169), (172),
% 194.32/31.41  | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.32/31.41  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 194.32/31.41  | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 194.32/31.41  | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 194.32/31.41  | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 194.32/31.41  | | | | | | | | | | |            (314), (315), (316), (317), (319), (321), (323),
% 194.32/31.41  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 194.32/31.41  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 194.32/31.41  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.32/31.41  | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.32/31.41  | | | | | | | | | | |            (427), (431), (459), (538), (539), (540), (541),
% 194.32/31.41  | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.32/31.41  | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.32/31.41  | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 194.32/31.41  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 194.32/31.41  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 194.32/31.41  | | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 194.32/31.41  | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 194.32/31.41  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 194.32/31.41  | | | | | | | | | | |            (610), (611), (612), (613), (670), (750), (772),
% 194.32/31.41  | | | | | | | | | | |            (773), (775), (776), (778), (2340), (2342),
% 194.32/31.41  | | | | | | | | | | |            (2748), (3058), (3059), (function-axioms) are
% 194.32/31.41  | | | | | | | | | | |            inconsistent by sub-proof #603.
% 194.32/31.41  | | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | End of split
% 194.32/31.41  | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | Case 2:
% 194.32/31.41  | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | |   (3060)  all_22_1 = e2
% 194.32/31.41  | | | | | | | | | |   (3061)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 194.32/31.41  | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | COMBINE_EQS: (658), (3060) imply:
% 194.32/31.41  | | | | | | | | | |   (3062)  all_6_1 = e2
% 194.32/31.41  | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | SIMP: (3062) implies:
% 194.32/31.41  | | | | | | | | | |   (3063)  all_6_1 = e2
% 194.32/31.41  | | | | | | | | | | 
% 194.32/31.41  | | | | | | | | | | REDUCE: (43), (3063) imply:
% 194.71/31.41  | | | | | | | | | |   (3064)  op(all_6_2, e3) = e2
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | REDUCE: (42), (3063) imply:
% 194.71/31.41  | | | | | | | | | |   (3065)  op(e3, e2) = all_6_0
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 194.71/31.41  | | | | | | | | | |            (52), (53), (61), (63), (104), (129), (153),
% 194.71/31.41  | | | | | | | | | |            (157), (158), (161), (162), (166), (167), (168),
% 194.71/31.41  | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 194.71/31.41  | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 194.71/31.41  | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (279),
% 194.71/31.41  | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 194.71/31.41  | | | | | | | | | |            (304), (306), (307), (309), (311), (313), (315),
% 194.71/31.41  | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 194.71/31.41  | | | | | | | | | |            (327), (328), (329), (331), (332), (333), (335),
% 194.71/31.41  | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 194.71/31.41  | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.71/31.41  | | | | | | | | | |            (415), (417), (421), (431), (522), (526), (538),
% 194.71/31.41  | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.71/31.41  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.71/31.41  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 194.71/31.41  | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 194.71/31.41  | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (582),
% 194.71/31.41  | | | | | | | | | |            (584), (586), (588), (590), (591), (592), (593),
% 194.71/31.41  | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 194.71/31.41  | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 194.71/31.41  | | | | | | | | | |            (610), (612), (613), (670), (687), (739), (767),
% 194.71/31.41  | | | | | | | | | |            (773), (775), (776), (2339), (2340), (2342),
% 194.71/31.41  | | | | | | | | | |            (3061), (3064), (3065), (function-axioms) are
% 194.71/31.41  | | | | | | | | | |            inconsistent by sub-proof #585.
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | End of split
% 194.71/31.41  | | | | | | | | | 
% 194.71/31.41  | | | | | | | | End of split
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | Case 2:
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | |   (3066)  all_16_0 = e2
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | COMBINE_EQS: (760), (3066) imply:
% 194.71/31.41  | | | | | | | |   (3067)  all_10_0 = e2
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | SIMP: (3067) implies:
% 194.71/31.41  | | | | | | | |   (3068)  all_10_0 = e2
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | COMBINE_EQS: (756), (3068) imply:
% 194.71/31.41  | | | | | | | |   (3069)  all_26_0 = e2
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | REDUCE: (776), (3068) imply:
% 194.71/31.41  | | | | | | | |   (3070)   ~ (e3 = e2)
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | REDUCE: (52), (3068) imply:
% 194.71/31.41  | | | | | | | |   (3071)  op(e1, all_10_1) = e2
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | BETA: splitting (79) gives:
% 194.71/31.41  | | | | | | | | 
% 194.71/31.41  | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | 
% 194.71/31.41  | | | | | | | | |   (3072)   ~ (all_20_0 = e3)
% 194.71/31.41  | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | REDUCE: (758), (3072) imply:
% 194.71/31.41  | | | | | | | | |   (3073)   ~ (all_4_0 = e3)
% 194.71/31.41  | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | BETA: splitting (84) gives:
% 194.71/31.41  | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | |   (3074)   ~ (all_22_1 = e2)
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | REDUCE: (658), (3074) imply:
% 194.71/31.41  | | | | | | | | | |   (3075)   ~ (all_6_1 = e2)
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | BETA: splitting (109) gives:
% 194.71/31.41  | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | |   (3076)   ~ (all_32_1 = e3)
% 194.71/31.41  | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | REDUCE: (663), (3076) imply:
% 194.71/31.41  | | | | | | | | | | |   (3077)   ~ (all_4_1 = e3)
% 194.71/31.41  | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | BETA: splitting (303) gives:
% 194.71/31.41  | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | |   (3078)  all_58_15 = e0
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (3078),
% 194.71/31.41  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.41  | | | | | | | | | | | |            #612.
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | Case 2:
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | |   (3079)   ~ (all_58_15 = e0)
% 194.71/31.41  | | | | | | | | | | | |   (3080)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.71/31.41  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.71/31.41  | | | | | | | | | | | |             e0)
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | ALPHA: (3080) implies:
% 194.71/31.41  | | | | | | | | | | | |   (3081)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.71/31.41  | | | | | | | | | | | |   (3082)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | REDUCE: (541), (3079) imply:
% 194.71/31.41  | | | | | | | | | | | |   (3083)   ~ (all_14_2 = e0)
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.71/31.41  | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | |   (3084)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.41  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.71/31.41  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.71/31.41  | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | BETA: splitting (3084) gives:
% 194.71/31.41  | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | |   (3085)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.41  | | | | | | | | | | | | | |           all_52_6 = e0
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | ALPHA: (3085) implies:
% 194.71/31.41  | | | | | | | | | | | | | |   (3086)  all_52_6 = e0
% 194.71/31.41  | | | | | | | | | | | | | |   (3087)  all_52_4 = e1
% 194.71/31.41  | | | | | | | | | | | | | |   (3088)  all_52_2 = e2
% 194.71/31.41  | | | | | | | | | | | | | |   (3089)  all_52_0 = e3
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | REDUCE: (185), (3088) imply:
% 194.71/31.41  | | | | | | | | | | | | | |   (3090)  op(all_52_3, all_52_3) = e2
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | REDUCE: (184), (3087) imply:
% 194.71/31.41  | | | | | | | | | | | | | |   (3091)  op(all_52_5, all_52_5) = e1
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | REDUCE: (183), (3086) imply:
% 194.71/31.41  | | | | | | | | | | | | | |   (3092)  op(all_52_7, all_52_7) = e0
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | REDUCE: (610), (3089) imply:
% 194.71/31.41  | | | | | | | | | | | | | |   (3093)  op(all_6_2, all_6_2) = e3
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.71/31.41  | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | Case 1:
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | |   (3094)  all_56_15 = e3
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (3094) imply:
% 194.71/31.41  | | | | | | | | | | | | | | |   (3095)  all_14_2 = e3
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | | SIMP: (3095) implies:
% 194.71/31.41  | | | | | | | | | | | | | | |   (3096)  all_14_2 = e3
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (41), (42), (43), (51),
% 194.71/31.41  | | | | | | | | | | | | | | |            (53), (61), (156), (161), (273), (277), (279),
% 194.71/31.41  | | | | | | | | | | | | | | |            (304), (305), (310), (317), (319), (321), (328),
% 194.71/31.41  | | | | | | | | | | | | | | |            (330), (332), (333), (351), (367), (372), (375),
% 194.71/31.41  | | | | | | | | | | | | | | |            (387), (393), (405), (417), (431), (541), (542),
% 194.71/31.41  | | | | | | | | | | | | | | |            (546), (547), (548), (551), (553), (555), (559),
% 194.71/31.41  | | | | | | | | | | | | | | |            (562), (564), (565), (567), (568), (569), (573),
% 194.71/31.41  | | | | | | | | | | | | | | |            (596), (597), (600), (608), (773), (3071), (3081),
% 194.71/31.41  | | | | | | | | | | | | | | |            (3083), (3090), (3091), (3092), (3093), (3096),
% 194.71/31.41  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.41  | | | | | | | | | | | | | | |            #584.
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | Case 2:
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.41  | | | | | | | | | | | | | | |   (3097)   ~ (all_56_15 = e3)
% 194.71/31.41  | | | | | | | | | | | | | | |   (3098)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 194.71/31.41  | | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | | | REDUCE: (538), (3097) imply:
% 194.71/31.42  | | | | | | | | | | | | | | |   (3099)   ~ (all_14_2 = e3)
% 194.71/31.42  | | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 194.71/31.42  | | | | | | | | | | | | | | |            (51), (61), (157), (161), (169), (175), (180),
% 194.71/31.42  | | | | | | | | | | | | | | |            (182), (272), (273), (280), (281), (284), (304),
% 194.71/31.42  | | | | | | | | | | | | | | |            (305), (306), (319), (320), (321), (324), (325),
% 194.71/31.42  | | | | | | | | | | | | | | |            (330), (332), (346), (351), (366), (387), (394),
% 194.71/31.42  | | | | | | | | | | | | | | |            (405), (411), (431), (538), (539), (541), (542),
% 194.71/31.42  | | | | | | | | | | | | | | |            (543), (547), (548), (549), (551), (555), (557),
% 194.71/31.42  | | | | | | | | | | | | | | |            (562), (563), (564), (569), (571), (572), (573),
% 194.71/31.42  | | | | | | | | | | | | | | |            (574), (576), (582), (590), (591), (600), (613),
% 194.71/31.42  | | | | | | | | | | | | | | |            (772), (3073), (3077), (3081), (3083), (3090),
% 194.71/31.42  | | | | | | | | | | | | | | |            (3091), (3092), (3093), (3098), (3099),
% 194.71/31.42  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.42  | | | | | | | | | | | | | | |            #1145.
% 194.71/31.42  | | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | | End of split
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | Case 2:
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | |   (3100)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.71/31.42  | | | | | | | | | | | | | |           all_52_14 = e0
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 194.71/31.42  | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 194.71/31.42  | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 194.71/31.42  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 194.71/31.42  | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 194.71/31.42  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 194.71/31.42  | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 194.71/31.42  | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 194.71/31.42  | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 194.71/31.42  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.71/31.42  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.71/31.42  | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 194.71/31.42  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.71/31.42  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 194.71/31.42  | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 194.71/31.42  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 194.71/31.42  | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 194.71/31.42  | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 194.71/31.42  | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 194.71/31.42  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 194.71/31.42  | | | | | | | | | | | | | |            (773), (775), (778), (3075), (3081), (3082),
% 194.71/31.42  | | | | | | | | | | | | | |            (3083), (3100), (function-axioms) are inconsistent
% 194.71/31.42  | | | | | | | | | | | | | |            by sub-proof #731.
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | End of split
% 194.71/31.42  | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | Case 2:
% 194.71/31.42  | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | |   (3101)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.71/31.42  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.71/31.42  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.71/31.42  | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | BETA: splitting (3101) gives:
% 194.71/31.42  | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | Case 1:
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | |   (3102)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.71/31.42  | | | | | | | | | | | | | |           all_52_22 = e0
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.71/31.42  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.71/31.42  | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.71/31.42  | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.71/31.42  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.71/31.42  | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.71/31.42  | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.71/31.42  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.71/31.42  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.71/31.42  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.71/31.42  | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.71/31.42  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.71/31.42  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.71/31.42  | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.71/31.42  | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.71/31.42  | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.71/31.42  | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.71/31.42  | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.71/31.42  | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (3075),
% 194.71/31.42  | | | | | | | | | | | | | |            (3081), (3082), (3102), (function-axioms) are
% 194.71/31.42  | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | Case 2:
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | |   (3103)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.71/31.42  | | | | | | | | | | | | | |           all_52_30 = e0
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.71/31.42  | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.71/31.42  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.71/31.42  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.71/31.42  | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.71/31.42  | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.71/31.42  | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.71/31.42  | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.71/31.42  | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.71/31.42  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.71/31.42  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.71/31.42  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.71/31.42  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.71/31.42  | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.71/31.42  | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.71/31.42  | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.71/31.42  | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.71/31.42  | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.71/31.42  | | | | | | | | | | | | | |            (775), (778), (3075), (3081), (3083), (3103),
% 194.71/31.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.42  | | | | | | | | | | | | | |            #1008.
% 194.71/31.42  | | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | | End of split
% 194.71/31.42  | | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | | End of split
% 194.71/31.42  | | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | End of split
% 194.71/31.42  | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | Case 2:
% 194.71/31.42  | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | |   (3104)  all_32_1 = e3
% 194.71/31.42  | | | | | | | | | | |   (3105)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 194.71/31.42  | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | COMBINE_EQS: (663), (3104) imply:
% 194.71/31.42  | | | | | | | | | | |   (3106)  all_4_1 = e3
% 194.71/31.42  | | | | | | | | | | | 
% 194.71/31.42  | | | | | | | | | | | SIMP: (3106) implies:
% 194.71/31.42  | | | | | | | | | | |   (3107)  all_4_1 = e3
% 194.71/31.42  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 194.71/31.43  | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (124), (158),
% 194.71/31.43  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 194.71/31.43  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 194.71/31.43  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 194.71/31.43  | | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 194.71/31.43  | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 194.71/31.43  | | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (314),
% 194.71/31.43  | | | | | | | | | | |            (315), (316), (317), (318), (319), (321), (323),
% 194.71/31.43  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 194.71/31.43  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 194.71/31.43  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.71/31.43  | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.71/31.43  | | | | | | | | | | |            (431), (523), (525), (538), (539), (540), (541),
% 194.71/31.43  | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.71/31.43  | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.71/31.43  | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 194.71/31.43  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 194.71/31.43  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 194.71/31.43  | | | | | | | | | | |            (587), (588), (590), (591), (592), (593), (594),
% 194.71/31.43  | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 194.71/31.43  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 194.71/31.43  | | | | | | | | | | |            (611), (612), (613), (686), (721), (766), (772),
% 194.71/31.43  | | | | | | | | | | |            (773), (775), (778), (2340), (3073), (3075),
% 194.71/31.43  | | | | | | | | | | |            (3105), (3107), (function-axioms) are inconsistent
% 194.71/31.43  | | | | | | | | | | |            by sub-proof #604.
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | End of split
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | Case 2:
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | |   (3108)  all_22_1 = e2
% 194.71/31.43  | | | | | | | | | |   (3109)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 194.71/31.43  | | | | | | | | | |            (53), (61), (63), (94), (158), (161), (162),
% 194.71/31.43  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 194.71/31.43  | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 194.71/31.43  | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 194.71/31.43  | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 194.71/31.43  | | | | | | | | | |            (303), (304), (306), (307), (308), (309), (311),
% 194.71/31.43  | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 194.71/31.43  | | | | | | | | | |            (325), (326), (327), (328), (329), (331), (332),
% 194.71/31.43  | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 194.71/31.43  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 194.71/31.43  | | | | | | | | | |            (411), (415), (431), (512), (522), (538), (539),
% 194.71/31.43  | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 194.71/31.43  | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 194.71/31.43  | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 194.71/31.43  | | | | | | | | | |            (567), (568), (569), (570), (572), (573), (574),
% 194.71/31.43  | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 194.71/31.43  | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 194.71/31.43  | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 194.71/31.43  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 194.71/31.43  | | | | | | | | | |            (612), (613), (658), (676), (739), (773), (775),
% 194.71/31.43  | | | | | | | | | |            (778), (2340), (3069), (3071), (3108), (3109),
% 194.71/31.43  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.43  | | | | | | | | | |            #582.
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | End of split
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | Case 2:
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | |   (3110)  all_20_0 = e3
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | COMBINE_EQS: (758), (3110) imply:
% 194.71/31.43  | | | | | | | | |   (3111)  all_4_0 = e3
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | SIMP: (3111) implies:
% 194.71/31.43  | | | | | | | | |   (3112)  all_4_0 = e3
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | REDUCE: (37), (3112) imply:
% 194.71/31.43  | | | | | | | | |   (3113)  op(e2, all_4_1) = e3
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | BETA: splitting (84) gives:
% 194.71/31.43  | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | Case 1:
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | |   (3114)   ~ (all_22_1 = e2)
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | REDUCE: (658), (3114) imply:
% 194.71/31.43  | | | | | | | | | |   (3115)   ~ (all_6_1 = e2)
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | BETA: splitting (303) gives:
% 194.71/31.43  | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | Case 1:
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | |   (3116)  all_58_15 = e0
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (2340), (3116),
% 194.71/31.43  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.43  | | | | | | | | | | |            #612.
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | Case 2:
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | |   (3117)   ~ (all_58_15 = e0)
% 194.71/31.43  | | | | | | | | | | |   (3118)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.71/31.43  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.71/31.43  | | | | | | | | | | |             e0)
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | ALPHA: (3118) implies:
% 194.71/31.43  | | | | | | | | | | |   (3119)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.71/31.43  | | | | | | | | | | |   (3120)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | REDUCE: (541), (3117) imply:
% 194.71/31.43  | | | | | | | | | | |   (3121)   ~ (all_14_2 = e0)
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | BETA: splitting (187) gives:
% 194.71/31.43  | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | Case 1:
% 194.71/31.43  | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | |   (3122)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.43  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.71/31.43  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.71/31.43  | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | BETA: splitting (3122) gives:
% 194.71/31.43  | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | Case 1:
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | |   (3123)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.43  | | | | | | | | | | | | |           all_52_6 = e0
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | ALPHA: (3123) implies:
% 194.71/31.43  | | | | | | | | | | | | |   (3124)  all_52_6 = e0
% 194.71/31.43  | | | | | | | | | | | | |   (3125)  all_52_4 = e1
% 194.71/31.43  | | | | | | | | | | | | |   (3126)  all_52_2 = e2
% 194.71/31.43  | | | | | | | | | | | | |   (3127)  all_52_0 = e3
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | REDUCE: (185), (3126) imply:
% 194.71/31.43  | | | | | | | | | | | | |   (3128)  op(all_52_3, all_52_3) = e2
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | REDUCE: (184), (3125) imply:
% 194.71/31.43  | | | | | | | | | | | | |   (3129)  op(all_52_5, all_52_5) = e1
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | REDUCE: (183), (3124) imply:
% 194.71/31.43  | | | | | | | | | | | | |   (3130)  op(all_52_7, all_52_7) = e0
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | REDUCE: (610), (3127) imply:
% 194.71/31.43  | | | | | | | | | | | | |   (3131)  op(all_6_2, all_6_2) = e3
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | BETA: splitting (270) gives:
% 194.71/31.43  | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | Case 1:
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | |   (3132)  all_56_15 = e3
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | COMBINE_EQS: (538), (3132) imply:
% 194.71/31.43  | | | | | | | | | | | | | |   (3133)  all_14_2 = e3
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (41), (42), (43), (51),
% 194.71/31.43  | | | | | | | | | | | | | |            (53), (61), (156), (161), (273), (277), (279),
% 194.71/31.43  | | | | | | | | | | | | | |            (304), (305), (310), (317), (319), (321), (328),
% 194.71/31.43  | | | | | | | | | | | | | |            (330), (332), (333), (351), (367), (372), (375),
% 194.71/31.43  | | | | | | | | | | | | | |            (387), (393), (405), (417), (431), (541), (542),
% 194.71/31.43  | | | | | | | | | | | | | |            (546), (547), (548), (551), (553), (555), (559),
% 194.71/31.43  | | | | | | | | | | | | | |            (562), (564), (565), (567), (568), (569), (573),
% 194.71/31.43  | | | | | | | | | | | | | |            (596), (597), (600), (608), (773), (3071), (3119),
% 194.71/31.43  | | | | | | | | | | | | | |            (3121), (3128), (3129), (3130), (3131), (3133),
% 194.71/31.43  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.43  | | | | | | | | | | | | | |            #584.
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | Case 2:
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | |   (3134)   ~ (all_56_15 = e3)
% 194.71/31.43  | | | | | | | | | | | | | |   (3135)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | REDUCE: (538), (3134) imply:
% 194.71/31.43  | | | | | | | | | | | | | |   (3136)   ~ (all_14_2 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.71/31.43  | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | Case 1:
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | |   (3137)  all_56_13 = e3
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | COMBINE_EQS: (346), (3137) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3138)  all_52_15 = e3
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3139)  all_58_13 = e3
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (571), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3140)   ~ (all_52_7 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (576), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3141)   ~ (all_52_9 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (587), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3142)   ~ (all_52_13 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (590), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3143)   ~ (all_52_23 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | SIMP: (3143) implies:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3144)   ~ (all_52_23 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (591), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3145)   ~ (all_14_2 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (582), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3146)   ~ (all_4_2 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | SIMP: (3146) implies:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3147)   ~ (all_4_2 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (179), (3138) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3148)  op(e3, e3) = all_52_14
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.71/31.43  | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (3148)
% 194.71/31.43  | | | | | | | | | | | | | | |              gives:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3149)  all_52_14 = all_6_2
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 194.71/31.43  | | | | | | | | | | | | | | |            (53), (61), (63), (159), (168), (172), (177),
% 194.71/31.43  | | | | | | | | | | | | | | |            (180), (182), (273), (274), (275), (276), (281),
% 194.71/31.43  | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 194.71/31.43  | | | | | | | | | | | | | | |            (311), (312), (313), (315), (317), (319), (320),
% 194.71/31.43  | | | | | | | | | | | | | | |            (321), (323), (324), (328), (330), (332), (333),
% 194.71/31.43  | | | | | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 194.71/31.43  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (421), (431), (541),
% 194.71/31.43  | | | | | | | | | | | | | | |            (542), (544), (545), (546), (547), (548), (549),
% 194.71/31.43  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 194.71/31.43  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (573),
% 194.71/31.43  | | | | | | | | | | | | | | |            (574), (575), (577), (578), (580), (588), (589),
% 194.71/31.43  | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (607), (608),
% 194.71/31.43  | | | | | | | | | | | | | | |            (612), (613), (773), (775), (2338), (3119),
% 194.71/31.43  | | | | | | | | | | | | | | |            (3128), (3129), (3130), (3131), (3136), (3139),
% 194.71/31.43  | | | | | | | | | | | | | | |            (3140), (3141), (3142), (3144), (3147),
% 194.71/31.43  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.43  | | | | | | | | | | | | | | |            #581.
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | Case 2:
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | |   (3150)   ~ (all_56_13 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.43  | | | | | | | | | | | | | | | REDUCE: (346), (3150) imply:
% 194.71/31.43  | | | | | | | | | | | | | | |   (3151)   ~ (all_52_15 = e3)
% 194.71/31.43  | | | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 194.71/31.44  | | | | | | | | | | | | | | |            (53), (61), (63), (158), (163), (169), (175),
% 194.71/31.44  | | | | | | | | | | | | | | |            (182), (273), (276), (277), (280), (281), (283),
% 194.71/31.44  | | | | | | | | | | | | | | |            (284), (304), (305), (306), (311), (312), (313),
% 194.71/31.44  | | | | | | | | | | | | | | |            (314), (319), (320), (321), (328), (331), (332),
% 194.71/31.44  | | | | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (393),
% 194.71/31.44  | | | | | | | | | | | | | | |            (394), (405), (411), (415), (421), (431), (538),
% 194.71/31.44  | | | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 194.71/31.44  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 194.71/31.44  | | | | | | | | | | | | | | |            (559), (563), (564), (565), (566), (568), (569),
% 194.71/31.44  | | | | | | | | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 194.71/31.44  | | | | | | | | | | | | | | |            (588), (589), (593), (594), (595), (596), (597),
% 194.71/31.44  | | | | | | | | | | | | | | |            (600), (605), (606), (607), (608), (609), (612),
% 194.71/31.44  | | | | | | | | | | | | | | |            (613), (772), (773), (2340), (3113), (3120),
% 194.71/31.44  | | | | | | | | | | | | | | |            (3121), (3128), (3129), (3130), (3131), (3135),
% 194.71/31.44  | | | | | | | | | | | | | | |            (3136), (3151), (function-axioms) are inconsistent
% 194.71/31.44  | | | | | | | | | | | | | | |            by sub-proof #579.
% 194.71/31.44  | | | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | Case 2:
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | |   (3152)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.71/31.44  | | | | | | | | | | | | |           all_52_14 = e0
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 194.71/31.44  | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 194.71/31.44  | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 194.71/31.44  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 194.71/31.44  | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 194.71/31.44  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 194.71/31.44  | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 194.71/31.44  | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 194.71/31.44  | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 194.71/31.44  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.71/31.44  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.71/31.44  | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 194.71/31.44  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.71/31.44  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 194.71/31.44  | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 194.71/31.44  | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 194.71/31.44  | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 194.71/31.44  | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 194.71/31.44  | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 194.71/31.44  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 194.71/31.44  | | | | | | | | | | | | |            (773), (775), (778), (3115), (3119), (3120),
% 194.71/31.44  | | | | | | | | | | | | |            (3121), (3152), (function-axioms) are inconsistent
% 194.71/31.44  | | | | | | | | | | | | |            by sub-proof #731.
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | Case 2:
% 194.71/31.44  | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | |   (3153)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.71/31.44  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.71/31.44  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.71/31.44  | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | BETA: splitting (3153) gives:
% 194.71/31.44  | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | Case 1:
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | |   (3154)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.71/31.44  | | | | | | | | | | | | |           all_52_22 = e0
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.71/31.44  | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.71/31.44  | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 194.71/31.44  | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 194.71/31.44  | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 194.71/31.44  | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 194.71/31.44  | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 194.71/31.44  | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 194.71/31.44  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 194.71/31.44  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 194.71/31.44  | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 194.71/31.44  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 194.71/31.44  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 194.71/31.44  | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 194.71/31.44  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 194.71/31.44  | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 194.71/31.44  | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 194.71/31.44  | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 194.71/31.44  | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (778), (3115),
% 194.71/31.44  | | | | | | | | | | | | |            (3119), (3120), (3154), (function-axioms) are
% 194.71/31.44  | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | Case 2:
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | |   (3155)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.71/31.44  | | | | | | | | | | | | |           all_52_30 = e0
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.71/31.44  | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.71/31.44  | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.71/31.44  | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.71/31.44  | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.71/31.44  | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.71/31.44  | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.71/31.44  | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.71/31.44  | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.71/31.44  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.71/31.44  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.71/31.44  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.71/31.44  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.71/31.44  | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.71/31.44  | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.71/31.44  | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.71/31.44  | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.71/31.44  | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.71/31.44  | | | | | | | | | | | | |            (775), (778), (3115), (3119), (3121), (3155),
% 194.71/31.44  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.44  | | | | | | | | | | | | |            #1008.
% 194.71/31.44  | | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | Case 2:
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | |   (3156)  all_22_1 = e2
% 194.71/31.44  | | | | | | | | | |   (3157)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | COMBINE_EQS: (658), (3156) imply:
% 194.71/31.44  | | | | | | | | | |   (3158)  all_6_1 = e2
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | REDUCE: (43), (3158) imply:
% 194.71/31.44  | | | | | | | | | |   (3159)  op(all_6_2, e3) = e2
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | REDUCE: (42), (3158) imply:
% 194.71/31.44  | | | | | | | | | |   (3160)  op(e3, e2) = all_6_0
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 194.71/31.44  | | | | | | | | | |            (53), (61), (63), (94), (158), (161), (162),
% 194.71/31.44  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 194.71/31.44  | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 194.71/31.44  | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 194.71/31.44  | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 194.71/31.44  | | | | | | | | | |            (303), (304), (306), (307), (308), (309), (311),
% 194.71/31.44  | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 194.71/31.44  | | | | | | | | | |            (325), (326), (327), (328), (329), (331), (332),
% 194.71/31.44  | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 194.71/31.44  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 194.71/31.44  | | | | | | | | | |            (411), (415), (431), (512), (522), (538), (539),
% 194.71/31.44  | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 194.71/31.44  | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 194.71/31.44  | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 194.71/31.44  | | | | | | | | | |            (567), (568), (569), (570), (572), (573), (574),
% 194.71/31.44  | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 194.71/31.44  | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 194.71/31.44  | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 194.71/31.44  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 194.71/31.44  | | | | | | | | | |            (612), (613), (676), (739), (773), (775), (2340),
% 194.71/31.44  | | | | | | | | | |            (3069), (3071), (3157), (3159), (3160),
% 194.71/31.44  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.44  | | | | | | | | | |            #583.
% 194.71/31.44  | | | | | | | | | | 
% 194.71/31.44  | | | | | | | | | End of split
% 194.71/31.44  | | | | | | | | | 
% 194.71/31.45  | | | | | | | | End of split
% 194.71/31.45  | | | | | | | | 
% 194.71/31.45  | | | | | | | End of split
% 194.71/31.45  | | | | | | | 
% 194.71/31.45  | | | | | | End of split
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | Case 2:
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | |   (3161)  all_12_1 = e1
% 194.71/31.45  | | | | | |   (3162)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | COMBINE_EQS: (683), (3161) imply:
% 194.71/31.45  | | | | | |   (3163)  all_6_1 = e1
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | SIMP: (3163) implies:
% 194.71/31.45  | | | | | |   (3164)  all_6_1 = e1
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | REDUCE: (43), (3164) imply:
% 194.71/31.45  | | | | | |   (3165)  op(all_6_2, e3) = e1
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | REDUCE: (42), (3164) imply:
% 194.71/31.45  | | | | | |   (3166)  op(e3, e1) = all_6_0
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | REF_CLOSE: (5), (6), (7), (8), (36), (38), (41), (51), (61), (62),
% 194.71/31.45  | | | | | |            (63), (64), (74), (153), (156), (158), (162), (166),
% 194.71/31.45  | | | | | |            (167), (168), (169), (172), (173), (174), (175), (178),
% 194.71/31.45  | | | | | |            (179), (180), (182), (183), (184), (185), (187), (270),
% 194.71/31.45  | | | | | |            (273), (276), (277), (278), (281), (282), (283), (284),
% 194.71/31.45  | | | | | |            (285), (303), (305), (306), (307), (308), (309), (313),
% 194.71/31.45  | | | | | |            (317), (321), (323), (325), (329), (331), (332), (333),
% 194.71/31.45  | | | | | |            (335), (351), (366), (367), (372), (375), (387), (388),
% 194.71/31.45  | | | | | |            (393), (394), (405), (411), (415), (421), (427), (431),
% 194.71/31.45  | | | | | |            (483), (538), (540), (541), (542), (543), (544), (545),
% 194.71/31.45  | | | | | |            (546), (547), (548), (549), (551), (553), (555), (557),
% 194.71/31.45  | | | | | |            (559), (561), (562), (563), (564), (567), (568), (569),
% 194.71/31.45  | | | | | |            (570), (571), (573), (574), (575), (576), (577), (578),
% 194.71/31.45  | | | | | |            (580), (582), (587), (588), (589), (590), (591), (592),
% 194.71/31.45  | | | | | |            (593), (594), (595), (598), (603), (604), (605), (606),
% 194.71/31.45  | | | | | |            (607), (608), (609), (610), (611), (613), (690), (761),
% 194.71/31.45  | | | | | |            (763), (771), (772), (773), (775), (3162), (3165),
% 194.71/31.45  | | | | | |            (3166), (function-axioms) are inconsistent by sub-proof
% 194.71/31.45  | | | | | |            #552.
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | End of split
% 194.71/31.45  | | | | | 
% 194.71/31.45  | | | | Case 2:
% 194.71/31.45  | | | | | 
% 194.71/31.45  | | | | |   (3167)  all_10_0 = e3
% 194.71/31.45  | | | | |   (3168)   ~ (all_10_1 = e0) |  ~ (all_10_2 = e2)
% 194.71/31.45  | | | | | 
% 194.71/31.45  | | | | | COMBINE_EQS: (717), (3167) imply:
% 194.71/31.45  | | | | |   (3169)  all_36_0 = e3
% 194.71/31.45  | | | | | 
% 194.71/31.45  | | | | | REDUCE: (52), (3167) imply:
% 194.71/31.45  | | | | |   (3170)  op(e1, all_10_1) = e3
% 194.71/31.45  | | | | | 
% 194.71/31.45  | | | | | BETA: splitting (59) gives:
% 194.71/31.45  | | | | | 
% 194.71/31.45  | | | | | Case 1:
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | |   (3171)   ~ (all_12_1 = e1)
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | REDUCE: (683), (3171) imply:
% 194.71/31.45  | | | | | |   (3172)   ~ (all_6_1 = e1)
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | BETA: splitting (64) gives:
% 194.71/31.45  | | | | | | 
% 194.71/31.45  | | | | | | Case 1:
% 194.71/31.45  | | | | | | | 
% 194.71/31.45  | | | | | | |   (3173)   ~ (all_14_0 = e2)
% 194.71/31.45  | | | | | | | 
% 194.71/31.45  | | | | | | | BETA: splitting (74) gives:
% 194.71/31.45  | | | | | | | 
% 194.71/31.45  | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | 
% 194.71/31.45  | | | | | | | |   (3174)   ~ (all_18_0 = e3)
% 194.71/31.45  | | | | | | | | 
% 194.71/31.45  | | | | | | | | REDUCE: (761), (3174) imply:
% 194.71/31.45  | | | | | | | |   (3175)   ~ (all_14_0 = e3)
% 194.71/31.45  | | | | | | | | 
% 194.71/31.45  | | | | | | | | BETA: splitting (79) gives:
% 194.71/31.45  | | | | | | | | 
% 194.71/31.45  | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | 
% 194.71/31.45  | | | | | | | | |   (3176)   ~ (all_20_0 = e3)
% 194.71/31.45  | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | REDUCE: (758), (3176) imply:
% 194.71/31.45  | | | | | | | | |   (3177)   ~ (all_4_0 = e3)
% 194.71/31.45  | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | BETA: splitting (84) gives:
% 194.71/31.45  | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | |   (3178)   ~ (all_22_1 = e2)
% 194.71/31.45  | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | REDUCE: (658), (3178) imply:
% 194.71/31.45  | | | | | | | | | |   (3179)   ~ (all_6_1 = e2)
% 194.71/31.45  | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | BETA: splitting (89) gives:
% 194.71/31.45  | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | |   (3180)   ~ (all_24_0 = e1)
% 194.71/31.45  | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | REDUCE: (711), (3180) imply:
% 194.71/31.45  | | | | | | | | | | |   (3181)   ~ (all_14_0 = e1)
% 194.71/31.45  | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | BETA: splitting (109) gives:
% 194.71/31.45  | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | |   (3182)   ~ (all_32_1 = e3)
% 194.71/31.45  | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | REDUCE: (663), (3182) imply:
% 194.71/31.45  | | | | | | | | | | | |   (3183)   ~ (all_4_1 = e3)
% 194.71/31.45  | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | BETA: splitting (119) gives:
% 194.71/31.45  | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | |   (3184)   ~ (all_36_0 = e3)
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | REDUCE: (3169), (3184) imply:
% 194.71/31.45  | | | | | | | | | | | | |   (3185)  $false
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | CLOSE: (3185) is inconsistent.
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | Case 2:
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | |   (3186)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.71/31.45  | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | |   (3187)  all_58_15 = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | COMBINE_EQS: (541), (3187) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3188)  all_14_2 = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (573), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3189)   ~ (all_52_7 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (591), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3190)   ~ (all_52_15 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (603), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3191)   ~ (all_52_23 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (606), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3192)   ~ (all_52_25 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (608), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3193)   ~ (all_52_27 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (609), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3194)   ~ (all_52_29 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (613), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3195)  op(e0, e0) = all_52_30
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (63), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3196)  op(e0, e0) = all_14_1
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (61), (3188) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3197)  op(e0, e0) = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 194.71/31.45  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3195), (3196)
% 194.71/31.45  | | | | | | | | | | | | | |              gives:
% 194.71/31.45  | | | | | | | | | | | | | |   (3198)  all_52_30 = all_14_1
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 194.71/31.45  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3195), (3197)
% 194.71/31.45  | | | | | | | | | | | | | |              gives:
% 194.71/31.45  | | | | | | | | | | | | | |   (3199)  all_52_30 = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | COMBINE_EQS: (3198), (3199) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3200)  all_14_1 = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | SIMP: (3200) implies:
% 194.71/31.45  | | | | | | | | | | | | | |   (3201)  all_14_1 = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (62), (3201) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3202)  op(e0, e0) = all_14_0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 194.71/31.45  | | | | | | | | | | | | | |              e0, e0, simplifying with (3197), (3202) gives:
% 194.71/31.45  | | | | | | | | | | | | | |   (3203)  all_14_0 = e0
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (3175), (3203) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3204)   ~ (e3 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (3173), (3203) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3205)   ~ (e2 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | REDUCE: (3181), (3203) imply:
% 194.71/31.45  | | | | | | | | | | | | | |   (3206)   ~ (e1 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.71/31.45  | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | |   (3207)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.45  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.71/31.45  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | BETA: splitting (3207) gives:
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3208)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.45  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | ALPHA: (3208) implies:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3209)  all_52_6 = e0
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3210)  all_52_4 = e1
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3211)  all_52_2 = e2
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3212)  all_52_0 = e3
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (185), (3211) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3213)  op(all_52_3, all_52_3) = e2
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (184), (3210) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3214)  op(all_52_5, all_52_5) = e1
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (183), (3209) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3215)  op(all_52_7, all_52_7) = e0
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (610), (3212) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3216)  op(all_6_2, all_6_2) = e3
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (51), (53),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (61), (156), (157), (162), (175), (272), (273),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (304), (305), (306), (321), (332), (346), (351),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (387), (405), (431), (524), (542), (543), (547),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (555), (564), (569), (571), (572), (573), (645),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (772), (3170), (3183), (3186), (3187), (3189),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (3190), (3213), (3214), (3215), (3216),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.45  | | | | | | | | | | | | | | | |            #547.
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | Case 2:
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3217)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.71/31.45  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | ALPHA: (3217) implies:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3218)  all_52_14 = e0
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3219)  all_52_12 = e1
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3220)  all_52_10 = e2
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3221)  all_52_8 = e3
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (182), (3221) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3222)  op(all_52_9, all_52_9) = e3
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (180), (3219) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3223)  op(all_52_13, all_52_13) = e1
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (179), (3218) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3224)  op(all_52_15, all_52_15) = e0
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (611), (3220) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3225)  op(all_4_2, all_4_2) = e2
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (36), (38), (41), (43), (51), (53),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (178), (183), (272), (273), (276), (277), (278),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (304), (305),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (306), (309), (313), (314), (317), (322), (324),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (325), (327), (333), (346), (351), (366), (367),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (411),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (415), (421), (427), (431), (539), (542), (543),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (564), (567), (568), (571), (572), (574), (575),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (588), (589), (595), (604), (605), (612), (772),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (3170), (3172), (3179), (3187), (3189), (3190),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (3192), (3197), (3222), (3223), (3224), (3225),
% 194.71/31.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.45  | | | | | | | | | | | | | | | |            #544.
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | End of split
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | Case 2:
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | |   (3226)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.71/31.45  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.71/31.45  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | BETA: splitting (3226) gives:
% 194.71/31.45  | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | Case 1:
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3227)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.71/31.45  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | ALPHA: (3227) implies:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3228)  all_52_22 = e0
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3229)  all_52_20 = e1
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3230)  all_52_18 = e2
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3231)  all_52_16 = e3
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (178), (3231) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3232)  op(all_52_17, all_52_17) = e3
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (177), (3230) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3233)  op(all_52_19, all_52_19) = e2
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (175), (3228) imply:
% 194.71/31.45  | | | | | | | | | | | | | | | |   (3234)  op(all_52_23, all_52_23) = e0
% 194.71/31.45  | | | | | | | | | | | | | | | | 
% 194.71/31.45  | | | | | | | | | | | | | | | | REDUCE: (612), (3229) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3235)  op(all_10_2, all_10_2) = e1
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (36), (38), (41), (43), (51), (53),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (157), (158), (162), (168), (169), (172), (173),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (174), (180), (182), (183), (271), (272), (273),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (277), (278), (280), (282), (283), (284), (304),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (306), (309), (313), (317), (322), (325), (331),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (366), (367), (372),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (375), (388), (393), (394), (405), (415), (427),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (431), (539), (542), (543), (544), (545), (546),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (559),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (561), (567), (568), (569), (571), (572), (577),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (578), (580), (584), (588), (589), (590), (593),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (604),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (605), (611), (3172), (3179), (3183), (3187),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3189), (3190), (3191), (3192), (3197), (3232),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3233), (3234), (3235), (function-axioms) are
% 194.71/31.46  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1249.
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | Case 2:
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3236)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.71/31.46  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | ALPHA: (3236) implies:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3237)  all_52_28 = e1
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3238)  all_52_26 = e2
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3239)  all_52_24 = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (174), (3239) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3240)  op(all_52_25, all_52_25) = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (173), (3238) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3241)  op(all_52_27, all_52_27) = e2
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (172), (3237) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3242)  op(all_52_29, all_52_29) = e1
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (175),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (179), (183), (272), (273), (274), (278), (281),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (282), (304), (305), (306), (307), (308), (309),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (313), (318), (321), (326), (330), (332), (333),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (346), (351), (352), (366), (372), (375), (387),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (388), (393), (405), (411), (427), (431), (542),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (551), (553), (555), (561), (563), (564), (567),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (569), (570), (571), (572), (576), (582), (587),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (588), (593), (595), (596), (600), (602), (604),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (605), (608), (610), (773), (775), (3179), (3187),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3189), (3190), (3191), (3192), (3193), (3194),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3240), (3241), (3242), (function-axioms) are
% 194.71/31.46  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | End of split
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | End of split
% 194.71/31.46  | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | Case 2:
% 194.71/31.46  | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | |   (3243)   ~ (all_58_15 = e0)
% 194.71/31.46  | | | | | | | | | | | | | |   (3244)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.71/31.46  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.71/31.46  | | | | | | | | | | | | | |             e0)
% 194.71/31.46  | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | ALPHA: (3244) implies:
% 194.71/31.46  | | | | | | | | | | | | | |   (3245)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.71/31.46  | | | | | | | | | | | | | |   (3246)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.71/31.46  | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | REDUCE: (541), (3243) imply:
% 194.71/31.46  | | | | | | | | | | | | | |   (3247)   ~ (all_14_2 = e0)
% 194.71/31.46  | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.71/31.46  | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | Case 1:
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | |   (3248)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.46  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.71/31.46  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | BETA: splitting (3248) gives:
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | Case 1:
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3249)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.46  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | ALPHA: (3249) implies:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3250)  all_52_6 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3251)  all_52_4 = e1
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3252)  all_52_2 = e2
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3253)  all_52_0 = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (185), (3252) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3254)  op(all_52_3, all_52_3) = e2
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (184), (3251) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3255)  op(all_52_5, all_52_5) = e1
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (183), (3250) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3256)  op(all_52_7, all_52_7) = e0
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (610), (3253) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3257)  op(all_6_2, all_6_2) = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (62), (63), (156),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (157), (161), (167), (169), (174), (175), (180),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (182), (270), (271), (272), (273), (275), (280),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (281), (282), (284), (304), (305), (306), (307),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (308), (312), (313), (317), (319), (320), (321),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (323), (324), (325), (327), (330), (332), (333),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (343), (346), (351), (361), (366), (372), (375),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (431),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (524), (538), (539), (541), (542), (543), (544),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (567), (569), (571), (572), (573), (574), (576),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (578), (580), (582), (588), (590), (591), (593),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (596), (597), (600), (603), (604), (605), (606),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (608), (609), (611), (612), (613), (645), (772),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (773), (3175), (3177), (3183), (3186), (3245),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3247), (3254), (3255), (3256), (3257),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.46  | | | | | | | | | | | | | | | |            #537.
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | Case 2:
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3258)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.71/31.46  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | ALPHA: (3258) implies:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3259)  all_52_14 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3260)  all_52_12 = e1
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3261)  all_52_10 = e2
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3262)  all_52_8 = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (182), (3262) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3263)  op(all_52_9, all_52_9) = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (180), (3260) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3264)  op(all_52_13, all_52_13) = e1
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (179), (3259) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3265)  op(all_52_15, all_52_15) = e0
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (611), (3261) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3266)  op(all_4_2, all_4_2) = e2
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (177), (178), (183), (184), (185), (270), (272),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (280),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (281), (282), (284), (304), (306), (309), (313),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (421), (427), (431),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (538), (539), (541), (542), (543), (544), (545),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (567), (568), (570), (571), (572), (573), (574),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (575), (577), (578), (580), (584), (586), (588),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (597), (603), (604), (605), (606), (607), (608),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (609), (610), (612), (613), (772), (773), (775),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3172), (3179), (3183), (3245), (3246), (3247),
% 194.71/31.46  | | | | | | | | | | | | | | | |            (3263), (3264), (3265), (3266), (function-axioms)
% 194.71/31.46  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1092.
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | End of split
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | Case 2:
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | |   (3267)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.71/31.46  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.71/31.46  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | BETA: splitting (3267) gives:
% 194.71/31.46  | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | Case 1:
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3268)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.71/31.46  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | ALPHA: (3268) implies:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3269)  all_52_22 = e0
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3270)  all_52_20 = e1
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3271)  all_52_18 = e2
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3272)  all_52_16 = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (178), (3272) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3273)  op(all_52_17, all_52_17) = e3
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (177), (3271) imply:
% 194.71/31.46  | | | | | | | | | | | | | | | |   (3274)  op(all_52_19, all_52_19) = e2
% 194.71/31.46  | | | | | | | | | | | | | | | | 
% 194.71/31.46  | | | | | | | | | | | | | | | | REDUCE: (175), (3269) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | |   (3275)  op(all_52_23, all_52_23) = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | REDUCE: (612), (3270) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | |   (3276)  op(all_10_2, all_10_2) = e1
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (180), (182),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (183), (184), (185), (270), (272), (273), (274),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (275), (276), (277), (279), (281), (282), (283),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (284), (285), (304), (306), (313), (315), (317),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (329),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (431), (538), (540), (541), (542), (543), (544),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (565), (566), (567), (569), (570), (571), (572),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (602), (603), (605),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (606), (608), (609), (610), (611), (613), (773),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (775), (3172), (3179), (3245), (3246), (3273),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (3274), (3275), (3276), (function-axioms) are
% 194.71/31.47  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | Case 2:
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | |   (3277)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.71/31.47  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (775), (3172), (3179), (3245), (3247), (3277),
% 194.71/31.47  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.47  | | | | | | | | | | | | | | | |            #1008.
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | End of split
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | End of split
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | End of split
% 194.71/31.47  | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | End of split
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | Case 2:
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | |   (3278)  all_32_1 = e3
% 194.71/31.47  | | | | | | | | | | | |   (3279)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | COMBINE_EQS: (663), (3278) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3280)  all_4_1 = e3
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | SIMP: (3280) implies:
% 194.71/31.47  | | | | | | | | | | | |   (3281)  all_4_1 = e3
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | COMBINE_EQS: (686), (3281) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3282)  all_38_1 = e3
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (38), (3281) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3283)  op(all_4_2, e2) = e3
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (37), (3281) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3284)  op(e2, e3) = all_4_0
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 194.71/31.47  | | | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (3284)
% 194.71/31.47  | | | | | | | | | | | |              gives:
% 194.71/31.47  | | | | | | | | | | | |   (3285)  all_52_3 = all_4_0
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | COMBINE_EQS: (411), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3286)  all_56_4 = all_4_0
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | COMBINE_EQS: (387), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3287)  all_58_2 = all_4_0
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (562), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3288)   ~ (all_52_5 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | SIMP: (3288) implies:
% 194.71/31.47  | | | | | | | | | | | |   (3289)   ~ (all_52_5 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (563), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3290)   ~ (all_52_7 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | SIMP: (3290) implies:
% 194.71/31.47  | | | | | | | | | | | |   (3291)   ~ (all_52_7 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (565), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3292)   ~ (all_52_19 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | SIMP: (3292) implies:
% 194.71/31.47  | | | | | | | | | | | |   (3293)   ~ (all_52_19 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (566), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3294)   ~ (all_52_27 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | SIMP: (3294) implies:
% 194.71/31.47  | | | | | | | | | | | |   (3295)   ~ (all_52_27 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (551), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3296)   ~ (all_6_2 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | SIMP: (3296) implies:
% 194.71/31.47  | | | | | | | | | | | |   (3297)   ~ (all_6_2 = all_4_0)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (564), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3298)   ~ (all_4_0 = all_4_2)
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | REDUCE: (185), (3285) imply:
% 194.71/31.47  | | | | | | | | | | | |   (3299)  op(all_4_0, all_4_0) = all_52_2
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | BETA: splitting (124) gives:
% 194.71/31.47  | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | |   (3300)   ~ (all_38_0 = e1)
% 194.71/31.47  | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | REDUCE: (766), (3300) imply:
% 194.71/31.47  | | | | | | | | | | | | |   (3301)   ~ (all_4_0 = e1)
% 194.71/31.47  | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 194.71/31.47  | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | |   (3302)  all_58_15 = e0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | COMBINE_EQS: (541), (3302) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3303)  all_14_2 = e0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (573), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3304)   ~ (all_52_7 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (591), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3305)   ~ (all_52_15 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (603), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3306)   ~ (all_52_23 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (606), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3307)   ~ (all_52_25 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (608), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3308)   ~ (all_52_27 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (609), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3309)   ~ (all_52_29 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (613), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3310)  op(e0, e0) = all_52_30
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (63), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3311)  op(e0, e0) = all_14_1
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (61), (3303) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3312)  op(e0, e0) = e0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 194.71/31.47  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3310), (3311)
% 194.71/31.47  | | | | | | | | | | | | | |              gives:
% 194.71/31.47  | | | | | | | | | | | | | |   (3313)  all_52_30 = all_14_1
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 194.71/31.47  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3310), (3312)
% 194.71/31.47  | | | | | | | | | | | | | |              gives:
% 194.71/31.47  | | | | | | | | | | | | | |   (3314)  all_52_30 = e0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | COMBINE_EQS: (3313), (3314) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3315)  all_14_1 = e0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (62), (3315) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3316)  op(e0, e0) = all_14_0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 194.71/31.47  | | | | | | | | | | | | | |              e0, e0, simplifying with (3312), (3316) gives:
% 194.71/31.47  | | | | | | | | | | | | | |   (3317)  all_14_0 = e0
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (3175), (3317) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3318)   ~ (e3 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (3173), (3317) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3319)   ~ (e2 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | REDUCE: (3181), (3317) imply:
% 194.71/31.47  | | | | | | | | | | | | | |   (3320)   ~ (e1 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 194.71/31.47  | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | |   (3321)  all_56_4 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | REF_CLOSE: (3177), (3286), (3321) are inconsistent by
% 194.71/31.47  | | | | | | | | | | | | | | |            sub-proof #980.
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | Case 2:
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | |   (3322)   ~ (all_56_4 = e3)
% 194.71/31.47  | | | | | | | | | | | | | | |   (3323)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 194.71/31.47  | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | |   (3324)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.47  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 194.71/31.47  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | BETA: splitting (3324) gives:
% 194.71/31.47  | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3325)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 194.71/31.47  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | ALPHA: (3325) implies:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3326)  all_52_6 = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3327)  all_52_4 = e1
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3328)  all_52_0 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (184), (3327) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3329)  op(all_52_5, all_52_5) = e1
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (183), (3326) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3330)  op(all_52_7, all_52_7) = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (610), (3328) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3331)  op(all_6_2, all_6_2) = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (43), (51), (162), (167), (169), (172), (173),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (174), (273), (277), (278), (280), (282), (304),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (306), (307), (308), (309), (312), (326), (328),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (330), (332), (351), (367), (372), (388), (405),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (427), (431), (523), (539), (544), (545), (547),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (555), (561), (567), (569), (570), (574), (604),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (605), (607), (611), (721), (775), (3177), (3179),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (3279), (3283), (3286), (3287), (3289), (3291),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (3295), (3297), (3298), (3301), (3302), (3304),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (3307), (3308), (3309), (3323), (3329), (3330),
% 194.71/31.47  | | | | | | | | | | | | | | | | |            (3331), (function-axioms) are inconsistent by
% 194.71/31.47  | | | | | | | | | | | | | | | | |            sub-proof #638.
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3332)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 194.71/31.47  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | ALPHA: (3332) implies:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3333)  all_52_14 = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3334)  all_52_12 = e1
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3335)  all_52_10 = e2
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3336)  all_52_8 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (182), (3336) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3337)  op(all_52_9, all_52_9) = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (180), (3334) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3338)  op(all_52_13, all_52_13) = e1
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (179), (3333) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3339)  op(all_52_15, all_52_15) = e0
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | REDUCE: (611), (3335) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | |   (3340)  op(all_4_2, all_4_2) = e2
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 194.71/31.47  | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3341)  all_56_7 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (3341) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3342)  all_52_27 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | SIMP: (3342) implies:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3343)  all_52_27 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | REDUCE: (604), (3343) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3344)   ~ (all_52_25 = e3)
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | REDUCE: (586), (3343) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3345)   ~ (all_4_2 = e3)
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | SIMP: (3345) implies:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3346)   ~ (all_4_2 = e3)
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | REDUCE: (173), (3343) imply:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3347)  op(e3, e3) = all_52_26
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.71/31.47  | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (41), (3347)
% 194.71/31.47  | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.47  | | | | | | | | | | | | | | | | | |   (3348)  all_52_26 = all_6_2
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 194.71/31.47  | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.47  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | |   (3349)  all_56_3 = e3
% 194.71/31.47  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (3344), (3349) are inconsistent by
% 194.71/31.47  | | | | | | | | | | | | | | | | | | |            sub-proof #1339.
% 194.71/31.47  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.47  | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.47  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | |   (3350)   ~ (all_56_3 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | |   (3351)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3352)  all_58_9 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3352) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3353)  all_52_25 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | SIMP: (3353) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3354)  all_52_25 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (3354) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3355)   ~ (all_6_2 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | SIMP: (3355) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3356)   ~ (all_6_2 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (3344), (3354) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3357)   ~ (e3 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (3354) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3358)  op(e3, e0) = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (36), (41), (42), (43), (158),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (162), (169), (272), (273), (280), (325), (326),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (328), (330), (346), (351), (366), (405), (431),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (523), (539), (543), (547), (548), (549), (555),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (557), (571), (574), (611), (721), (775), (3172),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (3179), (3279), (3283), (3286), (3291), (3297),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (3298), (3304), (3323), (3337), (3338), (3339),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (3346), (3356), (3358), (function-axioms) are
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #536.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3359)   ~ (all_58_9 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (158), (272), (273), (307), (325),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (346), (366), (388), (431), (543), (545), (548),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (549), (555), (557), (561), (571), (3172), (3179),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (3307), (3337), (3338), (3339), (3346), (3351),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            (3359), (function-axioms) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |            sub-proof #891.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.48  | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | |   (3360)   ~ (all_56_7 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | |   (3361)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | REDUCE: (427), (3360) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | |   (3362)   ~ (all_52_27 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | |   (3363)  all_58_2 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3177), (3287), (3363) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | |            sub-proof #948.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | |   (3364)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3365)  all_58_9 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3365) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3366)  all_52_25 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | SIMP: (3366) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3367)  all_52_25 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (3367) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3368)   ~ (all_52_17 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (3367) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3369)   ~ (all_52_27 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (3367) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3370)   ~ (all_6_2 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | SIMP: (3370) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3371)   ~ (all_6_2 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (3367) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3372)  op(e3, e3) = all_52_24
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (3372)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | |   (3373)  all_52_24 = all_6_2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | |   (3374)  all_58_9 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3365), (3374) are inconsistent by sub-proof
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | |            #840.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | |   (3375)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | |   (3376)  all_58_0 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (3376) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | |   (3377)  all_6_2 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3371), (3377) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | |   (3378)  $false
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3378) is inconsistent.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | |   (3379)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | |   (3380)  all_58_9 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3365), (3380) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | |   (3381)  e3 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3381) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | |   (3382)  e3 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (3382) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | |   (3383)  $false
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3383) is inconsistent.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | |   (3384)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3385)  all_56_13 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (3385) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3386)  all_52_15 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3386) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3387)  all_52_15 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (3387) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3388)   ~ (all_52_7 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (3387) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3389)   ~ (all_4_2 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3389) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3390)   ~ (all_4_2 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3339), (3387) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3391)  op(e3, e3) = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3364) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3392)  all_58_3 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (3392) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3393)  all_4_2 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3390), (3393) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3394)  $false
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3394) is inconsistent.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3395)  all_58_5 = e3 | all_58_10 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3395) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3396)  all_58_5 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (3396) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3397)  all_52_19 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3397) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3398)  all_52_19 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3293), (3398) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3399)   ~ (all_4_0 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (3398) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3400)  op(e3, e3) = all_52_18
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3379) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3401)  all_58_2 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3177), (3287), (3401) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #948.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3402)  all_58_6 = e3 | all_58_12 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3403)  all_58_6 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (3403) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3404)  all_52_5 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3404) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3405)  all_52_5 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (3405) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3406)   ~ (all_52_7 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (3405) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3407)  op(e3, e3) = all_52_4
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_18, e3, e3, simplifying with (3391), (3400)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3408)  all_52_18 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_4, e3, e3, simplifying with (41), (3407)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3409)  all_52_4 = all_6_2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_18,
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_4, e3, e3, simplifying with (3400), (3407)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3410)  all_52_4 = all_52_18
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3409), (3410) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3411)  all_52_18 = all_6_2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3411) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3412)  all_52_18 = all_6_2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3408), (3412) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3413)  all_6_2 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3413) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3414)  all_6_2 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (3414) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3415)  op(e0, e3) = all_6_1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (273), (431), (3172), (3179), (3304),
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3388), (3415), (function-axioms) are inconsistent
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1343.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3416)   ~ (all_58_6 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (547), (3388), (3402), (3416) are
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #594.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3417)  all_58_10 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (3362), (3417) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3418)   ~ (all_56_13 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3419)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3418) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | |   (3420)   ~ (all_52_15 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3421)  all_58_12 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (3421) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3422)  all_52_7 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3422) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3423)  all_52_7 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (3423) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3424)   ~ (all_52_5 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (3423) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3425)   ~ (all_52_15 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (3423) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3426)   ~ (all_52_23 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3426) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3427)   ~ (all_52_23 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (3423) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3428)  op(e3, e3) = all_52_6
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (3428)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (3429)  all_52_6 = all_6_2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3430)  all_58_0 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (3430) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3431)  all_6_2 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (3431) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3432)   ~ (all_52_5 = e1)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3297), (3431) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3433)   ~ (all_4_0 = e1)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (3431) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3434)  op(e1, e3) = all_6_1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_6_1, e3, e1, simplifying with (162), (3434)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3435)  all_52_5 = all_6_1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (3435) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3436)  all_56_8 = all_6_1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (3435) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3437)   ~ (all_52_29 = all_6_1)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3437) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3438)   ~ (all_52_29 = all_6_1)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3289), (3435) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3439)   ~ (all_6_1 = all_4_0)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3424), (3435) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3440)   ~ (all_6_1 = e3)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (3435) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3441)  op(all_6_1, all_6_1) = all_52_4
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3442)  all_56_8 = e3
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3436), (3440), (3442) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1101.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3443)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3443) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3444)  all_56_8 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3179), (3436), (3444) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1321.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3445)  all_56_8 = e1 | all_56_8 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3445) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3446)  all_56_8 = e1
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3172), (3436), (3446) are inconsistent by
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1320.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3447)  all_56_8 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3436), (3447) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3448)  all_6_1 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3448) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3449)  all_6_1 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3439), (3449) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3450)   ~ (all_4_0 = e0)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3450) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3451)   ~ (all_4_0 = e0)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3441), (3449) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3452)  op(e0, e0) = all_52_4
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3323) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3453)  all_56_4 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3286), (3453) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3454)  all_4_0 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3454) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3455)  all_4_0 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3287), (3455) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3456)  all_58_2 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3295), (3455) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3457)   ~ (all_52_27 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3298), (3455) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3458)   ~ (all_4_2 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3458) implies:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3459)   ~ (all_4_2 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3299), (3455) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3460)  op(e2, e2) = all_52_2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3361) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3461)  all_56_7 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (3461) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3462)  all_52_27 = e2
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3457), (3462) imply:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3463)  $false
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3463) is inconsistent.
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3464)   ~ (all_56_7 = e2)
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3465)  all_56_7 = e1 | all_56_7 = e0
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3375) gives:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3466)  all_58_10 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (3457), (3466) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #539.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3467)  all_58_11 = e2 | all_58_15 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3467) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3468)  all_58_11 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3468) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3469)  all_52_29 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3469) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3470)  all_52_29 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (3470) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3471)  op(e2, e2) = all_52_28
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3384) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3472)  all_58_10 = e1
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (3472) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3473)  all_52_27 = e1
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3473) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3474)  all_52_27 = e1
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (3474) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3475)   ~ (all_4_2 = e1)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3475) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3476)   ~ (all_4_2 = e1)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_4,
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (3312), (3452) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3477)  all_52_4 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_2, e2, e2, simplifying with (36), (3460)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3478)  all_52_2 = all_4_2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_28,
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_2, e2, e2, simplifying with (3460), (3471)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3479)  all_52_2 = all_52_28
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3478), (3479) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3480)  all_52_28 = all_4_2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3480) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3481)  all_52_28 = all_4_2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3482)  all_56_10 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (3482) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3483)  all_10_2 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (3483) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3484)   ~ (all_52_19 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (372), (375), (548), (574), (3283), (3362),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3364), (3484), (function-axioms) are inconsistent
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #945.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3485)   ~ (all_56_10 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (3485) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3486)   ~ (all_10_2 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3487)  all_58_4 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (3487) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3488)  all_52_17 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3368), (3488) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3489)  $false
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3489) is inconsistent.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3490)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3490) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3491)  all_58_5 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (3491) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3492)  all_52_19 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (3492) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3493)   ~ (all_4_2 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3493) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3494)   ~ (all_4_2 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3495)  all_58_2 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3456), (3495) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3496)  e2 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3496) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3497)  $false
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3497) is inconsistent.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3498)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3499)  all_56_5 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (539), (3494), (3499) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1319.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3500)   ~ (all_56_5 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3501)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3498) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3502)  all_58_3 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (548), (3312), (3340), (3459), (3502),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1316.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3503)   ~ (all_58_3 = e0)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (3503) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3504)   ~ (all_4_2 = e0)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (539), (611), (3283), (3476), (3494),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3501), (3504), (function-axioms) are inconsistent
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #974.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3505)  all_58_8 = e3 | all_58_14 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (546), (3427), (3486), (3505) are
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1304.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3506)   ~ (all_58_10 = e1)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3506) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3507)   ~ (all_52_27 = e1)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3465) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3508)  all_56_7 = e1
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (3507), (3508) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #903.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3509)  all_56_7 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (3308), (3509) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #906.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3510)  all_58_15 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3302), (3510) are inconsistent by sub-proof
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1223.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3511)  all_56_4 = e1 | all_56_4 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3286), (3301), (3451), (3511) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #674.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3512)   ~ (all_58_0 = e1)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (3512) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3513)   ~ (all_6_2 = e1)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (169), (276), (325), (366), (421), (543),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            (548), (549), (557), (574), (3283), (3337),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3338), (3420), (3428), (3513), (function-axioms)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #932.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (3514)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (51), (53), (156), (162), (183),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (273), (276), (304), (305), (346), (351), (421),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (431), (542), (543), (568), (571), (572), (582),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (587), (588), (3170), (3302), (3304), (3305),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (3312), (3338), (3339), (3340), (3419), (3420),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (3514), (function-axioms) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #545.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | |   (3515)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3515) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | |   (3516)  all_58_10 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (3362), (3516) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | |   (3517)  all_58_11 = e3 | all_58_15 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3517) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3518)  all_58_11 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3518) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3519)  all_52_29 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3519) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3520)  all_52_29 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (3520) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3521)   ~ (all_52_25 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (3520) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3522)  op(e3, e3) = all_52_28
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e3, simplifying with (41), (3522)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3523)  all_52_28 = all_6_2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | |   (3524)  all_56_3 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (3521), (3524) are inconsistent by
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1339.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | |   (3525)   ~ (all_56_3 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | |   (3526)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3527)  all_58_9 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3527) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3528)  all_52_25 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3528) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3529)  all_52_25 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (3529) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3530)   ~ (all_6_2 = e2)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3530) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3531)   ~ (all_6_2 = e2)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3521), (3529) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3532)   ~ (e3 = e2)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (3529) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3533)  op(e3, e0) = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (3534)  all_56_5 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (539), (574), (3283), (3534),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            #976.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (3535)   ~ (all_56_5 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (3535) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (3536)   ~ (all_4_2 = e3)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (36), (41), (42), (43), (158),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (169), (272), (273), (280), (325), (326),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (328), (330), (346), (351), (366), (405), (431),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (523), (539), (543), (547), (548), (549), (555),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (557), (571), (574), (611), (721), (775), (3172),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (3179), (3279), (3283), (3286), (3291), (3297),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (3298), (3304), (3323), (3337), (3338), (3339),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3533), (3536), (function-axioms) are
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #536.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3537)   ~ (all_58_9 = e2)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (3537) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |   (3538)   ~ (all_52_25 = e2)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (388), (427), (523), (539),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |            (574), (604), (611), (721), (3279), (3283),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |            (3286), (3295), (3298), (3301), (3307), (3308),
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |            (3323), (3361), (3526), (3538), (function-axioms)
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #639.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |   (3539)  all_58_15 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3302), (3539) are inconsistent by sub-proof
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | |            #1350.
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | End of split
% 194.71/31.49  | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | Case 2:
% 194.71/31.49  | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | |   (3540)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 194.71/31.49  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 194.71/31.49  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 194.71/31.49  | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | BETA: splitting (3540) gives:
% 194.71/31.49  | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | Case 1:
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3541)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 194.71/31.49  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | ALPHA: (3541) implies:
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3542)  all_52_22 = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3543)  all_52_20 = e1
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3544)  all_52_18 = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3545)  all_52_16 = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | REDUCE: (178), (3545) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3546)  op(all_52_17, all_52_17) = e3
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | REDUCE: (177), (3544) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3547)  op(all_52_19, all_52_19) = e2
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | REDUCE: (175), (3542) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3548)  op(all_52_23, all_52_23) = e0
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.49  | | | | | | | | | | | | | | | | | REDUCE: (612), (3543) imply:
% 194.71/31.49  | | | | | | | | | | | | | | | | |   (3549)  op(all_10_2, all_10_2) = e1
% 194.71/31.49  | | | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (42), (43),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (51), (158), (162), (167), (169), (172), (173),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (174), (180), (182), (183), (271), (272), (273),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (276), (278), (279), (280), (282), (283), (284),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (304), (307), (308), (317), (319), (321), (323),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (325), (326), (328), (330), (331), (332), (333),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (343), (346), (351), (366), (372), (375), (388),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (393), (394), (405), (415), (417), (421), (427),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (431), (523), (539), (542), (543), (544), (545),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (561), (570), (571), (572), (574), (575), (576),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (578), (580), (584), (586), (587), (588), (589),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (590), (595), (597), (598), (600), (604), (605),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (607), (610), (611), (721), (775), (3172), (3177),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (3179), (3279), (3283), (3286), (3287), (3291),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (3297), (3298), (3301), (3302), (3304), (3305),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (3306), (3307), (3309), (3312), (3323), (3546),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (3547), (3548), (3549), (function-axioms) are
% 194.71/31.50  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #943.
% 194.71/31.50  | | | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | | | Case 2:
% 194.71/31.50  | | | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | | | |   (3550)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 194.71/31.50  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 194.71/31.50  | | | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (278), (280), (282), (309), (321), (332), (372),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (375), (388), (405), (427), (523), (539), (544),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (545), (548), (561), (574), (584), (586), (605),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (607), (610), (611), (721), (3177), (3279),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (3283), (3286), (3287), (3297), (3298), (3301),
% 194.71/31.50  | | | | | | | | | | | | | | | | |            (3302), (3307), (3323), (3550), (function-axioms)
% 194.71/31.50  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #940.
% 194.71/31.50  | | | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | | | End of split
% 194.71/31.50  | | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | | End of split
% 194.71/31.50  | | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | End of split
% 194.71/31.50  | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | Case 2:
% 194.71/31.50  | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | |   (3551)   ~ (all_58_15 = e0)
% 194.71/31.50  | | | | | | | | | | | | | |   (3552)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 194.71/31.50  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 194.71/31.50  | | | | | | | | | | | | | |             e0)
% 194.71/31.50  | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | ALPHA: (3552) implies:
% 194.71/31.50  | | | | | | | | | | | | | |   (3553)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 194.71/31.50  | | | | | | | | | | | | | |   (3554)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 194.71/31.50  | | | | | | | | | | | | | | 
% 194.71/31.50  | | | | | | | | | | | | | | REDUCE: (541), (3551) imply:
% 194.71/31.50  | | | | | | | | | | | | | |   (3555)   ~ (all_14_2 = e0)
% 194.71/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.07/31.50  | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (158), (162), (166),
% 195.07/31.50  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 195.07/31.50  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.07/31.50  | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 195.07/31.50  | | | | | | | | | | | | | |            (275), (276), (277), (279), (280), (281), (282),
% 195.07/31.50  | | | | | | | | | | | | | |            (283), (284), (285), (304), (306), (307), (309),
% 195.07/31.50  | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 195.07/31.50  | | | | | | | | | | | | | |            (318), (319), (321), (323), (324), (325), (326),
% 195.07/31.50  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 195.07/31.50  | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 195.07/31.50  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.07/31.50  | | | | | | | | | | | | | |            (411), (415), (417), (421), (431), (523), (538),
% 195.07/31.50  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.07/31.50  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.07/31.50  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 195.07/31.50  | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 195.07/31.50  | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 195.07/31.50  | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 195.07/31.50  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.07/31.50  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.07/31.50  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (721),
% 195.07/31.50  | | | | | | | | | | | | | |            (772), (773), (775), (3172), (3177), (3179),
% 195.07/31.50  | | | | | | | | | | | | | |            (3279), (3283), (3286), (3287), (3289), (3291),
% 195.07/31.50  | | | | | | | | | | | | | |            (3297), (3298), (3299), (3301), (3553), (3554),
% 195.07/31.50  | | | | | | | | | | | | | |            (3555), (function-axioms) are inconsistent by
% 195.07/31.50  | | | | | | | | | | | | | |            sub-proof #670.
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | End of split
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | Case 2:
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | |   (3556)  all_38_0 = e1
% 195.07/31.50  | | | | | | | | | | | | |   (3557)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | COMBINE_EQS: (766), (3556) imply:
% 195.07/31.50  | | | | | | | | | | | | |   (3558)  all_4_0 = e1
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 195.07/31.50  | | | | | | | | | | | | |            (3282), (3283), (3298), (3557), (3558),
% 195.07/31.50  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.50  | | | | | | | | | | | | |            #927.
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | End of split
% 195.07/31.50  | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | End of split
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | Case 2:
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | |   (3559)  all_24_0 = e1
% 195.07/31.50  | | | | | | | | | | |   (3560)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | COMBINE_EQS: (711), (3559) imply:
% 195.07/31.50  | | | | | | | | | | |   (3561)  all_14_0 = e1
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | SIMP: (3561) implies:
% 195.07/31.50  | | | | | | | | | | |   (3562)  all_14_0 = e1
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | COMBINE_EQS: (765), (3562) imply:
% 195.07/31.50  | | | | | | | | | | |   (3563)  all_34_0 = e1
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | REDUCE: (3175), (3562) imply:
% 195.07/31.50  | | | | | | | | | | |   (3564)   ~ (e3 = e1)
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | REDUCE: (3173), (3562) imply:
% 195.07/31.50  | | | | | | | | | | |   (3565)   ~ (e2 = e1)
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | REDUCE: (62), (3562) imply:
% 195.07/31.50  | | | | | | | | | | |   (3566)  op(e0, all_14_1) = e1
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 195.07/31.50  | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (63), (109),
% 195.07/31.50  | | | | | | | | | | |            (114), (124), (156), (157), (158), (159), (161),
% 195.07/31.50  | | | | | | | | | | |            (162), (163), (166), (167), (168), (169), (172),
% 195.07/31.50  | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.07/31.50  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 195.07/31.50  | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 195.07/31.50  | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 195.07/31.50  | | | | | | | | | | |            (303), (304), (305), (306), (307), (308), (309),
% 195.07/31.50  | | | | | | | | | | |            (310), (311), (313), (315), (316), (317), (319),
% 195.07/31.50  | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 195.07/31.50  | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 195.07/31.50  | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.07/31.50  | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.07/31.50  | | | | | | | | | | |            (415), (417), (421), (427), (431), (491), (508),
% 195.07/31.50  | | | | | | | | | | |            (525), (538), (539), (540), (541), (542), (543),
% 195.07/31.50  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.07/31.50  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 195.07/31.50  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 195.07/31.50  | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 195.07/31.50  | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 195.07/31.50  | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.07/31.50  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.07/31.50  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.07/31.50  | | | | | | | | | | |            (612), (613), (649), (663), (685), (686), (766),
% 195.07/31.50  | | | | | | | | | | |            (772), (773), (775), (3172), (3177), (3179),
% 195.07/31.50  | | | | | | | | | | |            (3560), (3563), (3566), (function-axioms) are
% 195.07/31.50  | | | | | | | | | | |            inconsistent by sub-proof #837.
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | End of split
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | Case 2:
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | |   (3567)  all_22_1 = e2
% 195.07/31.50  | | | | | | | | | |   (3568)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | COMBINE_EQS: (658), (3567) imply:
% 195.07/31.50  | | | | | | | | | |   (3569)  all_6_1 = e2
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (43), (3569) imply:
% 195.07/31.50  | | | | | | | | | |   (3570)  op(all_6_2, e3) = e2
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (42), (3569) imply:
% 195.07/31.50  | | | | | | | | | |   (3571)  op(e3, e2) = all_6_0
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 195.07/31.50  | | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (3571)
% 195.07/31.50  | | | | | | | | | |              gives:
% 195.07/31.50  | | | | | | | | | |   (3572)  all_52_9 = all_6_0
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | COMBINE_EQS: (394), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3573)  all_56_1 = all_6_0
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | COMBINE_EQS: (549), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3574)  all_58_1 = all_6_0
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (575), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3575)   ~ (all_52_13 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | SIMP: (3575) implies:
% 195.07/31.50  | | | | | | | | | |   (3576)   ~ (all_52_13 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (576), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3577)   ~ (all_52_15 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | SIMP: (3577) implies:
% 195.07/31.50  | | | | | | | | | |   (3578)   ~ (all_52_15 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (577), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3579)   ~ (all_52_17 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | SIMP: (3579) implies:
% 195.07/31.50  | | | | | | | | | |   (3580)   ~ (all_52_17 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (578), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3581)   ~ (all_52_25 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | SIMP: (3581) implies:
% 195.07/31.50  | | | | | | | | | |   (3582)   ~ (all_52_25 = all_6_0)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (557), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3583)   ~ (all_6_0 = all_6_2)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (574), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3584)   ~ (all_6_0 = all_4_2)
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | REDUCE: (182), (3572) imply:
% 195.07/31.50  | | | | | | | | | |   (3585)  op(all_6_0, all_6_0) = all_52_8
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | BETA: splitting (89) gives:
% 195.07/31.50  | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | Case 1:
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | |   (3586)   ~ (all_24_0 = e1)
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | REDUCE: (711), (3586) imply:
% 195.07/31.50  | | | | | | | | | | |   (3587)   ~ (all_14_0 = e1)
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | BETA: splitting (109) gives:
% 195.07/31.50  | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | Case 1:
% 195.07/31.50  | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | |   (3588)   ~ (all_32_1 = e3)
% 195.07/31.50  | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | REDUCE: (663), (3588) imply:
% 195.07/31.50  | | | | | | | | | | | |   (3589)   ~ (all_4_1 = e3)
% 195.07/31.50  | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | BETA: splitting (119) gives:
% 195.07/31.50  | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | Case 1:
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | |   (3590)   ~ (all_36_0 = e3)
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | REDUCE: (3169), (3590) imply:
% 195.07/31.50  | | | | | | | | | | | | |   (3591)  $false
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | CLOSE: (3591) is inconsistent.
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | Case 2:
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | |   (3592)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.50  | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | Case 1:
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | |   (3593)  all_58_15 = e0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | COMBINE_EQS: (541), (3593) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3594)  all_14_2 = e0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (573), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3595)   ~ (all_52_7 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (591), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3596)   ~ (all_52_15 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (603), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3597)   ~ (all_52_23 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (606), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3598)   ~ (all_52_25 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (613), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3599)  op(e0, e0) = all_52_30
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (63), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3600)  op(e0, e0) = all_14_1
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (61), (3594) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3601)  op(e0, e0) = e0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.07/31.50  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3599), (3600)
% 195.07/31.50  | | | | | | | | | | | | | |              gives:
% 195.07/31.50  | | | | | | | | | | | | | |   (3602)  all_52_30 = all_14_1
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.07/31.50  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3599), (3601)
% 195.07/31.50  | | | | | | | | | | | | | |              gives:
% 195.07/31.50  | | | | | | | | | | | | | |   (3603)  all_52_30 = e0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | COMBINE_EQS: (3602), (3603) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3604)  all_14_1 = e0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (62), (3604) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3605)  op(e0, e0) = all_14_0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.07/31.50  | | | | | | | | | | | | | |              e0, e0, simplifying with (3601), (3605) gives:
% 195.07/31.50  | | | | | | | | | | | | | |   (3606)  all_14_0 = e0
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (3175), (3606) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3607)   ~ (e3 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (3173), (3606) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3608)   ~ (e2 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | REDUCE: (3587), (3606) imply:
% 195.07/31.50  | | | | | | | | | | | | | |   (3609)   ~ (e1 = e0)
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 195.07/31.50  | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | Case 1:
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | |   (3610)  all_56_1 = e3
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | COMBINE_EQS: (3573), (3610) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3611)  all_6_0 = e3
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | SIMP: (3611) implies:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3612)  all_6_0 = e3
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | COMBINE_EQS: (3574), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3613)  all_58_1 = e3
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | REDUCE: (3576), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3614)   ~ (all_52_13 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | REDUCE: (3578), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3615)   ~ (all_52_15 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | REDUCE: (3580), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3616)   ~ (all_52_17 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | REDUCE: (3582), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3617)   ~ (all_52_25 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | REDUCE: (3583), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3618)   ~ (all_6_2 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | SIMP: (3618) implies:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3619)   ~ (all_6_2 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | REDUCE: (3584), (3612) imply:
% 195.07/31.50  | | | | | | | | | | | | | | |   (3620)   ~ (all_4_2 = e3)
% 195.07/31.50  | | | | | | | | | | | | | | | 
% 195.07/31.50  | | | | | | | | | | | | | | | SIMP: (3620) implies:
% 195.07/31.51  | | | | | | | | | | | | | | |   (3621)   ~ (all_4_2 = e3)
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | REDUCE: (3585), (3612) imply:
% 195.07/31.51  | | | | | | | | | | | | | | |   (3622)  op(e3, e3) = all_52_8
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.07/31.51  | | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (3622)
% 195.07/31.51  | | | | | | | | | | | | | | |              gives:
% 195.07/31.51  | | | | | | | | | | | | | | |   (3623)  all_52_8 = all_6_2
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | Case 1:
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | |   (3624)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.51  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.51  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | BETA: splitting (3624) gives:
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3625)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.51  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (51), (53),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (61), (156), (157), (162), (175), (183), (184),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (185), (272), (273), (304), (305), (306), (321),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (332), (346), (351), (387), (405), (431), (524),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (542), (543), (547), (555), (564), (569), (571),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (572), (573), (610), (645), (772), (3170), (3589),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (3592), (3593), (3595), (3596), (3625),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.51  | | | | | | | | | | | | | | | | |            #535.
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3626)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.51  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (3619), (3623), (3626) are inconsistent by
% 195.07/31.51  | | | | | | | | | | | | | | | | |            sub-proof #791.
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | |   (3627)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.51  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.51  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | BETA: splitting (3627) gives:
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3628)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.07/31.51  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | ALPHA: (3628) implies:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3629)  all_52_22 = e0
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3630)  all_52_20 = e1
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3631)  all_52_18 = e2
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3632)  all_52_16 = e3
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (178), (3632) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3633)  op(all_52_17, all_52_17) = e3
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (177), (3631) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3634)  op(all_52_19, all_52_19) = e2
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (175), (3629) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3635)  op(all_52_23, all_52_23) = e0
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (612), (3630) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3636)  op(all_10_2, all_10_2) = e1
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (53),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (61), (158), (166), (168), (182), (183), (184),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (274), (278), (282), (283), (306), (307), (313),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (315), (317), (321), (325), (327), (329), (331),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (351), (352), (366), (372), (375), (387), (388),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (393), (405), (415), (427), (542), (543), (544),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (557),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (559), (561), (563), (572), (590), (592), (593),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (609), (610), (3570), (3593), (3595), (3598),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (3601), (3613), (3614), (3615), (3616), (3617),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (3621), (3622), (3633), (3634), (3635), (3636),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.51  | | | | | | | | | | | | | | | | |            #826.
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3637)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.07/31.51  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | ALPHA: (3637) implies:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3638)  all_52_28 = e1
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3639)  all_52_26 = e2
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3640)  all_52_24 = e3
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (174), (3640) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3641)  op(all_52_25, all_52_25) = e3
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (173), (3639) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3642)  op(all_52_27, all_52_27) = e2
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REDUCE: (172), (3638) imply:
% 195.07/31.51  | | | | | | | | | | | | | | | | |   (3643)  op(all_52_29, all_52_29) = e1
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (51), (166), (175), (183),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (278), (282), (306), (307), (309), (317), (321),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (332), (351), (372), (375), (387), (388), (393),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (405), (427), (542), (543), (544), (545), (546),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (547), (548), (551), (561), (563), (564), (570),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (572), (584), (596), (598), (600), (604), (605),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (612), (3570), (3593), (3597), (3598), (3615),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (3616), (3617), (3621), (3641), (3642), (3643),
% 195.07/31.51  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.51  | | | | | | | | | | | | | | | | |            #823.
% 195.07/31.51  | | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | |   (3644)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 195.07/31.51  | | | | | | | | | | | | | | |            (610), (739), (773), (775), (3568), (3570),
% 195.07/31.51  | | | | | | | | | | | | | | |            (3573), (3583), (3644), (function-axioms) are
% 195.07/31.51  | | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 195.07/31.51  | | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | |   (3645)   ~ (all_58_15 = e0)
% 195.07/31.51  | | | | | | | | | | | | | |   (3646)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.51  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.51  | | | | | | | | | | | | | |             e0)
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | ALPHA: (3646) implies:
% 195.07/31.51  | | | | | | | | | | | | | |   (3647)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.51  | | | | | | | | | | | | | |   (3648)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | REDUCE: (541), (3645) imply:
% 195.07/31.51  | | | | | | | | | | | | | |   (3649)   ~ (all_14_2 = e0)
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 195.07/31.51  | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (62), (63), (156),
% 195.07/31.51  | | | | | | | | | | | | | |            (157), (158), (159), (161), (162), (166), (167),
% 195.07/31.51  | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 195.07/31.51  | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (187),
% 195.07/31.51  | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (277),
% 195.07/31.51  | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 195.07/31.51  | | | | | | | | | | | | | |            (305), (306), (307), (308), (309), (311), (312),
% 195.07/31.51  | | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (320), (321),
% 195.07/31.51  | | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 195.07/31.51  | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 195.07/31.51  | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.07/31.51  | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 195.07/31.51  | | | | | | | | | | | | | |            (522), (524), (538), (539), (540), (541), (542),
% 195.07/31.51  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.07/31.51  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.07/31.51  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (569), (570),
% 195.07/31.51  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (578),
% 195.07/31.51  | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (590), (591),
% 195.07/31.51  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.07/31.51  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.07/31.51  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (645),
% 195.07/31.51  | | | | | | | | | | | | | |            (739), (772), (773), (775), (3170), (3175),
% 195.07/31.51  | | | | | | | | | | | | | |            (3177), (3568), (3570), (3573), (3574), (3576),
% 195.07/31.51  | | | | | | | | | | | | | |            (3578), (3580), (3582), (3583), (3584), (3585),
% 195.07/31.51  | | | | | | | | | | | | | |            (3589), (3592), (3647), (3648), (3649),
% 195.07/31.51  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.51  | | | | | | | | | | | | | |            #530.
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | |   (3650)  all_32_1 = e3
% 195.07/31.51  | | | | | | | | | | | |   (3651)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | COMBINE_EQS: (663), (3650) imply:
% 195.07/31.51  | | | | | | | | | | | |   (3652)  all_4_1 = e3
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | SIMP: (3652) implies:
% 195.07/31.51  | | | | | | | | | | | |   (3653)  all_4_1 = e3
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (36), (37), (38), (41), (51), (61),
% 195.07/31.51  | | | | | | | | | | | |            (124), (158), (162), (166), (169), (173), (174),
% 195.07/31.51  | | | | | | | | | | | |            (175), (177), (182), (183), (184), (187), (270),
% 195.07/31.51  | | | | | | | | | | | |            (280), (281), (282), (284), (285), (306), (307),
% 195.07/31.51  | | | | | | | | | | | |            (309), (313), (321), (325), (328), (330), (332),
% 195.07/31.51  | | | | | | | | | | | |            (333), (351), (366), (372), (375), (387), (388),
% 195.07/31.51  | | | | | | | | | | | |            (393), (405), (411), (522), (523), (525), (538),
% 195.07/31.51  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.07/31.51  | | | | | | | | | | | |            (547), (548), (549), (551), (555), (561), (562),
% 195.07/31.51  | | | | | | | | | | | |            (563), (564), (569), (570), (571), (573), (574),
% 195.07/31.51  | | | | | | | | | | | |            (578), (584), (586), (593), (595), (598), (604),
% 195.07/31.51  | | | | | | | | | | | |            (608), (610), (611), (613), (686), (721), (739),
% 195.07/31.51  | | | | | | | | | | | |            (766), (773), (775), (3177), (3568), (3570),
% 195.07/31.51  | | | | | | | | | | | |            (3573), (3574), (3576), (3578), (3582), (3583),
% 195.07/31.51  | | | | | | | | | | | |            (3584), (3585), (3651), (3653), (function-axioms)
% 195.07/31.51  | | | | | | | | | | | |            are inconsistent by sub-proof #593.
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | End of split
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | |   (3654)  all_24_0 = e1
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | COMBINE_EQS: (711), (3654) imply:
% 195.07/31.51  | | | | | | | | | | |   (3655)  all_14_0 = e1
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | SIMP: (3655) implies:
% 195.07/31.51  | | | | | | | | | | |   (3656)  all_14_0 = e1
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | REDUCE: (3173), (3656) imply:
% 195.07/31.51  | | | | | | | | | | |   (3657)   ~ (e2 = e1)
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | REDUCE: (62), (3656) imply:
% 195.07/31.51  | | | | | | | | | | |   (3658)  op(e0, all_14_1) = e1
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | BETA: splitting (109) gives:
% 195.07/31.51  | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | Case 1:
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | |   (3659)   ~ (all_32_1 = e3)
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | REDUCE: (663), (3659) imply:
% 195.07/31.51  | | | | | | | | | | | |   (3660)   ~ (all_4_1 = e3)
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | BETA: splitting (119) gives:
% 195.07/31.51  | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | Case 1:
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | |   (3661)   ~ (all_36_0 = e3)
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | REDUCE: (3169), (3661) imply:
% 195.07/31.51  | | | | | | | | | | | | |   (3662)  $false
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | CLOSE: (3662) is inconsistent.
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | |   (3663)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.51  | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | Case 1:
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | |   (3664)  all_58_15 = e0
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (3658), (3664),
% 195.07/31.51  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.51  | | | | | | | | | | | | | |            #877.
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | Case 2:
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | |   (3665)   ~ (all_58_15 = e0)
% 195.07/31.51  | | | | | | | | | | | | | |   (3666)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.51  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.51  | | | | | | | | | | | | | |             e0)
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | ALPHA: (3666) implies:
% 195.07/31.51  | | | | | | | | | | | | | |   (3667)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.51  | | | | | | | | | | | | | |   (3668)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.51  | | | | | | | | | | | | | | REDUCE: (541), (3665) imply:
% 195.07/31.51  | | | | | | | | | | | | | |   (3669)   ~ (all_14_2 = e0)
% 195.07/31.51  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 195.07/31.52  | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (62), (63), (156),
% 195.07/31.52  | | | | | | | | | | | | | |            (157), (158), (159), (161), (162), (166), (167),
% 195.07/31.52  | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 195.07/31.52  | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (187),
% 195.07/31.52  | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (277),
% 195.07/31.52  | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 195.07/31.52  | | | | | | | | | | | | | |            (305), (306), (307), (308), (309), (311), (312),
% 195.07/31.52  | | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (320), (321),
% 195.07/31.52  | | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 195.07/31.52  | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 195.07/31.52  | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.07/31.52  | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 195.07/31.52  | | | | | | | | | | | | | |            (522), (524), (538), (539), (540), (541), (542),
% 195.07/31.52  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.07/31.52  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.07/31.52  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (569), (570),
% 195.07/31.52  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (578),
% 195.07/31.52  | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (590), (591),
% 195.07/31.52  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.07/31.52  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.07/31.52  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (645),
% 195.07/31.52  | | | | | | | | | | | | | |            (739), (772), (773), (775), (3170), (3175),
% 195.07/31.52  | | | | | | | | | | | | | |            (3177), (3568), (3570), (3573), (3574), (3576),
% 195.07/31.52  | | | | | | | | | | | | | |            (3578), (3580), (3582), (3583), (3584), (3585),
% 195.07/31.52  | | | | | | | | | | | | | |            (3660), (3663), (3667), (3668), (3669),
% 195.07/31.52  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.52  | | | | | | | | | | | | | |            #530.
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | Case 2:
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | |   (3670)  all_32_1 = e3
% 195.07/31.52  | | | | | | | | | | | |   (3671)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | COMBINE_EQS: (663), (3670) imply:
% 195.07/31.52  | | | | | | | | | | | |   (3672)  all_4_1 = e3
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (36), (37), (38), (41), (51), (61),
% 195.07/31.52  | | | | | | | | | | | |            (124), (158), (162), (166), (169), (173), (174),
% 195.07/31.52  | | | | | | | | | | | |            (175), (177), (182), (183), (184), (187), (270),
% 195.07/31.52  | | | | | | | | | | | |            (280), (281), (282), (284), (285), (306), (307),
% 195.07/31.52  | | | | | | | | | | | |            (309), (313), (321), (325), (328), (330), (332),
% 195.07/31.52  | | | | | | | | | | | |            (333), (351), (366), (372), (375), (387), (388),
% 195.07/31.52  | | | | | | | | | | | |            (393), (405), (411), (522), (523), (525), (538),
% 195.07/31.52  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.07/31.52  | | | | | | | | | | | |            (547), (548), (549), (551), (555), (561), (562),
% 195.07/31.52  | | | | | | | | | | | |            (563), (564), (569), (570), (571), (573), (574),
% 195.07/31.52  | | | | | | | | | | | |            (578), (584), (586), (593), (595), (598), (604),
% 195.07/31.52  | | | | | | | | | | | |            (608), (610), (611), (613), (686), (721), (739),
% 195.07/31.52  | | | | | | | | | | | |            (766), (773), (775), (3177), (3568), (3570),
% 195.07/31.52  | | | | | | | | | | | |            (3573), (3574), (3576), (3578), (3582), (3583),
% 195.07/31.52  | | | | | | | | | | | |            (3584), (3585), (3671), (3672), (function-axioms)
% 195.07/31.52  | | | | | | | | | | | |            are inconsistent by sub-proof #593.
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | Case 2:
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | |   (3673)  all_20_0 = e3
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | COMBINE_EQS: (758), (3673) imply:
% 195.07/31.52  | | | | | | | | |   (3674)  all_4_0 = e3
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | SIMP: (3674) implies:
% 195.07/31.52  | | | | | | | | |   (3675)  all_4_0 = e3
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | REDUCE: (37), (3675) imply:
% 195.07/31.52  | | | | | | | | |   (3676)  op(e2, all_4_1) = e3
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | BETA: splitting (84) gives:
% 195.07/31.52  | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | |   (3677)   ~ (all_22_1 = e2)
% 195.07/31.52  | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | REDUCE: (658), (3677) imply:
% 195.07/31.52  | | | | | | | | | |   (3678)   ~ (all_6_1 = e2)
% 195.07/31.52  | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | BETA: splitting (89) gives:
% 195.07/31.52  | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | |   (3679)   ~ (all_24_0 = e1)
% 195.07/31.52  | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | REDUCE: (711), (3679) imply:
% 195.07/31.52  | | | | | | | | | | |   (3680)   ~ (all_14_0 = e1)
% 195.07/31.52  | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | BETA: splitting (119) gives:
% 195.07/31.52  | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | |   (3681)   ~ (all_36_0 = e3)
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | REDUCE: (3169), (3681) imply:
% 195.07/31.52  | | | | | | | | | | | |   (3682)  $false
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | CLOSE: (3682) is inconsistent.
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | Case 2:
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | |   (3683)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.52  | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | |   (3684)  all_58_15 = e0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | COMBINE_EQS: (541), (3684) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3685)  all_14_2 = e0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (573), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3686)   ~ (all_52_7 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (591), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3687)   ~ (all_52_15 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (603), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3688)   ~ (all_52_23 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (606), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3689)   ~ (all_52_25 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (608), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3690)   ~ (all_52_27 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (609), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3691)   ~ (all_52_29 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (613), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3692)  op(e0, e0) = all_52_30
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (63), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3693)  op(e0, e0) = all_14_1
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (61), (3685) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3694)  op(e0, e0) = e0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.07/31.52  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3692), (3693)
% 195.07/31.52  | | | | | | | | | | | | |              gives:
% 195.07/31.52  | | | | | | | | | | | | |   (3695)  all_52_30 = all_14_1
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.07/31.52  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3692), (3694)
% 195.07/31.52  | | | | | | | | | | | | |              gives:
% 195.07/31.52  | | | | | | | | | | | | |   (3696)  all_52_30 = e0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | COMBINE_EQS: (3695), (3696) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3697)  all_14_1 = e0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (62), (3697) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3698)  op(e0, e0) = all_14_0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.07/31.52  | | | | | | | | | | | | |              e0, e0, simplifying with (3694), (3698) gives:
% 195.07/31.52  | | | | | | | | | | | | |   (3699)  all_14_0 = e0
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (3175), (3699) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3700)   ~ (e3 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (3173), (3699) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3701)   ~ (e2 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | REDUCE: (3680), (3699) imply:
% 195.07/31.52  | | | | | | | | | | | | |   (3702)   ~ (e1 = e0)
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.52  | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | |   (3703)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.52  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.52  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | BETA: splitting (3703) gives:
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | |   (3704)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.52  | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | ALPHA: (3704) implies:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3705)  all_52_6 = e0
% 195.07/31.52  | | | | | | | | | | | | | | |   (3706)  all_52_4 = e1
% 195.07/31.52  | | | | | | | | | | | | | | |   (3707)  all_52_2 = e2
% 195.07/31.52  | | | | | | | | | | | | | | |   (3708)  all_52_0 = e3
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (185), (3707) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3709)  op(all_52_3, all_52_3) = e2
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (184), (3706) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3710)  op(all_52_5, all_52_5) = e1
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (183), (3705) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3711)  op(all_52_7, all_52_7) = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (610), (3708) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3712)  op(all_6_2, all_6_2) = e3
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.07/31.52  | | | | | | | | | | | | | | |            (51), (53), (61), (156), (157), (162), (166),
% 195.07/31.52  | | | | | | | | | | | | | | |            (175), (179), (272), (273), (304), (305), (306),
% 195.07/31.52  | | | | | | | | | | | | | | |            (321), (332), (346), (351), (387), (405), (431),
% 195.07/31.52  | | | | | | | | | | | | | | |            (524), (542), (543), (547), (555), (564), (569),
% 195.07/31.52  | | | | | | | | | | | | | | |            (571), (572), (573), (645), (772), (3170), (3676),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3683), (3684), (3686), (3687), (3709), (3710),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3711), (3712), (function-axioms) are inconsistent
% 195.07/31.52  | | | | | | | | | | | | | | |            by sub-proof #528.
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | Case 2:
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | |   (3713)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.52  | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | ALPHA: (3713) implies:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3714)  all_52_14 = e0
% 195.07/31.52  | | | | | | | | | | | | | | |   (3715)  all_52_12 = e1
% 195.07/31.52  | | | | | | | | | | | | | | |   (3716)  all_52_10 = e2
% 195.07/31.52  | | | | | | | | | | | | | | |   (3717)  all_52_8 = e3
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (182), (3717) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3718)  op(all_52_9, all_52_9) = e3
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (180), (3715) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3719)  op(all_52_13, all_52_13) = e1
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (179), (3714) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3720)  op(all_52_15, all_52_15) = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (611), (3716) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3721)  op(all_4_2, all_4_2) = e2
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (36), (38), (41), (43), (51), (53),
% 195.07/31.52  | | | | | | | | | | | | | | |            (156), (158), (162), (169), (173), (174), (177),
% 195.07/31.52  | | | | | | | | | | | | | | |            (178), (183), (272), (273), (276), (277), (278),
% 195.07/31.52  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (304), (305),
% 195.07/31.52  | | | | | | | | | | | | | | |            (306), (309), (313), (314), (317), (322), (324),
% 195.07/31.52  | | | | | | | | | | | | | | |            (325), (327), (333), (346), (351), (366), (367),
% 195.07/31.52  | | | | | | | | | | | | | | |            (372), (375), (388), (393), (394), (405), (411),
% 195.07/31.52  | | | | | | | | | | | | | | |            (415), (421), (427), (431), (539), (542), (543),
% 195.07/31.52  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.07/31.52  | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 195.07/31.52  | | | | | | | | | | | | | | |            (564), (567), (568), (571), (572), (574), (575),
% 195.07/31.52  | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.07/31.52  | | | | | | | | | | | | | | |            (588), (589), (595), (604), (605), (612), (772),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3170), (3172), (3678), (3684), (3686), (3687),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3689), (3694), (3718), (3719), (3720), (3721),
% 195.07/31.52  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.52  | | | | | | | | | | | | | | |            #544.
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | Case 2:
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | |   (3722)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.52  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.52  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | BETA: splitting (3722) gives:
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | Case 1:
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | |   (3723)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.07/31.52  | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | ALPHA: (3723) implies:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3724)  all_52_22 = e0
% 195.07/31.52  | | | | | | | | | | | | | | |   (3725)  all_52_20 = e1
% 195.07/31.52  | | | | | | | | | | | | | | |   (3726)  all_52_18 = e2
% 195.07/31.52  | | | | | | | | | | | | | | |   (3727)  all_52_16 = e3
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (178), (3727) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3728)  op(all_52_17, all_52_17) = e3
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (177), (3726) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3729)  op(all_52_19, all_52_19) = e2
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (175), (3724) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3730)  op(all_52_23, all_52_23) = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REDUCE: (612), (3725) imply:
% 195.07/31.52  | | | | | | | | | | | | | | |   (3731)  op(all_10_2, all_10_2) = e1
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (43), (51),
% 195.07/31.52  | | | | | | | | | | | | | | |            (53), (157), (158), (162), (166), (168), (169),
% 195.07/31.52  | | | | | | | | | | | | | | |            (172), (173), (174), (179), (180), (182), (183),
% 195.07/31.52  | | | | | | | | | | | | | | |            (271), (272), (273), (277), (278), (279), (280),
% 195.07/31.52  | | | | | | | | | | | | | | |            (282), (283), (284), (304), (305), (306), (309),
% 195.07/31.52  | | | | | | | | | | | | | | |            (313), (317), (322), (325), (331), (333), (343),
% 195.07/31.52  | | | | | | | | | | | | | | |            (346), (351), (366), (367), (372), (375), (388),
% 195.07/31.52  | | | | | | | | | | | | | | |            (393), (394), (405), (415), (417), (427), (431),
% 195.07/31.52  | | | | | | | | | | | | | | |            (539), (542), (543), (544), (545), (546), (547),
% 195.07/31.52  | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 195.07/31.52  | | | | | | | | | | | | | | |            (561), (565), (567), (568), (569), (571), (572),
% 195.07/31.52  | | | | | | | | | | | | | | |            (577), (578), (580), (584), (588), (589), (590),
% 195.07/31.52  | | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.07/31.52  | | | | | | | | | | | | | | |            (600), (602), (604), (605), (611), (3172), (3676),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3678), (3684), (3686), (3687), (3688), (3689),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3694), (3728), (3729), (3730), (3731),
% 195.07/31.52  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.52  | | | | | | | | | | | | | | |            #764.
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | Case 2:
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | |   (3732)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.07/31.52  | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 195.07/31.52  | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (172),
% 195.07/31.52  | | | | | | | | | | | | | | |            (173), (174), (175), (179), (183), (272), (273),
% 195.07/31.52  | | | | | | | | | | | | | | |            (274), (278), (281), (282), (304), (305), (306),
% 195.07/31.52  | | | | | | | | | | | | | | |            (307), (308), (309), (313), (318), (321), (326),
% 195.07/31.52  | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (352), (366),
% 195.07/31.52  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 195.07/31.52  | | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 195.07/31.52  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (561),
% 195.07/31.52  | | | | | | | | | | | | | | |            (563), (564), (567), (569), (570), (571), (572),
% 195.07/31.52  | | | | | | | | | | | | | | |            (576), (582), (587), (588), (593), (595), (596),
% 195.07/31.52  | | | | | | | | | | | | | | |            (600), (602), (604), (605), (608), (610), (773),
% 195.07/31.52  | | | | | | | | | | | | | | |            (775), (3678), (3684), (3686), (3687), (3688),
% 195.07/31.52  | | | | | | | | | | | | | | |            (3689), (3690), (3691), (3732), (function-axioms)
% 195.07/31.52  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 195.07/31.52  | | | | | | | | | | | | | | | 
% 195.07/31.52  | | | | | | | | | | | | | | End of split
% 195.07/31.52  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | End of split
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | |   (3733)   ~ (all_58_15 = e0)
% 195.07/31.53  | | | | | | | | | | | | |   (3734)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.53  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.53  | | | | | | | | | | | | |             e0)
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | ALPHA: (3734) implies:
% 195.07/31.53  | | | | | | | | | | | | |   (3735)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.53  | | | | | | | | | | | | |   (3736)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | REDUCE: (541), (3733) imply:
% 195.07/31.53  | | | | | | | | | | | | |   (3737)   ~ (all_14_2 = e0)
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | Case 1:
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | |   (3738)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.53  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.53  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | BETA: splitting (3738) gives:
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | Case 1:
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | |   (3739)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.53  | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | ALPHA: (3739) implies:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3740)  all_52_6 = e0
% 195.07/31.53  | | | | | | | | | | | | | | |   (3741)  all_52_4 = e1
% 195.07/31.53  | | | | | | | | | | | | | | |   (3742)  all_52_2 = e2
% 195.07/31.53  | | | | | | | | | | | | | | |   (3743)  all_52_0 = e3
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (185), (3742) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3744)  op(all_52_3, all_52_3) = e2
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (184), (3741) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3745)  op(all_52_5, all_52_5) = e1
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (183), (3740) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3746)  op(all_52_7, all_52_7) = e0
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (610), (3743) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3747)  op(all_6_2, all_6_2) = e3
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (38), (41), (42), (43),
% 195.07/31.53  | | | | | | | | | | | | | | |            (51), (53), (61), (62), (63), (156), (157), (158),
% 195.07/31.53  | | | | | | | | | | | | | | |            (159), (161), (163), (167), (168), (169), (172),
% 195.07/31.53  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.07/31.53  | | | | | | | | | | | | | | |            (182), (270), (271), (272), (273), (274), (275),
% 195.07/31.53  | | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 195.07/31.53  | | | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (307), (308),
% 195.07/31.53  | | | | | | | | | | | | | | |            (309), (311), (312), (313), (314), (315), (317),
% 195.07/31.53  | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (327),
% 195.07/31.53  | | | | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 195.07/31.53  | | | | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 195.07/31.53  | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 195.07/31.53  | | | | | | | | | | | | | | |            (417), (421), (431), (524), (538), (539), (540),
% 195.07/31.53  | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 195.07/31.53  | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 195.07/31.53  | | | | | | | | | | | | | | |            (561), (563), (564), (565), (566), (567), (568),
% 195.07/31.53  | | | | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 195.07/31.53  | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 195.07/31.53  | | | | | | | | | | | | | | |            (587), (588), (589), (590), (591), (593), (594),
% 195.07/31.53  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.07/31.53  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (611),
% 195.07/31.53  | | | | | | | | | | | | | | |            (612), (613), (645), (772), (773), (775), (3170),
% 195.07/31.53  | | | | | | | | | | | | | | |            (3173), (3175), (3676), (3680), (3683), (3735),
% 195.07/31.53  | | | | | | | | | | | | | | |            (3736), (3737), (3744), (3745), (3746), (3747),
% 195.07/31.53  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.53  | | | | | | | | | | | | | | |            #518.
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | |   (3748)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.53  | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | ALPHA: (3748) implies:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3749)  all_52_14 = e0
% 195.07/31.53  | | | | | | | | | | | | | | |   (3750)  all_52_12 = e1
% 195.07/31.53  | | | | | | | | | | | | | | |   (3751)  all_52_10 = e2
% 195.07/31.53  | | | | | | | | | | | | | | |   (3752)  all_52_8 = e3
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (182), (3752) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3753)  op(all_52_9, all_52_9) = e3
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (180), (3750) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3754)  op(all_52_13, all_52_13) = e1
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (179), (3749) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3755)  op(all_52_15, all_52_15) = e0
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REDUCE: (611), (3751) imply:
% 195.07/31.53  | | | | | | | | | | | | | | |   (3756)  op(all_4_2, all_4_2) = e2
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 195.07/31.53  | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 195.07/31.53  | | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 195.07/31.53  | | | | | | | | | | | | | | |            (177), (178), (183), (184), (185), (270), (272),
% 195.07/31.53  | | | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 195.07/31.53  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 195.07/31.53  | | | | | | | | | | | | | | |            (306), (309), (313), (314), (317), (319), (321),
% 195.07/31.53  | | | | | | | | | | | | | | |            (323), (325), (326), (328), (330), (331), (332),
% 195.07/31.53  | | | | | | | | | | | | | | |            (333), (346), (351), (352), (361), (366), (367),
% 195.07/31.53  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.07/31.53  | | | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (538),
% 195.07/31.53  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.07/31.53  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.07/31.53  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 195.07/31.53  | | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 195.07/31.53  | | | | | | | | | | | | | | |            (574), (575), (577), (578), (580), (582), (584),
% 195.07/31.53  | | | | | | | | | | | | | | |            (586), (588), (589), (590), (591), (592), (593),
% 195.07/31.53  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (603),
% 195.07/31.53  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.07/31.53  | | | | | | | | | | | | | | |            (612), (613), (772), (773), (775), (3172), (3678),
% 195.07/31.53  | | | | | | | | | | | | | | |            (3735), (3736), (3737), (3753), (3754), (3755),
% 195.07/31.53  | | | | | | | | | | | | | | |            (3756), (function-axioms) are inconsistent by
% 195.07/31.53  | | | | | | | | | | | | | | |            sub-proof #732.
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | End of split
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | |   (3757)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.53  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.53  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | BETA: splitting (3757) gives:
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | Case 1:
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | |   (3758)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.07/31.53  | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 195.07/31.53  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 195.07/31.53  | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 195.07/31.53  | | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 195.07/31.53  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 195.07/31.53  | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 195.07/31.53  | | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 195.07/31.53  | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 195.07/31.53  | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.07/31.53  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.07/31.53  | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 195.07/31.53  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.07/31.53  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.07/31.53  | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.07/31.53  | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.07/31.53  | | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 195.07/31.53  | | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 195.07/31.53  | | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 195.07/31.53  | | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (3172), (3678),
% 195.07/31.53  | | | | | | | | | | | | | | |            (3735), (3736), (3758), (function-axioms) are
% 195.07/31.53  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | |   (3759)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.07/31.53  | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 195.07/31.53  | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 195.07/31.53  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.07/31.53  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 195.07/31.53  | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 195.07/31.53  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 195.07/31.53  | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 195.07/31.53  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 195.07/31.53  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 195.07/31.53  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 195.07/31.53  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.07/31.53  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.07/31.53  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 195.07/31.53  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 195.07/31.53  | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 195.07/31.53  | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 195.07/31.53  | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 195.07/31.53  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 195.07/31.53  | | | | | | | | | | | | | | |            (775), (3172), (3678), (3735), (3737), (3759),
% 195.07/31.53  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.53  | | | | | | | | | | | | | | |            #1008.
% 195.07/31.53  | | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | | End of split
% 195.07/31.53  | | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | End of split
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | End of split
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | End of split
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | |   (3760)  all_24_0 = e1
% 195.07/31.53  | | | | | | | | | | |   (3761)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | COMBINE_EQS: (711), (3760) imply:
% 195.07/31.53  | | | | | | | | | | |   (3762)  all_14_0 = e1
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | SIMP: (3762) implies:
% 195.07/31.53  | | | | | | | | | | |   (3763)  all_14_0 = e1
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | COMBINE_EQS: (765), (3763) imply:
% 195.07/31.53  | | | | | | | | | | |   (3764)  all_34_0 = e1
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | REDUCE: (3175), (3763) imply:
% 195.07/31.53  | | | | | | | | | | |   (3765)   ~ (e3 = e1)
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | REDUCE: (3173), (3763) imply:
% 195.07/31.53  | | | | | | | | | | |   (3766)   ~ (e2 = e1)
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | REDUCE: (62), (3763) imply:
% 195.07/31.53  | | | | | | | | | | |   (3767)  op(e0, all_14_1) = e1
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | BETA: splitting (114) gives:
% 195.07/31.53  | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | Case 1:
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | |   (3768)   ~ (all_34_0 = e1)
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | REDUCE: (3764), (3768) imply:
% 195.07/31.53  | | | | | | | | | | | |   (3769)  $false
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | CLOSE: (3769) is inconsistent.
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | |   (3770)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.53  | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | Case 1:
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | |   (3771)  all_58_15 = e0
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (3767), (3771),
% 195.07/31.53  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.53  | | | | | | | | | | | | |            #877.
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | Case 2:
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | |   (3772)   ~ (all_58_15 = e0)
% 195.07/31.53  | | | | | | | | | | | | |   (3773)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.53  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.53  | | | | | | | | | | | | |             e0)
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | ALPHA: (3773) implies:
% 195.07/31.53  | | | | | | | | | | | | |   (3774)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.53  | | | | | | | | | | | | |   (3775)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.53  | | | | | | | | | | | | | REDUCE: (541), (3772) imply:
% 195.07/31.53  | | | | | | | | | | | | |   (3776)   ~ (all_14_2 = e0)
% 195.07/31.53  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | Case 1:
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | |   (3777)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.54  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.54  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | BETA: splitting (3777) gives:
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | Case 1:
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | |   (3778)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.54  | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | ALPHA: (3778) implies:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3779)  all_52_6 = e0
% 195.07/31.54  | | | | | | | | | | | | | | |   (3780)  all_52_4 = e1
% 195.07/31.54  | | | | | | | | | | | | | | |   (3781)  all_52_2 = e2
% 195.07/31.54  | | | | | | | | | | | | | | |   (3782)  all_52_0 = e3
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (185), (3781) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3783)  op(all_52_3, all_52_3) = e2
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (184), (3780) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3784)  op(all_52_5, all_52_5) = e1
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (183), (3779) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3785)  op(all_52_7, all_52_7) = e0
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (610), (3782) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3786)  op(all_6_2, all_6_2) = e3
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.07/31.54  | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (156), (157),
% 195.07/31.54  | | | | | | | | | | | | | | |            (158), (159), (161), (163), (167), (168), (169),
% 195.07/31.54  | | | | | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 195.07/31.54  | | | | | | | | | | | | | | |            (180), (182), (270), (272), (273), (274), (275),
% 195.07/31.54  | | | | | | | | | | | | | | |            (276), (277), (280), (281), (282), (283), (284),
% 195.07/31.54  | | | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 195.07/31.54  | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 195.07/31.54  | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (328),
% 195.07/31.54  | | | | | | | | | | | | | | |            (329), (330), (331), (332), (333), (346), (351),
% 195.07/31.54  | | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.07/31.54  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (421),
% 195.07/31.54  | | | | | | | | | | | | | | |            (431), (491), (508), (538), (539), (541), (542),
% 195.07/31.54  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.07/31.54  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.07/31.54  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.07/31.54  | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.07/31.54  | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.07/31.54  | | | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (594), (595),
% 195.07/31.54  | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.07/31.54  | | | | | | | | | | | | | | |            (605), (606), (608), (609), (611), (612), (613),
% 195.07/31.54  | | | | | | | | | | | | | | |            (649), (685), (772), (773), (775), (3170), (3676),
% 195.07/31.54  | | | | | | | | | | | | | | |            (3761), (3767), (3770), (3774), (3775), (3776),
% 195.07/31.54  | | | | | | | | | | | | | | |            (3783), (3784), (3785), (3786), (function-axioms)
% 195.07/31.54  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #515.
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | Case 2:
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | |   (3787)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.54  | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | ALPHA: (3787) implies:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3788)  all_52_14 = e0
% 195.07/31.54  | | | | | | | | | | | | | | |   (3789)  all_52_12 = e1
% 195.07/31.54  | | | | | | | | | | | | | | |   (3790)  all_52_10 = e2
% 195.07/31.54  | | | | | | | | | | | | | | |   (3791)  all_52_8 = e3
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (182), (3791) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3792)  op(all_52_9, all_52_9) = e3
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (180), (3789) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3793)  op(all_52_13, all_52_13) = e1
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (179), (3788) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3794)  op(all_52_15, all_52_15) = e0
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REDUCE: (611), (3790) imply:
% 195.07/31.54  | | | | | | | | | | | | | | |   (3795)  op(all_4_2, all_4_2) = e2
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.07/31.54  | | | | | | | | | | | | | | |            (42), (43), (51), (61), (63), (158), (161), (162),
% 195.07/31.54  | | | | | | | | | | | | | | |            (163), (166), (167), (169), (172), (173), (174),
% 195.07/31.54  | | | | | | | | | | | | | | |            (175), (177), (178), (183), (184), (185), (270),
% 195.07/31.54  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 195.07/31.54  | | | | | | | | | | | | | | |            (279), (280), (281), (282), (284), (304), (306),
% 195.07/31.54  | | | | | | | | | | | | | | |            (308), (309), (313), (317), (319), (321), (323),
% 195.07/31.54  | | | | | | | | | | | | | | |            (325), (326), (328), (330), (331), (332), (333),
% 195.07/31.54  | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.07/31.54  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.07/31.54  | | | | | | | | | | | | | | |            (417), (421), (427), (431), (538), (539), (541),
% 195.07/31.54  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.07/31.54  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.07/31.54  | | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 195.07/31.54  | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (577),
% 195.07/31.54  | | | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 195.07/31.54  | | | | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.07/31.54  | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.07/31.54  | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 195.07/31.54  | | | | | | | | | | | | | | |            (613), (772), (773), (775), (3172), (3678),
% 195.07/31.54  | | | | | | | | | | | | | | |            (3767), (3774), (3775), (3776), (3792), (3793),
% 195.07/31.54  | | | | | | | | | | | | | | |            (3794), (3795), (function-axioms) are inconsistent
% 195.07/31.54  | | | | | | | | | | | | | | |            by sub-proof #618.
% 195.07/31.54  | | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | End of split
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | Case 2:
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | |   (3796)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.54  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.54  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 195.07/31.54  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (156), (158), (162),
% 195.07/31.54  | | | | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 195.07/31.54  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.07/31.54  | | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (275),
% 195.07/31.54  | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 195.07/31.54  | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 195.07/31.54  | | | | | | | | | | | | | |            (315), (316), (317), (319), (321), (323), (324),
% 195.07/31.54  | | | | | | | | | | | | | |            (325), (327), (328), (329), (330), (331), (332),
% 195.07/31.54  | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 195.07/31.54  | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 195.07/31.54  | | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (431), (491),
% 195.07/31.54  | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 195.07/31.54  | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.07/31.54  | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 195.07/31.54  | | | | | | | | | | | | | |            (565), (566), (567), (569), (570), (571), (572),
% 195.07/31.54  | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 195.07/31.54  | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 195.07/31.54  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.07/31.54  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.07/31.54  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (685),
% 195.07/31.54  | | | | | | | | | | | | | |            (773), (775), (3172), (3678), (3767), (3770),
% 195.07/31.54  | | | | | | | | | | | | | |            (3774), (3775), (3776), (3796), (function-axioms)
% 195.07/31.54  | | | | | | | | | | | | | |            are inconsistent by sub-proof #838.
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | End of split
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | End of split
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | End of split
% 195.07/31.54  | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | End of split
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | Case 2:
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | |   (3797)  all_22_1 = e2
% 195.07/31.54  | | | | | | | | | |   (3798)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | COMBINE_EQS: (658), (3797) imply:
% 195.07/31.54  | | | | | | | | | |   (3799)  all_6_1 = e2
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | SIMP: (3799) implies:
% 195.07/31.54  | | | | | | | | | |   (3800)  all_6_1 = e2
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (43), (3800) imply:
% 195.07/31.54  | | | | | | | | | |   (3801)  op(all_6_2, e3) = e2
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (42), (3800) imply:
% 195.07/31.54  | | | | | | | | | |   (3802)  op(e3, e2) = all_6_0
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 195.07/31.54  | | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (3802)
% 195.07/31.54  | | | | | | | | | |              gives:
% 195.07/31.54  | | | | | | | | | |   (3803)  all_52_9 = all_6_0
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | COMBINE_EQS: (394), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3804)  all_56_1 = all_6_0
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | COMBINE_EQS: (549), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3805)  all_58_1 = all_6_0
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (575), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3806)   ~ (all_52_13 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | SIMP: (3806) implies:
% 195.07/31.54  | | | | | | | | | |   (3807)   ~ (all_52_13 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (576), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3808)   ~ (all_52_15 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | SIMP: (3808) implies:
% 195.07/31.54  | | | | | | | | | |   (3809)   ~ (all_52_15 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (577), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3810)   ~ (all_52_17 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | SIMP: (3810) implies:
% 195.07/31.54  | | | | | | | | | |   (3811)   ~ (all_52_17 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (578), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3812)   ~ (all_52_25 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | SIMP: (3812) implies:
% 195.07/31.54  | | | | | | | | | |   (3813)   ~ (all_52_25 = all_6_0)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (557), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3814)   ~ (all_6_0 = all_6_2)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (574), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3815)   ~ (all_6_0 = all_4_2)
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | REDUCE: (182), (3803) imply:
% 195.07/31.54  | | | | | | | | | |   (3816)  op(all_6_0, all_6_0) = all_52_8
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | BETA: splitting (89) gives:
% 195.07/31.54  | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | Case 1:
% 195.07/31.54  | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | |   (3817)   ~ (all_24_0 = e1)
% 195.07/31.54  | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | REDUCE: (711), (3817) imply:
% 195.07/31.54  | | | | | | | | | | |   (3818)   ~ (all_14_0 = e1)
% 195.07/31.54  | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | BETA: splitting (119) gives:
% 195.07/31.54  | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | Case 1:
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | |   (3819)   ~ (all_36_0 = e3)
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | REDUCE: (3169), (3819) imply:
% 195.07/31.54  | | | | | | | | | | | |   (3820)  $false
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | CLOSE: (3820) is inconsistent.
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | Case 2:
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | |   (3821)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.54  | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | Case 1:
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | |   (3822)  all_58_15 = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | COMBINE_EQS: (541), (3822) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3823)  all_14_2 = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (573), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3824)   ~ (all_52_7 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (591), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3825)   ~ (all_52_15 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (603), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3826)   ~ (all_52_23 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (606), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3827)   ~ (all_52_25 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (613), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3828)  op(e0, e0) = all_52_30
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (63), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3829)  op(e0, e0) = all_14_1
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (61), (3823) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3830)  op(e0, e0) = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.07/31.54  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3828), (3829)
% 195.07/31.54  | | | | | | | | | | | | |              gives:
% 195.07/31.54  | | | | | | | | | | | | |   (3831)  all_52_30 = all_14_1
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.07/31.54  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (3828), (3830)
% 195.07/31.54  | | | | | | | | | | | | |              gives:
% 195.07/31.54  | | | | | | | | | | | | |   (3832)  all_52_30 = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | COMBINE_EQS: (3831), (3832) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3833)  all_14_1 = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | SIMP: (3833) implies:
% 195.07/31.54  | | | | | | | | | | | | |   (3834)  all_14_1 = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (62), (3834) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3835)  op(e0, e0) = all_14_0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.07/31.54  | | | | | | | | | | | | |              e0, e0, simplifying with (3830), (3835) gives:
% 195.07/31.54  | | | | | | | | | | | | |   (3836)  all_14_0 = e0
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (3175), (3836) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3837)   ~ (e3 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (3173), (3836) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3838)   ~ (e2 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | REDUCE: (3818), (3836) imply:
% 195.07/31.54  | | | | | | | | | | | | |   (3839)   ~ (e1 = e0)
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | BETA: splitting (284) gives:
% 195.07/31.54  | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | Case 1:
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | |   (3840)  all_56_1 = e3
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | COMBINE_EQS: (3804), (3840) imply:
% 195.07/31.54  | | | | | | | | | | | | | |   (3841)  all_6_0 = e3
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | COMBINE_EQS: (3805), (3841) imply:
% 195.07/31.54  | | | | | | | | | | | | | |   (3842)  all_58_1 = e3
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | REDUCE: (3807), (3841) imply:
% 195.07/31.54  | | | | | | | | | | | | | |   (3843)   ~ (all_52_13 = e3)
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | REDUCE: (3809), (3841) imply:
% 195.07/31.54  | | | | | | | | | | | | | |   (3844)   ~ (all_52_15 = e3)
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | REDUCE: (3811), (3841) imply:
% 195.07/31.54  | | | | | | | | | | | | | |   (3845)   ~ (all_52_17 = e3)
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | REDUCE: (3813), (3841) imply:
% 195.07/31.54  | | | | | | | | | | | | | |   (3846)   ~ (all_52_25 = e3)
% 195.07/31.54  | | | | | | | | | | | | | | 
% 195.07/31.54  | | | | | | | | | | | | | | REDUCE: (3814), (3841) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3847)   ~ (all_6_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | SIMP: (3847) implies:
% 195.07/31.55  | | | | | | | | | | | | | |   (3848)   ~ (all_6_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3815), (3841) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3849)   ~ (all_4_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | SIMP: (3849) implies:
% 195.07/31.55  | | | | | | | | | | | | | |   (3850)   ~ (all_4_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3816), (3841) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3851)  op(e3, e3) = all_52_8
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.07/31.55  | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (3851)
% 195.07/31.55  | | | | | | | | | | | | | |              gives:
% 195.07/31.55  | | | | | | | | | | | | | |   (3852)  all_52_8 = all_6_2
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | |   (3853)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.55  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.55  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | BETA: splitting (3853) gives:
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3854)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.55  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (51), (53), (61), (156), (157), (162), (166),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (175), (179), (183), (184), (185), (272), (273),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (304), (305), (306), (321), (332), (346), (351),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (387), (405), (431), (524), (542), (543), (547),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (555), (564), (569), (571), (572), (573), (610),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (645), (772), (3170), (3676), (3821), (3822),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (3824), (3825), (3854), (function-axioms) are
% 195.07/31.55  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #514.
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3855)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.55  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REF_CLOSE: (3848), (3852), (3855) are inconsistent by
% 195.07/31.55  | | | | | | | | | | | | | | | |            sub-proof #834.
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | |   (3856)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.55  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.55  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (53),
% 195.07/31.55  | | | | | | | | | | | | | | |            (61), (158), (166), (168), (172), (173), (174),
% 195.07/31.55  | | | | | | | | | | | | | | |            (175), (177), (178), (182), (183), (184), (274),
% 195.07/31.55  | | | | | | | | | | | | | | |            (278), (282), (283), (306), (307), (309), (313),
% 195.07/31.55  | | | | | | | | | | | | | | |            (315), (317), (321), (325), (327), (329), (331),
% 195.07/31.55  | | | | | | | | | | | | | | |            (332), (351), (352), (366), (372), (375), (387),
% 195.07/31.55  | | | | | | | | | | | | | | |            (388), (393), (405), (415), (427), (542), (543),
% 195.07/31.55  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.07/31.55  | | | | | | | | | | | | | | |            (557), (559), (561), (563), (564), (570), (572),
% 195.07/31.55  | | | | | | | | | | | | | | |            (584), (590), (592), (593), (594), (595), (596),
% 195.07/31.55  | | | | | | | | | | | | | | |            (597), (598), (600), (602), (604), (605), (609),
% 195.07/31.55  | | | | | | | | | | | | | | |            (610), (612), (3801), (3822), (3824), (3826),
% 195.07/31.55  | | | | | | | | | | | | | | |            (3827), (3830), (3842), (3843), (3844), (3845),
% 195.07/31.55  | | | | | | | | | | | | | | |            (3846), (3850), (3851), (3856), (function-axioms)
% 195.07/31.55  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #822.
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | |   (3857)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 195.07/31.55  | | | | | | | | | | | | | |            (610), (739), (773), (775), (3798), (3801),
% 195.07/31.55  | | | | | | | | | | | | | |            (3804), (3814), (3857), (function-axioms) are
% 195.07/31.55  | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | |   (3858)   ~ (all_58_15 = e0)
% 195.07/31.55  | | | | | | | | | | | | |   (3859)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.55  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.55  | | | | | | | | | | | | |             e0)
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | ALPHA: (3859) implies:
% 195.07/31.55  | | | | | | | | | | | | |   (3860)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.55  | | | | | | | | | | | | |   (3861)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | REDUCE: (541), (3858) imply:
% 195.07/31.55  | | | | | | | | | | | | |   (3862)   ~ (all_14_2 = e0)
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | BETA: splitting (284) gives:
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | |   (3863)  all_56_1 = e3
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | COMBINE_EQS: (3804), (3863) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3864)  all_6_0 = e3
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | COMBINE_EQS: (3805), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3865)  all_58_1 = e3
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3807), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3866)   ~ (all_52_13 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3809), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3867)   ~ (all_52_15 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3811), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3868)   ~ (all_52_17 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3813), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3869)   ~ (all_52_25 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3814), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3870)   ~ (all_6_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | SIMP: (3870) implies:
% 195.07/31.55  | | | | | | | | | | | | | |   (3871)   ~ (all_6_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3815), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3872)   ~ (all_4_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | SIMP: (3872) implies:
% 195.07/31.55  | | | | | | | | | | | | | |   (3873)   ~ (all_4_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3816), (3864) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3874)  op(e3, e3) = all_52_8
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.07/31.55  | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (3874)
% 195.07/31.55  | | | | | | | | | | | | | |              gives:
% 195.07/31.55  | | | | | | | | | | | | | |   (3875)  all_52_8 = all_6_2
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | |   (3876)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.55  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.55  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | BETA: splitting (3876) gives:
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3877)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.55  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | ALPHA: (3877) implies:
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3878)  all_52_6 = e0
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3879)  all_52_4 = e1
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3880)  all_52_2 = e2
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3881)  all_52_0 = e3
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REDUCE: (185), (3880) imply:
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3882)  op(all_52_3, all_52_3) = e2
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REDUCE: (184), (3879) imply:
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3883)  op(all_52_5, all_52_5) = e1
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REDUCE: (183), (3878) imply:
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3884)  op(all_52_7, all_52_7) = e0
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REDUCE: (610), (3881) imply:
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3885)  op(all_6_2, all_6_2) = e3
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (38), (41), (42), (43),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (51), (53), (61), (62), (63), (156), (157), (158),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (159), (161), (163), (167), (168), (169), (172),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (182), (270), (271), (272), (273), (274), (275),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (307), (308),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (309), (311), (312), (313), (314), (315), (317),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (327),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (417), (421), (431), (524), (538), (539), (540),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (561), (563), (564), (565), (566), (567), (568),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (587), (588), (589), (590), (591), (593), (594),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (611),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (612), (613), (645), (772), (773), (775), (3170),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (3173), (3175), (3676), (3818), (3821), (3860),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (3861), (3862), (3882), (3883), (3884), (3885),
% 195.07/31.55  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.55  | | | | | | | | | | | | | | | |            #518.
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | |   (3886)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.55  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | | REF_CLOSE: (3871), (3875), (3886) are inconsistent by
% 195.07/31.55  | | | | | | | | | | | | | | | |            sub-proof #834.
% 195.07/31.55  | | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | |   (3887)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.55  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.55  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 195.07/31.55  | | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 195.07/31.55  | | | | | | | | | | | | | | |            (162), (166), (167), (168), (172), (173), (174),
% 195.07/31.55  | | | | | | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 195.07/31.55  | | | | | | | | | | | | | | |            (185), (270), (271), (273), (274), (275), (277),
% 195.07/31.55  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (306), (307),
% 195.07/31.55  | | | | | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 195.07/31.55  | | | | | | | | | | | | | | |            (321), (324), (325), (326), (327), (328), (329),
% 195.07/31.55  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (351), (352), (361),
% 195.07/31.55  | | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 195.07/31.55  | | | | | | | | | | | | | | |            (405), (411), (415), (431), (538), (539), (541),
% 195.07/31.55  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.07/31.55  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (559), (561), (562),
% 195.07/31.55  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (569), (570),
% 195.07/31.55  | | | | | | | | | | | | | | |            (572), (573), (574), (575), (578), (582), (584),
% 195.07/31.55  | | | | | | | | | | | | | | |            (586), (588), (590), (591), (592), (593), (594),
% 195.07/31.55  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.07/31.55  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.07/31.55  | | | | | | | | | | | | | | |            (612), (613), (3170), (3801), (3860), (3861),
% 195.07/31.55  | | | | | | | | | | | | | | |            (3862), (3865), (3866), (3867), (3868), (3869),
% 195.07/31.55  | | | | | | | | | | | | | | |            (3871), (3873), (3874), (3887), (function-axioms)
% 195.07/31.55  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #513.
% 195.07/31.55  | | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | |   (3888)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 195.07/31.55  | | | | | | | | | | | | | |            (610), (739), (773), (775), (3798), (3801),
% 195.07/31.55  | | | | | | | | | | | | | |            (3804), (3814), (3888), (function-axioms) are
% 195.07/31.55  | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | End of split
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | |   (3889)  all_24_0 = e1
% 195.07/31.55  | | | | | | | | | | |   (3890)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | COMBINE_EQS: (711), (3889) imply:
% 195.07/31.55  | | | | | | | | | | |   (3891)  all_14_0 = e1
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | COMBINE_EQS: (765), (3891) imply:
% 195.07/31.55  | | | | | | | | | | |   (3892)  all_34_0 = e1
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | REDUCE: (3173), (3891) imply:
% 195.07/31.55  | | | | | | | | | | |   (3893)   ~ (e2 = e1)
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | REDUCE: (62), (3891) imply:
% 195.07/31.55  | | | | | | | | | | |   (3894)  op(e0, all_14_1) = e1
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | BETA: splitting (114) gives:
% 195.07/31.55  | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | |   (3895)   ~ (all_34_0 = e1)
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | REDUCE: (3892), (3895) imply:
% 195.07/31.55  | | | | | | | | | | | |   (3896)  $false
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | CLOSE: (3896) is inconsistent.
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | |   (3897)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.55  | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | |   (3898)  all_58_15 = e0
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (3894), (3898),
% 195.07/31.55  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.55  | | | | | | | | | | | | |            #877.
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | Case 2:
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | |   (3899)   ~ (all_58_15 = e0)
% 195.07/31.55  | | | | | | | | | | | | |   (3900)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.55  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.55  | | | | | | | | | | | | |             e0)
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | ALPHA: (3900) implies:
% 195.07/31.55  | | | | | | | | | | | | |   (3901)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.55  | | | | | | | | | | | | |   (3902)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | REDUCE: (541), (3899) imply:
% 195.07/31.55  | | | | | | | | | | | | |   (3903)   ~ (all_14_2 = e0)
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | BETA: splitting (284) gives:
% 195.07/31.55  | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | Case 1:
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | |   (3904)  all_56_1 = e3
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | COMBINE_EQS: (3804), (3904) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3905)  all_6_0 = e3
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | COMBINE_EQS: (3805), (3905) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3906)  all_58_1 = e3
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3807), (3905) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3907)   ~ (all_52_13 = e3)
% 195.07/31.55  | | | | | | | | | | | | | | 
% 195.07/31.55  | | | | | | | | | | | | | | REDUCE: (3809), (3905) imply:
% 195.07/31.55  | | | | | | | | | | | | | |   (3908)   ~ (all_52_15 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | REDUCE: (3811), (3905) imply:
% 195.07/31.56  | | | | | | | | | | | | | |   (3909)   ~ (all_52_17 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | REDUCE: (3813), (3905) imply:
% 195.07/31.56  | | | | | | | | | | | | | |   (3910)   ~ (all_52_25 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | REDUCE: (3814), (3905) imply:
% 195.07/31.56  | | | | | | | | | | | | | |   (3911)   ~ (all_6_2 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | SIMP: (3911) implies:
% 195.07/31.56  | | | | | | | | | | | | | |   (3912)   ~ (all_6_2 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | REDUCE: (3815), (3905) imply:
% 195.07/31.56  | | | | | | | | | | | | | |   (3913)   ~ (all_4_2 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | SIMP: (3913) implies:
% 195.07/31.56  | | | | | | | | | | | | | |   (3914)   ~ (all_4_2 = e3)
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | REDUCE: (3816), (3905) imply:
% 195.07/31.56  | | | | | | | | | | | | | |   (3915)  op(e3, e3) = all_52_8
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.07/31.56  | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (3915)
% 195.07/31.56  | | | | | | | | | | | | | |              gives:
% 195.07/31.56  | | | | | | | | | | | | | |   (3916)  all_52_8 = all_6_2
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | |   (3917)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.56  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.56  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | BETA: splitting (3917) gives:
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3918)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.56  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | ALPHA: (3918) implies:
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3919)  all_52_6 = e0
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3920)  all_52_4 = e1
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3921)  all_52_2 = e2
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3922)  all_52_0 = e3
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | REDUCE: (185), (3921) imply:
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3923)  op(all_52_3, all_52_3) = e2
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | REDUCE: (184), (3920) imply:
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3924)  op(all_52_5, all_52_5) = e1
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | REDUCE: (183), (3919) imply:
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3925)  op(all_52_7, all_52_7) = e0
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | REDUCE: (610), (3922) imply:
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3926)  op(all_6_2, all_6_2) = e3
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (156), (157),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (158), (159), (161), (163), (167), (168), (169),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (180), (182), (270), (272), (273), (274), (275),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (276), (277), (280), (281), (282), (283), (284),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (328),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (329), (330), (331), (332), (333), (346), (351),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (421),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (431), (491), (508), (538), (539), (541), (542),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (594), (595),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (605), (606), (608), (609), (611), (612), (613),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (649), (685), (772), (773), (775), (3170), (3676),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (3890), (3894), (3897), (3901), (3902), (3903),
% 195.07/31.56  | | | | | | | | | | | | | | | |            (3923), (3924), (3925), (3926), (function-axioms)
% 195.07/31.56  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #515.
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | |   (3927)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.07/31.56  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | | REF_CLOSE: (3912), (3916), (3927) are inconsistent by
% 195.07/31.56  | | | | | | | | | | | | | | | |            sub-proof #834.
% 195.07/31.56  | | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | |   (3928)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.07/31.56  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.07/31.56  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 195.07/31.56  | | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 195.07/31.56  | | | | | | | | | | | | | | |            (162), (166), (167), (168), (172), (173), (174),
% 195.07/31.56  | | | | | | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 195.07/31.56  | | | | | | | | | | | | | | |            (185), (270), (271), (273), (274), (275), (277),
% 195.07/31.56  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (306), (307),
% 195.07/31.56  | | | | | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 195.07/31.56  | | | | | | | | | | | | | | |            (321), (324), (325), (326), (327), (328), (329),
% 195.07/31.56  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (351), (352), (361),
% 195.07/31.56  | | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 195.07/31.56  | | | | | | | | | | | | | | |            (405), (411), (415), (431), (538), (539), (541),
% 195.07/31.56  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.07/31.56  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (559), (561), (562),
% 195.07/31.56  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (569), (570),
% 195.07/31.56  | | | | | | | | | | | | | | |            (572), (573), (574), (575), (578), (582), (584),
% 195.07/31.56  | | | | | | | | | | | | | | |            (586), (588), (590), (591), (592), (593), (594),
% 195.07/31.56  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.07/31.56  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.07/31.56  | | | | | | | | | | | | | | |            (612), (613), (3170), (3801), (3901), (3902),
% 195.07/31.56  | | | | | | | | | | | | | | |            (3903), (3906), (3907), (3908), (3909), (3910),
% 195.07/31.56  | | | | | | | | | | | | | | |            (3912), (3914), (3915), (3928), (function-axioms)
% 195.07/31.56  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #513.
% 195.07/31.56  | | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | |   (3929)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (166), (285), (522), (540), (551),
% 195.07/31.56  | | | | | | | | | | | | | |            (610), (739), (773), (775), (3798), (3801),
% 195.07/31.56  | | | | | | | | | | | | | |            (3804), (3814), (3929), (function-axioms) are
% 195.07/31.56  | | | | | | | | | | | | | |            inconsistent by sub-proof #820.
% 195.07/31.56  | | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | 
% 195.07/31.56  | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | |   (3930)  all_18_0 = e3
% 195.07/31.56  | | | | | | | |   (3931)   ~ (all_18_1 = e2) |  ~ (all_18_2 = e1)
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | | COMBINE_EQS: (761), (3930) imply:
% 195.07/31.56  | | | | | | | |   (3932)  all_14_0 = e3
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | | SIMP: (3932) implies:
% 195.07/31.56  | | | | | | | |   (3933)  all_14_0 = e3
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | | REDUCE: (62), (3933) imply:
% 195.07/31.56  | | | | | | | |   (3934)  op(e0, all_14_1) = e3
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | | BETA: splitting (79) gives:
% 195.07/31.56  | | | | | | | | 
% 195.07/31.56  | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | 
% 195.07/31.56  | | | | | | | | |   (3935)   ~ (all_20_0 = e3)
% 195.07/31.56  | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | REDUCE: (758), (3935) imply:
% 195.07/31.56  | | | | | | | | |   (3936)   ~ (all_4_0 = e3)
% 195.07/31.56  | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | BETA: splitting (84) gives:
% 195.07/31.56  | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | |   (3937)   ~ (all_22_1 = e2)
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | REDUCE: (658), (3937) imply:
% 195.07/31.56  | | | | | | | | | |   (3938)   ~ (all_6_1 = e2)
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | BETA: splitting (109) gives:
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | |   (3939)   ~ (all_32_1 = e3)
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | REDUCE: (663), (3939) imply:
% 195.07/31.56  | | | | | | | | | | |   (3940)   ~ (all_4_1 = e3)
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | BETA: splitting (119) gives:
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | |   (3941)   ~ (all_36_0 = e3)
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | REDUCE: (3169), (3941) imply:
% 195.07/31.56  | | | | | | | | | | | |   (3942)  $false
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | CLOSE: (3942) is inconsistent.
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | |   (3943)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | Case 1:
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | |   (3944)  all_58_15 = e0
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (3934), (3944),
% 195.07/31.56  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.56  | | | | | | | | | | | | |            #678.
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | |   (3945)   ~ (all_58_15 = e0)
% 195.07/31.56  | | | | | | | | | | | | |   (3946)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.56  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.56  | | | | | | | | | | | | |             e0)
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | ALPHA: (3946) implies:
% 195.07/31.56  | | | | | | | | | | | | |   (3947)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.56  | | | | | | | | | | | | |   (3948)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | REDUCE: (541), (3945) imply:
% 195.07/31.56  | | | | | | | | | | | | |   (3949)   ~ (all_14_2 = e0)
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 195.07/31.56  | | | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (63), (156),
% 195.07/31.56  | | | | | | | | | | | | |            (157), (158), (161), (162), (166), (167), (168),
% 195.07/31.56  | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 195.07/31.56  | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 195.07/31.56  | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (276),
% 195.07/31.56  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 195.07/31.56  | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (307), (309),
% 195.07/31.56  | | | | | | | | | | | | |            (311), (312), (313), (315), (316), (317), (319),
% 195.07/31.56  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 195.07/31.56  | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 195.07/31.56  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.07/31.56  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.07/31.56  | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (524), (538),
% 195.07/31.56  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.07/31.56  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.07/31.56  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 195.07/31.56  | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 195.07/31.56  | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 195.07/31.56  | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (590),
% 195.07/31.56  | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 195.07/31.56  | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 195.07/31.56  | | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 195.07/31.56  | | | | | | | | | | | | |            (645), (772), (773), (775), (3168), (3172),
% 195.07/31.56  | | | | | | | | | | | | |            (3936), (3938), (3940), (3943), (3947), (3948),
% 195.07/31.56  | | | | | | | | | | | | |            (3949), (function-axioms) are inconsistent by
% 195.07/31.56  | | | | | | | | | | | | |            sub-proof #510.
% 195.07/31.56  | | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | |   (3950)  all_32_1 = e3
% 195.07/31.56  | | | | | | | | | | |   (3951)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 195.07/31.56  | | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (124), (158),
% 195.07/31.56  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.07/31.56  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 195.07/31.56  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 195.07/31.56  | | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 195.07/31.56  | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 195.07/31.56  | | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (314),
% 195.07/31.56  | | | | | | | | | | |            (315), (316), (317), (318), (319), (321), (323),
% 195.07/31.56  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 195.07/31.56  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 195.07/31.56  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.07/31.56  | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 195.07/31.56  | | | | | | | | | | |            (431), (523), (525), (538), (539), (540), (541),
% 195.07/31.56  | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.07/31.56  | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.07/31.56  | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 195.07/31.56  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 195.07/31.56  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 195.07/31.56  | | | | | | | | | | |            (587), (588), (590), (591), (592), (593), (594),
% 195.07/31.56  | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.07/31.56  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.07/31.56  | | | | | | | | | | |            (611), (612), (613), (663), (686), (721), (766),
% 195.07/31.56  | | | | | | | | | | |            (772), (773), (775), (3172), (3934), (3936),
% 195.07/31.56  | | | | | | | | | | |            (3938), (3950), (3951), (function-axioms) are
% 195.07/31.56  | | | | | | | | | | |            inconsistent by sub-proof #668.
% 195.07/31.56  | | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | End of split
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | Case 2:
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | |   (3952)  all_22_1 = e2
% 195.07/31.56  | | | | | | | | | |   (3953)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | COMBINE_EQS: (658), (3952) imply:
% 195.07/31.56  | | | | | | | | | |   (3954)  all_6_1 = e2
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.56  | | | | | | | | | | SIMP: (3954) implies:
% 195.07/31.56  | | | | | | | | | |   (3955)  all_6_1 = e2
% 195.07/31.56  | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 195.07/31.57  | | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 195.07/31.57  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.07/31.57  | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 195.07/31.57  | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 195.07/31.57  | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 195.07/31.57  | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 195.07/31.57  | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 195.07/31.57  | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 195.07/31.57  | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 195.07/31.57  | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.07/31.57  | | | | | | | | | |            (415), (431), (522), (538), (539), (540), (541),
% 195.07/31.57  | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.07/31.57  | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.07/31.57  | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.07/31.57  | | | | | | | | | |            (570), (572), (573), (574), (575), (576), (577),
% 195.07/31.57  | | | | | | | | | |            (578), (582), (584), (586), (588), (590), (591),
% 195.07/31.57  | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.07/31.57  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.07/31.57  | | | | | | | | | |            (608), (609), (610), (612), (613), (739), (773),
% 195.07/31.57  | | | | | | | | | |            (775), (3170), (3172), (3934), (3953), (3955),
% 195.07/31.57  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.57  | | | | | | | | | |            #508.
% 195.07/31.57  | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | End of split
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | |   (3956)  all_20_0 = e3
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | COMBINE_EQS: (758), (3956) imply:
% 195.07/31.57  | | | | | | | | |   (3957)  all_4_0 = e3
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | SIMP: (3957) implies:
% 195.07/31.57  | | | | | | | | |   (3958)  all_4_0 = e3
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | REDUCE: (37), (3958) imply:
% 195.07/31.57  | | | | | | | | |   (3959)  op(e2, all_4_1) = e3
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | BETA: splitting (84) gives:
% 195.07/31.57  | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | |   (3960)   ~ (all_22_1 = e2)
% 195.07/31.57  | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | REDUCE: (658), (3960) imply:
% 195.07/31.57  | | | | | | | | | |   (3961)   ~ (all_6_1 = e2)
% 195.07/31.57  | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | BETA: splitting (119) gives:
% 195.07/31.57  | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | |   (3962)   ~ (all_36_0 = e3)
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | REDUCE: (3169), (3962) imply:
% 195.07/31.57  | | | | | | | | | | |   (3963)  $false
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | CLOSE: (3963) is inconsistent.
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | |   (3964)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | BETA: splitting (303) gives:
% 195.07/31.57  | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | |   (3965)  all_58_15 = e0
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (3934), (3965),
% 195.07/31.57  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.57  | | | | | | | | | | | |            #693.
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | |   (3966)   ~ (all_58_15 = e0)
% 195.07/31.57  | | | | | | | | | | | |   (3967)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.07/31.57  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.07/31.57  | | | | | | | | | | | |             e0)
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | ALPHA: (3967) implies:
% 195.07/31.57  | | | | | | | | | | | |   (3968)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.07/31.57  | | | | | | | | | | | |   (3969)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | REDUCE: (541), (3966) imply:
% 195.07/31.57  | | | | | | | | | | | |   (3970)   ~ (all_14_2 = e0)
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.07/31.57  | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | |   (3971)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.57  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.07/31.57  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.07/31.57  | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | BETA: splitting (3971) gives:
% 195.07/31.57  | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | |   (3972)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.07/31.57  | | | | | | | | | | | | | |           all_52_6 = e0
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | ALPHA: (3972) implies:
% 195.07/31.57  | | | | | | | | | | | | | |   (3973)  all_52_6 = e0
% 195.07/31.57  | | | | | | | | | | | | | |   (3974)  all_52_4 = e1
% 195.07/31.57  | | | | | | | | | | | | | |   (3975)  all_52_2 = e2
% 195.07/31.57  | | | | | | | | | | | | | |   (3976)  all_52_0 = e3
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | REDUCE: (185), (3975) imply:
% 195.07/31.57  | | | | | | | | | | | | | |   (3977)  op(all_52_3, all_52_3) = e2
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | REDUCE: (184), (3974) imply:
% 195.07/31.57  | | | | | | | | | | | | | |   (3978)  op(all_52_5, all_52_5) = e1
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | REDUCE: (183), (3973) imply:
% 195.07/31.57  | | | | | | | | | | | | | |   (3979)  op(all_52_7, all_52_7) = e0
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | REDUCE: (610), (3976) imply:
% 195.07/31.57  | | | | | | | | | | | | | |   (3980)  op(all_6_2, all_6_2) = e3
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 195.07/31.57  | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | |   (3981)  all_56_15 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (3981) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3982)  all_14_2 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (573), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3983)   ~ (all_52_7 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (591), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3984)   ~ (all_52_15 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (603), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3985)   ~ (all_52_23 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (608), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3986)   ~ (all_52_27 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (609), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3987)   ~ (all_52_29 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (613), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3988)  op(e3, e3) = all_52_30
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (61), (3982) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3989)  op(e0, e0) = e3
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (42), (43), (51), (53),
% 195.07/31.57  | | | | | | | | | | | | | | |            (61), (156), (157), (173), (182), (271), (272),
% 195.07/31.57  | | | | | | | | | | | | | | |            (273), (277), (278), (279), (281), (304), (305),
% 195.07/31.57  | | | | | | | | | | | | | | |            (311), (312), (313), (320), (321), (324), (330),
% 195.07/31.57  | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (367),
% 195.07/31.57  | | | | | | | | | | | | | | |            (372), (375), (387), (405), (411), (417), (427),
% 195.07/31.57  | | | | | | | | | | | | | | |            (431), (524), (543), (544), (546), (547), (548),
% 195.07/31.57  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (562), (563), (564),
% 195.07/31.57  | | | | | | | | | | | | | | |            (565), (566), (567), (569), (571), (572), (573),
% 195.07/31.57  | | | | | | | | | | | | | | |            (574), (575), (582), (586), (596), (598), (600),
% 195.07/31.57  | | | | | | | | | | | | | | |            (607), (612), (645), (772), (775), (3168), (3964),
% 195.07/31.57  | | | | | | | | | | | | | | |            (3977), (3978), (3979), (3980), (3983), (3984),
% 195.07/31.57  | | | | | | | | | | | | | | |            (3985), (3986), (3987), (3988), (3989),
% 195.07/31.57  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.57  | | | | | | | | | | | | | | |            #512.
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | |   (3990)   ~ (all_56_15 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | |   (3991)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | REDUCE: (538), (3990) imply:
% 195.07/31.57  | | | | | | | | | | | | | | |   (3992)   ~ (all_14_2 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | |   (3993)  all_56_13 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (53), (61), (62), (63), (158), (159), (161),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (168), (172), (173), (177), (178), (180), (182),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (273), (274), (276), (277), (279), (280), (281),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (283), (284), (285), (304), (306), (307), (308),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (309), (311), (312), (313), (315), (317), (319),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (320), (321), (323), (324), (328), (330), (331),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (332), (333), (346), (351), (352), (366), (367),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (405), (411),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (539), (540),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (561), (563), (564), (565), (566), (567), (568),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (569), (570), (571), (573), (574), (575), (576),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (586), (587), (588),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (589), (590), (591), (595), (596), (597), (598),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (600), (602), (606), (607), (608), (609), (611),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (612), (613), (773), (775), (3170), (3173),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (3968), (3969), (3970), (3977), (3978), (3979),
% 195.07/31.57  | | | | | | | | | | | | | | | |            (3980), (3991), (3993), (function-axioms) are
% 195.07/31.57  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #507.
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | |   (3994)   ~ (all_56_13 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | REDUCE: (346), (3994) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | |   (3995)   ~ (all_52_15 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | |   (3996)  all_58_12 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (3996) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | |   (3997)  all_52_7 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 195.07/31.57  | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (555), (564), (569),
% 195.07/31.57  | | | | | | | | | | | | | | | | |            (573), (3977), (3978), (3979), (3980), (3997),
% 195.07/31.57  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.57  | | | | | | | | | | | | | | | | |            #1361.
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | |   (3998)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | BETA: splitting (3998) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | |   (3999)  all_58_13 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (3995), (3999) are inconsistent by
% 195.07/31.57  | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | |   (4000)  all_58_14 = e3 | all_58_15 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | BETA: splitting (4000) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4001)  all_58_14 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (4001) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4002)  all_52_23 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | SIMP: (4002) implies:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4003)  all_52_23 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | REDUCE: (572), (4003) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4004)   ~ (all_52_7 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | REDUCE: (594), (4003) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4005)   ~ (all_52_17 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | REDUCE: (597), (4003) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4006)   ~ (all_52_19 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | REDUCE: (600), (4003) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4007)   ~ (all_10_2 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | SIMP: (4007) implies:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4008)   ~ (all_10_2 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (4003) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4009)  op(e3, e3) = all_52_22
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (4009)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |              gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | |   (4010)  all_52_22 = all_6_2
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | |   (4011)  all_56_6 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (417), (4006), (4011) are inconsistent by
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | |   (4012)   ~ (all_56_6 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | |   (4013)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | |   (4014)  all_56_12 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (4004), (4014) are inconsistent by
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | |   (4015)   ~ (all_56_12 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | |   (4016)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | |   (4017)  all_56_2 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (4017) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | |   (4018)  all_52_17 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4005), (4018) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | |   (4019)  $false
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4019) is inconsistent.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | |   (4020)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |   (4021)  all_56_8 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (4021) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |   (4022)  all_52_5 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4022) implies:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |   (4023)  all_52_5 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (553), (564), (567), (569), (3977),
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |            (3978), (3980), (4023), (function-axioms) are
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | |   (4024)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4025)  all_58_0 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (4025) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4026)  all_6_2 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (4026) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4027)   ~ (all_52_3 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (4026) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4028)   ~ (all_52_5 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (4026) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4029)   ~ (all_52_9 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (4026) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4030)  op(e3, e3) = all_6_1
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (4026) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4031)  op(e3, e3) = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (4030), (4031) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4032)  all_6_1 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (4032) imply:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4033)  op(e3, e3) = all_6_0
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (4031), (4033) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | |   (4034)  all_6_0 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (4035)  all_58_6 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (4028), (4035) are inconsistent by
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (4036)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4037)  all_58_2 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (4027), (4037) are inconsistent by
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1369.
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4038)   ~ (all_58_2 = e3)
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4039)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 195.07/31.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4040)  all_56_4 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (4027), (4040) are inconsistent by
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4041)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4042)  all_56_1 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (4042) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4043)  all_52_9 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4029), (4043) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4044)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4044) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4045)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4046)  all_58_4 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (4046) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4047)  all_52_17 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4047) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4048)  all_52_17 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (4048) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4049)   ~ (all_52_19 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4049) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4050)   ~ (all_52_19 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (4048) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4051)   ~ (all_10_2 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4051) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4052)   ~ (all_10_2 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4005), (4048) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4053)   ~ (e3 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (178), (4048) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4054)  op(e2, e2) = all_52_16
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_16, e2, e2, simplifying with (36), (4054)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4055)  all_52_16 = all_4_2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4056)  all_56_5 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (61), (169), (182), (276), (305),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (314), (319), (320), (351), (366), (367),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (411), (415),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (421), (431), (539), (544), (545), (546), (547),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (573),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (575), (577), (578), (580), (588), (589), (595),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (605), (772), (3959), (3969), (3977), (3978),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3979), (4001), (4005), (4008), (4016), (4020),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4024), (4036), (4041), (4045), (4056),
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #703.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4057)   ~ (all_56_5 = e3)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (4057) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4058)   ~ (all_4_2 = e3)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4039) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4059)  all_58_3 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4059) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4060)  all_4_2 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4058), (4060) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4061)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4061) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4062)  all_58_5 = e3 | all_58_10 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4062) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4063)  all_58_5 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (375), (4006), (4063) are inconsistent by
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4064)  all_58_10 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4064) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4065)  all_52_27 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4065) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4066)  all_52_27 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (4066) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4067)   ~ (all_52_29 = e3)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4067) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4068)   ~ (all_52_29 = e3)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (608), (4066) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4069)   ~ (all_14_2 = e3)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4036) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4070)  all_58_7 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (4070) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4071)  all_52_13 = e3
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (4071) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4072)   ~ (all_4_2 = e3)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4073)  all_58_6 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4073) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4074)  all_52_5 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4074) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4075)  all_52_5 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (4075) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4076)   ~ (all_52_3 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4075) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4077)   ~ (all_52_7 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4077) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4078)   ~ (all_52_7 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3978), (4075) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4079)  op(e2, e2) = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4080)  all_58_2 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (4076), (4080) are inconsistent by
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1156.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4081)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4081) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4082)  all_58_3 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4082) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4083)  all_4_2 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (4083) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4084)   ~ (all_52_15 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (4083) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4085)  op(e2, e2) = all_52_10
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (4083) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4086)  op(e2, e2) = all_4_1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4083) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4087)  op(e2, e2) = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4088)  all_58_12 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (4078), (4088) are inconsistent by
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #506.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4089)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4089) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4090)  all_58_13 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (4084), (4090) are inconsistent by
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #784.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4091)  all_58_14 = e2 | all_58_15 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4091) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4092)  all_58_14 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4001), (4092) are inconsistent by sub-proof
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #701.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4093)  all_58_15 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4093) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4094)  all_14_2 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (4094) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4095)  op(e2, e2) = all_52_30
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_4_1,
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (4079), (4086) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4096)  all_4_1 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_30, e2, e2, simplifying with (4086), (4095)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4097)  all_52_30 = all_4_1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_30,
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e2, e2, simplifying with (4085), (4095)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4098)  all_52_10 = all_52_30
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e2, e2, simplifying with (4085), (4087)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4099)  all_52_10 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4098), (4099) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4100)  all_52_30 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4100) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4101)  all_52_30 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4097), (4101) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4102)  all_4_1 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4102) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4103)  all_4_1 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4096), (4103) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4104)  e2 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (4104) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4105)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4105) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4106)  all_58_5 = e2 | all_58_10 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (375), (4050), (4064), (4106) are
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #760.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4107)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4107) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4108)  all_58_7 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4070), (4108) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4109)  e3 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4109) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4110)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4110) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4111)  all_58_8 = e2 | all_58_11 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4111) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4112)  all_58_8 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (4112) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4113)  all_10_2 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4052), (4113) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4114)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4114) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4115)  all_58_11 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4115) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4116)  all_52_29 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4116) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4117)  all_52_29 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (609), (4117) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4118)   ~ (all_14_2 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4118) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4119)   ~ (all_14_2 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (4117) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4120)  op(e1, e0) = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3969) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4121)  all_58_9 = e0
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4122)  all_58_9 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4121), (4122) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4123)  e1 = e0
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (4123) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4124)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4124) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4125)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4125) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4126)  all_58_10 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4064), (4126) are inconsistent by sub-proof
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #968.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4127)  all_58_11 = e1 | all_58_15 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4127) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4128)  all_58_11 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4115), (4128) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4129)  e2 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4129) implies:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4130)  e2 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (4130) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4131)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4131) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4132)  all_58_15 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4132) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4133)  all_14_2 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (517), (4133) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4134)  all_18_2 = e1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (4133) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4135)  op(e1, e0) = all_14_1
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3931) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4136)   ~ (all_18_1 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (681), (4136) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4137)   ~ (all_14_1 = e2)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_14_1,
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (4120), (4135) gives:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4138)  all_14_1 = e2
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4137), (4138) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4139)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4139) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4140)   ~ (all_18_2 = e1)
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4134), (4140) imply:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4141)  $false
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4141) is inconsistent.
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.07/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4142)  all_58_10 = e0 | all_58_11 = e0
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (51), (53), (311), (328), (351), (387),
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (538), (544), (546), (547), (569), (573), (609),
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (612), (613), (3977), (3978), (3991), (3992),
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4025), (4064), (4070), (4119), (4142),
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #747.
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4143)  all_58_8 = e3 | all_58_11 = e3
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (546), (4008), (4068), (4143) are
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4144)   ~ (all_58_4 = e2)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (4144) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4145)   ~ (all_52_17 = e2)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4146)  all_56_5 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (61), (169), (182), (276), (305),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (314), (319), (320), (351), (366), (367),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (411), (415),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (421), (431), (539), (544), (545), (546), (547),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (568), (569), (573),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (575), (577), (578), (580), (588), (589), (595),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (605), (772), (3959), (3969), (3977), (3978),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3979), (4001), (4005), (4008), (4016), (4020),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4024), (4036), (4041), (4045), (4146),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #703.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4147)   ~ (all_56_5 = e3)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (4147) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4148)   ~ (all_4_2 = e3)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4039) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4149)  all_58_3 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4149) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4150)  all_4_2 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4148), (4150) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4151)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4151) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4152)  all_58_5 = e3 | all_58_10 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4152) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4153)  all_58_5 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (375), (4006), (4153) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4154)  all_58_10 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4154) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4155)  all_52_27 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4155) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4156)  all_52_27 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (4156) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4157)   ~ (all_52_29 = e3)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4157) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4158)   ~ (all_52_29 = e3)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4036) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4159)  all_58_7 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (4159) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4160)  all_52_13 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (4160) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4161)  op(e1, e2) = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4162)  all_58_4 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (4162) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4163)  all_52_17 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4163) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4164)  all_52_17 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (4164) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4165)   ~ (all_52_9 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (4164) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4166)   ~ (all_52_19 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4166) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4167)   ~ (all_52_19 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4005), (4164) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4168)   ~ (e3 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4169)  all_58_1 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (4169) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4170)  all_52_9 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4165), (4170) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4171)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4171) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4172)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4173)  all_58_2 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (4173) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4174)  all_52_3 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4174) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4175)  all_52_3 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (4175) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4176)   ~ (all_4_2 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4176) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4177)   ~ (all_4_2 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4172) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4178)  all_58_3 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4178) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4179)  all_4_2 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4177), (4179) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4180)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4180) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4181)  all_58_7 = e1 | all_58_13 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4181) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4182)  all_58_7 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4159), (4182) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4183)  e3 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4183) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4184)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4184) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4185)  all_58_13 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (61), (157), (305), (351), (431),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (543), (571), (573), (772), (3979), (4016),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4185), (function-axioms) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #646.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4186)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4186) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4187)  all_58_3 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4187) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4188)  all_4_2 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (4188) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4189)  op(e1, e2) = all_4_1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_1,
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (4161), (4189) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4190)  all_4_1 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3959), (4190) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4191)  op(e2, e3) = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (4191) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4192)  all_52_3 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4027), (4192) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4193)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4193) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4194)  all_58_5 = e1 | all_58_10 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4195)  all_58_5 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (375), (4167), (4195) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #857.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4196)  all_58_10 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4154), (4196) are inconsistent by sub-proof
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #968.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4197)   ~ (all_58_4 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (4197) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4198)   ~ (all_52_17 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4020) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4199)  all_56_2 = e2
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (4145), (4199) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1264.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4200)  all_56_2 = e1 | all_56_2 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4200) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4201)  all_56_2 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (4198), (4201) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1263.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4202)  all_56_2 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (4202) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4203)  all_52_17 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4203) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4204)  all_52_17 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (4204) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4205)   ~ (all_52_19 = e0)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4205) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4206)   ~ (all_52_19 = e0)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (4204) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4207)   ~ (all_52_25 = e0)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4207) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4208)   ~ (all_52_25 = e0)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4005), (4204) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4209)   ~ (e3 = e0)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4198), (4204) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4210)   ~ (e1 = e0)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3969) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4211)  all_58_9 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (4208), (4211) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #523.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4212)  all_58_10 = e0 | all_58_11 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4212) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4213)  all_58_10 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4154), (4213) are inconsistent by sub-proof
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #750.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4214)  all_58_11 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4215)  all_58_6 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4215) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4216)  all_52_5 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4216) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4217)  all_52_5 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (569), (3978), (4217), (function-axioms) are
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4218)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4218) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4219)  all_58_7 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4159), (4219) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4220)  e3 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4220) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4221)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4221) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4222)  all_58_8 = e1 | all_58_11 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4222) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4223)  all_58_8 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (4223) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4224)  all_10_2 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4224) implies:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4225)  all_10_2 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (4225) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4226)   ~ (all_52_19 = e1)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (4225) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4227)  op(e1, e1) = all_52_20
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (4225) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4228)  op(e1, e1) = all_10_1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (4225) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4229)  op(e1, e1) = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4013) gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e1, e1, simplifying with (4227), (4228)
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4230)  all_52_20 = all_10_1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (3170), (4008), (4227), (4229), (4230),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #524.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4231)  all_56_6 = e1 | all_56_6 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (417), (4206), (4226), (4231) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #757.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4232)  all_58_11 = e1
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4214), (4232) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4233)  e1 = e0
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (4233) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4234)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4234) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4235)  all_58_8 = e3 | all_58_11 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (546), (4008), (4158), (4235) are
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | |   (4236)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (351), (387), (547),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | |            (564), (569), (3977), (3978), (3980), (4004),
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | |            (4236), (function-axioms) are inconsistent by
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1364.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | |   (4237)  all_58_15 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4237) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | |   (4238)  all_14_2 = e3
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | REDUCE: (3992), (4238) imply:
% 195.42/31.59  | | | | | | | | | | | | | | | | | | |   (4239)  $false
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | CLOSE: (4239) is inconsistent.
% 195.42/31.59  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | | End of split
% 195.42/31.59  | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | Case 2:
% 195.42/31.59  | | | | | | | | | | | | | | 
% 195.42/31.59  | | | | | | | | | | | | | |   (4240)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.42/31.59  | | | | | | | | | | | | | |           all_52_14 = e0
% 195.42/31.59  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 195.42/31.60  | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 195.42/31.60  | | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 195.42/31.60  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.42/31.60  | | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 195.42/31.60  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 195.42/31.60  | | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 195.42/31.60  | | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 195.42/31.60  | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 195.42/31.60  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.42/31.60  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 195.42/31.60  | | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 195.42/31.60  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.42/31.60  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.42/31.60  | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 195.42/31.60  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 195.42/31.60  | | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 195.42/31.60  | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 195.42/31.60  | | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 195.42/31.60  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 195.42/31.60  | | | | | | | | | | | | | |            (773), (775), (3172), (3961), (3968), (3969),
% 195.42/31.60  | | | | | | | | | | | | | |            (3970), (4240), (function-axioms) are inconsistent
% 195.42/31.60  | | | | | | | | | | | | | |            by sub-proof #731.
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | |   (4241)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.42/31.60  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.42/31.60  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.42/31.60  | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | BETA: splitting (4241) gives:
% 195.42/31.60  | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | Case 1:
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | |   (4242)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.42/31.60  | | | | | | | | | | | | | |           all_52_22 = e0
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 195.42/31.60  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 195.42/31.60  | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 195.42/31.60  | | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 195.42/31.60  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 195.42/31.60  | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 195.42/31.60  | | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 195.42/31.60  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 195.42/31.60  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.42/31.60  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.60  | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 195.42/31.60  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.42/31.60  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.42/31.60  | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.42/31.60  | | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.42/31.60  | | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 195.42/31.60  | | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 195.42/31.60  | | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 195.42/31.60  | | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (3172), (3961),
% 195.42/31.60  | | | | | | | | | | | | | |            (3968), (3969), (4242), (function-axioms) are
% 195.42/31.60  | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | |   (4243)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.42/31.60  | | | | | | | | | | | | | |           all_52_30 = e0
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 195.42/31.60  | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 195.42/31.60  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.42/31.60  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 195.42/31.60  | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 195.42/31.60  | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 195.42/31.60  | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 195.42/31.60  | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 195.42/31.60  | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 195.42/31.60  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 195.42/31.60  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.42/31.60  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.42/31.60  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 195.42/31.60  | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 195.42/31.60  | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 195.42/31.60  | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 195.42/31.60  | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 195.42/31.60  | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 195.42/31.60  | | | | | | | | | | | | | |            (775), (3172), (3961), (3968), (3970), (4243),
% 195.42/31.60  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.60  | | | | | | | | | | | | | |            #1008.
% 195.42/31.60  | | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | |   (4244)  all_22_1 = e2
% 195.42/31.60  | | | | | | | | | |   (4245)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | COMBINE_EQS: (658), (4244) imply:
% 195.42/31.60  | | | | | | | | | |   (4246)  all_6_1 = e2
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 195.42/31.60  | | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 195.42/31.60  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.42/31.60  | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 195.42/31.60  | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 195.42/31.60  | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 195.42/31.60  | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 195.42/31.60  | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 195.42/31.60  | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 195.42/31.60  | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 195.42/31.60  | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.60  | | | | | | | | | |            (415), (431), (522), (538), (539), (540), (541),
% 195.42/31.60  | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.42/31.60  | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.42/31.60  | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.42/31.60  | | | | | | | | | |            (570), (572), (573), (574), (575), (576), (577),
% 195.42/31.60  | | | | | | | | | |            (578), (582), (584), (586), (588), (590), (591),
% 195.42/31.60  | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.42/31.60  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.42/31.60  | | | | | | | | | |            (608), (609), (610), (612), (613), (739), (773),
% 195.42/31.60  | | | | | | | | | |            (775), (3170), (3172), (3934), (4245), (4246),
% 195.42/31.60  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.60  | | | | | | | | | |            #508.
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.60  | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | 
% 195.42/31.60  | | | | | | | End of split
% 195.42/31.60  | | | | | | | 
% 195.42/31.60  | | | | | | Case 2:
% 195.42/31.60  | | | | | | | 
% 195.42/31.60  | | | | | | |   (4247)  all_14_0 = e2
% 195.42/31.60  | | | | | | | 
% 195.42/31.60  | | | | | | | REDUCE: (62), (4247) imply:
% 195.42/31.60  | | | | | | |   (4248)  op(e0, all_14_1) = e2
% 195.42/31.60  | | | | | | | 
% 195.42/31.60  | | | | | | | BETA: splitting (79) gives:
% 195.42/31.60  | | | | | | | 
% 195.42/31.60  | | | | | | | Case 1:
% 195.42/31.60  | | | | | | | | 
% 195.42/31.60  | | | | | | | |   (4249)   ~ (all_20_0 = e3)
% 195.42/31.60  | | | | | | | | 
% 195.42/31.60  | | | | | | | | REDUCE: (758), (4249) imply:
% 195.42/31.60  | | | | | | | |   (4250)   ~ (all_4_0 = e3)
% 195.42/31.60  | | | | | | | | 
% 195.42/31.60  | | | | | | | | BETA: splitting (84) gives:
% 195.42/31.60  | | | | | | | | 
% 195.42/31.60  | | | | | | | | Case 1:
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.60  | | | | | | | | |   (4251)   ~ (all_22_1 = e2)
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | REDUCE: (658), (4251) imply:
% 195.42/31.60  | | | | | | | | |   (4252)   ~ (all_6_1 = e2)
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | BETA: splitting (109) gives:
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | Case 1:
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | |   (4253)   ~ (all_32_1 = e3)
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | REDUCE: (663), (4253) imply:
% 195.42/31.60  | | | | | | | | | |   (4254)   ~ (all_4_1 = e3)
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | BETA: splitting (119) gives:
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | Case 1:
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | |   (4255)   ~ (all_36_0 = e3)
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | REDUCE: (3169), (4255) imply:
% 195.42/31.60  | | | | | | | | | | |   (4256)  $false
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | CLOSE: (4256) is inconsistent.
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | |   (4257)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | BETA: splitting (303) gives:
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | Case 1:
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | |   (4258)  all_58_15 = e0
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (4248), (4258),
% 195.42/31.60  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.60  | | | | | | | | | | | |            #612.
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | |   (4259)   ~ (all_58_15 = e0)
% 195.42/31.60  | | | | | | | | | | | |   (4260)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.42/31.60  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.42/31.60  | | | | | | | | | | | |             e0)
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | ALPHA: (4260) implies:
% 195.42/31.60  | | | | | | | | | | | |   (4261)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.42/31.60  | | | | | | | | | | | |   (4262)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | REDUCE: (541), (4259) imply:
% 195.42/31.60  | | | | | | | | | | | |   (4263)   ~ (all_14_2 = e0)
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 195.42/31.60  | | | | | | | | | | | |            (41), (42), (43), (51), (53), (61), (63), (156),
% 195.42/31.60  | | | | | | | | | | | |            (157), (158), (161), (162), (166), (167), (168),
% 195.42/31.60  | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 195.42/31.60  | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 195.42/31.60  | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (276),
% 195.42/31.60  | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 195.42/31.60  | | | | | | | | | | | |            (284), (285), (304), (305), (306), (307), (309),
% 195.42/31.60  | | | | | | | | | | | |            (311), (312), (313), (315), (316), (317), (319),
% 195.42/31.60  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 195.42/31.60  | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 195.42/31.60  | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.42/31.60  | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.60  | | | | | | | | | | | |            (415), (417), (421), (427), (431), (524), (538),
% 195.42/31.60  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.42/31.60  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.42/31.60  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 195.42/31.60  | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 195.42/31.60  | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 195.42/31.60  | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (590),
% 195.42/31.60  | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 195.42/31.60  | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 195.42/31.60  | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 195.42/31.60  | | | | | | | | | | | |            (645), (772), (773), (775), (3168), (3172),
% 195.42/31.60  | | | | | | | | | | | |            (4250), (4252), (4254), (4257), (4261), (4262),
% 195.42/31.60  | | | | | | | | | | | |            (4263), (function-axioms) are inconsistent by
% 195.42/31.60  | | | | | | | | | | | |            sub-proof #510.
% 195.42/31.60  | | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | |   (4264)  all_32_1 = e3
% 195.42/31.60  | | | | | | | | | |   (4265)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | COMBINE_EQS: (663), (4264) imply:
% 195.42/31.60  | | | | | | | | | |   (4266)  all_4_1 = e3
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 195.42/31.60  | | | | | | | | | |            (42), (43), (51), (53), (61), (63), (124), (158),
% 195.42/31.60  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.42/31.60  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 195.42/31.60  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 195.42/31.60  | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 195.42/31.60  | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 195.42/31.60  | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (314),
% 195.42/31.60  | | | | | | | | | |            (315), (316), (317), (318), (319), (321), (323),
% 195.42/31.60  | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 195.42/31.60  | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 195.42/31.60  | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.42/31.60  | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 195.42/31.60  | | | | | | | | | |            (431), (523), (525), (538), (539), (540), (541),
% 195.42/31.60  | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.42/31.60  | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.42/31.60  | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 195.42/31.60  | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 195.42/31.60  | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 195.42/31.60  | | | | | | | | | |            (587), (588), (590), (591), (592), (593), (594),
% 195.42/31.60  | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.42/31.60  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.42/31.60  | | | | | | | | | |            (611), (612), (613), (686), (721), (766), (772),
% 195.42/31.60  | | | | | | | | | |            (773), (775), (3172), (4248), (4250), (4252),
% 195.42/31.60  | | | | | | | | | |            (4265), (4266), (function-axioms) are inconsistent
% 195.42/31.60  | | | | | | | | | |            by sub-proof #604.
% 195.42/31.60  | | | | | | | | | | 
% 195.42/31.60  | | | | | | | | | End of split
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.60  | | | | | | | | Case 2:
% 195.42/31.60  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | |   (4267)  all_22_1 = e2
% 195.42/31.61  | | | | | | | | |   (4268)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | COMBINE_EQS: (658), (4267) imply:
% 195.42/31.61  | | | | | | | | |   (4269)  all_6_1 = e2
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 195.42/31.61  | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 195.42/31.61  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.42/31.61  | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 195.42/31.61  | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 195.42/31.61  | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 195.42/31.61  | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 195.42/31.61  | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 195.42/31.61  | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 195.42/31.61  | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 195.42/31.61  | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.61  | | | | | | | | |            (415), (431), (522), (538), (539), (540), (541),
% 195.42/31.61  | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.42/31.61  | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.42/31.61  | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.42/31.61  | | | | | | | | |            (570), (572), (573), (574), (575), (576), (577),
% 195.42/31.61  | | | | | | | | |            (578), (582), (584), (586), (588), (590), (591),
% 195.42/31.61  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.42/31.61  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.42/31.61  | | | | | | | | |            (608), (609), (610), (612), (613), (739), (773),
% 195.42/31.61  | | | | | | | | |            (775), (3170), (3172), (4248), (4268), (4269),
% 195.42/31.61  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.61  | | | | | | | | |            #504.
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | End of split
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | |   (4270)  all_20_0 = e3
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | | COMBINE_EQS: (758), (4270) imply:
% 195.42/31.61  | | | | | | | |   (4271)  all_4_0 = e3
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | | SIMP: (4271) implies:
% 195.42/31.61  | | | | | | | |   (4272)  all_4_0 = e3
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | | REDUCE: (37), (4272) imply:
% 195.42/31.61  | | | | | | | |   (4273)  op(e2, all_4_1) = e3
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | | BETA: splitting (84) gives:
% 195.42/31.61  | | | | | | | | 
% 195.42/31.61  | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | |   (4274)   ~ (all_22_1 = e2)
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | REDUCE: (658), (4274) imply:
% 195.42/31.61  | | | | | | | | |   (4275)   ~ (all_6_1 = e2)
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | BETA: splitting (119) gives:
% 195.42/31.61  | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | |   (4276)   ~ (all_36_0 = e3)
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | REDUCE: (3169), (4276) imply:
% 195.42/31.61  | | | | | | | | | |   (4277)  $false
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | CLOSE: (4277) is inconsistent.
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | |   (4278)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | BETA: splitting (303) gives:
% 195.42/31.61  | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | |   (4279)  all_58_15 = e0
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (4248), (4279),
% 195.42/31.61  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.61  | | | | | | | | | | |            #612.
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | |   (4280)   ~ (all_58_15 = e0)
% 195.42/31.61  | | | | | | | | | | |   (4281)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.42/31.61  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.42/31.61  | | | | | | | | | | |             e0)
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | ALPHA: (4281) implies:
% 195.42/31.61  | | | | | | | | | | |   (4282)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.42/31.61  | | | | | | | | | | |   (4283)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | REDUCE: (541), (4280) imply:
% 195.42/31.61  | | | | | | | | | | |   (4284)   ~ (all_14_2 = e0)
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | BETA: splitting (187) gives:
% 195.42/31.61  | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | |   (4285)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.42/31.61  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.42/31.61  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.42/31.61  | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | BETA: splitting (4285) gives:
% 195.42/31.61  | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | |   (4286)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.42/31.61  | | | | | | | | | | | | |           all_52_6 = e0
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | ALPHA: (4286) implies:
% 195.42/31.61  | | | | | | | | | | | | |   (4287)  all_52_6 = e0
% 195.42/31.61  | | | | | | | | | | | | |   (4288)  all_52_4 = e1
% 195.42/31.61  | | | | | | | | | | | | |   (4289)  all_52_2 = e2
% 195.42/31.61  | | | | | | | | | | | | |   (4290)  all_52_0 = e3
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | REDUCE: (185), (4289) imply:
% 195.42/31.61  | | | | | | | | | | | | |   (4291)  op(all_52_3, all_52_3) = e2
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | REDUCE: (184), (4288) imply:
% 195.42/31.61  | | | | | | | | | | | | |   (4292)  op(all_52_5, all_52_5) = e1
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | REDUCE: (183), (4287) imply:
% 195.42/31.61  | | | | | | | | | | | | |   (4293)  op(all_52_7, all_52_7) = e0
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | REDUCE: (610), (4290) imply:
% 195.42/31.61  | | | | | | | | | | | | |   (4294)  op(all_6_2, all_6_2) = e3
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | BETA: splitting (270) gives:
% 195.42/31.61  | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | |   (4295)  all_56_15 = e3
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (42), (43), (51), (53), (61),
% 195.42/31.61  | | | | | | | | | | | | | |            (156), (157), (173), (182), (271), (272), (273),
% 195.42/31.61  | | | | | | | | | | | | | |            (277), (278), (279), (281), (304), (305), (311),
% 195.42/31.61  | | | | | | | | | | | | | |            (312), (313), (320), (321), (324), (330), (332),
% 195.42/31.61  | | | | | | | | | | | | | |            (333), (343), (346), (351), (366), (367), (372),
% 195.42/31.61  | | | | | | | | | | | | | |            (375), (387), (405), (411), (417), (427), (431),
% 195.42/31.61  | | | | | | | | | | | | | |            (524), (538), (543), (544), (546), (547), (548),
% 195.42/31.61  | | | | | | | | | | | | | |            (549), (551), (553), (555), (562), (563), (564),
% 195.42/31.61  | | | | | | | | | | | | | |            (565), (566), (567), (569), (571), (572), (573),
% 195.42/31.61  | | | | | | | | | | | | | |            (574), (575), (582), (586), (591), (596), (598),
% 195.42/31.61  | | | | | | | | | | | | | |            (600), (603), (607), (608), (609), (612), (613),
% 195.42/31.61  | | | | | | | | | | | | | |            (645), (772), (775), (3168), (4278), (4284),
% 195.42/31.61  | | | | | | | | | | | | | |            (4291), (4292), (4293), (4294), (4295),
% 195.42/31.61  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.61  | | | | | | | | | | | | | |            #511.
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | |   (4296)   ~ (all_56_15 = e3)
% 195.42/31.61  | | | | | | | | | | | | | |   (4297)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | REDUCE: (538), (4296) imply:
% 195.42/31.61  | | | | | | | | | | | | | |   (4298)   ~ (all_14_2 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.42/31.61  | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | |   (4299)  all_56_13 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | COMBINE_EQS: (346), (4299) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4300)  all_52_15 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | SIMP: (4300) implies:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4301)  all_52_15 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | COMBINE_EQS: (543), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4302)  all_58_13 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (571), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4303)   ~ (all_52_7 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (576), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4304)   ~ (all_52_9 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (587), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4305)   ~ (all_52_13 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (590), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4306)   ~ (all_52_23 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | SIMP: (4306) implies:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4307)   ~ (all_52_23 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (591), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4308)   ~ (all_14_2 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (582), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4309)   ~ (all_4_2 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | SIMP: (4309) implies:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4310)   ~ (all_4_2 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (179), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4311)  op(e3, e3) = all_52_14
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | REDUCE: (157), (4301) imply:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4312)  op(e0, e2) = e3
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.42/31.61  | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (4311)
% 195.42/31.61  | | | | | | | | | | | | | | |              gives:
% 195.42/31.61  | | | | | | | | | | | | | | |   (4313)  all_52_14 = all_6_2
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | |   (4314)  all_56_9 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | REF_CLOSE: (421), (4305), (4314) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | |            sub-proof #958.
% 195.42/31.61  | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | |   (4315)   ~ (all_56_9 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | |   (4316)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.42/31.61  | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | |   (4317)  all_56_5 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (539), (4310), (4317) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | |            sub-proof #1319.
% 195.42/31.61  | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | |   (4318)   ~ (all_56_5 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | |   (4319)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 195.42/31.61  | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | |   (4320)  all_56_12 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (4303), (4320) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | |   (4321)   ~ (all_56_12 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | |   (4322)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 195.42/31.61  | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | |   (4323)  all_56_1 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (394), (4304), (4323) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | | | |            sub-proof #1326.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | |   (4324)   ~ (all_56_1 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | |   (4325)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |   (4326)  all_58_1 = e1
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (53), (168), (177), (274), (283), (304), (307),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (309), (311), (313), (315), (317), (319), (321),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (351), (352), (366),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (405), (415), (541),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (542), (544), (545), (546), (547), (548), (549),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (553), (559), (561), (564), (565), (566), (569),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (570), (574), (575), (577), (578), (596), (597),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (598), (600), (602), (608), (612), (613), (773),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (775), (4282), (4291), (4292), (4293), (4294),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (4298), (4302), (4303), (4305), (4307), (4326),
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |            #708.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |   (4327)   ~ (all_58_1 = e1)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |   (4328)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (4327) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | |   (4329)   ~ (all_52_9 = e1)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4330)  all_56_6 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (4330) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4331)  all_52_19 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | SIMP: (4331) implies:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4332)  all_52_19 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (4332) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4333)  all_58_5 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (4332) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4334)   ~ (all_52_27 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | SIMP: (4334) implies:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4335)   ~ (all_52_27 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (4332) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4336)  op(e3, e3) = all_52_18
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (4332) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4337)  op(e2, e1) = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |              all_52_18, e3, e3, simplifying with (41), (4336)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | |   (4338)  all_52_18 = all_6_2
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | |   (4339)  all_58_0 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (4339) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | |   (4340)  all_6_2 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (4340) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | |   (4341)   ~ (all_52_3 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (4340) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | |   (4342)   ~ (all_52_25 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (4340) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | |   (4343)  op(e3, e3) = all_6_1
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (4340) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | |   (4344)  op(e3, e3) = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | |   (4345)  all_58_9 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (4342), (4345) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1300.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | |   (4346)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4346) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | |   (4347)  all_58_10 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (4335), (4347) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | |   (4348)  all_58_11 = e3 | all_58_15 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4348) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4349)  all_58_11 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4349) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4350)  all_52_29 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4350) implies:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4351)  all_52_29 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (4351) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4352)   ~ (all_52_5 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (602), (4351) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4353)   ~ (all_10_2 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4353) implies:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4354)   ~ (all_10_2 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (4351) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4355)  op(e3, e3) = all_52_28
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e3, simplifying with (4343), (4355)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4356)  all_52_28 = all_6_1
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e3, simplifying with (4344), (4355)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4357)  all_52_28 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4356), (4357) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4358)  all_6_1 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (4358) imply:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4359)  op(e3, e3) = all_6_0
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (4344), (4359) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (4360)  all_6_0 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4361)  all_56_4 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (4341), (4361) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4362)   ~ (all_56_4 = e3)
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4363)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4364)  all_56_7 = e3
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (4335), (4364) are inconsistent by
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #609.
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4365)   ~ (all_56_7 = e3)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4366)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4367)  all_56_10 = e3
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (361), (4354), (4367) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #913.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4368)   ~ (all_56_10 = e3)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4369)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4370)  all_56_8 = e3
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (4352), (4370) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4371)   ~ (all_56_8 = e3)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4372)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4373)  all_58_6 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4373) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4374)  all_52_5 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4374) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4375)  all_52_5 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (569), (4292), (4375), (function-axioms) are
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4376)   ~ (all_58_6 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (4376) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4377)   ~ (all_52_5 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4378)  all_58_1 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (4378) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4379)  all_52_9 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (4379) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4380)   ~ (all_52_13 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4380) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4381)   ~ (all_52_13 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (4379) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4382)   ~ (all_4_2 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4382) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4383)   ~ (all_4_2 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (4379) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4384)  op(e2, e2) = all_52_8
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_8, e2, e2, simplifying with (36), (4384)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4385)  all_52_8 = all_4_2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4386)  all_58_6 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4386) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4387)  all_52_5 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4387) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4388)  all_52_5 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4388) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4389)   ~ (all_52_7 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4389) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4390)   ~ (all_52_7 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (61), (304), (351), (431), (542),
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (573), (600), (4282), (4293), (4302), (4322),
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4390), (function-axioms) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1169.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4391)   ~ (all_58_6 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (4391) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4392)   ~ (all_52_5 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4372) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4393)  all_56_8 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (4392), (4393) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1022.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4394)   ~ (all_56_8 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4395)  all_56_8 = e1 | all_56_8 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4395) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4396)  all_56_8 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (4377), (4396) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #707.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4397)  all_56_8 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (4397) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4398)  all_52_5 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4398) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4399)  all_52_5 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4400)   ~ (all_52_7 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4400) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4401)   ~ (all_52_7 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4402)   ~ (all_52_13 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4402) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4403)   ~ (all_52_13 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4404)   ~ (all_10_2 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4404) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4405)   ~ (all_10_2 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4352), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4406)   ~ (e3 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4392), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4407)   ~ (e2 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4292), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4408)  op(e0, e0) = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (4399) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4409)  op(e1, e3) = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4316) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4410)  all_56_9 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (421), (4381), (4410) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #955.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4411)  all_56_9 = e1 | all_56_9 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4411) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4412)  all_56_9 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (4412) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4413)  all_52_13 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4413) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4414)  all_52_13 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (4414) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4415)   ~ (all_10_2 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4415) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4416)   ~ (all_10_2 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (4414) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4417)   ~ (all_4_2 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4417) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4418)   ~ (all_4_2 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4419)  all_58_1 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4378), (4419) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4420)  e2 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (4420) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4421)  $false
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4421) is inconsistent.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4422)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4369) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4423)  all_56_10 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (4423) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4424)  all_10_2 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4424) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4425)  all_10_2 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (4425) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4426)  op(e2, e1) = all_10_1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4282) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4427)  all_58_12 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (4401), (4427) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1067.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4428)  all_58_13 = e0 | all_58_14 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4428) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4429)  all_58_13 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4302), (4429) are inconsistent by sub-proof
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4430)  all_58_14 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (4430) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4431)  all_52_23 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4431) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4432)  all_52_23 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (4432) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4433)  op(e0, e0) = all_52_22
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4319) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4434)  all_56_5 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (539), (4383), (4434) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1315.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4435)  all_56_5 = e1 | all_56_5 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4422) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4436)  all_58_3 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4436) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4437)  all_4_2 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (4437) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4438)   ~ (all_52_3 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (4437) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4439)   ~ (all_52_27 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (4437) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4440)  op(e0, e0) = all_52_10
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (4437) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4441)  op(e0, e2) = all_4_1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4283) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4442)  all_58_9 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4442) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4443)  all_52_25 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4443) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4444)  all_52_25 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (4444) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4445)   ~ (all_52_27 = e0)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (4444) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4446)  op(e0, e0) = all_52_24
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_22, e0, e0, simplifying with (61), (4433)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4447)  all_52_22 = all_14_2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_22,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e0, e0, simplifying with (4433), (4440)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4448)  all_52_10 = all_52_22
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_24,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e0, e0, simplifying with (4440), (4446)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4449)  all_52_10 = all_52_24
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e0, e0, simplifying with (4408), (4440)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4450)  all_52_10 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_1,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (4312), (4441) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4451)  all_4_1 = e3
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_10_1,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (4337), (4426) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4452)  all_10_1 = e3
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4448), (4449) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4453)  all_52_22 = all_52_24
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4453) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4454)  all_52_22 = all_52_24
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4449), (4450) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4455)  all_52_24 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4447), (4454) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4456)  all_52_24 = all_14_2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4456) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4457)  all_52_24 = all_14_2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4455), (4457) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4458)  all_14_2 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4458) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4459)  all_58_15 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (4458) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4460)   ~ (all_52_7 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4273), (4451) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4461)  op(e2, e3) = e3
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3170), (4452) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4462)  op(e1, e3) = e3
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4322) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4463)  all_56_12 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (4463) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4464)  all_52_7 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4464) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4465)  all_52_7 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (4465) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4466)   ~ (all_52_3 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4467)  all_58_2 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (4467) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4468)  all_52_3 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (4468) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4469)   ~ (all_52_27 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4469) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4470)   ~ (all_52_27 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4341), (4468) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4471)   ~ (e3 = e1)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (4468) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4472)  op(e2, e3) = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4366) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4473)  all_56_7 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (4473) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4474)  all_52_27 = e2
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4335), (4474) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4475)   ~ (e3 = e2)
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e3,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (4409), (4462) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4476)  e3 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e3,
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (4461), (4472) gives:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4477)  e3 = e1
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4476), (4477) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4478)  e1 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4478) implies:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4479)  e1 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4459), (4479) imply:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4480)  all_58_15 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (51),
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (53), (156), (166), (273), (304), (305), (351),
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (431), (524), (542), (555), (645), (4273), (4278),
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4291), (4293), (4302), (4303), (4312), (4401),
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4480), (function-axioms) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #529.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4481)  all_56_7 = e1 | all_56_7 = e0
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (427), (4439), (4470), (4481) are inconsistent by
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #902.
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4482)   ~ (all_58_2 = e1)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (4482) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4483)   ~ (all_52_3 = e1)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (4363), (4438), (4466), (4483) are
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4484)  all_56_12 = e1 | all_56_12 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (4401), (4460), (4484) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1374.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4485)  all_58_10 = e0 | all_58_11 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (372), (4349), (4439), (4485) are
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #802.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4486)   ~ (all_58_3 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (4486) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4487)   ~ (all_4_2 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (539), (4418), (4435), (4487) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1021.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4488)  all_56_10 = e1 | all_56_10 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4488) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4489)  all_56_10 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (4489) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4490)  all_10_2 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4490) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4491)  all_10_2 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4416), (4491) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4492)  $false
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4492) is inconsistent.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4493)  all_56_10 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (361), (4405), (4493) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #911.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4494)  all_56_9 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (421), (4403), (4494) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #953.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4495)   ~ (all_58_1 = e2)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (4495) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4496)   ~ (all_52_9 = e2)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4325) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4497)  all_56_1 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (394), (4496), (4497) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1194.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4498)   ~ (all_56_1 = e2)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4499)  all_56_1 = e1 | all_56_1 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4499) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4500)  all_56_1 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (394), (4329), (4500) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1061.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4501)  all_56_1 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (4501) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4502)  all_52_9 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4502) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4503)  all_52_9 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4503) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4504)   ~ (all_52_25 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4504) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4505)   ~ (all_52_25 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4304), (4503) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4506)   ~ (e3 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4496), (4503) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4507)   ~ (e2 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4283) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4508)  all_58_9 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (4505), (4508) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #523.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4509)  all_58_10 = e0 | all_58_11 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4509) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4510)  all_58_10 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4510) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4511)  all_52_27 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4511) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4512)  all_52_27 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (4512) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4513)   ~ (all_52_3 = e0)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4514)  all_58_2 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (4514) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4515)  all_52_3 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (564), (4291), (4515), (function-axioms) are
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4516)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4516) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4517)  all_58_3 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4517) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4518)  all_4_2 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (4518) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4519)   ~ (all_52_3 = e2)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (4518) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4520)  op(e2, e2) = all_52_10
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (4518) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4521)  op(e2, e2) = all_4_1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4518) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4522)  op(e2, e2) = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4523)  all_58_2 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (4523) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4524)  all_52_3 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4524) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4525)  all_52_3 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4341), (4525) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4526)   ~ (e3 = e1)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4519), (4525) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4527)   ~ (e2 = e1)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4291), (4525) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4528)  op(e1, e1) = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4328) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4529)  all_58_3 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4517), (4529) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4530)  e2 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (4530) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4531)  $false
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4531) is inconsistent.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4532)  all_58_7 = e1 | all_58_13 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4532) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4533)  all_58_7 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (4533) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4534)  all_52_13 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (4534) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4535)  op(e1, e1) = all_52_12
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e1, e1, simplifying with (51), (4535)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4536)  all_52_12 = all_10_2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e1, e1, simplifying with (4528), (4535)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4537)  all_52_12 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e2, e2, simplifying with (4520), (4521)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4538)  all_52_10 = all_4_1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_10, e2, e2, simplifying with (4520), (4522)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4539)  all_52_10 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4538), (4539) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4540)  all_4_1 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4536), (4537) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4541)  all_10_2 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4541) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4542)  all_10_2 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4354), (4542) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4543)   ~ (e3 = e2)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4273), (4520), (4521), (4540),
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #722.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4544)  all_58_13 = e1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4302), (4544) are inconsistent by sub-proof
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #770.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4545)   ~ (all_58_2 = e1)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (4545) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4546)   ~ (all_52_3 = e1)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (4363), (4513), (4519), (4546) are
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4547)  all_58_5 = e2 | all_58_10 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4547) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4548)  all_58_5 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4333), (4548) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4549)  e3 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4549) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4550)  $false
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4550) is inconsistent.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4551)  all_58_10 = e2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (4349), (4509), (4551) are inconsistent
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #522.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4552)  all_58_11 = e0
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4349), (4552) are inconsistent by sub-proof
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #863.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4553)  all_58_15 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4553) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4554)  all_14_2 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4298), (4554) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4555)  $false
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4555) is inconsistent.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |   (4556)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (351), (387), (547),
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |            (564), (569), (4291), (4292), (4294), (4303),
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |            (4556), (function-axioms) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1364.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | |   (4557)   ~ (all_56_6 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (4557) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | |   (4558)   ~ (all_52_19 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |   (4559)  all_58_2 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (387), (564), (4291), (4294), (4559),
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |            #1159.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | |   (4560)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4560) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | |   (4561)  all_58_3 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4561) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | |   (4562)  all_4_2 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4310), (4562) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | |   (4563)  $false
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4563) is inconsistent.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | |   (4564)  all_58_5 = e3 | all_58_10 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4564) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4565)  all_58_5 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (375), (4558), (4565) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4566)  all_58_10 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4566) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4567)  all_52_27 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4567) implies:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4568)  all_52_27 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (4568) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4569)   ~ (all_52_25 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4568) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4570)  op(e3, e3) = all_52_26
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (41), (4570)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | |   (4571)  all_52_26 = all_6_2
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4572)  all_58_4 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (4572) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4573)  all_52_17 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (559), (564), (569), (4291), (4292),
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (4294), (4303), (4573), (function-axioms) are
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1199.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4574)   ~ (all_58_4 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4575)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (4574) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (4576)   ~ (all_52_17 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4575) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4577)  all_58_5 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (375), (4558), (4577) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4578)  all_58_8 = e3 | all_58_14 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4579)  all_58_0 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (4579) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4580)  all_6_2 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (4580) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4581)   ~ (all_52_3 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (4580) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4582)   ~ (all_52_5 = e3)
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (4580) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4583)  op(e3, e3) = all_6_1
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (4580) imply:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4584)  op(e3, e3) = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4585)  all_58_6 = e3
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (4582), (4585) are inconsistent by
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4586)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4578) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4587)  all_58_8 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (4587) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4588)  all_10_2 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (4588) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4589)  op(e3, e3) = all_52_20
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (4588) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4590)  op(e3, e1) = all_10_1
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (4590)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4591)  all_52_17 = all_10_1
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (4583), (4589)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4592)  all_52_20 = all_6_1
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (4584), (4589)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4593)  all_52_20 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4592), (4593) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4594)  all_6_1 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4594) implies:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4595)  all_6_1 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (4591) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4596)  all_56_2 = all_10_1
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (4591) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4597)  all_58_4 = all_10_1
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (4591) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4598)   ~ (all_52_9 = all_10_1)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (4591) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4599)   ~ (all_52_25 = all_10_1)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4599) implies:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4600)   ~ (all_52_25 = all_10_1)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4576), (4591) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4601)   ~ (all_10_1 = e3)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (178), (4591) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4602)  op(all_10_1, all_10_1) = all_52_16
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (4595) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4603)  op(e3, e3) = all_6_0
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (4584), (4603) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4604)  all_6_0 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4605)  all_56_4 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (4581), (4605) are inconsistent by
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4606)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4607)  all_56_2 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4596), (4601), (4607) are inconsistent by
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1029.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4608)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4609)  all_56_8 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (4582), (4609) are inconsistent by
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4610)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4611)  all_58_0 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4579), (4611) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4612)  e3 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4612) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4613)  $false
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4613) is inconsistent.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4614)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4615)  all_58_9 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4615) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4616)  all_52_25 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4616) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4617)   ~ (all_52_9 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4569), (4616) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4618)   ~ (e3 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (61), (161), (172), (182), (308), (311),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (331), (367), (394), (421), (431), (538), (539),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (544), (545), (547), (549), (567), (568), (570),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (573), (574), (578), (580), (589), (606), (609),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (611), (613), (3170), (4283), (4292), (4293),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4297), (4304), (4305), (4310), (4316), (4319),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4322), (4325), (4329), (4566), (4579), (4596),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4597), (4598), (4600), (4602), (4608), (4610),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4617), (function-axioms) are inconsistent by
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #517.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4619)   ~ (all_58_9 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (4619) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4620)   ~ (all_52_25 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4614) gives:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4621)  all_58_1 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (4621) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4622)  all_52_9 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4622) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4623)   ~ (all_52_25 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (4622) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4624)   ~ (all_4_2 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4624) implies:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4625)   ~ (all_4_2 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4304), (4622) imply:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4626)   ~ (e3 = e2)
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (51), (61), (172),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (177), (180), (304), (306), (308), (312), (313),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (319), (320), (321), (330), (332), (351), (366),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (405), (411), (421), (431),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (541), (542), (544), (545), (546), (547), (548),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (553), (563), (564), (565), (567), (569), (573),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (580), (588), (589), (596), (600), (602), (607),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4282), (4291), (4292), (4293), (4294), (4302),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4303), (4305), (4316), (4322), (4558), (4564),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4579), (4586), (4606), (4620), (4625),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #624.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4627)  all_58_4 = e2 | all_58_9 = e2
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (545), (3170), (4305), (4597), (4620),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4627), (function-axioms) are inconsistent by
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #521.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4628)  all_58_14 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (4307), (4628) are inconsistent by
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4629)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (393), (545), (549), (4304), (4569), (4576),
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4629) are inconsistent by sub-proof #744.
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | |   (4630)   ~ (all_56_13 = e3)
% 195.42/31.64  | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | REDUCE: (346), (4630) imply:
% 195.42/31.64  | | | | | | | | | | | | | | |   (4631)   ~ (all_52_15 = e3)
% 195.42/31.64  | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (38), (41), (42), (43), (51),
% 195.42/31.64  | | | | | | | | | | | | | | |            (53), (61), (63), (158), (163), (169), (175),
% 195.42/31.64  | | | | | | | | | | | | | | |            (182), (273), (276), (277), (280), (281), (283),
% 195.42/31.64  | | | | | | | | | | | | | | |            (284), (304), (305), (306), (311), (312), (313),
% 195.42/31.64  | | | | | | | | | | | | | | |            (314), (319), (320), (321), (328), (331), (332),
% 195.42/31.64  | | | | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (393),
% 195.42/31.64  | | | | | | | | | | | | | | |            (394), (405), (411), (415), (421), (431), (538),
% 195.42/31.64  | | | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 195.42/31.64  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 195.42/31.64  | | | | | | | | | | | | | | |            (559), (563), (564), (565), (566), (568), (569),
% 195.42/31.64  | | | | | | | | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 195.42/31.64  | | | | | | | | | | | | | | |            (588), (589), (593), (594), (595), (596), (597),
% 195.42/31.64  | | | | | | | | | | | | | | |            (600), (605), (606), (607), (608), (609), (612),
% 195.42/31.64  | | | | | | | | | | | | | | |            (613), (772), (773), (4248), (4273), (4283),
% 195.42/31.64  | | | | | | | | | | | | | | |            (4284), (4291), (4292), (4293), (4294), (4297),
% 195.42/31.64  | | | | | | | | | | | | | | |            (4298), (4631), (function-axioms) are inconsistent
% 195.42/31.64  | | | | | | | | | | | | | | |            by sub-proof #579.
% 195.42/31.64  | | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | |   (4632)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.42/31.64  | | | | | | | | | | | | |           all_52_14 = e0
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (38), (41), (42),
% 195.42/31.64  | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (161), (162),
% 195.42/31.64  | | | | | | | | | | | | |            (166), (167), (169), (172), (173), (174), (175),
% 195.42/31.64  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.42/31.64  | | | | | | | | | | | | |            (185), (270), (272), (273), (274), (275), (276),
% 195.42/31.64  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 195.42/31.64  | | | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (314),
% 195.42/31.64  | | | | | | | | | | | | |            (317), (319), (321), (323), (325), (326), (328),
% 195.42/31.64  | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 195.42/31.64  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.42/31.64  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 195.42/31.64  | | | | | | | | | | | | |            (427), (431), (538), (539), (540), (541), (542),
% 195.42/31.64  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.42/31.64  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.42/31.64  | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 195.42/31.64  | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 195.42/31.64  | | | | | | | | | | | | |            (580), (582), (584), (586), (588), (589), (590),
% 195.42/31.64  | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 195.42/31.64  | | | | | | | | | | | | |            (598), (600), (603), (604), (605), (606), (607),
% 195.42/31.64  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (772),
% 195.42/31.64  | | | | | | | | | | | | |            (773), (775), (3172), (4275), (4282), (4283),
% 195.42/31.64  | | | | | | | | | | | | |            (4284), (4632), (function-axioms) are inconsistent
% 195.42/31.64  | | | | | | | | | | | | |            by sub-proof #731.
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | |   (4633)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.42/31.64  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.42/31.64  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.42/31.64  | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | BETA: splitting (4633) gives:
% 195.42/31.64  | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | Case 1:
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | |   (4634)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.42/31.64  | | | | | | | | | | | | |           all_52_22 = e0
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 195.42/31.64  | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 195.42/31.64  | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (175), (177),
% 195.42/31.64  | | | | | | | | | | | | |            (178), (180), (182), (183), (184), (185), (270),
% 195.42/31.64  | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (279),
% 195.42/31.64  | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 195.42/31.64  | | | | | | | | | | | | |            (313), (315), (317), (321), (323), (324), (325),
% 195.42/31.64  | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 195.42/31.64  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.42/31.64  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.64  | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (540), (541),
% 195.42/31.64  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.42/31.64  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.42/31.64  | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.42/31.64  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.42/31.64  | | | | | | | | | | | | |            (577), (578), (580), (586), (587), (588), (589),
% 195.42/31.64  | | | | | | | | | | | | |            (590), (591), (592), (595), (596), (597), (598),
% 195.42/31.64  | | | | | | | | | | | | |            (602), (603), (605), (606), (608), (609), (610),
% 195.42/31.64  | | | | | | | | | | | | |            (611), (612), (613), (773), (775), (3172), (4275),
% 195.42/31.64  | | | | | | | | | | | | |            (4282), (4283), (4634), (function-axioms) are
% 195.42/31.64  | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | |   (4635)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.42/31.64  | | | | | | | | | | | | |           all_52_30 = e0
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 195.42/31.64  | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 195.42/31.64  | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.42/31.64  | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 195.42/31.64  | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 195.42/31.64  | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 195.42/31.64  | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 195.42/31.64  | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 195.42/31.64  | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 195.42/31.64  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 195.42/31.64  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 195.42/31.64  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.42/31.64  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 195.42/31.64  | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 195.42/31.64  | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 195.42/31.64  | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 195.42/31.64  | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 195.42/31.64  | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (773),
% 195.42/31.64  | | | | | | | | | | | | |            (775), (3172), (4275), (4282), (4284), (4635),
% 195.42/31.64  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.64  | | | | | | | | | | | | |            #1008.
% 195.42/31.64  | | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | End of split
% 195.42/31.64  | | | | | | | | | 
% 195.42/31.64  | | | | | | | | Case 2:
% 195.42/31.64  | | | | | | | | | 
% 195.42/31.64  | | | | | | | | |   (4636)  all_22_1 = e2
% 195.42/31.64  | | | | | | | | |   (4637)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 195.42/31.64  | | | | | | | | | 
% 195.42/31.64  | | | | | | | | | COMBINE_EQS: (658), (4636) imply:
% 195.42/31.65  | | | | | | | | |   (4638)  all_6_1 = e2
% 195.42/31.65  | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 195.42/31.65  | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 195.42/31.65  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.42/31.65  | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 195.42/31.65  | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 195.42/31.65  | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 195.42/31.65  | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 195.42/31.65  | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 195.42/31.65  | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 195.42/31.65  | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 195.42/31.65  | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.65  | | | | | | | | |            (415), (431), (522), (538), (539), (540), (541),
% 195.42/31.65  | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.42/31.65  | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.42/31.65  | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 195.42/31.65  | | | | | | | | |            (570), (572), (573), (574), (575), (576), (577),
% 195.42/31.65  | | | | | | | | |            (578), (582), (584), (586), (588), (590), (591),
% 195.42/31.65  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.42/31.65  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.42/31.65  | | | | | | | | |            (608), (609), (610), (612), (613), (739), (773),
% 195.42/31.65  | | | | | | | | |            (775), (3170), (3172), (4248), (4637), (4638),
% 195.42/31.65  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.65  | | | | | | | | |            #504.
% 195.42/31.65  | | | | | | | | | 
% 195.42/31.65  | | | | | | | | End of split
% 195.42/31.65  | | | | | | | | 
% 195.42/31.65  | | | | | | | End of split
% 195.42/31.65  | | | | | | | 
% 195.42/31.65  | | | | | | End of split
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | Case 2:
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | |   (4639)  all_12_1 = e1
% 195.42/31.65  | | | | | |   (4640)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | COMBINE_EQS: (683), (4639) imply:
% 195.42/31.65  | | | | | |   (4641)  all_6_1 = e1
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | SIMP: (4641) implies:
% 195.42/31.65  | | | | | |   (4642)  all_6_1 = e1
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | REDUCE: (43), (4642) imply:
% 195.42/31.65  | | | | | |   (4643)  op(all_6_2, e3) = e1
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | REDUCE: (42), (4642) imply:
% 195.42/31.65  | | | | | |   (4644)  op(e3, e1) = all_6_0
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | REF_CLOSE: (5), (6), (7), (8), (36), (38), (41), (51), (61), (62),
% 195.42/31.65  | | | | | |            (63), (64), (74), (153), (156), (158), (162), (166),
% 195.42/31.65  | | | | | |            (167), (168), (169), (172), (173), (174), (175), (178),
% 195.42/31.65  | | | | | |            (179), (180), (182), (183), (184), (185), (187), (270),
% 195.42/31.65  | | | | | |            (273), (276), (277), (278), (281), (282), (283), (284),
% 195.42/31.65  | | | | | |            (285), (303), (305), (306), (307), (308), (309), (313),
% 195.42/31.65  | | | | | |            (317), (321), (323), (325), (329), (331), (332), (333),
% 195.42/31.65  | | | | | |            (335), (351), (366), (367), (372), (375), (387), (388),
% 195.42/31.65  | | | | | |            (393), (394), (405), (411), (415), (421), (427), (431),
% 195.42/31.65  | | | | | |            (483), (538), (540), (541), (542), (543), (544), (545),
% 195.42/31.65  | | | | | |            (546), (547), (548), (549), (551), (553), (555), (557),
% 195.42/31.65  | | | | | |            (559), (561), (562), (563), (564), (567), (568), (569),
% 195.42/31.65  | | | | | |            (570), (571), (573), (574), (575), (576), (577), (578),
% 195.42/31.65  | | | | | |            (580), (582), (587), (588), (589), (590), (591), (592),
% 195.42/31.65  | | | | | |            (593), (594), (595), (598), (603), (604), (605), (606),
% 195.42/31.65  | | | | | |            (607), (608), (609), (610), (611), (613), (690), (761),
% 195.42/31.65  | | | | | |            (763), (771), (772), (773), (775), (4640), (4643),
% 195.42/31.65  | | | | | |            (4644), (function-axioms) are inconsistent by sub-proof
% 195.42/31.65  | | | | | |            #552.
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | End of split
% 195.42/31.65  | | | | | 
% 195.42/31.65  | | | | End of split
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | Case 2:
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | |   (4645)  all_8_0 = e2
% 195.42/31.65  | | | |   (4646)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | | COMBINE_EQS: (764), (4645) imply:
% 195.42/31.65  | | | |   (4647)  all_6_0 = e2
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | | COMBINE_EQS: (727), (4647) imply:
% 195.42/31.65  | | | |   (4648)  all_44_0 = e2
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | | REDUCE: (42), (4647) imply:
% 195.42/31.65  | | | |   (4649)  op(e3, all_6_1) = e2
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | | BETA: splitting (54) gives:
% 195.42/31.65  | | | | 
% 195.42/31.65  | | | | Case 1:
% 195.42/31.65  | | | | | 
% 195.42/31.65  | | | | |   (4650)   ~ (all_10_0 = e3)
% 195.42/31.65  | | | | | 
% 195.42/31.65  | | | | | BETA: splitting (64) gives:
% 195.42/31.65  | | | | | 
% 195.42/31.65  | | | | | Case 1:
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | |   (4651)   ~ (all_14_0 = e2)
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | BETA: splitting (69) gives:
% 195.42/31.65  | | | | | | 
% 195.42/31.65  | | | | | | Case 1:
% 195.42/31.65  | | | | | | | 
% 195.42/31.65  | | | | | | |   (4652)   ~ (all_16_0 = e2)
% 195.42/31.65  | | | | | | | 
% 195.42/31.65  | | | | | | | REDUCE: (760), (4652) imply:
% 195.42/31.65  | | | | | | |   (4653)   ~ (all_10_0 = e2)
% 195.42/31.65  | | | | | | | 
% 195.42/31.65  | | | | | | | BETA: splitting (74) gives:
% 195.42/31.65  | | | | | | | 
% 195.42/31.65  | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | 
% 195.42/31.65  | | | | | | | |   (4654)   ~ (all_18_0 = e3)
% 195.42/31.65  | | | | | | | | 
% 195.42/31.65  | | | | | | | | REDUCE: (761), (4654) imply:
% 195.42/31.65  | | | | | | | |   (4655)   ~ (all_14_0 = e3)
% 195.42/31.65  | | | | | | | | 
% 195.42/31.65  | | | | | | | | BETA: splitting (79) gives:
% 195.42/31.65  | | | | | | | | 
% 195.42/31.65  | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | 
% 195.42/31.65  | | | | | | | | |   (4656)   ~ (all_20_0 = e3)
% 195.42/31.65  | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | REDUCE: (758), (4656) imply:
% 195.42/31.65  | | | | | | | | |   (4657)   ~ (all_4_0 = e3)
% 195.42/31.65  | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | BETA: splitting (89) gives:
% 195.42/31.65  | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | |   (4658)   ~ (all_24_0 = e1)
% 195.42/31.65  | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | REDUCE: (711), (4658) imply:
% 195.42/31.65  | | | | | | | | | |   (4659)   ~ (all_14_0 = e1)
% 195.42/31.65  | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | BETA: splitting (104) gives:
% 195.42/31.65  | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | |   (4660)   ~ (all_30_1 = e3)
% 195.42/31.65  | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | REDUCE: (670), (4660) imply:
% 195.42/31.65  | | | | | | | | | | |   (4661)   ~ (all_10_1 = e3)
% 195.42/31.65  | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | BETA: splitting (109) gives:
% 195.42/31.65  | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | |   (4662)   ~ (all_32_1 = e3)
% 195.42/31.65  | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | REDUCE: (663), (4662) imply:
% 195.42/31.65  | | | | | | | | | | | |   (4663)   ~ (all_4_1 = e3)
% 195.42/31.65  | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | BETA: splitting (129) gives:
% 195.42/31.65  | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | |   (4664)   ~ (all_40_1 = e2)
% 195.42/31.65  | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | REDUCE: (687), (4664) imply:
% 195.42/31.65  | | | | | | | | | | | | |   (4665)   ~ (all_10_1 = e2)
% 195.42/31.65  | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.42/31.65  | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | |   (4666)   ~ (all_44_0 = e2)
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | REDUCE: (4648), (4666) imply:
% 195.42/31.65  | | | | | | | | | | | | | |   (4667)  $false
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | CLOSE: (4667) is inconsistent.
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | Case 2:
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | |   (4668)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.42/31.65  | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | |   (4669)  all_58_15 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4669) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4670)  all_14_2 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (573), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4671)   ~ (all_52_7 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (591), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4672)   ~ (all_52_15 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (603), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4673)   ~ (all_52_23 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (606), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4674)   ~ (all_52_25 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (609), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4675)   ~ (all_52_29 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (613), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4676)  op(e0, e0) = all_52_30
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (63), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4677)  op(e0, e0) = all_14_1
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (61), (4670) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4678)  op(e0, e0) = e0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.42/31.65  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (4676), (4677)
% 195.42/31.65  | | | | | | | | | | | | | | |              gives:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4679)  all_52_30 = all_14_1
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.42/31.65  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (4676), (4678)
% 195.42/31.65  | | | | | | | | | | | | | | |              gives:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4680)  all_52_30 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | COMBINE_EQS: (4679), (4680) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4681)  all_14_1 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (62), (4681) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4682)  op(e0, e0) = all_14_0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.42/31.65  | | | | | | | | | | | | | | |              e0, e0, simplifying with (4678), (4682) gives:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4683)  all_14_0 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (4655), (4683) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4684)   ~ (e3 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (4651), (4683) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4685)   ~ (e2 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | REDUCE: (4659), (4683) imply:
% 195.42/31.65  | | | | | | | | | | | | | | |   (4686)   ~ (e1 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.42/31.65  | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | |   (4687)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.42/31.65  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.42/31.65  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | BETA: splitting (4687) gives:
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4688)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.42/31.65  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (4649), (4688), (function-axioms) are inconsistent
% 195.42/31.65  | | | | | | | | | | | | | | | | |            by sub-proof #501.
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4689)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.42/31.65  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | ALPHA: (4689) implies:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4690)  all_52_14 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4691)  all_52_12 = e1
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4692)  all_52_10 = e2
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4693)  all_52_8 = e3
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (182), (4693) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4694)  op(all_52_9, all_52_9) = e3
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (180), (4691) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4695)  op(all_52_13, all_52_13) = e1
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (179), (4690) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4696)  op(all_52_15, all_52_15) = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (611), (4692) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4697)  op(all_4_2, all_4_2) = e2
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (166), (167),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (178), (183),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (281), (282),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (309), (313),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (317), (319), (325), (326), (327), (329), (330),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (372), (387), (388), (393), (394), (405), (411),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (431), (521), (528), (540), (542), (543), (544),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (567), (570),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (571), (572), (575), (576), (577), (578), (582),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (589), (590), (593), (595), (600), (604), (605),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (607), (610), (684), (688), (772), (4646), (4649),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (4661), (4665), (4668), (4669), (4671), (4672),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (4673), (4674), (4675), (4678), (4694), (4695),
% 195.42/31.65  | | | | | | | | | | | | | | | | |            (4696), (4697), (function-axioms) are inconsistent
% 195.42/31.65  | | | | | | | | | | | | | | | | |            by sub-proof #487.
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | End of split
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | Case 2:
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | |   (4698)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.42/31.65  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.42/31.65  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | BETA: splitting (4698) gives:
% 195.42/31.65  | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4699)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.42/31.65  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | ALPHA: (4699) implies:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4700)  all_52_22 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4701)  all_52_20 = e1
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4702)  all_52_18 = e2
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4703)  all_52_16 = e3
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (178), (4703) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4704)  op(all_52_17, all_52_17) = e3
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (177), (4702) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4705)  op(all_52_19, all_52_19) = e2
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (175), (4700) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4706)  op(all_52_23, all_52_23) = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | REDUCE: (612), (4701) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | |   (4707)  op(all_10_2, all_10_2) = e1
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | |   (4708)  all_56_13 = e3
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (51), (157), (271), (273), (304),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (343), (346), (351), (431), (571), (572), (590),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (600), (4663), (4671), (4673), (4678), (4706),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (4707), (4708), (function-axioms) are inconsistent
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            by sub-proof #1281.
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | |   (4709)   ~ (all_56_13 = e3)
% 195.42/31.65  | | | | | | | | | | | | | | | | | |   (4710)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | | REDUCE: (346), (4709) imply:
% 195.42/31.65  | | | | | | | | | | | | | | | | | |   (4711)   ~ (all_52_15 = e3)
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (41), (43), (51), (53), (158),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (174),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (179), (182), (183), (185), (273), (274), (277),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (285), (304), (306), (309),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (313), (317), (319), (325), (326), (329), (330),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (333), (346), (351), (352), (366), (367), (375),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (431),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (521), (528), (540), (541), (542), (543), (544),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (567),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (570), (571), (572), (575), (577), (584), (589),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (605), (613),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (4665), (4668),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (4669), (4674), (4675), (4678), (4704), (4705),
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            (4706), (4707), (4710), (4711), (function-axioms)
% 195.42/31.65  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #477.
% 195.42/31.65  | | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | | End of split
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.65  | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.65  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4712)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.42/31.66  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | ALPHA: (4712) implies:
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4713)  all_52_28 = e1
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4714)  all_52_26 = e2
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4715)  all_52_24 = e3
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REDUCE: (174), (4715) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4716)  op(all_52_25, all_52_25) = e3
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REDUCE: (173), (4714) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4717)  op(all_52_27, all_52_27) = e2
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REDUCE: (172), (4713) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4718)  op(all_52_29, all_52_29) = e1
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (175), (177),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (178), (183), (185), (272), (274), (276), (277),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (279), (281), (282), (306), (307), (308), (309),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (310), (311), (313), (317), (320), (321), (326),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (332), (333), (346), (351), (352), (366), (367),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (417), (421), (528), (542), (543), (544), (545),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (561), (562), (564), (565), (566), (567), (568),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (569), (570), (572), (576), (578), (580), (582),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (584), (587), (588), (589), (592), (593), (595),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (596), (600), (604), (605), (608), (609), (610),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (688), (4649), (4668), (4669), (4671), (4672),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (4673), (4674), (4675), (4716), (4717), (4718),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.66  | | | | | | | | | | | | | | | | |            #469.
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | End of split
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | End of split
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | Case 2:
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | |   (4719)   ~ (all_58_15 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | |   (4720)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.42/31.66  | | | | | | | | | | | | | | |             e0)
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | ALPHA: (4720) implies:
% 195.42/31.66  | | | | | | | | | | | | | | |   (4721)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.42/31.66  | | | | | | | | | | | | | | |   (4722)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | REDUCE: (541), (4719) imply:
% 195.42/31.66  | | | | | | | | | | | | | | |   (4723)   ~ (all_14_2 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.42/31.66  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 195.42/31.66  | | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 195.42/31.66  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.42/31.66  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 195.42/31.66  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 195.42/31.66  | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 195.42/31.66  | | | | | | | | | | | | | | |            (304), (305), (306), (307), (309), (311), (313),
% 195.42/31.66  | | | | | | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 195.42/31.66  | | | | | | | | | | | | | | |            (326), (327), (329), (331), (332), (333), (343),
% 195.42/31.66  | | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.42/31.66  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.42/31.66  | | | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (521), (528),
% 195.42/31.66  | | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 195.42/31.66  | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.42/31.66  | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 195.42/31.66  | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (570), (571),
% 195.42/31.66  | | | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 195.42/31.66  | | | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 195.42/31.66  | | | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 195.42/31.66  | | | | | | | | | | | | | | |            (597), (598), (600), (602), (603), (604), (605),
% 195.42/31.66  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 195.42/31.66  | | | | | | | | | | | | | | |            (613), (684), (688), (772), (4646), (4649),
% 195.42/31.66  | | | | | | | | | | | | | | |            (4651), (4659), (4665), (4668), (4721), (4722),
% 195.42/31.66  | | | | | | | | | | | | | | |            (4723), (function-axioms) are inconsistent by
% 195.42/31.66  | | | | | | | | | | | | | | |            sub-proof #433.
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | End of split
% 195.42/31.66  | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | End of split
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | Case 2:
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | |   (4724)  all_40_1 = e2
% 195.42/31.66  | | | | | | | | | | | | |   (4725)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | COMBINE_EQS: (687), (4724) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4726)  all_10_1 = e2
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (4661), (4726) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4727)   ~ (e3 = e2)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (53), (4726) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4728)  op(all_10_2, e1) = e2
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (52), (4726) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4729)  op(e1, e2) = all_10_0
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 195.42/31.66  | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (4729)
% 195.42/31.66  | | | | | | | | | | | | |              gives:
% 195.42/31.66  | | | | | | | | | | | | |   (4730)  all_52_13 = all_10_0
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | COMBINE_EQS: (421), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4731)  all_56_9 = all_10_0
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | COMBINE_EQS: (366), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4732)  all_58_7 = all_10_0
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (568), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4733)   ~ (all_52_5 = all_10_0)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (575), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4734)   ~ (all_52_9 = all_10_0)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (587), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4735)   ~ (all_52_15 = all_10_0)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | SIMP: (4735) implies:
% 195.42/31.66  | | | | | | | | | | | | |   (4736)   ~ (all_52_15 = all_10_0)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (589), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4737)   ~ (all_52_29 = all_10_0)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | SIMP: (4737) implies:
% 195.42/31.66  | | | | | | | | | | | | |   (4738)   ~ (all_52_29 = all_10_0)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (588), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4739)   ~ (all_10_0 = all_10_2)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (580), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4740)   ~ (all_10_0 = all_4_2)
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | REDUCE: (180), (4730) imply:
% 195.42/31.66  | | | | | | | | | | | | |   (4741)  op(all_10_0, all_10_0) = all_52_12
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 195.42/31.66  | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | Case 1:
% 195.42/31.66  | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | |   (4742)   ~ (all_42_0 = e1)
% 195.42/31.66  | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | REDUCE: (768), (4742) imply:
% 195.42/31.66  | | | | | | | | | | | | | |   (4743)   ~ (all_4_0 = e1)
% 195.42/31.66  | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.42/31.66  | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | Case 1:
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | |   (4744)   ~ (all_44_0 = e2)
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | REDUCE: (4648), (4744) imply:
% 195.42/31.66  | | | | | | | | | | | | | | |   (4745)  $false
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | CLOSE: (4745) is inconsistent.
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | Case 2:
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | |   (4746)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.42/31.66  | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | Case 1:
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4747)  all_58_15 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4747) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4748)  all_14_2 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (573), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4749)   ~ (all_52_7 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (591), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4750)   ~ (all_52_15 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (603), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4751)   ~ (all_52_23 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (606), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4752)   ~ (all_52_25 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (608), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4753)   ~ (all_52_27 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (609), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4754)   ~ (all_52_29 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (613), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4755)  op(e0, e0) = all_52_30
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (63), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4756)  op(e0, e0) = all_14_1
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (61), (4748) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4757)  op(e0, e0) = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.42/31.66  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (4755), (4756)
% 195.42/31.66  | | | | | | | | | | | | | | | |              gives:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4758)  all_52_30 = all_14_1
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.42/31.66  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (4755), (4757)
% 195.42/31.66  | | | | | | | | | | | | | | | |              gives:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4759)  all_52_30 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | COMBINE_EQS: (4758), (4759) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4760)  all_14_1 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | SIMP: (4760) implies:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4761)  all_14_1 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (62), (4761) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4762)  op(e0, e0) = all_14_0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.42/31.66  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (4757), (4762) gives:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4763)  all_14_0 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (4655), (4763) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4764)   ~ (e3 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (4651), (4763) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4765)   ~ (e2 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (4659), (4763) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4766)   ~ (e1 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4767)  all_56_9 = e3
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (4650), (4731), (4767) are inconsistent by
% 195.42/31.66  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4768)   ~ (all_56_9 = e3)
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4769)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (43), (51), (61), (157), (158), (162), (164),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (182), (183), (184),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (276), (277), (278), (279), (281), (282), (283),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (284), (285), (304), (306), (307), (308), (309),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (317), (319), (320),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (321), (325), (326), (327), (328), (331), (332),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (521),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (526), (528), (538), (540), (541), (542), (543),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (576), (577), (578),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (598), (600), (602), (604), (605), (606), (607),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (688), (767), (772), (4646), (4649), (4650),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (4653), (4663), (4725), (4728), (4731), (4732),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (4733), (4734), (4738), (4739), (4741), (4746),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (4747), (4749), (4750), (4751), (4752), (4753),
% 195.42/31.66  | | | | | | | | | | | | | | | | |            (4754), (4757), (4769), (function-axioms) are
% 195.42/31.66  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #417.
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | End of split
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | Case 2:
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4770)   ~ (all_58_15 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4771)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.42/31.66  | | | | | | | | | | | | | | | |             e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | ALPHA: (4771) implies:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4772)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4773)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | REDUCE: (541), (4770) imply:
% 195.42/31.66  | | | | | | | | | | | | | | | |   (4774)   ~ (all_14_2 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.42/31.66  | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4775)  all_56_9 = e3
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (4650), (4731), (4775) are inconsistent by
% 195.42/31.66  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4776)   ~ (all_56_9 = e3)
% 195.42/31.66  | | | | | | | | | | | | | | | | |   (4777)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.42/31.66  | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.66  | | | | | | | | | | | | | | | | | | 
% 195.42/31.66  | | | | | | | | | | | | | | | | | |   (4778)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.42/31.66  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.42/31.66  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.42/31.66  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (61),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (158), (169), (178), (179), (182), (183), (184),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (284), (285), (306),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (317), (321), (325), (327), (332), (333), (346),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (351), (387), (393), (394), (405), (431), (521),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (538), (540), (543), (545), (547), (548), (549),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (555), (557), (564), (569), (571), (573), (574),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (577), (582), (591), (606), (610), (611), (684),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (772), (4646), (4649), (4650), (4653), (4731),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (4732), (4734), (4739), (4741), (4777), (4778),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            #429.
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | |   (4779)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.42/31.67  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.42/31.67  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | BETA: splitting (4779) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4780)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | ALPHA: (4780) implies:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4781)  all_52_22 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4782)  all_52_20 = e1
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4783)  all_52_18 = e2
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4784)  all_52_16 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (178), (4784) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4785)  op(all_52_17, all_52_17) = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (177), (4783) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4786)  op(all_52_19, all_52_19) = e2
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (4781) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4787)  op(all_52_23, all_52_23) = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (612), (4782) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4788)  op(all_10_2, all_10_2) = e1
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (41), (43), (51), (61), (63), (158), (166), (167),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (168), (169), (172), (174), (179), (182), (183),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (184), (185), (270), (272), (273), (274), (281),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (306), (309),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (313), (315), (317), (319), (322), (323), (324),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (325), (326), (327), (329), (332), (333), (346),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (351), (352), (372), (375), (387), (388), (393),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (431), (521), (526),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (538), (540), (541), (542), (543), (544), (545),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (564), (565), (566),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (567), (569), (571), (572), (573), (574), (576),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (577), (578), (582), (584), (590), (591), (592),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (600), (602),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (603), (605), (606), (609), (610), (611), (613),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (684), (767), (4646), (4649), (4650), (4653),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (4657), (4725), (4728), (4731), (4732), (4734),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (4736), (4740), (4741), (4743), (4772), (4777),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (4785), (4786), (4787), (4788), (function-axioms)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #406.
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4789)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (4746), (4772),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            (4773), (4774), (4789), (function-axioms) are
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | End of split
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | End of split
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | End of split
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | End of split
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | |   (4790)  all_42_0 = e1
% 195.42/31.67  | | | | | | | | | | | | | |   (4791)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | COMBINE_EQS: (768), (4790) imply:
% 195.42/31.67  | | | | | | | | | | | | | |   (4792)  all_4_0 = e1
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | REDUCE: (4657), (4792) imply:
% 195.42/31.67  | | | | | | | | | | | | | |   (4793)   ~ (e3 = e1)
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | REDUCE: (37), (4792) imply:
% 195.42/31.67  | | | | | | | | | | | | | |   (4794)  op(e2, all_4_1) = e1
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.42/31.67  | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | |   (4795)   ~ (all_44_0 = e2)
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | REDUCE: (4648), (4795) imply:
% 195.42/31.67  | | | | | | | | | | | | | | |   (4796)  $false
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | CLOSE: (4796) is inconsistent.
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | |   (4797)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4798)  all_58_15 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4798) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4799)  all_14_2 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (573), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4800)   ~ (all_52_7 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (591), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4801)   ~ (all_52_15 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (603), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4802)   ~ (all_52_23 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (606), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4803)   ~ (all_52_25 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (609), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4804)   ~ (all_52_29 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (613), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4805)  op(e0, e0) = all_52_30
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (63), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4806)  op(e0, e0) = all_14_1
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (61), (4799) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4807)  op(e0, e0) = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.42/31.67  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (4805), (4806)
% 195.42/31.67  | | | | | | | | | | | | | | | |              gives:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4808)  all_52_30 = all_14_1
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.42/31.67  | | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (4805), (4807)
% 195.42/31.67  | | | | | | | | | | | | | | | |              gives:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4809)  all_52_30 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | COMBINE_EQS: (4808), (4809) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4810)  all_14_1 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (62), (4810) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4811)  op(e0, e0) = all_14_0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.42/31.67  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (4807), (4811) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4812)  all_14_0 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (4655), (4812) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4813)   ~ (e3 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (4651), (4812) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4814)   ~ (e2 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | REDUCE: (4659), (4812) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | |   (4815)   ~ (e1 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | |   (4816)  all_56_9 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (4650), (4731), (4816) are inconsistent by
% 195.42/31.67  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | |   (4817)   ~ (all_56_9 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | |   (4818)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | |   (4819)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.42/31.67  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.42/31.67  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (61),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (158), (169), (178), (179), (182), (183), (184),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (284), (285), (306),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (317), (321), (325), (327), (332), (333), (346),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (351), (387), (393), (394), (405), (431), (521),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (538), (540), (543), (545), (547), (548), (549),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (555), (557), (564), (569), (571), (573), (574),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (577), (582), (591), (606), (610), (611), (684),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (772), (4646), (4649), (4650), (4653), (4731),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (4732), (4734), (4739), (4741), (4818), (4819),
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.67  | | | | | | | | | | | | | | | | | |            #429.
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | |   (4820)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.42/31.67  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.42/31.67  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | BETA: splitting (4820) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4821)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | ALPHA: (4821) implies:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4822)  all_52_22 = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4823)  all_52_20 = e1
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4824)  all_52_18 = e2
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4825)  all_52_16 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (178), (4825) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4826)  op(all_52_17, all_52_17) = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (177), (4824) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4827)  op(all_52_19, all_52_19) = e2
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (4822) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4828)  op(all_52_23, all_52_23) = e0
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | REDUCE: (612), (4823) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | |   (4829)  op(all_10_2, all_10_2) = e1
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4830)  all_56_7 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (4830) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4831)  all_52_27 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | SIMP: (4831) implies:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4832)  all_52_27 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4832) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4833)  all_58_10 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (4832) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4834)   ~ (all_52_19 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (4832) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4835)   ~ (all_52_25 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (4832) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4836)   ~ (all_52_29 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | SIMP: (4836) implies:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4837)   ~ (all_52_29 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (4832) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4838)   ~ (all_4_2 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | SIMP: (4838) implies:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4839)   ~ (all_4_2 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4832) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4840)  op(e3, e3) = all_52_26
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (41), (164), (168),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (172), (182), (184), (274), (282), (307), (312),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (313), (317), (331), (333), (352), (375), (388),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (393), (405), (526), (542), (544), (545), (546),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (547), (549), (553), (559), (569), (570), (574),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (596), (605), (767), (4650), (4653), (4725),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (4728), (4731), (4732), (4738), (4798), (4803),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (4804), (4818), (4826), (4828), (4833), (4834),
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            (4835), (4837), (4839), (4840), (function-axioms)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #424.
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4841)   ~ (all_56_7 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (4841) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | |   (4842)   ~ (all_52_27 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | |   (4843)  all_58_9 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4843) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | |   (4844)  all_52_25 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4844) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | |   (4845)   ~ (all_52_9 = e3)
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | |   (4846)  all_58_1 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (4846) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | |   (4847)  all_52_9 = e3
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4845), (4847) imply:
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | |   (4848)  $false
% 195.42/31.67  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4848) is inconsistent.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | |   (4849)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |   (4850)  all_56_13 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (51), (157), (271), (273), (304),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            (343), (346), (351), (431), (571), (572), (590),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            (600), (4663), (4800), (4802), (4807), (4828),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            (4829), (4850), (function-axioms) are inconsistent
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1281.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |   (4851)   ~ (all_56_13 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (4851) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |   (4852)   ~ (all_52_15 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (169), (182), (284), (394),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            (527), (543), (548), (574), (637), (772), (4650),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            (4732), (4791), (4794), (4849), (4852),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            #607.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4853)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (38), (41), (43), (51), (157),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (158), (164), (169), (172), (179), (182), (183),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (184), (271), (272), (273), (282), (283), (304),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (312), (317), (325), (343), (346), (351), (366),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (372), (375), (388), (393), (415), (431), (521),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (546), (547), (548),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (549), (555), (557), (559), (561), (567), (571),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (572), (577), (584), (589), (590), (594), (595),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (596), (600), (602), (605), (613), (684), (4646),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (4649), (4653), (4663), (4728), (4732), (4798),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (4800), (4801), (4802), (4803), (4807), (4826),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (4827), (4828), (4829), (4842), (4853),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |            #419.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4854)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | ALPHA: (4854) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4855)  all_52_28 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4856)  all_52_26 = e2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4857)  all_52_24 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | REDUCE: (174), (4857) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4858)  op(all_52_25, all_52_25) = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4856) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4859)  op(all_52_27, all_52_27) = e2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | REDUCE: (172), (4855) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | |   (4860)  op(all_52_29, all_52_29) = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |   (4861)  all_56_13 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (41), (43), (51), (61), (162), (169),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (177), (178), (183), (185), (277), (279), (282),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (307), (309), (313), (317), (321), (326), (333),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (346), (351), (366), (367), (372), (375), (387),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (388), (393), (405), (417), (528), (544), (545),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (561),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (562), (567), (570), (576), (578), (582), (587),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (592), (593), (595), (604), (605), (608), (609),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (688), (4649), (4797), (4801), (4858), (4859),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            (4860), (4861), (function-axioms) are inconsistent
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |            by sub-proof #473.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |   (4862)   ~ (all_56_13 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (4862) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | |   (4863)   ~ (all_52_15 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4864)  all_58_12 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (4864) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4865)  all_52_7 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | SIMP: (4865) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4866)  all_52_7 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (4866) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4867)   ~ (all_52_3 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4866) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4868)   ~ (all_52_5 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (4866) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4869)   ~ (all_6_2 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | SIMP: (4869) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4870)   ~ (all_6_2 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (4866) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4871)  op(e3, e3) = all_52_6
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (4871)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | |   (4872)  all_52_6 = all_6_2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | |   (4873)  all_56_8 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (4868), (4873) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | |   (4874)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |   (4875)  all_56_4 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (4867), (4875) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |   (4876)   ~ (all_56_4 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | |   (4877)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4878)  all_56_7 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (4878) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4879)  all_52_27 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4879) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4880)  all_52_27 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4880) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4881)  all_58_10 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (604), (4880) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4882)   ~ (all_52_25 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4859), (4880) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4883)  op(e3, e3) = e2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (41), (43), (51), (166), (167), (276),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (279), (282), (308), (310), (311), (320), (326),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (366), (367), (375), (387), (388), (405), (411),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (417), (421), (544), (545), (547), (548), (551),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (561), (562), (565), (568), (570), (580), (584),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (588), (589), (596), (610), (4649), (4798),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (4803), (4804), (4858), (4860), (4870), (4874),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            (4877), (4881), (4882), (4883), (function-axioms)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #470.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4884)   ~ (all_56_7 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (4884) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4885)   ~ (all_52_27 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (4886)  all_58_2 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (4867), (4886) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1369.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (4887)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4888)  all_58_9 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4888) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4889)  all_52_25 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (561), (4858), (4889), (function-axioms) are
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1246.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4890)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4890) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4891)  all_58_10 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (4885), (4891) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4892)  all_58_11 = e3 | all_58_15 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4892) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4893)  all_58_11 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4893) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4894)  all_52_29 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4894) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4895)  all_52_29 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (4895) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4896)   ~ (all_52_25 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (602), (4895) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4897)   ~ (all_10_2 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4897) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4898)   ~ (all_10_2 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4860), (4895) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4899)  op(e3, e3) = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (41), (4899) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4900)  all_6_2 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (4900) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4901)   ~ (all_52_25 = e1)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4902)  all_56_3 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (4896), (4902) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1339.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4903)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4904)  all_58_9 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (4901), (4904) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #856.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4905)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4905) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4906)  all_58_10 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (4906) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4907)  all_52_27 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4907) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4908)  all_52_27 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (4908) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4909)   ~ (all_4_2 = e1)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4909) implies:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4910)   ~ (all_4_2 = e1)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4911)  all_58_9 = e2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4911) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4912)  all_52_25 = e2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4858), (4912) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4913)  op(e2, e2) = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3,
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (4913) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4914)  all_4_2 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (4914) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4915)   ~ (all_52_19 = e3)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4887) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4916)  all_58_3 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (169), (182), (284), (394),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (527), (548), (574), (637), (772), (4791), (4794),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4916), (function-axioms) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #606.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4917)  all_58_5 = e3 | all_58_10 = e3
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (375), (4885), (4915), (4917) are
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1132.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4918)   ~ (all_58_9 = e2)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (4918) imply:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4919)   ~ (all_52_25 = e2)
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4903) gives:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4920)  all_56_3 = e2
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (4919), (4920) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1259.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4921)  all_56_3 = e1 | all_56_3 = e0
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (307), (388), (545), (4803), (4858), (4898),
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4921), (function-axioms) are inconsistent by
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1245.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4922)  all_58_11 = e1 | all_58_15 = e1
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (4798), (4893), (4922) are inconsistent
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1206.
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.42/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4923)  all_58_15 = e3
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4798), (4923) are inconsistent by sub-proof
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1350.
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |   (4924)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (51), (175), (282), (307),
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |            (309), (332), (351), (372), (387), (388), (405),
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (547), (561), (564),
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |            (570), (572), (600), (604), (605), (4798), (4802),
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |            (4803), (4858), (4859), (4860), (4863), (4924),
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | |            #1205.
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | End of split
% 195.72/31.68  | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | Case 2:
% 195.72/31.68  | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | |   (4925)   ~ (all_58_15 = e0)
% 195.72/31.68  | | | | | | | | | | | | | | | |   (4926)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.72/31.68  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.72/31.68  | | | | | | | | | | | | | | | |             e0)
% 195.72/31.68  | | | | | | | | | | | | | | | | 
% 195.72/31.68  | | | | | | | | | | | | | | | | ALPHA: (4926) implies:
% 195.72/31.69  | | | | | | | | | | | | | | | |   (4927)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.72/31.69  | | | | | | | | | | | | | | | |   (4928)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.72/31.69  | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | REDUCE: (541), (4925) imply:
% 195.72/31.69  | | | | | | | | | | | | | | | |   (4929)   ~ (all_14_2 = e0)
% 195.72/31.69  | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.72/31.69  | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | Case 1:
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | |   (4930)  all_56_9 = e3
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | REF_CLOSE: (4650), (4731), (4930) are inconsistent by
% 195.72/31.69  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | |   (4931)   ~ (all_56_9 = e3)
% 195.72/31.69  | | | | | | | | | | | | | | | | |   (4932)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | Case 1:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | |   (4933)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.72/31.69  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.72/31.69  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (61),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (158), (169), (178), (179), (182), (183), (184),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (284), (285), (306),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (317), (321), (325), (327), (332), (333), (346),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (351), (387), (393), (394), (405), (431), (521),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (538), (540), (543), (545), (547), (548), (549),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (555), (557), (564), (569), (571), (573), (574),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (577), (582), (591), (606), (610), (611), (684),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (772), (4646), (4649), (4650), (4653), (4731),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (4732), (4734), (4739), (4741), (4932), (4933),
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.72/31.69  | | | | | | | | | | | | | | | | | |            #429.
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | |   (4934)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.72/31.69  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.72/31.69  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | BETA: splitting (4934) gives:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | Case 1:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4935)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | ALPHA: (4935) implies:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4936)  all_52_22 = e0
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4937)  all_52_20 = e1
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4938)  all_52_18 = e2
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4939)  all_52_16 = e3
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | REDUCE: (178), (4939) imply:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4940)  op(all_52_17, all_52_17) = e3
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | REDUCE: (177), (4938) imply:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4941)  op(all_52_19, all_52_19) = e2
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (4936) imply:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4942)  op(all_52_23, all_52_23) = e0
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | REDUCE: (612), (4937) imply:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4943)  op(all_10_2, all_10_2) = e1
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (166), (167),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (168), (169), (179), (182), (183), (184), (270),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (272), (273), (274), (281), (282), (283), (284),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (285), (304), (306), (313), (315), (317), (319),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (329), (332), (333),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (346), (351), (352), (375), (387), (388), (393),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (431), (521), (526),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (527), (538), (540), (541), (542), (543), (544),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (555),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (557), (559), (561), (564), (565), (567), (569),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (576), (577), (594),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (600), (602), (603), (606),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (609), (610), (611), (613), (637), (684), (767),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (772), (4646), (4649), (4650), (4653), (4725),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (4728), (4731), (4732), (4734), (4791), (4794),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (4927), (4932), (4940), (4941), (4942), (4943),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            #405.
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |   (4944)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (4797), (4927),
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            (4928), (4929), (4944), (function-axioms) are
% 195.72/31.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 195.72/31.69  | | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | |   (4945)  all_32_1 = e3
% 195.72/31.69  | | | | | | | | | | | |   (4946)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | COMBINE_EQS: (663), (4945) imply:
% 195.72/31.69  | | | | | | | | | | | |   (4947)  all_4_1 = e3
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | COMBINE_EQS: (686), (4947) imply:
% 195.72/31.69  | | | | | | | | | | | |   (4948)  all_38_1 = e3
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | REDUCE: (38), (4947) imply:
% 195.72/31.69  | | | | | | | | | | | |   (4949)  op(all_4_2, e2) = e3
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | REDUCE: (37), (4947) imply:
% 195.72/31.69  | | | | | | | | | | | |   (4950)  op(e2, e3) = all_4_0
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 195.72/31.69  | | | | | | | | | | | |            (51), (53), (61), (62), (63), (124), (139), (158),
% 195.72/31.69  | | | | | | | | | | | |            (162), (166), (168), (169), (172), (173), (174),
% 195.72/31.69  | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 195.72/31.69  | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 195.72/31.69  | | | | | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 195.72/31.69  | | | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 195.72/31.69  | | | | | | | | | | | |            (306), (307), (308), (309), (311), (312), (313),
% 195.72/31.69  | | | | | | | | | | | |            (316), (317), (319), (320), (321), (324), (325),
% 195.72/31.69  | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (332),
% 195.72/31.69  | | | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 195.72/31.69  | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 195.72/31.69  | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 195.72/31.69  | | | | | | | | | | | |            (521), (523), (525), (528), (538), (539), (540),
% 195.72/31.69  | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 195.72/31.69  | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 195.72/31.69  | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 195.72/31.69  | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 195.72/31.69  | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 195.72/31.69  | | | | | | | | | | | |            (586), (589), (590), (591), (592), (593), (594),
% 195.72/31.69  | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.72/31.69  | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.72/31.69  | | | | | | | | | | | |            (611), (612), (613), (684), (688), (721), (766),
% 195.72/31.69  | | | | | | | | | | | |            (4646), (4648), (4649), (4651), (4655), (4657),
% 195.72/31.69  | | | | | | | | | | | |            (4659), (4946), (4948), (4949), (4950),
% 195.72/31.69  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.72/31.69  | | | | | | | | | | | |            #388.
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | |   (4951)  all_30_1 = e3
% 195.72/31.69  | | | | | | | | | | |   (4952)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | COMBINE_EQS: (670), (4951) imply:
% 195.72/31.69  | | | | | | | | | | |   (4953)  all_10_1 = e3
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | SIMP: (4953) implies:
% 195.72/31.69  | | | | | | | | | | |   (4954)  all_10_1 = e3
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.72/31.69  | | | | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (139),
% 195.72/31.69  | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 195.72/31.69  | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.72/31.69  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 195.72/31.69  | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 195.72/31.69  | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 195.72/31.69  | | | | | | | | | | |            (304), (305), (306), (307), (309), (311), (313),
% 195.72/31.69  | | | | | | | | | | |            (314), (315), (316), (317), (319), (321), (324),
% 195.72/31.69  | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (332),
% 195.72/31.69  | | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 195.72/31.69  | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 195.72/31.69  | | | | | | | | | | |            (405), (411), (415), (417), (427), (431), (459),
% 195.72/31.69  | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 195.72/31.69  | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.72/31.69  | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.72/31.69  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.72/31.69  | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.72/31.69  | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.72/31.69  | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 195.72/31.69  | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.72/31.69  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.72/31.69  | | | | | | | | | | |            (611), (612), (613), (684), (688), (750), (772),
% 195.72/31.69  | | | | | | | | | | |            (4646), (4648), (4649), (4650), (4651), (4653),
% 195.72/31.69  | | | | | | | | | | |            (4655), (4659), (4952), (4954), (function-axioms)
% 195.72/31.69  | | | | | | | | | | |            are inconsistent by sub-proof #367.
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | End of split
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | |   (4955)  all_24_0 = e1
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | COMBINE_EQS: (711), (4955) imply:
% 195.72/31.69  | | | | | | | | | |   (4956)  all_14_0 = e1
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | SIMP: (4956) implies:
% 195.72/31.69  | | | | | | | | | |   (4957)  all_14_0 = e1
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | COMBINE_EQS: (765), (4957) imply:
% 195.72/31.69  | | | | | | | | | |   (4958)  all_34_0 = e1
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | REDUCE: (4655), (4957) imply:
% 195.72/31.69  | | | | | | | | | |   (4959)   ~ (e3 = e1)
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | REDUCE: (4651), (4957) imply:
% 195.72/31.69  | | | | | | | | | |   (4960)   ~ (e2 = e1)
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | REDUCE: (62), (4957) imply:
% 195.72/31.69  | | | | | | | | | |   (4961)  op(e0, all_14_1) = e1
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | BETA: splitting (104) gives:
% 195.72/31.69  | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | Case 1:
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | |   (4962)   ~ (all_30_1 = e3)
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | REDUCE: (670), (4962) imply:
% 195.72/31.69  | | | | | | | | | | |   (4963)   ~ (all_10_1 = e3)
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | BETA: splitting (114) gives:
% 195.72/31.69  | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | Case 1:
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | |   (4964)   ~ (all_34_0 = e1)
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | REDUCE: (4958), (4964) imply:
% 195.72/31.69  | | | | | | | | | | | |   (4965)  $false
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | CLOSE: (4965) is inconsistent.
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | Case 2:
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | |   (4966)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | BETA: splitting (129) gives:
% 195.72/31.69  | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | Case 1:
% 195.72/31.69  | | | | | | | | | | | | | 
% 195.72/31.69  | | | | | | | | | | | | |   (4967)   ~ (all_40_1 = e2)
% 195.72/31.69  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.72/31.70  | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (139), (156), (158),
% 195.72/31.70  | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.72/31.70  | | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 195.72/31.70  | | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 195.72/31.70  | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 195.72/31.70  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 195.72/31.70  | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 195.72/31.70  | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 195.72/31.70  | | | | | | | | | | | | |            (325), (326), (327), (329), (331), (332), (333),
% 195.72/31.70  | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 195.72/31.70  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.72/31.70  | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (491),
% 195.72/31.70  | | | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 195.72/31.70  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.72/31.70  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.72/31.70  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.72/31.70  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.72/31.70  | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.72/31.70  | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 195.72/31.70  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.72/31.70  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.72/31.70  | | | | | | | | | | | | |            (611), (612), (613), (684), (685), (687), (688),
% 195.72/31.70  | | | | | | | | | | | | |            (772), (4646), (4648), (4649), (4961), (4966),
% 195.72/31.70  | | | | | | | | | | | | |            (4967), (function-axioms) are inconsistent by
% 195.72/31.70  | | | | | | | | | | | | |            sub-proof #361.
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | Case 2:
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | |   (4968)  all_40_1 = e2
% 195.72/31.70  | | | | | | | | | | | | |   (4969)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | COMBINE_EQS: (687), (4968) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4970)  all_10_1 = e2
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | SIMP: (4970) implies:
% 195.72/31.70  | | | | | | | | | | | | |   (4971)  all_10_1 = e2
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (4963), (4971) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4972)   ~ (e3 = e2)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (53), (4971) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4973)  op(all_10_2, e1) = e2
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (52), (4971) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4974)  op(e1, e2) = all_10_0
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 195.72/31.70  | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (4974)
% 195.72/31.70  | | | | | | | | | | | | |              gives:
% 195.72/31.70  | | | | | | | | | | | | |   (4975)  all_52_13 = all_10_0
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | COMBINE_EQS: (421), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4976)  all_56_9 = all_10_0
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | COMBINE_EQS: (366), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4977)  all_58_7 = all_10_0
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (575), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4978)   ~ (all_52_9 = all_10_0)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (587), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4979)   ~ (all_52_15 = all_10_0)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | SIMP: (4979) implies:
% 195.72/31.70  | | | | | | | | | | | | |   (4980)   ~ (all_52_15 = all_10_0)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (588), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4981)   ~ (all_10_0 = all_10_2)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (580), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4982)   ~ (all_10_0 = all_4_2)
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | REDUCE: (180), (4975) imply:
% 195.72/31.70  | | | | | | | | | | | | |   (4983)  op(all_10_0, all_10_0) = all_52_12
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 195.72/31.70  | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | Case 1:
% 195.72/31.70  | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | |   (4984)   ~ (all_42_0 = e1)
% 195.72/31.70  | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | REDUCE: (768), (4984) imply:
% 195.72/31.70  | | | | | | | | | | | | | |   (4985)   ~ (all_4_0 = e1)
% 195.72/31.70  | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.72/31.70  | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | Case 1:
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | |   (4986)   ~ (all_44_0 = e2)
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | | REDUCE: (4648), (4986) imply:
% 195.72/31.70  | | | | | | | | | | | | | | |   (4987)  $false
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | | CLOSE: (4987) is inconsistent.
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | Case 2:
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | |   (4988)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.72/31.70  | | | | | | | | | | | | | | | 
% 195.72/31.70  | | | | | | | | | | | | | | | Case 1:
% 195.72/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | |   (4989)  all_58_15 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (4961), (4989),
% 195.76/31.70  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.70  | | | | | | | | | | | | | | | |            #877.
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | |   (4990)   ~ (all_58_15 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | |   (4991)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.70  | | | | | | | | | | | | | | | |             e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | ALPHA: (4991) implies:
% 195.76/31.70  | | | | | | | | | | | | | | | |   (4992)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | |   (4993)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | REDUCE: (541), (4990) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | |   (4994)   ~ (all_14_2 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | |   (4995)  all_56_9 = e3
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (4650), (4976), (4995) are inconsistent by
% 195.76/31.70  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | |   (4996)   ~ (all_56_9 = e3)
% 195.76/31.70  | | | | | | | | | | | | | | | | |   (4997)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | |   (4998)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.70  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | BETA: splitting (4998) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (4999)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4649), (4999), (function-axioms) are inconsistent
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            by sub-proof #501.
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5000)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | ALPHA: (5000) implies:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5001)  all_52_14 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5002)  all_52_12 = e1
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5003)  all_52_10 = e2
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5004)  all_52_8 = e3
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (182), (5004) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5005)  op(all_52_9, all_52_9) = e3
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (179), (5001) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5006)  op(all_52_15, all_52_15) = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (4983), (5002) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5007)  op(all_10_0, all_10_0) = e1
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (611), (5003) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5008)  op(all_4_2, all_4_2) = e2
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (61),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (158), (169), (178), (183), (270), (272), (273),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (284), (317), (325), (327), (333), (346), (393),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (394), (405), (431), (521), (538), (543), (545),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (548), (549), (555), (557), (571), (573), (574),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (577), (582), (591), (606), (684), (772), (4646),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4649), (4650), (4653), (4976), (4977), (4978),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4981), (4997), (5005), (5006), (5007), (5008),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            #430.
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | |   (5009)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.70  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.70  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | BETA: splitting (5009) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5010)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | ALPHA: (5010) implies:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5011)  all_52_22 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5012)  all_52_20 = e1
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5013)  all_52_18 = e2
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5014)  all_52_16 = e3
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (178), (5014) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5015)  op(all_52_17, all_52_17) = e3
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (177), (5013) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5016)  op(all_52_19, all_52_19) = e2
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (5011) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5017)  op(all_52_23, all_52_23) = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REDUCE: (612), (5012) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5018)  op(all_10_2, all_10_2) = e1
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (41), (43), (51), (61), (63), (158), (166), (167),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (168), (169), (172), (174), (179), (182), (183),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (184), (185), (270), (272), (273), (274), (281),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (282), (283), (284), (285), (304), (306), (309),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (313), (315), (317), (319), (322), (323), (324),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (325), (326), (327), (329), (332), (333), (346),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (351), (352), (372), (375), (387), (388), (393),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (431), (521), (526),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (538), (540), (541), (542), (543), (544), (545),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (564), (565), (566),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (567), (569), (571), (572), (573), (574), (576),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (577), (578), (582), (584), (590), (591), (592),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (600), (602),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (603), (605), (606), (609), (610), (611), (613),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (684), (767), (4646), (4649), (4650), (4653),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4657), (4969), (4973), (4976), (4977), (4978),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4980), (4982), (4983), (4985), (4992), (4997),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (5015), (5016), (5017), (5018), (function-axioms)
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #406.
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5019)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (61), (63), (156), (158), (162), (166), (167),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (177), (178),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (270),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (271), (274), (276), (277), (278), (279), (280),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (282), (283), (285), (305), (306), (307), (308),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (309), (311), (313), (316), (317), (319), (321),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (332), (333), (343),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (388), (393), (405), (415), (417), (421), (427),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (491), (528), (538), (539), (540), (541), (542),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (551), (553), (555), (559), (561), (562), (563),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (572),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (573), (574), (575), (578), (580), (582), (584),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (586), (587), (589), (590), (592), (593), (594),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (602), (603), (604),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (685), (688), (4649), (4961), (4966), (4988),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4992), (4993), (4994), (5019), (function-axioms)
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #360.
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | End of split
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | End of split
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | End of split
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | End of split
% 195.76/31.70  | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | |   (5020)  all_42_0 = e1
% 195.76/31.70  | | | | | | | | | | | | | |   (5021)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 195.76/31.70  | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | COMBINE_EQS: (768), (5020) imply:
% 195.76/31.70  | | | | | | | | | | | | | |   (5022)  all_4_0 = e1
% 195.76/31.70  | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | REDUCE: (37), (5022) imply:
% 195.76/31.70  | | | | | | | | | | | | | |   (5023)  op(e2, all_4_1) = e1
% 195.76/31.70  | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.70  | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | |   (5024)   ~ (all_44_0 = e2)
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | REDUCE: (4648), (5024) imply:
% 195.76/31.70  | | | | | | | | | | | | | | |   (5025)  $false
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | CLOSE: (5025) is inconsistent.
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | |   (5026)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | |   (5027)  all_58_15 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (4961), (5027),
% 195.76/31.70  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.70  | | | | | | | | | | | | | | | |            #877.
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | |   (5028)   ~ (all_58_15 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | |   (5029)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.70  | | | | | | | | | | | | | | | |             e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | ALPHA: (5029) implies:
% 195.76/31.70  | | | | | | | | | | | | | | | |   (5030)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | |   (5031)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | REDUCE: (541), (5028) imply:
% 195.76/31.70  | | | | | | | | | | | | | | | |   (5032)   ~ (all_14_2 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | |   (5033)  all_56_9 = e3
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (4650), (4976), (5033) are inconsistent by
% 195.76/31.70  | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | |   (5034)   ~ (all_56_9 = e3)
% 195.76/31.70  | | | | | | | | | | | | | | | | |   (5035)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | |   (5036)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.70  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | BETA: splitting (5036) gives:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5037)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            (4649), (5037), (function-axioms) are inconsistent
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |            by sub-proof #501.
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.70  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |   (5038)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.76/31.70  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | ALPHA: (5038) implies:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5039)  all_52_14 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5040)  all_52_8 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REDUCE: (182), (5040) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5041)  op(all_52_9, all_52_9) = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REDUCE: (179), (5039) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5042)  op(all_52_15, all_52_15) = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |   (5043)  all_56_15 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5043) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |   (5044)  all_14_2 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | SIMP: (5044) implies:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |   (5045)  all_14_2 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (5045) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |   (5046)   ~ (all_52_15 = e3)
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (169), (182), (284), (325),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |            (394), (527), (543), (548), (549), (557), (574),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |            (637), (772), (4650), (4977), (5021), (5023),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |            (5041), (5046), (function-axioms) are inconsistent
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |            by sub-proof #359.
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | |   (5047)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |   (5048)  all_56_13 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (5048) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |   (5049)  all_52_15 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (158), (169), (183), (273),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            (431), (521), (538), (555), (571), (573), (582),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            (684), (4646), (4649), (5041), (5042), (5047),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            (5049), (function-axioms) are inconsistent by
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            sub-proof #432.
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |   (5050)   ~ (all_56_13 = e3)
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (5050) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |   (5051)   ~ (all_52_15 = e3)
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (169), (182), (284), (325),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            (394), (527), (543), (548), (549), (557), (574),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            (637), (772), (4650), (4977), (5021), (5023),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            (5041), (5051), (function-axioms) are inconsistent
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #359.
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | |   (5052)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.71  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.71  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | BETA: splitting (5052) gives:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5053)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | ALPHA: (5053) implies:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5054)  all_52_22 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5055)  all_52_20 = e1
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5056)  all_52_18 = e2
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5057)  all_52_16 = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REDUCE: (178), (5057) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5058)  op(all_52_17, all_52_17) = e3
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REDUCE: (177), (5056) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5059)  op(all_52_19, all_52_19) = e2
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (5054) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5060)  op(all_52_23, all_52_23) = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REDUCE: (612), (5055) imply:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5061)  op(all_10_2, all_10_2) = e1
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (166), (167),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (168), (169), (179), (182), (183), (184), (270),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (272), (273), (274), (281), (282), (283), (284),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (285), (304), (306), (313), (315), (317), (319),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (329), (332), (333),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (346), (351), (352), (375), (387), (388), (393),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (394), (405), (411), (415), (431), (521), (526),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (527), (538), (540), (541), (542), (543), (544),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (555),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (557), (559), (561), (564), (565), (567), (569),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (576), (577), (594),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (600), (602), (603), (606),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (609), (610), (611), (613), (637), (684), (767),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (772), (4646), (4649), (4650), (4653), (4969),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (4973), (4976), (4977), (4978), (5021), (5023),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (5030), (5035), (5058), (5059), (5060), (5061),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            #405.
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |   (5062)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (61), (63), (156), (158), (162), (166), (167),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (177), (178),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (270),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (271), (274), (276), (277), (278), (279), (280),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (282), (283), (285), (305), (306), (307), (308),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (309), (311), (313), (316), (317), (319), (321),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (332), (333), (343),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (388), (393), (405), (415), (417), (421), (427),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (491), (528), (538), (539), (540), (541), (542),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (551), (553), (555), (559), (561), (562), (563),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (572),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (573), (574), (575), (578), (580), (582), (584),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (586), (587), (589), (590), (592), (593), (594),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (602), (603), (604),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (685), (688), (4649), (4961), (4966), (5026),
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            (5030), (5031), (5032), (5062), (function-axioms)
% 195.76/31.71  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #360.
% 195.76/31.71  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | |   (5063)  all_30_1 = e3
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | COMBINE_EQS: (670), (5063) imply:
% 195.76/31.71  | | | | | | | | | | |   (5064)  all_10_1 = e3
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | SIMP: (5064) implies:
% 195.76/31.71  | | | | | | | | | | |   (5065)  all_10_1 = e3
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | REDUCE: (53), (5065) imply:
% 195.76/31.71  | | | | | | | | | | |   (5066)  op(all_10_2, e1) = e3
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | REDUCE: (52), (5065) imply:
% 195.76/31.71  | | | | | | | | | | |   (5067)  op(e1, e3) = all_10_0
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.71  | | | | | | | | | | |            (43), (51), (53), (61), (63), (114), (139), (156),
% 195.76/31.71  | | | | | | | | | | |            (158), (159), (162), (166), (167), (168), (169),
% 195.76/31.71  | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 195.76/31.71  | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 195.76/31.71  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 195.76/31.71  | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (284),
% 195.76/31.71  | | | | | | | | | | |            (285), (303), (304), (305), (306), (307), (308),
% 195.76/31.71  | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 195.76/31.71  | | | | | | | | | | |            (321), (324), (325), (326), (327), (329), (330),
% 195.76/31.71  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 195.76/31.71  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.76/31.71  | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 195.76/31.71  | | | | | | | | | | |            (427), (431), (491), (521), (528), (538), (539),
% 195.76/31.71  | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.71  | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 195.76/31.71  | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 195.76/31.71  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 195.76/31.71  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 195.76/31.71  | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 195.76/31.71  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.76/31.71  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.76/31.71  | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 195.76/31.71  | | | | | | | | | | |            (685), (688), (772), (4646), (4648), (4649),
% 195.76/31.71  | | | | | | | | | | |            (4650), (4653), (4958), (4961), (5066), (5067),
% 195.76/31.71  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.71  | | | | | | | | | | |            #355.
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | End of split
% 195.76/31.71  | | | | | | | | | 
% 195.76/31.71  | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | 
% 195.76/31.71  | | | | | | | | |   (5068)  all_20_0 = e3
% 195.76/31.71  | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | COMBINE_EQS: (758), (5068) imply:
% 195.76/31.71  | | | | | | | | |   (5069)  all_4_0 = e3
% 195.76/31.71  | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | REDUCE: (37), (5069) imply:
% 195.76/31.71  | | | | | | | | |   (5070)  op(e2, all_4_1) = e3
% 195.76/31.71  | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | BETA: splitting (89) gives:
% 195.76/31.71  | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | |   (5071)   ~ (all_24_0 = e1)
% 195.76/31.71  | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | REDUCE: (711), (5071) imply:
% 195.76/31.71  | | | | | | | | | |   (5072)   ~ (all_14_0 = e1)
% 195.76/31.71  | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | BETA: splitting (104) gives:
% 195.76/31.71  | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | |   (5073)   ~ (all_30_1 = e3)
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | REDUCE: (670), (5073) imply:
% 195.76/31.71  | | | | | | | | | | |   (5074)   ~ (all_10_1 = e3)
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | BETA: splitting (129) gives:
% 195.76/31.71  | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | |   (5075)   ~ (all_40_1 = e2)
% 195.76/31.71  | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | REDUCE: (687), (5075) imply:
% 195.76/31.71  | | | | | | | | | | | |   (5076)   ~ (all_10_1 = e2)
% 195.76/31.71  | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.71  | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | |   (5077)   ~ (all_44_0 = e2)
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | REDUCE: (4648), (5077) imply:
% 195.76/31.71  | | | | | | | | | | | | |   (5078)  $false
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | CLOSE: (5078) is inconsistent.
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | |   (5079)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.71  | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | |   (5080)  all_58_15 = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | COMBINE_EQS: (541), (5080) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5081)  all_14_2 = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (573), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5082)   ~ (all_52_7 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (591), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5083)   ~ (all_52_15 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (603), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5084)   ~ (all_52_23 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (606), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5085)   ~ (all_52_25 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (609), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5086)   ~ (all_52_29 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (613), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5087)  op(e0, e0) = all_52_30
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (63), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5088)  op(e0, e0) = all_14_1
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (61), (5081) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5089)  op(e0, e0) = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.76/31.71  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5087), (5088)
% 195.76/31.71  | | | | | | | | | | | | | |              gives:
% 195.76/31.71  | | | | | | | | | | | | | |   (5090)  all_52_30 = all_14_1
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.76/31.71  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5087), (5089)
% 195.76/31.71  | | | | | | | | | | | | | |              gives:
% 195.76/31.71  | | | | | | | | | | | | | |   (5091)  all_52_30 = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | COMBINE_EQS: (5090), (5091) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5092)  all_14_1 = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | SIMP: (5092) implies:
% 195.76/31.71  | | | | | | | | | | | | | |   (5093)  all_14_1 = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (62), (5093) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5094)  op(e0, e0) = all_14_0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.76/31.71  | | | | | | | | | | | | | |              e0, e0, simplifying with (5089), (5094) gives:
% 195.76/31.71  | | | | | | | | | | | | | |   (5095)  all_14_0 = e0
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (4655), (5095) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5096)   ~ (e3 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (4651), (5095) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5097)   ~ (e2 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | REDUCE: (5072), (5095) imply:
% 195.76/31.71  | | | | | | | | | | | | | |   (5098)   ~ (e1 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.71  | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | |   (5099)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.71  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.71  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.71  | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | BETA: splitting (5099) gives:
% 195.76/31.71  | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.71  | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | |   (5100)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.71  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 195.76/31.71  | | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 195.76/31.71  | | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 195.76/31.71  | | | | | | | | | | | | | | | |            (4649), (5100), (function-axioms) are inconsistent
% 195.76/31.71  | | | | | | | | | | | | | | | |            by sub-proof #501.
% 195.76/31.71  | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.71  | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | |   (5101)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.76/31.71  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.76/31.71  | | | | | | | | | | | | | | | | 
% 195.76/31.71  | | | | | | | | | | | | | | | | ALPHA: (5101) implies:
% 195.76/31.71  | | | | | | | | | | | | | | | |   (5102)  all_52_14 = e0
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5103)  all_52_12 = e1
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5104)  all_52_10 = e2
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5105)  all_52_8 = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (182), (5105) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5106)  op(all_52_9, all_52_9) = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (180), (5103) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5107)  op(all_52_13, all_52_13) = e1
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (179), (5102) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5108)  op(all_52_15, all_52_15) = e0
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (611), (5104) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5109)  op(all_4_2, all_4_2) = e2
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (166), (167),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (178), (183),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (281), (282),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (284), (285), (304), (305), (306), (309), (313),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (317), (319), (325), (326), (327), (329), (330),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (372), (387), (388), (393), (394), (405), (411),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (431), (521), (528), (540), (542), (543), (544),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (567), (570),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (571), (572), (575), (576), (577), (578), (582),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (589), (590), (593), (595), (600), (604), (605),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (607), (610), (684), (688), (772), (4646), (4649),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (5074), (5076), (5079), (5080), (5082), (5083),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (5084), (5085), (5086), (5089), (5106), (5107),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (5108), (5109), (function-axioms) are inconsistent
% 195.76/31.72  | | | | | | | | | | | | | | | |            by sub-proof #487.
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | End of split
% 195.76/31.72  | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | Case 2:
% 195.76/31.72  | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | |   (5110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.72  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.72  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | BETA: splitting (5110) gives:
% 195.76/31.72  | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5111)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.72  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | ALPHA: (5111) implies:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5112)  all_52_22 = e0
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5113)  all_52_20 = e1
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5114)  all_52_18 = e2
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5115)  all_52_16 = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (178), (5115) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5116)  op(all_52_17, all_52_17) = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (177), (5114) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5117)  op(all_52_19, all_52_19) = e2
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (175), (5112) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5118)  op(all_52_23, all_52_23) = e0
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REDUCE: (612), (5113) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5119)  op(all_10_2, all_10_2) = e1
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5120)  all_56_13 = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (5120) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5121)  all_52_15 = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | SIMP: (5121) implies:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5122)  all_52_15 = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (5122) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5123)  all_58_13 = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REDUCE: (571), (5122) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5124)   ~ (all_52_7 = e3)
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REDUCE: (590), (5122) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5125)   ~ (all_52_23 = e3)
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | SIMP: (5125) implies:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5126)   ~ (all_52_23 = e3)
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REDUCE: (179), (5122) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5127)  op(e3, e3) = all_52_14
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REDUCE: (157), (5122) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5128)  op(e0, e2) = e3
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (38), (41), (51), (166),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (271), (273), (279), (283), (304), (305), (343),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (351), (415), (417), (431), (542), (551), (565),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (572), (584), (592), (594), (597), (600), (611),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (5070), (5080), (5082), (5084), (5089), (5116),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (5118), (5119), (5123), (5124), (5126), (5127),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (5128), (function-axioms) are inconsistent by
% 195.76/31.72  | | | | | | | | | | | | | | | | |            sub-proof #766.
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5129)   ~ (all_56_13 = e3)
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5130)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REDUCE: (346), (5129) imply:
% 195.76/31.72  | | | | | | | | | | | | | | | | |   (5131)   ~ (all_52_15 = e3)
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (41), (43), (51), (53), (158),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (174),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (179), (182), (183), (185), (273), (274), (277),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (281), (282), (283), (285), (304), (306), (309),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (313), (317), (319), (325), (326), (329), (330),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (333), (346), (351), (352), (366), (367), (375),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (431),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (521), (528), (540), (541), (542), (543), (544),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (567),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (570), (571), (572), (575), (577), (584), (589),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (605), (613),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (5076), (5079),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (5080), (5085), (5086), (5089), (5116), (5117),
% 195.76/31.72  | | | | | | | | | | | | | | | | |            (5118), (5119), (5130), (5131), (function-axioms)
% 195.76/31.72  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #477.
% 195.76/31.72  | | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | End of split
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | |   (5132)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.72  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (608), (609), (610), (688), (4649), (5079),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (5080), (5082), (5083), (5084), (5085), (5086),
% 195.76/31.72  | | | | | | | | | | | | | | | |            (5132), (function-axioms) are inconsistent by
% 195.76/31.72  | | | | | | | | | | | | | | | |            sub-proof #418.
% 195.76/31.72  | | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | | End of split
% 195.76/31.72  | | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | End of split
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | Case 2:
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | |   (5133)   ~ (all_58_15 = e0)
% 195.76/31.72  | | | | | | | | | | | | | |   (5134)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.72  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.72  | | | | | | | | | | | | | |             e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | ALPHA: (5134) implies:
% 195.76/31.72  | | | | | | | | | | | | | |   (5135)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.72  | | | | | | | | | | | | | |   (5136)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (541), (5133) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5137)   ~ (all_14_2 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.72  | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 195.76/31.72  | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 195.76/31.72  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.76/31.72  | | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 195.76/31.72  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 195.76/31.72  | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 195.76/31.72  | | | | | | | | | | | | | |            (304), (305), (306), (307), (309), (311), (313),
% 195.76/31.72  | | | | | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 195.76/31.72  | | | | | | | | | | | | | |            (326), (327), (329), (331), (332), (333), (343),
% 195.76/31.72  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.76/31.72  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.76/31.72  | | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (521), (528),
% 195.76/31.72  | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 195.76/31.72  | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 195.76/31.72  | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 195.76/31.72  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (570), (571),
% 195.76/31.72  | | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 195.76/31.72  | | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 195.76/31.72  | | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 195.76/31.72  | | | | | | | | | | | | | |            (597), (598), (600), (602), (603), (604), (605),
% 195.76/31.72  | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 195.76/31.72  | | | | | | | | | | | | | |            (613), (684), (688), (772), (4646), (4649),
% 195.76/31.72  | | | | | | | | | | | | | |            (4651), (5072), (5076), (5079), (5135), (5136),
% 195.76/31.72  | | | | | | | | | | | | | |            (5137), (function-axioms) are inconsistent by
% 195.76/31.72  | | | | | | | | | | | | | |            sub-proof #433.
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | End of split
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | End of split
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | Case 2:
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | |   (5138)  all_40_1 = e2
% 195.76/31.72  | | | | | | | | | | | |   (5139)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | COMBINE_EQS: (687), (5138) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5140)  all_10_1 = e2
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (5074), (5140) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5141)   ~ (e3 = e2)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (53), (5140) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5142)  op(all_10_2, e1) = e2
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (52), (5140) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5143)  op(e1, e2) = all_10_0
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 195.76/31.72  | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (5143)
% 195.76/31.72  | | | | | | | | | | | |              gives:
% 195.76/31.72  | | | | | | | | | | | |   (5144)  all_52_13 = all_10_0
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | COMBINE_EQS: (421), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5145)  all_56_9 = all_10_0
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | COMBINE_EQS: (366), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5146)  all_58_7 = all_10_0
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (568), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5147)   ~ (all_52_5 = all_10_0)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (575), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5148)   ~ (all_52_9 = all_10_0)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (589), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5149)   ~ (all_52_29 = all_10_0)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | SIMP: (5149) implies:
% 195.76/31.72  | | | | | | | | | | | |   (5150)   ~ (all_52_29 = all_10_0)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (588), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5151)   ~ (all_10_0 = all_10_2)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (580), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5152)   ~ (all_10_0 = all_4_2)
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | REDUCE: (180), (5144) imply:
% 195.76/31.72  | | | | | | | | | | | |   (5153)  op(all_10_0, all_10_0) = all_52_12
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.72  | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | Case 1:
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | |   (5154)   ~ (all_44_0 = e2)
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | REDUCE: (4648), (5154) imply:
% 195.76/31.72  | | | | | | | | | | | | |   (5155)  $false
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | CLOSE: (5155) is inconsistent.
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | Case 2:
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | |   (5156)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.72  | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | Case 1:
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | |   (5157)  all_58_15 = e0
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | COMBINE_EQS: (541), (5157) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5158)  all_14_2 = e0
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (573), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5159)   ~ (all_52_7 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (591), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5160)   ~ (all_52_15 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (603), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5161)   ~ (all_52_23 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (606), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5162)   ~ (all_52_25 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (608), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5163)   ~ (all_52_27 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (609), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5164)   ~ (all_52_29 = e0)
% 195.76/31.72  | | | | | | | | | | | | | | 
% 195.76/31.72  | | | | | | | | | | | | | | REDUCE: (613), (5158) imply:
% 195.76/31.72  | | | | | | | | | | | | | |   (5165)  op(e0, e0) = all_52_30
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (63), (5158) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5166)  op(e0, e0) = all_14_1
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (61), (5158) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5167)  op(e0, e0) = e0
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.76/31.73  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5165), (5166)
% 195.76/31.73  | | | | | | | | | | | | | |              gives:
% 195.76/31.73  | | | | | | | | | | | | | |   (5168)  all_52_30 = all_14_1
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.76/31.73  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5165), (5167)
% 195.76/31.73  | | | | | | | | | | | | | |              gives:
% 195.76/31.73  | | | | | | | | | | | | | |   (5169)  all_52_30 = e0
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | COMBINE_EQS: (5168), (5169) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5170)  all_14_1 = e0
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (62), (5170) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5171)  op(e0, e0) = all_14_0
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.76/31.73  | | | | | | | | | | | | | |              e0, e0, simplifying with (5167), (5171) gives:
% 195.76/31.73  | | | | | | | | | | | | | |   (5172)  all_14_0 = e0
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (4655), (5172) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5173)   ~ (e3 = e0)
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (4651), (5172) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5174)   ~ (e2 = e0)
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (5072), (5172) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5175)   ~ (e1 = e0)
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | |   (5176)  all_56_9 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | REF_CLOSE: (4650), (5145), (5176) are inconsistent by
% 195.76/31.73  | | | | | | | | | | | | | | |            sub-proof #1006.
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | |   (5177)   ~ (all_56_9 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | |   (5178)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | |   (5179)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.73  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.73  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (61),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (158), (169), (178), (179), (182), (183), (184),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (284), (285), (306),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (317), (321), (325), (327), (332), (333), (346),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (351), (387), (393), (394), (405), (431), (521),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (538), (540), (543), (545), (547), (548), (549),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (555), (557), (564), (569), (571), (573), (574),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (577), (582), (591), (606), (610), (611), (684),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (772), (4646), (4649), (4650), (4653), (5145),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (5146), (5148), (5151), (5153), (5178), (5179),
% 195.76/31.73  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.73  | | | | | | | | | | | | | | | |            #429.
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | |   (5180)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.73  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.73  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | BETA: splitting (5180) gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5181)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.73  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | ALPHA: (5181) implies:
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5182)  all_52_22 = e0
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5183)  all_52_20 = e1
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5184)  all_52_18 = e2
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5185)  all_52_16 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | REDUCE: (178), (5185) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5186)  op(all_52_17, all_52_17) = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | REDUCE: (177), (5184) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5187)  op(all_52_19, all_52_19) = e2
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | REDUCE: (175), (5182) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5188)  op(all_52_23, all_52_23) = e0
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | REDUCE: (612), (5183) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5189)  op(all_10_2, all_10_2) = e1
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | |   (5190)  all_56_13 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (38), (41), (51), (157),
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            (166), (179), (271), (273), (279), (283), (304),
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            (305), (343), (346), (351), (415), (417), (431),
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            (542), (543), (551), (565), (571), (572), (584),
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            (590), (592), (594), (597), (600), (611), (5070),
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            (5157), (5159), (5161), (5167), (5186), (5188),
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            (5189), (5190), (function-axioms) are inconsistent
% 195.76/31.73  | | | | | | | | | | | | | | | | | |            by sub-proof #765.
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | |   (5191)   ~ (all_56_13 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | |   (5192)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | REDUCE: (346), (5191) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | |   (5193)   ~ (all_52_15 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5194)  all_58_1 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (5194) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5195)  all_52_9 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | REDUCE: (576), (5195) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5196)   ~ (all_52_15 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | REDUCE: (577), (5195) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5197)   ~ (all_52_17 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | SIMP: (5197) implies:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5198)   ~ (all_52_17 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | REDUCE: (5148), (5195) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5199)   ~ (all_10_0 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | REDUCE: (574), (5195) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5200)   ~ (all_4_2 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | SIMP: (5200) implies:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5201)   ~ (all_4_2 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | REDUCE: (182), (5195) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5202)  op(e3, e3) = all_52_8
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (5202)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5203)  all_52_8 = all_6_2
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5204)  all_58_12 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (5204) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5205)  all_52_7 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | SIMP: (5205) implies:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5206)  all_52_7 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (5206) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5207)   ~ (all_52_5 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (5206) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5208)   ~ (all_52_23 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | SIMP: (5208) implies:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5209)   ~ (all_52_23 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (61),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (168), (274), (313), (315), (317), (327), (329),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (352), (375), (393), (405), (526), (542), (544),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (545), (546), (547), (596), (597), (602), (609),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (767), (4650), (4653), (5139), (5142), (5145),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (5146), (5178), (5186), (5187), (5194), (5198),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (5201), (5202), (5207), (5209), (function-axioms)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #788.
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5210)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (41), (43), (51), (158), (169),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (179), (273), (283), (304), (346), (351), (415),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (431), (521), (541), (542), (543), (555), (559),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (571), (572), (577), (594), (600), (613), (684),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (4646), (4649), (5157), (5186), (5188), (5192),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (5193), (5210), (function-axioms) are inconsistent
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            by sub-proof #478.
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | |   (5211)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (5211) gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5212)  all_58_3 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (5212) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5213)  all_4_2 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (5213) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5214)   ~ (all_52_9 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (5213) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5215)  op(e3, e3) = all_52_10
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (5213) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5216)  op(e3, e2) = all_4_1
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |              all_4_1, e2, e3, simplifying with (169), (5216)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5217)  all_52_9 = all_4_1
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |              all_52_10, e3, e3, simplifying with (41), (5215)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5218)  all_52_10 = all_6_2
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (5214), (5217) imply:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5219)   ~ (all_4_1 = e3)
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (43), (51), (61), (157), (158), (162), (164),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (175), (177), (178), (179), (182), (183), (184),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (276), (277), (278), (279), (281), (282), (283),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (284), (285), (304), (306), (307), (308), (309),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (317), (319), (320),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (321), (325), (326), (327), (328), (331), (332),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (521),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (526), (528), (538), (540), (541), (542), (543),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (571), (572), (573), (574), (576), (577), (578),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (598), (600), (602), (604), (605), (606), (607),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (688), (767), (772), (4646), (4649), (4650),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (4653), (5139), (5142), (5145), (5146), (5147),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (5148), (5150), (5151), (5153), (5156), (5157),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (5159), (5160), (5161), (5162), (5163), (5164),
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            (5167), (5178), (5219), (function-axioms) are
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #417.
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |   (5220)  all_58_7 = e3 | all_58_13 = e3
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (4650), (5146), (5193), (5220) are
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #717.
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | |   (5221)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.73  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (608), (609), (610), (688), (4649), (5156),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (5157), (5159), (5160), (5161), (5162), (5164),
% 195.76/31.73  | | | | | | | | | | | | | | | | |            (5221), (function-axioms) are inconsistent by
% 195.76/31.73  | | | | | | | | | | | | | | | | |            sub-proof #418.
% 195.76/31.73  | | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | End of split
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | Case 2:
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | |   (5222)   ~ (all_58_15 = e0)
% 195.76/31.73  | | | | | | | | | | | | | |   (5223)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.73  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.73  | | | | | | | | | | | | | |             e0)
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | ALPHA: (5223) implies:
% 195.76/31.73  | | | | | | | | | | | | | |   (5224)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.73  | | | | | | | | | | | | | |   (5225)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.73  | | | | | | | | | | | | | | REDUCE: (541), (5222) imply:
% 195.76/31.73  | | | | | | | | | | | | | |   (5226)   ~ (all_14_2 = e0)
% 195.76/31.73  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.74  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (164),
% 195.76/31.74  | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.76/31.74  | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 195.76/31.74  | | | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 195.76/31.74  | | | | | | | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 195.76/31.74  | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 195.76/31.74  | | | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (315),
% 195.76/31.74  | | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 195.76/31.74  | | | | | | | | | | | | | |            (327), (329), (332), (333), (343), (346), (351),
% 195.76/31.74  | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.76/31.74  | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 195.76/31.74  | | | | | | | | | | | | | |            (427), (431), (521), (526), (528), (538), (539),
% 195.76/31.74  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.74  | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 195.76/31.74  | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 195.76/31.74  | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 195.76/31.74  | | | | | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 195.76/31.74  | | | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.76/31.74  | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.76/31.74  | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.76/31.74  | | | | | | | | | | | | | |            (612), (613), (684), (688), (767), (772), (4646),
% 195.76/31.74  | | | | | | | | | | | | | |            (4649), (4650), (4653), (5139), (5142), (5145),
% 195.76/31.74  | | | | | | | | | | | | | |            (5146), (5147), (5148), (5150), (5151), (5152),
% 195.76/31.74  | | | | | | | | | | | | | |            (5153), (5156), (5224), (5225), (5226),
% 195.76/31.74  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.74  | | | | | | | | | | | | | |            #351.
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | |   (5227)  all_30_1 = e3
% 195.76/31.74  | | | | | | | | | | |   (5228)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | COMBINE_EQS: (670), (5227) imply:
% 195.76/31.74  | | | | | | | | | | |   (5229)  all_10_1 = e3
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.74  | | | | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (139),
% 195.76/31.74  | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 195.76/31.74  | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 195.76/31.74  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 195.76/31.74  | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 195.76/31.74  | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 195.76/31.74  | | | | | | | | | | |            (304), (305), (306), (307), (309), (311), (313),
% 195.76/31.74  | | | | | | | | | | |            (314), (315), (316), (317), (319), (321), (324),
% 195.76/31.74  | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (332),
% 195.76/31.74  | | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 195.76/31.74  | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 195.76/31.74  | | | | | | | | | | |            (405), (411), (415), (417), (427), (431), (459),
% 195.76/31.74  | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 195.76/31.74  | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.74  | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.76/31.74  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.76/31.74  | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.76/31.74  | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.76/31.74  | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 195.76/31.74  | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.76/31.74  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.76/31.74  | | | | | | | | | | |            (611), (612), (613), (684), (688), (750), (772),
% 195.76/31.74  | | | | | | | | | | |            (4646), (4648), (4649), (4650), (4651), (4653),
% 195.76/31.74  | | | | | | | | | | |            (4655), (5072), (5228), (5229), (function-axioms)
% 195.76/31.74  | | | | | | | | | | |            are inconsistent by sub-proof #367.
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | |   (5230)  all_24_0 = e1
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | COMBINE_EQS: (711), (5230) imply:
% 195.76/31.74  | | | | | | | | | |   (5231)  all_14_0 = e1
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | SIMP: (5231) implies:
% 195.76/31.74  | | | | | | | | | |   (5232)  all_14_0 = e1
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | COMBINE_EQS: (765), (5232) imply:
% 195.76/31.74  | | | | | | | | | |   (5233)  all_34_0 = e1
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | REDUCE: (4655), (5232) imply:
% 195.76/31.74  | | | | | | | | | |   (5234)   ~ (e3 = e1)
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | REDUCE: (4651), (5232) imply:
% 195.76/31.74  | | | | | | | | | |   (5235)   ~ (e2 = e1)
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | REDUCE: (62), (5232) imply:
% 195.76/31.74  | | | | | | | | | |   (5236)  op(e0, all_14_1) = e1
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | BETA: splitting (104) gives:
% 195.76/31.74  | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | Case 1:
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | |   (5237)   ~ (all_30_1 = e3)
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | REDUCE: (670), (5237) imply:
% 195.76/31.74  | | | | | | | | | | |   (5238)   ~ (all_10_1 = e3)
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | BETA: splitting (114) gives:
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | Case 1:
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | |   (5239)   ~ (all_34_0 = e1)
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | REDUCE: (5233), (5239) imply:
% 195.76/31.74  | | | | | | | | | | | |   (5240)  $false
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | CLOSE: (5240) is inconsistent.
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | |   (5241)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | BETA: splitting (129) gives:
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | Case 1:
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | |   (5242)   ~ (all_40_1 = e2)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.74  | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (139), (156), (158),
% 195.76/31.74  | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.76/31.74  | | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 195.76/31.74  | | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 195.76/31.74  | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 195.76/31.74  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 195.76/31.74  | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 195.76/31.74  | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 195.76/31.74  | | | | | | | | | | | | |            (325), (326), (327), (329), (331), (332), (333),
% 195.76/31.74  | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 195.76/31.74  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.76/31.74  | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (491),
% 195.76/31.74  | | | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 195.76/31.74  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.74  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.76/31.74  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.76/31.74  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.76/31.74  | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 195.76/31.74  | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 195.76/31.74  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 195.76/31.74  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 195.76/31.74  | | | | | | | | | | | | |            (611), (612), (613), (684), (685), (687), (688),
% 195.76/31.74  | | | | | | | | | | | | |            (772), (4646), (4648), (4649), (5236), (5241),
% 195.76/31.74  | | | | | | | | | | | | |            (5242), (function-axioms) are inconsistent by
% 195.76/31.74  | | | | | | | | | | | | |            sub-proof #361.
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | |   (5243)  all_40_1 = e2
% 195.76/31.74  | | | | | | | | | | | | |   (5244)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | COMBINE_EQS: (687), (5243) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5245)  all_10_1 = e2
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | SIMP: (5245) implies:
% 195.76/31.74  | | | | | | | | | | | | |   (5246)  all_10_1 = e2
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (5238), (5246) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5247)   ~ (e3 = e2)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (53), (5246) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5248)  op(all_10_2, e1) = e2
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (52), (5246) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5249)  op(e1, e2) = all_10_0
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 195.76/31.74  | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (5249)
% 195.76/31.74  | | | | | | | | | | | | |              gives:
% 195.76/31.74  | | | | | | | | | | | | |   (5250)  all_52_13 = all_10_0
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | COMBINE_EQS: (421), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5251)  all_56_9 = all_10_0
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | COMBINE_EQS: (366), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5252)  all_58_7 = all_10_0
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (568), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5253)   ~ (all_52_5 = all_10_0)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (575), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5254)   ~ (all_52_9 = all_10_0)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (589), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5255)   ~ (all_52_29 = all_10_0)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | SIMP: (5255) implies:
% 195.76/31.74  | | | | | | | | | | | | |   (5256)   ~ (all_52_29 = all_10_0)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (588), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5257)   ~ (all_10_0 = all_10_2)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (580), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5258)   ~ (all_10_0 = all_4_2)
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | REDUCE: (180), (5250) imply:
% 195.76/31.74  | | | | | | | | | | | | |   (5259)  op(all_10_0, all_10_0) = all_52_12
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | Case 1:
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | |   (5260)   ~ (all_44_0 = e2)
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | REDUCE: (4648), (5260) imply:
% 195.76/31.74  | | | | | | | | | | | | | |   (5261)  $false
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | CLOSE: (5261) is inconsistent.
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | |   (5262)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | Case 1:
% 195.76/31.74  | | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | |   (5263)  all_58_15 = e0
% 195.76/31.74  | | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (5236), (5263),
% 195.76/31.74  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.74  | | | | | | | | | | | | | | |            #877.
% 195.76/31.74  | | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | |   (5264)   ~ (all_58_15 = e0)
% 195.76/31.74  | | | | | | | | | | | | | | |   (5265)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.74  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.74  | | | | | | | | | | | | | | |             e0)
% 195.76/31.74  | | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.74  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (164),
% 195.76/31.74  | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.76/31.74  | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 195.76/31.74  | | | | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 195.76/31.74  | | | | | | | | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 195.76/31.74  | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 195.76/31.74  | | | | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (315),
% 195.76/31.74  | | | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 195.76/31.74  | | | | | | | | | | | | | | |            (327), (329), (332), (333), (343), (346), (351),
% 195.76/31.74  | | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.76/31.74  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 195.76/31.74  | | | | | | | | | | | | | | |            (427), (431), (521), (526), (528), (538), (539),
% 195.76/31.74  | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.74  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 195.76/31.74  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 195.76/31.74  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 195.76/31.74  | | | | | | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 195.76/31.74  | | | | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.76/31.74  | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.76/31.74  | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.76/31.74  | | | | | | | | | | | | | | |            (612), (613), (684), (688), (767), (772), (4646),
% 195.76/31.74  | | | | | | | | | | | | | | |            (4649), (4650), (4653), (5244), (5248), (5251),
% 195.76/31.74  | | | | | | | | | | | | | | |            (5252), (5253), (5254), (5256), (5257), (5258),
% 195.76/31.74  | | | | | | | | | | | | | | |            (5259), (5262), (5264), (5265), (function-axioms)
% 195.76/31.74  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #350.
% 195.76/31.74  | | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | End of split
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | Case 2:
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | |   (5266)  all_30_1 = e3
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | COMBINE_EQS: (670), (5266) imply:
% 195.76/31.74  | | | | | | | | | | |   (5267)  all_10_1 = e3
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | SIMP: (5267) implies:
% 195.76/31.74  | | | | | | | | | | |   (5268)  all_10_1 = e3
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | REDUCE: (53), (5268) imply:
% 195.76/31.74  | | | | | | | | | | |   (5269)  op(all_10_2, e1) = e3
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.74  | | | | | | | | | | | REDUCE: (52), (5268) imply:
% 195.76/31.74  | | | | | | | | | | |   (5270)  op(e1, e3) = all_10_0
% 195.76/31.74  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.75  | | | | | | | | | | |            (43), (51), (53), (61), (63), (114), (139), (156),
% 195.76/31.75  | | | | | | | | | | |            (158), (159), (162), (166), (167), (168), (169),
% 195.76/31.75  | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 195.76/31.75  | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 195.76/31.75  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 195.76/31.75  | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (284),
% 195.76/31.75  | | | | | | | | | | |            (285), (303), (304), (305), (306), (307), (308),
% 195.76/31.75  | | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 195.76/31.75  | | | | | | | | | | |            (321), (324), (325), (326), (327), (329), (330),
% 195.76/31.75  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 195.76/31.75  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.76/31.75  | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 195.76/31.75  | | | | | | | | | | |            (427), (431), (491), (521), (528), (538), (539),
% 195.76/31.75  | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.75  | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 195.76/31.75  | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 195.76/31.75  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 195.76/31.75  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 195.76/31.75  | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 195.76/31.75  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 195.76/31.75  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 195.76/31.75  | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 195.76/31.75  | | | | | | | | | | |            (685), (688), (772), (4646), (4648), (4649),
% 195.76/31.75  | | | | | | | | | | |            (4650), (4653), (5233), (5236), (5269), (5270),
% 195.76/31.75  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.75  | | | | | | | | | | |            #355.
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | 
% 195.76/31.75  | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | 
% 195.76/31.75  | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | 
% 195.76/31.75  | | | | | | | |   (5271)  all_18_0 = e3
% 195.76/31.75  | | | | | | | | 
% 195.76/31.75  | | | | | | | | COMBINE_EQS: (761), (5271) imply:
% 195.76/31.75  | | | | | | | |   (5272)  all_14_0 = e3
% 195.76/31.75  | | | | | | | | 
% 195.76/31.75  | | | | | | | | REDUCE: (62), (5272) imply:
% 195.76/31.75  | | | | | | | |   (5273)  op(e0, all_14_1) = e3
% 195.76/31.75  | | | | | | | | 
% 195.76/31.75  | | | | | | | | BETA: splitting (104) gives:
% 195.76/31.75  | | | | | | | | 
% 195.76/31.75  | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | 
% 195.76/31.75  | | | | | | | | |   (5274)   ~ (all_30_1 = e3)
% 195.76/31.75  | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | REDUCE: (670), (5274) imply:
% 195.76/31.75  | | | | | | | | |   (5275)   ~ (all_10_1 = e3)
% 195.76/31.75  | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | BETA: splitting (129) gives:
% 195.76/31.75  | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | |   (5276)   ~ (all_40_1 = e2)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (687), (5276) imply:
% 195.76/31.75  | | | | | | | | | |   (5277)   ~ (all_10_1 = e2)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | |   (5278)   ~ (all_44_0 = e2)
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | REDUCE: (4648), (5278) imply:
% 195.76/31.75  | | | | | | | | | | |   (5279)  $false
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | CLOSE: (5279) is inconsistent.
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | |   (5280)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | |   (5281)  all_58_15 = e0
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (5273), (5281),
% 195.76/31.75  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.75  | | | | | | | | | | | |            #678.
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | |   (5282)   ~ (all_58_15 = e0)
% 195.76/31.75  | | | | | | | | | | | |   (5283)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.75  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.75  | | | | | | | | | | | |             e0)
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | ALPHA: (5283) implies:
% 195.76/31.75  | | | | | | | | | | | |   (5284)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.75  | | | | | | | | | | | |   (5285)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | REDUCE: (541), (5282) imply:
% 195.76/31.75  | | | | | | | | | | | |   (5286)   ~ (all_14_2 = e0)
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | |   (5287)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.75  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.75  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 195.76/31.75  | | | | | | | | | | | | |            (61), (62), (63), (156), (158), (162), (166),
% 195.76/31.75  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 195.76/31.75  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.76/31.75  | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (275), (276),
% 195.76/31.75  | | | | | | | | | | | | |            (277), (278), (281), (282), (284), (285), (304),
% 195.76/31.75  | | | | | | | | | | | | |            (305), (306), (309), (311), (313), (317), (319),
% 195.76/31.75  | | | | | | | | | | | | |            (321), (325), (326), (332), (333), (343), (346),
% 195.76/31.75  | | | | | | | | | | | | |            (351), (361), (366), (367), (372), (375), (387),
% 195.76/31.75  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (421), (427),
% 195.76/31.75  | | | | | | | | | | | | |            (431), (521), (528), (538), (540), (541), (542),
% 195.76/31.75  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.75  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.76/31.75  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.76/31.75  | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 195.76/31.75  | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 195.76/31.75  | | | | | | | | | | | | |            (590), (591), (592), (594), (595), (596), (597),
% 195.76/31.75  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 195.76/31.75  | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (684), (688),
% 195.76/31.75  | | | | | | | | | | | | |            (772), (4646), (4649), (4651), (5280), (5285),
% 195.76/31.75  | | | | | | | | | | | | |            (5287), (function-axioms) are inconsistent by
% 195.76/31.75  | | | | | | | | | | | | |            sub-proof #349.
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | |   (5288)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.75  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.75  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | BETA: splitting (5288) gives:
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | |   (5289)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.75  | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | ALPHA: (5289) implies:
% 195.76/31.75  | | | | | | | | | | | | | |   (5290)  all_52_22 = e0
% 195.76/31.75  | | | | | | | | | | | | | |   (5291)  all_52_20 = e1
% 195.76/31.75  | | | | | | | | | | | | | |   (5292)  all_52_18 = e2
% 195.76/31.75  | | | | | | | | | | | | | |   (5293)  all_52_16 = e3
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | REDUCE: (178), (5293) imply:
% 195.76/31.75  | | | | | | | | | | | | | |   (5294)  op(all_52_17, all_52_17) = e3
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | REDUCE: (177), (5292) imply:
% 195.76/31.75  | | | | | | | | | | | | | |   (5295)  op(all_52_19, all_52_19) = e2
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | REDUCE: (175), (5290) imply:
% 195.76/31.75  | | | | | | | | | | | | | |   (5296)  op(all_52_23, all_52_23) = e0
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | REDUCE: (612), (5291) imply:
% 195.76/31.75  | | | | | | | | | | | | | |   (5297)  op(all_10_2, all_10_2) = e1
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | |   (5298)  all_56_15 = e3
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5298) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5299)  all_14_2 = e3
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | SIMP: (5299) implies:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5300)  all_14_2 = e3
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (573), (5300) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5301)   ~ (all_52_7 = e3)
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (591), (5300) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5302)   ~ (all_52_15 = e3)
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (603), (5300) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5303)   ~ (all_52_23 = e3)
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (613), (5300) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5304)  op(e3, e3) = all_52_30
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (63), (5300) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5305)  op(e3, e0) = all_14_1
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 195.76/31.75  | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (5305)
% 195.76/31.75  | | | | | | | | | | | | | | |              gives:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5306)  all_52_25 = all_14_1
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.75  | | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (5304)
% 195.76/31.75  | | | | | | | | | | | | | | |              gives:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5307)  all_52_30 = all_6_2
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | COMBINE_EQS: (545), (5306) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5308)  all_58_9 = all_14_1
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (561), (5306) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5309)   ~ (all_14_1 = all_6_2)
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5310)  all_58_9 = e2
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | COMBINE_EQS: (5308), (5310) imply:
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5311)  all_14_1 = e2
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | SIMP: (5311) implies:
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5312)  all_14_1 = e2
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | REDUCE: (5273), (5312) imply:
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5313)  op(e0, e2) = e3
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_15,
% 195.76/31.75  | | | | | | | | | | | | | | | |              e3, e2, e0, simplifying with (157), (5313) gives:
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5314)  all_52_15 = e3
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | REDUCE: (5302), (5314) imply:
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5315)  $false
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | CLOSE: (5315) is inconsistent.
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5316)   ~ (all_58_9 = e2)
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | REDUCE: (5308), (5316) imply:
% 195.76/31.75  | | | | | | | | | | | | | | | |   (5317)   ~ (all_14_1 = e2)
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (41), (43), (53), (166),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (168), (279), (281), (317), (319), (325), (326),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (331), (332), (351), (366), (375), (387), (393),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (405), (411), (417), (542), (543), (546), (547),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (548), (549), (551), (559), (564), (565), (569),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (588), (4649), (5277), (5294), (5295), (5297),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (5301), (5302), (5303), (5305), (5308), (5309),
% 195.76/31.75  | | | | | | | | | | | | | | | |            (5317), (function-axioms) are inconsistent by
% 195.76/31.75  | | | | | | | | | | | | | | | |            sub-proof #363.
% 195.76/31.75  | | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | |   (5318)   ~ (all_56_15 = e3)
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REDUCE: (538), (5318) imply:
% 195.76/31.75  | | | | | | | | | | | | | | |   (5319)   ~ (all_14_2 = e3)
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (43), (51),
% 195.76/31.75  | | | | | | | | | | | | | | |            (53), (61), (158), (166), (167), (168), (169),
% 195.76/31.75  | | | | | | | | | | | | | | |            (172), (173), (174), (179), (180), (182), (183),
% 195.76/31.75  | | | | | | | | | | | | | | |            (185), (272), (273), (275), (278), (279), (281),
% 195.76/31.75  | | | | | | | | | | | | | | |            (282), (283), (304), (306), (309), (313), (315),
% 195.76/31.75  | | | | | | | | | | | | | | |            (317), (319), (321), (325), (326), (327), (329),
% 195.76/31.75  | | | | | | | | | | | | | | |            (332), (333), (346), (351), (361), (366), (372),
% 195.76/31.75  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 195.76/31.75  | | | | | | | | | | | | | | |            (417), (427), (431), (521), (541), (542), (543),
% 195.76/31.75  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.76/31.75  | | | | | | | | | | | | | | |            (553), (555), (559), (561), (562), (563), (565),
% 195.76/31.75  | | | | | | | | | | | | | | |            (567), (569), (571), (572), (573), (575), (576),
% 195.76/31.75  | | | | | | | | | | | | | | |            (577), (582), (588), (590), (591), (592), (593),
% 195.76/31.75  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (600), (602), (604),
% 195.76/31.75  | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (611), (613),
% 195.76/31.75  | | | | | | | | | | | | | | |            (684), (4646), (4649), (5277), (5284), (5294),
% 195.76/31.75  | | | | | | | | | | | | | | |            (5295), (5296), (5297), (5319), (function-axioms)
% 195.76/31.75  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #436.
% 195.76/31.75  | | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | |   (5320)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.75  | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.76/31.75  | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 195.76/31.75  | | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 195.76/31.75  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 195.76/31.75  | | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 195.76/31.75  | | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 195.76/31.75  | | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 195.76/31.75  | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 195.76/31.75  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 195.76/31.75  | | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 195.76/31.75  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.75  | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 195.76/31.75  | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 195.76/31.75  | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 195.76/31.75  | | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 195.76/31.75  | | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 195.76/31.75  | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.76/31.75  | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (5280), (5284),
% 195.76/31.75  | | | | | | | | | | | | | |            (5285), (5286), (5320), (function-axioms) are
% 195.76/31.75  | | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 195.76/31.75  | | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | End of split
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | |   (5321)  all_40_1 = e2
% 195.76/31.75  | | | | | | | | | |   (5322)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | COMBINE_EQS: (687), (5321) imply:
% 195.76/31.75  | | | | | | | | | |   (5323)  all_10_1 = e2
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | SIMP: (5323) implies:
% 195.76/31.75  | | | | | | | | | |   (5324)  all_10_1 = e2
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (5275), (5324) imply:
% 195.76/31.75  | | | | | | | | | |   (5325)   ~ (e3 = e2)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (53), (5324) imply:
% 195.76/31.75  | | | | | | | | | |   (5326)  op(all_10_2, e1) = e2
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (52), (5324) imply:
% 195.76/31.75  | | | | | | | | | |   (5327)  op(e1, e2) = all_10_0
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 195.76/31.75  | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (5327)
% 195.76/31.75  | | | | | | | | | |              gives:
% 195.76/31.75  | | | | | | | | | |   (5328)  all_52_13 = all_10_0
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | COMBINE_EQS: (421), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5329)  all_56_9 = all_10_0
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | COMBINE_EQS: (366), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5330)  all_58_7 = all_10_0
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (568), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5331)   ~ (all_52_5 = all_10_0)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (575), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5332)   ~ (all_52_9 = all_10_0)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (589), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5333)   ~ (all_52_29 = all_10_0)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | SIMP: (5333) implies:
% 195.76/31.75  | | | | | | | | | |   (5334)   ~ (all_52_29 = all_10_0)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (588), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5335)   ~ (all_10_0 = all_10_2)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (580), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5336)   ~ (all_10_0 = all_4_2)
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | REDUCE: (180), (5328) imply:
% 195.76/31.75  | | | | | | | | | |   (5337)  op(all_10_0, all_10_0) = all_52_12
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.75  | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | |   (5338)   ~ (all_44_0 = e2)
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | REDUCE: (4648), (5338) imply:
% 195.76/31.75  | | | | | | | | | | |   (5339)  $false
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | CLOSE: (5339) is inconsistent.
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | |   (5340)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.75  | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | Case 1:
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | |   (5341)  all_58_15 = e0
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (5273), (5341),
% 195.76/31.75  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.75  | | | | | | | | | | | |            #678.
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.75  | | | | | | | | | | | Case 2:
% 195.76/31.75  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | |   (5342)   ~ (all_58_15 = e0)
% 195.76/31.76  | | | | | | | | | | | |   (5343)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.76  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.76  | | | | | | | | | | | |             e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.76  | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (164),
% 195.76/31.76  | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.76/31.76  | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 195.76/31.76  | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 195.76/31.76  | | | | | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 195.76/31.76  | | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 195.76/31.76  | | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (315),
% 195.76/31.76  | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 195.76/31.76  | | | | | | | | | | | |            (327), (329), (332), (333), (343), (346), (351),
% 195.76/31.76  | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 195.76/31.76  | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 195.76/31.76  | | | | | | | | | | | |            (427), (431), (521), (526), (528), (538), (539),
% 195.76/31.76  | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.76  | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 195.76/31.76  | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 195.76/31.76  | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 195.76/31.76  | | | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 195.76/31.76  | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.76/31.76  | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.76/31.76  | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.76/31.76  | | | | | | | | | | | |            (612), (613), (684), (688), (767), (772), (4646),
% 195.76/31.76  | | | | | | | | | | | |            (4649), (4650), (4653), (5322), (5326), (5329),
% 195.76/31.76  | | | | | | | | | | | |            (5330), (5331), (5332), (5334), (5335), (5336),
% 195.76/31.76  | | | | | | | | | | | |            (5337), (5340), (5342), (5343), (function-axioms)
% 195.76/31.76  | | | | | | | | | | | |            are inconsistent by sub-proof #350.
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | End of split
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | End of split
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | End of split
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | |   (5344)  all_30_1 = e3
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | COMBINE_EQS: (670), (5344) imply:
% 195.76/31.76  | | | | | | | | |   (5345)  all_10_1 = e3
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | SIMP: (5345) implies:
% 195.76/31.76  | | | | | | | | |   (5346)  all_10_1 = e3
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | REDUCE: (53), (5346) imply:
% 195.76/31.76  | | | | | | | | |   (5347)  op(all_10_2, e1) = e3
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | REDUCE: (52), (5346) imply:
% 195.76/31.76  | | | | | | | | |   (5348)  op(e1, e3) = all_10_0
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 195.76/31.76  | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (5348)
% 195.76/31.76  | | | | | | | | |              gives:
% 195.76/31.76  | | | | | | | | |   (5349)  all_52_5 = all_10_0
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | COMBINE_EQS: (367), (5349) imply:
% 195.76/31.76  | | | | | | | | |   (5350)  all_56_8 = all_10_0
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | COMBINE_EQS: (547), (5349) imply:
% 195.76/31.76  | | | | | | | | |   (5351)  all_58_6 = all_10_0
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | REDUCE: (567), (5349) imply:
% 195.76/31.76  | | | | | | | | |   (5352)   ~ (all_52_7 = all_10_0)
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | SIMP: (5352) implies:
% 195.76/31.76  | | | | | | | | |   (5353)   ~ (all_52_7 = all_10_0)
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | REDUCE: (553), (5349) imply:
% 195.76/31.76  | | | | | | | | |   (5354)   ~ (all_10_0 = all_6_2)
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | REDUCE: (184), (5349) imply:
% 195.76/31.76  | | | | | | | | |   (5355)  op(all_10_0, all_10_0) = all_52_4
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | |   (5356)   ~ (all_44_0 = e2)
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | REDUCE: (4648), (5356) imply:
% 195.76/31.76  | | | | | | | | | |   (5357)  $false
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | CLOSE: (5357) is inconsistent.
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | |   (5358)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | |   (5359)  all_58_15 = e0
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (5273), (5359),
% 195.76/31.76  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.76  | | | | | | | | | | |            #678.
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | |   (5360)   ~ (all_58_15 = e0)
% 195.76/31.76  | | | | | | | | | | |   (5361)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.76  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.76  | | | | | | | | | | |             e0)
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.76  | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 195.76/31.76  | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 195.76/31.76  | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.76/31.76  | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 195.76/31.76  | | | | | | | | | | |            (275), (277), (278), (279), (280), (281), (282),
% 195.76/31.76  | | | | | | | | | | |            (283), (284), (285), (304), (306), (307), (309),
% 195.76/31.76  | | | | | | | | | | |            (311), (313), (315), (316), (317), (319), (321),
% 195.76/31.76  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 195.76/31.76  | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (361),
% 195.76/31.76  | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 195.76/31.76  | | | | | | | | | | |            (394), (405), (411), (415), (417), (427), (431),
% 195.76/31.76  | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 195.76/31.76  | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.76  | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.76/31.76  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.76/31.76  | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 195.76/31.76  | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (588),
% 195.76/31.76  | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.76/31.76  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.76/31.76  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.76/31.76  | | | | | | | | | | |            (612), (613), (684), (688), (772), (4646), (4649),
% 195.76/31.76  | | | | | | | | | | |            (4650), (4653), (5347), (5348), (5350), (5351),
% 195.76/31.76  | | | | | | | | | | |            (5353), (5354), (5355), (5358), (5360), (5361),
% 195.76/31.76  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.76  | | | | | | | | | | |            #348.
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | End of split
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | End of split
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | End of split
% 195.76/31.76  | | | | | | | | 
% 195.76/31.76  | | | | | | | End of split
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | Case 2:
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | |   (5362)  all_16_0 = e2
% 195.76/31.76  | | | | | | |   (5363)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | | COMBINE_EQS: (760), (5362) imply:
% 195.76/31.76  | | | | | | |   (5364)  all_10_0 = e2
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | | SIMP: (5364) implies:
% 195.76/31.76  | | | | | | |   (5365)  all_10_0 = e2
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | | COMBINE_EQS: (756), (5365) imply:
% 195.76/31.76  | | | | | | |   (5366)  all_26_0 = e2
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | | REDUCE: (4650), (5365) imply:
% 195.76/31.76  | | | | | | |   (5367)   ~ (e3 = e2)
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | | BETA: splitting (74) gives:
% 195.76/31.76  | | | | | | | 
% 195.76/31.76  | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | 
% 195.76/31.76  | | | | | | | |   (5368)   ~ (all_18_0 = e3)
% 195.76/31.76  | | | | | | | | 
% 195.76/31.76  | | | | | | | | REDUCE: (761), (5368) imply:
% 195.76/31.76  | | | | | | | |   (5369)   ~ (all_14_0 = e3)
% 195.76/31.76  | | | | | | | | 
% 195.76/31.76  | | | | | | | | BETA: splitting (94) gives:
% 195.76/31.76  | | | | | | | | 
% 195.76/31.76  | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | |   (5370)   ~ (all_26_0 = e2)
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | REDUCE: (5366), (5370) imply:
% 195.76/31.76  | | | | | | | | |   (5371)  $false
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | CLOSE: (5371) is inconsistent.
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | |   (5372)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | BETA: splitting (89) gives:
% 195.76/31.76  | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | |   (5373)   ~ (all_24_0 = e1)
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | REDUCE: (711), (5373) imply:
% 195.76/31.76  | | | | | | | | | |   (5374)   ~ (all_14_0 = e1)
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.76  | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | |   (5375)   ~ (all_44_0 = e2)
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | REDUCE: (4648), (5375) imply:
% 195.76/31.76  | | | | | | | | | | |   (5376)  $false
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | CLOSE: (5376) is inconsistent.
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | |   (5377)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.76  | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | |   (5378)  all_58_15 = e0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | COMBINE_EQS: (541), (5378) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5379)  all_14_2 = e0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (573), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5380)   ~ (all_52_7 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (591), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5381)   ~ (all_52_15 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (603), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5382)   ~ (all_52_23 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (606), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5383)   ~ (all_52_25 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (609), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5384)   ~ (all_52_29 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (613), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5385)  op(e0, e0) = all_52_30
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (63), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5386)  op(e0, e0) = all_14_1
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (61), (5379) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5387)  op(e0, e0) = e0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 195.76/31.76  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5385), (5386)
% 195.76/31.76  | | | | | | | | | | | |              gives:
% 195.76/31.76  | | | | | | | | | | | |   (5388)  all_52_30 = all_14_1
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 195.76/31.76  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5385), (5387)
% 195.76/31.76  | | | | | | | | | | | |              gives:
% 195.76/31.76  | | | | | | | | | | | |   (5389)  all_52_30 = e0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | COMBINE_EQS: (5388), (5389) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5390)  all_14_1 = e0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (62), (5390) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5391)  op(e0, e0) = all_14_0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 195.76/31.76  | | | | | | | | | | | |              e0, e0, simplifying with (5387), (5391) gives:
% 195.76/31.76  | | | | | | | | | | | |   (5392)  all_14_0 = e0
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (5369), (5392) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5393)   ~ (e3 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (4651), (5392) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5394)   ~ (e2 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | REDUCE: (5374), (5392) imply:
% 195.76/31.76  | | | | | | | | | | | |   (5395)   ~ (e1 = e0)
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.76  | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | |   (5396)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.76  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.76  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.76  | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | BETA: splitting (5396) gives:
% 195.76/31.76  | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | |   (5397)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.76  | | | | | | | | | | | | | |           all_52_6 = e0
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 195.76/31.76  | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 195.76/31.76  | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 195.76/31.76  | | | | | | | | | | | | | |            (4649), (5397), (function-axioms) are inconsistent
% 195.76/31.76  | | | | | | | | | | | | | |            by sub-proof #501.
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | |   (5398)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.76/31.76  | | | | | | | | | | | | | |           all_52_14 = e0
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | ALPHA: (5398) implies:
% 195.76/31.76  | | | | | | | | | | | | | |   (5399)  all_52_14 = e0
% 195.76/31.76  | | | | | | | | | | | | | |   (5400)  all_52_12 = e1
% 195.76/31.76  | | | | | | | | | | | | | |   (5401)  all_52_10 = e2
% 195.76/31.76  | | | | | | | | | | | | | |   (5402)  all_52_8 = e3
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | REDUCE: (182), (5402) imply:
% 195.76/31.76  | | | | | | | | | | | | | |   (5403)  op(all_52_9, all_52_9) = e3
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | REDUCE: (180), (5400) imply:
% 195.76/31.76  | | | | | | | | | | | | | |   (5404)  op(all_52_13, all_52_13) = e1
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | REDUCE: (179), (5399) imply:
% 195.76/31.76  | | | | | | | | | | | | | |   (5405)  op(all_52_15, all_52_15) = e0
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | REDUCE: (611), (5401) imply:
% 195.76/31.76  | | | | | | | | | | | | | |   (5406)  op(all_4_2, all_4_2) = e2
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.76/31.76  | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | |   (5407)  all_56_13 = e3
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | COMBINE_EQS: (346), (5407) imply:
% 195.76/31.76  | | | | | | | | | | | | | | |   (5408)  all_52_15 = e3
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (158), (169), (183), (271),
% 195.76/31.76  | | | | | | | | | | | | | | |            (273), (343), (431), (521), (555), (571), (572),
% 195.76/31.76  | | | | | | | | | | | | | | |            (582), (590), (684), (4646), (4649), (5382),
% 195.76/31.76  | | | | | | | | | | | | | | |            (5403), (5405), (5408), (function-axioms) are
% 195.76/31.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #499.
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | Case 2:
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | |   (5409)   ~ (all_56_13 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | |   (5410)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | REDUCE: (346), (5409) imply:
% 195.76/31.76  | | | | | | | | | | | | | | |   (5411)   ~ (all_52_15 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 195.76/31.76  | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5412)  all_58_12 = e3
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (5412) imply:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5413)  all_52_7 = e3
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | SIMP: (5413) implies:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5414)  all_52_7 = e3
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | REDUCE: (567), (5414) imply:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5415)   ~ (all_52_5 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | REDUCE: (571), (5414) imply:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5416)   ~ (all_52_15 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | REDUCE: (572), (5414) imply:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5417)   ~ (all_52_23 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | SIMP: (5417) implies:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5418)   ~ (all_52_23 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | REDUCE: (555), (5414) imply:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5419)   ~ (all_6_2 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | SIMP: (5419) implies:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5420)   ~ (all_6_2 = e3)
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | REDUCE: (183), (5414) imply:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5421)  op(e3, e3) = all_52_6
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.76  | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (5421)
% 195.76/31.76  | | | | | | | | | | | | | | | |              gives:
% 195.76/31.76  | | | | | | | | | | | | | | | |   (5422)  all_52_6 = all_6_2
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 195.76/31.76  | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.76  | | | | | | | | | | | | | | | | | 
% 195.76/31.76  | | | | | | | | | | | | | | | | |   (5423)  all_56_7 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (5423) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5424)  all_52_27 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | SIMP: (5424) implies:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5425)  all_52_27 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | REDUCE: (604), (5425) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5426)   ~ (all_52_25 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | REDUCE: (607), (5425) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5427)   ~ (all_52_29 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | SIMP: (5427) implies:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5428)   ~ (all_52_29 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | REDUCE: (173), (5425) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5429)  op(e3, e3) = all_52_26
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (41), (43), (178), (282), (284), (313),
% 195.76/31.77  | | | | | | | | | | | | | | | | |            (325), (327), (333), (366), (388), (393), (394),
% 195.76/31.77  | | | | | | | | | | | | | | | | |            (405), (544), (545), (546), (547), (549), (557),
% 195.76/31.77  | | | | | | | | | | | | | | | | |            (561), (575), (578), (593), (595), (4649), (5383),
% 195.76/31.77  | | | | | | | | | | | | | | | | |            (5387), (5403), (5404), (5415), (5420), (5426),
% 195.76/31.77  | | | | | | | | | | | | | | | | |            (5428), (5429), (function-axioms) are inconsistent
% 195.76/31.77  | | | | | | | | | | | | | | | | |            by sub-proof #490.
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5430)   ~ (all_56_7 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | REDUCE: (427), (5430) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | |   (5431)   ~ (all_52_27 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5432)  all_58_9 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (5432) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5433)  all_52_25 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | SIMP: (5433) implies:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5434)  all_52_25 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | REDUCE: (578), (5434) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5435)   ~ (all_52_9 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | REDUCE: (595), (5434) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5436)   ~ (all_52_17 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | REDUCE: (605), (5434) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5437)   ~ (all_52_29 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | SIMP: (5437) implies:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5438)   ~ (all_52_29 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | REDUCE: (174), (5434) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5439)  op(e3, e3) = all_52_24
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.77  | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (5439)
% 195.76/31.77  | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5440)  all_52_24 = all_6_2
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |   (5441)  all_58_1 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (5441) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |   (5442)  all_52_9 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | REDUCE: (5435), (5442) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |   (5443)  $false
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | CLOSE: (5443) is inconsistent.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |   (5444)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | |   (5445)  all_58_4 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (393), (5436), (5445) are inconsistent by
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | |            sub-proof #1302.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | |   (5446)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | |   (5447)  all_58_6 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (5415), (5447) are inconsistent by
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | |   (5448)   ~ (all_58_6 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | |   (5449)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | |   (5450)  all_56_8 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (5415), (5450) are inconsistent by
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | |   (5451)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5452)  all_56_5 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (5452) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5453)  all_4_2 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5453) implies:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5454)  all_4_2 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (5454) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5455)   ~ (all_52_13 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5406), (5454) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5456)  op(e3, e3) = e2
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5449) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | |   (5457)  all_58_7 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (5457) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | |   (5458)  all_52_13 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5455), (5458) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | |   (5459)  $false
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5459) is inconsistent.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | |   (5460)  all_58_8 = e3 | all_58_11 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5460) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (5461)  all_58_8 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (5461) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (5462)  all_10_2 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (512), (5462) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (5463)  all_26_2 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (5462) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (5464)  op(e3, e3) = all_52_20
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (5462) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (5465)  op(e3, e1) = all_10_1
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5372) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5466)   ~ (all_26_2 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5463), (5466) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5467)  $false
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5467) is inconsistent.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (5465)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5468)  all_52_17 = all_10_1
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (41), (5464)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5469)  all_52_20 = all_6_2
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (5456), (5464)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5470)  all_52_20 = e2
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5469), (5470) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5471)  all_6_2 = e2
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5468), (5471) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5472)   ~ (all_10_1 = e2)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5436), (5468) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5473)   ~ (all_10_1 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (166), (167),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (178), (183),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (271), (273), (274), (277), (281), (282), (284),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (285), (304), (305), (306), (309), (313), (317),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (319), (325), (326), (327), (329), (330), (333),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (431),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (521), (528), (540), (542), (543), (544), (545),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (557), (559), (561), (563), (567), (570), (571),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (572), (575), (576), (577), (578), (582), (589),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (590), (593), (595), (600), (604), (605), (607),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (610), (688), (772), (4646), (4649), (5377),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5378), (5380), (5381), (5383), (5384), (5387),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5403), (5404), (5405), (5406), (5410), (5411),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5472), (5473), (function-axioms) are inconsistent
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #488.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (5474)  all_58_11 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (5438), (5474) are inconsistent by
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1323.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5475)   ~ (all_56_5 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (5475) imply:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |   (5476)   ~ (all_4_2 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (41), (43), (162), (169), (177),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |            (184), (326), (366), (367), (375), (405), (528),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |            (542), (543), (546), (547), (548), (553), (584),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |            (588), (688), (4649), (5377), (5403), (5404),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |            (5411), (5412), (5418), (5444), (5446), (5451),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |            (5476), (function-axioms) are inconsistent by
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #346.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | |   (5477)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | BETA: splitting (5477) gives:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |   (5478)  all_58_10 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (5431), (5478) are inconsistent by
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |   (5479)  all_58_11 = e3 | all_58_15 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (38), (41), (169), (178), (284), (317),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |            (325), (333), (366), (393), (394), (405), (543),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |            (544), (545), (548), (549), (557), (577), (589),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |            (605), (772), (5378), (5387), (5403), (5406),
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |            (5411), (5420), (5479), (function-axioms) are
% 195.76/31.77  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1295.
% 195.76/31.77  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | |   (5480)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (51), (53), (156), (273), (305), (346),
% 195.76/31.77  | | | | | | | | | | | | | | | |            (351), (431), (515), (542), (543), (571), (572),
% 195.76/31.77  | | | | | | | | | | | | | | | |            (582), (680), (5363), (5378), (5380), (5381),
% 195.76/31.77  | | | | | | | | | | | | | | | |            (5387), (5405), (5406), (5410), (5411), (5480),
% 195.76/31.77  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.77  | | | | | | | | | | | | | | | |            #648.
% 195.76/31.77  | | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | End of split
% 195.76/31.77  | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | |   (5481)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.77  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.77  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.77  | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | BETA: splitting (5481) gives:
% 195.76/31.77  | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | |   (5482)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.77  | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | ALPHA: (5482) implies:
% 195.76/31.77  | | | | | | | | | | | | | |   (5483)  all_52_22 = e0
% 195.76/31.77  | | | | | | | | | | | | | |   (5484)  all_52_20 = e1
% 195.76/31.77  | | | | | | | | | | | | | |   (5485)  all_52_18 = e2
% 195.76/31.77  | | | | | | | | | | | | | |   (5486)  all_52_16 = e3
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | REDUCE: (178), (5486) imply:
% 195.76/31.77  | | | | | | | | | | | | | |   (5487)  op(all_52_17, all_52_17) = e3
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | REDUCE: (177), (5485) imply:
% 195.76/31.77  | | | | | | | | | | | | | |   (5488)  op(all_52_19, all_52_19) = e2
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | REDUCE: (175), (5483) imply:
% 195.76/31.77  | | | | | | | | | | | | | |   (5489)  op(all_52_23, all_52_23) = e0
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | REDUCE: (612), (5484) imply:
% 195.76/31.77  | | | | | | | | | | | | | |   (5490)  op(all_10_2, all_10_2) = e1
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 195.76/31.77  | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | Case 1:
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | |   (5491)  all_56_13 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | COMBINE_EQS: (346), (5491) imply:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5492)  all_52_15 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | SIMP: (5492) implies:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5493)  all_52_15 = e3
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | REDUCE: (576), (5493) imply:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5494)   ~ (all_52_9 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | REDUCE: (587), (5493) imply:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5495)   ~ (all_52_13 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | REDUCE: (582), (5493) imply:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5496)   ~ (all_4_2 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | SIMP: (5496) implies:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5497)   ~ (all_4_2 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (53),
% 195.76/31.77  | | | | | | | | | | | | | | |            (166), (167), (168), (173), (174), (185), (281),
% 195.76/31.77  | | | | | | | | | | | | | | |            (309), (313), (317), (319), (321), (326), (327),
% 195.76/31.77  | | | | | | | | | | | | | | |            (331), (332), (333), (351), (366), (372), (375),
% 195.76/31.77  | | | | | | | | | | | | | | |            (387), (393), (405), (411), (512), (544), (545),
% 195.76/31.77  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (559),
% 195.76/31.77  | | | | | | | | | | | | | | |            (562), (563), (564), (565), (567), (578), (588),
% 195.76/31.77  | | | | | | | | | | | | | | |            (592), (596), (604), (605), (676), (4649), (5372),
% 195.76/31.77  | | | | | | | | | | | | | | |            (5487), (5488), (5490), (5494), (5495), (5497),
% 195.76/31.77  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.77  | | | | | | | | | | | | | | |            #343.
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | Case 2:
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | |   (5498)   ~ (all_56_13 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | |   (5499)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.77  | | | | | | | | | | | | | | | REDUCE: (346), (5498) imply:
% 195.76/31.77  | | | | | | | | | | | | | | |   (5500)   ~ (all_52_15 = e3)
% 195.76/31.77  | | | | | | | | | | | | | | | 
% 195.76/31.78  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (41), (43), (51), (53), (158),
% 195.76/31.78  | | | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.76/31.78  | | | | | | | | | | | | | | |            (174), (179), (182), (183), (185), (273), (274),
% 195.76/31.78  | | | | | | | | | | | | | | |            (277), (278), (281), (282), (283), (285), (304),
% 195.76/31.78  | | | | | | | | | | | | | | |            (306), (309), (317), (319), (325), (326), (329),
% 195.76/31.78  | | | | | | | | | | | | | | |            (330), (333), (346), (351), (352), (366), (367),
% 195.76/31.78  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 195.76/31.78  | | | | | | | | | | | | | | |            (415), (427), (431), (521), (528), (540), (541),
% 195.76/31.78  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 195.76/31.78  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 195.76/31.78  | | | | | | | | | | | | | | |            (562), (563), (567), (570), (571), (572), (577),
% 195.76/31.78  | | | | | | | | | | | | | | |            (584), (589), (593), (594), (595), (598), (600),
% 195.76/31.78  | | | | | | | | | | | | | | |            (602), (604), (605), (613), (684), (688), (4646),
% 195.76/31.78  | | | | | | | | | | | | | | |            (4649), (5377), (5378), (5380), (5383), (5384),
% 195.76/31.78  | | | | | | | | | | | | | | |            (5387), (5487), (5488), (5489), (5490), (5499),
% 195.76/31.78  | | | | | | | | | | | | | | |            (5500), (function-axioms) are inconsistent by
% 195.76/31.78  | | | | | | | | | | | | | | |            sub-proof #342.
% 195.76/31.78  | | | | | | | | | | | | | | | 
% 195.76/31.78  | | | | | | | | | | | | | | End of split
% 195.76/31.78  | | | | | | | | | | | | | | 
% 195.76/31.78  | | | | | | | | | | | | | Case 2:
% 195.76/31.78  | | | | | | | | | | | | | | 
% 195.76/31.78  | | | | | | | | | | | | | |   (5501)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.78  | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.78  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 195.76/31.80  | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 195.76/31.80  | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 195.76/31.80  | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 195.76/31.80  | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 195.76/31.80  | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 195.76/31.80  | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 195.76/31.80  | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 195.76/31.80  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.80  | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 195.76/31.80  | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 195.76/31.80  | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 195.76/31.80  | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 195.76/31.80  | | | | | | | | | | | | | |            (608), (609), (610), (688), (4649), (5377),
% 195.76/31.80  | | | | | | | | | | | | | |            (5378), (5380), (5381), (5382), (5383), (5384),
% 195.76/31.80  | | | | | | | | | | | | | |            (5501), (function-axioms) are inconsistent by
% 195.76/31.80  | | | | | | | | | | | | | |            sub-proof #418.
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | End of split
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | End of split
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | |   (5502)   ~ (all_58_15 = e0)
% 195.76/31.80  | | | | | | | | | | | |   (5503)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.80  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.80  | | | | | | | | | | | |             e0)
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | ALPHA: (5503) implies:
% 195.76/31.80  | | | | | | | | | | | |   (5504)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.80  | | | | | | | | | | | |   (5505)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | REDUCE: (541), (5502) imply:
% 195.76/31.80  | | | | | | | | | | | |   (5506)   ~ (all_14_2 = e0)
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.80  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 195.76/31.80  | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.76/31.80  | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 195.76/31.80  | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 195.76/31.80  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 195.76/31.80  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 195.76/31.80  | | | | | | | | | | | |            (305), (306), (307), (309), (311), (313), (315),
% 195.76/31.80  | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 195.76/31.80  | | | | | | | | | | | |            (327), (328), (329), (331), (332), (333), (343),
% 195.76/31.80  | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.76/31.80  | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.76/31.80  | | | | | | | | | | | |            (415), (417), (421), (427), (431), (512), (521),
% 195.76/31.80  | | | | | | | | | | | |            (528), (538), (539), (540), (541), (542), (543),
% 195.76/31.80  | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.76/31.80  | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 195.76/31.80  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 195.76/31.80  | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 195.76/31.80  | | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 195.76/31.80  | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.76/31.80  | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.76/31.80  | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.76/31.80  | | | | | | | | | | | |            (612), (613), (676), (684), (688), (772), (4646),
% 195.76/31.80  | | | | | | | | | | | |            (4649), (4651), (5372), (5377), (5504), (5505),
% 195.76/31.80  | | | | | | | | | | | |            (5506), (function-axioms) are inconsistent by
% 195.76/31.80  | | | | | | | | | | | |            sub-proof #336.
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | End of split
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | End of split
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | |   (5507)  all_24_0 = e1
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | COMBINE_EQS: (711), (5507) imply:
% 195.76/31.80  | | | | | | | | | |   (5508)  all_14_0 = e1
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | COMBINE_EQS: (765), (5508) imply:
% 195.76/31.80  | | | | | | | | | |   (5509)  all_34_0 = e1
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | REDUCE: (5369), (5508) imply:
% 195.76/31.80  | | | | | | | | | |   (5510)   ~ (e3 = e1)
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | REDUCE: (4651), (5508) imply:
% 195.76/31.80  | | | | | | | | | |   (5511)   ~ (e2 = e1)
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | REDUCE: (62), (5508) imply:
% 195.76/31.80  | | | | | | | | | |   (5512)  op(e0, all_14_1) = e1
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | BETA: splitting (114) gives:
% 195.76/31.80  | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | Case 1:
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | |   (5513)   ~ (all_34_0 = e1)
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | REDUCE: (5509), (5513) imply:
% 195.76/31.80  | | | | | | | | | | |   (5514)  $false
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | CLOSE: (5514) is inconsistent.
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | |   (5515)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.80  | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | Case 1:
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | |   (5516)   ~ (all_44_0 = e2)
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | REDUCE: (4648), (5516) imply:
% 195.76/31.80  | | | | | | | | | | | |   (5517)  $false
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | CLOSE: (5517) is inconsistent.
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | |   (5518)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.80  | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | Case 1:
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | |   (5519)  all_58_15 = e0
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (5512), (5519),
% 195.76/31.80  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.80  | | | | | | | | | | | | |            #877.
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | |   (5520)   ~ (all_58_15 = e0)
% 195.76/31.80  | | | | | | | | | | | | |   (5521)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.80  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.80  | | | | | | | | | | | | |             e0)
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | ALPHA: (5521) implies:
% 195.76/31.80  | | | | | | | | | | | | |   (5522)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.80  | | | | | | | | | | | | |   (5523)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | REDUCE: (541), (5520) imply:
% 195.76/31.80  | | | | | | | | | | | | |   (5524)   ~ (all_14_2 = e0)
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.80  | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | Case 1:
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | |   (5525)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.80  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.80  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | BETA: splitting (5525) gives:
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | Case 1:
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | |   (5526)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.80  | | | | | | | | | | | | | | |           all_52_6 = e0
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 195.76/31.80  | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 195.76/31.80  | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 195.76/31.80  | | | | | | | | | | | | | | |            (4649), (5526), (function-axioms) are inconsistent
% 195.76/31.80  | | | | | | | | | | | | | | |            by sub-proof #501.
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | |   (5527)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 195.76/31.80  | | | | | | | | | | | | | | |           all_52_14 = e0
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.80  | | | | | | | | | | | | | | |            (43), (51), (61), (63), (156), (158), (162),
% 195.76/31.80  | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 195.76/31.80  | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 195.76/31.80  | | | | | | | | | | | | | | |            (184), (185), (270), (272), (273), (275), (276),
% 195.76/31.80  | | | | | | | | | | | | | | |            (277), (278), (281), (282), (284), (285), (305),
% 195.76/31.80  | | | | | | | | | | | | | | |            (306), (309), (311), (313), (317), (319), (321),
% 195.76/31.80  | | | | | | | | | | | | | | |            (325), (326), (329), (332), (333), (346), (351),
% 195.76/31.80  | | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 195.76/31.80  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (421), (427), (431),
% 195.76/31.80  | | | | | | | | | | | | | | |            (491), (521), (528), (538), (540), (541), (542),
% 195.76/31.80  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.80  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 195.76/31.80  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 195.76/31.80  | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 195.76/31.80  | | | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 195.76/31.80  | | | | | | | | | | | | | | |            (590), (591), (592), (594), (595), (596), (597),
% 195.76/31.80  | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 195.76/31.80  | | | | | | | | | | | | | | |            (609), (611), (612), (613), (684), (688), (772),
% 195.76/31.80  | | | | | | | | | | | | | | |            (4646), (4649), (5512), (5515), (5518), (5523),
% 195.76/31.80  | | | | | | | | | | | | | | |            (5527), (function-axioms) are inconsistent by
% 195.76/31.80  | | | | | | | | | | | | | | |            sub-proof #358.
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | End of split
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | Case 2:
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | |   (5528)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.80  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.80  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | BETA: splitting (5528) gives:
% 195.76/31.80  | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | Case 1:
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | |   (5529)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.80  | | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.80  | | | | | | | | | | | | | | | 
% 195.76/31.80  | | | | | | | | | | | | | | | ALPHA: (5529) implies:
% 195.76/31.80  | | | | | | | | | | | | | | |   (5530)  all_52_22 = e0
% 195.76/31.81  | | | | | | | | | | | | | | |   (5531)  all_52_20 = e1
% 195.76/31.81  | | | | | | | | | | | | | | |   (5532)  all_52_18 = e2
% 195.76/31.81  | | | | | | | | | | | | | | |   (5533)  all_52_16 = e3
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | REDUCE: (178), (5533) imply:
% 195.76/31.81  | | | | | | | | | | | | | | |   (5534)  op(all_52_17, all_52_17) = e3
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | REDUCE: (177), (5532) imply:
% 195.76/31.81  | | | | | | | | | | | | | | |   (5535)  op(all_52_19, all_52_19) = e2
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | REDUCE: (175), (5530) imply:
% 195.76/31.81  | | | | | | | | | | | | | | |   (5536)  op(all_52_23, all_52_23) = e0
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | REDUCE: (612), (5531) imply:
% 195.76/31.81  | | | | | | | | | | | | | | |   (5537)  op(all_10_2, all_10_2) = e1
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5538)  all_56_15 = e3
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5538) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5539)  all_14_2 = e3
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | SIMP: (5539) implies:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5540)  all_14_2 = e3
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (491), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5541)  all_34_2 = e3
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (573), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5542)   ~ (all_52_7 = e3)
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (603), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5543)   ~ (all_52_23 = e3)
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (606), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5544)   ~ (all_52_25 = e3)
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (609), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5545)   ~ (all_52_29 = e3)
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (613), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5546)  op(e3, e3) = all_52_30
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (63), (5540) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5547)  op(e3, e0) = all_14_1
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (41), (43), (166), (167),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (168), (182), (185), (281), (284), (313), (317),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (319), (325), (326), (330), (331), (332), (333),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (351), (366), (375), (387), (393), (394), (405),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (411), (542), (543), (544), (545), (546), (547),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (548), (549), (551), (557), (559), (561), (565),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (569), (574), (575), (576), (577), (685), (4649),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (5515), (5534), (5535), (5537), (5541), (5542),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (5543), (5544), (5545), (5546), (5547),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.81  | | | | | | | | | | | | | | | |            #335.
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5548)   ~ (all_56_15 = e3)
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REDUCE: (538), (5548) imply:
% 195.76/31.81  | | | | | | | | | | | | | | | |   (5549)   ~ (all_14_2 = e3)
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (51), (53), (61), (158), (162), (166), (167),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (179), (180),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (182), (183), (185), (272), (273), (275), (277),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (278), (279), (281), (283), (284), (304), (306),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (309), (313), (315), (317), (319), (321), (325),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (346), (351), (361), (366), (367), (372), (375),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (387), (393), (394), (405), (411), (415), (417),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (427), (431), (512), (521), (528), (541), (542),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (551), (553), (555), (559), (561), (562), (563),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (564), (565), (567), (571), (572), (573), (574),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (586), (587),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (588), (592), (594), (595), (596), (597), (600),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (602), (604), (605), (608), (609), (613), (676),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (5372), (5518),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (5522), (5534), (5535), (5536), (5537), (5549),
% 195.76/31.81  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.81  | | | | | | | | | | | | | | | |            #338.
% 195.76/31.81  | | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | |   (5550)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.81  | | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.76/31.81  | | | | | | | | | | | | | | |            (61), (63), (156), (158), (162), (166), (167),
% 195.76/31.81  | | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (177), (178),
% 195.76/31.81  | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (270),
% 195.76/31.81  | | | | | | | | | | | | | | |            (271), (274), (276), (277), (278), (279), (280),
% 195.76/31.81  | | | | | | | | | | | | | | |            (282), (283), (285), (305), (306), (307), (308),
% 195.76/31.81  | | | | | | | | | | | | | | |            (309), (311), (313), (316), (317), (319), (321),
% 195.76/31.81  | | | | | | | | | | | | | | |            (324), (325), (326), (327), (332), (333), (343),
% 195.76/31.81  | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 195.76/31.81  | | | | | | | | | | | | | | |            (388), (393), (405), (415), (417), (421), (427),
% 195.76/31.81  | | | | | | | | | | | | | | |            (491), (528), (538), (539), (540), (541), (542),
% 195.76/31.81  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 195.76/31.81  | | | | | | | | | | | | | | |            (551), (553), (555), (559), (561), (562), (563),
% 195.76/31.81  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (572),
% 195.76/31.81  | | | | | | | | | | | | | | |            (573), (574), (575), (578), (580), (582), (584),
% 195.76/31.81  | | | | | | | | | | | | | | |            (586), (587), (589), (590), (592), (593), (594),
% 195.76/31.81  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (602), (603), (604),
% 195.76/31.81  | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.76/31.81  | | | | | | | | | | | | | | |            (685), (688), (4649), (5512), (5515), (5518),
% 195.76/31.81  | | | | | | | | | | | | | | |            (5522), (5523), (5524), (5550), (function-axioms)
% 195.76/31.81  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #360.
% 195.76/31.81  | | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | |   (5551)  all_18_0 = e3
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | COMBINE_EQS: (761), (5551) imply:
% 195.76/31.81  | | | | | | | |   (5552)  all_14_0 = e3
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | SIMP: (5552) implies:
% 195.76/31.81  | | | | | | | |   (5553)  all_14_0 = e3
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | REDUCE: (62), (5553) imply:
% 195.76/31.81  | | | | | | | |   (5554)  op(e0, all_14_1) = e3
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | BETA: splitting (94) gives:
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | |   (5555)   ~ (all_26_0 = e2)
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | REDUCE: (5366), (5555) imply:
% 195.76/31.81  | | | | | | | | |   (5556)  $false
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | CLOSE: (5556) is inconsistent.
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | |   (5557)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | |   (5558)   ~ (all_44_0 = e2)
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | REDUCE: (4648), (5558) imply:
% 195.76/31.81  | | | | | | | | | |   (5559)  $false
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | CLOSE: (5559) is inconsistent.
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | |   (5560)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | |   (5561)  all_58_15 = e0
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (5554), (5561),
% 195.76/31.81  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.81  | | | | | | | | | | |            #678.
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | |   (5562)   ~ (all_58_15 = e0)
% 195.76/31.81  | | | | | | | | | | |   (5563)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.81  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.81  | | | | | | | | | | |             e0)
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | ALPHA: (5563) implies:
% 195.76/31.81  | | | | | | | | | | |   (5564)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.81  | | | | | | | | | | |   (5565)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | REDUCE: (541), (5562) imply:
% 195.76/31.81  | | | | | | | | | | |   (5566)   ~ (all_14_2 = e0)
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.81  | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 195.76/31.81  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 195.76/31.81  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 195.76/31.81  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 195.76/31.81  | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 195.76/31.81  | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 195.76/31.81  | | | | | | | | | | |            (305), (306), (307), (309), (311), (313), (315),
% 195.76/31.81  | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 195.76/31.81  | | | | | | | | | | |            (327), (328), (329), (331), (332), (333), (343),
% 195.76/31.81  | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 195.76/31.81  | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 195.76/31.81  | | | | | | | | | | |            (415), (417), (421), (427), (431), (512), (521),
% 195.76/31.81  | | | | | | | | | | |            (528), (538), (539), (540), (541), (542), (543),
% 195.76/31.81  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.76/31.81  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 195.76/31.81  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 195.76/31.81  | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 195.76/31.81  | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 195.76/31.81  | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 195.76/31.81  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 195.76/31.81  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 195.76/31.81  | | | | | | | | | | |            (612), (613), (676), (684), (688), (772), (4646),
% 195.76/31.81  | | | | | | | | | | |            (4649), (4651), (5557), (5560), (5564), (5565),
% 195.76/31.81  | | | | | | | | | | |            (5566), (function-axioms) are inconsistent by
% 195.76/31.81  | | | | | | | | | | |            sub-proof #336.
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | End of split
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | End of split
% 195.76/31.81  | | | | | | | 
% 195.76/31.81  | | | | | | End of split
% 195.76/31.81  | | | | | | 
% 195.76/31.81  | | | | | Case 2:
% 195.76/31.81  | | | | | | 
% 195.76/31.81  | | | | | |   (5567)  all_14_0 = e2
% 195.76/31.81  | | | | | | 
% 195.76/31.81  | | | | | | COMBINE_EQS: (771), (5567) imply:
% 195.76/31.81  | | | | | |   (5568)  all_50_0 = e2
% 195.76/31.81  | | | | | | 
% 195.76/31.81  | | | | | | REDUCE: (62), (5567) imply:
% 195.76/31.81  | | | | | |   (5569)  op(e0, all_14_1) = e2
% 195.76/31.81  | | | | | | 
% 195.76/31.81  | | | | | | BETA: splitting (69) gives:
% 195.76/31.81  | | | | | | 
% 195.76/31.81  | | | | | | Case 1:
% 195.76/31.81  | | | | | | | 
% 195.76/31.81  | | | | | | |   (5570)   ~ (all_16_0 = e2)
% 195.76/31.81  | | | | | | | 
% 195.76/31.81  | | | | | | | REDUCE: (760), (5570) imply:
% 195.76/31.81  | | | | | | |   (5571)   ~ (all_10_0 = e2)
% 195.76/31.81  | | | | | | | 
% 195.76/31.81  | | | | | | | BETA: splitting (104) gives:
% 195.76/31.81  | | | | | | | 
% 195.76/31.81  | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | |   (5572)   ~ (all_30_1 = e3)
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | REDUCE: (670), (5572) imply:
% 195.76/31.81  | | | | | | | |   (5573)   ~ (all_10_1 = e3)
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | BETA: splitting (129) gives:
% 195.76/31.81  | | | | | | | | 
% 195.76/31.81  | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | |   (5574)   ~ (all_40_1 = e2)
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | REDUCE: (687), (5574) imply:
% 195.76/31.81  | | | | | | | | |   (5575)   ~ (all_10_1 = e2)
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | BETA: splitting (139) gives:
% 195.76/31.81  | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | |   (5576)   ~ (all_44_0 = e2)
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | REDUCE: (4648), (5576) imply:
% 195.76/31.81  | | | | | | | | | |   (5577)  $false
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | CLOSE: (5577) is inconsistent.
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | |   (5578)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | BETA: splitting (153) gives:
% 195.76/31.81  | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | |   (5579)   ~ (all_50_0 = e2)
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | REDUCE: (5568), (5579) imply:
% 195.76/31.81  | | | | | | | | | | |   (5580)  $false
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | CLOSE: (5580) is inconsistent.
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | |   (5581)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | BETA: splitting (303) gives:
% 195.76/31.81  | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | |   (5582)  all_58_15 = e0
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (5569), (5582),
% 195.76/31.81  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.81  | | | | | | | | | | | |            #612.
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | Case 2:
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | |   (5583)   ~ (all_58_15 = e0)
% 195.76/31.81  | | | | | | | | | | | |   (5584)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 195.76/31.81  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 195.76/31.81  | | | | | | | | | | | |             e0)
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | ALPHA: (5584) implies:
% 195.76/31.81  | | | | | | | | | | | |   (5585)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 195.76/31.81  | | | | | | | | | | | |   (5586)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | REDUCE: (541), (5583) imply:
% 195.76/31.81  | | | | | | | | | | | |   (5587)   ~ (all_14_2 = e0)
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | BETA: splitting (187) gives:
% 195.76/31.81  | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | Case 1:
% 195.76/31.81  | | | | | | | | | | | | | 
% 195.76/31.81  | | | | | | | | | | | | |   (5588)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 195.76/31.81  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 195.76/31.81  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 195.76/31.81  | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 195.76/31.82  | | | | | | | | | | | | |            (43), (51), (61), (63), (158), (162), (166),
% 195.76/31.82  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 195.76/31.82  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 195.76/31.82  | | | | | | | | | | | | |            (185), (270), (272), (273), (275), (277), (278),
% 195.76/31.82  | | | | | | | | | | | | |            (281), (282), (284), (285), (306), (309), (313),
% 195.76/31.82  | | | | | | | | | | | | |            (317), (319), (321), (325), (326), (329), (332),
% 195.76/31.82  | | | | | | | | | | | | |            (333), (335), (346), (351), (361), (366), (367),
% 195.76/31.82  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 195.76/31.82  | | | | | | | | | | | | |            (411), (427), (431), (521), (528), (538), (540),
% 195.76/31.82  | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 195.76/31.82  | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 195.76/31.82  | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 195.76/31.82  | | | | | | | | | | | | |            (568), (569), (571), (572), (573), (574), (577),
% 195.76/31.82  | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (588), (589),
% 195.76/31.82  | | | | | | | | | | | | |            (590), (591), (592), (594), (595), (596), (597),
% 195.76/31.82  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 195.76/31.82  | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (684), (688),
% 195.76/31.82  | | | | | | | | | | | | |            (690), (772), (4646), (4649), (5578), (5581),
% 195.76/31.82  | | | | | | | | | | | | |            (5586), (5588), (function-axioms) are inconsistent
% 195.76/31.82  | | | | | | | | | | | | |            by sub-proof #333.
% 195.76/31.82  | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | |   (5589)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 195.76/31.82  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 195.76/31.82  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 195.76/31.82  | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | BETA: splitting (5589) gives:
% 195.76/31.82  | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | |   (5590)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 195.76/31.82  | | | | | | | | | | | | | |           all_52_22 = e0
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | ALPHA: (5590) implies:
% 195.76/31.82  | | | | | | | | | | | | | |   (5591)  all_52_22 = e0
% 195.76/31.82  | | | | | | | | | | | | | |   (5592)  all_52_20 = e1
% 195.76/31.82  | | | | | | | | | | | | | |   (5593)  all_52_18 = e2
% 195.76/31.82  | | | | | | | | | | | | | |   (5594)  all_52_16 = e3
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | REDUCE: (178), (5594) imply:
% 195.76/31.82  | | | | | | | | | | | | | |   (5595)  op(all_52_17, all_52_17) = e3
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | REDUCE: (177), (5593) imply:
% 195.76/31.82  | | | | | | | | | | | | | |   (5596)  op(all_52_19, all_52_19) = e2
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | REDUCE: (175), (5591) imply:
% 195.76/31.82  | | | | | | | | | | | | | |   (5597)  op(all_52_23, all_52_23) = e0
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | REDUCE: (612), (5592) imply:
% 195.76/31.82  | | | | | | | | | | | | | |   (5598)  op(all_10_2, all_10_2) = e1
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | |   (5599)  all_56_15 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5599) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5600)  all_14_2 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (603), (5600) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5601)   ~ (all_52_23 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (606), (5600) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5602)   ~ (all_52_25 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (609), (5600) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5603)   ~ (all_52_29 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (613), (5600) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5604)  op(e3, e3) = all_52_30
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (63), (5600) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5605)  op(e3, e0) = all_14_1
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 195.76/31.82  | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (5605)
% 195.76/31.82  | | | | | | | | | | | | | | |              gives:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5606)  all_52_25 = all_14_1
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 195.76/31.82  | | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (5604)
% 195.76/31.82  | | | | | | | | | | | | | | |              gives:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5607)  all_52_30 = all_6_2
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | COMBINE_EQS: (388), (5606) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5608)  all_56_3 = all_14_1
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (595), (5606) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5609)   ~ (all_52_17 = all_14_1)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (561), (5606) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5610)   ~ (all_14_1 = all_6_2)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (5602), (5606) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5611)   ~ (all_14_1 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (174), (5606) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5612)  op(all_14_1, all_14_1) = all_52_24
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | |   (5613)  all_56_3 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | REF_CLOSE: (5608), (5611), (5613) are inconsistent by
% 195.76/31.82  | | | | | | | | | | | | | | | |            sub-proof #1200.
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | |   (5614)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | |   (5615)  all_56_14 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (343), (5601), (5615) are inconsistent by
% 195.76/31.82  | | | | | | | | | | | | | | | | |            sub-proof #1286.
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | |   (5616)   ~ (all_56_14 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | |   (5617)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5618)  all_56_9 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (5618) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5619)  all_52_13 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | SIMP: (5619) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5620)  all_52_13 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | REDUCE: (588), (5620) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5621)   ~ (all_10_2 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | SIMP: (5621) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5622)   ~ (all_10_2 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (41), (43), (166), (168), (182), (281),
% 195.76/31.82  | | | | | | | | | | | | | | | | | |            (317), (319), (325), (326), (333), (375), (387),
% 195.76/31.82  | | | | | | | | | | | | | | | | | |            (393), (405), (411), (542), (545), (546), (549),
% 195.76/31.82  | | | | | | | | | | | | | | | | | |            (551), (559), (565), (577), (4649), (5595),
% 195.76/31.82  | | | | | | | | | | | | | | | | | |            (5596), (5601), (5602), (5605), (5610), (5622),
% 195.76/31.82  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.82  | | | | | | | | | | | | | | | | | |            #416.
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5623)   ~ (all_56_9 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | REDUCE: (421), (5623) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | |   (5624)   ~ (all_52_13 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |   (5625)  all_58_6 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (5625) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |   (5626)  all_52_5 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | SIMP: (5626) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |   (5627)  all_52_5 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5627) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |   (5628)   ~ (all_10_2 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | SIMP: (5628) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |   (5629)   ~ (all_10_2 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (41), (43), (166), (168), (182), (281),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |            (317), (319), (325), (326), (333), (375), (387),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |            (393), (405), (411), (542), (545), (546), (549),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |            (551), (559), (565), (577), (4649), (5595),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |            (5596), (5601), (5602), (5605), (5610), (5629),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |            #416.
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | |   (5630)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (5630) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | |   (5631)  all_58_7 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (5631) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | |   (5632)  all_52_13 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (5624), (5632) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | |   (5633)  $false
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | CLOSE: (5633) is inconsistent.
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | |   (5634)  all_58_8 = e3 | all_58_11 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5634) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5635)  all_58_8 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (5635) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5636)  all_10_2 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (5636) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5637)   ~ (all_52_17 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (5636) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5638)   ~ (all_52_19 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (5598), (5636) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5639)  op(e3, e3) = e1
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (5636) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5640)  op(e3, e1) = all_10_1
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (5640)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |              gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5641)  all_52_17 = all_10_1
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (41), (5639) gives:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5642)  all_6_2 = e1
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (5641) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5643)  all_56_2 = all_10_1
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (5641) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5644)   ~ (all_52_19 = all_10_1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | SIMP: (5644) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5645)   ~ (all_52_19 = all_10_1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (5641) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5646)   ~ (all_52_23 = all_10_1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | SIMP: (5646) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5647)   ~ (all_52_23 = all_10_1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (5609), (5641) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5648)   ~ (all_14_1 = all_10_1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | SIMP: (5648) implies:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5649)   ~ (all_14_1 = all_10_1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5641), (5642) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5650)   ~ (all_10_1 = e1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (5642) imply:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5651)   ~ (all_14_1 = e1)
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (157), (279), (283), (343), (417), (582),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |            (590), (597), (5569), (5573), (5575), (5596),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |            (5608), (5612), (5614), (5617), (5638), (5643),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |            (5645), (5647), (5649), (5650), (5651),
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |            #332.
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |   (5652)  all_58_11 = e3
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (5603), (5652) are inconsistent by
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1323.
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | |   (5653)   ~ (all_56_15 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REDUCE: (538), (5653) imply:
% 195.76/31.82  | | | | | | | | | | | | | | |   (5654)   ~ (all_14_2 = e3)
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (43), (51),
% 195.76/31.82  | | | | | | | | | | | | | | |            (53), (61), (158), (166), (167), (168), (169),
% 195.76/31.82  | | | | | | | | | | | | | | |            (172), (173), (174), (179), (180), (182), (183),
% 195.76/31.82  | | | | | | | | | | | | | | |            (185), (272), (273), (275), (278), (279), (281),
% 195.76/31.82  | | | | | | | | | | | | | | |            (282), (283), (304), (306), (309), (313), (315),
% 195.76/31.82  | | | | | | | | | | | | | | |            (317), (319), (321), (325), (326), (327), (329),
% 195.76/31.82  | | | | | | | | | | | | | | |            (332), (333), (346), (351), (361), (366), (372),
% 195.76/31.82  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 195.76/31.82  | | | | | | | | | | | | | | |            (417), (427), (431), (521), (541), (542), (543),
% 195.76/31.82  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 195.76/31.82  | | | | | | | | | | | | | | |            (553), (555), (559), (561), (562), (563), (565),
% 195.76/31.82  | | | | | | | | | | | | | | |            (567), (569), (571), (572), (573), (575), (576),
% 195.76/31.82  | | | | | | | | | | | | | | |            (577), (582), (588), (590), (591), (592), (593),
% 195.76/31.82  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (600), (602), (604),
% 195.76/31.82  | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (611), (613),
% 195.76/31.82  | | | | | | | | | | | | | | |            (684), (4646), (4649), (5575), (5585), (5595),
% 195.76/31.82  | | | | | | | | | | | | | | |            (5596), (5597), (5598), (5654), (function-axioms)
% 195.76/31.82  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #436.
% 195.76/31.82  | | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | |   (5655)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 195.76/31.82  | | | | | | | | | | | | | |           all_52_30 = e0
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 195.76/31.82  | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 195.76/31.82  | | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 195.76/31.82  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 195.76/31.82  | | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 195.76/31.82  | | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 195.76/31.82  | | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 195.76/31.82  | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 195.76/31.82  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 195.76/31.82  | | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 195.76/31.82  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 195.76/31.82  | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 195.76/31.82  | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 195.76/31.82  | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 195.76/31.82  | | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 195.76/31.82  | | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 195.76/31.82  | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 195.76/31.82  | | | | | | | | | | | | | |            (684), (688), (4646), (4649), (5578), (5585),
% 195.76/31.82  | | | | | | | | | | | | | |            (5586), (5587), (5655), (function-axioms) are
% 195.76/31.82  | | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 195.76/31.82  | | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | End of split
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.82  | | | | | | | | Case 2:
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.82  | | | | | | | | |   (5656)  all_40_1 = e2
% 195.76/31.82  | | | | | | | | |   (5657)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | COMBINE_EQS: (687), (5656) imply:
% 195.76/31.82  | | | | | | | | |   (5658)  all_10_1 = e2
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | REDUCE: (5573), (5658) imply:
% 195.76/31.82  | | | | | | | | |   (5659)   ~ (e3 = e2)
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | REDUCE: (53), (5658) imply:
% 195.76/31.82  | | | | | | | | |   (5660)  op(all_10_2, e1) = e2
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.82  | | | | | | | | | REDUCE: (52), (5658) imply:
% 195.76/31.82  | | | | | | | | |   (5661)  op(e1, e2) = all_10_0
% 195.76/31.82  | | | | | | | | | 
% 195.76/31.83  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 195.76/31.83  | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (5661)
% 195.76/31.83  | | | | | | | | |              gives:
% 195.76/31.83  | | | | | | | | |   (5662)  all_52_13 = all_10_0
% 195.76/31.83  | | | | | | | | | 
% 195.76/31.83  | | | | | | | | | COMBINE_EQS: (421), (5662) imply:
% 195.76/31.83  | | | | | | | | |   (5663)  all_56_9 = all_10_0
% 195.76/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | COMBINE_EQS: (366), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5664)  all_58_7 = all_10_0
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (568), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5665)   ~ (all_52_5 = all_10_0)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (575), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5666)   ~ (all_52_9 = all_10_0)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (589), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5667)   ~ (all_52_29 = all_10_0)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | SIMP: (5667) implies:
% 196.10/31.83  | | | | | | | | |   (5668)   ~ (all_52_29 = all_10_0)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (588), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5669)   ~ (all_10_0 = all_10_2)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (580), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5670)   ~ (all_10_0 = all_4_2)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (180), (5662) imply:
% 196.10/31.83  | | | | | | | | |   (5671)  op(all_10_0, all_10_0) = all_52_12
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | BETA: splitting (139) gives:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | |   (5672)   ~ (all_44_0 = e2)
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | REDUCE: (4648), (5672) imply:
% 196.10/31.83  | | | | | | | | | |   (5673)  $false
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | CLOSE: (5673) is inconsistent.
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | |   (5674)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | |   (5675)  all_58_15 = e0
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (5569), (5675),
% 196.10/31.83  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.83  | | | | | | | | | | |            #612.
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | |   (5676)   ~ (all_58_15 = e0)
% 196.10/31.83  | | | | | | | | | | |   (5677)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.83  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.83  | | | | | | | | | | |             e0)
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.83  | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (164),
% 196.10/31.83  | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.10/31.83  | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.10/31.83  | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.10/31.83  | | | | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 196.10/31.83  | | | | | | | | | | |            (281), (282), (283), (284), (285), (304), (306),
% 196.10/31.83  | | | | | | | | | | |            (307), (309), (310), (311), (312), (313), (315),
% 196.10/31.83  | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 196.10/31.83  | | | | | | | | | | |            (327), (329), (332), (333), (343), (346), (351),
% 196.10/31.83  | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.10/31.83  | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.10/31.83  | | | | | | | | | | |            (427), (431), (521), (526), (528), (538), (539),
% 196.10/31.83  | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.10/31.83  | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.10/31.83  | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.10/31.83  | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 196.10/31.83  | | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 196.10/31.83  | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 196.10/31.83  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 196.10/31.83  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 196.10/31.83  | | | | | | | | | | |            (612), (613), (684), (688), (767), (772), (4646),
% 196.10/31.83  | | | | | | | | | | |            (4649), (4650), (5571), (5657), (5660), (5663),
% 196.10/31.83  | | | | | | | | | | |            (5664), (5665), (5666), (5668), (5669), (5670),
% 196.10/31.83  | | | | | | | | | | |            (5671), (5674), (5676), (5677), (function-axioms)
% 196.10/31.83  | | | | | | | | | | |            are inconsistent by sub-proof #350.
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | End of split
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | End of split
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | End of split
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | |   (5678)  all_30_1 = e3
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | COMBINE_EQS: (670), (5678) imply:
% 196.10/31.83  | | | | | | | |   (5679)  all_10_1 = e3
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | SIMP: (5679) implies:
% 196.10/31.83  | | | | | | | |   (5680)  all_10_1 = e3
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | REDUCE: (53), (5680) imply:
% 196.10/31.83  | | | | | | | |   (5681)  op(all_10_2, e1) = e3
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | REDUCE: (52), (5680) imply:
% 196.10/31.83  | | | | | | | |   (5682)  op(e1, e3) = all_10_0
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.10/31.83  | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (5682)
% 196.10/31.83  | | | | | | | |              gives:
% 196.10/31.83  | | | | | | | |   (5683)  all_52_5 = all_10_0
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | COMBINE_EQS: (367), (5683) imply:
% 196.10/31.83  | | | | | | | |   (5684)  all_56_8 = all_10_0
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | COMBINE_EQS: (547), (5683) imply:
% 196.10/31.83  | | | | | | | |   (5685)  all_58_6 = all_10_0
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | REDUCE: (567), (5683) imply:
% 196.10/31.83  | | | | | | | |   (5686)   ~ (all_52_7 = all_10_0)
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | SIMP: (5686) implies:
% 196.10/31.83  | | | | | | | |   (5687)   ~ (all_52_7 = all_10_0)
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | REDUCE: (553), (5683) imply:
% 196.10/31.83  | | | | | | | |   (5688)   ~ (all_10_0 = all_6_2)
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | REDUCE: (184), (5683) imply:
% 196.10/31.83  | | | | | | | |   (5689)  op(all_10_0, all_10_0) = all_52_4
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | BETA: splitting (139) gives:
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | |   (5690)   ~ (all_44_0 = e2)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (4648), (5690) imply:
% 196.10/31.83  | | | | | | | | |   (5691)  $false
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | CLOSE: (5691) is inconsistent.
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | |   (5692)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | |   (5693)  all_58_15 = e0
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (5569), (5693),
% 196.10/31.83  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.83  | | | | | | | | | |            #612.
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | |   (5694)   ~ (all_58_15 = e0)
% 196.10/31.83  | | | | | | | | | |   (5695)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.83  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.83  | | | | | | | | | |             e0)
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.83  | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.10/31.83  | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.83  | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.10/31.83  | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.10/31.83  | | | | | | | | | |            (275), (277), (278), (279), (280), (281), (282),
% 196.10/31.83  | | | | | | | | | |            (283), (284), (285), (304), (306), (307), (309),
% 196.10/31.83  | | | | | | | | | |            (311), (313), (315), (316), (317), (319), (321),
% 196.10/31.83  | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 196.10/31.83  | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (361),
% 196.10/31.83  | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 196.10/31.83  | | | | | | | | | |            (394), (405), (411), (415), (417), (427), (431),
% 196.10/31.83  | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 196.10/31.83  | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 196.10/31.83  | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 196.10/31.83  | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 196.10/31.83  | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 196.10/31.83  | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (588),
% 196.10/31.83  | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 196.10/31.83  | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 196.10/31.83  | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 196.10/31.83  | | | | | | | | | |            (612), (613), (684), (688), (772), (4646), (4649),
% 196.10/31.83  | | | | | | | | | |            (4650), (5571), (5681), (5682), (5684), (5685),
% 196.10/31.83  | | | | | | | | | |            (5687), (5688), (5689), (5692), (5694), (5695),
% 196.10/31.83  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.83  | | | | | | | | | |            #348.
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | End of split
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | End of split
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | End of split
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | Case 2:
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | |   (5696)  all_16_0 = e2
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | | COMBINE_EQS: (760), (5696) imply:
% 196.10/31.83  | | | | | | |   (5697)  all_10_0 = e2
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | | SIMP: (5697) implies:
% 196.10/31.83  | | | | | | |   (5698)  all_10_0 = e2
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | | COMBINE_EQS: (756), (5698) imply:
% 196.10/31.83  | | | | | | |   (5699)  all_26_0 = e2
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | | REDUCE: (4650), (5698) imply:
% 196.10/31.83  | | | | | | |   (5700)   ~ (e3 = e2)
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | | BETA: splitting (94) gives:
% 196.10/31.83  | | | | | | | 
% 196.10/31.83  | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | |   (5701)   ~ (all_26_0 = e2)
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | REDUCE: (5699), (5701) imply:
% 196.10/31.83  | | | | | | | |   (5702)  $false
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | CLOSE: (5702) is inconsistent.
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | |   (5703)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | BETA: splitting (139) gives:
% 196.10/31.83  | | | | | | | | 
% 196.10/31.83  | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | |   (5704)   ~ (all_44_0 = e2)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | REDUCE: (4648), (5704) imply:
% 196.10/31.83  | | | | | | | | |   (5705)  $false
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | CLOSE: (5705) is inconsistent.
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | |   (5706)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | BETA: splitting (153) gives:
% 196.10/31.83  | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | |   (5707)   ~ (all_50_0 = e2)
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | REDUCE: (5568), (5707) imply:
% 196.10/31.83  | | | | | | | | | |   (5708)  $false
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | CLOSE: (5708) is inconsistent.
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | |   (5709)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.83  | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | |   (5710)  all_58_15 = e0
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (5569), (5710),
% 196.10/31.83  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.83  | | | | | | | | | | |            #612.
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | |   (5711)   ~ (all_58_15 = e0)
% 196.10/31.83  | | | | | | | | | | |   (5712)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.83  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.83  | | | | | | | | | | |             e0)
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | ALPHA: (5712) implies:
% 196.10/31.83  | | | | | | | | | | |   (5713)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.10/31.83  | | | | | | | | | | |   (5714)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | REDUCE: (541), (5711) imply:
% 196.10/31.83  | | | | | | | | | | |   (5715)   ~ (all_14_2 = e0)
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.83  | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | |   (5716)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.83  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.83  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.83  | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | BETA: splitting (5716) gives:
% 196.10/31.83  | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | Case 1:
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | |   (5717)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.83  | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 196.10/31.83  | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 196.10/31.83  | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 196.10/31.83  | | | | | | | | | | | | |            (4649), (5717), (function-axioms) are inconsistent
% 196.10/31.83  | | | | | | | | | | | | |            by sub-proof #501.
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | |   (5718)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.83  | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | ALPHA: (5718) implies:
% 196.10/31.83  | | | | | | | | | | | | |   (5719)  all_52_14 = e0
% 196.10/31.83  | | | | | | | | | | | | |   (5720)  all_52_12 = e1
% 196.10/31.83  | | | | | | | | | | | | |   (5721)  all_52_10 = e2
% 196.10/31.83  | | | | | | | | | | | | |   (5722)  all_52_8 = e3
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | REDUCE: (182), (5722) imply:
% 196.10/31.83  | | | | | | | | | | | | |   (5723)  op(all_52_9, all_52_9) = e3
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | REDUCE: (180), (5720) imply:
% 196.10/31.83  | | | | | | | | | | | | |   (5724)  op(all_52_13, all_52_13) = e1
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | REDUCE: (179), (5719) imply:
% 196.10/31.83  | | | | | | | | | | | | |   (5725)  op(all_52_15, all_52_15) = e0
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | REDUCE: (611), (5721) imply:
% 196.10/31.83  | | | | | | | | | | | | |   (5726)  op(all_4_2, all_4_2) = e2
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.83  | | | | | | | | | | | | |            (43), (61), (63), (158), (162), (166), (167),
% 196.10/31.83  | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 196.10/31.83  | | | | | | | | | | | | |            (178), (183), (184), (185), (270), (272), (273),
% 196.10/31.83  | | | | | | | | | | | | |            (275), (277), (278), (281), (282), (284), (285),
% 196.10/31.83  | | | | | | | | | | | | |            (306), (309), (313), (317), (319), (321), (325),
% 196.10/31.83  | | | | | | | | | | | | |            (326), (329), (332), (333), (335), (346), (351),
% 196.10/31.83  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.10/31.83  | | | | | | | | | | | | |            (393), (394), (405), (411), (427), (431), (521),
% 196.10/31.83  | | | | | | | | | | | | |            (528), (538), (540), (541), (542), (543), (544),
% 196.10/31.83  | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.10/31.83  | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.10/31.83  | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (572),
% 196.10/31.83  | | | | | | | | | | | | |            (573), (574), (577), (578), (580), (582), (584),
% 196.10/31.83  | | | | | | | | | | | | |            (586), (588), (589), (590), (591), (592), (594),
% 196.10/31.83  | | | | | | | | | | | | |            (595), (596), (597), (600), (602), (603), (604),
% 196.10/31.83  | | | | | | | | | | | | |            (605), (606), (608), (609), (612), (613), (684),
% 196.10/31.83  | | | | | | | | | | | | |            (688), (690), (772), (4646), (4649), (5706),
% 196.10/31.83  | | | | | | | | | | | | |            (5709), (5714), (5723), (5724), (5725), (5726),
% 196.10/31.83  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.83  | | | | | | | | | | | | |            #334.
% 196.10/31.83  | | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | | End of split
% 196.10/31.83  | | | | | | | | | | | | 
% 196.10/31.83  | | | | | | | | | | | Case 2:
% 196.10/31.83  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | |   (5727)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.84  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.84  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | BETA: splitting (5727) gives:
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | |   (5728)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.10/31.84  | | | | | | | | | | | | |           all_52_22 = e0
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | ALPHA: (5728) implies:
% 196.10/31.84  | | | | | | | | | | | | |   (5729)  all_52_22 = e0
% 196.10/31.84  | | | | | | | | | | | | |   (5730)  all_52_20 = e1
% 196.10/31.84  | | | | | | | | | | | | |   (5731)  all_52_18 = e2
% 196.10/31.84  | | | | | | | | | | | | |   (5732)  all_52_16 = e3
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | REDUCE: (178), (5732) imply:
% 196.10/31.84  | | | | | | | | | | | | |   (5733)  op(all_52_17, all_52_17) = e3
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | REDUCE: (177), (5731) imply:
% 196.10/31.84  | | | | | | | | | | | | |   (5734)  op(all_52_19, all_52_19) = e2
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | REDUCE: (175), (5729) imply:
% 196.10/31.84  | | | | | | | | | | | | |   (5735)  op(all_52_23, all_52_23) = e0
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | REDUCE: (612), (5730) imply:
% 196.10/31.84  | | | | | | | | | | | | |   (5736)  op(all_10_2, all_10_2) = e1
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.10/31.84  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 196.10/31.84  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (179),
% 196.10/31.84  | | | | | | | | | | | | |            (180), (182), (183), (185), (270), (272), (273),
% 196.10/31.84  | | | | | | | | | | | | |            (275), (277), (278), (279), (281), (283), (284),
% 196.10/31.84  | | | | | | | | | | | | |            (304), (306), (309), (313), (315), (317), (319),
% 196.10/31.84  | | | | | | | | | | | | |            (321), (325), (326), (327), (328), (329), (331),
% 196.10/31.84  | | | | | | | | | | | | |            (332), (333), (346), (351), (361), (366), (367),
% 196.10/31.84  | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (405), (411),
% 196.10/31.84  | | | | | | | | | | | | |            (415), (417), (427), (431), (512), (521), (528),
% 196.10/31.84  | | | | | | | | | | | | |            (538), (541), (542), (543), (544), (545), (546),
% 196.10/31.84  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.10/31.84  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (567),
% 196.10/31.84  | | | | | | | | | | | | |            (569), (571), (572), (573), (574), (575), (576),
% 196.10/31.84  | | | | | | | | | | | | |            (577), (578), (580), (582), (586), (587), (588),
% 196.10/31.84  | | | | | | | | | | | | |            (592), (594), (595), (596), (597), (600), (602),
% 196.10/31.84  | | | | | | | | | | | | |            (604), (605), (606), (608), (609), (613), (676),
% 196.10/31.84  | | | | | | | | | | | | |            (684), (688), (4646), (4649), (5703), (5706),
% 196.10/31.84  | | | | | | | | | | | | |            (5713), (5715), (5733), (5734), (5735), (5736),
% 196.10/31.84  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.84  | | | | | | | | | | | | |            #337.
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | Case 2:
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | |   (5737)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.10/31.84  | | | | | | | | | | | | |           all_52_30 = e0
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 196.10/31.84  | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 196.10/31.84  | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 196.10/31.84  | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 196.10/31.84  | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 196.10/31.84  | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 196.10/31.84  | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 196.10/31.84  | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 196.10/31.84  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 196.10/31.84  | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 196.10/31.84  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.10/31.84  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 196.10/31.84  | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 196.10/31.84  | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 196.10/31.84  | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 196.10/31.84  | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 196.10/31.84  | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 196.10/31.84  | | | | | | | | | | | | |            (684), (688), (4646), (4649), (5706), (5713),
% 196.10/31.84  | | | | | | | | | | | | |            (5714), (5715), (5737), (function-axioms) are
% 196.10/31.84  | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | End of split
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | End of split
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | End of split
% 196.10/31.84  | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | End of split
% 196.10/31.84  | | | | | | | | | 
% 196.10/31.84  | | | | | | | | End of split
% 196.10/31.84  | | | | | | | | 
% 196.10/31.84  | | | | | | | End of split
% 196.10/31.84  | | | | | | | 
% 196.10/31.84  | | | | | | End of split
% 196.10/31.84  | | | | | | 
% 196.10/31.84  | | | | | End of split
% 196.10/31.84  | | | | | 
% 196.10/31.84  | | | | Case 2:
% 196.10/31.84  | | | | | 
% 196.10/31.84  | | | | |   (5738)  all_10_0 = e3
% 196.10/31.84  | | | | | 
% 196.10/31.84  | | | | | REDUCE: (52), (5738) imply:
% 196.10/31.84  | | | | |   (5739)  op(e1, all_10_1) = e3
% 196.10/31.84  | | | | | 
% 196.10/31.84  | | | | | BETA: splitting (64) gives:
% 196.10/31.84  | | | | | 
% 196.10/31.84  | | | | | Case 1:
% 196.10/31.84  | | | | | | 
% 196.10/31.84  | | | | | |   (5740)   ~ (all_14_0 = e2)
% 196.10/31.84  | | | | | | 
% 196.10/31.84  | | | | | | BETA: splitting (74) gives:
% 196.10/31.84  | | | | | | 
% 196.10/31.84  | | | | | | Case 1:
% 196.10/31.84  | | | | | | | 
% 196.10/31.84  | | | | | | |   (5741)   ~ (all_18_0 = e3)
% 196.10/31.84  | | | | | | | 
% 196.10/31.84  | | | | | | | REDUCE: (761), (5741) imply:
% 196.10/31.84  | | | | | | |   (5742)   ~ (all_14_0 = e3)
% 196.10/31.84  | | | | | | | 
% 196.10/31.84  | | | | | | | BETA: splitting (79) gives:
% 196.10/31.84  | | | | | | | 
% 196.10/31.84  | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | 
% 196.10/31.84  | | | | | | | |   (5743)   ~ (all_20_0 = e3)
% 196.10/31.84  | | | | | | | | 
% 196.10/31.84  | | | | | | | | REDUCE: (758), (5743) imply:
% 196.10/31.84  | | | | | | | |   (5744)   ~ (all_4_0 = e3)
% 196.10/31.84  | | | | | | | | 
% 196.10/31.84  | | | | | | | | BETA: splitting (89) gives:
% 196.10/31.84  | | | | | | | | 
% 196.10/31.84  | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | 
% 196.10/31.84  | | | | | | | | |   (5745)   ~ (all_24_0 = e1)
% 196.10/31.84  | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | REDUCE: (711), (5745) imply:
% 196.10/31.84  | | | | | | | | |   (5746)   ~ (all_14_0 = e1)
% 196.10/31.84  | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | BETA: splitting (109) gives:
% 196.10/31.84  | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | |   (5747)   ~ (all_32_1 = e3)
% 196.10/31.84  | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | REDUCE: (663), (5747) imply:
% 196.10/31.84  | | | | | | | | | |   (5748)   ~ (all_4_1 = e3)
% 196.10/31.84  | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | BETA: splitting (139) gives:
% 196.10/31.84  | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | |   (5749)   ~ (all_44_0 = e2)
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | REDUCE: (4648), (5749) imply:
% 196.10/31.84  | | | | | | | | | | |   (5750)  $false
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | CLOSE: (5750) is inconsistent.
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | Case 2:
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | |   (5751)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.84  | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | |   (5752)  all_58_15 = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | COMBINE_EQS: (541), (5752) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5753)  all_14_2 = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (573), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5754)   ~ (all_52_7 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (591), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5755)   ~ (all_52_15 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (603), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5756)   ~ (all_52_23 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (606), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5757)   ~ (all_52_25 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (609), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5758)   ~ (all_52_29 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (613), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5759)  op(e0, e0) = all_52_30
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (63), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5760)  op(e0, e0) = all_14_1
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (61), (5753) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5761)  op(e0, e0) = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.84  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5759), (5760)
% 196.10/31.84  | | | | | | | | | | | |              gives:
% 196.10/31.84  | | | | | | | | | | | |   (5762)  all_52_30 = all_14_1
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.84  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5759), (5761)
% 196.10/31.84  | | | | | | | | | | | |              gives:
% 196.10/31.84  | | | | | | | | | | | |   (5763)  all_52_30 = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | COMBINE_EQS: (5762), (5763) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5764)  all_14_1 = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | SIMP: (5764) implies:
% 196.10/31.84  | | | | | | | | | | | |   (5765)  all_14_1 = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (62), (5765) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5766)  op(e0, e0) = all_14_0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.84  | | | | | | | | | | | |              e0, e0, simplifying with (5761), (5766) gives:
% 196.10/31.84  | | | | | | | | | | | |   (5767)  all_14_0 = e0
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (5742), (5767) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5768)   ~ (e3 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (5740), (5767) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5769)   ~ (e2 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | REDUCE: (5746), (5767) imply:
% 196.10/31.84  | | | | | | | | | | | |   (5770)   ~ (e1 = e0)
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.84  | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | |   (5771)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.84  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.84  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | BETA: splitting (5771) gives:
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | |   (5772)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.84  | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 196.10/31.84  | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 196.10/31.84  | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 196.10/31.84  | | | | | | | | | | | | | |            (4649), (5772), (function-axioms) are inconsistent
% 196.10/31.84  | | | | | | | | | | | | | |            by sub-proof #501.
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | Case 2:
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | |   (5773)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.84  | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | ALPHA: (5773) implies:
% 196.10/31.84  | | | | | | | | | | | | | |   (5774)  all_52_14 = e0
% 196.10/31.84  | | | | | | | | | | | | | |   (5775)  all_52_12 = e1
% 196.10/31.84  | | | | | | | | | | | | | |   (5776)  all_52_10 = e2
% 196.10/31.84  | | | | | | | | | | | | | |   (5777)  all_52_8 = e3
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (182), (5777) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5778)  op(all_52_9, all_52_9) = e3
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (180), (5775) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5779)  op(all_52_13, all_52_13) = e1
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (179), (5774) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5780)  op(all_52_15, all_52_15) = e0
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (611), (5776) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5781)  op(all_4_2, all_4_2) = e2
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 196.10/31.84  | | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (166), (167),
% 196.10/31.84  | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (177), (178),
% 196.10/31.84  | | | | | | | | | | | | | |            (183), (184), (271), (272), (273), (274), (276),
% 196.10/31.84  | | | | | | | | | | | | | |            (277), (280), (281), (282), (284), (285), (304),
% 196.10/31.84  | | | | | | | | | | | | | |            (305), (306), (309), (313), (317), (319), (325),
% 196.10/31.84  | | | | | | | | | | | | | |            (326), (327), (329), (330), (333), (343), (346),
% 196.10/31.84  | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.10/31.84  | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (421), (431),
% 196.10/31.84  | | | | | | | | | | | | | |            (521), (528), (539), (540), (542), (543), (544),
% 196.10/31.84  | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.10/31.84  | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (567), (568),
% 196.10/31.84  | | | | | | | | | | | | | |            (570), (571), (572), (575), (576), (577), (578),
% 196.10/31.84  | | | | | | | | | | | | | |            (582), (584), (587), (588), (589), (590), (593),
% 196.10/31.84  | | | | | | | | | | | | | |            (595), (600), (604), (605), (607), (610), (612),
% 196.10/31.84  | | | | | | | | | | | | | |            (684), (688), (772), (4646), (4649), (5739),
% 196.10/31.84  | | | | | | | | | | | | | |            (5751), (5752), (5754), (5755), (5756), (5757),
% 196.10/31.84  | | | | | | | | | | | | | |            (5758), (5761), (5778), (5779), (5780), (5781),
% 196.10/31.84  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.84  | | | | | | | | | | | | | |            #331.
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | End of split
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | Case 2:
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | |   (5782)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.84  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.84  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | BETA: splitting (5782) gives:
% 196.10/31.84  | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | |   (5783)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.10/31.84  | | | | | | | | | | | | | |           all_52_22 = e0
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | ALPHA: (5783) implies:
% 196.10/31.84  | | | | | | | | | | | | | |   (5784)  all_52_22 = e0
% 196.10/31.84  | | | | | | | | | | | | | |   (5785)  all_52_20 = e1
% 196.10/31.84  | | | | | | | | | | | | | |   (5786)  all_52_18 = e2
% 196.10/31.84  | | | | | | | | | | | | | |   (5787)  all_52_16 = e3
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (178), (5787) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5788)  op(all_52_17, all_52_17) = e3
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (177), (5786) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5789)  op(all_52_19, all_52_19) = e2
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (175), (5784) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5790)  op(all_52_23, all_52_23) = e0
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | REDUCE: (612), (5785) imply:
% 196.10/31.84  | | | | | | | | | | | | | |   (5791)  op(all_10_2, all_10_2) = e1
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.10/31.84  | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | Case 1:
% 196.10/31.84  | | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | |   (5792)  all_56_13 = e3
% 196.10/31.84  | | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (51), (157), (271), (273), (304),
% 196.10/31.84  | | | | | | | | | | | | | | |            (343), (346), (351), (431), (571), (572), (590),
% 196.10/31.84  | | | | | | | | | | | | | | |            (600), (5748), (5754), (5756), (5761), (5790),
% 196.10/31.84  | | | | | | | | | | | | | | |            (5791), (5792), (function-axioms) are inconsistent
% 196.10/31.84  | | | | | | | | | | | | | | |            by sub-proof #1281.
% 196.10/31.84  | | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | Case 2:
% 196.10/31.84  | | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | |   (5793)   ~ (all_56_13 = e3)
% 196.10/31.84  | | | | | | | | | | | | | | |   (5794)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 196.10/31.84  | | | | | | | | | | | | | | | 
% 196.10/31.84  | | | | | | | | | | | | | | | REDUCE: (346), (5793) imply:
% 196.10/31.84  | | | | | | | | | | | | | | |   (5795)   ~ (all_52_15 = e3)
% 196.10/31.84  | | | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (41), (43), (51), (53), (158),
% 196.10/31.85  | | | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.85  | | | | | | | | | | | | | | |            (174), (179), (182), (183), (185), (273), (274),
% 196.10/31.85  | | | | | | | | | | | | | | |            (277), (278), (281), (282), (283), (285), (304),
% 196.10/31.85  | | | | | | | | | | | | | | |            (306), (309), (317), (319), (325), (326), (329),
% 196.10/31.85  | | | | | | | | | | | | | | |            (330), (333), (346), (351), (352), (366), (367),
% 196.10/31.85  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 196.10/31.85  | | | | | | | | | | | | | | |            (415), (427), (431), (521), (528), (540), (541),
% 196.10/31.85  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.10/31.85  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.10/31.85  | | | | | | | | | | | | | | |            (562), (563), (567), (570), (571), (572), (577),
% 196.10/31.85  | | | | | | | | | | | | | | |            (584), (589), (593), (594), (595), (598), (600),
% 196.10/31.85  | | | | | | | | | | | | | | |            (602), (604), (605), (613), (684), (688), (4646),
% 196.10/31.85  | | | | | | | | | | | | | | |            (4649), (5751), (5752), (5754), (5757), (5758),
% 196.10/31.85  | | | | | | | | | | | | | | |            (5761), (5788), (5789), (5790), (5791), (5794),
% 196.10/31.85  | | | | | | | | | | | | | | |            (5795), (function-axioms) are inconsistent by
% 196.10/31.85  | | | | | | | | | | | | | | |            sub-proof #342.
% 196.10/31.85  | | | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | |   (5796)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.10/31.85  | | | | | | | | | | | | | |           all_52_30 = e0
% 196.10/31.85  | | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 196.10/31.85  | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 196.10/31.85  | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 196.10/31.85  | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 196.10/31.85  | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 196.10/31.85  | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 196.10/31.85  | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.10/31.85  | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 196.10/31.85  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 196.10/31.85  | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 196.10/31.85  | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 196.10/31.85  | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 196.10/31.85  | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 196.10/31.85  | | | | | | | | | | | | | |            (608), (609), (610), (688), (4649), (5751),
% 196.10/31.85  | | | | | | | | | | | | | |            (5752), (5754), (5755), (5756), (5757), (5758),
% 196.10/31.85  | | | | | | | | | | | | | |            (5796), (function-axioms) are inconsistent by
% 196.10/31.85  | | | | | | | | | | | | | |            sub-proof #418.
% 196.10/31.85  | | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | |   (5797)   ~ (all_58_15 = e0)
% 196.10/31.85  | | | | | | | | | | | |   (5798)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.85  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.85  | | | | | | | | | | | |             e0)
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | ALPHA: (5798) implies:
% 196.10/31.85  | | | | | | | | | | | |   (5799)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.10/31.85  | | | | | | | | | | | |   (5800)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | REDUCE: (541), (5797) imply:
% 196.10/31.85  | | | | | | | | | | | |   (5801)   ~ (all_14_2 = e0)
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.85  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.10/31.85  | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.85  | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.85  | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.85  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.85  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.10/31.85  | | | | | | | | | | | |            (305), (306), (307), (309), (311), (313), (315),
% 196.10/31.85  | | | | | | | | | | | |            (316), (317), (319), (321), (323), (324), (325),
% 196.10/31.85  | | | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 196.10/31.85  | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.10/31.85  | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.10/31.85  | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (521),
% 196.10/31.85  | | | | | | | | | | | |            (528), (538), (539), (540), (541), (542), (543),
% 196.10/31.85  | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.85  | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.10/31.85  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 196.10/31.85  | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 196.10/31.85  | | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 196.10/31.85  | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 196.10/31.85  | | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 196.10/31.85  | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 196.10/31.85  | | | | | | | | | | | |            (612), (613), (684), (688), (772), (4646), (4649),
% 196.10/31.85  | | | | | | | | | | | |            (5740), (5751), (5799), (5800), (5801),
% 196.10/31.85  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.85  | | | | | | | | | | | |            #327.
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | |   (5802)  all_32_1 = e3
% 196.10/31.85  | | | | | | | | | |   (5803)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | COMBINE_EQS: (663), (5802) imply:
% 196.10/31.85  | | | | | | | | | |   (5804)  all_4_1 = e3
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | COMBINE_EQS: (686), (5804) imply:
% 196.10/31.85  | | | | | | | | | |   (5805)  all_38_1 = e3
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | REDUCE: (38), (5804) imply:
% 196.10/31.85  | | | | | | | | | |   (5806)  op(all_4_2, e2) = e3
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | REDUCE: (37), (5804) imply:
% 196.10/31.85  | | | | | | | | | |   (5807)  op(e2, e3) = all_4_0
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.10/31.85  | | | | | | | | | |            (51), (53), (61), (62), (63), (124), (139), (158),
% 196.10/31.85  | | | | | | | | | |            (162), (166), (168), (169), (172), (173), (174),
% 196.10/31.85  | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.10/31.85  | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.10/31.85  | | | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 196.10/31.85  | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 196.10/31.85  | | | | | | | | | |            (306), (307), (308), (309), (311), (312), (313),
% 196.10/31.85  | | | | | | | | | |            (316), (317), (319), (320), (321), (324), (325),
% 196.10/31.85  | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (332),
% 196.10/31.85  | | | | | | | | | |            (333), (343), (346), (351), (352), (361), (366),
% 196.10/31.85  | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 196.10/31.85  | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 196.10/31.85  | | | | | | | | | |            (521), (523), (525), (528), (538), (539), (540),
% 196.10/31.85  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.10/31.85  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.10/31.85  | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 196.10/31.85  | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 196.10/31.85  | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 196.10/31.85  | | | | | | | | | |            (586), (589), (590), (591), (592), (593), (594),
% 196.10/31.85  | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 196.10/31.85  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 196.10/31.85  | | | | | | | | | |            (611), (612), (613), (684), (688), (721), (766),
% 196.10/31.85  | | | | | | | | | |            (4646), (4648), (4649), (5740), (5742), (5744),
% 196.10/31.85  | | | | | | | | | |            (5746), (5803), (5805), (5806), (5807),
% 196.10/31.85  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.85  | | | | | | | | | |            #388.
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | |   (5808)  all_24_0 = e1
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.10/31.85  | | | | | | | | |            (53), (61), (62), (63), (114), (139), (156), (158),
% 196.10/31.85  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.85  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.85  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.85  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.85  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.10/31.85  | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 196.10/31.85  | | | | | | | | |            (313), (315), (316), (317), (319), (321), (323),
% 196.10/31.85  | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 196.10/31.85  | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.10/31.85  | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.10/31.85  | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 196.10/31.85  | | | | | | | | |            (427), (431), (491), (521), (528), (538), (539),
% 196.10/31.85  | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.10/31.85  | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.10/31.85  | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.10/31.85  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.85  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.85  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.10/31.85  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.10/31.85  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.10/31.85  | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 196.10/31.85  | | | | | | | | |            (685), (688), (711), (765), (772), (4646), (4648),
% 196.10/31.85  | | | | | | | | |            (4649), (5740), (5742), (5808), (function-axioms)
% 196.10/31.85  | | | | | | | | |            are inconsistent by sub-proof #326.
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | End of split
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | |   (5809)  all_20_0 = e3
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | | COMBINE_EQS: (758), (5809) imply:
% 196.10/31.85  | | | | | | | |   (5810)  all_4_0 = e3
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | | SIMP: (5810) implies:
% 196.10/31.85  | | | | | | | |   (5811)  all_4_0 = e3
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | | REDUCE: (37), (5811) imply:
% 196.10/31.85  | | | | | | | |   (5812)  op(e2, all_4_1) = e3
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | | BETA: splitting (89) gives:
% 196.10/31.85  | | | | | | | | 
% 196.10/31.85  | | | | | | | | Case 1:
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | |   (5813)   ~ (all_24_0 = e1)
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | REDUCE: (711), (5813) imply:
% 196.10/31.85  | | | | | | | | |   (5814)   ~ (all_14_0 = e1)
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | BETA: splitting (139) gives:
% 196.10/31.85  | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | Case 1:
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | |   (5815)   ~ (all_44_0 = e2)
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | REDUCE: (4648), (5815) imply:
% 196.10/31.85  | | | | | | | | | |   (5816)  $false
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | CLOSE: (5816) is inconsistent.
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | |   (5817)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.85  | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | Case 1:
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | |   (5818)  all_58_15 = e0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | COMBINE_EQS: (541), (5818) imply:
% 196.10/31.85  | | | | | | | | | | |   (5819)  all_14_2 = e0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (573), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5820)   ~ (all_52_7 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (591), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5821)   ~ (all_52_15 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (603), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5822)   ~ (all_52_23 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (606), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5823)   ~ (all_52_25 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (609), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5824)   ~ (all_52_29 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (613), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5825)  op(e0, e0) = all_52_30
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (63), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5826)  op(e0, e0) = all_14_1
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (61), (5819) imply:
% 196.10/31.85  | | | | | | | | | | |   (5827)  op(e0, e0) = e0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.85  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5825), (5826)
% 196.10/31.85  | | | | | | | | | | |              gives:
% 196.10/31.85  | | | | | | | | | | |   (5828)  all_52_30 = all_14_1
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.85  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5825), (5827)
% 196.10/31.85  | | | | | | | | | | |              gives:
% 196.10/31.85  | | | | | | | | | | |   (5829)  all_52_30 = e0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | COMBINE_EQS: (5828), (5829) imply:
% 196.10/31.85  | | | | | | | | | | |   (5830)  all_14_1 = e0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (62), (5830) imply:
% 196.10/31.85  | | | | | | | | | | |   (5831)  op(e0, e0) = all_14_0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.85  | | | | | | | | | | |              e0, e0, simplifying with (5827), (5831) gives:
% 196.10/31.85  | | | | | | | | | | |   (5832)  all_14_0 = e0
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (5742), (5832) imply:
% 196.10/31.85  | | | | | | | | | | |   (5833)   ~ (e3 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (5740), (5832) imply:
% 196.10/31.85  | | | | | | | | | | |   (5834)   ~ (e2 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | REDUCE: (5814), (5832) imply:
% 196.10/31.85  | | | | | | | | | | |   (5835)   ~ (e1 = e0)
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.85  | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | Case 1:
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | |   (5836)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.85  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.85  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | BETA: splitting (5836) gives:
% 196.10/31.85  | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | Case 1:
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | |   (5837)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.85  | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 196.10/31.85  | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 196.10/31.85  | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 196.10/31.85  | | | | | | | | | | | | |            (4649), (5837), (function-axioms) are inconsistent
% 196.10/31.85  | | | | | | | | | | | | |            by sub-proof #501.
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | Case 2:
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | |   (5838)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.85  | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | ALPHA: (5838) implies:
% 196.10/31.85  | | | | | | | | | | | | |   (5839)  all_52_14 = e0
% 196.10/31.85  | | | | | | | | | | | | |   (5840)  all_52_12 = e1
% 196.10/31.85  | | | | | | | | | | | | |   (5841)  all_52_10 = e2
% 196.10/31.85  | | | | | | | | | | | | |   (5842)  all_52_8 = e3
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | REDUCE: (182), (5842) imply:
% 196.10/31.85  | | | | | | | | | | | | |   (5843)  op(all_52_9, all_52_9) = e3
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | REDUCE: (180), (5840) imply:
% 196.10/31.85  | | | | | | | | | | | | |   (5844)  op(all_52_13, all_52_13) = e1
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | REDUCE: (179), (5839) imply:
% 196.10/31.85  | | | | | | | | | | | | |   (5845)  op(all_52_15, all_52_15) = e0
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.85  | | | | | | | | | | | | | REDUCE: (611), (5841) imply:
% 196.10/31.85  | | | | | | | | | | | | |   (5846)  op(all_4_2, all_4_2) = e2
% 196.10/31.85  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 196.10/31.86  | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (166), (167),
% 196.10/31.86  | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (177), (178),
% 196.10/31.86  | | | | | | | | | | | | |            (183), (184), (271), (272), (273), (274), (276),
% 196.10/31.86  | | | | | | | | | | | | |            (277), (280), (281), (282), (284), (285), (304),
% 196.10/31.86  | | | | | | | | | | | | |            (305), (306), (309), (313), (317), (319), (325),
% 196.10/31.86  | | | | | | | | | | | | |            (326), (327), (329), (330), (333), (343), (346),
% 196.10/31.86  | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.10/31.86  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (421), (431),
% 196.10/31.86  | | | | | | | | | | | | |            (521), (528), (539), (540), (542), (543), (544),
% 196.10/31.86  | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.10/31.86  | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (567), (568),
% 196.10/31.86  | | | | | | | | | | | | |            (570), (571), (572), (575), (576), (577), (578),
% 196.10/31.86  | | | | | | | | | | | | |            (582), (584), (587), (588), (589), (590), (593),
% 196.10/31.86  | | | | | | | | | | | | |            (595), (600), (604), (605), (607), (610), (612),
% 196.10/31.86  | | | | | | | | | | | | |            (684), (688), (772), (4646), (4649), (5739),
% 196.10/31.86  | | | | | | | | | | | | |            (5817), (5818), (5820), (5821), (5822), (5823),
% 196.10/31.86  | | | | | | | | | | | | |            (5824), (5827), (5843), (5844), (5845), (5846),
% 196.10/31.86  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.86  | | | | | | | | | | | | |            #331.
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | |   (5847)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.86  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.86  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.86  | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | BETA: splitting (5847) gives:
% 196.10/31.86  | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | Case 1:
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | |   (5848)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.10/31.86  | | | | | | | | | | | | |           all_52_22 = e0
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | ALPHA: (5848) implies:
% 196.10/31.86  | | | | | | | | | | | | |   (5849)  all_52_22 = e0
% 196.10/31.86  | | | | | | | | | | | | |   (5850)  all_52_20 = e1
% 196.10/31.86  | | | | | | | | | | | | |   (5851)  all_52_18 = e2
% 196.10/31.86  | | | | | | | | | | | | |   (5852)  all_52_16 = e3
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | REDUCE: (178), (5852) imply:
% 196.10/31.86  | | | | | | | | | | | | |   (5853)  op(all_52_17, all_52_17) = e3
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | REDUCE: (177), (5851) imply:
% 196.10/31.86  | | | | | | | | | | | | |   (5854)  op(all_52_19, all_52_19) = e2
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | REDUCE: (175), (5849) imply:
% 196.10/31.86  | | | | | | | | | | | | |   (5855)  op(all_52_23, all_52_23) = e0
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | REDUCE: (612), (5850) imply:
% 196.10/31.86  | | | | | | | | | | | | |   (5856)  op(all_10_2, all_10_2) = e1
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | Case 1:
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | |   (5857)  all_56_13 = e3
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (38), (41), (51), (157),
% 196.10/31.86  | | | | | | | | | | | | | |            (166), (179), (271), (273), (279), (283), (304),
% 196.10/31.86  | | | | | | | | | | | | | |            (305), (343), (346), (351), (415), (417), (431),
% 196.10/31.86  | | | | | | | | | | | | | |            (542), (543), (551), (565), (571), (572), (584),
% 196.10/31.86  | | | | | | | | | | | | | |            (590), (592), (594), (597), (600), (611), (5812),
% 196.10/31.86  | | | | | | | | | | | | | |            (5818), (5820), (5822), (5827), (5853), (5855),
% 196.10/31.86  | | | | | | | | | | | | | |            (5856), (5857), (function-axioms) are inconsistent
% 196.10/31.86  | | | | | | | | | | | | | |            by sub-proof #765.
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | |   (5858)   ~ (all_56_13 = e3)
% 196.10/31.86  | | | | | | | | | | | | | |   (5859)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | | REDUCE: (346), (5858) imply:
% 196.10/31.86  | | | | | | | | | | | | | |   (5860)   ~ (all_52_15 = e3)
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (41), (43), (51), (53), (158),
% 196.10/31.86  | | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.86  | | | | | | | | | | | | | |            (174), (179), (182), (183), (185), (273), (274),
% 196.10/31.86  | | | | | | | | | | | | | |            (277), (278), (281), (282), (283), (285), (304),
% 196.10/31.86  | | | | | | | | | | | | | |            (306), (309), (317), (319), (325), (326), (329),
% 196.10/31.86  | | | | | | | | | | | | | |            (330), (333), (346), (351), (352), (366), (367),
% 196.10/31.86  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 196.10/31.86  | | | | | | | | | | | | | |            (415), (427), (431), (521), (528), (540), (541),
% 196.10/31.86  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.10/31.86  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.10/31.86  | | | | | | | | | | | | | |            (562), (563), (567), (570), (571), (572), (577),
% 196.10/31.86  | | | | | | | | | | | | | |            (584), (589), (593), (594), (595), (598), (600),
% 196.10/31.86  | | | | | | | | | | | | | |            (602), (604), (605), (613), (684), (688), (4646),
% 196.10/31.86  | | | | | | | | | | | | | |            (4649), (5817), (5818), (5820), (5823), (5824),
% 196.10/31.86  | | | | | | | | | | | | | |            (5827), (5853), (5854), (5855), (5856), (5859),
% 196.10/31.86  | | | | | | | | | | | | | |            (5860), (function-axioms) are inconsistent by
% 196.10/31.86  | | | | | | | | | | | | | |            sub-proof #342.
% 196.10/31.86  | | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | |   (5861)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.10/31.86  | | | | | | | | | | | | |           all_52_30 = e0
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 196.10/31.86  | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 196.10/31.86  | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 196.10/31.86  | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 196.10/31.86  | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 196.10/31.86  | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 196.10/31.86  | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.10/31.86  | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 196.10/31.86  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 196.10/31.86  | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 196.10/31.86  | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 196.10/31.86  | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 196.10/31.86  | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 196.10/31.86  | | | | | | | | | | | | |            (608), (609), (610), (688), (4649), (5817),
% 196.10/31.86  | | | | | | | | | | | | |            (5818), (5820), (5821), (5822), (5823), (5824),
% 196.10/31.86  | | | | | | | | | | | | |            (5861), (function-axioms) are inconsistent by
% 196.10/31.86  | | | | | | | | | | | | |            sub-proof #418.
% 196.10/31.86  | | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | |   (5862)   ~ (all_58_15 = e0)
% 196.10/31.86  | | | | | | | | | | |   (5863)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.86  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.86  | | | | | | | | | | |             e0)
% 196.10/31.86  | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.86  | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.10/31.86  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.86  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.86  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.86  | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.86  | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.10/31.86  | | | | | | | | | | |            (305), (306), (307), (309), (311), (313), (315),
% 196.10/31.86  | | | | | | | | | | |            (316), (317), (319), (321), (323), (324), (325),
% 196.10/31.86  | | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 196.10/31.86  | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.10/31.86  | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.10/31.86  | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (521),
% 196.10/31.86  | | | | | | | | | | |            (528), (538), (539), (540), (541), (542), (543),
% 196.10/31.86  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.86  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.10/31.86  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 196.10/31.86  | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 196.10/31.86  | | | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 196.10/31.86  | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 196.10/31.86  | | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 196.10/31.86  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 196.10/31.86  | | | | | | | | | | |            (612), (613), (684), (688), (772), (4646), (4649),
% 196.10/31.86  | | | | | | | | | | |            (5740), (5817), (5862), (5863), (function-axioms)
% 196.10/31.86  | | | | | | | | | | |            are inconsistent by sub-proof #325.
% 196.10/31.86  | | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | |   (5864)  all_24_0 = e1
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.10/31.86  | | | | | | | | |            (53), (61), (62), (63), (114), (139), (156), (158),
% 196.10/31.86  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.86  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.86  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.86  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.86  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.10/31.86  | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 196.10/31.86  | | | | | | | | |            (313), (315), (316), (317), (319), (321), (323),
% 196.10/31.86  | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 196.10/31.86  | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.10/31.86  | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.10/31.86  | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 196.10/31.86  | | | | | | | | |            (427), (431), (491), (521), (528), (538), (539),
% 196.10/31.86  | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.10/31.86  | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.10/31.86  | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.10/31.86  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.86  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.86  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.10/31.86  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.10/31.86  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.10/31.86  | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 196.10/31.86  | | | | | | | | |            (685), (688), (711), (765), (772), (4646), (4648),
% 196.10/31.86  | | | | | | | | |            (4649), (5740), (5742), (5864), (function-axioms)
% 196.10/31.86  | | | | | | | | |            are inconsistent by sub-proof #326.
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | End of split
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | Case 2:
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | |   (5865)  all_18_0 = e3
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | COMBINE_EQS: (761), (5865) imply:
% 196.10/31.86  | | | | | | |   (5866)  all_14_0 = e3
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | SIMP: (5866) implies:
% 196.10/31.86  | | | | | | |   (5867)  all_14_0 = e3
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | REDUCE: (62), (5867) imply:
% 196.10/31.86  | | | | | | |   (5868)  op(e0, all_14_1) = e3
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | BETA: splitting (139) gives:
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | Case 1:
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | |   (5869)   ~ (all_44_0 = e2)
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | REDUCE: (4648), (5869) imply:
% 196.10/31.86  | | | | | | | |   (5870)  $false
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | CLOSE: (5870) is inconsistent.
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | |   (5871)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | Case 1:
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | |   (5872)  all_58_15 = e0
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (5868), (5872),
% 196.10/31.86  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.86  | | | | | | | | |            #678.
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | |   (5873)   ~ (all_58_15 = e0)
% 196.10/31.86  | | | | | | | | |   (5874)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 196.10/31.86  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.86  | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.10/31.86  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.86  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.86  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.86  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.86  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.10/31.86  | | | | | | | | |            (305), (306), (307), (309), (311), (313), (315),
% 196.10/31.86  | | | | | | | | |            (316), (317), (319), (321), (323), (324), (325),
% 196.10/31.86  | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 196.10/31.86  | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.10/31.86  | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.10/31.86  | | | | | | | | |            (411), (415), (417), (421), (427), (431), (521),
% 196.10/31.86  | | | | | | | | |            (528), (538), (539), (540), (541), (542), (543),
% 196.10/31.86  | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.86  | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.10/31.86  | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 196.10/31.86  | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 196.10/31.86  | | | | | | | | |            (578), (580), (582), (584), (586), (587), (588),
% 196.10/31.86  | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 196.10/31.86  | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 196.10/31.86  | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 196.10/31.86  | | | | | | | | |            (612), (613), (684), (688), (772), (4646), (4649),
% 196.10/31.86  | | | | | | | | |            (5740), (5871), (5873), (5874), (function-axioms)
% 196.10/31.86  | | | | | | | | |            are inconsistent by sub-proof #325.
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | End of split
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | End of split
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | End of split
% 196.10/31.86  | | | | | | 
% 196.10/31.86  | | | | | Case 2:
% 196.10/31.86  | | | | | | 
% 196.10/31.86  | | | | | |   (5875)  all_14_0 = e2
% 196.10/31.86  | | | | | | 
% 196.10/31.86  | | | | | | COMBINE_EQS: (771), (5875) imply:
% 196.10/31.86  | | | | | |   (5876)  all_50_0 = e2
% 196.10/31.86  | | | | | | 
% 196.10/31.86  | | | | | | REDUCE: (62), (5875) imply:
% 196.10/31.86  | | | | | |   (5877)  op(e0, all_14_1) = e2
% 196.10/31.86  | | | | | | 
% 196.10/31.86  | | | | | | BETA: splitting (139) gives:
% 196.10/31.86  | | | | | | 
% 196.10/31.86  | | | | | | Case 1:
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | |   (5878)   ~ (all_44_0 = e2)
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | REDUCE: (4648), (5878) imply:
% 196.10/31.86  | | | | | | |   (5879)  $false
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | CLOSE: (5879) is inconsistent.
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | Case 2:
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | |   (5880)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | BETA: splitting (153) gives:
% 196.10/31.86  | | | | | | | 
% 196.10/31.86  | | | | | | | Case 1:
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | |   (5881)   ~ (all_50_0 = e2)
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | REDUCE: (5876), (5881) imply:
% 196.10/31.86  | | | | | | | |   (5882)  $false
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | CLOSE: (5882) is inconsistent.
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | |   (5883)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.86  | | | | | | | | 
% 196.10/31.86  | | | | | | | | Case 1:
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | |   (5884)  all_58_15 = e0
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (5877), (5884),
% 196.10/31.86  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.86  | | | | | | | | |            #612.
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.86  | | | | | | | | Case 2:
% 196.10/31.86  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | |   (5885)   ~ (all_58_15 = e0)
% 196.10/31.87  | | | | | | | | |   (5886)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 196.10/31.87  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | ALPHA: (5886) implies:
% 196.10/31.87  | | | | | | | | |   (5887)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.10/31.87  | | | | | | | | |   (5888)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | REDUCE: (541), (5885) imply:
% 196.10/31.87  | | | | | | | | |   (5889)   ~ (all_14_2 = e0)
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | |   (5890)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.87  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.87  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.87  | | | | | | | | | |            (43), (51), (61), (63), (158), (162), (166),
% 196.10/31.87  | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.87  | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.10/31.87  | | | | | | | | | |            (185), (270), (272), (273), (275), (277), (278),
% 196.10/31.87  | | | | | | | | | |            (281), (282), (284), (285), (306), (309), (313),
% 196.10/31.87  | | | | | | | | | |            (317), (319), (321), (325), (326), (329), (332),
% 196.10/31.87  | | | | | | | | | |            (333), (335), (346), (351), (361), (366), (367),
% 196.10/31.87  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.10/31.87  | | | | | | | | | |            (411), (427), (431), (521), (528), (538), (540),
% 196.10/31.87  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.10/31.87  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.10/31.87  | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 196.10/31.87  | | | | | | | | | |            (568), (569), (571), (572), (573), (574), (577),
% 196.10/31.87  | | | | | | | | | |            (578), (580), (582), (584), (586), (588), (589),
% 196.10/31.87  | | | | | | | | | |            (590), (591), (592), (594), (595), (596), (597),
% 196.10/31.87  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 196.10/31.87  | | | | | | | | | |            (609), (610), (611), (612), (613), (684), (688),
% 196.10/31.87  | | | | | | | | | |            (690), (772), (4646), (4649), (5880), (5883),
% 196.10/31.87  | | | | | | | | | |            (5888), (5890), (function-axioms) are inconsistent
% 196.10/31.87  | | | | | | | | | |            by sub-proof #333.
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | Case 2:
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | |   (5891)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.87  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.87  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | BETA: splitting (5891) gives:
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | |   (5892)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.10/31.87  | | | | | | | | | | |           all_52_22 = e0
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | ALPHA: (5892) implies:
% 196.10/31.87  | | | | | | | | | | |   (5893)  all_52_22 = e0
% 196.10/31.87  | | | | | | | | | | |   (5894)  all_52_20 = e1
% 196.10/31.87  | | | | | | | | | | |   (5895)  all_52_18 = e2
% 196.10/31.87  | | | | | | | | | | |   (5896)  all_52_16 = e3
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REDUCE: (178), (5896) imply:
% 196.10/31.87  | | | | | | | | | | |   (5897)  op(all_52_17, all_52_17) = e3
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REDUCE: (177), (5895) imply:
% 196.10/31.87  | | | | | | | | | | |   (5898)  op(all_52_19, all_52_19) = e2
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REDUCE: (175), (5893) imply:
% 196.10/31.87  | | | | | | | | | | |   (5899)  op(all_52_23, all_52_23) = e0
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REDUCE: (612), (5894) imply:
% 196.10/31.87  | | | | | | | | | | |   (5900)  op(all_10_2, all_10_2) = e1
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.10/31.87  | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 196.10/31.87  | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (179),
% 196.10/31.87  | | | | | | | | | | |            (180), (182), (183), (185), (270), (272), (273),
% 196.10/31.87  | | | | | | | | | | |            (275), (277), (278), (279), (281), (282), (283),
% 196.10/31.87  | | | | | | | | | | |            (284), (285), (304), (306), (309), (313), (315),
% 196.10/31.87  | | | | | | | | | | |            (317), (319), (321), (323), (324), (325), (326),
% 196.10/31.87  | | | | | | | | | | |            (327), (328), (329), (331), (332), (333), (346),
% 196.10/31.87  | | | | | | | | | | |            (351), (361), (366), (367), (372), (375), (387),
% 196.10/31.87  | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.10/31.87  | | | | | | | | | | |            (427), (431), (521), (528), (538), (540), (541),
% 196.10/31.87  | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.10/31.87  | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.10/31.87  | | | | | | | | | | |            (562), (563), (564), (565), (567), (569), (571),
% 196.10/31.87  | | | | | | | | | | |            (572), (573), (574), (576), (577), (580), (582),
% 196.10/31.87  | | | | | | | | | | |            (586), (587), (588), (592), (594), (595), (596),
% 196.10/31.87  | | | | | | | | | | |            (597), (600), (602), (603), (604), (605), (606),
% 196.10/31.87  | | | | | | | | | | |            (608), (609), (610), (613), (684), (688), (4646),
% 196.10/31.87  | | | | | | | | | | |            (4649), (5880), (5887), (5897), (5898), (5899),
% 196.10/31.87  | | | | | | | | | | |            (5900), (function-axioms) are inconsistent by
% 196.10/31.87  | | | | | | | | | | |            sub-proof #328.
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | Case 2:
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | |   (5901)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.10/31.87  | | | | | | | | | | |           all_52_30 = e0
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 196.10/31.87  | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 196.10/31.87  | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 196.10/31.87  | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 196.10/31.87  | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 196.10/31.87  | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 196.10/31.87  | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 196.10/31.87  | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 196.10/31.87  | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 196.10/31.87  | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 196.10/31.87  | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.10/31.87  | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 196.10/31.87  | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 196.10/31.87  | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 196.10/31.87  | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 196.10/31.87  | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 196.10/31.87  | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 196.10/31.87  | | | | | | | | | | |            (684), (688), (4646), (4649), (5880), (5887),
% 196.10/31.87  | | | | | | | | | | |            (5888), (5889), (5901), (function-axioms) are
% 196.10/31.87  | | | | | | | | | | |            inconsistent by sub-proof #434.
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | End of split
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | End of split
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | End of split
% 196.10/31.87  | | | | | | | | 
% 196.10/31.87  | | | | | | | End of split
% 196.10/31.87  | | | | | | | 
% 196.10/31.87  | | | | | | End of split
% 196.10/31.87  | | | | | | 
% 196.10/31.87  | | | | | End of split
% 196.10/31.87  | | | | | 
% 196.10/31.87  | | | | End of split
% 196.10/31.87  | | | | 
% 196.10/31.87  | | | End of split
% 196.10/31.87  | | | 
% 196.10/31.87  | | Case 2:
% 196.10/31.87  | | | 
% 196.10/31.87  | | |   (5902)  all_6_0 = e1
% 196.10/31.87  | | |   (5903)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 196.10/31.87  | | | 
% 196.10/31.87  | | | COMBINE_EQS: (769), (5902) imply:
% 196.10/31.87  | | |   (5904)  all_46_0 = e1
% 196.10/31.87  | | | 
% 196.10/31.87  | | | REDUCE: (42), (5902) imply:
% 196.10/31.87  | | |   (5905)  op(e3, all_6_1) = e1
% 196.10/31.87  | | | 
% 196.10/31.87  | | | BETA: splitting (54) gives:
% 196.10/31.87  | | | 
% 196.10/31.87  | | | Case 1:
% 196.10/31.87  | | | | 
% 196.10/31.87  | | | |   (5906)   ~ (all_10_0 = e3)
% 196.10/31.87  | | | | 
% 196.10/31.87  | | | | BETA: splitting (64) gives:
% 196.10/31.87  | | | | 
% 196.10/31.87  | | | | Case 1:
% 196.10/31.87  | | | | | 
% 196.10/31.87  | | | | |   (5907)   ~ (all_14_0 = e2)
% 196.10/31.87  | | | | | 
% 196.10/31.87  | | | | | BETA: splitting (69) gives:
% 196.10/31.87  | | | | | 
% 196.10/31.87  | | | | | Case 1:
% 196.10/31.87  | | | | | | 
% 196.10/31.87  | | | | | |   (5908)   ~ (all_16_0 = e2)
% 196.10/31.87  | | | | | | 
% 196.10/31.87  | | | | | | REDUCE: (760), (5908) imply:
% 196.10/31.87  | | | | | |   (5909)   ~ (all_10_0 = e2)
% 196.10/31.87  | | | | | | 
% 196.10/31.87  | | | | | | BETA: splitting (74) gives:
% 196.10/31.87  | | | | | | 
% 196.10/31.87  | | | | | | Case 1:
% 196.10/31.87  | | | | | | | 
% 196.10/31.87  | | | | | | |   (5910)   ~ (all_18_0 = e3)
% 196.10/31.87  | | | | | | | 
% 196.10/31.87  | | | | | | | REDUCE: (761), (5910) imply:
% 196.10/31.87  | | | | | | |   (5911)   ~ (all_14_0 = e3)
% 196.10/31.87  | | | | | | | 
% 196.10/31.87  | | | | | | | BETA: splitting (79) gives:
% 196.10/31.87  | | | | | | | 
% 196.10/31.87  | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | 
% 196.10/31.87  | | | | | | | |   (5912)   ~ (all_20_0 = e3)
% 196.10/31.87  | | | | | | | | 
% 196.10/31.87  | | | | | | | | REDUCE: (758), (5912) imply:
% 196.10/31.87  | | | | | | | |   (5913)   ~ (all_4_0 = e3)
% 196.10/31.87  | | | | | | | | 
% 196.10/31.87  | | | | | | | | BETA: splitting (89) gives:
% 196.10/31.87  | | | | | | | | 
% 196.10/31.87  | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | |   (5914)   ~ (all_24_0 = e1)
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | REDUCE: (711), (5914) imply:
% 196.10/31.87  | | | | | | | | |   (5915)   ~ (all_14_0 = e1)
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | BETA: splitting (104) gives:
% 196.10/31.87  | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | |   (5916)   ~ (all_30_1 = e3)
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | REDUCE: (670), (5916) imply:
% 196.10/31.87  | | | | | | | | | |   (5917)   ~ (all_10_1 = e3)
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | BETA: splitting (109) gives:
% 196.10/31.87  | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | |   (5918)   ~ (all_32_1 = e3)
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | REDUCE: (663), (5918) imply:
% 196.10/31.87  | | | | | | | | | | |   (5919)   ~ (all_4_1 = e3)
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | BETA: splitting (129) gives:
% 196.10/31.87  | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | |   (5920)   ~ (all_40_1 = e2)
% 196.10/31.87  | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | REDUCE: (687), (5920) imply:
% 196.10/31.87  | | | | | | | | | | | |   (5921)   ~ (all_10_1 = e2)
% 196.10/31.87  | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.87  | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | |   (5922)   ~ (all_46_0 = e1)
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | REDUCE: (5904), (5922) imply:
% 196.10/31.87  | | | | | | | | | | | | |   (5923)  $false
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | CLOSE: (5923) is inconsistent.
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | Case 2:
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | |   (5924)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.87  | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | |   (5925)  all_58_15 = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | COMBINE_EQS: (541), (5925) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5926)  all_14_2 = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (573), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5927)   ~ (all_52_7 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (591), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5928)   ~ (all_52_15 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (603), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5929)   ~ (all_52_23 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (606), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5930)   ~ (all_52_25 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (609), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5931)   ~ (all_52_29 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (613), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5932)  op(e0, e0) = all_52_30
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (63), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5933)  op(e0, e0) = all_14_1
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (61), (5926) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5934)  op(e0, e0) = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.87  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5932), (5933)
% 196.10/31.87  | | | | | | | | | | | | | |              gives:
% 196.10/31.87  | | | | | | | | | | | | | |   (5935)  all_52_30 = all_14_1
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.87  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5932), (5934)
% 196.10/31.87  | | | | | | | | | | | | | |              gives:
% 196.10/31.87  | | | | | | | | | | | | | |   (5936)  all_52_30 = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | COMBINE_EQS: (5935), (5936) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5937)  all_14_1 = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | SIMP: (5937) implies:
% 196.10/31.87  | | | | | | | | | | | | | |   (5938)  all_14_1 = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (62), (5938) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5939)  op(e0, e0) = all_14_0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.87  | | | | | | | | | | | | | |              e0, e0, simplifying with (5934), (5939) gives:
% 196.10/31.87  | | | | | | | | | | | | | |   (5940)  all_14_0 = e0
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (5911), (5940) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5941)   ~ (e3 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (5907), (5940) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5942)   ~ (e2 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | REDUCE: (5915), (5940) imply:
% 196.10/31.87  | | | | | | | | | | | | | |   (5943)   ~ (e1 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.87  | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | |   (5944)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.87  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.87  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.87  | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | BETA: splitting (5944) gives:
% 196.10/31.87  | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | Case 1:
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5945)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.87  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | ALPHA: (5945) implies:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5946)  all_52_6 = e0
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5947)  all_52_4 = e1
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5948)  all_52_2 = e2
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5949)  all_52_0 = e3
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (185), (5948) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5950)  op(all_52_3, all_52_3) = e2
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (184), (5947) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5951)  op(all_52_5, all_52_5) = e1
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (183), (5946) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5952)  op(all_52_7, all_52_7) = e0
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (610), (5949) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5953)  op(all_6_2, all_6_2) = e3
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (51), (53), (61), (156),
% 196.10/31.87  | | | | | | | | | | | | | | | |            (157), (271), (272), (273), (304), (306), (321),
% 196.10/31.87  | | | | | | | | | | | | | | | |            (332), (343), (346), (351), (387), (405), (431),
% 196.10/31.87  | | | | | | | | | | | | | | | |            (542), (543), (547), (555), (564), (569), (571),
% 196.10/31.87  | | | | | | | | | | | | | | | |            (572), (573), (600), (772), (5917), (5919),
% 196.10/31.87  | | | | | | | | | | | | | | | |            (5921), (5925), (5927), (5928), (5950), (5951),
% 196.10/31.87  | | | | | | | | | | | | | | | |            (5952), (5953), (function-axioms) are inconsistent
% 196.10/31.87  | | | | | | | | | | | | | | | |            by sub-proof #1348.
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | Case 2:
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5954)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.87  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | ALPHA: (5954) implies:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5955)  all_52_14 = e0
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5956)  all_52_12 = e1
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5957)  all_52_10 = e2
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5958)  all_52_8 = e3
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (182), (5958) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5959)  op(all_52_9, all_52_9) = e3
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (180), (5956) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5960)  op(all_52_13, all_52_13) = e1
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (179), (5955) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5961)  op(all_52_15, all_52_15) = e0
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.87  | | | | | | | | | | | | | | | | REDUCE: (611), (5957) imply:
% 196.10/31.87  | | | | | | | | | | | | | | | |   (5962)  op(all_4_2, all_4_2) = e2
% 196.10/31.87  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (51), (53), (156), (158), (168), (169), (174),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (175), (177), (178), (272), (273), (278), (279),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (282), (283), (284), (304), (305), (306), (308),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (309), (313), (314), (317), (321), (325), (327),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (333), (346), (351), (366), (372), (375), (387),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (415), (417), (427),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (431), (542), (543), (544), (545), (546), (547),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (548), (549), (555), (557), (559), (561), (563),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (567), (571), (572), (574), (575), (576), (577),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (578), (580), (582), (586), (589), (595), (596),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (604), (605), (612), (772), (5903), (5905),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (5917), (5925), (5927), (5928), (5930), (5934),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (5959), (5960), (5961), (5962), (function-axioms)
% 196.10/31.88  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #316.
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | |   (5963)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.88  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.88  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.88  | | | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.10/31.88  | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.88  | | | | | | | | | | | | | | |            (177), (178), (180), (182), (183), (271), (272),
% 196.10/31.88  | | | | | | | | | | | | | | |            (273), (278), (279), (281), (282), (283), (284),
% 196.10/31.88  | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (313), (317),
% 196.10/31.88  | | | | | | | | | | | | | | |            (320), (321), (322), (325), (326), (330), (331),
% 196.10/31.88  | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (372),
% 196.10/31.88  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.88  | | | | | | | | | | | | | | |            (415), (417), (427), (431), (529), (542), (543),
% 196.10/31.88  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.88  | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (566),
% 196.10/31.88  | | | | | | | | | | | | | | |            (567), (570), (571), (572), (576), (577), (578),
% 196.10/31.88  | | | | | | | | | | | | | | |            (580), (582), (584), (588), (589), (590), (593),
% 196.10/31.88  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 196.10/31.88  | | | | | | | | | | | | | | |            (604), (605), (610), (611), (612), (641), (5903),
% 196.10/31.88  | | | | | | | | | | | | | | |            (5905), (5919), (5924), (5925), (5927), (5928),
% 196.10/31.88  | | | | | | | | | | | | | | |            (5929), (5930), (5931), (5934), (5963),
% 196.10/31.88  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.88  | | | | | | | | | | | | | | |            #303.
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | |   (5964)   ~ (all_58_15 = e0)
% 196.10/31.88  | | | | | | | | | | | | | |   (5965)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.88  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.88  | | | | | | | | | | | | | |             e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | ALPHA: (5965) implies:
% 196.10/31.88  | | | | | | | | | | | | | |   (5966)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.10/31.88  | | | | | | | | | | | | | |   (5967)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (541), (5964) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5968)   ~ (all_14_2 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.88  | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 196.10/31.88  | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 196.10/31.88  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.10/31.88  | | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.10/31.88  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 196.10/31.88  | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.10/31.88  | | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 196.10/31.88  | | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.10/31.88  | | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.10/31.88  | | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.10/31.88  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.10/31.88  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.88  | | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (529), (538),
% 196.10/31.88  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.10/31.88  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.10/31.88  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.10/31.88  | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.88  | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.88  | | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.10/31.88  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.10/31.88  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.10/31.88  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.10/31.88  | | | | | | | | | | | | | |            (772), (5903), (5905), (5907), (5911), (5915),
% 196.10/31.88  | | | | | | | | | | | | | |            (5924), (5966), (5967), (5968), (function-axioms)
% 196.10/31.88  | | | | | | | | | | | | | |            are inconsistent by sub-proof #270.
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | |   (5969)  all_40_1 = e2
% 196.10/31.88  | | | | | | | | | | | |   (5970)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | COMBINE_EQS: (687), (5969) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5971)  all_10_1 = e2
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | SIMP: (5971) implies:
% 196.10/31.88  | | | | | | | | | | | |   (5972)  all_10_1 = e2
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (5917), (5972) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5973)   ~ (e3 = e2)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (53), (5972) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5974)  op(all_10_2, e1) = e2
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (52), (5972) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5975)  op(e1, e2) = all_10_0
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.10/31.88  | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (5975)
% 196.10/31.88  | | | | | | | | | | | |              gives:
% 196.10/31.88  | | | | | | | | | | | |   (5976)  all_52_13 = all_10_0
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | COMBINE_EQS: (421), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5977)  all_56_9 = all_10_0
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | COMBINE_EQS: (366), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5978)  all_58_7 = all_10_0
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (568), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5979)   ~ (all_52_5 = all_10_0)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (575), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5980)   ~ (all_52_9 = all_10_0)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (589), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5981)   ~ (all_52_29 = all_10_0)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | SIMP: (5981) implies:
% 196.10/31.88  | | | | | | | | | | | |   (5982)   ~ (all_52_29 = all_10_0)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (588), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5983)   ~ (all_10_0 = all_10_2)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (580), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5984)   ~ (all_10_0 = all_4_2)
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | REDUCE: (180), (5976) imply:
% 196.10/31.88  | | | | | | | | | | | |   (5985)  op(all_10_0, all_10_0) = all_52_12
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.88  | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | Case 1:
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | |   (5986)   ~ (all_46_0 = e1)
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | REDUCE: (5904), (5986) imply:
% 196.10/31.88  | | | | | | | | | | | | |   (5987)  $false
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | CLOSE: (5987) is inconsistent.
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | |   (5988)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.88  | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | Case 1:
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | |   (5989)  all_58_15 = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | COMBINE_EQS: (541), (5989) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5990)  all_14_2 = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (573), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5991)   ~ (all_52_7 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (591), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5992)   ~ (all_52_15 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (603), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5993)   ~ (all_52_23 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (606), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5994)   ~ (all_52_25 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (609), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5995)   ~ (all_52_29 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (613), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5996)  op(e0, e0) = all_52_30
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (63), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5997)  op(e0, e0) = all_14_1
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (61), (5990) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (5998)  op(e0, e0) = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.88  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5996), (5997)
% 196.10/31.88  | | | | | | | | | | | | | |              gives:
% 196.10/31.88  | | | | | | | | | | | | | |   (5999)  all_52_30 = all_14_1
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.88  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (5996), (5998)
% 196.10/31.88  | | | | | | | | | | | | | |              gives:
% 196.10/31.88  | | | | | | | | | | | | | |   (6000)  all_52_30 = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | COMBINE_EQS: (5999), (6000) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (6001)  all_14_1 = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (62), (6001) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (6002)  op(e0, e0) = all_14_0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.88  | | | | | | | | | | | | | |              e0, e0, simplifying with (5998), (6002) gives:
% 196.10/31.88  | | | | | | | | | | | | | |   (6003)  all_14_0 = e0
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (5911), (6003) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (6004)   ~ (e3 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (5907), (6003) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (6005)   ~ (e2 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | REDUCE: (5915), (6003) imply:
% 196.10/31.88  | | | | | | | | | | | | | |   (6006)   ~ (e1 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | Case 1:
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | |   (6007)  all_56_9 = e3
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | REF_CLOSE: (5906), (5977), (6007) are inconsistent by
% 196.10/31.88  | | | | | | | | | | | | | | |            sub-proof #1006.
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | |   (6008)   ~ (all_56_9 = e3)
% 196.10/31.88  | | | | | | | | | | | | | | |   (6009)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | Case 1:
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | |   (6010)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.88  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.88  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | BETA: splitting (6010) gives:
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6011)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.88  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (183),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (184), (185), (273), (274), (277), (278), (282),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (310), (311),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (312), (317), (321), (325), (332), (351), (352),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (427), (431), (526), (542), (543), (544), (545),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (561), (564), (566), (567), (569), (570), (571),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (573), (586), (590), (596), (598), (604), (605),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (607), (610), (611), (612), (767), (5906), (5909),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (5970), (5974), (5977), (5978), (5979), (5982),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (5984), (5989), (5991), (5994), (5995), (5998),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (6009), (6011), (function-axioms) are inconsistent
% 196.10/31.88  | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6012)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.88  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | ALPHA: (6012) implies:
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6013)  all_52_14 = e0
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6014)  all_52_12 = e1
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6015)  all_52_10 = e2
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6016)  all_52_8 = e3
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | REDUCE: (182), (6016) imply:
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6017)  op(all_52_9, all_52_9) = e3
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | REDUCE: (179), (6013) imply:
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6018)  op(all_52_15, all_52_15) = e0
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | REDUCE: (5985), (6014) imply:
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6019)  op(all_10_0, all_10_0) = e1
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | REDUCE: (611), (6015) imply:
% 196.10/31.88  | | | | | | | | | | | | | | | | |   (6020)  op(all_4_2, all_4_2) = e2
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (158),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (168), (169), (175), (272), (273), (284), (305),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (325), (327), (346), (351), (394), (405), (431),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (542), (543), (548), (549), (555), (557), (571),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (574), (576), (577), (582), (772), (5903), (5905),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (5906), (5909), (5977), (5978), (5980), (5983),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (5989), (6009), (6017), (6018), (6019), (6020),
% 196.10/31.88  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.88  | | | | | | | | | | | | | | | | |            #268.
% 196.10/31.88  | | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | |   (6021)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.88  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.88  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (177), (178), (180), (182), (183), (271), (272),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (273), (278), (279), (281), (282), (283), (284),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (313), (317),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (320), (321), (322), (325), (326), (330), (331),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (372),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (415), (417), (427), (431), (529), (542), (543),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (566),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (567), (570), (571), (572), (576), (577), (578),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (580), (582), (584), (588), (589), (590), (593),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (604), (605), (610), (611), (612), (641), (5903),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (5905), (5919), (5988), (5989), (5991), (5992),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (5993), (5994), (5995), (5998), (6021),
% 196.10/31.88  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.88  | | | | | | | | | | | | | | | |            #303.
% 196.10/31.88  | | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | | End of split
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | Case 2:
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.88  | | | | | | | | | | | | | |   (6022)   ~ (all_58_15 = e0)
% 196.10/31.88  | | | | | | | | | | | | | |   (6023)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.88  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.88  | | | | | | | | | | | | | |             e0)
% 196.10/31.88  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.89  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.10/31.89  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.89  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.10/31.89  | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.10/31.89  | | | | | | | | | | | | | |            (275), (276), (277), (280), (281), (282), (283),
% 196.10/31.89  | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.10/31.89  | | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 196.10/31.89  | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 196.10/31.89  | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.10/31.89  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.10/31.89  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (526),
% 196.10/31.89  | | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.10/31.89  | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.89  | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.10/31.89  | | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (571),
% 196.10/31.89  | | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.10/31.89  | | | | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 196.10/31.89  | | | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 196.10/31.89  | | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.10/31.89  | | | | | | | | | | | | | |            (610), (611), (612), (613), (641), (767), (772),
% 196.10/31.89  | | | | | | | | | | | | | |            (5903), (5905), (5906), (5909), (5970), (5974),
% 196.10/31.89  | | | | | | | | | | | | | |            (5977), (5978), (5979), (5980), (5983), (5985),
% 196.10/31.89  | | | | | | | | | | | | | |            (5988), (6022), (6023), (function-axioms) are
% 196.10/31.89  | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | |   (6024)  all_32_1 = e3
% 196.10/31.89  | | | | | | | | | | |   (6025)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | COMBINE_EQS: (663), (6024) imply:
% 196.10/31.89  | | | | | | | | | | |   (6026)  all_4_1 = e3
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | COMBINE_EQS: (686), (6026) imply:
% 196.10/31.89  | | | | | | | | | | |   (6027)  all_38_1 = e3
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (38), (6026) imply:
% 196.10/31.89  | | | | | | | | | | |   (6028)  op(all_4_2, e2) = e3
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (37), (6026) imply:
% 196.10/31.89  | | | | | | | | | | |   (6029)  op(e2, e3) = all_4_0
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 196.10/31.89  | | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (6029)
% 196.10/31.89  | | | | | | | | | | |              gives:
% 196.10/31.89  | | | | | | | | | | |   (6030)  all_52_3 = all_4_0
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | COMBINE_EQS: (411), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6031)  all_56_4 = all_4_0
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | COMBINE_EQS: (387), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6032)  all_58_2 = all_4_0
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (562), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6033)   ~ (all_52_5 = all_4_0)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | SIMP: (6033) implies:
% 196.10/31.89  | | | | | | | | | | |   (6034)   ~ (all_52_5 = all_4_0)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (563), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6035)   ~ (all_52_7 = all_4_0)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | SIMP: (6035) implies:
% 196.10/31.89  | | | | | | | | | | |   (6036)   ~ (all_52_7 = all_4_0)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (551), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6037)   ~ (all_6_2 = all_4_0)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | SIMP: (6037) implies:
% 196.10/31.89  | | | | | | | | | | |   (6038)   ~ (all_6_2 = all_4_0)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (564), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6039)   ~ (all_4_0 = all_4_2)
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | REDUCE: (185), (6030) imply:
% 196.10/31.89  | | | | | | | | | | |   (6040)  op(all_4_0, all_4_0) = all_52_2
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | BETA: splitting (124) gives:
% 196.10/31.89  | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | |   (6041)   ~ (all_38_0 = e1)
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | REDUCE: (766), (6041) imply:
% 196.10/31.89  | | | | | | | | | | | |   (6042)   ~ (all_4_0 = e1)
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | |   (6043)   ~ (all_46_0 = e1)
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | REDUCE: (5904), (6043) imply:
% 196.10/31.89  | | | | | | | | | | | | |   (6044)  $false
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | CLOSE: (6044) is inconsistent.
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | |   (6045)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | |   (6046)  all_58_15 = e0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | COMBINE_EQS: (541), (6046) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6047)  all_14_2 = e0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (573), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6048)   ~ (all_52_7 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (591), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6049)   ~ (all_52_15 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (606), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6050)   ~ (all_52_25 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (609), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6051)   ~ (all_52_29 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (613), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6052)  op(e0, e0) = all_52_30
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (63), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6053)  op(e0, e0) = all_14_1
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (61), (6047) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6054)  op(e0, e0) = e0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.89  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6052), (6053)
% 196.10/31.89  | | | | | | | | | | | | | |              gives:
% 196.10/31.89  | | | | | | | | | | | | | |   (6055)  all_52_30 = all_14_1
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.89  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6052), (6054)
% 196.10/31.89  | | | | | | | | | | | | | |              gives:
% 196.10/31.89  | | | | | | | | | | | | | |   (6056)  all_52_30 = e0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | COMBINE_EQS: (6055), (6056) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6057)  all_14_1 = e0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (62), (6057) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6058)  op(e0, e0) = all_14_0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.89  | | | | | | | | | | | | | |              e0, e0, simplifying with (6054), (6058) gives:
% 196.10/31.89  | | | | | | | | | | | | | |   (6059)  all_14_0 = e0
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (5911), (6059) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6060)   ~ (e3 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (5907), (6059) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6061)   ~ (e2 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REDUCE: (5915), (6059) imply:
% 196.10/31.89  | | | | | | | | | | | | | |   (6062)   ~ (e1 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | |   (6063)  all_56_4 = e3
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | REF_CLOSE: (5913), (6031), (6063) are inconsistent by
% 196.10/31.89  | | | | | | | | | | | | | | |            sub-proof #980.
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | |   (6064)   ~ (all_56_4 = e3)
% 196.10/31.89  | | | | | | | | | | | | | | |   (6065)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | |   (6066)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.89  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.89  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | BETA: splitting (6066) gives:
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6067)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.89  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (611), (721), (6025), (6028), (6031), (6032),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (6039), (6040), (6042), (6065), (6067),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.89  | | | | | | | | | | | | | | | | |            #970.
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6068)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.89  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | ALPHA: (6068) implies:
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6069)  all_52_14 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6070)  all_52_12 = e1
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6071)  all_52_10 = e2
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6072)  all_52_8 = e3
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REDUCE: (182), (6072) imply:
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6073)  op(all_52_9, all_52_9) = e3
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REDUCE: (180), (6070) imply:
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6074)  op(all_52_13, all_52_13) = e1
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REDUCE: (179), (6069) imply:
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6075)  op(all_52_15, all_52_15) = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REDUCE: (611), (6071) imply:
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6076)  op(all_4_2, all_4_2) = e2
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | |   (6077)  all_56_13 = e3
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (41), (43), (158), (168), (175),
% 196.10/31.89  | | | | | | | | | | | | | | | | | |            (273), (284), (305), (346), (351), (394), (431),
% 196.10/31.89  | | | | | | | | | | | | | | | | | |            (542), (543), (555), (557), (571), (576), (577),
% 196.10/31.89  | | | | | | | | | | | | | | | | | |            (582), (5903), (5905), (6046), (6073), (6075),
% 196.10/31.89  | | | | | | | | | | | | | | | | | |            (6077), (function-axioms) are inconsistent by
% 196.10/31.89  | | | | | | | | | | | | | | | | | |            sub-proof #321.
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | |   (6078)   ~ (all_56_13 = e3)
% 196.10/31.89  | | | | | | | | | | | | | | | | | |   (6079)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | REDUCE: (346), (6078) imply:
% 196.10/31.89  | | | | | | | | | | | | | | | | | |   (6080)   ~ (all_52_15 = e3)
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |   (6081)  all_58_12 = e3
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (41), (43), (162), (167),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (169), (183), (276), (320), (325), (326), (328),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (330), (351), (366), (387), (405), (421), (543),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (557), (561), (571), (574),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (5905), (6028), (6048), (6073), (6074), (6081),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            #262.
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |   (6082)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (51), (53), (156), (273), (304),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (305), (346), (351), (431), (542), (543), (571),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (572), (582), (5917), (6046), (6048), (6049),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (6054), (6075), (6076), (6079), (6080), (6082),
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.89  | | | | | | | | | | | | | | | | | | |            #1288.
% 196.10/31.89  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | |   (6083)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.89  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.89  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | BETA: splitting (6083) gives:
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6084)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.10/31.89  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (51), (53), (158), (162), (167), (168), (169),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (172), (173), (175), (177), (178), (179), (182),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (183), (184), (272), (273), (274), (277), (278),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (279), (280), (282), (283), (304), (306), (312),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (317), (320), (321), (326), (328), (330), (332),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (333), (346), (351), (352), (367), (372), (375),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (387), (388), (393), (405), (415), (417), (427),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (431), (523), (539), (542), (543), (545), (546),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (559),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (561), (567), (569), (570), (572), (574), (584),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (590), (593), (595), (598), (604), (607), (610),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (611), (612), (721), (5905), (5913), (6025),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (6028), (6031), (6032), (6034), (6036), (6038),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (6039), (6042), (6046), (6048), (6049), (6050),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (6051), (6054), (6065), (6084), (function-axioms)
% 196.10/31.89  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #259.
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | |   (6085)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.10/31.89  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (309), (321), (332),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (372), (375), (388), (405), (427), (523), (539),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (544), (545), (548), (561), (574), (584), (586),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (605), (607), (610), (611), (721), (5913), (6025),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (6028), (6031), (6032), (6038), (6039), (6042),
% 196.10/31.89  | | | | | | | | | | | | | | | | |            (6046), (6050), (6085), (function-axioms) are
% 196.10/31.89  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 196.10/31.89  | | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | |   (6086)   ~ (all_58_15 = e0)
% 196.10/31.89  | | | | | | | | | | | | | |   (6087)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.89  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.89  | | | | | | | | | | | | | |             e0)
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.89  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.10/31.89  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.89  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.10/31.89  | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.10/31.89  | | | | | | | | | | | | | |            (275), (277), (278), (279), (280), (281), (282),
% 196.10/31.89  | | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 196.10/31.89  | | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.10/31.89  | | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.10/31.89  | | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.10/31.89  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.10/31.89  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.89  | | | | | | | | | | | | | |            (415), (417), (427), (431), (523), (529), (538),
% 196.10/31.89  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.10/31.89  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.10/31.89  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.10/31.89  | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.89  | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.89  | | | | | | | | | | | | | |            (584), (586), (587), (589), (590), (591), (592),
% 196.10/31.89  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.10/31.89  | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.10/31.89  | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (641), (721),
% 196.10/31.89  | | | | | | | | | | | | | |            (772), (5903), (5905), (5913), (6025), (6028),
% 196.10/31.89  | | | | | | | | | | | | | |            (6031), (6032), (6038), (6039), (6040), (6042),
% 196.10/31.89  | | | | | | | | | | | | | |            (6045), (6086), (6087), (function-axioms) are
% 196.10/31.89  | | | | | | | | | | | | | |            inconsistent by sub-proof #255.
% 196.10/31.89  | | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | | End of split
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | Case 2:
% 196.10/31.89  | | | | | | | | | | | | 
% 196.10/31.89  | | | | | | | | | | | |   (6088)  all_38_0 = e1
% 196.10/31.90  | | | | | | | | | | | |   (6089)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | COMBINE_EQS: (766), (6088) imply:
% 196.10/31.90  | | | | | | | | | | | |   (6090)  all_4_0 = e1
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | SIMP: (6090) implies:
% 196.10/31.90  | | | | | | | | | | | |   (6091)  all_4_0 = e1
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 196.10/31.90  | | | | | | | | | | | |            (6027), (6028), (6039), (6089), (6091),
% 196.10/31.90  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.90  | | | | | | | | | | | |            #927.
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | |   (6092)  all_30_1 = e3
% 196.10/31.90  | | | | | | | | | |   (6093)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | COMBINE_EQS: (670), (6092) imply:
% 196.10/31.90  | | | | | | | | | |   (6094)  all_10_1 = e3
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | REDUCE: (53), (6094) imply:
% 196.10/31.90  | | | | | | | | | |   (6095)  op(all_10_2, e1) = e3
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | REDUCE: (52), (6094) imply:
% 196.10/31.90  | | | | | | | | | |   (6096)  op(e1, e3) = all_10_0
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.10/31.90  | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (6096)
% 196.10/31.90  | | | | | | | | | |              gives:
% 196.10/31.90  | | | | | | | | | |   (6097)  all_52_5 = all_10_0
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | COMBINE_EQS: (367), (6097) imply:
% 196.10/31.90  | | | | | | | | | |   (6098)  all_56_8 = all_10_0
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | COMBINE_EQS: (547), (6097) imply:
% 196.10/31.90  | | | | | | | | | |   (6099)  all_58_6 = all_10_0
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | REDUCE: (568), (6097) imply:
% 196.10/31.90  | | | | | | | | | |   (6100)   ~ (all_52_13 = all_10_0)
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | SIMP: (6100) implies:
% 196.10/31.90  | | | | | | | | | |   (6101)   ~ (all_52_13 = all_10_0)
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | REDUCE: (570), (6097) imply:
% 196.10/31.90  | | | | | | | | | |   (6102)   ~ (all_52_29 = all_10_0)
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | SIMP: (6102) implies:
% 196.10/31.90  | | | | | | | | | |   (6103)   ~ (all_52_29 = all_10_0)
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | REDUCE: (569), (6097) imply:
% 196.10/31.90  | | | | | | | | | |   (6104)   ~ (all_10_0 = all_10_2)
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | REDUCE: (184), (6097) imply:
% 196.10/31.90  | | | | | | | | | |   (6105)  op(all_10_0, all_10_0) = all_52_4
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | BETA: splitting (109) gives:
% 196.10/31.90  | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | |   (6106)   ~ (all_32_1 = e3)
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | REDUCE: (663), (6106) imply:
% 196.10/31.90  | | | | | | | | | | |   (6107)   ~ (all_4_1 = e3)
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | |   (6108)   ~ (all_46_0 = e1)
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | REDUCE: (5904), (6108) imply:
% 196.10/31.90  | | | | | | | | | | | |   (6109)  $false
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | CLOSE: (6109) is inconsistent.
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | |   (6110)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | |   (6111)  all_58_15 = e0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | COMBINE_EQS: (541), (6111) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6112)  all_14_2 = e0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (573), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6113)   ~ (all_52_7 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (591), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6114)   ~ (all_52_15 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (603), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6115)   ~ (all_52_23 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (606), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6116)   ~ (all_52_25 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (608), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6117)   ~ (all_52_27 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (609), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6118)   ~ (all_52_29 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (613), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6119)  op(e0, e0) = all_52_30
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (63), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6120)  op(e0, e0) = all_14_1
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (61), (6112) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6121)  op(e0, e0) = e0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.90  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6119), (6120)
% 196.10/31.90  | | | | | | | | | | | | |              gives:
% 196.10/31.90  | | | | | | | | | | | | |   (6122)  all_52_30 = all_14_1
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.90  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6119), (6121)
% 196.10/31.90  | | | | | | | | | | | | |              gives:
% 196.10/31.90  | | | | | | | | | | | | |   (6123)  all_52_30 = e0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | COMBINE_EQS: (6122), (6123) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6124)  all_14_1 = e0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (62), (6124) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6125)  op(e0, e0) = all_14_0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.90  | | | | | | | | | | | | |              e0, e0, simplifying with (6121), (6125) gives:
% 196.10/31.90  | | | | | | | | | | | | |   (6126)  all_14_0 = e0
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (5911), (6126) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6127)   ~ (e3 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (5907), (6126) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6128)   ~ (e2 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (5915), (6126) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6129)   ~ (e1 = e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | BETA: splitting (277) gives:
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | |   (6130)  all_56_8 = e3
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | REF_CLOSE: (5906), (6098), (6130) are inconsistent by
% 196.10/31.90  | | | | | | | | | | | | | |            sub-proof #926.
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | |   (6131)   ~ (all_56_8 = e3)
% 196.10/31.90  | | | | | | | | | | | | | |   (6132)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | |   (6133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.90  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.90  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | BETA: splitting (6133) gives:
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6134)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.90  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (311), (361), (459), (593),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (750), (5909), (6093), (6095), (6098), (6099),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (6104), (6105), (6132), (6134), (function-axioms)
% 196.10/31.90  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #667.
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6135)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.90  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | ALPHA: (6135) implies:
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6136)  all_52_14 = e0
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6137)  all_52_12 = e1
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6138)  all_52_10 = e2
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6139)  all_52_8 = e3
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | REDUCE: (182), (6139) imply:
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6140)  op(all_52_9, all_52_9) = e3
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | REDUCE: (180), (6137) imply:
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6141)  op(all_52_13, all_52_13) = e1
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | REDUCE: (179), (6136) imply:
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6142)  op(all_52_15, all_52_15) = e0
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | REDUCE: (611), (6138) imply:
% 196.10/31.90  | | | | | | | | | | | | | | | |   (6143)  op(all_4_2, all_4_2) = e2
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (43),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (51), (158), (166), (168), (169), (172), (173),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (271),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (272), (273), (275), (278), (279), (282), (283),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (284), (305), (306), (307), (308), (309), (313),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (314), (317), (321), (325), (326), (327), (330),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (361), (366),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (415), (417), (427), (431), (459), (529), (542),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (548), (549), (551),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (565), (566),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (571), (572), (574), (575), (576), (577), (578),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (580), (582), (586), (588), (589), (590), (593),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (594), (595), (596), (600), (602), (604), (605),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (607), (612), (641), (750), (772), (5903), (5905),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (5906), (5909), (6093), (6095), (6099), (6101),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (6103), (6104), (6110), (6111), (6113), (6114),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (6115), (6116), (6117), (6121), (6140), (6141),
% 196.10/31.90  | | | | | | | | | | | | | | | |            (6142), (6143), (function-axioms) are inconsistent
% 196.10/31.90  | | | | | | | | | | | | | | | |            by sub-proof #252.
% 196.10/31.90  | | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | |   (6144)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.90  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.90  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.90  | | | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.10/31.90  | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.90  | | | | | | | | | | | | | | |            (177), (178), (180), (182), (183), (271), (272),
% 196.10/31.90  | | | | | | | | | | | | | | |            (273), (278), (279), (281), (282), (283), (284),
% 196.10/31.90  | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (313), (317),
% 196.10/31.90  | | | | | | | | | | | | | | |            (320), (321), (322), (325), (326), (330), (331),
% 196.10/31.90  | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (372),
% 196.10/31.90  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.90  | | | | | | | | | | | | | | |            (415), (417), (427), (431), (529), (542), (543),
% 196.10/31.90  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.10/31.90  | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (566),
% 196.10/31.90  | | | | | | | | | | | | | | |            (567), (570), (571), (572), (576), (577), (578),
% 196.10/31.90  | | | | | | | | | | | | | | |            (580), (582), (584), (588), (589), (590), (593),
% 196.10/31.90  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 196.10/31.90  | | | | | | | | | | | | | | |            (604), (605), (610), (611), (612), (641), (5903),
% 196.10/31.90  | | | | | | | | | | | | | | |            (5905), (6107), (6110), (6111), (6113), (6114),
% 196.10/31.90  | | | | | | | | | | | | | | |            (6115), (6116), (6118), (6121), (6144),
% 196.10/31.90  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.90  | | | | | | | | | | | | | | |            #303.
% 196.10/31.90  | | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | |   (6145)   ~ (all_58_15 = e0)
% 196.10/31.90  | | | | | | | | | | | | |   (6146)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.90  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.90  | | | | | | | | | | | | |             e0)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.90  | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.10/31.90  | | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.90  | | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.90  | | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.90  | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.90  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.10/31.90  | | | | | | | | | | | | |            (305), (306), (307), (309), (311), (312), (313),
% 196.10/31.90  | | | | | | | | | | | | |            (314), (315), (316), (317), (319), (320), (321),
% 196.10/31.90  | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 196.10/31.90  | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.10/31.90  | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.10/31.90  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.10/31.90  | | | | | | | | | | | | |            (421), (427), (431), (459), (529), (538), (539),
% 196.10/31.90  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.10/31.90  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.10/31.90  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.10/31.90  | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.90  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.90  | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.10/31.90  | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.10/31.90  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.10/31.90  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.10/31.90  | | | | | | | | | | | | |            (750), (772), (5903), (5905), (5906), (5907),
% 196.10/31.90  | | | | | | | | | | | | |            (5909), (6093), (6095), (6098), (6099), (6104),
% 196.10/31.90  | | | | | | | | | | | | |            (6105), (6110), (6145), (6146), (function-axioms)
% 196.10/31.90  | | | | | | | | | | | | |            are inconsistent by sub-proof #250.
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | End of split
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | |   (6147)  all_32_1 = e3
% 196.10/31.90  | | | | | | | | | | |   (6148)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | COMBINE_EQS: (663), (6147) imply:
% 196.10/31.90  | | | | | | | | | | |   (6149)  all_4_1 = e3
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | SIMP: (6149) implies:
% 196.10/31.90  | | | | | | | | | | |   (6150)  all_4_1 = e3
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | COMBINE_EQS: (686), (6150) imply:
% 196.10/31.90  | | | | | | | | | | |   (6151)  all_38_1 = e3
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | REDUCE: (38), (6150) imply:
% 196.10/31.90  | | | | | | | | | | |   (6152)  op(all_4_2, e2) = e3
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | REDUCE: (37), (6150) imply:
% 196.10/31.90  | | | | | | | | | | |   (6153)  op(e2, e3) = all_4_0
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 196.10/31.90  | | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (6153)
% 196.10/31.90  | | | | | | | | | | |              gives:
% 196.10/31.90  | | | | | | | | | | |   (6154)  all_52_3 = all_4_0
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | COMBINE_EQS: (411), (6154) imply:
% 196.10/31.90  | | | | | | | | | | |   (6155)  all_56_4 = all_4_0
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | COMBINE_EQS: (387), (6154) imply:
% 196.10/31.90  | | | | | | | | | | |   (6156)  all_58_2 = all_4_0
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | REDUCE: (551), (6154) imply:
% 196.10/31.90  | | | | | | | | | | |   (6157)   ~ (all_6_2 = all_4_0)
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | SIMP: (6157) implies:
% 196.10/31.90  | | | | | | | | | | |   (6158)   ~ (all_6_2 = all_4_0)
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | REDUCE: (564), (6154) imply:
% 196.10/31.90  | | | | | | | | | | |   (6159)   ~ (all_4_0 = all_4_2)
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | REDUCE: (185), (6154) imply:
% 196.10/31.90  | | | | | | | | | | |   (6160)  op(all_4_0, all_4_0) = all_52_2
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | BETA: splitting (124) gives:
% 196.10/31.90  | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | |   (6161)   ~ (all_38_0 = e1)
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | REDUCE: (766), (6161) imply:
% 196.10/31.90  | | | | | | | | | | | |   (6162)   ~ (all_4_0 = e1)
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.90  | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | |   (6163)   ~ (all_46_0 = e1)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | REDUCE: (5904), (6163) imply:
% 196.10/31.90  | | | | | | | | | | | | |   (6164)  $false
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | CLOSE: (6164) is inconsistent.
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | Case 2:
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | |   (6165)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.90  | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | Case 1:
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | |   (6166)  all_58_15 = e0
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | COMBINE_EQS: (541), (6166) imply:
% 196.10/31.90  | | | | | | | | | | | | | |   (6167)  all_14_2 = e0
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | REDUCE: (573), (6167) imply:
% 196.10/31.90  | | | | | | | | | | | | | |   (6168)   ~ (all_52_7 = e0)
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | REDUCE: (603), (6167) imply:
% 196.10/31.90  | | | | | | | | | | | | | |   (6169)   ~ (all_52_23 = e0)
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | REDUCE: (606), (6167) imply:
% 196.10/31.90  | | | | | | | | | | | | | |   (6170)   ~ (all_52_25 = e0)
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | REDUCE: (613), (6167) imply:
% 196.10/31.90  | | | | | | | | | | | | | |   (6171)  op(e0, e0) = all_52_30
% 196.10/31.90  | | | | | | | | | | | | | | 
% 196.10/31.90  | | | | | | | | | | | | | | REDUCE: (63), (6167) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6172)  op(e0, e0) = all_14_1
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | REDUCE: (61), (6167) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6173)  op(e0, e0) = e0
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.91  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6171), (6172)
% 196.10/31.91  | | | | | | | | | | | | | |              gives:
% 196.10/31.91  | | | | | | | | | | | | | |   (6174)  all_52_30 = all_14_1
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.91  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6171), (6173)
% 196.10/31.91  | | | | | | | | | | | | | |              gives:
% 196.10/31.91  | | | | | | | | | | | | | |   (6175)  all_52_30 = e0
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | COMBINE_EQS: (6174), (6175) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6176)  all_14_1 = e0
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | SIMP: (6176) implies:
% 196.10/31.91  | | | | | | | | | | | | | |   (6177)  all_14_1 = e0
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | REDUCE: (62), (6177) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6178)  op(e0, e0) = all_14_0
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.91  | | | | | | | | | | | | | |              e0, e0, simplifying with (6173), (6178) gives:
% 196.10/31.91  | | | | | | | | | | | | | |   (6179)  all_14_0 = e0
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | REDUCE: (5911), (6179) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6180)   ~ (e3 = e0)
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | REDUCE: (5907), (6179) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6181)   ~ (e2 = e0)
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | REDUCE: (5915), (6179) imply:
% 196.10/31.91  | | | | | | | | | | | | | |   (6182)   ~ (e1 = e0)
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | |   (6183)  all_56_4 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | REF_CLOSE: (5913), (6155), (6183) are inconsistent by
% 196.10/31.91  | | | | | | | | | | | | | | |            sub-proof #980.
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | |   (6184)   ~ (all_56_4 = e3)
% 196.10/31.91  | | | | | | | | | | | | | | |   (6185)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | |   (6186)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.91  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.91  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | BETA: splitting (6186) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6187)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.91  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (611), (721), (6148), (6152), (6155), (6156),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (6159), (6160), (6162), (6185), (6187),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.91  | | | | | | | | | | | | | | | | |            #970.
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6188)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.91  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | ALPHA: (6188) implies:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6189)  all_52_12 = e1
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6190)  all_52_8 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REDUCE: (182), (6190) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6191)  op(all_52_9, all_52_9) = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REDUCE: (180), (6189) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6192)  op(all_52_13, all_52_13) = e1
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | |   (6193)  all_58_0 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (6193) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | | |   (6194)  all_6_2 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (41), (43), (5905), (6194), (function-axioms)
% 196.10/31.91  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #310.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | |   (6195)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | BETA: splitting (6195) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | |   (6196)  all_58_2 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5913), (6156), (6196) are inconsistent by
% 196.10/31.91  | | | | | | | | | | | | | | | | | | |            sub-proof #948.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | |   (6197)  all_58_6 = e3 | all_58_12 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (6197) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6198)  all_58_6 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5906), (6099), (6198) are inconsistent by
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            sub-proof #922.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6199)  all_58_12 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (41), (43), (162), (167),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (169), (183), (276), (320), (325), (326), (328),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (330), (351), (366), (387), (405), (421), (543),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (557), (561), (571), (574),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (5905), (6152), (6168), (6191), (6192), (6199),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            #262.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | |   (6200)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.91  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.91  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | BETA: splitting (6200) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6201)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.10/31.91  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | ALPHA: (6201) implies:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6202)  all_52_22 = e0
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6203)  all_52_20 = e1
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6204)  all_52_18 = e2
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6205)  all_52_16 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REDUCE: (178), (6205) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6206)  op(all_52_17, all_52_17) = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REDUCE: (177), (6204) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6207)  op(all_52_19, all_52_19) = e2
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REDUCE: (175), (6202) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6208)  op(all_52_23, all_52_23) = e0
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REDUCE: (612), (6203) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6209)  op(all_10_2, all_10_2) = e1
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | |   (6210)  all_58_0 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (6210) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | | |   (6211)  all_6_2 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (41), (43), (5905), (6211), (function-axioms)
% 196.10/31.91  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #310.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | |   (6212)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | BETA: splitting (6212) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | |   (6213)  all_58_2 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5913), (6156), (6213) are inconsistent by
% 196.10/31.91  | | | | | | | | | | | | | | | | | | |            sub-proof #948.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | |   (6214)  all_58_6 = e3 | all_58_12 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (6214) gives:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6215)  all_58_6 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5906), (6099), (6215) are inconsistent by
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            sub-proof #922.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6216)  all_58_12 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (6216) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6217)  all_52_7 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | SIMP: (6217) implies:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6218)  all_52_7 = e3
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (6218) imply:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6219)   ~ (all_52_15 = e3)
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | SIMP: (6219) implies:
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |   (6220)   ~ (all_52_15 = e3)
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (38), (41), (43), (51), (53),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (158), (168), (169), (172), (173), (174), (180),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (182), (183), (271), (273), (278), (279), (282),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (283), (284), (306), (309), (313), (317), (321),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (322), (325), (331), (333), (343), (351), (366),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (415), (417), (427), (431), (542), (543), (544),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (555), (557),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (559), (561), (563), (567), (571), (572), (577),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (578), (580), (584), (588), (589), (593), (594),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (604),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (605), (611), (5903), (5905), (6166), (6168),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (6169), (6170), (6173), (6206), (6207), (6208),
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            (6209), (6220), (function-axioms) are inconsistent
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | |            by sub-proof #313.
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | |   (6221)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.10/31.91  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (278), (280), (281), (282), (309), (321), (332),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (372), (375), (388), (405), (427), (523), (539),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (544), (545), (548), (561), (574), (584), (586),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (605), (607), (610), (611), (721), (5913), (6148),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (6152), (6155), (6156), (6158), (6159), (6162),
% 196.10/31.91  | | | | | | | | | | | | | | | | |            (6166), (6170), (6221), (function-axioms) are
% 196.10/31.91  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 196.10/31.91  | | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | |   (6222)   ~ (all_58_15 = e0)
% 196.10/31.91  | | | | | | | | | | | | | |   (6223)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.91  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.91  | | | | | | | | | | | | | |             e0)
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.91  | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.10/31.91  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.91  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.10/31.91  | | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.10/31.91  | | | | | | | | | | | | | |            (275), (277), (278), (279), (280), (281), (282),
% 196.10/31.91  | | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 196.10/31.91  | | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.10/31.91  | | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.10/31.91  | | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.10/31.91  | | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.10/31.91  | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.91  | | | | | | | | | | | | | |            (415), (417), (427), (431), (523), (529), (538),
% 196.10/31.91  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.10/31.91  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.10/31.91  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.10/31.91  | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.91  | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.91  | | | | | | | | | | | | | |            (584), (586), (587), (589), (590), (591), (592),
% 196.10/31.91  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.10/31.91  | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.10/31.91  | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (641), (721),
% 196.10/31.91  | | | | | | | | | | | | | |            (772), (5903), (5905), (5913), (6148), (6152),
% 196.10/31.91  | | | | | | | | | | | | | |            (6155), (6156), (6158), (6159), (6160), (6162),
% 196.10/31.91  | | | | | | | | | | | | | |            (6165), (6222), (6223), (function-axioms) are
% 196.10/31.91  | | | | | | | | | | | | | |            inconsistent by sub-proof #255.
% 196.10/31.91  | | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | |   (6224)  all_38_0 = e1
% 196.10/31.91  | | | | | | | | | | | |   (6225)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | COMBINE_EQS: (766), (6224) imply:
% 196.10/31.91  | | | | | | | | | | | |   (6226)  all_4_0 = e1
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 196.10/31.91  | | | | | | | | | | | |            (6151), (6152), (6159), (6225), (6226),
% 196.10/31.91  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.91  | | | | | | | | | | | |            #927.
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | |   (6227)  all_24_0 = e1
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.10/31.91  | | | | | | | | |            (53), (61), (62), (63), (114), (144), (156), (158),
% 196.10/31.91  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.10/31.91  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.10/31.91  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.10/31.91  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.10/31.91  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.10/31.91  | | | | | | | | |            (304), (305), (306), (307), (309), (311), (312),
% 196.10/31.91  | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 196.10/31.91  | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 196.10/31.91  | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 196.10/31.91  | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 196.10/31.91  | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 196.10/31.91  | | | | | | | | |            (417), (421), (427), (431), (491), (529), (538),
% 196.10/31.91  | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.10/31.91  | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.10/31.91  | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.10/31.91  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.91  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.91  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.10/31.91  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.10/31.91  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.10/31.91  | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.10/31.91  | | | | | | | | |            (685), (711), (765), (772), (5903), (5904), (5905),
% 196.10/31.91  | | | | | | | | |            (5907), (5911), (6227), (function-axioms) are
% 196.10/31.91  | | | | | | | | |            inconsistent by sub-proof #245.
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | End of split
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | |   (6228)  all_20_0 = e3
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | | COMBINE_EQS: (758), (6228) imply:
% 196.10/31.91  | | | | | | | |   (6229)  all_4_0 = e3
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | | SIMP: (6229) implies:
% 196.10/31.91  | | | | | | | |   (6230)  all_4_0 = e3
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | | REDUCE: (37), (6230) imply:
% 196.10/31.91  | | | | | | | |   (6231)  op(e2, all_4_1) = e3
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | | BETA: splitting (89) gives:
% 196.10/31.91  | | | | | | | | 
% 196.10/31.91  | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | |   (6232)   ~ (all_24_0 = e1)
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | REDUCE: (711), (6232) imply:
% 196.10/31.91  | | | | | | | | |   (6233)   ~ (all_14_0 = e1)
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | BETA: splitting (104) gives:
% 196.10/31.91  | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | |   (6234)   ~ (all_30_1 = e3)
% 196.10/31.91  | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | REDUCE: (670), (6234) imply:
% 196.10/31.91  | | | | | | | | | |   (6235)   ~ (all_10_1 = e3)
% 196.10/31.91  | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | BETA: splitting (129) gives:
% 196.10/31.91  | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | |   (6236)   ~ (all_40_1 = e2)
% 196.10/31.91  | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | REDUCE: (687), (6236) imply:
% 196.10/31.91  | | | | | | | | | | |   (6237)   ~ (all_10_1 = e2)
% 196.10/31.91  | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.91  | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | |   (6238)   ~ (all_46_0 = e1)
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | REDUCE: (5904), (6238) imply:
% 196.10/31.91  | | | | | | | | | | | |   (6239)  $false
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | CLOSE: (6239) is inconsistent.
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | Case 2:
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | |   (6240)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.91  | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | Case 1:
% 196.10/31.91  | | | | | | | | | | | | | 
% 196.10/31.91  | | | | | | | | | | | | |   (6241)  all_58_15 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | COMBINE_EQS: (541), (6241) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6242)  all_14_2 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (573), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6243)   ~ (all_52_7 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (591), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6244)   ~ (all_52_15 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (603), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6245)   ~ (all_52_23 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (606), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6246)   ~ (all_52_25 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (609), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6247)   ~ (all_52_29 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (613), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6248)  op(e0, e0) = all_52_30
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (63), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6249)  op(e0, e0) = all_14_1
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (61), (6242) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6250)  op(e0, e0) = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.92  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6248), (6249)
% 196.10/31.92  | | | | | | | | | | | | |              gives:
% 196.10/31.92  | | | | | | | | | | | | |   (6251)  all_52_30 = all_14_1
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.92  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6248), (6250)
% 196.10/31.92  | | | | | | | | | | | | |              gives:
% 196.10/31.92  | | | | | | | | | | | | |   (6252)  all_52_30 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | COMBINE_EQS: (6251), (6252) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6253)  all_14_1 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (62), (6253) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6254)  op(e0, e0) = all_14_0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.92  | | | | | | | | | | | | |              e0, e0, simplifying with (6250), (6254) gives:
% 196.10/31.92  | | | | | | | | | | | | |   (6255)  all_14_0 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (5911), (6255) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6256)   ~ (e3 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (5907), (6255) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6257)   ~ (e2 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (6233), (6255) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6258)   ~ (e1 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | |   (6259)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.92  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.92  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | BETA: splitting (6259) gives:
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | |   (6260)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.92  | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | ALPHA: (6260) implies:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6261)  all_52_6 = e0
% 196.10/31.92  | | | | | | | | | | | | | | |   (6262)  all_52_4 = e1
% 196.10/31.92  | | | | | | | | | | | | | | |   (6263)  all_52_2 = e2
% 196.10/31.92  | | | | | | | | | | | | | | |   (6264)  all_52_0 = e3
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (185), (6263) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6265)  op(all_52_3, all_52_3) = e2
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (184), (6262) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6266)  op(all_52_5, all_52_5) = e1
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (183), (6261) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6267)  op(all_52_7, all_52_7) = e0
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (610), (6264) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6268)  op(all_6_2, all_6_2) = e3
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (38), (41), (51), (53), (61),
% 196.10/31.92  | | | | | | | | | | | | | | |            (156), (157), (166), (179), (271), (272), (273),
% 196.10/31.92  | | | | | | | | | | | | | | |            (304), (306), (321), (332), (343), (346), (351),
% 196.10/31.92  | | | | | | | | | | | | | | |            (387), (405), (431), (542), (543), (547), (555),
% 196.10/31.92  | | | | | | | | | | | | | | |            (564), (569), (571), (572), (573), (600), (772),
% 196.10/31.92  | | | | | | | | | | | | | | |            (6231), (6235), (6237), (6241), (6243), (6244),
% 196.10/31.92  | | | | | | | | | | | | | | |            (6265), (6266), (6267), (6268), (function-axioms)
% 196.10/31.92  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #767.
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | Case 2:
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | |   (6269)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.92  | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | ALPHA: (6269) implies:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6270)  all_52_14 = e0
% 196.10/31.92  | | | | | | | | | | | | | | |   (6271)  all_52_12 = e1
% 196.10/31.92  | | | | | | | | | | | | | | |   (6272)  all_52_10 = e2
% 196.10/31.92  | | | | | | | | | | | | | | |   (6273)  all_52_8 = e3
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (182), (6273) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6274)  op(all_52_9, all_52_9) = e3
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (180), (6271) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6275)  op(all_52_13, all_52_13) = e1
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (179), (6270) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6276)  op(all_52_15, all_52_15) = e0
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REDUCE: (611), (6272) imply:
% 196.10/31.92  | | | | | | | | | | | | | | |   (6277)  op(all_4_2, all_4_2) = e2
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 196.10/31.92  | | | | | | | | | | | | | | |            (51), (53), (156), (158), (168), (169), (174),
% 196.10/31.92  | | | | | | | | | | | | | | |            (175), (177), (178), (272), (273), (278), (279),
% 196.10/31.92  | | | | | | | | | | | | | | |            (282), (283), (284), (304), (305), (306), (308),
% 196.10/31.92  | | | | | | | | | | | | | | |            (309), (313), (314), (317), (321), (325), (327),
% 196.10/31.92  | | | | | | | | | | | | | | |            (333), (346), (351), (366), (372), (375), (387),
% 196.10/31.92  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (415), (417), (427),
% 196.10/31.92  | | | | | | | | | | | | | | |            (431), (542), (543), (544), (545), (546), (547),
% 196.10/31.92  | | | | | | | | | | | | | | |            (548), (549), (555), (557), (559), (561), (563),
% 196.10/31.92  | | | | | | | | | | | | | | |            (567), (571), (572), (574), (575), (576), (577),
% 196.10/31.92  | | | | | | | | | | | | | | |            (578), (580), (582), (586), (589), (595), (596),
% 196.10/31.92  | | | | | | | | | | | | | | |            (604), (605), (612), (772), (5903), (5905),
% 196.10/31.92  | | | | | | | | | | | | | | |            (6235), (6241), (6243), (6244), (6246), (6250),
% 196.10/31.92  | | | | | | | | | | | | | | |            (6274), (6275), (6276), (6277), (function-axioms)
% 196.10/31.92  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #316.
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | End of split
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | Case 2:
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | |   (6278)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.92  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.92  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.92  | | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.10/31.92  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.10/31.92  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (271),
% 196.10/31.92  | | | | | | | | | | | | | |            (272), (273), (278), (279), (281), (282), (283),
% 196.10/31.92  | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 196.10/31.92  | | | | | | | | | | | | | |            (313), (317), (320), (321), (322), (325), (326),
% 196.10/31.92  | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.10/31.92  | | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (394),
% 196.10/31.92  | | | | | | | | | | | | | |            (405), (411), (415), (417), (427), (431), (529),
% 196.10/31.92  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.10/31.92  | | | | | | | | | | | | | |            (549), (551), (555), (557), (559), (561), (563),
% 196.10/31.92  | | | | | | | | | | | | | |            (564), (565), (566), (567), (570), (571), (572),
% 196.10/31.92  | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (588),
% 196.10/31.92  | | | | | | | | | | | | | |            (589), (590), (592), (593), (594), (595), (596),
% 196.10/31.92  | | | | | | | | | | | | | |            (597), (598), (600), (602), (604), (605), (610),
% 196.10/31.92  | | | | | | | | | | | | | |            (611), (612), (641), (5903), (5905), (6231),
% 196.10/31.92  | | | | | | | | | | | | | |            (6240), (6241), (6243), (6244), (6245), (6246),
% 196.10/31.92  | | | | | | | | | | | | | |            (6247), (6250), (6278), (function-axioms) are
% 196.10/31.92  | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | End of split
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | Case 2:
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | |   (6279)   ~ (all_58_15 = e0)
% 196.10/31.92  | | | | | | | | | | | | |   (6280)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.10/31.92  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.10/31.92  | | | | | | | | | | | | |             e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.10/31.92  | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 196.10/31.92  | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 196.10/31.92  | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.10/31.92  | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.10/31.92  | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 196.10/31.92  | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.10/31.92  | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 196.10/31.92  | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.10/31.92  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.10/31.92  | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.10/31.92  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.10/31.92  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.10/31.92  | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (529), (538),
% 196.10/31.92  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.10/31.92  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.10/31.92  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.10/31.92  | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.10/31.92  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.10/31.92  | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.10/31.92  | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.10/31.92  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.10/31.92  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.10/31.92  | | | | | | | | | | | | |            (772), (5903), (5905), (5907), (5911), (6233),
% 196.10/31.92  | | | | | | | | | | | | |            (6240), (6279), (6280), (function-axioms) are
% 196.10/31.92  | | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | End of split
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | End of split
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | Case 2:
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | |   (6281)  all_40_1 = e2
% 196.10/31.92  | | | | | | | | | | |   (6282)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | COMBINE_EQS: (687), (6281) imply:
% 196.10/31.92  | | | | | | | | | | |   (6283)  all_10_1 = e2
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | SIMP: (6283) implies:
% 196.10/31.92  | | | | | | | | | | |   (6284)  all_10_1 = e2
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (6235), (6284) imply:
% 196.10/31.92  | | | | | | | | | | |   (6285)   ~ (e3 = e2)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (53), (6284) imply:
% 196.10/31.92  | | | | | | | | | | |   (6286)  op(all_10_2, e1) = e2
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (52), (6284) imply:
% 196.10/31.92  | | | | | | | | | | |   (6287)  op(e1, e2) = all_10_0
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.10/31.92  | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (6287)
% 196.10/31.92  | | | | | | | | | | |              gives:
% 196.10/31.92  | | | | | | | | | | |   (6288)  all_52_13 = all_10_0
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | COMBINE_EQS: (421), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6289)  all_56_9 = all_10_0
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | COMBINE_EQS: (366), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6290)  all_58_7 = all_10_0
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (568), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6291)   ~ (all_52_5 = all_10_0)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (575), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6292)   ~ (all_52_9 = all_10_0)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (589), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6293)   ~ (all_52_29 = all_10_0)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | SIMP: (6293) implies:
% 196.10/31.92  | | | | | | | | | | |   (6294)   ~ (all_52_29 = all_10_0)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (588), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6295)   ~ (all_10_0 = all_10_2)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (580), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6296)   ~ (all_10_0 = all_4_2)
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | REDUCE: (180), (6288) imply:
% 196.10/31.92  | | | | | | | | | | |   (6297)  op(all_10_0, all_10_0) = all_52_12
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | BETA: splitting (144) gives:
% 196.10/31.92  | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | |   (6298)   ~ (all_46_0 = e1)
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | REDUCE: (5904), (6298) imply:
% 196.10/31.92  | | | | | | | | | | | |   (6299)  $false
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | CLOSE: (6299) is inconsistent.
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | Case 2:
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | |   (6300)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.10/31.92  | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | |   (6301)  all_58_15 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | COMBINE_EQS: (541), (6301) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6302)  all_14_2 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (573), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6303)   ~ (all_52_7 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (591), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6304)   ~ (all_52_15 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (603), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6305)   ~ (all_52_23 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (606), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6306)   ~ (all_52_25 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (609), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6307)   ~ (all_52_29 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (613), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6308)  op(e0, e0) = all_52_30
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (63), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6309)  op(e0, e0) = all_14_1
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (61), (6302) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6310)  op(e0, e0) = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.10/31.92  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6308), (6309)
% 196.10/31.92  | | | | | | | | | | | | |              gives:
% 196.10/31.92  | | | | | | | | | | | | |   (6311)  all_52_30 = all_14_1
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.10/31.92  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6308), (6310)
% 196.10/31.92  | | | | | | | | | | | | |              gives:
% 196.10/31.92  | | | | | | | | | | | | |   (6312)  all_52_30 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | COMBINE_EQS: (6311), (6312) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6313)  all_14_1 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | SIMP: (6313) implies:
% 196.10/31.92  | | | | | | | | | | | | |   (6314)  all_14_1 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (62), (6314) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6315)  op(e0, e0) = all_14_0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.10/31.92  | | | | | | | | | | | | |              e0, e0, simplifying with (6310), (6315) gives:
% 196.10/31.92  | | | | | | | | | | | | |   (6316)  all_14_0 = e0
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (5911), (6316) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6317)   ~ (e3 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (5907), (6316) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6318)   ~ (e2 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | REDUCE: (6233), (6316) imply:
% 196.10/31.92  | | | | | | | | | | | | |   (6319)   ~ (e1 = e0)
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | BETA: splitting (276) gives:
% 196.10/31.92  | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | |   (6320)  all_56_9 = e3
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | REF_CLOSE: (5906), (6289), (6320) are inconsistent by
% 196.10/31.92  | | | | | | | | | | | | | |            sub-proof #1006.
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | Case 2:
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | |   (6321)   ~ (all_56_9 = e3)
% 196.10/31.92  | | | | | | | | | | | | | |   (6322)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.10/31.92  | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | |   (6323)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.92  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.10/31.92  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | BETA: splitting (6323) gives:
% 196.10/31.92  | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | Case 1:
% 196.10/31.92  | | | | | | | | | | | | | | | | 
% 196.10/31.92  | | | | | | | | | | | | | | | |   (6324)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.10/31.92  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.10/31.92  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (183),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (184), (185), (273), (274), (277), (278), (282),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (310), (311),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (312), (317), (321), (325), (332), (351), (352),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (427), (431), (526), (542), (543), (544), (545),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (561), (564), (566), (567), (569), (570), (571),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (573), (586), (590), (596), (598), (604), (605),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (607), (610), (611), (612), (767), (5906), (5909),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (6282), (6286), (6289), (6290), (6291), (6294),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (6296), (6301), (6303), (6306), (6307), (6310),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (6322), (6324), (function-axioms) are inconsistent
% 196.10/31.93  | | | | | | | | | | | | | | | |            by sub-proof #729.
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | Case 2:
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6325)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.10/31.93  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | ALPHA: (6325) implies:
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6326)  all_52_14 = e0
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6327)  all_52_12 = e1
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6328)  all_52_10 = e2
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6329)  all_52_8 = e3
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | REDUCE: (182), (6329) imply:
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6330)  op(all_52_9, all_52_9) = e3
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | REDUCE: (179), (6326) imply:
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6331)  op(all_52_15, all_52_15) = e0
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | REDUCE: (6297), (6327) imply:
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6332)  op(all_10_0, all_10_0) = e1
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | REDUCE: (611), (6328) imply:
% 196.10/31.93  | | | | | | | | | | | | | | | |   (6333)  op(all_4_2, all_4_2) = e2
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (38), (41), (43), (51), (158),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (168), (169), (175), (272), (273), (284), (305),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (325), (327), (346), (351), (394), (405), (431),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (542), (543), (548), (549), (555), (557), (571),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (574), (576), (577), (582), (772), (5903), (5905),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (5906), (5909), (6289), (6290), (6292), (6295),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (6301), (6322), (6330), (6331), (6332), (6333),
% 196.10/31.93  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.10/31.93  | | | | | | | | | | | | | | | |            #268.
% 196.10/31.93  | | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | | End of split
% 196.10/31.93  | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | Case 2:
% 196.10/31.93  | | | | | | | | | | | | | | | 
% 196.10/31.93  | | | | | | | | | | | | | | |   (6334)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.10/31.93  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.10/31.93  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.10/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.93  | | | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.58/31.93  | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.93  | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (271),
% 196.58/31.93  | | | | | | | | | | | | | | |            (272), (273), (278), (279), (281), (282), (283),
% 196.58/31.93  | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 196.58/31.93  | | | | | | | | | | | | | | |            (313), (317), (320), (321), (322), (325), (326),
% 196.58/31.93  | | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.58/31.93  | | | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (394),
% 196.58/31.93  | | | | | | | | | | | | | | |            (405), (411), (415), (417), (427), (431), (529),
% 196.58/31.93  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.58/31.93  | | | | | | | | | | | | | | |            (549), (551), (555), (557), (559), (561), (563),
% 196.58/31.93  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (570), (571), (572),
% 196.58/31.93  | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (588),
% 196.58/31.93  | | | | | | | | | | | | | | |            (589), (590), (592), (593), (594), (595), (596),
% 196.58/31.93  | | | | | | | | | | | | | | |            (597), (598), (600), (602), (604), (605), (610),
% 196.58/31.93  | | | | | | | | | | | | | | |            (611), (612), (641), (5903), (5905), (6231),
% 196.58/31.93  | | | | | | | | | | | | | | |            (6300), (6301), (6303), (6304), (6305), (6306),
% 196.58/31.93  | | | | | | | | | | | | | | |            (6307), (6310), (6334), (function-axioms) are
% 196.58/31.93  | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | End of split
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | End of split
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | Case 2:
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | |   (6335)   ~ (all_58_15 = e0)
% 196.58/31.93  | | | | | | | | | | | | |   (6336)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.93  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.93  | | | | | | | | | | | | |             e0)
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.93  | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.58/31.93  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.93  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.58/31.93  | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.58/31.93  | | | | | | | | | | | | |            (275), (276), (277), (280), (281), (282), (283),
% 196.58/31.93  | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.58/31.93  | | | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 196.58/31.93  | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 196.58/31.93  | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.58/31.93  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.58/31.93  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (526),
% 196.58/31.93  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.58/31.93  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.58/31.93  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.58/31.93  | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (571),
% 196.58/31.93  | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.58/31.93  | | | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 196.58/31.93  | | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 196.58/31.93  | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.58/31.93  | | | | | | | | | | | | |            (610), (611), (612), (613), (641), (767), (772),
% 196.58/31.93  | | | | | | | | | | | | |            (5903), (5905), (5906), (5909), (6282), (6286),
% 196.58/31.93  | | | | | | | | | | | | |            (6289), (6290), (6291), (6292), (6295), (6297),
% 196.58/31.93  | | | | | | | | | | | | |            (6300), (6335), (6336), (function-axioms) are
% 196.58/31.93  | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | End of split
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | End of split
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | End of split
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | Case 2:
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | |   (6337)  all_30_1 = e3
% 196.58/31.93  | | | | | | | | | |   (6338)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | COMBINE_EQS: (670), (6337) imply:
% 196.58/31.93  | | | | | | | | | |   (6339)  all_10_1 = e3
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | REDUCE: (53), (6339) imply:
% 196.58/31.93  | | | | | | | | | |   (6340)  op(all_10_2, e1) = e3
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | REDUCE: (52), (6339) imply:
% 196.58/31.93  | | | | | | | | | |   (6341)  op(e1, e3) = all_10_0
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.58/31.93  | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (6341)
% 196.58/31.93  | | | | | | | | | |              gives:
% 196.58/31.93  | | | | | | | | | |   (6342)  all_52_5 = all_10_0
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | COMBINE_EQS: (367), (6342) imply:
% 196.58/31.93  | | | | | | | | | |   (6343)  all_56_8 = all_10_0
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | COMBINE_EQS: (547), (6342) imply:
% 196.58/31.93  | | | | | | | | | |   (6344)  all_58_6 = all_10_0
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | REDUCE: (568), (6342) imply:
% 196.58/31.93  | | | | | | | | | |   (6345)   ~ (all_52_13 = all_10_0)
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | SIMP: (6345) implies:
% 196.58/31.93  | | | | | | | | | |   (6346)   ~ (all_52_13 = all_10_0)
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | REDUCE: (570), (6342) imply:
% 196.58/31.93  | | | | | | | | | |   (6347)   ~ (all_52_29 = all_10_0)
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | SIMP: (6347) implies:
% 196.58/31.93  | | | | | | | | | |   (6348)   ~ (all_52_29 = all_10_0)
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | REDUCE: (569), (6342) imply:
% 196.58/31.93  | | | | | | | | | |   (6349)   ~ (all_10_0 = all_10_2)
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | REDUCE: (184), (6342) imply:
% 196.58/31.93  | | | | | | | | | |   (6350)  op(all_10_0, all_10_0) = all_52_4
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.93  | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | Case 1:
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | |   (6351)   ~ (all_46_0 = e1)
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | REDUCE: (5904), (6351) imply:
% 196.58/31.93  | | | | | | | | | | |   (6352)  $false
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | CLOSE: (6352) is inconsistent.
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | Case 2:
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | |   (6353)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.93  | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | Case 1:
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | |   (6354)  all_58_15 = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | COMBINE_EQS: (541), (6354) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6355)  all_14_2 = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (573), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6356)   ~ (all_52_7 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (591), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6357)   ~ (all_52_15 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (603), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6358)   ~ (all_52_23 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (606), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6359)   ~ (all_52_25 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (608), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6360)   ~ (all_52_27 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (609), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6361)   ~ (all_52_29 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (613), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6362)  op(e0, e0) = all_52_30
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (63), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6363)  op(e0, e0) = all_14_1
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (61), (6355) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6364)  op(e0, e0) = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.58/31.93  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6362), (6363)
% 196.58/31.93  | | | | | | | | | | | |              gives:
% 196.58/31.93  | | | | | | | | | | | |   (6365)  all_52_30 = all_14_1
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.58/31.93  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6362), (6364)
% 196.58/31.93  | | | | | | | | | | | |              gives:
% 196.58/31.93  | | | | | | | | | | | |   (6366)  all_52_30 = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | COMBINE_EQS: (6365), (6366) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6367)  all_14_1 = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | SIMP: (6367) implies:
% 196.58/31.93  | | | | | | | | | | | |   (6368)  all_14_1 = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (62), (6368) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6369)  op(e0, e0) = all_14_0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.58/31.93  | | | | | | | | | | | |              e0, e0, simplifying with (6364), (6369) gives:
% 196.58/31.93  | | | | | | | | | | | |   (6370)  all_14_0 = e0
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (5911), (6370) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6371)   ~ (e3 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (5907), (6370) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6372)   ~ (e2 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | REDUCE: (6233), (6370) imply:
% 196.58/31.93  | | | | | | | | | | | |   (6373)   ~ (e1 = e0)
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | BETA: splitting (277) gives:
% 196.58/31.93  | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | Case 1:
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | |   (6374)  all_56_8 = e3
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | REF_CLOSE: (5906), (6343), (6374) are inconsistent by
% 196.58/31.93  | | | | | | | | | | | | |            sub-proof #926.
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | Case 2:
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | |   (6375)   ~ (all_56_8 = e3)
% 196.58/31.93  | | | | | | | | | | | | |   (6376)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.93  | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | Case 1:
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | |   (6377)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.93  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/31.93  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | BETA: splitting (6377) gives:
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | Case 1:
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | |   (6378)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.93  | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (311), (361), (459), (593),
% 196.58/31.93  | | | | | | | | | | | | | | |            (750), (5909), (6338), (6340), (6343), (6344),
% 196.58/31.93  | | | | | | | | | | | | | | |            (6349), (6350), (6376), (6378), (function-axioms)
% 196.58/31.93  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #667.
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | Case 2:
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | |   (6379)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.93  | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | ALPHA: (6379) implies:
% 196.58/31.93  | | | | | | | | | | | | | | |   (6380)  all_52_14 = e0
% 196.58/31.93  | | | | | | | | | | | | | | |   (6381)  all_52_12 = e1
% 196.58/31.93  | | | | | | | | | | | | | | |   (6382)  all_52_10 = e2
% 196.58/31.93  | | | | | | | | | | | | | | |   (6383)  all_52_8 = e3
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REDUCE: (182), (6383) imply:
% 196.58/31.93  | | | | | | | | | | | | | | |   (6384)  op(all_52_9, all_52_9) = e3
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REDUCE: (180), (6381) imply:
% 196.58/31.93  | | | | | | | | | | | | | | |   (6385)  op(all_52_13, all_52_13) = e1
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REDUCE: (179), (6380) imply:
% 196.58/31.93  | | | | | | | | | | | | | | |   (6386)  op(all_52_15, all_52_15) = e0
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REDUCE: (611), (6382) imply:
% 196.58/31.93  | | | | | | | | | | | | | | |   (6387)  op(all_4_2, all_4_2) = e2
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (43),
% 196.58/31.93  | | | | | | | | | | | | | | |            (51), (158), (166), (168), (169), (172), (173),
% 196.58/31.93  | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (271),
% 196.58/31.93  | | | | | | | | | | | | | | |            (272), (273), (275), (278), (279), (282), (283),
% 196.58/31.93  | | | | | | | | | | | | | | |            (284), (305), (306), (307), (308), (309), (313),
% 196.58/31.93  | | | | | | | | | | | | | | |            (314), (317), (321), (325), (326), (327), (330),
% 196.58/31.93  | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (361), (366),
% 196.58/31.93  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.58/31.93  | | | | | | | | | | | | | | |            (415), (417), (427), (431), (459), (529), (542),
% 196.58/31.93  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (548), (549), (551),
% 196.58/31.93  | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (565), (566),
% 196.58/31.93  | | | | | | | | | | | | | | |            (571), (572), (574), (575), (576), (577), (578),
% 196.58/31.93  | | | | | | | | | | | | | | |            (580), (582), (586), (588), (589), (590), (593),
% 196.58/31.93  | | | | | | | | | | | | | | |            (594), (595), (596), (600), (602), (604), (605),
% 196.58/31.93  | | | | | | | | | | | | | | |            (607), (612), (641), (750), (772), (5903), (5905),
% 196.58/31.93  | | | | | | | | | | | | | | |            (5906), (5909), (6338), (6340), (6344), (6346),
% 196.58/31.93  | | | | | | | | | | | | | | |            (6348), (6349), (6353), (6354), (6356), (6357),
% 196.58/31.93  | | | | | | | | | | | | | | |            (6358), (6359), (6360), (6364), (6384), (6385),
% 196.58/31.93  | | | | | | | | | | | | | | |            (6386), (6387), (function-axioms) are inconsistent
% 196.58/31.93  | | | | | | | | | | | | | | |            by sub-proof #252.
% 196.58/31.93  | | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | | End of split
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | Case 2:
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.93  | | | | | | | | | | | | | |   (6388)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/31.93  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/31.93  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.93  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.94  | | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.58/31.94  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.94  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (271),
% 196.58/31.94  | | | | | | | | | | | | | |            (272), (273), (278), (279), (281), (282), (283),
% 196.58/31.94  | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 196.58/31.94  | | | | | | | | | | | | | |            (313), (317), (320), (321), (322), (325), (326),
% 196.58/31.94  | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.58/31.94  | | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (394),
% 196.58/31.94  | | | | | | | | | | | | | |            (405), (411), (415), (417), (427), (431), (529),
% 196.58/31.94  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.58/31.94  | | | | | | | | | | | | | |            (549), (551), (555), (557), (559), (561), (563),
% 196.58/31.94  | | | | | | | | | | | | | |            (564), (565), (566), (567), (570), (571), (572),
% 196.58/31.94  | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (588),
% 196.58/31.94  | | | | | | | | | | | | | |            (589), (590), (592), (593), (594), (595), (596),
% 196.58/31.94  | | | | | | | | | | | | | |            (597), (598), (600), (602), (604), (605), (610),
% 196.58/31.94  | | | | | | | | | | | | | |            (611), (612), (641), (5903), (5905), (6231),
% 196.58/31.94  | | | | | | | | | | | | | |            (6353), (6354), (6356), (6357), (6358), (6359),
% 196.58/31.94  | | | | | | | | | | | | | |            (6361), (6364), (6388), (function-axioms) are
% 196.58/31.94  | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | |   (6389)   ~ (all_58_15 = e0)
% 196.58/31.94  | | | | | | | | | | | |   (6390)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.94  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.94  | | | | | | | | | | | |             e0)
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.94  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.58/31.94  | | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.58/31.94  | | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.58/31.94  | | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.58/31.94  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.58/31.94  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.58/31.94  | | | | | | | | | | | |            (305), (306), (307), (309), (311), (312), (313),
% 196.58/31.94  | | | | | | | | | | | |            (314), (315), (316), (317), (319), (320), (321),
% 196.58/31.94  | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 196.58/31.94  | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.58/31.94  | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.58/31.94  | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.58/31.94  | | | | | | | | | | | |            (421), (427), (431), (459), (529), (538), (539),
% 196.58/31.94  | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.58/31.94  | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.58/31.94  | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.58/31.94  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.94  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.94  | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.94  | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.94  | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.94  | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.94  | | | | | | | | | | | |            (750), (772), (5903), (5905), (5906), (5907),
% 196.58/31.94  | | | | | | | | | | | |            (5909), (6338), (6340), (6343), (6344), (6349),
% 196.58/31.94  | | | | | | | | | | | |            (6350), (6353), (6389), (6390), (function-axioms)
% 196.58/31.94  | | | | | | | | | | | |            are inconsistent by sub-proof #250.
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | |   (6391)  all_24_0 = e1
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.58/31.94  | | | | | | | | |            (53), (61), (62), (63), (114), (144), (156), (158),
% 196.58/31.94  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.58/31.94  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.58/31.94  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.58/31.94  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.58/31.94  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.58/31.94  | | | | | | | | |            (304), (305), (306), (307), (309), (311), (312),
% 196.58/31.94  | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 196.58/31.94  | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 196.58/31.94  | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 196.58/31.94  | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 196.58/31.94  | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 196.58/31.94  | | | | | | | | |            (417), (421), (427), (431), (491), (529), (538),
% 196.58/31.94  | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/31.94  | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/31.94  | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/31.94  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.94  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.94  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.94  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.94  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.94  | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.94  | | | | | | | | |            (685), (711), (765), (772), (5903), (5904), (5905),
% 196.58/31.94  | | | | | | | | |            (5907), (5911), (6391), (function-axioms) are
% 196.58/31.94  | | | | | | | | |            inconsistent by sub-proof #245.
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | 
% 196.58/31.94  | | | | | | | End of split
% 196.58/31.94  | | | | | | | 
% 196.58/31.94  | | | | | | Case 2:
% 196.58/31.94  | | | | | | | 
% 196.58/31.94  | | | | | | |   (6392)  all_18_0 = e3
% 196.58/31.94  | | | | | | | 
% 196.58/31.94  | | | | | | | COMBINE_EQS: (761), (6392) imply:
% 196.58/31.94  | | | | | | |   (6393)  all_14_0 = e3
% 196.58/31.94  | | | | | | | 
% 196.58/31.94  | | | | | | | REDUCE: (62), (6393) imply:
% 196.58/31.94  | | | | | | |   (6394)  op(e0, all_14_1) = e3
% 196.58/31.94  | | | | | | | 
% 196.58/31.94  | | | | | | | BETA: splitting (104) gives:
% 196.58/31.94  | | | | | | | 
% 196.58/31.94  | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | 
% 196.58/31.94  | | | | | | | |   (6395)   ~ (all_30_1 = e3)
% 196.58/31.94  | | | | | | | | 
% 196.58/31.94  | | | | | | | | REDUCE: (670), (6395) imply:
% 196.58/31.94  | | | | | | | |   (6396)   ~ (all_10_1 = e3)
% 196.58/31.94  | | | | | | | | 
% 196.58/31.94  | | | | | | | | BETA: splitting (129) gives:
% 196.58/31.94  | | | | | | | | 
% 196.58/31.94  | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | |   (6397)   ~ (all_40_1 = e2)
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | REDUCE: (687), (6397) imply:
% 196.58/31.94  | | | | | | | | |   (6398)   ~ (all_10_1 = e2)
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.94  | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | |   (6399)   ~ (all_46_0 = e1)
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | REDUCE: (5904), (6399) imply:
% 196.58/31.94  | | | | | | | | | |   (6400)  $false
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | CLOSE: (6400) is inconsistent.
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | |   (6401)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.94  | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | |   (6402)  all_58_15 = e0
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (6394), (6402),
% 196.58/31.94  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.94  | | | | | | | | | | |            #678.
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | |   (6403)   ~ (all_58_15 = e0)
% 196.58/31.94  | | | | | | | | | | |   (6404)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.94  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.94  | | | | | | | | | | |             e0)
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | ALPHA: (6404) implies:
% 196.58/31.94  | | | | | | | | | | |   (6405)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.58/31.94  | | | | | | | | | | |   (6406)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | REDUCE: (541), (6403) imply:
% 196.58/31.94  | | | | | | | | | | |   (6407)   ~ (all_14_2 = e0)
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.94  | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | |   (6408)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.94  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/31.94  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | BETA: splitting (6408) gives:
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | |   (6409)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.94  | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.58/31.94  | | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.58/31.94  | | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.58/31.94  | | | | | | | | | | | | |            (5905), (6409), (function-axioms) are inconsistent
% 196.58/31.94  | | | | | | | | | | | | |            by sub-proof #302.
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | |   (6410)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.94  | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.94  | | | | | | | | | | | | |            (43), (51), (61), (62), (63), (156), (158), (162),
% 196.58/31.94  | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (174), (175),
% 196.58/31.94  | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 196.58/31.94  | | | | | | | | | | | | |            (270), (272), (273), (276), (277), (278), (279),
% 196.58/31.94  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.58/31.94  | | | | | | | | | | | | |            (305), (306), (309), (312), (313), (314), (315),
% 196.58/31.94  | | | | | | | | | | | | |            (316), (317), (320), (321), (323), (325), (326),
% 196.58/31.94  | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (346),
% 196.58/31.94  | | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (388),
% 196.58/31.94  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 196.58/31.94  | | | | | | | | | | | | |            (427), (431), (529), (538), (539), (540), (541),
% 196.58/31.94  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.58/31.94  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.58/31.94  | | | | | | | | | | | | |            (562), (563), (564), (567), (568), (570), (571),
% 196.58/31.94  | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.58/31.94  | | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 196.58/31.94  | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (597),
% 196.58/31.94  | | | | | | | | | | | | |            (600), (603), (604), (605), (606), (608), (609),
% 196.58/31.94  | | | | | | | | | | | | |            (610), (611), (612), (613), (641), (772), (5903),
% 196.58/31.94  | | | | | | | | | | | | |            (5905), (5907), (6401), (6405), (6406), (6410),
% 196.58/31.94  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.94  | | | | | | | | | | | | |            #286.
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | |   (6411)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/31.94  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/31.94  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | BETA: splitting (6411) gives:
% 196.58/31.94  | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | |   (6412)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/31.94  | | | | | | | | | | | | |           all_52_22 = e0
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | ALPHA: (6412) implies:
% 196.58/31.94  | | | | | | | | | | | | |   (6413)  all_52_22 = e0
% 196.58/31.94  | | | | | | | | | | | | |   (6414)  all_52_20 = e1
% 196.58/31.94  | | | | | | | | | | | | |   (6415)  all_52_18 = e2
% 196.58/31.94  | | | | | | | | | | | | |   (6416)  all_52_16 = e3
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | REDUCE: (178), (6416) imply:
% 196.58/31.94  | | | | | | | | | | | | |   (6417)  op(all_52_17, all_52_17) = e3
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | REDUCE: (177), (6415) imply:
% 196.58/31.94  | | | | | | | | | | | | |   (6418)  op(all_52_19, all_52_19) = e2
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | REDUCE: (175), (6413) imply:
% 196.58/31.94  | | | | | | | | | | | | |   (6419)  op(all_52_23, all_52_23) = e0
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | REDUCE: (612), (6414) imply:
% 196.58/31.94  | | | | | | | | | | | | |   (6420)  op(all_10_2, all_10_2) = e1
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.58/31.94  | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | |   (6421)  all_56_15 = e3
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | COMBINE_EQS: (538), (6421) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6422)  all_14_2 = e3
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | SIMP: (6422) implies:
% 196.58/31.94  | | | | | | | | | | | | | |   (6423)  all_14_2 = e3
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REDUCE: (573), (6423) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6424)   ~ (all_52_7 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REDUCE: (591), (6423) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6425)   ~ (all_52_15 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REDUCE: (603), (6423) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6426)   ~ (all_52_23 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REDUCE: (613), (6423) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6427)  op(e3, e3) = all_52_30
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REDUCE: (63), (6423) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6428)  op(e3, e0) = all_14_1
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 196.58/31.94  | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (6428)
% 196.58/31.94  | | | | | | | | | | | | | |              gives:
% 196.58/31.94  | | | | | | | | | | | | | |   (6429)  all_52_25 = all_14_1
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.58/31.94  | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (6427)
% 196.58/31.94  | | | | | | | | | | | | | |              gives:
% 196.58/31.94  | | | | | | | | | | | | | |   (6430)  all_52_30 = all_6_2
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | COMBINE_EQS: (545), (6429) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6431)  all_58_9 = all_14_1
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | |   (6432)  all_56_12 = e3
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | REF_CLOSE: (431), (6424), (6432) are inconsistent by
% 196.58/31.94  | | | | | | | | | | | | | | |            sub-proof #1383.
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | |   (6433)   ~ (all_56_12 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | |   (6434)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6435)  all_58_9 = e2
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (6431), (6435) imply:
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6436)  all_14_1 = e2
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | SIMP: (6436) implies:
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6437)  all_14_1 = e2
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | REDUCE: (6394), (6437) imply:
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6438)  op(e0, e2) = e3
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_15,
% 196.58/31.94  | | | | | | | | | | | | | | | |              e3, e2, e0, simplifying with (157), (6438) gives:
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6439)  all_52_15 = e3
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | REDUCE: (6425), (6439) imply:
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6440)  $false
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | CLOSE: (6440) is inconsistent.
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6441)   ~ (all_58_9 = e2)
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | REDUCE: (6431), (6441) imply:
% 196.58/31.94  | | | | | | | | | | | | | | | |   (6442)   ~ (all_14_1 = e2)
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | Case 1:
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | |   (6443)  all_56_6 = e3
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (51), (166), (168), (185), (281),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (411), (417), (431), (529), (551), (555), (563),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (565), (596), (641), (5905), (6401), (6417),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (6418), (6434), (6443), (function-axioms) are
% 196.58/31.94  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #240.
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | |   (6444)   ~ (all_56_6 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | | REDUCE: (417), (6444) imply:
% 196.58/31.94  | | | | | | | | | | | | | | | | |   (6445)   ~ (all_52_19 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (41), (53), (168), (317), (325),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (331), (332), (351), (366), (375), (387), (393),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (405), (542), (543), (546), (547), (548), (549),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (559), (564), (569), (588), (6398), (6417),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (6420), (6424), (6425), (6426), (6431), (6442),
% 196.58/31.94  | | | | | | | | | | | | | | | | |            (6445), (function-axioms) are inconsistent by
% 196.58/31.94  | | | | | | | | | | | | | | | | |            sub-proof #364.
% 196.58/31.94  | | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | End of split
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | Case 2:
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | |   (6446)   ~ (all_56_15 = e3)
% 196.58/31.94  | | | | | | | | | | | | | |   (6447)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.94  | | | | | | | | | | | | | | REDUCE: (538), (6446) imply:
% 196.58/31.94  | | | | | | | | | | | | | |   (6448)   ~ (all_14_2 = e3)
% 196.58/31.94  | | | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/31.95  | | | | | | | | | | | | | |            (51), (53), (61), (158), (162), (167), (168),
% 196.58/31.95  | | | | | | | | | | | | | |            (169), (172), (174), (182), (183), (184), (185),
% 196.58/31.95  | | | | | | | | | | | | | |            (272), (273), (274), (275), (282), (283), (284),
% 196.58/31.95  | | | | | | | | | | | | | |            (285), (306), (309), (313), (315), (317), (320),
% 196.58/31.95  | | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (329), (330),
% 196.58/31.95  | | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (352), (361),
% 196.58/31.95  | | | | | | | | | | | | | |            (366), (375), (387), (388), (393), (394), (405),
% 196.58/31.95  | | | | | | | | | | | | | |            (415), (431), (538), (540), (541), (542), (543),
% 196.58/31.95  | | | | | | | | | | | | | |            (544), (545), (546), (547), (549), (553), (555),
% 196.58/31.95  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (569),
% 196.58/31.95  | | | | | | | | | | | | | |            (571), (572), (573), (576), (577), (578), (587),
% 196.58/31.95  | | | | | | | | | | | | | |            (590), (595), (596), (600), (602), (603), (605),
% 196.58/31.95  | | | | | | | | | | | | | |            (606), (610), (5903), (5905), (6405), (6407),
% 196.58/31.95  | | | | | | | | | | | | | |            (6417), (6418), (6419), (6420), (6447), (6448),
% 196.58/31.95  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.95  | | | | | | | | | | | | | |            #274.
% 196.58/31.95  | | | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | |   (6449)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.58/31.95  | | | | | | | | | | | | |           all_52_30 = e0
% 196.58/31.95  | | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/31.95  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 196.58/31.95  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.95  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.58/31.95  | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 196.58/31.95  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.58/31.95  | | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 196.58/31.95  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.58/31.95  | | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 196.58/31.95  | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.58/31.95  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 196.58/31.95  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.58/31.95  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.58/31.95  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.58/31.95  | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 196.58/31.95  | | | | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 196.58/31.95  | | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 196.58/31.95  | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 196.58/31.95  | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 196.58/31.95  | | | | | | | | | | | | |            (641), (5903), (5905), (6401), (6405), (6407),
% 196.58/31.95  | | | | | | | | | | | | |            (6449), (function-axioms) are inconsistent by
% 196.58/31.95  | | | | | | | | | | | | |            sub-proof #271.
% 196.58/31.95  | | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | |   (6450)  all_40_1 = e2
% 196.58/31.95  | | | | | | | | |   (6451)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | COMBINE_EQS: (687), (6450) imply:
% 196.58/31.95  | | | | | | | | |   (6452)  all_10_1 = e2
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (6396), (6452) imply:
% 196.58/31.95  | | | | | | | | |   (6453)   ~ (e3 = e2)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (53), (6452) imply:
% 196.58/31.95  | | | | | | | | |   (6454)  op(all_10_2, e1) = e2
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (52), (6452) imply:
% 196.58/31.95  | | | | | | | | |   (6455)  op(e1, e2) = all_10_0
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.58/31.95  | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (6455)
% 196.58/31.95  | | | | | | | | |              gives:
% 196.58/31.95  | | | | | | | | |   (6456)  all_52_13 = all_10_0
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | COMBINE_EQS: (421), (6456) imply:
% 196.58/31.95  | | | | | | | | |   (6457)  all_56_9 = all_10_0
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | COMBINE_EQS: (366), (6456) imply:
% 196.58/31.95  | | | | | | | | |   (6458)  all_58_7 = all_10_0
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (568), (6456) imply:
% 196.58/31.95  | | | | | | | | |   (6459)   ~ (all_52_5 = all_10_0)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (575), (6456) imply:
% 196.58/31.95  | | | | | | | | |   (6460)   ~ (all_52_9 = all_10_0)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (588), (6456) imply:
% 196.58/31.95  | | | | | | | | |   (6461)   ~ (all_10_0 = all_10_2)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (180), (6456) imply:
% 196.58/31.95  | | | | | | | | |   (6462)  op(all_10_0, all_10_0) = all_52_12
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | |   (6463)   ~ (all_46_0 = e1)
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | REDUCE: (5904), (6463) imply:
% 196.58/31.95  | | | | | | | | | |   (6464)  $false
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | CLOSE: (6464) is inconsistent.
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | |   (6465)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | |   (6466)  all_58_15 = e0
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (6394), (6466),
% 196.58/31.95  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.95  | | | | | | | | | | |            #678.
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | |   (6467)   ~ (all_58_15 = e0)
% 196.58/31.95  | | | | | | | | | | |   (6468)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.95  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.95  | | | | | | | | | | |             e0)
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | ALPHA: (6468) implies:
% 196.58/31.95  | | | | | | | | | | |   (6469)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | REDUCE: (541), (6467) imply:
% 196.58/31.95  | | | | | | | | | | |   (6470)   ~ (all_14_2 = e0)
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.95  | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.58/31.95  | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.95  | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.58/31.95  | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.58/31.95  | | | | | | | | | | |            (275), (276), (277), (280), (281), (282), (283),
% 196.58/31.95  | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.58/31.95  | | | | | | | | | | |            (315), (316), (317), (319), (320), (321), (323),
% 196.58/31.95  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 196.58/31.95  | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.58/31.95  | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.58/31.95  | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (526),
% 196.58/31.95  | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.58/31.95  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.58/31.95  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.58/31.95  | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (571),
% 196.58/31.95  | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.58/31.95  | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 196.58/31.95  | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 196.58/31.95  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.58/31.95  | | | | | | | | | | |            (610), (611), (612), (613), (641), (767), (772),
% 196.58/31.95  | | | | | | | | | | |            (5903), (5905), (5906), (5909), (6451), (6454),
% 196.58/31.95  | | | | | | | | | | |            (6457), (6458), (6459), (6460), (6461), (6462),
% 196.58/31.95  | | | | | | | | | | |            (6465), (6469), (6470), (function-axioms) are
% 196.58/31.95  | | | | | | | | | | |            inconsistent by sub-proof #265.
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | |   (6471)  all_30_1 = e3
% 196.58/31.95  | | | | | | | |   (6472)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | COMBINE_EQS: (670), (6471) imply:
% 196.58/31.95  | | | | | | | |   (6473)  all_10_1 = e3
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | SIMP: (6473) implies:
% 196.58/31.95  | | | | | | | |   (6474)  all_10_1 = e3
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | REDUCE: (53), (6474) imply:
% 196.58/31.95  | | | | | | | |   (6475)  op(all_10_2, e1) = e3
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | REDUCE: (52), (6474) imply:
% 196.58/31.95  | | | | | | | |   (6476)  op(e1, e3) = all_10_0
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.58/31.95  | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (6476)
% 196.58/31.95  | | | | | | | |              gives:
% 196.58/31.95  | | | | | | | |   (6477)  all_52_5 = all_10_0
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | COMBINE_EQS: (367), (6477) imply:
% 196.58/31.95  | | | | | | | |   (6478)  all_56_8 = all_10_0
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | COMBINE_EQS: (547), (6477) imply:
% 196.58/31.95  | | | | | | | |   (6479)  all_58_6 = all_10_0
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | REDUCE: (569), (6477) imply:
% 196.58/31.95  | | | | | | | |   (6480)   ~ (all_10_0 = all_10_2)
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | REDUCE: (184), (6477) imply:
% 196.58/31.95  | | | | | | | |   (6481)  op(all_10_0, all_10_0) = all_52_4
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | |   (6482)   ~ (all_46_0 = e1)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (5904), (6482) imply:
% 196.58/31.95  | | | | | | | | |   (6483)  $false
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | CLOSE: (6483) is inconsistent.
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | |   (6484)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | |   (6485)  all_58_15 = e0
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (6394), (6485),
% 196.58/31.95  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.95  | | | | | | | | | |            #678.
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | |   (6486)   ~ (all_58_15 = e0)
% 196.58/31.95  | | | | | | | | | |   (6487)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.95  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.95  | | | | | | | | | |             e0)
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | ALPHA: (6487) implies:
% 196.58/31.95  | | | | | | | | | |   (6488)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.58/31.95  | | | | | | | | | |   (6489)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | REDUCE: (541), (6486) imply:
% 196.58/31.95  | | | | | | | | | |   (6490)   ~ (all_14_2 = e0)
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.95  | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.58/31.95  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.58/31.95  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.58/31.95  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.58/31.95  | | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.58/31.95  | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.58/31.95  | | | | | | | | | |            (305), (306), (307), (309), (311), (312), (313),
% 196.58/31.95  | | | | | | | | | |            (314), (315), (316), (317), (319), (320), (321),
% 196.58/31.95  | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 196.58/31.95  | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.58/31.95  | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.58/31.95  | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.58/31.95  | | | | | | | | | |            (421), (427), (431), (459), (529), (538), (539),
% 196.58/31.95  | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.58/31.95  | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.58/31.95  | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.58/31.95  | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.95  | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.95  | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.95  | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.95  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.95  | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.95  | | | | | | | | | |            (750), (772), (5903), (5905), (5906), (5907),
% 196.58/31.95  | | | | | | | | | |            (5909), (6472), (6475), (6478), (6479), (6480),
% 196.58/31.95  | | | | | | | | | |            (6481), (6484), (6488), (6489), (6490),
% 196.58/31.95  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.95  | | | | | | | | | |            #251.
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | End of split
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | End of split
% 196.58/31.95  | | | | | | | 
% 196.58/31.95  | | | | | | End of split
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | Case 2:
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | |   (6491)  all_16_0 = e2
% 196.58/31.95  | | | | | |   (6492)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | COMBINE_EQS: (760), (6491) imply:
% 196.58/31.95  | | | | | |   (6493)  all_10_0 = e2
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | SIMP: (6493) implies:
% 196.58/31.95  | | | | | |   (6494)  all_10_0 = e2
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | COMBINE_EQS: (756), (6494) imply:
% 196.58/31.95  | | | | | |   (6495)  all_26_0 = e2
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | REDUCE: (5906), (6494) imply:
% 196.58/31.95  | | | | | |   (6496)   ~ (e3 = e2)
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | REDUCE: (52), (6494) imply:
% 196.58/31.95  | | | | | |   (6497)  op(e1, all_10_1) = e2
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | BETA: splitting (74) gives:
% 196.58/31.95  | | | | | | 
% 196.58/31.95  | | | | | | Case 1:
% 196.58/31.95  | | | | | | | 
% 196.58/31.95  | | | | | | |   (6498)   ~ (all_18_0 = e3)
% 196.58/31.95  | | | | | | | 
% 196.58/31.95  | | | | | | | REDUCE: (761), (6498) imply:
% 196.58/31.95  | | | | | | |   (6499)   ~ (all_14_0 = e3)
% 196.58/31.95  | | | | | | | 
% 196.58/31.95  | | | | | | | BETA: splitting (79) gives:
% 196.58/31.95  | | | | | | | 
% 196.58/31.95  | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | |   (6500)   ~ (all_20_0 = e3)
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | REDUCE: (758), (6500) imply:
% 196.58/31.95  | | | | | | | |   (6501)   ~ (all_4_0 = e3)
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | BETA: splitting (89) gives:
% 196.58/31.95  | | | | | | | | 
% 196.58/31.95  | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | |   (6502)   ~ (all_24_0 = e1)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | REDUCE: (711), (6502) imply:
% 196.58/31.95  | | | | | | | | |   (6503)   ~ (all_14_0 = e1)
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | BETA: splitting (109) gives:
% 196.58/31.95  | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | |   (6504)   ~ (all_32_1 = e3)
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | REDUCE: (663), (6504) imply:
% 196.58/31.95  | | | | | | | | | |   (6505)   ~ (all_4_1 = e3)
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.95  | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | |   (6506)   ~ (all_46_0 = e1)
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | REDUCE: (5904), (6506) imply:
% 196.58/31.95  | | | | | | | | | | |   (6507)  $false
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | CLOSE: (6507) is inconsistent.
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | Case 2:
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | |   (6508)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.95  | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | Case 1:
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | |   (6509)  all_58_15 = e0
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | COMBINE_EQS: (541), (6509) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6510)  all_14_2 = e0
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (573), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6511)   ~ (all_52_7 = e0)
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (591), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6512)   ~ (all_52_15 = e0)
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (603), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6513)   ~ (all_52_23 = e0)
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (606), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6514)   ~ (all_52_25 = e0)
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (609), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6515)   ~ (all_52_29 = e0)
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (613), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6516)  op(e0, e0) = all_52_30
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (63), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6517)  op(e0, e0) = all_14_1
% 196.58/31.95  | | | | | | | | | | | | 
% 196.58/31.95  | | | | | | | | | | | | REDUCE: (61), (6510) imply:
% 196.58/31.95  | | | | | | | | | | | |   (6518)  op(e0, e0) = e0
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.58/31.96  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6516), (6517)
% 196.58/31.96  | | | | | | | | | | | |              gives:
% 196.58/31.96  | | | | | | | | | | | |   (6519)  all_52_30 = all_14_1
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.58/31.96  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6516), (6518)
% 196.58/31.96  | | | | | | | | | | | |              gives:
% 196.58/31.96  | | | | | | | | | | | |   (6520)  all_52_30 = e0
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | COMBINE_EQS: (6519), (6520) imply:
% 196.58/31.96  | | | | | | | | | | | |   (6521)  all_14_1 = e0
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | SIMP: (6521) implies:
% 196.58/31.96  | | | | | | | | | | | |   (6522)  all_14_1 = e0
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | REDUCE: (62), (6522) imply:
% 196.58/31.96  | | | | | | | | | | | |   (6523)  op(e0, e0) = all_14_0
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.58/31.96  | | | | | | | | | | | |              e0, e0, simplifying with (6518), (6523) gives:
% 196.58/31.96  | | | | | | | | | | | |   (6524)  all_14_0 = e0
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | REDUCE: (6499), (6524) imply:
% 196.58/31.96  | | | | | | | | | | | |   (6525)   ~ (e3 = e0)
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | REDUCE: (5907), (6524) imply:
% 196.58/31.96  | | | | | | | | | | | |   (6526)   ~ (e2 = e0)
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | REDUCE: (6503), (6524) imply:
% 196.58/31.96  | | | | | | | | | | | |   (6527)   ~ (e1 = e0)
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | |   (6528)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.96  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/31.96  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | BETA: splitting (6528) gives:
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | |   (6529)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.96  | | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | ALPHA: (6529) implies:
% 196.58/31.96  | | | | | | | | | | | | | |   (6530)  all_52_6 = e0
% 196.58/31.96  | | | | | | | | | | | | | |   (6531)  all_52_4 = e1
% 196.58/31.96  | | | | | | | | | | | | | |   (6532)  all_52_2 = e2
% 196.58/31.96  | | | | | | | | | | | | | |   (6533)  all_52_0 = e3
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REDUCE: (185), (6532) imply:
% 196.58/31.96  | | | | | | | | | | | | | |   (6534)  op(all_52_3, all_52_3) = e2
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REDUCE: (184), (6531) imply:
% 196.58/31.96  | | | | | | | | | | | | | |   (6535)  op(all_52_5, all_52_5) = e1
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REDUCE: (183), (6530) imply:
% 196.58/31.96  | | | | | | | | | | | | | |   (6536)  op(all_52_7, all_52_7) = e0
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REDUCE: (610), (6533) imply:
% 196.58/31.96  | | | | | | | | | | | | | |   (6537)  op(all_6_2, all_6_2) = e3
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (51), (53),
% 196.58/31.96  | | | | | | | | | | | | | |            (61), (156), (157), (161), (179), (272), (273),
% 196.58/31.96  | | | | | | | | | | | | | |            (277), (304), (305), (306), (321), (332), (346),
% 196.58/31.96  | | | | | | | | | | | | | |            (351), (367), (387), (405), (431), (515), (542),
% 196.58/31.96  | | | | | | | | | | | | | |            (543), (547), (555), (564), (567), (568), (569),
% 196.58/31.96  | | | | | | | | | | | | | |            (571), (572), (573), (680), (772), (6492), (6497),
% 196.58/31.96  | | | | | | | | | | | | | |            (6505), (6509), (6511), (6512), (6534), (6535),
% 196.58/31.96  | | | | | | | | | | | | | |            (6536), (6537), (function-axioms) are inconsistent
% 196.58/31.96  | | | | | | | | | | | | | |            by sub-proof #649.
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | |   (6538)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.96  | | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.58/31.96  | | | | | | | | | | | | | |            (53), (156), (158), (168), (169), (174), (175),
% 196.58/31.96  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (272), (273),
% 196.58/31.96  | | | | | | | | | | | | | |            (278), (279), (282), (283), (284), (305), (306),
% 196.58/31.96  | | | | | | | | | | | | | |            (308), (309), (313), (314), (317), (321), (325),
% 196.58/31.96  | | | | | | | | | | | | | |            (327), (333), (346), (351), (366), (372), (375),
% 196.58/31.96  | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (415), (417),
% 196.58/31.96  | | | | | | | | | | | | | |            (427), (431), (515), (542), (543), (544), (545),
% 196.58/31.96  | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 196.58/31.96  | | | | | | | | | | | | | |            (561), (563), (567), (571), (572), (574), (575),
% 196.58/31.96  | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (586), (589),
% 196.58/31.96  | | | | | | | | | | | | | |            (595), (596), (604), (605), (611), (612), (680),
% 196.58/31.96  | | | | | | | | | | | | | |            (772), (5903), (5905), (6492), (6509), (6511),
% 196.58/31.96  | | | | | | | | | | | | | |            (6512), (6514), (6518), (6538), (function-axioms)
% 196.58/31.96  | | | | | | | | | | | | | |            are inconsistent by sub-proof #238.
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | End of split
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | |   (6539)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/31.96  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/31.96  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.96  | | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.58/31.96  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.96  | | | | | | | | | | | | |            (177), (178), (180), (182), (183), (271), (272),
% 196.58/31.96  | | | | | | | | | | | | |            (273), (278), (279), (281), (282), (283), (284),
% 196.58/31.96  | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (313), (317),
% 196.58/31.96  | | | | | | | | | | | | |            (320), (321), (322), (325), (326), (330), (331),
% 196.58/31.96  | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (366), (372),
% 196.58/31.96  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.58/31.96  | | | | | | | | | | | | |            (415), (417), (427), (431), (529), (542), (543),
% 196.58/31.96  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.58/31.96  | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (566),
% 196.58/31.96  | | | | | | | | | | | | |            (567), (570), (571), (572), (576), (577), (578),
% 196.58/31.96  | | | | | | | | | | | | |            (580), (582), (584), (588), (589), (590), (593),
% 196.58/31.96  | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 196.58/31.96  | | | | | | | | | | | | |            (604), (605), (610), (611), (612), (641), (5903),
% 196.58/31.96  | | | | | | | | | | | | |            (5905), (6505), (6508), (6509), (6511), (6512),
% 196.58/31.96  | | | | | | | | | | | | |            (6513), (6514), (6515), (6518), (6539),
% 196.58/31.96  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.96  | | | | | | | | | | | | |            #303.
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | End of split
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | |   (6540)   ~ (all_58_15 = e0)
% 196.58/31.96  | | | | | | | | | | | |   (6541)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.96  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.96  | | | | | | | | | | | |             e0)
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.96  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 196.58/31.96  | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 196.58/31.96  | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.58/31.96  | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.58/31.96  | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 196.58/31.96  | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.58/31.96  | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 196.58/31.96  | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.58/31.96  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.58/31.96  | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.58/31.96  | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.58/31.96  | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.58/31.96  | | | | | | | | | | | |            (415), (417), (421), (427), (431), (529), (538),
% 196.58/31.96  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/31.96  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/31.96  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/31.96  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.96  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.96  | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.96  | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.96  | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.96  | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.96  | | | | | | | | | | | |            (772), (5903), (5905), (5907), (6499), (6503),
% 196.58/31.96  | | | | | | | | | | | |            (6508), (6540), (6541), (function-axioms) are
% 196.58/31.96  | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | End of split
% 196.58/31.96  | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | End of split
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | |   (6542)  all_32_1 = e3
% 196.58/31.96  | | | | | | | | | |   (6543)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | COMBINE_EQS: (663), (6542) imply:
% 196.58/31.96  | | | | | | | | | |   (6544)  all_4_1 = e3
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | SIMP: (6544) implies:
% 196.58/31.96  | | | | | | | | | |   (6545)  all_4_1 = e3
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | COMBINE_EQS: (686), (6545) imply:
% 196.58/31.96  | | | | | | | | | |   (6546)  all_38_1 = e3
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (38), (6545) imply:
% 196.58/31.96  | | | | | | | | | |   (6547)  op(all_4_2, e2) = e3
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (37), (6545) imply:
% 196.58/31.96  | | | | | | | | | |   (6548)  op(e2, e3) = all_4_0
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 196.58/31.96  | | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (6548)
% 196.58/31.96  | | | | | | | | | |              gives:
% 196.58/31.96  | | | | | | | | | |   (6549)  all_52_3 = all_4_0
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | COMBINE_EQS: (411), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6550)  all_56_4 = all_4_0
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | COMBINE_EQS: (387), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6551)  all_58_2 = all_4_0
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (562), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6552)   ~ (all_52_5 = all_4_0)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | SIMP: (6552) implies:
% 196.58/31.96  | | | | | | | | | |   (6553)   ~ (all_52_5 = all_4_0)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (563), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6554)   ~ (all_52_7 = all_4_0)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | SIMP: (6554) implies:
% 196.58/31.96  | | | | | | | | | |   (6555)   ~ (all_52_7 = all_4_0)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (551), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6556)   ~ (all_6_2 = all_4_0)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | SIMP: (6556) implies:
% 196.58/31.96  | | | | | | | | | |   (6557)   ~ (all_6_2 = all_4_0)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (564), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6558)   ~ (all_4_0 = all_4_2)
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | REDUCE: (185), (6549) imply:
% 196.58/31.96  | | | | | | | | | |   (6559)  op(all_4_0, all_4_0) = all_52_2
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | BETA: splitting (124) gives:
% 196.58/31.96  | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | |   (6560)   ~ (all_38_0 = e1)
% 196.58/31.96  | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | REDUCE: (766), (6560) imply:
% 196.58/31.96  | | | | | | | | | | |   (6561)   ~ (all_4_0 = e1)
% 196.58/31.96  | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.96  | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | |   (6562)   ~ (all_46_0 = e1)
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | REDUCE: (5904), (6562) imply:
% 196.58/31.96  | | | | | | | | | | | |   (6563)  $false
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | CLOSE: (6563) is inconsistent.
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | |   (6564)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.96  | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | |   (6565)  all_58_15 = e0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | COMBINE_EQS: (541), (6565) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6566)  all_14_2 = e0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (573), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6567)   ~ (all_52_7 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (591), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6568)   ~ (all_52_15 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (606), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6569)   ~ (all_52_25 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (609), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6570)   ~ (all_52_29 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (613), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6571)  op(e0, e0) = all_52_30
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (63), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6572)  op(e0, e0) = all_14_1
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (61), (6566) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6573)  op(e0, e0) = e0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.58/31.96  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6571), (6572)
% 196.58/31.96  | | | | | | | | | | | | |              gives:
% 196.58/31.96  | | | | | | | | | | | | |   (6574)  all_52_30 = all_14_1
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.58/31.96  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6571), (6573)
% 196.58/31.96  | | | | | | | | | | | | |              gives:
% 196.58/31.96  | | | | | | | | | | | | |   (6575)  all_52_30 = e0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | COMBINE_EQS: (6574), (6575) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6576)  all_14_1 = e0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (62), (6576) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6577)  op(e0, e0) = all_14_0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.58/31.96  | | | | | | | | | | | | |              e0, e0, simplifying with (6573), (6577) gives:
% 196.58/31.96  | | | | | | | | | | | | |   (6578)  all_14_0 = e0
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (6499), (6578) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6579)   ~ (e3 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (5907), (6578) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6580)   ~ (e2 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | REDUCE: (6503), (6578) imply:
% 196.58/31.96  | | | | | | | | | | | | |   (6581)   ~ (e1 = e0)
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | BETA: splitting (281) gives:
% 196.58/31.96  | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | |   (6582)  all_56_4 = e3
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | REF_CLOSE: (6501), (6550), (6582) are inconsistent by
% 196.58/31.96  | | | | | | | | | | | | | |            sub-proof #980.
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | |   (6583)   ~ (all_56_4 = e3)
% 196.58/31.96  | | | | | | | | | | | | | |   (6584)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.96  | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | |   (6585)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.96  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/31.96  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | BETA: splitting (6585) gives:
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | |   (6586)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.96  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (611), (721), (6543), (6547), (6550), (6551),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (6558), (6559), (6561), (6584), (6586),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.96  | | | | | | | | | | | | | | | |            #970.
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | |   (6587)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.96  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (53), (156), (158), (168), (169), (174), (175),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (272), (273),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (278), (279), (282), (283), (284), (305), (306),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (308), (309), (313), (314), (317), (321), (325),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (327), (333), (346), (351), (366), (372), (375),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (415), (417),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (427), (431), (515), (542), (543), (544), (545),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (561), (563), (567), (571), (572), (574), (575),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (586), (589),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (595), (596), (604), (605), (611), (612), (680),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (772), (5903), (5905), (6492), (6565), (6567),
% 196.58/31.96  | | | | | | | | | | | | | | | |            (6568), (6569), (6573), (6587), (function-axioms)
% 196.58/31.96  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #238.
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | End of split
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | Case 2:
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | |   (6588)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/31.96  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/31.96  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | BETA: splitting (6588) gives:
% 196.58/31.96  | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | Case 1:
% 196.58/31.96  | | | | | | | | | | | | | | | | 
% 196.58/31.96  | | | | | | | | | | | | | | | |   (6589)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/31.96  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.58/31.97  | | | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (51), (53), (158), (162), (167), (168), (169),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (172), (173), (175), (177), (178), (179), (182),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (183), (184), (272), (273), (274), (277), (278),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (279), (280), (282), (283), (304), (306), (312),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (317), (320), (321), (326), (328), (330), (332),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (333), (346), (351), (352), (367), (372), (375),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (387), (388), (393), (405), (415), (417), (427),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (431), (523), (539), (542), (543), (545), (546),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (559),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (561), (567), (569), (570), (572), (574), (584),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (590), (593), (595), (598), (604), (607), (610),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (611), (612), (721), (5905), (6501), (6543),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (6547), (6550), (6551), (6553), (6555), (6557),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (6558), (6561), (6565), (6567), (6568), (6569),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (6570), (6573), (6584), (6589), (function-axioms)
% 196.58/31.97  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #259.
% 196.58/31.97  | | | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | | | |   (6590)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.58/31.97  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.58/31.97  | | | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (278), (280), (282), (309), (321), (332), (372),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (375), (388), (405), (427), (523), (539), (544),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (545), (548), (561), (574), (584), (586), (605),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (607), (610), (611), (721), (6501), (6543),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (6547), (6550), (6551), (6557), (6558), (6561),
% 196.58/31.97  | | | | | | | | | | | | | | | |            (6565), (6569), (6584), (6590), (function-axioms)
% 196.58/31.97  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #940.
% 196.58/31.97  | | | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | |   (6591)   ~ (all_58_15 = e0)
% 196.58/31.97  | | | | | | | | | | | | |   (6592)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.97  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.97  | | | | | | | | | | | | |             e0)
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.97  | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.58/31.97  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.97  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.58/31.97  | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 196.58/31.97  | | | | | | | | | | | | |            (275), (277), (278), (279), (280), (281), (282),
% 196.58/31.97  | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 196.58/31.97  | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.58/31.97  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.58/31.97  | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.58/31.97  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.58/31.97  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.58/31.97  | | | | | | | | | | | | |            (415), (417), (427), (431), (523), (529), (538),
% 196.58/31.97  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/31.97  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/31.97  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/31.97  | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.97  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.97  | | | | | | | | | | | | |            (584), (586), (587), (589), (590), (591), (592),
% 196.58/31.97  | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.58/31.97  | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.58/31.97  | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (641), (721),
% 196.58/31.97  | | | | | | | | | | | | |            (772), (5903), (5905), (6501), (6543), (6547),
% 196.58/31.97  | | | | | | | | | | | | |            (6550), (6551), (6557), (6558), (6559), (6561),
% 196.58/31.97  | | | | | | | | | | | | |            (6564), (6591), (6592), (function-axioms) are
% 196.58/31.97  | | | | | | | | | | | | |            inconsistent by sub-proof #255.
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | |   (6593)  all_38_0 = e1
% 196.58/31.97  | | | | | | | | | | |   (6594)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | COMBINE_EQS: (766), (6593) imply:
% 196.58/31.97  | | | | | | | | | | |   (6595)  all_4_0 = e1
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 196.58/31.97  | | | | | | | | | | |            (6546), (6547), (6558), (6594), (6595),
% 196.58/31.97  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.97  | | | | | | | | | | |            #927.
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | |   (6596)  all_24_0 = e1
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.58/31.97  | | | | | | | | |            (53), (61), (62), (63), (114), (144), (156), (158),
% 196.58/31.97  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.58/31.97  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.58/31.97  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.58/31.97  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.58/31.97  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.58/31.97  | | | | | | | | |            (304), (305), (306), (307), (309), (311), (312),
% 196.58/31.97  | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 196.58/31.97  | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 196.58/31.97  | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 196.58/31.97  | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 196.58/31.97  | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 196.58/31.97  | | | | | | | | |            (417), (421), (427), (431), (491), (529), (538),
% 196.58/31.97  | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/31.97  | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/31.97  | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/31.97  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.97  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.97  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.97  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.97  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.97  | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.97  | | | | | | | | |            (685), (711), (765), (772), (5903), (5904), (5905),
% 196.58/31.97  | | | | | | | | |            (5907), (6499), (6596), (function-axioms) are
% 196.58/31.97  | | | | | | | | |            inconsistent by sub-proof #245.
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | |   (6597)  all_20_0 = e3
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | | COMBINE_EQS: (758), (6597) imply:
% 196.58/31.97  | | | | | | | |   (6598)  all_4_0 = e3
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | | SIMP: (6598) implies:
% 196.58/31.97  | | | | | | | |   (6599)  all_4_0 = e3
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | | REDUCE: (37), (6599) imply:
% 196.58/31.97  | | | | | | | |   (6600)  op(e2, all_4_1) = e3
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | | BETA: splitting (89) gives:
% 196.58/31.97  | | | | | | | | 
% 196.58/31.97  | | | | | | | | Case 1:
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | |   (6601)   ~ (all_24_0 = e1)
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | REDUCE: (711), (6601) imply:
% 196.58/31.97  | | | | | | | | |   (6602)   ~ (all_14_0 = e1)
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.97  | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | Case 1:
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | |   (6603)   ~ (all_46_0 = e1)
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | REDUCE: (5904), (6603) imply:
% 196.58/31.97  | | | | | | | | | |   (6604)  $false
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | CLOSE: (6604) is inconsistent.
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | |   (6605)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.97  | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | Case 1:
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | |   (6606)  all_58_15 = e0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | COMBINE_EQS: (541), (6606) imply:
% 196.58/31.97  | | | | | | | | | | |   (6607)  all_14_2 = e0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (573), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6608)   ~ (all_52_7 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (591), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6609)   ~ (all_52_15 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (603), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6610)   ~ (all_52_23 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (606), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6611)   ~ (all_52_25 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (609), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6612)   ~ (all_52_29 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (613), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6613)  op(e0, e0) = all_52_30
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (63), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6614)  op(e0, e0) = all_14_1
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (61), (6607) imply:
% 196.58/31.97  | | | | | | | | | | |   (6615)  op(e0, e0) = e0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.58/31.97  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6613), (6614)
% 196.58/31.97  | | | | | | | | | | |              gives:
% 196.58/31.97  | | | | | | | | | | |   (6616)  all_52_30 = all_14_1
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.58/31.97  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6613), (6615)
% 196.58/31.97  | | | | | | | | | | |              gives:
% 196.58/31.97  | | | | | | | | | | |   (6617)  all_52_30 = e0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | COMBINE_EQS: (6616), (6617) imply:
% 196.58/31.97  | | | | | | | | | | |   (6618)  all_14_1 = e0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (62), (6618) imply:
% 196.58/31.97  | | | | | | | | | | |   (6619)  op(e0, e0) = all_14_0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.58/31.97  | | | | | | | | | | |              e0, e0, simplifying with (6615), (6619) gives:
% 196.58/31.97  | | | | | | | | | | |   (6620)  all_14_0 = e0
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (6499), (6620) imply:
% 196.58/31.97  | | | | | | | | | | |   (6621)   ~ (e3 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (5907), (6620) imply:
% 196.58/31.97  | | | | | | | | | | |   (6622)   ~ (e2 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | REDUCE: (6602), (6620) imply:
% 196.58/31.97  | | | | | | | | | | |   (6623)   ~ (e1 = e0)
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.97  | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | Case 1:
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | |   (6624)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.97  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/31.97  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | BETA: splitting (6624) gives:
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | Case 1:
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | |   (6625)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.97  | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | ALPHA: (6625) implies:
% 196.58/31.97  | | | | | | | | | | | | |   (6626)  all_52_6 = e0
% 196.58/31.97  | | | | | | | | | | | | |   (6627)  all_52_4 = e1
% 196.58/31.97  | | | | | | | | | | | | |   (6628)  all_52_2 = e2
% 196.58/31.97  | | | | | | | | | | | | |   (6629)  all_52_0 = e3
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (185), (6628) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6630)  op(all_52_3, all_52_3) = e2
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (184), (6627) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6631)  op(all_52_5, all_52_5) = e1
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (183), (6626) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6632)  op(all_52_7, all_52_7) = e0
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (610), (6629) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6633)  op(all_6_2, all_6_2) = e3
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.97  | | | | | | | | | | | | |            (51), (53), (61), (156), (157), (161), (166),
% 196.58/31.97  | | | | | | | | | | | | |            (179), (272), (273), (277), (304), (305), (306),
% 196.58/31.97  | | | | | | | | | | | | |            (321), (332), (346), (351), (367), (387), (405),
% 196.58/31.97  | | | | | | | | | | | | |            (431), (515), (542), (543), (547), (555), (564),
% 196.58/31.97  | | | | | | | | | | | | |            (567), (568), (569), (571), (572), (573), (680),
% 196.58/31.97  | | | | | | | | | | | | |            (772), (6492), (6497), (6600), (6606), (6608),
% 196.58/31.97  | | | | | | | | | | | | |            (6609), (6630), (6631), (6632), (6633),
% 196.58/31.97  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.97  | | | | | | | | | | | | |            #626.
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | |   (6634)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.97  | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | ALPHA: (6634) implies:
% 196.58/31.97  | | | | | | | | | | | | |   (6635)  all_52_14 = e0
% 196.58/31.97  | | | | | | | | | | | | |   (6636)  all_52_12 = e1
% 196.58/31.97  | | | | | | | | | | | | |   (6637)  all_52_10 = e2
% 196.58/31.97  | | | | | | | | | | | | |   (6638)  all_52_8 = e3
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (182), (6638) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6639)  op(all_52_9, all_52_9) = e3
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (180), (6636) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6640)  op(all_52_13, all_52_13) = e1
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (179), (6635) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6641)  op(all_52_15, all_52_15) = e0
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REDUCE: (611), (6637) imply:
% 196.58/31.97  | | | | | | | | | | | | |   (6642)  op(all_4_2, all_4_2) = e2
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.58/31.97  | | | | | | | | | | | | |            (53), (156), (158), (168), (169), (174), (175),
% 196.58/31.97  | | | | | | | | | | | | |            (177), (178), (272), (273), (278), (279), (282),
% 196.58/31.97  | | | | | | | | | | | | |            (283), (284), (305), (306), (308), (309), (313),
% 196.58/31.97  | | | | | | | | | | | | |            (314), (317), (321), (325), (327), (333), (346),
% 196.58/31.97  | | | | | | | | | | | | |            (351), (366), (372), (375), (387), (388), (393),
% 196.58/31.97  | | | | | | | | | | | | |            (394), (405), (415), (417), (427), (431), (515),
% 196.58/31.97  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.58/31.97  | | | | | | | | | | | | |            (549), (555), (557), (559), (561), (563), (567),
% 196.58/31.97  | | | | | | | | | | | | |            (571), (572), (574), (575), (576), (577), (578),
% 196.58/31.97  | | | | | | | | | | | | |            (580), (582), (586), (589), (595), (596), (604),
% 196.58/31.97  | | | | | | | | | | | | |            (605), (612), (680), (772), (5903), (5905),
% 196.58/31.97  | | | | | | | | | | | | |            (6492), (6606), (6608), (6609), (6611), (6615),
% 196.58/31.97  | | | | | | | | | | | | |            (6639), (6640), (6641), (6642), (function-axioms)
% 196.58/31.97  | | | | | | | | | | | | |            are inconsistent by sub-proof #239.
% 196.58/31.97  | | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | | End of split
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | Case 2:
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.97  | | | | | | | | | | | |   (6643)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/31.97  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/31.97  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.97  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.98  | | | | | | | | | | | |            (43), (51), (53), (157), (158), (162), (166),
% 196.58/31.98  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.98  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (271),
% 196.58/31.98  | | | | | | | | | | | |            (272), (273), (278), (279), (281), (282), (283),
% 196.58/31.98  | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 196.58/31.98  | | | | | | | | | | | |            (313), (317), (320), (321), (322), (325), (326),
% 196.58/31.98  | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.58/31.98  | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (394),
% 196.58/31.98  | | | | | | | | | | | |            (405), (411), (415), (417), (427), (431), (529),
% 196.58/31.98  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.58/31.98  | | | | | | | | | | | |            (549), (551), (555), (557), (559), (561), (563),
% 196.58/31.98  | | | | | | | | | | | |            (564), (565), (566), (567), (570), (571), (572),
% 196.58/31.98  | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (588),
% 196.58/31.98  | | | | | | | | | | | |            (589), (590), (592), (593), (594), (595), (596),
% 196.58/31.98  | | | | | | | | | | | |            (597), (598), (600), (602), (604), (605), (610),
% 196.58/31.98  | | | | | | | | | | | |            (611), (612), (641), (5903), (5905), (6600),
% 196.58/31.98  | | | | | | | | | | | |            (6605), (6606), (6608), (6609), (6610), (6611),
% 196.58/31.98  | | | | | | | | | | | |            (6612), (6615), (6643), (function-axioms) are
% 196.58/31.98  | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | End of split
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | |   (6644)   ~ (all_58_15 = e0)
% 196.58/31.98  | | | | | | | | | | |   (6645)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.98  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.98  | | | | | | | | | | |             e0)
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.98  | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 196.58/31.98  | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 196.58/31.98  | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.58/31.98  | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.58/31.98  | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 196.58/31.98  | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.58/31.98  | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (311),
% 196.58/31.98  | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 196.58/31.98  | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.58/31.98  | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 196.58/31.98  | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 196.58/31.98  | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.58/31.98  | | | | | | | | | | |            (415), (417), (421), (427), (431), (529), (538),
% 196.58/31.98  | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/31.98  | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/31.98  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/31.98  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.98  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.98  | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.98  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.98  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.98  | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.98  | | | | | | | | | | |            (772), (5903), (5905), (5907), (6499), (6602),
% 196.58/31.98  | | | | | | | | | | |            (6605), (6644), (6645), (function-axioms) are
% 196.58/31.98  | | | | | | | | | | |            inconsistent by sub-proof #242.
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | End of split
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | End of split
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | |   (6646)  all_24_0 = e1
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (38), (41), (43), (51),
% 196.58/31.98  | | | | | | | | |            (53), (61), (62), (63), (114), (144), (156), (158),
% 196.58/31.98  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.58/31.98  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 196.58/31.98  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 196.58/31.98  | | | | | | | | |            (273), (274), (275), (276), (277), (278), (279),
% 196.58/31.98  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.58/31.98  | | | | | | | | |            (304), (305), (306), (307), (309), (311), (312),
% 196.58/31.98  | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 196.58/31.98  | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 196.58/31.98  | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 196.58/31.98  | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 196.58/31.98  | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 196.58/31.98  | | | | | | | | |            (417), (421), (427), (431), (491), (529), (538),
% 196.58/31.98  | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/31.98  | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/31.98  | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/31.98  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/31.98  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.58/31.98  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.58/31.98  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.58/31.98  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.58/31.98  | | | | | | | | |            (608), (609), (610), (611), (612), (613), (641),
% 196.58/31.98  | | | | | | | | |            (685), (711), (765), (772), (5903), (5904), (5905),
% 196.58/31.98  | | | | | | | | |            (5907), (6499), (6646), (function-axioms) are
% 196.58/31.98  | | | | | | | | |            inconsistent by sub-proof #245.
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | End of split
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | End of split
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | Case 2:
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | |   (6647)  all_18_0 = e3
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | | COMBINE_EQS: (761), (6647) imply:
% 196.58/31.98  | | | | | | |   (6648)  all_14_0 = e3
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | | SIMP: (6648) implies:
% 196.58/31.98  | | | | | | |   (6649)  all_14_0 = e3
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | | REDUCE: (62), (6649) imply:
% 196.58/31.98  | | | | | | |   (6650)  op(e0, all_14_1) = e3
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | | BETA: splitting (94) gives:
% 196.58/31.98  | | | | | | | 
% 196.58/31.98  | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | |   (6651)   ~ (all_26_0 = e2)
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | | REDUCE: (6495), (6651) imply:
% 196.58/31.98  | | | | | | | |   (6652)  $false
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | | CLOSE: (6652) is inconsistent.
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | |   (6653)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | | BETA: splitting (144) gives:
% 196.58/31.98  | | | | | | | | 
% 196.58/31.98  | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | |   (6654)   ~ (all_46_0 = e1)
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | REDUCE: (5904), (6654) imply:
% 196.58/31.98  | | | | | | | | |   (6655)  $false
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | CLOSE: (6655) is inconsistent.
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | |   (6656)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | BETA: splitting (303) gives:
% 196.58/31.98  | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | |   (6657)  all_58_15 = e0
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (6650), (6657),
% 196.58/31.98  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.98  | | | | | | | | | |            #678.
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | |   (6658)   ~ (all_58_15 = e0)
% 196.58/31.98  | | | | | | | | | |   (6659)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/31.98  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/31.98  | | | | | | | | | |             e0)
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | ALPHA: (6659) implies:
% 196.58/31.98  | | | | | | | | | |   (6660)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.58/31.98  | | | | | | | | | |   (6661)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | REDUCE: (541), (6658) imply:
% 196.58/31.98  | | | | | | | | | |   (6662)   ~ (all_14_2 = e0)
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.98  | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | |   (6663)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.98  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/31.98  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | BETA: splitting (6663) gives:
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | |   (6664)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.98  | | | | | | | | | | | |           all_52_6 = e0
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.58/31.98  | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.58/31.98  | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.58/31.98  | | | | | | | | | | | |            (5905), (6664), (function-axioms) are inconsistent
% 196.58/31.98  | | | | | | | | | | | |            by sub-proof #302.
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | |   (6665)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.98  | | | | | | | | | | | |           all_52_14 = e0
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.98  | | | | | | | | | | | |            (43), (51), (61), (62), (63), (156), (158), (162),
% 196.58/31.98  | | | | | | | | | | | |            (166), (167), (168), (169), (172), (174), (175),
% 196.58/31.98  | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 196.58/31.98  | | | | | | | | | | | |            (270), (272), (273), (276), (277), (278), (279),
% 196.58/31.98  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.58/31.98  | | | | | | | | | | | |            (305), (306), (309), (312), (313), (314), (315),
% 196.58/31.98  | | | | | | | | | | | |            (316), (317), (320), (321), (323), (325), (326),
% 196.58/31.98  | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (346),
% 196.58/31.98  | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (388),
% 196.58/31.98  | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (421),
% 196.58/31.98  | | | | | | | | | | | |            (427), (431), (529), (538), (539), (540), (541),
% 196.58/31.98  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.58/31.98  | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.58/31.98  | | | | | | | | | | | |            (562), (563), (564), (567), (568), (570), (571),
% 196.58/31.98  | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.58/31.98  | | | | | | | | | | | |            (580), (582), (584), (586), (587), (588), (589),
% 196.58/31.98  | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (597),
% 196.58/31.98  | | | | | | | | | | | |            (600), (603), (604), (605), (606), (608), (609),
% 196.58/31.98  | | | | | | | | | | | |            (610), (611), (612), (613), (641), (772), (5903),
% 196.58/31.98  | | | | | | | | | | | |            (5905), (5907), (6656), (6660), (6661), (6665),
% 196.58/31.98  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.98  | | | | | | | | | | | |            #286.
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | End of split
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | |   (6666)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/31.98  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/31.98  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | BETA: splitting (6666) gives:
% 196.58/31.98  | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | |   (6667)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/31.98  | | | | | | | | | | | |           all_52_22 = e0
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | ALPHA: (6667) implies:
% 196.58/31.98  | | | | | | | | | | | |   (6668)  all_52_22 = e0
% 196.58/31.98  | | | | | | | | | | | |   (6669)  all_52_20 = e1
% 196.58/31.98  | | | | | | | | | | | |   (6670)  all_52_18 = e2
% 196.58/31.98  | | | | | | | | | | | |   (6671)  all_52_16 = e3
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REDUCE: (178), (6671) imply:
% 196.58/31.98  | | | | | | | | | | | |   (6672)  op(all_52_17, all_52_17) = e3
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REDUCE: (177), (6670) imply:
% 196.58/31.98  | | | | | | | | | | | |   (6673)  op(all_52_19, all_52_19) = e2
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REDUCE: (175), (6668) imply:
% 196.58/31.98  | | | | | | | | | | | |   (6674)  op(all_52_23, all_52_23) = e0
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | REDUCE: (612), (6669) imply:
% 196.58/31.98  | | | | | | | | | | | |   (6675)  op(all_10_2, all_10_2) = e1
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.58/31.98  | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | |   (6676)  all_56_15 = e3
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | COMBINE_EQS: (538), (6676) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6677)  all_14_2 = e3
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | SIMP: (6677) implies:
% 196.58/31.98  | | | | | | | | | | | | |   (6678)  all_14_2 = e3
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (573), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6679)   ~ (all_52_7 = e3)
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (603), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6680)   ~ (all_52_23 = e3)
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (606), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6681)   ~ (all_52_25 = e3)
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (608), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6682)   ~ (all_52_27 = e3)
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (609), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6683)   ~ (all_52_29 = e3)
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (613), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6684)  op(e3, e3) = all_52_30
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | REDUCE: (63), (6678) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6685)  op(e3, e0) = all_14_1
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 196.58/31.98  | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (6685)
% 196.58/31.98  | | | | | | | | | | | | |              gives:
% 196.58/31.98  | | | | | | | | | | | | |   (6686)  all_52_25 = all_14_1
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.58/31.98  | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (6684)
% 196.58/31.98  | | | | | | | | | | | | |              gives:
% 196.58/31.98  | | | | | | | | | | | | |   (6687)  all_52_30 = all_6_2
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | COMBINE_EQS: (545), (6686) imply:
% 196.58/31.98  | | | | | | | | | | | | |   (6688)  all_58_9 = all_14_1
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | BETA: splitting (273) gives:
% 196.58/31.98  | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | |   (6689)  all_56_12 = e3
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | COMBINE_EQS: (431), (6689) imply:
% 196.58/31.98  | | | | | | | | | | | | | |   (6690)  all_52_7 = e3
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | REDUCE: (6679), (6690) imply:
% 196.58/31.98  | | | | | | | | | | | | | |   (6691)  $false
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | CLOSE: (6691) is inconsistent.
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | |   (6692)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 196.58/31.98  | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | |   (6693)  all_56_6 = e3
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (51), (166), (168), (185), (281),
% 196.58/31.98  | | | | | | | | | | | | | | |            (411), (417), (431), (529), (551), (555), (563),
% 196.58/31.98  | | | | | | | | | | | | | | |            (565), (596), (641), (5905), (6656), (6672),
% 196.58/31.98  | | | | | | | | | | | | | | |            (6673), (6692), (6693), (function-axioms) are
% 196.58/31.98  | | | | | | | | | | | | | | |            inconsistent by sub-proof #240.
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | |   (6694)   ~ (all_56_6 = e3)
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | REDUCE: (417), (6694) imply:
% 196.58/31.98  | | | | | | | | | | | | | | |   (6695)   ~ (all_52_19 = e3)
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 196.58/31.98  | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | |   (6696)  all_58_2 = e3
% 196.58/31.98  | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (53), (168),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (182), (185), (313), (317), (325), (327), (331),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (332), (333), (351), (366), (387), (393), (405),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (512), (543), (544), (545), (546), (547), (548),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (549), (551), (557), (559), (562), (563), (564),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (569), (574), (575), (576), (588), (676), (6653),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (6672), (6675), (6681), (6683), (6688), (6696),
% 196.58/31.98  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.98  | | | | | | | | | | | | | | | |            #237.
% 196.58/31.98  | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | Case 2:
% 196.58/31.98  | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | |   (6697)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 196.58/31.98  | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | BETA: splitting (6697) gives:
% 196.58/31.98  | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | Case 1:
% 196.58/31.98  | | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | |   (6698)  all_58_3 = e3
% 196.58/31.98  | | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (6698) imply:
% 196.58/31.98  | | | | | | | | | | | | | | | | |   (6699)  all_4_2 = e3
% 196.58/31.98  | | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | | REDUCE: (574), (6699) imply:
% 196.58/31.98  | | | | | | | | | | | | | | | | |   (6700)   ~ (all_52_9 = e3)
% 196.58/31.98  | | | | | | | | | | | | | | | | | 
% 196.58/31.98  | | | | | | | | | | | | | | | | | REDUCE: (580), (6699) imply:
% 196.58/31.98  | | | | | | | | | | | | | | | | |   (6701)   ~ (all_52_13 = e3)
% 196.58/31.98  | | | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (41), (172), (274), (313), (317), (333),
% 196.58/31.99  | | | | | | | | | | | | | | | | |            (352), (366), (375), (393), (405), (542), (544),
% 196.58/31.99  | | | | | | | | | | | | | | | | |            (545), (546), (547), (549), (553), (559), (602),
% 196.58/31.99  | | | | | | | | | | | | | | | | |            (610), (6672), (6673), (6675), (6680), (6681),
% 196.58/31.99  | | | | | | | | | | | | | | | | |            (6700), (6701), (function-axioms) are inconsistent
% 196.58/31.99  | | | | | | | | | | | | | | | | |            by sub-proof #281.
% 196.58/31.99  | | | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | | | |   (6702)  all_58_5 = e3 | all_58_10 = e3
% 196.58/31.99  | | | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (375), (6682), (6695), (6702) are
% 196.58/31.99  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1132.
% 196.58/31.99  | | | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | |   (6703)   ~ (all_56_15 = e3)
% 196.58/31.99  | | | | | | | | | | | | |   (6704)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.58/31.99  | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | REDUCE: (538), (6703) imply:
% 196.58/31.99  | | | | | | | | | | | | |   (6705)   ~ (all_14_2 = e3)
% 196.58/31.99  | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/31.99  | | | | | | | | | | | | |            (51), (53), (61), (158), (162), (167), (168),
% 196.58/31.99  | | | | | | | | | | | | |            (169), (172), (174), (182), (183), (184), (185),
% 196.58/31.99  | | | | | | | | | | | | |            (272), (273), (274), (275), (282), (283), (284),
% 196.58/31.99  | | | | | | | | | | | | |            (285), (306), (309), (313), (315), (317), (320),
% 196.58/31.99  | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (329), (330),
% 196.58/31.99  | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (352), (361),
% 196.58/31.99  | | | | | | | | | | | | |            (366), (375), (387), (388), (393), (394), (405),
% 196.58/31.99  | | | | | | | | | | | | |            (415), (431), (538), (540), (541), (542), (543),
% 196.58/31.99  | | | | | | | | | | | | |            (544), (545), (546), (547), (549), (553), (555),
% 196.58/31.99  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (569),
% 196.58/31.99  | | | | | | | | | | | | |            (571), (572), (573), (576), (577), (578), (587),
% 196.58/31.99  | | | | | | | | | | | | |            (590), (595), (596), (600), (602), (603), (605),
% 196.58/31.99  | | | | | | | | | | | | |            (606), (610), (5903), (5905), (6660), (6662),
% 196.58/31.99  | | | | | | | | | | | | |            (6672), (6673), (6674), (6675), (6704), (6705),
% 196.58/31.99  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.99  | | | | | | | | | | | | |            #274.
% 196.58/31.99  | | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | |   (6706)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.58/31.99  | | | | | | | | | | | |           all_52_30 = e0
% 196.58/31.99  | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/31.99  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 196.58/31.99  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.58/31.99  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.58/31.99  | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 196.58/31.99  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.58/31.99  | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 196.58/31.99  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.58/31.99  | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 196.58/31.99  | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.58/31.99  | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 196.58/31.99  | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.58/31.99  | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.58/31.99  | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.58/31.99  | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 196.58/31.99  | | | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 196.58/31.99  | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 196.58/31.99  | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 196.58/31.99  | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 196.58/31.99  | | | | | | | | | | | |            (641), (5903), (5905), (6656), (6660), (6662),
% 196.58/31.99  | | | | | | | | | | | |            (6706), (function-axioms) are inconsistent by
% 196.58/31.99  | | | | | | | | | | | |            sub-proof #271.
% 196.58/31.99  | | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | End of split
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | End of split
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | End of split
% 196.58/31.99  | | | | | 
% 196.58/31.99  | | | | Case 2:
% 196.58/31.99  | | | | | 
% 196.58/31.99  | | | | |   (6707)  all_14_0 = e2
% 196.58/31.99  | | | | | 
% 196.58/31.99  | | | | | COMBINE_EQS: (771), (6707) imply:
% 196.58/31.99  | | | | |   (6708)  all_50_0 = e2
% 196.58/31.99  | | | | | 
% 196.58/31.99  | | | | | REDUCE: (62), (6707) imply:
% 196.58/31.99  | | | | |   (6709)  op(e0, all_14_1) = e2
% 196.58/31.99  | | | | | 
% 196.58/31.99  | | | | | BETA: splitting (144) gives:
% 196.58/31.99  | | | | | 
% 196.58/31.99  | | | | | Case 1:
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | |   (6710)   ~ (all_46_0 = e1)
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | | REDUCE: (5904), (6710) imply:
% 196.58/31.99  | | | | | |   (6711)  $false
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | | CLOSE: (6711) is inconsistent.
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | Case 2:
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | |   (6712)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | | BETA: splitting (153) gives:
% 196.58/31.99  | | | | | | 
% 196.58/31.99  | | | | | | Case 1:
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | |   (6713)   ~ (all_50_0 = e2)
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | | REDUCE: (6708), (6713) imply:
% 196.58/31.99  | | | | | | |   (6714)  $false
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | | CLOSE: (6714) is inconsistent.
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | Case 2:
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | |   (6715)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | | BETA: splitting (303) gives:
% 196.58/31.99  | | | | | | | 
% 196.58/31.99  | | | | | | | Case 1:
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | |   (6716)  all_58_15 = e0
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (6709), (6716),
% 196.58/31.99  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #612.
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | |   (6717)   ~ (all_58_15 = e0)
% 196.58/31.99  | | | | | | | |   (6718)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 196.58/31.99  | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | | ALPHA: (6718) implies:
% 196.58/31.99  | | | | | | | |   (6719)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.58/31.99  | | | | | | | |   (6720)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | | REDUCE: (541), (6717) imply:
% 196.58/31.99  | | | | | | | |   (6721)   ~ (all_14_2 = e0)
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | | BETA: splitting (187) gives:
% 196.58/31.99  | | | | | | | | 
% 196.58/31.99  | | | | | | | | Case 1:
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | |   (6722)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.99  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 196.58/31.99  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | BETA: splitting (6722) gives:
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | Case 1:
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | |   (6723)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/31.99  | | | | | | | | | |           all_52_6 = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.58/31.99  | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.58/31.99  | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.58/31.99  | | | | | | | | | |            (5905), (6723), (function-axioms) are inconsistent
% 196.58/31.99  | | | | | | | | | |            by sub-proof #302.
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | |   (6724)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/31.99  | | | | | | | | | |           all_52_14 = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | ALPHA: (6724) implies:
% 196.58/31.99  | | | | | | | | | |   (6725)  all_52_14 = e0
% 196.58/31.99  | | | | | | | | | |   (6726)  all_52_12 = e1
% 196.58/31.99  | | | | | | | | | |   (6727)  all_52_10 = e2
% 196.58/31.99  | | | | | | | | | |   (6728)  all_52_8 = e3
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (182), (6728) imply:
% 196.58/31.99  | | | | | | | | | |   (6729)  op(all_52_9, all_52_9) = e3
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (180), (6726) imply:
% 196.58/31.99  | | | | | | | | | |   (6730)  op(all_52_13, all_52_13) = e1
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (179), (6725) imply:
% 196.58/31.99  | | | | | | | | | |   (6731)  op(all_52_15, all_52_15) = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (611), (6727) imply:
% 196.58/31.99  | | | | | | | | | |   (6732)  op(all_4_2, all_4_2) = e2
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/31.99  | | | | | | | | | |            (43), (51), (61), (63), (157), (158), (162),
% 196.58/31.99  | | | | | | | | | |            (166), (167), (168), (169), (172), (174), (175),
% 196.58/31.99  | | | | | | | | | |            (178), (183), (184), (185), (270), (272), (273),
% 196.58/31.99  | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 196.58/31.99  | | | | | | | | | |            (284), (285), (306), (309), (312), (313), (314),
% 196.58/31.99  | | | | | | | | | |            (315), (316), (317), (320), (321), (323), (324),
% 196.58/31.99  | | | | | | | | | |            (325), (326), (328), (329), (330), (332), (333),
% 196.58/31.99  | | | | | | | | | |            (335), (346), (351), (366), (367), (372), (375),
% 196.58/31.99  | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 196.58/31.99  | | | | | | | | | |            (417), (427), (431), (529), (538), (539), (540),
% 196.58/31.99  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.58/31.99  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.58/31.99  | | | | | | | | | |            (561), (562), (563), (564), (567), (570), (571),
% 196.58/31.99  | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.58/31.99  | | | | | | | | | |            (580), (582), (584), (586), (589), (590), (592),
% 196.58/31.99  | | | | | | | | | |            (593), (594), (595), (597), (600), (603), (604),
% 196.58/31.99  | | | | | | | | | |            (605), (606), (608), (609), (610), (612), (613),
% 196.58/31.99  | | | | | | | | | |            (641), (690), (772), (5903), (5905), (6709),
% 196.58/31.99  | | | | | | | | | |            (6712), (6715), (6719), (6720), (6729), (6730),
% 196.58/31.99  | | | | | | | | | |            (6731), (6732), (function-axioms) are inconsistent
% 196.58/31.99  | | | | | | | | | |            by sub-proof #234.
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | |   (6733)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/31.99  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 196.58/31.99  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | BETA: splitting (6733) gives:
% 196.58/31.99  | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | Case 1:
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | |   (6734)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/31.99  | | | | | | | | | |           all_52_22 = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | ALPHA: (6734) implies:
% 196.58/31.99  | | | | | | | | | |   (6735)  all_52_22 = e0
% 196.58/31.99  | | | | | | | | | |   (6736)  all_52_20 = e1
% 196.58/31.99  | | | | | | | | | |   (6737)  all_52_18 = e2
% 196.58/31.99  | | | | | | | | | |   (6738)  all_52_16 = e3
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (178), (6738) imply:
% 196.58/31.99  | | | | | | | | | |   (6739)  op(all_52_17, all_52_17) = e3
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (177), (6737) imply:
% 196.58/31.99  | | | | | | | | | |   (6740)  op(all_52_19, all_52_19) = e2
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (175), (6735) imply:
% 196.58/31.99  | | | | | | | | | |   (6741)  op(all_52_23, all_52_23) = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (612), (6736) imply:
% 196.58/31.99  | | | | | | | | | |   (6742)  op(all_10_2, all_10_2) = e1
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | BETA: splitting (270) gives:
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | Case 1:
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | |   (6743)  all_56_15 = e3
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | COMBINE_EQS: (538), (6743) imply:
% 196.58/31.99  | | | | | | | | | | |   (6744)  all_14_2 = e3
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | SIMP: (6744) implies:
% 196.58/31.99  | | | | | | | | | | |   (6745)  all_14_2 = e3
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | COMBINE_EQS: (335), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6746)  all_50_2 = e3
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | COMBINE_EQS: (541), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6747)  all_58_15 = e3
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (573), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6748)   ~ (all_52_7 = e3)
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (603), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6749)   ~ (all_52_23 = e3)
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (606), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6750)   ~ (all_52_25 = e3)
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (608), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6751)   ~ (all_52_27 = e3)
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (609), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6752)   ~ (all_52_29 = e3)
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (613), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6753)  op(e3, e3) = all_52_30
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (63), (6745) imply:
% 196.58/31.99  | | | | | | | | | | |   (6754)  op(e3, e0) = all_14_1
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (41), (43), (51), (53),
% 196.58/31.99  | | | | | | | | | | |            (61), (157), (162), (166), (167), (168), (172),
% 196.58/31.99  | | | | | | | | | | |            (173), (174), (179), (180), (182), (183), (184),
% 196.58/31.99  | | | | | | | | | | |            (185), (271), (274), (277), (279), (281), (282),
% 196.58/31.99  | | | | | | | | | | |            (283), (304), (308), (313), (317), (321), (325),
% 196.58/31.99  | | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 196.58/31.99  | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.58/31.99  | | | | | | | | | | |            (393), (405), (411), (415), (417), (542), (543),
% 196.58/31.99  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.58/31.99  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (564),
% 196.58/31.99  | | | | | | | | | | |            (565), (567), (568), (569), (574), (575), (576),
% 196.58/31.99  | | | | | | | | | | |            (577), (580), (582), (586), (588), (589), (590),
% 196.58/31.99  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (602),
% 196.58/31.99  | | | | | | | | | | |            (608), (610), (690), (5905), (6709), (6715),
% 196.58/31.99  | | | | | | | | | | |            (6739), (6740), (6742), (6746), (6747), (6748),
% 196.58/31.99  | | | | | | | | | | |            (6749), (6750), (6751), (6752), (6753), (6754),
% 196.58/31.99  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.99  | | | | | | | | | | |            #230.
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | |   (6755)   ~ (all_56_15 = e3)
% 196.58/31.99  | | | | | | | | | | |   (6756)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REDUCE: (538), (6755) imply:
% 196.58/31.99  | | | | | | | | | | |   (6757)   ~ (all_14_2 = e3)
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/31.99  | | | | | | | | | | |            (51), (53), (61), (158), (162), (167), (168),
% 196.58/31.99  | | | | | | | | | | |            (169), (172), (174), (182), (183), (184), (185),
% 196.58/31.99  | | | | | | | | | | |            (272), (273), (274), (275), (282), (283), (284),
% 196.58/31.99  | | | | | | | | | | |            (285), (306), (309), (313), (315), (317), (320),
% 196.58/31.99  | | | | | | | | | | |            (323), (324), (326), (327), (328), (329), (330),
% 196.58/31.99  | | | | | | | | | | |            (331), (332), (333), (346), (351), (352), (361),
% 196.58/31.99  | | | | | | | | | | |            (366), (375), (387), (388), (393), (394), (405),
% 196.58/31.99  | | | | | | | | | | |            (415), (431), (538), (540), (541), (542), (543),
% 196.58/31.99  | | | | | | | | | | |            (544), (545), (546), (547), (549), (553), (555),
% 196.58/31.99  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (569),
% 196.58/31.99  | | | | | | | | | | |            (571), (572), (573), (576), (577), (578), (587),
% 196.58/31.99  | | | | | | | | | | |            (590), (595), (596), (600), (602), (603), (605),
% 196.58/31.99  | | | | | | | | | | |            (606), (610), (5903), (5905), (6719), (6721),
% 196.58/31.99  | | | | | | | | | | |            (6739), (6740), (6741), (6742), (6756), (6757),
% 196.58/31.99  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/31.99  | | | | | | | | | | |            #274.
% 196.58/31.99  | | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | End of split
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | Case 2:
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | |   (6758)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.58/31.99  | | | | | | | | | |           all_52_30 = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | ALPHA: (6758) implies:
% 196.58/31.99  | | | | | | | | | |   (6759)  all_52_30 = e0
% 196.58/31.99  | | | | | | | | | |   (6760)  all_52_28 = e1
% 196.58/31.99  | | | | | | | | | |   (6761)  all_52_26 = e2
% 196.58/31.99  | | | | | | | | | |   (6762)  all_52_24 = e3
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (174), (6762) imply:
% 196.58/31.99  | | | | | | | | | |   (6763)  op(all_52_25, all_52_25) = e3
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (173), (6761) imply:
% 196.58/31.99  | | | | | | | | | |   (6764)  op(all_52_27, all_52_27) = e2
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (172), (6760) imply:
% 196.58/31.99  | | | | | | | | | |   (6765)  op(all_52_29, all_52_29) = e1
% 196.58/31.99  | | | | | | | | | | 
% 196.58/31.99  | | | | | | | | | | REDUCE: (613), (6759) imply:
% 196.58/31.99  | | | | | | | | | |   (6766)  op(all_14_2, all_14_2) = e0
% 196.58/31.99  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/32.00  | | | | | | | | | |            (43), (51), (53), (61), (63), (157), (158), (162),
% 196.58/32.00  | | | | | | | | | |            (166), (167), (168), (169), (175), (177), (178),
% 196.58/32.00  | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (270),
% 196.58/32.00  | | | | | | | | | |            (271), (272), (273), (274), (277), (280), (281),
% 196.58/32.00  | | | | | | | | | |            (282), (283), (284), (285), (306), (307), (309),
% 196.58/32.00  | | | | | | | | | |            (311), (313), (315), (316), (319), (320), (321),
% 196.58/32.00  | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 196.58/32.00  | | | | | | | | | |            (332), (333), (335), (343), (346), (351), (352),
% 196.58/32.00  | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 196.58/32.00  | | | | | | | | | |            (394), (405), (411), (415), (431), (529), (538),
% 196.58/32.00  | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.58/32.00  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.58/32.00  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.58/32.00  | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.58/32.00  | | | | | | | | | |            (574), (575), (576), (578), (582), (584), (586),
% 196.58/32.00  | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 196.58/32.00  | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 196.58/32.00  | | | | | | | | | |            (606), (607), (608), (609), (610), (641), (690),
% 196.58/32.00  | | | | | | | | | |            (772), (5905), (6709), (6712), (6715), (6719),
% 196.58/32.00  | | | | | | | | | |            (6721), (6763), (6764), (6765), (6766),
% 196.58/32.00  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/32.00  | | | | | | | | | |            #229.
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | 
% 196.58/32.00  | | | | | | | End of split
% 196.58/32.00  | | | | | | | 
% 196.58/32.00  | | | | | | End of split
% 196.58/32.00  | | | | | | 
% 196.58/32.00  | | | | | End of split
% 196.58/32.00  | | | | | 
% 196.58/32.00  | | | | End of split
% 196.58/32.00  | | | | 
% 196.58/32.00  | | | Case 2:
% 196.58/32.00  | | | | 
% 196.58/32.00  | | | |   (6767)  all_10_0 = e3
% 196.58/32.00  | | | | 
% 196.58/32.00  | | | | COMBINE_EQS: (717), (6767) imply:
% 196.58/32.00  | | | |   (6768)  all_36_0 = e3
% 196.58/32.00  | | | | 
% 196.58/32.00  | | | | REDUCE: (52), (6767) imply:
% 196.58/32.00  | | | |   (6769)  op(e1, all_10_1) = e3
% 196.58/32.00  | | | | 
% 196.58/32.00  | | | | BETA: splitting (64) gives:
% 196.58/32.00  | | | | 
% 196.58/32.00  | | | | Case 1:
% 196.58/32.00  | | | | | 
% 196.58/32.00  | | | | |   (6770)   ~ (all_14_0 = e2)
% 196.58/32.00  | | | | | 
% 196.58/32.00  | | | | | BETA: splitting (74) gives:
% 196.58/32.00  | | | | | 
% 196.58/32.00  | | | | | Case 1:
% 196.58/32.00  | | | | | | 
% 196.58/32.00  | | | | | |   (6771)   ~ (all_18_0 = e3)
% 196.58/32.00  | | | | | | 
% 196.58/32.00  | | | | | | REDUCE: (761), (6771) imply:
% 196.58/32.00  | | | | | |   (6772)   ~ (all_14_0 = e3)
% 196.58/32.00  | | | | | | 
% 196.58/32.00  | | | | | | BETA: splitting (79) gives:
% 196.58/32.00  | | | | | | 
% 196.58/32.00  | | | | | | Case 1:
% 196.58/32.00  | | | | | | | 
% 196.58/32.00  | | | | | | |   (6773)   ~ (all_20_0 = e3)
% 196.58/32.00  | | | | | | | 
% 196.58/32.00  | | | | | | | REDUCE: (758), (6773) imply:
% 196.58/32.00  | | | | | | |   (6774)   ~ (all_4_0 = e3)
% 196.58/32.00  | | | | | | | 
% 196.58/32.00  | | | | | | | BETA: splitting (89) gives:
% 196.58/32.00  | | | | | | | 
% 196.58/32.00  | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | 
% 196.58/32.00  | | | | | | | |   (6775)   ~ (all_24_0 = e1)
% 196.58/32.00  | | | | | | | | 
% 196.58/32.00  | | | | | | | | REDUCE: (711), (6775) imply:
% 196.58/32.00  | | | | | | | |   (6776)   ~ (all_14_0 = e1)
% 196.58/32.00  | | | | | | | | 
% 196.58/32.00  | | | | | | | | BETA: splitting (109) gives:
% 196.58/32.00  | | | | | | | | 
% 196.58/32.00  | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | |   (6777)   ~ (all_32_1 = e3)
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | REDUCE: (663), (6777) imply:
% 196.58/32.00  | | | | | | | | |   (6778)   ~ (all_4_1 = e3)
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | BETA: splitting (119) gives:
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | |   (6779)   ~ (all_36_0 = e3)
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | REDUCE: (6768), (6779) imply:
% 196.58/32.00  | | | | | | | | | |   (6780)  $false
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | CLOSE: (6780) is inconsistent.
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | |   (6781)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | BETA: splitting (144) gives:
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | |   (6782)   ~ (all_46_0 = e1)
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | REDUCE: (5904), (6782) imply:
% 196.58/32.00  | | | | | | | | | | |   (6783)  $false
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | CLOSE: (6783) is inconsistent.
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | |   (6784)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | |   (6785)  all_58_15 = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | COMBINE_EQS: (541), (6785) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6786)  all_14_2 = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (573), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6787)   ~ (all_52_7 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (591), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6788)   ~ (all_52_15 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (603), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6789)   ~ (all_52_23 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (606), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6790)   ~ (all_52_25 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (609), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6791)   ~ (all_52_29 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (613), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6792)  op(e0, e0) = all_52_30
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (63), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6793)  op(e0, e0) = all_14_1
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (61), (6786) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6794)  op(e0, e0) = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.58/32.00  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6792), (6793)
% 196.58/32.00  | | | | | | | | | | | |              gives:
% 196.58/32.00  | | | | | | | | | | | |   (6795)  all_52_30 = all_14_1
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.58/32.00  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6792), (6794)
% 196.58/32.00  | | | | | | | | | | | |              gives:
% 196.58/32.00  | | | | | | | | | | | |   (6796)  all_52_30 = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | COMBINE_EQS: (6795), (6796) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6797)  all_14_1 = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (62), (6797) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6798)  op(e0, e0) = all_14_0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.58/32.00  | | | | | | | | | | | |              e0, e0, simplifying with (6794), (6798) gives:
% 196.58/32.00  | | | | | | | | | | | |   (6799)  all_14_0 = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (6772), (6799) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6800)   ~ (e3 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (6770), (6799) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6801)   ~ (e2 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (6776), (6799) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6802)   ~ (e1 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | |   (6803)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/32.00  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/32.00  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | BETA: splitting (6803) gives:
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | |   (6804)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/32.00  | | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (51), (53),
% 196.58/32.00  | | | | | | | | | | | | | |            (61), (156), (157), (162), (175), (183), (184),
% 196.58/32.00  | | | | | | | | | | | | | |            (185), (272), (273), (304), (305), (306), (321),
% 196.58/32.00  | | | | | | | | | | | | | |            (332), (346), (351), (387), (405), (431), (524),
% 196.58/32.00  | | | | | | | | | | | | | |            (542), (543), (547), (555), (564), (569), (571),
% 196.58/32.00  | | | | | | | | | | | | | |            (572), (573), (610), (645), (772), (6769), (6778),
% 196.58/32.00  | | | | | | | | | | | | | |            (6781), (6785), (6787), (6788), (6804),
% 196.58/32.00  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/32.00  | | | | | | | | | | | | | |            #535.
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | |   (6805)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/32.00  | | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | ALPHA: (6805) implies:
% 196.58/32.00  | | | | | | | | | | | | | |   (6806)  all_52_14 = e0
% 196.58/32.00  | | | | | | | | | | | | | |   (6807)  all_52_12 = e1
% 196.58/32.00  | | | | | | | | | | | | | |   (6808)  all_52_10 = e2
% 196.58/32.00  | | | | | | | | | | | | | |   (6809)  all_52_8 = e3
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (182), (6809) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6810)  op(all_52_9, all_52_9) = e3
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (180), (6807) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6811)  op(all_52_13, all_52_13) = e1
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (179), (6806) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6812)  op(all_52_15, all_52_15) = e0
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (611), (6808) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6813)  op(all_4_2, all_4_2) = e2
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 196.58/32.00  | | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (168), (169),
% 196.58/32.00  | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (272), (273),
% 196.58/32.00  | | | | | | | | | | | | | |            (276), (278), (279), (282), (283), (284), (304),
% 196.58/32.00  | | | | | | | | | | | | | |            (305), (306), (308), (309), (313), (314), (317),
% 196.58/32.00  | | | | | | | | | | | | | |            (321), (325), (327), (333), (346), (351), (366),
% 196.58/32.00  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.58/32.00  | | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (542), (543),
% 196.58/32.00  | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (555),
% 196.58/32.00  | | | | | | | | | | | | | |            (557), (559), (561), (563), (567), (568), (571),
% 196.58/32.00  | | | | | | | | | | | | | |            (572), (574), (575), (576), (577), (578), (580),
% 196.58/32.00  | | | | | | | | | | | | | |            (582), (586), (587), (588), (589), (595), (596),
% 196.58/32.00  | | | | | | | | | | | | | |            (604), (605), (612), (772), (5903), (5905),
% 196.58/32.00  | | | | | | | | | | | | | |            (6769), (6785), (6787), (6788), (6790), (6794),
% 196.58/32.00  | | | | | | | | | | | | | |            (6810), (6811), (6812), (6813), (function-axioms)
% 196.58/32.00  | | | | | | | | | | | | | |            are inconsistent by sub-proof #228.
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | |   (6814)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/32.00  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/32.00  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | BETA: splitting (6814) gives:
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | Case 1:
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | |   (6815)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/32.00  | | | | | | | | | | | | | |           all_52_22 = e0
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | ALPHA: (6815) implies:
% 196.58/32.00  | | | | | | | | | | | | | |   (6816)  all_52_22 = e0
% 196.58/32.00  | | | | | | | | | | | | | |   (6817)  all_52_20 = e1
% 196.58/32.00  | | | | | | | | | | | | | |   (6818)  all_52_18 = e2
% 196.58/32.00  | | | | | | | | | | | | | |   (6819)  all_52_16 = e3
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (178), (6819) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6820)  op(all_52_17, all_52_17) = e3
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (177), (6818) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6821)  op(all_52_19, all_52_19) = e2
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (175), (6816) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6822)  op(all_52_23, all_52_23) = e0
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (612), (6817) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6823)  op(all_10_2, all_10_2) = e1
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (43), (51),
% 196.58/32.00  | | | | | | | | | | | | | |            (53), (157), (158), (168), (169), (172), (173),
% 196.58/32.00  | | | | | | | | | | | | | |            (174), (180), (182), (183), (271), (272), (273),
% 196.58/32.00  | | | | | | | | | | | | | |            (278), (279), (282), (283), (284), (304), (306),
% 196.58/32.00  | | | | | | | | | | | | | |            (309), (313), (317), (321), (322), (325), (331),
% 196.58/32.00  | | | | | | | | | | | | | |            (333), (343), (346), (351), (366), (372), (375),
% 196.58/32.00  | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (415), (417),
% 196.58/32.00  | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 196.58/32.00  | | | | | | | | | | | | | |            (547), (548), (549), (555), (557), (559), (561),
% 196.58/32.00  | | | | | | | | | | | | | |            (563), (567), (571), (572), (577), (578), (580),
% 196.58/32.00  | | | | | | | | | | | | | |            (584), (588), (589), (590), (593), (594), (595),
% 196.58/32.00  | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (604), (605),
% 196.58/32.00  | | | | | | | | | | | | | |            (611), (5903), (5905), (6778), (6785), (6787),
% 196.58/32.00  | | | | | | | | | | | | | |            (6789), (6790), (6794), (6820), (6821), (6822),
% 196.58/32.00  | | | | | | | | | | | | | |            (6823), (function-axioms) are inconsistent by
% 196.58/32.00  | | | | | | | | | | | | | |            sub-proof #312.
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | |   (6824)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.58/32.00  | | | | | | | | | | | | | |           all_52_30 = e0
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | ALPHA: (6824) implies:
% 196.58/32.00  | | | | | | | | | | | | | |   (6825)  all_52_28 = e1
% 196.58/32.00  | | | | | | | | | | | | | |   (6826)  all_52_26 = e2
% 196.58/32.00  | | | | | | | | | | | | | |   (6827)  all_52_24 = e3
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (174), (6827) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6828)  op(all_52_25, all_52_25) = e3
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (173), (6826) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6829)  op(all_52_27, all_52_27) = e2
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REDUCE: (172), (6825) imply:
% 196.58/32.00  | | | | | | | | | | | | | |   (6830)  op(all_52_29, all_52_29) = e1
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.58/32.00  | | | | | | | | | | | | | |            (51), (162), (166), (167), (169), (175), (183),
% 196.58/32.00  | | | | | | | | | | | | | |            (272), (273), (278), (281), (282), (304), (306),
% 196.58/32.00  | | | | | | | | | | | | | |            (307), (308), (309), (320), (326), (330), (332),
% 196.58/32.00  | | | | | | | | | | | | | |            (333), (346), (351), (372), (387), (388), (393),
% 196.58/32.00  | | | | | | | | | | | | | |            (405), (411), (427), (431), (529), (542), (543),
% 196.58/32.00  | | | | | | | | | | | | | |            (544), (545), (547), (549), (551), (555), (557),
% 196.58/32.00  | | | | | | | | | | | | | |            (561), (564), (566), (570), (571), (572), (576),
% 196.58/32.00  | | | | | | | | | | | | | |            (582), (593), (600), (604), (605), (610), (641),
% 196.58/32.00  | | | | | | | | | | | | | |            (5905), (6784), (6785), (6787), (6788), (6789),
% 196.58/32.00  | | | | | | | | | | | | | |            (6790), (6791), (6828), (6829), (6830),
% 196.58/32.00  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/32.00  | | | | | | | | | | | | | |            #305.
% 196.58/32.00  | | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | |   (6831)   ~ (all_58_15 = e0)
% 196.58/32.00  | | | | | | | | | | | |   (6832)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.58/32.00  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.58/32.00  | | | | | | | | | | | |             e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | ALPHA: (6832) implies:
% 196.58/32.00  | | | | | | | | | | | |   (6833)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.58/32.00  | | | | | | | | | | | |   (6834)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REDUCE: (541), (6831) imply:
% 196.58/32.00  | | | | | | | | | | | |   (6835)   ~ (all_14_2 = e0)
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.58/32.00  | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 196.58/32.00  | | | | | | | | | | | |            (158), (161), (162), (166), (167), (168), (169),
% 196.58/32.00  | | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 196.58/32.00  | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.58/32.00  | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 196.58/32.00  | | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (284),
% 196.58/32.00  | | | | | | | | | | | |            (285), (304), (305), (306), (307), (308), (309),
% 196.58/32.00  | | | | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 196.58/32.00  | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 196.58/32.00  | | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 196.58/32.00  | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.58/32.00  | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.58/32.00  | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (529),
% 196.58/32.00  | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.58/32.00  | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.58/32.00  | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.58/32.00  | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 196.58/32.00  | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.58/32.00  | | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (590),
% 196.58/32.00  | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 196.58/32.00  | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 196.58/32.00  | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 196.58/32.00  | | | | | | | | | | | |            (641), (772), (5903), (5905), (6769), (6770),
% 196.58/32.00  | | | | | | | | | | | |            (6772), (6776), (6784), (6833), (6834), (6835),
% 196.58/32.00  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/32.00  | | | | | | | | | | | |            #224.
% 196.58/32.00  | | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | End of split
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | Case 2:
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | |   (6836)  all_32_1 = e3
% 196.58/32.00  | | | | | | | | |   (6837)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | COMBINE_EQS: (663), (6836) imply:
% 196.58/32.00  | | | | | | | | |   (6838)  all_4_1 = e3
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | COMBINE_EQS: (686), (6838) imply:
% 196.58/32.00  | | | | | | | | |   (6839)  all_38_1 = e3
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | REDUCE: (38), (6838) imply:
% 196.58/32.00  | | | | | | | | |   (6840)  op(all_4_2, e2) = e3
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | REDUCE: (37), (6838) imply:
% 196.58/32.00  | | | | | | | | |   (6841)  op(e2, e3) = all_4_0
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 196.58/32.00  | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (6841)
% 196.58/32.00  | | | | | | | | |              gives:
% 196.58/32.00  | | | | | | | | |   (6842)  all_52_3 = all_4_0
% 196.58/32.00  | | | | | | | | | 
% 196.58/32.00  | | | | | | | | | COMBINE_EQS: (411), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6843)  all_56_4 = all_4_0
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | COMBINE_EQS: (387), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6844)  all_58_2 = all_4_0
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | REDUCE: (562), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6845)   ~ (all_52_5 = all_4_0)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | SIMP: (6845) implies:
% 196.58/32.01  | | | | | | | | |   (6846)   ~ (all_52_5 = all_4_0)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | REDUCE: (563), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6847)   ~ (all_52_7 = all_4_0)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | SIMP: (6847) implies:
% 196.58/32.01  | | | | | | | | |   (6848)   ~ (all_52_7 = all_4_0)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | REDUCE: (551), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6849)   ~ (all_6_2 = all_4_0)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | SIMP: (6849) implies:
% 196.58/32.01  | | | | | | | | |   (6850)   ~ (all_6_2 = all_4_0)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | REDUCE: (564), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6851)   ~ (all_4_0 = all_4_2)
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | REDUCE: (185), (6842) imply:
% 196.58/32.01  | | | | | | | | |   (6852)  op(all_4_0, all_4_0) = all_52_2
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | BETA: splitting (124) gives:
% 196.58/32.01  | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | |   (6853)   ~ (all_38_0 = e1)
% 196.58/32.01  | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | REDUCE: (766), (6853) imply:
% 196.58/32.01  | | | | | | | | | |   (6854)   ~ (all_4_0 = e1)
% 196.58/32.01  | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | BETA: splitting (144) gives:
% 196.58/32.01  | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | |   (6855)   ~ (all_46_0 = e1)
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | REDUCE: (5904), (6855) imply:
% 196.58/32.01  | | | | | | | | | | |   (6856)  $false
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | CLOSE: (6856) is inconsistent.
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | |   (6857)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.58/32.01  | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | |   (6858)  all_58_15 = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | COMBINE_EQS: (541), (6858) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6859)  all_14_2 = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (573), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6860)   ~ (all_52_7 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (591), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6861)   ~ (all_52_15 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (603), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6862)   ~ (all_52_23 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (606), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6863)   ~ (all_52_25 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (609), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6864)   ~ (all_52_29 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (613), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6865)  op(e0, e0) = all_52_30
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (63), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6866)  op(e0, e0) = all_14_1
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (61), (6859) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6867)  op(e0, e0) = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.58/32.01  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6865), (6866)
% 196.58/32.01  | | | | | | | | | | | |              gives:
% 196.58/32.01  | | | | | | | | | | | |   (6868)  all_52_30 = all_14_1
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.58/32.01  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (6865), (6867)
% 196.58/32.01  | | | | | | | | | | | |              gives:
% 196.58/32.01  | | | | | | | | | | | |   (6869)  all_52_30 = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | COMBINE_EQS: (6868), (6869) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6870)  all_14_1 = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | SIMP: (6870) implies:
% 196.58/32.01  | | | | | | | | | | | |   (6871)  all_14_1 = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (62), (6871) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6872)  op(e0, e0) = all_14_0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.58/32.01  | | | | | | | | | | | |              e0, e0, simplifying with (6867), (6872) gives:
% 196.58/32.01  | | | | | | | | | | | |   (6873)  all_14_0 = e0
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (6772), (6873) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6874)   ~ (e3 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (6770), (6873) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6875)   ~ (e2 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | REDUCE: (6776), (6873) imply:
% 196.58/32.01  | | | | | | | | | | | |   (6876)   ~ (e1 = e0)
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | BETA: splitting (281) gives:
% 196.58/32.01  | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | |   (6877)  all_56_4 = e3
% 196.58/32.01  | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | REF_CLOSE: (6774), (6843), (6877) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | |            sub-proof #980.
% 196.58/32.01  | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | |   (6878)   ~ (all_56_4 = e3)
% 196.58/32.01  | | | | | | | | | | | | |   (6879)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 196.58/32.01  | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.58/32.01  | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | |   (6880)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/32.01  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.58/32.01  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | BETA: splitting (6880) gives:
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | |   (6881)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.58/32.01  | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 196.58/32.01  | | | | | | | | | | | | | | |            (611), (721), (6837), (6840), (6843), (6844),
% 196.58/32.01  | | | | | | | | | | | | | | |            (6851), (6852), (6854), (6879), (6881),
% 196.58/32.01  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/32.01  | | | | | | | | | | | | | | |            #970.
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | |   (6882)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.58/32.01  | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | ALPHA: (6882) implies:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6883)  all_52_14 = e0
% 196.58/32.01  | | | | | | | | | | | | | | |   (6884)  all_52_12 = e1
% 196.58/32.01  | | | | | | | | | | | | | | |   (6885)  all_52_10 = e2
% 196.58/32.01  | | | | | | | | | | | | | | |   (6886)  all_52_8 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (182), (6886) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6887)  op(all_52_9, all_52_9) = e3
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (180), (6884) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6888)  op(all_52_13, all_52_13) = e1
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (179), (6883) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6889)  op(all_52_15, all_52_15) = e0
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (611), (6885) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6890)  op(all_4_2, all_4_2) = e2
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6891)  all_56_13 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (6891) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6892)  all_52_15 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | SIMP: (6892) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6893)  all_52_15 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (571), (6893) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6894)   ~ (all_52_7 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (576), (6893) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6895)   ~ (all_52_9 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (590), (6893) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6896)   ~ (all_52_23 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | SIMP: (6896) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6897)   ~ (all_52_23 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (6889), (6893) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6898)  op(e3, e3) = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 196.58/32.01  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (41), (6898) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6899)  all_6_2 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (557), (6899) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6900)   ~ (all_52_9 = e0)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (6850), (6899) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6901)   ~ (all_4_0 = e0)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | SIMP: (6901) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6902)   ~ (all_4_0 = e0)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (43), (6899) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6903)  op(e0, e3) = all_6_1
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | BETA: splitting (6879) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6904)  all_56_4 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | COMBINE_EQS: (6843), (6904) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6905)  all_4_0 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | SIMP: (6905) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6906)  all_4_0 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REDUCE: (6848), (6906) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6907)   ~ (all_52_7 = e2)
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REDUCE: (6852), (6906) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6908)  op(e2, e2) = all_52_2
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | |   (6909)  all_56_12 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (6894), (6909) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | |   (6910)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | BETA: splitting (6910) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | |   (6911)  all_56_12 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (6907), (6911) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | | | |            sub-proof #1178.
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | |   (6912)  all_56_12 = e1 | all_56_12 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (6912) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6913)  all_56_12 = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (6913) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6914)  all_52_7 = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | SIMP: (6914) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6915)  all_52_7 = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (6915) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6916)   ~ (all_52_23 = e1)
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | SIMP: (6916) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6917)   ~ (all_52_23 = e1)
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (6915) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6918)  op(e0, e3) = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | |   (6919)  all_56_14 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (343), (6897), (6919) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1286.
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | |   (6920)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6920) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6921)  all_56_14 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (6921) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6922)  all_52_23 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6922) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6923)  all_52_23 = e2
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (6923) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6924)  op(e2, e2) = all_52_22
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_1,
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (6903), (6918) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6925)  all_6_1 = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |              all_52_2, e2, e2, simplifying with (36), (6908)
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6926)  all_52_2 = all_4_2
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_22,
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |              all_52_2, e2, e2, simplifying with (6908), (6924)
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6927)  all_52_2 = all_52_22
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6926), (6927) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6928)  all_52_22 = all_4_2
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5905), (6925) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6929)  op(e3, e1) = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |              e1, e1, e3, simplifying with (168), (6929) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6930)  all_52_17 = e1
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (6930) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6931)   ~ (all_52_9 = e1)
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (284), (394), (6840), (6887), (6895),
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |            (6900), (6931), (function-axioms) are inconsistent
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #935.
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |   (6932)  all_56_14 = e1 | all_56_14 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (343), (6862), (6917), (6932) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1381.
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |   (6933)  all_56_12 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (6860), (6933) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | |            sub-proof #1375.
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6934)  all_56_4 = e1 | all_56_4 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (6843), (6854), (6902), (6934) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | |            sub-proof #674.
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6935)   ~ (all_56_13 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6936)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | REDUCE: (346), (6935) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | |   (6937)   ~ (all_52_15 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6938)  all_58_12 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (6938) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6939)  all_52_7 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | SIMP: (6939) implies:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6940)  all_52_7 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REDUCE: (571), (6940) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6941)   ~ (all_52_15 = e3)
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REDUCE: (183), (6940) imply:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6942)  op(e3, e3) = all_52_6
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.58/32.01  | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (6942)
% 196.58/32.01  | | | | | | | | | | | | | | | | |              gives:
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6943)  all_52_6 = all_6_2
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (41), (43), (162), (167),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (169), (276), (320), (325), (326), (328), (330),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (366), (387), (405), (421), (543), (547), (548),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (549), (557), (561), (574), (5905), (6840),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (6887), (6888), (6937), (6938), (6942),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.58/32.01  | | | | | | | | | | | | | | | | |            #263.
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | |   (6944)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (51), (53), (156), (162), (183),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (273), (276), (304), (305), (346), (351), (421),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (431), (542), (543), (568), (571), (572), (582),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (587), (588), (6769), (6858), (6860), (6861),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (6867), (6888), (6889), (6890), (6936), (6937),
% 196.58/32.01  | | | | | | | | | | | | | | | | |            (6944), (function-axioms) are inconsistent by
% 196.58/32.01  | | | | | | | | | | | | | | | | |            sub-proof #545.
% 196.58/32.01  | | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | End of split
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | Case 2:
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | |   (6945)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.58/32.01  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.58/32.01  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | BETA: splitting (6945) gives:
% 196.58/32.01  | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | Case 1:
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | |   (6946)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.58/32.01  | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | ALPHA: (6946) implies:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6947)  all_52_22 = e0
% 196.58/32.01  | | | | | | | | | | | | | | |   (6948)  all_52_20 = e1
% 196.58/32.01  | | | | | | | | | | | | | | |   (6949)  all_52_18 = e2
% 196.58/32.01  | | | | | | | | | | | | | | |   (6950)  all_52_16 = e3
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (178), (6950) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6951)  op(all_52_17, all_52_17) = e3
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (177), (6949) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6952)  op(all_52_19, all_52_19) = e2
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (175), (6947) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6953)  op(all_52_23, all_52_23) = e0
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.58/32.01  | | | | | | | | | | | | | | | REDUCE: (612), (6948) imply:
% 196.58/32.01  | | | | | | | | | | | | | | |   (6954)  op(all_10_2, all_10_2) = e1
% 196.58/32.01  | | | | | | | | | | | | | | | 
% 196.79/32.01  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.01  | | | | | | | | | | | | | | |            (51), (53), (158), (162), (167), (168), (169),
% 196.79/32.01  | | | | | | | | | | | | | | |            (172), (173), (179), (182), (183), (184), (272),
% 196.79/32.01  | | | | | | | | | | | | | | |            (273), (274), (277), (278), (279), (280), (282),
% 196.79/32.01  | | | | | | | | | | | | | | |            (283), (304), (306), (312), (317), (320), (321),
% 196.79/32.01  | | | | | | | | | | | | | | |            (326), (328), (330), (332), (333), (346), (351),
% 196.79/32.01  | | | | | | | | | | | | | | |            (352), (367), (372), (375), (387), (388), (393),
% 196.79/32.01  | | | | | | | | | | | | | | |            (405), (415), (417), (427), (431), (523), (539),
% 196.79/32.01  | | | | | | | | | | | | | | |            (542), (543), (545), (546), (547), (548), (549),
% 196.79/32.01  | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (567), (569),
% 196.79/32.01  | | | | | | | | | | | | | | |            (570), (572), (574), (584), (590), (593), (595),
% 196.79/32.01  | | | | | | | | | | | | | | |            (598), (604), (607), (610), (611), (721), (5905),
% 196.79/32.01  | | | | | | | | | | | | | | |            (6774), (6837), (6840), (6843), (6844), (6846),
% 196.79/32.01  | | | | | | | | | | | | | | |            (6848), (6850), (6851), (6854), (6858), (6860),
% 196.79/32.01  | | | | | | | | | | | | | | |            (6861), (6863), (6864), (6867), (6879), (6951),
% 196.79/32.01  | | | | | | | | | | | | | | |            (6952), (6953), (6954), (function-axioms) are
% 196.79/32.01  | | | | | | | | | | | | | | |            inconsistent by sub-proof #260.
% 196.79/32.01  | | | | | | | | | | | | | | | 
% 196.79/32.01  | | | | | | | | | | | | | | Case 2:
% 196.79/32.01  | | | | | | | | | | | | | | | 
% 196.79/32.01  | | | | | | | | | | | | | | |   (6955)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.01  | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.01  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (41), (169), (172), (173), (174),
% 196.79/32.02  | | | | | | | | | | | | | | |            (278), (280), (282), (309), (321), (332), (372),
% 196.79/32.02  | | | | | | | | | | | | | | |            (375), (388), (405), (427), (523), (539), (544),
% 196.79/32.02  | | | | | | | | | | | | | | |            (545), (548), (561), (574), (584), (586), (605),
% 196.79/32.02  | | | | | | | | | | | | | | |            (607), (610), (611), (721), (6774), (6837),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6840), (6843), (6844), (6850), (6851), (6854),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6858), (6863), (6879), (6955), (function-axioms)
% 196.79/32.02  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #940.
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | |   (6956)   ~ (all_58_15 = e0)
% 196.79/32.02  | | | | | | | | | | | |   (6957)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.79/32.02  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.79/32.02  | | | | | | | | | | | |             e0)
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | ALPHA: (6957) implies:
% 196.79/32.02  | | | | | | | | | | | |   (6958)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.02  | | | | | | | | | | | |   (6959)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | REDUCE: (541), (6956) imply:
% 196.79/32.02  | | | | | | | | | | | |   (6960)   ~ (all_14_2 = e0)
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | BETA: splitting (281) gives:
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | |   (6961)  all_56_4 = e3
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | REF_CLOSE: (6774), (6843), (6961) are inconsistent by
% 196.79/32.02  | | | | | | | | | | | | |            sub-proof #980.
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | |   (6962)   ~ (all_56_4 = e3)
% 196.79/32.02  | | | | | | | | | | | | |   (6963)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | |   (6964)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.02  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.02  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.02  | | | | | | | | | | | | | |            (43), (51), (61), (158), (162), (166), (168),
% 196.79/32.02  | | | | | | | | | | | | | |            (169), (172), (174), (175), (178), (179), (180),
% 196.79/32.02  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (272), (273),
% 196.79/32.02  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 196.79/32.02  | | | | | | | | | | | | | |            (284), (285), (306), (309), (312), (313), (314),
% 196.79/32.02  | | | | | | | | | | | | | |            (315), (316), (317), (320), (321), (323), (325),
% 196.79/32.02  | | | | | | | | | | | | | |            (326), (328), (329), (330), (332), (333), (346),
% 196.79/32.02  | | | | | | | | | | | | | |            (351), (366), (367), (372), (375), (387), (388),
% 196.79/32.02  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (417), (427),
% 196.79/32.02  | | | | | | | | | | | | | |            (431), (523), (529), (538), (539), (540), (541),
% 196.79/32.02  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.79/32.02  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.79/32.02  | | | | | | | | | | | | | |            (562), (563), (564), (567), (568), (570), (571),
% 196.79/32.02  | | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.79/32.02  | | | | | | | | | | | | | |            (580), (582), (584), (586), (589), (590), (591),
% 196.79/32.02  | | | | | | | | | | | | | |            (592), (593), (594), (595), (597), (600), (603),
% 196.79/32.02  | | | | | | | | | | | | | |            (604), (605), (606), (608), (609), (610), (611),
% 196.79/32.02  | | | | | | | | | | | | | |            (612), (613), (641), (721), (772), (5903), (5905),
% 196.79/32.02  | | | | | | | | | | | | | |            (6774), (6837), (6840), (6843), (6844), (6851),
% 196.79/32.02  | | | | | | | | | | | | | |            (6852), (6854), (6857), (6958), (6959), (6963),
% 196.79/32.02  | | | | | | | | | | | | | |            (6964), (function-axioms) are inconsistent by
% 196.79/32.02  | | | | | | | | | | | | | |            sub-proof #257.
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | |   (6965)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.02  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.02  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | BETA: splitting (6965) gives:
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | |   (6966)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.02  | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | ALPHA: (6966) implies:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6967)  all_52_22 = e0
% 196.79/32.02  | | | | | | | | | | | | | | |   (6968)  all_52_20 = e1
% 196.79/32.02  | | | | | | | | | | | | | | |   (6969)  all_52_18 = e2
% 196.79/32.02  | | | | | | | | | | | | | | |   (6970)  all_52_16 = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (178), (6970) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6971)  op(all_52_17, all_52_17) = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (177), (6969) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6972)  op(all_52_19, all_52_19) = e2
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (175), (6967) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6973)  op(all_52_23, all_52_23) = e0
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (612), (6968) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6974)  op(all_10_2, all_10_2) = e1
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.02  | | | | | | | | | | | | | | |            (51), (53), (61), (158), (161), (162), (168),
% 196.79/32.02  | | | | | | | | | | | | | | |            (169), (172), (173), (174), (179), (180), (182),
% 196.79/32.02  | | | | | | | | | | | | | | |            (183), (184), (185), (270), (272), (273), (274),
% 196.79/32.02  | | | | | | | | | | | | | | |            (275), (279), (280), (282), (283), (284), (285),
% 196.79/32.02  | | | | | | | | | | | | | | |            (306), (309), (313), (315), (316), (317), (321),
% 196.79/32.02  | | | | | | | | | | | | | | |            (323), (324), (327), (328), (329), (330), (331),
% 196.79/32.02  | | | | | | | | | | | | | | |            (332), (333), (346), (351), (352), (361), (366),
% 196.79/32.02  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.02  | | | | | | | | | | | | | | |            (415), (417), (431), (523), (538), (539), (540),
% 196.79/32.02  | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.79/32.02  | | | | | | | | | | | | | | |            (548), (549), (553), (555), (557), (559), (561),
% 196.79/32.02  | | | | | | | | | | | | | | |            (562), (563), (564), (567), (569), (571), (572),
% 196.79/32.02  | | | | | | | | | | | | | | |            (573), (574), (576), (577), (578), (580), (584),
% 196.79/32.02  | | | | | | | | | | | | | | |            (586), (587), (588), (590), (595), (596), (597),
% 196.79/32.02  | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 196.79/32.02  | | | | | | | | | | | | | | |            (610), (611), (721), (5903), (5905), (6769),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6774), (6837), (6840), (6843), (6844), (6850),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6851), (6854), (6958), (6960), (6963), (6971),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6972), (6973), (6974), (function-axioms) are
% 196.79/32.02  | | | | | | | | | | | | | | |            inconsistent by sub-proof #223.
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | |   (6975)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.02  | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | ALPHA: (6975) implies:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6976)  all_52_30 = e0
% 196.79/32.02  | | | | | | | | | | | | | | |   (6977)  all_52_28 = e1
% 196.79/32.02  | | | | | | | | | | | | | | |   (6978)  all_52_26 = e2
% 196.79/32.02  | | | | | | | | | | | | | | |   (6979)  all_52_24 = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (174), (6979) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6980)  op(all_52_25, all_52_25) = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (173), (6978) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6981)  op(all_52_27, all_52_27) = e2
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (172), (6977) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6982)  op(all_52_29, all_52_29) = e1
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (613), (6976) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (6983)  op(all_14_2, all_14_2) = e0
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.02  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (162), (166),
% 196.79/32.02  | | | | | | | | | | | | | | |            (167), (168), (169), (175), (177), (178), (179),
% 196.79/32.02  | | | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (270), (271),
% 196.79/32.02  | | | | | | | | | | | | | | |            (272), (274), (277), (280), (281), (282), (283),
% 196.79/32.02  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.79/32.02  | | | | | | | | | | | | | | |            (315), (316), (319), (320), (321), (323), (324),
% 196.79/32.02  | | | | | | | | | | | | | | |            (325), (326), (327), (328), (330), (332), (333),
% 196.79/32.02  | | | | | | | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 196.79/32.02  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.79/32.02  | | | | | | | | | | | | | | |            (415), (529), (538), (539), (540), (541), (542),
% 196.79/32.02  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 196.79/32.02  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 196.79/32.02  | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 196.79/32.02  | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (578),
% 196.79/32.02  | | | | | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 196.79/32.02  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 196.79/32.02  | | | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.79/32.02  | | | | | | | | | | | | | | |            (610), (641), (772), (5905), (6774), (6843),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6844), (6850), (6852), (6854), (6857), (6958),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6960), (6963), (6980), (6981), (6982), (6983),
% 196.79/32.02  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.02  | | | | | | | | | | | | | | |            #256.
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | |   (6984)  all_38_0 = e1
% 196.79/32.02  | | | | | | | | | |   (6985)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | COMBINE_EQS: (766), (6984) imply:
% 196.79/32.02  | | | | | | | | | |   (6986)  all_4_0 = e1
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 196.79/32.02  | | | | | | | | | |            (6839), (6840), (6851), (6985), (6986),
% 196.79/32.02  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.02  | | | | | | | | | |            #927.
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | | 
% 196.79/32.02  | | | | | | | | End of split
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | |   (6987)  all_24_0 = e1
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | COMBINE_EQS: (711), (6987) imply:
% 196.79/32.02  | | | | | | | |   (6988)  all_14_0 = e1
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | SIMP: (6988) implies:
% 196.79/32.02  | | | | | | | |   (6989)  all_14_0 = e1
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | COMBINE_EQS: (765), (6989) imply:
% 196.79/32.02  | | | | | | | |   (6990)  all_34_0 = e1
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | REDUCE: (6772), (6989) imply:
% 196.79/32.02  | | | | | | | |   (6991)   ~ (e3 = e1)
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | REDUCE: (6770), (6989) imply:
% 196.79/32.02  | | | | | | | |   (6992)   ~ (e2 = e1)
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | REDUCE: (62), (6989) imply:
% 196.79/32.02  | | | | | | | |   (6993)  op(e0, all_14_1) = e1
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | BETA: splitting (109) gives:
% 196.79/32.02  | | | | | | | | 
% 196.79/32.02  | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | 
% 196.79/32.02  | | | | | | | | |   (6994)   ~ (all_32_1 = e3)
% 196.79/32.02  | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | REDUCE: (663), (6994) imply:
% 196.79/32.02  | | | | | | | | |   (6995)   ~ (all_4_1 = e3)
% 196.79/32.02  | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | BETA: splitting (114) gives:
% 196.79/32.02  | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | |   (6996)   ~ (all_34_0 = e1)
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | REDUCE: (6990), (6996) imply:
% 196.79/32.02  | | | | | | | | | |   (6997)  $false
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | CLOSE: (6997) is inconsistent.
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | |   (6998)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | BETA: splitting (144) gives:
% 196.79/32.02  | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | |   (6999)   ~ (all_46_0 = e1)
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | REDUCE: (5904), (6999) imply:
% 196.79/32.02  | | | | | | | | | | |   (7000)  $false
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | CLOSE: (7000) is inconsistent.
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | |   (7001)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.79/32.02  | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | |   (7002)  all_58_15 = e0
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (6993), (7002),
% 196.79/32.02  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.02  | | | | | | | | | | | |            #877.
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | |   (7003)   ~ (all_58_15 = e0)
% 196.79/32.02  | | | | | | | | | | | |   (7004)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.79/32.02  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.79/32.02  | | | | | | | | | | | |             e0)
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | ALPHA: (7004) implies:
% 196.79/32.02  | | | | | | | | | | | |   (7005)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.02  | | | | | | | | | | | |   (7006)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | REDUCE: (541), (7003) imply:
% 196.79/32.02  | | | | | | | | | | | |   (7007)   ~ (all_14_2 = e0)
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.02  | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | |   (7008)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.02  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.02  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | BETA: splitting (7008) gives:
% 196.79/32.02  | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | |   (7009)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.02  | | | | | | | | | | | | | |           all_52_6 = e0
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.79/32.02  | | | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.79/32.02  | | | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.79/32.02  | | | | | | | | | | | | | |            (5905), (7009), (function-axioms) are inconsistent
% 196.79/32.02  | | | | | | | | | | | | | |            by sub-proof #302.
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | |   (7010)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.02  | | | | | | | | | | | | | |           all_52_14 = e0
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | ALPHA: (7010) implies:
% 196.79/32.02  | | | | | | | | | | | | | |   (7011)  all_52_14 = e0
% 196.79/32.02  | | | | | | | | | | | | | |   (7012)  all_52_12 = e1
% 196.79/32.02  | | | | | | | | | | | | | |   (7013)  all_52_10 = e2
% 196.79/32.02  | | | | | | | | | | | | | |   (7014)  all_52_8 = e3
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | REDUCE: (182), (7014) imply:
% 196.79/32.02  | | | | | | | | | | | | | |   (7015)  op(all_52_9, all_52_9) = e3
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | REDUCE: (180), (7012) imply:
% 196.79/32.02  | | | | | | | | | | | | | |   (7016)  op(all_52_13, all_52_13) = e1
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | REDUCE: (179), (7011) imply:
% 196.79/32.02  | | | | | | | | | | | | | |   (7017)  op(all_52_15, all_52_15) = e0
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | REDUCE: (611), (7013) imply:
% 196.79/32.02  | | | | | | | | | | | | | |   (7018)  op(all_4_2, all_4_2) = e2
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.79/32.02  | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | Case 1:
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | |   (7019)  all_56_15 = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (7019) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7020)  all_14_2 = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | COMBINE_EQS: (491), (7020) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7021)  all_34_2 = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (603), (7020) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7022)   ~ (all_52_23 = e3)
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (606), (7020) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7023)   ~ (all_52_25 = e3)
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (609), (7020) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7024)   ~ (all_52_29 = e3)
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (63), (7020) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7025)  op(e3, e0) = all_14_1
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REDUCE: (61), (7020) imply:
% 196.79/32.02  | | | | | | | | | | | | | | |   (7026)  op(e0, e0) = e3
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (38), (51), (156), (161), (167), (174),
% 196.79/32.02  | | | | | | | | | | | | | | |            (175), (184), (282), (307), (311), (313), (319),
% 196.79/32.02  | | | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (544), (545),
% 196.79/32.02  | | | | | | | | | | | | | | |            (546), (547), (548), (562), (580), (588), (597),
% 196.79/32.02  | | | | | | | | | | | | | | |            (600), (604), (605), (685), (6993), (6995),
% 196.79/32.02  | | | | | | | | | | | | | | |            (6998), (7016), (7018), (7021), (7022), (7023),
% 196.79/32.02  | | | | | | | | | | | | | | |            (7024), (7025), (7026), (function-axioms) are
% 196.79/32.02  | | | | | | | | | | | | | | |            inconsistent by sub-proof #855.
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | Case 2:
% 196.79/32.02  | | | | | | | | | | | | | | | 
% 196.79/32.02  | | | | | | | | | | | | | | |   (7027)   ~ (all_56_15 = e3)
% 196.79/32.03  | | | | | | | | | | | | | | |   (7028)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | REDUCE: (538), (7027) imply:
% 196.79/32.03  | | | | | | | | | | | | | | |   (7029)   ~ (all_14_2 = e3)
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.03  | | | | | | | | | | | | | | |            (43), (51), (61), (158), (162), (166), (168),
% 196.79/32.03  | | | | | | | | | | | | | | |            (169), (172), (174), (175), (178), (183), (184),
% 196.79/32.03  | | | | | | | | | | | | | | |            (185), (272), (273), (277), (278), (279), (280),
% 196.79/32.03  | | | | | | | | | | | | | | |            (281), (282), (283), (284), (285), (306), (309),
% 196.79/32.03  | | | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (320),
% 196.79/32.03  | | | | | | | | | | | | | | |            (321), (323), (325), (326), (328), (329), (330),
% 196.79/32.03  | | | | | | | | | | | | | | |            (332), (333), (346), (351), (366), (367), (372),
% 196.79/32.03  | | | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 196.79/32.03  | | | | | | | | | | | | | | |            (415), (417), (427), (431), (529), (538), (539),
% 196.79/32.03  | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.79/32.03  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.79/32.03  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (570),
% 196.79/32.03  | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 196.79/32.03  | | | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (589), (590),
% 196.79/32.03  | | | | | | | | | | | | | | |            (592), (593), (594), (595), (597), (600), (603),
% 196.79/32.03  | | | | | | | | | | | | | | |            (604), (605), (606), (608), (609), (610), (612),
% 196.79/32.03  | | | | | | | | | | | | | | |            (613), (641), (772), (5903), (5905), (7001),
% 196.79/32.03  | | | | | | | | | | | | | | |            (7005), (7006), (7015), (7016), (7017), (7018),
% 196.79/32.03  | | | | | | | | | | | | | | |            (7028), (7029), (function-axioms) are inconsistent
% 196.79/32.03  | | | | | | | | | | | | | | |            by sub-proof #288.
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | |   (7030)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.03  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.03  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | BETA: splitting (7030) gives:
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | |   (7031)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.03  | | | | | | | | | | | | | |           all_52_22 = e0
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | ALPHA: (7031) implies:
% 196.79/32.03  | | | | | | | | | | | | | |   (7032)  all_52_22 = e0
% 196.79/32.03  | | | | | | | | | | | | | |   (7033)  all_52_20 = e1
% 196.79/32.03  | | | | | | | | | | | | | |   (7034)  all_52_18 = e2
% 196.79/32.03  | | | | | | | | | | | | | |   (7035)  all_52_16 = e3
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (178), (7035) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7036)  op(all_52_17, all_52_17) = e3
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (177), (7034) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7037)  op(all_52_19, all_52_19) = e2
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (175), (7032) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7038)  op(all_52_23, all_52_23) = e0
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (612), (7033) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7039)  op(all_10_2, all_10_2) = e1
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.03  | | | | | | | | | | | | | |            (51), (53), (61), (63), (156), (158), (161),
% 196.79/32.03  | | | | | | | | | | | | | |            (162), (167), (168), (172), (173), (174), (179),
% 196.79/32.03  | | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (270), (272),
% 196.79/32.03  | | | | | | | | | | | | | |            (273), (274), (275), (279), (282), (283), (284),
% 196.79/32.03  | | | | | | | | | | | | | |            (285), (306), (307), (309), (313), (315), (316),
% 196.79/32.03  | | | | | | | | | | | | | |            (317), (321), (323), (324), (327), (328), (329),
% 196.79/32.03  | | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 196.79/32.03  | | | | | | | | | | | | | |            (361), (366), (372), (375), (387), (388), (393),
% 196.79/32.03  | | | | | | | | | | | | | |            (394), (405), (415), (417), (431), (491), (538),
% 196.79/32.03  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.79/32.03  | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (559),
% 196.79/32.03  | | | | | | | | | | | | | |            (561), (562), (563), (564), (567), (569), (571),
% 196.79/32.03  | | | | | | | | | | | | | |            (572), (573), (574), (576), (577), (578), (580),
% 196.79/32.03  | | | | | | | | | | | | | |            (586), (587), (588), (590), (595), (596), (597),
% 196.79/32.03  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 196.79/32.03  | | | | | | | | | | | | | |            (609), (610), (685), (5903), (5905), (6769),
% 196.79/32.03  | | | | | | | | | | | | | |            (6993), (6998), (7005), (7006), (7007), (7036),
% 196.79/32.03  | | | | | | | | | | | | | |            (7037), (7038), (7039), (function-axioms) are
% 196.79/32.03  | | | | | | | | | | | | | |            inconsistent by sub-proof #222.
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | |   (7040)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.03  | | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | ALPHA: (7040) implies:
% 196.79/32.03  | | | | | | | | | | | | | |   (7041)  all_52_30 = e0
% 196.79/32.03  | | | | | | | | | | | | | |   (7042)  all_52_28 = e1
% 196.79/32.03  | | | | | | | | | | | | | |   (7043)  all_52_26 = e2
% 196.79/32.03  | | | | | | | | | | | | | |   (7044)  all_52_24 = e3
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (174), (7044) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7045)  op(all_52_25, all_52_25) = e3
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (173), (7043) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7046)  op(all_52_27, all_52_27) = e2
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (172), (7042) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7047)  op(all_52_29, all_52_29) = e1
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REDUCE: (613), (7041) imply:
% 196.79/32.03  | | | | | | | | | | | | | |   (7048)  op(all_14_2, all_14_2) = e0
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.03  | | | | | | | | | | | | | |            (51), (53), (61), (63), (156), (158), (162),
% 196.79/32.03  | | | | | | | | | | | | | |            (166), (167), (168), (169), (175), (177), (178),
% 196.79/32.03  | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (270),
% 196.79/32.03  | | | | | | | | | | | | | |            (271), (272), (273), (274), (277), (280), (281),
% 196.79/32.03  | | | | | | | | | | | | | |            (282), (283), (284), (285), (306), (307), (309),
% 196.79/32.03  | | | | | | | | | | | | | |            (311), (313), (315), (316), (319), (320), (321),
% 196.79/32.03  | | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 196.79/32.03  | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 196.79/32.03  | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 196.79/32.03  | | | | | | | | | | | | | |            (405), (411), (415), (431), (491), (529), (538),
% 196.79/32.03  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.79/32.03  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.79/32.03  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.79/32.03  | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 196.79/32.03  | | | | | | | | | | | | | |            (575), (576), (578), (582), (584), (586), (587),
% 196.79/32.03  | | | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 196.79/32.03  | | | | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 196.79/32.03  | | | | | | | | | | | | | |            (607), (608), (609), (610), (641), (685), (5903),
% 196.79/32.03  | | | | | | | | | | | | | |            (5905), (6993), (6998), (7001), (7005), (7007),
% 196.79/32.03  | | | | | | | | | | | | | |            (7045), (7046), (7047), (7048), (function-axioms)
% 196.79/32.03  | | | | | | | | | | | | | |            are inconsistent by sub-proof #247.
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | |   (7049)  all_32_1 = e3
% 196.79/32.03  | | | | | | | | |   (7050)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | COMBINE_EQS: (663), (7049) imply:
% 196.79/32.03  | | | | | | | | |   (7051)  all_4_1 = e3
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | SIMP: (7051) implies:
% 196.79/32.03  | | | | | | | | |   (7052)  all_4_1 = e3
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | COMBINE_EQS: (686), (7052) imply:
% 196.79/32.03  | | | | | | | | |   (7053)  all_38_1 = e3
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | REDUCE: (38), (7052) imply:
% 196.79/32.03  | | | | | | | | |   (7054)  op(all_4_2, e2) = e3
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | REDUCE: (37), (7052) imply:
% 196.79/32.03  | | | | | | | | |   (7055)  op(e2, e3) = all_4_0
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 196.79/32.03  | | | | | | | | |              all_4_0, e3, e2, simplifying with (166), (7055)
% 196.79/32.03  | | | | | | | | |              gives:
% 196.79/32.03  | | | | | | | | |   (7056)  all_52_3 = all_4_0
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | COMBINE_EQS: (411), (7056) imply:
% 196.79/32.03  | | | | | | | | |   (7057)  all_56_4 = all_4_0
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | COMBINE_EQS: (387), (7056) imply:
% 196.79/32.03  | | | | | | | | |   (7058)  all_58_2 = all_4_0
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | REDUCE: (551), (7056) imply:
% 196.79/32.03  | | | | | | | | |   (7059)   ~ (all_6_2 = all_4_0)
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | SIMP: (7059) implies:
% 196.79/32.03  | | | | | | | | |   (7060)   ~ (all_6_2 = all_4_0)
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | REDUCE: (564), (7056) imply:
% 196.79/32.03  | | | | | | | | |   (7061)   ~ (all_4_0 = all_4_2)
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | REDUCE: (185), (7056) imply:
% 196.79/32.03  | | | | | | | | |   (7062)  op(all_4_0, all_4_0) = all_52_2
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | BETA: splitting (114) gives:
% 196.79/32.03  | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | |   (7063)   ~ (all_34_0 = e1)
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | REDUCE: (6990), (7063) imply:
% 196.79/32.03  | | | | | | | | | |   (7064)  $false
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | CLOSE: (7064) is inconsistent.
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | |   (7065)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | BETA: splitting (124) gives:
% 196.79/32.03  | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | |   (7066)   ~ (all_38_0 = e1)
% 196.79/32.03  | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | REDUCE: (766), (7066) imply:
% 196.79/32.03  | | | | | | | | | | |   (7067)   ~ (all_4_0 = e1)
% 196.79/32.03  | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | BETA: splitting (144) gives:
% 196.79/32.03  | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | |   (7068)   ~ (all_46_0 = e1)
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | REDUCE: (5904), (7068) imply:
% 196.79/32.03  | | | | | | | | | | | |   (7069)  $false
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | CLOSE: (7069) is inconsistent.
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | |   (7070)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.79/32.03  | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | |   (7071)  all_58_15 = e0
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (6993), (7071),
% 196.79/32.03  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.03  | | | | | | | | | | | | |            #877.
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | |   (7072)   ~ (all_58_15 = e0)
% 196.79/32.03  | | | | | | | | | | | | |   (7073)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.79/32.03  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.79/32.03  | | | | | | | | | | | | |             e0)
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | ALPHA: (7073) implies:
% 196.79/32.03  | | | | | | | | | | | | |   (7074)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.03  | | | | | | | | | | | | |   (7075)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | REDUCE: (541), (7072) imply:
% 196.79/32.03  | | | | | | | | | | | | |   (7076)   ~ (all_14_2 = e0)
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | BETA: splitting (281) gives:
% 196.79/32.03  | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | |   (7077)  all_56_4 = e3
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | REF_CLOSE: (6774), (7057), (7077) are inconsistent by
% 196.79/32.03  | | | | | | | | | | | | | |            sub-proof #980.
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | |   (7078)   ~ (all_56_4 = e3)
% 196.79/32.03  | | | | | | | | | | | | | |   (7079)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.03  | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | |   (7080)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.03  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.03  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | BETA: splitting (7080) gives:
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7081)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.03  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (320), (523), (539), (574),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (611), (721), (7050), (7054), (7057), (7058),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (7061), (7062), (7067), (7079), (7081),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.03  | | | | | | | | | | | | | | | |            #970.
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7082)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.03  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | ALPHA: (7082) implies:
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7083)  all_52_14 = e0
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7084)  all_52_12 = e1
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7085)  all_52_10 = e2
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7086)  all_52_8 = e3
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | REDUCE: (182), (7086) imply:
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7087)  op(all_52_9, all_52_9) = e3
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | REDUCE: (180), (7084) imply:
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7088)  op(all_52_13, all_52_13) = e1
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | REDUCE: (179), (7083) imply:
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7089)  op(all_52_15, all_52_15) = e0
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | REDUCE: (611), (7085) imply:
% 196.79/32.03  | | | | | | | | | | | | | | | |   (7090)  op(all_4_2, all_4_2) = e2
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (43), (51), (61), (158), (162), (166), (168),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (169), (172), (174), (175), (178), (183), (184),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (185), (270), (272), (273), (277), (278), (279),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (309), (312), (313), (314), (315), (316), (317),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (320), (321), (323), (325), (326), (328), (329),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (366), (367),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (529), (538),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (567),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (568), (570), (571), (572), (573), (574), (575),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (597), (600), (603), (604), (605), (606), (608),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (609), (610), (612), (613), (641), (772), (5903),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (5905), (6774), (7054), (7058), (7070), (7074),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (7075), (7087), (7088), (7089), (7090),
% 196.79/32.03  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.03  | | | | | | | | | | | | | | | |            #258.
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | End of split
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | Case 2:
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | |   (7091)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.03  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.03  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | BETA: splitting (7091) gives:
% 196.79/32.03  | | | | | | | | | | | | | | | 
% 196.79/32.03  | | | | | | | | | | | | | | | Case 1:
% 196.79/32.03  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7092)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.04  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | ALPHA: (7092) implies:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7093)  all_52_22 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7094)  all_52_20 = e1
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7095)  all_52_18 = e2
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7096)  all_52_16 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (178), (7096) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7097)  op(all_52_17, all_52_17) = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (177), (7095) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7098)  op(all_52_19, all_52_19) = e2
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (175), (7093) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7099)  op(all_52_23, all_52_23) = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (612), (7094) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7100)  op(all_10_2, all_10_2) = e1
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (51), (53), (61), (158), (161), (162), (168),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (169), (172), (173), (174), (179), (180), (182),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (183), (184), (185), (270), (272), (273), (274),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (275), (279), (280), (282), (283), (284), (285),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (306), (309), (313), (315), (316), (317), (321),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (323), (324), (327), (328), (329), (330), (331),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (332), (333), (346), (351), (352), (361), (366),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (415), (417), (431), (523), (538), (539), (540),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (548), (549), (553), (555), (557), (559), (561),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (562), (563), (564), (567), (569), (571), (572),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (573), (574), (576), (577), (578), (580), (584),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (586), (587), (588), (590), (595), (596), (597),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (610), (611), (721), (5903), (5905), (6769),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (6774), (7050), (7054), (7057), (7058), (7060),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (7061), (7067), (7074), (7076), (7079), (7097),
% 196.79/32.04  | | | | | | | | | | | | | | | |            (7098), (7099), (7100), (function-axioms) are
% 196.79/32.04  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #223.
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7101)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.04  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | ALPHA: (7101) implies:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7102)  all_52_30 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7103)  all_52_28 = e1
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7104)  all_52_26 = e2
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7105)  all_52_24 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (174), (7105) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7106)  op(all_52_25, all_52_25) = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (173), (7104) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7107)  op(all_52_27, all_52_27) = e2
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (172), (7103) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7108)  op(all_52_29, all_52_29) = e1
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | REDUCE: (613), (7102) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | |   (7109)  op(all_14_2, all_14_2) = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7110)  all_56_15 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (7110) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7111)  all_14_2 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | SIMP: (7111) implies:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7112)  all_14_2 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (491), (7112) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7113)  all_34_2 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | REDUCE: (573), (7112) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7114)   ~ (all_52_7 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | REDUCE: (606), (7112) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7115)   ~ (all_52_25 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | REDUCE: (7109), (7112) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7116)  op(e3, e3) = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | REDUCE: (63), (7112) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7117)  op(e3, e0) = all_14_1
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | BETA: splitting (7065) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7118)   ~ (all_34_1 = e2)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | REDUCE: (685), (7118) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7119)   ~ (all_14_1 = e2)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 196.79/32.04  | | | | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (7117)
% 196.79/32.04  | | | | | | | | | | | | | | | | | |              gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7120)  all_52_25 = all_14_1
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 196.79/32.04  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (41), (7116) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7121)  all_6_2 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (7120) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7122)  all_56_3 = all_14_1
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (7120) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7123)  all_58_9 = all_14_1
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (7121) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7124)  all_58_0 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | REDUCE: (561), (7120), (7121) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7125)   ~ (all_14_1 = e0)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | REDUCE: (7115), (7120) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7126)   ~ (all_14_1 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | REDUCE: (7106), (7120) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7127)  op(all_14_1, all_14_1) = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | |   (7128)  all_58_0 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7124), (7128) are inconsistent by sub-proof
% 196.79/32.04  | | | | | | | | | | | | | | | | | | |            #1015.
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | |   (7129)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (7129) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | |   (7130)  all_58_2 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6774), (7058), (7130) are inconsistent by
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | |            sub-proof #948.
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | |   (7131)  all_58_6 = e3 | all_58_12 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | |   (7132)  all_56_3 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7122), (7132) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | |   (7133)  all_14_1 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | REDUCE: (7126), (7133) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | |   (7134)  $false
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | CLOSE: (7134) is inconsistent.
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | |   (7135)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7131) gives:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |   (7136)  all_58_6 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (7136) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |   (7137)  all_52_5 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | SIMP: (7137) implies:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |   (7138)  all_52_5 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (7138) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |   (7139)   ~ (all_10_2 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | SIMP: (7139) implies:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |   (7140)   ~ (all_10_2 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (307), (7119), (7122), (7123), (7125),
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |            (7127), (7135), (7140), (function-axioms) are
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #560.
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |   (7141)  all_58_12 = e3
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (7114), (7141) are inconsistent by
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1367.
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7142)   ~ (all_34_2 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | REDUCE: (7113), (7142) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | | |   (7143)  $false
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | | CLOSE: (7143) is inconsistent.
% 196.79/32.04  | | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7144)   ~ (all_56_15 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7145)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | REDUCE: (538), (7144) imply:
% 196.79/32.04  | | | | | | | | | | | | | | | | |   (7146)   ~ (all_14_2 = e3)
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (51), (53), (61), (158), (162), (166), (167),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (168), (169), (175), (177), (178), (179), (180),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (271), (272), (274),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (327), (328), (330), (332), (333), (343), (346),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (529),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (566), (567), (569), (570), (571), (572), (573),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (574), (575), (576), (578), (582), (584), (586),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (641), (5905),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (7070), (7074), (7076), (7106), (7107), (7108),
% 196.79/32.04  | | | | | | | | | | | | | | | | |            (7109), (7145), (7146), (function-axioms) are
% 196.79/32.04  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #272.
% 196.79/32.04  | | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | |   (7147)  all_38_0 = e1
% 196.79/32.04  | | | | | | | | | | |   (7148)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | COMBINE_EQS: (766), (7147) imply:
% 196.79/32.04  | | | | | | | | | | |   (7149)  all_4_0 = e1
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REF_CLOSE: (36), (169), (280), (525), (539), (574), (611),
% 196.79/32.04  | | | | | | | | | | |            (7053), (7054), (7061), (7148), (7149),
% 196.79/32.04  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.04  | | | | | | | | | | |            #927.
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | 
% 196.79/32.04  | | | | | | | End of split
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | Case 2:
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | |   (7150)  all_20_0 = e3
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | | COMBINE_EQS: (758), (7150) imply:
% 196.79/32.04  | | | | | | |   (7151)  all_4_0 = e3
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | | SIMP: (7151) implies:
% 196.79/32.04  | | | | | | |   (7152)  all_4_0 = e3
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | | REDUCE: (37), (7152) imply:
% 196.79/32.04  | | | | | | |   (7153)  op(e2, all_4_1) = e3
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | | BETA: splitting (89) gives:
% 196.79/32.04  | | | | | | | 
% 196.79/32.04  | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | 
% 196.79/32.04  | | | | | | | |   (7154)   ~ (all_24_0 = e1)
% 196.79/32.04  | | | | | | | | 
% 196.79/32.04  | | | | | | | | REDUCE: (711), (7154) imply:
% 196.79/32.04  | | | | | | | |   (7155)   ~ (all_14_0 = e1)
% 196.79/32.04  | | | | | | | | 
% 196.79/32.04  | | | | | | | | BETA: splitting (119) gives:
% 196.79/32.04  | | | | | | | | 
% 196.79/32.04  | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | |   (7156)   ~ (all_36_0 = e3)
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | REDUCE: (6768), (7156) imply:
% 196.79/32.04  | | | | | | | | |   (7157)  $false
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | CLOSE: (7157) is inconsistent.
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | |   (7158)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | BETA: splitting (144) gives:
% 196.79/32.04  | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | |   (7159)   ~ (all_46_0 = e1)
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | REDUCE: (5904), (7159) imply:
% 196.79/32.04  | | | | | | | | | |   (7160)  $false
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | CLOSE: (7160) is inconsistent.
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | |   (7161)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | BETA: splitting (303) gives:
% 196.79/32.04  | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | |   (7162)  all_58_15 = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | COMBINE_EQS: (541), (7162) imply:
% 196.79/32.04  | | | | | | | | | | |   (7163)  all_14_2 = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (573), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7164)   ~ (all_52_7 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (591), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7165)   ~ (all_52_15 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (603), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7166)   ~ (all_52_23 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (606), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7167)   ~ (all_52_25 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (609), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7168)   ~ (all_52_29 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (613), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7169)  op(e0, e0) = all_52_30
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (63), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7170)  op(e0, e0) = all_14_1
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (61), (7163) imply:
% 196.79/32.04  | | | | | | | | | | |   (7171)  op(e0, e0) = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.79/32.04  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7169), (7170)
% 196.79/32.04  | | | | | | | | | | |              gives:
% 196.79/32.04  | | | | | | | | | | |   (7172)  all_52_30 = all_14_1
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.79/32.04  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7169), (7171)
% 196.79/32.04  | | | | | | | | | | |              gives:
% 196.79/32.04  | | | | | | | | | | |   (7173)  all_52_30 = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | COMBINE_EQS: (7172), (7173) imply:
% 196.79/32.04  | | | | | | | | | | |   (7174)  all_14_1 = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | SIMP: (7174) implies:
% 196.79/32.04  | | | | | | | | | | |   (7175)  all_14_1 = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (62), (7175) imply:
% 196.79/32.04  | | | | | | | | | | |   (7176)  op(e0, e0) = all_14_0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.79/32.04  | | | | | | | | | | |              e0, e0, simplifying with (7171), (7176) gives:
% 196.79/32.04  | | | | | | | | | | |   (7177)  all_14_0 = e0
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (6772), (7177) imply:
% 196.79/32.04  | | | | | | | | | | |   (7178)   ~ (e3 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (6770), (7177) imply:
% 196.79/32.04  | | | | | | | | | | |   (7179)   ~ (e2 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | REDUCE: (7155), (7177) imply:
% 196.79/32.04  | | | | | | | | | | |   (7180)   ~ (e1 = e0)
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.04  | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | |   (7181)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.04  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.04  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | BETA: splitting (7181) gives:
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | |   (7182)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.04  | | | | | | | | | | | | |           all_52_6 = e0
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.04  | | | | | | | | | | | | |            (51), (53), (61), (156), (157), (162), (166),
% 196.79/32.04  | | | | | | | | | | | | |            (175), (179), (183), (184), (185), (272), (273),
% 196.79/32.04  | | | | | | | | | | | | |            (304), (305), (306), (321), (332), (346), (351),
% 196.79/32.04  | | | | | | | | | | | | |            (387), (405), (431), (524), (542), (543), (547),
% 196.79/32.04  | | | | | | | | | | | | |            (555), (564), (569), (571), (572), (573), (610),
% 196.79/32.04  | | | | | | | | | | | | |            (645), (772), (6769), (7153), (7158), (7162),
% 196.79/32.04  | | | | | | | | | | | | |            (7164), (7165), (7182), (function-axioms) are
% 196.79/32.04  | | | | | | | | | | | | |            inconsistent by sub-proof #514.
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | |   (7183)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.04  | | | | | | | | | | | | |           all_52_14 = e0
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | ALPHA: (7183) implies:
% 196.79/32.04  | | | | | | | | | | | | |   (7184)  all_52_14 = e0
% 196.79/32.04  | | | | | | | | | | | | |   (7185)  all_52_12 = e1
% 196.79/32.04  | | | | | | | | | | | | |   (7186)  all_52_10 = e2
% 196.79/32.04  | | | | | | | | | | | | |   (7187)  all_52_8 = e3
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | REDUCE: (182), (7187) imply:
% 196.79/32.04  | | | | | | | | | | | | |   (7188)  op(all_52_9, all_52_9) = e3
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | REDUCE: (180), (7185) imply:
% 196.79/32.04  | | | | | | | | | | | | |   (7189)  op(all_52_13, all_52_13) = e1
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | REDUCE: (179), (7184) imply:
% 196.79/32.04  | | | | | | | | | | | | |   (7190)  op(all_52_15, all_52_15) = e0
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | REDUCE: (611), (7186) imply:
% 196.79/32.04  | | | | | | | | | | | | |   (7191)  op(all_4_2, all_4_2) = e2
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (38), (41), (43),
% 196.79/32.04  | | | | | | | | | | | | |            (51), (53), (156), (158), (162), (168), (169),
% 196.79/32.04  | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (272), (273),
% 196.79/32.04  | | | | | | | | | | | | |            (276), (278), (279), (282), (283), (284), (304),
% 196.79/32.04  | | | | | | | | | | | | |            (305), (306), (308), (309), (313), (314), (317),
% 196.79/32.04  | | | | | | | | | | | | |            (321), (325), (327), (333), (346), (351), (366),
% 196.79/32.04  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.04  | | | | | | | | | | | | |            (415), (417), (421), (427), (431), (542), (543),
% 196.79/32.04  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (555),
% 196.79/32.04  | | | | | | | | | | | | |            (557), (559), (561), (563), (567), (568), (571),
% 196.79/32.04  | | | | | | | | | | | | |            (572), (574), (575), (576), (577), (578), (580),
% 196.79/32.04  | | | | | | | | | | | | |            (582), (586), (587), (588), (589), (595), (596),
% 196.79/32.04  | | | | | | | | | | | | |            (604), (605), (612), (772), (5903), (5905),
% 196.79/32.04  | | | | | | | | | | | | |            (6769), (7162), (7164), (7165), (7167), (7171),
% 196.79/32.04  | | | | | | | | | | | | |            (7188), (7189), (7190), (7191), (function-axioms)
% 196.79/32.04  | | | | | | | | | | | | |            are inconsistent by sub-proof #228.
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | End of split
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | Case 2:
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | |   (7192)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.04  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.04  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | BETA: splitting (7192) gives:
% 196.79/32.04  | | | | | | | | | | | | 
% 196.79/32.04  | | | | | | | | | | | | Case 1:
% 196.79/32.04  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | |   (7193)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.05  | | | | | | | | | | | | |           all_52_22 = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | ALPHA: (7193) implies:
% 196.79/32.05  | | | | | | | | | | | | |   (7194)  all_52_22 = e0
% 196.79/32.05  | | | | | | | | | | | | |   (7195)  all_52_20 = e1
% 196.79/32.05  | | | | | | | | | | | | |   (7196)  all_52_18 = e2
% 196.79/32.05  | | | | | | | | | | | | |   (7197)  all_52_16 = e3
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (178), (7197) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7198)  op(all_52_17, all_52_17) = e3
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (177), (7196) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7199)  op(all_52_19, all_52_19) = e2
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (175), (7194) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7200)  op(all_52_23, all_52_23) = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (612), (7195) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7201)  op(all_10_2, all_10_2) = e1
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (41), (43), (51),
% 196.79/32.05  | | | | | | | | | | | | |            (53), (157), (158), (166), (168), (169), (172),
% 196.79/32.05  | | | | | | | | | | | | |            (173), (174), (179), (180), (182), (183), (271),
% 196.79/32.05  | | | | | | | | | | | | |            (272), (273), (278), (279), (282), (283), (284),
% 196.79/32.05  | | | | | | | | | | | | |            (304), (305), (306), (309), (313), (317), (321),
% 196.79/32.05  | | | | | | | | | | | | |            (322), (325), (331), (333), (343), (346), (351),
% 196.79/32.05  | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (394),
% 196.79/32.05  | | | | | | | | | | | | |            (405), (415), (417), (427), (431), (542), (543),
% 196.79/32.05  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.79/32.05  | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (565), (567),
% 196.79/32.05  | | | | | | | | | | | | |            (571), (572), (577), (578), (580), (584), (588),
% 196.79/32.05  | | | | | | | | | | | | |            (589), (590), (592), (593), (594), (595), (596),
% 196.79/32.05  | | | | | | | | | | | | |            (597), (598), (600), (602), (604), (605), (611),
% 196.79/32.05  | | | | | | | | | | | | |            (5903), (5905), (7153), (7162), (7164), (7166),
% 196.79/32.05  | | | | | | | | | | | | |            (7167), (7171), (7198), (7199), (7200), (7201),
% 196.79/32.05  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.05  | | | | | | | | | | | | |            #244.
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | |   (7202)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.05  | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.05  | | | | | | | | | | | | |            (51), (162), (166), (167), (169), (172), (173),
% 196.79/32.05  | | | | | | | | | | | | |            (174), (175), (183), (272), (273), (278), (281),
% 196.79/32.05  | | | | | | | | | | | | |            (282), (304), (306), (307), (308), (309), (320),
% 196.79/32.05  | | | | | | | | | | | | |            (326), (330), (332), (333), (346), (351), (372),
% 196.79/32.05  | | | | | | | | | | | | |            (387), (388), (393), (405), (411), (427), (431),
% 196.79/32.05  | | | | | | | | | | | | |            (529), (542), (543), (544), (545), (547), (549),
% 196.79/32.05  | | | | | | | | | | | | |            (551), (555), (557), (561), (564), (566), (570),
% 196.79/32.05  | | | | | | | | | | | | |            (571), (572), (576), (582), (593), (600), (604),
% 196.79/32.05  | | | | | | | | | | | | |            (605), (610), (641), (5905), (7161), (7162),
% 196.79/32.05  | | | | | | | | | | | | |            (7164), (7165), (7166), (7167), (7168), (7202),
% 196.79/32.05  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.05  | | | | | | | | | | | | |            #304.
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | |   (7203)   ~ (all_58_15 = e0)
% 196.79/32.05  | | | | | | | | | | |   (7204)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.79/32.05  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.79/32.05  | | | | | | | | | | |             e0)
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | ALPHA: (7204) implies:
% 196.79/32.05  | | | | | | | | | | |   (7205)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.05  | | | | | | | | | | |   (7206)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | REDUCE: (541), (7203) imply:
% 196.79/32.05  | | | | | | | | | | |   (7207)   ~ (all_14_2 = e0)
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.05  | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (157),
% 196.79/32.05  | | | | | | | | | | |            (158), (161), (162), (166), (167), (168), (169),
% 196.79/32.05  | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 196.79/32.05  | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.79/32.05  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 196.79/32.05  | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (284),
% 196.79/32.05  | | | | | | | | | | |            (285), (304), (305), (306), (307), (308), (309),
% 196.79/32.05  | | | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 196.79/32.05  | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 196.79/32.05  | | | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 196.79/32.05  | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.79/32.05  | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.05  | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (529),
% 196.79/32.05  | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.79/32.05  | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.79/32.05  | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.79/32.05  | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 196.79/32.05  | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.79/32.05  | | | | | | | | | | |            (582), (584), (586), (587), (588), (589), (590),
% 196.79/32.05  | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 196.79/32.05  | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 196.79/32.05  | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 196.79/32.05  | | | | | | | | | | |            (641), (772), (5903), (5905), (6769), (6770),
% 196.79/32.05  | | | | | | | | | | |            (6772), (7155), (7161), (7205), (7206), (7207),
% 196.79/32.05  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.05  | | | | | | | | | | |            #224.
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | |   (7208)  all_24_0 = e1
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | COMBINE_EQS: (711), (7208) imply:
% 196.79/32.05  | | | | | | | |   (7209)  all_14_0 = e1
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | SIMP: (7209) implies:
% 196.79/32.05  | | | | | | | |   (7210)  all_14_0 = e1
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | COMBINE_EQS: (765), (7210) imply:
% 196.79/32.05  | | | | | | | |   (7211)  all_34_0 = e1
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | REDUCE: (6772), (7210) imply:
% 196.79/32.05  | | | | | | | |   (7212)   ~ (e3 = e1)
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | REDUCE: (6770), (7210) imply:
% 196.79/32.05  | | | | | | | |   (7213)   ~ (e2 = e1)
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | REDUCE: (62), (7210) imply:
% 196.79/32.05  | | | | | | | |   (7214)  op(e0, all_14_1) = e1
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | BETA: splitting (114) gives:
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | |   (7215)   ~ (all_34_0 = e1)
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | REDUCE: (7211), (7215) imply:
% 196.79/32.05  | | | | | | | | |   (7216)  $false
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | CLOSE: (7216) is inconsistent.
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | |   (7217)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | BETA: splitting (144) gives:
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | |   (7218)   ~ (all_46_0 = e1)
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | REDUCE: (5904), (7218) imply:
% 196.79/32.05  | | | | | | | | | |   (7219)  $false
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | CLOSE: (7219) is inconsistent.
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | |   (7220)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | BETA: splitting (303) gives:
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | |   (7221)  all_58_15 = e0
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (7214), (7221),
% 196.79/32.05  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.05  | | | | | | | | | | |            #877.
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | |   (7222)   ~ (all_58_15 = e0)
% 196.79/32.05  | | | | | | | | | | |   (7223)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.79/32.05  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.79/32.05  | | | | | | | | | | |             e0)
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | ALPHA: (7223) implies:
% 196.79/32.05  | | | | | | | | | | |   (7224)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.05  | | | | | | | | | | |   (7225)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | REDUCE: (541), (7222) imply:
% 196.79/32.05  | | | | | | | | | | |   (7226)   ~ (all_14_2 = e0)
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | |   (7227)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.05  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.05  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | BETA: splitting (7227) gives:
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | |   (7228)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.05  | | | | | | | | | | | | |           all_52_6 = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.79/32.05  | | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.79/32.05  | | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.79/32.05  | | | | | | | | | | | | |            (5905), (7228), (function-axioms) are inconsistent
% 196.79/32.05  | | | | | | | | | | | | |            by sub-proof #302.
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | |   (7229)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.05  | | | | | | | | | | | | |           all_52_14 = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | ALPHA: (7229) implies:
% 196.79/32.05  | | | | | | | | | | | | |   (7230)  all_52_14 = e0
% 196.79/32.05  | | | | | | | | | | | | |   (7231)  all_52_12 = e1
% 196.79/32.05  | | | | | | | | | | | | |   (7232)  all_52_10 = e2
% 196.79/32.05  | | | | | | | | | | | | |   (7233)  all_52_8 = e3
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (182), (7233) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7234)  op(all_52_9, all_52_9) = e3
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (180), (7231) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7235)  op(all_52_13, all_52_13) = e1
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (179), (7230) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7236)  op(all_52_15, all_52_15) = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (611), (7232) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7237)  op(all_4_2, all_4_2) = e2
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.05  | | | | | | | | | | | | |            (43), (51), (61), (62), (63), (156), (158), (162),
% 196.79/32.05  | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (174), (175),
% 196.79/32.05  | | | | | | | | | | | | |            (178), (183), (184), (185), (270), (272), (273),
% 196.79/32.05  | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 196.79/32.05  | | | | | | | | | | | | |            (283), (284), (285), (304), (305), (306), (309),
% 196.79/32.05  | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (320),
% 196.79/32.05  | | | | | | | | | | | | |            (321), (323), (325), (326), (328), (329), (330),
% 196.79/32.05  | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (366), (367),
% 196.79/32.05  | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.05  | | | | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (491),
% 196.79/32.05  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.79/32.05  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.79/32.05  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.79/32.05  | | | | | | | | | | | | |            (564), (567), (568), (570), (571), (572), (573),
% 196.79/32.05  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.79/32.05  | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.79/32.05  | | | | | | | | | | | | |            (592), (593), (594), (595), (597), (600), (603),
% 196.79/32.05  | | | | | | | | | | | | |            (604), (605), (606), (608), (609), (610), (612),
% 196.79/32.05  | | | | | | | | | | | | |            (613), (641), (685), (772), (5903), (5905),
% 196.79/32.05  | | | | | | | | | | | | |            (6770), (7217), (7220), (7224), (7225), (7234),
% 196.79/32.05  | | | | | | | | | | | | |            (7235), (7236), (7237), (function-axioms) are
% 196.79/32.05  | | | | | | | | | | | | |            inconsistent by sub-proof #249.
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | |   (7238)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.05  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.05  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | BETA: splitting (7238) gives:
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | |   (7239)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.05  | | | | | | | | | | | | |           all_52_22 = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | ALPHA: (7239) implies:
% 196.79/32.05  | | | | | | | | | | | | |   (7240)  all_52_22 = e0
% 196.79/32.05  | | | | | | | | | | | | |   (7241)  all_52_20 = e1
% 196.79/32.05  | | | | | | | | | | | | |   (7242)  all_52_18 = e2
% 196.79/32.05  | | | | | | | | | | | | |   (7243)  all_52_16 = e3
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (178), (7243) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7244)  op(all_52_17, all_52_17) = e3
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (177), (7242) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7245)  op(all_52_19, all_52_19) = e2
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (175), (7240) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7246)  op(all_52_23, all_52_23) = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REDUCE: (612), (7241) imply:
% 196.79/32.05  | | | | | | | | | | | | |   (7247)  op(all_10_2, all_10_2) = e1
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.05  | | | | | | | | | | | | |            (51), (53), (61), (63), (156), (158), (161),
% 196.79/32.05  | | | | | | | | | | | | |            (162), (167), (168), (172), (173), (174), (179),
% 196.79/32.05  | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (270), (272),
% 196.79/32.05  | | | | | | | | | | | | |            (273), (274), (275), (279), (282), (283), (284),
% 196.79/32.05  | | | | | | | | | | | | |            (285), (306), (307), (309), (313), (315), (316),
% 196.79/32.05  | | | | | | | | | | | | |            (317), (321), (323), (324), (327), (328), (329),
% 196.79/32.05  | | | | | | | | | | | | |            (330), (331), (332), (333), (346), (351), (352),
% 196.79/32.05  | | | | | | | | | | | | |            (361), (366), (372), (375), (387), (388), (393),
% 196.79/32.05  | | | | | | | | | | | | |            (394), (405), (415), (417), (431), (491), (538),
% 196.79/32.05  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.79/32.05  | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (559),
% 196.79/32.05  | | | | | | | | | | | | |            (561), (562), (563), (564), (567), (569), (571),
% 196.79/32.05  | | | | | | | | | | | | |            (572), (573), (574), (576), (577), (578), (580),
% 196.79/32.05  | | | | | | | | | | | | |            (586), (587), (588), (590), (595), (596), (597),
% 196.79/32.05  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (608),
% 196.79/32.05  | | | | | | | | | | | | |            (609), (610), (685), (5903), (5905), (6769),
% 196.79/32.05  | | | | | | | | | | | | |            (7214), (7217), (7224), (7225), (7226), (7244),
% 196.79/32.05  | | | | | | | | | | | | |            (7245), (7246), (7247), (function-axioms) are
% 196.79/32.05  | | | | | | | | | | | | |            inconsistent by sub-proof #222.
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | Case 2:
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | |   (7248)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.05  | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.05  | | | | | | | | | | | | |            (51), (53), (61), (63), (156), (158), (162),
% 196.79/32.05  | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.79/32.05  | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.79/32.05  | | | | | | | | | | | | |            (184), (185), (270), (271), (272), (273), (274),
% 196.79/32.05  | | | | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 196.79/32.05  | | | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 196.79/32.05  | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 196.79/32.05  | | | | | | | | | | | | |            (327), (328), (330), (332), (333), (343), (346),
% 196.79/32.05  | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.79/32.05  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 196.79/32.05  | | | | | | | | | | | | |            (491), (529), (538), (539), (540), (541), (542),
% 196.79/32.05  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 196.79/32.05  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 196.79/32.05  | | | | | | | | | | | | |            (563), (564), (566), (567), (569), (570), (571),
% 196.79/32.05  | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (578), (582),
% 196.79/32.05  | | | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 196.79/32.05  | | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 196.79/32.05  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 196.79/32.05  | | | | | | | | | | | | |            (613), (641), (685), (5903), (5905), (7214),
% 196.79/32.05  | | | | | | | | | | | | |            (7217), (7220), (7224), (7226), (7248),
% 196.79/32.05  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.05  | | | | | | | | | | | | |            #246.
% 196.79/32.05  | | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | | 
% 196.79/32.05  | | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | | 
% 196.79/32.05  | | | | | | | | End of split
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | End of split
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | End of split
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | Case 2:
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | |   (7249)  all_18_0 = e3
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | | COMBINE_EQS: (761), (7249) imply:
% 196.79/32.05  | | | | | |   (7250)  all_14_0 = e3
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | | SIMP: (7250) implies:
% 196.79/32.05  | | | | | |   (7251)  all_14_0 = e3
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | | REDUCE: (62), (7251) imply:
% 196.79/32.05  | | | | | |   (7252)  op(e0, all_14_1) = e3
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | | BETA: splitting (144) gives:
% 196.79/32.05  | | | | | | 
% 196.79/32.05  | | | | | | Case 1:
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | |   (7253)   ~ (all_46_0 = e1)
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | | REDUCE: (5904), (7253) imply:
% 196.79/32.05  | | | | | | |   (7254)  $false
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | | CLOSE: (7254) is inconsistent.
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | Case 2:
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | |   (7255)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | | BETA: splitting (303) gives:
% 196.79/32.05  | | | | | | | 
% 196.79/32.05  | | | | | | | Case 1:
% 196.79/32.05  | | | | | | | | 
% 196.79/32.05  | | | | | | | |   (7256)  all_58_15 = e0
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (7252), (7256),
% 196.79/32.06  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #678.
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | |   (7257)   ~ (all_58_15 = e0)
% 196.79/32.06  | | | | | | | |   (7258)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 196.79/32.06  | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | | ALPHA: (7258) implies:
% 196.79/32.06  | | | | | | | |   (7259)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.06  | | | | | | | |   (7260)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | | REDUCE: (541), (7257) imply:
% 196.79/32.06  | | | | | | | |   (7261)   ~ (all_14_2 = e0)
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.06  | | | | | | | | 
% 196.79/32.06  | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | |   (7262)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.06  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 196.79/32.06  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | BETA: splitting (7262) gives:
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | |   (7263)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.06  | | | | | | | | | |           all_52_6 = e0
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.79/32.06  | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.79/32.06  | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.79/32.06  | | | | | | | | | |            (5905), (7263), (function-axioms) are inconsistent
% 196.79/32.06  | | | | | | | | | |            by sub-proof #302.
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | |   (7264)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.06  | | | | | | | | | |           all_52_14 = e0
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | ALPHA: (7264) implies:
% 196.79/32.06  | | | | | | | | | |   (7265)  all_52_14 = e0
% 196.79/32.06  | | | | | | | | | |   (7266)  all_52_12 = e1
% 196.79/32.06  | | | | | | | | | |   (7267)  all_52_10 = e2
% 196.79/32.06  | | | | | | | | | |   (7268)  all_52_8 = e3
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (182), (7268) imply:
% 196.79/32.06  | | | | | | | | | |   (7269)  op(all_52_9, all_52_9) = e3
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (180), (7266) imply:
% 196.79/32.06  | | | | | | | | | |   (7270)  op(all_52_13, all_52_13) = e1
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (179), (7265) imply:
% 196.79/32.06  | | | | | | | | | |   (7271)  op(all_52_15, all_52_15) = e0
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (611), (7267) imply:
% 196.79/32.06  | | | | | | | | | |   (7272)  op(all_4_2, all_4_2) = e2
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.06  | | | | | | | | | |            (43), (51), (61), (62), (63), (156), (158), (162),
% 196.79/32.06  | | | | | | | | | |            (166), (167), (168), (169), (172), (174), (175),
% 196.79/32.06  | | | | | | | | | |            (178), (183), (184), (185), (270), (272), (273),
% 196.79/32.06  | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 196.79/32.06  | | | | | | | | | |            (283), (284), (285), (304), (305), (306), (309),
% 196.79/32.06  | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (320),
% 196.79/32.06  | | | | | | | | | |            (321), (323), (325), (326), (328), (329), (330),
% 196.79/32.06  | | | | | | | | | |            (331), (332), (333), (346), (351), (366), (367),
% 196.79/32.06  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.06  | | | | | | | | | |            (411), (415), (417), (421), (427), (431), (529),
% 196.79/32.06  | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.79/32.06  | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.79/32.06  | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.79/32.06  | | | | | | | | | |            (567), (568), (570), (571), (572), (573), (574),
% 196.79/32.06  | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 196.79/32.06  | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 196.79/32.06  | | | | | | | | | |            (593), (594), (595), (597), (600), (603), (604),
% 196.79/32.06  | | | | | | | | | |            (605), (606), (608), (609), (610), (612), (613),
% 196.79/32.06  | | | | | | | | | |            (641), (772), (5903), (5905), (6770), (7255),
% 196.79/32.06  | | | | | | | | | |            (7259), (7260), (7269), (7270), (7271), (7272),
% 196.79/32.06  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.06  | | | | | | | | | |            #287.
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | |   (7273)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.06  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 196.79/32.06  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | BETA: splitting (7273) gives:
% 196.79/32.06  | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | |   (7274)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.06  | | | | | | | | | |           all_52_22 = e0
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | ALPHA: (7274) implies:
% 196.79/32.06  | | | | | | | | | |   (7275)  all_52_22 = e0
% 196.79/32.06  | | | | | | | | | |   (7276)  all_52_20 = e1
% 196.79/32.06  | | | | | | | | | |   (7277)  all_52_18 = e2
% 196.79/32.06  | | | | | | | | | |   (7278)  all_52_16 = e3
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (178), (7278) imply:
% 196.79/32.06  | | | | | | | | | |   (7279)  op(all_52_17, all_52_17) = e3
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (177), (7277) imply:
% 196.79/32.06  | | | | | | | | | |   (7280)  op(all_52_19, all_52_19) = e2
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (175), (7275) imply:
% 196.79/32.06  | | | | | | | | | |   (7281)  op(all_52_23, all_52_23) = e0
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | REDUCE: (612), (7276) imply:
% 196.79/32.06  | | | | | | | | | |   (7282)  op(all_10_2, all_10_2) = e1
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | BETA: splitting (270) gives:
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | |   (7283)  all_56_15 = e3
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | COMBINE_EQS: (538), (7283) imply:
% 196.79/32.06  | | | | | | | | | | |   (7284)  all_14_2 = e3
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | SIMP: (7284) implies:
% 196.79/32.06  | | | | | | | | | | |   (7285)  all_14_2 = e3
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REDUCE: (573), (7285) imply:
% 196.79/32.06  | | | | | | | | | | |   (7286)   ~ (all_52_7 = e3)
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REDUCE: (603), (7285) imply:
% 196.79/32.06  | | | | | | | | | | |   (7287)   ~ (all_52_23 = e3)
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REDUCE: (606), (7285) imply:
% 196.79/32.06  | | | | | | | | | | |   (7288)   ~ (all_52_25 = e3)
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REDUCE: (609), (7285) imply:
% 196.79/32.06  | | | | | | | | | | |   (7289)   ~ (all_52_29 = e3)
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REDUCE: (613), (7285) imply:
% 196.79/32.06  | | | | | | | | | | |   (7290)  op(e3, e3) = all_52_30
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.79/32.06  | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (7290)
% 196.79/32.06  | | | | | | | | | | |              gives:
% 196.79/32.06  | | | | | | | | | | |   (7291)  all_52_30 = all_6_2
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | BETA: splitting (273) gives:
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | |   (7292)  all_56_12 = e3
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | COMBINE_EQS: (431), (7292) imply:
% 196.79/32.06  | | | | | | | | | | | |   (7293)  all_52_7 = e3
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | REDUCE: (7286), (7293) imply:
% 196.79/32.06  | | | | | | | | | | | |   (7294)  $false
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | CLOSE: (7294) is inconsistent.
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | |   (7295)   ~ (all_56_12 = e3)
% 196.79/32.06  | | | | | | | | | | | |   (7296)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | BETA: splitting (276) gives:
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | |   (7297)  all_56_9 = e3
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | COMBINE_EQS: (421), (7297) imply:
% 196.79/32.06  | | | | | | | | | | | | |   (7298)  all_52_13 = e3
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | SIMP: (7298) implies:
% 196.79/32.06  | | | | | | | | | | | | |   (7299)  all_52_13 = e3
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | REDUCE: (575), (7299) imply:
% 196.79/32.06  | | | | | | | | | | | | |   (7300)   ~ (all_52_9 = e3)
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | REDUCE: (180), (7299) imply:
% 196.79/32.06  | | | | | | | | | | | | |   (7301)  op(e3, e3) = all_52_12
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.79/32.06  | | | | | | | | | | | | |              all_52_12, e3, e3, simplifying with (41), (7301)
% 196.79/32.06  | | | | | | | | | | | | |              gives:
% 196.79/32.06  | | | | | | | | | | | | |   (7302)  all_52_12 = all_6_2
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | |   (7303)  all_58_0 = e3
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | COMBINE_EQS: (405), (7303) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7304)  all_6_2 = e3
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REF_CLOSE: (8), (41), (43), (5905), (7304), (function-axioms)
% 196.79/32.06  | | | | | | | | | | | | | |            are inconsistent by sub-proof #310.
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | |   (7305)   ~ (all_58_0 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (405), (7305) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7306)   ~ (all_6_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REF_CLOSE: (41), (333), (393), (405), (545), (549), (559),
% 196.79/32.06  | | | | | | | | | | | | | |            (7279), (7288), (7300), (7306), (function-axioms)
% 196.79/32.06  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1071.
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | |   (7307)   ~ (all_56_9 = e3)
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | REDUCE: (421), (7307) imply:
% 196.79/32.06  | | | | | | | | | | | | |   (7308)   ~ (all_52_13 = e3)
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | BETA: splitting (325) gives:
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | |   (7309)  all_58_1 = e3
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | COMBINE_EQS: (549), (7309) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7310)  all_52_9 = e3
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (575), (7310) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7311)   ~ (all_52_13 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (576), (7310) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7312)   ~ (all_52_15 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | SIMP: (7312) implies:
% 196.79/32.06  | | | | | | | | | | | | | |   (7313)   ~ (all_52_15 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (577), (7310) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7314)   ~ (all_52_17 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | SIMP: (7314) implies:
% 196.79/32.06  | | | | | | | | | | | | | |   (7315)   ~ (all_52_17 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (557), (7310) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7316)   ~ (all_6_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | SIMP: (7316) implies:
% 196.79/32.06  | | | | | | | | | | | | | |   (7317)   ~ (all_6_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (182), (7310) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7318)  op(e3, e3) = all_52_8
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.79/32.06  | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (41), (7318)
% 196.79/32.06  | | | | | | | | | | | | | |              gives:
% 196.79/32.06  | | | | | | | | | | | | | |   (7319)  all_52_8 = all_6_2
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | |   (7320)  all_58_6 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | COMBINE_EQS: (547), (7320) imply:
% 196.79/32.06  | | | | | | | | | | | | | | |   (7321)  all_52_5 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | SIMP: (7321) implies:
% 196.79/32.06  | | | | | | | | | | | | | | |   (7322)  all_52_5 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | REDUCE: (569), (7322) imply:
% 196.79/32.06  | | | | | | | | | | | | | | |   (7323)   ~ (all_10_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | SIMP: (7323) implies:
% 196.79/32.06  | | | | | | | | | | | | | | |   (7324)   ~ (all_10_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | REDUCE: (184), (7322) imply:
% 196.79/32.06  | | | | | | | | | | | | | | |   (7325)  op(e3, e3) = all_52_4
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | |   (7326)  all_58_4 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | REF_CLOSE: (393), (7315), (7326) are inconsistent by
% 196.79/32.06  | | | | | | | | | | | | | | | |            sub-proof #1302.
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | |   (7327)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | BETA: splitting (7327) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7328)  all_58_5 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (7328) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7329)  all_52_19 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | SIMP: (7329) implies:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7330)  all_52_19 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (565), (7330) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7331)   ~ (all_52_3 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (7280), (7330) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7332)  op(e3, e3) = e2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.79/32.06  | | | | | | | | | | | | | | | | |              all_52_4, e3, e3, simplifying with (41), (7325)
% 196.79/32.06  | | | | | | | | | | | | | | | | |              gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7333)  all_52_4 = all_6_2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_4,
% 196.79/32.06  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (7325), (7332) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7334)  all_52_4 = e2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7333), (7334) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7335)  all_6_2 = e2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | SIMP: (7335) implies:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7336)  all_6_2 = e2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (7336) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7337)  all_46_2 = e2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (551), (7336) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7338)   ~ (all_52_3 = e2)
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (555), (7336) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7339)   ~ (all_52_7 = e2)
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (43), (7336) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7340)  op(e2, e3) = all_6_1
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | BETA: splitting (7255) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7341)   ~ (all_46_2 = e2)
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | REDUCE: (7337), (7341) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7342)  $false
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | CLOSE: (7342) is inconsistent.
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7343)   ~ (all_46_1 = e0)
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | REDUCE: (641), (7343) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7344)   ~ (all_6_1 = e0)
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (166), (168), (185), (281), (411), (431),
% 196.79/32.06  | | | | | | | | | | | | | | | | | |            (563), (5905), (7279), (7296), (7324), (7331),
% 196.79/32.06  | | | | | | | | | | | | | | | | | |            (7338), (7339), (7340), (7344), (function-axioms)
% 196.79/32.06  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #241.
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7345)  all_58_8 = e3 | all_58_14 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (546), (7287), (7324), (7345) are
% 196.79/32.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1304.
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | |   (7346)   ~ (all_58_6 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | |   (7347)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | REDUCE: (547), (7346) imply:
% 196.79/32.06  | | | | | | | | | | | | | | |   (7348)   ~ (all_52_5 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | |   (7349)  all_58_0 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (7349) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | |   (7350)  all_6_2 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | REDUCE: (7317), (7350) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | |   (7351)  $false
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | CLOSE: (7351) is inconsistent.
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | |   (7352)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | BETA: splitting (7352) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7353)  all_58_2 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (7353) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7354)  all_52_3 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | SIMP: (7354) implies:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7355)  all_52_3 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (563), (7355) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7356)   ~ (all_52_7 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (564), (7355) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7357)   ~ (all_4_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | SIMP: (7357) implies:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7358)   ~ (all_4_2 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REDUCE: (185), (7355) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7359)  op(e3, e3) = all_52_2
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | BETA: splitting (7347) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7360)  all_58_7 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (7360) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7361)  all_52_13 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | REDUCE: (7308), (7361) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7362)  $false
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | CLOSE: (7362) is inconsistent.
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | |   (7363)  all_58_8 = e3 | all_58_11 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | BETA: splitting (7363) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7364)  all_58_8 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (7364) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7365)  all_10_2 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | REDUCE: (7282), (7365) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7366)  op(e3, e3) = e1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | REDUCE: (53), (7365) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7367)  op(e3, e1) = all_10_1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (7367)
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |              gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7368)  all_52_17 = all_10_1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |              all_52_2, e3, e3, simplifying with (41), (7359)
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |              gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7369)  all_52_2 = all_6_2
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_2,
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (7359), (7366) gives:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7370)  all_52_2 = e1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7369), (7370) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7371)  all_6_2 = e1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | SIMP: (7371) implies:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7372)  all_6_2 = e1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (7368) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7373)  all_58_4 = all_10_1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (7372) imply:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7374)  all_58_0 = e1
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (159),
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            (168), (325), (327), (331), (332), (351), (366),
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            (387), (405), (543), (547), (548), (564), (6769),
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            (7279), (7286), (7289), (7308), (7309), (7313),
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            (7348), (7358), (7366), (7367), (7373), (7374),
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            #534.
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |   (7375)  all_58_11 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (7289), (7375) are inconsistent by
% 196.79/32.06  | | | | | | | | | | | | | | | | | | |            sub-proof #1323.
% 196.79/32.06  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | |   (7376)  all_58_6 = e3 | all_58_12 = e3
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (547), (7286), (7348), (7376) are
% 196.79/32.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1243.
% 196.79/32.06  | | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | |   (7377)   ~ (all_58_1 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REDUCE: (549), (7377) imply:
% 196.79/32.06  | | | | | | | | | | | | | |   (7378)   ~ (all_52_9 = e3)
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (41), (172), (274), (313), (317), (333),
% 196.79/32.06  | | | | | | | | | | | | | |            (352), (366), (375), (393), (405), (542), (544),
% 196.79/32.06  | | | | | | | | | | | | | |            (545), (546), (547), (549), (553), (559), (602),
% 196.79/32.06  | | | | | | | | | | | | | |            (610), (7279), (7280), (7282), (7287), (7288),
% 196.79/32.06  | | | | | | | | | | | | | |            (7308), (7378), (function-axioms) are inconsistent
% 196.79/32.06  | | | | | | | | | | | | | |            by sub-proof #281.
% 196.79/32.06  | | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | Case 2:
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | |   (7379)   ~ (all_56_15 = e3)
% 196.79/32.06  | | | | | | | | | | |   (7380)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REDUCE: (538), (7379) imply:
% 196.79/32.06  | | | | | | | | | | |   (7381)   ~ (all_14_2 = e3)
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.06  | | | | | | | | | | |            (51), (53), (61), (158), (161), (162), (168),
% 196.79/32.06  | | | | | | | | | | |            (172), (173), (174), (179), (180), (182), (183),
% 196.79/32.06  | | | | | | | | | | |            (184), (185), (272), (273), (274), (275), (279),
% 196.79/32.06  | | | | | | | | | | |            (282), (283), (284), (285), (306), (309), (313),
% 196.79/32.06  | | | | | | | | | | |            (315), (316), (317), (321), (323), (324), (327),
% 196.79/32.06  | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (346),
% 196.79/32.06  | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 196.79/32.06  | | | | | | | | | | |            (388), (393), (394), (405), (415), (417), (431),
% 196.79/32.06  | | | | | | | | | | |            (538), (540), (541), (542), (543), (544), (545),
% 196.79/32.06  | | | | | | | | | | |            (546), (547), (548), (549), (553), (555), (557),
% 196.79/32.06  | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (569),
% 196.79/32.06  | | | | | | | | | | |            (571), (572), (573), (574), (576), (577), (578),
% 196.79/32.06  | | | | | | | | | | |            (580), (586), (587), (588), (590), (595), (596),
% 196.79/32.06  | | | | | | | | | | |            (597), (600), (602), (603), (604), (605), (606),
% 196.79/32.06  | | | | | | | | | | |            (608), (610), (5903), (5905), (6769), (7259),
% 196.79/32.06  | | | | | | | | | | |            (7261), (7279), (7280), (7281), (7282), (7380),
% 196.79/32.06  | | | | | | | | | | |            (7381), (function-axioms) are inconsistent by
% 196.79/32.06  | | | | | | | | | | |            sub-proof #225.
% 196.79/32.06  | | | | | | | | | | | 
% 196.79/32.06  | | | | | | | | | | End of split
% 196.79/32.06  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | Case 2:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | |   (7382)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.07  | | | | | | | | | |           all_52_30 = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.07  | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 196.79/32.07  | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 196.79/32.07  | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 196.79/32.07  | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 196.79/32.07  | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.79/32.07  | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 196.79/32.07  | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 196.79/32.07  | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 196.79/32.07  | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 196.79/32.07  | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 196.79/32.07  | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 196.79/32.07  | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.79/32.07  | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.79/32.07  | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 196.79/32.07  | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 196.79/32.07  | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 196.79/32.07  | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 196.79/32.07  | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 196.79/32.07  | | | | | | | | | |            (641), (5903), (5905), (7255), (7259), (7261),
% 196.79/32.07  | | | | | | | | | |            (7382), (function-axioms) are inconsistent by
% 196.79/32.07  | | | | | | | | | |            sub-proof #271.
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | End of split
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | End of split
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | End of split
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | End of split
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | End of split
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | Case 2:
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | |   (7383)  all_14_0 = e2
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | | COMBINE_EQS: (771), (7383) imply:
% 196.79/32.07  | | | | |   (7384)  all_50_0 = e2
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | | REDUCE: (62), (7383) imply:
% 196.79/32.07  | | | | |   (7385)  op(e0, all_14_1) = e2
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | | BETA: splitting (144) gives:
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | | Case 1:
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | |   (7386)   ~ (all_46_0 = e1)
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | REDUCE: (5904), (7386) imply:
% 196.79/32.07  | | | | | |   (7387)  $false
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | CLOSE: (7387) is inconsistent.
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | Case 2:
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | |   (7388)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | BETA: splitting (153) gives:
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | Case 1:
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | |   (7389)   ~ (all_50_0 = e2)
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | | REDUCE: (7384), (7389) imply:
% 196.79/32.07  | | | | | | |   (7390)  $false
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | | CLOSE: (7390) is inconsistent.
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | Case 2:
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | |   (7391)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | | BETA: splitting (303) gives:
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | |   (7392)  all_58_15 = e0
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (7385), (7392),
% 196.79/32.07  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #612.
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | Case 2:
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | |   (7393)   ~ (all_58_15 = e0)
% 196.79/32.07  | | | | | | | |   (7394)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 196.79/32.07  | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | ALPHA: (7394) implies:
% 196.79/32.07  | | | | | | | |   (7395)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.79/32.07  | | | | | | | |   (7396)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | REDUCE: (541), (7393) imply:
% 196.79/32.07  | | | | | | | |   (7397)   ~ (all_14_2 = e0)
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | |   (7398)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.07  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 196.79/32.07  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | BETA: splitting (7398) gives:
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | |   (7399)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.07  | | | | | | | | | |           all_52_6 = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 196.79/32.07  | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 196.79/32.07  | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 196.79/32.07  | | | | | | | | | |            (5905), (7399), (function-axioms) are inconsistent
% 196.79/32.07  | | | | | | | | | |            by sub-proof #302.
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | Case 2:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | |   (7400)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.07  | | | | | | | | | |           all_52_14 = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | ALPHA: (7400) implies:
% 196.79/32.07  | | | | | | | | | |   (7401)  all_52_14 = e0
% 196.79/32.07  | | | | | | | | | |   (7402)  all_52_12 = e1
% 196.79/32.07  | | | | | | | | | |   (7403)  all_52_10 = e2
% 196.79/32.07  | | | | | | | | | |   (7404)  all_52_8 = e3
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (182), (7404) imply:
% 196.79/32.07  | | | | | | | | | |   (7405)  op(all_52_9, all_52_9) = e3
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (180), (7402) imply:
% 196.79/32.07  | | | | | | | | | |   (7406)  op(all_52_13, all_52_13) = e1
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (179), (7401) imply:
% 196.79/32.07  | | | | | | | | | |   (7407)  op(all_52_15, all_52_15) = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (611), (7403) imply:
% 196.79/32.07  | | | | | | | | | |   (7408)  op(all_4_2, all_4_2) = e2
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.07  | | | | | | | | | |            (43), (51), (61), (63), (157), (158), (162),
% 196.79/32.07  | | | | | | | | | |            (166), (167), (168), (169), (172), (174), (175),
% 196.79/32.07  | | | | | | | | | |            (178), (183), (184), (185), (270), (272), (273),
% 196.79/32.07  | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 196.79/32.07  | | | | | | | | | |            (284), (285), (306), (309), (312), (313), (314),
% 196.79/32.07  | | | | | | | | | |            (315), (316), (317), (320), (321), (323), (324),
% 196.79/32.07  | | | | | | | | | |            (325), (326), (328), (329), (330), (332), (333),
% 196.79/32.07  | | | | | | | | | |            (335), (346), (351), (366), (367), (372), (375),
% 196.79/32.07  | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 196.79/32.07  | | | | | | | | | |            (417), (427), (431), (529), (538), (539), (540),
% 196.79/32.07  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.79/32.07  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.79/32.07  | | | | | | | | | |            (561), (562), (563), (564), (567), (570), (571),
% 196.79/32.07  | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.79/32.07  | | | | | | | | | |            (580), (582), (584), (586), (589), (590), (592),
% 196.79/32.07  | | | | | | | | | |            (593), (594), (595), (597), (600), (603), (604),
% 196.79/32.07  | | | | | | | | | |            (605), (606), (608), (609), (610), (612), (613),
% 196.79/32.07  | | | | | | | | | |            (641), (690), (772), (5903), (5905), (7385),
% 196.79/32.07  | | | | | | | | | |            (7388), (7391), (7395), (7396), (7405), (7406),
% 196.79/32.07  | | | | | | | | | |            (7407), (7408), (function-axioms) are inconsistent
% 196.79/32.07  | | | | | | | | | |            by sub-proof #234.
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | End of split
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | Case 2:
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | |   (7409)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.07  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 196.79/32.07  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | BETA: splitting (7409) gives:
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | |   (7410)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.07  | | | | | | | | | |           all_52_22 = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | ALPHA: (7410) implies:
% 196.79/32.07  | | | | | | | | | |   (7411)  all_52_22 = e0
% 196.79/32.07  | | | | | | | | | |   (7412)  all_52_20 = e1
% 196.79/32.07  | | | | | | | | | |   (7413)  all_52_18 = e2
% 196.79/32.07  | | | | | | | | | |   (7414)  all_52_16 = e3
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (178), (7414) imply:
% 196.79/32.07  | | | | | | | | | |   (7415)  op(all_52_17, all_52_17) = e3
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (177), (7413) imply:
% 196.79/32.07  | | | | | | | | | |   (7416)  op(all_52_19, all_52_19) = e2
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (175), (7411) imply:
% 196.79/32.07  | | | | | | | | | |   (7417)  op(all_52_23, all_52_23) = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (612), (7412) imply:
% 196.79/32.07  | | | | | | | | | |   (7418)  op(all_10_2, all_10_2) = e1
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | BETA: splitting (270) gives:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | |   (7419)  all_56_15 = e3
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | COMBINE_EQS: (538), (7419) imply:
% 196.79/32.07  | | | | | | | | | | |   (7420)  all_14_2 = e3
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | COMBINE_EQS: (335), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7421)  all_50_2 = e3
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | COMBINE_EQS: (541), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7422)  all_58_15 = e3
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (573), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7423)   ~ (all_52_7 = e3)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (603), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7424)   ~ (all_52_23 = e3)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (606), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7425)   ~ (all_52_25 = e3)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (608), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7426)   ~ (all_52_27 = e3)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (609), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7427)   ~ (all_52_29 = e3)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (613), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7428)  op(e3, e3) = all_52_30
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (63), (7420) imply:
% 196.79/32.07  | | | | | | | | | | |   (7429)  op(e3, e0) = all_14_1
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (41), (43), (51), (53),
% 196.79/32.07  | | | | | | | | | | |            (61), (157), (162), (166), (167), (168), (172),
% 196.79/32.07  | | | | | | | | | | |            (173), (174), (179), (180), (182), (183), (184),
% 196.79/32.07  | | | | | | | | | | |            (185), (271), (274), (277), (279), (281), (282),
% 196.79/32.07  | | | | | | | | | | |            (283), (304), (308), (313), (317), (321), (325),
% 196.79/32.07  | | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 196.79/32.07  | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.79/32.07  | | | | | | | | | | |            (393), (405), (411), (415), (417), (542), (543),
% 196.79/32.07  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.79/32.07  | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (564),
% 196.79/32.07  | | | | | | | | | | |            (565), (567), (568), (569), (574), (575), (576),
% 196.79/32.07  | | | | | | | | | | |            (577), (580), (582), (586), (588), (589), (590),
% 196.79/32.07  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (602),
% 196.79/32.07  | | | | | | | | | | |            (608), (610), (690), (5905), (7385), (7391),
% 196.79/32.07  | | | | | | | | | | |            (7415), (7416), (7418), (7421), (7422), (7423),
% 196.79/32.07  | | | | | | | | | | |            (7424), (7425), (7426), (7427), (7428), (7429),
% 196.79/32.07  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.07  | | | | | | | | | | |            #230.
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | Case 2:
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | |   (7430)   ~ (all_56_15 = e3)
% 196.79/32.07  | | | | | | | | | | |   (7431)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (538), (7430) imply:
% 196.79/32.07  | | | | | | | | | | |   (7432)   ~ (all_14_2 = e3)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 196.79/32.07  | | | | | | | | | | |            (51), (53), (61), (158), (161), (162), (168),
% 196.79/32.07  | | | | | | | | | | |            (172), (173), (174), (179), (180), (182), (183),
% 196.79/32.07  | | | | | | | | | | |            (184), (185), (272), (273), (274), (275), (279),
% 196.79/32.07  | | | | | | | | | | |            (282), (283), (284), (285), (306), (309), (313),
% 196.79/32.07  | | | | | | | | | | |            (315), (316), (317), (321), (323), (324), (327),
% 196.79/32.07  | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (346),
% 196.79/32.07  | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 196.79/32.07  | | | | | | | | | | |            (388), (393), (394), (405), (415), (417), (431),
% 196.79/32.07  | | | | | | | | | | |            (538), (540), (541), (542), (543), (544), (545),
% 196.79/32.07  | | | | | | | | | | |            (546), (547), (548), (549), (553), (555), (557),
% 196.79/32.07  | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (569),
% 196.79/32.07  | | | | | | | | | | |            (571), (572), (573), (574), (576), (577), (578),
% 196.79/32.07  | | | | | | | | | | |            (580), (586), (587), (588), (590), (595), (596),
% 196.79/32.07  | | | | | | | | | | |            (597), (600), (602), (603), (604), (605), (606),
% 196.79/32.07  | | | | | | | | | | |            (608), (610), (5903), (5905), (6769), (7395),
% 196.79/32.07  | | | | | | | | | | |            (7397), (7415), (7416), (7417), (7418), (7431),
% 196.79/32.07  | | | | | | | | | | |            (7432), (function-axioms) are inconsistent by
% 196.79/32.07  | | | | | | | | | | |            sub-proof #225.
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | End of split
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | Case 2:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | |   (7433)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.07  | | | | | | | | | |           all_52_30 = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | ALPHA: (7433) implies:
% 196.79/32.07  | | | | | | | | | |   (7434)  all_52_30 = e0
% 196.79/32.07  | | | | | | | | | |   (7435)  all_52_28 = e1
% 196.79/32.07  | | | | | | | | | |   (7436)  all_52_26 = e2
% 196.79/32.07  | | | | | | | | | |   (7437)  all_52_24 = e3
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (174), (7437) imply:
% 196.79/32.07  | | | | | | | | | |   (7438)  op(all_52_25, all_52_25) = e3
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (173), (7436) imply:
% 196.79/32.07  | | | | | | | | | |   (7439)  op(all_52_27, all_52_27) = e2
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (172), (7435) imply:
% 196.79/32.07  | | | | | | | | | |   (7440)  op(all_52_29, all_52_29) = e1
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (613), (7434) imply:
% 196.79/32.07  | | | | | | | | | |   (7441)  op(all_14_2, all_14_2) = e0
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 196.79/32.07  | | | | | | | | | |            (43), (51), (53), (61), (63), (157), (158), (162),
% 196.79/32.07  | | | | | | | | | |            (166), (167), (168), (169), (175), (177), (178),
% 196.79/32.07  | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (270),
% 196.79/32.07  | | | | | | | | | |            (271), (272), (273), (274), (277), (280), (281),
% 196.79/32.07  | | | | | | | | | |            (282), (283), (284), (285), (306), (307), (309),
% 196.79/32.07  | | | | | | | | | |            (311), (313), (315), (316), (319), (320), (321),
% 196.79/32.07  | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 196.79/32.07  | | | | | | | | | |            (332), (333), (335), (343), (346), (351), (352),
% 196.79/32.07  | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 196.79/32.07  | | | | | | | | | |            (394), (405), (411), (415), (431), (529), (538),
% 196.79/32.07  | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.79/32.07  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.79/32.07  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.79/32.07  | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.79/32.07  | | | | | | | | | |            (574), (575), (576), (578), (582), (584), (586),
% 196.79/32.07  | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 196.79/32.07  | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 196.79/32.07  | | | | | | | | | |            (606), (607), (608), (609), (610), (641), (690),
% 196.79/32.07  | | | | | | | | | |            (772), (5905), (7385), (7388), (7391), (7395),
% 196.79/32.07  | | | | | | | | | |            (7397), (7438), (7439), (7440), (7441),
% 196.79/32.07  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.07  | | | | | | | | | |            #229.
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | End of split
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | End of split
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | End of split
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | End of split
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | End of split
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | End of split
% 196.79/32.07  | | | | 
% 196.79/32.07  | | | End of split
% 196.79/32.07  | | | 
% 196.79/32.07  | | End of split
% 196.79/32.07  | | 
% 196.79/32.07  | Case 2:
% 196.79/32.07  | | 
% 196.79/32.07  | |   (7442)  all_4_1 = e1
% 196.79/32.07  | |   (7443)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 196.79/32.07  | | 
% 196.79/32.07  | | COMBINE_EQS: (674), (7442) imply:
% 196.79/32.07  | |   (7444)  all_28_1 = e1
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (38), (7442) imply:
% 196.79/32.07  | |   (7445)  op(all_4_2, e2) = e1
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (37), (7442) imply:
% 196.79/32.07  | |   (7446)  op(e2, e1) = all_4_0
% 196.79/32.07  | | 
% 196.79/32.07  | | GROUND_INST: instantiating (function-axioms) with all_52_19, all_4_0, e1,
% 196.79/32.07  | |              e2, simplifying with (164), (7446) gives:
% 196.79/32.07  | |   (7447)  all_52_19 = all_4_0
% 196.79/32.07  | | 
% 196.79/32.07  | | COMBINE_EQS: (417), (7447) imply:
% 196.79/32.07  | |   (7448)  all_56_6 = all_4_0
% 196.79/32.07  | | 
% 196.79/32.07  | | COMBINE_EQS: (375), (7447) imply:
% 196.79/32.07  | |   (7449)  all_58_5 = all_4_0
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (565), (7447) imply:
% 196.79/32.07  | |   (7450)   ~ (all_52_3 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (592), (7447) imply:
% 196.79/32.07  | |   (7451)   ~ (all_52_17 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (597), (7447) imply:
% 196.79/32.07  | |   (7452)   ~ (all_52_23 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | SIMP: (7452) implies:
% 196.79/32.07  | |   (7453)   ~ (all_52_23 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (598), (7447) imply:
% 196.79/32.07  | |   (7454)   ~ (all_52_27 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | SIMP: (7454) implies:
% 196.79/32.07  | |   (7455)   ~ (all_52_27 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (596), (7447) imply:
% 196.79/32.07  | |   (7456)   ~ (all_10_2 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | SIMP: (7456) implies:
% 196.79/32.07  | |   (7457)   ~ (all_10_2 = all_4_0)
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (584), (7447) imply:
% 196.79/32.07  | |   (7458)   ~ (all_4_0 = all_4_2)
% 196.79/32.07  | | 
% 196.79/32.07  | | REDUCE: (177), (7447) imply:
% 196.79/32.07  | |   (7459)  op(all_4_0, all_4_0) = all_52_18
% 196.79/32.07  | | 
% 196.79/32.07  | | BETA: splitting (44) gives:
% 196.79/32.07  | | 
% 196.79/32.07  | | Case 1:
% 196.79/32.07  | | | 
% 196.79/32.07  | | |   (7460)   ~ (all_6_0 = e1)
% 196.79/32.07  | | | 
% 196.79/32.07  | | | BETA: splitting (49) gives:
% 196.79/32.07  | | | 
% 196.79/32.07  | | | Case 1:
% 196.79/32.07  | | | | 
% 196.79/32.07  | | | |   (7461)   ~ (all_8_0 = e2)
% 196.79/32.07  | | | | 
% 196.79/32.07  | | | | REDUCE: (764), (7461) imply:
% 196.79/32.07  | | | |   (7462)   ~ (all_6_0 = e2)
% 196.79/32.07  | | | | 
% 196.79/32.07  | | | | BETA: splitting (54) gives:
% 196.79/32.07  | | | | 
% 196.79/32.07  | | | | Case 1:
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | |   (7463)   ~ (all_10_0 = e3)
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | | BETA: splitting (59) gives:
% 196.79/32.07  | | | | | 
% 196.79/32.07  | | | | | Case 1:
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | |   (7464)   ~ (all_12_1 = e1)
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | REDUCE: (683), (7464) imply:
% 196.79/32.07  | | | | | |   (7465)   ~ (all_6_1 = e1)
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | BETA: splitting (64) gives:
% 196.79/32.07  | | | | | | 
% 196.79/32.07  | | | | | | Case 1:
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | |   (7466)   ~ (all_14_0 = e2)
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | | BETA: splitting (69) gives:
% 196.79/32.07  | | | | | | | 
% 196.79/32.07  | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | |   (7467)   ~ (all_16_0 = e2)
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | REDUCE: (760), (7467) imply:
% 196.79/32.07  | | | | | | | |   (7468)   ~ (all_10_0 = e2)
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | BETA: splitting (74) gives:
% 196.79/32.07  | | | | | | | | 
% 196.79/32.07  | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | |   (7469)   ~ (all_18_0 = e3)
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | REDUCE: (761), (7469) imply:
% 196.79/32.07  | | | | | | | | |   (7470)   ~ (all_14_0 = e3)
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | BETA: splitting (84) gives:
% 196.79/32.07  | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | |   (7471)   ~ (all_22_1 = e2)
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | REDUCE: (658), (7471) imply:
% 196.79/32.07  | | | | | | | | | |   (7472)   ~ (all_6_1 = e2)
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | BETA: splitting (89) gives:
% 196.79/32.07  | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | Case 1:
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | |   (7473)   ~ (all_24_0 = e1)
% 196.79/32.07  | | | | | | | | | | | 
% 196.79/32.07  | | | | | | | | | | | REDUCE: (711), (7473) imply:
% 196.79/32.08  | | | | | | | | | | |   (7474)   ~ (all_14_0 = e1)
% 196.79/32.08  | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | BETA: splitting (99) gives:
% 196.79/32.08  | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | |   (7475)   ~ (all_28_0 = e3)
% 196.79/32.08  | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | REDUCE: (754), (7475) imply:
% 196.79/32.08  | | | | | | | | | | | |   (7476)   ~ (all_4_0 = e3)
% 196.79/32.08  | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | BETA: splitting (104) gives:
% 196.79/32.08  | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | |   (7477)   ~ (all_30_1 = e3)
% 196.79/32.08  | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | REDUCE: (670), (7477) imply:
% 196.79/32.08  | | | | | | | | | | | | |   (7478)   ~ (all_10_1 = e3)
% 196.79/32.08  | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 196.79/32.08  | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | |   (7479)   ~ (all_40_1 = e2)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (687), (7479) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7480)   ~ (all_10_1 = e2)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | |   (7481)  all_58_15 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (7481) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7482)  all_14_2 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | SIMP: (7482) implies:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7483)  all_14_2 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (573), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7484)   ~ (all_52_7 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (591), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7485)   ~ (all_52_15 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (603), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7486)   ~ (all_52_23 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (606), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7487)   ~ (all_52_25 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (608), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7488)   ~ (all_52_27 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (609), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7489)   ~ (all_52_29 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (613), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7490)  op(e0, e0) = all_52_30
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (63), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7491)  op(e0, e0) = all_14_1
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (61), (7483) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7492)  op(e0, e0) = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.79/32.08  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7490), (7491)
% 196.79/32.08  | | | | | | | | | | | | | | |              gives:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7493)  all_52_30 = all_14_1
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.79/32.08  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7490), (7492)
% 196.79/32.08  | | | | | | | | | | | | | | |              gives:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7494)  all_52_30 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | COMBINE_EQS: (7493), (7494) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7495)  all_14_1 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | SIMP: (7495) implies:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7496)  all_14_1 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (62), (7496) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7497)  op(e0, e0) = all_14_0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.79/32.08  | | | | | | | | | | | | | | |              e0, e0, simplifying with (7492), (7497) gives:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7498)  all_14_0 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (7470), (7498) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7499)   ~ (e3 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (7466), (7498) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7500)   ~ (e2 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (7474), (7498) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7501)   ~ (e1 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | |   (7502)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.08  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | BETA: splitting (7502) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7503)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (41), (51), (53), (61),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (156), (175), (179), (183), (184), (185), (271),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (272), (273), (304), (305), (306), (321), (326),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (332), (343), (346), (351), (387), (405), (431),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (542), (543), (547), (555), (564), (569), (571),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (572), (573), (582), (590), (600), (610), (611),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (7478), (7480), (7481), (7484), (7486), (7492),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (7503), (function-axioms) are inconsistent by
% 196.79/32.08  | | | | | | | | | | | | | | | | |            sub-proof #216.
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7504)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | ALPHA: (7504) implies:
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7505)  all_52_14 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7506)  all_52_12 = e1
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7507)  all_52_10 = e2
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7508)  all_52_8 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REDUCE: (182), (7508) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7509)  op(all_52_9, all_52_9) = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REDUCE: (180), (7506) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7510)  op(all_52_13, all_52_13) = e1
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REDUCE: (179), (7505) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7511)  op(all_52_15, all_52_15) = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REDUCE: (611), (7507) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7512)  op(all_4_2, all_4_2) = e2
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | |   (7513)  all_56_13 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (158), (273), (346), (431), (555),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (571), (7465), (7472), (7511), (7513),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            #893.
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | |   (7514)   ~ (all_56_13 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | |   (7515)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | REDUCE: (346), (7514) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | |   (7516)   ~ (all_52_15 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7517)  all_58_12 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (7517) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7518)  all_52_7 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | SIMP: (7518) implies:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7519)  all_52_7 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (7519) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7520)   ~ (all_52_3 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REDUCE: (567), (7519) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7521)   ~ (all_52_5 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REDUCE: (571), (7519) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7522)   ~ (all_52_15 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REDUCE: (572), (7519) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7523)   ~ (all_52_23 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | SIMP: (7523) implies:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7524)   ~ (all_52_23 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REDUCE: (555), (7519) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7525)   ~ (all_6_2 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | SIMP: (7525) implies:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7526)   ~ (all_6_2 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (7519) imply:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7527)  op(e3, e3) = all_52_6
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (7527)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |              gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7528)  all_52_6 = all_6_2
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (41), (51), (53), (168), (169), (178),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (274), (282), (284), (310), (313), (314), (317),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (318), (321), (322), (325), (326), (327), (333),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (352), (366), (372), (387), (388), (393), (394),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (405), (542), (543), (544), (545), (546), (547),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (548), (549), (557), (559), (561), (562), (564),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (568), (574), (575), (577), (578), (580), (582),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (588), (593), (595), (602), (607), (612), (7443),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (7445), (7449), (7451), (7476), (7485), (7486),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (7487), (7492), (7509), (7510), (7516), (7517),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (7520), (7521), (7524), (7526), (function-axioms)
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #206.
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |   (7529)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (51), (53), (156), (273), (304),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (305), (346), (351), (431), (542), (543), (571),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (572), (582), (7478), (7481), (7484), (7485),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (7492), (7511), (7512), (7515), (7516), (7529),
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.08  | | | | | | | | | | | | | | | | | | |            #1288.
% 196.79/32.08  | | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | End of split
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | End of split
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | End of split
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | |   (7530)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.08  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.08  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | BETA: splitting (7530) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7531)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (42), (43), (53), (61),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (63), (158), (162), (167), (168), (169), (175),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (178), (183), (185), (270), (272), (273), (277),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (282), (283), (306), (317), (321), (325), (330),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (366), (367),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (431), (538), (541), (542), (543), (545), (546),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (559), (562), (563), (564), (566), (567), (572),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (573), (574), (576), (588), (590), (591), (593),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (596), (603), (606), (608), (611), (612), (613),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7458), (7462),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (7465), (7472), (7476), (7480), (7531),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.79/32.08  | | | | | | | | | | | | | | | | |            #200.
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7532)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (172),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (173), (174), (175), (179), (183), (272), (273),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (274), (278), (281), (282), (304), (305), (306),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (318), (321), (326),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (352), (366),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (561),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (563), (564), (567), (569), (570), (571), (572),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (576), (582), (587), (588), (593), (595), (596),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (600), (602), (604), (605), (608), (610), (7460),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (7462), (7472), (7481), (7484), (7485), (7486),
% 196.79/32.08  | | | | | | | | | | | | | | | | |            (7487), (7488), (7489), (7532), (function-axioms)
% 196.79/32.08  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | End of split
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | End of split
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | |   (7533)   ~ (all_58_15 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | |   (7534)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.79/32.08  | | | | | | | | | | | | | | |             e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.79/32.08  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.79/32.08  | | | | | | | | | | | | | | |            (159), (162), (166), (167), (168), (169), (172),
% 196.79/32.08  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.79/32.08  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.79/32.08  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 196.79/32.08  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.79/32.08  | | | | | | | | | | | | | | |            (305), (306), (307), (309), (310), (311), (313),
% 196.79/32.08  | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (323), (324),
% 196.79/32.08  | | | | | | | | | | | | | | |            (325), (327), (328), (330), (331), (332), (333),
% 196.79/32.08  | | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.79/32.08  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.79/32.08  | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (538), (539),
% 196.79/32.08  | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.79/32.08  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.79/32.08  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.79/32.08  | | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.79/32.08  | | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.79/32.08  | | | | | | | | | | | | | | |            (584), (586), (587), (588), (590), (591), (592),
% 196.79/32.08  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.79/32.08  | | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.79/32.08  | | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (7443), (7445),
% 196.79/32.08  | | | | | | | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 196.79/32.08  | | | | | | | | | | | | | | |            (7460), (7462), (7465), (7466), (7472), (7476),
% 196.79/32.08  | | | | | | | | | | | | | | |            (7478), (7480), (7533), (7534), (function-axioms)
% 196.79/32.08  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #186.
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | End of split
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | |   (7535)  all_40_1 = e2
% 196.79/32.08  | | | | | | | | | | | | | |   (7536)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | COMBINE_EQS: (687), (7535) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7537)  all_10_1 = e2
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (7478), (7537) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7538)   ~ (e3 = e2)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (53), (7537) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7539)  op(all_10_2, e1) = e2
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (52), (7537) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7540)  op(e1, e2) = all_10_0
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.79/32.08  | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (7540)
% 196.79/32.08  | | | | | | | | | | | | | |              gives:
% 196.79/32.08  | | | | | | | | | | | | | |   (7541)  all_52_13 = all_10_0
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | COMBINE_EQS: (421), (7541) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7542)  all_56_9 = all_10_0
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | COMBINE_EQS: (366), (7541) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7543)  all_58_7 = all_10_0
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (568), (7541) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7544)   ~ (all_52_5 = all_10_0)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (575), (7541) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7545)   ~ (all_52_9 = all_10_0)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (589), (7541) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7546)   ~ (all_52_29 = all_10_0)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | SIMP: (7546) implies:
% 196.79/32.08  | | | | | | | | | | | | | |   (7547)   ~ (all_52_29 = all_10_0)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | REDUCE: (580), (7541) imply:
% 196.79/32.08  | | | | | | | | | | | | | |   (7548)   ~ (all_10_0 = all_4_2)
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.79/32.08  | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | |   (7549)  all_58_15 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | COMBINE_EQS: (541), (7549) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7550)  all_14_2 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (573), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7551)   ~ (all_52_7 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (591), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7552)   ~ (all_52_15 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (603), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7553)   ~ (all_52_23 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (606), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7554)   ~ (all_52_25 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (608), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7555)   ~ (all_52_27 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (609), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7556)   ~ (all_52_29 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (613), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7557)  op(e0, e0) = all_52_30
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (63), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7558)  op(e0, e0) = all_14_1
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (61), (7550) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7559)  op(e0, e0) = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.79/32.08  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7557), (7558)
% 196.79/32.08  | | | | | | | | | | | | | | |              gives:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7560)  all_52_30 = all_14_1
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.79/32.08  | | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7557), (7559)
% 196.79/32.08  | | | | | | | | | | | | | | |              gives:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7561)  all_52_30 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | COMBINE_EQS: (7560), (7561) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7562)  all_14_1 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | SIMP: (7562) implies:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7563)  all_14_1 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (62), (7563) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7564)  op(e0, e0) = all_14_0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.79/32.08  | | | | | | | | | | | | | | |              e0, e0, simplifying with (7559), (7564) gives:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7565)  all_14_0 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (7470), (7565) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7566)   ~ (e3 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (7466), (7565) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7567)   ~ (e2 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | REDUCE: (7474), (7565) imply:
% 196.79/32.08  | | | | | | | | | | | | | | |   (7568)   ~ (e1 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | |   (7569)  all_56_9 = e3
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | REF_CLOSE: (7463), (7542), (7569) are inconsistent by
% 196.79/32.08  | | | | | | | | | | | | | | | |            sub-proof #1006.
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | |   (7570)   ~ (all_56_9 = e3)
% 196.79/32.08  | | | | | | | | | | | | | | | |   (7571)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | |   (7572)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.79/32.08  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | BETA: splitting (7572) gives:
% 196.79/32.08  | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | Case 1:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | |   (7573)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (183),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (184), (185), (273), (274), (277), (278), (282),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (310), (311),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (312), (317), (321), (325), (332), (351), (352),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (427), (431), (526), (542), (543), (544), (545),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (561), (564), (566), (567), (569), (570), (571),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (573), (586), (590), (596), (598), (604), (605),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (607), (610), (611), (612), (767), (7463), (7468),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (7536), (7539), (7542), (7543), (7544), (7547),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (7548), (7549), (7551), (7554), (7556), (7559),
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            (7571), (7573), (function-axioms) are inconsistent
% 196.79/32.08  | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.08  | | | | | | | | | | | | | | | | | |   (7574)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.79/32.08  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.79/32.08  | | | | | | | | | | | | | | | | | | 
% 196.79/32.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (158), (169), (179),
% 196.79/32.09  | | | | | | | | | | | | | | | | | |            (182), (273), (278), (321), (324), (325), (372),
% 196.79/32.09  | | | | | | | | | | | | | | | | | |            (387), (427), (431), (543), (548), (549), (555),
% 196.79/32.09  | | | | | | | | | | | | | | | | | |            (557), (564), (571), (586), (611), (7445), (7449),
% 196.79/32.09  | | | | | | | | | | | | | | | | | |            (7463), (7465), (7468), (7472), (7476), (7543),
% 196.79/32.09  | | | | | | | | | | | | | | | | | |            (7574), (function-axioms) are inconsistent by
% 196.79/32.09  | | | | | | | | | | | | | | | | | |            sub-proof #182.
% 196.79/32.09  | | | | | | | | | | | | | | | | | | 
% 196.79/32.09  | | | | | | | | | | | | | | | | | End of split
% 196.79/32.09  | | | | | | | | | | | | | | | | | 
% 196.79/32.09  | | | | | | | | | | | | | | | | Case 2:
% 196.79/32.09  | | | | | | | | | | | | | | | | | 
% 196.79/32.09  | | | | | | | | | | | | | | | | |   (7575)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.79/32.09  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.79/32.09  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.79/32.09  | | | | | | | | | | | | | | | | | 
% 196.79/32.09  | | | | | | | | | | | | | | | | | BETA: splitting (7575) gives:
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.09  | | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | |   (7576)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (158), (168), (169), (173),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (175), (178), (185), (270), (273), (278), (306),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (309), (313), (317), (321), (333), (351), (372),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (387), (393), (405), (427), (431), (526), (538),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (567), (572), (576), (582),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (586), (603), (604), (605), (607), (608), (611),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (612), (767), (7443), (7445), (7449), (7450),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (7458), (7463), (7465), (7468), (7472), (7476),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (7536), (7539), (7542), (7543), (7545), (7571),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (7576), (function-axioms) are inconsistent by
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            sub-proof #173.
% 196.95/32.09  | | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | |   (7577)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (172),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (173), (174), (175), (179), (183), (272), (273),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (274), (278), (281), (282), (304), (305), (306),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (318), (321), (326),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (352), (366),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (561),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (563), (564), (567), (569), (570), (571), (572),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (576), (582), (587), (588), (593), (595), (596),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (600), (602), (604), (605), (608), (610), (7460),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (7462), (7472), (7549), (7551), (7552), (7553),
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            (7554), (7555), (7556), (7577), (function-axioms)
% 196.95/32.09  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 196.95/32.09  | | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | |   (7578)   ~ (all_58_15 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | |   (7579)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.09  | | | | | | | | | | | | | | |             e0)
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | ALPHA: (7579) implies:
% 196.95/32.09  | | | | | | | | | | | | | | |   (7580)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.09  | | | | | | | | | | | | | | |   (7581)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | REDUCE: (541), (7578) imply:
% 196.95/32.09  | | | | | | | | | | | | | | |   (7582)   ~ (all_14_2 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (36), (41), (42), (43), (51),
% 196.95/32.09  | | | | | | | | | | | | | | |            (53), (61), (158), (162), (166), (167), (168),
% 196.95/32.09  | | | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 196.95/32.09  | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 196.95/32.09  | | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (276), (277),
% 196.95/32.09  | | | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (284), (285),
% 196.95/32.09  | | | | | | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (316),
% 196.95/32.09  | | | | | | | | | | | | | | |            (317), (319), (321), (323), (324), (325), (327),
% 196.95/32.09  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 196.95/32.09  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.95/32.09  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (427), (431),
% 196.95/32.09  | | | | | | | | | | | | | | |            (526), (538), (539), (540), (541), (542), (543),
% 196.95/32.09  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.95/32.09  | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.95/32.09  | | | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 196.95/32.09  | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.95/32.09  | | | | | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 196.95/32.09  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (602),
% 196.95/32.09  | | | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.95/32.09  | | | | | | | | | | | | | | |            (610), (611), (612), (613), (767), (7443), (7445),
% 196.95/32.09  | | | | | | | | | | | | | | |            (7449), (7450), (7457), (7458), (7460), (7462),
% 196.95/32.09  | | | | | | | | | | | | | | |            (7463), (7465), (7468), (7472), (7476), (7536),
% 196.95/32.09  | | | | | | | | | | | | | | |            (7539), (7542), (7543), (7544), (7545), (7548),
% 196.95/32.09  | | | | | | | | | | | | | | |            (7580), (7581), (7582), (function-axioms) are
% 196.95/32.09  | | | | | | | | | | | | | | |            inconsistent by sub-proof #170.
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | |   (7583)  all_30_1 = e3
% 196.95/32.09  | | | | | | | | | | | | |   (7584)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | COMBINE_EQS: (670), (7583) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7585)  all_10_1 = e3
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (53), (7585) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7586)  op(all_10_2, e1) = e3
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (52), (7585) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7587)  op(e1, e3) = all_10_0
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.95/32.09  | | | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (7587)
% 196.95/32.09  | | | | | | | | | | | | |              gives:
% 196.95/32.09  | | | | | | | | | | | | |   (7588)  all_52_5 = all_10_0
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | COMBINE_EQS: (367), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7589)  all_56_8 = all_10_0
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | COMBINE_EQS: (547), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7590)  all_58_6 = all_10_0
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (562), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7591)   ~ (all_52_3 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (567), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7592)   ~ (all_52_7 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | SIMP: (7592) implies:
% 196.95/32.09  | | | | | | | | | | | | |   (7593)   ~ (all_52_7 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (568), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7594)   ~ (all_52_13 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | SIMP: (7594) implies:
% 196.95/32.09  | | | | | | | | | | | | |   (7595)   ~ (all_52_13 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (570), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7596)   ~ (all_52_29 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | SIMP: (7596) implies:
% 196.95/32.09  | | | | | | | | | | | | |   (7597)   ~ (all_52_29 = all_10_0)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (569), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7598)   ~ (all_10_0 = all_10_2)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (553), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7599)   ~ (all_10_0 = all_6_2)
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | REDUCE: (184), (7588) imply:
% 196.95/32.09  | | | | | | | | | | | | |   (7600)  op(all_10_0, all_10_0) = all_52_4
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | Case 1:
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | |   (7601)  all_58_15 = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | COMBINE_EQS: (541), (7601) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7602)  all_14_2 = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (573), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7603)   ~ (all_52_7 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (591), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7604)   ~ (all_52_15 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (603), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7605)   ~ (all_52_23 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (606), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7606)   ~ (all_52_25 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (608), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7607)   ~ (all_52_27 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (609), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7608)   ~ (all_52_29 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (613), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7609)  op(e0, e0) = all_52_30
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (63), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7610)  op(e0, e0) = all_14_1
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (61), (7602) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7611)  op(e0, e0) = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.95/32.09  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7609), (7610)
% 196.95/32.09  | | | | | | | | | | | | | |              gives:
% 196.95/32.09  | | | | | | | | | | | | | |   (7612)  all_52_30 = all_14_1
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.95/32.09  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7609), (7611)
% 196.95/32.09  | | | | | | | | | | | | | |              gives:
% 196.95/32.09  | | | | | | | | | | | | | |   (7613)  all_52_30 = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | COMBINE_EQS: (7612), (7613) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7614)  all_14_1 = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | SIMP: (7614) implies:
% 196.95/32.09  | | | | | | | | | | | | | |   (7615)  all_14_1 = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (62), (7615) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7616)  op(e0, e0) = all_14_0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.95/32.09  | | | | | | | | | | | | | |              e0, e0, simplifying with (7611), (7616) gives:
% 196.95/32.09  | | | | | | | | | | | | | |   (7617)  all_14_0 = e0
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (7470), (7617) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7618)   ~ (e3 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (7466), (7617) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7619)   ~ (e2 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REDUCE: (7474), (7617) imply:
% 196.95/32.09  | | | | | | | | | | | | | |   (7620)   ~ (e1 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | Case 1:
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | |   (7621)  all_56_8 = e3
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | REF_CLOSE: (7463), (7589), (7621) are inconsistent by
% 196.95/32.09  | | | | | | | | | | | | | | |            sub-proof #926.
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | |   (7622)   ~ (all_56_8 = e3)
% 196.95/32.09  | | | | | | | | | | | | | | |   (7623)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | |   (7624)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.95/32.09  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | BETA: splitting (7624) gives:
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7625)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (311), (361), (459), (593),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (750), (7468), (7584), (7586), (7589), (7590),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7598), (7600), (7623), (7625), (function-axioms)
% 196.95/32.09  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #667.
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7626)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (51), (158), (166), (167), (168), (173), (175),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (179), (180), (182), (183), (185), (272), (273),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (274), (275), (276), (278), (280), (281), (282),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (317),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (321), (322), (323), (325), (328), (330), (346),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (421), (427),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (431), (459), (539), (542), (543), (544), (545),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (546), (548), (549), (551), (555), (557), (561),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (563), (564), (566), (571), (572), (578), (582),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (593), (595),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (596), (602), (604), (611), (612), (750), (7460),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7465), (7468), (7472), (7584), (7586), (7589),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7590), (7591), (7593), (7595), (7597), (7598),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7599), (7600), (7601), (7603), (7604), (7606),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7607), (7611), (7623), (7626), (function-axioms)
% 196.95/32.09  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #879.
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | |   (7627)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.95/32.09  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.95/32.09  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | BETA: splitting (7627) gives:
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7628)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | ALPHA: (7628) implies:
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7629)  all_52_22 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7630)  all_52_20 = e1
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7631)  all_52_16 = e3
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REDUCE: (178), (7631) imply:
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7632)  op(all_52_17, all_52_17) = e3
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REDUCE: (175), (7629) imply:
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7633)  op(all_52_23, all_52_23) = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REDUCE: (612), (7630) imply:
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7634)  op(all_10_2, all_10_2) = e1
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (42), (43), (53), (61),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (63), (158), (162), (166), (167), (168), (169),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (173), (183), (185), (270), (271), (272), (273),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (277), (280), (282), (283), (306), (313), (317),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (321), (325), (330), (331), (332), (333), (343),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (346), (351), (366), (367), (372), (375), (387),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (388), (393), (405), (415), (431), (538), (539),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (572), (574),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (576), (582), (586), (587), (588), (590), (593),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (594), (596), (603), (606), (607), (608), (611),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (613), (7443), (7445), (7449), (7450), (7453),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7458), (7462), (7463), (7465), (7468), (7472),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7476), (7586), (7590), (7593), (7599), (7632),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7633), (7634), (function-axioms) are inconsistent
% 196.95/32.09  | | | | | | | | | | | | | | | | |            by sub-proof #160.
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | |   (7635)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.95/32.09  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (172),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (173), (174), (175), (179), (183), (272), (273),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (274), (278), (281), (282), (304), (305), (306),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (318), (321), (326),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (352), (366),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (561),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (563), (564), (567), (569), (570), (571), (572),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (576), (582), (587), (588), (593), (595), (596),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (600), (602), (604), (605), (608), (610), (7460),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7462), (7472), (7601), (7603), (7604), (7605),
% 196.95/32.09  | | | | | | | | | | | | | | | | |            (7606), (7607), (7608), (7635), (function-axioms)
% 196.95/32.09  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 196.95/32.09  | | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | |   (7636)   ~ (all_58_15 = e0)
% 196.95/32.09  | | | | | | | | | | | | | |   (7637)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.09  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.09  | | | | | | | | | | | | | |             e0)
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 196.95/32.09  | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 196.95/32.09  | | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 196.95/32.09  | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 196.95/32.09  | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (277),
% 196.95/32.09  | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.95/32.09  | | | | | | | | | | | | | |            (307), (309), (311), (313), (316), (317), (319),
% 196.95/32.09  | | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (330),
% 196.95/32.09  | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.95/32.09  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.95/32.09  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (459),
% 196.95/32.09  | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.95/32.09  | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.95/32.09  | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.95/32.09  | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 196.95/32.09  | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.95/32.09  | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 196.95/32.09  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.09  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.09  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (750),
% 196.95/32.09  | | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7451), (7453),
% 196.95/32.09  | | | | | | | | | | | | | |            (7457), (7458), (7460), (7462), (7463), (7465),
% 196.95/32.09  | | | | | | | | | | | | | |            (7468), (7472), (7476), (7584), (7586), (7589),
% 196.95/32.09  | | | | | | | | | | | | | |            (7590), (7593), (7598), (7599), (7600), (7636),
% 196.95/32.09  | | | | | | | | | | | | | |            (7637), (function-axioms) are inconsistent by
% 196.95/32.09  | | | | | | | | | | | | | |            sub-proof #158.
% 196.95/32.09  | | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | | End of split
% 196.95/32.09  | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | Case 2:
% 196.95/32.09  | | | | | | | | | | | | 
% 196.95/32.09  | | | | | | | | | | | |   (7638)  all_28_0 = e3
% 196.95/32.09  | | | | | | | | | | | |   (7639)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 196.95/32.09  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.10  | | | | | | | | | | | |            (51), (53), (61), (62), (63), (158), (161), (162),
% 196.95/32.10  | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.10  | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.95/32.10  | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.95/32.10  | | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 196.95/32.10  | | | | | | | | | | | |            (284), (285), (303), (304), (305), (306), (307),
% 196.95/32.10  | | | | | | | | | | | |            (308), (309), (311), (313), (315), (316), (318),
% 196.95/32.10  | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 196.95/32.10  | | | | | | | | | | | |            (327), (328), (329), (330), (332), (333), (343),
% 196.95/32.10  | | | | | | | | | | | |            (346), (351), (352), (366), (367), (372), (375),
% 196.95/32.10  | | | | | | | | | | | |            (376), (387), (388), (393), (394), (405), (411),
% 196.95/32.10  | | | | | | | | | | | |            (415), (427), (431), (538), (539), (540), (541),
% 196.95/32.10  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.95/32.10  | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.95/32.10  | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 196.95/32.10  | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 196.95/32.10  | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 196.95/32.10  | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 196.95/32.10  | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 196.95/32.10  | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 196.95/32.10  | | | | | | | | | | | |            (613), (754), (7443), (7444), (7445), (7449),
% 196.95/32.10  | | | | | | | | | | | |            (7450), (7451), (7453), (7455), (7457), (7458),
% 196.95/32.10  | | | | | | | | | | | |            (7459), (7460), (7462), (7465), (7466), (7470),
% 196.95/32.10  | | | | | | | | | | | |            (7472), (7474), (7638), (7639), (function-axioms)
% 196.95/32.10  | | | | | | | | | | | |            are inconsistent by sub-proof #144.
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | |   (7640)  all_24_0 = e1
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | COMBINE_EQS: (711), (7640) imply:
% 196.95/32.10  | | | | | | | | | | |   (7641)  all_14_0 = e1
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | SIMP: (7641) implies:
% 196.95/32.10  | | | | | | | | | | |   (7642)  all_14_0 = e1
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | REDUCE: (7470), (7642) imply:
% 196.95/32.10  | | | | | | | | | | |   (7643)   ~ (e3 = e1)
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | REDUCE: (7466), (7642) imply:
% 196.95/32.10  | | | | | | | | | | |   (7644)   ~ (e2 = e1)
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | REDUCE: (62), (7642) imply:
% 196.95/32.10  | | | | | | | | | | |   (7645)  op(e0, all_14_1) = e1
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | |   (7646)   ~ (all_28_0 = e3)
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | REDUCE: (754), (7646) imply:
% 196.95/32.10  | | | | | | | | | | | |   (7647)   ~ (all_4_0 = e3)
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | BETA: splitting (104) gives:
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | |   (7648)   ~ (all_30_1 = e3)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (670), (7648) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7649)   ~ (all_10_1 = e3)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | |   (7650)   ~ (all_40_1 = e2)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (687), (7650) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7651)   ~ (all_10_1 = e2)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | |   (7652)  all_58_15 = e0
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (7645), (7652),
% 196.95/32.10  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.10  | | | | | | | | | | | | | | |            #877.
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | |   (7653)   ~ (all_58_15 = e0)
% 196.95/32.10  | | | | | | | | | | | | | | |   (7654)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.10  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.10  | | | | | | | | | | | | | | |             e0)
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.10  | | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.95/32.10  | | | | | | | | | | | | | | |            (159), (162), (166), (167), (168), (169), (172),
% 196.95/32.10  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.95/32.10  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.95/32.10  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 196.95/32.10  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.95/32.10  | | | | | | | | | | | | | | |            (305), (306), (307), (309), (310), (311), (313),
% 196.95/32.10  | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (323), (324),
% 196.95/32.10  | | | | | | | | | | | | | | |            (325), (327), (328), (330), (331), (332), (333),
% 196.95/32.10  | | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.95/32.10  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.95/32.10  | | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (538), (539),
% 196.95/32.10  | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.95/32.10  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.95/32.10  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.95/32.10  | | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.95/32.10  | | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.95/32.10  | | | | | | | | | | | | | | |            (584), (586), (587), (588), (590), (591), (592),
% 196.95/32.10  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.95/32.10  | | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.95/32.10  | | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (7443), (7445),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7460), (7462), (7465), (7466), (7472), (7647),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7649), (7651), (7653), (7654), (function-axioms)
% 196.95/32.10  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #186.
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | |   (7655)  all_40_1 = e2
% 196.95/32.10  | | | | | | | | | | | | | |   (7656)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | COMBINE_EQS: (687), (7655) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7657)  all_10_1 = e2
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | SIMP: (7657) implies:
% 196.95/32.10  | | | | | | | | | | | | | |   (7658)  all_10_1 = e2
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (7649), (7658) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7659)   ~ (e3 = e2)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (53), (7658) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7660)  op(all_10_2, e1) = e2
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (52), (7658) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7661)  op(e1, e2) = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.95/32.10  | | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (7661)
% 196.95/32.10  | | | | | | | | | | | | | |              gives:
% 196.95/32.10  | | | | | | | | | | | | | |   (7662)  all_52_13 = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | COMBINE_EQS: (421), (7662) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7663)  all_56_9 = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | COMBINE_EQS: (366), (7662) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7664)  all_58_7 = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (568), (7662) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7665)   ~ (all_52_5 = all_10_0)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (575), (7662) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7666)   ~ (all_52_9 = all_10_0)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REDUCE: (580), (7662) imply:
% 196.95/32.10  | | | | | | | | | | | | | |   (7667)   ~ (all_10_0 = all_4_2)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | |   (7668)  all_58_15 = e0
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (7645), (7668),
% 196.95/32.10  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.10  | | | | | | | | | | | | | | |            #877.
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | |   (7669)   ~ (all_58_15 = e0)
% 196.95/32.10  | | | | | | | | | | | | | | |   (7670)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.10  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.10  | | | | | | | | | | | | | | |             e0)
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | | ALPHA: (7670) implies:
% 196.95/32.10  | | | | | | | | | | | | | | |   (7671)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.10  | | | | | | | | | | | | | | |   (7672)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | | REDUCE: (541), (7669) imply:
% 196.95/32.10  | | | | | | | | | | | | | | |   (7673)   ~ (all_14_2 = e0)
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (36), (41), (42), (43), (51),
% 196.95/32.10  | | | | | | | | | | | | | | |            (53), (61), (158), (162), (166), (167), (168),
% 196.95/32.10  | | | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 196.95/32.10  | | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 196.95/32.10  | | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (276), (277),
% 196.95/32.10  | | | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (284), (285),
% 196.95/32.10  | | | | | | | | | | | | | | |            (306), (307), (309), (311), (312), (313), (316),
% 196.95/32.10  | | | | | | | | | | | | | | |            (317), (319), (321), (323), (324), (325), (327),
% 196.95/32.10  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 196.95/32.10  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.95/32.10  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (427), (431),
% 196.95/32.10  | | | | | | | | | | | | | | |            (526), (538), (539), (540), (541), (542), (543),
% 196.95/32.10  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.95/32.10  | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.95/32.10  | | | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 196.95/32.10  | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.95/32.10  | | | | | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 196.95/32.10  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (602),
% 196.95/32.10  | | | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.95/32.10  | | | | | | | | | | | | | | |            (610), (611), (612), (613), (767), (7443), (7445),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7449), (7450), (7457), (7458), (7460), (7462),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7463), (7465), (7468), (7472), (7647), (7656),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7660), (7663), (7664), (7665), (7666), (7667),
% 196.95/32.10  | | | | | | | | | | | | | | |            (7671), (7672), (7673), (function-axioms) are
% 196.95/32.10  | | | | | | | | | | | | | | |            inconsistent by sub-proof #170.
% 196.95/32.10  | | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | |   (7674)  all_30_1 = e3
% 196.95/32.10  | | | | | | | | | | | | |   (7675)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | COMBINE_EQS: (670), (7674) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7676)  all_10_1 = e3
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (53), (7676) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7677)  op(all_10_2, e1) = e3
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (52), (7676) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7678)  op(e1, e3) = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.95/32.10  | | | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (7678)
% 196.95/32.10  | | | | | | | | | | | | |              gives:
% 196.95/32.10  | | | | | | | | | | | | |   (7679)  all_52_5 = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | COMBINE_EQS: (367), (7679) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7680)  all_56_8 = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | COMBINE_EQS: (547), (7679) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7681)  all_58_6 = all_10_0
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (567), (7679) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7682)   ~ (all_52_7 = all_10_0)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | SIMP: (7682) implies:
% 196.95/32.10  | | | | | | | | | | | | |   (7683)   ~ (all_52_7 = all_10_0)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (569), (7679) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7684)   ~ (all_10_0 = all_10_2)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (553), (7679) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7685)   ~ (all_10_0 = all_6_2)
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | REDUCE: (184), (7679) imply:
% 196.95/32.10  | | | | | | | | | | | | |   (7686)  op(all_10_0, all_10_0) = all_52_4
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | |   (7687)  all_58_15 = e0
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (7645), (7687),
% 196.95/32.10  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.10  | | | | | | | | | | | | | |            #877.
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | |   (7688)   ~ (all_58_15 = e0)
% 196.95/32.10  | | | | | | | | | | | | | |   (7689)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.10  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.10  | | | | | | | | | | | | | |             e0)
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 196.95/32.10  | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 196.95/32.10  | | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 196.95/32.10  | | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 196.95/32.10  | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (277),
% 196.95/32.10  | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.95/32.10  | | | | | | | | | | | | | |            (307), (309), (311), (313), (316), (317), (319),
% 196.95/32.10  | | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (330),
% 196.95/32.10  | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.95/32.10  | | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.95/32.10  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (459),
% 196.95/32.10  | | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.95/32.10  | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.95/32.10  | | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.95/32.10  | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 196.95/32.10  | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.95/32.10  | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 196.95/32.10  | | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.10  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.10  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (750),
% 196.95/32.10  | | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7451), (7453),
% 196.95/32.10  | | | | | | | | | | | | | |            (7457), (7458), (7460), (7462), (7463), (7465),
% 196.95/32.10  | | | | | | | | | | | | | |            (7468), (7472), (7647), (7675), (7677), (7680),
% 196.95/32.10  | | | | | | | | | | | | | |            (7681), (7683), (7684), (7685), (7686), (7688),
% 196.95/32.10  | | | | | | | | | | | | | |            (7689), (function-axioms) are inconsistent by
% 196.95/32.10  | | | | | | | | | | | | | |            sub-proof #158.
% 196.95/32.10  | | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | |   (7690)  all_28_0 = e3
% 196.95/32.10  | | | | | | | | | | | |   (7691)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.10  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (161), (162),
% 196.95/32.10  | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.10  | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.95/32.10  | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.95/32.10  | | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 196.95/32.10  | | | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 196.95/32.10  | | | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 196.95/32.10  | | | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 196.95/32.10  | | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 196.95/32.10  | | | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 196.95/32.10  | | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 196.95/32.10  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.10  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.10  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.10  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.95/32.10  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.95/32.10  | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.95/32.10  | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.10  | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.10  | | | | | | | | | | | |            (608), (609), (610), (613), (754), (7443), (7444),
% 196.95/32.10  | | | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7455),
% 196.95/32.10  | | | | | | | | | | | |            (7457), (7458), (7459), (7460), (7462), (7465),
% 196.95/32.10  | | | | | | | | | | | |            (7472), (7645), (7690), (7691), (function-axioms)
% 196.95/32.10  | | | | | | | | | | | |            are inconsistent by sub-proof #142.
% 196.95/32.10  | | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | End of split
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | Case 2:
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | |   (7692)  all_22_1 = e2
% 196.95/32.10  | | | | | | | | | |   (7693)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | COMBINE_EQS: (658), (7692) imply:
% 196.95/32.10  | | | | | | | | | |   (7694)  all_6_1 = e2
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (43), (7694) imply:
% 196.95/32.10  | | | | | | | | | |   (7695)  op(all_6_2, e3) = e2
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (42), (7694) imply:
% 196.95/32.10  | | | | | | | | | |   (7696)  op(e3, e2) = all_6_0
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 196.95/32.10  | | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (7696)
% 196.95/32.10  | | | | | | | | | |              gives:
% 196.95/32.10  | | | | | | | | | |   (7697)  all_52_9 = all_6_0
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | COMBINE_EQS: (394), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7698)  all_56_1 = all_6_0
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | COMBINE_EQS: (549), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7699)  all_58_1 = all_6_0
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (575), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7700)   ~ (all_52_13 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | SIMP: (7700) implies:
% 196.95/32.10  | | | | | | | | | |   (7701)   ~ (all_52_13 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (576), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7702)   ~ (all_52_15 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | SIMP: (7702) implies:
% 196.95/32.10  | | | | | | | | | |   (7703)   ~ (all_52_15 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (577), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7704)   ~ (all_52_17 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | SIMP: (7704) implies:
% 196.95/32.10  | | | | | | | | | |   (7705)   ~ (all_52_17 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (578), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7706)   ~ (all_52_25 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | SIMP: (7706) implies:
% 196.95/32.10  | | | | | | | | | |   (7707)   ~ (all_52_25 = all_6_0)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (557), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7708)   ~ (all_6_0 = all_6_2)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (574), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7709)   ~ (all_6_0 = all_4_2)
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | REDUCE: (182), (7697) imply:
% 196.95/32.10  | | | | | | | | | |   (7710)  op(all_6_0, all_6_0) = all_52_8
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | BETA: splitting (89) gives:
% 196.95/32.10  | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | Case 1:
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | |   (7711)   ~ (all_24_0 = e1)
% 196.95/32.10  | | | | | | | | | | | 
% 196.95/32.10  | | | | | | | | | | | REDUCE: (711), (7711) imply:
% 196.95/32.11  | | | | | | | | | | |   (7712)   ~ (all_14_0 = e1)
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | |   (7713)   ~ (all_28_0 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (754), (7713) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7714)   ~ (all_4_0 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 196.95/32.11  | | | | | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (104),
% 196.95/32.11  | | | | | | | | | | | |            (129), (157), (158), (161), (162), (166), (167),
% 196.95/32.11  | | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 196.95/32.11  | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.95/32.11  | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (278),
% 196.95/32.11  | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.95/32.11  | | | | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 196.95/32.11  | | | | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 196.95/32.11  | | | | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 196.95/32.11  | | | | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 196.95/32.11  | | | | | | | | | | | |            (375), (387), (388), (393), (405), (411), (415),
% 196.95/32.11  | | | | | | | | | | | |            (417), (421), (427), (431), (522), (526), (538),
% 196.95/32.11  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.11  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.11  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (565),
% 196.95/32.11  | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 196.95/32.11  | | | | | | | | | | | |            (573), (574), (575), (577), (578), (580), (582),
% 196.95/32.11  | | | | | | | | | | | |            (584), (586), (588), (590), (591), (592), (593),
% 196.95/32.11  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (602),
% 196.95/32.11  | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 196.95/32.11  | | | | | | | | | | | |            (610), (611), (612), (613), (670), (687), (739),
% 196.95/32.11  | | | | | | | | | | | |            (767), (7460), (7462), (7463), (7466), (7468),
% 196.95/32.11  | | | | | | | | | | | |            (7470), (7693), (7695), (7698), (7699), (7701),
% 196.95/32.11  | | | | | | | | | | | |            (7703), (7705), (7707), (7708), (7709), (7710),
% 196.95/32.11  | | | | | | | | | | | |            (7712), (7714), (function-axioms) are inconsistent
% 196.95/32.11  | | | | | | | | | | | |            by sub-proof #776.
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | |   (7715)  all_28_0 = e3
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | COMBINE_EQS: (754), (7715) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7716)  all_4_0 = e3
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | SIMP: (7716) implies:
% 196.95/32.11  | | | | | | | | | | | |   (7717)  all_4_0 = e3
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (7450), (7717) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7718)   ~ (all_52_3 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (7455), (7717) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7719)   ~ (all_52_27 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (7459), (7717) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7720)  op(e3, e3) = all_52_18
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.11  | | | | | | | | | | | |              all_52_18, e3, e3, simplifying with (41), (7720)
% 196.95/32.11  | | | | | | | | | | | |              gives:
% 196.95/32.11  | | | | | | | | | | | |   (7721)  all_52_18 = all_6_2
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | |   (7722)  all_58_15 = e0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (53), (61), (62),
% 196.95/32.11  | | | | | | | | | | | | |            (63), (158), (166), (168), (172), (173), (174),
% 196.95/32.11  | | | | | | | | | | | | |            (175), (177), (178), (182), (183), (184), (185),
% 196.95/32.11  | | | | | | | | | | | | |            (187), (274), (278), (282), (283), (284), (285),
% 196.95/32.11  | | | | | | | | | | | | |            (306), (307), (309), (313), (315), (317), (321),
% 196.95/32.11  | | | | | | | | | | | | |            (325), (327), (329), (331), (332), (351), (352),
% 196.95/32.11  | | | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (405),
% 196.95/32.11  | | | | | | | | | | | | |            (415), (427), (522), (540), (541), (542), (543),
% 196.95/32.11  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.95/32.11  | | | | | | | | | | | | |            (557), (559), (561), (563), (564), (569), (570),
% 196.95/32.11  | | | | | | | | | | | | |            (572), (573), (584), (590), (592), (593), (594),
% 196.95/32.11  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 196.95/32.11  | | | | | | | | | | | | |            (604), (605), (606), (609), (610), (612), (613),
% 196.95/32.11  | | | | | | | | | | | | |            (739), (7460), (7462), (7466), (7470), (7693),
% 196.95/32.11  | | | | | | | | | | | | |            (7695), (7698), (7699), (7701), (7703), (7705),
% 196.95/32.11  | | | | | | | | | | | | |            (7707), (7708), (7709), (7710), (7712), (7722),
% 196.95/32.11  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.11  | | | | | | | | | | | | |            #818.
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | |   (7723)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.11  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.11  | | | | | | | | | | | | |             e0)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | ALPHA: (7723) implies:
% 196.95/32.11  | | | | | | | | | | | | |   (7724)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (51), (61), (63),
% 196.95/32.11  | | | | | | | | | | | | |            (162), (166), (167), (172), (174), (183), (184),
% 196.95/32.11  | | | | | | | | | | | | |            (185), (187), (282), (284), (285), (306), (307),
% 196.95/32.11  | | | | | | | | | | | | |            (309), (321), (326), (332), (351), (372), (387),
% 196.95/32.11  | | | | | | | | | | | | |            (388), (405), (522), (540), (541), (544), (545),
% 196.95/32.11  | | | | | | | | | | | | |            (547), (551), (561), (563), (564), (566), (569),
% 196.95/32.11  | | | | | | | | | | | | |            (570), (573), (606), (609), (610), (613), (739),
% 196.95/32.11  | | | | | | | | | | | | |            (7460), (7462), (7693), (7695), (7698), (7707),
% 196.95/32.11  | | | | | | | | | | | | |            (7708), (7709), (7710), (7718), (7719), (7721),
% 196.95/32.11  | | | | | | | | | | | | |            (7724), (function-axioms) are inconsistent by
% 196.95/32.11  | | | | | | | | | | | | |            sub-proof #141.
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | |   (7725)  all_24_0 = e1
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | COMBINE_EQS: (711), (7725) imply:
% 196.95/32.11  | | | | | | | | | | |   (7726)  all_14_0 = e1
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | SIMP: (7726) implies:
% 196.95/32.11  | | | | | | | | | | |   (7727)  all_14_0 = e1
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | REDUCE: (7466), (7727) imply:
% 196.95/32.11  | | | | | | | | | | |   (7728)   ~ (e2 = e1)
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | REDUCE: (62), (7727) imply:
% 196.95/32.11  | | | | | | | | | | |   (7729)  op(e0, all_14_1) = e1
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | |   (7730)   ~ (all_28_0 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (754), (7730) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7731)   ~ (all_4_0 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (37), (38), (41),
% 196.95/32.11  | | | | | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (104),
% 196.95/32.11  | | | | | | | | | | | |            (129), (157), (158), (161), (162), (166), (167),
% 196.95/32.11  | | | | | | | | | | | |            (168), (172), (173), (174), (175), (177), (178),
% 196.95/32.11  | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.95/32.11  | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (279),
% 196.95/32.11  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 196.95/32.11  | | | | | | | | | | | |            (304), (306), (307), (309), (311), (313), (315),
% 196.95/32.11  | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 196.95/32.11  | | | | | | | | | | | |            (327), (328), (329), (331), (332), (333), (343),
% 196.95/32.11  | | | | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 196.95/32.11  | | | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (417),
% 196.95/32.11  | | | | | | | | | | | |            (421), (431), (522), (526), (538), (539), (540),
% 196.95/32.11  | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.11  | | | | | | | | | | | |            (548), (549), (551), (553), (555), (559), (561),
% 196.95/32.11  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 196.95/32.11  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 196.95/32.11  | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (588),
% 196.95/32.11  | | | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 196.95/32.11  | | | | | | | | | | | |            (597), (598), (600), (602), (603), (604), (605),
% 196.95/32.11  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 196.95/32.11  | | | | | | | | | | | |            (613), (670), (687), (739), (767), (7460), (7462),
% 196.95/32.11  | | | | | | | | | | | |            (7463), (7466), (7468), (7693), (7695), (7698),
% 196.95/32.11  | | | | | | | | | | | |            (7699), (7701), (7703), (7705), (7707), (7708),
% 196.95/32.11  | | | | | | | | | | | |            (7709), (7710), (7729), (7731), (function-axioms)
% 196.95/32.11  | | | | | | | | | | | |            are inconsistent by sub-proof #771.
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | |   (7732)  all_28_0 = e3
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | COMBINE_EQS: (754), (7732) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7733)  all_4_0 = e3
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | SIMP: (7733) implies:
% 196.95/32.11  | | | | | | | | | | | |   (7734)  all_4_0 = e3
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (7450), (7734) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7735)   ~ (all_52_3 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (7455), (7734) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7736)   ~ (all_52_27 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (7459), (7734) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7737)  op(e3, e3) = all_52_18
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.11  | | | | | | | | | | | |              all_52_18, e3, e3, simplifying with (41), (7737)
% 196.95/32.11  | | | | | | | | | | | |              gives:
% 196.95/32.11  | | | | | | | | | | | |   (7738)  all_52_18 = all_6_2
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | |   (7739)  all_58_15 = e0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (7729), (7739),
% 196.95/32.11  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.11  | | | | | | | | | | | | |            #877.
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | |   (7740)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.11  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.11  | | | | | | | | | | | | |             e0)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | ALPHA: (7740) implies:
% 196.95/32.11  | | | | | | | | | | | | |   (7741)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (51), (61), (63),
% 196.95/32.11  | | | | | | | | | | | | |            (162), (166), (167), (172), (174), (183), (184),
% 196.95/32.11  | | | | | | | | | | | | |            (185), (187), (282), (284), (285), (306), (307),
% 196.95/32.11  | | | | | | | | | | | | |            (309), (321), (326), (332), (351), (372), (387),
% 196.95/32.11  | | | | | | | | | | | | |            (388), (405), (522), (540), (541), (544), (545),
% 196.95/32.11  | | | | | | | | | | | | |            (547), (551), (561), (563), (564), (566), (569),
% 196.95/32.11  | | | | | | | | | | | | |            (570), (573), (606), (609), (610), (613), (739),
% 196.95/32.11  | | | | | | | | | | | | |            (7460), (7462), (7693), (7695), (7698), (7707),
% 196.95/32.11  | | | | | | | | | | | | |            (7708), (7709), (7710), (7735), (7736), (7738),
% 196.95/32.11  | | | | | | | | | | | | |            (7741), (function-axioms) are inconsistent by
% 196.95/32.11  | | | | | | | | | | | | |            sub-proof #141.
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | |   (7742)  all_18_0 = e3
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | COMBINE_EQS: (761), (7742) imply:
% 196.95/32.11  | | | | | | | | |   (7743)  all_14_0 = e3
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | SIMP: (7743) implies:
% 196.95/32.11  | | | | | | | | |   (7744)  all_14_0 = e3
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | REDUCE: (62), (7744) imply:
% 196.95/32.11  | | | | | | | | |   (7745)  op(e0, all_14_1) = e3
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | BETA: splitting (84) gives:
% 196.95/32.11  | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | |   (7746)   ~ (all_22_1 = e2)
% 196.95/32.11  | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | REDUCE: (658), (7746) imply:
% 196.95/32.11  | | | | | | | | | |   (7747)   ~ (all_6_1 = e2)
% 196.95/32.11  | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.11  | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | |   (7748)   ~ (all_28_0 = e3)
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | REDUCE: (754), (7748) imply:
% 196.95/32.11  | | | | | | | | | | |   (7749)   ~ (all_4_0 = e3)
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | BETA: splitting (104) gives:
% 196.95/32.11  | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | |   (7750)   ~ (all_30_1 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | REDUCE: (670), (7750) imply:
% 196.95/32.11  | | | | | | | | | | | |   (7751)   ~ (all_10_1 = e3)
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | BETA: splitting (129) gives:
% 196.95/32.11  | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | |   (7752)   ~ (all_40_1 = e2)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (687), (7752) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7753)   ~ (all_10_1 = e2)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | |   (7754)  all_58_15 = e0
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (7745), (7754),
% 196.95/32.11  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.11  | | | | | | | | | | | | | |            #693.
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | |   (7755)   ~ (all_58_15 = e0)
% 196.95/32.11  | | | | | | | | | | | | | |   (7756)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.11  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.11  | | | | | | | | | | | | | |             e0)
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | ALPHA: (7756) implies:
% 196.95/32.11  | | | | | | | | | | | | | |   (7757)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.11  | | | | | | | | | | | | | |   (7758)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | REDUCE: (541), (7755) imply:
% 196.95/32.11  | | | | | | | | | | | | | |   (7759)   ~ (all_14_2 = e0)
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.11  | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.95/32.11  | | | | | | | | | | | | | |            (159), (162), (166), (167), (168), (169), (172),
% 196.95/32.11  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.95/32.11  | | | | | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.95/32.11  | | | | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 196.95/32.11  | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 196.95/32.11  | | | | | | | | | | | | | |            (305), (306), (307), (309), (310), (311), (313),
% 196.95/32.11  | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (323), (324),
% 196.95/32.11  | | | | | | | | | | | | | |            (325), (327), (328), (330), (331), (332), (333),
% 196.95/32.11  | | | | | | | | | | | | | |            (343), (346), (351), (352), (361), (366), (367),
% 196.95/32.11  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.95/32.11  | | | | | | | | | | | | | |            (411), (415), (417), (427), (431), (538), (539),
% 196.95/32.11  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.95/32.11  | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.95/32.11  | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.95/32.11  | | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.95/32.11  | | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.95/32.11  | | | | | | | | | | | | | |            (584), (586), (587), (588), (590), (591), (592),
% 196.95/32.11  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.95/32.11  | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.95/32.11  | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (7443), (7445),
% 196.95/32.11  | | | | | | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 196.95/32.11  | | | | | | | | | | | | | |            (7460), (7462), (7465), (7466), (7747), (7749),
% 196.95/32.11  | | | | | | | | | | | | | |            (7751), (7753), (7757), (7758), (7759),
% 196.95/32.11  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.11  | | | | | | | | | | | | | |            #187.
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | End of split
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | |   (7760)  all_40_1 = e2
% 196.95/32.11  | | | | | | | | | | | | |   (7761)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | COMBINE_EQS: (687), (7760) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7762)  all_10_1 = e2
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | SIMP: (7762) implies:
% 196.95/32.11  | | | | | | | | | | | | |   (7763)  all_10_1 = e2
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (7751), (7763) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7764)   ~ (e3 = e2)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (53), (7763) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7765)  op(all_10_2, e1) = e2
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (52), (7763) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7766)  op(e1, e2) = all_10_0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.95/32.11  | | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (7766)
% 196.95/32.11  | | | | | | | | | | | | |              gives:
% 196.95/32.11  | | | | | | | | | | | | |   (7767)  all_52_13 = all_10_0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | COMBINE_EQS: (421), (7767) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7768)  all_56_9 = all_10_0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | COMBINE_EQS: (366), (7767) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7769)  all_58_7 = all_10_0
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (568), (7767) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7770)   ~ (all_52_5 = all_10_0)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (575), (7767) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7771)   ~ (all_52_9 = all_10_0)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | REDUCE: (580), (7767) imply:
% 196.95/32.11  | | | | | | | | | | | | |   (7772)   ~ (all_10_0 = all_4_2)
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.11  | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | |   (7773)  all_58_15 = e0
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (7745), (7773),
% 196.95/32.11  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.11  | | | | | | | | | | | | | |            #678.
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | |   (7774)   ~ (all_58_15 = e0)
% 196.95/32.11  | | | | | | | | | | | | | |   (7775)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.11  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.11  | | | | | | | | | | | | | |             e0)
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | ALPHA: (7775) implies:
% 196.95/32.11  | | | | | | | | | | | | | |   (7776)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.11  | | | | | | | | | | | | | |   (7777)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | REDUCE: (541), (7774) imply:
% 196.95/32.11  | | | | | | | | | | | | | |   (7778)   ~ (all_14_2 = e0)
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 196.95/32.11  | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | |   (7779)  all_56_9 = e3
% 196.95/32.11  | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | REF_CLOSE: (7463), (7768), (7779) are inconsistent by
% 196.95/32.11  | | | | | | | | | | | | | | |            sub-proof #1006.
% 196.95/32.11  | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | |   (7780)   ~ (all_56_9 = e3)
% 196.95/32.11  | | | | | | | | | | | | | | |   (7781)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 196.95/32.11  | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.95/32.11  | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | |   (7782)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.11  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.95/32.11  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.95/32.11  | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | BETA: splitting (7782) gives:
% 196.95/32.11  | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7783)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.11  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | ALPHA: (7783) implies:
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7784)  all_52_6 = e0
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7785)  all_52_4 = e1
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7786)  all_52_2 = e2
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7787)  all_52_0 = e3
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | REDUCE: (185), (7786) imply:
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7788)  op(all_52_3, all_52_3) = e2
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | REDUCE: (184), (7785) imply:
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7789)  op(all_52_5, all_52_5) = e1
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | REDUCE: (183), (7784) imply:
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7790)  op(all_52_7, all_52_7) = e0
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | REDUCE: (610), (7787) imply:
% 196.95/32.11  | | | | | | | | | | | | | | | | |   (7791)  op(all_6_2, all_6_2) = e3
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.95/32.11  | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.11  | | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | |   (7792)  all_56_15 = e3
% 196.95/32.11  | | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (63), (156), (167), (168),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (178), (282), (284), (313), (321), (332), (351),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (387), (388), (394), (405), (526), (538), (544),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (546), (547), (553), (557), (564), (567), (569),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (573), (577), (578), (595), (600), (606), (609),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (612), (613), (767), (7463), (7468), (7745),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (7761), (7765), (7768), (7769), (7771), (7781),
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            (7788), (7789), (7791), (7792), (function-axioms)
% 196.95/32.11  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #676.
% 196.95/32.11  | | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.11  | | | | | | | | | | | | | | | | | | 
% 196.95/32.11  | | | | | | | | | | | | | | | | | |   (7793)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.95/32.11  | | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (61), (168), (169),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (173), (178), (273), (277), (278), (284), (306),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (312), (313), (321), (324), (332), (351), (367),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (372), (387), (394), (405), (427), (431), (526),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (538), (543), (544), (545), (546), (547), (548),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (549), (553), (555), (557), (564), (569), (570),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (571), (573), (577), (578), (591), (607), (611),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (612), (767), (7445), (7449), (7463), (7468),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (7749), (7761), (7765), (7768), (7769), (7770),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (7771), (7772), (7777), (7778), (7781), (7788),
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            (7789), (7790), (7791), (7793), (function-axioms)
% 196.95/32.12  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #172.
% 196.95/32.12  | | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | |   (7794)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.95/32.12  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (158), (169), (179),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (182), (273), (278), (321), (324), (325), (372),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (387), (427), (431), (543), (548), (549), (555),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (557), (564), (571), (586), (611), (7445), (7449),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (7463), (7465), (7468), (7747), (7749), (7769),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (7794), (function-axioms) are inconsistent by
% 196.95/32.12  | | | | | | | | | | | | | | | | |            sub-proof #182.
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7795)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.95/32.12  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.95/32.12  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | BETA: splitting (7795) gives:
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | |   (7796)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.12  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (158), (168), (169), (173),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (175), (178), (185), (270), (273), (278), (306),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (309), (313), (317), (321), (333), (351), (372),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (387), (393), (405), (427), (431), (526), (538),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (562), (563), (564), (567), (572), (576), (582),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (586), (603), (604), (605), (607), (608), (611),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (612), (767), (7443), (7445), (7449), (7450),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (7458), (7463), (7465), (7468), (7747), (7749),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (7761), (7765), (7768), (7769), (7771), (7781),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (7796), (function-axioms) are inconsistent by
% 196.95/32.12  | | | | | | | | | | | | | | | | |            sub-proof #173.
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | |   (7797)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.95/32.12  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (7462), (7465), (7747), (7776), (7778), (7797),
% 196.95/32.12  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.12  | | | | | | | | | | | | | | | | |            #1008.
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | |   (7798)  all_30_1 = e3
% 196.95/32.12  | | | | | | | | | | | |   (7799)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | COMBINE_EQS: (670), (7798) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7800)  all_10_1 = e3
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (53), (7800) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7801)  op(all_10_2, e1) = e3
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (52), (7800) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7802)  op(e1, e3) = all_10_0
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.95/32.12  | | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (7802)
% 196.95/32.12  | | | | | | | | | | | |              gives:
% 196.95/32.12  | | | | | | | | | | | |   (7803)  all_52_5 = all_10_0
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | COMBINE_EQS: (367), (7803) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7804)  all_56_8 = all_10_0
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | COMBINE_EQS: (547), (7803) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7805)  all_58_6 = all_10_0
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (567), (7803) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7806)   ~ (all_52_7 = all_10_0)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | SIMP: (7806) implies:
% 196.95/32.12  | | | | | | | | | | | |   (7807)   ~ (all_52_7 = all_10_0)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (569), (7803) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7808)   ~ (all_10_0 = all_10_2)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (553), (7803) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7809)   ~ (all_10_0 = all_6_2)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (184), (7803) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7810)  op(all_10_0, all_10_0) = all_52_4
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | |   (7811)  all_58_15 = e0
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (7745), (7811),
% 196.95/32.12  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.12  | | | | | | | | | | | | |            #678.
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | |   (7812)   ~ (all_58_15 = e0)
% 196.95/32.12  | | | | | | | | | | | | |   (7813)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.12  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.12  | | | | | | | | | | | | |             e0)
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | ALPHA: (7813) implies:
% 196.95/32.12  | | | | | | | | | | | | |   (7814)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.12  | | | | | | | | | | | | |   (7815)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | REDUCE: (541), (7812) imply:
% 196.95/32.12  | | | | | | | | | | | | |   (7816)   ~ (all_14_2 = e0)
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 196.95/32.12  | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 196.95/32.12  | | | | | | | | | | | | |            (169), (172), (173), (174), (175), (177), (178),
% 196.95/32.12  | | | | | | | | | | | | |            (179), (180), (182), (183), (184), (185), (187),
% 196.95/32.12  | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (277),
% 196.95/32.12  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 196.95/32.12  | | | | | | | | | | | | |            (307), (309), (311), (313), (316), (317), (319),
% 196.95/32.12  | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (330),
% 196.95/32.12  | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 196.95/32.12  | | | | | | | | | | | | |            (361), (366), (367), (372), (375), (387), (388),
% 196.95/32.12  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (459),
% 196.95/32.12  | | | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 196.95/32.12  | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 196.95/32.12  | | | | | | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 196.95/32.12  | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (571), (572),
% 196.95/32.12  | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.95/32.12  | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (590), (591),
% 196.95/32.12  | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.12  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.12  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (750),
% 196.95/32.12  | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7451), (7453),
% 196.95/32.12  | | | | | | | | | | | | |            (7457), (7458), (7460), (7462), (7463), (7465),
% 196.95/32.12  | | | | | | | | | | | | |            (7468), (7747), (7749), (7799), (7801), (7804),
% 196.95/32.12  | | | | | | | | | | | | |            (7805), (7807), (7808), (7809), (7810), (7814),
% 196.95/32.12  | | | | | | | | | | | | |            (7815), (7816), (function-axioms) are inconsistent
% 196.95/32.12  | | | | | | | | | | | | |            by sub-proof #159.
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | |   (7817)  all_28_0 = e3
% 196.95/32.12  | | | | | | | | | | |   (7818)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.12  | | | | | | | | | | |            (51), (53), (61), (63), (158), (161), (162),
% 196.95/32.12  | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.12  | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.95/32.12  | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.95/32.12  | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 196.95/32.12  | | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 196.95/32.12  | | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 196.95/32.12  | | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 196.95/32.12  | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 196.95/32.12  | | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 196.95/32.12  | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 196.95/32.12  | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.12  | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.12  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.12  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.95/32.12  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.95/32.12  | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.95/32.12  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.12  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.12  | | | | | | | | | | |            (608), (609), (610), (613), (754), (7443), (7444),
% 196.95/32.12  | | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7455),
% 196.95/32.12  | | | | | | | | | | |            (7457), (7458), (7459), (7460), (7462), (7465),
% 196.95/32.12  | | | | | | | | | | |            (7745), (7747), (7817), (7818), (function-axioms)
% 196.95/32.12  | | | | | | | | | | |            are inconsistent by sub-proof #137.
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | |   (7819)  all_22_1 = e2
% 196.95/32.12  | | | | | | | | | |   (7820)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | COMBINE_EQS: (658), (7819) imply:
% 196.95/32.12  | | | | | | | | | |   (7821)  all_6_1 = e2
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 196.95/32.12  | | | | | | | | | |            (52), (53), (61), (62), (63), (104), (129), (157),
% 196.95/32.12  | | | | | | | | | |            (158), (161), (162), (166), (167), (168), (169),
% 196.95/32.12  | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (180),
% 196.95/32.12  | | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 196.95/32.12  | | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 196.95/32.12  | | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 196.95/32.12  | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 196.95/32.12  | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 196.95/32.12  | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 196.95/32.12  | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.95/32.12  | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.95/32.12  | | | | | | | | | |            (421), (431), (522), (526), (538), (539), (540),
% 196.95/32.12  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.12  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.12  | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 196.95/32.12  | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 196.95/32.12  | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 196.95/32.12  | | | | | | | | | |            (588), (590), (591), (592), (593), (594), (595),
% 196.95/32.12  | | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 196.95/32.12  | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 196.95/32.12  | | | | | | | | | |            (613), (670), (687), (739), (767), (7460), (7462),
% 196.95/32.12  | | | | | | | | | |            (7463), (7465), (7466), (7468), (7745), (7820),
% 196.95/32.12  | | | | | | | | | |            (7821), (function-axioms) are inconsistent by
% 196.95/32.12  | | | | | | | | | |            sub-proof #662.
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | | 
% 196.95/32.12  | | | | | | | | End of split
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | |   (7822)  all_16_0 = e2
% 196.95/32.12  | | | | | | | |   (7823)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | COMBINE_EQS: (760), (7822) imply:
% 196.95/32.12  | | | | | | | |   (7824)  all_10_0 = e2
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | SIMP: (7824) implies:
% 196.95/32.12  | | | | | | | |   (7825)  all_10_0 = e2
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | COMBINE_EQS: (756), (7825) imply:
% 196.95/32.12  | | | | | | | |   (7826)  all_26_0 = e2
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | REDUCE: (7463), (7825) imply:
% 196.95/32.12  | | | | | | | |   (7827)   ~ (e3 = e2)
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | REDUCE: (52), (7825) imply:
% 196.95/32.12  | | | | | | | |   (7828)  op(e1, all_10_1) = e2
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | BETA: splitting (74) gives:
% 196.95/32.12  | | | | | | | | 
% 196.95/32.12  | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | 
% 196.95/32.12  | | | | | | | | |   (7829)   ~ (all_18_0 = e3)
% 196.95/32.12  | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | REDUCE: (761), (7829) imply:
% 196.95/32.12  | | | | | | | | |   (7830)   ~ (all_14_0 = e3)
% 196.95/32.12  | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | BETA: splitting (84) gives:
% 196.95/32.12  | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | |   (7831)   ~ (all_22_1 = e2)
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | REDUCE: (658), (7831) imply:
% 196.95/32.12  | | | | | | | | | |   (7832)   ~ (all_6_1 = e2)
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | BETA: splitting (89) gives:
% 196.95/32.12  | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | |   (7833)   ~ (all_24_0 = e1)
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | REDUCE: (711), (7833) imply:
% 196.95/32.12  | | | | | | | | | | |   (7834)   ~ (all_14_0 = e1)
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | BETA: splitting (94) gives:
% 196.95/32.12  | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | |   (7835)   ~ (all_26_0 = e2)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | REDUCE: (7826), (7835) imply:
% 196.95/32.12  | | | | | | | | | | | |   (7836)  $false
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | CLOSE: (7836) is inconsistent.
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | |   (7837)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.12  | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | |   (7838)   ~ (all_28_0 = e3)
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | REDUCE: (754), (7838) imply:
% 196.95/32.12  | | | | | | | | | | | | |   (7839)   ~ (all_4_0 = e3)
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.12  | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | |   (7840)  all_58_15 = e0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | COMBINE_EQS: (541), (7840) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7841)  all_14_2 = e0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (573), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7842)   ~ (all_52_7 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (591), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7843)   ~ (all_52_15 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (603), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7844)   ~ (all_52_23 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (606), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7845)   ~ (all_52_25 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (608), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7846)   ~ (all_52_27 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (609), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7847)   ~ (all_52_29 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (613), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7848)  op(e0, e0) = all_52_30
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (63), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7849)  op(e0, e0) = all_14_1
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (61), (7841) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7850)  op(e0, e0) = e0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 196.95/32.12  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7848), (7849)
% 196.95/32.12  | | | | | | | | | | | | | |              gives:
% 196.95/32.12  | | | | | | | | | | | | | |   (7851)  all_52_30 = all_14_1
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 196.95/32.12  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (7848), (7850)
% 196.95/32.12  | | | | | | | | | | | | | |              gives:
% 196.95/32.12  | | | | | | | | | | | | | |   (7852)  all_52_30 = e0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | COMBINE_EQS: (7851), (7852) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7853)  all_14_1 = e0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (62), (7853) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7854)  op(e0, e0) = all_14_0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 196.95/32.12  | | | | | | | | | | | | | |              e0, e0, simplifying with (7850), (7854) gives:
% 196.95/32.12  | | | | | | | | | | | | | |   (7855)  all_14_0 = e0
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (7830), (7855) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7856)   ~ (e3 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (7466), (7855) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7857)   ~ (e2 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | REDUCE: (7834), (7855) imply:
% 196.95/32.12  | | | | | | | | | | | | | |   (7858)   ~ (e1 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.95/32.12  | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | |   (7859)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.12  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.95/32.12  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.95/32.12  | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | BETA: splitting (7859) gives:
% 196.95/32.12  | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7860)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.12  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (53), (61), (156), (161), (175), (179), (183),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (184), (185), (271), (272), (273), (277), (304),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (305), (306), (321), (326), (332), (343), (346),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (351), (367), (387), (405), (431), (515), (542),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (543), (547), (555), (564), (567), (568), (569),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (571), (572), (573), (582), (590), (610), (611),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (680), (7823), (7828), (7840), (7842), (7844),
% 196.95/32.12  | | | | | | | | | | | | | | | |            (7850), (7860), (function-axioms) are inconsistent
% 196.95/32.12  | | | | | | | | | | | | | | | |            by sub-proof #136.
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7861)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.95/32.12  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | ALPHA: (7861) implies:
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7862)  all_52_14 = e0
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7863)  all_52_12 = e1
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7864)  all_52_10 = e2
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7865)  all_52_8 = e3
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | REDUCE: (182), (7865) imply:
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7866)  op(all_52_9, all_52_9) = e3
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | REDUCE: (180), (7863) imply:
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7867)  op(all_52_13, all_52_13) = e1
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | REDUCE: (179), (7862) imply:
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7868)  op(all_52_15, all_52_15) = e0
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | REDUCE: (611), (7864) imply:
% 196.95/32.12  | | | | | | | | | | | | | | | |   (7869)  op(all_4_2, all_4_2) = e2
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.95/32.12  | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | |   (7870)  all_56_13 = e3
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (7870) imply:
% 196.95/32.12  | | | | | | | | | | | | | | | | |   (7871)  all_52_15 = e3
% 196.95/32.12  | | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (158), (273), (431), (555), (571),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (7465), (7832), (7868), (7871), (function-axioms)
% 196.95/32.13  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1341.
% 196.95/32.13  | | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | |   (7872)   ~ (all_56_13 = e3)
% 196.95/32.13  | | | | | | | | | | | | | | | | |   (7873)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 196.95/32.13  | | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | | REDUCE: (346), (7872) imply:
% 196.95/32.13  | | | | | | | | | | | | | | | | |   (7874)   ~ (all_52_15 = e3)
% 196.95/32.13  | | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (41), (51), (53), (156), (168),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (169), (178), (183), (273), (274), (282), (284),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (305), (306), (313), (314), (317), (321), (325),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (327), (346), (351), (352), (366), (372), (387),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (388), (393), (394), (405), (431), (512), (515),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (542), (543), (544), (546), (547), (548), (549),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (557), (561), (563), (567), (571), (572), (575),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (588), (593), (595),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (602), (607), (612), (676), (680), (7443), (7445),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (7449), (7451), (7823), (7837), (7839), (7840),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (7842), (7843), (7844), (7845), (7850), (7866),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (7867), (7868), (7869), (7873), (7874),
% 196.95/32.13  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.13  | | | | | | | | | | | | | | | | |            #135.
% 196.95/32.13  | | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | |   (7875)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.95/32.13  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.95/32.13  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.95/32.13  | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | BETA: splitting (7875) gives:
% 196.95/32.13  | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | |   (7876)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.13  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (42), (43), (53), (63),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (158), (162), (167), (168), (169), (174), (175),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (178), (180), (182), (183), (185), (270), (273),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (275), (276), (277), (280), (282), (283), (306),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (309), (313), (317), (321), (325), (330), (331),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (332), (333), (351), (361), (366), (367), (372),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (415), (421),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (431), (512), (538), (539), (541), (542), (543),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (553), (555), (557), (559), (562), (563), (564),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (566), (567), (572), (574), (576), (577), (578),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (580), (582), (587), (588), (590), (593), (595),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (596), (603), (605), (606), (608), (611), (612),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (613), (676), (7443), (7445), (7449), (7450),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (7458), (7462), (7465), (7832), (7837), (7839),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (7876), (function-axioms) are inconsistent by
% 196.95/32.13  | | | | | | | | | | | | | | | |            sub-proof #127.
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | |   (7877)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.95/32.13  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (172),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (173), (174), (175), (179), (183), (272), (273),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (274), (278), (281), (282), (304), (305), (306),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (307), (308), (309), (313), (318), (321), (326),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (352), (366),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (561),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (563), (564), (567), (569), (570), (571), (572),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (576), (582), (587), (588), (593), (595), (596),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (600), (602), (604), (605), (608), (610), (7460),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (7462), (7832), (7840), (7842), (7843), (7844),
% 196.95/32.13  | | | | | | | | | | | | | | | |            (7845), (7846), (7847), (7877), (function-axioms)
% 196.95/32.13  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 196.95/32.13  | | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | |   (7878)   ~ (all_58_15 = e0)
% 196.95/32.13  | | | | | | | | | | | | | |   (7879)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.13  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.13  | | | | | | | | | | | | | |             e0)
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | ALPHA: (7879) implies:
% 196.95/32.13  | | | | | | | | | | | | | |   (7880)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.13  | | | | | | | | | | | | | |   (7881)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | REDUCE: (541), (7878) imply:
% 196.95/32.13  | | | | | | | | | | | | | |   (7882)   ~ (all_14_2 = e0)
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.13  | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.95/32.13  | | | | | | | | | | | | | |            (159), (161), (162), (166), (167), (168), (169),
% 196.95/32.13  | | | | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 196.95/32.13  | | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.95/32.13  | | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 196.95/32.13  | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.95/32.13  | | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 196.95/32.13  | | | | | | | | | | | | | |            (311), (312), (313), (316), (317), (319), (320),
% 196.95/32.13  | | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (329),
% 196.95/32.13  | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.95/32.13  | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.95/32.13  | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.95/32.13  | | | | | | | | | | | | | |            (421), (431), (512), (515), (538), (539), (540),
% 196.95/32.13  | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.13  | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.13  | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 196.95/32.13  | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 196.95/32.13  | | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 196.95/32.13  | | | | | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 196.95/32.13  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.95/32.13  | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.95/32.13  | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (676), (680),
% 196.95/32.13  | | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7451), (7453),
% 196.95/32.13  | | | | | | | | | | | | | |            (7457), (7458), (7460), (7462), (7465), (7466),
% 196.95/32.13  | | | | | | | | | | | | | |            (7823), (7828), (7832), (7837), (7839), (7880),
% 196.95/32.13  | | | | | | | | | | | | | |            (7881), (7882), (function-axioms) are inconsistent
% 196.95/32.13  | | | | | | | | | | | | | |            by sub-proof #126.
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | |   (7883)  all_28_0 = e3
% 196.95/32.13  | | | | | | | | | | | | |   (7884)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | COMBINE_EQS: (754), (7883) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7885)  all_4_0 = e3
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | COMBINE_EQS: (7449), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7886)  all_58_5 = e3
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7450), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7887)   ~ (all_52_3 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7451), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7888)   ~ (all_52_17 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7453), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7889)   ~ (all_52_23 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7455), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7890)   ~ (all_52_27 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7457), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7891)   ~ (all_10_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7458), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7892)   ~ (all_4_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | SIMP: (7892) implies:
% 196.95/32.13  | | | | | | | | | | | | |   (7893)   ~ (all_4_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7459), (7885) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7894)  op(e3, e3) = all_52_18
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.13  | | | | | | | | | | | | |            (51), (53), (61), (62), (63), (158), (161), (162),
% 196.95/32.13  | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.13  | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.95/32.13  | | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.95/32.13  | | | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 196.95/32.13  | | | | | | | | | | | | |            (284), (285), (303), (304), (305), (306), (307),
% 196.95/32.13  | | | | | | | | | | | | |            (308), (309), (311), (313), (315), (316), (318),
% 196.95/32.13  | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 196.95/32.13  | | | | | | | | | | | | |            (327), (328), (329), (330), (332), (333), (343),
% 196.95/32.13  | | | | | | | | | | | | |            (346), (351), (352), (366), (367), (372), (375),
% 196.95/32.13  | | | | | | | | | | | | |            (376), (387), (388), (393), (394), (405), (411),
% 196.95/32.13  | | | | | | | | | | | | |            (415), (427), (431), (538), (539), (540), (541),
% 196.95/32.13  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 196.95/32.13  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 196.95/32.13  | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 196.95/32.13  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 196.95/32.13  | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 196.95/32.13  | | | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 196.95/32.13  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 196.95/32.13  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 196.95/32.13  | | | | | | | | | | | | |            (613), (7443), (7444), (7445), (7449), (7453),
% 196.95/32.13  | | | | | | | | | | | | |            (7458), (7460), (7462), (7465), (7466), (7830),
% 196.95/32.13  | | | | | | | | | | | | |            (7832), (7834), (7884), (7886), (7887), (7888),
% 196.95/32.13  | | | | | | | | | | | | |            (7889), (7890), (7891), (7893), (7894),
% 196.95/32.13  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.13  | | | | | | | | | | | | |            #145.
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | |   (7895)  all_24_0 = e1
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | COMBINE_EQS: (711), (7895) imply:
% 196.95/32.13  | | | | | | | | | | |   (7896)  all_14_0 = e1
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | SIMP: (7896) implies:
% 196.95/32.13  | | | | | | | | | | |   (7897)  all_14_0 = e1
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | REDUCE: (7830), (7897) imply:
% 196.95/32.13  | | | | | | | | | | |   (7898)   ~ (e3 = e1)
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | REDUCE: (7466), (7897) imply:
% 196.95/32.13  | | | | | | | | | | |   (7899)   ~ (e2 = e1)
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | REDUCE: (62), (7897) imply:
% 196.95/32.13  | | | | | | | | | | |   (7900)  op(e0, all_14_1) = e1
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | BETA: splitting (94) gives:
% 196.95/32.13  | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | Case 1:
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | |   (7901)   ~ (all_26_0 = e2)
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | REDUCE: (7826), (7901) imply:
% 196.95/32.13  | | | | | | | | | | | |   (7902)  $false
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | CLOSE: (7902) is inconsistent.
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | |   (7903)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.13  | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | Case 1:
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | |   (7904)   ~ (all_28_0 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (754), (7904) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7905)   ~ (all_4_0 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | Case 1:
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | |   (7906)  all_58_15 = e0
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (7900), (7906),
% 196.95/32.13  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.13  | | | | | | | | | | | | | |            #877.
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | |   (7907)   ~ (all_58_15 = e0)
% 196.95/32.13  | | | | | | | | | | | | | |   (7908)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.13  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.13  | | | | | | | | | | | | | |             e0)
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.13  | | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.95/32.13  | | | | | | | | | | | | | |            (159), (161), (162), (166), (167), (168), (169),
% 196.95/32.13  | | | | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 196.95/32.13  | | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.95/32.13  | | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 196.95/32.13  | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.95/32.13  | | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 196.95/32.13  | | | | | | | | | | | | | |            (311), (312), (313), (316), (317), (319), (320),
% 196.95/32.13  | | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (329),
% 196.95/32.13  | | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.95/32.13  | | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.95/32.13  | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.95/32.13  | | | | | | | | | | | | | |            (421), (431), (512), (515), (538), (539), (540),
% 196.95/32.13  | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.13  | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.13  | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 196.95/32.13  | | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 196.95/32.13  | | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 196.95/32.13  | | | | | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 196.95/32.13  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.95/32.13  | | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.95/32.13  | | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (676), (680),
% 196.95/32.13  | | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7451), (7453),
% 196.95/32.13  | | | | | | | | | | | | | |            (7457), (7458), (7460), (7462), (7465), (7466),
% 196.95/32.13  | | | | | | | | | | | | | |            (7823), (7828), (7832), (7903), (7905), (7907),
% 196.95/32.13  | | | | | | | | | | | | | |            (7908), (function-axioms) are inconsistent by
% 196.95/32.13  | | | | | | | | | | | | | |            sub-proof #125.
% 196.95/32.13  | | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | End of split
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | Case 2:
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | |   (7909)  all_28_0 = e3
% 196.95/32.13  | | | | | | | | | | | | |   (7910)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | COMBINE_EQS: (754), (7909) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7911)  all_4_0 = e3
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | COMBINE_EQS: (7449), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7912)  all_58_5 = e3
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7450), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7913)   ~ (all_52_3 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7451), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7914)   ~ (all_52_17 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7455), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7915)   ~ (all_52_27 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7457), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7916)   ~ (all_10_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7458), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7917)   ~ (all_4_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | SIMP: (7917) implies:
% 196.95/32.13  | | | | | | | | | | | | |   (7918)   ~ (all_4_2 = e3)
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REDUCE: (7459), (7911) imply:
% 196.95/32.13  | | | | | | | | | | | | |   (7919)  op(e3, e3) = all_52_18
% 196.95/32.13  | | | | | | | | | | | | | 
% 196.95/32.13  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.13  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (161), (162),
% 196.95/32.13  | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.13  | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.95/32.13  | | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.95/32.13  | | | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 196.95/32.13  | | | | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 196.95/32.13  | | | | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 196.95/32.13  | | | | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 196.95/32.13  | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 196.95/32.13  | | | | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 196.95/32.13  | | | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 196.95/32.13  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.13  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.13  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.13  | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.95/32.13  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.95/32.13  | | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.95/32.13  | | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.13  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.13  | | | | | | | | | | | | |            (608), (609), (610), (613), (7443), (7444),
% 196.95/32.13  | | | | | | | | | | | | |            (7445), (7449), (7453), (7458), (7460), (7462),
% 196.95/32.13  | | | | | | | | | | | | |            (7465), (7832), (7900), (7910), (7912), (7913),
% 196.95/32.13  | | | | | | | | | | | | |            (7914), (7915), (7916), (7918), (7919),
% 196.95/32.13  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.14  | | | | | | | | | | | | |            #143.
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | |   (7920)  all_22_1 = e2
% 196.95/32.14  | | | | | | | | | |   (7921)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | COMBINE_EQS: (658), (7920) imply:
% 196.95/32.14  | | | | | | | | | |   (7922)  all_6_1 = e2
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 196.95/32.14  | | | | | | | | | |            (53), (61), (62), (63), (89), (94), (158), (161),
% 196.95/32.14  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 196.95/32.14  | | | | | | | | | |            (174), (175), (177), (178), (180), (182), (183),
% 196.95/32.14  | | | | | | | | | |            (184), (185), (187), (270), (271), (273), (274),
% 196.95/32.14  | | | | | | | | | |            (275), (277), (278), (280), (281), (282), (283),
% 196.95/32.14  | | | | | | | | | |            (284), (285), (303), (304), (306), (307), (308),
% 196.95/32.14  | | | | | | | | | |            (309), (311), (313), (315), (316), (317), (319),
% 196.95/32.14  | | | | | | | | | |            (321), (324), (325), (326), (327), (328), (329),
% 196.95/32.14  | | | | | | | | | |            (331), (332), (333), (343), (351), (352), (361),
% 196.95/32.14  | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 196.95/32.14  | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (512),
% 196.95/32.14  | | | | | | | | | |            (522), (538), (539), (540), (541), (542), (543),
% 196.95/32.14  | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.95/32.14  | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.95/32.14  | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (570),
% 196.95/32.14  | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 196.95/32.14  | | | | | | | | | |            (582), (584), (586), (588), (589), (590), (591),
% 196.95/32.14  | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.14  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.14  | | | | | | | | | |            (608), (609), (610), (612), (613), (676), (711),
% 196.95/32.14  | | | | | | | | | |            (739), (7460), (7462), (7465), (7466), (7826),
% 196.95/32.14  | | | | | | | | | |            (7828), (7830), (7921), (7922), (function-axioms)
% 196.95/32.14  | | | | | | | | | |            are inconsistent by sub-proof #617.
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | |   (7923)  all_18_0 = e3
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | COMBINE_EQS: (761), (7923) imply:
% 196.95/32.14  | | | | | | | | |   (7924)  all_14_0 = e3
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | SIMP: (7924) implies:
% 196.95/32.14  | | | | | | | | |   (7925)  all_14_0 = e3
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | REDUCE: (62), (7925) imply:
% 196.95/32.14  | | | | | | | | |   (7926)  op(e0, all_14_1) = e3
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | BETA: splitting (84) gives:
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | |   (7927)   ~ (all_22_1 = e2)
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | REDUCE: (658), (7927) imply:
% 196.95/32.14  | | | | | | | | | |   (7928)   ~ (all_6_1 = e2)
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | BETA: splitting (94) gives:
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | |   (7929)   ~ (all_26_0 = e2)
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | REDUCE: (7826), (7929) imply:
% 196.95/32.14  | | | | | | | | | | |   (7930)  $false
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | CLOSE: (7930) is inconsistent.
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | |   (7931)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | |   (7932)   ~ (all_28_0 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (754), (7932) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7933)   ~ (all_4_0 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | |   (7934)  all_58_15 = e0
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (7926), (7934),
% 196.95/32.14  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.14  | | | | | | | | | | | | |            #693.
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | |   (7935)   ~ (all_58_15 = e0)
% 196.95/32.14  | | | | | | | | | | | | |   (7936)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.14  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.14  | | | | | | | | | | | | |             e0)
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 196.95/32.14  | | | | | | | | | | | | |            (43), (51), (53), (61), (62), (63), (156), (158),
% 196.95/32.14  | | | | | | | | | | | | |            (159), (161), (162), (166), (167), (168), (169),
% 196.95/32.14  | | | | | | | | | | | | |            (172), (173), (174), (175), (177), (178), (179),
% 196.95/32.14  | | | | | | | | | | | | |            (180), (182), (183), (184), (185), (187), (270),
% 196.95/32.14  | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 196.95/32.14  | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (284), (285),
% 196.95/32.14  | | | | | | | | | | | | |            (304), (305), (306), (307), (308), (309), (310),
% 196.95/32.14  | | | | | | | | | | | | |            (311), (312), (313), (316), (317), (319), (320),
% 196.95/32.14  | | | | | | | | | | | | |            (321), (323), (324), (325), (327), (328), (329),
% 196.95/32.14  | | | | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 196.95/32.14  | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 196.95/32.14  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (417),
% 196.95/32.14  | | | | | | | | | | | | |            (421), (431), (512), (515), (538), (539), (540),
% 196.95/32.14  | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 196.95/32.14  | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 196.95/32.14  | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 196.95/32.14  | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 196.95/32.14  | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 196.95/32.14  | | | | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 196.95/32.14  | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 196.95/32.14  | | | | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 196.95/32.14  | | | | | | | | | | | | |            (609), (610), (611), (612), (613), (676), (680),
% 196.95/32.14  | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7451), (7453),
% 196.95/32.14  | | | | | | | | | | | | |            (7457), (7458), (7460), (7462), (7465), (7466),
% 196.95/32.14  | | | | | | | | | | | | |            (7823), (7828), (7928), (7931), (7933), (7935),
% 196.95/32.14  | | | | | | | | | | | | |            (7936), (function-axioms) are inconsistent by
% 196.95/32.14  | | | | | | | | | | | | |            sub-proof #125.
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | |   (7937)  all_28_0 = e3
% 196.95/32.14  | | | | | | | | | | | |   (7938)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | COMBINE_EQS: (754), (7937) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7939)  all_4_0 = e3
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | COMBINE_EQS: (7449), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7940)  all_58_5 = e3
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (7450), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7941)   ~ (all_52_3 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (7451), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7942)   ~ (all_52_17 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (7455), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7943)   ~ (all_52_27 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (7457), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7944)   ~ (all_10_2 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (7458), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7945)   ~ (all_4_2 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | SIMP: (7945) implies:
% 196.95/32.14  | | | | | | | | | | | |   (7946)   ~ (all_4_2 = e3)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (7459), (7939) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7947)  op(e3, e3) = all_52_18
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 196.95/32.14  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (161), (162),
% 196.95/32.14  | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.14  | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 196.95/32.14  | | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 196.95/32.14  | | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 196.95/32.14  | | | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 196.95/32.14  | | | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 196.95/32.14  | | | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 196.95/32.14  | | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 196.95/32.14  | | | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 196.95/32.14  | | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 196.95/32.14  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.14  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.14  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.14  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 196.95/32.14  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 196.95/32.14  | | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 196.95/32.14  | | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 196.95/32.14  | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 196.95/32.14  | | | | | | | | | | | |            (608), (609), (610), (613), (7443), (7444),
% 196.95/32.14  | | | | | | | | | | | |            (7445), (7449), (7453), (7458), (7460), (7462),
% 196.95/32.14  | | | | | | | | | | | |            (7465), (7926), (7928), (7938), (7940), (7941),
% 196.95/32.14  | | | | | | | | | | | |            (7942), (7943), (7944), (7946), (7947),
% 196.95/32.14  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.14  | | | | | | | | | | | |            #138.
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | |   (7948)  all_22_1 = e2
% 196.95/32.14  | | | | | | | | | |   (7949)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 196.95/32.14  | | | | | | | | | |            (53), (61), (63), (94), (158), (161), (162),
% 196.95/32.14  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 196.95/32.14  | | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 196.95/32.14  | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 196.95/32.14  | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 196.95/32.14  | | | | | | | | | |            (303), (304), (306), (307), (308), (309), (311),
% 196.95/32.14  | | | | | | | | | |            (313), (315), (316), (317), (319), (321), (324),
% 196.95/32.14  | | | | | | | | | |            (325), (326), (327), (328), (329), (331), (332),
% 196.95/32.14  | | | | | | | | | |            (333), (343), (351), (352), (361), (366), (367),
% 196.95/32.14  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 196.95/32.14  | | | | | | | | | |            (411), (415), (431), (512), (522), (538), (539),
% 196.95/32.14  | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 196.95/32.14  | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.95/32.14  | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 196.95/32.14  | | | | | | | | | |            (567), (568), (569), (570), (572), (573), (574),
% 196.95/32.14  | | | | | | | | | |            (575), (576), (577), (578), (582), (584), (586),
% 196.95/32.14  | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 196.95/32.14  | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 196.95/32.14  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 196.95/32.14  | | | | | | | | | |            (612), (613), (658), (676), (739), (7460), (7462),
% 196.95/32.14  | | | | | | | | | |            (7465), (7826), (7828), (7926), (7948), (7949),
% 196.95/32.14  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.14  | | | | | | | | | |            #613.
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | End of split
% 196.95/32.14  | | | | | | | | 
% 196.95/32.14  | | | | | | | End of split
% 196.95/32.14  | | | | | | | 
% 196.95/32.14  | | | | | | Case 2:
% 196.95/32.14  | | | | | | | 
% 196.95/32.14  | | | | | | |   (7950)  all_14_0 = e2
% 196.95/32.14  | | | | | | |   (7951)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 196.95/32.14  | | | | | | | 
% 196.95/32.14  | | | | | | | COMBINE_EQS: (771), (7950) imply:
% 196.95/32.14  | | | | | | |   (7952)  all_50_0 = e2
% 196.95/32.14  | | | | | | | 
% 196.95/32.14  | | | | | | | REDUCE: (62), (7950) imply:
% 196.95/32.14  | | | | | | |   (7953)  op(e0, all_14_1) = e2
% 196.95/32.14  | | | | | | | 
% 196.95/32.14  | | | | | | | BETA: splitting (69) gives:
% 196.95/32.14  | | | | | | | 
% 196.95/32.14  | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | 
% 196.95/32.14  | | | | | | | |   (7954)   ~ (all_16_0 = e2)
% 196.95/32.14  | | | | | | | | 
% 196.95/32.14  | | | | | | | | REDUCE: (760), (7954) imply:
% 196.95/32.14  | | | | | | | |   (7955)   ~ (all_10_0 = e2)
% 196.95/32.14  | | | | | | | | 
% 196.95/32.14  | | | | | | | | BETA: splitting (84) gives:
% 196.95/32.14  | | | | | | | | 
% 196.95/32.14  | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | |   (7956)   ~ (all_22_1 = e2)
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | REDUCE: (658), (7956) imply:
% 196.95/32.14  | | | | | | | | |   (7957)   ~ (all_6_1 = e2)
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | BETA: splitting (99) gives:
% 196.95/32.14  | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | |   (7958)   ~ (all_28_0 = e3)
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | REDUCE: (754), (7958) imply:
% 196.95/32.14  | | | | | | | | | |   (7959)   ~ (all_4_0 = e3)
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | BETA: splitting (104) gives:
% 196.95/32.14  | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | |   (7960)   ~ (all_30_1 = e3)
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | REDUCE: (670), (7960) imply:
% 196.95/32.14  | | | | | | | | | | |   (7961)   ~ (all_10_1 = e3)
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | BETA: splitting (129) gives:
% 196.95/32.14  | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | |   (7962)   ~ (all_40_1 = e2)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | REDUCE: (687), (7962) imply:
% 196.95/32.14  | | | | | | | | | | | |   (7963)   ~ (all_10_1 = e2)
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.14  | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | |   (7964)  all_58_15 = e0
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (7953), (7964),
% 196.95/32.14  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.14  | | | | | | | | | | | | |            #612.
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | |   (7965)   ~ (all_58_15 = e0)
% 196.95/32.14  | | | | | | | | | | | | |   (7966)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.14  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.14  | | | | | | | | | | | | |             e0)
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | ALPHA: (7966) implies:
% 196.95/32.14  | | | | | | | | | | | | |   (7967)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.14  | | | | | | | | | | | | |   (7968)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | REDUCE: (541), (7965) imply:
% 196.95/32.14  | | | | | | | | | | | | |   (7969)   ~ (all_14_2 = e0)
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.95/32.14  | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | |   (7970)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.14  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.95/32.14  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.95/32.14  | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | BETA: splitting (7970) gives:
% 196.95/32.14  | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | |   (7971)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.14  | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | ALPHA: (7971) implies:
% 196.95/32.14  | | | | | | | | | | | | | | |   (7972)  all_52_6 = e0
% 196.95/32.14  | | | | | | | | | | | | | | |   (7973)  all_52_4 = e1
% 196.95/32.14  | | | | | | | | | | | | | | |   (7974)  all_52_2 = e2
% 196.95/32.14  | | | | | | | | | | | | | | |   (7975)  all_52_0 = e3
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | REDUCE: (185), (7974) imply:
% 196.95/32.14  | | | | | | | | | | | | | | |   (7976)  op(all_52_3, all_52_3) = e2
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | REDUCE: (184), (7973) imply:
% 196.95/32.14  | | | | | | | | | | | | | | |   (7977)  op(all_52_5, all_52_5) = e1
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | REDUCE: (183), (7972) imply:
% 196.95/32.14  | | | | | | | | | | | | | | |   (7978)  op(all_52_7, all_52_7) = e0
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | REDUCE: (610), (7975) imply:
% 196.95/32.14  | | | | | | | | | | | | | | |   (7979)  op(all_6_2, all_6_2) = e3
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.95/32.14  | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | |   (7980)  all_56_15 = e3
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (43), (51), (53), (61),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (156), (169), (175), (182), (271), (273), (277),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (279), (304), (305), (310), (317), (319), (321),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (351), (367),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (405), (417), (431),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (538), (541), (542), (543), (546), (547), (548),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (551), (553), (559), (562), (564), (565), (569),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (572), (573), (574), (576), (586), (596), (597),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (600), (608), (611), (7443), (7445), (7449),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (7460), (7959), (7961), (7963), (7969), (7976),
% 196.95/32.14  | | | | | | | | | | | | | | | |            (7977), (7978), (7979), (7980), (function-axioms)
% 196.95/32.14  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #198.
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | |   (7981)   ~ (all_56_15 = e3)
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | REDUCE: (538), (7981) imply:
% 196.95/32.14  | | | | | | | | | | | | | | | |   (7982)   ~ (all_14_2 = e3)
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.95/32.14  | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.14  | | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | |   (7983)  all_56_13 = e3
% 196.95/32.14  | | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (7983) imply:
% 196.95/32.14  | | | | | | | | | | | | | | | | |   (7984)  all_52_15 = e3
% 196.95/32.14  | | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | | SIMP: (7984) implies:
% 196.95/32.14  | | | | | | | | | | | | | | | | |   (7985)  all_52_15 = e3
% 196.95/32.14  | | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (7985) imply:
% 196.95/32.14  | | | | | | | | | | | | | | | | |   (7986)  all_58_13 = e3
% 196.95/32.14  | | | | | | | | | | | | | | | | | 
% 196.95/32.14  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (53), (61), (63), (159), (168), (172), (177),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (180), (182), (273), (274), (275), (276), (281),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (311), (312), (313), (315), (317), (319), (320),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (321), (323), (324), (328), (330), (332), (333),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (351), (352), (361), (366), (372), (375), (387),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (421), (431), (541),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (542), (544), (545), (546), (547), (548), (549),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (563),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (569), (570), (571),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (582), (587), (588), (589), (590), (591), (596),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (597), (598), (600), (602), (607), (608), (612),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (613), (7460), (7462), (7951), (7967), (7976),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (7977), (7978), (7979), (7985), (7986),
% 196.95/32.14  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.14  | | | | | | | | | | | | | | | | |            #124.
% 196.95/32.14  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (7987)   ~ (all_56_13 = e3)
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (346), (7987) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (7988)   ~ (all_52_15 = e3)
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (41), (51), (53), (61), (156),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (273), (304), (305), (306), (321), (332), (351),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (387), (405), (431), (541), (542), (543), (547),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (555), (564), (569), (572), (573), (582), (7961),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7967), (7976), (7977), (7978), (7979), (7982),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7988), (function-axioms) are inconsistent by
% 196.95/32.15  | | | | | | | | | | | | | | | | |            sub-proof #196.
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (7989)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (42), (43),
% 196.95/32.15  | | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (167),
% 196.95/32.15  | | | | | | | | | | | | | | |            (168), (169), (173), (174), (175), (178), (179),
% 196.95/32.15  | | | | | | | | | | | | | | |            (180), (182), (183), (185), (270), (272), (273),
% 196.95/32.15  | | | | | | | | | | | | | | |            (275), (277), (280), (282), (283), (284), (306),
% 196.95/32.15  | | | | | | | | | | | | | | |            (309), (313), (317), (321), (325), (326), (330),
% 196.95/32.15  | | | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (361), (366),
% 196.95/32.15  | | | | | | | | | | | | | | |            (367), (372), (387), (388), (393), (394), (405),
% 196.95/32.15  | | | | | | | | | | | | | | |            (415), (431), (538), (539), (541), (542), (543),
% 196.95/32.15  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 196.95/32.15  | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 196.95/32.15  | | | | | | | | | | | | | | |            (564), (567), (568), (569), (570), (571), (572),
% 196.95/32.15  | | | | | | | | | | | | | | |            (575), (577), (578), (580), (582), (586), (588),
% 196.95/32.15  | | | | | | | | | | | | | | |            (590), (591), (593), (594), (595), (600), (602),
% 196.95/32.15  | | | | | | | | | | | | | | |            (604), (606), (607), (608), (609), (610), (611),
% 196.95/32.15  | | | | | | | | | | | | | | |            (612), (613), (7443), (7445), (7449), (7451),
% 196.95/32.15  | | | | | | | | | | | | | | |            (7453), (7457), (7458), (7460), (7462), (7465),
% 196.95/32.15  | | | | | | | | | | | | | | |            (7953), (7957), (7959), (7967), (7968), (7969),
% 196.95/32.15  | | | | | | | | | | | | | | |            (7989), (function-axioms) are inconsistent by
% 196.95/32.15  | | | | | | | | | | | | | | |            sub-proof #123.
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | |   (7990)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.95/32.15  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.95/32.15  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | BETA: splitting (7990) gives:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (7991)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (42), (43), (53), (61),
% 196.95/32.15  | | | | | | | | | | | | | | |            (63), (158), (162), (167), (168), (169), (175),
% 196.95/32.15  | | | | | | | | | | | | | | |            (178), (183), (185), (270), (272), (273), (277),
% 196.95/32.15  | | | | | | | | | | | | | | |            (282), (283), (306), (317), (321), (325), (330),
% 196.95/32.15  | | | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (366), (367),
% 196.95/32.15  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 196.95/32.15  | | | | | | | | | | | | | | |            (431), (538), (541), (542), (543), (545), (546),
% 196.95/32.15  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 196.95/32.15  | | | | | | | | | | | | | | |            (559), (562), (563), (564), (566), (567), (572),
% 196.95/32.15  | | | | | | | | | | | | | | |            (573), (574), (576), (588), (590), (591), (593),
% 196.95/32.15  | | | | | | | | | | | | | | |            (596), (603), (606), (608), (611), (612), (613),
% 196.95/32.15  | | | | | | | | | | | | | | |            (7443), (7445), (7449), (7450), (7458), (7462),
% 196.95/32.15  | | | | | | | | | | | | | | |            (7465), (7957), (7959), (7963), (7991),
% 196.95/32.15  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.15  | | | | | | | | | | | | | | |            #200.
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (7992)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 196.95/32.15  | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 196.95/32.15  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.95/32.15  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 196.95/32.15  | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 196.95/32.15  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.95/32.15  | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 196.95/32.15  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 196.95/32.15  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.95/32.15  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 196.95/32.15  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.15  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.15  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.15  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 196.95/32.15  | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 196.95/32.15  | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 196.95/32.15  | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 196.95/32.15  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 196.95/32.15  | | | | | | | | | | | | | | |            (7462), (7465), (7957), (7967), (7969), (7992),
% 196.95/32.15  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.15  | | | | | | | | | | | | | | |            #1008.
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | |   (7993)  all_40_1 = e2
% 196.95/32.15  | | | | | | | | | | | |   (7994)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | COMBINE_EQS: (687), (7993) imply:
% 196.95/32.15  | | | | | | | | | | | |   (7995)  all_10_1 = e2
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (7961), (7995) imply:
% 196.95/32.15  | | | | | | | | | | | |   (7996)   ~ (e3 = e2)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (53), (7995) imply:
% 196.95/32.15  | | | | | | | | | | | |   (7997)  op(all_10_2, e1) = e2
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (52), (7995) imply:
% 196.95/32.15  | | | | | | | | | | | |   (7998)  op(e1, e2) = all_10_0
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 196.95/32.15  | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (7998)
% 196.95/32.15  | | | | | | | | | | | |              gives:
% 196.95/32.15  | | | | | | | | | | | |   (7999)  all_52_13 = all_10_0
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | COMBINE_EQS: (421), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8000)  all_56_9 = all_10_0
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | COMBINE_EQS: (366), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8001)  all_58_7 = all_10_0
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (568), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8002)   ~ (all_52_5 = all_10_0)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (575), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8003)   ~ (all_52_9 = all_10_0)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (589), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8004)   ~ (all_52_29 = all_10_0)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | SIMP: (8004) implies:
% 196.95/32.15  | | | | | | | | | | | |   (8005)   ~ (all_52_29 = all_10_0)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (588), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8006)   ~ (all_10_0 = all_10_2)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (580), (7999) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8007)   ~ (all_10_0 = all_4_2)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | BETA: splitting (153) gives:
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | |   (8008)   ~ (all_50_0 = e2)
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | REDUCE: (7952), (8008) imply:
% 196.95/32.15  | | | | | | | | | | | | |   (8009)  $false
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | CLOSE: (8009) is inconsistent.
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | |   (8010)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | |   (8011)  all_58_15 = e0
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (7953), (8011),
% 196.95/32.15  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.15  | | | | | | | | | | | | | |            #612.
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | |   (8012)   ~ (all_58_15 = e0)
% 196.95/32.15  | | | | | | | | | | | | | |   (8013)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.15  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.15  | | | | | | | | | | | | | |             e0)
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | ALPHA: (8013) implies:
% 196.95/32.15  | | | | | | | | | | | | | |   (8014)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.15  | | | | | | | | | | | | | |   (8015)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | REDUCE: (541), (8012) imply:
% 196.95/32.15  | | | | | | | | | | | | | |   (8016)   ~ (all_14_2 = e0)
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (8017)  all_56_9 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REF_CLOSE: (7463), (8000), (8017) are inconsistent by
% 196.95/32.15  | | | | | | | | | | | | | | |            sub-proof #1006.
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (8018)   ~ (all_56_9 = e3)
% 196.95/32.15  | | | | | | | | | | | | | | |   (8019)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8020)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.95/32.15  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | BETA: splitting (8020) gives:
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8021)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | ALPHA: (8021) implies:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8022)  all_52_6 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8023)  all_52_4 = e1
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8024)  all_52_2 = e2
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8025)  all_52_0 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (185), (8024) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8026)  op(all_52_3, all_52_3) = e2
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (184), (8023) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8027)  op(all_52_5, all_52_5) = e1
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (183), (8022) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8028)  op(all_52_7, all_52_7) = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (610), (8025) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8029)  op(all_6_2, all_6_2) = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (61), (63), (167),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (168), (169), (173), (174), (178), (270), (273),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (277), (278), (282), (284), (306), (307), (312),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (313), (321), (324), (332), (335), (351), (367),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (372), (387), (388), (394), (405), (427), (431),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (526), (538), (541), (543), (544), (545), (546),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (564),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (569), (570), (571), (573), (577), (578), (591),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (593), (595), (604), (606), (607), (609), (611),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (612), (613), (690), (767), (7445), (7449),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7463), (7953), (7955), (7959), (7994), (7997),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (8000), (8001), (8002), (8003), (8005), (8006),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (8007), (8010), (8015), (8016), (8019), (8026),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (8027), (8028), (8029), (function-axioms) are
% 196.95/32.15  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #122.
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8030)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (158), (169), (179),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (182), (273), (278), (321), (324), (325), (372),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (387), (427), (431), (543), (548), (549), (555),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (557), (564), (571), (586), (611), (7445), (7449),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7463), (7465), (7955), (7957), (7959), (8001),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (8030), (function-axioms) are inconsistent by
% 196.95/32.15  | | | | | | | | | | | | | | | | |            sub-proof #182.
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8031)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.95/32.15  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.95/32.15  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | BETA: splitting (8031) gives:
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8032)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | ALPHA: (8032) implies:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8033)  all_52_22 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8034)  all_52_20 = e1
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8035)  all_52_16 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (178), (8035) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8036)  op(all_52_17, all_52_17) = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (175), (8033) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8037)  op(all_52_23, all_52_23) = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REDUCE: (612), (8034) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8038)  op(all_10_2, all_10_2) = e1
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (158), (168), (169), (173),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (185), (270), (273), (278), (306), (309), (313),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (317), (321), (333), (351), (372), (387), (393),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (405), (427), (431), (526), (538), (541), (542),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (562), (563),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (564), (567), (572), (576), (582), (586), (603),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (604), (605), (607), (608), (611), (767), (7443),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (7463), (7465),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7955), (7957), (7959), (7994), (7997), (8000),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (8001), (8003), (8019), (8036), (8037), (8038),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.15  | | | | | | | | | | | | | | | | |            #174.
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | |   (8039)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (7462), (7465), (7957), (8014), (8016), (8039),
% 196.95/32.15  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.15  | | | | | | | | | | | | | | | | |            #1008.
% 196.95/32.15  | | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | End of split
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | |   (8040)  all_30_1 = e3
% 196.95/32.15  | | | | | | | | | | |   (8041)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | COMBINE_EQS: (670), (8040) imply:
% 196.95/32.15  | | | | | | | | | | |   (8042)  all_10_1 = e3
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | SIMP: (8042) implies:
% 196.95/32.15  | | | | | | | | | | |   (8043)  all_10_1 = e3
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | REDUCE: (53), (8043) imply:
% 196.95/32.15  | | | | | | | | | | |   (8044)  op(all_10_2, e1) = e3
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | REDUCE: (52), (8043) imply:
% 196.95/32.15  | | | | | | | | | | |   (8045)  op(e1, e3) = all_10_0
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 196.95/32.15  | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (8045)
% 196.95/32.15  | | | | | | | | | | |              gives:
% 196.95/32.15  | | | | | | | | | | |   (8046)  all_52_5 = all_10_0
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | COMBINE_EQS: (367), (8046) imply:
% 196.95/32.15  | | | | | | | | | | |   (8047)  all_56_8 = all_10_0
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | COMBINE_EQS: (547), (8046) imply:
% 196.95/32.15  | | | | | | | | | | |   (8048)  all_58_6 = all_10_0
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | REDUCE: (567), (8046) imply:
% 196.95/32.15  | | | | | | | | | | |   (8049)   ~ (all_52_7 = all_10_0)
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | SIMP: (8049) implies:
% 196.95/32.15  | | | | | | | | | | |   (8050)   ~ (all_52_7 = all_10_0)
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | REDUCE: (569), (8046) imply:
% 196.95/32.15  | | | | | | | | | | |   (8051)   ~ (all_10_0 = all_10_2)
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | REDUCE: (553), (8046) imply:
% 196.95/32.15  | | | | | | | | | | |   (8052)   ~ (all_10_0 = all_6_2)
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | REDUCE: (184), (8046) imply:
% 196.95/32.15  | | | | | | | | | | |   (8053)  op(all_10_0, all_10_0) = all_52_4
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | BETA: splitting (303) gives:
% 196.95/32.15  | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | |   (8054)  all_58_15 = e0
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (7953), (8054),
% 196.95/32.15  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.15  | | | | | | | | | | | |            #612.
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | |   (8055)   ~ (all_58_15 = e0)
% 196.95/32.15  | | | | | | | | | | | |   (8056)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 196.95/32.15  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 196.95/32.15  | | | | | | | | | | | |             e0)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | ALPHA: (8056) implies:
% 196.95/32.15  | | | | | | | | | | | |   (8057)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | REDUCE: (541), (8055) imply:
% 196.95/32.15  | | | | | | | | | | | |   (8058)   ~ (all_14_2 = e0)
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | BETA: splitting (277) gives:
% 196.95/32.15  | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | |   (8059)  all_56_8 = e3
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | REF_CLOSE: (7463), (8047), (8059) are inconsistent by
% 196.95/32.15  | | | | | | | | | | | | |            sub-proof #926.
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | |   (8060)   ~ (all_56_8 = e3)
% 196.95/32.15  | | | | | | | | | | | | |   (8061)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 196.95/32.15  | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | |   (8062)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 196.95/32.15  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | BETA: splitting (8062) gives:
% 196.95/32.15  | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (8063)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | |           all_52_6 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (311), (361), (459), (593),
% 196.95/32.15  | | | | | | | | | | | | | | |            (750), (7955), (8041), (8044), (8047), (8048),
% 196.95/32.15  | | | | | | | | | | | | | | |            (8051), (8053), (8061), (8063), (function-axioms)
% 196.95/32.15  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #667.
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | Case 2:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | |   (8064)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 196.95/32.15  | | | | | | | | | | | | | | |           all_52_14 = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | ALPHA: (8064) implies:
% 196.95/32.15  | | | | | | | | | | | | | | |   (8065)  all_52_14 = e0
% 196.95/32.15  | | | | | | | | | | | | | | |   (8066)  all_52_12 = e1
% 196.95/32.15  | | | | | | | | | | | | | | |   (8067)  all_52_10 = e2
% 196.95/32.15  | | | | | | | | | | | | | | |   (8068)  all_52_8 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REDUCE: (182), (8068) imply:
% 196.95/32.15  | | | | | | | | | | | | | | |   (8069)  op(all_52_9, all_52_9) = e3
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REDUCE: (180), (8066) imply:
% 196.95/32.15  | | | | | | | | | | | | | | |   (8070)  op(all_52_13, all_52_13) = e1
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REDUCE: (179), (8065) imply:
% 196.95/32.15  | | | | | | | | | | | | | | |   (8071)  op(all_52_15, all_52_15) = e0
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | REDUCE: (611), (8067) imply:
% 196.95/32.15  | | | | | | | | | | | | | | |   (8072)  op(all_4_2, all_4_2) = e2
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.95/32.15  | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8073)  all_56_15 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8073) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8074)  all_14_2 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | SIMP: (8074) implies:
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8075)  all_14_2 = e3
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | REDUCE: (573), (8075) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8076)   ~ (all_52_7 = e3)
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | REDUCE: (591), (8075) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8077)   ~ (all_52_15 = e3)
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | REDUCE: (603), (8075) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8078)   ~ (all_52_23 = e3)
% 196.95/32.15  | | | | | | | | | | | | | | | | 
% 196.95/32.15  | | | | | | | | | | | | | | | | REDUCE: (606), (8075) imply:
% 196.95/32.15  | | | | | | | | | | | | | | | |   (8079)   ~ (all_52_25 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (609), (8075) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8080)   ~ (all_52_29 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (613), (8075) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8081)  op(e3, e3) = all_52_30
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (63), (8075) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8082)  op(e3, e0) = all_14_1
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 196.95/32.16  | | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (8082)
% 196.95/32.16  | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8083)  all_52_25 = all_14_1
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.16  | | | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (8081)
% 196.95/32.16  | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8084)  all_52_30 = all_6_2
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (8083) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8085)  all_56_3 = all_14_1
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (578), (8083) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8086)   ~ (all_52_9 = all_14_1)
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (561), (8083) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8087)   ~ (all_14_1 = all_6_2)
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (8079), (8083) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8088)   ~ (all_14_1 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8089)  all_56_3 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (8085), (8088), (8089) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | |            sub-proof #1200.
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8090)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8091)  all_58_0 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (42), (43), (275), (313), (325), (333),
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            (361), (366), (393), (405), (543), (544), (545),
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (553), (557), (559),
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            (588), (610), (612), (7460), (7462), (8069),
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            (8070), (8072), (8077), (8079), (8080), (8091),
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            #1136.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8092)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | BETA: splitting (8092) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8093)  all_58_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (8093) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8094)  all_52_3 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | SIMP: (8094) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8095)  all_52_3 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (8095) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8096)   ~ (all_52_7 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REDUCE: (7450), (8095) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8097)   ~ (all_4_0 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REDUCE: (564), (8095) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8098)   ~ (all_4_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | SIMP: (8098) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8099)   ~ (all_4_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REDUCE: (185), (8095) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8100)  op(e3, e3) = all_52_2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |              all_52_2, e3, e3, simplifying with (41), (8100)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8101)  all_52_2 = all_6_2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8102)  all_58_4 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (8102) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8103)  all_52_17 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8103) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8104)  all_52_17 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (8104) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8105)   ~ (all_52_9 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (8104) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8106)   ~ (all_6_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8106) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8107)   ~ (all_6_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (42), (43),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (162), (183), (284), (325), (326), (330), (331),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (332), (351), (366), (387), (394), (405), (543),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (555), (557), (564), (568),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (575), (7462), (7957), (8069), (8070), (8076),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (8077), (8082), (8085), (8086), (8087), (8090),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (8093), (8099), (8100), (8105), (8107),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            #1119.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8108)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (542), (546), (593), (7449), (7959),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (8044), (8078), (8108), (function-axioms) are
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #167.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8109)  all_58_6 = e3 | all_58_12 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (7463), (8048), (8076), (8109) are
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #921.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8110)   ~ (all_56_15 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8111)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | REDUCE: (538), (8110) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | |   (8112)   ~ (all_14_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8113)  all_58_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (8113) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8114)  all_52_3 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | SIMP: (8114) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8115)  all_52_3 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (563), (8115) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8116)   ~ (all_52_7 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | SIMP: (8116) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8117)   ~ (all_52_7 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (566), (8115) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8118)   ~ (all_52_27 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | SIMP: (8118) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8119)   ~ (all_52_27 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (7450), (8115) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8120)   ~ (all_4_0 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (564), (8115) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8121)   ~ (all_4_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | SIMP: (8121) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8122)   ~ (all_4_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (185), (8115) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8123)  op(e3, e3) = all_52_2
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (166), (8115) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8124)  op(e2, e3) = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.16  | | | | | | | | | | | | | | | | |              all_52_2, e3, e3, simplifying with (41), (8123)
% 196.95/32.16  | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8125)  all_52_2 = all_6_2
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8126)  all_58_0 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8126) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8127)  all_6_2 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REDUCE: (43), (8127) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8128)  op(e2, e3) = all_6_1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REDUCE: (41), (8127) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8129)  op(e3, e3) = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (7462), (8124), (8128), (8129),
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.16  | | | | | | | | | | | | | | | | | |            #169.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8130)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | BETA: splitting (8130) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8131)  all_58_2 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8113), (8131) are inconsistent by sub-proof
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |            #1124.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8132)  all_58_6 = e2 | all_58_12 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (8132) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8133)  all_58_6 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7955), (8048), (8133) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #917.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8134)  all_58_12 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8134) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8135)  all_52_7 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8135) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8136)  all_52_7 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (8136) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8137)   ~ (all_14_2 = e2)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8137) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8138)   ~ (all_14_2 = e2)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (8050), (8136) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8139)   ~ (all_10_0 = e2)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (8117), (8136) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8140)   ~ (e3 = e2)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8111) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8141)  all_56_15 = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8138), (8141) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #762.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8142)   ~ (all_56_15 = e2)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8143)  all_56_15 = e1 | all_56_15 = e0
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8143) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8144)  all_56_15 = e1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8144) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8145)  all_14_2 = e1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8145) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8146)  all_14_2 = e1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (8146) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8147)  all_58_15 = e1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (8146) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8148)   ~ (all_52_25 = e1)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8112), (8146) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8149)   ~ (e3 = e1)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8138), (8146) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8150)   ~ (e2 = e1)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (8146) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8151)  op(e1, e0) = all_14_1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7951) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8152)   ~ (all_14_1 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |              all_14_1, e0, e1, simplifying with (159), (8151)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8153)  all_52_29 = all_14_1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8153) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8154)  all_58_11 = all_14_1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8155)  all_58_9 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (8155) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8156)  all_52_25 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8156) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8157)  all_52_25 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (8157) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8158)   ~ (all_52_17 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (8157) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8159)  op(e3, e3) = all_52_24
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (8159)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8160)  all_52_24 = all_6_2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (8161)  all_56_13 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (317), (346), (393), (542), (546), (590),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | |            (593), (7449), (7959), (8044), (8158), (8161),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | |            #165.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (8162)   ~ (all_56_13 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (8162) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (8163)   ~ (all_52_15 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8164)  all_58_12 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7955), (8048), (8132), (8164) are
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #889.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8165)   ~ (all_58_12 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8166)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8166) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8167)  all_58_13 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (8167) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8168)  all_52_15 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8163), (8168) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8169)  $false
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8169) is inconsistent.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8170)   ~ (all_58_13 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8171)  all_58_14 = e3 | all_58_15 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8171) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8172)  all_58_14 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (41), (43), (61), (162), (277),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (325), (330), (332), (351), (366), (367), (387),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (405), (543), (547), (548), (549), (553), (557),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (562), (567), (568), (591), (7957), (8057),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8069), (8070), (8071), (8117), (8122), (8163),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8172), (function-axioms) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1098.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8173)  all_58_15 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8147), (8173) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8174)  e3 = e1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (8174) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8175)  $false
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8175) is inconsistent.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |   (8176)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (372), (8119), (8147), (8152), (8154), (8176)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #121.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8177)   ~ (all_14_2 = e1)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8058), (8143), (8177) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8178)  all_56_15 = e0
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8058), (8178) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1162.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8179)   ~ (all_58_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8180)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | REDUCE: (387), (8179) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | |   (8181)   ~ (all_52_3 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8182)  all_58_0 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8182) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8183)  all_6_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REDUCE: (610), (8183) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8184)  op(e3, e3) = all_52_0
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REDUCE: (43), (8183) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8185)  op(e3, e3) = all_6_1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REDUCE: (41), (8183) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8186)  op(e3, e3) = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 196.95/32.16  | | | | | | | | | | | | | | | | | |              all_52_0, e3, e3, simplifying with (8184), (8185)
% 196.95/32.16  | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8187)  all_52_0 = all_6_1
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_0,
% 196.95/32.16  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8184), (8186) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8188)  all_52_0 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8187), (8188) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8189)  all_6_1 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | SIMP: (8189) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8190)  all_6_1 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | REDUCE: (42), (8190) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8191)  op(e3, e3) = all_6_0
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 196.95/32.16  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8186), (8191) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8192)  all_6_0 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8193)  all_56_5 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (8193) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8194)  all_4_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | SIMP: (8194) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8195)  all_4_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REDUCE: (8072), (8195) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8196)  op(e3, e3) = e2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8184), (8186), (8196), (function-axioms) are
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #821.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8197)   ~ (all_56_5 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REDUCE: (539), (8197) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8198)   ~ (all_4_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (8180) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8199)  all_58_3 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8199) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8200)  all_4_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (8198), (8200) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8201)  $false
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | CLOSE: (8201) is inconsistent.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8202)  all_58_5 = e3 | all_58_10 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8202) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8203)  all_58_5 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7959), (8203) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8204)  all_58_10 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (8204) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8205)  all_52_27 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (8205) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8206)  all_52_27 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (8206) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8207)   ~ (all_52_29 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (8207) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8208)   ~ (all_52_29 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (8206) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8209)  op(e3, e3) = all_52_26
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (8186), (8209)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | |   (8210)  all_52_26 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8211)  all_58_6 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7463), (8048), (8211) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #922.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | |   (8212)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8213)  all_56_10 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (8213) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8214)  all_10_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8214) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8215)  all_10_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (593), (8044), (8215), (function-axioms)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #925.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8216)   ~ (all_56_10 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (8216) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |   (8217)   ~ (all_10_2 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (366), (544), (546), (8070), (8184), (8186),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |            (8208), (8212), (8217), (function-axioms) are
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1139.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | |   (8218)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | BETA: splitting (8218) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8219)  all_58_2 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (8181), (8219) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |            sub-proof #1369.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | |   (8220)  all_58_6 = e3 | all_58_12 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (8220) gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8221)  all_58_6 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7463), (8048), (8221) are inconsistent by
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #922.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8222)  all_58_12 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8222) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8223)  all_52_7 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8223) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8224)  all_52_7 = e3
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (8224) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8225)   ~ (all_52_15 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8225) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8226)   ~ (all_52_15 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (8224) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8227)   ~ (all_52_23 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | SIMP: (8227) implies:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8228)   ~ (all_52_23 = e3)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (8224) imply:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8229)  op(e3, e3) = all_52_6
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (8229)
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |   (8230)  all_52_6 = all_6_2
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (51), (168), (169), (178), (275), (278),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (317), (325), (328), (361), (366), (372), (393),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (405), (427), (459), (542), (543), (546), (548),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (549), (577), (580), (582), (586), (593), (750),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7955), (7959),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (8041), (8044), (8047), (8051), (8052), (8061),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (8069), (8070), (8180), (8226), (8228),
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | |            #119.
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | | 
% 196.95/32.16  | | | | | | | | | | | | | | | | End of split
% 196.95/32.16  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | End of split
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | End of split
% 196.95/32.17  | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | Case 2:
% 196.95/32.17  | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | |   (8231)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 196.95/32.17  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 196.95/32.17  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 196.95/32.17  | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | BETA: splitting (8231) gives:
% 196.95/32.17  | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | |   (8232)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 196.95/32.17  | | | | | | | | | | | | | | |           all_52_22 = e0
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | ALPHA: (8232) implies:
% 196.95/32.17  | | | | | | | | | | | | | | |   (8233)  all_52_22 = e0
% 196.95/32.17  | | | | | | | | | | | | | | |   (8234)  all_52_20 = e1
% 196.95/32.17  | | | | | | | | | | | | | | |   (8235)  all_52_16 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | REDUCE: (178), (8235) imply:
% 196.95/32.17  | | | | | | | | | | | | | | |   (8236)  op(all_52_17, all_52_17) = e3
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | REDUCE: (175), (8233) imply:
% 196.95/32.17  | | | | | | | | | | | | | | |   (8237)  op(all_52_23, all_52_23) = e0
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | REDUCE: (612), (8234) imply:
% 196.95/32.17  | | | | | | | | | | | | | | |   (8238)  op(all_10_2, all_10_2) = e1
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | |   (8239)  all_56_15 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | REF_CLOSE: (41), (168), (185), (317), (325), (332), (333),
% 196.95/32.17  | | | | | | | | | | | | | | | |            (351), (375), (387), (393), (405), (538), (542),
% 196.95/32.17  | | | | | | | | | | | | | | | |            (545), (546), (549), (551), (559), (565), (573),
% 196.95/32.17  | | | | | | | | | | | | | | | |            (577), (593), (603), (606), (7449), (7463),
% 196.95/32.17  | | | | | | | | | | | | | | | |            (7959), (8044), (8048), (8236), (8239),
% 196.95/32.17  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.17  | | | | | | | | | | | | | | | |            #118.
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | Case 2:
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | |   (8240)   ~ (all_56_15 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | |   (8241)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | REDUCE: (538), (8240) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | |   (8242)   ~ (all_14_2 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8243)  all_58_2 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (8243) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8244)  all_52_3 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | SIMP: (8244) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8245)  all_52_3 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | REDUCE: (563), (8245) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8246)   ~ (all_52_7 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | SIMP: (8246) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8247)   ~ (all_52_7 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | REDUCE: (566), (8245) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8248)   ~ (all_52_27 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | SIMP: (8248) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8249)   ~ (all_52_27 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | REDUCE: (7450), (8245) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8250)   ~ (all_4_0 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | REDUCE: (185), (8245) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8251)  op(e3, e3) = all_52_2
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | REDUCE: (166), (8245) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8252)  op(e2, e3) = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.17  | | | | | | | | | | | | | | | | |              all_52_2, e3, e3, simplifying with (41), (8251)
% 196.95/32.17  | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | |   (8253)  all_52_2 = all_6_2
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | |   (8254)  all_58_0 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (42), (43), (405), (7462), (8252), (8254),
% 196.95/32.17  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 196.95/32.17  | | | | | | | | | | | | | | | | | |            #168.
% 196.95/32.17  | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | |   (8255)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | BETA: splitting (8255) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | |   (8256)  all_58_2 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8243), (8256) are inconsistent by sub-proof
% 196.95/32.17  | | | | | | | | | | | | | | | | | | |            #1124.
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | |   (8257)  all_58_6 = e2 | all_58_12 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (8257) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8258)  all_58_6 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7955), (8048), (8258) are inconsistent by
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |            sub-proof #917.
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8259)  all_58_12 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8259) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8260)  all_52_7 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | SIMP: (8260) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8261)  all_52_7 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (8261) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8262)   ~ (all_14_2 = e2)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | SIMP: (8262) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8263)   ~ (all_14_2 = e2)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | REDUCE: (8050), (8261) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8264)   ~ (all_10_0 = e2)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | REDUCE: (8247), (8261) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | |   (8265)   ~ (e3 = e2)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8241) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | |   (8266)  all_56_15 = e2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8263), (8266) are inconsistent by
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | |            sub-proof #762.
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | |   (8267)  all_56_15 = e1 | all_56_15 = e0
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8267) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8268)  all_56_15 = e1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8268) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8269)  all_14_2 = e1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8269) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8270)  all_14_2 = e1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (8270) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8271)  all_58_15 = e1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8242), (8270) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8272)   ~ (e3 = e1)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (8270) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8273)  op(e1, e0) = all_14_1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7951) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | |   (8274)   ~ (all_14_1 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | |              all_14_1, e0, e1, simplifying with (159), (8273)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | |   (8275)  all_52_29 = all_14_1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8275) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | |   (8276)  all_58_11 = all_14_1
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8277)  all_58_9 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (8277) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8278)  all_52_25 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8278) implies:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8279)  all_52_25 = e3
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (8279) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8280)   ~ (all_52_17 = e3)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (8279) imply:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8281)  op(e3, e3) = all_52_24
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (8281)
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8282)  all_52_24 = all_6_2
% 196.95/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (43), (158), (168), (272), (273),
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |            (306), (317), (346), (393), (431), (541), (542),
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |            (543), (546), (555), (572), (590), (593), (7449),
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |            (7465), (7955), (7957), (7959), (8044), (8048),
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |            (8237), (8242), (8257), (8280), (function-axioms)
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #164.
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |   (8283)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (372), (8249), (8271), (8274), (8276), (8283)
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #121.
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | |   (8284)   ~ (all_14_2 = e1)
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8058), (8267), (8284) are inconsistent by
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | |   (8285)  all_56_15 = e0
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8058), (8285) are inconsistent by
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1162.
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | |   (8286)   ~ (all_58_2 = e3)
% 197.10/32.17  | | | | | | | | | | | | | | | | |   (8287)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.10/32.17  | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | REDUCE: (387), (8286) imply:
% 197.10/32.17  | | | | | | | | | | | | | | | | |   (8288)   ~ (all_52_3 = e3)
% 197.10/32.17  | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (53), (61), (158), (168), (173),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (183), (273), (280), (283), (306), (313), (317),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (332), (351), (366), (372), (375), (387), (393),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (405), (415), (431), (539), (541), (542), (543),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (544), (546), (548), (555), (559), (572), (582),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (586), (587), (593), (596), (607), (608), (7449),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (7463), (7465), (7957), (7959), (8044), (8048),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (8052), (8236), (8237), (8238), (8242), (8287),
% 197.10/32.17  | | | | | | | | | | | | | | | | |            (8288), (function-axioms) are inconsistent by
% 197.10/32.17  | | | | | | | | | | | | | | | | |            sub-proof #161.
% 197.10/32.17  | | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | |   (8289)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.10/32.17  | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.10/32.17  | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 197.10/32.17  | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 197.10/32.17  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 197.10/32.17  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 197.10/32.17  | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 197.10/32.17  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 197.10/32.17  | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 197.10/32.17  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 197.10/32.17  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.10/32.17  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 197.10/32.17  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.10/32.17  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.10/32.17  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.10/32.17  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 197.10/32.17  | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 197.10/32.17  | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.10/32.17  | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 197.10/32.17  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 197.10/32.17  | | | | | | | | | | | | | | |            (7462), (7465), (7957), (8057), (8058), (8289),
% 197.10/32.17  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.10/32.17  | | | | | | | | | | | | | | |            #1008.
% 197.10/32.17  | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | |   (8290)  all_28_0 = e3
% 197.10/32.17  | | | | | | | | | |   (8291)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | COMBINE_EQS: (754), (8290) imply:
% 197.10/32.17  | | | | | | | | | |   (8292)  all_4_0 = e3
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | COMBINE_EQS: (7449), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8293)  all_58_5 = e3
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (7450), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8294)   ~ (all_52_3 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (7451), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8295)   ~ (all_52_17 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (7455), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8296)   ~ (all_52_27 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (7457), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8297)   ~ (all_10_2 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (7458), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8298)   ~ (all_4_2 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | SIMP: (8298) implies:
% 197.10/32.17  | | | | | | | | | |   (8299)   ~ (all_4_2 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (7459), (8292) imply:
% 197.10/32.17  | | | | | | | | | |   (8300)  op(e3, e3) = all_52_18
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 197.10/32.17  | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (161), (162),
% 197.10/32.17  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.10/32.17  | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.10/32.17  | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.10/32.17  | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.10/32.17  | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.10/32.17  | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.10/32.17  | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 197.10/32.17  | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.10/32.17  | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.10/32.17  | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 197.10/32.17  | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.10/32.17  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.10/32.17  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.10/32.17  | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.10/32.17  | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.10/32.17  | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 197.10/32.17  | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 197.10/32.17  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.10/32.17  | | | | | | | | | |            (608), (609), (610), (613), (7443), (7444),
% 197.10/32.17  | | | | | | | | | |            (7445), (7449), (7453), (7458), (7460), (7462),
% 197.10/32.17  | | | | | | | | | |            (7465), (7953), (7957), (8291), (8293), (8294),
% 197.10/32.17  | | | | | | | | | |            (8295), (8296), (8297), (8299), (8300),
% 197.10/32.17  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.10/32.17  | | | | | | | | | |            #117.
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | |   (8301)  all_22_1 = e2
% 197.10/32.17  | | | | | | | | |   (8302)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | COMBINE_EQS: (658), (8301) imply:
% 197.10/32.17  | | | | | | | | |   (8303)  all_6_1 = e2
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | REDUCE: (43), (8303) imply:
% 197.10/32.17  | | | | | | | | |   (8304)  op(all_6_2, e3) = e2
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | REDUCE: (42), (8303) imply:
% 197.10/32.17  | | | | | | | | |   (8305)  op(e3, e2) = all_6_0
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 197.10/32.17  | | | | | | | | |            (52), (53), (61), (63), (104), (129), (153), (157),
% 197.10/32.17  | | | | | | | | |            (158), (161), (162), (166), (167), (168), (169),
% 197.10/32.17  | | | | | | | | |            (172), (173), (174), (175), (177), (178), (180),
% 197.10/32.17  | | | | | | | | |            (182), (183), (184), (185), (187), (270), (271),
% 197.10/32.17  | | | | | | | | |            (273), (274), (275), (276), (277), (279), (280),
% 197.10/32.17  | | | | | | | | |            (281), (282), (283), (284), (285), (303), (304),
% 197.10/32.17  | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 197.10/32.17  | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 197.10/32.17  | | | | | | | | |            (328), (329), (331), (332), (333), (335), (343),
% 197.10/32.17  | | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 197.10/32.17  | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 197.10/32.17  | | | | | | | | |            (417), (421), (431), (522), (526), (538), (539),
% 197.10/32.17  | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.10/32.17  | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.10/32.17  | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 197.10/32.17  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.10/32.17  | | | | | | | | |            (574), (575), (576), (577), (578), (582), (584),
% 197.10/32.17  | | | | | | | | |            (586), (588), (590), (591), (592), (593), (594),
% 197.10/32.17  | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 197.10/32.17  | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.10/32.17  | | | | | | | | |            (612), (613), (670), (687), (739), (767), (7460),
% 197.10/32.17  | | | | | | | | |            (7462), (7463), (7952), (7953), (7955), (8302),
% 197.10/32.17  | | | | | | | | |            (8304), (8305), (function-axioms) are inconsistent
% 197.10/32.17  | | | | | | | | |            by sub-proof #585.
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | End of split
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | |   (8306)  all_16_0 = e2
% 197.10/32.17  | | | | | | | |   (8307)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | COMBINE_EQS: (760), (8306) imply:
% 197.10/32.17  | | | | | | | |   (8308)  all_10_0 = e2
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | SIMP: (8308) implies:
% 197.10/32.17  | | | | | | | |   (8309)  all_10_0 = e2
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | COMBINE_EQS: (756), (8309) imply:
% 197.10/32.17  | | | | | | | |   (8310)  all_26_0 = e2
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | REDUCE: (7463), (8309) imply:
% 197.10/32.17  | | | | | | | |   (8311)   ~ (e3 = e2)
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | REDUCE: (52), (8309) imply:
% 197.10/32.17  | | | | | | | |   (8312)  op(e1, all_10_1) = e2
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | BETA: splitting (84) gives:
% 197.10/32.17  | | | | | | | | 
% 197.10/32.17  | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | |   (8313)   ~ (all_22_1 = e2)
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | REDUCE: (658), (8313) imply:
% 197.10/32.17  | | | | | | | | |   (8314)   ~ (all_6_1 = e2)
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | BETA: splitting (94) gives:
% 197.10/32.17  | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | |   (8315)   ~ (all_26_0 = e2)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | REDUCE: (8310), (8315) imply:
% 197.10/32.17  | | | | | | | | | |   (8316)  $false
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | CLOSE: (8316) is inconsistent.
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | |   (8317)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | BETA: splitting (99) gives:
% 197.10/32.17  | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | |   (8318)   ~ (all_28_0 = e3)
% 197.10/32.17  | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | REDUCE: (754), (8318) imply:
% 197.10/32.17  | | | | | | | | | | |   (8319)   ~ (all_4_0 = e3)
% 197.10/32.17  | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.10/32.17  | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | |   (8320)  all_58_15 = e0
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (7953), (8320),
% 197.10/32.17  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.10/32.17  | | | | | | | | | | | |            #612.
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | Case 2:
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | |   (8321)   ~ (all_58_15 = e0)
% 197.10/32.17  | | | | | | | | | | | |   (8322)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.10/32.17  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.10/32.17  | | | | | | | | | | | |             e0)
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | ALPHA: (8322) implies:
% 197.10/32.17  | | | | | | | | | | | |   (8323)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.10/32.17  | | | | | | | | | | | |   (8324)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | REDUCE: (541), (8321) imply:
% 197.10/32.17  | | | | | | | | | | | |   (8325)   ~ (all_14_2 = e0)
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.10/32.17  | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | |   (8326)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.10/32.17  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.10/32.17  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.10/32.17  | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | BETA: splitting (8326) gives:
% 197.10/32.17  | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | |   (8327)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.10/32.17  | | | | | | | | | | | | | |           all_52_6 = e0
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | ALPHA: (8327) implies:
% 197.10/32.17  | | | | | | | | | | | | | |   (8328)  all_52_6 = e0
% 197.10/32.17  | | | | | | | | | | | | | |   (8329)  all_52_4 = e1
% 197.10/32.17  | | | | | | | | | | | | | |   (8330)  all_52_2 = e2
% 197.10/32.17  | | | | | | | | | | | | | |   (8331)  all_52_0 = e3
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | REDUCE: (185), (8330) imply:
% 197.10/32.17  | | | | | | | | | | | | | |   (8332)  op(all_52_3, all_52_3) = e2
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | REDUCE: (184), (8329) imply:
% 197.10/32.17  | | | | | | | | | | | | | |   (8333)  op(all_52_5, all_52_5) = e1
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | REDUCE: (183), (8328) imply:
% 197.10/32.17  | | | | | | | | | | | | | |   (8334)  op(all_52_7, all_52_7) = e0
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | REDUCE: (610), (8331) imply:
% 197.10/32.17  | | | | | | | | | | | | | |   (8335)  op(all_6_2, all_6_2) = e3
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.10/32.17  | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | Case 1:
% 197.10/32.17  | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | |   (8336)  all_56_15 = e3
% 197.10/32.17  | | | | | | | | | | | | | | | 
% 197.10/32.17  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8336) imply:
% 197.10/32.18  | | | | | | | | | | | | | | |   (8337)  all_14_2 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | SIMP: (8337) implies:
% 197.10/32.18  | | | | | | | | | | | | | | |   (8338)  all_14_2 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (41), (42), (43), (51),
% 197.10/32.18  | | | | | | | | | | | | | | |            (53), (61), (156), (161), (273), (277), (279),
% 197.10/32.18  | | | | | | | | | | | | | | |            (304), (305), (310), (317), (319), (321), (328),
% 197.10/32.18  | | | | | | | | | | | | | | |            (330), (332), (333), (351), (367), (372), (375),
% 197.10/32.18  | | | | | | | | | | | | | | |            (387), (393), (405), (417), (431), (541), (542),
% 197.10/32.18  | | | | | | | | | | | | | | |            (546), (547), (548), (551), (553), (555), (559),
% 197.10/32.18  | | | | | | | | | | | | | | |            (562), (564), (565), (567), (568), (569), (573),
% 197.10/32.18  | | | | | | | | | | | | | | |            (596), (597), (600), (608), (7460), (8312),
% 197.10/32.18  | | | | | | | | | | | | | | |            (8323), (8325), (8332), (8333), (8334), (8335),
% 197.10/32.18  | | | | | | | | | | | | | | |            (8338), (function-axioms) are inconsistent by
% 197.10/32.18  | | | | | | | | | | | | | | |            sub-proof #584.
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | Case 2:
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | |   (8339)   ~ (all_56_15 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | REDUCE: (538), (8339) imply:
% 197.10/32.18  | | | | | | | | | | | | | | |   (8340)   ~ (all_14_2 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | Case 1:
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | |   (8341)  all_56_5 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (8341) imply:
% 197.10/32.18  | | | | | | | | | | | | | | | |   (8342)  all_4_2 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | SIMP: (8342) implies:
% 197.10/32.18  | | | | | | | | | | | | | | | |   (8343)  all_4_2 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | REDUCE: (582), (8343) imply:
% 197.10/32.18  | | | | | | | | | | | | | | | |   (8344)   ~ (all_52_15 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (41), (51), (53), (61), (156),
% 197.10/32.18  | | | | | | | | | | | | | | | |            (273), (304), (305), (306), (321), (332), (351),
% 197.10/32.18  | | | | | | | | | | | | | | | |            (387), (405), (431), (515), (541), (542), (543),
% 197.10/32.18  | | | | | | | | | | | | | | | |            (547), (555), (564), (569), (572), (573), (582),
% 197.10/32.18  | | | | | | | | | | | | | | | |            (680), (8307), (8323), (8332), (8333), (8334),
% 197.10/32.18  | | | | | | | | | | | | | | | |            (8335), (8340), (8344), (function-axioms) are
% 197.10/32.18  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #615.
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | Case 2:
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | |   (8345)   ~ (all_56_5 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | REDUCE: (539), (8345) imply:
% 197.10/32.18  | | | | | | | | | | | | | | | |   (8346)   ~ (all_4_2 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | Case 1:
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8347)  all_56_9 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (8347) imply:
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8348)  all_52_13 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | SIMP: (8348) implies:
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8349)  all_52_13 = e3
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | REDUCE: (587), (8349) imply:
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8350)   ~ (all_52_15 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | SIMP: (8350) implies:
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8351)   ~ (all_52_15 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (41), (51), (53), (61), (156),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (273), (304), (305), (306), (321), (332), (351),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (387), (405), (431), (515), (541), (542), (543),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (547), (555), (564), (569), (572), (573), (582),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (680), (8307), (8323), (8332), (8333), (8334),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (8335), (8340), (8351), (function-axioms) are
% 197.10/32.18  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #615.
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | Case 2:
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8352)   ~ (all_56_9 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | REDUCE: (421), (8352) imply:
% 197.10/32.18  | | | | | | | | | | | | | | | | |   (8353)   ~ (all_52_13 = e3)
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (53), (61), (63), (159), (168), (172), (177),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (180), (182), (273), (274), (275), (276), (281),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (311), (312), (313), (315), (317), (319), (320),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (321), (323), (324), (325), (328), (330), (332),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (333), (351), (352), (361), (366), (372), (375),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (387), (393), (394), (405), (411), (421), (431),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (561), (563), (564), (565), (566), (567), (569),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (570), (571), (573), (574), (575), (576), (577),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (578), (580), (582), (587), (588), (589), (590),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (591), (596), (597), (598), (600), (602), (607),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (608), (612), (613), (7460), (7462), (7951),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (8323), (8332), (8333), (8334), (8335), (8346),
% 197.10/32.18  | | | | | | | | | | | | | | | | |            (8353), (function-axioms) are inconsistent by
% 197.10/32.18  | | | | | | | | | | | | | | | | |            sub-proof #116.
% 197.10/32.18  | | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | | End of split
% 197.10/32.18  | | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | | End of split
% 197.10/32.18  | | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | End of split
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | Case 2:
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | |   (8354)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.10/32.18  | | | | | | | | | | | | | |           all_52_14 = e0
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (42), (43),
% 197.10/32.18  | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (167),
% 197.10/32.18  | | | | | | | | | | | | | |            (168), (169), (173), (174), (175), (178), (179),
% 197.10/32.18  | | | | | | | | | | | | | |            (180), (182), (183), (185), (270), (272), (273),
% 197.10/32.18  | | | | | | | | | | | | | |            (275), (277), (280), (282), (283), (284), (306),
% 197.10/32.18  | | | | | | | | | | | | | |            (309), (313), (317), (321), (325), (326), (330),
% 197.10/32.18  | | | | | | | | | | | | | |            (331), (332), (333), (346), (351), (361), (366),
% 197.10/32.18  | | | | | | | | | | | | | |            (367), (372), (387), (388), (393), (394), (405),
% 197.10/32.18  | | | | | | | | | | | | | |            (415), (431), (538), (539), (541), (542), (543),
% 197.10/32.18  | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.10/32.18  | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.10/32.18  | | | | | | | | | | | | | |            (564), (567), (568), (569), (570), (571), (572),
% 197.10/32.18  | | | | | | | | | | | | | |            (575), (577), (578), (580), (582), (586), (588),
% 197.10/32.18  | | | | | | | | | | | | | |            (590), (591), (593), (594), (595), (600), (602),
% 197.10/32.18  | | | | | | | | | | | | | |            (604), (606), (607), (608), (609), (610), (611),
% 197.10/32.18  | | | | | | | | | | | | | |            (612), (613), (7443), (7445), (7449), (7451),
% 197.10/32.18  | | | | | | | | | | | | | |            (7453), (7457), (7458), (7460), (7462), (7465),
% 197.10/32.18  | | | | | | | | | | | | | |            (7953), (8314), (8319), (8323), (8324), (8325),
% 197.10/32.18  | | | | | | | | | | | | | |            (8354), (function-axioms) are inconsistent by
% 197.10/32.18  | | | | | | | | | | | | | |            sub-proof #123.
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | End of split
% 197.10/32.18  | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | Case 2:
% 197.10/32.18  | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | |   (8355)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.10/32.18  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.10/32.18  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.10/32.18  | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | BETA: splitting (8355) gives:
% 197.10/32.18  | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | Case 1:
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | |   (8356)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.10/32.18  | | | | | | | | | | | | | |           all_52_22 = e0
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (42), (43), (53), (63),
% 197.10/32.18  | | | | | | | | | | | | | |            (158), (162), (167), (168), (169), (174), (175),
% 197.10/32.18  | | | | | | | | | | | | | |            (178), (180), (182), (183), (185), (270), (273),
% 197.10/32.18  | | | | | | | | | | | | | |            (275), (276), (277), (280), (282), (283), (306),
% 197.10/32.18  | | | | | | | | | | | | | |            (309), (313), (317), (321), (325), (330), (331),
% 197.10/32.18  | | | | | | | | | | | | | |            (332), (333), (351), (361), (366), (367), (372),
% 197.10/32.18  | | | | | | | | | | | | | |            (375), (387), (388), (393), (405), (415), (421),
% 197.10/32.18  | | | | | | | | | | | | | |            (431), (512), (538), (539), (541), (542), (543),
% 197.10/32.18  | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.10/32.18  | | | | | | | | | | | | | |            (553), (555), (557), (559), (562), (563), (564),
% 197.10/32.18  | | | | | | | | | | | | | |            (566), (567), (572), (574), (576), (577), (578),
% 197.10/32.18  | | | | | | | | | | | | | |            (580), (582), (587), (588), (590), (593), (595),
% 197.10/32.18  | | | | | | | | | | | | | |            (596), (603), (605), (606), (608), (611), (612),
% 197.10/32.18  | | | | | | | | | | | | | |            (613), (676), (7443), (7445), (7449), (7450),
% 197.10/32.18  | | | | | | | | | | | | | |            (7458), (7462), (7465), (8314), (8317), (8319),
% 197.10/32.18  | | | | | | | | | | | | | |            (8356), (function-axioms) are inconsistent by
% 197.10/32.18  | | | | | | | | | | | | | |            sub-proof #127.
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.10/32.18  | | | | | | | | | | | | | Case 2:
% 197.10/32.18  | | | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | | | |   (8357)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.11/32.18  | | | | | | | | | | | | | |           all_52_30 = e0
% 197.11/32.18  | | | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 197.11/32.18  | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 197.11/32.18  | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 197.11/32.18  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 197.11/32.18  | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 197.11/32.18  | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 197.11/32.18  | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 197.11/32.18  | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 197.11/32.18  | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.11/32.18  | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 197.11/32.18  | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.11/32.18  | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.11/32.18  | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.11/32.18  | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 197.11/32.18  | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 197.11/32.18  | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.11/32.18  | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 197.11/32.18  | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 197.11/32.18  | | | | | | | | | | | | | |            (7462), (7465), (8314), (8323), (8325), (8357),
% 197.11/32.18  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.18  | | | | | | | | | | | | | |            #1008.
% 197.11/32.18  | | | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | | | End of split
% 197.11/32.18  | | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | | End of split
% 197.11/32.18  | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | End of split
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | Case 2:
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | |   (8358)  all_28_0 = e3
% 197.11/32.18  | | | | | | | | | | |   (8359)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | COMBINE_EQS: (754), (8358) imply:
% 197.11/32.18  | | | | | | | | | | |   (8360)  all_4_0 = e3
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 197.11/32.18  | | | | | | | | | | |            (43), (51), (53), (61), (63), (158), (161), (162),
% 197.11/32.18  | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.11/32.18  | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.11/32.18  | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.11/32.18  | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.11/32.18  | | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.11/32.18  | | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.11/32.18  | | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 197.11/32.18  | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.11/32.18  | | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.11/32.18  | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 197.11/32.18  | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.11/32.18  | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.11/32.18  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.11/32.18  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.11/32.18  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.11/32.18  | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 197.11/32.18  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 197.11/32.18  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.11/32.18  | | | | | | | | | | |            (608), (609), (610), (613), (7443), (7444),
% 197.11/32.18  | | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7455),
% 197.11/32.18  | | | | | | | | | | |            (7457), (7458), (7459), (7460), (7462), (7465),
% 197.11/32.18  | | | | | | | | | | |            (7953), (8314), (8359), (8360), (function-axioms)
% 197.11/32.18  | | | | | | | | | | |            are inconsistent by sub-proof #115.
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | End of split
% 197.11/32.18  | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | End of split
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | Case 2:
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | |   (8361)  all_22_1 = e2
% 197.11/32.18  | | | | | | | | |   (8362)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 197.11/32.18  | | | | | | | | |            (53), (61), (63), (94), (158), (161), (162), (166),
% 197.11/32.18  | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.11/32.18  | | | | | | | | |            (177), (178), (180), (182), (183), (184), (185),
% 197.11/32.18  | | | | | | | | |            (187), (270), (271), (273), (274), (275), (277),
% 197.11/32.18  | | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 197.11/32.18  | | | | | | | | |            (304), (306), (307), (308), (309), (311), (313),
% 197.11/32.18  | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 197.11/32.18  | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 197.11/32.18  | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 197.11/32.18  | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.11/32.18  | | | | | | | | |            (415), (431), (512), (522), (538), (539), (540),
% 197.11/32.18  | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.11/32.18  | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.11/32.18  | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 197.11/32.18  | | | | | | | | |            (568), (569), (570), (572), (573), (574), (575),
% 197.11/32.18  | | | | | | | | |            (576), (577), (578), (582), (584), (586), (588),
% 197.11/32.18  | | | | | | | | |            (589), (590), (591), (592), (593), (594), (595),
% 197.11/32.18  | | | | | | | | |            (596), (597), (598), (600), (602), (603), (604),
% 197.11/32.18  | | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 197.11/32.18  | | | | | | | | |            (613), (658), (676), (739), (7460), (7462), (7465),
% 197.11/32.18  | | | | | | | | |            (7953), (8310), (8312), (8361), (8362),
% 197.11/32.18  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.18  | | | | | | | | |            #582.
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | End of split
% 197.11/32.18  | | | | | | | | 
% 197.11/32.18  | | | | | | | End of split
% 197.11/32.18  | | | | | | | 
% 197.11/32.18  | | | | | | End of split
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | Case 2:
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | |   (8363)  all_12_1 = e1
% 197.11/32.18  | | | | | |   (8364)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | COMBINE_EQS: (683), (8363) imply:
% 197.11/32.18  | | | | | |   (8365)  all_6_1 = e1
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | SIMP: (8365) implies:
% 197.11/32.18  | | | | | |   (8366)  all_6_1 = e1
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | REDUCE: (43), (8366) imply:
% 197.11/32.18  | | | | | |   (8367)  op(all_6_2, e3) = e1
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | REDUCE: (42), (8366) imply:
% 197.11/32.18  | | | | | |   (8368)  op(e3, e1) = all_6_0
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | REF_CLOSE: (5), (6), (7), (8), (36), (41), (42), (43), (51), (61),
% 197.11/32.18  | | | | | |            (62), (63), (64), (74), (153), (157), (158), (162),
% 197.11/32.18  | | | | | |            (167), (168), (169), (172), (173), (174), (175), (178),
% 197.11/32.18  | | | | | |            (179), (180), (182), (183), (184), (185), (187), (270),
% 197.11/32.18  | | | | | |            (274), (276), (277), (280), (281), (282), (283), (284),
% 197.11/32.18  | | | | | |            (285), (303), (305), (306), (307), (308), (309), (312),
% 197.11/32.18  | | | | | |            (313), (315), (318), (319), (321), (322), (323), (324),
% 197.11/32.18  | | | | | |            (325), (329), (331), (332), (333), (335), (351), (352),
% 197.11/32.18  | | | | | |            (366), (367), (372), (375), (387), (388), (393), (394),
% 197.11/32.18  | | | | | |            (405), (411), (415), (421), (483), (538), (539), (540),
% 197.11/32.18  | | | | | |            (541), (542), (543), (544), (545), (546), (547), (548),
% 197.11/32.18  | | | | | |            (549), (551), (553), (555), (557), (559), (561), (562),
% 197.11/32.18  | | | | | |            (563), (564), (566), (567), (568), (569), (570), (571),
% 197.11/32.18  | | | | | |            (572), (573), (574), (575), (576), (577), (578), (580),
% 197.11/32.18  | | | | | |            (582), (586), (587), (588), (589), (590), (591), (592),
% 197.11/32.18  | | | | | |            (593), (594), (595), (596), (598), (602), (603), (604),
% 197.11/32.18  | | | | | |            (605), (606), (607), (608), (609), (610), (611), (613),
% 197.11/32.18  | | | | | |            (690), (761), (763), (771), (7443), (7445), (7449),
% 197.11/32.18  | | | | | |            (7451), (7453), (7457), (7458), (7459), (7460), (7462),
% 197.11/32.18  | | | | | |            (8364), (8367), (8368), (function-axioms) are
% 197.11/32.18  | | | | | |            inconsistent by sub-proof #109.
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | End of split
% 197.11/32.18  | | | | | 
% 197.11/32.18  | | | | Case 2:
% 197.11/32.18  | | | | | 
% 197.11/32.18  | | | | |   (8369)  all_10_0 = e3
% 197.11/32.18  | | | | | 
% 197.11/32.18  | | | | | COMBINE_EQS: (717), (8369) imply:
% 197.11/32.18  | | | | |   (8370)  all_36_0 = e3
% 197.11/32.18  | | | | | 
% 197.11/32.18  | | | | | REDUCE: (52), (8369) imply:
% 197.11/32.18  | | | | |   (8371)  op(e1, all_10_1) = e3
% 197.11/32.18  | | | | | 
% 197.11/32.18  | | | | | BETA: splitting (59) gives:
% 197.11/32.18  | | | | | 
% 197.11/32.18  | | | | | Case 1:
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | |   (8372)   ~ (all_12_1 = e1)
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | REDUCE: (683), (8372) imply:
% 197.11/32.18  | | | | | |   (8373)   ~ (all_6_1 = e1)
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | BETA: splitting (64) gives:
% 197.11/32.18  | | | | | | 
% 197.11/32.18  | | | | | | Case 1:
% 197.11/32.18  | | | | | | | 
% 197.11/32.18  | | | | | | |   (8374)   ~ (all_14_0 = e2)
% 197.11/32.18  | | | | | | | 
% 197.11/32.18  | | | | | | | BETA: splitting (74) gives:
% 197.11/32.18  | | | | | | | 
% 197.11/32.18  | | | | | | | Case 1:
% 197.11/32.18  | | | | | | | | 
% 197.11/32.18  | | | | | | | |   (8375)   ~ (all_18_0 = e3)
% 197.11/32.18  | | | | | | | | 
% 197.11/32.18  | | | | | | | | REDUCE: (761), (8375) imply:
% 197.11/32.18  | | | | | | | |   (8376)   ~ (all_14_0 = e3)
% 197.11/32.18  | | | | | | | | 
% 197.11/32.18  | | | | | | | | BETA: splitting (84) gives:
% 197.11/32.18  | | | | | | | | 
% 197.11/32.18  | | | | | | | | Case 1:
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | |   (8377)   ~ (all_22_1 = e2)
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | REDUCE: (658), (8377) imply:
% 197.11/32.18  | | | | | | | | |   (8378)   ~ (all_6_1 = e2)
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | BETA: splitting (89) gives:
% 197.11/32.18  | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | Case 1:
% 197.11/32.18  | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | |   (8379)   ~ (all_24_0 = e1)
% 197.11/32.18  | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | REDUCE: (711), (8379) imply:
% 197.11/32.18  | | | | | | | | | |   (8380)   ~ (all_14_0 = e1)
% 197.11/32.18  | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | BETA: splitting (99) gives:
% 197.11/32.18  | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | Case 1:
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | |   (8381)   ~ (all_28_0 = e3)
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | REDUCE: (754), (8381) imply:
% 197.11/32.18  | | | | | | | | | | |   (8382)   ~ (all_4_0 = e3)
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | BETA: splitting (119) gives:
% 197.11/32.18  | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | Case 1:
% 197.11/32.18  | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | |   (8383)   ~ (all_36_0 = e3)
% 197.11/32.18  | | | | | | | | | | | | 
% 197.11/32.18  | | | | | | | | | | | | REDUCE: (8370), (8383) imply:
% 197.11/32.19  | | | | | | | | | | | |   (8384)  $false
% 197.11/32.19  | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | CLOSE: (8384) is inconsistent.
% 197.11/32.19  | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | |   (8385)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 197.11/32.19  | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.11/32.19  | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | |   (8386)  all_58_15 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | COMBINE_EQS: (541), (8386) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8387)  all_14_2 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (573), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8388)   ~ (all_52_7 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (591), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8389)   ~ (all_52_15 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (603), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8390)   ~ (all_52_23 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (606), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8391)   ~ (all_52_25 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (608), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8392)   ~ (all_52_27 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (609), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8393)   ~ (all_52_29 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (613), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8394)  op(e0, e0) = all_52_30
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (63), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8395)  op(e0, e0) = all_14_1
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (61), (8387) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8396)  op(e0, e0) = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.11/32.19  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (8394), (8395)
% 197.11/32.19  | | | | | | | | | | | | |              gives:
% 197.11/32.19  | | | | | | | | | | | | |   (8397)  all_52_30 = all_14_1
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.11/32.19  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (8394), (8396)
% 197.11/32.19  | | | | | | | | | | | | |              gives:
% 197.11/32.19  | | | | | | | | | | | | |   (8398)  all_52_30 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | COMBINE_EQS: (8397), (8398) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8399)  all_14_1 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | SIMP: (8399) implies:
% 197.11/32.19  | | | | | | | | | | | | |   (8400)  all_14_1 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (62), (8400) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8401)  op(e0, e0) = all_14_0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.11/32.19  | | | | | | | | | | | | |              e0, e0, simplifying with (8396), (8401) gives:
% 197.11/32.19  | | | | | | | | | | | | |   (8402)  all_14_0 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (8376), (8402) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8403)   ~ (e3 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (8374), (8402) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8404)   ~ (e2 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (8380), (8402) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8405)   ~ (e1 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | |   (8406)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.11/32.19  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | BETA: splitting (8406) gives:
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | |   (8407)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 197.11/32.19  | | | | | | | | | | | | | | |            (53), (61), (156), (162), (175), (179), (183),
% 197.11/32.19  | | | | | | | | | | | | | | |            (184), (185), (271), (272), (273), (304), (305),
% 197.11/32.19  | | | | | | | | | | | | | | |            (306), (321), (326), (332), (343), (346), (351),
% 197.11/32.19  | | | | | | | | | | | | | | |            (387), (405), (431), (524), (542), (543), (547),
% 197.11/32.19  | | | | | | | | | | | | | | |            (555), (564), (569), (571), (572), (573), (582),
% 197.11/32.19  | | | | | | | | | | | | | | |            (590), (610), (611), (645), (8371), (8385),
% 197.11/32.19  | | | | | | | | | | | | | | |            (8386), (8388), (8390), (8396), (8407),
% 197.11/32.19  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.19  | | | | | | | | | | | | | | |            #108.
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | |   (8408)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | ALPHA: (8408) implies:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8409)  all_52_14 = e0
% 197.11/32.19  | | | | | | | | | | | | | | |   (8410)  all_52_12 = e1
% 197.11/32.19  | | | | | | | | | | | | | | |   (8411)  all_52_10 = e2
% 197.11/32.19  | | | | | | | | | | | | | | |   (8412)  all_52_8 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (182), (8412) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8413)  op(all_52_9, all_52_9) = e3
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (180), (8410) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8414)  op(all_52_13, all_52_13) = e1
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (179), (8409) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8415)  op(all_52_15, all_52_15) = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (611), (8411) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8416)  op(all_4_2, all_4_2) = e2
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8417)  all_56_13 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (8417) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8418)  all_52_15 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (158), (273), (431), (555), (571),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (8373), (8378), (8415), (8418), (function-axioms)
% 197.11/32.19  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1341.
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8419)   ~ (all_56_13 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8420)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | REDUCE: (346), (8419) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8421)   ~ (all_52_15 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8422)  all_58_12 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8422) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8423)  all_52_7 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | SIMP: (8423) implies:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8424)  all_52_7 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REDUCE: (563), (8424) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8425)   ~ (all_52_3 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REDUCE: (567), (8424) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8426)   ~ (all_52_5 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REDUCE: (571), (8424) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8427)   ~ (all_52_15 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REDUCE: (572), (8424) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8428)   ~ (all_52_23 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | SIMP: (8428) implies:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8429)   ~ (all_52_23 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REDUCE: (555), (8424) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8430)   ~ (all_6_2 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | SIMP: (8430) implies:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8431)   ~ (all_6_2 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (41), (51), (53), (168), (169), (178),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (274), (282), (284), (310), (313), (314), (317),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (318), (321), (322), (325), (326), (327), (333),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (352), (366), (372), (387), (388), (393), (394),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (405), (542), (543), (544), (545), (546), (547),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (548), (549), (557), (559), (561), (562), (564),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (568), (574), (575), (577), (578), (580), (582),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (588), (593), (595), (602), (607), (612), (7443),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (7445), (7449), (7451), (8382), (8389), (8390),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (8391), (8396), (8413), (8414), (8421), (8422),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (8425), (8426), (8429), (8431), (function-axioms)
% 197.11/32.19  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #206.
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8432)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (51), (53), (156), (162), (183),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (273), (276), (304), (305), (346), (351), (421),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (431), (542), (543), (568), (571), (572), (582),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (587), (588), (8371), (8386), (8388), (8389),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (8396), (8414), (8415), (8416), (8420), (8421),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (8432), (function-axioms) are inconsistent by
% 197.11/32.19  | | | | | | | | | | | | | | | | |            sub-proof #545.
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | End of split
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | End of split
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | End of split
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | |   (8433)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.11/32.19  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.11/32.19  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | BETA: splitting (8433) gives:
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | |   (8434)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (36), (41), (42), (43), (53), (61),
% 197.11/32.19  | | | | | | | | | | | | | | |            (63), (158), (161), (162), (167), (168), (169),
% 197.11/32.19  | | | | | | | | | | | | | | |            (174), (175), (178), (179), (183), (184), (185),
% 197.11/32.19  | | | | | | | | | | | | | | |            (270), (271), (272), (273), (277), (282), (283),
% 197.11/32.19  | | | | | | | | | | | | | | |            (306), (309), (316), (317), (321), (325), (330),
% 197.11/32.19  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 197.11/32.19  | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.11/32.19  | | | | | | | | | | | | | | |            (415), (431), (538), (541), (542), (543), (545),
% 197.11/32.19  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.11/32.19  | | | | | | | | | | | | | | |            (557), (559), (562), (563), (564), (566), (567),
% 197.11/32.19  | | | | | | | | | | | | | | |            (569), (572), (573), (574), (576), (582), (588),
% 197.11/32.19  | | | | | | | | | | | | | | |            (590), (591), (593), (595), (596), (603), (604),
% 197.11/32.19  | | | | | | | | | | | | | | |            (606), (608), (610), (611), (612), (613), (7443),
% 197.11/32.19  | | | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (7462), (8371),
% 197.11/32.19  | | | | | | | | | | | | | | |            (8373), (8378), (8382), (8434), (function-axioms)
% 197.11/32.19  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #105.
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | |   (8435)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 197.11/32.19  | | | | | | | | | | | | | | |            (43), (51), (61), (162), (166), (167), (172),
% 197.11/32.19  | | | | | | | | | | | | | | |            (173), (174), (175), (179), (183), (272), (273),
% 197.11/32.19  | | | | | | | | | | | | | | |            (274), (278), (281), (282), (304), (305), (306),
% 197.11/32.19  | | | | | | | | | | | | | | |            (307), (308), (309), (313), (318), (321), (326),
% 197.11/32.19  | | | | | | | | | | | | | | |            (330), (332), (333), (346), (351), (352), (366),
% 197.11/32.19  | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (411),
% 197.11/32.19  | | | | | | | | | | | | | | |            (427), (431), (542), (543), (544), (545), (546),
% 197.11/32.19  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (561),
% 197.11/32.19  | | | | | | | | | | | | | | |            (563), (564), (567), (569), (570), (571), (572),
% 197.11/32.19  | | | | | | | | | | | | | | |            (576), (582), (587), (588), (593), (595), (596),
% 197.11/32.19  | | | | | | | | | | | | | | |            (600), (602), (604), (605), (608), (610), (7460),
% 197.11/32.19  | | | | | | | | | | | | | | |            (7462), (8378), (8386), (8388), (8389), (8390),
% 197.11/32.19  | | | | | | | | | | | | | | |            (8391), (8392), (8393), (8435), (function-axioms)
% 197.11/32.19  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | End of split
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | End of split
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | |   (8436)   ~ (all_58_15 = e0)
% 197.11/32.19  | | | | | | | | | | | | |   (8437)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.11/32.19  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.11/32.19  | | | | | | | | | | | | |             e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | ALPHA: (8437) implies:
% 197.11/32.19  | | | | | | | | | | | | |   (8438)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.11/32.19  | | | | | | | | | | | | |   (8439)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | REDUCE: (541), (8436) imply:
% 197.11/32.19  | | | | | | | | | | | | |   (8440)   ~ (all_14_2 = e0)
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.11/32.19  | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | |   (8441)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.11/32.19  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | BETA: splitting (8441) gives:
% 197.11/32.19  | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | |   (8442)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.11/32.19  | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | ALPHA: (8442) implies:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8443)  all_52_6 = e0
% 197.11/32.19  | | | | | | | | | | | | | | |   (8444)  all_52_4 = e1
% 197.11/32.19  | | | | | | | | | | | | | | |   (8445)  all_52_2 = e2
% 197.11/32.19  | | | | | | | | | | | | | | |   (8446)  all_52_0 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (185), (8445) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8447)  op(all_52_3, all_52_3) = e2
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (184), (8444) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8448)  op(all_52_5, all_52_5) = e1
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (183), (8443) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8449)  op(all_52_7, all_52_7) = e0
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | REDUCE: (610), (8446) imply:
% 197.11/32.19  | | | | | | | | | | | | | | |   (8450)  op(all_6_2, all_6_2) = e3
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8451)  all_56_15 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (43), (51), (53), (61),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (63), (167), (168), (169), (172), (175), (182),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (273), (277), (279), (304), (305), (307), (310),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (313), (315), (317), (319), (321), (328), (330),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (332), (333), (351), (366), (367), (372), (375),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (387), (393), (405), (417), (431), (538), (541),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (551), (553), (555), (559), (562), (564), (565),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (569), (572), (573), (576), (577), (578), (580),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (586), (596), (597), (608), (609), (611), (612),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (613), (7445), (7449), (7455), (7457), (7459),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (7460), (8382), (8440), (8447), (8448), (8449),
% 197.11/32.19  | | | | | | | | | | | | | | | |            (8450), (8451), (function-axioms) are inconsistent
% 197.11/32.19  | | | | | | | | | | | | | | | |            by sub-proof #103.
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8452)   ~ (all_56_15 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8453)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | REDUCE: (538), (8452) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | |   (8454)   ~ (all_14_2 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8455)  all_56_13 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (53), (61), (62), (63), (158), (159), (161),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (168), (172), (173), (177), (178), (180), (182),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (273), (274), (276), (277), (279), (280), (281),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (283), (284), (285), (304), (306), (307), (308),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (309), (311), (312), (313), (315), (317), (319),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (320), (321), (323), (324), (328), (330), (331),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (332), (333), (346), (351), (352), (366), (367),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (372), (375), (387), (393), (394), (405), (411),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (415), (417), (421), (431), (538), (539), (540),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (561), (563), (564), (565), (566), (567), (568),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (569), (570), (571), (573), (574), (575), (576),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (577), (578), (580), (582), (586), (587), (588),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (589), (590), (591), (595), (596), (597), (598),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (600), (602), (606), (607), (608), (609), (611),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (612), (613), (7460), (7462), (8371), (8374),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (8438), (8439), (8440), (8447), (8448), (8449),
% 197.11/32.19  | | | | | | | | | | | | | | | | |            (8450), (8453), (8455), (function-axioms) are
% 197.11/32.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #507.
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8456)   ~ (all_56_13 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | REDUCE: (346), (8456) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | |   (8457)   ~ (all_52_15 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | |   (8458)  all_58_12 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8458) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | |   (8459)  all_52_7 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 197.11/32.19  | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (555), (564), (569),
% 197.11/32.19  | | | | | | | | | | | | | | | | | |            (573), (8447), (8448), (8449), (8450), (8459),
% 197.11/32.19  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.19  | | | | | | | | | | | | | | | | | |            #1361.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | |   (8460)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | BETA: splitting (8460) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | |   (8461)  all_58_13 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8457), (8461) are inconsistent by
% 197.11/32.19  | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | |   (8462)  all_58_14 = e3 | all_58_15 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (8462) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8463)  all_58_14 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (8463) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8464)  all_52_23 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | SIMP: (8464) implies:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8465)  all_52_23 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (8465) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8466)   ~ (all_52_7 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | REDUCE: (603), (8465) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8467)   ~ (all_14_2 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (8465) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8468)  op(e3, e3) = all_52_22
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (8468)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |              gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | |   (8469)  all_52_22 = all_6_2
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | |   (8470)  all_56_12 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (8466), (8470) are inconsistent by
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | |   (8471)   ~ (all_56_12 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | |   (8472)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | |   (8473)  all_58_0 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8473) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | |   (8474)  all_6_2 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (8474) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | |   (8475)   ~ (all_52_3 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (8474) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | |   (8476)   ~ (all_52_5 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (8474) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | |   (8477)   ~ (all_52_9 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (8474) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | |   (8478)   ~ (all_52_17 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | |   (8479)  all_58_1 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (8479) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | |   (8480)  all_52_9 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8477), (8480) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | |   (8481)  $false
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8481) is inconsistent.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | |   (8482)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | |   (8483)  all_56_4 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (8475), (8483) are inconsistent by
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | |   (8484)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (8485)  all_56_8 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (8476), (8485) are inconsistent by
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (8486)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8487)  all_56_5 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (8487) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8488)  all_4_2 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8488) implies:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8489)  all_4_2 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8489) imply:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8490)  all_58_3 = e3
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (61), (169), (304), (305), (318),
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (320), (324), (351), (366), (367), (387), (411),
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (431), (538), (543), (549), (562), (563), (567),
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (573), (591), (7443), (7445), (8440),
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8447), (8449), (8453), (8454), (8472), (8475),
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8484), (8486), (8489), (8490), (function-axioms)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #102.
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8491)   ~ (all_56_5 = e3)
% 197.11/32.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (8491) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8492)   ~ (all_4_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8482) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8493)  all_58_3 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8493) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8494)  all_4_2 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8492), (8494) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8495)  $false
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8495) is inconsistent.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8496)  all_58_7 = e3 | all_58_13 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8496) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8497)  all_58_7 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (8497) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8498)  all_52_13 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (8498) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8499)   ~ (all_52_29 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8499) implies:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8500)   ~ (all_52_29 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (8498) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8501)   ~ (all_10_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8501) implies:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8502)   ~ (all_10_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (8498) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8503)  op(e3, e3) = all_52_12
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (41), (42), (43), (51), (53),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (62), (63), (158), (163), (173), (304),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (306), (309), (311), (320), (321), (328), (331),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (333), (351), (372), (375), (387), (393),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (405), (538), (541), (544), (545), (546), (547),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (548), (549), (561), (564), (569), (573), (574),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (586), (593), (596), (604), (606), (608), (609),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (612), (613), (7460), (8380), (8439), (8440),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8447), (8448), (8449), (8450), (8453), (8454),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8477), (8478), (8497), (8500), (8502), (8503),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #743.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8504)  all_58_13 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8457), (8504) are inconsistent by
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | |   (8505)   ~ (all_58_0 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (8505) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | |   (8506)   ~ (all_6_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (564), (569), (8447), (8448),
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | |            (8450), (8466), (8506), (function-axioms) are
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1363.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | |   (8507)  all_58_15 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (8507) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | |   (8508)  all_14_2 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | REDUCE: (8454), (8508) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | |   (8509)  $false
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | CLOSE: (8509) is inconsistent.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | |   (8510)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.11/32.20  | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 197.11/32.20  | | | | | | | | | | | | | | |            (61), (63), (158), (162), (167), (168), (169),
% 197.11/32.20  | | | | | | | | | | | | | | |            (173), (174), (175), (178), (179), (180), (182),
% 197.11/32.20  | | | | | | | | | | | | | | |            (183), (185), (270), (272), (273), (275), (277),
% 197.11/32.20  | | | | | | | | | | | | | | |            (280), (282), (283), (284), (306), (309), (313),
% 197.11/32.20  | | | | | | | | | | | | | | |            (317), (321), (325), (330), (331), (332), (333),
% 197.11/32.20  | | | | | | | | | | | | | | |            (346), (351), (361), (366), (367), (372), (387),
% 197.11/32.20  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (415), (431), (538),
% 197.11/32.20  | | | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 197.11/32.20  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.11/32.20  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (568),
% 197.11/32.20  | | | | | | | | | | | | | | |            (569), (570), (571), (572), (573), (575), (577),
% 197.11/32.20  | | | | | | | | | | | | | | |            (578), (580), (582), (586), (588), (590), (591),
% 197.11/32.20  | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (606),
% 197.11/32.20  | | | | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 197.11/32.20  | | | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7457),
% 197.11/32.20  | | | | | | | | | | | | | | |            (7458), (7460), (7462), (8373), (8378), (8382),
% 197.11/32.20  | | | | | | | | | | | | | | |            (8438), (8439), (8510), (function-axioms) are
% 197.11/32.20  | | | | | | | | | | | | | | |            inconsistent by sub-proof #188.
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | |   (8511)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.11/32.20  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.11/32.20  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | BETA: splitting (8511) gives:
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | |   (8512)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.11/32.20  | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (36), (41), (42), (43), (53), (61),
% 197.11/32.20  | | | | | | | | | | | | | | |            (63), (158), (161), (162), (167), (168), (169),
% 197.11/32.20  | | | | | | | | | | | | | | |            (174), (175), (178), (179), (183), (184), (185),
% 197.11/32.20  | | | | | | | | | | | | | | |            (270), (271), (272), (273), (277), (282), (283),
% 197.11/32.20  | | | | | | | | | | | | | | |            (306), (309), (316), (317), (321), (325), (330),
% 197.11/32.20  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 197.11/32.20  | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.11/32.20  | | | | | | | | | | | | | | |            (415), (431), (538), (541), (542), (543), (545),
% 197.11/32.20  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.11/32.20  | | | | | | | | | | | | | | |            (557), (559), (562), (563), (564), (566), (567),
% 197.11/32.20  | | | | | | | | | | | | | | |            (569), (572), (573), (574), (576), (582), (588),
% 197.11/32.20  | | | | | | | | | | | | | | |            (590), (591), (593), (595), (596), (603), (604),
% 197.11/32.20  | | | | | | | | | | | | | | |            (606), (608), (610), (611), (612), (613), (7443),
% 197.11/32.20  | | | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (7462), (8371),
% 197.11/32.20  | | | | | | | | | | | | | | |            (8373), (8378), (8382), (8512), (function-axioms)
% 197.11/32.20  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #105.
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | |   (8513)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.11/32.20  | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 197.11/32.20  | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 197.11/32.20  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 197.11/32.20  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 197.11/32.20  | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 197.11/32.20  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 197.11/32.20  | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 197.11/32.20  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 197.11/32.20  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.11/32.20  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 197.11/32.20  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.11/32.20  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.11/32.20  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.11/32.20  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 197.11/32.20  | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 197.11/32.20  | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.11/32.20  | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 197.11/32.20  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 197.11/32.20  | | | | | | | | | | | | | | |            (7462), (8373), (8378), (8438), (8440), (8513),
% 197.11/32.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.20  | | | | | | | | | | | | | | |            #1008.
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | |   (8514)  all_28_0 = e3
% 197.11/32.20  | | | | | | | | | | |   (8515)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 197.11/32.20  | | | | | | | | | | |            (51), (53), (61), (62), (63), (158), (161), (162),
% 197.11/32.20  | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.11/32.20  | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.11/32.20  | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.11/32.20  | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.11/32.20  | | | | | | | | | | |            (284), (285), (303), (304), (305), (306), (307),
% 197.11/32.20  | | | | | | | | | | |            (308), (309), (311), (313), (315), (316), (318),
% 197.11/32.20  | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 197.11/32.20  | | | | | | | | | | |            (327), (328), (329), (330), (332), (333), (343),
% 197.11/32.20  | | | | | | | | | | |            (346), (351), (352), (366), (367), (372), (375),
% 197.11/32.20  | | | | | | | | | | |            (376), (387), (388), (393), (394), (405), (411),
% 197.11/32.20  | | | | | | | | | | |            (415), (427), (431), (538), (539), (540), (541),
% 197.11/32.20  | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.11/32.20  | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.11/32.20  | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 197.11/32.20  | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 197.11/32.20  | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 197.11/32.20  | | | | | | | | | | |            (588), (589), (590), (591), (592), (593), (594),
% 197.11/32.20  | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 197.11/32.20  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.11/32.20  | | | | | | | | | | |            (613), (754), (7443), (7444), (7445), (7449),
% 197.11/32.20  | | | | | | | | | | |            (7450), (7451), (7453), (7455), (7457), (7458),
% 197.11/32.20  | | | | | | | | | | |            (7459), (7460), (7462), (8373), (8374), (8376),
% 197.11/32.20  | | | | | | | | | | |            (8378), (8380), (8514), (8515), (function-axioms)
% 197.11/32.20  | | | | | | | | | | |            are inconsistent by sub-proof #144.
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | End of split
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | |   (8516)  all_24_0 = e1
% 197.11/32.20  | | | | | | | | | |   (8517)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | COMBINE_EQS: (711), (8516) imply:
% 197.11/32.20  | | | | | | | | | |   (8518)  all_14_0 = e1
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | COMBINE_EQS: (765), (8518) imply:
% 197.11/32.20  | | | | | | | | | |   (8519)  all_34_0 = e1
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | REDUCE: (8376), (8518) imply:
% 197.11/32.20  | | | | | | | | | |   (8520)   ~ (e3 = e1)
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | REDUCE: (8374), (8518) imply:
% 197.11/32.20  | | | | | | | | | |   (8521)   ~ (e2 = e1)
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | REDUCE: (62), (8518) imply:
% 197.11/32.20  | | | | | | | | | |   (8522)  op(e0, all_14_1) = e1
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | BETA: splitting (99) gives:
% 197.11/32.20  | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | |   (8523)   ~ (all_28_0 = e3)
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | REDUCE: (754), (8523) imply:
% 197.11/32.20  | | | | | | | | | | |   (8524)   ~ (all_4_0 = e3)
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | BETA: splitting (114) gives:
% 197.11/32.20  | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | |   (8525)   ~ (all_34_0 = e1)
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | REDUCE: (8519), (8525) imply:
% 197.11/32.20  | | | | | | | | | | | |   (8526)  $false
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | CLOSE: (8526) is inconsistent.
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | |   (8527)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.11/32.20  | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | |   (8528)  all_58_15 = e0
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (8522), (8528),
% 197.11/32.20  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.20  | | | | | | | | | | | | |            #877.
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | |   (8529)   ~ (all_58_15 = e0)
% 197.11/32.20  | | | | | | | | | | | | |   (8530)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.11/32.20  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.11/32.20  | | | | | | | | | | | | |             e0)
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | ALPHA: (8530) implies:
% 197.11/32.20  | | | | | | | | | | | | |   (8531)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.11/32.20  | | | | | | | | | | | | |   (8532)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | REDUCE: (541), (8529) imply:
% 197.11/32.20  | | | | | | | | | | | | |   (8533)   ~ (all_14_2 = e0)
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.11/32.20  | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | |   (8534)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.11/32.20  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.11/32.20  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | BETA: splitting (8534) gives:
% 197.11/32.20  | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | |   (8535)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.11/32.20  | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | ALPHA: (8535) implies:
% 197.11/32.20  | | | | | | | | | | | | | | |   (8536)  all_52_6 = e0
% 197.11/32.20  | | | | | | | | | | | | | | |   (8537)  all_52_4 = e1
% 197.11/32.20  | | | | | | | | | | | | | | |   (8538)  all_52_2 = e2
% 197.11/32.20  | | | | | | | | | | | | | | |   (8539)  all_52_0 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REDUCE: (185), (8538) imply:
% 197.11/32.20  | | | | | | | | | | | | | | |   (8540)  op(all_52_3, all_52_3) = e2
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REDUCE: (184), (8537) imply:
% 197.11/32.20  | | | | | | | | | | | | | | |   (8541)  op(all_52_5, all_52_5) = e1
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REDUCE: (183), (8536) imply:
% 197.11/32.20  | | | | | | | | | | | | | | |   (8542)  op(all_52_7, all_52_7) = e0
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | REDUCE: (610), (8539) imply:
% 197.11/32.20  | | | | | | | | | | | | | | |   (8543)  op(all_6_2, all_6_2) = e3
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | |   (8544)  all_56_15 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8544) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | |   (8545)  all_14_2 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | SIMP: (8545) implies:
% 197.11/32.20  | | | | | | | | | | | | | | | |   (8546)  all_14_2 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (51), (61), (63), (156),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (167), (174), (175), (180), (282), (306), (307),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (311), (313), (319), (321), (332), (351), (366),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (405), (491), (544),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (553), (562), (564),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (569), (573), (580), (597), (600), (603), (604),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (605), (606), (609), (613), (685), (8522), (8527),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (8540), (8541), (8542), (8543), (8546),
% 197.11/32.20  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.20  | | | | | | | | | | | | | | | |            #713.
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | |   (8547)   ~ (all_56_15 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | |   (8548)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | REDUCE: (538), (8547) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | |   (8549)   ~ (all_14_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8550)  all_56_13 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (8550) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8551)  all_52_15 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | SIMP: (8551) implies:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8552)  all_52_15 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8553)  all_58_13 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (571), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8554)   ~ (all_52_7 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (576), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8555)   ~ (all_52_9 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (587), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8556)   ~ (all_52_13 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (590), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8557)   ~ (all_52_23 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | SIMP: (8557) implies:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8558)   ~ (all_52_23 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (591), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8559)   ~ (all_14_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (582), (8552) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8560)   ~ (all_4_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | SIMP: (8560) implies:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8561)   ~ (all_4_2 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (53), (61), (63), (157), (158), (159), (161),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (163), (168), (172), (173), (175), (177), (178),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (182), (273), (274), (275), (276), (277), (280),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (283), (284), (304), (307), (308), (309), (310),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (311), (312), (313), (315), (317), (319), (321),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (323), (324), (328), (329), (330), (331), (332),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (333), (351), (352), (361), (366), (367), (372),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (375), (387), (393), (394), (405), (415), (421),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (431), (508), (538), (539), (541), (542), (544),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (553), (557),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (559), (561), (564), (565), (566), (567), (568),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (569), (570), (573), (574), (575), (577), (578),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (580), (584), (586), (588), (589), (591), (595),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (602), (606), (608),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (609), (611), (612), (613), (649), (7460), (7462),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (8371), (8517), (8522), (8531), (8532), (8533),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (8540), (8541), (8542), (8543), (8548), (8549),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (8553), (8554), (8555), (8556), (8558), (8561),
% 197.11/32.20  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.20  | | | | | | | | | | | | | | | | |            #516.
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8562)   ~ (all_56_13 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | REDUCE: (346), (8562) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | |   (8563)   ~ (all_52_15 = e3)
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | |   (8564)  all_58_12 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8564) imply:
% 197.11/32.20  | | | | | | | | | | | | | | | | | |   (8565)  all_52_7 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 197.11/32.20  | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (555), (564), (569),
% 197.11/32.20  | | | | | | | | | | | | | | | | | |            (573), (8540), (8541), (8542), (8543), (8565),
% 197.11/32.20  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.11/32.20  | | | | | | | | | | | | | | | | | |            #1361.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | |   (8566)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | BETA: splitting (8566) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | |   (8567)  all_58_13 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8563), (8567) are inconsistent by
% 197.11/32.20  | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | |   (8568)  all_58_14 = e3 | all_58_15 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | BETA: splitting (8568) gives:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | |   (8569)  all_58_14 = e3
% 197.11/32.20  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (8569) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |   (8570)  all_52_23 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | SIMP: (8570) implies:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |   (8571)  all_52_23 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (8571) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |   (8572)   ~ (all_52_7 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (603), (8571) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |   (8573)   ~ (all_14_2 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (8571) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |   (8574)  op(e3, e3) = all_52_22
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (8574)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |              gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | |   (8575)  all_52_22 = all_6_2
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | |   (8576)  all_56_12 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (8572), (8576) are inconsistent by
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | |   (8577)   ~ (all_56_12 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | |   (8578)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8579)  all_56_0 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (8579) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8580)  all_6_2 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8581)  all_58_0 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8582)   ~ (all_52_3 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8583)   ~ (all_52_5 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8584)   ~ (all_52_9 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8585)   ~ (all_52_17 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8586)   ~ (all_52_25 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8587)  op(e3, e3) = all_6_1
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (8580) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8588)  op(e3, e3) = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8587), (8588) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8589)  all_6_1 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (8589) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8590)  op(e3, e3) = all_6_0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8588), (8590) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8591)  all_6_0 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | |   (8592)  all_58_9 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (8586), (8592) are inconsistent by
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1300.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | |   (8593)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | |   (8594)  all_58_2 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (8582), (8594) are inconsistent by
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1369.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | |   (8595)   ~ (all_58_2 = e3)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | |   (8596)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (8597)  all_58_1 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (8597) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (8598)  all_52_9 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8584), (8598) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (8599)  $false
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8599) is inconsistent.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (8600)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8601)  all_56_8 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (8583), (8601) are inconsistent by
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8602)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8603)  all_56_4 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (411), (8582), (8603) are inconsistent by
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1340.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8604)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8605)  all_58_12 = e2
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (351), (543), (582), (8531),
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8542), (8569), (8605), (function-axioms) are
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #702.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8606)   ~ (all_58_12 = e2)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (8606) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8607)   ~ (all_52_7 = e2)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8608)  all_58_12 = e1
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8531) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8609)  all_58_12 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8608), (8609) are inconsistent by sub-proof
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1173.
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8610)  all_58_13 = e0 | all_58_14 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8610) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8611)  all_58_13 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (8611) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8612)  all_52_15 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8612) implies:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8613)  all_52_15 = e0
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (8613) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8614)   ~ (all_14_2 = e0)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (8613) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8615)   ~ (all_4_2 = e0)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8615) implies:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8616)   ~ (all_4_2 = e0)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8563), (8613) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8617)   ~ (e3 = e0)
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8596) gives:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8618)  all_58_3 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8618) imply:
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8619)  all_4_2 = e3
% 197.11/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (61), (169), (304), (305), (318),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (320), (324), (351), (366), (367), (387), (411),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (431), (538), (543), (549), (562), (563), (567),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (573), (591), (7443), (7445), (8533),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8540), (8542), (8548), (8549), (8578), (8582),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8602), (8604), (8618), (8619), (function-axioms)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #102.
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8620)   ~ (all_58_3 = e3)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (8620) imply:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8621)   ~ (all_4_2 = e3)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (51), (53), (63), (163),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (178), (305), (311), (316), (320), (324), (328),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (331), (351), (366), (372), (375), (387), (393),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (508), (538), (541), (543), (544), (545), (546),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (564), (569), (573), (575),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (576), (582), (586), (589), (592), (606), (608),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (609), (612), (613), (649), (8517), (8531),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8532), (8540), (8541), (8542), (8548), (8549),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8563), (8569), (8581), (8585), (8593), (8600),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8621), (function-axioms) are inconsistent by
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #699.
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8622)  all_58_14 = e0
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8569), (8622) are inconsistent by sub-proof
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1151.
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8623)   ~ (all_58_12 = e1)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (8623) imply:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8624)   ~ (all_52_7 = e1)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (273), (306), (321),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (351), (387), (405), (431), (547), (555),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (564), (569), (573), (8540), (8541), (8542),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8543), (8607), (8624), (function-axioms) are
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8625)   ~ (all_56_0 = e3)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (8625) imply:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | |   (8626)   ~ (all_6_2 = e3)
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | |            (405), (547), (564), (569), (8540), (8541),
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | |            (8543), (8572), (8626), (function-axioms) are
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1363.
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | |   (8627)  all_58_15 = e3
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (8627) imply:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | |   (8628)  all_14_2 = e3
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (8549), (8628) imply:
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | |   (8629)  $false
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | CLOSE: (8629) is inconsistent.
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | |   (8630)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.16/32.21  | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 197.16/32.21  | | | | | | | | | | | | | | |            (61), (63), (158), (162), (167), (168), (169),
% 197.16/32.21  | | | | | | | | | | | | | | |            (173), (174), (175), (178), (179), (180), (182),
% 197.16/32.21  | | | | | | | | | | | | | | |            (183), (185), (270), (272), (273), (275), (277),
% 197.16/32.21  | | | | | | | | | | | | | | |            (280), (282), (283), (284), (306), (309), (313),
% 197.16/32.21  | | | | | | | | | | | | | | |            (317), (321), (325), (330), (331), (332), (333),
% 197.16/32.21  | | | | | | | | | | | | | | |            (346), (351), (361), (366), (367), (372), (387),
% 197.16/32.21  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (415), (431), (538),
% 197.16/32.21  | | | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 197.16/32.21  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.16/32.21  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (568),
% 197.16/32.21  | | | | | | | | | | | | | | |            (569), (570), (571), (572), (573), (575), (577),
% 197.16/32.21  | | | | | | | | | | | | | | |            (578), (580), (582), (586), (588), (590), (591),
% 197.16/32.21  | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (606),
% 197.16/32.21  | | | | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 197.16/32.21  | | | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7457),
% 197.16/32.21  | | | | | | | | | | | | | | |            (7458), (7460), (7462), (8373), (8378), (8524),
% 197.16/32.21  | | | | | | | | | | | | | | |            (8531), (8532), (8630), (function-axioms) are
% 197.16/32.21  | | | | | | | | | | | | | | |            inconsistent by sub-proof #188.
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | |   (8631)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.16/32.21  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.16/32.21  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.16/32.21  | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | BETA: splitting (8631) gives:
% 197.16/32.21  | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | Case 1:
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | |   (8632)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.16/32.21  | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (36), (41), (42), (43), (53), (61),
% 197.16/32.21  | | | | | | | | | | | | | | |            (63), (158), (161), (162), (167), (168), (169),
% 197.16/32.21  | | | | | | | | | | | | | | |            (174), (175), (178), (179), (183), (184), (185),
% 197.16/32.21  | | | | | | | | | | | | | | |            (270), (271), (272), (273), (277), (282), (283),
% 197.16/32.21  | | | | | | | | | | | | | | |            (306), (309), (316), (317), (321), (325), (330),
% 197.16/32.21  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 197.16/32.21  | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.16/32.21  | | | | | | | | | | | | | | |            (415), (431), (538), (541), (542), (543), (545),
% 197.16/32.21  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.16/32.21  | | | | | | | | | | | | | | |            (557), (559), (562), (563), (564), (566), (567),
% 197.16/32.21  | | | | | | | | | | | | | | |            (569), (572), (573), (574), (576), (582), (588),
% 197.16/32.21  | | | | | | | | | | | | | | |            (590), (591), (593), (595), (596), (603), (604),
% 197.16/32.21  | | | | | | | | | | | | | | |            (606), (608), (610), (611), (612), (613), (7443),
% 197.16/32.21  | | | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (7462), (8371),
% 197.16/32.21  | | | | | | | | | | | | | | |            (8373), (8378), (8524), (8632), (function-axioms)
% 197.16/32.21  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #105.
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | |   (8633)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.16/32.21  | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 197.16/32.21  | | | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 197.16/32.21  | | | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 197.16/32.21  | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 197.16/32.21  | | | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 197.16/32.21  | | | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 197.16/32.21  | | | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 197.16/32.21  | | | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 197.16/32.21  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.16/32.21  | | | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 197.16/32.21  | | | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.16/32.21  | | | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.16/32.21  | | | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.16/32.21  | | | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 197.16/32.21  | | | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 197.16/32.21  | | | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.16/32.21  | | | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 197.16/32.21  | | | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 197.16/32.21  | | | | | | | | | | | | | | |            (7462), (8373), (8378), (8531), (8533), (8633),
% 197.16/32.21  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.16/32.21  | | | | | | | | | | | | | | |            #1008.
% 197.16/32.21  | | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | |   (8634)  all_28_0 = e3
% 197.16/32.21  | | | | | | | | | | |   (8635)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.16/32.21  | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 197.16/32.21  | | | | | | | | | | |            (51), (53), (61), (63), (158), (161), (162),
% 197.16/32.21  | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.16/32.21  | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.16/32.21  | | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.16/32.21  | | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.16/32.21  | | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.16/32.21  | | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.16/32.21  | | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 197.16/32.21  | | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.16/32.21  | | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.16/32.21  | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 197.16/32.21  | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.16/32.21  | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.16/32.21  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.16/32.21  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.16/32.21  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.16/32.21  | | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 197.16/32.21  | | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 197.16/32.21  | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.16/32.21  | | | | | | | | | | |            (608), (609), (610), (613), (754), (7443), (7444),
% 197.16/32.21  | | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7455),
% 197.16/32.21  | | | | | | | | | | |            (7457), (7458), (7459), (7460), (7462), (8373),
% 197.16/32.21  | | | | | | | | | | |            (8378), (8522), (8634), (8635), (function-axioms)
% 197.16/32.21  | | | | | | | | | | |            are inconsistent by sub-proof #142.
% 197.16/32.21  | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | End of split
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | Case 2:
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | |   (8636)  all_22_1 = e2
% 197.16/32.21  | | | | | | | | |   (8637)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | COMBINE_EQS: (658), (8636) imply:
% 197.16/32.21  | | | | | | | | |   (8638)  all_6_1 = e2
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (43), (8638) imply:
% 197.16/32.21  | | | | | | | | |   (8639)  op(all_6_2, e3) = e2
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (42), (8638) imply:
% 197.16/32.21  | | | | | | | | |   (8640)  op(e3, e2) = all_6_0
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 197.16/32.21  | | | | | | | | |              all_6_0, e2, e3, simplifying with (169), (8640)
% 197.16/32.21  | | | | | | | | |              gives:
% 197.16/32.21  | | | | | | | | |   (8641)  all_52_9 = all_6_0
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | COMBINE_EQS: (394), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8642)  all_56_1 = all_6_0
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | COMBINE_EQS: (549), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8643)  all_58_1 = all_6_0
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (575), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8644)   ~ (all_52_13 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | SIMP: (8644) implies:
% 197.16/32.21  | | | | | | | | |   (8645)   ~ (all_52_13 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (576), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8646)   ~ (all_52_15 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | SIMP: (8646) implies:
% 197.16/32.21  | | | | | | | | |   (8647)   ~ (all_52_15 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (577), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8648)   ~ (all_52_17 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | SIMP: (8648) implies:
% 197.16/32.21  | | | | | | | | |   (8649)   ~ (all_52_17 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (578), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8650)   ~ (all_52_25 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | SIMP: (8650) implies:
% 197.16/32.21  | | | | | | | | |   (8651)   ~ (all_52_25 = all_6_0)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (557), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8652)   ~ (all_6_0 = all_6_2)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (574), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8653)   ~ (all_6_0 = all_4_2)
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | REDUCE: (182), (8641) imply:
% 197.16/32.21  | | | | | | | | |   (8654)  op(all_6_0, all_6_0) = all_52_8
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | BETA: splitting (89) gives:
% 197.16/32.21  | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | Case 1:
% 197.16/32.21  | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | |   (8655)   ~ (all_24_0 = e1)
% 197.16/32.21  | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | REDUCE: (711), (8655) imply:
% 197.16/32.21  | | | | | | | | | |   (8656)   ~ (all_14_0 = e1)
% 197.16/32.21  | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | BETA: splitting (303) gives:
% 197.16/32.21  | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | Case 1:
% 197.16/32.21  | | | | | | | | | | | 
% 197.16/32.21  | | | | | | | | | | |   (8657)  all_58_15 = e0
% 197.16/32.21  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (53), (61), (62),
% 197.16/32.22  | | | | | | | | | | |            (63), (158), (166), (168), (172), (173), (174),
% 197.16/32.22  | | | | | | | | | | |            (175), (177), (178), (182), (183), (184), (185),
% 197.16/32.22  | | | | | | | | | | |            (187), (274), (278), (282), (283), (284), (285),
% 197.16/32.22  | | | | | | | | | | |            (306), (307), (309), (313), (315), (317), (321),
% 197.16/32.22  | | | | | | | | | | |            (325), (327), (329), (331), (332), (351), (352),
% 197.16/32.22  | | | | | | | | | | |            (366), (372), (375), (387), (388), (393), (405),
% 197.16/32.22  | | | | | | | | | | |            (415), (427), (522), (540), (541), (542), (543),
% 197.16/32.22  | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.16/32.22  | | | | | | | | | | |            (557), (559), (561), (563), (564), (569), (570),
% 197.16/32.22  | | | | | | | | | | |            (572), (573), (584), (590), (592), (593), (594),
% 197.16/32.22  | | | | | | | | | | |            (595), (596), (597), (598), (600), (602), (603),
% 197.16/32.22  | | | | | | | | | | |            (604), (605), (606), (609), (610), (612), (613),
% 197.16/32.22  | | | | | | | | | | |            (739), (7460), (7462), (8374), (8376), (8637),
% 197.16/32.22  | | | | | | | | | | |            (8639), (8642), (8643), (8645), (8647), (8649),
% 197.16/32.22  | | | | | | | | | | |            (8651), (8652), (8653), (8654), (8656), (8657),
% 197.16/32.22  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.16/32.22  | | | | | | | | | | |            #818.
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | |   (8658)   ~ (all_58_15 = e0)
% 197.16/32.22  | | | | | | | | | | |   (8659)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.16/32.22  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.16/32.22  | | | | | | | | | | |             e0)
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 197.16/32.22  | | | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 197.16/32.22  | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 197.16/32.22  | | | | | | | | | | |            (177), (178), (180), (182), (183), (184), (185),
% 197.16/32.22  | | | | | | | | | | |            (187), (270), (271), (273), (274), (275), (277),
% 197.16/32.22  | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 197.16/32.22  | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 197.16/32.22  | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 197.16/32.22  | | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 197.16/32.22  | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 197.16/32.22  | | | | | | | | | | |            (388), (393), (405), (411), (415), (431), (522),
% 197.16/32.22  | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 197.16/32.22  | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.16/32.22  | | | | | | | | | | |            (555), (559), (561), (562), (563), (564), (565),
% 197.16/32.22  | | | | | | | | | | |            (566), (567), (569), (570), (572), (573), (574),
% 197.16/32.22  | | | | | | | | | | |            (575), (578), (582), (584), (586), (588), (590),
% 197.16/32.22  | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 197.16/32.22  | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 197.16/32.22  | | | | | | | | | | |            (607), (608), (609), (610), (612), (613), (739),
% 197.16/32.22  | | | | | | | | | | |            (7460), (7462), (8371), (8637), (8639), (8642),
% 197.16/32.22  | | | | | | | | | | |            (8643), (8645), (8647), (8649), (8651), (8652),
% 197.16/32.22  | | | | | | | | | | |            (8653), (8654), (8658), (8659), (function-axioms)
% 197.16/32.22  | | | | | | | | | | |            are inconsistent by sub-proof #505.
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | End of split
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | |   (8660)  all_24_0 = e1
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | COMBINE_EQS: (711), (8660) imply:
% 197.16/32.22  | | | | | | | | | |   (8661)  all_14_0 = e1
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | SIMP: (8661) implies:
% 197.16/32.22  | | | | | | | | | |   (8662)  all_14_0 = e1
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | REDUCE: (8374), (8662) imply:
% 197.16/32.22  | | | | | | | | | |   (8663)   ~ (e2 = e1)
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | REDUCE: (62), (8662) imply:
% 197.16/32.22  | | | | | | | | | |   (8664)  op(e0, all_14_1) = e1
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | BETA: splitting (303) gives:
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | |   (8665)  all_58_15 = e0
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (8664), (8665),
% 197.16/32.22  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.16/32.22  | | | | | | | | | | |            #877.
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | |   (8666)   ~ (all_58_15 = e0)
% 197.16/32.22  | | | | | | | | | | |   (8667)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.16/32.22  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.16/32.22  | | | | | | | | | | |             e0)
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 197.16/32.22  | | | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 197.16/32.22  | | | | | | | | | | |            (166), (167), (168), (172), (173), (174), (175),
% 197.16/32.22  | | | | | | | | | | |            (177), (178), (180), (182), (183), (184), (185),
% 197.16/32.22  | | | | | | | | | | |            (187), (270), (271), (273), (274), (275), (277),
% 197.16/32.22  | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (304),
% 197.16/32.22  | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 197.16/32.22  | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 197.16/32.22  | | | | | | | | | | |            (328), (329), (331), (332), (333), (343), (351),
% 197.16/32.22  | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 197.16/32.22  | | | | | | | | | | |            (388), (393), (405), (411), (415), (431), (522),
% 197.16/32.22  | | | | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 197.16/32.22  | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.16/32.22  | | | | | | | | | | |            (555), (559), (561), (562), (563), (564), (565),
% 197.16/32.22  | | | | | | | | | | |            (566), (567), (569), (570), (572), (573), (574),
% 197.16/32.22  | | | | | | | | | | |            (575), (578), (582), (584), (586), (588), (590),
% 197.16/32.22  | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (597),
% 197.16/32.22  | | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 197.16/32.22  | | | | | | | | | | |            (607), (608), (609), (610), (612), (613), (739),
% 197.16/32.22  | | | | | | | | | | |            (7460), (7462), (8371), (8637), (8639), (8642),
% 197.16/32.22  | | | | | | | | | | |            (8643), (8645), (8647), (8649), (8651), (8652),
% 197.16/32.22  | | | | | | | | | | |            (8653), (8654), (8666), (8667), (function-axioms)
% 197.16/32.22  | | | | | | | | | | |            are inconsistent by sub-proof #505.
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | End of split
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | End of split
% 197.16/32.22  | | | | | | | | | 
% 197.16/32.22  | | | | | | | | End of split
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | |   (8668)  all_18_0 = e3
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | | COMBINE_EQS: (761), (8668) imply:
% 197.16/32.22  | | | | | | | |   (8669)  all_14_0 = e3
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | | SIMP: (8669) implies:
% 197.16/32.22  | | | | | | | |   (8670)  all_14_0 = e3
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | | REDUCE: (62), (8670) imply:
% 197.16/32.22  | | | | | | | |   (8671)  op(e0, all_14_1) = e3
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | | BETA: splitting (84) gives:
% 197.16/32.22  | | | | | | | | 
% 197.16/32.22  | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | 
% 197.16/32.22  | | | | | | | | |   (8672)   ~ (all_22_1 = e2)
% 197.16/32.22  | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | REDUCE: (658), (8672) imply:
% 197.16/32.22  | | | | | | | | |   (8673)   ~ (all_6_1 = e2)
% 197.16/32.22  | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | BETA: splitting (99) gives:
% 197.16/32.22  | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | |   (8674)   ~ (all_28_0 = e3)
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | REDUCE: (754), (8674) imply:
% 197.16/32.22  | | | | | | | | | |   (8675)   ~ (all_4_0 = e3)
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | BETA: splitting (303) gives:
% 197.16/32.22  | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | |   (8676)  all_58_15 = e0
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (8671), (8676),
% 197.16/32.22  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.16/32.22  | | | | | | | | | | |            #678.
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | |   (8677)   ~ (all_58_15 = e0)
% 197.16/32.22  | | | | | | | | | | |   (8678)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.16/32.22  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.16/32.22  | | | | | | | | | | |             e0)
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | ALPHA: (8678) implies:
% 197.16/32.22  | | | | | | | | | | |   (8679)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.16/32.22  | | | | | | | | | | |   (8680)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | REDUCE: (541), (8677) imply:
% 197.16/32.22  | | | | | | | | | | |   (8681)   ~ (all_14_2 = e0)
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | BETA: splitting (187) gives:
% 197.16/32.22  | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | |   (8682)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.16/32.22  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.16/32.22  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.16/32.22  | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | BETA: splitting (8682) gives:
% 197.16/32.22  | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | |   (8683)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.16/32.22  | | | | | | | | | | | | |           all_52_6 = e0
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | ALPHA: (8683) implies:
% 197.16/32.22  | | | | | | | | | | | | |   (8684)  all_52_6 = e0
% 197.16/32.22  | | | | | | | | | | | | |   (8685)  all_52_4 = e1
% 197.16/32.22  | | | | | | | | | | | | |   (8686)  all_52_2 = e2
% 197.16/32.22  | | | | | | | | | | | | |   (8687)  all_52_0 = e3
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | REDUCE: (185), (8686) imply:
% 197.16/32.22  | | | | | | | | | | | | |   (8688)  op(all_52_3, all_52_3) = e2
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | REDUCE: (184), (8685) imply:
% 197.16/32.22  | | | | | | | | | | | | |   (8689)  op(all_52_5, all_52_5) = e1
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | REDUCE: (183), (8684) imply:
% 197.16/32.22  | | | | | | | | | | | | |   (8690)  op(all_52_7, all_52_7) = e0
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | REDUCE: (610), (8687) imply:
% 197.16/32.22  | | | | | | | | | | | | |   (8691)  op(all_6_2, all_6_2) = e3
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.16/32.22  | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | |   (8692)  all_56_15 = e3
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | COMBINE_EQS: (538), (8692) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8693)  all_14_2 = e3
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | SIMP: (8693) implies:
% 197.16/32.22  | | | | | | | | | | | | | |   (8694)  all_14_2 = e3
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | COMBINE_EQS: (541), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8695)  all_58_15 = e3
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (573), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8696)   ~ (all_52_7 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (608), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8697)   ~ (all_52_27 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (609), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8698)   ~ (all_52_29 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (613), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8699)  op(e3, e3) = all_52_30
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (63), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8700)  op(e3, e0) = all_14_1
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (61), (8694) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8701)  op(e0, e0) = e3
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (41), (42), (43), (51), (53),
% 197.16/32.22  | | | | | | | | | | | | | |            (61), (167), (168), (169), (172), (175), (182),
% 197.16/32.22  | | | | | | | | | | | | | |            (273), (277), (279), (304), (305), (307), (310),
% 197.16/32.22  | | | | | | | | | | | | | |            (313), (315), (317), (319), (321), (328), (330),
% 197.16/32.22  | | | | | | | | | | | | | |            (332), (333), (351), (366), (367), (372), (375),
% 197.16/32.22  | | | | | | | | | | | | | |            (387), (393), (405), (417), (431), (542), (543),
% 197.16/32.22  | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (551), (553),
% 197.16/32.22  | | | | | | | | | | | | | |            (555), (559), (562), (564), (565), (569), (572),
% 197.16/32.22  | | | | | | | | | | | | | |            (573), (576), (577), (578), (580), (586), (596),
% 197.16/32.22  | | | | | | | | | | | | | |            (597), (611), (612), (7445), (7449), (7455),
% 197.16/32.22  | | | | | | | | | | | | | |            (7457), (7459), (7460), (8675), (8688), (8689),
% 197.16/32.22  | | | | | | | | | | | | | |            (8690), (8691), (8695), (8696), (8697), (8698),
% 197.16/32.22  | | | | | | | | | | | | | |            (8699), (8700), (8701), (function-axioms) are
% 197.16/32.22  | | | | | | | | | | | | | |            inconsistent by sub-proof #104.
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | |   (8702)   ~ (all_56_15 = e3)
% 197.16/32.22  | | | | | | | | | | | | | |   (8703)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | REDUCE: (538), (8702) imply:
% 197.16/32.22  | | | | | | | | | | | | | |   (8704)   ~ (all_14_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.16/32.22  | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | |   (8705)  all_58_2 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (387), (564), (8688), (8691), (8705),
% 197.16/32.22  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.16/32.22  | | | | | | | | | | | | | | |            #1159.
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | |   (8706)   ~ (all_58_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | |   (8707)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | REDUCE: (387), (8706) imply:
% 197.16/32.22  | | | | | | | | | | | | | | |   (8708)   ~ (all_52_3 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | |   (8709)  all_56_4 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | REF_CLOSE: (411), (8708), (8709) are inconsistent by
% 197.16/32.22  | | | | | | | | | | | | | | | |            sub-proof #1340.
% 197.16/32.22  | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | |   (8710)   ~ (all_56_4 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | |   (8711)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 197.16/32.22  | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | |   (8712)  all_58_12 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8712) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | |   (8713)  all_52_7 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 197.16/32.22  | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (555), (564), (569),
% 197.16/32.22  | | | | | | | | | | | | | | | | |            (573), (8688), (8689), (8690), (8691), (8713),
% 197.16/32.22  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.16/32.22  | | | | | | | | | | | | | | | | |            #1361.
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | |   (8714)   ~ (all_58_12 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | |   (8715)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | REDUCE: (351), (8714) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | |   (8716)   ~ (all_52_7 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8717)  all_58_0 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8717) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8718)  all_6_2 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | REDUCE: (553), (8718) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8719)   ~ (all_52_5 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | REDUCE: (557), (8718) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8720)   ~ (all_52_9 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | REDUCE: (561), (8718) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8721)   ~ (all_52_25 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | REDUCE: (43), (8718) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8722)  op(e3, e3) = all_6_1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | REDUCE: (41), (8718) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8723)  op(e3, e3) = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 197.16/32.22  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8722), (8723) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8724)  all_6_1 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | REDUCE: (42), (8724) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8725)  op(e3, e3) = all_6_0
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 197.16/32.22  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8723), (8725) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | |   (8726)  all_6_0 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | |   (8727)  all_58_9 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (8721), (8727) are inconsistent by
% 197.16/32.22  | | | | | | | | | | | | | | | | | | |            sub-proof #1300.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | |   (8728)   ~ (all_58_9 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | |   (8729)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | |   (8730)  all_56_12 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (8716), (8730) are inconsistent by
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | |            sub-proof #1383.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | |   (8731)   ~ (all_56_12 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | |   (8732)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | |   (8733)  all_56_8 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (8719), (8733) are inconsistent by
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | |   (8734)   ~ (all_56_8 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | |   (8735)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | |   (8736)  all_56_3 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (8721), (8736) are inconsistent by
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1339.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | |   (8737)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | |   (8738)  all_56_1 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (8738) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | |   (8739)  all_52_9 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8720), (8739) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | |   (8740)  $false
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8740) is inconsistent.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | |   (8741)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8742)  all_56_7 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (8742) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8743)  all_52_27 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8743) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8744)  all_52_27 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (8744) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8745)  all_58_10 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (8744) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8746)   ~ (all_52_29 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8746) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8747)   ~ (all_52_29 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (608), (8744) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8748)   ~ (all_14_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (8744) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8749)  op(e2, e0) = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (8750)  all_58_6 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (8719), (8750) are inconsistent by
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (8751)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8752)  all_56_14 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (8752) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8753)  all_52_23 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8753) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8754)  all_52_23 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (600), (8754) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8755)   ~ (all_10_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8755) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8756)   ~ (all_10_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8751) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8757)  all_58_7 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (8757) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8758)  all_52_13 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (8758) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8759)   ~ (all_4_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8759) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8760)   ~ (all_4_2 = e3)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8761)  all_58_0 = e1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8717), (8761) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8762)  e3 = e1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (8762) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8763)  $false
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8763) is inconsistent.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8764)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8765)  all_58_12 = e1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8765) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8766)  all_52_7 = e1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8766) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8767)  all_52_7 = e1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (8767) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8768)   ~ (all_14_2 = e1)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8768) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8769)   ~ (all_14_2 = e1)
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8703) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8770)  all_56_15 = e2
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8770) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8771)  all_14_2 = e2
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8771) implies:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8772)  all_14_2 = e2
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (8772) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8773)  op(e2, e0) = all_14_1
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_14_1,
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (8749), (8773) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8774)  all_14_1 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8671), (8774) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8775)  op(e0, e3) = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (8775) gives:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8776)  all_52_7 = e3
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8716), (8776) imply:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8777)  $false
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8777) is inconsistent.
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.16/32.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8778)  all_56_15 = e1 | all_56_15 = e0
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8681), (8769), (8778) are inconsistent by
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.16/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8779)   ~ (all_58_12 = e1)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (8779) imply:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8780)   ~ (all_52_7 = e1)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (51), (53), (311), (320), (328),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (331), (351), (375), (387), (393), (538), (544),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (569), (573),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (574), (593), (596), (606), (609), (612), (613),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8680), (8688), (8689), (8703), (8704), (8717),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8745), (8756), (8757), (8760), (8764), (8780),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #745.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8781)  all_58_8 = e3 | all_58_11 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (546), (8747), (8756), (8781) are
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8782)   ~ (all_56_14 = e3)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8783)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (8782) imply:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8784)   ~ (all_52_23 = e3)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8715) gives:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8785)  all_58_13 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (61), (62), (63),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (182), (278), (279), (281), (304),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (305), (320), (323), (343), (351), (375), (387),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (388), (394), (411), (417), (427), (431), (538),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (541), (542), (544), (545), (548), (549), (563),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (572), (573), (574), (578),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (584), (586), (596), (598), (600), (604), (606),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (613), (8374), (8679), (8680), (8681), (8688),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8690), (8703), (8704), (8708), (8716), (8721),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8729), (8732), (8737), (8741), (8783), (8785),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #756.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8786)  all_58_14 = e3 | all_58_15 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (542), (8704), (8784), (8786) are
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #715.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | |   (8787)   ~ (all_56_7 = e3)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (8787) imply:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | |   (8788)   ~ (all_52_27 = e3)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8707) gives:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (8789)  all_58_3 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8789) imply:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (8790)  all_4_2 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (61), (169), (304), (305), (318),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (320), (324), (351), (366), (367), (387), (411),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (431), (538), (543), (549), (562), (563), (567),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (573), (591), (7443), (7445), (8681),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (8688), (8690), (8703), (8704), (8708), (8711),
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (8732), (8735), (8789), (8790), (function-axioms)
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #102.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (8791)  all_58_5 = e3 | all_58_10 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (7449), (8675), (8788), (8791) are
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #214.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | |   (8792)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 197.19/32.23  | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (51), (351), (387), (547), (569), (8689),
% 197.19/32.23  | | | | | | | | | | | | | | | | | |            (8691), (8708), (8716), (8792), (function-axioms)
% 197.19/32.23  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1365.
% 197.19/32.23  | | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | |   (8793)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.19/32.23  | | | | | | | | | | | | |           all_52_14 = e0
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 197.19/32.23  | | | | | | | | | | | | |            (61), (63), (158), (162), (167), (168), (169),
% 197.19/32.23  | | | | | | | | | | | | |            (173), (174), (175), (178), (179), (180), (182),
% 197.19/32.23  | | | | | | | | | | | | |            (183), (185), (270), (272), (273), (275), (277),
% 197.19/32.23  | | | | | | | | | | | | |            (280), (282), (283), (284), (306), (309), (313),
% 197.19/32.23  | | | | | | | | | | | | |            (317), (321), (325), (330), (331), (332), (333),
% 197.19/32.23  | | | | | | | | | | | | |            (346), (351), (361), (366), (367), (372), (387),
% 197.19/32.23  | | | | | | | | | | | | |            (388), (393), (394), (405), (415), (431), (538),
% 197.19/32.23  | | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 197.19/32.23  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.19/32.23  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (568),
% 197.19/32.23  | | | | | | | | | | | | |            (569), (570), (571), (572), (573), (575), (577),
% 197.19/32.23  | | | | | | | | | | | | |            (578), (580), (582), (586), (588), (590), (591),
% 197.19/32.23  | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (606),
% 197.19/32.23  | | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 197.19/32.23  | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7457),
% 197.19/32.23  | | | | | | | | | | | | |            (7458), (7460), (7462), (8373), (8673), (8675),
% 197.19/32.23  | | | | | | | | | | | | |            (8679), (8680), (8793), (function-axioms) are
% 197.19/32.23  | | | | | | | | | | | | |            inconsistent by sub-proof #188.
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | |   (8794)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.19/32.23  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.19/32.23  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | BETA: splitting (8794) gives:
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | |   (8795)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.19/32.23  | | | | | | | | | | | | |           all_52_22 = e0
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (36), (41), (42), (43), (53), (61),
% 197.19/32.23  | | | | | | | | | | | | |            (63), (158), (161), (162), (167), (168), (169),
% 197.19/32.23  | | | | | | | | | | | | |            (174), (175), (178), (179), (183), (184), (185),
% 197.19/32.23  | | | | | | | | | | | | |            (270), (271), (272), (273), (277), (282), (283),
% 197.19/32.23  | | | | | | | | | | | | |            (306), (309), (316), (317), (321), (325), (330),
% 197.19/32.23  | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 197.19/32.23  | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.19/32.23  | | | | | | | | | | | | |            (415), (431), (538), (541), (542), (543), (545),
% 197.19/32.23  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.23  | | | | | | | | | | | | |            (557), (559), (562), (563), (564), (566), (567),
% 197.19/32.23  | | | | | | | | | | | | |            (569), (572), (573), (574), (576), (582), (588),
% 197.19/32.23  | | | | | | | | | | | | |            (590), (591), (593), (595), (596), (603), (604),
% 197.19/32.23  | | | | | | | | | | | | |            (606), (608), (610), (611), (612), (613), (7443),
% 197.19/32.23  | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (7462), (8371),
% 197.19/32.23  | | | | | | | | | | | | |            (8373), (8673), (8675), (8795), (function-axioms)
% 197.19/32.23  | | | | | | | | | | | | |            are inconsistent by sub-proof #105.
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | |   (8796)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.19/32.23  | | | | | | | | | | | | |           all_52_30 = e0
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 197.19/32.23  | | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 197.19/32.23  | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 197.19/32.23  | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 197.19/32.23  | | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 197.19/32.23  | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 197.19/32.23  | | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 197.19/32.23  | | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 197.19/32.23  | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.19/32.23  | | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 197.19/32.23  | | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.19/32.23  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.23  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.19/32.23  | | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 197.19/32.23  | | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 197.19/32.23  | | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.19/32.23  | | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 197.19/32.23  | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 197.19/32.23  | | | | | | | | | | | | |            (7462), (8373), (8673), (8679), (8681), (8796),
% 197.19/32.23  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.23  | | | | | | | | | | | | |            #1008.
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | |   (8797)  all_28_0 = e3
% 197.19/32.23  | | | | | | | | | |   (8798)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (41), (42), (43),
% 197.19/32.23  | | | | | | | | | |            (51), (53), (61), (63), (158), (161), (162),
% 197.19/32.23  | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.19/32.23  | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.19/32.23  | | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.19/32.23  | | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.19/32.23  | | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.19/32.23  | | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.19/32.23  | | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 197.19/32.23  | | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.19/32.23  | | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.19/32.23  | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 197.19/32.23  | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.19/32.23  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.23  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.19/32.23  | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.19/32.23  | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.19/32.23  | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 197.19/32.23  | | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 197.19/32.23  | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.23  | | | | | | | | | |            (608), (609), (610), (613), (754), (7443), (7444),
% 197.19/32.23  | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7455),
% 197.19/32.23  | | | | | | | | | |            (7457), (7458), (7459), (7460), (7462), (8373),
% 197.19/32.23  | | | | | | | | | |            (8671), (8673), (8797), (8798), (function-axioms)
% 197.19/32.23  | | | | | | | | | |            are inconsistent by sub-proof #137.
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | |   (8799)  all_22_1 = e2
% 197.19/32.23  | | | | | | | | |   (8800)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | COMBINE_EQS: (658), (8799) imply:
% 197.19/32.23  | | | | | | | | |   (8801)  all_6_1 = e2
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | SIMP: (8801) implies:
% 197.19/32.23  | | | | | | | | |   (8802)  all_6_1 = e2
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 197.19/32.23  | | | | | | | | |            (53), (61), (63), (158), (159), (161), (162),
% 197.19/32.23  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.19/32.23  | | | | | | | | |            (175), (177), (178), (180), (182), (183), (184),
% 197.19/32.23  | | | | | | | | |            (185), (187), (270), (271), (273), (274), (275),
% 197.19/32.23  | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 197.19/32.23  | | | | | | | | |            (303), (304), (306), (307), (309), (311), (313),
% 197.19/32.23  | | | | | | | | |            (315), (316), (317), (319), (321), (324), (325),
% 197.19/32.23  | | | | | | | | |            (326), (327), (328), (329), (331), (332), (333),
% 197.19/32.23  | | | | | | | | |            (343), (351), (352), (361), (366), (367), (372),
% 197.19/32.23  | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.19/32.23  | | | | | | | | |            (415), (431), (522), (538), (539), (540), (541),
% 197.19/32.23  | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.23  | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.19/32.23  | | | | | | | | |            (562), (563), (564), (565), (566), (567), (569),
% 197.19/32.23  | | | | | | | | |            (570), (572), (573), (574), (575), (576), (577),
% 197.19/32.23  | | | | | | | | |            (578), (582), (584), (586), (588), (590), (591),
% 197.19/32.23  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 197.19/32.23  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.23  | | | | | | | | |            (608), (609), (610), (612), (613), (739), (7460),
% 197.19/32.23  | | | | | | | | |            (7462), (8371), (8373), (8671), (8800), (8802),
% 197.19/32.23  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.23  | | | | | | | | |            #508.
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | End of split
% 197.19/32.23  | | | | | | | | 
% 197.19/32.23  | | | | | | | End of split
% 197.19/32.23  | | | | | | | 
% 197.19/32.23  | | | | | | Case 2:
% 197.19/32.23  | | | | | | | 
% 197.19/32.23  | | | | | | |   (8803)  all_14_0 = e2
% 197.19/32.23  | | | | | | |   (8804)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 197.19/32.23  | | | | | | | 
% 197.19/32.23  | | | | | | | REDUCE: (62), (8803) imply:
% 197.19/32.23  | | | | | | |   (8805)  op(e0, all_14_1) = e2
% 197.19/32.23  | | | | | | | 
% 197.19/32.23  | | | | | | | BETA: splitting (84) gives:
% 197.19/32.23  | | | | | | | 
% 197.19/32.23  | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | 
% 197.19/32.23  | | | | | | | |   (8806)   ~ (all_22_1 = e2)
% 197.19/32.23  | | | | | | | | 
% 197.19/32.23  | | | | | | | | REDUCE: (658), (8806) imply:
% 197.19/32.23  | | | | | | | |   (8807)   ~ (all_6_1 = e2)
% 197.19/32.23  | | | | | | | | 
% 197.19/32.23  | | | | | | | | BETA: splitting (99) gives:
% 197.19/32.23  | | | | | | | | 
% 197.19/32.23  | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | |   (8808)   ~ (all_28_0 = e3)
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | REDUCE: (754), (8808) imply:
% 197.19/32.23  | | | | | | | | |   (8809)   ~ (all_4_0 = e3)
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.23  | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | |   (8810)  all_58_15 = e0
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (8805), (8810),
% 197.19/32.23  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.23  | | | | | | | | | |            #612.
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | |   (8811)   ~ (all_58_15 = e0)
% 197.19/32.23  | | | | | | | | | |   (8812)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.23  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.23  | | | | | | | | | |             e0)
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | ALPHA: (8812) implies:
% 197.19/32.23  | | | | | | | | | |   (8813)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.19/32.23  | | | | | | | | | |   (8814)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | REDUCE: (541), (8811) imply:
% 197.19/32.23  | | | | | | | | | |   (8815)   ~ (all_14_2 = e0)
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | BETA: splitting (187) gives:
% 197.19/32.23  | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | |   (8816)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.23  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.19/32.23  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.19/32.23  | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | BETA: splitting (8816) gives:
% 197.19/32.23  | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | |   (8817)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.23  | | | | | | | | | | | |           all_52_6 = e0
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | ALPHA: (8817) implies:
% 197.19/32.23  | | | | | | | | | | | |   (8818)  all_52_6 = e0
% 197.19/32.23  | | | | | | | | | | | |   (8819)  all_52_4 = e1
% 197.19/32.23  | | | | | | | | | | | |   (8820)  all_52_2 = e2
% 197.19/32.23  | | | | | | | | | | | |   (8821)  all_52_0 = e3
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | REDUCE: (185), (8820) imply:
% 197.19/32.23  | | | | | | | | | | | |   (8822)  op(all_52_3, all_52_3) = e2
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | REDUCE: (184), (8819) imply:
% 197.19/32.23  | | | | | | | | | | | |   (8823)  op(all_52_5, all_52_5) = e1
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | REDUCE: (183), (8818) imply:
% 197.19/32.23  | | | | | | | | | | | |   (8824)  op(all_52_7, all_52_7) = e0
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | REDUCE: (610), (8821) imply:
% 197.19/32.23  | | | | | | | | | | | |   (8825)  op(all_6_2, all_6_2) = e3
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | BETA: splitting (279) gives:
% 197.19/32.23  | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | |   (8826)  all_56_6 = e3
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | COMBINE_EQS: (7448), (8826) imply:
% 197.19/32.23  | | | | | | | | | | | | |   (8827)  all_4_0 = e3
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | SIMP: (8827) implies:
% 197.19/32.23  | | | | | | | | | | | | |   (8828)  all_4_0 = e3
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | REDUCE: (8809), (8828) imply:
% 197.19/32.23  | | | | | | | | | | | | |   (8829)  $false
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | CLOSE: (8829) is inconsistent.
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | Case 2:
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | |   (8830)   ~ (all_56_6 = e3)
% 197.19/32.23  | | | | | | | | | | | | |   (8831)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.19/32.23  | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | Case 1:
% 197.19/32.23  | | | | | | | | | | | | | | 
% 197.19/32.23  | | | | | | | | | | | | | |   (8832)  all_56_15 = e3
% 197.19/32.23  | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (43), (51), (53), (61),
% 197.19/32.24  | | | | | | | | | | | | | |            (63), (167), (168), (169), (172), (175), (182),
% 197.19/32.24  | | | | | | | | | | | | | |            (273), (277), (279), (304), (305), (307), (310),
% 197.19/32.24  | | | | | | | | | | | | | |            (313), (315), (317), (319), (321), (328), (330),
% 197.19/32.24  | | | | | | | | | | | | | |            (332), (333), (351), (366), (367), (372), (375),
% 197.19/32.24  | | | | | | | | | | | | | |            (387), (393), (405), (417), (431), (538), (541),
% 197.19/32.24  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.24  | | | | | | | | | | | | | |            (551), (553), (555), (559), (562), (564), (565),
% 197.19/32.24  | | | | | | | | | | | | | |            (569), (572), (573), (576), (577), (578), (580),
% 197.19/32.24  | | | | | | | | | | | | | |            (586), (596), (597), (608), (609), (611), (612),
% 197.19/32.24  | | | | | | | | | | | | | |            (613), (7445), (7449), (7455), (7457), (7459),
% 197.19/32.24  | | | | | | | | | | | | | |            (7460), (8809), (8815), (8822), (8823), (8824),
% 197.19/32.24  | | | | | | | | | | | | | |            (8825), (8832), (function-axioms) are inconsistent
% 197.19/32.24  | | | | | | | | | | | | | |            by sub-proof #103.
% 197.19/32.24  | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | |   (8833)   ~ (all_56_15 = e3)
% 197.19/32.24  | | | | | | | | | | | | | |   (8834)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.19/32.24  | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | REDUCE: (538), (8833) imply:
% 197.19/32.24  | | | | | | | | | | | | | |   (8835)   ~ (all_14_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.19/32.24  | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | |   (8836)  all_58_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (387), (564), (8822), (8825), (8836),
% 197.19/32.24  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.24  | | | | | | | | | | | | | | |            #1159.
% 197.19/32.24  | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | |   (8837)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8838)  all_56_5 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (8838) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8839)  all_4_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | SIMP: (8839) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8840)  all_4_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (574), (8840) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8841)   ~ (all_52_9 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (582), (8840) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8842)   ~ (all_52_15 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (586), (8840) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8843)   ~ (all_52_27 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (611), (8840) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8844)  op(e3, e3) = all_52_10
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (7445), (8840) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8845)  op(e3, e2) = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (36), (8840) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8846)  op(e2, e2) = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | BETA: splitting (7443) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8847)   ~ (all_4_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (8846), (8847), (function-axioms) are
% 197.19/32.24  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #211.
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8848)   ~ (all_4_0 = e0)
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 197.19/32.24  | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (8845) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8849)  all_52_9 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.24  | | | | | | | | | | | | | | | | |              all_52_10, e3, e3, simplifying with (41), (8844)
% 197.19/32.24  | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8850)  all_52_10 = all_6_2
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | REDUCE: (575), (8849) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8851)   ~ (all_52_13 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | SIMP: (8851) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8852)   ~ (all_52_13 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | REDUCE: (578), (8849) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8853)   ~ (all_52_25 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | SIMP: (8853) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8854)   ~ (all_52_25 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | REDUCE: (182), (8849) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8855)  op(e1, e1) = all_52_8
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 197.19/32.24  | | | | | | | | | | | | | | | | |              all_52_8, e1, e1, simplifying with (51), (8855)
% 197.19/32.24  | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8856)  all_52_8 = all_10_2
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8857)  all_58_12 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (8857) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8858)  all_52_7 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 197.19/32.24  | | | | | | | | | | | | | | | | | |            (351), (387), (405), (547), (555), (564), (569),
% 197.19/32.24  | | | | | | | | | | | | | | | | | |            (573), (8822), (8823), (8824), (8825), (8858),
% 197.19/32.24  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.24  | | | | | | | | | | | | | | | | | |            #1361.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8859)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | BETA: splitting (8859) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8860)  all_58_13 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8842), (8860) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8861)  all_58_14 = e3 | all_58_15 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (8861) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8862)  all_58_14 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (8862) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8863)  all_52_23 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | SIMP: (8863) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8864)  all_52_23 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (8864) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8865)   ~ (all_52_7 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (8864) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8866)   ~ (all_52_17 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (603), (8864) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8867)   ~ (all_14_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (8864) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8868)  op(e3, e3) = all_52_22
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (8868)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8869)  all_52_22 = all_6_2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8870)  all_56_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (8866), (8870) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1327.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8871)   ~ (all_56_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8872)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8873)  all_58_9 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (332), (351), (387),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |            (405), (545), (547), (561), (564), (569), (8822),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |            (8823), (8825), (8865), (8873), (function-axioms)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #660.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8874)   ~ (all_58_9 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8875)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (8874) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8876)   ~ (all_52_25 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | |   (8877)  all_58_0 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8877) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | |   (8878)  all_6_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (8878) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | |   (8879)  op(e3, e3) = all_6_1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (8878) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | |   (8880)  op(e3, e3) = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8875) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | |   (8881)  all_58_10 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (8843), (8881) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | |   (8882)  all_58_11 = e3 | all_58_15 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8882) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8883)  all_58_11 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8883) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8884)  all_52_29 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8884) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8885)  all_52_29 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (8885) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8886)   ~ (all_52_5 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (8885) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8887)  op(e3, e3) = all_52_28
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (8885) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8888)  op(e1, e0) = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e3, simplifying with (8879), (8887)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8889)  all_52_28 = all_6_1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e3, simplifying with (8880), (8887)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8890)  all_52_28 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8889), (8890) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8891)  all_6_1 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8891) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8892)  all_6_1 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (8892) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8893)  op(e3, e3) = all_6_0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0,
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (8880), (8893) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8894)  all_6_0 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8895)  all_56_3 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (8876), (8895) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1339.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8896)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8897)  all_58_6 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (8897) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8898)  all_52_5 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (569), (8823), (8898), (function-axioms) are
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8899)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8899) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8900)  all_58_7 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (8900) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8901)  all_52_13 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8852), (8901) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8902)  $false
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8902) is inconsistent.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8903)  all_58_8 = e1 | all_58_11 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8903) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8904)  all_58_8 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8904) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8905)  all_10_2 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (8905) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8906)   ~ (all_52_17 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7457), (8905) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8907)   ~ (all_4_0 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8907) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8908)   ~ (all_4_0 = e1)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8831) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8909)  all_56_6 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7448), (8909) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8910)  all_4_0 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8910) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8911)  all_4_0 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7451), (8911) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8912)   ~ (all_52_17 = e2)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8872) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8913)  all_56_2 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (8912), (8913) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1264.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8914)  all_56_2 = e1 | all_56_2 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8914) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8915)  all_56_2 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (8906), (8915) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1263.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8916)  all_56_2 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (8916) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8917)  all_52_17 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8917) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8918)  all_52_17 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (8918) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8919)   ~ (all_52_25 = e0)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8919) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8920)   ~ (all_52_25 = e0)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8896) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8921)  all_56_3 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (8921) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8922)  all_52_25 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8922) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8923)  all_52_25 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (8923) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8924)   ~ (all_14_2 = e2)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8924) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8925)   ~ (all_14_2 = e2)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8834) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8926)  all_56_15 = e2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8925), (8926) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #762.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8927)  all_56_15 = e1 | all_56_15 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8927) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8928)  all_56_15 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (8928) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8929)  all_14_2 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8929) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8930)  all_14_2 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (8930) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8931)  op(e1, e0) = all_14_1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8804), (8888), (8930), (8931), (function-axioms)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #590.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8932)  all_56_15 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (8815), (8932) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1162.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8933)  all_56_3 = e1 | all_56_3 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (388), (8854), (8920), (8933) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1330.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8934)  all_56_6 = e1 | all_56_6 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8934) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8935)  all_56_6 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7448), (8935) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8936)  all_4_0 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8936) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8937)  all_4_0 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8908), (8937) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8938)  $false
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8938) is inconsistent.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8939)  all_56_6 = e0
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7448), (8848), (8939) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #101.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8940)  all_58_11 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8883), (8940) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8941)  e3 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8877), (8941) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8942)  all_58_0 = e1
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (332), (351), (387), (547), (564),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8846), (8865), (8886), (8942), (function-axioms)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1241.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8943)  all_58_15 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (8835), (8943) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #197.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | |   (8944)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (393), (545), (549), (8841), (8866), (8876),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | |            (8944) are inconsistent by sub-proof #744.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8945)  all_58_15 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (8835), (8945) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            sub-proof #197.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8946)   ~ (all_56_5 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | REDUCE: (539), (8946) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | |   (8947)   ~ (all_4_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | BETA: splitting (8837) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8948)  all_58_3 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8948) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8949)  all_4_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | REDUCE: (8947), (8949) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8950)  $false
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | CLOSE: (8950) is inconsistent.
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | |   (8951)  all_58_5 = e3 | all_58_10 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | BETA: splitting (8951) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8952)  all_58_5 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (8809), (8952) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8953)  all_58_10 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (8953) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8954)  all_52_27 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | SIMP: (8954) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8955)  all_52_27 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REDUCE: (607), (8955) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8956)   ~ (all_52_29 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | SIMP: (8956) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8957)   ~ (all_52_29 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REDUCE: (7455), (8955) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8958)   ~ (all_4_0 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REDUCE: (586), (8955) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8959)   ~ (all_4_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REDUCE: (173), (8955) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8960)  op(e3, e3) = all_52_26
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | REDUCE: (163), (8955) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8961)  op(e2, e0) = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.24  | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (41), (8960)
% 197.19/32.24  | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | |   (8962)  all_52_26 = all_6_2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8963)  all_56_14 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (8963) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8964)  all_52_23 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | SIMP: (8964) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8965)  all_52_23 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | REDUCE: (572), (8965) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8966)   ~ (all_52_7 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | REDUCE: (603), (8965) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8967)   ~ (all_14_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | REDUCE: (600), (8965) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8968)   ~ (all_10_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | SIMP: (8968) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8969)   ~ (all_10_2 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | REDUCE: (175), (8965) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8970)  op(e3, e3) = all_52_22
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e3, simplifying with (41), (8970)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8971)  all_52_22 = all_6_2
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8972)  all_58_0 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (8972) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8973)  all_6_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (8973) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8974)   ~ (all_52_5 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8975)  all_58_6 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (8974), (8975) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8976)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (51), (53), (63), (158),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (304), (311), (320), (328), (331), (351), (366),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (375), (387), (393), (538), (544), (545), (546),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (547), (548), (549), (569), (573), (574), (580),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (588), (593), (596), (606), (609), (612), (613),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (8805), (8814), (8815), (8822), (8823), (8834),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (8835), (8953), (8957), (8961), (8969), (8972),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            (8976), (function-axioms) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #580.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8977)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (321), (351), (387), (547),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            (564), (569), (8822), (8823), (8825), (8966),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            (8977), (function-axioms) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            sub-proof #1364.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8978)   ~ (all_56_14 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | REDUCE: (343), (8978) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | |   (8979)   ~ (all_52_23 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8980)  all_58_4 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (61), (306), (321), (332),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            (351), (387), (393), (405), (547), (559), (564),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            (569), (573), (8822), (8823), (8824), (8825),
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            (8980), (function-axioms) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |            sub-proof #591.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | |   (8981)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8981) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8982)  all_58_5 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (8809), (8982) are inconsistent by
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | |   (8983)  all_58_8 = e3 | all_58_14 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8983) gives:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8984)  all_58_8 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8984) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8985)  all_10_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8985) implies:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8986)  all_10_2 = e3
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (8986) imply:
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | |   (8987)   ~ (all_52_13 = e3)
% 197.19/32.24  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (41), (42), (43), (51),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (53), (61), (63), (159), (168), (172), (177),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (180), (182), (273), (274), (275), (276), (281),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (284), (304), (305), (306), (307), (308), (309),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (311), (312), (313), (315), (317), (319), (320),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (321), (323), (324), (325), (328), (330), (332),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (333), (351), (352), (361), (366), (372), (375),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (387), (393), (394), (405), (411), (421), (431),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (561), (563), (564), (565), (566), (567), (569),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (570), (571), (573), (574), (575), (576), (577),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (578), (580), (582), (587), (588), (589), (590),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (591), (596), (597), (598), (600), (602), (607),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (608), (612), (613), (7460), (7462), (8804),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (8813), (8822), (8823), (8824), (8825), (8947),
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            (8987), (function-axioms) are inconsistent by
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #116.
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |   (8988)  all_58_14 = e3
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8979), (8988) are inconsistent by
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | |   (8989)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.19/32.25  | | | | | | | | | | | |           all_52_14 = e0
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (51), (53),
% 197.19/32.25  | | | | | | | | | | | |            (61), (63), (158), (162), (167), (168), (169),
% 197.19/32.25  | | | | | | | | | | | |            (173), (174), (175), (178), (179), (180), (182),
% 197.19/32.25  | | | | | | | | | | | |            (183), (185), (270), (272), (273), (275), (277),
% 197.19/32.25  | | | | | | | | | | | |            (280), (282), (283), (284), (306), (309), (313),
% 197.19/32.25  | | | | | | | | | | | |            (317), (321), (325), (330), (331), (332), (333),
% 197.19/32.25  | | | | | | | | | | | |            (346), (351), (361), (366), (367), (372), (387),
% 197.19/32.25  | | | | | | | | | | | |            (388), (393), (394), (405), (415), (431), (538),
% 197.19/32.25  | | | | | | | | | | | |            (539), (541), (542), (543), (544), (545), (546),
% 197.19/32.25  | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.19/32.25  | | | | | | | | | | | |            (559), (561), (562), (563), (564), (567), (568),
% 197.19/32.25  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (575), (577),
% 197.19/32.25  | | | | | | | | | | | |            (578), (580), (582), (586), (588), (590), (591),
% 197.19/32.25  | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (606),
% 197.19/32.25  | | | | | | | | | | | |            (607), (608), (609), (610), (611), (612), (613),
% 197.19/32.25  | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7457),
% 197.19/32.25  | | | | | | | | | | | |            (7458), (7460), (7462), (8373), (8807), (8809),
% 197.19/32.25  | | | | | | | | | | | |            (8813), (8814), (8989), (function-axioms) are
% 197.19/32.25  | | | | | | | | | | | |            inconsistent by sub-proof #188.
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | |   (8990)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.19/32.25  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.19/32.25  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | BETA: splitting (8990) gives:
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | |   (8991)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.19/32.25  | | | | | | | | | | | |           all_52_22 = e0
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (36), (41), (42), (43), (53), (61),
% 197.19/32.25  | | | | | | | | | | | |            (63), (158), (161), (162), (167), (168), (169),
% 197.19/32.25  | | | | | | | | | | | |            (174), (175), (178), (179), (183), (184), (185),
% 197.19/32.25  | | | | | | | | | | | |            (270), (271), (272), (273), (277), (282), (283),
% 197.19/32.25  | | | | | | | | | | | |            (306), (309), (316), (317), (321), (325), (330),
% 197.19/32.25  | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (366),
% 197.19/32.25  | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.19/32.25  | | | | | | | | | | | |            (415), (431), (538), (541), (542), (543), (545),
% 197.19/32.25  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.25  | | | | | | | | | | | |            (557), (559), (562), (563), (564), (566), (567),
% 197.19/32.25  | | | | | | | | | | | |            (569), (572), (573), (574), (576), (582), (588),
% 197.19/32.25  | | | | | | | | | | | |            (590), (591), (593), (595), (596), (603), (604),
% 197.19/32.25  | | | | | | | | | | | |            (606), (608), (610), (611), (612), (613), (7443),
% 197.19/32.25  | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (7462), (8371),
% 197.19/32.25  | | | | | | | | | | | |            (8373), (8807), (8809), (8991), (function-axioms)
% 197.19/32.25  | | | | | | | | | | | |            are inconsistent by sub-proof #105.
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | |   (8992)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.19/32.25  | | | | | | | | | | | |           all_52_30 = e0
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (51), (53),
% 197.19/32.25  | | | | | | | | | | | |            (61), (158), (162), (166), (167), (168), (172),
% 197.19/32.25  | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (180),
% 197.19/32.25  | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (272),
% 197.19/32.25  | | | | | | | | | | | |            (273), (274), (277), (280), (281), (282), (283),
% 197.19/32.25  | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (313),
% 197.19/32.25  | | | | | | | | | | | |            (316), (319), (321), (323), (324), (325), (327),
% 197.19/32.25  | | | | | | | | | | | |            (328), (330), (332), (333), (343), (346), (351),
% 197.19/32.25  | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.19/32.25  | | | | | | | | | | | |            (393), (394), (405), (411), (415), (431), (538),
% 197.19/32.25  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.19/32.25  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.25  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.19/32.25  | | | | | | | | | | | |            (567), (569), (570), (571), (572), (573), (574),
% 197.19/32.25  | | | | | | | | | | | |            (575), (576), (578), (580), (582), (584), (586),
% 197.19/32.25  | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.19/32.25  | | | | | | | | | | | |            (596), (597), (598), (602), (603), (604), (605),
% 197.19/32.25  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (613), (7460),
% 197.19/32.25  | | | | | | | | | | | |            (7462), (8373), (8807), (8813), (8815), (8992),
% 197.19/32.25  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.25  | | | | | | | | | | | |            #1008.
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | |   (8993)  all_28_0 = e3
% 197.19/32.25  | | | | | | | | |   (8994)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | COMBINE_EQS: (754), (8993) imply:
% 197.19/32.25  | | | | | | | | |   (8995)  all_4_0 = e3
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | SIMP: (8995) implies:
% 197.19/32.25  | | | | | | | | |   (8996)  all_4_0 = e3
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 197.19/32.25  | | | | | | | | |            (43), (51), (53), (61), (63), (158), (161), (162),
% 197.19/32.25  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.19/32.25  | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.19/32.25  | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.19/32.25  | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.19/32.25  | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.19/32.25  | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.19/32.25  | | | | | | | | |            (323), (324), (325), (327), (328), (329), (330),
% 197.19/32.25  | | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.19/32.25  | | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.19/32.25  | | | | | | | | |            (394), (405), (411), (415), (427), (431), (538),
% 197.19/32.25  | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.19/32.25  | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.25  | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.19/32.25  | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.19/32.25  | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.19/32.25  | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 197.19/32.25  | | | | | | | | |            (592), (593), (594), (595), (596), (597), (598),
% 197.19/32.25  | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.25  | | | | | | | | |            (608), (609), (610), (613), (7443), (7444), (7445),
% 197.19/32.25  | | | | | | | | |            (7449), (7450), (7451), (7453), (7455), (7457),
% 197.19/32.25  | | | | | | | | |            (7458), (7459), (7460), (7462), (8373), (8805),
% 197.19/32.25  | | | | | | | | |            (8807), (8994), (8996), (function-axioms) are
% 197.19/32.25  | | | | | | | | |            inconsistent by sub-proof #115.
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | End of split
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | |   (8997)  all_22_1 = e2
% 197.19/32.25  | | | | | | | |   (8998)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | | COMBINE_EQS: (658), (8997) imply:
% 197.19/32.25  | | | | | | | |   (8999)  all_6_1 = e2
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | | SIMP: (8999) implies:
% 197.19/32.25  | | | | | | | |   (9000)  all_6_1 = e2
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (42), (43), (51),
% 197.19/32.25  | | | | | | | |            (53), (61), (63), (158), (159), (161), (162), (166),
% 197.19/32.25  | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.19/32.25  | | | | | | | |            (177), (178), (180), (182), (183), (184), (185),
% 197.19/32.25  | | | | | | | |            (187), (270), (271), (273), (274), (275), (277),
% 197.19/32.25  | | | | | | | |            (280), (281), (282), (283), (284), (285), (303),
% 197.19/32.25  | | | | | | | |            (304), (306), (307), (309), (311), (313), (315),
% 197.19/32.25  | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.19/32.25  | | | | | | | |            (327), (328), (329), (331), (332), (333), (343),
% 197.19/32.25  | | | | | | | |            (351), (352), (361), (366), (367), (372), (375),
% 197.19/32.25  | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 197.19/32.25  | | | | | | | |            (431), (522), (538), (539), (540), (541), (542),
% 197.19/32.25  | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.25  | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.19/32.25  | | | | | | | |            (563), (564), (565), (566), (567), (569), (570),
% 197.19/32.25  | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 197.19/32.25  | | | | | | | |            (582), (584), (586), (588), (590), (591), (592),
% 197.19/32.25  | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 197.19/32.25  | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 197.19/32.25  | | | | | | | |            (609), (610), (612), (613), (739), (7460), (7462),
% 197.19/32.25  | | | | | | | |            (8371), (8373), (8805), (8998), (9000),
% 197.19/32.25  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #504.
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | End of split
% 197.19/32.25  | | | | | | | 
% 197.19/32.25  | | | | | | End of split
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | Case 2:
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | |   (9001)  all_12_1 = e1
% 197.19/32.25  | | | | | |   (9002)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | | COMBINE_EQS: (683), (9001) imply:
% 197.19/32.25  | | | | | |   (9003)  all_6_1 = e1
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | | REDUCE: (43), (9003) imply:
% 197.19/32.25  | | | | | |   (9004)  op(all_6_2, e3) = e1
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | | REDUCE: (42), (9003) imply:
% 197.19/32.25  | | | | | |   (9005)  op(e3, e1) = all_6_0
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | | REF_CLOSE: (5), (6), (7), (8), (36), (41), (42), (43), (51), (61),
% 197.19/32.25  | | | | | |            (62), (63), (64), (74), (153), (157), (158), (162),
% 197.19/32.25  | | | | | |            (167), (168), (169), (172), (173), (174), (175), (178),
% 197.19/32.25  | | | | | |            (179), (180), (182), (183), (184), (185), (187), (270),
% 197.19/32.25  | | | | | |            (274), (276), (277), (280), (281), (282), (283), (284),
% 197.19/32.25  | | | | | |            (285), (303), (305), (306), (307), (308), (309), (312),
% 197.19/32.25  | | | | | |            (313), (315), (318), (319), (321), (322), (323), (324),
% 197.19/32.25  | | | | | |            (325), (329), (331), (332), (333), (335), (351), (352),
% 197.19/32.25  | | | | | |            (366), (367), (372), (375), (387), (388), (393), (394),
% 197.19/32.25  | | | | | |            (405), (411), (415), (421), (483), (538), (539), (540),
% 197.19/32.25  | | | | | |            (541), (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.25  | | | | | |            (549), (551), (553), (555), (557), (559), (561), (562),
% 197.19/32.25  | | | | | |            (563), (564), (566), (567), (568), (569), (570), (571),
% 197.19/32.25  | | | | | |            (572), (573), (574), (575), (576), (577), (578), (580),
% 197.19/32.25  | | | | | |            (582), (586), (587), (588), (589), (590), (591), (592),
% 197.19/32.25  | | | | | |            (593), (594), (595), (596), (598), (602), (603), (604),
% 197.19/32.25  | | | | | |            (605), (606), (607), (608), (609), (610), (611), (613),
% 197.19/32.25  | | | | | |            (690), (761), (763), (771), (7443), (7445), (7449),
% 197.19/32.25  | | | | | |            (7451), (7453), (7457), (7458), (7459), (7460), (7462),
% 197.19/32.25  | | | | | |            (9002), (9004), (9005), (function-axioms) are
% 197.19/32.25  | | | | | |            inconsistent by sub-proof #109.
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | End of split
% 197.19/32.25  | | | | | 
% 197.19/32.25  | | | | End of split
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | Case 2:
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | |   (9006)  all_8_0 = e2
% 197.19/32.25  | | | |   (9007)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | | COMBINE_EQS: (764), (9006) imply:
% 197.19/32.25  | | | |   (9008)  all_6_0 = e2
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | | SIMP: (9008) implies:
% 197.19/32.25  | | | |   (9009)  all_6_0 = e2
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | | COMBINE_EQS: (727), (9009) imply:
% 197.19/32.25  | | | |   (9010)  all_44_0 = e2
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | | REDUCE: (42), (9009) imply:
% 197.19/32.25  | | | |   (9011)  op(e3, all_6_1) = e2
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | | BETA: splitting (54) gives:
% 197.19/32.25  | | | | 
% 197.19/32.25  | | | | Case 1:
% 197.19/32.25  | | | | | 
% 197.19/32.25  | | | | |   (9012)   ~ (all_10_0 = e3)
% 197.19/32.25  | | | | | 
% 197.19/32.25  | | | | | BETA: splitting (64) gives:
% 197.19/32.25  | | | | | 
% 197.19/32.25  | | | | | Case 1:
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | |   (9013)   ~ (all_14_0 = e2)
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | | BETA: splitting (69) gives:
% 197.19/32.25  | | | | | | 
% 197.19/32.25  | | | | | | Case 1:
% 197.19/32.25  | | | | | | | 
% 197.19/32.25  | | | | | | |   (9014)   ~ (all_16_0 = e2)
% 197.19/32.25  | | | | | | | 
% 197.19/32.25  | | | | | | | REDUCE: (760), (9014) imply:
% 197.19/32.25  | | | | | | |   (9015)   ~ (all_10_0 = e2)
% 197.19/32.25  | | | | | | | 
% 197.19/32.25  | | | | | | | BETA: splitting (74) gives:
% 197.19/32.25  | | | | | | | 
% 197.19/32.25  | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | |   (9016)   ~ (all_18_0 = e3)
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | | REDUCE: (761), (9016) imply:
% 197.19/32.25  | | | | | | | |   (9017)   ~ (all_14_0 = e3)
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | | BETA: splitting (89) gives:
% 197.19/32.25  | | | | | | | | 
% 197.19/32.25  | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | |   (9018)   ~ (all_24_0 = e1)
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | REDUCE: (711), (9018) imply:
% 197.19/32.25  | | | | | | | | |   (9019)   ~ (all_14_0 = e1)
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | BETA: splitting (99) gives:
% 197.19/32.25  | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | |   (9020)   ~ (all_28_0 = e3)
% 197.19/32.25  | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | REDUCE: (754), (9020) imply:
% 197.19/32.25  | | | | | | | | | |   (9021)   ~ (all_4_0 = e3)
% 197.19/32.25  | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | BETA: splitting (104) gives:
% 197.19/32.25  | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | |   (9022)   ~ (all_30_1 = e3)
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | REDUCE: (670), (9022) imply:
% 197.19/32.25  | | | | | | | | | | |   (9023)   ~ (all_10_1 = e3)
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | BETA: splitting (129) gives:
% 197.19/32.25  | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | |   (9024)   ~ (all_40_1 = e2)
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | REDUCE: (687), (9024) imply:
% 197.19/32.25  | | | | | | | | | | | |   (9025)   ~ (all_10_1 = e2)
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.25  | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | |   (9026)   ~ (all_44_0 = e2)
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | REDUCE: (9010), (9026) imply:
% 197.19/32.25  | | | | | | | | | | | | |   (9027)  $false
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | CLOSE: (9027) is inconsistent.
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | Case 2:
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | |   (9028)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.25  | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | Case 1:
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | |   (9029)  all_58_15 = e0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | COMBINE_EQS: (541), (9029) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9030)  all_14_2 = e0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (573), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9031)   ~ (all_52_7 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (591), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9032)   ~ (all_52_15 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (603), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9033)   ~ (all_52_23 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (606), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9034)   ~ (all_52_25 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (609), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9035)   ~ (all_52_29 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (613), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9036)  op(e0, e0) = all_52_30
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (63), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9037)  op(e0, e0) = all_14_1
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (61), (9030) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9038)  op(e0, e0) = e0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.19/32.25  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9036), (9037)
% 197.19/32.25  | | | | | | | | | | | | | |              gives:
% 197.19/32.25  | | | | | | | | | | | | | |   (9039)  all_52_30 = all_14_1
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.19/32.25  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9036), (9038)
% 197.19/32.25  | | | | | | | | | | | | | |              gives:
% 197.19/32.25  | | | | | | | | | | | | | |   (9040)  all_52_30 = e0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | COMBINE_EQS: (9039), (9040) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9041)  all_14_1 = e0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (62), (9041) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9042)  op(e0, e0) = all_14_0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.19/32.25  | | | | | | | | | | | | | |              e0, e0, simplifying with (9038), (9042) gives:
% 197.19/32.25  | | | | | | | | | | | | | |   (9043)  all_14_0 = e0
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (9017), (9043) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9044)   ~ (e3 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (9013), (9043) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9045)   ~ (e2 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | REDUCE: (9019), (9043) imply:
% 197.19/32.25  | | | | | | | | | | | | | |   (9046)   ~ (e1 = e0)
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.19/32.25  | | | | | | | | | | | | | | 
% 197.19/32.25  | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | |   (9047)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.26  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.19/32.26  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | BETA: splitting (9047) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9048)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.26  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (9011), (9048), (function-axioms) are inconsistent
% 197.19/32.26  | | | | | | | | | | | | | | | |            by sub-proof #501.
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9049)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.19/32.26  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | ALPHA: (9049) implies:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9050)  all_52_14 = e0
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9051)  all_52_12 = e1
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9052)  all_52_10 = e2
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9053)  all_52_8 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (182), (9053) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9054)  op(all_52_9, all_52_9) = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (180), (9051) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9055)  op(all_52_13, all_52_13) = e1
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (179), (9050) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9056)  op(all_52_15, all_52_15) = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (611), (9052) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9057)  op(all_4_2, all_4_2) = e2
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9058)  all_56_14 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (51), (53), (156), (272), (273), (304),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (305), (343), (346), (351), (431), (543), (571),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (572), (582), (590), (9023), (9031), (9032),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (9038), (9056), (9057), (9058), (function-axioms)
% 197.19/32.26  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #100.
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9059)   ~ (all_56_14 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (343), (9059) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9060)   ~ (all_52_23 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (43), (51), (53),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (174),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (178), (183), (184), (271), (273), (274), (277),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (281), (283), (306), (309), (313), (317), (319),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (321), (325), (326), (333), (343), (351), (352),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (366), (367), (372), (387), (393), (405), (411),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (415), (431), (521), (528), (542), (543), (544),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (571), (572), (574), (577), (580), (582), (590),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (607),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (610), (612), (684), (688), (7443), (7445),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (7449), (7451), (7457), (9007), (9011), (9021),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (9028), (9029), (9031), (9032), (9033), (9034),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (9054), (9055), (9056), (9057), (9060),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.26  | | | | | | | | | | | | | | | | |            #91.
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | |   (9061)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.19/32.26  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.19/32.26  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | BETA: splitting (9061) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9062)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.19/32.26  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | ALPHA: (9062) implies:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9063)  all_52_22 = e0
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9064)  all_52_20 = e1
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9065)  all_52_16 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (178), (9065) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9066)  op(all_52_17, all_52_17) = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (175), (9063) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9067)  op(all_52_23, all_52_23) = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REDUCE: (612), (9064) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9068)  op(all_10_2, all_10_2) = e1
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9069)  all_56_14 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (9069) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9070)  all_52_23 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | SIMP: (9070) implies:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9071)  all_52_23 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (9071) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9072)  all_58_14 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (572), (9071) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9073)   ~ (all_52_7 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (590), (9071) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9074)   ~ (all_52_15 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (594), (9071) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9075)   ~ (all_52_17 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (600), (9071) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9076)   ~ (all_10_2 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | SIMP: (9076) implies:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9077)   ~ (all_10_2 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (9067), (9071) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9078)  op(e3, e3) = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (41), (43), (51), (158), (169), (179),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (272), (273), (283), (304), (346), (351), (415),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (431), (521), (541), (543), (555), (559), (571),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (577), (613), (684), (9007), (9011), (9066),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (9072), (9073), (9074), (9075), (9077), (9078),
% 197.19/32.26  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.26  | | | | | | | | | | | | | | | | |            #90.
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9079)   ~ (all_56_14 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | REDUCE: (343), (9079) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | |   (9080)   ~ (all_52_23 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | |   (9081)  all_58_4 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9081) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | | |   (9082)  all_52_17 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | SIMP: (9082) implies:
% 197.19/32.26  | | | | | | | | | | | | | | | | | |   (9083)  all_52_17 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (559), (9066), (9083), (function-axioms) are
% 197.19/32.26  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1280.
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | |   (9084)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | BETA: splitting (9084) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | |   (9085)  all_58_5 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (9021), (9085) are inconsistent by
% 197.19/32.26  | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | |   (9086)  all_58_8 = e3 | all_58_14 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (9086) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9087)  all_58_8 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (9087) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9088)  all_10_2 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (9088) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9089)   ~ (all_52_17 = e3)
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (9068), (9088) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9090)  op(e3, e3) = e1
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (9088) imply:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9091)  op(e3, e1) = all_10_1
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (9091)
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9092)  all_52_17 = all_10_1
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (41), (9090) gives:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9093)  all_6_2 = e1
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (415), (559), (9025), (9038), (9066),
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |            (9089), (9092), (9093), (function-axioms) are
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #482.
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |   (9094)  all_58_14 = e3
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (9080), (9094) are inconsistent by
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | |   (9095)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.19/32.26  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (608), (609), (610), (688), (9011), (9028),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (9029), (9031), (9032), (9033), (9034), (9035),
% 197.19/32.26  | | | | | | | | | | | | | | | |            (9095), (function-axioms) are inconsistent by
% 197.19/32.26  | | | | | | | | | | | | | | | |            sub-proof #418.
% 197.19/32.26  | | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | |   (9096)   ~ (all_58_15 = e0)
% 197.19/32.26  | | | | | | | | | | | | | |   (9097)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.26  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.26  | | | | | | | | | | | | | |             e0)
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.26  | | | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.19/32.26  | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.19/32.26  | | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.19/32.26  | | | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (276),
% 197.19/32.26  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.26  | | | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.19/32.26  | | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.19/32.26  | | | | | | | | | | | | | |            (327), (332), (333), (343), (346), (351), (352),
% 197.19/32.26  | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.26  | | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.19/32.26  | | | | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 197.19/32.26  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.26  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.19/32.26  | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 197.19/32.26  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.19/32.26  | | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (588), (589),
% 197.19/32.26  | | | | | | | | | | | | | |            (590), (592), (593), (594), (595), (596), (598),
% 197.19/32.26  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.26  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.19/32.26  | | | | | | | | | | | | | |            (688), (7443), (7445), (7449), (7450), (7451),
% 197.19/32.26  | | | | | | | | | | | | | |            (9007), (9011), (9021), (9025), (9028), (9096),
% 197.19/32.26  | | | | | | | | | | | | | |            (9097), (function-axioms) are inconsistent by
% 197.19/32.26  | | | | | | | | | | | | | |            sub-proof #80.
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | End of split
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | |   (9098)  all_40_1 = e2
% 197.19/32.26  | | | | | | | | | | | |   (9099)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | COMBINE_EQS: (687), (9098) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9100)  all_10_1 = e2
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | SIMP: (9100) implies:
% 197.19/32.26  | | | | | | | | | | | |   (9101)  all_10_1 = e2
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (9023), (9101) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9102)   ~ (e3 = e2)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (53), (9101) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9103)  op(all_10_2, e1) = e2
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (52), (9101) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9104)  op(e1, e2) = all_10_0
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.19/32.26  | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (9104)
% 197.19/32.26  | | | | | | | | | | | |              gives:
% 197.19/32.26  | | | | | | | | | | | |   (9105)  all_52_13 = all_10_0
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | COMBINE_EQS: (421), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9106)  all_56_9 = all_10_0
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | COMBINE_EQS: (366), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9107)  all_58_7 = all_10_0
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (568), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9108)   ~ (all_52_5 = all_10_0)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (575), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9109)   ~ (all_52_9 = all_10_0)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (587), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9110)   ~ (all_52_15 = all_10_0)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | SIMP: (9110) implies:
% 197.19/32.26  | | | | | | | | | | | |   (9111)   ~ (all_52_15 = all_10_0)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (589), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9112)   ~ (all_52_29 = all_10_0)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | SIMP: (9112) implies:
% 197.19/32.26  | | | | | | | | | | | |   (9113)   ~ (all_52_29 = all_10_0)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (588), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9114)   ~ (all_10_0 = all_10_2)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (580), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9115)   ~ (all_10_0 = all_4_2)
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | REDUCE: (180), (9105) imply:
% 197.19/32.26  | | | | | | | | | | | |   (9116)  op(all_10_0, all_10_0) = all_52_12
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.26  | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | |   (9117)   ~ (all_44_0 = e2)
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | REDUCE: (9010), (9117) imply:
% 197.19/32.26  | | | | | | | | | | | | |   (9118)  $false
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | CLOSE: (9118) is inconsistent.
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | Case 2:
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | |   (9119)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.26  | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | Case 1:
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | |   (9120)  all_58_15 = e0
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | COMBINE_EQS: (541), (9120) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9121)  all_14_2 = e0
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (573), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9122)   ~ (all_52_7 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (591), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9123)   ~ (all_52_15 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (603), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9124)   ~ (all_52_23 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (606), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9125)   ~ (all_52_25 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (609), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9126)   ~ (all_52_29 = e0)
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (613), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9127)  op(e0, e0) = all_52_30
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (63), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9128)  op(e0, e0) = all_14_1
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | REDUCE: (61), (9121) imply:
% 197.19/32.26  | | | | | | | | | | | | | |   (9129)  op(e0, e0) = e0
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.19/32.26  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9127), (9128)
% 197.19/32.26  | | | | | | | | | | | | | |              gives:
% 197.19/32.26  | | | | | | | | | | | | | |   (9130)  all_52_30 = all_14_1
% 197.19/32.26  | | | | | | | | | | | | | | 
% 197.19/32.26  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.19/32.26  | | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9127), (9129)
% 197.19/32.26  | | | | | | | | | | | | | |              gives:
% 197.19/32.27  | | | | | | | | | | | | | |   (9131)  all_52_30 = e0
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | COMBINE_EQS: (9130), (9131) imply:
% 197.19/32.27  | | | | | | | | | | | | | |   (9132)  all_14_1 = e0
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | SIMP: (9132) implies:
% 197.19/32.27  | | | | | | | | | | | | | |   (9133)  all_14_1 = e0
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | REDUCE: (62), (9133) imply:
% 197.19/32.27  | | | | | | | | | | | | | |   (9134)  op(e0, e0) = all_14_0
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.19/32.27  | | | | | | | | | | | | | |              e0, e0, simplifying with (9129), (9134) gives:
% 197.19/32.27  | | | | | | | | | | | | | |   (9135)  all_14_0 = e0
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | REDUCE: (9017), (9135) imply:
% 197.19/32.27  | | | | | | | | | | | | | |   (9136)   ~ (e3 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | REDUCE: (9013), (9135) imply:
% 197.19/32.27  | | | | | | | | | | | | | |   (9137)   ~ (e2 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | REDUCE: (9019), (9135) imply:
% 197.19/32.27  | | | | | | | | | | | | | |   (9138)   ~ (e1 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 197.19/32.27  | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | |   (9139)  all_56_9 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | REF_CLOSE: (9012), (9106), (9139) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | |            sub-proof #1006.
% 197.19/32.27  | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | |   (9140)   ~ (all_56_9 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | |   (9141)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | |   (9142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.27  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.19/32.27  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | BETA: splitting (9142) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9143)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.27  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (183),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (184), (185), (273), (274), (277), (278), (282),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (310), (311),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (312), (317), (321), (325), (332), (351), (352),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (427), (431), (526), (542), (543), (544), (545),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (561), (564), (566), (567), (569), (570), (571),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (573), (586), (590), (596), (598), (604), (605),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (607), (610), (611), (612), (767), (9012), (9015),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (9099), (9103), (9106), (9107), (9108), (9113),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (9115), (9120), (9122), (9125), (9126), (9129),
% 197.19/32.27  | | | | | | | | | | | | | | | | |            (9141), (9143), (function-axioms) are inconsistent
% 197.19/32.27  | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9144)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.19/32.27  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | ALPHA: (9144) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9145)  all_52_14 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9146)  all_52_12 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9147)  all_52_10 = e2
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9148)  all_52_8 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REDUCE: (182), (9148) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9149)  op(all_52_9, all_52_9) = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REDUCE: (179), (9145) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9150)  op(all_52_15, all_52_15) = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REDUCE: (9116), (9146) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9151)  op(all_10_0, all_10_0) = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REDUCE: (611), (9147) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9152)  op(all_4_2, all_4_2) = e2
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9153)  all_56_13 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (9153) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9154)  all_52_15 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | SIMP: (9154) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9155)  all_52_15 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (571), (9155) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9156)   ~ (all_52_7 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (590), (9155) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9157)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | SIMP: (9157) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9158)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (41), (43), (158), (169), (183), (271),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (273), (306), (343), (351), (431), (521), (542),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (543), (555), (571), (572), (582), (590), (684),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (9007), (9011), (9120), (9124), (9149), (9150),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (9156), (9158), (function-axioms) are inconsistent
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            by sub-proof #79.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9159)   ~ (all_56_13 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9160)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (346), (9159) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9161)   ~ (all_52_15 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9162)  all_58_12 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (9162) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9163)  all_52_7 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | SIMP: (9163) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9164)  all_52_7 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (9164) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9165)   ~ (all_52_3 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REDUCE: (567), (9164) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9166)   ~ (all_52_5 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REDUCE: (572), (9164) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9167)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | SIMP: (9167) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9168)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (9164) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9169)  op(e3, e3) = all_52_6
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (9169)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9170)  all_52_6 = all_6_2
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9171)  all_58_4 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9171) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9172)  all_52_17 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | SIMP: (9172) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9173)  all_52_17 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (7451), (9173) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9174)   ~ (all_4_0 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | |   (9175)  all_58_6 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (9166), (9175) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | |   (9176)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9176) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9177)  all_58_7 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9107), (9177) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9178)  all_10_0 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9012), (9178) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9179)  $false
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9179) is inconsistent.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9180)  all_58_8 = e3 | all_58_11 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9180) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9181)  all_58_8 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (526), (546), (767), (9015), (9099), (9106),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |            (9114), (9141), (9151), (9181), (function-axioms)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #78.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9182)  all_58_11 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (9182) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9183)  all_52_29 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9183) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9184)  all_52_29 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (9184) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9185)   ~ (all_52_27 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | |   (9186)  all_58_2 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (9165), (9186) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1369.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | |   (9187)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9187) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9188)  all_58_3 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (9188) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9189)  all_4_2 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (9189) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9190)  op(e2, e2) = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7443) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9191)   ~ (all_4_2 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (9190), (9191), (function-axioms) are
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #211.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9192)   ~ (all_4_0 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9193)  all_58_4 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9171), (9193) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9194)  e3 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (9194) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9195)  $false
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9195) is inconsistent.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9196)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9196) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9197)  all_58_5 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (9192), (9197) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #209.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9198)  all_58_8 = e0 | all_58_14 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9198) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9199)  all_58_8 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (9199) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9200)  all_10_2 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9114), (9200) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9201)   ~ (all_10_0 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (9015), (9106), (9114), (9141), (9151),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9201), (function-axioms) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9202)  all_58_14 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (9124), (9202) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1019.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9203)  all_58_5 = e3 | all_58_10 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (372), (7449), (9021), (9185), (9203) are
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #214.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9204)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (53), (158), (166),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (174), (183), (271), (273),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (281), (283), (306), (309), (319), (321), (326),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (333), (343), (351), (372), (387), (393), (405),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (411), (415), (431), (521), (542), (543), (545),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (546), (548), (549), (551), (555), (557), (559),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (561), (563), (564), (571), (572), (574), (577),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (582), (590), (593), (600), (604), (610), (612),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (684), (7445), (7449), (7457), (9007), (9011),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (9021), (9120), (9123), (9124), (9125), (9149),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            (9150), (9152), (9168), (9204), (function-axioms)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #92.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9205)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (51), (53), (156), (273), (304),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |            (305), (346), (351), (431), (542), (543), (571),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |            (572), (582), (9023), (9120), (9122), (9123),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |            (9129), (9150), (9152), (9160), (9161), (9205),
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |            #1288.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | End of split
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | |   (9206)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.19/32.27  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | BETA: splitting (9206) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9207)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.19/32.27  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | ALPHA: (9207) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9208)  all_52_22 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9209)  all_52_16 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REDUCE: (178), (9209) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9210)  op(all_52_17, all_52_17) = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | REDUCE: (175), (9208) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | |   (9211)  op(all_52_23, all_52_23) = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9212)  all_56_13 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (9212) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9213)  all_52_15 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | SIMP: (9213) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9214)  all_52_15 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (590), (9214) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9215)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | SIMP: (9215) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9216)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (582), (9214) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9217)   ~ (all_4_2 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | SIMP: (9217) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9218)   ~ (all_4_2 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (179), (9214) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9219)  op(e3, e3) = all_52_14
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.27  | | | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (9219)
% 197.19/32.27  | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9220)  all_52_14 = all_6_2
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (168), (317), (393), (526), (542),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (546), (559), (767), (7449), (9015), (9021),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (9099), (9103), (9106), (9141), (9210), (9216),
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            (9218), (function-axioms) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | |            sub-proof #181.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9221)   ~ (all_56_13 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9222)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | REDUCE: (346), (9221) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | |   (9223)   ~ (all_52_15 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9224)  all_58_12 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (9224) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9225)  all_52_7 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | SIMP: (9225) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9226)  all_52_7 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REDUCE: (572), (9226) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9227)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | SIMP: (9227) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9228)   ~ (all_52_23 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (9226) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9229)  op(e3, e3) = all_52_6
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (9229)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | |   (9230)  all_52_6 = all_6_2
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9231)  all_58_4 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9231) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9232)  all_52_17 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | SIMP: (9232) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9233)  all_52_17 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (559), (9210), (9233), (function-axioms) are
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1280.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | |   (9234)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9234) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | |   (9235)  all_58_5 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (9021), (9235) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | |   (9236)  all_58_8 = e3 | all_58_14 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9236) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9237)  all_58_8 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (9237) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9238)  all_10_2 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (9238) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9239)  all_40_2 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (9238) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | |   (9240)  op(e1, e1) = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9099) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9241)   ~ (all_40_2 = e3)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9239), (9241) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9242)  $false
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9242) is inconsistent.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9243)   ~ (all_40_0 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (9243) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | |   (9244)   ~ (all_10_0 = e0)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9141) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | |   (9245)  all_56_9 = e2
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9015), (9106), (9245) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #991.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | |   (9246)  all_56_9 = e1 | all_56_9 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9246) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9247)  all_56_9 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9106), (9247) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9248)  all_10_0 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9248) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9249)  all_10_0 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9111), (9249) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9250)   ~ (all_52_15 = e1)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9012), (9249) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9251)   ~ (e3 = e1)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9116), (9249) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (9252)  op(e1, e1) = all_52_12
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9253)  all_58_12 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9224), (9253) are inconsistent by sub-proof
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            #894.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9254)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9254) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9255)  all_58_13 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (9250), (9255) are inconsistent by
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1133.
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9256)  all_58_14 = e1 | all_58_15 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9256) gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9257)  all_58_14 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (9257) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9258)  all_52_23 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9258) implies:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9259)  all_52_23 = e1
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9211), (9259) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9260)  op(e1, e1) = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e1, e1, simplifying with (9240), (9252)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9261)  all_52_12 = e3
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e1, e1, simplifying with (9252), (9260)
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9262)  all_52_12 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9261), (9262) imply:
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9263)  e3 = e0
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (9263) imply:
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9264)  $false
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9264) is inconsistent.
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9265)  all_58_15 = e1
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9120), (9265) are inconsistent by sub-proof
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1207.
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (9266)  all_56_9 = e0
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9106), (9244), (9266) are inconsistent by
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #989.
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | |   (9267)  all_58_14 = e3
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (9228), (9267) are inconsistent by
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |   (9268)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (41), (43), (51), (158), (169),
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |            (179), (273), (283), (304), (346), (351), (415),
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |            (431), (521), (541), (542), (543), (555), (559),
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |            (571), (572), (577), (594), (600), (613), (684),
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |            (9007), (9011), (9120), (9210), (9211), (9222),
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |            (9223), (9268), (function-axioms) are inconsistent
% 197.19/32.28  | | | | | | | | | | | | | | | | | | |            by sub-proof #478.
% 197.19/32.28  | | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | |   (9269)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.19/32.28  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.19/32.28  | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (608), (609), (610), (688), (9011), (9119),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (9120), (9122), (9123), (9124), (9125), (9126),
% 197.19/32.28  | | | | | | | | | | | | | | | | |            (9269), (function-axioms) are inconsistent by
% 197.19/32.28  | | | | | | | | | | | | | | | | |            sub-proof #418.
% 197.19/32.28  | | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | |   (9270)   ~ (all_58_15 = e0)
% 197.19/32.28  | | | | | | | | | | | | | |   (9271)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.28  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.28  | | | | | | | | | | | | | |             e0)
% 197.19/32.28  | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | ALPHA: (9271) implies:
% 197.19/32.28  | | | | | | | | | | | | | |   (9272)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.19/32.28  | | | | | | | | | | | | | |   (9273)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.19/32.28  | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | REDUCE: (541), (9270) imply:
% 197.19/32.28  | | | | | | | | | | | | | |   (9274)   ~ (all_14_2 = e0)
% 197.19/32.28  | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (43),
% 197.19/32.28  | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.19/32.28  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.19/32.28  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.19/32.28  | | | | | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (276),
% 197.19/32.28  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.28  | | | | | | | | | | | | | |            (284), (285), (304), (306), (307), (309), (311),
% 197.19/32.28  | | | | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.19/32.28  | | | | | | | | | | | | | |            (326), (327), (332), (333), (343), (351), (352),
% 197.19/32.28  | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.28  | | | | | | | | | | | | | |            (394), (405), (411), (415), (417), (427), (431),
% 197.19/32.28  | | | | | | | | | | | | | |            (521), (526), (528), (538), (539), (540), (541),
% 197.19/32.28  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.28  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.19/32.28  | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.19/32.28  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.19/32.28  | | | | | | | | | | | | | |            (578), (582), (584), (586), (588), (589), (590),
% 197.19/32.28  | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (598),
% 197.19/32.28  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.28  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.19/32.28  | | | | | | | | | | | | | |            (688), (767), (7443), (7445), (7449), (7450),
% 197.19/32.28  | | | | | | | | | | | | | |            (9007), (9011), (9012), (9015), (9021), (9099),
% 197.19/32.28  | | | | | | | | | | | | | |            (9103), (9106), (9107), (9108), (9109), (9111),
% 197.19/32.28  | | | | | | | | | | | | | |            (9115), (9119), (9272), (9273), (9274),
% 197.19/32.28  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.28  | | | | | | | | | | | | | |            #72.
% 197.19/32.28  | | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | |   (9275)  all_30_1 = e3
% 197.19/32.28  | | | | | | | | | | |   (9276)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | COMBINE_EQS: (670), (9275) imply:
% 197.19/32.28  | | | | | | | | | | |   (9277)  all_10_1 = e3
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (53), (9277) imply:
% 197.19/32.28  | | | | | | | | | | |   (9278)  op(all_10_2, e1) = e3
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (52), (9277) imply:
% 197.19/32.28  | | | | | | | | | | |   (9279)  op(e1, e3) = all_10_0
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.19/32.28  | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (9279)
% 197.19/32.28  | | | | | | | | | | |              gives:
% 197.19/32.28  | | | | | | | | | | |   (9280)  all_52_5 = all_10_0
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | COMBINE_EQS: (367), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9281)  all_56_8 = all_10_0
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | COMBINE_EQS: (547), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9282)  all_58_6 = all_10_0
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (562), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9283)   ~ (all_52_3 = all_10_0)
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (567), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9284)   ~ (all_52_7 = all_10_0)
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | SIMP: (9284) implies:
% 197.19/32.28  | | | | | | | | | | |   (9285)   ~ (all_52_7 = all_10_0)
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (569), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9286)   ~ (all_10_0 = all_10_2)
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (553), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9287)   ~ (all_10_0 = all_6_2)
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | REDUCE: (184), (9280) imply:
% 197.19/32.28  | | | | | | | | | | |   (9288)  op(all_10_0, all_10_0) = all_52_4
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | Case 1:
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | |   (9289)   ~ (all_44_0 = e2)
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | REDUCE: (9010), (9289) imply:
% 197.19/32.28  | | | | | | | | | | | |   (9290)  $false
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | CLOSE: (9290) is inconsistent.
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | |   (9291)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | Case 1:
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | |   (9292)  all_58_15 = e0
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | COMBINE_EQS: (541), (9292) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9293)  all_14_2 = e0
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (573), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9294)   ~ (all_52_7 = e0)
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (591), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9295)   ~ (all_52_15 = e0)
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (603), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9296)   ~ (all_52_23 = e0)
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (606), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9297)   ~ (all_52_25 = e0)
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (613), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9298)  op(e0, e0) = all_52_30
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (63), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9299)  op(e0, e0) = all_14_1
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REDUCE: (61), (9293) imply:
% 197.19/32.28  | | | | | | | | | | | | |   (9300)  op(e0, e0) = e0
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (43), (51), (61), (62),
% 197.19/32.28  | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (172),
% 197.19/32.28  | | | | | | | | | | | | |            (173), (174), (175), (177), (178), (179), (182),
% 197.19/32.28  | | | | | | | | | | | | |            (183), (185), (187), (271), (272), (273), (275),
% 197.19/32.28  | | | | | | | | | | | | |            (277), (279), (281), (282), (283), (284), (285),
% 197.19/32.28  | | | | | | | | | | | | |            (304), (305), (306), (307), (309), (313), (314),
% 197.19/32.28  | | | | | | | | | | | | |            (317), (319), (321), (326), (327), (328), (330),
% 197.19/32.28  | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (361), (366),
% 197.19/32.28  | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (394),
% 197.19/32.28  | | | | | | | | | | | | |            (405), (411), (415), (417), (431), (459), (521),
% 197.19/32.28  | | | | | | | | | | | | |            (528), (540), (541), (542), (543), (544), (545),
% 197.19/32.28  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.19/32.28  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (567),
% 197.19/32.28  | | | | | | | | | | | | |            (570), (571), (572), (576), (577), (578), (582),
% 197.19/32.28  | | | | | | | | | | | | |            (584), (587), (590), (592), (593), (594), (595),
% 197.19/32.28  | | | | | | | | | | | | |            (597), (600), (604), (605), (608), (609), (610),
% 197.19/32.28  | | | | | | | | | | | | |            (611), (613), (684), (688), (750), (9007), (9011),
% 197.19/32.28  | | | | | | | | | | | | |            (9012), (9013), (9015), (9017), (9019), (9276),
% 197.19/32.28  | | | | | | | | | | | | |            (9278), (9279), (9281), (9282), (9283), (9285),
% 197.19/32.28  | | | | | | | | | | | | |            (9286), (9287), (9288), (9291), (9292), (9294),
% 197.19/32.28  | | | | | | | | | | | | |            (9295), (9296), (9297), (9298), (9299), (9300),
% 197.19/32.28  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.28  | | | | | | | | | | | | |            #374.
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | |   (9301)   ~ (all_58_15 = e0)
% 197.19/32.28  | | | | | | | | | | | | |   (9302)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.28  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.28  | | | | | | | | | | | | |             e0)
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.28  | | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.19/32.28  | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.19/32.28  | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.19/32.28  | | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (275),
% 197.19/32.28  | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 197.19/32.28  | | | | | | | | | | | | |            (283), (285), (304), (306), (307), (309), (311),
% 197.19/32.28  | | | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.19/32.28  | | | | | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.19/32.28  | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 197.19/32.28  | | | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.19/32.28  | | | | | | | | | | | | |            (427), (431), (459), (521), (528), (538), (539),
% 197.19/32.28  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.19/32.28  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.19/32.28  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 197.19/32.28  | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.19/32.28  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.19/32.28  | | | | | | | | | | | | |            (584), (586), (588), (589), (590), (591), (592),
% 197.19/32.28  | | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.19/32.28  | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.19/32.28  | | | | | | | | | | | | |            (610), (611), (612), (613), (684), (688), (750),
% 197.19/32.28  | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (9007), (9011),
% 197.19/32.28  | | | | | | | | | | | | |            (9012), (9015), (9021), (9276), (9278), (9281),
% 197.19/32.28  | | | | | | | | | | | | |            (9282), (9283), (9285), (9286), (9287), (9288),
% 197.19/32.28  | | | | | | | | | | | | |            (9291), (9301), (9302), (function-axioms) are
% 197.19/32.28  | | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 197.19/32.28  | | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | |   (9303)  all_28_0 = e3
% 197.19/32.28  | | | | | | | | | |   (9304)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.19/32.28  | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | COMBINE_EQS: (754), (9303) imply:
% 197.19/32.28  | | | | | | | | | |   (9305)  all_4_0 = e3
% 197.19/32.28  | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | SIMP: (9305) implies:
% 197.19/32.28  | | | | | | | | | |   (9306)  all_4_0 = e3
% 197.19/32.28  | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.19/32.28  | | | | | | | | | |            (51), (53), (61), (62), (63), (139), (158), (161),
% 197.19/32.28  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.19/32.28  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.19/32.28  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 197.19/32.28  | | | | | | | | | |            (273), (274), (276), (277), (278), (279), (280),
% 197.19/32.28  | | | | | | | | | |            (281), (282), (283), (285), (303), (306), (307),
% 197.19/32.28  | | | | | | | | | |            (308), (309), (310), (311), (313), (315), (316),
% 197.19/32.28  | | | | | | | | | |            (317), (318), (319), (320), (321), (324), (325),
% 197.19/32.28  | | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.19/32.28  | | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.19/32.28  | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.19/32.28  | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.19/32.28  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.19/32.28  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.19/32.28  | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 197.19/32.28  | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.19/32.28  | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 197.19/32.28  | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 197.19/32.28  | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.19/32.28  | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.19/32.28  | | | | | | | | | |            (610), (612), (613), (684), (688), (7444), (7445),
% 197.19/32.28  | | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 197.19/32.28  | | | | | | | | | |            (7459), (9007), (9010), (9011), (9013), (9017),
% 197.19/32.28  | | | | | | | | | |            (9019), (9304), (9306), (function-axioms) are
% 197.19/32.28  | | | | | | | | | |            inconsistent by sub-proof #63.
% 197.19/32.28  | | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | End of split
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | Case 2:
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | |   (9307)  all_24_0 = e1
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | COMBINE_EQS: (711), (9307) imply:
% 197.19/32.28  | | | | | | | | |   (9308)  all_14_0 = e1
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | SIMP: (9308) implies:
% 197.19/32.28  | | | | | | | | |   (9309)  all_14_0 = e1
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | REDUCE: (9017), (9309) imply:
% 197.19/32.28  | | | | | | | | |   (9310)   ~ (e3 = e1)
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | REDUCE: (9013), (9309) imply:
% 197.19/32.28  | | | | | | | | |   (9311)   ~ (e2 = e1)
% 197.19/32.28  | | | | | | | | | 
% 197.19/32.28  | | | | | | | | | REDUCE: (62), (9309) imply:
% 197.19/32.29  | | | | | | | | |   (9312)  op(e0, all_14_1) = e1
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | BETA: splitting (99) gives:
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | |   (9313)   ~ (all_28_0 = e3)
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | REDUCE: (754), (9313) imply:
% 197.19/32.29  | | | | | | | | | |   (9314)   ~ (all_4_0 = e3)
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | BETA: splitting (104) gives:
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | |   (9315)   ~ (all_30_1 = e3)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (670), (9315) imply:
% 197.19/32.29  | | | | | | | | | | |   (9316)   ~ (all_10_1 = e3)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | BETA: splitting (129) gives:
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | |   (9317)   ~ (all_40_1 = e2)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (687), (9317) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9318)   ~ (all_10_1 = e2)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9319)   ~ (all_44_0 = e2)
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | REDUCE: (9010), (9319) imply:
% 197.19/32.29  | | | | | | | | | | | | |   (9320)  $false
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | CLOSE: (9320) is inconsistent.
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9321)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | |   (9322)  all_58_15 = e0
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (9312), (9322),
% 197.19/32.29  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.29  | | | | | | | | | | | | | |            #877.
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | |   (9323)   ~ (all_58_15 = e0)
% 197.19/32.29  | | | | | | | | | | | | | |   (9324)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.29  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.29  | | | | | | | | | | | | | |             e0)
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.29  | | | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.19/32.29  | | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.19/32.29  | | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.19/32.29  | | | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (276),
% 197.19/32.29  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.29  | | | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.19/32.29  | | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.19/32.29  | | | | | | | | | | | | | |            (327), (332), (333), (343), (346), (351), (352),
% 197.19/32.29  | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.29  | | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.19/32.29  | | | | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 197.19/32.29  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.29  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.19/32.29  | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 197.19/32.29  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.19/32.29  | | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (588), (589),
% 197.19/32.29  | | | | | | | | | | | | | |            (590), (592), (593), (594), (595), (596), (598),
% 197.19/32.29  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.29  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.19/32.29  | | | | | | | | | | | | | |            (688), (7443), (7445), (7449), (7450), (7451),
% 197.19/32.29  | | | | | | | | | | | | | |            (9007), (9011), (9314), (9318), (9321), (9323),
% 197.19/32.29  | | | | | | | | | | | | | |            (9324), (function-axioms) are inconsistent by
% 197.19/32.29  | | | | | | | | | | | | | |            sub-proof #80.
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | |   (9325)  all_40_1 = e2
% 197.19/32.29  | | | | | | | | | | | |   (9326)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | COMBINE_EQS: (687), (9325) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9327)  all_10_1 = e2
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | SIMP: (9327) implies:
% 197.19/32.29  | | | | | | | | | | | |   (9328)  all_10_1 = e2
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (9316), (9328) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9329)   ~ (e3 = e2)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (53), (9328) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9330)  op(all_10_2, e1) = e2
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (52), (9328) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9331)  op(e1, e2) = all_10_0
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.19/32.29  | | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (9331)
% 197.19/32.29  | | | | | | | | | | | |              gives:
% 197.19/32.29  | | | | | | | | | | | |   (9332)  all_52_13 = all_10_0
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | COMBINE_EQS: (421), (9332) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9333)  all_56_9 = all_10_0
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | COMBINE_EQS: (366), (9332) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9334)  all_58_7 = all_10_0
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (568), (9332) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9335)   ~ (all_52_5 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (575), (9332) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9336)   ~ (all_52_9 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (587), (9332) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9337)   ~ (all_52_15 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | SIMP: (9337) implies:
% 197.19/32.29  | | | | | | | | | | | |   (9338)   ~ (all_52_15 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (580), (9332) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9339)   ~ (all_10_0 = all_4_2)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9340)   ~ (all_44_0 = e2)
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | REDUCE: (9010), (9340) imply:
% 197.19/32.29  | | | | | | | | | | | | |   (9341)  $false
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | CLOSE: (9341) is inconsistent.
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9342)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | |   (9343)  all_58_15 = e0
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (9312), (9343),
% 197.19/32.29  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.29  | | | | | | | | | | | | | |            #877.
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | |   (9344)   ~ (all_58_15 = e0)
% 197.19/32.29  | | | | | | | | | | | | | |   (9345)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.29  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.29  | | | | | | | | | | | | | |             e0)
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (43),
% 197.19/32.29  | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.19/32.29  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.19/32.29  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.19/32.29  | | | | | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (276),
% 197.19/32.29  | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.29  | | | | | | | | | | | | | |            (284), (285), (304), (306), (307), (309), (311),
% 197.19/32.29  | | | | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.19/32.29  | | | | | | | | | | | | | |            (326), (327), (332), (333), (343), (351), (352),
% 197.19/32.29  | | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.29  | | | | | | | | | | | | | |            (394), (405), (411), (415), (417), (427), (431),
% 197.19/32.29  | | | | | | | | | | | | | |            (521), (526), (528), (538), (539), (540), (541),
% 197.19/32.29  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.29  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.19/32.29  | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.19/32.29  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.19/32.29  | | | | | | | | | | | | | |            (578), (582), (584), (586), (588), (589), (590),
% 197.19/32.29  | | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (598),
% 197.19/32.29  | | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.29  | | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.19/32.29  | | | | | | | | | | | | | |            (688), (767), (7443), (7445), (7449), (7450),
% 197.19/32.29  | | | | | | | | | | | | | |            (9007), (9011), (9012), (9015), (9314), (9326),
% 197.19/32.29  | | | | | | | | | | | | | |            (9330), (9333), (9334), (9335), (9336), (9338),
% 197.19/32.29  | | | | | | | | | | | | | |            (9339), (9342), (9344), (9345), (function-axioms)
% 197.19/32.29  | | | | | | | | | | | | | |            are inconsistent by sub-proof #62.
% 197.19/32.29  | | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | |   (9346)  all_30_1 = e3
% 197.19/32.29  | | | | | | | | | | |   (9347)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | COMBINE_EQS: (670), (9346) imply:
% 197.19/32.29  | | | | | | | | | | |   (9348)  all_10_1 = e3
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | SIMP: (9348) implies:
% 197.19/32.29  | | | | | | | | | | |   (9349)  all_10_1 = e3
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (53), (9349) imply:
% 197.19/32.29  | | | | | | | | | | |   (9350)  op(all_10_2, e1) = e3
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (52), (9349) imply:
% 197.19/32.29  | | | | | | | | | | |   (9351)  op(e1, e3) = all_10_0
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.19/32.29  | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (9351)
% 197.19/32.29  | | | | | | | | | | |              gives:
% 197.19/32.29  | | | | | | | | | | |   (9352)  all_52_5 = all_10_0
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | COMBINE_EQS: (367), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9353)  all_56_8 = all_10_0
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | COMBINE_EQS: (547), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9354)  all_58_6 = all_10_0
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (562), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9355)   ~ (all_52_3 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (567), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9356)   ~ (all_52_7 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | SIMP: (9356) implies:
% 197.19/32.29  | | | | | | | | | | |   (9357)   ~ (all_52_7 = all_10_0)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (569), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9358)   ~ (all_10_0 = all_10_2)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (553), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9359)   ~ (all_10_0 = all_6_2)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (184), (9352) imply:
% 197.19/32.29  | | | | | | | | | | |   (9360)  op(all_10_0, all_10_0) = all_52_4
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | |   (9361)   ~ (all_44_0 = e2)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (9010), (9361) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9362)  $false
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | CLOSE: (9362) is inconsistent.
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | |   (9363)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9364)  all_58_15 = e0
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (9312), (9364),
% 197.19/32.29  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.29  | | | | | | | | | | | | |            #877.
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9365)   ~ (all_58_15 = e0)
% 197.19/32.29  | | | | | | | | | | | | |   (9366)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.29  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.29  | | | | | | | | | | | | |             e0)
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.29  | | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.19/32.29  | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.19/32.29  | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.19/32.29  | | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (275),
% 197.19/32.29  | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 197.19/32.29  | | | | | | | | | | | | |            (283), (285), (304), (306), (307), (309), (311),
% 197.19/32.29  | | | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.19/32.29  | | | | | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.19/32.29  | | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 197.19/32.29  | | | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.19/32.29  | | | | | | | | | | | | |            (427), (431), (459), (521), (528), (538), (539),
% 197.19/32.29  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.19/32.29  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.19/32.29  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 197.19/32.29  | | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.19/32.29  | | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.19/32.29  | | | | | | | | | | | | |            (584), (586), (588), (589), (590), (591), (592),
% 197.19/32.29  | | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.19/32.29  | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.19/32.29  | | | | | | | | | | | | |            (610), (611), (612), (613), (684), (688), (750),
% 197.19/32.29  | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (9007), (9011),
% 197.19/32.29  | | | | | | | | | | | | |            (9012), (9015), (9314), (9347), (9350), (9353),
% 197.19/32.29  | | | | | | | | | | | | |            (9354), (9355), (9357), (9358), (9359), (9360),
% 197.19/32.29  | | | | | | | | | | | | |            (9363), (9365), (9366), (function-axioms) are
% 197.19/32.29  | | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | |   (9367)  all_28_0 = e3
% 197.19/32.29  | | | | | | | | | |   (9368)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.19/32.29  | | | | | | | | | |            (51), (53), (61), (63), (139), (158), (161),
% 197.19/32.29  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.19/32.29  | | | | | | | | | |            (174), (177), (178), (179), (180), (182), (183),
% 197.19/32.29  | | | | | | | | | |            (184), (185), (187), (270), (271), (273), (274),
% 197.19/32.29  | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.29  | | | | | | | | | |            (285), (303), (306), (307), (309), (311), (313),
% 197.19/32.29  | | | | | | | | | |            (315), (316), (317), (318), (319), (320), (321),
% 197.19/32.29  | | | | | | | | | |            (324), (325), (326), (327), (332), (333), (343),
% 197.19/32.29  | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (376),
% 197.19/32.29  | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (417),
% 197.19/32.29  | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.19/32.29  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.19/32.29  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.19/32.29  | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.19/32.29  | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (577),
% 197.19/32.29  | | | | | | | | | |            (578), (580), (582), (584), (586), (589), (590),
% 197.19/32.29  | | | | | | | | | |            (592), (593), (594), (595), (596), (598), (602),
% 197.19/32.29  | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.19/32.29  | | | | | | | | | |            (610), (612), (613), (684), (688), (754), (7444),
% 197.19/32.29  | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7457),
% 197.19/32.29  | | | | | | | | | |            (7458), (7459), (9007), (9010), (9011), (9312),
% 197.19/32.29  | | | | | | | | | |            (9367), (9368), (function-axioms) are inconsistent
% 197.19/32.29  | | | | | | | | | |            by sub-proof #60.
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | End of split
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | |   (9369)  all_18_0 = e3
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | | COMBINE_EQS: (761), (9369) imply:
% 197.19/32.29  | | | | | | | |   (9370)  all_14_0 = e3
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | | SIMP: (9370) implies:
% 197.19/32.29  | | | | | | | |   (9371)  all_14_0 = e3
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | | REDUCE: (62), (9371) imply:
% 197.19/32.29  | | | | | | | |   (9372)  op(e0, all_14_1) = e3
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | | BETA: splitting (99) gives:
% 197.19/32.29  | | | | | | | | 
% 197.19/32.29  | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | |   (9373)   ~ (all_28_0 = e3)
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | REDUCE: (754), (9373) imply:
% 197.19/32.29  | | | | | | | | |   (9374)   ~ (all_4_0 = e3)
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | BETA: splitting (104) gives:
% 197.19/32.29  | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | |   (9375)   ~ (all_30_1 = e3)
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | REDUCE: (670), (9375) imply:
% 197.19/32.29  | | | | | | | | | |   (9376)   ~ (all_10_1 = e3)
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | BETA: splitting (129) gives:
% 197.19/32.29  | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | |   (9377)   ~ (all_40_1 = e2)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | REDUCE: (687), (9377) imply:
% 197.19/32.29  | | | | | | | | | | |   (9378)   ~ (all_10_1 = e2)
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.29  | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | |   (9379)   ~ (all_44_0 = e2)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | REDUCE: (9010), (9379) imply:
% 197.19/32.29  | | | | | | | | | | | |   (9380)  $false
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | CLOSE: (9380) is inconsistent.
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | |   (9381)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.29  | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 1:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9382)  all_58_15 = e0
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (9372), (9382),
% 197.19/32.29  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.29  | | | | | | | | | | | | |            #693.
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | Case 2:
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.29  | | | | | | | | | | | | |   (9383)   ~ (all_58_15 = e0)
% 197.19/32.29  | | | | | | | | | | | | |   (9384)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.29  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.29  | | | | | | | | | | | | |             e0)
% 197.19/32.29  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.30  | | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.19/32.30  | | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.19/32.30  | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.19/32.30  | | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (276),
% 197.19/32.30  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.30  | | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.19/32.30  | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.19/32.30  | | | | | | | | | | | | |            (327), (332), (333), (343), (346), (351), (352),
% 197.19/32.30  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.30  | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.19/32.30  | | | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 197.19/32.30  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.30  | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.19/32.30  | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 197.19/32.30  | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.19/32.30  | | | | | | | | | | | | |            (578), (580), (582), (584), (586), (588), (589),
% 197.19/32.30  | | | | | | | | | | | | |            (590), (592), (593), (594), (595), (596), (598),
% 197.19/32.30  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.30  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.19/32.30  | | | | | | | | | | | | |            (688), (7443), (7445), (7449), (7450), (7451),
% 197.19/32.30  | | | | | | | | | | | | |            (9007), (9011), (9374), (9378), (9381), (9383),
% 197.19/32.30  | | | | | | | | | | | | |            (9384), (function-axioms) are inconsistent by
% 197.19/32.30  | | | | | | | | | | | | |            sub-proof #80.
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | |   (9385)  all_40_1 = e2
% 197.19/32.30  | | | | | | | | | | |   (9386)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | COMBINE_EQS: (687), (9385) imply:
% 197.19/32.30  | | | | | | | | | | |   (9387)  all_10_1 = e2
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (9376), (9387) imply:
% 197.19/32.30  | | | | | | | | | | |   (9388)   ~ (e3 = e2)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (53), (9387) imply:
% 197.19/32.30  | | | | | | | | | | |   (9389)  op(all_10_2, e1) = e2
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (52), (9387) imply:
% 197.19/32.30  | | | | | | | | | | |   (9390)  op(e1, e2) = all_10_0
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.19/32.30  | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (9390)
% 197.19/32.30  | | | | | | | | | | |              gives:
% 197.19/32.30  | | | | | | | | | | |   (9391)  all_52_13 = all_10_0
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | COMBINE_EQS: (421), (9391) imply:
% 197.19/32.30  | | | | | | | | | | |   (9392)  all_56_9 = all_10_0
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | COMBINE_EQS: (366), (9391) imply:
% 197.19/32.30  | | | | | | | | | | |   (9393)  all_58_7 = all_10_0
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (568), (9391) imply:
% 197.19/32.30  | | | | | | | | | | |   (9394)   ~ (all_52_5 = all_10_0)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (575), (9391) imply:
% 197.19/32.30  | | | | | | | | | | |   (9395)   ~ (all_52_9 = all_10_0)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (587), (9391) imply:
% 197.19/32.30  | | | | | | | | | | |   (9396)   ~ (all_52_15 = all_10_0)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | SIMP: (9396) implies:
% 197.19/32.30  | | | | | | | | | | |   (9397)   ~ (all_52_15 = all_10_0)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (580), (9391) imply:
% 197.19/32.30  | | | | | | | | | | |   (9398)   ~ (all_10_0 = all_4_2)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | |   (9399)   ~ (all_44_0 = e2)
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | REDUCE: (9010), (9399) imply:
% 197.19/32.30  | | | | | | | | | | | |   (9400)  $false
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | CLOSE: (9400) is inconsistent.
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | |   (9401)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | |   (9402)  all_58_15 = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (9372), (9402),
% 197.19/32.30  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.30  | | | | | | | | | | | | |            #678.
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | |   (9403)   ~ (all_58_15 = e0)
% 197.19/32.30  | | | | | | | | | | | | |   (9404)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.30  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.30  | | | | | | | | | | | | |             e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (43),
% 197.19/32.30  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.19/32.30  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.19/32.30  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.19/32.30  | | | | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (276),
% 197.19/32.30  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.30  | | | | | | | | | | | | |            (284), (285), (304), (306), (307), (309), (311),
% 197.19/32.30  | | | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.19/32.30  | | | | | | | | | | | | |            (326), (327), (332), (333), (343), (351), (352),
% 197.19/32.30  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.30  | | | | | | | | | | | | |            (394), (405), (411), (415), (417), (427), (431),
% 197.19/32.30  | | | | | | | | | | | | |            (521), (526), (528), (538), (539), (540), (541),
% 197.19/32.30  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.30  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.19/32.30  | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.19/32.30  | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.19/32.30  | | | | | | | | | | | | |            (578), (582), (584), (586), (588), (589), (590),
% 197.19/32.30  | | | | | | | | | | | | |            (591), (592), (593), (594), (595), (596), (598),
% 197.19/32.30  | | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.19/32.30  | | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.19/32.30  | | | | | | | | | | | | |            (688), (767), (7443), (7445), (7449), (7450),
% 197.19/32.30  | | | | | | | | | | | | |            (9007), (9011), (9012), (9015), (9374), (9386),
% 197.19/32.30  | | | | | | | | | | | | |            (9389), (9392), (9393), (9394), (9395), (9397),
% 197.19/32.30  | | | | | | | | | | | | |            (9398), (9401), (9403), (9404), (function-axioms)
% 197.19/32.30  | | | | | | | | | | | | |            are inconsistent by sub-proof #62.
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | |   (9405)  all_30_1 = e3
% 197.19/32.30  | | | | | | | | | |   (9406)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | COMBINE_EQS: (670), (9405) imply:
% 197.19/32.30  | | | | | | | | | |   (9407)  all_10_1 = e3
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | SIMP: (9407) implies:
% 197.19/32.30  | | | | | | | | | |   (9408)  all_10_1 = e3
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (53), (9408) imply:
% 197.19/32.30  | | | | | | | | | |   (9409)  op(all_10_2, e1) = e3
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (52), (9408) imply:
% 197.19/32.30  | | | | | | | | | |   (9410)  op(e1, e3) = all_10_0
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.19/32.30  | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (9410)
% 197.19/32.30  | | | | | | | | | |              gives:
% 197.19/32.30  | | | | | | | | | |   (9411)  all_52_5 = all_10_0
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | COMBINE_EQS: (367), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9412)  all_56_8 = all_10_0
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | COMBINE_EQS: (547), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9413)  all_58_6 = all_10_0
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (562), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9414)   ~ (all_52_3 = all_10_0)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (567), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9415)   ~ (all_52_7 = all_10_0)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | SIMP: (9415) implies:
% 197.19/32.30  | | | | | | | | | |   (9416)   ~ (all_52_7 = all_10_0)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (569), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9417)   ~ (all_10_0 = all_10_2)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (553), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9418)   ~ (all_10_0 = all_6_2)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (184), (9411) imply:
% 197.19/32.30  | | | | | | | | | |   (9419)  op(all_10_0, all_10_0) = all_52_4
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | |   (9420)   ~ (all_44_0 = e2)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (9010), (9420) imply:
% 197.19/32.30  | | | | | | | | | | |   (9421)  $false
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | CLOSE: (9421) is inconsistent.
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | |   (9422)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | |   (9423)  all_58_15 = e0
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (9372), (9423),
% 197.19/32.30  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.30  | | | | | | | | | | | |            #678.
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | |   (9424)   ~ (all_58_15 = e0)
% 197.19/32.30  | | | | | | | | | | | |   (9425)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.30  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.30  | | | | | | | | | | | |             e0)
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.30  | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.19/32.30  | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.19/32.30  | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.19/32.30  | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (275),
% 197.19/32.30  | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 197.19/32.30  | | | | | | | | | | | |            (283), (285), (304), (306), (307), (309), (311),
% 197.19/32.30  | | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.19/32.30  | | | | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.19/32.30  | | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 197.19/32.30  | | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.19/32.30  | | | | | | | | | | | |            (427), (431), (459), (521), (528), (538), (539),
% 197.19/32.30  | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.19/32.30  | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.19/32.30  | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 197.19/32.30  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.19/32.30  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.19/32.30  | | | | | | | | | | | |            (584), (586), (588), (589), (590), (591), (592),
% 197.19/32.30  | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.19/32.30  | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.19/32.30  | | | | | | | | | | | |            (610), (611), (612), (613), (684), (688), (750),
% 197.19/32.30  | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (9007), (9011),
% 197.19/32.30  | | | | | | | | | | | |            (9012), (9015), (9374), (9406), (9409), (9412),
% 197.19/32.30  | | | | | | | | | | | |            (9413), (9414), (9416), (9417), (9418), (9419),
% 197.19/32.30  | | | | | | | | | | | |            (9422), (9424), (9425), (function-axioms) are
% 197.19/32.30  | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | |   (9426)  all_28_0 = e3
% 197.19/32.30  | | | | | | | | |   (9427)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.19/32.30  | | | | | | | | |            (51), (53), (61), (63), (139), (158), (161), (162),
% 197.19/32.30  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.19/32.30  | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.19/32.30  | | | | | | | | |            (185), (187), (270), (271), (273), (274), (277),
% 197.19/32.30  | | | | | | | | |            (278), (279), (280), (281), (282), (283), (285),
% 197.19/32.30  | | | | | | | | |            (303), (306), (307), (309), (311), (313), (315),
% 197.19/32.30  | | | | | | | | |            (316), (317), (318), (319), (320), (321), (324),
% 197.19/32.30  | | | | | | | | |            (325), (326), (327), (332), (333), (343), (351),
% 197.19/32.30  | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.19/32.30  | | | | | | | | |            (388), (393), (405), (411), (415), (417), (427),
% 197.19/32.30  | | | | | | | | |            (431), (521), (528), (538), (539), (540), (541),
% 197.19/32.30  | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.30  | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.19/32.30  | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.19/32.30  | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 197.19/32.30  | | | | | | | | |            (580), (582), (584), (586), (589), (590), (592),
% 197.19/32.30  | | | | | | | | |            (593), (594), (595), (596), (598), (602), (603),
% 197.19/32.30  | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.19/32.30  | | | | | | | | |            (612), (613), (684), (688), (754), (7444), (7445),
% 197.19/32.30  | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 197.19/32.30  | | | | | | | | |            (7459), (9007), (9010), (9011), (9372), (9426),
% 197.19/32.30  | | | | | | | | |            (9427), (function-axioms) are inconsistent by
% 197.19/32.30  | | | | | | | | |            sub-proof #58.
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | End of split
% 197.19/32.30  | | | | | | | | 
% 197.19/32.30  | | | | | | | End of split
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | Case 2:
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | |   (9428)  all_16_0 = e2
% 197.19/32.30  | | | | | | |   (9429)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | | COMBINE_EQS: (760), (9428) imply:
% 197.19/32.30  | | | | | | |   (9430)  all_10_0 = e2
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | | SIMP: (9430) implies:
% 197.19/32.30  | | | | | | |   (9431)  all_10_0 = e2
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | | COMBINE_EQS: (756), (9431) imply:
% 197.19/32.30  | | | | | | |   (9432)  all_26_0 = e2
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | | REDUCE: (9012), (9431) imply:
% 197.19/32.30  | | | | | | |   (9433)   ~ (e3 = e2)
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | | BETA: splitting (74) gives:
% 197.19/32.30  | | | | | | | 
% 197.19/32.30  | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | 
% 197.19/32.30  | | | | | | | |   (9434)   ~ (all_18_0 = e3)
% 197.19/32.30  | | | | | | | | 
% 197.19/32.30  | | | | | | | | REDUCE: (761), (9434) imply:
% 197.19/32.30  | | | | | | | |   (9435)   ~ (all_14_0 = e3)
% 197.19/32.30  | | | | | | | | 
% 197.19/32.30  | | | | | | | | BETA: splitting (89) gives:
% 197.19/32.30  | | | | | | | | 
% 197.19/32.30  | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | |   (9436)   ~ (all_24_0 = e1)
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | REDUCE: (711), (9436) imply:
% 197.19/32.30  | | | | | | | | |   (9437)   ~ (all_14_0 = e1)
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | BETA: splitting (94) gives:
% 197.19/32.30  | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | |   (9438)   ~ (all_26_0 = e2)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | REDUCE: (9432), (9438) imply:
% 197.19/32.30  | | | | | | | | | |   (9439)  $false
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | CLOSE: (9439) is inconsistent.
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | |   (9440)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | BETA: splitting (99) gives:
% 197.19/32.30  | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | |   (9441)   ~ (all_28_0 = e3)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | REDUCE: (754), (9441) imply:
% 197.19/32.30  | | | | | | | | | | |   (9442)   ~ (all_4_0 = e3)
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.30  | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | |   (9443)   ~ (all_44_0 = e2)
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | REDUCE: (9010), (9443) imply:
% 197.19/32.30  | | | | | | | | | | | |   (9444)  $false
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | CLOSE: (9444) is inconsistent.
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | |   (9445)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.30  | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | |   (9446)  all_58_15 = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | COMBINE_EQS: (541), (9446) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9447)  all_14_2 = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (573), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9448)   ~ (all_52_7 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (591), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9449)   ~ (all_52_15 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (603), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9450)   ~ (all_52_23 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (606), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9451)   ~ (all_52_25 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (609), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9452)   ~ (all_52_29 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (613), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9453)  op(e0, e0) = all_52_30
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (63), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9454)  op(e0, e0) = all_14_1
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (61), (9447) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9455)  op(e0, e0) = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.19/32.30  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9453), (9454)
% 197.19/32.30  | | | | | | | | | | | | |              gives:
% 197.19/32.30  | | | | | | | | | | | | |   (9456)  all_52_30 = all_14_1
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.19/32.30  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9453), (9455)
% 197.19/32.30  | | | | | | | | | | | | |              gives:
% 197.19/32.30  | | | | | | | | | | | | |   (9457)  all_52_30 = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | COMBINE_EQS: (9456), (9457) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9458)  all_14_1 = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (62), (9458) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9459)  op(e0, e0) = all_14_0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.19/32.30  | | | | | | | | | | | | |              e0, e0, simplifying with (9455), (9459) gives:
% 197.19/32.30  | | | | | | | | | | | | |   (9460)  all_14_0 = e0
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (9435), (9460) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9461)   ~ (e3 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (9013), (9460) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9462)   ~ (e2 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | REDUCE: (9437), (9460) imply:
% 197.19/32.30  | | | | | | | | | | | | |   (9463)   ~ (e1 = e0)
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.19/32.30  | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | |   (9464)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.30  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.19/32.30  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.19/32.30  | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | BETA: splitting (9464) gives:
% 197.19/32.30  | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | |   (9465)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.19/32.30  | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 197.19/32.30  | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 197.19/32.30  | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 197.19/32.30  | | | | | | | | | | | | | | |            (9011), (9465), (function-axioms) are inconsistent
% 197.19/32.30  | | | | | | | | | | | | | | |            by sub-proof #501.
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | Case 2:
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | |   (9466)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.19/32.30  | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | ALPHA: (9466) implies:
% 197.19/32.30  | | | | | | | | | | | | | | |   (9467)  all_52_14 = e0
% 197.19/32.30  | | | | | | | | | | | | | | |   (9468)  all_52_12 = e1
% 197.19/32.30  | | | | | | | | | | | | | | |   (9469)  all_52_10 = e2
% 197.19/32.30  | | | | | | | | | | | | | | |   (9470)  all_52_8 = e3
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | REDUCE: (182), (9470) imply:
% 197.19/32.30  | | | | | | | | | | | | | | |   (9471)  op(all_52_9, all_52_9) = e3
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | REDUCE: (180), (9468) imply:
% 197.19/32.30  | | | | | | | | | | | | | | |   (9472)  op(all_52_13, all_52_13) = e1
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | REDUCE: (179), (9467) imply:
% 197.19/32.30  | | | | | | | | | | | | | | |   (9473)  op(all_52_15, all_52_15) = e0
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | REDUCE: (611), (9469) imply:
% 197.19/32.30  | | | | | | | | | | | | | | |   (9474)  op(all_4_2, all_4_2) = e2
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.19/32.30  | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | Case 1:
% 197.19/32.30  | | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | |   (9475)  all_56_13 = e3
% 197.19/32.30  | | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (9475) imply:
% 197.19/32.30  | | | | | | | | | | | | | | | |   (9476)  all_52_15 = e3
% 197.19/32.30  | | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | | SIMP: (9476) implies:
% 197.19/32.30  | | | | | | | | | | | | | | | |   (9477)  all_52_15 = e3
% 197.19/32.30  | | | | | | | | | | | | | | | | 
% 197.19/32.30  | | | | | | | | | | | | | | | | REDUCE: (590), (9477) imply:
% 197.19/32.30  | | | | | | | | | | | | | | | |   (9478)   ~ (all_52_23 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | SIMP: (9478) implies:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9479)   ~ (all_52_23 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (43), (51), (53),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (174),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (178), (183), (184), (271), (273), (274), (277),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (281), (283), (306), (309), (313), (317), (319),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (321), (325), (326), (333), (343), (351), (352),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (366), (367), (372), (387), (393), (405), (411),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (415), (431), (521), (528), (542), (543), (544),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (571), (572), (574), (577), (580), (582), (590),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (607),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (610), (612), (684), (688), (7443), (7445),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (7449), (7451), (7457), (9007), (9011), (9442),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (9445), (9446), (9448), (9449), (9450), (9451),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (9471), (9472), (9473), (9474), (9479),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.31  | | | | | | | | | | | | | | | |            #91.
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9480)   ~ (all_56_13 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9481)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | REDUCE: (346), (9480) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9482)   ~ (all_52_15 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9483)  all_58_12 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (9483) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9484)  all_52_7 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | SIMP: (9484) implies:
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9485)  all_52_7 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | REDUCE: (572), (9485) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9486)   ~ (all_52_23 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | SIMP: (9486) implies:
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9487)   ~ (all_52_23 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (43), (51), (53),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (174),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (178), (183), (184), (271), (273), (274), (277),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (281), (283), (306), (309), (313), (317), (319),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (321), (325), (326), (333), (343), (351), (352),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (366), (367), (372), (387), (393), (405), (411),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (415), (431), (521), (528), (542), (543), (544),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (555), (557), (559), (561), (563), (564), (567),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (571), (572), (574), (577), (580), (582), (590),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (593), (594), (595), (600), (602), (604), (607),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (610), (612), (684), (688), (7443), (7445),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (7449), (7451), (7457), (9007), (9011), (9442),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (9445), (9446), (9448), (9449), (9450), (9451),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (9471), (9472), (9473), (9474), (9487),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.31  | | | | | | | | | | | | | | | | |            #91.
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9488)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (51), (53), (156), (273), (305), (346),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (351), (431), (515), (542), (543), (571), (572),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (582), (680), (9429), (9446), (9448), (9449),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (9455), (9473), (9474), (9481), (9482), (9488),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.31  | | | | | | | | | | | | | | | | |            #648.
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | |   (9489)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.19/32.31  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.19/32.31  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.19/32.31  | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | BETA: splitting (9489) gives:
% 197.19/32.31  | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | |   (9490)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.19/32.31  | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | ALPHA: (9490) implies:
% 197.19/32.31  | | | | | | | | | | | | | | |   (9491)  all_52_22 = e0
% 197.19/32.31  | | | | | | | | | | | | | | |   (9492)  all_52_20 = e1
% 197.19/32.31  | | | | | | | | | | | | | | |   (9493)  all_52_16 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | REDUCE: (178), (9493) imply:
% 197.19/32.31  | | | | | | | | | | | | | | |   (9494)  op(all_52_17, all_52_17) = e3
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | REDUCE: (175), (9491) imply:
% 197.19/32.31  | | | | | | | | | | | | | | |   (9495)  op(all_52_23, all_52_23) = e0
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | REDUCE: (612), (9492) imply:
% 197.19/32.31  | | | | | | | | | | | | | | |   (9496)  op(all_10_2, all_10_2) = e1
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9497)  all_56_13 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (9497) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9498)  all_52_15 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | SIMP: (9498) implies:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9499)  all_52_15 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | REDUCE: (590), (9499) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9500)   ~ (all_52_23 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | SIMP: (9500) implies:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9501)   ~ (all_52_23 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | REDUCE: (179), (9499) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9502)  op(e3, e3) = all_52_14
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.19/32.31  | | | | | | | | | | | | | | | |              all_52_14, e3, e3, simplifying with (41), (9502)
% 197.19/32.31  | | | | | | | | | | | | | | | |              gives:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9503)  all_52_14 = all_6_2
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (53), (168), (169), (283), (317),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (393), (415), (512), (542), (546), (557), (559),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (593), (676), (7445), (7449), (9440), (9442),
% 197.19/32.31  | | | | | | | | | | | | | | | |            (9494), (9496), (9501), (function-axioms) are
% 197.19/32.31  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9504)   ~ (all_56_13 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9505)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | REDUCE: (346), (9504) imply:
% 197.19/32.31  | | | | | | | | | | | | | | | |   (9506)   ~ (all_52_15 = e3)
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9507)  all_58_12 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (53), (168), (169), (183), (283),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (317), (351), (393), (415), (512), (542), (546),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (557), (559), (572), (593), (676), (7445), (7449),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (9440), (9442), (9494), (9496), (9507),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.31  | | | | | | | | | | | | | | | | |            #130.
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | |   (9508)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (41), (43), (51), (158), (169),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (179), (273), (283), (304), (346), (351), (415),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (431), (521), (541), (542), (543), (555), (559),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (571), (572), (577), (594), (600), (613), (684),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (9007), (9011), (9446), (9494), (9495), (9505),
% 197.19/32.31  | | | | | | | | | | | | | | | | |            (9506), (9508), (function-axioms) are inconsistent
% 197.19/32.31  | | | | | | | | | | | | | | | | |            by sub-proof #478.
% 197.19/32.31  | | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | |   (9509)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.19/32.31  | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.19/32.31  | | | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 197.19/32.31  | | | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 197.19/32.31  | | | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 197.19/32.31  | | | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 197.19/32.31  | | | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 197.19/32.31  | | | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.19/32.31  | | | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 197.19/32.31  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.19/32.31  | | | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 197.19/32.31  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 197.19/32.31  | | | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 197.19/32.31  | | | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 197.19/32.31  | | | | | | | | | | | | | | |            (608), (609), (610), (688), (9011), (9445),
% 197.19/32.31  | | | | | | | | | | | | | | |            (9446), (9448), (9449), (9450), (9451), (9452),
% 197.19/32.31  | | | | | | | | | | | | | | |            (9509), (function-axioms) are inconsistent by
% 197.19/32.31  | | | | | | | | | | | | | | |            sub-proof #418.
% 197.19/32.31  | | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | |   (9510)   ~ (all_58_15 = e0)
% 197.19/32.31  | | | | | | | | | | | | |   (9511)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.31  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.31  | | | | | | | | | | | | |             e0)
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.19/32.31  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.19/32.31  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.19/32.31  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.19/32.31  | | | | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (276),
% 197.19/32.31  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.19/32.31  | | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.19/32.31  | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.19/32.31  | | | | | | | | | | | | |            (327), (331), (332), (333), (343), (351), (352),
% 197.19/32.31  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.19/32.31  | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.19/32.31  | | | | | | | | | | | | |            (512), (521), (528), (538), (539), (540), (541),
% 197.19/32.31  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.19/32.31  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.19/32.31  | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 197.19/32.31  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 197.19/32.31  | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 197.19/32.31  | | | | | | | | | | | | |            (588), (589), (590), (592), (593), (594), (595),
% 197.19/32.31  | | | | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 197.19/32.31  | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 197.19/32.31  | | | | | | | | | | | | |            (613), (676), (684), (688), (7443), (7445),
% 197.19/32.31  | | | | | | | | | | | | |            (7449), (7450), (7451), (9007), (9011), (9440),
% 197.19/32.31  | | | | | | | | | | | | |            (9442), (9445), (9510), (9511), (function-axioms)
% 197.19/32.31  | | | | | | | | | | | | |            are inconsistent by sub-proof #54.
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | |   (9512)  all_28_0 = e3
% 197.19/32.31  | | | | | | | | | | |   (9513)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | COMBINE_EQS: (754), (9512) imply:
% 197.19/32.31  | | | | | | | | | | |   (9514)  all_4_0 = e3
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.19/32.31  | | | | | | | | | | |            (51), (53), (61), (62), (63), (139), (158), (161),
% 197.19/32.31  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.19/32.31  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.19/32.31  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 197.19/32.31  | | | | | | | | | | |            (273), (274), (276), (277), (278), (279), (280),
% 197.19/32.31  | | | | | | | | | | |            (281), (282), (283), (285), (303), (306), (307),
% 197.19/32.31  | | | | | | | | | | |            (308), (309), (310), (311), (313), (315), (316),
% 197.19/32.31  | | | | | | | | | | |            (317), (318), (319), (320), (321), (324), (325),
% 197.19/32.31  | | | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.19/32.31  | | | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.19/32.31  | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.19/32.31  | | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.19/32.31  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.19/32.31  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.19/32.31  | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 197.19/32.31  | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.19/32.31  | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 197.19/32.31  | | | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 197.19/32.31  | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.19/32.31  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.19/32.31  | | | | | | | | | | |            (610), (612), (613), (684), (688), (7444), (7445),
% 197.19/32.31  | | | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 197.19/32.31  | | | | | | | | | | |            (7459), (9007), (9010), (9011), (9013), (9435),
% 197.19/32.31  | | | | | | | | | | |            (9437), (9513), (9514), (function-axioms) are
% 197.19/32.31  | | | | | | | | | | |            inconsistent by sub-proof #63.
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | End of split
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | |   (9515)  all_24_0 = e1
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | COMBINE_EQS: (711), (9515) imply:
% 197.19/32.31  | | | | | | | | |   (9516)  all_14_0 = e1
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | SIMP: (9516) implies:
% 197.19/32.31  | | | | | | | | |   (9517)  all_14_0 = e1
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | REDUCE: (9435), (9517) imply:
% 197.19/32.31  | | | | | | | | |   (9518)   ~ (e3 = e1)
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | REDUCE: (9013), (9517) imply:
% 197.19/32.31  | | | | | | | | |   (9519)   ~ (e2 = e1)
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | REDUCE: (62), (9517) imply:
% 197.19/32.31  | | | | | | | | |   (9520)  op(e0, all_14_1) = e1
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | BETA: splitting (94) gives:
% 197.19/32.31  | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | |   (9521)   ~ (all_26_0 = e2)
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | REDUCE: (9432), (9521) imply:
% 197.19/32.31  | | | | | | | | | |   (9522)  $false
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | CLOSE: (9522) is inconsistent.
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | |   (9523)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | BETA: splitting (99) gives:
% 197.19/32.31  | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | |   (9524)   ~ (all_28_0 = e3)
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | REDUCE: (754), (9524) imply:
% 197.19/32.31  | | | | | | | | | | |   (9525)   ~ (all_4_0 = e3)
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | BETA: splitting (139) gives:
% 197.19/32.31  | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | |   (9526)   ~ (all_44_0 = e2)
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | REDUCE: (9010), (9526) imply:
% 197.19/32.31  | | | | | | | | | | | |   (9527)  $false
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | CLOSE: (9527) is inconsistent.
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | |   (9528)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.19/32.31  | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | Case 1:
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | |   (9529)  all_58_15 = e0
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (9520), (9529),
% 197.19/32.31  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.19/32.31  | | | | | | | | | | | | |            #877.
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | Case 2:
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.19/32.31  | | | | | | | | | | | | |   (9530)   ~ (all_58_15 = e0)
% 197.19/32.31  | | | | | | | | | | | | |   (9531)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.19/32.31  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.19/32.31  | | | | | | | | | | | | |             e0)
% 197.19/32.31  | | | | | | | | | | | | | 
% 197.44/32.31  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.31  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.44/32.31  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.44/32.31  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.44/32.31  | | | | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (276),
% 197.44/32.31  | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.44/32.31  | | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.44/32.31  | | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.44/32.31  | | | | | | | | | | | | |            (327), (331), (332), (333), (343), (351), (352),
% 197.44/32.31  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.44/32.31  | | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.44/32.31  | | | | | | | | | | | | |            (512), (521), (528), (538), (539), (540), (541),
% 197.44/32.31  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.44/32.31  | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.44/32.31  | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 197.44/32.31  | | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 197.44/32.31  | | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 197.44/32.31  | | | | | | | | | | | | |            (588), (589), (590), (592), (593), (594), (595),
% 197.44/32.31  | | | | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 197.44/32.31  | | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 197.44/32.31  | | | | | | | | | | | | |            (613), (676), (684), (688), (7443), (7445),
% 197.44/32.31  | | | | | | | | | | | | |            (7449), (7450), (7451), (9007), (9011), (9523),
% 197.44/32.31  | | | | | | | | | | | | |            (9525), (9528), (9530), (9531), (function-axioms)
% 197.44/32.31  | | | | | | | | | | | | |            are inconsistent by sub-proof #54.
% 197.44/32.31  | | | | | | | | | | | | | 
% 197.44/32.31  | | | | | | | | | | | | End of split
% 197.44/32.31  | | | | | | | | | | | | 
% 197.44/32.31  | | | | | | | | | | | End of split
% 197.44/32.31  | | | | | | | | | | | 
% 197.44/32.31  | | | | | | | | | | Case 2:
% 197.44/32.31  | | | | | | | | | | | 
% 197.44/32.31  | | | | | | | | | | |   (9532)  all_28_0 = e3
% 197.44/32.31  | | | | | | | | | | |   (9533)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.31  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.32  | | | | | | | | | | |            (51), (53), (61), (63), (139), (158), (161),
% 197.44/32.32  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.32  | | | | | | | | | | |            (174), (177), (178), (179), (180), (182), (183),
% 197.44/32.32  | | | | | | | | | | |            (184), (185), (187), (270), (271), (273), (274),
% 197.44/32.32  | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.44/32.32  | | | | | | | | | | |            (285), (303), (306), (307), (309), (311), (313),
% 197.44/32.32  | | | | | | | | | | |            (315), (316), (317), (318), (319), (320), (321),
% 197.44/32.32  | | | | | | | | | | |            (324), (325), (326), (327), (332), (333), (343),
% 197.44/32.32  | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (376),
% 197.44/32.32  | | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (417),
% 197.44/32.32  | | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.44/32.32  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.32  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.32  | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.44/32.32  | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (577),
% 197.44/32.32  | | | | | | | | | | |            (578), (580), (582), (584), (586), (589), (590),
% 197.44/32.32  | | | | | | | | | | |            (592), (593), (594), (595), (596), (598), (602),
% 197.44/32.32  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.44/32.32  | | | | | | | | | | |            (610), (612), (613), (684), (688), (754), (7444),
% 197.44/32.32  | | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7457),
% 197.44/32.32  | | | | | | | | | | |            (7458), (7459), (9007), (9010), (9011), (9520),
% 197.44/32.32  | | | | | | | | | | |            (9532), (9533), (function-axioms) are inconsistent
% 197.44/32.32  | | | | | | | | | | |            by sub-proof #60.
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | |   (9534)  all_18_0 = e3
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | COMBINE_EQS: (761), (9534) imply:
% 197.44/32.32  | | | | | | | |   (9535)  all_14_0 = e3
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | SIMP: (9535) implies:
% 197.44/32.32  | | | | | | | |   (9536)  all_14_0 = e3
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | REDUCE: (62), (9536) imply:
% 197.44/32.32  | | | | | | | |   (9537)  op(e0, all_14_1) = e3
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | BETA: splitting (94) gives:
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | |   (9538)   ~ (all_26_0 = e2)
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | REDUCE: (9432), (9538) imply:
% 197.44/32.32  | | | | | | | | |   (9539)  $false
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | CLOSE: (9539) is inconsistent.
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | |   (9540)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | BETA: splitting (99) gives:
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | |   (9541)   ~ (all_28_0 = e3)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (754), (9541) imply:
% 197.44/32.32  | | | | | | | | | |   (9542)   ~ (all_4_0 = e3)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | |   (9543)   ~ (all_44_0 = e2)
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | REDUCE: (9010), (9543) imply:
% 197.44/32.32  | | | | | | | | | | |   (9544)  $false
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | CLOSE: (9544) is inconsistent.
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | |   (9545)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | |   (9546)  all_58_15 = e0
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (9537), (9546),
% 197.44/32.32  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.32  | | | | | | | | | | | |            #678.
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | |   (9547)   ~ (all_58_15 = e0)
% 197.44/32.32  | | | | | | | | | | | |   (9548)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.32  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.32  | | | | | | | | | | | |             e0)
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | ALPHA: (9548) implies:
% 197.44/32.32  | | | | | | | | | | | |   (9549)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.32  | | | | | | | | | | | |   (9550)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REDUCE: (541), (9547) imply:
% 197.44/32.32  | | | | | | | | | | | |   (9551)   ~ (all_14_2 = e0)
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.32  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.44/32.32  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.44/32.32  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.44/32.32  | | | | | | | | | | | |            (185), (187), (270), (271), (273), (274), (276),
% 197.44/32.32  | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.44/32.32  | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.44/32.32  | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.44/32.32  | | | | | | | | | | | |            (327), (331), (332), (333), (343), (351), (352),
% 197.44/32.32  | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.44/32.32  | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.44/32.32  | | | | | | | | | | | |            (512), (521), (528), (538), (539), (540), (541),
% 197.44/32.32  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.44/32.32  | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.44/32.32  | | | | | | | | | | | |            (562), (563), (564), (566), (567), (568), (569),
% 197.44/32.32  | | | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 197.44/32.32  | | | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 197.44/32.32  | | | | | | | | | | | |            (588), (589), (590), (592), (593), (594), (595),
% 197.44/32.32  | | | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 197.44/32.32  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 197.44/32.32  | | | | | | | | | | | |            (613), (676), (684), (688), (7443), (7445),
% 197.44/32.32  | | | | | | | | | | | |            (7449), (7450), (7451), (9007), (9011), (9540),
% 197.44/32.32  | | | | | | | | | | | |            (9542), (9545), (9549), (9550), (9551),
% 197.44/32.32  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.32  | | | | | | | | | | | |            #55.
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | |   (9552)  all_28_0 = e3
% 197.44/32.32  | | | | | | | | | |   (9553)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.32  | | | | | | | | | |            (51), (53), (61), (63), (139), (158), (161),
% 197.44/32.32  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.32  | | | | | | | | | |            (174), (177), (178), (179), (180), (182), (183),
% 197.44/32.32  | | | | | | | | | |            (184), (185), (187), (270), (271), (273), (274),
% 197.44/32.32  | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.44/32.32  | | | | | | | | | |            (285), (303), (306), (307), (309), (311), (313),
% 197.44/32.32  | | | | | | | | | |            (315), (316), (317), (318), (319), (320), (321),
% 197.44/32.32  | | | | | | | | | |            (324), (325), (326), (327), (332), (333), (343),
% 197.44/32.32  | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (376),
% 197.44/32.32  | | | | | | | | | |            (387), (388), (393), (405), (411), (415), (417),
% 197.44/32.32  | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.44/32.32  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.32  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.32  | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.44/32.32  | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (577),
% 197.44/32.32  | | | | | | | | | |            (578), (580), (582), (584), (586), (589), (590),
% 197.44/32.32  | | | | | | | | | |            (592), (593), (594), (595), (596), (598), (602),
% 197.44/32.32  | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.44/32.32  | | | | | | | | | |            (610), (612), (613), (684), (688), (754), (7444),
% 197.44/32.32  | | | | | | | | | |            (7445), (7449), (7450), (7451), (7453), (7457),
% 197.44/32.32  | | | | | | | | | |            (7458), (7459), (9007), (9010), (9011), (9537),
% 197.44/32.32  | | | | | | | | | |            (9552), (9553), (function-axioms) are inconsistent
% 197.44/32.32  | | | | | | | | | |            by sub-proof #58.
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | End of split
% 197.44/32.32  | | | | | | | 
% 197.44/32.32  | | | | | | End of split
% 197.44/32.32  | | | | | | 
% 197.44/32.32  | | | | | Case 2:
% 197.44/32.32  | | | | | | 
% 197.44/32.32  | | | | | |   (9554)  all_14_0 = e2
% 197.44/32.32  | | | | | | 
% 197.44/32.32  | | | | | | COMBINE_EQS: (771), (9554) imply:
% 197.44/32.32  | | | | | |   (9555)  all_50_0 = e2
% 197.44/32.32  | | | | | | 
% 197.44/32.32  | | | | | | REDUCE: (62), (9554) imply:
% 197.44/32.32  | | | | | |   (9556)  op(e0, all_14_1) = e2
% 197.44/32.32  | | | | | | 
% 197.44/32.32  | | | | | | BETA: splitting (69) gives:
% 197.44/32.32  | | | | | | 
% 197.44/32.32  | | | | | | Case 1:
% 197.44/32.32  | | | | | | | 
% 197.44/32.32  | | | | | | |   (9557)   ~ (all_16_0 = e2)
% 197.44/32.32  | | | | | | | 
% 197.44/32.32  | | | | | | | REDUCE: (760), (9557) imply:
% 197.44/32.32  | | | | | | |   (9558)   ~ (all_10_0 = e2)
% 197.44/32.32  | | | | | | | 
% 197.44/32.32  | | | | | | | BETA: splitting (99) gives:
% 197.44/32.32  | | | | | | | 
% 197.44/32.32  | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | |   (9559)   ~ (all_28_0 = e3)
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | REDUCE: (754), (9559) imply:
% 197.44/32.32  | | | | | | | |   (9560)   ~ (all_4_0 = e3)
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | BETA: splitting (104) gives:
% 197.44/32.32  | | | | | | | | 
% 197.44/32.32  | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | |   (9561)   ~ (all_30_1 = e3)
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | REDUCE: (670), (9561) imply:
% 197.44/32.32  | | | | | | | | |   (9562)   ~ (all_10_1 = e3)
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | BETA: splitting (129) gives:
% 197.44/32.32  | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | |   (9563)   ~ (all_40_1 = e2)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (687), (9563) imply:
% 197.44/32.32  | | | | | | | | | |   (9564)   ~ (all_10_1 = e2)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | |   (9565)   ~ (all_44_0 = e2)
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | REDUCE: (9010), (9565) imply:
% 197.44/32.32  | | | | | | | | | | |   (9566)  $false
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | CLOSE: (9566) is inconsistent.
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | |   (9567)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | |   (9568)  all_58_15 = e0
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (9556), (9568),
% 197.44/32.32  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.32  | | | | | | | | | | | |            #612.
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | |   (9569)   ~ (all_58_15 = e0)
% 197.44/32.32  | | | | | | | | | | | |   (9570)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.32  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.32  | | | | | | | | | | | |             e0)
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | ALPHA: (9570) implies:
% 197.44/32.32  | | | | | | | | | | | |   (9571)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.32  | | | | | | | | | | | |   (9572)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REDUCE: (541), (9569) imply:
% 197.44/32.32  | | | | | | | | | | | |   (9573)   ~ (all_14_2 = e0)
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.44/32.32  | | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.44/32.32  | | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.44/32.32  | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.44/32.32  | | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (276),
% 197.44/32.32  | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 197.44/32.32  | | | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.44/32.32  | | | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.44/32.32  | | | | | | | | | | | |            (327), (332), (333), (343), (346), (351), (352),
% 197.44/32.32  | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.44/32.32  | | | | | | | | | | | |            (405), (411), (415), (417), (421), (427), (431),
% 197.44/32.32  | | | | | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 197.44/32.32  | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.44/32.32  | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.44/32.32  | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (570),
% 197.44/32.32  | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.44/32.32  | | | | | | | | | | | |            (578), (580), (582), (584), (586), (588), (589),
% 197.44/32.32  | | | | | | | | | | | |            (590), (592), (593), (594), (595), (596), (598),
% 197.44/32.32  | | | | | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 197.44/32.32  | | | | | | | | | | | |            (608), (609), (610), (611), (612), (613), (684),
% 197.44/32.32  | | | | | | | | | | | |            (688), (7443), (7445), (7449), (7450), (7451),
% 197.44/32.32  | | | | | | | | | | | |            (9007), (9011), (9560), (9564), (9567), (9571),
% 197.44/32.32  | | | | | | | | | | | |            (9572), (9573), (function-axioms) are inconsistent
% 197.44/32.32  | | | | | | | | | | | |            by sub-proof #81.
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | End of split
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | |   (9574)  all_40_1 = e2
% 197.44/32.32  | | | | | | | | | |   (9575)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | COMBINE_EQS: (687), (9574) imply:
% 197.44/32.32  | | | | | | | | | |   (9576)  all_10_1 = e2
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (9562), (9576) imply:
% 197.44/32.32  | | | | | | | | | |   (9577)   ~ (e3 = e2)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (53), (9576) imply:
% 197.44/32.32  | | | | | | | | | |   (9578)  op(all_10_2, e1) = e2
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (52), (9576) imply:
% 197.44/32.32  | | | | | | | | | |   (9579)  op(e1, e2) = all_10_0
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.44/32.32  | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (9579)
% 197.44/32.32  | | | | | | | | | |              gives:
% 197.44/32.32  | | | | | | | | | |   (9580)  all_52_13 = all_10_0
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | COMBINE_EQS: (421), (9580) imply:
% 197.44/32.32  | | | | | | | | | |   (9581)  all_56_9 = all_10_0
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | COMBINE_EQS: (366), (9580) imply:
% 197.44/32.32  | | | | | | | | | |   (9582)  all_58_7 = all_10_0
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (568), (9580) imply:
% 197.44/32.32  | | | | | | | | | |   (9583)   ~ (all_52_5 = all_10_0)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (575), (9580) imply:
% 197.44/32.32  | | | | | | | | | |   (9584)   ~ (all_52_9 = all_10_0)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (587), (9580) imply:
% 197.44/32.32  | | | | | | | | | |   (9585)   ~ (all_52_15 = all_10_0)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | SIMP: (9585) implies:
% 197.44/32.32  | | | | | | | | | |   (9586)   ~ (all_52_15 = all_10_0)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | REDUCE: (580), (9580) imply:
% 197.44/32.32  | | | | | | | | | |   (9587)   ~ (all_10_0 = all_4_2)
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.32  | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | |   (9588)   ~ (all_44_0 = e2)
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | REDUCE: (9010), (9588) imply:
% 197.44/32.32  | | | | | | | | | | |   (9589)  $false
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | CLOSE: (9589) is inconsistent.
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | |   (9590)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | BETA: splitting (153) gives:
% 197.44/32.32  | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | |   (9591)   ~ (all_50_0 = e2)
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | REDUCE: (9555), (9591) imply:
% 197.44/32.32  | | | | | | | | | | | |   (9592)  $false
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | CLOSE: (9592) is inconsistent.
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | |   (9593)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.32  | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | |   (9594)  all_58_15 = e0
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (9556), (9594),
% 197.44/32.32  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.32  | | | | | | | | | | | | |            #612.
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | |   (9595)   ~ (all_58_15 = e0)
% 197.44/32.32  | | | | | | | | | | | | |   (9596)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.32  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.32  | | | | | | | | | | | | |             e0)
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | ALPHA: (9596) implies:
% 197.44/32.32  | | | | | | | | | | | | |   (9597)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.32  | | | | | | | | | | | | |   (9598)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | REDUCE: (541), (9595) imply:
% 197.44/32.32  | | | | | | | | | | | | |   (9599)   ~ (all_14_2 = e0)
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | BETA: splitting (276) gives:
% 197.44/32.32  | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | |   (9600)  all_56_9 = e3
% 197.44/32.32  | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | REF_CLOSE: (9012), (9581), (9600) are inconsistent by
% 197.44/32.32  | | | | | | | | | | | | | |            sub-proof #1006.
% 197.44/32.32  | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | |   (9601)   ~ (all_56_9 = e3)
% 197.44/32.32  | | | | | | | | | | | | | |   (9602)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 197.44/32.32  | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.44/32.32  | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | |   (9603)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.32  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.44/32.32  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.44/32.32  | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | BETA: splitting (9603) gives:
% 197.44/32.32  | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9604)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.32  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 197.44/32.32  | | | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 197.44/32.32  | | | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 197.44/32.32  | | | | | | | | | | | | | | | |            (9011), (9604), (function-axioms) are inconsistent
% 197.44/32.32  | | | | | | | | | | | | | | | |            by sub-proof #501.
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9605)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.44/32.32  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | ALPHA: (9605) implies:
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9606)  all_52_14 = e0
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9607)  all_52_10 = e2
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9608)  all_52_8 = e3
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | REDUCE: (182), (9608) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9609)  op(all_52_9, all_52_9) = e3
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | REDUCE: (179), (9606) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9610)  op(all_52_15, all_52_15) = e0
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | REDUCE: (611), (9607) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | |   (9611)  op(all_4_2, all_4_2) = e2
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.44/32.32  | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | |   (9612)  all_56_15 = e3
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (9612) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | | |   (9613)  all_14_2 = e3
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (9613) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | | |   (9614)  all_50_2 = e3
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | REDUCE: (591), (9613) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | | |   (9615)   ~ (all_52_15 = e3)
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | REDUCE: (613), (9613) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | | |   (9616)  op(e3, e3) = all_52_30
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | REDUCE: (63), (9613) imply:
% 197.44/32.32  | | | | | | | | | | | | | | | | |   (9617)  op(e3, e0) = all_14_1
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | BETA: splitting (9593) gives:
% 197.44/32.32  | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.32  | | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 197.44/32.32  | | | | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (9617)
% 197.44/32.32  | | | | | | | | | | | | | | | | | |              gives:
% 197.44/32.32  | | | | | | | | | | | | | | | | | |   (9618)  all_52_25 = all_14_1
% 197.44/32.32  | | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (41), (43), (166), (167), (168), (281),
% 197.44/32.32  | | | | | | | | | | | | | | | | | |            (319), (325), (326), (387), (405), (411), (543),
% 197.44/32.32  | | | | | | | | | | | | | | | | | |            (548), (549), (551), (557), (559), (561), (564),
% 197.44/32.32  | | | | | | | | | | | | | | | | | |            (7443), (9011), (9012), (9582), (9609), (9611),
% 197.44/32.32  | | | | | | | | | | | | | | | | | |            (9615), (9616), (9618), (function-axioms) are
% 197.44/32.32  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #77.
% 197.44/32.32  | | | | | | | | | | | | | | | | | | 
% 197.44/32.32  | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.32  | | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | | |   (9619)   ~ (all_50_2 = e3)
% 197.44/32.33  | | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | | | REDUCE: (9614), (9619) imply:
% 197.44/32.33  | | | | | | | | | | | | | | | | | |   (9620)  $false
% 197.44/32.33  | | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | | | CLOSE: (9620) is inconsistent.
% 197.44/32.33  | | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | |   (9621)   ~ (all_56_15 = e3)
% 197.44/32.33  | | | | | | | | | | | | | | | | |   (9622)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.44/32.33  | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (51), (158), (169),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (183), (184), (185), (273), (277), (284), (306),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (313), (317), (321), (324), (325), (332), (351),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (367), (387), (393), (394), (405), (431), (521),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (538), (541), (542), (543), (546), (547), (548),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (549), (553), (555), (557), (564), (567), (569),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (571), (572), (573), (582), (590), (594), (684),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (7445), (7449), (9007), (9011), (9012), (9558),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (9560), (9582), (9583), (9609), (9610), (9611),
% 197.44/32.33  | | | | | | | | | | | | | | | | |            (9621), (9622), (function-axioms) are inconsistent
% 197.44/32.33  | | | | | | | | | | | | | | | | |            by sub-proof #75.
% 197.44/32.33  | | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | |   (9623)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.44/32.33  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.44/32.33  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.44/32.33  | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | BETA: splitting (9623) gives:
% 197.44/32.33  | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9624)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.44/32.33  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | ALPHA: (9624) implies:
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9625)  all_52_22 = e0
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9626)  all_52_20 = e1
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9627)  all_52_16 = e3
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | REDUCE: (178), (9627) imply:
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9628)  op(all_52_17, all_52_17) = e3
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | REDUCE: (175), (9625) imply:
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9629)  op(all_52_23, all_52_23) = e0
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | REDUCE: (612), (9626) imply:
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9630)  op(all_10_2, all_10_2) = e1
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (38), (41), (43), (51),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (61), (158), (162), (168), (169), (173), (174),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (179), (182), (183), (184), (185), (270), (273),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (277), (283), (284), (304), (306), (309), (313),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (317), (321), (324), (325), (332), (333), (351),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (366), (367), (372), (387), (393), (394), (405),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (415), (431), (521), (526), (528), (538), (541),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (562),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (563), (564), (567), (569), (571), (572), (573),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (574), (576), (577), (578), (582), (586), (588),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (591), (593), (594), (600), (603), (604), (605),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (606), (607), (608), (611), (613), (684), (688),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (767), (7449), (7450), (9007), (9011), (9012),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (9558), (9560), (9575), (9578), (9581), (9582),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (9584), (9586), (9587), (9590), (9597), (9599),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (9602), (9628), (9629), (9630), (function-axioms)
% 197.44/32.33  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #73.
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | |   (9631)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.44/32.33  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (684), (688), (9007), (9011), (9590), (9597),
% 197.44/32.33  | | | | | | | | | | | | | | | |            (9598), (9599), (9631), (function-axioms) are
% 197.44/32.33  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 197.44/32.33  | | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | |   (9632)  all_30_1 = e3
% 197.44/32.33  | | | | | | | | |   (9633)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | COMBINE_EQS: (670), (9632) imply:
% 197.44/32.33  | | | | | | | | |   (9634)  all_10_1 = e3
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | SIMP: (9634) implies:
% 197.44/32.33  | | | | | | | | |   (9635)  all_10_1 = e3
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (53), (9635) imply:
% 197.44/32.33  | | | | | | | | |   (9636)  op(all_10_2, e1) = e3
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (52), (9635) imply:
% 197.44/32.33  | | | | | | | | |   (9637)  op(e1, e3) = all_10_0
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.44/32.33  | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (9637)
% 197.44/32.33  | | | | | | | | |              gives:
% 197.44/32.33  | | | | | | | | |   (9638)  all_52_5 = all_10_0
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | COMBINE_EQS: (367), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9639)  all_56_8 = all_10_0
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | COMBINE_EQS: (547), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9640)  all_58_6 = all_10_0
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (562), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9641)   ~ (all_52_3 = all_10_0)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (567), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9642)   ~ (all_52_7 = all_10_0)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | SIMP: (9642) implies:
% 197.44/32.33  | | | | | | | | |   (9643)   ~ (all_52_7 = all_10_0)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (569), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9644)   ~ (all_10_0 = all_10_2)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (553), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9645)   ~ (all_10_0 = all_6_2)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (184), (9638) imply:
% 197.44/32.33  | | | | | | | | |   (9646)  op(all_10_0, all_10_0) = all_52_4
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | |   (9647)   ~ (all_44_0 = e2)
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | REDUCE: (9010), (9647) imply:
% 197.44/32.33  | | | | | | | | | |   (9648)  $false
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | CLOSE: (9648) is inconsistent.
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | |   (9649)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | |   (9650)  all_58_15 = e0
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (9556), (9650),
% 197.44/32.33  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.33  | | | | | | | | | | |            #612.
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | |   (9651)   ~ (all_58_15 = e0)
% 197.44/32.33  | | | | | | | | | | |   (9652)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.33  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.33  | | | | | | | | | | |             e0)
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | ALPHA: (9652) implies:
% 197.44/32.33  | | | | | | | | | | |   (9653)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.33  | | | | | | | | | | |   (9654)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | REDUCE: (541), (9651) imply:
% 197.44/32.33  | | | | | | | | | | |   (9655)   ~ (all_14_2 = e0)
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.44/32.33  | | | | | | | | | | |            (53), (61), (63), (158), (162), (166), (167),
% 197.44/32.33  | | | | | | | | | | |            (168), (169), (172), (173), (174), (175), (177),
% 197.44/32.33  | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.44/32.33  | | | | | | | | | | |            (187), (270), (271), (272), (273), (274), (275),
% 197.44/32.33  | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 197.44/32.33  | | | | | | | | | | |            (283), (285), (304), (306), (307), (309), (311),
% 197.44/32.33  | | | | | | | | | | |            (313), (316), (317), (319), (321), (324), (325),
% 197.44/32.33  | | | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.44/32.33  | | | | | | | | | | |            (352), (361), (366), (367), (372), (375), (387),
% 197.44/32.33  | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.44/32.33  | | | | | | | | | | |            (427), (431), (459), (521), (528), (538), (539),
% 197.44/32.33  | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.44/32.33  | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.44/32.33  | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 197.44/32.33  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.44/32.33  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.44/32.33  | | | | | | | | | | |            (584), (586), (588), (589), (590), (591), (592),
% 197.44/32.33  | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.44/32.33  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.44/32.33  | | | | | | | | | | |            (610), (611), (612), (613), (684), (688), (750),
% 197.44/32.33  | | | | | | | | | | |            (7443), (7445), (7449), (7451), (9007), (9011),
% 197.44/32.33  | | | | | | | | | | |            (9012), (9558), (9560), (9633), (9636), (9639),
% 197.44/32.33  | | | | | | | | | | |            (9640), (9641), (9643), (9644), (9645), (9646),
% 197.44/32.33  | | | | | | | | | | |            (9649), (9653), (9654), (9655), (function-axioms)
% 197.44/32.33  | | | | | | | | | | |            are inconsistent by sub-proof #70.
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | |   (9656)  all_28_0 = e3
% 197.44/32.33  | | | | | | | |   (9657)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 197.44/32.33  | | | | | | | |            (53), (61), (63), (139), (158), (161), (162), (166),
% 197.44/32.33  | | | | | | | |            (167), (168), (169), (172), (173), (174), (177),
% 197.44/32.33  | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.44/32.33  | | | | | | | |            (187), (270), (271), (273), (274), (277), (278),
% 197.44/32.33  | | | | | | | |            (279), (280), (281), (282), (283), (285), (303),
% 197.44/32.33  | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 197.44/32.33  | | | | | | | |            (317), (318), (319), (320), (321), (324), (325),
% 197.44/32.33  | | | | | | | |            (326), (327), (332), (333), (343), (351), (352),
% 197.44/32.33  | | | | | | | |            (366), (367), (372), (375), (376), (387), (388),
% 197.44/32.33  | | | | | | | |            (393), (405), (411), (415), (417), (427), (431),
% 197.44/32.33  | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 197.44/32.33  | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.44/32.33  | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.44/32.33  | | | | | | | |            (563), (564), (566), (567), (569), (570), (571),
% 197.44/32.33  | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 197.44/32.33  | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 197.44/32.33  | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 197.44/32.33  | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 197.44/32.33  | | | | | | | |            (613), (684), (688), (754), (7444), (7445), (7449),
% 197.44/32.33  | | | | | | | |            (7450), (7451), (7453), (7457), (7458), (7459),
% 197.44/32.33  | | | | | | | |            (9007), (9010), (9011), (9556), (9656), (9657),
% 197.44/32.33  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #52.
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | End of split
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | Case 2:
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | |   (9658)  all_16_0 = e2
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | | COMBINE_EQS: (760), (9658) imply:
% 197.44/32.33  | | | | | | |   (9659)  all_10_0 = e2
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | | SIMP: (9659) implies:
% 197.44/32.33  | | | | | | |   (9660)  all_10_0 = e2
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | | COMBINE_EQS: (756), (9660) imply:
% 197.44/32.33  | | | | | | |   (9661)  all_26_0 = e2
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | | REDUCE: (9012), (9660) imply:
% 197.44/32.33  | | | | | | |   (9662)   ~ (e3 = e2)
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | | BETA: splitting (94) gives:
% 197.44/32.33  | | | | | | | 
% 197.44/32.33  | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | |   (9663)   ~ (all_26_0 = e2)
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | | REDUCE: (9661), (9663) imply:
% 197.44/32.33  | | | | | | | |   (9664)  $false
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | | CLOSE: (9664) is inconsistent.
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | |   (9665)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | | BETA: splitting (99) gives:
% 197.44/32.33  | | | | | | | | 
% 197.44/32.33  | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | |   (9666)   ~ (all_28_0 = e3)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | REDUCE: (754), (9666) imply:
% 197.44/32.33  | | | | | | | | |   (9667)   ~ (all_4_0 = e3)
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.33  | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | |   (9668)   ~ (all_44_0 = e2)
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | REDUCE: (9010), (9668) imply:
% 197.44/32.33  | | | | | | | | | |   (9669)  $false
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | CLOSE: (9669) is inconsistent.
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | |   (9670)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | BETA: splitting (153) gives:
% 197.44/32.33  | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | |   (9671)   ~ (all_50_0 = e2)
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | REDUCE: (9555), (9671) imply:
% 197.44/32.33  | | | | | | | | | | |   (9672)  $false
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | CLOSE: (9672) is inconsistent.
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | |   (9673)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.33  | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | |   (9674)  all_58_15 = e0
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (9556), (9674),
% 197.44/32.33  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.33  | | | | | | | | | | | |            #612.
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | |   (9675)   ~ (all_58_15 = e0)
% 197.44/32.33  | | | | | | | | | | | |   (9676)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.33  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.33  | | | | | | | | | | | |             e0)
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | ALPHA: (9676) implies:
% 197.44/32.33  | | | | | | | | | | | |   (9677)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.33  | | | | | | | | | | | |   (9678)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | REDUCE: (541), (9675) imply:
% 197.44/32.33  | | | | | | | | | | | |   (9679)   ~ (all_14_2 = e0)
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.44/32.33  | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | |   (9680)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.33  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.44/32.33  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | BETA: splitting (9680) gives:
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | |   (9681)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.33  | | | | | | | | | | | | | |           all_52_6 = e0
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 197.44/32.33  | | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 197.44/32.33  | | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 197.44/32.33  | | | | | | | | | | | | | |            (9011), (9681), (function-axioms) are inconsistent
% 197.44/32.33  | | | | | | | | | | | | | |            by sub-proof #501.
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | |   (9682)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.44/32.33  | | | | | | | | | | | | | |           all_52_14 = e0
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (63),
% 197.44/32.33  | | | | | | | | | | | | | |            (158), (162), (166), (167), (168), (169), (174),
% 197.44/32.33  | | | | | | | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.44/32.33  | | | | | | | | | | | | | |            (270), (273), (274), (276), (277), (278), (281),
% 197.44/32.33  | | | | | | | | | | | | | |            (283), (306), (309), (313), (317), (319), (321),
% 197.44/32.33  | | | | | | | | | | | | | |            (325), (326), (333), (351), (352), (366), (367),
% 197.44/32.33  | | | | | | | | | | | | | |            (372), (387), (393), (405), (411), (415), (421),
% 197.44/32.33  | | | | | | | | | | | | | |            (427), (431), (521), (528), (538), (541), (542),
% 197.44/32.33  | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.44/32.33  | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.44/32.33  | | | | | | | | | | | | | |            (563), (564), (567), (568), (571), (573), (574),
% 197.44/32.33  | | | | | | | | | | | | | |            (577), (578), (580), (582), (593), (594), (595),
% 197.44/32.33  | | | | | | | | | | | | | |            (602), (604), (606), (607), (608), (609), (611),
% 197.44/32.33  | | | | | | | | | | | | | |            (613), (684), (688), (7443), (7445), (7449),
% 197.44/32.33  | | | | | | | | | | | | | |            (7451), (9007), (9011), (9667), (9670), (9679),
% 197.44/32.33  | | | | | | | | | | | | | |            (9682), (function-axioms) are inconsistent by
% 197.44/32.33  | | | | | | | | | | | | | |            sub-proof #86.
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | End of split
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | Case 2:
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | |   (9683)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.44/32.33  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.44/32.33  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | BETA: splitting (9683) gives:
% 197.44/32.33  | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | Case 1:
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | |   (9684)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.44/32.33  | | | | | | | | | | | | | |           all_52_22 = e0
% 197.44/32.33  | | | | | | | | | | | | | | 
% 197.44/32.33  | | | | | | | | | | | | | | ALPHA: (9684) implies:
% 197.44/32.33  | | | | | | | | | | | | | |   (9685)  all_52_22 = e0
% 197.44/32.34  | | | | | | | | | | | | | |   (9686)  all_52_20 = e1
% 197.44/32.34  | | | | | | | | | | | | | |   (9687)  all_52_16 = e3
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (178), (9687) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9688)  op(all_52_17, all_52_17) = e3
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (175), (9685) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9689)  op(all_52_23, all_52_23) = e0
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (612), (9686) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9690)  op(all_10_2, all_10_2) = e1
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | |   (9691)  all_56_15 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | COMBINE_EQS: (538), (9691) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9692)  all_14_2 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | SIMP: (9692) implies:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9693)  all_14_2 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | COMBINE_EQS: (335), (9693) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9694)  all_50_2 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (573), (9693) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9695)   ~ (all_52_7 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (606), (9693) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9696)   ~ (all_52_25 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (609), (9693) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9697)   ~ (all_52_29 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (613), (9693) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9698)  op(e3, e3) = all_52_30
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (63), (9693) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9699)  op(e3, e0) = all_14_1
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | BETA: splitting (9673) gives:
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 197.44/32.34  | | | | | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (9699)
% 197.44/32.34  | | | | | | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9700)  all_52_25 = all_14_1
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.44/32.34  | | | | | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (9698)
% 197.44/32.34  | | | | | | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9701)  all_52_30 = all_6_2
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (9700) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9702)  all_58_9 = all_14_1
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9703)  all_58_2 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (53), (168),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (182), (185), (313), (317), (325), (327), (331),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (332), (333), (351), (366), (387), (393), (405),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (512), (543), (544), (545), (546), (547), (548),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (549), (551), (557), (559), (562), (563), (564),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (569), (574), (575), (576), (588), (676), (9665),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (9688), (9690), (9696), (9697), (9702), (9703),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.34  | | | | | | | | | | | | | | | | |            #237.
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9704)   ~ (all_58_2 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REDUCE: (387), (9704) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9705)   ~ (all_52_3 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (41), (43), (51), (158),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (169), (184), (273), (283), (304), (317), (332),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (351), (387), (393), (405), (415), (431), (521),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (541), (542), (543), (546), (547), (555), (559),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (569), (571), (572), (577), (594), (600), (613),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (684), (7449), (9007), (9011), (9667), (9677),
% 197.44/32.34  | | | | | | | | | | | | | | | | |            (9688), (9689), (9695), (9705), (function-axioms)
% 197.44/32.34  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #83.
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9706)   ~ (all_50_2 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | REDUCE: (9694), (9706) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9707)  $false
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | CLOSE: (9707) is inconsistent.
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | |   (9708)   ~ (all_56_15 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (538), (9708) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9709)   ~ (all_14_2 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.34  | | | | | | | | | | | | | | |            (51), (53), (158), (168), (169), (173), (174),
% 197.44/32.34  | | | | | | | | | | | | | | |            (183), (184), (185), (271), (273), (283), (304),
% 197.44/32.34  | | | | | | | | | | | | | | |            (306), (309), (313), (317), (321), (325), (327),
% 197.44/32.34  | | | | | | | | | | | | | | |            (331), (332), (333), (343), (351), (366), (372),
% 197.44/32.34  | | | | | | | | | | | | | | |            (375), (387), (393), (405), (415), (431), (512),
% 197.44/32.34  | | | | | | | | | | | | | | |            (521), (541), (542), (543), (544), (545), (546),
% 197.44/32.34  | | | | | | | | | | | | | | |            (547), (548), (549), (551), (555), (557), (559),
% 197.44/32.34  | | | | | | | | | | | | | | |            (562), (563), (564), (569), (571), (572), (576),
% 197.44/32.34  | | | | | | | | | | | | | | |            (577), (582), (587), (588), (593), (594), (596),
% 197.44/32.34  | | | | | | | | | | | | | | |            (600), (604), (605), (606), (613), (676), (684),
% 197.44/32.34  | | | | | | | | | | | | | | |            (7445), (7449), (9007), (9011), (9665), (9667),
% 197.44/32.34  | | | | | | | | | | | | | | |            (9677), (9688), (9689), (9690), (9709),
% 197.44/32.34  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.34  | | | | | | | | | | | | | | |            #56.
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | |   (9710)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.44/32.34  | | | | | | | | | | | | | |           all_52_30 = e0
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (41), (43), (51), (53),
% 197.44/32.34  | | | | | | | | | | | | | |            (61), (63), (158), (162), (166), (167), (168),
% 197.44/32.34  | | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (180),
% 197.44/32.34  | | | | | | | | | | | | | |            (182), (183), (184), (185), (270), (271), (273),
% 197.44/32.34  | | | | | | | | | | | | | |            (274), (277), (278), (279), (280), (282), (283),
% 197.44/32.34  | | | | | | | | | | | | | |            (285), (306), (307), (309), (311), (313), (316),
% 197.44/32.34  | | | | | | | | | | | | | |            (317), (319), (321), (324), (325), (326), (327),
% 197.44/32.34  | | | | | | | | | | | | | |            (332), (333), (343), (351), (352), (366), (367),
% 197.44/32.34  | | | | | | | | | | | | | |            (372), (375), (387), (388), (393), (405), (415),
% 197.44/32.34  | | | | | | | | | | | | | |            (417), (427), (431), (521), (528), (538), (539),
% 197.44/32.34  | | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.44/32.34  | | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (559),
% 197.44/32.34  | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.44/32.34  | | | | | | | | | | | | | |            (570), (572), (573), (574), (575), (577), (578),
% 197.44/32.34  | | | | | | | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 197.44/32.34  | | | | | | | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 197.44/32.34  | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 197.44/32.34  | | | | | | | | | | | | | |            (684), (688), (9007), (9011), (9670), (9677),
% 197.44/32.34  | | | | | | | | | | | | | |            (9678), (9679), (9710), (function-axioms) are
% 197.44/32.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #434.
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | |   (9711)  all_28_0 = e3
% 197.44/32.34  | | | | | | | | |   (9712)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.34  | | | | | | | | |            (51), (53), (61), (63), (139), (158), (161), (162),
% 197.44/32.34  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.44/32.34  | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.44/32.34  | | | | | | | | |            (185), (187), (270), (271), (273), (274), (277),
% 197.44/32.34  | | | | | | | | |            (278), (279), (280), (281), (282), (283), (285),
% 197.44/32.34  | | | | | | | | |            (303), (306), (307), (309), (311), (313), (315),
% 197.44/32.34  | | | | | | | | |            (316), (317), (318), (319), (320), (321), (324),
% 197.44/32.34  | | | | | | | | |            (325), (326), (327), (332), (333), (343), (351),
% 197.44/32.34  | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.44/32.34  | | | | | | | | |            (388), (393), (405), (411), (415), (417), (427),
% 197.44/32.34  | | | | | | | | |            (431), (521), (528), (538), (539), (540), (541),
% 197.44/32.34  | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.44/32.34  | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.44/32.34  | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.44/32.34  | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 197.44/32.34  | | | | | | | | |            (580), (582), (584), (586), (589), (590), (592),
% 197.44/32.34  | | | | | | | | |            (593), (594), (595), (596), (598), (602), (603),
% 197.44/32.34  | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.44/32.34  | | | | | | | | |            (612), (613), (684), (688), (754), (7444), (7445),
% 197.44/32.34  | | | | | | | | |            (7449), (7450), (7451), (7453), (7457), (7458),
% 197.44/32.34  | | | | | | | | |            (7459), (9007), (9010), (9011), (9556), (9711),
% 197.44/32.34  | | | | | | | | |            (9712), (function-axioms) are inconsistent by
% 197.44/32.34  | | | | | | | | |            sub-proof #52.
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | End of split
% 197.44/32.34  | | | | | | | | 
% 197.44/32.34  | | | | | | | End of split
% 197.44/32.34  | | | | | | | 
% 197.44/32.34  | | | | | | End of split
% 197.44/32.34  | | | | | | 
% 197.44/32.34  | | | | | End of split
% 197.44/32.34  | | | | | 
% 197.44/32.34  | | | | Case 2:
% 197.44/32.34  | | | | | 
% 197.44/32.34  | | | | |   (9713)  all_10_0 = e3
% 197.44/32.34  | | | | | 
% 197.44/32.34  | | | | | REDUCE: (52), (9713) imply:
% 197.44/32.34  | | | | |   (9714)  op(e1, all_10_1) = e3
% 197.44/32.34  | | | | | 
% 197.44/32.34  | | | | | BETA: splitting (64) gives:
% 197.44/32.34  | | | | | 
% 197.44/32.34  | | | | | Case 1:
% 197.44/32.34  | | | | | | 
% 197.44/32.34  | | | | | |   (9715)   ~ (all_14_0 = e2)
% 197.44/32.34  | | | | | | 
% 197.44/32.34  | | | | | | BETA: splitting (74) gives:
% 197.44/32.34  | | | | | | 
% 197.44/32.34  | | | | | | Case 1:
% 197.44/32.34  | | | | | | | 
% 197.44/32.34  | | | | | | |   (9716)   ~ (all_18_0 = e3)
% 197.44/32.34  | | | | | | | 
% 197.44/32.34  | | | | | | | REDUCE: (761), (9716) imply:
% 197.44/32.34  | | | | | | |   (9717)   ~ (all_14_0 = e3)
% 197.44/32.34  | | | | | | | 
% 197.44/32.34  | | | | | | | BETA: splitting (89) gives:
% 197.44/32.34  | | | | | | | 
% 197.44/32.34  | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | 
% 197.44/32.34  | | | | | | | |   (9718)   ~ (all_24_0 = e1)
% 197.44/32.34  | | | | | | | | 
% 197.44/32.34  | | | | | | | | REDUCE: (711), (9718) imply:
% 197.44/32.34  | | | | | | | |   (9719)   ~ (all_14_0 = e1)
% 197.44/32.34  | | | | | | | | 
% 197.44/32.34  | | | | | | | | BETA: splitting (99) gives:
% 197.44/32.34  | | | | | | | | 
% 197.44/32.34  | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | |   (9720)   ~ (all_28_0 = e3)
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | REDUCE: (754), (9720) imply:
% 197.44/32.34  | | | | | | | | |   (9721)   ~ (all_4_0 = e3)
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.34  | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | |   (9722)   ~ (all_44_0 = e2)
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | REDUCE: (9010), (9722) imply:
% 197.44/32.34  | | | | | | | | | |   (9723)  $false
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | CLOSE: (9723) is inconsistent.
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | |   (9724)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.34  | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | |   (9725)  all_58_15 = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | COMBINE_EQS: (541), (9725) imply:
% 197.44/32.34  | | | | | | | | | | |   (9726)  all_14_2 = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (573), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9727)   ~ (all_52_7 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (591), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9728)   ~ (all_52_15 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (603), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9729)   ~ (all_52_23 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (606), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9730)   ~ (all_52_25 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (609), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9731)   ~ (all_52_29 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (613), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9732)  op(e0, e0) = all_52_30
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (63), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9733)  op(e0, e0) = all_14_1
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (61), (9726) imply:
% 197.44/32.34  | | | | | | | | | | |   (9734)  op(e0, e0) = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.44/32.34  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9732), (9733)
% 197.44/32.34  | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | |   (9735)  all_52_30 = all_14_1
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.44/32.34  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (9732), (9734)
% 197.44/32.34  | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | |   (9736)  all_52_30 = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | COMBINE_EQS: (9735), (9736) imply:
% 197.44/32.34  | | | | | | | | | | |   (9737)  all_14_1 = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | SIMP: (9737) implies:
% 197.44/32.34  | | | | | | | | | | |   (9738)  all_14_1 = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (62), (9738) imply:
% 197.44/32.34  | | | | | | | | | | |   (9739)  op(e0, e0) = all_14_0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.44/32.34  | | | | | | | | | | |              e0, e0, simplifying with (9734), (9739) gives:
% 197.44/32.34  | | | | | | | | | | |   (9740)  all_14_0 = e0
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (9717), (9740) imply:
% 197.44/32.34  | | | | | | | | | | |   (9741)   ~ (e3 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (9715), (9740) imply:
% 197.44/32.34  | | | | | | | | | | |   (9742)   ~ (e2 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | REDUCE: (9719), (9740) imply:
% 197.44/32.34  | | | | | | | | | | |   (9743)   ~ (e1 = e0)
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | BETA: splitting (187) gives:
% 197.44/32.34  | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | |   (9744)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.34  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.44/32.34  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.44/32.34  | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | BETA: splitting (9744) gives:
% 197.44/32.34  | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | |   (9745)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.34  | | | | | | | | | | | | |           all_52_6 = e0
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 197.44/32.34  | | | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 197.44/32.34  | | | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 197.44/32.34  | | | | | | | | | | | | |            (9011), (9745), (function-axioms) are inconsistent
% 197.44/32.34  | | | | | | | | | | | | |            by sub-proof #501.
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | |   (9746)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.44/32.34  | | | | | | | | | | | | |           all_52_14 = e0
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | ALPHA: (9746) implies:
% 197.44/32.34  | | | | | | | | | | | | |   (9747)  all_52_14 = e0
% 197.44/32.34  | | | | | | | | | | | | |   (9748)  all_52_12 = e1
% 197.44/32.34  | | | | | | | | | | | | |   (9749)  all_52_10 = e2
% 197.44/32.34  | | | | | | | | | | | | |   (9750)  all_52_8 = e3
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | REDUCE: (182), (9750) imply:
% 197.44/32.34  | | | | | | | | | | | | |   (9751)  op(all_52_9, all_52_9) = e3
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | REDUCE: (180), (9748) imply:
% 197.44/32.34  | | | | | | | | | | | | |   (9752)  op(all_52_13, all_52_13) = e1
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | REDUCE: (179), (9747) imply:
% 197.44/32.34  | | | | | | | | | | | | |   (9753)  op(all_52_15, all_52_15) = e0
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | REDUCE: (611), (9749) imply:
% 197.44/32.34  | | | | | | | | | | | | |   (9754)  op(all_4_2, all_4_2) = e2
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.44/32.34  | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | |   (9755)  all_56_14 = e3
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | COMBINE_EQS: (343), (9755) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9756)  all_52_23 = e3
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | SIMP: (9756) implies:
% 197.44/32.34  | | | | | | | | | | | | | |   (9757)  all_52_23 = e3
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (572), (9757) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9758)   ~ (all_52_7 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (590), (9757) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9759)   ~ (all_52_15 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (156), (9757) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9760)  op(e0, e1) = e3
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (51), (53), (162), (183), (272), (273),
% 197.44/32.34  | | | | | | | | | | | | | |            (276), (304), (305), (346), (351), (421), (431),
% 197.44/32.34  | | | | | | | | | | | | | |            (543), (568), (571), (582), (587), (588), (9714),
% 197.44/32.34  | | | | | | | | | | | | | |            (9727), (9728), (9734), (9752), (9753), (9754),
% 197.44/32.34  | | | | | | | | | | | | | |            (9758), (9759), (9760), (function-axioms) are
% 197.44/32.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #51.
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | |   (9761)   ~ (all_56_14 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | REDUCE: (343), (9761) imply:
% 197.44/32.34  | | | | | | | | | | | | | |   (9762)   ~ (all_52_23 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.44/32.34  | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | |   (9763)  all_58_4 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9763) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9764)  all_52_17 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | SIMP: (9764) implies:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9765)  all_52_17 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (577), (9765) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9766)   ~ (all_52_9 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (594), (9765) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9767)   ~ (all_52_23 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (595), (9765) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9768)   ~ (all_52_25 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | SIMP: (9768) implies:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9769)   ~ (all_52_25 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (7451), (9765) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9770)   ~ (all_4_0 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REDUCE: (178), (9765) imply:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9771)  op(e3, e3) = all_52_16
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.44/32.34  | | | | | | | | | | | | | | |              all_52_16, e3, e3, simplifying with (41), (9771)
% 197.44/32.34  | | | | | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | | | | | |   (9772)  all_52_16 = all_6_2
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (43), (51), (158),
% 197.44/32.34  | | | | | | | | | | | | | | |            (162), (169), (183), (184), (271), (273), (274),
% 197.44/32.34  | | | | | | | | | | | | | | |            (277), (306), (313), (321), (325), (326), (333),
% 197.44/32.34  | | | | | | | | | | | | | | |            (343), (351), (352), (366), (367), (372), (387),
% 197.44/32.34  | | | | | | | | | | | | | | |            (393), (405), (431), (521), (528), (542), (543),
% 197.44/32.34  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (553),
% 197.44/32.34  | | | | | | | | | | | | | | |            (555), (557), (563), (567), (571), (572), (580),
% 197.44/32.34  | | | | | | | | | | | | | | |            (582), (590), (593), (602), (607), (684), (688),
% 197.44/32.34  | | | | | | | | | | | | | | |            (7443), (7445), (7449), (9007), (9011), (9721),
% 197.44/32.34  | | | | | | | | | | | | | | |            (9724), (9725), (9727), (9729), (9751), (9752),
% 197.44/32.34  | | | | | | | | | | | | | | |            (9753), (9762), (9766), (9769), (9771),
% 197.44/32.34  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.34  | | | | | | | | | | | | | | |            #97.
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | |   (9773)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | BETA: splitting (9773) gives:
% 197.44/32.34  | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9774)  all_58_5 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (9721), (9774) are inconsistent by
% 197.44/32.34  | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | |   (9775)  all_58_8 = e3 | all_58_14 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | BETA: splitting (9775) gives:
% 197.44/32.34  | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9776)  all_58_8 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (9776) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9777)  all_10_2 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REDUCE: (593), (9777) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9778)   ~ (all_52_17 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REDUCE: (7457), (9777) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9779)   ~ (all_4_0 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REDUCE: (612), (9777) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9780)  op(e3, e3) = all_52_20
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | REDUCE: (53), (9777) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9781)  op(e3, e1) = all_10_1
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 197.44/32.34  | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (9781)
% 197.44/32.34  | | | | | | | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9782)  all_52_17 = all_10_1
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.44/32.34  | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (41), (9780)
% 197.44/32.34  | | | | | | | | | | | | | | | | |              gives:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9783)  all_52_20 = all_6_2
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9782) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | |   (9784)  all_58_4 = all_10_1
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 197.44/32.34  | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.34  | | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | |   (9785)  all_58_9 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (9785) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | | |   (9786)  all_52_25 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | | SIMP: (9786) implies:
% 197.44/32.34  | | | | | | | | | | | | | | | | | |   (9787)  all_52_25 = e3
% 197.44/32.34  | | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | | REDUCE: (604), (9787) imply:
% 197.44/32.34  | | | | | | | | | | | | | | | | | |   (9788)   ~ (all_52_27 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | | SIMP: (9788) implies:
% 197.44/32.34  | | | | | | | | | | | | | | | | | |   (9789)   ~ (all_52_27 = e3)
% 197.44/32.34  | | | | | | | | | | | | | | | | | | 
% 197.44/32.34  | | | | | | | | | | | | | | | | | | REDUCE: (605), (9787) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9790)   ~ (all_52_29 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | SIMP: (9790) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9791)   ~ (all_52_29 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REDUCE: (174), (9787) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9792)  op(e3, e3) = all_52_24
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.44/32.35  | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (9792)
% 197.44/32.35  | | | | | | | | | | | | | | | | | |              gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9793)  all_52_24 = all_6_2
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9794)  all_58_2 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (9794) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9795)  all_52_3 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | SIMP: (9795) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9796)  all_52_3 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (9796) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9797)   ~ (all_52_7 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | SIMP: (9797) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9798)   ~ (all_52_7 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (41), (43), (158), (169), (183), (271),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            (273), (306), (343), (351), (431), (521), (542),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            (543), (555), (571), (572), (582), (590), (684),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            (9007), (9011), (9725), (9729), (9751), (9753),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            (9762), (9798), (function-axioms) are inconsistent
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            by sub-proof #79.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9799)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (159), (314), (372), (542), (548),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            (7443), (7449), (9714), (9721), (9729), (9776),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            (9784), (9789), (9791), (9799), (function-axioms)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #49.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9800)   ~ (all_58_9 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (43), (306), (333), (351), (393),
% 197.44/32.35  | | | | | | | | | | | | | | | | | |            (405), (542), (543), (545), (549), (555), (557),
% 197.44/32.35  | | | | | | | | | | | | | | | | | |            (610), (9725), (9728), (9751), (9753), (9762),
% 197.44/32.35  | | | | | | | | | | | | | | | | | |            (9778), (9800), (function-axioms) are inconsistent
% 197.44/32.35  | | | | | | | | | | | | | | | | | |            by sub-proof #93.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9801)  all_58_14 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (9762), (9801) are inconsistent by
% 197.44/32.35  | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | |   (9802)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.44/32.35  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.44/32.35  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.44/32.35  | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | BETA: splitting (9802) gives:
% 197.44/32.35  | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | |   (9803)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.44/32.35  | | | | | | | | | | | | |           all_52_22 = e0
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | ALPHA: (9803) implies:
% 197.44/32.35  | | | | | | | | | | | | |   (9804)  all_52_22 = e0
% 197.44/32.35  | | | | | | | | | | | | |   (9805)  all_52_20 = e1
% 197.44/32.35  | | | | | | | | | | | | |   (9806)  all_52_16 = e3
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | REDUCE: (178), (9806) imply:
% 197.44/32.35  | | | | | | | | | | | | |   (9807)  op(all_52_17, all_52_17) = e3
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | REDUCE: (175), (9804) imply:
% 197.44/32.35  | | | | | | | | | | | | |   (9808)  op(all_52_23, all_52_23) = e0
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | REDUCE: (612), (9805) imply:
% 197.44/32.35  | | | | | | | | | | | | |   (9809)  op(all_10_2, all_10_2) = e1
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | |   (9810)  all_56_14 = e3
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | COMBINE_EQS: (343), (9810) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9811)  all_52_23 = e3
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | SIMP: (9811) implies:
% 197.44/32.35  | | | | | | | | | | | | | |   (9812)  all_52_23 = e3
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | COMBINE_EQS: (542), (9812) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9813)  all_58_14 = e3
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REDUCE: (572), (9812) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9814)   ~ (all_52_7 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REDUCE: (590), (9812) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9815)   ~ (all_52_15 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REDUCE: (594), (9812) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9816)   ~ (all_52_17 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REDUCE: (600), (9812) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9817)   ~ (all_10_2 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | SIMP: (9817) implies:
% 197.44/32.35  | | | | | | | | | | | | | |   (9818)   ~ (all_10_2 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REDUCE: (9808), (9812) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9819)  op(e3, e3) = e0
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (41), (43), (51), (158), (169), (179),
% 197.44/32.35  | | | | | | | | | | | | | |            (272), (273), (283), (304), (346), (351), (415),
% 197.44/32.35  | | | | | | | | | | | | | |            (431), (521), (541), (543), (555), (559), (571),
% 197.44/32.35  | | | | | | | | | | | | | |            (577), (613), (684), (9007), (9011), (9807),
% 197.44/32.35  | | | | | | | | | | | | | |            (9813), (9814), (9815), (9816), (9818), (9819),
% 197.44/32.35  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.35  | | | | | | | | | | | | | |            #90.
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | |   (9820)   ~ (all_56_14 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | REDUCE: (343), (9820) imply:
% 197.44/32.35  | | | | | | | | | | | | | |   (9821)   ~ (all_52_23 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | |   (9822)  all_58_4 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9822) imply:
% 197.44/32.35  | | | | | | | | | | | | | | |   (9823)  all_52_17 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | SIMP: (9823) implies:
% 197.44/32.35  | | | | | | | | | | | | | | |   (9824)  all_52_17 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | REF_CLOSE: (41), (559), (9807), (9824), (function-axioms) are
% 197.44/32.35  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1280.
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | |   (9825)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | BETA: splitting (9825) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | |   (9826)  all_58_5 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (9721), (9826) are inconsistent by
% 197.44/32.35  | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | |   (9827)  all_58_8 = e3 | all_58_14 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | BETA: splitting (9827) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9828)  all_58_8 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (9828) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9829)  all_10_2 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (569), (9829) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9830)   ~ (all_52_5 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (602), (9829) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9831)   ~ (all_52_29 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (9809), (9829) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9832)  op(e3, e3) = e1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (53), (9829) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9833)  op(e3, e1) = all_10_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 197.44/32.35  | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (9833)
% 197.44/32.35  | | | | | | | | | | | | | | | | |              gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9834)  all_52_17 = all_10_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 197.44/32.35  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (41), (9832) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9835)  all_6_2 = e1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | COMBINE_EQS: (528), (9835) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9836)  all_44_2 = e1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (9834) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9837)  all_58_4 = all_10_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (9835) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9838)  all_58_0 = e1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (553), (9835) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9839)   ~ (all_52_5 = e1)
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (555), (9835) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9840)   ~ (all_52_7 = e1)
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REDUCE: (43), (9835) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9841)  op(e1, e3) = all_6_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | BETA: splitting (9724) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9842)   ~ (all_44_2 = e1)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REDUCE: (9836), (9842) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9843)  $false
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | CLOSE: (9843) is inconsistent.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9844)   ~ (all_44_1 = e0)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REDUCE: (688), (9844) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9845)   ~ (all_6_1 = e0)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.44/32.35  | | | | | | | | | | | | | | | | | |              all_6_1, e3, e1, simplifying with (162), (9841)
% 197.44/32.35  | | | | | | | | | | | | | | | | | |              gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9846)  all_52_5 = all_6_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (9846) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9847)  all_56_8 = all_6_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (9846) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9848)  all_58_6 = all_6_1
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REDUCE: (567), (9846) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9849)   ~ (all_52_7 = all_6_1)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | SIMP: (9849) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9850)   ~ (all_52_7 = all_6_1)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REDUCE: (9830), (9846) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9851)   ~ (all_6_1 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | REDUCE: (9839), (9846) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | |   (9852)   ~ (all_6_1 = e1)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9853)  all_56_8 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9847), (9851), (9853) are inconsistent by
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |            sub-proof #1101.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | |   (9854)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | |   (9855)  all_58_0 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9838), (9855) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | |   (9856)  e1 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (9856) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | |   (9857)  $false
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | CLOSE: (9857) is inconsistent.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | |   (9858)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9854) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | |   (9859)  all_56_8 = e2
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9847), (9859) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | |   (9860)  all_6_1 = e2
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | SIMP: (9860) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | |   (9861)  all_6_1 = e2
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9850), (9861) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | |   (9862)   ~ (all_52_7 = e2)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |   (9863)  all_56_12 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (9863) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |   (9864)  all_52_7 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | SIMP: (9864) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |   (9865)  all_52_7 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (9865) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |   (9866)  all_58_12 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (9865) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |   (9867)   ~ (all_52_3 = e3)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9858) gives:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |   (9868)  all_58_2 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (9868) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |   (9869)  all_52_3 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9869) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |   (9870)  all_52_3 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7450), (9870) imply:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |   (9871)   ~ (all_4_0 = e0)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9871) implies:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |   (9872)   ~ (all_4_0 = e0)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (314), (542), (7449), (9714), (9729),
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |            (9828), (9831), (9837), (9872), (function-axioms)
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |   (9873)  all_58_6 = e0 | all_58_12 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9845), (9848), (9866), (9873) are
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #485.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |   (9874)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (9727), (9840), (9862), (9874) are
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #155.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | |   (9875)  all_56_8 = e1 | all_56_8 = e0
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9845), (9847), (9852), (9875) are inconsistent by
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | |            sub-proof #495.
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | |   (9876)  all_58_14 = e3
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (9821), (9876) are inconsistent by
% 197.44/32.35  | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 197.44/32.35  | | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | |   (9877)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.44/32.35  | | | | | | | | | | | | |           all_52_30 = e0
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (41), (43), (51),
% 197.44/32.35  | | | | | | | | | | | | |            (61), (162), (166), (167), (169), (172), (173),
% 197.44/32.35  | | | | | | | | | | | | |            (174), (175), (177), (178), (183), (185), (272),
% 197.44/32.35  | | | | | | | | | | | | |            (274), (276), (277), (279), (281), (282), (306),
% 197.44/32.35  | | | | | | | | | | | | |            (307), (308), (309), (310), (311), (313), (317),
% 197.44/32.35  | | | | | | | | | | | | |            (320), (321), (326), (332), (333), (346), (351),
% 197.44/32.35  | | | | | | | | | | | | |            (352), (366), (367), (372), (375), (387), (388),
% 197.44/32.35  | | | | | | | | | | | | |            (393), (405), (411), (417), (421), (528), (542),
% 197.44/32.35  | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.44/32.35  | | | | | | | | | | | | |            (551), (553), (555), (561), (562), (564), (565),
% 197.44/32.35  | | | | | | | | | | | | |            (566), (567), (568), (569), (570), (572), (576),
% 197.44/32.35  | | | | | | | | | | | | |            (578), (580), (582), (584), (587), (588), (589),
% 197.44/32.35  | | | | | | | | | | | | |            (592), (593), (595), (596), (600), (604), (605),
% 197.44/32.35  | | | | | | | | | | | | |            (608), (609), (610), (688), (9011), (9724),
% 197.44/32.35  | | | | | | | | | | | | |            (9725), (9727), (9728), (9729), (9730), (9731),
% 197.44/32.35  | | | | | | | | | | | | |            (9877), (function-axioms) are inconsistent by
% 197.44/32.35  | | | | | | | | | | | | |            sub-proof #418.
% 197.44/32.35  | | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | |   (9878)   ~ (all_58_15 = e0)
% 197.44/32.35  | | | | | | | | | | |   (9879)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.35  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.35  | | | | | | | | | | |             e0)
% 197.44/32.35  | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.35  | | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 197.44/32.35  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.35  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.44/32.35  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (273),
% 197.44/32.35  | | | | | | | | | | |            (274), (276), (277), (278), (279), (280), (281),
% 197.44/32.35  | | | | | | | | | | |            (282), (283), (285), (304), (306), (307), (309),
% 197.44/32.35  | | | | | | | | | | |            (311), (313), (316), (317), (319), (321), (324),
% 197.44/32.35  | | | | | | | | | | |            (325), (326), (327), (331), (332), (333), (343),
% 197.44/32.35  | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.44/32.35  | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.44/32.35  | | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.44/32.35  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.35  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.35  | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 197.44/32.35  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 197.44/32.35  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 197.44/32.35  | | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 197.44/32.35  | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.44/32.35  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.44/32.35  | | | | | | | | | | |            (611), (612), (613), (684), (688), (7443), (7445),
% 197.44/32.35  | | | | | | | | | | |            (7449), (7450), (7451), (7458), (9007), (9011),
% 197.44/32.35  | | | | | | | | | | |            (9714), (9721), (9724), (9878), (9879),
% 197.44/32.35  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.35  | | | | | | | | | | |            #43.
% 197.44/32.35  | | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | End of split
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | Case 2:
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | |   (9880)  all_28_0 = e3
% 197.44/32.35  | | | | | | | | |   (9881)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | COMBINE_EQS: (754), (9880) imply:
% 197.44/32.35  | | | | | | | | |   (9882)  all_4_0 = e3
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | SIMP: (9882) implies:
% 197.44/32.35  | | | | | | | | |   (9883)  all_4_0 = e3
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | COMBINE_EQS: (7449), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9884)  all_58_5 = e3
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REDUCE: (7450), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9885)   ~ (all_52_3 = e3)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REDUCE: (7451), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9886)   ~ (all_52_17 = e3)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REDUCE: (7453), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9887)   ~ (all_52_23 = e3)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REDUCE: (7457), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9888)   ~ (all_10_2 = e3)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REDUCE: (7458), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9889)   ~ (all_4_2 = e3)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | SIMP: (9889) implies:
% 197.44/32.35  | | | | | | | | |   (9890)   ~ (all_4_2 = e3)
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REDUCE: (7459), (9883) imply:
% 197.44/32.35  | | | | | | | | |   (9891)  op(e3, e3) = all_52_18
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.35  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.35  | | | | | | | | |            (51), (53), (61), (62), (63), (139), (158), (161),
% 197.44/32.35  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.35  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.44/32.35  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 197.44/32.35  | | | | | | | | |            (273), (274), (276), (277), (278), (279), (280),
% 197.44/32.35  | | | | | | | | |            (281), (282), (283), (285), (303), (306), (307),
% 197.44/32.35  | | | | | | | | |            (308), (309), (310), (311), (313), (315), (316),
% 197.44/32.35  | | | | | | | | |            (317), (318), (319), (320), (321), (324), (325),
% 197.44/32.35  | | | | | | | | |            (326), (327), (332), (333), (343), (346), (351),
% 197.44/32.35  | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.44/32.35  | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.44/32.35  | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.44/32.35  | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.35  | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.35  | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 197.44/32.35  | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.44/32.35  | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 197.44/32.35  | | | | | | | | |            (586), (587), (588), (589), (590), (591), (592),
% 197.44/32.35  | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.44/32.35  | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.44/32.35  | | | | | | | | |            (610), (612), (613), (684), (688), (7444), (7445),
% 197.44/32.35  | | | | | | | | |            (9007), (9010), (9011), (9715), (9717), (9719),
% 197.44/32.35  | | | | | | | | |            (9881), (9884), (9885), (9886), (9887), (9888),
% 197.44/32.35  | | | | | | | | |            (9890), (9891), (function-axioms) are inconsistent
% 197.44/32.35  | | | | | | | | |            by sub-proof #64.
% 197.44/32.35  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | End of split
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | |   (9892)  all_24_0 = e1
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | COMBINE_EQS: (711), (9892) imply:
% 197.44/32.36  | | | | | | | |   (9893)  all_14_0 = e1
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | SIMP: (9893) implies:
% 197.44/32.36  | | | | | | | |   (9894)  all_14_0 = e1
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (9717), (9894) imply:
% 197.44/32.36  | | | | | | | |   (9895)   ~ (e3 = e1)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (9715), (9894) imply:
% 197.44/32.36  | | | | | | | |   (9896)   ~ (e2 = e1)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (62), (9894) imply:
% 197.44/32.36  | | | | | | | |   (9897)  op(e0, all_14_1) = e1
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | BETA: splitting (99) gives:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | |   (9898)   ~ (all_28_0 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (754), (9898) imply:
% 197.44/32.36  | | | | | | | | |   (9899)   ~ (all_4_0 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | |   (9900)   ~ (all_44_0 = e2)
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | REDUCE: (9010), (9900) imply:
% 197.44/32.36  | | | | | | | | | |   (9901)  $false
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | CLOSE: (9901) is inconsistent.
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | |   (9902)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | |   (9903)  all_58_15 = e0
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (9897), (9903),
% 197.44/32.36  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.36  | | | | | | | | | | |            #877.
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | |   (9904)   ~ (all_58_15 = e0)
% 197.44/32.36  | | | | | | | | | | |   (9905)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.36  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.36  | | | | | | | | | | |             e0)
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.36  | | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 197.44/32.36  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.36  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.44/32.36  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (273),
% 197.44/32.36  | | | | | | | | | | |            (274), (276), (277), (278), (279), (280), (281),
% 197.44/32.36  | | | | | | | | | | |            (282), (283), (285), (304), (306), (307), (309),
% 197.44/32.36  | | | | | | | | | | |            (311), (313), (316), (317), (319), (321), (324),
% 197.44/32.36  | | | | | | | | | | |            (325), (326), (327), (331), (332), (333), (343),
% 197.44/32.36  | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.44/32.36  | | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.44/32.36  | | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.44/32.36  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.36  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.36  | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 197.44/32.36  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 197.44/32.36  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 197.44/32.36  | | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 197.44/32.36  | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.44/32.36  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.44/32.36  | | | | | | | | | | |            (611), (612), (613), (684), (688), (7443), (7445),
% 197.44/32.36  | | | | | | | | | | |            (7449), (7450), (7451), (7458), (9007), (9011),
% 197.44/32.36  | | | | | | | | | | |            (9714), (9899), (9902), (9904), (9905),
% 197.44/32.36  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.36  | | | | | | | | | | |            #43.
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | End of split
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | End of split
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | |   (9906)  all_28_0 = e3
% 197.44/32.36  | | | | | | | | |   (9907)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | COMBINE_EQS: (754), (9906) imply:
% 197.44/32.36  | | | | | | | | |   (9908)  all_4_0 = e3
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | SIMP: (9908) implies:
% 197.44/32.36  | | | | | | | | |   (9909)  all_4_0 = e3
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | COMBINE_EQS: (7449), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9910)  all_58_5 = e3
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (7450), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9911)   ~ (all_52_3 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (7451), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9912)   ~ (all_52_17 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (7453), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9913)   ~ (all_52_23 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (7457), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9914)   ~ (all_10_2 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (7458), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9915)   ~ (all_4_2 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | SIMP: (9915) implies:
% 197.44/32.36  | | | | | | | | |   (9916)   ~ (all_4_2 = e3)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (7459), (9909) imply:
% 197.44/32.36  | | | | | | | | |   (9917)  op(e3, e3) = all_52_18
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.36  | | | | | | | | |            (51), (53), (61), (63), (139), (158), (161), (162),
% 197.44/32.36  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.44/32.36  | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.44/32.36  | | | | | | | | |            (185), (187), (270), (271), (273), (274), (277),
% 197.44/32.36  | | | | | | | | |            (278), (279), (280), (281), (282), (283), (285),
% 197.44/32.36  | | | | | | | | |            (303), (306), (307), (309), (311), (313), (315),
% 197.44/32.36  | | | | | | | | |            (316), (317), (318), (319), (320), (321), (324),
% 197.44/32.36  | | | | | | | | |            (325), (326), (327), (332), (333), (343), (351),
% 197.44/32.36  | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.44/32.36  | | | | | | | | |            (388), (393), (405), (411), (415), (417), (427),
% 197.44/32.36  | | | | | | | | |            (431), (521), (528), (538), (539), (540), (541),
% 197.44/32.36  | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.44/32.36  | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.44/32.36  | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.44/32.36  | | | | | | | | |            (571), (572), (573), (574), (575), (577), (578),
% 197.44/32.36  | | | | | | | | |            (580), (582), (584), (586), (589), (590), (592),
% 197.44/32.36  | | | | | | | | |            (593), (594), (595), (596), (598), (602), (603),
% 197.44/32.36  | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.44/32.36  | | | | | | | | |            (612), (613), (684), (688), (7444), (7445), (9007),
% 197.44/32.36  | | | | | | | | |            (9010), (9011), (9897), (9907), (9910), (9911),
% 197.44/32.36  | | | | | | | | |            (9912), (9913), (9914), (9916), (9917),
% 197.44/32.36  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.36  | | | | | | | | |            #61.
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | End of split
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | End of split
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | Case 2:
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | |   (9918)  all_18_0 = e3
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | COMBINE_EQS: (761), (9918) imply:
% 197.44/32.36  | | | | | | |   (9919)  all_14_0 = e3
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | SIMP: (9919) implies:
% 197.44/32.36  | | | | | | |   (9920)  all_14_0 = e3
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | REDUCE: (62), (9920) imply:
% 197.44/32.36  | | | | | | |   (9921)  op(e0, all_14_1) = e3
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | BETA: splitting (99) gives:
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | |   (9922)   ~ (all_28_0 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (754), (9922) imply:
% 197.44/32.36  | | | | | | | |   (9923)   ~ (all_4_0 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | BETA: splitting (139) gives:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | |   (9924)   ~ (all_44_0 = e2)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (9010), (9924) imply:
% 197.44/32.36  | | | | | | | | |   (9925)  $false
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | CLOSE: (9925) is inconsistent.
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | |   (9926)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | |   (9927)  all_58_15 = e0
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (9921), (9927),
% 197.44/32.36  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.36  | | | | | | | | | |            #678.
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | |   (9928)   ~ (all_58_15 = e0)
% 197.44/32.36  | | | | | | | | | |   (9929)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.36  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.36  | | | | | | | | | |             e0)
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | ALPHA: (9929) implies:
% 197.44/32.36  | | | | | | | | | |   (9930)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.36  | | | | | | | | | |   (9931)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | REDUCE: (541), (9928) imply:
% 197.44/32.36  | | | | | | | | | |   (9932)   ~ (all_14_2 = e0)
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.36  | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 197.44/32.36  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.36  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.44/32.36  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (273),
% 197.44/32.36  | | | | | | | | | |            (274), (276), (277), (278), (279), (280), (281),
% 197.44/32.36  | | | | | | | | | |            (282), (283), (285), (304), (306), (307), (309),
% 197.44/32.36  | | | | | | | | | |            (311), (313), (316), (317), (319), (321), (324),
% 197.44/32.36  | | | | | | | | | |            (325), (326), (327), (331), (332), (333), (343),
% 197.44/32.36  | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.44/32.36  | | | | | | | | | |            (388), (393), (405), (411), (415), (417), (421),
% 197.44/32.36  | | | | | | | | | |            (427), (431), (521), (528), (538), (539), (540),
% 197.44/32.36  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.36  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.36  | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 197.44/32.36  | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 197.44/32.36  | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 197.44/32.36  | | | | | | | | | |            (587), (588), (589), (590), (591), (592), (593),
% 197.44/32.36  | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.44/32.36  | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.44/32.36  | | | | | | | | | |            (611), (612), (613), (684), (688), (7443), (7445),
% 197.44/32.36  | | | | | | | | | |            (7449), (7450), (7451), (7458), (9007), (9011),
% 197.44/32.36  | | | | | | | | | |            (9714), (9923), (9926), (9930), (9931), (9932),
% 197.44/32.36  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.36  | | | | | | | | | |            #44.
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | End of split
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | End of split
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | |   (9933)  all_28_0 = e3
% 197.44/32.36  | | | | | | | |   (9934)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | COMBINE_EQS: (754), (9933) imply:
% 197.44/32.36  | | | | | | | |   (9935)  all_4_0 = e3
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | SIMP: (9935) implies:
% 197.44/32.36  | | | | | | | |   (9936)  all_4_0 = e3
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | COMBINE_EQS: (7449), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9937)  all_58_5 = e3
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (7450), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9938)   ~ (all_52_3 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (7451), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9939)   ~ (all_52_17 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (7453), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9940)   ~ (all_52_23 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (7457), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9941)   ~ (all_10_2 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (7458), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9942)   ~ (all_4_2 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | SIMP: (9942) implies:
% 197.44/32.36  | | | | | | | |   (9943)   ~ (all_4_2 = e3)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (7459), (9936) imply:
% 197.44/32.36  | | | | | | | |   (9944)  op(e3, e3) = all_52_18
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 197.44/32.36  | | | | | | | |            (53), (61), (63), (139), (158), (161), (162), (166),
% 197.44/32.36  | | | | | | | |            (167), (168), (169), (172), (173), (174), (177),
% 197.44/32.36  | | | | | | | |            (178), (179), (180), (182), (183), (184), (185),
% 197.44/32.36  | | | | | | | |            (187), (270), (271), (273), (274), (277), (278),
% 197.44/32.36  | | | | | | | |            (279), (280), (281), (282), (283), (285), (303),
% 197.44/32.36  | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 197.44/32.36  | | | | | | | |            (317), (318), (319), (320), (321), (324), (325),
% 197.44/32.36  | | | | | | | |            (326), (327), (332), (333), (343), (351), (352),
% 197.44/32.36  | | | | | | | |            (366), (367), (372), (375), (376), (387), (388),
% 197.44/32.36  | | | | | | | |            (393), (405), (411), (415), (417), (427), (431),
% 197.44/32.36  | | | | | | | |            (521), (528), (538), (539), (540), (541), (542),
% 197.44/32.36  | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.44/32.36  | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.44/32.36  | | | | | | | |            (563), (564), (566), (567), (569), (570), (571),
% 197.44/32.36  | | | | | | | |            (572), (573), (574), (575), (577), (578), (580),
% 197.44/32.36  | | | | | | | |            (582), (584), (586), (589), (590), (592), (593),
% 197.44/32.36  | | | | | | | |            (594), (595), (596), (598), (602), (603), (604),
% 197.44/32.36  | | | | | | | |            (605), (606), (607), (608), (609), (610), (612),
% 197.44/32.36  | | | | | | | |            (613), (684), (688), (7444), (7445), (9007), (9010),
% 197.44/32.36  | | | | | | | |            (9011), (9921), (9934), (9937), (9938), (9939),
% 197.44/32.36  | | | | | | | |            (9940), (9941), (9943), (9944), (function-axioms) are
% 197.44/32.36  | | | | | | | |            inconsistent by sub-proof #59.
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | End of split
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | End of split
% 197.44/32.36  | | | | | | 
% 197.44/32.36  | | | | | Case 2:
% 197.44/32.36  | | | | | | 
% 197.44/32.36  | | | | | |   (9945)  all_14_0 = e2
% 197.44/32.36  | | | | | | 
% 197.44/32.36  | | | | | | REDUCE: (62), (9945) imply:
% 197.44/32.36  | | | | | |   (9946)  op(e0, all_14_1) = e2
% 197.44/32.36  | | | | | | 
% 197.44/32.36  | | | | | | BETA: splitting (99) gives:
% 197.44/32.36  | | | | | | 
% 197.44/32.36  | | | | | | Case 1:
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | |   (9947)   ~ (all_28_0 = e3)
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | REDUCE: (754), (9947) imply:
% 197.44/32.36  | | | | | | |   (9948)   ~ (all_4_0 = e3)
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | BETA: splitting (139) gives:
% 197.44/32.36  | | | | | | | 
% 197.44/32.36  | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | |   (9949)   ~ (all_44_0 = e2)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | REDUCE: (9010), (9949) imply:
% 197.44/32.36  | | | | | | | |   (9950)  $false
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | CLOSE: (9950) is inconsistent.
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | |   (9951)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.36  | | | | | | | | 
% 197.44/32.36  | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | |   (9952)  all_58_15 = e0
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (9946), (9952),
% 197.44/32.36  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.36  | | | | | | | | |            #612.
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | |   (9953)   ~ (all_58_15 = e0)
% 197.44/32.36  | | | | | | | | |   (9954)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 197.44/32.36  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | ALPHA: (9954) implies:
% 197.44/32.36  | | | | | | | | |   (9955)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.36  | | | | | | | | |   (9956)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | REDUCE: (541), (9953) imply:
% 197.44/32.36  | | | | | | | | |   (9957)   ~ (all_14_2 = e0)
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | BETA: splitting (187) gives:
% 197.44/32.36  | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | |   (9958)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.36  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.44/32.36  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | BETA: splitting (9958) gives:
% 197.44/32.36  | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | |   (9959)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.36  | | | | | | | | | | |           all_52_6 = e0
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (43), (51), (61), (183), (184),
% 197.44/32.36  | | | | | | | | | | |            (185), (285), (306), (321), (332), (351), (387),
% 197.44/32.36  | | | | | | | | | | |            (405), (540), (547), (564), (569), (573), (610),
% 197.44/32.36  | | | | | | | | | | |            (9011), (9959), (function-axioms) are inconsistent
% 197.44/32.36  | | | | | | | | | | |            by sub-proof #501.
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | |   (9960)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.44/32.36  | | | | | | | | | | |           all_52_14 = e0
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | ALPHA: (9960) implies:
% 197.44/32.36  | | | | | | | | | | |   (9961)  all_52_14 = e0
% 197.44/32.36  | | | | | | | | | | |   (9962)  all_52_12 = e1
% 197.44/32.36  | | | | | | | | | | |   (9963)  all_52_10 = e2
% 197.44/32.36  | | | | | | | | | | |   (9964)  all_52_8 = e3
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REDUCE: (182), (9964) imply:
% 197.44/32.36  | | | | | | | | | | |   (9965)  op(all_52_9, all_52_9) = e3
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REDUCE: (180), (9962) imply:
% 197.44/32.36  | | | | | | | | | | |   (9966)  op(all_52_13, all_52_13) = e1
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REDUCE: (179), (9961) imply:
% 197.44/32.36  | | | | | | | | | | |   (9967)  op(all_52_15, all_52_15) = e0
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | REDUCE: (611), (9963) imply:
% 197.44/32.36  | | | | | | | | | | |   (9968)  op(all_4_2, all_4_2) = e2
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | BETA: splitting (270) gives:
% 197.44/32.36  | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | |   (9969)  all_56_15 = e3
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | COMBINE_EQS: (538), (9969) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9970)  all_14_2 = e3
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (573), (9970) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9971)   ~ (all_52_7 = e3)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (606), (9970) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9972)   ~ (all_52_25 = e3)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (608), (9970) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9973)   ~ (all_52_27 = e3)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (609), (9970) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9974)   ~ (all_52_29 = e3)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (613), (9970) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9975)  op(e3, e3) = all_52_30
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (63), (9970) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9976)  op(e3, e0) = all_14_1
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 197.44/32.36  | | | | | | | | | | | |              all_14_1, e0, e3, simplifying with (167), (9976)
% 197.44/32.36  | | | | | | | | | | | |              gives:
% 197.44/32.36  | | | | | | | | | | | |   (9977)  all_52_25 = all_14_1
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.44/32.36  | | | | | | | | | | | |              all_52_30, e3, e3, simplifying with (41), (9975)
% 197.44/32.36  | | | | | | | | | | | |              gives:
% 197.44/32.36  | | | | | | | | | | | |   (9978)  all_52_30 = all_6_2
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | COMBINE_EQS: (388), (9977) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9979)  all_56_3 = all_14_1
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (578), (9977) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9980)   ~ (all_52_9 = all_14_1)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (561), (9977) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9981)   ~ (all_14_1 = all_6_2)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (9972), (9977) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9982)   ~ (all_14_1 = e3)
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | REDUCE: (174), (9977) imply:
% 197.44/32.36  | | | | | | | | | | | |   (9983)  op(all_14_1, all_14_1) = all_52_24
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | BETA: splitting (282) gives:
% 197.44/32.36  | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | Case 1:
% 197.44/32.36  | | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | |   (9984)  all_56_3 = e3
% 197.44/32.36  | | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | | REF_CLOSE: (9979), (9982), (9984) are inconsistent by
% 197.44/32.36  | | | | | | | | | | | | |            sub-proof #1200.
% 197.44/32.36  | | | | | | | | | | | | | 
% 197.44/32.36  | | | | | | | | | | | | Case 2:
% 197.44/32.36  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | |   (9985)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | |   (9986)  all_58_4 = e3
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | COMBINE_EQS: (393), (9986) imply:
% 197.44/32.37  | | | | | | | | | | | | | |   (9987)  all_52_17 = e3
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | SIMP: (9987) implies:
% 197.44/32.37  | | | | | | | | | | | | | |   (9988)  all_52_17 = e3
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | REDUCE: (559), (9988) imply:
% 197.44/32.37  | | | | | | | | | | | | | |   (9989)   ~ (all_6_2 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | SIMP: (9989) implies:
% 197.44/32.37  | | | | | | | | | | | | | |   (9990)   ~ (all_6_2 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | REDUCE: (7451), (9988) imply:
% 197.44/32.37  | | | | | | | | | | | | | |   (9991)   ~ (all_4_0 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | REDUCE: (178), (9988) imply:
% 197.44/32.37  | | | | | | | | | | | | | |   (9992)  op(e3, e3) = all_52_16
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.44/32.37  | | | | | | | | | | | | | |              all_52_16, e3, e3, simplifying with (41), (9992)
% 197.44/32.37  | | | | | | | | | | | | | |              gives:
% 197.44/32.37  | | | | | | | | | | | | | |   (9993)  all_52_16 = all_6_2
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | |   (9994)  all_58_2 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | COMBINE_EQS: (387), (9994) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (9995)  all_52_3 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | SIMP: (9995) implies:
% 197.44/32.37  | | | | | | | | | | | | | | |   (9996)  all_52_3 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (562), (9996) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (9997)   ~ (all_52_5 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | SIMP: (9997) implies:
% 197.44/32.37  | | | | | | | | | | | | | | |   (9998)   ~ (all_52_5 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (563), (9996) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (9999)   ~ (all_52_7 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (185), (9996) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (10000)  op(e3, e3) = all_52_2
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | |   (10001)  all_58_6 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | REF_CLOSE: (547), (9998), (10001) are inconsistent by
% 197.44/32.37  | | | | | | | | | | | | | | | |            sub-proof #1328.
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | |   (10002)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | BETA: splitting (10002) gives:
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | |   (10003)  all_58_7 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (10003) imply:
% 197.44/32.37  | | | | | | | | | | | | | | | | |   (10004)  all_52_13 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | | REDUCE: (575), (10004) imply:
% 197.44/32.37  | | | | | | | | | | | | | | | | |   (10005)   ~ (all_52_9 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | | REDUCE: (9966), (10004) imply:
% 197.44/32.37  | | | | | | | | | | | | | | | | |   (10006)  op(e3, e3) = e1
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (157), (284), (324), (332), (351),
% 197.44/32.37  | | | | | | | | | | | | | | | | |            (387), (394), (405), (547), (549), (557), (564),
% 197.44/32.37  | | | | | | | | | | | | | | | | |            (574), (9946), (9965), (9967), (9971), (9979),
% 197.44/32.37  | | | | | | | | | | | | | | | | |            (9980), (9981), (9983), (9985), (9990), (9998),
% 197.44/32.37  | | | | | | | | | | | | | | | | |            (10000), (10005), (10006), (function-axioms) are
% 197.44/32.37  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #235.
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | |   (10007)  all_58_8 = e3 | all_58_11 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (43), (333), (393), (405), (544),
% 197.44/32.37  | | | | | | | | | | | | | | | | |            (545), (546), (549), (557), (593), (9011), (9965),
% 197.44/32.37  | | | | | | | | | | | | | | | | |            (9972), (9974), (10007), (function-axioms) are
% 197.44/32.37  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #491.
% 197.44/32.37  | | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | |   (10008)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REF_CLOSE: (36), (51), (169), (313), (332), (351), (372),
% 197.44/32.37  | | | | | | | | | | | | | | |            (387), (405), (547), (548), (564), (569), (7445),
% 197.44/32.37  | | | | | | | | | | | | | | |            (7449), (9948), (9965), (9971), (9973), (9990),
% 197.44/32.37  | | | | | | | | | | | | | | |            (10008), (function-axioms) are inconsistent by
% 197.44/32.37  | | | | | | | | | | | | | | |            sub-proof #42.
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | |   (10009)   ~ (all_58_4 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | REDUCE: (393), (10009) imply:
% 197.44/32.37  | | | | | | | | | | | | | |   (10010)   ~ (all_52_17 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (43), (333), (393), (405), (545),
% 197.44/32.37  | | | | | | | | | | | | | |            (549), (557), (9011), (9965), (9972), (10010),
% 197.44/32.37  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.37  | | | | | | | | | | | | | |            #492.
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | |   (10011)   ~ (all_56_15 = e3)
% 197.44/32.37  | | | | | | | | | | | |   (10012)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | REDUCE: (538), (10011) imply:
% 197.44/32.37  | | | | | | | | | | | |   (10013)   ~ (all_14_2 = e3)
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (41), (43), (51), (158),
% 197.44/32.37  | | | | | | | | | | | |            (162), (166), (167), (168), (169), (174), (178),
% 197.44/32.37  | | | | | | | | | | | |            (183), (184), (185), (273), (274), (276), (277),
% 197.44/32.37  | | | | | | | | | | | |            (278), (281), (283), (306), (309), (313), (317),
% 197.44/32.37  | | | | | | | | | | | |            (319), (321), (325), (326), (333), (351), (352),
% 197.44/32.37  | | | | | | | | | | | |            (366), (367), (372), (387), (393), (405), (411),
% 197.44/32.37  | | | | | | | | | | | |            (415), (421), (427), (431), (521), (528), (538),
% 197.44/32.37  | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.44/32.37  | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.44/32.37  | | | | | | | | | | | |            (561), (563), (564), (567), (568), (571), (573),
% 197.44/32.37  | | | | | | | | | | | |            (574), (577), (578), (580), (582), (593), (594),
% 197.44/32.37  | | | | | | | | | | | |            (595), (602), (604), (607), (684), (688), (7443),
% 197.44/32.37  | | | | | | | | | | | |            (7445), (7449), (7451), (9007), (9011), (9948),
% 197.44/32.37  | | | | | | | | | | | |            (9951), (9965), (9966), (9967), (9968), (10012),
% 197.44/32.37  | | | | | | | | | | | |            (10013), (function-axioms) are inconsistent by
% 197.44/32.37  | | | | | | | | | | | |            sub-proof #87.
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | |   (10014)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.44/32.37  | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.44/32.37  | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.37  | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 197.44/32.37  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.44/32.37  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.44/32.37  | | | | | | | | | |            (183), (184), (185), (270), (271), (273), (274),
% 197.44/32.37  | | | | | | | | | |            (276), (277), (278), (279), (280), (282), (283),
% 197.44/32.37  | | | | | | | | | |            (285), (304), (306), (307), (309), (311), (313),
% 197.44/32.37  | | | | | | | | | |            (316), (317), (319), (321), (324), (325), (326),
% 197.44/32.37  | | | | | | | | | |            (327), (331), (332), (333), (343), (351), (352),
% 197.44/32.37  | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.44/32.37  | | | | | | | | | |            (405), (415), (417), (421), (427), (431), (521),
% 197.44/32.37  | | | | | | | | | |            (528), (538), (539), (540), (541), (542), (543),
% 197.44/32.37  | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.44/32.37  | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.44/32.37  | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.44/32.37  | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (582),
% 197.44/32.37  | | | | | | | | | |            (584), (586), (587), (588), (589), (590), (591),
% 197.44/32.37  | | | | | | | | | |            (592), (593), (594), (595), (596), (598), (600),
% 197.44/32.37  | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 197.44/32.37  | | | | | | | | | |            (609), (610), (611), (612), (613), (684), (688),
% 197.44/32.37  | | | | | | | | | |            (7443), (7445), (7449), (7450), (7458), (9007),
% 197.44/32.37  | | | | | | | | | |            (9011), (9714), (9948), (9951), (9955), (9956),
% 197.44/32.37  | | | | | | | | | |            (9957), (10014), (function-axioms) are
% 197.44/32.37  | | | | | | | | | |            inconsistent by sub-proof #45.
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | | 
% 197.44/32.37  | | | | | | | | End of split
% 197.44/32.37  | | | | | | | | 
% 197.44/32.37  | | | | | | | End of split
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | Case 2:
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | |   (10015)  all_28_0 = e3
% 197.44/32.37  | | | | | | |   (10016)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | COMBINE_EQS: (754), (10015) imply:
% 197.44/32.37  | | | | | | |   (10017)  all_4_0 = e3
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | SIMP: (10017) implies:
% 197.44/32.37  | | | | | | |   (10018)  all_4_0 = e3
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | COMBINE_EQS: (7449), (10018) imply:
% 197.44/32.37  | | | | | | |   (10019)  all_58_5 = e3
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (7450), (10018) imply:
% 197.44/32.37  | | | | | | |   (10020)   ~ (all_52_3 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (7451), (10018) imply:
% 197.44/32.37  | | | | | | |   (10021)   ~ (all_52_17 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (7453), (10018) imply:
% 197.44/32.37  | | | | | | |   (10022)   ~ (all_52_23 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (7457), (10018) imply:
% 197.44/32.37  | | | | | | |   (10023)   ~ (all_10_2 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (7458), (10018) imply:
% 197.44/32.37  | | | | | | |   (10024)   ~ (all_4_2 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | SIMP: (10024) implies:
% 197.44/32.37  | | | | | | |   (10025)   ~ (all_4_2 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (7459), (10018) imply:
% 197.44/32.37  | | | | | | |   (10026)  op(e3, e3) = all_52_18
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 197.44/32.37  | | | | | | |            (53), (61), (63), (139), (158), (161), (162), (166),
% 197.44/32.37  | | | | | | |            (167), (168), (169), (172), (173), (174), (177), (178),
% 197.44/32.37  | | | | | | |            (179), (180), (182), (183), (184), (185), (187), (270),
% 197.44/32.37  | | | | | | |            (271), (273), (274), (277), (278), (279), (280), (281),
% 197.44/32.37  | | | | | | |            (282), (283), (285), (303), (306), (307), (309), (311),
% 197.44/32.37  | | | | | | |            (313), (315), (316), (317), (318), (319), (320), (321),
% 197.44/32.37  | | | | | | |            (324), (325), (326), (327), (332), (333), (343), (351),
% 197.44/32.37  | | | | | | |            (352), (366), (367), (372), (375), (376), (387), (388),
% 197.44/32.37  | | | | | | |            (393), (405), (411), (415), (417), (427), (431), (521),
% 197.44/32.37  | | | | | | |            (528), (538), (539), (540), (541), (542), (543), (544),
% 197.44/32.37  | | | | | | |            (545), (546), (547), (548), (549), (551), (553), (555),
% 197.44/32.37  | | | | | | |            (557), (559), (561), (562), (563), (564), (566), (567),
% 197.44/32.37  | | | | | | |            (569), (570), (571), (572), (573), (574), (575), (577),
% 197.44/32.37  | | | | | | |            (578), (580), (582), (584), (586), (589), (590), (592),
% 197.44/32.37  | | | | | | |            (593), (594), (595), (596), (598), (602), (603), (604),
% 197.44/32.37  | | | | | | |            (605), (606), (607), (608), (609), (610), (612), (613),
% 197.44/32.37  | | | | | | |            (684), (688), (7444), (7445), (9007), (9010), (9011),
% 197.44/32.37  | | | | | | |            (9946), (10016), (10019), (10020), (10021), (10022),
% 197.44/32.37  | | | | | | |            (10023), (10025), (10026), (function-axioms) are
% 197.44/32.37  | | | | | | |            inconsistent by sub-proof #53.
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | End of split
% 197.44/32.37  | | | | | | 
% 197.44/32.37  | | | | | End of split
% 197.44/32.37  | | | | | 
% 197.44/32.37  | | | | End of split
% 197.44/32.37  | | | | 
% 197.44/32.37  | | | End of split
% 197.44/32.37  | | | 
% 197.44/32.37  | | Case 2:
% 197.44/32.37  | | | 
% 197.44/32.37  | | |   (10027)  all_6_0 = e1
% 197.44/32.37  | | |   (10028)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 197.44/32.37  | | | 
% 197.44/32.37  | | | COMBINE_EQS: (769), (10027) imply:
% 197.44/32.37  | | |   (10029)  all_46_0 = e1
% 197.44/32.37  | | | 
% 197.44/32.37  | | | REDUCE: (42), (10027) imply:
% 197.44/32.37  | | |   (10030)  op(e3, all_6_1) = e1
% 197.44/32.37  | | | 
% 197.44/32.37  | | | BETA: splitting (54) gives:
% 197.44/32.37  | | | 
% 197.44/32.37  | | | Case 1:
% 197.44/32.37  | | | | 
% 197.44/32.37  | | | |   (10031)   ~ (all_10_0 = e3)
% 197.44/32.37  | | | | 
% 197.44/32.37  | | | | BETA: splitting (64) gives:
% 197.44/32.37  | | | | 
% 197.44/32.37  | | | | Case 1:
% 197.44/32.37  | | | | | 
% 197.44/32.37  | | | | |   (10032)   ~ (all_14_0 = e2)
% 197.44/32.37  | | | | | 
% 197.44/32.37  | | | | | BETA: splitting (69) gives:
% 197.44/32.37  | | | | | 
% 197.44/32.37  | | | | | Case 1:
% 197.44/32.37  | | | | | | 
% 197.44/32.37  | | | | | |   (10033)   ~ (all_16_0 = e2)
% 197.44/32.37  | | | | | | 
% 197.44/32.37  | | | | | | REDUCE: (760), (10033) imply:
% 197.44/32.37  | | | | | |   (10034)   ~ (all_10_0 = e2)
% 197.44/32.37  | | | | | | 
% 197.44/32.37  | | | | | | BETA: splitting (74) gives:
% 197.44/32.37  | | | | | | 
% 197.44/32.37  | | | | | | Case 1:
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | |   (10035)   ~ (all_18_0 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | REDUCE: (761), (10035) imply:
% 197.44/32.37  | | | | | | |   (10036)   ~ (all_14_0 = e3)
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | BETA: splitting (89) gives:
% 197.44/32.37  | | | | | | | 
% 197.44/32.37  | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | 
% 197.44/32.37  | | | | | | | |   (10037)   ~ (all_24_0 = e1)
% 197.44/32.37  | | | | | | | | 
% 197.44/32.37  | | | | | | | | REDUCE: (711), (10037) imply:
% 197.44/32.37  | | | | | | | |   (10038)   ~ (all_14_0 = e1)
% 197.44/32.37  | | | | | | | | 
% 197.44/32.37  | | | | | | | | BETA: splitting (99) gives:
% 197.44/32.37  | | | | | | | | 
% 197.44/32.37  | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | 
% 197.44/32.37  | | | | | | | | |   (10039)   ~ (all_28_0 = e3)
% 197.44/32.37  | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | REDUCE: (754), (10039) imply:
% 197.44/32.37  | | | | | | | | |   (10040)   ~ (all_4_0 = e3)
% 197.44/32.37  | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | BETA: splitting (104) gives:
% 197.44/32.37  | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | |   (10041)   ~ (all_30_1 = e3)
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | REDUCE: (670), (10041) imply:
% 197.44/32.37  | | | | | | | | | |   (10042)   ~ (all_10_1 = e3)
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | BETA: splitting (129) gives:
% 197.44/32.37  | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | |   (10043)   ~ (all_40_1 = e2)
% 197.44/32.37  | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | REDUCE: (687), (10043) imply:
% 197.44/32.37  | | | | | | | | | | |   (10044)   ~ (all_10_1 = e2)
% 197.44/32.37  | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | BETA: splitting (144) gives:
% 197.44/32.37  | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | |   (10045)   ~ (all_46_0 = e1)
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | REDUCE: (10029), (10045) imply:
% 197.44/32.37  | | | | | | | | | | | |   (10046)  $false
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | CLOSE: (10046) is inconsistent.
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | |   (10047)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.37  | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | |   (10048)  all_58_15 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | COMBINE_EQS: (541), (10048) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10049)  all_14_2 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (573), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10050)   ~ (all_52_7 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (591), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10051)   ~ (all_52_15 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (603), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10052)   ~ (all_52_23 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (606), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10053)   ~ (all_52_25 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (609), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10054)   ~ (all_52_29 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (613), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10055)  op(e0, e0) = all_52_30
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (63), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10056)  op(e0, e0) = all_14_1
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (61), (10049) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10057)  op(e0, e0) = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.44/32.37  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10055),
% 197.44/32.37  | | | | | | | | | | | | |              (10056) gives:
% 197.44/32.37  | | | | | | | | | | | | |   (10058)  all_52_30 = all_14_1
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.44/32.37  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10055),
% 197.44/32.37  | | | | | | | | | | | | |              (10057) gives:
% 197.44/32.37  | | | | | | | | | | | | |   (10059)  all_52_30 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | COMBINE_EQS: (10058), (10059) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10060)  all_14_1 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | SIMP: (10060) implies:
% 197.44/32.37  | | | | | | | | | | | | |   (10061)  all_14_1 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (62), (10061) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10062)  op(e0, e0) = all_14_0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.44/32.37  | | | | | | | | | | | | |              e0, e0, simplifying with (10057), (10062) gives:
% 197.44/32.37  | | | | | | | | | | | | |   (10063)  all_14_0 = e0
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (10036), (10063) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10064)   ~ (e3 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (10032), (10063) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10065)   ~ (e2 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | REDUCE: (10038), (10063) imply:
% 197.44/32.37  | | | | | | | | | | | | |   (10066)   ~ (e1 = e0)
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.44/32.37  | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | |   (10067)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.37  | | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.44/32.37  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | BETA: splitting (10067) gives:
% 197.44/32.37  | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | |   (10068)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.37  | | | | | | | | | | | | | | |            all_52_6 = e0
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (41), (51), (53), (61),
% 197.44/32.37  | | | | | | | | | | | | | | |            (156), (175), (179), (183), (184), (185), (271),
% 197.44/32.37  | | | | | | | | | | | | | | |            (272), (273), (304), (305), (306), (321), (326),
% 197.44/32.37  | | | | | | | | | | | | | | |            (332), (343), (346), (351), (387), (405), (431),
% 197.44/32.37  | | | | | | | | | | | | | | |            (542), (543), (547), (555), (564), (569), (571),
% 197.44/32.37  | | | | | | | | | | | | | | |            (572), (573), (582), (590), (600), (610), (611),
% 197.44/32.37  | | | | | | | | | | | | | | |            (10042), (10044), (10048), (10050), (10052),
% 197.44/32.37  | | | | | | | | | | | | | | |            (10057), (10068), (function-axioms) are
% 197.44/32.37  | | | | | | | | | | | | | | |            inconsistent by sub-proof #216.
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | |   (10069)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.44/32.37  | | | | | | | | | | | | | | |            all_52_14 = e0
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | ALPHA: (10069) implies:
% 197.44/32.37  | | | | | | | | | | | | | | |   (10070)  all_52_14 = e0
% 197.44/32.37  | | | | | | | | | | | | | | |   (10071)  all_52_12 = e1
% 197.44/32.37  | | | | | | | | | | | | | | |   (10072)  all_52_10 = e2
% 197.44/32.37  | | | | | | | | | | | | | | |   (10073)  all_52_8 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (182), (10073) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (10074)  op(all_52_9, all_52_9) = e3
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (180), (10071) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (10075)  op(all_52_13, all_52_13) = e1
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (179), (10070) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (10076)  op(all_52_15, all_52_15) = e0
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | REDUCE: (611), (10072) imply:
% 197.44/32.37  | | | | | | | | | | | | | | |   (10077)  op(all_4_2, all_4_2) = e2
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.44/32.37  | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | |   (10078)  all_56_14 = e3
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (51), (53), (156), (272), (273), (304),
% 197.44/32.37  | | | | | | | | | | | | | | | |            (305), (343), (346), (351), (431), (543), (571),
% 197.44/32.37  | | | | | | | | | | | | | | | |            (572), (582), (590), (10042), (10050), (10051),
% 197.44/32.37  | | | | | | | | | | | | | | | |            (10057), (10076), (10077), (10078),
% 197.44/32.37  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.37  | | | | | | | | | | | | | | | |            #100.
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | |   (10079)   ~ (all_56_14 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.37  | | | | | | | | | | | | | | | | REDUCE: (343), (10079) imply:
% 197.44/32.37  | | | | | | | | | | | | | | | |   (10080)   ~ (all_52_23 = e3)
% 197.44/32.37  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (53), (158), (162), (167), (168), (169), (175),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (273), (278), (284), (305), (306), (310), (314),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (317), (318), (320), (321), (322), (325), (326),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (329), (330), (333), (351), (366), (372), (387),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (393), (394), (405), (427), (431), (542), (543),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (555), (557),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (568), (571),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (572), (574), (576), (577), (580), (582), (586),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (588), (593), (594), (595), (612), (7443), (7445),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (7449), (7451), (10028), (10030), (10040),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (10048), (10050), (10051), (10052), (10053),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (10057), (10074), (10075), (10076), (10080),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.38  | | | | | | | | | | | | | | | |            #38.
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | |   (10081)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.44/32.38  | | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.44/32.38  | | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | BETA: splitting (10081) gives:
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | |   (10082)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.44/32.38  | | | | | | | | | | | | | | |            all_52_22 = e0
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (51), (53), (61), (63), (158), (162),
% 197.44/32.38  | | | | | | | | | | | | | | |            (167), (168), (169), (175), (178), (183), (270),
% 197.44/32.38  | | | | | | | | | | | | | | |            (273), (275), (277), (283), (312), (317), (361),
% 197.44/32.38  | | | | | | | | | | | | | | |            (367), (393), (415), (431), (538), (542), (546),
% 197.44/32.38  | | | | | | | | | | | | | | |            (547), (553), (555), (557), (559), (561), (569),
% 197.44/32.38  | | | | | | | | | | | | | | |            (572), (593), (600), (603), (612), (613), (7449),
% 197.44/32.38  | | | | | | | | | | | | | | |            (10028), (10030), (10040), (10044), (10082),
% 197.44/32.38  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.38  | | | | | | | | | | | | | | |            #35.
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | |   (10083)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.44/32.38  | | | | | | | | | | | | | | |            all_52_30 = e0
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.38  | | | | | | | | | | | | | | |            (51), (162), (166), (167), (169), (172), (173),
% 197.44/32.38  | | | | | | | | | | | | | | |            (174), (175), (183), (272), (273), (278), (281),
% 197.44/32.38  | | | | | | | | | | | | | | |            (282), (304), (306), (307), (308), (309), (320),
% 197.44/32.38  | | | | | | | | | | | | | | |            (326), (330), (332), (333), (346), (351), (372),
% 197.44/32.38  | | | | | | | | | | | | | | |            (387), (388), (393), (405), (411), (427), (431),
% 197.44/32.38  | | | | | | | | | | | | | | |            (529), (542), (543), (544), (545), (547), (549),
% 197.44/32.38  | | | | | | | | | | | | | | |            (551), (555), (557), (561), (564), (566), (570),
% 197.44/32.38  | | | | | | | | | | | | | | |            (571), (572), (576), (582), (593), (600), (604),
% 197.44/32.38  | | | | | | | | | | | | | | |            (605), (610), (641), (10030), (10047), (10048),
% 197.44/32.38  | | | | | | | | | | | | | | |            (10050), (10051), (10052), (10053), (10054),
% 197.44/32.38  | | | | | | | | | | | | | | |            (10083), (function-axioms) are inconsistent by
% 197.44/32.38  | | | | | | | | | | | | | | |            sub-proof #304.
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | |   (10084)   ~ (all_58_15 = e0)
% 197.44/32.38  | | | | | | | | | | | | |   (10085)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.38  | | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.38  | | | | | | | | | | | | |              e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.38  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.44/32.38  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.44/32.38  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.44/32.38  | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.44/32.38  | | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 197.44/32.38  | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 197.44/32.38  | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 197.44/32.38  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.44/32.38  | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 197.44/32.38  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 197.44/32.38  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.44/32.38  | | | | | | | | | | | | |            (415), (421), (427), (431), (529), (538), (539),
% 197.44/32.38  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.44/32.38  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.44/32.38  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (566), (567),
% 197.44/32.38  | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.44/32.38  | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 197.44/32.38  | | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.44/32.38  | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.44/32.38  | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 197.44/32.38  | | | | | | | | | | | | |            (612), (613), (641), (7443), (7445), (7449),
% 197.44/32.38  | | | | | | | | | | | | |            (7451), (7453), (7458), (10028), (10030), (10040),
% 197.44/32.38  | | | | | | | | | | | | |            (10044), (10047), (10084), (10085),
% 197.44/32.38  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.38  | | | | | | | | | | | | |            #30.
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | |   (10086)  all_40_1 = e2
% 197.44/32.38  | | | | | | | | | | |   (10087)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | COMBINE_EQS: (687), (10086) imply:
% 197.44/32.38  | | | | | | | | | | |   (10088)  all_10_1 = e2
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (10042), (10088) imply:
% 197.44/32.38  | | | | | | | | | | |   (10089)   ~ (e3 = e2)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (53), (10088) imply:
% 197.44/32.38  | | | | | | | | | | |   (10090)  op(all_10_2, e1) = e2
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (52), (10088) imply:
% 197.44/32.38  | | | | | | | | | | |   (10091)  op(e1, e2) = all_10_0
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.44/32.38  | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (10091)
% 197.44/32.38  | | | | | | | | | | |              gives:
% 197.44/32.38  | | | | | | | | | | |   (10092)  all_52_13 = all_10_0
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | COMBINE_EQS: (421), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10093)  all_56_9 = all_10_0
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | COMBINE_EQS: (366), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10094)  all_58_7 = all_10_0
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (568), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10095)   ~ (all_52_5 = all_10_0)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (575), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10096)   ~ (all_52_9 = all_10_0)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (589), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10097)   ~ (all_52_29 = all_10_0)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | SIMP: (10097) implies:
% 197.44/32.38  | | | | | | | | | | |   (10098)   ~ (all_52_29 = all_10_0)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (588), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10099)   ~ (all_10_0 = all_10_2)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (580), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10100)   ~ (all_10_0 = all_4_2)
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | REDUCE: (180), (10092) imply:
% 197.44/32.38  | | | | | | | | | | |   (10101)  op(all_10_0, all_10_0) = all_52_12
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | BETA: splitting (144) gives:
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | |   (10102)   ~ (all_46_0 = e1)
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | REDUCE: (10029), (10102) imply:
% 197.44/32.38  | | | | | | | | | | | |   (10103)  $false
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | CLOSE: (10103) is inconsistent.
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | |   (10104)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | |   (10105)  all_58_15 = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | COMBINE_EQS: (541), (10105) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10106)  all_14_2 = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (573), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10107)   ~ (all_52_7 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (591), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10108)   ~ (all_52_15 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (603), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10109)   ~ (all_52_23 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (606), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10110)   ~ (all_52_25 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (609), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10111)   ~ (all_52_29 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (613), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10112)  op(e0, e0) = all_52_30
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (63), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10113)  op(e0, e0) = all_14_1
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (61), (10106) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10114)  op(e0, e0) = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.44/32.38  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10112),
% 197.44/32.38  | | | | | | | | | | | | |              (10113) gives:
% 197.44/32.38  | | | | | | | | | | | | |   (10115)  all_52_30 = all_14_1
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.44/32.38  | | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10112),
% 197.44/32.38  | | | | | | | | | | | | |              (10114) gives:
% 197.44/32.38  | | | | | | | | | | | | |   (10116)  all_52_30 = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | COMBINE_EQS: (10115), (10116) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10117)  all_14_1 = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (62), (10117) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10118)  op(e0, e0) = all_14_0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.44/32.38  | | | | | | | | | | | | |              e0, e0, simplifying with (10114), (10118) gives:
% 197.44/32.38  | | | | | | | | | | | | |   (10119)  all_14_0 = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (10036), (10119) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10120)   ~ (e3 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (10032), (10119) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10121)   ~ (e2 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (10038), (10119) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10122)   ~ (e1 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | BETA: splitting (276) gives:
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | |   (10123)  all_56_9 = e3
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | REF_CLOSE: (10031), (10093), (10123) are inconsistent by
% 197.44/32.38  | | | | | | | | | | | | | |            sub-proof #1006.
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | |   (10124)   ~ (all_56_9 = e3)
% 197.44/32.38  | | | | | | | | | | | | | |   (10125)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | |   (10126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.38  | | | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.44/32.38  | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | BETA: splitting (10126) gives:
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10127)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.44/32.38  | | | | | | | | | | | | | | | |            all_52_6 = e0
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (61), (164), (172), (173), (174), (179), (183),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (184), (185), (273), (274), (277), (278), (282),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (304), (306), (307), (308), (309), (310), (311),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (312), (317), (321), (325), (332), (351), (352),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (367), (372), (375), (387), (388), (393), (405),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (427), (431), (526), (542), (543), (544), (545),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (546), (547), (548), (549), (555), (557), (559),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (561), (564), (566), (567), (569), (570), (571),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (573), (586), (590), (596), (598), (604), (605),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (607), (610), (611), (612), (767), (10031),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (10034), (10087), (10090), (10093), (10094),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (10095), (10098), (10100), (10105), (10107),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (10110), (10111), (10114), (10125), (10127),
% 197.44/32.38  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.38  | | | | | | | | | | | | | | | |            #729.
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10128)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.44/32.38  | | | | | | | | | | | | | | | |            all_52_14 = e0
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | ALPHA: (10128) implies:
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10129)  all_52_14 = e0
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10130)  all_52_10 = e2
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10131)  all_52_8 = e3
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | REDUCE: (182), (10131) imply:
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10132)  op(all_52_9, all_52_9) = e3
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | REDUCE: (179), (10129) imply:
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10133)  op(all_52_15, all_52_15) = e0
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | REDUCE: (611), (10130) imply:
% 197.44/32.38  | | | | | | | | | | | | | | | |   (10134)  op(all_4_2, all_4_2) = e2
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | Case 1:
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | |   (10135)  all_56_13 = e3
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (41), (43), (158), (168), (175),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (273), (284), (305), (346), (351), (394), (431),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (542), (543), (555), (557), (571), (576), (577),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (582), (10028), (10030), (10105), (10132),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (10133), (10135), (function-axioms) are
% 197.44/32.38  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | |   (10136)   ~ (all_56_13 = e3)
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | | REDUCE: (346), (10136) imply:
% 197.44/32.38  | | | | | | | | | | | | | | | | |   (10137)   ~ (all_52_15 = e3)
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (169), (324), (325), (543),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (548), (549), (557), (7445), (10031), (10034),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (10094), (10132), (10133), (10134), (10137),
% 197.44/32.38  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.44/32.38  | | | | | | | | | | | | | | | | |            #28.
% 197.44/32.38  | | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | |   (10138)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.44/32.38  | | | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.44/32.38  | | | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.38  | | | | | | | | | | | | | | |            (51), (158), (162), (166), (167), (168), (169),
% 197.44/32.38  | | | | | | | | | | | | | | |            (172), (173), (174), (175), (178), (183), (271),
% 197.44/32.38  | | | | | | | | | | | | | | |            (272), (273), (278), (281), (282), (304), (306),
% 197.44/32.38  | | | | | | | | | | | | | | |            (307), (308), (309), (317), (320), (326), (330),
% 197.44/32.38  | | | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (372), (387),
% 197.44/32.38  | | | | | | | | | | | | | | |            (388), (393), (405), (411), (427), (431), (529),
% 197.44/32.38  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (549),
% 197.44/32.38  | | | | | | | | | | | | | | |            (551), (555), (557), (559), (561), (564), (566),
% 197.44/32.38  | | | | | | | | | | | | | | |            (570), (571), (572), (576), (582), (593), (600),
% 197.44/32.38  | | | | | | | | | | | | | | |            (604), (605), (610), (612), (641), (7449),
% 197.44/32.38  | | | | | | | | | | | | | | |            (10028), (10030), (10040), (10104), (10105),
% 197.44/32.38  | | | | | | | | | | | | | | |            (10107), (10108), (10109), (10110), (10111),
% 197.44/32.38  | | | | | | | | | | | | | | |            (10114), (10138), (function-axioms) are
% 197.44/32.38  | | | | | | | | | | | | | | |            inconsistent by sub-proof #27.
% 197.44/32.38  | | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | |   (10139)   ~ (all_58_15 = e0)
% 197.44/32.38  | | | | | | | | | | | | |   (10140)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.44/32.38  | | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.44/32.38  | | | | | | | | | | | | |              e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | ALPHA: (10140) implies:
% 197.44/32.38  | | | | | | | | | | | | |   (10141)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.44/32.38  | | | | | | | | | | | | |   (10142)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REDUCE: (541), (10139) imply:
% 197.44/32.38  | | | | | | | | | | | | |   (10143)   ~ (all_14_2 = e0)
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.44/32.38  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.44/32.38  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.44/32.38  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.44/32.38  | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.44/32.38  | | | | | | | | | | | | |            (276), (277), (278), (280), (281), (282), (283),
% 197.44/32.38  | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (312),
% 197.44/32.38  | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (320), (321),
% 197.44/32.38  | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 197.44/32.38  | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 197.44/32.38  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.44/32.38  | | | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (526),
% 197.44/32.38  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.44/32.38  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.44/32.38  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.44/32.38  | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.44/32.38  | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (582),
% 197.44/32.38  | | | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.44/32.38  | | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.44/32.38  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.44/32.38  | | | | | | | | | | | | |            (611), (612), (613), (641), (767), (7443), (7445),
% 197.44/32.38  | | | | | | | | | | | | |            (7449), (7450), (7457), (7458), (10028), (10030),
% 197.44/32.38  | | | | | | | | | | | | |            (10031), (10034), (10040), (10087), (10090),
% 197.44/32.38  | | | | | | | | | | | | |            (10093), (10094), (10095), (10096), (10099),
% 197.44/32.38  | | | | | | | | | | | | |            (10100), (10101), (10104), (10141), (10142),
% 197.44/32.38  | | | | | | | | | | | | |            (10143), (function-axioms) are inconsistent by
% 197.44/32.38  | | | | | | | | | | | | |            sub-proof #22.
% 197.44/32.38  | | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | End of split
% 197.44/32.38  | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | Case 2:
% 197.44/32.38  | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | |   (10144)  all_30_1 = e3
% 197.44/32.38  | | | | | | | | | |   (10145)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.44/32.38  | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | COMBINE_EQS: (670), (10144) imply:
% 197.44/32.38  | | | | | | | | | |   (10146)  all_10_1 = e3
% 197.44/32.38  | | | | | | | | | | 
% 197.44/32.38  | | | | | | | | | | SIMP: (10146) implies:
% 197.68/32.38  | | | | | | | | | |   (10147)  all_10_1 = e3
% 197.68/32.38  | | | | | | | | | | 
% 197.68/32.38  | | | | | | | | | | REDUCE: (53), (10147) imply:
% 197.68/32.38  | | | | | | | | | |   (10148)  op(all_10_2, e1) = e3
% 197.68/32.38  | | | | | | | | | | 
% 197.68/32.38  | | | | | | | | | | REDUCE: (52), (10147) imply:
% 197.68/32.38  | | | | | | | | | |   (10149)  op(e1, e3) = all_10_0
% 197.68/32.38  | | | | | | | | | | 
% 197.68/32.38  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.68/32.38  | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (10149)
% 197.68/32.39  | | | | | | | | | |              gives:
% 197.68/32.39  | | | | | | | | | |   (10150)  all_52_5 = all_10_0
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | COMBINE_EQS: (367), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10151)  all_56_8 = all_10_0
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | COMBINE_EQS: (547), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10152)  all_58_6 = all_10_0
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (567), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10153)   ~ (all_52_7 = all_10_0)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | SIMP: (10153) implies:
% 197.68/32.39  | | | | | | | | | |   (10154)   ~ (all_52_7 = all_10_0)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (568), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10155)   ~ (all_52_13 = all_10_0)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | SIMP: (10155) implies:
% 197.68/32.39  | | | | | | | | | |   (10156)   ~ (all_52_13 = all_10_0)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (570), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10157)   ~ (all_52_29 = all_10_0)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | SIMP: (10157) implies:
% 197.68/32.39  | | | | | | | | | |   (10158)   ~ (all_52_29 = all_10_0)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (569), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10159)   ~ (all_10_0 = all_10_2)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (553), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10160)   ~ (all_10_0 = all_6_2)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (184), (10150) imply:
% 197.68/32.39  | | | | | | | | | |   (10161)  op(all_10_0, all_10_0) = all_52_4
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | |   (10162)   ~ (all_46_0 = e1)
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | REDUCE: (10029), (10162) imply:
% 197.68/32.39  | | | | | | | | | | |   (10163)  $false
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | CLOSE: (10163) is inconsistent.
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | |   (10164)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | |   (10165)  all_58_15 = e0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | COMBINE_EQS: (541), (10165) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10166)  all_14_2 = e0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (573), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10167)   ~ (all_52_7 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (591), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10168)   ~ (all_52_15 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (603), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10169)   ~ (all_52_23 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (606), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10170)   ~ (all_52_25 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (609), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10171)   ~ (all_52_29 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (613), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10172)  op(e0, e0) = all_52_30
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (63), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10173)  op(e0, e0) = all_14_1
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (61), (10166) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10174)  op(e0, e0) = e0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.68/32.39  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10172),
% 197.68/32.39  | | | | | | | | | | | |              (10173) gives:
% 197.68/32.39  | | | | | | | | | | | |   (10175)  all_52_30 = all_14_1
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.68/32.39  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10172),
% 197.68/32.39  | | | | | | | | | | | |              (10174) gives:
% 197.68/32.39  | | | | | | | | | | | |   (10176)  all_52_30 = e0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | COMBINE_EQS: (10175), (10176) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10177)  all_14_1 = e0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (62), (10177) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10178)  op(e0, e0) = all_14_0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.68/32.39  | | | | | | | | | | | |              e0, e0, simplifying with (10174), (10178) gives:
% 197.68/32.39  | | | | | | | | | | | |   (10179)  all_14_0 = e0
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (10036), (10179) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10180)   ~ (e3 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (10032), (10179) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10181)   ~ (e2 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (10038), (10179) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10182)   ~ (e1 = e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | BETA: splitting (277) gives:
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | |   (10183)  all_56_8 = e3
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | REF_CLOSE: (10031), (10151), (10183) are inconsistent by
% 197.68/32.39  | | | | | | | | | | | | |            sub-proof #926.
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | |   (10184)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | |   (10185)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.39  | | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.39  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | BETA: splitting (10185) gives:
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | |   (10186)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.39  | | | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (311), (361), (459), (593),
% 197.68/32.39  | | | | | | | | | | | | | | |            (750), (10034), (10145), (10148), (10151),
% 197.68/32.39  | | | | | | | | | | | | | | |            (10152), (10159), (10161), (10184), (10186),
% 197.68/32.39  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.39  | | | | | | | | | | | | | | |            #667.
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | |   (10187)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.39  | | | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | ALPHA: (10187) implies:
% 197.68/32.39  | | | | | | | | | | | | | | |   (10188)  all_52_14 = e0
% 197.68/32.39  | | | | | | | | | | | | | | |   (10189)  all_52_12 = e1
% 197.68/32.39  | | | | | | | | | | | | | | |   (10190)  all_52_10 = e2
% 197.68/32.39  | | | | | | | | | | | | | | |   (10191)  all_52_8 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REDUCE: (182), (10191) imply:
% 197.68/32.39  | | | | | | | | | | | | | | |   (10192)  op(all_52_9, all_52_9) = e3
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REDUCE: (180), (10189) imply:
% 197.68/32.39  | | | | | | | | | | | | | | |   (10193)  op(all_52_13, all_52_13) = e1
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REDUCE: (179), (10188) imply:
% 197.68/32.39  | | | | | | | | | | | | | | |   (10194)  op(all_52_15, all_52_15) = e0
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REDUCE: (611), (10190) imply:
% 197.68/32.39  | | | | | | | | | | | | | | |   (10195)  op(all_4_2, all_4_2) = e2
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | |   (10196)  all_56_13 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (41), (43), (158), (168), (175),
% 197.68/32.39  | | | | | | | | | | | | | | | |            (273), (284), (305), (346), (351), (394), (431),
% 197.68/32.39  | | | | | | | | | | | | | | | |            (542), (543), (555), (557), (571), (576), (577),
% 197.68/32.39  | | | | | | | | | | | | | | | |            (582), (10028), (10030), (10165), (10192),
% 197.68/32.39  | | | | | | | | | | | | | | | |            (10194), (10196), (function-axioms) are
% 197.68/32.39  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | |   (10197)   ~ (all_56_13 = e3)
% 197.68/32.39  | | | | | | | | | | | | | | | |   (10198)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | REDUCE: (346), (10197) imply:
% 197.68/32.39  | | | | | | | | | | | | | | | |   (10199)   ~ (all_52_15 = e3)
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10200)  all_58_12 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (10200) imply:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10201)  all_52_7 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | SIMP: (10201) implies:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10202)  all_52_7 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | REDUCE: (563), (10202) imply:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10203)   ~ (all_52_3 = e3)
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | REDUCE: (571), (10202) imply:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10204)   ~ (all_52_15 = e3)
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | REDUCE: (572), (10202) imply:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10205)   ~ (all_52_23 = e3)
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | SIMP: (10205) implies:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10206)   ~ (all_52_23 = e3)
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | REDUCE: (183), (10202) imply:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10207)  op(e3, e3) = all_52_6
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.39  | | | | | | | | | | | | | | | | |              all_52_6, e3, e3, simplifying with (41), (10207)
% 197.68/32.39  | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10208)  all_52_6 = all_6_2
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | |   (10209)  all_58_2 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (387), (10203), (10209) are inconsistent by
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            sub-proof #1369.
% 197.68/32.39  | | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | |   (10210)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (51), (168), (169), (178), (275), (278),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (317), (325), (328), (361), (366), (372), (393),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (405), (427), (459), (542), (543), (546), (548),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (549), (577), (580), (582), (586), (593), (750),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (10034), (10040),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (10145), (10148), (10151), (10159), (10160),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (10184), (10192), (10193), (10199), (10206),
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            (10210), (function-axioms) are inconsistent by
% 197.68/32.39  | | | | | | | | | | | | | | | | | |            sub-proof #119.
% 197.68/32.39  | | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | |   (10211)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (41), (51), (175), (183), (273), (274),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (276), (304), (305), (346), (351), (352), (421),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (431), (542), (543), (571), (572), (582), (587),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (588), (589), (602), (612), (10151), (10154),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (10156), (10158), (10159), (10160), (10165),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (10167), (10168), (10174), (10184), (10193),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (10194), (10195), (10198), (10199), (10211),
% 197.68/32.39  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.39  | | | | | | | | | | | | | | | | |            #881.
% 197.68/32.39  | | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | |   (10212)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.39  | | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.39  | | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | BETA: splitting (10212) gives:
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | |   (10213)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.68/32.39  | | | | | | | | | | | | | | |            all_52_22 = e0
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (51), (158), (168), (175), (178),
% 197.68/32.39  | | | | | | | | | | | | | | |            (183), (273), (275), (317), (361), (393), (431),
% 197.68/32.39  | | | | | | | | | | | | | | |            (542), (546), (555), (559), (572), (593), (600),
% 197.68/32.39  | | | | | | | | | | | | | | |            (7449), (10028), (10030), (10040), (10148),
% 197.68/32.39  | | | | | | | | | | | | | | |            (10213), (function-axioms) are inconsistent by
% 197.68/32.39  | | | | | | | | | | | | | | |            sub-proof #21.
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | |   (10214)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.68/32.39  | | | | | | | | | | | | | | |            all_52_30 = e0
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.39  | | | | | | | | | | | | | | |            (51), (162), (166), (167), (169), (172), (173),
% 197.68/32.39  | | | | | | | | | | | | | | |            (174), (175), (183), (272), (273), (278), (281),
% 197.68/32.39  | | | | | | | | | | | | | | |            (282), (304), (306), (307), (308), (309), (320),
% 197.68/32.39  | | | | | | | | | | | | | | |            (326), (330), (332), (333), (346), (351), (372),
% 197.68/32.39  | | | | | | | | | | | | | | |            (387), (388), (393), (405), (411), (427), (431),
% 197.68/32.39  | | | | | | | | | | | | | | |            (529), (542), (543), (544), (545), (547), (549),
% 197.68/32.39  | | | | | | | | | | | | | | |            (551), (555), (557), (561), (564), (566), (570),
% 197.68/32.39  | | | | | | | | | | | | | | |            (571), (572), (576), (582), (593), (600), (604),
% 197.68/32.39  | | | | | | | | | | | | | | |            (605), (610), (641), (10030), (10164), (10165),
% 197.68/32.39  | | | | | | | | | | | | | | |            (10167), (10168), (10169), (10170), (10171),
% 197.68/32.39  | | | | | | | | | | | | | | |            (10214), (function-axioms) are inconsistent by
% 197.68/32.39  | | | | | | | | | | | | | | |            sub-proof #304.
% 197.68/32.39  | | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | |   (10215)   ~ (all_58_15 = e0)
% 197.68/32.39  | | | | | | | | | | | |   (10216)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.39  | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.39  | | | | | | | | | | | |              e0)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.39  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.39  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.39  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.39  | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.39  | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 197.68/32.39  | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 197.68/32.39  | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 197.68/32.39  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.39  | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 197.68/32.39  | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 197.68/32.39  | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.68/32.39  | | | | | | | | | | | |            (415), (421), (427), (431), (459), (529), (538),
% 197.68/32.39  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.68/32.39  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.68/32.39  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.68/32.39  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.68/32.39  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.68/32.39  | | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.39  | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.39  | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.39  | | | | | | | | | | | |            (611), (613), (641), (750), (7443), (7445),
% 197.68/32.39  | | | | | | | | | | | |            (7449), (7451), (7453), (7458), (10028), (10030),
% 197.68/32.39  | | | | | | | | | | | |            (10031), (10034), (10040), (10145), (10148),
% 197.68/32.39  | | | | | | | | | | | |            (10151), (10152), (10159), (10161), (10164),
% 197.68/32.39  | | | | | | | | | | | |            (10215), (10216), (function-axioms) are
% 197.68/32.39  | | | | | | | | | | | |            inconsistent by sub-proof #19.
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | |   (10217)  all_28_0 = e3
% 197.68/32.39  | | | | | | | | |   (10218)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.39  | | | | | | | | |            (51), (53), (61), (62), (63), (144), (158), (161),
% 197.68/32.39  | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.68/32.39  | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.68/32.39  | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 197.68/32.39  | | | | | | | | |            (273), (274), (277), (278), (280), (281), (282),
% 197.68/32.39  | | | | | | | | |            (283), (284), (285), (303), (304), (306), (307),
% 197.68/32.39  | | | | | | | | |            (308), (309), (311), (313), (315), (316), (318),
% 197.68/32.39  | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 197.68/32.39  | | | | | | | | |            (327), (328), (330), (331), (332), (333), (343),
% 197.68/32.39  | | | | | | | | |            (346), (351), (352), (366), (367), (372), (375),
% 197.68/32.39  | | | | | | | | |            (376), (387), (388), (393), (394), (405), (411),
% 197.68/32.39  | | | | | | | | |            (415), (427), (431), (529), (538), (539), (540),
% 197.68/32.39  | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.68/32.39  | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.68/32.39  | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.68/32.39  | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 197.68/32.39  | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 197.68/32.39  | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 197.68/32.39  | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 197.68/32.39  | | | | | | | | |            (607), (608), (609), (610), (613), (641), (754),
% 197.68/32.39  | | | | | | | | |            (7444), (7445), (7449), (7450), (7451), (7453),
% 197.68/32.39  | | | | | | | | |            (7455), (7458), (7459), (10028), (10029), (10030),
% 197.68/32.39  | | | | | | | | |            (10032), (10036), (10038), (10217), (10218),
% 197.68/32.39  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.39  | | | | | | | | |            #14.
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | End of split
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | |   (10219)  all_24_0 = e1
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | COMBINE_EQS: (711), (10219) imply:
% 197.68/32.39  | | | | | | | |   (10220)  all_14_0 = e1
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | SIMP: (10220) implies:
% 197.68/32.39  | | | | | | | |   (10221)  all_14_0 = e1
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | REDUCE: (10036), (10221) imply:
% 197.68/32.39  | | | | | | | |   (10222)   ~ (e3 = e1)
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | REDUCE: (10032), (10221) imply:
% 197.68/32.39  | | | | | | | |   (10223)   ~ (e2 = e1)
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | REDUCE: (62), (10221) imply:
% 197.68/32.39  | | | | | | | |   (10224)  op(e0, all_14_1) = e1
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | BETA: splitting (99) gives:
% 197.68/32.39  | | | | | | | | 
% 197.68/32.39  | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | |   (10225)   ~ (all_28_0 = e3)
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | REDUCE: (754), (10225) imply:
% 197.68/32.39  | | | | | | | | |   (10226)   ~ (all_4_0 = e3)
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | BETA: splitting (104) gives:
% 197.68/32.39  | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | |   (10227)   ~ (all_30_1 = e3)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | REDUCE: (670), (10227) imply:
% 197.68/32.39  | | | | | | | | | |   (10228)   ~ (all_10_1 = e3)
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | BETA: splitting (129) gives:
% 197.68/32.39  | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | |   (10229)   ~ (all_40_1 = e2)
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | REDUCE: (687), (10229) imply:
% 197.68/32.39  | | | | | | | | | | |   (10230)   ~ (all_10_1 = e2)
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.39  | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | |   (10231)   ~ (all_46_0 = e1)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | REDUCE: (10029), (10231) imply:
% 197.68/32.39  | | | | | | | | | | | |   (10232)  $false
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | CLOSE: (10232) is inconsistent.
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | |   (10233)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.39  | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | Case 1:
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | |   (10234)  all_58_15 = e0
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (10224), (10234),
% 197.68/32.39  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.39  | | | | | | | | | | | | |            #877.
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | Case 2:
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.39  | | | | | | | | | | | | |   (10235)   ~ (all_58_15 = e0)
% 197.68/32.39  | | | | | | | | | | | | |   (10236)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.39  | | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.39  | | | | | | | | | | | | |              e0)
% 197.68/32.39  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.40  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.40  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.40  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.40  | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.40  | | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 197.68/32.40  | | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 197.68/32.40  | | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 197.68/32.40  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.40  | | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 197.68/32.40  | | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 197.68/32.40  | | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.68/32.40  | | | | | | | | | | | | |            (415), (421), (427), (431), (529), (538), (539),
% 197.68/32.40  | | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.68/32.40  | | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.68/32.40  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (566), (567),
% 197.68/32.40  | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.68/32.40  | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 197.68/32.40  | | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.68/32.40  | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.40  | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 197.68/32.40  | | | | | | | | | | | | |            (612), (613), (641), (7443), (7445), (7449),
% 197.68/32.40  | | | | | | | | | | | | |            (7451), (7453), (7458), (10028), (10030), (10226),
% 197.68/32.40  | | | | | | | | | | | | |            (10230), (10233), (10235), (10236),
% 197.68/32.40  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.40  | | | | | | | | | | | | |            #30.
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | |   (10237)  all_40_1 = e2
% 197.68/32.40  | | | | | | | | | | |   (10238)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | COMBINE_EQS: (687), (10237) imply:
% 197.68/32.40  | | | | | | | | | | |   (10239)  all_10_1 = e2
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (10228), (10239) imply:
% 197.68/32.40  | | | | | | | | | | |   (10240)   ~ (e3 = e2)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (53), (10239) imply:
% 197.68/32.40  | | | | | | | | | | |   (10241)  op(all_10_2, e1) = e2
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (52), (10239) imply:
% 197.68/32.40  | | | | | | | | | | |   (10242)  op(e1, e2) = all_10_0
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.68/32.40  | | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (10242)
% 197.68/32.40  | | | | | | | | | | |              gives:
% 197.68/32.40  | | | | | | | | | | |   (10243)  all_52_13 = all_10_0
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | COMBINE_EQS: (421), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10244)  all_56_9 = all_10_0
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | COMBINE_EQS: (366), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10245)  all_58_7 = all_10_0
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (568), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10246)   ~ (all_52_5 = all_10_0)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (575), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10247)   ~ (all_52_9 = all_10_0)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (588), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10248)   ~ (all_10_0 = all_10_2)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (580), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10249)   ~ (all_10_0 = all_4_2)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (180), (10243) imply:
% 197.68/32.40  | | | | | | | | | | |   (10250)  op(all_10_0, all_10_0) = all_52_12
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | |   (10251)   ~ (all_46_0 = e1)
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | REDUCE: (10029), (10251) imply:
% 197.68/32.40  | | | | | | | | | | | |   (10252)  $false
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | CLOSE: (10252) is inconsistent.
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | |   (10253)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | |   (10254)  all_58_15 = e0
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (10224), (10254),
% 197.68/32.40  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.40  | | | | | | | | | | | | |            #877.
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | |   (10255)   ~ (all_58_15 = e0)
% 197.68/32.40  | | | | | | | | | | | | |   (10256)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.40  | | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.40  | | | | | | | | | | | | |              e0)
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | | ALPHA: (10256) implies:
% 197.68/32.40  | | | | | | | | | | | | |   (10257)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.40  | | | | | | | | | | | | |   (10258)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | | REDUCE: (541), (10255) imply:
% 197.68/32.40  | | | | | | | | | | | | |   (10259)   ~ (all_14_2 = e0)
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.40  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.40  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.40  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.40  | | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.40  | | | | | | | | | | | | |            (276), (277), (278), (280), (281), (282), (283),
% 197.68/32.40  | | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (312),
% 197.68/32.40  | | | | | | | | | | | | |            (313), (315), (316), (317), (319), (320), (321),
% 197.68/32.40  | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 197.68/32.40  | | | | | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 197.68/32.40  | | | | | | | | | | | | |            (366), (367), (372), (375), (387), (388), (393),
% 197.68/32.40  | | | | | | | | | | | | |            (394), (405), (411), (415), (427), (431), (526),
% 197.68/32.40  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.40  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.40  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.40  | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.40  | | | | | | | | | | | | |            (573), (574), (575), (576), (577), (578), (582),
% 197.68/32.40  | | | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.40  | | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.40  | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.40  | | | | | | | | | | | | |            (611), (612), (613), (641), (767), (7443), (7445),
% 197.68/32.40  | | | | | | | | | | | | |            (7449), (7450), (7457), (7458), (10028), (10030),
% 197.68/32.40  | | | | | | | | | | | | |            (10031), (10034), (10226), (10238), (10241),
% 197.68/32.40  | | | | | | | | | | | | |            (10244), (10245), (10246), (10247), (10248),
% 197.68/32.40  | | | | | | | | | | | | |            (10249), (10250), (10253), (10257), (10258),
% 197.68/32.40  | | | | | | | | | | | | |            (10259), (function-axioms) are inconsistent by
% 197.68/32.40  | | | | | | | | | | | | |            sub-proof #22.
% 197.68/32.40  | | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | |   (10260)  all_30_1 = e3
% 197.68/32.40  | | | | | | | | | |   (10261)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | COMBINE_EQS: (670), (10260) imply:
% 197.68/32.40  | | | | | | | | | |   (10262)  all_10_1 = e3
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | SIMP: (10262) implies:
% 197.68/32.40  | | | | | | | | | |   (10263)  all_10_1 = e3
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | REDUCE: (53), (10263) imply:
% 197.68/32.40  | | | | | | | | | |   (10264)  op(all_10_2, e1) = e3
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | REDUCE: (52), (10263) imply:
% 197.68/32.40  | | | | | | | | | |   (10265)  op(e1, e3) = all_10_0
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.68/32.40  | | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (10265)
% 197.68/32.40  | | | | | | | | | |              gives:
% 197.68/32.40  | | | | | | | | | |   (10266)  all_52_5 = all_10_0
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | COMBINE_EQS: (367), (10266) imply:
% 197.68/32.40  | | | | | | | | | |   (10267)  all_56_8 = all_10_0
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | COMBINE_EQS: (547), (10266) imply:
% 197.68/32.40  | | | | | | | | | |   (10268)  all_58_6 = all_10_0
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | REDUCE: (569), (10266) imply:
% 197.68/32.40  | | | | | | | | | |   (10269)   ~ (all_10_0 = all_10_2)
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | REDUCE: (184), (10266) imply:
% 197.68/32.40  | | | | | | | | | |   (10270)  op(all_10_0, all_10_0) = all_52_4
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | |   (10271)   ~ (all_46_0 = e1)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (10029), (10271) imply:
% 197.68/32.40  | | | | | | | | | | |   (10272)  $false
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | CLOSE: (10272) is inconsistent.
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | |   (10273)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | |   (10274)  all_58_15 = e0
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (10224), (10274),
% 197.68/32.40  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.40  | | | | | | | | | | | |            #877.
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | |   (10275)   ~ (all_58_15 = e0)
% 197.68/32.40  | | | | | | | | | | | |   (10276)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.40  | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.40  | | | | | | | | | | | |              e0)
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.40  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.40  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.40  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.40  | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.40  | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 197.68/32.40  | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 197.68/32.40  | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 197.68/32.40  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.40  | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 197.68/32.40  | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 197.68/32.40  | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.68/32.40  | | | | | | | | | | | |            (415), (421), (427), (431), (459), (529), (538),
% 197.68/32.40  | | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.68/32.40  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.68/32.40  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.68/32.40  | | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.68/32.40  | | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.68/32.40  | | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.40  | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.40  | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.40  | | | | | | | | | | | |            (611), (613), (641), (750), (7443), (7445),
% 197.68/32.40  | | | | | | | | | | | |            (7449), (7451), (7453), (7458), (10028), (10030),
% 197.68/32.40  | | | | | | | | | | | |            (10031), (10034), (10226), (10261), (10264),
% 197.68/32.40  | | | | | | | | | | | |            (10267), (10268), (10269), (10270), (10273),
% 197.68/32.40  | | | | | | | | | | | |            (10275), (10276), (function-axioms) are
% 197.68/32.40  | | | | | | | | | | | |            inconsistent by sub-proof #19.
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | |   (10277)  all_28_0 = e3
% 197.68/32.40  | | | | | | | | |   (10278)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.40  | | | | | | | | |            (51), (53), (61), (63), (144), (158), (161), (162),
% 197.68/32.40  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.68/32.40  | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.68/32.40  | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.68/32.40  | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.68/32.40  | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.68/32.40  | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.68/32.40  | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 197.68/32.40  | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 197.68/32.40  | | | | | | | | |            (366), (367), (372), (375), (376), (387), (388),
% 197.68/32.40  | | | | | | | | |            (393), (394), (405), (411), (415), (427), (431),
% 197.68/32.40  | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.40  | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.40  | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.40  | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.40  | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 197.68/32.40  | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 197.68/32.40  | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.68/32.40  | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.68/32.40  | | | | | | | | |            (610), (613), (641), (754), (7444), (7445), (7449),
% 197.68/32.40  | | | | | | | | |            (7450), (7451), (7453), (7455), (7458), (7459),
% 197.68/32.40  | | | | | | | | |            (10028), (10029), (10030), (10224), (10277),
% 197.68/32.40  | | | | | | | | |            (10278), (function-axioms) are inconsistent by
% 197.68/32.40  | | | | | | | | |            sub-proof #12.
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | 
% 197.68/32.40  | | | | | | | End of split
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | Case 2:
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | |   (10279)  all_18_0 = e3
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | | COMBINE_EQS: (761), (10279) imply:
% 197.68/32.40  | | | | | | |   (10280)  all_14_0 = e3
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | | SIMP: (10280) implies:
% 197.68/32.40  | | | | | | |   (10281)  all_14_0 = e3
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | | REDUCE: (62), (10281) imply:
% 197.68/32.40  | | | | | | |   (10282)  op(e0, all_14_1) = e3
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | | BETA: splitting (99) gives:
% 197.68/32.40  | | | | | | | 
% 197.68/32.40  | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | 
% 197.68/32.40  | | | | | | | |   (10283)   ~ (all_28_0 = e3)
% 197.68/32.40  | | | | | | | | 
% 197.68/32.40  | | | | | | | | REDUCE: (754), (10283) imply:
% 197.68/32.40  | | | | | | | |   (10284)   ~ (all_4_0 = e3)
% 197.68/32.40  | | | | | | | | 
% 197.68/32.40  | | | | | | | | BETA: splitting (104) gives:
% 197.68/32.40  | | | | | | | | 
% 197.68/32.40  | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | |   (10285)   ~ (all_30_1 = e3)
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | REDUCE: (670), (10285) imply:
% 197.68/32.40  | | | | | | | | |   (10286)   ~ (all_10_1 = e3)
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | BETA: splitting (129) gives:
% 197.68/32.40  | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | |   (10287)   ~ (all_40_1 = e2)
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | REDUCE: (687), (10287) imply:
% 197.68/32.40  | | | | | | | | | |   (10288)   ~ (all_10_1 = e2)
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | |   (10289)   ~ (all_46_0 = e1)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | REDUCE: (10029), (10289) imply:
% 197.68/32.40  | | | | | | | | | | |   (10290)  $false
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | CLOSE: (10290) is inconsistent.
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | |   (10291)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | Case 1:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | |   (10292)  all_58_15 = e0
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (10282), (10292),
% 197.68/32.40  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.40  | | | | | | | | | | | |            #678.
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | |   (10293)   ~ (all_58_15 = e0)
% 197.68/32.40  | | | | | | | | | | | |   (10294)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.40  | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.40  | | | | | | | | | | | |              e0)
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | ALPHA: (10294) implies:
% 197.68/32.40  | | | | | | | | | | | |   (10295)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.40  | | | | | | | | | | | |   (10296)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | REDUCE: (541), (10293) imply:
% 197.68/32.40  | | | | | | | | | | | |   (10297)   ~ (all_14_2 = e0)
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.40  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.40  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.40  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.40  | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.40  | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 197.68/32.40  | | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 197.68/32.40  | | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 197.68/32.40  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.40  | | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 197.68/32.40  | | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 197.68/32.40  | | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.68/32.40  | | | | | | | | | | | |            (415), (421), (427), (431), (529), (538), (539),
% 197.68/32.40  | | | | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 197.68/32.40  | | | | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 197.68/32.40  | | | | | | | | | | | |            (559), (561), (562), (563), (564), (566), (567),
% 197.68/32.40  | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.68/32.40  | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 197.68/32.40  | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.68/32.40  | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.40  | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (611),
% 197.68/32.40  | | | | | | | | | | | |            (612), (613), (641), (7443), (7445), (7449),
% 197.68/32.40  | | | | | | | | | | | |            (7451), (7453), (7458), (10028), (10030), (10284),
% 197.68/32.40  | | | | | | | | | | | |            (10288), (10291), (10295), (10296), (10297),
% 197.68/32.40  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.40  | | | | | | | | | | | |            #31.
% 197.68/32.40  | | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | End of split
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | Case 2:
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | |   (10298)  all_40_1 = e2
% 197.68/32.40  | | | | | | | | | |   (10299)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.40  | | | | | | | | | | COMBINE_EQS: (687), (10298) imply:
% 197.68/32.40  | | | | | | | | | |   (10300)  all_10_1 = e2
% 197.68/32.40  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (10286), (10300) imply:
% 197.68/32.41  | | | | | | | | | |   (10301)   ~ (e3 = e2)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (53), (10300) imply:
% 197.68/32.41  | | | | | | | | | |   (10302)  op(all_10_2, e1) = e2
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (52), (10300) imply:
% 197.68/32.41  | | | | | | | | | |   (10303)  op(e1, e2) = all_10_0
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.68/32.41  | | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (10303)
% 197.68/32.41  | | | | | | | | | |              gives:
% 197.68/32.41  | | | | | | | | | |   (10304)  all_52_13 = all_10_0
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | COMBINE_EQS: (421), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10305)  all_56_9 = all_10_0
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | COMBINE_EQS: (366), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10306)  all_58_7 = all_10_0
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (568), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10307)   ~ (all_52_5 = all_10_0)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (575), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10308)   ~ (all_52_9 = all_10_0)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (588), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10309)   ~ (all_10_0 = all_10_2)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (580), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10310)   ~ (all_10_0 = all_4_2)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (180), (10304) imply:
% 197.68/32.41  | | | | | | | | | |   (10311)  op(all_10_0, all_10_0) = all_52_12
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | |   (10312)   ~ (all_46_0 = e1)
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | REDUCE: (10029), (10312) imply:
% 197.68/32.41  | | | | | | | | | | |   (10313)  $false
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | CLOSE: (10313) is inconsistent.
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | |   (10314)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | |   (10315)  all_58_15 = e0
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (10282), (10315),
% 197.68/32.41  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.41  | | | | | | | | | | | |            #693.
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | |   (10316)   ~ (all_58_15 = e0)
% 197.68/32.41  | | | | | | | | | | | |   (10317)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.41  | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.41  | | | | | | | | | | | |              e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | ALPHA: (10317) implies:
% 197.68/32.41  | | | | | | | | | | | |   (10318)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.41  | | | | | | | | | | | |   (10319)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (541), (10316) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10320)   ~ (all_14_2 = e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | BETA: splitting (276) gives:
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | |   (10321)  all_56_9 = e3
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | REF_CLOSE: (10031), (10305), (10321) are inconsistent by
% 197.68/32.41  | | | | | | | | | | | | |            sub-proof #1006.
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | |   (10322)   ~ (all_56_9 = e3)
% 197.68/32.41  | | | | | | | | | | | | |   (10323)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | |   (10324)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.41  | | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.41  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | BETA: splitting (10324) gives:
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | |   (10325)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.41  | | | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | ALPHA: (10325) implies:
% 197.68/32.41  | | | | | | | | | | | | | | |   (10326)  all_52_6 = e0
% 197.68/32.41  | | | | | | | | | | | | | | |   (10327)  all_52_4 = e1
% 197.68/32.41  | | | | | | | | | | | | | | |   (10328)  all_52_2 = e2
% 197.68/32.41  | | | | | | | | | | | | | | |   (10329)  all_52_0 = e3
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | REDUCE: (185), (10328) imply:
% 197.68/32.41  | | | | | | | | | | | | | | |   (10330)  op(all_52_3, all_52_3) = e2
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | REDUCE: (184), (10327) imply:
% 197.68/32.41  | | | | | | | | | | | | | | |   (10331)  op(all_52_5, all_52_5) = e1
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | REDUCE: (183), (10326) imply:
% 197.68/32.41  | | | | | | | | | | | | | | |   (10332)  op(all_52_7, all_52_7) = e0
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | REDUCE: (610), (10329) imply:
% 197.68/32.41  | | | | | | | | | | | | | | |   (10333)  op(all_6_2, all_6_2) = e3
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | |   (10334)  all_56_15 = e3
% 197.68/32.41  | | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (51), (63), (156), (167), (168),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (178), (282), (284), (313), (321), (332), (351),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (387), (388), (394), (405), (526), (538), (544),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (546), (547), (553), (557), (564), (567), (569),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (573), (577), (578), (595), (600), (606), (609),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (612), (613), (767), (10031), (10034), (10282),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (10299), (10302), (10305), (10306), (10308),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (10323), (10330), (10331), (10333), (10334),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.41  | | | | | | | | | | | | | | | |            #676.
% 197.68/32.41  | | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | |   (10335)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.68/32.41  | | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (61), (168), (169),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (173), (178), (273), (277), (278), (284), (306),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (312), (313), (321), (324), (332), (351), (367),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (372), (387), (394), (405), (427), (431), (526),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (538), (543), (544), (545), (546), (547), (548),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (549), (553), (555), (557), (564), (569), (570),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (571), (573), (577), (578), (591), (607), (611),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (612), (767), (7445), (7449), (10031), (10034),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (10284), (10299), (10302), (10305), (10306),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (10307), (10308), (10310), (10319), (10320),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (10323), (10330), (10331), (10332), (10333),
% 197.68/32.41  | | | | | | | | | | | | | | | |            (10335), (function-axioms) are inconsistent by
% 197.68/32.41  | | | | | | | | | | | | | | | |            sub-proof #172.
% 197.68/32.41  | | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | |   (10336)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.41  | | | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (51), (158), (168),
% 197.68/32.41  | | | | | | | | | | | | | | |            (169), (175), (179), (182), (183), (270), (271),
% 197.68/32.41  | | | | | | | | | | | | | | |            (273), (284), (306), (317), (324), (325), (343),
% 197.68/32.41  | | | | | | | | | | | | | | |            (351), (393), (394), (431), (526), (538), (541),
% 197.68/32.41  | | | | | | | | | | | | | | |            (542), (543), (546), (548), (549), (555), (557),
% 197.68/32.41  | | | | | | | | | | | | | | |            (571), (572), (573), (576), (577), (582), (590),
% 197.68/32.41  | | | | | | | | | | | | | | |            (591), (603), (611), (613), (767), (7445), (7449),
% 197.68/32.41  | | | | | | | | | | | | | | |            (10028), (10030), (10031), (10034), (10284),
% 197.68/32.41  | | | | | | | | | | | | | | |            (10299), (10305), (10306), (10309), (10311),
% 197.68/32.41  | | | | | | | | | | | | | | |            (10318), (10320), (10323), (10336),
% 197.68/32.41  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.41  | | | | | | | | | | | | | | |            #25.
% 197.68/32.41  | | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | |   (10337)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.41  | | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.41  | | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.41  | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.41  | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.41  | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.41  | | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 197.68/32.41  | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 197.68/32.41  | | | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (317),
% 197.68/32.41  | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 197.68/32.41  | | | | | | | | | | | | | |            (327), (328), (330), (331), (332), (333), (343),
% 197.68/32.41  | | | | | | | | | | | | | |            (346), (351), (352), (366), (367), (372), (375),
% 197.68/32.41  | | | | | | | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 197.68/32.41  | | | | | | | | | | | | | |            (431), (526), (529), (538), (539), (540), (541),
% 197.68/32.41  | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.68/32.41  | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.68/32.41  | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 197.68/32.41  | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (578),
% 197.68/32.41  | | | | | | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 197.68/32.41  | | | | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.68/32.41  | | | | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.68/32.41  | | | | | | | | | | | | | |            (610), (611), (612), (613), (641), (767), (7443),
% 197.68/32.41  | | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (10028), (10030),
% 197.68/32.41  | | | | | | | | | | | | | |            (10034), (10284), (10299), (10302), (10305),
% 197.68/32.41  | | | | | | | | | | | | | |            (10314), (10318), (10320), (10323), (10337),
% 197.68/32.41  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.41  | | | | | | | | | | | | | |            #23.
% 197.68/32.41  | | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | |   (10338)  all_30_1 = e3
% 197.68/32.41  | | | | | | | | |   (10339)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | COMBINE_EQS: (670), (10338) imply:
% 197.68/32.41  | | | | | | | | |   (10340)  all_10_1 = e3
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | SIMP: (10340) implies:
% 197.68/32.41  | | | | | | | | |   (10341)  all_10_1 = e3
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | REDUCE: (53), (10341) imply:
% 197.68/32.41  | | | | | | | | |   (10342)  op(all_10_2, e1) = e3
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | REDUCE: (52), (10341) imply:
% 197.68/32.41  | | | | | | | | |   (10343)  op(e1, e3) = all_10_0
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.68/32.41  | | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (10343)
% 197.68/32.41  | | | | | | | | |              gives:
% 197.68/32.41  | | | | | | | | |   (10344)  all_52_5 = all_10_0
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | COMBINE_EQS: (367), (10344) imply:
% 197.68/32.41  | | | | | | | | |   (10345)  all_56_8 = all_10_0
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | COMBINE_EQS: (547), (10344) imply:
% 197.68/32.41  | | | | | | | | |   (10346)  all_58_6 = all_10_0
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | REDUCE: (569), (10344) imply:
% 197.68/32.41  | | | | | | | | |   (10347)   ~ (all_10_0 = all_10_2)
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | REDUCE: (184), (10344) imply:
% 197.68/32.41  | | | | | | | | |   (10348)  op(all_10_0, all_10_0) = all_52_4
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | |   (10349)   ~ (all_46_0 = e1)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (10029), (10349) imply:
% 197.68/32.41  | | | | | | | | | |   (10350)  $false
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | CLOSE: (10350) is inconsistent.
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | |   (10351)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | |   (10352)  all_58_15 = e0
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (10282), (10352),
% 197.68/32.41  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.41  | | | | | | | | | | |            #693.
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | |   (10353)   ~ (all_58_15 = e0)
% 197.68/32.41  | | | | | | | | | | |   (10354)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.41  | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.41  | | | | | | | | | | |              e0)
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | ALPHA: (10354) implies:
% 197.68/32.41  | | | | | | | | | | |   (10355)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.41  | | | | | | | | | | |   (10356)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | REDUCE: (541), (10353) imply:
% 197.68/32.41  | | | | | | | | | | |   (10357)   ~ (all_14_2 = e0)
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.41  | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.41  | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.41  | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.41  | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.41  | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 197.68/32.41  | | | | | | | | | | |            (283), (284), (285), (306), (307), (309), (311),
% 197.68/32.41  | | | | | | | | | | |            (312), (313), (314), (315), (316), (317), (319),
% 197.68/32.41  | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.41  | | | | | | | | | | |            (328), (329), (330), (331), (332), (333), (343),
% 197.68/32.41  | | | | | | | | | | |            (346), (351), (352), (361), (366), (367), (372),
% 197.68/32.41  | | | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 197.68/32.41  | | | | | | | | | | |            (415), (421), (427), (431), (459), (529), (538),
% 197.68/32.41  | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 197.68/32.41  | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.68/32.41  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 197.68/32.41  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 197.68/32.41  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.68/32.41  | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.41  | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.41  | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.41  | | | | | | | | | | |            (611), (613), (641), (750), (7443), (7445),
% 197.68/32.41  | | | | | | | | | | |            (7449), (7451), (7453), (7458), (10028), (10030),
% 197.68/32.41  | | | | | | | | | | |            (10031), (10034), (10284), (10339), (10342),
% 197.68/32.41  | | | | | | | | | | |            (10345), (10346), (10347), (10348), (10351),
% 197.68/32.41  | | | | | | | | | | |            (10355), (10356), (10357), (function-axioms) are
% 197.68/32.41  | | | | | | | | | | |            inconsistent by sub-proof #20.
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | End of split
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | |   (10358)  all_28_0 = e3
% 197.68/32.41  | | | | | | | |   (10359)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 197.68/32.41  | | | | | | | |            (53), (61), (63), (144), (158), (161), (162), (166),
% 197.68/32.41  | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.41  | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.41  | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.41  | | | | | | | |            (277), (278), (280), (281), (282), (283), (284),
% 197.68/32.41  | | | | | | | |            (285), (303), (306), (307), (309), (311), (313),
% 197.68/32.41  | | | | | | | |            (315), (316), (318), (319), (320), (321), (323),
% 197.68/32.41  | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 197.68/32.41  | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.68/32.41  | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.68/32.41  | | | | | | | |            (394), (405), (411), (415), (427), (431), (529),
% 197.68/32.41  | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 197.68/32.41  | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.68/32.41  | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 197.68/32.41  | | | | | | | |            (566), (567), (569), (570), (571), (572), (573),
% 197.68/32.41  | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.68/32.41  | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.41  | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.41  | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.41  | | | | | | | |            (613), (641), (754), (7444), (7445), (7449), (7450),
% 197.68/32.41  | | | | | | | |            (7451), (7453), (7455), (7458), (7459), (10028),
% 197.68/32.41  | | | | | | | |            (10029), (10030), (10282), (10358), (10359),
% 197.68/32.41  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #10.
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | End of split
% 197.68/32.41  | | | | | | | 
% 197.68/32.41  | | | | | | End of split
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | Case 2:
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | |   (10360)  all_16_0 = e2
% 197.68/32.41  | | | | | |   (10361)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | COMBINE_EQS: (760), (10360) imply:
% 197.68/32.41  | | | | | |   (10362)  all_10_0 = e2
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | SIMP: (10362) implies:
% 197.68/32.41  | | | | | |   (10363)  all_10_0 = e2
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | COMBINE_EQS: (756), (10363) imply:
% 197.68/32.41  | | | | | |   (10364)  all_26_0 = e2
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | REDUCE: (10031), (10363) imply:
% 197.68/32.41  | | | | | |   (10365)   ~ (e3 = e2)
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | REDUCE: (52), (10363) imply:
% 197.68/32.41  | | | | | |   (10366)  op(e1, all_10_1) = e2
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | BETA: splitting (74) gives:
% 197.68/32.41  | | | | | | 
% 197.68/32.41  | | | | | | Case 1:
% 197.68/32.41  | | | | | | | 
% 197.68/32.41  | | | | | | |   (10367)   ~ (all_18_0 = e3)
% 197.68/32.41  | | | | | | | 
% 197.68/32.41  | | | | | | | REDUCE: (761), (10367) imply:
% 197.68/32.41  | | | | | | |   (10368)   ~ (all_14_0 = e3)
% 197.68/32.41  | | | | | | | 
% 197.68/32.41  | | | | | | | BETA: splitting (89) gives:
% 197.68/32.41  | | | | | | | 
% 197.68/32.41  | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | |   (10369)   ~ (all_24_0 = e1)
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | | REDUCE: (711), (10369) imply:
% 197.68/32.41  | | | | | | | |   (10370)   ~ (all_14_0 = e1)
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | | BETA: splitting (94) gives:
% 197.68/32.41  | | | | | | | | 
% 197.68/32.41  | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | |   (10371)   ~ (all_26_0 = e2)
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | REDUCE: (10364), (10371) imply:
% 197.68/32.41  | | | | | | | | |   (10372)  $false
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | CLOSE: (10372) is inconsistent.
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | |   (10373)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | BETA: splitting (99) gives:
% 197.68/32.41  | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | |   (10374)   ~ (all_28_0 = e3)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | REDUCE: (754), (10374) imply:
% 197.68/32.41  | | | | | | | | | |   (10375)   ~ (all_4_0 = e3)
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.41  | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | |   (10376)   ~ (all_46_0 = e1)
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | REDUCE: (10029), (10376) imply:
% 197.68/32.41  | | | | | | | | | | |   (10377)  $false
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | CLOSE: (10377) is inconsistent.
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | Case 2:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | |   (10378)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.41  | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | Case 1:
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | |   (10379)  all_58_15 = e0
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | COMBINE_EQS: (541), (10379) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10380)  all_14_2 = e0
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (573), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10381)   ~ (all_52_7 = e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (591), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10382)   ~ (all_52_15 = e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (603), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10383)   ~ (all_52_23 = e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (606), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10384)   ~ (all_52_25 = e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (609), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10385)   ~ (all_52_29 = e0)
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (613), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10386)  op(e0, e0) = all_52_30
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (63), (10380) imply:
% 197.68/32.41  | | | | | | | | | | | |   (10387)  op(e0, e0) = all_14_1
% 197.68/32.41  | | | | | | | | | | | | 
% 197.68/32.41  | | | | | | | | | | | | REDUCE: (61), (10380) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10388)  op(e0, e0) = e0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.68/32.42  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10386),
% 197.68/32.42  | | | | | | | | | | | |              (10387) gives:
% 197.68/32.42  | | | | | | | | | | | |   (10389)  all_52_30 = all_14_1
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.68/32.42  | | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10386),
% 197.68/32.42  | | | | | | | | | | | |              (10388) gives:
% 197.68/32.42  | | | | | | | | | | | |   (10390)  all_52_30 = e0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | COMBINE_EQS: (10389), (10390) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10391)  all_14_1 = e0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | SIMP: (10391) implies:
% 197.68/32.42  | | | | | | | | | | | |   (10392)  all_14_1 = e0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REDUCE: (62), (10392) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10393)  op(e0, e0) = all_14_0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.68/32.42  | | | | | | | | | | | |              e0, e0, simplifying with (10388), (10393) gives:
% 197.68/32.42  | | | | | | | | | | | |   (10394)  all_14_0 = e0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REDUCE: (10368), (10394) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10395)   ~ (e3 = e0)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REDUCE: (10032), (10394) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10396)   ~ (e2 = e0)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REDUCE: (10370), (10394) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10397)   ~ (e1 = e0)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | |   (10398)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.42  | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.42  | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | BETA: splitting (10398) gives:
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | |   (10399)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 197.68/32.42  | | | | | | | | | | | | | |            (53), (61), (156), (161), (175), (179), (183),
% 197.68/32.42  | | | | | | | | | | | | | |            (184), (185), (271), (272), (273), (277), (304),
% 197.68/32.42  | | | | | | | | | | | | | |            (305), (306), (321), (326), (332), (343), (346),
% 197.68/32.42  | | | | | | | | | | | | | |            (351), (367), (387), (405), (431), (515), (542),
% 197.68/32.42  | | | | | | | | | | | | | |            (543), (547), (555), (564), (567), (568), (569),
% 197.68/32.42  | | | | | | | | | | | | | |            (571), (572), (573), (582), (590), (610), (611),
% 197.68/32.42  | | | | | | | | | | | | | |            (680), (10361), (10366), (10379), (10381),
% 197.68/32.42  | | | | | | | | | | | | | |            (10383), (10388), (10399), (function-axioms) are
% 197.68/32.42  | | | | | | | | | | | | | |            inconsistent by sub-proof #136.
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | |   (10400)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | ALPHA: (10400) implies:
% 197.68/32.42  | | | | | | | | | | | | | |   (10401)  all_52_14 = e0
% 197.68/32.42  | | | | | | | | | | | | | |   (10402)  all_52_12 = e1
% 197.68/32.42  | | | | | | | | | | | | | |   (10403)  all_52_10 = e2
% 197.68/32.42  | | | | | | | | | | | | | |   (10404)  all_52_8 = e3
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | REDUCE: (182), (10404) imply:
% 197.68/32.42  | | | | | | | | | | | | | |   (10405)  op(all_52_9, all_52_9) = e3
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | REDUCE: (180), (10402) imply:
% 197.68/32.42  | | | | | | | | | | | | | |   (10406)  op(all_52_13, all_52_13) = e1
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | REDUCE: (179), (10401) imply:
% 197.68/32.42  | | | | | | | | | | | | | |   (10407)  op(all_52_15, all_52_15) = e0
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | REDUCE: (611), (10403) imply:
% 197.68/32.42  | | | | | | | | | | | | | |   (10408)  op(all_4_2, all_4_2) = e2
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | |   (10409)  all_56_13 = e3
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | COMBINE_EQS: (346), (10409) imply:
% 197.68/32.42  | | | | | | | | | | | | | | |   (10410)  all_52_15 = e3
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | SIMP: (10410) implies:
% 197.68/32.42  | | | | | | | | | | | | | | |   (10411)  all_52_15 = e3
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REDUCE: (590), (10411) imply:
% 197.68/32.42  | | | | | | | | | | | | | | |   (10412)   ~ (all_52_23 = e3)
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | SIMP: (10412) implies:
% 197.68/32.42  | | | | | | | | | | | | | | |   (10413)   ~ (all_52_23 = e3)
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 197.68/32.42  | | | | | | | | | | | | | | |            (53), (158), (162), (167), (168), (169), (175),
% 197.68/32.42  | | | | | | | | | | | | | | |            (273), (278), (284), (305), (306), (310), (314),
% 197.68/32.42  | | | | | | | | | | | | | | |            (317), (318), (320), (321), (322), (325), (326),
% 197.68/32.42  | | | | | | | | | | | | | | |            (329), (330), (333), (351), (366), (372), (387),
% 197.68/32.42  | | | | | | | | | | | | | | |            (393), (394), (405), (427), (431), (542), (543),
% 197.68/32.42  | | | | | | | | | | | | | | |            (545), (546), (547), (548), (549), (555), (557),
% 197.68/32.42  | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (568), (571),
% 197.68/32.42  | | | | | | | | | | | | | | |            (572), (574), (576), (577), (580), (582), (586),
% 197.68/32.42  | | | | | | | | | | | | | | |            (588), (593), (594), (595), (612), (7443), (7445),
% 197.68/32.42  | | | | | | | | | | | | | | |            (7449), (7451), (10028), (10030), (10375),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10379), (10381), (10382), (10383), (10384),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10388), (10405), (10406), (10407), (10413),
% 197.68/32.42  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.42  | | | | | | | | | | | | | | |            #38.
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | |   (10414)   ~ (all_56_13 = e3)
% 197.68/32.42  | | | | | | | | | | | | | | |   (10415)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REDUCE: (346), (10414) imply:
% 197.68/32.42  | | | | | | | | | | | | | | |   (10416)   ~ (all_52_15 = e3)
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (36), (41), (51), (53), (156), (168),
% 197.68/32.42  | | | | | | | | | | | | | | |            (169), (178), (183), (273), (274), (282), (284),
% 197.68/32.42  | | | | | | | | | | | | | | |            (305), (306), (313), (314), (317), (321), (325),
% 197.68/32.42  | | | | | | | | | | | | | | |            (327), (346), (351), (352), (366), (372), (387),
% 197.68/32.42  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (431), (512), (515),
% 197.68/32.42  | | | | | | | | | | | | | | |            (542), (543), (544), (546), (547), (548), (549),
% 197.68/32.42  | | | | | | | | | | | | | | |            (557), (561), (563), (567), (571), (572), (575),
% 197.68/32.42  | | | | | | | | | | | | | | |            (577), (578), (580), (582), (588), (593), (595),
% 197.68/32.42  | | | | | | | | | | | | | | |            (602), (607), (612), (676), (680), (7443), (7445),
% 197.68/32.42  | | | | | | | | | | | | | | |            (7449), (7451), (10361), (10373), (10375),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10379), (10381), (10382), (10383), (10384),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10388), (10405), (10406), (10407), (10408),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10415), (10416), (function-axioms) are
% 197.68/32.42  | | | | | | | | | | | | | | |            inconsistent by sub-proof #135.
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | |   (10417)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.42  | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.42  | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.42  | | | | | | | | | | | | |            (51), (158), (162), (166), (167), (168), (169),
% 197.68/32.42  | | | | | | | | | | | | |            (172), (173), (174), (175), (178), (183), (271),
% 197.68/32.42  | | | | | | | | | | | | |            (272), (273), (278), (281), (282), (304), (306),
% 197.68/32.42  | | | | | | | | | | | | |            (307), (308), (309), (317), (320), (326), (330),
% 197.68/32.42  | | | | | | | | | | | | |            (332), (333), (343), (346), (351), (372), (387),
% 197.68/32.42  | | | | | | | | | | | | |            (388), (393), (405), (411), (427), (431), (529),
% 197.68/32.42  | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (549),
% 197.68/32.42  | | | | | | | | | | | | |            (551), (555), (557), (559), (561), (564), (566),
% 197.68/32.42  | | | | | | | | | | | | |            (570), (571), (572), (576), (582), (593), (600),
% 197.68/32.42  | | | | | | | | | | | | |            (604), (605), (610), (612), (641), (7449),
% 197.68/32.42  | | | | | | | | | | | | |            (10028), (10030), (10375), (10378), (10379),
% 197.68/32.42  | | | | | | | | | | | | |            (10381), (10382), (10383), (10384), (10385),
% 197.68/32.42  | | | | | | | | | | | | |            (10388), (10417), (function-axioms) are
% 197.68/32.42  | | | | | | | | | | | | |            inconsistent by sub-proof #27.
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | |   (10418)   ~ (all_58_15 = e0)
% 197.68/32.42  | | | | | | | | | | | |   (10419)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.42  | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.42  | | | | | | | | | | | |              e0)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | ALPHA: (10419) implies:
% 197.68/32.42  | | | | | | | | | | | |   (10420)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.42  | | | | | | | | | | | |   (10421)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REDUCE: (541), (10418) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10422)   ~ (all_14_2 = e0)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.42  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.42  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.42  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.42  | | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.42  | | | | | | | | | | | |            (276), (277), (278), (280), (281), (282), (283),
% 197.68/32.42  | | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (312),
% 197.68/32.42  | | | | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 197.68/32.42  | | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 197.68/32.42  | | | | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 197.68/32.42  | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.42  | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (421),
% 197.68/32.42  | | | | | | | | | | | |            (427), (431), (512), (529), (538), (539), (540),
% 197.68/32.42  | | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.68/32.42  | | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.68/32.42  | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 197.68/32.42  | | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 197.68/32.42  | | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 197.68/32.42  | | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.68/32.42  | | | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 197.68/32.42  | | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 197.68/32.42  | | | | | | | | | | | |            (613), (641), (676), (7443), (7445), (7449),
% 197.68/32.42  | | | | | | | | | | | |            (7451), (7453), (7458), (10028), (10030), (10373),
% 197.68/32.42  | | | | | | | | | | | |            (10375), (10378), (10420), (10421), (10422),
% 197.68/32.42  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.42  | | | | | | | | | | | |            #7.
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | |   (10423)  all_28_0 = e3
% 197.68/32.42  | | | | | | | | | |   (10424)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.42  | | | | | | | | | |            (51), (53), (61), (62), (63), (144), (158), (161),
% 197.68/32.42  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.68/32.42  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.68/32.42  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 197.68/32.42  | | | | | | | | | |            (273), (274), (277), (278), (280), (281), (282),
% 197.68/32.42  | | | | | | | | | |            (283), (284), (285), (303), (304), (306), (307),
% 197.68/32.42  | | | | | | | | | |            (308), (309), (311), (313), (315), (316), (318),
% 197.68/32.42  | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 197.68/32.42  | | | | | | | | | |            (327), (328), (330), (331), (332), (333), (343),
% 197.68/32.42  | | | | | | | | | |            (346), (351), (352), (366), (367), (372), (375),
% 197.68/32.42  | | | | | | | | | |            (376), (387), (388), (393), (394), (405), (411),
% 197.68/32.42  | | | | | | | | | |            (415), (427), (431), (529), (538), (539), (540),
% 197.68/32.42  | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.68/32.42  | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.68/32.42  | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (569),
% 197.68/32.42  | | | | | | | | | |            (570), (571), (572), (573), (574), (575), (576),
% 197.68/32.42  | | | | | | | | | |            (577), (578), (580), (582), (584), (586), (587),
% 197.68/32.42  | | | | | | | | | |            (590), (591), (592), (593), (594), (595), (596),
% 197.68/32.42  | | | | | | | | | |            (598), (600), (602), (603), (604), (605), (606),
% 197.68/32.42  | | | | | | | | | |            (607), (608), (609), (610), (613), (641), (754),
% 197.68/32.42  | | | | | | | | | |            (7444), (7445), (7449), (7450), (7451), (7453),
% 197.68/32.42  | | | | | | | | | |            (7455), (7458), (7459), (10028), (10029), (10030),
% 197.68/32.42  | | | | | | | | | |            (10032), (10368), (10370), (10423), (10424),
% 197.68/32.42  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.42  | | | | | | | | | |            #14.
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | |   (10425)  all_24_0 = e1
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | COMBINE_EQS: (711), (10425) imply:
% 197.68/32.42  | | | | | | | |   (10426)  all_14_0 = e1
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | SIMP: (10426) implies:
% 197.68/32.42  | | | | | | | |   (10427)  all_14_0 = e1
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | COMBINE_EQS: (765), (10427) imply:
% 197.68/32.42  | | | | | | | |   (10428)  all_34_0 = e1
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | REDUCE: (10368), (10427) imply:
% 197.68/32.42  | | | | | | | |   (10429)   ~ (e3 = e1)
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | REDUCE: (10032), (10427) imply:
% 197.68/32.42  | | | | | | | |   (10430)   ~ (e2 = e1)
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | REDUCE: (62), (10427) imply:
% 197.68/32.42  | | | | | | | |   (10431)  op(e0, all_14_1) = e1
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | BETA: splitting (94) gives:
% 197.68/32.42  | | | | | | | | 
% 197.68/32.42  | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | |   (10432)   ~ (all_26_0 = e2)
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | REDUCE: (10364), (10432) imply:
% 197.68/32.42  | | | | | | | | |   (10433)  $false
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | CLOSE: (10433) is inconsistent.
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | |   (10434)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | BETA: splitting (99) gives:
% 197.68/32.42  | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | |   (10435)   ~ (all_28_0 = e3)
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | REDUCE: (754), (10435) imply:
% 197.68/32.42  | | | | | | | | | |   (10436)   ~ (all_4_0 = e3)
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | BETA: splitting (114) gives:
% 197.68/32.42  | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | |   (10437)   ~ (all_34_0 = e1)
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | REDUCE: (10428), (10437) imply:
% 197.68/32.42  | | | | | | | | | | |   (10438)  $false
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | CLOSE: (10438) is inconsistent.
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | |   (10439)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.42  | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | |   (10440)   ~ (all_46_0 = e1)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | REDUCE: (10029), (10440) imply:
% 197.68/32.42  | | | | | | | | | | | |   (10441)  $false
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | CLOSE: (10441) is inconsistent.
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | |   (10442)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.42  | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | |   (10443)  all_58_15 = e0
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (10431), (10443),
% 197.68/32.42  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.42  | | | | | | | | | | | | |            #877.
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | |   (10444)   ~ (all_58_15 = e0)
% 197.68/32.42  | | | | | | | | | | | | |   (10445)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.42  | | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.42  | | | | | | | | | | | | |              e0)
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | ALPHA: (10445) implies:
% 197.68/32.42  | | | | | | | | | | | | |   (10446)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.42  | | | | | | | | | | | | |   (10447)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | REDUCE: (541), (10444) imply:
% 197.68/32.42  | | | | | | | | | | | | |   (10448)   ~ (all_14_2 = e0)
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.42  | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | |   (10449)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.42  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | BETA: splitting (10449) gives:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | |   (10450)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 197.68/32.42  | | | | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 197.68/32.42  | | | | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10030), (10450), (function-axioms) are
% 197.68/32.42  | | | | | | | | | | | | | | |            inconsistent by sub-proof #302.
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | |   (10451)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.42  | | | | | | | | | | | | | | |            (51), (61), (63), (158), (162), (166), (167),
% 197.68/32.42  | | | | | | | | | | | | | | |            (168), (169), (173), (174), (175), (178), (179),
% 197.68/32.42  | | | | | | | | | | | | | | |            (180), (182), (183), (185), (270), (273), (276),
% 197.68/32.42  | | | | | | | | | | | | | | |            (277), (278), (280), (283), (284), (306), (309),
% 197.68/32.42  | | | | | | | | | | | | | | |            (312), (313), (314), (316), (317), (320), (321),
% 197.68/32.42  | | | | | | | | | | | | | | |            (325), (326), (329), (330), (332), (333), (351),
% 197.68/32.42  | | | | | | | | | | | | | | |            (366), (367), (372), (387), (393), (394), (405),
% 197.68/32.42  | | | | | | | | | | | | | | |            (415), (421), (427), (431), (538), (539), (541),
% 197.68/32.42  | | | | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 197.68/32.42  | | | | | | | | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 197.68/32.42  | | | | | | | | | | | | | | |            (562), (563), (564), (567), (568), (569), (570),
% 197.68/32.42  | | | | | | | | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 197.68/32.42  | | | | | | | | | | | | | | |            (578), (580), (582), (586), (587), (590), (591),
% 197.68/32.42  | | | | | | | | | | | | | | |            (593), (594), (600), (603), (604), (606), (607),
% 197.68/32.42  | | | | | | | | | | | | | | |            (608), (609), (610), (611), (613), (7443), (7445),
% 197.68/32.42  | | | | | | | | | | | | | | |            (7449), (7451), (7453), (7458), (10028), (10030),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10436), (10446), (10447), (10451),
% 197.68/32.42  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.42  | | | | | | | | | | | | | | |            #32.
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | End of split
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | |   (10452)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.42  | | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.42  | | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | BETA: splitting (10452) gives:
% 197.68/32.42  | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | Case 1:
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | |   (10453)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | | |            all_52_22 = e0
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (51), (53), (158), (168), (169),
% 197.68/32.42  | | | | | | | | | | | | | | |            (175), (178), (183), (270), (271), (273), (283),
% 197.68/32.42  | | | | | | | | | | | | | | |            (317), (343), (393), (415), (431), (512), (538),
% 197.68/32.42  | | | | | | | | | | | | | | |            (542), (546), (555), (557), (559), (572), (573),
% 197.68/32.42  | | | | | | | | | | | | | | |            (593), (600), (603), (612), (676), (7445), (7449),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10028), (10030), (10434), (10436), (10448),
% 197.68/32.42  | | | | | | | | | | | | | | |            (10453), (function-axioms) are inconsistent by
% 197.68/32.42  | | | | | | | | | | | | | | |            sub-proof #8.
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | Case 2:
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.42  | | | | | | | | | | | | | | |   (10454)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.68/32.42  | | | | | | | | | | | | | | |            all_52_30 = e0
% 197.68/32.42  | | | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.43  | | | | | | | | | | | | | | |            (51), (53), (61), (63), (156), (158), (162),
% 197.68/32.43  | | | | | | | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.68/32.43  | | | | | | | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.68/32.43  | | | | | | | | | | | | | | |            (184), (185), (270), (271), (272), (273), (274),
% 197.68/32.43  | | | | | | | | | | | | | | |            (277), (280), (281), (282), (283), (284), (285),
% 197.68/32.43  | | | | | | | | | | | | | | |            (306), (307), (309), (311), (313), (315), (316),
% 197.68/32.43  | | | | | | | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 197.68/32.43  | | | | | | | | | | | | | | |            (327), (328), (330), (332), (333), (343), (346),
% 197.68/32.43  | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.43  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 197.68/32.43  | | | | | | | | | | | | | | |            (491), (529), (538), (539), (540), (541), (542),
% 197.68/32.43  | | | | | | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.68/32.43  | | | | | | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.68/32.43  | | | | | | | | | | | | | | |            (563), (564), (566), (567), (569), (570), (571),
% 197.68/32.43  | | | | | | | | | | | | | | |            (572), (573), (574), (575), (576), (578), (582),
% 197.68/32.43  | | | | | | | | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.43  | | | | | | | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.43  | | | | | | | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.43  | | | | | | | | | | | | | | |            (613), (641), (685), (10028), (10030), (10431),
% 197.68/32.43  | | | | | | | | | | | | | | |            (10439), (10442), (10446), (10448), (10454),
% 197.68/32.43  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.43  | | | | | | | | | | | | | | |            #246.
% 197.68/32.43  | | | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | |   (10455)  all_28_0 = e3
% 197.68/32.43  | | | | | | | | | |   (10456)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.43  | | | | | | | | | |            (51), (53), (61), (63), (144), (158), (161),
% 197.68/32.43  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 197.68/32.43  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 197.68/32.43  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 197.68/32.43  | | | | | | | | | |            (273), (274), (277), (278), (280), (281), (282),
% 197.68/32.43  | | | | | | | | | |            (283), (284), (285), (303), (306), (307), (309),
% 197.68/32.43  | | | | | | | | | |            (311), (313), (315), (316), (318), (319), (320),
% 197.68/32.43  | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 197.68/32.43  | | | | | | | | | |            (330), (331), (332), (333), (343), (346), (351),
% 197.68/32.43  | | | | | | | | | |            (352), (366), (367), (372), (375), (376), (387),
% 197.68/32.43  | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (427),
% 197.68/32.43  | | | | | | | | | |            (431), (529), (538), (539), (540), (541), (542),
% 197.68/32.43  | | | | | | | | | |            (543), (544), (545), (546), (547), (548), (549),
% 197.68/32.43  | | | | | | | | | |            (551), (553), (555), (557), (559), (561), (562),
% 197.68/32.43  | | | | | | | | | |            (563), (564), (566), (567), (569), (570), (571),
% 197.68/32.43  | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 197.68/32.43  | | | | | | | | | |            (580), (582), (584), (586), (587), (590), (591),
% 197.68/32.43  | | | | | | | | | |            (592), (593), (594), (595), (596), (598), (600),
% 197.68/32.43  | | | | | | | | | |            (602), (603), (604), (605), (606), (607), (608),
% 197.68/32.43  | | | | | | | | | |            (609), (610), (613), (641), (754), (7444), (7445),
% 197.68/32.43  | | | | | | | | | |            (7449), (7450), (7451), (7453), (7455), (7458),
% 197.68/32.43  | | | | | | | | | |            (7459), (10028), (10029), (10030), (10431),
% 197.68/32.43  | | | | | | | | | |            (10455), (10456), (function-axioms) are
% 197.68/32.43  | | | | | | | | | |            inconsistent by sub-proof #12.
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | End of split
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | Case 2:
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | |   (10457)  all_18_0 = e3
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | COMBINE_EQS: (761), (10457) imply:
% 197.68/32.43  | | | | | | |   (10458)  all_14_0 = e3
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | SIMP: (10458) implies:
% 197.68/32.43  | | | | | | |   (10459)  all_14_0 = e3
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | REDUCE: (62), (10459) imply:
% 197.68/32.43  | | | | | | |   (10460)  op(e0, all_14_1) = e3
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | BETA: splitting (94) gives:
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | |   (10461)   ~ (all_26_0 = e2)
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | REDUCE: (10364), (10461) imply:
% 197.68/32.43  | | | | | | | |   (10462)  $false
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | CLOSE: (10462) is inconsistent.
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | |   (10463)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | BETA: splitting (99) gives:
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | |   (10464)   ~ (all_28_0 = e3)
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | REDUCE: (754), (10464) imply:
% 197.68/32.43  | | | | | | | | |   (10465)   ~ (all_4_0 = e3)
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | |   (10466)   ~ (all_46_0 = e1)
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | REDUCE: (10029), (10466) imply:
% 197.68/32.43  | | | | | | | | | |   (10467)  $false
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | CLOSE: (10467) is inconsistent.
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | |   (10468)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | |   (10469)  all_58_15 = e0
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (10460), (10469),
% 197.68/32.43  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.43  | | | | | | | | | | |            #678.
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | |   (10470)   ~ (all_58_15 = e0)
% 197.68/32.43  | | | | | | | | | | |   (10471)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.43  | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.43  | | | | | | | | | | |              e0)
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | ALPHA: (10471) implies:
% 197.68/32.43  | | | | | | | | | | |   (10472)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.43  | | | | | | | | | | |   (10473)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | REDUCE: (541), (10470) imply:
% 197.68/32.43  | | | | | | | | | | |   (10474)   ~ (all_14_2 = e0)
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.43  | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.43  | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.43  | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.43  | | | | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.43  | | | | | | | | | | |            (276), (277), (278), (280), (281), (282), (283),
% 197.68/32.43  | | | | | | | | | | |            (284), (285), (306), (307), (309), (311), (312),
% 197.68/32.43  | | | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 197.68/32.43  | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 197.68/32.43  | | | | | | | | | | |            (329), (330), (331), (332), (333), (343), (346),
% 197.68/32.43  | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.43  | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (421),
% 197.68/32.43  | | | | | | | | | | |            (427), (431), (512), (529), (538), (539), (540),
% 197.68/32.43  | | | | | | | | | | |            (541), (542), (543), (544), (545), (546), (547),
% 197.68/32.43  | | | | | | | | | | |            (548), (549), (551), (553), (555), (557), (559),
% 197.68/32.43  | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 197.68/32.43  | | | | | | | | | | |            (569), (570), (571), (572), (573), (574), (575),
% 197.68/32.43  | | | | | | | | | | |            (576), (577), (578), (580), (582), (584), (586),
% 197.68/32.43  | | | | | | | | | | |            (587), (590), (591), (592), (593), (594), (595),
% 197.68/32.43  | | | | | | | | | | |            (596), (598), (600), (602), (603), (604), (605),
% 197.68/32.43  | | | | | | | | | | |            (606), (607), (608), (609), (610), (611), (612),
% 197.68/32.43  | | | | | | | | | | |            (613), (641), (676), (7443), (7445), (7449),
% 197.68/32.43  | | | | | | | | | | |            (7451), (7453), (7458), (10028), (10030), (10463),
% 197.68/32.43  | | | | | | | | | | |            (10465), (10468), (10472), (10473), (10474),
% 197.68/32.43  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.43  | | | | | | | | | | |            #7.
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | |   (10475)  all_28_0 = e3
% 197.68/32.43  | | | | | | | | |   (10476)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.43  | | | | | | | | |            (51), (53), (61), (63), (144), (158), (161), (162),
% 197.68/32.43  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 197.68/32.43  | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 197.68/32.43  | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 197.68/32.43  | | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 197.68/32.43  | | | | | | | | |            (284), (285), (303), (306), (307), (309), (311),
% 197.68/32.43  | | | | | | | | |            (313), (315), (316), (318), (319), (320), (321),
% 197.68/32.43  | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 197.68/32.43  | | | | | | | | |            (331), (332), (333), (343), (346), (351), (352),
% 197.68/32.43  | | | | | | | | |            (366), (367), (372), (375), (376), (387), (388),
% 197.68/32.43  | | | | | | | | |            (393), (394), (405), (411), (415), (427), (431),
% 197.68/32.43  | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.43  | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.43  | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.43  | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.43  | | | | | | | | |            (573), (574), (575), (576), (577), (578), (580),
% 197.68/32.43  | | | | | | | | |            (582), (584), (586), (587), (590), (591), (592),
% 197.68/32.43  | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 197.68/32.43  | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 197.68/32.43  | | | | | | | | |            (610), (613), (641), (754), (7444), (7445), (7449),
% 197.68/32.43  | | | | | | | | |            (7450), (7451), (7453), (7455), (7458), (7459),
% 197.68/32.43  | | | | | | | | |            (10028), (10029), (10030), (10460), (10475),
% 197.68/32.43  | | | | | | | | |            (10476), (function-axioms) are inconsistent by
% 197.68/32.43  | | | | | | | | |            sub-proof #10.
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | End of split
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | End of split
% 197.68/32.43  | | | | | | 
% 197.68/32.43  | | | | | End of split
% 197.68/32.43  | | | | | 
% 197.68/32.43  | | | | Case 2:
% 197.68/32.43  | | | | | 
% 197.68/32.43  | | | | |   (10477)  all_14_0 = e2
% 197.68/32.43  | | | | |   (10478)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 197.68/32.43  | | | | | 
% 197.68/32.43  | | | | | COMBINE_EQS: (771), (10477) imply:
% 197.68/32.43  | | | | |   (10479)  all_50_0 = e2
% 197.68/32.43  | | | | | 
% 197.68/32.43  | | | | | REDUCE: (62), (10477) imply:
% 197.68/32.43  | | | | |   (10480)  op(e0, all_14_1) = e2
% 197.68/32.43  | | | | | 
% 197.68/32.43  | | | | | BETA: splitting (69) gives:
% 197.68/32.43  | | | | | 
% 197.68/32.43  | | | | | Case 1:
% 197.68/32.43  | | | | | | 
% 197.68/32.43  | | | | | |   (10481)   ~ (all_16_0 = e2)
% 197.68/32.43  | | | | | | 
% 197.68/32.43  | | | | | | REDUCE: (760), (10481) imply:
% 197.68/32.43  | | | | | |   (10482)   ~ (all_10_0 = e2)
% 197.68/32.43  | | | | | | 
% 197.68/32.43  | | | | | | BETA: splitting (99) gives:
% 197.68/32.43  | | | | | | 
% 197.68/32.43  | | | | | | Case 1:
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | |   (10483)   ~ (all_28_0 = e3)
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | REDUCE: (754), (10483) imply:
% 197.68/32.43  | | | | | | |   (10484)   ~ (all_4_0 = e3)
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | BETA: splitting (104) gives:
% 197.68/32.43  | | | | | | | 
% 197.68/32.43  | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | |   (10485)   ~ (all_30_1 = e3)
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | REDUCE: (670), (10485) imply:
% 197.68/32.43  | | | | | | | |   (10486)   ~ (all_10_1 = e3)
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | BETA: splitting (129) gives:
% 197.68/32.43  | | | | | | | | 
% 197.68/32.43  | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | |   (10487)   ~ (all_40_1 = e2)
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | REDUCE: (687), (10487) imply:
% 197.68/32.43  | | | | | | | | |   (10488)   ~ (all_10_1 = e2)
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.43  | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | |   (10489)   ~ (all_46_0 = e1)
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | REDUCE: (10029), (10489) imply:
% 197.68/32.43  | | | | | | | | | |   (10490)  $false
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | CLOSE: (10490) is inconsistent.
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | |   (10491)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.43  | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | |   (10492)  all_58_15 = e0
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (10480), (10492),
% 197.68/32.43  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.43  | | | | | | | | | | |            #612.
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | |   (10493)   ~ (all_58_15 = e0)
% 197.68/32.43  | | | | | | | | | | |   (10494)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.43  | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.43  | | | | | | | | | | |              e0)
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | ALPHA: (10494) implies:
% 197.68/32.43  | | | | | | | | | | |   (10495)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.43  | | | | | | | | | | |   (10496)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | REDUCE: (541), (10493) imply:
% 197.68/32.43  | | | | | | | | | | |   (10497)   ~ (all_14_2 = e0)
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.43  | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | |   (10498)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.43  | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.43  | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | BETA: splitting (10498) gives:
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | |   (10499)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.43  | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 197.68/32.43  | | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 197.68/32.43  | | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 197.68/32.43  | | | | | | | | | | | | |            (10030), (10499), (function-axioms) are
% 197.68/32.43  | | | | | | | | | | | | |            inconsistent by sub-proof #302.
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | |   (10500)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.43  | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.43  | | | | | | | | | | | | |            (51), (61), (63), (157), (158), (162), (166),
% 197.68/32.43  | | | | | | | | | | | | |            (167), (168), (169), (173), (174), (175), (178),
% 197.68/32.43  | | | | | | | | | | | | |            (179), (180), (182), (183), (185), (270), (273),
% 197.68/32.43  | | | | | | | | | | | | |            (276), (277), (278), (280), (282), (283), (284),
% 197.68/32.43  | | | | | | | | | | | | |            (306), (309), (313), (314), (316), (317), (320),
% 197.68/32.43  | | | | | | | | | | | | |            (321), (324), (325), (326), (329), (330), (332),
% 197.68/32.43  | | | | | | | | | | | | |            (333), (351), (366), (367), (372), (387), (388),
% 197.68/32.43  | | | | | | | | | | | | |            (393), (394), (405), (415), (421), (427), (431),
% 197.68/32.43  | | | | | | | | | | | | |            (538), (539), (541), (542), (543), (544), (545),
% 197.68/32.43  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.68/32.43  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (567),
% 197.68/32.43  | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.68/32.43  | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (586),
% 197.68/32.43  | | | | | | | | | | | | |            (587), (590), (591), (593), (594), (600), (603),
% 197.68/32.43  | | | | | | | | | | | | |            (604), (606), (607), (608), (610), (611), (613),
% 197.68/32.43  | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7458),
% 197.68/32.43  | | | | | | | | | | | | |            (10028), (10030), (10480), (10484), (10495),
% 197.68/32.43  | | | | | | | | | | | | |            (10496), (10500), (function-axioms) are
% 197.68/32.43  | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | End of split
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | |   (10501)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.43  | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.43  | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | BETA: splitting (10501) gives:
% 197.68/32.43  | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | Case 1:
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | |   (10502)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.68/32.43  | | | | | | | | | | | | |            all_52_22 = e0
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | | REF_CLOSE: (41), (43), (51), (53), (61), (63), (158), (162),
% 197.68/32.43  | | | | | | | | | | | | |            (167), (168), (169), (175), (178), (183), (270),
% 197.68/32.43  | | | | | | | | | | | | |            (273), (275), (277), (283), (312), (317), (361),
% 197.68/32.43  | | | | | | | | | | | | |            (367), (393), (415), (431), (538), (542), (546),
% 197.68/32.43  | | | | | | | | | | | | |            (547), (553), (555), (557), (559), (561), (569),
% 197.68/32.43  | | | | | | | | | | | | |            (572), (593), (600), (603), (612), (613), (7449),
% 197.68/32.43  | | | | | | | | | | | | |            (10028), (10030), (10484), (10488), (10502),
% 197.68/32.43  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.43  | | | | | | | | | | | | |            #35.
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | Case 2:
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.43  | | | | | | | | | | | | |   (10503)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.68/32.43  | | | | | | | | | | | | |            all_52_30 = e0
% 197.68/32.43  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.44  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.44  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.44  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.44  | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 197.68/32.44  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 197.68/32.44  | | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 197.68/32.44  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.44  | | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 197.68/32.44  | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.44  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 197.68/32.44  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.44  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.44  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.44  | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.44  | | | | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 197.68/32.44  | | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.68/32.44  | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.44  | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 197.68/32.44  | | | | | | | | | | | | |            (641), (10028), (10030), (10491), (10495),
% 197.68/32.44  | | | | | | | | | | | | |            (10497), (10503), (function-axioms) are
% 197.68/32.44  | | | | | | | | | | | | |            inconsistent by sub-proof #271.
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | |   (10504)  all_40_1 = e2
% 197.68/32.44  | | | | | | | | |   (10505)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | COMBINE_EQS: (687), (10504) imply:
% 197.68/32.44  | | | | | | | | |   (10506)  all_10_1 = e2
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | SIMP: (10506) implies:
% 197.68/32.44  | | | | | | | | |   (10507)  all_10_1 = e2
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (10486), (10507) imply:
% 197.68/32.44  | | | | | | | | |   (10508)   ~ (e3 = e2)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (53), (10507) imply:
% 197.68/32.44  | | | | | | | | |   (10509)  op(all_10_2, e1) = e2
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (52), (10507) imply:
% 197.68/32.44  | | | | | | | | |   (10510)  op(e1, e2) = all_10_0
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 197.68/32.44  | | | | | | | | |              all_10_0, e2, e1, simplifying with (161), (10510)
% 197.68/32.44  | | | | | | | | |              gives:
% 197.68/32.44  | | | | | | | | |   (10511)  all_52_13 = all_10_0
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | COMBINE_EQS: (421), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10512)  all_56_9 = all_10_0
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | COMBINE_EQS: (366), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10513)  all_58_7 = all_10_0
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (568), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10514)   ~ (all_52_5 = all_10_0)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (575), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10515)   ~ (all_52_9 = all_10_0)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (589), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10516)   ~ (all_52_29 = all_10_0)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | SIMP: (10516) implies:
% 197.68/32.44  | | | | | | | | |   (10517)   ~ (all_52_29 = all_10_0)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (588), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10518)   ~ (all_10_0 = all_10_2)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (580), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10519)   ~ (all_10_0 = all_4_2)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (180), (10511) imply:
% 197.68/32.44  | | | | | | | | |   (10520)  op(all_10_0, all_10_0) = all_52_12
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | |   (10521)   ~ (all_46_0 = e1)
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | REDUCE: (10029), (10521) imply:
% 197.68/32.44  | | | | | | | | | |   (10522)  $false
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | CLOSE: (10522) is inconsistent.
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | |   (10523)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | BETA: splitting (153) gives:
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | |   (10524)   ~ (all_50_0 = e2)
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | REDUCE: (10479), (10524) imply:
% 197.68/32.44  | | | | | | | | | | |   (10525)  $false
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | CLOSE: (10525) is inconsistent.
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | |   (10526)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | |   (10527)  all_58_15 = e0
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (10480), (10527),
% 197.68/32.44  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.44  | | | | | | | | | | | |            #612.
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | |   (10528)   ~ (all_58_15 = e0)
% 197.68/32.44  | | | | | | | | | | | |   (10529)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.44  | | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.44  | | | | | | | | | | | |              e0)
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | ALPHA: (10529) implies:
% 197.68/32.44  | | | | | | | | | | | |   (10530)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.44  | | | | | | | | | | | |   (10531)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | REDUCE: (541), (10528) imply:
% 197.68/32.44  | | | | | | | | | | | |   (10532)   ~ (all_14_2 = e0)
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | BETA: splitting (276) gives:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | |   (10533)  all_56_9 = e3
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | REF_CLOSE: (10031), (10512), (10533) are inconsistent by
% 197.68/32.44  | | | | | | | | | | | | |            sub-proof #1006.
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | |   (10534)   ~ (all_56_9 = e3)
% 197.68/32.44  | | | | | | | | | | | | |   (10535)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | |   (10536)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.44  | | | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.44  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | BETA: splitting (10536) gives:
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | |   (10537)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.44  | | | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | ALPHA: (10537) implies:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10538)  all_52_6 = e0
% 197.68/32.44  | | | | | | | | | | | | | | |   (10539)  all_52_4 = e1
% 197.68/32.44  | | | | | | | | | | | | | | |   (10540)  all_52_2 = e2
% 197.68/32.44  | | | | | | | | | | | | | | |   (10541)  all_52_0 = e3
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (185), (10540) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10542)  op(all_52_3, all_52_3) = e2
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (184), (10539) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10543)  op(all_52_5, all_52_5) = e1
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (183), (10538) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10544)  op(all_52_7, all_52_7) = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (610), (10541) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10545)  op(all_6_2, all_6_2) = e3
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (41), (51), (61), (63), (167),
% 197.68/32.44  | | | | | | | | | | | | | | |            (168), (169), (173), (174), (178), (270), (273),
% 197.68/32.44  | | | | | | | | | | | | | | |            (277), (278), (282), (284), (306), (307), (312),
% 197.68/32.44  | | | | | | | | | | | | | | |            (313), (321), (324), (332), (335), (351), (367),
% 197.68/32.44  | | | | | | | | | | | | | | |            (372), (387), (388), (394), (405), (427), (431),
% 197.68/32.44  | | | | | | | | | | | | | | |            (526), (538), (541), (543), (544), (545), (546),
% 197.68/32.44  | | | | | | | | | | | | | | |            (547), (548), (549), (553), (555), (557), (564),
% 197.68/32.44  | | | | | | | | | | | | | | |            (569), (570), (571), (573), (577), (578), (591),
% 197.68/32.44  | | | | | | | | | | | | | | |            (593), (595), (604), (606), (607), (609), (611),
% 197.68/32.44  | | | | | | | | | | | | | | |            (612), (613), (690), (767), (7445), (7449),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10031), (10480), (10482), (10484), (10505),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10509), (10512), (10513), (10514), (10515),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10517), (10518), (10519), (10526), (10531),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10532), (10535), (10542), (10543), (10544),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10545), (function-axioms) are inconsistent by
% 197.68/32.44  | | | | | | | | | | | | | | |            sub-proof #122.
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | |   (10546)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.44  | | | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | ALPHA: (10546) implies:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10547)  all_52_14 = e0
% 197.68/32.44  | | | | | | | | | | | | | | |   (10548)  all_52_12 = e1
% 197.68/32.44  | | | | | | | | | | | | | | |   (10549)  all_52_10 = e2
% 197.68/32.44  | | | | | | | | | | | | | | |   (10550)  all_52_8 = e3
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (182), (10550) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10551)  op(all_52_9, all_52_9) = e3
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (179), (10547) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10552)  op(all_52_15, all_52_15) = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (10520), (10548) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10553)  op(all_10_0, all_10_0) = e1
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (611), (10549) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10554)  op(all_4_2, all_4_2) = e2
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (41), (43), (51), (158), (168),
% 197.68/32.44  | | | | | | | | | | | | | | |            (169), (175), (183), (270), (271), (273), (284),
% 197.68/32.44  | | | | | | | | | | | | | | |            (306), (317), (324), (325), (343), (351), (393),
% 197.68/32.44  | | | | | | | | | | | | | | |            (394), (431), (526), (538), (541), (542), (543),
% 197.68/32.44  | | | | | | | | | | | | | | |            (546), (548), (549), (555), (557), (571), (572),
% 197.68/32.44  | | | | | | | | | | | | | | |            (573), (576), (577), (582), (590), (591), (603),
% 197.68/32.44  | | | | | | | | | | | | | | |            (613), (767), (7445), (7449), (10028), (10030),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10031), (10482), (10484), (10505), (10512),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10513), (10518), (10530), (10532), (10535),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10551), (10552), (10553), (10554),
% 197.68/32.44  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.44  | | | | | | | | | | | | | | |            #26.
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | |   (10555)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.44  | | | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.44  | | | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | BETA: splitting (10555) gives:
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | |   (10556)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.68/32.44  | | | | | | | | | | | | | | |            all_52_22 = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | ALPHA: (10556) implies:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10557)  all_52_22 = e0
% 197.68/32.44  | | | | | | | | | | | | | | |   (10558)  all_52_20 = e1
% 197.68/32.44  | | | | | | | | | | | | | | |   (10559)  all_52_16 = e3
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (178), (10559) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10560)  op(all_52_17, all_52_17) = e3
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (175), (10557) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10561)  op(all_52_23, all_52_23) = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REDUCE: (612), (10558) imply:
% 197.68/32.44  | | | | | | | | | | | | | | |   (10562)  op(all_10_2, all_10_2) = e1
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (41), (43), (51), (158), (162),
% 197.68/32.44  | | | | | | | | | | | | | | |            (167), (168), (169), (183), (270), (273), (306),
% 197.68/32.44  | | | | | | | | | | | | | | |            (317), (320), (321), (326), (330), (351), (372),
% 197.68/32.44  | | | | | | | | | | | | | | |            (387), (393), (405), (431), (526), (538), (541),
% 197.68/32.44  | | | | | | | | | | | | | | |            (542), (543), (546), (547), (548), (555), (557),
% 197.68/32.44  | | | | | | | | | | | | | | |            (559), (561), (564), (572), (573), (582), (590),
% 197.68/32.44  | | | | | | | | | | | | | | |            (593), (600), (603), (608), (611), (767), (7443),
% 197.68/32.44  | | | | | | | | | | | | | | |            (7445), (7449), (7450), (7458), (10028), (10030),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10482), (10484), (10505), (10509), (10512),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10532), (10535), (10560), (10561), (10562),
% 197.68/32.44  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.44  | | | | | | | | | | | | | | |            #24.
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | |   (10563)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.68/32.44  | | | | | | | | | | | | | | |            all_52_30 = e0
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.44  | | | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.44  | | | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.44  | | | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.44  | | | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 197.68/32.44  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 197.68/32.44  | | | | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 197.68/32.44  | | | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.44  | | | | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 197.68/32.44  | | | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.44  | | | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 197.68/32.44  | | | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.44  | | | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.44  | | | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.44  | | | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.44  | | | | | | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 197.68/32.44  | | | | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.68/32.44  | | | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.44  | | | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 197.68/32.44  | | | | | | | | | | | | | | |            (641), (10028), (10030), (10523), (10530),
% 197.68/32.44  | | | | | | | | | | | | | | |            (10532), (10563), (function-axioms) are
% 197.68/32.44  | | | | | | | | | | | | | | |            inconsistent by sub-proof #271.
% 197.68/32.44  | | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | |   (10564)  all_30_1 = e3
% 197.68/32.44  | | | | | | | |   (10565)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | COMBINE_EQS: (670), (10564) imply:
% 197.68/32.44  | | | | | | | |   (10566)  all_10_1 = e3
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | SIMP: (10566) implies:
% 197.68/32.44  | | | | | | | |   (10567)  all_10_1 = e3
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | REDUCE: (53), (10567) imply:
% 197.68/32.44  | | | | | | | |   (10568)  op(all_10_2, e1) = e3
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | REDUCE: (52), (10567) imply:
% 197.68/32.44  | | | | | | | |   (10569)  op(e1, e3) = all_10_0
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 197.68/32.44  | | | | | | | |              all_10_0, e3, e1, simplifying with (162), (10569)
% 197.68/32.44  | | | | | | | |              gives:
% 197.68/32.44  | | | | | | | |   (10570)  all_52_5 = all_10_0
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | COMBINE_EQS: (367), (10570) imply:
% 197.68/32.44  | | | | | | | |   (10571)  all_56_8 = all_10_0
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | COMBINE_EQS: (547), (10570) imply:
% 197.68/32.44  | | | | | | | |   (10572)  all_58_6 = all_10_0
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | REDUCE: (567), (10570) imply:
% 197.68/32.44  | | | | | | | |   (10573)   ~ (all_52_7 = all_10_0)
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | SIMP: (10573) implies:
% 197.68/32.44  | | | | | | | |   (10574)   ~ (all_52_7 = all_10_0)
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | REDUCE: (569), (10570) imply:
% 197.68/32.44  | | | | | | | |   (10575)   ~ (all_10_0 = all_10_2)
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | REDUCE: (184), (10570) imply:
% 197.68/32.44  | | | | | | | |   (10576)  op(all_10_0, all_10_0) = all_52_4
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.44  | | | | | | | | 
% 197.68/32.44  | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | |   (10577)   ~ (all_46_0 = e1)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | REDUCE: (10029), (10577) imply:
% 197.68/32.44  | | | | | | | | |   (10578)  $false
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | CLOSE: (10578) is inconsistent.
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | |   (10579)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.44  | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | |   (10580)  all_58_15 = e0
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (10480), (10580),
% 197.68/32.44  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.44  | | | | | | | | | |            #612.
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | |   (10581)   ~ (all_58_15 = e0)
% 197.68/32.44  | | | | | | | | | |   (10582)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.44  | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.44  | | | | | | | | | |              e0)
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | ALPHA: (10582) implies:
% 197.68/32.44  | | | | | | | | | |   (10583)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.44  | | | | | | | | | |   (10584)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | REDUCE: (541), (10581) imply:
% 197.68/32.44  | | | | | | | | | |   (10585)   ~ (all_14_2 = e0)
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | BETA: splitting (277) gives:
% 197.68/32.44  | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | |   (10586)  all_56_8 = e3
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | REF_CLOSE: (10031), (10571), (10586) are inconsistent by
% 197.68/32.44  | | | | | | | | | | |            sub-proof #926.
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | |   (10587)   ~ (all_56_8 = e3)
% 197.68/32.44  | | | | | | | | | | |   (10588)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.44  | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | |   (10589)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.44  | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.44  | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | BETA: splitting (10589) gives:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | |   (10590)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.44  | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | REF_CLOSE: (51), (168), (275), (311), (361), (459), (593),
% 197.68/32.44  | | | | | | | | | | | | |            (750), (10482), (10565), (10568), (10571),
% 197.68/32.44  | | | | | | | | | | | | |            (10572), (10575), (10576), (10588), (10590),
% 197.68/32.44  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.44  | | | | | | | | | | | | |            #667.
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | |   (10591)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.44  | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.44  | | | | | | | | | | | | |            (51), (61), (63), (157), (158), (162), (166),
% 197.68/32.44  | | | | | | | | | | | | |            (167), (168), (169), (173), (174), (175), (178),
% 197.68/32.44  | | | | | | | | | | | | |            (179), (180), (182), (183), (185), (270), (273),
% 197.68/32.44  | | | | | | | | | | | | |            (276), (277), (278), (280), (282), (283), (284),
% 197.68/32.44  | | | | | | | | | | | | |            (306), (309), (313), (314), (316), (317), (320),
% 197.68/32.44  | | | | | | | | | | | | |            (321), (324), (325), (326), (329), (330), (332),
% 197.68/32.44  | | | | | | | | | | | | |            (333), (351), (366), (367), (372), (387), (388),
% 197.68/32.44  | | | | | | | | | | | | |            (393), (394), (405), (415), (421), (427), (431),
% 197.68/32.44  | | | | | | | | | | | | |            (538), (539), (541), (542), (543), (544), (545),
% 197.68/32.44  | | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.68/32.44  | | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (567),
% 197.68/32.44  | | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.68/32.44  | | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (586),
% 197.68/32.44  | | | | | | | | | | | | |            (587), (590), (591), (593), (594), (600), (603),
% 197.68/32.44  | | | | | | | | | | | | |            (604), (606), (607), (608), (610), (611), (613),
% 197.68/32.44  | | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7458),
% 197.68/32.44  | | | | | | | | | | | | |            (10028), (10030), (10480), (10484), (10583),
% 197.68/32.44  | | | | | | | | | | | | |            (10584), (10591), (function-axioms) are
% 197.68/32.44  | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | End of split
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | Case 2:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | |   (10592)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.44  | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.44  | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | BETA: splitting (10592) gives:
% 197.68/32.44  | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | |   (10593)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.68/32.44  | | | | | | | | | | | | |            all_52_22 = e0
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | ALPHA: (10593) implies:
% 197.68/32.44  | | | | | | | | | | | | |   (10594)  all_52_22 = e0
% 197.68/32.44  | | | | | | | | | | | | |   (10595)  all_52_16 = e3
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | REDUCE: (178), (10595) imply:
% 197.68/32.44  | | | | | | | | | | | | |   (10596)  op(all_52_17, all_52_17) = e3
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | REDUCE: (175), (10594) imply:
% 197.68/32.44  | | | | | | | | | | | | |   (10597)  op(all_52_23, all_52_23) = e0
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | BETA: splitting (270) gives:
% 197.68/32.44  | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | Case 1:
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.44  | | | | | | | | | | | | | |   (10598)  all_56_15 = e3
% 197.68/32.44  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | REF_CLOSE: (41), (168), (185), (317), (325), (332), (333),
% 197.68/32.45  | | | | | | | | | | | | | |            (351), (375), (387), (393), (405), (538), (542),
% 197.68/32.45  | | | | | | | | | | | | | |            (545), (546), (549), (551), (559), (565), (573),
% 197.68/32.45  | | | | | | | | | | | | | |            (577), (593), (603), (606), (7449), (10031),
% 197.68/32.45  | | | | | | | | | | | | | |            (10484), (10568), (10572), (10596), (10598),
% 197.68/32.45  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.45  | | | | | | | | | | | | | |            #118.
% 197.68/32.45  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | |   (10599)   ~ (all_56_15 = e3)
% 197.68/32.45  | | | | | | | | | | | | | |   (10600)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 197.68/32.45  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | REDUCE: (538), (10599) imply:
% 197.68/32.45  | | | | | | | | | | | | | |   (10601)   ~ (all_14_2 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 197.68/32.45  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | |   (10602)  all_56_5 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | COMBINE_EQS: (539), (10602) imply:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10603)  all_4_2 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | SIMP: (10603) implies:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10604)  all_4_2 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | REDUCE: (564), (10604) imply:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10605)   ~ (all_52_3 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | REDUCE: (611), (10604) imply:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10606)  op(e3, e3) = all_52_10
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | REDUCE: (7445), (10604) imply:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10607)  op(e3, e2) = e1
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 197.68/32.45  | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (10607) gives:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10608)  all_52_9 = e1
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.45  | | | | | | | | | | | | | | |              all_52_10, e3, e3, simplifying with (41), (10606)
% 197.68/32.45  | | | | | | | | | | | | | | |              gives:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10609)  all_52_10 = all_6_2
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | REDUCE: (557), (10608) imply:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10610)   ~ (all_6_2 = e1)
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | SIMP: (10610) implies:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10611)   ~ (all_6_2 = e1)
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10612)  all_58_0 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (10612) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10613)  all_6_2 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (41), (43), (10030), (10613),
% 197.68/32.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.45  | | | | | | | | | | | | | | | |            #310.
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10614)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REF_CLOSE: (41), (168), (183), (283), (317), (351), (387),
% 197.68/32.45  | | | | | | | | | | | | | | | |            (393), (415), (542), (546), (555), (572), (593),
% 197.68/32.45  | | | | | | | | | | | | | | | |            (7449), (10031), (10484), (10568), (10572),
% 197.68/32.45  | | | | | | | | | | | | | | | |            (10596), (10605), (10614), (function-axioms) are
% 197.68/32.45  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #162.
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | |   (10615)   ~ (all_56_5 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | REDUCE: (539), (10615) imply:
% 197.68/32.45  | | | | | | | | | | | | | | |   (10616)   ~ (all_4_2 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10617)  all_58_2 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (10617) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10618)  all_52_3 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | SIMP: (10618) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10619)  all_52_3 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REDUCE: (563), (10619) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10620)   ~ (all_52_7 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | SIMP: (10620) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10621)   ~ (all_52_7 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REDUCE: (566), (10619) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10622)   ~ (all_52_27 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | SIMP: (10622) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10623)   ~ (all_52_27 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REDUCE: (7450), (10619) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10624)   ~ (all_4_0 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REDUCE: (185), (10619) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10625)  op(e3, e3) = all_52_2
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | REDUCE: (166), (10619) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10626)  op(e2, e3) = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.45  | | | | | | | | | | | | | | | |              all_52_2, e3, e3, simplifying with (41), (10625)
% 197.68/32.45  | | | | | | | | | | | | | | | |              gives:
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10627)  all_52_2 = all_6_2
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10628)  all_58_0 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (10628) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10629)  all_6_2 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | REDUCE: (43), (10629) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10630)  op(e2, e3) = all_6_1
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | REDUCE: (41), (10629) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10631)  op(e3, e3) = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 197.68/32.45  | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (10626), (10630) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10632)  all_6_1 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | REDUCE: (10030), (10632) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10633)  op(e3, e3) = e1
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e1, e3,
% 197.68/32.45  | | | | | | | | | | | | | | | | |              e3, simplifying with (10631), (10633) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10634)  e2 = e1
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | REDUCE: (6), (10634) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10635)  $false
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | CLOSE: (10635) is inconsistent.
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10636)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | BETA: splitting (10636) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10637)  all_58_2 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10617), (10637) are inconsistent by
% 197.68/32.45  | | | | | | | | | | | | | | | | | |            sub-proof #1124.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10638)  all_58_6 = e2 | all_58_12 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | BETA: splitting (10638) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10639)  all_58_6 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10482), (10572), (10639) are inconsistent by
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            sub-proof #917.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10640)  all_58_12 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (10640) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10641)  all_52_7 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | SIMP: (10641) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10642)  all_52_7 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | REDUCE: (573), (10642) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10643)   ~ (all_14_2 = e2)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | SIMP: (10643) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10644)   ~ (all_14_2 = e2)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (10600) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | |   (10645)  all_56_15 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (10645) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | |   (10646)  all_14_2 = e2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | REDUCE: (10644), (10646) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | |   (10647)  $false
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | CLOSE: (10647) is inconsistent.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | |   (10648)  all_56_15 = e1 | all_56_15 = e0
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10648) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10649)  all_56_15 = e1
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (10649) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10650)  all_14_2 = e1
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (10650) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10651)  all_58_15 = e1
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10601), (10650) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10652)   ~ (e3 = e1)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (10650) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10653)  op(e1, e1) = all_52_30
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (10650) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10654)  op(e1, e0) = all_14_1
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10478) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |   (10655)   ~ (all_14_1 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |              all_14_1, e0, e1, simplifying with (159), (10654)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |   (10656)  all_52_29 = all_14_1
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |              all_52_30, e1, e1, simplifying with (51), (10653)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |   (10657)  all_52_30 = all_10_2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (10656) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |   (10658)  all_58_11 = all_14_1
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10659)  all_58_9 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (10659) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10660)  all_52_25 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (10660) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10661)   ~ (all_6_2 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10661) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10662)   ~ (all_6_2 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (10660) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10663)  op(e3, e3) = all_52_24
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (10663)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10664)  all_52_24 = all_6_2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |   (10665)  all_56_14 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (10665) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |   (10666)  all_52_23 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10666) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |   (10667)  all_52_23 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (51), (158), (168), (183), (273),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            (431), (538), (555), (573), (600), (10028),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            (10030), (10585), (10596), (10597), (10600),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            (10621), (10667), (function-axioms) are
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #9.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |   (10668)   ~ (all_56_14 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (10668) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |   (10669)   ~ (all_52_23 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (168), (283), (317), (393), (415), (542),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            (546), (593), (7449), (10484), (10568), (10596),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            (10662), (10669), (function-axioms) are
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #163.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |   (10670)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (372), (10623), (10651), (10655), (10658),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | |            (10670) are inconsistent by sub-proof #121.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |   (10671)   ~ (all_14_2 = e1)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (10585), (10648), (10671) are inconsistent
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1161.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10672)  all_56_15 = e0
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (10672) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10673)  all_14_2 = e0
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10585), (10673) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | |   (10674)  $false
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | CLOSE: (10674) is inconsistent.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | |   (10675)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | BETA: splitting (10675) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10676)  all_58_3 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (10676) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10677)  all_4_2 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | REDUCE: (10616), (10677) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10678)  $false
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | CLOSE: (10678) is inconsistent.
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | |   (10679)  all_58_5 = e3 | all_58_10 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | BETA: splitting (10679) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10680)  all_58_5 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (10484), (10680) are inconsistent by
% 197.68/32.45  | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10681)  all_58_10 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (10681) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10682)  all_52_27 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | SIMP: (10682) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10683)  all_52_27 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | REDUCE: (566), (10683) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10684)   ~ (all_52_3 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | REDUCE: (604), (10683) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10685)   ~ (all_52_25 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | REDUCE: (607), (10683) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10686)   ~ (all_52_29 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | SIMP: (10686) implies:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10687)   ~ (all_52_29 = e3)
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | REDUCE: (173), (10683) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10688)  op(e3, e3) = all_52_26
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.45  | | | | | | | | | | | | | | | | | |              all_52_26, e3, e3, simplifying with (41), (10688)
% 197.68/32.45  | | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | |   (10689)  all_52_26 = all_6_2
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10690)  all_58_0 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (10690) imply:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10691)  all_6_2 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (41), (43), (10030), (10691),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            #310.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |   (10692)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (168), (183), (313), (325), (333), (351),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            (366), (387), (393), (405), (544), (545), (546),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            (549), (555), (559), (575), (593), (10031),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            (10568), (10572), (10574), (10596), (10684),
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            (10685), (10687), (10692), (function-axioms) are
% 197.68/32.45  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #71.
% 197.68/32.45  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | |   (10693)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.68/32.45  | | | | | | | | | | | | |            all_52_30 = e0
% 197.68/32.45  | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.45  | | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.45  | | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.45  | | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.45  | | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 197.68/32.45  | | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 197.68/32.45  | | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 197.68/32.45  | | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.45  | | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 197.68/32.45  | | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.45  | | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 197.68/32.45  | | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.45  | | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.45  | | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.45  | | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.45  | | | | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 197.68/32.45  | | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.68/32.45  | | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.45  | | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 197.68/32.45  | | | | | | | | | | | | |            (641), (10028), (10030), (10579), (10583),
% 197.68/32.45  | | | | | | | | | | | | |            (10585), (10693), (function-axioms) are
% 197.68/32.45  | | | | | | | | | | | | |            inconsistent by sub-proof #271.
% 197.68/32.45  | | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.45  | | | | | | | | End of split
% 197.68/32.45  | | | | | | | | 
% 197.68/32.45  | | | | | | | End of split
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | Case 2:
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | |   (10694)  all_28_0 = e3
% 197.68/32.45  | | | | | | |   (10695)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | COMBINE_EQS: (754), (10694) imply:
% 197.68/32.45  | | | | | | |   (10696)  all_4_0 = e3
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | SIMP: (10696) implies:
% 197.68/32.45  | | | | | | |   (10697)  all_4_0 = e3
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 197.68/32.45  | | | | | | |            (53), (61), (63), (144), (158), (161), (162), (166),
% 197.68/32.45  | | | | | | |            (167), (168), (169), (172), (173), (174), (175), (177),
% 197.68/32.45  | | | | | | |            (178), (179), (180), (182), (183), (184), (185), (187),
% 197.68/32.45  | | | | | | |            (270), (271), (272), (273), (274), (277), (278), (280),
% 197.68/32.45  | | | | | | |            (281), (282), (283), (284), (285), (303), (306), (307),
% 197.68/32.45  | | | | | | |            (309), (311), (313), (315), (316), (318), (319), (320),
% 197.68/32.45  | | | | | | |            (321), (323), (324), (325), (326), (327), (328), (330),
% 197.68/32.45  | | | | | | |            (331), (332), (333), (343), (346), (351), (352), (366),
% 197.68/32.45  | | | | | | |            (367), (372), (375), (376), (387), (388), (393), (394),
% 197.68/32.45  | | | | | | |            (405), (411), (415), (427), (431), (529), (538), (539),
% 197.68/32.45  | | | | | | |            (540), (541), (542), (543), (544), (545), (546), (547),
% 197.68/32.45  | | | | | | |            (548), (549), (551), (553), (555), (557), (559), (561),
% 197.68/32.45  | | | | | | |            (562), (563), (564), (566), (567), (569), (570), (571),
% 197.68/32.45  | | | | | | |            (572), (573), (574), (575), (576), (577), (578), (580),
% 197.68/32.45  | | | | | | |            (582), (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.45  | | | | | | |            (594), (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.45  | | | | | | |            (605), (606), (607), (608), (609), (610), (613), (641),
% 197.68/32.45  | | | | | | |            (7444), (7445), (7449), (7450), (7451), (7453), (7455),
% 197.68/32.45  | | | | | | |            (7458), (7459), (10028), (10029), (10030), (10480),
% 197.68/32.45  | | | | | | |            (10695), (10697), (function-axioms) are inconsistent by
% 197.68/32.45  | | | | | | |            sub-proof #4.
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | End of split
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | Case 2:
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | |   (10698)  all_16_0 = e2
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | | COMBINE_EQS: (760), (10698) imply:
% 197.68/32.45  | | | | | |   (10699)  all_10_0 = e2
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | | SIMP: (10699) implies:
% 197.68/32.45  | | | | | |   (10700)  all_10_0 = e2
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | | COMBINE_EQS: (756), (10700) imply:
% 197.68/32.45  | | | | | |   (10701)  all_26_0 = e2
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | | REDUCE: (10031), (10700) imply:
% 197.68/32.45  | | | | | |   (10702)   ~ (e3 = e2)
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | | BETA: splitting (94) gives:
% 197.68/32.45  | | | | | | 
% 197.68/32.45  | | | | | | Case 1:
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | |   (10703)   ~ (all_26_0 = e2)
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | REDUCE: (10701), (10703) imply:
% 197.68/32.45  | | | | | | |   (10704)  $false
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | CLOSE: (10704) is inconsistent.
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | Case 2:
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | |   (10705)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | BETA: splitting (99) gives:
% 197.68/32.45  | | | | | | | 
% 197.68/32.45  | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | 
% 197.68/32.45  | | | | | | | |   (10706)   ~ (all_28_0 = e3)
% 197.68/32.45  | | | | | | | | 
% 197.68/32.45  | | | | | | | | REDUCE: (754), (10706) imply:
% 197.68/32.45  | | | | | | | |   (10707)   ~ (all_4_0 = e3)
% 197.68/32.45  | | | | | | | | 
% 197.68/32.45  | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.45  | | | | | | | | 
% 197.68/32.45  | | | | | | | | Case 1:
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.45  | | | | | | | | |   (10708)   ~ (all_46_0 = e1)
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | REDUCE: (10029), (10708) imply:
% 197.68/32.45  | | | | | | | | |   (10709)  $false
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.45  | | | | | | | | | CLOSE: (10709) is inconsistent.
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.45  | | | | | | | | Case 2:
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.45  | | | | | | | | |   (10710)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.45  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | |   (10711)  all_58_15 = e0
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (10480), (10711),
% 197.68/32.46  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.46  | | | | | | | | | |            #612.
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | |   (10712)   ~ (all_58_15 = e0)
% 197.68/32.46  | | | | | | | | | |   (10713)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.46  | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.46  | | | | | | | | | |              e0)
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | ALPHA: (10713) implies:
% 197.68/32.46  | | | | | | | | | |   (10714)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 197.68/32.46  | | | | | | | | | |   (10715)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | REDUCE: (541), (10712) imply:
% 197.68/32.46  | | | | | | | | | |   (10716)   ~ (all_14_2 = e0)
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | |   (10717)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.46  | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.46  | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | BETA: splitting (10717) gives:
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | |   (10718)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.46  | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 197.68/32.46  | | | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 197.68/32.46  | | | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 197.68/32.46  | | | | | | | | | | | |            (10030), (10718), (function-axioms) are
% 197.68/32.46  | | | | | | | | | | | |            inconsistent by sub-proof #302.
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | |   (10719)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.46  | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.46  | | | | | | | | | | | |            (51), (61), (63), (157), (158), (162), (166),
% 197.68/32.46  | | | | | | | | | | | |            (167), (168), (169), (173), (174), (175), (178),
% 197.68/32.46  | | | | | | | | | | | |            (179), (180), (182), (183), (185), (270), (273),
% 197.68/32.46  | | | | | | | | | | | |            (276), (277), (278), (280), (282), (283), (284),
% 197.68/32.46  | | | | | | | | | | | |            (306), (309), (313), (314), (316), (317), (320),
% 197.68/32.46  | | | | | | | | | | | |            (321), (324), (325), (326), (329), (330), (332),
% 197.68/32.46  | | | | | | | | | | | |            (333), (351), (366), (367), (372), (387), (388),
% 197.68/32.46  | | | | | | | | | | | |            (393), (394), (405), (415), (421), (427), (431),
% 197.68/32.46  | | | | | | | | | | | |            (538), (539), (541), (542), (543), (544), (545),
% 197.68/32.46  | | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 197.68/32.46  | | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (567),
% 197.68/32.46  | | | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 197.68/32.46  | | | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (586),
% 197.68/32.46  | | | | | | | | | | | |            (587), (590), (591), (593), (594), (600), (603),
% 197.68/32.46  | | | | | | | | | | | |            (604), (606), (607), (608), (610), (611), (613),
% 197.68/32.46  | | | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7458),
% 197.68/32.46  | | | | | | | | | | | |            (10028), (10030), (10480), (10707), (10714),
% 197.68/32.46  | | | | | | | | | | | |            (10715), (10719), (function-axioms) are
% 197.68/32.46  | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | End of split
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | |   (10720)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.46  | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.46  | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | BETA: splitting (10720) gives:
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | |   (10721)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 197.68/32.46  | | | | | | | | | | | |            all_52_22 = e0
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (51), (53), (158), (168), (169),
% 197.68/32.46  | | | | | | | | | | | |            (175), (178), (183), (270), (271), (273), (283),
% 197.68/32.46  | | | | | | | | | | | |            (317), (343), (393), (415), (431), (512), (538),
% 197.68/32.46  | | | | | | | | | | | |            (542), (546), (555), (557), (559), (572), (573),
% 197.68/32.46  | | | | | | | | | | | |            (593), (600), (603), (612), (676), (7445), (7449),
% 197.68/32.46  | | | | | | | | | | | |            (10028), (10030), (10705), (10707), (10716),
% 197.68/32.46  | | | | | | | | | | | |            (10721), (function-axioms) are inconsistent by
% 197.68/32.46  | | | | | | | | | | | |            sub-proof #8.
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | |   (10722)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 197.68/32.46  | | | | | | | | | | | |            all_52_30 = e0
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.46  | | | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 197.68/32.46  | | | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.46  | | | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.46  | | | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 197.68/32.46  | | | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 197.68/32.46  | | | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 197.68/32.46  | | | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 197.68/32.46  | | | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 197.68/32.46  | | | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 197.68/32.46  | | | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 197.68/32.46  | | | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 197.68/32.46  | | | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 197.68/32.46  | | | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 197.68/32.46  | | | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 197.68/32.46  | | | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 197.68/32.46  | | | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 197.68/32.46  | | | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 197.68/32.46  | | | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 197.68/32.46  | | | | | | | | | | | |            (641), (10028), (10030), (10710), (10714),
% 197.68/32.46  | | | | | | | | | | | |            (10716), (10722), (function-axioms) are
% 197.68/32.46  | | | | | | | | | | | |            inconsistent by sub-proof #271.
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | End of split
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | End of split
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | End of split
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | End of split
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | |   (10723)  all_28_0 = e3
% 197.68/32.46  | | | | | | | |   (10724)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | | COMBINE_EQS: (754), (10723) imply:
% 197.68/32.46  | | | | | | | |   (10725)  all_4_0 = e3
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 197.68/32.46  | | | | | | | |            (53), (61), (63), (144), (158), (161), (162), (166),
% 197.68/32.46  | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 197.68/32.46  | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 197.68/32.46  | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 197.68/32.46  | | | | | | | |            (277), (278), (280), (281), (282), (283), (284),
% 197.68/32.46  | | | | | | | |            (285), (303), (306), (307), (309), (311), (313),
% 197.68/32.46  | | | | | | | |            (315), (316), (318), (319), (320), (321), (323),
% 197.68/32.46  | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 197.68/32.46  | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 197.68/32.46  | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 197.68/32.46  | | | | | | | |            (394), (405), (411), (415), (427), (431), (529),
% 197.68/32.46  | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 197.68/32.46  | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 197.68/32.46  | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 197.68/32.46  | | | | | | | |            (566), (567), (569), (570), (571), (572), (573),
% 197.68/32.46  | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 197.68/32.46  | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 197.68/32.46  | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 197.68/32.46  | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 197.68/32.46  | | | | | | | |            (613), (641), (7444), (7445), (7449), (7450), (7451),
% 197.68/32.46  | | | | | | | |            (7453), (7455), (7458), (7459), (10028), (10029),
% 197.68/32.46  | | | | | | | |            (10030), (10480), (10724), (10725), (function-axioms)
% 197.68/32.46  | | | | | | | |            are inconsistent by sub-proof #4.
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | End of split
% 197.68/32.46  | | | | | | | 
% 197.68/32.46  | | | | | | End of split
% 197.68/32.46  | | | | | | 
% 197.68/32.46  | | | | | End of split
% 197.68/32.46  | | | | | 
% 197.68/32.46  | | | | End of split
% 197.68/32.46  | | | | 
% 197.68/32.46  | | | Case 2:
% 197.68/32.46  | | | | 
% 197.68/32.46  | | | |   (10726)  all_10_0 = e3
% 197.68/32.46  | | | | 
% 197.68/32.46  | | | | COMBINE_EQS: (717), (10726) imply:
% 197.68/32.46  | | | |   (10727)  all_36_0 = e3
% 197.68/32.46  | | | | 
% 197.68/32.46  | | | | REDUCE: (52), (10726) imply:
% 197.68/32.46  | | | |   (10728)  op(e1, all_10_1) = e3
% 197.68/32.46  | | | | 
% 197.68/32.46  | | | | BETA: splitting (64) gives:
% 197.68/32.46  | | | | 
% 197.68/32.46  | | | | Case 1:
% 197.68/32.46  | | | | | 
% 197.68/32.46  | | | | |   (10729)   ~ (all_14_0 = e2)
% 197.68/32.46  | | | | | 
% 197.68/32.46  | | | | | BETA: splitting (74) gives:
% 197.68/32.46  | | | | | 
% 197.68/32.46  | | | | | Case 1:
% 197.68/32.46  | | | | | | 
% 197.68/32.46  | | | | | |   (10730)   ~ (all_18_0 = e3)
% 197.68/32.46  | | | | | | 
% 197.68/32.46  | | | | | | REDUCE: (761), (10730) imply:
% 197.68/32.46  | | | | | |   (10731)   ~ (all_14_0 = e3)
% 197.68/32.46  | | | | | | 
% 197.68/32.46  | | | | | | BETA: splitting (89) gives:
% 197.68/32.46  | | | | | | 
% 197.68/32.46  | | | | | | Case 1:
% 197.68/32.46  | | | | | | | 
% 197.68/32.46  | | | | | | |   (10732)   ~ (all_24_0 = e1)
% 197.68/32.46  | | | | | | | 
% 197.68/32.46  | | | | | | | REDUCE: (711), (10732) imply:
% 197.68/32.46  | | | | | | |   (10733)   ~ (all_14_0 = e1)
% 197.68/32.46  | | | | | | | 
% 197.68/32.46  | | | | | | | BETA: splitting (99) gives:
% 197.68/32.46  | | | | | | | 
% 197.68/32.46  | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | |   (10734)   ~ (all_28_0 = e3)
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | | REDUCE: (754), (10734) imply:
% 197.68/32.46  | | | | | | | |   (10735)   ~ (all_4_0 = e3)
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | | BETA: splitting (119) gives:
% 197.68/32.46  | | | | | | | | 
% 197.68/32.46  | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | |   (10736)   ~ (all_36_0 = e3)
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | REDUCE: (10727), (10736) imply:
% 197.68/32.46  | | | | | | | | |   (10737)  $false
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | CLOSE: (10737) is inconsistent.
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | |   (10738)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | BETA: splitting (144) gives:
% 197.68/32.46  | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | |   (10739)   ~ (all_46_0 = e1)
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | REDUCE: (10029), (10739) imply:
% 197.68/32.46  | | | | | | | | | |   (10740)  $false
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | CLOSE: (10740) is inconsistent.
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | |   (10741)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | BETA: splitting (303) gives:
% 197.68/32.46  | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | |   (10742)  all_58_15 = e0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | COMBINE_EQS: (541), (10742) imply:
% 197.68/32.46  | | | | | | | | | | |   (10743)  all_14_2 = e0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (573), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10744)   ~ (all_52_7 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (591), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10745)   ~ (all_52_15 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (603), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10746)   ~ (all_52_23 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (606), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10747)   ~ (all_52_25 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (609), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10748)   ~ (all_52_29 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (613), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10749)  op(e0, e0) = all_52_30
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (63), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10750)  op(e0, e0) = all_14_1
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (61), (10743) imply:
% 197.68/32.46  | | | | | | | | | | |   (10751)  op(e0, e0) = e0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 197.68/32.46  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10749),
% 197.68/32.46  | | | | | | | | | | |              (10750) gives:
% 197.68/32.46  | | | | | | | | | | |   (10752)  all_52_30 = all_14_1
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 197.68/32.46  | | | | | | | | | | |              all_52_30, e0, e0, simplifying with (10749),
% 197.68/32.46  | | | | | | | | | | |              (10751) gives:
% 197.68/32.46  | | | | | | | | | | |   (10753)  all_52_30 = e0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | COMBINE_EQS: (10752), (10753) imply:
% 197.68/32.46  | | | | | | | | | | |   (10754)  all_14_1 = e0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (62), (10754) imply:
% 197.68/32.46  | | | | | | | | | | |   (10755)  op(e0, e0) = all_14_0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 197.68/32.46  | | | | | | | | | | |              e0, e0, simplifying with (10751), (10755) gives:
% 197.68/32.46  | | | | | | | | | | |   (10756)  all_14_0 = e0
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (10731), (10756) imply:
% 197.68/32.46  | | | | | | | | | | |   (10757)   ~ (e3 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (10729), (10756) imply:
% 197.68/32.46  | | | | | | | | | | |   (10758)   ~ (e2 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | REDUCE: (10733), (10756) imply:
% 197.68/32.46  | | | | | | | | | | |   (10759)   ~ (e1 = e0)
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | BETA: splitting (187) gives:
% 197.68/32.46  | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | |   (10760)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.46  | | | | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 197.68/32.46  | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | BETA: splitting (10760) gives:
% 197.68/32.46  | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | |   (10761)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 197.68/32.46  | | | | | | | | | | | | |            all_52_6 = e0
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (51),
% 197.68/32.46  | | | | | | | | | | | | |            (53), (61), (156), (162), (175), (179), (183),
% 197.68/32.46  | | | | | | | | | | | | |            (184), (185), (271), (272), (273), (304), (305),
% 197.68/32.46  | | | | | | | | | | | | |            (306), (321), (326), (332), (343), (346), (351),
% 197.68/32.46  | | | | | | | | | | | | |            (387), (405), (431), (524), (542), (543), (547),
% 197.68/32.46  | | | | | | | | | | | | |            (555), (564), (569), (571), (572), (573), (582),
% 197.68/32.46  | | | | | | | | | | | | |            (590), (610), (611), (645), (10728), (10738),
% 197.68/32.46  | | | | | | | | | | | | |            (10742), (10744), (10746), (10751), (10761),
% 197.68/32.46  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.46  | | | | | | | | | | | | |            #108.
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | |   (10762)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 197.68/32.46  | | | | | | | | | | | | |            all_52_14 = e0
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | ALPHA: (10762) implies:
% 197.68/32.46  | | | | | | | | | | | | |   (10763)  all_52_14 = e0
% 197.68/32.46  | | | | | | | | | | | | |   (10764)  all_52_12 = e1
% 197.68/32.46  | | | | | | | | | | | | |   (10765)  all_52_10 = e2
% 197.68/32.46  | | | | | | | | | | | | |   (10766)  all_52_8 = e3
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | REDUCE: (182), (10766) imply:
% 197.68/32.46  | | | | | | | | | | | | |   (10767)  op(all_52_9, all_52_9) = e3
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | REDUCE: (180), (10764) imply:
% 197.68/32.46  | | | | | | | | | | | | |   (10768)  op(all_52_13, all_52_13) = e1
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | REDUCE: (179), (10763) imply:
% 197.68/32.46  | | | | | | | | | | | | |   (10769)  op(all_52_15, all_52_15) = e0
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | REDUCE: (611), (10765) imply:
% 197.68/32.46  | | | | | | | | | | | | |   (10770)  op(all_4_2, all_4_2) = e2
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | BETA: splitting (271) gives:
% 197.68/32.46  | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | |   (10771)  all_56_14 = e3
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | COMBINE_EQS: (343), (10771) imply:
% 197.68/32.46  | | | | | | | | | | | | | |   (10772)  all_52_23 = e3
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | SIMP: (10772) implies:
% 197.68/32.46  | | | | | | | | | | | | | |   (10773)  all_52_23 = e3
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | REDUCE: (572), (10773) imply:
% 197.68/32.46  | | | | | | | | | | | | | |   (10774)   ~ (all_52_7 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | REDUCE: (590), (10773) imply:
% 197.68/32.46  | | | | | | | | | | | | | |   (10775)   ~ (all_52_15 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | REDUCE: (156), (10773) imply:
% 197.68/32.46  | | | | | | | | | | | | | |   (10776)  op(e0, e1) = e3
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (51), (53), (162), (183), (272), (273),
% 197.68/32.46  | | | | | | | | | | | | | |            (276), (304), (305), (346), (351), (421), (431),
% 197.68/32.46  | | | | | | | | | | | | | |            (543), (568), (571), (582), (587), (588), (10728),
% 197.68/32.46  | | | | | | | | | | | | | |            (10744), (10745), (10751), (10768), (10769),
% 197.68/32.46  | | | | | | | | | | | | | |            (10770), (10774), (10775), (10776),
% 197.68/32.46  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.46  | | | | | | | | | | | | | |            #51.
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | |   (10777)   ~ (all_56_14 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | REDUCE: (343), (10777) imply:
% 197.68/32.46  | | | | | | | | | | | | | |   (10778)   ~ (all_52_23 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 197.68/32.46  | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | |   (10779)  all_58_4 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | COMBINE_EQS: (393), (10779) imply:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10780)  all_52_17 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | SIMP: (10780) implies:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10781)  all_52_17 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | REDUCE: (577), (10781) imply:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10782)   ~ (all_52_9 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | REDUCE: (594), (10781) imply:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10783)   ~ (all_52_23 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | REDUCE: (593), (10781) imply:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10784)   ~ (all_10_2 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | SIMP: (10784) implies:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10785)   ~ (all_10_2 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | REDUCE: (7451), (10781) imply:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10786)   ~ (all_4_0 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | REDUCE: (178), (10781) imply:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10787)  op(e3, e3) = all_52_16
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.46  | | | | | | | | | | | | | | |              all_52_16, e3, e3, simplifying with (41), (10787)
% 197.68/32.46  | | | | | | | | | | | | | | |              gives:
% 197.68/32.46  | | | | | | | | | | | | | | |   (10788)  all_52_16 = all_6_2
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (41), (43), (51),
% 197.68/32.46  | | | | | | | | | | | | | | |            (158), (162), (167), (168), (169), (175), (273),
% 197.68/32.46  | | | | | | | | | | | | | | |            (278), (284), (305), (306), (320), (321), (325),
% 197.68/32.46  | | | | | | | | | | | | | | |            (326), (329), (330), (351), (366), (372), (387),
% 197.68/32.46  | | | | | | | | | | | | | | |            (394), (405), (427), (431), (542), (543), (547),
% 197.68/32.46  | | | | | | | | | | | | | | |            (548), (549), (555), (557), (561), (563), (571),
% 197.68/32.46  | | | | | | | | | | | | | | |            (576), (577), (580), (582), (586), (7443), (7445),
% 197.68/32.46  | | | | | | | | | | | | | | |            (7449), (10028), (10030), (10735), (10742),
% 197.68/32.46  | | | | | | | | | | | | | | |            (10744), (10767), (10768), (10769), (10778),
% 197.68/32.46  | | | | | | | | | | | | | | |            (10782), (10785), (function-axioms) are
% 197.68/32.46  | | | | | | | | | | | | | | |            inconsistent by sub-proof #39.
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | |   (10789)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | BETA: splitting (10789) gives:
% 197.68/32.46  | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | |   (10790)  all_58_5 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (10735), (10790) are inconsistent by
% 197.68/32.46  | | | | | | | | | | | | | | | |            sub-proof #215.
% 197.68/32.46  | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | Case 2:
% 197.68/32.46  | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | |   (10791)  all_58_8 = e3 | all_58_14 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | BETA: splitting (10791) gives:
% 197.68/32.46  | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10792)  all_58_8 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (10792) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10793)  all_10_2 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | REDUCE: (593), (10793) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10794)   ~ (all_52_17 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | REDUCE: (7457), (10793) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10795)   ~ (all_4_0 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | REDUCE: (612), (10793) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10796)  op(e3, e3) = all_52_20
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | REDUCE: (53), (10793) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10797)  op(e3, e1) = all_10_1
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 197.68/32.46  | | | | | | | | | | | | | | | | |              all_10_1, e1, e3, simplifying with (168), (10797)
% 197.68/32.46  | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10798)  all_52_17 = all_10_1
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.46  | | | | | | | | | | | | | | | | |              all_52_20, e3, e3, simplifying with (41), (10796)
% 197.68/32.46  | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10799)  all_52_20 = all_6_2
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (393), (10798) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | |   (10800)  all_58_4 = all_10_1
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 197.68/32.46  | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10801)  all_58_9 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (10801) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10802)  all_52_25 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | SIMP: (10802) implies:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10803)  all_52_25 = e3
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | REDUCE: (604), (10803) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10804)   ~ (all_52_27 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | SIMP: (10804) implies:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10805)   ~ (all_52_27 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | REDUCE: (605), (10803) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10806)   ~ (all_52_29 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | SIMP: (10806) implies:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10807)   ~ (all_52_29 = e3)
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | REDUCE: (174), (10803) imply:
% 197.68/32.46  | | | | | | | | | | | | | | | | | |   (10808)  op(e3, e3) = all_52_24
% 197.68/32.46  | | | | | | | | | | | | | | | | | | 
% 197.68/32.46  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 197.68/32.46  | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (41), (10808)
% 197.68/32.46  | | | | | | | | | | | | | | | | | |              gives:
% 197.68/32.47  | | | | | | | | | | | | | | | | | |   (10809)  all_52_24 = all_6_2
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |   (10810)  all_58_2 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (10810) imply:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |   (10811)  all_52_3 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | SIMP: (10811) implies:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |   (10812)  all_52_3 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (10812) imply:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |   (10813)   ~ (all_52_7 = e3)
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | SIMP: (10813) implies:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |   (10814)   ~ (all_52_7 = e3)
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |   (10815)  all_58_12 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (10814), (10815) are inconsistent by
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |            sub-proof #1367.
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |   (10816)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (41), (43), (158), (168),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |            (175), (273), (284), (305), (351), (394), (431),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |            (542), (543), (555), (557), (571), (576), (577),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |            (582), (10028), (10030), (10742), (10767),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |            (10769), (10778), (10816), (function-axioms) are
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #40.
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |   (10817)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (159), (314), (372), (542), (548),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |            (7443), (7449), (10728), (10735), (10746),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |            (10792), (10800), (10805), (10807), (10817),
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 197.68/32.47  | | | | | | | | | | | | | | | | | | |            #49.
% 197.68/32.47  | | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | |   (10818)   ~ (all_58_9 = e3)
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | REDUCE: (545), (10818) imply:
% 197.68/32.47  | | | | | | | | | | | | | | | | | |   (10819)   ~ (all_52_25 = e3)
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (41), (43), (333), (393), (405), (545),
% 197.68/32.47  | | | | | | | | | | | | | | | | | |            (549), (557), (610), (10030), (10767), (10794),
% 197.68/32.47  | | | | | | | | | | | | | | | | | |            (10819), (function-axioms) are inconsistent by
% 197.68/32.47  | | | | | | | | | | | | | | | | | |            sub-proof #289.
% 197.68/32.47  | | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | Case 2:
% 197.68/32.47  | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | |   (10820)  all_58_14 = e3
% 197.68/32.47  | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (10778), (10820) are inconsistent by
% 197.68/32.47  | | | | | | | | | | | | | | | | |            sub-proof #1305.
% 197.68/32.47  | | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | Case 2:
% 197.68/32.47  | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | |   (10821)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 197.68/32.47  | | | | | | | | | | | |              & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 197.68/32.47  | | | | | | | | | | | |              = e2 & all_52_28 = e1 & all_52_30 = e0)
% 197.68/32.47  | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 197.68/32.47  | | | | | | | | | | | |            (51), (158), (162), (166), (167), (168), (169),
% 197.68/32.47  | | | | | | | | | | | |            (172), (173), (174), (175), (178), (183), (271),
% 197.68/32.47  | | | | | | | | | | | |            (272), (273), (278), (281), (282), (304), (306),
% 197.68/32.47  | | | | | | | | | | | |            (307), (308), (309), (317), (320), (326), (330),
% 197.68/32.47  | | | | | | | | | | | |            (332), (333), (343), (346), (351), (372), (387),
% 197.68/32.47  | | | | | | | | | | | |            (388), (393), (405), (411), (427), (431), (529),
% 197.68/32.47  | | | | | | | | | | | |            (542), (543), (544), (545), (546), (547), (549),
% 197.68/32.47  | | | | | | | | | | | |            (551), (555), (557), (559), (561), (564), (566),
% 197.68/32.47  | | | | | | | | | | | |            (570), (571), (572), (576), (582), (593), (600),
% 197.68/32.47  | | | | | | | | | | | |            (604), (605), (610), (612), (641), (7449),
% 197.68/32.47  | | | | | | | | | | | |            (10028), (10030), (10735), (10741), (10742),
% 197.68/32.47  | | | | | | | | | | | |            (10744), (10745), (10746), (10747), (10748),
% 197.68/32.47  | | | | | | | | | | | |            (10751), (10821), (function-axioms) are
% 197.68/32.47  | | | | | | | | | | | |            inconsistent by sub-proof #27.
% 197.68/32.47  | | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | | End of split
% 197.68/32.47  | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | Case 2:
% 197.68/32.47  | | | | | | | | | | | 
% 197.68/32.47  | | | | | | | | | | |   (10822)   ~ (all_58_15 = e0)
% 197.68/32.47  | | | | | | | | | | |   (10823)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 197.68/32.47  | | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 197.68/32.47  | | | | | | | | | | |              e0)
% 197.68/32.47  | | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 198.01/32.47  | | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 198.01/32.47  | | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 198.01/32.47  | | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 198.01/32.47  | | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 198.01/32.47  | | | | | | | | | | |            (273), (274), (276), (277), (278), (279), (280),
% 198.01/32.47  | | | | | | | | | | |            (281), (282), (283), (284), (285), (306), (307),
% 198.01/32.47  | | | | | | | | | | |            (309), (311), (312), (313), (314), (315), (316),
% 198.01/32.47  | | | | | | | | | | |            (317), (319), (320), (321), (323), (324), (325),
% 198.01/32.47  | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (332),
% 198.01/32.47  | | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 198.01/32.47  | | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 198.01/32.47  | | | | | | | | | | |            (411), (415), (421), (427), (431), (529), (538),
% 198.01/32.47  | | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 198.01/32.47  | | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 198.01/32.47  | | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 198.01/32.47  | | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 198.01/32.47  | | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 198.01/32.47  | | | | | | | | | | |            (584), (586), (587), (588), (590), (591), (592),
% 198.01/32.47  | | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 198.01/32.47  | | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 198.01/32.47  | | | | | | | | | | |            (610), (611), (612), (613), (641), (7443), (7445),
% 198.01/32.47  | | | | | | | | | | |            (7448), (7449), (7450), (7451), (7453), (7458),
% 198.01/32.47  | | | | | | | | | | |            (7459), (10028), (10030), (10728), (10735),
% 198.01/32.47  | | | | | | | | | | |            (10741), (10822), (10823), (function-axioms) are
% 198.01/32.47  | | | | | | | | | | |            inconsistent by sub-proof #1.
% 198.01/32.47  | | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | | End of split
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | End of split
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | End of split
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | Case 2:
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | |   (10824)  all_28_0 = e3
% 198.01/32.47  | | | | | | | |   (10825)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | COMBINE_EQS: (754), (10824) imply:
% 198.01/32.47  | | | | | | | |   (10826)  all_4_0 = e3
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | SIMP: (10826) implies:
% 198.01/32.47  | | | | | | | |   (10827)  all_4_0 = e3
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | COMBINE_EQS: (7449), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10828)  all_58_5 = e3
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7450), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10829)   ~ (all_52_3 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7451), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10830)   ~ (all_52_17 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7453), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10831)   ~ (all_52_23 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7455), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10832)   ~ (all_52_27 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7458), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10833)   ~ (all_4_2 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | SIMP: (10833) implies:
% 198.01/32.47  | | | | | | | |   (10834)   ~ (all_4_2 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7459), (10827) imply:
% 198.01/32.47  | | | | | | | |   (10835)  op(e3, e3) = all_52_18
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 198.01/32.47  | | | | | | | |            (53), (61), (62), (63), (144), (158), (161), (162),
% 198.01/32.47  | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 198.01/32.47  | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 198.01/32.47  | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 198.01/32.47  | | | | | | | |            (274), (277), (278), (280), (281), (282), (283),
% 198.01/32.47  | | | | | | | |            (284), (285), (303), (304), (306), (307), (308),
% 198.01/32.47  | | | | | | | |            (309), (311), (313), (315), (316), (318), (319),
% 198.01/32.47  | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 198.01/32.47  | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 198.01/32.47  | | | | | | | |            (351), (352), (366), (367), (372), (375), (376),
% 198.01/32.47  | | | | | | | |            (387), (388), (393), (394), (405), (411), (415),
% 198.01/32.47  | | | | | | | |            (427), (431), (529), (538), (539), (540), (541),
% 198.01/32.47  | | | | | | | |            (542), (543), (544), (545), (546), (547), (548),
% 198.01/32.47  | | | | | | | |            (549), (551), (553), (555), (557), (559), (561),
% 198.01/32.47  | | | | | | | |            (562), (563), (564), (566), (567), (569), (570),
% 198.01/32.47  | | | | | | | |            (571), (572), (573), (574), (575), (576), (577),
% 198.01/32.47  | | | | | | | |            (578), (580), (582), (584), (586), (587), (590),
% 198.01/32.47  | | | | | | | |            (591), (592), (593), (594), (595), (596), (598),
% 198.01/32.47  | | | | | | | |            (600), (602), (603), (604), (605), (606), (607),
% 198.01/32.47  | | | | | | | |            (608), (609), (610), (613), (641), (7444), (7445),
% 198.01/32.47  | | | | | | | |            (10028), (10029), (10030), (10729), (10731), (10733),
% 198.01/32.47  | | | | | | | |            (10825), (10828), (10829), (10830), (10831), (10832),
% 198.01/32.47  | | | | | | | |            (10834), (10835), (function-axioms) are inconsistent
% 198.01/32.47  | | | | | | | |            by sub-proof #15.
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | End of split
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | Case 2:
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | |   (10836)  all_24_0 = e1
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | COMBINE_EQS: (711), (10836) imply:
% 198.01/32.47  | | | | | | |   (10837)  all_14_0 = e1
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | SIMP: (10837) implies:
% 198.01/32.47  | | | | | | |   (10838)  all_14_0 = e1
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | REDUCE: (10731), (10838) imply:
% 198.01/32.47  | | | | | | |   (10839)   ~ (e3 = e1)
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | REDUCE: (10729), (10838) imply:
% 198.01/32.47  | | | | | | |   (10840)   ~ (e2 = e1)
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | REDUCE: (62), (10838) imply:
% 198.01/32.47  | | | | | | |   (10841)  op(e0, all_14_1) = e1
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | BETA: splitting (99) gives:
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | | Case 1:
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | |   (10842)   ~ (all_28_0 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (754), (10842) imply:
% 198.01/32.47  | | | | | | | |   (10843)   ~ (all_4_0 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | BETA: splitting (144) gives:
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | Case 1:
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | |   (10844)   ~ (all_46_0 = e1)
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | REDUCE: (10029), (10844) imply:
% 198.01/32.47  | | | | | | | | |   (10845)  $false
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | CLOSE: (10845) is inconsistent.
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | Case 2:
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | |   (10846)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | BETA: splitting (303) gives:
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | Case 1:
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | |   (10847)  all_58_15 = e0
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | | REF_CLOSE: (4), (61), (63), (541), (613), (10841), (10847),
% 198.01/32.47  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 198.01/32.47  | | | | | | | | | |            #877.
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | Case 2:
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | |   (10848)   ~ (all_58_15 = e0)
% 198.01/32.47  | | | | | | | | | |   (10849)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 198.01/32.47  | | | | | | | | | |            & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 198.01/32.47  | | | | | | | | | |              e0)
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 198.01/32.47  | | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161),
% 198.01/32.47  | | | | | | | | | |            (162), (166), (167), (168), (169), (172), (173),
% 198.01/32.47  | | | | | | | | | |            (174), (175), (177), (178), (179), (180), (182),
% 198.01/32.47  | | | | | | | | | |            (183), (184), (185), (187), (270), (271), (272),
% 198.01/32.47  | | | | | | | | | |            (273), (274), (276), (277), (278), (279), (280),
% 198.01/32.47  | | | | | | | | | |            (281), (282), (283), (284), (285), (306), (307),
% 198.01/32.47  | | | | | | | | | |            (309), (311), (312), (313), (314), (315), (316),
% 198.01/32.47  | | | | | | | | | |            (317), (319), (320), (321), (323), (324), (325),
% 198.01/32.47  | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (332),
% 198.01/32.47  | | | | | | | | | |            (333), (343), (346), (351), (352), (366), (367),
% 198.01/32.47  | | | | | | | | | |            (372), (375), (387), (388), (393), (394), (405),
% 198.01/32.47  | | | | | | | | | |            (411), (415), (421), (427), (431), (529), (538),
% 198.01/32.47  | | | | | | | | | |            (539), (540), (541), (542), (543), (544), (545),
% 198.01/32.47  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 198.01/32.47  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (566),
% 198.01/32.47  | | | | | | | | | |            (567), (568), (569), (570), (571), (572), (573),
% 198.01/32.47  | | | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 198.01/32.47  | | | | | | | | | |            (584), (586), (587), (588), (590), (591), (592),
% 198.01/32.47  | | | | | | | | | |            (593), (594), (595), (596), (598), (600), (602),
% 198.01/32.47  | | | | | | | | | |            (603), (604), (605), (606), (607), (608), (609),
% 198.01/32.47  | | | | | | | | | |            (610), (611), (612), (613), (641), (7443), (7445),
% 198.01/32.47  | | | | | | | | | |            (7448), (7449), (7450), (7451), (7453), (7458),
% 198.01/32.47  | | | | | | | | | |            (7459), (10028), (10030), (10728), (10843),
% 198.01/32.47  | | | | | | | | | |            (10846), (10848), (10849), (function-axioms) are
% 198.01/32.47  | | | | | | | | | |            inconsistent by sub-proof #1.
% 198.01/32.47  | | | | | | | | | | 
% 198.01/32.47  | | | | | | | | | End of split
% 198.01/32.47  | | | | | | | | | 
% 198.01/32.47  | | | | | | | | End of split
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | Case 2:
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | |   (10850)  all_28_0 = e3
% 198.01/32.47  | | | | | | | |   (10851)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | COMBINE_EQS: (754), (10850) imply:
% 198.01/32.47  | | | | | | | |   (10852)  all_4_0 = e3
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | SIMP: (10852) implies:
% 198.01/32.47  | | | | | | | |   (10853)  all_4_0 = e3
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | COMBINE_EQS: (7449), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10854)  all_58_5 = e3
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7450), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10855)   ~ (all_52_3 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7451), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10856)   ~ (all_52_17 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7453), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10857)   ~ (all_52_23 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7455), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10858)   ~ (all_52_27 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7458), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10859)   ~ (all_4_2 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | SIMP: (10859) implies:
% 198.01/32.47  | | | | | | | |   (10860)   ~ (all_4_2 = e3)
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REDUCE: (7459), (10853) imply:
% 198.01/32.47  | | | | | | | |   (10861)  op(e3, e3) = all_52_18
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 198.01/32.47  | | | | | | | |            (53), (61), (63), (144), (158), (161), (162), (166),
% 198.01/32.47  | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 198.01/32.47  | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 198.01/32.47  | | | | | | | |            (185), (187), (270), (271), (272), (273), (274),
% 198.01/32.47  | | | | | | | |            (277), (278), (280), (281), (282), (283), (284),
% 198.01/32.47  | | | | | | | |            (285), (303), (306), (307), (309), (311), (313),
% 198.01/32.47  | | | | | | | |            (315), (316), (318), (319), (320), (321), (323),
% 198.01/32.47  | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 198.01/32.47  | | | | | | | |            (332), (333), (343), (346), (351), (352), (366),
% 198.01/32.47  | | | | | | | |            (367), (372), (375), (376), (387), (388), (393),
% 198.01/32.47  | | | | | | | |            (394), (405), (411), (415), (427), (431), (529),
% 198.01/32.47  | | | | | | | |            (538), (539), (540), (541), (542), (543), (544),
% 198.01/32.47  | | | | | | | |            (545), (546), (547), (548), (549), (551), (553),
% 198.01/32.47  | | | | | | | |            (555), (557), (559), (561), (562), (563), (564),
% 198.01/32.47  | | | | | | | |            (566), (567), (569), (570), (571), (572), (573),
% 198.01/32.47  | | | | | | | |            (574), (575), (576), (577), (578), (580), (582),
% 198.01/32.47  | | | | | | | |            (584), (586), (587), (590), (591), (592), (593),
% 198.01/32.47  | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 198.01/32.47  | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 198.01/32.47  | | | | | | | |            (613), (641), (7444), (7445), (10028), (10029),
% 198.01/32.47  | | | | | | | |            (10030), (10841), (10851), (10854), (10855), (10856),
% 198.01/32.47  | | | | | | | |            (10857), (10858), (10860), (10861), (function-axioms)
% 198.01/32.47  | | | | | | | |            are inconsistent by sub-proof #13.
% 198.01/32.47  | | | | | | | | 
% 198.01/32.47  | | | | | | | End of split
% 198.01/32.47  | | | | | | | 
% 198.01/32.47  | | | | | | End of split
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | Case 2:
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | |   (10862)  all_18_0 = e3
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | | COMBINE_EQS: (761), (10862) imply:
% 198.01/32.47  | | | | | |   (10863)  all_14_0 = e3
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | | SIMP: (10863) implies:
% 198.01/32.47  | | | | | |   (10864)  all_14_0 = e3
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | | REDUCE: (62), (10864) imply:
% 198.01/32.47  | | | | | |   (10865)  op(e0, all_14_1) = e3
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | | BETA: splitting (99) gives:
% 198.01/32.47  | | | | | | 
% 198.01/32.47  | | | | | | Case 1:
% 198.01/32.47  | | | | | | | 
% 198.01/32.48  | | | | | | |   (10866)   ~ (all_28_0 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (754), (10866) imply:
% 198.01/32.48  | | | | | | |   (10867)   ~ (all_4_0 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | BETA: splitting (144) gives:
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | Case 1:
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | |   (10868)   ~ (all_46_0 = e1)
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | REDUCE: (10029), (10868) imply:
% 198.01/32.48  | | | | | | | |   (10869)  $false
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | CLOSE: (10869) is inconsistent.
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | Case 2:
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | |   (10870)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | BETA: splitting (303) gives:
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | Case 1:
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | |   (10871)  all_58_15 = e0
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | REF_CLOSE: (7), (61), (63), (541), (613), (10865), (10871),
% 198.01/32.48  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 198.01/32.48  | | | | | | | | |            #693.
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | Case 2:
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | |   (10872)   ~ (all_58_15 = e0)
% 198.01/32.48  | | | | | | | | |   (10873)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.48  | | | | | | | | |            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | ALPHA: (10873) implies:
% 198.01/32.48  | | | | | | | | |   (10874)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.48  | | | | | | | | |   (10875)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | REDUCE: (541), (10872) imply:
% 198.01/32.48  | | | | | | | | |   (10876)   ~ (all_14_2 = e0)
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 198.01/32.48  | | | | | | | | |            (51), (53), (61), (63), (158), (159), (161), (162),
% 198.01/32.48  | | | | | | | | |            (166), (167), (168), (169), (172), (173), (174),
% 198.01/32.48  | | | | | | | | |            (175), (177), (178), (179), (180), (182), (183),
% 198.01/32.48  | | | | | | | | |            (184), (185), (187), (270), (271), (272), (273),
% 198.01/32.48  | | | | | | | | |            (274), (276), (277), (278), (279), (280), (281),
% 198.01/32.48  | | | | | | | | |            (282), (283), (284), (285), (306), (307), (309),
% 198.01/32.48  | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 198.01/32.48  | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 198.01/32.48  | | | | | | | | |            (327), (328), (329), (330), (331), (332), (333),
% 198.01/32.48  | | | | | | | | |            (343), (346), (351), (352), (366), (367), (372),
% 198.01/32.48  | | | | | | | | |            (375), (387), (388), (393), (394), (405), (411),
% 198.01/32.48  | | | | | | | | |            (415), (421), (427), (431), (529), (538), (539),
% 198.01/32.48  | | | | | | | | |            (540), (541), (542), (543), (544), (545), (546),
% 198.01/32.48  | | | | | | | | |            (547), (548), (549), (551), (553), (555), (557),
% 198.01/32.48  | | | | | | | | |            (559), (561), (562), (563), (564), (566), (567),
% 198.01/32.48  | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 198.01/32.48  | | | | | | | | |            (575), (576), (577), (578), (580), (582), (584),
% 198.01/32.48  | | | | | | | | |            (586), (587), (588), (590), (591), (592), (593),
% 198.01/32.48  | | | | | | | | |            (594), (595), (596), (598), (600), (602), (603),
% 198.01/32.48  | | | | | | | | |            (604), (605), (606), (607), (608), (609), (610),
% 198.01/32.48  | | | | | | | | |            (611), (612), (613), (641), (7443), (7445), (7448),
% 198.01/32.48  | | | | | | | | |            (7449), (7450), (7451), (7453), (7458), (7459),
% 198.01/32.48  | | | | | | | | |            (10028), (10030), (10728), (10867), (10870),
% 198.01/32.48  | | | | | | | | |            (10874), (10875), (10876), (function-axioms) are
% 198.01/32.48  | | | | | | | | |            inconsistent by sub-proof #2.
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | End of split
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | End of split
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | Case 2:
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | |   (10877)  all_28_0 = e3
% 198.01/32.48  | | | | | | |   (10878)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | COMBINE_EQS: (754), (10877) imply:
% 198.01/32.48  | | | | | | |   (10879)  all_4_0 = e3
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | SIMP: (10879) implies:
% 198.01/32.48  | | | | | | |   (10880)  all_4_0 = e3
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | COMBINE_EQS: (7449), (10880) imply:
% 198.01/32.48  | | | | | | |   (10881)  all_58_5 = e3
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (7450), (10880) imply:
% 198.01/32.48  | | | | | | |   (10882)   ~ (all_52_3 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (7451), (10880) imply:
% 198.01/32.48  | | | | | | |   (10883)   ~ (all_52_17 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (7453), (10880) imply:
% 198.01/32.48  | | | | | | |   (10884)   ~ (all_52_23 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (7455), (10880) imply:
% 198.01/32.48  | | | | | | |   (10885)   ~ (all_52_27 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (7458), (10880) imply:
% 198.01/32.48  | | | | | | |   (10886)   ~ (all_4_2 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | SIMP: (10886) implies:
% 198.01/32.48  | | | | | | |   (10887)   ~ (all_4_2 = e3)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (7459), (10880) imply:
% 198.01/32.48  | | | | | | |   (10888)  op(e3, e3) = all_52_18
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 198.01/32.48  | | | | | | |            (53), (61), (63), (144), (158), (161), (162), (166),
% 198.01/32.48  | | | | | | |            (167), (168), (169), (172), (173), (174), (175), (177),
% 198.01/32.48  | | | | | | |            (178), (179), (180), (182), (183), (184), (185), (187),
% 198.01/32.48  | | | | | | |            (270), (271), (272), (273), (274), (277), (278), (280),
% 198.01/32.48  | | | | | | |            (281), (282), (283), (284), (285), (303), (306), (307),
% 198.01/32.48  | | | | | | |            (309), (311), (313), (315), (316), (318), (319), (320),
% 198.01/32.48  | | | | | | |            (321), (323), (324), (325), (326), (327), (328), (330),
% 198.01/32.48  | | | | | | |            (331), (332), (333), (343), (346), (351), (352), (366),
% 198.01/32.48  | | | | | | |            (367), (372), (375), (376), (387), (388), (393), (394),
% 198.01/32.48  | | | | | | |            (405), (411), (415), (427), (431), (529), (538), (539),
% 198.01/32.48  | | | | | | |            (540), (541), (542), (543), (544), (545), (546), (547),
% 198.01/32.48  | | | | | | |            (548), (549), (551), (553), (555), (557), (559), (561),
% 198.01/32.48  | | | | | | |            (562), (563), (564), (566), (567), (569), (570), (571),
% 198.01/32.48  | | | | | | |            (572), (573), (574), (575), (576), (577), (578), (580),
% 198.01/32.48  | | | | | | |            (582), (584), (586), (587), (590), (591), (592), (593),
% 198.01/32.48  | | | | | | |            (594), (595), (596), (598), (600), (602), (603), (604),
% 198.01/32.48  | | | | | | |            (605), (606), (607), (608), (609), (610), (613), (641),
% 198.01/32.48  | | | | | | |            (7444), (7445), (10028), (10029), (10030), (10865),
% 198.01/32.48  | | | | | | |            (10878), (10881), (10882), (10883), (10884), (10885),
% 198.01/32.48  | | | | | | |            (10887), (10888), (function-axioms) are inconsistent by
% 198.01/32.48  | | | | | | |            sub-proof #11.
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | End of split
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | End of split
% 198.01/32.48  | | | | | 
% 198.01/32.48  | | | | Case 2:
% 198.01/32.48  | | | | | 
% 198.01/32.48  | | | | |   (10889)  all_14_0 = e2
% 198.01/32.48  | | | | | 
% 198.01/32.48  | | | | | REDUCE: (62), (10889) imply:
% 198.01/32.48  | | | | |   (10890)  op(e0, all_14_1) = e2
% 198.01/32.48  | | | | | 
% 198.01/32.48  | | | | | BETA: splitting (99) gives:
% 198.01/32.48  | | | | | 
% 198.01/32.48  | | | | | Case 1:
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | |   (10891)   ~ (all_28_0 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (754), (10891) imply:
% 198.01/32.48  | | | | | |   (10892)   ~ (all_4_0 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | BETA: splitting (144) gives:
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | Case 1:
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | |   (10893)   ~ (all_46_0 = e1)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | REDUCE: (10029), (10893) imply:
% 198.01/32.48  | | | | | | |   (10894)  $false
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | CLOSE: (10894) is inconsistent.
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | Case 2:
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | |   (10895)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | BETA: splitting (303) gives:
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | | Case 1:
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | |   (10896)  all_58_15 = e0
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | REF_CLOSE: (5), (61), (63), (541), (613), (10890), (10896),
% 198.01/32.48  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #612.
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | Case 2:
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | |   (10897)   ~ (all_58_15 = e0)
% 198.01/32.48  | | | | | | | |   (10898)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.48  | | | | | | | |            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | ALPHA: (10898) implies:
% 198.01/32.48  | | | | | | | |   (10899)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.48  | | | | | | | |   (10900)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | REDUCE: (541), (10897) imply:
% 198.01/32.48  | | | | | | | |   (10901)   ~ (all_14_2 = e0)
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | BETA: splitting (187) gives:
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | | Case 1:
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | |   (10902)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 198.01/32.48  | | | | | | | | |              all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 198.01/32.48  | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0)
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | BETA: splitting (10902) gives:
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | Case 1:
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | |   (10903)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 198.01/32.48  | | | | | | | | | |            all_52_6 = e0
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REF_CLOSE: (8), (36), (41), (43), (51), (61), (183), (184),
% 198.01/32.48  | | | | | | | | | |            (185), (306), (321), (332), (333), (351), (387),
% 198.01/32.48  | | | | | | | | | |            (405), (547), (555), (564), (569), (573), (610),
% 198.01/32.48  | | | | | | | | | |            (10030), (10903), (function-axioms) are
% 198.01/32.48  | | | | | | | | | |            inconsistent by sub-proof #302.
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | Case 2:
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | |   (10904)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 198.01/32.48  | | | | | | | | | |            all_52_14 = e0
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 198.01/32.48  | | | | | | | | | |            (51), (61), (63), (157), (158), (162), (166),
% 198.01/32.48  | | | | | | | | | |            (167), (168), (169), (173), (174), (175), (178),
% 198.01/32.48  | | | | | | | | | |            (179), (180), (182), (183), (185), (270), (273),
% 198.01/32.48  | | | | | | | | | |            (276), (277), (278), (280), (282), (283), (284),
% 198.01/32.48  | | | | | | | | | |            (306), (309), (313), (314), (316), (317), (320),
% 198.01/32.48  | | | | | | | | | |            (321), (324), (325), (326), (329), (330), (332),
% 198.01/32.48  | | | | | | | | | |            (333), (351), (366), (367), (372), (387), (388),
% 198.01/32.48  | | | | | | | | | |            (393), (394), (405), (415), (421), (427), (431),
% 198.01/32.48  | | | | | | | | | |            (538), (539), (541), (542), (543), (544), (545),
% 198.01/32.48  | | | | | | | | | |            (546), (547), (548), (549), (551), (553), (555),
% 198.01/32.48  | | | | | | | | | |            (557), (559), (561), (562), (563), (564), (567),
% 198.01/32.48  | | | | | | | | | |            (568), (569), (570), (571), (572), (573), (574),
% 198.01/32.48  | | | | | | | | | |            (575), (576), (577), (578), (580), (582), (586),
% 198.01/32.48  | | | | | | | | | |            (587), (590), (591), (593), (594), (600), (603),
% 198.01/32.48  | | | | | | | | | |            (604), (606), (607), (608), (610), (611), (613),
% 198.01/32.48  | | | | | | | | | |            (7443), (7445), (7449), (7451), (7453), (7458),
% 198.01/32.48  | | | | | | | | | |            (10028), (10030), (10890), (10892), (10899),
% 198.01/32.48  | | | | | | | | | |            (10900), (10904), (function-axioms) are
% 198.01/32.48  | | | | | | | | | |            inconsistent by sub-proof #6.
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | End of split
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | Case 2:
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | |   (10905)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 198.01/32.48  | | | | | | | | |              all_52_22 = e0) | (all_52_24 = e3 & all_52_26 =
% 198.01/32.48  | | | | | | | | |              e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | BETA: splitting (10905) gives:
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | Case 1:
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | |   (10906)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 198.01/32.48  | | | | | | | | | |            all_52_22 = e0
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | ALPHA: (10906) implies:
% 198.01/32.48  | | | | | | | | | |   (10907)  all_52_22 = e0
% 198.01/32.48  | | | | | | | | | |   (10908)  all_52_20 = e1
% 198.01/32.48  | | | | | | | | | |   (10909)  all_52_18 = e2
% 198.01/32.48  | | | | | | | | | |   (10910)  all_52_16 = e3
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REDUCE: (178), (10910) imply:
% 198.01/32.48  | | | | | | | | | |   (10911)  op(all_52_17, all_52_17) = e3
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REDUCE: (175), (10907) imply:
% 198.01/32.48  | | | | | | | | | |   (10912)  op(all_52_23, all_52_23) = e0
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REDUCE: (612), (10908) imply:
% 198.01/32.48  | | | | | | | | | |   (10913)  op(all_10_2, all_10_2) = e1
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REDUCE: (7459), (10909) imply:
% 198.01/32.48  | | | | | | | | | |   (10914)  op(all_4_0, all_4_0) = e2
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (41), (43), (51),
% 198.01/32.48  | | | | | | | | | |            (53), (61), (158), (159), (161), (168), (169),
% 198.01/32.48  | | | | | | | | | |            (173), (174), (179), (182), (183), (185), (270),
% 198.01/32.48  | | | | | | | | | |            (273), (276), (278), (279), (283), (285), (306),
% 198.01/32.48  | | | | | | | | | |            (309), (313), (316), (317), (321), (325), (327),
% 198.01/32.48  | | | | | | | | | |            (331), (332), (333), (351), (366), (372), (375),
% 198.01/32.48  | | | | | | | | | |            (387), (393), (405), (415), (421), (427), (431),
% 198.01/32.48  | | | | | | | | | |            (538), (540), (541), (542), (543), (544), (545),
% 198.01/32.48  | | | | | | | | | |            (546), (547), (548), (549), (551), (555), (557),
% 198.01/32.48  | | | | | | | | | |            (559), (561), (563), (564), (566), (567), (569),
% 198.01/32.48  | | | | | | | | | |            (572), (573), (574), (575), (576), (577), (578),
% 198.01/32.48  | | | | | | | | | |            (586), (587), (588), (590), (591), (593), (596),
% 198.01/32.48  | | | | | | | | | |            (600), (602), (603), (604), (606), (607), (608),
% 198.01/32.48  | | | | | | | | | |            (611), (7443), (7445), (7448), (7449), (7450),
% 198.01/32.48  | | | | | | | | | |            (7451), (10028), (10030), (10728), (10892),
% 198.01/32.48  | | | | | | | | | |            (10901), (10911), (10912), (10913), (10914),
% 198.01/32.48  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 198.01/32.48  | | | | | | | | | |            #3.
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | Case 2:
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | |   (10915)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 198.01/32.48  | | | | | | | | | |            all_52_30 = e0
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43),
% 198.01/32.48  | | | | | | | | | |            (51), (53), (61), (63), (158), (162), (166),
% 198.01/32.48  | | | | | | | | | |            (167), (168), (169), (172), (173), (174), (175),
% 198.01/32.48  | | | | | | | | | |            (177), (178), (179), (180), (182), (183), (184),
% 198.01/32.48  | | | | | | | | | |            (185), (270), (271), (272), (273), (274), (277),
% 198.01/32.48  | | | | | | | | | |            (280), (281), (282), (283), (284), (285), (306),
% 198.01/32.48  | | | | | | | | | |            (307), (309), (311), (313), (315), (316), (319),
% 198.01/32.48  | | | | | | | | | |            (320), (321), (323), (324), (325), (326), (327),
% 198.01/32.48  | | | | | | | | | |            (328), (330), (331), (332), (333), (343), (346),
% 198.01/32.48  | | | | | | | | | |            (351), (352), (366), (367), (372), (375), (387),
% 198.01/32.48  | | | | | | | | | |            (388), (393), (394), (405), (411), (415), (431),
% 198.01/32.48  | | | | | | | | | |            (529), (538), (539), (540), (541), (542), (543),
% 198.01/32.48  | | | | | | | | | |            (544), (545), (546), (547), (548), (549), (551),
% 198.01/32.48  | | | | | | | | | |            (553), (555), (557), (559), (561), (562), (563),
% 198.01/32.48  | | | | | | | | | |            (564), (566), (567), (569), (570), (571), (572),
% 198.01/32.48  | | | | | | | | | |            (573), (574), (575), (576), (578), (582), (584),
% 198.01/32.48  | | | | | | | | | |            (586), (587), (590), (591), (592), (593), (594),
% 198.01/32.48  | | | | | | | | | |            (595), (596), (598), (600), (602), (603), (604),
% 198.01/32.48  | | | | | | | | | |            (605), (606), (607), (608), (609), (610), (613),
% 198.01/32.48  | | | | | | | | | |            (641), (10028), (10030), (10895), (10899),
% 198.01/32.48  | | | | | | | | | |            (10901), (10915), (function-axioms) are
% 198.01/32.48  | | | | | | | | | |            inconsistent by sub-proof #271.
% 198.01/32.48  | | | | | | | | | | 
% 198.01/32.48  | | | | | | | | | End of split
% 198.01/32.48  | | | | | | | | | 
% 198.01/32.48  | | | | | | | | End of split
% 198.01/32.48  | | | | | | | | 
% 198.01/32.48  | | | | | | | End of split
% 198.01/32.48  | | | | | | | 
% 198.01/32.48  | | | | | | End of split
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | Case 2:
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | |   (10916)  all_28_0 = e3
% 198.01/32.48  | | | | | |   (10917)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | COMBINE_EQS: (754), (10916) imply:
% 198.01/32.48  | | | | | |   (10918)  all_4_0 = e3
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | COMBINE_EQS: (7449), (10918) imply:
% 198.01/32.48  | | | | | |   (10919)  all_58_5 = e3
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (7450), (10918) imply:
% 198.01/32.48  | | | | | |   (10920)   ~ (all_52_3 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (7451), (10918) imply:
% 198.01/32.48  | | | | | |   (10921)   ~ (all_52_17 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (7453), (10918) imply:
% 198.01/32.48  | | | | | |   (10922)   ~ (all_52_23 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (7455), (10918) imply:
% 198.01/32.48  | | | | | |   (10923)   ~ (all_52_27 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (7458), (10918) imply:
% 198.01/32.48  | | | | | |   (10924)   ~ (all_4_2 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | SIMP: (10924) implies:
% 198.01/32.48  | | | | | |   (10925)   ~ (all_4_2 = e3)
% 198.01/32.48  | | | | | | 
% 198.01/32.48  | | | | | | REDUCE: (7459), (10918) imply:
% 198.01/32.48  | | | | | |   (10926)  op(e3, e3) = all_52_18
% 198.01/32.48  | | | | | | 
% 198.01/32.49  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (43), (51),
% 198.01/32.49  | | | | | |            (53), (61), (63), (144), (158), (161), (162), (166),
% 198.01/32.49  | | | | | |            (167), (168), (169), (172), (173), (174), (175), (177),
% 198.01/32.49  | | | | | |            (178), (179), (180), (182), (183), (184), (185), (187),
% 198.01/32.49  | | | | | |            (270), (271), (272), (273), (274), (277), (278), (280),
% 198.01/32.49  | | | | | |            (281), (282), (283), (284), (285), (303), (306), (307),
% 198.01/32.49  | | | | | |            (309), (311), (313), (315), (316), (318), (319), (320),
% 198.01/32.49  | | | | | |            (321), (323), (324), (325), (326), (327), (328), (330),
% 198.01/32.49  | | | | | |            (331), (332), (333), (343), (346), (351), (352), (366),
% 198.01/32.49  | | | | | |            (367), (372), (375), (376), (387), (388), (393), (394),
% 198.01/32.49  | | | | | |            (405), (411), (415), (427), (431), (529), (538), (539),
% 198.01/32.49  | | | | | |            (540), (541), (542), (543), (544), (545), (546), (547),
% 198.01/32.49  | | | | | |            (548), (549), (551), (553), (555), (557), (559), (561),
% 198.01/32.49  | | | | | |            (562), (563), (564), (566), (567), (569), (570), (571),
% 198.01/32.49  | | | | | |            (572), (573), (574), (575), (576), (577), (578), (580),
% 198.01/32.49  | | | | | |            (582), (584), (586), (587), (590), (591), (592), (593),
% 198.01/32.49  | | | | | |            (594), (595), (596), (598), (600), (602), (603), (604),
% 198.01/32.49  | | | | | |            (605), (606), (607), (608), (609), (610), (613), (641),
% 198.01/32.49  | | | | | |            (7444), (7445), (10028), (10029), (10030), (10890),
% 198.01/32.49  | | | | | |            (10917), (10919), (10920), (10921), (10922), (10923),
% 198.01/32.49  | | | | | |            (10925), (10926), (function-axioms) are inconsistent by
% 198.01/32.49  | | | | | |            sub-proof #5.
% 198.01/32.49  | | | | | | 
% 198.01/32.49  | | | | | End of split
% 198.01/32.49  | | | | | 
% 198.01/32.49  | | | | End of split
% 198.01/32.49  | | | | 
% 198.01/32.49  | | | End of split
% 198.01/32.49  | | | 
% 198.01/32.49  | | End of split
% 198.01/32.49  | | 
% 198.01/32.49  | End of split
% 198.01/32.49  | 
% 198.01/32.49  End of proof
% 198.01/32.49  
% 198.01/32.49  Sub-proof #1 shows that the following formulas are inconsistent:
% 198.01/32.49  ----------------------------------------------------------------
% 198.01/32.49    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.49    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.49    (3)  all_58_14 = all_52_23
% 198.01/32.49    (4)   ~ (e3 = e1)
% 198.01/32.49    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.49    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.01/32.49    (7)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.49    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.49    (9)   ~ (all_52_5 = all_52_13)
% 198.01/32.49    (10)  all_58_1 = all_52_9
% 198.01/32.49    (11)   ~ (all_52_9 = all_52_13)
% 198.01/32.49    (12)   ~ (e3 = e0)
% 198.01/32.49    (13)  op(e2, e3) = all_52_3
% 198.01/32.49    (14)   ~ (all_52_23 = all_4_0)
% 198.01/32.49    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.49    (16)   ~ (all_52_7 = all_52_15)
% 198.01/32.49    (17)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.49    (18)   ~ (all_52_17 = all_52_25)
% 198.01/32.49    (19)   ~ (all_52_3 = all_6_2)
% 198.01/32.49    (20)  all_58_0 = all_6_2
% 198.01/32.49    (21)  op(all_14_2, e0) = all_14_1
% 198.01/32.49    (22)  all_56_4 = all_52_3
% 198.01/32.49    (23)  op(e3, all_6_1) = e1
% 198.01/32.49    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.49    (25)  op(e3, e0) = all_52_25
% 198.01/32.49    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.49    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.49    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.49    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.49    (30)  all_58_13 = all_52_15
% 198.01/32.49    (31)  op(all_10_2, all_10_2) = all_52_20
% 198.01/32.49    (32)  all_58_9 = all_52_25
% 198.01/32.49    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.01/32.49    (34)   ~ (all_52_29 = all_14_2)
% 198.01/32.49    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.49    (36)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.49    (37)  op(e1, e3) = all_52_5
% 198.01/32.49    (38)  op(e2, e2) = all_4_2
% 198.01/32.49    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.49    (40)   ~ (all_52_3 = all_52_5)
% 198.01/32.49    (41)  op(all_4_2, e2) = e1
% 198.01/32.49    (42)  all_58_11 = all_52_29
% 198.01/32.49    (43)  all_56_5 = all_4_2
% 198.01/32.49    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.49    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.49    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.49    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.49    (48)  all_46_2 = all_6_2
% 198.01/32.49    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.49    (50)   ~ (all_52_7 = all_6_2)
% 198.01/32.49    (51)  op(e0, e0) = all_14_2
% 198.01/32.49    (52)  all_56_15 = all_14_2
% 198.01/32.49    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.49    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.49    (55)  op(e1, e0) = all_52_29
% 198.01/32.49    (56)   ~ (all_58_15 = e0)
% 198.01/32.49    (57)  all_56_11 = all_52_29
% 198.01/32.49    (58)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.49    (59)   ~ (all_4_0 = e3)
% 198.01/32.49    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.49    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.49    (62)  op(e1, all_10_1) = e3
% 198.01/32.49    (63)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.49    (64)  all_56_9 = all_52_13
% 198.01/32.49    (65)   ~ (e2 = e1)
% 198.01/32.49    (66)   ~ (all_52_13 = all_10_2)
% 198.01/32.49    (67)  all_58_10 = all_52_27
% 198.01/32.49    (68)  all_56_8 = all_52_5
% 198.01/32.49    (69)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.49    (70)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.49    (71)   ~ (all_52_25 = all_52_29)
% 198.01/32.49    (72)   ~ (all_52_29 = all_10_2)
% 198.01/32.49    (73)  all_58_7 = all_52_13
% 198.01/32.49    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.49    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.49    (76)   ~ (all_52_5 = all_52_7)
% 198.01/32.49    (77)  all_58_12 = all_52_7
% 198.01/32.49    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.49    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.49    (80)   ~ (all_52_7 = all_14_2)
% 198.01/32.49    (81)  all_58_2 = all_52_3
% 198.01/32.49    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.01/32.49    (83)  all_56_2 = all_52_17
% 198.01/32.49    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.49    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.49    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.49    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.49    (88)  all_56_7 = all_52_27
% 198.01/32.49    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.49    (90)   ~ (e2 = e0)
% 198.01/32.49    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.49    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.01/32.49    (93)   ~ (all_52_5 = all_52_29)
% 198.01/32.49    (94)   ~ (all_52_15 = all_14_2)
% 198.01/32.49    (95)   ~ (all_52_19 = all_52_27)
% 198.01/32.49    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.49    (97)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.49    (98)   ~ (all_52_13 = all_4_2)
% 198.01/32.49    (99)  op(e3, e1) = all_52_17
% 198.01/32.49    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.49    (101)  op(e0, e3) = all_52_7
% 198.01/32.49    (102)  op(e1, e2) = all_52_13
% 198.01/32.49    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.49    (104)   ~ (all_52_9 = all_52_25)
% 198.01/32.49    (105)  all_58_15 = all_14_2
% 198.01/32.49    (106)   ~ (all_52_19 = all_10_2)
% 198.01/32.49    (107)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.49    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.49    (109)  all_58_8 = all_10_2
% 198.01/32.49    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.49    (111)   ~ (all_52_5 = all_10_2)
% 198.01/32.49    (112)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.49    (113)   ~ (all_52_23 = all_14_2)
% 198.01/32.49    (114)  all_56_12 = all_52_7
% 198.01/32.49    (115)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.49    (116)  all_58_5 = all_4_0
% 198.01/32.49    (117)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.49    (118)   ~ (all_52_25 = all_6_2)
% 198.01/32.49    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.49    (120)   ~ (all_52_9 = all_4_2)
% 198.01/32.49    (121)   ~ (all_52_5 = all_6_2)
% 198.01/32.49    (122)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.49    (123)   ~ (all_52_9 = all_6_2)
% 198.01/32.49    (124)   ~ (all_52_13 = all_52_15)
% 198.01/32.49    (125)  all_56_0 = all_6_2
% 198.01/32.49    (126)  op(all_4_0, all_4_0) = all_52_18
% 198.01/32.49    (127)  op(e3, e3) = all_6_2
% 198.01/32.49    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.49    (129)   ~ (all_52_27 = all_14_2)
% 198.01/32.49    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.49    (131)  all_56_14 = all_52_23
% 198.01/32.49    (132)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.49    (133)  all_56_3 = all_52_25
% 198.01/32.49    (134)   ~ (all_52_3 = all_52_7)
% 198.01/32.49    (135)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.49    (136)  all_58_5 = all_52_19
% 198.01/32.49    (137)  all_56_1 = all_52_9
% 198.01/32.49    (138)   ~ (all_52_15 = all_4_2)
% 198.01/32.49    (139)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.49           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.49           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.49           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.49    (140)   ~ (all_52_27 = all_4_2)
% 198.01/32.49    (141)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 198.01/32.49             all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.49    (142)  all_58_6 = all_52_5
% 198.01/32.49    (143)   ~ (all_4_0 = all_4_2)
% 198.01/32.49    (144)  op(e3, e2) = all_52_9
% 198.01/32.49    (145)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.49    (146)  all_56_6 = all_4_0
% 198.01/32.49    (147)   ~ (all_52_17 = all_6_2)
% 198.01/32.49    (148)   ~ (e1 = e0)
% 198.01/32.49    (149)   ~ (e3 = e2)
% 198.01/32.49    (150)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.49    (151)   ~ (all_52_9 = all_52_17)
% 198.01/32.49    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.49    (153)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.49    (154)   ~ (all_52_3 = all_4_0)
% 198.01/32.49    (155)  all_46_1 = all_6_1
% 198.01/32.49    (156)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.49    (157)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.49    (158)  op(e1, e1) = all_10_2
% 198.01/32.49    (159)   ~ (all_52_23 = all_10_2)
% 198.01/32.49    (160)   ~ (all_52_7 = all_52_23)
% 198.01/32.49    (161)   ~ (all_52_17 = all_52_19)
% 198.01/32.49    (162)  all_58_3 = all_4_2
% 198.01/32.49    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.49    (164)  all_56_13 = all_52_15
% 198.01/32.49    (165)   ~ (all_52_3 = all_4_2)
% 198.01/32.49    (166)   ~ (all_52_19 = all_4_2)
% 198.01/32.49    (167)   ~ (all_52_17 = all_52_23)
% 198.01/32.49    (168)  op(all_6_2, e3) = all_6_1
% 198.01/32.49    (169)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.49    (170)  all_58_4 = all_52_17
% 198.01/32.49    (171)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.49  
% 198.01/32.49  Begin of proof
% 198.01/32.49  | 
% 198.01/32.49  | ALPHA: (141) implies:
% 198.01/32.49  |   (172)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.49  |   (173)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.49  | 
% 198.01/32.49  | REDUCE: (56), (105) imply:
% 198.01/32.49  |   (174)   ~ (all_14_2 = e0)
% 198.01/32.49  | 
% 198.01/32.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.49  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 198.01/32.49  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.01/32.49  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.01/32.49  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (57),
% 198.01/32.49  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 198.01/32.49  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 198.01/32.49  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 198.01/32.49  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 198.01/32.49  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 198.01/32.49  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 198.01/32.49  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 198.01/32.49  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 198.01/32.49  |            (138), (139), (140), (142), (143), (144), (145), (146), (147),
% 198.01/32.49  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 198.01/32.49  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 198.01/32.49  |            (166), (167), (168), (169), (170), (171), (172), (173), (174) are
% 198.01/32.49  |            inconsistent by sub-proof #2.
% 198.01/32.49  | 
% 198.01/32.49  End of proof
% 198.01/32.49  
% 198.01/32.49  Sub-proof #2 shows that the following formulas are inconsistent:
% 198.01/32.49  ----------------------------------------------------------------
% 198.01/32.49    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.49    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.49    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.49    (4)  all_58_14 = all_52_23
% 198.01/32.49    (5)   ~ (e3 = e1)
% 198.01/32.49    (6)   ~ (all_52_17 = all_4_0)
% 198.01/32.49    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.01/32.49    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.49    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.49    (10)   ~ (all_52_5 = all_52_13)
% 198.01/32.49    (11)  all_58_1 = all_52_9
% 198.01/32.49    (12)   ~ (all_52_9 = all_52_13)
% 198.01/32.49    (13)   ~ (e3 = e0)
% 198.01/32.49    (14)  op(e2, e3) = all_52_3
% 198.01/32.49    (15)   ~ (all_52_23 = all_4_0)
% 198.01/32.49    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.49    (17)   ~ (all_52_7 = all_52_15)
% 198.01/32.49    (18)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.49    (19)   ~ (all_52_17 = all_52_25)
% 198.01/32.49    (20)   ~ (all_52_3 = all_6_2)
% 198.01/32.49    (21)  all_58_0 = all_6_2
% 198.01/32.49    (22)  op(all_14_2, e0) = all_14_1
% 198.01/32.49    (23)  all_56_4 = all_52_3
% 198.01/32.49    (24)  op(e3, all_6_1) = e1
% 198.01/32.49    (25)   ~ (all_52_17 = all_10_2)
% 198.01/32.49    (26)  op(e3, e0) = all_52_25
% 198.01/32.49    (27)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.49    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.49    (29)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.49    (30)   ~ (all_52_27 = all_52_29)
% 198.01/32.49    (31)  all_58_13 = all_52_15
% 198.01/32.49    (32)  op(all_10_2, all_10_2) = all_52_20
% 198.01/32.49    (33)  all_58_9 = all_52_25
% 198.01/32.49    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.01/32.49    (35)   ~ (all_52_29 = all_14_2)
% 198.01/32.49    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.49    (37)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.49    (38)  op(e1, e3) = all_52_5
% 198.01/32.49    (39)  op(e2, e2) = all_4_2
% 198.01/32.49    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.50    (41)   ~ (all_52_3 = all_52_5)
% 198.01/32.50    (42)  op(all_4_2, e2) = e1
% 198.01/32.50    (43)  all_58_11 = all_52_29
% 198.01/32.50    (44)  all_56_5 = all_4_2
% 198.01/32.50    (45)   ~ (all_52_25 = all_14_2)
% 198.01/32.50    (46)   ~ (all_52_9 = all_52_15)
% 198.01/32.50    (47)   ~ (all_52_3 = all_52_27)
% 198.01/32.50    (48)  op(all_10_2, e1) = all_10_1
% 198.01/32.50    (49)  all_46_2 = all_6_2
% 198.01/32.50    (50)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.50    (51)   ~ (all_52_7 = all_6_2)
% 198.01/32.50    (52)  op(e0, e0) = all_14_2
% 198.01/32.50    (53)  all_56_15 = all_14_2
% 198.01/32.50    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.50    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.50    (56)  op(e1, e0) = all_52_29
% 198.01/32.50    (57)  all_56_11 = all_52_29
% 198.01/32.50    (58)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.50    (59)   ~ (all_4_0 = e3)
% 198.01/32.50    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.50    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.50    (62)  op(e1, all_10_1) = e3
% 198.01/32.50    (63)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.50    (64)  all_56_9 = all_52_13
% 198.01/32.50    (65)   ~ (e2 = e1)
% 198.01/32.50    (66)   ~ (all_52_13 = all_10_2)
% 198.01/32.50    (67)  all_58_10 = all_52_27
% 198.01/32.50    (68)  all_56_8 = all_52_5
% 198.01/32.50    (69)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.50    (70)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.50    (71)   ~ (all_52_25 = all_52_29)
% 198.01/32.50    (72)   ~ (all_52_29 = all_10_2)
% 198.01/32.50    (73)  all_58_7 = all_52_13
% 198.01/32.50    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.50    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.50    (76)   ~ (all_52_5 = all_52_7)
% 198.01/32.50    (77)  all_58_12 = all_52_7
% 198.01/32.50    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.50    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.50    (80)   ~ (all_52_7 = all_14_2)
% 198.01/32.50    (81)   ~ (all_14_2 = e0)
% 198.01/32.50    (82)  all_58_2 = all_52_3
% 198.01/32.50    (83)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.01/32.50    (84)  all_56_2 = all_52_17
% 198.01/32.50    (85)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.50    (86)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.50    (87)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.50    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.50    (89)  all_56_7 = all_52_27
% 198.01/32.50    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.50    (91)   ~ (e2 = e0)
% 198.01/32.50    (92)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.50    (93)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.01/32.50    (94)   ~ (all_52_5 = all_52_29)
% 198.01/32.50    (95)   ~ (all_52_15 = all_14_2)
% 198.01/32.50    (96)   ~ (all_52_19 = all_52_27)
% 198.01/32.50    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.50    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.50    (99)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.50    (100)   ~ (all_52_13 = all_4_2)
% 198.01/32.50    (101)  op(e3, e1) = all_52_17
% 198.01/32.50    (102)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.50    (103)  op(e0, e3) = all_52_7
% 198.01/32.50    (104)  op(e1, e2) = all_52_13
% 198.01/32.50    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.50    (106)   ~ (all_52_9 = all_52_25)
% 198.01/32.50    (107)  all_58_15 = all_14_2
% 198.01/32.50    (108)   ~ (all_52_19 = all_10_2)
% 198.01/32.50    (109)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.50    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.50    (111)  all_58_8 = all_10_2
% 198.01/32.50    (112)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.50    (113)   ~ (all_52_5 = all_10_2)
% 198.01/32.50    (114)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.50    (115)   ~ (all_52_23 = all_14_2)
% 198.01/32.50    (116)  all_56_12 = all_52_7
% 198.01/32.50    (117)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.50    (118)  all_58_5 = all_4_0
% 198.01/32.50    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.50    (120)   ~ (all_52_25 = all_6_2)
% 198.01/32.50    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.50    (122)   ~ (all_52_9 = all_4_2)
% 198.01/32.50    (123)   ~ (all_52_5 = all_6_2)
% 198.01/32.50    (124)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.50    (125)   ~ (all_52_9 = all_6_2)
% 198.01/32.50    (126)   ~ (all_52_13 = all_52_15)
% 198.01/32.50    (127)  all_56_0 = all_6_2
% 198.01/32.50    (128)  op(all_4_0, all_4_0) = all_52_18
% 198.01/32.50    (129)  op(e3, e3) = all_6_2
% 198.01/32.50    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.50    (131)   ~ (all_52_27 = all_14_2)
% 198.01/32.50    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.50    (133)  all_56_14 = all_52_23
% 198.01/32.50    (134)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.50    (135)  all_56_3 = all_52_25
% 198.01/32.50    (136)   ~ (all_52_3 = all_52_7)
% 198.01/32.50    (137)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.50    (138)  all_58_5 = all_52_19
% 198.01/32.50    (139)  all_56_1 = all_52_9
% 198.01/32.50    (140)   ~ (all_52_15 = all_4_2)
% 198.01/32.50    (141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.50           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.50           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.50           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.50    (142)   ~ (all_52_27 = all_4_2)
% 198.01/32.50    (143)  all_58_6 = all_52_5
% 198.01/32.50    (144)   ~ (all_4_0 = all_4_2)
% 198.01/32.50    (145)  op(e3, e2) = all_52_9
% 198.01/32.50    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.50    (147)  all_56_6 = all_4_0
% 198.01/32.50    (148)   ~ (all_52_17 = all_6_2)
% 198.01/32.50    (149)   ~ (e1 = e0)
% 198.01/32.50    (150)   ~ (e3 = e2)
% 198.01/32.50    (151)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.50    (152)   ~ (all_52_9 = all_52_17)
% 198.01/32.50    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.50    (154)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.50    (155)   ~ (all_52_3 = all_4_0)
% 198.01/32.50    (156)  all_46_1 = all_6_1
% 198.01/32.50    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.50    (158)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.50    (159)  op(e1, e1) = all_10_2
% 198.01/32.50    (160)   ~ (all_52_23 = all_10_2)
% 198.01/32.50    (161)   ~ (all_52_7 = all_52_23)
% 198.01/32.50    (162)   ~ (all_52_17 = all_52_19)
% 198.01/32.50    (163)  all_58_3 = all_4_2
% 198.01/32.50    (164)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.50    (165)  all_56_13 = all_52_15
% 198.01/32.50    (166)   ~ (all_52_3 = all_4_2)
% 198.01/32.50    (167)   ~ (all_52_19 = all_4_2)
% 198.01/32.50    (168)   ~ (all_52_17 = all_52_23)
% 198.01/32.50    (169)  op(all_6_2, e3) = all_6_1
% 198.01/32.50    (170)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.50    (171)  all_58_4 = all_52_17
% 198.01/32.50    (172)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.50  
% 198.01/32.50  Begin of proof
% 198.01/32.50  | 
% 198.01/32.50  | BETA: splitting (141) gives:
% 198.01/32.50  | 
% 198.01/32.50  | Case 1:
% 198.01/32.50  | | 
% 198.01/32.50  | |   (173)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.50  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 198.01/32.50  | | 
% 198.01/32.50  | | BETA: splitting (173) gives:
% 198.01/32.50  | | 
% 198.01/32.50  | | Case 1:
% 198.01/32.50  | | | 
% 198.01/32.50  | | |   (174)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REF_CLOSE: (5), (8), (9), (18), (21), (24), (27), (39), (50), (51), (52),
% 198.01/32.50  | | |            (54), (77), (80), (82), (86), (113), (129), (132), (143),
% 198.01/32.50  | | |            (146), (159), (166), (169), (174) are inconsistent by sub-proof
% 198.01/32.50  | | |            #302.
% 198.01/32.50  | | | 
% 198.01/32.50  | | Case 2:
% 198.01/32.50  | | | 
% 198.01/32.50  | | |   (175)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.50  | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (24),
% 198.01/32.50  | | |            (25), (26), (28), (30), (31), (33), (34), (35), (37), (38),
% 198.01/32.50  | | |            (39), (40), (41), (42), (43), (44), (45), (46), (50), (51),
% 198.01/32.50  | | |            (52), (53), (54), (59), (61), (64), (65), (67), (68), (69),
% 198.01/32.50  | | |            (70), (73), (76), (77), (78), (79), (80), (82), (84), (86),
% 198.01/32.50  | | |            (89), (91), (92), (93), (94), (95), (98), (99), (100), (101),
% 198.01/32.50  | | |            (102), (103), (105), (106), (107), (109), (110), (111), (112),
% 198.01/32.50  | | |            (113), (115), (116), (117), (118), (120), (122), (123), (124),
% 198.01/32.50  | | |            (125), (126), (129), (130), (131), (132), (134), (136), (137),
% 198.01/32.50  | | |            (139), (140), (142), (143), (144), (145), (146), (148), (149),
% 198.01/32.50  | | |            (150), (151), (152), (153), (154), (158), (159), (160), (161),
% 198.01/32.50  | | |            (163), (166), (168), (169), (170), (171), (172), (175) are
% 198.01/32.50  | | |            inconsistent by sub-proof #32.
% 198.01/32.50  | | | 
% 198.01/32.50  | | End of split
% 198.01/32.50  | | 
% 198.01/32.50  | Case 2:
% 198.01/32.50  | | 
% 198.01/32.50  | |   (176)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 198.01/32.50  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 198.01/32.50  | |            e0)
% 198.01/32.50  | | 
% 198.01/32.50  | | BETA: splitting (176) gives:
% 198.01/32.50  | | 
% 198.01/32.50  | | Case 1:
% 198.01/32.50  | | | 
% 198.01/32.50  | | |   (177)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.01/32.50  | | | 
% 198.01/32.50  | | | ALPHA: (177) implies:
% 198.01/32.50  | | |   (178)  all_52_22 = e0
% 198.01/32.50  | | |   (179)  all_52_20 = e1
% 198.01/32.50  | | |   (180)  all_52_18 = e2
% 198.01/32.50  | | |   (181)  all_52_16 = e3
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REDUCE: (117), (181) imply:
% 198.01/32.50  | | |   (182)  op(all_52_17, all_52_17) = e3
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REDUCE: (109), (178) imply:
% 198.01/32.50  | | |   (183)  op(all_52_23, all_52_23) = e0
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REDUCE: (32), (179) imply:
% 198.01/32.50  | | |   (184)  op(all_10_2, all_10_2) = e1
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REDUCE: (128), (180) imply:
% 198.01/32.50  | | |   (185)  op(all_4_0, all_4_0) = e2
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (11), (12), (16), (18),
% 198.01/32.50  | | |            (20), (21), (24), (25), (28), (30), (31), (33), (37), (39),
% 198.01/32.50  | | |            (42), (43), (45), (46), (47), (48), (51), (52), (53), (54),
% 198.01/32.50  | | |            (56), (59), (61), (62), (64), (65), (66), (67), (69), (70),
% 198.01/32.50  | | |            (72), (73), (76), (77), (78), (79), (80), (81), (82), (83),
% 198.01/32.50  | | |            (84), (85), (86), (87), (89), (91), (95), (101), (102), (103),
% 198.01/32.50  | | |            (104), (105), (106), (107), (108), (111), (112), (113), (115),
% 198.01/32.50  | | |            (116), (118), (120), (122), (124), (125), (126), (127), (129),
% 198.01/32.50  | | |            (130), (131), (132), (134), (136), (138), (142), (143), (145),
% 198.01/32.50  | | |            (146), (147), (148), (149), (150), (152), (153), (154), (155),
% 198.01/32.50  | | |            (157), (159), (160), (161), (163), (166), (169), (171), (172),
% 198.01/32.50  | | |            (182), (183), (184), (185) are inconsistent by sub-proof #3.
% 198.01/32.50  | | | 
% 198.01/32.50  | | Case 2:
% 198.01/32.50  | | | 
% 198.01/32.50  | | |   (186)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (12), (13), (14), (16),
% 198.01/32.50  | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 198.01/32.50  | | |            (27), (29), (30), (31), (33), (35), (36), (37), (38), (39),
% 198.01/32.50  | | |            (40), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 198.01/32.50  | | |            (51), (52), (53), (54), (55), (57), (58), (60), (61), (63),
% 198.01/32.50  | | |            (65), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 198.01/32.50  | | |            (76), (77), (78), (79), (80), (81), (82), (84), (85), (86),
% 198.01/32.50  | | |            (87), (88), (90), (91), (92), (94), (95), (96), (97), (98),
% 198.01/32.50  | | |            (99), (101), (102), (103), (105), (106), (107), (108), (109),
% 198.01/32.50  | | |            (110), (111), (112), (113), (114), (115), (116), (117), (119),
% 198.01/32.50  | | |            (120), (121), (122), (123), (125), (126), (127), (129), (130),
% 198.01/32.50  | | |            (131), (132), (133), (135), (136), (137), (138), (139), (140),
% 198.01/32.50  | | |            (142), (143), (145), (146), (148), (149), (150), (151), (156),
% 198.01/32.50  | | |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 198.01/32.50  | | |            (166), (167), (168), (169), (170), (171), (172), (186) are
% 198.01/32.50  | | |            inconsistent by sub-proof #271.
% 198.01/32.50  | | | 
% 198.01/32.50  | | End of split
% 198.01/32.50  | | 
% 198.01/32.50  | End of split
% 198.01/32.50  | 
% 198.01/32.50  End of proof
% 198.01/32.50  
% 198.01/32.50  Sub-proof #3 shows that the following formulas are inconsistent:
% 198.01/32.50  ----------------------------------------------------------------
% 198.01/32.50    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.50    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.50    (3)  all_58_14 = all_52_23
% 198.01/32.50    (4)   ~ (e3 = e1)
% 198.01/32.50    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.50    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.50    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.50    (8)  all_58_1 = all_52_9
% 198.01/32.50    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.50    (10)  op(all_52_23, all_52_23) = e0
% 198.01/32.50    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.50    (12)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.50    (13)   ~ (all_52_3 = all_6_2)
% 198.01/32.50    (14)  all_58_0 = all_6_2
% 198.01/32.50    (15)  op(e3, all_6_1) = e1
% 198.01/32.50    (16)   ~ (all_52_17 = all_10_2)
% 198.01/32.50    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.50    (18)   ~ (all_52_27 = all_52_29)
% 198.01/32.50    (19)  all_58_13 = all_52_15
% 198.01/32.50    (20)  all_58_9 = all_52_25
% 198.01/32.50    (21)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.50    (22)  op(e2, e2) = all_4_2
% 198.01/32.50    (23)  op(all_4_2, e2) = e1
% 198.01/32.50    (24)  all_58_11 = all_52_29
% 198.01/32.50    (25)   ~ (all_52_25 = all_14_2)
% 198.01/32.50    (26)   ~ (all_52_9 = all_52_15)
% 198.01/32.50    (27)   ~ (all_52_3 = all_52_27)
% 198.01/32.50    (28)  op(all_10_2, e1) = all_10_1
% 198.01/32.50    (29)   ~ (all_52_7 = all_6_2)
% 198.01/32.50    (30)  op(e0, e0) = all_14_2
% 198.01/32.50    (31)  all_56_15 = all_14_2
% 198.01/32.50    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.50    (33)  op(e1, e0) = all_52_29
% 198.01/32.50    (34)   ~ (all_4_0 = e3)
% 198.01/32.50    (35)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.50    (36)  op(e1, all_10_1) = e3
% 198.01/32.50    (37)  all_56_9 = all_52_13
% 198.01/32.50    (38)   ~ (e2 = e1)
% 198.01/32.50    (39)   ~ (all_52_13 = all_10_2)
% 198.01/32.50    (40)  op(all_10_2, all_10_2) = e1
% 198.01/32.50    (41)  all_58_10 = all_52_27
% 198.01/32.50    (42)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.50    (43)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.50    (44)   ~ (all_52_29 = all_10_2)
% 198.01/32.50    (45)  all_58_7 = all_52_13
% 198.01/32.50    (46)  op(all_4_0, all_4_0) = e2
% 198.01/32.50    (47)   ~ (all_52_5 = all_52_7)
% 198.01/32.50    (48)  all_58_12 = all_52_7
% 198.01/32.50    (49)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.50    (50)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.50    (51)   ~ (all_52_7 = all_14_2)
% 198.01/32.50    (52)   ~ (all_14_2 = e0)
% 198.01/32.50    (53)  all_58_2 = all_52_3
% 198.01/32.50    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.01/32.50    (55)  all_56_2 = all_52_17
% 198.01/32.50    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.50    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.50    (58)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.50    (59)  all_56_7 = all_52_27
% 198.01/32.50    (60)   ~ (e2 = e0)
% 198.01/32.50    (61)   ~ (all_52_15 = all_14_2)
% 198.01/32.50    (62)  op(e3, e1) = all_52_17
% 198.01/32.50    (63)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.50    (64)  op(e0, e3) = all_52_7
% 198.01/32.50    (65)  op(e1, e2) = all_52_13
% 198.01/32.50    (66)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.50    (67)   ~ (all_52_9 = all_52_25)
% 198.01/32.50    (68)  all_58_15 = all_14_2
% 198.01/32.50    (69)   ~ (all_52_19 = all_10_2)
% 198.01/32.50    (70)  all_58_8 = all_10_2
% 198.01/32.50    (71)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.50    (72)   ~ (all_52_5 = all_10_2)
% 198.01/32.50    (73)   ~ (all_52_23 = all_14_2)
% 198.01/32.50    (74)  all_56_12 = all_52_7
% 198.01/32.50    (75)  all_58_5 = all_4_0
% 198.01/32.50    (76)   ~ (all_52_25 = all_6_2)
% 198.01/32.50    (77)   ~ (all_52_9 = all_4_2)
% 198.01/32.50    (78)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.50    (79)   ~ (all_52_9 = all_6_2)
% 198.01/32.50    (80)   ~ (all_52_13 = all_52_15)
% 198.01/32.50    (81)  all_56_0 = all_6_2
% 198.01/32.50    (82)  op(e3, e3) = all_6_2
% 198.01/32.50    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.50    (84)   ~ (all_52_27 = all_14_2)
% 198.01/32.50    (85)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.50    (86)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.50    (87)   ~ (all_52_3 = all_52_7)
% 198.01/32.50    (88)  all_58_5 = all_52_19
% 198.01/32.50    (89)   ~ (all_52_27 = all_4_2)
% 198.01/32.50    (90)  op(all_52_17, all_52_17) = e3
% 198.01/32.50    (91)  all_58_6 = all_52_5
% 198.01/32.50    (92)  op(e3, e2) = all_52_9
% 198.01/32.50    (93)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.50    (94)  all_56_6 = all_4_0
% 198.01/32.50    (95)   ~ (all_52_17 = all_6_2)
% 198.01/32.50    (96)   ~ (e1 = e0)
% 198.01/32.50    (97)   ~ (e3 = e2)
% 198.01/32.50    (98)   ~ (all_52_9 = all_52_17)
% 198.01/32.50    (99)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.50    (100)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.50    (101)   ~ (all_52_3 = all_4_0)
% 198.01/32.50    (102)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.50    (103)  op(e1, e1) = all_10_2
% 198.01/32.50    (104)   ~ (all_52_23 = all_10_2)
% 198.01/32.50    (105)   ~ (all_52_7 = all_52_23)
% 198.01/32.50    (106)  all_58_3 = all_4_2
% 198.01/32.50    (107)   ~ (all_52_3 = all_4_2)
% 198.01/32.50    (108)  op(all_6_2, e3) = all_6_1
% 198.01/32.50    (109)  all_58_4 = all_52_17
% 198.01/32.50    (110)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.50  
% 198.01/32.50  Begin of proof
% 198.01/32.50  | 
% 198.01/32.50  | BETA: splitting (54) gives:
% 198.01/32.50  | 
% 198.01/32.50  | Case 1:
% 198.01/32.50  | | 
% 198.01/32.50  | |   (111)  all_56_6 = e3
% 198.01/32.50  | | 
% 198.01/32.50  | | COMBINE_EQS: (94), (111) imply:
% 198.01/32.50  | |   (112)  all_4_0 = e3
% 198.01/32.50  | | 
% 198.01/32.50  | | REDUCE: (34), (112) imply:
% 198.01/32.50  | |   (113)  $false
% 198.01/32.50  | | 
% 198.01/32.50  | | CLOSE: (113) is inconsistent.
% 198.01/32.50  | | 
% 198.01/32.50  | Case 2:
% 198.01/32.50  | | 
% 198.01/32.50  | |   (114)   ~ (all_56_6 = e3)
% 198.01/32.50  | |   (115)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.01/32.50  | | 
% 198.01/32.50  | | BETA: splitting (71) gives:
% 198.01/32.50  | | 
% 198.01/32.50  | | Case 1:
% 198.01/32.50  | | | 
% 198.01/32.50  | | |   (116)  all_56_15 = e3
% 198.01/32.50  | | | 
% 198.01/32.50  | | | COMBINE_EQS: (31), (116) imply:
% 198.01/32.50  | | |   (117)  all_14_2 = e3
% 198.01/32.50  | | | 
% 198.01/32.50  | | | SIMP: (117) implies:
% 198.01/32.50  | | |   (118)  all_14_2 = e3
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REF_CLOSE: (3), (4), (7), (8), (9), (14), (16), (19), (20), (22), (25),
% 198.01/32.50  | | |            (26), (28), (33), (34), (36), (38), (40), (44), (45), (48),
% 198.01/32.50  | | |            (51), (52), (53), (56), (57), (58), (60), (62), (66), (70),
% 198.01/32.50  | | |            (72), (73), (75), (77), (79), (82), (85), (90), (91), (95),
% 198.01/32.50  | | |            (96), (97), (99), (106), (107), (109), (118) are inconsistent
% 198.01/32.50  | | |            by sub-proof #48.
% 198.01/32.50  | | | 
% 198.01/32.50  | | Case 2:
% 198.01/32.50  | | | 
% 198.01/32.50  | | |   (119)   ~ (all_56_15 = e3)
% 198.01/32.50  | | |   (120)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.50  | | | 
% 198.01/32.50  | | | REDUCE: (31), (119) imply:
% 198.01/32.50  | | |   (121)   ~ (all_14_2 = e3)
% 198.01/32.50  | | | 
% 198.01/32.50  | | | BETA: splitting (99) gives:
% 198.01/32.50  | | | 
% 198.01/32.50  | | | Case 1:
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | |   (122)  all_58_4 = e3
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | | COMBINE_EQS: (109), (122) imply:
% 198.01/32.50  | | | |   (123)  all_52_17 = e3
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | | SIMP: (123) implies:
% 198.01/32.50  | | | |   (124)  all_52_17 = e3
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | | REF_CLOSE: (7), (82), (90), (95), (124) are inconsistent by sub-proof
% 198.01/32.50  | | | |            #1280.
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | Case 2:
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | |   (125)   ~ (all_58_4 = e3)
% 198.01/32.50  | | | |   (126)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | | REDUCE: (109), (125) imply:
% 198.01/32.50  | | | |   (127)   ~ (all_52_17 = e3)
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | | BETA: splitting (35) gives:
% 198.01/32.50  | | | | 
% 198.01/32.50  | | | | Case 1:
% 198.01/32.50  | | | | | 
% 198.01/32.50  | | | | |   (128)  all_56_2 = e3
% 198.01/32.50  | | | | | 
% 198.01/32.50  | | | | | REF_CLOSE: (55), (127), (128) are inconsistent by sub-proof #1327.
% 198.01/32.50  | | | | | 
% 198.01/32.51  | | | | Case 2:
% 198.01/32.51  | | | | | 
% 198.01/32.51  | | | | |   (129)   ~ (all_56_2 = e3)
% 198.01/32.51  | | | | |   (130)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.51  | | | | | 
% 198.01/32.51  | | | | | BETA: splitting (17) gives:
% 198.01/32.51  | | | | | 
% 198.01/32.51  | | | | | Case 1:
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | |   (131)  all_56_7 = e3
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | COMBINE_EQS: (59), (131) imply:
% 198.01/32.51  | | | | | |   (132)  all_52_27 = e3
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | SIMP: (132) implies:
% 198.01/32.51  | | | | | |   (133)  all_52_27 = e3
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | REDUCE: (27), (133) imply:
% 198.01/32.51  | | | | | |   (134)   ~ (all_52_3 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | REDUCE: (2), (133) imply:
% 198.01/32.51  | | | | | |   (135)   ~ (all_52_25 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | REDUCE: (18), (133) imply:
% 198.01/32.51  | | | | | |   (136)   ~ (all_52_29 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | SIMP: (136) implies:
% 198.01/32.51  | | | | | |   (137)   ~ (all_52_29 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | REDUCE: (84), (133) imply:
% 198.01/32.51  | | | | | |   (138)   ~ (all_14_2 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | REDUCE: (21), (133) imply:
% 198.01/32.51  | | | | | |   (139)  op(e3, e3) = all_52_26
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_26, e3, e3,
% 198.01/32.51  | | | | | |              simplifying with (82), (139) gives:
% 198.01/32.51  | | | | | |   (140)  all_52_26 = all_6_2
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | BETA: splitting (85) gives:
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | Case 1:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | |   (141)  all_58_0 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | COMBINE_EQS: (14), (141) imply:
% 198.01/32.51  | | | | | | |   (142)  all_6_2 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | REF_CLOSE: (4), (7), (15), (82), (108), (142) are inconsistent by
% 198.01/32.51  | | | | | | |            sub-proof #310.
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | Case 2:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | |   (143)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | BETA: splitting (143) gives:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | |   (144)  all_58_1 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | COMBINE_EQS: (8), (144) imply:
% 198.01/32.51  | | | | | | | |   (145)  all_52_9 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (9), (145) imply:
% 198.01/32.51  | | | | | | | |   (146)   ~ (all_52_13 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | SIMP: (146) implies:
% 198.01/32.51  | | | | | | | |   (147)   ~ (all_52_13 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (26), (145) imply:
% 198.01/32.51  | | | | | | | |   (148)   ~ (all_52_15 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | SIMP: (148) implies:
% 198.01/32.51  | | | | | | | |   (149)   ~ (all_52_15 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (77), (145) imply:
% 198.01/32.51  | | | | | | | |   (150)   ~ (all_4_2 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | SIMP: (150) implies:
% 198.01/32.51  | | | | | | | |   (151)   ~ (all_4_2 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (42), (145) imply:
% 198.01/32.51  | | | | | | | |   (152)  op(e3, e3) = all_52_8
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3,
% 198.01/32.51  | | | | | | | |              simplifying with (82), (152) gives:
% 198.01/32.51  | | | | | | | |   (153)  all_52_8 = all_6_2
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | BETA: splitting (50) gives:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (154)  all_58_6 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | COMBINE_EQS: (91), (154) imply:
% 198.01/32.51  | | | | | | | | |   (155)  all_52_5 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | SIMP: (155) implies:
% 198.01/32.51  | | | | | | | | |   (156)  all_52_5 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REDUCE: (47), (156) imply:
% 198.01/32.51  | | | | | | | | |   (157)   ~ (all_52_7 = e3)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | SIMP: (157) implies:
% 198.01/32.51  | | | | | | | | |   (158)   ~ (all_52_7 = e3)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | BETA: splitting (93) gives:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (159)  all_58_12 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | REF_CLOSE: (48), (158), (159) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | |            #1367.
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (160)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | REF_CLOSE: (3), (7), (10), (11), (12), (15), (19), (29),
% 198.01/32.51  | | | | | | | | | |            (31), (49), (51), (52), (62), (64), (68), (74),
% 198.01/32.51  | | | | | | | | | |            (82), (90), (103), (104), (105), (108), (120),
% 198.01/32.51  | | | | | | | | | |            (121), (149), (160) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | |            #275.
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (161)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REF_CLOSE: (7), (21), (22), (24), (28), (30), (32), (40),
% 198.01/32.51  | | | | | | | | |            (41), (45), (53), (55), (62), (69), (70), (82),
% 198.01/32.51  | | | | | | | | |            (84), (88), (89), (90), (95), (106), (130), (134),
% 198.01/32.51  | | | | | | | | |            (137), (147), (151), (161) are inconsistent by
% 198.01/32.51  | | | | | | | | |            sub-proof #47.
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | |   (162)  all_58_4 = e3 | all_58_9 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REF_CLOSE: (7), (20), (82), (90), (95), (109), (135), (162) are
% 198.01/32.51  | | | | | | | |            inconsistent by sub-proof #1080.
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | End of split
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | End of split
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | Case 2:
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | |   (163)   ~ (all_56_7 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | REDUCE: (59), (163) imply:
% 198.01/32.51  | | | | | |   (164)   ~ (all_52_27 = e3)
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | BETA: splitting (32) gives:
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | | Case 1:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | |   (165)  all_58_2 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | COMBINE_EQS: (53), (165) imply:
% 198.01/32.51  | | | | | | |   (166)  all_52_3 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | SIMP: (166) implies:
% 198.01/32.51  | | | | | | |   (167)  all_52_3 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | REDUCE: (87), (167) imply:
% 198.01/32.51  | | | | | | |   (168)   ~ (all_52_7 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | SIMP: (168) implies:
% 198.01/32.51  | | | | | | |   (169)   ~ (all_52_7 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | REDUCE: (13), (167) imply:
% 198.01/32.51  | | | | | | |   (170)   ~ (all_6_2 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | SIMP: (170) implies:
% 198.01/32.51  | | | | | | |   (171)   ~ (all_6_2 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | REDUCE: (101), (167) imply:
% 198.01/32.51  | | | | | | |   (172)   ~ (all_4_0 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | REDUCE: (107), (167) imply:
% 198.01/32.51  | | | | | | |   (173)   ~ (all_4_2 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | SIMP: (173) implies:
% 198.01/32.51  | | | | | | |   (174)   ~ (all_4_2 = e3)
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | REDUCE: (6), (167) imply:
% 198.01/32.51  | | | | | | |   (175)  op(e3, e3) = all_52_2
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_2, e3, e3,
% 198.01/32.51  | | | | | | |              simplifying with (82), (175) gives:
% 198.01/32.51  | | | | | | |   (176)  all_52_2 = all_6_2
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | BETA: splitting (83) gives:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | |   (177)  all_58_9 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | COMBINE_EQS: (20), (177) imply:
% 198.01/32.51  | | | | | | | |   (178)  all_52_25 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | SIMP: (178) implies:
% 198.01/32.51  | | | | | | | |   (179)  all_52_25 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (67), (179) imply:
% 198.01/32.51  | | | | | | | |   (180)   ~ (all_52_9 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (25), (179) imply:
% 198.01/32.51  | | | | | | | |   (181)   ~ (all_14_2 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (110), (179) imply:
% 198.01/32.51  | | | | | | | |   (182)  op(e3, e3) = all_52_24
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 198.01/32.51  | | | | | | | |              simplifying with (82), (182) gives:
% 198.01/32.51  | | | | | | | |   (183)  all_52_24 = all_6_2
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | BETA: splitting (93) gives:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (184)  all_58_12 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REF_CLOSE: (48), (169), (184) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | |            #1367.
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (185)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | BETA: splitting (66) gives:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (186)  all_58_1 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | COMBINE_EQS: (8), (186) imply:
% 198.01/32.51  | | | | | | | | | |   (187)  all_52_9 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | REDUCE: (180), (187) imply:
% 198.01/32.51  | | | | | | | | | |   (188)  $false
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | CLOSE: (188) is inconsistent.
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (189)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | BETA: splitting (100) gives:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | |   (190)  all_56_9 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | COMBINE_EQS: (37), (190) imply:
% 198.01/32.51  | | | | | | | | | | |   (191)  all_52_13 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | SIMP: (191) implies:
% 198.01/32.51  | | | | | | | | | | |   (192)  all_52_13 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | REDUCE: (80), (192) imply:
% 198.01/32.51  | | | | | | | | | | |   (193)   ~ (all_52_15 = e3)
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | SIMP: (193) implies:
% 198.01/32.51  | | | | | | | | | | |   (194)   ~ (all_52_15 = e3)
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | BETA: splitting (185) gives:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | |   (195)  all_58_13 = e3
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | REF_CLOSE: (19), (194), (195) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | | |            #1360.
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | |   (196)  all_58_14 = e3 | all_58_15 = e3
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (11), (12), (15), (29), (31),
% 198.01/32.51  | | | | | | | | | | | |            (49), (51), (52), (62), (64), (68), (74), (82),
% 198.01/32.51  | | | | | | | | | | | |            (90), (103), (104), (105), (108), (120), (121),
% 198.01/32.51  | | | | | | | | | | | |            (196) are inconsistent by sub-proof #276.
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | |   (197)   ~ (all_56_9 = e3)
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (19), (28), (30), (34), (36), (37),
% 198.01/32.51  | | | | | | | | | | |            (39), (40), (43), (45), (55), (61), (62), (63),
% 198.01/32.51  | | | | | | | | | | |            (65), (70), (75), (82), (90), (95), (106), (109),
% 198.01/32.51  | | | | | | | | | | |            (126), (130), (174), (189), (197) are inconsistent
% 198.01/32.51  | | | | | | | | | | |            by sub-proof #46.
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | |   (198)   ~ (all_58_9 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (20), (198) imply:
% 198.01/32.51  | | | | | | | |   (199)   ~ (all_52_25 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | BETA: splitting (85) gives:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (200)  all_58_0 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | COMBINE_EQS: (14), (200) imply:
% 198.01/32.51  | | | | | | | | |   (201)  all_6_2 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REDUCE: (171), (201) imply:
% 198.01/32.51  | | | | | | | | |   (202)  $false
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | CLOSE: (202) is inconsistent.
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (203)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | BETA: splitting (203) gives:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (204)  all_58_1 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | COMBINE_EQS: (8), (204) imply:
% 198.01/32.51  | | | | | | | | | |   (205)  all_52_9 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | REDUCE: (26), (205) imply:
% 198.01/32.51  | | | | | | | | | |   (206)   ~ (all_52_15 = e3)
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | SIMP: (206) implies:
% 198.01/32.51  | | | | | | | | | |   (207)   ~ (all_52_15 = e3)
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | BETA: splitting (93) gives:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | |   (208)  all_58_12 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | REF_CLOSE: (48), (169), (208) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | |            #1367.
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | |   (209)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (11), (12), (15), (19), (29),
% 198.01/32.51  | | | | | | | | | | |            (31), (49), (51), (52), (62), (64), (68), (74),
% 198.01/32.51  | | | | | | | | | | |            (82), (90), (103), (104), (105), (108), (120),
% 198.01/32.51  | | | | | | | | | | |            (121), (207), (209) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | |            #275.
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (210)  all_58_4 = e3 | all_58_9 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | REF_CLOSE: (7), (20), (82), (90), (95), (109), (199), (210)
% 198.01/32.51  | | | | | | | | | |            are inconsistent by sub-proof #1080.
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | End of split
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | Case 2:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | |   (211)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | BETA: splitting (211) gives:
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | |   (212)  all_58_3 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | COMBINE_EQS: (106), (212) imply:
% 198.01/32.51  | | | | | | | |   (213)  all_4_2 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (77), (213) imply:
% 198.01/32.51  | | | | | | | |   (214)   ~ (all_52_9 = e3)
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (86), (213) imply:
% 198.01/32.51  | | | | | | | |   (215)  op(e3, e3) = all_52_10
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (23), (213) imply:
% 198.01/32.51  | | | | | | | |   (216)  op(e3, e2) = e1
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REDUCE: (22), (213) imply:
% 198.01/32.51  | | | | | | | |   (217)  op(e2, e2) = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | BETA: splitting (78) gives:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (218)   ~ (all_4_2 = e3)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REF_CLOSE: (7), (22), (217), (218) are inconsistent by
% 198.01/32.51  | | | | | | | | |            sub-proof #211.
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | |   (219)   ~ (all_4_0 = e0)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | GROUND_INST: instantiating (7) with all_52_9, e1, e2, e3,
% 198.01/32.51  | | | | | | | | |              simplifying with (92), (216) gives:
% 198.01/32.51  | | | | | | | | |   (220)  all_52_9 = e1
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_10, e3, e3,
% 198.01/32.51  | | | | | | | | |              simplifying with (82), (215) gives:
% 198.01/32.51  | | | | | | | | |   (221)  all_52_10 = all_6_2
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | COMBINE_EQS: (8), (220) imply:
% 198.01/32.51  | | | | | | | | |   (222)  all_58_1 = e1
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REDUCE: (98), (220) imply:
% 198.01/32.51  | | | | | | | | |   (223)   ~ (all_52_17 = e1)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | SIMP: (223) implies:
% 198.01/32.51  | | | | | | | | |   (224)   ~ (all_52_17 = e1)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REDUCE: (79), (220) imply:
% 198.01/32.51  | | | | | | | | |   (225)   ~ (all_6_2 = e1)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | SIMP: (225) implies:
% 198.01/32.51  | | | | | | | | |   (226)   ~ (all_6_2 = e1)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REDUCE: (214), (220) imply:
% 198.01/32.51  | | | | | | | | |   (227)   ~ (e3 = e1)
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | REDUCE: (42), (220) imply:
% 198.01/32.51  | | | | | | | | |   (228)  op(e1, e1) = all_52_8
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_8, e1, e1,
% 198.01/32.51  | | | | | | | | |              simplifying with (103), (228) gives:
% 198.01/32.51  | | | | | | | | |   (229)  all_52_8 = all_10_2
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | BETA: splitting (85) gives:
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (230)  all_58_0 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | COMBINE_EQS: (14), (230) imply:
% 198.01/32.51  | | | | | | | | | |   (231)  all_6_2 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | REF_CLOSE: (4), (7), (15), (82), (108), (231) are
% 198.01/32.51  | | | | | | | | | |            inconsistent by sub-proof #310.
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | |   (232)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | BETA: splitting (232) gives:
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | |   (233)  all_58_1 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | REF_CLOSE: (4), (222), (233) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | |            #96.
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | |   (234)  all_58_4 = e3 | all_58_9 = e3
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | BETA: splitting (234) gives:
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | |   (235)  all_58_4 = e3
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | REF_CLOSE: (109), (127), (235) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | | |            #1302.
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | |   (236)  all_58_9 = e3
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | COMBINE_EQS: (20), (236) imply:
% 198.01/32.51  | | | | | | | | | | | |   (237)  all_52_25 = e3
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | SIMP: (237) implies:
% 198.01/32.51  | | | | | | | | | | | |   (238)  all_52_25 = e3
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | REDUCE: (25), (238) imply:
% 198.01/32.51  | | | | | | | | | | | |   (239)   ~ (all_14_2 = e3)
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | REDUCE: (76), (238) imply:
% 198.01/32.51  | | | | | | | | | | | |   (240)   ~ (all_6_2 = e3)
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | SIMP: (240) implies:
% 198.01/32.51  | | | | | | | | | | | |   (241)   ~ (all_6_2 = e3)
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | REDUCE: (110), (238) imply:
% 198.01/32.51  | | | | | | | | | | | |   (242)  op(e3, e3) = all_52_24
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 198.01/32.51  | | | | | | | | | | | |              simplifying with (82), (242) gives:
% 198.01/32.51  | | | | | | | | | | | |   (243)  all_52_24 = all_6_2
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | BETA: splitting (102) gives:
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | |   (244)  all_56_0 = e3
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | REF_CLOSE: (81), (241), (244) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | | | |            #598.
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | |   (245)   ~ (all_56_0 = e3)
% 198.01/32.51  | | | | | | | | | | | | |   (246)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | BETA: splitting (56) gives:
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | |   (247)  all_58_0 = e2
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | COMBINE_EQS: (14), (247) imply:
% 198.01/32.51  | | | | | | | | | | | | | |   (248)  all_6_2 = e2
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | REDUCE: (95), (248) imply:
% 198.01/32.51  | | | | | | | | | | | | | |   (249)   ~ (all_52_17 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | REF_CLOSE: (7), (30), (35), (55), (82), (90), (121), (224),
% 198.01/32.51  | | | | | | | | | | | | | |            (241), (249) are inconsistent by sub-proof #340.
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | |   (250)   ~ (all_58_0 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | REDUCE: (14), (250) imply:
% 198.01/32.51  | | | | | | | | | | | | | |   (251)   ~ (all_6_2 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | |   (252)  all_56_0 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | REF_CLOSE: (81), (251), (252) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | | | | | |            #597.
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | |   (253)  all_56_0 = e1 | all_56_0 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | |   (254)  all_56_0 = e1
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | REF_CLOSE: (81), (226), (254) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | | | | | | |            #596.
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | |   (255)  all_56_0 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (255) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | |   (256)  all_6_2 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 198.01/32.51  | | | | | | | | | | | | | | | |   (257)  all_6_2 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | REDUCE: (95), (257) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | |   (258)   ~ (all_52_17 = e0)
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (259)  all_56_2 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (259) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (260)  all_52_17 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | SIMP: (260) implies:
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (261)  all_52_17 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | REDUCE: (16), (261) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (262)   ~ (all_10_2 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (263)   ~ (all_10_2 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | REDUCE: (5), (261) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (264)   ~ (all_4_0 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | SIMP: (264) implies:
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (265)   ~ (all_4_0 = e2)
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | |   (266)  all_56_6 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (266) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | | |   (267)  all_4_0 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | SIMP: (267) implies:
% 198.01/32.51  | | | | | | | | | | | | | | | | | |   (268)  all_4_0 = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | REDUCE: (265), (268) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | | |   (269)  $false
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent.
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | |   (270)  all_56_6 = e1 | all_56_6 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | Case 1:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |   (271)  all_56_6 = e1
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (271) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |   (272)  all_4_0 = e1
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |   (273)  all_4_0 = e1
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | REDUCE: (46), (273) imply:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |   (274)  op(e1, e1) = e2
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (103), (228), (263), (274) are inconsistent
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |            by sub-proof #962.
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |   (275)  all_56_6 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (219), (275) are inconsistent by sub-proof
% 198.01/32.51  | | | | | | | | | | | | | | | | | | |            #101.
% 198.01/32.51  | | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | |   (276)  all_56_2 = e1 | all_56_2 = e0
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (224), (258), (276) are inconsistent by
% 198.01/32.51  | | | | | | | | | | | | | | | | |            sub-proof #1307.
% 198.01/32.51  | | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | | 
% 198.01/32.51  | | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | | 
% 198.01/32.51  | | | | | | | | End of split
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | Case 2:
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | |   (277)  all_58_5 = e3 | all_58_10 = e3
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | | REF_CLOSE: (34), (41), (75), (164), (277) are inconsistent by
% 198.01/32.51  | | | | | | | |            sub-proof #214.
% 198.01/32.51  | | | | | | | | 
% 198.01/32.51  | | | | | | | End of split
% 198.01/32.51  | | | | | | | 
% 198.01/32.51  | | | | | | End of split
% 198.01/32.51  | | | | | | 
% 198.01/32.51  | | | | | End of split
% 198.01/32.51  | | | | | 
% 198.01/32.51  | | | | End of split
% 198.01/32.51  | | | | 
% 198.01/32.51  | | | End of split
% 198.01/32.51  | | | 
% 198.01/32.51  | | End of split
% 198.01/32.51  | | 
% 198.01/32.51  | End of split
% 198.01/32.51  | 
% 198.01/32.51  End of proof
% 198.01/32.51  
% 198.01/32.51  Sub-proof #4 shows that the following formulas are inconsistent:
% 198.01/32.51  ----------------------------------------------------------------
% 198.01/32.51    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.51    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.51    (3)  all_58_14 = all_52_23
% 198.01/32.51    (4)   ~ (e3 = e1)
% 198.01/32.51    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.51    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.51    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.51    (8)  all_58_1 = all_52_9
% 198.01/32.51    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.51    (10)   ~ (e3 = e0)
% 198.01/32.51    (11)  op(e2, e3) = all_52_3
% 198.01/32.51    (12)   ~ (all_52_23 = all_4_0)
% 198.01/32.51    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.51    (14)   ~ (all_52_7 = all_52_15)
% 198.01/32.51    (15)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.51    (16)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.51    (17)   ~ (all_52_17 = all_52_25)
% 198.01/32.51    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.51    (19)  all_58_0 = all_6_2
% 198.01/32.51    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.51    (21)  all_46_0 = e1
% 198.01/32.51    (22)  all_56_4 = all_52_3
% 198.01/32.51    (23)  op(e3, all_6_1) = e1
% 198.01/32.51    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.51    (25)  op(e3, e0) = all_52_25
% 198.01/32.51    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.52    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.52    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.52    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.52    (30)  all_58_13 = all_52_15
% 198.01/32.52    (31)  all_58_9 = all_52_25
% 198.01/32.52    (32)   ~ (all_52_29 = all_14_2)
% 198.01/32.52    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.52    (34)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.52    (35)  op(e1, e3) = all_52_5
% 198.01/32.52    (36)  op(e2, e2) = all_4_2
% 198.01/32.52    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.52    (38)   ~ (all_52_3 = all_52_5)
% 198.01/32.52    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.52    (40)  op(all_4_2, e2) = e1
% 198.01/32.52    (41)  all_58_11 = all_52_29
% 198.01/32.52    (42)  all_56_5 = all_4_2
% 198.01/32.52    (43)   ~ (all_52_25 = all_14_2)
% 198.01/32.52    (44)   ~ (all_52_9 = all_52_15)
% 198.01/32.52    (45)   ~ (all_52_3 = all_52_27)
% 198.01/32.52    (46)  op(all_10_2, e1) = all_10_1
% 198.01/32.52    (47)  all_46_2 = all_6_2
% 198.01/32.52    (48)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.52    (49)   ~ (all_52_7 = all_6_2)
% 198.01/32.52    (50)  op(e0, e0) = all_14_2
% 198.01/32.52    (51)  all_56_15 = all_14_2
% 198.01/32.52    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.52    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.52    (54)  all_56_11 = all_52_29
% 198.01/32.52    (55)  all_4_0 = e3
% 198.01/32.52    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.52    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.52    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.52    (59)   ~ (e2 = e1)
% 198.01/32.52    (60)  all_58_10 = all_52_27
% 198.01/32.52    (61)  all_56_8 = all_52_5
% 198.01/32.52    (62)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.52    (63)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.52    (64)   ~ (all_52_25 = all_52_29)
% 198.01/32.52    (65)   ~ (all_52_29 = all_10_2)
% 198.01/32.52    (66)  all_58_7 = all_52_13
% 198.01/32.52    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.52    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.52    (69)   ~ (all_52_5 = all_52_7)
% 198.01/32.52    (70)  all_58_12 = all_52_7
% 198.01/32.52    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.52    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.52    (73)   ~ (all_52_7 = all_14_2)
% 198.01/32.52    (74)  all_58_2 = all_52_3
% 198.01/32.52    (75)  all_56_2 = all_52_17
% 198.01/32.52    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.52    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.52    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.52    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.52    (80)  all_56_7 = all_52_27
% 198.01/32.52    (81)  all_28_2 = all_4_2
% 198.01/32.52    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.52    (83)   ~ (e2 = e0)
% 198.01/32.52    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.52    (85)   ~ (all_52_5 = all_52_29)
% 198.01/32.52    (86)   ~ (all_52_15 = all_14_2)
% 198.01/32.52    (87)   ~ (all_52_19 = all_52_27)
% 198.01/32.52    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.52    (89)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.52    (90)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.52            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.52    (91)   ~ (all_52_13 = all_4_2)
% 198.01/32.52    (92)  op(e3, e1) = all_52_17
% 198.01/32.52    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.52    (94)  op(e0, e3) = all_52_7
% 198.01/32.52    (95)  op(e1, e2) = all_52_13
% 198.01/32.52    (96)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.52    (97)   ~ (all_52_9 = all_52_25)
% 198.01/32.52    (98)  all_58_15 = all_14_2
% 198.01/32.52    (99)   ~ (all_52_19 = all_10_2)
% 198.01/32.52    (100)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.52    (101)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.52    (102)  all_58_8 = all_10_2
% 198.01/32.52    (103)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.52    (104)   ~ (all_52_5 = all_10_2)
% 198.01/32.52    (105)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.52    (106)   ~ (all_52_23 = all_14_2)
% 198.01/32.52    (107)  all_56_12 = all_52_7
% 198.01/32.52    (108)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.52    (109)  all_58_5 = all_4_0
% 198.01/32.52    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.52    (111)   ~ (all_52_25 = all_6_2)
% 198.01/32.52    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.52    (113)   ~ (all_52_9 = all_4_2)
% 198.01/32.52    (114)   ~ (all_52_5 = all_6_2)
% 198.01/32.52    (115)   ~ (all_52_9 = all_6_2)
% 198.01/32.52    (116)   ~ (all_52_13 = all_52_15)
% 198.01/32.52    (117)  all_56_0 = all_6_2
% 198.01/32.52    (118)  op(all_4_0, all_4_0) = all_52_18
% 198.01/32.52    (119)  op(e3, e3) = all_6_2
% 198.01/32.52    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.52    (121)   ~ (all_52_27 = all_14_2)
% 198.01/32.52    (122)   ~ (all_52_27 = all_4_0)
% 198.01/32.52    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.52    (124)  all_56_14 = all_52_23
% 198.01/32.52    (125)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.52    (126)  all_56_3 = all_52_25
% 198.01/32.52    (127)  op(e0, all_14_1) = e2
% 198.01/32.52    (128)   ~ (all_52_3 = all_52_7)
% 198.01/32.52    (129)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.52    (130)  all_58_5 = all_52_19
% 198.01/32.52    (131)  all_56_1 = all_52_9
% 198.01/32.52    (132)   ~ (all_52_15 = all_4_2)
% 198.01/32.52    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.52           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.52           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.52           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.52    (134)   ~ (all_52_27 = all_4_2)
% 198.01/32.52    (135)  all_58_6 = all_52_5
% 198.01/32.52    (136)   ~ (all_4_0 = all_4_2)
% 198.01/32.52    (137)  op(e3, e2) = all_52_9
% 198.01/32.52    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.52    (139)   ~ (all_52_17 = all_6_2)
% 198.01/32.52    (140)   ~ (e1 = e0)
% 198.01/32.52    (141)   ~ (e3 = e2)
% 198.01/32.52    (142)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.52    (143)   ~ (all_52_9 = all_52_17)
% 198.01/32.52    (144)   ~ (all_52_3 = all_4_0)
% 198.01/32.52    (145)  all_46_1 = all_6_1
% 198.01/32.52    (146)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.52    (147)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.52    (148)  op(e1, e1) = all_10_2
% 198.01/32.52    (149)   ~ (all_52_23 = all_10_2)
% 198.01/32.52    (150)   ~ (all_52_7 = all_52_23)
% 198.01/32.52    (151)   ~ (all_52_17 = all_52_19)
% 198.01/32.52    (152)  all_58_3 = all_4_2
% 198.01/32.52    (153)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.52    (154)  all_56_13 = all_52_15
% 198.01/32.52    (155)   ~ (all_52_3 = all_4_2)
% 198.01/32.52    (156)  all_28_1 = e1
% 198.01/32.52    (157)   ~ (all_52_19 = all_4_2)
% 198.01/32.52    (158)   ~ (all_52_17 = all_52_23)
% 198.01/32.52    (159)  op(all_6_2, e3) = all_6_1
% 198.01/32.52    (160)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.52    (161)  all_58_4 = all_52_17
% 198.01/32.52    (162)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.52  
% 198.01/32.52  Begin of proof
% 198.01/32.52  | 
% 198.01/32.52  | COMBINE_EQS: (55), (109) imply:
% 198.01/32.52  |   (163)  all_58_5 = e3
% 198.01/32.52  | 
% 198.01/32.52  | REDUCE: (55), (144) imply:
% 198.01/32.52  |   (164)   ~ (all_52_3 = e3)
% 198.01/32.52  | 
% 198.01/32.52  | REDUCE: (5), (55) imply:
% 198.01/32.52  |   (165)   ~ (all_52_17 = e3)
% 198.01/32.52  | 
% 198.01/32.52  | REDUCE: (12), (55) imply:
% 198.01/32.52  |   (166)   ~ (all_52_23 = e3)
% 198.01/32.52  | 
% 198.01/32.52  | REDUCE: (55), (122) imply:
% 198.01/32.52  |   (167)   ~ (all_52_27 = e3)
% 198.01/32.52  | 
% 198.01/32.52  | REDUCE: (55), (136) imply:
% 198.01/32.52  |   (168)   ~ (all_4_2 = e3)
% 198.01/32.52  | 
% 198.01/32.52  | SIMP: (168) implies:
% 198.01/32.52  |   (169)   ~ (all_4_2 = e3)
% 198.01/32.52  | 
% 198.01/32.52  | REDUCE: (55), (118) imply:
% 198.01/32.52  |   (170)  op(e3, e3) = all_52_18
% 198.01/32.52  | 
% 198.01/32.52  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 198.01/32.52  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 198.01/32.52  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 198.01/32.52  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 198.01/32.52  |            (48), (49), (50), (51), (52), (53), (54), (56), (57), (58), (59),
% 198.01/32.52  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 198.01/32.52  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 198.01/32.52  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 198.01/32.52  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 198.01/32.52  |            (103), (104), (105), (106), (107), (108), (110), (111), (112),
% 198.01/32.52  |            (113), (114), (115), (116), (117), (119), (120), (121), (123),
% 198.01/32.52  |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 198.01/32.52  |            (133), (134), (135), (137), (138), (139), (140), (141), (142),
% 198.01/32.52  |            (143), (145), (146), (147), (148), (149), (150), (151), (152),
% 198.01/32.52  |            (153), (154), (155), (156), (157), (158), (159), (160), (161),
% 198.01/32.52  |            (162), (163), (164), (165), (166), (167), (169), (170) are
% 198.01/32.52  |            inconsistent by sub-proof #5.
% 198.01/32.52  | 
% 198.01/32.52  End of proof
% 198.01/32.52  
% 198.01/32.52  Sub-proof #5 shows that the following formulas are inconsistent:
% 198.01/32.52  ----------------------------------------------------------------
% 198.01/32.52    (1)  op(e3, e3) = all_52_18
% 198.01/32.52    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.52    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.52    (4)  all_58_14 = all_52_23
% 198.01/32.52    (5)   ~ (e3 = e1)
% 198.01/32.52    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.52    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.52    (8)  all_58_1 = all_52_9
% 198.01/32.52    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.52    (10)   ~ (e3 = e0)
% 198.01/32.52    (11)  op(e2, e3) = all_52_3
% 198.01/32.52    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.52    (13)   ~ (all_52_7 = all_52_15)
% 198.01/32.52    (14)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.52    (15)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.52    (16)   ~ (all_52_17 = all_52_25)
% 198.01/32.52    (17)   ~ (all_4_2 = e3)
% 198.01/32.52    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.52    (19)  all_58_0 = all_6_2
% 198.01/32.52    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.52    (21)  all_46_0 = e1
% 198.01/32.52    (22)  all_56_4 = all_52_3
% 198.01/32.52    (23)  op(e3, all_6_1) = e1
% 198.01/32.52    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.52    (25)  op(e3, e0) = all_52_25
% 198.01/32.52    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.52    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.52    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.52    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.52    (30)  all_58_13 = all_52_15
% 198.01/32.52    (31)  all_58_9 = all_52_25
% 198.01/32.52    (32)   ~ (all_52_29 = all_14_2)
% 198.01/32.52    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.52    (34)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.52    (35)  op(e1, e3) = all_52_5
% 198.01/32.52    (36)  op(e2, e2) = all_4_2
% 198.01/32.52    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.52    (38)   ~ (all_52_3 = all_52_5)
% 198.01/32.52    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.52    (40)  op(all_4_2, e2) = e1
% 198.01/32.52    (41)  all_58_11 = all_52_29
% 198.01/32.52    (42)   ~ (all_52_3 = e3)
% 198.01/32.52    (43)  all_56_5 = all_4_2
% 198.01/32.52    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.52    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.52    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.52    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.52    (48)  all_46_2 = all_6_2
% 198.01/32.52    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.52    (50)   ~ (all_52_7 = all_6_2)
% 198.01/32.52    (51)  op(e0, e0) = all_14_2
% 198.01/32.52    (52)  all_56_15 = all_14_2
% 198.01/32.52    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.52    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.52    (55)  all_56_11 = all_52_29
% 198.01/32.52    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.52    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.52    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.52    (59)   ~ (e2 = e1)
% 198.01/32.52    (60)  all_58_10 = all_52_27
% 198.01/32.52    (61)  all_56_8 = all_52_5
% 198.01/32.52    (62)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.52    (63)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.52    (64)   ~ (all_52_25 = all_52_29)
% 198.01/32.52    (65)   ~ (all_52_29 = all_10_2)
% 198.01/32.52    (66)  all_58_7 = all_52_13
% 198.01/32.52    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.52    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.52    (69)   ~ (all_52_5 = all_52_7)
% 198.01/32.52    (70)  all_58_12 = all_52_7
% 198.01/32.52    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.52    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.52    (73)   ~ (all_52_7 = all_14_2)
% 198.01/32.52    (74)  all_58_2 = all_52_3
% 198.01/32.52    (75)  all_56_2 = all_52_17
% 198.01/32.52    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.52    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.52    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.52    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.52    (80)  all_56_7 = all_52_27
% 198.01/32.52    (81)  all_28_2 = all_4_2
% 198.01/32.52    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.52    (83)   ~ (e2 = e0)
% 198.01/32.52    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.52    (85)   ~ (all_52_23 = e3)
% 198.01/32.52    (86)   ~ (all_52_5 = all_52_29)
% 198.01/32.52    (87)   ~ (all_52_15 = all_14_2)
% 198.01/32.52    (88)   ~ (all_52_19 = all_52_27)
% 198.01/32.52    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.52    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.52    (91)   ~ (all_52_27 = e3)
% 198.01/32.52    (92)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.52            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.52    (93)   ~ (all_52_13 = all_4_2)
% 198.01/32.52    (94)  op(e3, e1) = all_52_17
% 198.01/32.52    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.52    (96)  op(e0, e3) = all_52_7
% 198.01/32.52    (97)  op(e1, e2) = all_52_13
% 198.01/32.52    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.52    (99)   ~ (all_52_9 = all_52_25)
% 198.01/32.52    (100)  all_58_15 = all_14_2
% 198.01/32.52    (101)   ~ (all_52_19 = all_10_2)
% 198.01/32.52    (102)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.52    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.52    (104)  all_58_8 = all_10_2
% 198.01/32.52    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.52    (106)   ~ (all_52_5 = all_10_2)
% 198.01/32.52    (107)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.52    (108)   ~ (all_52_23 = all_14_2)
% 198.01/32.52    (109)  all_56_12 = all_52_7
% 198.01/32.52    (110)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.52    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.52    (112)   ~ (all_52_25 = all_6_2)
% 198.01/32.52    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.52    (114)   ~ (all_52_9 = all_4_2)
% 198.01/32.52    (115)   ~ (all_52_5 = all_6_2)
% 198.01/32.52    (116)   ~ (all_52_9 = all_6_2)
% 198.01/32.52    (117)   ~ (all_52_13 = all_52_15)
% 198.01/32.52    (118)  all_56_0 = all_6_2
% 198.01/32.52    (119)  op(e3, e3) = all_6_2
% 198.01/32.52    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.52    (121)   ~ (all_52_27 = all_14_2)
% 198.01/32.52    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.52    (123)  all_58_5 = e3
% 198.01/32.52    (124)  all_56_14 = all_52_23
% 198.01/32.52    (125)   ~ (all_52_17 = e3)
% 198.01/32.52    (126)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.52    (127)  all_56_3 = all_52_25
% 198.01/32.52    (128)  op(e0, all_14_1) = e2
% 198.01/32.52    (129)   ~ (all_52_3 = all_52_7)
% 198.01/32.52    (130)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.52    (131)  all_58_5 = all_52_19
% 198.01/32.52    (132)  all_56_1 = all_52_9
% 198.01/32.52    (133)   ~ (all_52_15 = all_4_2)
% 198.01/32.52    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.52           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.52           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.52           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.52    (135)   ~ (all_52_27 = all_4_2)
% 198.01/32.52    (136)  all_58_6 = all_52_5
% 198.01/32.52    (137)  op(e3, e2) = all_52_9
% 198.01/32.52    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.52    (139)   ~ (all_52_17 = all_6_2)
% 198.01/32.52    (140)   ~ (e1 = e0)
% 198.01/32.52    (141)   ~ (e3 = e2)
% 198.01/32.52    (142)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.52    (143)   ~ (all_52_9 = all_52_17)
% 198.01/32.52    (144)  all_46_1 = all_6_1
% 198.01/32.52    (145)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.52    (146)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.52    (147)  op(e1, e1) = all_10_2
% 198.01/32.52    (148)   ~ (all_52_23 = all_10_2)
% 198.01/32.52    (149)   ~ (all_52_7 = all_52_23)
% 198.01/32.52    (150)   ~ (all_52_17 = all_52_19)
% 198.01/32.52    (151)  all_58_3 = all_4_2
% 198.01/32.52    (152)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.52    (153)  all_56_13 = all_52_15
% 198.01/32.52    (154)   ~ (all_52_3 = all_4_2)
% 198.01/32.52    (155)  all_28_1 = e1
% 198.01/32.52    (156)   ~ (all_52_19 = all_4_2)
% 198.01/32.52    (157)   ~ (all_52_17 = all_52_23)
% 198.01/32.52    (158)  op(all_6_2, e3) = all_6_1
% 198.01/32.52    (159)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.52    (160)  all_58_4 = all_52_17
% 198.01/32.52    (161)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.52  
% 198.01/32.52  Begin of proof
% 198.01/32.52  | 
% 198.01/32.52  | BETA: splitting (126) gives:
% 198.01/32.52  | 
% 198.01/32.52  | Case 1:
% 198.01/32.52  | | 
% 198.01/32.52  | |   (162)   ~ (all_28_1 = e1)
% 198.01/32.52  | | 
% 198.01/32.52  | | REDUCE: (155), (162) imply:
% 198.01/32.52  | |   (163)  $false
% 198.01/32.52  | | 
% 198.01/32.52  | | CLOSE: (163) is inconsistent.
% 198.01/32.52  | | 
% 198.01/32.52  | Case 2:
% 198.01/32.52  | | 
% 198.01/32.52  | |   (164)   ~ (all_28_2 = e0)
% 198.01/32.52  | | 
% 198.01/32.52  | | REDUCE: (81), (164) imply:
% 198.01/32.52  | |   (165)   ~ (all_4_2 = e0)
% 198.01/32.52  | | 
% 198.01/32.52  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 198.01/32.52  | |              with (1), (119) gives:
% 198.01/32.52  | |   (166)  all_52_18 = all_6_2
% 198.01/32.52  | | 
% 198.01/32.52  | | BETA: splitting (14) gives:
% 198.01/32.52  | | 
% 198.01/32.52  | | Case 1:
% 198.01/32.52  | | | 
% 198.01/32.52  | | |   (167)   ~ (all_46_0 = e1)
% 198.01/32.52  | | | 
% 198.01/32.52  | | | REDUCE: (21), (167) imply:
% 198.01/32.52  | | |   (168)  $false
% 198.01/32.52  | | | 
% 198.01/32.52  | | | CLOSE: (168) is inconsistent.
% 198.01/32.52  | | | 
% 198.01/32.52  | | Case 2:
% 198.01/32.52  | | | 
% 198.01/32.52  | | |   (169)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.52  | | | 
% 198.01/32.52  | | | BETA: splitting (92) gives:
% 198.01/32.52  | | | 
% 198.01/32.52  | | | Case 1:
% 198.01/32.52  | | | | 
% 198.01/32.52  | | | |   (170)  all_58_15 = e0
% 198.01/32.52  | | | | 
% 198.01/32.52  | | | | REF_CLOSE: (7), (20), (51), (83), (100), (128), (130), (170) are
% 198.01/32.52  | | | |            inconsistent by sub-proof #612.
% 198.01/32.52  | | | | 
% 198.01/32.52  | | | Case 2:
% 198.01/32.52  | | | | 
% 198.01/32.53  | | | |   (171)   ~ (all_58_15 = e0)
% 198.01/32.53  | | | |   (172)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 198.01/32.53  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | ALPHA: (172) implies:
% 198.01/32.53  | | | |   (173)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REDUCE: (100), (171) imply:
% 198.01/32.53  | | | |   (174)   ~ (all_14_2 = e0)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.53  | | | |            (13), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 198.01/32.53  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.01/32.53  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 198.01/32.53  | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 198.01/32.53  | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 198.01/32.53  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 198.01/32.53  | | | |            (75), (76), (77), (78), (79), (80), (82), (83), (84), (85),
% 198.01/32.53  | | | |            (86), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 198.01/32.53  | | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 198.01/32.53  | | | |            (106), (107), (108), (109), (110), (111), (112), (113),
% 198.01/32.53  | | | |            (114), (115), (116), (117), (118), (119), (120), (121),
% 198.01/32.53  | | | |            (122), (123), (124), (125), (127), (129), (130), (131),
% 198.01/32.53  | | | |            (132), (133), (134), (135), (136), (137), (138), (139),
% 198.01/32.53  | | | |            (140), (141), (142), (143), (144), (145), (146), (147),
% 198.01/32.53  | | | |            (148), (149), (150), (151), (152), (153), (154), (156),
% 198.01/32.53  | | | |            (157), (158), (159), (160), (161), (165), (166), (169),
% 198.01/32.53  | | | |            (173), (174) are inconsistent by sub-proof #17.
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | End of split
% 198.01/32.53  | | | 
% 198.01/32.53  | | End of split
% 198.01/32.53  | | 
% 198.01/32.53  | End of split
% 198.01/32.53  | 
% 198.01/32.53  End of proof
% 198.01/32.53  
% 198.01/32.53  Sub-proof #6 shows that the following formulas are inconsistent:
% 198.01/32.53  ----------------------------------------------------------------
% 198.01/32.53    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.53    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.53    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.53    (4)  all_58_14 = all_52_23
% 198.01/32.53    (5)   ~ (e3 = e1)
% 198.01/32.53    (6)   ~ (all_52_17 = all_4_0)
% 198.01/32.53    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.01/32.53    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.53    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.53    (10)   ~ (all_52_5 = all_52_13)
% 198.01/32.53    (11)  all_58_1 = all_52_9
% 198.01/32.53    (12)   ~ (all_52_9 = all_52_13)
% 198.01/32.53    (13)   ~ (e3 = e0)
% 198.01/32.53    (14)  op(e2, e3) = all_52_3
% 198.01/32.53    (15)   ~ (all_52_23 = all_4_0)
% 198.01/32.53    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.53    (17)  op(e0, e2) = all_52_15
% 198.01/32.53    (18)   ~ (all_52_7 = all_52_15)
% 198.01/32.53    (19)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.53    (20)   ~ (all_52_3 = all_6_2)
% 198.01/32.53    (21)  all_58_0 = all_6_2
% 198.01/32.53    (22)  op(all_14_2, e0) = all_14_1
% 198.01/32.53    (23)  op(e3, all_6_1) = e1
% 198.01/32.53    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.53    (25)  op(e3, e0) = all_52_25
% 198.01/32.53    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.53    (27)   ~ (all_52_27 = all_52_29)
% 198.01/32.53    (28)  all_58_13 = all_52_15
% 198.01/32.53    (29)  all_58_9 = all_52_25
% 198.01/32.53    (30)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.53    (31)  op(e1, e3) = all_52_5
% 198.01/32.53    (32)  op(e2, e2) = all_4_2
% 198.01/32.53    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.53    (34)   ~ (all_52_3 = all_52_5)
% 198.01/32.53    (35)  op(all_4_2, e2) = e1
% 198.01/32.53    (36)  all_58_11 = all_52_29
% 198.01/32.53    (37)  all_56_5 = all_4_2
% 198.01/32.53    (38)   ~ (all_52_25 = all_14_2)
% 198.01/32.53    (39)   ~ (all_52_9 = all_52_15)
% 198.01/32.53    (40)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.53    (41)   ~ (all_52_7 = all_6_2)
% 198.01/32.53    (42)  op(e0, e0) = all_14_2
% 198.01/32.53    (43)  all_56_15 = all_14_2
% 198.01/32.53    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.53    (45)   ~ (all_4_0 = e3)
% 198.01/32.53    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.53    (47)  all_56_9 = all_52_13
% 198.01/32.53    (48)   ~ (e2 = e1)
% 198.01/32.53    (49)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.01/32.53    (50)  all_58_10 = all_52_27
% 198.01/32.53    (51)  all_56_8 = all_52_5
% 198.01/32.53    (52)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.53    (53)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.53    (54)  all_58_7 = all_52_13
% 198.01/32.53    (55)   ~ (all_52_5 = all_52_7)
% 198.01/32.53    (56)  all_58_12 = all_52_7
% 198.01/32.53    (57)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.53    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.53    (59)   ~ (all_52_7 = all_14_2)
% 198.01/32.53    (60)  all_58_2 = all_52_3
% 198.01/32.53    (61)  all_56_2 = all_52_17
% 198.01/32.53    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.53    (63)  all_56_7 = all_52_27
% 198.01/32.53    (64)   ~ (e2 = e0)
% 198.01/32.53    (65)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.53    (66)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.01/32.53    (67)   ~ (all_52_5 = all_52_29)
% 198.01/32.53    (68)   ~ (all_52_15 = all_14_2)
% 198.01/32.53    (69)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.53    (70)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.53    (71)   ~ (all_52_13 = all_4_2)
% 198.01/32.53    (72)  op(e3, e1) = all_52_17
% 198.01/32.53    (73)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.53    (74)  op(e0, e3) = all_52_7
% 198.01/32.53    (75)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.53    (76)   ~ (all_52_9 = all_52_25)
% 198.01/32.53    (77)  all_58_15 = all_14_2
% 198.01/32.53    (78)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.53    (79)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.53    (80)  all_58_8 = all_10_2
% 198.01/32.53    (81)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.53    (82)   ~ (all_52_5 = all_10_2)
% 198.01/32.53    (83)   ~ (all_52_23 = all_14_2)
% 198.01/32.53    (84)  all_56_12 = all_52_7
% 198.01/32.53    (85)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.53    (86)  all_58_5 = all_4_0
% 198.01/32.53    (87)   ~ (all_52_25 = all_6_2)
% 198.01/32.53    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.53    (89)   ~ (all_52_9 = all_4_2)
% 198.01/32.53    (90)   ~ (all_52_5 = all_6_2)
% 198.01/32.53    (91)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.53    (92)   ~ (all_52_9 = all_6_2)
% 198.01/32.53    (93)   ~ (all_52_13 = all_52_15)
% 198.01/32.53    (94)  op(e3, e3) = all_6_2
% 198.01/32.53    (95)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.53    (96)   ~ (all_52_27 = all_14_2)
% 198.01/32.53    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.53    (98)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.53    (99)  all_56_3 = all_52_25
% 198.01/32.53    (100)  op(e0, all_14_1) = e2
% 198.01/32.53    (101)   ~ (all_52_3 = all_52_7)
% 198.01/32.53    (102)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.53    (103)  all_56_1 = all_52_9
% 198.01/32.53    (104)   ~ (all_52_15 = all_4_2)
% 198.01/32.53    (105)   ~ (all_52_27 = all_4_2)
% 198.01/32.53    (106)  all_58_6 = all_52_5
% 198.01/32.53    (107)   ~ (all_4_0 = all_4_2)
% 198.01/32.53    (108)  op(e3, e2) = all_52_9
% 198.01/32.53    (109)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.53    (110)   ~ (all_52_17 = all_6_2)
% 198.01/32.53    (111)   ~ (e1 = e0)
% 198.01/32.53    (112)   ~ (e3 = e2)
% 198.01/32.53    (113)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.53    (114)   ~ (all_52_9 = all_52_17)
% 198.01/32.53    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.53    (116)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.53    (117)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.53    (118)  op(e1, e1) = all_10_2
% 198.01/32.53    (119)   ~ (all_52_23 = all_10_2)
% 198.01/32.53    (120)   ~ (all_52_7 = all_52_23)
% 198.01/32.53    (121)  all_58_3 = all_4_2
% 198.01/32.53    (122)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.53    (123)   ~ (all_52_3 = all_4_2)
% 198.01/32.53    (124)   ~ (all_52_17 = all_52_23)
% 198.01/32.53    (125)  op(all_6_2, e3) = all_6_1
% 198.01/32.53    (126)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.53    (127)  all_58_4 = all_52_17
% 198.01/32.53    (128)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.53  
% 198.01/32.53  Begin of proof
% 198.01/32.53  | 
% 198.01/32.53  | ALPHA: (49) implies:
% 198.01/32.53  |   (129)  all_52_14 = e0
% 198.01/32.53  |   (130)  all_52_12 = e1
% 198.01/32.53  |   (131)  all_52_10 = e2
% 198.01/32.53  |   (132)  all_52_8 = e3
% 198.01/32.53  | 
% 198.01/32.53  | REDUCE: (52), (132) imply:
% 198.01/32.53  |   (133)  op(all_52_9, all_52_9) = e3
% 198.01/32.53  | 
% 198.01/32.53  | REDUCE: (117), (130) imply:
% 198.01/32.53  |   (134)  op(all_52_13, all_52_13) = e1
% 198.01/32.53  | 
% 198.01/32.53  | REDUCE: (53), (129) imply:
% 198.01/32.53  |   (135)  op(all_52_15, all_52_15) = e0
% 198.01/32.53  | 
% 198.01/32.53  | REDUCE: (98), (131) imply:
% 198.01/32.53  |   (136)  op(all_4_2, all_4_2) = e2
% 198.01/32.53  | 
% 198.01/32.53  | BETA: splitting (81) gives:
% 198.01/32.53  | 
% 198.01/32.53  | Case 1:
% 198.01/32.53  | | 
% 198.01/32.53  | |   (137)  all_56_15 = e3
% 198.01/32.53  | | 
% 198.01/32.53  | | COMBINE_EQS: (43), (137) imply:
% 198.01/32.53  | |   (138)  all_14_2 = e3
% 198.01/32.53  | | 
% 198.01/32.53  | | SIMP: (138) implies:
% 198.01/32.53  | |   (139)  all_14_2 = e3
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (59), (139) imply:
% 198.01/32.53  | |   (140)   ~ (all_52_7 = e3)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (68), (139) imply:
% 198.01/32.53  | |   (141)   ~ (all_52_15 = e3)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (38), (139) imply:
% 198.01/32.53  | |   (142)   ~ (all_52_25 = e3)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (96), (139) imply:
% 198.01/32.53  | |   (143)   ~ (all_52_27 = e3)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (102), (139) imply:
% 198.01/32.53  | |   (144)  op(e3, e3) = all_52_30
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (22), (139) imply:
% 198.01/32.53  | |   (145)  op(e3, e0) = all_14_1
% 198.01/32.53  | | 
% 198.01/32.53  | | GROUND_INST: instantiating (9) with all_52_25, all_14_1, e0, e3, simplifying
% 198.01/32.53  | |              with (25), (145) gives:
% 198.01/32.53  | |   (146)  all_52_25 = all_14_1
% 198.01/32.53  | | 
% 198.01/32.53  | | GROUND_INST: instantiating (9) with all_6_2, all_52_30, e3, e3, simplifying
% 198.01/32.53  | |              with (94), (144) gives:
% 198.01/32.53  | |   (147)  all_52_30 = all_6_2
% 198.01/32.53  | | 
% 198.01/32.53  | | COMBINE_EQS: (99), (146) imply:
% 198.01/32.53  | |   (148)  all_56_3 = all_14_1
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (76), (146) imply:
% 198.01/32.53  | |   (149)   ~ (all_52_9 = all_14_1)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (87), (146) imply:
% 198.01/32.53  | |   (150)   ~ (all_14_1 = all_6_2)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (142), (146) imply:
% 198.01/32.53  | |   (151)   ~ (all_14_1 = e3)
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (128), (146) imply:
% 198.01/32.53  | |   (152)  op(all_14_1, all_14_1) = all_52_24
% 198.01/32.53  | | 
% 198.01/32.53  | | BETA: splitting (88) gives:
% 198.01/32.53  | | 
% 198.01/32.53  | | Case 1:
% 198.01/32.53  | | | 
% 198.01/32.53  | | |   (153)  all_56_3 = e3
% 198.01/32.53  | | | 
% 198.01/32.53  | | | REF_CLOSE: (148), (151), (153) are inconsistent by sub-proof #1200.
% 198.01/32.53  | | | 
% 198.01/32.53  | | Case 2:
% 198.01/32.53  | | | 
% 198.01/32.53  | | |   (154)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.53  | | | 
% 198.01/32.53  | | | BETA: splitting (115) gives:
% 198.01/32.53  | | | 
% 198.01/32.53  | | | Case 1:
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | |   (155)  all_58_4 = e3
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | COMBINE_EQS: (127), (155) imply:
% 198.01/32.53  | | | |   (156)  all_52_17 = e3
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | SIMP: (156) implies:
% 198.01/32.53  | | | |   (157)  all_52_17 = e3
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REDUCE: (114), (157) imply:
% 198.01/32.53  | | | |   (158)   ~ (all_52_9 = e3)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REDUCE: (110), (157) imply:
% 198.01/32.53  | | | |   (159)   ~ (all_6_2 = e3)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | SIMP: (159) implies:
% 198.01/32.53  | | | |   (160)   ~ (all_6_2 = e3)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REDUCE: (6), (157) imply:
% 198.01/32.53  | | | |   (161)   ~ (all_4_0 = e3)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REDUCE: (85), (157) imply:
% 198.01/32.53  | | | |   (162)  op(e3, e3) = all_52_16
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_16, e3, e3,
% 198.01/32.53  | | | |              simplifying with (94), (162) gives:
% 198.01/32.53  | | | |   (163)  all_52_16 = all_6_2
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | BETA: splitting (44) gives:
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | Case 1:
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | |   (164)  all_58_2 = e3
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | COMBINE_EQS: (60), (164) imply:
% 198.01/32.53  | | | | |   (165)  all_52_3 = e3
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | SIMP: (165) implies:
% 198.01/32.53  | | | | |   (166)  all_52_3 = e3
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | REDUCE: (101), (166) imply:
% 198.01/32.53  | | | | |   (167)   ~ (all_52_7 = e3)
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | REDUCE: (123), (166) imply:
% 198.01/32.53  | | | | |   (168)   ~ (all_4_2 = e3)
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | SIMP: (168) implies:
% 198.01/32.53  | | | | |   (169)   ~ (all_4_2 = e3)
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | REDUCE: (8), (166) imply:
% 198.01/32.53  | | | | |   (170)  op(e3, e3) = all_52_2
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | BETA: splitting (75) gives:
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | Case 1:
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | |   (171)  all_58_1 = e3
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | | COMBINE_EQS: (11), (171) imply:
% 198.01/32.53  | | | | | |   (172)  all_52_9 = e3
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | | REDUCE: (158), (172) imply:
% 198.01/32.53  | | | | | |   (173)  $false
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | | CLOSE: (173) is inconsistent.
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | Case 2:
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | |   (174)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | | BETA: splitting (174) gives:
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | | Case 1:
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | |   (175)  all_58_3 = e3
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | | COMBINE_EQS: (121), (175) imply:
% 198.01/32.53  | | | | | | |   (176)  all_4_2 = e3
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | | REDUCE: (169), (176) imply:
% 198.01/32.53  | | | | | | |   (177)  $false
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | | CLOSE: (177) is inconsistent.
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | Case 2:
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | |   (178)  all_58_7 = e3 | all_58_13 = e3
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | | BETA: splitting (178) gives:
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | | Case 1:
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | |   (179)  all_58_7 = e3
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | COMBINE_EQS: (54), (179) imply:
% 198.01/32.53  | | | | | | | |   (180)  all_52_13 = e3
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | REDUCE: (10), (180) imply:
% 198.01/32.53  | | | | | | | |   (181)   ~ (all_52_5 = e3)
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | REDUCE: (134), (180) imply:
% 198.01/32.53  | | | | | | | |   (182)  op(e3, e3) = e1
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_2, e3, e3,
% 198.01/32.53  | | | | | | | |              simplifying with (94), (170) gives:
% 198.01/32.53  | | | | | | | |   (183)  all_52_2 = all_6_2
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | GROUND_INST: instantiating (9) with e1, all_52_2, e3, e3,
% 198.01/32.53  | | | | | | | |              simplifying with (170), (182) gives:
% 198.01/32.53  | | | | | | | |   (184)  all_52_2 = e1
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | COMBINE_EQS: (183), (184) imply:
% 198.01/32.53  | | | | | | | |   (185)  all_6_2 = e1
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | REF_CLOSE: (9), (11), (17), (21), (32), (56), (60), (62), (89),
% 198.01/32.53  | | | | | | | |            (92), (100), (103), (106), (113), (122), (123),
% 198.01/32.53  | | | | | | | |            (133), (135), (140), (148), (149), (150), (152),
% 198.01/32.53  | | | | | | | |            (154), (158), (160), (181), (185) are inconsistent by
% 198.01/32.53  | | | | | | | |            sub-proof #236.
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | Case 2:
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | |   (186)  all_58_13 = e3
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | | REF_CLOSE: (28), (141), (186) are inconsistent by sub-proof
% 198.01/32.53  | | | | | | | |            #1360.
% 198.01/32.53  | | | | | | | | 
% 198.01/32.53  | | | | | | | End of split
% 198.01/32.53  | | | | | | | 
% 198.01/32.53  | | | | | | End of split
% 198.01/32.53  | | | | | | 
% 198.01/32.53  | | | | | End of split
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | Case 2:
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | |   (187)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | | REF_CLOSE: (9), (21), (32), (35), (45), (50), (56), (58), (60), (62),
% 198.01/32.53  | | | | |            (82), (86), (106), (108), (118), (121), (123), (133),
% 198.01/32.53  | | | | |            (140), (143), (160), (187) are inconsistent by sub-proof
% 198.01/32.53  | | | | |            #42.
% 198.01/32.53  | | | | | 
% 198.01/32.53  | | | | End of split
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | Case 2:
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | |   (188)   ~ (all_58_4 = e3)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REDUCE: (127), (188) imply:
% 198.01/32.53  | | | |   (189)   ~ (all_52_17 = e3)
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | | REF_CLOSE: (5), (9), (11), (21), (23), (29), (40), (92), (94), (97),
% 198.01/32.53  | | | |            (125), (127), (133), (142), (189) are inconsistent by
% 198.01/32.53  | | | |            sub-proof #289.
% 198.01/32.53  | | | | 
% 198.01/32.53  | | | End of split
% 198.01/32.53  | | | 
% 198.01/32.53  | | End of split
% 198.01/32.53  | | 
% 198.01/32.53  | Case 2:
% 198.01/32.53  | | 
% 198.01/32.53  | |   (190)   ~ (all_56_15 = e3)
% 198.01/32.53  | |   (191)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.53  | | 
% 198.01/32.53  | | REDUCE: (43), (190) imply:
% 198.01/32.53  | |   (192)   ~ (all_14_2 = e3)
% 198.01/32.53  | | 
% 198.01/32.53  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.53  | |            (13), (14), (15), (16), (18), (19), (20), (21), (23), (24), (25),
% 198.01/32.53  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 198.01/32.53  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 198.01/32.53  | |            (48), (50), (51), (54), (55), (56), (57), (58), (59), (60), (61),
% 198.01/32.53  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 198.01/32.53  | |            (73), (74), (75), (76), (77), (78), (79), (80), (82), (83), (84),
% 198.01/32.53  | |            (85), (86), (87), (89), (90), (91), (92), (93), (94), (95), (97),
% 198.01/32.53  | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 198.01/32.53  | |            (110), (111), (112), (113), (114), (115), (116), (118), (119),
% 198.01/32.53  | |            (120), (121), (123), (124), (125), (126), (127), (128), (133),
% 198.01/32.53  | |            (134), (135), (136), (191), (192) are inconsistent by sub-proof
% 198.01/32.53  | |            #33.
% 198.01/32.53  | | 
% 198.01/32.53  | End of split
% 198.01/32.53  | 
% 198.01/32.53  End of proof
% 198.01/32.53  
% 198.01/32.53  Sub-proof #7 shows that the following formulas are inconsistent:
% 198.01/32.53  ----------------------------------------------------------------
% 198.01/32.53    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.53    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.53    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.53    (4)  all_58_14 = all_52_23
% 198.01/32.53    (5)   ~ (e3 = e1)
% 198.01/32.53    (6)   ~ (all_52_17 = all_4_0)
% 198.01/32.53    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.01/32.53    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.53    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.53    (10)   ~ (all_52_5 = all_52_13)
% 198.01/32.53    (11)  all_58_1 = all_52_9
% 198.01/32.53    (12)   ~ (all_52_9 = all_52_13)
% 198.01/32.53    (13)   ~ (e3 = e0)
% 198.01/32.53    (14)  op(e2, e3) = all_52_3
% 198.01/32.53    (15)   ~ (all_52_23 = all_4_0)
% 198.01/32.53    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.53    (17)   ~ (all_52_7 = all_52_15)
% 198.01/32.53    (18)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.53    (19)   ~ (all_52_17 = all_52_25)
% 198.01/32.53    (20)   ~ (all_52_3 = all_6_2)
% 198.01/32.53    (21)  all_58_0 = all_6_2
% 198.01/32.53    (22)  op(all_14_2, e0) = all_14_1
% 198.01/32.53    (23)  all_56_4 = all_52_3
% 198.01/32.53    (24)  op(e3, all_6_1) = e1
% 198.01/32.53    (25)   ~ (all_52_17 = all_10_2)
% 198.01/32.53    (26)  all_26_1 = all_10_1
% 198.01/32.53    (27)  op(e3, e0) = all_52_25
% 198.01/32.53    (28)  all_26_2 = all_10_2
% 198.01/32.53    (29)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.53    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.53    (31)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.53    (32)   ~ (all_52_27 = all_52_29)
% 198.01/32.53    (33)  all_58_13 = all_52_15
% 198.01/32.53    (34)  op(all_10_2, all_10_2) = all_52_20
% 198.01/32.53    (35)  all_58_9 = all_52_25
% 198.01/32.53    (36)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.01/32.53    (37)   ~ (all_52_29 = all_14_2)
% 198.01/32.54    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.54    (39)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.54    (40)  op(e1, e3) = all_52_5
% 198.01/32.54    (41)  op(e2, e2) = all_4_2
% 198.01/32.54    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.54    (43)   ~ (all_52_3 = all_52_5)
% 198.01/32.54    (44)  op(all_4_2, e2) = e1
% 198.01/32.54    (45)  all_58_11 = all_52_29
% 198.01/32.54    (46)  all_56_5 = all_4_2
% 198.01/32.54    (47)   ~ (all_52_25 = all_14_2)
% 198.01/32.54    (48)   ~ (all_52_9 = all_52_15)
% 198.01/32.54    (49)   ~ (all_52_3 = all_52_27)
% 198.01/32.54    (50)  op(all_10_2, e1) = all_10_1
% 198.01/32.54    (51)  all_46_2 = all_6_2
% 198.01/32.54    (52)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.54    (53)   ~ (all_52_7 = all_6_2)
% 198.01/32.54    (54)  op(e0, e0) = all_14_2
% 198.01/32.54    (55)  all_56_15 = all_14_2
% 198.01/32.54    (56)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.54    (57)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.54    (58)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 198.01/32.54    (59)  all_56_11 = all_52_29
% 198.01/32.54    (60)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.54    (61)   ~ (all_4_0 = e3)
% 198.01/32.54    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.54    (63)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.54    (64)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.54    (65)  all_56_9 = all_52_13
% 198.01/32.54    (66)   ~ (e2 = e1)
% 198.01/32.54    (67)  all_58_10 = all_52_27
% 198.01/32.54    (68)  all_56_8 = all_52_5
% 198.01/32.54    (69)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.54    (70)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.54    (71)   ~ (all_52_25 = all_52_29)
% 198.01/32.54    (72)   ~ (all_52_29 = all_10_2)
% 198.01/32.54    (73)  all_58_7 = all_52_13
% 198.01/32.54    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.54    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.54    (76)   ~ (all_52_5 = all_52_7)
% 198.01/32.54    (77)  all_58_12 = all_52_7
% 198.01/32.54    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.54    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.54    (80)   ~ (all_52_7 = all_14_2)
% 198.01/32.54    (81)   ~ (all_14_2 = e0)
% 198.01/32.54    (82)  all_58_2 = all_52_3
% 198.01/32.54    (83)  all_56_2 = all_52_17
% 198.01/32.54    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.54    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.54    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.54    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.54    (88)  all_56_7 = all_52_27
% 198.01/32.54    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.54    (90)   ~ (e2 = e0)
% 198.01/32.54    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.54    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.01/32.54    (93)   ~ (all_52_5 = all_52_29)
% 198.01/32.54    (94)   ~ (all_52_15 = all_14_2)
% 198.01/32.54    (95)   ~ (all_52_19 = all_52_27)
% 198.01/32.54    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.54    (97)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.54    (98)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.54    (99)   ~ (all_52_13 = all_4_2)
% 198.01/32.54    (100)  op(e3, e1) = all_52_17
% 198.01/32.54    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.54    (102)  op(e0, e3) = all_52_7
% 198.01/32.54    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.54    (104)   ~ (all_52_9 = all_52_25)
% 198.01/32.54    (105)  all_58_15 = all_14_2
% 198.01/32.54    (106)   ~ (all_52_19 = all_10_2)
% 198.01/32.54    (107)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.54    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.54    (109)  all_58_8 = all_10_2
% 198.01/32.54    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.54    (111)   ~ (all_52_5 = all_10_2)
% 198.01/32.54    (112)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.54    (113)   ~ (all_52_23 = all_14_2)
% 198.01/32.54    (114)  all_56_12 = all_52_7
% 198.01/32.54    (115)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.54    (116)  all_58_5 = all_4_0
% 198.01/32.54    (117)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.54    (118)   ~ (all_52_25 = all_6_2)
% 198.01/32.54    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.54    (120)   ~ (all_52_9 = all_4_2)
% 198.01/32.54    (121)   ~ (all_52_5 = all_6_2)
% 198.01/32.54    (122)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.54    (123)   ~ (all_52_9 = all_6_2)
% 198.01/32.54    (124)   ~ (all_52_13 = all_52_15)
% 198.01/32.54    (125)  all_56_0 = all_6_2
% 198.01/32.54    (126)  op(e3, e3) = all_6_2
% 198.01/32.54    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.54    (128)   ~ (all_52_27 = all_14_2)
% 198.01/32.54    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.54    (130)  all_56_14 = all_52_23
% 198.01/32.54    (131)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.54    (132)  all_56_3 = all_52_25
% 198.01/32.54    (133)   ~ (all_52_3 = all_52_7)
% 198.01/32.54    (134)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.54    (135)  all_58_5 = all_52_19
% 198.01/32.54    (136)  all_56_1 = all_52_9
% 198.01/32.54    (137)   ~ (all_52_15 = all_4_2)
% 198.01/32.54    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.54           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.54           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.54           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.54    (139)   ~ (all_52_27 = all_4_2)
% 198.01/32.54    (140)  all_58_6 = all_52_5
% 198.01/32.54    (141)   ~ (all_4_0 = all_4_2)
% 198.01/32.54    (142)  op(e3, e2) = all_52_9
% 198.01/32.54    (143)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.54    (144)   ~ (all_52_17 = all_6_2)
% 198.01/32.54    (145)   ~ (e1 = e0)
% 198.01/32.54    (146)   ~ (e3 = e2)
% 198.01/32.54    (147)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.54    (148)   ~ (all_52_9 = all_52_17)
% 198.01/32.54    (149)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.54    (150)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.54    (151)  all_46_1 = all_6_1
% 198.01/32.54    (152)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.54    (153)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.54    (154)  op(e1, e1) = all_10_2
% 198.01/32.54    (155)   ~ (all_52_23 = all_10_2)
% 198.01/32.54    (156)   ~ (all_52_7 = all_52_23)
% 198.01/32.54    (157)   ~ (all_52_17 = all_52_19)
% 198.01/32.54    (158)  all_58_3 = all_4_2
% 198.01/32.54    (159)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.54    (160)  all_56_13 = all_52_15
% 198.01/32.54    (161)   ~ (all_52_3 = all_4_2)
% 198.01/32.54    (162)   ~ (all_52_19 = all_4_2)
% 198.01/32.54    (163)   ~ (all_52_17 = all_52_23)
% 198.01/32.54    (164)  op(all_6_2, e3) = all_6_1
% 198.01/32.54    (165)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.54    (166)  all_58_4 = all_52_17
% 198.01/32.54    (167)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.54  
% 198.01/32.54  Begin of proof
% 198.01/32.54  | 
% 198.01/32.54  | BETA: splitting (138) gives:
% 198.01/32.54  | 
% 198.01/32.54  | Case 1:
% 198.01/32.54  | | 
% 198.01/32.54  | |   (168)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.54  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 198.01/32.54  | | 
% 198.01/32.54  | | BETA: splitting (168) gives:
% 198.01/32.54  | | 
% 198.01/32.54  | | Case 1:
% 198.01/32.54  | | | 
% 198.01/32.54  | | |   (169)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REF_CLOSE: (5), (8), (9), (18), (21), (24), (29), (41), (52), (53), (54),
% 198.01/32.54  | | |            (56), (77), (80), (82), (85), (111), (126), (129), (140),
% 198.01/32.54  | | |            (143), (154), (161), (164), (169) are inconsistent by sub-proof
% 198.01/32.54  | | |            #302.
% 198.01/32.54  | | | 
% 198.01/32.54  | | Case 2:
% 198.01/32.54  | | | 
% 198.01/32.54  | | |   (170)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.54  | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (24),
% 198.01/32.54  | | |            (25), (27), (30), (32), (33), (35), (36), (37), (39), (40),
% 198.01/32.54  | | |            (41), (42), (43), (44), (45), (46), (47), (48), (52), (53),
% 198.01/32.54  | | |            (54), (55), (56), (61), (63), (65), (66), (67), (68), (69),
% 198.01/32.54  | | |            (70), (73), (76), (77), (78), (79), (80), (82), (83), (85),
% 198.01/32.54  | | |            (88), (90), (91), (92), (93), (94), (97), (98), (99), (100),
% 198.01/32.54  | | |            (101), (102), (103), (104), (105), (107), (108), (109), (110),
% 198.01/32.54  | | |            (111), (113), (114), (115), (116), (118), (120), (121), (122),
% 198.01/32.54  | | |            (123), (124), (126), (127), (128), (129), (131), (133), (134),
% 198.01/32.54  | | |            (136), (137), (139), (140), (141), (142), (143), (144), (145),
% 198.01/32.54  | | |            (146), (147), (148), (149), (150), (153), (154), (155), (156),
% 198.01/32.54  | | |            (158), (161), (163), (164), (165), (166), (167), (170) are
% 198.01/32.54  | | |            inconsistent by sub-proof #32.
% 198.01/32.54  | | | 
% 198.01/32.54  | | End of split
% 198.01/32.54  | | 
% 198.01/32.54  | Case 2:
% 198.01/32.54  | | 
% 198.01/32.54  | |   (171)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 198.01/32.54  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 198.01/32.54  | |            e0)
% 198.01/32.54  | | 
% 198.01/32.54  | | BETA: splitting (171) gives:
% 198.01/32.54  | | 
% 198.01/32.54  | | Case 1:
% 198.01/32.54  | | | 
% 198.01/32.54  | | |   (172)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REF_CLOSE: (4), (9), (16), (18), (24), (25), (26), (28), (34), (41), (44),
% 198.01/32.54  | | |            (50), (53), (55), (58), (61), (63), (74), (78), (80), (81),
% 198.01/32.54  | | |            (83), (100), (102), (107), (109), (110), (113), (114), (115),
% 198.01/32.54  | | |            (116), (123), (126), (130), (142), (144), (149), (154), (155),
% 198.01/32.54  | | |            (156), (164), (166), (172) are inconsistent by sub-proof #8.
% 198.01/32.54  | | | 
% 198.01/32.54  | | Case 2:
% 198.01/32.54  | | | 
% 198.01/32.54  | | |   (173)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (12), (13), (14), (16),
% 198.01/32.54  | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 198.01/32.54  | | |            (29), (31), (32), (33), (35), (37), (38), (39), (40), (41),
% 198.01/32.54  | | |            (42), (43), (45), (46), (47), (48), (49), (50), (51), (52),
% 198.01/32.54  | | |            (53), (54), (55), (56), (57), (59), (60), (62), (63), (64),
% 198.01/32.54  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 198.01/32.54  | | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 198.01/32.54  | | |            (86), (87), (89), (90), (91), (93), (94), (95), (96), (97),
% 198.01/32.54  | | |            (98), (100), (101), (102), (103), (104), (105), (106), (107),
% 198.01/32.54  | | |            (108), (109), (110), (111), (112), (113), (114), (115), (117),
% 198.01/32.54  | | |            (118), (119), (120), (121), (123), (124), (125), (126), (127),
% 198.01/32.54  | | |            (128), (129), (130), (132), (133), (134), (135), (136), (137),
% 198.01/32.54  | | |            (139), (140), (142), (143), (144), (145), (146), (147), (151),
% 198.01/32.54  | | |            (152), (153), (154), (155), (156), (157), (158), (159), (160),
% 198.01/32.54  | | |            (161), (162), (163), (164), (165), (166), (167), (173) are
% 198.01/32.54  | | |            inconsistent by sub-proof #271.
% 198.01/32.54  | | | 
% 198.01/32.54  | | End of split
% 198.01/32.54  | | 
% 198.01/32.54  | End of split
% 198.01/32.54  | 
% 198.01/32.54  End of proof
% 198.01/32.54  
% 198.01/32.54  Sub-proof #8 shows that the following formulas are inconsistent:
% 198.01/32.54  ----------------------------------------------------------------
% 198.01/32.54    (1)  all_58_14 = all_52_23
% 198.01/32.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.54    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.54    (4)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.54    (5)  op(e3, all_6_1) = e1
% 198.01/32.54    (6)   ~ (all_52_17 = all_10_2)
% 198.01/32.54    (7)  all_26_1 = all_10_1
% 198.01/32.54    (8)  all_26_2 = all_10_2
% 198.01/32.54    (9)  op(all_10_2, all_10_2) = all_52_20
% 198.01/32.54    (10)  op(e2, e2) = all_4_2
% 198.01/32.54    (11)  op(all_4_2, e2) = e1
% 198.01/32.54    (12)  op(all_10_2, e1) = all_10_1
% 198.01/32.54    (13)   ~ (all_52_7 = all_6_2)
% 198.01/32.54    (14)  all_56_15 = all_14_2
% 198.01/32.54    (15)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 198.01/32.54    (16)   ~ (all_4_0 = e3)
% 198.01/32.54    (17)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.54    (18)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.54    (19)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.54    (20)   ~ (all_52_7 = all_14_2)
% 198.01/32.54    (21)   ~ (all_14_2 = e0)
% 198.01/32.54    (22)  all_56_2 = all_52_17
% 198.01/32.54    (23)  op(e3, e1) = all_52_17
% 198.01/32.54    (24)  op(e0, e3) = all_52_7
% 198.01/32.54    (25)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.54    (26)  all_58_8 = all_10_2
% 198.01/32.54    (27)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.54    (28)   ~ (all_52_23 = all_14_2)
% 198.01/32.54    (29)  all_56_12 = all_52_7
% 198.01/32.54    (30)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.54    (31)  all_58_5 = all_4_0
% 198.01/32.54    (32)   ~ (all_52_9 = all_6_2)
% 198.01/32.54    (33)  op(e3, e3) = all_6_2
% 198.01/32.54    (34)  all_56_14 = all_52_23
% 198.01/32.54    (35)  op(e3, e2) = all_52_9
% 198.01/32.54    (36)   ~ (all_52_17 = all_6_2)
% 198.01/32.54    (37)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.54    (38)  op(e1, e1) = all_10_2
% 198.01/32.54    (39)   ~ (all_52_23 = all_10_2)
% 198.01/32.54    (40)   ~ (all_52_7 = all_52_23)
% 198.01/32.54    (41)  op(all_6_2, e3) = all_6_1
% 198.01/32.54    (42)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.01/32.54    (43)  all_58_4 = all_52_17
% 198.01/32.54  
% 198.01/32.54  Begin of proof
% 198.01/32.54  | 
% 198.01/32.54  | ALPHA: (42) implies:
% 198.01/32.54  |   (44)  all_52_22 = e0
% 198.01/32.54  |   (45)  all_52_20 = e1
% 198.01/32.54  |   (46)  all_52_16 = e3
% 198.01/32.54  | 
% 198.01/32.54  | REDUCE: (30), (46) imply:
% 198.01/32.54  |   (47)  op(all_52_17, all_52_17) = e3
% 198.01/32.54  | 
% 198.01/32.54  | REDUCE: (25), (44) imply:
% 198.01/32.54  |   (48)  op(all_52_23, all_52_23) = e0
% 198.01/32.54  | 
% 198.01/32.54  | REDUCE: (9), (45) imply:
% 198.01/32.54  |   (49)  op(all_10_2, all_10_2) = e1
% 198.01/32.54  | 
% 198.01/32.54  | BETA: splitting (27) gives:
% 198.01/32.54  | 
% 198.01/32.54  | Case 1:
% 198.01/32.54  | | 
% 198.01/32.54  | |   (50)  all_56_15 = e3
% 198.01/32.54  | | 
% 198.01/32.54  | | COMBINE_EQS: (14), (50) imply:
% 198.01/32.54  | |   (51)  all_14_2 = e3
% 198.01/32.54  | | 
% 198.01/32.54  | | REDUCE: (28), (51) imply:
% 198.01/32.54  | |   (52)   ~ (all_52_23 = e3)
% 198.01/32.54  | | 
% 198.01/32.54  | | REF_CLOSE: (1), (2), (6), (7), (8), (10), (11), (12), (15), (16), (17),
% 198.01/32.54  | |            (22), (23), (26), (31), (32), (33), (35), (36), (37), (43), (47),
% 198.01/32.54  | |            (49), (52) are inconsistent by sub-proof #129.
% 198.01/32.54  | | 
% 198.01/32.54  | Case 2:
% 198.01/32.54  | | 
% 198.01/32.54  | |   (53)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.54  | | 
% 198.01/32.54  | | BETA: splitting (18) gives:
% 198.01/32.54  | | 
% 198.01/32.54  | | Case 1:
% 198.01/32.54  | | | 
% 198.01/32.54  | | |   (54)  all_56_14 = e3
% 198.01/32.54  | | | 
% 198.01/32.54  | | | COMBINE_EQS: (34), (54) imply:
% 198.01/32.54  | | |   (55)  all_52_23 = e3
% 198.01/32.54  | | | 
% 198.01/32.54  | | | SIMP: (55) implies:
% 198.01/32.54  | | |   (56)  all_52_23 = e3
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REDUCE: (40), (56) imply:
% 198.01/32.54  | | |   (57)   ~ (all_52_7 = e3)
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REF_CLOSE: (2), (3), (4), (5), (13), (14), (19), (20), (21), (23), (24),
% 198.01/32.54  | | |            (29), (33), (38), (39), (41), (47), (48), (53), (56), (57) are
% 198.01/32.54  | | |            inconsistent by sub-proof #9.
% 198.01/32.54  | | | 
% 198.01/32.54  | | Case 2:
% 198.01/32.54  | | | 
% 198.01/32.54  | | |   (58)   ~ (all_56_14 = e3)
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REDUCE: (34), (58) imply:
% 198.01/32.54  | | |   (59)   ~ (all_52_23 = e3)
% 198.01/32.54  | | | 
% 198.01/32.54  | | | REF_CLOSE: (1), (2), (6), (7), (8), (10), (11), (12), (15), (16), (17),
% 198.01/32.54  | | |            (22), (23), (26), (31), (32), (33), (35), (36), (37), (43),
% 198.01/32.54  | | |            (47), (49), (59) are inconsistent by sub-proof #129.
% 198.01/32.54  | | | 
% 198.01/32.54  | | End of split
% 198.01/32.54  | | 
% 198.01/32.54  | End of split
% 198.01/32.54  | 
% 198.01/32.54  End of proof
% 198.01/32.54  
% 198.01/32.54  Sub-proof #9 shows that the following formulas are inconsistent:
% 198.01/32.54  ----------------------------------------------------------------
% 198.01/32.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.54    (2)  op(all_52_23, all_52_23) = e0
% 198.01/32.54    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.54    (4)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.54    (5)  op(e3, all_6_1) = e1
% 198.01/32.54    (6)   ~ (all_52_7 = all_6_2)
% 198.01/32.54    (7)  all_56_15 = all_14_2
% 198.01/32.54    (8)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.54    (9)   ~ (all_52_7 = e3)
% 198.01/32.54    (10)   ~ (all_52_7 = all_14_2)
% 198.01/32.54    (11)   ~ (all_14_2 = e0)
% 198.01/32.54    (12)  all_52_23 = e3
% 198.01/32.54    (13)  op(e3, e1) = all_52_17
% 198.01/32.54    (14)  op(e0, e3) = all_52_7
% 198.01/32.54    (15)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.54    (16)  all_56_12 = all_52_7
% 198.01/32.54    (17)  op(e3, e3) = all_6_2
% 198.01/32.54    (18)  op(all_52_17, all_52_17) = e3
% 198.01/32.54    (19)  op(e1, e1) = all_10_2
% 198.01/32.54    (20)   ~ (all_52_23 = all_10_2)
% 198.01/32.54    (21)  op(all_6_2, e3) = all_6_1
% 198.01/32.54  
% 198.01/32.54  Begin of proof
% 198.01/32.54  | 
% 198.01/32.54  | REDUCE: (12), (20) imply:
% 198.01/32.54  |   (22)   ~ (all_10_2 = e3)
% 198.01/32.54  | 
% 198.01/32.54  | SIMP: (22) implies:
% 198.01/32.54  |   (23)   ~ (all_10_2 = e3)
% 198.01/32.54  | 
% 198.01/32.54  | REDUCE: (2), (12) imply:
% 198.01/32.54  |   (24)  op(e3, e3) = e0
% 198.01/32.54  | 
% 198.01/32.54  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 198.01/32.54  |            (15), (16), (17), (18), (19), (21), (23), (24) are inconsistent by
% 198.01/32.54  |            sub-proof #277.
% 198.01/32.54  | 
% 198.01/32.54  End of proof
% 198.01/32.54  
% 198.01/32.54  Sub-proof #10 shows that the following formulas are inconsistent:
% 198.01/32.54  ----------------------------------------------------------------
% 198.01/32.54    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.54    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.54    (3)  all_58_14 = all_52_23
% 198.01/32.54    (4)   ~ (e3 = e1)
% 198.01/32.54    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.54    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.54    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.54    (8)  all_58_1 = all_52_9
% 198.01/32.54    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.54    (10)   ~ (e3 = e0)
% 198.01/32.54    (11)  op(e2, e3) = all_52_3
% 198.01/32.54    (12)   ~ (all_52_23 = all_4_0)
% 198.01/32.54    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.54    (14)   ~ (all_52_7 = all_52_15)
% 198.01/32.54    (15)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.54    (16)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.54    (17)   ~ (all_52_17 = all_52_25)
% 198.01/32.54    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.54    (19)  all_58_0 = all_6_2
% 198.01/32.54    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.54    (21)  all_46_0 = e1
% 198.01/32.54    (22)  all_56_4 = all_52_3
% 198.01/32.54    (23)  op(e3, all_6_1) = e1
% 198.01/32.54    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.54    (25)  op(e3, e0) = all_52_25
% 198.01/32.54    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.54    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.54    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.54    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.54    (30)  all_58_13 = all_52_15
% 198.01/32.54    (31)  all_58_9 = all_52_25
% 198.01/32.54    (32)   ~ (all_52_29 = all_14_2)
% 198.01/32.54    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.54    (34)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.54    (35)  op(e1, e3) = all_52_5
% 198.01/32.54    (36)  op(e2, e2) = all_4_2
% 198.01/32.54    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.54    (38)   ~ (all_52_3 = all_52_5)
% 198.01/32.54    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.54    (40)  op(all_4_2, e2) = e1
% 198.01/32.54    (41)  all_58_11 = all_52_29
% 198.01/32.54    (42)  all_56_5 = all_4_2
% 198.01/32.54    (43)   ~ (all_52_25 = all_14_2)
% 198.01/32.54    (44)   ~ (all_52_9 = all_52_15)
% 198.01/32.55    (45)   ~ (all_52_3 = all_52_27)
% 198.01/32.55    (46)  op(all_10_2, e1) = all_10_1
% 198.01/32.55    (47)  all_46_2 = all_6_2
% 198.01/32.55    (48)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.55    (49)   ~ (all_52_7 = all_6_2)
% 198.01/32.55    (50)  op(e0, e0) = all_14_2
% 198.01/32.55    (51)  all_56_15 = all_14_2
% 198.01/32.55    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.55    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.55    (54)  all_56_11 = all_52_29
% 198.01/32.55    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.55    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.55    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.55    (58)   ~ (e2 = e1)
% 198.01/32.55    (59)  all_58_10 = all_52_27
% 198.01/32.55    (60)  all_56_8 = all_52_5
% 198.01/32.55    (61)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.55    (62)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.55    (63)   ~ (all_52_25 = all_52_29)
% 198.01/32.55    (64)   ~ (all_52_29 = all_10_2)
% 198.01/32.55    (65)  all_58_7 = all_52_13
% 198.01/32.55    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.55    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.55    (68)   ~ (all_52_5 = all_52_7)
% 198.01/32.55    (69)  all_58_12 = all_52_7
% 198.01/32.55    (70)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.55    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.55    (72)   ~ (all_52_7 = all_14_2)
% 198.01/32.55    (73)  all_58_2 = all_52_3
% 198.01/32.55    (74)  all_56_2 = all_52_17
% 198.01/32.55    (75)  all_28_0 = all_4_0
% 198.01/32.55    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.55    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.55    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.55    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.55    (80)  all_56_7 = all_52_27
% 198.01/32.55    (81)  all_28_2 = all_4_2
% 198.01/32.55    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.55    (83)   ~ (e2 = e0)
% 198.01/32.55    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.55    (85)   ~ (all_52_5 = all_52_29)
% 198.01/32.55    (86)   ~ (all_52_15 = all_14_2)
% 198.01/32.55    (87)   ~ (all_52_19 = all_52_27)
% 198.01/32.55    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.55    (89)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.55    (90)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.55            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.55    (91)   ~ (all_52_13 = all_4_2)
% 198.01/32.55    (92)  op(e3, e1) = all_52_17
% 198.01/32.55    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.55    (94)  op(e0, e3) = all_52_7
% 198.01/32.55    (95)  op(e1, e2) = all_52_13
% 198.01/32.55    (96)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.55    (97)   ~ (all_52_9 = all_52_25)
% 198.01/32.55    (98)  all_58_15 = all_14_2
% 198.01/32.55    (99)   ~ (all_52_19 = all_10_2)
% 198.01/32.55    (100)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.55    (101)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.55    (102)  all_58_8 = all_10_2
% 198.01/32.55    (103)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.55    (104)   ~ (all_52_5 = all_10_2)
% 198.01/32.55    (105)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.55    (106)   ~ (all_52_23 = all_14_2)
% 198.01/32.55    (107)  all_56_12 = all_52_7
% 198.01/32.55    (108)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.55    (109)  all_58_5 = all_4_0
% 198.01/32.55    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.55    (111)   ~ (all_52_25 = all_6_2)
% 198.01/32.55    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.55    (113)   ~ (all_52_9 = all_4_2)
% 198.01/32.55    (114)   ~ (all_52_5 = all_6_2)
% 198.01/32.55    (115)   ~ (all_52_9 = all_6_2)
% 198.01/32.55    (116)   ~ (all_52_13 = all_52_15)
% 198.01/32.55    (117)  all_56_0 = all_6_2
% 198.01/32.55    (118)  op(all_4_0, all_4_0) = all_52_18
% 198.01/32.55    (119)  op(e3, e3) = all_6_2
% 198.01/32.55    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.55    (121)   ~ (all_52_27 = all_14_2)
% 198.01/32.55    (122)   ~ (all_52_27 = all_4_0)
% 198.01/32.55    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.55    (124)  all_56_14 = all_52_23
% 198.01/32.55    (125)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.55    (126)  all_56_3 = all_52_25
% 198.01/32.55    (127)  all_28_0 = e3
% 198.01/32.55    (128)   ~ (all_52_3 = all_52_7)
% 198.01/32.55    (129)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.55    (130)  all_58_5 = all_52_19
% 198.01/32.55    (131)  all_56_1 = all_52_9
% 198.01/32.55    (132)   ~ (all_52_15 = all_4_2)
% 198.01/32.55    (133)  op(e0, all_14_1) = e3
% 198.01/32.55    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.55           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.55           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.55           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.55    (135)   ~ (all_52_27 = all_4_2)
% 198.01/32.55    (136)  all_58_6 = all_52_5
% 198.01/32.55    (137)   ~ (all_4_0 = all_4_2)
% 198.01/32.55    (138)  op(e3, e2) = all_52_9
% 198.01/32.55    (139)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.55    (140)   ~ (all_52_17 = all_6_2)
% 198.01/32.55    (141)   ~ (e1 = e0)
% 198.01/32.55    (142)   ~ (e3 = e2)
% 198.01/32.55    (143)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.55    (144)   ~ (all_52_9 = all_52_17)
% 198.01/32.55    (145)   ~ (all_52_3 = all_4_0)
% 198.01/32.55    (146)  all_46_1 = all_6_1
% 198.01/32.55    (147)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.55    (148)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.55    (149)  op(e1, e1) = all_10_2
% 198.01/32.55    (150)   ~ (all_52_23 = all_10_2)
% 198.01/32.55    (151)   ~ (all_52_7 = all_52_23)
% 198.01/32.55    (152)   ~ (all_52_17 = all_52_19)
% 198.01/32.55    (153)  all_58_3 = all_4_2
% 198.01/32.55    (154)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.55    (155)  all_56_13 = all_52_15
% 198.01/32.55    (156)   ~ (all_52_3 = all_4_2)
% 198.01/32.55    (157)  all_28_1 = e1
% 198.01/32.55    (158)   ~ (all_52_19 = all_4_2)
% 198.01/32.55    (159)   ~ (all_52_17 = all_52_23)
% 198.01/32.55    (160)  op(all_6_2, e3) = all_6_1
% 198.01/32.55    (161)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.55    (162)  all_58_4 = all_52_17
% 198.01/32.55    (163)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.55  
% 198.01/32.55  Begin of proof
% 198.01/32.55  | 
% 198.01/32.55  | COMBINE_EQS: (75), (127) imply:
% 198.01/32.55  |   (164)  all_4_0 = e3
% 198.01/32.55  | 
% 198.01/32.55  | SIMP: (164) implies:
% 198.01/32.55  |   (165)  all_4_0 = e3
% 198.01/32.55  | 
% 198.01/32.55  | COMBINE_EQS: (109), (165) imply:
% 198.01/32.55  |   (166)  all_58_5 = e3
% 198.01/32.55  | 
% 198.01/32.55  | REDUCE: (145), (165) imply:
% 198.01/32.55  |   (167)   ~ (all_52_3 = e3)
% 198.01/32.55  | 
% 198.01/32.55  | REDUCE: (5), (165) imply:
% 198.01/32.55  |   (168)   ~ (all_52_17 = e3)
% 198.01/32.55  | 
% 198.01/32.55  | REDUCE: (12), (165) imply:
% 198.01/32.55  |   (169)   ~ (all_52_23 = e3)
% 198.01/32.55  | 
% 198.01/32.55  | REDUCE: (122), (165) imply:
% 198.01/32.55  |   (170)   ~ (all_52_27 = e3)
% 198.01/32.55  | 
% 198.01/32.55  | REDUCE: (137), (165) imply:
% 198.01/32.55  |   (171)   ~ (all_4_2 = e3)
% 198.01/32.55  | 
% 198.01/32.55  | SIMP: (171) implies:
% 198.01/32.55  |   (172)   ~ (all_4_2 = e3)
% 198.01/32.55  | 
% 198.01/32.55  | REDUCE: (118), (165) imply:
% 198.01/32.55  |   (173)  op(e3, e3) = all_52_18
% 198.01/32.55  | 
% 198.01/32.55  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 198.01/32.55  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 198.01/32.55  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 198.01/32.55  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 198.01/32.55  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 198.01/32.55  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 198.01/32.55  |            (70), (71), (72), (73), (74), (76), (77), (78), (79), (80), (81),
% 198.01/32.55  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 198.01/32.55  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 198.01/32.55  |            (103), (104), (105), (106), (107), (108), (110), (111), (112),
% 198.01/32.55  |            (113), (114), (115), (116), (117), (119), (120), (121), (123),
% 198.01/32.55  |            (124), (125), (126), (128), (129), (130), (131), (132), (133),
% 198.01/32.55  |            (134), (135), (136), (138), (139), (140), (141), (142), (143),
% 198.01/32.55  |            (144), (146), (147), (148), (149), (150), (151), (152), (153),
% 198.01/32.55  |            (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 198.01/32.55  |            (163), (166), (167), (168), (169), (170), (172), (173) are
% 198.01/32.55  |            inconsistent by sub-proof #11.
% 198.01/32.55  | 
% 198.01/32.55  End of proof
% 198.01/32.55  
% 198.01/32.55  Sub-proof #11 shows that the following formulas are inconsistent:
% 198.01/32.55  ----------------------------------------------------------------
% 198.01/32.55    (1)  op(e3, e3) = all_52_18
% 198.01/32.55    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.55    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.55    (4)  all_58_14 = all_52_23
% 198.01/32.55    (5)   ~ (e3 = e1)
% 198.01/32.55    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.55    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.55    (8)  all_58_1 = all_52_9
% 198.01/32.55    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.55    (10)   ~ (e3 = e0)
% 198.01/32.55    (11)  op(e2, e3) = all_52_3
% 198.01/32.55    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.55    (13)   ~ (all_52_7 = all_52_15)
% 198.01/32.55    (14)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.55    (15)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.55    (16)   ~ (all_52_17 = all_52_25)
% 198.01/32.55    (17)   ~ (all_4_2 = e3)
% 198.01/32.55    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.55    (19)  all_58_0 = all_6_2
% 198.01/32.55    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.55    (21)  all_46_0 = e1
% 198.01/32.55    (22)  all_56_4 = all_52_3
% 198.01/32.55    (23)  op(e3, all_6_1) = e1
% 198.01/32.55    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.55    (25)  op(e3, e0) = all_52_25
% 198.01/32.55    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.55    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.55    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.55    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.55    (30)  all_58_13 = all_52_15
% 198.01/32.55    (31)  all_58_9 = all_52_25
% 198.01/32.55    (32)   ~ (all_52_29 = all_14_2)
% 198.01/32.55    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.55    (34)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.55    (35)  op(e1, e3) = all_52_5
% 198.01/32.55    (36)  op(e2, e2) = all_4_2
% 198.01/32.55    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.55    (38)   ~ (all_52_3 = all_52_5)
% 198.01/32.55    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.55    (40)  op(all_4_2, e2) = e1
% 198.01/32.55    (41)  all_58_11 = all_52_29
% 198.01/32.55    (42)   ~ (all_52_3 = e3)
% 198.01/32.55    (43)  all_56_5 = all_4_2
% 198.01/32.55    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.55    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.55    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.55    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.55    (48)  all_46_2 = all_6_2
% 198.01/32.55    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.55    (50)   ~ (all_52_7 = all_6_2)
% 198.01/32.55    (51)  op(e0, e0) = all_14_2
% 198.01/32.55    (52)  all_56_15 = all_14_2
% 198.01/32.55    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.55    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.55    (55)  all_56_11 = all_52_29
% 198.01/32.55    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.55    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.55    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.55    (59)   ~ (e2 = e1)
% 198.01/32.55    (60)  all_58_10 = all_52_27
% 198.01/32.55    (61)  all_56_8 = all_52_5
% 198.01/32.55    (62)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.55    (63)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.55    (64)   ~ (all_52_25 = all_52_29)
% 198.01/32.55    (65)   ~ (all_52_29 = all_10_2)
% 198.01/32.55    (66)  all_58_7 = all_52_13
% 198.01/32.55    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.55    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.55    (69)   ~ (all_52_5 = all_52_7)
% 198.01/32.55    (70)  all_58_12 = all_52_7
% 198.01/32.55    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.55    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.55    (73)   ~ (all_52_7 = all_14_2)
% 198.01/32.55    (74)  all_58_2 = all_52_3
% 198.01/32.55    (75)  all_56_2 = all_52_17
% 198.01/32.55    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.55    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.55    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.55    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.55    (80)  all_56_7 = all_52_27
% 198.01/32.55    (81)  all_28_2 = all_4_2
% 198.01/32.55    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.55    (83)   ~ (e2 = e0)
% 198.01/32.55    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.55    (85)   ~ (all_52_23 = e3)
% 198.01/32.55    (86)   ~ (all_52_5 = all_52_29)
% 198.01/32.55    (87)   ~ (all_52_15 = all_14_2)
% 198.01/32.55    (88)   ~ (all_52_19 = all_52_27)
% 198.01/32.55    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.55    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.55    (91)   ~ (all_52_27 = e3)
% 198.01/32.55    (92)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.55            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.55    (93)   ~ (all_52_13 = all_4_2)
% 198.01/32.55    (94)  op(e3, e1) = all_52_17
% 198.01/32.55    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.55    (96)  op(e0, e3) = all_52_7
% 198.01/32.55    (97)  op(e1, e2) = all_52_13
% 198.01/32.55    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.55    (99)   ~ (all_52_9 = all_52_25)
% 198.01/32.55    (100)  all_58_15 = all_14_2
% 198.01/32.55    (101)   ~ (all_52_19 = all_10_2)
% 198.01/32.55    (102)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.55    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.55    (104)  all_58_8 = all_10_2
% 198.01/32.55    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.55    (106)   ~ (all_52_5 = all_10_2)
% 198.01/32.55    (107)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.55    (108)   ~ (all_52_23 = all_14_2)
% 198.01/32.55    (109)  all_56_12 = all_52_7
% 198.01/32.55    (110)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.55    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.55    (112)   ~ (all_52_25 = all_6_2)
% 198.01/32.55    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.55    (114)   ~ (all_52_9 = all_4_2)
% 198.01/32.55    (115)   ~ (all_52_5 = all_6_2)
% 198.01/32.55    (116)   ~ (all_52_9 = all_6_2)
% 198.01/32.55    (117)   ~ (all_52_13 = all_52_15)
% 198.01/32.55    (118)  all_56_0 = all_6_2
% 198.01/32.55    (119)  op(e3, e3) = all_6_2
% 198.01/32.55    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.55    (121)   ~ (all_52_27 = all_14_2)
% 198.01/32.55    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.55    (123)  all_58_5 = e3
% 198.01/32.55    (124)  all_56_14 = all_52_23
% 198.01/32.55    (125)   ~ (all_52_17 = e3)
% 198.01/32.55    (126)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.55    (127)  all_56_3 = all_52_25
% 198.01/32.55    (128)   ~ (all_52_3 = all_52_7)
% 198.01/32.55    (129)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.55    (130)  all_58_5 = all_52_19
% 198.01/32.55    (131)  all_56_1 = all_52_9
% 198.01/32.55    (132)   ~ (all_52_15 = all_4_2)
% 198.01/32.55    (133)  op(e0, all_14_1) = e3
% 198.01/32.55    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.55           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.55           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.55           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.55    (135)   ~ (all_52_27 = all_4_2)
% 198.01/32.55    (136)  all_58_6 = all_52_5
% 198.01/32.55    (137)  op(e3, e2) = all_52_9
% 198.01/32.55    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.55    (139)   ~ (all_52_17 = all_6_2)
% 198.01/32.55    (140)   ~ (e1 = e0)
% 198.01/32.55    (141)   ~ (e3 = e2)
% 198.01/32.55    (142)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.55    (143)   ~ (all_52_9 = all_52_17)
% 198.01/32.55    (144)  all_46_1 = all_6_1
% 198.01/32.55    (145)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.55    (146)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.55    (147)  op(e1, e1) = all_10_2
% 198.01/32.55    (148)   ~ (all_52_23 = all_10_2)
% 198.01/32.55    (149)   ~ (all_52_7 = all_52_23)
% 198.01/32.55    (150)   ~ (all_52_17 = all_52_19)
% 198.01/32.55    (151)  all_58_3 = all_4_2
% 198.01/32.55    (152)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.55    (153)  all_56_13 = all_52_15
% 198.01/32.55    (154)   ~ (all_52_3 = all_4_2)
% 198.01/32.55    (155)  all_28_1 = e1
% 198.01/32.55    (156)   ~ (all_52_19 = all_4_2)
% 198.01/32.55    (157)   ~ (all_52_17 = all_52_23)
% 198.01/32.55    (158)  op(all_6_2, e3) = all_6_1
% 198.01/32.55    (159)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.55    (160)  all_58_4 = all_52_17
% 198.01/32.55    (161)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.55  
% 198.01/32.55  Begin of proof
% 198.01/32.55  | 
% 198.01/32.55  | BETA: splitting (126) gives:
% 198.01/32.55  | 
% 198.01/32.55  | Case 1:
% 198.01/32.55  | | 
% 198.01/32.55  | |   (162)   ~ (all_28_1 = e1)
% 198.01/32.55  | | 
% 198.01/32.55  | | REDUCE: (155), (162) imply:
% 198.01/32.55  | |   (163)  $false
% 198.01/32.55  | | 
% 198.01/32.55  | | CLOSE: (163) is inconsistent.
% 198.01/32.55  | | 
% 198.01/32.55  | Case 2:
% 198.01/32.55  | | 
% 198.01/32.55  | |   (164)   ~ (all_28_2 = e0)
% 198.01/32.55  | | 
% 198.01/32.55  | | REDUCE: (81), (164) imply:
% 198.01/32.55  | |   (165)   ~ (all_4_2 = e0)
% 198.01/32.55  | | 
% 198.01/32.55  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 198.01/32.55  | |              with (1), (119) gives:
% 198.01/32.55  | |   (166)  all_52_18 = all_6_2
% 198.01/32.55  | | 
% 198.01/32.55  | | BETA: splitting (14) gives:
% 198.01/32.55  | | 
% 198.01/32.55  | | Case 1:
% 198.01/32.55  | | | 
% 198.01/32.55  | | |   (167)   ~ (all_46_0 = e1)
% 198.01/32.55  | | | 
% 198.01/32.55  | | | REDUCE: (21), (167) imply:
% 198.01/32.55  | | |   (168)  $false
% 198.01/32.55  | | | 
% 198.01/32.55  | | | CLOSE: (168) is inconsistent.
% 198.01/32.55  | | | 
% 198.01/32.55  | | Case 2:
% 198.01/32.55  | | | 
% 198.01/32.55  | | |   (169)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.55  | | | 
% 198.01/32.55  | | | BETA: splitting (92) gives:
% 198.01/32.55  | | | 
% 198.01/32.55  | | | Case 1:
% 198.01/32.55  | | | | 
% 198.01/32.55  | | | |   (170)  all_58_15 = e0
% 198.01/32.55  | | | | 
% 198.01/32.55  | | | | REF_CLOSE: (6), (7), (10), (20), (39), (42), (51), (60), (74), (100),
% 198.01/32.55  | | | |            (121), (123), (129), (133), (151), (165), (170) are
% 198.01/32.55  | | | |            inconsistent by sub-proof #139.
% 198.01/32.55  | | | | 
% 198.01/32.55  | | | Case 2:
% 198.01/32.55  | | | | 
% 198.01/32.55  | | | |   (171)   ~ (all_58_15 = e0)
% 198.01/32.56  | | | |   (172)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 198.01/32.56  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.56  | | | | 
% 198.01/32.56  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.56  | | | |            (13), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 198.01/32.56  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.01/32.56  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 198.01/32.56  | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 198.01/32.56  | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 198.01/32.56  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 198.01/32.56  | | | |            (75), (76), (77), (78), (79), (80), (82), (83), (84), (85),
% 198.01/32.56  | | | |            (86), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 198.01/32.56  | | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 198.01/32.56  | | | |            (106), (107), (108), (109), (110), (111), (112), (113),
% 198.01/32.56  | | | |            (114), (115), (116), (117), (118), (119), (120), (121),
% 198.01/32.56  | | | |            (122), (123), (124), (125), (127), (128), (129), (130),
% 198.01/32.56  | | | |            (131), (132), (134), (135), (136), (137), (138), (139),
% 198.01/32.56  | | | |            (140), (141), (142), (143), (144), (145), (146), (147),
% 198.01/32.56  | | | |            (148), (149), (150), (151), (152), (153), (154), (156),
% 198.01/32.56  | | | |            (157), (158), (159), (160), (161), (165), (166), (169),
% 198.01/32.56  | | | |            (171), (172) are inconsistent by sub-proof #16.
% 198.01/32.56  | | | | 
% 198.01/32.56  | | | End of split
% 198.01/32.56  | | | 
% 198.01/32.56  | | End of split
% 198.01/32.56  | | 
% 198.01/32.56  | End of split
% 198.01/32.56  | 
% 198.01/32.56  End of proof
% 198.01/32.56  
% 198.01/32.56  Sub-proof #12 shows that the following formulas are inconsistent:
% 198.01/32.56  ----------------------------------------------------------------
% 198.01/32.56    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.56    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.56    (3)  all_58_14 = all_52_23
% 198.01/32.56    (4)   ~ (e3 = e1)
% 198.01/32.56    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.56    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.56    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.56    (8)  all_58_1 = all_52_9
% 198.01/32.56    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.56    (10)   ~ (e3 = e0)
% 198.01/32.56    (11)  op(e2, e3) = all_52_3
% 198.01/32.56    (12)   ~ (all_52_23 = all_4_0)
% 198.01/32.56    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.56    (14)   ~ (all_52_7 = all_52_15)
% 198.01/32.56    (15)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.56    (16)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.56    (17)   ~ (all_52_17 = all_52_25)
% 198.01/32.56    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.56    (19)  all_58_0 = all_6_2
% 198.01/32.56    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.56    (21)  all_46_0 = e1
% 198.01/32.56    (22)  all_56_4 = all_52_3
% 198.01/32.56    (23)  op(e3, all_6_1) = e1
% 198.01/32.56    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.56    (25)  op(e3, e0) = all_52_25
% 198.01/32.56    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.56    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.56    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.56    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.56    (30)  all_58_13 = all_52_15
% 198.01/32.56    (31)  op(e0, all_14_1) = e1
% 198.01/32.56    (32)  all_58_9 = all_52_25
% 198.01/32.56    (33)   ~ (all_52_29 = all_14_2)
% 198.01/32.56    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.56    (35)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.56    (36)  op(e1, e3) = all_52_5
% 198.01/32.56    (37)  op(e2, e2) = all_4_2
% 198.01/32.56    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.56    (39)   ~ (all_52_3 = all_52_5)
% 198.01/32.56    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.56    (41)  op(all_4_2, e2) = e1
% 198.01/32.56    (42)  all_58_11 = all_52_29
% 198.01/32.56    (43)  all_56_5 = all_4_2
% 198.01/32.56    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.56    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.56    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.56    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.56    (48)  all_46_2 = all_6_2
% 198.01/32.56    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.56    (50)   ~ (all_52_7 = all_6_2)
% 198.01/32.56    (51)  op(e0, e0) = all_14_2
% 198.01/32.56    (52)  all_56_15 = all_14_2
% 198.01/32.56    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.56    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.56    (55)  all_56_11 = all_52_29
% 198.01/32.56    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.56    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.56    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.56    (59)   ~ (e2 = e1)
% 198.01/32.56    (60)  all_58_10 = all_52_27
% 198.01/32.56    (61)  all_56_8 = all_52_5
% 198.01/32.56    (62)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.56    (63)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.56    (64)   ~ (all_52_25 = all_52_29)
% 198.01/32.56    (65)   ~ (all_52_29 = all_10_2)
% 198.01/32.56    (66)  all_58_7 = all_52_13
% 198.01/32.56    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.56    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.56    (69)   ~ (all_52_5 = all_52_7)
% 198.01/32.56    (70)  all_58_12 = all_52_7
% 198.01/32.56    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.56    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.56    (73)   ~ (all_52_7 = all_14_2)
% 198.01/32.56    (74)  all_58_2 = all_52_3
% 198.01/32.56    (75)  all_56_2 = all_52_17
% 198.01/32.56    (76)  all_28_0 = all_4_0
% 198.01/32.56    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.56    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.56    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.56    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.56    (81)  all_56_7 = all_52_27
% 198.01/32.56    (82)  all_28_2 = all_4_2
% 198.01/32.56    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.56    (84)   ~ (e2 = e0)
% 198.01/32.56    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.56    (86)   ~ (all_52_5 = all_52_29)
% 198.01/32.56    (87)   ~ (all_52_15 = all_14_2)
% 198.01/32.56    (88)   ~ (all_52_19 = all_52_27)
% 198.01/32.56    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.56    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.56    (91)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.56            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.56    (92)   ~ (all_52_13 = all_4_2)
% 198.01/32.56    (93)  op(e3, e1) = all_52_17
% 198.01/32.56    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.56    (95)  op(e0, e3) = all_52_7
% 198.01/32.56    (96)  op(e1, e2) = all_52_13
% 198.01/32.56    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.56    (98)   ~ (all_52_9 = all_52_25)
% 198.01/32.56    (99)  all_58_15 = all_14_2
% 198.01/32.56    (100)   ~ (all_52_19 = all_10_2)
% 198.01/32.56    (101)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.56    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.56    (103)  all_58_8 = all_10_2
% 198.01/32.56    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.56    (105)   ~ (all_52_5 = all_10_2)
% 198.01/32.56    (106)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.56    (107)   ~ (all_52_23 = all_14_2)
% 198.01/32.56    (108)  all_56_12 = all_52_7
% 198.01/32.56    (109)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.56    (110)  all_58_5 = all_4_0
% 198.01/32.56    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.56    (112)   ~ (all_52_25 = all_6_2)
% 198.01/32.56    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.56    (114)   ~ (all_52_9 = all_4_2)
% 198.01/32.56    (115)   ~ (all_52_5 = all_6_2)
% 198.01/32.56    (116)   ~ (all_52_9 = all_6_2)
% 198.01/32.56    (117)   ~ (all_52_13 = all_52_15)
% 198.01/32.56    (118)  all_56_0 = all_6_2
% 198.01/32.56    (119)  op(all_4_0, all_4_0) = all_52_18
% 198.01/32.56    (120)  op(e3, e3) = all_6_2
% 198.01/32.56    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.56    (122)   ~ (all_52_27 = all_14_2)
% 198.01/32.56    (123)   ~ (all_52_27 = all_4_0)
% 198.01/32.56    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.56    (125)  all_56_14 = all_52_23
% 198.01/32.56    (126)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.56    (127)  all_56_3 = all_52_25
% 198.01/32.56    (128)  all_28_0 = e3
% 198.01/32.56    (129)   ~ (all_52_3 = all_52_7)
% 198.01/32.56    (130)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.56    (131)  all_58_5 = all_52_19
% 198.01/32.56    (132)  all_56_1 = all_52_9
% 198.01/32.56    (133)   ~ (all_52_15 = all_4_2)
% 198.01/32.56    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.56           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.56           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.56           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.56    (135)   ~ (all_52_27 = all_4_2)
% 198.01/32.56    (136)  all_58_6 = all_52_5
% 198.01/32.56    (137)   ~ (all_4_0 = all_4_2)
% 198.01/32.56    (138)  op(e3, e2) = all_52_9
% 198.01/32.56    (139)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.56    (140)   ~ (all_52_17 = all_6_2)
% 198.01/32.56    (141)   ~ (e1 = e0)
% 198.01/32.56    (142)   ~ (e3 = e2)
% 198.01/32.56    (143)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.56    (144)   ~ (all_52_9 = all_52_17)
% 198.01/32.56    (145)   ~ (all_52_3 = all_4_0)
% 198.01/32.56    (146)  all_46_1 = all_6_1
% 198.01/32.56    (147)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.56    (148)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.56    (149)  op(e1, e1) = all_10_2
% 198.01/32.56    (150)   ~ (all_52_23 = all_10_2)
% 198.01/32.56    (151)   ~ (all_52_7 = all_52_23)
% 198.01/32.56    (152)   ~ (all_52_17 = all_52_19)
% 198.01/32.56    (153)  all_58_3 = all_4_2
% 198.01/32.56    (154)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.56    (155)  all_56_13 = all_52_15
% 198.01/32.56    (156)   ~ (all_52_3 = all_4_2)
% 198.01/32.56    (157)  all_28_1 = e1
% 198.01/32.56    (158)   ~ (all_52_19 = all_4_2)
% 198.01/32.56    (159)   ~ (all_52_17 = all_52_23)
% 198.01/32.56    (160)  op(all_6_2, e3) = all_6_1
% 198.01/32.56    (161)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.56    (162)  all_58_4 = all_52_17
% 198.01/32.56    (163)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.56  
% 198.01/32.56  Begin of proof
% 198.01/32.56  | 
% 198.01/32.56  | COMBINE_EQS: (76), (128) imply:
% 198.01/32.56  |   (164)  all_4_0 = e3
% 198.01/32.56  | 
% 198.01/32.56  | SIMP: (164) implies:
% 198.01/32.56  |   (165)  all_4_0 = e3
% 198.01/32.56  | 
% 198.01/32.56  | COMBINE_EQS: (110), (165) imply:
% 198.01/32.56  |   (166)  all_58_5 = e3
% 198.01/32.56  | 
% 198.01/32.56  | REDUCE: (145), (165) imply:
% 198.01/32.56  |   (167)   ~ (all_52_3 = e3)
% 198.01/32.56  | 
% 198.01/32.56  | REDUCE: (5), (165) imply:
% 198.01/32.56  |   (168)   ~ (all_52_17 = e3)
% 198.01/32.56  | 
% 198.01/32.56  | REDUCE: (12), (165) imply:
% 198.01/32.56  |   (169)   ~ (all_52_23 = e3)
% 198.01/32.56  | 
% 198.01/32.56  | REDUCE: (123), (165) imply:
% 198.01/32.56  |   (170)   ~ (all_52_27 = e3)
% 198.01/32.56  | 
% 198.01/32.56  | REDUCE: (137), (165) imply:
% 198.01/32.56  |   (171)   ~ (all_4_2 = e3)
% 198.01/32.56  | 
% 198.01/32.56  | SIMP: (171) implies:
% 198.01/32.56  |   (172)   ~ (all_4_2 = e3)
% 198.01/32.56  | 
% 198.01/32.56  | REDUCE: (119), (165) imply:
% 198.01/32.56  |   (173)  op(e3, e3) = all_52_18
% 198.01/32.56  | 
% 198.01/32.56  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 198.01/32.56  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 198.01/32.56  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 198.01/32.56  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 198.01/32.56  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 198.01/32.56  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 198.01/32.56  |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (80), (81),
% 198.01/32.56  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 198.01/32.56  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 198.01/32.56  |            (103), (104), (105), (106), (107), (108), (109), (111), (112),
% 198.01/32.56  |            (113), (114), (115), (116), (117), (118), (120), (121), (122),
% 198.01/32.56  |            (124), (125), (126), (127), (129), (130), (131), (132), (133),
% 198.01/32.56  |            (134), (135), (136), (138), (139), (140), (141), (142), (143),
% 198.01/32.56  |            (144), (146), (147), (148), (149), (150), (151), (152), (153),
% 198.01/32.56  |            (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 198.01/32.56  |            (163), (166), (167), (168), (169), (170), (172), (173) are
% 198.01/32.56  |            inconsistent by sub-proof #13.
% 198.01/32.56  | 
% 198.01/32.56  End of proof
% 198.01/32.56  
% 198.01/32.56  Sub-proof #13 shows that the following formulas are inconsistent:
% 198.01/32.56  ----------------------------------------------------------------
% 198.01/32.56    (1)  op(e3, e3) = all_52_18
% 198.01/32.56    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.56    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.56    (4)  all_58_14 = all_52_23
% 198.01/32.56    (5)   ~ (e3 = e1)
% 198.01/32.56    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.56    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.56    (8)  all_58_1 = all_52_9
% 198.01/32.56    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.56    (10)   ~ (e3 = e0)
% 198.01/32.56    (11)  op(e2, e3) = all_52_3
% 198.01/32.56    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.56    (13)   ~ (all_52_7 = all_52_15)
% 198.01/32.56    (14)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.56    (15)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.56    (16)   ~ (all_52_17 = all_52_25)
% 198.01/32.56    (17)   ~ (all_4_2 = e3)
% 198.01/32.56    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.56    (19)  all_58_0 = all_6_2
% 198.01/32.56    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.56    (21)  all_46_0 = e1
% 198.01/32.56    (22)  all_56_4 = all_52_3
% 198.01/32.56    (23)  op(e3, all_6_1) = e1
% 198.01/32.56    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.56    (25)  op(e3, e0) = all_52_25
% 198.01/32.56    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.56    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.56    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.56    (29)   ~ (all_52_27 = all_52_29)
% 198.01/32.56    (30)  all_58_13 = all_52_15
% 198.01/32.56    (31)  op(e0, all_14_1) = e1
% 198.01/32.56    (32)  all_58_9 = all_52_25
% 198.01/32.56    (33)   ~ (all_52_29 = all_14_2)
% 198.01/32.56    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.56    (35)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.56    (36)  op(e1, e3) = all_52_5
% 198.01/32.56    (37)  op(e2, e2) = all_4_2
% 198.01/32.56    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.56    (39)   ~ (all_52_3 = all_52_5)
% 198.01/32.56    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.56    (41)  op(all_4_2, e2) = e1
% 198.01/32.56    (42)  all_58_11 = all_52_29
% 198.01/32.56    (43)   ~ (all_52_3 = e3)
% 198.01/32.56    (44)  all_56_5 = all_4_2
% 198.01/32.56    (45)   ~ (all_52_25 = all_14_2)
% 198.01/32.56    (46)   ~ (all_52_9 = all_52_15)
% 198.01/32.56    (47)   ~ (all_52_3 = all_52_27)
% 198.01/32.56    (48)  op(all_10_2, e1) = all_10_1
% 198.01/32.56    (49)  all_46_2 = all_6_2
% 198.01/32.56    (50)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.56    (51)   ~ (all_52_7 = all_6_2)
% 198.01/32.56    (52)  op(e0, e0) = all_14_2
% 198.01/32.56    (53)  all_56_15 = all_14_2
% 198.01/32.56    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.56    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.56    (56)  all_56_11 = all_52_29
% 198.01/32.56    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.56    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.56    (59)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.56    (60)   ~ (e2 = e1)
% 198.01/32.56    (61)  all_58_10 = all_52_27
% 198.01/32.56    (62)  all_56_8 = all_52_5
% 198.01/32.56    (63)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.56    (64)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.56    (65)   ~ (all_52_25 = all_52_29)
% 198.01/32.56    (66)   ~ (all_52_29 = all_10_2)
% 198.01/32.56    (67)  all_58_7 = all_52_13
% 198.01/32.56    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.56    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.56    (70)   ~ (all_52_5 = all_52_7)
% 198.01/32.56    (71)  all_58_12 = all_52_7
% 198.01/32.56    (72)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.56    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.56    (74)   ~ (all_52_7 = all_14_2)
% 198.01/32.56    (75)  all_58_2 = all_52_3
% 198.01/32.56    (76)  all_56_2 = all_52_17
% 198.01/32.56    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.56    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.56    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.56    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.56    (81)  all_56_7 = all_52_27
% 198.01/32.56    (82)  all_28_2 = all_4_2
% 198.01/32.56    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.56    (84)   ~ (e2 = e0)
% 198.01/32.56    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.56    (86)   ~ (all_52_23 = e3)
% 198.01/32.56    (87)   ~ (all_52_5 = all_52_29)
% 198.01/32.56    (88)   ~ (all_52_15 = all_14_2)
% 198.01/32.56    (89)   ~ (all_52_19 = all_52_27)
% 198.01/32.56    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.56    (91)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.56    (92)   ~ (all_52_27 = e3)
% 198.01/32.56    (93)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.56            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.56    (94)   ~ (all_52_13 = all_4_2)
% 198.01/32.56    (95)  op(e3, e1) = all_52_17
% 198.01/32.56    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.56    (97)  op(e0, e3) = all_52_7
% 198.01/32.56    (98)  op(e1, e2) = all_52_13
% 198.01/32.56    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.56    (100)   ~ (all_52_9 = all_52_25)
% 198.01/32.56    (101)  all_58_15 = all_14_2
% 198.01/32.56    (102)   ~ (all_52_19 = all_10_2)
% 198.01/32.56    (103)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.56    (104)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.56    (105)  all_58_8 = all_10_2
% 198.01/32.56    (106)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.56    (107)   ~ (all_52_5 = all_10_2)
% 198.01/32.56    (108)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.56    (109)   ~ (all_52_23 = all_14_2)
% 198.01/32.56    (110)  all_56_12 = all_52_7
% 198.01/32.56    (111)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.57    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.57    (113)   ~ (all_52_25 = all_6_2)
% 198.01/32.57    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.57    (115)   ~ (all_52_9 = all_4_2)
% 198.01/32.57    (116)   ~ (all_52_5 = all_6_2)
% 198.01/32.57    (117)   ~ (all_52_9 = all_6_2)
% 198.01/32.57    (118)   ~ (all_52_13 = all_52_15)
% 198.01/32.57    (119)  all_56_0 = all_6_2
% 198.01/32.57    (120)  op(e3, e3) = all_6_2
% 198.01/32.57    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.57    (122)   ~ (all_52_27 = all_14_2)
% 198.01/32.57    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.57    (124)  all_58_5 = e3
% 198.01/32.57    (125)  all_56_14 = all_52_23
% 198.01/32.57    (126)   ~ (all_52_17 = e3)
% 198.01/32.57    (127)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.57    (128)  all_56_3 = all_52_25
% 198.01/32.57    (129)   ~ (all_52_3 = all_52_7)
% 198.01/32.57    (130)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.57    (131)  all_58_5 = all_52_19
% 198.01/32.57    (132)  all_56_1 = all_52_9
% 198.01/32.57    (133)   ~ (all_52_15 = all_4_2)
% 198.01/32.57    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.57           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.57           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.57           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.57    (135)   ~ (all_52_27 = all_4_2)
% 198.01/32.57    (136)  all_58_6 = all_52_5
% 198.01/32.57    (137)  op(e3, e2) = all_52_9
% 198.01/32.57    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.57    (139)   ~ (all_52_17 = all_6_2)
% 198.01/32.57    (140)   ~ (e1 = e0)
% 198.01/32.57    (141)   ~ (e3 = e2)
% 198.01/32.57    (142)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.57    (143)   ~ (all_52_9 = all_52_17)
% 198.01/32.57    (144)  all_46_1 = all_6_1
% 198.01/32.57    (145)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.57    (146)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.57    (147)  op(e1, e1) = all_10_2
% 198.01/32.57    (148)   ~ (all_52_23 = all_10_2)
% 198.01/32.57    (149)   ~ (all_52_7 = all_52_23)
% 198.01/32.57    (150)   ~ (all_52_17 = all_52_19)
% 198.01/32.57    (151)  all_58_3 = all_4_2
% 198.01/32.57    (152)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.57    (153)  all_56_13 = all_52_15
% 198.01/32.57    (154)   ~ (all_52_3 = all_4_2)
% 198.01/32.57    (155)  all_28_1 = e1
% 198.01/32.57    (156)   ~ (all_52_19 = all_4_2)
% 198.01/32.57    (157)   ~ (all_52_17 = all_52_23)
% 198.01/32.57    (158)  op(all_6_2, e3) = all_6_1
% 198.01/32.57    (159)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.57    (160)  all_58_4 = all_52_17
% 198.01/32.57    (161)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.57  
% 198.01/32.57  Begin of proof
% 198.01/32.57  | 
% 198.01/32.57  | BETA: splitting (127) gives:
% 198.01/32.57  | 
% 198.01/32.57  | Case 1:
% 198.01/32.57  | | 
% 198.01/32.57  | |   (162)   ~ (all_28_1 = e1)
% 198.01/32.57  | | 
% 198.01/32.57  | | REDUCE: (155), (162) imply:
% 198.01/32.57  | |   (163)  $false
% 198.01/32.57  | | 
% 198.01/32.57  | | CLOSE: (163) is inconsistent.
% 198.01/32.57  | | 
% 198.01/32.57  | Case 2:
% 198.01/32.57  | | 
% 198.01/32.57  | |   (164)   ~ (all_28_2 = e0)
% 198.01/32.57  | | 
% 198.01/32.57  | | REDUCE: (82), (164) imply:
% 198.01/32.57  | |   (165)   ~ (all_4_2 = e0)
% 198.01/32.57  | | 
% 198.01/32.57  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 198.01/32.57  | |              with (1), (120) gives:
% 198.01/32.57  | |   (166)  all_52_18 = all_6_2
% 198.01/32.57  | | 
% 198.01/32.57  | | BETA: splitting (14) gives:
% 198.01/32.57  | | 
% 198.01/32.57  | | Case 1:
% 198.01/32.57  | | | 
% 198.01/32.57  | | |   (167)   ~ (all_46_0 = e1)
% 198.01/32.57  | | | 
% 198.01/32.57  | | | REDUCE: (21), (167) imply:
% 198.01/32.57  | | |   (168)  $false
% 198.01/32.57  | | | 
% 198.01/32.57  | | | CLOSE: (168) is inconsistent.
% 198.01/32.57  | | | 
% 198.01/32.57  | | Case 2:
% 198.01/32.57  | | | 
% 198.01/32.57  | | |   (169)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.57  | | | 
% 198.01/32.57  | | | BETA: splitting (93) gives:
% 198.01/32.57  | | | 
% 198.01/32.57  | | | Case 1:
% 198.01/32.57  | | | | 
% 198.01/32.57  | | | |   (170)  all_58_15 = e0
% 198.01/32.57  | | | | 
% 198.01/32.57  | | | | REF_CLOSE: (7), (20), (31), (52), (101), (130), (140), (170) are
% 198.01/32.57  | | | |            inconsistent by sub-proof #877.
% 198.01/32.57  | | | | 
% 198.01/32.57  | | | Case 2:
% 198.01/32.57  | | | | 
% 198.01/32.57  | | | |   (171)   ~ (all_58_15 = e0)
% 198.01/32.57  | | | |   (172)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 198.01/32.57  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.57  | | | | 
% 198.01/32.57  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.57  | | | |            (13), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 198.01/32.57  | | | |            (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 198.01/32.57  | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.01/32.57  | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 198.01/32.57  | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 198.01/32.57  | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 198.01/32.57  | | | |            (76), (77), (78), (79), (80), (81), (83), (84), (85), (86),
% 198.01/32.57  | | | |            (87), (88), (89), (90), (91), (92), (94), (95), (96), (97),
% 198.01/32.57  | | | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 198.01/32.57  | | | |            (107), (108), (109), (110), (111), (112), (113), (114),
% 198.01/32.57  | | | |            (115), (116), (117), (118), (119), (120), (121), (122),
% 198.01/32.57  | | | |            (123), (124), (125), (126), (128), (129), (130), (131),
% 198.01/32.57  | | | |            (132), (133), (134), (135), (136), (137), (138), (139),
% 198.01/32.57  | | | |            (140), (141), (142), (143), (144), (145), (146), (147),
% 198.01/32.57  | | | |            (148), (149), (150), (151), (152), (153), (154), (156),
% 198.01/32.57  | | | |            (157), (158), (159), (160), (161), (165), (166), (169),
% 198.01/32.57  | | | |            (171), (172) are inconsistent by sub-proof #16.
% 198.01/32.57  | | | | 
% 198.01/32.57  | | | End of split
% 198.01/32.57  | | | 
% 198.01/32.57  | | End of split
% 198.01/32.57  | | 
% 198.01/32.57  | End of split
% 198.01/32.57  | 
% 198.01/32.57  End of proof
% 198.01/32.57  
% 198.01/32.57  Sub-proof #14 shows that the following formulas are inconsistent:
% 198.01/32.57  ----------------------------------------------------------------
% 198.01/32.57    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.57    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.57    (3)  all_58_14 = all_52_23
% 198.01/32.57    (4)   ~ (e3 = e1)
% 198.01/32.57    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.57    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.57    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.57    (8)  all_58_1 = all_52_9
% 198.01/32.57    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.57    (10)   ~ (e3 = e0)
% 198.01/32.57    (11)  op(e2, e3) = all_52_3
% 198.01/32.57    (12)   ~ (all_52_23 = all_4_0)
% 198.01/32.57    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.57    (14)   ~ (all_52_7 = all_52_15)
% 198.01/32.57    (15)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.57    (16)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.57    (17)   ~ (all_52_17 = all_52_25)
% 198.01/32.57    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.57    (19)  all_58_0 = all_6_2
% 198.01/32.57    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.57    (21)  all_46_0 = e1
% 198.01/32.57    (22)  all_56_4 = all_52_3
% 198.01/32.57    (23)  op(e3, all_6_1) = e1
% 198.01/32.57    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.57    (25)  op(e3, e0) = all_52_25
% 198.01/32.57    (26)  op(e0, all_14_1) = all_14_0
% 198.01/32.57    (27)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.57    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.57    (29)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.57    (30)   ~ (all_52_27 = all_52_29)
% 198.01/32.57    (31)  all_58_13 = all_52_15
% 198.01/32.57    (32)  all_58_9 = all_52_25
% 198.01/32.57    (33)   ~ (all_52_29 = all_14_2)
% 198.01/32.57    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.57    (35)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.57    (36)  op(e1, e3) = all_52_5
% 198.01/32.57    (37)  op(e2, e2) = all_4_2
% 198.01/32.57    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.57    (39)   ~ (all_52_3 = all_52_5)
% 198.01/32.57    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.57    (41)  op(all_4_2, e2) = e1
% 198.01/32.57    (42)  all_58_11 = all_52_29
% 198.01/32.57    (43)  all_56_5 = all_4_2
% 198.01/32.57    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.57    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.57    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.57    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.57    (48)  all_46_2 = all_6_2
% 198.01/32.57    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.57    (50)   ~ (all_52_7 = all_6_2)
% 198.01/32.57    (51)  op(e0, e0) = all_14_2
% 198.01/32.57    (52)  all_56_15 = all_14_2
% 198.01/32.57    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.57    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.57    (55)  all_56_11 = all_52_29
% 198.01/32.57    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.57    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.57    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.57    (59)   ~ (e2 = e1)
% 198.01/32.57    (60)  all_58_10 = all_52_27
% 198.01/32.57    (61)  all_56_8 = all_52_5
% 198.01/32.57    (62)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.57    (63)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.57    (64)   ~ (all_52_25 = all_52_29)
% 198.01/32.57    (65)   ~ (all_52_29 = all_10_2)
% 198.01/32.57    (66)  all_58_7 = all_52_13
% 198.01/32.57    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.57    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.57    (69)   ~ (all_52_5 = all_52_7)
% 198.01/32.57    (70)  all_58_12 = all_52_7
% 198.01/32.57    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.57    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.57    (73)   ~ (all_52_7 = all_14_2)
% 198.01/32.57    (74)  all_58_2 = all_52_3
% 198.01/32.57    (75)  all_56_2 = all_52_17
% 198.01/32.57    (76)  all_28_0 = all_4_0
% 198.01/32.57    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.57    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.57    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.57    (80)   ~ (all_14_0 = e3)
% 198.01/32.57    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.57    (82)  all_56_7 = all_52_27
% 198.01/32.57    (83)  all_28_2 = all_4_2
% 198.01/32.57    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.57    (85)   ~ (e2 = e0)
% 198.01/32.57    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.57    (87)   ~ (all_52_5 = all_52_29)
% 198.01/32.57    (88)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 198.01/32.57    (89)   ~ (all_52_15 = all_14_2)
% 198.01/32.57    (90)   ~ (all_52_19 = all_52_27)
% 198.01/32.57    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.57    (92)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.57    (93)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.57            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.57    (94)   ~ (all_52_13 = all_4_2)
% 198.01/32.57    (95)  op(e3, e1) = all_52_17
% 198.01/32.57    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.57    (97)  op(e0, e3) = all_52_7
% 198.01/32.57    (98)  op(e1, e2) = all_52_13
% 198.01/32.57    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.57    (100)   ~ (all_52_9 = all_52_25)
% 198.01/32.57    (101)  all_58_15 = all_14_2
% 198.01/32.57    (102)   ~ (all_52_19 = all_10_2)
% 198.01/32.57    (103)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.57    (104)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.57    (105)  all_58_8 = all_10_2
% 198.01/32.57    (106)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.57    (107)   ~ (all_52_5 = all_10_2)
% 198.01/32.57    (108)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.57    (109)   ~ (all_52_23 = all_14_2)
% 198.01/32.57    (110)  all_56_12 = all_52_7
% 198.01/32.57    (111)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.57    (112)  all_58_5 = all_4_0
% 198.01/32.57    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.57    (114)   ~ (all_52_25 = all_6_2)
% 198.01/32.57    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.57    (116)   ~ (all_52_9 = all_4_2)
% 198.01/32.57    (117)   ~ (all_52_5 = all_6_2)
% 198.01/32.57    (118)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 198.01/32.57    (119)   ~ (all_52_9 = all_6_2)
% 198.01/32.57    (120)   ~ (all_52_13 = all_52_15)
% 198.01/32.57    (121)  all_56_0 = all_6_2
% 198.01/32.57    (122)  op(all_4_0, all_4_0) = all_52_18
% 198.01/32.57    (123)  op(e3, e3) = all_6_2
% 198.01/32.57    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.57    (125)   ~ (all_52_27 = all_14_2)
% 198.01/32.57    (126)   ~ (all_52_27 = all_4_0)
% 198.01/32.57    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.57    (128)  all_56_14 = all_52_23
% 198.01/32.57    (129)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.57    (130)  all_56_3 = all_52_25
% 198.01/32.57    (131)  all_28_0 = e3
% 198.01/32.57    (132)   ~ (all_52_3 = all_52_7)
% 198.01/32.57    (133)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.57    (134)  all_58_5 = all_52_19
% 198.01/32.57    (135)  all_56_1 = all_52_9
% 198.01/32.57    (136)   ~ (all_52_15 = all_4_2)
% 198.01/32.57    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.57           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.57           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.57           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.57    (138)   ~ (all_52_27 = all_4_2)
% 198.01/32.57    (139)  all_58_6 = all_52_5
% 198.01/32.57    (140)   ~ (all_4_0 = all_4_2)
% 198.01/32.57    (141)  op(e3, e2) = all_52_9
% 198.01/32.57    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.57    (143)   ~ (all_52_17 = all_6_2)
% 198.01/32.57    (144)   ~ (e1 = e0)
% 198.01/32.57    (145)   ~ (e3 = e2)
% 198.01/32.57    (146)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.57    (147)   ~ (all_52_9 = all_52_17)
% 198.01/32.57    (148)   ~ (all_52_3 = all_4_0)
% 198.01/32.57    (149)  all_46_1 = all_6_1
% 198.01/32.57    (150)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.57    (151)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.57    (152)  op(e1, e1) = all_10_2
% 198.01/32.57    (153)   ~ (all_52_23 = all_10_2)
% 198.01/32.57    (154)   ~ (all_52_7 = all_52_23)
% 198.01/32.57    (155)   ~ (all_52_17 = all_52_19)
% 198.01/32.57    (156)  all_58_3 = all_4_2
% 198.01/32.57    (157)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.57    (158)  all_56_13 = all_52_15
% 198.01/32.57    (159)   ~ (all_52_3 = all_4_2)
% 198.01/32.57    (160)  all_28_1 = e1
% 198.01/32.57    (161)   ~ (all_52_19 = all_4_2)
% 198.01/32.57    (162)   ~ (all_52_17 = all_52_23)
% 198.01/32.57    (163)  op(all_6_2, e3) = all_6_1
% 198.01/32.57    (164)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.57    (165)  all_58_4 = all_52_17
% 198.01/32.57    (166)   ~ (all_14_0 = e1)
% 198.01/32.57    (167)   ~ (all_14_0 = e2)
% 198.01/32.57    (168)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.57  
% 198.01/32.57  Begin of proof
% 198.01/32.57  | 
% 198.01/32.57  | COMBINE_EQS: (76), (131) imply:
% 198.01/32.57  |   (169)  all_4_0 = e3
% 198.01/32.57  | 
% 198.01/32.57  | COMBINE_EQS: (112), (169) imply:
% 198.01/32.57  |   (170)  all_58_5 = e3
% 198.01/32.57  | 
% 198.01/32.57  | REDUCE: (148), (169) imply:
% 198.01/32.57  |   (171)   ~ (all_52_3 = e3)
% 198.01/32.57  | 
% 198.01/32.57  | REDUCE: (5), (169) imply:
% 198.01/32.57  |   (172)   ~ (all_52_17 = e3)
% 198.01/32.57  | 
% 198.01/32.57  | REDUCE: (12), (169) imply:
% 198.01/32.57  |   (173)   ~ (all_52_23 = e3)
% 198.01/32.57  | 
% 198.01/32.57  | REDUCE: (126), (169) imply:
% 198.01/32.57  |   (174)   ~ (all_52_27 = e3)
% 198.01/32.57  | 
% 198.01/32.57  | REDUCE: (140), (169) imply:
% 198.01/32.57  |   (175)   ~ (all_4_2 = e3)
% 198.01/32.57  | 
% 198.01/32.57  | SIMP: (175) implies:
% 198.01/32.57  |   (176)   ~ (all_4_2 = e3)
% 198.01/32.57  | 
% 198.01/32.57  | REDUCE: (122), (169) imply:
% 198.01/32.57  |   (177)  op(e3, e3) = all_52_18
% 198.01/32.57  | 
% 198.01/32.57  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 198.01/32.57  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 198.01/32.57  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 198.01/32.57  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 198.01/32.57  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 198.01/32.57  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 198.01/32.57  |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (80), (81),
% 198.01/32.57  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 198.01/32.57  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 198.01/32.57  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 198.01/32.57  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 198.01/32.57  |            (123), (124), (125), (127), (128), (129), (130), (132), (133),
% 198.01/32.57  |            (134), (135), (136), (137), (138), (139), (141), (142), (143),
% 198.01/32.57  |            (144), (145), (146), (147), (149), (150), (151), (152), (153),
% 198.01/32.57  |            (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 198.01/32.57  |            (163), (164), (165), (166), (167), (168), (170), (171), (172),
% 198.01/32.57  |            (173), (174), (176), (177) are inconsistent by sub-proof #15.
% 198.01/32.57  | 
% 198.01/32.57  End of proof
% 198.01/32.57  
% 198.01/32.57  Sub-proof #15 shows that the following formulas are inconsistent:
% 198.01/32.57  ----------------------------------------------------------------
% 198.01/32.57    (1)  op(e3, e3) = all_52_18
% 198.01/32.57    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.57    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.57    (4)  all_58_14 = all_52_23
% 198.01/32.57    (5)   ~ (e3 = e1)
% 198.01/32.57    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.57    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.57    (8)  all_58_1 = all_52_9
% 198.01/32.57    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.57    (10)   ~ (e3 = e0)
% 198.01/32.57    (11)  op(e2, e3) = all_52_3
% 198.01/32.57    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.57    (13)   ~ (all_52_7 = all_52_15)
% 198.01/32.57    (14)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.57    (15)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.57    (16)   ~ (all_52_17 = all_52_25)
% 198.01/32.57    (17)   ~ (all_4_2 = e3)
% 198.01/32.57    (18)   ~ (all_52_3 = all_6_2)
% 198.01/32.57    (19)  all_58_0 = all_6_2
% 198.01/32.57    (20)  op(all_14_2, e0) = all_14_1
% 198.01/32.57    (21)  all_46_0 = e1
% 198.01/32.57    (22)  all_56_4 = all_52_3
% 198.01/32.57    (23)  op(e3, all_6_1) = e1
% 198.01/32.57    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.57    (25)  op(e3, e0) = all_52_25
% 198.01/32.57    (26)  op(e0, all_14_1) = all_14_0
% 198.01/32.57    (27)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.57    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.57    (29)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.57    (30)   ~ (all_52_27 = all_52_29)
% 198.01/32.57    (31)  all_58_13 = all_52_15
% 198.01/32.57    (32)  all_58_9 = all_52_25
% 198.01/32.57    (33)   ~ (all_52_29 = all_14_2)
% 198.01/32.57    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.57    (35)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.57    (36)  op(e1, e3) = all_52_5
% 198.01/32.57    (37)  op(e2, e2) = all_4_2
% 198.01/32.58    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.58    (39)   ~ (all_52_3 = all_52_5)
% 198.01/32.58    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.58    (41)  op(all_4_2, e2) = e1
% 198.01/32.58    (42)  all_58_11 = all_52_29
% 198.01/32.58    (43)   ~ (all_52_3 = e3)
% 198.01/32.58    (44)  all_56_5 = all_4_2
% 198.01/32.58    (45)   ~ (all_52_25 = all_14_2)
% 198.01/32.58    (46)   ~ (all_52_9 = all_52_15)
% 198.01/32.58    (47)   ~ (all_52_3 = all_52_27)
% 198.01/32.58    (48)  op(all_10_2, e1) = all_10_1
% 198.01/32.58    (49)  all_46_2 = all_6_2
% 198.01/32.58    (50)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.58    (51)   ~ (all_52_7 = all_6_2)
% 198.01/32.58    (52)  op(e0, e0) = all_14_2
% 198.01/32.58    (53)  all_56_15 = all_14_2
% 198.01/32.58    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.58    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.58    (56)  all_56_11 = all_52_29
% 198.01/32.58    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.58    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.58    (59)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.58    (60)   ~ (e2 = e1)
% 198.01/32.58    (61)  all_58_10 = all_52_27
% 198.01/32.58    (62)  all_56_8 = all_52_5
% 198.01/32.58    (63)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.58    (64)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.58    (65)   ~ (all_52_25 = all_52_29)
% 198.01/32.58    (66)   ~ (all_52_29 = all_10_2)
% 198.01/32.58    (67)  all_58_7 = all_52_13
% 198.01/32.58    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.58    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.58    (70)   ~ (all_52_5 = all_52_7)
% 198.01/32.58    (71)  all_58_12 = all_52_7
% 198.01/32.58    (72)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.58    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.58    (74)   ~ (all_52_7 = all_14_2)
% 198.01/32.58    (75)  all_58_2 = all_52_3
% 198.01/32.58    (76)  all_56_2 = all_52_17
% 198.01/32.58    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.58    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.58    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.58    (80)   ~ (all_14_0 = e3)
% 198.01/32.58    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.58    (82)  all_56_7 = all_52_27
% 198.01/32.58    (83)  all_28_2 = all_4_2
% 198.01/32.58    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.58    (85)   ~ (e2 = e0)
% 198.01/32.58    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.58    (87)   ~ (all_52_23 = e3)
% 198.01/32.58    (88)   ~ (all_52_5 = all_52_29)
% 198.01/32.58    (89)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 198.01/32.58    (90)   ~ (all_52_15 = all_14_2)
% 198.01/32.58    (91)   ~ (all_52_19 = all_52_27)
% 198.01/32.58    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.58    (93)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.58    (94)   ~ (all_52_27 = e3)
% 198.01/32.58    (95)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 198.01/32.58            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 198.01/32.58    (96)   ~ (all_52_13 = all_4_2)
% 198.01/32.58    (97)  op(e3, e1) = all_52_17
% 198.01/32.58    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.58    (99)  op(e0, e3) = all_52_7
% 198.01/32.58    (100)  op(e1, e2) = all_52_13
% 198.01/32.58    (101)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.58    (102)   ~ (all_52_9 = all_52_25)
% 198.01/32.58    (103)  all_58_15 = all_14_2
% 198.01/32.58    (104)   ~ (all_52_19 = all_10_2)
% 198.01/32.58    (105)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.58    (106)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.58    (107)  all_58_8 = all_10_2
% 198.01/32.58    (108)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.58    (109)   ~ (all_52_5 = all_10_2)
% 198.01/32.58    (110)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.58    (111)   ~ (all_52_23 = all_14_2)
% 198.01/32.58    (112)  all_56_12 = all_52_7
% 198.01/32.58    (113)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.58    (114)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.58    (115)   ~ (all_52_25 = all_6_2)
% 198.01/32.58    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.58    (117)   ~ (all_52_9 = all_4_2)
% 198.01/32.58    (118)   ~ (all_52_5 = all_6_2)
% 198.01/32.58    (119)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 198.01/32.58    (120)   ~ (all_52_9 = all_6_2)
% 198.01/32.58    (121)   ~ (all_52_13 = all_52_15)
% 198.01/32.58    (122)  all_56_0 = all_6_2
% 198.01/32.58    (123)  op(e3, e3) = all_6_2
% 198.01/32.58    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.58    (125)   ~ (all_52_27 = all_14_2)
% 198.01/32.58    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.58    (127)  all_58_5 = e3
% 198.01/32.58    (128)  all_56_14 = all_52_23
% 198.01/32.58    (129)   ~ (all_52_17 = e3)
% 198.01/32.58    (130)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 198.01/32.58    (131)  all_56_3 = all_52_25
% 198.01/32.58    (132)   ~ (all_52_3 = all_52_7)
% 198.01/32.58    (133)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.58    (134)  all_58_5 = all_52_19
% 198.01/32.58    (135)  all_56_1 = all_52_9
% 198.01/32.58    (136)   ~ (all_52_15 = all_4_2)
% 198.01/32.58    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.58           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.58           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.58           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.58    (138)   ~ (all_52_27 = all_4_2)
% 198.01/32.58    (139)  all_58_6 = all_52_5
% 198.01/32.58    (140)  op(e3, e2) = all_52_9
% 198.01/32.58    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.58    (142)   ~ (all_52_17 = all_6_2)
% 198.01/32.58    (143)   ~ (e1 = e0)
% 198.01/32.58    (144)   ~ (e3 = e2)
% 198.01/32.58    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.58    (146)   ~ (all_52_9 = all_52_17)
% 198.01/32.58    (147)  all_46_1 = all_6_1
% 198.01/32.58    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.58    (149)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.58    (150)  op(e1, e1) = all_10_2
% 198.01/32.58    (151)   ~ (all_52_23 = all_10_2)
% 198.01/32.58    (152)   ~ (all_52_7 = all_52_23)
% 198.01/32.58    (153)   ~ (all_52_17 = all_52_19)
% 198.01/32.58    (154)  all_58_3 = all_4_2
% 198.01/32.58    (155)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.58    (156)  all_56_13 = all_52_15
% 198.01/32.58    (157)   ~ (all_52_3 = all_4_2)
% 198.01/32.58    (158)  all_28_1 = e1
% 198.01/32.58    (159)   ~ (all_52_19 = all_4_2)
% 198.01/32.58    (160)   ~ (all_52_17 = all_52_23)
% 198.01/32.58    (161)  op(all_6_2, e3) = all_6_1
% 198.01/32.58    (162)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.58    (163)  all_58_4 = all_52_17
% 198.01/32.58    (164)   ~ (all_14_0 = e1)
% 198.01/32.58    (165)   ~ (all_14_0 = e2)
% 198.01/32.58    (166)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.58  
% 198.01/32.58  Begin of proof
% 198.01/32.58  | 
% 198.01/32.58  | BETA: splitting (130) gives:
% 198.01/32.58  | 
% 198.01/32.58  | Case 1:
% 198.01/32.58  | | 
% 198.01/32.58  | |   (167)   ~ (all_28_1 = e1)
% 198.01/32.58  | | 
% 198.01/32.58  | | REDUCE: (158), (167) imply:
% 198.01/32.58  | |   (168)  $false
% 198.01/32.58  | | 
% 198.01/32.58  | | CLOSE: (168) is inconsistent.
% 198.01/32.58  | | 
% 198.01/32.58  | Case 2:
% 198.01/32.58  | | 
% 198.01/32.58  | |   (169)   ~ (all_28_2 = e0)
% 198.01/32.58  | | 
% 198.01/32.58  | | REDUCE: (83), (169) imply:
% 198.01/32.58  | |   (170)   ~ (all_4_2 = e0)
% 198.01/32.58  | | 
% 198.01/32.58  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 198.01/32.58  | |              with (1), (123) gives:
% 198.01/32.58  | |   (171)  all_52_18 = all_6_2
% 198.01/32.58  | | 
% 198.01/32.58  | | BETA: splitting (14) gives:
% 198.01/32.58  | | 
% 198.01/32.58  | | Case 1:
% 198.01/32.58  | | | 
% 198.01/32.58  | | |   (172)   ~ (all_46_0 = e1)
% 198.01/32.58  | | | 
% 198.01/32.58  | | | REDUCE: (21), (172) imply:
% 198.01/32.58  | | |   (173)  $false
% 198.01/32.58  | | | 
% 198.01/32.58  | | | CLOSE: (173) is inconsistent.
% 198.01/32.58  | | | 
% 198.01/32.58  | | Case 2:
% 198.01/32.58  | | | 
% 198.01/32.58  | | |   (174)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.58  | | | 
% 198.01/32.58  | | | BETA: splitting (95) gives:
% 198.01/32.58  | | | 
% 198.01/32.58  | | | Case 1:
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | |   (175)  all_58_15 = e0
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | COMBINE_EQS: (103), (175) imply:
% 198.01/32.58  | | | |   (176)  all_14_2 = e0
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (90), (176) imply:
% 198.01/32.58  | | | |   (177)   ~ (all_52_15 = e0)
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (111), (176) imply:
% 198.01/32.58  | | | |   (178)   ~ (all_52_23 = e0)
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (45), (176) imply:
% 198.01/32.58  | | | |   (179)   ~ (all_52_25 = e0)
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (125), (176) imply:
% 198.01/32.58  | | | |   (180)   ~ (all_52_27 = e0)
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (33), (176) imply:
% 198.01/32.58  | | | |   (181)   ~ (all_52_29 = e0)
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (133), (176) imply:
% 198.01/32.58  | | | |   (182)  op(e0, e0) = all_52_30
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (20), (176) imply:
% 198.01/32.58  | | | |   (183)  op(e0, e0) = all_14_1
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REDUCE: (52), (176) imply:
% 198.01/32.58  | | | |   (184)  op(e0, e0) = e0
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | BETA: splitting (40) gives:
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | Case 1:
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | |   (185)  all_58_2 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | COMBINE_EQS: (75), (185) imply:
% 198.01/32.58  | | | | |   (186)  all_52_3 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | SIMP: (186) implies:
% 198.01/32.58  | | | | |   (187)  all_52_3 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (132), (187) imply:
% 198.01/32.58  | | | | |   (188)   ~ (all_52_7 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | SIMP: (188) implies:
% 198.01/32.58  | | | | |   (189)   ~ (all_52_7 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (18), (187) imply:
% 198.01/32.58  | | | | |   (190)   ~ (all_6_2 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | SIMP: (190) implies:
% 198.01/32.58  | | | | |   (191)   ~ (all_6_2 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (6), (187) imply:
% 198.01/32.58  | | | | |   (192)  op(e0, e0) = all_52_2
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (11), (187) imply:
% 198.01/32.58  | | | | |   (193)  op(e2, e3) = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | GROUND_INST: instantiating (7) with e0, all_52_30, e0, e0, simplifying
% 198.01/32.58  | | | | |              with (182), (184) gives:
% 198.01/32.58  | | | | |   (194)  all_52_30 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | GROUND_INST: instantiating (7) with all_52_30, all_52_2, e0, e0,
% 198.01/32.58  | | | | |              simplifying with (182), (192) gives:
% 198.01/32.58  | | | | |   (195)  all_52_2 = all_52_30
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | GROUND_INST: instantiating (7) with all_14_1, all_52_2, e0, e0,
% 198.01/32.58  | | | | |              simplifying with (183), (192) gives:
% 198.01/32.58  | | | | |   (196)  all_52_2 = all_14_1
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | COMBINE_EQS: (195), (196) imply:
% 198.01/32.58  | | | | |   (197)  all_52_30 = all_14_1
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | SIMP: (197) implies:
% 198.01/32.58  | | | | |   (198)  all_52_30 = all_14_1
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | COMBINE_EQS: (194), (198) imply:
% 198.01/32.58  | | | | |   (199)  all_14_1 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | SIMP: (199) implies:
% 198.01/32.58  | | | | |   (200)  all_14_1 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | COMBINE_EQS: (196), (200) imply:
% 198.01/32.58  | | | | |   (201)  all_52_2 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (26), (200) imply:
% 198.01/32.58  | | | | |   (202)  op(e0, e0) = all_14_0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | GROUND_INST: instantiating (7) with e0, all_14_0, e0, e0, simplifying
% 198.01/32.58  | | | | |              with (184), (202) gives:
% 198.01/32.58  | | | | |   (203)  all_14_0 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (80), (203) imply:
% 198.01/32.58  | | | | |   (204)   ~ (e3 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (165), (203) imply:
% 198.01/32.58  | | | | |   (205)   ~ (e2 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REDUCE: (164), (203) imply:
% 198.01/32.58  | | | | |   (206)   ~ (e1 = e0)
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | BETA: splitting (137) gives:
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | Case 1:
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | |   (207)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 198.01/32.58  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 198.01/32.58  | | | | | |            all_52_14 = e0)
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | | BETA: splitting (207) gives:
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | | Case 1:
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | |   (208)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 198.01/32.58  | | | | | | |          = e0
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | REF_CLOSE: (85), (201), (208) are inconsistent by sub-proof #68.
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | Case 2:
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | |   (209)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 198.01/32.58  | | | | | | |          all_52_14 = e0
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | ALPHA: (209) implies:
% 198.01/32.58  | | | | | | |   (210)  all_52_14 = e0
% 198.01/32.58  | | | | | | |   (211)  all_52_12 = e1
% 198.01/32.58  | | | | | | |   (212)  all_52_8 = e3
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | REDUCE: (63), (212) imply:
% 198.01/32.58  | | | | | | |   (213)  op(all_52_9, all_52_9) = e3
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | REDUCE: (149), (211) imply:
% 198.01/32.58  | | | | | | |   (214)  op(all_52_13, all_52_13) = e1
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | REDUCE: (64), (210) imply:
% 198.01/32.58  | | | | | | |   (215)  op(all_52_15, all_52_15) = e0
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | BETA: splitting (141) gives:
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | Case 1:
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | |   (216)  all_58_12 = e3
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | COMBINE_EQS: (71), (216) imply:
% 198.01/32.58  | | | | | | | |   (217)  all_52_7 = e3
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | SIMP: (217) implies:
% 198.01/32.58  | | | | | | | |   (218)  all_52_7 = e3
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | REDUCE: (13), (218) imply:
% 198.01/32.58  | | | | | | | |   (219)   ~ (all_52_15 = e3)
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | SIMP: (219) implies:
% 198.01/32.58  | | | | | | | |   (220)   ~ (all_52_15 = e3)
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | REF_CLOSE: (7), (8), (10), (17), (19), (23), (25), (31), (36),
% 198.01/32.58  | | | | | | | |            (38), (60), (67), (75), (81), (85), (93), (101),
% 198.01/32.58  | | | | | | | |            (115), (120), (123), (139), (140), (144), (154),
% 198.01/32.58  | | | | | | | |            (161), (162), (191), (213), (214), (216), (220) are
% 198.01/32.58  | | | | | | | |            inconsistent by sub-proof #18.
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | Case 2:
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | |   (221)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | REF_CLOSE: (4), (7), (10), (31), (87), (123), (175), (191),
% 198.01/32.58  | | | | | | | |            (215), (221) are inconsistent by sub-proof #156.
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | End of split
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | End of split
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | Case 2:
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | |   (222)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 198.01/32.58  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 198.01/32.58  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | | BETA: splitting (222) gives:
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | | Case 1:
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | |   (223)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 198.01/32.58  | | | | | | |          all_52_22 = e0
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | ALPHA: (223) implies:
% 198.01/32.58  | | | | | | |   (224)  all_52_18 = e2
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | COMBINE_EQS: (171), (224) imply:
% 198.01/32.58  | | | | | | |   (225)  all_6_2 = e2
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | COMBINE_EQS: (49), (225) imply:
% 198.01/32.58  | | | | | | |   (226)  all_46_2 = e2
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | REDUCE: (161), (225) imply:
% 198.01/32.58  | | | | | | |   (227)  op(e2, e3) = all_6_1
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | BETA: splitting (174) gives:
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | Case 1:
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | |   (228)   ~ (all_46_2 = e2)
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | REDUCE: (226), (228) imply:
% 198.01/32.58  | | | | | | | |   (229)  $false
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | CLOSE: (229) is inconsistent.
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | Case 2:
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | |   (230)   ~ (all_46_1 = e0)
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | REDUCE: (147), (230) imply:
% 198.01/32.58  | | | | | | | |   (231)   ~ (all_6_1 = e0)
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | GROUND_INST: instantiating (7) with e0, all_6_1, e3, e2,
% 198.01/32.58  | | | | | | | |              simplifying with (193), (227) gives:
% 198.01/32.58  | | | | | | | |   (232)  all_6_1 = e0
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | REDUCE: (231), (232) imply:
% 198.01/32.58  | | | | | | | |   (233)  $false
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | | CLOSE: (233) is inconsistent.
% 198.01/32.58  | | | | | | | | 
% 198.01/32.58  | | | | | | | End of split
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | Case 2:
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | |   (234)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 198.01/32.58  | | | | | | |          all_52_30 = e0
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (10), (11), (12), (13), (15),
% 198.01/32.58  | | | | | | |            (18), (19), (22), (23), (24), (25), (28), (31), (32),
% 198.01/32.58  | | | | | | |            (35), (36), (37), (38), (42), (46), (47), (49), (50),
% 198.01/32.58  | | | | | | |            (51), (55), (57), (60), (61), (65), (71), (75), (78),
% 198.01/32.58  | | | | | | |            (82), (84), (85), (88), (89), (93), (105), (110),
% 198.01/32.58  | | | | | | |            (112), (115), (116), (119), (120), (123), (124), (126),
% 198.01/32.58  | | | | | | |            (131), (136), (139), (140), (141), (143), (144), (147),
% 198.01/32.58  | | | | | | |            (150), (151), (152), (156), (157), (161), (162), (163),
% 198.01/32.58  | | | | | | |            (166), (174), (175), (177), (178), (179), (181), (189),
% 198.01/32.58  | | | | | | |            (234) are inconsistent by sub-proof #304.
% 198.01/32.58  | | | | | | | 
% 198.01/32.58  | | | | | | End of split
% 198.01/32.58  | | | | | | 
% 198.01/32.58  | | | | | End of split
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | Case 2:
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | |   (235)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | | REF_CLOSE: (10), (61), (127), (154), (170), (180), (235) are
% 198.01/32.58  | | | | |            inconsistent by sub-proof #152.
% 198.01/32.58  | | | | | 
% 198.01/32.58  | | | | End of split
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | Case 2:
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | |   (236)   ~ (all_58_15 = e0)
% 198.01/32.58  | | | |   (237)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 198.01/32.58  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.58  | | | |            (13), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 198.01/32.58  | | | |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 198.01/32.58  | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.01/32.58  | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 198.01/32.58  | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 198.01/32.58  | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 198.01/32.58  | | | |            (76), (77), (78), (79), (81), (82), (84), (85), (86), (87),
% 198.01/32.58  | | | |            (88), (90), (91), (92), (93), (94), (96), (97), (98), (99),
% 198.01/32.58  | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 198.01/32.58  | | | |            (108), (109), (110), (111), (112), (113), (114), (115),
% 198.01/32.58  | | | |            (116), (117), (118), (120), (121), (122), (123), (124),
% 198.01/32.58  | | | |            (125), (126), (127), (128), (129), (131), (132), (133),
% 198.01/32.58  | | | |            (134), (135), (136), (137), (138), (139), (140), (141),
% 198.01/32.58  | | | |            (142), (143), (144), (145), (146), (147), (148), (149),
% 198.01/32.58  | | | |            (150), (151), (152), (153), (154), (155), (156), (157),
% 198.01/32.58  | | | |            (159), (160), (161), (162), (163), (166), (170), (171),
% 198.01/32.58  | | | |            (174), (236), (237) are inconsistent by sub-proof #16.
% 198.01/32.58  | | | | 
% 198.01/32.58  | | | End of split
% 198.01/32.58  | | | 
% 198.01/32.58  | | End of split
% 198.01/32.58  | | 
% 198.01/32.58  | End of split
% 198.01/32.58  | 
% 198.01/32.58  End of proof
% 198.01/32.58  
% 198.01/32.58  Sub-proof #16 shows that the following formulas are inconsistent:
% 198.01/32.58  ----------------------------------------------------------------
% 198.01/32.58    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.58    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.58    (3)  all_58_14 = all_52_23
% 198.01/32.58    (4)   ~ (e3 = e1)
% 198.01/32.58    (5)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.58    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.58    (7)  all_58_1 = all_52_9
% 198.01/32.58    (8)   ~ (all_52_9 = all_52_13)
% 198.01/32.58    (9)   ~ (e3 = e0)
% 198.01/32.58    (10)  op(e2, e3) = all_52_3
% 198.01/32.58    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.58    (12)   ~ (all_52_7 = all_52_15)
% 198.01/32.58    (13)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.58    (14)   ~ (all_52_17 = all_52_25)
% 198.01/32.58    (15)   ~ (all_4_2 = e3)
% 198.01/32.58    (16)   ~ (all_52_3 = all_6_2)
% 198.01/32.58    (17)  all_58_0 = all_6_2
% 198.01/32.58    (18)  op(all_14_2, e0) = all_14_1
% 198.01/32.58    (19)  all_56_4 = all_52_3
% 198.01/32.58    (20)  op(e3, all_6_1) = e1
% 198.01/32.58    (21)   ~ (all_52_17 = all_10_2)
% 198.01/32.58    (22)  op(e3, e0) = all_52_25
% 198.01/32.58    (23)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.58    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.58    (25)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.58    (26)   ~ (all_52_27 = all_52_29)
% 198.01/32.58    (27)  all_58_13 = all_52_15
% 198.01/32.58    (28)   ~ (all_4_2 = e0)
% 198.01/32.58    (29)  all_58_9 = all_52_25
% 198.01/32.59    (30)   ~ (all_52_29 = all_14_2)
% 198.01/32.59    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.59    (32)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.59    (33)  op(e1, e3) = all_52_5
% 198.01/32.59    (34)  op(e2, e2) = all_4_2
% 198.01/32.59    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.59    (36)   ~ (all_52_3 = all_52_5)
% 198.01/32.59    (37)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.59    (38)  op(all_4_2, e2) = e1
% 198.01/32.59    (39)  all_58_11 = all_52_29
% 198.01/32.59    (40)   ~ (all_52_3 = e3)
% 198.01/32.59    (41)  all_56_5 = all_4_2
% 198.01/32.59    (42)   ~ (all_52_25 = all_14_2)
% 198.01/32.59    (43)   ~ (all_52_9 = all_52_15)
% 198.01/32.59    (44)   ~ (all_52_3 = all_52_27)
% 198.01/32.59    (45)  op(all_10_2, e1) = all_10_1
% 198.01/32.59    (46)  all_46_2 = all_6_2
% 198.01/32.59    (47)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.59    (48)   ~ (all_52_7 = all_6_2)
% 198.01/32.59    (49)  op(e0, e0) = all_14_2
% 198.01/32.59    (50)  all_56_15 = all_14_2
% 198.01/32.59    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.59    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.59    (53)   ~ (all_58_15 = e0)
% 198.01/32.59    (54)  all_56_11 = all_52_29
% 198.01/32.59    (55)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.59    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.59    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.59    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.59    (59)   ~ (e2 = e1)
% 198.01/32.59    (60)  all_58_10 = all_52_27
% 198.01/32.59    (61)  all_56_8 = all_52_5
% 198.01/32.59    (62)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.59    (63)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.59    (64)   ~ (all_52_25 = all_52_29)
% 198.01/32.59    (65)   ~ (all_52_29 = all_10_2)
% 198.01/32.59    (66)  all_58_7 = all_52_13
% 198.01/32.59    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.59    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.59    (69)   ~ (all_52_5 = all_52_7)
% 198.01/32.59    (70)  all_58_12 = all_52_7
% 198.01/32.59    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.59    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.59    (73)   ~ (all_52_7 = all_14_2)
% 198.01/32.59    (74)  all_52_18 = all_6_2
% 198.01/32.59    (75)  all_58_2 = all_52_3
% 198.01/32.59    (76)  all_56_2 = all_52_17
% 198.01/32.59    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.59    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.59    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.59    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.59    (81)  all_56_7 = all_52_27
% 198.01/32.59    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.59    (83)   ~ (e2 = e0)
% 198.01/32.59    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.59    (85)   ~ (all_52_23 = e3)
% 198.01/32.59    (86)   ~ (all_52_5 = all_52_29)
% 198.01/32.59    (87)   ~ (all_52_15 = all_14_2)
% 198.01/32.59    (88)   ~ (all_52_19 = all_52_27)
% 198.01/32.59    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.59    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.59    (91)   ~ (all_52_27 = e3)
% 198.01/32.59    (92)   ~ (all_52_13 = all_4_2)
% 198.01/32.59    (93)  op(e3, e1) = all_52_17
% 198.01/32.59    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.59    (95)  op(e0, e3) = all_52_7
% 198.01/32.59    (96)  op(e1, e2) = all_52_13
% 198.01/32.59    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.59    (98)   ~ (all_52_9 = all_52_25)
% 198.01/32.59    (99)  all_58_15 = all_14_2
% 198.01/32.59    (100)   ~ (all_52_19 = all_10_2)
% 198.01/32.59    (101)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.59    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.59    (103)  all_58_8 = all_10_2
% 198.01/32.59    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.59    (105)   ~ (all_52_5 = all_10_2)
% 198.01/32.59    (106)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.59    (107)   ~ (all_52_23 = all_14_2)
% 198.01/32.59    (108)  all_56_12 = all_52_7
% 198.01/32.59    (109)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.59    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.59    (111)   ~ (all_52_25 = all_6_2)
% 198.01/32.59    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.59    (113)   ~ (all_52_9 = all_4_2)
% 198.01/32.59    (114)   ~ (all_52_5 = all_6_2)
% 198.01/32.59    (115)   ~ (all_52_9 = all_6_2)
% 198.01/32.59    (116)   ~ (all_52_13 = all_52_15)
% 198.01/32.59    (117)  all_56_0 = all_6_2
% 198.01/32.59    (118)  op(e3, e3) = all_6_2
% 198.01/32.59    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.59    (120)   ~ (all_52_27 = all_14_2)
% 198.01/32.59    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.59    (122)  all_58_5 = e3
% 198.01/32.59    (123)  all_56_14 = all_52_23
% 198.01/32.59    (124)   ~ (all_52_17 = e3)
% 198.01/32.59    (125)  all_56_3 = all_52_25
% 198.01/32.59    (126)   ~ (all_52_3 = all_52_7)
% 198.01/32.59    (127)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.59    (128)  all_58_5 = all_52_19
% 198.01/32.59    (129)  all_56_1 = all_52_9
% 198.01/32.59    (130)   ~ (all_52_15 = all_4_2)
% 198.01/32.59    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.59           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.59           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.59           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.59    (132)   ~ (all_52_27 = all_4_2)
% 198.01/32.59    (133)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 198.01/32.59             all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.59    (134)  all_58_6 = all_52_5
% 198.01/32.59    (135)  op(e3, e2) = all_52_9
% 198.01/32.59    (136)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.59    (137)   ~ (all_52_17 = all_6_2)
% 198.01/32.59    (138)   ~ (e1 = e0)
% 198.01/32.59    (139)   ~ (e3 = e2)
% 198.01/32.59    (140)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.59    (141)   ~ (all_52_9 = all_52_17)
% 198.01/32.59    (142)  all_46_1 = all_6_1
% 198.01/32.59    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.59    (144)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.59    (145)  op(e1, e1) = all_10_2
% 198.01/32.59    (146)   ~ (all_52_23 = all_10_2)
% 198.01/32.59    (147)   ~ (all_52_7 = all_52_23)
% 198.01/32.59    (148)   ~ (all_52_17 = all_52_19)
% 198.01/32.59    (149)  all_58_3 = all_4_2
% 198.01/32.59    (150)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.59    (151)  all_56_13 = all_52_15
% 198.01/32.59    (152)   ~ (all_52_3 = all_4_2)
% 198.01/32.59    (153)   ~ (all_52_19 = all_4_2)
% 198.01/32.59    (154)   ~ (all_52_17 = all_52_23)
% 198.01/32.59    (155)  op(all_6_2, e3) = all_6_1
% 198.01/32.59    (156)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.59    (157)  all_58_4 = all_52_17
% 198.01/32.59    (158)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.59  
% 198.01/32.59  Begin of proof
% 198.01/32.59  | 
% 198.01/32.59  | ALPHA: (133) implies:
% 198.01/32.59  |   (159)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.59  | 
% 198.01/32.59  | REDUCE: (53), (99) imply:
% 198.01/32.59  |   (160)   ~ (all_14_2 = e0)
% 198.01/32.59  | 
% 198.01/32.59  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.59  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 198.01/32.59  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.01/32.59  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.01/32.59  |            (46), (47), (48), (49), (50), (51), (52), (54), (55), (56), (57),
% 198.01/32.59  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 198.01/32.59  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 198.01/32.59  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 198.01/32.59  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 198.01/32.59  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 198.01/32.59  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 198.01/32.59  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 198.01/32.59  |            (129), (130), (131), (132), (134), (135), (136), (137), (138),
% 198.01/32.59  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 198.01/32.59  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 198.01/32.59  |            (157), (158), (159), (160) are inconsistent by sub-proof #17.
% 198.01/32.59  | 
% 198.01/32.59  End of proof
% 198.01/32.59  
% 198.01/32.59  Sub-proof #17 shows that the following formulas are inconsistent:
% 198.01/32.59  ----------------------------------------------------------------
% 198.01/32.59    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.59    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.59    (3)  all_58_14 = all_52_23
% 198.01/32.59    (4)   ~ (e3 = e1)
% 198.01/32.59    (5)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.59    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.59    (7)  all_58_1 = all_52_9
% 198.01/32.59    (8)   ~ (all_52_9 = all_52_13)
% 198.01/32.59    (9)   ~ (e3 = e0)
% 198.01/32.59    (10)  op(e2, e3) = all_52_3
% 198.01/32.59    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.59    (12)   ~ (all_52_7 = all_52_15)
% 198.01/32.59    (13)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.59    (14)   ~ (all_52_17 = all_52_25)
% 198.01/32.59    (15)   ~ (all_4_2 = e3)
% 198.01/32.59    (16)   ~ (all_52_3 = all_6_2)
% 198.01/32.59    (17)  all_58_0 = all_6_2
% 198.01/32.59    (18)  op(all_14_2, e0) = all_14_1
% 198.01/32.59    (19)  all_56_4 = all_52_3
% 198.01/32.59    (20)  op(e3, all_6_1) = e1
% 198.01/32.59    (21)   ~ (all_52_17 = all_10_2)
% 198.01/32.59    (22)  op(e3, e0) = all_52_25
% 198.01/32.59    (23)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.59    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.59    (25)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.59    (26)   ~ (all_52_27 = all_52_29)
% 198.01/32.59    (27)  all_58_13 = all_52_15
% 198.01/32.59    (28)   ~ (all_4_2 = e0)
% 198.01/32.59    (29)  all_58_9 = all_52_25
% 198.01/32.59    (30)   ~ (all_52_29 = all_14_2)
% 198.01/32.59    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.59    (32)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.59    (33)  op(e1, e3) = all_52_5
% 198.01/32.59    (34)  op(e2, e2) = all_4_2
% 198.01/32.59    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.59    (36)   ~ (all_52_3 = all_52_5)
% 198.01/32.59    (37)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.59    (38)  op(all_4_2, e2) = e1
% 198.01/32.59    (39)  all_58_11 = all_52_29
% 198.01/32.59    (40)   ~ (all_52_3 = e3)
% 198.01/32.59    (41)  all_56_5 = all_4_2
% 198.01/32.59    (42)   ~ (all_52_25 = all_14_2)
% 198.01/32.59    (43)   ~ (all_52_9 = all_52_15)
% 198.01/32.59    (44)   ~ (all_52_3 = all_52_27)
% 198.01/32.59    (45)  op(all_10_2, e1) = all_10_1
% 198.01/32.59    (46)  all_46_2 = all_6_2
% 198.01/32.59    (47)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.59    (48)   ~ (all_52_7 = all_6_2)
% 198.01/32.59    (49)  op(e0, e0) = all_14_2
% 198.01/32.59    (50)  all_56_15 = all_14_2
% 198.01/32.59    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.59    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.59    (53)  all_56_11 = all_52_29
% 198.01/32.59    (54)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.59    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.59    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.59    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.59    (58)   ~ (e2 = e1)
% 198.01/32.59    (59)  all_58_10 = all_52_27
% 198.01/32.59    (60)  all_56_8 = all_52_5
% 198.01/32.59    (61)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.59    (62)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.59    (63)   ~ (all_52_25 = all_52_29)
% 198.01/32.59    (64)   ~ (all_52_29 = all_10_2)
% 198.01/32.59    (65)  all_58_7 = all_52_13
% 198.01/32.59    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.59    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.59    (68)   ~ (all_52_5 = all_52_7)
% 198.01/32.59    (69)  all_58_12 = all_52_7
% 198.01/32.59    (70)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.59    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.59    (72)   ~ (all_52_7 = all_14_2)
% 198.01/32.59    (73)   ~ (all_14_2 = e0)
% 198.01/32.59    (74)  all_52_18 = all_6_2
% 198.01/32.59    (75)  all_58_2 = all_52_3
% 198.01/32.59    (76)  all_56_2 = all_52_17
% 198.01/32.59    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.59    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.59    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.59    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.59    (81)  all_56_7 = all_52_27
% 198.01/32.59    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.59    (83)   ~ (e2 = e0)
% 198.01/32.59    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.59    (85)   ~ (all_52_23 = e3)
% 198.01/32.59    (86)   ~ (all_52_5 = all_52_29)
% 198.01/32.59    (87)   ~ (all_52_15 = all_14_2)
% 198.01/32.59    (88)   ~ (all_52_19 = all_52_27)
% 198.01/32.59    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.59    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.59    (91)   ~ (all_52_27 = e3)
% 198.01/32.59    (92)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.59    (93)   ~ (all_52_13 = all_4_2)
% 198.01/32.59    (94)  op(e3, e1) = all_52_17
% 198.01/32.59    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.59    (96)  op(e0, e3) = all_52_7
% 198.01/32.59    (97)  op(e1, e2) = all_52_13
% 198.01/32.59    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.59    (99)   ~ (all_52_9 = all_52_25)
% 198.01/32.59    (100)  all_58_15 = all_14_2
% 198.01/32.59    (101)   ~ (all_52_19 = all_10_2)
% 198.01/32.59    (102)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.59    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.59    (104)  all_58_8 = all_10_2
% 198.01/32.59    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.59    (106)   ~ (all_52_5 = all_10_2)
% 198.01/32.59    (107)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.59    (108)   ~ (all_52_23 = all_14_2)
% 198.01/32.59    (109)  all_56_12 = all_52_7
% 198.01/32.59    (110)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.59    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.59    (112)   ~ (all_52_25 = all_6_2)
% 198.01/32.59    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.59    (114)   ~ (all_52_9 = all_4_2)
% 198.01/32.59    (115)   ~ (all_52_5 = all_6_2)
% 198.01/32.59    (116)   ~ (all_52_9 = all_6_2)
% 198.01/32.59    (117)   ~ (all_52_13 = all_52_15)
% 198.01/32.59    (118)  all_56_0 = all_6_2
% 198.01/32.59    (119)  op(e3, e3) = all_6_2
% 198.01/32.59    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.59    (121)   ~ (all_52_27 = all_14_2)
% 198.01/32.59    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.59    (123)  all_58_5 = e3
% 198.01/32.59    (124)  all_56_14 = all_52_23
% 198.01/32.59    (125)   ~ (all_52_17 = e3)
% 198.01/32.59    (126)  all_56_3 = all_52_25
% 198.01/32.59    (127)   ~ (all_52_3 = all_52_7)
% 198.01/32.59    (128)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.59    (129)  all_58_5 = all_52_19
% 198.01/32.59    (130)  all_56_1 = all_52_9
% 198.01/32.59    (131)   ~ (all_52_15 = all_4_2)
% 198.01/32.59    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.59           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.59           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.59           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.59    (133)   ~ (all_52_27 = all_4_2)
% 198.01/32.59    (134)  all_58_6 = all_52_5
% 198.01/32.59    (135)  op(e3, e2) = all_52_9
% 198.01/32.59    (136)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.59    (137)   ~ (all_52_17 = all_6_2)
% 198.01/32.59    (138)   ~ (e1 = e0)
% 198.01/32.59    (139)   ~ (e3 = e2)
% 198.01/32.59    (140)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.59    (141)   ~ (all_52_9 = all_52_17)
% 198.01/32.59    (142)  all_46_1 = all_6_1
% 198.01/32.59    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.59    (144)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.59    (145)  op(e1, e1) = all_10_2
% 198.01/32.59    (146)   ~ (all_52_23 = all_10_2)
% 198.01/32.59    (147)   ~ (all_52_7 = all_52_23)
% 198.01/32.59    (148)   ~ (all_52_17 = all_52_19)
% 198.01/32.59    (149)  all_58_3 = all_4_2
% 198.01/32.59    (150)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.59    (151)  all_56_13 = all_52_15
% 198.01/32.59    (152)   ~ (all_52_3 = all_4_2)
% 198.01/32.59    (153)   ~ (all_52_19 = all_4_2)
% 198.01/32.59    (154)   ~ (all_52_17 = all_52_23)
% 198.01/32.59    (155)  op(all_6_2, e3) = all_6_1
% 198.01/32.59    (156)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.59    (157)  all_58_4 = all_52_17
% 198.01/32.59    (158)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.59  
% 198.01/32.59  Begin of proof
% 198.01/32.59  | 
% 198.01/32.59  | BETA: splitting (84) gives:
% 198.01/32.59  | 
% 198.01/32.59  | Case 1:
% 198.01/32.59  | | 
% 198.01/32.59  | |   (159)  all_56_5 = e3
% 198.01/32.59  | | 
% 198.01/32.59  | | REF_CLOSE: (15), (41), (159) are inconsistent by sub-proof #1319.
% 198.01/32.59  | | 
% 198.01/32.59  | Case 2:
% 198.01/32.59  | | 
% 198.01/32.59  | |   (160)   ~ (all_56_5 = e3)
% 198.01/32.59  | |   (161)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.59  | | 
% 198.01/32.59  | | BETA: splitting (132) gives:
% 198.01/32.59  | | 
% 198.01/32.59  | | Case 1:
% 198.01/32.59  | | | 
% 198.01/32.59  | | |   (162)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.59  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 198.01/32.59  | | |            e0)
% 198.01/32.59  | | | 
% 198.01/32.59  | | | BETA: splitting (162) gives:
% 198.01/32.59  | | | 
% 198.01/32.59  | | | Case 1:
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | |   (163)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | ALPHA: (163) implies:
% 198.01/32.59  | | | |   (164)  all_52_2 = e2
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | REDUCE: (5), (164) imply:
% 198.01/32.59  | | | |   (165)  op(all_52_3, all_52_3) = e2
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | REF_CLOSE: (4), (6), (9), (24), (28), (34), (37), (38), (41), (49),
% 198.01/32.59  | | | |            (58), (59), (67), (73), (75), (81), (91), (93), (97), (121),
% 198.01/32.59  | | | |            (123), (133), (138), (149), (152), (156), (161), (165) are
% 198.01/32.59  | | | |            inconsistent by sub-proof #148.
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | Case 2:
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | |   (166)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 198.01/32.59  | | | |          e0
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | ALPHA: (166) implies:
% 198.01/32.59  | | | |   (167)  all_52_14 = e0
% 198.01/32.59  | | | |   (168)  all_52_12 = e1
% 198.01/32.59  | | | |   (169)  all_52_8 = e3
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | REDUCE: (61), (169) imply:
% 198.01/32.59  | | | |   (170)  op(all_52_9, all_52_9) = e3
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | REDUCE: (144), (168) imply:
% 198.01/32.59  | | | |   (171)  op(all_52_13, all_52_13) = e1
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | REDUCE: (62), (167) imply:
% 198.01/32.59  | | | |   (172)  op(all_52_15, all_52_15) = e0
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | BETA: splitting (37) gives:
% 198.01/32.59  | | | | 
% 198.01/32.59  | | | | Case 1:
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | |   (173)  all_58_2 = e0
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | | COMBINE_EQS: (75), (173) imply:
% 198.01/32.59  | | | | |   (174)  all_52_3 = e0
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | | SIMP: (174) implies:
% 198.01/32.59  | | | | |   (175)  all_52_3 = e0
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | | REDUCE: (127), (175) imply:
% 198.01/32.59  | | | | |   (176)   ~ (all_52_7 = e0)
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | | SIMP: (176) implies:
% 198.01/32.59  | | | | |   (177)   ~ (all_52_7 = e0)
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | | REDUCE: (16), (175) imply:
% 198.01/32.59  | | | | |   (178)   ~ (all_6_2 = e0)
% 198.01/32.59  | | | | | 
% 198.01/32.59  | | | | | SIMP: (178) implies:
% 198.01/32.60  | | | | |   (179)   ~ (all_6_2 = e0)
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | REDUCE: (40), (175) imply:
% 198.01/32.60  | | | | |   (180)   ~ (e3 = e0)
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | BETA: splitting (105) gives:
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | Case 1:
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | |   (181)  all_56_15 = e3
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | COMBINE_EQS: (50), (181) imply:
% 198.01/32.60  | | | | | |   (182)  all_14_2 = e3
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | SIMP: (182) implies:
% 198.01/32.60  | | | | | |   (183)  all_14_2 = e3
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | REDUCE: (42), (183) imply:
% 198.01/32.60  | | | | | |   (184)   ~ (all_52_25 = e3)
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | REF_CLOSE: (4), (6), (7), (17), (20), (29), (47), (116), (119),
% 198.01/32.60  | | | | | |            (122), (125), (155), (157), (170), (184) are inconsistent
% 198.01/32.60  | | | | | |            by sub-proof #289.
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | Case 2:
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | |   (185)   ~ (all_56_15 = e3)
% 198.01/32.60  | | | | | |   (186)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | REDUCE: (50), (185) imply:
% 198.01/32.60  | | | | | |   (187)   ~ (all_14_2 = e3)
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | BETA: splitting (136) gives:
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | Case 1:
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | |   (188)  all_58_12 = e3
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | COMBINE_EQS: (69), (188) imply:
% 198.01/32.60  | | | | | | |   (189)  all_52_7 = e3
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | SIMP: (189) implies:
% 198.01/32.60  | | | | | | |   (190)  all_52_7 = e3
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | REDUCE: (12), (190) imply:
% 198.01/32.60  | | | | | | |   (191)   ~ (all_52_15 = e3)
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | SIMP: (191) implies:
% 198.01/32.60  | | | | | | |   (192)   ~ (all_52_15 = e3)
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | REDUCE: (13), (190) imply:
% 198.01/32.60  | | | | | | |   (193)  op(e3, e3) = all_52_6
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3,
% 198.01/32.60  | | | | | | |              simplifying with (119), (193) gives:
% 198.01/32.60  | | | | | | |   (194)  all_52_6 = all_6_2
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | REF_CLOSE: (6), (7), (9), (15), (17), (20), (22), (27), (33),
% 198.01/32.60  | | | | | | |            (35), (58), (65), (75), (80), (83), (90), (98), (112),
% 198.01/32.60  | | | | | | |            (116), (119), (134), (135), (139), (149), (155), (156),
% 198.01/32.60  | | | | | | |            (170), (171), (179), (188), (192) are inconsistent by
% 198.01/32.60  | | | | | | |            sub-proof #18.
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | Case 2:
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | |   (195)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | | REF_CLOSE: (3), (6), (9), (11), (12), (20), (27), (34), (43),
% 198.01/32.60  | | | | | | |            (48), (50), (69), (70), (72), (85), (92), (94), (96),
% 198.01/32.60  | | | | | | |            (100), (108), (109), (116), (119), (128), (130), (131),
% 198.01/32.60  | | | | | | |            (140), (141), (147), (155), (170), (172), (186), (187),
% 198.01/32.60  | | | | | | |            (195) are inconsistent by sub-proof #34.
% 198.01/32.60  | | | | | | | 
% 198.01/32.60  | | | | | | End of split
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | End of split
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | Case 2:
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | |   (196)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | REF_CLOSE: (4), (6), (9), (28), (34), (38), (41), (58), (59), (67),
% 198.01/32.60  | | | | |            (75), (93), (97), (123), (133), (138), (149), (152), (156),
% 198.01/32.60  | | | | |            (161), (196) are inconsistent by sub-proof #149.
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | End of split
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | End of split
% 198.01/32.60  | | | 
% 198.01/32.60  | | Case 2:
% 198.01/32.60  | | | 
% 198.01/32.60  | | |   (197)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 198.01/32.60  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 198.01/32.60  | | |            all_52_30 = e0)
% 198.01/32.60  | | | 
% 198.01/32.60  | | | BETA: splitting (197) gives:
% 198.01/32.60  | | | 
% 198.01/32.60  | | | Case 1:
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | |   (198)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 198.01/32.60  | | | |          e0
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | ALPHA: (198) implies:
% 198.01/32.60  | | | |   (199)  all_52_18 = e2
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | COMBINE_EQS: (74), (199) imply:
% 198.01/32.60  | | | |   (200)  all_6_2 = e2
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | COMBINE_EQS: (46), (200) imply:
% 198.01/32.60  | | | |   (201)  all_46_2 = e2
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | REDUCE: (47), (200) imply:
% 198.01/32.60  | | | |   (202)  op(e2, e2) = all_52_0
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | REDUCE: (155), (200) imply:
% 198.01/32.60  | | | |   (203)  op(e2, e3) = all_6_1
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | BETA: splitting (54) gives:
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | Case 1:
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | |   (204)   ~ (all_46_2 = e2)
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | REDUCE: (201), (204) imply:
% 198.01/32.60  | | | | |   (205)  $false
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | CLOSE: (205) is inconsistent.
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | Case 2:
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | |   (206)   ~ (all_46_1 = e0)
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | REDUCE: (142), (206) imply:
% 198.01/32.60  | | | | |   (207)   ~ (all_6_1 = e0)
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | GROUND_INST: instantiating (6) with all_4_2, all_52_0, e2, e2,
% 198.01/32.60  | | | | |              simplifying with (34), (202) gives:
% 198.01/32.60  | | | | |   (208)  all_52_0 = all_4_2
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | GROUND_INST: instantiating (6) with all_52_3, all_6_1, e3, e2,
% 198.01/32.60  | | | | |              simplifying with (10), (203) gives:
% 198.01/32.60  | | | | |   (209)  all_52_3 = all_6_1
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | COMBINE_EQS: (75), (209) imply:
% 198.01/32.60  | | | | |   (210)  all_58_2 = all_6_1
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | BETA: splitting (37) gives:
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | | Case 1:
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | |   (211)  all_58_2 = e0
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | REF_CLOSE: (207), (210), (211) are inconsistent by sub-proof #295.
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | Case 2:
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | |   (212)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | | REF_CLOSE: (4), (6), (9), (28), (34), (38), (41), (58), (59), (67),
% 198.01/32.60  | | | | | |            (75), (93), (97), (123), (133), (138), (149), (152),
% 198.01/32.60  | | | | | |            (156), (161), (212) are inconsistent by sub-proof #149.
% 198.01/32.60  | | | | | | 
% 198.01/32.60  | | | | | End of split
% 198.01/32.60  | | | | | 
% 198.01/32.60  | | | | End of split
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | Case 2:
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | |   (213)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 198.01/32.60  | | | |          e0
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 198.01/32.60  | | | |            (12), (13), (14), (16), (17), (18), (19), (20), (21), (22),
% 198.01/32.60  | | | |            (23), (25), (26), (27), (29), (30), (31), (32), (33), (34),
% 198.01/32.60  | | | |            (35), (36), (39), (41), (42), (43), (44), (45), (46), (47),
% 198.01/32.60  | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 198.01/32.60  | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 198.01/32.60  | | | |            (68), (69), (70), (71), (72), (73), (75), (76), (77), (78),
% 198.01/32.60  | | | |            (79), (80), (82), (83), (84), (86), (87), (88), (89), (90),
% 198.01/32.60  | | | |            (92), (94), (95), (96), (98), (99), (100), (101), (102),
% 198.01/32.60  | | | |            (103), (104), (105), (106), (107), (108), (109), (110),
% 198.01/32.60  | | | |            (111), (112), (113), (114), (115), (116), (117), (118),
% 198.01/32.60  | | | |            (119), (120), (121), (122), (124), (126), (127), (128),
% 198.01/32.60  | | | |            (129), (130), (131), (133), (134), (135), (136), (137),
% 198.01/32.60  | | | |            (138), (139), (140), (142), (143), (144), (145), (146),
% 198.01/32.60  | | | |            (147), (148), (149), (150), (151), (152), (153), (154),
% 198.01/32.60  | | | |            (155), (156), (157), (158), (213) are inconsistent by
% 198.01/32.60  | | | |            sub-proof #271.
% 198.01/32.60  | | | | 
% 198.01/32.60  | | | End of split
% 198.01/32.60  | | | 
% 198.01/32.60  | | End of split
% 198.01/32.60  | | 
% 198.01/32.60  | End of split
% 198.01/32.60  | 
% 198.01/32.60  End of proof
% 198.01/32.60  
% 198.01/32.60  Sub-proof #18 shows that the following formulas are inconsistent:
% 198.01/32.60  ----------------------------------------------------------------
% 198.01/32.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.60    (2)  all_58_1 = all_52_9
% 198.01/32.60    (3)   ~ (e3 = e0)
% 198.01/32.60    (4)   ~ (all_4_2 = e3)
% 198.01/32.60    (5)  all_58_0 = all_6_2
% 198.01/32.60    (6)  op(e3, all_6_1) = e1
% 198.01/32.60    (7)  op(e3, e0) = all_52_25
% 198.01/32.60    (8)  all_58_13 = all_52_15
% 198.01/32.60    (9)  op(all_52_13, all_52_13) = e1
% 198.01/32.60    (10)   ~ (all_52_15 = e3)
% 198.01/32.60    (11)  op(e1, e3) = all_52_5
% 198.01/32.60    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.60    (13)   ~ (e2 = e1)
% 198.01/32.60    (14)   ~ (all_6_2 = e0)
% 198.01/32.60    (15)  all_58_7 = all_52_13
% 198.01/32.60    (16)  all_58_2 = all_52_3
% 198.01/32.60    (17)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.60    (18)   ~ (e2 = e0)
% 198.01/32.60    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.60    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.60    (21)   ~ (all_52_25 = all_6_2)
% 198.01/32.60    (22)   ~ (all_52_9 = all_6_2)
% 198.01/32.60    (23)  op(e3, e3) = all_6_2
% 198.01/32.60    (24)  all_58_6 = all_52_5
% 198.01/32.60    (25)  op(e3, e2) = all_52_9
% 198.01/32.60    (26)   ~ (e3 = e2)
% 198.01/32.60    (27)  all_58_12 = e3
% 198.01/32.60    (28)  op(all_52_9, all_52_9) = e3
% 198.01/32.60    (29)  all_58_3 = all_4_2
% 198.01/32.60    (30)  op(all_6_2, e3) = all_6_1
% 198.01/32.60    (31)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.60  
% 198.01/32.60  Begin of proof
% 198.01/32.60  | 
% 198.01/32.60  | BETA: splitting (17) gives:
% 198.01/32.60  | 
% 198.01/32.60  | Case 1:
% 198.01/32.60  | | 
% 198.01/32.60  | |   (32)  all_58_0 = e1
% 198.01/32.60  | | 
% 198.01/32.60  | | COMBINE_EQS: (5), (32) imply:
% 198.01/32.60  | |   (33)  all_6_2 = e1
% 198.01/32.60  | | 
% 198.01/32.60  | | REDUCE: (22), (33) imply:
% 198.01/32.60  | |   (34)   ~ (all_52_9 = e1)
% 198.01/32.60  | | 
% 198.01/32.60  | | REDUCE: (21), (33) imply:
% 198.01/32.60  | |   (35)   ~ (all_52_25 = e1)
% 198.01/32.60  | | 
% 198.01/32.60  | | REDUCE: (14), (33) imply:
% 198.01/32.60  | |   (36)   ~ (e1 = e0)
% 198.01/32.60  | | 
% 198.01/32.60  | | REDUCE: (30), (33) imply:
% 198.01/32.60  | |   (37)  op(e1, e3) = all_6_1
% 198.01/32.60  | | 
% 198.01/32.60  | | REF_CLOSE: (1), (3), (6), (7), (11), (12), (13), (16), (18), (19), (24),
% 198.01/32.60  | |            (25), (26), (27), (31), (32), (34), (35), (36), (37) are
% 198.01/32.60  | |            inconsistent by sub-proof #307.
% 198.01/32.60  | | 
% 198.01/32.60  | Case 2:
% 198.01/32.60  | | 
% 198.01/32.60  | |   (38)   ~ (all_58_0 = e1)
% 198.01/32.60  | | 
% 198.01/32.60  | | REDUCE: (5), (38) imply:
% 198.01/32.60  | |   (39)   ~ (all_6_2 = e1)
% 198.01/32.60  | | 
% 198.01/32.60  | | REF_CLOSE: (1), (2), (4), (8), (9), (10), (15), (20), (22), (23), (28),
% 198.01/32.60  | |            (29), (39) are inconsistent by sub-proof #1142.
% 198.01/32.60  | | 
% 198.01/32.60  | End of split
% 198.01/32.60  | 
% 198.01/32.60  End of proof
% 198.01/32.60  
% 198.01/32.60  Sub-proof #19 shows that the following formulas are inconsistent:
% 198.01/32.60  ----------------------------------------------------------------
% 198.01/32.60    (1)   ~ (all_52_15 = all_52_23)
% 198.01/32.60    (2)   ~ (all_52_25 = all_52_27)
% 198.01/32.60    (3)  all_58_14 = all_52_23
% 198.01/32.60    (4)   ~ (e3 = e1)
% 198.01/32.60    (5)   ~ (all_52_17 = all_4_0)
% 198.01/32.60    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.01/32.60    (7)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.60    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.60    (9)   ~ (all_52_5 = all_52_13)
% 198.01/32.60    (10)  all_58_1 = all_52_9
% 198.01/32.60    (11)   ~ (all_52_9 = all_52_13)
% 198.01/32.60    (12)   ~ (e3 = e0)
% 198.01/32.60    (13)  op(e2, e3) = all_52_3
% 198.01/32.60    (14)   ~ (all_52_23 = all_4_0)
% 198.01/32.60    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.60    (16)   ~ (all_52_7 = all_52_15)
% 198.01/32.60    (17)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.60    (18)   ~ (all_52_17 = all_52_25)
% 198.01/32.60    (19)   ~ (all_52_3 = all_6_2)
% 198.01/32.60    (20)  all_58_0 = all_6_2
% 198.01/32.60    (21)  op(all_14_2, e0) = all_14_1
% 198.01/32.60    (22)  all_56_4 = all_52_3
% 198.01/32.60    (23)  op(e3, all_6_1) = e1
% 198.01/32.60    (24)   ~ (all_52_17 = all_10_2)
% 198.01/32.60    (25)   ~ (all_10_0 = e3)
% 198.01/32.60    (26)  op(e3, e0) = all_52_25
% 198.01/32.60    (27)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.60    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.60    (29)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.60    (30)   ~ (all_52_27 = all_52_29)
% 198.01/32.60    (31)  all_58_13 = all_52_15
% 198.01/32.60    (32)  all_58_9 = all_52_25
% 198.01/32.60    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.01/32.60    (34)   ~ (all_52_29 = all_14_2)
% 198.01/32.60    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.60    (36)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.60    (37)  op(e1, e3) = all_52_5
% 198.01/32.60    (38)  op(e2, e2) = all_4_2
% 198.01/32.60    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.60    (40)   ~ (all_52_3 = all_52_5)
% 198.01/32.60    (41)  op(all_4_2, e2) = e1
% 198.01/32.60    (42)  all_58_11 = all_52_29
% 198.01/32.60    (43)  all_56_5 = all_4_2
% 198.01/32.60    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.60    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.60    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.60    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.60    (48)  all_46_2 = all_6_2
% 198.01/32.60    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.60    (50)   ~ (all_52_7 = all_6_2)
% 198.01/32.60    (51)  op(e0, e0) = all_14_2
% 198.01/32.60    (52)  all_56_15 = all_14_2
% 198.01/32.60    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.60    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.60    (55)   ~ (all_58_15 = e0)
% 198.01/32.60    (56)  all_56_11 = all_52_29
% 198.01/32.60    (57)   ~ (all_10_0 = e2)
% 198.01/32.60    (58)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.60    (59)   ~ (all_4_0 = e3)
% 198.01/32.60    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.60    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.60    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.60    (63)  all_56_9 = all_52_13
% 198.01/32.60    (64)   ~ (e2 = e1)
% 198.01/32.60    (65)  all_58_10 = all_52_27
% 198.01/32.60    (66)  all_56_8 = all_52_5
% 198.01/32.60    (67)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.60    (68)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.60    (69)   ~ (all_52_25 = all_52_29)
% 198.01/32.60    (70)   ~ (all_52_29 = all_10_2)
% 198.01/32.60    (71)  op(all_10_2, e1) = e3
% 198.01/32.60    (72)  all_58_7 = all_52_13
% 198.01/32.60    (73)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 198.01/32.60    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.60    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.60    (76)   ~ (all_52_5 = all_52_7)
% 198.01/32.60    (77)  all_58_12 = all_52_7
% 198.01/32.60    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.60    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.60    (80)   ~ (all_52_7 = all_14_2)
% 198.01/32.60    (81)  all_30_2 = all_10_2
% 198.01/32.60    (82)  all_58_2 = all_52_3
% 198.01/32.60    (83)  all_56_2 = all_52_17
% 198.01/32.60    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.60    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.60    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.60    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.60    (88)  all_56_7 = all_52_27
% 198.01/32.60    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.60    (90)   ~ (e2 = e0)
% 198.01/32.60    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.60    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.01/32.60    (93)   ~ (all_52_5 = all_52_29)
% 198.01/32.60    (94)  all_56_8 = all_10_0
% 198.01/32.60    (95)   ~ (all_52_15 = all_14_2)
% 198.01/32.60    (96)   ~ (all_52_19 = all_52_27)
% 198.01/32.60    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.60    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.60    (99)   ~ (all_52_13 = all_4_2)
% 198.01/32.60    (100)  op(e3, e1) = all_52_17
% 198.01/32.60    (101)  all_30_0 = all_10_0
% 198.01/32.60    (102)  all_58_6 = all_10_0
% 198.01/32.60    (103)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.60    (104)  op(e0, e3) = all_52_7
% 198.01/32.60    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.60    (106)   ~ (all_52_9 = all_52_25)
% 198.01/32.60    (107)  all_58_15 = all_14_2
% 198.01/32.60    (108)   ~ (all_52_19 = all_10_2)
% 198.01/32.60    (109)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.60    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.60    (111)   ~ (all_10_0 = all_10_2)
% 198.01/32.60    (112)  all_58_8 = all_10_2
% 198.01/32.60    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.60    (114)   ~ (all_52_5 = all_10_2)
% 198.01/32.60    (115)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.60    (116)   ~ (all_52_23 = all_14_2)
% 198.01/32.60    (117)  all_56_12 = all_52_7
% 198.01/32.60    (118)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.60    (119)  all_58_5 = all_4_0
% 198.01/32.60    (120)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.60    (121)   ~ (all_52_25 = all_6_2)
% 198.01/32.60    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.60    (123)   ~ (all_52_9 = all_4_2)
% 198.01/32.60    (124)   ~ (all_52_5 = all_6_2)
% 198.01/32.60    (125)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.60    (126)   ~ (all_52_9 = all_6_2)
% 198.01/32.60    (127)   ~ (all_52_13 = all_52_15)
% 198.01/32.60    (128)  all_56_0 = all_6_2
% 198.01/32.60    (129)  op(e3, e3) = all_6_2
% 198.01/32.60    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.60    (131)   ~ (all_52_27 = all_14_2)
% 198.01/32.60    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.60    (133)  all_56_14 = all_52_23
% 198.01/32.60    (134)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.60    (135)  all_56_3 = all_52_25
% 198.01/32.60    (136)   ~ (all_52_3 = all_52_7)
% 198.01/32.60    (137)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.60    (138)  all_58_5 = all_52_19
% 198.01/32.60    (139)  op(all_10_0, all_10_0) = all_52_4
% 198.01/32.60    (140)  all_56_1 = all_52_9
% 198.01/32.60    (141)   ~ (all_52_15 = all_4_2)
% 198.01/32.60    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.60           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.60           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.60           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.60    (143)   ~ (all_52_27 = all_4_2)
% 198.01/32.60    (144)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 198.01/32.60             all_58_13 = e0 | all_58_14 = e0)
% 198.01/32.60    (145)  all_58_6 = all_52_5
% 198.01/32.60    (146)   ~ (all_4_0 = all_4_2)
% 198.01/32.60    (147)  op(e3, e2) = all_52_9
% 198.01/32.60    (148)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.60    (149)   ~ (all_52_17 = all_6_2)
% 198.01/32.60    (150)   ~ (e1 = e0)
% 198.01/32.60    (151)   ~ (e3 = e2)
% 198.01/32.60    (152)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.60    (153)   ~ (all_52_9 = all_52_17)
% 198.01/32.60    (154)  all_56_10 = all_10_2
% 198.01/32.61    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.61    (156)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.61    (157)  all_46_1 = all_6_1
% 198.01/32.61    (158)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.61    (159)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.61    (160)  op(e1, e1) = all_10_2
% 198.01/32.61    (161)   ~ (all_52_23 = all_10_2)
% 198.01/32.61    (162)   ~ (all_52_7 = all_52_23)
% 198.01/32.61    (163)   ~ (all_52_17 = all_52_19)
% 198.01/32.61    (164)  all_58_3 = all_4_2
% 198.01/32.61    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.61    (166)  all_56_13 = all_52_15
% 198.01/32.61    (167)   ~ (all_52_3 = all_4_2)
% 198.01/32.61    (168)   ~ (all_52_19 = all_4_2)
% 198.01/32.61    (169)   ~ (all_52_17 = all_52_23)
% 198.01/32.61    (170)  op(all_6_2, e3) = all_6_1
% 198.01/32.61    (171)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.61    (172)  all_58_4 = all_52_17
% 198.01/32.61    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 198.01/32.61    (174)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.61  
% 198.01/32.61  Begin of proof
% 198.01/32.61  | 
% 198.01/32.61  | ALPHA: (144) implies:
% 198.01/32.61  |   (175)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.61  |   (176)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.61  | 
% 198.01/32.61  | REDUCE: (55), (107) imply:
% 198.01/32.61  |   (177)   ~ (all_14_2 = e0)
% 198.01/32.61  | 
% 198.01/32.61  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.01/32.61  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 198.01/32.61  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.01/32.61  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.01/32.61  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 198.01/32.61  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 198.01/32.61  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 198.01/32.61  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 198.01/32.61  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 198.01/32.61  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 198.01/32.61  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 198.01/32.61  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 198.01/32.61  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 198.01/32.61  |            (138), (139), (140), (141), (142), (143), (145), (146), (147),
% 198.01/32.61  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 198.01/32.61  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 198.01/32.61  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 198.01/32.61  |            (175), (176), (177) are inconsistent by sub-proof #20.
% 198.01/32.61  | 
% 198.01/32.61  End of proof
% 198.01/32.61  
% 198.01/32.61  Sub-proof #20 shows that the following formulas are inconsistent:
% 198.01/32.61  ----------------------------------------------------------------
% 198.01/32.61    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.61    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.61    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.61    (4)  all_58_14 = all_52_23
% 198.01/32.61    (5)   ~ (e3 = e1)
% 198.01/32.61    (6)   ~ (all_52_17 = all_4_0)
% 198.01/32.61    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.01/32.61    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.61    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.61    (10)   ~ (all_52_5 = all_52_13)
% 198.01/32.61    (11)  all_58_1 = all_52_9
% 198.01/32.61    (12)   ~ (all_52_9 = all_52_13)
% 198.01/32.61    (13)   ~ (e3 = e0)
% 198.01/32.61    (14)  op(e2, e3) = all_52_3
% 198.01/32.61    (15)   ~ (all_52_23 = all_4_0)
% 198.01/32.61    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.61    (17)   ~ (all_52_7 = all_52_15)
% 198.01/32.61    (18)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.61    (19)   ~ (all_52_17 = all_52_25)
% 198.01/32.61    (20)   ~ (all_52_3 = all_6_2)
% 198.01/32.61    (21)  all_58_0 = all_6_2
% 198.01/32.61    (22)  op(all_14_2, e0) = all_14_1
% 198.01/32.61    (23)  all_56_4 = all_52_3
% 198.01/32.61    (24)  op(e3, all_6_1) = e1
% 198.01/32.61    (25)   ~ (all_52_17 = all_10_2)
% 198.01/32.61    (26)   ~ (all_10_0 = e3)
% 198.01/32.61    (27)  op(e3, e0) = all_52_25
% 198.01/32.61    (28)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.61    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.61    (30)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.61    (31)   ~ (all_52_27 = all_52_29)
% 198.01/32.61    (32)  all_58_13 = all_52_15
% 198.01/32.61    (33)  all_58_9 = all_52_25
% 198.01/32.61    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.01/32.61    (35)   ~ (all_52_29 = all_14_2)
% 198.01/32.61    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.61    (37)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.61    (38)  op(e1, e3) = all_52_5
% 198.01/32.61    (39)  op(e2, e2) = all_4_2
% 198.01/32.61    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.61    (41)   ~ (all_52_3 = all_52_5)
% 198.01/32.61    (42)  op(all_4_2, e2) = e1
% 198.01/32.61    (43)  all_58_11 = all_52_29
% 198.01/32.61    (44)  all_56_5 = all_4_2
% 198.01/32.61    (45)   ~ (all_52_25 = all_14_2)
% 198.01/32.61    (46)   ~ (all_52_9 = all_52_15)
% 198.01/32.61    (47)   ~ (all_52_3 = all_52_27)
% 198.01/32.61    (48)  op(all_10_2, e1) = all_10_1
% 198.01/32.61    (49)  all_46_2 = all_6_2
% 198.01/32.61    (50)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.61    (51)   ~ (all_52_7 = all_6_2)
% 198.01/32.61    (52)  op(e0, e0) = all_14_2
% 198.01/32.61    (53)  all_56_15 = all_14_2
% 198.01/32.61    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.61    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.61    (56)  all_56_11 = all_52_29
% 198.01/32.61    (57)   ~ (all_10_0 = e2)
% 198.01/32.61    (58)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.61    (59)   ~ (all_4_0 = e3)
% 198.01/32.61    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.61    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.61    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.61    (63)  all_56_9 = all_52_13
% 198.01/32.61    (64)   ~ (e2 = e1)
% 198.01/32.61    (65)  all_58_10 = all_52_27
% 198.01/32.61    (66)  all_56_8 = all_52_5
% 198.01/32.61    (67)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.61    (68)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.61    (69)   ~ (all_52_25 = all_52_29)
% 198.01/32.61    (70)   ~ (all_52_29 = all_10_2)
% 198.01/32.61    (71)  op(all_10_2, e1) = e3
% 198.01/32.61    (72)  all_58_7 = all_52_13
% 198.01/32.61    (73)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 198.01/32.61    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.61    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.61    (76)   ~ (all_52_5 = all_52_7)
% 198.01/32.61    (77)  all_58_12 = all_52_7
% 198.01/32.61    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.61    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.61    (80)   ~ (all_52_7 = all_14_2)
% 198.01/32.61    (81)   ~ (all_14_2 = e0)
% 198.01/32.61    (82)  all_30_2 = all_10_2
% 198.01/32.61    (83)  all_58_2 = all_52_3
% 198.01/32.61    (84)  all_56_2 = all_52_17
% 198.01/32.61    (85)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.61    (86)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.61    (87)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.01/32.61    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.01/32.61    (89)  all_56_7 = all_52_27
% 198.01/32.61    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.01/32.61    (91)   ~ (e2 = e0)
% 198.01/32.61    (92)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.01/32.61    (93)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.01/32.61    (94)   ~ (all_52_5 = all_52_29)
% 198.01/32.61    (95)  all_56_8 = all_10_0
% 198.01/32.61    (96)   ~ (all_52_15 = all_14_2)
% 198.01/32.61    (97)   ~ (all_52_19 = all_52_27)
% 198.01/32.61    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.01/32.61    (99)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.01/32.61    (100)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.01/32.61    (101)   ~ (all_52_13 = all_4_2)
% 198.01/32.61    (102)  op(e3, e1) = all_52_17
% 198.01/32.61    (103)  all_30_0 = all_10_0
% 198.01/32.61    (104)  all_58_6 = all_10_0
% 198.01/32.61    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.01/32.61    (106)  op(e0, e3) = all_52_7
% 198.01/32.61    (107)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.01/32.61    (108)   ~ (all_52_9 = all_52_25)
% 198.01/32.61    (109)  all_58_15 = all_14_2
% 198.01/32.61    (110)   ~ (all_52_19 = all_10_2)
% 198.01/32.61    (111)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.61    (112)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.61    (113)   ~ (all_10_0 = all_10_2)
% 198.01/32.61    (114)  all_58_8 = all_10_2
% 198.01/32.61    (115)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.01/32.61    (116)   ~ (all_52_5 = all_10_2)
% 198.01/32.61    (117)  op(all_52_29, all_52_29) = all_52_28
% 198.01/32.61    (118)   ~ (all_52_23 = all_14_2)
% 198.01/32.61    (119)  all_56_12 = all_52_7
% 198.01/32.61    (120)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.61    (121)  all_58_5 = all_4_0
% 198.01/32.61    (122)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.01/32.61    (123)   ~ (all_52_25 = all_6_2)
% 198.01/32.61    (124)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.01/32.61    (125)   ~ (all_52_9 = all_4_2)
% 198.01/32.61    (126)   ~ (all_52_5 = all_6_2)
% 198.01/32.61    (127)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.01/32.61    (128)   ~ (all_52_9 = all_6_2)
% 198.01/32.61    (129)   ~ (all_52_13 = all_52_15)
% 198.01/32.61    (130)  all_56_0 = all_6_2
% 198.01/32.61    (131)  op(e3, e3) = all_6_2
% 198.01/32.61    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.01/32.61    (133)   ~ (all_52_27 = all_14_2)
% 198.01/32.61    (134)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.01/32.61    (135)  all_56_14 = all_52_23
% 198.01/32.61    (136)  op(all_4_2, all_4_2) = all_52_10
% 198.01/32.61    (137)  all_56_3 = all_52_25
% 198.01/32.61    (138)   ~ (all_52_3 = all_52_7)
% 198.01/32.61    (139)  op(all_14_2, all_14_2) = all_52_30
% 198.01/32.61    (140)  all_58_5 = all_52_19
% 198.01/32.61    (141)  op(all_10_0, all_10_0) = all_52_4
% 198.01/32.61    (142)  all_56_1 = all_52_9
% 198.01/32.61    (143)   ~ (all_52_15 = all_4_2)
% 198.01/32.61    (144)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.61           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.01/32.61           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.01/32.61           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.01/32.61    (145)   ~ (all_52_27 = all_4_2)
% 198.01/32.61    (146)  all_58_6 = all_52_5
% 198.01/32.61    (147)   ~ (all_4_0 = all_4_2)
% 198.01/32.61    (148)  op(e3, e2) = all_52_9
% 198.01/32.61    (149)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.01/32.61    (150)   ~ (all_52_17 = all_6_2)
% 198.01/32.61    (151)   ~ (e1 = e0)
% 198.01/32.61    (152)   ~ (e3 = e2)
% 198.01/32.61    (153)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.01/32.61    (154)   ~ (all_52_9 = all_52_17)
% 198.01/32.61    (155)  all_56_10 = all_10_2
% 198.01/32.61    (156)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.61    (157)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.01/32.61    (158)  all_46_1 = all_6_1
% 198.01/32.61    (159)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.01/32.61    (160)  op(all_52_13, all_52_13) = all_52_12
% 198.01/32.61    (161)  op(e1, e1) = all_10_2
% 198.01/32.61    (162)   ~ (all_52_23 = all_10_2)
% 198.01/32.61    (163)   ~ (all_52_7 = all_52_23)
% 198.01/32.61    (164)   ~ (all_52_17 = all_52_19)
% 198.01/32.61    (165)  all_58_3 = all_4_2
% 198.01/32.61    (166)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.01/32.61    (167)  all_56_13 = all_52_15
% 198.01/32.61    (168)   ~ (all_52_3 = all_4_2)
% 198.01/32.61    (169)   ~ (all_52_19 = all_4_2)
% 198.01/32.61    (170)   ~ (all_52_17 = all_52_23)
% 198.01/32.61    (171)  op(all_6_2, e3) = all_6_1
% 198.01/32.61    (172)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.01/32.61    (173)  all_58_4 = all_52_17
% 198.01/32.61    (174)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 198.01/32.61    (175)  op(all_52_25, all_52_25) = all_52_24
% 198.01/32.61  
% 198.01/32.61  Begin of proof
% 198.01/32.61  | 
% 198.01/32.61  | BETA: splitting (112) gives:
% 198.01/32.61  | 
% 198.01/32.61  | Case 1:
% 198.01/32.61  | | 
% 198.01/32.61  | |   (176)  all_56_8 = e3
% 198.01/32.61  | | 
% 198.01/32.61  | | REF_CLOSE: (26), (95), (176) are inconsistent by sub-proof #926.
% 198.01/32.61  | | 
% 198.01/32.61  | Case 2:
% 198.01/32.61  | | 
% 198.01/32.61  | |   (177)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.01/32.61  | | 
% 198.01/32.61  | | BETA: splitting (144) gives:
% 198.01/32.61  | | 
% 198.01/32.61  | | Case 1:
% 198.01/32.61  | | | 
% 198.01/32.61  | | |   (178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.01/32.61  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 198.01/32.61  | | |            e0)
% 198.01/32.61  | | | 
% 198.01/32.61  | | | BETA: splitting (178) gives:
% 198.01/32.61  | | | 
% 198.01/32.61  | | | Case 1:
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | |   (179)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | | REF_CLOSE: (9), (25), (57), (71), (73), (82), (95), (102), (103), (104),
% 198.01/32.61  | | | |            (113), (122), (141), (155), (161), (174), (177), (179) are
% 198.01/32.61  | | | |            inconsistent by sub-proof #667.
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | Case 2:
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | |   (180)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 198.01/32.61  | | | |          e0
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 198.01/32.61  | | | |            (12), (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 198.01/32.61  | | | |            (24), (25), (27), (29), (31), (32), (33), (34), (35), (37),
% 198.01/32.61  | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (50),
% 198.01/32.61  | | | |            (51), (52), (53), (54), (59), (61), (63), (64), (65), (66),
% 198.01/32.61  | | | |            (67), (68), (72), (76), (77), (78), (79), (80), (83), (84),
% 198.01/32.61  | | | |            (86), (89), (91), (92), (93), (94), (96), (99), (100), (101),
% 198.01/32.61  | | | |            (102), (105), (106), (107), (108), (109), (111), (112),
% 198.01/32.61  | | | |            (114), (115), (116), (118), (119), (120), (121), (123),
% 198.01/32.61  | | | |            (125), (126), (127), (128), (129), (131), (132), (133),
% 198.01/32.61  | | | |            (134), (136), (138), (139), (142), (143), (145), (146),
% 198.01/32.61  | | | |            (147), (148), (149), (150), (151), (152), (153), (154),
% 198.01/32.61  | | | |            (156), (157), (160), (161), (162), (163), (165), (168),
% 198.01/32.61  | | | |            (170), (171), (172), (173), (175), (180) are inconsistent by
% 198.01/32.61  | | | |            sub-proof #32.
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | End of split
% 198.01/32.61  | | | 
% 198.01/32.61  | | Case 2:
% 198.01/32.61  | | | 
% 198.01/32.61  | | |   (181)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 198.01/32.61  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 198.01/32.61  | | |            all_52_30 = e0)
% 198.01/32.61  | | | 
% 198.01/32.61  | | | BETA: splitting (181) gives:
% 198.01/32.61  | | | 
% 198.01/32.61  | | | Case 1:
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | |   (182)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 198.01/32.61  | | | |          e0
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | | REF_CLOSE: (4), (9), (16), (18), (24), (25), (51), (59), (71), (78),
% 198.01/32.61  | | | |            (102), (106), (111), (114), (119), (120), (121), (131),
% 198.01/32.61  | | | |            (150), (155), (156), (161), (162), (163), (171), (173),
% 198.01/32.61  | | | |            (174), (182) are inconsistent by sub-proof #21.
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | Case 2:
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | |   (183)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 198.01/32.61  | | | |          e0
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (12), (13), (14), (16),
% 198.01/32.61  | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 198.01/32.61  | | | |            (28), (30), (31), (32), (33), (35), (36), (37), (38), (39),
% 198.01/32.61  | | | |            (40), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 198.01/32.61  | | | |            (51), (52), (53), (54), (55), (56), (58), (60), (61), (62),
% 198.01/32.61  | | | |            (64), (65), (66), (67), (68), (69), (70), (72), (74), (75),
% 198.01/32.61  | | | |            (76), (77), (78), (79), (80), (81), (83), (84), (85), (86),
% 198.01/32.61  | | | |            (87), (88), (90), (91), (92), (94), (96), (97), (98), (99),
% 198.01/32.61  | | | |            (100), (102), (105), (106), (107), (108), (109), (110),
% 198.01/32.61  | | | |            (111), (112), (114), (115), (116), (117), (118), (119),
% 198.01/32.61  | | | |            (120), (122), (123), (124), (125), (126), (128), (129),
% 198.01/32.61  | | | |            (130), (131), (132), (133), (134), (135), (137), (138),
% 198.01/32.61  | | | |            (139), (140), (142), (143), (145), (146), (148), (149),
% 198.01/32.61  | | | |            (150), (151), (152), (153), (158), (159), (160), (161),
% 198.01/32.61  | | | |            (162), (163), (164), (165), (166), (167), (168), (169),
% 198.01/32.61  | | | |            (170), (171), (172), (173), (175), (183) are inconsistent by
% 198.01/32.61  | | | |            sub-proof #271.
% 198.01/32.61  | | | | 
% 198.01/32.61  | | | End of split
% 198.01/32.61  | | | 
% 198.01/32.61  | | End of split
% 198.01/32.61  | | 
% 198.01/32.61  | End of split
% 198.01/32.61  | 
% 198.01/32.61  End of proof
% 198.01/32.61  
% 198.01/32.61  Sub-proof #21 shows that the following formulas are inconsistent:
% 198.01/32.61  ----------------------------------------------------------------
% 198.01/32.61    (1)  all_58_14 = all_52_23
% 198.01/32.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.61    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.61    (4)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.61    (5)  op(e3, all_6_1) = e1
% 198.01/32.61    (6)   ~ (all_52_17 = all_10_2)
% 198.01/32.61    (7)   ~ (all_52_7 = all_6_2)
% 198.01/32.61    (8)   ~ (all_4_0 = e3)
% 198.01/32.61    (9)  op(all_10_2, e1) = e3
% 198.01/32.61    (10)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.61    (11)  op(e3, e1) = all_52_17
% 198.01/32.61    (12)  op(e0, e3) = all_52_7
% 198.01/32.61    (13)  op(all_52_23, all_52_23) = all_52_22
% 198.01/32.61    (14)  all_58_8 = all_10_2
% 198.01/32.61    (15)  all_56_12 = all_52_7
% 198.01/32.61    (16)  op(all_52_17, all_52_17) = all_52_16
% 198.01/32.61    (17)  all_58_5 = all_4_0
% 198.01/32.61    (18)  op(e3, e3) = all_6_2
% 198.01/32.61    (19)   ~ (all_52_17 = all_6_2)
% 198.01/32.61    (20)  all_56_10 = all_10_2
% 198.01/32.61    (21)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.61    (22)  op(e1, e1) = all_10_2
% 198.01/32.61    (23)   ~ (all_52_23 = all_10_2)
% 198.01/32.61    (24)   ~ (all_52_7 = all_52_23)
% 198.01/32.61    (25)  op(all_6_2, e3) = all_6_1
% 198.01/32.61    (26)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.01/32.61    (27)  all_58_4 = all_52_17
% 198.01/32.61    (28)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 198.01/32.61  
% 198.01/32.61  Begin of proof
% 198.01/32.61  | 
% 198.01/32.61  | ALPHA: (26) implies:
% 198.01/32.61  |   (29)  all_52_22 = e0
% 198.01/32.61  |   (30)  all_52_16 = e3
% 198.01/32.61  | 
% 198.01/32.61  | REDUCE: (16), (30) imply:
% 198.01/32.61  |   (31)  op(all_52_17, all_52_17) = e3
% 198.01/32.61  | 
% 198.01/32.61  | REDUCE: (13), (29) imply:
% 198.01/32.61  |   (32)  op(all_52_23, all_52_23) = e0
% 198.01/32.61  | 
% 198.01/32.61  | BETA: splitting (21) gives:
% 198.01/32.61  | 
% 198.01/32.61  | Case 1:
% 198.01/32.61  | | 
% 198.01/32.61  | |   (33)  all_58_4 = e3
% 198.01/32.61  | | 
% 198.01/32.61  | | COMBINE_EQS: (27), (33) imply:
% 198.01/32.61  | |   (34)  all_52_17 = e3
% 198.01/32.61  | | 
% 198.01/32.61  | | REF_CLOSE: (2), (18), (19), (31), (34) are inconsistent by sub-proof #1280.
% 198.01/32.61  | | 
% 198.01/32.61  | Case 2:
% 198.01/32.61  | | 
% 198.01/32.61  | |   (35)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.01/32.61  | | 
% 198.01/32.61  | | BETA: splitting (28) gives:
% 198.01/32.61  | | 
% 198.01/32.61  | | Case 1:
% 198.01/32.61  | | | 
% 198.01/32.61  | | |   (36)  all_56_10 = e3
% 198.01/32.61  | | | 
% 198.01/32.61  | | | COMBINE_EQS: (20), (36) imply:
% 198.01/32.61  | | |   (37)  all_10_2 = e3
% 198.01/32.61  | | | 
% 198.01/32.61  | | | SIMP: (37) implies:
% 198.01/32.61  | | |   (38)  all_10_2 = e3
% 198.01/32.61  | | | 
% 198.01/32.61  | | | REF_CLOSE: (2), (6), (9), (11), (38) are inconsistent by sub-proof #925.
% 198.01/32.61  | | | 
% 198.01/32.61  | | Case 2:
% 198.01/32.61  | | | 
% 198.01/32.61  | | |   (39)   ~ (all_56_10 = e3)
% 198.01/32.61  | | | 
% 198.01/32.61  | | | REDUCE: (20), (39) imply:
% 198.01/32.61  | | |   (40)   ~ (all_10_2 = e3)
% 198.01/32.61  | | | 
% 198.01/32.61  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (14),
% 198.01/32.61  | | |            (15), (17), (18), (22), (23), (24), (25), (31), (32), (35),
% 198.01/32.61  | | |            (40) are inconsistent by sub-proof #36.
% 198.01/32.61  | | | 
% 198.01/32.61  | | End of split
% 198.01/32.61  | | 
% 198.01/32.61  | End of split
% 198.01/32.61  | 
% 198.01/32.62  End of proof
% 198.01/32.62  
% 198.01/32.62  Sub-proof #22 shows that the following formulas are inconsistent:
% 198.01/32.62  ----------------------------------------------------------------
% 198.01/32.62    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.01/32.62    (2)   ~ (all_52_15 = all_52_23)
% 198.01/32.62    (3)   ~ (all_52_25 = all_52_27)
% 198.01/32.62    (4)  all_58_14 = all_52_23
% 198.01/32.62    (5)   ~ (e3 = e1)
% 198.01/32.62    (6)  op(all_52_3, all_52_3) = all_52_2
% 198.01/32.62    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.01/32.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.01/32.62    (8)  all_58_1 = all_52_9
% 198.01/32.62    (9)   ~ (all_52_9 = all_52_13)
% 198.01/32.62    (10)   ~ (e3 = e0)
% 198.01/32.62    (11)  op(e2, e3) = all_52_3
% 198.01/32.62    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.01/32.62    (13)   ~ (all_52_7 = all_52_15)
% 198.01/32.62    (14)  op(all_52_7, all_52_7) = all_52_6
% 198.01/32.62    (15)   ~ (all_52_17 = all_52_25)
% 198.01/32.62    (16)   ~ (all_52_3 = all_6_2)
% 198.01/32.62    (17)  all_58_0 = all_6_2
% 198.01/32.62    (18)  op(all_14_2, e0) = all_14_1
% 198.01/32.62    (19)  all_56_4 = all_52_3
% 198.01/32.62    (20)  op(e3, all_6_1) = e1
% 198.01/32.62    (21)   ~ (all_52_17 = all_10_2)
% 198.01/32.62    (22)   ~ (all_10_0 = e3)
% 198.01/32.62    (23)  all_40_2 = all_10_2
% 198.01/32.62    (24)  op(e3, e0) = all_52_25
% 198.01/32.62    (25)  op(all_52_5, all_52_5) = all_52_4
% 198.01/32.62    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.01/32.62    (27)  op(all_52_19, all_52_19) = all_52_18
% 198.01/32.62    (28)   ~ (all_52_27 = all_52_29)
% 198.01/32.62    (29)  all_58_13 = all_52_15
% 198.01/32.62    (30)  op(all_10_2, all_10_2) = all_52_20
% 198.01/32.62    (31)  all_58_9 = all_52_25
% 198.01/32.62    (32)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.01/32.62    (33)   ~ (all_52_29 = all_14_2)
% 198.01/32.62    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.01/32.62    (35)  op(all_52_27, all_52_27) = all_52_26
% 198.01/32.62    (36)  op(e1, e3) = all_52_5
% 198.01/32.62    (37)  op(e2, e2) = all_4_2
% 198.01/32.62    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.01/32.62    (39)  all_58_7 = all_10_0
% 198.01/32.62    (40)   ~ (all_52_3 = all_52_5)
% 198.01/32.62    (41)  op(all_4_2, e2) = e1
% 198.01/32.62    (42)  all_58_11 = all_52_29
% 198.01/32.62    (43)  all_56_5 = all_4_2
% 198.01/32.62    (44)   ~ (all_52_25 = all_14_2)
% 198.01/32.62    (45)   ~ (all_52_9 = all_52_15)
% 198.01/32.62    (46)   ~ (all_52_3 = all_52_27)
% 198.01/32.62    (47)  op(all_10_2, e1) = all_10_1
% 198.01/32.62    (48)   ~ (all_10_2 = all_4_0)
% 198.01/32.62    (49)  all_46_2 = all_6_2
% 198.01/32.62    (50)  op(all_6_2, all_6_2) = all_52_0
% 198.01/32.62    (51)   ~ (all_52_7 = all_6_2)
% 198.01/32.62    (52)  op(e0, e0) = all_14_2
% 198.01/32.62    (53)  all_56_15 = all_14_2
% 198.01/32.62    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.01/32.62    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.01/32.62    (56)  all_56_11 = all_52_29
% 198.01/32.62    (57)   ~ (all_10_0 = e2)
% 198.01/32.62    (58)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.01/32.62    (59)   ~ (all_4_0 = e3)
% 198.01/32.62    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.01/32.62    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.01/32.62    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.01/32.62    (63)   ~ (e2 = e1)
% 198.01/32.62    (64)  all_58_10 = all_52_27
% 198.01/32.62    (65)  all_56_8 = all_52_5
% 198.01/32.62    (66)  op(all_52_9, all_52_9) = all_52_8
% 198.01/32.62    (67)  op(all_52_15, all_52_15) = all_52_14
% 198.01/32.62    (68)  all_56_9 = all_10_0
% 198.01/32.62    (69)   ~ (all_52_25 = all_52_29)
% 198.01/32.62    (70)   ~ (all_52_29 = all_10_2)
% 198.01/32.62    (71)  all_58_7 = all_52_13
% 198.01/32.62    (72)   ~ (all_10_0 = all_4_2)
% 198.01/32.62    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.01/32.62    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.01/32.62    (75)   ~ (all_52_5 = all_52_7)
% 198.01/32.62    (76)  all_58_12 = all_52_7
% 198.01/32.62    (77)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.01/32.62    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.01/32.62    (79)   ~ (all_52_7 = all_14_2)
% 198.01/32.62    (80)   ~ (all_14_2 = e0)
% 198.01/32.62    (81)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 198.01/32.62    (82)  all_58_2 = all_52_3
% 198.01/32.62    (83)  all_56_2 = all_52_17
% 198.01/32.62    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.01/32.62    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.01/32.62    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.47/32.62    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.47/32.62    (88)  all_56_7 = all_52_27
% 198.47/32.62    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.47/32.62    (90)   ~ (e2 = e0)
% 198.47/32.62    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.47/32.62    (92)   ~ (all_52_5 = all_52_29)
% 198.47/32.62    (93)   ~ (all_52_15 = all_14_2)
% 198.47/32.62    (94)   ~ (all_52_19 = all_52_27)
% 198.47/32.62    (95)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.47/32.62    (96)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.47/32.62    (97)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.47/32.62    (98)  op(e3, e1) = all_52_17
% 198.47/32.62    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.47/32.62    (100)  op(e0, e3) = all_52_7
% 198.47/32.62    (101)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.62    (102)   ~ (all_52_9 = all_52_25)
% 198.47/32.62    (103)  all_58_15 = all_14_2
% 198.47/32.62    (104)   ~ (all_52_19 = all_10_2)
% 198.47/32.62    (105)  op(all_52_23, all_52_23) = all_52_22
% 198.47/32.62    (106)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.47/32.62    (107)   ~ (all_10_0 = all_10_2)
% 198.47/32.62    (108)  all_58_8 = all_10_2
% 198.47/32.62    (109)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.62    (110)   ~ (all_52_5 = all_10_2)
% 198.47/32.62    (111)  op(all_52_29, all_52_29) = all_52_28
% 198.47/32.62    (112)   ~ (all_52_23 = all_14_2)
% 198.47/32.62    (113)  all_56_12 = all_52_7
% 198.47/32.62    (114)  op(all_52_17, all_52_17) = all_52_16
% 198.47/32.62    (115)  all_58_5 = all_4_0
% 198.47/32.62    (116)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.47/32.62    (117)   ~ (all_52_25 = all_6_2)
% 198.47/32.62    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.47/32.62    (119)   ~ (all_52_9 = all_4_2)
% 198.47/32.62    (120)   ~ (all_52_5 = all_6_2)
% 198.47/32.62    (121)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.47/32.62    (122)   ~ (all_52_9 = all_6_2)
% 198.47/32.62    (123)   ~ (all_52_13 = all_52_15)
% 198.47/32.62    (124)  all_56_0 = all_6_2
% 198.47/32.62    (125)  op(e3, e3) = all_6_2
% 198.47/32.62    (126)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.47/32.62    (127)   ~ (all_52_27 = all_14_2)
% 198.47/32.62    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.47/32.62    (129)  all_56_14 = all_52_23
% 198.47/32.62    (130)  op(all_4_2, all_4_2) = all_52_10
% 198.47/32.62    (131)  all_40_0 = all_10_0
% 198.47/32.62    (132)  all_56_3 = all_52_25
% 198.47/32.62    (133)   ~ (all_52_3 = all_52_7)
% 198.47/32.62    (134)  op(all_14_2, all_14_2) = all_52_30
% 198.47/32.62    (135)  all_58_5 = all_52_19
% 198.47/32.62    (136)  all_56_1 = all_52_9
% 198.47/32.62    (137)   ~ (all_52_15 = all_4_2)
% 198.47/32.62    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.47/32.62           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.47/32.62           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.47/32.62           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.47/32.62    (139)   ~ (all_52_27 = all_4_2)
% 198.47/32.62    (140)  all_58_6 = all_52_5
% 198.47/32.62    (141)  op(all_10_2, e1) = e2
% 198.47/32.62    (142)   ~ (all_4_0 = all_4_2)
% 198.47/32.62    (143)  op(e3, e2) = all_52_9
% 198.47/32.62    (144)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.62    (145)   ~ (all_52_17 = all_6_2)
% 198.47/32.62    (146)   ~ (e1 = e0)
% 198.47/32.62    (147)   ~ (e3 = e2)
% 198.47/32.62    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.47/32.62    (149)   ~ (all_52_9 = all_52_17)
% 198.47/32.62    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.62    (151)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.47/32.62    (152)   ~ (all_52_3 = all_4_0)
% 198.47/32.62    (153)  all_46_1 = all_6_1
% 198.47/32.62    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.47/32.62    (155)  op(all_52_13, all_52_13) = all_52_12
% 198.47/32.62    (156)  op(all_10_0, all_10_0) = all_52_12
% 198.47/32.62    (157)  op(e1, e1) = all_10_2
% 198.47/32.62    (158)   ~ (all_52_23 = all_10_2)
% 198.47/32.62    (159)   ~ (all_52_7 = all_52_23)
% 198.47/32.62    (160)   ~ (all_52_17 = all_52_19)
% 198.47/32.62    (161)   ~ (all_52_5 = all_10_0)
% 198.47/32.62    (162)  all_58_3 = all_4_2
% 198.47/32.62    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.47/32.62    (164)  all_56_13 = all_52_15
% 198.47/32.62    (165)   ~ (all_52_3 = all_4_2)
% 198.47/32.62    (166)   ~ (all_52_9 = all_10_0)
% 198.47/32.62    (167)   ~ (all_52_19 = all_4_2)
% 198.47/32.62    (168)   ~ (all_52_17 = all_52_23)
% 198.47/32.62    (169)  op(all_6_2, e3) = all_6_1
% 198.47/32.62    (170)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.47/32.62    (171)  all_58_4 = all_52_17
% 198.47/32.62    (172)  op(all_52_25, all_52_25) = all_52_24
% 198.47/32.62  
% 198.47/32.62  Begin of proof
% 198.47/32.62  | 
% 198.47/32.62  | BETA: splitting (151) gives:
% 198.47/32.62  | 
% 198.47/32.62  | Case 1:
% 198.47/32.62  | | 
% 198.47/32.62  | |   (173)  all_56_9 = e3
% 198.47/32.62  | | 
% 198.47/32.62  | | REF_CLOSE: (22), (68), (173) are inconsistent by sub-proof #1006.
% 198.47/32.62  | | 
% 198.47/32.62  | Case 2:
% 198.47/32.62  | | 
% 198.47/32.62  | |   (174)   ~ (all_56_9 = e3)
% 198.47/32.62  | |   (175)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.47/32.62  | | 
% 198.47/32.62  | | BETA: splitting (138) gives:
% 198.47/32.62  | | 
% 198.47/32.62  | | Case 1:
% 198.47/32.62  | | | 
% 198.47/32.62  | | |   (176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.47/32.62  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 198.47/32.62  | | |            e0)
% 198.47/32.62  | | | 
% 198.47/32.62  | | | BETA: splitting (176) gives:
% 198.47/32.62  | | | 
% 198.47/32.62  | | | Case 1:
% 198.47/32.62  | | | | 
% 198.47/32.62  | | | |   (177)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.47/32.62  | | | | 
% 198.47/32.62  | | | | REF_CLOSE: (1), (4), (6), (7), (8), (12), (13), (14), (16), (17), (21),
% 198.47/32.62  | | | |            (22), (23), (25), (26), (28), (29), (30), (31), (32), (35),
% 198.47/32.62  | | | |            (37), (39), (41), (42), (44), (48), (50), (51), (52), (53),
% 198.47/32.62  | | | |            (54), (57), (59), (63), (64), (65), (68), (72), (76), (78),
% 198.47/32.62  | | | |            (79), (80), (81), (82), (85), (88), (92), (93), (98), (102),
% 198.47/32.62  | | | |            (106), (108), (109), (110), (112), (113), (114), (115),
% 198.47/32.62  | | | |            (120), (122), (125), (127), (128), (130), (131), (134),
% 198.47/32.62  | | | |            (136), (140), (141), (143), (144), (145), (147), (148),
% 198.47/32.62  | | | |            (149), (150), (157), (161), (162), (163), (165), (166),
% 198.47/32.62  | | | |            (171), (175), (177) are inconsistent by sub-proof #171.
% 198.47/32.62  | | | | 
% 198.47/32.62  | | | Case 2:
% 198.47/32.62  | | | | 
% 198.47/32.62  | | | |   (178)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 198.47/32.62  | | | |          e0
% 198.47/32.62  | | | | 
% 198.47/32.62  | | | | REF_CLOSE: (2), (4), (7), (8), (10), (12), (13), (14), (20), (22), (23),
% 198.47/32.62  | | | |            (29), (37), (39), (41), (45), (51), (53), (57), (59), (66),
% 198.47/32.62  | | | |            (67), (68), (73), (76), (77), (79), (80), (81), (93), (97),
% 198.47/32.62  | | | |            (98), (100), (101), (103), (105), (107), (108), (109), (112),
% 198.47/32.62  | | | |            (113), (115), (122), (125), (129), (130), (131), (134),
% 198.47/32.62  | | | |            (136), (137), (143), (144), (147), (148), (149), (150),
% 198.47/32.62  | | | |            (156), (157), (159), (162), (163), (169), (171), (175), (178)
% 198.47/32.62  | | | |            are inconsistent by sub-proof #25.
% 198.47/32.62  | | | | 
% 198.47/32.62  | | | End of split
% 198.47/32.62  | | | 
% 198.47/32.62  | | Case 2:
% 198.47/32.62  | | | 
% 198.47/32.62  | | |   (179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 198.47/32.62  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 198.47/32.62  | | |            all_52_30 = e0)
% 198.47/32.62  | | | 
% 198.47/32.62  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 198.47/32.62  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 198.47/32.62  | | |            (25), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 198.47/32.62  | | |            (37), (38), (40), (41), (42), (43), (44), (45), (46), (47),
% 198.47/32.62  | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 198.47/32.62  | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 198.47/32.62  | | |            (69), (70), (71), (73), (74), (75), (76), (77), (78), (79),
% 198.47/32.62  | | |            (80), (81), (82), (83), (84), (85), (86), (87), (89), (90),
% 198.47/32.62  | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 198.47/32.62  | | |            (101), (102), (103), (104), (105), (106), (108), (109), (110),
% 198.47/32.62  | | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 198.47/32.62  | | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 198.47/32.62  | | |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 198.47/32.62  | | |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 198.47/32.62  | | |            (148), (150), (152), (153), (154), (155), (157), (158), (159),
% 198.47/32.62  | | |            (160), (162), (163), (164), (165), (167), (168), (169), (170),
% 198.47/32.62  | | |            (171), (172), (175), (179) are inconsistent by sub-proof #23.
% 198.47/32.62  | | | 
% 198.47/32.62  | | End of split
% 198.47/32.62  | | 
% 198.47/32.62  | End of split
% 198.47/32.62  | 
% 198.47/32.62  End of proof
% 198.47/32.62  
% 198.47/32.62  Sub-proof #23 shows that the following formulas are inconsistent:
% 198.47/32.62  ----------------------------------------------------------------
% 198.47/32.62    (1)   ~ (all_52_15 = all_52_23)
% 198.47/32.62    (2)   ~ (all_52_25 = all_52_27)
% 198.47/32.62    (3)  all_58_14 = all_52_23
% 198.47/32.62    (4)   ~ (e3 = e1)
% 198.47/32.62    (5)  op(all_52_3, all_52_3) = all_52_2
% 198.47/32.62    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.62    (7)  all_58_1 = all_52_9
% 198.47/32.62    (8)   ~ (all_52_9 = all_52_13)
% 198.47/32.62    (9)   ~ (e3 = e0)
% 198.47/32.62    (10)  op(e2, e3) = all_52_3
% 198.47/32.62    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.47/32.62    (12)   ~ (all_52_7 = all_52_15)
% 198.47/32.62    (13)  op(all_52_7, all_52_7) = all_52_6
% 198.47/32.62    (14)   ~ (all_52_17 = all_52_25)
% 198.47/32.62    (15)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.47/32.62    (16)   ~ (all_52_3 = all_6_2)
% 198.47/32.62    (17)  all_58_0 = all_6_2
% 198.47/32.62    (18)  op(all_14_2, e0) = all_14_1
% 198.47/32.62    (19)  all_56_4 = all_52_3
% 198.47/32.62    (20)  op(e3, all_6_1) = e1
% 198.47/32.62    (21)   ~ (all_52_17 = all_10_2)
% 198.47/32.62    (22)  all_40_2 = all_10_2
% 198.47/32.62    (23)  op(e3, e0) = all_52_25
% 198.47/32.62    (24)  op(all_52_5, all_52_5) = all_52_4
% 198.47/32.62    (25)  op(all_52_19, all_52_19) = all_52_18
% 198.47/32.62    (26)   ~ (all_52_27 = all_52_29)
% 198.47/32.62    (27)  all_58_13 = all_52_15
% 198.47/32.62    (28)  op(all_10_2, all_10_2) = all_52_20
% 198.47/32.62    (29)  all_58_9 = all_52_25
% 198.47/32.62    (30)   ~ (all_52_29 = all_14_2)
% 198.47/32.62    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.47/32.62    (32)  op(all_52_27, all_52_27) = all_52_26
% 198.47/32.62    (33)  op(e1, e3) = all_52_5
% 198.47/32.62    (34)  op(e2, e2) = all_4_2
% 198.47/32.62    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.47/32.62    (36)   ~ (all_52_3 = all_52_5)
% 198.47/32.62    (37)  op(all_4_2, e2) = e1
% 198.47/32.62    (38)  all_58_11 = all_52_29
% 198.47/32.62    (39)  all_56_5 = all_4_2
% 198.47/32.62    (40)   ~ (all_52_25 = all_14_2)
% 198.47/32.62    (41)   ~ (all_52_9 = all_52_15)
% 198.47/32.62    (42)   ~ (all_52_3 = all_52_27)
% 198.47/32.62    (43)  op(all_10_2, e1) = all_10_1
% 198.47/32.62    (44)  all_46_2 = all_6_2
% 198.47/32.62    (45)  op(all_6_2, all_6_2) = all_52_0
% 198.47/32.62    (46)   ~ (all_52_7 = all_6_2)
% 198.47/32.62    (47)  op(e0, e0) = all_14_2
% 198.47/32.62    (48)  all_56_15 = all_14_2
% 198.47/32.62    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.47/32.62    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.47/32.62    (51)  all_56_11 = all_52_29
% 198.47/32.62    (52)   ~ (all_10_0 = e2)
% 198.47/32.62    (53)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.47/32.62    (54)   ~ (all_4_0 = e3)
% 198.47/32.62    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.47/32.62    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.47/32.62    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.47/32.62    (58)   ~ (e2 = e1)
% 198.47/32.62    (59)  all_58_10 = all_52_27
% 198.47/32.62    (60)  all_56_8 = all_52_5
% 198.47/32.62    (61)  op(all_52_9, all_52_9) = all_52_8
% 198.47/32.62    (62)  op(all_52_15, all_52_15) = all_52_14
% 198.47/32.62    (63)  all_56_9 = all_10_0
% 198.47/32.62    (64)   ~ (all_52_25 = all_52_29)
% 198.47/32.62    (65)   ~ (all_52_29 = all_10_2)
% 198.47/32.62    (66)  all_58_7 = all_52_13
% 198.47/32.62    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.47/32.62    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.47/32.62    (69)   ~ (all_52_5 = all_52_7)
% 198.47/32.62    (70)  all_58_12 = all_52_7
% 198.47/32.62    (71)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.47/32.62    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.47/32.62    (73)   ~ (all_52_7 = all_14_2)
% 198.47/32.62    (74)   ~ (all_14_2 = e0)
% 198.47/32.62    (75)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 198.47/32.62    (76)  all_58_2 = all_52_3
% 198.47/32.62    (77)  all_56_2 = all_52_17
% 198.47/32.62    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.47/32.62    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.47/32.62    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.47/32.62    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.47/32.62    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.47/32.62    (83)   ~ (e2 = e0)
% 198.47/32.62    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.47/32.62    (85)   ~ (all_52_5 = all_52_29)
% 198.47/32.62    (86)   ~ (all_52_15 = all_14_2)
% 198.47/32.62    (87)   ~ (all_52_19 = all_52_27)
% 198.47/32.62    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.47/32.62    (89)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.47/32.62    (90)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.47/32.62    (91)  op(e3, e1) = all_52_17
% 198.47/32.62    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.47/32.62    (93)  op(e0, e3) = all_52_7
% 198.47/32.62    (94)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.62    (95)   ~ (all_52_9 = all_52_25)
% 198.47/32.62    (96)  all_58_15 = all_14_2
% 198.47/32.62    (97)   ~ (all_52_19 = all_10_2)
% 198.47/32.62    (98)  op(all_52_23, all_52_23) = all_52_22
% 198.47/32.62    (99)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.47/32.62    (100)  all_58_8 = all_10_2
% 198.47/32.62    (101)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.62    (102)   ~ (all_52_5 = all_10_2)
% 198.47/32.62    (103)  op(all_52_29, all_52_29) = all_52_28
% 198.47/32.62    (104)   ~ (all_52_23 = all_14_2)
% 198.47/32.62    (105)  all_56_12 = all_52_7
% 198.47/32.62    (106)  op(all_52_17, all_52_17) = all_52_16
% 198.47/32.62    (107)  all_58_5 = all_4_0
% 198.47/32.62    (108)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.47/32.62    (109)   ~ (all_52_25 = all_6_2)
% 198.47/32.62    (110)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.47/32.62    (111)   ~ (all_52_9 = all_4_2)
% 198.47/32.62    (112)   ~ (all_52_5 = all_6_2)
% 198.47/32.62    (113)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.47/32.62    (114)   ~ (all_52_9 = all_6_2)
% 198.47/32.63    (115)   ~ (all_52_13 = all_52_15)
% 198.47/32.63    (116)  all_56_0 = all_6_2
% 198.47/32.63    (117)  op(e3, e3) = all_6_2
% 198.47/32.63    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.47/32.63    (119)   ~ (all_52_27 = all_14_2)
% 198.47/32.63    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.47/32.63    (121)  all_56_14 = all_52_23
% 198.47/32.63    (122)  op(all_4_2, all_4_2) = all_52_10
% 198.47/32.63    (123)  all_40_0 = all_10_0
% 198.47/32.63    (124)  all_56_3 = all_52_25
% 198.47/32.63    (125)   ~ (all_52_3 = all_52_7)
% 198.47/32.63    (126)  op(all_14_2, all_14_2) = all_52_30
% 198.47/32.63    (127)  all_58_5 = all_52_19
% 198.47/32.63    (128)  all_56_1 = all_52_9
% 198.47/32.63    (129)   ~ (all_52_15 = all_4_2)
% 198.47/32.63    (130)   ~ (all_52_27 = all_4_2)
% 198.47/32.63    (131)  all_58_6 = all_52_5
% 198.47/32.63    (132)  op(all_10_2, e1) = e2
% 198.47/32.63    (133)   ~ (all_4_0 = all_4_2)
% 198.47/32.63    (134)  op(e3, e2) = all_52_9
% 198.47/32.63    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.63    (136)   ~ (all_52_17 = all_6_2)
% 198.47/32.63    (137)   ~ (e1 = e0)
% 198.47/32.63    (138)   ~ (e3 = e2)
% 198.47/32.63    (139)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.47/32.63    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.63    (141)   ~ (all_52_3 = all_4_0)
% 198.47/32.63    (142)  all_46_1 = all_6_1
% 198.47/32.63    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.47/32.63    (144)  op(all_52_13, all_52_13) = all_52_12
% 198.47/32.63    (145)  op(e1, e1) = all_10_2
% 198.47/32.63    (146)   ~ (all_52_23 = all_10_2)
% 198.47/32.63    (147)   ~ (all_52_7 = all_52_23)
% 198.47/32.63    (148)   ~ (all_52_17 = all_52_19)
% 198.47/32.63    (149)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.47/32.63           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.47/32.63    (150)  all_58_3 = all_4_2
% 198.47/32.63    (151)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.47/32.63    (152)  all_56_13 = all_52_15
% 198.47/32.63    (153)   ~ (all_52_3 = all_4_2)
% 198.47/32.63    (154)   ~ (all_52_19 = all_4_2)
% 198.47/32.63    (155)   ~ (all_52_17 = all_52_23)
% 198.47/32.63    (156)  op(all_6_2, e3) = all_6_1
% 198.47/32.63    (157)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.47/32.63    (158)  all_58_4 = all_52_17
% 198.47/32.63    (159)  op(all_52_25, all_52_25) = all_52_24
% 198.47/32.63  
% 198.47/32.63  Begin of proof
% 198.47/32.63  | 
% 198.47/32.63  | BETA: splitting (149) gives:
% 198.47/32.63  | 
% 198.47/32.63  | Case 1:
% 198.47/32.63  | | 
% 198.47/32.63  | |   (160)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.47/32.63  | | 
% 198.47/32.63  | | ALPHA: (160) implies:
% 198.47/32.63  | |   (161)  all_52_22 = e0
% 198.47/32.63  | |   (162)  all_52_20 = e1
% 198.47/32.63  | |   (163)  all_52_16 = e3
% 198.47/32.63  | | 
% 198.47/32.63  | | REDUCE: (106), (163) imply:
% 198.47/32.63  | |   (164)  op(all_52_17, all_52_17) = e3
% 198.47/32.63  | | 
% 198.47/32.63  | | REDUCE: (98), (161) imply:
% 198.47/32.63  | |   (165)  op(all_52_23, all_52_23) = e0
% 198.47/32.63  | | 
% 198.47/32.63  | | REDUCE: (28), (162) imply:
% 198.47/32.63  | |   (166)  op(all_10_2, all_10_2) = e1
% 198.47/32.63  | | 
% 198.47/32.63  | | REF_CLOSE: (1), (3), (6), (9), (11), (13), (15), (17), (20), (21), (22),
% 198.47/32.63  | |            (23), (27), (33), (34), (35), (37), (46), (48), (49), (52), (54),
% 198.47/32.63  | |            (59), (63), (70), (71), (73), (74), (75), (76), (83), (89), (91),
% 198.47/32.63  | |            (93), (96), (100), (101), (104), (105), (107), (109), (113),
% 198.47/32.63  | |            (114), (117), (119), (122), (123), (129), (131), (132), (133),
% 198.47/32.63  | |            (134), (135), (136), (140), (141), (145), (146), (147), (150),
% 198.47/32.63  | |            (153), (156), (157), (158), (164), (165), (166) are inconsistent
% 198.47/32.63  | |            by sub-proof #24.
% 198.47/32.63  | | 
% 198.47/32.63  | Case 2:
% 198.47/32.63  | | 
% 198.47/32.63  | |   (167)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 198.47/32.63  | | 
% 198.47/32.63  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.47/32.63  | |            (13), (14), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 198.47/32.63  | |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (38),
% 198.47/32.63  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 198.47/32.63  | |            (50), (51), (53), (55), (56), (57), (58), (59), (60), (61), (62),
% 198.47/32.63  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 198.47/32.63  | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 198.47/32.63  | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 198.47/32.63  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 198.47/32.63  | |            (108), (109), (110), (111), (112), (114), (115), (116), (117),
% 198.47/32.63  | |            (118), (119), (120), (121), (124), (125), (126), (127), (128),
% 198.47/32.63  | |            (129), (130), (131), (134), (135), (136), (137), (138), (139),
% 198.47/32.63  | |            (142), (143), (144), (145), (146), (147), (148), (150), (151),
% 198.47/32.63  | |            (152), (153), (154), (155), (156), (157), (158), (159), (167) are
% 198.47/32.63  | |            inconsistent by sub-proof #271.
% 198.47/32.63  | | 
% 198.47/32.63  | End of split
% 198.47/32.63  | 
% 198.47/32.63  End of proof
% 198.47/32.63  
% 198.47/32.63  Sub-proof #24 shows that the following formulas are inconsistent:
% 198.47/32.63  ----------------------------------------------------------------
% 198.47/32.63    (1)   ~ (all_52_15 = all_52_23)
% 198.47/32.63    (2)  all_58_14 = all_52_23
% 198.47/32.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.63    (4)   ~ (e3 = e0)
% 198.47/32.63    (5)  op(all_52_23, all_52_23) = e0
% 198.47/32.63    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.47/32.63    (7)  op(all_52_7, all_52_7) = all_52_6
% 198.47/32.63    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.47/32.63    (9)  all_58_0 = all_6_2
% 198.47/32.63    (10)  op(e3, all_6_1) = e1
% 198.47/32.63    (11)   ~ (all_52_17 = all_10_2)
% 198.47/32.63    (12)  all_40_2 = all_10_2
% 198.47/32.63    (13)  op(e3, e0) = all_52_25
% 198.47/32.63    (14)  all_58_13 = all_52_15
% 198.47/32.63    (15)  op(e1, e3) = all_52_5
% 198.47/32.63    (16)  op(e2, e2) = all_4_2
% 198.47/32.63    (17)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.47/32.63    (18)  op(all_4_2, e2) = e1
% 198.47/32.63    (19)   ~ (all_52_7 = all_6_2)
% 198.47/32.63    (20)  all_56_15 = all_14_2
% 198.47/32.63    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.47/32.63    (22)   ~ (all_10_0 = e2)
% 198.47/32.63    (23)   ~ (all_4_0 = e3)
% 198.47/32.63    (24)  op(all_10_2, all_10_2) = e1
% 198.47/32.63    (25)  all_58_10 = all_52_27
% 198.47/32.63    (26)  all_56_9 = all_10_0
% 198.47/32.63    (27)  all_58_12 = all_52_7
% 198.47/32.63    (28)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.47/32.63    (29)   ~ (all_52_7 = all_14_2)
% 198.47/32.63    (30)   ~ (all_14_2 = e0)
% 198.47/32.63    (31)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 198.47/32.63    (32)  all_58_2 = all_52_3
% 198.47/32.63    (33)   ~ (e2 = e0)
% 198.47/32.63    (34)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.47/32.63    (35)  op(e3, e1) = all_52_17
% 198.47/32.63    (36)  op(e0, e3) = all_52_7
% 198.47/32.63    (37)  all_58_15 = all_14_2
% 198.47/32.63    (38)  all_58_8 = all_10_2
% 198.47/32.63    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.63    (40)   ~ (all_52_23 = all_14_2)
% 198.47/32.63    (41)  all_56_12 = all_52_7
% 198.47/32.63    (42)  all_58_5 = all_4_0
% 198.47/32.63    (43)   ~ (all_52_25 = all_6_2)
% 198.47/32.63    (44)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.47/32.63    (45)   ~ (all_52_9 = all_6_2)
% 198.47/32.63    (46)  op(e3, e3) = all_6_2
% 198.47/32.63    (47)   ~ (all_52_27 = all_14_2)
% 198.47/32.63    (48)  op(all_4_2, all_4_2) = all_52_10
% 198.47/32.63    (49)  all_40_0 = all_10_0
% 198.47/32.63    (50)   ~ (all_52_15 = all_4_2)
% 198.47/32.63    (51)  op(all_52_17, all_52_17) = e3
% 198.47/32.63    (52)  all_58_6 = all_52_5
% 198.47/32.63    (53)  op(all_10_2, e1) = e2
% 198.47/32.63    (54)   ~ (all_4_0 = all_4_2)
% 198.47/32.63    (55)  op(e3, e2) = all_52_9
% 198.47/32.63    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.63    (57)   ~ (all_52_17 = all_6_2)
% 198.47/32.63    (58)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.63    (59)   ~ (all_52_3 = all_4_0)
% 198.47/32.63    (60)  op(e1, e1) = all_10_2
% 198.47/32.63    (61)   ~ (all_52_23 = all_10_2)
% 198.47/32.63    (62)   ~ (all_52_7 = all_52_23)
% 198.47/32.63    (63)  all_58_3 = all_4_2
% 198.47/32.63    (64)   ~ (all_52_3 = all_4_2)
% 198.47/32.63    (65)  op(all_6_2, e3) = all_6_1
% 198.47/32.63    (66)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.47/32.63    (67)  all_58_4 = all_52_17
% 198.47/32.63  
% 198.47/32.63  Begin of proof
% 198.47/32.63  | 
% 198.47/32.63  | BETA: splitting (39) gives:
% 198.47/32.63  | 
% 198.47/32.63  | Case 1:
% 198.47/32.63  | | 
% 198.47/32.63  | |   (68)  all_56_15 = e3
% 198.47/32.63  | | 
% 198.47/32.63  | | REF_CLOSE: (2), (3), (8), (12), (16), (18), (20), (21), (22), (23), (24),
% 198.47/32.63  | |            (25), (26), (31), (32), (35), (38), (40), (42), (44), (45), (46),
% 198.47/32.63  | |            (47), (48), (49), (51), (53), (54), (55), (57), (58), (59), (63),
% 198.47/32.63  | |            (64), (67), (68) are inconsistent by sub-proof #180.
% 198.47/32.63  | | 
% 198.47/32.63  | Case 2:
% 198.47/32.63  | | 
% 198.47/32.63  | |   (69)   ~ (all_56_15 = e3)
% 198.47/32.63  | |   (70)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.63  | | 
% 198.47/32.63  | | REDUCE: (20), (69) imply:
% 198.47/32.63  | |   (71)   ~ (all_14_2 = e3)
% 198.47/32.63  | | 
% 198.47/32.63  | | BETA: splitting (56) gives:
% 198.47/32.63  | | 
% 198.47/32.63  | | Case 1:
% 198.47/32.63  | | | 
% 198.47/32.63  | | |   (72)  all_58_12 = e3
% 198.47/32.63  | | | 
% 198.47/32.63  | | | COMBINE_EQS: (27), (72) imply:
% 198.47/32.63  | | |   (73)  all_52_7 = e3
% 198.47/32.63  | | | 
% 198.47/32.63  | | | SIMP: (73) implies:
% 198.47/32.63  | | |   (74)  all_52_7 = e3
% 198.47/32.63  | | | 
% 198.47/32.63  | | | REDUCE: (62), (74) imply:
% 198.47/32.63  | | |   (75)   ~ (all_52_23 = e3)
% 198.47/32.63  | | | 
% 198.47/32.63  | | | SIMP: (75) implies:
% 198.47/32.63  | | |   (76)   ~ (all_52_23 = e3)
% 198.47/32.63  | | | 
% 198.47/32.63  | | | REDUCE: (7), (74) imply:
% 198.47/32.63  | | |   (77)  op(e3, e3) = all_52_6
% 198.47/32.63  | | | 
% 198.47/32.63  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_6, e3, e3, simplifying
% 198.47/32.63  | | |              with (46), (77) gives:
% 198.47/32.63  | | |   (78)  all_52_6 = all_6_2
% 198.47/32.63  | | | 
% 198.47/32.63  | | | BETA: splitting (58) gives:
% 198.47/32.63  | | | 
% 198.47/32.63  | | | Case 1:
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | |   (79)  all_58_4 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | COMBINE_EQS: (67), (79) imply:
% 198.47/32.63  | | | |   (80)  all_52_17 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | SIMP: (80) implies:
% 198.47/32.63  | | | |   (81)  all_52_17 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | REF_CLOSE: (3), (46), (51), (57), (81) are inconsistent by sub-proof
% 198.47/32.63  | | | |            #1280.
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | Case 2:
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | |   (82)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | BETA: splitting (82) gives:
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | Case 1:
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | |   (83)  all_58_5 = e3
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | | REF_CLOSE: (23), (42), (83) are inconsistent by sub-proof #215.
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | Case 2:
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | |   (84)  all_58_8 = e3 | all_58_14 = e3
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | | BETA: splitting (84) gives:
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | | Case 1:
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | |   (85)  all_58_8 = e3
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | COMBINE_EQS: (38), (85) imply:
% 198.47/32.63  | | | | | |   (86)  all_10_2 = e3
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | COMBINE_EQS: (12), (86) imply:
% 198.47/32.63  | | | | | |   (87)  all_40_2 = e3
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | REDUCE: (11), (86) imply:
% 198.47/32.63  | | | | | |   (88)   ~ (all_52_17 = e3)
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | REDUCE: (24), (86) imply:
% 198.47/32.63  | | | | | |   (89)  op(e3, e3) = e1
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | REDUCE: (53), (86) imply:
% 198.47/32.63  | | | | | |   (90)  op(e3, e1) = e2
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | BETA: splitting (31) gives:
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | Case 1:
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | |   (91)   ~ (all_40_2 = e3)
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | | REDUCE: (87), (91) imply:
% 198.47/32.63  | | | | | | |   (92)  $false
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | | CLOSE: (92) is inconsistent.
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | Case 2:
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | |   (93)   ~ (all_40_0 = e0)
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | | REDUCE: (49), (93) imply:
% 198.47/32.63  | | | | | | |   (94)   ~ (all_10_0 = e0)
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | | BETA: splitting (8) gives:
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | | Case 1:
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | |   (95)  all_56_9 = e2
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | | REF_CLOSE: (22), (26), (95) are inconsistent by sub-proof #991.
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | Case 2:
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | |   (96)  all_56_9 = e1 | all_56_9 = e0
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | | BETA: splitting (96) gives:
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | | Case 1:
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | |   (97)  all_56_9 = e1
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | COMBINE_EQS: (26), (97) imply:
% 198.47/32.63  | | | | | | | | |   (98)  all_10_0 = e1
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | SIMP: (98) implies:
% 198.47/32.63  | | | | | | | | |   (99)  all_10_0 = e1
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | REDUCE: (94), (99) imply:
% 198.47/32.63  | | | | | | | | |   (100)   ~ (e1 = e0)
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | GROUND_INST: instantiating (3) with all_52_17, e2, e1, e3,
% 198.47/32.63  | | | | | | | | |              simplifying with (35), (90) gives:
% 198.47/32.63  | | | | | | | | |   (101)  all_52_17 = e2
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, e1, e3, e3,
% 198.47/32.63  | | | | | | | | |              simplifying with (46), (89) gives:
% 198.47/32.63  | | | | | | | | |   (102)  all_6_2 = e1
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | COMBINE_EQS: (9), (102) imply:
% 198.47/32.63  | | | | | | | | |   (103)  all_58_0 = e1
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | REDUCE: (45), (102) imply:
% 198.47/32.63  | | | | | | | | |   (104)   ~ (all_52_9 = e1)
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | REDUCE: (57), (101), (102) imply:
% 198.47/32.63  | | | | | | | | |   (105)   ~ (e2 = e1)
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | REDUCE: (88), (101) imply:
% 198.47/32.63  | | | | | | | | |   (106)   ~ (e3 = e2)
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | SIMP: (106) implies:
% 198.47/32.63  | | | | | | | | |   (107)   ~ (e3 = e2)
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | REF_CLOSE: (3), (4), (10), (13), (15), (17), (32), (33), (34),
% 198.47/32.63  | | | | | | | | |            (43), (52), (55), (65), (66), (72), (100), (102),
% 198.47/32.63  | | | | | | | | |            (103), (104), (105), (107) are inconsistent by
% 198.47/32.63  | | | | | | | | |            sub-proof #306.
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | Case 2:
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | |   (108)  all_56_9 = e0
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | | REF_CLOSE: (26), (94), (108) are inconsistent by sub-proof
% 198.47/32.63  | | | | | | | | |            #989.
% 198.47/32.63  | | | | | | | | | 
% 198.47/32.63  | | | | | | | | End of split
% 198.47/32.63  | | | | | | | | 
% 198.47/32.63  | | | | | | | End of split
% 198.47/32.63  | | | | | | | 
% 198.47/32.63  | | | | | | End of split
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | Case 2:
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | |   (109)  all_58_14 = e3
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | | REF_CLOSE: (2), (76), (109) are inconsistent by sub-proof #1305.
% 198.47/32.63  | | | | | | 
% 198.47/32.63  | | | | | End of split
% 198.47/32.63  | | | | | 
% 198.47/32.63  | | | | End of split
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | End of split
% 198.47/32.63  | | | 
% 198.47/32.63  | | Case 2:
% 198.47/32.63  | | | 
% 198.47/32.63  | | |   (110)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.63  | | | 
% 198.47/32.63  | | | BETA: splitting (110) gives:
% 198.47/32.63  | | | 
% 198.47/32.63  | | | Case 1:
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | |   (111)  all_58_13 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | COMBINE_EQS: (14), (111) imply:
% 198.47/32.63  | | | |   (112)  all_52_15 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | SIMP: (112) implies:
% 198.47/32.63  | | | |   (113)  all_52_15 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | REDUCE: (1), (113) imply:
% 198.47/32.63  | | | |   (114)   ~ (all_52_23 = e3)
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | SIMP: (114) implies:
% 198.47/32.63  | | | |   (115)   ~ (all_52_23 = e3)
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | REDUCE: (50), (113) imply:
% 198.47/32.63  | | | |   (116)   ~ (all_4_2 = e3)
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | SIMP: (116) implies:
% 198.47/32.63  | | | |   (117)   ~ (all_4_2 = e3)
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | REF_CLOSE: (2), (3), (8), (12), (16), (22), (23), (26), (31), (35),
% 198.47/32.63  | | | |            (38), (42), (46), (49), (51), (53), (57), (58), (67), (115),
% 198.47/32.63  | | | |            (117) are inconsistent by sub-proof #181.
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | Case 2:
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | |   (118)  all_58_14 = e3 | all_58_15 = e3
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (19), (20), (28), (29), (30),
% 198.47/32.63  | | | |            (35), (36), (37), (41), (46), (51), (60), (61), (62), (65),
% 198.47/32.63  | | | |            (70), (71), (118) are inconsistent by sub-proof #276.
% 198.47/32.63  | | | | 
% 198.47/32.63  | | | End of split
% 198.47/32.63  | | | 
% 198.47/32.63  | | End of split
% 198.47/32.63  | | 
% 198.47/32.63  | End of split
% 198.47/32.63  | 
% 198.47/32.63  End of proof
% 198.47/32.63  
% 198.47/32.63  Sub-proof #25 shows that the following formulas are inconsistent:
% 198.47/32.63  ----------------------------------------------------------------
% 198.47/32.63    (1)   ~ (all_52_15 = all_52_23)
% 198.47/32.63    (2)  all_58_14 = all_52_23
% 198.47/32.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.63    (4)  all_58_1 = all_52_9
% 198.47/32.63    (5)   ~ (e3 = e0)
% 198.47/32.63    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.47/32.63    (7)   ~ (all_52_7 = all_52_15)
% 198.47/32.63    (8)  op(all_52_7, all_52_7) = all_52_6
% 198.47/32.63    (9)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.47/32.63    (10)  op(e3, all_6_1) = e1
% 198.47/32.63    (11)   ~ (all_10_0 = e3)
% 198.47/32.63    (12)  all_40_2 = all_10_2
% 198.47/32.63    (13)  all_58_13 = all_52_15
% 198.47/32.63    (14)  op(e2, e2) = all_4_2
% 198.47/32.63    (15)  all_58_7 = all_10_0
% 198.47/32.63    (16)  op(all_4_2, e2) = e1
% 198.47/32.63    (17)   ~ (all_52_9 = all_52_15)
% 198.47/32.63    (18)   ~ (all_52_7 = all_6_2)
% 198.47/32.63    (19)  all_56_15 = all_14_2
% 198.47/32.63    (20)   ~ (all_10_0 = e2)
% 198.47/32.63    (21)   ~ (all_4_0 = e3)
% 198.47/32.63    (22)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.47/32.63    (23)  op(all_52_9, all_52_9) = all_52_8
% 198.47/32.63    (24)  op(all_52_15, all_52_15) = all_52_14
% 198.47/32.63    (25)  all_56_9 = all_10_0
% 198.47/32.63    (26)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.47/32.63    (27)  all_58_12 = all_52_7
% 198.47/32.63    (28)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.47/32.63    (29)   ~ (all_52_7 = all_14_2)
% 198.47/32.63    (30)   ~ (all_14_2 = e0)
% 198.47/32.63    (31)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 198.47/32.63    (32)   ~ (all_52_15 = all_14_2)
% 198.47/32.63    (33)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.47/32.63    (34)  op(e3, e1) = all_52_17
% 198.47/32.63    (35)  op(e0, e3) = all_52_7
% 198.47/32.63    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.63    (37)  all_58_15 = all_14_2
% 198.47/32.63    (38)  op(all_52_23, all_52_23) = all_52_22
% 198.47/32.63    (39)   ~ (all_10_0 = all_10_2)
% 198.47/32.63    (40)  all_58_8 = all_10_2
% 198.47/32.63    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.63    (42)   ~ (all_52_23 = all_14_2)
% 198.47/32.63    (43)  all_56_12 = all_52_7
% 198.47/32.63    (44)  all_58_5 = all_4_0
% 198.47/32.63    (45)   ~ (all_52_9 = all_6_2)
% 198.47/32.63    (46)  op(e3, e3) = all_6_2
% 198.47/32.63    (47)  all_56_14 = all_52_23
% 198.47/32.63    (48)  op(all_4_2, all_4_2) = all_52_10
% 198.47/32.63    (49)  all_40_0 = all_10_0
% 198.47/32.63    (50)  op(all_14_2, all_14_2) = all_52_30
% 198.47/32.63    (51)  all_56_1 = all_52_9
% 198.47/32.63    (52)   ~ (all_52_15 = all_4_2)
% 198.47/32.63    (53)  op(e3, e2) = all_52_9
% 198.47/32.63    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.63    (55)   ~ (e3 = e2)
% 198.47/32.63    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.47/32.63    (57)   ~ (all_52_9 = all_52_17)
% 198.47/32.63    (58)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.63    (59)  op(all_10_0, all_10_0) = all_52_12
% 198.47/32.63    (60)  op(e1, e1) = all_10_2
% 198.47/32.63    (61)   ~ (all_52_7 = all_52_23)
% 198.47/32.63    (62)  all_58_3 = all_4_2
% 198.47/32.63    (63)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.47/32.63    (64)  op(all_6_2, e3) = all_6_1
% 198.47/32.63    (65)  all_58_4 = all_52_17
% 198.47/32.63  
% 198.47/32.63  Begin of proof
% 198.47/32.63  | 
% 198.47/32.63  | ALPHA: (22) implies:
% 198.47/32.63  |   (66)  all_52_14 = e0
% 198.47/32.63  |   (67)  all_52_12 = e1
% 198.47/32.63  |   (68)  all_52_10 = e2
% 198.47/32.63  |   (69)  all_52_8 = e3
% 198.47/32.63  | 
% 198.47/32.63  | REDUCE: (23), (69) imply:
% 198.47/32.63  |   (70)  op(all_52_9, all_52_9) = e3
% 198.47/32.63  | 
% 198.47/32.63  | REDUCE: (24), (66) imply:
% 198.47/32.63  |   (71)  op(all_52_15, all_52_15) = e0
% 198.47/32.63  | 
% 198.47/32.63  | REDUCE: (59), (67) imply:
% 198.47/32.63  |   (72)  op(all_10_0, all_10_0) = e1
% 198.47/32.63  | 
% 198.47/32.63  | REDUCE: (48), (68) imply:
% 198.47/32.63  |   (73)  op(all_4_2, all_4_2) = e2
% 198.47/32.63  | 
% 198.47/32.64  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.47/32.64  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (25), (26),
% 198.47/32.64  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 198.47/32.64  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 198.47/32.64  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (60), (61),
% 198.47/32.64  |            (62), (63), (64), (65), (70), (71), (72), (73) are inconsistent by
% 198.47/32.64  |            sub-proof #26.
% 198.47/32.64  | 
% 198.47/32.64  End of proof
% 198.47/32.64  
% 198.47/32.64  Sub-proof #26 shows that the following formulas are inconsistent:
% 198.47/32.64  ----------------------------------------------------------------
% 198.47/32.64    (1)   ~ (all_52_15 = all_52_23)
% 198.47/32.64    (2)  all_58_14 = all_52_23
% 198.47/32.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.64    (4)  all_58_1 = all_52_9
% 198.47/32.64    (5)   ~ (e3 = e0)
% 198.47/32.64    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.47/32.64    (7)   ~ (all_52_7 = all_52_15)
% 198.47/32.64    (8)  op(all_52_15, all_52_15) = e0
% 198.47/32.64    (9)  op(all_52_7, all_52_7) = all_52_6
% 198.47/32.64    (10)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.47/32.64    (11)  op(e3, all_6_1) = e1
% 198.47/32.64    (12)   ~ (all_10_0 = e3)
% 198.47/32.64    (13)  all_40_2 = all_10_2
% 198.47/32.64    (14)  all_58_13 = all_52_15
% 198.47/32.64    (15)  op(all_10_0, all_10_0) = e1
% 198.47/32.64    (16)  op(e2, e2) = all_4_2
% 198.47/32.64    (17)  all_58_7 = all_10_0
% 198.47/32.64    (18)  op(all_4_2, e2) = e1
% 198.47/32.64    (19)   ~ (all_52_9 = all_52_15)
% 198.47/32.64    (20)   ~ (all_52_7 = all_6_2)
% 198.47/32.64    (21)  all_56_15 = all_14_2
% 198.47/32.64    (22)   ~ (all_10_0 = e2)
% 198.47/32.64    (23)   ~ (all_4_0 = e3)
% 198.47/32.64    (24)  all_56_9 = all_10_0
% 198.47/32.64    (25)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.47/32.64    (26)  all_58_12 = all_52_7
% 198.47/32.64    (27)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.47/32.64    (28)   ~ (all_52_7 = all_14_2)
% 198.47/32.64    (29)   ~ (all_14_2 = e0)
% 198.47/32.64    (30)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 198.47/32.64    (31)   ~ (all_52_15 = all_14_2)
% 198.47/32.64    (32)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.47/32.64    (33)  op(e3, e1) = all_52_17
% 198.47/32.64    (34)  op(e0, e3) = all_52_7
% 198.47/32.64    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.64    (36)  all_58_15 = all_14_2
% 198.47/32.64    (37)  op(all_52_23, all_52_23) = all_52_22
% 198.47/32.64    (38)   ~ (all_10_0 = all_10_2)
% 198.47/32.64    (39)  all_58_8 = all_10_2
% 198.47/32.64    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.64    (41)   ~ (all_52_23 = all_14_2)
% 198.47/32.64    (42)  all_56_12 = all_52_7
% 198.47/32.64    (43)  all_58_5 = all_4_0
% 198.47/32.64    (44)  op(all_4_2, all_4_2) = e2
% 198.47/32.64    (45)   ~ (all_52_9 = all_6_2)
% 198.47/32.64    (46)  op(e3, e3) = all_6_2
% 198.47/32.64    (47)  all_56_14 = all_52_23
% 198.47/32.64    (48)  all_40_0 = all_10_0
% 198.47/32.64    (49)  op(all_14_2, all_14_2) = all_52_30
% 198.47/32.64    (50)  all_56_1 = all_52_9
% 198.47/32.64    (51)   ~ (all_52_15 = all_4_2)
% 198.47/32.64    (52)  op(e3, e2) = all_52_9
% 198.47/32.64    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.64    (54)   ~ (e3 = e2)
% 198.47/32.64    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.47/32.64    (56)   ~ (all_52_9 = all_52_17)
% 198.47/32.64    (57)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.64    (58)  op(e1, e1) = all_10_2
% 198.47/32.64    (59)  op(all_52_9, all_52_9) = e3
% 198.47/32.64    (60)   ~ (all_52_7 = all_52_23)
% 198.47/32.64    (61)  all_58_3 = all_4_2
% 198.47/32.64    (62)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.47/32.64    (63)  op(all_6_2, e3) = all_6_1
% 198.47/32.64    (64)  all_58_4 = all_52_17
% 198.47/32.64  
% 198.47/32.64  Begin of proof
% 198.47/32.64  | 
% 198.47/32.64  | BETA: splitting (40) gives:
% 198.47/32.64  | 
% 198.47/32.64  | Case 1:
% 198.47/32.64  | | 
% 198.47/32.64  | |   (65)  all_56_15 = e3
% 198.47/32.64  | | 
% 198.47/32.64  | | COMBINE_EQS: (21), (65) imply:
% 198.47/32.64  | |   (66)  all_14_2 = e3
% 198.47/32.64  | | 
% 198.47/32.64  | | SIMP: (66) implies:
% 198.47/32.64  | |   (67)  all_14_2 = e3
% 198.47/32.64  | | 
% 198.47/32.64  | | REDUCE: (31), (67) imply:
% 198.47/32.64  | |   (68)   ~ (all_52_15 = e3)
% 198.47/32.64  | | 
% 198.47/32.64  | | REF_CLOSE: (3), (4), (5), (8), (12), (14), (16), (17), (18), (22), (35),
% 198.47/32.64  | |            (44), (45), (46), (52), (54), (59), (61), (62), (68) are
% 198.47/32.64  | |            inconsistent by sub-proof #28.
% 198.47/32.64  | | 
% 198.47/32.64  | Case 2:
% 198.47/32.64  | | 
% 198.47/32.64  | |   (69)   ~ (all_56_15 = e3)
% 198.47/32.64  | |   (70)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.47/32.64  | | 
% 198.47/32.64  | | REDUCE: (21), (69) imply:
% 198.47/32.64  | |   (71)   ~ (all_14_2 = e3)
% 198.47/32.64  | | 
% 198.47/32.64  | | BETA: splitting (25) gives:
% 198.47/32.64  | | 
% 198.47/32.64  | | Case 1:
% 198.47/32.64  | | | 
% 198.47/32.64  | | |   (72)  all_56_14 = e3
% 198.47/32.64  | | | 
% 198.47/32.64  | | | COMBINE_EQS: (47), (72) imply:
% 198.47/32.64  | | |   (73)  all_52_23 = e3
% 198.47/32.64  | | | 
% 198.47/32.64  | | | REDUCE: (1), (73) imply:
% 198.47/32.64  | | |   (74)   ~ (all_52_15 = e3)
% 198.47/32.64  | | | 
% 198.47/32.64  | | | REDUCE: (37), (73) imply:
% 198.47/32.64  | | |   (75)  op(e3, e3) = all_52_22
% 198.47/32.64  | | | 
% 198.47/32.64  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_22, e3, e3,
% 198.47/32.64  | | |              simplifying with (46), (75) gives:
% 198.47/32.64  | | |   (76)  all_52_22 = all_6_2
% 198.47/32.64  | | | 
% 198.47/32.64  | | | REF_CLOSE: (3), (4), (5), (8), (12), (14), (16), (17), (18), (22), (35),
% 198.47/32.64  | | |            (44), (45), (46), (52), (54), (59), (61), (62), (74) are
% 198.47/32.64  | | |            inconsistent by sub-proof #28.
% 198.47/32.64  | | | 
% 198.47/32.64  | | Case 2:
% 198.47/32.64  | | | 
% 198.47/32.64  | | |   (77)   ~ (all_56_14 = e3)
% 198.47/32.64  | | | 
% 198.47/32.64  | | | REDUCE: (47), (77) imply:
% 198.47/32.64  | | |   (78)   ~ (all_52_23 = e3)
% 198.47/32.64  | | | 
% 198.47/32.64  | | | BETA: splitting (53) gives:
% 198.47/32.64  | | | 
% 198.47/32.64  | | | Case 1:
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | |   (79)  all_58_12 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | COMBINE_EQS: (26), (79) imply:
% 198.47/32.64  | | | |   (80)  all_52_7 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | SIMP: (80) implies:
% 198.47/32.64  | | | |   (81)  all_52_7 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | REDUCE: (7), (81) imply:
% 198.47/32.64  | | | |   (82)   ~ (all_52_15 = e3)
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | SIMP: (82) implies:
% 198.47/32.64  | | | |   (83)   ~ (all_52_15 = e3)
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | REDUCE: (60), (81) imply:
% 198.47/32.64  | | | |   (84)   ~ (all_52_23 = e3)
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | REDUCE: (9), (81) imply:
% 198.47/32.64  | | | |   (85)  op(e3, e3) = all_52_6
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_6, e3, e3,
% 198.47/32.64  | | | |              simplifying with (46), (85) gives:
% 198.47/32.64  | | | |   (86)  all_52_6 = all_6_2
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | BETA: splitting (57) gives:
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | Case 1:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | |   (87)  all_58_4 = e3
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | COMBINE_EQS: (64), (87) imply:
% 198.47/32.64  | | | | |   (88)  all_52_17 = e3
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | SIMP: (88) implies:
% 198.47/32.64  | | | | |   (89)  all_52_17 = e3
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | REDUCE: (56), (89) imply:
% 198.47/32.64  | | | | |   (90)   ~ (all_52_9 = e3)
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | BETA: splitting (35) gives:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | Case 1:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | |   (91)  all_58_1 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | COMBINE_EQS: (4), (91) imply:
% 198.47/32.64  | | | | | |   (92)  all_52_9 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REDUCE: (90), (92) imply:
% 198.47/32.64  | | | | | |   (93)  $false
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | CLOSE: (93) is inconsistent.
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | Case 2:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | |   (94)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REF_CLOSE: (3), (4), (5), (8), (12), (14), (16), (17), (18), (22),
% 198.47/32.64  | | | | | |            (44), (45), (46), (52), (54), (61), (62), (83), (94) are
% 198.47/32.64  | | | | | |            inconsistent by sub-proof #29.
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | End of split
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | Case 2:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | |   (95)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | BETA: splitting (95) gives:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | Case 1:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | |   (96)  all_58_5 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REF_CLOSE: (23), (43), (96) are inconsistent by sub-proof #215.
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | Case 2:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | |   (97)  all_58_8 = e3 | all_58_14 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | BETA: splitting (97) gives:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | Case 1:
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | |   (98)  all_58_8 = e3
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | | REF_CLOSE: (3), (10), (13), (15), (22), (24), (30), (38), (39),
% 198.47/32.64  | | | | | | |            (48), (58), (98) are inconsistent by sub-proof #78.
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | Case 2:
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | |   (99)  all_58_14 = e3
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | | REF_CLOSE: (2), (78), (99) are inconsistent by sub-proof #1305.
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | End of split
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | End of split
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | End of split
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | Case 2:
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | |   (100)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (11), (14), (16), (19), (20),
% 198.47/32.64  | | | |            (21), (26), (27), (28), (32), (33), (34), (36), (41), (42),
% 198.47/32.64  | | | |            (45), (46), (49), (50), (51), (55), (56), (59), (60), (63),
% 198.47/32.64  | | | |            (70), (71), (78), (100) are inconsistent by sub-proof #34.
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | End of split
% 198.47/32.64  | | | 
% 198.47/32.64  | | End of split
% 198.47/32.64  | | 
% 198.47/32.64  | End of split
% 198.47/32.64  | 
% 198.47/32.64  End of proof
% 198.47/32.64  
% 198.47/32.64  Sub-proof #27 shows that the following formulas are inconsistent:
% 198.47/32.64  ----------------------------------------------------------------
% 198.47/32.64    (1)   ~ (all_52_25 = all_52_27)
% 198.47/32.64    (2)  all_58_14 = all_52_23
% 198.47/32.64    (3)   ~ (e3 = e1)
% 198.47/32.64    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.64    (5)  all_58_1 = all_52_9
% 198.47/32.64    (6)   ~ (e3 = e0)
% 198.47/32.64    (7)  op(e2, e3) = all_52_3
% 198.47/32.64    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.47/32.64    (9)   ~ (all_52_7 = all_52_15)
% 198.47/32.64    (10)  op(all_52_7, all_52_7) = all_52_6
% 198.47/32.64    (11)   ~ (all_52_3 = all_6_2)
% 198.47/32.64    (12)  all_58_0 = all_6_2
% 198.47/32.64    (13)  all_56_4 = all_52_3
% 198.47/32.64    (14)  op(e3, all_6_1) = e1
% 198.47/32.64    (15)   ~ (all_52_17 = all_10_2)
% 198.47/32.64    (16)  op(e3, e0) = all_52_25
% 198.47/32.64    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.47/32.64    (18)  all_58_13 = all_52_15
% 198.47/32.64    (19)  op(all_10_2, all_10_2) = all_52_20
% 198.47/32.64    (20)  all_58_9 = all_52_25
% 198.47/32.64    (21)  op(all_52_27, all_52_27) = all_52_26
% 198.47/32.64    (22)  op(e1, e3) = all_52_5
% 198.47/32.64    (23)  op(e2, e2) = all_4_2
% 198.47/32.64    (24)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.47/32.64    (25)  all_58_11 = all_52_29
% 198.47/32.64    (26)   ~ (all_52_9 = all_52_15)
% 198.47/32.64    (27)   ~ (all_52_3 = all_52_27)
% 198.47/32.64    (28)  all_46_2 = all_6_2
% 198.47/32.64    (29)  op(all_6_2, all_6_2) = all_52_0
% 198.47/32.64    (30)   ~ (all_52_7 = all_6_2)
% 198.47/32.64    (31)   ~ (all_52_15 = e0)
% 198.47/32.64    (32)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.47/32.64    (33)  all_58_15 = e0
% 198.47/32.64    (34)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.47/32.64    (35)   ~ (all_4_0 = e3)
% 198.47/32.64    (36)   ~ (all_52_25 = e0)
% 198.47/32.64    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.47/32.64    (38)   ~ (e2 = e1)
% 198.47/32.64    (39)  op(e0, e0) = e0
% 198.47/32.64    (40)  all_58_10 = all_52_27
% 198.47/32.64    (41)   ~ (all_52_25 = all_52_29)
% 198.47/32.64    (42)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.47/32.64    (43)  all_58_12 = all_52_7
% 198.47/32.64    (44)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.47/32.64    (45)  all_58_2 = all_52_3
% 198.47/32.64    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.47/32.64    (47)  all_56_7 = all_52_27
% 198.47/32.64    (48)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.47/32.64    (49)   ~ (e2 = e0)
% 198.47/32.64    (50)   ~ (all_52_5 = all_52_29)
% 198.47/32.64    (51)   ~ (all_52_29 = e0)
% 198.47/32.64    (52)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 198.47/32.64    (53)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.47/32.64    (54)  op(e3, e1) = all_52_17
% 198.47/32.64    (55)  op(e0, e3) = all_52_7
% 198.47/32.64    (56)  op(all_52_23, all_52_23) = all_52_22
% 198.47/32.64    (57)  all_58_8 = all_10_2
% 198.47/32.64    (58)   ~ (all_52_23 = e0)
% 198.47/32.64    (59)  op(all_52_29, all_52_29) = all_52_28
% 198.47/32.64    (60)  all_56_12 = all_52_7
% 198.47/32.64    (61)  op(all_52_17, all_52_17) = all_52_16
% 198.47/32.64    (62)  all_58_5 = all_4_0
% 198.47/32.64    (63)   ~ (all_52_25 = all_6_2)
% 198.47/32.64    (64)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.47/32.64    (65)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 198.47/32.64    (66)   ~ (all_52_9 = all_6_2)
% 198.47/32.64    (67)  op(e3, e3) = all_6_2
% 198.47/32.64    (68)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.47/32.64    (69)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.47/32.64    (70)  all_56_14 = all_52_23
% 198.47/32.64    (71)  all_56_3 = all_52_25
% 198.47/32.64    (72)   ~ (all_52_15 = all_4_2)
% 198.47/32.64    (73)  all_58_6 = all_52_5
% 198.47/32.64    (74)  op(e3, e2) = all_52_9
% 198.47/32.64    (75)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.47/32.64    (76)   ~ (all_52_17 = all_6_2)
% 198.47/32.64    (77)   ~ (e1 = e0)
% 198.47/32.64    (78)   ~ (e3 = e2)
% 198.47/32.64    (79)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.64    (80)  all_46_1 = all_6_1
% 198.47/32.64    (81)  op(e1, e1) = all_10_2
% 198.47/32.64    (82)   ~ (all_52_23 = all_10_2)
% 198.47/32.64    (83)   ~ (all_52_7 = all_52_23)
% 198.47/32.64    (84)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.47/32.64          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.47/32.64    (85)  all_56_13 = all_52_15
% 198.47/32.64    (86)   ~ (all_52_3 = all_4_2)
% 198.47/32.64    (87)  op(all_6_2, e3) = all_6_1
% 198.47/32.64    (88)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.47/32.64    (89)  all_58_4 = all_52_17
% 198.47/32.64    (90)   ~ (all_52_7 = e0)
% 198.47/32.64    (91)  op(all_52_25, all_52_25) = all_52_24
% 198.47/32.64  
% 198.47/32.64  Begin of proof
% 198.47/32.64  | 
% 198.47/32.64  | BETA: splitting (84) gives:
% 198.47/32.64  | 
% 198.47/32.64  | Case 1:
% 198.47/32.64  | | 
% 198.47/32.64  | |   (92)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.47/32.64  | | 
% 198.47/32.64  | | ALPHA: (92) implies:
% 198.47/32.64  | |   (93)  all_52_22 = e0
% 198.47/32.64  | |   (94)  all_52_20 = e1
% 198.47/32.64  | |   (95)  all_52_16 = e3
% 198.47/32.64  | | 
% 198.47/32.64  | | REDUCE: (61), (95) imply:
% 198.47/32.64  | |   (96)  op(all_52_17, all_52_17) = e3
% 198.47/32.64  | | 
% 198.47/32.64  | | REDUCE: (56), (93) imply:
% 198.47/32.64  | |   (97)  op(all_52_23, all_52_23) = e0
% 198.47/32.64  | | 
% 198.47/32.64  | | REDUCE: (19), (94) imply:
% 198.47/32.64  | |   (98)  op(all_10_2, all_10_2) = e1
% 198.47/32.64  | | 
% 198.47/32.64  | | BETA: splitting (42) gives:
% 198.47/32.64  | | 
% 198.47/32.64  | | Case 1:
% 198.47/32.64  | | | 
% 198.47/32.64  | | |   (99)  all_56_14 = e3
% 198.47/32.64  | | | 
% 198.47/32.64  | | | COMBINE_EQS: (70), (99) imply:
% 198.47/32.64  | | |   (100)  all_52_23 = e3
% 198.47/32.64  | | | 
% 198.47/32.64  | | | REF_CLOSE: (4), (8), (10), (14), (30), (44), (54), (55), (60), (67), (81),
% 198.47/32.64  | | |            (82), (83), (87), (96), (97), (100) are inconsistent by
% 198.47/32.64  | | |            sub-proof #37.
% 198.47/32.64  | | | 
% 198.47/32.64  | | Case 2:
% 198.47/32.64  | | | 
% 198.47/32.64  | | |   (101)   ~ (all_56_14 = e3)
% 198.47/32.64  | | |   (102)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.47/32.64  | | | 
% 198.47/32.64  | | | REDUCE: (70), (101) imply:
% 198.47/32.64  | | |   (103)   ~ (all_52_23 = e3)
% 198.47/32.64  | | | 
% 198.47/32.64  | | | BETA: splitting (79) gives:
% 198.47/32.64  | | | 
% 198.47/32.64  | | | Case 1:
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | |   (104)  all_58_4 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | COMBINE_EQS: (89), (104) imply:
% 198.47/32.64  | | | |   (105)  all_52_17 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | SIMP: (105) implies:
% 198.47/32.64  | | | |   (106)  all_52_17 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | REF_CLOSE: (4), (67), (76), (96), (106) are inconsistent by sub-proof
% 198.47/32.64  | | | |            #1280.
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | Case 2:
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | |   (107)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | BETA: splitting (107) gives:
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | | Case 1:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | |   (108)  all_58_5 = e3
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | REF_CLOSE: (35), (62), (108) are inconsistent by sub-proof #215.
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | Case 2:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | |   (109)  all_58_8 = e3 | all_58_14 = e3
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | BETA: splitting (109) gives:
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | | Case 1:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | |   (110)  all_58_8 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | COMBINE_EQS: (57), (110) imply:
% 198.47/32.64  | | | | | |   (111)  all_10_2 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REDUCE: (98), (111) imply:
% 198.47/32.64  | | | | | |   (112)  op(e3, e3) = e1
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | GROUND_INST: instantiating (4) with all_6_2, e1, e3, e3, simplifying
% 198.47/32.64  | | | | | |              with (67), (112) gives:
% 198.47/32.64  | | | | | |   (113)  all_6_2 = e1
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | COMBINE_EQS: (12), (113) imply:
% 198.47/32.64  | | | | | |   (114)  all_58_0 = e1
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REDUCE: (30), (113) imply:
% 198.47/32.64  | | | | | |   (115)   ~ (all_52_7 = e1)
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REDUCE: (66), (113) imply:
% 198.47/32.64  | | | | | |   (116)   ~ (all_52_9 = e1)
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REDUCE: (63), (113) imply:
% 198.47/32.64  | | | | | |   (117)   ~ (all_52_25 = e1)
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REDUCE: (87), (113) imply:
% 198.47/32.64  | | | | | |   (118)  op(e1, e3) = all_6_1
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | GROUND_INST: instantiating (4) with all_52_5, all_6_1, e3, e1,
% 198.47/32.64  | | | | | |              simplifying with (22), (118) gives:
% 198.47/32.64  | | | | | |   (119)  all_52_5 = all_6_1
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | BETA: splitting (8) gives:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | Case 1:
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | |   (120)  all_56_12 = e3
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | | COMBINE_EQS: (60), (120) imply:
% 198.47/32.64  | | | | | | |   (121)  all_52_7 = e3
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | | COMBINE_EQS: (43), (121) imply:
% 198.47/32.64  | | | | | | |   (122)  all_58_12 = e3
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | | REF_CLOSE: (4), (6), (14), (16), (22), (24), (38), (45), (49),
% 198.47/32.64  | | | | | | |            (53), (73), (74), (77), (78), (88), (114), (116),
% 198.47/32.64  | | | | | | |            (117), (118), (122) are inconsistent by sub-proof #307.
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | Case 2:
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | |   (123)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | | REF_CLOSE: (4), (39), (58), (60), (70), (81), (82), (83), (90),
% 198.47/32.64  | | | | | | |            (97), (98), (102), (115), (123) are inconsistent by
% 198.47/32.64  | | | | | | |            sub-proof #1283.
% 198.47/32.64  | | | | | | | 
% 198.47/32.64  | | | | | | End of split
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | Case 2:
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | |   (124)  all_58_14 = e3
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | | REF_CLOSE: (2), (103), (124) are inconsistent by sub-proof #1305.
% 198.47/32.64  | | | | | | 
% 198.47/32.64  | | | | | End of split
% 198.47/32.64  | | | | | 
% 198.47/32.64  | | | | End of split
% 198.47/32.64  | | | | 
% 198.47/32.64  | | | End of split
% 198.47/32.64  | | | 
% 198.47/32.64  | | End of split
% 198.47/32.64  | | 
% 198.47/32.64  | Case 2:
% 198.47/32.64  | | 
% 198.47/32.64  | |   (125)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 198.47/32.64  | | 
% 198.47/32.64  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.47/32.64  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 198.47/32.64  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 198.47/32.64  | |            (37), (38), (40), (41), (43), (45), (46), (47), (48), (49), (50),
% 198.47/32.64  | |            (51), (52), (53), (56), (58), (59), (60), (63), (64), (65), (66),
% 198.47/32.64  | |            (67), (68), (69), (71), (72), (73), (74), (75), (77), (78), (80),
% 198.47/32.64  | |            (81), (82), (83), (85), (86), (87), (88), (89), (90), (91), (125)
% 198.47/32.64  | |            are inconsistent by sub-proof #304.
% 198.47/32.64  | | 
% 198.47/32.64  | End of split
% 198.47/32.64  | 
% 198.47/32.64  End of proof
% 198.47/32.64  
% 198.47/32.64  Sub-proof #28 shows that the following formulas are inconsistent:
% 198.47/32.64  ----------------------------------------------------------------
% 198.47/32.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.64    (2)  all_58_1 = all_52_9
% 198.47/32.65    (3)   ~ (e3 = e0)
% 198.47/32.65    (4)  op(all_52_15, all_52_15) = e0
% 198.47/32.65    (5)   ~ (all_10_0 = e3)
% 198.47/32.65    (6)  all_58_13 = all_52_15
% 198.47/32.65    (7)   ~ (all_52_15 = e3)
% 198.47/32.65    (8)  op(e2, e2) = all_4_2
% 198.47/32.65    (9)  all_58_7 = all_10_0
% 198.47/32.65    (10)  op(all_4_2, e2) = e1
% 198.47/32.65    (11)   ~ (all_10_0 = e2)
% 198.47/32.65    (12)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.65    (13)  op(all_4_2, all_4_2) = e2
% 198.47/32.65    (14)   ~ (all_52_9 = all_6_2)
% 198.47/32.65    (15)  op(e3, e3) = all_6_2
% 198.47/32.65    (16)  op(e3, e2) = all_52_9
% 198.47/32.65    (17)   ~ (e3 = e2)
% 198.47/32.65    (18)  op(all_52_9, all_52_9) = e3
% 198.47/32.65    (19)  all_58_3 = all_4_2
% 198.47/32.65    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.47/32.65  
% 198.47/32.65  Begin of proof
% 198.47/32.65  | 
% 198.47/32.65  | BETA: splitting (12) gives:
% 198.47/32.65  | 
% 198.47/32.65  | Case 1:
% 198.47/32.65  | | 
% 198.47/32.65  | |   (21)  all_58_1 = e3
% 198.47/32.65  | | 
% 198.47/32.65  | | COMBINE_EQS: (2), (21) imply:
% 198.47/32.65  | |   (22)  all_52_9 = e3
% 198.47/32.65  | | 
% 198.47/32.65  | | REF_CLOSE: (1), (14), (15), (18), (22) are inconsistent by sub-proof #1337.
% 198.47/32.65  | | 
% 198.47/32.65  | Case 2:
% 198.47/32.65  | | 
% 198.47/32.65  | |   (23)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.47/32.65  | | 
% 198.47/32.65  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 198.47/32.65  | |            (14), (15), (16), (17), (19), (20), (23) are inconsistent by
% 198.47/32.65  | |            sub-proof #29.
% 198.47/32.65  | | 
% 198.47/32.65  | End of split
% 198.47/32.65  | 
% 198.47/32.65  End of proof
% 198.47/32.65  
% 198.47/32.65  Sub-proof #29 shows that the following formulas are inconsistent:
% 198.47/32.65  ----------------------------------------------------------------
% 198.47/32.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.47/32.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.47/32.65    (2)  all_58_1 = all_52_9
% 198.47/32.65    (3)   ~ (e3 = e0)
% 198.47/32.65    (4)  op(all_52_15, all_52_15) = e0
% 198.47/32.65    (5)   ~ (all_10_0 = e3)
% 198.47/32.65    (6)  all_58_13 = all_52_15
% 198.47/32.65    (7)   ~ (all_52_15 = e3)
% 198.47/32.65    (8)  op(e2, e2) = all_4_2
% 198.47/32.65    (9)  all_58_7 = all_10_0
% 198.47/32.65    (10)  op(all_4_2, e2) = e1
% 198.47/32.65    (11)   ~ (all_10_0 = e2)
% 198.47/32.65    (12)  op(all_4_2, all_4_2) = e2
% 198.75/32.65    (13)   ~ (all_52_9 = all_6_2)
% 198.75/32.65    (14)  op(e3, e3) = all_6_2
% 198.75/32.65    (15)  op(e3, e2) = all_52_9
% 198.75/32.65    (16)   ~ (e3 = e2)
% 198.75/32.65    (17)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.75/32.65    (18)  all_58_3 = all_4_2
% 198.75/32.65    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.75/32.65  
% 198.75/32.65  Begin of proof
% 198.75/32.65  | 
% 198.75/32.65  | BETA: splitting (17) gives:
% 198.75/32.65  | 
% 198.75/32.65  | Case 1:
% 198.75/32.65  | | 
% 198.75/32.65  | |   (20)  all_58_3 = e3
% 198.75/32.65  | | 
% 198.75/32.65  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 198.75/32.65  | |            (15), (16), (18), (19), (20) are inconsistent by sub-proof #183.
% 198.75/32.65  | | 
% 198.75/32.65  | Case 2:
% 198.75/32.65  | | 
% 198.75/32.65  | |   (21)  all_58_7 = e3 | all_58_13 = e3
% 198.75/32.65  | | 
% 198.75/32.65  | | REF_CLOSE: (5), (6), (7), (9), (21) are inconsistent by sub-proof #717.
% 198.75/32.65  | | 
% 198.75/32.65  | End of split
% 198.75/32.65  | 
% 198.75/32.65  End of proof
% 198.75/32.65  
% 198.75/32.65  Sub-proof #30 shows that the following formulas are inconsistent:
% 198.75/32.65  ----------------------------------------------------------------
% 198.75/32.65    (1)   ~ (all_52_15 = all_52_23)
% 198.75/32.65    (2)   ~ (all_52_25 = all_52_27)
% 198.75/32.65    (3)  all_58_14 = all_52_23
% 198.75/32.65    (4)   ~ (e3 = e1)
% 198.75/32.65    (5)   ~ (all_52_17 = all_4_0)
% 198.75/32.65    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.75/32.65    (7)  op(all_52_3, all_52_3) = all_52_2
% 198.75/32.65    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.75/32.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.75/32.65    (9)   ~ (all_52_5 = all_52_13)
% 198.75/32.65    (10)  all_58_1 = all_52_9
% 198.75/32.65    (11)   ~ (all_52_9 = all_52_13)
% 198.75/32.65    (12)   ~ (e3 = e0)
% 198.75/32.65    (13)  op(e2, e3) = all_52_3
% 198.75/32.65    (14)   ~ (all_52_23 = all_4_0)
% 198.75/32.65    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.75/32.65    (16)   ~ (all_52_7 = all_52_15)
% 198.75/32.65    (17)  op(all_52_7, all_52_7) = all_52_6
% 198.75/32.65    (18)   ~ (all_52_17 = all_52_25)
% 198.75/32.65    (19)   ~ (all_52_3 = all_6_2)
% 198.75/32.65    (20)  all_58_0 = all_6_2
% 198.75/32.65    (21)  op(all_14_2, e0) = all_14_1
% 198.75/32.65    (22)  all_56_4 = all_52_3
% 198.75/32.65    (23)  op(e3, all_6_1) = e1
% 198.75/32.65    (24)   ~ (all_52_17 = all_10_2)
% 198.75/32.65    (25)  op(e3, e0) = all_52_25
% 198.75/32.65    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.75/32.65    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.75/32.65    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.75/32.65    (29)   ~ (all_52_27 = all_52_29)
% 198.75/32.65    (30)  all_58_13 = all_52_15
% 198.75/32.65    (31)  op(all_10_2, all_10_2) = all_52_20
% 198.75/32.65    (32)  all_58_9 = all_52_25
% 198.75/32.65    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.75/32.65    (34)   ~ (all_52_29 = all_14_2)
% 198.75/32.65    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.75/32.65    (36)  op(all_52_27, all_52_27) = all_52_26
% 198.75/32.65    (37)  op(e1, e3) = all_52_5
% 198.75/32.65    (38)  op(e2, e2) = all_4_2
% 198.75/32.65    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.75/32.65    (40)   ~ (all_52_3 = all_52_5)
% 198.75/32.65    (41)  op(all_4_2, e2) = e1
% 198.75/32.65    (42)  all_58_11 = all_52_29
% 198.75/32.65    (43)  all_56_5 = all_4_2
% 198.75/32.65    (44)   ~ (all_52_25 = all_14_2)
% 198.75/32.65    (45)   ~ (all_52_9 = all_52_15)
% 198.75/32.65    (46)   ~ (all_52_3 = all_52_27)
% 198.75/32.65    (47)  op(all_10_2, e1) = all_10_1
% 198.75/32.65    (48)  all_46_2 = all_6_2
% 198.75/32.65    (49)  op(all_6_2, all_6_2) = all_52_0
% 198.75/32.65    (50)   ~ (all_52_7 = all_6_2)
% 198.75/32.65    (51)  op(e0, e0) = all_14_2
% 198.75/32.65    (52)  all_56_15 = all_14_2
% 198.75/32.65    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.75/32.65    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.75/32.65    (55)   ~ (all_58_15 = e0)
% 198.75/32.65    (56)  all_56_11 = all_52_29
% 198.75/32.65    (57)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.75/32.65    (58)   ~ (all_4_0 = e3)
% 198.75/32.65    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.75/32.65    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.75/32.65    (61)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.75/32.65    (62)  all_56_9 = all_52_13
% 198.75/32.65    (63)   ~ (e2 = e1)
% 198.75/32.65    (64)  all_58_10 = all_52_27
% 198.75/32.65    (65)  all_56_8 = all_52_5
% 198.75/32.65    (66)  op(all_52_9, all_52_9) = all_52_8
% 198.75/32.65    (67)  op(all_52_15, all_52_15) = all_52_14
% 198.75/32.65    (68)   ~ (all_52_25 = all_52_29)
% 198.75/32.65    (69)   ~ (all_52_29 = all_10_2)
% 198.75/32.65    (70)  all_58_7 = all_52_13
% 198.75/32.65    (71)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.75/32.65    (72)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.75/32.65    (73)   ~ (all_52_5 = all_52_7)
% 198.75/32.65    (74)  all_58_12 = all_52_7
% 198.75/32.65    (75)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.75/32.65    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.75/32.65    (77)   ~ (all_52_7 = all_14_2)
% 198.75/32.65    (78)  all_58_2 = all_52_3
% 198.75/32.65    (79)  all_56_2 = all_52_17
% 198.75/32.65    (80)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.75/32.65    (81)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.75/32.65    (82)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.75/32.65    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.75/32.65    (84)  all_56_7 = all_52_27
% 198.75/32.65    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.75/32.65    (86)   ~ (e2 = e0)
% 198.75/32.65    (87)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.75/32.65    (88)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.75/32.65    (89)   ~ (all_52_5 = all_52_29)
% 198.75/32.65    (90)   ~ (all_52_15 = all_14_2)
% 198.75/32.65    (91)   ~ (all_52_19 = all_52_27)
% 198.75/32.65    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.75/32.65    (93)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.75/32.65    (94)   ~ (all_52_13 = all_4_2)
% 198.75/32.65    (95)  op(e3, e1) = all_52_17
% 198.75/32.65    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.75/32.65    (97)  op(e0, e3) = all_52_7
% 198.75/32.65    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.75/32.65    (99)   ~ (all_52_9 = all_52_25)
% 198.75/32.65    (100)  all_58_15 = all_14_2
% 198.75/32.65    (101)   ~ (all_52_19 = all_10_2)
% 198.75/32.65    (102)  op(all_52_23, all_52_23) = all_52_22
% 198.75/32.65    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.75/32.65    (104)   ~ (all_10_1 = e2)
% 198.75/32.65    (105)  all_58_8 = all_10_2
% 198.75/32.65    (106)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.75/32.65    (107)   ~ (all_52_5 = all_10_2)
% 198.75/32.65    (108)  op(all_52_29, all_52_29) = all_52_28
% 198.75/32.65    (109)   ~ (all_52_23 = all_14_2)
% 198.75/32.65    (110)  all_56_12 = all_52_7
% 198.75/32.65    (111)  op(all_52_17, all_52_17) = all_52_16
% 198.75/32.65    (112)  all_58_5 = all_4_0
% 198.75/32.65    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.75/32.65    (114)   ~ (all_52_25 = all_6_2)
% 198.75/32.65    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.75/32.65    (116)   ~ (all_52_9 = all_4_2)
% 198.75/32.65    (117)   ~ (all_52_5 = all_6_2)
% 198.75/32.65    (118)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.75/32.65    (119)   ~ (all_52_9 = all_6_2)
% 198.75/32.65    (120)   ~ (all_52_13 = all_52_15)
% 198.75/32.65    (121)  all_56_0 = all_6_2
% 198.75/32.65    (122)  op(e3, e3) = all_6_2
% 198.75/32.65    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.75/32.65    (124)   ~ (all_52_27 = all_14_2)
% 198.75/32.65    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.75/32.65    (126)  all_56_14 = all_52_23
% 198.75/32.65    (127)  op(all_4_2, all_4_2) = all_52_10
% 198.75/32.65    (128)  all_56_3 = all_52_25
% 198.75/32.65    (129)   ~ (all_52_3 = all_52_7)
% 198.75/32.65    (130)  op(all_14_2, all_14_2) = all_52_30
% 198.75/32.65    (131)  all_58_5 = all_52_19
% 198.75/32.65    (132)  all_56_1 = all_52_9
% 198.75/32.65    (133)   ~ (all_52_15 = all_4_2)
% 198.75/32.65    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.75/32.65           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.75/32.65           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.75/32.65           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.75/32.65    (135)   ~ (all_52_27 = all_4_2)
% 198.75/32.65    (136)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 198.75/32.65             all_58_13 = e0 | all_58_14 = e0)
% 198.75/32.65    (137)  all_58_6 = all_52_5
% 198.75/32.65    (138)   ~ (all_4_0 = all_4_2)
% 198.75/32.65    (139)  op(e3, e2) = all_52_9
% 198.75/32.65    (140)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.75/32.65    (141)   ~ (all_52_17 = all_6_2)
% 198.75/32.65    (142)   ~ (e1 = e0)
% 198.75/32.65    (143)   ~ (e3 = e2)
% 198.75/32.65    (144)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.75/32.65    (145)   ~ (all_52_9 = all_52_17)
% 198.75/32.65    (146)  all_56_10 = all_10_2
% 198.75/32.65    (147)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.75/32.65    (148)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.75/32.65    (149)  all_46_1 = all_6_1
% 198.75/32.65    (150)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.75/32.65    (151)  op(all_52_13, all_52_13) = all_52_12
% 198.75/32.65    (152)  op(e1, e1) = all_10_2
% 198.75/32.65    (153)   ~ (all_52_23 = all_10_2)
% 198.75/32.65    (154)   ~ (all_52_7 = all_52_23)
% 198.75/32.65    (155)   ~ (all_52_17 = all_52_19)
% 198.75/32.65    (156)  all_58_3 = all_4_2
% 198.75/32.65    (157)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.75/32.65    (158)  all_56_13 = all_52_15
% 198.75/32.65    (159)   ~ (all_52_3 = all_4_2)
% 198.75/32.65    (160)   ~ (all_52_19 = all_4_2)
% 198.75/32.65    (161)   ~ (all_52_17 = all_52_23)
% 198.75/32.65    (162)  op(all_6_2, e3) = all_6_1
% 198.75/32.65    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.75/32.65    (164)  all_58_4 = all_52_17
% 198.75/32.65    (165)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 198.75/32.65    (166)  op(all_52_25, all_52_25) = all_52_24
% 198.75/32.65  
% 198.75/32.65  Begin of proof
% 198.75/32.65  | 
% 198.75/32.65  | ALPHA: (136) implies:
% 198.75/32.65  |   (167)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.75/32.65  |   (168)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.75/32.65  | 
% 198.75/32.65  | REDUCE: (55), (100) imply:
% 198.75/32.65  |   (169)   ~ (all_14_2 = e0)
% 198.75/32.65  | 
% 198.75/32.65  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.75/32.65  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 198.75/32.65  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.75/32.65  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.75/32.65  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 198.75/32.65  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 198.75/32.65  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 198.75/32.65  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 198.75/32.65  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 198.75/32.65  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 198.75/32.65  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 198.75/32.65  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 198.75/32.65  |            (129), (130), (131), (132), (133), (134), (135), (137), (138),
% 198.75/32.65  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 198.75/32.65  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 198.75/32.65  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 198.75/32.65  |            (166), (167), (168), (169) are inconsistent by sub-proof #31.
% 198.75/32.65  | 
% 198.75/32.65  End of proof
% 198.75/32.65  
% 198.75/32.65  Sub-proof #31 shows that the following formulas are inconsistent:
% 198.75/32.65  ----------------------------------------------------------------
% 198.75/32.65    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.75/32.65    (2)   ~ (all_52_15 = all_52_23)
% 198.75/32.65    (3)   ~ (all_52_25 = all_52_27)
% 198.75/32.65    (4)  all_58_14 = all_52_23
% 198.75/32.65    (5)   ~ (e3 = e1)
% 198.75/32.65    (6)   ~ (all_52_17 = all_4_0)
% 198.75/32.65    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.75/32.65    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.75/32.65    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.75/32.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.75/32.65    (10)   ~ (all_52_5 = all_52_13)
% 198.75/32.65    (11)  all_58_1 = all_52_9
% 198.75/32.65    (12)   ~ (all_52_9 = all_52_13)
% 198.75/32.65    (13)   ~ (e3 = e0)
% 198.75/32.65    (14)  op(e2, e3) = all_52_3
% 198.75/32.65    (15)   ~ (all_52_23 = all_4_0)
% 198.75/32.65    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.75/32.65    (17)   ~ (all_52_7 = all_52_15)
% 198.75/32.65    (18)  op(all_52_7, all_52_7) = all_52_6
% 198.75/32.65    (19)   ~ (all_52_17 = all_52_25)
% 198.75/32.65    (20)   ~ (all_52_3 = all_6_2)
% 198.75/32.65    (21)  all_58_0 = all_6_2
% 198.75/32.65    (22)  op(all_14_2, e0) = all_14_1
% 198.75/32.65    (23)  all_56_4 = all_52_3
% 198.75/32.65    (24)  op(e3, all_6_1) = e1
% 198.75/32.65    (25)   ~ (all_52_17 = all_10_2)
% 198.75/32.65    (26)  op(e3, e0) = all_52_25
% 198.75/32.65    (27)  op(all_52_5, all_52_5) = all_52_4
% 198.75/32.65    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.75/32.65    (29)  op(all_52_19, all_52_19) = all_52_18
% 198.75/32.65    (30)   ~ (all_52_27 = all_52_29)
% 198.75/32.65    (31)  all_58_13 = all_52_15
% 198.75/32.65    (32)  op(all_10_2, all_10_2) = all_52_20
% 198.75/32.65    (33)  all_58_9 = all_52_25
% 198.75/32.65    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.75/32.65    (35)   ~ (all_52_29 = all_14_2)
% 198.75/32.65    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 198.75/32.65    (37)  op(all_52_27, all_52_27) = all_52_26
% 198.75/32.65    (38)  op(e1, e3) = all_52_5
% 198.75/32.65    (39)  op(e2, e2) = all_4_2
% 198.75/32.65    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.75/32.65    (41)   ~ (all_52_3 = all_52_5)
% 198.75/32.65    (42)  op(all_4_2, e2) = e1
% 198.75/32.65    (43)  all_58_11 = all_52_29
% 198.75/32.65    (44)  all_56_5 = all_4_2
% 198.75/32.65    (45)   ~ (all_52_25 = all_14_2)
% 198.75/32.65    (46)   ~ (all_52_9 = all_52_15)
% 198.75/32.65    (47)   ~ (all_52_3 = all_52_27)
% 198.75/32.65    (48)  op(all_10_2, e1) = all_10_1
% 198.75/32.65    (49)  all_46_2 = all_6_2
% 198.75/32.65    (50)  op(all_6_2, all_6_2) = all_52_0
% 198.75/32.65    (51)   ~ (all_52_7 = all_6_2)
% 198.75/32.65    (52)  op(e0, e0) = all_14_2
% 198.75/32.65    (53)  all_56_15 = all_14_2
% 198.75/32.65    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.75/32.65    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.75/32.65    (56)  all_56_11 = all_52_29
% 198.75/32.65    (57)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 198.75/32.65    (58)   ~ (all_4_0 = e3)
% 198.75/32.65    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 198.75/32.65    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.75/32.65    (61)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 198.75/32.65    (62)  all_56_9 = all_52_13
% 198.75/32.65    (63)   ~ (e2 = e1)
% 198.75/32.65    (64)  all_58_10 = all_52_27
% 198.75/32.65    (65)  all_56_8 = all_52_5
% 198.75/32.65    (66)  op(all_52_9, all_52_9) = all_52_8
% 198.75/32.65    (67)  op(all_52_15, all_52_15) = all_52_14
% 198.75/32.65    (68)   ~ (all_52_25 = all_52_29)
% 198.75/32.65    (69)   ~ (all_52_29 = all_10_2)
% 198.75/32.65    (70)  all_58_7 = all_52_13
% 198.75/32.65    (71)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.75/32.65    (72)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.75/32.65    (73)   ~ (all_52_5 = all_52_7)
% 198.75/32.65    (74)  all_58_12 = all_52_7
% 198.75/32.65    (75)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.75/32.65    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.75/32.65    (77)   ~ (all_52_7 = all_14_2)
% 198.75/32.65    (78)   ~ (all_14_2 = e0)
% 198.75/32.65    (79)  all_58_2 = all_52_3
% 198.75/32.65    (80)  all_56_2 = all_52_17
% 198.75/32.65    (81)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.75/32.65    (82)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.75/32.65    (83)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.75/32.65    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 198.75/32.65    (85)  all_56_7 = all_52_27
% 198.75/32.65    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.75/32.65    (87)   ~ (e2 = e0)
% 198.75/32.65    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.75/32.65    (89)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.75/32.65    (90)   ~ (all_52_5 = all_52_29)
% 198.75/32.65    (91)   ~ (all_52_15 = all_14_2)
% 198.75/32.66    (92)   ~ (all_52_19 = all_52_27)
% 198.75/32.66    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.75/32.66    (94)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.75/32.66    (95)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.75/32.66    (96)   ~ (all_52_13 = all_4_2)
% 198.75/32.66    (97)  op(e3, e1) = all_52_17
% 198.75/32.66    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.75/32.66    (99)  op(e0, e3) = all_52_7
% 198.75/32.66    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.75/32.66    (101)   ~ (all_52_9 = all_52_25)
% 198.75/32.66    (102)  all_58_15 = all_14_2
% 198.75/32.66    (103)   ~ (all_52_19 = all_10_2)
% 198.75/32.66    (104)  op(all_52_23, all_52_23) = all_52_22
% 198.75/32.66    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.75/32.66    (106)   ~ (all_10_1 = e2)
% 198.75/32.66    (107)  all_58_8 = all_10_2
% 198.75/32.66    (108)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.75/32.66    (109)   ~ (all_52_5 = all_10_2)
% 198.75/32.66    (110)  op(all_52_29, all_52_29) = all_52_28
% 198.75/32.66    (111)   ~ (all_52_23 = all_14_2)
% 198.75/32.66    (112)  all_56_12 = all_52_7
% 198.75/32.66    (113)  op(all_52_17, all_52_17) = all_52_16
% 198.75/32.66    (114)  all_58_5 = all_4_0
% 198.75/32.66    (115)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.75/32.66    (116)   ~ (all_52_25 = all_6_2)
% 198.75/32.66    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.75/32.66    (118)   ~ (all_52_9 = all_4_2)
% 198.75/32.66    (119)   ~ (all_52_5 = all_6_2)
% 198.75/32.66    (120)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.75/32.66    (121)   ~ (all_52_9 = all_6_2)
% 198.75/32.66    (122)   ~ (all_52_13 = all_52_15)
% 198.75/32.66    (123)  all_56_0 = all_6_2
% 198.75/32.66    (124)  op(e3, e3) = all_6_2
% 198.75/32.66    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.75/32.66    (126)   ~ (all_52_27 = all_14_2)
% 198.75/32.66    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.75/32.66    (128)  all_56_14 = all_52_23
% 198.75/32.66    (129)  op(all_4_2, all_4_2) = all_52_10
% 198.75/32.66    (130)  all_56_3 = all_52_25
% 198.75/32.66    (131)   ~ (all_52_3 = all_52_7)
% 198.75/32.66    (132)  op(all_14_2, all_14_2) = all_52_30
% 198.75/32.66    (133)  all_58_5 = all_52_19
% 198.75/32.66    (134)  all_56_1 = all_52_9
% 198.75/32.66    (135)   ~ (all_52_15 = all_4_2)
% 198.75/32.66    (136)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.75/32.66           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.75/32.66           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.75/32.66           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.75/32.66    (137)   ~ (all_52_27 = all_4_2)
% 198.75/32.66    (138)  all_58_6 = all_52_5
% 198.75/32.66    (139)   ~ (all_4_0 = all_4_2)
% 198.75/32.66    (140)  op(e3, e2) = all_52_9
% 198.75/32.66    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.75/32.66    (142)   ~ (all_52_17 = all_6_2)
% 198.75/32.66    (143)   ~ (e1 = e0)
% 198.75/32.66    (144)   ~ (e3 = e2)
% 198.75/32.66    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.75/32.66    (146)   ~ (all_52_9 = all_52_17)
% 198.75/32.66    (147)  all_56_10 = all_10_2
% 198.75/32.66    (148)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.75/32.66    (149)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.75/32.66    (150)  all_46_1 = all_6_1
% 198.75/32.66    (151)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.75/32.66    (152)  op(all_52_13, all_52_13) = all_52_12
% 198.75/32.66    (153)  op(e1, e1) = all_10_2
% 198.75/32.66    (154)   ~ (all_52_23 = all_10_2)
% 198.75/32.66    (155)   ~ (all_52_7 = all_52_23)
% 198.75/32.66    (156)   ~ (all_52_17 = all_52_19)
% 198.75/32.66    (157)  all_58_3 = all_4_2
% 198.75/32.66    (158)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.75/32.66    (159)  all_56_13 = all_52_15
% 198.75/32.66    (160)   ~ (all_52_3 = all_4_2)
% 198.75/32.66    (161)   ~ (all_52_19 = all_4_2)
% 198.75/32.66    (162)   ~ (all_52_17 = all_52_23)
% 198.75/32.66    (163)  op(all_6_2, e3) = all_6_1
% 198.75/32.66    (164)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.75/32.66    (165)  all_58_4 = all_52_17
% 198.75/32.66    (166)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 198.75/32.66    (167)  op(all_52_25, all_52_25) = all_52_24
% 198.75/32.66  
% 198.75/32.66  Begin of proof
% 198.75/32.66  | 
% 198.75/32.66  | BETA: splitting (136) gives:
% 198.75/32.66  | 
% 198.75/32.66  | Case 1:
% 198.75/32.66  | | 
% 198.75/32.66  | |   (168)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.75/32.66  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 198.75/32.66  | | 
% 198.75/32.66  | | BETA: splitting (168) gives:
% 198.75/32.66  | | 
% 198.75/32.66  | | Case 1:
% 198.75/32.66  | | | 
% 198.75/32.66  | | |   (169)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REF_CLOSE: (5), (8), (9), (18), (21), (24), (27), (39), (50), (51), (52),
% 198.75/32.66  | | |            (54), (74), (77), (79), (82), (109), (124), (127), (138),
% 198.75/32.66  | | |            (141), (153), (160), (163), (169) are inconsistent by sub-proof
% 198.75/32.66  | | |            #302.
% 198.75/32.66  | | | 
% 198.75/32.66  | | Case 2:
% 198.75/32.66  | | | 
% 198.75/32.66  | | |   (170)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.75/32.66  | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (24),
% 198.75/32.66  | | |            (25), (26), (28), (30), (31), (33), (34), (35), (37), (38),
% 198.75/32.66  | | |            (39), (40), (41), (42), (43), (44), (45), (46), (50), (51),
% 198.75/32.66  | | |            (52), (53), (54), (58), (60), (62), (63), (64), (65), (66),
% 198.75/32.66  | | |            (67), (70), (73), (74), (75), (76), (77), (79), (80), (82),
% 198.75/32.66  | | |            (85), (87), (88), (89), (90), (91), (94), (95), (96), (97),
% 198.75/32.66  | | |            (98), (99), (100), (101), (102), (104), (105), (107), (108),
% 198.75/32.66  | | |            (109), (111), (112), (113), (114), (116), (118), (119), (120),
% 198.75/32.66  | | |            (121), (122), (124), (125), (126), (127), (129), (131), (132),
% 198.75/32.66  | | |            (134), (135), (137), (138), (139), (140), (141), (142), (143),
% 198.75/32.66  | | |            (144), (145), (146), (148), (149), (152), (153), (154), (155),
% 198.75/32.66  | | |            (157), (160), (162), (163), (164), (165), (167), (170) are
% 198.75/32.66  | | |            inconsistent by sub-proof #32.
% 198.75/32.66  | | | 
% 198.75/32.66  | | End of split
% 198.75/32.66  | | 
% 198.75/32.66  | Case 2:
% 198.75/32.66  | | 
% 198.75/32.66  | |   (171)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 198.75/32.66  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 198.75/32.66  | |            e0)
% 198.75/32.66  | | 
% 198.75/32.66  | | BETA: splitting (171) gives:
% 198.75/32.66  | | 
% 198.75/32.66  | | Case 1:
% 198.75/32.66  | | | 
% 198.75/32.66  | | |   (172)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REF_CLOSE: (4), (9), (16), (18), (22), (24), (25), (26), (32), (34), (38),
% 198.75/32.66  | | |            (48), (51), (52), (53), (58), (60), (65), (75), (80), (97),
% 198.75/32.66  | | |            (99), (104), (105), (106), (107), (108), (109), (111), (112),
% 198.75/32.66  | | |            (113), (114), (116), (119), (121), (124), (132), (138), (140),
% 198.75/32.66  | | |            (142), (147), (148), (153), (154), (155), (163), (165), (166),
% 198.75/32.66  | | |            (172) are inconsistent by sub-proof #35.
% 198.75/32.66  | | | 
% 198.75/32.66  | | Case 2:
% 198.75/32.66  | | | 
% 198.75/32.66  | | |   (173)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (12), (13), (14), (16),
% 198.75/32.66  | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 198.75/32.66  | | |            (27), (29), (30), (31), (33), (35), (36), (37), (38), (39),
% 198.75/32.66  | | |            (40), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 198.75/32.66  | | |            (51), (52), (53), (54), (55), (56), (57), (59), (60), (61),
% 198.75/32.66  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 198.75/32.66  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 198.75/32.66  | | |            (83), (84), (86), (87), (88), (90), (91), (92), (93), (94),
% 198.75/32.66  | | |            (95), (97), (98), (99), (100), (101), (102), (103), (104),
% 198.75/32.66  | | |            (105), (107), (108), (109), (110), (111), (112), (113), (115),
% 198.75/32.66  | | |            (116), (117), (118), (119), (121), (122), (123), (124), (125),
% 198.75/32.66  | | |            (126), (127), (128), (130), (131), (132), (133), (134), (135),
% 198.75/32.66  | | |            (137), (138), (140), (141), (142), (143), (144), (145), (150),
% 198.75/32.66  | | |            (151), (152), (153), (154), (155), (156), (157), (158), (159),
% 198.75/32.66  | | |            (160), (161), (162), (163), (164), (165), (167), (173) are
% 198.75/32.66  | | |            inconsistent by sub-proof #271.
% 198.75/32.66  | | | 
% 198.75/32.66  | | End of split
% 198.75/32.66  | | 
% 198.75/32.66  | End of split
% 198.75/32.66  | 
% 198.75/32.66  End of proof
% 198.75/32.66  
% 198.75/32.66  Sub-proof #32 shows that the following formulas are inconsistent:
% 198.75/32.66  ----------------------------------------------------------------
% 198.75/32.66    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.75/32.66    (2)   ~ (all_52_15 = all_52_23)
% 198.75/32.66    (3)   ~ (all_52_25 = all_52_27)
% 198.75/32.66    (4)  all_58_14 = all_52_23
% 198.75/32.66    (5)   ~ (e3 = e1)
% 198.75/32.66    (6)   ~ (all_52_17 = all_4_0)
% 198.75/32.66    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.75/32.66    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.75/32.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.75/32.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.75/32.66    (10)   ~ (all_52_5 = all_52_13)
% 198.75/32.66    (11)  all_58_1 = all_52_9
% 198.75/32.66    (12)   ~ (all_52_9 = all_52_13)
% 198.75/32.66    (13)   ~ (e3 = e0)
% 198.75/32.66    (14)  op(e2, e3) = all_52_3
% 198.75/32.66    (15)   ~ (all_52_23 = all_4_0)
% 198.75/32.66    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.75/32.66    (17)   ~ (all_52_7 = all_52_15)
% 198.75/32.66    (18)  op(all_52_7, all_52_7) = all_52_6
% 198.75/32.66    (19)   ~ (all_52_3 = all_6_2)
% 198.75/32.66    (20)  all_58_0 = all_6_2
% 198.75/32.66    (21)  op(all_14_2, e0) = all_14_1
% 198.75/32.66    (22)  op(e3, all_6_1) = e1
% 198.75/32.66    (23)   ~ (all_52_17 = all_10_2)
% 198.75/32.66    (24)  op(e3, e0) = all_52_25
% 198.75/32.66    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.75/32.66    (26)   ~ (all_52_27 = all_52_29)
% 198.75/32.66    (27)  all_58_13 = all_52_15
% 198.75/32.66    (28)  all_58_9 = all_52_25
% 198.75/32.66    (29)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.75/32.66    (30)   ~ (all_52_29 = all_14_2)
% 198.75/32.66    (31)  op(all_52_27, all_52_27) = all_52_26
% 198.75/32.66    (32)  op(e1, e3) = all_52_5
% 198.75/32.66    (33)  op(e2, e2) = all_4_2
% 198.75/32.66    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.75/32.66    (35)   ~ (all_52_3 = all_52_5)
% 198.75/32.66    (36)  op(all_4_2, e2) = e1
% 198.75/32.66    (37)  all_58_11 = all_52_29
% 198.75/32.66    (38)  all_56_5 = all_4_2
% 198.75/32.66    (39)   ~ (all_52_25 = all_14_2)
% 198.75/32.66    (40)   ~ (all_52_9 = all_52_15)
% 198.75/32.66    (41)  op(all_6_2, all_6_2) = all_52_0
% 198.75/32.66    (42)   ~ (all_52_7 = all_6_2)
% 198.75/32.66    (43)  op(e0, e0) = all_14_2
% 198.75/32.66    (44)  all_56_15 = all_14_2
% 198.75/32.66    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.75/32.66    (46)   ~ (all_4_0 = e3)
% 198.75/32.66    (47)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.75/32.66    (48)  all_56_9 = all_52_13
% 198.75/32.66    (49)   ~ (e2 = e1)
% 198.75/32.66    (50)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.75/32.66    (51)  all_58_10 = all_52_27
% 198.75/32.66    (52)  all_56_8 = all_52_5
% 198.75/32.66    (53)  op(all_52_9, all_52_9) = all_52_8
% 198.75/32.66    (54)  op(all_52_15, all_52_15) = all_52_14
% 198.75/32.66    (55)  all_58_7 = all_52_13
% 198.75/32.66    (56)   ~ (all_52_5 = all_52_7)
% 198.75/32.66    (57)  all_58_12 = all_52_7
% 198.75/32.66    (58)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.75/32.66    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.75/32.66    (60)   ~ (all_52_7 = all_14_2)
% 198.75/32.66    (61)  all_58_2 = all_52_3
% 198.75/32.66    (62)  all_56_2 = all_52_17
% 198.75/32.66    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.75/32.66    (64)  all_56_7 = all_52_27
% 198.75/32.66    (65)   ~ (e2 = e0)
% 198.75/32.66    (66)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.75/32.66    (67)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.75/32.66    (68)   ~ (all_52_5 = all_52_29)
% 198.75/32.66    (69)   ~ (all_52_15 = all_14_2)
% 198.75/32.66    (70)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.75/32.66    (71)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.75/32.66    (72)   ~ (all_52_13 = all_4_2)
% 198.75/32.66    (73)  op(e3, e1) = all_52_17
% 198.75/32.66    (74)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.75/32.66    (75)  op(e0, e3) = all_52_7
% 198.75/32.66    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.75/32.66    (77)   ~ (all_52_9 = all_52_25)
% 198.75/32.66    (78)  all_58_15 = all_14_2
% 198.75/32.66    (79)  op(all_52_23, all_52_23) = all_52_22
% 198.75/32.66    (80)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.75/32.66    (81)  all_58_8 = all_10_2
% 198.75/32.66    (82)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.75/32.66    (83)   ~ (all_52_5 = all_10_2)
% 198.75/32.66    (84)   ~ (all_52_23 = all_14_2)
% 198.75/32.66    (85)  all_56_12 = all_52_7
% 198.75/32.66    (86)  op(all_52_17, all_52_17) = all_52_16
% 198.75/32.66    (87)  all_58_5 = all_4_0
% 198.75/32.66    (88)   ~ (all_52_25 = all_6_2)
% 198.75/32.66    (89)   ~ (all_52_9 = all_4_2)
% 198.75/32.66    (90)   ~ (all_52_5 = all_6_2)
% 198.75/32.66    (91)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.75/32.66    (92)   ~ (all_52_9 = all_6_2)
% 198.75/32.66    (93)   ~ (all_52_13 = all_52_15)
% 198.75/32.66    (94)  op(e3, e3) = all_6_2
% 198.75/32.66    (95)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.75/32.66    (96)   ~ (all_52_27 = all_14_2)
% 198.75/32.66    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.75/32.66    (98)  op(all_4_2, all_4_2) = all_52_10
% 198.75/32.66    (99)   ~ (all_52_3 = all_52_7)
% 198.75/32.66    (100)  op(all_14_2, all_14_2) = all_52_30
% 198.75/32.66    (101)  all_56_1 = all_52_9
% 198.75/32.66    (102)   ~ (all_52_15 = all_4_2)
% 198.75/32.66    (103)   ~ (all_52_27 = all_4_2)
% 198.75/32.66    (104)  all_58_6 = all_52_5
% 198.75/32.66    (105)   ~ (all_4_0 = all_4_2)
% 198.75/32.66    (106)  op(e3, e2) = all_52_9
% 198.75/32.66    (107)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.75/32.66    (108)   ~ (all_52_17 = all_6_2)
% 198.75/32.66    (109)   ~ (e1 = e0)
% 198.75/32.66    (110)   ~ (e3 = e2)
% 198.75/32.66    (111)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.75/32.66    (112)   ~ (all_52_9 = all_52_17)
% 198.75/32.66    (113)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.75/32.66    (114)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.75/32.66    (115)  op(all_52_13, all_52_13) = all_52_12
% 198.75/32.66    (116)  op(e1, e1) = all_10_2
% 198.75/32.66    (117)   ~ (all_52_23 = all_10_2)
% 198.75/32.66    (118)   ~ (all_52_7 = all_52_23)
% 198.75/32.66    (119)  all_58_3 = all_4_2
% 198.75/32.66    (120)   ~ (all_52_3 = all_4_2)
% 198.75/32.66    (121)   ~ (all_52_17 = all_52_23)
% 198.75/32.66    (122)  op(all_6_2, e3) = all_6_1
% 198.75/32.66    (123)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.75/32.66    (124)  all_58_4 = all_52_17
% 198.75/32.66    (125)  op(all_52_25, all_52_25) = all_52_24
% 198.75/32.66  
% 198.75/32.66  Begin of proof
% 198.75/32.66  | 
% 198.75/32.66  | ALPHA: (50) implies:
% 198.75/32.66  |   (126)  all_52_14 = e0
% 198.75/32.66  |   (127)  all_52_12 = e1
% 198.75/32.66  |   (128)  all_52_10 = e2
% 198.75/32.66  |   (129)  all_52_8 = e3
% 198.75/32.66  | 
% 198.75/32.66  | REDUCE: (53), (129) imply:
% 198.75/32.66  |   (130)  op(all_52_9, all_52_9) = e3
% 198.75/32.66  | 
% 198.75/32.66  | REDUCE: (115), (127) imply:
% 198.75/32.66  |   (131)  op(all_52_13, all_52_13) = e1
% 198.75/32.66  | 
% 198.75/32.66  | REDUCE: (54), (126) imply:
% 198.75/32.66  |   (132)  op(all_52_15, all_52_15) = e0
% 198.75/32.66  | 
% 198.75/32.66  | REDUCE: (98), (128) imply:
% 198.75/32.66  |   (133)  op(all_4_2, all_4_2) = e2
% 198.75/32.66  | 
% 198.75/32.66  | BETA: splitting (82) gives:
% 198.75/32.66  | 
% 198.75/32.66  | Case 1:
% 198.75/32.66  | | 
% 198.75/32.66  | |   (134)  all_56_15 = e3
% 198.75/32.66  | | 
% 198.75/32.66  | | COMBINE_EQS: (44), (134) imply:
% 198.75/32.66  | |   (135)  all_14_2 = e3
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (60), (135) imply:
% 198.75/32.66  | |   (136)   ~ (all_52_7 = e3)
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (39), (135) imply:
% 198.75/32.66  | |   (137)   ~ (all_52_25 = e3)
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (96), (135) imply:
% 198.75/32.66  | |   (138)   ~ (all_52_27 = e3)
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (30), (135) imply:
% 198.75/32.66  | |   (139)   ~ (all_52_29 = e3)
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (100), (135) imply:
% 198.75/32.66  | |   (140)  op(e3, e3) = all_52_30
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (21), (135) imply:
% 198.75/32.66  | |   (141)  op(e3, e0) = all_14_1
% 198.75/32.66  | | 
% 198.75/32.66  | | GROUND_INST: instantiating (9) with all_52_25, all_14_1, e0, e3, simplifying
% 198.75/32.66  | |              with (24), (141) gives:
% 198.75/32.66  | |   (142)  all_52_25 = all_14_1
% 198.75/32.66  | | 
% 198.75/32.66  | | GROUND_INST: instantiating (9) with all_6_2, all_52_30, e3, e3, simplifying
% 198.75/32.66  | |              with (94), (140) gives:
% 198.75/32.66  | |   (143)  all_52_30 = all_6_2
% 198.75/32.66  | | 
% 198.75/32.66  | | REDUCE: (88), (142) imply:
% 198.75/32.66  | |   (144)   ~ (all_14_1 = all_6_2)
% 198.75/32.66  | | 
% 198.75/32.66  | | BETA: splitting (45) gives:
% 198.75/32.66  | | 
% 198.75/32.66  | | Case 1:
% 198.75/32.66  | | | 
% 198.75/32.66  | | |   (145)  all_58_2 = e3
% 198.75/32.66  | | | 
% 198.75/32.66  | | | COMBINE_EQS: (61), (145) imply:
% 198.75/32.66  | | |   (146)  all_52_3 = e3
% 198.75/32.66  | | | 
% 198.75/32.66  | | | SIMP: (146) implies:
% 198.75/32.66  | | |   (147)  all_52_3 = e3
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REDUCE: (35), (147) imply:
% 198.75/32.66  | | |   (148)   ~ (all_52_5 = e3)
% 198.75/32.66  | | | 
% 198.75/32.66  | | | SIMP: (148) implies:
% 198.75/32.66  | | |   (149)   ~ (all_52_5 = e3)
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REDUCE: (19), (147) imply:
% 198.75/32.66  | | |   (150)   ~ (all_6_2 = e3)
% 198.75/32.66  | | | 
% 198.75/32.66  | | | SIMP: (150) implies:
% 198.75/32.66  | | |   (151)   ~ (all_6_2 = e3)
% 198.75/32.66  | | | 
% 198.75/32.66  | | | REDUCE: (8), (147) imply:
% 198.75/32.66  | | |   (152)  op(e3, e3) = all_52_2
% 198.75/32.66  | | | 
% 198.75/32.66  | | | GROUND_INST: instantiating (9) with all_6_2, all_52_2, e3, e3, simplifying
% 198.75/32.66  | | |              with (94), (152) gives:
% 198.75/32.66  | | |   (153)  all_52_2 = all_6_2
% 198.75/32.66  | | | 
% 198.75/32.66  | | | BETA: splitting (113) gives:
% 198.75/32.66  | | | 
% 198.75/32.66  | | | Case 1:
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | |   (154)  all_58_4 = e3
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | COMBINE_EQS: (124), (154) imply:
% 198.75/32.66  | | | |   (155)  all_52_17 = e3
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | SIMP: (155) implies:
% 198.75/32.66  | | | |   (156)  all_52_17 = e3
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | REDUCE: (23), (156) imply:
% 198.75/32.66  | | | |   (157)   ~ (all_10_2 = e3)
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | SIMP: (157) implies:
% 198.75/32.66  | | | |   (158)   ~ (all_10_2 = e3)
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | REDUCE: (86), (156) imply:
% 198.75/32.66  | | | |   (159)  op(e3, e3) = all_52_16
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | BETA: splitting (59) gives:
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | Case 1:
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | |   (160)  all_58_6 = e3
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | | REF_CLOSE: (104), (149), (160) are inconsistent by sub-proof #1328.
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | Case 2:
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | |   (161)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | | BETA: splitting (161) gives:
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | | Case 1:
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | |   (162)  all_58_7 = e3
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | COMBINE_EQS: (55), (162) imply:
% 198.75/32.66  | | | | | |   (163)  all_52_13 = e3
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | REDUCE: (131), (163) imply:
% 198.75/32.66  | | | | | |   (164)  op(e3, e3) = e1
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_16, e3, e3,
% 198.75/32.66  | | | | | |              simplifying with (94), (159) gives:
% 198.75/32.66  | | | | | |   (165)  all_52_16 = all_6_2
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | GROUND_INST: instantiating (9) with e1, all_52_16, e3, e3,
% 198.75/32.66  | | | | | |              simplifying with (159), (164) gives:
% 198.75/32.66  | | | | | |   (166)  all_52_16 = e1
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | COMBINE_EQS: (165), (166) imply:
% 198.75/32.66  | | | | | |   (167)  all_6_2 = e1
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | REF_CLOSE: (9), (22), (29), (32), (52), (80), (90), (92), (104),
% 198.75/32.66  | | | | | |            (106), (122), (141), (144), (149), (167) are inconsistent
% 198.75/32.66  | | | | | |            by sub-proof #301.
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | Case 2:
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | |   (168)  all_58_8 = e3 | all_58_11 = e3
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | | REF_CLOSE: (37), (81), (139), (158), (168) are inconsistent by
% 198.75/32.66  | | | | | |            sub-proof #1140.
% 198.75/32.66  | | | | | | 
% 198.75/32.66  | | | | | End of split
% 198.75/32.66  | | | | | 
% 198.75/32.66  | | | | End of split
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | Case 2:
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | |   (169)   ~ (all_58_4 = e3)
% 198.75/32.66  | | | | 
% 198.75/32.66  | | | | REDUCE: (124), (169) imply:
% 198.82/32.66  | | | |   (170)   ~ (all_52_17 = e3)
% 198.82/32.66  | | | | 
% 198.82/32.66  | | | | REF_CLOSE: (9), (11), (20), (28), (92), (94), (97), (124), (130), (137),
% 198.82/32.66  | | | |            (151), (170) are inconsistent by sub-proof #254.
% 198.82/32.66  | | | | 
% 198.82/32.66  | | | End of split
% 198.82/32.66  | | | 
% 198.82/32.66  | | Case 2:
% 198.82/32.66  | | | 
% 198.82/32.66  | | |   (171)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.66  | | | 
% 198.82/32.66  | | | REF_CLOSE: (9), (20), (33), (36), (46), (51), (57), (59), (61), (63),
% 198.82/32.66  | | |            (83), (87), (94), (104), (106), (110), (116), (119), (120),
% 198.82/32.66  | | |            (130), (133), (136), (138), (171) are inconsistent by sub-proof
% 198.82/32.66  | | |            #194.
% 198.82/32.66  | | | 
% 198.82/32.66  | | End of split
% 198.82/32.66  | | 
% 198.82/32.66  | Case 2:
% 198.82/32.66  | | 
% 198.82/32.66  | |   (172)   ~ (all_56_15 = e3)
% 198.82/32.66  | |   (173)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.66  | | 
% 198.82/32.66  | | REDUCE: (44), (172) imply:
% 198.82/32.66  | |   (174)   ~ (all_14_2 = e3)
% 198.82/32.66  | | 
% 198.82/32.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.82/32.66  | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 198.82/32.66  | |            (25), (26), (27), (28), (31), (32), (33), (34), (35), (36), (37),
% 198.82/32.66  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 198.82/32.66  | |            (49), (51), (52), (55), (56), (57), (58), (59), (60), (61), (62),
% 198.82/32.66  | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 198.82/32.66  | |            (74), (75), (76), (77), (78), (79), (80), (81), (83), (84), (85),
% 198.82/32.66  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (97),
% 198.82/32.66  | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 198.82/32.66  | |            (108), (109), (110), (111), (112), (113), (114), (116), (117),
% 198.82/32.66  | |            (118), (119), (120), (121), (122), (123), (124), (125), (130),
% 198.82/32.66  | |            (131), (132), (133), (173), (174) are inconsistent by sub-proof
% 198.82/32.66  | |            #33.
% 198.82/32.66  | | 
% 198.82/32.66  | End of split
% 198.82/32.66  | 
% 198.82/32.66  End of proof
% 198.82/32.66  
% 198.82/32.66  Sub-proof #33 shows that the following formulas are inconsistent:
% 198.82/32.66  ----------------------------------------------------------------
% 198.82/32.66    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.82/32.66    (2)   ~ (all_52_15 = all_52_23)
% 198.82/32.66    (3)   ~ (all_52_25 = all_52_27)
% 198.82/32.66    (4)  all_58_14 = all_52_23
% 198.82/32.66    (5)   ~ (e3 = e1)
% 198.82/32.66    (6)   ~ (all_52_17 = all_4_0)
% 198.82/32.66    (7)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.82/32.67    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.82/32.67    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.67    (10)   ~ (all_52_5 = all_52_13)
% 198.82/32.67    (11)  all_58_1 = all_52_9
% 198.82/32.67    (12)   ~ (all_52_9 = all_52_13)
% 198.82/32.67    (13)   ~ (e3 = e0)
% 198.82/32.67    (14)  op(e2, e3) = all_52_3
% 198.82/32.67    (15)   ~ (all_52_23 = all_4_0)
% 198.82/32.67    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.67    (17)   ~ (all_52_7 = all_52_15)
% 198.82/32.67    (18)  op(all_52_15, all_52_15) = e0
% 198.82/32.67    (19)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.67    (20)   ~ (all_52_3 = all_6_2)
% 198.82/32.67    (21)  all_58_0 = all_6_2
% 198.82/32.67    (22)  op(e3, all_6_1) = e1
% 198.82/32.67    (23)   ~ (all_52_17 = all_10_2)
% 198.82/32.67    (24)  op(e3, e0) = all_52_25
% 198.82/32.67    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.67    (26)   ~ (all_52_27 = all_52_29)
% 198.82/32.67    (27)  all_58_13 = all_52_15
% 198.82/32.67    (28)  op(all_52_13, all_52_13) = e1
% 198.82/32.67    (29)  all_58_9 = all_52_25
% 198.82/32.67    (30)  op(all_52_27, all_52_27) = all_52_26
% 198.82/32.67    (31)  op(e1, e3) = all_52_5
% 198.82/32.67    (32)  op(e2, e2) = all_4_2
% 198.82/32.67    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.67    (34)   ~ (all_52_3 = all_52_5)
% 198.82/32.67    (35)  op(all_4_2, e2) = e1
% 198.82/32.67    (36)  all_58_11 = all_52_29
% 198.82/32.67    (37)  all_56_5 = all_4_2
% 198.82/32.67    (38)   ~ (all_52_25 = all_14_2)
% 198.82/32.67    (39)   ~ (all_52_9 = all_52_15)
% 198.82/32.67    (40)  op(all_6_2, all_6_2) = all_52_0
% 198.82/32.67    (41)   ~ (all_52_7 = all_6_2)
% 198.82/32.67    (42)  op(e0, e0) = all_14_2
% 198.82/32.67    (43)  all_56_15 = all_14_2
% 198.82/32.67    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.67    (45)   ~ (all_4_0 = e3)
% 198.82/32.67    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.67    (47)  all_56_9 = all_52_13
% 198.82/32.67    (48)   ~ (e2 = e1)
% 198.82/32.67    (49)  all_58_10 = all_52_27
% 198.82/32.67    (50)  all_56_8 = all_52_5
% 198.82/32.67    (51)  all_58_7 = all_52_13
% 198.82/32.67    (52)   ~ (all_52_5 = all_52_7)
% 198.82/32.67    (53)  all_58_12 = all_52_7
% 198.82/32.67    (54)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.67    (55)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.82/32.67    (56)   ~ (all_52_7 = all_14_2)
% 198.82/32.67    (57)  all_58_2 = all_52_3
% 198.82/32.67    (58)  all_56_2 = all_52_17
% 198.82/32.67    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.82/32.67    (60)  all_56_7 = all_52_27
% 198.82/32.67    (61)   ~ (e2 = e0)
% 198.82/32.67    (62)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.82/32.67    (63)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.82/32.67    (64)   ~ (all_52_5 = all_52_29)
% 198.82/32.67    (65)   ~ (all_52_15 = all_14_2)
% 198.82/32.67    (66)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.82/32.67    (67)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.82/32.67    (68)   ~ (all_52_13 = all_4_2)
% 198.82/32.67    (69)  op(e3, e1) = all_52_17
% 198.82/32.67    (70)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.82/32.67    (71)  op(e0, e3) = all_52_7
% 198.82/32.67    (72)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.67    (73)   ~ (all_52_9 = all_52_25)
% 198.82/32.67    (74)  all_58_15 = all_14_2
% 198.82/32.67    (75)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.67    (76)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.82/32.67    (77)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.67    (78)  all_58_8 = all_10_2
% 198.82/32.67    (79)   ~ (all_52_5 = all_10_2)
% 198.82/32.67    (80)   ~ (all_52_23 = all_14_2)
% 198.82/32.67    (81)  all_56_12 = all_52_7
% 198.82/32.67    (82)  op(all_52_17, all_52_17) = all_52_16
% 198.82/32.67    (83)  all_58_5 = all_4_0
% 198.82/32.67    (84)   ~ (all_52_25 = all_6_2)
% 198.82/32.67    (85)   ~ (all_52_9 = all_4_2)
% 198.82/32.67    (86)   ~ (all_52_5 = all_6_2)
% 198.82/32.67    (87)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.67    (88)  op(all_4_2, all_4_2) = e2
% 198.82/32.67    (89)   ~ (all_52_9 = all_6_2)
% 198.82/32.67    (90)   ~ (all_52_13 = all_52_15)
% 198.82/32.67    (91)  op(e3, e3) = all_6_2
% 198.82/32.67    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.82/32.67    (93)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.67    (94)   ~ (all_52_3 = all_52_7)
% 198.82/32.67    (95)  op(all_14_2, all_14_2) = all_52_30
% 198.82/32.67    (96)  all_56_1 = all_52_9
% 198.82/32.67    (97)   ~ (all_52_15 = all_4_2)
% 198.82/32.67    (98)   ~ (all_52_27 = all_4_2)
% 198.82/32.67    (99)  all_58_6 = all_52_5
% 198.82/32.67    (100)   ~ (all_4_0 = all_4_2)
% 198.82/32.67    (101)  op(e3, e2) = all_52_9
% 198.82/32.67    (102)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.67    (103)   ~ (all_52_17 = all_6_2)
% 198.82/32.67    (104)   ~ (e1 = e0)
% 198.82/32.67    (105)   ~ (e3 = e2)
% 198.82/32.67    (106)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.82/32.67    (107)   ~ (all_52_9 = all_52_17)
% 198.82/32.67    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.67    (109)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.82/32.67    (110)  op(e1, e1) = all_10_2
% 198.82/32.67    (111)  op(all_52_9, all_52_9) = e3
% 198.82/32.67    (112)   ~ (all_52_23 = all_10_2)
% 198.82/32.67    (113)   ~ (all_52_7 = all_52_23)
% 198.82/32.67    (114)  all_58_3 = all_4_2
% 198.82/32.67    (115)   ~ (all_52_3 = all_4_2)
% 198.82/32.67    (116)   ~ (all_52_17 = all_52_23)
% 198.82/32.67    (117)  op(all_6_2, e3) = all_6_1
% 198.82/32.67    (118)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.82/32.67    (119)  all_58_4 = all_52_17
% 198.82/32.67    (120)  op(all_52_25, all_52_25) = all_52_24
% 198.82/32.67    (121)   ~ (all_14_2 = e3)
% 198.82/32.67  
% 198.82/32.67  Begin of proof
% 198.82/32.67  | 
% 198.82/32.67  | BETA: splitting (108) gives:
% 198.82/32.67  | 
% 198.82/32.67  | Case 1:
% 198.82/32.67  | | 
% 198.82/32.67  | |   (122)  all_58_4 = e3
% 198.82/32.67  | | 
% 198.82/32.67  | | COMBINE_EQS: (119), (122) imply:
% 198.82/32.67  | |   (123)  all_52_17 = e3
% 198.82/32.67  | | 
% 198.82/32.67  | | SIMP: (123) implies:
% 198.82/32.67  | |   (124)  all_52_17 = e3
% 198.82/32.67  | | 
% 198.82/32.67  | | REDUCE: (107), (124) imply:
% 198.82/32.67  | |   (125)   ~ (all_52_9 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | REDUCE: (116), (124) imply:
% 198.82/32.67  | |   (126)   ~ (all_52_23 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | SIMP: (126) implies:
% 198.82/32.67  | |   (127)   ~ (all_52_23 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | REDUCE: (23), (124) imply:
% 198.82/32.67  | |   (128)   ~ (all_10_2 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | SIMP: (128) implies:
% 198.82/32.67  | |   (129)   ~ (all_10_2 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | REDUCE: (6), (124) imply:
% 198.82/32.67  | |   (130)   ~ (all_4_0 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | REDUCE: (82), (124) imply:
% 198.82/32.67  | |   (131)  op(e3, e3) = all_52_16
% 198.82/32.67  | | 
% 198.82/32.67  | | GROUND_INST: instantiating (9) with all_6_2, all_52_16, e3, e3, simplifying
% 198.82/32.67  | |              with (91), (131) gives:
% 198.82/32.67  | |   (132)  all_52_16 = all_6_2
% 198.82/32.67  | | 
% 198.82/32.67  | | BETA: splitting (102) gives:
% 198.82/32.67  | | 
% 198.82/32.67  | | Case 1:
% 198.82/32.67  | | | 
% 198.82/32.67  | | |   (133)  all_58_12 = e3
% 198.82/32.67  | | | 
% 198.82/32.67  | | | COMBINE_EQS: (53), (133) imply:
% 198.82/32.67  | | |   (134)  all_52_7 = e3
% 198.82/32.67  | | | 
% 198.82/32.67  | | | SIMP: (134) implies:
% 198.82/32.67  | | |   (135)  all_52_7 = e3
% 198.82/32.67  | | | 
% 198.82/32.67  | | | REDUCE: (94), (135) imply:
% 198.82/32.67  | | |   (136)   ~ (all_52_3 = e3)
% 198.82/32.67  | | | 
% 198.82/32.67  | | | REDUCE: (17), (135) imply:
% 198.82/32.67  | | |   (137)   ~ (all_52_15 = e3)
% 198.82/32.67  | | | 
% 198.82/32.67  | | | SIMP: (137) implies:
% 198.82/32.67  | | |   (138)   ~ (all_52_15 = e3)
% 198.82/32.67  | | | 
% 198.82/32.67  | | | REDUCE: (19), (135) imply:
% 198.82/32.67  | | |   (139)  op(e3, e3) = all_52_6
% 198.82/32.67  | | | 
% 198.82/32.67  | | | GROUND_INST: instantiating (9) with all_6_2, all_52_6, e3, e3, simplifying
% 198.82/32.67  | | |              with (91), (139) gives:
% 198.82/32.67  | | |   (140)  all_52_6 = all_6_2
% 198.82/32.67  | | | 
% 198.82/32.67  | | | REF_CLOSE: (9), (11), (13), (21), (22), (24), (25), (27), (28), (31),
% 198.82/32.67  | | |            (33), (35), (44), (45), (48), (49), (51), (57), (60), (61),
% 198.82/32.67  | | |            (63), (66), (68), (72), (83), (84), (87), (89), (91), (97),
% 198.82/32.67  | | |            (98), (99), (101), (104), (105), (110), (111), (114), (117),
% 198.82/32.67  | | |            (118), (125), (129), (133), (136), (138) are inconsistent by
% 198.82/32.67  | | |            sub-proof #41.
% 198.82/32.67  | | | 
% 198.82/32.67  | | Case 2:
% 198.82/32.67  | | | 
% 198.82/32.67  | | |   (141)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.67  | | | 
% 198.82/32.67  | | | REF_CLOSE: (4), (9), (13), (16), (17), (18), (22), (27), (32), (39), (41),
% 198.82/32.67  | | |            (43), (53), (54), (56), (67), (69), (71), (74), (77), (80),
% 198.82/32.67  | | |            (81), (89), (91), (95), (96), (97), (106), (107), (111), (113),
% 198.82/32.67  | | |            (117), (121), (127), (141) are inconsistent by sub-proof #34.
% 198.82/32.67  | | | 
% 198.82/32.67  | | End of split
% 198.82/32.67  | | 
% 198.82/32.67  | Case 2:
% 198.82/32.67  | | 
% 198.82/32.67  | |   (142)   ~ (all_58_4 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | REDUCE: (119), (142) imply:
% 198.82/32.67  | |   (143)   ~ (all_52_17 = e3)
% 198.82/32.67  | | 
% 198.82/32.67  | | BETA: splitting (46) gives:
% 198.82/32.67  | | 
% 198.82/32.67  | | Case 1:
% 198.82/32.67  | | | 
% 198.82/32.67  | | |   (144)  all_56_2 = e3
% 198.82/32.67  | | | 
% 198.82/32.67  | | | REF_CLOSE: (58), (143), (144) are inconsistent by sub-proof #1327.
% 198.82/32.67  | | | 
% 198.82/32.67  | | Case 2:
% 198.82/32.67  | | | 
% 198.82/32.67  | | |   (145)   ~ (all_56_2 = e3)
% 198.82/32.67  | | |   (146)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.67  | | | 
% 198.82/32.67  | | | BETA: splitting (25) gives:
% 198.82/32.67  | | | 
% 198.82/32.67  | | | Case 1:
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | |   (147)  all_56_7 = e3
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | COMBINE_EQS: (60), (147) imply:
% 198.82/32.67  | | | |   (148)  all_52_27 = e3
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | SIMP: (148) implies:
% 198.82/32.67  | | | |   (149)  all_52_27 = e3
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | REDUCE: (3), (149) imply:
% 198.82/32.67  | | | |   (150)   ~ (all_52_25 = e3)
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | REF_CLOSE: (5), (9), (11), (21), (22), (29), (40), (89), (91), (93),
% 198.82/32.67  | | | |            (111), (117), (119), (143), (150) are inconsistent by
% 198.82/32.67  | | | |            sub-proof #289.
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | Case 2:
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | |   (151)   ~ (all_56_7 = e3)
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | REDUCE: (60), (151) imply:
% 198.82/32.67  | | | |   (152)   ~ (all_52_27 = e3)
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | BETA: splitting (44) gives:
% 198.82/32.67  | | | | 
% 198.82/32.67  | | | | Case 1:
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | |   (153)  all_58_2 = e3
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | COMBINE_EQS: (57), (153) imply:
% 198.82/32.67  | | | | |   (154)  all_52_3 = e3
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | SIMP: (154) implies:
% 198.82/32.67  | | | | |   (155)  all_52_3 = e3
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | REDUCE: (94), (155) imply:
% 198.82/32.67  | | | | |   (156)   ~ (all_52_7 = e3)
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | SIMP: (156) implies:
% 198.82/32.67  | | | | |   (157)   ~ (all_52_7 = e3)
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | REDUCE: (20), (155) imply:
% 198.82/32.67  | | | | |   (158)   ~ (all_6_2 = e3)
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | SIMP: (158) implies:
% 198.82/32.67  | | | | |   (159)   ~ (all_6_2 = e3)
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | REDUCE: (115), (155) imply:
% 198.82/32.67  | | | | |   (160)   ~ (all_4_2 = e3)
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | SIMP: (160) implies:
% 198.82/32.67  | | | | |   (161)   ~ (all_4_2 = e3)
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | REDUCE: (8), (155) imply:
% 198.82/32.67  | | | | |   (162)  op(e3, e3) = all_52_2
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_2, e3, e3,
% 198.82/32.67  | | | | |              simplifying with (91), (162) gives:
% 198.82/32.67  | | | | |   (163)  all_52_2 = all_6_2
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | BETA: splitting (92) gives:
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | Case 1:
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | |   (164)  all_58_9 = e3
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | COMBINE_EQS: (29), (164) imply:
% 198.82/32.67  | | | | | |   (165)  all_52_25 = e3
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | SIMP: (165) implies:
% 198.82/32.67  | | | | | |   (166)  all_52_25 = e3
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (73), (166) imply:
% 198.82/32.67  | | | | | |   (167)   ~ (all_52_9 = e3)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (38), (166) imply:
% 198.82/32.67  | | | | | |   (168)   ~ (all_14_2 = e3)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (120), (166) imply:
% 198.82/32.67  | | | | | |   (169)  op(e3, e3) = all_52_24
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_24, e3, e3,
% 198.82/32.67  | | | | | |              simplifying with (91), (169) gives:
% 198.82/32.67  | | | | | |   (170)  all_52_24 = all_6_2
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | BETA: splitting (102) gives:
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | Case 1:
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | |   (171)  all_58_12 = e3
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | | REF_CLOSE: (53), (157), (171) are inconsistent by sub-proof #1367.
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | Case 2:
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | |   (172)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | | BETA: splitting (72) gives:
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | |   (173)  all_58_1 = e3
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | COMBINE_EQS: (11), (173) imply:
% 198.82/32.67  | | | | | | | |   (174)  all_52_9 = e3
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | REDUCE: (167), (174) imply:
% 198.82/32.67  | | | | | | | |   (175)  $false
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | CLOSE: (175) is inconsistent.
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | |   (176)   ~ (all_58_1 = e3)
% 198.82/32.67  | | | | | | | |   (177)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | BETA: splitting (106) gives:
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | |   (178)  all_56_1 = e3
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | REF_CLOSE: (96), (167), (178) are inconsistent by sub-proof
% 198.82/32.67  | | | | | | | | |            #1326.
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | |   (179)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | BETA: splitting (109) gives:
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | |   (180)  all_56_9 = e3
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | COMBINE_EQS: (47), (180) imply:
% 198.82/32.67  | | | | | | | | | |   (181)  all_52_13 = e3
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | SIMP: (181) implies:
% 198.82/32.67  | | | | | | | | | |   (182)  all_52_13 = e3
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | REDUCE: (90), (182) imply:
% 198.82/32.67  | | | | | | | | | |   (183)   ~ (all_52_15 = e3)
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | SIMP: (183) implies:
% 198.82/32.67  | | | | | | | | | |   (184)   ~ (all_52_15 = e3)
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | REDUCE: (28), (182) imply:
% 198.82/32.67  | | | | | | | | | |   (185)  op(e3, e3) = e1
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | BETA: splitting (172) gives:
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | |   (186)  all_58_13 = e3
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | REF_CLOSE: (27), (184), (186) are inconsistent by sub-proof
% 198.82/32.67  | | | | | | | | | | |            #1360.
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | |   (187)  all_58_14 = e3 | all_58_15 = e3
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | BETA: splitting (187) gives:
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | |   (188)  all_58_14 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | COMBINE_EQS: (4), (188) imply:
% 198.82/32.67  | | | | | | | | | | | |   (189)  all_52_23 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | SIMP: (189) implies:
% 198.82/32.67  | | | | | | | | | | | |   (190)  all_52_23 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | REDUCE: (75), (190) imply:
% 198.82/32.67  | | | | | | | | | | | |   (191)  op(e3, e3) = all_52_22
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_22, e3, e3,
% 198.82/32.67  | | | | | | | | | | | |              simplifying with (91), (191) gives:
% 198.82/32.67  | | | | | | | | | | | |   (192)  all_52_22 = all_6_2
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | GROUND_INST: instantiating (9) with e1, all_52_22, e3, e3,
% 198.82/32.67  | | | | | | | | | | | |              simplifying with (185), (191) gives:
% 198.82/32.67  | | | | | | | | | | | |   (193)  all_52_22 = e1
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | COMBINE_EQS: (192), (193) imply:
% 198.82/32.67  | | | | | | | | | | | |   (194)  all_6_2 = e1
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | REDUCE: (89), (194) imply:
% 198.82/32.67  | | | | | | | | | | | |   (195)   ~ (all_52_9 = e1)
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | REDUCE: (103), (194) imply:
% 198.82/32.67  | | | | | | | | | | | |   (196)   ~ (all_52_17 = e1)
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | BETA: splitting (70) gives:
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | |   (197)  all_58_4 = e2
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | | COMBINE_EQS: (119), (197) imply:
% 198.82/32.67  | | | | | | | | | | | | |   (198)  all_52_17 = e2
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | | REDUCE: (107), (198) imply:
% 198.82/32.67  | | | | | | | | | | | | |   (199)   ~ (all_52_9 = e2)
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | | REF_CLOSE: (9), (42), (96), (111), (121), (179), (195), (199)
% 198.82/32.67  | | | | | | | | | | | | |            are inconsistent by sub-proof #293.
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | |   (200)   ~ (all_58_4 = e2)
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | | REDUCE: (119), (200) imply:
% 198.82/32.67  | | | | | | | | | | | | |   (201)   ~ (all_52_17 = e2)
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | | REF_CLOSE: (7), (9), (32), (58), (96), (106), (107), (111),
% 198.82/32.67  | | | | | | | | | | | | |            (119), (146), (161), (167), (195), (196), (201)
% 198.82/32.67  | | | | | | | | | | | | |            are inconsistent by sub-proof #736.
% 198.82/32.67  | | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | |   (202)  all_58_15 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | COMBINE_EQS: (74), (202) imply:
% 198.82/32.67  | | | | | | | | | | | |   (203)  all_14_2 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | REDUCE: (121), (203) imply:
% 198.82/32.67  | | | | | | | | | | | |   (204)  $false
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | |   (205)   ~ (all_56_9 = e3)
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | REDUCE: (47), (205) imply:
% 198.82/32.67  | | | | | | | | | |   (206)   ~ (all_52_13 = e3)
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | BETA: splitting (177) gives:
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | |   (207)  all_58_3 = e3
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | COMBINE_EQS: (114), (207) imply:
% 198.82/32.67  | | | | | | | | | | |   (208)  all_4_2 = e3
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | REDUCE: (161), (208) imply:
% 198.82/32.67  | | | | | | | | | | |   (209)  $false
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | |   (210)  all_58_7 = e3 | all_58_13 = e3
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | BETA: splitting (210) gives:
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | |   (211)  all_58_7 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | COMBINE_EQS: (51), (211) imply:
% 198.82/32.67  | | | | | | | | | | | |   (212)  all_52_13 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | REDUCE: (206), (212) imply:
% 198.82/32.67  | | | | | | | | | | | |   (213)  $false
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | |   (214)  all_58_13 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | COMBINE_EQS: (27), (214) imply:
% 198.82/32.67  | | | | | | | | | | | |   (215)  all_52_15 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | SIMP: (215) implies:
% 198.82/32.67  | | | | | | | | | | | |   (216)  all_52_15 = e3
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | | REF_CLOSE: (4), (9), (13), (16), (17), (18), (22), (32),
% 198.82/32.67  | | | | | | | | | | | |            (39), (41), (43), (53), (54), (56), (67), (69),
% 198.82/32.67  | | | | | | | | | | | |            (71), (77), (80), (81), (89), (91), (95), (96),
% 198.82/32.67  | | | | | | | | | | | |            (97), (106), (107), (111), (113), (117), (214),
% 198.82/32.67  | | | | | | | | | | | |            (216) are inconsistent by sub-proof #267.
% 198.82/32.67  | | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | End of split
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | End of split
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | End of split
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | Case 2:
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | |   (217)   ~ (all_58_9 = e3)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (29), (217) imply:
% 198.82/32.67  | | | | | |   (218)   ~ (all_52_25 = e3)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REF_CLOSE: (9), (11), (21), (29), (89), (91), (93), (111), (119),
% 198.82/32.67  | | | | | |            (143), (159), (218) are inconsistent by sub-proof #254.
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | End of split
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | Case 2:
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | |   (219)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | BETA: splitting (219) gives:
% 198.82/32.67  | | | | | 
% 198.82/32.67  | | | | | Case 1:
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | |   (220)  all_58_3 = e3
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | COMBINE_EQS: (114), (220) imply:
% 198.82/32.67  | | | | | |   (221)  all_4_2 = e3
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (85), (221) imply:
% 198.82/32.67  | | | | | |   (222)   ~ (all_52_9 = e3)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (97), (221) imply:
% 198.82/32.67  | | | | | |   (223)   ~ (all_52_15 = e3)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (88), (221) imply:
% 198.82/32.67  | | | | | |   (224)  op(e3, e3) = e2
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (35), (221) imply:
% 198.82/32.67  | | | | | |   (225)  op(e3, e2) = e1
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | GROUND_INST: instantiating (9) with all_52_9, e1, e2, e3,
% 198.82/32.67  | | | | | |              simplifying with (101), (225) gives:
% 198.82/32.67  | | | | | |   (226)  all_52_9 = e1
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | GROUND_INST: instantiating (9) with all_6_2, e2, e3, e3, simplifying
% 198.82/32.67  | | | | | |              with (91), (224) gives:
% 198.82/32.67  | | | | | |   (227)  all_6_2 = e2
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | COMBINE_EQS: (11), (226) imply:
% 198.82/32.67  | | | | | |   (228)  all_58_1 = e1
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | COMBINE_EQS: (21), (227) imply:
% 198.82/32.67  | | | | | |   (229)  all_58_0 = e2
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (20), (227) imply:
% 198.82/32.67  | | | | | |   (230)   ~ (all_52_3 = e2)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (107), (226) imply:
% 198.82/32.67  | | | | | |   (231)   ~ (all_52_17 = e1)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | SIMP: (231) implies:
% 198.82/32.67  | | | | | |   (232)   ~ (all_52_17 = e1)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (73), (226) imply:
% 198.82/32.67  | | | | | |   (233)   ~ (all_52_25 = e1)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | SIMP: (233) implies:
% 198.82/32.67  | | | | | |   (234)   ~ (all_52_25 = e1)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (89), (226), (227) imply:
% 198.82/32.67  | | | | | |   (235)   ~ (e2 = e1)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (222), (226) imply:
% 198.82/32.67  | | | | | |   (236)   ~ (e3 = e1)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (103), (227) imply:
% 198.82/32.67  | | | | | |   (237)   ~ (all_52_17 = e2)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (84), (227) imply:
% 198.82/32.67  | | | | | |   (238)   ~ (all_52_25 = e2)
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (111), (226) imply:
% 198.82/32.67  | | | | | |   (239)  op(e1, e1) = e3
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | REDUCE: (117), (227) imply:
% 198.82/32.67  | | | | | |   (240)  op(e2, e3) = all_6_1
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | BETA: splitting (93) gives:
% 198.82/32.67  | | | | | | 
% 198.82/32.67  | | | | | | Case 1:
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | |   (241)  all_58_0 = e3
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | | REF_CLOSE: (105), (229), (241) are inconsistent by sub-proof
% 198.82/32.67  | | | | | | |            #1235.
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | Case 2:
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | |   (242)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | | BETA: splitting (146) gives:
% 198.82/32.67  | | | | | | | 
% 198.82/32.67  | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | |   (243)  all_56_2 = e2
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | COMBINE_EQS: (58), (243) imply:
% 198.82/32.67  | | | | | | | |   (244)  all_52_17 = e2
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | REDUCE: (237), (244) imply:
% 198.82/32.67  | | | | | | | |   (245)  $false
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | CLOSE: (245) is inconsistent.
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | Case 2:
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | |   (246)  all_56_2 = e1 | all_56_2 = e0
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | BETA: splitting (246) gives:
% 198.82/32.67  | | | | | | | | 
% 198.82/32.67  | | | | | | | | Case 1:
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | |   (247)  all_56_2 = e1
% 198.82/32.67  | | | | | | | | | 
% 198.82/32.67  | | | | | | | | | COMBINE_EQS: (58), (247) imply:
% 198.82/32.68  | | | | | | | | |   (248)  all_52_17 = e1
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | REDUCE: (232), (248) imply:
% 198.82/32.68  | | | | | | | | |   (249)  $false
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | CLOSE: (249) is inconsistent.
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | |   (250)  all_56_2 = e0
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | COMBINE_EQS: (58), (250) imply:
% 198.82/32.68  | | | | | | | | |   (251)  all_52_17 = e0
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | COMBINE_EQS: (119), (251) imply:
% 198.82/32.68  | | | | | | | | |   (252)  all_58_4 = e0
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | REDUCE: (116), (251) imply:
% 198.82/32.68  | | | | | | | | |   (253)   ~ (all_52_23 = e0)
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | SIMP: (253) implies:
% 198.82/32.68  | | | | | | | | |   (254)   ~ (all_52_23 = e0)
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | REDUCE: (23), (251) imply:
% 198.82/32.68  | | | | | | | | |   (255)   ~ (all_10_2 = e0)
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | SIMP: (255) implies:
% 198.82/32.68  | | | | | | | | |   (256)   ~ (all_10_2 = e0)
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | REDUCE: (143), (251) imply:
% 198.82/32.68  | | | | | | | | |   (257)   ~ (e3 = e0)
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | REDUCE: (82), (251) imply:
% 198.82/32.68  | | | | | | | | |   (258)  op(e0, e0) = all_52_16
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | BETA: splitting (242) gives:
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | Case 1:
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | |   (259)  all_58_1 = e3
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | REF_CLOSE: (5), (228), (259) are inconsistent by sub-proof
% 198.82/32.68  | | | | | | | | | |            #96.
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | |   (260)  all_58_4 = e3 | all_58_9 = e3
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | BETA: splitting (260) gives:
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | Case 1:
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | |   (261)  all_58_4 = e3
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | REF_CLOSE: (13), (252), (261) are inconsistent by sub-proof
% 198.82/32.68  | | | | | | | | | | |            #95.
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | |   (262)  all_58_9 = e3
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | COMBINE_EQS: (29), (262) imply:
% 198.82/32.68  | | | | | | | | | | |   (263)  all_52_25 = e3
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | REDUCE: (38), (263) imply:
% 198.82/32.68  | | | | | | | | | | |   (264)   ~ (all_14_2 = e3)
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | GROUND_INST: instantiating (9) with all_14_2, all_52_16, e0,
% 198.82/32.68  | | | | | | | | | | |              e0, simplifying with (42), (258) gives:
% 198.82/32.68  | | | | | | | | | | |   (265)  all_52_16 = all_14_2
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | GROUND_INST: instantiating (9) with all_10_2, e3, e1, e1,
% 198.82/32.68  | | | | | | | | | | |              simplifying with (110), (239) gives:
% 198.82/32.68  | | | | | | | | | | |   (266)  all_10_2 = e3
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | GROUND_INST: instantiating (9) with all_52_3, all_6_1, e3, e2,
% 198.82/32.68  | | | | | | | | | | |              simplifying with (14), (240) gives:
% 198.82/32.68  | | | | | | | | | | |   (267)  all_52_3 = all_6_1
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | REDUCE: (230), (267) imply:
% 198.82/32.68  | | | | | | | | | | |   (268)   ~ (all_6_1 = e2)
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | BETA: splitting (102) gives:
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | Case 1:
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | |   (269)  all_58_12 = e3
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | BETA: splitting (67) gives:
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | Case 1:
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | |   (270)  all_58_12 = e0
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | COMBINE_EQS: (269), (270) imply:
% 198.82/32.68  | | | | | | | | | | | | |   (271)  e3 = e0
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | COMBINE_EQS: (262), (271) imply:
% 198.82/32.68  | | | | | | | | | | | | |   (272)  all_58_9 = e0
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | REF_CLOSE: (13), (119), (143), (260), (272) are inconsistent
% 198.82/32.68  | | | | | | | | | | | | |            by sub-proof #210.
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | |   (273)  all_58_13 = e0 | all_58_14 = e0
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | BETA: splitting (273) gives:
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | Case 1:
% 198.82/32.68  | | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | |   (274)  all_58_13 = e0
% 198.82/32.68  | | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | | REF_CLOSE: (9), (18), (27), (42), (65), (274) are
% 198.82/32.68  | | | | | | | | | | | | | |            inconsistent by sub-proof #1100.
% 198.82/32.68  | | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | |   (275)  all_58_14 = e0
% 198.82/32.68  | | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | | REF_CLOSE: (4), (254), (275) are inconsistent by sub-proof
% 198.82/32.68  | | | | | | | | | | | | | |            #1019.
% 198.82/32.68  | | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | |   (276)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | BETA: splitting (276) gives:
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | Case 1:
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | |   (277)  all_58_13 = e3
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | REF_CLOSE: (27), (223), (277) are inconsistent by sub-proof
% 198.82/32.68  | | | | | | | | | | | | |            #1360.
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | Case 2:
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | |   (278)  all_58_14 = e3 | all_58_15 = e3
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (11), (15), (18),
% 198.82/32.68  | | | | | | | | | | | | |            (21), (26), (27), (28), (29), (30), (31), (32),
% 198.82/32.68  | | | | | | | | | | | | |            (34), (35), (36), (37), (42), (44), (48), (49),
% 198.82/32.68  | | | | | | | | | | | | |            (50), (51), (52), (53), (55), (57), (59), (62),
% 198.82/32.68  | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (72), (73), (74),
% 198.82/32.68  | | | | | | | | | | | | |            (75), (76), (78), (79), (83), (86), (87), (89),
% 198.82/32.68  | | | | | | | | | | | | |            (91), (94), (96), (97), (98), (99), (100), (101),
% 198.82/32.68  | | | | | | | | | | | | |            (105), (106), (110), (111), (112), (113), (114),
% 198.82/32.68  | | | | | | | | | | | | |            (115), (117), (121), (268), (278) are inconsistent
% 198.82/32.68  | | | | | | | | | | | | |            by sub-proof #190.
% 198.82/32.68  | | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | | | 
% 198.82/32.68  | | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | | 
% 198.82/32.68  | | | | | | | | End of split
% 198.82/32.68  | | | | | | | | 
% 198.82/32.68  | | | | | | | End of split
% 198.82/32.68  | | | | | | | 
% 198.82/32.68  | | | | | | End of split
% 198.82/32.68  | | | | | | 
% 198.82/32.68  | | | | | Case 2:
% 198.82/32.68  | | | | | | 
% 198.82/32.68  | | | | | |   (279)  all_58_5 = e3 | all_58_10 = e3
% 198.82/32.68  | | | | | | 
% 198.82/32.68  | | | | | | REF_CLOSE: (45), (49), (83), (152), (279) are inconsistent by
% 198.82/32.68  | | | | | |            sub-proof #214.
% 198.82/32.68  | | | | | | 
% 198.82/32.68  | | | | | End of split
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | End of split
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | End of split
% 198.82/32.68  | | | 
% 198.82/32.68  | | End of split
% 198.82/32.68  | | 
% 198.82/32.68  | End of split
% 198.82/32.68  | 
% 198.82/32.68  End of proof
% 198.82/32.68  
% 198.82/32.68  Sub-proof #34 shows that the following formulas are inconsistent:
% 198.82/32.68  ----------------------------------------------------------------
% 198.82/32.68    (1)  all_58_14 = all_52_23
% 198.82/32.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.68    (3)   ~ (e3 = e0)
% 198.82/32.68    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.68    (5)   ~ (all_52_7 = all_52_15)
% 198.82/32.68    (6)  op(all_52_15, all_52_15) = e0
% 198.82/32.68    (7)  op(e3, all_6_1) = e1
% 198.82/32.68    (8)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.68    (9)  all_58_13 = all_52_15
% 198.82/32.68    (10)  op(e2, e2) = all_4_2
% 198.82/32.68    (11)   ~ (all_52_9 = all_52_15)
% 198.82/32.68    (12)   ~ (all_52_7 = all_6_2)
% 198.82/32.68    (13)  all_56_15 = all_14_2
% 198.82/32.68    (14)  all_58_12 = all_52_7
% 198.82/32.68    (15)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.68    (16)   ~ (all_52_7 = all_14_2)
% 198.82/32.68    (17)   ~ (all_52_23 = e3)
% 198.82/32.68    (18)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.82/32.68    (19)  op(e3, e1) = all_52_17
% 198.82/32.68    (20)  op(e0, e3) = all_52_7
% 198.82/32.68    (21)  all_58_15 = all_14_2
% 198.82/32.68    (22)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.68    (23)   ~ (all_52_23 = all_14_2)
% 198.82/32.68    (24)  all_56_12 = all_52_7
% 198.82/32.68    (25)   ~ (all_52_9 = all_6_2)
% 198.82/32.68    (26)  op(e3, e3) = all_6_2
% 198.82/32.68    (27)  op(all_14_2, all_14_2) = all_52_30
% 198.82/32.68    (28)  all_56_1 = all_52_9
% 198.82/32.68    (29)   ~ (all_52_15 = all_4_2)
% 198.82/32.68    (30)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.82/32.68    (31)   ~ (all_52_9 = all_52_17)
% 198.82/32.68    (32)  op(all_52_9, all_52_9) = e3
% 198.82/32.68    (33)   ~ (all_52_7 = all_52_23)
% 198.82/32.68    (34)  op(all_6_2, e3) = all_6_1
% 198.82/32.68    (35)   ~ (all_14_2 = e3)
% 198.82/32.68  
% 198.82/32.68  Begin of proof
% 198.82/32.68  | 
% 198.82/32.68  | BETA: splitting (8) gives:
% 198.82/32.68  | 
% 198.82/32.68  | Case 1:
% 198.82/32.68  | | 
% 198.82/32.68  | |   (36)  all_58_13 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | COMBINE_EQS: (9), (36) imply:
% 198.82/32.68  | |   (37)  all_52_15 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | SIMP: (37) implies:
% 198.82/32.68  | |   (38)  all_52_15 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 198.82/32.68  | |            (15), (16), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 198.82/32.68  | |            (28), (29), (30), (31), (32), (33), (34), (36), (38) are
% 198.82/32.68  | |            inconsistent by sub-proof #267.
% 198.82/32.68  | | 
% 198.82/32.68  | Case 2:
% 198.82/32.68  | | 
% 198.82/32.68  | |   (39)  all_58_14 = e3 | all_58_15 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | REF_CLOSE: (1), (17), (21), (35), (39) are inconsistent by sub-proof #715.
% 198.82/32.68  | | 
% 198.82/32.68  | End of split
% 198.82/32.68  | 
% 198.82/32.68  End of proof
% 198.82/32.68  
% 198.82/32.68  Sub-proof #35 shows that the following formulas are inconsistent:
% 198.82/32.68  ----------------------------------------------------------------
% 198.82/32.68    (1)  all_58_14 = all_52_23
% 198.82/32.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.68    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.68    (4)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.68    (5)  op(all_14_2, e0) = all_14_1
% 198.82/32.68    (6)  op(e3, all_6_1) = e1
% 198.82/32.68    (7)   ~ (all_52_17 = all_10_2)
% 198.82/32.68    (8)  op(e3, e0) = all_52_25
% 198.82/32.68    (9)  op(all_10_2, all_10_2) = all_52_20
% 198.82/32.68    (10)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 198.82/32.68    (11)  op(e1, e3) = all_52_5
% 198.82/32.68    (12)  op(all_10_2, e1) = all_10_1
% 198.82/32.68    (13)   ~ (all_52_7 = all_6_2)
% 198.82/32.68    (14)  op(e0, e0) = all_14_2
% 198.82/32.68    (15)  all_56_15 = all_14_2
% 198.82/32.68    (16)   ~ (all_4_0 = e3)
% 198.82/32.68    (17)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.68    (18)  all_56_8 = all_52_5
% 198.82/32.68    (19)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.68    (20)  all_56_2 = all_52_17
% 198.82/32.68    (21)  op(e3, e1) = all_52_17
% 198.82/32.68    (22)  op(e0, e3) = all_52_7
% 198.82/32.68    (23)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.68    (24)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.82/32.68    (25)   ~ (all_10_1 = e2)
% 198.82/32.68    (26)  all_58_8 = all_10_2
% 198.82/32.68    (27)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.68    (28)   ~ (all_52_5 = all_10_2)
% 198.82/32.68    (29)   ~ (all_52_23 = all_14_2)
% 198.82/32.68    (30)  all_56_12 = all_52_7
% 198.82/32.68    (31)  op(all_52_17, all_52_17) = all_52_16
% 198.82/32.68    (32)  all_58_5 = all_4_0
% 198.82/32.68    (33)   ~ (all_52_25 = all_6_2)
% 198.82/32.68    (34)   ~ (all_52_5 = all_6_2)
% 198.82/32.68    (35)   ~ (all_52_9 = all_6_2)
% 198.82/32.68    (36)  op(e3, e3) = all_6_2
% 198.82/32.68    (37)  op(all_14_2, all_14_2) = all_52_30
% 198.82/32.68    (38)  all_58_6 = all_52_5
% 198.82/32.68    (39)  op(e3, e2) = all_52_9
% 198.82/32.68    (40)   ~ (all_52_17 = all_6_2)
% 198.82/32.68    (41)  all_56_10 = all_10_2
% 198.82/32.68    (42)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.68    (43)  op(e1, e1) = all_10_2
% 198.82/32.68    (44)   ~ (all_52_23 = all_10_2)
% 198.82/32.68    (45)   ~ (all_52_7 = all_52_23)
% 198.82/32.68    (46)  op(all_6_2, e3) = all_6_1
% 198.82/32.68    (47)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.82/32.68    (48)  all_58_4 = all_52_17
% 198.82/32.68    (49)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 198.82/32.68  
% 198.82/32.68  Begin of proof
% 198.82/32.68  | 
% 198.82/32.68  | ALPHA: (47) implies:
% 198.82/32.68  |   (50)  all_52_22 = e0
% 198.82/32.68  |   (51)  all_52_20 = e1
% 198.82/32.68  |   (52)  all_52_16 = e3
% 198.82/32.68  | 
% 198.82/32.68  | REDUCE: (31), (52) imply:
% 198.82/32.68  |   (53)  op(all_52_17, all_52_17) = e3
% 198.82/32.68  | 
% 198.82/32.68  | REDUCE: (23), (50) imply:
% 198.82/32.68  |   (54)  op(all_52_23, all_52_23) = e0
% 198.82/32.68  | 
% 198.82/32.68  | REDUCE: (9), (51) imply:
% 198.82/32.68  |   (55)  op(all_10_2, all_10_2) = e1
% 198.82/32.68  | 
% 198.82/32.68  | BETA: splitting (27) gives:
% 198.82/32.68  | 
% 198.82/32.68  | Case 1:
% 198.82/32.68  | | 
% 198.82/32.68  | |   (56)  all_56_15 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | COMBINE_EQS: (15), (56) imply:
% 198.82/32.68  | |   (57)  all_14_2 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | SIMP: (57) implies:
% 198.82/32.68  | |   (58)  all_14_2 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | REDUCE: (29), (58) imply:
% 198.82/32.68  | |   (59)   ~ (all_52_23 = e3)
% 198.82/32.68  | | 
% 198.82/32.68  | | REDUCE: (37), (58) imply:
% 198.82/32.68  | |   (60)  op(e3, e3) = all_52_30
% 198.82/32.68  | | 
% 198.82/32.68  | | REDUCE: (5), (58) imply:
% 198.82/32.68  | |   (61)  op(e3, e0) = all_14_1
% 198.82/32.68  | | 
% 198.82/32.68  | | GROUND_INST: instantiating (2) with all_52_25, all_14_1, e0, e3, simplifying
% 198.82/32.68  | |              with (8), (61) gives:
% 198.82/32.68  | |   (62)  all_52_25 = all_14_1
% 198.82/32.68  | | 
% 198.82/32.68  | | GROUND_INST: instantiating (2) with all_6_2, all_52_30, e3, e3, simplifying
% 198.82/32.68  | |              with (36), (60) gives:
% 198.82/32.68  | |   (63)  all_52_30 = all_6_2
% 198.82/32.68  | | 
% 198.82/32.68  | | REDUCE: (33), (62) imply:
% 198.82/32.68  | |   (64)   ~ (all_14_1 = all_6_2)
% 198.82/32.68  | | 
% 198.82/32.68  | | BETA: splitting (42) gives:
% 198.82/32.68  | | 
% 198.82/32.68  | | Case 1:
% 198.82/32.68  | | | 
% 198.82/32.68  | | |   (65)  all_58_4 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | COMBINE_EQS: (48), (65) imply:
% 198.82/32.68  | | |   (66)  all_52_17 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | SIMP: (66) implies:
% 198.82/32.68  | | |   (67)  all_52_17 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | REF_CLOSE: (2), (36), (40), (53), (67) are inconsistent by sub-proof
% 198.82/32.68  | | |            #1280.
% 198.82/32.68  | | | 
% 198.82/32.68  | | Case 2:
% 198.82/32.68  | | | 
% 198.82/32.68  | | |   (68)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | BETA: splitting (68) gives:
% 198.82/32.68  | | | 
% 198.82/32.68  | | | Case 1:
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | |   (69)  all_58_5 = e3
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REF_CLOSE: (16), (32), (69) are inconsistent by sub-proof #215.
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | Case 2:
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | |   (70)  all_58_8 = e3 | all_58_14 = e3
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | BETA: splitting (70) gives:
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | Case 1:
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | |   (71)  all_58_8 = e3
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | COMBINE_EQS: (26), (71) imply:
% 198.82/32.68  | | | | |   (72)  all_10_2 = e3
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | SIMP: (72) implies:
% 198.82/32.68  | | | | |   (73)  all_10_2 = e3
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | REDUCE: (28), (73) imply:
% 198.82/32.68  | | | | |   (74)   ~ (all_52_5 = e3)
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | REDUCE: (55), (73) imply:
% 198.82/32.68  | | | | |   (75)  op(e3, e3) = e1
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | GROUND_INST: instantiating (2) with all_6_2, e1, e3, e3, simplifying
% 198.82/32.68  | | | | |              with (36), (75) gives:
% 198.82/32.68  | | | | |   (76)  all_6_2 = e1
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | REF_CLOSE: (2), (6), (10), (11), (18), (24), (34), (35), (38), (39),
% 198.82/32.68  | | | | |            (46), (61), (64), (74), (76) are inconsistent by sub-proof
% 198.82/32.68  | | | | |            #301.
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | Case 2:
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | |   (77)  all_58_14 = e3
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | | REF_CLOSE: (1), (59), (77) are inconsistent by sub-proof #1305.
% 198.82/32.68  | | | | | 
% 198.82/32.68  | | | | End of split
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | End of split
% 198.82/32.68  | | | 
% 198.82/32.68  | | End of split
% 198.82/32.68  | | 
% 198.82/32.68  | Case 2:
% 198.82/32.68  | | 
% 198.82/32.68  | |   (78)   ~ (all_56_15 = e3)
% 198.82/32.68  | | 
% 198.82/32.68  | | REDUCE: (15), (78) imply:
% 198.82/32.68  | |   (79)   ~ (all_14_2 = e3)
% 198.82/32.68  | | 
% 198.82/32.68  | | BETA: splitting (42) gives:
% 198.82/32.68  | | 
% 198.82/32.68  | | Case 1:
% 198.82/32.68  | | | 
% 198.82/32.68  | | |   (80)  all_58_4 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | COMBINE_EQS: (48), (80) imply:
% 198.82/32.68  | | |   (81)  all_52_17 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | SIMP: (81) implies:
% 198.82/32.68  | | |   (82)  all_52_17 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | REF_CLOSE: (2), (36), (40), (53), (82) are inconsistent by sub-proof
% 198.82/32.68  | | |            #1280.
% 198.82/32.68  | | | 
% 198.82/32.68  | | Case 2:
% 198.82/32.68  | | | 
% 198.82/32.68  | | |   (83)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | BETA: splitting (49) gives:
% 198.82/32.68  | | | 
% 198.82/32.68  | | | Case 1:
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | |   (84)  all_56_10 = e3
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | COMBINE_EQS: (41), (84) imply:
% 198.82/32.68  | | | |   (85)  all_10_2 = e3
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | SIMP: (85) implies:
% 198.82/32.68  | | | |   (86)  all_10_2 = e3
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REDUCE: (7), (86) imply:
% 198.82/32.68  | | | |   (87)   ~ (all_52_17 = e3)
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REDUCE: (55), (86) imply:
% 198.82/32.68  | | | |   (88)  op(e3, e3) = e1
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REDUCE: (12), (86) imply:
% 198.82/32.68  | | | |   (89)  op(e3, e1) = all_10_1
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REF_CLOSE: (2), (14), (17), (20), (21), (25), (36), (40), (53), (79),
% 198.82/32.68  | | | |            (87), (88), (89) are inconsistent by sub-proof #202.
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | Case 2:
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | |   (90)   ~ (all_56_10 = e3)
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REDUCE: (41), (90) imply:
% 198.82/32.68  | | | |   (91)   ~ (all_10_2 = e3)
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (13), (16), (19), (21), (22), (26),
% 198.82/32.68  | | | |            (30), (32), (36), (43), (44), (45), (46), (53), (54), (83),
% 198.82/32.68  | | | |            (91) are inconsistent by sub-proof #36.
% 198.82/32.68  | | | | 
% 198.82/32.68  | | | End of split
% 198.82/32.68  | | | 
% 198.82/32.68  | | End of split
% 198.82/32.68  | | 
% 198.82/32.68  | End of split
% 198.82/32.68  | 
% 198.82/32.68  End of proof
% 198.82/32.68  
% 198.82/32.68  Sub-proof #36 shows that the following formulas are inconsistent:
% 198.82/32.68  ----------------------------------------------------------------
% 198.82/32.68    (1)  all_58_14 = all_52_23
% 198.82/32.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.68    (3)  op(all_52_23, all_52_23) = e0
% 198.82/32.68    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.68    (5)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.68    (6)  op(e3, all_6_1) = e1
% 198.82/32.68    (7)   ~ (all_52_7 = all_6_2)
% 198.82/32.68    (8)   ~ (all_4_0 = e3)
% 198.82/32.68    (9)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.68    (10)   ~ (all_10_2 = e3)
% 198.82/32.68    (11)  op(e3, e1) = all_52_17
% 198.82/32.68    (12)  op(e0, e3) = all_52_7
% 198.82/32.68    (13)  all_58_8 = all_10_2
% 198.82/32.68    (14)  all_56_12 = all_52_7
% 198.82/32.68    (15)  all_58_5 = all_4_0
% 198.82/32.68    (16)  op(e3, e3) = all_6_2
% 198.82/32.68    (17)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.68    (18)  op(all_52_17, all_52_17) = e3
% 198.82/32.68    (19)  op(e1, e1) = all_10_2
% 198.82/32.68    (20)   ~ (all_52_23 = all_10_2)
% 198.82/32.68    (21)   ~ (all_52_7 = all_52_23)
% 198.82/32.68    (22)  op(all_6_2, e3) = all_6_1
% 198.82/32.68  
% 198.82/32.68  Begin of proof
% 198.82/32.68  | 
% 198.82/32.68  | BETA: splitting (17) gives:
% 198.82/32.68  | 
% 198.82/32.68  | Case 1:
% 198.82/32.68  | | 
% 198.82/32.68  | |   (23)  all_58_5 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | REF_CLOSE: (8), (15), (23) are inconsistent by sub-proof #215.
% 198.82/32.68  | | 
% 198.82/32.68  | Case 2:
% 198.82/32.68  | | 
% 198.82/32.68  | |   (24)  all_58_8 = e3 | all_58_14 = e3
% 198.82/32.68  | | 
% 198.82/32.68  | | BETA: splitting (24) gives:
% 198.82/32.68  | | 
% 198.82/32.68  | | Case 1:
% 198.82/32.68  | | | 
% 198.82/32.68  | | |   (25)  all_58_8 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | REF_CLOSE: (10), (13), (25) are inconsistent by sub-proof #950.
% 198.82/32.68  | | | 
% 198.82/32.68  | | Case 2:
% 198.82/32.68  | | | 
% 198.82/32.68  | | |   (26)  all_58_14 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | COMBINE_EQS: (1), (26) imply:
% 198.82/32.68  | | |   (27)  all_52_23 = e3
% 198.82/32.68  | | | 
% 198.82/32.68  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (12), (14), (16),
% 198.82/32.68  | | |            (18), (19), (20), (21), (22), (27) are inconsistent by
% 198.82/32.68  | | |            sub-proof #37.
% 198.82/32.68  | | | 
% 198.82/32.68  | | End of split
% 198.82/32.68  | | 
% 198.82/32.68  | End of split
% 198.82/32.68  | 
% 198.82/32.68  End of proof
% 198.82/32.68  
% 198.82/32.68  Sub-proof #37 shows that the following formulas are inconsistent:
% 198.82/32.68  ----------------------------------------------------------------
% 198.82/32.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.68    (2)  op(all_52_23, all_52_23) = e0
% 198.82/32.68    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.68    (4)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.68    (5)  op(e3, all_6_1) = e1
% 198.82/32.68    (6)   ~ (all_52_7 = all_6_2)
% 198.82/32.68    (7)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.68    (8)  op(e3, e1) = all_52_17
% 198.82/32.68    (9)  op(e0, e3) = all_52_7
% 198.82/32.68    (10)  all_56_12 = all_52_7
% 198.82/32.68    (11)  op(e3, e3) = all_6_2
% 198.82/32.68    (12)  op(all_52_17, all_52_17) = e3
% 198.82/32.68    (13)  all_52_23 = e3
% 198.82/32.68    (14)  op(e1, e1) = all_10_2
% 198.82/32.68    (15)   ~ (all_52_23 = all_10_2)
% 198.82/32.68    (16)   ~ (all_52_7 = all_52_23)
% 198.82/32.68    (17)  op(all_6_2, e3) = all_6_1
% 198.82/32.68  
% 198.82/32.68  Begin of proof
% 198.82/32.68  | 
% 198.82/32.68  | SIMP: (13) implies:
% 198.82/32.68  |   (18)  all_52_23 = e3
% 198.82/32.68  | 
% 198.82/32.68  | REDUCE: (16), (18) imply:
% 198.82/32.68  |   (19)   ~ (all_52_7 = e3)
% 198.82/32.68  | 
% 198.82/32.68  | REDUCE: (15), (18) imply:
% 198.82/32.68  |   (20)   ~ (all_10_2 = e3)
% 198.82/32.68  | 
% 198.82/32.68  | SIMP: (20) implies:
% 198.82/32.68  |   (21)   ~ (all_10_2 = e3)
% 198.82/32.68  | 
% 198.82/32.68  | REDUCE: (2), (18) imply:
% 198.82/32.68  |   (22)  op(e3, e3) = e0
% 198.82/32.68  | 
% 198.82/32.68  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 198.82/32.68  |            (17), (19), (21), (22) are inconsistent by sub-proof #314.
% 198.82/32.68  | 
% 198.82/32.68  End of proof
% 198.82/32.68  
% 198.82/32.68  Sub-proof #38 shows that the following formulas are inconsistent:
% 198.82/32.68  ----------------------------------------------------------------
% 198.82/32.68    (1)  all_58_14 = all_52_23
% 198.82/32.68    (2)   ~ (all_52_17 = all_4_0)
% 198.82/32.68    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 198.82/32.68    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.68    (5)   ~ (all_52_5 = all_52_13)
% 198.82/32.68    (6)  all_58_1 = all_52_9
% 198.82/32.68    (7)   ~ (e3 = e0)
% 198.82/32.68    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.68    (9)   ~ (all_52_7 = all_52_15)
% 198.82/32.68    (10)  op(all_52_15, all_52_15) = e0
% 198.82/32.68    (11)   ~ (all_52_17 = all_52_25)
% 198.82/32.68    (12)  all_58_0 = all_6_2
% 198.82/32.68    (13)  op(e3, all_6_1) = e1
% 198.82/32.68    (14)   ~ (all_52_17 = all_10_2)
% 198.82/32.68    (15)  op(e3, e0) = all_52_25
% 198.82/32.68    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.68    (17)  all_58_13 = all_52_15
% 198.82/32.68    (18)  op(all_52_13, all_52_13) = e1
% 198.82/32.68    (19)  op(all_10_2, all_10_2) = all_52_20
% 198.82/32.68    (20)  all_58_9 = all_52_25
% 198.82/32.68    (21)  op(e1, e3) = all_52_5
% 198.82/32.68    (22)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 198.82/32.68    (23)  op(e2, e2) = all_4_2
% 198.82/32.68    (24)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.68    (25)   ~ (all_52_3 = all_52_5)
% 198.82/32.68    (26)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 198.82/32.68    (27)  op(all_4_2, e2) = e1
% 198.82/32.68    (28)   ~ (all_52_9 = all_52_15)
% 198.82/32.69    (29)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 198.82/32.69    (30)  op(all_10_2, e1) = all_10_1
% 198.82/32.69    (31)   ~ (all_52_7 = all_6_2)
% 198.82/32.69    (32)   ~ (all_52_15 = e0)
% 198.82/32.69    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.69    (34)  all_58_15 = e0
% 198.82/32.69    (35)   ~ (all_4_0 = e3)
% 198.82/32.69    (36)   ~ (all_52_25 = e0)
% 198.82/32.69    (37)   ~ (e2 = e1)
% 198.82/32.69    (38)   ~ (all_52_13 = all_10_2)
% 198.82/32.69    (39)  op(e0, e0) = e0
% 198.82/32.69    (40)  all_58_10 = all_52_27
% 198.82/32.69    (41)  all_58_7 = all_52_13
% 198.82/32.69    (42)  all_58_12 = all_52_7
% 198.82/32.69    (43)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.69    (44)  all_58_2 = all_52_3
% 198.82/32.69    (45)  all_56_7 = all_52_27
% 198.82/32.69    (46)   ~ (e2 = e0)
% 198.82/32.69    (47)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.82/32.69    (48)   ~ (all_52_23 = e3)
% 198.82/32.69    (49)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.82/32.69    (50)   ~ (all_52_13 = all_4_2)
% 198.82/32.69    (51)  op(e3, e1) = all_52_17
% 198.82/32.69    (52)  op(e0, e3) = all_52_7
% 198.82/32.69    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.69    (54)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.69    (55)  all_58_8 = all_10_2
% 198.82/32.69    (56)   ~ (all_52_23 = e0)
% 198.82/32.69    (57)  all_56_12 = all_52_7
% 198.82/32.69    (58)  all_58_5 = all_4_0
% 198.82/32.69    (59)   ~ (all_52_25 = all_6_2)
% 198.82/32.69    (60)   ~ (all_52_9 = all_4_2)
% 198.82/32.69    (61)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.69    (62)   ~ (all_52_9 = all_6_2)
% 198.82/32.69    (63)  op(e3, e3) = all_6_2
% 198.82/32.69    (64)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.69    (65)   ~ (all_52_3 = all_52_7)
% 198.82/32.69    (66)  all_56_1 = all_52_9
% 198.82/32.69    (67)   ~ (all_52_15 = all_4_2)
% 198.82/32.69    (68)   ~ (all_52_27 = all_4_2)
% 198.82/32.69    (69)  all_58_6 = all_52_5
% 198.82/32.69    (70)  op(e3, e2) = all_52_9
% 198.82/32.69    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.69    (72)   ~ (all_52_17 = all_6_2)
% 198.82/32.69    (73)   ~ (e1 = e0)
% 198.82/32.69    (74)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 198.82/32.69    (75)   ~ (e3 = e2)
% 198.82/32.69    (76)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.82/32.69    (77)   ~ (all_52_9 = all_52_17)
% 198.82/32.69    (78)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.69    (79)  op(e1, e1) = all_10_2
% 198.82/32.69    (80)  op(all_52_9, all_52_9) = e3
% 198.82/32.69    (81)   ~ (all_52_7 = all_52_23)
% 198.82/32.69    (82)  all_58_3 = all_4_2
% 198.82/32.69    (83)   ~ (all_52_3 = all_4_2)
% 198.82/32.69    (84)   ~ (all_52_17 = all_52_23)
% 198.82/32.69    (85)  op(all_6_2, e3) = all_6_1
% 198.82/32.69    (86)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.82/32.69    (87)  all_58_4 = all_52_17
% 198.82/32.69    (88)   ~ (all_52_7 = e0)
% 198.82/32.69  
% 198.82/32.69  Begin of proof
% 198.82/32.69  | 
% 198.82/32.69  | BETA: splitting (78) gives:
% 198.82/32.69  | 
% 198.82/32.69  | Case 1:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (89)  all_58_4 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | COMBINE_EQS: (87), (89) imply:
% 198.82/32.69  | |   (90)  all_52_17 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | SIMP: (90) implies:
% 198.82/32.69  | |   (91)  all_52_17 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (77), (91) imply:
% 198.82/32.69  | |   (92)   ~ (all_52_9 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (84), (91) imply:
% 198.82/32.69  | |   (93)   ~ (all_52_23 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (14), (91) imply:
% 198.82/32.69  | |   (94)   ~ (all_10_2 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | SIMP: (94) implies:
% 198.82/32.69  | |   (95)   ~ (all_10_2 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (2), (91) imply:
% 198.82/32.69  | |   (96)   ~ (all_4_0 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13), (15), (16), (17),
% 198.82/32.69  | |            (18), (21), (23), (24), (27), (28), (29), (31), (33), (34), (35),
% 198.82/32.69  | |            (37), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 198.82/32.69  | |            (50), (51), (52), (53), (54), (57), (58), (59), (61), (62), (63),
% 198.82/32.69  | |            (65), (66), (67), (68), (69), (70), (71), (73), (75), (76), (77),
% 198.82/32.69  | |            (79), (80), (82), (85), (86), (88), (92), (95) are inconsistent
% 198.82/32.69  | |            by sub-proof #39.
% 198.82/32.69  | | 
% 198.82/32.69  | Case 2:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (97)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | BETA: splitting (71) gives:
% 198.82/32.69  | | 
% 198.82/32.69  | | Case 1:
% 198.82/32.69  | | | 
% 198.82/32.69  | | |   (98)  all_58_12 = e3
% 198.82/32.69  | | | 
% 198.82/32.69  | | | COMBINE_EQS: (42), (98) imply:
% 198.82/32.69  | | |   (99)  all_52_7 = e3
% 198.82/32.69  | | | 
% 198.82/32.69  | | | SIMP: (99) implies:
% 198.82/32.69  | | |   (100)  all_52_7 = e3
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REDUCE: (9), (100) imply:
% 198.82/32.69  | | |   (101)   ~ (all_52_15 = e3)
% 198.82/32.69  | | | 
% 198.82/32.69  | | | SIMP: (101) implies:
% 198.82/32.69  | | |   (102)   ~ (all_52_15 = e3)
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REDUCE: (81), (100) imply:
% 198.82/32.69  | | |   (103)   ~ (all_52_23 = e3)
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REDUCE: (31), (100) imply:
% 198.82/32.69  | | |   (104)   ~ (all_6_2 = e3)
% 198.82/32.69  | | | 
% 198.82/32.69  | | | SIMP: (104) implies:
% 198.82/32.69  | | |   (105)   ~ (all_6_2 = e3)
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REF_CLOSE: (1), (3), (4), (5), (6), (11), (12), (14), (17), (18), (19),
% 198.82/32.69  | | |            (20), (22), (23), (24), (25), (26), (30), (32), (35), (36),
% 198.82/32.69  | | |            (38), (39), (41), (44), (48), (51), (53), (55), (56), (58),
% 198.82/32.69  | | |            (60), (61), (62), (63), (64), (69), (72), (73), (74), (77),
% 198.82/32.69  | | |            (80), (82), (83), (87), (97), (98), (102), (105) are
% 198.82/32.69  | | |            inconsistent by sub-proof #207.
% 198.82/32.69  | | | 
% 198.82/32.69  | | Case 2:
% 198.82/32.69  | | | 
% 198.82/32.69  | | |   (106)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (13), (17), (23), (28), (29),
% 198.82/32.69  | | |            (31), (34), (42), (43), (46), (48), (51), (52), (54), (57),
% 198.82/32.69  | | |            (62), (63), (66), (67), (75), (76), (77), (80), (85), (106) are
% 198.82/32.69  | | |            inconsistent by sub-proof #40.
% 198.82/32.69  | | | 
% 198.82/32.69  | | End of split
% 198.82/32.69  | | 
% 198.82/32.69  | End of split
% 198.82/32.69  | 
% 198.82/32.69  End of proof
% 198.82/32.69  
% 198.82/32.69  Sub-proof #39 shows that the following formulas are inconsistent:
% 198.82/32.69  ----------------------------------------------------------------
% 198.82/32.69    (1)  all_58_14 = all_52_23
% 198.82/32.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.69    (3)  all_58_1 = all_52_9
% 198.82/32.69    (4)   ~ (e3 = e0)
% 198.82/32.69    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.69    (6)   ~ (all_52_7 = all_52_15)
% 198.82/32.69    (7)  op(all_52_15, all_52_15) = e0
% 198.82/32.69    (8)  all_58_0 = all_6_2
% 198.82/32.69    (9)  op(e3, all_6_1) = e1
% 198.82/32.69    (10)  op(e3, e0) = all_52_25
% 198.82/32.69    (11)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.69    (12)  all_58_13 = all_52_15
% 198.82/32.69    (13)  op(all_52_13, all_52_13) = e1
% 198.82/32.69    (14)  op(e1, e3) = all_52_5
% 198.82/32.69    (15)  op(e2, e2) = all_4_2
% 198.82/32.69    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.69    (17)  op(all_4_2, e2) = e1
% 198.82/32.69    (18)   ~ (all_52_9 = all_52_15)
% 198.82/32.69    (19)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 198.82/32.69    (20)   ~ (all_52_7 = all_6_2)
% 198.82/32.69    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.69    (22)  all_58_15 = e0
% 198.82/32.69    (23)   ~ (all_4_0 = e3)
% 198.82/32.69    (24)   ~ (e2 = e1)
% 198.82/32.69    (25)  all_58_10 = all_52_27
% 198.82/32.69    (26)  all_58_7 = all_52_13
% 198.82/32.69    (27)  all_58_12 = all_52_7
% 198.82/32.69    (28)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.69    (29)  all_58_2 = all_52_3
% 198.82/32.69    (30)  all_56_7 = all_52_27
% 198.82/32.69    (31)   ~ (e2 = e0)
% 198.82/32.69    (32)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.82/32.69    (33)   ~ (all_52_23 = e3)
% 198.82/32.69    (34)   ~ (all_10_2 = e3)
% 198.82/32.69    (35)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.82/32.69    (36)   ~ (all_52_9 = e3)
% 198.82/32.69    (37)   ~ (all_52_13 = all_4_2)
% 198.82/32.69    (38)  op(e3, e1) = all_52_17
% 198.82/32.69    (39)  op(e0, e3) = all_52_7
% 198.82/32.69    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.69    (41)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.69    (42)  all_56_12 = all_52_7
% 198.82/32.69    (43)  all_58_5 = all_4_0
% 198.82/32.69    (44)   ~ (all_52_25 = all_6_2)
% 198.82/32.69    (45)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.69    (46)   ~ (all_52_9 = all_6_2)
% 198.82/32.69    (47)  op(e3, e3) = all_6_2
% 198.82/32.69    (48)   ~ (all_52_3 = all_52_7)
% 198.82/32.69    (49)  all_56_1 = all_52_9
% 198.82/32.69    (50)   ~ (all_52_15 = all_4_2)
% 198.82/32.69    (51)   ~ (all_52_27 = all_4_2)
% 198.82/32.69    (52)  all_58_6 = all_52_5
% 198.82/32.69    (53)  op(e3, e2) = all_52_9
% 198.82/32.69    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.69    (55)   ~ (e1 = e0)
% 198.82/32.69    (56)   ~ (e3 = e2)
% 198.82/32.69    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.82/32.69    (58)   ~ (all_52_9 = all_52_17)
% 198.82/32.69    (59)  op(e1, e1) = all_10_2
% 198.82/32.69    (60)  op(all_52_9, all_52_9) = e3
% 198.82/32.69    (61)  all_58_3 = all_4_2
% 198.82/32.69    (62)  op(all_6_2, e3) = all_6_1
% 198.82/32.69    (63)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.82/32.69    (64)   ~ (all_52_7 = e0)
% 198.82/32.69  
% 198.82/32.69  Begin of proof
% 198.82/32.69  | 
% 198.82/32.69  | BETA: splitting (54) gives:
% 198.82/32.69  | 
% 198.82/32.69  | Case 1:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (65)  all_58_12 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | COMBINE_EQS: (27), (65) imply:
% 198.82/32.69  | |   (66)  all_52_7 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | SIMP: (66) implies:
% 198.82/32.69  | |   (67)  all_52_7 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (48), (67) imply:
% 198.82/32.69  | |   (68)   ~ (all_52_3 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (6), (67) imply:
% 198.82/32.69  | |   (69)   ~ (all_52_15 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | SIMP: (69) implies:
% 198.82/32.69  | |   (70)   ~ (all_52_15 = e3)
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (11), (12), (13), (14), (16),
% 198.82/32.69  | |            (17), (21), (23), (24), (25), (26), (29), (30), (31), (32), (34),
% 198.82/32.69  | |            (35), (36), (37), (40), (43), (44), (45), (46), (47), (50), (51),
% 198.82/32.69  | |            (52), (53), (55), (56), (59), (60), (61), (62), (63), (65), (68),
% 198.82/32.69  | |            (70) are inconsistent by sub-proof #41.
% 198.82/32.69  | | 
% 198.82/32.69  | Case 2:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (71)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (12), (15), (18), (19), (20),
% 198.82/32.69  | |            (22), (27), (28), (31), (33), (38), (39), (41), (42), (46), (47),
% 198.82/32.69  | |            (49), (50), (56), (57), (58), (60), (62), (71) are inconsistent
% 198.82/32.69  | |            by sub-proof #40.
% 198.82/32.69  | | 
% 198.82/32.69  | End of split
% 198.82/32.69  | 
% 198.82/32.69  End of proof
% 198.82/32.69  
% 198.82/32.69  Sub-proof #40 shows that the following formulas are inconsistent:
% 198.82/32.69  ----------------------------------------------------------------
% 198.82/32.69    (1)  all_58_14 = all_52_23
% 198.82/32.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.69    (3)   ~ (e3 = e0)
% 198.82/32.69    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.69    (5)   ~ (all_52_7 = all_52_15)
% 198.82/32.69    (6)  op(all_52_15, all_52_15) = e0
% 198.82/32.69    (7)  op(e3, all_6_1) = e1
% 198.82/32.69    (8)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.69    (9)  all_58_13 = all_52_15
% 198.82/32.69    (10)  op(e2, e2) = all_4_2
% 198.82/32.69    (11)   ~ (all_52_9 = all_52_15)
% 198.82/32.69    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 198.82/32.69    (13)   ~ (all_52_7 = all_6_2)
% 198.82/32.69    (14)  all_58_15 = e0
% 198.82/32.69    (15)  all_58_12 = all_52_7
% 198.82/32.69    (16)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 198.82/32.69    (17)   ~ (e2 = e0)
% 198.82/32.69    (18)   ~ (all_52_23 = e3)
% 198.82/32.69    (19)  op(e3, e1) = all_52_17
% 198.82/32.69    (20)  op(e0, e3) = all_52_7
% 198.82/32.69    (21)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.69    (22)  all_56_12 = all_52_7
% 198.82/32.69    (23)   ~ (all_52_9 = all_6_2)
% 198.82/32.69    (24)  op(e3, e3) = all_6_2
% 198.82/32.69    (25)  all_56_1 = all_52_9
% 198.82/32.69    (26)   ~ (all_52_15 = all_4_2)
% 198.82/32.69    (27)   ~ (e3 = e2)
% 198.82/32.69    (28)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 198.82/32.69    (29)   ~ (all_52_9 = all_52_17)
% 198.82/32.69    (30)  op(all_52_9, all_52_9) = e3
% 198.82/32.69    (31)  op(all_6_2, e3) = all_6_1
% 198.82/32.69  
% 198.82/32.69  Begin of proof
% 198.82/32.69  | 
% 198.82/32.69  | BETA: splitting (8) gives:
% 198.82/32.69  | 
% 198.82/32.69  | Case 1:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (32)  all_58_13 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | COMBINE_EQS: (9), (32) imply:
% 198.82/32.69  | |   (33)  all_52_15 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | SIMP: (33) implies:
% 198.82/32.69  | |   (34)  all_52_15 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 198.82/32.69  | |            (16), (17), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 198.82/32.69  | |            (28), (29), (30), (31), (32), (34) are inconsistent by sub-proof
% 198.82/32.69  | |            #322.
% 198.82/32.69  | | 
% 198.82/32.69  | Case 2:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (35)  all_58_14 = e3 | all_58_15 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (1), (3), (14), (18), (35) are inconsistent by sub-proof #983.
% 198.82/32.69  | | 
% 198.82/32.69  | End of split
% 198.82/32.69  | 
% 198.82/32.69  End of proof
% 198.82/32.69  
% 198.82/32.69  Sub-proof #41 shows that the following formulas are inconsistent:
% 198.82/32.69  ----------------------------------------------------------------
% 198.82/32.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.69    (2)  all_58_1 = all_52_9
% 198.82/32.69    (3)   ~ (e3 = e0)
% 198.82/32.69    (4)  all_58_0 = all_6_2
% 198.82/32.69    (5)  op(e3, all_6_1) = e1
% 198.82/32.69    (6)  op(e3, e0) = all_52_25
% 198.82/32.69    (7)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.69    (8)  all_58_13 = all_52_15
% 198.82/32.69    (9)  op(all_52_13, all_52_13) = e1
% 198.82/32.69    (10)   ~ (all_52_15 = e3)
% 198.82/32.69    (11)  op(e1, e3) = all_52_5
% 198.82/32.69    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.69    (13)  op(all_4_2, e2) = e1
% 198.82/32.69    (14)   ~ (all_52_3 = e3)
% 198.82/32.69    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.69    (16)   ~ (all_4_0 = e3)
% 198.82/32.69    (17)   ~ (e2 = e1)
% 198.82/32.69    (18)  all_58_10 = all_52_27
% 198.82/32.69    (19)  all_58_7 = all_52_13
% 198.82/32.69    (20)  all_58_2 = all_52_3
% 198.82/32.69    (21)  all_56_7 = all_52_27
% 198.82/32.69    (22)   ~ (e2 = e0)
% 198.82/32.69    (23)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 198.82/32.69    (24)   ~ (all_10_2 = e3)
% 198.82/32.69    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 198.82/32.69    (26)   ~ (all_52_9 = e3)
% 198.82/32.69    (27)   ~ (all_52_13 = all_4_2)
% 198.82/32.69    (28)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.69    (29)  all_58_5 = all_4_0
% 198.82/32.69    (30)   ~ (all_52_25 = all_6_2)
% 198.82/32.69    (31)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.69    (32)   ~ (all_52_9 = all_6_2)
% 198.82/32.69    (33)  op(e3, e3) = all_6_2
% 198.82/32.69    (34)   ~ (all_52_15 = all_4_2)
% 198.82/32.69    (35)   ~ (all_52_27 = all_4_2)
% 198.82/32.69    (36)  all_58_6 = all_52_5
% 198.82/32.69    (37)  op(e3, e2) = all_52_9
% 198.82/32.69    (38)   ~ (e1 = e0)
% 198.82/32.69    (39)   ~ (e3 = e2)
% 198.82/32.69    (40)  all_58_12 = e3
% 198.82/32.69    (41)  op(e1, e1) = all_10_2
% 198.82/32.69    (42)  op(all_52_9, all_52_9) = e3
% 198.82/32.69    (43)  all_58_3 = all_4_2
% 198.82/32.69    (44)  op(all_6_2, e3) = all_6_1
% 198.82/32.69    (45)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 198.82/32.69  
% 198.82/32.69  Begin of proof
% 198.82/32.69  | 
% 198.82/32.69  | BETA: splitting (15) gives:
% 198.82/32.69  | 
% 198.82/32.69  | Case 1:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (46)  all_58_2 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (14), (20), (46) are inconsistent by sub-proof #1369.
% 198.82/32.69  | | 
% 198.82/32.69  | Case 2:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (47)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | BETA: splitting (23) gives:
% 198.82/32.69  | | 
% 198.82/32.69  | | Case 1:
% 198.82/32.69  | | | 
% 198.82/32.69  | | |   (48)  all_58_0 = e1
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REF_CLOSE: (1), (3), (4), (5), (6), (11), (12), (17), (20), (22), (25),
% 198.82/32.69  | | |            (30), (32), (36), (37), (38), (39), (40), (44), (45), (48) are
% 198.82/32.69  | | |            inconsistent by sub-proof #279.
% 198.82/32.69  | | | 
% 198.82/32.69  | | Case 2:
% 198.82/32.69  | | | 
% 198.82/32.69  | | |   (49)   ~ (all_58_0 = e1)
% 198.82/32.69  | | | 
% 198.82/32.69  | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (13), (16), (18), (19),
% 198.82/32.69  | | |            (21), (24), (26), (27), (28), (29), (31), (33), (34), (35),
% 198.82/32.69  | | |            (37), (41), (42), (43), (47), (49) are inconsistent by
% 198.82/32.69  | | |            sub-proof #120.
% 198.82/32.69  | | | 
% 198.82/32.69  | | End of split
% 198.82/32.69  | | 
% 198.82/32.69  | End of split
% 198.82/32.69  | 
% 198.82/32.69  End of proof
% 198.82/32.69  
% 198.82/32.69  Sub-proof #42 shows that the following formulas are inconsistent:
% 198.82/32.69  ----------------------------------------------------------------
% 198.82/32.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.69    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.69    (3)  all_58_0 = all_6_2
% 198.82/32.69    (4)  op(e2, e2) = all_4_2
% 198.82/32.69    (5)  op(all_4_2, e2) = e1
% 198.82/32.69    (6)   ~ (all_4_0 = e3)
% 198.82/32.69    (7)   ~ (all_6_2 = e3)
% 198.82/32.69    (8)  all_58_10 = all_52_27
% 198.82/32.69    (9)  all_58_12 = all_52_7
% 198.82/32.69    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.82/32.69    (11)   ~ (all_52_7 = e3)
% 198.82/32.69    (12)  all_58_2 = all_52_3
% 198.82/32.69    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.82/32.69    (14)   ~ (all_52_27 = e3)
% 198.82/32.69    (15)   ~ (all_52_5 = all_10_2)
% 198.82/32.69    (16)  all_58_5 = all_4_0
% 198.82/32.69    (17)  all_58_6 = all_52_5
% 198.82/32.69    (18)  op(e3, e2) = all_52_9
% 198.82/32.69    (19)  op(e1, e1) = all_10_2
% 198.82/32.69    (20)  op(all_52_9, all_52_9) = e3
% 198.82/32.69    (21)  all_58_3 = all_4_2
% 198.82/32.69    (22)   ~ (all_52_3 = all_4_2)
% 198.82/32.69  
% 198.82/32.69  Begin of proof
% 198.82/32.69  | 
% 198.82/32.69  | BETA: splitting (2) gives:
% 198.82/32.69  | 
% 198.82/32.69  | Case 1:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (23)  all_58_3 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | COMBINE_EQS: (21), (23) imply:
% 198.82/32.69  | |   (24)  all_4_2 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (5), (24) imply:
% 198.82/32.69  | |   (25)  op(e3, e2) = e1
% 198.82/32.69  | | 
% 198.82/32.69  | | REDUCE: (4), (24) imply:
% 198.82/32.69  | |   (26)  op(e2, e2) = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (1), (3), (4), (7), (9), (10), (11), (12), (13), (15), (17),
% 198.82/32.69  | |            (18), (19), (20), (22), (25), (26) are inconsistent by sub-proof
% 198.82/32.69  | |            #76.
% 198.82/32.69  | | 
% 198.82/32.69  | Case 2:
% 198.82/32.69  | | 
% 198.82/32.69  | |   (27)  all_58_5 = e3 | all_58_10 = e3
% 198.82/32.69  | | 
% 198.82/32.69  | | REF_CLOSE: (6), (8), (14), (16), (27) are inconsistent by sub-proof #214.
% 198.82/32.69  | | 
% 198.82/32.69  | End of split
% 198.82/32.69  | 
% 198.82/32.69  End of proof
% 198.82/32.69  
% 198.82/32.69  Sub-proof #43 shows that the following formulas are inconsistent:
% 198.82/32.69  ----------------------------------------------------------------
% 198.82/32.69    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 198.82/32.69    (2)   ~ (all_52_15 = all_52_23)
% 198.82/32.69    (3)   ~ (all_52_25 = all_52_27)
% 198.82/32.69    (4)  all_58_14 = all_52_23
% 198.82/32.69    (5)   ~ (e3 = e1)
% 198.82/32.69    (6)   ~ (all_52_17 = all_4_0)
% 198.82/32.69    (7)  op(all_52_3, all_52_3) = all_52_2
% 198.82/32.69    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.69    (9)   ~ (all_52_5 = all_52_13)
% 198.82/32.69    (10)  all_58_1 = all_52_9
% 198.82/32.69    (11)   ~ (all_52_9 = all_52_13)
% 198.82/32.69    (12)   ~ (e3 = e0)
% 198.82/32.69    (13)  op(e2, e3) = all_52_3
% 198.82/32.69    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.69    (15)   ~ (all_52_7 = all_52_15)
% 198.82/32.69    (16)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.69    (17)   ~ (all_52_17 = all_52_25)
% 198.82/32.69    (18)   ~ (all_52_3 = all_6_2)
% 198.82/32.69    (19)  all_44_2 = all_6_2
% 198.82/32.69    (20)  all_58_0 = all_6_2
% 198.82/32.69    (21)  op(all_14_2, e0) = all_14_1
% 198.82/32.69    (22)  all_56_4 = all_52_3
% 198.82/32.69    (23)   ~ (all_52_17 = all_10_2)
% 198.82/32.69    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 198.82/32.69    (25)  op(e3, e0) = all_52_25
% 198.82/32.69    (26)  op(all_52_5, all_52_5) = all_52_4
% 198.82/32.69    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.69    (28)  op(all_52_19, all_52_19) = all_52_18
% 198.82/32.69    (29)   ~ (all_52_27 = all_52_29)
% 198.82/32.69    (30)  all_58_13 = all_52_15
% 198.82/32.69    (31)  op(all_10_2, all_10_2) = all_52_20
% 198.82/32.69    (32)  all_58_9 = all_52_25
% 198.82/32.69    (33)   ~ (all_52_29 = all_14_2)
% 198.82/32.69    (34)  op(all_52_27, all_52_27) = all_52_26
% 198.82/32.69    (35)  op(e1, e3) = all_52_5
% 198.82/32.69    (36)  op(e2, e2) = all_4_2
% 198.82/32.69    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.69    (38)   ~ (all_52_3 = all_52_5)
% 198.82/32.69    (39)  op(all_4_2, e2) = e1
% 198.82/32.70    (40)  all_58_11 = all_52_29
% 198.82/32.70    (41)  all_56_5 = all_4_2
% 198.82/32.70    (42)   ~ (all_52_25 = all_14_2)
% 198.82/32.70    (43)   ~ (all_52_9 = all_52_15)
% 198.82/32.70    (44)   ~ (all_52_3 = all_52_27)
% 198.82/32.70    (45)  op(all_10_2, e1) = all_10_1
% 198.82/32.70    (46)  op(all_6_2, all_6_2) = all_52_0
% 198.82/32.70    (47)   ~ (all_52_7 = all_6_2)
% 198.82/32.70    (48)  op(e0, e0) = all_14_2
% 198.82/32.70    (49)  all_56_15 = all_14_2
% 198.82/32.70    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.70    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.82/32.70    (52)  op(e1, e0) = all_52_29
% 198.82/32.70    (53)   ~ (all_58_15 = e0)
% 198.82/32.70    (54)  all_56_11 = all_52_29
% 198.82/32.70    (55)   ~ (all_4_0 = e3)
% 198.82/32.70    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.70    (57)  op(e1, all_10_1) = e3
% 198.82/32.70    (58)  all_56_9 = all_52_13
% 198.82/32.70    (59)   ~ (e2 = e1)
% 198.82/32.70    (60)   ~ (all_52_13 = all_10_2)
% 198.82/32.70    (61)  all_58_10 = all_52_27
% 198.82/32.70    (62)  all_56_8 = all_52_5
% 198.82/32.70    (63)  op(all_52_9, all_52_9) = all_52_8
% 198.82/32.70    (64)  op(all_52_15, all_52_15) = all_52_14
% 198.82/32.70    (65)   ~ (all_52_25 = all_52_29)
% 198.82/32.70    (66)   ~ (all_52_29 = all_10_2)
% 198.82/32.70    (67)  all_58_7 = all_52_13
% 198.82/32.70    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.82/32.70    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.82/32.70    (70)   ~ (all_52_5 = all_52_7)
% 198.82/32.70    (71)  all_58_12 = all_52_7
% 198.82/32.70    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.82/32.70    (73)   ~ (all_52_7 = all_14_2)
% 198.82/32.70    (74)  all_58_2 = all_52_3
% 198.82/32.70    (75)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.82/32.70    (76)  all_56_2 = all_52_17
% 198.82/32.70    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.82/32.70    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.82/32.70    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.82/32.70    (80)  all_56_7 = all_52_27
% 198.82/32.70    (81)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.82/32.70    (82)   ~ (e2 = e0)
% 198.82/32.70    (83)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.82/32.70    (84)   ~ (all_52_5 = all_52_29)
% 198.82/32.70    (85)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 198.82/32.70    (86)  all_56_6 = all_52_19
% 198.82/32.70    (87)   ~ (all_52_15 = all_14_2)
% 198.82/32.70    (88)   ~ (all_52_19 = all_52_27)
% 198.82/32.70    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.82/32.70    (90)   ~ (all_52_13 = all_4_2)
% 198.82/32.70    (91)  op(e3, e1) = all_52_17
% 198.82/32.70    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.82/32.70    (93)  op(e0, e3) = all_52_7
% 198.82/32.70    (94)  op(e1, e2) = all_52_13
% 198.82/32.70    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.70    (96)   ~ (all_52_9 = all_52_25)
% 198.82/32.70    (97)  all_58_15 = all_14_2
% 198.82/32.70    (98)   ~ (all_52_19 = all_10_2)
% 198.82/32.70    (99)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.70    (100)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.82/32.70    (101)  all_58_8 = all_10_2
% 198.82/32.70    (102)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.70    (103)   ~ (all_52_5 = all_10_2)
% 198.82/32.70    (104)  op(all_52_29, all_52_29) = all_52_28
% 198.82/32.70    (105)   ~ (all_52_23 = all_14_2)
% 198.82/32.70    (106)  all_56_12 = all_52_7
% 198.82/32.70    (107)  op(all_52_17, all_52_17) = all_52_16
% 198.82/32.70    (108)  all_58_5 = all_4_0
% 198.82/32.70    (109)  all_8_2 = all_6_2
% 198.82/32.70    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.82/32.70    (111)   ~ (all_52_25 = all_6_2)
% 198.82/32.70    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.82/32.70    (113)   ~ (all_52_9 = all_4_2)
% 198.82/32.70    (114)   ~ (all_52_5 = all_6_2)
% 198.82/32.70    (115)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.70    (116)   ~ (all_52_9 = all_6_2)
% 198.82/32.70    (117)   ~ (all_52_13 = all_52_15)
% 198.82/32.70    (118)  op(e3, all_6_1) = e2
% 198.82/32.70    (119)  all_56_0 = all_6_2
% 198.82/32.70    (120)  op(e3, e3) = all_6_2
% 198.82/32.70    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.82/32.70    (122)   ~ (all_52_27 = all_14_2)
% 198.82/32.70    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.70    (124)  all_56_14 = all_52_23
% 198.82/32.70    (125)  op(all_4_2, all_4_2) = all_52_10
% 198.82/32.70    (126)  all_56_3 = all_52_25
% 198.82/32.70    (127)   ~ (all_52_3 = all_52_7)
% 198.82/32.70    (128)  op(all_14_2, all_14_2) = all_52_30
% 198.82/32.70    (129)  all_58_5 = all_52_19
% 198.82/32.70    (130)   ~ (all_52_15 = all_4_2)
% 198.82/32.70    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.82/32.70           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.82/32.70           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.82/32.70           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.82/32.70    (132)   ~ (all_52_27 = all_4_2)
% 198.82/32.70    (133)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 198.82/32.70             all_58_13 = e0 | all_58_14 = e0)
% 198.82/32.70    (134)  all_58_6 = all_52_5
% 198.82/32.70    (135)   ~ (all_4_0 = all_4_2)
% 198.82/32.70    (136)  op(e3, e2) = all_52_9
% 198.82/32.70    (137)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.70    (138)   ~ (all_52_17 = all_6_2)
% 198.82/32.70    (139)   ~ (e1 = e0)
% 198.82/32.70    (140)   ~ (e3 = e2)
% 198.82/32.70    (141)  all_44_1 = all_6_1
% 198.82/32.70    (142)   ~ (all_52_9 = all_52_17)
% 198.82/32.70    (143)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.70    (144)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.82/32.70    (145)   ~ (all_52_3 = all_4_0)
% 198.82/32.70    (146)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.82/32.70    (147)  op(all_52_13, all_52_13) = all_52_12
% 198.82/32.70    (148)  op(e1, e1) = all_10_2
% 198.82/32.70    (149)   ~ (all_52_23 = all_10_2)
% 198.82/32.70    (150)   ~ (all_52_7 = all_52_23)
% 198.82/32.70    (151)   ~ (all_52_17 = all_52_19)
% 198.82/32.70    (152)  all_58_3 = all_4_2
% 198.82/32.70    (153)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.82/32.70    (154)   ~ (all_52_3 = all_4_2)
% 198.82/32.70    (155)   ~ (all_52_19 = all_4_2)
% 198.82/32.70    (156)   ~ (all_52_17 = all_52_23)
% 198.82/32.70    (157)  all_8_1 = all_6_1
% 198.82/32.70    (158)  op(all_6_2, e3) = all_6_1
% 198.82/32.70    (159)   ~ (all_52_13 = all_52_29)
% 198.82/32.70    (160)  all_58_4 = all_52_17
% 198.82/32.70    (161)  op(all_52_25, all_52_25) = all_52_24
% 198.82/32.70  
% 198.82/32.70  Begin of proof
% 198.82/32.70  | 
% 198.82/32.70  | ALPHA: (133) implies:
% 198.82/32.70  |   (162)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.82/32.70  |   (163)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.82/32.70  | 
% 198.82/32.70  | REDUCE: (53), (97) imply:
% 198.82/32.70  |   (164)   ~ (all_14_2 = e0)
% 198.82/32.70  | 
% 198.82/32.70  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 198.82/32.70  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 198.82/32.70  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 198.82/32.70  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 198.82/32.70  |            (46), (47), (48), (49), (50), (51), (52), (54), (55), (56), (57),
% 198.82/32.70  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 198.82/32.70  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 198.82/32.70  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 198.82/32.70  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 198.82/32.70  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 198.82/32.70  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 198.82/32.70  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 198.82/32.70  |            (129), (130), (131), (132), (134), (135), (136), (137), (138),
% 198.82/32.70  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 198.82/32.70  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 198.82/32.70  |            (157), (158), (159), (160), (161), (162), (163), (164) are
% 198.82/32.70  |            inconsistent by sub-proof #44.
% 198.82/32.70  | 
% 198.82/32.70  End of proof
% 198.82/32.70  
% 198.82/32.70  Sub-proof #44 shows that the following formulas are inconsistent:
% 198.82/32.70  ----------------------------------------------------------------
% 198.82/32.70    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.82/32.70    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 198.82/32.70    (3)   ~ (all_52_15 = all_52_23)
% 198.82/32.70    (4)   ~ (all_52_25 = all_52_27)
% 198.82/32.70    (5)  all_58_14 = all_52_23
% 198.82/32.70    (6)   ~ (e3 = e1)
% 198.82/32.70    (7)   ~ (all_52_17 = all_4_0)
% 198.82/32.70    (8)  op(all_52_3, all_52_3) = all_52_2
% 198.82/32.70    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.70    (10)   ~ (all_52_5 = all_52_13)
% 198.82/32.70    (11)  all_58_1 = all_52_9
% 198.82/32.70    (12)   ~ (all_52_9 = all_52_13)
% 198.82/32.70    (13)   ~ (e3 = e0)
% 198.82/32.70    (14)  op(e2, e3) = all_52_3
% 198.82/32.70    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.70    (16)   ~ (all_52_7 = all_52_15)
% 198.82/32.70    (17)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.70    (18)   ~ (all_52_17 = all_52_25)
% 198.82/32.70    (19)   ~ (all_52_3 = all_6_2)
% 198.82/32.70    (20)  all_44_2 = all_6_2
% 198.82/32.70    (21)  all_58_0 = all_6_2
% 198.82/32.70    (22)  op(all_14_2, e0) = all_14_1
% 198.82/32.70    (23)  all_56_4 = all_52_3
% 198.82/32.70    (24)   ~ (all_52_17 = all_10_2)
% 198.82/32.70    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 198.82/32.70    (26)  op(e3, e0) = all_52_25
% 198.82/32.70    (27)  op(all_52_5, all_52_5) = all_52_4
% 198.82/32.70    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.70    (29)  op(all_52_19, all_52_19) = all_52_18
% 198.82/32.70    (30)   ~ (all_52_27 = all_52_29)
% 198.82/32.70    (31)  all_58_13 = all_52_15
% 198.82/32.70    (32)  op(all_10_2, all_10_2) = all_52_20
% 198.82/32.70    (33)  all_58_9 = all_52_25
% 198.82/32.70    (34)   ~ (all_52_29 = all_14_2)
% 198.82/32.70    (35)  op(all_52_27, all_52_27) = all_52_26
% 198.82/32.70    (36)  op(e1, e3) = all_52_5
% 198.82/32.70    (37)  op(e2, e2) = all_4_2
% 198.82/32.70    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.70    (39)   ~ (all_52_3 = all_52_5)
% 198.82/32.70    (40)  op(all_4_2, e2) = e1
% 198.82/32.70    (41)  all_58_11 = all_52_29
% 198.82/32.70    (42)  all_56_5 = all_4_2
% 198.82/32.70    (43)   ~ (all_52_25 = all_14_2)
% 198.82/32.70    (44)   ~ (all_52_9 = all_52_15)
% 198.82/32.70    (45)   ~ (all_52_3 = all_52_27)
% 198.82/32.70    (46)  op(all_10_2, e1) = all_10_1
% 198.82/32.70    (47)  op(all_6_2, all_6_2) = all_52_0
% 198.82/32.70    (48)   ~ (all_52_7 = all_6_2)
% 198.82/32.70    (49)  op(e0, e0) = all_14_2
% 198.82/32.70    (50)  all_56_15 = all_14_2
% 198.82/32.70    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.70    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.82/32.70    (53)  op(e1, e0) = all_52_29
% 198.82/32.70    (54)  all_56_11 = all_52_29
% 198.82/32.70    (55)   ~ (all_4_0 = e3)
% 198.82/32.70    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.70    (57)  op(e1, all_10_1) = e3
% 198.82/32.70    (58)  all_56_9 = all_52_13
% 198.82/32.70    (59)   ~ (e2 = e1)
% 198.82/32.70    (60)   ~ (all_52_13 = all_10_2)
% 198.82/32.70    (61)  all_58_10 = all_52_27
% 198.82/32.70    (62)  all_56_8 = all_52_5
% 198.82/32.70    (63)  op(all_52_9, all_52_9) = all_52_8
% 198.82/32.70    (64)  op(all_52_15, all_52_15) = all_52_14
% 198.82/32.70    (65)   ~ (all_52_25 = all_52_29)
% 198.82/32.70    (66)   ~ (all_52_29 = all_10_2)
% 198.82/32.70    (67)  all_58_7 = all_52_13
% 198.82/32.70    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.82/32.70    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.82/32.70    (70)   ~ (all_52_5 = all_52_7)
% 198.82/32.70    (71)  all_58_12 = all_52_7
% 198.82/32.70    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.82/32.70    (73)   ~ (all_52_7 = all_14_2)
% 198.82/32.70    (74)   ~ (all_14_2 = e0)
% 198.82/32.70    (75)  all_58_2 = all_52_3
% 198.82/32.70    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.82/32.70    (77)  all_56_2 = all_52_17
% 198.82/32.70    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.82/32.70    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.82/32.70    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.82/32.70    (81)  all_56_7 = all_52_27
% 198.82/32.70    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 198.82/32.70    (83)   ~ (e2 = e0)
% 198.82/32.70    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.82/32.70    (85)   ~ (all_52_5 = all_52_29)
% 198.82/32.70    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 198.82/32.70    (87)  all_56_6 = all_52_19
% 198.82/32.70    (88)   ~ (all_52_15 = all_14_2)
% 198.82/32.70    (89)   ~ (all_52_19 = all_52_27)
% 198.82/32.70    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.82/32.70    (91)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.82/32.70    (92)   ~ (all_52_13 = all_4_2)
% 198.82/32.70    (93)  op(e3, e1) = all_52_17
% 198.82/32.70    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.82/32.70    (95)  op(e0, e3) = all_52_7
% 198.82/32.70    (96)  op(e1, e2) = all_52_13
% 198.82/32.70    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.70    (98)   ~ (all_52_9 = all_52_25)
% 198.82/32.70    (99)  all_58_15 = all_14_2
% 198.82/32.70    (100)   ~ (all_52_19 = all_10_2)
% 198.82/32.70    (101)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.70    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.82/32.70    (103)  all_58_8 = all_10_2
% 198.82/32.70    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.70    (105)   ~ (all_52_5 = all_10_2)
% 198.82/32.70    (106)  op(all_52_29, all_52_29) = all_52_28
% 198.82/32.70    (107)   ~ (all_52_23 = all_14_2)
% 198.82/32.70    (108)  all_56_12 = all_52_7
% 198.82/32.70    (109)  op(all_52_17, all_52_17) = all_52_16
% 198.82/32.70    (110)  all_58_5 = all_4_0
% 198.82/32.70    (111)  all_8_2 = all_6_2
% 198.82/32.70    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.82/32.70    (113)   ~ (all_52_25 = all_6_2)
% 198.82/32.70    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.82/32.70    (115)   ~ (all_52_9 = all_4_2)
% 198.82/32.70    (116)   ~ (all_52_5 = all_6_2)
% 198.82/32.70    (117)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.70    (118)   ~ (all_52_9 = all_6_2)
% 198.82/32.70    (119)   ~ (all_52_13 = all_52_15)
% 198.82/32.70    (120)  op(e3, all_6_1) = e2
% 198.82/32.70    (121)  all_56_0 = all_6_2
% 198.82/32.70    (122)  op(e3, e3) = all_6_2
% 198.82/32.70    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.82/32.70    (124)   ~ (all_52_27 = all_14_2)
% 198.82/32.70    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.70    (126)  all_56_14 = all_52_23
% 198.82/32.70    (127)  op(all_4_2, all_4_2) = all_52_10
% 198.82/32.70    (128)  all_56_3 = all_52_25
% 198.82/32.70    (129)   ~ (all_52_3 = all_52_7)
% 198.82/32.70    (130)  op(all_14_2, all_14_2) = all_52_30
% 198.82/32.70    (131)  all_58_5 = all_52_19
% 198.82/32.70    (132)   ~ (all_52_15 = all_4_2)
% 198.82/32.70    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.82/32.70           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 198.82/32.70           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.82/32.70           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.82/32.70    (134)   ~ (all_52_27 = all_4_2)
% 198.82/32.70    (135)  all_58_6 = all_52_5
% 198.82/32.70    (136)   ~ (all_4_0 = all_4_2)
% 198.82/32.70    (137)  op(e3, e2) = all_52_9
% 198.82/32.70    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.70    (139)   ~ (all_52_17 = all_6_2)
% 198.82/32.70    (140)   ~ (e1 = e0)
% 198.82/32.70    (141)   ~ (e3 = e2)
% 198.82/32.70    (142)  all_44_1 = all_6_1
% 198.82/32.70    (143)   ~ (all_52_9 = all_52_17)
% 198.82/32.70    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.70    (145)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.82/32.70    (146)   ~ (all_52_3 = all_4_0)
% 198.82/32.70    (147)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.82/32.70    (148)  op(all_52_13, all_52_13) = all_52_12
% 198.82/32.70    (149)  op(e1, e1) = all_10_2
% 198.82/32.70    (150)   ~ (all_52_23 = all_10_2)
% 198.82/32.70    (151)   ~ (all_52_7 = all_52_23)
% 198.82/32.70    (152)   ~ (all_52_17 = all_52_19)
% 198.82/32.70    (153)  all_58_3 = all_4_2
% 198.82/32.70    (154)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.82/32.70    (155)   ~ (all_52_3 = all_4_2)
% 198.82/32.70    (156)   ~ (all_52_19 = all_4_2)
% 198.82/32.70    (157)   ~ (all_52_17 = all_52_23)
% 198.82/32.70    (158)  all_8_1 = all_6_1
% 198.82/32.70    (159)  op(all_6_2, e3) = all_6_1
% 198.82/32.70    (160)   ~ (all_52_13 = all_52_29)
% 198.82/32.70    (161)  all_58_4 = all_52_17
% 198.82/32.70    (162)  op(all_52_25, all_52_25) = all_52_24
% 198.82/32.70  
% 198.82/32.70  Begin of proof
% 198.82/32.70  | 
% 198.82/32.70  | BETA: splitting (133) gives:
% 198.82/32.70  | 
% 198.82/32.70  | Case 1:
% 198.82/32.70  | | 
% 198.82/32.70  | |   (163)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 198.82/32.70  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 198.82/32.70  | | 
% 198.82/32.70  | | BETA: splitting (163) gives:
% 198.82/32.70  | | 
% 198.82/32.70  | | Case 1:
% 198.82/32.70  | | | 
% 198.82/32.70  | | |   (164)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 198.82/32.70  | | | 
% 198.82/32.70  | | | REF_CLOSE: (8), (9), (17), (21), (27), (37), (47), (49), (51), (71), (73),
% 198.82/32.70  | | |            (75), (79), (105), (120), (121), (122), (135), (138), (141),
% 198.82/32.70  | | |            (147), (149), (155), (159), (164) are inconsistent by sub-proof
% 198.82/32.70  | | |            #501.
% 198.82/32.70  | | | 
% 198.82/32.70  | | Case 2:
% 198.82/32.70  | | | 
% 198.82/32.70  | | |   (165)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 198.82/32.70  | | | 
% 198.82/32.70  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 198.82/32.70  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 198.82/32.70  | | |            (26), (27), (28), (30), (31), (33), (34), (36), (37), (38),
% 198.82/32.70  | | |            (39), (40), (41), (43), (48), (50), (51), (54), (55), (56),
% 198.82/32.70  | | |            (58), (61), (62), (63), (64), (66), (67), (69), (70), (71),
% 198.82/32.70  | | |            (72), (73), (74), (75), (77), (81), (82), (83), (90), (92),
% 198.82/32.70  | | |            (93), (95), (97), (98), (99), (102), (103), (104), (108),
% 198.82/32.70  | | |            (109), (110), (111), (113), (115), (116), (117), (118), (120),
% 198.82/32.70  | | |            (122), (123), (124), (125), (127), (129), (130), (132), (135),
% 198.82/32.70  | | |            (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 198.82/32.70  | | |            (148), (149), (153), (155), (157), (158), (159), (161), (162),
% 198.82/32.70  | | |            (165) are inconsistent by sub-proof #86.
% 198.82/32.70  | | | 
% 198.82/32.70  | | End of split
% 198.82/32.70  | | 
% 198.82/32.70  | Case 2:
% 198.82/32.70  | | 
% 198.82/32.70  | |   (166)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 198.82/32.70  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 198.82/32.70  | |            e0)
% 198.82/32.70  | | 
% 198.82/32.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 198.82/32.70  | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 198.82/32.70  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 198.82/32.70  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 198.82/32.70  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 198.82/32.70  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 198.82/32.70  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 198.82/32.70  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (93), (94),
% 198.82/32.70  | |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 198.82/32.70  | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 198.82/32.70  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 198.82/32.70  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 198.82/32.70  | |            (132), (134), (135), (136), (137), (138), (139), (140), (141),
% 198.82/32.70  | |            (142), (143), (144), (145), (146), (147), (148), (149), (150),
% 198.82/32.70  | |            (151), (152), (153), (154), (155), (156), (157), (158), (159),
% 198.82/32.70  | |            (160), (161), (162), (166) are inconsistent by sub-proof #45.
% 198.82/32.70  | | 
% 198.82/32.70  | End of split
% 198.82/32.70  | 
% 198.82/32.70  End of proof
% 198.82/32.70  
% 198.82/32.70  Sub-proof #45 shows that the following formulas are inconsistent:
% 198.82/32.70  ----------------------------------------------------------------
% 198.82/32.70    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 198.82/32.70    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 198.82/32.70    (3)   ~ (all_52_15 = all_52_23)
% 198.82/32.70    (4)   ~ (all_52_25 = all_52_27)
% 198.82/32.70    (5)  all_58_14 = all_52_23
% 198.82/32.70    (6)   ~ (e3 = e1)
% 198.82/32.70    (7)  op(all_52_3, all_52_3) = all_52_2
% 198.82/32.70    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 198.82/32.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 198.82/32.70    (9)  all_58_1 = all_52_9
% 198.82/32.70    (10)   ~ (all_52_9 = all_52_13)
% 198.82/32.70    (11)   ~ (e3 = e0)
% 198.82/32.70    (12)  op(e2, e3) = all_52_3
% 198.82/32.70    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 198.82/32.70    (14)   ~ (all_52_7 = all_52_15)
% 198.82/32.70    (15)  op(all_52_7, all_52_7) = all_52_6
% 198.82/32.70    (16)   ~ (all_52_17 = all_52_25)
% 198.82/32.70    (17)   ~ (all_52_3 = all_6_2)
% 198.82/32.70    (18)  all_44_2 = all_6_2
% 198.82/32.70    (19)  all_58_0 = all_6_2
% 198.82/32.70    (20)  op(all_14_2, e0) = all_14_1
% 198.82/32.70    (21)   ~ (all_52_17 = all_10_2)
% 198.82/32.70    (22)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 198.82/32.70    (23)  op(e3, e0) = all_52_25
% 198.82/32.70    (24)  op(all_52_5, all_52_5) = all_52_4
% 198.82/32.70    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 198.82/32.70    (26)  op(all_52_19, all_52_19) = all_52_18
% 198.82/32.70    (27)   ~ (all_52_27 = all_52_29)
% 198.82/32.70    (28)  all_58_13 = all_52_15
% 198.82/32.70    (29)  op(all_10_2, all_10_2) = all_52_20
% 198.82/32.70    (30)  all_58_9 = all_52_25
% 198.82/32.70    (31)   ~ (all_52_29 = all_14_2)
% 198.82/32.70    (32)  op(all_52_27, all_52_27) = all_52_26
% 198.82/32.70    (33)  op(e1, e3) = all_52_5
% 198.82/32.70    (34)  op(e2, e2) = all_4_2
% 198.82/32.70    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 198.82/32.70    (36)   ~ (all_52_3 = all_52_5)
% 198.82/32.70    (37)  op(all_4_2, e2) = e1
% 198.82/32.70    (38)  all_58_11 = all_52_29
% 198.82/32.70    (39)  all_56_5 = all_4_2
% 198.82/32.70    (40)   ~ (all_52_25 = all_14_2)
% 198.82/32.70    (41)   ~ (all_52_9 = all_52_15)
% 198.82/32.70    (42)   ~ (all_52_3 = all_52_27)
% 198.82/32.70    (43)  op(all_10_2, e1) = all_10_1
% 198.82/32.70    (44)  op(all_6_2, all_6_2) = all_52_0
% 198.82/32.70    (45)   ~ (all_52_7 = all_6_2)
% 198.82/32.70    (46)  op(e0, e0) = all_14_2
% 198.82/32.70    (47)  all_56_15 = all_14_2
% 198.82/32.70    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 198.82/32.70    (49)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 198.82/32.71    (50)  op(e1, e0) = all_52_29
% 198.82/32.71    (51)  all_56_11 = all_52_29
% 198.82/32.71    (52)   ~ (all_4_0 = e3)
% 198.82/32.71    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.71    (54)  op(e1, all_10_1) = e3
% 198.82/32.71    (55)  all_56_9 = all_52_13
% 198.82/32.71    (56)   ~ (e2 = e1)
% 198.82/32.71    (57)   ~ (all_52_13 = all_10_2)
% 198.82/32.71    (58)  all_58_10 = all_52_27
% 198.82/32.71    (59)  all_56_8 = all_52_5
% 198.82/32.71    (60)  op(all_52_9, all_52_9) = all_52_8
% 198.82/32.71    (61)  op(all_52_15, all_52_15) = all_52_14
% 198.82/32.71    (62)   ~ (all_52_25 = all_52_29)
% 198.82/32.71    (63)   ~ (all_52_29 = all_10_2)
% 198.82/32.71    (64)  all_58_7 = all_52_13
% 198.82/32.71    (65)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 198.82/32.71    (66)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 198.82/32.71    (67)   ~ (all_52_5 = all_52_7)
% 198.82/32.71    (68)  all_58_12 = all_52_7
% 198.82/32.71    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.82/32.71    (70)   ~ (all_52_7 = all_14_2)
% 198.82/32.71    (71)   ~ (all_14_2 = e0)
% 198.82/32.71    (72)  all_58_2 = all_52_3
% 198.82/32.71    (73)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 198.82/32.71    (74)  all_56_2 = all_52_17
% 198.82/32.71    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 198.82/32.71    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 198.82/32.71    (77)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 198.82/32.71    (78)  all_56_7 = all_52_27
% 198.82/32.71    (79)   ~ (e2 = e0)
% 198.82/32.71    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 198.82/32.71    (81)   ~ (all_52_5 = all_52_29)
% 198.82/32.71    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 198.82/32.71    (83)  all_56_6 = all_52_19
% 198.82/32.71    (84)   ~ (all_52_15 = all_14_2)
% 198.82/32.71    (85)   ~ (all_52_19 = all_52_27)
% 198.82/32.71    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 198.82/32.71    (87)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 198.82/32.71    (88)  op(e3, e1) = all_52_17
% 198.82/32.71    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 198.82/32.71    (90)  op(e0, e3) = all_52_7
% 198.82/32.71    (91)  op(e1, e2) = all_52_13
% 198.82/32.71    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 198.82/32.71    (93)   ~ (all_52_9 = all_52_25)
% 198.82/32.71    (94)  all_58_15 = all_14_2
% 198.82/32.71    (95)   ~ (all_52_19 = all_10_2)
% 198.82/32.71    (96)  op(all_52_23, all_52_23) = all_52_22
% 198.82/32.71    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 198.82/32.71    (98)  all_58_8 = all_10_2
% 198.82/32.71    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 198.82/32.71    (100)   ~ (all_52_5 = all_10_2)
% 198.82/32.71    (101)  op(all_52_29, all_52_29) = all_52_28
% 198.82/32.71    (102)   ~ (all_52_23 = all_14_2)
% 198.82/32.71    (103)  all_56_12 = all_52_7
% 198.82/32.71    (104)  op(all_52_17, all_52_17) = all_52_16
% 198.82/32.71    (105)  all_58_5 = all_4_0
% 198.82/32.71    (106)  all_8_2 = all_6_2
% 198.82/32.71    (107)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 198.82/32.71    (108)   ~ (all_52_25 = all_6_2)
% 198.82/32.71    (109)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 198.82/32.71    (110)   ~ (all_52_9 = all_4_2)
% 198.82/32.71    (111)   ~ (all_52_5 = all_6_2)
% 198.82/32.71    (112)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 198.82/32.71    (113)   ~ (all_52_9 = all_6_2)
% 198.82/32.71    (114)   ~ (all_52_13 = all_52_15)
% 198.82/32.71    (115)  op(e3, all_6_1) = e2
% 198.82/32.71    (116)  all_56_0 = all_6_2
% 198.82/32.71    (117)  op(e3, e3) = all_6_2
% 198.82/32.71    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 198.82/32.71    (119)   ~ (all_52_27 = all_14_2)
% 198.82/32.71    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.71    (121)  all_56_14 = all_52_23
% 198.82/32.71    (122)  op(all_4_2, all_4_2) = all_52_10
% 198.82/32.71    (123)  all_56_3 = all_52_25
% 198.82/32.71    (124)   ~ (all_52_3 = all_52_7)
% 198.82/32.71    (125)  op(all_14_2, all_14_2) = all_52_30
% 198.82/32.71    (126)  all_58_5 = all_52_19
% 198.82/32.71    (127)   ~ (all_52_15 = all_4_2)
% 198.82/32.71    (128)   ~ (all_52_27 = all_4_2)
% 198.82/32.71    (129)  all_58_6 = all_52_5
% 198.82/32.71    (130)   ~ (all_4_0 = all_4_2)
% 198.82/32.71    (131)  op(e3, e2) = all_52_9
% 198.82/32.71    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 198.82/32.71    (133)   ~ (all_52_17 = all_6_2)
% 198.82/32.71    (134)   ~ (e1 = e0)
% 198.82/32.71    (135)   ~ (e3 = e2)
% 198.82/32.71    (136)  all_44_1 = all_6_1
% 198.82/32.71    (137)   ~ (all_52_9 = all_52_17)
% 198.82/32.71    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.71    (139)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 198.82/32.71    (140)   ~ (all_52_3 = all_4_0)
% 198.82/32.71    (141)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 198.82/32.71    (142)  op(all_52_13, all_52_13) = all_52_12
% 198.82/32.71    (143)  op(e1, e1) = all_10_2
% 198.82/32.71    (144)   ~ (all_52_23 = all_10_2)
% 198.82/32.71    (145)   ~ (all_52_7 = all_52_23)
% 198.82/32.71    (146)   ~ (all_52_17 = all_52_19)
% 198.82/32.71    (147)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 198.82/32.71           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 198.82/32.71    (148)  all_58_3 = all_4_2
% 198.82/32.71    (149)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 198.82/32.71    (150)   ~ (all_52_3 = all_4_2)
% 198.82/32.71    (151)   ~ (all_52_19 = all_4_2)
% 198.82/32.71    (152)   ~ (all_52_17 = all_52_23)
% 198.82/32.71    (153)  all_8_1 = all_6_1
% 198.82/32.71    (154)  op(all_6_2, e3) = all_6_1
% 198.82/32.71    (155)   ~ (all_52_13 = all_52_29)
% 198.82/32.71    (156)  all_58_4 = all_52_17
% 198.82/32.71    (157)  op(all_52_25, all_52_25) = all_52_24
% 198.82/32.71  
% 198.82/32.71  Begin of proof
% 198.82/32.71  | 
% 198.82/32.71  | BETA: splitting (147) gives:
% 198.82/32.71  | 
% 198.82/32.71  | Case 1:
% 198.82/32.71  | | 
% 198.82/32.71  | |   (158)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 198.82/32.71  | | 
% 198.82/32.71  | | ALPHA: (158) implies:
% 198.82/32.71  | |   (159)  all_52_22 = e0
% 198.82/32.71  | |   (160)  all_52_20 = e1
% 198.82/32.71  | |   (161)  all_52_16 = e3
% 198.82/32.71  | | 
% 198.82/32.71  | | REDUCE: (104), (161) imply:
% 198.82/32.71  | |   (162)  op(all_52_17, all_52_17) = e3
% 198.82/32.71  | | 
% 198.82/32.71  | | REDUCE: (96), (159) imply:
% 198.82/32.71  | |   (163)  op(all_52_23, all_52_23) = e0
% 198.82/32.71  | | 
% 198.82/32.71  | | REDUCE: (29), (160) imply:
% 198.82/32.71  | |   (164)  op(all_10_2, all_10_2) = e1
% 198.82/32.71  | | 
% 198.82/32.71  | | BETA: splitting (99) gives:
% 198.82/32.71  | | 
% 198.82/32.71  | | Case 1:
% 198.82/32.71  | | | 
% 198.82/32.71  | | |   (165)  all_56_15 = e3
% 198.82/32.71  | | | 
% 198.82/32.71  | | | COMBINE_EQS: (47), (165) imply:
% 198.82/32.71  | | |   (166)  all_14_2 = e3
% 198.82/32.71  | | | 
% 198.82/32.71  | | | REF_CLOSE: (5), (6), (8), (9), (10), (19), (21), (28), (30), (34), (40),
% 198.82/32.71  | | |            (41), (43), (50), (52), (54), (56), (63), (64), (68), (70),
% 198.82/32.71  | | |            (71), (72), (75), (76), (77), (79), (88), (92), (98), (100),
% 198.82/32.71  | | |            (102), (105), (110), (113), (117), (120), (129), (133), (134),
% 198.82/32.71  | | |            (135), (138), (148), (150), (156), (162), (164), (166) are
% 198.82/32.71  | | |            inconsistent by sub-proof #48.
% 198.82/32.71  | | | 
% 198.82/32.71  | | Case 2:
% 198.82/32.71  | | | 
% 198.82/32.71  | | |   (167)   ~ (all_56_15 = e3)
% 198.82/32.71  | | | 
% 198.82/32.71  | | | REDUCE: (47), (167) imply:
% 198.82/32.71  | | |   (168)   ~ (all_14_2 = e3)
% 198.82/32.71  | | | 
% 198.82/32.71  | | | BETA: splitting (138) gives:
% 198.82/32.71  | | | 
% 198.82/32.71  | | | Case 1:
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | |   (169)  all_58_4 = e3
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | | COMBINE_EQS: (156), (169) imply:
% 198.82/32.71  | | | |   (170)  all_52_17 = e3
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | | SIMP: (170) implies:
% 198.82/32.71  | | | |   (171)  all_52_17 = e3
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | | REF_CLOSE: (8), (117), (133), (162), (171) are inconsistent by sub-proof
% 198.82/32.71  | | | |            #1280.
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | Case 2:
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | |   (172)   ~ (all_58_4 = e3)
% 198.82/32.71  | | | |   (173)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | | REDUCE: (156), (172) imply:
% 198.82/32.71  | | | |   (174)   ~ (all_52_17 = e3)
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | | BETA: splitting (53) gives:
% 198.82/32.71  | | | | 
% 198.82/32.71  | | | | Case 1:
% 198.82/32.71  | | | | | 
% 198.82/32.71  | | | | |   (175)  all_56_2 = e3
% 198.82/32.71  | | | | | 
% 198.82/32.71  | | | | | REF_CLOSE: (74), (174), (175) are inconsistent by sub-proof #1327.
% 198.82/32.71  | | | | | 
% 198.82/32.71  | | | | Case 2:
% 198.82/32.71  | | | | | 
% 198.82/32.71  | | | | |   (176)   ~ (all_56_2 = e3)
% 198.82/32.71  | | | | |   (177)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 198.82/32.71  | | | | | 
% 198.82/32.71  | | | | | BETA: splitting (25) gives:
% 198.82/32.71  | | | | | 
% 198.82/32.71  | | | | | Case 1:
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | |   (178)  all_56_7 = e3
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | COMBINE_EQS: (78), (178) imply:
% 198.82/32.71  | | | | | |   (179)  all_52_27 = e3
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | SIMP: (179) implies:
% 198.82/32.71  | | | | | |   (180)  all_52_27 = e3
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | REDUCE: (42), (180) imply:
% 198.82/32.71  | | | | | |   (181)   ~ (all_52_3 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | REDUCE: (4), (180) imply:
% 198.82/32.71  | | | | | |   (182)   ~ (all_52_25 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | REDUCE: (27), (180) imply:
% 198.82/32.71  | | | | | |   (183)   ~ (all_52_29 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | SIMP: (183) implies:
% 198.82/32.71  | | | | | |   (184)   ~ (all_52_29 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | REDUCE: (119), (180) imply:
% 198.82/32.71  | | | | | |   (185)   ~ (all_14_2 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | REDUCE: (32), (180) imply:
% 198.82/32.71  | | | | | |   (186)  op(e3, e3) = all_52_26
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_26, e3, e3,
% 198.82/32.71  | | | | | |              simplifying with (117), (186) gives:
% 198.82/32.71  | | | | | |   (187)  all_52_26 = all_6_2
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | BETA: splitting (120) gives:
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | Case 1:
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | |   (188)  all_58_0 = e3
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | COMBINE_EQS: (19), (188) imply:
% 198.82/32.71  | | | | | | |   (189)  all_6_2 = e3
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | REF_CLOSE: (8), (115), (117), (135), (154), (189) are inconsistent
% 198.82/32.71  | | | | | | |            by sub-proof #502.
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | Case 2:
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | |   (190)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | BETA: splitting (190) gives:
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | Case 1:
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | |   (191)  all_58_1 = e3
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | COMBINE_EQS: (9), (191) imply:
% 198.82/32.71  | | | | | | | |   (192)  all_52_9 = e3
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (10), (192) imply:
% 198.82/32.71  | | | | | | | |   (193)   ~ (all_52_13 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | SIMP: (193) implies:
% 198.82/32.71  | | | | | | | |   (194)   ~ (all_52_13 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (93), (192) imply:
% 198.82/32.71  | | | | | | | |   (195)   ~ (all_52_25 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (110), (192) imply:
% 198.82/32.71  | | | | | | | |   (196)   ~ (all_4_2 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | SIMP: (196) implies:
% 198.82/32.71  | | | | | | | |   (197)   ~ (all_4_2 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (60), (192) imply:
% 198.82/32.71  | | | | | | | |   (198)  op(e3, e3) = all_52_8
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_8, e3, e3,
% 198.82/32.71  | | | | | | | |              simplifying with (117), (198) gives:
% 198.82/32.71  | | | | | | | |   (199)  all_52_8 = all_6_2
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | BETA: splitting (69) gives:
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | Case 1:
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | |   (200)  all_58_6 = e3
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | | COMBINE_EQS: (129), (200) imply:
% 198.82/32.71  | | | | | | | | |   (201)  all_52_5 = e3
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | | SIMP: (201) implies:
% 198.82/32.71  | | | | | | | | |   (202)  all_52_5 = e3
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | | REDUCE: (67), (202) imply:
% 198.82/32.71  | | | | | | | | |   (203)   ~ (all_52_7 = e3)
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | | SIMP: (203) implies:
% 198.82/32.71  | | | | | | | | |   (204)   ~ (all_52_7 = e3)
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (13), (14), (19),
% 198.82/32.71  | | | | | | | | |            (28), (30), (41), (45), (53), (68), (74), (82),
% 198.82/32.71  | | | | | | | | |            (87), (90), (92), (94), (103), (106), (115), (117),
% 198.82/32.71  | | | | | | | | |            (120), (125), (131), (132), (133), (134), (135),
% 198.82/32.71  | | | | | | | | |            (137), (138), (143), (144), (145), (152), (153),
% 198.82/32.71  | | | | | | | | |            (154), (156), (162), (163), (168), (182), (204) are
% 198.82/32.71  | | | | | | | | |            inconsistent by sub-proof #57.
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | Case 2:
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | |   (205)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | | REF_CLOSE: (8), (32), (34), (38), (43), (46), (48), (58),
% 198.82/32.71  | | | | | | | | |            (64), (72), (74), (88), (95), (98), (117), (119),
% 198.82/32.71  | | | | | | | | |            (126), (128), (133), (148), (162), (164), (177),
% 198.82/32.71  | | | | | | | | |            (181), (184), (194), (197), (205) are inconsistent
% 198.82/32.71  | | | | | | | | |            by sub-proof #47.
% 198.82/32.71  | | | | | | | | | 
% 198.82/32.71  | | | | | | | | End of split
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | Case 2:
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | |   (206)  all_58_4 = e3 | all_58_9 = e3
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REF_CLOSE: (30), (156), (174), (182), (206) are inconsistent by
% 198.82/32.71  | | | | | | | |            sub-proof #1276.
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | End of split
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | End of split
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | Case 2:
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | |   (207)   ~ (all_56_7 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | REDUCE: (78), (207) imply:
% 198.82/32.71  | | | | | |   (208)   ~ (all_52_27 = e3)
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | BETA: splitting (48) gives:
% 198.82/32.71  | | | | | | 
% 198.82/32.71  | | | | | | Case 1:
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | |   (209)  all_58_2 = e3
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | COMBINE_EQS: (72), (209) imply:
% 198.82/32.71  | | | | | | |   (210)  all_52_3 = e3
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | SIMP: (210) implies:
% 198.82/32.71  | | | | | | |   (211)  all_52_3 = e3
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | REDUCE: (124), (211) imply:
% 198.82/32.71  | | | | | | |   (212)   ~ (all_52_7 = e3)
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | SIMP: (212) implies:
% 198.82/32.71  | | | | | | |   (213)   ~ (all_52_7 = e3)
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | REDUCE: (140), (211) imply:
% 198.82/32.71  | | | | | | |   (214)   ~ (all_4_0 = e3)
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | REDUCE: (150), (211) imply:
% 198.82/32.71  | | | | | | |   (215)   ~ (all_4_2 = e3)
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | SIMP: (215) implies:
% 198.82/32.71  | | | | | | |   (216)   ~ (all_4_2 = e3)
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | REDUCE: (7), (211) imply:
% 198.82/32.71  | | | | | | |   (217)  op(e3, e3) = all_52_2
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3,
% 198.82/32.71  | | | | | | |              simplifying with (117), (217) gives:
% 198.82/32.71  | | | | | | |   (218)  all_52_2 = all_6_2
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | BETA: splitting (118) gives:
% 198.82/32.71  | | | | | | | 
% 198.82/32.71  | | | | | | | Case 1:
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | |   (219)  all_58_9 = e3
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | COMBINE_EQS: (30), (219) imply:
% 198.82/32.71  | | | | | | | |   (220)  all_52_25 = e3
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | SIMP: (220) implies:
% 198.82/32.71  | | | | | | | |   (221)  all_52_25 = e3
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (93), (221) imply:
% 198.82/32.71  | | | | | | | |   (222)   ~ (all_52_9 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (40), (221) imply:
% 198.82/32.71  | | | | | | | |   (223)   ~ (all_14_2 = e3)
% 198.82/32.71  | | | | | | | | 
% 198.82/32.71  | | | | | | | | REDUCE: (157), (221) imply:
% 198.82/32.71  | | | | | | | |   (224)  op(e3, e3) = all_52_24
% 198.82/32.71  | | | | | | | | 
% 199.02/32.72  | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_24, e3, e3,
% 199.02/32.72  | | | | | | | |              simplifying with (117), (224) gives:
% 199.02/32.72  | | | | | | | |   (225)  all_52_24 = all_6_2
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | BETA: splitting (132) gives:
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | |   (226)  all_58_12 = e3
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REF_CLOSE: (68), (213), (226) are inconsistent by sub-proof
% 199.02/32.72  | | | | | | | | |            #1367.
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | |   (227)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | BETA: splitting (92) gives:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | |   (228)  all_58_1 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | COMBINE_EQS: (9), (228) imply:
% 199.02/32.72  | | | | | | | | | |   (229)  all_52_9 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | REDUCE: (222), (229) imply:
% 199.02/32.72  | | | | | | | | | |   (230)  $false
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | CLOSE: (230) is inconsistent.
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | |   (231)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | BETA: splitting (139) gives:
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | |   (232)  all_56_9 = e3
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | COMBINE_EQS: (55), (232) imply:
% 199.02/32.72  | | | | | | | | | | |   (233)  all_52_13 = e3
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | SIMP: (233) implies:
% 199.02/32.72  | | | | | | | | | | |   (234)  all_52_13 = e3
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | REDUCE: (114), (234) imply:
% 199.02/32.72  | | | | | | | | | | |   (235)   ~ (all_52_15 = e3)
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | SIMP: (235) implies:
% 199.02/32.72  | | | | | | | | | | |   (236)   ~ (all_52_15 = e3)
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (11), (13), (14), (28), (45),
% 199.02/32.72  | | | | | | | | | | |            (53), (68), (74), (82), (87), (90), (94), (103),
% 199.02/32.72  | | | | | | | | | | |            (106), (115), (117), (125), (131), (133), (134),
% 199.02/32.72  | | | | | | | | | | |            (137), (143), (144), (145), (152), (153), (154),
% 199.02/32.72  | | | | | | | | | | |            (162), (163), (168), (227), (236) are inconsistent
% 199.02/32.72  | | | | | | | | | | |            by sub-proof #437.
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | |   (237)   ~ (all_56_9 = e3)
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | REF_CLOSE: (3), (5), (8), (28), (43), (46), (52), (54), (55),
% 199.02/32.72  | | | | | | | | | | |            (57), (61), (64), (74), (84), (88), (89), (91),
% 199.02/32.72  | | | | | | | | | | |            (98), (105), (117), (133), (148), (156), (162),
% 199.02/32.72  | | | | | | | | | | |            (164), (173), (177), (216), (231), (237) are
% 199.02/32.72  | | | | | | | | | | |            inconsistent by sub-proof #46.
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | |   (238)   ~ (all_58_9 = e3)
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REDUCE: (30), (238) imply:
% 199.02/32.72  | | | | | | | |   (239)   ~ (all_52_25 = e3)
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (13), (14), (19),
% 199.02/32.72  | | | | | | | |            (28), (30), (41), (45), (53), (68), (74), (82), (87),
% 199.02/32.72  | | | | | | | |            (90), (92), (94), (103), (106), (115), (117), (120),
% 199.02/32.72  | | | | | | | |            (125), (131), (132), (133), (134), (135), (137),
% 199.02/32.72  | | | | | | | |            (138), (143), (144), (145), (152), (153), (154),
% 199.02/32.72  | | | | | | | |            (156), (162), (163), (168), (213), (239) are
% 199.02/32.72  | | | | | | | |            inconsistent by sub-proof #57.
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | End of split
% 199.02/32.72  | | | | | | | 
% 199.02/32.72  | | | | | | Case 2:
% 199.02/32.72  | | | | | | | 
% 199.02/32.72  | | | | | | |   (240)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.72  | | | | | | | 
% 199.02/32.72  | | | | | | | BETA: splitting (240) gives:
% 199.02/32.72  | | | | | | | 
% 199.02/32.72  | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | |   (241)  all_58_3 = e3
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | COMBINE_EQS: (148), (241) imply:
% 199.02/32.72  | | | | | | | |   (242)  all_4_2 = e3
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REDUCE: (110), (242) imply:
% 199.02/32.72  | | | | | | | |   (243)   ~ (all_52_9 = e3)
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REDUCE: (127), (242) imply:
% 199.02/32.72  | | | | | | | |   (244)   ~ (all_52_15 = e3)
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REDUCE: (122), (242) imply:
% 199.02/32.72  | | | | | | | |   (245)  op(e3, e3) = all_52_10
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REDUCE: (37), (242) imply:
% 199.02/32.72  | | | | | | | |   (246)  op(e3, e2) = e1
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | REDUCE: (34), (242) imply:
% 199.02/32.72  | | | | | | | |   (247)  op(e2, e2) = e3
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | BETA: splitting (112) gives:
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | |   (248)   ~ (all_4_2 = e3)
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REF_CLOSE: (8), (34), (247), (248) are inconsistent by
% 199.02/32.72  | | | | | | | | |            sub-proof #211.
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | GROUND_INST: instantiating (8) with all_52_9, e1, e2, e3,
% 199.02/32.72  | | | | | | | | |              simplifying with (131), (246) gives:
% 199.02/32.72  | | | | | | | | |   (249)  all_52_9 = e1
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_10, e3, e3,
% 199.02/32.72  | | | | | | | | |              simplifying with (117), (245) gives:
% 199.02/32.72  | | | | | | | | |   (250)  all_52_10 = all_6_2
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REDUCE: (113), (249) imply:
% 199.02/32.72  | | | | | | | | |   (251)   ~ (all_6_2 = e1)
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | SIMP: (251) implies:
% 199.02/32.72  | | | | | | | | |   (252)   ~ (all_6_2 = e1)
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REDUCE: (243), (249) imply:
% 199.02/32.72  | | | | | | | | |   (253)   ~ (e3 = e1)
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REDUCE: (60), (249) imply:
% 199.02/32.72  | | | | | | | | |   (254)  op(e1, e1) = all_52_8
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, all_52_8, e1, e1,
% 199.02/32.72  | | | | | | | | |              simplifying with (143), (254) gives:
% 199.02/32.72  | | | | | | | | |   (255)  all_52_8 = all_10_2
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | BETA: splitting (132) gives:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | |   (256)  all_58_12 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | COMBINE_EQS: (68), (256) imply:
% 199.02/32.72  | | | | | | | | | |   (257)  all_52_7 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | SIMP: (257) implies:
% 199.02/32.72  | | | | | | | | | |   (258)  all_52_7 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | REDUCE: (145), (258) imply:
% 199.02/32.72  | | | | | | | | | |   (259)   ~ (all_52_23 = e3)
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | SIMP: (259) implies:
% 199.02/32.72  | | | | | | | | | |   (260)   ~ (all_52_23 = e3)
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | BETA: splitting (173) gives:
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | |   (261)  all_58_5 = e3
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | REF_CLOSE: (52), (105), (261) are inconsistent by sub-proof
% 199.02/32.72  | | | | | | | | | | |            #215.
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | |   (262)  all_58_8 = e3 | all_58_14 = e3
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | | REF_CLOSE: (5), (8), (98), (117), (164), (252), (260), (262)
% 199.02/32.72  | | | | | | | | | | |            are inconsistent by sub-proof #283.
% 199.02/32.72  | | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | |   (263)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (11), (13), (14), (28), (45),
% 199.02/32.72  | | | | | | | | | |            (53), (68), (74), (82), (87), (90), (94), (103),
% 199.02/32.72  | | | | | | | | | |            (106), (115), (117), (125), (131), (133), (134),
% 199.02/32.72  | | | | | | | | | |            (137), (143), (144), (145), (152), (153), (154),
% 199.02/32.72  | | | | | | | | | |            (162), (163), (168), (244), (263) are inconsistent
% 199.02/32.72  | | | | | | | | | |            by sub-proof #437.
% 199.02/32.72  | | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | |   (264)  all_58_5 = e3 | all_58_10 = e3
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | BETA: splitting (264) gives:
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | | Case 1:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | |   (265)  all_58_5 = e3
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REF_CLOSE: (52), (105), (265) are inconsistent by sub-proof
% 199.02/32.72  | | | | | | | | |            #215.
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | Case 2:
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | |   (266)  all_58_10 = e3
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | | REF_CLOSE: (58), (208), (266) are inconsistent by sub-proof
% 199.02/32.72  | | | | | | | | |            #1301.
% 199.02/32.72  | | | | | | | | | 
% 199.02/32.72  | | | | | | | | End of split
% 199.02/32.72  | | | | | | | | 
% 199.02/32.72  | | | | | | | End of split
% 199.02/32.72  | | | | | | | 
% 199.02/32.72  | | | | | | End of split
% 199.02/32.72  | | | | | | 
% 199.02/32.72  | | | | | End of split
% 199.02/32.72  | | | | | 
% 199.02/32.72  | | | | End of split
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | End of split
% 199.02/32.72  | | | 
% 199.02/32.72  | | End of split
% 199.02/32.72  | | 
% 199.02/32.72  | Case 2:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (267)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 199.02/32.72  | | 
% 199.02/32.72  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 199.02/32.72  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.02/32.72  | |            (26), (27), (28), (30), (31), (32), (33), (34), (35), (36), (38),
% 199.02/32.72  | |            (39), (40), (42), (43), (44), (45), (46), (47), (48), (49), (51),
% 199.02/32.72  | |            (53), (58), (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 199.02/32.72  | |            (69), (70), (71), (72), (73), (74), (76), (77), (78), (79), (80),
% 199.02/32.72  | |            (81), (83), (85), (86), (87), (88), (89), (90), (92), (93), (94),
% 199.02/32.72  | |            (95), (97), (98), (99), (100), (101), (102), (103), (104), (106),
% 199.02/32.72  | |            (107), (108), (109), (110), (111), (115), (116), (117), (118),
% 199.02/32.72  | |            (119), (120), (121), (123), (124), (125), (126), (127), (128),
% 199.02/32.72  | |            (129), (131), (132), (133), (134), (135), (136), (137), (138),
% 199.02/32.72  | |            (141), (142), (143), (145), (146), (148), (149), (150), (151),
% 199.02/32.72  | |            (152), (153), (154), (155), (156), (157), (267) are inconsistent
% 199.02/32.72  | |            by sub-proof #434.
% 199.02/32.72  | | 
% 199.02/32.72  | End of split
% 199.02/32.72  | 
% 199.02/32.72  End of proof
% 199.02/32.72  
% 199.02/32.72  Sub-proof #46 shows that the following formulas are inconsistent:
% 199.02/32.72  ----------------------------------------------------------------
% 199.02/32.72    (1)   ~ (all_52_15 = all_52_23)
% 199.02/32.72    (2)  all_58_14 = all_52_23
% 199.02/32.72    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.72    (4)   ~ (all_4_2 = e3)
% 199.02/32.72    (5)  all_58_13 = all_52_15
% 199.02/32.72    (6)  op(all_10_2, e1) = all_10_1
% 199.02/32.72    (7)  op(e0, e0) = all_14_2
% 199.02/32.72    (8)   ~ (all_4_0 = e3)
% 199.02/32.72    (9)  op(e1, all_10_1) = e3
% 199.02/32.72    (10)  all_56_9 = all_52_13
% 199.02/32.72    (11)   ~ (all_52_13 = all_10_2)
% 199.02/32.72    (12)  op(all_10_2, all_10_2) = e1
% 199.02/32.72    (13)  op(all_52_15, all_52_15) = all_52_14
% 199.02/32.72    (14)  all_58_7 = all_52_13
% 199.02/32.72    (15)   ~ (all_56_9 = e3)
% 199.02/32.72    (16)  all_56_2 = all_52_17
% 199.02/32.72    (17)   ~ (all_52_15 = all_14_2)
% 199.02/32.72    (18)  op(e3, e1) = all_52_17
% 199.02/32.72    (19)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.02/32.72    (20)  op(e1, e2) = all_52_13
% 199.02/32.72    (21)  all_58_8 = all_10_2
% 199.02/32.72    (22)  all_58_5 = all_4_0
% 199.02/32.72    (23)  op(e3, e3) = all_6_2
% 199.02/32.72    (24)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.72    (25)  op(all_52_17, all_52_17) = e3
% 199.02/32.72    (26)   ~ (all_52_17 = all_6_2)
% 199.02/32.72    (27)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.02/32.72    (28)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.72    (29)  all_58_3 = all_4_2
% 199.02/32.72    (30)  all_58_4 = all_52_17
% 199.02/32.72  
% 199.02/32.72  Begin of proof
% 199.02/32.72  | 
% 199.02/32.72  | REDUCE: (10), (15) imply:
% 199.02/32.72  |   (31)   ~ (all_52_13 = e3)
% 199.02/32.72  | 
% 199.02/32.72  | BETA: splitting (28) gives:
% 199.02/32.72  | 
% 199.02/32.72  | Case 1:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (32)  all_58_3 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | COMBINE_EQS: (29), (32) imply:
% 199.02/32.72  | |   (33)  all_4_2 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | REDUCE: (4), (33) imply:
% 199.02/32.72  | |   (34)  $false
% 199.02/32.72  | | 
% 199.02/32.72  | | CLOSE: (34) is inconsistent.
% 199.02/32.72  | | 
% 199.02/32.72  | Case 2:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (35)  all_58_7 = e3 | all_58_13 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | BETA: splitting (35) gives:
% 199.02/32.72  | | 
% 199.02/32.72  | | Case 1:
% 199.02/32.72  | | | 
% 199.02/32.72  | | |   (36)  all_58_7 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | COMBINE_EQS: (14), (36) imply:
% 199.02/32.72  | | |   (37)  all_52_13 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | REDUCE: (31), (37) imply:
% 199.02/32.72  | | |   (38)  $false
% 199.02/32.72  | | | 
% 199.02/32.72  | | | CLOSE: (38) is inconsistent.
% 199.02/32.72  | | | 
% 199.02/32.72  | | Case 2:
% 199.02/32.72  | | | 
% 199.02/32.72  | | |   (39)  all_58_13 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | COMBINE_EQS: (5), (39) imply:
% 199.02/32.72  | | |   (40)  all_52_15 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | SIMP: (40) implies:
% 199.02/32.72  | | |   (41)  all_52_15 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | REDUCE: (1), (41) imply:
% 199.02/32.72  | | |   (42)   ~ (all_52_23 = e3)
% 199.02/32.72  | | | 
% 199.02/32.72  | | | SIMP: (42) implies:
% 199.02/32.72  | | |   (43)   ~ (all_52_23 = e3)
% 199.02/32.72  | | | 
% 199.02/32.72  | | | REDUCE: (17), (41) imply:
% 199.02/32.72  | | |   (44)   ~ (all_14_2 = e3)
% 199.02/32.72  | | | 
% 199.02/32.72  | | | SIMP: (44) implies:
% 199.02/32.72  | | |   (45)   ~ (all_14_2 = e3)
% 199.02/32.72  | | | 
% 199.02/32.72  | | | REDUCE: (13), (41) imply:
% 199.02/32.72  | | |   (46)  op(e3, e3) = all_52_14
% 199.02/32.72  | | | 
% 199.02/32.72  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (11), (12), (16), (18), (19),
% 199.02/32.72  | | |            (20), (21), (22), (23), (24), (25), (26), (27), (30), (43),
% 199.02/32.72  | | |            (45), (46) are inconsistent by sub-proof #107.
% 199.02/32.72  | | | 
% 199.02/32.72  | | End of split
% 199.02/32.72  | | 
% 199.02/32.72  | End of split
% 199.02/32.72  | 
% 199.02/32.72  End of proof
% 199.02/32.72  
% 199.02/32.72  Sub-proof #47 shows that the following formulas are inconsistent:
% 199.02/32.72  ----------------------------------------------------------------
% 199.02/32.72    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.72    (2)   ~ (all_4_2 = e3)
% 199.02/32.72    (3)  op(all_52_27, all_52_27) = all_52_26
% 199.02/32.72    (4)  op(e2, e2) = all_4_2
% 199.02/32.72    (5)  all_58_11 = all_52_29
% 199.02/32.72    (6)   ~ (all_52_3 = e3)
% 199.02/32.72    (7)  op(all_10_2, e1) = all_10_1
% 199.02/32.72    (8)  op(e0, e0) = all_14_2
% 199.02/32.72    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.72    (10)  op(all_10_2, all_10_2) = e1
% 199.02/32.72    (11)  all_58_10 = all_52_27
% 199.02/32.72    (12)  all_58_7 = all_52_13
% 199.02/32.72    (13)  all_58_2 = all_52_3
% 199.02/32.72    (14)  all_56_2 = all_52_17
% 199.02/32.72    (15)   ~ (all_52_29 = e3)
% 199.02/32.72    (16)  op(e3, e1) = all_52_17
% 199.02/32.72    (17)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.02/32.72    (18)   ~ (all_52_19 = all_10_2)
% 199.02/32.72    (19)  all_58_8 = all_10_2
% 199.02/32.72    (20)  op(e3, e3) = all_6_2
% 199.02/32.72    (21)   ~ (all_52_13 = e3)
% 199.02/32.72    (22)   ~ (all_52_27 = all_14_2)
% 199.02/32.72    (23)  all_58_5 = all_52_19
% 199.02/32.72    (24)   ~ (all_52_27 = all_4_2)
% 199.02/32.72    (25)  op(all_52_17, all_52_17) = e3
% 199.02/32.72    (26)   ~ (all_52_17 = all_6_2)
% 199.02/32.72    (27)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.02/32.72    (28)  all_58_3 = all_4_2
% 199.02/32.72  
% 199.02/32.72  Begin of proof
% 199.02/32.72  | 
% 199.02/32.72  | BETA: splitting (17) gives:
% 199.02/32.72  | 
% 199.02/32.72  | Case 1:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (29)  all_58_7 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | COMBINE_EQS: (12), (29) imply:
% 199.02/32.72  | |   (30)  all_52_13 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | REDUCE: (21), (30) imply:
% 199.02/32.72  | |   (31)  $false
% 199.02/32.72  | | 
% 199.02/32.72  | | CLOSE: (31) is inconsistent.
% 199.02/32.72  | | 
% 199.02/32.72  | Case 2:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (32)  all_58_8 = e3 | all_58_11 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 199.02/32.72  | |            (14), (15), (16), (18), (19), (20), (22), (23), (24), (25), (26),
% 199.02/32.72  | |            (27), (28), (32) are inconsistent by sub-proof #232.
% 199.02/32.72  | | 
% 199.02/32.72  | End of split
% 199.02/32.72  | 
% 199.02/32.72  End of proof
% 199.02/32.72  
% 199.02/32.72  Sub-proof #48 shows that the following formulas are inconsistent:
% 199.02/32.72  ----------------------------------------------------------------
% 199.02/32.72    (1)  all_58_14 = all_52_23
% 199.02/32.72    (2)   ~ (e3 = e1)
% 199.02/32.72    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.72    (4)  all_58_1 = all_52_9
% 199.02/32.72    (5)   ~ (all_52_9 = all_52_13)
% 199.02/32.72    (6)  all_58_0 = all_6_2
% 199.02/32.72    (7)   ~ (all_52_17 = all_10_2)
% 199.02/32.72    (8)  all_58_13 = all_52_15
% 199.02/32.72    (9)  all_58_9 = all_52_25
% 199.02/32.72    (10)  op(e2, e2) = all_4_2
% 199.02/32.72    (11)   ~ (all_52_25 = all_14_2)
% 199.02/32.72    (12)   ~ (all_52_9 = all_52_15)
% 199.02/32.72    (13)  op(all_10_2, e1) = all_10_1
% 199.02/32.72    (14)  op(e1, e0) = all_52_29
% 199.02/32.72    (15)   ~ (all_4_0 = e3)
% 199.02/32.72    (16)  op(e1, all_10_1) = e3
% 199.02/32.72    (17)   ~ (e2 = e1)
% 199.02/32.72    (18)  op(all_10_2, all_10_2) = e1
% 199.02/32.72    (19)   ~ (all_52_29 = all_10_2)
% 199.02/32.72    (20)  all_58_7 = all_52_13
% 199.02/32.72    (21)  all_58_12 = all_52_7
% 199.02/32.72    (22)   ~ (all_52_7 = all_14_2)
% 199.02/32.72    (23)   ~ (all_14_2 = e0)
% 199.02/32.72    (24)  all_58_2 = all_52_3
% 199.02/32.72    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 199.02/32.72    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.02/32.72    (27)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.02/32.72    (28)   ~ (e2 = e0)
% 199.02/32.72    (29)  op(e3, e1) = all_52_17
% 199.02/32.72    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.72    (31)  all_58_8 = all_10_2
% 199.02/32.72    (32)   ~ (all_52_5 = all_10_2)
% 199.02/32.72    (33)   ~ (all_52_23 = all_14_2)
% 199.02/32.72    (34)  all_58_5 = all_4_0
% 199.02/32.72    (35)   ~ (all_52_9 = all_4_2)
% 199.02/32.72    (36)   ~ (all_52_9 = all_6_2)
% 199.02/32.72    (37)  op(e3, e3) = all_6_2
% 199.02/32.72    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.02/32.72    (39)  op(all_52_17, all_52_17) = e3
% 199.02/32.72    (40)  all_58_6 = all_52_5
% 199.02/32.72    (41)   ~ (all_52_17 = all_6_2)
% 199.02/32.72    (42)   ~ (e1 = e0)
% 199.02/32.72    (43)   ~ (e3 = e2)
% 199.02/32.72    (44)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.72    (45)  all_58_3 = all_4_2
% 199.02/32.72    (46)   ~ (all_52_3 = all_4_2)
% 199.02/32.72    (47)  all_58_4 = all_52_17
% 199.02/32.72    (48)  all_14_2 = e3
% 199.02/32.72  
% 199.02/32.72  Begin of proof
% 199.02/32.72  | 
% 199.02/32.72  | REDUCE: (22), (48) imply:
% 199.02/32.72  |   (49)   ~ (all_52_7 = e3)
% 199.02/32.72  | 
% 199.02/32.72  | REDUCE: (33), (48) imply:
% 199.02/32.72  |   (50)   ~ (all_52_23 = e3)
% 199.02/32.72  | 
% 199.02/32.72  | REDUCE: (11), (48) imply:
% 199.02/32.72  |   (51)   ~ (all_52_25 = e3)
% 199.02/32.72  | 
% 199.02/32.72  | REDUCE: (23), (48) imply:
% 199.02/32.72  |   (52)   ~ (e3 = e0)
% 199.02/32.72  | 
% 199.02/32.72  | BETA: splitting (44) gives:
% 199.02/32.72  | 
% 199.02/32.72  | Case 1:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (53)  all_58_4 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | COMBINE_EQS: (47), (53) imply:
% 199.02/32.72  | |   (54)  all_52_17 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | SIMP: (54) implies:
% 199.02/32.72  | |   (55)  all_52_17 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | REF_CLOSE: (3), (37), (39), (41), (55) are inconsistent by sub-proof #1280.
% 199.02/32.72  | | 
% 199.02/32.72  | Case 2:
% 199.02/32.72  | | 
% 199.02/32.72  | |   (56)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.72  | | 
% 199.02/32.72  | | BETA: splitting (56) gives:
% 199.02/32.72  | | 
% 199.02/32.72  | | Case 1:
% 199.02/32.72  | | | 
% 199.02/32.72  | | |   (57)  all_58_5 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | REF_CLOSE: (15), (34), (57) are inconsistent by sub-proof #215.
% 199.02/32.72  | | | 
% 199.02/32.72  | | Case 2:
% 199.02/32.72  | | | 
% 199.02/32.72  | | |   (58)  all_58_8 = e3 | all_58_14 = e3
% 199.02/32.72  | | | 
% 199.02/32.72  | | | BETA: splitting (58) gives:
% 199.02/32.72  | | | 
% 199.02/32.72  | | | Case 1:
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | |   (59)  all_58_8 = e3
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | | COMBINE_EQS: (31), (59) imply:
% 199.02/32.72  | | | |   (60)  all_10_2 = e3
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | | REDUCE: (32), (60) imply:
% 199.02/32.72  | | | |   (61)   ~ (all_52_5 = e3)
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | | REDUCE: (7), (60) imply:
% 199.02/32.72  | | | |   (62)   ~ (all_52_17 = e3)
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | | REDUCE: (19), (60) imply:
% 199.02/32.72  | | | |   (63)   ~ (all_52_29 = e3)
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | | REDUCE: (18), (60) imply:
% 199.02/32.72  | | | |   (64)  op(e3, e3) = e1
% 199.02/32.72  | | | | 
% 199.02/32.72  | | | | REDUCE: (13), (60) imply:
% 199.02/32.72  | | | |   (65)  op(e3, e1) = all_10_1
% 199.02/32.72  | | | | 
% 199.02/32.73  | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 199.02/32.73  | | | |              simplifying with (29), (65) gives:
% 199.02/32.73  | | | |   (66)  all_52_17 = all_10_1
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | GROUND_INST: instantiating (3) with all_6_2, e1, e3, e3, simplifying
% 199.02/32.73  | | | |              with (37), (64) gives:
% 199.02/32.73  | | | |   (67)  all_6_2 = e1
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | COMBINE_EQS: (47), (66) imply:
% 199.02/32.73  | | | |   (68)  all_58_4 = all_10_1
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | COMBINE_EQS: (6), (67) imply:
% 199.02/32.73  | | | |   (69)  all_58_0 = e1
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | REDUCE: (36), (67) imply:
% 199.02/32.73  | | | |   (70)   ~ (all_52_9 = e1)
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | BETA: splitting (38) gives:
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | Case 1:
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | |   (71)  all_58_0 = e3
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | | REF_CLOSE: (2), (69), (71) are inconsistent by sub-proof #1244.
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | Case 2:
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | |   (72)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | | BETA: splitting (72) gives:
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | | Case 1:
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | |   (73)  all_58_1 = e3
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | COMBINE_EQS: (4), (73) imply:
% 199.02/32.73  | | | | | |   (74)  all_52_9 = e3
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | REDUCE: (5), (74) imply:
% 199.02/32.73  | | | | | |   (75)   ~ (all_52_13 = e3)
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | SIMP: (75) implies:
% 199.02/32.73  | | | | | |   (76)   ~ (all_52_13 = e3)
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | REDUCE: (12), (74) imply:
% 199.02/32.73  | | | | | |   (77)   ~ (all_52_15 = e3)
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | SIMP: (77) implies:
% 199.02/32.73  | | | | | |   (78)   ~ (all_52_15 = e3)
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | REDUCE: (35), (74) imply:
% 199.02/32.73  | | | | | |   (79)   ~ (all_4_2 = e3)
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | SIMP: (79) implies:
% 199.02/32.73  | | | | | |   (80)   ~ (all_4_2 = e3)
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | REF_CLOSE: (2), (3), (6), (8), (10), (14), (16), (17), (20), (21),
% 199.02/32.73  | | | | | |            (24), (25), (26), (27), (28), (29), (30), (37), (39),
% 199.02/32.73  | | | | | |            (40), (42), (43), (45), (46), (49), (52), (61), (63),
% 199.02/32.73  | | | | | |            (64), (65), (68), (69), (73), (76), (78), (80) are
% 199.02/32.73  | | | | | |            inconsistent by sub-proof #534.
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | Case 2:
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | |   (81)  all_58_4 = e3 | all_58_9 = e3
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | | REF_CLOSE: (9), (47), (51), (62), (81) are inconsistent by sub-proof
% 199.02/32.73  | | | | | |            #1276.
% 199.02/32.73  | | | | | | 
% 199.02/32.73  | | | | | End of split
% 199.02/32.73  | | | | | 
% 199.02/32.73  | | | | End of split
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | Case 2:
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | |   (82)  all_58_14 = e3
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | | REF_CLOSE: (1), (50), (82) are inconsistent by sub-proof #1305.
% 199.02/32.73  | | | | 
% 199.02/32.73  | | | End of split
% 199.02/32.73  | | | 
% 199.02/32.73  | | End of split
% 199.02/32.73  | | 
% 199.02/32.73  | End of split
% 199.02/32.73  | 
% 199.02/32.73  End of proof
% 199.02/32.73  
% 199.02/32.73  Sub-proof #49 shows that the following formulas are inconsistent:
% 199.02/32.73  ----------------------------------------------------------------
% 199.02/32.73    (1)  all_58_14 = all_52_23
% 199.02/32.73    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 199.02/32.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.73    (4)   ~ (e3 = e0)
% 199.02/32.73    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.73    (6)  op(e2, e2) = all_4_2
% 199.02/32.73    (7)  all_58_8 = e3
% 199.02/32.73    (8)  all_58_4 = all_10_1
% 199.02/32.73    (9)  op(e1, e0) = all_52_29
% 199.02/32.73    (10)   ~ (all_4_0 = e3)
% 199.02/32.73    (11)  op(e1, all_10_1) = e3
% 199.02/32.73    (12)  all_58_10 = all_52_27
% 199.02/32.73    (13)   ~ (all_52_29 = e3)
% 199.02/32.73    (14)   ~ (all_52_27 = e3)
% 199.02/32.73    (15)   ~ (all_52_23 = e0)
% 199.02/32.73    (16)  all_58_5 = all_4_0
% 199.02/32.73    (17)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.02/32.73    (18)  all_58_3 = all_4_2
% 199.02/32.73  
% 199.02/32.73  Begin of proof
% 199.02/32.73  | 
% 199.02/32.73  | BETA: splitting (5) gives:
% 199.02/32.73  | 
% 199.02/32.73  | Case 1:
% 199.02/32.73  | | 
% 199.02/32.73  | |   (19)  all_58_3 = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | COMBINE_EQS: (18), (19) imply:
% 199.02/32.73  | |   (20)  all_4_2 = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | REDUCE: (6), (20) imply:
% 199.02/32.73  | |   (21)  op(e2, e2) = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | BETA: splitting (17) gives:
% 199.02/32.73  | | 
% 199.02/32.73  | | Case 1:
% 199.02/32.73  | | | 
% 199.02/32.73  | | |   (22)   ~ (all_4_2 = e3)
% 199.02/32.73  | | | 
% 199.02/32.73  | | | REF_CLOSE: (3), (6), (21), (22) are inconsistent by sub-proof #211.
% 199.02/32.73  | | | 
% 199.02/32.73  | | Case 2:
% 199.02/32.73  | | | 
% 199.02/32.73  | | |   (23)   ~ (all_4_0 = e0)
% 199.02/32.73  | | | 
% 199.02/32.73  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (13), (15), (16), (23)
% 199.02/32.73  | | |            are inconsistent by sub-proof #50.
% 199.02/32.73  | | | 
% 199.02/32.73  | | End of split
% 199.02/32.73  | | 
% 199.02/32.73  | Case 2:
% 199.02/32.73  | | 
% 199.02/32.73  | |   (24)  all_58_5 = e3 | all_58_10 = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | REF_CLOSE: (10), (12), (14), (16), (24) are inconsistent by sub-proof #214.
% 199.02/32.73  | | 
% 199.02/32.73  | End of split
% 199.02/32.73  | 
% 199.02/32.73  End of proof
% 199.02/32.73  
% 199.02/32.73  Sub-proof #50 shows that the following formulas are inconsistent:
% 199.02/32.73  ----------------------------------------------------------------
% 199.02/32.73    (1)  all_58_14 = all_52_23
% 199.02/32.73    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 199.02/32.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.73    (4)   ~ (e3 = e0)
% 199.02/32.73    (5)  all_58_8 = e3
% 199.02/32.73    (6)  all_58_4 = all_10_1
% 199.02/32.73    (7)  op(e1, e0) = all_52_29
% 199.02/32.73    (8)  op(e1, all_10_1) = e3
% 199.02/32.73    (9)   ~ (all_52_29 = e3)
% 199.02/32.73    (10)   ~ (all_52_23 = e0)
% 199.02/32.73    (11)  all_58_5 = all_4_0
% 199.02/32.73    (12)   ~ (all_4_0 = e0)
% 199.02/32.73  
% 199.02/32.73  Begin of proof
% 199.02/32.73  | 
% 199.02/32.73  | BETA: splitting (2) gives:
% 199.02/32.73  | 
% 199.02/32.73  | Case 1:
% 199.02/32.73  | | 
% 199.02/32.73  | |   (13)  all_58_4 = e0
% 199.02/32.73  | | 
% 199.02/32.73  | | COMBINE_EQS: (6), (13) imply:
% 199.02/32.73  | |   (14)  all_10_1 = e0
% 199.02/32.73  | | 
% 199.02/32.73  | | SIMP: (14) implies:
% 199.02/32.73  | |   (15)  all_10_1 = e0
% 199.02/32.73  | | 
% 199.02/32.73  | | REDUCE: (8), (15) imply:
% 199.02/32.73  | |   (16)  op(e1, e0) = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | GROUND_INST: instantiating (3) with all_52_29, e3, e0, e1, simplifying with
% 199.02/32.73  | |              (7), (16) gives:
% 199.02/32.73  | |   (17)  all_52_29 = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | REDUCE: (9), (17) imply:
% 199.02/32.73  | |   (18)  $false
% 199.02/32.73  | | 
% 199.02/32.73  | | CLOSE: (18) is inconsistent.
% 199.02/32.73  | | 
% 199.02/32.73  | Case 2:
% 199.02/32.73  | | 
% 199.02/32.73  | |   (19)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 199.02/32.73  | | 
% 199.02/32.73  | | REF_CLOSE: (1), (4), (5), (10), (11), (12), (19) are inconsistent by
% 199.02/32.73  | |            sub-proof #208.
% 199.02/32.73  | | 
% 199.02/32.73  | End of split
% 199.02/32.73  | 
% 199.02/32.73  End of proof
% 199.02/32.73  
% 199.02/32.73  Sub-proof #51 shows that the following formulas are inconsistent:
% 199.02/32.73  ----------------------------------------------------------------
% 199.02/32.73    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.73    (2)   ~ (all_52_5 = all_52_13)
% 199.02/32.73    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.02/32.73    (4)   ~ (all_52_7 = all_52_15)
% 199.02/32.73    (5)  op(all_52_15, all_52_15) = e0
% 199.02/32.73    (6)  op(all_52_7, all_52_7) = all_52_6
% 199.02/32.73    (7)  all_58_13 = all_52_15
% 199.02/32.73    (8)  op(all_52_13, all_52_13) = e1
% 199.02/32.73    (9)   ~ (all_52_15 = e3)
% 199.02/32.73    (10)  op(e1, e3) = all_52_5
% 199.02/32.73    (11)  op(e2, e2) = all_4_2
% 199.02/32.73    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.02/32.73    (13)  op(all_10_2, e1) = all_10_1
% 199.02/32.73    (14)   ~ (all_52_15 = e0)
% 199.02/32.73    (15)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.02/32.73    (16)  op(e1, all_10_1) = e3
% 199.02/32.73    (17)  all_56_9 = all_52_13
% 199.02/32.73    (18)   ~ (e2 = e1)
% 199.02/32.73    (19)   ~ (all_52_13 = all_10_2)
% 199.02/32.73    (20)  op(e0, e0) = e0
% 199.02/32.73    (21)  all_58_12 = all_52_7
% 199.02/32.73    (22)   ~ (all_52_7 = e3)
% 199.02/32.73    (23)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.02/32.73    (24)  all_56_12 = all_52_7
% 199.02/32.73    (25)  op(all_4_2, all_4_2) = e2
% 199.02/32.73    (26)   ~ (all_52_13 = all_52_15)
% 199.02/32.73    (27)   ~ (all_52_15 = all_4_2)
% 199.02/32.73    (28)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.02/32.73    (29)  op(e1, e1) = all_10_2
% 199.02/32.73    (30)  all_56_13 = all_52_15
% 199.02/32.73    (31)  op(e0, e1) = e3
% 199.02/32.73    (32)   ~ (all_52_7 = e0)
% 199.02/32.73  
% 199.02/32.73  Begin of proof
% 199.02/32.73  | 
% 199.02/32.73  | BETA: splitting (15) gives:
% 199.02/32.73  | 
% 199.02/32.73  | Case 1:
% 199.02/32.73  | | 
% 199.02/32.73  | |   (33)  all_56_13 = e3
% 199.02/32.73  | | 
% 199.02/32.73  | | REF_CLOSE: (9), (30), (33) are inconsistent by sub-proof #1201.
% 199.02/32.73  | | 
% 199.02/32.73  | Case 2:
% 199.02/32.73  | | 
% 199.02/32.73  | |   (34)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.02/32.73  | | 
% 199.02/32.73  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 199.02/32.73  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.02/32.73  | |            (26), (27), (28), (29), (30), (31), (32), (34) are inconsistent
% 199.02/32.73  | |            by sub-proof #546.
% 199.02/32.73  | | 
% 199.02/32.73  | End of split
% 199.02/32.73  | 
% 199.02/32.73  End of proof
% 199.02/32.73  
% 199.02/32.73  Sub-proof #52 shows that the following formulas are inconsistent:
% 199.02/32.73  ----------------------------------------------------------------
% 199.02/32.73    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.02/32.73    (2)   ~ (all_52_15 = all_52_23)
% 199.02/32.73    (3)   ~ (all_52_25 = all_52_27)
% 199.02/32.73    (4)  all_58_14 = all_52_23
% 199.02/32.73    (5)   ~ (e3 = e1)
% 199.02/32.73    (6)   ~ (all_52_17 = all_4_0)
% 199.02/32.73    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.02/32.73    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.73    (9)  all_58_1 = all_52_9
% 199.02/32.73    (10)   ~ (all_52_9 = all_52_13)
% 199.02/32.73    (11)   ~ (e3 = e0)
% 199.02/32.73    (12)  op(e2, e3) = all_52_3
% 199.02/32.73    (13)   ~ (all_52_23 = all_4_0)
% 199.02/32.73    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.02/32.73    (15)   ~ (all_52_7 = all_52_15)
% 199.02/32.73    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.02/32.73    (17)   ~ (all_52_17 = all_52_25)
% 199.02/32.73    (18)   ~ (all_52_3 = all_6_2)
% 199.02/32.73    (19)  all_44_2 = all_6_2
% 199.02/32.73    (20)  all_58_0 = all_6_2
% 199.02/32.73    (21)  op(all_14_2, e0) = all_14_1
% 199.02/32.73    (22)  all_56_4 = all_52_3
% 199.02/32.73    (23)   ~ (all_52_17 = all_10_2)
% 199.02/32.73    (24)  op(e3, e0) = all_52_25
% 199.02/32.73    (25)  op(all_52_5, all_52_5) = all_52_4
% 199.02/32.73    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.02/32.73    (27)  op(all_52_19, all_52_19) = all_52_18
% 199.02/32.73    (28)   ~ (all_52_27 = all_52_29)
% 199.02/32.73    (29)  all_58_13 = all_52_15
% 199.02/32.73    (30)  op(all_10_2, all_10_2) = all_52_20
% 199.02/32.73    (31)  all_58_9 = all_52_25
% 199.02/32.73    (32)   ~ (all_52_29 = all_14_2)
% 199.02/32.73    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.02/32.73    (34)  op(all_52_27, all_52_27) = all_52_26
% 199.02/32.73    (35)  op(e1, e3) = all_52_5
% 199.02/32.73    (36)  op(e2, e2) = all_4_2
% 199.02/32.73    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.02/32.73    (38)   ~ (all_52_3 = all_52_5)
% 199.02/32.73    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.02/32.73    (40)  op(all_4_2, e2) = e1
% 199.02/32.73    (41)  all_58_11 = all_52_29
% 199.02/32.73    (42)  all_56_5 = all_4_2
% 199.02/32.73    (43)   ~ (all_52_25 = all_14_2)
% 199.02/32.73    (44)   ~ (all_52_3 = all_52_27)
% 199.02/32.73    (45)  op(all_10_2, e1) = all_10_1
% 199.02/32.73    (46)   ~ (all_10_2 = all_4_0)
% 199.02/32.73    (47)  op(all_6_2, all_6_2) = all_52_0
% 199.02/32.73    (48)   ~ (all_52_7 = all_6_2)
% 199.02/32.73    (49)  op(e0, e0) = all_14_2
% 199.02/32.73    (50)  all_56_15 = all_14_2
% 199.02/32.73    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.73    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.02/32.73    (53)  all_56_11 = all_52_29
% 199.02/32.73    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.02/32.73    (55)   ~ (e2 = e1)
% 199.02/32.73    (56)  all_58_10 = all_52_27
% 199.02/32.73    (57)  all_56_8 = all_52_5
% 199.02/32.73    (58)  op(all_52_9, all_52_9) = all_52_8
% 199.02/32.73    (59)  op(all_52_15, all_52_15) = all_52_14
% 199.02/32.73    (60)   ~ (all_52_25 = all_52_29)
% 199.02/32.73    (61)   ~ (all_52_29 = all_10_2)
% 199.02/32.73    (62)  all_58_7 = all_52_13
% 199.02/32.73    (63)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.02/32.73    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.02/32.73    (65)   ~ (all_52_5 = all_52_7)
% 199.02/32.73    (66)  all_58_12 = all_52_7
% 199.02/32.73    (67)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.02/32.73    (68)   ~ (all_52_7 = all_14_2)
% 199.02/32.73    (69)  all_58_2 = all_52_3
% 199.02/32.73    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.02/32.73    (71)  all_56_2 = all_52_17
% 199.02/32.73    (72)  all_28_0 = all_4_0
% 199.02/32.73    (73)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.02/32.73    (74)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.02/32.73    (75)  all_56_7 = all_52_27
% 199.02/32.73    (76)  all_28_2 = all_4_2
% 199.02/32.73    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.02/32.73    (78)   ~ (e2 = e0)
% 199.02/32.73    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.02/32.73    (80)   ~ (all_52_5 = all_52_29)
% 199.02/32.73    (81)  all_56_6 = all_52_19
% 199.02/32.73    (82)   ~ (all_52_19 = all_52_27)
% 199.02/32.73    (83)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.02/32.73    (84)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.02/32.73            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.02/32.73    (85)   ~ (all_52_13 = all_4_2)
% 199.02/32.73    (86)  op(e3, e1) = all_52_17
% 199.02/32.73    (87)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.02/32.73    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.02/32.73    (89)  op(e0, e3) = all_52_7
% 199.02/32.73    (90)  op(e1, e2) = all_52_13
% 199.02/32.73    (91)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.73    (92)   ~ (all_52_9 = all_52_25)
% 199.02/32.73    (93)  all_58_15 = all_14_2
% 199.02/32.73    (94)   ~ (all_52_19 = all_10_2)
% 199.02/32.73    (95)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.02/32.73    (96)  all_58_8 = all_10_2
% 199.02/32.73    (97)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.02/32.73    (98)   ~ (all_52_5 = all_10_2)
% 199.02/32.73    (99)  op(all_52_29, all_52_29) = all_52_28
% 199.02/32.73    (100)   ~ (all_52_23 = all_14_2)
% 199.02/32.73    (101)  all_56_12 = all_52_7
% 199.02/32.73    (102)  op(all_52_17, all_52_17) = all_52_16
% 199.02/32.73    (103)  all_58_5 = all_4_0
% 199.02/32.73    (104)  all_8_2 = all_6_2
% 199.02/32.73    (105)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.02/32.73    (106)   ~ (all_52_25 = all_6_2)
% 199.02/32.73    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.02/32.73    (108)   ~ (all_52_9 = all_4_2)
% 199.02/32.73    (109)   ~ (all_52_5 = all_6_2)
% 199.02/32.73    (110)   ~ (all_52_9 = all_6_2)
% 199.02/32.73    (111)  op(e3, all_6_1) = e2
% 199.02/32.73    (112)  all_56_0 = all_6_2
% 199.02/32.73    (113)  op(all_4_0, all_4_0) = all_52_18
% 199.02/32.73    (114)  op(e3, e3) = all_6_2
% 199.02/32.73    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.02/32.73    (116)   ~ (all_52_27 = all_14_2)
% 199.02/32.73    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.02/32.73    (118)  all_56_14 = all_52_23
% 199.02/32.73    (119)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.02/32.73    (120)  all_56_3 = all_52_25
% 199.02/32.73    (121)  all_28_0 = e3
% 199.02/32.73    (122)  op(e0, all_14_1) = e2
% 199.02/32.73    (123)   ~ (all_52_3 = all_52_7)
% 199.02/32.73    (124)  op(all_14_2, all_14_2) = all_52_30
% 199.02/32.73    (125)  all_58_5 = all_52_19
% 199.02/32.73    (126)   ~ (all_52_15 = all_4_2)
% 199.02/32.73    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.02/32.73           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.02/32.73           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.02/32.73           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.02/32.73    (128)   ~ (all_52_27 = all_4_2)
% 199.02/32.73    (129)  all_58_6 = all_52_5
% 199.02/32.73    (130)   ~ (all_4_0 = all_4_2)
% 199.02/32.73    (131)  op(e3, e2) = all_52_9
% 199.02/32.73    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.02/32.73    (133)   ~ (all_52_17 = all_6_2)
% 199.02/32.73    (134)   ~ (e1 = e0)
% 199.02/32.73    (135)   ~ (e3 = e2)
% 199.02/32.73    (136)  all_44_1 = all_6_1
% 199.02/32.73    (137)   ~ (all_52_9 = all_52_17)
% 199.02/32.73    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.73    (139)   ~ (all_52_3 = all_4_0)
% 199.02/32.73    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.02/32.73    (141)  all_44_0 = e2
% 199.02/32.73    (142)  op(all_52_13, all_52_13) = all_52_12
% 199.02/32.73    (143)  op(e1, e1) = all_10_2
% 199.02/32.73    (144)   ~ (all_52_7 = all_52_23)
% 199.02/32.73    (145)   ~ (all_52_17 = all_52_19)
% 199.02/32.73    (146)  all_58_3 = all_4_2
% 199.02/32.73    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.02/32.73    (148)   ~ (all_52_3 = all_4_2)
% 199.02/32.73    (149)  all_28_1 = e1
% 199.02/32.73    (150)   ~ (all_52_19 = all_4_2)
% 199.02/32.73    (151)   ~ (all_52_17 = all_52_23)
% 199.02/32.73    (152)  all_8_1 = all_6_1
% 199.02/32.73    (153)  op(all_6_2, e3) = all_6_1
% 199.02/32.73    (154)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.02/32.73    (155)   ~ (all_52_13 = all_52_29)
% 199.02/32.73    (156)  all_58_4 = all_52_17
% 199.02/32.73    (157)  op(all_52_25, all_52_25) = all_52_24
% 199.02/32.73  
% 199.02/32.73  Begin of proof
% 199.02/32.73  | 
% 199.02/32.73  | COMBINE_EQS: (72), (121) imply:
% 199.02/32.73  |   (158)  all_4_0 = e3
% 199.02/32.73  | 
% 199.02/32.73  | SIMP: (158) implies:
% 199.02/32.73  |   (159)  all_4_0 = e3
% 199.02/32.73  | 
% 199.02/32.73  | COMBINE_EQS: (103), (159) imply:
% 199.02/32.73  |   (160)  all_58_5 = e3
% 199.02/32.73  | 
% 199.02/32.73  | REDUCE: (139), (159) imply:
% 199.02/32.73  |   (161)   ~ (all_52_3 = e3)
% 199.02/32.73  | 
% 199.02/32.73  | REDUCE: (6), (159) imply:
% 199.02/32.73  |   (162)   ~ (all_52_17 = e3)
% 199.02/32.73  | 
% 199.02/32.73  | REDUCE: (13), (159) imply:
% 199.02/32.73  |   (163)   ~ (all_52_23 = e3)
% 199.02/32.73  | 
% 199.02/32.73  | REDUCE: (46), (159) imply:
% 199.02/32.73  |   (164)   ~ (all_10_2 = e3)
% 199.02/32.73  | 
% 199.02/32.73  | REDUCE: (130), (159) imply:
% 199.02/32.73  |   (165)   ~ (all_4_2 = e3)
% 199.02/32.73  | 
% 199.02/32.73  | SIMP: (165) implies:
% 199.02/32.73  |   (166)   ~ (all_4_2 = e3)
% 199.02/32.73  | 
% 199.02/32.73  | REDUCE: (113), (159) imply:
% 199.02/32.73  |   (167)  op(e3, e3) = all_52_18
% 199.02/32.73  | 
% 199.02/32.73  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 199.02/32.73  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.02/32.73  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 199.02/32.73  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 199.02/32.73  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 199.02/32.73  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 199.02/32.73  |            (71), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 199.02/32.73  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 199.02/32.73  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (104),
% 199.02/32.73  |            (105), (106), (107), (108), (109), (110), (111), (112), (114),
% 199.02/32.73  |            (115), (116), (117), (118), (119), (120), (122), (123), (124),
% 199.02/32.73  |            (125), (126), (127), (128), (129), (131), (132), (133), (134),
% 199.02/32.73  |            (135), (136), (137), (138), (140), (141), (142), (143), (144),
% 199.02/32.73  |            (145), (146), (147), (148), (149), (150), (151), (152), (153),
% 199.02/32.73  |            (154), (155), (156), (157), (160), (161), (162), (163), (164),
% 199.02/32.73  |            (166), (167) are inconsistent by sub-proof #53.
% 199.02/32.73  | 
% 199.02/32.73  End of proof
% 199.02/32.73  
% 199.02/32.73  Sub-proof #53 shows that the following formulas are inconsistent:
% 199.02/32.73  ----------------------------------------------------------------
% 199.02/32.73    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.02/32.73    (2)  op(e3, e3) = all_52_18
% 199.02/32.73    (3)   ~ (all_52_15 = all_52_23)
% 199.02/32.73    (4)   ~ (all_52_25 = all_52_27)
% 199.02/32.73    (5)  all_58_14 = all_52_23
% 199.02/32.73    (6)   ~ (e3 = e1)
% 199.02/32.73    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.02/32.73    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.73    (9)  all_58_1 = all_52_9
% 199.02/32.73    (10)   ~ (all_52_9 = all_52_13)
% 199.02/32.73    (11)   ~ (e3 = e0)
% 199.02/32.73    (12)  op(e2, e3) = all_52_3
% 199.02/32.73    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.02/32.73    (14)   ~ (all_52_7 = all_52_15)
% 199.02/32.73    (15)  op(all_52_7, all_52_7) = all_52_6
% 199.02/32.73    (16)   ~ (all_52_17 = all_52_25)
% 199.02/32.73    (17)   ~ (all_4_2 = e3)
% 199.02/32.73    (18)   ~ (all_52_3 = all_6_2)
% 199.02/32.73    (19)  all_44_2 = all_6_2
% 199.02/32.73    (20)  all_58_0 = all_6_2
% 199.02/32.73    (21)  op(all_14_2, e0) = all_14_1
% 199.02/32.73    (22)  all_56_4 = all_52_3
% 199.02/32.73    (23)   ~ (all_52_17 = all_10_2)
% 199.02/32.73    (24)  op(e3, e0) = all_52_25
% 199.02/32.73    (25)  op(all_52_5, all_52_5) = all_52_4
% 199.02/32.73    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.02/32.73    (27)  op(all_52_19, all_52_19) = all_52_18
% 199.02/32.73    (28)   ~ (all_52_27 = all_52_29)
% 199.02/32.73    (29)  all_58_13 = all_52_15
% 199.02/32.73    (30)  op(all_10_2, all_10_2) = all_52_20
% 199.02/32.73    (31)  all_58_9 = all_52_25
% 199.02/32.73    (32)   ~ (all_52_29 = all_14_2)
% 199.02/32.73    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.02/32.73    (34)  op(all_52_27, all_52_27) = all_52_26
% 199.02/32.73    (35)  op(e1, e3) = all_52_5
% 199.02/32.73    (36)  op(e2, e2) = all_4_2
% 199.02/32.74    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.02/32.74    (38)   ~ (all_52_3 = all_52_5)
% 199.02/32.74    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.02/32.74    (40)  op(all_4_2, e2) = e1
% 199.02/32.74    (41)  all_58_11 = all_52_29
% 199.02/32.74    (42)   ~ (all_52_3 = e3)
% 199.02/32.74    (43)  all_56_5 = all_4_2
% 199.02/32.74    (44)   ~ (all_52_25 = all_14_2)
% 199.02/32.74    (45)   ~ (all_52_3 = all_52_27)
% 199.02/32.74    (46)  op(all_10_2, e1) = all_10_1
% 199.02/32.74    (47)  op(all_6_2, all_6_2) = all_52_0
% 199.02/32.74    (48)   ~ (all_52_7 = all_6_2)
% 199.02/32.74    (49)  op(e0, e0) = all_14_2
% 199.02/32.74    (50)  all_56_15 = all_14_2
% 199.02/32.74    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.74    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.02/32.74    (53)  all_56_11 = all_52_29
% 199.02/32.74    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.02/32.74    (55)   ~ (e2 = e1)
% 199.02/32.74    (56)  all_58_10 = all_52_27
% 199.02/32.74    (57)  all_56_8 = all_52_5
% 199.02/32.74    (58)  op(all_52_9, all_52_9) = all_52_8
% 199.02/32.74    (59)  op(all_52_15, all_52_15) = all_52_14
% 199.02/32.74    (60)   ~ (all_52_25 = all_52_29)
% 199.02/32.74    (61)   ~ (all_52_29 = all_10_2)
% 199.02/32.74    (62)  all_58_7 = all_52_13
% 199.02/32.74    (63)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.02/32.74    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.02/32.74    (65)   ~ (all_52_5 = all_52_7)
% 199.02/32.74    (66)  all_58_12 = all_52_7
% 199.02/32.74    (67)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.02/32.74    (68)   ~ (all_52_7 = all_14_2)
% 199.02/32.74    (69)  all_58_2 = all_52_3
% 199.02/32.74    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.02/32.74    (71)  all_56_2 = all_52_17
% 199.02/32.74    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.02/32.74    (73)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.02/32.74    (74)  all_56_7 = all_52_27
% 199.02/32.74    (75)  all_28_2 = all_4_2
% 199.02/32.74    (76)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.02/32.74    (77)   ~ (e2 = e0)
% 199.02/32.74    (78)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.02/32.74    (79)   ~ (all_52_23 = e3)
% 199.02/32.74    (80)   ~ (all_52_5 = all_52_29)
% 199.02/32.74    (81)  all_56_6 = all_52_19
% 199.02/32.74    (82)   ~ (all_10_2 = e3)
% 199.02/32.74    (83)   ~ (all_52_19 = all_52_27)
% 199.02/32.74    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.02/32.74    (85)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.02/32.74            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.02/32.74    (86)   ~ (all_52_13 = all_4_2)
% 199.02/32.74    (87)  op(e3, e1) = all_52_17
% 199.02/32.74    (88)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.02/32.74    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.02/32.74    (90)  op(e0, e3) = all_52_7
% 199.02/32.74    (91)  op(e1, e2) = all_52_13
% 199.02/32.74    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.74    (93)   ~ (all_52_9 = all_52_25)
% 199.02/32.74    (94)  all_58_15 = all_14_2
% 199.02/32.74    (95)   ~ (all_52_19 = all_10_2)
% 199.02/32.74    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.02/32.74    (97)  all_58_8 = all_10_2
% 199.02/32.74    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.02/32.74    (99)   ~ (all_52_5 = all_10_2)
% 199.02/32.74    (100)  op(all_52_29, all_52_29) = all_52_28
% 199.02/32.74    (101)   ~ (all_52_23 = all_14_2)
% 199.02/32.74    (102)  all_56_12 = all_52_7
% 199.02/32.74    (103)  op(all_52_17, all_52_17) = all_52_16
% 199.02/32.74    (104)  all_8_2 = all_6_2
% 199.02/32.74    (105)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.02/32.74    (106)   ~ (all_52_25 = all_6_2)
% 199.02/32.74    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.02/32.74    (108)   ~ (all_52_9 = all_4_2)
% 199.02/32.74    (109)   ~ (all_52_5 = all_6_2)
% 199.02/32.74    (110)   ~ (all_52_9 = all_6_2)
% 199.02/32.74    (111)  op(e3, all_6_1) = e2
% 199.02/32.74    (112)  all_56_0 = all_6_2
% 199.02/32.74    (113)  op(e3, e3) = all_6_2
% 199.02/32.74    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.02/32.74    (115)   ~ (all_52_27 = all_14_2)
% 199.02/32.74    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.02/32.74    (117)  all_58_5 = e3
% 199.02/32.74    (118)  all_56_14 = all_52_23
% 199.02/32.74    (119)   ~ (all_52_17 = e3)
% 199.02/32.74    (120)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.02/32.74    (121)  all_56_3 = all_52_25
% 199.02/32.74    (122)  op(e0, all_14_1) = e2
% 199.02/32.74    (123)   ~ (all_52_3 = all_52_7)
% 199.02/32.74    (124)  op(all_14_2, all_14_2) = all_52_30
% 199.02/32.74    (125)  all_58_5 = all_52_19
% 199.02/32.74    (126)   ~ (all_52_15 = all_4_2)
% 199.02/32.74    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.02/32.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.02/32.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.02/32.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.02/32.74    (128)   ~ (all_52_27 = all_4_2)
% 199.02/32.74    (129)  all_58_6 = all_52_5
% 199.02/32.74    (130)  op(e3, e2) = all_52_9
% 199.02/32.74    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.02/32.74    (132)   ~ (all_52_17 = all_6_2)
% 199.02/32.74    (133)   ~ (e1 = e0)
% 199.02/32.74    (134)   ~ (e3 = e2)
% 199.02/32.74    (135)  all_44_1 = all_6_1
% 199.02/32.74    (136)   ~ (all_52_9 = all_52_17)
% 199.02/32.74    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.74    (138)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.02/32.74    (139)  all_44_0 = e2
% 199.02/32.74    (140)  op(all_52_13, all_52_13) = all_52_12
% 199.02/32.74    (141)  op(e1, e1) = all_10_2
% 199.02/32.74    (142)   ~ (all_52_7 = all_52_23)
% 199.02/32.74    (143)   ~ (all_52_17 = all_52_19)
% 199.02/32.74    (144)  all_58_3 = all_4_2
% 199.02/32.74    (145)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.02/32.74    (146)   ~ (all_52_3 = all_4_2)
% 199.02/32.74    (147)  all_28_1 = e1
% 199.02/32.74    (148)   ~ (all_52_19 = all_4_2)
% 199.02/32.74    (149)   ~ (all_52_17 = all_52_23)
% 199.02/32.74    (150)  all_8_1 = all_6_1
% 199.02/32.74    (151)  op(all_6_2, e3) = all_6_1
% 199.02/32.74    (152)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.02/32.74    (153)   ~ (all_52_13 = all_52_29)
% 199.02/32.74    (154)  all_58_4 = all_52_17
% 199.02/32.74    (155)  op(all_52_25, all_52_25) = all_52_24
% 199.02/32.74  
% 199.02/32.74  Begin of proof
% 199.02/32.74  | 
% 199.02/32.74  | BETA: splitting (120) gives:
% 199.02/32.74  | 
% 199.02/32.74  | Case 1:
% 199.02/32.74  | | 
% 199.02/32.74  | |   (156)   ~ (all_28_1 = e1)
% 199.02/32.74  | | 
% 199.02/32.74  | | REDUCE: (147), (156) imply:
% 199.02/32.74  | |   (157)  $false
% 199.02/32.74  | | 
% 199.02/32.74  | | CLOSE: (157) is inconsistent.
% 199.02/32.74  | | 
% 199.02/32.74  | Case 2:
% 199.02/32.74  | | 
% 199.02/32.74  | |   (158)   ~ (all_28_2 = e0)
% 199.02/32.74  | | 
% 199.02/32.74  | | REDUCE: (75), (158) imply:
% 199.02/32.74  | |   (159)   ~ (all_4_2 = e0)
% 199.02/32.74  | | 
% 199.02/32.74  | | GROUND_INST: instantiating (8) with all_6_2, all_52_18, e3, e3, simplifying
% 199.02/32.74  | |              with (2), (113) gives:
% 199.02/32.74  | |   (160)  all_52_18 = all_6_2
% 199.02/32.74  | | 
% 199.02/32.74  | | BETA: splitting (88) gives:
% 199.02/32.74  | | 
% 199.02/32.74  | | Case 1:
% 199.02/32.74  | | | 
% 199.02/32.74  | | |   (161)   ~ (all_44_0 = e2)
% 199.02/32.74  | | | 
% 199.02/32.74  | | | REDUCE: (139), (161) imply:
% 199.02/32.74  | | |   (162)  $false
% 199.02/32.74  | | | 
% 199.02/32.74  | | | CLOSE: (162) is inconsistent.
% 199.02/32.74  | | | 
% 199.02/32.74  | | Case 2:
% 199.02/32.74  | | | 
% 199.02/32.74  | | |   (163)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.02/32.74  | | | 
% 199.02/32.74  | | | BETA: splitting (85) gives:
% 199.02/32.74  | | | 
% 199.02/32.74  | | | Case 1:
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | |   (164)  all_58_15 = e0
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | | REF_CLOSE: (8), (21), (49), (77), (94), (122), (124), (164) are
% 199.02/32.74  | | | |            inconsistent by sub-proof #612.
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | Case 2:
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | |   (165)   ~ (all_58_15 = e0)
% 199.02/32.74  | | | |   (166)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.02/32.74  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | | ALPHA: (166) implies:
% 199.02/32.74  | | | |   (167)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.02/32.74  | | | |   (168)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | | REDUCE: (94), (165) imply:
% 199.02/32.74  | | | |   (169)   ~ (all_14_2 = e0)
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 199.02/32.74  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 199.02/32.74  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 199.02/32.74  | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 199.02/32.74  | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 199.02/32.74  | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 199.02/32.74  | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 199.02/32.74  | | | |            (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 199.02/32.74  | | | |            (83), (84), (86), (87), (89), (90), (91), (92), (93), (94),
% 199.02/32.74  | | | |            (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 199.02/32.74  | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 199.02/32.74  | | | |            (112), (113), (114), (115), (116), (117), (118), (119),
% 199.02/32.74  | | | |            (121), (123), (124), (125), (126), (127), (128), (129),
% 199.02/32.74  | | | |            (130), (131), (132), (133), (134), (135), (136), (137),
% 199.02/32.74  | | | |            (138), (140), (141), (142), (143), (144), (145), (146),
% 199.02/32.74  | | | |            (148), (149), (150), (151), (152), (153), (154), (155),
% 199.02/32.74  | | | |            (159), (160), (163), (167), (168), (169) are inconsistent by
% 199.02/32.74  | | | |            sub-proof #66.
% 199.02/32.74  | | | | 
% 199.02/32.74  | | | End of split
% 199.02/32.74  | | | 
% 199.02/32.74  | | End of split
% 199.02/32.74  | | 
% 199.02/32.74  | End of split
% 199.02/32.74  | 
% 199.02/32.74  End of proof
% 199.02/32.74  
% 199.02/32.74  Sub-proof #54 shows that the following formulas are inconsistent:
% 199.02/32.74  ----------------------------------------------------------------
% 199.02/32.74    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.02/32.74    (2)   ~ (all_52_15 = all_52_23)
% 199.02/32.74    (3)   ~ (all_52_25 = all_52_27)
% 199.02/32.74    (4)  all_58_14 = all_52_23
% 199.02/32.74    (5)   ~ (e3 = e1)
% 199.02/32.74    (6)   ~ (all_52_17 = all_4_0)
% 199.02/32.74    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.02/32.74    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.74    (9)   ~ (all_52_5 = all_52_13)
% 199.02/32.74    (10)  all_58_1 = all_52_9
% 199.02/32.74    (11)   ~ (all_52_9 = all_52_13)
% 199.02/32.74    (12)   ~ (e3 = e0)
% 199.02/32.74    (13)  op(e2, e3) = all_52_3
% 199.02/32.74    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.02/32.74    (15)   ~ (all_52_7 = all_52_15)
% 199.02/32.74    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.02/32.74    (17)   ~ (all_52_17 = all_52_25)
% 199.02/32.74    (18)   ~ (all_52_3 = all_6_2)
% 199.02/32.74    (19)  all_44_2 = all_6_2
% 199.02/32.74    (20)  all_58_0 = all_6_2
% 199.02/32.74    (21)  op(all_14_2, e0) = all_14_1
% 199.02/32.74    (22)  all_56_4 = all_52_3
% 199.02/32.74    (23)   ~ (all_52_17 = all_10_2)
% 199.02/32.74    (24)  all_26_1 = all_10_1
% 199.02/32.74    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.02/32.74    (26)  op(e3, e0) = all_52_25
% 199.02/32.74    (27)  all_26_2 = all_10_2
% 199.02/32.74    (28)  op(all_52_5, all_52_5) = all_52_4
% 199.02/32.74    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.02/32.74    (30)  op(all_52_19, all_52_19) = all_52_18
% 199.02/32.74    (31)   ~ (all_52_27 = all_52_29)
% 199.02/32.74    (32)  all_58_13 = all_52_15
% 199.02/32.74    (33)  op(all_10_2, all_10_2) = all_52_20
% 199.02/32.74    (34)  all_58_9 = all_52_25
% 199.02/32.74    (35)   ~ (all_52_29 = all_14_2)
% 199.02/32.74    (36)  op(all_52_27, all_52_27) = all_52_26
% 199.02/32.74    (37)  op(e1, e3) = all_52_5
% 199.02/32.74    (38)  op(e2, e2) = all_4_2
% 199.02/32.74    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.02/32.74    (40)   ~ (all_52_3 = all_52_5)
% 199.02/32.74    (41)  op(all_4_2, e2) = e1
% 199.02/32.74    (42)  all_58_11 = all_52_29
% 199.02/32.74    (43)  all_56_5 = all_4_2
% 199.02/32.74    (44)   ~ (all_52_25 = all_14_2)
% 199.02/32.74    (45)   ~ (all_52_9 = all_52_15)
% 199.02/32.74    (46)   ~ (all_52_3 = all_52_27)
% 199.02/32.74    (47)  op(all_10_2, e1) = all_10_1
% 199.02/32.74    (48)  op(all_6_2, all_6_2) = all_52_0
% 199.02/32.74    (49)   ~ (all_52_7 = all_6_2)
% 199.02/32.74    (50)  op(e0, e0) = all_14_2
% 199.02/32.74    (51)  all_56_15 = all_14_2
% 199.02/32.74    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.74    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.02/32.74    (54)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 199.02/32.74    (55)   ~ (all_58_15 = e0)
% 199.02/32.74    (56)  all_56_11 = all_52_29
% 199.02/32.74    (57)   ~ (all_4_0 = e3)
% 199.02/32.74    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.02/32.74    (59)  all_56_9 = all_52_13
% 199.02/32.74    (60)   ~ (e2 = e1)
% 199.02/32.74    (61)   ~ (all_52_13 = all_10_2)
% 199.02/32.74    (62)  all_58_10 = all_52_27
% 199.02/32.74    (63)  all_56_8 = all_52_5
% 199.02/32.74    (64)  op(all_52_9, all_52_9) = all_52_8
% 199.02/32.74    (65)  op(all_52_15, all_52_15) = all_52_14
% 199.02/32.74    (66)   ~ (all_52_25 = all_52_29)
% 199.02/32.74    (67)   ~ (all_52_29 = all_10_2)
% 199.02/32.74    (68)  all_58_7 = all_52_13
% 199.02/32.74    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.02/32.74    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.02/32.74    (71)   ~ (all_52_5 = all_52_7)
% 199.02/32.74    (72)  all_58_12 = all_52_7
% 199.02/32.74    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.02/32.74    (74)   ~ (all_52_7 = all_14_2)
% 199.02/32.74    (75)  all_58_2 = all_52_3
% 199.02/32.74    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.02/32.74    (77)  all_56_2 = all_52_17
% 199.02/32.74    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 199.02/32.74    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.02/32.74    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.02/32.74    (81)  all_56_7 = all_52_27
% 199.02/32.74    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.02/32.74    (83)   ~ (e2 = e0)
% 199.02/32.74    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.02/32.74    (85)   ~ (all_52_5 = all_52_29)
% 199.02/32.74    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.02/32.74    (87)  all_56_6 = all_52_19
% 199.02/32.74    (88)   ~ (all_52_19 = all_52_27)
% 199.02/32.74    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.02/32.74    (90)   ~ (all_52_13 = all_4_2)
% 199.02/32.74    (91)  op(e3, e1) = all_52_17
% 199.02/32.74    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.02/32.74    (93)  op(e0, e3) = all_52_7
% 199.02/32.74    (94)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.74    (95)   ~ (all_52_9 = all_52_25)
% 199.02/32.74    (96)  all_58_15 = all_14_2
% 199.02/32.74    (97)   ~ (all_52_19 = all_10_2)
% 199.02/32.74    (98)  op(all_52_23, all_52_23) = all_52_22
% 199.02/32.74    (99)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.02/32.74    (100)  all_58_8 = all_10_2
% 199.02/32.74    (101)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.02/32.74    (102)   ~ (all_52_5 = all_10_2)
% 199.02/32.74    (103)  op(all_52_29, all_52_29) = all_52_28
% 199.02/32.74    (104)   ~ (all_52_23 = all_14_2)
% 199.02/32.74    (105)  all_56_12 = all_52_7
% 199.02/32.74    (106)  op(all_52_17, all_52_17) = all_52_16
% 199.02/32.74    (107)  all_58_5 = all_4_0
% 199.02/32.74    (108)  all_8_2 = all_6_2
% 199.02/32.74    (109)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.02/32.74    (110)   ~ (all_52_25 = all_6_2)
% 199.02/32.74    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.02/32.74    (112)   ~ (all_52_9 = all_4_2)
% 199.02/32.74    (113)   ~ (all_52_5 = all_6_2)
% 199.02/32.74    (114)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.02/32.74    (115)   ~ (all_52_9 = all_6_2)
% 199.02/32.74    (116)   ~ (all_52_13 = all_52_15)
% 199.02/32.74    (117)  op(e3, all_6_1) = e2
% 199.02/32.74    (118)  all_56_0 = all_6_2
% 199.02/32.74    (119)  op(e3, e3) = all_6_2
% 199.02/32.74    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.02/32.74    (121)   ~ (all_52_27 = all_14_2)
% 199.02/32.74    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.02/32.74    (123)  all_56_14 = all_52_23
% 199.02/32.74    (124)  op(all_4_2, all_4_2) = all_52_10
% 199.02/32.74    (125)  all_56_3 = all_52_25
% 199.02/32.74    (126)   ~ (all_52_3 = all_52_7)
% 199.02/32.74    (127)  op(all_14_2, all_14_2) = all_52_30
% 199.02/32.74    (128)  all_58_5 = all_52_19
% 199.02/32.74    (129)   ~ (all_52_15 = all_4_2)
% 199.02/32.74    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.02/32.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.02/32.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.02/32.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.02/32.74    (131)   ~ (all_52_27 = all_4_2)
% 199.02/32.74    (132)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 199.02/32.74             all_58_13 = e0 | all_58_14 = e0)
% 199.02/32.74    (133)  all_58_6 = all_52_5
% 199.02/32.74    (134)  op(e3, e2) = all_52_9
% 199.02/32.74    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.02/32.74    (136)   ~ (all_52_17 = all_6_2)
% 199.02/32.74    (137)   ~ (e1 = e0)
% 199.02/32.74    (138)   ~ (e3 = e2)
% 199.02/32.74    (139)  all_44_1 = all_6_1
% 199.02/32.74    (140)   ~ (all_52_9 = all_52_17)
% 199.02/32.74    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.74    (142)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.02/32.74    (143)   ~ (all_52_3 = all_4_0)
% 199.02/32.74    (144)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.02/32.74    (145)  op(all_52_13, all_52_13) = all_52_12
% 199.02/32.74    (146)  op(e1, e1) = all_10_2
% 199.02/32.74    (147)   ~ (all_52_23 = all_10_2)
% 199.02/32.74    (148)   ~ (all_52_7 = all_52_23)
% 199.02/32.74    (149)   ~ (all_52_17 = all_52_19)
% 199.02/32.74    (150)  all_58_3 = all_4_2
% 199.02/32.74    (151)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.02/32.74    (152)   ~ (all_52_3 = all_4_2)
% 199.02/32.74    (153)   ~ (all_52_19 = all_4_2)
% 199.02/32.74    (154)   ~ (all_52_17 = all_52_23)
% 199.02/32.74    (155)  all_8_1 = all_6_1
% 199.02/32.74    (156)  op(all_6_2, e3) = all_6_1
% 199.02/32.74    (157)   ~ (all_52_13 = all_52_29)
% 199.02/32.74    (158)  all_58_4 = all_52_17
% 199.02/32.74    (159)  op(all_52_25, all_52_25) = all_52_24
% 199.02/32.74  
% 199.02/32.74  Begin of proof
% 199.02/32.74  | 
% 199.02/32.74  | ALPHA: (132) implies:
% 199.02/32.74  |   (160)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.02/32.74  |   (161)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.02/32.74  | 
% 199.02/32.74  | REDUCE: (55), (96) imply:
% 199.02/32.74  |   (162)   ~ (all_14_2 = e0)
% 199.02/32.74  | 
% 199.02/32.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.02/32.74  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 199.02/32.74  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 199.02/32.74  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.02/32.74  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 199.02/32.74  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 199.02/32.74  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 199.02/32.74  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 199.02/32.74  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 199.02/32.74  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 199.02/32.74  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 199.02/32.74  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 199.02/32.74  |            (129), (130), (131), (133), (134), (135), (136), (137), (138),
% 199.02/32.74  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 199.02/32.74  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 199.02/32.74  |            (157), (158), (159), (160), (161), (162) are inconsistent by
% 199.02/32.74  |            sub-proof #55.
% 199.02/32.74  | 
% 199.02/32.74  End of proof
% 199.02/32.74  
% 199.02/32.74  Sub-proof #55 shows that the following formulas are inconsistent:
% 199.02/32.74  ----------------------------------------------------------------
% 199.02/32.74    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.02/32.74    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.02/32.74    (3)   ~ (all_52_15 = all_52_23)
% 199.02/32.74    (4)   ~ (all_52_25 = all_52_27)
% 199.02/32.74    (5)  all_58_14 = all_52_23
% 199.02/32.74    (6)   ~ (e3 = e1)
% 199.02/32.74    (7)   ~ (all_52_17 = all_4_0)
% 199.02/32.74    (8)  op(all_52_3, all_52_3) = all_52_2
% 199.02/32.74    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.02/32.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.02/32.74    (10)   ~ (all_52_5 = all_52_13)
% 199.02/32.74    (11)  all_58_1 = all_52_9
% 199.02/32.74    (12)   ~ (all_52_9 = all_52_13)
% 199.02/32.74    (13)   ~ (e3 = e0)
% 199.02/32.74    (14)  op(e2, e3) = all_52_3
% 199.02/32.74    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.02/32.74    (16)   ~ (all_52_7 = all_52_15)
% 199.02/32.74    (17)  op(all_52_7, all_52_7) = all_52_6
% 199.02/32.74    (18)   ~ (all_52_17 = all_52_25)
% 199.02/32.74    (19)   ~ (all_52_3 = all_6_2)
% 199.02/32.74    (20)  all_44_2 = all_6_2
% 199.02/32.74    (21)  all_58_0 = all_6_2
% 199.02/32.74    (22)  op(all_14_2, e0) = all_14_1
% 199.02/32.74    (23)  all_56_4 = all_52_3
% 199.02/32.74    (24)   ~ (all_52_17 = all_10_2)
% 199.02/32.74    (25)  all_26_1 = all_10_1
% 199.02/32.74    (26)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.02/32.74    (27)  op(e3, e0) = all_52_25
% 199.02/32.74    (28)  all_26_2 = all_10_2
% 199.02/32.74    (29)  op(all_52_5, all_52_5) = all_52_4
% 199.02/32.74    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.02/32.74    (31)  op(all_52_19, all_52_19) = all_52_18
% 199.02/32.74    (32)   ~ (all_52_27 = all_52_29)
% 199.02/32.74    (33)  all_58_13 = all_52_15
% 199.02/32.74    (34)  op(all_10_2, all_10_2) = all_52_20
% 199.02/32.74    (35)  all_58_9 = all_52_25
% 199.02/32.74    (36)   ~ (all_52_29 = all_14_2)
% 199.02/32.74    (37)  op(all_52_27, all_52_27) = all_52_26
% 199.02/32.74    (38)  op(e1, e3) = all_52_5
% 199.02/32.75    (39)  op(e2, e2) = all_4_2
% 199.02/32.75    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.02/32.75    (41)   ~ (all_52_3 = all_52_5)
% 199.02/32.75    (42)  op(all_4_2, e2) = e1
% 199.02/32.75    (43)  all_58_11 = all_52_29
% 199.02/32.75    (44)  all_56_5 = all_4_2
% 199.02/32.75    (45)   ~ (all_52_25 = all_14_2)
% 199.02/32.75    (46)   ~ (all_52_9 = all_52_15)
% 199.02/32.75    (47)   ~ (all_52_3 = all_52_27)
% 199.02/32.75    (48)  op(all_10_2, e1) = all_10_1
% 199.02/32.75    (49)  op(all_6_2, all_6_2) = all_52_0
% 199.02/32.75    (50)   ~ (all_52_7 = all_6_2)
% 199.02/32.75    (51)  op(e0, e0) = all_14_2
% 199.02/32.75    (52)  all_56_15 = all_14_2
% 199.02/32.75    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.02/32.75    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.02/32.75    (55)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 199.02/32.75    (56)  all_56_11 = all_52_29
% 199.02/32.75    (57)   ~ (all_4_0 = e3)
% 199.02/32.75    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.02/32.75    (59)  all_56_9 = all_52_13
% 199.02/32.75    (60)   ~ (e2 = e1)
% 199.02/32.75    (61)   ~ (all_52_13 = all_10_2)
% 199.02/32.75    (62)  all_58_10 = all_52_27
% 199.02/32.75    (63)  all_56_8 = all_52_5
% 199.02/32.75    (64)  op(all_52_9, all_52_9) = all_52_8
% 199.02/32.75    (65)  op(all_52_15, all_52_15) = all_52_14
% 199.02/32.75    (66)   ~ (all_52_25 = all_52_29)
% 199.02/32.75    (67)   ~ (all_52_29 = all_10_2)
% 199.02/32.75    (68)  all_58_7 = all_52_13
% 199.02/32.75    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.02/32.75    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.02/32.75    (71)   ~ (all_52_5 = all_52_7)
% 199.02/32.75    (72)  all_58_12 = all_52_7
% 199.02/32.75    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.02/32.75    (74)   ~ (all_52_7 = all_14_2)
% 199.02/32.75    (75)   ~ (all_14_2 = e0)
% 199.02/32.75    (76)  all_58_2 = all_52_3
% 199.02/32.75    (77)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.02/32.75    (78)  all_56_2 = all_52_17
% 199.02/32.75    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 199.02/32.75    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.02/32.75    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.02/32.75    (82)  all_56_7 = all_52_27
% 199.02/32.75    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.02/32.75    (84)   ~ (e2 = e0)
% 199.02/32.75    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.02/32.75    (86)   ~ (all_52_5 = all_52_29)
% 199.02/32.75    (87)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.02/32.75    (88)  all_56_6 = all_52_19
% 199.02/32.75    (89)   ~ (all_52_19 = all_52_27)
% 199.02/32.75    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.02/32.75    (91)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.02/32.75    (92)   ~ (all_52_13 = all_4_2)
% 199.02/32.75    (93)  op(e3, e1) = all_52_17
% 199.02/32.75    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.02/32.75    (95)  op(e0, e3) = all_52_7
% 199.02/32.75    (96)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.02/32.75    (97)   ~ (all_52_9 = all_52_25)
% 199.02/32.75    (98)  all_58_15 = all_14_2
% 199.02/32.75    (99)   ~ (all_52_19 = all_10_2)
% 199.02/32.75    (100)  op(all_52_23, all_52_23) = all_52_22
% 199.02/32.75    (101)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.02/32.75    (102)  all_58_8 = all_10_2
% 199.02/32.75    (103)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.02/32.75    (104)   ~ (all_52_5 = all_10_2)
% 199.02/32.75    (105)  op(all_52_29, all_52_29) = all_52_28
% 199.02/32.75    (106)   ~ (all_52_23 = all_14_2)
% 199.02/32.75    (107)  all_56_12 = all_52_7
% 199.02/32.75    (108)  op(all_52_17, all_52_17) = all_52_16
% 199.02/32.75    (109)  all_58_5 = all_4_0
% 199.02/32.75    (110)  all_8_2 = all_6_2
% 199.02/32.75    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.02/32.75    (112)   ~ (all_52_25 = all_6_2)
% 199.02/32.75    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.02/32.75    (114)   ~ (all_52_9 = all_4_2)
% 199.02/32.75    (115)   ~ (all_52_5 = all_6_2)
% 199.02/32.75    (116)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.02/32.75    (117)   ~ (all_52_9 = all_6_2)
% 199.02/32.75    (118)   ~ (all_52_13 = all_52_15)
% 199.02/32.75    (119)  op(e3, all_6_1) = e2
% 199.02/32.75    (120)  all_56_0 = all_6_2
% 199.02/32.75    (121)  op(e3, e3) = all_6_2
% 199.02/32.75    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.02/32.75    (123)   ~ (all_52_27 = all_14_2)
% 199.02/32.75    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.02/32.75    (125)  all_56_14 = all_52_23
% 199.02/32.75    (126)  op(all_4_2, all_4_2) = all_52_10
% 199.02/32.75    (127)  all_56_3 = all_52_25
% 199.02/32.75    (128)   ~ (all_52_3 = all_52_7)
% 199.02/32.75    (129)  op(all_14_2, all_14_2) = all_52_30
% 199.02/32.75    (130)  all_58_5 = all_52_19
% 199.02/32.75    (131)   ~ (all_52_15 = all_4_2)
% 199.02/32.75    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.02/32.75           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.02/32.75           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.02/32.75           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.02/32.75    (133)   ~ (all_52_27 = all_4_2)
% 199.02/32.75    (134)  all_58_6 = all_52_5
% 199.02/32.75    (135)  op(e3, e2) = all_52_9
% 199.02/32.75    (136)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.02/32.75    (137)   ~ (all_52_17 = all_6_2)
% 199.02/32.75    (138)   ~ (e1 = e0)
% 199.02/32.75    (139)   ~ (e3 = e2)
% 199.02/32.75    (140)  all_44_1 = all_6_1
% 199.02/32.75    (141)   ~ (all_52_9 = all_52_17)
% 199.02/32.75    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.02/32.75    (143)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.02/32.75    (144)   ~ (all_52_3 = all_4_0)
% 199.02/32.75    (145)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.02/32.75    (146)  op(all_52_13, all_52_13) = all_52_12
% 199.02/32.75    (147)  op(e1, e1) = all_10_2
% 199.02/32.75    (148)   ~ (all_52_23 = all_10_2)
% 199.02/32.75    (149)   ~ (all_52_7 = all_52_23)
% 199.02/32.75    (150)   ~ (all_52_17 = all_52_19)
% 199.02/32.75    (151)  all_58_3 = all_4_2
% 199.02/32.75    (152)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.02/32.75    (153)   ~ (all_52_3 = all_4_2)
% 199.02/32.75    (154)   ~ (all_52_19 = all_4_2)
% 199.02/32.75    (155)   ~ (all_52_17 = all_52_23)
% 199.02/32.75    (156)  all_8_1 = all_6_1
% 199.02/32.75    (157)  op(all_6_2, e3) = all_6_1
% 199.02/32.75    (158)   ~ (all_52_13 = all_52_29)
% 199.02/32.75    (159)  all_58_4 = all_52_17
% 199.02/32.75    (160)  op(all_52_25, all_52_25) = all_52_24
% 199.02/32.75  
% 199.02/32.75  Begin of proof
% 199.02/32.75  | 
% 199.02/32.75  | BETA: splitting (132) gives:
% 199.02/32.75  | 
% 199.02/32.75  | Case 1:
% 199.02/32.75  | | 
% 199.02/32.75  | |   (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.02/32.75  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 199.02/32.75  | | 
% 199.02/32.75  | | BETA: splitting (161) gives:
% 199.02/32.75  | | 
% 199.02/32.75  | | Case 1:
% 199.02/32.75  | | | 
% 199.02/32.75  | | |   (162)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.02/32.75  | | | 
% 199.02/32.75  | | | REF_CLOSE: (8), (9), (17), (21), (29), (39), (49), (51), (53), (72), (74),
% 199.02/32.75  | | |            (76), (80), (104), (119), (120), (121), (134), (136), (139),
% 199.02/32.75  | | |            (145), (147), (153), (157), (162) are inconsistent by sub-proof
% 199.02/32.75  | | |            #501.
% 199.02/32.75  | | | 
% 199.02/32.75  | | Case 2:
% 199.02/32.75  | | | 
% 199.02/32.75  | | |   (163)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 199.02/32.75  | | | 
% 199.02/32.75  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 199.02/32.75  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 199.02/32.75  | | |            (27), (29), (30), (32), (33), (35), (36), (38), (39), (40),
% 199.02/32.75  | | |            (41), (42), (43), (45), (50), (52), (53), (56), (57), (58),
% 199.02/32.75  | | |            (59), (62), (63), (64), (65), (67), (68), (70), (71), (72),
% 199.02/32.75  | | |            (73), (74), (75), (76), (78), (82), (83), (84), (90), (92),
% 199.02/32.75  | | |            (93), (95), (96), (97), (98), (101), (102), (103), (107),
% 199.02/32.75  | | |            (108), (109), (110), (112), (114), (115), (116), (117), (119),
% 199.02/32.75  | | |            (121), (122), (123), (124), (126), (128), (129), (131), (134),
% 199.02/32.75  | | |            (135), (136), (137), (138), (139), (140), (141), (142), (143),
% 199.02/32.75  | | |            (146), (147), (151), (153), (155), (156), (157), (159), (160),
% 199.02/32.75  | | |            (163) are inconsistent by sub-proof #86.
% 199.02/32.75  | | | 
% 199.02/32.75  | | End of split
% 199.02/32.75  | | 
% 199.02/32.75  | Case 2:
% 199.02/32.75  | | 
% 199.02/32.75  | |   (164)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 199.02/32.75  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 199.02/32.75  | |            e0)
% 199.02/32.75  | | 
% 199.02/32.75  | | BETA: splitting (164) gives:
% 199.02/32.75  | | 
% 199.02/32.75  | | Case 1:
% 199.02/32.75  | | | 
% 199.02/32.75  | | |   (165)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 199.02/32.75  | | | 
% 199.02/32.75  | | | ALPHA: (165) implies:
% 199.02/32.75  | | |   (166)  all_52_22 = e0
% 199.02/32.75  | | |   (167)  all_52_20 = e1
% 199.02/32.75  | | |   (168)  all_52_16 = e3
% 199.02/32.75  | | | 
% 199.02/32.75  | | | REDUCE: (108), (168) imply:
% 199.02/32.75  | | |   (169)  op(all_52_17, all_52_17) = e3
% 199.02/32.75  | | | 
% 199.02/32.75  | | | REDUCE: (100), (166) imply:
% 199.02/32.75  | | |   (170)  op(all_52_23, all_52_23) = e0
% 199.02/32.75  | | | 
% 199.02/32.75  | | | REDUCE: (34), (167) imply:
% 199.02/32.75  | | |   (171)  op(all_10_2, all_10_2) = e1
% 199.02/32.75  | | | 
% 199.02/32.75  | | | BETA: splitting (103) gives:
% 199.02/32.75  | | | 
% 199.02/32.75  | | | Case 1:
% 199.02/32.75  | | | | 
% 199.02/32.75  | | | |   (172)  all_56_15 = e3
% 199.02/32.75  | | | | 
% 199.02/32.75  | | | | COMBINE_EQS: (52), (172) imply:
% 199.02/32.75  | | | |   (173)  all_14_2 = e3
% 199.02/32.75  | | | | 
% 199.02/32.75  | | | | SIMP: (173) implies:
% 199.02/32.75  | | | |   (174)  all_14_2 = e3
% 199.02/32.75  | | | | 
% 199.16/32.75  | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (15), (16), (19), (20), (21),
% 199.16/32.75  | | | |            (26), (29), (33), (35), (38), (45), (46), (50), (53), (57),
% 199.16/32.75  | | | |            (58), (61), (63), (64), (68), (71), (72), (74), (75), (76),
% 199.16/32.75  | | | |            (78), (80), (87), (91), (95), (96), (98), (101), (102),
% 199.16/32.75  | | | |            (104), (106), (107), (109), (110), (114), (115), (119),
% 199.16/32.75  | | | |            (121), (124), (128), (129), (134), (135), (137), (138),
% 199.16/32.75  | | | |            (139), (140), (141), (142), (144), (147), (148), (149),
% 199.16/32.75  | | | |            (151), (155), (156), (157), (159), (169), (170), (171), (174)
% 199.16/32.75  | | | |            are inconsistent by sub-proof #82.
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | Case 2:
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | |   (175)   ~ (all_56_15 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REDUCE: (52), (175) imply:
% 199.16/32.75  | | | |   (176)   ~ (all_14_2 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (13), (15), (16), (17),
% 199.16/32.75  | | | |            (19), (21), (24), (25), (28), (29), (33), (35), (37), (39),
% 199.16/32.75  | | | |            (41), (42), (43), (45), (46), (48), (50), (53), (55), (57),
% 199.16/32.75  | | | |            (58), (60), (61), (62), (66), (68), (69), (72), (73), (76),
% 199.16/32.75  | | | |            (78), (79), (80), (81), (84), (87), (91), (93), (95), (96),
% 199.16/32.75  | | | |            (98), (99), (102), (104), (107), (109), (110), (117), (118),
% 199.16/32.75  | | | |            (119), (121), (122), (124), (125), (128), (129), (130),
% 199.16/32.75  | | | |            (131), (134), (135), (136), (137), (138), (139), (141),
% 199.16/32.75  | | | |            (142), (147), (148), (149), (151), (153), (155), (156),
% 199.16/32.75  | | | |            (157), (159), (160), (169), (170), (171), (176) are
% 199.16/32.75  | | | |            inconsistent by sub-proof #56.
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | End of split
% 199.16/32.75  | | | 
% 199.16/32.75  | | Case 2:
% 199.16/32.75  | | | 
% 199.16/32.75  | | |   (177)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 199.16/32.75  | | | 
% 199.16/32.75  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (13), (14),
% 199.16/32.75  | | |            (15), (17), (18), (19), (20), (21), (22), (24), (26), (27),
% 199.16/32.75  | | |            (29), (30), (31), (32), (33), (35), (36), (37), (38), (39),
% 199.16/32.75  | | |            (40), (41), (43), (44), (45), (47), (48), (49), (50), (51),
% 199.16/32.75  | | |            (52), (53), (54), (56), (58), (62), (63), (64), (66), (67),
% 199.16/32.75  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 199.16/32.75  | | |            (78), (80), (81), (82), (84), (85), (86), (88), (89), (90),
% 199.16/32.75  | | |            (91), (93), (94), (95), (96), (97), (98), (99), (101), (102),
% 199.16/32.75  | | |            (103), (104), (105), (106), (107), (108), (110), (111), (112),
% 199.16/32.75  | | |            (113), (114), (115), (119), (120), (121), (122), (123), (124),
% 199.16/32.75  | | |            (125), (127), (128), (129), (130), (131), (133), (134), (135),
% 199.16/32.75  | | |            (136), (137), (138), (139), (140), (141), (142), (145), (146),
% 199.16/32.75  | | |            (147), (149), (150), (151), (152), (153), (154), (155), (156),
% 199.16/32.75  | | |            (157), (158), (159), (160), (177) are inconsistent by sub-proof
% 199.16/32.75  | | |            #434.
% 199.16/32.75  | | | 
% 199.16/32.75  | | End of split
% 199.16/32.75  | | 
% 199.16/32.75  | End of split
% 199.16/32.75  | 
% 199.16/32.75  End of proof
% 199.16/32.75  
% 199.16/32.75  Sub-proof #56 shows that the following formulas are inconsistent:
% 199.16/32.75  ----------------------------------------------------------------
% 199.16/32.75    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.75    (2)   ~ (all_52_25 = all_52_27)
% 199.16/32.75    (3)  all_58_14 = all_52_23
% 199.16/32.75    (4)   ~ (e3 = e1)
% 199.16/32.75    (5)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.75    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.75    (7)  all_58_1 = all_52_9
% 199.16/32.75    (8)   ~ (e3 = e0)
% 199.16/32.75    (9)  op(all_52_23, all_52_23) = e0
% 199.16/32.75    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.75    (11)   ~ (all_52_7 = all_52_15)
% 199.16/32.75    (12)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.75    (13)   ~ (all_52_3 = all_6_2)
% 199.16/32.75    (14)  all_58_0 = all_6_2
% 199.16/32.75    (15)   ~ (all_52_17 = all_10_2)
% 199.16/32.75    (16)  all_26_1 = all_10_1
% 199.16/32.75    (17)  all_26_2 = all_10_2
% 199.16/32.75    (18)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.75    (19)  all_58_13 = all_52_15
% 199.16/32.75    (20)  all_58_9 = all_52_25
% 199.16/32.75    (21)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.75    (22)  op(e2, e2) = all_4_2
% 199.16/32.75    (23)   ~ (all_52_3 = all_52_5)
% 199.16/32.75    (24)  op(all_4_2, e2) = e1
% 199.16/32.75    (25)  all_58_11 = all_52_29
% 199.16/32.75    (26)   ~ (all_52_25 = all_14_2)
% 199.16/32.75    (27)   ~ (all_52_9 = all_52_15)
% 199.16/32.75    (28)  op(all_10_2, e1) = all_10_1
% 199.16/32.75    (29)   ~ (all_52_7 = all_6_2)
% 199.16/32.75    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.75    (31)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 199.16/32.75    (32)   ~ (all_4_0 = e3)
% 199.16/32.75    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.75    (34)   ~ (e2 = e1)
% 199.16/32.75    (35)   ~ (all_52_13 = all_10_2)
% 199.16/32.75    (36)  op(all_10_2, all_10_2) = e1
% 199.16/32.75    (37)  all_58_10 = all_52_27
% 199.16/32.75    (38)   ~ (all_52_25 = all_52_29)
% 199.16/32.75    (39)  all_58_7 = all_52_13
% 199.16/32.75    (40)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.75    (41)  all_58_12 = all_52_7
% 199.16/32.75    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.75    (43)  all_58_2 = all_52_3
% 199.16/32.75    (44)  all_56_2 = all_52_17
% 199.16/32.75    (45)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 199.16/32.75    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.75    (47)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.75    (48)   ~ (e2 = e0)
% 199.16/32.75    (49)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.16/32.75    (50)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.75    (51)  op(e3, e1) = all_52_17
% 199.16/32.75    (52)  op(e0, e3) = all_52_7
% 199.16/32.75    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.75    (54)  all_58_15 = all_14_2
% 199.16/32.75    (55)   ~ (all_52_19 = all_10_2)
% 199.16/32.75    (56)  all_58_8 = all_10_2
% 199.16/32.75    (57)   ~ (all_52_5 = all_10_2)
% 199.16/32.75    (58)  all_56_12 = all_52_7
% 199.16/32.75    (59)  all_58_5 = all_4_0
% 199.16/32.75    (60)  all_8_2 = all_6_2
% 199.16/32.75    (61)   ~ (all_52_9 = all_6_2)
% 199.16/32.75    (62)   ~ (all_52_13 = all_52_15)
% 199.16/32.75    (63)  op(e3, all_6_1) = e2
% 199.16/32.75    (64)  op(e3, e3) = all_6_2
% 199.16/32.75    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.75    (66)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.75    (67)  all_56_14 = all_52_23
% 199.16/32.75    (68)   ~ (all_52_3 = all_52_7)
% 199.16/32.75    (69)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.75    (70)  all_58_5 = all_52_19
% 199.16/32.75    (71)   ~ (all_52_15 = all_4_2)
% 199.16/32.75    (72)  op(all_52_17, all_52_17) = e3
% 199.16/32.75    (73)  all_58_6 = all_52_5
% 199.16/32.75    (74)  op(e3, e2) = all_52_9
% 199.16/32.75    (75)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.75    (76)   ~ (all_52_17 = all_6_2)
% 199.16/32.75    (77)   ~ (e1 = e0)
% 199.16/32.75    (78)   ~ (e3 = e2)
% 199.16/32.75    (79)   ~ (all_52_9 = all_52_17)
% 199.16/32.75    (80)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.75    (81)  op(e1, e1) = all_10_2
% 199.16/32.75    (82)   ~ (all_52_23 = all_10_2)
% 199.16/32.75    (83)   ~ (all_52_7 = all_52_23)
% 199.16/32.75    (84)  all_58_3 = all_4_2
% 199.16/32.75    (85)   ~ (all_52_3 = all_4_2)
% 199.16/32.75    (86)   ~ (all_52_17 = all_52_23)
% 199.16/32.75    (87)  all_8_1 = all_6_1
% 199.16/32.75    (88)  op(all_6_2, e3) = all_6_1
% 199.16/32.75    (89)  all_58_4 = all_52_17
% 199.16/32.75    (90)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.75    (91)   ~ (all_14_2 = e3)
% 199.16/32.75  
% 199.16/32.75  Begin of proof
% 199.16/32.75  | 
% 199.16/32.75  | BETA: splitting (30) gives:
% 199.16/32.75  | 
% 199.16/32.75  | Case 1:
% 199.16/32.75  | | 
% 199.16/32.75  | |   (92)  all_58_2 = e3
% 199.16/32.75  | | 
% 199.16/32.75  | | COMBINE_EQS: (43), (92) imply:
% 199.16/32.75  | |   (93)  all_52_3 = e3
% 199.16/32.75  | | 
% 199.16/32.75  | | SIMP: (93) implies:
% 199.16/32.75  | |   (94)  all_52_3 = e3
% 199.16/32.75  | | 
% 199.16/32.75  | | REDUCE: (23), (94) imply:
% 199.16/32.75  | |   (95)   ~ (all_52_5 = e3)
% 199.16/32.75  | | 
% 199.16/32.75  | | SIMP: (95) implies:
% 199.16/32.75  | |   (96)   ~ (all_52_5 = e3)
% 199.16/32.75  | | 
% 199.16/32.75  | | REDUCE: (68), (94) imply:
% 199.16/32.75  | |   (97)   ~ (all_52_7 = e3)
% 199.16/32.75  | | 
% 199.16/32.75  | | SIMP: (97) implies:
% 199.16/32.75  | |   (98)   ~ (all_52_7 = e3)
% 199.16/32.75  | | 
% 199.16/32.75  | | REDUCE: (5), (94) imply:
% 199.16/32.75  | |   (99)  op(e3, e3) = all_52_2
% 199.16/32.75  | | 
% 199.16/32.75  | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3, simplifying
% 199.16/32.75  | |              with (64), (99) gives:
% 199.16/32.75  | |   (100)  all_52_2 = all_6_2
% 199.16/32.75  | | 
% 199.16/32.75  | | BETA: splitting (75) gives:
% 199.16/32.75  | | 
% 199.16/32.75  | | Case 1:
% 199.16/32.75  | | | 
% 199.16/32.75  | | |   (101)  all_58_12 = e3
% 199.16/32.75  | | | 
% 199.16/32.75  | | | REF_CLOSE: (41), (98), (101) are inconsistent by sub-proof #1367.
% 199.16/32.75  | | | 
% 199.16/32.75  | | Case 2:
% 199.16/32.75  | | | 
% 199.16/32.75  | | |   (102)   ~ (all_58_12 = e3)
% 199.16/32.75  | | |   (103)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.75  | | | 
% 199.16/32.75  | | | BETA: splitting (65) gives:
% 199.16/32.75  | | | 
% 199.16/32.75  | | | Case 1:
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | |   (104)  all_58_9 = e3
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | COMBINE_EQS: (20), (104) imply:
% 199.16/32.75  | | | |   (105)  all_52_25 = e3
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REDUCE: (38), (105) imply:
% 199.16/32.75  | | | |   (106)   ~ (all_52_29 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | SIMP: (106) implies:
% 199.16/32.75  | | | |   (107)   ~ (all_52_29 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REDUCE: (26), (105) imply:
% 199.16/32.75  | | | |   (108)   ~ (all_14_2 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REDUCE: (90), (105) imply:
% 199.16/32.75  | | | |   (109)  op(e3, e3) = all_52_24
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 199.16/32.75  | | | |              simplifying with (64), (109) gives:
% 199.16/32.75  | | | |   (110)  all_52_24 = all_6_2
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | BETA: splitting (42) gives:
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | Case 1:
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | |   (111)  all_58_6 = e3
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | | REF_CLOSE: (73), (96), (111) are inconsistent by sub-proof #1328.
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | Case 2:
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | |   (112)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | | BETA: splitting (40) gives:
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | | Case 1:
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | |   (113)  all_56_14 = e3
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | COMBINE_EQS: (67), (113) imply:
% 199.16/32.75  | | | | | |   (114)  all_52_23 = e3
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | SIMP: (114) implies:
% 199.16/32.75  | | | | | |   (115)  all_52_23 = e3
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | COMBINE_EQS: (3), (115) imply:
% 199.16/32.75  | | | | | |   (116)  all_58_14 = e3
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (19), (29), (33),
% 199.16/32.75  | | | | | |            (41), (44), (49), (50), (52), (54), (58), (60), (63),
% 199.16/32.75  | | | | | |            (64), (69), (72), (74), (76), (77), (79), (81), (82),
% 199.16/32.75  | | | | | |            (83), (86), (87), (88), (115), (116) are inconsistent by
% 199.16/32.75  | | | | | |            sub-proof #85.
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | Case 2:
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | |   (117)   ~ (all_56_14 = e3)
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | REDUCE: (67), (117) imply:
% 199.16/32.75  | | | | | |   (118)   ~ (all_52_23 = e3)
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | BETA: splitting (103) gives:
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | | Case 1:
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | |   (119)  all_58_13 = e3
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | COMBINE_EQS: (19), (119) imply:
% 199.16/32.75  | | | | | | |   (120)  all_52_15 = e3
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | SIMP: (120) implies:
% 199.16/32.75  | | | | | | |   (121)  all_52_15 = e3
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | REDUCE: (27), (121) imply:
% 199.16/32.75  | | | | | | |   (122)   ~ (all_52_9 = e3)
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | REDUCE: (62), (121) imply:
% 199.16/32.75  | | | | | | |   (123)   ~ (all_52_13 = e3)
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | REDUCE: (71), (121) imply:
% 199.16/32.75  | | | | | | |   (124)   ~ (all_4_2 = e3)
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | SIMP: (124) implies:
% 199.16/32.75  | | | | | | |   (125)   ~ (all_4_2 = e3)
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (13), (14), (16), (17), (20),
% 199.16/32.75  | | | | | | |            (21), (22), (23), (25), (28), (30), (31), (34), (35),
% 199.16/32.75  | | | | | | |            (36), (37), (38), (39), (41), (43), (45), (46), (47),
% 199.16/32.75  | | | | | | |            (48), (51), (55), (56), (63), (64), (66), (68), (70),
% 199.16/32.75  | | | | | | |            (72), (73), (76), (77), (78), (80), (84), (85), (88),
% 199.16/32.75  | | | | | | |            (89), (104), (107), (112), (122), (123), (125) are
% 199.16/32.75  | | | | | | |            inconsistent by sub-proof #344.
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | Case 2:
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | |   (126)  all_58_14 = e3 | all_58_15 = e3
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | | REF_CLOSE: (3), (54), (91), (118), (126) are inconsistent by
% 199.16/32.75  | | | | | | |            sub-proof #715.
% 199.16/32.75  | | | | | | | 
% 199.16/32.75  | | | | | | End of split
% 199.16/32.75  | | | | | | 
% 199.16/32.75  | | | | | End of split
% 199.16/32.75  | | | | | 
% 199.16/32.75  | | | | End of split
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | Case 2:
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | |   (127)   ~ (all_58_9 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REDUCE: (20), (127) imply:
% 199.16/32.75  | | | |   (128)   ~ (all_52_25 = e3)
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (14), (19),
% 199.16/32.75  | | | |            (20), (27), (29), (33), (41), (44), (49), (50), (52), (53),
% 199.16/32.75  | | | |            (54), (58), (60), (63), (64), (66), (69), (72), (74), (75),
% 199.16/32.75  | | | |            (76), (77), (78), (79), (80), (81), (82), (83), (86), (87),
% 199.16/32.75  | | | |            (88), (89), (91), (98), (128) are inconsistent by sub-proof
% 199.16/32.75  | | | |            #57.
% 199.16/32.75  | | | | 
% 199.16/32.75  | | | End of split
% 199.16/32.75  | | | 
% 199.16/32.75  | | End of split
% 199.16/32.75  | | 
% 199.16/32.75  | Case 2:
% 199.16/32.75  | | 
% 199.16/32.75  | |   (129)   ~ (all_58_2 = e3)
% 199.16/32.76  | | 
% 199.16/32.76  | | REDUCE: (43), (129) imply:
% 199.16/32.76  | |   (130)   ~ (all_52_3 = e3)
% 199.16/32.76  | | 
% 199.16/32.76  | | BETA: splitting (75) gives:
% 199.16/32.76  | | 
% 199.16/32.76  | | Case 1:
% 199.16/32.76  | | | 
% 199.16/32.76  | | |   (131)  all_58_12 = e3
% 199.16/32.76  | | | 
% 199.16/32.76  | | | COMBINE_EQS: (41), (131) imply:
% 199.16/32.76  | | |   (132)  all_52_7 = e3
% 199.16/32.76  | | | 
% 199.16/32.76  | | | SIMP: (132) implies:
% 199.16/32.76  | | |   (133)  all_52_7 = e3
% 199.16/32.76  | | | 
% 199.16/32.76  | | | REDUCE: (83), (133) imply:
% 199.16/32.76  | | |   (134)   ~ (all_52_23 = e3)
% 199.16/32.76  | | | 
% 199.16/32.76  | | | SIMP: (134) implies:
% 199.16/32.76  | | |   (135)   ~ (all_52_23 = e3)
% 199.16/32.76  | | | 
% 199.16/32.76  | | | REDUCE: (12), (133) imply:
% 199.16/32.76  | | |   (136)  op(e3, e3) = all_52_6
% 199.16/32.76  | | | 
% 199.16/32.76  | | | REF_CLOSE: (3), (6), (15), (16), (17), (22), (24), (28), (31), (32), (33),
% 199.16/32.76  | | |            (36), (44), (51), (56), (59), (61), (64), (72), (74), (76),
% 199.16/32.76  | | |            (80), (89), (135), (136) are inconsistent by sub-proof #131.
% 199.16/32.76  | | | 
% 199.16/32.76  | | Case 2:
% 199.16/32.76  | | | 
% 199.16/32.76  | | |   (137)   ~ (all_58_12 = e3)
% 199.16/32.76  | | | 
% 199.16/32.76  | | | REDUCE: (41), (137) imply:
% 199.16/32.76  | | |   (138)   ~ (all_52_7 = e3)
% 199.16/32.76  | | | 
% 199.16/32.76  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (14), (18), (19),
% 199.16/32.76  | | |            (29), (32), (33), (41), (43), (44), (46), (49), (50), (52),
% 199.16/32.76  | | |            (54), (56), (57), (58), (59), (60), (63), (64), (69), (72),
% 199.16/32.76  | | |            (73), (74), (76), (77), (78), (79), (80), (81), (82), (83),
% 199.16/32.76  | | |            (86), (87), (88), (89), (130), (138) are inconsistent by
% 199.16/32.76  | | |            sub-proof #83.
% 199.16/32.76  | | | 
% 199.16/32.76  | | End of split
% 199.16/32.76  | | 
% 199.16/32.76  | End of split
% 199.16/32.76  | 
% 199.16/32.76  End of proof
% 199.16/32.76  
% 199.16/32.76  Sub-proof #57 shows that the following formulas are inconsistent:
% 199.16/32.76  ----------------------------------------------------------------
% 199.16/32.76    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.76    (2)  all_58_14 = all_52_23
% 199.16/32.76    (3)   ~ (e3 = e1)
% 199.16/32.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.76    (5)  all_58_1 = all_52_9
% 199.16/32.76    (6)   ~ (e3 = e0)
% 199.16/32.76    (7)  op(all_52_23, all_52_23) = e0
% 199.16/32.76    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.76    (9)   ~ (all_52_7 = all_52_15)
% 199.16/32.76    (10)  all_58_0 = all_6_2
% 199.16/32.76    (11)  all_58_13 = all_52_15
% 199.16/32.76    (12)  all_58_9 = all_52_25
% 199.16/32.76    (13)   ~ (all_52_9 = all_52_15)
% 199.16/32.76    (14)   ~ (all_52_7 = all_6_2)
% 199.16/32.76    (15)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.76    (16)  all_58_12 = all_52_7
% 199.16/32.76    (17)   ~ (all_52_7 = e3)
% 199.16/32.76    (18)  all_56_2 = all_52_17
% 199.16/32.76    (19)   ~ (all_52_25 = e3)
% 199.16/32.76    (20)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.16/32.76    (21)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.76    (22)  op(e0, e3) = all_52_7
% 199.16/32.76    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.76    (24)  all_58_15 = all_14_2
% 199.16/32.76    (25)  all_56_12 = all_52_7
% 199.16/32.76    (26)  all_8_2 = all_6_2
% 199.16/32.76    (27)  op(e3, all_6_1) = e2
% 199.16/32.76    (28)  op(e3, e3) = all_6_2
% 199.16/32.76    (29)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.76    (30)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.76    (31)  op(all_52_17, all_52_17) = e3
% 199.16/32.76    (32)  op(e3, e2) = all_52_9
% 199.16/32.76    (33)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.76    (34)   ~ (all_52_17 = all_6_2)
% 199.16/32.76    (35)   ~ (e1 = e0)
% 199.16/32.76    (36)   ~ (e3 = e2)
% 199.16/32.76    (37)   ~ (all_52_9 = all_52_17)
% 199.16/32.76    (38)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.76    (39)  op(e1, e1) = all_10_2
% 199.16/32.76    (40)   ~ (all_52_23 = all_10_2)
% 199.16/32.76    (41)   ~ (all_52_7 = all_52_23)
% 199.16/32.76    (42)   ~ (all_52_17 = all_52_23)
% 199.16/32.76    (43)  all_8_1 = all_6_1
% 199.16/32.76    (44)  op(all_6_2, e3) = all_6_1
% 199.16/32.76    (45)  all_58_4 = all_52_17
% 199.16/32.76    (46)   ~ (all_14_2 = e3)
% 199.16/32.76  
% 199.16/32.76  Begin of proof
% 199.16/32.76  | 
% 199.16/32.76  | BETA: splitting (33) gives:
% 199.16/32.76  | 
% 199.16/32.76  | Case 1:
% 199.16/32.76  | | 
% 199.16/32.76  | |   (47)  all_58_12 = e3
% 199.16/32.76  | | 
% 199.16/32.76  | | REF_CLOSE: (16), (17), (47) are inconsistent by sub-proof #1367.
% 199.16/32.76  | | 
% 199.16/32.76  | Case 2:
% 199.16/32.76  | | 
% 199.16/32.76  | |   (48)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.76  | | 
% 199.16/32.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.16/32.76  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 199.16/32.76  | |            (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 199.16/32.76  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (48)
% 199.16/32.76  | |            are inconsistent by sub-proof #372.
% 199.16/32.76  | | 
% 199.16/32.76  | End of split
% 199.16/32.76  | 
% 199.16/32.76  End of proof
% 199.16/32.76  
% 199.16/32.76  Sub-proof #58 shows that the following formulas are inconsistent:
% 199.16/32.76  ----------------------------------------------------------------
% 199.16/32.76    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.76    (2)   ~ (all_52_15 = all_52_23)
% 199.16/32.76    (3)   ~ (all_52_25 = all_52_27)
% 199.16/32.76    (4)  all_58_14 = all_52_23
% 199.16/32.76    (5)   ~ (e3 = e1)
% 199.16/32.76    (6)   ~ (all_52_17 = all_4_0)
% 199.16/32.76    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.76    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.76    (9)  all_58_1 = all_52_9
% 199.16/32.76    (10)   ~ (all_52_9 = all_52_13)
% 199.16/32.76    (11)   ~ (e3 = e0)
% 199.16/32.76    (12)  op(e2, e3) = all_52_3
% 199.16/32.76    (13)   ~ (all_52_23 = all_4_0)
% 199.16/32.76    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.76    (15)   ~ (all_52_7 = all_52_15)
% 199.16/32.76    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.76    (17)   ~ (all_52_17 = all_52_25)
% 199.16/32.76    (18)   ~ (all_52_3 = all_6_2)
% 199.16/32.76    (19)  all_44_2 = all_6_2
% 199.16/32.76    (20)  all_58_0 = all_6_2
% 199.16/32.76    (21)  op(all_14_2, e0) = all_14_1
% 199.16/32.76    (22)  all_56_4 = all_52_3
% 199.16/32.76    (23)   ~ (all_52_17 = all_10_2)
% 199.16/32.76    (24)  op(e3, e0) = all_52_25
% 199.16/32.76    (25)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.76    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.76    (27)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.76    (28)   ~ (all_52_27 = all_52_29)
% 199.16/32.76    (29)  all_58_13 = all_52_15
% 199.16/32.76    (30)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.76    (31)  all_58_9 = all_52_25
% 199.16/32.76    (32)   ~ (all_52_29 = all_14_2)
% 199.16/32.76    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.76    (34)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.76    (35)  op(e1, e3) = all_52_5
% 199.16/32.76    (36)  op(e2, e2) = all_4_2
% 199.16/32.76    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.76    (38)   ~ (all_52_3 = all_52_5)
% 199.16/32.76    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.76    (40)  op(all_4_2, e2) = e1
% 199.16/32.76    (41)  all_58_11 = all_52_29
% 199.16/32.76    (42)  all_56_5 = all_4_2
% 199.16/32.76    (43)   ~ (all_52_25 = all_14_2)
% 199.16/32.76    (44)   ~ (all_52_3 = all_52_27)
% 199.16/32.76    (45)  op(all_10_2, e1) = all_10_1
% 199.16/32.76    (46)   ~ (all_10_2 = all_4_0)
% 199.16/32.76    (47)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.76    (48)   ~ (all_52_7 = all_6_2)
% 199.16/32.76    (49)  op(e0, e0) = all_14_2
% 199.16/32.76    (50)  all_56_15 = all_14_2
% 199.16/32.76    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.76    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.76    (53)  all_56_11 = all_52_29
% 199.16/32.76    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.76    (55)   ~ (e2 = e1)
% 199.16/32.76    (56)  all_58_10 = all_52_27
% 199.16/32.76    (57)  all_56_8 = all_52_5
% 199.16/32.76    (58)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.76    (59)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.76    (60)   ~ (all_52_25 = all_52_29)
% 199.16/32.76    (61)   ~ (all_52_29 = all_10_2)
% 199.16/32.76    (62)  all_58_7 = all_52_13
% 199.16/32.76    (63)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.76    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.76    (65)   ~ (all_52_5 = all_52_7)
% 199.16/32.76    (66)  all_58_12 = all_52_7
% 199.16/32.76    (67)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.76    (68)   ~ (all_52_7 = all_14_2)
% 199.16/32.76    (69)  all_58_2 = all_52_3
% 199.16/32.76    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.76    (71)  all_56_2 = all_52_17
% 199.16/32.76    (72)  all_28_0 = all_4_0
% 199.16/32.76    (73)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.76    (74)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.76    (75)  all_56_7 = all_52_27
% 199.16/32.76    (76)  all_28_2 = all_4_2
% 199.16/32.76    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.76    (78)   ~ (e2 = e0)
% 199.16/32.76    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.76    (80)   ~ (all_52_5 = all_52_29)
% 199.16/32.76    (81)  all_56_6 = all_52_19
% 199.16/32.76    (82)   ~ (all_52_19 = all_52_27)
% 199.16/32.76    (83)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.76    (84)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.16/32.76            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.16/32.76    (85)   ~ (all_52_13 = all_4_2)
% 199.16/32.76    (86)  op(e3, e1) = all_52_17
% 199.16/32.76    (87)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.76    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.76    (89)  op(e0, e3) = all_52_7
% 199.16/32.76    (90)  op(e1, e2) = all_52_13
% 199.16/32.76    (91)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.76    (92)   ~ (all_52_9 = all_52_25)
% 199.16/32.76    (93)  all_58_15 = all_14_2
% 199.16/32.76    (94)   ~ (all_52_19 = all_10_2)
% 199.16/32.76    (95)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.76    (96)  all_58_8 = all_10_2
% 199.16/32.76    (97)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.76    (98)   ~ (all_52_5 = all_10_2)
% 199.16/32.76    (99)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.76    (100)   ~ (all_52_23 = all_14_2)
% 199.16/32.76    (101)  all_56_12 = all_52_7
% 199.16/32.76    (102)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.76    (103)  all_58_5 = all_4_0
% 199.16/32.76    (104)  all_8_2 = all_6_2
% 199.16/32.76    (105)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.76    (106)   ~ (all_52_25 = all_6_2)
% 199.16/32.76    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.76    (108)   ~ (all_52_9 = all_4_2)
% 199.16/32.76    (109)   ~ (all_52_5 = all_6_2)
% 199.16/32.76    (110)   ~ (all_52_9 = all_6_2)
% 199.16/32.76    (111)  op(e3, all_6_1) = e2
% 199.16/32.76    (112)  all_56_0 = all_6_2
% 199.16/32.76    (113)  op(all_4_0, all_4_0) = all_52_18
% 199.16/32.76    (114)  op(e3, e3) = all_6_2
% 199.16/32.76    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.76    (116)   ~ (all_52_27 = all_14_2)
% 199.16/32.76    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.76    (118)  all_56_14 = all_52_23
% 199.16/32.76    (119)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.16/32.76    (120)  all_56_3 = all_52_25
% 199.16/32.76    (121)  all_28_0 = e3
% 199.16/32.76    (122)   ~ (all_52_3 = all_52_7)
% 199.16/32.76    (123)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.76    (124)  all_58_5 = all_52_19
% 199.16/32.76    (125)   ~ (all_52_15 = all_4_2)
% 199.16/32.76    (126)  op(e0, all_14_1) = e3
% 199.16/32.76    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.76           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.76           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.76           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.76    (128)   ~ (all_52_27 = all_4_2)
% 199.16/32.76    (129)  all_58_6 = all_52_5
% 199.16/32.76    (130)   ~ (all_4_0 = all_4_2)
% 199.16/32.76    (131)  op(e3, e2) = all_52_9
% 199.16/32.76    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.76    (133)   ~ (all_52_17 = all_6_2)
% 199.16/32.76    (134)   ~ (e1 = e0)
% 199.16/32.76    (135)   ~ (e3 = e2)
% 199.16/32.76    (136)  all_44_1 = all_6_1
% 199.16/32.76    (137)   ~ (all_52_9 = all_52_17)
% 199.16/32.76    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.76    (139)   ~ (all_52_3 = all_4_0)
% 199.16/32.76    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.76    (141)  all_44_0 = e2
% 199.16/32.76    (142)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.76    (143)  op(e1, e1) = all_10_2
% 199.16/32.76    (144)   ~ (all_52_7 = all_52_23)
% 199.16/32.76    (145)   ~ (all_52_17 = all_52_19)
% 199.16/32.76    (146)  all_58_3 = all_4_2
% 199.16/32.76    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.76    (148)   ~ (all_52_3 = all_4_2)
% 199.16/32.76    (149)  all_28_1 = e1
% 199.16/32.76    (150)   ~ (all_52_19 = all_4_2)
% 199.16/32.76    (151)   ~ (all_52_17 = all_52_23)
% 199.16/32.76    (152)  all_8_1 = all_6_1
% 199.16/32.76    (153)  op(all_6_2, e3) = all_6_1
% 199.16/32.76    (154)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.76    (155)   ~ (all_52_13 = all_52_29)
% 199.16/32.76    (156)  all_58_4 = all_52_17
% 199.16/32.76    (157)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.76  
% 199.16/32.76  Begin of proof
% 199.16/32.76  | 
% 199.16/32.76  | COMBINE_EQS: (72), (121) imply:
% 199.16/32.76  |   (158)  all_4_0 = e3
% 199.16/32.76  | 
% 199.16/32.76  | SIMP: (158) implies:
% 199.16/32.76  |   (159)  all_4_0 = e3
% 199.16/32.76  | 
% 199.16/32.76  | COMBINE_EQS: (103), (159) imply:
% 199.16/32.76  |   (160)  all_58_5 = e3
% 199.16/32.76  | 
% 199.16/32.76  | REDUCE: (139), (159) imply:
% 199.16/32.76  |   (161)   ~ (all_52_3 = e3)
% 199.16/32.76  | 
% 199.16/32.76  | REDUCE: (6), (159) imply:
% 199.16/32.76  |   (162)   ~ (all_52_17 = e3)
% 199.16/32.76  | 
% 199.16/32.76  | REDUCE: (13), (159) imply:
% 199.16/32.76  |   (163)   ~ (all_52_23 = e3)
% 199.16/32.76  | 
% 199.16/32.76  | REDUCE: (46), (159) imply:
% 199.16/32.76  |   (164)   ~ (all_10_2 = e3)
% 199.16/32.76  | 
% 199.16/32.76  | REDUCE: (130), (159) imply:
% 199.16/32.76  |   (165)   ~ (all_4_2 = e3)
% 199.16/32.76  | 
% 199.16/32.76  | SIMP: (165) implies:
% 199.16/32.76  |   (166)   ~ (all_4_2 = e3)
% 199.16/32.76  | 
% 199.16/32.76  | REDUCE: (113), (159) imply:
% 199.16/32.76  |   (167)  op(e3, e3) = all_52_18
% 199.16/32.76  | 
% 199.16/32.76  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 199.16/32.76  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.16/32.76  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 199.16/32.76  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 199.16/32.76  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 199.16/32.76  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 199.16/32.76  |            (71), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 199.16/32.76  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 199.16/32.76  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (104),
% 199.16/32.76  |            (105), (106), (107), (108), (109), (110), (111), (112), (114),
% 199.16/32.76  |            (115), (116), (117), (118), (119), (120), (122), (123), (124),
% 199.16/32.76  |            (125), (126), (127), (128), (129), (131), (132), (133), (134),
% 199.16/32.76  |            (135), (136), (137), (138), (140), (141), (142), (143), (144),
% 199.16/32.76  |            (145), (146), (147), (148), (149), (150), (151), (152), (153),
% 199.16/32.76  |            (154), (155), (156), (157), (160), (161), (162), (163), (164),
% 199.16/32.76  |            (166), (167) are inconsistent by sub-proof #59.
% 199.16/32.76  | 
% 199.16/32.76  End of proof
% 199.16/32.76  
% 199.16/32.76  Sub-proof #59 shows that the following formulas are inconsistent:
% 199.16/32.76  ----------------------------------------------------------------
% 199.16/32.76    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.76    (2)  op(e3, e3) = all_52_18
% 199.16/32.76    (3)   ~ (all_52_15 = all_52_23)
% 199.16/32.76    (4)   ~ (all_52_25 = all_52_27)
% 199.16/32.76    (5)  all_58_14 = all_52_23
% 199.16/32.76    (6)   ~ (e3 = e1)
% 199.16/32.76    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.76    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.76    (9)  all_58_1 = all_52_9
% 199.16/32.76    (10)   ~ (all_52_9 = all_52_13)
% 199.16/32.76    (11)   ~ (e3 = e0)
% 199.16/32.76    (12)  op(e2, e3) = all_52_3
% 199.16/32.76    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.76    (14)   ~ (all_52_7 = all_52_15)
% 199.16/32.76    (15)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.76    (16)   ~ (all_52_17 = all_52_25)
% 199.16/32.76    (17)   ~ (all_4_2 = e3)
% 199.16/32.76    (18)   ~ (all_52_3 = all_6_2)
% 199.16/32.76    (19)  all_44_2 = all_6_2
% 199.16/32.76    (20)  all_58_0 = all_6_2
% 199.16/32.76    (21)  op(all_14_2, e0) = all_14_1
% 199.16/32.76    (22)  all_56_4 = all_52_3
% 199.16/32.76    (23)   ~ (all_52_17 = all_10_2)
% 199.16/32.76    (24)  op(e3, e0) = all_52_25
% 199.16/32.76    (25)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.76    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.76    (27)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.76    (28)   ~ (all_52_27 = all_52_29)
% 199.16/32.76    (29)  all_58_13 = all_52_15
% 199.16/32.76    (30)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.76    (31)  all_58_9 = all_52_25
% 199.16/32.76    (32)   ~ (all_52_29 = all_14_2)
% 199.16/32.76    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.76    (34)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.76    (35)  op(e1, e3) = all_52_5
% 199.16/32.76    (36)  op(e2, e2) = all_4_2
% 199.16/32.76    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.76    (38)   ~ (all_52_3 = all_52_5)
% 199.16/32.76    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.76    (40)  op(all_4_2, e2) = e1
% 199.16/32.76    (41)  all_58_11 = all_52_29
% 199.16/32.76    (42)   ~ (all_52_3 = e3)
% 199.16/32.76    (43)  all_56_5 = all_4_2
% 199.16/32.76    (44)   ~ (all_52_25 = all_14_2)
% 199.16/32.76    (45)   ~ (all_52_3 = all_52_27)
% 199.16/32.76    (46)  op(all_10_2, e1) = all_10_1
% 199.16/32.76    (47)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.76    (48)   ~ (all_52_7 = all_6_2)
% 199.16/32.76    (49)  op(e0, e0) = all_14_2
% 199.16/32.76    (50)  all_56_15 = all_14_2
% 199.16/32.76    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.76    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.76    (53)  all_56_11 = all_52_29
% 199.16/32.76    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.76    (55)   ~ (e2 = e1)
% 199.16/32.76    (56)  all_58_10 = all_52_27
% 199.16/32.76    (57)  all_56_8 = all_52_5
% 199.16/32.76    (58)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.76    (59)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.76    (60)   ~ (all_52_25 = all_52_29)
% 199.16/32.76    (61)   ~ (all_52_29 = all_10_2)
% 199.16/32.76    (62)  all_58_7 = all_52_13
% 199.16/32.76    (63)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.76    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.76    (65)   ~ (all_52_5 = all_52_7)
% 199.16/32.76    (66)  all_58_12 = all_52_7
% 199.16/32.76    (67)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.76    (68)   ~ (all_52_7 = all_14_2)
% 199.16/32.76    (69)  all_58_2 = all_52_3
% 199.16/32.76    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.76    (71)  all_56_2 = all_52_17
% 199.16/32.76    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.76    (73)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.76    (74)  all_56_7 = all_52_27
% 199.16/32.76    (75)  all_28_2 = all_4_2
% 199.16/32.76    (76)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.76    (77)   ~ (e2 = e0)
% 199.16/32.76    (78)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.76    (79)   ~ (all_52_23 = e3)
% 199.16/32.76    (80)   ~ (all_52_5 = all_52_29)
% 199.16/32.76    (81)  all_56_6 = all_52_19
% 199.16/32.76    (82)   ~ (all_10_2 = e3)
% 199.16/32.76    (83)   ~ (all_52_19 = all_52_27)
% 199.16/32.76    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.76    (85)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.16/32.76            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.16/32.76    (86)   ~ (all_52_13 = all_4_2)
% 199.16/32.76    (87)  op(e3, e1) = all_52_17
% 199.16/32.76    (88)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.76    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.76    (90)  op(e0, e3) = all_52_7
% 199.16/32.76    (91)  op(e1, e2) = all_52_13
% 199.16/32.76    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.76    (93)   ~ (all_52_9 = all_52_25)
% 199.16/32.76    (94)  all_58_15 = all_14_2
% 199.16/32.76    (95)   ~ (all_52_19 = all_10_2)
% 199.16/32.76    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.76    (97)  all_58_8 = all_10_2
% 199.16/32.76    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.76    (99)   ~ (all_52_5 = all_10_2)
% 199.16/32.76    (100)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.76    (101)   ~ (all_52_23 = all_14_2)
% 199.16/32.76    (102)  all_56_12 = all_52_7
% 199.16/32.76    (103)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.76    (104)  all_8_2 = all_6_2
% 199.16/32.76    (105)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.76    (106)   ~ (all_52_25 = all_6_2)
% 199.16/32.76    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.76    (108)   ~ (all_52_9 = all_4_2)
% 199.16/32.76    (109)   ~ (all_52_5 = all_6_2)
% 199.16/32.76    (110)   ~ (all_52_9 = all_6_2)
% 199.16/32.76    (111)  op(e3, all_6_1) = e2
% 199.16/32.76    (112)  all_56_0 = all_6_2
% 199.16/32.77    (113)  op(e3, e3) = all_6_2
% 199.16/32.77    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.77    (115)   ~ (all_52_27 = all_14_2)
% 199.16/32.77    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.77    (117)  all_58_5 = e3
% 199.16/32.77    (118)  all_56_14 = all_52_23
% 199.16/32.77    (119)   ~ (all_52_17 = e3)
% 199.16/32.77    (120)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.16/32.77    (121)  all_56_3 = all_52_25
% 199.16/32.77    (122)   ~ (all_52_3 = all_52_7)
% 199.16/32.77    (123)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.77    (124)  all_58_5 = all_52_19
% 199.16/32.77    (125)   ~ (all_52_15 = all_4_2)
% 199.16/32.77    (126)  op(e0, all_14_1) = e3
% 199.16/32.77    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.77           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.77           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.77           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.77    (128)   ~ (all_52_27 = all_4_2)
% 199.16/32.77    (129)  all_58_6 = all_52_5
% 199.16/32.77    (130)  op(e3, e2) = all_52_9
% 199.16/32.77    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.77    (132)   ~ (all_52_17 = all_6_2)
% 199.16/32.77    (133)   ~ (e1 = e0)
% 199.16/32.77    (134)   ~ (e3 = e2)
% 199.16/32.77    (135)  all_44_1 = all_6_1
% 199.16/32.77    (136)   ~ (all_52_9 = all_52_17)
% 199.16/32.77    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.77    (138)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.77    (139)  all_44_0 = e2
% 199.16/32.77    (140)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.77    (141)  op(e1, e1) = all_10_2
% 199.16/32.77    (142)   ~ (all_52_7 = all_52_23)
% 199.16/32.77    (143)   ~ (all_52_17 = all_52_19)
% 199.16/32.77    (144)  all_58_3 = all_4_2
% 199.16/32.77    (145)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.77    (146)   ~ (all_52_3 = all_4_2)
% 199.16/32.77    (147)  all_28_1 = e1
% 199.16/32.77    (148)   ~ (all_52_19 = all_4_2)
% 199.16/32.77    (149)   ~ (all_52_17 = all_52_23)
% 199.16/32.77    (150)  all_8_1 = all_6_1
% 199.16/32.77    (151)  op(all_6_2, e3) = all_6_1
% 199.16/32.77    (152)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.77    (153)   ~ (all_52_13 = all_52_29)
% 199.16/32.77    (154)  all_58_4 = all_52_17
% 199.16/32.77    (155)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.77  
% 199.16/32.77  Begin of proof
% 199.16/32.77  | 
% 199.16/32.77  | BETA: splitting (120) gives:
% 199.16/32.77  | 
% 199.16/32.77  | Case 1:
% 199.16/32.77  | | 
% 199.16/32.77  | |   (156)   ~ (all_28_1 = e1)
% 199.16/32.77  | | 
% 199.16/32.77  | | REDUCE: (147), (156) imply:
% 199.16/32.77  | |   (157)  $false
% 199.16/32.77  | | 
% 199.16/32.77  | | CLOSE: (157) is inconsistent.
% 199.16/32.77  | | 
% 199.16/32.77  | Case 2:
% 199.16/32.77  | | 
% 199.16/32.77  | |   (158)   ~ (all_28_2 = e0)
% 199.16/32.77  | | 
% 199.16/32.77  | | REDUCE: (75), (158) imply:
% 199.16/32.77  | |   (159)   ~ (all_4_2 = e0)
% 199.16/32.77  | | 
% 199.16/32.77  | | GROUND_INST: instantiating (8) with all_6_2, all_52_18, e3, e3, simplifying
% 199.16/32.77  | |              with (2), (113) gives:
% 199.16/32.77  | |   (160)  all_52_18 = all_6_2
% 199.16/32.77  | | 
% 199.16/32.77  | | BETA: splitting (88) gives:
% 199.16/32.77  | | 
% 199.16/32.77  | | Case 1:
% 199.16/32.77  | | | 
% 199.16/32.77  | | |   (161)   ~ (all_44_0 = e2)
% 199.16/32.77  | | | 
% 199.16/32.77  | | | REDUCE: (139), (161) imply:
% 199.16/32.77  | | |   (162)  $false
% 199.16/32.77  | | | 
% 199.16/32.77  | | | CLOSE: (162) is inconsistent.
% 199.16/32.77  | | | 
% 199.16/32.77  | | Case 2:
% 199.16/32.77  | | | 
% 199.16/32.77  | | |   (163)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.77  | | | 
% 199.16/32.77  | | | BETA: splitting (85) gives:
% 199.16/32.77  | | | 
% 199.16/32.77  | | | Case 1:
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | |   (164)  all_58_15 = e0
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | COMBINE_EQS: (94), (164) imply:
% 199.16/32.77  | | | |   (165)  all_14_2 = e0
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | REDUCE: (115), (165) imply:
% 199.16/32.77  | | | |   (166)   ~ (all_52_27 = e0)
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | REDUCE: (123), (165) imply:
% 199.16/32.77  | | | |   (167)  op(e0, e0) = all_52_30
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | REDUCE: (21), (165) imply:
% 199.16/32.77  | | | |   (168)  op(e0, e0) = all_14_1
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | REDUCE: (49), (165) imply:
% 199.16/32.77  | | | |   (169)  op(e0, e0) = e0
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | REF_CLOSE: (7), (8), (11), (39), (42), (56), (69), (117), (126), (144),
% 199.16/32.77  | | | |            (159), (166), (167), (168), (169) are inconsistent by
% 199.16/32.77  | | | |            sub-proof #140.
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | Case 2:
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | |   (170)   ~ (all_58_15 = e0)
% 199.16/32.77  | | | |   (171)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.16/32.77  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 199.16/32.77  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 199.16/32.77  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 199.16/32.77  | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 199.16/32.77  | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 199.16/32.77  | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 199.16/32.77  | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 199.16/32.77  | | | |            (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 199.16/32.77  | | | |            (83), (84), (86), (87), (89), (90), (91), (92), (93), (94),
% 199.16/32.77  | | | |            (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 199.16/32.77  | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 199.16/32.77  | | | |            (112), (113), (114), (115), (116), (117), (118), (119),
% 199.16/32.77  | | | |            (121), (122), (123), (124), (125), (127), (128), (129),
% 199.16/32.77  | | | |            (130), (131), (132), (133), (134), (135), (136), (137),
% 199.16/32.77  | | | |            (138), (140), (141), (142), (143), (144), (145), (146),
% 199.16/32.77  | | | |            (148), (149), (150), (151), (152), (153), (154), (155),
% 199.16/32.77  | | | |            (159), (160), (163), (170), (171) are inconsistent by
% 199.16/32.77  | | | |            sub-proof #65.
% 199.16/32.77  | | | | 
% 199.16/32.77  | | | End of split
% 199.16/32.77  | | | 
% 199.16/32.77  | | End of split
% 199.16/32.77  | | 
% 199.16/32.77  | End of split
% 199.16/32.77  | 
% 199.16/32.77  End of proof
% 199.16/32.77  
% 199.16/32.77  Sub-proof #60 shows that the following formulas are inconsistent:
% 199.16/32.77  ----------------------------------------------------------------
% 199.16/32.77    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.77    (2)   ~ (all_52_15 = all_52_23)
% 199.16/32.77    (3)   ~ (all_52_25 = all_52_27)
% 199.16/32.77    (4)  all_58_14 = all_52_23
% 199.16/32.77    (5)   ~ (e3 = e1)
% 199.16/32.77    (6)   ~ (all_52_17 = all_4_0)
% 199.16/32.77    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.77    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.77    (9)  all_58_1 = all_52_9
% 199.16/32.77    (10)   ~ (all_52_9 = all_52_13)
% 199.16/32.77    (11)   ~ (e3 = e0)
% 199.16/32.77    (12)  op(e2, e3) = all_52_3
% 199.16/32.77    (13)   ~ (all_52_23 = all_4_0)
% 199.16/32.77    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.77    (15)   ~ (all_52_7 = all_52_15)
% 199.16/32.77    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.77    (17)   ~ (all_52_17 = all_52_25)
% 199.16/32.77    (18)   ~ (all_52_3 = all_6_2)
% 199.16/32.77    (19)  all_44_2 = all_6_2
% 199.16/32.77    (20)  all_58_0 = all_6_2
% 199.16/32.77    (21)  op(all_14_2, e0) = all_14_1
% 199.16/32.77    (22)  all_56_4 = all_52_3
% 199.16/32.77    (23)   ~ (all_52_17 = all_10_2)
% 199.16/32.77    (24)  op(e3, e0) = all_52_25
% 199.16/32.77    (25)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.77    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.77    (27)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.77    (28)   ~ (all_52_27 = all_52_29)
% 199.16/32.77    (29)  all_58_13 = all_52_15
% 199.16/32.77    (30)  op(e0, all_14_1) = e1
% 199.16/32.77    (31)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.77    (32)  all_58_9 = all_52_25
% 199.16/32.77    (33)   ~ (all_52_29 = all_14_2)
% 199.16/32.77    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.77    (35)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.77    (36)  op(e1, e3) = all_52_5
% 199.16/32.77    (37)  op(e2, e2) = all_4_2
% 199.16/32.77    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.77    (39)   ~ (all_52_3 = all_52_5)
% 199.16/32.77    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.77    (41)  op(all_4_2, e2) = e1
% 199.16/32.77    (42)  all_58_11 = all_52_29
% 199.16/32.77    (43)  all_56_5 = all_4_2
% 199.16/32.77    (44)   ~ (all_52_25 = all_14_2)
% 199.16/32.77    (45)   ~ (all_52_3 = all_52_27)
% 199.16/32.77    (46)  op(all_10_2, e1) = all_10_1
% 199.16/32.77    (47)   ~ (all_10_2 = all_4_0)
% 199.16/32.77    (48)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.77    (49)   ~ (all_52_7 = all_6_2)
% 199.16/32.77    (50)  op(e0, e0) = all_14_2
% 199.16/32.77    (51)  all_56_15 = all_14_2
% 199.16/32.77    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.77    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.77    (54)  all_56_11 = all_52_29
% 199.16/32.77    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.77    (56)   ~ (e2 = e1)
% 199.16/32.77    (57)  all_58_10 = all_52_27
% 199.16/32.77    (58)  all_56_8 = all_52_5
% 199.16/32.77    (59)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.77    (60)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.77    (61)   ~ (all_52_25 = all_52_29)
% 199.16/32.77    (62)   ~ (all_52_29 = all_10_2)
% 199.16/32.77    (63)  all_58_7 = all_52_13
% 199.16/32.77    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.77    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.77    (66)   ~ (all_52_5 = all_52_7)
% 199.16/32.77    (67)  all_58_12 = all_52_7
% 199.16/32.77    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.77    (69)   ~ (all_52_7 = all_14_2)
% 199.16/32.77    (70)  all_58_2 = all_52_3
% 199.16/32.77    (71)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.77    (72)  all_56_2 = all_52_17
% 199.16/32.77    (73)  all_28_0 = all_4_0
% 199.16/32.77    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.77    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.77    (76)  all_56_7 = all_52_27
% 199.16/32.77    (77)  all_28_2 = all_4_2
% 199.16/32.77    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.77    (79)   ~ (e2 = e0)
% 199.16/32.77    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.77    (81)   ~ (all_52_5 = all_52_29)
% 199.16/32.77    (82)  all_56_6 = all_52_19
% 199.16/32.77    (83)   ~ (all_52_19 = all_52_27)
% 199.16/32.77    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.77    (85)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.16/32.77            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.16/32.77    (86)   ~ (all_52_13 = all_4_2)
% 199.16/32.77    (87)  op(e3, e1) = all_52_17
% 199.16/32.77    (88)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.77    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.77    (90)  op(e0, e3) = all_52_7
% 199.16/32.77    (91)  op(e1, e2) = all_52_13
% 199.16/32.77    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.77    (93)   ~ (all_52_9 = all_52_25)
% 199.16/32.77    (94)  all_58_15 = all_14_2
% 199.16/32.77    (95)   ~ (all_52_19 = all_10_2)
% 199.16/32.77    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.77    (97)  all_58_8 = all_10_2
% 199.16/32.77    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.77    (99)   ~ (all_52_5 = all_10_2)
% 199.16/32.77    (100)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.77    (101)   ~ (all_52_23 = all_14_2)
% 199.16/32.77    (102)  all_56_12 = all_52_7
% 199.16/32.77    (103)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.77    (104)  all_58_5 = all_4_0
% 199.16/32.77    (105)  all_8_2 = all_6_2
% 199.16/32.77    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.77    (107)   ~ (all_52_25 = all_6_2)
% 199.16/32.77    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.77    (109)   ~ (all_52_9 = all_4_2)
% 199.16/32.77    (110)   ~ (all_52_5 = all_6_2)
% 199.16/32.77    (111)   ~ (all_52_9 = all_6_2)
% 199.16/32.77    (112)  op(e3, all_6_1) = e2
% 199.16/32.77    (113)  all_56_0 = all_6_2
% 199.16/32.77    (114)  op(all_4_0, all_4_0) = all_52_18
% 199.16/32.77    (115)  op(e3, e3) = all_6_2
% 199.16/32.77    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.77    (117)   ~ (all_52_27 = all_14_2)
% 199.16/32.77    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.77    (119)  all_56_14 = all_52_23
% 199.16/32.77    (120)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.16/32.77    (121)  all_56_3 = all_52_25
% 199.16/32.77    (122)  all_28_0 = e3
% 199.16/32.77    (123)   ~ (all_52_3 = all_52_7)
% 199.16/32.77    (124)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.77    (125)  all_58_5 = all_52_19
% 199.16/32.77    (126)   ~ (all_52_15 = all_4_2)
% 199.16/32.77    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.77           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.77           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.77           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.77    (128)   ~ (all_52_27 = all_4_2)
% 199.16/32.77    (129)  all_58_6 = all_52_5
% 199.16/32.77    (130)   ~ (all_4_0 = all_4_2)
% 199.16/32.77    (131)  op(e3, e2) = all_52_9
% 199.16/32.77    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.77    (133)   ~ (all_52_17 = all_6_2)
% 199.16/32.77    (134)   ~ (e1 = e0)
% 199.16/32.77    (135)   ~ (e3 = e2)
% 199.16/32.77    (136)  all_44_1 = all_6_1
% 199.16/32.77    (137)   ~ (all_52_9 = all_52_17)
% 199.16/32.77    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.77    (139)   ~ (all_52_3 = all_4_0)
% 199.16/32.77    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.77    (141)  all_44_0 = e2
% 199.16/32.77    (142)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.77    (143)  op(e1, e1) = all_10_2
% 199.16/32.77    (144)   ~ (all_52_7 = all_52_23)
% 199.16/32.77    (145)   ~ (all_52_17 = all_52_19)
% 199.16/32.77    (146)  all_58_3 = all_4_2
% 199.16/32.77    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.77    (148)   ~ (all_52_3 = all_4_2)
% 199.16/32.77    (149)  all_28_1 = e1
% 199.16/32.77    (150)   ~ (all_52_19 = all_4_2)
% 199.16/32.77    (151)   ~ (all_52_17 = all_52_23)
% 199.16/32.77    (152)  all_8_1 = all_6_1
% 199.16/32.77    (153)  op(all_6_2, e3) = all_6_1
% 199.16/32.77    (154)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.77    (155)   ~ (all_52_13 = all_52_29)
% 199.16/32.77    (156)  all_58_4 = all_52_17
% 199.16/32.77    (157)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.77  
% 199.16/32.77  Begin of proof
% 199.16/32.77  | 
% 199.16/32.77  | COMBINE_EQS: (73), (122) imply:
% 199.16/32.77  |   (158)  all_4_0 = e3
% 199.16/32.77  | 
% 199.16/32.77  | SIMP: (158) implies:
% 199.16/32.77  |   (159)  all_4_0 = e3
% 199.16/32.77  | 
% 199.16/32.77  | COMBINE_EQS: (104), (159) imply:
% 199.16/32.77  |   (160)  all_58_5 = e3
% 199.16/32.77  | 
% 199.16/32.77  | REDUCE: (139), (159) imply:
% 199.16/32.77  |   (161)   ~ (all_52_3 = e3)
% 199.16/32.77  | 
% 199.16/32.77  | REDUCE: (6), (159) imply:
% 199.16/32.77  |   (162)   ~ (all_52_17 = e3)
% 199.16/32.77  | 
% 199.16/32.77  | REDUCE: (13), (159) imply:
% 199.16/32.77  |   (163)   ~ (all_52_23 = e3)
% 199.16/32.77  | 
% 199.16/32.77  | REDUCE: (47), (159) imply:
% 199.16/32.77  |   (164)   ~ (all_10_2 = e3)
% 199.16/32.77  | 
% 199.16/32.77  | REDUCE: (130), (159) imply:
% 199.16/32.77  |   (165)   ~ (all_4_2 = e3)
% 199.16/32.77  | 
% 199.16/32.77  | SIMP: (165) implies:
% 199.16/32.77  |   (166)   ~ (all_4_2 = e3)
% 199.16/32.77  | 
% 199.16/32.77  | REDUCE: (114), (159) imply:
% 199.16/32.77  |   (167)  op(e3, e3) = all_52_18
% 199.16/32.77  | 
% 199.16/32.77  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 199.16/32.77  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.16/32.77  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 199.16/32.77  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (48),
% 199.16/32.77  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 199.16/32.77  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 199.16/32.77  |            (71), (72), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 199.16/32.77  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 199.16/32.77  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 199.16/32.77  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 199.16/32.77  |            (115), (116), (117), (118), (119), (120), (121), (123), (124),
% 199.16/32.77  |            (125), (126), (127), (128), (129), (131), (132), (133), (134),
% 199.16/32.77  |            (135), (136), (137), (138), (140), (141), (142), (143), (144),
% 199.16/32.77  |            (145), (146), (147), (148), (149), (150), (151), (152), (153),
% 199.16/32.77  |            (154), (155), (156), (157), (160), (161), (162), (163), (164),
% 199.16/32.77  |            (166), (167) are inconsistent by sub-proof #61.
% 199.16/32.77  | 
% 199.16/32.77  End of proof
% 199.16/32.77  
% 199.16/32.77  Sub-proof #61 shows that the following formulas are inconsistent:
% 199.16/32.77  ----------------------------------------------------------------
% 199.16/32.77    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.77    (2)  op(e3, e3) = all_52_18
% 199.16/32.77    (3)   ~ (all_52_15 = all_52_23)
% 199.16/32.77    (4)   ~ (all_52_25 = all_52_27)
% 199.16/32.77    (5)  all_58_14 = all_52_23
% 199.16/32.77    (6)   ~ (e3 = e1)
% 199.16/32.77    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.77    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.77    (9)  all_58_1 = all_52_9
% 199.16/32.77    (10)   ~ (all_52_9 = all_52_13)
% 199.16/32.77    (11)   ~ (e3 = e0)
% 199.16/32.77    (12)  op(e2, e3) = all_52_3
% 199.16/32.77    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.77    (14)   ~ (all_52_7 = all_52_15)
% 199.16/32.77    (15)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.77    (16)   ~ (all_52_17 = all_52_25)
% 199.16/32.77    (17)   ~ (all_4_2 = e3)
% 199.16/32.77    (18)   ~ (all_52_3 = all_6_2)
% 199.16/32.77    (19)  all_44_2 = all_6_2
% 199.16/32.77    (20)  all_58_0 = all_6_2
% 199.16/32.77    (21)  op(all_14_2, e0) = all_14_1
% 199.16/32.77    (22)  all_56_4 = all_52_3
% 199.16/32.77    (23)   ~ (all_52_17 = all_10_2)
% 199.16/32.77    (24)  op(e3, e0) = all_52_25
% 199.16/32.77    (25)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.77    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.77    (27)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.77    (28)   ~ (all_52_27 = all_52_29)
% 199.16/32.77    (29)  all_58_13 = all_52_15
% 199.16/32.77    (30)  op(e0, all_14_1) = e1
% 199.16/32.77    (31)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.77    (32)  all_58_9 = all_52_25
% 199.16/32.77    (33)   ~ (all_52_29 = all_14_2)
% 199.16/32.77    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.77    (35)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.77    (36)  op(e1, e3) = all_52_5
% 199.16/32.77    (37)  op(e2, e2) = all_4_2
% 199.16/32.77    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.77    (39)   ~ (all_52_3 = all_52_5)
% 199.16/32.77    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.77    (41)  op(all_4_2, e2) = e1
% 199.16/32.77    (42)  all_58_11 = all_52_29
% 199.16/32.77    (43)   ~ (all_52_3 = e3)
% 199.16/32.77    (44)  all_56_5 = all_4_2
% 199.16/32.77    (45)   ~ (all_52_25 = all_14_2)
% 199.16/32.77    (46)   ~ (all_52_3 = all_52_27)
% 199.16/32.77    (47)  op(all_10_2, e1) = all_10_1
% 199.16/32.77    (48)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.77    (49)   ~ (all_52_7 = all_6_2)
% 199.16/32.77    (50)  op(e0, e0) = all_14_2
% 199.16/32.77    (51)  all_56_15 = all_14_2
% 199.16/32.77    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.77    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.77    (54)  all_56_11 = all_52_29
% 199.16/32.77    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.77    (56)   ~ (e2 = e1)
% 199.16/32.77    (57)  all_58_10 = all_52_27
% 199.16/32.77    (58)  all_56_8 = all_52_5
% 199.16/32.77    (59)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.77    (60)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.77    (61)   ~ (all_52_25 = all_52_29)
% 199.16/32.77    (62)   ~ (all_52_29 = all_10_2)
% 199.16/32.77    (63)  all_58_7 = all_52_13
% 199.16/32.77    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.77    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.77    (66)   ~ (all_52_5 = all_52_7)
% 199.16/32.77    (67)  all_58_12 = all_52_7
% 199.16/32.77    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.77    (69)   ~ (all_52_7 = all_14_2)
% 199.16/32.77    (70)  all_58_2 = all_52_3
% 199.16/32.77    (71)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.77    (72)  all_56_2 = all_52_17
% 199.16/32.77    (73)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.77    (74)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.77    (75)  all_56_7 = all_52_27
% 199.16/32.77    (76)  all_28_2 = all_4_2
% 199.16/32.77    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.77    (78)   ~ (e2 = e0)
% 199.16/32.77    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.77    (80)   ~ (all_52_23 = e3)
% 199.16/32.77    (81)   ~ (all_52_5 = all_52_29)
% 199.16/32.77    (82)  all_56_6 = all_52_19
% 199.16/32.77    (83)   ~ (all_10_2 = e3)
% 199.16/32.77    (84)   ~ (all_52_19 = all_52_27)
% 199.16/32.77    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.77    (86)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.16/32.77            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.16/32.77    (87)   ~ (all_52_13 = all_4_2)
% 199.16/32.77    (88)  op(e3, e1) = all_52_17
% 199.16/32.77    (89)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.77    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.77    (91)  op(e0, e3) = all_52_7
% 199.16/32.77    (92)  op(e1, e2) = all_52_13
% 199.16/32.77    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.77    (94)   ~ (all_52_9 = all_52_25)
% 199.16/32.77    (95)  all_58_15 = all_14_2
% 199.16/32.77    (96)   ~ (all_52_19 = all_10_2)
% 199.16/32.77    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.77    (98)  all_58_8 = all_10_2
% 199.16/32.77    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.77    (100)   ~ (all_52_5 = all_10_2)
% 199.16/32.77    (101)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.77    (102)   ~ (all_52_23 = all_14_2)
% 199.16/32.77    (103)  all_56_12 = all_52_7
% 199.16/32.77    (104)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.77    (105)  all_8_2 = all_6_2
% 199.16/32.77    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.77    (107)   ~ (all_52_25 = all_6_2)
% 199.16/32.77    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.77    (109)   ~ (all_52_9 = all_4_2)
% 199.16/32.77    (110)   ~ (all_52_5 = all_6_2)
% 199.16/32.77    (111)   ~ (all_52_9 = all_6_2)
% 199.16/32.77    (112)  op(e3, all_6_1) = e2
% 199.16/32.77    (113)  all_56_0 = all_6_2
% 199.16/32.77    (114)  op(e3, e3) = all_6_2
% 199.16/32.78    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.78    (116)   ~ (all_52_27 = all_14_2)
% 199.16/32.78    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.78    (118)  all_58_5 = e3
% 199.16/32.78    (119)  all_56_14 = all_52_23
% 199.16/32.78    (120)   ~ (all_52_17 = e3)
% 199.16/32.78    (121)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.16/32.78    (122)  all_56_3 = all_52_25
% 199.16/32.78    (123)   ~ (all_52_3 = all_52_7)
% 199.16/32.78    (124)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.78    (125)  all_58_5 = all_52_19
% 199.16/32.78    (126)   ~ (all_52_15 = all_4_2)
% 199.16/32.78    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.78           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.78           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.78           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.78    (128)   ~ (all_52_27 = all_4_2)
% 199.16/32.78    (129)  all_58_6 = all_52_5
% 199.16/32.78    (130)  op(e3, e2) = all_52_9
% 199.16/32.78    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.78    (132)   ~ (all_52_17 = all_6_2)
% 199.16/32.78    (133)   ~ (e1 = e0)
% 199.16/32.78    (134)   ~ (e3 = e2)
% 199.16/32.78    (135)  all_44_1 = all_6_1
% 199.16/32.78    (136)   ~ (all_52_9 = all_52_17)
% 199.16/32.78    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.78    (138)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.78    (139)  all_44_0 = e2
% 199.16/32.78    (140)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.78    (141)  op(e1, e1) = all_10_2
% 199.16/32.78    (142)   ~ (all_52_7 = all_52_23)
% 199.16/32.78    (143)   ~ (all_52_17 = all_52_19)
% 199.16/32.78    (144)  all_58_3 = all_4_2
% 199.16/32.78    (145)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.78    (146)   ~ (all_52_3 = all_4_2)
% 199.16/32.78    (147)  all_28_1 = e1
% 199.16/32.78    (148)   ~ (all_52_19 = all_4_2)
% 199.16/32.78    (149)   ~ (all_52_17 = all_52_23)
% 199.16/32.78    (150)  all_8_1 = all_6_1
% 199.16/32.78    (151)  op(all_6_2, e3) = all_6_1
% 199.16/32.78    (152)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.78    (153)   ~ (all_52_13 = all_52_29)
% 199.16/32.78    (154)  all_58_4 = all_52_17
% 199.16/32.78    (155)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.78  
% 199.16/32.78  Begin of proof
% 199.16/32.78  | 
% 199.16/32.78  | BETA: splitting (121) gives:
% 199.16/32.78  | 
% 199.16/32.78  | Case 1:
% 199.16/32.78  | | 
% 199.16/32.78  | |   (156)   ~ (all_28_1 = e1)
% 199.16/32.78  | | 
% 199.16/32.78  | | REDUCE: (147), (156) imply:
% 199.16/32.78  | |   (157)  $false
% 199.16/32.78  | | 
% 199.16/32.78  | | CLOSE: (157) is inconsistent.
% 199.16/32.78  | | 
% 199.16/32.78  | Case 2:
% 199.16/32.78  | | 
% 199.16/32.78  | |   (158)   ~ (all_28_2 = e0)
% 199.16/32.78  | | 
% 199.16/32.78  | | REDUCE: (76), (158) imply:
% 199.16/32.78  | |   (159)   ~ (all_4_2 = e0)
% 199.16/32.78  | | 
% 199.16/32.78  | | GROUND_INST: instantiating (8) with all_6_2, all_52_18, e3, e3, simplifying
% 199.16/32.78  | |              with (2), (114) gives:
% 199.16/32.78  | |   (160)  all_52_18 = all_6_2
% 199.16/32.78  | | 
% 199.16/32.78  | | BETA: splitting (89) gives:
% 199.16/32.78  | | 
% 199.16/32.78  | | Case 1:
% 199.16/32.78  | | | 
% 199.16/32.78  | | |   (161)   ~ (all_44_0 = e2)
% 199.16/32.78  | | | 
% 199.16/32.78  | | | REDUCE: (139), (161) imply:
% 199.16/32.78  | | |   (162)  $false
% 199.16/32.78  | | | 
% 199.16/32.78  | | | CLOSE: (162) is inconsistent.
% 199.16/32.78  | | | 
% 199.16/32.78  | | Case 2:
% 199.16/32.78  | | | 
% 199.16/32.78  | | |   (163)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.78  | | | 
% 199.16/32.78  | | | BETA: splitting (86) gives:
% 199.16/32.78  | | | 
% 199.16/32.78  | | | Case 1:
% 199.16/32.78  | | | | 
% 199.16/32.78  | | | |   (164)  all_58_15 = e0
% 199.16/32.78  | | | | 
% 199.16/32.78  | | | | REF_CLOSE: (8), (21), (30), (50), (95), (124), (133), (164) are
% 199.16/32.78  | | | |            inconsistent by sub-proof #877.
% 199.16/32.78  | | | | 
% 199.16/32.78  | | | Case 2:
% 199.16/32.78  | | | | 
% 199.16/32.78  | | | |   (165)   ~ (all_58_15 = e0)
% 199.16/32.78  | | | |   (166)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.16/32.78  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.16/32.78  | | | | 
% 199.16/32.78  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 199.16/32.78  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 199.16/32.78  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 199.16/32.78  | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 199.16/32.78  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 199.16/32.78  | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 199.16/32.78  | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 199.16/32.78  | | | |            (73), (74), (75), (77), (78), (79), (80), (81), (82), (83),
% 199.16/32.78  | | | |            (84), (85), (87), (88), (90), (91), (92), (93), (94), (95),
% 199.16/32.78  | | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 199.16/32.78  | | | |            (105), (106), (107), (108), (109), (110), (111), (112),
% 199.16/32.78  | | | |            (113), (114), (115), (116), (117), (118), (119), (120),
% 199.16/32.78  | | | |            (122), (123), (124), (125), (126), (127), (128), (129),
% 199.16/32.78  | | | |            (130), (131), (132), (133), (134), (135), (136), (137),
% 199.16/32.78  | | | |            (138), (140), (141), (142), (143), (144), (145), (146),
% 199.16/32.78  | | | |            (148), (149), (150), (151), (152), (153), (154), (155),
% 199.16/32.78  | | | |            (159), (160), (163), (165), (166) are inconsistent by
% 199.16/32.78  | | | |            sub-proof #65.
% 199.16/32.78  | | | | 
% 199.16/32.78  | | | End of split
% 199.16/32.78  | | | 
% 199.16/32.78  | | End of split
% 199.16/32.78  | | 
% 199.16/32.78  | End of split
% 199.16/32.78  | 
% 199.16/32.78  End of proof
% 199.16/32.78  
% 199.16/32.78  Sub-proof #62 shows that the following formulas are inconsistent:
% 199.16/32.78  ----------------------------------------------------------------
% 199.16/32.78    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.78    (2)   ~ (all_52_15 = all_52_23)
% 199.16/32.78    (3)   ~ (all_52_25 = all_52_27)
% 199.16/32.78    (4)  all_58_14 = all_52_23
% 199.16/32.78    (5)   ~ (e3 = e1)
% 199.16/32.78    (6)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.78    (8)  all_58_1 = all_52_9
% 199.16/32.78    (9)   ~ (all_52_9 = all_52_13)
% 199.16/32.78    (10)   ~ (e3 = e0)
% 199.16/32.78    (11)  op(e2, e3) = all_52_3
% 199.16/32.78    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.78    (13)   ~ (all_52_7 = all_52_15)
% 199.16/32.78    (14)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.78    (15)   ~ (all_52_17 = all_52_25)
% 199.16/32.78    (16)   ~ (all_52_3 = all_6_2)
% 199.16/32.78    (17)  all_44_2 = all_6_2
% 199.16/32.78    (18)  all_58_0 = all_6_2
% 199.16/32.78    (19)  op(all_14_2, e0) = all_14_1
% 199.16/32.78    (20)  all_56_4 = all_52_3
% 199.16/32.78    (21)   ~ (all_52_17 = all_10_2)
% 199.16/32.78    (22)   ~ (all_10_0 = e3)
% 199.16/32.78    (23)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.78    (24)  all_40_2 = all_10_2
% 199.16/32.78    (25)  op(e3, e0) = all_52_25
% 199.16/32.78    (26)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.78    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.78    (28)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.78    (29)   ~ (all_52_27 = all_52_29)
% 199.16/32.78    (30)  all_58_13 = all_52_15
% 199.16/32.78    (31)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.78    (32)  all_58_9 = all_52_25
% 199.16/32.78    (33)   ~ (all_52_29 = all_14_2)
% 199.16/32.78    (34)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.78    (35)  op(e1, e3) = all_52_5
% 199.16/32.78    (36)  op(e2, e2) = all_4_2
% 199.16/32.78    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.78    (38)  all_58_7 = all_10_0
% 199.16/32.78    (39)   ~ (all_52_3 = all_52_5)
% 199.16/32.78    (40)  op(all_4_2, e2) = e1
% 199.16/32.78    (41)  all_58_11 = all_52_29
% 199.16/32.78    (42)  all_56_5 = all_4_2
% 199.16/32.78    (43)   ~ (all_52_25 = all_14_2)
% 199.16/32.78    (44)   ~ (all_52_9 = all_52_15)
% 199.16/32.78    (45)   ~ (all_52_3 = all_52_27)
% 199.16/32.78    (46)  op(all_10_2, e1) = all_10_1
% 199.16/32.78    (47)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.78    (48)   ~ (all_52_7 = all_6_2)
% 199.16/32.78    (49)  op(e0, e0) = all_14_2
% 199.16/32.78    (50)  all_56_15 = all_14_2
% 199.16/32.78    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.78    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.78    (53)   ~ (all_58_15 = e0)
% 199.16/32.78    (54)  all_56_11 = all_52_29
% 199.16/32.78    (55)   ~ (all_10_0 = e2)
% 199.16/32.78    (56)   ~ (all_4_0 = e3)
% 199.16/32.78    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.78    (58)   ~ (all_52_13 = all_10_2)
% 199.16/32.78    (59)  all_58_10 = all_52_27
% 199.16/32.78    (60)  all_56_8 = all_52_5
% 199.16/32.78    (61)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.78    (62)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.78    (63)  all_56_9 = all_10_0
% 199.16/32.78    (64)   ~ (all_52_25 = all_52_29)
% 199.16/32.78    (65)   ~ (all_52_29 = all_10_2)
% 199.16/32.78    (66)  all_58_7 = all_52_13
% 199.16/32.78    (67)   ~ (all_10_0 = all_4_2)
% 199.16/32.78    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.78    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.78    (70)   ~ (all_52_5 = all_52_7)
% 199.16/32.78    (71)  all_58_12 = all_52_7
% 199.16/32.78    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.78    (73)   ~ (all_52_7 = all_14_2)
% 199.16/32.78    (74)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 199.16/32.78    (75)  all_58_2 = all_52_3
% 199.16/32.78    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.78    (77)  all_56_2 = all_52_17
% 199.16/32.78    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.78    (79)   ~ (all_52_15 = all_10_0)
% 199.16/32.78    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.78    (81)  all_56_7 = all_52_27
% 199.16/32.78    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.78    (83)   ~ (e2 = e0)
% 199.16/32.78    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.78    (85)  op(all_4_2, e2) = all_4_1
% 199.16/32.78    (86)   ~ (all_52_5 = all_52_29)
% 199.16/32.78    (87)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.16/32.78    (88)  all_56_6 = all_52_19
% 199.16/32.78    (89)   ~ (all_52_15 = all_14_2)
% 199.16/32.78    (90)   ~ (all_52_19 = all_52_27)
% 199.16/32.78    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.78    (92)  op(e3, e1) = all_52_17
% 199.16/32.78    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.78    (94)  op(e0, e3) = all_52_7
% 199.16/32.78    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.78    (96)   ~ (all_52_9 = all_52_25)
% 199.16/32.78    (97)  all_58_15 = all_14_2
% 199.16/32.78    (98)   ~ (all_52_19 = all_10_2)
% 199.16/32.78    (99)  op(all_52_23, all_52_23) = all_52_22
% 199.16/32.78    (100)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.78    (101)  all_58_8 = all_10_2
% 199.16/32.78    (102)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.78    (103)   ~ (all_52_5 = all_10_2)
% 199.16/32.78    (104)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.78    (105)   ~ (all_52_23 = all_14_2)
% 199.16/32.78    (106)  all_56_12 = all_52_7
% 199.16/32.78    (107)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.78    (108)  all_58_5 = all_4_0
% 199.16/32.78    (109)  all_8_2 = all_6_2
% 199.16/32.78    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.78    (111)   ~ (all_52_25 = all_6_2)
% 199.16/32.78    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.78    (113)   ~ (all_52_9 = all_4_2)
% 199.16/32.78    (114)   ~ (all_52_5 = all_6_2)
% 199.16/32.78    (115)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.16/32.78    (116)   ~ (all_52_9 = all_6_2)
% 199.16/32.78    (117)  op(e3, all_6_1) = e2
% 199.16/32.78    (118)  all_56_0 = all_6_2
% 199.16/32.78    (119)  op(e3, e3) = all_6_2
% 199.16/32.78    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.78    (121)   ~ (all_52_27 = all_14_2)
% 199.16/32.78    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.78    (123)  all_56_14 = all_52_23
% 199.16/32.78    (124)  op(all_4_2, all_4_2) = all_52_10
% 199.16/32.78    (125)  all_40_0 = all_10_0
% 199.16/32.78    (126)  all_56_3 = all_52_25
% 199.16/32.78    (127)   ~ (all_52_3 = all_52_7)
% 199.16/32.78    (128)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.78    (129)  all_58_5 = all_52_19
% 199.16/32.78    (130)  all_56_1 = all_52_9
% 199.16/32.78    (131)   ~ (all_52_15 = all_4_2)
% 199.16/32.78    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.78           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.78           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.78           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.78    (133)   ~ (all_52_27 = all_4_2)
% 199.16/32.78    (134)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 199.16/32.78             all_58_13 = e0 | all_58_14 = e0)
% 199.16/32.78    (135)  all_58_6 = all_52_5
% 199.16/32.78    (136)  op(all_10_2, e1) = e2
% 199.16/32.78    (137)  op(e3, e2) = all_52_9
% 199.16/32.78    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.78    (139)   ~ (all_52_17 = all_6_2)
% 199.16/32.78    (140)   ~ (e1 = e0)
% 199.16/32.78    (141)   ~ (e3 = e2)
% 199.16/32.78    (142)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 199.16/32.78    (143)  all_44_1 = all_6_1
% 199.16/32.78    (144)   ~ (all_52_9 = all_52_17)
% 199.16/32.78    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.78    (146)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.16/32.78    (147)   ~ (all_52_3 = all_4_0)
% 199.16/32.78    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.78    (149)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.78    (150)  op(e1, e1) = all_10_2
% 199.16/32.78    (151)   ~ (all_52_23 = all_10_2)
% 199.16/32.78    (152)   ~ (all_52_7 = all_52_23)
% 199.16/32.78    (153)   ~ (all_52_17 = all_52_19)
% 199.16/32.78    (154)   ~ (all_52_5 = all_10_0)
% 199.16/32.78    (155)  all_58_3 = all_4_2
% 199.16/32.78    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.78    (157)   ~ (all_52_3 = all_4_2)
% 199.16/32.78    (158)   ~ (all_52_9 = all_10_0)
% 199.16/32.78    (159)   ~ (all_52_19 = all_4_2)
% 199.16/32.78    (160)   ~ (all_52_17 = all_52_23)
% 199.16/32.78    (161)  all_8_1 = all_6_1
% 199.16/32.78    (162)  op(all_6_2, e3) = all_6_1
% 199.16/32.78    (163)   ~ (all_52_13 = all_52_29)
% 199.16/32.78    (164)  all_58_4 = all_52_17
% 199.16/32.78    (165)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.78  
% 199.16/32.78  Begin of proof
% 199.16/32.78  | 
% 199.16/32.78  | ALPHA: (134) implies:
% 199.16/32.78  |   (166)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.78  |   (167)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.16/32.78  | 
% 199.16/32.78  | REDUCE: (53), (97) imply:
% 199.16/32.78  |   (168)   ~ (all_14_2 = e0)
% 199.16/32.78  | 
% 199.16/32.78  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.16/32.78  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 199.16/32.78  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 199.16/32.78  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.16/32.78  |            (46), (47), (48), (49), (50), (51), (52), (54), (55), (56), (57),
% 199.16/32.78  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 199.16/32.78  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 199.16/32.78  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 199.16/32.78  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 199.16/32.78  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 199.16/32.78  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 199.16/32.78  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 199.16/32.78  |            (129), (130), (131), (132), (133), (135), (136), (137), (138),
% 199.16/32.78  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 199.16/32.78  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 199.16/32.78  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 199.16/32.78  |            (166), (167), (168) are inconsistent by sub-proof #72.
% 199.16/32.78  | 
% 199.16/32.78  End of proof
% 199.16/32.78  
% 199.16/32.78  Sub-proof #63 shows that the following formulas are inconsistent:
% 199.16/32.78  ----------------------------------------------------------------
% 199.16/32.78    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.78    (2)   ~ (all_52_15 = all_52_23)
% 199.16/32.78    (3)   ~ (all_52_25 = all_52_27)
% 199.16/32.78    (4)  all_58_14 = all_52_23
% 199.16/32.78    (5)   ~ (e3 = e1)
% 199.16/32.78    (6)   ~ (all_52_17 = all_4_0)
% 199.16/32.78    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.78    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.78    (9)   ~ (all_52_5 = all_52_13)
% 199.16/32.78    (10)  all_58_1 = all_52_9
% 199.16/32.78    (11)   ~ (all_52_9 = all_52_13)
% 199.16/32.78    (12)   ~ (e3 = e0)
% 199.16/32.78    (13)  op(e2, e3) = all_52_3
% 199.16/32.78    (14)   ~ (all_52_23 = all_4_0)
% 199.16/32.78    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.78    (16)   ~ (all_52_7 = all_52_15)
% 199.16/32.78    (17)   ~ (all_52_3 = all_52_19)
% 199.16/32.78    (18)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.78    (19)   ~ (all_52_17 = all_52_25)
% 199.16/32.78    (20)   ~ (all_52_3 = all_6_2)
% 199.16/32.78    (21)  all_44_2 = all_6_2
% 199.16/32.78    (22)  all_58_0 = all_6_2
% 199.16/32.78    (23)  op(all_14_2, e0) = all_14_1
% 199.16/32.78    (24)  all_56_4 = all_52_3
% 199.16/32.78    (25)   ~ (all_52_17 = all_10_2)
% 199.16/32.78    (26)  op(e3, e0) = all_52_25
% 199.16/32.78    (27)  op(e0, all_14_1) = all_14_0
% 199.16/32.78    (28)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.78    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.78    (30)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.78    (31)   ~ (all_52_27 = all_52_29)
% 199.16/32.78    (32)  all_58_13 = all_52_15
% 199.16/32.78    (33)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.78    (34)  all_58_9 = all_52_25
% 199.16/32.78    (35)   ~ (all_52_29 = all_14_2)
% 199.16/32.78    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.78    (37)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.78    (38)  op(e1, e3) = all_52_5
% 199.16/32.78    (39)  op(e2, e2) = all_4_2
% 199.16/32.78    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.78    (41)   ~ (all_52_3 = all_52_5)
% 199.16/32.78    (42)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.78    (43)  op(all_4_2, e2) = e1
% 199.16/32.78    (44)  all_58_11 = all_52_29
% 199.16/32.78    (45)  all_56_5 = all_4_2
% 199.16/32.78    (46)   ~ (all_52_25 = all_14_2)
% 199.16/32.78    (47)   ~ (all_52_9 = all_52_15)
% 199.16/32.78    (48)   ~ (all_52_3 = all_52_27)
% 199.16/32.78    (49)  op(all_10_2, e1) = all_10_1
% 199.16/32.78    (50)   ~ (all_10_2 = all_4_0)
% 199.16/32.78    (51)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.78    (52)   ~ (all_52_7 = all_6_2)
% 199.16/32.78    (53)  op(e0, e0) = all_14_2
% 199.16/32.78    (54)  all_56_15 = all_14_2
% 199.16/32.78    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.78    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.78    (57)  all_56_11 = all_52_29
% 199.16/32.78    (58)  all_4_0 = e3
% 199.16/32.78    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.16/32.78    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.78    (61)  all_56_9 = all_52_13
% 199.16/32.78    (62)   ~ (e2 = e1)
% 199.16/32.78    (63)   ~ (all_52_13 = all_10_2)
% 199.16/32.78    (64)  all_58_10 = all_52_27
% 199.16/32.78    (65)  all_56_8 = all_52_5
% 199.16/32.78    (66)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.78    (67)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.78    (68)   ~ (all_52_25 = all_52_29)
% 199.16/32.78    (69)   ~ (all_52_29 = all_10_2)
% 199.16/32.78    (70)  all_58_7 = all_52_13
% 199.16/32.78    (71)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.78    (72)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.78    (73)   ~ (all_52_5 = all_52_7)
% 199.16/32.78    (74)  all_58_12 = all_52_7
% 199.16/32.78    (75)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.78    (76)   ~ (all_52_7 = all_14_2)
% 199.16/32.78    (77)  all_58_2 = all_52_3
% 199.16/32.78    (78)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.78    (79)  all_56_2 = all_52_17
% 199.16/32.78    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.78    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.78    (82)   ~ (all_14_0 = e3)
% 199.16/32.78    (83)  all_56_7 = all_52_27
% 199.16/32.78    (84)  all_28_2 = all_4_2
% 199.16/32.78    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.78    (86)   ~ (e2 = e0)
% 199.16/32.78    (87)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.78    (88)   ~ (all_52_5 = all_52_29)
% 199.16/32.78    (89)  all_56_6 = all_52_19
% 199.16/32.78    (90)   ~ (all_52_15 = all_14_2)
% 199.16/32.78    (91)   ~ (all_52_19 = all_52_27)
% 199.16/32.78    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.78    (93)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.16/32.78            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.16/32.78    (94)   ~ (all_52_13 = all_4_2)
% 199.16/32.78    (95)  op(e3, e1) = all_52_17
% 199.16/32.78    (96)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.78    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.78    (98)  op(e0, e3) = all_52_7
% 199.16/32.78    (99)  op(e1, e2) = all_52_13
% 199.16/32.78    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.78    (101)   ~ (all_52_9 = all_52_25)
% 199.16/32.78    (102)  all_58_15 = all_14_2
% 199.16/32.78    (103)   ~ (all_52_19 = all_10_2)
% 199.16/32.78    (104)  op(all_52_23, all_52_23) = all_52_22
% 199.16/32.78    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.78    (106)  all_58_8 = all_10_2
% 199.16/32.78    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.78    (108)   ~ (all_52_5 = all_10_2)
% 199.16/32.78    (109)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.78    (110)   ~ (all_52_23 = all_14_2)
% 199.16/32.78    (111)  all_56_12 = all_52_7
% 199.16/32.78    (112)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.78    (113)  all_58_5 = all_4_0
% 199.16/32.78    (114)  all_8_2 = all_6_2
% 199.16/32.78    (115)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.78    (116)   ~ (all_52_25 = all_6_2)
% 199.16/32.78    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.78    (118)   ~ (all_52_9 = all_4_2)
% 199.16/32.78    (119)   ~ (all_52_5 = all_6_2)
% 199.16/32.78    (120)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 199.16/32.78    (121)   ~ (all_52_9 = all_6_2)
% 199.16/32.78    (122)   ~ (all_52_13 = all_52_15)
% 199.16/32.78    (123)  op(e3, all_6_1) = e2
% 199.16/32.78    (124)  all_56_0 = all_6_2
% 199.16/32.78    (125)  op(all_4_0, all_4_0) = all_52_18
% 199.16/32.78    (126)  op(e3, e3) = all_6_2
% 199.16/32.78    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.78    (128)   ~ (all_52_27 = all_14_2)
% 199.16/32.78    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.78    (130)  all_56_14 = all_52_23
% 199.16/32.78    (131)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.16/32.78    (132)  all_56_3 = all_52_25
% 199.16/32.78    (133)   ~ (all_52_3 = all_52_7)
% 199.16/32.78    (134)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.78    (135)  all_58_5 = all_52_19
% 199.16/32.78    (136)   ~ (all_52_15 = all_4_2)
% 199.16/32.78    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.78           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.78           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.78           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.78    (138)   ~ (all_52_27 = all_4_2)
% 199.16/32.78    (139)  all_58_6 = all_52_5
% 199.16/32.79    (140)   ~ (all_4_0 = all_4_2)
% 199.16/32.79    (141)  op(e3, e2) = all_52_9
% 199.16/32.79    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.79    (143)   ~ (all_52_17 = all_6_2)
% 199.16/32.79    (144)   ~ (e1 = e0)
% 199.16/32.79    (145)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 199.16/32.79    (146)   ~ (e3 = e2)
% 199.16/32.79    (147)  all_44_1 = all_6_1
% 199.16/32.79    (148)   ~ (all_52_9 = all_52_17)
% 199.16/32.79    (149)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.79    (150)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.16/32.79    (151)   ~ (all_52_3 = all_4_0)
% 199.16/32.79    (152)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.79    (153)  all_44_0 = e2
% 199.16/32.79    (154)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.79    (155)  op(e1, e1) = all_10_2
% 199.16/32.79    (156)   ~ (all_52_23 = all_10_2)
% 199.16/32.79    (157)   ~ (all_52_7 = all_52_23)
% 199.16/32.79    (158)   ~ (all_52_17 = all_52_19)
% 199.16/32.79    (159)  all_58_3 = all_4_2
% 199.16/32.79    (160)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.79    (161)  all_56_13 = all_52_15
% 199.16/32.79    (162)   ~ (all_52_3 = all_4_2)
% 199.16/32.79    (163)  all_28_1 = e1
% 199.16/32.79    (164)   ~ (all_52_19 = all_4_2)
% 199.16/32.79    (165)   ~ (all_52_17 = all_52_23)
% 199.16/32.79    (166)  all_8_1 = all_6_1
% 199.16/32.79    (167)  op(all_6_2, e3) = all_6_1
% 199.16/32.79    (168)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.79    (169)   ~ (all_52_13 = all_52_29)
% 199.16/32.79    (170)  all_58_4 = all_52_17
% 199.16/32.79    (171)   ~ (all_14_0 = e1)
% 199.16/32.79    (172)   ~ (all_14_0 = e2)
% 199.16/32.79    (173)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.79  
% 199.16/32.79  Begin of proof
% 199.16/32.79  | 
% 199.16/32.79  | COMBINE_EQS: (58), (113) imply:
% 199.16/32.79  |   (174)  all_58_5 = e3
% 199.16/32.79  | 
% 199.16/32.79  | REDUCE: (58), (151) imply:
% 199.16/32.79  |   (175)   ~ (all_52_3 = e3)
% 199.16/32.79  | 
% 199.16/32.79  | REDUCE: (6), (58) imply:
% 199.16/32.79  |   (176)   ~ (all_52_17 = e3)
% 199.16/32.79  | 
% 199.16/32.79  | REDUCE: (14), (58) imply:
% 199.16/32.79  |   (177)   ~ (all_52_23 = e3)
% 199.16/32.79  | 
% 199.16/32.79  | REDUCE: (50), (58) imply:
% 199.16/32.79  |   (178)   ~ (all_10_2 = e3)
% 199.16/32.79  | 
% 199.16/32.79  | REDUCE: (58), (140) imply:
% 199.16/32.79  |   (179)   ~ (all_4_2 = e3)
% 199.16/32.79  | 
% 199.16/32.79  | SIMP: (179) implies:
% 199.16/32.79  |   (180)   ~ (all_4_2 = e3)
% 199.16/32.79  | 
% 199.16/32.79  | REDUCE: (58), (125) imply:
% 199.16/32.79  |   (181)  op(e3, e3) = all_52_18
% 199.16/32.79  | 
% 199.16/32.79  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 199.16/32.79  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.16/32.79  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 199.16/32.79  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 199.16/32.79  |            (48), (49), (51), (52), (53), (54), (55), (56), (57), (59), (60),
% 199.16/32.79  |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 199.16/32.79  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 199.16/32.79  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 199.16/32.79  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 199.16/32.79  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 199.16/32.79  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 199.16/32.79  |            (123), (124), (126), (127), (128), (129), (130), (131), (132),
% 199.16/32.79  |            (133), (134), (135), (136), (137), (138), (139), (141), (142),
% 199.16/32.79  |            (143), (144), (145), (146), (147), (148), (149), (150), (152),
% 199.16/32.79  |            (153), (154), (155), (156), (157), (158), (159), (160), (161),
% 199.16/32.79  |            (162), (163), (164), (165), (166), (167), (168), (169), (170),
% 199.16/32.79  |            (171), (172), (173), (174), (175), (176), (177), (178), (180),
% 199.16/32.79  |            (181) are inconsistent by sub-proof #64.
% 199.16/32.79  | 
% 199.16/32.79  End of proof
% 199.16/32.79  
% 199.16/32.79  Sub-proof #64 shows that the following formulas are inconsistent:
% 199.16/32.79  ----------------------------------------------------------------
% 199.16/32.79    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.79    (2)  op(e3, e3) = all_52_18
% 199.16/32.79    (3)   ~ (all_52_15 = all_52_23)
% 199.16/32.79    (4)   ~ (all_52_25 = all_52_27)
% 199.16/32.79    (5)  all_58_14 = all_52_23
% 199.16/32.79    (6)   ~ (e3 = e1)
% 199.16/32.79    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.79    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.79    (9)   ~ (all_52_5 = all_52_13)
% 199.16/32.79    (10)  all_58_1 = all_52_9
% 199.16/32.79    (11)   ~ (all_52_9 = all_52_13)
% 199.16/32.79    (12)   ~ (e3 = e0)
% 199.16/32.79    (13)  op(e2, e3) = all_52_3
% 199.16/32.79    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.79    (15)   ~ (all_52_7 = all_52_15)
% 199.16/32.79    (16)   ~ (all_52_3 = all_52_19)
% 199.16/32.79    (17)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.79    (18)   ~ (all_52_17 = all_52_25)
% 199.16/32.79    (19)   ~ (all_4_2 = e3)
% 199.16/32.79    (20)   ~ (all_52_3 = all_6_2)
% 199.16/32.79    (21)  all_44_2 = all_6_2
% 199.16/32.79    (22)  all_58_0 = all_6_2
% 199.16/32.79    (23)  op(all_14_2, e0) = all_14_1
% 199.16/32.79    (24)  all_56_4 = all_52_3
% 199.16/32.79    (25)   ~ (all_52_17 = all_10_2)
% 199.16/32.79    (26)  op(e3, e0) = all_52_25
% 199.16/32.79    (27)  op(e0, all_14_1) = all_14_0
% 199.16/32.79    (28)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.79    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.79    (30)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.79    (31)   ~ (all_52_27 = all_52_29)
% 199.16/32.79    (32)  all_58_13 = all_52_15
% 199.16/32.79    (33)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.79    (34)  all_58_9 = all_52_25
% 199.16/32.79    (35)   ~ (all_52_29 = all_14_2)
% 199.16/32.79    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.79    (37)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.79    (38)  op(e1, e3) = all_52_5
% 199.16/32.79    (39)  op(e2, e2) = all_4_2
% 199.16/32.79    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.79    (41)   ~ (all_52_3 = all_52_5)
% 199.16/32.79    (42)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.79    (43)  op(all_4_2, e2) = e1
% 199.16/32.79    (44)  all_58_11 = all_52_29
% 199.16/32.79    (45)   ~ (all_52_3 = e3)
% 199.16/32.79    (46)  all_56_5 = all_4_2
% 199.16/32.79    (47)   ~ (all_52_25 = all_14_2)
% 199.16/32.79    (48)   ~ (all_52_9 = all_52_15)
% 199.16/32.79    (49)   ~ (all_52_3 = all_52_27)
% 199.16/32.79    (50)  op(all_10_2, e1) = all_10_1
% 199.16/32.79    (51)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.79    (52)   ~ (all_52_7 = all_6_2)
% 199.16/32.79    (53)  op(e0, e0) = all_14_2
% 199.16/32.79    (54)  all_56_15 = all_14_2
% 199.16/32.79    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.79    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.79    (57)  all_56_11 = all_52_29
% 199.16/32.79    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.16/32.79    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.79    (60)  all_56_9 = all_52_13
% 199.16/32.79    (61)   ~ (e2 = e1)
% 199.16/32.79    (62)   ~ (all_52_13 = all_10_2)
% 199.16/32.79    (63)  all_58_10 = all_52_27
% 199.16/32.79    (64)  all_56_8 = all_52_5
% 199.16/32.79    (65)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.79    (66)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.79    (67)   ~ (all_52_25 = all_52_29)
% 199.16/32.79    (68)   ~ (all_52_29 = all_10_2)
% 199.16/32.79    (69)  all_58_7 = all_52_13
% 199.16/32.79    (70)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.79    (71)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.79    (72)   ~ (all_52_5 = all_52_7)
% 199.16/32.79    (73)  all_58_12 = all_52_7
% 199.16/32.79    (74)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.79    (75)   ~ (all_52_7 = all_14_2)
% 199.16/32.79    (76)  all_58_2 = all_52_3
% 199.16/32.79    (77)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.79    (78)  all_56_2 = all_52_17
% 199.16/32.79    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.79    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.79    (81)   ~ (all_14_0 = e3)
% 199.16/32.79    (82)  all_56_7 = all_52_27
% 199.16/32.79    (83)  all_28_2 = all_4_2
% 199.16/32.79    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.79    (85)   ~ (e2 = e0)
% 199.16/32.79    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.79    (87)   ~ (all_52_23 = e3)
% 199.16/32.79    (88)   ~ (all_52_5 = all_52_29)
% 199.16/32.79    (89)  all_56_6 = all_52_19
% 199.16/32.79    (90)   ~ (all_10_2 = e3)
% 199.16/32.79    (91)   ~ (all_52_15 = all_14_2)
% 199.16/32.79    (92)   ~ (all_52_19 = all_52_27)
% 199.16/32.79    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.79    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.16/32.79            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.16/32.79    (95)   ~ (all_52_13 = all_4_2)
% 199.16/32.79    (96)  op(e3, e1) = all_52_17
% 199.16/32.79    (97)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.79    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.79    (99)  op(e0, e3) = all_52_7
% 199.16/32.79    (100)  op(e1, e2) = all_52_13
% 199.16/32.79    (101)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.79    (102)   ~ (all_52_9 = all_52_25)
% 199.16/32.79    (103)  all_58_15 = all_14_2
% 199.16/32.79    (104)   ~ (all_52_19 = all_10_2)
% 199.16/32.79    (105)  op(all_52_23, all_52_23) = all_52_22
% 199.16/32.79    (106)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.79    (107)  all_58_8 = all_10_2
% 199.16/32.79    (108)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.79    (109)   ~ (all_52_5 = all_10_2)
% 199.16/32.79    (110)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.79    (111)   ~ (all_52_23 = all_14_2)
% 199.16/32.79    (112)  all_56_12 = all_52_7
% 199.16/32.79    (113)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.79    (114)  all_8_2 = all_6_2
% 199.16/32.79    (115)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.79    (116)   ~ (all_52_25 = all_6_2)
% 199.16/32.79    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.79    (118)   ~ (all_52_9 = all_4_2)
% 199.16/32.79    (119)   ~ (all_52_5 = all_6_2)
% 199.16/32.79    (120)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 199.16/32.79    (121)   ~ (all_52_9 = all_6_2)
% 199.16/32.79    (122)   ~ (all_52_13 = all_52_15)
% 199.16/32.79    (123)  op(e3, all_6_1) = e2
% 199.16/32.79    (124)  all_56_0 = all_6_2
% 199.16/32.79    (125)  op(e3, e3) = all_6_2
% 199.16/32.79    (126)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.79    (127)   ~ (all_52_27 = all_14_2)
% 199.16/32.79    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.79    (129)  all_58_5 = e3
% 199.16/32.79    (130)  all_56_14 = all_52_23
% 199.16/32.79    (131)   ~ (all_52_17 = e3)
% 199.16/32.79    (132)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 199.16/32.79    (133)  all_56_3 = all_52_25
% 199.16/32.79    (134)   ~ (all_52_3 = all_52_7)
% 199.16/32.79    (135)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.79    (136)  all_58_5 = all_52_19
% 199.16/32.79    (137)   ~ (all_52_15 = all_4_2)
% 199.16/32.79    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.79           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.79           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.79           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.79    (139)   ~ (all_52_27 = all_4_2)
% 199.16/32.79    (140)  all_58_6 = all_52_5
% 199.16/32.79    (141)  op(e3, e2) = all_52_9
% 199.16/32.79    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.79    (143)   ~ (all_52_17 = all_6_2)
% 199.16/32.79    (144)   ~ (e1 = e0)
% 199.16/32.79    (145)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 199.16/32.79    (146)   ~ (e3 = e2)
% 199.16/32.79    (147)  all_44_1 = all_6_1
% 199.16/32.79    (148)   ~ (all_52_9 = all_52_17)
% 199.16/32.79    (149)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.79    (150)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.16/32.79    (151)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.79    (152)  all_44_0 = e2
% 199.16/32.79    (153)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.79    (154)  op(e1, e1) = all_10_2
% 199.16/32.79    (155)   ~ (all_52_23 = all_10_2)
% 199.16/32.79    (156)   ~ (all_52_7 = all_52_23)
% 199.16/32.79    (157)   ~ (all_52_17 = all_52_19)
% 199.16/32.79    (158)  all_58_3 = all_4_2
% 199.16/32.79    (159)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.79    (160)  all_56_13 = all_52_15
% 199.16/32.79    (161)   ~ (all_52_3 = all_4_2)
% 199.16/32.79    (162)  all_28_1 = e1
% 199.16/32.79    (163)   ~ (all_52_19 = all_4_2)
% 199.16/32.79    (164)   ~ (all_52_17 = all_52_23)
% 199.16/32.79    (165)  all_8_1 = all_6_1
% 199.16/32.79    (166)  op(all_6_2, e3) = all_6_1
% 199.16/32.79    (167)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.79    (168)   ~ (all_52_13 = all_52_29)
% 199.16/32.79    (169)  all_58_4 = all_52_17
% 199.16/32.79    (170)   ~ (all_14_0 = e1)
% 199.16/32.79    (171)   ~ (all_14_0 = e2)
% 199.16/32.79    (172)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.79  
% 199.16/32.79  Begin of proof
% 199.16/32.79  | 
% 199.16/32.79  | BETA: splitting (132) gives:
% 199.16/32.79  | 
% 199.16/32.79  | Case 1:
% 199.16/32.79  | | 
% 199.16/32.79  | |   (173)   ~ (all_28_1 = e1)
% 199.16/32.79  | | 
% 199.16/32.79  | | REDUCE: (162), (173) imply:
% 199.16/32.79  | |   (174)  $false
% 199.16/32.79  | | 
% 199.16/32.79  | | CLOSE: (174) is inconsistent.
% 199.16/32.79  | | 
% 199.16/32.79  | Case 2:
% 199.16/32.79  | | 
% 199.16/32.79  | |   (175)   ~ (all_28_2 = e0)
% 199.16/32.79  | | 
% 199.16/32.79  | | REDUCE: (83), (175) imply:
% 199.16/32.79  | |   (176)   ~ (all_4_2 = e0)
% 199.16/32.79  | | 
% 199.16/32.79  | | GROUND_INST: instantiating (8) with all_6_2, all_52_18, e3, e3, simplifying
% 199.16/32.79  | |              with (2), (125) gives:
% 199.16/32.79  | |   (177)  all_52_18 = all_6_2
% 199.16/32.79  | | 
% 199.16/32.79  | | BETA: splitting (97) gives:
% 199.16/32.79  | | 
% 199.16/32.79  | | Case 1:
% 199.16/32.79  | | | 
% 199.16/32.79  | | |   (178)   ~ (all_44_0 = e2)
% 199.16/32.79  | | | 
% 199.16/32.79  | | | REDUCE: (152), (178) imply:
% 199.16/32.79  | | |   (179)  $false
% 199.16/32.79  | | | 
% 199.16/32.79  | | | CLOSE: (179) is inconsistent.
% 199.16/32.79  | | | 
% 199.16/32.79  | | Case 2:
% 199.16/32.79  | | | 
% 199.16/32.79  | | |   (180)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.79  | | | 
% 199.16/32.79  | | | BETA: splitting (94) gives:
% 199.16/32.79  | | | 
% 199.16/32.79  | | | Case 1:
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | |   (181)  all_58_15 = e0
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | COMBINE_EQS: (103), (181) imply:
% 199.16/32.79  | | | |   (182)  all_14_2 = e0
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (91), (182) imply:
% 199.16/32.79  | | | |   (183)   ~ (all_52_15 = e0)
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (111), (182) imply:
% 199.16/32.79  | | | |   (184)   ~ (all_52_23 = e0)
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (47), (182) imply:
% 199.16/32.79  | | | |   (185)   ~ (all_52_25 = e0)
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (127), (182) imply:
% 199.16/32.79  | | | |   (186)   ~ (all_52_27 = e0)
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (35), (182) imply:
% 199.16/32.79  | | | |   (187)   ~ (all_52_29 = e0)
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (135), (182) imply:
% 199.16/32.79  | | | |   (188)  op(e0, e0) = all_52_30
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (23), (182) imply:
% 199.16/32.79  | | | |   (189)  op(e0, e0) = all_14_1
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | REDUCE: (53), (182) imply:
% 199.16/32.79  | | | |   (190)  op(e0, e0) = e0
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | BETA: splitting (42) gives:
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | | Case 1:
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | |   (191)  all_58_2 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | COMBINE_EQS: (76), (191) imply:
% 199.16/32.79  | | | | |   (192)  all_52_3 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | SIMP: (192) implies:
% 199.16/32.79  | | | | |   (193)  all_52_3 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (134), (193) imply:
% 199.16/32.79  | | | | |   (194)   ~ (all_52_7 = e0)
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | SIMP: (194) implies:
% 199.16/32.79  | | | | |   (195)   ~ (all_52_7 = e0)
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (7), (193) imply:
% 199.16/32.79  | | | | |   (196)  op(e0, e0) = all_52_2
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (13), (193) imply:
% 199.16/32.79  | | | | |   (197)  op(e2, e3) = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | GROUND_INST: instantiating (8) with all_14_1, all_52_30, e0, e0,
% 199.16/32.79  | | | | |              simplifying with (188), (189) gives:
% 199.16/32.79  | | | | |   (198)  all_52_30 = all_14_1
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | GROUND_INST: instantiating (8) with all_52_30, all_52_2, e0, e0,
% 199.16/32.79  | | | | |              simplifying with (188), (196) gives:
% 199.16/32.79  | | | | |   (199)  all_52_2 = all_52_30
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | GROUND_INST: instantiating (8) with e0, all_52_2, e0, e0, simplifying
% 199.16/32.79  | | | | |              with (190), (196) gives:
% 199.16/32.79  | | | | |   (200)  all_52_2 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | COMBINE_EQS: (199), (200) imply:
% 199.16/32.79  | | | | |   (201)  all_52_30 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | SIMP: (201) implies:
% 199.16/32.79  | | | | |   (202)  all_52_30 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | COMBINE_EQS: (198), (202) imply:
% 199.16/32.79  | | | | |   (203)  all_14_1 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | SIMP: (203) implies:
% 199.16/32.79  | | | | |   (204)  all_14_1 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (27), (204) imply:
% 199.16/32.79  | | | | |   (205)  op(e0, e0) = all_14_0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | GROUND_INST: instantiating (8) with e0, all_14_0, e0, e0, simplifying
% 199.16/32.79  | | | | |              with (190), (205) gives:
% 199.16/32.79  | | | | |   (206)  all_14_0 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (81), (206) imply:
% 199.16/32.79  | | | | |   (207)   ~ (e3 = e0)
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (171), (206) imply:
% 199.16/32.79  | | | | |   (208)   ~ (e2 = e0)
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REDUCE: (170), (206) imply:
% 199.16/32.79  | | | | |   (209)   ~ (e1 = e0)
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | BETA: splitting (138) gives:
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | Case 1:
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | |   (210)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 199.16/32.79  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 199.16/32.79  | | | | | |            all_52_14 = e0)
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | | BETA: splitting (210) gives:
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | | Case 1:
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | |   (211)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 199.16/32.79  | | | | | | |          = e0
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REF_CLOSE: (85), (200), (211) are inconsistent by sub-proof #68.
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | Case 2:
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | |   (212)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 199.16/32.79  | | | | | | |          all_52_14 = e0
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | ALPHA: (212) implies:
% 199.16/32.79  | | | | | | |   (213)  all_52_14 = e0
% 199.16/32.79  | | | | | | |   (214)  all_52_12 = e1
% 199.16/32.79  | | | | | | |   (215)  all_52_8 = e3
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (65), (215) imply:
% 199.16/32.79  | | | | | | |   (216)  op(all_52_9, all_52_9) = e3
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (153), (214) imply:
% 199.16/32.79  | | | | | | |   (217)  op(all_52_13, all_52_13) = e1
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (66), (213) imply:
% 199.16/32.79  | | | | | | |   (218)  op(all_52_15, all_52_15) = e0
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REF_CLOSE: (1), (2), (5), (8), (10), (14), (15), (17), (19), (21),
% 199.16/32.79  | | | | | | |            (22), (28), (32), (34), (38), (39), (40), (47), (52),
% 199.16/32.79  | | | | | | |            (54), (64), (69), (72), (73), (75), (87), (95), (99),
% 199.16/32.79  | | | | | | |            (101), (103), (106), (108), (112), (114), (119), (121),
% 199.16/32.79  | | | | | | |            (123), (125), (128), (131), (137), (140), (141), (142),
% 199.16/32.79  | | | | | | |            (144), (146), (147), (158), (165), (166), (169), (180),
% 199.16/32.79  | | | | | | |            (195), (216), (217), (218) are inconsistent by
% 199.16/32.79  | | | | | | |            sub-proof #67.
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | End of split
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | Case 2:
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | |   (219)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 199.16/32.79  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 199.16/32.79  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | | BETA: splitting (219) gives:
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | | Case 1:
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | |   (220)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 199.16/32.79  | | | | | | |          all_52_22 = e0
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | ALPHA: (220) implies:
% 199.16/32.79  | | | | | | |   (221)  all_52_18 = e2
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | COMBINE_EQS: (177), (221) imply:
% 199.16/32.79  | | | | | | |   (222)  all_6_2 = e2
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (116), (222) imply:
% 199.16/32.79  | | | | | | |   (223)   ~ (all_52_25 = e2)
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (166), (222) imply:
% 199.16/32.79  | | | | | | |   (224)  op(e2, e3) = all_6_1
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | GROUND_INST: instantiating (8) with e0, all_6_1, e3, e2,
% 199.16/32.79  | | | | | | |              simplifying with (197), (224) gives:
% 199.16/32.79  | | | | | | |   (225)  all_6_1 = e0
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (123), (225) imply:
% 199.16/32.79  | | | | | | |   (226)  op(e3, e0) = e2
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | GROUND_INST: instantiating (8) with all_52_25, e2, e0, e3,
% 199.16/32.79  | | | | | | |              simplifying with (26), (226) gives:
% 199.16/32.79  | | | | | | |   (227)  all_52_25 = e2
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REDUCE: (223), (227) imply:
% 199.16/32.79  | | | | | | |   (228)  $false
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | CLOSE: (228) is inconsistent.
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | Case 2:
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | |   (229)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 199.16/32.79  | | | | | | |          all_52_30 = e0
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (12), (13), (16),
% 199.16/32.79  | | | | | | |            (17), (18), (20), (21), (22), (24), (25), (26), (30),
% 199.16/32.79  | | | | | | |            (32), (34), (35), (37), (38), (39), (40), (41), (44),
% 199.16/32.79  | | | | | | |            (48), (49), (51), (52), (53), (55), (56), (57), (58),
% 199.16/32.79  | | | | | | |            (60), (62), (63), (64), (67), (69), (72), (73), (74),
% 199.16/32.79  | | | | | | |            (76), (77), (79), (84), (85), (88), (89), (93), (95),
% 199.16/32.79  | | | | | | |            (102), (104), (105), (106), (107), (109), (110), (113),
% 199.16/32.79  | | | | | | |            (115), (116), (117), (119), (120), (122), (123), (125),
% 199.16/32.79  | | | | | | |            (126), (127), (128), (133), (136), (137), (140), (141),
% 199.16/32.79  | | | | | | |            (142), (144), (145), (146), (147), (149), (150), (154),
% 199.16/32.79  | | | | | | |            (155), (156), (157), (158), (160), (161), (163), (166),
% 199.16/32.79  | | | | | | |            (167), (168), (169), (172), (180), (181), (183), (184),
% 199.16/32.79  | | | | | | |            (185), (187), (195), (229) are inconsistent by
% 199.16/32.79  | | | | | | |            sub-proof #418.
% 199.16/32.79  | | | | | | | 
% 199.16/32.79  | | | | | | End of split
% 199.16/32.79  | | | | | | 
% 199.16/32.79  | | | | | End of split
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | Case 2:
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | |   (230)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | | REF_CLOSE: (12), (63), (129), (158), (176), (186), (230) are
% 199.16/32.79  | | | | |            inconsistent by sub-proof #152.
% 199.16/32.79  | | | | | 
% 199.16/32.79  | | | | End of split
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | Case 2:
% 199.16/32.79  | | | | 
% 199.16/32.79  | | | |   (231)   ~ (all_58_15 = e0)
% 199.16/32.79  | | | |   (232)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.16/32.79  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.16/32.79  | | | | 
% 199.16/32.80  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 199.16/32.80  | | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 199.16/32.80  | | | |            (24), (25), (26), (28), (29), (30), (31), (32), (33), (34),
% 199.16/32.80  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 199.16/32.80  | | | |            (45), (46), (47), (49), (50), (51), (52), (53), (54), (55),
% 199.16/32.80  | | | |            (56), (57), (59), (61), (63), (64), (65), (66), (67), (68),
% 199.16/32.80  | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 199.16/32.80  | | | |            (79), (80), (82), (84), (85), (86), (87), (88), (89), (90),
% 199.16/32.80  | | | |            (92), (93), (95), (96), (98), (99), (100), (101), (102),
% 199.16/32.80  | | | |            (103), (104), (106), (107), (108), (109), (110), (111),
% 199.16/32.80  | | | |            (112), (113), (114), (115), (116), (117), (118), (119),
% 199.16/32.80  | | | |            (121), (123), (124), (125), (126), (127), (128), (129),
% 199.16/32.80  | | | |            (130), (131), (133), (134), (135), (136), (137), (138),
% 199.16/32.80  | | | |            (139), (140), (141), (142), (143), (144), (146), (147),
% 199.16/32.80  | | | |            (148), (149), (151), (153), (154), (156), (157), (158),
% 199.16/32.80  | | | |            (159), (161), (163), (164), (165), (166), (167), (168),
% 199.16/32.80  | | | |            (169), (172), (176), (177), (180), (231), (232) are
% 199.16/32.80  | | | |            inconsistent by sub-proof #65.
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | End of split
% 199.16/32.80  | | | 
% 199.16/32.80  | | End of split
% 199.16/32.80  | | 
% 199.16/32.80  | End of split
% 199.16/32.80  | 
% 199.16/32.80  End of proof
% 199.16/32.80  
% 199.16/32.80  Sub-proof #65 shows that the following formulas are inconsistent:
% 199.16/32.80  ----------------------------------------------------------------
% 199.16/32.80    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.80    (2)  op(e3, e3) = all_52_18
% 199.16/32.80    (3)   ~ (all_52_15 = all_52_23)
% 199.16/32.80    (4)   ~ (all_52_25 = all_52_27)
% 199.16/32.80    (5)  all_58_14 = all_52_23
% 199.16/32.80    (6)   ~ (e3 = e1)
% 199.16/32.80    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.80    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.80    (9)  all_58_1 = all_52_9
% 199.16/32.80    (10)   ~ (all_52_9 = all_52_13)
% 199.16/32.80    (11)   ~ (e3 = e0)
% 199.16/32.80    (12)  op(e2, e3) = all_52_3
% 199.16/32.80    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.80    (14)   ~ (all_52_7 = all_52_15)
% 199.16/32.80    (15)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.80    (16)   ~ (all_52_17 = all_52_25)
% 199.16/32.80    (17)   ~ (all_4_2 = e3)
% 199.16/32.80    (18)   ~ (all_52_3 = all_6_2)
% 199.16/32.80    (19)  all_44_2 = all_6_2
% 199.16/32.80    (20)  all_58_0 = all_6_2
% 199.16/32.80    (21)  op(all_14_2, e0) = all_14_1
% 199.16/32.80    (22)  all_56_4 = all_52_3
% 199.16/32.80    (23)   ~ (all_52_17 = all_10_2)
% 199.16/32.80    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.80    (25)  op(e3, e0) = all_52_25
% 199.16/32.80    (26)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.80    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.80    (28)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.80    (29)   ~ (all_52_27 = all_52_29)
% 199.16/32.80    (30)  all_58_13 = all_52_15
% 199.16/32.80    (31)   ~ (all_4_2 = e0)
% 199.16/32.80    (32)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.80    (33)  all_58_9 = all_52_25
% 199.16/32.80    (34)   ~ (all_52_29 = all_14_2)
% 199.16/32.80    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.80    (36)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.80    (37)  op(e1, e3) = all_52_5
% 199.16/32.80    (38)  op(e2, e2) = all_4_2
% 199.16/32.80    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.80    (40)   ~ (all_52_3 = all_52_5)
% 199.16/32.80    (41)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.80    (42)  op(all_4_2, e2) = e1
% 199.16/32.80    (43)  all_58_11 = all_52_29
% 199.16/32.80    (44)   ~ (all_52_3 = e3)
% 199.16/32.80    (45)  all_56_5 = all_4_2
% 199.16/32.80    (46)   ~ (all_52_25 = all_14_2)
% 199.16/32.80    (47)   ~ (all_52_3 = all_52_27)
% 199.16/32.80    (48)  op(all_10_2, e1) = all_10_1
% 199.16/32.80    (49)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.80    (50)   ~ (all_52_7 = all_6_2)
% 199.16/32.80    (51)  op(e0, e0) = all_14_2
% 199.16/32.80    (52)  all_56_15 = all_14_2
% 199.16/32.80    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.80    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.80    (55)   ~ (all_58_15 = e0)
% 199.16/32.80    (56)  all_56_11 = all_52_29
% 199.16/32.80    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.80    (58)   ~ (e2 = e1)
% 199.16/32.80    (59)  all_58_10 = all_52_27
% 199.16/32.80    (60)  all_56_8 = all_52_5
% 199.16/32.80    (61)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.80    (62)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.80    (63)   ~ (all_52_25 = all_52_29)
% 199.16/32.80    (64)   ~ (all_52_29 = all_10_2)
% 199.16/32.80    (65)  all_58_7 = all_52_13
% 199.16/32.80    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.80    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.80    (68)   ~ (all_52_5 = all_52_7)
% 199.16/32.80    (69)  all_58_12 = all_52_7
% 199.16/32.80    (70)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.80    (71)   ~ (all_52_7 = all_14_2)
% 199.16/32.80    (72)  all_52_18 = all_6_2
% 199.16/32.80    (73)  all_58_2 = all_52_3
% 199.16/32.80    (74)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.80    (75)  all_56_2 = all_52_17
% 199.16/32.80    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.80    (77)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.80    (78)  all_56_7 = all_52_27
% 199.16/32.80    (79)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.80    (80)   ~ (e2 = e0)
% 199.16/32.80    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.80    (82)   ~ (all_52_23 = e3)
% 199.16/32.80    (83)   ~ (all_52_5 = all_52_29)
% 199.16/32.80    (84)  all_56_6 = all_52_19
% 199.16/32.80    (85)   ~ (all_10_2 = e3)
% 199.16/32.80    (86)   ~ (all_52_19 = all_52_27)
% 199.16/32.80    (87)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.80    (88)   ~ (all_52_13 = all_4_2)
% 199.16/32.80    (89)  op(e3, e1) = all_52_17
% 199.16/32.80    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.80    (91)  op(e0, e3) = all_52_7
% 199.16/32.80    (92)  op(e1, e2) = all_52_13
% 199.16/32.80    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.80    (94)   ~ (all_52_9 = all_52_25)
% 199.16/32.80    (95)  all_58_15 = all_14_2
% 199.16/32.80    (96)   ~ (all_52_19 = all_10_2)
% 199.16/32.80    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.80    (98)  all_58_8 = all_10_2
% 199.16/32.80    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.80    (100)   ~ (all_52_5 = all_10_2)
% 199.16/32.80    (101)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.80    (102)   ~ (all_52_23 = all_14_2)
% 199.16/32.80    (103)  all_56_12 = all_52_7
% 199.16/32.80    (104)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.80    (105)  all_8_2 = all_6_2
% 199.16/32.80    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.80    (107)   ~ (all_52_25 = all_6_2)
% 199.16/32.80    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.80    (109)   ~ (all_52_9 = all_4_2)
% 199.16/32.80    (110)   ~ (all_52_5 = all_6_2)
% 199.16/32.80    (111)   ~ (all_52_9 = all_6_2)
% 199.16/32.80    (112)  op(e3, all_6_1) = e2
% 199.16/32.80    (113)  all_56_0 = all_6_2
% 199.16/32.80    (114)  op(e3, e3) = all_6_2
% 199.16/32.80    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.80    (116)   ~ (all_52_27 = all_14_2)
% 199.16/32.80    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.80    (118)  all_58_5 = e3
% 199.16/32.80    (119)  all_56_14 = all_52_23
% 199.16/32.80    (120)   ~ (all_52_17 = e3)
% 199.16/32.80    (121)  all_56_3 = all_52_25
% 199.16/32.80    (122)   ~ (all_52_3 = all_52_7)
% 199.16/32.80    (123)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.80    (124)  all_58_5 = all_52_19
% 199.16/32.80    (125)   ~ (all_52_15 = all_4_2)
% 199.16/32.80    (126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.80           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.80           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.80           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.80    (127)   ~ (all_52_27 = all_4_2)
% 199.16/32.80    (128)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 199.16/32.80             all_58_13 = e0 | all_58_14 = e0)
% 199.16/32.80    (129)  all_58_6 = all_52_5
% 199.16/32.80    (130)  op(e3, e2) = all_52_9
% 199.16/32.80    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.80    (132)   ~ (all_52_17 = all_6_2)
% 199.16/32.80    (133)   ~ (e1 = e0)
% 199.16/32.80    (134)   ~ (e3 = e2)
% 199.16/32.80    (135)  all_44_1 = all_6_1
% 199.16/32.80    (136)   ~ (all_52_9 = all_52_17)
% 199.16/32.80    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.80    (138)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.80    (139)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.80    (140)  op(e1, e1) = all_10_2
% 199.16/32.80    (141)   ~ (all_52_7 = all_52_23)
% 199.16/32.80    (142)   ~ (all_52_17 = all_52_19)
% 199.16/32.80    (143)  all_58_3 = all_4_2
% 199.16/32.80    (144)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.80    (145)   ~ (all_52_3 = all_4_2)
% 199.16/32.80    (146)   ~ (all_52_19 = all_4_2)
% 199.16/32.80    (147)   ~ (all_52_17 = all_52_23)
% 199.16/32.80    (148)  all_8_1 = all_6_1
% 199.16/32.80    (149)  op(all_6_2, e3) = all_6_1
% 199.16/32.80    (150)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.80    (151)   ~ (all_52_13 = all_52_29)
% 199.16/32.80    (152)  all_58_4 = all_52_17
% 199.16/32.80    (153)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.80  
% 199.16/32.80  Begin of proof
% 199.16/32.80  | 
% 199.16/32.80  | ALPHA: (128) implies:
% 199.16/32.80  |   (154)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.80  |   (155)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.16/32.80  | 
% 199.16/32.80  | REDUCE: (55), (95) imply:
% 199.16/32.80  |   (156)   ~ (all_14_2 = e0)
% 199.16/32.80  | 
% 199.16/32.80  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.16/32.80  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 199.16/32.80  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 199.16/32.80  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.16/32.80  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 199.16/32.80  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 199.16/32.80  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 199.16/32.80  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 199.16/32.80  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 199.16/32.80  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 199.16/32.80  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 199.16/32.80  |            (120), (121), (122), (123), (124), (125), (126), (127), (129),
% 199.16/32.80  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 199.16/32.80  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 199.16/32.80  |            (148), (149), (150), (151), (152), (153), (154), (155), (156) are
% 199.16/32.80  |            inconsistent by sub-proof #66.
% 199.16/32.80  | 
% 199.16/32.80  End of proof
% 199.16/32.80  
% 199.16/32.80  Sub-proof #66 shows that the following formulas are inconsistent:
% 199.16/32.80  ----------------------------------------------------------------
% 199.16/32.80    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.16/32.80    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.80    (3)  op(e3, e3) = all_52_18
% 199.16/32.80    (4)   ~ (all_52_15 = all_52_23)
% 199.16/32.80    (5)   ~ (all_52_25 = all_52_27)
% 199.16/32.80    (6)  all_58_14 = all_52_23
% 199.16/32.80    (7)   ~ (e3 = e1)
% 199.16/32.80    (8)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.80    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.80    (10)  all_58_1 = all_52_9
% 199.16/32.80    (11)   ~ (all_52_9 = all_52_13)
% 199.16/32.80    (12)   ~ (e3 = e0)
% 199.16/32.80    (13)  op(e2, e3) = all_52_3
% 199.16/32.80    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.80    (15)   ~ (all_52_7 = all_52_15)
% 199.16/32.80    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.80    (17)   ~ (all_52_17 = all_52_25)
% 199.16/32.80    (18)   ~ (all_4_2 = e3)
% 199.16/32.80    (19)   ~ (all_52_3 = all_6_2)
% 199.16/32.80    (20)  all_44_2 = all_6_2
% 199.16/32.80    (21)  all_58_0 = all_6_2
% 199.16/32.80    (22)  op(all_14_2, e0) = all_14_1
% 199.16/32.80    (23)  all_56_4 = all_52_3
% 199.16/32.80    (24)   ~ (all_52_17 = all_10_2)
% 199.16/32.80    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.80    (26)  op(e3, e0) = all_52_25
% 199.16/32.80    (27)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.80    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.80    (29)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.80    (30)   ~ (all_52_27 = all_52_29)
% 199.16/32.80    (31)  all_58_13 = all_52_15
% 199.16/32.80    (32)   ~ (all_4_2 = e0)
% 199.16/32.80    (33)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.80    (34)  all_58_9 = all_52_25
% 199.16/32.80    (35)   ~ (all_52_29 = all_14_2)
% 199.16/32.80    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.16/32.80    (37)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.80    (38)  op(e1, e3) = all_52_5
% 199.16/32.80    (39)  op(e2, e2) = all_4_2
% 199.16/32.80    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.80    (41)   ~ (all_52_3 = all_52_5)
% 199.16/32.80    (42)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.80    (43)  op(all_4_2, e2) = e1
% 199.16/32.80    (44)  all_58_11 = all_52_29
% 199.16/32.80    (45)   ~ (all_52_3 = e3)
% 199.16/32.80    (46)  all_56_5 = all_4_2
% 199.16/32.80    (47)   ~ (all_52_25 = all_14_2)
% 199.16/32.80    (48)   ~ (all_52_3 = all_52_27)
% 199.16/32.80    (49)  op(all_10_2, e1) = all_10_1
% 199.16/32.80    (50)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.80    (51)   ~ (all_52_7 = all_6_2)
% 199.16/32.80    (52)  op(e0, e0) = all_14_2
% 199.16/32.80    (53)  all_56_15 = all_14_2
% 199.16/32.80    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.80    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.80    (56)  all_56_11 = all_52_29
% 199.16/32.80    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.80    (58)   ~ (e2 = e1)
% 199.16/32.80    (59)  all_58_10 = all_52_27
% 199.16/32.80    (60)  all_56_8 = all_52_5
% 199.16/32.80    (61)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.80    (62)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.80    (63)   ~ (all_52_25 = all_52_29)
% 199.16/32.80    (64)   ~ (all_52_29 = all_10_2)
% 199.16/32.80    (65)  all_58_7 = all_52_13
% 199.16/32.80    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.80    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.80    (68)   ~ (all_52_5 = all_52_7)
% 199.16/32.80    (69)  all_58_12 = all_52_7
% 199.16/32.80    (70)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.80    (71)   ~ (all_52_7 = all_14_2)
% 199.16/32.80    (72)   ~ (all_14_2 = e0)
% 199.16/32.80    (73)  all_52_18 = all_6_2
% 199.16/32.80    (74)  all_58_2 = all_52_3
% 199.16/32.80    (75)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.80    (76)  all_56_2 = all_52_17
% 199.16/32.80    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.80    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.80    (79)  all_56_7 = all_52_27
% 199.16/32.80    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.80    (81)   ~ (e2 = e0)
% 199.16/32.80    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.80    (83)   ~ (all_52_23 = e3)
% 199.16/32.80    (84)   ~ (all_52_5 = all_52_29)
% 199.16/32.80    (85)  all_56_6 = all_52_19
% 199.16/32.80    (86)   ~ (all_10_2 = e3)
% 199.16/32.80    (87)   ~ (all_52_19 = all_52_27)
% 199.16/32.80    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.80    (89)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.80    (90)   ~ (all_52_13 = all_4_2)
% 199.16/32.80    (91)  op(e3, e1) = all_52_17
% 199.16/32.80    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.80    (93)  op(e0, e3) = all_52_7
% 199.16/32.80    (94)  op(e1, e2) = all_52_13
% 199.16/32.80    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.80    (96)   ~ (all_52_9 = all_52_25)
% 199.16/32.80    (97)  all_58_15 = all_14_2
% 199.16/32.80    (98)   ~ (all_52_19 = all_10_2)
% 199.16/32.80    (99)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.80    (100)  all_58_8 = all_10_2
% 199.16/32.80    (101)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.80    (102)   ~ (all_52_5 = all_10_2)
% 199.16/32.80    (103)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.80    (104)   ~ (all_52_23 = all_14_2)
% 199.16/32.80    (105)  all_56_12 = all_52_7
% 199.16/32.80    (106)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.80    (107)  all_8_2 = all_6_2
% 199.16/32.80    (108)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.80    (109)   ~ (all_52_25 = all_6_2)
% 199.16/32.80    (110)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.80    (111)   ~ (all_52_9 = all_4_2)
% 199.16/32.80    (112)   ~ (all_52_5 = all_6_2)
% 199.16/32.80    (113)   ~ (all_52_9 = all_6_2)
% 199.16/32.80    (114)  op(e3, all_6_1) = e2
% 199.16/32.80    (115)  all_56_0 = all_6_2
% 199.16/32.80    (116)  op(e3, e3) = all_6_2
% 199.16/32.80    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.80    (118)   ~ (all_52_27 = all_14_2)
% 199.16/32.80    (119)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.80    (120)  all_58_5 = e3
% 199.16/32.80    (121)  all_56_14 = all_52_23
% 199.16/32.80    (122)   ~ (all_52_17 = e3)
% 199.16/32.80    (123)  all_56_3 = all_52_25
% 199.16/32.80    (124)   ~ (all_52_3 = all_52_7)
% 199.16/32.80    (125)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.80    (126)  all_58_5 = all_52_19
% 199.16/32.80    (127)   ~ (all_52_15 = all_4_2)
% 199.16/32.80    (128)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.80           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.80           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.80           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.80    (129)   ~ (all_52_27 = all_4_2)
% 199.16/32.80    (130)  all_58_6 = all_52_5
% 199.16/32.80    (131)  op(e3, e2) = all_52_9
% 199.16/32.80    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.80    (133)   ~ (all_52_17 = all_6_2)
% 199.16/32.80    (134)   ~ (e1 = e0)
% 199.16/32.80    (135)   ~ (e3 = e2)
% 199.16/32.80    (136)  all_44_1 = all_6_1
% 199.16/32.80    (137)   ~ (all_52_9 = all_52_17)
% 199.16/32.80    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.80    (139)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.80    (140)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.80    (141)  op(e1, e1) = all_10_2
% 199.16/32.80    (142)   ~ (all_52_7 = all_52_23)
% 199.16/32.80    (143)   ~ (all_52_17 = all_52_19)
% 199.16/32.80    (144)  all_58_3 = all_4_2
% 199.16/32.80    (145)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.80    (146)   ~ (all_52_3 = all_4_2)
% 199.16/32.80    (147)   ~ (all_52_19 = all_4_2)
% 199.16/32.80    (148)   ~ (all_52_17 = all_52_23)
% 199.16/32.80    (149)  all_8_1 = all_6_1
% 199.16/32.80    (150)  op(all_6_2, e3) = all_6_1
% 199.16/32.80    (151)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.16/32.80    (152)   ~ (all_52_13 = all_52_29)
% 199.16/32.80    (153)  all_58_4 = all_52_17
% 199.16/32.80    (154)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.80  
% 199.16/32.80  Begin of proof
% 199.16/32.80  | 
% 199.16/32.80  | BETA: splitting (82) gives:
% 199.16/32.80  | 
% 199.16/32.80  | Case 1:
% 199.16/32.80  | | 
% 199.16/32.80  | |   (155)  all_56_5 = e3
% 199.16/32.80  | | 
% 199.16/32.80  | | REF_CLOSE: (18), (46), (155) are inconsistent by sub-proof #1319.
% 199.16/32.80  | | 
% 199.16/32.80  | Case 2:
% 199.16/32.80  | | 
% 199.16/32.80  | |   (156)   ~ (all_56_5 = e3)
% 199.16/32.80  | |   (157)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.80  | | 
% 199.16/32.80  | | BETA: splitting (128) gives:
% 199.16/32.80  | | 
% 199.16/32.80  | | Case 1:
% 199.16/32.80  | | | 
% 199.16/32.80  | | |   (158)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.80  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 199.16/32.80  | | |            e0)
% 199.16/32.80  | | | 
% 199.16/32.80  | | | BETA: splitting (158) gives:
% 199.16/32.80  | | | 
% 199.16/32.80  | | | Case 1:
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | |   (159)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REF_CLOSE: (8), (9), (16), (21), (27), (39), (50), (52), (54), (69),
% 199.16/32.80  | | | |            (71), (74), (77), (102), (114), (115), (116), (130), (132),
% 199.16/32.80  | | | |            (135), (139), (141), (146), (150), (159) are inconsistent by
% 199.16/32.80  | | | |            sub-proof #501.
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | Case 2:
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | |   (160)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 199.16/32.80  | | | |          e0
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | ALPHA: (160) implies:
% 199.16/32.80  | | | |   (161)  all_52_14 = e0
% 199.16/32.80  | | | |   (162)  all_52_12 = e1
% 199.16/32.80  | | | |   (163)  all_52_8 = e3
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (61), (163) imply:
% 199.16/32.80  | | | |   (164)  op(all_52_9, all_52_9) = e3
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (140), (162) imply:
% 199.16/32.80  | | | |   (165)  op(all_52_13, all_52_13) = e1
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (62), (161) imply:
% 199.16/32.80  | | | |   (166)  op(all_52_15, all_52_15) = e0
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | BETA: splitting (42) gives:
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | Case 1:
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | |   (167)  all_58_2 = e0
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | | COMBINE_EQS: (74), (167) imply:
% 199.16/32.80  | | | | |   (168)  all_52_3 = e0
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | | SIMP: (168) implies:
% 199.16/32.80  | | | | |   (169)  all_52_3 = e0
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | | REDUCE: (124), (169) imply:
% 199.16/32.80  | | | | |   (170)   ~ (all_52_7 = e0)
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | | SIMP: (170) implies:
% 199.16/32.80  | | | | |   (171)   ~ (all_52_7 = e0)
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | | REF_CLOSE: (2), (3), (6), (9), (10), (14), (15), (16), (18), (20),
% 199.16/32.80  | | | | |            (21), (25), (27), (31), (34), (38), (39), (40), (47), (51),
% 199.16/32.80  | | | | |            (53), (60), (65), (68), (69), (71), (83), (90), (93), (95),
% 199.16/32.80  | | | | |            (97), (99), (101), (105), (107), (112), (113), (114),
% 199.16/32.80  | | | | |            (116), (119), (122), (127), (130), (131), (132), (134),
% 199.16/32.80  | | | | |            (135), (136), (144), (149), (150), (153), (164), (165),
% 199.16/32.80  | | | | |            (166), (171) are inconsistent by sub-proof #67.
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | Case 2:
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | |   (172)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | | REF_CLOSE: (7), (9), (12), (32), (39), (43), (46), (58), (59), (67),
% 199.16/32.80  | | | | |            (74), (90), (94), (120), (129), (134), (144), (146), (151),
% 199.16/32.80  | | | | |            (157), (172) are inconsistent by sub-proof #149.
% 199.16/32.80  | | | | | 
% 199.16/32.80  | | | | End of split
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | End of split
% 199.16/32.80  | | | 
% 199.16/32.80  | | Case 2:
% 199.16/32.80  | | | 
% 199.16/32.80  | | |   (173)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 199.16/32.80  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 199.16/32.80  | | |            all_52_30 = e0)
% 199.16/32.80  | | | 
% 199.16/32.80  | | | BETA: splitting (173) gives:
% 199.16/32.80  | | | 
% 199.16/32.80  | | | Case 1:
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | |   (174)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 199.16/32.80  | | | |          e0
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | ALPHA: (174) implies:
% 199.16/32.80  | | | |   (175)  all_52_20 = e1
% 199.16/32.80  | | | |   (176)  all_52_18 = e2
% 199.16/32.80  | | | |   (177)  all_52_16 = e3
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | COMBINE_EQS: (73), (176) imply:
% 199.16/32.80  | | | |   (178)  all_6_2 = e2
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | COMBINE_EQS: (21), (178) imply:
% 199.16/32.80  | | | |   (179)  all_58_0 = e2
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (19), (178) imply:
% 199.16/32.80  | | | |   (180)   ~ (all_52_3 = e2)
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (133), (178) imply:
% 199.16/32.80  | | | |   (181)   ~ (all_52_17 = e2)
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (109), (178) imply:
% 199.16/32.80  | | | |   (182)   ~ (all_52_25 = e2)
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (106), (177) imply:
% 199.16/32.80  | | | |   (183)  op(all_52_17, all_52_17) = e3
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (33), (175) imply:
% 199.16/32.80  | | | |   (184)  op(all_10_2, all_10_2) = e1
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (150), (178) imply:
% 199.16/32.80  | | | |   (185)  op(e2, e3) = all_6_1
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | REDUCE: (116), (178) imply:
% 199.16/32.80  | | | |   (186)  op(e3, e3) = e2
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | GROUND_INST: instantiating (9) with all_52_3, all_6_1, e3, e2,
% 199.16/32.80  | | | |              simplifying with (13), (185) gives:
% 199.16/32.80  | | | |   (187)  all_52_3 = all_6_1
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | BETA: splitting (57) gives:
% 199.16/32.80  | | | | 
% 199.16/32.80  | | | | Case 1:
% 199.16/32.80  | | | | | 
% 199.16/32.81  | | | | |   (188)  all_56_2 = e3
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | REF_CLOSE: (76), (122), (188) are inconsistent by sub-proof #1327.
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | Case 2:
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | |   (189)   ~ (all_56_2 = e3)
% 199.16/32.81  | | | | |   (190)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | BETA: splitting (119) gives:
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | Case 1:
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | |   (191)  all_58_0 = e3
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | REF_CLOSE: (135), (179), (191) are inconsistent by sub-proof #1235.
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | Case 2:
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | |   (192)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | BETA: splitting (101) gives:
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | Case 1:
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | |   (193)  all_56_15 = e3
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | COMBINE_EQS: (53), (193) imply:
% 199.16/32.81  | | | | | | |   (194)  all_14_2 = e3
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | SIMP: (194) implies:
% 199.16/32.81  | | | | | | |   (195)  all_14_2 = e3
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REDUCE: (47), (195) imply:
% 199.16/32.81  | | | | | | |   (196)   ~ (all_52_25 = e3)
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REDUCE: (35), (195) imply:
% 199.16/32.81  | | | | | | |   (197)   ~ (all_52_29 = e3)
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REDUCE: (22), (195) imply:
% 199.16/32.81  | | | | | | |   (198)  op(e3, e0) = all_14_1
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | BETA: splitting (192) gives:
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | Case 1:
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | |   (199)  all_58_1 = e3
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | COMBINE_EQS: (10), (199) imply:
% 199.16/32.81  | | | | | | | |   (200)  all_52_9 = e3
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | REDUCE: (11), (200) imply:
% 199.16/32.81  | | | | | | | |   (201)   ~ (all_52_13 = e3)
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | SIMP: (201) implies:
% 199.16/32.81  | | | | | | | |   (202)   ~ (all_52_13 = e3)
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | REDUCE: (61), (200) imply:
% 199.16/32.81  | | | | | | | |   (203)  op(e3, e3) = all_52_8
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | BETA: splitting (70) gives:
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | Case 1:
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | | GROUND_INST: instantiating (9) with all_52_25, all_14_1, e0,
% 199.16/32.81  | | | | | | | | |              e3, simplifying with (26), (198) gives:
% 199.16/32.81  | | | | | | | | |   (204)  all_52_25 = all_14_1
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | | REDUCE: (182), (204) imply:
% 199.16/32.81  | | | | | | | | |   (205)   ~ (all_14_1 = e2)
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | | REF_CLOSE: (9), (13), (23), (40), (45), (67), (74), (80),
% 199.16/32.81  | | | | | | | | |            (81), (91), (114), (179), (180), (181), (185),
% 199.16/32.81  | | | | | | | | |            (198), (205) are inconsistent by sub-proof #450.
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | Case 2:
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | |   (206)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | | REF_CLOSE: (9), (44), (58), (65), (100), (184), (186), (197),
% 199.16/32.81  | | | | | | | | |            (202), (203), (206) are inconsistent by sub-proof
% 199.16/32.81  | | | | | | | | |            #830.
% 199.16/32.81  | | | | | | | | | 
% 199.16/32.81  | | | | | | | | End of split
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | Case 2:
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | |   (207)  all_58_4 = e3 | all_58_9 = e3
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | | REF_CLOSE: (34), (122), (153), (196), (207) are inconsistent by
% 199.16/32.81  | | | | | | | |            sub-proof #1276.
% 199.16/32.81  | | | | | | | | 
% 199.16/32.81  | | | | | | | End of split
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | Case 2:
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | |   (208)   ~ (all_56_15 = e3)
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REDUCE: (53), (208) imply:
% 199.16/32.81  | | | | | | |   (209)   ~ (all_14_2 = e3)
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REF_CLOSE: (9), (36), (52), (76), (86), (141), (153), (181),
% 199.16/32.81  | | | | | | |            (183), (190), (209) are inconsistent by sub-proof
% 199.16/32.81  | | | | | | |            #1058.
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | End of split
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | End of split
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | End of split
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | Case 2:
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | |   (210)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 199.16/32.81  | | | |          e0
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 199.16/32.81  | | | |            (14), (16), (17), (19), (20), (21), (22), (24), (25), (26),
% 199.16/32.81  | | | |            (27), (28), (29), (30), (31), (34), (35), (37), (38), (39),
% 199.16/32.81  | | | |            (40), (41), (44), (46), (47), (48), (49), (50), (51), (52),
% 199.16/32.81  | | | |            (53), (54), (55), (56), (57), (59), (60), (61), (63), (64),
% 199.16/32.81  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (74), (75),
% 199.16/32.81  | | | |            (76), (77), (78), (79), (81), (82), (84), (85), (87), (88),
% 199.16/32.81  | | | |            (89), (91), (92), (93), (95), (96), (97), (98), (99), (100),
% 199.16/32.81  | | | |            (101), (102), (103), (104), (105), (106), (107), (108),
% 199.16/32.81  | | | |            (109), (110), (111), (112), (114), (115), (116), (117),
% 199.16/32.81  | | | |            (118), (119), (121), (123), (124), (125), (126), (127),
% 199.16/32.81  | | | |            (129), (130), (131), (132), (133), (134), (135), (136),
% 199.16/32.81  | | | |            (137), (138), (139), (140), (141), (142), (143), (144),
% 199.16/32.81  | | | |            (145), (146), (147), (148), (149), (150), (152), (153),
% 199.16/32.81  | | | |            (154), (210) are inconsistent by sub-proof #434.
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | End of split
% 199.16/32.81  | | | 
% 199.16/32.81  | | End of split
% 199.16/32.81  | | 
% 199.16/32.81  | End of split
% 199.16/32.81  | 
% 199.16/32.81  End of proof
% 199.16/32.81  
% 199.16/32.81  Sub-proof #67 shows that the following formulas are inconsistent:
% 199.16/32.81  ----------------------------------------------------------------
% 199.16/32.81    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.81    (2)  op(e3, e3) = all_52_18
% 199.16/32.81    (3)  all_58_14 = all_52_23
% 199.16/32.81    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.81    (5)  all_58_1 = all_52_9
% 199.16/32.81    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.81    (7)   ~ (all_52_7 = all_52_15)
% 199.16/32.81    (8)  op(all_52_15, all_52_15) = e0
% 199.16/32.81    (9)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.81    (10)   ~ (all_4_2 = e3)
% 199.16/32.81    (11)  all_44_2 = all_6_2
% 199.16/32.81    (12)  all_58_0 = all_6_2
% 199.16/32.81    (13)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.81    (14)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.81    (15)  all_58_13 = all_52_15
% 199.16/32.81    (16)  op(all_52_13, all_52_13) = e1
% 199.16/32.81    (17)  all_58_9 = all_52_25
% 199.16/32.81    (18)  op(e1, e3) = all_52_5
% 199.16/32.81    (19)  op(e2, e2) = all_4_2
% 199.16/32.81    (20)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.81    (21)   ~ (all_52_25 = all_14_2)
% 199.16/32.81    (22)   ~ (all_52_7 = all_6_2)
% 199.16/32.81    (23)  all_56_15 = all_14_2
% 199.16/32.81    (24)  all_56_8 = all_52_5
% 199.16/32.81    (25)  all_58_7 = all_52_13
% 199.16/32.81    (26)   ~ (all_52_5 = all_52_7)
% 199.16/32.81    (27)  all_58_12 = all_52_7
% 199.16/32.81    (28)   ~ (all_52_7 = all_14_2)
% 199.16/32.81    (29)   ~ (all_52_23 = e3)
% 199.16/32.81    (30)   ~ (all_52_13 = all_4_2)
% 199.16/32.81    (31)  op(e0, e3) = all_52_7
% 199.16/32.81    (32)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.81    (33)  all_58_15 = all_14_2
% 199.16/32.81    (34)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.81    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.81    (36)  all_56_12 = all_52_7
% 199.16/32.81    (37)  all_8_2 = all_6_2
% 199.16/32.81    (38)   ~ (all_52_5 = all_6_2)
% 199.16/32.81    (39)   ~ (all_52_9 = all_6_2)
% 199.16/32.81    (40)  op(e3, all_6_1) = e2
% 199.16/32.81    (41)  op(e3, e3) = all_6_2
% 199.16/32.81    (42)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.81    (43)   ~ (all_52_17 = e3)
% 199.16/32.81    (44)   ~ (all_52_15 = all_4_2)
% 199.16/32.81    (45)  all_58_6 = all_52_5
% 199.16/32.81    (46)  op(e3, e2) = all_52_9
% 199.16/32.81    (47)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.81    (48)   ~ (e1 = e0)
% 199.16/32.81    (49)   ~ (e3 = e2)
% 199.16/32.81    (50)  all_44_1 = all_6_1
% 199.16/32.81    (51)  op(all_52_9, all_52_9) = e3
% 199.16/32.81    (52)  all_58_3 = all_4_2
% 199.16/32.81    (53)  all_8_1 = all_6_1
% 199.16/32.81    (54)  op(all_6_2, e3) = all_6_1
% 199.16/32.81    (55)  all_58_4 = all_52_17
% 199.16/32.81    (56)   ~ (all_52_7 = e0)
% 199.16/32.81  
% 199.16/32.81  Begin of proof
% 199.16/32.81  | 
% 199.16/32.81  | BETA: splitting (35) gives:
% 199.16/32.81  | 
% 199.16/32.81  | Case 1:
% 199.16/32.81  | | 
% 199.16/32.81  | |   (57)  all_56_15 = e3
% 199.16/32.81  | | 
% 199.16/32.81  | | COMBINE_EQS: (23), (57) imply:
% 199.16/32.81  | |   (58)  all_14_2 = e3
% 199.16/32.81  | | 
% 199.16/32.81  | | SIMP: (58) implies:
% 199.16/32.81  | |   (59)  all_14_2 = e3
% 199.16/32.81  | | 
% 199.16/32.81  | | REDUCE: (21), (59) imply:
% 199.16/32.81  | |   (60)   ~ (all_52_25 = e3)
% 199.16/32.81  | | 
% 199.16/32.81  | | REF_CLOSE: (4), (5), (12), (17), (39), (40), (41), (42), (43), (49), (51),
% 199.16/32.81  | |            (54), (55), (60) are inconsistent by sub-proof #492.
% 199.16/32.81  | | 
% 199.16/32.81  | Case 2:
% 199.16/32.81  | | 
% 199.16/32.81  | |   (61)   ~ (all_56_15 = e3)
% 199.16/32.81  | |   (62)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.81  | | 
% 199.16/32.81  | | REDUCE: (23), (61) imply:
% 199.16/32.81  | |   (63)   ~ (all_14_2 = e3)
% 199.16/32.81  | | 
% 199.16/32.81  | | BETA: splitting (47) gives:
% 199.16/32.81  | | 
% 199.16/32.81  | | Case 1:
% 199.16/32.81  | | | 
% 199.16/32.81  | | |   (64)  all_58_12 = e3
% 199.16/32.81  | | | 
% 199.16/32.81  | | | COMBINE_EQS: (27), (64) imply:
% 199.16/32.81  | | |   (65)  all_52_7 = e3
% 199.16/32.81  | | | 
% 199.16/32.81  | | | SIMP: (65) implies:
% 199.16/32.81  | | |   (66)  all_52_7 = e3
% 199.16/32.81  | | | 
% 199.16/32.81  | | | REDUCE: (26), (66) imply:
% 199.16/32.81  | | |   (67)   ~ (all_52_5 = e3)
% 199.16/32.81  | | | 
% 199.16/32.81  | | | REDUCE: (7), (66) imply:
% 199.16/32.81  | | |   (68)   ~ (all_52_15 = e3)
% 199.16/32.81  | | | 
% 199.16/32.81  | | | SIMP: (68) implies:
% 199.16/32.81  | | |   (69)   ~ (all_52_15 = e3)
% 199.16/32.81  | | | 
% 199.16/32.81  | | | REDUCE: (56), (66) imply:
% 199.16/32.81  | | |   (70)   ~ (e3 = e0)
% 199.16/32.81  | | | 
% 199.16/32.81  | | | REDUCE: (9), (66) imply:
% 199.16/32.81  | | |   (71)  op(e3, e3) = all_52_6
% 199.16/32.81  | | | 
% 199.16/32.81  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 199.16/32.81  | | |              with (41), (71) gives:
% 199.16/32.81  | | |   (72)  all_52_6 = all_6_2
% 199.16/32.81  | | | 
% 199.16/32.81  | | | BETA: splitting (34) gives:
% 199.16/32.81  | | | 
% 199.16/32.81  | | | Case 1:
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | |   (73)  all_56_8 = e3
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | | REF_CLOSE: (24), (67), (73) are inconsistent by sub-proof #1325.
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | Case 2:
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | |   (74)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | | BETA: splitting (32) gives:
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | | Case 1:
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | |   (75)  all_58_1 = e3
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | COMBINE_EQS: (5), (75) imply:
% 199.16/32.81  | | | | |   (76)  all_52_9 = e3
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | REF_CLOSE: (4), (39), (41), (51), (76) are inconsistent by sub-proof
% 199.16/32.81  | | | | |            #1337.
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | Case 2:
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | |   (77)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | BETA: splitting (77) gives:
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | | Case 1:
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | |   (78)  all_58_3 = e3
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | COMBINE_EQS: (52), (78) imply:
% 199.16/32.81  | | | | | |   (79)  all_4_2 = e3
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | REDUCE: (10), (79) imply:
% 199.16/32.81  | | | | | |   (80)  $false
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | CLOSE: (80) is inconsistent.
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | Case 2:
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | |   (81)  all_58_7 = e3 | all_58_13 = e3
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | BETA: splitting (81) gives:
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | | Case 1:
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | |   (82)  all_58_7 = e3
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | COMBINE_EQS: (25), (82) imply:
% 199.16/32.81  | | | | | | |   (83)  all_52_13 = e3
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REDUCE: (30), (83) imply:
% 199.16/32.81  | | | | | | |   (84)   ~ (all_4_2 = e3)
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REDUCE: (16), (83) imply:
% 199.16/32.81  | | | | | | |   (85)  op(e3, e3) = e1
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REF_CLOSE: (2), (4), (10), (11), (12), (13), (14), (18), (19),
% 199.16/32.81  | | | | | | |            (20), (24), (38), (40), (41), (45), (46), (48), (50),
% 199.16/32.81  | | | | | | |            (51), (54), (64), (70), (74), (85) are inconsistent by
% 199.16/32.81  | | | | | | |            sub-proof #347.
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | Case 2:
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | |   (86)  all_58_13 = e3
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | | REF_CLOSE: (15), (69), (86) are inconsistent by sub-proof #1360.
% 199.16/32.81  | | | | | | | 
% 199.16/32.81  | | | | | | End of split
% 199.16/32.81  | | | | | | 
% 199.16/32.81  | | | | | End of split
% 199.16/32.81  | | | | | 
% 199.16/32.81  | | | | End of split
% 199.16/32.81  | | | | 
% 199.16/32.81  | | | End of split
% 199.16/32.81  | | | 
% 199.16/32.81  | | Case 2:
% 199.16/32.81  | | | 
% 199.16/32.81  | | |   (87)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.81  | | | 
% 199.16/32.81  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (15), (19), (22), (23),
% 199.16/32.81  | | |            (28), (29), (31), (33), (36), (37), (40), (41), (44), (46),
% 199.16/32.81  | | |            (51), (53), (54), (62), (63), (87) are inconsistent by
% 199.16/32.81  | | |            sub-proof #88.
% 199.16/32.81  | | | 
% 199.16/32.81  | | End of split
% 199.16/32.81  | | 
% 199.16/32.81  | End of split
% 199.16/32.81  | 
% 199.16/32.81  End of proof
% 199.16/32.81  
% 199.16/32.81  Sub-proof #68 shows that the following formulas are inconsistent:
% 199.16/32.81  ----------------------------------------------------------------
% 199.16/32.81    (1)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.16/32.81    (2)  all_52_2 = e0
% 199.16/32.81    (3)   ~ (e2 = e0)
% 199.16/32.81  
% 199.16/32.81  Begin of proof
% 199.16/32.81  | 
% 199.16/32.81  | ALPHA: (1) implies:
% 199.16/32.81  |   (4)  all_52_2 = e2
% 199.16/32.81  | 
% 199.16/32.81  | COMBINE_EQS: (2), (4) imply:
% 199.16/32.81  |   (5)  e2 = e0
% 199.16/32.81  | 
% 199.16/32.81  | SIMP: (5) implies:
% 199.16/32.81  |   (6)  e2 = e0
% 199.16/32.81  | 
% 199.16/32.81  | REDUCE: (3), (6) imply:
% 199.16/32.81  |   (7)  $false
% 199.16/32.81  | 
% 199.16/32.81  | CLOSE: (7) is inconsistent.
% 199.16/32.81  | 
% 199.16/32.81  End of proof
% 199.16/32.81  
% 199.16/32.81  Sub-proof #69 shows that the following formulas are inconsistent:
% 199.16/32.81  ----------------------------------------------------------------
% 199.16/32.81    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.81    (2)   ~ (all_52_15 = all_52_23)
% 199.16/32.81    (3)   ~ (all_52_25 = all_52_27)
% 199.16/32.81    (4)  all_58_14 = all_52_23
% 199.16/32.81    (5)   ~ (e3 = e1)
% 199.16/32.81    (6)   ~ (all_52_17 = all_4_0)
% 199.16/32.81    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.81    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.81    (9)   ~ (all_52_7 = all_10_0)
% 199.16/32.81    (10)   ~ (all_52_5 = all_52_13)
% 199.16/32.81    (11)  all_58_1 = all_52_9
% 199.16/32.81    (12)   ~ (all_52_9 = all_52_13)
% 199.16/32.81    (13)   ~ (e3 = e0)
% 199.16/32.81    (14)  op(e2, e3) = all_52_3
% 199.16/32.81    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.81    (16)   ~ (all_52_7 = all_52_15)
% 199.16/32.81    (17)   ~ (all_52_3 = all_52_19)
% 199.16/32.81    (18)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.81    (19)   ~ (all_52_17 = all_52_25)
% 199.16/32.81    (20)   ~ (all_52_3 = all_6_2)
% 199.16/32.81    (21)  all_44_2 = all_6_2
% 199.16/32.81    (22)  all_58_0 = all_6_2
% 199.16/32.81    (23)  op(all_14_2, e0) = all_14_1
% 199.16/32.81    (24)  all_56_4 = all_52_3
% 199.16/32.81    (25)   ~ (all_52_17 = all_10_2)
% 199.16/32.81    (26)   ~ (all_10_0 = e3)
% 199.16/32.81    (27)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.81    (28)  op(e3, e0) = all_52_25
% 199.16/32.81    (29)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.81    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.81    (31)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.81    (32)   ~ (all_52_27 = all_52_29)
% 199.16/32.81    (33)  all_58_13 = all_52_15
% 199.16/32.81    (34)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.81    (35)  all_58_9 = all_52_25
% 199.16/32.81    (36)   ~ (all_52_29 = all_14_2)
% 199.16/32.81    (37)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.81    (38)  op(e1, e3) = all_52_5
% 199.16/32.81    (39)  op(e2, e2) = all_4_2
% 199.16/32.81    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.81    (41)   ~ (all_52_3 = all_52_5)
% 199.16/32.81    (42)  op(all_4_2, e2) = e1
% 199.16/32.81    (43)  all_58_11 = all_52_29
% 199.16/32.81    (44)  all_56_5 = all_4_2
% 199.16/32.81    (45)   ~ (all_52_25 = all_14_2)
% 199.16/32.81    (46)   ~ (all_52_9 = all_52_15)
% 199.16/32.81    (47)   ~ (all_52_3 = all_52_27)
% 199.16/32.81    (48)  op(all_10_2, e1) = all_10_1
% 199.16/32.81    (49)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.81    (50)   ~ (all_52_7 = all_6_2)
% 199.16/32.81    (51)  op(e0, e0) = all_14_2
% 199.16/32.81    (52)   ~ (all_10_0 = all_6_2)
% 199.16/32.81    (53)  all_56_15 = all_14_2
% 199.16/32.81    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.81    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.81    (56)   ~ (all_58_15 = e0)
% 199.16/32.81    (57)  all_56_11 = all_52_29
% 199.16/32.81    (58)   ~ (all_10_0 = e2)
% 199.16/32.81    (59)   ~ (all_4_0 = e3)
% 199.16/32.81    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.16/32.81    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.81    (62)  all_56_9 = all_52_13
% 199.16/32.81    (63)   ~ (all_52_13 = all_10_2)
% 199.16/32.81    (64)  all_58_10 = all_52_27
% 199.16/32.81    (65)   ~ (all_52_3 = all_10_0)
% 199.16/32.81    (66)  all_56_8 = all_52_5
% 199.16/32.81    (67)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.81    (68)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.81    (69)   ~ (all_52_25 = all_52_29)
% 199.16/32.81    (70)   ~ (all_52_29 = all_10_2)
% 199.16/32.81    (71)  op(all_10_2, e1) = e3
% 199.16/32.81    (72)  all_58_7 = all_52_13
% 199.16/32.81    (73)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 199.16/32.81    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.81    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.81    (76)   ~ (all_52_5 = all_52_7)
% 199.16/32.81    (77)  all_58_12 = all_52_7
% 199.16/32.81    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.81    (79)   ~ (all_52_7 = all_14_2)
% 199.16/32.81    (80)  all_30_2 = all_10_2
% 199.16/32.81    (81)  all_58_2 = all_52_3
% 199.16/32.81    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.81    (83)  all_56_2 = all_52_17
% 199.16/32.81    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.81    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.81    (86)  all_56_7 = all_52_27
% 199.16/32.81    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.81    (88)   ~ (e2 = e0)
% 199.16/32.81    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.81    (90)   ~ (all_52_5 = all_52_29)
% 199.16/32.81    (91)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.16/32.81    (92)  all_56_6 = all_52_19
% 199.16/32.81    (93)  all_56_8 = all_10_0
% 199.16/32.81    (94)   ~ (all_52_15 = all_14_2)
% 199.16/32.81    (95)   ~ (all_52_19 = all_52_27)
% 199.16/32.81    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.81    (97)   ~ (all_52_13 = all_4_2)
% 199.16/32.81    (98)  op(e3, e1) = all_52_17
% 199.16/32.81    (99)  all_30_0 = all_10_0
% 199.16/32.81    (100)  all_58_6 = all_10_0
% 199.16/32.81    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.81    (102)  op(e0, e3) = all_52_7
% 199.16/32.81    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.81    (104)   ~ (all_52_9 = all_52_25)
% 199.16/32.81    (105)  all_58_15 = all_14_2
% 199.16/32.81    (106)   ~ (all_52_19 = all_10_2)
% 199.16/32.81    (107)  op(all_52_23, all_52_23) = all_52_22
% 199.16/32.81    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.81    (109)   ~ (all_10_0 = all_10_2)
% 199.16/32.81    (110)  all_58_8 = all_10_2
% 199.16/32.81    (111)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.81    (112)   ~ (all_52_5 = all_10_2)
% 199.16/32.81    (113)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.81    (114)   ~ (all_52_23 = all_14_2)
% 199.16/32.81    (115)  all_56_12 = all_52_7
% 199.16/32.81    (116)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.81    (117)  all_58_5 = all_4_0
% 199.16/32.81    (118)  all_8_2 = all_6_2
% 199.16/32.81    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.81    (120)   ~ (all_52_25 = all_6_2)
% 199.16/32.81    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.81    (122)   ~ (all_52_9 = all_4_2)
% 199.16/32.81    (123)   ~ (all_52_5 = all_6_2)
% 199.16/32.81    (124)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.16/32.81    (125)   ~ (all_52_9 = all_6_2)
% 199.16/32.81    (126)  op(e3, all_6_1) = e2
% 199.16/32.81    (127)  all_56_0 = all_6_2
% 199.16/32.81    (128)  op(e3, e3) = all_6_2
% 199.16/32.81    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.81    (130)   ~ (all_52_27 = all_14_2)
% 199.16/32.81    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.81    (132)  all_56_14 = all_52_23
% 199.16/32.81    (133)  op(all_4_2, all_4_2) = all_52_10
% 199.16/32.81    (134)  all_56_3 = all_52_25
% 199.16/32.81    (135)   ~ (all_52_3 = all_52_7)
% 199.16/32.81    (136)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.81    (137)  all_58_5 = all_52_19
% 199.16/32.81    (138)  op(all_10_0, all_10_0) = all_52_4
% 199.16/32.81    (139)   ~ (all_52_15 = all_4_2)
% 199.16/32.81    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.81           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.81           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.81           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.81    (141)   ~ (all_52_27 = all_4_2)
% 199.16/32.81    (142)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 199.16/32.81             all_58_13 = e0 | all_58_14 = e0)
% 199.16/32.81    (143)  all_58_6 = all_52_5
% 199.16/32.81    (144)  op(e3, e2) = all_52_9
% 199.16/32.81    (145)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.81    (146)   ~ (all_52_17 = all_6_2)
% 199.16/32.81    (147)   ~ (e1 = e0)
% 199.16/32.81    (148)   ~ (e3 = e2)
% 199.16/32.81    (149)  all_44_1 = all_6_1
% 199.16/32.81    (150)   ~ (all_52_9 = all_52_17)
% 199.16/32.81    (151)  all_56_10 = all_10_2
% 199.16/32.81    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.81    (153)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.16/32.81    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.81    (155)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.81    (156)  op(e1, e1) = all_10_2
% 199.16/32.81    (157)   ~ (all_52_23 = all_10_2)
% 199.16/32.81    (158)   ~ (all_52_7 = all_52_23)
% 199.16/32.81    (159)   ~ (all_52_17 = all_52_19)
% 199.16/32.81    (160)  all_58_3 = all_4_2
% 199.16/32.81    (161)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.81    (162)  all_56_13 = all_52_15
% 199.16/32.81    (163)   ~ (all_52_3 = all_4_2)
% 199.16/32.81    (164)   ~ (all_52_19 = all_4_2)
% 199.16/32.81    (165)   ~ (all_52_17 = all_52_23)
% 199.16/32.81    (166)  all_8_1 = all_6_1
% 199.16/32.81    (167)  op(all_6_2, e3) = all_6_1
% 199.16/32.81    (168)   ~ (all_52_13 = all_52_29)
% 199.16/32.81    (169)  all_58_4 = all_52_17
% 199.16/32.81    (170)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 199.16/32.81    (171)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.81  
% 199.16/32.81  Begin of proof
% 199.16/32.81  | 
% 199.16/32.81  | ALPHA: (142) implies:
% 199.16/32.81  |   (172)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.81  |   (173)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.16/32.81  | 
% 199.16/32.81  | REDUCE: (56), (105) imply:
% 199.16/32.81  |   (174)   ~ (all_14_2 = e0)
% 199.16/32.81  | 
% 199.16/32.81  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.16/32.81  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 199.16/32.81  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 199.16/32.81  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.16/32.81  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (57),
% 199.16/32.81  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 199.16/32.81  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 199.16/32.81  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 199.16/32.81  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 199.16/32.81  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 199.16/32.81  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 199.16/32.81  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 199.16/32.81  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 199.16/32.81  |            (138), (139), (140), (141), (143), (144), (145), (146), (147),
% 199.16/32.81  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 199.16/32.81  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 199.16/32.81  |            (166), (167), (168), (169), (170), (171), (172), (173), (174) are
% 199.16/32.81  |            inconsistent by sub-proof #70.
% 199.16/32.81  | 
% 199.16/32.81  End of proof
% 199.16/32.81  
% 199.16/32.81  Sub-proof #70 shows that the following formulas are inconsistent:
% 199.16/32.81  ----------------------------------------------------------------
% 199.16/32.81    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.16/32.81    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.81    (3)   ~ (all_52_15 = all_52_23)
% 199.16/32.81    (4)   ~ (all_52_25 = all_52_27)
% 199.16/32.81    (5)  all_58_14 = all_52_23
% 199.16/32.81    (6)   ~ (e3 = e1)
% 199.16/32.81    (7)   ~ (all_52_17 = all_4_0)
% 199.16/32.82    (8)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.82    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.82    (10)   ~ (all_52_7 = all_10_0)
% 199.16/32.82    (11)   ~ (all_52_5 = all_52_13)
% 199.16/32.82    (12)  all_58_1 = all_52_9
% 199.16/32.82    (13)   ~ (all_52_9 = all_52_13)
% 199.16/32.82    (14)   ~ (e3 = e0)
% 199.16/32.82    (15)  op(e2, e3) = all_52_3
% 199.16/32.82    (16)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.82    (17)   ~ (all_52_7 = all_52_15)
% 199.16/32.82    (18)   ~ (all_52_3 = all_52_19)
% 199.16/32.82    (19)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.82    (20)   ~ (all_52_17 = all_52_25)
% 199.16/32.82    (21)   ~ (all_52_3 = all_6_2)
% 199.16/32.82    (22)  all_44_2 = all_6_2
% 199.16/32.82    (23)  all_58_0 = all_6_2
% 199.16/32.82    (24)  op(all_14_2, e0) = all_14_1
% 199.16/32.82    (25)  all_56_4 = all_52_3
% 199.16/32.82    (26)   ~ (all_52_17 = all_10_2)
% 199.16/32.82    (27)   ~ (all_10_0 = e3)
% 199.16/32.82    (28)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.82    (29)  op(e3, e0) = all_52_25
% 199.16/32.82    (30)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.82    (31)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.82    (32)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.82    (33)   ~ (all_52_27 = all_52_29)
% 199.16/32.82    (34)  all_58_13 = all_52_15
% 199.16/32.82    (35)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.82    (36)  all_58_9 = all_52_25
% 199.16/32.82    (37)   ~ (all_52_29 = all_14_2)
% 199.16/32.82    (38)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.82    (39)  op(e1, e3) = all_52_5
% 199.16/32.82    (40)  op(e2, e2) = all_4_2
% 199.16/32.82    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.82    (42)   ~ (all_52_3 = all_52_5)
% 199.16/32.82    (43)  op(all_4_2, e2) = e1
% 199.16/32.82    (44)  all_58_11 = all_52_29
% 199.16/32.82    (45)  all_56_5 = all_4_2
% 199.16/32.82    (46)   ~ (all_52_25 = all_14_2)
% 199.16/32.82    (47)   ~ (all_52_9 = all_52_15)
% 199.16/32.82    (48)   ~ (all_52_3 = all_52_27)
% 199.16/32.82    (49)  op(all_10_2, e1) = all_10_1
% 199.16/32.82    (50)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.82    (51)   ~ (all_52_7 = all_6_2)
% 199.16/32.82    (52)  op(e0, e0) = all_14_2
% 199.16/32.82    (53)   ~ (all_10_0 = all_6_2)
% 199.16/32.82    (54)  all_56_15 = all_14_2
% 199.16/32.82    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.82    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.82    (57)  all_56_11 = all_52_29
% 199.16/32.82    (58)   ~ (all_10_0 = e2)
% 199.16/32.82    (59)   ~ (all_4_0 = e3)
% 199.16/32.82    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.16/32.82    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.82    (62)  all_56_9 = all_52_13
% 199.16/32.82    (63)   ~ (all_52_13 = all_10_2)
% 199.16/32.82    (64)  all_58_10 = all_52_27
% 199.16/32.82    (65)   ~ (all_52_3 = all_10_0)
% 199.16/32.82    (66)  all_56_8 = all_52_5
% 199.16/32.82    (67)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.82    (68)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.82    (69)   ~ (all_52_25 = all_52_29)
% 199.16/32.82    (70)   ~ (all_52_29 = all_10_2)
% 199.16/32.82    (71)  op(all_10_2, e1) = e3
% 199.16/32.82    (72)  all_58_7 = all_52_13
% 199.16/32.82    (73)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 199.16/32.82    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.82    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.82    (76)   ~ (all_52_5 = all_52_7)
% 199.16/32.82    (77)  all_58_12 = all_52_7
% 199.16/32.82    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.82    (79)   ~ (all_52_7 = all_14_2)
% 199.16/32.82    (80)   ~ (all_14_2 = e0)
% 199.16/32.82    (81)  all_30_2 = all_10_2
% 199.16/32.82    (82)  all_58_2 = all_52_3
% 199.16/32.82    (83)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.82    (84)  all_56_2 = all_52_17
% 199.16/32.82    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.82    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.82    (87)  all_56_7 = all_52_27
% 199.16/32.82    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.82    (89)   ~ (e2 = e0)
% 199.16/32.82    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.82    (91)   ~ (all_52_5 = all_52_29)
% 199.16/32.82    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.16/32.82    (93)  all_56_6 = all_52_19
% 199.16/32.82    (94)  all_56_8 = all_10_0
% 199.16/32.82    (95)   ~ (all_52_15 = all_14_2)
% 199.16/32.82    (96)   ~ (all_52_19 = all_52_27)
% 199.16/32.82    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.82    (98)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.82    (99)   ~ (all_52_13 = all_4_2)
% 199.16/32.82    (100)  op(e3, e1) = all_52_17
% 199.16/32.82    (101)  all_30_0 = all_10_0
% 199.16/32.82    (102)  all_58_6 = all_10_0
% 199.16/32.82    (103)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.82    (104)  op(e0, e3) = all_52_7
% 199.16/32.82    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.82    (106)   ~ (all_52_9 = all_52_25)
% 199.16/32.82    (107)  all_58_15 = all_14_2
% 199.16/32.82    (108)   ~ (all_52_19 = all_10_2)
% 199.16/32.82    (109)  op(all_52_23, all_52_23) = all_52_22
% 199.16/32.82    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.82    (111)   ~ (all_10_0 = all_10_2)
% 199.16/32.82    (112)  all_58_8 = all_10_2
% 199.16/32.82    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.82    (114)   ~ (all_52_5 = all_10_2)
% 199.16/32.82    (115)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.82    (116)   ~ (all_52_23 = all_14_2)
% 199.16/32.82    (117)  all_56_12 = all_52_7
% 199.16/32.82    (118)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.82    (119)  all_58_5 = all_4_0
% 199.16/32.82    (120)  all_8_2 = all_6_2
% 199.16/32.82    (121)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.82    (122)   ~ (all_52_25 = all_6_2)
% 199.16/32.82    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.82    (124)   ~ (all_52_9 = all_4_2)
% 199.16/32.82    (125)   ~ (all_52_5 = all_6_2)
% 199.16/32.82    (126)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.16/32.82    (127)   ~ (all_52_9 = all_6_2)
% 199.16/32.82    (128)  op(e3, all_6_1) = e2
% 199.16/32.82    (129)  all_56_0 = all_6_2
% 199.16/32.82    (130)  op(e3, e3) = all_6_2
% 199.16/32.82    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.82    (132)   ~ (all_52_27 = all_14_2)
% 199.16/32.82    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.82    (134)  all_56_14 = all_52_23
% 199.16/32.82    (135)  op(all_4_2, all_4_2) = all_52_10
% 199.16/32.82    (136)  all_56_3 = all_52_25
% 199.16/32.82    (137)   ~ (all_52_3 = all_52_7)
% 199.16/32.82    (138)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.82    (139)  all_58_5 = all_52_19
% 199.16/32.82    (140)  op(all_10_0, all_10_0) = all_52_4
% 199.16/32.82    (141)   ~ (all_52_15 = all_4_2)
% 199.16/32.82    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.82           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.82           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.82           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.82    (143)   ~ (all_52_27 = all_4_2)
% 199.16/32.82    (144)  all_58_6 = all_52_5
% 199.16/32.82    (145)  op(e3, e2) = all_52_9
% 199.16/32.82    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.82    (147)   ~ (all_52_17 = all_6_2)
% 199.16/32.82    (148)   ~ (e1 = e0)
% 199.16/32.82    (149)   ~ (e3 = e2)
% 199.16/32.82    (150)  all_44_1 = all_6_1
% 199.16/32.82    (151)   ~ (all_52_9 = all_52_17)
% 199.16/32.82    (152)  all_56_10 = all_10_2
% 199.16/32.82    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.16/32.82    (154)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.16/32.82    (155)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.16/32.82    (156)  op(all_52_13, all_52_13) = all_52_12
% 199.16/32.82    (157)  op(e1, e1) = all_10_2
% 199.16/32.82    (158)   ~ (all_52_23 = all_10_2)
% 199.16/32.82    (159)   ~ (all_52_7 = all_52_23)
% 199.16/32.82    (160)   ~ (all_52_17 = all_52_19)
% 199.16/32.82    (161)  all_58_3 = all_4_2
% 199.16/32.82    (162)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.16/32.82    (163)  all_56_13 = all_52_15
% 199.16/32.82    (164)   ~ (all_52_3 = all_4_2)
% 199.16/32.82    (165)   ~ (all_52_19 = all_4_2)
% 199.16/32.82    (166)   ~ (all_52_17 = all_52_23)
% 199.16/32.82    (167)  all_8_1 = all_6_1
% 199.16/32.82    (168)  op(all_6_2, e3) = all_6_1
% 199.16/32.82    (169)   ~ (all_52_13 = all_52_29)
% 199.16/32.82    (170)  all_58_4 = all_52_17
% 199.16/32.82    (171)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 199.16/32.82    (172)  op(all_52_25, all_52_25) = all_52_24
% 199.16/32.82  
% 199.16/32.82  Begin of proof
% 199.16/32.82  | 
% 199.16/32.82  | BETA: splitting (110) gives:
% 199.16/32.82  | 
% 199.16/32.82  | Case 1:
% 199.16/32.82  | | 
% 199.16/32.82  | |   (173)  all_56_8 = e3
% 199.16/32.82  | | 
% 199.16/32.82  | | REF_CLOSE: (27), (94), (173) are inconsistent by sub-proof #926.
% 199.16/32.82  | | 
% 199.16/32.82  | Case 2:
% 199.16/32.82  | | 
% 199.16/32.82  | |   (174)   ~ (all_56_8 = e3)
% 199.16/32.82  | |   (175)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.82  | | 
% 199.16/32.82  | | BETA: splitting (142) gives:
% 199.16/32.82  | | 
% 199.16/32.82  | | Case 1:
% 199.16/32.82  | | | 
% 199.16/32.82  | | |   (176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.82  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 199.16/32.82  | | |            e0)
% 199.16/32.82  | | | 
% 199.16/32.82  | | | BETA: splitting (176) gives:
% 199.16/32.82  | | | 
% 199.16/32.82  | | | Case 1:
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | |   (177)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REF_CLOSE: (9), (26), (58), (71), (73), (81), (94), (100), (101), (102),
% 199.16/32.82  | | | |            (111), (121), (140), (152), (157), (171), (175), (177) are
% 199.16/32.82  | | | |            inconsistent by sub-proof #667.
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | Case 2:
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | |   (178)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 199.16/32.82  | | | |          e0
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (11), (12), (14), (15), (16),
% 199.16/32.82  | | | |            (17), (19), (20), (21), (22), (23), (24), (25), (26), (28),
% 199.16/32.82  | | | |            (29), (30), (31), (33), (34), (36), (37), (39), (40), (41),
% 199.16/32.82  | | | |            (42), (43), (44), (46), (51), (54), (55), (57), (59), (61),
% 199.16/32.82  | | | |            (62), (64), (66), (67), (68), (70), (72), (75), (76), (77),
% 199.16/32.82  | | | |            (78), (79), (80), (82), (84), (87), (88), (89), (97), (99),
% 199.16/32.82  | | | |            (100), (104), (105), (106), (107), (110), (112), (113),
% 199.16/32.82  | | | |            (117), (118), (119), (120), (122), (124), (125), (126),
% 199.16/32.82  | | | |            (127), (128), (130), (131), (132), (133), (135), (137),
% 199.16/32.82  | | | |            (138), (141), (144), (145), (146), (147), (148), (149),
% 199.16/32.82  | | | |            (150), (151), (153), (154), (156), (157), (161), (164),
% 199.16/32.82  | | | |            (166), (167), (168), (170), (172), (178) are inconsistent by
% 199.16/32.82  | | | |            sub-proof #86.
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | End of split
% 199.16/32.82  | | | 
% 199.16/32.82  | | Case 2:
% 199.16/32.82  | | | 
% 199.16/32.82  | | |   (179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 199.16/32.82  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 199.16/32.82  | | |            all_52_30 = e0)
% 199.16/32.82  | | | 
% 199.16/32.82  | | | BETA: splitting (179) gives:
% 199.16/32.82  | | | 
% 199.16/32.82  | | | Case 1:
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | |   (180)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 199.16/32.82  | | | |          e0
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | ALPHA: (180) implies:
% 199.16/32.82  | | | |   (181)  all_52_22 = e0
% 199.16/32.82  | | | |   (182)  all_52_20 = e1
% 199.16/32.82  | | | |   (183)  all_52_16 = e3
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (118), (183) imply:
% 199.16/32.82  | | | |   (184)  op(all_52_17, all_52_17) = e3
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (109), (181) imply:
% 199.16/32.82  | | | |   (185)  op(all_52_23, all_52_23) = e0
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (35), (182) imply:
% 199.16/32.82  | | | |   (186)  op(all_10_2, all_10_2) = e1
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | BETA: splitting (113) gives:
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | Case 1:
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | |   (187)  all_56_15 = e3
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | COMBINE_EQS: (54), (187) imply:
% 199.16/32.82  | | | | |   (188)  all_14_2 = e3
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | REDUCE: (79), (188) imply:
% 199.16/32.82  | | | | |   (189)   ~ (all_52_7 = e3)
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | REDUCE: (116), (188) imply:
% 199.16/32.82  | | | | |   (190)   ~ (all_52_23 = e3)
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | REDUCE: (46), (188) imply:
% 199.16/32.82  | | | | |   (191)   ~ (all_52_25 = e3)
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | REF_CLOSE: (5), (8), (9), (12), (18), (21), (23), (26), (27), (36),
% 199.16/32.82  | | | | |            (71), (77), (82), (85), (100), (102), (105), (112), (128),
% 199.16/32.82  | | | | |            (130), (133), (139), (147), (149), (151), (153), (168),
% 199.16/32.82  | | | | |            (170), (184), (189), (190), (191) are inconsistent by
% 199.16/32.82  | | | | |            sub-proof #373.
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | Case 2:
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | |   (192)   ~ (all_56_15 = e3)
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | REDUCE: (54), (192) imply:
% 199.16/32.82  | | | | |   (193)   ~ (all_14_2 = e3)
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | BETA: splitting (90) gives:
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | | Case 1:
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | |   (194)  all_56_5 = e3
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | COMBINE_EQS: (45), (194) imply:
% 199.16/32.82  | | | | | |   (195)  all_4_2 = e3
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | SIMP: (195) implies:
% 199.16/32.82  | | | | | |   (196)  all_4_2 = e3
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (124), (196) imply:
% 199.16/32.82  | | | | | |   (197)   ~ (all_52_9 = e3)
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (99), (196) imply:
% 199.16/32.82  | | | | | |   (198)   ~ (all_52_13 = e3)
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (141), (196) imply:
% 199.16/32.82  | | | | | |   (199)   ~ (all_52_15 = e3)
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (135), (196) imply:
% 199.16/32.82  | | | | | |   (200)  op(e3, e3) = all_52_10
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (43), (196) imply:
% 199.16/32.82  | | | | | |   (201)  op(e3, e2) = e1
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (40), (196) imply:
% 199.16/32.82  | | | | | |   (202)  op(e2, e2) = e3
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | BETA: splitting (126) gives:
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | Case 1:
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | |   (203)   ~ (all_4_2 = e3)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REF_CLOSE: (9), (40), (202), (203) are inconsistent by sub-proof
% 199.16/32.82  | | | | | | |            #211.
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | Case 2:
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | GROUND_INST: instantiating (9) with all_52_9, e1, e2, e3,
% 199.16/32.82  | | | | | | |              simplifying with (145), (201) gives:
% 199.16/32.82  | | | | | | |   (204)  all_52_9 = e1
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_10, e3, e3,
% 199.16/32.82  | | | | | | |              simplifying with (130), (200) gives:
% 199.16/32.82  | | | | | | |   (205)  all_52_10 = all_6_2
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REDUCE: (127), (204) imply:
% 199.16/32.82  | | | | | | |   (206)   ~ (all_6_2 = e1)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | SIMP: (206) implies:
% 199.16/32.82  | | | | | | |   (207)   ~ (all_6_2 = e1)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REDUCE: (197), (204) imply:
% 199.16/32.82  | | | | | | |   (208)   ~ (e3 = e1)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REDUCE: (67), (204) imply:
% 199.16/32.82  | | | | | | |   (209)  op(e1, e1) = all_52_8
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | GROUND_INST: instantiating (9) with all_10_2, all_52_8, e1, e1,
% 199.16/32.82  | | | | | | |              simplifying with (157), (209) gives:
% 199.16/32.82  | | | | | | |   (210)  all_52_8 = all_10_2
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | BETA: splitting (146) gives:
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | Case 1:
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | |   (211)  all_58_12 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | COMBINE_EQS: (77), (211) imply:
% 199.16/32.82  | | | | | | | |   (212)  all_52_7 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | SIMP: (212) implies:
% 199.16/32.82  | | | | | | | |   (213)  all_52_7 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | REDUCE: (10), (213) imply:
% 199.16/32.82  | | | | | | | |   (214)   ~ (all_10_0 = e3)
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | REDUCE: (51), (213) imply:
% 199.16/32.82  | | | | | | | |   (215)   ~ (all_6_2 = e3)
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | SIMP: (215) implies:
% 199.16/32.82  | | | | | | | |   (216)   ~ (all_6_2 = e3)
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | REDUCE: (19), (213) imply:
% 199.16/32.82  | | | | | | | |   (217)  op(e3, e3) = all_52_6
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_6, e3, e3,
% 199.16/32.82  | | | | | | | |              simplifying with (130), (217) gives:
% 199.16/32.82  | | | | | | | |   (218)  all_52_6 = all_6_2
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | BETA: splitting (78) gives:
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | Case 1:
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | |   (219)  all_58_6 = e3
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | REF_CLOSE: (27), (102), (219) are inconsistent by sub-proof
% 199.16/32.82  | | | | | | | | |            #922.
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | Case 2:
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | |   (220)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | BETA: splitting (131) gives:
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | Case 1:
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | |   (221)  all_58_9 = e3
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | COMBINE_EQS: (36), (221) imply:
% 199.16/32.82  | | | | | | | | | |   (222)  all_52_25 = e3
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | SIMP: (222) implies:
% 199.16/32.82  | | | | | | | | | |   (223)  all_52_25 = e3
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | REDUCE: (69), (223) imply:
% 199.16/32.82  | | | | | | | | | |   (224)   ~ (all_52_29 = e3)
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | SIMP: (224) implies:
% 199.16/32.82  | | | | | | | | | |   (225)   ~ (all_52_29 = e3)
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | REF_CLOSE: (9), (44), (72), (112), (130), (152), (171),
% 199.16/32.82  | | | | | | | | | |            (186), (198), (207), (217), (220), (225) are
% 199.16/32.82  | | | | | | | | | |            inconsistent by sub-proof #396.
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | Case 2:
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | |   (226)   ~ (all_58_9 = e3)
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | REDUCE: (36), (226) imply:
% 199.16/32.82  | | | | | | | | | |   (227)   ~ (all_52_25 = e3)
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | REF_CLOSE: (9), (12), (23), (36), (130), (133), (147), (170),
% 199.16/32.82  | | | | | | | | | |            (184), (197), (216), (227) are inconsistent by
% 199.16/32.82  | | | | | | | | | |            sub-proof #1071.
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | End of split
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | End of split
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | Case 2:
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | |   (228)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | REF_CLOSE: (2), (5), (6), (9), (14), (16), (17), (34), (51),
% 199.16/32.82  | | | | | | | |            (61), (77), (84), (92), (98), (104), (107), (117),
% 199.16/32.82  | | | | | | | |            (120), (128), (130), (138), (145), (147), (148),
% 199.16/32.82  | | | | | | | |            (151), (157), (158), (159), (166), (167), (168),
% 199.16/32.82  | | | | | | | |            (184), (185), (193), (199), (228) are inconsistent by
% 199.16/32.82  | | | | | | | |            sub-proof #437.
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | End of split
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | End of split
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | Case 2:
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | |   (229)   ~ (all_56_5 = e3)
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | REDUCE: (45), (229) imply:
% 199.16/32.82  | | | | | |   (230)   ~ (all_4_2 = e3)
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | BETA: splitting (55) gives:
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | | Case 1:
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | |   (231)  all_58_2 = e3
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | COMBINE_EQS: (82), (231) imply:
% 199.16/32.82  | | | | | | |   (232)  all_52_3 = e3
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | SIMP: (232) implies:
% 199.16/32.82  | | | | | | |   (233)  all_52_3 = e3
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REDUCE: (137), (233) imply:
% 199.16/32.82  | | | | | | |   (234)   ~ (all_52_7 = e3)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | SIMP: (234) implies:
% 199.16/32.82  | | | | | | |   (235)   ~ (all_52_7 = e3)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REDUCE: (65), (233) imply:
% 199.16/32.82  | | | | | | |   (236)   ~ (all_10_0 = e3)
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | REF_CLOSE: (2), (3), (5), (6), (9), (12), (14), (16), (17), (18),
% 199.16/32.82  | | | | | | |            (20), (23), (26), (27), (34), (36), (46), (47), (51),
% 199.16/32.82  | | | | | | |            (60), (61), (71), (77), (82), (84), (85), (92), (98),
% 199.16/32.82  | | | | | | |            (100), (102), (104), (105), (107), (112), (117), (120),
% 199.16/32.82  | | | | | | |            (128), (130), (131), (133), (137), (138), (139), (145),
% 199.16/32.82  | | | | | | |            (146), (147), (148), (149), (151), (153), (157), (158),
% 199.16/32.82  | | | | | | |            (159), (163), (166), (167), (168), (170), (184), (185),
% 199.16/32.82  | | | | | | |            (193), (235) are inconsistent by sub-proof #370.
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | Case 2:
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | |   (237)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | BETA: splitting (237) gives:
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | | Case 1:
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | |   (238)  all_58_3 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | COMBINE_EQS: (161), (238) imply:
% 199.16/32.82  | | | | | | | |   (239)  all_4_2 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | REDUCE: (230), (239) imply:
% 199.16/32.82  | | | | | | | |   (240)  $false
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | CLOSE: (240) is inconsistent.
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | Case 2:
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | |   (241)  all_58_5 = e3 | all_58_10 = e3
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | BETA: splitting (241) gives:
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | | Case 1:
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | |   (242)  all_58_5 = e3
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | REF_CLOSE: (59), (119), (242) are inconsistent by sub-proof
% 199.16/32.82  | | | | | | | | |            #215.
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | Case 2:
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | |   (243)  all_58_10 = e3
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | COMBINE_EQS: (64), (243) imply:
% 199.16/32.82  | | | | | | | | |   (244)  all_52_27 = e3
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | SIMP: (244) implies:
% 199.16/32.82  | | | | | | | | |   (245)  all_52_27 = e3
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | REDUCE: (48), (245) imply:
% 199.16/32.82  | | | | | | | | |   (246)   ~ (all_52_3 = e3)
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | REDUCE: (4), (245) imply:
% 199.16/32.82  | | | | | | | | |   (247)   ~ (all_52_25 = e3)
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | REDUCE: (33), (245) imply:
% 199.16/32.82  | | | | | | | | |   (248)   ~ (all_52_29 = e3)
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | SIMP: (248) implies:
% 199.16/32.82  | | | | | | | | |   (249)   ~ (all_52_29 = e3)
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | REDUCE: (38), (245) imply:
% 199.16/32.82  | | | | | | | | |   (250)  op(e3, e3) = all_52_26
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_26, e3, e3,
% 199.16/32.82  | | | | | | | | |              simplifying with (130), (250) gives:
% 199.16/32.82  | | | | | | | | |   (251)  all_52_26 = all_6_2
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | BETA: splitting (85) gives:
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | Case 1:
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | |   (252)  all_58_0 = e3
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | COMBINE_EQS: (23), (252) imply:
% 199.16/32.82  | | | | | | | | | |   (253)  all_6_2 = e3
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | REF_CLOSE: (9), (128), (130), (149), (168), (253) are
% 199.16/32.82  | | | | | | | | | |            inconsistent by sub-proof #502.
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | Case 2:
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | |   (254)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | | REF_CLOSE: (9), (10), (12), (13), (19), (23), (26), (27),
% 199.16/32.82  | | | | | | | | | |            (36), (44), (51), (71), (72), (77), (78), (82),
% 199.16/32.82  | | | | | | | | | |            (100), (102), (105), (112), (130), (133), (147),
% 199.16/32.82  | | | | | | | | | |            (170), (184), (246), (247), (249), (254) are
% 199.16/32.82  | | | | | | | | | |            inconsistent by sub-proof #71.
% 199.16/32.82  | | | | | | | | | | 
% 199.16/32.82  | | | | | | | | | End of split
% 199.16/32.82  | | | | | | | | | 
% 199.16/32.82  | | | | | | | | End of split
% 199.16/32.82  | | | | | | | | 
% 199.16/32.82  | | | | | | | End of split
% 199.16/32.82  | | | | | | | 
% 199.16/32.82  | | | | | | End of split
% 199.16/32.82  | | | | | | 
% 199.16/32.82  | | | | | End of split
% 199.16/32.82  | | | | | 
% 199.16/32.82  | | | | End of split
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | Case 2:
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | |   (255)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 199.16/32.82  | | | |          e0
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | ALPHA: (255) implies:
% 199.16/32.82  | | | |   (256)  all_52_30 = e0
% 199.16/32.82  | | | |   (257)  all_52_28 = e1
% 199.16/32.82  | | | |   (258)  all_52_26 = e2
% 199.16/32.82  | | | |   (259)  all_52_24 = e3
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (172), (259) imply:
% 199.16/32.82  | | | |   (260)  op(all_52_25, all_52_25) = e3
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (38), (258) imply:
% 199.16/32.82  | | | |   (261)  op(all_52_27, all_52_27) = e2
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (115), (257) imply:
% 199.16/32.82  | | | |   (262)  op(all_52_29, all_52_29) = e1
% 199.16/32.82  | | | | 
% 199.16/32.82  | | | | REDUCE: (138), (256) imply:
% 199.16/32.82  | | | |   (263)  op(all_14_2, all_14_2) = e0
% 199.16/32.82  | | | | 
% 199.16/32.83  | | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (12), (13), (14), (15),
% 199.16/32.83  | | | |            (16), (19), (20), (21), (22), (23), (24), (26), (27), (28),
% 199.16/32.83  | | | |            (29), (30), (31), (32), (33), (34), (36), (37), (39), (40),
% 199.16/32.83  | | | |            (41), (42), (44), (45), (46), (48), (49), (50), (51), (52),
% 199.16/32.83  | | | |            (53), (54), (55), (56), (57), (58), (61), (63), (64), (66),
% 199.16/32.83  | | | |            (67), (69), (70), (72), (74), (75), (76), (77), (78), (79),
% 199.16/32.83  | | | |            (80), (82), (83), (84), (85), (86), (87), (89), (90), (91),
% 199.16/32.83  | | | |            (93), (94), (95), (96), (97), (98), (100), (102), (103),
% 199.16/32.83  | | | |            (104), (105), (106), (107), (108), (110), (112), (113),
% 199.16/32.83  | | | |            (114), (116), (117), (118), (121), (122), (123), (124),
% 199.16/32.83  | | | |            (125), (128), (129), (130), (131), (132), (133), (134),
% 199.16/32.83  | | | |            (136), (137), (139), (140), (141), (143), (144), (145),
% 199.16/32.83  | | | |            (146), (147), (148), (149), (150), (153), (155), (156),
% 199.16/32.83  | | | |            (157), (159), (160), (161), (162), (164), (165), (166),
% 199.16/32.83  | | | |            (168), (169), (170), (175), (260), (261), (262), (263) are
% 199.16/32.83  | | | |            inconsistent by sub-proof #369.
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | End of split
% 199.16/32.83  | | | 
% 199.16/32.83  | | End of split
% 199.16/32.83  | | 
% 199.16/32.83  | End of split
% 199.16/32.83  | 
% 199.16/32.83  End of proof
% 199.16/32.83  
% 199.16/32.83  Sub-proof #71 shows that the following formulas are inconsistent:
% 199.16/32.83  ----------------------------------------------------------------
% 199.16/32.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.83    (2)   ~ (all_52_7 = all_10_0)
% 199.16/32.83    (3)  all_58_1 = all_52_9
% 199.16/32.83    (4)   ~ (all_52_9 = all_52_13)
% 199.16/32.83    (5)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.83    (6)  all_58_0 = all_6_2
% 199.16/32.83    (7)   ~ (all_52_17 = all_10_2)
% 199.16/32.83    (8)   ~ (all_10_0 = e3)
% 199.16/32.83    (9)  all_58_9 = all_52_25
% 199.16/32.83    (10)  all_58_11 = all_52_29
% 199.16/32.83    (11)   ~ (all_52_3 = e3)
% 199.16/32.83    (12)   ~ (all_52_7 = all_6_2)
% 199.16/32.83    (13)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.83    (14)  op(all_10_2, e1) = e3
% 199.16/32.83    (15)  all_58_7 = all_52_13
% 199.16/32.83    (16)  all_58_12 = all_52_7
% 199.16/32.83    (17)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.83    (18)  all_58_2 = all_52_3
% 199.16/32.83    (19)   ~ (all_52_29 = e3)
% 199.16/32.83    (20)   ~ (all_52_25 = e3)
% 199.16/32.83    (21)  op(e3, e1) = all_52_17
% 199.16/32.83    (22)  all_58_6 = all_10_0
% 199.16/32.83    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.83    (24)  all_58_8 = all_10_2
% 199.16/32.83    (25)  op(e3, e3) = all_6_2
% 199.16/32.83    (26)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.83    (27)  op(all_52_17, all_52_17) = e3
% 199.16/32.83    (28)   ~ (all_52_17 = all_6_2)
% 199.16/32.83    (29)  all_58_4 = all_52_17
% 199.16/32.83  
% 199.16/32.83  Begin of proof
% 199.16/32.83  | 
% 199.16/32.83  | BETA: splitting (13) gives:
% 199.16/32.83  | 
% 199.16/32.83  | Case 1:
% 199.16/32.83  | | 
% 199.16/32.83  | |   (30)  all_58_2 = e3
% 199.16/32.83  | | 
% 199.16/32.83  | | REF_CLOSE: (11), (18), (30) are inconsistent by sub-proof #1369.
% 199.16/32.83  | | 
% 199.16/32.83  | Case 2:
% 199.16/32.83  | | 
% 199.16/32.83  | |   (31)  all_58_6 = e3 | all_58_12 = e3
% 199.16/32.83  | | 
% 199.16/32.83  | | BETA: splitting (31) gives:
% 199.16/32.83  | | 
% 199.16/32.83  | | Case 1:
% 199.16/32.83  | | | 
% 199.16/32.83  | | |   (32)  all_58_6 = e3
% 199.16/32.83  | | | 
% 199.16/32.83  | | | REF_CLOSE: (8), (22), (32) are inconsistent by sub-proof #922.
% 199.16/32.83  | | | 
% 199.16/32.83  | | Case 2:
% 199.16/32.83  | | | 
% 199.16/32.83  | | |   (33)  all_58_12 = e3
% 199.16/32.83  | | | 
% 199.16/32.83  | | | COMBINE_EQS: (16), (33) imply:
% 199.16/32.83  | | |   (34)  all_52_7 = e3
% 199.16/32.83  | | | 
% 199.16/32.83  | | | SIMP: (34) implies:
% 199.16/32.83  | | |   (35)  all_52_7 = e3
% 199.16/32.83  | | | 
% 199.16/32.83  | | | REDUCE: (2), (35) imply:
% 199.16/32.83  | | |   (36)   ~ (all_10_0 = e3)
% 199.16/32.83  | | | 
% 199.16/32.83  | | | REDUCE: (12), (35) imply:
% 199.16/32.83  | | |   (37)   ~ (all_6_2 = e3)
% 199.16/32.83  | | | 
% 199.16/32.83  | | | SIMP: (37) implies:
% 199.16/32.83  | | |   (38)   ~ (all_6_2 = e3)
% 199.16/32.83  | | | 
% 199.16/32.83  | | | REDUCE: (5), (35) imply:
% 199.16/32.83  | | |   (39)  op(e3, e3) = all_52_6
% 199.16/32.83  | | | 
% 199.16/32.83  | | | GROUND_INST: instantiating (1) with all_6_2, all_52_6, e3, e3, simplifying
% 199.16/32.83  | | |              with (25), (39) gives:
% 199.16/32.83  | | |   (40)  all_52_6 = all_6_2
% 199.16/32.83  | | | 
% 199.16/32.83  | | | BETA: splitting (26) gives:
% 199.16/32.83  | | | 
% 199.16/32.83  | | | Case 1:
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | |   (41)  all_58_0 = e3
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | | COMBINE_EQS: (6), (41) imply:
% 199.16/32.83  | | | |   (42)  all_6_2 = e3
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | | REDUCE: (38), (42) imply:
% 199.16/32.83  | | | |   (43)  $false
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | | CLOSE: (43) is inconsistent.
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | Case 2:
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | |   (44)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | | BETA: splitting (17) gives:
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | | Case 1:
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | |   (45)  all_58_6 = e3
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | | REF_CLOSE: (8), (22), (45) are inconsistent by sub-proof #922.
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | Case 2:
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | |   (46)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | | BETA: splitting (23) gives:
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | | Case 1:
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | |   (47)  all_58_1 = e3
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | COMBINE_EQS: (3), (47) imply:
% 199.16/32.83  | | | | | |   (48)  all_52_9 = e3
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | REDUCE: (4), (48) imply:
% 199.16/32.83  | | | | | |   (49)   ~ (all_52_13 = e3)
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | SIMP: (49) implies:
% 199.16/32.83  | | | | | |   (50)   ~ (all_52_13 = e3)
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | BETA: splitting (46) gives:
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | Case 1:
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | |   (51)  all_58_7 = e3
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | | COMBINE_EQS: (15), (51) imply:
% 199.16/32.83  | | | | | | |   (52)  all_52_13 = e3
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | | REDUCE: (50), (52) imply:
% 199.16/32.83  | | | | | | |   (53)  $false
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | | CLOSE: (53) is inconsistent.
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | Case 2:
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | |   (54)  all_58_8 = e3 | all_58_11 = e3
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | | BETA: splitting (54) gives:
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | | Case 1:
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | |   (55)  all_58_8 = e3
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | | COMBINE_EQS: (24), (55) imply:
% 199.16/32.83  | | | | | | | |   (56)  all_10_2 = e3
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | | REF_CLOSE: (1), (7), (14), (21), (56) are inconsistent by
% 199.16/32.83  | | | | | | | |            sub-proof #925.
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | Case 2:
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | |   (57)  all_58_11 = e3
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | | REF_CLOSE: (10), (19), (57) are inconsistent by sub-proof #1323.
% 199.16/32.83  | | | | | | | | 
% 199.16/32.83  | | | | | | | End of split
% 199.16/32.83  | | | | | | | 
% 199.16/32.83  | | | | | | End of split
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | Case 2:
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | |   (58)   ~ (all_58_1 = e3)
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | REDUCE: (3), (58) imply:
% 199.16/32.83  | | | | | |   (59)   ~ (all_52_9 = e3)
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | | REF_CLOSE: (1), (3), (9), (20), (25), (27), (28), (29), (44), (59)
% 199.16/32.83  | | | | | |            are inconsistent by sub-proof #1072.
% 199.16/32.83  | | | | | | 
% 199.16/32.83  | | | | | End of split
% 199.16/32.83  | | | | | 
% 199.16/32.83  | | | | End of split
% 199.16/32.83  | | | | 
% 199.16/32.83  | | | End of split
% 199.16/32.83  | | | 
% 199.16/32.83  | | End of split
% 199.16/32.83  | | 
% 199.16/32.83  | End of split
% 199.16/32.83  | 
% 199.16/32.83  End of proof
% 199.16/32.83  
% 199.16/32.83  Sub-proof #72 shows that the following formulas are inconsistent:
% 199.16/32.83  ----------------------------------------------------------------
% 199.16/32.83    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.16/32.83    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.16/32.83    (3)   ~ (all_52_15 = all_52_23)
% 199.16/32.83    (4)   ~ (all_52_25 = all_52_27)
% 199.16/32.83    (5)  all_58_14 = all_52_23
% 199.16/32.83    (6)   ~ (e3 = e1)
% 199.16/32.83    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.16/32.83    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.16/32.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.16/32.83    (9)  all_58_1 = all_52_9
% 199.16/32.83    (10)   ~ (all_52_9 = all_52_13)
% 199.16/32.83    (11)   ~ (e3 = e0)
% 199.16/32.83    (12)  op(e2, e3) = all_52_3
% 199.16/32.83    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.16/32.83    (14)   ~ (all_52_7 = all_52_15)
% 199.16/32.83    (15)  op(all_52_7, all_52_7) = all_52_6
% 199.16/32.83    (16)   ~ (all_52_17 = all_52_25)
% 199.16/32.83    (17)   ~ (all_52_3 = all_6_2)
% 199.16/32.83    (18)  all_44_2 = all_6_2
% 199.16/32.83    (19)  all_58_0 = all_6_2
% 199.16/32.83    (20)  op(all_14_2, e0) = all_14_1
% 199.16/32.83    (21)  all_56_4 = all_52_3
% 199.16/32.83    (22)   ~ (all_52_17 = all_10_2)
% 199.16/32.83    (23)   ~ (all_10_0 = e3)
% 199.16/32.83    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.16/32.83    (25)  all_40_2 = all_10_2
% 199.16/32.83    (26)  op(e3, e0) = all_52_25
% 199.16/32.83    (27)  op(all_52_5, all_52_5) = all_52_4
% 199.16/32.83    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.16/32.83    (29)  op(all_52_19, all_52_19) = all_52_18
% 199.16/32.83    (30)   ~ (all_52_27 = all_52_29)
% 199.16/32.83    (31)  all_58_13 = all_52_15
% 199.16/32.83    (32)  op(all_10_2, all_10_2) = all_52_20
% 199.16/32.83    (33)  all_58_9 = all_52_25
% 199.16/32.83    (34)   ~ (all_52_29 = all_14_2)
% 199.16/32.83    (35)  op(all_52_27, all_52_27) = all_52_26
% 199.16/32.83    (36)  op(e1, e3) = all_52_5
% 199.16/32.83    (37)  op(e2, e2) = all_4_2
% 199.16/32.83    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.16/32.83    (39)  all_58_7 = all_10_0
% 199.16/32.83    (40)   ~ (all_52_3 = all_52_5)
% 199.16/32.83    (41)  op(all_4_2, e2) = e1
% 199.16/32.83    (42)  all_58_11 = all_52_29
% 199.16/32.83    (43)  all_56_5 = all_4_2
% 199.16/32.83    (44)   ~ (all_52_25 = all_14_2)
% 199.16/32.83    (45)   ~ (all_52_9 = all_52_15)
% 199.16/32.83    (46)   ~ (all_52_3 = all_52_27)
% 199.16/32.83    (47)  op(all_10_2, e1) = all_10_1
% 199.16/32.83    (48)  op(all_6_2, all_6_2) = all_52_0
% 199.16/32.83    (49)   ~ (all_52_7 = all_6_2)
% 199.16/32.83    (50)  op(e0, e0) = all_14_2
% 199.16/32.83    (51)  all_56_15 = all_14_2
% 199.16/32.83    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.16/32.83    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.16/32.83    (54)  all_56_11 = all_52_29
% 199.16/32.83    (55)   ~ (all_10_0 = e2)
% 199.16/32.83    (56)   ~ (all_4_0 = e3)
% 199.16/32.83    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.16/32.83    (58)   ~ (all_52_13 = all_10_2)
% 199.16/32.83    (59)  all_58_10 = all_52_27
% 199.16/32.83    (60)  all_56_8 = all_52_5
% 199.16/32.83    (61)  op(all_52_9, all_52_9) = all_52_8
% 199.16/32.83    (62)  op(all_52_15, all_52_15) = all_52_14
% 199.16/32.83    (63)  all_56_9 = all_10_0
% 199.16/32.83    (64)   ~ (all_52_25 = all_52_29)
% 199.16/32.83    (65)   ~ (all_52_29 = all_10_2)
% 199.16/32.83    (66)  all_58_7 = all_52_13
% 199.16/32.83    (67)   ~ (all_10_0 = all_4_2)
% 199.16/32.83    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.16/32.83    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.16/32.83    (70)   ~ (all_52_5 = all_52_7)
% 199.16/32.83    (71)  all_58_12 = all_52_7
% 199.16/32.83    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.16/32.83    (73)   ~ (all_52_7 = all_14_2)
% 199.16/32.83    (74)   ~ (all_14_2 = e0)
% 199.16/32.83    (75)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 199.16/32.83    (76)  all_58_2 = all_52_3
% 199.16/32.83    (77)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.16/32.83    (78)  all_56_2 = all_52_17
% 199.16/32.83    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.16/32.83    (80)   ~ (all_52_15 = all_10_0)
% 199.16/32.83    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.16/32.83    (82)  all_56_7 = all_52_27
% 199.16/32.83    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.16/32.83    (84)   ~ (e2 = e0)
% 199.16/32.83    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.16/32.83    (86)  op(all_4_2, e2) = all_4_1
% 199.16/32.83    (87)   ~ (all_52_5 = all_52_29)
% 199.16/32.83    (88)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.16/32.83    (89)  all_56_6 = all_52_19
% 199.16/32.83    (90)   ~ (all_52_15 = all_14_2)
% 199.16/32.83    (91)   ~ (all_52_19 = all_52_27)
% 199.16/32.83    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.16/32.83    (93)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.16/32.83    (94)  op(e3, e1) = all_52_17
% 199.16/32.83    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.16/32.83    (96)  op(e0, e3) = all_52_7
% 199.16/32.83    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.16/32.83    (98)   ~ (all_52_9 = all_52_25)
% 199.16/32.83    (99)  all_58_15 = all_14_2
% 199.16/32.83    (100)   ~ (all_52_19 = all_10_2)
% 199.16/32.83    (101)  op(all_52_23, all_52_23) = all_52_22
% 199.16/32.83    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.16/32.83    (103)  all_58_8 = all_10_2
% 199.16/32.83    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.16/32.83    (105)   ~ (all_52_5 = all_10_2)
% 199.16/32.83    (106)  op(all_52_29, all_52_29) = all_52_28
% 199.16/32.83    (107)   ~ (all_52_23 = all_14_2)
% 199.16/32.83    (108)  all_56_12 = all_52_7
% 199.16/32.83    (109)  op(all_52_17, all_52_17) = all_52_16
% 199.16/32.83    (110)  all_58_5 = all_4_0
% 199.16/32.83    (111)  all_8_2 = all_6_2
% 199.16/32.83    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.16/32.83    (113)   ~ (all_52_25 = all_6_2)
% 199.16/32.83    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.16/32.83    (115)   ~ (all_52_9 = all_4_2)
% 199.16/32.83    (116)   ~ (all_52_5 = all_6_2)
% 199.16/32.83    (117)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.16/32.83    (118)   ~ (all_52_9 = all_6_2)
% 199.16/32.83    (119)  op(e3, all_6_1) = e2
% 199.16/32.83    (120)  all_56_0 = all_6_2
% 199.16/32.83    (121)  op(e3, e3) = all_6_2
% 199.16/32.83    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.16/32.83    (123)   ~ (all_52_27 = all_14_2)
% 199.16/32.83    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.16/32.83    (125)  all_56_14 = all_52_23
% 199.16/32.83    (126)  op(all_4_2, all_4_2) = all_52_10
% 199.16/32.83    (127)  all_40_0 = all_10_0
% 199.16/32.83    (128)  all_56_3 = all_52_25
% 199.16/32.83    (129)   ~ (all_52_3 = all_52_7)
% 199.16/32.83    (130)  op(all_14_2, all_14_2) = all_52_30
% 199.16/32.83    (131)  all_58_5 = all_52_19
% 199.16/32.83    (132)  all_56_1 = all_52_9
% 199.16/32.83    (133)   ~ (all_52_15 = all_4_2)
% 199.16/32.83    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.16/32.83           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.16/32.83           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.16/32.83           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.16/32.83    (135)   ~ (all_52_27 = all_4_2)
% 199.16/32.83    (136)  all_58_6 = all_52_5
% 199.16/32.83    (137)  op(all_10_2, e1) = e2
% 199.16/32.83    (138)  op(e3, e2) = all_52_9
% 199.16/32.83    (139)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.16/32.83    (140)   ~ (all_52_17 = all_6_2)
% 199.49/32.83    (141)   ~ (e1 = e0)
% 199.49/32.83    (142)   ~ (e3 = e2)
% 199.49/32.83    (143)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 199.49/32.83    (144)  all_44_1 = all_6_1
% 199.49/32.83    (145)   ~ (all_52_9 = all_52_17)
% 199.49/32.83    (146)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.83    (147)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.83    (148)   ~ (all_52_3 = all_4_0)
% 199.49/32.83    (149)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.49/32.83    (150)  op(all_52_13, all_52_13) = all_52_12
% 199.49/32.83    (151)  op(e1, e1) = all_10_2
% 199.49/32.83    (152)   ~ (all_52_23 = all_10_2)
% 199.49/32.83    (153)   ~ (all_52_7 = all_52_23)
% 199.49/32.83    (154)   ~ (all_52_17 = all_52_19)
% 199.49/32.83    (155)   ~ (all_52_5 = all_10_0)
% 199.49/32.83    (156)  all_58_3 = all_4_2
% 199.49/32.83    (157)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.83    (158)   ~ (all_52_3 = all_4_2)
% 199.49/32.83    (159)   ~ (all_52_9 = all_10_0)
% 199.49/32.83    (160)   ~ (all_52_19 = all_4_2)
% 199.49/32.83    (161)   ~ (all_52_17 = all_52_23)
% 199.49/32.83    (162)  all_8_1 = all_6_1
% 199.49/32.83    (163)  op(all_6_2, e3) = all_6_1
% 199.49/32.83    (164)   ~ (all_52_13 = all_52_29)
% 199.49/32.83    (165)  all_58_4 = all_52_17
% 199.49/32.83    (166)  op(all_52_25, all_52_25) = all_52_24
% 199.49/32.83  
% 199.49/32.83  Begin of proof
% 199.49/32.83  | 
% 199.49/32.83  | BETA: splitting (147) gives:
% 199.49/32.83  | 
% 199.49/32.83  | Case 1:
% 199.49/32.83  | | 
% 199.49/32.83  | |   (167)  all_56_9 = e3
% 199.49/32.83  | | 
% 199.49/32.83  | | REF_CLOSE: (23), (63), (167) are inconsistent by sub-proof #1006.
% 199.49/32.83  | | 
% 199.49/32.83  | Case 2:
% 199.49/32.83  | | 
% 199.49/32.83  | |   (168)   ~ (all_56_9 = e3)
% 199.49/32.83  | |   (169)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.83  | | 
% 199.49/32.83  | | BETA: splitting (134) gives:
% 199.49/32.83  | | 
% 199.49/32.83  | | Case 1:
% 199.49/32.83  | | | 
% 199.49/32.83  | | |   (170)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.49/32.83  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 199.49/32.83  | | |            e0)
% 199.49/32.83  | | | 
% 199.49/32.83  | | | BETA: splitting (170) gives:
% 199.49/32.83  | | | 
% 199.49/32.83  | | | Case 1:
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | |   (171)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REF_CLOSE: (7), (8), (15), (19), (27), (37), (48), (50), (52), (71),
% 199.49/32.83  | | | |            (73), (76), (79), (105), (119), (120), (121), (136), (139),
% 199.49/32.83  | | | |            (142), (149), (151), (158), (163), (171) are inconsistent by
% 199.49/32.83  | | | |            sub-proof #501.
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | Case 2:
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | |   (172)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 199.49/32.83  | | | |          e0
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | ALPHA: (172) implies:
% 199.49/32.83  | | | |   (173)  all_52_14 = e0
% 199.49/32.83  | | | |   (174)  all_52_10 = e2
% 199.49/32.83  | | | |   (175)  all_52_8 = e3
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REDUCE: (61), (175) imply:
% 199.49/32.83  | | | |   (176)  op(all_52_9, all_52_9) = e3
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REDUCE: (62), (173) imply:
% 199.49/32.83  | | | |   (177)  op(all_52_15, all_52_15) = e0
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REDUCE: (126), (174) imply:
% 199.49/32.83  | | | |   (178)  op(all_4_2, all_4_2) = e2
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | BETA: splitting (104) gives:
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | Case 1:
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | |   (179)  all_56_15 = e3
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | COMBINE_EQS: (51), (179) imply:
% 199.49/32.83  | | | | |   (180)  all_14_2 = e3
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | SIMP: (180) implies:
% 199.49/32.83  | | | | |   (181)  all_14_2 = e3
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | REDUCE: (90), (181) imply:
% 199.49/32.83  | | | | |   (182)   ~ (all_52_15 = e3)
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | REDUCE: (130), (181) imply:
% 199.49/32.83  | | | | |   (183)  op(e3, e3) = all_52_30
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | REDUCE: (20), (181) imply:
% 199.49/32.83  | | | | |   (184)  op(e3, e0) = all_14_1
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 199.49/32.83  | | | | |              simplifying with (26), (184) gives:
% 199.49/32.83  | | | | |   (185)  all_52_25 = all_14_1
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | REF_CLOSE: (8), (9), (12), (17), (19), (21), (23), (26), (31), (37),
% 199.49/32.83  | | | | |            (38), (39), (69), (76), (83), (84), (94), (97), (113),
% 199.49/32.83  | | | | |            (117), (118), (119), (121), (140), (156), (158), (163),
% 199.49/32.83  | | | | |            (176), (178), (182), (183), (185) are inconsistent by
% 199.49/32.83  | | | | |            sub-proof #77.
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | Case 2:
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | |   (186)   ~ (all_56_15 = e3)
% 199.49/32.83  | | | | |   (187)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (11), (13), (14), (15), (19),
% 199.49/32.83  | | | | |            (23), (27), (31), (37), (39), (41), (49), (51), (52), (55),
% 199.49/32.83  | | | | |            (56), (60), (70), (71), (72), (73), (76), (79), (96), (97),
% 199.49/32.83  | | | | |            (99), (102), (103), (105), (108), (110), (111), (116),
% 199.49/32.83  | | | | |            (118), (119), (121), (132), (133), (136), (138), (139),
% 199.49/32.83  | | | | |            (142), (143), (146), (151), (153), (155), (156), (157),
% 199.49/32.83  | | | | |            (158), (161), (162), (163), (165), (176), (177), (178),
% 199.49/32.83  | | | | |            (186), (187) are inconsistent by sub-proof #75.
% 199.49/32.83  | | | | | 
% 199.49/32.83  | | | | End of split
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | End of split
% 199.49/32.83  | | | 
% 199.49/32.83  | | Case 2:
% 199.49/32.83  | | | 
% 199.49/32.83  | | |   (188)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 199.49/32.83  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 199.49/32.83  | | |            all_52_30 = e0)
% 199.49/32.83  | | | 
% 199.49/32.83  | | | BETA: splitting (188) gives:
% 199.49/32.83  | | | 
% 199.49/32.83  | | | Case 1:
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | |   (189)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 199.49/32.83  | | | |          e0
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | ALPHA: (189) implies:
% 199.49/32.83  | | | |   (190)  all_52_22 = e0
% 199.49/32.83  | | | |   (191)  all_52_20 = e1
% 199.49/32.83  | | | |   (192)  all_52_16 = e3
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REDUCE: (109), (192) imply:
% 199.49/32.83  | | | |   (193)  op(all_52_17, all_52_17) = e3
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REDUCE: (101), (190) imply:
% 199.49/32.83  | | | |   (194)  op(all_52_23, all_52_23) = e0
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REDUCE: (32), (191) imply:
% 199.49/32.83  | | | |   (195)  op(all_10_2, all_10_2) = e1
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 199.49/32.83  | | | |            (17), (18), (19), (22), (23), (24), (25), (27), (30), (31),
% 199.49/32.83  | | | |            (33), (35), (36), (37), (39), (40), (42), (44), (45), (49),
% 199.49/32.83  | | | |            (50), (51), (52), (55), (56), (57), (58), (59), (60), (61),
% 199.49/32.83  | | | |            (62), (63), (64), (66), (67), (70), (71), (72), (73), (74),
% 199.49/32.83  | | | |            (75), (76), (78), (79), (80), (86), (88), (90), (93), (94),
% 199.49/32.83  | | | |            (96), (97), (98), (99), (102), (103), (104), (105), (107),
% 199.49/32.83  | | | |            (108), (110), (111), (115), (116), (118), (119), (121),
% 199.49/32.83  | | | |            (122), (123), (124), (126), (127), (129), (130), (132),
% 199.49/32.83  | | | |            (133), (135), (136), (137), (138), (139), (140), (141),
% 199.49/32.83  | | | |            (142), (143), (144), (145), (146), (148), (151), (152),
% 199.49/32.83  | | | |            (153), (156), (157), (158), (159), (161), (162), (163),
% 199.49/32.83  | | | |            (165), (166), (169), (193), (194), (195) are inconsistent by
% 199.49/32.83  | | | |            sub-proof #73.
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | Case 2:
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | |   (196)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 199.49/32.83  | | | |          e0
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 199.49/32.83  | | | |            (13), (15), (16), (17), (18), (19), (20), (22), (24), (26),
% 199.49/32.83  | | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 199.49/32.83  | | | |            (38), (40), (42), (43), (44), (46), (47), (48), (49), (50),
% 199.49/32.83  | | | |            (51), (52), (53), (54), (57), (59), (60), (61), (64), (65),
% 199.49/32.83  | | | |            (66), (68), (69), (70), (71), (72), (73), (74), (76), (77),
% 199.49/32.83  | | | |            (78), (79), (81), (82), (84), (85), (87), (89), (91), (92),
% 199.49/32.83  | | | |            (93), (94), (95), (96), (97), (98), (99), (100), (102),
% 199.49/32.83  | | | |            (103), (104), (105), (106), (107), (108), (109), (111),
% 199.49/32.83  | | | |            (112), (113), (114), (115), (116), (119), (120), (121),
% 199.49/32.83  | | | |            (122), (123), (124), (125), (128), (129), (130), (131),
% 199.49/32.83  | | | |            (133), (135), (136), (138), (139), (140), (141), (142),
% 199.49/32.83  | | | |            (144), (145), (146), (149), (150), (151), (153), (154),
% 199.49/32.83  | | | |            (156), (157), (158), (160), (161), (162), (163), (164),
% 199.49/32.83  | | | |            (165), (166), (196) are inconsistent by sub-proof #434.
% 199.49/32.83  | | | | 
% 199.49/32.83  | | | End of split
% 199.49/32.83  | | | 
% 199.49/32.83  | | End of split
% 199.49/32.83  | | 
% 199.49/32.83  | End of split
% 199.49/32.83  | 
% 199.49/32.83  End of proof
% 199.49/32.83  
% 199.49/32.83  Sub-proof #73 shows that the following formulas are inconsistent:
% 199.49/32.83  ----------------------------------------------------------------
% 199.49/32.83    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.83    (2)   ~ (all_52_25 = all_52_27)
% 199.49/32.83    (3)  all_58_14 = all_52_23
% 199.49/32.83    (4)   ~ (e3 = e1)
% 199.49/32.83    (5)  op(all_52_3, all_52_3) = all_52_2
% 199.49/32.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.83    (7)  all_58_1 = all_52_9
% 199.49/32.83    (8)   ~ (e3 = e0)
% 199.49/32.83    (9)  op(all_52_23, all_52_23) = e0
% 199.49/32.83    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.83    (11)   ~ (all_52_7 = all_52_15)
% 199.49/32.83    (12)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.83    (13)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.83    (14)   ~ (all_52_3 = all_6_2)
% 199.49/32.84    (15)  all_44_2 = all_6_2
% 199.49/32.84    (16)  all_58_0 = all_6_2
% 199.49/32.84    (17)   ~ (all_52_17 = all_10_2)
% 199.49/32.84    (18)   ~ (all_10_0 = e3)
% 199.49/32.84    (19)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.49/32.84    (20)  all_40_2 = all_10_2
% 199.49/32.84    (21)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.84    (22)   ~ (all_52_27 = all_52_29)
% 199.49/32.84    (23)  all_58_13 = all_52_15
% 199.49/32.84    (24)  all_58_9 = all_52_25
% 199.49/32.84    (25)  op(all_52_27, all_52_27) = all_52_26
% 199.49/32.84    (26)  op(e1, e3) = all_52_5
% 199.49/32.84    (27)  op(e2, e2) = all_4_2
% 199.49/32.84    (28)  all_58_7 = all_10_0
% 199.49/32.84    (29)   ~ (all_52_3 = all_52_5)
% 199.49/32.84    (30)  all_58_11 = all_52_29
% 199.49/32.84    (31)   ~ (all_52_25 = all_14_2)
% 199.49/32.84    (32)   ~ (all_52_9 = all_52_15)
% 199.49/32.84    (33)   ~ (all_52_7 = all_6_2)
% 199.49/32.84    (34)  op(e0, e0) = all_14_2
% 199.49/32.84    (35)  all_56_15 = all_14_2
% 199.49/32.84    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.49/32.84    (37)   ~ (all_10_0 = e2)
% 199.49/32.84    (38)   ~ (all_4_0 = e3)
% 199.49/32.84    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.84    (40)   ~ (all_52_13 = all_10_2)
% 199.49/32.84    (41)  op(all_10_2, all_10_2) = e1
% 199.49/32.84    (42)  all_58_10 = all_52_27
% 199.49/32.84    (43)  all_56_8 = all_52_5
% 199.49/32.84    (44)  op(all_52_9, all_52_9) = all_52_8
% 199.49/32.84    (45)  op(all_52_15, all_52_15) = all_52_14
% 199.49/32.84    (46)  all_56_9 = all_10_0
% 199.49/32.84    (47)   ~ (all_52_25 = all_52_29)
% 199.49/32.84    (48)  all_58_7 = all_52_13
% 199.49/32.84    (49)   ~ (all_10_0 = all_4_2)
% 199.49/32.84    (50)   ~ (all_52_5 = all_52_7)
% 199.49/32.84    (51)  all_58_12 = all_52_7
% 199.49/32.84    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.84    (53)   ~ (all_52_7 = all_14_2)
% 199.49/32.84    (54)   ~ (all_14_2 = e0)
% 199.49/32.84    (55)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 199.49/32.84    (56)  all_58_2 = all_52_3
% 199.49/32.84    (57)  all_56_2 = all_52_17
% 199.49/32.84    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.84    (59)   ~ (all_52_15 = all_10_0)
% 199.49/32.84    (60)  op(all_4_2, e2) = all_4_1
% 199.49/32.84    (61)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.84    (62)   ~ (all_52_15 = all_14_2)
% 199.49/32.84    (63)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.84    (64)  op(e3, e1) = all_52_17
% 199.49/32.84    (65)  op(e0, e3) = all_52_7
% 199.49/32.84    (66)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.84    (67)   ~ (all_52_9 = all_52_25)
% 199.49/32.84    (68)  all_58_15 = all_14_2
% 199.49/32.84    (69)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.49/32.84    (70)  all_58_8 = all_10_2
% 199.49/32.84    (71)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.84    (72)   ~ (all_52_5 = all_10_2)
% 199.49/32.84    (73)   ~ (all_52_23 = all_14_2)
% 199.49/32.84    (74)  all_56_12 = all_52_7
% 199.49/32.84    (75)  all_58_5 = all_4_0
% 199.49/32.84    (76)  all_8_2 = all_6_2
% 199.49/32.84    (77)   ~ (all_52_9 = all_4_2)
% 199.49/32.84    (78)   ~ (all_52_5 = all_6_2)
% 199.49/32.84    (79)   ~ (all_52_9 = all_6_2)
% 199.49/32.84    (80)  op(e3, all_6_1) = e2
% 199.49/32.84    (81)  op(e3, e3) = all_6_2
% 199.49/32.84    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.49/32.84    (83)   ~ (all_52_27 = all_14_2)
% 199.49/32.84    (84)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.84    (85)  op(all_4_2, all_4_2) = all_52_10
% 199.49/32.84    (86)  all_40_0 = all_10_0
% 199.49/32.84    (87)   ~ (all_52_3 = all_52_7)
% 199.49/32.84    (88)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.84    (89)  all_56_1 = all_52_9
% 199.49/32.84    (90)   ~ (all_52_15 = all_4_2)
% 199.49/32.84    (91)   ~ (all_52_27 = all_4_2)
% 199.49/32.84    (92)  op(all_52_17, all_52_17) = e3
% 199.49/32.84    (93)  all_58_6 = all_52_5
% 199.49/32.84    (94)  op(all_10_2, e1) = e2
% 199.49/32.84    (95)  op(e3, e2) = all_52_9
% 199.49/32.84    (96)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.84    (97)   ~ (all_52_17 = all_6_2)
% 199.49/32.84    (98)   ~ (e1 = e0)
% 199.49/32.84    (99)   ~ (e3 = e2)
% 199.49/32.84    (100)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 199.49/32.84    (101)  all_44_1 = all_6_1
% 199.49/32.84    (102)   ~ (all_52_9 = all_52_17)
% 199.49/32.84    (103)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.84    (104)   ~ (all_52_3 = all_4_0)
% 199.49/32.84    (105)  op(e1, e1) = all_10_2
% 199.49/32.84    (106)   ~ (all_52_23 = all_10_2)
% 199.49/32.84    (107)   ~ (all_52_7 = all_52_23)
% 199.49/32.84    (108)  all_58_3 = all_4_2
% 199.49/32.84    (109)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.84    (110)   ~ (all_52_3 = all_4_2)
% 199.49/32.84    (111)   ~ (all_52_9 = all_10_0)
% 199.49/32.84    (112)   ~ (all_52_17 = all_52_23)
% 199.49/32.84    (113)  all_8_1 = all_6_1
% 199.49/32.84    (114)  op(all_6_2, e3) = all_6_1
% 199.49/32.84    (115)  all_58_4 = all_52_17
% 199.49/32.84    (116)  op(all_52_25, all_52_25) = all_52_24
% 199.49/32.84  
% 199.49/32.84  Begin of proof
% 199.49/32.84  | 
% 199.49/32.84  | BETA: splitting (71) gives:
% 199.49/32.84  | 
% 199.49/32.84  | Case 1:
% 199.49/32.84  | | 
% 199.49/32.84  | |   (117)  all_56_15 = e3
% 199.49/32.84  | | 
% 199.49/32.84  | | COMBINE_EQS: (35), (117) imply:
% 199.49/32.84  | |   (118)  all_14_2 = e3
% 199.49/32.84  | | 
% 199.49/32.84  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (14), (15), (16),
% 199.49/32.84  | |            (19), (21), (23), (24), (26), (31), (32), (33), (36), (38), (39),
% 199.49/32.84  | |            (40), (41), (43), (44), (48), (50), (51), (53), (54), (56), (57),
% 199.49/32.84  | |            (58), (61), (63), (65), (66), (68), (69), (70), (72), (73), (74),
% 199.49/32.84  | |            (75), (76), (77), (78), (80), (81), (84), (87), (88), (92), (93),
% 199.49/32.84  | |            (95), (97), (98), (99), (101), (102), (103), (104), (105), (106),
% 199.49/32.84  | |            (107), (108), (112), (113), (114), (115), (118) are inconsistent
% 199.49/32.84  | |            by sub-proof #82.
% 199.49/32.84  | | 
% 199.49/32.84  | Case 2:
% 199.49/32.84  | | 
% 199.49/32.84  | |   (119)   ~ (all_56_15 = e3)
% 199.49/32.84  | |   (120)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.84  | | 
% 199.49/32.84  | | REDUCE: (35), (119) imply:
% 199.49/32.84  | |   (121)   ~ (all_14_2 = e3)
% 199.49/32.84  | | 
% 199.49/32.84  | | BETA: splitting (36) gives:
% 199.49/32.84  | | 
% 199.49/32.84  | | Case 1:
% 199.49/32.84  | | | 
% 199.49/32.84  | | |   (122)  all_58_2 = e3
% 199.49/32.84  | | | 
% 199.49/32.84  | | | COMBINE_EQS: (56), (122) imply:
% 199.49/32.84  | | |   (123)  all_52_3 = e3
% 199.49/32.84  | | | 
% 199.49/32.84  | | | SIMP: (123) implies:
% 199.49/32.84  | | |   (124)  all_52_3 = e3
% 199.49/32.84  | | | 
% 199.49/32.84  | | | REDUCE: (29), (124) imply:
% 199.49/32.84  | | |   (125)   ~ (all_52_5 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | SIMP: (125) implies:
% 199.49/32.84  | | |   (126)   ~ (all_52_5 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | REDUCE: (87), (124) imply:
% 199.49/32.84  | | |   (127)   ~ (all_52_7 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | SIMP: (127) implies:
% 199.49/32.84  | | |   (128)   ~ (all_52_7 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | REDUCE: (14), (124) imply:
% 199.49/32.84  | | |   (129)   ~ (all_6_2 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | SIMP: (129) implies:
% 199.49/32.84  | | |   (130)   ~ (all_6_2 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | REDUCE: (110), (124) imply:
% 199.49/32.84  | | |   (131)   ~ (all_4_2 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | SIMP: (131) implies:
% 199.49/32.84  | | |   (132)   ~ (all_4_2 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | REDUCE: (5), (124) imply:
% 199.49/32.84  | | |   (133)  op(e3, e3) = all_52_2
% 199.49/32.84  | | | 
% 199.49/32.84  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3, simplifying
% 199.49/32.84  | | |              with (81), (133) gives:
% 199.49/32.84  | | |   (134)  all_52_2 = all_6_2
% 199.49/32.84  | | | 
% 199.49/32.84  | | | BETA: splitting (96) gives:
% 199.49/32.84  | | | 
% 199.49/32.84  | | | Case 1:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | |   (135)  all_58_12 = e3
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | REF_CLOSE: (51), (128), (135) are inconsistent by sub-proof #1367.
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | Case 2:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | |   (136)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | BETA: splitting (52) gives:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | Case 1:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | |   (137)  all_58_6 = e3
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REF_CLOSE: (93), (126), (137) are inconsistent by sub-proof #1328.
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | Case 2:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | |   (138)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | BETA: splitting (66) gives:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | Case 1:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | |   (139)  all_58_1 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | COMBINE_EQS: (7), (139) imply:
% 199.49/32.84  | | | | | |   (140)  all_52_9 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | REDUCE: (67), (140) imply:
% 199.49/32.84  | | | | | |   (141)   ~ (all_52_25 = e3)
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | SIMP: (141) implies:
% 199.49/32.84  | | | | | |   (142)   ~ (all_52_25 = e3)
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (16),
% 199.49/32.84  | | | | | |            (23), (24), (32), (33), (39), (51), (57), (61), (63),
% 199.49/32.84  | | | | | |            (65), (66), (68), (74), (76), (80), (81), (84), (88),
% 199.49/32.84  | | | | | |            (92), (95), (97), (98), (99), (102), (103), (105), (106),
% 199.49/32.84  | | | | | |            (107), (112), (113), (114), (115), (121), (136), (142)
% 199.49/32.84  | | | | | |            are inconsistent by sub-proof #372.
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | Case 2:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | |   (143)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | BETA: splitting (143) gives:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | Case 1:
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | |   (144)  all_58_3 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | COMBINE_EQS: (108), (144) imply:
% 199.49/32.84  | | | | | | |   (145)  all_4_2 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | REDUCE: (132), (145) imply:
% 199.49/32.84  | | | | | | |   (146)  $false
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | CLOSE: (146) is inconsistent.
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | Case 2:
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | |   (147)  all_58_7 = e3 | all_58_13 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | BETA: splitting (147) gives:
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | Case 1:
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | |   (148)  all_58_7 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | COMBINE_EQS: (28), (148) imply:
% 199.49/32.84  | | | | | | | |   (149)  all_10_0 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REDUCE: (18), (149) imply:
% 199.49/32.84  | | | | | | | |   (150)  $false
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | CLOSE: (150) is inconsistent.
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | Case 2:
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | |   (151)  all_58_13 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | COMBINE_EQS: (23), (151) imply:
% 199.49/32.84  | | | | | | | |   (152)  all_52_15 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | SIMP: (152) implies:
% 199.49/32.84  | | | | | | | |   (153)  all_52_15 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REDUCE: (32), (153) imply:
% 199.49/32.84  | | | | | | | |   (154)   ~ (all_52_9 = e3)
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REDUCE: (59), (153) imply:
% 199.49/32.84  | | | | | | | |   (155)   ~ (all_10_0 = e3)
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REDUCE: (45), (153) imply:
% 199.49/32.84  | | | | | | | |   (156)  op(e3, e3) = all_52_14
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3,
% 199.49/32.84  | | | | | | | |              simplifying with (81), (156) gives:
% 199.49/32.84  | | | | | | | |   (157)  all_52_14 = all_6_2
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | BETA: splitting (84) gives:
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | Case 1:
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | |   (158)  all_58_0 = e3
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | COMBINE_EQS: (16), (158) imply:
% 199.49/32.84  | | | | | | | | |   (159)  all_6_2 = e3
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | REDUCE: (130), (159) imply:
% 199.49/32.84  | | | | | | | | |   (160)  $false
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | CLOSE: (160) is inconsistent.
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | Case 2:
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | |   (161)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | BETA: splitting (103) gives:
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | Case 1:
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | |   (162)  all_58_4 = e3
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | COMBINE_EQS: (115), (162) imply:
% 199.49/32.84  | | | | | | | | | |   (163)  all_52_17 = e3
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | SIMP: (163) implies:
% 199.49/32.84  | | | | | | | | | |   (164)  all_52_17 = e3
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | REF_CLOSE: (6), (81), (92), (97), (164) are inconsistent by
% 199.49/32.84  | | | | | | | | | |            sub-proof #1280.
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | Case 2:
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | |   (165)   ~ (all_58_4 = e3)
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | REDUCE: (115), (165) imply:
% 199.49/32.84  | | | | | | | | | |   (166)   ~ (all_52_17 = e3)
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | BETA: splitting (161) gives:
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | Case 1:
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | |   (167)  all_58_1 = e3
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | COMBINE_EQS: (7), (167) imply:
% 199.49/32.84  | | | | | | | | | | |   (168)  all_52_9 = e3
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | REDUCE: (154), (168) imply:
% 199.49/32.84  | | | | | | | | | | |   (169)  $false
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | Case 2:
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | |   (170)  all_58_4 = e3 | all_58_9 = e3
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | BETA: splitting (170) gives:
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | Case 1:
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | |   (171)  all_58_4 = e3
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | | REF_CLOSE: (115), (166), (171) are inconsistent by sub-proof
% 199.49/32.84  | | | | | | | | | | | |            #1302.
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | Case 2:
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | |   (172)  all_58_9 = e3
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | | COMBINE_EQS: (24), (172) imply:
% 199.49/32.84  | | | | | | | | | | | |   (173)  all_52_25 = e3
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | | SIMP: (173) implies:
% 199.49/32.84  | | | | | | | | | | | |   (174)  all_52_25 = e3
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | | REDUCE: (47), (174) imply:
% 199.49/32.84  | | | | | | | | | | | |   (175)   ~ (all_52_29 = e3)
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | | SIMP: (175) implies:
% 199.49/32.84  | | | | | | | | | | | |   (176)   ~ (all_52_29 = e3)
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | | REF_CLOSE: (4), (6), (16), (18), (27), (28), (30), (41),
% 199.49/32.84  | | | | | | | | | | | |            (51), (56), (58), (64), (70), (72), (81), (92),
% 199.49/32.84  | | | | | | | | | | | |            (93), (94), (110), (128), (138), (176) are
% 199.49/32.84  | | | | | | | | | | | |            inconsistent by sub-proof #415.
% 199.49/32.84  | | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | | End of split
% 199.49/32.84  | | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | | End of split
% 199.49/32.84  | | | | | | | | | | 
% 199.49/32.84  | | | | | | | | | End of split
% 199.49/32.84  | | | | | | | | | 
% 199.49/32.84  | | | | | | | | End of split
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | End of split
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | End of split
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | End of split
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | End of split
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | End of split
% 199.49/32.84  | | | 
% 199.49/32.84  | | Case 2:
% 199.49/32.84  | | | 
% 199.49/32.84  | | |   (177)   ~ (all_58_2 = e3)
% 199.49/32.84  | | |   (178)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.49/32.84  | | | 
% 199.49/32.84  | | | REDUCE: (56), (177) imply:
% 199.49/32.84  | | |   (179)   ~ (all_52_3 = e3)
% 199.49/32.84  | | | 
% 199.49/32.84  | | | BETA: splitting (109) gives:
% 199.49/32.84  | | | 
% 199.49/32.84  | | | Case 1:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | |   (180)  all_58_1 = e2
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | COMBINE_EQS: (7), (180) imply:
% 199.49/32.84  | | | |   (181)  all_52_9 = e2
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | REDUCE: (111), (181) imply:
% 199.49/32.84  | | | |   (182)   ~ (all_10_0 = e2)
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | BETA: splitting (66) gives:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | Case 1:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | |   (183)  all_58_1 = e3
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REF_CLOSE: (99), (180), (183) are inconsistent by sub-proof #1090.
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | Case 2:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | |   (184)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 199.49/32.84  | | | | |            (16), (17), (18), (20), (21), (23), (24), (28), (30), (31),
% 199.49/32.84  | | | | |            (32), (33), (34), (35), (37), (38), (39), (41), (43), (44),
% 199.49/32.84  | | | | |            (46), (47), (49), (50), (51), (52), (55), (56), (57), (58),
% 199.49/32.84  | | | | |            (60), (61), (62), (63), (64), (65), (67), (68), (69), (70),
% 199.49/32.84  | | | | |            (72), (73), (74), (75), (76), (77), (79), (80), (81), (82),
% 199.49/32.84  | | | | |            (84), (85), (86), (88), (89), (90), (92), (93), (94), (95),
% 199.49/32.84  | | | | |            (96), (97), (98), (99), (100), (102), (103), (105), (106),
% 199.49/32.84  | | | | |            (107), (108), (109), (112), (113), (114), (115), (116),
% 199.49/32.84  | | | | |            (120), (179), (184) are inconsistent by sub-proof #74.
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | End of split
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | Case 2:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | |   (185)   ~ (all_58_1 = e2)
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | REDUCE: (7), (185) imply:
% 199.49/32.84  | | | |   (186)   ~ (all_52_9 = e2)
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | BETA: splitting (100) gives:
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | | Case 1:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | |   (187)  all_56_1 = e3
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | COMBINE_EQS: (89), (187) imply:
% 199.49/32.84  | | | | |   (188)  all_52_9 = e3
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REDUCE: (111), (188) imply:
% 199.49/32.84  | | | | |   (189)   ~ (all_10_0 = e3)
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REDUCE: (77), (188) imply:
% 199.49/32.84  | | | | |   (190)   ~ (all_4_2 = e3)
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | SIMP: (190) implies:
% 199.49/32.84  | | | | |   (191)   ~ (all_4_2 = e3)
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REDUCE: (44), (188) imply:
% 199.49/32.84  | | | | |   (192)  op(e3, e3) = all_52_8
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | BETA: splitting (178) gives:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | Case 1:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | |   (193)  all_58_3 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | COMBINE_EQS: (108), (193) imply:
% 199.49/32.84  | | | | | |   (194)  all_4_2 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | REDUCE: (191), (194) imply:
% 199.49/32.84  | | | | | |   (195)  $false
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | CLOSE: (195) is inconsistent.
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | Case 2:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | |   (196)  all_58_5 = e3 | all_58_10 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | BETA: splitting (196) gives:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | Case 1:
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | |   (197)  all_58_5 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | REF_CLOSE: (38), (75), (197) are inconsistent by sub-proof #215.
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | Case 2:
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | |   (198)  all_58_10 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | COMBINE_EQS: (42), (198) imply:
% 199.49/32.84  | | | | | | |   (199)  all_52_27 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | SIMP: (199) implies:
% 199.49/32.84  | | | | | | |   (200)  all_52_27 = e3
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | REDUCE: (2), (200) imply:
% 199.49/32.84  | | | | | | |   (201)   ~ (all_52_25 = e3)
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | REDUCE: (22), (200) imply:
% 199.49/32.84  | | | | | | |   (202)   ~ (all_52_29 = e3)
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | SIMP: (202) implies:
% 199.49/32.84  | | | | | | |   (203)   ~ (all_52_29 = e3)
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | REDUCE: (83), (200) imply:
% 199.49/32.84  | | | | | | |   (204)   ~ (all_14_2 = e3)
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | REDUCE: (25), (200) imply:
% 199.49/32.84  | | | | | | |   (205)  op(e3, e3) = all_52_26
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 199.49/32.84  | | | | | | |              simplifying with (81), (192) gives:
% 199.49/32.84  | | | | | | |   (206)  all_52_8 = all_6_2
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | GROUND_INST: instantiating (6) with all_52_26, all_52_8, e3, e3,
% 199.49/32.84  | | | | | | |              simplifying with (192), (205) gives:
% 199.49/32.84  | | | | | | |   (207)  all_52_8 = all_52_26
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | COMBINE_EQS: (206), (207) imply:
% 199.49/32.84  | | | | | | |   (208)  all_52_26 = all_6_2
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | BETA: splitting (96) gives:
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | | Case 1:
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | |   (209)  all_58_12 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | COMBINE_EQS: (51), (209) imply:
% 199.49/32.84  | | | | | | | |   (210)  all_52_7 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | SIMP: (210) implies:
% 199.49/32.84  | | | | | | | |   (211)  all_52_7 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REDUCE: (50), (211) imply:
% 199.49/32.84  | | | | | | | |   (212)   ~ (all_52_5 = e3)
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REF_CLOSE: (6), (13), (18), (20), (27), (28), (30), (37), (46),
% 199.49/32.84  | | | | | | | |            (52), (55), (64), (70), (86), (92), (93), (94),
% 199.49/32.84  | | | | | | | |            (191), (203), (212) are inconsistent by sub-proof
% 199.49/32.84  | | | | | | | |            #176.
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | Case 2:
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | |   (213)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (16),
% 199.49/32.84  | | | | | | | |            (23), (24), (32), (33), (39), (51), (57), (61), (63),
% 199.49/32.84  | | | | | | | |            (65), (66), (68), (74), (76), (80), (81), (84), (88),
% 199.49/32.84  | | | | | | | |            (92), (95), (97), (98), (99), (102), (103), (105),
% 199.49/32.84  | | | | | | | |            (106), (107), (112), (113), (114), (115), (121),
% 199.49/32.84  | | | | | | | |            (201), (213) are inconsistent by sub-proof #372.
% 199.49/32.84  | | | | | | | | 
% 199.49/32.84  | | | | | | | End of split
% 199.49/32.84  | | | | | | | 
% 199.49/32.84  | | | | | | End of split
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | End of split
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | Case 2:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | |   (214)   ~ (all_56_1 = e3)
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | REDUCE: (89), (214) imply:
% 199.49/32.84  | | | | |   (215)   ~ (all_52_9 = e3)
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | BETA: splitting (66) gives:
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | | Case 1:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | |   (216)  all_58_1 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | COMBINE_EQS: (7), (216) imply:
% 199.49/32.84  | | | | | |   (217)  all_52_9 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | REDUCE: (215), (217) imply:
% 199.49/32.84  | | | | | |   (218)  $false
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | CLOSE: (218) is inconsistent.
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | Case 2:
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | |   (219)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 199.49/32.84  | | | | | |            (13), (16), (17), (18), (20), (21), (23), (24), (28),
% 199.49/32.84  | | | | | |            (30), (31), (32), (33), (34), (35), (37), (38), (39),
% 199.49/32.84  | | | | | |            (41), (43), (44), (46), (47), (49), (50), (51), (52),
% 199.49/32.84  | | | | | |            (55), (56), (57), (58), (60), (61), (62), (63), (64),
% 199.49/32.84  | | | | | |            (65), (67), (68), (69), (70), (72), (73), (74), (75),
% 199.49/32.84  | | | | | |            (76), (77), (79), (80), (81), (82), (84), (85), (86),
% 199.49/32.84  | | | | | |            (88), (89), (90), (92), (93), (94), (95), (96), (97),
% 199.49/32.84  | | | | | |            (98), (99), (100), (102), (103), (105), (106), (107),
% 199.49/32.84  | | | | | |            (108), (109), (112), (113), (114), (115), (116), (120),
% 199.49/32.84  | | | | | |            (179), (219) are inconsistent by sub-proof #74.
% 199.49/32.84  | | | | | | 
% 199.49/32.84  | | | | | End of split
% 199.49/32.84  | | | | | 
% 199.49/32.84  | | | | End of split
% 199.49/32.84  | | | | 
% 199.49/32.84  | | | End of split
% 199.49/32.84  | | | 
% 199.49/32.84  | | End of split
% 199.49/32.84  | | 
% 199.49/32.84  | End of split
% 199.49/32.84  | 
% 199.49/32.84  End of proof
% 199.49/32.84  
% 199.49/32.84  Sub-proof #74 shows that the following formulas are inconsistent:
% 199.49/32.84  ----------------------------------------------------------------
% 199.49/32.84    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.84    (2)  all_58_14 = all_52_23
% 199.49/32.84    (3)   ~ (e3 = e1)
% 199.49/32.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.84    (5)  all_58_1 = all_52_9
% 199.49/32.84    (6)   ~ (e3 = e0)
% 199.49/32.84    (7)  op(all_52_23, all_52_23) = e0
% 199.49/32.84    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.84    (9)   ~ (all_52_7 = all_52_15)
% 199.49/32.84    (10)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.84    (11)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.84    (12)  all_58_0 = all_6_2
% 199.49/32.84    (13)   ~ (all_52_17 = all_10_2)
% 199.49/32.84    (14)   ~ (all_10_0 = e3)
% 199.49/32.84    (15)  all_40_2 = all_10_2
% 199.49/32.84    (16)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.84    (17)  all_58_13 = all_52_15
% 199.49/32.84    (18)  all_58_9 = all_52_25
% 199.49/32.84    (19)  all_58_7 = all_10_0
% 199.49/32.84    (20)  all_58_11 = all_52_29
% 199.49/32.84    (21)   ~ (all_52_3 = e3)
% 199.49/32.84    (22)   ~ (all_52_25 = all_14_2)
% 199.49/32.84    (23)   ~ (all_52_9 = all_52_15)
% 199.49/32.84    (24)   ~ (all_52_7 = all_6_2)
% 199.49/32.84    (25)  op(e0, e0) = all_14_2
% 199.49/32.84    (26)  all_56_15 = all_14_2
% 199.49/32.84    (27)   ~ (all_10_0 = e2)
% 199.49/32.84    (28)   ~ (all_4_0 = e3)
% 199.49/32.84    (29)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.84    (30)  op(all_10_2, all_10_2) = e1
% 199.49/32.84    (31)  all_56_8 = all_52_5
% 199.49/32.84    (32)  op(all_52_9, all_52_9) = all_52_8
% 199.49/32.84    (33)  all_56_9 = all_10_0
% 199.49/32.84    (34)   ~ (all_52_25 = all_52_29)
% 199.49/32.84    (35)   ~ (all_10_0 = all_4_2)
% 199.49/32.84    (36)   ~ (all_52_5 = all_52_7)
% 199.49/32.84    (37)  all_58_12 = all_52_7
% 199.49/32.84    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.84    (39)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 199.49/32.84    (40)  all_58_2 = all_52_3
% 199.49/32.84    (41)  all_56_2 = all_52_17
% 199.49/32.84    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.84    (43)  op(all_4_2, e2) = all_4_1
% 199.49/32.84    (44)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.84    (45)   ~ (all_52_15 = all_14_2)
% 199.49/32.84    (46)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.84    (47)  op(e3, e1) = all_52_17
% 199.49/32.84    (48)  op(e0, e3) = all_52_7
% 199.49/32.84    (49)   ~ (all_52_9 = all_52_25)
% 199.49/32.84    (50)  all_58_15 = all_14_2
% 199.49/32.84    (51)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.49/32.84    (52)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.84    (53)  all_58_8 = all_10_2
% 199.49/32.84    (54)   ~ (all_52_5 = all_10_2)
% 199.49/32.84    (55)   ~ (all_52_23 = all_14_2)
% 199.49/32.84    (56)  all_56_12 = all_52_7
% 199.49/32.84    (57)  all_58_5 = all_4_0
% 199.49/32.84    (58)  all_8_2 = all_6_2
% 199.49/32.84    (59)   ~ (all_52_9 = all_4_2)
% 199.49/32.84    (60)   ~ (all_52_9 = all_6_2)
% 199.49/32.84    (61)  op(e3, all_6_1) = e2
% 199.49/32.84    (62)  op(e3, e3) = all_6_2
% 199.49/32.84    (63)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.49/32.84    (64)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.85    (65)  op(all_4_2, all_4_2) = all_52_10
% 199.49/32.85    (66)  all_40_0 = all_10_0
% 199.49/32.85    (67)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.85    (68)  all_56_1 = all_52_9
% 199.49/32.85    (69)   ~ (all_52_15 = all_4_2)
% 199.49/32.85    (70)  op(all_52_17, all_52_17) = e3
% 199.49/32.85    (71)  all_58_6 = all_52_5
% 199.49/32.85    (72)  op(all_10_2, e1) = e2
% 199.49/32.85    (73)  op(e3, e2) = all_52_9
% 199.49/32.85    (74)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.85    (75)   ~ (all_52_17 = all_6_2)
% 199.49/32.85    (76)   ~ (e1 = e0)
% 199.49/32.85    (77)   ~ (e3 = e2)
% 199.49/32.85    (78)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85    (79)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 199.49/32.85    (80)   ~ (all_52_9 = all_52_17)
% 199.49/32.85    (81)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.85    (82)  op(e1, e1) = all_10_2
% 199.49/32.85    (83)   ~ (all_52_23 = all_10_2)
% 199.49/32.85    (84)   ~ (all_52_7 = all_52_23)
% 199.49/32.85    (85)  all_58_3 = all_4_2
% 199.49/32.85    (86)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.85    (87)   ~ (all_52_17 = all_52_23)
% 199.49/32.85    (88)  all_8_1 = all_6_1
% 199.49/32.85    (89)  op(all_6_2, e3) = all_6_1
% 199.49/32.85    (90)  all_58_4 = all_52_17
% 199.49/32.85    (91)  op(all_52_25, all_52_25) = all_52_24
% 199.49/32.85  
% 199.49/32.85  Begin of proof
% 199.49/32.85  | 
% 199.49/32.85  | BETA: splitting (51) gives:
% 199.49/32.85  | 
% 199.49/32.85  | Case 1:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (92)  all_56_8 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | COMBINE_EQS: (31), (92) imply:
% 199.49/32.85  | |   (93)  all_52_5 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | SIMP: (93) implies:
% 199.49/32.85  | |   (94)  all_52_5 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (54), (94) imply:
% 199.49/32.85  | |   (95)   ~ (all_10_2 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | SIMP: (95) implies:
% 199.49/32.85  | |   (96)   ~ (all_10_2 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (16), (94) imply:
% 199.49/32.85  | |   (97)  op(e3, e3) = all_52_4
% 199.49/32.85  | | 
% 199.49/32.85  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (17), (24), (28), (29),
% 199.49/32.85  | |            (37), (41), (44), (46), (48), (50), (53), (56), (57), (58), (61),
% 199.49/32.85  | |            (62), (67), (70), (73), (75), (76), (80), (81), (82), (83), (84),
% 199.49/32.85  | |            (87), (88), (89), (90), (96), (97) are inconsistent by sub-proof
% 199.49/32.85  | |            #84.
% 199.49/32.85  | | 
% 199.49/32.85  | Case 2:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (98)   ~ (all_56_8 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (31), (98) imply:
% 199.49/32.85  | |   (99)   ~ (all_52_5 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | BETA: splitting (42) gives:
% 199.49/32.85  | | 
% 199.49/32.85  | | Case 1:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (100)  all_58_0 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | COMBINE_EQS: (12), (100) imply:
% 199.49/32.85  | | |   (101)  all_6_2 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REF_CLOSE: (4), (61), (62), (77), (89), (101) are inconsistent by
% 199.49/32.85  | | |            sub-proof #502.
% 199.49/32.85  | | | 
% 199.49/32.85  | | Case 2:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (102)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | BETA: splitting (102) gives:
% 199.49/32.85  | | | 
% 199.49/32.85  | | | Case 1:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | |   (103)  all_58_2 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | REF_CLOSE: (21), (40), (103) are inconsistent by sub-proof #1369.
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | Case 2:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | |   (104)  all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | BETA: splitting (104) gives:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | Case 1:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | |   (105)  all_58_6 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | REF_CLOSE: (71), (99), (105) are inconsistent by sub-proof #1328.
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | Case 2:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | |   (106)  all_58_12 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | COMBINE_EQS: (37), (106) imply:
% 199.49/32.85  | | | | |   (107)  all_52_7 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | SIMP: (107) implies:
% 199.49/32.85  | | | | |   (108)  all_52_7 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | REDUCE: (9), (108) imply:
% 199.49/32.85  | | | | |   (109)   ~ (all_52_15 = e3)
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | SIMP: (109) implies:
% 199.49/32.85  | | | | |   (110)   ~ (all_52_15 = e3)
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 199.49/32.85  | | | | |            (12), (13), (14), (15), (17), (18), (19), (20), (22), (23),
% 199.49/32.85  | | | | |            (24), (25), (26), (27), (29), (30), (32), (33), (34), (35),
% 199.49/32.85  | | | | |            (36), (37), (38), (39), (41), (43), (44), (45), (46), (47),
% 199.49/32.85  | | | | |            (48), (49), (50), (52), (53), (55), (56), (58), (59), (60),
% 199.49/32.85  | | | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 199.49/32.85  | | | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 199.49/32.85  | | | | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 199.49/32.85  | | | | |            (91), (110) are inconsistent by sub-proof #407.
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | End of split
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | End of split
% 199.49/32.85  | | | 
% 199.49/32.85  | | End of split
% 199.49/32.85  | | 
% 199.49/32.85  | End of split
% 199.49/32.85  | 
% 199.49/32.85  End of proof
% 199.49/32.85  
% 199.49/32.85  Sub-proof #75 shows that the following formulas are inconsistent:
% 199.49/32.85  ----------------------------------------------------------------
% 199.49/32.85    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.85    (2)   ~ (all_52_15 = all_52_23)
% 199.49/32.85    (3)  all_58_14 = all_52_23
% 199.49/32.85    (4)  op(all_52_3, all_52_3) = all_52_2
% 199.49/32.85    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.85    (6)  all_58_1 = all_52_9
% 199.49/32.85    (7)   ~ (e3 = e0)
% 199.49/32.85    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.85    (9)   ~ (all_52_7 = all_52_15)
% 199.49/32.85    (10)  op(all_52_15, all_52_15) = e0
% 199.49/32.85    (11)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.85    (12)  all_58_0 = all_6_2
% 199.49/32.85    (13)   ~ (all_10_0 = e3)
% 199.49/32.85    (14)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.85    (15)  all_58_13 = all_52_15
% 199.49/32.85    (16)  op(e2, e2) = all_4_2
% 199.49/32.85    (17)  all_58_7 = all_10_0
% 199.49/32.85    (18)  op(all_4_2, e2) = e1
% 199.49/32.85    (19)   ~ (all_52_7 = all_6_2)
% 199.49/32.85    (20)  all_56_15 = all_14_2
% 199.49/32.85    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.49/32.85    (22)   ~ (all_10_0 = e2)
% 199.49/32.85    (23)   ~ (all_4_0 = e3)
% 199.49/32.85    (24)  all_56_8 = all_52_5
% 199.49/32.85    (25)   ~ (all_52_5 = all_52_7)
% 199.49/32.85    (26)  all_58_12 = all_52_7
% 199.49/32.85    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.85    (28)   ~ (all_52_7 = all_14_2)
% 199.49/32.85    (29)  all_58_2 = all_52_3
% 199.49/32.85    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85    (31)  op(e0, e3) = all_52_7
% 199.49/32.85    (32)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85    (33)  all_58_15 = all_14_2
% 199.49/32.85    (34)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.49/32.85    (35)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.85    (36)  all_58_8 = all_10_2
% 199.49/32.85    (37)   ~ (all_52_5 = all_10_2)
% 199.49/32.85    (38)  all_56_12 = all_52_7
% 199.49/32.85    (39)  all_58_5 = all_4_0
% 199.49/32.85    (40)  all_8_2 = all_6_2
% 199.49/32.85    (41)   ~ (all_52_5 = all_6_2)
% 199.49/32.85    (42)  op(all_4_2, all_4_2) = e2
% 199.49/32.85    (43)   ~ (all_52_9 = all_6_2)
% 199.49/32.85    (44)  op(e3, all_6_1) = e2
% 199.49/32.85    (45)  op(e3, e3) = all_6_2
% 199.49/32.85    (46)   ~ (all_56_15 = e3)
% 199.49/32.85    (47)  all_56_1 = all_52_9
% 199.49/32.85    (48)   ~ (all_52_15 = all_4_2)
% 199.49/32.85    (49)  all_58_6 = all_52_5
% 199.49/32.85    (50)  op(e3, e2) = all_52_9
% 199.49/32.85    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.85    (52)   ~ (e3 = e2)
% 199.49/32.85    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 199.49/32.85    (54)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.85    (55)  op(e1, e1) = all_10_2
% 199.49/32.85    (56)  op(all_52_9, all_52_9) = e3
% 199.49/32.85    (57)   ~ (all_52_7 = all_52_23)
% 199.49/32.85    (58)   ~ (all_52_5 = all_10_0)
% 199.49/32.85    (59)  all_58_3 = all_4_2
% 199.49/32.85    (60)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.85    (61)   ~ (all_52_3 = all_4_2)
% 199.49/32.85    (62)   ~ (all_52_17 = all_52_23)
% 199.49/32.85    (63)  all_8_1 = all_6_1
% 199.49/32.85    (64)  op(all_6_2, e3) = all_6_1
% 199.49/32.85    (65)  all_58_4 = all_52_17
% 199.49/32.85  
% 199.49/32.85  Begin of proof
% 199.49/32.85  | 
% 199.49/32.85  | REDUCE: (20), (46) imply:
% 199.49/32.85  |   (66)   ~ (all_14_2 = e3)
% 199.49/32.85  | 
% 199.49/32.85  | BETA: splitting (21) gives:
% 199.49/32.85  | 
% 199.49/32.85  | Case 1:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (67)  all_58_2 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | COMBINE_EQS: (29), (67) imply:
% 199.49/32.85  | |   (68)  all_52_3 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | SIMP: (68) implies:
% 199.49/32.85  | |   (69)  all_52_3 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (61), (69) imply:
% 199.49/32.85  | |   (70)   ~ (all_4_2 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | SIMP: (70) implies:
% 199.49/32.85  | |   (71)   ~ (all_4_2 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (4), (69) imply:
% 199.49/32.85  | |   (72)  op(e3, e3) = all_52_2
% 199.49/32.85  | | 
% 199.49/32.85  | | GROUND_INST: instantiating (5) with all_6_2, all_52_2, e3, e3, simplifying
% 199.49/32.85  | |              with (45), (72) gives:
% 199.49/32.85  | |   (73)  all_52_2 = all_6_2
% 199.49/32.85  | | 
% 199.49/32.85  | | BETA: splitting (32) gives:
% 199.49/32.85  | | 
% 199.49/32.85  | | Case 1:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (74)  all_58_1 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | COMBINE_EQS: (6), (74) imply:
% 199.49/32.85  | | |   (75)  all_52_9 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REF_CLOSE: (5), (43), (45), (56), (75) are inconsistent by sub-proof
% 199.49/32.85  | | |            #1337.
% 199.49/32.85  | | | 
% 199.49/32.85  | | Case 2:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (76)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | BETA: splitting (76) gives:
% 199.49/32.85  | | | 
% 199.49/32.85  | | | Case 1:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | |   (77)  all_58_3 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | COMBINE_EQS: (59), (77) imply:
% 199.49/32.85  | | | |   (78)  all_4_2 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | REDUCE: (71), (78) imply:
% 199.49/32.85  | | | |   (79)  $false
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | CLOSE: (79) is inconsistent.
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | Case 2:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | |   (80)  all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | BETA: splitting (80) gives:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | Case 1:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | |   (81)  all_58_7 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | COMBINE_EQS: (17), (81) imply:
% 199.49/32.85  | | | | |   (82)  all_10_0 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | REDUCE: (13), (82) imply:
% 199.49/32.85  | | | | |   (83)  $false
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | CLOSE: (83) is inconsistent.
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | Case 2:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | |   (84)  all_58_13 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | COMBINE_EQS: (15), (84) imply:
% 199.49/32.85  | | | | |   (85)  all_52_15 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | REF_CLOSE: (1), (5), (8), (9), (10), (11), (16), (19), (20), (28),
% 199.49/32.85  | | | | |            (31), (35), (38), (40), (44), (45), (48), (50), (56), (63),
% 199.49/32.85  | | | | |            (64), (85) are inconsistent by sub-proof #432.
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | End of split
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | End of split
% 199.49/32.85  | | | 
% 199.49/32.85  | | End of split
% 199.49/32.85  | | 
% 199.49/32.85  | Case 2:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (86)   ~ (all_58_2 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (29), (86) imply:
% 199.49/32.85  | |   (87)   ~ (all_52_3 = e3)
% 199.49/32.85  | | 
% 199.49/32.85  | | BETA: splitting (60) gives:
% 199.49/32.85  | | 
% 199.49/32.85  | | Case 1:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (88)  all_58_1 = e2
% 199.49/32.85  | | | 
% 199.49/32.85  | | | COMBINE_EQS: (6), (88) imply:
% 199.49/32.85  | | |   (89)  all_52_9 = e2
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REDUCE: (43), (89) imply:
% 199.49/32.85  | | |   (90)   ~ (all_6_2 = e2)
% 199.49/32.85  | | | 
% 199.49/32.85  | | | SIMP: (90) implies:
% 199.49/32.85  | | |   (91)   ~ (all_6_2 = e2)
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REDUCE: (56), (89) imply:
% 199.49/32.85  | | |   (92)  op(e2, e2) = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | GROUND_INST: instantiating (5) with all_4_2, e3, e2, e2, simplifying with
% 199.49/32.85  | | |              (16), (92) gives:
% 199.49/32.85  | | |   (93)  all_4_2 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REDUCE: (42), (93) imply:
% 199.49/32.85  | | |   (94)  op(e3, e3) = e2
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REF_CLOSE: (5), (45), (91), (94) are inconsistent by sub-proof #769.
% 199.49/32.85  | | | 
% 199.49/32.85  | | Case 2:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (95)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.85  | | | 
% 199.49/32.85  | | | BETA: splitting (53) gives:
% 199.49/32.85  | | | 
% 199.49/32.85  | | | Case 1:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | |   (96)  all_56_1 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | COMBINE_EQS: (47), (96) imply:
% 199.49/32.85  | | | |   (97)  all_52_9 = e3
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | REF_CLOSE: (5), (43), (45), (56), (97) are inconsistent by sub-proof
% 199.49/32.85  | | | |            #1337.
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | Case 2:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | |   (98)   ~ (all_56_1 = e3)
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | REDUCE: (47), (98) imply:
% 199.49/32.85  | | | |   (99)   ~ (all_52_9 = e3)
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | BETA: splitting (32) gives:
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | | Case 1:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | |   (100)  all_58_1 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | COMBINE_EQS: (6), (100) imply:
% 199.49/32.85  | | | | |   (101)  all_52_9 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | REDUCE: (99), (101) imply:
% 199.49/32.85  | | | | |   (102)  $false
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | CLOSE: (102) is inconsistent.
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | Case 2:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | |   (103)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | BETA: splitting (34) gives:
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | | Case 1:
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | |   (104)  all_56_8 = e3
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | COMBINE_EQS: (24), (104) imply:
% 199.49/32.85  | | | | | |   (105)  all_52_5 = e3
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | SIMP: (105) implies:
% 199.49/32.85  | | | | | |   (106)  all_52_5 = e3
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | REDUCE: (25), (106) imply:
% 199.49/32.85  | | | | | |   (107)   ~ (all_52_7 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | SIMP: (107) implies:
% 199.49/32.85  | | | | | |   (108)   ~ (all_52_7 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | REDUCE: (58), (106) imply:
% 199.49/32.85  | | | | | |   (109)   ~ (all_10_0 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | REDUCE: (37), (106) imply:
% 199.49/32.85  | | | | | |   (110)   ~ (all_10_2 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | SIMP: (110) implies:
% 199.49/32.85  | | | | | |   (111)   ~ (all_10_2 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | REDUCE: (41), (106) imply:
% 199.49/32.85  | | | | | |   (112)   ~ (all_6_2 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | SIMP: (112) implies:
% 199.49/32.85  | | | | | |   (113)   ~ (all_6_2 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | REDUCE: (14), (106) imply:
% 199.49/32.85  | | | | | |   (114)  op(e3, e3) = all_52_4
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 199.49/32.85  | | | | | |              simplifying with (45), (114) gives:
% 199.49/32.85  | | | | | |   (115)  all_52_4 = all_6_2
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | BETA: splitting (51) gives:
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | Case 1:
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | |   (116)  all_58_12 = e3
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | REF_CLOSE: (26), (108), (116) are inconsistent by sub-proof #1367.
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | Case 2:
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | |   (117)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | BETA: splitting (54) gives:
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | |   (118)  all_58_4 = e3
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | COMBINE_EQS: (65), (118) imply:
% 199.49/32.85  | | | | | | | |   (119)  all_52_17 = e3
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | SIMP: (119) implies:
% 199.49/32.85  | | | | | | | |   (120)  all_52_17 = e3
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | REDUCE: (62), (120) imply:
% 199.49/32.85  | | | | | | | |   (121)   ~ (all_52_23 = e3)
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | SIMP: (121) implies:
% 199.49/32.85  | | | | | | | |   (122)   ~ (all_52_23 = e3)
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (11), (15), (16),
% 199.49/32.85  | | | | | | | |            (19), (20), (28), (31), (33), (35), (38), (40), (44),
% 199.49/32.85  | | | | | | | |            (45), (48), (50), (56), (63), (64), (66), (117),
% 199.49/32.85  | | | | | | | |            (122) are inconsistent by sub-proof #88.
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | |   (123)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | BETA: splitting (123) gives:
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | |   (124)  all_58_5 = e3
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | REF_CLOSE: (23), (39), (124) are inconsistent by sub-proof
% 199.49/32.85  | | | | | | | | |            #215.
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | |   (125)  all_58_8 = e3 | all_58_14 = e3
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | BETA: splitting (125) gives:
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | |   (126)  all_58_8 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | COMBINE_EQS: (36), (126) imply:
% 199.49/32.85  | | | | | | | | | |   (127)  all_10_2 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | REDUCE: (111), (127) imply:
% 199.49/32.85  | | | | | | | | | |   (128)  $false
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | CLOSE: (128) is inconsistent.
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | |   (129)  all_58_14 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | COMBINE_EQS: (3), (129) imply:
% 199.49/32.85  | | | | | | | | | |   (130)  all_52_23 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | SIMP: (130) implies:
% 199.49/32.85  | | | | | | | | | |   (131)  all_52_23 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | REDUCE: (2), (131) imply:
% 199.49/32.85  | | | | | | | | | |   (132)   ~ (all_52_15 = e3)
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | BETA: splitting (103) gives:
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | |   (133)  all_58_3 = e3
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | | COMBINE_EQS: (59), (133) imply:
% 199.49/32.85  | | | | | | | | | | |   (134)  all_4_2 = e3
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | | REDUCE: (18), (134) imply:
% 199.49/32.85  | | | | | | | | | | |   (135)  op(e3, e2) = e1
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | | REDUCE: (16), (134) imply:
% 199.49/32.85  | | | | | | | | | | |   (136)  op(e2, e2) = e3
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | | REF_CLOSE: (5), (12), (16), (26), (27), (29), (30), (37),
% 199.49/32.85  | | | | | | | | | | |            (49), (50), (55), (56), (61), (108), (113), (135),
% 199.49/32.85  | | | | | | | | | | |            (136) are inconsistent by sub-proof #76.
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | |   (137)  all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | | REF_CLOSE: (13), (15), (17), (132), (137) are inconsistent by
% 199.49/32.85  | | | | | | | | | | |            sub-proof #717.
% 199.49/32.85  | | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | End of split
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | End of split
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | End of split
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | End of split
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | End of split
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | Case 2:
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | |   (138)   ~ (all_56_8 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | REDUCE: (24), (138) imply:
% 199.49/32.85  | | | | | |   (139)   ~ (all_52_5 = e3)
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | BETA: splitting (30) gives:
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | | Case 1:
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | |   (140)  all_58_0 = e3
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | COMBINE_EQS: (12), (140) imply:
% 199.49/32.85  | | | | | | |   (141)  all_6_2 = e3
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | REF_CLOSE: (5), (44), (45), (52), (64), (141) are inconsistent by
% 199.49/32.85  | | | | | | |            sub-proof #502.
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | Case 2:
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | |   (142)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | BETA: splitting (142) gives:
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | |   (143)  all_58_2 = e3
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | REF_CLOSE: (29), (87), (143) are inconsistent by sub-proof
% 199.49/32.85  | | | | | | | |            #1369.
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | |   (144)  all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | BETA: splitting (144) gives:
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | |   (145)  all_58_6 = e3
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | REF_CLOSE: (49), (139), (145) are inconsistent by sub-proof
% 199.49/32.85  | | | | | | | | |            #1328.
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | |   (146)  all_58_12 = e3
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | COMBINE_EQS: (26), (146) imply:
% 199.49/32.85  | | | | | | | | |   (147)  all_52_7 = e3
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | SIMP: (147) implies:
% 199.49/32.85  | | | | | | | | |   (148)  all_52_7 = e3
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | REDUCE: (9), (148) imply:
% 199.49/32.85  | | | | | | | | |   (149)   ~ (all_52_15 = e3)
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | SIMP: (149) implies:
% 199.49/32.85  | | | | | | | | |   (150)   ~ (all_52_15 = e3)
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | BETA: splitting (103) gives:
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | Case 1:
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | |   (151)  all_58_3 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | COMBINE_EQS: (59), (151) imply:
% 199.49/32.85  | | | | | | | | | |   (152)  all_4_2 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | REDUCE: (16), (152) imply:
% 199.49/32.85  | | | | | | | | | |   (153)  op(e2, e2) = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | REF_CLOSE: (5), (7), (10), (15), (17), (22), (52), (95),
% 199.49/32.85  | | | | | | | | | |            (151), (153) are inconsistent by sub-proof #184.
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | Case 2:
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | |   (154)  all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | | REF_CLOSE: (13), (15), (17), (150), (154) are inconsistent by
% 199.49/32.85  | | | | | | | | | |            sub-proof #717.
% 199.49/32.85  | | | | | | | | | | 
% 199.49/32.85  | | | | | | | | | End of split
% 199.49/32.85  | | | | | | | | | 
% 199.49/32.85  | | | | | | | | End of split
% 199.49/32.85  | | | | | | | | 
% 199.49/32.85  | | | | | | | End of split
% 199.49/32.85  | | | | | | | 
% 199.49/32.85  | | | | | | End of split
% 199.49/32.85  | | | | | | 
% 199.49/32.85  | | | | | End of split
% 199.49/32.85  | | | | | 
% 199.49/32.85  | | | | End of split
% 199.49/32.85  | | | | 
% 199.49/32.85  | | | End of split
% 199.49/32.85  | | | 
% 199.49/32.85  | | End of split
% 199.49/32.85  | | 
% 199.49/32.85  | End of split
% 199.49/32.85  | 
% 199.49/32.85  End of proof
% 199.49/32.85  
% 199.49/32.85  Sub-proof #76 shows that the following formulas are inconsistent:
% 199.49/32.85  ----------------------------------------------------------------
% 199.49/32.85    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.85    (2)  op(e3, e2) = e1
% 199.49/32.85    (3)  all_58_0 = all_6_2
% 199.49/32.85    (4)  op(e2, e2) = all_4_2
% 199.49/32.85    (5)   ~ (all_6_2 = e3)
% 199.49/32.85    (6)  all_58_12 = all_52_7
% 199.49/32.85    (7)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.85    (8)   ~ (all_52_7 = e3)
% 199.49/32.85    (9)  all_58_2 = all_52_3
% 199.49/32.85    (10)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85    (11)   ~ (all_52_5 = all_10_2)
% 199.49/32.85    (12)  op(e2, e2) = e3
% 199.49/32.85    (13)  all_58_6 = all_52_5
% 199.49/32.85    (14)  op(e3, e2) = all_52_9
% 199.49/32.85    (15)  op(e1, e1) = all_10_2
% 199.49/32.85    (16)  op(all_52_9, all_52_9) = e3
% 199.49/32.85    (17)   ~ (all_52_3 = all_4_2)
% 199.49/32.85  
% 199.49/32.85  Begin of proof
% 199.49/32.85  | 
% 199.49/32.85  | BETA: splitting (10) gives:
% 199.49/32.85  | 
% 199.49/32.85  | Case 1:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (18)  all_58_0 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | COMBINE_EQS: (3), (18) imply:
% 199.49/32.85  | |   (19)  all_6_2 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | REDUCE: (5), (19) imply:
% 199.49/32.85  | |   (20)  $false
% 199.49/32.85  | | 
% 199.49/32.85  | | CLOSE: (20) is inconsistent.
% 199.49/32.85  | | 
% 199.49/32.85  | Case 2:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (21)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15),
% 199.49/32.85  | |            (16), (17), (21) are inconsistent by sub-proof #195.
% 199.49/32.85  | | 
% 199.49/32.85  | End of split
% 199.49/32.85  | 
% 199.49/32.85  End of proof
% 199.49/32.85  
% 199.49/32.85  Sub-proof #77 shows that the following formulas are inconsistent:
% 199.49/32.85  ----------------------------------------------------------------
% 199.49/32.85    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.85    (2)  all_58_1 = all_52_9
% 199.49/32.85    (3)  op(e2, e3) = all_52_3
% 199.49/32.85    (4)   ~ (all_52_3 = all_6_2)
% 199.49/32.85    (5)  all_58_0 = all_6_2
% 199.49/32.85    (6)  all_56_4 = all_52_3
% 199.49/32.85    (7)   ~ (all_10_0 = e3)
% 199.49/32.85    (8)  op(e3, e0) = all_52_25
% 199.49/32.85    (9)  all_58_13 = all_52_15
% 199.49/32.85    (10)   ~ (all_52_15 = e3)
% 199.49/32.85    (11)  op(e2, e2) = all_4_2
% 199.49/32.85    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.49/32.85    (13)  all_58_7 = all_10_0
% 199.49/32.85    (14)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.49/32.85    (15)  all_58_2 = all_52_3
% 199.49/32.85    (16)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.49/32.85    (17)   ~ (e2 = e0)
% 199.49/32.85    (18)  op(e3, e3) = all_52_30
% 199.49/32.85    (19)  op(e3, e1) = all_52_17
% 199.49/32.85    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85    (21)  all_52_25 = all_14_1
% 199.49/32.85    (22)   ~ (all_52_25 = all_6_2)
% 199.49/32.85    (23)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.49/32.85    (24)  op(all_4_2, all_4_2) = e2
% 199.49/32.85    (25)   ~ (all_52_9 = all_6_2)
% 199.49/32.85    (26)  op(e3, all_6_1) = e2
% 199.49/32.85    (27)  op(e3, e3) = all_6_2
% 199.49/32.85    (28)   ~ (all_52_17 = all_6_2)
% 199.49/32.85    (29)  op(all_52_9, all_52_9) = e3
% 199.49/32.85    (30)  all_58_3 = all_4_2
% 199.49/32.85    (31)   ~ (all_52_3 = all_4_2)
% 199.49/32.85    (32)  op(all_6_2, e3) = all_6_1
% 199.49/32.85  
% 199.49/32.85  Begin of proof
% 199.49/32.85  | 
% 199.49/32.85  | GROUND_INST: instantiating (1) with all_6_2, all_52_30, e3, e3, simplifying
% 199.49/32.85  |              with (18), (27) gives:
% 199.49/32.85  |   (33)  all_52_30 = all_6_2
% 199.49/32.85  | 
% 199.49/32.85  | REDUCE: (21), (22) imply:
% 199.49/32.85  |   (34)   ~ (all_14_1 = all_6_2)
% 199.49/32.85  | 
% 199.49/32.85  | REDUCE: (8), (21) imply:
% 199.49/32.85  |   (35)  op(e3, e0) = all_14_1
% 199.49/32.85  | 
% 199.49/32.85  | BETA: splitting (20) gives:
% 199.49/32.85  | 
% 199.49/32.85  | Case 1:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (36)  all_58_1 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | COMBINE_EQS: (2), (36) imply:
% 199.49/32.85  | |   (37)  all_52_9 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | REF_CLOSE: (1), (25), (27), (29), (37) are inconsistent by sub-proof #1337.
% 199.49/32.85  | | 
% 199.49/32.85  | Case 2:
% 199.49/32.85  | | 
% 199.49/32.85  | |   (38)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.85  | | 
% 199.49/32.85  | | BETA: splitting (38) gives:
% 199.49/32.85  | | 
% 199.49/32.85  | | Case 1:
% 199.49/32.85  | | | 
% 199.49/32.85  | | |   (39)  all_58_3 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | COMBINE_EQS: (30), (39) imply:
% 199.49/32.85  | | |   (40)  all_4_2 = e3
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REDUCE: (31), (40) imply:
% 199.49/32.85  | | |   (41)   ~ (all_52_3 = e3)
% 199.49/32.85  | | | 
% 199.49/32.85  | | | REDUCE: (24), (40) imply:
% 199.49/32.85  | | |   (42)  op(e3, e3) = e2
% 199.49/32.85  | | | 
% 199.49/32.86  | | | REDUCE: (11), (40) imply:
% 199.49/32.86  | | |   (43)  op(e2, e2) = e3
% 199.49/32.86  | | | 
% 199.49/32.86  | | | REF_CLOSE: (1), (3), (4), (5), (6), (11), (12), (14), (15), (16), (17),
% 199.49/32.86  | | |            (19), (23), (26), (27), (28), (32), (34), (35), (41), (42),
% 199.49/32.86  | | |            (43) are inconsistent by sub-proof #89.
% 199.49/32.86  | | | 
% 199.49/32.86  | | Case 2:
% 199.49/32.86  | | | 
% 199.49/32.86  | | |   (44)  all_58_7 = e3 | all_58_13 = e3
% 199.49/32.86  | | | 
% 199.49/32.86  | | | REF_CLOSE: (7), (9), (10), (13), (44) are inconsistent by sub-proof #717.
% 199.49/32.86  | | | 
% 199.49/32.86  | | End of split
% 199.49/32.86  | | 
% 199.49/32.86  | End of split
% 199.49/32.86  | 
% 199.49/32.86  End of proof
% 199.49/32.86  
% 199.49/32.86  Sub-proof #78 shows that the following formulas are inconsistent:
% 199.49/32.86  ----------------------------------------------------------------
% 199.49/32.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.86    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.86    (3)  all_40_2 = all_10_2
% 199.49/32.86    (4)  op(all_10_0, all_10_0) = e1
% 199.49/32.86    (5)  all_58_8 = e3
% 199.49/32.86    (6)   ~ (all_10_0 = e2)
% 199.49/32.86    (7)  all_56_9 = all_10_0
% 199.49/32.86    (8)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 199.49/32.86    (9)   ~ (all_10_0 = all_10_2)
% 199.49/32.86    (10)  all_58_8 = all_10_2
% 199.49/32.86    (11)  all_40_0 = all_10_0
% 199.49/32.86    (12)  op(e1, e1) = all_10_2
% 199.49/32.86  
% 199.49/32.86  Begin of proof
% 199.49/32.86  | 
% 199.49/32.86  | COMBINE_EQS: (5), (10) imply:
% 199.49/32.86  |   (13)  all_10_2 = e3
% 199.49/32.86  | 
% 199.49/32.86  | COMBINE_EQS: (3), (13) imply:
% 199.49/32.86  |   (14)  all_40_2 = e3
% 199.49/32.86  | 
% 199.49/32.86  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (12), (14) are
% 199.49/32.86  |            inconsistent by sub-proof #987.
% 199.49/32.86  | 
% 199.49/32.86  End of proof
% 199.49/32.86  
% 199.49/32.86  Sub-proof #79 shows that the following formulas are inconsistent:
% 199.49/32.86  ----------------------------------------------------------------
% 199.49/32.86    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.86    (2)   ~ (all_52_15 = all_52_23)
% 199.49/32.86    (3)  all_58_14 = all_52_23
% 199.49/32.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.86    (5)   ~ (e3 = e0)
% 199.49/32.86    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.86    (7)   ~ (all_52_7 = all_52_15)
% 199.49/32.86    (8)  op(all_52_15, all_52_15) = e0
% 199.49/32.86    (9)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.86    (10)  all_58_13 = all_52_15
% 199.49/32.86    (11)  op(e2, e2) = all_4_2
% 199.49/32.86    (12)   ~ (all_52_7 = all_6_2)
% 199.49/32.86    (13)  all_58_15 = e0
% 199.49/32.86    (14)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.49/32.86    (15)  all_58_12 = all_52_7
% 199.49/32.86    (16)   ~ (all_52_7 = e3)
% 199.49/32.86    (17)   ~ (all_52_23 = e3)
% 199.49/32.86    (18)  op(e0, e3) = all_52_7
% 199.49/32.86    (19)   ~ (all_52_23 = e0)
% 199.49/32.86    (20)  all_56_12 = all_52_7
% 199.49/32.86    (21)  all_8_2 = all_6_2
% 199.49/32.86    (22)  op(e3, all_6_1) = e2
% 199.49/32.86    (23)  op(e3, e3) = all_6_2
% 199.49/32.86    (24)  all_56_14 = all_52_23
% 199.49/32.86    (25)   ~ (all_52_15 = all_4_2)
% 199.49/32.86    (26)  op(e3, e2) = all_52_9
% 199.49/32.86    (27)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.86    (28)  op(all_52_9, all_52_9) = e3
% 199.49/32.86    (29)   ~ (all_52_7 = all_52_23)
% 199.49/32.86    (30)  all_8_1 = all_6_1
% 199.49/32.86    (31)  op(all_6_2, e3) = all_6_1
% 199.49/32.86  
% 199.49/32.86  Begin of proof
% 199.49/32.86  | 
% 199.49/32.86  | BETA: splitting (27) gives:
% 199.49/32.86  | 
% 199.49/32.86  | Case 1:
% 199.49/32.86  | | 
% 199.49/32.86  | |   (32)  all_58_12 = e3
% 199.49/32.86  | | 
% 199.49/32.86  | | REF_CLOSE: (15), (16), (32) are inconsistent by sub-proof #1367.
% 199.49/32.86  | | 
% 199.49/32.86  | Case 2:
% 199.49/32.86  | | 
% 199.49/32.86  | |   (33)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.86  | | 
% 199.49/32.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.49/32.86  | |            (13), (14), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.49/32.86  | |            (26), (28), (29), (30), (31), (33) are inconsistent by sub-proof
% 199.49/32.86  | |            #98.
% 199.49/32.86  | | 
% 199.49/32.86  | End of split
% 199.49/32.86  | 
% 199.49/32.86  End of proof
% 199.49/32.86  
% 199.49/32.86  Sub-proof #80 shows that the following formulas are inconsistent:
% 199.49/32.86  ----------------------------------------------------------------
% 199.49/32.86    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.86    (2)   ~ (all_52_15 = all_52_23)
% 199.49/32.86    (3)   ~ (all_52_25 = all_52_27)
% 199.49/32.86    (4)  all_58_14 = all_52_23
% 199.49/32.86    (5)   ~ (e3 = e1)
% 199.49/32.86    (6)   ~ (all_52_17 = all_4_0)
% 199.49/32.86    (7)  op(all_52_3, all_52_3) = all_52_2
% 199.49/32.86    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.86    (9)   ~ (all_52_5 = all_52_13)
% 199.49/32.86    (10)  all_58_1 = all_52_9
% 199.49/32.86    (11)   ~ (all_52_9 = all_52_13)
% 199.49/32.86    (12)   ~ (e3 = e0)
% 199.49/32.86    (13)  op(e2, e3) = all_52_3
% 199.49/32.86    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.86    (15)   ~ (all_52_7 = all_52_15)
% 199.49/32.86    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.86    (17)   ~ (all_52_17 = all_52_25)
% 199.49/32.86    (18)   ~ (all_52_3 = all_6_2)
% 199.49/32.86    (19)  all_44_2 = all_6_2
% 199.49/32.86    (20)  all_58_0 = all_6_2
% 199.49/32.86    (21)  op(all_14_2, e0) = all_14_1
% 199.49/32.86    (22)  all_56_4 = all_52_3
% 199.49/32.86    (23)   ~ (all_52_17 = all_10_2)
% 199.49/32.86    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.49/32.86    (25)  op(e3, e0) = all_52_25
% 199.49/32.86    (26)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.86    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.49/32.86    (28)  op(all_52_19, all_52_19) = all_52_18
% 199.49/32.86    (29)   ~ (all_52_27 = all_52_29)
% 199.49/32.86    (30)  all_58_13 = all_52_15
% 199.49/32.86    (31)  op(all_10_2, all_10_2) = all_52_20
% 199.49/32.86    (32)  all_58_9 = all_52_25
% 199.49/32.86    (33)   ~ (all_52_29 = all_14_2)
% 199.49/32.86    (34)  op(all_52_27, all_52_27) = all_52_26
% 199.49/32.86    (35)  op(e1, e3) = all_52_5
% 199.49/32.86    (36)  op(e2, e2) = all_4_2
% 199.49/32.86    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.49/32.86    (38)   ~ (all_52_3 = all_52_5)
% 199.49/32.86    (39)  op(all_4_2, e2) = e1
% 199.49/32.86    (40)  all_58_11 = all_52_29
% 199.49/32.86    (41)  all_56_5 = all_4_2
% 199.49/32.86    (42)   ~ (all_52_25 = all_14_2)
% 199.49/32.86    (43)   ~ (all_52_9 = all_52_15)
% 199.49/32.86    (44)   ~ (all_52_3 = all_52_27)
% 199.49/32.86    (45)  op(all_10_2, e1) = all_10_1
% 199.49/32.86    (46)  op(all_6_2, all_6_2) = all_52_0
% 199.49/32.86    (47)   ~ (all_52_7 = all_6_2)
% 199.49/32.86    (48)  op(e0, e0) = all_14_2
% 199.49/32.86    (49)  all_56_15 = all_14_2
% 199.49/32.86    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.49/32.86    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.49/32.86    (52)   ~ (all_58_15 = e0)
% 199.49/32.86    (53)  all_56_11 = all_52_29
% 199.49/32.86    (54)   ~ (all_4_0 = e3)
% 199.49/32.86    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.49/32.86    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.86    (57)  all_56_9 = all_52_13
% 199.49/32.86    (58)   ~ (all_52_13 = all_10_2)
% 199.49/32.86    (59)  all_58_10 = all_52_27
% 199.49/32.86    (60)  all_56_8 = all_52_5
% 199.49/32.86    (61)  op(all_52_9, all_52_9) = all_52_8
% 199.49/32.86    (62)  op(all_52_15, all_52_15) = all_52_14
% 199.49/32.86    (63)   ~ (all_52_25 = all_52_29)
% 199.49/32.86    (64)   ~ (all_52_29 = all_10_2)
% 199.49/32.86    (65)  all_58_7 = all_52_13
% 199.49/32.86    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.49/32.86    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.49/32.86    (68)   ~ (all_52_5 = all_52_7)
% 199.49/32.86    (69)  all_58_12 = all_52_7
% 199.49/32.86    (70)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.86    (71)   ~ (all_52_7 = all_14_2)
% 199.49/32.86    (72)  all_58_2 = all_52_3
% 199.49/32.86    (73)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.49/32.86    (74)  all_56_2 = all_52_17
% 199.49/32.86    (75)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.86    (76)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.49/32.86    (77)  all_56_7 = all_52_27
% 199.49/32.86    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.49/32.86    (79)   ~ (e2 = e0)
% 199.49/32.86    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.49/32.86    (81)   ~ (all_52_5 = all_52_29)
% 199.49/32.86    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.86    (83)  all_56_6 = all_52_19
% 199.49/32.86    (84)   ~ (all_52_19 = all_52_27)
% 199.49/32.86    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.49/32.86    (86)   ~ (all_52_13 = all_4_2)
% 199.49/32.86    (87)  op(e3, e1) = all_52_17
% 199.49/32.86    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.49/32.86    (89)  op(e0, e3) = all_52_7
% 199.49/32.86    (90)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.86    (91)   ~ (all_52_9 = all_52_25)
% 199.49/32.86    (92)  all_58_15 = all_14_2
% 199.49/32.86    (93)   ~ (all_52_19 = all_10_2)
% 199.49/32.86    (94)  op(all_52_23, all_52_23) = all_52_22
% 199.49/32.86    (95)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.49/32.86    (96)   ~ (all_10_1 = e2)
% 199.49/32.86    (97)  all_58_8 = all_10_2
% 199.49/32.86    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.86    (99)   ~ (all_52_5 = all_10_2)
% 199.49/32.86    (100)  op(all_52_29, all_52_29) = all_52_28
% 199.49/32.86    (101)   ~ (all_52_23 = all_14_2)
% 199.49/32.86    (102)  all_56_12 = all_52_7
% 199.49/32.86    (103)  op(all_52_17, all_52_17) = all_52_16
% 199.49/32.86    (104)  all_58_5 = all_4_0
% 199.49/32.86    (105)  all_8_2 = all_6_2
% 199.49/32.86    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.49/32.86    (107)   ~ (all_52_25 = all_6_2)
% 199.49/32.86    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.49/32.86    (109)   ~ (all_52_9 = all_4_2)
% 199.49/32.86    (110)   ~ (all_52_5 = all_6_2)
% 199.49/32.86    (111)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.49/32.86    (112)   ~ (all_52_9 = all_6_2)
% 199.49/32.86    (113)  op(e3, all_6_1) = e2
% 199.49/32.86    (114)  all_56_0 = all_6_2
% 199.49/32.86    (115)  op(e3, e3) = all_6_2
% 199.49/32.86    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.49/32.86    (117)   ~ (all_52_27 = all_14_2)
% 199.49/32.86    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.86    (119)  all_56_14 = all_52_23
% 199.49/32.86    (120)  op(all_4_2, all_4_2) = all_52_10
% 199.49/32.86    (121)  all_56_3 = all_52_25
% 199.49/32.86    (122)   ~ (all_52_3 = all_52_7)
% 199.49/32.86    (123)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.86    (124)  all_58_5 = all_52_19
% 199.49/32.86    (125)   ~ (all_52_15 = all_4_2)
% 199.49/32.86    (126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.49/32.86           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.49/32.86           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.49/32.86           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.49/32.86    (127)   ~ (all_52_27 = all_4_2)
% 199.49/32.86    (128)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 199.49/32.86             all_58_13 = e0 | all_58_14 = e0)
% 199.49/32.86    (129)  all_58_6 = all_52_5
% 199.49/32.86    (130)  op(e3, e2) = all_52_9
% 199.49/32.86    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.86    (132)   ~ (all_52_17 = all_6_2)
% 199.49/32.86    (133)   ~ (e1 = e0)
% 199.49/32.86    (134)   ~ (e3 = e2)
% 199.49/32.86    (135)  all_44_1 = all_6_1
% 199.49/32.86    (136)   ~ (all_52_9 = all_52_17)
% 199.49/32.86    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.86    (138)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.86    (139)   ~ (all_52_3 = all_4_0)
% 199.49/32.86    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.49/32.86    (141)  op(all_52_13, all_52_13) = all_52_12
% 199.49/32.86    (142)  op(e1, e1) = all_10_2
% 199.49/32.86    (143)   ~ (all_52_23 = all_10_2)
% 199.49/32.86    (144)   ~ (all_52_7 = all_52_23)
% 199.49/32.86    (145)   ~ (all_52_17 = all_52_19)
% 199.49/32.86    (146)  all_58_3 = all_4_2
% 199.49/32.86    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.86    (148)  all_56_13 = all_52_15
% 199.49/32.86    (149)   ~ (all_52_3 = all_4_2)
% 199.49/32.86    (150)   ~ (all_52_19 = all_4_2)
% 199.49/32.86    (151)   ~ (all_52_17 = all_52_23)
% 199.49/32.86    (152)  all_8_1 = all_6_1
% 199.49/32.86    (153)  op(all_6_2, e3) = all_6_1
% 199.49/32.86    (154)   ~ (all_52_13 = all_52_29)
% 199.49/32.86    (155)  all_58_4 = all_52_17
% 199.49/32.86    (156)  op(all_52_25, all_52_25) = all_52_24
% 199.49/32.86  
% 199.49/32.86  Begin of proof
% 199.49/32.86  | 
% 199.49/32.86  | ALPHA: (128) implies:
% 199.49/32.86  |   (157)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.86  |   (158)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.49/32.86  | 
% 199.49/32.86  | REDUCE: (52), (92) imply:
% 199.49/32.86  |   (159)   ~ (all_14_2 = e0)
% 199.49/32.86  | 
% 199.49/32.86  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.49/32.86  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 199.49/32.86  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 199.49/32.86  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.49/32.86  |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 199.49/32.86  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 199.49/32.86  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 199.49/32.86  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 199.49/32.86  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 199.49/32.86  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 199.49/32.86  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 199.49/32.86  |            (120), (121), (122), (123), (124), (125), (126), (127), (129),
% 199.49/32.86  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 199.49/32.86  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 199.49/32.86  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 199.49/32.86  |            (157), (158), (159) are inconsistent by sub-proof #81.
% 199.49/32.86  | 
% 199.49/32.86  End of proof
% 199.49/32.86  
% 199.49/32.86  Sub-proof #81 shows that the following formulas are inconsistent:
% 199.49/32.86  ----------------------------------------------------------------
% 199.49/32.86    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.49/32.86    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.86    (3)   ~ (all_52_15 = all_52_23)
% 199.49/32.86    (4)   ~ (all_52_25 = all_52_27)
% 199.49/32.86    (5)  all_58_14 = all_52_23
% 199.49/32.86    (6)   ~ (e3 = e1)
% 199.49/32.86    (7)   ~ (all_52_17 = all_4_0)
% 199.49/32.86    (8)  op(all_52_3, all_52_3) = all_52_2
% 199.49/32.86    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.86    (10)   ~ (all_52_5 = all_52_13)
% 199.49/32.86    (11)  all_58_1 = all_52_9
% 199.49/32.86    (12)   ~ (all_52_9 = all_52_13)
% 199.49/32.86    (13)   ~ (e3 = e0)
% 199.49/32.86    (14)  op(e2, e3) = all_52_3
% 199.49/32.86    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.86    (16)   ~ (all_52_7 = all_52_15)
% 199.49/32.86    (17)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.86    (18)   ~ (all_52_17 = all_52_25)
% 199.49/32.86    (19)   ~ (all_52_3 = all_6_2)
% 199.49/32.86    (20)  all_44_2 = all_6_2
% 199.49/32.86    (21)  all_58_0 = all_6_2
% 199.49/32.86    (22)  op(all_14_2, e0) = all_14_1
% 199.49/32.86    (23)  all_56_4 = all_52_3
% 199.49/32.86    (24)   ~ (all_52_17 = all_10_2)
% 199.49/32.86    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.49/32.86    (26)  op(e3, e0) = all_52_25
% 199.49/32.86    (27)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.86    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.49/32.86    (29)  op(all_52_19, all_52_19) = all_52_18
% 199.49/32.86    (30)   ~ (all_52_27 = all_52_29)
% 199.49/32.86    (31)  all_58_13 = all_52_15
% 199.49/32.86    (32)  op(all_10_2, all_10_2) = all_52_20
% 199.49/32.86    (33)  all_58_9 = all_52_25
% 199.49/32.86    (34)   ~ (all_52_29 = all_14_2)
% 199.49/32.86    (35)  op(all_52_27, all_52_27) = all_52_26
% 199.49/32.86    (36)  op(e1, e3) = all_52_5
% 199.49/32.86    (37)  op(e2, e2) = all_4_2
% 199.49/32.86    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.49/32.86    (39)   ~ (all_52_3 = all_52_5)
% 199.49/32.86    (40)  op(all_4_2, e2) = e1
% 199.49/32.86    (41)  all_58_11 = all_52_29
% 199.49/32.86    (42)  all_56_5 = all_4_2
% 199.49/32.86    (43)   ~ (all_52_25 = all_14_2)
% 199.49/32.86    (44)   ~ (all_52_9 = all_52_15)
% 199.49/32.86    (45)   ~ (all_52_3 = all_52_27)
% 199.49/32.86    (46)  op(all_10_2, e1) = all_10_1
% 199.49/32.86    (47)  op(all_6_2, all_6_2) = all_52_0
% 199.49/32.86    (48)   ~ (all_52_7 = all_6_2)
% 199.49/32.86    (49)  op(e0, e0) = all_14_2
% 199.49/32.86    (50)  all_56_15 = all_14_2
% 199.49/32.86    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.49/32.86    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.49/32.86    (53)  all_56_11 = all_52_29
% 199.49/32.86    (54)   ~ (all_4_0 = e3)
% 199.49/32.86    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.49/32.86    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.86    (57)  all_56_9 = all_52_13
% 199.49/32.86    (58)   ~ (all_52_13 = all_10_2)
% 199.49/32.86    (59)  all_58_10 = all_52_27
% 199.49/32.86    (60)  all_56_8 = all_52_5
% 199.49/32.86    (61)  op(all_52_9, all_52_9) = all_52_8
% 199.49/32.86    (62)  op(all_52_15, all_52_15) = all_52_14
% 199.49/32.86    (63)   ~ (all_52_25 = all_52_29)
% 199.49/32.86    (64)   ~ (all_52_29 = all_10_2)
% 199.49/32.86    (65)  all_58_7 = all_52_13
% 199.49/32.86    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.49/32.86    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.49/32.86    (68)   ~ (all_52_5 = all_52_7)
% 199.49/32.86    (69)  all_58_12 = all_52_7
% 199.49/32.86    (70)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.49/32.86    (71)   ~ (all_52_7 = all_14_2)
% 199.49/32.86    (72)   ~ (all_14_2 = e0)
% 199.49/32.86    (73)  all_58_2 = all_52_3
% 199.49/32.86    (74)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.49/32.86    (75)  all_56_2 = all_52_17
% 199.49/32.86    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.86    (77)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 199.49/32.86    (78)  all_56_7 = all_52_27
% 199.49/32.86    (79)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.49/32.86    (80)   ~ (e2 = e0)
% 199.49/32.86    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.49/32.86    (82)   ~ (all_52_5 = all_52_29)
% 199.49/32.86    (83)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.86    (84)  all_56_6 = all_52_19
% 199.49/32.86    (85)   ~ (all_52_19 = all_52_27)
% 199.49/32.86    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.49/32.86    (87)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.86    (88)   ~ (all_52_13 = all_4_2)
% 199.49/32.86    (89)  op(e3, e1) = all_52_17
% 199.49/32.86    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.49/32.86    (91)  op(e0, e3) = all_52_7
% 199.49/32.86    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.86    (93)   ~ (all_52_9 = all_52_25)
% 199.49/32.86    (94)  all_58_15 = all_14_2
% 199.49/32.86    (95)   ~ (all_52_19 = all_10_2)
% 199.49/32.86    (96)  op(all_52_23, all_52_23) = all_52_22
% 199.49/32.86    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.49/32.86    (98)   ~ (all_10_1 = e2)
% 199.49/32.86    (99)  all_58_8 = all_10_2
% 199.49/32.86    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.49/32.86    (101)   ~ (all_52_5 = all_10_2)
% 199.49/32.86    (102)  op(all_52_29, all_52_29) = all_52_28
% 199.49/32.86    (103)   ~ (all_52_23 = all_14_2)
% 199.49/32.86    (104)  all_56_12 = all_52_7
% 199.49/32.86    (105)  op(all_52_17, all_52_17) = all_52_16
% 199.49/32.86    (106)  all_58_5 = all_4_0
% 199.49/32.86    (107)  all_8_2 = all_6_2
% 199.49/32.86    (108)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 199.49/32.86    (109)   ~ (all_52_25 = all_6_2)
% 199.49/32.86    (110)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.49/32.86    (111)   ~ (all_52_9 = all_4_2)
% 199.49/32.86    (112)   ~ (all_52_5 = all_6_2)
% 199.49/32.86    (113)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.49/32.86    (114)   ~ (all_52_9 = all_6_2)
% 199.49/32.86    (115)  op(e3, all_6_1) = e2
% 199.49/32.86    (116)  all_56_0 = all_6_2
% 199.49/32.86    (117)  op(e3, e3) = all_6_2
% 199.49/32.86    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.49/32.86    (119)   ~ (all_52_27 = all_14_2)
% 199.49/32.86    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.86    (121)  all_56_14 = all_52_23
% 199.49/32.86    (122)  op(all_4_2, all_4_2) = all_52_10
% 199.49/32.86    (123)  all_56_3 = all_52_25
% 199.49/32.86    (124)   ~ (all_52_3 = all_52_7)
% 199.49/32.86    (125)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.86    (126)  all_58_5 = all_52_19
% 199.49/32.86    (127)   ~ (all_52_15 = all_4_2)
% 199.49/32.86    (128)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.49/32.86           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.49/32.86           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.49/32.86           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.49/32.86    (129)   ~ (all_52_27 = all_4_2)
% 199.49/32.86    (130)  all_58_6 = all_52_5
% 199.49/32.86    (131)  op(e3, e2) = all_52_9
% 199.49/32.86    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.86    (133)   ~ (all_52_17 = all_6_2)
% 199.49/32.86    (134)   ~ (e1 = e0)
% 199.49/32.86    (135)   ~ (e3 = e2)
% 199.49/32.86    (136)  all_44_1 = all_6_1
% 199.49/32.86    (137)   ~ (all_52_9 = all_52_17)
% 199.49/32.86    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.86    (139)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.49/32.86    (140)   ~ (all_52_3 = all_4_0)
% 199.49/32.86    (141)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.49/32.86    (142)  op(all_52_13, all_52_13) = all_52_12
% 199.49/32.86    (143)  op(e1, e1) = all_10_2
% 199.49/32.86    (144)   ~ (all_52_23 = all_10_2)
% 199.49/32.86    (145)   ~ (all_52_7 = all_52_23)
% 199.49/32.86    (146)   ~ (all_52_17 = all_52_19)
% 199.49/32.86    (147)  all_58_3 = all_4_2
% 199.49/32.86    (148)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.49/32.86    (149)  all_56_13 = all_52_15
% 199.49/32.86    (150)   ~ (all_52_3 = all_4_2)
% 199.49/32.86    (151)   ~ (all_52_19 = all_4_2)
% 199.49/32.86    (152)   ~ (all_52_17 = all_52_23)
% 199.49/32.86    (153)  all_8_1 = all_6_1
% 199.49/32.86    (154)  op(all_6_2, e3) = all_6_1
% 199.49/32.86    (155)   ~ (all_52_13 = all_52_29)
% 199.49/32.86    (156)  all_58_4 = all_52_17
% 199.49/32.86    (157)  op(all_52_25, all_52_25) = all_52_24
% 199.49/32.86  
% 199.49/32.86  Begin of proof
% 199.49/32.86  | 
% 199.49/32.86  | BETA: splitting (128) gives:
% 199.49/32.86  | 
% 199.49/32.86  | Case 1:
% 199.49/32.86  | | 
% 199.49/32.86  | |   (158)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.49/32.86  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 199.49/32.86  | | 
% 199.49/32.86  | | BETA: splitting (158) gives:
% 199.49/32.86  | | 
% 199.49/32.86  | | Case 1:
% 199.49/32.86  | | | 
% 199.49/32.86  | | |   (159)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.49/32.86  | | | 
% 199.49/32.86  | | | REF_CLOSE: (8), (9), (17), (21), (27), (37), (47), (49), (51), (69), (71),
% 199.49/32.86  | | |            (73), (76), (101), (115), (116), (117), (130), (132), (135),
% 199.49/32.86  | | |            (141), (143), (150), (154), (159) are inconsistent by sub-proof
% 199.49/32.86  | | |            #501.
% 199.49/32.86  | | | 
% 199.49/32.86  | | Case 2:
% 199.49/32.86  | | | 
% 199.49/32.86  | | |   (160)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 199.49/32.86  | | | 
% 199.49/32.87  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 199.49/32.87  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.49/32.87  | | |            (26), (27), (28), (30), (31), (33), (34), (36), (37), (38),
% 199.49/32.87  | | |            (39), (40), (41), (43), (48), (50), (51), (53), (54), (56),
% 199.49/32.87  | | |            (57), (59), (60), (61), (62), (64), (65), (67), (68), (69),
% 199.49/32.87  | | |            (70), (71), (72), (73), (75), (78), (79), (80), (86), (88),
% 199.49/32.87  | | |            (89), (91), (92), (93), (94), (97), (99), (100), (104), (105),
% 199.49/32.87  | | |            (106), (107), (109), (111), (112), (113), (114), (115), (117),
% 199.49/32.87  | | |            (118), (119), (120), (122), (124), (125), (127), (130), (131),
% 199.49/32.87  | | |            (132), (133), (134), (135), (136), (137), (138), (139), (142),
% 199.49/32.87  | | |            (143), (147), (150), (152), (153), (154), (156), (157), (160)
% 199.49/32.87  | | |            are inconsistent by sub-proof #86.
% 199.49/32.87  | | | 
% 199.49/32.87  | | End of split
% 199.49/32.87  | | 
% 199.49/32.87  | Case 2:
% 199.49/32.87  | | 
% 199.49/32.87  | |   (161)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 199.49/32.87  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 199.49/32.87  | |            e0)
% 199.49/32.87  | | 
% 199.49/32.87  | | BETA: splitting (161) gives:
% 199.49/32.87  | | 
% 199.49/32.87  | | Case 1:
% 199.49/32.87  | | | 
% 199.49/32.87  | | |   (162)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 199.49/32.87  | | | 
% 199.49/32.87  | | | ALPHA: (162) implies:
% 199.49/32.87  | | |   (163)  all_52_22 = e0
% 199.49/32.87  | | |   (164)  all_52_20 = e1
% 199.49/32.87  | | |   (165)  all_52_16 = e3
% 199.49/32.87  | | | 
% 199.49/32.87  | | | REDUCE: (105), (165) imply:
% 199.49/32.87  | | |   (166)  op(all_52_17, all_52_17) = e3
% 199.49/32.87  | | | 
% 199.49/32.87  | | | REDUCE: (96), (163) imply:
% 199.49/32.87  | | |   (167)  op(all_52_23, all_52_23) = e0
% 199.49/32.87  | | | 
% 199.49/32.87  | | | REDUCE: (32), (164) imply:
% 199.49/32.87  | | |   (168)  op(all_10_2, all_10_2) = e1
% 199.49/32.87  | | | 
% 199.49/32.87  | | | BETA: splitting (100) gives:
% 199.49/32.87  | | | 
% 199.49/32.87  | | | Case 1:
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | |   (169)  all_56_15 = e3
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | COMBINE_EQS: (50), (169) imply:
% 199.49/32.87  | | | |   (170)  all_14_2 = e3
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | SIMP: (170) implies:
% 199.49/32.87  | | | |   (171)  all_14_2 = e3
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (15), (16), (19), (20), (21),
% 199.49/32.87  | | | |            (25), (27), (31), (33), (36), (43), (44), (48), (51), (54),
% 199.49/32.87  | | | |            (56), (58), (60), (61), (65), (68), (69), (71), (72), (73),
% 199.49/32.87  | | | |            (75), (76), (83), (87), (91), (92), (94), (97), (99), (101),
% 199.49/32.87  | | | |            (103), (104), (106), (107), (111), (112), (115), (117),
% 199.49/32.87  | | | |            (120), (124), (125), (130), (131), (133), (134), (135),
% 199.49/32.87  | | | |            (136), (137), (138), (140), (143), (144), (145), (147),
% 199.49/32.87  | | | |            (152), (153), (154), (156), (166), (167), (168), (171) are
% 199.49/32.87  | | | |            inconsistent by sub-proof #82.
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | Case 2:
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | |   (172)   ~ (all_56_15 = e3)
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | REDUCE: (50), (172) imply:
% 199.49/32.87  | | | |   (173)   ~ (all_14_2 = e3)
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | BETA: splitting (55) gives:
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | Case 1:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | |   (174)  all_56_13 = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | COMBINE_EQS: (149), (174) imply:
% 199.49/32.87  | | | | |   (175)  all_52_15 = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | SIMP: (175) implies:
% 199.49/32.87  | | | | |   (176)  all_52_15 = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (16), (176) imply:
% 199.49/32.87  | | | | |   (177)   ~ (all_52_7 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (44), (176) imply:
% 199.49/32.87  | | | | |   (178)   ~ (all_52_9 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (3), (176) imply:
% 199.49/32.87  | | | | |   (179)   ~ (all_52_23 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | SIMP: (179) implies:
% 199.49/32.87  | | | | |   (180)   ~ (all_52_23 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (62), (176) imply:
% 199.49/32.87  | | | | |   (181)  op(e3, e3) = all_52_14
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_14, e3, e3,
% 199.49/32.87  | | | | |              simplifying with (117), (181) gives:
% 199.49/32.87  | | | | |   (182)  all_52_14 = all_6_2
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | BETA: splitting (51) gives:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | Case 1:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | |   (183)  all_58_2 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | COMBINE_EQS: (73), (183) imply:
% 199.49/32.87  | | | | | |   (184)  all_52_3 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | SIMP: (184) implies:
% 199.49/32.87  | | | | | |   (185)  all_52_3 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (19), (185) imply:
% 199.49/32.87  | | | | | |   (186)   ~ (all_6_2 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | SIMP: (186) implies:
% 199.49/32.87  | | | | | |   (187)   ~ (all_6_2 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (140), (185) imply:
% 199.49/32.87  | | | | | |   (188)   ~ (all_4_0 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (8), (185) imply:
% 199.49/32.87  | | | | | |   (189)  op(e3, e3) = all_52_2
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_2, e3, e3,
% 199.49/32.87  | | | | | |              simplifying with (117), (189) gives:
% 199.49/32.87  | | | | | |   (190)  all_52_2 = all_6_2
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | BETA: splitting (138) gives:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | Case 1:
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | |   (191)  all_58_4 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | COMBINE_EQS: (156), (191) imply:
% 199.49/32.87  | | | | | | |   (192)  all_52_17 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | SIMP: (192) implies:
% 199.49/32.87  | | | | | | |   (193)  all_52_17 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REF_CLOSE: (9), (117), (133), (166), (193) are inconsistent by
% 199.49/32.87  | | | | | | |            sub-proof #1280.
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | Case 2:
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | |   (194)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | BETA: splitting (120) gives:
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | Case 1:
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | |   (195)  all_58_0 = e3
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | COMBINE_EQS: (21), (195) imply:
% 199.49/32.87  | | | | | | | |   (196)  all_6_2 = e3
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | REDUCE: (187), (196) imply:
% 199.49/32.87  | | | | | | | |   (197)  $false
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | CLOSE: (197) is inconsistent.
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | Case 2:
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | |   (198)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | BETA: splitting (194) gives:
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | Case 1:
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | |   (199)  all_58_5 = e3
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | REF_CLOSE: (54), (106), (199) are inconsistent by sub-proof
% 199.49/32.87  | | | | | | | | |            #215.
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | Case 2:
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | |   (200)  all_58_8 = e3 | all_58_14 = e3
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | BETA: splitting (200) gives:
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | Case 1:
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | |   (201)  all_58_8 = e3
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | COMBINE_EQS: (99), (201) imply:
% 199.49/32.87  | | | | | | | | | |   (202)  all_10_2 = e3
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | SIMP: (202) implies:
% 199.49/32.87  | | | | | | | | | |   (203)  all_10_2 = e3
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | REDUCE: (168), (203) imply:
% 199.49/32.87  | | | | | | | | | |   (204)  op(e3, e3) = e1
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | REDUCE: (46), (203) imply:
% 199.49/32.87  | | | | | | | | | |   (205)  op(e3, e1) = all_10_1
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | BETA: splitting (118) gives:
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | Case 1:
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | |   (206)  all_58_9 = e3
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | COMBINE_EQS: (33), (206) imply:
% 199.49/32.87  | | | | | | | | | | |   (207)  all_52_25 = e3
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | SIMP: (207) implies:
% 199.49/32.87  | | | | | | | | | | |   (208)  all_52_25 = e3
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | REDUCE: (18), (208) imply:
% 199.49/32.87  | | | | | | | | | | |   (209)   ~ (all_52_17 = e3)
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | REDUCE: (43), (208) imply:
% 199.49/32.87  | | | | | | | | | | |   (210)   ~ (all_14_2 = e3)
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | REDUCE: (157), (208) imply:
% 199.49/32.87  | | | | | | | | | | |   (211)  op(e3, e3) = all_52_24
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | REF_CLOSE: (9), (49), (56), (75), (89), (98), (117), (133),
% 199.49/32.87  | | | | | | | | | | |            (166), (173), (204), (205), (209), (211) are
% 199.49/32.87  | | | | | | | | | | |            inconsistent by sub-proof #444.
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | Case 2:
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | |   (212)   ~ (all_58_9 = e3)
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | REDUCE: (33), (212) imply:
% 199.49/32.87  | | | | | | | | | | |   (213)   ~ (all_52_25 = e3)
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | | REF_CLOSE: (9), (11), (33), (117), (133), (156), (166),
% 199.49/32.87  | | | | | | | | | | |            (178), (198), (213) are inconsistent by sub-proof
% 199.49/32.87  | | | | | | | | | | |            #1072.
% 199.49/32.87  | | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | End of split
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | Case 2:
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | |   (214)  all_58_14 = e3
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | | REF_CLOSE: (5), (180), (214) are inconsistent by sub-proof
% 199.49/32.87  | | | | | | | | | |            #1305.
% 199.49/32.87  | | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | End of split
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | End of split
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | End of split
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | End of split
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | Case 2:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | |   (215)   ~ (all_58_2 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (73), (215) imply:
% 199.49/32.87  | | | | | |   (216)   ~ (all_52_3 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REF_CLOSE: (2), (5), (6), (9), (13), (15), (16), (21), (27), (31),
% 199.49/32.87  | | | | | |            (48), (54), (56), (69), (73), (75), (76), (83), (87),
% 199.49/32.87  | | | | | |            (91), (94), (99), (101), (104), (106), (107), (115),
% 199.49/32.87  | | | | | |            (117), (125), (130), (131), (133), (134), (135), (137),
% 199.49/32.87  | | | | | |            (138), (143), (144), (145), (152), (153), (154), (156),
% 199.49/32.87  | | | | | |            (166), (167), (177), (216) are inconsistent by sub-proof
% 199.49/32.87  | | | | | |            #83.
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | End of split
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | Case 2:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | |   (217)   ~ (all_56_13 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (149), (217) imply:
% 199.49/32.87  | | | | |   (218)   ~ (all_52_15 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | BETA: splitting (132) gives:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | Case 1:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | |   (219)  all_58_12 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | COMBINE_EQS: (69), (219) imply:
% 199.49/32.87  | | | | | |   (220)  all_52_7 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | SIMP: (220) implies:
% 199.49/32.87  | | | | | |   (221)  all_52_7 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (145), (221) imply:
% 199.49/32.87  | | | | | |   (222)   ~ (all_52_23 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | SIMP: (222) implies:
% 199.49/32.87  | | | | | |   (223)   ~ (all_52_23 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (71), (221) imply:
% 199.49/32.87  | | | | | |   (224)   ~ (all_14_2 = e3)
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REDUCE: (17), (221) imply:
% 199.49/32.87  | | | | | |   (225)  op(e3, e3) = all_52_6
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | GROUND_INST: instantiating (9) with all_6_2, all_52_6, e3, e3,
% 199.49/32.87  | | | | | |              simplifying with (117), (225) gives:
% 199.49/32.87  | | | | | |   (226)  all_52_6 = all_6_2
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REF_CLOSE: (5), (9), (24), (46), (49), (54), (56), (75), (89), (98),
% 199.49/32.87  | | | | | |            (99), (106), (117), (133), (138), (156), (166), (168),
% 199.49/32.87  | | | | | |            (173), (223) are inconsistent by sub-proof #201.
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | Case 2:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | |   (227)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REF_CLOSE: (2), (5), (6), (9), (13), (15), (16), (31), (48), (56),
% 199.49/32.87  | | | | | |            (69), (75), (83), (87), (91), (94), (104), (107), (115),
% 199.49/32.87  | | | | | |            (117), (125), (131), (133), (134), (137), (143), (144),
% 199.49/32.87  | | | | | |            (145), (152), (153), (154), (166), (167), (173), (218),
% 199.49/32.87  | | | | | |            (227) are inconsistent by sub-proof #437.
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | End of split
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | End of split
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | End of split
% 199.49/32.87  | | | 
% 199.49/32.87  | | Case 2:
% 199.49/32.87  | | | 
% 199.49/32.87  | | |   (228)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 199.49/32.87  | | | 
% 199.49/32.87  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (13), (14),
% 199.49/32.87  | | |            (15), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 199.49/32.87  | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 199.49/32.87  | | |            (38), (39), (41), (42), (43), (45), (46), (47), (48), (49),
% 199.49/32.87  | | |            (50), (51), (52), (53), (56), (59), (60), (61), (63), (64),
% 199.49/32.87  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 199.49/32.87  | | |            (75), (76), (77), (78), (80), (81), (82), (84), (85), (86),
% 199.49/32.87  | | |            (87), (89), (90), (91), (92), (93), (94), (95), (97), (99),
% 199.49/32.87  | | |            (100), (101), (102), (103), (104), (105), (107), (108), (109),
% 199.49/32.87  | | |            (110), (111), (112), (115), (116), (117), (118), (119), (120),
% 199.49/32.87  | | |            (121), (123), (124), (125), (126), (127), (129), (130), (131),
% 199.49/32.87  | | |            (132), (133), (134), (135), (136), (137), (138), (141), (142),
% 199.49/32.87  | | |            (143), (145), (146), (147), (148), (150), (151), (152), (153),
% 199.49/32.87  | | |            (154), (155), (156), (157), (228) are inconsistent by sub-proof
% 199.49/32.87  | | |            #434.
% 199.49/32.87  | | | 
% 199.49/32.87  | | End of split
% 199.49/32.87  | | 
% 199.49/32.87  | End of split
% 199.49/32.87  | 
% 199.49/32.87  End of proof
% 199.49/32.87  
% 199.49/32.87  Sub-proof #82 shows that the following formulas are inconsistent:
% 199.49/32.87  ----------------------------------------------------------------
% 199.49/32.87    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.87    (2)  all_58_14 = all_52_23
% 199.49/32.87    (3)   ~ (e3 = e1)
% 199.49/32.87    (4)  op(all_52_3, all_52_3) = all_52_2
% 199.49/32.87    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.87    (6)  all_58_1 = all_52_9
% 199.49/32.87    (7)  op(all_52_23, all_52_23) = e0
% 199.49/32.87    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.87    (9)   ~ (all_52_7 = all_52_15)
% 199.49/32.87    (10)   ~ (all_52_3 = all_6_2)
% 199.49/32.87    (11)  all_44_2 = all_6_2
% 199.49/32.87    (12)  all_58_0 = all_6_2
% 199.49/32.87    (13)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.49/32.87    (14)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.87    (15)  all_58_13 = all_52_15
% 199.49/32.87    (16)  all_58_9 = all_52_25
% 199.49/32.87    (17)  op(e1, e3) = all_52_5
% 199.49/32.87    (18)   ~ (all_52_25 = all_14_2)
% 199.49/32.87    (19)   ~ (all_52_9 = all_52_15)
% 199.49/32.87    (20)   ~ (all_52_7 = all_6_2)
% 199.49/32.87    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.49/32.87    (22)   ~ (all_4_0 = e3)
% 199.49/32.87    (23)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.87    (24)   ~ (all_52_13 = all_10_2)
% 199.49/32.87    (25)  op(all_10_2, all_10_2) = e1
% 199.49/32.87    (26)  all_56_8 = all_52_5
% 199.49/32.87    (27)  op(all_52_9, all_52_9) = all_52_8
% 199.49/32.87    (28)  all_58_7 = all_52_13
% 199.49/32.87    (29)   ~ (all_52_5 = all_52_7)
% 199.49/32.87    (30)  all_58_12 = all_52_7
% 199.49/32.87    (31)   ~ (all_52_7 = all_14_2)
% 199.49/32.87    (32)   ~ (all_14_2 = e0)
% 199.49/32.87    (33)  all_58_2 = all_52_3
% 199.49/32.87    (34)  all_56_2 = all_52_17
% 199.49/32.87    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.87    (36)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.87    (37)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.87    (38)  op(e0, e3) = all_52_7
% 199.49/32.87    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.49/32.87    (40)  all_58_15 = all_14_2
% 199.49/32.87    (41)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.49/32.87    (42)  all_58_8 = all_10_2
% 199.49/32.87    (43)   ~ (all_52_5 = all_10_2)
% 199.49/32.87    (44)   ~ (all_52_23 = all_14_2)
% 199.49/32.87    (45)  all_56_12 = all_52_7
% 199.49/32.87    (46)  all_58_5 = all_4_0
% 199.49/32.87    (47)  all_8_2 = all_6_2
% 199.49/32.87    (48)   ~ (all_52_9 = all_4_2)
% 199.49/32.87    (49)   ~ (all_52_5 = all_6_2)
% 199.49/32.87    (50)  op(e3, all_6_1) = e2
% 199.49/32.87    (51)  op(e3, e3) = all_6_2
% 199.49/32.87    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.87    (53)   ~ (all_52_3 = all_52_7)
% 199.49/32.87    (54)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.87    (55)  op(all_52_17, all_52_17) = e3
% 199.49/32.87    (56)  all_58_6 = all_52_5
% 199.49/32.87    (57)  op(e3, e2) = all_52_9
% 199.49/32.87    (58)   ~ (all_52_17 = all_6_2)
% 199.49/32.87    (59)   ~ (e1 = e0)
% 199.49/32.87    (60)   ~ (e3 = e2)
% 199.49/32.87    (61)  all_44_1 = all_6_1
% 199.49/32.87    (62)   ~ (all_52_9 = all_52_17)
% 199.49/32.87    (63)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.87    (64)   ~ (all_52_3 = all_4_0)
% 199.49/32.87    (65)  op(e1, e1) = all_10_2
% 199.49/32.87    (66)   ~ (all_52_23 = all_10_2)
% 199.49/32.87    (67)   ~ (all_52_7 = all_52_23)
% 199.49/32.87    (68)  all_58_3 = all_4_2
% 199.49/32.87    (69)   ~ (all_52_17 = all_52_23)
% 199.49/32.87    (70)  all_8_1 = all_6_1
% 199.49/32.87    (71)  op(all_6_2, e3) = all_6_1
% 199.49/32.87    (72)  all_58_4 = all_52_17
% 199.49/32.87    (73)  all_14_2 = e3
% 199.49/32.87  
% 199.49/32.87  Begin of proof
% 199.49/32.87  | 
% 199.49/32.87  | REDUCE: (31), (73) imply:
% 199.49/32.87  |   (74)   ~ (all_52_7 = e3)
% 199.49/32.87  | 
% 199.49/32.87  | REDUCE: (44), (73) imply:
% 199.49/32.87  |   (75)   ~ (all_52_23 = e3)
% 199.49/32.87  | 
% 199.49/32.87  | REDUCE: (18), (73) imply:
% 199.49/32.87  |   (76)   ~ (all_52_25 = e3)
% 199.49/32.87  | 
% 199.49/32.87  | REDUCE: (32), (73) imply:
% 199.49/32.87  |   (77)   ~ (e3 = e0)
% 199.49/32.87  | 
% 199.49/32.87  | BETA: splitting (21) gives:
% 199.49/32.87  | 
% 199.49/32.87  | Case 1:
% 199.49/32.87  | | 
% 199.49/32.87  | |   (78)  all_58_2 = e3
% 199.49/32.87  | | 
% 199.49/32.87  | | COMBINE_EQS: (33), (78) imply:
% 199.49/32.87  | |   (79)  all_52_3 = e3
% 199.49/32.87  | | 
% 199.49/32.87  | | SIMP: (79) implies:
% 199.49/32.87  | |   (80)  all_52_3 = e3
% 199.49/32.87  | | 
% 199.49/32.87  | | REDUCE: (53), (80) imply:
% 199.49/32.87  | |   (81)   ~ (all_52_7 = e3)
% 199.49/32.87  | | 
% 199.49/32.87  | | REDUCE: (10), (80) imply:
% 199.49/32.87  | |   (82)   ~ (all_6_2 = e3)
% 199.49/32.87  | | 
% 199.49/32.87  | | SIMP: (82) implies:
% 199.49/32.87  | |   (83)   ~ (all_6_2 = e3)
% 199.49/32.87  | | 
% 199.49/32.87  | | REDUCE: (64), (80) imply:
% 199.49/32.87  | |   (84)   ~ (all_4_0 = e3)
% 199.49/32.87  | | 
% 199.49/32.87  | | REDUCE: (4), (80) imply:
% 199.49/32.87  | |   (85)  op(e3, e3) = all_52_2
% 199.49/32.87  | | 
% 199.49/32.87  | | GROUND_INST: instantiating (5) with all_6_2, all_52_2, e3, e3, simplifying
% 199.49/32.87  | |              with (51), (85) gives:
% 199.49/32.87  | |   (86)  all_52_2 = all_6_2
% 199.49/32.87  | | 
% 199.49/32.87  | | BETA: splitting (63) gives:
% 199.49/32.87  | | 
% 199.49/32.87  | | Case 1:
% 199.49/32.87  | | | 
% 199.49/32.87  | | |   (87)  all_58_4 = e3
% 199.49/32.87  | | | 
% 199.49/32.87  | | | COMBINE_EQS: (72), (87) imply:
% 199.49/32.87  | | |   (88)  all_52_17 = e3
% 199.49/32.87  | | | 
% 199.49/32.87  | | | SIMP: (88) implies:
% 199.49/32.87  | | |   (89)  all_52_17 = e3
% 199.49/32.87  | | | 
% 199.49/32.87  | | | REF_CLOSE: (5), (51), (55), (58), (89) are inconsistent by sub-proof
% 199.49/32.87  | | |            #1280.
% 199.49/32.87  | | | 
% 199.49/32.87  | | Case 2:
% 199.49/32.87  | | | 
% 199.49/32.87  | | |   (90)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.87  | | | 
% 199.49/32.87  | | | BETA: splitting (52) gives:
% 199.49/32.87  | | | 
% 199.49/32.87  | | | Case 1:
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | |   (91)  all_58_0 = e3
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | COMBINE_EQS: (12), (91) imply:
% 199.49/32.87  | | | |   (92)  all_6_2 = e3
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | REDUCE: (83), (92) imply:
% 199.49/32.87  | | | |   (93)  $false
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | CLOSE: (93) is inconsistent.
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | Case 2:
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | |   (94)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | BETA: splitting (94) gives:
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | | Case 1:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | |   (95)  all_58_1 = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | COMBINE_EQS: (6), (95) imply:
% 199.49/32.87  | | | | |   (96)  all_52_9 = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (19), (96) imply:
% 199.49/32.87  | | | | |   (97)   ~ (all_52_15 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | SIMP: (97) implies:
% 199.49/32.87  | | | | |   (98)   ~ (all_52_15 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (48), (96) imply:
% 199.49/32.87  | | | | |   (99)   ~ (all_4_2 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | SIMP: (99) implies:
% 199.49/32.87  | | | | |   (100)   ~ (all_4_2 = e3)
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (27), (96) imply:
% 199.49/32.87  | | | | |   (101)  op(e3, e3) = all_52_8
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REDUCE: (57), (96) imply:
% 199.49/32.87  | | | | |   (102)  op(e3, e2) = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | BETA: splitting (90) gives:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | Case 1:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | |   (103)  all_58_5 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | REF_CLOSE: (22), (46), (103) are inconsistent by sub-proof #215.
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | Case 2:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | |   (104)  all_58_8 = e3 | all_58_14 = e3
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | BETA: splitting (104) gives:
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | | Case 1:
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | |   (105)  all_58_8 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | COMBINE_EQS: (42), (105) imply:
% 199.49/32.87  | | | | | | |   (106)  all_10_2 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REDUCE: (43), (106) imply:
% 199.49/32.87  | | | | | | |   (107)   ~ (all_52_5 = e3)
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REDUCE: (24), (106) imply:
% 199.49/32.87  | | | | | | |   (108)   ~ (all_52_13 = e3)
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REDUCE: (25), (106) imply:
% 199.49/32.87  | | | | | | |   (109)  op(e3, e3) = e1
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_8, e3, e3,
% 199.49/32.87  | | | | | | |              simplifying with (51), (101) gives:
% 199.49/32.87  | | | | | | |   (110)  all_52_8 = all_6_2
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | GROUND_INST: instantiating (5) with e1, all_52_8, e3, e3,
% 199.49/32.87  | | | | | | |              simplifying with (101), (109) gives:
% 199.49/32.87  | | | | | | |   (111)  all_52_8 = e1
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | COMBINE_EQS: (110), (111) imply:
% 199.49/32.87  | | | | | | |   (112)  all_6_2 = e1
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | SIMP: (112) implies:
% 199.49/32.87  | | | | | | |   (113)  all_6_2 = e1
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | COMBINE_EQS: (11), (113) imply:
% 199.49/32.87  | | | | | | |   (114)  all_44_2 = e1
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REDUCE: (49), (113) imply:
% 199.49/32.87  | | | | | | |   (115)   ~ (all_52_5 = e1)
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REDUCE: (20), (113) imply:
% 199.49/32.87  | | | | | | |   (116)   ~ (all_52_7 = e1)
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REDUCE: (71), (113) imply:
% 199.49/32.87  | | | | | | |   (117)  op(e1, e3) = all_6_1
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | BETA: splitting (13) gives:
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | Case 1:
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | |   (118)   ~ (all_44_2 = e1)
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | REDUCE: (114), (118) imply:
% 199.49/32.87  | | | | | | | |   (119)  $false
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | CLOSE: (119) is inconsistent.
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | Case 2:
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | |   (120)   ~ (all_44_1 = e0)
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | REDUCE: (61), (120) imply:
% 199.49/32.87  | | | | | | | |   (121)   ~ (all_6_1 = e0)
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | GROUND_INST: instantiating (5) with all_52_5, all_6_1, e3, e1,
% 199.49/32.87  | | | | | | | |              simplifying with (17), (117) gives:
% 199.49/32.87  | | | | | | | |   (122)  all_52_5 = all_6_1
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | BETA: splitting (8) gives:
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | | Case 1:
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | |   (123)  all_56_12 = e3
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | REF_CLOSE: (45), (74), (123) are inconsistent by sub-proof
% 199.49/32.87  | | | | | | | | |            #1383.
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | Case 2:
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | |   (124)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | | REF_CLOSE: (5), (15), (17), (26), (28), (29), (39), (41),
% 199.49/32.87  | | | | | | | | |            (45), (50), (68), (95), (98), (100), (102), (107),
% 199.49/32.87  | | | | | | | | |            (108), (115), (116), (117), (121), (124) are
% 199.49/32.87  | | | | | | | | |            inconsistent by sub-proof #330.
% 199.49/32.87  | | | | | | | | | 
% 199.49/32.87  | | | | | | | | End of split
% 199.49/32.87  | | | | | | | | 
% 199.49/32.87  | | | | | | | End of split
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | Case 2:
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | |   (125)  all_58_14 = e3
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | | REF_CLOSE: (2), (75), (125) are inconsistent by sub-proof #1305.
% 199.49/32.87  | | | | | | | 
% 199.49/32.87  | | | | | | End of split
% 199.49/32.87  | | | | | | 
% 199.49/32.87  | | | | | End of split
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | Case 2:
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | |   (126)  all_58_4 = e3 | all_58_9 = e3
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | | REF_CLOSE: (5), (16), (51), (55), (58), (72), (76), (126) are
% 199.49/32.87  | | | | |            inconsistent by sub-proof #1080.
% 199.49/32.87  | | | | | 
% 199.49/32.87  | | | | End of split
% 199.49/32.87  | | | | 
% 199.49/32.87  | | | End of split
% 199.49/32.87  | | | 
% 199.49/32.87  | | End of split
% 199.49/32.87  | | 
% 199.49/32.87  | Case 2:
% 199.49/32.87  | | 
% 199.49/32.87  | |   (127)   ~ (all_58_2 = e3)
% 199.49/32.87  | | 
% 199.49/32.87  | | REDUCE: (33), (127) imply:
% 199.49/32.87  | |   (128)   ~ (all_52_3 = e3)
% 199.49/32.87  | | 
% 199.49/32.87  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (12), (14), (15), (20), (22),
% 199.49/32.87  | |            (23), (30), (33), (34), (35), (36), (37), (38), (40), (42), (43),
% 199.49/32.87  | |            (45), (46), (47), (50), (51), (54), (55), (56), (57), (58), (59),
% 199.49/32.87  | |            (60), (62), (63), (65), (66), (67), (69), (70), (71), (72), (74),
% 199.49/32.87  | |            (77), (128) are inconsistent by sub-proof #83.
% 199.49/32.87  | | 
% 199.49/32.87  | End of split
% 199.49/32.87  | 
% 199.49/32.87  End of proof
% 199.49/32.87  
% 199.49/32.87  Sub-proof #83 shows that the following formulas are inconsistent:
% 199.49/32.87  ----------------------------------------------------------------
% 199.49/32.87    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.87    (2)  all_58_14 = all_52_23
% 199.49/32.87    (3)   ~ (e3 = e1)
% 199.49/32.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.87    (5)   ~ (e3 = e0)
% 199.49/32.87    (6)  op(all_52_23, all_52_23) = e0
% 199.49/32.87    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.87    (8)   ~ (all_52_7 = all_52_15)
% 199.49/32.87    (9)  all_58_0 = all_6_2
% 199.49/32.87    (10)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.87    (11)  all_58_13 = all_52_15
% 199.49/32.87    (12)   ~ (all_52_3 = e3)
% 199.49/32.87    (13)   ~ (all_52_7 = all_6_2)
% 199.49/32.87    (14)   ~ (all_4_0 = e3)
% 199.49/32.87    (15)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.87    (16)  all_58_12 = all_52_7
% 199.49/32.87    (17)   ~ (all_52_7 = e3)
% 199.49/32.87    (18)  all_58_2 = all_52_3
% 199.49/32.87    (19)  all_56_2 = all_52_17
% 199.49/32.87    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.87    (21)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.87    (22)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.87    (23)  op(e0, e3) = all_52_7
% 199.49/32.88    (24)  all_58_15 = all_14_2
% 199.49/32.88    (25)  all_58_8 = all_10_2
% 199.49/32.88    (26)   ~ (all_52_5 = all_10_2)
% 199.49/32.88    (27)  all_56_12 = all_52_7
% 199.49/32.88    (28)  all_58_5 = all_4_0
% 199.49/32.88    (29)  all_8_2 = all_6_2
% 199.49/32.88    (30)  op(e3, all_6_1) = e2
% 199.49/32.88    (31)  op(e3, e3) = all_6_2
% 199.49/32.88    (32)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.88    (33)  op(all_52_17, all_52_17) = e3
% 199.49/32.88    (34)  all_58_6 = all_52_5
% 199.49/32.88    (35)  op(e3, e2) = all_52_9
% 199.49/32.88    (36)   ~ (all_52_17 = all_6_2)
% 199.49/32.88    (37)   ~ (e1 = e0)
% 199.49/32.88    (38)   ~ (e3 = e2)
% 199.49/32.88    (39)   ~ (all_52_9 = all_52_17)
% 199.49/32.88    (40)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.88    (41)  op(e1, e1) = all_10_2
% 199.49/32.88    (42)   ~ (all_52_23 = all_10_2)
% 199.49/32.88    (43)   ~ (all_52_7 = all_52_23)
% 199.49/32.88    (44)   ~ (all_52_17 = all_52_23)
% 199.49/32.88    (45)  all_8_1 = all_6_1
% 199.49/32.88    (46)  op(all_6_2, e3) = all_6_1
% 199.49/32.88    (47)  all_58_4 = all_52_17
% 199.49/32.88  
% 199.49/32.88  Begin of proof
% 199.49/32.88  | 
% 199.49/32.88  | BETA: splitting (20) gives:
% 199.49/32.88  | 
% 199.49/32.88  | Case 1:
% 199.49/32.88  | | 
% 199.49/32.88  | |   (48)  all_58_0 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | COMBINE_EQS: (9), (48) imply:
% 199.49/32.88  | |   (49)  all_6_2 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | REF_CLOSE: (4), (30), (31), (38), (46), (49) are inconsistent by sub-proof
% 199.49/32.88  | |            #502.
% 199.49/32.88  | | 
% 199.49/32.88  | Case 2:
% 199.49/32.88  | | 
% 199.49/32.88  | |   (50)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | BETA: splitting (50) gives:
% 199.49/32.88  | | 
% 199.49/32.88  | | Case 1:
% 199.49/32.88  | | | 
% 199.49/32.88  | | |   (51)  all_58_2 = e3
% 199.49/32.88  | | | 
% 199.49/32.88  | | | REF_CLOSE: (12), (18), (51) are inconsistent by sub-proof #1369.
% 199.49/32.88  | | | 
% 199.49/32.88  | | Case 2:
% 199.49/32.88  | | | 
% 199.49/32.88  | | |   (52)  all_58_6 = e3 | all_58_12 = e3
% 199.49/32.88  | | | 
% 199.49/32.88  | | | BETA: splitting (52) gives:
% 199.49/32.88  | | | 
% 199.49/32.88  | | | Case 1:
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | |   (53)  all_58_6 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | COMBINE_EQS: (34), (53) imply:
% 199.49/32.88  | | | |   (54)  all_52_5 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | SIMP: (54) implies:
% 199.49/32.88  | | | |   (55)  all_52_5 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | REDUCE: (26), (55) imply:
% 199.49/32.88  | | | |   (56)   ~ (all_10_2 = e3)
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | SIMP: (56) implies:
% 199.49/32.88  | | | |   (57)   ~ (all_10_2 = e3)
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | REDUCE: (10), (55) imply:
% 199.49/32.88  | | | |   (58)  op(e3, e3) = all_52_4
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (13), (14),
% 199.49/32.88  | | | |            (15), (16), (19), (21), (22), (23), (24), (25), (27), (28),
% 199.49/32.88  | | | |            (29), (30), (31), (32), (33), (35), (36), (37), (39), (40),
% 199.49/32.88  | | | |            (41), (42), (43), (44), (45), (46), (47), (57), (58) are
% 199.49/32.88  | | | |            inconsistent by sub-proof #84.
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | Case 2:
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | |   (59)  all_58_12 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | REF_CLOSE: (16), (17), (59) are inconsistent by sub-proof #1367.
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | End of split
% 199.49/32.88  | | | 
% 199.49/32.88  | | End of split
% 199.49/32.88  | | 
% 199.49/32.88  | End of split
% 199.49/32.88  | 
% 199.49/32.88  End of proof
% 199.49/32.88  
% 199.49/32.88  Sub-proof #84 shows that the following formulas are inconsistent:
% 199.49/32.88  ----------------------------------------------------------------
% 199.49/32.88    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.88    (2)  all_58_14 = all_52_23
% 199.49/32.88    (3)   ~ (e3 = e1)
% 199.49/32.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.88    (5)   ~ (e3 = e0)
% 199.49/32.88    (6)  op(all_52_23, all_52_23) = e0
% 199.49/32.88    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.88    (8)   ~ (all_52_7 = all_52_15)
% 199.49/32.88    (9)  all_58_13 = all_52_15
% 199.49/32.88    (10)   ~ (all_52_7 = all_6_2)
% 199.49/32.88    (11)   ~ (all_4_0 = e3)
% 199.49/32.88    (12)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.88    (13)  all_58_12 = all_52_7
% 199.49/32.88    (14)  all_56_2 = all_52_17
% 199.49/32.88    (15)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.88    (16)   ~ (all_10_2 = e3)
% 199.49/32.88    (17)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.88    (18)  op(e0, e3) = all_52_7
% 199.49/32.88    (19)  all_58_15 = all_14_2
% 199.49/32.88    (20)  all_58_8 = all_10_2
% 199.49/32.88    (21)  all_56_12 = all_52_7
% 199.49/32.88    (22)  op(e3, e3) = all_52_4
% 199.49/32.88    (23)  all_58_5 = all_4_0
% 199.49/32.88    (24)  all_8_2 = all_6_2
% 199.49/32.88    (25)  op(e3, all_6_1) = e2
% 199.49/32.88    (26)  op(e3, e3) = all_6_2
% 199.49/32.88    (27)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.88    (28)  op(all_52_17, all_52_17) = e3
% 199.49/32.88    (29)  op(e3, e2) = all_52_9
% 199.49/32.88    (30)   ~ (all_52_17 = all_6_2)
% 199.49/32.88    (31)   ~ (e1 = e0)
% 199.49/32.88    (32)   ~ (all_52_9 = all_52_17)
% 199.49/32.88    (33)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.88    (34)  op(e1, e1) = all_10_2
% 199.49/32.88    (35)   ~ (all_52_23 = all_10_2)
% 199.49/32.88    (36)   ~ (all_52_7 = all_52_23)
% 199.49/32.88    (37)   ~ (all_52_17 = all_52_23)
% 199.49/32.88    (38)  all_8_1 = all_6_1
% 199.49/32.88    (39)  op(all_6_2, e3) = all_6_1
% 199.49/32.88    (40)  all_58_4 = all_52_17
% 199.49/32.88  
% 199.49/32.88  Begin of proof
% 199.49/32.88  | 
% 199.49/32.88  | GROUND_INST: instantiating (4) with all_6_2, all_52_4, e3, e3, simplifying
% 199.49/32.88  |              with (22), (26) gives:
% 199.49/32.88  |   (41)  all_52_4 = all_6_2
% 199.49/32.88  | 
% 199.49/32.88  | BETA: splitting (33) gives:
% 199.49/32.88  | 
% 199.49/32.88  | Case 1:
% 199.49/32.88  | | 
% 199.49/32.88  | |   (42)  all_58_4 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | COMBINE_EQS: (40), (42) imply:
% 199.49/32.88  | |   (43)  all_52_17 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | SIMP: (43) implies:
% 199.49/32.88  | |   (44)  all_52_17 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | REF_CLOSE: (4), (26), (28), (30), (44) are inconsistent by sub-proof #1280.
% 199.49/32.88  | | 
% 199.49/32.88  | Case 2:
% 199.49/32.88  | | 
% 199.49/32.88  | |   (45)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.49/32.88  | | 
% 199.49/32.88  | | BETA: splitting (45) gives:
% 199.49/32.88  | | 
% 199.49/32.88  | | Case 1:
% 199.49/32.88  | | | 
% 199.49/32.88  | | |   (46)  all_58_5 = e3
% 199.49/32.88  | | | 
% 199.49/32.88  | | | REF_CLOSE: (11), (23), (46) are inconsistent by sub-proof #215.
% 199.49/32.88  | | | 
% 199.49/32.88  | | Case 2:
% 199.49/32.88  | | | 
% 199.49/32.88  | | |   (47)  all_58_8 = e3 | all_58_14 = e3
% 199.49/32.88  | | | 
% 199.49/32.88  | | | BETA: splitting (47) gives:
% 199.49/32.88  | | | 
% 199.49/32.88  | | | Case 1:
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | |   (48)  all_58_8 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | COMBINE_EQS: (20), (48) imply:
% 199.49/32.88  | | | |   (49)  all_10_2 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | REDUCE: (16), (49) imply:
% 199.49/32.88  | | | |   (50)  $false
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | CLOSE: (50) is inconsistent.
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | Case 2:
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | |   (51)  all_58_14 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | COMBINE_EQS: (2), (51) imply:
% 199.49/32.88  | | | |   (52)  all_52_23 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | SIMP: (52) implies:
% 199.49/32.88  | | | |   (53)  all_52_23 = e3
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 199.49/32.88  | | | |            (14), (15), (17), (18), (19), (21), (24), (25), (26), (27),
% 199.49/32.88  | | | |            (28), (29), (30), (31), (32), (34), (35), (36), (37), (38),
% 199.49/32.88  | | | |            (39), (51), (53) are inconsistent by sub-proof #85.
% 199.49/32.88  | | | | 
% 199.49/32.88  | | | End of split
% 199.49/32.88  | | | 
% 199.49/32.88  | | End of split
% 199.49/32.88  | | 
% 199.49/32.88  | End of split
% 199.49/32.88  | 
% 199.49/32.88  End of proof
% 199.49/32.88  
% 199.49/32.88  Sub-proof #85 shows that the following formulas are inconsistent:
% 199.49/32.88  ----------------------------------------------------------------
% 199.49/32.88    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.88    (2)   ~ (e3 = e1)
% 199.49/32.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.88    (4)   ~ (e3 = e0)
% 199.49/32.88    (5)  op(all_52_23, all_52_23) = e0
% 199.49/32.88    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.88    (7)   ~ (all_52_7 = all_52_15)
% 199.49/32.88    (8)  all_58_13 = all_52_15
% 199.49/32.88    (9)   ~ (all_52_7 = all_6_2)
% 199.49/32.88    (10)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.49/32.88    (11)  all_58_12 = all_52_7
% 199.49/32.88    (12)  all_56_2 = all_52_17
% 199.49/32.88    (13)  all_52_23 = e3
% 199.49/32.88    (14)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.49/32.88    (15)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.49/32.88    (16)  op(e0, e3) = all_52_7
% 199.49/32.88    (17)  all_58_15 = all_14_2
% 199.49/32.88    (18)  all_56_12 = all_52_7
% 199.49/32.88    (19)  all_8_2 = all_6_2
% 199.49/32.88    (20)  op(e3, all_6_1) = e2
% 199.49/32.88    (21)  op(e3, e3) = all_6_2
% 199.49/32.88    (22)  op(all_14_2, all_14_2) = all_52_30
% 199.49/32.88    (23)  op(all_52_17, all_52_17) = e3
% 199.49/32.88    (24)  op(e3, e2) = all_52_9
% 199.49/32.88    (25)   ~ (all_52_17 = all_6_2)
% 199.49/32.88    (26)   ~ (e1 = e0)
% 199.49/32.88    (27)   ~ (all_52_9 = all_52_17)
% 199.49/32.88    (28)  op(e1, e1) = all_10_2
% 199.49/32.88    (29)  all_58_14 = e3
% 199.49/32.88    (30)   ~ (all_52_23 = all_10_2)
% 199.49/32.88    (31)   ~ (all_52_7 = all_52_23)
% 199.49/32.88    (32)   ~ (all_52_17 = all_52_23)
% 199.49/32.88    (33)  all_8_1 = all_6_1
% 199.49/32.88    (34)  op(all_6_2, e3) = all_6_1
% 199.49/32.88  
% 199.49/32.88  Begin of proof
% 199.49/32.88  | 
% 199.49/32.88  | REDUCE: (13), (31) imply:
% 199.49/32.88  |   (35)   ~ (all_52_7 = e3)
% 199.49/32.88  | 
% 199.49/32.88  | REDUCE: (13), (32) imply:
% 199.49/32.88  |   (36)   ~ (all_52_17 = e3)
% 199.49/32.88  | 
% 199.49/32.88  | REDUCE: (13), (30) imply:
% 199.49/32.88  |   (37)   ~ (all_10_2 = e3)
% 199.49/32.88  | 
% 199.49/32.88  | SIMP: (37) implies:
% 199.49/32.88  |   (38)   ~ (all_10_2 = e3)
% 199.49/32.88  | 
% 199.49/32.88  | REDUCE: (5), (13) imply:
% 199.49/32.88  |   (39)  op(e3, e3) = e0
% 199.49/32.88  | 
% 199.49/32.88  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 199.49/32.88  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.49/32.88  |            (26), (27), (28), (29), (33), (34), (35), (36), (38), (39) are
% 199.49/32.88  |            inconsistent by sub-proof #438.
% 199.49/32.88  | 
% 199.49/32.88  End of proof
% 199.49/32.88  
% 199.49/32.88  Sub-proof #86 shows that the following formulas are inconsistent:
% 199.49/32.88  ----------------------------------------------------------------
% 199.49/32.88    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.49/32.88    (2)   ~ (all_52_25 = all_52_27)
% 199.49/32.88    (3)  all_58_14 = all_52_23
% 199.49/32.88    (4)   ~ (all_52_17 = all_4_0)
% 199.49/32.88    (5)  op(all_52_3, all_52_3) = all_52_2
% 199.49/32.88    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.49/32.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.49/32.88    (7)   ~ (all_52_5 = all_52_13)
% 199.49/32.88    (8)  all_58_1 = all_52_9
% 199.49/32.88    (9)   ~ (e3 = e0)
% 199.49/32.88    (10)  op(e2, e3) = all_52_3
% 199.49/32.88    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.49/32.88    (12)   ~ (all_52_7 = all_52_15)
% 199.49/32.88    (13)  op(all_52_7, all_52_7) = all_52_6
% 199.49/32.88    (14)   ~ (all_52_17 = all_52_25)
% 199.49/32.88    (15)   ~ (all_52_3 = all_6_2)
% 199.49/32.88    (16)  all_44_2 = all_6_2
% 199.49/32.88    (17)  all_58_0 = all_6_2
% 199.49/32.88    (18)  op(all_14_2, e0) = all_14_1
% 199.49/32.88    (19)  all_56_4 = all_52_3
% 199.49/32.88    (20)   ~ (all_52_17 = all_10_2)
% 199.49/32.88    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.49/32.88    (22)  op(e3, e0) = all_52_25
% 199.49/32.88    (23)  op(all_52_5, all_52_5) = all_52_4
% 199.49/32.88    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.49/32.88    (25)   ~ (all_52_27 = all_52_29)
% 199.49/32.88    (26)  all_58_13 = all_52_15
% 199.49/32.88    (27)  all_58_9 = all_52_25
% 199.49/32.88    (28)   ~ (all_52_29 = all_14_2)
% 199.49/32.88    (29)  op(e1, e3) = all_52_5
% 199.49/32.88    (30)  op(e2, e2) = all_4_2
% 199.49/32.88    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.49/32.88    (32)   ~ (all_52_3 = all_52_5)
% 199.49/32.88    (33)  op(all_4_2, e2) = e1
% 199.49/32.88    (34)  all_58_11 = all_52_29
% 199.49/32.88    (35)   ~ (all_52_25 = all_14_2)
% 199.49/32.88    (36)   ~ (all_52_7 = all_6_2)
% 199.49/32.88    (37)  all_56_15 = all_14_2
% 199.69/32.88    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.88    (39)  all_56_11 = all_52_29
% 199.69/32.88    (40)   ~ (all_4_0 = e3)
% 199.69/32.88    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.88    (42)  all_56_9 = all_52_13
% 199.69/32.88    (43)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 199.69/32.88    (44)  all_58_10 = all_52_27
% 199.69/32.88    (45)  all_56_8 = all_52_5
% 199.69/32.88    (46)  op(all_52_9, all_52_9) = all_52_8
% 199.69/32.88    (47)  op(all_52_15, all_52_15) = all_52_14
% 199.69/32.88    (48)   ~ (all_52_29 = all_10_2)
% 199.69/32.88    (49)  all_58_7 = all_52_13
% 199.69/32.88    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.88    (51)   ~ (all_52_5 = all_52_7)
% 199.69/32.88    (52)  all_58_12 = all_52_7
% 199.69/32.88    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.88    (54)   ~ (all_52_7 = all_14_2)
% 199.69/32.88    (55)   ~ (all_14_2 = e0)
% 199.69/32.88    (56)  all_58_2 = all_52_3
% 199.69/32.88    (57)  all_56_2 = all_52_17
% 199.69/32.88    (58)  all_56_7 = all_52_27
% 199.69/32.88    (59)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.88    (60)   ~ (e2 = e0)
% 199.69/32.88    (61)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.69/32.88    (62)   ~ (all_52_13 = all_4_2)
% 199.69/32.88    (63)  op(e3, e1) = all_52_17
% 199.69/32.88    (64)  op(e0, e3) = all_52_7
% 199.69/32.88    (65)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.88    (66)   ~ (all_52_9 = all_52_25)
% 199.69/32.88    (67)  all_58_15 = all_14_2
% 199.69/32.88    (68)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.88    (69)  all_58_8 = all_10_2
% 199.69/32.88    (70)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.69/32.88    (71)  all_56_12 = all_52_7
% 199.69/32.88    (72)  op(all_52_17, all_52_17) = all_52_16
% 199.69/32.88    (73)  all_58_5 = all_4_0
% 199.69/32.88    (74)  all_8_2 = all_6_2
% 199.69/32.88    (75)   ~ (all_52_25 = all_6_2)
% 199.69/32.88    (76)   ~ (all_52_9 = all_4_2)
% 199.69/32.88    (77)   ~ (all_52_5 = all_6_2)
% 199.69/32.88    (78)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.88    (79)   ~ (all_52_9 = all_6_2)
% 199.69/32.88    (80)  op(e3, all_6_1) = e2
% 199.69/32.88    (81)  op(e3, e3) = all_6_2
% 199.69/32.88    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.69/32.88    (83)   ~ (all_52_27 = all_14_2)
% 199.69/32.88    (84)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.88    (85)  op(all_4_2, all_4_2) = all_52_10
% 199.69/32.88    (86)   ~ (all_52_3 = all_52_7)
% 199.69/32.88    (87)  op(all_14_2, all_14_2) = all_52_30
% 199.69/32.88    (88)   ~ (all_52_15 = all_4_2)
% 199.69/32.88    (89)  all_58_6 = all_52_5
% 199.69/32.88    (90)  op(e3, e2) = all_52_9
% 199.69/32.88    (91)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.88    (92)   ~ (all_52_17 = all_6_2)
% 199.69/32.88    (93)   ~ (e1 = e0)
% 199.69/32.88    (94)   ~ (e3 = e2)
% 199.69/32.88    (95)  all_44_1 = all_6_1
% 199.69/32.88    (96)   ~ (all_52_9 = all_52_17)
% 199.69/32.88    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.88    (98)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.69/32.88    (99)  op(all_52_13, all_52_13) = all_52_12
% 199.69/32.88    (100)  op(e1, e1) = all_10_2
% 199.69/32.88    (101)  all_58_3 = all_4_2
% 199.69/32.88    (102)   ~ (all_52_3 = all_4_2)
% 199.69/32.88    (103)   ~ (all_52_17 = all_52_23)
% 199.69/32.88    (104)  all_8_1 = all_6_1
% 199.69/32.88    (105)  op(all_6_2, e3) = all_6_1
% 199.69/32.88    (106)  all_58_4 = all_52_17
% 199.69/32.88    (107)  op(all_52_25, all_52_25) = all_52_24
% 199.69/32.88  
% 199.69/32.88  Begin of proof
% 199.69/32.88  | 
% 199.69/32.88  | ALPHA: (43) implies:
% 199.69/32.88  |   (108)  all_52_14 = e0
% 199.69/32.88  |   (109)  all_52_12 = e1
% 199.69/32.88  |   (110)  all_52_10 = e2
% 199.69/32.88  |   (111)  all_52_8 = e3
% 199.69/32.88  | 
% 199.69/32.88  | REDUCE: (46), (111) imply:
% 199.69/32.88  |   (112)  op(all_52_9, all_52_9) = e3
% 199.69/32.88  | 
% 199.69/32.88  | REDUCE: (99), (109) imply:
% 199.69/32.88  |   (113)  op(all_52_13, all_52_13) = e1
% 199.69/32.88  | 
% 199.69/32.88  | REDUCE: (47), (108) imply:
% 199.69/32.88  |   (114)  op(all_52_15, all_52_15) = e0
% 199.69/32.88  | 
% 199.69/32.88  | REDUCE: (85), (110) imply:
% 199.69/32.88  |   (115)  op(all_4_2, all_4_2) = e2
% 199.69/32.88  | 
% 199.69/32.88  | BETA: splitting (70) gives:
% 199.69/32.88  | 
% 199.69/32.88  | Case 1:
% 199.69/32.88  | | 
% 199.69/32.88  | |   (116)  all_56_15 = e3
% 199.69/32.88  | | 
% 199.69/32.88  | | COMBINE_EQS: (37), (116) imply:
% 199.69/32.88  | |   (117)  all_14_2 = e3
% 199.69/32.88  | | 
% 199.69/32.88  | | SIMP: (117) implies:
% 199.69/32.88  | |   (118)  all_14_2 = e3
% 199.69/32.88  | | 
% 199.69/32.88  | | REDUCE: (35), (118) imply:
% 199.69/32.88  | |   (119)   ~ (all_52_25 = e3)
% 199.69/32.88  | | 
% 199.69/32.88  | | REDUCE: (83), (118) imply:
% 199.69/32.88  | |   (120)   ~ (all_52_27 = e3)
% 199.69/32.88  | | 
% 199.69/32.88  | | REDUCE: (28), (118) imply:
% 199.69/32.88  | |   (121)   ~ (all_52_29 = e3)
% 199.69/32.88  | | 
% 199.69/32.88  | | REDUCE: (87), (118) imply:
% 199.69/32.88  | |   (122)  op(e3, e3) = all_52_30
% 199.69/32.88  | | 
% 199.69/32.88  | | REDUCE: (18), (118) imply:
% 199.69/32.88  | |   (123)  op(e3, e0) = all_14_1
% 199.69/32.88  | | 
% 199.69/32.88  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 199.69/32.88  | |              with (22), (123) gives:
% 199.69/32.88  | |   (124)  all_52_25 = all_14_1
% 199.69/32.88  | | 
% 199.69/32.88  | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3, simplifying
% 199.69/32.88  | |              with (81), (122) gives:
% 199.69/32.88  | |   (125)  all_52_30 = all_6_2
% 199.69/32.88  | | 
% 199.69/32.88  | | REDUCE: (75), (124) imply:
% 199.69/32.88  | |   (126)   ~ (all_14_1 = all_6_2)
% 199.69/32.88  | | 
% 199.69/32.88  | | BETA: splitting (38) gives:
% 199.69/32.88  | | 
% 199.69/32.88  | | Case 1:
% 199.69/32.88  | | | 
% 199.69/32.88  | | |   (127)  all_58_2 = e3
% 199.69/32.88  | | | 
% 199.69/32.88  | | | COMBINE_EQS: (56), (127) imply:
% 199.69/32.88  | | |   (128)  all_52_3 = e3
% 199.69/32.88  | | | 
% 199.69/32.88  | | | SIMP: (128) implies:
% 199.69/32.88  | | |   (129)  all_52_3 = e3
% 199.69/32.88  | | | 
% 199.69/32.88  | | | REDUCE: (32), (129) imply:
% 199.69/32.88  | | |   (130)   ~ (all_52_5 = e3)
% 199.69/32.88  | | | 
% 199.69/32.88  | | | SIMP: (130) implies:
% 199.69/32.88  | | |   (131)   ~ (all_52_5 = e3)
% 199.69/32.88  | | | 
% 199.69/32.88  | | | REDUCE: (15), (129) imply:
% 199.69/32.88  | | |   (132)   ~ (all_6_2 = e3)
% 199.69/32.88  | | | 
% 199.69/32.88  | | | SIMP: (132) implies:
% 199.69/32.88  | | |   (133)   ~ (all_6_2 = e3)
% 199.69/32.88  | | | 
% 199.69/32.88  | | | REDUCE: (5), (129) imply:
% 199.69/32.88  | | |   (134)  op(e3, e3) = all_52_2
% 199.69/32.88  | | | 
% 199.69/32.88  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3, simplifying
% 199.69/32.88  | | |              with (81), (134) gives:
% 199.69/32.88  | | |   (135)  all_52_2 = all_6_2
% 199.69/32.88  | | | 
% 199.69/32.88  | | | BETA: splitting (97) gives:
% 199.69/32.88  | | | 
% 199.69/32.88  | | | Case 1:
% 199.69/32.88  | | | | 
% 199.69/32.88  | | | |   (136)  all_58_4 = e3
% 199.69/32.88  | | | | 
% 199.69/32.88  | | | | COMBINE_EQS: (106), (136) imply:
% 199.69/32.88  | | | |   (137)  all_52_17 = e3
% 199.69/32.88  | | | | 
% 199.69/32.88  | | | | SIMP: (137) implies:
% 199.69/32.88  | | | |   (138)  all_52_17 = e3
% 199.69/32.88  | | | | 
% 199.69/32.88  | | | | REDUCE: (72), (138) imply:
% 199.69/32.88  | | | |   (139)  op(e3, e3) = all_52_16
% 199.69/32.88  | | | | 
% 199.69/32.88  | | | | BETA: splitting (53) gives:
% 199.69/32.88  | | | | 
% 199.69/32.88  | | | | Case 1:
% 199.69/32.88  | | | | | 
% 199.69/32.88  | | | | |   (140)  all_58_6 = e3
% 199.69/32.88  | | | | | 
% 199.69/32.88  | | | | | REF_CLOSE: (89), (131), (140) are inconsistent by sub-proof #1328.
% 199.69/32.88  | | | | | 
% 199.69/32.88  | | | | Case 2:
% 199.69/32.88  | | | | | 
% 199.69/32.88  | | | | |   (141)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.88  | | | | | 
% 199.69/32.88  | | | | | BETA: splitting (141) gives:
% 199.69/32.88  | | | | | 
% 199.69/32.88  | | | | | Case 1:
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | |   (142)  all_58_7 = e3
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | COMBINE_EQS: (49), (142) imply:
% 199.69/32.88  | | | | | |   (143)  all_52_13 = e3
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | REDUCE: (62), (143) imply:
% 199.69/32.88  | | | | | |   (144)   ~ (all_4_2 = e3)
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | SIMP: (144) implies:
% 199.69/32.88  | | | | | |   (145)   ~ (all_4_2 = e3)
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | REDUCE: (113), (143) imply:
% 199.69/32.88  | | | | | |   (146)  op(e3, e3) = e1
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_16, e3, e3,
% 199.69/32.88  | | | | | |              simplifying with (81), (139) gives:
% 199.69/32.88  | | | | | |   (147)  all_52_16 = all_6_2
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | GROUND_INST: instantiating (6) with e1, all_52_16, e3, e3,
% 199.69/32.88  | | | | | |              simplifying with (139), (146) gives:
% 199.69/32.88  | | | | | |   (148)  all_52_16 = e1
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | COMBINE_EQS: (147), (148) imply:
% 199.69/32.88  | | | | | |   (149)  all_6_2 = e1
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | COMBINE_EQS: (16), (149) imply:
% 199.69/32.88  | | | | | |   (150)  all_44_2 = e1
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | COMBINE_EQS: (17), (149) imply:
% 199.69/32.88  | | | | | |   (151)  all_58_0 = e1
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | REDUCE: (77), (149) imply:
% 199.69/32.88  | | | | | |   (152)   ~ (all_52_5 = e1)
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | REDUCE: (105), (149) imply:
% 199.69/32.88  | | | | | |   (153)  op(e1, e3) = all_6_1
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | BETA: splitting (21) gives:
% 199.69/32.88  | | | | | | 
% 199.69/32.88  | | | | | | Case 1:
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | |   (154)   ~ (all_44_2 = e1)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | REDUCE: (150), (154) imply:
% 199.69/32.88  | | | | | | |   (155)  $false
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | CLOSE: (155) is inconsistent.
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | Case 2:
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | |   (156)   ~ (all_44_1 = e0)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | REDUCE: (95), (156) imply:
% 199.69/32.88  | | | | | | |   (157)   ~ (all_6_1 = e0)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 199.69/32.88  | | | | | | |              simplifying with (29), (153) gives:
% 199.69/32.88  | | | | | | |   (158)  all_52_5 = all_6_1
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | COMBINE_EQS: (45), (158) imply:
% 199.69/32.88  | | | | | | |   (159)  all_56_8 = all_6_1
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | COMBINE_EQS: (89), (158) imply:
% 199.69/32.88  | | | | | | |   (160)  all_58_6 = all_6_1
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | REDUCE: (51), (158) imply:
% 199.69/32.88  | | | | | | |   (161)   ~ (all_52_7 = all_6_1)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | SIMP: (161) implies:
% 199.69/32.88  | | | | | | |   (162)   ~ (all_52_7 = all_6_1)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | REDUCE: (131), (158) imply:
% 199.69/32.88  | | | | | | |   (163)   ~ (all_6_1 = e3)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | REDUCE: (152), (158) imply:
% 199.69/32.88  | | | | | | |   (164)   ~ (all_6_1 = e1)
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | REDUCE: (23), (158) imply:
% 199.69/32.88  | | | | | | |   (165)  op(all_6_1, all_6_1) = all_52_4
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | BETA: splitting (31) gives:
% 199.69/32.88  | | | | | | | 
% 199.69/32.88  | | | | | | | Case 1:
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | |   (166)  all_58_0 = e0
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | | COMBINE_EQS: (151), (166) imply:
% 199.69/32.88  | | | | | | | |   (167)  e1 = e0
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | | REDUCE: (93), (167) imply:
% 199.69/32.88  | | | | | | | |   (168)  $false
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | | CLOSE: (168) is inconsistent.
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | Case 2:
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | |   (169)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | | BETA: splitting (68) gives:
% 199.69/32.88  | | | | | | | | 
% 199.69/32.88  | | | | | | | | Case 1:
% 199.69/32.88  | | | | | | | | | 
% 199.69/32.88  | | | | | | | | |   (170)  all_56_8 = e3
% 199.69/32.88  | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | REF_CLOSE: (159), (163), (170) are inconsistent by sub-proof
% 199.69/32.88  | | | | | | | | |            #1101.
% 199.69/32.88  | | | | | | | | | 
% 199.69/32.88  | | | | | | | | Case 2:
% 199.69/32.88  | | | | | | | | | 
% 199.69/32.88  | | | | | | | | |   (171)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.88  | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | BETA: splitting (171) gives:
% 199.69/32.88  | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | Case 1:
% 199.69/32.88  | | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | |   (172)  all_56_8 = e2
% 199.69/32.88  | | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | | COMBINE_EQS: (159), (172) imply:
% 199.69/32.88  | | | | | | | | | |   (173)  all_6_1 = e2
% 199.69/32.88  | | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | | SIMP: (173) implies:
% 199.69/32.88  | | | | | | | | | |   (174)  all_6_1 = e2
% 199.69/32.88  | | | | | | | | | | 
% 199.69/32.88  | | | | | | | | | | COMBINE_EQS: (160), (174) imply:
% 199.69/32.89  | | | | | | | | | |   (175)  all_58_6 = e2
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | REDUCE: (162), (174) imply:
% 199.69/32.89  | | | | | | | | | |   (176)   ~ (all_52_7 = e2)
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | REDUCE: (165), (174) imply:
% 199.69/32.89  | | | | | | | | | |   (177)  op(e2, e2) = all_52_4
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | REDUCE: (80), (174) imply:
% 199.69/32.89  | | | | | | | | | |   (178)  op(e3, e2) = e2
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | BETA: splitting (11) gives:
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | Case 1:
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | |   (179)  all_56_12 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | COMBINE_EQS: (71), (179) imply:
% 199.69/32.89  | | | | | | | | | | |   (180)  all_52_7 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | SIMP: (180) implies:
% 199.69/32.89  | | | | | | | | | | |   (181)  all_52_7 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | COMBINE_EQS: (52), (181) imply:
% 199.69/32.89  | | | | | | | | | | |   (182)  all_58_12 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | REF_CLOSE: (6), (9), (30), (60), (90), (112), (145), (169),
% 199.69/32.89  | | | | | | | | | | |            (175), (177), (178), (182) are inconsistent by
% 199.69/32.89  | | | | | | | | | | |            sub-proof #460.
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | |   (183)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | BETA: splitting (183) gives:
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | Case 1:
% 199.69/32.89  | | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | |   (184)  all_56_12 = e2
% 199.69/32.89  | | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | | REF_CLOSE: (71), (176), (184) are inconsistent by sub-proof
% 199.69/32.89  | | | | | | | | | | | |            #1178.
% 199.69/32.89  | | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | | REF_CLOSE: (6), (30), (90), (112), (145), (177), (178) are
% 199.69/32.89  | | | | | | | | | | | |            inconsistent by sub-proof #464.
% 199.69/32.89  | | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | |   (185)  all_56_8 = e1 | all_56_8 = e0
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | REF_CLOSE: (157), (159), (164), (185) are inconsistent by
% 199.69/32.89  | | | | | | | | | |            sub-proof #495.
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | End of split
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | End of split
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | Case 2:
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | |   (186)  all_58_8 = e3 | all_58_11 = e3
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | REF_CLOSE: (6), (8), (17), (20), (27), (34), (69), (79), (80), (81),
% 199.69/32.89  | | | | | |            (84), (94), (105), (106), (112), (119), (121), (186) are
% 199.69/32.89  | | | | | |            inconsistent by sub-proof #491.
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | End of split
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | End of split
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | Case 2:
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | |   (187)   ~ (all_58_4 = e3)
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REDUCE: (106), (187) imply:
% 199.69/32.89  | | | |   (188)   ~ (all_52_17 = e3)
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REF_CLOSE: (6), (8), (17), (27), (79), (81), (84), (106), (112), (119),
% 199.69/32.89  | | | |            (133), (188) are inconsistent by sub-proof #254.
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | End of split
% 199.69/32.89  | | | 
% 199.69/32.89  | | Case 2:
% 199.69/32.89  | | | 
% 199.69/32.89  | | |   (189)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.89  | | | 
% 199.69/32.89  | | | BETA: splitting (189) gives:
% 199.69/32.89  | | | 
% 199.69/32.89  | | | Case 1:
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | |   (190)  all_58_3 = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | COMBINE_EQS: (101), (190) imply:
% 199.69/32.89  | | | |   (191)  all_4_2 = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REDUCE: (102), (191) imply:
% 199.69/32.89  | | | |   (192)   ~ (all_52_3 = e3)
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REDUCE: (115), (191) imply:
% 199.69/32.89  | | | |   (193)  op(e3, e3) = e2
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REDUCE: (30), (191) imply:
% 199.69/32.89  | | | |   (194)  op(e2, e2) = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REF_CLOSE: (6), (10), (15), (17), (19), (30), (31), (50), (56), (59),
% 199.69/32.89  | | | |            (60), (63), (78), (80), (81), (92), (105), (123), (126),
% 199.69/32.89  | | | |            (192), (193), (194) are inconsistent by sub-proof #89.
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | Case 2:
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | |   (195)  all_58_5 = e3 | all_58_10 = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REF_CLOSE: (40), (44), (73), (120), (195) are inconsistent by sub-proof
% 199.69/32.89  | | | |            #214.
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | End of split
% 199.69/32.89  | | | 
% 199.69/32.89  | | End of split
% 199.69/32.89  | | 
% 199.69/32.89  | Case 2:
% 199.69/32.89  | | 
% 199.69/32.89  | |   (196)   ~ (all_56_15 = e3)
% 199.69/32.89  | |   (197)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (37), (196) imply:
% 199.69/32.89  | |   (198)   ~ (all_14_2 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 199.69/32.89  | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 199.69/32.89  | |            (25), (26), (27), (29), (30), (31), (33), (34), (36), (37), (38),
% 199.69/32.89  | |            (39), (40), (41), (42), (44), (45), (48), (49), (50), (51), (52),
% 199.69/32.89  | |            (53), (54), (56), (57), (58), (59), (61), (62), (63), (64), (65),
% 199.69/32.89  | |            (66), (67), (68), (69), (71), (72), (73), (74), (75), (76), (77),
% 199.69/32.89  | |            (78), (79), (80), (81), (82), (84), (86), (88), (89), (90), (91),
% 199.69/32.89  | |            (92), (93), (94), (95), (96), (97), (98), (100), (101), (102),
% 199.69/32.89  | |            (103), (104), (105), (106), (107), (112), (113), (114), (115),
% 199.69/32.89  | |            (197), (198) are inconsistent by sub-proof #87.
% 199.69/32.89  | | 
% 199.69/32.89  | End of split
% 199.69/32.89  | 
% 199.69/32.89  End of proof
% 199.69/32.89  
% 199.69/32.89  Sub-proof #87 shows that the following formulas are inconsistent:
% 199.69/32.89  ----------------------------------------------------------------
% 199.69/32.89    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.89    (2)   ~ (all_52_25 = all_52_27)
% 199.69/32.89    (3)  all_58_14 = all_52_23
% 199.69/32.89    (4)   ~ (all_52_17 = all_4_0)
% 199.69/32.89    (5)  op(all_52_3, all_52_3) = all_52_2
% 199.69/32.89    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.89    (7)   ~ (all_52_5 = all_52_13)
% 199.69/32.89    (8)  all_58_1 = all_52_9
% 199.69/32.89    (9)   ~ (e3 = e0)
% 199.69/32.89    (10)  op(e2, e3) = all_52_3
% 199.69/32.89    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.89    (12)   ~ (all_52_7 = all_52_15)
% 199.69/32.89    (13)  op(all_52_15, all_52_15) = e0
% 199.69/32.89    (14)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.89    (15)   ~ (all_52_17 = all_52_25)
% 199.69/32.89    (16)   ~ (all_52_3 = all_6_2)
% 199.69/32.89    (17)  all_44_2 = all_6_2
% 199.69/32.89    (18)  all_58_0 = all_6_2
% 199.69/32.89    (19)  all_56_4 = all_52_3
% 199.69/32.89    (20)   ~ (all_52_17 = all_10_2)
% 199.69/32.89    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.69/32.89    (22)  op(e3, e0) = all_52_25
% 199.69/32.89    (23)  op(all_52_5, all_52_5) = all_52_4
% 199.69/32.89    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 199.69/32.89    (25)   ~ (all_52_27 = all_52_29)
% 199.69/32.89    (26)  all_58_13 = all_52_15
% 199.69/32.89    (27)  op(all_52_13, all_52_13) = e1
% 199.69/32.89    (28)  all_58_9 = all_52_25
% 199.69/32.89    (29)  op(e1, e3) = all_52_5
% 199.69/32.89    (30)  op(e2, e2) = all_4_2
% 199.69/32.89    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.89    (32)  op(all_4_2, e2) = e1
% 199.69/32.89    (33)  all_58_11 = all_52_29
% 199.69/32.89    (34)   ~ (all_52_7 = all_6_2)
% 199.69/32.89    (35)  all_56_15 = all_14_2
% 199.69/32.89    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.89    (37)  all_56_11 = all_52_29
% 199.69/32.89    (38)   ~ (all_4_0 = e3)
% 199.69/32.89    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.89    (40)  all_56_9 = all_52_13
% 199.69/32.89    (41)  all_58_10 = all_52_27
% 199.69/32.89    (42)  all_56_8 = all_52_5
% 199.69/32.89    (43)   ~ (all_52_29 = all_10_2)
% 199.69/32.89    (44)  all_58_7 = all_52_13
% 199.69/32.89    (45)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.89    (46)   ~ (all_52_5 = all_52_7)
% 199.69/32.89    (47)  all_58_12 = all_52_7
% 199.69/32.89    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.89    (49)   ~ (all_52_7 = all_14_2)
% 199.69/32.89    (50)  all_58_2 = all_52_3
% 199.69/32.89    (51)  all_56_2 = all_52_17
% 199.69/32.89    (52)  all_56_7 = all_52_27
% 199.69/32.89    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.89    (54)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.69/32.89    (55)   ~ (all_52_13 = all_4_2)
% 199.69/32.89    (56)  op(e3, e1) = all_52_17
% 199.69/32.89    (57)  op(e0, e3) = all_52_7
% 199.69/32.89    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.89    (59)   ~ (all_52_9 = all_52_25)
% 199.69/32.89    (60)  all_58_15 = all_14_2
% 199.69/32.89    (61)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.89    (62)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.69/32.89    (63)  all_58_8 = all_10_2
% 199.69/32.89    (64)  all_56_12 = all_52_7
% 199.69/32.89    (65)  op(all_52_17, all_52_17) = all_52_16
% 199.69/32.89    (66)  all_58_5 = all_4_0
% 199.69/32.89    (67)  all_8_2 = all_6_2
% 199.69/32.89    (68)   ~ (all_52_25 = all_6_2)
% 199.69/32.89    (69)   ~ (all_52_9 = all_4_2)
% 199.69/32.89    (70)   ~ (all_52_5 = all_6_2)
% 199.69/32.89    (71)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.89    (72)  op(all_4_2, all_4_2) = e2
% 199.69/32.89    (73)   ~ (all_52_9 = all_6_2)
% 199.69/32.89    (74)  op(e3, all_6_1) = e2
% 199.69/32.89    (75)  op(e3, e3) = all_6_2
% 199.69/32.89    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.69/32.89    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.89    (78)   ~ (all_52_3 = all_52_7)
% 199.69/32.89    (79)   ~ (all_52_15 = all_4_2)
% 199.69/32.89    (80)  all_58_6 = all_52_5
% 199.69/32.89    (81)  op(e3, e2) = all_52_9
% 199.69/32.89    (82)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.89    (83)   ~ (all_52_17 = all_6_2)
% 199.69/32.89    (84)   ~ (e1 = e0)
% 199.69/32.89    (85)   ~ (e3 = e2)
% 199.69/32.89    (86)  all_44_1 = all_6_1
% 199.69/32.89    (87)   ~ (all_52_9 = all_52_17)
% 199.69/32.89    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.89    (89)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.69/32.89    (90)  op(e1, e1) = all_10_2
% 199.69/32.89    (91)  op(all_52_9, all_52_9) = e3
% 199.69/32.89    (92)  all_58_3 = all_4_2
% 199.69/32.89    (93)   ~ (all_52_3 = all_4_2)
% 199.69/32.89    (94)   ~ (all_52_17 = all_52_23)
% 199.69/32.89    (95)  all_8_1 = all_6_1
% 199.69/32.89    (96)  op(all_6_2, e3) = all_6_1
% 199.69/32.89    (97)  all_58_4 = all_52_17
% 199.69/32.89    (98)  op(all_52_25, all_52_25) = all_52_24
% 199.69/32.89    (99)   ~ (all_14_2 = e3)
% 199.69/32.89  
% 199.69/32.89  Begin of proof
% 199.69/32.89  | 
% 199.69/32.89  | BETA: splitting (88) gives:
% 199.69/32.89  | 
% 199.69/32.89  | Case 1:
% 199.69/32.89  | | 
% 199.69/32.89  | |   (100)  all_58_4 = e3
% 199.69/32.89  | | 
% 199.69/32.89  | | COMBINE_EQS: (97), (100) imply:
% 199.69/32.89  | |   (101)  all_52_17 = e3
% 199.69/32.89  | | 
% 199.69/32.89  | | SIMP: (101) implies:
% 199.69/32.89  | |   (102)  all_52_17 = e3
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (87), (102) imply:
% 199.69/32.89  | |   (103)   ~ (all_52_9 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (94), (102) imply:
% 199.69/32.89  | |   (104)   ~ (all_52_23 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | SIMP: (104) implies:
% 199.69/32.89  | |   (105)   ~ (all_52_23 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (15), (102) imply:
% 199.69/32.89  | |   (106)   ~ (all_52_25 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | SIMP: (106) implies:
% 199.69/32.89  | |   (107)   ~ (all_52_25 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (4), (102) imply:
% 199.69/32.89  | |   (108)   ~ (all_4_0 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (65), (102) imply:
% 199.69/32.89  | |   (109)  op(e3, e3) = all_52_16
% 199.69/32.89  | | 
% 199.69/32.89  | | GROUND_INST: instantiating (6) with all_6_2, all_52_16, e3, e3, simplifying
% 199.69/32.89  | |              with (75), (109) gives:
% 199.69/32.89  | |   (110)  all_52_16 = all_6_2
% 199.69/32.89  | | 
% 199.69/32.89  | | BETA: splitting (82) gives:
% 199.69/32.89  | | 
% 199.69/32.89  | | Case 1:
% 199.69/32.89  | | | 
% 199.69/32.89  | | |   (111)  all_58_12 = e3
% 199.69/32.89  | | | 
% 199.69/32.89  | | | COMBINE_EQS: (47), (111) imply:
% 199.69/32.89  | | |   (112)  all_52_7 = e3
% 199.69/32.89  | | | 
% 199.69/32.89  | | | SIMP: (112) implies:
% 199.69/32.89  | | |   (113)  all_52_7 = e3
% 199.69/32.89  | | | 
% 199.69/32.89  | | | REDUCE: (78), (113) imply:
% 199.69/32.89  | | |   (114)   ~ (all_52_3 = e3)
% 199.69/32.89  | | | 
% 199.69/32.89  | | | REDUCE: (46), (113) imply:
% 199.69/32.89  | | |   (115)   ~ (all_52_5 = e3)
% 199.69/32.89  | | | 
% 199.69/32.89  | | | REDUCE: (14), (113) imply:
% 199.69/32.89  | | |   (116)  op(e3, e3) = all_52_6
% 199.69/32.89  | | | 
% 199.69/32.89  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 199.69/32.89  | | |              with (75), (116) gives:
% 199.69/32.89  | | |   (117)  all_52_6 = all_6_2
% 199.69/32.89  | | | 
% 199.69/32.89  | | | REF_CLOSE: (6), (8), (9), (17), (18), (20), (21), (23), (25), (26), (27),
% 199.69/32.89  | | |            (28), (29), (30), (31), (32), (33), (36), (37), (38), (41),
% 199.69/32.89  | | |            (42), (43), (44), (48), (50), (54), (55), (58), (61), (63),
% 199.69/32.89  | | |            (66), (70), (71), (73), (74), (75), (77), (79), (80), (81),
% 199.69/32.89  | | |            (84), (85), (86), (90), (91), (92), (96), (97), (103), (107),
% 199.69/32.89  | | |            (109), (111), (114), (115) are inconsistent by sub-proof #99.
% 199.69/32.89  | | | 
% 199.69/32.89  | | Case 2:
% 199.69/32.89  | | | 
% 199.69/32.89  | | |   (118)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.89  | | | 
% 199.69/32.89  | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (26), (30), (34), (35),
% 199.69/32.89  | | |            (49), (57), (60), (62), (64), (67), (74), (75), (79), (81),
% 199.69/32.89  | | |            (91), (95), (96), (99), (105), (118) are inconsistent by
% 199.69/32.89  | | |            sub-proof #88.
% 199.69/32.89  | | | 
% 199.69/32.89  | | End of split
% 199.69/32.89  | | 
% 199.69/32.89  | Case 2:
% 199.69/32.89  | | 
% 199.69/32.89  | |   (119)   ~ (all_58_4 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | REDUCE: (97), (119) imply:
% 199.69/32.89  | |   (120)   ~ (all_52_17 = e3)
% 199.69/32.89  | | 
% 199.69/32.89  | | BETA: splitting (39) gives:
% 199.69/32.89  | | 
% 199.69/32.89  | | Case 1:
% 199.69/32.89  | | | 
% 199.69/32.89  | | |   (121)  all_56_2 = e3
% 199.69/32.89  | | | 
% 199.69/32.89  | | | REF_CLOSE: (51), (120), (121) are inconsistent by sub-proof #1327.
% 199.69/32.89  | | | 
% 199.69/32.89  | | Case 2:
% 199.69/32.89  | | | 
% 199.69/32.89  | | |   (122)   ~ (all_56_2 = e3)
% 199.69/32.89  | | |   (123)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.89  | | | 
% 199.69/32.89  | | | BETA: splitting (24) gives:
% 199.69/32.89  | | | 
% 199.69/32.89  | | | Case 1:
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | |   (124)  all_56_7 = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | COMBINE_EQS: (52), (124) imply:
% 199.69/32.89  | | | |   (125)  all_52_27 = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | SIMP: (125) implies:
% 199.69/32.89  | | | |   (126)  all_52_27 = e3
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REDUCE: (2), (126) imply:
% 199.69/32.89  | | | |   (127)   ~ (all_52_25 = e3)
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REF_CLOSE: (6), (8), (18), (28), (73), (74), (75), (77), (85), (91),
% 199.69/32.89  | | | |            (96), (97), (120), (127) are inconsistent by sub-proof #492.
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | Case 2:
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | |   (128)   ~ (all_56_7 = e3)
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | REDUCE: (52), (128) imply:
% 199.69/32.89  | | | |   (129)   ~ (all_52_27 = e3)
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | BETA: splitting (36) gives:
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | | Case 1:
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | |   (130)  all_58_2 = e3
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | COMBINE_EQS: (50), (130) imply:
% 199.69/32.89  | | | | |   (131)  all_52_3 = e3
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | SIMP: (131) implies:
% 199.69/32.89  | | | | |   (132)  all_52_3 = e3
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | REDUCE: (78), (132) imply:
% 199.69/32.89  | | | | |   (133)   ~ (all_52_7 = e3)
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | SIMP: (133) implies:
% 199.69/32.89  | | | | |   (134)   ~ (all_52_7 = e3)
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | REDUCE: (16), (132) imply:
% 199.69/32.89  | | | | |   (135)   ~ (all_6_2 = e3)
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | SIMP: (135) implies:
% 199.69/32.89  | | | | |   (136)   ~ (all_6_2 = e3)
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | REDUCE: (93), (132) imply:
% 199.69/32.89  | | | | |   (137)   ~ (all_4_2 = e3)
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | SIMP: (137) implies:
% 199.69/32.89  | | | | |   (138)   ~ (all_4_2 = e3)
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | REDUCE: (5), (132) imply:
% 199.69/32.89  | | | | |   (139)  op(e3, e3) = all_52_2
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3,
% 199.69/32.89  | | | | |              simplifying with (75), (139) gives:
% 199.69/32.89  | | | | |   (140)  all_52_2 = all_6_2
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | BETA: splitting (76) gives:
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | Case 1:
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | |   (141)  all_58_9 = e3
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | COMBINE_EQS: (28), (141) imply:
% 199.69/32.89  | | | | | |   (142)  all_52_25 = e3
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | SIMP: (142) implies:
% 199.69/32.89  | | | | | |   (143)  all_52_25 = e3
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | REDUCE: (59), (143) imply:
% 199.69/32.89  | | | | | |   (144)   ~ (all_52_9 = e3)
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | REDUCE: (98), (143) imply:
% 199.69/32.89  | | | | | |   (145)  op(e3, e3) = all_52_24
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 199.69/32.89  | | | | | |              simplifying with (75), (145) gives:
% 199.69/32.89  | | | | | |   (146)  all_52_24 = all_6_2
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | BETA: splitting (58) gives:
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | Case 1:
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | |   (147)  all_58_1 = e3
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | | COMBINE_EQS: (8), (147) imply:
% 199.69/32.89  | | | | | | |   (148)  all_52_9 = e3
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | | REDUCE: (144), (148) imply:
% 199.69/32.89  | | | | | | |   (149)  $false
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | | CLOSE: (149) is inconsistent.
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | Case 2:
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | |   (150)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | | BETA: splitting (11) gives:
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | | Case 1:
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | |   (151)  all_56_12 = e3
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | | REF_CLOSE: (64), (134), (151) are inconsistent by sub-proof
% 199.69/32.89  | | | | | | | |            #1383.
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | |   (152)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | | BETA: splitting (89) gives:
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | | Case 1:
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | |   (153)  all_56_9 = e3
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | COMBINE_EQS: (40), (153) imply:
% 199.69/32.89  | | | | | | | | |   (154)  all_52_13 = e3
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | SIMP: (154) implies:
% 199.69/32.89  | | | | | | | | |   (155)  all_52_13 = e3
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | REDUCE: (7), (155) imply:
% 199.69/32.89  | | | | | | | | |   (156)   ~ (all_52_5 = e3)
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | REDUCE: (27), (155) imply:
% 199.69/32.89  | | | | | | | | |   (157)  op(e3, e3) = e1
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | REF_CLOSE: (6), (17), (21), (23), (29), (30), (42), (46),
% 199.69/32.89  | | | | | | | | |            (61), (64), (70), (74), (75), (81), (86), (91),
% 199.69/32.89  | | | | | | | | |            (96), (138), (145), (152), (156), (157) are
% 199.69/32.89  | | | | | | | | |            inconsistent by sub-proof #457.
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | |   (158)   ~ (all_56_9 = e3)
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | REDUCE: (40), (158) imply:
% 199.69/32.89  | | | | | | | | |   (159)   ~ (all_52_13 = e3)
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | BETA: splitting (150) gives:
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | Case 1:
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | |   (160)  all_58_3 = e3
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | COMBINE_EQS: (92), (160) imply:
% 199.69/32.89  | | | | | | | | | |   (161)  all_4_2 = e3
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | REDUCE: (138), (161) imply:
% 199.69/32.89  | | | | | | | | | |   (162)  $false
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | CLOSE: (162) is inconsistent.
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | |   (163)  all_58_7 = e3 | all_58_13 = e3
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | BETA: splitting (163) gives:
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | Case 1:
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | |   (164)  all_58_7 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | COMBINE_EQS: (44), (164) imply:
% 199.69/32.89  | | | | | | | | | | |   (165)  all_52_13 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | REDUCE: (159), (165) imply:
% 199.69/32.89  | | | | | | | | | | |   (166)  $false
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | Case 2:
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | |   (167)  all_58_13 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | COMBINE_EQS: (26), (167) imply:
% 199.69/32.89  | | | | | | | | | | |   (168)  all_52_15 = e3
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | | REF_CLOSE: (1), (6), (11), (12), (13), (14), (30), (34),
% 199.69/32.89  | | | | | | | | | | |            (35), (49), (57), (62), (64), (67), (74), (75),
% 199.69/32.89  | | | | | | | | | | |            (79), (81), (91), (95), (96), (168) are
% 199.69/32.89  | | | | | | | | | | |            inconsistent by sub-proof #432.
% 199.69/32.89  | | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | | | 
% 199.69/32.89  | | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | | 
% 199.69/32.89  | | | | | | | | End of split
% 199.69/32.89  | | | | | | | | 
% 199.69/32.89  | | | | | | | End of split
% 199.69/32.89  | | | | | | | 
% 199.69/32.89  | | | | | | End of split
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | Case 2:
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | |   (169)   ~ (all_58_9 = e3)
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | REDUCE: (28), (169) imply:
% 199.69/32.89  | | | | | |   (170)   ~ (all_52_25 = e3)
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | | REF_CLOSE: (6), (8), (18), (28), (73), (75), (77), (91), (97),
% 199.69/32.89  | | | | | |            (120), (136), (170) are inconsistent by sub-proof #254.
% 199.69/32.89  | | | | | | 
% 199.69/32.89  | | | | | End of split
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | Case 2:
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | |   (171)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | | REF_CLOSE: (6), (8), (10), (16), (18), (19), (22), (28), (31), (32),
% 199.69/32.89  | | | | |            (38), (41), (45), (50), (51), (53), (56), (66), (68), (69),
% 199.69/32.89  | | | | |            (72), (74), (75), (77), (81), (83), (85), (87), (92), (93),
% 199.69/32.89  | | | | |            (96), (97), (120), (123), (129), (171) are inconsistent by
% 199.69/32.89  | | | | |            sub-proof #94.
% 199.69/32.89  | | | | | 
% 199.69/32.89  | | | | End of split
% 199.69/32.89  | | | | 
% 199.69/32.89  | | | End of split
% 199.69/32.89  | | | 
% 199.69/32.89  | | End of split
% 199.69/32.89  | | 
% 199.69/32.89  | End of split
% 199.69/32.89  | 
% 199.69/32.89  End of proof
% 199.69/32.89  
% 199.69/32.89  Sub-proof #88 shows that the following formulas are inconsistent:
% 199.69/32.89  ----------------------------------------------------------------
% 199.69/32.89    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.89    (2)  all_58_14 = all_52_23
% 199.69/32.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.89    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.89    (5)   ~ (all_52_7 = all_52_15)
% 199.69/32.89    (6)  op(all_52_15, all_52_15) = e0
% 199.69/32.89    (7)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.89    (8)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.89    (9)  all_58_13 = all_52_15
% 199.69/32.89    (10)  op(e2, e2) = all_4_2
% 199.69/32.89    (11)   ~ (all_52_7 = all_6_2)
% 199.69/32.89    (12)  all_56_15 = all_14_2
% 199.69/32.89    (13)   ~ (all_52_7 = all_14_2)
% 199.69/32.89    (14)   ~ (all_52_23 = e3)
% 199.69/32.89    (15)  op(e0, e3) = all_52_7
% 199.69/32.89    (16)  all_58_15 = all_14_2
% 199.69/32.89    (17)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.69/32.89    (18)  all_56_12 = all_52_7
% 199.69/32.89    (19)  all_8_2 = all_6_2
% 199.69/32.89    (20)  op(e3, all_6_1) = e2
% 199.69/32.89    (21)  op(e3, e3) = all_6_2
% 199.69/32.89    (22)   ~ (all_52_15 = all_4_2)
% 199.69/32.89    (23)  op(e3, e2) = all_52_9
% 199.69/32.89    (24)  op(all_52_9, all_52_9) = e3
% 199.69/32.89    (25)  all_8_1 = all_6_1
% 199.69/32.89    (26)  op(all_6_2, e3) = all_6_1
% 199.69/32.89    (27)   ~ (all_14_2 = e3)
% 199.69/32.89  
% 199.69/32.89  Begin of proof
% 199.69/32.89  | 
% 199.69/32.89  | BETA: splitting (8) gives:
% 199.69/32.89  | 
% 199.69/32.89  | Case 1:
% 199.69/32.89  | | 
% 199.69/32.89  | |   (28)  all_58_13 = e3
% 199.69/32.89  | | 
% 199.69/32.89  | | COMBINE_EQS: (9), (28) imply:
% 199.69/32.89  | |   (29)  all_52_15 = e3
% 199.69/32.89  | | 
% 199.69/32.89  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (15), (17),
% 199.69/32.89  | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (29) are
% 199.69/32.89  | |            inconsistent by sub-proof #432.
% 199.69/32.89  | | 
% 199.69/32.89  | Case 2:
% 199.69/32.89  | | 
% 199.69/32.89  | |   (30)  all_58_14 = e3 | all_58_15 = e3
% 199.69/32.89  | | 
% 199.69/32.89  | | REF_CLOSE: (2), (14), (16), (27), (30) are inconsistent by sub-proof #715.
% 199.69/32.89  | | 
% 199.69/32.89  | End of split
% 199.69/32.89  | 
% 199.69/32.89  End of proof
% 199.69/32.89  
% 199.69/32.89  Sub-proof #89 shows that the following formulas are inconsistent:
% 199.69/32.89  ----------------------------------------------------------------
% 199.69/32.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.89    (2)  op(e2, e3) = all_52_3
% 199.69/32.89    (3)   ~ (all_52_3 = all_6_2)
% 199.69/32.89    (4)  all_58_0 = all_6_2
% 199.69/32.89    (5)  all_56_4 = all_52_3
% 199.69/32.90    (6)  op(e2, e2) = all_4_2
% 199.69/32.90    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.90    (8)   ~ (all_52_3 = e3)
% 199.69/32.90    (9)  op(e3, e3) = e2
% 199.69/32.90    (10)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.90    (11)  all_58_2 = all_52_3
% 199.69/32.90    (12)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.90    (13)   ~ (e2 = e0)
% 199.69/32.90    (14)   ~ (all_14_1 = all_6_2)
% 199.69/32.90    (15)  op(e3, e1) = all_52_17
% 199.69/32.90    (16)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.90    (17)  op(e3, all_6_1) = e2
% 199.69/32.90    (18)  op(e3, e3) = all_6_2
% 199.69/32.90    (19)  op(e3, e0) = all_14_1
% 199.69/32.90    (20)  op(e2, e2) = e3
% 199.69/32.90    (21)   ~ (all_52_17 = all_6_2)
% 199.69/32.90    (22)  op(all_6_2, e3) = all_6_1
% 199.69/32.90  
% 199.69/32.90  Begin of proof
% 199.69/32.90  | 
% 199.69/32.90  | BETA: splitting (16) gives:
% 199.69/32.90  | 
% 199.69/32.90  | Case 1:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (23)   ~ (all_4_2 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | REF_CLOSE: (1), (6), (20), (23) are inconsistent by sub-proof #211.
% 199.69/32.90  | | 
% 199.69/32.90  | Case 2:
% 199.69/32.90  | | 
% 199.69/32.90  | | 
% 199.69/32.90  | | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 199.69/32.90  | |              (9), (18) gives:
% 199.69/32.90  | |   (24)  all_6_2 = e2
% 199.69/32.90  | | 
% 199.69/32.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 199.69/32.90  | |            (15), (17), (19), (21), (22), (24) are inconsistent by sub-proof
% 199.69/32.90  | |            #449.
% 199.69/32.90  | | 
% 199.69/32.90  | End of split
% 199.69/32.90  | 
% 199.69/32.90  End of proof
% 199.69/32.90  
% 199.69/32.90  Sub-proof #90 shows that the following formulas are inconsistent:
% 199.69/32.90  ----------------------------------------------------------------
% 199.69/32.90    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.90    (2)   ~ (e3 = e1)
% 199.69/32.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.90    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.90    (5)   ~ (all_52_7 = all_52_15)
% 199.69/32.90    (6)  all_58_13 = all_52_15
% 199.69/32.90    (7)   ~ (all_52_15 = e3)
% 199.69/32.90    (8)   ~ (all_52_7 = all_6_2)
% 199.69/32.90    (9)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.69/32.90    (10)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.90    (11)  op(all_52_15, all_52_15) = all_52_14
% 199.69/32.90    (12)  all_58_12 = all_52_7
% 199.69/32.90    (13)   ~ (all_52_7 = e3)
% 199.69/32.90    (14)  all_56_2 = all_52_17
% 199.69/32.90    (15)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.90    (16)   ~ (all_10_2 = e3)
% 199.69/32.90    (17)  op(e0, e3) = all_52_7
% 199.69/32.90    (18)  all_58_15 = all_14_2
% 199.69/32.90    (19)  all_56_12 = all_52_7
% 199.69/32.90    (20)  all_8_2 = all_6_2
% 199.69/32.90    (21)  op(e3, all_6_1) = e2
% 199.69/32.90    (22)  op(e3, e3) = e0
% 199.69/32.90    (23)  op(e3, e3) = all_6_2
% 199.69/32.90    (24)   ~ (all_52_17 = e3)
% 199.69/32.90    (25)  op(all_14_2, all_14_2) = all_52_30
% 199.69/32.90    (26)  op(all_52_17, all_52_17) = e3
% 199.69/32.90    (27)  op(e3, e2) = all_52_9
% 199.69/32.90    (28)   ~ (all_52_17 = all_6_2)
% 199.69/32.90    (29)   ~ (e1 = e0)
% 199.69/32.90    (30)   ~ (all_52_9 = all_52_17)
% 199.69/32.90    (31)  op(e1, e1) = all_10_2
% 199.69/32.90    (32)  all_58_14 = e3
% 199.69/32.90    (33)  all_56_13 = all_52_15
% 199.69/32.90    (34)  all_8_1 = all_6_1
% 199.69/32.90    (35)  op(all_6_2, e3) = all_6_1
% 199.69/32.90  
% 199.69/32.90  Begin of proof
% 199.69/32.90  | 
% 199.69/32.90  | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying with
% 199.69/32.90  |              (22), (23) gives:
% 199.69/32.90  |   (36)  all_6_2 = e0
% 199.69/32.90  | 
% 199.69/32.90  | COMBINE_EQS: (20), (36) imply:
% 199.69/32.90  |   (37)  all_8_2 = e0
% 199.69/32.90  | 
% 199.69/32.90  | REDUCE: (8), (36) imply:
% 199.69/32.90  |   (38)   ~ (all_52_7 = e0)
% 199.69/32.90  | 
% 199.69/32.90  | REDUCE: (28), (36) imply:
% 199.69/32.90  |   (39)   ~ (all_52_17 = e0)
% 199.69/32.90  | 
% 199.69/32.90  | REDUCE: (35), (36) imply:
% 199.69/32.90  |   (40)  op(e0, e3) = all_6_1
% 199.69/32.90  | 
% 199.69/32.90  | BETA: splitting (1) gives:
% 199.69/32.90  | 
% 199.69/32.90  | Case 1:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (41)   ~ (all_8_1 = e1)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (34), (41) imply:
% 199.69/32.90  | |   (42)   ~ (all_6_1 = e1)
% 199.69/32.90  | | 
% 199.69/32.90  | | GROUND_INST: instantiating (3) with all_52_7, all_6_1, e3, e0, simplifying
% 199.69/32.90  | |              with (17), (40) gives:
% 199.69/32.90  | |   (43)  all_52_7 = all_6_1
% 199.69/32.90  | | 
% 199.69/32.90  | | COMBINE_EQS: (19), (43) imply:
% 199.69/32.90  | |   (44)  all_56_12 = all_6_1
% 199.69/32.90  | | 
% 199.69/32.90  | | COMBINE_EQS: (12), (43) imply:
% 199.69/32.90  | |   (45)  all_58_12 = all_6_1
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (5), (43) imply:
% 199.69/32.90  | |   (46)   ~ (all_52_15 = all_6_1)
% 199.69/32.90  | | 
% 199.69/32.90  | | SIMP: (46) implies:
% 199.69/32.90  | |   (47)   ~ (all_52_15 = all_6_1)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (13), (43) imply:
% 199.69/32.90  | |   (48)   ~ (all_6_1 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (38), (43) imply:
% 199.69/32.90  | |   (49)   ~ (all_6_1 = e0)
% 199.69/32.90  | | 
% 199.69/32.90  | | BETA: splitting (4) gives:
% 199.69/32.90  | | 
% 199.69/32.90  | | Case 1:
% 199.69/32.90  | | | 
% 199.69/32.90  | | |   (50)  all_56_12 = e3
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REF_CLOSE: (44), (48), (50) are inconsistent by sub-proof #1347.
% 199.69/32.90  | | | 
% 199.69/32.90  | | Case 2:
% 199.69/32.90  | | | 
% 199.69/32.90  | | |   (51)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.90  | | | 
% 199.69/32.90  | | | BETA: splitting (9) gives:
% 199.69/32.90  | | | 
% 199.69/32.90  | | | Case 1:
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | |   (52)  all_56_13 = e3
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | | REF_CLOSE: (7), (33), (52) are inconsistent by sub-proof #1201.
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | Case 2:
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | |   (53)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | | REF_CLOSE: (2), (3), (6), (10), (11), (14), (15), (16), (18), (21),
% 199.69/32.90  | | | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (39),
% 199.69/32.90  | | | |            (42), (44), (45), (47), (49), (51), (53) are inconsistent by
% 199.69/32.90  | | | |            sub-proof #480.
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | End of split
% 199.69/32.90  | | | 
% 199.69/32.90  | | End of split
% 199.69/32.90  | | 
% 199.69/32.90  | Case 2:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (54)   ~ (all_8_2 = e0)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (37), (54) imply:
% 199.69/32.90  | |   (55)  $false
% 199.69/32.90  | | 
% 199.69/32.90  | | CLOSE: (55) is inconsistent.
% 199.69/32.90  | | 
% 199.69/32.90  | End of split
% 199.69/32.90  | 
% 199.69/32.90  End of proof
% 199.69/32.90  
% 199.69/32.90  Sub-proof #91 shows that the following formulas are inconsistent:
% 199.69/32.90  ----------------------------------------------------------------
% 199.69/32.90    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.90    (2)   ~ (all_52_15 = all_52_23)
% 199.69/32.90    (3)   ~ (all_52_25 = all_52_27)
% 199.69/32.90    (4)  all_58_14 = all_52_23
% 199.69/32.90    (5)   ~ (all_52_17 = all_4_0)
% 199.69/32.90    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.90    (7)  all_58_1 = all_52_9
% 199.69/32.90    (8)   ~ (e3 = e0)
% 199.69/32.90    (9)  op(e2, e3) = all_52_3
% 199.69/32.90    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.90    (11)   ~ (all_52_7 = all_52_15)
% 199.69/32.90    (12)  op(all_52_15, all_52_15) = e0
% 199.69/32.90    (13)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.90    (14)   ~ (all_52_17 = all_52_25)
% 199.69/32.90    (15)   ~ (all_52_3 = all_6_2)
% 199.69/32.90    (16)  all_44_2 = all_6_2
% 199.69/32.90    (17)  all_58_0 = all_6_2
% 199.69/32.90    (18)  all_56_4 = all_52_3
% 199.69/32.90    (19)   ~ (all_52_17 = all_10_2)
% 199.69/32.90    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.69/32.90    (21)  op(e3, e0) = all_52_25
% 199.69/32.90    (22)  op(all_52_5, all_52_5) = all_52_4
% 199.69/32.90    (23)   ~ (all_52_27 = all_52_29)
% 199.69/32.90    (24)  all_58_13 = all_52_15
% 199.69/32.90    (25)  op(all_52_13, all_52_13) = e1
% 199.69/32.90    (26)  op(all_10_2, all_10_2) = all_52_20
% 199.69/32.90    (27)  all_58_9 = all_52_25
% 199.69/32.90    (28)  op(e1, e3) = all_52_5
% 199.69/32.90    (29)  op(e2, e2) = all_4_2
% 199.69/32.90    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.90    (31)  op(all_4_2, e2) = e1
% 199.69/32.90    (32)  all_58_11 = all_52_29
% 199.69/32.90    (33)  op(all_10_2, e1) = all_10_1
% 199.69/32.90    (34)   ~ (all_10_2 = all_4_0)
% 199.69/32.90    (35)  op(all_6_2, all_6_2) = all_52_0
% 199.69/32.90    (36)   ~ (all_52_7 = all_6_2)
% 199.69/32.90    (37)   ~ (all_52_15 = e0)
% 199.69/32.90    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.90    (39)  all_58_15 = e0
% 199.69/32.90    (40)  all_56_11 = all_52_29
% 199.69/32.90    (41)   ~ (all_4_0 = e3)
% 199.69/32.90    (42)   ~ (all_52_25 = e0)
% 199.69/32.90    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.90    (44)  all_58_10 = all_52_27
% 199.69/32.90    (45)  all_56_8 = all_52_5
% 199.69/32.90    (46)   ~ (all_52_29 = all_10_2)
% 199.69/32.90    (47)  all_58_7 = all_52_13
% 199.69/32.90    (48)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.69/32.90    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.90    (50)   ~ (all_52_5 = all_52_7)
% 199.69/32.90    (51)  all_58_12 = all_52_7
% 199.69/32.90    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.90    (53)  all_58_2 = all_52_3
% 199.69/32.90    (54)  all_56_2 = all_52_17
% 199.69/32.90    (55)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.90    (56)   ~ (all_52_23 = e3)
% 199.69/32.90    (57)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.69/32.90    (58)   ~ (all_52_13 = all_4_2)
% 199.69/32.90    (59)  op(e3, e1) = all_52_17
% 199.69/32.90    (60)  op(e0, e3) = all_52_7
% 199.69/32.90    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.90    (62)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.90    (63)  all_58_8 = all_10_2
% 199.69/32.90    (64)   ~ (all_52_23 = e0)
% 199.69/32.90    (65)  all_56_12 = all_52_7
% 199.69/32.90    (66)  op(all_52_17, all_52_17) = all_52_16
% 199.69/32.90    (67)  all_58_5 = all_4_0
% 199.69/32.90    (68)  all_8_2 = all_6_2
% 199.69/32.90    (69)   ~ (all_52_25 = all_6_2)
% 199.69/32.90    (70)   ~ (all_52_9 = all_4_2)
% 199.69/32.90    (71)   ~ (all_52_5 = all_6_2)
% 199.69/32.90    (72)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.90    (73)  op(all_4_2, all_4_2) = e2
% 199.69/32.90    (74)   ~ (all_52_9 = all_6_2)
% 199.69/32.90    (75)  op(e3, all_6_1) = e2
% 199.69/32.90    (76)  op(e3, e3) = all_6_2
% 199.69/32.90    (77)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.69/32.90    (78)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.90    (79)  all_56_14 = all_52_23
% 199.69/32.90    (80)   ~ (all_52_3 = all_52_7)
% 199.69/32.90    (81)   ~ (all_52_15 = all_4_2)
% 199.69/32.90    (82)  all_58_6 = all_52_5
% 199.69/32.90    (83)  op(e3, e2) = all_52_9
% 199.69/32.90    (84)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.90    (85)   ~ (all_52_17 = all_6_2)
% 199.69/32.90    (86)   ~ (e1 = e0)
% 199.69/32.90    (87)   ~ (e3 = e2)
% 199.69/32.90    (88)  all_44_1 = all_6_1
% 199.69/32.90    (89)   ~ (all_52_9 = all_52_17)
% 199.69/32.90    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.90    (91)  op(e1, e1) = all_10_2
% 199.69/32.90    (92)  op(all_52_9, all_52_9) = e3
% 199.69/32.90    (93)   ~ (all_52_23 = all_10_2)
% 199.69/32.90    (94)   ~ (all_52_7 = all_52_23)
% 199.69/32.90    (95)  all_58_3 = all_4_2
% 199.69/32.90    (96)   ~ (all_52_3 = all_4_2)
% 199.69/32.90    (97)   ~ (all_52_17 = all_52_23)
% 199.69/32.90    (98)  all_8_1 = all_6_1
% 199.69/32.90    (99)  op(all_6_2, e3) = all_6_1
% 199.69/32.90    (100)  all_58_4 = all_52_17
% 199.69/32.90    (101)   ~ (all_52_7 = e0)
% 199.69/32.90    (102)  op(all_52_25, all_52_25) = all_52_24
% 199.69/32.90  
% 199.69/32.90  Begin of proof
% 199.69/32.90  | 
% 199.69/32.90  | BETA: splitting (90) gives:
% 199.69/32.90  | 
% 199.69/32.90  | Case 1:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (103)  all_58_4 = e3
% 199.69/32.90  | | 
% 199.69/32.90  | | COMBINE_EQS: (100), (103) imply:
% 199.69/32.90  | |   (104)  all_52_17 = e3
% 199.69/32.90  | | 
% 199.69/32.90  | | SIMP: (104) implies:
% 199.69/32.90  | |   (105)  all_52_17 = e3
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (89), (105) imply:
% 199.69/32.90  | |   (106)   ~ (all_52_9 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (97), (105) imply:
% 199.69/32.90  | |   (107)   ~ (all_52_23 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (14), (105) imply:
% 199.69/32.90  | |   (108)   ~ (all_52_25 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | SIMP: (108) implies:
% 199.69/32.90  | |   (109)   ~ (all_52_25 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (5), (105) imply:
% 199.69/32.90  | |   (110)   ~ (all_4_0 = e3)
% 199.69/32.90  | | 
% 199.69/32.90  | | REDUCE: (66), (105) imply:
% 199.69/32.90  | |   (111)  op(e3, e3) = all_52_16
% 199.69/32.90  | | 
% 199.69/32.90  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (13), (16), (17),
% 199.69/32.90  | |            (19), (20), (22), (23), (24), (25), (27), (28), (29), (30), (31),
% 199.69/32.90  | |            (32), (36), (38), (39), (40), (41), (44), (45), (46), (47), (48),
% 199.69/32.90  | |            (50), (51), (52), (53), (56), (57), (58), (60), (61), (62), (63),
% 199.69/32.90  | |            (64), (65), (67), (68), (71), (72), (74), (75), (76), (78), (79),
% 199.69/32.90  | |            (80), (81), (82), (83), (84), (86), (87), (88), (91), (92), (94),
% 199.69/32.90  | |            (95), (98), (99), (100), (101), (106), (109), (111) are
% 199.69/32.90  | |            inconsistent by sub-proof #97.
% 199.69/32.90  | | 
% 199.69/32.90  | Case 2:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (112)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.90  | | 
% 199.69/32.90  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 199.69/32.90  | |            (15), (17), (18), (19), (21), (24), (26), (27), (29), (30), (31),
% 199.69/32.90  | |            (33), (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 199.69/32.90  | |            (48), (49), (51), (53), (54), (55), (56), (59), (60), (63), (64),
% 199.69/32.90  | |            (65), (67), (68), (69), (70), (73), (74), (75), (76), (77), (78),
% 199.69/32.90  | |            (79), (80), (81), (83), (84), (85), (87), (89), (92), (93), (94),
% 199.69/32.90  | |            (95), (96), (98), (99), (100), (102), (112) are inconsistent by
% 199.69/32.90  | |            sub-proof #92.
% 199.69/32.90  | | 
% 199.69/32.90  | End of split
% 199.69/32.90  | 
% 199.69/32.90  End of proof
% 199.69/32.90  
% 199.69/32.90  Sub-proof #92 shows that the following formulas are inconsistent:
% 199.69/32.90  ----------------------------------------------------------------
% 199.69/32.90    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.90    (2)   ~ (all_52_15 = all_52_23)
% 199.69/32.90    (3)   ~ (all_52_25 = all_52_27)
% 199.69/32.90    (4)  all_58_14 = all_52_23
% 199.69/32.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.90    (6)  all_58_1 = all_52_9
% 199.69/32.90    (7)   ~ (e3 = e0)
% 199.69/32.90    (8)  op(e2, e3) = all_52_3
% 199.69/32.90    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.90    (10)   ~ (all_52_7 = all_52_15)
% 199.69/32.90    (11)  op(all_52_15, all_52_15) = e0
% 199.69/32.90    (12)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.90    (13)   ~ (all_52_3 = all_6_2)
% 199.69/32.90    (14)  all_58_0 = all_6_2
% 199.69/32.90    (15)  all_56_4 = all_52_3
% 199.69/32.90    (16)   ~ (all_52_17 = all_10_2)
% 199.69/32.90    (17)  op(e3, e0) = all_52_25
% 199.69/32.90    (18)  all_58_13 = all_52_15
% 199.69/32.90    (19)  op(all_10_2, all_10_2) = all_52_20
% 199.69/32.90    (20)  all_58_9 = all_52_25
% 199.69/32.90    (21)  op(e2, e2) = all_4_2
% 199.69/32.90    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.90    (23)  op(all_4_2, e2) = e1
% 199.69/32.90    (24)  op(all_10_2, e1) = all_10_1
% 199.69/32.90    (25)   ~ (all_10_2 = all_4_0)
% 199.69/32.90    (26)  op(all_6_2, all_6_2) = all_52_0
% 199.69/32.90    (27)   ~ (all_52_7 = all_6_2)
% 199.69/32.90    (28)   ~ (all_52_15 = e0)
% 199.69/32.90    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.90    (30)  all_58_15 = e0
% 199.69/32.90    (31)   ~ (all_4_0 = e3)
% 199.69/32.90    (32)   ~ (all_52_25 = e0)
% 199.69/32.90    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.90    (34)  all_58_10 = all_52_27
% 199.69/32.90    (35)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.69/32.90    (36)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.90    (37)  all_58_12 = all_52_7
% 199.69/32.90    (38)  all_58_2 = all_52_3
% 199.69/32.90    (39)  all_56_2 = all_52_17
% 199.69/32.90    (40)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.90    (41)   ~ (all_52_23 = e3)
% 199.69/32.90    (42)  op(e3, e1) = all_52_17
% 199.69/32.90    (43)  op(e0, e3) = all_52_7
% 199.69/32.90    (44)  all_58_8 = all_10_2
% 199.69/32.90    (45)   ~ (all_52_23 = e0)
% 199.69/32.90    (46)  all_56_12 = all_52_7
% 199.69/32.90    (47)  all_58_5 = all_4_0
% 199.69/32.90    (48)  all_8_2 = all_6_2
% 199.69/32.90    (49)   ~ (all_52_25 = all_6_2)
% 199.69/32.90    (50)   ~ (all_52_9 = all_4_2)
% 199.69/32.90    (51)  op(all_4_2, all_4_2) = e2
% 199.69/32.90    (52)   ~ (all_52_9 = all_6_2)
% 199.69/32.90    (53)  op(e3, all_6_1) = e2
% 199.69/32.90    (54)  op(e3, e3) = all_6_2
% 199.69/32.90    (55)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.69/32.90    (56)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.90    (57)  all_56_14 = all_52_23
% 199.69/32.90    (58)   ~ (all_52_3 = all_52_7)
% 199.69/32.90    (59)   ~ (all_52_15 = all_4_2)
% 199.69/32.90    (60)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.90    (61)  op(e3, e2) = all_52_9
% 199.69/32.90    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.90    (63)   ~ (all_52_17 = all_6_2)
% 199.69/32.90    (64)   ~ (e3 = e2)
% 199.69/32.90    (65)   ~ (all_52_9 = all_52_17)
% 199.69/32.90    (66)  op(all_52_9, all_52_9) = e3
% 199.69/32.90    (67)   ~ (all_52_23 = all_10_2)
% 199.69/32.90    (68)   ~ (all_52_7 = all_52_23)
% 199.69/32.90    (69)  all_58_3 = all_4_2
% 199.69/32.90    (70)   ~ (all_52_3 = all_4_2)
% 199.69/32.90    (71)  all_8_1 = all_6_1
% 199.69/32.90    (72)  op(all_6_2, e3) = all_6_1
% 199.69/32.90    (73)  all_58_4 = all_52_17
% 199.69/32.90    (74)  op(all_52_25, all_52_25) = all_52_24
% 199.69/32.90  
% 199.69/32.90  Begin of proof
% 199.69/32.90  | 
% 199.69/32.90  | BETA: splitting (60) gives:
% 199.69/32.90  | 
% 199.69/32.90  | Case 1:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (75)  all_58_5 = e3
% 199.69/32.90  | | 
% 199.69/32.90  | | REF_CLOSE: (31), (47), (75) are inconsistent by sub-proof #215.
% 199.69/32.90  | | 
% 199.69/32.90  | Case 2:
% 199.69/32.90  | | 
% 199.69/32.90  | |   (76)  all_58_8 = e3 | all_58_14 = e3
% 199.69/32.90  | | 
% 199.69/32.90  | | BETA: splitting (76) gives:
% 199.69/32.90  | | 
% 199.69/32.90  | | Case 1:
% 199.69/32.90  | | | 
% 199.69/32.90  | | |   (77)  all_58_8 = e3
% 199.69/32.90  | | | 
% 199.69/32.90  | | | COMBINE_EQS: (44), (77) imply:
% 199.69/32.90  | | |   (78)  all_10_2 = e3
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REDUCE: (16), (78) imply:
% 199.69/32.90  | | |   (79)   ~ (all_52_17 = e3)
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REDUCE: (25), (78) imply:
% 199.69/32.90  | | |   (80)   ~ (all_4_0 = e3)
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REDUCE: (19), (78) imply:
% 199.69/32.90  | | |   (81)  op(e3, e3) = all_52_20
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REDUCE: (24), (78) imply:
% 199.69/32.90  | | |   (82)  op(e3, e1) = all_10_1
% 199.69/32.90  | | | 
% 199.69/32.90  | | | GROUND_INST: instantiating (5) with all_52_17, all_10_1, e1, e3,
% 199.69/32.90  | | |              simplifying with (42), (82) gives:
% 199.69/32.90  | | |   (83)  all_52_17 = all_10_1
% 199.69/32.90  | | | 
% 199.69/32.90  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_20, e3, e3,
% 199.69/32.90  | | |              simplifying with (54), (81) gives:
% 199.69/32.90  | | |   (84)  all_52_20 = all_6_2
% 199.69/32.90  | | | 
% 199.69/32.90  | | | COMBINE_EQS: (39), (83) imply:
% 199.69/32.90  | | |   (85)  all_56_2 = all_10_1
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REDUCE: (79), (83) imply:
% 199.69/32.90  | | |   (86)   ~ (all_10_1 = e3)
% 199.69/32.90  | | | 
% 199.69/32.90  | | | BETA: splitting (33) gives:
% 199.69/32.90  | | | 
% 199.69/32.90  | | | Case 1:
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | |   (87)  all_56_2 = e3
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | | REF_CLOSE: (85), (86), (87) are inconsistent by sub-proof #1029.
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | Case 2:
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | |   (88)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | | BETA: splitting (55) gives:
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | | Case 1:
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | |   (89)  all_58_9 = e3
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | COMBINE_EQS: (20), (89) imply:
% 199.69/32.90  | | | | |   (90)  all_52_25 = e3
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | SIMP: (90) implies:
% 199.69/32.90  | | | | |   (91)  all_52_25 = e3
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | REDUCE: (3), (91) imply:
% 199.69/32.90  | | | | |   (92)   ~ (all_52_27 = e3)
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | SIMP: (92) implies:
% 199.69/32.90  | | | | |   (93)   ~ (all_52_27 = e3)
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | REDUCE: (74), (91) imply:
% 199.69/32.90  | | | | |   (94)  op(e3, e3) = all_52_24
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 199.69/32.90  | | | | |              simplifying with (54), (94) gives:
% 199.69/32.90  | | | | |   (95)  all_52_24 = all_6_2
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | BETA: splitting (62) gives:
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | Case 1:
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | |   (96)  all_58_12 = e3
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | | COMBINE_EQS: (37), (96) imply:
% 199.69/32.90  | | | | | |   (97)  all_52_7 = e3
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | | SIMP: (97) implies:
% 199.69/32.90  | | | | | |   (98)  all_52_7 = e3
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | | REDUCE: (58), (98) imply:
% 199.69/32.90  | | | | | |   (99)   ~ (all_52_3 = e3)
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | | BETA: splitting (29) gives:
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | | Case 1:
% 199.69/32.90  | | | | | | | 
% 199.69/32.90  | | | | | | |   (100)  all_58_2 = e3
% 199.69/32.90  | | | | | | | 
% 199.69/32.90  | | | | | | | REF_CLOSE: (38), (99), (100) are inconsistent by sub-proof #1369.
% 199.69/32.90  | | | | | | | 
% 199.69/32.90  | | | | | | Case 2:
% 199.69/32.90  | | | | | | | 
% 199.69/32.90  | | | | | | |   (101)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.90  | | | | | | | 
% 199.69/32.90  | | | | | | | REF_CLOSE: (5), (6), (8), (13), (14), (15), (17), (20), (22),
% 199.69/32.90  | | | | | | |            (23), (31), (34), (36), (38), (39), (40), (42), (47),
% 199.69/32.90  | | | | | | |            (49), (50), (51), (53), (54), (56), (61), (63), (64),
% 199.69/32.90  | | | | | | |            (65), (69), (70), (72), (73), (79), (88), (93), (101)
% 199.69/32.90  | | | | | | |            are inconsistent by sub-proof #94.
% 199.69/32.90  | | | | | | | 
% 199.69/32.90  | | | | | | End of split
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | Case 2:
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | |   (102)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12), (18),
% 199.69/32.90  | | | | | |            (21), (27), (30), (35), (41), (43), (45), (46), (48),
% 199.69/32.90  | | | | | |            (53), (54), (57), (59), (61), (66), (68), (71), (72),
% 199.69/32.90  | | | | | |            (102) are inconsistent by sub-proof #98.
% 199.69/32.90  | | | | | | 
% 199.69/32.90  | | | | | End of split
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | Case 2:
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | |   (103)   ~ (all_58_9 = e3)
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | | REF_CLOSE: (4), (5), (6), (7), (11), (14), (18), (20), (26), (27),
% 199.69/32.90  | | | | |            (28), (30), (37), (41), (52), (54), (56), (62), (66), (72),
% 199.69/32.90  | | | | |            (73), (79), (103) are inconsistent by sub-proof #93.
% 199.69/32.90  | | | | | 
% 199.69/32.90  | | | | End of split
% 199.69/32.90  | | | | 
% 199.69/32.90  | | | End of split
% 199.69/32.90  | | | 
% 199.69/32.90  | | Case 2:
% 199.69/32.90  | | | 
% 199.69/32.90  | | |   (104)  all_58_14 = e3
% 199.69/32.90  | | | 
% 199.69/32.90  | | | REF_CLOSE: (4), (41), (104) are inconsistent by sub-proof #1305.
% 199.69/32.90  | | | 
% 199.69/32.90  | | End of split
% 199.69/32.90  | | 
% 199.69/32.90  | End of split
% 199.69/32.90  | 
% 199.69/32.90  End of proof
% 199.69/32.90  
% 199.69/32.90  Sub-proof #93 shows that the following formulas are inconsistent:
% 199.69/32.90  ----------------------------------------------------------------
% 199.69/32.90    (1)  all_58_14 = all_52_23
% 199.69/32.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.90    (3)  all_58_1 = all_52_9
% 199.69/32.90    (4)   ~ (e3 = e0)
% 199.69/32.90    (5)   ~ (all_58_9 = e3)
% 199.69/32.91    (6)  op(all_52_15, all_52_15) = e0
% 199.69/32.91    (7)  all_58_0 = all_6_2
% 199.69/32.91    (8)  all_58_13 = all_52_15
% 199.69/32.91    (9)  all_58_9 = all_52_25
% 199.69/32.91    (10)  op(all_6_2, all_6_2) = all_52_0
% 199.69/32.91    (11)   ~ (all_52_7 = all_6_2)
% 199.69/32.91    (12)   ~ (all_52_15 = e0)
% 199.69/32.91    (13)  all_58_15 = e0
% 199.69/32.91    (14)  all_58_12 = all_52_7
% 199.69/32.91    (15)   ~ (all_52_23 = e3)
% 199.69/32.91    (16)   ~ (all_52_9 = all_6_2)
% 199.69/32.91    (17)  op(e3, e3) = all_6_2
% 199.69/32.91    (18)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91    (19)   ~ (all_52_17 = e3)
% 199.69/32.91    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91    (21)  op(all_52_9, all_52_9) = e3
% 199.69/32.91    (22)  op(all_6_2, e3) = all_6_1
% 199.69/32.91    (23)  all_58_4 = all_52_17
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | REDUCE: (5), (9) imply:
% 199.69/32.91  |   (24)   ~ (all_52_25 = e3)
% 199.69/32.91  | 
% 199.69/32.91  | BETA: splitting (18) gives:
% 199.69/32.91  | 
% 199.69/32.91  | Case 1:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (25)  all_58_0 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | COMBINE_EQS: (7), (25) imply:
% 199.69/32.91  | |   (26)  all_6_2 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (11), (26) imply:
% 199.69/32.91  | |   (27)   ~ (all_52_7 = e3)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (10), (26) imply:
% 199.69/32.91  | |   (28)  op(e3, e3) = all_52_0
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (22), (26) imply:
% 199.69/32.91  | |   (29)  op(e3, e3) = all_6_1
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (17), (26) imply:
% 199.69/32.91  | |   (30)  op(e3, e3) = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | BETA: splitting (20) gives:
% 199.69/32.91  | | 
% 199.69/32.91  | | Case 1:
% 199.69/32.91  | | | 
% 199.69/32.91  | | |   (31)  all_58_12 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | COMBINE_EQS: (14), (31) imply:
% 199.69/32.91  | | |   (32)  all_52_7 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | REDUCE: (27), (32) imply:
% 199.69/32.91  | | |   (33)  $false
% 199.69/32.91  | | | 
% 199.69/32.91  | | | CLOSE: (33) is inconsistent.
% 199.69/32.91  | | | 
% 199.69/32.91  | | Case 2:
% 199.69/32.91  | | | 
% 199.69/32.91  | | |   (34)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | BETA: splitting (34) gives:
% 199.69/32.91  | | | 
% 199.69/32.91  | | | Case 1:
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | |   (35)  all_58_13 = e3
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | COMBINE_EQS: (8), (35) imply:
% 199.69/32.91  | | | |   (36)  all_52_15 = e3
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | REDUCE: (6), (36) imply:
% 199.69/32.91  | | | |   (37)  op(e3, e3) = e0
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | REF_CLOSE: (2), (4), (28), (29), (30), (37) are inconsistent by
% 199.69/32.91  | | | |            sub-proof #949.
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | Case 2:
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | |   (38)  all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | REF_CLOSE: (1), (4), (13), (15), (38) are inconsistent by sub-proof
% 199.69/32.91  | | | |            #983.
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | End of split
% 199.69/32.91  | | | 
% 199.69/32.91  | | End of split
% 199.69/32.91  | | 
% 199.69/32.91  | Case 2:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (39)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (2), (3), (9), (16), (17), (19), (21), (23), (24), (39) are
% 199.69/32.91  | |            inconsistent by sub-proof #1138.
% 199.69/32.91  | | 
% 199.69/32.91  | End of split
% 199.69/32.91  | 
% 199.69/32.91  End of proof
% 199.69/32.91  
% 199.69/32.91  Sub-proof #94 shows that the following formulas are inconsistent:
% 199.69/32.91  ----------------------------------------------------------------
% 199.69/32.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.91    (2)  all_58_1 = all_52_9
% 199.69/32.91    (3)  op(e2, e3) = all_52_3
% 199.69/32.91    (4)   ~ (all_52_3 = all_6_2)
% 199.69/32.91    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.91    (6)  all_58_0 = all_6_2
% 199.69/32.91    (7)  all_56_4 = all_52_3
% 199.69/32.91    (8)  op(e3, e0) = all_52_25
% 199.69/32.91    (9)  all_58_9 = all_52_25
% 199.69/32.91    (10)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.91    (11)  op(all_4_2, e2) = e1
% 199.69/32.91    (12)   ~ (all_4_0 = e3)
% 199.69/32.91    (13)  all_58_10 = all_52_27
% 199.69/32.91    (14)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.91    (15)  all_58_2 = all_52_3
% 199.69/32.91    (16)  all_56_2 = all_52_17
% 199.69/32.91    (17)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.91    (18)   ~ (all_52_27 = e3)
% 199.69/32.91    (19)  op(e3, e1) = all_52_17
% 199.69/32.91    (20)  all_58_5 = all_4_0
% 199.69/32.91    (21)   ~ (all_52_25 = all_6_2)
% 199.69/32.91    (22)   ~ (all_52_9 = all_4_2)
% 199.69/32.91    (23)  op(all_4_2, all_4_2) = e2
% 199.69/32.91    (24)  op(e3, all_6_1) = e2
% 199.69/32.91    (25)  op(e3, e3) = all_6_2
% 199.69/32.91    (26)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91    (27)   ~ (all_52_17 = e3)
% 199.69/32.91    (28)  op(e3, e2) = all_52_9
% 199.69/32.91    (29)   ~ (all_52_17 = all_6_2)
% 199.69/32.91    (30)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.91    (31)   ~ (e3 = e2)
% 199.69/32.91    (32)   ~ (all_52_9 = all_52_17)
% 199.69/32.91    (33)  all_58_3 = all_4_2
% 199.69/32.91    (34)   ~ (all_52_3 = all_4_2)
% 199.69/32.91    (35)  op(all_6_2, e3) = all_6_1
% 199.69/32.91    (36)  all_58_4 = all_52_17
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | BETA: splitting (5) gives:
% 199.69/32.91  | 
% 199.69/32.91  | Case 1:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (37)  all_58_3 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | COMBINE_EQS: (33), (37) imply:
% 199.69/32.91  | |   (38)  all_4_2 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (34), (38) imply:
% 199.69/32.91  | |   (39)   ~ (all_52_3 = e3)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (22), (38) imply:
% 199.69/32.91  | |   (40)   ~ (all_52_9 = e3)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (23), (38) imply:
% 199.69/32.91  | |   (41)  op(e3, e3) = e2
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (11), (38) imply:
% 199.69/32.91  | |   (42)  op(e3, e2) = e1
% 199.69/32.91  | | 
% 199.69/32.91  | | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 199.69/32.91  | |              (28), (42) gives:
% 199.69/32.91  | |   (43)  all_52_9 = e1
% 199.69/32.91  | | 
% 199.69/32.91  | | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 199.69/32.91  | |              (25), (41) gives:
% 199.69/32.91  | |   (44)  all_6_2 = e2
% 199.69/32.91  | | 
% 199.69/32.91  | | COMBINE_EQS: (2), (43) imply:
% 199.69/32.91  | |   (45)  all_58_1 = e1
% 199.69/32.91  | | 
% 199.69/32.91  | | COMBINE_EQS: (6), (44) imply:
% 199.69/32.91  | |   (46)  all_58_0 = e2
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (4), (44) imply:
% 199.69/32.91  | |   (47)   ~ (all_52_3 = e2)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (32), (43) imply:
% 199.69/32.91  | |   (48)   ~ (all_52_17 = e1)
% 199.69/32.91  | | 
% 199.69/32.91  | | SIMP: (48) implies:
% 199.69/32.91  | |   (49)   ~ (all_52_17 = e1)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (40), (43) imply:
% 199.69/32.91  | |   (50)   ~ (e3 = e1)
% 199.69/32.91  | | 
% 199.69/32.91  | | SIMP: (50) implies:
% 199.69/32.91  | |   (51)   ~ (e3 = e1)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (29), (44) imply:
% 199.69/32.91  | |   (52)   ~ (all_52_17 = e2)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (21), (44) imply:
% 199.69/32.91  | |   (53)   ~ (all_52_25 = e2)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (35), (44) imply:
% 199.69/32.91  | |   (54)  op(e2, e3) = all_6_1
% 199.69/32.91  | | 
% 199.69/32.91  | | BETA: splitting (26) gives:
% 199.69/32.91  | | 
% 199.69/32.91  | | Case 1:
% 199.69/32.91  | | | 
% 199.69/32.91  | | |   (55)  all_58_0 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | REF_CLOSE: (31), (46), (55) are inconsistent by sub-proof #1235.
% 199.69/32.91  | | | 
% 199.69/32.91  | | Case 2:
% 199.69/32.91  | | | 
% 199.69/32.91  | | |   (56)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | BETA: splitting (30) gives:
% 199.69/32.91  | | | 
% 199.69/32.91  | | | Case 1:
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | |   (57)  all_56_2 = e2
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | COMBINE_EQS: (16), (57) imply:
% 199.69/32.91  | | | |   (58)  all_52_17 = e2
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | REDUCE: (52), (58) imply:
% 199.69/32.91  | | | |   (59)  $false
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | CLOSE: (59) is inconsistent.
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | Case 2:
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | |   (60)   ~ (all_56_2 = e2)
% 199.69/32.91  | | | |   (61)  all_56_2 = e1 | all_56_2 = e0
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | BETA: splitting (61) gives:
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | | Case 1:
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | |   (62)  all_56_2 = e1
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | COMBINE_EQS: (16), (62) imply:
% 199.69/32.91  | | | | |   (63)  all_52_17 = e1
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | REDUCE: (49), (63) imply:
% 199.69/32.91  | | | | |   (64)  $false
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | CLOSE: (64) is inconsistent.
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | Case 2:
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | |   (65)  all_56_2 = e0
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | COMBINE_EQS: (16), (65) imply:
% 199.69/32.91  | | | | |   (66)  all_52_17 = e0
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | COMBINE_EQS: (36), (66) imply:
% 199.69/32.91  | | | | |   (67)  all_58_4 = e0
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | REDUCE: (27), (66) imply:
% 199.69/32.91  | | | | |   (68)   ~ (e3 = e0)
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | SIMP: (68) implies:
% 199.69/32.91  | | | | |   (69)   ~ (e3 = e0)
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | REDUCE: (52), (66) imply:
% 199.69/32.91  | | | | |   (70)   ~ (e2 = e0)
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | SIMP: (70) implies:
% 199.69/32.91  | | | | |   (71)   ~ (e2 = e0)
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | BETA: splitting (56) gives:
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | | Case 1:
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | |   (72)  all_58_1 = e3
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | | REF_CLOSE: (45), (51), (72) are inconsistent by sub-proof #96.
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | Case 2:
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | |   (73)  all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | | BETA: splitting (73) gives:
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | | Case 1:
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | |   (74)  all_58_4 = e3
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | | REF_CLOSE: (67), (69), (74) are inconsistent by sub-proof #95.
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | Case 2:
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | |   (75)  all_58_9 = e3
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | | COMBINE_EQS: (9), (75) imply:
% 199.69/32.91  | | | | | | |   (76)  all_52_25 = e3
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | | REDUCE: (8), (76) imply:
% 199.69/32.91  | | | | | | |   (77)  op(e3, e0) = e3
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | | REF_CLOSE: (1), (3), (7), (10), (14), (15), (17), (19), (24),
% 199.69/32.91  | | | | | | |            (31), (39), (46), (47), (52), (54), (71), (77) are
% 199.69/32.91  | | | | | | |            inconsistent by sub-proof #455.
% 199.69/32.91  | | | | | | | 
% 199.69/32.91  | | | | | | End of split
% 199.69/32.91  | | | | | | 
% 199.69/32.91  | | | | | End of split
% 199.69/32.91  | | | | | 
% 199.69/32.91  | | | | End of split
% 199.69/32.91  | | | | 
% 199.69/32.91  | | | End of split
% 199.69/32.91  | | | 
% 199.69/32.91  | | End of split
% 199.69/32.91  | | 
% 199.69/32.91  | Case 2:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (78)  all_58_5 = e3 | all_58_10 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (12), (13), (18), (20), (78) are inconsistent by sub-proof #214.
% 199.69/32.91  | | 
% 199.69/32.91  | End of split
% 199.69/32.91  | 
% 199.69/32.91  End of proof
% 199.69/32.91  
% 199.69/32.91  Sub-proof #95 shows that the following formulas are inconsistent:
% 199.69/32.91  ----------------------------------------------------------------
% 199.69/32.91    (1)  all_58_4 = e3
% 199.69/32.91    (2)  all_58_4 = e0
% 199.69/32.91    (3)   ~ (e3 = e0)
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | COMBINE_EQS: (1), (2) imply:
% 199.69/32.91  |   (4)  e3 = e0
% 199.69/32.91  | 
% 199.69/32.91  | SIMP: (4) implies:
% 199.69/32.91  |   (5)  e3 = e0
% 199.69/32.91  | 
% 199.69/32.91  | REDUCE: (3), (5) imply:
% 199.69/32.91  |   (6)  $false
% 199.69/32.91  | 
% 199.69/32.91  | CLOSE: (6) is inconsistent.
% 199.69/32.91  | 
% 199.69/32.91  End of proof
% 199.69/32.91  
% 199.69/32.91  Sub-proof #96 shows that the following formulas are inconsistent:
% 199.69/32.91  ----------------------------------------------------------------
% 199.69/32.91    (1)  all_58_1 = e3
% 199.69/32.91    (2)  all_58_1 = e1
% 199.69/32.91    (3)   ~ (e3 = e1)
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | COMBINE_EQS: (1), (2) imply:
% 199.69/32.91  |   (4)  e3 = e1
% 199.69/32.91  | 
% 199.69/32.91  | SIMP: (4) implies:
% 199.69/32.91  |   (5)  e3 = e1
% 199.69/32.91  | 
% 199.69/32.91  | REDUCE: (3), (5) imply:
% 199.69/32.91  |   (6)  $false
% 199.69/32.91  | 
% 199.69/32.91  | CLOSE: (6) is inconsistent.
% 199.69/32.91  | 
% 199.69/32.91  End of proof
% 199.69/32.91  
% 199.69/32.91  Sub-proof #97 shows that the following formulas are inconsistent:
% 199.69/32.91  ----------------------------------------------------------------
% 199.69/32.91    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.91    (2)   ~ (all_52_15 = all_52_23)
% 199.69/32.91    (3)  all_58_14 = all_52_23
% 199.69/32.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.91    (5)  all_58_1 = all_52_9
% 199.69/32.91    (6)   ~ (e3 = e0)
% 199.69/32.91    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.91    (8)   ~ (all_52_7 = all_52_15)
% 199.69/32.91    (9)  op(all_52_15, all_52_15) = e0
% 199.69/32.91    (10)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.91    (11)  all_44_2 = all_6_2
% 199.69/32.91    (12)  all_58_0 = all_6_2
% 199.69/32.91    (13)   ~ (all_52_17 = all_10_2)
% 199.69/32.91    (14)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.69/32.91    (15)  op(all_52_5, all_52_5) = all_52_4
% 199.69/32.91    (16)   ~ (all_52_27 = all_52_29)
% 199.69/32.91    (17)  all_58_13 = all_52_15
% 199.69/32.91    (18)  op(all_52_13, all_52_13) = e1
% 199.69/32.91    (19)  all_58_9 = all_52_25
% 199.69/32.91    (20)  op(e1, e3) = all_52_5
% 199.69/32.91    (21)  op(e2, e2) = all_4_2
% 199.69/32.91    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.91    (23)  op(all_4_2, e2) = e1
% 199.69/32.91    (24)  all_58_11 = all_52_29
% 199.69/32.91    (25)   ~ (all_52_7 = all_6_2)
% 199.69/32.91    (26)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.91    (27)  all_58_15 = e0
% 199.69/32.91    (28)  all_56_11 = all_52_29
% 199.69/32.91    (29)   ~ (all_4_0 = e3)
% 199.69/32.91    (30)  all_58_10 = all_52_27
% 199.69/32.91    (31)  all_56_8 = all_52_5
% 199.69/32.91    (32)   ~ (all_52_29 = all_10_2)
% 199.69/32.91    (33)  all_58_7 = all_52_13
% 199.69/32.91    (34)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.69/32.91    (35)   ~ (all_52_5 = all_52_7)
% 199.69/32.91    (36)  all_58_12 = all_52_7
% 199.69/32.91    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.91    (38)  all_58_2 = all_52_3
% 199.69/32.91    (39)  op(e3, e3) = all_52_16
% 199.69/32.91    (40)   ~ (all_52_25 = e3)
% 199.69/32.91    (41)   ~ (all_52_23 = e3)
% 199.69/32.91    (42)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.69/32.91    (43)   ~ (all_52_9 = e3)
% 199.69/32.91    (44)   ~ (all_52_13 = all_4_2)
% 199.69/32.91    (45)  op(e0, e3) = all_52_7
% 199.69/32.91    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.91    (47)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.91    (48)  all_58_8 = all_10_2
% 199.69/32.91    (49)   ~ (all_52_23 = e0)
% 199.69/32.91    (50)  all_56_12 = all_52_7
% 199.69/32.91    (51)  all_58_5 = all_4_0
% 199.69/32.91    (52)  all_8_2 = all_6_2
% 199.69/32.91    (53)   ~ (all_52_5 = all_6_2)
% 199.69/32.91    (54)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.91    (55)   ~ (all_52_9 = all_6_2)
% 199.69/32.91    (56)  op(e3, all_6_1) = e2
% 199.69/32.91    (57)  op(e3, e3) = all_6_2
% 199.69/32.91    (58)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91    (59)  all_56_14 = all_52_23
% 199.69/32.91    (60)   ~ (all_52_3 = all_52_7)
% 199.69/32.91    (61)   ~ (all_52_15 = all_4_2)
% 199.69/32.91    (62)  all_58_6 = all_52_5
% 199.69/32.91    (63)  op(e3, e2) = all_52_9
% 199.69/32.91    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91    (65)   ~ (e1 = e0)
% 199.69/32.91    (66)   ~ (e3 = e2)
% 199.69/32.91    (67)  all_44_1 = all_6_1
% 199.69/32.91    (68)  op(e1, e1) = all_10_2
% 199.69/32.91    (69)  op(all_52_9, all_52_9) = e3
% 199.69/32.91    (70)   ~ (all_52_7 = all_52_23)
% 199.69/32.91    (71)  all_58_3 = all_4_2
% 199.69/32.91    (72)  all_8_1 = all_6_1
% 199.69/32.91    (73)  op(all_6_2, e3) = all_6_1
% 199.69/32.91    (74)  all_58_4 = all_52_17
% 199.69/32.91    (75)   ~ (all_52_7 = e0)
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | BETA: splitting (64) gives:
% 199.69/32.91  | 
% 199.69/32.91  | Case 1:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (76)  all_58_12 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | COMBINE_EQS: (36), (76) imply:
% 199.69/32.91  | |   (77)  all_52_7 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | SIMP: (77) implies:
% 199.69/32.91  | |   (78)  all_52_7 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (60), (78) imply:
% 199.69/32.91  | |   (79)   ~ (all_52_3 = e3)
% 199.69/32.91  | | 
% 199.69/32.91  | | REDUCE: (35), (78) imply:
% 199.69/32.91  | |   (80)   ~ (all_52_5 = e3)
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (4), (5), (6), (11), (12), (13), (14), (15), (16), (17), (18),
% 199.69/32.91  | |            (19), (20), (21), (22), (23), (24), (26), (28), (29), (30), (31),
% 199.69/32.91  | |            (32), (33), (37), (38), (39), (40), (42), (43), (44), (46), (47),
% 199.69/32.91  | |            (48), (51), (53), (54), (55), (56), (57), (58), (61), (62), (63),
% 199.69/32.91  | |            (65), (66), (67), (68), (69), (71), (73), (74), (76), (79), (80)
% 199.69/32.91  | |            are inconsistent by sub-proof #99.
% 199.69/32.91  | | 
% 199.69/32.91  | Case 2:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (81)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (17), (21), (25),
% 199.69/32.91  | |            (27), (34), (41), (45), (49), (50), (52), (56), (57), (59), (61),
% 199.69/32.91  | |            (63), (69), (70), (72), (73), (81) are inconsistent by sub-proof
% 199.69/32.91  | |            #98.
% 199.69/32.91  | | 
% 199.69/32.91  | End of split
% 199.69/32.91  | 
% 199.69/32.91  End of proof
% 199.69/32.91  
% 199.69/32.91  Sub-proof #98 shows that the following formulas are inconsistent:
% 199.69/32.91  ----------------------------------------------------------------
% 199.69/32.91    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 199.69/32.91    (2)   ~ (all_52_15 = all_52_23)
% 199.69/32.91    (3)  all_58_14 = all_52_23
% 199.69/32.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.91    (5)   ~ (e3 = e0)
% 199.69/32.91    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.91    (7)   ~ (all_52_7 = all_52_15)
% 199.69/32.91    (8)  op(all_52_15, all_52_15) = e0
% 199.69/32.91    (9)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.91    (10)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91    (11)  all_58_13 = all_52_15
% 199.69/32.91    (12)  op(e2, e2) = all_4_2
% 199.69/32.91    (13)   ~ (all_52_7 = all_6_2)
% 199.69/32.91    (14)  all_58_15 = e0
% 199.69/32.91    (15)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.69/32.91    (16)   ~ (all_52_23 = e3)
% 199.69/32.91    (17)  op(e0, e3) = all_52_7
% 199.69/32.91    (18)   ~ (all_52_23 = e0)
% 199.69/32.91    (19)  all_56_12 = all_52_7
% 199.69/32.91    (20)  all_8_2 = all_6_2
% 199.69/32.91    (21)  op(e3, all_6_1) = e2
% 199.69/32.91    (22)  op(e3, e3) = all_6_2
% 199.69/32.91    (23)  all_56_14 = all_52_23
% 199.69/32.91    (24)   ~ (all_52_15 = all_4_2)
% 199.69/32.91    (25)  op(e3, e2) = all_52_9
% 199.69/32.91    (26)  op(all_52_9, all_52_9) = e3
% 199.69/32.91    (27)   ~ (all_52_7 = all_52_23)
% 199.69/32.91    (28)  all_8_1 = all_6_1
% 199.69/32.91    (29)  op(all_6_2, e3) = all_6_1
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | BETA: splitting (10) gives:
% 199.69/32.91  | 
% 199.69/32.91  | Case 1:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (30)  all_58_13 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | COMBINE_EQS: (11), (30) imply:
% 199.69/32.91  | |   (31)  all_52_15 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (12), (13), (15), (17), (18),
% 199.69/32.91  | |            (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 199.69/32.91  | |            (31) are inconsistent by sub-proof #499.
% 199.69/32.91  | | 
% 199.69/32.91  | Case 2:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (32)  all_58_14 = e3 | all_58_15 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (3), (5), (14), (16), (32) are inconsistent by sub-proof #983.
% 199.69/32.91  | | 
% 199.69/32.91  | End of split
% 199.69/32.91  | 
% 199.69/32.91  End of proof
% 199.69/32.91  
% 199.69/32.91  Sub-proof #99 shows that the following formulas are inconsistent:
% 199.69/32.91  ----------------------------------------------------------------
% 199.69/32.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.91    (2)  all_58_1 = all_52_9
% 199.69/32.91    (3)   ~ (e3 = e0)
% 199.69/32.91    (4)  all_44_2 = all_6_2
% 199.69/32.91    (5)  all_58_0 = all_6_2
% 199.69/32.91    (6)   ~ (all_52_17 = all_10_2)
% 199.69/32.91    (7)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 199.69/32.91    (8)  op(all_52_5, all_52_5) = all_52_4
% 199.69/32.91    (9)   ~ (all_52_27 = all_52_29)
% 199.69/32.91    (10)  all_58_13 = all_52_15
% 199.69/32.91    (11)  op(all_52_13, all_52_13) = e1
% 199.69/32.91    (12)  all_58_9 = all_52_25
% 199.69/32.91    (13)  op(e1, e3) = all_52_5
% 199.69/32.91    (14)  op(e2, e2) = all_4_2
% 199.69/32.91    (15)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.91    (16)  op(all_4_2, e2) = e1
% 199.69/32.91    (17)  all_58_11 = all_52_29
% 199.69/32.91    (18)   ~ (all_52_3 = e3)
% 199.69/32.91    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.91    (20)  all_56_11 = all_52_29
% 199.69/32.91    (21)   ~ (all_4_0 = e3)
% 199.69/32.91    (22)  all_58_10 = all_52_27
% 199.69/32.91    (23)  all_56_8 = all_52_5
% 199.69/32.91    (24)   ~ (all_52_29 = all_10_2)
% 199.69/32.91    (25)  all_58_7 = all_52_13
% 199.69/32.91    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.91    (27)  all_58_2 = all_52_3
% 199.69/32.91    (28)  op(e3, e3) = all_52_16
% 199.69/32.91    (29)   ~ (all_52_25 = e3)
% 199.69/32.91    (30)   ~ (all_52_5 = e3)
% 199.69/32.91    (31)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.69/32.91    (32)   ~ (all_52_9 = e3)
% 199.69/32.91    (33)   ~ (all_52_13 = all_4_2)
% 199.69/32.91    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.91    (35)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.91    (36)  all_58_8 = all_10_2
% 199.69/32.91    (37)  all_58_5 = all_4_0
% 199.69/32.91    (38)   ~ (all_52_5 = all_6_2)
% 199.69/32.91    (39)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.91    (40)   ~ (all_52_9 = all_6_2)
% 199.69/32.91    (41)  op(e3, all_6_1) = e2
% 199.69/32.91    (42)  op(e3, e3) = all_6_2
% 199.69/32.91    (43)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.91    (44)   ~ (all_52_15 = all_4_2)
% 199.69/32.91    (45)  all_58_6 = all_52_5
% 199.69/32.91    (46)  op(e3, e2) = all_52_9
% 199.69/32.91    (47)   ~ (e1 = e0)
% 199.69/32.91    (48)   ~ (e3 = e2)
% 199.69/32.91    (49)  all_44_1 = all_6_1
% 199.69/32.91    (50)  all_58_12 = e3
% 199.69/32.91    (51)  op(e1, e1) = all_10_2
% 199.69/32.91    (52)  op(all_52_9, all_52_9) = e3
% 199.69/32.91    (53)  all_58_3 = all_4_2
% 199.69/32.91    (54)  op(all_6_2, e3) = all_6_1
% 199.69/32.91    (55)  all_58_4 = all_52_17
% 199.69/32.91  
% 199.69/32.91  Begin of proof
% 199.69/32.91  | 
% 199.69/32.91  | BETA: splitting (19) gives:
% 199.69/32.91  | 
% 199.69/32.91  | Case 1:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (56)  all_58_2 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | REF_CLOSE: (18), (27), (56) are inconsistent by sub-proof #1369.
% 199.69/32.91  | | 
% 199.69/32.91  | Case 2:
% 199.69/32.91  | | 
% 199.69/32.91  | |   (57)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.91  | | 
% 199.69/32.91  | | BETA: splitting (26) gives:
% 199.69/32.91  | | 
% 199.69/32.91  | | Case 1:
% 199.69/32.91  | | | 
% 199.69/32.91  | | |   (58)  all_58_6 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | REF_CLOSE: (30), (45), (58) are inconsistent by sub-proof #1328.
% 199.69/32.91  | | | 
% 199.69/32.91  | | Case 2:
% 199.69/32.91  | | | 
% 199.69/32.91  | | |   (59)   ~ (all_58_6 = e3)
% 199.69/32.91  | | |   (60)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.91  | | | 
% 199.69/32.91  | | | BETA: splitting (34) gives:
% 199.69/32.91  | | | 
% 199.69/32.92  | | | Case 1:
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | |   (61)  all_58_1 = e3
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | COMBINE_EQS: (2), (61) imply:
% 199.69/32.92  | | | |   (62)  all_52_9 = e3
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | REDUCE: (32), (62) imply:
% 199.69/32.92  | | | |   (63)  $false
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | CLOSE: (63) is inconsistent.
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | Case 2:
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | |   (64)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | BETA: splitting (35) gives:
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | Case 1:
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | |   (65)  all_56_8 = e3
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | | REF_CLOSE: (23), (30), (65) are inconsistent by sub-proof #1325.
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | Case 2:
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | |   (66)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | | BETA: splitting (31) gives:
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | | Case 1:
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | |   (67)  all_56_11 = e3
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | COMBINE_EQS: (20), (67) imply:
% 199.69/32.92  | | | | | |   (68)  all_52_29 = e3
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | SIMP: (68) implies:
% 199.69/32.92  | | | | | |   (69)  all_52_29 = e3
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | REDUCE: (9), (69) imply:
% 199.69/32.92  | | | | | |   (70)   ~ (all_52_27 = e3)
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | REDUCE: (24), (69) imply:
% 199.69/32.92  | | | | | |   (71)   ~ (all_10_2 = e3)
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | SIMP: (71) implies:
% 199.69/32.92  | | | | | |   (72)   ~ (all_10_2 = e3)
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | REF_CLOSE: (1), (10), (16), (21), (22), (25), (33), (37), (39),
% 199.69/32.92  | | | | | |            (44), (46), (51), (52), (53), (57), (64), (70), (72) are
% 199.69/32.92  | | | | | |            inconsistent by sub-proof #213.
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | Case 2:
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | |   (73)   ~ (all_56_11 = e3)
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | REDUCE: (20), (73) imply:
% 199.69/32.92  | | | | | |   (74)   ~ (all_52_29 = e3)
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | BETA: splitting (60) gives:
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | Case 1:
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | |   (75)  all_58_7 = e3
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | COMBINE_EQS: (25), (75) imply:
% 199.69/32.92  | | | | | | |   (76)  all_52_13 = e3
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | REDUCE: (33), (76) imply:
% 199.69/32.92  | | | | | | |   (77)   ~ (all_4_2 = e3)
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | SIMP: (77) implies:
% 199.69/32.92  | | | | | | |   (78)   ~ (all_4_2 = e3)
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | REDUCE: (11), (76) imply:
% 199.69/32.92  | | | | | | |   (79)  op(e3, e3) = e1
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (13), (14), (15), (23),
% 199.69/32.92  | | | | | | |            (28), (38), (41), (42), (45), (46), (47), (49), (50),
% 199.69/32.92  | | | | | | |            (52), (54), (66), (78), (79) are inconsistent by
% 199.69/32.92  | | | | | | |            sub-proof #458.
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | Case 2:
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | |   (80)  all_58_8 = e3 | all_58_11 = e3
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | REF_CLOSE: (1), (2), (5), (6), (12), (17), (29), (36), (40), (41),
% 199.69/32.92  | | | | | | |            (42), (43), (48), (52), (54), (55), (74), (80) are
% 199.69/32.92  | | | | | | |            inconsistent by sub-proof #491.
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | End of split
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | End of split
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | End of split
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | End of split
% 199.69/32.92  | | | 
% 199.69/32.92  | | End of split
% 199.69/32.92  | | 
% 199.69/32.92  | End of split
% 199.69/32.92  | 
% 199.69/32.92  End of proof
% 199.69/32.92  
% 199.69/32.92  Sub-proof #100 shows that the following formulas are inconsistent:
% 199.69/32.92  ----------------------------------------------------------------
% 199.69/32.92    (1)   ~ (all_52_15 = all_52_23)
% 199.69/32.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.92    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.92    (4)   ~ (all_52_7 = all_52_15)
% 199.69/32.92    (5)  op(all_52_15, all_52_15) = e0
% 199.69/32.92    (6)  all_58_13 = all_52_15
% 199.69/32.92    (7)  op(e2, e2) = all_4_2
% 199.69/32.92    (8)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.69/32.92    (9)  op(all_10_2, e1) = all_10_1
% 199.69/32.92    (10)  op(e0, e1) = all_52_23
% 199.69/32.92    (11)   ~ (all_52_15 = e0)
% 199.69/32.92    (12)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.69/32.92    (13)   ~ (e2 = e1)
% 199.69/32.92    (14)  op(e0, e0) = e0
% 199.69/32.92    (15)  all_58_12 = all_52_7
% 199.69/32.92    (16)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.92    (17)  all_56_12 = all_52_7
% 199.69/32.92    (18)  op(all_4_2, all_4_2) = e2
% 199.69/32.92    (19)  all_56_14 = e3
% 199.69/32.92    (20)  all_56_14 = all_52_23
% 199.69/32.92    (21)   ~ (all_10_1 = e3)
% 199.69/32.92    (22)   ~ (all_52_15 = all_4_2)
% 199.69/32.92    (23)  op(e1, e1) = all_10_2
% 199.69/32.92    (24)   ~ (all_52_7 = all_52_23)
% 199.69/32.92    (25)  all_56_13 = all_52_15
% 199.69/32.92    (26)   ~ (all_52_7 = e0)
% 199.69/32.92  
% 199.69/32.92  Begin of proof
% 199.69/32.92  | 
% 199.69/32.92  | COMBINE_EQS: (19), (20) imply:
% 199.69/32.92  |   (27)  all_52_23 = e3
% 199.69/32.92  | 
% 199.69/32.92  | SIMP: (27) implies:
% 199.69/32.92  |   (28)  all_52_23 = e3
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (24), (28) imply:
% 199.69/32.92  |   (29)   ~ (all_52_7 = e3)
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (1), (28) imply:
% 199.69/32.92  |   (30)   ~ (all_52_15 = e3)
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (10), (28) imply:
% 199.69/32.92  |   (31)  op(e0, e1) = e3
% 199.69/32.92  | 
% 199.69/32.92  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 199.69/32.92  |            (15), (16), (17), (18), (21), (22), (23), (25), (26), (29), (30),
% 199.69/32.92  |            (31) are inconsistent by sub-proof #985.
% 199.69/32.92  | 
% 199.69/32.92  End of proof
% 199.69/32.92  
% 199.69/32.92  Sub-proof #101 shows that the following formulas are inconsistent:
% 199.69/32.92  ----------------------------------------------------------------
% 199.69/32.92    (1)  all_56_6 = all_4_0
% 199.69/32.92    (2)  all_56_6 = e0
% 199.69/32.92    (3)   ~ (all_4_0 = e0)
% 199.69/32.92  
% 199.69/32.92  Begin of proof
% 199.69/32.92  | 
% 199.69/32.92  | COMBINE_EQS: (1), (2) imply:
% 199.69/32.92  |   (4)  all_4_0 = e0
% 199.69/32.92  | 
% 199.69/32.92  | SIMP: (4) implies:
% 199.69/32.92  |   (5)  all_4_0 = e0
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (3), (5) imply:
% 199.69/32.92  |   (6)  $false
% 199.69/32.92  | 
% 199.69/32.92  | CLOSE: (6) is inconsistent.
% 199.69/32.92  | 
% 199.69/32.92  End of proof
% 199.69/32.92  
% 199.69/32.92  Sub-proof #102 shows that the following formulas are inconsistent:
% 199.69/32.92  ----------------------------------------------------------------
% 199.69/32.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.92    (2)   ~ (all_52_5 = all_52_13)
% 199.69/32.92    (3)  op(all_52_7, all_52_7) = e0
% 199.69/32.92    (4)  all_58_1 = all_52_9
% 199.69/32.92    (5)   ~ (e3 = e0)
% 199.69/32.92    (6)  all_4_2 = e3
% 199.69/32.92    (7)  all_56_4 = all_52_3
% 199.69/32.92    (8)  all_58_3 = e3
% 199.69/32.92    (9)  all_58_13 = all_52_15
% 199.69/32.92    (10)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.92    (11)  op(e2, e2) = all_4_2
% 199.69/32.92    (12)   ~ (all_52_3 = all_52_5)
% 199.69/32.92    (13)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.69/32.92    (14)  op(all_4_2, e2) = e1
% 199.69/32.92    (15)   ~ (all_52_3 = e3)
% 199.69/32.92    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.69/32.92    (17)  op(e0, e0) = all_14_2
% 199.69/32.92    (18)  all_56_15 = all_14_2
% 199.69/32.92    (19)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.92    (20)  all_56_8 = all_52_5
% 199.69/32.92    (21)  all_58_7 = all_52_13
% 199.69/32.92    (22)   ~ (all_52_5 = all_52_7)
% 199.69/32.92    (23)  all_58_12 = all_52_7
% 199.69/32.92    (24)   ~ (all_52_7 = all_14_2)
% 199.69/32.92    (25)   ~ (all_14_2 = e0)
% 199.69/32.92    (26)  all_58_2 = all_52_3
% 199.69/32.92    (27)  op(all_52_3, all_52_3) = e2
% 199.69/32.92    (28)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.92    (29)   ~ (all_52_15 = all_14_2)
% 199.69/32.92    (30)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.69/32.92    (31)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.69/32.92    (32)  all_56_12 = all_52_7
% 199.69/32.92    (33)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.92    (34)   ~ (all_52_3 = all_52_7)
% 199.69/32.92    (35)  op(e3, e2) = all_52_9
% 199.69/32.92    (36)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.69/32.92    (37)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 199.69/32.92    (38)   ~ (all_14_2 = e3)
% 199.69/32.92  
% 199.69/32.92  Begin of proof
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (6), (14) imply:
% 199.69/32.92  |   (39)  op(e3, e2) = e1
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (6), (11) imply:
% 199.69/32.92  |   (40)  op(e2, e2) = e3
% 199.69/32.92  | 
% 199.69/32.92  | BETA: splitting (33) gives:
% 199.69/32.92  | 
% 199.69/32.92  | Case 1:
% 199.69/32.92  | | 
% 199.69/32.92  | |   (41)   ~ (all_4_2 = e3)
% 199.69/32.92  | | 
% 199.69/32.92  | | REF_CLOSE: (1), (11), (40), (41) are inconsistent by sub-proof #211.
% 199.69/32.92  | | 
% 199.69/32.92  | Case 2:
% 199.69/32.92  | | 
% 199.69/32.92  | | 
% 199.69/32.92  | | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 199.69/32.92  | |              (35), (39) gives:
% 199.69/32.92  | |   (42)  all_52_9 = e1
% 199.69/32.92  | | 
% 199.69/32.92  | | COMBINE_EQS: (4), (42) imply:
% 199.69/32.92  | |   (43)  all_58_1 = e1
% 199.69/32.92  | | 
% 199.69/32.92  | | BETA: splitting (28) gives:
% 199.69/32.92  | | 
% 199.69/32.92  | | Case 1:
% 199.69/32.92  | | | 
% 199.69/32.92  | | |   (44)  all_58_12 = e1
% 199.69/32.92  | | | 
% 199.69/32.92  | | | COMBINE_EQS: (23), (44) imply:
% 199.69/32.92  | | |   (45)  all_52_7 = e1
% 199.69/32.92  | | | 
% 199.69/32.92  | | | SIMP: (45) implies:
% 199.69/32.92  | | |   (46)  all_52_7 = e1
% 199.69/32.92  | | | 
% 199.69/32.92  | | | REDUCE: (34), (46) imply:
% 199.69/32.92  | | |   (47)   ~ (all_52_3 = e1)
% 199.69/32.92  | | | 
% 199.69/32.92  | | | REDUCE: (22), (46) imply:
% 199.69/32.92  | | |   (48)   ~ (all_52_5 = e1)
% 199.69/32.92  | | | 
% 199.69/32.92  | | | REDUCE: (24), (46) imply:
% 199.69/32.92  | | |   (49)   ~ (all_14_2 = e1)
% 199.69/32.92  | | | 
% 199.69/32.92  | | | SIMP: (49) implies:
% 199.69/32.92  | | |   (50)   ~ (all_14_2 = e1)
% 199.69/32.92  | | | 
% 199.69/32.92  | | | BETA: splitting (31) gives:
% 199.69/32.92  | | | 
% 199.69/32.92  | | | Case 1:
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | |   (51)  all_56_15 = e2
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | COMBINE_EQS: (18), (51) imply:
% 199.69/32.92  | | | |   (52)  all_14_2 = e2
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | SIMP: (52) implies:
% 199.69/32.92  | | | |   (53)  all_14_2 = e2
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | REDUCE: (29), (53) imply:
% 199.69/32.92  | | | |   (54)   ~ (all_52_15 = e2)
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | REDUCE: (38), (53) imply:
% 199.69/32.92  | | | |   (55)   ~ (e3 = e2)
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | SIMP: (55) implies:
% 199.69/32.92  | | | |   (56)   ~ (e3 = e2)
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | REDUCE: (50), (53) imply:
% 199.69/32.92  | | | |   (57)   ~ (e2 = e1)
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | BETA: splitting (36) gives:
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | Case 1:
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | |   (58)  all_58_1 = e2
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | | REF_CLOSE: (43), (57), (58) are inconsistent by sub-proof #185.
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | Case 2:
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | |   (59)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | | BETA: splitting (59) gives:
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | | Case 1:
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | |   (60)  all_58_3 = e2
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | COMBINE_EQS: (8), (60) imply:
% 199.69/32.92  | | | | | |   (61)  e3 = e2
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | REDUCE: (56), (61) imply:
% 199.69/32.92  | | | | | |   (62)  $false
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | CLOSE: (62) is inconsistent.
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | Case 2:
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | |   (63)  all_58_7 = e2 | all_58_13 = e2
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | BETA: splitting (13) gives:
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | | Case 1:
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | |   (64)  all_58_2 = e0
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | COMBINE_EQS: (26), (64) imply:
% 199.69/32.92  | | | | | | |   (65)  all_52_3 = e0
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | SIMP: (65) implies:
% 199.69/32.92  | | | | | | |   (66)  all_52_3 = e0
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | REDUCE: (12), (66) imply:
% 199.69/32.92  | | | | | | |   (67)   ~ (all_52_5 = e0)
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | SIMP: (67) implies:
% 199.69/32.92  | | | | | | |   (68)   ~ (all_52_5 = e0)
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | BETA: splitting (19) gives:
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | Case 1:
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | |   (69)  all_56_8 = e2
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | COMBINE_EQS: (20), (69) imply:
% 199.69/32.92  | | | | | | | |   (70)  all_52_5 = e2
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | SIMP: (70) implies:
% 199.69/32.92  | | | | | | | |   (71)  all_52_5 = e2
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | REDUCE: (2), (71) imply:
% 199.69/32.92  | | | | | | | |   (72)   ~ (all_52_13 = e2)
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | SIMP: (72) implies:
% 199.69/32.92  | | | | | | | |   (73)   ~ (all_52_13 = e2)
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | REF_CLOSE: (9), (21), (54), (63), (73) are inconsistent by
% 199.69/32.92  | | | | | | | |            sub-proof #389.
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | Case 2:
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | |   (74)  all_56_8 = e1 | all_56_8 = e0
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | REF_CLOSE: (20), (48), (68), (74) are inconsistent by sub-proof
% 199.69/32.92  | | | | | | | |            #1020.
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | End of split
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | Case 2:
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | |   (75)   ~ (all_58_2 = e0)
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | REDUCE: (26), (75) imply:
% 199.69/32.92  | | | | | | |   (76)   ~ (all_52_3 = e0)
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | BETA: splitting (37) gives:
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | | Case 1:
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | |   (77)  all_58_2 = e2
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | COMBINE_EQS: (26), (77) imply:
% 199.69/32.92  | | | | | | | |   (78)  all_52_3 = e2
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | SIMP: (78) implies:
% 199.69/32.92  | | | | | | | |   (79)  all_52_3 = e2
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | REF_CLOSE: (1), (15), (27), (40), (79) are inconsistent by
% 199.69/32.92  | | | | | | | |            sub-proof #687.
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | Case 2:
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | |   (80)   ~ (all_58_2 = e2)
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | REDUCE: (26), (80) imply:
% 199.69/32.92  | | | | | | | |   (81)   ~ (all_52_3 = e2)
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | | REF_CLOSE: (7), (30), (47), (76), (81) are inconsistent by
% 199.69/32.92  | | | | | | | |            sub-proof #724.
% 199.69/32.92  | | | | | | | | 
% 199.69/32.92  | | | | | | | End of split
% 199.69/32.92  | | | | | | | 
% 199.69/32.92  | | | | | | End of split
% 199.69/32.92  | | | | | | 
% 199.69/32.92  | | | | | End of split
% 199.69/32.92  | | | | | 
% 199.69/32.92  | | | | End of split
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | Case 2:
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | |   (82)  all_56_15 = e1 | all_56_15 = e0
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | | REF_CLOSE: (18), (25), (50), (82) are inconsistent by sub-proof #1161.
% 199.69/32.92  | | | | 
% 199.69/32.92  | | | End of split
% 199.69/32.92  | | | 
% 199.69/32.92  | | Case 2:
% 199.69/32.92  | | | 
% 199.69/32.92  | | |   (83)   ~ (all_58_12 = e1)
% 199.69/32.92  | | | 
% 199.69/32.92  | | | REDUCE: (23), (83) imply:
% 199.69/32.92  | | |   (84)   ~ (all_52_7 = e1)
% 199.69/32.92  | | | 
% 199.69/32.92  | | | REF_CLOSE: (1), (3), (5), (10), (16), (17), (23), (24), (32), (40), (84)
% 199.69/32.92  | | |            are inconsistent by sub-proof #1160.
% 199.69/32.92  | | | 
% 199.69/32.92  | | End of split
% 199.69/32.92  | | 
% 199.69/32.92  | End of split
% 199.69/32.92  | 
% 199.69/32.92  End of proof
% 199.69/32.92  
% 199.69/32.92  Sub-proof #103 shows that the following formulas are inconsistent:
% 199.69/32.92  ----------------------------------------------------------------
% 199.69/32.92    (1)  all_58_14 = all_52_23
% 199.69/32.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.92    (3)  op(all_52_7, all_52_7) = e0
% 199.69/32.92    (4)  op(all_52_5, all_52_5) = e1
% 199.69/32.92    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.92    (6)   ~ (all_52_3 = all_52_19)
% 199.69/32.92    (7)   ~ (all_52_3 = all_6_2)
% 199.69/32.92    (8)  all_58_0 = all_6_2
% 199.69/32.92    (9)  op(all_14_2, e0) = all_14_1
% 199.69/32.92    (10)  op(e3, e0) = all_52_25
% 199.69/32.92    (11)  all_58_13 = all_52_15
% 199.69/32.92    (12)  op(all_10_2, all_10_2) = all_52_20
% 199.69/32.92    (13)  all_58_9 = all_52_25
% 199.69/32.92    (14)   ~ (all_52_29 = all_14_2)
% 199.69/32.92    (15)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.69/32.92    (16)  op(e2, e2) = all_4_2
% 199.69/32.92    (17)   ~ (all_52_3 = all_52_5)
% 199.69/32.92    (18)  op(all_4_2, e2) = e1
% 199.69/32.92    (19)  all_58_11 = all_52_29
% 199.69/32.92    (20)   ~ (all_52_9 = all_52_15)
% 199.69/32.92    (21)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.69/32.92    (22)  op(all_10_2, e1) = all_10_1
% 199.69/32.92    (23)   ~ (all_10_2 = all_4_0)
% 199.69/32.92    (24)   ~ (all_52_7 = all_6_2)
% 199.69/32.92    (25)  op(e0, e0) = all_14_2
% 199.69/32.92    (26)  all_56_15 = all_14_2
% 199.69/32.92    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.92    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.69/32.92    (29)   ~ (all_4_0 = e3)
% 199.69/32.92    (30)   ~ (e2 = e1)
% 199.69/32.92    (31)   ~ (all_6_0 = e1)
% 199.69/32.92    (32)  all_58_10 = all_52_27
% 199.69/32.92    (33)  all_56_8 = all_52_5
% 199.69/32.92    (34)  op(all_52_9, all_52_9) = all_52_8
% 199.69/32.92    (35)   ~ (all_52_19 = all_52_23)
% 199.69/32.92    (36)  all_58_7 = all_52_13
% 199.69/32.92    (37)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.92    (38)  op(all_6_2, all_6_2) = e3
% 199.69/32.92    (39)  all_58_12 = all_52_7
% 199.69/32.92    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.92    (41)   ~ (all_52_7 = all_14_2)
% 199.69/32.92    (42)   ~ (all_14_2 = e0)
% 199.69/32.92    (43)  all_58_2 = all_52_3
% 199.69/32.92    (44)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.69/32.92    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.69/32.92    (46)  op(e3, all_6_1) = all_6_0
% 199.69/32.92    (47)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 199.69/32.92    (48)  op(all_52_3, all_52_3) = e2
% 199.69/32.92    (49)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.92    (50)  all_56_6 = all_52_19
% 199.69/32.92    (51)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 199.69/32.92    (52)   ~ (all_52_13 = all_4_2)
% 199.69/32.92    (53)  op(e3, e1) = all_52_17
% 199.69/32.92    (54)   ~ (all_52_9 = all_52_25)
% 199.69/32.92    (55)  all_58_15 = all_14_2
% 199.69/32.92    (56)   ~ (all_52_19 = all_10_2)
% 199.69/32.92    (57)  op(all_52_23, all_52_23) = all_52_22
% 199.69/32.92    (58)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.92    (59)  all_58_8 = all_10_2
% 199.69/32.92    (60)   ~ (all_52_5 = all_10_2)
% 199.69/32.92    (61)  op(all_52_29, all_52_29) = all_52_28
% 199.69/32.92    (62)  all_56_12 = all_52_7
% 199.69/32.92    (63)  all_58_5 = all_4_0
% 199.69/32.92    (64)   ~ (all_52_5 = all_6_2)
% 199.69/32.92    (65)  op(all_4_0, all_4_0) = all_52_18
% 199.69/32.92    (66)  op(e3, e3) = all_6_2
% 199.69/32.92    (67)  all_56_15 = e3
% 199.69/32.92    (68)   ~ (all_52_27 = all_14_2)
% 199.69/32.92    (69)   ~ (all_52_27 = all_4_0)
% 199.69/32.92    (70)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.92    (71)  op(all_4_2, all_4_2) = all_52_10
% 199.69/32.92    (72)  op(all_14_2, all_14_2) = all_52_30
% 199.69/32.92    (73)  all_58_5 = all_52_19
% 199.69/32.92    (74)   ~ (all_52_27 = all_4_2)
% 199.69/32.92    (75)  all_58_6 = all_52_5
% 199.69/32.92    (76)  op(e3, e2) = all_52_9
% 199.69/32.92    (77)   ~ (all_52_17 = all_6_2)
% 199.69/32.92    (78)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 199.69/32.92    (79)   ~ (all_52_9 = all_52_17)
% 199.69/32.92    (80)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.92    (81)  op(e1, e1) = all_10_2
% 199.69/32.92    (82)   ~ (all_52_7 = all_52_23)
% 199.69/32.92    (83)  all_58_3 = all_4_2
% 199.69/32.92    (84)   ~ (all_52_3 = all_4_2)
% 199.69/32.92    (85)  op(all_6_2, e3) = all_6_1
% 199.69/32.92    (86)  all_58_4 = all_52_17
% 199.69/32.92  
% 199.69/32.92  Begin of proof
% 199.69/32.92  | 
% 199.69/32.92  | COMBINE_EQS: (26), (67) imply:
% 199.69/32.92  |   (87)  all_14_2 = e3
% 199.69/32.92  | 
% 199.69/32.92  | SIMP: (87) implies:
% 199.69/32.92  |   (88)  all_14_2 = e3
% 199.69/32.92  | 
% 199.69/32.92  | COMBINE_EQS: (55), (88) imply:
% 199.69/32.92  |   (89)  all_58_15 = e3
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (41), (88) imply:
% 199.69/32.92  |   (90)   ~ (all_52_7 = e3)
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (68), (88) imply:
% 199.69/32.92  |   (91)   ~ (all_52_27 = e3)
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (14), (88) imply:
% 199.69/32.92  |   (92)   ~ (all_52_29 = e3)
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (42), (88) imply:
% 199.69/32.92  |   (93)   ~ (e3 = e0)
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (72), (88) imply:
% 199.69/32.92  |   (94)  op(e3, e3) = all_52_30
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (9), (88) imply:
% 199.69/32.92  |   (95)  op(e3, e0) = all_14_1
% 199.69/32.92  | 
% 199.69/32.92  | REDUCE: (25), (88) imply:
% 199.69/32.92  |   (96)  op(e0, e0) = e3
% 199.69/32.92  | 
% 199.69/32.92  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 199.69/32.92  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 199.69/32.92  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 199.69/32.92  |            (38), (39), (40), (41), (43), (44), (45), (46), (47), (48), (49),
% 199.69/32.92  |            (50), (51), (52), (53), (54), (56), (57), (58), (59), (60), (61),
% 199.69/32.92  |            (62), (63), (64), (65), (66), (69), (70), (71), (73), (74), (75),
% 199.69/32.92  |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 199.69/32.92  |            (89), (90), (91), (92), (93), (94), (95), (96) are inconsistent by
% 199.69/32.92  |            sub-proof #104.
% 199.69/32.92  | 
% 199.69/32.92  End of proof
% 199.69/32.92  
% 199.69/32.92  Sub-proof #104 shows that the following formulas are inconsistent:
% 199.69/32.92  ----------------------------------------------------------------
% 199.69/32.92    (1)  all_58_14 = all_52_23
% 199.69/32.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.92    (3)  op(all_52_7, all_52_7) = e0
% 199.69/32.92    (4)  op(all_52_5, all_52_5) = e1
% 199.69/32.92    (5)   ~ (e3 = e0)
% 199.69/32.92    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.92    (7)   ~ (all_52_3 = all_52_19)
% 199.69/32.92    (8)   ~ (all_52_3 = all_6_2)
% 199.69/32.92    (9)  all_58_0 = all_6_2
% 199.69/32.92    (10)  op(e3, e0) = all_52_25
% 199.69/32.92    (11)  all_58_13 = all_52_15
% 199.69/32.92    (12)  op(all_10_2, all_10_2) = all_52_20
% 199.69/32.92    (13)  all_58_9 = all_52_25
% 199.69/32.92    (14)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.69/32.92    (15)  op(e2, e2) = all_4_2
% 199.69/32.92    (16)   ~ (all_52_3 = all_52_5)
% 199.69/32.92    (17)  op(all_4_2, e2) = e1
% 199.69/32.92    (18)  all_58_11 = all_52_29
% 199.69/32.92    (19)   ~ (all_52_9 = all_52_15)
% 199.69/32.92    (20)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.69/32.92    (21)  op(all_10_2, e1) = all_10_1
% 199.69/32.92    (22)   ~ (all_10_2 = all_4_0)
% 199.69/32.92    (23)   ~ (all_52_7 = all_6_2)
% 199.69/32.92    (24)  op(e0, e0) = all_14_2
% 199.69/32.92    (25)  all_58_15 = e3
% 199.69/32.92    (26)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.92    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.69/32.92    (28)  op(e0, e0) = e3
% 199.69/32.92    (29)   ~ (all_4_0 = e3)
% 199.69/32.92    (30)   ~ (e2 = e1)
% 199.69/32.92    (31)   ~ (all_6_0 = e1)
% 199.69/32.92    (32)  all_58_10 = all_52_27
% 199.69/32.92    (33)  all_56_8 = all_52_5
% 199.69/32.92    (34)  op(all_52_9, all_52_9) = all_52_8
% 199.69/32.92    (35)   ~ (all_52_19 = all_52_23)
% 199.69/32.92    (36)  all_58_7 = all_52_13
% 199.69/32.92    (37)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.69/32.92    (38)  op(all_6_2, all_6_2) = e3
% 199.69/32.92    (39)  all_58_12 = all_52_7
% 199.69/32.92    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.92    (41)   ~ (all_52_7 = e3)
% 199.69/32.92    (42)   ~ (all_52_7 = all_14_2)
% 199.69/32.92    (43)  all_58_2 = all_52_3
% 199.69/32.92    (44)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 199.69/32.93    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.69/32.93    (46)   ~ (all_52_29 = e3)
% 199.69/32.93    (47)  op(e3, all_6_1) = all_6_0
% 199.69/32.93    (48)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 199.69/32.93    (49)  op(all_52_3, all_52_3) = e2
% 199.69/32.93    (50)  op(e3, e3) = all_52_30
% 199.69/32.93    (51)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.93    (52)  all_56_6 = all_52_19
% 199.69/32.93    (53)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 199.69/32.93    (54)   ~ (all_52_27 = e3)
% 199.69/32.93    (55)   ~ (all_52_13 = all_4_2)
% 199.69/32.93    (56)  op(e3, e1) = all_52_17
% 199.69/32.93    (57)   ~ (all_52_9 = all_52_25)
% 199.69/32.93    (58)   ~ (all_52_19 = all_10_2)
% 199.69/32.93    (59)  op(all_52_23, all_52_23) = all_52_22
% 199.69/32.93    (60)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.93    (61)  all_58_8 = all_10_2
% 199.69/32.93    (62)   ~ (all_52_5 = all_10_2)
% 199.69/32.93    (63)  op(all_52_29, all_52_29) = all_52_28
% 199.69/32.93    (64)  all_56_12 = all_52_7
% 199.69/32.93    (65)  all_58_5 = all_4_0
% 199.69/32.93    (66)   ~ (all_52_5 = all_6_2)
% 199.69/32.93    (67)  op(all_4_0, all_4_0) = all_52_18
% 199.69/32.93    (68)  op(e3, e3) = all_6_2
% 199.69/32.93    (69)  op(e3, e0) = all_14_1
% 199.69/32.93    (70)   ~ (all_52_27 = all_4_0)
% 199.69/32.93    (71)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.93    (72)  op(all_4_2, all_4_2) = all_52_10
% 199.69/32.93    (73)  all_58_5 = all_52_19
% 199.69/32.93    (74)   ~ (all_52_27 = all_4_2)
% 199.69/32.93    (75)  all_58_6 = all_52_5
% 199.69/32.93    (76)  op(e3, e2) = all_52_9
% 199.69/32.93    (77)   ~ (all_52_17 = all_6_2)
% 199.69/32.93    (78)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 199.69/32.93    (79)   ~ (all_52_9 = all_52_17)
% 199.69/32.93    (80)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.93    (81)  op(e1, e1) = all_10_2
% 199.69/32.93    (82)   ~ (all_52_7 = all_52_23)
% 199.69/32.93    (83)  all_58_3 = all_4_2
% 199.69/32.93    (84)   ~ (all_52_3 = all_4_2)
% 199.69/32.93    (85)  op(all_6_2, e3) = all_6_1
% 199.69/32.93    (86)  all_58_4 = all_52_17
% 199.69/32.93  
% 199.69/32.93  Begin of proof
% 199.69/32.93  | 
% 199.69/32.93  | GROUND_INST: instantiating (2) with all_52_25, all_14_1, e0, e3, simplifying
% 199.69/32.93  |              with (10), (69) gives:
% 199.69/32.93  |   (87)  all_52_25 = all_14_1
% 199.69/32.93  | 
% 199.69/32.93  | GROUND_INST: instantiating (2) with all_6_2, all_52_30, e3, e3, simplifying
% 199.69/32.93  |              with (50), (68) gives:
% 199.69/32.93  |   (88)  all_52_30 = all_6_2
% 199.69/32.93  | 
% 199.69/32.93  | COMBINE_EQS: (13), (87) imply:
% 199.69/32.93  |   (89)  all_58_9 = all_14_1
% 199.69/32.93  | 
% 199.69/32.93  | REDUCE: (57), (87) imply:
% 199.69/32.93  |   (90)   ~ (all_52_9 = all_14_1)
% 199.69/32.93  | 
% 199.69/32.93  | BETA: splitting (26) gives:
% 199.69/32.93  | 
% 199.69/32.93  | Case 1:
% 199.69/32.93  | | 
% 199.69/32.93  | |   (91)  all_58_2 = e3
% 199.69/32.93  | | 
% 199.69/32.93  | | REF_CLOSE: (2), (15), (38), (43), (49), (68), (84), (91) are inconsistent by
% 199.69/32.93  | |            sub-proof #1159.
% 199.69/32.93  | | 
% 199.69/32.93  | Case 2:
% 199.69/32.93  | | 
% 199.69/32.93  | |   (92)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.93  | | 
% 199.69/32.93  | | BETA: splitting (92) gives:
% 199.69/32.93  | | 
% 199.69/32.93  | | Case 1:
% 199.69/32.93  | | | 
% 199.69/32.93  | | |   (93)  all_58_3 = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | COMBINE_EQS: (83), (93) imply:
% 199.69/32.93  | | |   (94)  all_4_2 = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (55), (94) imply:
% 199.69/32.93  | | |   (95)   ~ (all_52_13 = e3)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (72), (94) imply:
% 199.69/32.93  | | |   (96)  op(e3, e3) = all_52_10
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (17), (94) imply:
% 199.69/32.93  | | |   (97)  op(e3, e2) = e1
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (15), (94) imply:
% 199.69/32.93  | | |   (98)  op(e2, e2) = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | GROUND_INST: instantiating (2) with all_52_9, e1, e2, e3, simplifying with
% 199.69/32.93  | | |              (76), (97) gives:
% 199.69/32.93  | | |   (99)  all_52_9 = e1
% 199.69/32.93  | | | 
% 199.69/32.93  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_10, e3, e3,
% 199.69/32.93  | | |              simplifying with (68), (96) gives:
% 199.69/32.93  | | |   (100)  all_52_10 = all_6_2
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (19), (99) imply:
% 199.69/32.93  | | |   (101)   ~ (all_52_15 = e1)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | SIMP: (101) implies:
% 199.69/32.93  | | |   (102)   ~ (all_52_15 = e1)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (79), (99) imply:
% 199.69/32.93  | | |   (103)   ~ (all_52_17 = e1)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | SIMP: (103) implies:
% 199.69/32.93  | | |   (104)   ~ (all_52_17 = e1)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (90), (99) imply:
% 199.69/32.93  | | |   (105)   ~ (all_14_1 = e1)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | SIMP: (105) implies:
% 199.69/32.93  | | |   (106)   ~ (all_14_1 = e1)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (34), (99) imply:
% 199.69/32.93  | | |   (107)  op(e1, e1) = all_52_8
% 199.69/32.93  | | | 
% 199.69/32.93  | | | GROUND_INST: instantiating (2) with all_10_2, all_52_8, e1, e1,
% 199.69/32.93  | | |              simplifying with (81), (107) gives:
% 199.69/32.93  | | |   (108)  all_52_8 = all_10_2
% 199.69/32.93  | | | 
% 199.69/32.93  | | | BETA: splitting (71) gives:
% 199.69/32.93  | | | 
% 199.69/32.93  | | | Case 1:
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | |   (109)  all_58_0 = e3
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | COMBINE_EQS: (9), (109) imply:
% 199.69/32.93  | | | |   (110)  all_6_2 = e3
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | REDUCE: (66), (110) imply:
% 199.69/32.93  | | | |   (111)   ~ (all_52_5 = e3)
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | REDUCE: (85), (110) imply:
% 199.69/32.93  | | | |   (112)  op(e3, e3) = all_6_1
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | REDUCE: (68), (110) imply:
% 199.69/32.93  | | | |   (113)  op(e3, e3) = e3
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | BETA: splitting (40) gives:
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | Case 1:
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | |   (114)  all_58_6 = e3
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | | REF_CLOSE: (75), (111), (114) are inconsistent by sub-proof #1328.
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | Case 2:
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | |   (115)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | | BETA: splitting (115) gives:
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | | Case 1:
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | |   (116)  all_58_7 = e3
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | | COMBINE_EQS: (36), (116) imply:
% 199.69/32.93  | | | | | |   (117)  all_52_13 = e3
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | | REDUCE: (95), (117) imply:
% 199.69/32.93  | | | | | |   (118)  $false
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | | CLOSE: (118) is inconsistent.
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | Case 2:
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | |   (119)  all_58_8 = e3 | all_58_11 = e3
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | | BETA: splitting (119) gives:
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | | Case 1:
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | |   (120)  all_58_8 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | COMBINE_EQS: (61), (120) imply:
% 199.69/32.93  | | | | | | |   (121)  all_10_2 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | SIMP: (121) implies:
% 199.69/32.93  | | | | | | |   (122)  all_10_2 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (22), (122) imply:
% 199.69/32.93  | | | | | | |   (123)   ~ (all_4_0 = e3)
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (12), (122) imply:
% 199.69/32.93  | | | | | | |   (124)  op(e3, e3) = all_52_20
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (21), (122) imply:
% 199.69/32.93  | | | | | | |   (125)  op(e3, e1) = all_10_1
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (81), (122) imply:
% 199.69/32.93  | | | | | | |   (126)  op(e1, e1) = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | GROUND_INST: instantiating (2) with all_52_17, all_10_1, e1, e3,
% 199.69/32.93  | | | | | | |              simplifying with (56), (125) gives:
% 199.69/32.93  | | | | | | |   (127)  all_52_17 = all_10_1
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | GROUND_INST: instantiating (2) with all_6_1, all_52_20, e3, e3,
% 199.69/32.93  | | | | | | |              simplifying with (112), (124) gives:
% 199.69/32.93  | | | | | | |   (128)  all_52_20 = all_6_1
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | GROUND_INST: instantiating (2) with e3, all_52_20, e3, e3,
% 199.69/32.93  | | | | | | |              simplifying with (113), (124) gives:
% 199.69/32.93  | | | | | | |   (129)  all_52_20 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | COMBINE_EQS: (128), (129) imply:
% 199.69/32.93  | | | | | | |   (130)  all_6_1 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | COMBINE_EQS: (86), (127) imply:
% 199.69/32.93  | | | | | | |   (131)  all_58_4 = all_10_1
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (104), (127) imply:
% 199.69/32.93  | | | | | | |   (132)   ~ (all_10_1 = e1)
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (47), (130) imply:
% 199.69/32.93  | | | | | | |   (133)  op(e3, e3) = all_6_0
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | GROUND_INST: instantiating (2) with e3, all_6_0, e3, e3,
% 199.69/32.93  | | | | | | |              simplifying with (113), (133) gives:
% 199.69/32.93  | | | | | | |   (134)  all_6_0 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REDUCE: (31), (134) imply:
% 199.69/32.93  | | | | | | |   (135)   ~ (e3 = e1)
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | BETA: splitting (51) gives:
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | |   (136)  all_58_12 = e1
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | COMBINE_EQS: (39), (136) imply:
% 199.69/32.93  | | | | | | | |   (137)  all_52_7 = e1
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | REDUCE: (82), (137) imply:
% 199.69/32.93  | | | | | | | |   (138)   ~ (all_52_23 = e1)
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | SIMP: (138) implies:
% 199.69/32.93  | | | | | | | |   (139)   ~ (all_52_23 = e1)
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | REDUCE: (41), (137) imply:
% 199.69/32.93  | | | | | | | |   (140)   ~ (e3 = e1)
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | REDUCE: (3), (137) imply:
% 199.69/32.93  | | | | | | | |   (141)  op(e1, e1) = e0
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | BETA: splitting (14) gives:
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | |   (142)  all_58_4 = e1
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | COMBINE_EQS: (131), (142) imply:
% 199.69/32.93  | | | | | | | | |   (143)  all_10_1 = e1
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | REDUCE: (132), (143) imply:
% 199.69/32.93  | | | | | | | | |   (144)  $false
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | CLOSE: (144) is inconsistent.
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | |   (145)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | BETA: splitting (145) gives:
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | |   (146)  all_58_5 = e1
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | COMBINE_EQS: (65), (146) imply:
% 199.69/32.93  | | | | | | | | | |   (147)  all_4_0 = e1
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | REDUCE: (70), (147) imply:
% 199.69/32.93  | | | | | | | | | |   (148)   ~ (all_52_27 = e1)
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | REDUCE: (67), (147) imply:
% 199.69/32.93  | | | | | | | | | |   (149)  op(e1, e1) = all_52_18
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | BETA: splitting (27) gives:
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | |   (150)  all_58_9 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | COMBINE_EQS: (89), (150) imply:
% 199.69/32.93  | | | | | | | | | | |   (151)  all_14_1 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | REDUCE: (106), (151) imply:
% 199.69/32.93  | | | | | | | | | | |   (152)  $false
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | |   (153)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | BETA: splitting (153) gives:
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | |   (154)  all_58_10 = e1
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | COMBINE_EQS: (32), (154) imply:
% 199.69/32.93  | | | | | | | | | | | |   (155)  all_52_27 = e1
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | REDUCE: (148), (155) imply:
% 199.69/32.93  | | | | | | | | | | | |   (156)  $false
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | |   (157)  all_58_11 = e1 | all_58_15 = e1
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | BETA: splitting (157) gives:
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | |   (158)  all_58_11 = e1
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | COMBINE_EQS: (18), (158) imply:
% 199.69/32.93  | | | | | | | | | | | | |   (159)  all_52_29 = e1
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | REDUCE: (63), (159) imply:
% 199.69/32.93  | | | | | | | | | | | | |   (160)  op(e1, e1) = all_52_28
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_52_28, e1, e1,
% 199.69/32.93  | | | | | | | | | | | | |              simplifying with (141), (160) gives:
% 199.69/32.93  | | | | | | | | | | | | |   (161)  all_52_28 = e0
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e3, all_52_18, e1, e1,
% 199.69/32.93  | | | | | | | | | | | | |              simplifying with (126), (149) gives:
% 199.69/32.93  | | | | | | | | | | | | |   (162)  all_52_18 = e3
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_28, all_52_18, e1,
% 199.69/32.93  | | | | | | | | | | | | |              e1, simplifying with (149), (160) gives:
% 199.69/32.93  | | | | | | | | | | | | |   (163)  all_52_18 = all_52_28
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply:
% 199.69/32.93  | | | | | | | | | | | | |   (164)  all_52_28 = e3
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | SIMP: (164) implies:
% 199.69/32.93  | | | | | | | | | | | | |   (165)  all_52_28 = e3
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | COMBINE_EQS: (161), (165) imply:
% 199.69/32.93  | | | | | | | | | | | | |   (166)  e3 = e0
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | SIMP: (166) implies:
% 199.69/32.93  | | | | | | | | | | | | |   (167)  e3 = e0
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | REDUCE: (5), (167) imply:
% 199.69/32.93  | | | | | | | | | | | | |   (168)  $false
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | |   (169)  all_58_15 = e1
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | COMBINE_EQS: (25), (169) imply:
% 199.69/32.93  | | | | | | | | | | | | |   (170)  e3 = e1
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | | REF_CLOSE: (2), (15), (39), (41), (43), (45), (75), (84),
% 199.69/32.93  | | | | | | | | | | | | |            (98), (109), (111), (135), (170) are inconsistent
% 199.69/32.93  | | | | | | | | | | | | |            by sub-proof #860.
% 199.69/32.93  | | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | | End of split
% 199.69/32.93  | | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | End of split
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | End of split
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | |   (171)  all_58_8 = e1 | all_58_14 = e1
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | BETA: splitting (171) gives:
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | Case 1:
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | |   (172)  all_58_8 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | COMBINE_EQS: (120), (172) imply:
% 199.69/32.93  | | | | | | | | | | |   (173)  e3 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | COMBINE_EQS: (109), (173) imply:
% 199.69/32.93  | | | | | | | | | | |   (174)  all_58_0 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | REF_CLOSE: (2), (15), (39), (41), (43), (45), (75), (84),
% 199.69/32.93  | | | | | | | | | | |            (98), (111), (135), (174) are inconsistent by
% 199.69/32.93  | | | | | | | | | | |            sub-proof #1241.
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | |   (175)  all_58_14 = e1
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | | REF_CLOSE: (1), (139), (175) are inconsistent by sub-proof
% 199.69/32.93  | | | | | | | | | | |            #231.
% 199.69/32.93  | | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | | End of split
% 199.69/32.93  | | | | | | | | | | 
% 199.69/32.93  | | | | | | | | | End of split
% 199.69/32.93  | | | | | | | | | 
% 199.69/32.93  | | | | | | | | End of split
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | Case 2:
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | |   (176)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 199.69/32.93  | | | | | | | |            (15), (16), (20), (24), (25), (26), (28), (30), (31),
% 199.69/32.93  | | | | | | | |            (32), (33), (35), (37), (38), (39), (41), (42), (43),
% 199.69/32.93  | | | | | | | |            (44), (45), (47), (48), (49), (52), (53), (54), (58),
% 199.69/32.93  | | | | | | | |            (59), (60), (61), (62), (64), (66), (68), (71), (73),
% 199.69/32.93  | | | | | | | |            (75), (77), (78), (80), (81), (82), (83), (84), (85),
% 199.69/32.93  | | | | | | | |            (86), (102), (135), (176) are inconsistent by
% 199.69/32.93  | | | | | | | |            sub-proof #199.
% 199.69/32.93  | | | | | | | | 
% 199.69/32.93  | | | | | | | End of split
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | Case 2:
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | |   (177)  all_58_11 = e3
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | | REF_CLOSE: (18), (46), (177) are inconsistent by sub-proof #1323.
% 199.69/32.93  | | | | | | | 
% 199.69/32.93  | | | | | | End of split
% 199.69/32.93  | | | | | | 
% 199.69/32.93  | | | | | End of split
% 199.69/32.93  | | | | | 
% 199.69/32.93  | | | | End of split
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | Case 2:
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | |   (178)   ~ (all_58_0 = e3)
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | REDUCE: (9), (178) imply:
% 199.69/32.93  | | | |   (179)   ~ (all_6_2 = e3)
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | | REF_CLOSE: (2), (4), (9), (15), (26), (38), (39), (41), (43), (45),
% 199.69/32.93  | | | |            (49), (62), (68), (75), (81), (84), (179) are inconsistent by
% 199.69/32.93  | | | |            sub-proof #1363.
% 199.69/32.93  | | | | 
% 199.69/32.93  | | | End of split
% 199.69/32.93  | | | 
% 199.69/32.93  | | Case 2:
% 199.69/32.93  | | | 
% 199.69/32.93  | | |   (180)  all_58_5 = e3 | all_58_10 = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REF_CLOSE: (29), (32), (54), (65), (180) are inconsistent by sub-proof
% 199.69/32.93  | | |            #214.
% 199.69/32.93  | | | 
% 199.69/32.93  | | End of split
% 199.69/32.93  | | 
% 199.69/32.93  | End of split
% 199.69/32.93  | 
% 199.69/32.93  End of proof
% 199.69/32.93  
% 199.69/32.93  Sub-proof #105 shows that the following formulas are inconsistent:
% 199.69/32.93  ----------------------------------------------------------------
% 199.69/32.93    (1)   ~ (all_52_15 = all_52_23)
% 199.69/32.93    (2)   ~ (all_52_25 = all_52_27)
% 199.69/32.93    (3)  all_58_14 = all_52_23
% 199.69/32.93    (4)  op(all_52_3, all_52_3) = all_52_2
% 199.69/32.93    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.93    (6)  all_58_1 = all_52_9
% 199.69/32.93    (7)   ~ (e3 = e0)
% 199.69/32.93    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.93    (9)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.93    (10)   ~ (all_52_17 = all_52_25)
% 199.69/32.93    (11)   ~ (all_52_3 = all_6_2)
% 199.69/32.93    (12)  all_58_0 = all_6_2
% 199.69/32.93    (13)  op(all_14_2, e0) = all_14_1
% 199.69/32.93    (14)   ~ (all_52_17 = all_10_2)
% 199.69/32.93    (15)  op(e3, e0) = all_52_25
% 199.69/32.93    (16)  op(all_52_5, all_52_5) = all_52_4
% 199.69/32.93    (17)  all_58_13 = all_52_15
% 199.69/32.93    (18)  op(all_10_2, all_10_2) = all_52_20
% 199.69/32.93    (19)  all_58_9 = all_52_25
% 199.69/32.93    (20)   ~ (all_6_1 = e1)
% 199.69/32.93    (21)  op(e1, e3) = all_52_5
% 199.69/32.93    (22)  op(e2, e2) = all_4_2
% 199.69/32.93    (23)   ~ (all_52_3 = all_52_5)
% 199.69/32.93    (24)  op(all_4_2, e2) = e1
% 199.69/32.93    (25)   ~ (all_52_25 = all_14_2)
% 199.69/32.93    (26)   ~ (all_52_9 = all_52_15)
% 199.69/32.93    (27)   ~ (all_52_3 = all_52_27)
% 199.69/32.93    (28)  op(all_10_2, e1) = all_10_1
% 199.69/32.93    (29)  op(all_6_2, all_6_2) = all_52_0
% 199.69/32.93    (30)   ~ (all_52_7 = all_6_2)
% 199.69/32.93    (31)  op(e0, e0) = all_14_2
% 199.69/32.93    (32)  all_56_15 = all_14_2
% 199.69/32.93    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.93    (34)   ~ (all_4_0 = e3)
% 199.69/32.93    (35)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.69/32.93    (36)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.93    (37)  op(e1, all_10_1) = e3
% 199.69/32.93    (38)   ~ (e2 = e1)
% 199.69/32.93    (39)   ~ (all_52_13 = all_10_2)
% 199.69/32.93    (40)  all_58_10 = all_52_27
% 199.69/32.93    (41)  all_56_8 = all_52_5
% 199.69/32.93    (42)  op(all_52_15, all_52_15) = all_52_14
% 199.69/32.93    (43)  all_58_7 = all_52_13
% 199.69/32.93    (44)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.69/32.93    (45)   ~ (all_52_5 = all_52_7)
% 199.69/32.93    (46)  all_58_12 = all_52_7
% 199.69/32.93    (47)   ~ (all_52_7 = all_14_2)
% 199.69/32.93    (48)  all_58_2 = all_52_3
% 199.69/32.93    (49)  all_56_2 = all_52_17
% 199.69/32.93    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 199.69/32.93    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.69/32.93    (52)  op(e3, all_6_1) = all_6_0
% 199.69/32.93    (53)   ~ (all_52_15 = all_14_2)
% 199.69/32.93    (54)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 199.69/32.93    (55)   ~ (all_6_0 = e2)
% 199.69/32.93    (56)  op(e3, e1) = all_52_17
% 199.69/32.93    (57)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.69/32.93    (58)  op(e0, e3) = all_52_7
% 199.69/32.93    (59)  op(e1, e2) = all_52_13
% 199.69/32.93    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.69/32.93    (61)  all_58_15 = all_14_2
% 199.69/32.93    (62)   ~ (all_52_19 = all_10_2)
% 199.69/32.93    (63)  op(all_52_23, all_52_23) = all_52_22
% 199.69/32.93    (64)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.69/32.93    (65)  all_58_8 = all_10_2
% 199.69/32.93    (66)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.69/32.93    (67)   ~ (all_52_5 = all_10_2)
% 199.69/32.93    (68)   ~ (all_52_23 = all_14_2)
% 199.69/32.93    (69)  all_56_12 = all_52_7
% 199.69/32.93    (70)  op(all_52_17, all_52_17) = all_52_16
% 199.69/32.93    (71)  all_58_5 = all_4_0
% 199.69/32.93    (72)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.69/32.93    (73)   ~ (all_52_9 = all_4_2)
% 199.69/32.93    (74)   ~ (all_52_5 = all_6_2)
% 199.69/32.93    (75)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.69/32.93    (76)   ~ (all_52_9 = all_6_2)
% 199.69/32.93    (77)  op(e3, e3) = all_6_2
% 199.69/32.93    (78)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.69/32.93    (79)   ~ (all_52_27 = all_14_2)
% 199.69/32.93    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.69/32.93    (81)  all_56_14 = all_52_23
% 199.69/32.93    (82)  op(all_4_2, all_4_2) = all_52_10
% 199.69/32.93    (83)  all_56_3 = all_52_25
% 199.69/32.93    (84)   ~ (all_52_3 = all_52_7)
% 199.69/32.93    (85)  op(all_14_2, all_14_2) = all_52_30
% 199.69/32.93    (86)  all_58_5 = all_52_19
% 199.69/32.93    (87)   ~ (all_52_15 = all_4_2)
% 199.69/32.93    (88)  all_58_6 = all_52_5
% 199.69/32.93    (89)   ~ (all_4_0 = all_4_2)
% 199.69/32.93    (90)  op(e3, e2) = all_52_9
% 199.69/32.93    (91)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.93    (92)   ~ (all_52_17 = all_6_2)
% 199.69/32.93    (93)   ~ (e3 = e2)
% 199.69/32.93    (94)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.93    (95)   ~ (all_52_3 = all_4_0)
% 199.69/32.93    (96)   ~ (all_6_1 = e2)
% 199.69/32.93    (97)   ~ (all_52_7 = all_52_23)
% 199.69/32.93    (98)  all_58_3 = all_4_2
% 199.69/32.93    (99)  all_56_13 = all_52_15
% 199.69/32.93    (100)   ~ (all_52_3 = all_4_2)
% 199.69/32.93    (101)  op(all_6_2, e3) = all_6_1
% 199.69/32.93    (102)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 199.69/32.93    (103)  all_58_4 = all_52_17
% 199.69/32.93    (104)  op(all_52_25, all_52_25) = all_52_24
% 199.69/32.93  
% 199.69/32.93  Begin of proof
% 199.69/32.93  | 
% 199.69/32.93  | ALPHA: (102) implies:
% 199.69/32.93  |   (105)  all_52_22 = e0
% 199.69/32.93  |   (106)  all_52_20 = e1
% 199.69/32.93  |   (107)  all_52_16 = e3
% 199.69/32.93  | 
% 199.69/32.93  | REDUCE: (70), (107) imply:
% 199.69/32.93  |   (108)  op(all_52_17, all_52_17) = e3
% 199.69/32.93  | 
% 199.69/32.93  | REDUCE: (63), (105) imply:
% 199.69/32.93  |   (109)  op(all_52_23, all_52_23) = e0
% 199.69/32.93  | 
% 199.69/32.93  | REDUCE: (18), (106) imply:
% 199.69/32.93  |   (110)  op(all_10_2, all_10_2) = e1
% 199.69/32.93  | 
% 199.69/32.93  | BETA: splitting (66) gives:
% 199.69/32.93  | 
% 199.69/32.93  | Case 1:
% 199.69/32.93  | | 
% 199.69/32.93  | |   (111)  all_56_15 = e3
% 199.69/32.93  | | 
% 199.69/32.93  | | REF_CLOSE: (3), (4), (5), (6), (9), (11), (12), (13), (15), (17), (19),
% 199.69/32.93  | |            (21), (22), (23), (24), (25), (26), (27), (28), (30), (32), (33),
% 199.69/32.93  | |            (34), (38), (39), (40), (41), (43), (45), (46), (48), (50), (51),
% 199.69/32.93  | |            (52), (54), (55), (56), (60), (62), (64), (65), (68), (71), (72),
% 199.69/32.93  | |            (73), (74), (75), (76), (77), (79), (80), (82), (83), (84), (85),
% 199.69/32.93  | |            (86), (88), (89), (90), (92), (93), (94), (95), (96), (98),
% 199.69/32.93  | |            (100), (101), (103), (108), (110), (111) are inconsistent by
% 199.69/32.93  | |            sub-proof #203.
% 199.69/32.93  | | 
% 199.69/32.93  | Case 2:
% 199.69/32.93  | | 
% 199.69/32.93  | |   (112)   ~ (all_56_15 = e3)
% 199.69/32.93  | | 
% 199.69/32.93  | | REDUCE: (32), (112) imply:
% 199.69/32.93  | |   (113)   ~ (all_14_2 = e3)
% 199.69/32.93  | | 
% 199.69/32.93  | | BETA: splitting (33) gives:
% 199.69/32.93  | | 
% 199.69/32.93  | | Case 1:
% 199.69/32.93  | | | 
% 199.69/32.93  | | |   (114)  all_58_2 = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | COMBINE_EQS: (48), (114) imply:
% 199.69/32.93  | | |   (115)  all_52_3 = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | SIMP: (115) implies:
% 199.69/32.93  | | |   (116)  all_52_3 = e3
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (84), (116) imply:
% 199.69/32.93  | | |   (117)   ~ (all_52_7 = e3)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | SIMP: (117) implies:
% 199.69/32.93  | | |   (118)   ~ (all_52_7 = e3)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (11), (116) imply:
% 199.69/32.93  | | |   (119)   ~ (all_6_2 = e3)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | SIMP: (119) implies:
% 199.69/32.93  | | |   (120)   ~ (all_6_2 = e3)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (95), (116) imply:
% 199.69/32.93  | | |   (121)   ~ (all_4_0 = e3)
% 199.69/32.93  | | | 
% 199.69/32.93  | | | REDUCE: (4), (116) imply:
% 199.69/32.93  | | |   (122)  op(e3, e3) = all_52_2
% 199.69/32.94  | | | 
% 199.69/32.94  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_2, e3, e3, simplifying
% 199.69/32.94  | | |              with (77), (122) gives:
% 199.69/32.94  | | |   (123)  all_52_2 = all_6_2
% 199.69/32.94  | | | 
% 199.69/32.94  | | | BETA: splitting (78) gives:
% 199.69/32.94  | | | 
% 199.69/32.94  | | | Case 1:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | |   (124)  all_58_9 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | COMBINE_EQS: (19), (124) imply:
% 199.69/32.94  | | | |   (125)  all_52_25 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | SIMP: (125) implies:
% 199.69/32.94  | | | |   (126)  all_52_25 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (10), (126) imply:
% 199.69/32.94  | | | |   (127)   ~ (all_52_17 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (25), (126) imply:
% 199.69/32.94  | | | |   (128)   ~ (all_14_2 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (104), (126) imply:
% 199.69/32.94  | | | |   (129)  op(e3, e3) = all_52_24
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 199.69/32.94  | | | |              simplifying with (77), (129) gives:
% 199.69/32.94  | | | |   (130)  all_52_24 = all_6_2
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | BETA: splitting (94) gives:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | Case 1:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | |   (131)  all_58_4 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REF_CLOSE: (103), (127), (131) are inconsistent by sub-proof #1302.
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | Case 2:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | |   (132)   ~ (all_58_4 = e3)
% 199.69/32.94  | | | | |   (133)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | BETA: splitting (36) gives:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | Case 1:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | |   (134)  all_56_2 = e3
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | REF_CLOSE: (49), (127), (134) are inconsistent by sub-proof #1327.
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | Case 2:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | |   (135)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | BETA: splitting (35) gives:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | Case 1:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | |   (136)  all_56_13 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | COMBINE_EQS: (99), (136) imply:
% 199.69/32.94  | | | | | | |   (137)  all_52_15 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | SIMP: (137) implies:
% 199.69/32.94  | | | | | | |   (138)  all_52_15 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (1), (138) imply:
% 199.69/32.94  | | | | | | |   (139)   ~ (all_52_23 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | SIMP: (139) implies:
% 199.69/32.94  | | | | | | |   (140)   ~ (all_52_23 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (42), (138) imply:
% 199.69/32.94  | | | | | | |   (141)  op(e3, e3) = all_52_14
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REF_CLOSE: (3), (5), (28), (31), (34), (37), (39), (49), (56),
% 199.69/32.94  | | | | | | |            (57), (59), (65), (71), (77), (92), (103), (108),
% 199.69/32.94  | | | | | | |            (110), (113), (133), (135), (140), (141) are
% 199.69/32.94  | | | | | | |            inconsistent by sub-proof #107.
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | Case 2:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | |   (142)   ~ (all_56_13 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (99), (142) imply:
% 199.69/32.94  | | | | | | |   (143)   ~ (all_52_15 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REF_CLOSE: (3), (5), (8), (17), (20), (30), (46), (58), (61),
% 199.69/32.94  | | | | | | |            (69), (77), (91), (96), (97), (101), (109), (113),
% 199.69/32.94  | | | | | | |            (118), (143) are inconsistent by sub-proof #179.
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | End of split
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | End of split
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | End of split
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | Case 2:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | |   (144)   ~ (all_58_9 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (19), (144) imply:
% 199.69/32.94  | | | |   (145)   ~ (all_52_25 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REF_CLOSE: (3), (5), (6), (8), (12), (17), (19), (20), (26), (30), (46),
% 199.69/32.94  | | | |            (58), (61), (69), (77), (80), (91), (92), (96), (97), (101),
% 199.69/32.94  | | | |            (103), (108), (109), (113), (118), (120), (145) are
% 199.69/32.94  | | | |            inconsistent by sub-proof #178.
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | End of split
% 199.69/32.94  | | | 
% 199.69/32.94  | | Case 2:
% 199.69/32.94  | | | 
% 199.69/32.94  | | |   (146)   ~ (all_58_2 = e3)
% 199.69/32.94  | | |   (147)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (48), (146) imply:
% 199.69/32.94  | | |   (148)   ~ (all_52_3 = e3)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | BETA: splitting (91) gives:
% 199.69/32.94  | | | 
% 199.69/32.94  | | | Case 1:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | |   (149)  all_58_12 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | COMBINE_EQS: (46), (149) imply:
% 199.69/32.94  | | | |   (150)  all_52_7 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | SIMP: (150) implies:
% 199.69/32.94  | | | |   (151)  all_52_7 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (97), (151) imply:
% 199.69/32.94  | | | |   (152)   ~ (all_52_23 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | SIMP: (152) implies:
% 199.69/32.94  | | | |   (153)   ~ (all_52_23 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (47), (151) imply:
% 199.69/32.94  | | | |   (154)   ~ (all_14_2 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (9), (151) imply:
% 199.69/32.94  | | | |   (155)  op(e3, e3) = all_52_6
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3,
% 199.69/32.94  | | | |              simplifying with (77), (155) gives:
% 199.69/32.94  | | | |   (156)  all_52_6 = all_6_2
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | BETA: splitting (94) gives:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | Case 1:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | |   (157)  all_58_4 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | COMBINE_EQS: (103), (157) imply:
% 199.69/32.94  | | | | |   (158)  all_52_17 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | SIMP: (158) implies:
% 199.69/32.94  | | | | |   (159)  all_52_17 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REF_CLOSE: (5), (77), (92), (108), (159) are inconsistent by sub-proof
% 199.69/32.94  | | | | |            #1280.
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | Case 2:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | |   (160)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REF_CLOSE: (3), (5), (14), (28), (31), (34), (36), (37), (39), (49),
% 199.69/32.94  | | | | |            (56), (57), (59), (65), (71), (77), (92), (103), (108),
% 199.69/32.94  | | | | |            (110), (113), (153), (160) are inconsistent by sub-proof
% 199.69/32.94  | | | | |            #106.
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | End of split
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | Case 2:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | |   (161)   ~ (all_58_12 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REDUCE: (46), (161) imply:
% 199.69/32.94  | | | |   (162)   ~ (all_52_7 = e3)
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | BETA: splitting (51) gives:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | Case 1:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | |   (163)  all_58_0 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | COMBINE_EQS: (12), (163) imply:
% 199.69/32.94  | | | | |   (164)  all_6_2 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REDUCE: (92), (164) imply:
% 199.69/32.94  | | | | |   (165)   ~ (all_52_17 = e3)
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REDUCE: (29), (164) imply:
% 199.69/32.94  | | | | |   (166)  op(e3, e3) = all_52_0
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REDUCE: (101), (164) imply:
% 199.69/32.94  | | | | |   (167)  op(e3, e3) = all_6_1
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REDUCE: (77), (164) imply:
% 199.69/32.94  | | | | |   (168)  op(e3, e3) = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | GROUND_INST: instantiating (5) with all_6_1, all_52_0, e3, e3,
% 199.69/32.94  | | | | |              simplifying with (166), (167) gives:
% 199.69/32.94  | | | | |   (169)  all_52_0 = all_6_1
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | GROUND_INST: instantiating (5) with e3, all_52_0, e3, e3, simplifying
% 199.69/32.94  | | | | |              with (166), (168) gives:
% 199.69/32.94  | | | | |   (170)  all_52_0 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | COMBINE_EQS: (169), (170) imply:
% 199.69/32.94  | | | | |   (171)  all_6_1 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | SIMP: (171) implies:
% 199.69/32.94  | | | | |   (172)  all_6_1 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | REDUCE: (52), (172) imply:
% 199.69/32.94  | | | | |   (173)  op(e3, e3) = all_6_0
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | GROUND_INST: instantiating (5) with e3, all_6_0, e3, e3, simplifying
% 199.69/32.94  | | | | |              with (168), (173) gives:
% 199.69/32.94  | | | | |   (174)  all_6_0 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | BETA: splitting (94) gives:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | Case 1:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | |   (175)  all_58_4 = e3
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | REF_CLOSE: (103), (165), (175) are inconsistent by sub-proof #1302.
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | Case 2:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | |   (176)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | BETA: splitting (44) gives:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | Case 1:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | |   (177)  all_56_14 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | COMBINE_EQS: (81), (177) imply:
% 199.69/32.94  | | | | | | |   (178)  all_52_23 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | SIMP: (178) implies:
% 199.69/32.94  | | | | | | |   (179)  all_52_23 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (109), (179) imply:
% 199.69/32.94  | | | | | | |   (180)  op(e3, e3) = e0
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REF_CLOSE: (5), (7), (166), (167), (168), (180) are inconsistent
% 199.69/32.94  | | | | | | |            by sub-proof #949.
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | Case 2:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | |   (181)   ~ (all_56_14 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (81), (181) imply:
% 199.69/32.94  | | | | | | |   (182)   ~ (all_52_23 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REF_CLOSE: (3), (5), (14), (28), (31), (34), (36), (37), (39),
% 199.69/32.94  | | | | | | |            (49), (56), (57), (59), (65), (71), (77), (92), (103),
% 199.69/32.94  | | | | | | |            (108), (110), (113), (176), (182) are inconsistent by
% 199.69/32.94  | | | | | | |            sub-proof #106.
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | End of split
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | End of split
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | Case 2:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | |   (183)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | BETA: splitting (183) gives:
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | | Case 1:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | |   (184)  all_58_2 = e3
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | REF_CLOSE: (48), (148), (184) are inconsistent by sub-proof #1369.
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | Case 2:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | |   (185)  all_58_6 = e3 | all_58_12 = e3
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | BETA: splitting (185) gives:
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | | Case 1:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | |   (186)  all_58_6 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | COMBINE_EQS: (88), (186) imply:
% 199.69/32.94  | | | | | | |   (187)  all_52_5 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | SIMP: (187) implies:
% 199.69/32.94  | | | | | | |   (188)  all_52_5 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (45), (188) imply:
% 199.69/32.94  | | | | | | |   (189)   ~ (all_52_7 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (67), (188) imply:
% 199.69/32.94  | | | | | | |   (190)   ~ (all_10_2 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | SIMP: (190) implies:
% 199.69/32.94  | | | | | | |   (191)   ~ (all_10_2 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (74), (188) imply:
% 199.69/32.94  | | | | | | |   (192)   ~ (all_6_2 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | SIMP: (192) implies:
% 199.69/32.94  | | | | | | |   (193)   ~ (all_6_2 = e3)
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REDUCE: (16), (188) imply:
% 199.69/32.94  | | | | | | |   (194)  op(e3, e3) = all_52_4
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 199.69/32.94  | | | | | | |              simplifying with (77), (194) gives:
% 199.69/32.94  | | | | | | |   (195)  all_52_4 = all_6_2
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | BETA: splitting (78) gives:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | Case 1:
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | |   (196)  all_58_9 = e3
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | COMBINE_EQS: (19), (196) imply:
% 199.69/32.94  | | | | | | | |   (197)  all_52_25 = e3
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | SIMP: (197) implies:
% 199.69/32.94  | | | | | | | |   (198)  all_52_25 = e3
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | REDUCE: (10), (198) imply:
% 199.69/32.94  | | | | | | | |   (199)   ~ (all_52_17 = e3)
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | REDUCE: (2), (198) imply:
% 199.69/32.94  | | | | | | | |   (200)   ~ (all_52_27 = e3)
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | SIMP: (200) implies:
% 199.69/32.94  | | | | | | | |   (201)   ~ (all_52_27 = e3)
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | REDUCE: (25), (198) imply:
% 199.69/32.94  | | | | | | | |   (202)   ~ (all_14_2 = e3)
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | BETA: splitting (94) gives:
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | Case 1:
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | |   (203)  all_58_4 = e3
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | REF_CLOSE: (103), (199), (203) are inconsistent by sub-proof
% 199.69/32.94  | | | | | | | | |            #1302.
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | Case 2:
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | |   (204)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | BETA: splitting (147) gives:
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | Case 1:
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | |   (205)  all_58_3 = e3
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | | COMBINE_EQS: (98), (205) imply:
% 199.69/32.94  | | | | | | | | | |   (206)  all_4_2 = e3
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | | REDUCE: (87), (206) imply:
% 199.69/32.94  | | | | | | | | | |   (207)   ~ (all_52_15 = e3)
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | | REF_CLOSE: (3), (5), (8), (17), (20), (30), (34), (46), (58),
% 199.69/32.94  | | | | | | | | | |            (61), (65), (69), (71), (77), (91), (96), (97),
% 199.69/32.94  | | | | | | | | | |            (101), (109), (113), (191), (204), (207) are
% 199.69/32.94  | | | | | | | | | |            inconsistent by sub-proof #175.
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | Case 2:
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | |   (208)  all_58_5 = e3 | all_58_10 = e3
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | | REF_CLOSE: (34), (40), (71), (201), (208) are inconsistent by
% 199.69/32.94  | | | | | | | | | |            sub-proof #214.
% 199.69/32.94  | | | | | | | | | | 
% 199.69/32.94  | | | | | | | | | End of split
% 199.69/32.94  | | | | | | | | | 
% 199.69/32.94  | | | | | | | | End of split
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | Case 2:
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | |   (209)   ~ (all_58_9 = e3)
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | REDUCE: (19), (209) imply:
% 199.69/32.94  | | | | | | | |   (210)   ~ (all_52_25 = e3)
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (12), (17), (19), (20), (26),
% 199.69/32.94  | | | | | | | |            (30), (46), (58), (61), (69), (77), (80), (91), (92),
% 199.69/32.94  | | | | | | | |            (96), (97), (101), (103), (108), (109), (113), (162),
% 199.69/32.94  | | | | | | | |            (193), (210) are inconsistent by sub-proof #178.
% 199.69/32.94  | | | | | | | | 
% 199.69/32.94  | | | | | | | End of split
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | Case 2:
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | |   (211)  all_58_12 = e3
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | | REF_CLOSE: (46), (162), (211) are inconsistent by sub-proof #1367.
% 199.69/32.94  | | | | | | | 
% 199.69/32.94  | | | | | | End of split
% 199.69/32.94  | | | | | | 
% 199.69/32.94  | | | | | End of split
% 199.69/32.94  | | | | | 
% 199.69/32.94  | | | | End of split
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | End of split
% 199.69/32.94  | | | 
% 199.69/32.94  | | End of split
% 199.69/32.94  | | 
% 199.69/32.94  | End of split
% 199.69/32.94  | 
% 199.69/32.94  End of proof
% 199.69/32.94  
% 199.69/32.94  Sub-proof #106 shows that the following formulas are inconsistent:
% 199.69/32.94  ----------------------------------------------------------------
% 199.69/32.94    (1)  all_58_14 = all_52_23
% 199.69/32.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.94    (3)   ~ (all_52_17 = all_10_2)
% 199.69/32.94    (4)  op(all_10_2, e1) = all_10_1
% 199.69/32.94    (5)  op(e0, e0) = all_14_2
% 199.69/32.94    (6)   ~ (all_4_0 = e3)
% 199.69/32.94    (7)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.94    (8)  op(e1, all_10_1) = e3
% 199.69/32.94    (9)   ~ (all_52_13 = all_10_2)
% 199.69/32.94    (10)  op(all_10_2, all_10_2) = e1
% 199.69/32.94    (11)  all_56_2 = all_52_17
% 199.69/32.94    (12)   ~ (all_52_23 = e3)
% 199.69/32.94    (13)  op(e3, e1) = all_52_17
% 199.69/32.94    (14)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.69/32.94    (15)  op(e1, e2) = all_52_13
% 199.69/32.94    (16)  all_58_8 = all_10_2
% 199.69/32.94    (17)  all_58_5 = all_4_0
% 199.69/32.94    (18)  op(e3, e3) = all_6_2
% 199.69/32.94    (19)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94    (20)  op(all_52_17, all_52_17) = e3
% 199.69/32.94    (21)   ~ (all_52_17 = all_6_2)
% 199.69/32.94    (22)  all_58_4 = all_52_17
% 199.69/32.94    (23)   ~ (all_14_2 = e3)
% 199.69/32.94  
% 199.69/32.94  Begin of proof
% 199.69/32.94  | 
% 199.69/32.94  | BETA: splitting (19) gives:
% 199.69/32.94  | 
% 199.69/32.94  | Case 1:
% 199.69/32.94  | | 
% 199.69/32.94  | |   (24)  all_58_5 = e3
% 199.69/32.94  | | 
% 199.69/32.94  | | REF_CLOSE: (6), (17), (24) are inconsistent by sub-proof #215.
% 199.69/32.94  | | 
% 199.69/32.94  | Case 2:
% 199.69/32.94  | | 
% 199.69/32.94  | |   (25)  all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94  | | 
% 199.69/32.94  | | BETA: splitting (25) gives:
% 199.69/32.94  | | 
% 199.69/32.94  | | Case 1:
% 199.69/32.94  | | | 
% 199.69/32.94  | | |   (26)  all_58_8 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (16), (26) imply:
% 199.69/32.94  | | |   (27)  all_10_2 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (9), (27) imply:
% 199.69/32.94  | | |   (28)   ~ (all_52_13 = e3)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (3), (27) imply:
% 199.69/32.94  | | |   (29)   ~ (all_52_17 = e3)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (10), (27) imply:
% 199.69/32.94  | | |   (30)  op(e3, e3) = e1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (4), (27) imply:
% 199.69/32.94  | | |   (31)  op(e3, e1) = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | GROUND_INST: instantiating (2) with all_52_17, all_10_1, e1, e3,
% 199.69/32.94  | | |              simplifying with (13), (31) gives:
% 199.69/32.94  | | |   (32)  all_52_17 = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | GROUND_INST: instantiating (2) with all_6_2, e1, e3, e3, simplifying with
% 199.69/32.94  | | |              (18), (30) gives:
% 199.69/32.94  | | |   (33)  all_6_2 = e1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (11), (32) imply:
% 199.69/32.94  | | |   (34)  all_56_2 = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (22), (32) imply:
% 199.69/32.94  | | |   (35)  all_58_4 = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (21), (32), (33) imply:
% 199.69/32.94  | | |   (36)   ~ (all_10_1 = e1)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (29), (32) imply:
% 199.69/32.94  | | |   (37)   ~ (all_10_1 = e3)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (20), (32) imply:
% 199.69/32.94  | | |   (38)  op(all_10_1, all_10_1) = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | BETA: splitting (7) gives:
% 199.69/32.94  | | | 
% 199.69/32.94  | | | Case 1:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | |   (39)  all_56_2 = e3
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REF_CLOSE: (34), (37), (39) are inconsistent by sub-proof #1029.
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | Case 2:
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | |   (40)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | | REF_CLOSE: (2), (5), (8), (14), (15), (23), (28), (34), (35), (36),
% 199.69/32.94  | | | |            (38), (40) are inconsistent by sub-proof #226.
% 199.69/32.94  | | | | 
% 199.69/32.94  | | | End of split
% 199.69/32.94  | | | 
% 199.69/32.94  | | Case 2:
% 199.69/32.94  | | | 
% 199.69/32.94  | | |   (41)  all_58_14 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REF_CLOSE: (1), (12), (41) are inconsistent by sub-proof #1305.
% 199.69/32.94  | | | 
% 199.69/32.94  | | End of split
% 199.69/32.94  | | 
% 199.69/32.94  | End of split
% 199.69/32.94  | 
% 199.69/32.94  End of proof
% 199.69/32.94  
% 199.69/32.94  Sub-proof #107 shows that the following formulas are inconsistent:
% 199.69/32.94  ----------------------------------------------------------------
% 199.69/32.94    (1)  all_58_14 = all_52_23
% 199.69/32.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.94    (3)  op(all_10_2, e1) = all_10_1
% 199.69/32.94    (4)  op(e0, e0) = all_14_2
% 199.69/32.94    (5)  op(e3, e3) = all_52_14
% 199.69/32.94    (6)   ~ (all_4_0 = e3)
% 199.69/32.94    (7)  op(e1, all_10_1) = e3
% 199.69/32.94    (8)   ~ (all_52_13 = all_10_2)
% 199.69/32.94    (9)  op(all_10_2, all_10_2) = e1
% 199.69/32.94    (10)  all_56_2 = all_52_17
% 199.69/32.94    (11)   ~ (all_52_23 = e3)
% 199.69/32.94    (12)  op(e3, e1) = all_52_17
% 199.69/32.94    (13)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 199.69/32.94    (14)  op(e1, e2) = all_52_13
% 199.69/32.94    (15)  all_58_8 = all_10_2
% 199.69/32.94    (16)  all_58_5 = all_4_0
% 199.69/32.94    (17)  op(e3, e3) = all_6_2
% 199.69/32.94    (18)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94    (19)  op(all_52_17, all_52_17) = e3
% 199.69/32.94    (20)   ~ (all_52_17 = all_6_2)
% 199.69/32.94    (21)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.69/32.94    (22)  all_58_4 = all_52_17
% 199.69/32.94    (23)   ~ (all_14_2 = e3)
% 199.69/32.94  
% 199.69/32.94  Begin of proof
% 199.69/32.94  | 
% 199.69/32.94  | BETA: splitting (18) gives:
% 199.69/32.94  | 
% 199.69/32.94  | Case 1:
% 199.69/32.94  | | 
% 199.69/32.94  | |   (24)  all_58_5 = e3
% 199.69/32.94  | | 
% 199.69/32.94  | | REF_CLOSE: (6), (16), (24) are inconsistent by sub-proof #215.
% 199.69/32.94  | | 
% 199.69/32.94  | Case 2:
% 199.69/32.94  | | 
% 199.69/32.94  | |   (25)  all_58_8 = e3 | all_58_14 = e3
% 199.69/32.94  | | 
% 199.69/32.94  | | BETA: splitting (25) gives:
% 199.69/32.94  | | 
% 199.69/32.94  | | Case 1:
% 199.69/32.94  | | | 
% 199.69/32.94  | | |   (26)  all_58_8 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (15), (26) imply:
% 199.69/32.94  | | |   (27)  all_10_2 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (8), (27) imply:
% 199.69/32.94  | | |   (28)   ~ (all_52_13 = e3)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (9), (27) imply:
% 199.69/32.94  | | |   (29)  op(e3, e3) = e1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (3), (27) imply:
% 199.69/32.94  | | |   (30)  op(e3, e1) = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | GROUND_INST: instantiating (2) with all_52_17, all_10_1, e1, e3,
% 199.69/32.94  | | |              simplifying with (12), (30) gives:
% 199.69/32.94  | | |   (31)  all_52_17 = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_14, e3, e3,
% 199.69/32.94  | | |              simplifying with (5), (17) gives:
% 199.69/32.94  | | |   (32)  all_52_14 = all_6_2
% 199.69/32.94  | | | 
% 199.69/32.94  | | | GROUND_INST: instantiating (2) with e1, all_52_14, e3, e3, simplifying
% 199.69/32.94  | | |              with (5), (29) gives:
% 199.69/32.94  | | |   (33)  all_52_14 = e1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (32), (33) imply:
% 199.69/32.94  | | |   (34)  all_6_2 = e1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | SIMP: (34) implies:
% 199.69/32.94  | | |   (35)  all_6_2 = e1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (10), (31) imply:
% 199.69/32.94  | | |   (36)  all_56_2 = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | COMBINE_EQS: (22), (31) imply:
% 199.69/32.94  | | |   (37)  all_58_4 = all_10_1
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (20), (31), (35) imply:
% 199.69/32.94  | | |   (38)   ~ (all_10_1 = e1)
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REDUCE: (19), (31) imply:
% 199.69/32.94  | | |   (39)  op(all_10_1, all_10_1) = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REF_CLOSE: (2), (4), (7), (13), (14), (21), (23), (28), (36), (37), (38),
% 199.69/32.94  | | |            (39) are inconsistent by sub-proof #226.
% 199.69/32.94  | | | 
% 199.69/32.94  | | Case 2:
% 199.69/32.94  | | | 
% 199.69/32.94  | | |   (40)  all_58_14 = e3
% 199.69/32.94  | | | 
% 199.69/32.94  | | | REF_CLOSE: (1), (11), (40) are inconsistent by sub-proof #1305.
% 199.69/32.94  | | | 
% 199.69/32.94  | | End of split
% 199.69/32.94  | | 
% 199.69/32.94  | End of split
% 199.69/32.94  | 
% 199.69/32.94  End of proof
% 199.69/32.94  
% 199.69/32.94  Sub-proof #108 shows that the following formulas are inconsistent:
% 199.69/32.94  ----------------------------------------------------------------
% 199.69/32.94    (1)   ~ (all_52_15 = all_52_23)
% 199.69/32.94    (2)  all_58_14 = all_52_23
% 199.69/32.94    (3)   ~ (e3 = e1)
% 199.69/32.94    (4)  op(all_52_3, all_52_3) = all_52_2
% 199.69/32.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.69/32.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.69/32.94    (6)   ~ (e3 = e0)
% 199.69/32.94    (7)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 199.69/32.94    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.69/32.94    (9)   ~ (all_52_7 = all_52_15)
% 199.69/32.94    (10)  op(all_52_7, all_52_7) = all_52_6
% 199.69/32.94    (11)  all_58_0 = all_6_2
% 199.69/32.94    (12)  op(all_52_5, all_52_5) = all_52_4
% 199.69/32.94    (13)  all_58_13 = all_52_15
% 199.69/32.94    (14)  op(e1, e3) = all_52_5
% 199.69/32.94    (15)  op(e2, e2) = all_4_2
% 199.69/32.94    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 199.69/32.94    (17)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.69/32.94    (18)  op(all_10_2, e1) = all_10_1
% 199.69/32.94    (19)  op(all_6_2, all_6_2) = all_52_0
% 199.69/32.94    (20)   ~ (all_52_7 = all_6_2)
% 199.69/32.94    (21)  op(e0, e0) = all_14_2
% 199.69/32.94    (22)  op(e0, e1) = all_52_23
% 199.69/32.94    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.69/32.94    (24)  all_58_15 = e0
% 199.69/32.94    (25)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 199.69/32.94    (26)  op(e1, all_10_1) = e3
% 199.69/32.94    (27)   ~ (e2 = e1)
% 199.69/32.94    (28)  op(e0, e0) = e0
% 199.69/32.94    (29)  op(all_52_15, all_52_15) = all_52_14
% 199.69/32.94    (30)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.69/32.94    (31)  all_36_2 = all_10_2
% 199.69/32.94    (32)  all_36_1 = all_10_1
% 199.69/32.94    (33)  all_58_12 = all_52_7
% 199.69/32.94    (34)   ~ (all_52_7 = all_14_2)
% 199.69/32.94    (35)  all_58_2 = all_52_3
% 199.69/32.94    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.69/32.94    (37)   ~ (e2 = e0)
% 199.69/32.94    (38)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.69/32.94    (39)  op(all_52_23, all_52_23) = all_52_22
% 199.69/32.94    (40)   ~ (all_52_23 = e0)
% 199.69/32.94    (41)   ~ (all_52_5 = all_10_2)
% 199.69/32.94    (42)  all_56_12 = all_52_7
% 199.69/32.94    (43)  op(e3, e3) = all_6_2
% 199.69/32.94    (44)  all_56_14 = all_52_23
% 199.69/32.94    (45)  op(all_4_2, all_4_2) = all_52_10
% 199.69/32.94    (46)   ~ (all_52_15 = all_4_2)
% 199.69/32.94    (47)  all_58_6 = all_52_5
% 199.69/32.94    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.69/32.95    (49)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 199.69/32.95    (50)   ~ (e1 = e0)
% 199.69/32.95    (51)   ~ (e3 = e2)
% 199.69/32.95    (52)  op(e1, e1) = all_10_2
% 199.69/32.95    (53)   ~ (all_52_7 = all_52_23)
% 199.69/32.95    (54)  all_56_13 = all_52_15
% 199.69/32.95    (55)   ~ (all_52_3 = all_4_2)
% 199.69/32.95    (56)   ~ (all_52_7 = e0)
% 199.69/32.95  
% 199.69/32.95  Begin of proof
% 199.69/32.95  | 
% 199.69/32.95  | ALPHA: (7) implies:
% 199.69/32.95  |   (57)  all_52_6 = e0
% 199.69/32.95  |   (58)  all_52_4 = e1
% 199.69/32.95  |   (59)  all_52_2 = e2
% 199.69/32.95  |   (60)  all_52_0 = e3
% 199.69/32.95  | 
% 199.69/32.95  | REDUCE: (4), (59) imply:
% 199.69/32.95  |   (61)  op(all_52_3, all_52_3) = e2
% 199.69/32.95  | 
% 199.69/32.95  | REDUCE: (12), (58) imply:
% 199.69/32.95  |   (62)  op(all_52_5, all_52_5) = e1
% 199.69/32.95  | 
% 199.69/32.95  | REDUCE: (10), (57) imply:
% 199.69/32.95  |   (63)  op(all_52_7, all_52_7) = e0
% 199.69/32.95  | 
% 199.69/32.95  | REDUCE: (19), (60) imply:
% 199.69/32.95  |   (64)  op(all_6_2, all_6_2) = e3
% 199.69/32.95  | 
% 199.69/32.95  | BETA: splitting (25) gives:
% 199.69/32.95  | 
% 199.69/32.95  | Case 1:
% 199.69/32.95  | | 
% 199.69/32.95  | |   (65)  all_56_13 = e3
% 199.69/32.95  | | 
% 199.69/32.95  | | COMBINE_EQS: (54), (65) imply:
% 199.69/32.95  | |   (66)  all_52_15 = e3
% 199.69/32.95  | | 
% 199.69/32.95  | | SIMP: (66) implies:
% 199.69/32.95  | |   (67)  all_52_15 = e3
% 199.69/32.95  | | 
% 199.69/32.95  | | COMBINE_EQS: (13), (67) imply:
% 199.69/32.95  | |   (68)  all_58_13 = e3
% 199.95/32.95  | | 
% 199.95/32.95  | | REDUCE: (9), (67) imply:
% 199.95/32.95  | |   (69)   ~ (all_52_7 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | REDUCE: (1), (67) imply:
% 199.95/32.95  | |   (70)   ~ (all_52_23 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | SIMP: (70) implies:
% 199.95/32.95  | |   (71)   ~ (all_52_23 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | REDUCE: (46), (67) imply:
% 199.95/32.95  | |   (72)   ~ (all_4_2 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | SIMP: (72) implies:
% 199.95/32.95  | |   (73)   ~ (all_4_2 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | REDUCE: (29), (67) imply:
% 199.95/32.95  | |   (74)  op(e3, e3) = all_52_14
% 199.95/32.95  | | 
% 199.95/32.95  | | GROUND_INST: instantiating (5) with all_6_2, all_52_14, e3, e3, simplifying
% 199.95/32.95  | |              with (43), (74) gives:
% 199.95/32.95  | |   (75)  all_52_14 = all_6_2
% 199.95/32.95  | | 
% 199.95/32.95  | | BETA: splitting (30) gives:
% 199.95/32.95  | | 
% 199.95/32.95  | | Case 1:
% 199.95/32.95  | | | 
% 199.95/32.95  | | |   (76)  all_56_14 = e3
% 199.95/32.95  | | | 
% 199.95/32.95  | | | REF_CLOSE: (44), (71), (76) are inconsistent by sub-proof #1286.
% 199.95/32.95  | | | 
% 199.95/32.95  | | Case 2:
% 199.95/32.95  | | | 
% 199.95/32.95  | | |   (77)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 199.95/32.95  | | | 
% 199.95/32.95  | | | BETA: splitting (8) gives:
% 199.95/32.95  | | | 
% 199.95/32.95  | | | Case 1:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | |   (78)  all_56_12 = e3
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REF_CLOSE: (42), (69), (78) are inconsistent by sub-proof #1383.
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | Case 2:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | |   (79)   ~ (all_56_12 = e3)
% 199.95/32.95  | | | |   (80)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | BETA: splitting (38) gives:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | Case 1:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | |   (81)  all_58_12 = e1
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | COMBINE_EQS: (33), (81) imply:
% 199.95/32.95  | | | | |   (82)  all_52_7 = e1
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (63), (82) imply:
% 199.95/32.95  | | | | |   (83)  op(e1, e1) = e0
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REF_CLOSE: (2), (5), (17), (18), (22), (24), (27), (31), (32), (37),
% 199.95/32.95  | | | | |            (49), (51), (52), (68), (81), (83) are inconsistent by
% 199.95/32.95  | | | | |            sub-proof #550.
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | Case 2:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | |   (84)   ~ (all_58_12 = e1)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REF_CLOSE: (5), (11), (15), (16), (23), (28), (33), (35), (36), (39),
% 199.95/32.95  | | | | |            (40), (41), (42), (43), (44), (47), (52), (53), (55), (56),
% 199.95/32.95  | | | | |            (61), (62), (63), (64), (69), (73), (77), (80), (84) are
% 199.95/32.95  | | | | |            inconsistent by sub-proof #219.
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | End of split
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | End of split
% 199.95/32.95  | | | 
% 199.95/32.95  | | End of split
% 199.95/32.95  | | 
% 199.95/32.95  | Case 2:
% 199.95/32.95  | | 
% 199.95/32.95  | |   (85)   ~ (all_56_13 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | REDUCE: (54), (85) imply:
% 199.95/32.95  | |   (86)   ~ (all_52_15 = e3)
% 199.95/32.95  | | 
% 199.95/32.95  | | BETA: splitting (48) gives:
% 199.95/32.95  | | 
% 199.95/32.95  | | Case 1:
% 199.95/32.95  | | | 
% 199.95/32.95  | | |   (87)  all_58_12 = e3
% 199.95/32.95  | | | 
% 199.95/32.95  | | | COMBINE_EQS: (33), (87) imply:
% 199.95/32.95  | | |   (88)  all_52_7 = e3
% 199.95/32.95  | | | 
% 199.95/32.95  | | | REF_CLOSE: (5), (11), (15), (20), (21), (23), (33), (34), (35), (36),
% 199.95/32.95  | | |            (41), (43), (47), (48), (52), (55), (61), (62), (63), (64),
% 199.95/32.95  | | |            (88) are inconsistent by sub-proof #1361.
% 199.95/32.95  | | | 
% 199.95/32.95  | | Case 2:
% 199.95/32.95  | | | 
% 199.95/32.95  | | |   (89)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.95/32.95  | | | 
% 199.95/32.95  | | | BETA: splitting (89) gives:
% 199.95/32.95  | | | 
% 199.95/32.95  | | | Case 1:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | |   (90)  all_58_13 = e3
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REF_CLOSE: (13), (86), (90) are inconsistent by sub-proof #1360.
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | Case 2:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | |   (91)  all_58_14 = e3 | all_58_15 = e3
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | BETA: splitting (91) gives:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | Case 1:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | |   (92)  all_58_14 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | COMBINE_EQS: (2), (92) imply:
% 199.95/32.95  | | | | |   (93)  all_52_23 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | SIMP: (93) implies:
% 199.95/32.95  | | | | |   (94)  all_52_23 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (53), (94) imply:
% 199.95/32.95  | | | | |   (95)   ~ (all_52_7 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (39), (94) imply:
% 199.95/32.95  | | | | |   (96)  op(e3, e3) = all_52_22
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (22), (94) imply:
% 199.95/32.95  | | | | |   (97)  op(e0, e1) = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3,
% 199.95/32.95  | | | | |              simplifying with (43), (96) gives:
% 199.95/32.95  | | | | |   (98)  all_52_22 = all_6_2
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | BETA: splitting (8) gives:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | Case 1:
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | |   (99)  all_56_12 = e3
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | | REF_CLOSE: (42), (95), (99) are inconsistent by sub-proof #1383.
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | Case 2:
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | |   (100)   ~ (all_56_12 = e3)
% 199.95/32.95  | | | | | |   (101)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | | BETA: splitting (38) gives:
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | | Case 1:
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | |   (102)  all_58_12 = e1
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | REF_CLOSE: (5), (14), (18), (20), (26), (31), (33), (43), (49),
% 199.95/32.95  | | | | | | |            (52), (62), (63), (97), (102) are inconsistent by
% 199.95/32.95  | | | | | | |            sub-proof #549.
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | Case 2:
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | |   (103)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | REF_CLOSE: (3), (5), (6), (9), (11), (13), (15), (16), (17), (23),
% 199.95/32.95  | | | | | | |            (24), (28), (29), (33), (35), (36), (41), (42), (43),
% 199.95/32.95  | | | | | | |            (45), (46), (47), (50), (52), (55), (56), (61), (62),
% 199.95/32.95  | | | | | | |            (63), (64), (92), (95), (101), (103) are inconsistent
% 199.95/32.95  | | | | | | |            by sub-proof #217.
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | End of split
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | End of split
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | Case 2:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | |   (104)  all_58_15 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REF_CLOSE: (6), (24), (104) are inconsistent by sub-proof #1350.
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | End of split
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | End of split
% 199.95/32.95  | | | 
% 199.95/32.95  | | End of split
% 199.95/32.95  | | 
% 199.95/32.95  | End of split
% 199.95/32.95  | 
% 199.95/32.95  End of proof
% 199.95/32.95  
% 199.95/32.95  Sub-proof #109 shows that the following formulas are inconsistent:
% 199.95/32.95  ----------------------------------------------------------------
% 199.95/32.95    (1)   ~ (all_52_15 = all_52_23)
% 199.95/32.95    (2)   ~ (all_52_25 = all_52_27)
% 199.95/32.95    (3)  all_58_14 = all_52_23
% 199.95/32.95    (4)   ~ (e3 = e1)
% 199.95/32.95    (5)   ~ (all_52_17 = all_4_0)
% 199.95/32.95    (6)  op(all_52_3, all_52_3) = all_52_2
% 199.95/32.95    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 199.95/32.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 199.95/32.95    (8)   ~ (all_52_5 = all_52_13)
% 199.95/32.95    (9)  all_58_1 = all_52_9
% 199.95/32.95    (10)   ~ (all_52_9 = all_52_13)
% 199.95/32.95    (11)   ~ (e3 = e0)
% 199.95/32.95    (12)   ~ (all_52_23 = all_4_0)
% 199.95/32.95    (13)  op(e0, e2) = all_52_15
% 199.95/32.95    (14)   ~ (all_52_7 = all_52_15)
% 199.95/32.95    (15)  all_18_0 = all_14_0
% 199.95/32.95    (16)  op(all_52_7, all_52_7) = all_52_6
% 199.95/32.95    (17)   ~ (all_52_17 = all_52_25)
% 199.95/32.95    (18)   ~ (all_52_3 = all_6_2)
% 199.95/32.95    (19)  all_50_1 = all_14_1
% 199.95/32.95    (20)  all_58_0 = all_6_2
% 199.95/32.95    (21)  op(all_14_2, e0) = all_14_1
% 199.95/32.95    (22)  all_56_4 = all_52_3
% 199.95/32.95    (23)   ~ (all_52_17 = all_10_2)
% 199.95/32.95    (24)  op(all_6_2, e3) = e1
% 199.95/32.95    (25)  op(e3, e0) = all_52_25
% 199.95/32.95    (26)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 199.95/32.95    (27)  op(e0, all_14_1) = all_14_0
% 199.95/32.95    (28)  op(all_52_5, all_52_5) = all_52_4
% 199.95/32.95    (29)   ~ (all_52_27 = all_52_29)
% 199.95/32.95    (30)  all_58_13 = all_52_15
% 199.95/32.95    (31)  all_58_9 = all_52_25
% 199.95/32.95    (32)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 199.95/32.95    (33)   ~ (all_52_29 = all_14_2)
% 199.95/32.95    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 199.95/32.95    (35)  op(all_52_27, all_52_27) = all_52_26
% 199.95/32.95    (36)  op(e1, e3) = all_52_5
% 199.95/32.95    (37)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 199.95/32.95    (38)  op(e2, e2) = all_4_2
% 199.95/32.95    (39)  all_12_0 = all_6_0
% 199.95/32.95    (40)   ~ (all_52_3 = all_52_5)
% 199.95/32.95    (41)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 199.95/32.95    (42)  op(all_4_2, e2) = e1
% 199.95/32.95    (43)  all_58_11 = all_52_29
% 199.95/32.95    (44)  all_56_5 = all_4_2
% 199.95/32.95    (45)   ~ (all_52_25 = all_14_2)
% 199.95/32.95    (46)   ~ (all_52_9 = all_52_15)
% 199.95/32.95    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 199.95/32.95    (48)   ~ (all_52_3 = all_52_27)
% 199.95/32.95    (49)   ~ (all_10_2 = all_4_0)
% 199.95/32.95    (50)  op(all_6_2, all_6_2) = all_52_0
% 199.95/32.95    (51)   ~ (all_52_7 = all_6_2)
% 199.95/32.95    (52)  op(e0, e0) = all_14_2
% 199.95/32.95    (53)  all_56_15 = all_14_2
% 199.95/32.95    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 199.95/32.95    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 199.95/32.95    (56)  all_56_11 = all_52_29
% 199.95/32.95    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.95/32.95    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 199.95/32.95    (59)  all_56_9 = all_52_13
% 199.95/32.95    (60)   ~ (e2 = e1)
% 199.95/32.95    (61)   ~ (all_52_13 = all_10_2)
% 199.95/32.95    (62)   ~ (all_6_0 = e1)
% 199.95/32.95    (63)  all_12_2 = all_6_2
% 199.95/32.95    (64)  all_58_10 = all_52_27
% 199.95/32.95    (65)  all_56_8 = all_52_5
% 199.95/32.95    (66)  op(all_52_9, all_52_9) = all_52_8
% 199.95/32.95    (67)  op(all_52_15, all_52_15) = all_52_14
% 199.95/32.95    (68)   ~ (all_52_25 = all_52_29)
% 199.95/32.95    (69)   ~ (all_52_29 = all_10_2)
% 199.95/32.95    (70)  all_58_7 = all_52_13
% 199.95/32.95    (71)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 199.95/32.95    (72)  all_50_0 = all_14_0
% 199.95/32.95    (73)   ~ (all_52_5 = all_52_7)
% 199.95/32.95    (74)  all_58_12 = all_52_7
% 199.95/32.95    (75)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.95/32.95    (76)   ~ (all_52_7 = all_14_2)
% 199.95/32.95    (77)  all_58_2 = all_52_3
% 199.95/32.95    (78)  all_56_2 = all_52_17
% 199.95/32.95    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 199.95/32.95    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 199.95/32.95    (81)  op(e3, all_6_1) = all_6_0
% 199.95/32.95    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 199.95/32.95    (83)   ~ (e2 = e0)
% 199.95/32.95    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 199.95/32.95    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 199.95/32.95    (86)   ~ (all_14_0 = e2) |  ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 199.95/32.95    (87)   ~ (all_52_5 = all_52_29)
% 199.95/32.95    (88)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 199.95/32.95    (89)   ~ (all_52_15 = all_14_2)
% 199.95/32.95    (90)   ~ (all_52_19 = all_52_27)
% 199.95/32.95    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 199.95/32.95    (92)   ~ (all_6_0 = e2)
% 199.95/32.95    (93)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 199.95/32.95            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 199.95/32.95    (94)   ~ (all_52_13 = all_4_2)
% 199.95/32.95    (95)  op(e3, e1) = all_52_17
% 199.95/32.95    (96)  op(e0, e3) = all_52_7
% 199.95/32.95    (97)  op(e3, e1) = all_6_0
% 199.95/32.95    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.95/32.95    (99)   ~ (all_52_9 = all_52_25)
% 199.95/32.95    (100)  all_58_15 = all_14_2
% 199.95/32.95    (101)   ~ (all_52_19 = all_10_2)
% 199.95/32.95    (102)  op(all_52_23, all_52_23) = all_52_22
% 199.95/32.95    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 199.95/32.95    (104)  all_58_8 = all_10_2
% 199.95/32.95    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 199.95/32.95    (106)   ~ (all_52_5 = all_10_2)
% 199.95/32.95    (107)  op(all_52_29, all_52_29) = all_52_28
% 199.95/32.95    (108)   ~ (all_52_23 = all_14_2)
% 199.95/32.95    (109)  op(all_52_17, all_52_17) = all_52_16
% 199.95/32.95    (110)  all_58_5 = all_4_0
% 199.95/32.95    (111)   ~ (all_52_25 = all_6_2)
% 199.95/32.95    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.95/32.95    (113)   ~ (all_52_9 = all_4_2)
% 199.95/32.95    (114)   ~ (all_52_5 = all_6_2)
% 199.95/32.95    (115)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 199.95/32.95    (116)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 199.95/32.95    (117)   ~ (all_52_9 = all_6_2)
% 199.95/32.95    (118)   ~ (all_52_13 = all_52_15)
% 199.95/32.95    (119)  all_56_0 = all_6_2
% 199.95/32.95    (120)   ~ (all_18_0 = e3) |  ~ (all_18_1 = e2) |  ~ (all_18_2 = e1)
% 199.95/32.95    (121)  op(all_4_0, all_4_0) = all_52_18
% 199.95/32.95    (122)  op(e3, e3) = all_6_2
% 199.95/32.95    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 199.95/32.95    (124)   ~ (all_52_27 = all_14_2)
% 199.95/32.95    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 199.95/32.95    (126)  op(all_4_2, all_4_2) = all_52_10
% 199.95/32.95    (127)  all_56_3 = all_52_25
% 199.95/32.95    (128)   ~ (all_52_3 = all_52_7)
% 199.95/32.95    (129)  op(all_14_2, all_14_2) = all_52_30
% 199.95/32.95    (130)  all_58_5 = all_52_19
% 199.95/32.95    (131)  all_56_1 = all_52_9
% 199.95/32.95    (132)   ~ (all_52_15 = all_4_2)
% 199.95/32.95    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 199.95/32.95           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 199.95/32.95           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 199.95/32.95           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 199.95/32.95    (134)   ~ (all_52_27 = all_4_2)
% 199.95/32.95    (135)  all_58_6 = all_52_5
% 199.95/32.95    (136)   ~ (all_4_0 = all_4_2)
% 199.95/32.95    (137)  op(e3, e2) = all_52_9
% 199.95/32.95    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.95/32.95    (139)   ~ (all_52_17 = all_6_2)
% 199.95/32.95    (140)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 199.95/32.95    (141)   ~ (all_52_9 = all_52_17)
% 199.95/32.95    (142)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 199.95/32.95    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 199.95/32.95    (144)  op(all_52_13, all_52_13) = all_52_12
% 199.95/32.95    (145)  op(e1, e1) = all_10_2
% 199.95/32.95    (146)   ~ (all_52_7 = all_52_23)
% 199.95/32.95    (147)   ~ (all_52_17 = all_52_19)
% 199.95/32.95    (148)  all_58_3 = all_4_2
% 199.95/32.95    (149)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 199.95/32.95    (150)   ~ (all_52_3 = all_4_2)
% 199.95/32.95    (151)   ~ (all_52_17 = all_52_23)
% 199.95/32.95    (152)  op(all_6_2, e3) = all_6_1
% 199.95/32.95    (153)   ~ (all_52_13 = all_52_29)
% 199.95/32.95    (154)  all_58_4 = all_52_17
% 199.95/32.95    (155)  all_50_2 = all_14_2
% 199.95/32.95    (156)  op(all_52_25, all_52_25) = all_52_24
% 199.95/32.95  
% 199.95/32.95  Begin of proof
% 199.95/32.95  | 
% 199.95/32.95  | GROUND_INST: instantiating (7) with all_52_17, all_6_0, e1, e3, simplifying
% 199.95/32.95  |              with (95), (97) gives:
% 199.95/32.95  |   (157)  all_52_17 = all_6_0
% 199.95/32.95  | 
% 199.95/32.95  | COMBINE_EQS: (78), (157) imply:
% 199.95/32.95  |   (158)  all_56_2 = all_6_0
% 199.95/32.95  | 
% 199.95/32.95  | COMBINE_EQS: (154), (157) imply:
% 199.95/32.95  |   (159)  all_58_4 = all_6_0
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (141), (157) imply:
% 199.95/32.95  |   (160)   ~ (all_52_9 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (151), (157) imply:
% 199.95/32.95  |   (161)   ~ (all_52_23 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | SIMP: (161) implies:
% 199.95/32.95  |   (162)   ~ (all_52_23 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (17), (157) imply:
% 199.95/32.95  |   (163)   ~ (all_52_25 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | SIMP: (163) implies:
% 199.95/32.95  |   (164)   ~ (all_52_25 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (23), (157) imply:
% 199.95/32.95  |   (165)   ~ (all_10_2 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | SIMP: (165) implies:
% 199.95/32.95  |   (166)   ~ (all_10_2 = all_6_0)
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (139), (157) imply:
% 199.95/32.95  |   (167)   ~ (all_6_0 = all_6_2)
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (5), (157) imply:
% 199.95/32.95  |   (168)   ~ (all_6_0 = all_4_0)
% 199.95/32.95  | 
% 199.95/32.95  | REDUCE: (109), (157) imply:
% 199.95/32.95  |   (169)  op(all_6_0, all_6_0) = all_52_16
% 199.95/32.95  | 
% 199.95/32.95  | BETA: splitting (86) gives:
% 199.95/32.95  | 
% 199.95/32.95  | Case 1:
% 199.95/32.95  | | 
% 199.95/32.95  | |   (170)   ~ (all_14_0 = e2)
% 199.95/32.95  | | 
% 199.95/32.95  | | BETA: splitting (120) gives:
% 199.95/32.95  | | 
% 199.95/32.95  | | Case 1:
% 199.95/32.95  | | | 
% 199.95/32.95  | | |   (171)   ~ (all_18_0 = e3)
% 199.95/32.95  | | | 
% 199.95/32.95  | | | REDUCE: (15), (171) imply:
% 199.95/32.95  | | |   (172)   ~ (all_14_0 = e3)
% 199.95/32.95  | | | 
% 199.95/32.95  | | | BETA: splitting (93) gives:
% 199.95/32.95  | | | 
% 199.95/32.95  | | | Case 1:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | |   (173)  all_58_15 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | COMBINE_EQS: (100), (173) imply:
% 199.95/32.95  | | | |   (174)  all_14_2 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (108), (174) imply:
% 199.95/32.95  | | | |   (175)   ~ (all_52_23 = e0)
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (45), (174) imply:
% 199.95/32.95  | | | |   (176)   ~ (all_52_25 = e0)
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (129), (174) imply:
% 199.95/32.95  | | | |   (177)  op(e0, e0) = all_52_30
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (21), (174) imply:
% 199.95/32.95  | | | |   (178)  op(e0, e0) = all_14_1
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (52), (174) imply:
% 199.95/32.95  | | | |   (179)  op(e0, e0) = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | GROUND_INST: instantiating (7) with all_14_1, all_52_30, e0, e0,
% 199.95/32.95  | | | |              simplifying with (177), (178) gives:
% 199.95/32.95  | | | |   (180)  all_52_30 = all_14_1
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | GROUND_INST: instantiating (7) with e0, all_52_30, e0, e0, simplifying
% 199.95/32.95  | | | |              with (177), (179) gives:
% 199.95/32.95  | | | |   (181)  all_52_30 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | COMBINE_EQS: (180), (181) imply:
% 199.95/32.95  | | | |   (182)  all_14_1 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | SIMP: (182) implies:
% 199.95/32.95  | | | |   (183)  all_14_1 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (27), (183) imply:
% 199.95/32.95  | | | |   (184)  op(e0, e0) = all_14_0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | GROUND_INST: instantiating (7) with e0, all_14_0, e0, e0, simplifying
% 199.95/32.95  | | | |              with (179), (184) gives:
% 199.95/32.95  | | | |   (185)  all_14_0 = e0
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (172), (185) imply:
% 199.95/32.95  | | | |   (186)   ~ (e3 = e0)
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | REDUCE: (170), (185) imply:
% 199.95/32.95  | | | |   (187)   ~ (e2 = e0)
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | BETA: splitting (57) gives:
% 199.95/32.95  | | | | 
% 199.95/32.95  | | | | Case 1:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | |   (188)  all_56_2 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | COMBINE_EQS: (158), (188) imply:
% 199.95/32.95  | | | | |   (189)  all_6_0 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | SIMP: (189) implies:
% 199.95/32.95  | | | | |   (190)  all_6_0 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | COMBINE_EQS: (159), (190) imply:
% 199.95/32.95  | | | | |   (191)  all_58_4 = e3
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (160), (190) imply:
% 199.95/32.95  | | | | |   (192)   ~ (all_52_9 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (162), (190) imply:
% 199.95/32.95  | | | | |   (193)   ~ (all_52_23 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (164), (190) imply:
% 199.95/32.95  | | | | |   (194)   ~ (all_52_25 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (166), (190) imply:
% 199.95/32.95  | | | | |   (195)   ~ (all_10_2 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (167), (190) imply:
% 199.95/32.95  | | | | |   (196)   ~ (all_6_2 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | SIMP: (196) implies:
% 199.95/32.95  | | | | |   (197)   ~ (all_6_2 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (168), (190) imply:
% 199.95/32.95  | | | | |   (198)   ~ (all_4_0 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | SIMP: (198) implies:
% 199.95/32.95  | | | | |   (199)   ~ (all_4_0 = e3)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (92), (190) imply:
% 199.95/32.95  | | | | |   (200)   ~ (e3 = e2)
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | REDUCE: (169), (190) imply:
% 199.95/32.95  | | | | |   (201)  op(e3, e3) = all_52_16
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_16, e3, e3,
% 199.95/32.95  | | | | |              simplifying with (122), (201) gives:
% 199.95/32.95  | | | | |   (202)  all_52_16 = all_6_2
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | BETA: splitting (133) gives:
% 199.95/32.95  | | | | | 
% 199.95/32.95  | | | | | Case 1:
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | |   (203)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 199.95/32.95  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 199.95/32.95  | | | | | |            all_52_14 = e0)
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | | BETA: splitting (203) gives:
% 199.95/32.95  | | | | | | 
% 199.95/32.95  | | | | | | Case 1:
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | |   (204)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 199.95/32.95  | | | | | | |          = e0
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | REF_CLOSE: (6), (7), (16), (20), (28), (38), (50), (52), (54),
% 199.95/32.95  | | | | | | |            (74), (76), (77), (80), (106), (122), (135), (138),
% 199.95/32.95  | | | | | | |            (145), (150), (197), (204) are inconsistent by
% 199.95/32.95  | | | | | | |            sub-proof #835.
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | Case 2:
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | |   (205)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 199.95/32.95  | | | | | | |          all_52_14 = e0
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | ALPHA: (205) implies:
% 199.95/32.95  | | | | | | |   (206)  all_52_14 = e0
% 199.95/32.95  | | | | | | |   (207)  all_52_12 = e1
% 199.95/32.95  | | | | | | |   (208)  all_52_8 = e3
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | REDUCE: (66), (208) imply:
% 199.95/32.95  | | | | | | |   (209)  op(all_52_9, all_52_9) = e3
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | REDUCE: (144), (207) imply:
% 199.95/32.95  | | | | | | |   (210)  op(all_52_13, all_52_13) = e1
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | REDUCE: (67), (206) imply:
% 199.95/32.95  | | | | | | |   (211)  op(all_52_15, all_52_15) = e0
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | BETA: splitting (138) gives:
% 199.95/32.95  | | | | | | | 
% 199.95/32.95  | | | | | | | Case 1:
% 199.95/32.95  | | | | | | | | 
% 199.95/32.95  | | | | | | | |   (212)  all_58_12 = e3
% 199.95/32.95  | | | | | | | | 
% 199.95/32.95  | | | | | | | | COMBINE_EQS: (74), (212) imply:
% 199.95/32.95  | | | | | | | |   (213)  all_52_7 = e3
% 199.95/32.95  | | | | | | | | 
% 199.95/32.95  | | | | | | | | REDUCE: (128), (213) imply:
% 199.95/32.95  | | | | | | | |   (214)   ~ (all_52_3 = e3)
% 199.95/32.95  | | | | | | | | 
% 199.95/32.95  | | | | | | | | REDUCE: (14), (213) imply:
% 199.95/32.95  | | | | | | | |   (215)   ~ (all_52_15 = e3)
% 199.95/32.95  | | | | | | | | 
% 199.95/32.96  | | | | | | | | SIMP: (215) implies:
% 199.95/32.96  | | | | | | | |   (216)   ~ (all_52_15 = e3)
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | | REF_CLOSE: (7), (9), (24), (30), (35), (36), (42), (44), (54),
% 199.95/32.96  | | | | | | | |            (64), (70), (77), (84), (94), (98), (110), (114),
% 199.95/32.96  | | | | | | | |            (115), (122), (132), (134), (136), (137), (145),
% 199.95/32.96  | | | | | | | |            (148), (192), (195), (199), (209), (210), (214),
% 199.95/32.96  | | | | | | | |            (216) are inconsistent by sub-proof #114.
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | |   (217)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | | REF_CLOSE: (1), (3), (7), (9), (11), (16), (20), (24), (30),
% 199.95/32.96  | | | | | | | |            (31), (38), (46), (47), (58), (60), (74), (79), (83),
% 199.95/32.96  | | | | | | | |            (96), (99), (102), (116), (117), (122), (131), (132),
% 199.95/32.96  | | | | | | | |            (140), (145), (173), (175), (191), (193), (195),
% 199.95/32.96  | | | | | | | |            (200), (209), (211), (217) are inconsistent by
% 199.95/32.96  | | | | | | | |            sub-proof #574.
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | End of split
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | End of split
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | Case 2:
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | |   (218)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 199.95/32.96  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 199.95/32.96  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | | BETA: splitting (218) gives:
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | | Case 1:
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | |   (219)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 199.95/32.96  | | | | | | |          all_52_22 = e0
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REF_CLOSE: (197), (202), (219) are inconsistent by sub-proof #573.
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | Case 2:
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | |   (220)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 199.95/32.96  | | | | | | |          all_52_30 = e0
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | ALPHA: (220) implies:
% 199.95/32.96  | | | | | | |   (221)  all_52_28 = e1
% 199.95/32.96  | | | | | | |   (222)  all_52_26 = e2
% 199.95/32.96  | | | | | | |   (223)  all_52_24 = e3
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REDUCE: (156), (223) imply:
% 199.95/32.96  | | | | | | |   (224)  op(all_52_25, all_52_25) = e3
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REDUCE: (35), (222) imply:
% 199.95/32.96  | | | | | | |   (225)  op(all_52_27, all_52_27) = e2
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REDUCE: (107), (221) imply:
% 199.95/32.96  | | | | | | |   (226)  op(all_52_29, all_52_29) = e1
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | BETA: splitting (112) gives:
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | Case 1:
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | |   (227)  all_56_3 = e3
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | | REF_CLOSE: (127), (194), (227) are inconsistent by sub-proof
% 199.95/32.96  | | | | | | | |            #1339.
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | |   (228)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | | BETA: splitting (138) gives:
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | | Case 1:
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | |   (229)  all_58_12 = e3
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | COMBINE_EQS: (74), (229) imply:
% 199.95/32.96  | | | | | | | | |   (230)  all_52_7 = e3
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | REDUCE: (73), (230) imply:
% 199.95/32.96  | | | | | | | | |   (231)   ~ (all_52_5 = e3)
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | REDUCE: (14), (230) imply:
% 199.95/32.96  | | | | | | | | |   (232)   ~ (all_52_15 = e3)
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | SIMP: (232) implies:
% 199.95/32.96  | | | | | | | | |   (233)   ~ (all_52_15 = e3)
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | REDUCE: (16), (230) imply:
% 199.95/32.96  | | | | | | | | |   (234)  op(e3, e3) = all_52_6
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 199.95/32.96  | | | | | | | | |              simplifying with (122), (234) gives:
% 199.95/32.96  | | | | | | | | |   (235)  all_52_6 = all_6_2
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | BETA: splitting (98) gives:
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | Case 1:
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | |   (236)  all_58_1 = e3
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | COMBINE_EQS: (9), (236) imply:
% 199.95/32.96  | | | | | | | | | |   (237)  all_52_9 = e3
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | REDUCE: (192), (237) imply:
% 199.95/32.96  | | | | | | | | | |   (238)  $false
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | CLOSE: (238) is inconsistent.
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | |   (239)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | BETA: splitting (75) gives:
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | Case 1:
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | |   (240)  all_58_6 = e3
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | COMBINE_EQS: (135), (240) imply:
% 199.95/32.96  | | | | | | | | | | |   (241)  all_52_5 = e3
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | REDUCE: (231), (241) imply:
% 199.95/32.96  | | | | | | | | | | |   (242)  $false
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | |   (243)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | BETA: splitting (91) gives:
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | Case 1:
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | |   (244)  all_56_11 = e3
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | COMBINE_EQS: (56), (244) imply:
% 199.95/32.96  | | | | | | | | | | | |   (245)  all_52_29 = e3
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | SIMP: (245) implies:
% 199.95/32.96  | | | | | | | | | | | |   (246)  all_52_29 = e3
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | REDUCE: (153), (246) imply:
% 199.95/32.96  | | | | | | | | | | | |   (247)   ~ (all_52_13 = e3)
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | REDUCE: (69), (246) imply:
% 199.95/32.96  | | | | | | | | | | | |   (248)   ~ (all_10_2 = e3)
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | REF_CLOSE: (7), (24), (30), (36), (43), (70), (104), (114),
% 199.95/32.96  | | | | | | | | | | | |            (122), (126), (148), (195), (226), (233), (239),
% 199.95/32.96  | | | | | | | | | | | |            (243), (247) are inconsistent by sub-proof #572.
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | |   (249)   ~ (all_56_11 = e3)
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | REDUCE: (56), (249) imply:
% 199.95/32.96  | | | | | | | | | | | |   (250)   ~ (all_52_29 = e3)
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | BETA: splitting (243) gives:
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | Case 1:
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | |   (251)  all_58_7 = e3
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | | COMBINE_EQS: (70), (251) imply:
% 199.95/32.96  | | | | | | | | | | | | |   (252)  all_52_13 = e3
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | | REDUCE: (61), (252) imply:
% 199.95/32.96  | | | | | | | | | | | | |   (253)   ~ (all_10_2 = e3)
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | | REDUCE: (94), (252) imply:
% 199.95/32.96  | | | | | | | | | | | | |   (254)   ~ (all_4_2 = e3)
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | | SIMP: (254) implies:
% 199.95/32.96  | | | | | | | | | | | | |   (255)   ~ (all_4_2 = e3)
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | | REF_CLOSE: (7), (31), (38), (55), (127), (145), (176), (195),
% 199.95/32.96  | | | | | | | | | | | | |            (224), (228), (255) are inconsistent by sub-proof
% 199.95/32.96  | | | | | | | | | | | | |            #824.
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | |   (256)  all_58_8 = e3 | all_58_11 = e3
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | | REF_CLOSE: (43), (104), (195), (250), (256) are inconsistent
% 199.95/32.96  | | | | | | | | | | | | |            by sub-proof #1140.
% 199.95/32.96  | | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | | End of split
% 199.95/32.96  | | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | | End of split
% 199.95/32.96  | | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | | End of split
% 199.95/32.96  | | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | End of split
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | Case 2:
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | |   (257)   ~ (all_58_12 = e3)
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | REDUCE: (74), (257) imply:
% 199.95/32.96  | | | | | | | | |   (258)   ~ (all_52_7 = e3)
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | | REF_CLOSE: (2), (4), (7), (11), (20), (31), (38), (43), (55),
% 199.95/32.96  | | | | | | | | |            (64), (68), (74), (77), (80), (87), (111), (112),
% 199.95/32.96  | | | | | | | | |            (122), (123), (127), (135), (145), (150), (173),
% 199.95/32.96  | | | | | | | | |            (176), (195), (224), (225), (226), (258) are
% 199.95/32.96  | | | | | | | | |            inconsistent by sub-proof #1238.
% 199.95/32.96  | | | | | | | | | 
% 199.95/32.96  | | | | | | | | End of split
% 199.95/32.96  | | | | | | | | 
% 199.95/32.96  | | | | | | | End of split
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | End of split
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | End of split
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | Case 2:
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | |   (259)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REF_CLOSE: (4), (7), (24), (36), (39), (50), (62), (63), (88), (92),
% 199.95/32.96  | | | | |            (114), (119), (122), (143), (158), (167), (259) are
% 199.95/32.96  | | | | |            inconsistent by sub-proof #569.
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | End of split
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | Case 2:
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | |   (260)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.95/32.96  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | ALPHA: (260) implies:
% 199.95/32.96  | | | |   (261)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (14), (16), (17), (18),
% 199.95/32.96  | | | |            (20), (21), (22), (23), (24), (25), (28), (30), (31), (33),
% 199.95/32.96  | | | |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.95/32.96  | | | |            (46), (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 199.95/32.96  | | | |            (58), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 199.95/32.96  | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 199.95/32.96  | | | |            (84), (87), (88), (89), (90), (91), (92), (94), (96), (98),
% 199.95/32.96  | | | |            (99), (100), (101), (103), (104), (105), (106), (107), (108),
% 199.95/32.96  | | | |            (109), (110), (111), (112), (114), (115), (117), (118),
% 199.95/32.96  | | | |            (119), (122), (123), (124), (125), (126), (127), (128),
% 199.95/32.96  | | | |            (129), (130), (131), (132), (133), (134), (135), (136),
% 199.95/32.96  | | | |            (137), (138), (139), (140), (143), (144), (145), (147),
% 199.95/32.96  | | | |            (148), (149), (150), (152), (153), (154), (156), (158),
% 199.95/32.96  | | | |            (159), (160), (162), (164), (166), (167), (168), (169), (261)
% 199.95/32.96  | | | |            are inconsistent by sub-proof #111.
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | End of split
% 199.95/32.96  | | | 
% 199.95/32.96  | | Case 2:
% 199.95/32.96  | | | 
% 199.95/32.96  | | |   (262)  all_18_0 = e3
% 199.95/32.96  | | | 
% 199.95/32.96  | | | COMBINE_EQS: (15), (262) imply:
% 199.95/32.96  | | |   (263)  all_14_0 = e3
% 199.95/32.96  | | | 
% 199.95/32.96  | | | SIMP: (263) implies:
% 199.95/32.96  | | |   (264)  all_14_0 = e3
% 199.95/32.96  | | | 
% 199.95/32.96  | | | REDUCE: (27), (264) imply:
% 199.95/32.96  | | |   (265)  op(e0, all_14_1) = e3
% 199.95/32.96  | | | 
% 199.95/32.96  | | | BETA: splitting (93) gives:
% 199.95/32.96  | | | 
% 199.95/32.96  | | | Case 1:
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | |   (266)  all_58_15 = e0
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | REF_CLOSE: (7), (11), (21), (52), (100), (129), (265), (266) are
% 199.95/32.96  | | | |            inconsistent by sub-proof #693.
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | Case 2:
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | |   (267)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.95/32.96  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | ALPHA: (267) implies:
% 199.95/32.96  | | | |   (268)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (14), (16), (17), (18),
% 199.95/32.96  | | | |            (20), (21), (22), (23), (24), (25), (28), (30), (31), (33),
% 199.95/32.96  | | | |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 199.95/32.96  | | | |            (46), (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 199.95/32.96  | | | |            (58), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 199.95/32.96  | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 199.95/32.96  | | | |            (84), (87), (88), (89), (90), (91), (92), (94), (96), (98),
% 199.95/32.96  | | | |            (99), (100), (101), (103), (104), (105), (106), (107), (108),
% 199.95/32.96  | | | |            (109), (110), (111), (112), (114), (115), (117), (118),
% 199.95/32.96  | | | |            (119), (122), (123), (124), (125), (126), (127), (128),
% 199.95/32.96  | | | |            (129), (130), (131), (132), (133), (134), (135), (136),
% 199.95/32.96  | | | |            (137), (138), (139), (140), (143), (144), (145), (147),
% 199.95/32.96  | | | |            (148), (149), (150), (152), (153), (154), (156), (158),
% 199.95/32.96  | | | |            (159), (160), (162), (164), (166), (167), (168), (169), (268)
% 199.95/32.96  | | | |            are inconsistent by sub-proof #111.
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | End of split
% 199.95/32.96  | | | 
% 199.95/32.96  | | End of split
% 199.95/32.96  | | 
% 199.95/32.96  | Case 2:
% 199.95/32.96  | | 
% 199.95/32.96  | |   (269)  all_14_0 = e2
% 199.95/32.96  | | 
% 199.95/32.96  | | COMBINE_EQS: (72), (269) imply:
% 199.95/32.96  | |   (270)  all_50_0 = e2
% 199.95/32.96  | | 
% 199.95/32.96  | | REDUCE: (27), (269) imply:
% 199.95/32.96  | |   (271)  op(e0, all_14_1) = e2
% 199.95/32.96  | | 
% 199.95/32.96  | | BETA: splitting (26) gives:
% 199.95/32.96  | | 
% 199.95/32.96  | | Case 1:
% 199.95/32.96  | | | 
% 199.95/32.96  | | |   (272)   ~ (all_50_0 = e2)
% 199.95/32.96  | | | 
% 199.95/32.96  | | | REDUCE: (270), (272) imply:
% 199.95/32.96  | | |   (273)  $false
% 199.95/32.96  | | | 
% 199.95/32.96  | | | CLOSE: (273) is inconsistent.
% 199.95/32.96  | | | 
% 199.95/32.96  | | Case 2:
% 199.95/32.96  | | | 
% 199.95/32.96  | | |   (274)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 199.95/32.96  | | | 
% 199.95/32.96  | | | BETA: splitting (93) gives:
% 199.95/32.96  | | | 
% 199.95/32.96  | | | Case 1:
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | |   (275)  all_58_15 = e0
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | REF_CLOSE: (7), (21), (52), (83), (100), (129), (271), (275) are
% 199.95/32.96  | | | |            inconsistent by sub-proof #612.
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | Case 2:
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | |   (276)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 199.95/32.96  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | ALPHA: (276) implies:
% 199.95/32.96  | | | |   (277)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 199.95/32.96  | | | |   (278)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | BETA: splitting (57) gives:
% 199.95/32.96  | | | | 
% 199.95/32.96  | | | | Case 1:
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | |   (279)  all_56_2 = e3
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | COMBINE_EQS: (158), (279) imply:
% 199.95/32.96  | | | | |   (280)  all_6_0 = e3
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | SIMP: (280) implies:
% 199.95/32.96  | | | | |   (281)  all_6_0 = e3
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | COMBINE_EQS: (159), (281) imply:
% 199.95/32.96  | | | | |   (282)  all_58_4 = e3
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (160), (281) imply:
% 199.95/32.96  | | | | |   (283)   ~ (all_52_9 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (162), (281) imply:
% 199.95/32.96  | | | | |   (284)   ~ (all_52_23 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (164), (281) imply:
% 199.95/32.96  | | | | |   (285)   ~ (all_52_25 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (166), (281) imply:
% 199.95/32.96  | | | | |   (286)   ~ (all_10_2 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (167), (281) imply:
% 199.95/32.96  | | | | |   (287)   ~ (all_6_2 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | SIMP: (287) implies:
% 199.95/32.96  | | | | |   (288)   ~ (all_6_2 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (168), (281) imply:
% 199.95/32.96  | | | | |   (289)   ~ (all_4_0 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | SIMP: (289) implies:
% 199.95/32.96  | | | | |   (290)   ~ (all_4_0 = e3)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (92), (281) imply:
% 199.95/32.96  | | | | |   (291)   ~ (e3 = e2)
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | REDUCE: (169), (281) imply:
% 199.95/32.96  | | | | |   (292)  op(e3, e3) = all_52_16
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_16, e3, e3,
% 199.95/32.96  | | | | |              simplifying with (122), (292) gives:
% 199.95/32.96  | | | | |   (293)  all_52_16 = all_6_2
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | BETA: splitting (133) gives:
% 199.95/32.96  | | | | | 
% 199.95/32.96  | | | | | Case 1:
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | |   (294)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 199.95/32.96  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 199.95/32.96  | | | | | |            all_52_14 = e0)
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | | BETA: splitting (294) gives:
% 199.95/32.96  | | | | | | 
% 199.95/32.96  | | | | | | Case 1:
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | |   (295)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 199.95/32.96  | | | | | | |          = e0
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REF_CLOSE: (6), (7), (16), (20), (28), (38), (50), (52), (54),
% 199.95/32.96  | | | | | | |            (74), (76), (77), (80), (106), (122), (135), (138),
% 199.95/32.96  | | | | | | |            (145), (150), (288), (295) are inconsistent by
% 199.95/32.96  | | | | | | |            sub-proof #835.
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | Case 2:
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | |   (296)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 199.95/32.96  | | | | | | |          all_52_14 = e0
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | ALPHA: (296) implies:
% 199.95/32.96  | | | | | | |   (297)  all_52_14 = e0
% 199.95/32.96  | | | | | | |   (298)  all_52_12 = e1
% 199.95/32.96  | | | | | | |   (299)  all_52_8 = e3
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REDUCE: (66), (299) imply:
% 199.95/32.96  | | | | | | |   (300)  op(all_52_9, all_52_9) = e3
% 199.95/32.96  | | | | | | | 
% 199.95/32.96  | | | | | | | REDUCE: (144), (298) imply:
% 200.02/32.96  | | | | | | |   (301)  op(all_52_13, all_52_13) = e1
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | REDUCE: (67), (297) imply:
% 200.02/32.96  | | | | | | |   (302)  op(all_52_15, all_52_15) = e0
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | BETA: splitting (105) gives:
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | |   (303)  all_56_15 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | COMBINE_EQS: (53), (303) imply:
% 200.02/32.96  | | | | | | | |   (304)  all_14_2 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | SIMP: (304) implies:
% 200.02/32.96  | | | | | | | |   (305)  all_14_2 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | COMBINE_EQS: (155), (305) imply:
% 200.02/32.96  | | | | | | | |   (306)  all_50_2 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | REDUCE: (21), (305) imply:
% 200.02/32.96  | | | | | | | |   (307)  op(e3, e0) = all_14_1
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | BETA: splitting (274) gives:
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | |   (308)   ~ (all_50_1 = e1)
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | REDUCE: (19), (308) imply:
% 200.02/32.96  | | | | | | | | |   (309)   ~ (all_14_1 = e1)
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0,
% 200.02/32.96  | | | | | | | | |              e3, simplifying with (25), (307) gives:
% 200.02/32.96  | | | | | | | | |   (310)  all_52_25 = all_14_1
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | COMBINE_EQS: (31), (310) imply:
% 200.02/32.96  | | | | | | | | |   (311)  all_58_9 = all_14_1
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | BETA: splitting (85) gives:
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | |   (312)  all_58_0 = e1
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | COMBINE_EQS: (20), (312) imply:
% 200.02/32.96  | | | | | | | | | |   (313)  all_6_2 = e1
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | REF_CLOSE: (7), (24), (36), (114), (313) are inconsistent by
% 200.02/32.96  | | | | | | | | | |            sub-proof #578.
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | Case 2:
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | |   (314)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | BETA: splitting (314) gives:
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | |   (315)  all_58_1 = e1
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | COMBINE_EQS: (9), (315) imply:
% 200.02/32.96  | | | | | | | | | | |   (316)  all_52_9 = e1
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | REDUCE: (300), (316) imply:
% 200.02/32.96  | | | | | | | | | | |   (317)  op(e1, e1) = e3
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | REF_CLOSE: (7), (145), (286), (317) are inconsistent by
% 200.02/32.96  | | | | | | | | | | |            sub-proof #1368.
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | Case 2:
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | |   (318)  all_58_4 = e1 | all_58_9 = e1
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | BETA: splitting (318) gives:
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | |   (319)  all_58_4 = e1
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | | COMBINE_EQS: (282), (319) imply:
% 200.02/32.96  | | | | | | | | | | | |   (320)  e3 = e1
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | | REDUCE: (4), (320) imply:
% 200.02/32.96  | | | | | | | | | | | |   (321)  $false
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | Case 2:
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | |   (322)  all_58_9 = e1
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | | COMBINE_EQS: (311), (322) imply:
% 200.02/32.96  | | | | | | | | | | | |   (323)  all_14_1 = e1
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | | REDUCE: (309), (323) imply:
% 200.02/32.96  | | | | | | | | | | | |   (324)  $false
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 200.02/32.96  | | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | | End of split
% 200.02/32.96  | | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | | End of split
% 200.02/32.96  | | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | End of split
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | Case 2:
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | |   (325)   ~ (all_50_2 = e3)
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | REDUCE: (306), (325) imply:
% 200.02/32.96  | | | | | | | | |   (326)  $false
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | CLOSE: (326) is inconsistent.
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | End of split
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | Case 2:
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | |   (327)   ~ (all_56_15 = e3)
% 200.02/32.96  | | | | | | | |   (328)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | REDUCE: (53), (327) imply:
% 200.02/32.96  | | | | | | | |   (329)   ~ (all_14_2 = e3)
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | REF_CLOSE: (3), (7), (9), (14), (16), (20), (24), (30), (31),
% 200.02/32.96  | | | | | | | |            (35), (36), (38), (42), (44), (45), (51), (53), (54),
% 200.02/32.96  | | | | | | | |            (64), (70), (74), (76), (77), (79), (84), (89), (94),
% 200.02/32.96  | | | | | | | |            (96), (98), (100), (108), (110), (114), (115), (122),
% 200.02/32.96  | | | | | | | |            (128), (132), (134), (136), (137), (138), (145),
% 200.02/32.96  | | | | | | | |            (148), (277), (282), (283), (284), (286), (288),
% 200.02/32.96  | | | | | | | |            (290), (300), (301), (302), (328), (329) are
% 200.02/32.96  | | | | | | | |            inconsistent by sub-proof #113.
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | End of split
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | End of split
% 200.02/32.96  | | | | | | 
% 200.02/32.96  | | | | | Case 2:
% 200.02/32.96  | | | | | | 
% 200.02/32.96  | | | | | |   (330)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 200.02/32.96  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 200.02/32.96  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 200.02/32.96  | | | | | | 
% 200.02/32.96  | | | | | | BETA: splitting (330) gives:
% 200.02/32.96  | | | | | | 
% 200.02/32.96  | | | | | | Case 1:
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | |   (331)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 200.02/32.96  | | | | | | |          all_52_22 = e0
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | REF_CLOSE: (288), (293), (331) are inconsistent by sub-proof #573.
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | Case 2:
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | |   (332)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.02/32.96  | | | | | | |          all_52_30 = e0
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | ALPHA: (332) implies:
% 200.02/32.96  | | | | | | |   (333)  all_52_30 = e0
% 200.02/32.96  | | | | | | |   (334)  all_52_28 = e1
% 200.02/32.96  | | | | | | |   (335)  all_52_26 = e2
% 200.02/32.96  | | | | | | |   (336)  all_52_24 = e3
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | REDUCE: (156), (336) imply:
% 200.02/32.96  | | | | | | |   (337)  op(all_52_25, all_52_25) = e3
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | REDUCE: (35), (335) imply:
% 200.02/32.96  | | | | | | |   (338)  op(all_52_27, all_52_27) = e2
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | REDUCE: (107), (334) imply:
% 200.02/32.96  | | | | | | |   (339)  op(all_52_29, all_52_29) = e1
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | REDUCE: (129), (333) imply:
% 200.02/32.96  | | | | | | |   (340)  op(all_14_2, all_14_2) = e0
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | BETA: splitting (105) gives:
% 200.02/32.96  | | | | | | | 
% 200.02/32.96  | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | |   (341)  all_56_15 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | COMBINE_EQS: (53), (341) imply:
% 200.02/32.96  | | | | | | | |   (342)  all_14_2 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | SIMP: (342) implies:
% 200.02/32.96  | | | | | | | |   (343)  all_14_2 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | COMBINE_EQS: (155), (343) imply:
% 200.02/32.96  | | | | | | | |   (344)  all_50_2 = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | REDUCE: (340), (343) imply:
% 200.02/32.96  | | | | | | | |   (345)  op(e3, e3) = e0
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | REDUCE: (21), (343) imply:
% 200.02/32.96  | | | | | | | |   (346)  op(e3, e0) = all_14_1
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | REDUCE: (52), (343) imply:
% 200.02/32.96  | | | | | | | |   (347)  op(e0, e0) = e3
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | BETA: splitting (274) gives:
% 200.02/32.96  | | | | | | | | 
% 200.02/32.96  | | | | | | | | Case 1:
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | |   (348)   ~ (all_50_1 = e1)
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | REDUCE: (19), (348) imply:
% 200.02/32.96  | | | | | | | | |   (349)   ~ (all_14_1 = e1)
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0,
% 200.02/32.96  | | | | | | | | |              e3, simplifying with (25), (346) gives:
% 200.02/32.96  | | | | | | | | |   (350)  all_52_25 = all_14_1
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, e0, e3, e3,
% 200.02/32.96  | | | | | | | | |              simplifying with (122), (345) gives:
% 200.02/32.96  | | | | | | | | |   (351)  all_6_2 = e0
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | COMBINE_EQS: (127), (350) imply:
% 200.02/32.96  | | | | | | | | |   (352)  all_56_3 = all_14_1
% 200.02/32.96  | | | | | | | | | 
% 200.02/32.96  | | | | | | | | | COMBINE_EQS: (31), (350) imply:
% 200.02/32.97  | | | | | | | | |   (353)  all_58_9 = all_14_1
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | COMBINE_EQS: (20), (351) imply:
% 200.02/32.97  | | | | | | | | |   (354)  all_58_0 = e0
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (18), (351) imply:
% 200.02/32.97  | | | | | | | | |   (355)   ~ (all_52_3 = e0)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (51), (351) imply:
% 200.02/32.97  | | | | | | | | |   (356)   ~ (all_52_7 = e0)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (99), (350) imply:
% 200.02/32.97  | | | | | | | | |   (357)   ~ (all_52_9 = all_14_1)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (117), (351) imply:
% 200.02/32.97  | | | | | | | | |   (358)   ~ (all_52_9 = e0)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (68), (350) imply:
% 200.02/32.97  | | | | | | | | |   (359)   ~ (all_52_29 = all_14_1)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | SIMP: (359) implies:
% 200.02/32.97  | | | | | | | | |   (360)   ~ (all_52_29 = all_14_1)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (111), (350), (351) imply:
% 200.02/32.97  | | | | | | | | |   (361)   ~ (all_14_1 = e0)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (285), (350) imply:
% 200.02/32.97  | | | | | | | | |   (362)   ~ (all_14_1 = e3)
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (337), (350) imply:
% 200.02/32.97  | | | | | | | | |   (363)  op(all_14_1, all_14_1) = e3
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (50), (351) imply:
% 200.02/32.97  | | | | | | | | |   (364)  op(e0, e0) = all_52_0
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | REDUCE: (24), (351) imply:
% 200.02/32.97  | | | | | | | | |   (365)  op(e0, e3) = e1
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | BETA: splitting (112) gives:
% 200.02/32.97  | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | |   (366)  all_56_3 = e3
% 200.02/32.97  | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | REF_CLOSE: (352), (362), (366) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | |            #1200.
% 200.02/32.97  | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | |   (367)   ~ (all_56_3 = e3)
% 200.02/32.97  | | | | | | | | | |   (368)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.02/32.97  | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | BETA: splitting (368) gives:
% 200.02/32.97  | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | |   (369)  all_56_3 = e2
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | COMBINE_EQS: (352), (369) imply:
% 200.02/32.97  | | | | | | | | | | |   (370)  all_14_1 = e2
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | SIMP: (370) implies:
% 200.02/32.97  | | | | | | | | | | |   (371)  all_14_1 = e2
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | COMBINE_EQS: (353), (371) imply:
% 200.02/32.97  | | | | | | | | | | |   (372)  all_58_9 = e2
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | REDUCE: (357), (371) imply:
% 200.02/32.97  | | | | | | | | | | |   (373)   ~ (all_52_9 = e2)
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | REDUCE: (360), (371) imply:
% 200.02/32.97  | | | | | | | | | | |   (374)   ~ (all_52_29 = e2)
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | REDUCE: (363), (371) imply:
% 200.02/32.97  | | | | | | | | | | |   (375)  op(e2, e2) = e3
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | REDUCE: (271), (371) imply:
% 200.02/32.97  | | | | | | | | | | |   (376)  op(e0, e2) = e2
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | BETA: splitting (140) gives:
% 200.02/32.97  | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | |   (377)  all_56_1 = e3
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | COMBINE_EQS: (131), (377) imply:
% 200.02/32.97  | | | | | | | | | | | |   (378)  all_52_9 = e3
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | REDUCE: (283), (378) imply:
% 200.02/32.97  | | | | | | | | | | | |   (379)  $false
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | CLOSE: (379) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | |   (380)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | BETA: splitting (380) gives:
% 200.02/32.97  | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | |   (381)  all_56_1 = e2
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | COMBINE_EQS: (131), (381) imply:
% 200.02/32.97  | | | | | | | | | | | | |   (382)  all_52_9 = e2
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | REDUCE: (373), (382) imply:
% 200.02/32.97  | | | | | | | | | | | | |   (383)  $false
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | CLOSE: (383) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | |   (384)  all_56_1 = e1 | all_56_1 = e0
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | BETA: splitting (384) gives:
% 200.02/32.97  | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | |   (385)  all_56_1 = e1
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | COMBINE_EQS: (131), (385) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (386)  all_52_9 = e1
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | COMBINE_EQS: (9), (386) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (387)  all_58_1 = e1
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (10), (386) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (388)   ~ (all_52_13 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | SIMP: (388) implies:
% 200.02/32.97  | | | | | | | | | | | | | |   (389)   ~ (all_52_13 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (66), (386) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (390)  op(e1, e1) = all_52_8
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_52_0, e0, e0,
% 200.02/32.97  | | | | | | | | | | | | | |              simplifying with (347), (364) gives:
% 200.02/32.97  | | | | | | | | | | | | | |   (391)  all_52_0 = e3
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_15, e2, e2, e0,
% 200.02/32.97  | | | | | | | | | | | | | |              simplifying with (13), (376) gives:
% 200.02/32.97  | | | | | | | | | | | | | |   (392)  all_52_15 = e2
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_7, e1, e3, e0,
% 200.02/32.97  | | | | | | | | | | | | | |              simplifying with (96), (365) gives:
% 200.02/32.97  | | | | | | | | | | | | | |   (393)  all_52_7 = e1
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_8, e1, e1,
% 200.02/32.97  | | | | | | | | | | | | | |              simplifying with (145), (390) gives:
% 200.02/32.97  | | | | | | | | | | | | | |   (394)  all_52_8 = all_10_2
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, e3, e2, e2,
% 200.02/32.97  | | | | | | | | | | | | | |              simplifying with (38), (375) gives:
% 200.02/32.97  | | | | | | | | | | | | | |   (395)  all_4_2 = e3
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | COMBINE_EQS: (30), (392) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (396)  all_58_13 = e2
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | COMBINE_EQS: (74), (393) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (397)  all_58_12 = e1
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | COMBINE_EQS: (148), (395) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (398)  all_58_3 = e3
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (128), (393) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (399)   ~ (all_52_3 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (150), (395) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (400)   ~ (all_52_3 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (73), (393) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (401)   ~ (all_52_5 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (146), (393) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (402)   ~ (all_52_23 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | SIMP: (402) implies:
% 200.02/32.97  | | | | | | | | | | | | | |   (403)   ~ (all_52_23 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (356), (393) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (404)   ~ (e1 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (118), (392) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (405)   ~ (all_52_13 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (94), (395) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (406)   ~ (all_52_13 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (1), (392) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (407)   ~ (all_52_23 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | SIMP: (407) implies:
% 200.02/32.97  | | | | | | | | | | | | | |   (408)   ~ (all_52_23 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (134), (395) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (409)   ~ (all_52_27 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | REDUCE: (16), (393) imply:
% 200.02/32.97  | | | | | | | | | | | | | |   (410)  op(e1, e1) = all_52_6
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 200.02/32.97  | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | |   (411)  all_58_6 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | COMBINE_EQS: (135), (411) imply:
% 200.02/32.97  | | | | | | | | | | | | | | |   (412)  all_52_5 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | SIMP: (412) implies:
% 200.02/32.97  | | | | | | | | | | | | | | |   (413)  all_52_5 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | REDUCE: (8), (413) imply:
% 200.02/32.97  | | | | | | | | | | | | | | |   (414)   ~ (all_52_13 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | REDUCE: (87), (413) imply:
% 200.02/32.97  | | | | | | | | | | | | | | |   (415)   ~ (all_52_29 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | SIMP: (415) implies:
% 200.02/32.97  | | | | | | | | | | | | | | |   (416)   ~ (all_52_29 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | REDUCE: (106), (413) imply:
% 200.02/32.97  | | | | | | | | | | | | | | |   (417)   ~ (all_10_2 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | |   (418)  all_56_4 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (418) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | |   (419)  all_52_3 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | REDUCE: (400), (419) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | |   (420)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | |   (421)   ~ (all_56_4 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | |   (422)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | BETA: splitting (422) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (423)  all_56_4 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (423) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (424)  all_52_3 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (424) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (425)  all_58_2 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | REDUCE: (48), (424) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (426)   ~ (all_52_27 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | SIMP: (426) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (427)   ~ (all_52_27 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | REDUCE: (400), (424) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (428)   ~ (e3 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | |   (429)  all_58_6 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (291), (411), (429) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | |            #428.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | |   (430)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | |   (431)  all_58_12 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (397), (404), (431) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | | |            #1173.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | |   (432)  all_58_13 = e0 | all_58_14 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (433)  all_58_13 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (396), (433) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |            #110.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (434)  all_58_14 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (434) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (435)  all_52_23 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | SIMP: (435) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (436)  all_52_23 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (436) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (437)   ~ (all_4_0 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | SIMP: (437) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (438)   ~ (all_4_0 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (284), (436) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (439)   ~ (e3 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (408), (436) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (440)   ~ (e2 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (436) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (441)   ~ (e1 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (436) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | |   (442)  op(e0, e0) = all_52_22
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | |   (443)  all_58_1 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (443) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | |   (444)  e1 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | REDUCE: (404), (444) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | |   (445)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | CLOSE: (445) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | |   (446)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | |   (447)  all_58_3 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (447) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | |   (448)  e3 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (448) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | |   (449)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | |   (450)  all_58_7 = e0 | all_58_13 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_58_7 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (451) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_52_13 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (452) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | |   (453)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (453) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | |   (454)  all_58_8 = e2 | all_58_11 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (455)  all_58_7 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (455) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (456)  all_52_13 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (456) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (457)   ~ (all_52_29 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (457) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (458)   ~ (all_52_29 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (456) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (459)   ~ (all_10_2 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (459) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (460)   ~ (all_10_2 = e0)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (456) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (461)  op(e0, e0) = all_52_12
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_56_11 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (462) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_52_29 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (463) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (464) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (465)   ~ (all_56_11 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  all_58_8 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (467) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_10_2 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (468) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)   ~ (all_4_0 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (469) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)   ~ (all_4_0 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (468) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  op(e1, e1) = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  all_56_11 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (374), (472) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1024.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)   ~ (all_56_11 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  all_56_11 = e1 | all_56_11 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  all_56_11 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (475) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  all_52_29 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (476) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_52_29 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (477) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  all_58_11 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (477) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)   ~ (all_52_27 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (477) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)   ~ (e3 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (477) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)   ~ (e2 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (477) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  op(e1, e1) = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_58_4 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (30), (38), (46), (60),
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (79), (83), (98), (113), (125), (148),
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (291), (353), (354), (362), (363), (483) are
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #273.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)   ~ (all_58_4 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_58_2 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (486) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  e2 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (487) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (488) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)   ~ (all_58_2 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_58_3 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (491) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  e3 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (492) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_58_4 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (30), (38), (46), (60),
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (79), (83), (98), (113), (125), (148),
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (291), (353), (354), (362), (363), (493) are
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #273.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  all_58_5 = e1 | all_58_10 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  all_58_9 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (495) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  e2 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (496) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (497) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_58_10 = e0 | all_58_11 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (485) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_58_5 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (499) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  all_4_0 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (500) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  op(e1, e1) = all_52_18
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_58_10 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (502) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_52_27 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (503) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  op(e0, e0) = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_52_22, e0, e0,
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (347), (442) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_52_22 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_22, all_52_12, e0,
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (442), (461) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  all_52_12 = all_52_22
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_12, e0, e0,
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (461), (504) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  all_52_12 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_18, e1, e1,
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (482), (501) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  all_52_18 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_18, all_52_6, e1,
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (410), (501) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_52_6 = all_52_18
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_6, e1, e1,
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (410), (471) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_52_6 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (509), (510) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  all_52_18 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  all_52_18 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (506), (507) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_52_22 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (513) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  all_52_22 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (508), (512) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  e2 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (505), (514) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  e3 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (516) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  e3 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (515), (517) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  e3 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (518) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  all_58_4 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (30), (38), (46), (60),
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (79), (83), (98), (113), (125), (148),
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (291), (353), (354), (362), (363), (519) are
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #273.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  all_58_11 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (520) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  e1 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (404), (521) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (522) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)   ~ (all_58_5 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (523) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)   ~ (all_4_0 = e1)
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (494) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  all_58_5 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (525) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  all_4_0 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (524), (526) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (527) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  all_58_10 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (528) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (529)  all_52_27 = e1
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (529) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (530)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (530) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (531)  all_56_11 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (458), (531) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1002.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (532)  all_58_11 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (532) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (533)  all_52_29 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (533) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (534)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (534) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |   (535)  all_58_13 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (396), (535) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | |            #110.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (536)  all_56_4 = e1 | all_56_4 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (355), (399), (536) are inconsistent by
% 200.02/32.97  | | | | | | | | | | | | | | | | |            sub-proof #1308.
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | End of split
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | |   (537)   ~ (all_58_6 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | REDUCE: (135), (537) imply:
% 200.02/32.97  | | | | | | | | | | | | | | |   (538)   ~ (all_52_5 = e3)
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | |   (539)  all_56_4 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (539) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | |   (540)  all_52_3 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | REDUCE: (400), (540) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | |   (541)  $false
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | CLOSE: (541) is inconsistent.
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | |   (542)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | BETA: splitting (542) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (543)  all_56_4 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (543) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (544)  all_52_3 = e2
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | REDUCE: (40), (544) imply:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (545)   ~ (all_52_5 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | SIMP: (545) implies:
% 200.02/32.97  | | | | | | | | | | | | | | | | |   (546)   ~ (all_52_5 = e2)
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | |   (547)  all_56_9 = e3
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (406), (547) are inconsistent by sub-proof
% 200.02/32.97  | | | | | | | | | | | | | | | | | |            #958.
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | |   (548)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | 
% 200.02/32.97  | | | | | | | | | | | | | | | | | | Case 1:
% 200.02/32.97  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | | |   (549)  all_56_8 = e3
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (538), (549) are inconsistent by sub-proof
% 200.02/32.98  | | | | | | | | | | | | | | | | | | |            #1325.
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | | |   (550)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (59), (65), (389), (401), (405), (546),
% 200.02/32.98  | | | | | | | | | | | | | | | | | | |            (548), (550) are inconsistent by sub-proof #471.
% 200.02/32.98  | | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | |   (551)  all_56_4 = e1 | all_56_4 = e0
% 200.02/32.98  | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (355), (399), (551) are inconsistent by
% 200.02/32.98  | | | | | | | | | | | | | | | | |            sub-proof #1308.
% 200.02/32.98  | | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | |   (552)  all_56_1 = e0
% 200.02/32.98  | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | COMBINE_EQS: (131), (552) imply:
% 200.02/32.98  | | | | | | | | | | | | | |   (553)  all_52_9 = e0
% 200.02/32.98  | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | REDUCE: (358), (553) imply:
% 200.02/32.98  | | | | | | | | | | | | | |   (554)  $false
% 200.02/32.98  | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | | CLOSE: (554) is inconsistent.
% 200.02/32.98  | | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | |   (555)  all_56_3 = e1 | all_56_3 = e0
% 200.02/32.98  | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | | REF_CLOSE: (349), (352), (361), (555) are inconsistent by
% 200.02/32.98  | | | | | | | | | | |            sub-proof #806.
% 200.02/32.98  | | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | | 
% 200.02/32.98  | | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | | 
% 200.02/32.98  | | | | | | | | |   (556)   ~ (all_50_2 = e3)
% 200.02/32.98  | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | REDUCE: (344), (556) imply:
% 200.02/32.98  | | | | | | | | |   (557)  $false
% 200.02/32.98  | | | | | | | | | 
% 200.02/32.98  | | | | | | | | | CLOSE: (557) is inconsistent.
% 200.02/32.98  | | | | | | | | | 
% 200.02/32.98  | | | | | | | | End of split
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | |   (558)   ~ (all_56_15 = e3)
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | | REDUCE: (53), (558) imply:
% 200.02/32.98  | | | | | | | |   (559)   ~ (all_14_2 = e3)
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | | REF_CLOSE: (2), (3), (4), (7), (9), (14), (16), (17), (18),
% 200.02/32.98  | | | | | | | |            (20), (23), (24), (28), (30), (31), (36), (38), (40),
% 200.02/32.98  | | | | | | | |            (43), (44), (46), (48), (50), (52), (54), (55), (56),
% 200.02/32.98  | | | | | | | |            (57), (58), (61), (62), (64), (66), (67), (68), (70),
% 200.02/32.98  | | | | | | | |            (73), (74), (75), (76), (77), (78), (80), (81), (84),
% 200.02/32.98  | | | | | | | |            (87), (89), (90), (91), (92), (94), (98), (99),
% 200.02/32.98  | | | | | | | |            (100), (101), (104), (106), (109), (111), (112),
% 200.02/32.98  | | | | | | | |            (114), (117), (118), (122), (123), (124), (125),
% 200.02/32.98  | | | | | | | |            (126), (127), (128), (130), (131), (132), (134),
% 200.02/32.98  | | | | | | | |            (135), (138), (139), (140), (145), (147), (148),
% 200.02/32.98  | | | | | | | |            (149), (150), (152), (153), (154), (283), (284),
% 200.02/32.98  | | | | | | | |            (285), (286), (291), (337), (338), (339), (559) are
% 200.02/32.98  | | | | | | | |            inconsistent by sub-proof #112.
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | End of split
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | End of split
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | End of split
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | Case 2:
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | |   (560)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REF_CLOSE: (4), (7), (24), (36), (39), (50), (62), (63), (88), (92),
% 200.02/32.98  | | | | |            (114), (119), (122), (143), (158), (167), (560) are
% 200.02/32.98  | | | | |            inconsistent by sub-proof #569.
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | End of split
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | End of split
% 200.02/32.98  | | | 
% 200.02/32.98  | | End of split
% 200.02/32.98  | | 
% 200.02/32.98  | End of split
% 200.02/32.98  | 
% 200.02/32.98  End of proof
% 200.02/32.98  
% 200.02/32.98  Sub-proof #110 shows that the following formulas are inconsistent:
% 200.02/32.98  ----------------------------------------------------------------
% 200.02/32.98    (1)  all_58_13 = e2
% 200.02/32.98    (2)  all_58_13 = e0
% 200.02/32.98    (3)   ~ (e2 = e0)
% 200.02/32.98  
% 200.02/32.98  Begin of proof
% 200.02/32.98  | 
% 200.02/32.98  | COMBINE_EQS: (1), (2) imply:
% 200.02/32.98  |   (4)  e2 = e0
% 200.02/32.98  | 
% 200.02/32.98  | SIMP: (4) implies:
% 200.02/32.98  |   (5)  e2 = e0
% 200.02/32.98  | 
% 200.02/32.98  | REDUCE: (3), (5) imply:
% 200.02/32.98  |   (6)  $false
% 200.02/32.98  | 
% 200.02/32.98  | CLOSE: (6) is inconsistent.
% 200.02/32.98  | 
% 200.02/32.98  End of proof
% 200.02/32.98  
% 200.02/32.98  Sub-proof #111 shows that the following formulas are inconsistent:
% 200.02/32.98  ----------------------------------------------------------------
% 200.02/32.98    (1)   ~ (all_52_25 = all_6_0)
% 200.02/32.98    (2)   ~ (all_52_25 = all_52_27)
% 200.02/32.98    (3)  all_58_14 = all_52_23
% 200.02/32.98    (4)   ~ (e3 = e1)
% 200.02/32.98    (5)  op(all_52_3, all_52_3) = all_52_2
% 200.02/32.98    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/32.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/32.98    (7)   ~ (all_52_5 = all_52_13)
% 200.02/32.98    (8)  all_58_1 = all_52_9
% 200.02/32.98    (9)   ~ (all_52_7 = all_52_15)
% 200.02/32.98    (10)  op(all_52_7, all_52_7) = all_52_6
% 200.02/32.98    (11)   ~ (all_52_17 = all_52_25)
% 200.02/32.98    (12)   ~ (all_52_3 = all_6_2)
% 200.02/32.98    (13)  all_58_0 = all_6_2
% 200.02/32.98    (14)  op(all_14_2, e0) = all_14_1
% 200.02/32.98    (15)  all_56_4 = all_52_3
% 200.02/32.98    (16)   ~ (all_52_17 = all_10_2)
% 200.02/32.98    (17)  op(all_6_0, all_6_0) = all_52_16
% 200.02/32.98    (18)  op(all_6_2, e3) = e1
% 200.02/32.98    (19)  op(e3, e0) = all_52_25
% 200.02/32.98    (20)  op(all_52_5, all_52_5) = all_52_4
% 200.02/32.98    (21)   ~ (all_10_2 = all_6_0)
% 200.02/32.98    (22)  all_58_13 = all_52_15
% 200.02/32.98    (23)  all_58_9 = all_52_25
% 200.02/32.98    (24)   ~ (all_52_29 = all_14_2)
% 200.02/32.98    (25)  op(all_52_27, all_52_27) = all_52_26
% 200.02/32.98    (26)  op(e1, e3) = all_52_5
% 200.02/32.98    (27)  op(e2, e2) = all_4_2
% 200.02/32.98    (28)  all_12_0 = all_6_0
% 200.02/32.98    (29)   ~ (all_52_3 = all_52_5)
% 200.02/32.98    (30)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.02/32.98    (31)  op(all_4_2, e2) = e1
% 200.02/32.98    (32)  all_58_11 = all_52_29
% 200.02/32.98    (33)  all_56_5 = all_4_2
% 200.02/32.98    (34)   ~ (all_52_25 = all_14_2)
% 200.02/32.98    (35)   ~ (all_52_9 = all_52_15)
% 200.02/32.98    (36)   ~ (all_52_3 = all_52_27)
% 200.02/32.98    (37)  op(all_6_2, all_6_2) = all_52_0
% 200.02/32.98    (38)   ~ (all_52_7 = all_6_2)
% 200.02/32.98    (39)  op(e0, e0) = all_14_2
% 200.02/32.98    (40)  all_56_2 = all_6_0
% 200.02/32.98    (41)  all_56_15 = all_14_2
% 200.02/32.98    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/32.98    (43)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.02/32.98    (44)  all_56_11 = all_52_29
% 200.02/32.98    (45)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.02/32.98    (46)  all_58_4 = all_6_0
% 200.02/32.98    (47)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.02/32.98    (48)   ~ (all_52_13 = all_10_2)
% 200.02/32.98    (49)   ~ (all_6_0 = e1)
% 200.02/32.98    (50)  all_12_2 = all_6_2
% 200.02/32.98    (51)  all_58_10 = all_52_27
% 200.02/32.98    (52)  all_56_8 = all_52_5
% 200.02/32.98    (53)  op(all_52_9, all_52_9) = all_52_8
% 200.02/32.98    (54)  op(all_52_15, all_52_15) = all_52_14
% 200.02/32.98    (55)   ~ (all_52_25 = all_52_29)
% 200.02/32.98    (56)  all_58_7 = all_52_13
% 200.02/32.98    (57)   ~ (all_52_5 = all_52_7)
% 200.02/32.98    (58)  all_58_12 = all_52_7
% 200.02/32.98    (59)   ~ (all_6_0 = all_4_0)
% 200.02/32.98    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/32.98    (61)   ~ (all_52_7 = all_14_2)
% 200.02/32.98    (62)  all_58_2 = all_52_3
% 200.02/32.98    (63)  all_56_2 = all_52_17
% 200.02/32.98    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.02/32.98    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/32.98    (66)  op(e3, all_6_1) = all_6_0
% 200.02/32.98    (67)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/32.98    (68)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.02/32.98    (69)   ~ (all_52_5 = all_52_29)
% 200.02/32.98    (70)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 200.02/32.98    (71)   ~ (all_52_15 = all_14_2)
% 200.02/32.98    (72)   ~ (all_52_19 = all_52_27)
% 200.02/32.98    (73)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.02/32.98    (74)   ~ (all_6_0 = e2)
% 200.02/32.98    (75)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.02/32.98    (76)   ~ (all_52_13 = all_4_2)
% 200.02/32.98    (77)  op(e0, e3) = all_52_7
% 200.02/32.98    (78)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/32.98    (79)   ~ (all_52_9 = all_52_25)
% 200.02/32.98    (80)  all_58_15 = all_14_2
% 200.02/32.98    (81)   ~ (all_52_19 = all_10_2)
% 200.02/32.98    (82)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.02/32.98    (83)   ~ (all_52_23 = all_6_0)
% 200.02/32.98    (84)  all_58_8 = all_10_2
% 200.02/32.98    (85)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.02/32.98    (86)   ~ (all_52_9 = all_6_0)
% 200.02/32.98    (87)   ~ (all_52_5 = all_10_2)
% 200.02/32.98    (88)  op(all_52_29, all_52_29) = all_52_28
% 200.02/32.98    (89)   ~ (all_52_23 = all_14_2)
% 200.02/32.98    (90)  op(all_52_17, all_52_17) = all_52_16
% 200.02/32.98    (91)  all_58_5 = all_4_0
% 200.02/32.98    (92)   ~ (all_52_25 = all_6_2)
% 200.02/32.98    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.02/32.98    (94)   ~ (all_52_5 = all_6_2)
% 200.02/32.98    (95)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.02/32.98    (96)   ~ (all_52_9 = all_6_2)
% 200.02/32.98    (97)   ~ (all_52_13 = all_52_15)
% 200.02/32.98    (98)  all_56_0 = all_6_2
% 200.02/32.98    (99)  op(e3, e3) = all_6_2
% 200.02/32.98    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.02/32.98    (101)   ~ (all_52_27 = all_14_2)
% 200.02/32.98    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.02/32.98    (103)  op(all_4_2, all_4_2) = all_52_10
% 200.02/32.98    (104)  all_56_3 = all_52_25
% 200.02/32.98    (105)   ~ (all_52_3 = all_52_7)
% 200.02/32.98    (106)   ~ (all_6_0 = all_6_2)
% 200.02/32.98    (107)  op(all_14_2, all_14_2) = all_52_30
% 200.02/32.98    (108)  all_58_5 = all_52_19
% 200.02/32.98    (109)  all_56_1 = all_52_9
% 200.02/32.98    (110)   ~ (all_52_15 = all_4_2)
% 200.02/32.98    (111)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.02/32.98           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.02/32.98           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.02/32.98           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.02/32.98    (112)   ~ (all_52_27 = all_4_2)
% 200.02/32.98    (113)  all_58_6 = all_52_5
% 200.02/32.98    (114)   ~ (all_4_0 = all_4_2)
% 200.02/32.98    (115)  op(e3, e2) = all_52_9
% 200.02/32.98    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/32.98    (117)   ~ (all_52_17 = all_6_2)
% 200.02/32.98    (118)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.02/32.98    (119)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.02/32.98    (120)  op(all_52_13, all_52_13) = all_52_12
% 200.02/32.98    (121)  op(e1, e1) = all_10_2
% 200.02/32.98    (122)   ~ (all_52_17 = all_52_19)
% 200.02/32.98    (123)  all_58_3 = all_4_2
% 200.02/32.98    (124)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.02/32.98    (125)   ~ (all_52_3 = all_4_2)
% 200.02/32.98    (126)  op(all_6_2, e3) = all_6_1
% 200.02/32.98    (127)   ~ (all_52_13 = all_52_29)
% 200.02/32.98    (128)  all_58_4 = all_52_17
% 200.02/32.98    (129)  op(all_52_25, all_52_25) = all_52_24
% 200.02/32.98  
% 200.02/32.98  Begin of proof
% 200.02/32.98  | 
% 200.02/32.98  | BETA: splitting (45) gives:
% 200.02/32.98  | 
% 200.02/32.98  | Case 1:
% 200.02/32.98  | | 
% 200.02/32.98  | |   (130)  all_56_2 = e3
% 200.02/32.98  | | 
% 200.02/32.98  | | COMBINE_EQS: (40), (130) imply:
% 200.02/32.98  | |   (131)  all_6_0 = e3
% 200.02/32.98  | | 
% 200.02/32.98  | | SIMP: (131) implies:
% 200.02/32.98  | |   (132)  all_6_0 = e3
% 200.02/32.98  | | 
% 200.02/32.98  | | COMBINE_EQS: (46), (132) imply:
% 200.02/32.98  | |   (133)  all_58_4 = e3
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (86), (132) imply:
% 200.02/32.98  | |   (134)   ~ (all_52_9 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (83), (132) imply:
% 200.02/32.98  | |   (135)   ~ (all_52_23 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (1), (132) imply:
% 200.02/32.98  | |   (136)   ~ (all_52_25 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (21), (132) imply:
% 200.02/32.98  | |   (137)   ~ (all_10_2 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (106), (132) imply:
% 200.02/32.98  | |   (138)   ~ (all_6_2 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | SIMP: (138) implies:
% 200.02/32.98  | |   (139)   ~ (all_6_2 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (59), (132) imply:
% 200.02/32.98  | |   (140)   ~ (all_4_0 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | SIMP: (140) implies:
% 200.02/32.98  | |   (141)   ~ (all_4_0 = e3)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (74), (132) imply:
% 200.02/32.98  | |   (142)   ~ (e3 = e2)
% 200.02/32.98  | | 
% 200.02/32.98  | | REDUCE: (17), (132) imply:
% 200.02/32.98  | |   (143)  op(e3, e3) = all_52_16
% 200.02/32.98  | | 
% 200.02/32.98  | | GROUND_INST: instantiating (6) with all_6_2, all_52_16, e3, e3, simplifying
% 200.02/32.98  | |              with (99), (143) gives:
% 200.02/32.98  | |   (144)  all_52_16 = all_6_2
% 200.02/32.98  | | 
% 200.02/32.98  | | BETA: splitting (111) gives:
% 200.02/32.98  | | 
% 200.02/32.98  | | Case 1:
% 200.02/32.98  | | | 
% 200.02/32.98  | | |   (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.02/32.98  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.02/32.98  | | |            e0)
% 200.02/32.98  | | | 
% 200.02/32.98  | | | BETA: splitting (145) gives:
% 200.02/32.98  | | | 
% 200.02/32.98  | | | Case 1:
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | |   (146)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REF_CLOSE: (5), (6), (10), (13), (20), (27), (37), (39), (42), (58),
% 200.02/32.98  | | | |            (61), (62), (65), (87), (99), (113), (116), (121), (125),
% 200.02/32.98  | | | |            (139), (146) are inconsistent by sub-proof #835.
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | Case 2:
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | |   (147)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.02/32.98  | | | |          e0
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | ALPHA: (147) implies:
% 200.02/32.98  | | | |   (148)  all_52_14 = e0
% 200.02/32.98  | | | |   (149)  all_52_12 = e1
% 200.02/32.98  | | | |   (150)  all_52_8 = e3
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (53), (150) imply:
% 200.02/32.98  | | | |   (151)  op(all_52_9, all_52_9) = e3
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (120), (149) imply:
% 200.02/32.98  | | | |   (152)  op(all_52_13, all_52_13) = e1
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (54), (148) imply:
% 200.02/32.98  | | | |   (153)  op(all_52_15, all_52_15) = e0
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | BETA: splitting (85) gives:
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | Case 1:
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | |   (154)  all_56_15 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | COMBINE_EQS: (41), (154) imply:
% 200.02/32.98  | | | | |   (155)  all_14_2 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | SIMP: (155) implies:
% 200.02/32.98  | | | | |   (156)  all_14_2 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (101), (156) imply:
% 200.02/32.98  | | | | |   (157)   ~ (all_52_27 = e3)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (24), (156) imply:
% 200.02/32.98  | | | | |   (158)   ~ (all_52_29 = e3)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (107), (156) imply:
% 200.02/32.98  | | | | |   (159)  op(e3, e3) = all_52_30
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3,
% 200.02/32.98  | | | | |              simplifying with (99), (159) gives:
% 200.02/32.98  | | | | |   (160)  all_52_30 = all_6_2
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | BETA: splitting (78) gives:
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | Case 1:
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | |   (161)  all_58_1 = e3
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | COMBINE_EQS: (8), (161) imply:
% 200.02/32.98  | | | | | |   (162)  all_52_9 = e3
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | REDUCE: (134), (162) imply:
% 200.02/32.98  | | | | | |   (163)  $false
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | CLOSE: (163) is inconsistent.
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | Case 2:
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | |   (164)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | BETA: splitting (42) gives:
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | Case 1:
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | |   (165)  all_58_2 = e3
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | COMBINE_EQS: (62), (165) imply:
% 200.02/32.98  | | | | | | |   (166)  all_52_3 = e3
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | REDUCE: (29), (166) imply:
% 200.02/32.98  | | | | | | |   (167)   ~ (all_52_5 = e3)
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | SIMP: (167) implies:
% 200.02/32.98  | | | | | | |   (168)   ~ (all_52_5 = e3)
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | REDUCE: (105), (166) imply:
% 200.02/32.98  | | | | | | |   (169)   ~ (all_52_7 = e3)
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | SIMP: (169) implies:
% 200.02/32.98  | | | | | | |   (170)   ~ (all_52_7 = e3)
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | BETA: splitting (60) gives:
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | Case 1:
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | |   (171)  all_58_6 = e3
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | | REF_CLOSE: (113), (168), (171) are inconsistent by sub-proof
% 200.02/32.98  | | | | | | | |            #1328.
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | Case 2:
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | |   (172)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | | REF_CLOSE: (5), (6), (7), (13), (18), (26), (32), (56), (58),
% 200.02/32.98  | | | | | | | |            (62), (65), (84), (94), (99), (113), (137), (139),
% 200.02/32.98  | | | | | | | |            (152), (158), (170), (172) are inconsistent by
% 200.02/32.98  | | | | | | | |            sub-proof #565.
% 200.02/32.98  | | | | | | | | 
% 200.02/32.98  | | | | | | | End of split
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | Case 2:
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | |   (173)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | REF_CLOSE: (6), (22), (31), (51), (56), (76), (91), (95), (110),
% 200.02/32.98  | | | | | | |            (115), (121), (123), (137), (141), (151), (157), (164),
% 200.02/32.98  | | | | | | |            (173) are inconsistent by sub-proof #213.
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | End of split
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | End of split
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | Case 2:
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | |   (174)   ~ (all_56_15 = e3)
% 200.02/32.98  | | | | |   (175)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (41), (174) imply:
% 200.02/32.98  | | | | |   (176)   ~ (all_14_2 = e3)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REF_CLOSE: (3), (6), (8), (9), (10), (13), (18), (22), (23), (25),
% 200.02/32.98  | | | | |            (26), (27), (31), (33), (34), (38), (41), (42), (51), (56),
% 200.02/32.98  | | | | |            (58), (61), (62), (64), (68), (71), (75), (76), (77), (78),
% 200.02/32.98  | | | | |            (80), (89), (91), (94), (95), (99), (105), (110), (112),
% 200.02/32.98  | | | | |            (114), (115), (116), (121), (123), (133), (134), (135),
% 200.02/32.98  | | | | |            (137), (139), (141), (151), (152), (153), (175), (176) are
% 200.02/32.98  | | | | |            inconsistent by sub-proof #113.
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | End of split
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | End of split
% 200.02/32.98  | | | 
% 200.02/32.98  | | Case 2:
% 200.02/32.98  | | | 
% 200.02/32.98  | | |   (177)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.02/32.98  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.02/32.98  | | |            all_52_30 = e0)
% 200.02/32.98  | | | 
% 200.02/32.98  | | | BETA: splitting (177) gives:
% 200.02/32.98  | | | 
% 200.02/32.98  | | | Case 1:
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | |   (178)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.02/32.98  | | | |          e0
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REF_CLOSE: (139), (144), (178) are inconsistent by sub-proof #553.
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | Case 2:
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | |   (179)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.02/32.98  | | | |          e0
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | ALPHA: (179) implies:
% 200.02/32.98  | | | |   (180)  all_52_30 = e0
% 200.02/32.98  | | | |   (181)  all_52_28 = e1
% 200.02/32.98  | | | |   (182)  all_52_26 = e2
% 200.02/32.98  | | | |   (183)  all_52_24 = e3
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (129), (183) imply:
% 200.02/32.98  | | | |   (184)  op(all_52_25, all_52_25) = e3
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (25), (182) imply:
% 200.02/32.98  | | | |   (185)  op(all_52_27, all_52_27) = e2
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (88), (181) imply:
% 200.02/32.98  | | | |   (186)  op(all_52_29, all_52_29) = e1
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | REDUCE: (107), (180) imply:
% 200.02/32.98  | | | |   (187)  op(all_14_2, all_14_2) = e0
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | BETA: splitting (85) gives:
% 200.02/32.98  | | | | 
% 200.02/32.98  | | | | Case 1:
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | |   (188)  all_56_15 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | COMBINE_EQS: (41), (188) imply:
% 200.02/32.98  | | | | |   (189)  all_14_2 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | SIMP: (189) implies:
% 200.02/32.98  | | | | |   (190)  all_14_2 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (61), (190) imply:
% 200.02/32.98  | | | | |   (191)   ~ (all_52_7 = e3)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (71), (190) imply:
% 200.02/32.98  | | | | |   (192)   ~ (all_52_15 = e3)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (187), (190) imply:
% 200.02/32.98  | | | | |   (193)  op(e3, e3) = e0
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (14), (190) imply:
% 200.02/32.98  | | | | |   (194)  op(e3, e0) = all_14_1
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (39), (190) imply:
% 200.02/32.98  | | | | |   (195)  op(e0, e0) = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3,
% 200.02/32.98  | | | | |              simplifying with (19), (194) gives:
% 200.02/32.98  | | | | |   (196)  all_52_25 = all_14_1
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying
% 200.02/32.98  | | | | |              with (99), (193) gives:
% 200.02/32.98  | | | | |   (197)  all_6_2 = e0
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | COMBINE_EQS: (104), (196) imply:
% 200.02/32.98  | | | | |   (198)  all_56_3 = all_14_1
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | COMBINE_EQS: (23), (196) imply:
% 200.02/32.98  | | | | |   (199)  all_58_9 = all_14_1
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | COMBINE_EQS: (13), (197) imply:
% 200.02/32.98  | | | | |   (200)  all_58_0 = e0
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (12), (197) imply:
% 200.02/32.98  | | | | |   (201)   ~ (all_52_3 = e0)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (94), (197) imply:
% 200.02/32.98  | | | | |   (202)   ~ (all_52_5 = e0)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (92), (196), (197) imply:
% 200.02/32.98  | | | | |   (203)   ~ (all_14_1 = e0)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (136), (196) imply:
% 200.02/32.98  | | | | |   (204)   ~ (all_14_1 = e3)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (139), (197) imply:
% 200.02/32.98  | | | | |   (205)   ~ (e3 = e0)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | SIMP: (205) implies:
% 200.02/32.98  | | | | |   (206)   ~ (e3 = e0)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (184), (196) imply:
% 200.02/32.98  | | | | |   (207)  op(all_14_1, all_14_1) = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (37), (197) imply:
% 200.02/32.98  | | | | |   (208)  op(e0, e0) = all_52_0
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (18), (197) imply:
% 200.02/32.98  | | | | |   (209)  op(e0, e3) = e1
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e0, e0, simplifying
% 200.02/32.98  | | | | |              with (195), (208) gives:
% 200.02/32.98  | | | | |   (210)  all_52_0 = e3
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | GROUND_INST: instantiating (6) with all_52_7, e1, e3, e0, simplifying
% 200.02/32.98  | | | | |              with (77), (209) gives:
% 200.02/32.98  | | | | |   (211)  all_52_7 = e1
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (105), (211) imply:
% 200.02/32.98  | | | | |   (212)   ~ (all_52_3 = e1)
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | REDUCE: (10), (211) imply:
% 200.02/32.98  | | | | |   (213)  op(e1, e1) = all_52_6
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_6, e1, e1,
% 200.02/32.98  | | | | |              simplifying with (121), (213) gives:
% 200.02/32.98  | | | | |   (214)  all_52_6 = all_10_2
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | BETA: splitting (93) gives:
% 200.02/32.98  | | | | | 
% 200.02/32.98  | | | | | Case 1:
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | |   (215)  all_56_3 = e3
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | REF_CLOSE: (198), (204), (215) are inconsistent by sub-proof #1200.
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | Case 2:
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | |   (216)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | BETA: splitting (82) gives:
% 200.02/32.98  | | | | | | 
% 200.02/32.98  | | | | | | Case 1:
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | |   (217)  all_56_8 = e3
% 200.02/32.98  | | | | | | | 
% 200.02/32.98  | | | | | | | COMBINE_EQS: (52), (217) imply:
% 200.02/32.98  | | | | | | |   (218)  all_52_5 = e3
% 200.02/32.98  | | | | | | | 
% 200.02/32.99  | | | | | | | SIMP: (218) implies:
% 200.02/32.99  | | | | | | |   (219)  all_52_5 = e3
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | REDUCE: (29), (219) imply:
% 200.02/32.99  | | | | | | |   (220)   ~ (all_52_3 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | REDUCE: (7), (219) imply:
% 200.02/32.99  | | | | | | |   (221)   ~ (all_52_13 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | SIMP: (221) implies:
% 200.02/32.99  | | | | | | |   (222)   ~ (all_52_13 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | BETA: splitting (67) gives:
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | |   (223)  all_56_4 = e3
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | REF_CLOSE: (15), (220), (223) are inconsistent by sub-proof
% 200.02/32.99  | | | | | | | |            #1340.
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | |   (224)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | BETA: splitting (224) gives:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | |   (225)  all_56_4 = e2
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | COMBINE_EQS: (15), (225) imply:
% 200.02/32.99  | | | | | | | | |   (226)  all_52_3 = e2
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | SIMP: (226) implies:
% 200.02/32.99  | | | | | | | | |   (227)  all_52_3 = e2
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | COMBINE_EQS: (62), (227) imply:
% 200.02/32.99  | | | | | | | | |   (228)  all_58_2 = e2
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REDUCE: (125), (227) imply:
% 200.02/32.99  | | | | | | | | |   (229)   ~ (all_4_2 = e2)
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | SIMP: (229) implies:
% 200.02/32.99  | | | | | | | | |   (230)   ~ (all_4_2 = e2)
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REDUCE: (201), (227) imply:
% 200.02/32.99  | | | | | | | | |   (231)   ~ (e2 = e0)
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | BETA: splitting (78) gives:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | |   (232)  all_58_1 = e3
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | COMBINE_EQS: (8), (232) imply:
% 200.02/32.99  | | | | | | | | | |   (233)  all_52_9 = e3
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | REDUCE: (134), (233) imply:
% 200.02/32.99  | | | | | | | | | |   (234)  $false
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | CLOSE: (234) is inconsistent.
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | |   (235)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | BETA: splitting (235) gives:
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | |   (236)  all_58_3 = e3
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | COMBINE_EQS: (123), (236) imply:
% 200.02/32.99  | | | | | | | | | | |   (237)  all_4_2 = e3
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | REDUCE: (27), (237) imply:
% 200.02/32.99  | | | | | | | | | | |   (238)  op(e2, e2) = e3
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | BETA: splitting (95) gives:
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | |   (239)   ~ (all_4_2 = e3)
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | REF_CLOSE: (6), (27), (238), (239) are inconsistent by
% 200.02/32.99  | | | | | | | | | | | |            sub-proof #211.
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | |   (240)   ~ (all_4_0 = e0)
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | BETA: splitting (30) gives:
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | |   (241)  all_58_2 = e0
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | REF_CLOSE: (228), (231), (241) are inconsistent by sub-proof
% 200.02/32.99  | | | | | | | | | | | | |            #1213.
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | |   (242)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | BETA: splitting (242) gives:
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | |   (243)  all_58_3 = e0
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | COMBINE_EQS: (236), (243) imply:
% 200.02/32.99  | | | | | | | | | | | | | |   (244)  e3 = e0
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | REDUCE: (206), (244) imply:
% 200.02/32.99  | | | | | | | | | | | | | |   (245)  $false
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | |   (246)  all_58_5 = e0 | all_58_10 = e0
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | |   (247)  all_58_5 = e0
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | REF_CLOSE: (91), (240), (247) are inconsistent by sub-proof
% 200.02/32.99  | | | | | | | | | | | | | | |            #209.
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | |   (248)  all_58_10 = e0
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | COMBINE_EQS: (51), (248) imply:
% 200.02/32.99  | | | | | | | | | | | | | | |   (249)  all_52_27 = e0
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | SIMP: (249) implies:
% 200.02/32.99  | | | | | | | | | | | | | | |   (250)  all_52_27 = e0
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | REDUCE: (185), (250) imply:
% 200.02/32.99  | | | | | | | | | | | | | | |   (251)  op(e0, e0) = e2
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, e2, e0, e0, simplifying
% 200.02/32.99  | | | | | | | | | | | | | | |              with (195), (251) gives:
% 200.02/32.99  | | | | | | | | | | | | | | |   (252)  e3 = e2
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | REDUCE: (142), (252) imply:
% 200.02/32.99  | | | | | | | | | | | | | | |   (253)  $false
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 200.02/32.99  | | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | |   (254)  all_58_7 = e3 | all_58_13 = e3
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | | REF_CLOSE: (22), (56), (192), (222), (254) are inconsistent
% 200.02/32.99  | | | | | | | | | | |            by sub-proof #1298.
% 200.02/32.99  | | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | |   (255)  all_56_4 = e1 | all_56_4 = e0
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REF_CLOSE: (15), (201), (212), (255) are inconsistent by
% 200.02/32.99  | | | | | | | | |            sub-proof #1308.
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | End of split
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | Case 2:
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | |   (256)   ~ (all_56_8 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | REDUCE: (52), (256) imply:
% 200.02/32.99  | | | | | | |   (257)   ~ (all_52_5 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | BETA: splitting (65) gives:
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | |   (258)  all_58_0 = e3
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | REF_CLOSE: (200), (206), (258) are inconsistent by sub-proof
% 200.02/32.99  | | | | | | | |            #1015.
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | |   (259)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | BETA: splitting (259) gives:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | |   (260)  all_58_2 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | COMBINE_EQS: (62), (260) imply:
% 200.02/32.99  | | | | | | | | |   (261)  all_52_3 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REF_CLOSE: (6), (27), (43), (121), (125), (137), (198), (199),
% 200.02/32.99  | | | | | | | | |            (203), (207), (216), (261) are inconsistent by
% 200.02/32.99  | | | | | | | | |            sub-proof #561.
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | |   (262)  all_58_6 = e3 | all_58_12 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REF_CLOSE: (58), (113), (191), (257), (262) are inconsistent
% 200.02/32.99  | | | | | | | | |            by sub-proof #1243.
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | End of split
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | End of split
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | End of split
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | Case 2:
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | |   (263)   ~ (all_56_15 = e3)
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | REDUCE: (41), (263) imply:
% 200.02/32.99  | | | | |   (264)   ~ (all_14_2 = e3)
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (16),
% 200.02/32.99  | | | | |            (18), (20), (22), (23), (26), (27), (29), (32), (33), (35),
% 200.02/32.99  | | | | |            (36), (37), (39), (42), (43), (44), (45), (47), (48), (49),
% 200.02/32.99  | | | | |            (51), (53), (54), (55), (56), (57), (58), (60), (61), (62),
% 200.02/32.99  | | | | |            (63), (65), (66), (68), (69), (71), (72), (73), (74), (76),
% 200.02/32.99  | | | | |            (78), (79), (80), (81), (84), (87), (90), (92), (93), (94),
% 200.02/32.99  | | | | |            (96), (97), (99), (100), (101), (102), (103), (104), (105),
% 200.02/32.99  | | | | |            (108), (109), (110), (112), (113), (116), (117), (118),
% 200.02/32.99  | | | | |            (121), (122), (123), (124), (125), (126), (127), (128),
% 200.02/32.99  | | | | |            (134), (135), (136), (137), (142), (184), (185), (186),
% 200.02/32.99  | | | | |            (264) are inconsistent by sub-proof #112.
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | End of split
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | End of split
% 200.02/32.99  | | | 
% 200.02/32.99  | | End of split
% 200.02/32.99  | | 
% 200.02/32.99  | Case 2:
% 200.02/32.99  | | 
% 200.02/32.99  | |   (265)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.02/32.99  | | 
% 200.02/32.99  | | REF_CLOSE: (4), (6), (18), (26), (28), (37), (40), (49), (50), (70), (74),
% 200.02/32.99  | |            (94), (98), (99), (106), (119), (265) are inconsistent by
% 200.02/32.99  | |            sub-proof #569.
% 200.02/32.99  | | 
% 200.02/32.99  | End of split
% 200.02/32.99  | 
% 200.02/32.99  End of proof
% 200.02/32.99  
% 200.02/32.99  Sub-proof #112 shows that the following formulas are inconsistent:
% 200.02/32.99  ----------------------------------------------------------------
% 200.02/32.99    (1)   ~ (all_52_25 = all_52_27)
% 200.02/32.99    (2)  all_58_14 = all_52_23
% 200.02/32.99    (3)   ~ (e3 = e1)
% 200.02/32.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/32.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/32.99    (5)  all_58_1 = all_52_9
% 200.02/32.99    (6)   ~ (all_52_7 = all_52_15)
% 200.02/32.99    (7)  op(all_52_7, all_52_7) = all_52_6
% 200.02/32.99    (8)   ~ (all_52_17 = all_52_25)
% 200.02/32.99    (9)   ~ (all_52_3 = all_6_2)
% 200.02/32.99    (10)  all_58_0 = all_6_2
% 200.02/32.99    (11)   ~ (all_52_17 = all_10_2)
% 200.02/32.99    (12)  op(all_6_2, e3) = e1
% 200.02/32.99    (13)  op(all_52_5, all_52_5) = all_52_4
% 200.02/32.99    (14)  all_58_13 = all_52_15
% 200.02/32.99    (15)  all_58_9 = all_52_25
% 200.02/32.99    (16)  op(e1, e3) = all_52_5
% 200.02/32.99    (17)  op(e2, e2) = all_4_2
% 200.02/32.99    (18)   ~ (all_52_3 = all_52_5)
% 200.02/32.99    (19)  all_58_11 = all_52_29
% 200.02/32.99    (20)  all_56_5 = all_4_2
% 200.02/32.99    (21)   ~ (all_52_9 = all_52_15)
% 200.02/32.99    (22)   ~ (all_52_3 = all_52_27)
% 200.02/32.99    (23)  op(all_6_2, all_6_2) = all_52_0
% 200.02/32.99    (24)  op(e0, e0) = all_14_2
% 200.02/32.99    (25)  op(all_52_29, all_52_29) = e1
% 200.02/32.99    (26)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/32.99    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.02/32.99    (28)  all_56_11 = all_52_29
% 200.02/32.99    (29)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.02/32.99    (30)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.02/32.99    (31)   ~ (all_52_13 = all_10_2)
% 200.02/32.99    (32)   ~ (all_6_0 = e1)
% 200.02/32.99    (33)  all_58_10 = all_52_27
% 200.02/32.99    (34)  op(all_52_9, all_52_9) = all_52_8
% 200.02/32.99    (35)  op(all_52_15, all_52_15) = all_52_14
% 200.02/32.99    (36)   ~ (all_52_25 = all_52_29)
% 200.02/32.99    (37)  all_58_7 = all_52_13
% 200.02/32.99    (38)   ~ (all_52_5 = all_52_7)
% 200.02/32.99    (39)  all_58_12 = all_52_7
% 200.02/32.99    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/32.99    (41)   ~ (all_52_7 = all_14_2)
% 200.02/32.99    (42)  all_58_2 = all_52_3
% 200.02/32.99    (43)  all_56_2 = all_52_17
% 200.02/32.99    (44)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/32.99    (45)  op(e3, all_6_1) = all_6_0
% 200.02/32.99    (46)   ~ (all_52_25 = e3)
% 200.02/32.99    (47)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.02/32.99    (48)   ~ (all_52_23 = e3)
% 200.02/32.99    (49)  op(all_52_25, all_52_25) = e3
% 200.02/32.99    (50)   ~ (all_52_5 = all_52_29)
% 200.02/32.99    (51)   ~ (all_10_2 = e3)
% 200.02/32.99    (52)   ~ (all_52_15 = all_14_2)
% 200.02/32.99    (53)   ~ (all_52_19 = all_52_27)
% 200.02/32.99    (54)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.02/32.99    (55)   ~ (all_6_0 = e2)
% 200.02/32.99    (56)   ~ (all_52_9 = e3)
% 200.02/32.99    (57)   ~ (all_52_13 = all_4_2)
% 200.02/32.99    (58)  op(all_52_27, all_52_27) = e2
% 200.02/32.99    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/32.99    (60)   ~ (all_52_9 = all_52_25)
% 200.02/32.99    (61)  all_58_15 = all_14_2
% 200.02/32.99    (62)   ~ (all_52_19 = all_10_2)
% 200.02/32.99    (63)  all_58_8 = all_10_2
% 200.02/32.99    (64)   ~ (all_52_5 = all_10_2)
% 200.02/32.99    (65)  op(all_52_17, all_52_17) = all_52_16
% 200.02/32.99    (66)   ~ (all_52_25 = all_6_2)
% 200.02/32.99    (67)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.02/32.99    (68)   ~ (all_52_5 = all_6_2)
% 200.02/32.99    (69)   ~ (all_52_9 = all_6_2)
% 200.02/32.99    (70)   ~ (all_52_13 = all_52_15)
% 200.02/32.99    (71)  op(e3, e3) = all_6_2
% 200.02/32.99    (72)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.02/32.99    (73)   ~ (all_52_27 = all_14_2)
% 200.02/32.99    (74)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.02/32.99    (75)  op(all_4_2, all_4_2) = all_52_10
% 200.02/32.99    (76)  all_56_3 = all_52_25
% 200.02/32.99    (77)   ~ (all_52_3 = all_52_7)
% 200.02/32.99    (78)  all_58_5 = all_52_19
% 200.02/32.99    (79)  all_56_1 = all_52_9
% 200.02/32.99    (80)   ~ (all_52_15 = all_4_2)
% 200.02/32.99    (81)   ~ (all_52_27 = all_4_2)
% 200.02/32.99    (82)  all_58_6 = all_52_5
% 200.02/32.99    (83)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/32.99    (84)   ~ (all_52_17 = all_6_2)
% 200.02/32.99    (85)   ~ (e3 = e2)
% 200.02/32.99    (86)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.02/32.99    (87)  op(e1, e1) = all_10_2
% 200.02/32.99    (88)   ~ (all_52_17 = all_52_19)
% 200.02/32.99    (89)  all_58_3 = all_4_2
% 200.02/32.99    (90)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.02/32.99    (91)   ~ (all_52_3 = all_4_2)
% 200.02/32.99    (92)  op(all_6_2, e3) = all_6_1
% 200.02/32.99    (93)   ~ (all_52_13 = all_52_29)
% 200.02/32.99    (94)  all_58_4 = all_52_17
% 200.02/32.99    (95)   ~ (all_14_2 = e3)
% 200.02/32.99  
% 200.02/32.99  Begin of proof
% 200.02/32.99  | 
% 200.02/32.99  | BETA: splitting (83) gives:
% 200.02/32.99  | 
% 200.02/32.99  | Case 1:
% 200.02/32.99  | | 
% 200.02/32.99  | |   (96)  all_58_12 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | COMBINE_EQS: (39), (96) imply:
% 200.02/32.99  | |   (97)  all_52_7 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | SIMP: (97) implies:
% 200.02/32.99  | |   (98)  all_52_7 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (77), (98) imply:
% 200.02/32.99  | |   (99)   ~ (all_52_3 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (38), (98) imply:
% 200.02/32.99  | |   (100)   ~ (all_52_5 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (6), (98) imply:
% 200.02/32.99  | |   (101)   ~ (all_52_15 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | SIMP: (101) implies:
% 200.02/32.99  | |   (102)   ~ (all_52_15 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (41), (98) imply:
% 200.02/32.99  | |   (103)   ~ (all_14_2 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (7), (98) imply:
% 200.02/32.99  | |   (104)  op(e3, e3) = all_52_6
% 200.02/32.99  | | 
% 200.02/32.99  | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 200.02/32.99  | |              with (71), (104) gives:
% 200.02/32.99  | |   (105)  all_52_6 = all_6_2
% 200.02/32.99  | | 
% 200.02/32.99  | | BETA: splitting (72) gives:
% 200.02/32.99  | | 
% 200.02/32.99  | | Case 1:
% 200.02/32.99  | | | 
% 200.02/32.99  | | |   (106)  all_58_9 = e3
% 200.02/32.99  | | | 
% 200.02/32.99  | | | COMBINE_EQS: (15), (106) imply:
% 200.02/32.99  | | |   (107)  all_52_25 = e3
% 200.02/32.99  | | | 
% 200.02/32.99  | | | REDUCE: (46), (107) imply:
% 200.02/32.99  | | |   (108)  $false
% 200.02/32.99  | | | 
% 200.02/32.99  | | | CLOSE: (108) is inconsistent.
% 200.02/32.99  | | | 
% 200.02/32.99  | | Case 2:
% 200.02/32.99  | | | 
% 200.02/32.99  | | |   (109)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.02/32.99  | | | 
% 200.02/32.99  | | | BETA: splitting (26) gives:
% 200.02/32.99  | | | 
% 200.02/32.99  | | | Case 1:
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | |   (110)  all_58_2 = e3
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | | COMBINE_EQS: (42), (110) imply:
% 200.02/32.99  | | | |   (111)  all_52_3 = e3
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | | REDUCE: (99), (111) imply:
% 200.02/32.99  | | | |   (112)  $false
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | | CLOSE: (112) is inconsistent.
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | Case 2:
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | |   (113)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | | BETA: splitting (40) gives:
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | | Case 1:
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | |   (114)  all_58_6 = e3
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | COMBINE_EQS: (82), (114) imply:
% 200.02/32.99  | | | | |   (115)  all_52_5 = e3
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | REDUCE: (100), (115) imply:
% 200.02/32.99  | | | | |   (116)  $false
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | CLOSE: (116) is inconsistent.
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | Case 2:
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | |   (117)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | BETA: splitting (59) gives:
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | | Case 1:
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | |   (118)  all_58_1 = e3
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | | COMBINE_EQS: (5), (118) imply:
% 200.02/32.99  | | | | | |   (119)  all_52_9 = e3
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | | REDUCE: (56), (119) imply:
% 200.02/32.99  | | | | | |   (120)  $false
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | | CLOSE: (120) is inconsistent.
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | Case 2:
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | |   (121)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | | BETA: splitting (47) gives:
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | | Case 1:
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | |   (122)  all_56_5 = e3
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | COMBINE_EQS: (20), (122) imply:
% 200.02/32.99  | | | | | | |   (123)  all_4_2 = e3
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | SIMP: (123) implies:
% 200.02/32.99  | | | | | | |   (124)  all_4_2 = e3
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | REDUCE: (57), (124) imply:
% 200.02/32.99  | | | | | | |   (125)   ~ (all_52_13 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | REF_CLOSE: (4), (12), (14), (16), (19), (25), (37), (51), (63),
% 200.02/32.99  | | | | | | |            (68), (71), (75), (89), (102), (117), (121), (125) are
% 200.02/32.99  | | | | | | |            inconsistent by sub-proof #572.
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | Case 2:
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | |   (126)   ~ (all_56_5 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | REDUCE: (20), (126) imply:
% 200.02/32.99  | | | | | | |   (127)   ~ (all_4_2 = e3)
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | BETA: splitting (121) gives:
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | |   (128)  all_58_3 = e3
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | COMBINE_EQS: (89), (128) imply:
% 200.02/32.99  | | | | | | | |   (129)  all_4_2 = e3
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | REDUCE: (127), (129) imply:
% 200.02/32.99  | | | | | | | |   (130)  $false
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | CLOSE: (130) is inconsistent.
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | |   (131)  all_58_7 = e3 | all_58_13 = e3
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | BETA: splitting (131) gives:
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | | Case 1:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | |   (132)  all_58_7 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | COMBINE_EQS: (37), (132) imply:
% 200.02/32.99  | | | | | | | | |   (133)  all_52_13 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REDUCE: (93), (133) imply:
% 200.02/32.99  | | | | | | | | |   (134)   ~ (all_52_29 = e3)
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | SIMP: (134) implies:
% 200.02/32.99  | | | | | | | | |   (135)   ~ (all_52_29 = e3)
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REDUCE: (31), (133) imply:
% 200.02/32.99  | | | | | | | | |   (136)   ~ (all_10_2 = e3)
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REF_CLOSE: (1), (4), (5), (8), (10), (11), (15), (19), (24),
% 200.02/32.99  | | | | | | | | |            (27), (33), (34), (49), (51), (53), (58), (59),
% 200.02/32.99  | | | | | | | | |            (60), (61), (66), (67), (71), (73), (74), (76),
% 200.02/32.99  | | | | | | | | |            (78), (81), (85), (87), (89), (94), (95), (109),
% 200.02/32.99  | | | | | | | | |            (113), (135) are inconsistent by sub-proof #1041.
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | Case 2:
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | |   (137)  all_58_13 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | COMBINE_EQS: (14), (137) imply:
% 200.02/32.99  | | | | | | | | |   (138)  all_52_15 = e3
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | REDUCE: (102), (138) imply:
% 200.02/32.99  | | | | | | | | |   (139)  $false
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | | CLOSE: (139) is inconsistent.
% 200.02/32.99  | | | | | | | | | 
% 200.02/32.99  | | | | | | | | End of split
% 200.02/32.99  | | | | | | | | 
% 200.02/32.99  | | | | | | | End of split
% 200.02/32.99  | | | | | | | 
% 200.02/32.99  | | | | | | End of split
% 200.02/32.99  | | | | | | 
% 200.02/32.99  | | | | | End of split
% 200.02/32.99  | | | | | 
% 200.02/32.99  | | | | End of split
% 200.02/32.99  | | | | 
% 200.02/32.99  | | | End of split
% 200.02/32.99  | | | 
% 200.02/32.99  | | End of split
% 200.02/32.99  | | 
% 200.02/32.99  | Case 2:
% 200.02/32.99  | | 
% 200.02/32.99  | |   (140)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | BETA: splitting (140) gives:
% 200.02/32.99  | | 
% 200.02/32.99  | | Case 1:
% 200.02/32.99  | | | 
% 200.02/32.99  | | |   (141)  all_58_13 = e3
% 200.02/32.99  | | | 
% 200.02/32.99  | | | COMBINE_EQS: (14), (141) imply:
% 200.02/32.99  | | |   (142)  all_52_15 = e3
% 200.02/32.99  | | | 
% 200.02/32.99  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (13), (15),
% 200.02/32.99  | | |            (17), (18), (19), (21), (22), (23), (24), (25), (26), (27),
% 200.02/32.99  | | |            (28), (29), (30), (32), (33), (34), (35), (36), (37), (39),
% 200.02/32.99  | | |            (40), (42), (43), (44), (45), (49), (50), (52), (53), (54),
% 200.02/32.99  | | |            (55), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 200.02/32.99  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (76), (77),
% 200.02/32.99  | | |            (78), (79), (80), (81), (82), (84), (85), (86), (87), (88),
% 200.02/32.99  | | |            (89), (90), (91), (92), (94), (142) are inconsistent by
% 200.02/32.99  | | |            sub-proof #1033.
% 200.02/32.99  | | | 
% 200.02/32.99  | | Case 2:
% 200.02/32.99  | | | 
% 200.02/32.99  | | |   (143)  all_58_14 = e3 | all_58_15 = e3
% 200.02/32.99  | | | 
% 200.02/32.99  | | | REF_CLOSE: (2), (48), (61), (95), (143) are inconsistent by sub-proof
% 200.02/32.99  | | |            #715.
% 200.02/32.99  | | | 
% 200.02/32.99  | | End of split
% 200.02/32.99  | | 
% 200.02/32.99  | End of split
% 200.02/32.99  | 
% 200.02/32.99  End of proof
% 200.02/32.99  
% 200.02/32.99  Sub-proof #113 shows that the following formulas are inconsistent:
% 200.02/32.99  ----------------------------------------------------------------
% 200.02/32.99    (1)  all_58_14 = all_52_23
% 200.02/32.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/32.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/32.99    (3)  all_58_1 = all_52_9
% 200.02/32.99    (4)   ~ (all_52_7 = all_52_15)
% 200.02/32.99    (5)  op(all_52_15, all_52_15) = e0
% 200.02/32.99    (6)  op(all_52_7, all_52_7) = all_52_6
% 200.02/32.99    (7)  all_58_0 = all_6_2
% 200.02/32.99    (8)  op(all_6_2, e3) = e1
% 200.02/32.99    (9)  all_58_13 = all_52_15
% 200.02/32.99    (10)  op(all_52_13, all_52_13) = e1
% 200.02/32.99    (11)  all_58_9 = all_52_25
% 200.02/32.99    (12)  op(all_52_27, all_52_27) = all_52_26
% 200.02/32.99    (13)  op(e1, e3) = all_52_5
% 200.02/32.99    (14)  op(e2, e2) = all_4_2
% 200.02/32.99    (15)  op(all_4_2, e2) = e1
% 200.02/32.99    (16)  all_56_5 = all_4_2
% 200.02/32.99    (17)   ~ (all_52_25 = all_14_2)
% 200.02/32.99    (18)   ~ (all_52_7 = all_6_2)
% 200.02/32.99    (19)  all_56_15 = all_14_2
% 200.02/32.99    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/32.99    (21)   ~ (all_4_0 = e3)
% 200.02/32.99    (22)   ~ (all_6_2 = e3)
% 200.02/32.99    (23)  all_58_10 = all_52_27
% 200.02/32.99    (24)  all_58_7 = all_52_13
% 200.02/32.99    (25)  all_58_12 = all_52_7
% 200.02/32.99    (26)   ~ (all_52_7 = all_14_2)
% 200.02/32.99    (27)  all_58_2 = all_52_3
% 200.02/32.99    (28)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.02/32.99    (29)  all_58_4 = e3
% 200.02/32.99    (30)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.02/32.99    (31)   ~ (all_52_23 = e3)
% 200.02/32.99    (32)   ~ (all_10_2 = e3)
% 200.02/32.99    (33)   ~ (all_52_15 = all_14_2)
% 200.02/32.99    (34)   ~ (all_52_9 = e3)
% 200.02/32.99    (35)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.02/32.99    (36)   ~ (all_52_13 = all_4_2)
% 200.02/32.99    (37)  op(e0, e3) = all_52_7
% 200.02/32.99    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/32.99    (39)  all_58_15 = all_14_2
% 200.02/32.99    (40)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.02/32.99    (41)   ~ (all_52_23 = all_14_2)
% 200.02/32.99    (42)  all_58_5 = all_4_0
% 200.02/32.99    (43)   ~ (all_52_5 = all_6_2)
% 200.02/32.99    (44)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.02/32.99    (45)  op(e3, e3) = all_6_2
% 200.02/32.99    (46)   ~ (all_52_3 = all_52_7)
% 200.02/32.99    (47)   ~ (all_52_15 = all_4_2)
% 200.02/32.99    (48)   ~ (all_52_27 = all_4_2)
% 200.02/32.99    (49)   ~ (all_4_0 = all_4_2)
% 200.02/32.99    (50)  op(e3, e2) = all_52_9
% 200.02/32.99    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/32.99    (52)  op(e1, e1) = all_10_2
% 200.02/32.99    (53)  op(all_52_9, all_52_9) = e3
% 200.02/32.99    (54)  all_58_3 = all_4_2
% 200.02/32.99    (55)   ~ (all_14_2 = e3)
% 200.02/32.99  
% 200.02/32.99  Begin of proof
% 200.02/32.99  | 
% 200.02/32.99  | BETA: splitting (51) gives:
% 200.02/32.99  | 
% 200.02/32.99  | Case 1:
% 200.02/32.99  | | 
% 200.02/32.99  | |   (56)  all_58_12 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | COMBINE_EQS: (25), (56) imply:
% 200.02/32.99  | |   (57)  all_52_7 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | SIMP: (57) implies:
% 200.02/32.99  | |   (58)  all_52_7 = e3
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (46), (58) imply:
% 200.02/32.99  | |   (59)   ~ (all_52_3 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (4), (58) imply:
% 200.02/32.99  | |   (60)   ~ (all_52_15 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | SIMP: (60) implies:
% 200.02/32.99  | |   (61)   ~ (all_52_15 = e3)
% 200.02/32.99  | | 
% 200.02/32.99  | | REDUCE: (6), (58) imply:
% 200.02/32.99  | |   (62)  op(e3, e3) = all_52_6
% 200.02/32.99  | | 
% 200.02/32.99  | | GROUND_INST: instantiating (2) with all_6_2, all_52_6, e3, e3, simplifying
% 200.02/32.99  | |              with (45), (62) gives:
% 200.02/32.99  | |   (63)  all_52_6 = all_6_2
% 200.02/32.99  | | 
% 200.02/33.00  | | REF_CLOSE: (2), (3), (8), (9), (10), (12), (13), (15), (16), (20), (21),
% 200.02/33.00  | |            (23), (24), (27), (30), (32), (34), (36), (38), (42), (43), (44),
% 200.02/33.00  | |            (45), (47), (48), (49), (50), (52), (53), (54), (59), (61) are
% 200.02/33.00  | |            inconsistent by sub-proof #114.
% 200.02/33.00  | | 
% 200.02/33.00  | Case 2:
% 200.02/33.00  | | 
% 200.02/33.00  | |   (64)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/33.00  | | 
% 200.02/33.00  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (14), (17), (18), (19),
% 200.02/33.00  | |            (22), (25), (26), (28), (29), (31), (33), (35), (37), (39), (40),
% 200.02/33.00  | |            (41), (45), (47), (53), (55), (64) are inconsistent by sub-proof
% 200.02/33.00  | |            #563.
% 200.02/33.00  | | 
% 200.02/33.00  | End of split
% 200.02/33.00  | 
% 200.02/33.00  End of proof
% 200.02/33.00  
% 200.02/33.00  Sub-proof #114 shows that the following formulas are inconsistent:
% 200.02/33.00  ----------------------------------------------------------------
% 200.02/33.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/33.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/33.00    (2)  all_58_1 = all_52_9
% 200.02/33.00    (3)  op(all_6_2, e3) = e1
% 200.02/33.00    (4)  all_58_13 = all_52_15
% 200.02/33.00    (5)  op(all_52_13, all_52_13) = e1
% 200.02/33.00    (6)   ~ (all_52_15 = e3)
% 200.02/33.00    (7)  op(all_52_27, all_52_27) = all_52_26
% 200.02/33.00    (8)  op(e1, e3) = all_52_5
% 200.02/33.00    (9)  op(all_4_2, e2) = e1
% 200.02/33.00    (10)   ~ (all_52_3 = e3)
% 200.02/33.00    (11)  all_56_5 = all_4_2
% 200.02/33.00    (12)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/33.00    (13)   ~ (all_4_0 = e3)
% 200.02/33.00    (14)  all_58_10 = all_52_27
% 200.02/33.00    (15)  all_58_7 = all_52_13
% 200.02/33.00    (16)  all_58_2 = all_52_3
% 200.02/33.00    (17)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.02/33.00    (18)   ~ (all_10_2 = e3)
% 200.02/33.00    (19)   ~ (all_52_9 = e3)
% 200.02/33.00    (20)   ~ (all_52_13 = all_4_2)
% 200.02/33.00    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.00    (22)  all_58_5 = all_4_0
% 200.02/33.00    (23)   ~ (all_52_5 = all_6_2)
% 200.02/33.00    (24)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.02/33.00    (25)  op(e3, e3) = all_6_2
% 200.02/33.00    (26)   ~ (all_52_15 = all_4_2)
% 200.02/33.00    (27)   ~ (all_52_27 = all_4_2)
% 200.02/33.00    (28)   ~ (all_4_0 = all_4_2)
% 200.02/33.00    (29)  op(e3, e2) = all_52_9
% 200.02/33.00    (30)  op(e1, e1) = all_10_2
% 200.02/33.00    (31)  op(all_52_9, all_52_9) = e3
% 200.02/33.00    (32)  all_58_3 = all_4_2
% 200.02/33.00  
% 200.02/33.00  Begin of proof
% 200.02/33.00  | 
% 200.02/33.00  | BETA: splitting (12) gives:
% 200.02/33.00  | 
% 200.02/33.00  | Case 1:
% 200.02/33.00  | | 
% 200.02/33.00  | |   (33)  all_58_2 = e3
% 200.02/33.00  | | 
% 200.02/33.00  | | COMBINE_EQS: (16), (33) imply:
% 200.02/33.00  | |   (34)  all_52_3 = e3
% 200.02/33.00  | | 
% 200.02/33.00  | | REDUCE: (10), (34) imply:
% 200.02/33.00  | |   (35)  $false
% 200.02/33.00  | | 
% 200.02/33.00  | | CLOSE: (35) is inconsistent.
% 200.02/33.00  | | 
% 200.02/33.00  | Case 2:
% 200.02/33.00  | | 
% 200.02/33.00  | |   (36)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/33.00  | | 
% 200.02/33.00  | | BETA: splitting (21) gives:
% 200.02/33.00  | | 
% 200.02/33.00  | | Case 1:
% 200.02/33.00  | | | 
% 200.02/33.00  | | |   (37)  all_58_1 = e3
% 200.02/33.00  | | | 
% 200.02/33.00  | | | COMBINE_EQS: (2), (37) imply:
% 200.02/33.00  | | |   (38)  all_52_9 = e3
% 200.02/33.00  | | | 
% 200.02/33.00  | | | REDUCE: (19), (38) imply:
% 200.02/33.00  | | |   (39)  $false
% 200.02/33.00  | | | 
% 200.02/33.00  | | | CLOSE: (39) is inconsistent.
% 200.02/33.00  | | | 
% 200.02/33.00  | | Case 2:
% 200.02/33.00  | | | 
% 200.02/33.00  | | |   (40)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.00  | | | 
% 200.02/33.00  | | | BETA: splitting (17) gives:
% 200.02/33.00  | | | 
% 200.02/33.00  | | | Case 1:
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | |   (41)  all_56_5 = e3
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | | REF_CLOSE: (1), (4), (9), (11), (14), (15), (18), (20), (22), (24),
% 200.02/33.00  | | | |            (26), (27), (28), (29), (30), (31), (32), (36), (40), (41)
% 200.02/33.00  | | | |            are inconsistent by sub-proof #193.
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | Case 2:
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | |   (42)   ~ (all_56_5 = e3)
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | | REDUCE: (11), (42) imply:
% 200.02/33.00  | | | |   (43)   ~ (all_4_2 = e3)
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | | BETA: splitting (36) gives:
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | | Case 1:
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | |   (44)  all_58_3 = e3
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | | COMBINE_EQS: (32), (44) imply:
% 200.02/33.00  | | | | |   (45)  all_4_2 = e3
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | | REDUCE: (43), (45) imply:
% 200.02/33.00  | | | | |   (46)  $false
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | | CLOSE: (46) is inconsistent.
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | Case 2:
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | |   (47)   ~ (all_58_3 = e3)
% 200.02/33.00  | | | | |   (48)  all_58_5 = e3 | all_58_10 = e3
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | | BETA: splitting (40) gives:
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | | Case 1:
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | |   (49)  all_58_3 = e3
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | | COMBINE_EQS: (32), (49) imply:
% 200.02/33.00  | | | | | |   (50)  all_4_2 = e3
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | | REDUCE: (43), (50) imply:
% 200.02/33.00  | | | | | |   (51)  $false
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | | CLOSE: (51) is inconsistent.
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | Case 2:
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | |   (52)  all_58_7 = e3 | all_58_13 = e3
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | | BETA: splitting (52) gives:
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | | Case 1:
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | |   (53)  all_58_7 = e3
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | COMBINE_EQS: (15), (53) imply:
% 200.02/33.00  | | | | | | |   (54)  all_52_13 = e3
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | REDUCE: (5), (54) imply:
% 200.02/33.00  | | | | | | |   (55)  op(e3, e3) = e1
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | BETA: splitting (48) gives:
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | Case 1:
% 200.02/33.00  | | | | | | | | 
% 200.02/33.00  | | | | | | | |   (56)  all_58_5 = e3
% 200.02/33.00  | | | | | | | | 
% 200.02/33.00  | | | | | | | | REF_CLOSE: (13), (22), (56) are inconsistent by sub-proof #215.
% 200.02/33.00  | | | | | | | | 
% 200.02/33.00  | | | | | | | Case 2:
% 200.02/33.00  | | | | | | | | 
% 200.02/33.00  | | | | | | | |   (57)  all_58_10 = e3
% 200.02/33.00  | | | | | | | | 
% 200.02/33.00  | | | | | | | | REF_CLOSE: (1), (3), (7), (8), (14), (23), (25), (55), (57) are
% 200.02/33.00  | | | | | | | |            inconsistent by sub-proof #577.
% 200.02/33.00  | | | | | | | | 
% 200.02/33.00  | | | | | | | End of split
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | Case 2:
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | |   (58)  all_58_13 = e3
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | COMBINE_EQS: (4), (58) imply:
% 200.02/33.00  | | | | | | |   (59)  all_52_15 = e3
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | REDUCE: (6), (59) imply:
% 200.02/33.00  | | | | | | |   (60)  $false
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | | CLOSE: (60) is inconsistent.
% 200.02/33.00  | | | | | | | 
% 200.02/33.00  | | | | | | End of split
% 200.02/33.00  | | | | | | 
% 200.02/33.00  | | | | | End of split
% 200.02/33.00  | | | | | 
% 200.02/33.00  | | | | End of split
% 200.02/33.00  | | | | 
% 200.02/33.00  | | | End of split
% 200.02/33.00  | | | 
% 200.02/33.00  | | End of split
% 200.02/33.00  | | 
% 200.02/33.00  | End of split
% 200.02/33.00  | 
% 200.02/33.00  End of proof
% 200.02/33.00  
% 200.02/33.00  Sub-proof #115 shows that the following formulas are inconsistent:
% 200.02/33.00  ----------------------------------------------------------------
% 200.02/33.00    (1)   ~ (all_52_15 = all_52_23)
% 200.02/33.00    (2)   ~ (all_52_25 = all_52_27)
% 200.02/33.00    (3)  all_58_14 = all_52_23
% 200.02/33.00    (4)   ~ (e3 = e1)
% 200.02/33.00    (5)   ~ (all_52_17 = all_4_0)
% 200.02/33.00    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.02/33.00    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/33.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/33.00    (8)   ~ (all_52_5 = all_52_13)
% 200.02/33.00    (9)  all_58_1 = all_52_9
% 200.02/33.00    (10)   ~ (all_52_9 = all_52_13)
% 200.02/33.00    (11)   ~ (e3 = e0)
% 200.02/33.00    (12)  op(e2, e3) = all_52_3
% 200.02/33.00    (13)   ~ (all_52_23 = all_4_0)
% 200.02/33.00    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.02/33.00    (15)   ~ (all_52_7 = all_52_15)
% 200.02/33.00    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.02/33.00    (17)   ~ (all_52_17 = all_52_25)
% 200.02/33.00    (18)   ~ (all_52_3 = all_6_2)
% 200.02/33.00    (19)  all_58_0 = all_6_2
% 200.02/33.00    (20)  op(all_14_2, e0) = all_14_1
% 200.02/33.00    (21)  all_56_4 = all_52_3
% 200.02/33.00    (22)   ~ (all_52_17 = all_10_2)
% 200.02/33.00    (23)  op(e3, e0) = all_52_25
% 200.02/33.00    (24)  op(all_52_5, all_52_5) = all_52_4
% 200.02/33.00    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.02/33.00    (26)  op(all_52_19, all_52_19) = all_52_18
% 200.02/33.00    (27)   ~ (all_52_27 = all_52_29)
% 200.02/33.00    (28)  all_58_13 = all_52_15
% 200.02/33.00    (29)  all_58_9 = all_52_25
% 200.02/33.00    (30)   ~ (all_6_1 = e1)
% 200.02/33.00    (31)   ~ (all_52_29 = all_14_2)
% 200.02/33.00    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.02/33.00    (33)  op(all_52_27, all_52_27) = all_52_26
% 200.02/33.00    (34)  op(e1, e3) = all_52_5
% 200.02/33.00    (35)  op(e2, e2) = all_4_2
% 200.02/33.00    (36)   ~ (all_52_3 = all_52_5)
% 200.02/33.00    (37)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.02/33.00    (38)  op(all_4_2, e2) = e1
% 200.02/33.00    (39)  all_58_11 = all_52_29
% 200.02/33.00    (40)  all_56_5 = all_4_2
% 200.02/33.00    (41)   ~ (all_52_25 = all_14_2)
% 200.02/33.00    (42)   ~ (all_52_9 = all_52_15)
% 200.02/33.00    (43)   ~ (all_52_3 = all_52_27)
% 200.02/33.00    (44)  op(all_10_2, e1) = all_10_1
% 200.02/33.00    (45)   ~ (all_10_2 = all_4_0)
% 200.02/33.00    (46)  op(all_6_2, all_6_2) = all_52_0
% 200.02/33.00    (47)   ~ (all_52_7 = all_6_2)
% 200.02/33.00    (48)  op(e0, e0) = all_14_2
% 200.02/33.00    (49)  all_56_15 = all_14_2
% 200.02/33.00    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/33.00    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.02/33.00    (52)  all_56_11 = all_52_29
% 200.02/33.00    (53)  all_4_0 = e3
% 200.02/33.00    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.02/33.00    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.02/33.00    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.02/33.00    (57)   ~ (e2 = e1)
% 200.02/33.00    (58)   ~ (all_52_13 = all_10_2)
% 200.02/33.00    (59)   ~ (all_6_0 = e1)
% 200.02/33.00    (60)  all_58_10 = all_52_27
% 200.02/33.00    (61)  all_56_8 = all_52_5
% 200.02/33.00    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.02/33.00    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.02/33.00    (64)   ~ (all_52_19 = all_52_23)
% 200.02/33.00    (65)   ~ (all_52_25 = all_52_29)
% 200.02/33.00    (66)   ~ (all_52_29 = all_10_2)
% 200.02/33.00    (67)  all_58_7 = all_52_13
% 200.02/33.00    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.02/33.00    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.02/33.00    (70)   ~ (all_52_5 = all_52_7)
% 200.02/33.00    (71)  all_58_12 = all_52_7
% 200.02/33.00    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/33.00    (73)   ~ (all_52_7 = all_14_2)
% 200.02/33.00    (74)  all_58_2 = all_52_3
% 200.02/33.00    (75)  all_56_2 = all_52_17
% 200.02/33.00    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/33.00    (77)  op(e3, all_6_1) = all_6_0
% 200.02/33.00    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.02/33.00    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.02/33.00    (80)  all_56_7 = all_52_27
% 200.02/33.00    (81)  all_28_2 = all_4_2
% 200.02/33.00    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/33.00    (83)   ~ (e2 = e0)
% 200.02/33.00    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.02/33.00    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.02/33.00    (86)   ~ (all_52_5 = all_52_29)
% 200.02/33.00    (87)   ~ (all_52_15 = all_14_2)
% 200.02/33.00    (88)   ~ (all_52_19 = all_52_27)
% 200.02/33.00    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.02/33.00    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.02/33.00    (91)   ~ (all_6_0 = e2)
% 200.02/33.00    (92)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.02/33.00            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.02/33.00    (93)   ~ (all_52_13 = all_4_2)
% 200.02/33.00    (94)  op(e3, e1) = all_52_17
% 200.02/33.00    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.02/33.00    (96)  op(e0, e3) = all_52_7
% 200.02/33.00    (97)  op(e1, e2) = all_52_13
% 200.02/33.00    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.00    (99)   ~ (all_52_9 = all_52_25)
% 200.02/33.00    (100)  all_58_15 = all_14_2
% 200.02/33.00    (101)   ~ (all_52_19 = all_10_2)
% 200.02/33.00    (102)  op(all_52_23, all_52_23) = all_52_22
% 200.02/33.00    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.02/33.00    (104)  all_58_8 = all_10_2
% 200.02/33.00    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.02/33.00    (106)   ~ (all_52_5 = all_10_2)
% 200.02/33.00    (107)  op(all_52_29, all_52_29) = all_52_28
% 200.02/33.00    (108)   ~ (all_52_23 = all_14_2)
% 200.02/33.00    (109)  all_56_12 = all_52_7
% 200.02/33.00    (110)  op(all_52_17, all_52_17) = all_52_16
% 200.02/33.00    (111)  all_58_5 = all_4_0
% 200.02/33.00    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.02/33.00    (113)   ~ (all_52_25 = all_6_2)
% 200.02/33.00    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.02/33.00    (115)   ~ (all_52_9 = all_4_2)
% 200.02/33.00    (116)   ~ (all_52_5 = all_6_2)
% 200.02/33.00    (117)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.02/33.00    (118)   ~ (all_52_9 = all_6_2)
% 200.02/33.00    (119)   ~ (all_52_13 = all_52_15)
% 200.02/33.00    (120)  all_56_0 = all_6_2
% 200.02/33.00    (121)  op(all_4_0, all_4_0) = all_52_18
% 200.02/33.00    (122)  op(e3, e3) = all_6_2
% 200.02/33.00    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.02/33.00    (124)   ~ (all_52_27 = all_14_2)
% 200.02/33.00    (125)   ~ (all_52_27 = all_4_0)
% 200.02/33.00    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.02/33.00    (127)  all_56_14 = all_52_23
% 200.02/33.00    (128)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.02/33.00    (129)  all_56_3 = all_52_25
% 200.02/33.00    (130)  op(e0, all_14_1) = e2
% 200.02/33.00    (131)   ~ (all_52_3 = all_52_7)
% 200.02/33.00    (132)  op(all_14_2, all_14_2) = all_52_30
% 200.02/33.00    (133)  all_58_5 = all_52_19
% 200.02/33.00    (134)  all_56_1 = all_52_9
% 200.02/33.00    (135)   ~ (all_52_15 = all_4_2)
% 200.02/33.00    (136)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.02/33.00           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.02/33.00           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.02/33.00           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.02/33.00    (137)   ~ (all_52_27 = all_4_2)
% 200.02/33.00    (138)  all_58_6 = all_52_5
% 200.02/33.00    (139)   ~ (all_4_0 = all_4_2)
% 200.02/33.00    (140)  op(e3, e2) = all_52_9
% 200.02/33.00    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/33.00    (142)   ~ (all_52_17 = all_6_2)
% 200.02/33.00    (143)   ~ (e1 = e0)
% 200.02/33.00    (144)   ~ (e3 = e2)
% 200.02/33.00    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.02/33.00    (146)   ~ (all_52_9 = all_52_17)
% 200.02/33.00    (147)   ~ (all_52_3 = all_4_0)
% 200.02/33.00    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.02/33.00    (149)  op(all_52_13, all_52_13) = all_52_12
% 200.02/33.00    (150)   ~ (all_6_1 = e2)
% 200.02/33.00    (151)  op(e1, e1) = all_10_2
% 200.02/33.00    (152)   ~ (all_52_23 = all_10_2)
% 200.02/33.00    (153)   ~ (all_52_7 = all_52_23)
% 200.02/33.00    (154)   ~ (all_52_17 = all_52_19)
% 200.02/33.00    (155)  all_58_3 = all_4_2
% 200.02/33.00    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.02/33.00    (157)  all_56_13 = all_52_15
% 200.02/33.00    (158)   ~ (all_52_3 = all_4_2)
% 200.02/33.00    (159)  all_28_1 = e1
% 200.02/33.00    (160)   ~ (all_52_19 = all_4_2)
% 200.02/33.00    (161)   ~ (all_52_17 = all_52_23)
% 200.02/33.00    (162)  op(all_6_2, e3) = all_6_1
% 200.02/33.00    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.02/33.00    (164)   ~ (all_52_13 = all_52_29)
% 200.02/33.00    (165)  all_58_4 = all_52_17
% 200.02/33.00    (166)  op(all_52_25, all_52_25) = all_52_24
% 200.02/33.00  
% 200.02/33.00  Begin of proof
% 200.02/33.00  | 
% 200.02/33.00  | COMBINE_EQS: (53), (111) imply:
% 200.02/33.00  |   (167)  all_58_5 = e3
% 200.02/33.00  | 
% 200.02/33.00  | REDUCE: (53), (147) imply:
% 200.02/33.00  |   (168)   ~ (all_52_3 = e3)
% 200.02/33.00  | 
% 200.02/33.00  | REDUCE: (5), (53) imply:
% 200.02/33.00  |   (169)   ~ (all_52_17 = e3)
% 200.02/33.00  | 
% 200.02/33.00  | REDUCE: (53), (125) imply:
% 200.02/33.00  |   (170)   ~ (all_52_27 = e3)
% 200.02/33.00  | 
% 200.02/33.00  | REDUCE: (45), (53) imply:
% 200.02/33.00  |   (171)   ~ (all_10_2 = e3)
% 200.02/33.00  | 
% 200.02/33.00  | REDUCE: (53), (139) imply:
% 200.02/33.00  |   (172)   ~ (all_4_2 = e3)
% 200.02/33.00  | 
% 200.02/33.00  | SIMP: (172) implies:
% 200.02/33.00  |   (173)   ~ (all_4_2 = e3)
% 200.02/33.00  | 
% 200.02/33.00  | REDUCE: (53), (121) imply:
% 200.02/33.00  |   (174)  op(e3, e3) = all_52_18
% 200.02/33.00  | 
% 200.02/33.00  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.02/33.00  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 200.02/33.00  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 200.02/33.00  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 200.02/33.00  |            (48), (49), (50), (51), (52), (54), (55), (56), (57), (58), (59),
% 200.02/33.00  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 200.02/33.00  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 200.02/33.00  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 200.02/33.00  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 200.02/33.00  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 200.02/33.00  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 200.02/33.00  |            (122), (123), (124), (126), (127), (128), (129), (130), (131),
% 200.02/33.00  |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 200.02/33.00  |            (141), (142), (143), (144), (145), (146), (148), (149), (150),
% 200.02/33.00  |            (151), (152), (153), (154), (155), (156), (157), (158), (159),
% 200.02/33.00  |            (160), (161), (162), (163), (164), (165), (166), (167), (168),
% 200.02/33.00  |            (169), (170), (171), (173), (174) are inconsistent by sub-proof
% 200.02/33.00  |            #117.
% 200.02/33.00  | 
% 200.02/33.00  End of proof
% 200.02/33.00  
% 200.02/33.00  Sub-proof #116 shows that the following formulas are inconsistent:
% 200.02/33.00  ----------------------------------------------------------------
% 200.02/33.00    (1)   ~ (all_52_15 = all_52_23)
% 200.02/33.00    (2)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 200.02/33.00    (3)  all_58_14 = all_52_23
% 200.02/33.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/33.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/33.00    (5)  op(all_52_7, all_52_7) = e0
% 200.02/33.00    (6)  all_58_1 = all_52_9
% 200.02/33.00    (7)   ~ (all_52_9 = all_52_13)
% 200.02/33.00    (8)  op(all_52_5, all_52_5) = e1
% 200.02/33.00    (9)   ~ (e3 = e0)
% 200.02/33.00    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.02/33.00    (11)   ~ (all_52_7 = all_52_15)
% 200.02/33.00    (12)   ~ (all_52_3 = all_52_19)
% 200.02/33.00    (13)   ~ (all_4_2 = e3)
% 200.02/33.00    (14)   ~ (all_52_3 = all_6_2)
% 200.02/33.00    (15)  all_58_0 = all_6_2
% 200.02/33.00    (16)  op(all_14_2, e0) = all_14_1
% 200.02/33.00    (17)  all_56_4 = all_52_3
% 200.02/33.00    (18)  op(all_52_19, all_52_19) = all_52_18
% 200.02/33.00    (19)   ~ (all_52_27 = all_52_29)
% 200.02/33.00    (20)  all_58_13 = all_52_15
% 200.02/33.00    (21)  op(all_10_2, all_10_2) = all_52_20
% 200.02/33.00    (22)  all_58_9 = all_52_25
% 200.02/33.00    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.02/33.00    (24)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.02/33.00    (25)  op(e2, e2) = all_4_2
% 200.02/33.00    (26)  all_58_11 = all_52_29
% 200.02/33.00    (27)   ~ (all_52_9 = all_52_15)
% 200.02/33.00    (28)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.02/33.00    (29)   ~ (all_52_3 = all_52_27)
% 200.02/33.00    (30)  op(all_10_2, e1) = all_10_1
% 200.02/33.00    (31)   ~ (all_52_7 = all_6_2)
% 200.02/33.00    (32)  op(e0, e0) = all_14_2
% 200.02/33.00    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/33.00    (34)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.02/33.00    (35)  op(e1, e0) = all_52_29
% 200.02/33.00    (36)  all_56_11 = all_52_29
% 200.02/33.00    (37)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.02/33.00    (38)  all_56_9 = all_52_13
% 200.02/33.00    (39)   ~ (e2 = e1)
% 200.02/33.00    (40)   ~ (all_52_13 = all_10_2)
% 200.02/33.00    (41)   ~ (all_6_0 = e1)
% 200.02/33.00    (42)  all_58_10 = all_52_27
% 200.02/33.00    (43)  op(all_52_9, all_52_9) = all_52_8
% 200.02/33.00    (44)   ~ (all_52_19 = all_52_23)
% 200.02/33.00    (45)   ~ (all_52_29 = all_10_2)
% 200.02/33.00    (46)  all_58_7 = all_52_13
% 200.02/33.00    (47)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.02/33.00    (48)  op(all_6_2, all_6_2) = e3
% 200.02/33.00    (49)   ~ (all_52_5 = all_52_7)
% 200.02/33.00    (50)  all_58_12 = all_52_7
% 200.02/33.00    (51)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/33.00    (52)   ~ (all_52_7 = all_14_2)
% 200.02/33.00    (53)  all_58_2 = all_52_3
% 200.02/33.00    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/33.00    (55)  op(e3, all_6_1) = all_6_0
% 200.02/33.00    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.02/33.00    (57)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/33.00    (58)   ~ (e2 = e0)
% 200.02/33.00    (59)  op(all_52_3, all_52_3) = e2
% 200.02/33.00    (60)   ~ (all_52_5 = all_52_29)
% 200.02/33.00    (61)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.02/33.00    (62)   ~ (all_52_15 = all_14_2)
% 200.02/33.00    (63)   ~ (all_52_19 = all_52_27)
% 200.02/33.00    (64)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.02/33.00    (65)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.02/33.00    (66)   ~ (all_6_0 = e2)
% 200.02/33.00    (67)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.02/33.00    (68)   ~ (all_52_13 = all_4_2)
% 200.02/33.00    (69)  op(e3, e1) = all_52_17
% 200.02/33.00    (70)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.00    (71)   ~ (all_52_9 = all_52_25)
% 200.02/33.00    (72)  all_58_15 = all_14_2
% 200.02/33.00    (73)   ~ (all_52_19 = all_10_2)
% 200.02/33.00    (74)  all_58_8 = all_10_2
% 200.02/33.00    (75)   ~ (all_52_5 = all_10_2)
% 200.02/33.00    (76)  op(all_52_29, all_52_29) = all_52_28
% 200.02/33.00    (77)  all_56_12 = all_52_7
% 200.02/33.00    (78)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.02/33.00    (79)   ~ (all_52_25 = all_6_2)
% 200.02/33.00    (80)   ~ (all_52_9 = all_4_2)
% 200.02/33.00    (81)   ~ (all_52_5 = all_6_2)
% 200.02/33.00    (82)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 200.02/33.00    (83)   ~ (all_52_9 = all_6_2)
% 200.02/33.00    (84)   ~ (all_52_13 = all_52_15)
% 200.02/33.00    (85)  op(e3, e3) = all_6_2
% 200.02/33.00    (86)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.02/33.00    (87)   ~ (all_52_13 = e3)
% 200.02/33.00    (88)   ~ (all_52_27 = all_14_2)
% 200.02/33.00    (89)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.02/33.00    (90)   ~ (all_52_3 = all_52_7)
% 200.02/33.00    (91)  op(all_14_2, all_14_2) = all_52_30
% 200.02/33.00    (92)  all_58_5 = all_52_19
% 200.02/33.00    (93)  all_56_1 = all_52_9
% 200.02/33.00    (94)   ~ (all_52_15 = all_4_2)
% 200.02/33.00    (95)  all_58_6 = all_52_5
% 200.02/33.00    (96)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/33.00    (97)   ~ (all_52_17 = all_6_2)
% 200.02/33.00    (98)   ~ (e1 = e0)
% 200.02/33.00    (99)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.02/33.00    (100)   ~ (all_52_9 = all_52_17)
% 200.02/33.00    (101)  all_56_10 = all_10_2
% 200.02/33.00    (102)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.02/33.00    (103)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.02/33.01    (104)  op(all_52_13, all_52_13) = all_52_12
% 200.02/33.01    (105)  op(e1, e1) = all_10_2
% 200.02/33.01    (106)   ~ (all_52_23 = all_10_2)
% 200.02/33.01    (107)  all_58_3 = all_4_2
% 200.02/33.01    (108)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.02/33.01    (109)   ~ (all_52_3 = all_4_2)
% 200.02/33.01    (110)  op(all_6_2, e3) = all_6_1
% 200.02/33.01    (111)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.02/33.01    (112)   ~ (all_52_13 = all_52_29)
% 200.02/33.01    (113)  all_58_4 = all_52_17
% 200.02/33.01    (114)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.02/33.01  
% 200.02/33.01  Begin of proof
% 200.02/33.01  | 
% 200.02/33.01  | BETA: splitting (70) gives:
% 200.02/33.01  | 
% 200.02/33.01  | Case 1:
% 200.02/33.01  | | 
% 200.02/33.01  | |   (115)  all_58_1 = e3
% 200.02/33.01  | | 
% 200.02/33.01  | | REF_CLOSE: (4), (5), (6), (8), (15), (25), (32), (33), (48), (50), (52),
% 200.02/33.01  | |            (53), (54), (59), (75), (83), (85), (95), (96), (105), (109),
% 200.02/33.01  | |            (115) are inconsistent by sub-proof #1005.
% 200.02/33.01  | | 
% 200.02/33.01  | Case 2:
% 200.02/33.01  | | 
% 200.02/33.01  | |   (116)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.01  | | 
% 200.02/33.01  | | BETA: splitting (116) gives:
% 200.02/33.01  | | 
% 200.02/33.01  | | Case 1:
% 200.02/33.01  | | | 
% 200.02/33.01  | | |   (117)  all_58_3 = e3
% 200.02/33.01  | | | 
% 200.02/33.01  | | | COMBINE_EQS: (107), (117) imply:
% 200.02/33.01  | | |   (118)  all_4_2 = e3
% 200.02/33.01  | | | 
% 200.02/33.01  | | | REDUCE: (13), (118) imply:
% 200.02/33.01  | | |   (119)  $false
% 200.02/33.01  | | | 
% 200.02/33.01  | | | CLOSE: (119) is inconsistent.
% 200.02/33.01  | | | 
% 200.02/33.01  | | Case 2:
% 200.02/33.01  | | | 
% 200.02/33.01  | | |   (120)  all_58_7 = e3 | all_58_13 = e3
% 200.02/33.01  | | | 
% 200.02/33.01  | | | BETA: splitting (120) gives:
% 200.02/33.01  | | | 
% 200.02/33.01  | | | Case 1:
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | |   (121)  all_58_7 = e3
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | | COMBINE_EQS: (46), (121) imply:
% 200.02/33.01  | | | |   (122)  all_52_13 = e3
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | | REDUCE: (87), (122) imply:
% 200.02/33.01  | | | |   (123)  $false
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | | CLOSE: (123) is inconsistent.
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | Case 2:
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | |   (124)  all_58_13 = e3
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | | COMBINE_EQS: (20), (124) imply:
% 200.02/33.01  | | | |   (125)  all_52_15 = e3
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | | SIMP: (125) implies:
% 200.02/33.01  | | | |   (126)  all_52_15 = e3
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 200.02/33.01  | | | |            (12), (14), (15), (16), (17), (18), (19), (21), (22), (23),
% 200.02/33.01  | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 200.02/33.01  | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 200.02/33.01  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 200.02/33.01  | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 200.02/33.01  | | | |            (64), (65), (66), (67), (68), (69), (71), (72), (73), (74),
% 200.02/33.01  | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 200.02/33.01  | | | |            (85), (86), (88), (89), (90), (91), (92), (93), (94), (95),
% 200.02/33.01  | | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 200.02/33.01  | | | |            (105), (106), (107), (108), (109), (110), (111), (112),
% 200.02/33.01  | | | |            (113), (114), (124), (126) are inconsistent by sub-proof
% 200.02/33.01  | | | |            #124.
% 200.02/33.01  | | | | 
% 200.02/33.01  | | | End of split
% 200.02/33.01  | | | 
% 200.02/33.01  | | End of split
% 200.02/33.01  | | 
% 200.02/33.01  | End of split
% 200.02/33.01  | 
% 200.02/33.01  End of proof
% 200.02/33.01  
% 200.02/33.01  Sub-proof #117 shows that the following formulas are inconsistent:
% 200.02/33.01  ----------------------------------------------------------------
% 200.02/33.01    (1)  op(e3, e3) = all_52_18
% 200.02/33.01    (2)   ~ (all_52_15 = all_52_23)
% 200.02/33.01    (3)   ~ (all_52_25 = all_52_27)
% 200.02/33.01    (4)  all_58_14 = all_52_23
% 200.02/33.01    (5)   ~ (e3 = e1)
% 200.02/33.01    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.02/33.01    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/33.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/33.01    (8)   ~ (all_52_5 = all_52_13)
% 200.02/33.01    (9)  all_58_1 = all_52_9
% 200.02/33.01    (10)   ~ (all_52_9 = all_52_13)
% 200.02/33.01    (11)   ~ (e3 = e0)
% 200.02/33.01    (12)  op(e2, e3) = all_52_3
% 200.02/33.01    (13)   ~ (all_52_23 = all_4_0)
% 200.02/33.01    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.02/33.01    (15)   ~ (all_52_7 = all_52_15)
% 200.02/33.01    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.02/33.01    (17)   ~ (all_52_17 = all_52_25)
% 200.02/33.01    (18)   ~ (all_4_2 = e3)
% 200.02/33.01    (19)   ~ (all_52_3 = all_6_2)
% 200.02/33.01    (20)  all_58_0 = all_6_2
% 200.02/33.01    (21)  op(all_14_2, e0) = all_14_1
% 200.02/33.01    (22)  all_56_4 = all_52_3
% 200.02/33.01    (23)   ~ (all_52_17 = all_10_2)
% 200.02/33.01    (24)  op(e3, e0) = all_52_25
% 200.02/33.01    (25)  op(all_52_5, all_52_5) = all_52_4
% 200.02/33.01    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.02/33.01    (27)  op(all_52_19, all_52_19) = all_52_18
% 200.02/33.01    (28)   ~ (all_52_27 = all_52_29)
% 200.02/33.01    (29)  all_58_13 = all_52_15
% 200.02/33.01    (30)  all_58_9 = all_52_25
% 200.02/33.01    (31)   ~ (all_6_1 = e1)
% 200.02/33.01    (32)   ~ (all_52_29 = all_14_2)
% 200.02/33.01    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.02/33.01    (34)  op(all_52_27, all_52_27) = all_52_26
% 200.02/33.01    (35)  op(e1, e3) = all_52_5
% 200.02/33.01    (36)  op(e2, e2) = all_4_2
% 200.02/33.01    (37)   ~ (all_52_3 = all_52_5)
% 200.02/33.01    (38)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.02/33.01    (39)  op(all_4_2, e2) = e1
% 200.02/33.01    (40)  all_58_11 = all_52_29
% 200.02/33.01    (41)   ~ (all_52_3 = e3)
% 200.02/33.01    (42)  all_56_5 = all_4_2
% 200.02/33.01    (43)   ~ (all_52_25 = all_14_2)
% 200.02/33.01    (44)   ~ (all_52_9 = all_52_15)
% 200.02/33.01    (45)   ~ (all_52_3 = all_52_27)
% 200.02/33.01    (46)  op(all_10_2, e1) = all_10_1
% 200.02/33.01    (47)  op(all_6_2, all_6_2) = all_52_0
% 200.02/33.01    (48)   ~ (all_52_7 = all_6_2)
% 200.02/33.01    (49)  op(e0, e0) = all_14_2
% 200.02/33.01    (50)  all_56_15 = all_14_2
% 200.02/33.01    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.02/33.01    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.02/33.01    (53)  all_56_11 = all_52_29
% 200.02/33.01    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.02/33.01    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.02/33.01    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.02/33.01    (57)   ~ (e2 = e1)
% 200.02/33.01    (58)   ~ (all_52_13 = all_10_2)
% 200.02/33.01    (59)   ~ (all_6_0 = e1)
% 200.02/33.01    (60)  all_58_10 = all_52_27
% 200.02/33.01    (61)  all_56_8 = all_52_5
% 200.02/33.01    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.02/33.01    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.02/33.01    (64)   ~ (all_52_19 = all_52_23)
% 200.02/33.01    (65)   ~ (all_52_25 = all_52_29)
% 200.02/33.01    (66)   ~ (all_52_29 = all_10_2)
% 200.02/33.01    (67)  all_58_7 = all_52_13
% 200.02/33.01    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.02/33.01    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.02/33.01    (70)   ~ (all_52_5 = all_52_7)
% 200.02/33.01    (71)  all_58_12 = all_52_7
% 200.02/33.01    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.02/33.01    (73)   ~ (all_52_7 = all_14_2)
% 200.02/33.01    (74)  all_58_2 = all_52_3
% 200.02/33.01    (75)  all_56_2 = all_52_17
% 200.02/33.01    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/33.01    (77)  op(e3, all_6_1) = all_6_0
% 200.02/33.01    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.02/33.01    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.02/33.01    (80)  all_56_7 = all_52_27
% 200.02/33.01    (81)  all_28_2 = all_4_2
% 200.02/33.01    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.02/33.01    (83)   ~ (e2 = e0)
% 200.02/33.01    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.02/33.01    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.02/33.01    (86)   ~ (all_52_5 = all_52_29)
% 200.02/33.01    (87)   ~ (all_10_2 = e3)
% 200.02/33.01    (88)   ~ (all_52_15 = all_14_2)
% 200.02/33.01    (89)   ~ (all_52_19 = all_52_27)
% 200.02/33.01    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.02/33.01    (91)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.02/33.01    (92)   ~ (all_52_27 = e3)
% 200.02/33.01    (93)   ~ (all_6_0 = e2)
% 200.02/33.01    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.02/33.01            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.02/33.01    (95)   ~ (all_52_13 = all_4_2)
% 200.02/33.01    (96)  op(e3, e1) = all_52_17
% 200.02/33.01    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.02/33.01    (98)  op(e0, e3) = all_52_7
% 200.02/33.01    (99)  op(e1, e2) = all_52_13
% 200.02/33.01    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.01    (101)   ~ (all_52_9 = all_52_25)
% 200.02/33.01    (102)  all_58_15 = all_14_2
% 200.02/33.01    (103)   ~ (all_52_19 = all_10_2)
% 200.02/33.01    (104)  op(all_52_23, all_52_23) = all_52_22
% 200.02/33.01    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.02/33.01    (106)  all_58_8 = all_10_2
% 200.02/33.01    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.02/33.01    (108)   ~ (all_52_5 = all_10_2)
% 200.02/33.01    (109)  op(all_52_29, all_52_29) = all_52_28
% 200.02/33.01    (110)   ~ (all_52_23 = all_14_2)
% 200.02/33.01    (111)  all_56_12 = all_52_7
% 200.02/33.01    (112)  op(all_52_17, all_52_17) = all_52_16
% 200.02/33.01    (113)  all_58_5 = all_4_0
% 200.02/33.01    (114)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.02/33.01    (115)   ~ (all_52_25 = all_6_2)
% 200.02/33.01    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.02/33.01    (117)   ~ (all_52_9 = all_4_2)
% 200.02/33.01    (118)   ~ (all_52_5 = all_6_2)
% 200.02/33.01    (119)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.02/33.01    (120)   ~ (all_52_9 = all_6_2)
% 200.02/33.01    (121)   ~ (all_52_13 = all_52_15)
% 200.02/33.01    (122)  all_56_0 = all_6_2
% 200.02/33.01    (123)  op(e3, e3) = all_6_2
% 200.02/33.01    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.02/33.01    (125)   ~ (all_52_27 = all_14_2)
% 200.02/33.01    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.02/33.01    (127)  all_58_5 = e3
% 200.02/33.01    (128)  all_56_14 = all_52_23
% 200.02/33.01    (129)   ~ (all_52_17 = e3)
% 200.02/33.01    (130)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.02/33.01    (131)  all_56_3 = all_52_25
% 200.02/33.01    (132)  op(e0, all_14_1) = e2
% 200.02/33.01    (133)   ~ (all_52_3 = all_52_7)
% 200.02/33.01    (134)  op(all_14_2, all_14_2) = all_52_30
% 200.02/33.01    (135)  all_58_5 = all_52_19
% 200.02/33.01    (136)  all_56_1 = all_52_9
% 200.02/33.01    (137)   ~ (all_52_15 = all_4_2)
% 200.02/33.01    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.02/33.01           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.02/33.01           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.02/33.01           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.02/33.01    (139)   ~ (all_52_27 = all_4_2)
% 200.02/33.01    (140)  all_58_6 = all_52_5
% 200.02/33.01    (141)   ~ (all_4_0 = all_4_2)
% 200.02/33.01    (142)  op(e3, e2) = all_52_9
% 200.02/33.01    (143)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.02/33.01    (144)   ~ (all_52_17 = all_6_2)
% 200.02/33.01    (145)   ~ (e1 = e0)
% 200.02/33.01    (146)   ~ (e3 = e2)
% 200.02/33.01    (147)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.02/33.01    (148)   ~ (all_52_9 = all_52_17)
% 200.02/33.01    (149)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.02/33.01    (150)  op(all_52_13, all_52_13) = all_52_12
% 200.02/33.01    (151)   ~ (all_6_1 = e2)
% 200.02/33.01    (152)  op(e1, e1) = all_10_2
% 200.02/33.01    (153)   ~ (all_52_23 = all_10_2)
% 200.02/33.01    (154)   ~ (all_52_7 = all_52_23)
% 200.02/33.01    (155)   ~ (all_52_17 = all_52_19)
% 200.02/33.01    (156)  all_58_3 = all_4_2
% 200.02/33.01    (157)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.02/33.01    (158)  all_56_13 = all_52_15
% 200.02/33.01    (159)   ~ (all_52_3 = all_4_2)
% 200.02/33.01    (160)  all_28_1 = e1
% 200.02/33.01    (161)   ~ (all_52_19 = all_4_2)
% 200.02/33.01    (162)   ~ (all_52_17 = all_52_23)
% 200.02/33.01    (163)  op(all_6_2, e3) = all_6_1
% 200.02/33.01    (164)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.02/33.01    (165)   ~ (all_52_13 = all_52_29)
% 200.02/33.01    (166)  all_58_4 = all_52_17
% 200.02/33.01    (167)  op(all_52_25, all_52_25) = all_52_24
% 200.02/33.01  
% 200.02/33.01  Begin of proof
% 200.02/33.01  | 
% 200.02/33.01  | BETA: splitting (130) gives:
% 200.02/33.01  | 
% 200.02/33.01  | Case 1:
% 200.02/33.01  | | 
% 200.02/33.01  | |   (168)   ~ (all_28_1 = e1)
% 200.02/33.01  | | 
% 200.02/33.01  | | REDUCE: (160), (168) imply:
% 200.02/33.01  | |   (169)  $false
% 200.02/33.01  | | 
% 200.02/33.01  | | CLOSE: (169) is inconsistent.
% 200.02/33.01  | | 
% 200.02/33.01  | Case 2:
% 200.02/33.01  | | 
% 200.02/33.01  | |   (170)   ~ (all_28_2 = e0)
% 200.02/33.01  | | 
% 200.02/33.01  | | REDUCE: (81), (170) imply:
% 200.02/33.01  | |   (171)   ~ (all_4_2 = e0)
% 200.02/33.01  | | 
% 200.02/33.01  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 200.02/33.01  | |              with (1), (123) gives:
% 200.02/33.01  | |   (172)  all_52_18 = all_6_2
% 200.02/33.01  | | 
% 200.02/33.01  | | BETA: splitting (94) gives:
% 200.02/33.01  | | 
% 200.02/33.01  | | Case 1:
% 200.02/33.01  | | | 
% 200.02/33.01  | | |   (173)  all_58_15 = e0
% 200.02/33.01  | | | 
% 200.02/33.01  | | | REF_CLOSE: (7), (21), (49), (83), (102), (132), (134), (173) are
% 200.02/33.01  | | |            inconsistent by sub-proof #612.
% 200.02/33.01  | | | 
% 200.02/33.01  | | Case 2:
% 200.02/33.01  | | | 
% 200.02/33.01  | | |   (174)   ~ (all_58_15 = e0)
% 200.02/33.01  | | |   (175)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 200.02/33.01  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 200.02/33.01  | | | 
% 200.02/33.01  | | | ALPHA: (175) implies:
% 200.02/33.01  | | |   (176)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.02/33.01  | | |   (177)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.02/33.01  | | | 
% 200.02/33.01  | | | REDUCE: (102), (174) imply:
% 200.02/33.01  | | |   (178)   ~ (all_14_2 = e0)
% 200.02/33.01  | | | 
% 200.02/33.01  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.02/33.01  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 200.02/33.01  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 200.02/33.01  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 200.02/33.01  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 200.02/33.01  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 200.02/33.01  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 200.02/33.01  | | |            (75), (76), (77), (78), (79), (80), (82), (84), (85), (86),
% 200.02/33.01  | | |            (87), (88), (89), (90), (91), (92), (93), (95), (96), (97),
% 200.02/33.01  | | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 200.02/33.01  | | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 200.02/33.01  | | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 200.02/33.01  | | |            (125), (126), (127), (128), (129), (131), (133), (134), (135),
% 200.02/33.01  | | |            (136), (137), (138), (139), (140), (141), (142), (143), (144),
% 200.02/33.01  | | |            (145), (146), (147), (148), (149), (150), (151), (152), (153),
% 200.02/33.01  | | |            (154), (155), (156), (157), (158), (159), (161), (162), (163),
% 200.02/33.01  | | |            (164), (165), (166), (167), (171), (172), (176), (177), (178)
% 200.02/33.01  | | |            are inconsistent by sub-proof #147.
% 200.02/33.01  | | | 
% 200.02/33.01  | | End of split
% 200.02/33.01  | | 
% 200.02/33.01  | End of split
% 200.02/33.01  | 
% 200.02/33.01  End of proof
% 200.02/33.01  
% 200.02/33.01  Sub-proof #118 shows that the following formulas are inconsistent:
% 200.02/33.01  ----------------------------------------------------------------
% 200.02/33.01    (1)  all_58_14 = all_52_23
% 200.02/33.01    (2)  op(all_52_3, all_52_3) = all_52_2
% 200.02/33.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.02/33.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.02/33.01    (4)  all_58_1 = all_52_9
% 200.02/33.01    (5)   ~ (all_52_3 = all_52_19)
% 200.02/33.01    (6)   ~ (all_52_3 = all_6_2)
% 200.02/33.01    (7)  all_58_0 = all_6_2
% 200.02/33.01    (8)   ~ (all_52_17 = all_10_2)
% 200.02/33.01    (9)   ~ (all_10_0 = e3)
% 200.02/33.01    (10)  all_58_9 = all_52_25
% 200.02/33.01    (11)   ~ (all_52_25 = all_14_2)
% 200.02/33.01    (12)  all_56_15 = all_14_2
% 200.02/33.01    (13)   ~ (all_4_0 = e3)
% 200.02/33.01    (14)  op(all_10_2, e1) = e3
% 200.02/33.01    (15)  all_58_12 = all_52_7
% 200.02/33.01    (16)   ~ (all_52_7 = all_14_2)
% 200.02/33.01    (17)  all_58_2 = all_52_3
% 200.02/33.01    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.02/33.01    (19)  op(e3, e1) = all_52_17
% 200.02/33.01    (20)  all_58_6 = all_10_0
% 200.02/33.01    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.02/33.01    (22)  all_58_8 = all_10_2
% 200.02/33.01    (23)   ~ (all_52_23 = all_14_2)
% 200.02/33.01    (24)  all_58_5 = all_4_0
% 200.02/33.01    (25)  op(e3, e3) = all_6_2
% 200.02/33.01    (26)  all_56_15 = e3
% 200.02/33.01    (27)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.02/33.01    (28)  all_58_5 = all_52_19
% 200.02/33.01    (29)  op(all_52_17, all_52_17) = e3
% 200.02/33.01    (30)   ~ (all_52_17 = all_6_2)
% 200.02/33.01    (31)   ~ (all_52_9 = all_52_17)
% 200.02/33.01    (32)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.02/33.01    (33)  all_58_4 = all_52_17
% 200.02/33.01  
% 200.02/33.01  Begin of proof
% 200.02/33.01  | 
% 200.02/33.01  | COMBINE_EQS: (12), (26) imply:
% 200.02/33.01  |   (34)  all_14_2 = e3
% 200.02/33.01  | 
% 200.02/33.01  | SIMP: (34) implies:
% 200.02/33.01  |   (35)  all_14_2 = e3
% 200.02/33.01  | 
% 200.02/33.01  | REDUCE: (16), (35) imply:
% 200.02/33.01  |   (36)   ~ (all_52_7 = e3)
% 200.02/33.01  | 
% 200.02/33.01  | REDUCE: (23), (35) imply:
% 200.02/33.01  |   (37)   ~ (all_52_23 = e3)
% 200.02/33.01  | 
% 200.02/33.01  | REDUCE: (11), (35) imply:
% 200.02/33.01  |   (38)   ~ (all_52_25 = e3)
% 200.02/33.01  | 
% 200.02/33.01  | BETA: splitting (18) gives:
% 200.02/33.01  | 
% 200.02/33.01  | Case 1:
% 200.02/33.01  | | 
% 200.02/33.01  | |   (39)  all_58_0 = e3
% 200.02/33.01  | | 
% 200.02/33.01  | | COMBINE_EQS: (7), (39) imply:
% 200.02/33.01  | |   (40)  all_6_2 = e3
% 200.02/33.01  | | 
% 200.02/33.01  | | REDUCE: (30), (40) imply:
% 200.02/33.01  | |   (41)   ~ (all_52_17 = e3)
% 200.02/33.01  | | 
% 200.22/33.01  | | REF_CLOSE: (1), (3), (8), (13), (14), (19), (22), (24), (32), (33), (37),
% 200.22/33.01  | |            (41) are inconsistent by sub-proof #166.
% 200.22/33.01  | | 
% 200.22/33.01  | Case 2:
% 200.22/33.01  | | 
% 200.22/33.01  | |   (42)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.01  | | 
% 200.22/33.01  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (14), (15),
% 200.22/33.01  | |            (17), (19), (20), (21), (22), (25), (27), (28), (29), (30), (31),
% 200.22/33.01  | |            (32), (33), (36), (37), (38), (42) are inconsistent by sub-proof
% 200.22/33.01  | |            #780.
% 200.22/33.01  | | 
% 200.22/33.01  | End of split
% 200.22/33.01  | 
% 200.22/33.01  End of proof
% 200.22/33.01  
% 200.22/33.01  Sub-proof #119 shows that the following formulas are inconsistent:
% 200.22/33.01  ----------------------------------------------------------------
% 200.22/33.01    (1)  all_58_14 = all_52_23
% 200.22/33.01    (2)   ~ (all_52_17 = all_4_0)
% 200.22/33.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.01    (4)  all_58_1 = all_52_9
% 200.22/33.01    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.01    (6)  all_58_0 = all_6_2
% 200.22/33.01    (7)   ~ (all_52_17 = all_10_2)
% 200.22/33.01    (8)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.22/33.01    (9)  all_58_13 = all_52_15
% 200.22/33.01    (10)  op(all_52_13, all_52_13) = e1
% 200.22/33.01    (11)   ~ (all_52_15 = e3)
% 200.22/33.01    (12)  op(all_4_2, e2) = e1
% 200.22/33.01    (13)   ~ (all_10_0 = all_6_2)
% 200.22/33.01    (14)   ~ (all_10_0 = e2)
% 200.22/33.01    (15)   ~ (all_4_0 = e3)
% 200.22/33.01    (16)  all_58_10 = all_52_27
% 200.22/33.01    (17)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.22/33.01    (18)  op(all_10_2, e1) = e3
% 200.22/33.01    (19)  all_58_7 = all_52_13
% 200.22/33.01    (20)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 200.22/33.01    (21)  all_30_2 = all_10_2
% 200.22/33.01    (22)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.22/33.01    (23)  all_56_7 = all_52_27
% 200.22/33.01    (24)   ~ (all_52_23 = e3)
% 200.22/33.01    (25)  all_56_8 = all_10_0
% 200.22/33.01    (26)   ~ (all_52_13 = all_4_2)
% 200.22/33.01    (27)  op(e3, e1) = all_52_17
% 200.22/33.01    (28)  all_30_0 = all_10_0
% 200.22/33.01    (29)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.01    (30)   ~ (all_10_0 = all_10_2)
% 200.22/33.01    (31)  all_58_8 = all_10_2
% 200.22/33.01    (32)  op(all_52_17, all_52_17) = all_52_16
% 200.22/33.01    (33)  all_58_5 = all_4_0
% 200.22/33.01    (34)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.22/33.01    (35)  op(e3, e3) = all_6_2
% 200.22/33.01    (36)   ~ (all_52_15 = all_4_2)
% 200.22/33.01    (37)   ~ (all_52_27 = all_4_2)
% 200.22/33.01    (38)  op(e3, e2) = all_52_9
% 200.22/33.01    (39)   ~ (all_52_9 = all_52_17)
% 200.22/33.01    (40)  all_56_10 = all_10_2
% 200.22/33.01    (41)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.01    (42)  op(e1, e1) = all_10_2
% 200.22/33.01    (43)  op(all_52_9, all_52_9) = e3
% 200.22/33.01    (44)  all_58_3 = all_4_2
% 200.22/33.01    (45)  all_58_4 = all_52_17
% 200.22/33.01    (46)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.22/33.01  
% 200.22/33.01  Begin of proof
% 200.22/33.01  | 
% 200.22/33.01  | BETA: splitting (41) gives:
% 200.22/33.01  | 
% 200.22/33.01  | Case 1:
% 200.22/33.01  | | 
% 200.22/33.01  | |   (47)  all_58_4 = e3
% 200.22/33.01  | | 
% 200.22/33.01  | | COMBINE_EQS: (45), (47) imply:
% 200.22/33.01  | |   (48)  all_52_17 = e3
% 200.22/33.01  | | 
% 200.22/33.01  | | SIMP: (48) implies:
% 200.22/33.01  | |   (49)  all_52_17 = e3
% 200.22/33.01  | | 
% 200.22/33.01  | | REDUCE: (39), (49) imply:
% 200.22/33.01  | |   (50)   ~ (all_52_9 = e3)
% 200.22/33.01  | | 
% 200.22/33.01  | | REDUCE: (7), (49) imply:
% 200.22/33.01  | |   (51)   ~ (all_10_2 = e3)
% 200.22/33.01  | | 
% 200.22/33.01  | | SIMP: (51) implies:
% 200.22/33.01  | |   (52)   ~ (all_10_2 = e3)
% 200.22/33.01  | | 
% 200.22/33.01  | | REDUCE: (2), (49) imply:
% 200.22/33.01  | |   (53)   ~ (all_4_0 = e3)
% 200.22/33.01  | | 
% 200.22/33.01  | | REDUCE: (32), (49) imply:
% 200.22/33.01  | |   (54)  op(e3, e3) = all_52_16
% 200.22/33.01  | | 
% 200.22/33.01  | | GROUND_INST: instantiating (3) with all_6_2, all_52_16, e3, e3, simplifying
% 200.22/33.01  | |              with (35), (54) gives:
% 200.22/33.01  | |   (55)  all_52_16 = all_6_2
% 200.22/33.01  | | 
% 200.22/33.01  | | BETA: splitting (22) gives:
% 200.22/33.01  | | 
% 200.22/33.01  | | Case 1:
% 200.22/33.01  | | | 
% 200.22/33.01  | | |   (56)  all_58_0 = e1
% 200.22/33.01  | | | 
% 200.22/33.01  | | | COMBINE_EQS: (6), (56) imply:
% 200.22/33.01  | | |   (57)  all_6_2 = e1
% 200.22/33.01  | | | 
% 200.22/33.01  | | | REDUCE: (13), (57) imply:
% 200.22/33.01  | | |   (58)   ~ (all_10_0 = e1)
% 200.22/33.01  | | | 
% 200.22/33.01  | | | REF_CLOSE: (3), (7), (14), (17), (18), (20), (21), (25), (27), (28), (30),
% 200.22/33.01  | | |            (40), (42), (46), (58) are inconsistent by sub-proof #909.
% 200.22/33.01  | | | 
% 200.22/33.01  | | Case 2:
% 200.22/33.01  | | | 
% 200.22/33.01  | | |   (59)   ~ (all_58_0 = e1)
% 200.22/33.01  | | | 
% 200.22/33.01  | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (12), (15), (16),
% 200.22/33.01  | | |            (19), (23), (26), (29), (33), (34), (35), (36), (37), (38),
% 200.22/33.01  | | |            (42), (43), (44), (50), (52), (59) are inconsistent by
% 200.22/33.01  | | |            sub-proof #120.
% 200.22/33.01  | | | 
% 200.22/33.02  | | End of split
% 200.22/33.02  | | 
% 200.22/33.02  | Case 2:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (60)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | REF_CLOSE: (1), (3), (7), (15), (18), (24), (27), (31), (33), (60) are
% 200.22/33.02  | |            inconsistent by sub-proof #167.
% 200.22/33.02  | | 
% 200.22/33.02  | End of split
% 200.22/33.02  | 
% 200.22/33.02  End of proof
% 200.22/33.02  
% 200.22/33.02  Sub-proof #120 shows that the following formulas are inconsistent:
% 200.22/33.02  ----------------------------------------------------------------
% 200.22/33.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.02    (2)  all_58_1 = all_52_9
% 200.22/33.02    (3)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.02    (4)  all_58_0 = all_6_2
% 200.22/33.02    (5)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.22/33.02    (6)  all_58_13 = all_52_15
% 200.22/33.02    (7)  op(all_52_13, all_52_13) = e1
% 200.22/33.02    (8)   ~ (all_52_15 = e3)
% 200.22/33.02    (9)  op(all_4_2, e2) = e1
% 200.22/33.02    (10)   ~ (all_4_0 = e3)
% 200.22/33.02    (11)  all_58_10 = all_52_27
% 200.22/33.02    (12)  all_58_7 = all_52_13
% 200.22/33.02    (13)  all_56_7 = all_52_27
% 200.22/33.02    (14)   ~ (all_10_2 = e3)
% 200.22/33.02    (15)   ~ (all_52_9 = e3)
% 200.22/33.02    (16)   ~ (all_52_13 = all_4_2)
% 200.22/33.02    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.02    (18)  all_58_5 = all_4_0
% 200.22/33.02    (19)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.22/33.02    (20)  op(e3, e3) = all_6_2
% 200.22/33.02    (21)   ~ (all_52_15 = all_4_2)
% 200.22/33.02    (22)   ~ (all_52_27 = all_4_2)
% 200.22/33.02    (23)  op(e3, e2) = all_52_9
% 200.22/33.02    (24)  op(e1, e1) = all_10_2
% 200.22/33.02    (25)  op(all_52_9, all_52_9) = e3
% 200.22/33.02    (26)  all_58_3 = all_4_2
% 200.22/33.02    (27)   ~ (all_58_0 = e1)
% 200.22/33.02  
% 200.22/33.02  Begin of proof
% 200.22/33.02  | 
% 200.22/33.02  | REDUCE: (4), (27) imply:
% 200.22/33.02  |   (28)   ~ (all_6_2 = e1)
% 200.22/33.02  | 
% 200.22/33.02  | BETA: splitting (17) gives:
% 200.22/33.02  | 
% 200.22/33.02  | Case 1:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (29)  all_58_1 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | COMBINE_EQS: (2), (29) imply:
% 200.22/33.02  | |   (30)  all_52_9 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (15), (30) imply:
% 200.22/33.02  | |   (31)  $false
% 200.22/33.02  | | 
% 200.22/33.02  | | CLOSE: (31) is inconsistent.
% 200.22/33.02  | | 
% 200.22/33.02  | Case 2:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (32)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | BETA: splitting (5) gives:
% 200.22/33.02  | | 
% 200.22/33.02  | | Case 1:
% 200.22/33.02  | | | 
% 200.22/33.02  | | |   (33)  all_56_7 = e3
% 200.22/33.02  | | | 
% 200.22/33.02  | | | COMBINE_EQS: (13), (33) imply:
% 200.22/33.02  | | |   (34)  all_52_27 = e3
% 200.22/33.02  | | | 
% 200.22/33.02  | | | SIMP: (34) implies:
% 200.22/33.02  | | |   (35)  all_52_27 = e3
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REDUCE: (22), (35) imply:
% 200.22/33.02  | | |   (36)   ~ (all_4_2 = e3)
% 200.22/33.02  | | | 
% 200.22/33.02  | | | SIMP: (36) implies:
% 200.22/33.02  | | |   (37)   ~ (all_4_2 = e3)
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REF_CLOSE: (1), (6), (7), (8), (12), (20), (26), (28), (32), (37) are
% 200.22/33.02  | | |            inconsistent by sub-proof #1143.
% 200.22/33.02  | | | 
% 200.22/33.02  | | Case 2:
% 200.22/33.02  | | | 
% 200.22/33.02  | | |   (38)   ~ (all_56_7 = e3)
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REDUCE: (13), (38) imply:
% 200.22/33.02  | | |   (39)   ~ (all_52_27 = e3)
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REF_CLOSE: (1), (3), (6), (9), (10), (11), (12), (14), (16), (18), (19),
% 200.22/33.02  | | |            (21), (23), (24), (25), (26), (32), (39) are inconsistent by
% 200.22/33.02  | | |            sub-proof #213.
% 200.22/33.02  | | | 
% 200.22/33.02  | | End of split
% 200.22/33.02  | | 
% 200.22/33.02  | End of split
% 200.22/33.02  | 
% 200.22/33.02  End of proof
% 200.22/33.02  
% 200.22/33.02  Sub-proof #121 shows that the following formulas are inconsistent:
% 200.22/33.02  ----------------------------------------------------------------
% 200.22/33.02    (1)   ~ (e3 = e1)
% 200.22/33.02    (2)   ~ (all_14_1 = e3)
% 200.22/33.02    (3)  all_58_10 = all_52_27
% 200.22/33.02    (4)  all_58_15 = e1
% 200.22/33.02    (5)   ~ (all_52_27 = e3)
% 200.22/33.02    (6)  all_58_11 = all_14_1
% 200.22/33.02    (7)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.22/33.02  
% 200.22/33.02  Begin of proof
% 200.22/33.02  | 
% 200.22/33.02  | BETA: splitting (7) gives:
% 200.22/33.02  | 
% 200.22/33.02  | Case 1:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (8)  all_58_10 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1301.
% 200.22/33.02  | | 
% 200.22/33.02  | Case 2:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (9)  all_58_11 = e3 | all_58_15 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | BETA: splitting (9) gives:
% 200.22/33.02  | | 
% 200.22/33.02  | | Case 1:
% 200.22/33.02  | | | 
% 200.22/33.02  | | |   (10)  all_58_11 = e3
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #587.
% 200.22/33.02  | | | 
% 200.22/33.02  | | Case 2:
% 200.22/33.02  | | | 
% 200.22/33.02  | | |   (11)  all_58_15 = e3
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #586.
% 200.22/33.02  | | | 
% 200.22/33.02  | | End of split
% 200.22/33.02  | | 
% 200.22/33.02  | End of split
% 200.22/33.02  | 
% 200.22/33.02  End of proof
% 200.22/33.02  
% 200.22/33.02  Sub-proof #122 shows that the following formulas are inconsistent:
% 200.22/33.02  ----------------------------------------------------------------
% 200.22/33.02    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.22/33.02    (2)   ~ (all_52_25 = all_52_27)
% 200.22/33.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.02    (4)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 200.22/33.02    (5)  op(all_52_7, all_52_7) = e0
% 200.22/33.02    (6)  all_58_1 = all_52_9
% 200.22/33.02    (7)  op(all_52_5, all_52_5) = e1
% 200.22/33.02    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.22/33.02    (9)   ~ (all_52_7 = all_52_15)
% 200.22/33.02    (10)   ~ (all_52_17 = all_52_25)
% 200.22/33.02    (11)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.22/33.02    (12)  all_50_1 = all_14_1
% 200.22/33.02    (13)  all_58_0 = all_6_2
% 200.22/33.02    (14)  op(all_14_2, e0) = all_14_1
% 200.22/33.02    (15)   ~ (all_52_17 = all_10_2)
% 200.22/33.02    (16)   ~ (all_10_0 = e3)
% 200.22/33.02    (17)  all_40_2 = all_10_2
% 200.22/33.02    (18)  op(e3, e0) = all_52_25
% 200.22/33.02    (19)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.22/33.02    (20)   ~ (all_52_27 = all_52_29)
% 200.22/33.02    (21)  all_58_13 = all_52_15
% 200.22/33.02    (22)  op(all_10_2, all_10_2) = all_52_20
% 200.22/33.02    (23)  all_58_9 = all_52_25
% 200.22/33.02    (24)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.22/33.02    (25)   ~ (all_52_29 = all_14_2)
% 200.22/33.02    (26)  op(all_52_27, all_52_27) = all_52_26
% 200.22/33.02    (27)  op(e2, e2) = all_4_2
% 200.22/33.02    (28)  all_58_7 = all_10_0
% 200.22/33.02    (29)  op(all_4_2, e2) = e1
% 200.22/33.02    (30)  all_58_11 = all_52_29
% 200.22/33.02    (31)   ~ (all_52_25 = all_14_2)
% 200.22/33.02    (32)   ~ (all_52_7 = all_6_2)
% 200.22/33.02    (33)  op(e0, e0) = all_14_2
% 200.22/33.02    (34)  all_56_15 = all_14_2
% 200.22/33.02    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.02    (36)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.22/33.02    (37)   ~ (all_10_0 = e2)
% 200.22/33.02    (38)   ~ (all_4_0 = e3)
% 200.22/33.02    (39)   ~ (e2 = e1)
% 200.22/33.02    (40)  all_58_10 = all_52_27
% 200.22/33.02    (41)  all_56_8 = all_52_5
% 200.22/33.02    (42)  all_56_9 = all_10_0
% 200.22/33.02    (43)   ~ (all_10_0 = all_4_2)
% 200.22/33.02    (44)  op(all_6_2, all_6_2) = e3
% 200.22/33.02    (45)  all_58_12 = all_52_7
% 200.22/33.02    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.02    (47)   ~ (all_52_7 = all_14_2)
% 200.22/33.02    (48)   ~ (all_14_2 = e0)
% 200.22/33.02    (49)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.22/33.02    (50)  all_58_2 = all_52_3
% 200.22/33.02    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.02    (52)  all_56_7 = all_52_27
% 200.22/33.02    (53)  op(all_52_3, all_52_3) = e2
% 200.22/33.02    (54)   ~ (all_52_5 = all_52_29)
% 200.22/33.02    (55)   ~ (all_52_15 = all_14_2)
% 200.22/33.02    (56)  op(e3, e1) = all_52_17
% 200.22/33.02    (57)   ~ (all_52_9 = all_52_25)
% 200.22/33.02    (58)  all_58_15 = all_14_2
% 200.22/33.02    (59)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.22/33.02    (60)   ~ (all_10_0 = all_10_2)
% 200.22/33.02    (61)  all_58_8 = all_10_2
% 200.22/33.02    (62)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.22/33.02    (63)   ~ (all_52_5 = all_10_2)
% 200.22/33.02    (64)  all_56_12 = all_52_7
% 200.22/33.02    (65)  op(all_52_17, all_52_17) = all_52_16
% 200.22/33.02    (66)  all_58_5 = all_4_0
% 200.22/33.02    (67)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.22/33.02    (68)   ~ (all_52_5 = all_6_2)
% 200.22/33.02    (69)   ~ (all_52_9 = all_6_2)
% 200.22/33.02    (70)  op(e3, e3) = all_6_2
% 200.22/33.02    (71)   ~ (all_52_29 = all_10_0)
% 200.22/33.02    (72)  op(all_4_2, all_4_2) = all_52_10
% 200.22/33.02    (73)  all_40_0 = all_10_0
% 200.22/33.02    (74)  all_56_3 = all_52_25
% 200.22/33.02    (75)  op(e0, all_14_1) = e2
% 200.22/33.02    (76)  op(all_14_2, all_14_2) = all_52_30
% 200.22/33.02    (77)  all_56_1 = all_52_9
% 200.22/33.02    (78)  all_58_6 = all_52_5
% 200.22/33.02    (79)  op(all_10_2, e1) = e2
% 200.22/33.02    (80)  op(e3, e2) = all_52_9
% 200.22/33.02    (81)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.22/33.02    (82)   ~ (e3 = e2)
% 200.22/33.02    (83)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.22/33.02    (84)   ~ (all_52_9 = all_52_17)
% 200.22/33.02    (85)  op(e1, e1) = all_10_2
% 200.22/33.02    (86)   ~ (all_52_5 = all_10_0)
% 200.22/33.02    (87)  all_58_3 = all_4_2
% 200.22/33.02    (88)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.22/33.02    (89)   ~ (all_52_3 = all_4_2)
% 200.22/33.02    (90)   ~ (all_52_9 = all_10_0)
% 200.22/33.02    (91)  all_50_2 = all_14_2
% 200.22/33.02    (92)  op(all_52_25, all_52_25) = all_52_24
% 200.22/33.02  
% 200.22/33.02  Begin of proof
% 200.22/33.02  | 
% 200.22/33.02  | BETA: splitting (62) gives:
% 200.22/33.02  | 
% 200.22/33.02  | Case 1:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (93)  all_56_15 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | COMBINE_EQS: (34), (93) imply:
% 200.22/33.02  | |   (94)  all_14_2 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | SIMP: (94) implies:
% 200.22/33.02  | |   (95)  all_14_2 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | COMBINE_EQS: (91), (95) imply:
% 200.22/33.02  | |   (96)  all_50_2 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | COMBINE_EQS: (58), (95) imply:
% 200.22/33.02  | |   (97)  all_58_15 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (31), (95) imply:
% 200.22/33.02  | |   (98)   ~ (all_52_25 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (25), (95) imply:
% 200.22/33.02  | |   (99)   ~ (all_52_29 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (76), (95) imply:
% 200.22/33.02  | |   (100)  op(e3, e3) = all_52_30
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (14), (95) imply:
% 200.22/33.02  | |   (101)  op(e3, e0) = all_14_1
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (33), (95) imply:
% 200.22/33.02  | |   (102)  op(e0, e0) = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (11), (12), (13), (15), (16),
% 200.22/33.02  | |            (17), (18), (23), (27), (28), (30), (33), (35), (36), (37), (40),
% 200.22/33.02  | |            (42), (44), (45), (46), (47), (49), (50), (51), (53), (56), (60),
% 200.22/33.02  | |            (61), (63), (67), (68), (70), (71), (73), (74), (75), (78), (79),
% 200.22/33.02  | |            (81), (85), (89), (92), (96), (97), (98), (99), (100), (101),
% 200.22/33.02  | |            (102) are inconsistent by sub-proof #588.
% 200.22/33.02  | | 
% 200.22/33.02  | Case 2:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (103)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.22/33.02  | | 
% 200.22/33.02  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (11), (13), (16), (17), (19),
% 200.22/33.02  | |            (20), (21), (22), (23), (24), (26), (27), (28), (29), (30), (32),
% 200.22/33.02  | |            (33), (34), (35), (37), (38), (39), (40), (41), (42), (43), (44),
% 200.22/33.02  | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 200.22/33.02  | |            (56), (57), (59), (61), (63), (64), (65), (66), (68), (69), (70),
% 200.22/33.02  | |            (72), (73), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 200.22/33.02  | |            (86), (87), (88), (89), (90), (103) are inconsistent by sub-proof
% 200.22/33.02  | |            #172.
% 200.22/33.02  | | 
% 200.22/33.02  | End of split
% 200.22/33.02  | 
% 200.22/33.02  End of proof
% 200.22/33.02  
% 200.22/33.02  Sub-proof #123 shows that the following formulas are inconsistent:
% 200.22/33.02  ----------------------------------------------------------------
% 200.22/33.02    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.22/33.02    (2)   ~ (all_52_15 = all_52_23)
% 200.22/33.02    (3)   ~ (all_52_25 = all_52_27)
% 200.22/33.02    (4)  all_58_14 = all_52_23
% 200.22/33.02    (5)   ~ (e3 = e1)
% 200.22/33.02    (6)   ~ (all_52_17 = all_4_0)
% 200.22/33.02    (7)  op(all_52_3, all_52_3) = all_52_2
% 200.22/33.02    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.02    (9)   ~ (all_52_5 = all_52_13)
% 200.22/33.02    (10)  all_58_1 = all_52_9
% 200.22/33.02    (11)   ~ (all_52_9 = all_52_13)
% 200.22/33.02    (12)   ~ (all_52_23 = all_4_0)
% 200.22/33.02    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.22/33.02    (14)   ~ (all_52_7 = all_52_15)
% 200.22/33.02    (15)  op(all_52_7, all_52_7) = all_52_6
% 200.22/33.02    (16)   ~ (all_52_17 = all_52_25)
% 200.22/33.02    (17)   ~ (all_52_3 = all_6_2)
% 200.22/33.02    (18)  all_58_0 = all_6_2
% 200.22/33.02    (19)  op(all_14_2, e0) = all_14_1
% 200.22/33.02    (20)   ~ (all_52_17 = all_10_2)
% 200.22/33.02    (21)  op(e3, e0) = all_52_25
% 200.22/33.02    (22)   ~ (all_52_27 = all_52_29)
% 200.22/33.02    (23)  all_58_13 = all_52_15
% 200.22/33.02    (24)  op(all_10_2, all_10_2) = all_52_20
% 200.22/33.02    (25)  all_58_9 = all_52_25
% 200.22/33.02    (26)   ~ (all_6_1 = e1)
% 200.22/33.02    (27)   ~ (all_52_29 = all_14_2)
% 200.22/33.02    (28)  op(all_52_27, all_52_27) = all_52_26
% 200.22/33.02    (29)  op(e1, e3) = all_52_5
% 200.22/33.02    (30)  op(e2, e2) = all_4_2
% 200.22/33.02    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 200.22/33.02    (32)   ~ (all_52_3 = all_52_5)
% 200.22/33.02    (33)  op(all_4_2, e2) = e1
% 200.22/33.02    (34)  all_58_11 = all_52_29
% 200.22/33.02    (35)  all_56_5 = all_4_2
% 200.22/33.02    (36)   ~ (all_52_25 = all_14_2)
% 200.22/33.02    (37)  op(all_10_2, e1) = all_10_1
% 200.22/33.02    (38)   ~ (all_10_2 = all_4_0)
% 200.22/33.02    (39)  op(all_6_2, all_6_2) = all_52_0
% 200.22/33.02    (40)   ~ (all_52_7 = all_6_2)
% 200.22/33.02    (41)  op(e0, e0) = all_14_2
% 200.22/33.02    (42)  all_56_15 = all_14_2
% 200.22/33.02    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.02    (44)   ~ (all_4_0 = e3)
% 200.22/33.02    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.22/33.02    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.22/33.02    (47)   ~ (e2 = e1)
% 200.22/33.02    (48)   ~ (all_52_13 = all_10_2)
% 200.22/33.02    (49)   ~ (all_6_0 = e1)
% 200.22/33.02    (50)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 200.22/33.02    (51)  all_58_10 = all_52_27
% 200.22/33.02    (52)  all_56_8 = all_52_5
% 200.22/33.02    (53)  op(all_52_9, all_52_9) = all_52_8
% 200.22/33.02    (54)  op(all_52_15, all_52_15) = all_52_14
% 200.22/33.02    (55)   ~ (all_52_29 = all_10_2)
% 200.22/33.02    (56)  all_58_7 = all_52_13
% 200.22/33.02    (57)   ~ (all_52_5 = all_52_7)
% 200.22/33.02    (58)  all_58_12 = all_52_7
% 200.22/33.02    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.02    (60)   ~ (all_14_2 = e0)
% 200.22/33.02    (61)  all_58_2 = all_52_3
% 200.22/33.02    (62)  all_56_2 = all_52_17
% 200.22/33.02    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.22/33.02    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.02    (65)  op(e3, all_6_1) = all_6_0
% 200.22/33.02    (66)   ~ (e2 = e0)
% 200.22/33.02    (67)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.22/33.02    (68)   ~ (all_52_5 = all_52_29)
% 200.22/33.02    (69)   ~ (all_52_15 = all_14_2)
% 200.22/33.02    (70)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.22/33.02    (71)   ~ (all_6_0 = e2)
% 200.22/33.02    (72)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.22/33.02    (73)   ~ (all_52_13 = all_4_2)
% 200.22/33.02    (74)  op(e3, e1) = all_52_17
% 200.22/33.02    (75)  op(e0, e3) = all_52_7
% 200.22/33.02    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.02    (77)   ~ (all_52_9 = all_52_25)
% 200.22/33.02    (78)  all_58_15 = all_14_2
% 200.22/33.02    (79)  op(all_52_23, all_52_23) = all_52_22
% 200.22/33.02    (80)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.22/33.02    (81)  all_58_8 = all_10_2
% 200.22/33.02    (82)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.22/33.02    (83)   ~ (all_52_5 = all_10_2)
% 200.22/33.02    (84)  all_56_12 = all_52_7
% 200.22/33.02    (85)  op(all_52_17, all_52_17) = all_52_16
% 200.22/33.02    (86)  all_58_5 = all_4_0
% 200.22/33.02    (87)   ~ (all_52_25 = all_6_2)
% 200.22/33.02    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.22/33.02    (89)   ~ (all_52_5 = all_6_2)
% 200.22/33.02    (90)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.22/33.02    (91)   ~ (all_52_9 = all_6_2)
% 200.22/33.02    (92)  op(e3, e3) = all_6_2
% 200.22/33.02    (93)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.22/33.02    (94)   ~ (all_52_27 = all_14_2)
% 200.22/33.02    (95)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.22/33.02    (96)  op(all_4_2, all_4_2) = all_52_10
% 200.22/33.02    (97)  all_56_3 = all_52_25
% 200.22/33.02    (98)  op(e0, all_14_1) = e2
% 200.22/33.02    (99)   ~ (all_52_3 = all_52_7)
% 200.22/33.02    (100)  op(all_14_2, all_14_2) = all_52_30
% 200.22/33.02    (101)  all_56_1 = all_52_9
% 200.22/33.02    (102)   ~ (all_52_15 = all_4_2)
% 200.22/33.02    (103)   ~ (all_52_27 = all_4_2)
% 200.22/33.02    (104)  all_58_6 = all_52_5
% 200.22/33.02    (105)   ~ (all_4_0 = all_4_2)
% 200.22/33.02    (106)  op(e3, e2) = all_52_9
% 200.22/33.02    (107)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.22/33.02    (108)   ~ (all_52_17 = all_6_2)
% 200.22/33.02    (109)   ~ (e1 = e0)
% 200.22/33.02    (110)   ~ (e3 = e2)
% 200.22/33.02    (111)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.22/33.02    (112)   ~ (all_52_9 = all_52_17)
% 200.22/33.02    (113)  all_56_10 = all_10_2
% 200.22/33.02    (114)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.02    (115)  op(all_52_13, all_52_13) = all_52_12
% 200.22/33.02    (116)   ~ (all_6_1 = e2)
% 200.22/33.02    (117)  op(e1, e1) = all_10_2
% 200.22/33.02    (118)   ~ (all_52_23 = all_10_2)
% 200.22/33.02    (119)   ~ (all_52_7 = all_52_23)
% 200.22/33.02    (120)  all_58_3 = all_4_2
% 200.22/33.02    (121)  all_56_13 = all_52_15
% 200.22/33.02    (122)   ~ (all_52_3 = all_4_2)
% 200.22/33.02    (123)   ~ (all_52_17 = all_52_23)
% 200.22/33.02    (124)  op(all_6_2, e3) = all_6_1
% 200.22/33.02    (125)  all_58_4 = all_52_17
% 200.22/33.02    (126)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.22/33.02    (127)  op(all_52_25, all_52_25) = all_52_24
% 200.22/33.02  
% 200.22/33.02  Begin of proof
% 200.22/33.02  | 
% 200.22/33.02  | ALPHA: (50) implies:
% 200.22/33.02  |   (128)  all_52_14 = e0
% 200.22/33.02  |   (129)  all_52_12 = e1
% 200.22/33.02  |   (130)  all_52_10 = e2
% 200.22/33.02  |   (131)  all_52_8 = e3
% 200.22/33.02  | 
% 200.22/33.02  | REDUCE: (53), (131) imply:
% 200.22/33.02  |   (132)  op(all_52_9, all_52_9) = e3
% 200.22/33.02  | 
% 200.22/33.02  | REDUCE: (115), (129) imply:
% 200.22/33.02  |   (133)  op(all_52_13, all_52_13) = e1
% 200.22/33.02  | 
% 200.22/33.02  | REDUCE: (54), (128) imply:
% 200.22/33.02  |   (134)  op(all_52_15, all_52_15) = e0
% 200.22/33.02  | 
% 200.22/33.02  | REDUCE: (96), (130) imply:
% 200.22/33.02  |   (135)  op(all_4_2, all_4_2) = e2
% 200.22/33.02  | 
% 200.22/33.02  | BETA: splitting (82) gives:
% 200.22/33.02  | 
% 200.22/33.02  | Case 1:
% 200.22/33.02  | | 
% 200.22/33.02  | |   (136)  all_56_15 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | COMBINE_EQS: (42), (136) imply:
% 200.22/33.02  | |   (137)  all_14_2 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | SIMP: (137) implies:
% 200.22/33.02  | |   (138)  all_14_2 = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (69), (138) imply:
% 200.22/33.02  | |   (139)   ~ (all_52_15 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (36), (138) imply:
% 200.22/33.02  | |   (140)   ~ (all_52_25 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (94), (138) imply:
% 200.22/33.02  | |   (141)   ~ (all_52_27 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (27), (138) imply:
% 200.22/33.02  | |   (142)   ~ (all_52_29 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (60), (138) imply:
% 200.22/33.02  | |   (143)   ~ (e3 = e0)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (100), (138) imply:
% 200.22/33.02  | |   (144)  op(e3, e3) = all_52_30
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (19), (138) imply:
% 200.22/33.02  | |   (145)  op(e3, e0) = all_14_1
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (41), (138) imply:
% 200.22/33.02  | |   (146)  op(e0, e0) = e3
% 200.22/33.02  | | 
% 200.22/33.02  | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3, simplifying
% 200.22/33.02  | |              with (21), (145) gives:
% 200.22/33.02  | |   (147)  all_52_25 = all_14_1
% 200.22/33.02  | | 
% 200.22/33.02  | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3, simplifying
% 200.22/33.02  | |              with (92), (144) gives:
% 200.22/33.02  | |   (148)  all_52_30 = all_6_2
% 200.22/33.02  | | 
% 200.22/33.02  | | COMBINE_EQS: (97), (147) imply:
% 200.22/33.02  | |   (149)  all_56_3 = all_14_1
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (77), (147) imply:
% 200.22/33.02  | |   (150)   ~ (all_52_9 = all_14_1)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (87), (147) imply:
% 200.22/33.02  | |   (151)   ~ (all_14_1 = all_6_2)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (140), (147) imply:
% 200.22/33.02  | |   (152)   ~ (all_14_1 = e3)
% 200.22/33.02  | | 
% 200.22/33.02  | | REDUCE: (127), (147) imply:
% 200.22/33.02  | |   (153)  op(all_14_1, all_14_1) = all_52_24
% 200.22/33.02  | | 
% 200.22/33.02  | | BETA: splitting (88) gives:
% 200.22/33.02  | | 
% 200.22/33.02  | | Case 1:
% 200.22/33.02  | | | 
% 200.22/33.02  | | |   (154)  all_56_3 = e3
% 200.22/33.02  | | | 
% 200.22/33.02  | | | REF_CLOSE: (149), (152), (154) are inconsistent by sub-proof #1200.
% 200.22/33.02  | | | 
% 200.22/33.02  | | Case 2:
% 200.22/33.02  | | | 
% 200.22/33.02  | | |   (155)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.22/33.02  | | | 
% 200.22/33.02  | | | BETA: splitting (43) gives:
% 200.22/33.02  | | | 
% 200.22/33.02  | | | Case 1:
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | |   (156)  all_58_2 = e3
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | COMBINE_EQS: (61), (156) imply:
% 200.22/33.02  | | | |   (157)  all_52_3 = e3
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | SIMP: (157) implies:
% 200.22/33.02  | | | |   (158)  all_52_3 = e3
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | REDUCE: (32), (158) imply:
% 200.22/33.02  | | | |   (159)   ~ (all_52_5 = e3)
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | SIMP: (159) implies:
% 200.22/33.02  | | | |   (160)   ~ (all_52_5 = e3)
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | REDUCE: (99), (158) imply:
% 200.22/33.02  | | | |   (161)   ~ (all_52_7 = e3)
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | SIMP: (161) implies:
% 200.22/33.02  | | | |   (162)   ~ (all_52_7 = e3)
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | REDUCE: (7), (158) imply:
% 200.22/33.02  | | | |   (163)  op(e3, e3) = all_52_2
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3,
% 200.22/33.02  | | | |              simplifying with (92), (163) gives:
% 200.22/33.02  | | | |   (164)  all_52_2 = all_6_2
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | BETA: splitting (114) gives:
% 200.22/33.02  | | | | 
% 200.22/33.02  | | | | Case 1:
% 200.22/33.02  | | | | | 
% 200.22/33.02  | | | | |   (165)  all_58_4 = e3
% 200.22/33.02  | | | | | 
% 200.22/33.02  | | | | | COMBINE_EQS: (125), (165) imply:
% 200.22/33.02  | | | | |   (166)  all_52_17 = e3
% 200.22/33.02  | | | | | 
% 200.22/33.02  | | | | | REDUCE: (112), (166) imply:
% 200.22/33.02  | | | | |   (167)   ~ (all_52_9 = e3)
% 200.22/33.02  | | | | | 
% 200.22/33.02  | | | | | REDUCE: (108), (166) imply:
% 200.22/33.03  | | | | |   (168)   ~ (all_6_2 = e3)
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | SIMP: (168) implies:
% 200.22/33.03  | | | | |   (169)   ~ (all_6_2 = e3)
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (15), (17), (18), (23), (29),
% 200.22/33.03  | | | | |            (30), (31), (40), (47), (56), (58), (61), (63), (64), (65),
% 200.22/33.03  | | | | |            (66), (70), (71), (76), (91), (92), (99), (101), (104),
% 200.22/33.03  | | | | |            (109), (110), (111), (116), (120), (122), (124), (132),
% 200.22/33.03  | | | | |            (133), (139), (143), (145), (149), (150), (151), (155),
% 200.22/33.03  | | | | |            (160), (162), (167), (169) are inconsistent by sub-proof
% 200.22/33.03  | | | | |            #1118.
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | Case 2:
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | |   (170)   ~ (all_58_4 = e3)
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REDUCE: (125), (170) imply:
% 200.22/33.03  | | | | |   (171)   ~ (all_52_17 = e3)
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REF_CLOSE: (8), (10), (18), (23), (24), (25), (34), (39), (48), (49),
% 200.22/33.03  | | | | |            (56), (59), (65), (71), (76), (81), (89), (91), (92), (95),
% 200.22/33.03  | | | | |            (104), (113), (120), (124), (125), (126), (132), (133),
% 200.22/33.03  | | | | |            (135), (139), (140), (142), (171) are inconsistent by
% 200.22/33.03  | | | | |            sub-proof #1137.
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | End of split
% 200.22/33.03  | | | | 
% 200.22/33.03  | | | Case 2:
% 200.22/33.03  | | | | 
% 200.22/33.03  | | | |   (172)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.03  | | | | 
% 200.22/33.03  | | | | BETA: splitting (172) gives:
% 200.22/33.03  | | | | 
% 200.22/33.03  | | | | Case 1:
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | |   (173)  all_58_3 = e3
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | COMBINE_EQS: (120), (173) imply:
% 200.22/33.03  | | | | |   (174)  all_4_2 = e3
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REDUCE: (135), (174) imply:
% 200.22/33.03  | | | | |   (175)  op(e3, e3) = e2
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REDUCE: (33), (174) imply:
% 200.22/33.03  | | | | |   (176)  op(e3, e2) = e1
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REDUCE: (30), (174) imply:
% 200.22/33.03  | | | | |   (177)  op(e2, e2) = e3
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | BETA: splitting (90) gives:
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | Case 1:
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | |   (178)   ~ (all_4_2 = e3)
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | REF_CLOSE: (8), (30), (177), (178) are inconsistent by sub-proof
% 200.22/33.03  | | | | | |            #211.
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | Case 2:
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | GROUND_INST: instantiating (8) with all_52_9, e1, e2, e3,
% 200.22/33.03  | | | | | |              simplifying with (106), (176) gives:
% 200.22/33.03  | | | | | |   (179)  all_52_9 = e1
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | GROUND_INST: instantiating (8) with all_6_2, e2, e3, e3, simplifying
% 200.22/33.03  | | | | | |              with (92), (175) gives:
% 200.22/33.03  | | | | | |   (180)  all_6_2 = e2
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | REDUCE: (150), (179) imply:
% 200.22/33.03  | | | | | |   (181)   ~ (all_14_1 = e1)
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | SIMP: (181) implies:
% 200.22/33.03  | | | | | |   (182)   ~ (all_14_1 = e1)
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | REDUCE: (151), (180) imply:
% 200.22/33.03  | | | | | |   (183)   ~ (all_14_1 = e2)
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | | REF_CLOSE: (8), (98), (110), (146), (149), (153), (155), (182),
% 200.22/33.03  | | | | | |            (183) are inconsistent by sub-proof #611.
% 200.22/33.03  | | | | | | 
% 200.22/33.03  | | | | | End of split
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | Case 2:
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | |   (184)  all_58_5 = e3 | all_58_10 = e3
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | | REF_CLOSE: (44), (51), (86), (141), (184) are inconsistent by
% 200.22/33.03  | | | | |            sub-proof #214.
% 200.22/33.03  | | | | | 
% 200.22/33.03  | | | | End of split
% 200.22/33.03  | | | | 
% 200.22/33.03  | | | End of split
% 200.22/33.03  | | | 
% 200.22/33.03  | | End of split
% 200.22/33.03  | | 
% 200.22/33.03  | Case 2:
% 200.22/33.03  | | 
% 200.22/33.03  | |   (185)   ~ (all_56_15 = e3)
% 200.22/33.03  | | 
% 200.22/33.03  | | REDUCE: (42), (185) imply:
% 200.22/33.03  | |   (186)   ~ (all_14_2 = e3)
% 200.22/33.03  | | 
% 200.22/33.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 200.22/33.03  | |            (15), (16), (18), (20), (22), (23), (24), (25), (26), (28), (29),
% 200.22/33.03  | |            (30), (32), (33), (34), (35), (37), (38), (39), (40), (41), (43),
% 200.22/33.03  | |            (44), (45), (46), (47), (48), (49), (51), (52), (55), (56), (57),
% 200.22/33.03  | |            (58), (59), (61), (62), (64), (65), (67), (68), (69), (70), (71),
% 200.22/33.03  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (83),
% 200.22/33.03  | |            (84), (85), (86), (87), (89), (90), (91), (92), (93), (95), (99),
% 200.22/33.03  | |            (101), (102), (103), (104), (105), (106), (107), (108), (110),
% 200.22/33.03  | |            (111), (112), (113), (114), (116), (117), (118), (119), (120),
% 200.22/33.03  | |            (121), (122), (123), (124), (125), (126), (127), (132), (133),
% 200.22/33.03  | |            (134), (135), (186) are inconsistent by sub-proof #189.
% 200.22/33.03  | | 
% 200.22/33.03  | End of split
% 200.22/33.03  | 
% 200.22/33.03  End of proof
% 200.22/33.03  
% 200.22/33.03  Sub-proof #124 shows that the following formulas are inconsistent:
% 200.22/33.03  ----------------------------------------------------------------
% 200.22/33.03    (1)   ~ (all_52_15 = all_52_23)
% 200.22/33.03    (2)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 200.22/33.03    (3)  all_58_14 = all_52_23
% 200.22/33.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.03    (5)  op(all_52_7, all_52_7) = e0
% 200.22/33.03    (6)  all_58_1 = all_52_9
% 200.22/33.03    (7)   ~ (all_52_9 = all_52_13)
% 200.22/33.03    (8)  op(all_52_5, all_52_5) = e1
% 200.22/33.03    (9)   ~ (e3 = e0)
% 200.22/33.03    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.22/33.03    (11)   ~ (all_52_7 = all_52_15)
% 200.22/33.03    (12)   ~ (all_52_3 = all_52_19)
% 200.22/33.03    (13)   ~ (all_52_3 = all_6_2)
% 200.22/33.03    (14)  all_58_0 = all_6_2
% 200.22/33.03    (15)  op(all_14_2, e0) = all_14_1
% 200.22/33.03    (16)  all_56_4 = all_52_3
% 200.22/33.03    (17)  all_58_13 = e3
% 200.22/33.03    (18)  op(all_52_19, all_52_19) = all_52_18
% 200.22/33.03    (19)   ~ (all_52_27 = all_52_29)
% 200.22/33.03    (20)  op(all_10_2, all_10_2) = all_52_20
% 200.22/33.03    (21)  all_58_9 = all_52_25
% 200.22/33.03    (22)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.22/33.03    (23)  all_52_15 = e3
% 200.22/33.03    (24)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.22/33.03    (25)  op(e2, e2) = all_4_2
% 200.22/33.03    (26)  all_58_11 = all_52_29
% 200.22/33.03    (27)   ~ (all_52_9 = all_52_15)
% 200.22/33.03    (28)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.22/33.03    (29)   ~ (all_52_3 = all_52_27)
% 200.22/33.03    (30)  op(all_10_2, e1) = all_10_1
% 200.22/33.03    (31)   ~ (all_52_7 = all_6_2)
% 200.22/33.03    (32)  op(e0, e0) = all_14_2
% 200.22/33.03    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.03    (34)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.22/33.03    (35)  op(e1, e0) = all_52_29
% 200.22/33.03    (36)  all_56_11 = all_52_29
% 200.22/33.03    (37)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.22/33.03    (38)  all_56_9 = all_52_13
% 200.22/33.03    (39)   ~ (e2 = e1)
% 200.22/33.03    (40)   ~ (all_52_13 = all_10_2)
% 200.22/33.03    (41)   ~ (all_6_0 = e1)
% 200.22/33.03    (42)  all_58_10 = all_52_27
% 200.22/33.03    (43)  op(all_52_9, all_52_9) = all_52_8
% 200.22/33.03    (44)   ~ (all_52_19 = all_52_23)
% 200.22/33.03    (45)   ~ (all_52_29 = all_10_2)
% 200.22/33.03    (46)  all_58_7 = all_52_13
% 200.22/33.03    (47)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.22/33.03    (48)  op(all_6_2, all_6_2) = e3
% 200.22/33.03    (49)   ~ (all_52_5 = all_52_7)
% 200.22/33.03    (50)  all_58_12 = all_52_7
% 200.22/33.03    (51)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.03    (52)   ~ (all_52_7 = all_14_2)
% 200.22/33.03    (53)  all_58_2 = all_52_3
% 200.22/33.03    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.03    (55)  op(e3, all_6_1) = all_6_0
% 200.22/33.03    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.22/33.03    (57)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.22/33.03    (58)   ~ (e2 = e0)
% 200.22/33.03    (59)  op(all_52_3, all_52_3) = e2
% 200.22/33.03    (60)   ~ (all_52_5 = all_52_29)
% 200.22/33.03    (61)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.22/33.03    (62)   ~ (all_52_15 = all_14_2)
% 200.22/33.03    (63)   ~ (all_52_19 = all_52_27)
% 200.22/33.03    (64)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.22/33.03    (65)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.22/33.03    (66)   ~ (all_6_0 = e2)
% 200.22/33.03    (67)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.22/33.03    (68)   ~ (all_52_13 = all_4_2)
% 200.22/33.03    (69)  op(e3, e1) = all_52_17
% 200.22/33.03    (70)   ~ (all_52_9 = all_52_25)
% 200.22/33.03    (71)  all_58_15 = all_14_2
% 200.22/33.03    (72)   ~ (all_52_19 = all_10_2)
% 200.22/33.03    (73)  all_58_8 = all_10_2
% 200.22/33.03    (74)   ~ (all_52_5 = all_10_2)
% 200.22/33.03    (75)  op(all_52_29, all_52_29) = all_52_28
% 200.22/33.03    (76)  all_56_12 = all_52_7
% 200.22/33.03    (77)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.22/33.03    (78)   ~ (all_52_25 = all_6_2)
% 200.22/33.03    (79)   ~ (all_52_9 = all_4_2)
% 200.22/33.03    (80)   ~ (all_52_5 = all_6_2)
% 200.22/33.03    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 200.22/33.03    (82)   ~ (all_52_9 = all_6_2)
% 200.22/33.03    (83)   ~ (all_52_13 = all_52_15)
% 200.22/33.03    (84)  op(e3, e3) = all_6_2
% 200.22/33.03    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.22/33.03    (86)   ~ (all_52_27 = all_14_2)
% 200.22/33.03    (87)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.22/33.03    (88)   ~ (all_52_3 = all_52_7)
% 200.22/33.03    (89)  op(all_14_2, all_14_2) = all_52_30
% 200.22/33.03    (90)  all_58_5 = all_52_19
% 200.22/33.03    (91)  all_56_1 = all_52_9
% 200.22/33.03    (92)   ~ (all_52_15 = all_4_2)
% 200.22/33.03    (93)  all_58_6 = all_52_5
% 200.22/33.03    (94)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.22/33.03    (95)   ~ (all_52_17 = all_6_2)
% 200.22/33.03    (96)   ~ (e1 = e0)
% 200.22/33.03    (97)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.22/33.03    (98)   ~ (all_52_9 = all_52_17)
% 200.22/33.03    (99)  all_56_10 = all_10_2
% 200.22/33.03    (100)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.03    (101)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.22/33.03    (102)  op(all_52_13, all_52_13) = all_52_12
% 200.22/33.03    (103)  op(e1, e1) = all_10_2
% 200.22/33.03    (104)   ~ (all_52_23 = all_10_2)
% 200.22/33.03    (105)  all_58_3 = all_4_2
% 200.22/33.03    (106)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.22/33.03    (107)   ~ (all_52_3 = all_4_2)
% 200.22/33.03    (108)  op(all_6_2, e3) = all_6_1
% 200.22/33.03    (109)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.22/33.03    (110)   ~ (all_52_13 = all_52_29)
% 200.22/33.03    (111)  all_58_4 = all_52_17
% 200.22/33.03    (112)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.22/33.03  
% 200.22/33.03  Begin of proof
% 200.22/33.03  | 
% 200.22/33.03  | REDUCE: (11), (23) imply:
% 200.22/33.03  |   (113)   ~ (all_52_7 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | REDUCE: (23), (27) imply:
% 200.22/33.03  |   (114)   ~ (all_52_9 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | REDUCE: (23), (83) imply:
% 200.22/33.03  |   (115)   ~ (all_52_13 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | REDUCE: (1), (23) imply:
% 200.22/33.03  |   (116)   ~ (all_52_23 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | SIMP: (116) implies:
% 200.22/33.03  |   (117)   ~ (all_52_23 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | REDUCE: (23), (62) imply:
% 200.22/33.03  |   (118)   ~ (all_14_2 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | SIMP: (118) implies:
% 200.22/33.03  |   (119)   ~ (all_14_2 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | REDUCE: (23), (92) imply:
% 200.22/33.03  |   (120)   ~ (all_4_2 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | SIMP: (120) implies:
% 200.22/33.03  |   (121)   ~ (all_4_2 = e3)
% 200.22/33.03  | 
% 200.22/33.03  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 200.22/33.03  |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 200.22/33.03  |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 200.22/33.03  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 200.22/33.03  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 200.22/33.03  |            (61), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 200.22/33.03  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (84),
% 200.22/33.03  |            (85), (86), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 200.22/33.03  |            (97), (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 200.22/33.03  |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 200.22/33.03  |            (117), (119), (121) are inconsistent by sub-proof #581.
% 200.22/33.03  | 
% 200.22/33.03  End of proof
% 200.22/33.03  
% 200.22/33.03  Sub-proof #125 shows that the following formulas are inconsistent:
% 200.22/33.03  ----------------------------------------------------------------
% 200.22/33.03    (1)   ~ (all_52_15 = all_52_23)
% 200.22/33.03    (2)   ~ (all_52_25 = all_52_27)
% 200.22/33.03    (3)  all_58_14 = all_52_23
% 200.22/33.03    (4)   ~ (e3 = e1)
% 200.22/33.03    (5)   ~ (all_52_17 = all_4_0)
% 200.22/33.03    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.22/33.03    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.03    (8)   ~ (all_52_5 = all_52_13)
% 200.22/33.03    (9)  all_58_1 = all_52_9
% 200.22/33.03    (10)   ~ (all_52_9 = all_52_13)
% 200.22/33.03    (11)   ~ (e3 = e0)
% 200.22/33.03    (12)  op(e2, e3) = all_52_3
% 200.22/33.03    (13)   ~ (all_52_23 = all_4_0)
% 200.22/33.03    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.22/33.03    (15)   ~ (all_52_7 = all_52_15)
% 200.22/33.03    (16)   ~ (all_52_3 = all_52_19)
% 200.22/33.03    (17)  op(all_52_7, all_52_7) = all_52_6
% 200.22/33.03    (18)   ~ (all_52_17 = all_52_25)
% 200.22/33.03    (19)  all_16_1 = all_10_1
% 200.22/33.03    (20)   ~ (all_52_3 = all_6_2)
% 200.22/33.03    (21)  all_58_0 = all_6_2
% 200.22/33.03    (22)  op(all_14_2, e0) = all_14_1
% 200.22/33.03    (23)  all_56_4 = all_52_3
% 200.22/33.03    (24)   ~ (all_52_17 = all_10_2)
% 200.22/33.03    (25)  all_26_1 = all_10_1
% 200.22/33.03    (26)  op(e3, e0) = all_52_25
% 200.22/33.03    (27)  all_26_2 = all_10_2
% 200.22/33.03    (28)  op(e0, all_14_1) = all_14_0
% 200.22/33.03    (29)  op(all_52_5, all_52_5) = all_52_4
% 200.22/33.03    (30)  op(all_52_19, all_52_19) = all_52_18
% 200.22/33.03    (31)   ~ (all_52_27 = all_52_29)
% 200.22/33.03    (32)  all_58_13 = all_52_15
% 200.22/33.03    (33)  op(all_10_2, all_10_2) = all_52_20
% 200.22/33.03    (34)  all_58_9 = all_52_25
% 200.22/33.03    (35)   ~ (all_6_1 = e1)
% 200.22/33.03    (36)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.22/33.03    (37)   ~ (all_52_29 = all_14_2)
% 200.22/33.03    (38)  op(all_52_27, all_52_27) = all_52_26
% 200.22/33.03    (39)  op(e1, e3) = all_52_5
% 200.22/33.03    (40)  op(e2, e2) = all_4_2
% 200.22/33.03    (41)   ~ (all_52_3 = all_52_5)
% 200.22/33.03    (42)  op(all_4_2, e2) = e1
% 200.22/33.03    (43)  all_58_11 = all_52_29
% 200.22/33.03    (44)  all_56_5 = all_4_2
% 200.22/33.03    (45)   ~ (all_52_25 = all_14_2)
% 200.22/33.03    (46)   ~ (all_52_9 = all_52_15)
% 200.22/33.03    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.22/33.03    (48)   ~ (all_52_3 = all_52_27)
% 200.22/33.03    (49)  op(all_10_2, e1) = all_10_1
% 200.22/33.03    (50)   ~ (all_10_2 = all_4_0)
% 200.22/33.03    (51)  op(all_6_2, all_6_2) = all_52_0
% 200.22/33.03    (52)   ~ (all_52_7 = all_6_2)
% 200.22/33.03    (53)  op(e0, e0) = all_14_2
% 200.22/33.03    (54)  op(e0, e1) = all_52_23
% 200.22/33.03    (55)  all_56_15 = all_14_2
% 200.22/33.03    (56)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.03    (57)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.22/33.03    (58)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.22/33.03    (59)  op(e1, e0) = all_52_29
% 200.22/33.03    (60)   ~ (all_58_15 = e0)
% 200.22/33.03    (61)  all_56_11 = all_52_29
% 200.22/33.03    (62)   ~ (all_4_0 = e3)
% 200.22/33.03    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.22/33.03    (64)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.22/33.03    (65)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.22/33.03    (66)  all_56_9 = all_52_13
% 200.22/33.03    (67)   ~ (e2 = e1)
% 200.22/33.03    (68)   ~ (all_52_13 = all_10_2)
% 200.22/33.03    (69)   ~ (all_6_0 = e1)
% 200.22/33.03    (70)  all_58_10 = all_52_27
% 200.22/33.03    (71)  all_56_8 = all_52_5
% 200.22/33.03    (72)  op(all_52_9, all_52_9) = all_52_8
% 200.22/33.03    (73)  op(all_52_15, all_52_15) = all_52_14
% 200.22/33.03    (74)   ~ (all_52_19 = all_52_23)
% 200.22/33.03    (75)   ~ (all_52_25 = all_52_29)
% 200.22/33.03    (76)  all_16_2 = all_10_2
% 200.22/33.03    (77)   ~ (all_52_29 = all_10_2)
% 200.22/33.03    (78)  all_58_7 = all_52_13
% 200.22/33.03    (79)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.22/33.03    (80)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.22/33.03    (81)   ~ (all_52_5 = all_52_7)
% 200.22/33.03    (82)  all_58_12 = all_52_7
% 200.22/33.03    (83)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.03    (84)   ~ (all_52_7 = all_14_2)
% 200.22/33.03    (85)  all_58_2 = all_52_3
% 200.22/33.03    (86)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 200.22/33.03    (87)  all_56_2 = all_52_17
% 200.22/33.03    (88)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.22/33.03    (89)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.03    (90)  op(e3, all_6_1) = all_6_0
% 200.22/33.03    (91)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.22/33.03    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.22/33.03    (93)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.22/33.03    (94)   ~ (e2 = e0)
% 200.22/33.03    (95)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.22/33.03    (96)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.22/33.03    (97)   ~ (all_52_5 = all_52_29)
% 200.22/33.03    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.22/33.03    (99)  all_56_6 = all_52_19
% 200.22/33.03    (100)   ~ (all_52_15 = all_14_2)
% 200.22/33.03    (101)   ~ (all_52_19 = all_52_27)
% 200.22/33.03    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.22/33.03    (103)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.22/33.03    (104)   ~ (all_6_0 = e2)
% 200.22/33.03    (105)   ~ (all_52_13 = all_4_2)
% 200.22/33.03    (106)  op(e3, e1) = all_52_17
% 200.22/33.03    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.22/33.03    (108)  op(e0, e3) = all_52_7
% 200.22/33.03    (109)  op(e1, e2) = all_52_13
% 200.22/33.03    (110)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.03    (111)   ~ (all_52_9 = all_52_25)
% 200.22/33.03    (112)  all_58_15 = all_14_2
% 200.22/33.03    (113)   ~ (all_52_19 = all_10_2)
% 200.22/33.03    (114)  op(all_52_23, all_52_23) = all_52_22
% 200.22/33.03    (115)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.22/33.03    (116)  all_58_8 = all_10_2
% 200.22/33.03    (117)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.22/33.03    (118)   ~ (all_52_5 = all_10_2)
% 200.22/33.03    (119)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 200.22/33.03    (120)  op(all_52_29, all_52_29) = all_52_28
% 200.22/33.03    (121)   ~ (all_52_23 = all_14_2)
% 200.22/33.03    (122)  all_56_12 = all_52_7
% 200.22/33.03    (123)  op(all_52_17, all_52_17) = all_52_16
% 200.22/33.03    (124)  all_58_5 = all_4_0
% 200.22/33.03    (125)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.22/33.03    (126)   ~ (all_52_25 = all_6_2)
% 200.22/33.03    (127)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.22/33.03    (128)   ~ (all_52_9 = all_4_2)
% 200.22/33.03    (129)   ~ (all_52_5 = all_6_2)
% 200.22/33.03    (130)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.22/33.03    (131)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 200.22/33.03    (132)   ~ (all_52_9 = all_6_2)
% 200.22/33.03    (133)   ~ (all_52_13 = all_52_15)
% 200.22/33.03    (134)  op(e1, all_10_1) = e2
% 200.22/33.03    (135)  all_56_0 = all_6_2
% 200.22/33.03    (136)  op(e3, e3) = all_6_2
% 200.22/33.03    (137)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.22/33.03    (138)   ~ (all_52_27 = all_14_2)
% 200.22/33.03    (139)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.22/33.03    (140)  all_56_14 = all_52_23
% 200.22/33.03    (141)  op(all_4_2, all_4_2) = all_52_10
% 200.22/33.03    (142)  all_56_3 = all_52_25
% 200.22/33.03    (143)   ~ (all_52_3 = all_52_7)
% 200.22/33.03    (144)  op(all_14_2, all_14_2) = all_52_30
% 200.22/33.03    (145)  all_58_5 = all_52_19
% 200.22/33.03    (146)  all_56_1 = all_52_9
% 200.22/33.03    (147)   ~ (all_52_15 = all_4_2)
% 200.22/33.03    (148)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.22/33.03           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.22/33.03           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.22/33.03           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.22/33.03    (149)   ~ (all_52_27 = all_4_2)
% 200.22/33.03    (150)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 200.22/33.03             all_58_13 = e0 | all_58_14 = e0)
% 200.22/33.03    (151)  all_58_6 = all_52_5
% 200.22/33.03    (152)   ~ (all_4_0 = all_4_2)
% 200.22/33.03    (153)  op(e3, e2) = all_52_9
% 200.22/33.03    (154)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.22/33.03    (155)   ~ (all_52_17 = all_6_2)
% 200.22/33.03    (156)   ~ (e1 = e0)
% 200.22/33.03    (157)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 200.22/33.03    (158)   ~ (e3 = e2)
% 200.22/33.03    (159)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.22/33.03    (160)   ~ (all_52_9 = all_52_17)
% 200.22/33.03    (161)  all_56_10 = all_10_2
% 200.22/33.03    (162)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.03    (163)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.22/33.03    (164)   ~ (all_52_3 = all_4_0)
% 200.22/33.03    (165)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.22/33.03    (166)  op(all_52_13, all_52_13) = all_52_12
% 200.22/33.03    (167)   ~ (all_6_1 = e2)
% 200.22/33.03    (168)  op(e1, e1) = all_10_2
% 200.22/33.03    (169)   ~ (all_52_23 = all_10_2)
% 200.22/33.03    (170)   ~ (all_52_7 = all_52_23)
% 200.22/33.03    (171)   ~ (all_52_17 = all_52_19)
% 200.22/33.03    (172)  all_58_3 = all_4_2
% 200.22/33.03    (173)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.22/33.03    (174)  all_56_13 = all_52_15
% 200.22/33.03    (175)   ~ (all_52_3 = all_4_2)
% 200.22/33.03    (176)   ~ (all_52_19 = all_4_2)
% 200.22/33.03    (177)   ~ (all_52_17 = all_52_23)
% 200.22/33.03    (178)  op(all_6_2, e3) = all_6_1
% 200.22/33.03    (179)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.22/33.03    (180)   ~ (all_52_13 = all_52_29)
% 200.22/33.03    (181)  all_58_4 = all_52_17
% 200.22/33.03    (182)   ~ (all_14_0 = e2)
% 200.22/33.03    (183)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.22/33.03    (184)  op(all_52_25, all_52_25) = all_52_24
% 200.22/33.03  
% 200.22/33.03  Begin of proof
% 200.22/33.03  | 
% 200.22/33.03  | ALPHA: (150) implies:
% 200.22/33.03  |   (185)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.22/33.04  |   (186)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.22/33.04  | 
% 200.22/33.04  | REDUCE: (60), (112) imply:
% 200.22/33.04  |   (187)   ~ (all_14_2 = e0)
% 200.22/33.04  | 
% 200.22/33.04  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 200.22/33.04  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 200.22/33.04  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 200.22/33.04  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 200.22/33.04  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 200.22/33.04  |            (57), (58), (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 200.22/33.04  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 200.22/33.04  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 200.22/33.04  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 200.22/33.04  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 200.22/33.04  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 200.22/33.04  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 200.22/33.04  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 200.22/33.04  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 200.22/33.04  |            (147), (148), (149), (151), (152), (153), (154), (155), (156),
% 200.22/33.04  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 200.22/33.04  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 200.22/33.04  |            (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 200.22/33.04  |            (184), (185), (186), (187) are inconsistent by sub-proof #126.
% 200.22/33.04  | 
% 200.22/33.04  End of proof
% 200.22/33.04  
% 200.22/33.04  Sub-proof #126 shows that the following formulas are inconsistent:
% 200.22/33.04  ----------------------------------------------------------------
% 200.22/33.04    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.22/33.04    (2)   ~ (all_52_15 = all_52_23)
% 200.22/33.04    (3)   ~ (all_52_25 = all_52_27)
% 200.22/33.04    (4)  all_58_14 = all_52_23
% 200.22/33.04    (5)   ~ (e3 = e1)
% 200.22/33.04    (6)   ~ (all_52_17 = all_4_0)
% 200.22/33.04    (7)  op(all_52_3, all_52_3) = all_52_2
% 200.22/33.04    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.04    (9)   ~ (all_52_5 = all_52_13)
% 200.22/33.04    (10)  all_58_1 = all_52_9
% 200.22/33.04    (11)   ~ (all_52_9 = all_52_13)
% 200.22/33.04    (12)   ~ (e3 = e0)
% 200.22/33.04    (13)  op(e2, e3) = all_52_3
% 200.22/33.04    (14)   ~ (all_52_23 = all_4_0)
% 200.22/33.04    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.22/33.04    (16)   ~ (all_52_7 = all_52_15)
% 200.22/33.04    (17)   ~ (all_52_3 = all_52_19)
% 200.22/33.04    (18)  op(all_52_7, all_52_7) = all_52_6
% 200.22/33.04    (19)   ~ (all_52_17 = all_52_25)
% 200.22/33.04    (20)  all_16_1 = all_10_1
% 200.22/33.04    (21)   ~ (all_52_3 = all_6_2)
% 200.22/33.04    (22)  all_58_0 = all_6_2
% 200.22/33.04    (23)  op(all_14_2, e0) = all_14_1
% 200.22/33.04    (24)  all_56_4 = all_52_3
% 200.22/33.04    (25)   ~ (all_52_17 = all_10_2)
% 200.22/33.04    (26)  all_26_1 = all_10_1
% 200.22/33.04    (27)  op(e3, e0) = all_52_25
% 200.22/33.04    (28)  all_26_2 = all_10_2
% 200.22/33.04    (29)  op(e0, all_14_1) = all_14_0
% 200.22/33.04    (30)  op(all_52_5, all_52_5) = all_52_4
% 200.22/33.04    (31)  op(all_52_19, all_52_19) = all_52_18
% 200.22/33.04    (32)   ~ (all_52_27 = all_52_29)
% 200.22/33.04    (33)  all_58_13 = all_52_15
% 200.22/33.04    (34)  op(all_10_2, all_10_2) = all_52_20
% 200.22/33.04    (35)  all_58_9 = all_52_25
% 200.22/33.04    (36)   ~ (all_6_1 = e1)
% 200.22/33.04    (37)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.22/33.04    (38)   ~ (all_52_29 = all_14_2)
% 200.22/33.04    (39)  op(all_52_27, all_52_27) = all_52_26
% 200.22/33.04    (40)  op(e1, e3) = all_52_5
% 200.22/33.04    (41)  op(e2, e2) = all_4_2
% 200.22/33.04    (42)   ~ (all_52_3 = all_52_5)
% 200.22/33.04    (43)  op(all_4_2, e2) = e1
% 200.22/33.04    (44)  all_58_11 = all_52_29
% 200.22/33.04    (45)  all_56_5 = all_4_2
% 200.22/33.04    (46)   ~ (all_52_25 = all_14_2)
% 200.22/33.04    (47)   ~ (all_52_9 = all_52_15)
% 200.22/33.04    (48)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.22/33.04    (49)   ~ (all_52_3 = all_52_27)
% 200.22/33.04    (50)  op(all_10_2, e1) = all_10_1
% 200.22/33.04    (51)   ~ (all_10_2 = all_4_0)
% 200.22/33.04    (52)  op(all_6_2, all_6_2) = all_52_0
% 200.22/33.04    (53)   ~ (all_52_7 = all_6_2)
% 200.22/33.04    (54)  op(e0, e0) = all_14_2
% 200.22/33.04    (55)  op(e0, e1) = all_52_23
% 200.22/33.04    (56)  all_56_15 = all_14_2
% 200.22/33.04    (57)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.04    (58)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.22/33.04    (59)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.22/33.04    (60)  op(e1, e0) = all_52_29
% 200.22/33.04    (61)  all_56_11 = all_52_29
% 200.22/33.04    (62)   ~ (all_4_0 = e3)
% 200.22/33.04    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.22/33.04    (64)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.22/33.04    (65)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.22/33.04    (66)  all_56_9 = all_52_13
% 200.22/33.04    (67)   ~ (e2 = e1)
% 200.22/33.04    (68)   ~ (all_52_13 = all_10_2)
% 200.22/33.04    (69)   ~ (all_6_0 = e1)
% 200.22/33.04    (70)  all_58_10 = all_52_27
% 200.22/33.04    (71)  all_56_8 = all_52_5
% 200.22/33.04    (72)  op(all_52_9, all_52_9) = all_52_8
% 200.22/33.04    (73)  op(all_52_15, all_52_15) = all_52_14
% 200.22/33.04    (74)   ~ (all_52_19 = all_52_23)
% 200.22/33.04    (75)   ~ (all_52_25 = all_52_29)
% 200.22/33.04    (76)  all_16_2 = all_10_2
% 200.22/33.04    (77)   ~ (all_52_29 = all_10_2)
% 200.22/33.04    (78)  all_58_7 = all_52_13
% 200.22/33.04    (79)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.22/33.04    (80)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.22/33.04    (81)   ~ (all_52_5 = all_52_7)
% 200.22/33.04    (82)  all_58_12 = all_52_7
% 200.22/33.04    (83)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.04    (84)   ~ (all_52_7 = all_14_2)
% 200.22/33.04    (85)   ~ (all_14_2 = e0)
% 200.22/33.04    (86)  all_58_2 = all_52_3
% 200.22/33.04    (87)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 200.22/33.04    (88)  all_56_2 = all_52_17
% 200.22/33.04    (89)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.22/33.04    (90)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.04    (91)  op(e3, all_6_1) = all_6_0
% 200.22/33.04    (92)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.22/33.04    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.22/33.04    (94)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.22/33.04    (95)   ~ (e2 = e0)
% 200.22/33.04    (96)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.22/33.04    (97)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.22/33.04    (98)   ~ (all_52_5 = all_52_29)
% 200.22/33.04    (99)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.22/33.04    (100)  all_56_6 = all_52_19
% 200.22/33.04    (101)   ~ (all_52_15 = all_14_2)
% 200.22/33.04    (102)   ~ (all_52_19 = all_52_27)
% 200.22/33.04    (103)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.22/33.04    (104)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.22/33.04    (105)   ~ (all_6_0 = e2)
% 200.22/33.04    (106)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.22/33.04    (107)   ~ (all_52_13 = all_4_2)
% 200.22/33.04    (108)  op(e3, e1) = all_52_17
% 200.22/33.04    (109)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.22/33.04    (110)  op(e0, e3) = all_52_7
% 200.22/33.04    (111)  op(e1, e2) = all_52_13
% 200.22/33.04    (112)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.04    (113)   ~ (all_52_9 = all_52_25)
% 200.22/33.04    (114)  all_58_15 = all_14_2
% 200.22/33.04    (115)   ~ (all_52_19 = all_10_2)
% 200.22/33.04    (116)  op(all_52_23, all_52_23) = all_52_22
% 200.22/33.04    (117)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.22/33.04    (118)  all_58_8 = all_10_2
% 200.22/33.04    (119)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.22/33.04    (120)   ~ (all_52_5 = all_10_2)
% 200.22/33.04    (121)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 200.22/33.04    (122)  op(all_52_29, all_52_29) = all_52_28
% 200.22/33.04    (123)   ~ (all_52_23 = all_14_2)
% 200.22/33.04    (124)  all_56_12 = all_52_7
% 200.22/33.04    (125)  op(all_52_17, all_52_17) = all_52_16
% 200.22/33.04    (126)  all_58_5 = all_4_0
% 200.22/33.04    (127)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.22/33.04    (128)   ~ (all_52_25 = all_6_2)
% 200.22/33.04    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.22/33.04    (130)   ~ (all_52_9 = all_4_2)
% 200.22/33.04    (131)   ~ (all_52_5 = all_6_2)
% 200.22/33.04    (132)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.22/33.04    (133)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 200.22/33.04    (134)   ~ (all_52_9 = all_6_2)
% 200.22/33.04    (135)   ~ (all_52_13 = all_52_15)
% 200.22/33.04    (136)  op(e1, all_10_1) = e2
% 200.22/33.04    (137)  all_56_0 = all_6_2
% 200.22/33.04    (138)  op(e3, e3) = all_6_2
% 200.22/33.04    (139)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.22/33.04    (140)   ~ (all_52_27 = all_14_2)
% 200.22/33.04    (141)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.22/33.04    (142)  all_56_14 = all_52_23
% 200.22/33.04    (143)  op(all_4_2, all_4_2) = all_52_10
% 200.22/33.04    (144)  all_56_3 = all_52_25
% 200.22/33.04    (145)   ~ (all_52_3 = all_52_7)
% 200.22/33.04    (146)  op(all_14_2, all_14_2) = all_52_30
% 200.22/33.04    (147)  all_58_5 = all_52_19
% 200.22/33.04    (148)  all_56_1 = all_52_9
% 200.22/33.04    (149)   ~ (all_52_15 = all_4_2)
% 200.22/33.04    (150)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.22/33.04           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.22/33.04           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.22/33.04           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.22/33.04    (151)   ~ (all_52_27 = all_4_2)
% 200.22/33.04    (152)  all_58_6 = all_52_5
% 200.22/33.04    (153)   ~ (all_4_0 = all_4_2)
% 200.22/33.04    (154)  op(e3, e2) = all_52_9
% 200.22/33.04    (155)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.22/33.04    (156)   ~ (all_52_17 = all_6_2)
% 200.22/33.04    (157)   ~ (e1 = e0)
% 200.22/33.04    (158)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 200.22/33.04    (159)   ~ (e3 = e2)
% 200.22/33.04    (160)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.22/33.04    (161)   ~ (all_52_9 = all_52_17)
% 200.22/33.04    (162)  all_56_10 = all_10_2
% 200.22/33.04    (163)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.04    (164)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.22/33.04    (165)   ~ (all_52_3 = all_4_0)
% 200.22/33.04    (166)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.22/33.04    (167)  op(all_52_13, all_52_13) = all_52_12
% 200.22/33.04    (168)   ~ (all_6_1 = e2)
% 200.22/33.04    (169)  op(e1, e1) = all_10_2
% 200.22/33.04    (170)   ~ (all_52_23 = all_10_2)
% 200.22/33.04    (171)   ~ (all_52_7 = all_52_23)
% 200.22/33.04    (172)   ~ (all_52_17 = all_52_19)
% 200.22/33.04    (173)  all_58_3 = all_4_2
% 200.22/33.04    (174)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.22/33.04    (175)  all_56_13 = all_52_15
% 200.22/33.04    (176)   ~ (all_52_3 = all_4_2)
% 200.22/33.04    (177)   ~ (all_52_19 = all_4_2)
% 200.22/33.04    (178)   ~ (all_52_17 = all_52_23)
% 200.22/33.04    (179)  op(all_6_2, e3) = all_6_1
% 200.22/33.04    (180)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.22/33.04    (181)   ~ (all_52_13 = all_52_29)
% 200.22/33.04    (182)  all_58_4 = all_52_17
% 200.22/33.04    (183)   ~ (all_14_0 = e2)
% 200.22/33.04    (184)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.22/33.04    (185)  op(all_52_25, all_52_25) = all_52_24
% 200.22/33.04  
% 200.22/33.04  Begin of proof
% 200.22/33.04  | 
% 200.22/33.04  | BETA: splitting (150) gives:
% 200.22/33.04  | 
% 200.22/33.04  | Case 1:
% 200.22/33.04  | | 
% 200.22/33.04  | |   (186)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.22/33.04  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 200.22/33.04  | | 
% 200.22/33.04  | | BETA: splitting (186) gives:
% 200.22/33.04  | | 
% 200.22/33.04  | | Case 1:
% 200.22/33.04  | | | 
% 200.22/33.04  | | |   (187)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.22/33.04  | | | 
% 200.22/33.04  | | | ALPHA: (187) implies:
% 200.22/33.04  | | |   (188)  all_52_6 = e0
% 200.22/33.04  | | |   (189)  all_52_4 = e1
% 200.22/33.04  | | |   (190)  all_52_2 = e2
% 200.22/33.04  | | |   (191)  all_52_0 = e3
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REDUCE: (7), (190) imply:
% 200.22/33.04  | | |   (192)  op(all_52_3, all_52_3) = e2
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REDUCE: (30), (189) imply:
% 200.22/33.04  | | |   (193)  op(all_52_5, all_52_5) = e1
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REDUCE: (18), (188) imply:
% 200.22/33.04  | | |   (194)  op(all_52_7, all_52_7) = e0
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REDUCE: (52), (191) imply:
% 200.22/33.04  | | |   (195)  op(all_6_2, all_6_2) = e3
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (12), (15), (16), (17),
% 200.22/33.04  | | |            (19), (20), (21), (22), (23), (24), (26), (28), (29), (31),
% 200.22/33.04  | | |            (32), (33), (35), (37), (41), (42), (44), (46), (48), (49),
% 200.22/33.04  | | |            (50), (53), (54), (55), (56), (57), (59), (60), (63), (64),
% 200.22/33.04  | | |            (65), (66), (67), (68), (69), (70), (71), (74), (76), (77),
% 200.22/33.04  | | |            (78), (80), (81), (82), (83), (84), (85), (86), (87), (88),
% 200.22/33.04  | | |            (90), (91), (92), (93), (94), (95), (97), (99), (100), (101),
% 200.22/33.04  | | |            (102), (104), (105), (106), (107), (108), (110), (111), (113),
% 200.22/33.04  | | |            (114), (115), (117), (118), (119), (120), (121), (122), (124),
% 200.22/33.04  | | |            (125), (128), (129), (131), (133), (135), (136), (138), (139),
% 200.22/33.04  | | |            (140), (141), (144), (145), (146), (147), (149), (151), (152),
% 200.22/33.04  | | |            (155), (156), (157), (158), (159), (161), (162), (163), (164),
% 200.22/33.04  | | |            (167), (169), (170), (171), (173), (175), (176), (179), (180),
% 200.22/33.04  | | |            (181), (182), (183), (184), (185), (192), (193), (194), (195)
% 200.22/33.04  | | |            are inconsistent by sub-proof #614.
% 200.22/33.04  | | | 
% 200.22/33.04  | | Case 2:
% 200.22/33.04  | | | 
% 200.22/33.04  | | |   (196)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14),
% 200.22/33.04  | | |            (15), (16), (18), (19), (21), (22), (23), (25), (27), (32),
% 200.22/33.04  | | |            (33), (34), (35), (36), (38), (39), (40), (41), (42), (43),
% 200.22/33.04  | | |            (44), (45), (46), (50), (51), (52), (53), (54), (56), (57),
% 200.22/33.04  | | |            (62), (63), (64), (67), (68), (69), (70), (71), (72), (73),
% 200.22/33.04  | | |            (77), (78), (81), (82), (83), (84), (86), (88), (89), (90),
% 200.22/33.04  | | |            (91), (96), (98), (101), (104), (105), (106), (107), (108),
% 200.22/33.04  | | |            (110), (112), (113), (114), (116), (117), (118), (119), (120),
% 200.22/33.04  | | |            (124), (125), (126), (128), (129), (131), (132), (134), (138),
% 200.22/33.04  | | |            (139), (140), (141), (143), (144), (145), (146), (148), (149),
% 200.22/33.04  | | |            (151), (152), (153), (154), (155), (156), (159), (160), (161),
% 200.22/33.04  | | |            (162), (163), (167), (168), (169), (170), (171), (173), (175),
% 200.22/33.04  | | |            (176), (178), (179), (182), (184), (185), (196) are
% 200.22/33.04  | | |            inconsistent by sub-proof #188.
% 200.22/33.04  | | | 
% 200.22/33.04  | | End of split
% 200.22/33.04  | | 
% 200.22/33.04  | Case 2:
% 200.22/33.04  | | 
% 200.22/33.04  | |   (197)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 200.22/33.04  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.22/33.04  | |            e0)
% 200.22/33.04  | | 
% 200.22/33.04  | | BETA: splitting (197) gives:
% 200.22/33.04  | | 
% 200.22/33.04  | | Case 1:
% 200.22/33.04  | | | 
% 200.22/33.04  | | |   (198)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REF_CLOSE: (2), (4), (7), (8), (10), (15), (18), (19), (21), (22), (23),
% 200.22/33.04  | | |            (25), (26), (27), (28), (33), (34), (35), (36), (40), (41),
% 200.22/33.04  | | |            (42), (43), (44), (45), (46), (47), (49), (50), (53), (56),
% 200.22/33.04  | | |            (57), (59), (62), (64), (66), (67), (68), (70), (71), (72),
% 200.22/33.04  | | |            (75), (78), (81), (82), (83), (86), (88), (89), (90), (91),
% 200.22/33.04  | | |            (96), (104), (105), (107), (108), (110), (112), (113), (114),
% 200.22/33.04  | | |            (115), (116), (117), (118), (119), (123), (124), (125), (126),
% 200.22/33.04  | | |            (129), (130), (131), (132), (134), (135), (138), (139), (140),
% 200.22/33.04  | | |            (141), (143), (144), (145), (146), (147), (149), (152), (153),
% 200.22/33.04  | | |            (154), (155), (156), (159), (161), (162), (163), (164), (165),
% 200.22/33.04  | | |            (167), (168), (171), (173), (176), (179), (182), (184), (185),
% 200.22/33.04  | | |            (198) are inconsistent by sub-proof #127.
% 200.22/33.04  | | | 
% 200.22/33.04  | | Case 2:
% 200.22/33.04  | | | 
% 200.22/33.04  | | |   (199)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (13), (15), (16),
% 200.22/33.04  | | |            (18), (19), (21), (22), (24), (25), (27), (30), (31), (32),
% 200.22/33.04  | | |            (33), (35), (36), (38), (39), (40), (41), (42), (44), (45),
% 200.22/33.04  | | |            (46), (47), (49), (50), (52), (53), (54), (56), (57), (58),
% 200.22/33.04  | | |            (61), (63), (64), (65), (69), (70), (71), (72), (73), (74),
% 200.22/33.04  | | |            (75), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 200.22/33.04  | | |            (86), (88), (90), (91), (92), (93), (94), (96), (98), (101),
% 200.22/33.04  | | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 200.22/33.04  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 200.22/33.04  | | |            (122), (123), (124), (125), (127), (128), (129), (130), (131),
% 200.22/33.04  | | |            (134), (135), (137), (138), (139), (140), (141), (142), (144),
% 200.22/33.04  | | |            (145), (146), (147), (148), (149), (151), (152), (155), (156),
% 200.22/33.04  | | |            (159), (160), (166), (167), (168), (169), (171), (172), (173),
% 200.22/33.04  | | |            (174), (175), (176), (177), (178), (179), (182), (185), (199)
% 200.22/33.04  | | |            are inconsistent by sub-proof #1008.
% 200.22/33.04  | | | 
% 200.22/33.04  | | End of split
% 200.22/33.04  | | 
% 200.22/33.04  | End of split
% 200.22/33.04  | 
% 200.22/33.04  End of proof
% 200.22/33.04  
% 200.22/33.04  Sub-proof #127 shows that the following formulas are inconsistent:
% 200.22/33.04  ----------------------------------------------------------------
% 200.22/33.04    (1)   ~ (all_52_15 = all_52_23)
% 200.22/33.04    (2)  all_58_14 = all_52_23
% 200.22/33.04    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.22/33.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.22/33.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.22/33.04    (5)  all_58_1 = all_52_9
% 200.22/33.04    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.22/33.04    (7)  op(all_52_7, all_52_7) = all_52_6
% 200.22/33.04    (8)   ~ (all_52_17 = all_52_25)
% 200.22/33.04    (9)   ~ (all_52_3 = all_6_2)
% 200.22/33.04    (10)  all_58_0 = all_6_2
% 200.22/33.04    (11)  op(all_14_2, e0) = all_14_1
% 200.22/33.04    (12)   ~ (all_52_17 = all_10_2)
% 200.22/33.04    (13)  all_26_1 = all_10_1
% 200.22/33.04    (14)  op(e3, e0) = all_52_25
% 200.22/33.04    (15)  all_26_2 = all_10_2
% 200.22/33.04    (16)  all_58_13 = all_52_15
% 200.22/33.04    (17)  op(all_10_2, all_10_2) = all_52_20
% 200.22/33.04    (18)  all_58_9 = all_52_25
% 200.22/33.04    (19)   ~ (all_6_1 = e1)
% 200.22/33.04    (20)  op(e1, e3) = all_52_5
% 200.22/33.04    (21)  op(e2, e2) = all_4_2
% 200.22/33.04    (22)   ~ (all_52_3 = all_52_5)
% 200.22/33.04    (23)  op(all_4_2, e2) = e1
% 200.22/33.04    (24)  all_58_11 = all_52_29
% 200.22/33.04    (25)  all_56_5 = all_4_2
% 200.22/33.04    (26)   ~ (all_52_25 = all_14_2)
% 200.22/33.04    (27)   ~ (all_52_9 = all_52_15)
% 200.22/33.04    (28)   ~ (all_52_3 = all_52_27)
% 200.22/33.04    (29)  op(all_10_2, e1) = all_10_1
% 200.22/33.04    (30)   ~ (all_52_7 = all_6_2)
% 200.22/33.04    (31)  all_56_15 = all_14_2
% 200.22/33.04    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.22/33.04    (33)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.22/33.04    (34)   ~ (all_4_0 = e3)
% 200.22/33.04    (35)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.22/33.04    (36)  all_56_9 = all_52_13
% 200.22/33.04    (37)   ~ (e2 = e1)
% 200.22/33.04    (38)   ~ (all_52_13 = all_10_2)
% 200.22/33.04    (39)  all_58_10 = all_52_27
% 200.22/33.04    (40)  all_56_8 = all_52_5
% 200.22/33.04    (41)  op(all_52_9, all_52_9) = all_52_8
% 200.22/33.04    (42)   ~ (all_52_25 = all_52_29)
% 200.22/33.04    (43)  all_58_7 = all_52_13
% 200.22/33.04    (44)   ~ (all_52_5 = all_52_7)
% 200.22/33.04    (45)  all_58_12 = all_52_7
% 200.22/33.04    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.04    (47)  all_58_2 = all_52_3
% 200.22/33.04    (48)  all_56_2 = all_52_17
% 200.22/33.04    (49)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.22/33.04    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.22/33.04    (51)  op(e3, all_6_1) = all_6_0
% 200.22/33.04    (52)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.22/33.04    (53)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.22/33.04    (54)   ~ (all_6_0 = e2)
% 200.22/33.04    (55)   ~ (all_52_13 = all_4_2)
% 200.22/33.04    (56)  op(e3, e1) = all_52_17
% 200.22/33.04    (57)  op(e0, e3) = all_52_7
% 200.22/33.04    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.22/33.04    (59)   ~ (all_52_9 = all_52_25)
% 200.22/33.04    (60)  all_58_15 = all_14_2
% 200.22/33.04    (61)   ~ (all_52_19 = all_10_2)
% 200.22/33.04    (62)  op(all_52_23, all_52_23) = all_52_22
% 200.22/33.04    (63)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.22/33.04    (64)  all_58_8 = all_10_2
% 200.22/33.04    (65)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.22/33.04    (66)   ~ (all_52_23 = all_14_2)
% 200.22/33.04    (67)  all_56_12 = all_52_7
% 200.22/33.04    (68)  op(all_52_17, all_52_17) = all_52_16
% 200.22/33.04    (69)  all_58_5 = all_4_0
% 200.22/33.04    (70)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.22/33.04    (71)   ~ (all_52_9 = all_4_2)
% 200.22/33.04    (72)   ~ (all_52_5 = all_6_2)
% 200.22/33.04    (73)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.22/33.04    (74)   ~ (all_52_9 = all_6_2)
% 200.22/33.04    (75)   ~ (all_52_13 = all_52_15)
% 200.22/33.04    (76)  op(e3, e3) = all_6_2
% 200.22/33.04    (77)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.22/33.04    (78)   ~ (all_52_27 = all_14_2)
% 200.22/33.04    (79)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.22/33.04    (80)  op(all_4_2, all_4_2) = all_52_10
% 200.22/33.04    (81)  all_56_3 = all_52_25
% 200.22/33.04    (82)   ~ (all_52_3 = all_52_7)
% 200.22/33.04    (83)  op(all_14_2, all_14_2) = all_52_30
% 200.22/33.04    (84)  all_58_5 = all_52_19
% 200.22/33.04    (85)   ~ (all_52_15 = all_4_2)
% 200.22/33.04    (86)  all_58_6 = all_52_5
% 200.22/33.04    (87)   ~ (all_4_0 = all_4_2)
% 200.22/33.04    (88)  op(e3, e2) = all_52_9
% 200.22/33.04    (89)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.22/33.04    (90)   ~ (all_52_17 = all_6_2)
% 200.22/33.04    (91)   ~ (e3 = e2)
% 200.22/33.04    (92)   ~ (all_52_9 = all_52_17)
% 200.22/33.04    (93)  all_56_10 = all_10_2
% 200.22/33.04    (94)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.22/33.04    (95)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.22/33.04    (96)   ~ (all_52_3 = all_4_0)
% 200.22/33.04    (97)  op(all_52_13, all_52_13) = all_52_12
% 200.22/33.04    (98)   ~ (all_6_1 = e2)
% 200.22/33.04    (99)   ~ (all_52_7 = all_52_23)
% 200.22/33.04    (100)  all_58_3 = all_4_2
% 200.22/33.04    (101)   ~ (all_52_3 = all_4_2)
% 200.22/33.04    (102)  op(all_6_2, e3) = all_6_1
% 200.22/33.04    (103)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 200.22/33.04    (104)  all_58_4 = all_52_17
% 200.22/33.04    (105)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.22/33.04    (106)  op(all_52_25, all_52_25) = all_52_24
% 200.22/33.04  
% 200.22/33.04  Begin of proof
% 200.22/33.04  | 
% 200.22/33.04  | ALPHA: (103) implies:
% 200.22/33.04  |   (107)  all_52_22 = e0
% 200.22/33.04  |   (108)  all_52_20 = e1
% 200.22/33.04  |   (109)  all_52_16 = e3
% 200.22/33.04  | 
% 200.22/33.04  | REDUCE: (68), (109) imply:
% 200.22/33.04  |   (110)  op(all_52_17, all_52_17) = e3
% 200.22/33.04  | 
% 200.22/33.04  | REDUCE: (62), (107) imply:
% 200.22/33.04  |   (111)  op(all_52_23, all_52_23) = e0
% 200.22/33.04  | 
% 200.22/33.04  | REDUCE: (17), (108) imply:
% 200.22/33.04  |   (112)  op(all_10_2, all_10_2) = e1
% 200.22/33.04  | 
% 200.22/33.04  | BETA: splitting (65) gives:
% 200.22/33.04  | 
% 200.22/33.04  | Case 1:
% 200.22/33.04  | | 
% 200.22/33.04  | |   (113)  all_56_15 = e3
% 200.22/33.04  | | 
% 200.22/33.04  | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (14), (16), (18), (20),
% 200.22/33.04  | |            (21), (22), (23), (26), (27), (28), (29), (30), (31), (32), (34),
% 200.22/33.04  | |            (37), (38), (39), (40), (43), (44), (45), (47), (49), (50), (51),
% 200.22/33.04  | |            (53), (54), (56), (58), (61), (63), (64), (66), (69), (70), (71),
% 200.22/33.04  | |            (72), (73), (74), (76), (78), (79), (80), (81), (82), (83), (84),
% 200.22/33.04  | |            (86), (87), (88), (90), (91), (94), (96), (98), (100), (101),
% 200.22/33.04  | |            (102), (104), (110), (112), (113) are inconsistent by sub-proof
% 200.22/33.04  | |            #203.
% 200.22/33.04  | | 
% 200.22/33.04  | Case 2:
% 200.22/33.04  | | 
% 200.22/33.04  | |   (114)   ~ (all_56_15 = e3)
% 200.22/33.04  | | 
% 200.22/33.04  | | REDUCE: (31), (114) imply:
% 200.22/33.04  | |   (115)   ~ (all_14_2 = e3)
% 200.22/33.04  | | 
% 200.22/33.04  | | BETA: splitting (32) gives:
% 200.22/33.04  | | 
% 200.22/33.04  | | Case 1:
% 200.22/33.04  | | | 
% 200.22/33.04  | | |   (116)  all_58_2 = e3
% 200.22/33.04  | | | 
% 200.22/33.04  | | | COMBINE_EQS: (47), (116) imply:
% 200.22/33.04  | | |   (117)  all_52_3 = e3
% 200.22/33.04  | | | 
% 200.22/33.04  | | | SIMP: (117) implies:
% 200.22/33.04  | | |   (118)  all_52_3 = e3
% 200.22/33.04  | | | 
% 200.22/33.04  | | | REDUCE: (22), (118) imply:
% 200.22/33.05  | | |   (119)   ~ (all_52_5 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | SIMP: (119) implies:
% 200.22/33.05  | | |   (120)   ~ (all_52_5 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | REDUCE: (82), (118) imply:
% 200.22/33.05  | | |   (121)   ~ (all_52_7 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | SIMP: (121) implies:
% 200.22/33.05  | | |   (122)   ~ (all_52_7 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | REDUCE: (9), (118) imply:
% 200.22/33.05  | | |   (123)   ~ (all_6_2 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | SIMP: (123) implies:
% 200.22/33.05  | | |   (124)   ~ (all_6_2 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | REDUCE: (96), (118) imply:
% 200.22/33.05  | | |   (125)   ~ (all_4_0 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | REDUCE: (3), (118) imply:
% 200.22/33.05  | | |   (126)  op(e3, e3) = all_52_2
% 200.22/33.05  | | | 
% 200.22/33.05  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_2, e3, e3, simplifying
% 200.22/33.05  | | |              with (76), (126) gives:
% 200.22/33.05  | | |   (127)  all_52_2 = all_6_2
% 200.22/33.05  | | | 
% 200.22/33.05  | | | BETA: splitting (77) gives:
% 200.22/33.05  | | | 
% 200.22/33.05  | | | Case 1:
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | |   (128)  all_58_9 = e3
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | COMBINE_EQS: (18), (128) imply:
% 200.22/33.05  | | | |   (129)  all_52_25 = e3
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | SIMP: (129) implies:
% 200.22/33.05  | | | |   (130)  all_52_25 = e3
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | REDUCE: (42), (130) imply:
% 200.22/33.05  | | | |   (131)   ~ (all_52_29 = e3)
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | SIMP: (131) implies:
% 200.22/33.05  | | | |   (132)   ~ (all_52_29 = e3)
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | REDUCE: (26), (130) imply:
% 200.22/33.05  | | | |   (133)   ~ (all_14_2 = e3)
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | REDUCE: (106), (130) imply:
% 200.22/33.05  | | | |   (134)  op(e3, e3) = all_52_24
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_24, e3, e3,
% 200.22/33.05  | | | |              simplifying with (76), (134) gives:
% 200.22/33.05  | | | |   (135)  all_52_24 = all_6_2
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | BETA: splitting (46) gives:
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | Case 1:
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | |   (136)  all_58_6 = e3
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | | REF_CLOSE: (86), (120), (136) are inconsistent by sub-proof #1328.
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | Case 2:
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | |   (137)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | | BETA: splitting (105) gives:
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | | Case 1:
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | |   (138)  all_56_10 = e3
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | COMBINE_EQS: (93), (138) imply:
% 200.22/33.05  | | | | | |   (139)  all_10_2 = e3
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | SIMP: (139) implies:
% 200.22/33.05  | | | | | |   (140)  all_10_2 = e3
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | COMBINE_EQS: (15), (140) imply:
% 200.22/33.05  | | | | | |   (141)  all_26_2 = e3
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | REDUCE: (12), (140) imply:
% 200.22/33.05  | | | | | |   (142)   ~ (all_52_17 = e3)
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | REDUCE: (112), (140) imply:
% 200.22/33.05  | | | | | |   (143)  op(e3, e3) = e1
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | REDUCE: (29), (140) imply:
% 200.22/33.05  | | | | | |   (144)  op(e3, e1) = all_10_1
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | REF_CLOSE: (4), (13), (21), (23), (33), (35), (48), (56), (74),
% 200.22/33.05  | | | | | |            (76), (88), (90), (110), (141), (142), (143), (144) are
% 200.22/33.05  | | | | | |            inconsistent by sub-proof #134.
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | Case 2:
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | |   (145)   ~ (all_56_10 = e3)
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | REDUCE: (93), (145) imply:
% 200.22/33.05  | | | | | |   (146)   ~ (all_10_2 = e3)
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | BETA: splitting (137) gives:
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | | Case 1:
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | |   (147)  all_58_7 = e3
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | COMBINE_EQS: (43), (147) imply:
% 200.22/33.05  | | | | | | |   (148)  all_52_13 = e3
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | REDUCE: (75), (148) imply:
% 200.22/33.05  | | | | | | |   (149)   ~ (all_52_15 = e3)
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | SIMP: (149) implies:
% 200.22/33.05  | | | | | | |   (150)   ~ (all_52_15 = e3)
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | REDUCE: (38), (148) imply:
% 200.22/33.05  | | | | | | |   (151)   ~ (all_10_2 = e3)
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | REDUCE: (97), (148) imply:
% 200.22/33.05  | | | | | | |   (152)  op(e3, e3) = all_52_12
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (16), (18), (19), (30),
% 200.22/33.05  | | | | | | |            (34), (45), (57), (60), (64), (67), (69), (76), (79),
% 200.22/33.05  | | | | | | |            (89), (90), (92), (94), (98), (99), (102), (104),
% 200.22/33.05  | | | | | | |            (110), (111), (115), (146), (150), (152) are
% 200.22/33.05  | | | | | | |            inconsistent by sub-proof #133.
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | Case 2:
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | |   (153)  all_58_8 = e3 | all_58_11 = e3
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | | REF_CLOSE: (24), (64), (132), (146), (153) are inconsistent by
% 200.22/33.05  | | | | | | |            sub-proof #1140.
% 200.22/33.05  | | | | | | | 
% 200.22/33.05  | | | | | | End of split
% 200.22/33.05  | | | | | | 
% 200.22/33.05  | | | | | End of split
% 200.22/33.05  | | | | | 
% 200.22/33.05  | | | | End of split
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | Case 2:
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | |   (154)   ~ (all_58_9 = e3)
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | REDUCE: (18), (154) imply:
% 200.22/33.05  | | | |   (155)   ~ (all_52_25 = e3)
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | | REF_CLOSE: (2), (4), (5), (6), (10), (16), (18), (19), (27), (30), (45),
% 200.22/33.05  | | | |            (57), (60), (67), (76), (79), (89), (90), (98), (99), (102),
% 200.22/33.05  | | | |            (104), (110), (111), (115), (122), (124), (155) are
% 200.22/33.05  | | | |            inconsistent by sub-proof #178.
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | End of split
% 200.22/33.05  | | | 
% 200.22/33.05  | | Case 2:
% 200.22/33.05  | | | 
% 200.22/33.05  | | |   (156)   ~ (all_58_2 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | REDUCE: (47), (156) imply:
% 200.22/33.05  | | |   (157)   ~ (all_52_3 = e3)
% 200.22/33.05  | | | 
% 200.22/33.05  | | | BETA: splitting (52) gives:
% 200.22/33.05  | | | 
% 200.22/33.05  | | | Case 1:
% 200.22/33.05  | | | | 
% 200.22/33.05  | | | |   (158)  all_56_5 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | COMBINE_EQS: (25), (158) imply:
% 200.36/33.05  | | | |   (159)  all_4_2 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | SIMP: (159) implies:
% 200.36/33.05  | | | |   (160)  all_4_2 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (55), (160) imply:
% 200.36/33.05  | | | |   (161)   ~ (all_52_13 = e3)
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (85), (160) imply:
% 200.36/33.05  | | | |   (162)   ~ (all_52_15 = e3)
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (80), (160) imply:
% 200.36/33.05  | | | |   (163)  op(e3, e3) = all_52_10
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (23), (160) imply:
% 200.36/33.05  | | | |   (164)  op(e3, e2) = e1
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | BETA: splitting (73) gives:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | Case 1:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | |   (165)   ~ (all_4_2 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (12), (13), (15), (16),
% 200.36/33.05  | | | | |            (18), (19), (21), (23), (27), (29), (30), (33), (34), (35),
% 200.36/33.05  | | | | |            (41), (43), (44), (45), (46), (47), (48), (50), (56), (57),
% 200.36/33.05  | | | | |            (58), (59), (60), (64), (67), (69), (72), (74), (76), (79),
% 200.36/33.05  | | | | |            (86), (88), (89), (90), (94), (98), (99), (100), (102),
% 200.36/33.05  | | | | |            (104), (110), (111), (112), (115), (157), (161), (165) are
% 200.36/33.05  | | | | |            inconsistent by sub-proof #128.
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | Case 2:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | GROUND_INST: instantiating (4) with all_52_9, e1, e2, e3, simplifying
% 200.36/33.05  | | | | |              with (88), (164) gives:
% 200.36/33.05  | | | | |   (166)  all_52_9 = e1
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_10, e3, e3,
% 200.36/33.05  | | | | |              simplifying with (76), (163) gives:
% 200.36/33.05  | | | | |   (167)  all_52_10 = all_6_2
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REDUCE: (74), (166) imply:
% 200.36/33.05  | | | | |   (168)   ~ (all_6_2 = e1)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | SIMP: (168) implies:
% 200.36/33.05  | | | | |   (169)   ~ (all_6_2 = e1)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | BETA: splitting (89) gives:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | Case 1:
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | |   (170)  all_58_12 = e3
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | COMBINE_EQS: (45), (170) imply:
% 200.36/33.05  | | | | | |   (171)  all_52_7 = e3
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | SIMP: (171) implies:
% 200.36/33.05  | | | | | |   (172)  all_52_7 = e3
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | REDUCE: (99), (172) imply:
% 200.36/33.05  | | | | | |   (173)   ~ (all_52_23 = e3)
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | SIMP: (173) implies:
% 200.36/33.05  | | | | | |   (174)   ~ (all_52_23 = e3)
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | REF_CLOSE: (2), (4), (34), (64), (69), (76), (90), (94), (104),
% 200.36/33.05  | | | | | |            (110), (112), (169), (174) are inconsistent by sub-proof
% 200.36/33.05  | | | | | |            #205.
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | Case 2:
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | |   (175)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | REF_CLOSE: (2), (4), (6), (16), (19), (30), (57), (60), (67), (76),
% 200.36/33.05  | | | | | |            (98), (99), (102), (111), (115), (162), (175) are
% 200.36/33.05  | | | | | |            inconsistent by sub-proof #1045.
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | End of split
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | End of split
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | Case 2:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | |   (176)   ~ (all_56_5 = e3)
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (25), (176) imply:
% 200.36/33.05  | | | |   (177)   ~ (all_4_2 = e3)
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | BETA: splitting (95) gives:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | Case 1:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | |   (178)  all_56_9 = e3
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | COMBINE_EQS: (36), (178) imply:
% 200.36/33.05  | | | | |   (179)  all_52_13 = e3
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | SIMP: (179) implies:
% 200.36/33.05  | | | | |   (180)  all_52_13 = e3
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REDUCE: (75), (180) imply:
% 200.36/33.05  | | | | |   (181)   ~ (all_52_15 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | SIMP: (181) implies:
% 200.36/33.05  | | | | |   (182)   ~ (all_52_15 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REDUCE: (38), (180) imply:
% 200.36/33.05  | | | | |   (183)   ~ (all_10_2 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | SIMP: (183) implies:
% 200.36/33.05  | | | | |   (184)   ~ (all_10_2 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REDUCE: (97), (180) imply:
% 200.36/33.05  | | | | |   (185)  op(e3, e3) = all_52_12
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (16), (18), (19), (30),
% 200.36/33.05  | | | | |            (34), (45), (57), (60), (64), (67), (69), (76), (79), (89),
% 200.36/33.05  | | | | |            (90), (92), (94), (98), (99), (102), (104), (110), (111),
% 200.36/33.05  | | | | |            (115), (182), (184), (185) are inconsistent by sub-proof
% 200.36/33.05  | | | | |            #133.
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | Case 2:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | |   (186)   ~ (all_56_9 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REDUCE: (36), (186) imply:
% 200.36/33.05  | | | | |   (187)   ~ (all_52_13 = e3)
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (12), (13), (15), (16),
% 200.36/33.05  | | | | |            (18), (19), (21), (23), (27), (29), (30), (33), (34), (35),
% 200.36/33.05  | | | | |            (41), (43), (44), (45), (46), (47), (48), (50), (56), (57),
% 200.36/33.05  | | | | |            (58), (59), (60), (64), (67), (69), (72), (74), (76), (79),
% 200.36/33.05  | | | | |            (86), (88), (89), (90), (94), (98), (99), (100), (102),
% 200.36/33.05  | | | | |            (104), (110), (111), (112), (115), (157), (177), (187) are
% 200.36/33.05  | | | | |            inconsistent by sub-proof #128.
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | End of split
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | End of split
% 200.36/33.05  | | | 
% 200.36/33.05  | | End of split
% 200.36/33.05  | | 
% 200.36/33.05  | End of split
% 200.36/33.05  | 
% 200.36/33.05  End of proof
% 200.36/33.05  
% 200.36/33.05  Sub-proof #128 shows that the following formulas are inconsistent:
% 200.36/33.05  ----------------------------------------------------------------
% 200.36/33.05    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.05    (2)  all_58_14 = all_52_23
% 200.36/33.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.05    (4)  all_58_1 = all_52_9
% 200.36/33.05    (5)  op(all_52_23, all_52_23) = e0
% 200.36/33.05    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.05    (7)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.05    (8)   ~ (all_4_2 = e3)
% 200.36/33.05    (9)  all_58_0 = all_6_2
% 200.36/33.05    (10)   ~ (all_52_17 = all_10_2)
% 200.36/33.05    (11)  all_26_1 = all_10_1
% 200.36/33.05    (12)  all_26_2 = all_10_2
% 200.36/33.05    (13)  all_58_13 = all_52_15
% 200.36/33.05    (14)  all_58_9 = all_52_25
% 200.36/33.05    (15)   ~ (all_6_1 = e1)
% 200.36/33.05    (16)  op(e2, e2) = all_4_2
% 200.36/33.05    (17)  op(all_4_2, e2) = e1
% 200.36/33.05    (18)   ~ (all_52_3 = e3)
% 200.36/33.05    (19)   ~ (all_52_9 = all_52_15)
% 200.36/33.05    (20)  op(all_10_2, e1) = all_10_1
% 200.36/33.05    (21)   ~ (all_52_7 = all_6_2)
% 200.36/33.05    (22)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.05    (23)   ~ (all_4_0 = e3)
% 200.36/33.05    (24)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.05    (25)  op(all_10_2, all_10_2) = e1
% 200.36/33.05    (26)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.05    (27)  all_58_7 = all_52_13
% 200.36/33.05    (28)   ~ (all_52_5 = all_52_7)
% 200.36/33.05    (29)  all_58_12 = all_52_7
% 200.36/33.05    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.05    (31)  all_58_2 = all_52_3
% 200.36/33.05    (32)  all_56_2 = all_52_17
% 200.36/33.05    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.05    (34)  op(e3, e1) = all_52_17
% 200.36/33.05    (35)  op(e0, e3) = all_52_7
% 200.36/33.05    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.05    (37)   ~ (all_52_9 = all_52_25)
% 200.36/33.05    (38)  all_58_15 = all_14_2
% 200.36/33.05    (39)  all_58_8 = all_10_2
% 200.36/33.05    (40)  all_56_12 = all_52_7
% 200.36/33.05    (41)  all_58_5 = all_4_0
% 200.36/33.05    (42)   ~ (all_52_5 = all_6_2)
% 200.36/33.05    (43)   ~ (all_52_9 = all_6_2)
% 200.36/33.05    (44)  op(e3, e3) = all_6_2
% 200.36/33.05    (45)   ~ (all_52_13 = e3)
% 200.36/33.05    (46)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.05    (47)  op(all_52_17, all_52_17) = e3
% 200.36/33.05    (48)  all_58_6 = all_52_5
% 200.36/33.05    (49)  op(e3, e2) = all_52_9
% 200.36/33.05    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.05    (51)   ~ (all_52_17 = all_6_2)
% 200.36/33.05    (52)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.05    (53)   ~ (all_6_1 = e2)
% 200.36/33.05    (54)   ~ (all_52_7 = all_52_23)
% 200.36/33.05    (55)  all_58_3 = all_4_2
% 200.36/33.05    (56)  op(all_6_2, e3) = all_6_1
% 200.36/33.05    (57)  all_58_4 = all_52_17
% 200.36/33.05    (58)   ~ (all_14_2 = e3)
% 200.36/33.05  
% 200.36/33.05  Begin of proof
% 200.36/33.05  | 
% 200.36/33.05  | BETA: splitting (36) gives:
% 200.36/33.05  | 
% 200.36/33.05  | Case 1:
% 200.36/33.05  | | 
% 200.36/33.05  | |   (59)  all_58_1 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | COMBINE_EQS: (4), (59) imply:
% 200.36/33.05  | |   (60)  all_52_9 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | REDUCE: (37), (60) imply:
% 200.36/33.05  | |   (61)   ~ (all_52_25 = e3)
% 200.36/33.05  | | 
% 200.36/33.05  | | SIMP: (61) implies:
% 200.36/33.05  | |   (62)   ~ (all_52_25 = e3)
% 200.36/33.05  | | 
% 200.36/33.05  | | REDUCE: (43), (60) imply:
% 200.36/33.05  | |   (63)   ~ (all_6_2 = e3)
% 200.36/33.05  | | 
% 200.36/33.05  | | SIMP: (63) implies:
% 200.36/33.05  | |   (64)   ~ (all_6_2 = e3)
% 200.36/33.05  | | 
% 200.36/33.05  | | REDUCE: (26), (60) imply:
% 200.36/33.05  | |   (65)  op(e3, e3) = all_52_8
% 200.36/33.05  | | 
% 200.36/33.05  | | GROUND_INST: instantiating (3) with all_6_2, all_52_8, e3, e3, simplifying
% 200.36/33.05  | |              with (44), (65) gives:
% 200.36/33.05  | |   (66)  all_52_8 = all_6_2
% 200.36/33.05  | | 
% 200.36/33.05  | | BETA: splitting (30) gives:
% 200.36/33.05  | | 
% 200.36/33.05  | | Case 1:
% 200.36/33.05  | | | 
% 200.36/33.05  | | |   (67)  all_58_6 = e3
% 200.36/33.05  | | | 
% 200.36/33.05  | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (13), (14), (15), (19), (21),
% 200.36/33.05  | | |            (28), (29), (35), (38), (40), (42), (44), (46), (47), (48),
% 200.36/33.05  | | |            (50), (51), (53), (54), (56), (57), (58), (62), (67) are
% 200.36/33.05  | | |            inconsistent by sub-proof #177.
% 200.36/33.05  | | | 
% 200.36/33.05  | | Case 2:
% 200.36/33.05  | | | 
% 200.36/33.05  | | |   (68)   ~ (all_58_6 = e3)
% 200.36/33.05  | | | 
% 200.36/33.05  | | | REDUCE: (48), (68) imply:
% 200.36/33.05  | | |   (69)   ~ (all_52_5 = e3)
% 200.36/33.05  | | | 
% 200.36/33.05  | | | BETA: splitting (33) gives:
% 200.36/33.05  | | | 
% 200.36/33.05  | | | Case 1:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | |   (70)  all_58_0 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | COMBINE_EQS: (9), (70) imply:
% 200.36/33.05  | | | |   (71)  all_6_2 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (64), (71) imply:
% 200.36/33.05  | | | |   (72)  $false
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | CLOSE: (72) is inconsistent.
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | Case 2:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | |   (73)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | BETA: splitting (73) gives:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | Case 1:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | |   (74)  all_58_2 = e3
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | REF_CLOSE: (18), (31), (74) are inconsistent by sub-proof #1369.
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | Case 2:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | |   (75)  all_58_6 = e3 | all_58_12 = e3
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | BETA: splitting (75) gives:
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | | Case 1:
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | |   (76)  all_58_6 = e3
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | REF_CLOSE: (48), (69), (76) are inconsistent by sub-proof #1328.
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | Case 2:
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | |   (77)  all_58_12 = e3
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | | REF_CLOSE: (2), (3), (7), (10), (11), (12), (16), (17), (20), (22),
% 200.36/33.05  | | | | | |            (23), (24), (25), (29), (32), (34), (39), (41), (43),
% 200.36/33.05  | | | | | |            (44), (47), (49), (51), (52), (54), (57), (77) are
% 200.36/33.05  | | | | | |            inconsistent by sub-proof #130.
% 200.36/33.05  | | | | | | 
% 200.36/33.05  | | | | | End of split
% 200.36/33.05  | | | | | 
% 200.36/33.05  | | | | End of split
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | End of split
% 200.36/33.05  | | | 
% 200.36/33.05  | | End of split
% 200.36/33.05  | | 
% 200.36/33.05  | Case 2:
% 200.36/33.05  | | 
% 200.36/33.05  | |   (78)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | BETA: splitting (78) gives:
% 200.36/33.05  | | 
% 200.36/33.05  | | Case 1:
% 200.36/33.05  | | | 
% 200.36/33.05  | | |   (79)  all_58_3 = e3
% 200.36/33.05  | | | 
% 200.36/33.05  | | | COMBINE_EQS: (55), (79) imply:
% 200.36/33.05  | | |   (80)  all_4_2 = e3
% 200.36/33.05  | | | 
% 200.36/33.05  | | | REDUCE: (8), (80) imply:
% 200.36/33.05  | | |   (81)  $false
% 200.36/33.05  | | | 
% 200.36/33.05  | | | CLOSE: (81) is inconsistent.
% 200.36/33.05  | | | 
% 200.36/33.05  | | Case 2:
% 200.36/33.05  | | | 
% 200.36/33.05  | | |   (82)  all_58_7 = e3 | all_58_13 = e3
% 200.36/33.05  | | | 
% 200.36/33.05  | | | BETA: splitting (82) gives:
% 200.36/33.05  | | | 
% 200.36/33.05  | | | Case 1:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | |   (83)  all_58_7 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | COMBINE_EQS: (27), (83) imply:
% 200.36/33.05  | | | |   (84)  all_52_13 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (45), (84) imply:
% 200.36/33.05  | | | |   (85)  $false
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | CLOSE: (85) is inconsistent.
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | Case 2:
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | |   (86)  all_58_13 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | COMBINE_EQS: (13), (86) imply:
% 200.36/33.05  | | | |   (87)  all_52_15 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | SIMP: (87) implies:
% 200.36/33.05  | | | |   (88)  all_52_15 = e3
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REDUCE: (1), (88) imply:
% 200.36/33.05  | | | |   (89)   ~ (all_52_23 = e3)
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | SIMP: (89) implies:
% 200.36/33.05  | | | |   (90)   ~ (all_52_23 = e3)
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | | REF_CLOSE: (2), (3), (10), (11), (12), (16), (17), (20), (22), (23),
% 200.36/33.05  | | | |            (24), (25), (32), (34), (39), (41), (43), (44), (47), (49),
% 200.36/33.05  | | | |            (51), (52), (57), (90) are inconsistent by sub-proof #129.
% 200.36/33.05  | | | | 
% 200.36/33.05  | | | End of split
% 200.36/33.05  | | | 
% 200.36/33.05  | | End of split
% 200.36/33.05  | | 
% 200.36/33.05  | End of split
% 200.36/33.05  | 
% 200.36/33.05  End of proof
% 200.36/33.05  
% 200.36/33.05  Sub-proof #129 shows that the following formulas are inconsistent:
% 200.36/33.05  ----------------------------------------------------------------
% 200.36/33.05    (1)  all_58_14 = all_52_23
% 200.36/33.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.05    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.05    (4)  all_26_1 = all_10_1
% 200.36/33.05    (5)  all_26_2 = all_10_2
% 200.36/33.05    (6)  op(e2, e2) = all_4_2
% 200.36/33.05    (7)  op(all_4_2, e2) = e1
% 200.36/33.05    (8)  op(all_10_2, e1) = all_10_1
% 200.36/33.05    (9)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.05    (10)   ~ (all_4_0 = e3)
% 200.36/33.05    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.05    (12)  op(all_10_2, all_10_2) = e1
% 200.36/33.05    (13)  all_56_2 = all_52_17
% 200.36/33.05    (14)   ~ (all_52_23 = e3)
% 200.36/33.05    (15)  op(e3, e1) = all_52_17
% 200.36/33.05    (16)  all_58_8 = all_10_2
% 200.36/33.05    (17)  all_58_5 = all_4_0
% 200.36/33.05    (18)   ~ (all_52_9 = all_6_2)
% 200.36/33.05    (19)  op(e3, e3) = all_6_2
% 200.36/33.05    (20)  op(all_52_17, all_52_17) = e3
% 200.36/33.05    (21)  op(e3, e2) = all_52_9
% 200.36/33.05    (22)   ~ (all_52_17 = all_6_2)
% 200.36/33.05    (23)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.05    (24)  all_58_4 = all_52_17
% 200.36/33.05  
% 200.36/33.05  Begin of proof
% 200.36/33.05  | 
% 200.36/33.05  | BETA: splitting (23) gives:
% 200.36/33.05  | 
% 200.36/33.05  | Case 1:
% 200.36/33.05  | | 
% 200.36/33.05  | |   (25)  all_58_4 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | COMBINE_EQS: (24), (25) imply:
% 200.36/33.05  | |   (26)  all_52_17 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | SIMP: (26) implies:
% 200.36/33.05  | |   (27)  all_52_17 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | REF_CLOSE: (2), (19), (20), (22), (27) are inconsistent by sub-proof #1280.
% 200.36/33.05  | | 
% 200.36/33.05  | Case 2:
% 200.36/33.05  | | 
% 200.36/33.05  | |   (28)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.05  | | 
% 200.36/33.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 200.36/33.05  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (28)
% 200.36/33.05  | |            are inconsistent by sub-proof #132.
% 200.36/33.05  | | 
% 200.36/33.05  | End of split
% 200.36/33.05  | 
% 200.36/33.05  End of proof
% 200.36/33.05  
% 200.36/33.05  Sub-proof #130 shows that the following formulas are inconsistent:
% 200.36/33.05  ----------------------------------------------------------------
% 200.36/33.05    (1)  all_58_14 = all_52_23
% 200.36/33.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.05    (3)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.05    (4)   ~ (all_52_17 = all_10_2)
% 200.36/33.05    (5)  all_26_1 = all_10_1
% 200.36/33.05    (6)  all_26_2 = all_10_2
% 200.36/33.05    (7)  op(e2, e2) = all_4_2
% 200.36/33.05    (8)  op(all_4_2, e2) = e1
% 200.36/33.05    (9)  op(all_10_2, e1) = all_10_1
% 200.36/33.05    (10)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.05    (11)   ~ (all_4_0 = e3)
% 200.36/33.05    (12)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.05    (13)  op(all_10_2, all_10_2) = e1
% 200.36/33.05    (14)  all_58_12 = all_52_7
% 200.36/33.05    (15)  all_56_2 = all_52_17
% 200.36/33.05    (16)  op(e3, e1) = all_52_17
% 200.36/33.05    (17)  all_58_8 = all_10_2
% 200.36/33.05    (18)  all_58_5 = all_4_0
% 200.36/33.05    (19)   ~ (all_52_9 = all_6_2)
% 200.36/33.05    (20)  op(e3, e3) = all_6_2
% 200.36/33.05    (21)  op(all_52_17, all_52_17) = e3
% 200.36/33.05    (22)  op(e3, e2) = all_52_9
% 200.36/33.05    (23)   ~ (all_52_17 = all_6_2)
% 200.36/33.05    (24)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.05    (25)  all_58_12 = e3
% 200.36/33.05    (26)   ~ (all_52_7 = all_52_23)
% 200.36/33.05    (27)  all_58_4 = all_52_17
% 200.36/33.05  
% 200.36/33.05  Begin of proof
% 200.36/33.05  | 
% 200.36/33.05  | COMBINE_EQS: (14), (25) imply:
% 200.36/33.05  |   (28)  all_52_7 = e3
% 200.36/33.05  | 
% 200.36/33.05  | SIMP: (28) implies:
% 200.36/33.05  |   (29)  all_52_7 = e3
% 200.36/33.05  | 
% 200.36/33.05  | REDUCE: (26), (29) imply:
% 200.36/33.05  |   (30)   ~ (all_52_23 = e3)
% 200.36/33.05  | 
% 200.36/33.05  | SIMP: (30) implies:
% 200.36/33.05  |   (31)   ~ (all_52_23 = e3)
% 200.36/33.05  | 
% 200.36/33.05  | REDUCE: (3), (29) imply:
% 200.36/33.05  |   (32)  op(e3, e3) = all_52_6
% 200.36/33.05  | 
% 200.36/33.05  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.05  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (27),
% 200.36/33.05  |            (31), (32) are inconsistent by sub-proof #131.
% 200.36/33.05  | 
% 200.36/33.05  End of proof
% 200.36/33.05  
% 200.36/33.05  Sub-proof #131 shows that the following formulas are inconsistent:
% 200.36/33.05  ----------------------------------------------------------------
% 200.36/33.05    (1)  all_58_14 = all_52_23
% 200.36/33.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.05    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.05    (4)  all_26_1 = all_10_1
% 200.36/33.05    (5)  op(e3, e3) = all_52_6
% 200.36/33.05    (6)  all_26_2 = all_10_2
% 200.36/33.05    (7)  op(e2, e2) = all_4_2
% 200.36/33.05    (8)  op(all_4_2, e2) = e1
% 200.36/33.05    (9)  op(all_10_2, e1) = all_10_1
% 200.36/33.05    (10)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.05    (11)   ~ (all_4_0 = e3)
% 200.36/33.05    (12)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.05    (13)  op(all_10_2, all_10_2) = e1
% 200.36/33.05    (14)  all_56_2 = all_52_17
% 200.36/33.05    (15)   ~ (all_52_23 = e3)
% 200.36/33.05    (16)  op(e3, e1) = all_52_17
% 200.36/33.05    (17)  all_58_8 = all_10_2
% 200.36/33.05    (18)  all_58_5 = all_4_0
% 200.36/33.06    (19)   ~ (all_52_9 = all_6_2)
% 200.36/33.06    (20)  op(e3, e3) = all_6_2
% 200.36/33.06    (21)  op(all_52_17, all_52_17) = e3
% 200.36/33.06    (22)  op(e3, e2) = all_52_9
% 200.36/33.06    (23)   ~ (all_52_17 = all_6_2)
% 200.36/33.06    (24)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06    (25)  all_58_4 = all_52_17
% 200.36/33.06  
% 200.36/33.06  Begin of proof
% 200.36/33.06  | 
% 200.36/33.06  | GROUND_INST: instantiating (2) with all_6_2, all_52_6, e3, e3, simplifying
% 200.36/33.06  |              with (5), (20) gives:
% 200.36/33.06  |   (26)  all_52_6 = all_6_2
% 200.36/33.06  | 
% 200.36/33.06  | BETA: splitting (24) gives:
% 200.36/33.06  | 
% 200.36/33.06  | Case 1:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (27)  all_58_4 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | COMBINE_EQS: (25), (27) imply:
% 200.36/33.06  | |   (28)  all_52_17 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REF_CLOSE: (2), (20), (21), (23), (28) are inconsistent by sub-proof #1280.
% 200.36/33.06  | | 
% 200.36/33.06  | Case 2:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (29)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.06  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (29)
% 200.36/33.06  | |            are inconsistent by sub-proof #132.
% 200.36/33.06  | | 
% 200.36/33.06  | End of split
% 200.36/33.06  | 
% 200.36/33.06  End of proof
% 200.36/33.06  
% 200.36/33.06  Sub-proof #132 shows that the following formulas are inconsistent:
% 200.36/33.06  ----------------------------------------------------------------
% 200.36/33.06    (1)  all_58_14 = all_52_23
% 200.36/33.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.06    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.06    (4)  all_26_1 = all_10_1
% 200.36/33.06    (5)  all_26_2 = all_10_2
% 200.36/33.06    (6)  op(e2, e2) = all_4_2
% 200.36/33.06    (7)  op(all_4_2, e2) = e1
% 200.36/33.06    (8)  op(all_10_2, e1) = all_10_1
% 200.36/33.06    (9)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.06    (10)   ~ (all_4_0 = e3)
% 200.36/33.06    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.06    (12)  op(all_10_2, all_10_2) = e1
% 200.36/33.06    (13)  all_56_2 = all_52_17
% 200.36/33.06    (14)   ~ (all_52_23 = e3)
% 200.36/33.06    (15)  op(e3, e1) = all_52_17
% 200.36/33.06    (16)  all_58_8 = all_10_2
% 200.36/33.06    (17)  all_58_5 = all_4_0
% 200.36/33.06    (18)   ~ (all_52_9 = all_6_2)
% 200.36/33.06    (19)  op(e3, e3) = all_6_2
% 200.36/33.06    (20)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06    (21)  op(all_52_17, all_52_17) = e3
% 200.36/33.06    (22)  op(e3, e2) = all_52_9
% 200.36/33.06    (23)   ~ (all_52_17 = all_6_2)
% 200.36/33.06  
% 200.36/33.06  Begin of proof
% 200.36/33.06  | 
% 200.36/33.06  | BETA: splitting (20) gives:
% 200.36/33.06  | 
% 200.36/33.06  | Case 1:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (24)  all_58_5 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REF_CLOSE: (10), (17), (24) are inconsistent by sub-proof #215.
% 200.36/33.06  | | 
% 200.36/33.06  | Case 2:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (25)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | BETA: splitting (25) gives:
% 200.36/33.06  | | 
% 200.36/33.06  | | Case 1:
% 200.36/33.06  | | | 
% 200.36/33.06  | | |   (26)  all_58_8 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | COMBINE_EQS: (16), (26) imply:
% 200.36/33.06  | | |   (27)  all_10_2 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | COMBINE_EQS: (5), (27) imply:
% 200.36/33.06  | | |   (28)  all_26_2 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (3), (27) imply:
% 200.36/33.06  | | |   (29)   ~ (all_52_17 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (12), (27) imply:
% 200.36/33.06  | | |   (30)  op(e3, e3) = e1
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (8), (27) imply:
% 200.36/33.06  | | |   (31)  op(e3, e1) = all_10_1
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (13), (15), (18), (19), (21),
% 200.36/33.06  | | |            (22), (23), (28), (29), (30), (31) are inconsistent by
% 200.36/33.06  | | |            sub-proof #134.
% 200.36/33.06  | | | 
% 200.36/33.06  | | Case 2:
% 200.36/33.06  | | | 
% 200.36/33.06  | | |   (32)  all_58_14 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REF_CLOSE: (1), (14), (32) are inconsistent by sub-proof #1305.
% 200.36/33.06  | | | 
% 200.36/33.06  | | End of split
% 200.36/33.06  | | 
% 200.36/33.06  | End of split
% 200.36/33.06  | 
% 200.36/33.06  End of proof
% 200.36/33.06  
% 200.36/33.06  Sub-proof #133 shows that the following formulas are inconsistent:
% 200.36/33.06  ----------------------------------------------------------------
% 200.36/33.06    (1)  all_58_14 = all_52_23
% 200.36/33.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.06    (3)  all_58_1 = all_52_9
% 200.36/33.06    (4)  op(all_52_23, all_52_23) = e0
% 200.36/33.06    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.06    (6)   ~ (all_52_17 = all_52_25)
% 200.36/33.06    (7)  all_58_0 = all_6_2
% 200.36/33.06    (8)  all_58_13 = all_52_15
% 200.36/33.06    (9)  all_58_9 = all_52_25
% 200.36/33.06    (10)   ~ (all_6_1 = e1)
% 200.36/33.06    (11)   ~ (all_52_15 = e3)
% 200.36/33.06    (12)  op(e3, e3) = all_52_12
% 200.36/33.06    (13)   ~ (all_52_7 = all_6_2)
% 200.36/33.06    (14)   ~ (all_4_0 = e3)
% 200.36/33.06    (15)  all_58_12 = all_52_7
% 200.36/33.06    (16)   ~ (all_10_2 = e3)
% 200.36/33.06    (17)  op(e0, e3) = all_52_7
% 200.36/33.06    (18)  all_58_15 = all_14_2
% 200.36/33.06    (19)  all_58_8 = all_10_2
% 200.36/33.06    (20)  all_56_12 = all_52_7
% 200.36/33.06    (21)  all_58_5 = all_4_0
% 200.36/33.06    (22)  op(e3, e3) = all_6_2
% 200.36/33.06    (23)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.06    (24)  op(all_52_17, all_52_17) = e3
% 200.36/33.06    (25)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.06    (26)   ~ (all_52_17 = all_6_2)
% 200.36/33.06    (27)   ~ (all_52_9 = all_52_17)
% 200.36/33.06    (28)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06    (29)   ~ (all_6_1 = e2)
% 200.36/33.06    (30)   ~ (all_52_7 = all_52_23)
% 200.36/33.06    (31)  op(all_6_2, e3) = all_6_1
% 200.36/33.06    (32)  all_58_4 = all_52_17
% 200.36/33.06    (33)   ~ (all_14_2 = e3)
% 200.36/33.06  
% 200.36/33.06  Begin of proof
% 200.36/33.06  | 
% 200.36/33.06  | GROUND_INST: instantiating (2) with all_6_2, all_52_12, e3, e3, simplifying
% 200.36/33.06  |              with (12), (22) gives:
% 200.36/33.06  |   (34)  all_52_12 = all_6_2
% 200.36/33.06  | 
% 200.36/33.06  | BETA: splitting (28) gives:
% 200.36/33.06  | 
% 200.36/33.06  | Case 1:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (35)  all_58_4 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | COMBINE_EQS: (32), (35) imply:
% 200.36/33.06  | |   (36)  all_52_17 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | SIMP: (36) implies:
% 200.36/33.06  | |   (37)  all_52_17 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (27), (37) imply:
% 200.36/33.06  | |   (38)   ~ (all_52_9 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (6), (37) imply:
% 200.36/33.06  | |   (39)   ~ (all_52_25 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | SIMP: (39) implies:
% 200.36/33.06  | |   (40)   ~ (all_52_25 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (26), (37) imply:
% 200.36/33.06  | |   (41)   ~ (all_6_2 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | SIMP: (41) implies:
% 200.36/33.06  | |   (42)   ~ (all_6_2 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REF_CLOSE: (2), (3), (7), (9), (22), (23), (24), (26), (32), (38), (40),
% 200.36/33.06  | |            (42) are inconsistent by sub-proof #1071.
% 200.36/33.06  | | 
% 200.36/33.06  | Case 2:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (43)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REF_CLOSE: (1), (2), (4), (5), (8), (10), (11), (13), (14), (15), (16),
% 200.36/33.06  | |            (17), (18), (19), (20), (21), (22), (25), (29), (30), (31), (33),
% 200.36/33.06  | |            (43) are inconsistent by sub-proof #175.
% 200.36/33.06  | | 
% 200.36/33.06  | End of split
% 200.36/33.06  | 
% 200.36/33.06  End of proof
% 200.36/33.06  
% 200.36/33.06  Sub-proof #134 shows that the following formulas are inconsistent:
% 200.36/33.06  ----------------------------------------------------------------
% 200.36/33.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.06    (2)  all_26_1 = all_10_1
% 200.36/33.06    (3)  op(e2, e2) = all_4_2
% 200.36/33.06    (4)  op(all_4_2, e2) = e1
% 200.36/33.06    (5)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.06    (6)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.06    (7)  all_26_2 = e3
% 200.36/33.06    (8)  all_56_2 = all_52_17
% 200.36/33.06    (9)  op(e3, e1) = all_10_1
% 200.36/33.06    (10)  op(e3, e1) = all_52_17
% 200.36/33.06    (11)   ~ (all_52_9 = all_6_2)
% 200.36/33.06    (12)  op(e3, e3) = all_6_2
% 200.36/33.06    (13)   ~ (all_52_17 = e3)
% 200.36/33.06    (14)  op(e3, e3) = e1
% 200.36/33.06    (15)  op(all_52_17, all_52_17) = e3
% 200.36/33.06    (16)  op(e3, e2) = all_52_9
% 200.36/33.06    (17)   ~ (all_52_17 = all_6_2)
% 200.36/33.06  
% 200.36/33.06  Begin of proof
% 200.36/33.06  | 
% 200.36/33.06  | BETA: splitting (5) gives:
% 200.36/33.06  | 
% 200.36/33.06  | Case 1:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (18)   ~ (all_26_2 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (7), (18) imply:
% 200.36/33.06  | |   (19)  $false
% 200.36/33.06  | | 
% 200.36/33.06  | | CLOSE: (19) is inconsistent.
% 200.36/33.06  | | 
% 200.36/33.06  | Case 2:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (20)   ~ (all_26_1 = e0)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (2), (20) imply:
% 200.36/33.06  | |   (21)   ~ (all_10_1 = e0)
% 200.36/33.06  | | 
% 200.36/33.06  | | GROUND_INST: instantiating (1) with all_52_17, all_10_1, e1, e3, simplifying
% 200.36/33.06  | |              with (9), (10) gives:
% 200.36/33.06  | |   (22)  all_52_17 = all_10_1
% 200.36/33.06  | | 
% 200.36/33.06  | | GROUND_INST: instantiating (1) with all_6_2, e1, e3, e3, simplifying with
% 200.36/33.06  | |              (12), (14) gives:
% 200.36/33.06  | |   (23)  all_6_2 = e1
% 200.36/33.06  | | 
% 200.36/33.06  | | COMBINE_EQS: (8), (22) imply:
% 200.36/33.06  | |   (24)  all_56_2 = all_10_1
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (11), (23) imply:
% 200.36/33.06  | |   (25)   ~ (all_52_9 = e1)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (17), (22), (23) imply:
% 200.36/33.06  | |   (26)   ~ (all_10_1 = e1)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (13), (22) imply:
% 200.36/33.06  | |   (27)   ~ (all_10_1 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (15), (22) imply:
% 200.36/33.06  | |   (28)  op(all_10_1, all_10_1) = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | BETA: splitting (6) gives:
% 200.36/33.06  | | 
% 200.36/33.06  | | Case 1:
% 200.36/33.06  | | | 
% 200.36/33.06  | | |   (29)  all_56_2 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | COMBINE_EQS: (24), (29) imply:
% 200.36/33.06  | | |   (30)  all_10_1 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (27), (30) imply:
% 200.36/33.06  | | |   (31)  $false
% 200.36/33.06  | | | 
% 200.36/33.06  | | | CLOSE: (31) is inconsistent.
% 200.36/33.06  | | | 
% 200.36/33.06  | | Case 2:
% 200.36/33.06  | | | 
% 200.36/33.06  | | |   (32)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.06  | | | 
% 200.36/33.06  | | | BETA: splitting (32) gives:
% 200.36/33.06  | | | 
% 200.36/33.06  | | | Case 1:
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | |   (33)  all_56_2 = e2
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | COMBINE_EQS: (24), (33) imply:
% 200.36/33.06  | | | |   (34)  all_10_1 = e2
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | REDUCE: (28), (34) imply:
% 200.36/33.06  | | | |   (35)  op(e2, e2) = e3
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying
% 200.36/33.06  | | | |              with (3), (35) gives:
% 200.36/33.06  | | | |   (36)  all_4_2 = e3
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | REDUCE: (4), (36) imply:
% 200.36/33.06  | | | |   (37)  op(e3, e2) = e1
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | REF_CLOSE: (1), (16), (25), (37) are inconsistent by sub-proof #309.
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | Case 2:
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | |   (38)  all_56_2 = e1 | all_56_2 = e0
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | BETA: splitting (38) gives:
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | Case 1:
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | |   (39)  all_56_2 = e1
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | REF_CLOSE: (24), (26), (39) are inconsistent by sub-proof #1025.
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | Case 2:
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | |   (40)  all_56_2 = e0
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | REF_CLOSE: (21), (24), (40) are inconsistent by sub-proof #809.
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | End of split
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | End of split
% 200.36/33.06  | | | 
% 200.36/33.06  | | End of split
% 200.36/33.06  | | 
% 200.36/33.06  | End of split
% 200.36/33.06  | 
% 200.36/33.06  End of proof
% 200.36/33.06  
% 200.36/33.06  Sub-proof #135 shows that the following formulas are inconsistent:
% 200.36/33.06  ----------------------------------------------------------------
% 200.36/33.06    (1)  all_58_14 = all_52_23
% 200.36/33.06    (2)   ~ (all_52_17 = all_4_0)
% 200.36/33.06    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 200.36/33.06    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.06    (5)  all_58_1 = all_52_9
% 200.36/33.06    (6)   ~ (all_52_9 = all_52_13)
% 200.36/33.06    (7)   ~ (e3 = e0)
% 200.36/33.06    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.06    (9)   ~ (all_52_7 = all_52_15)
% 200.36/33.06    (10)  op(all_52_15, all_52_15) = e0
% 200.36/33.06    (11)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.06    (12)   ~ (all_52_17 = all_52_25)
% 200.36/33.06    (13)  all_16_1 = all_10_1
% 200.36/33.06    (14)  all_58_0 = all_6_2
% 200.36/33.06    (15)   ~ (all_52_17 = all_10_2)
% 200.36/33.06    (16)  all_26_1 = all_10_1
% 200.36/33.06    (17)  all_26_2 = all_10_2
% 200.36/33.06    (18)   ~ (all_52_27 = all_52_29)
% 200.36/33.06    (19)  all_58_13 = all_52_15
% 200.36/33.06    (20)  op(all_52_13, all_52_13) = e1
% 200.36/33.06    (21)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.06    (22)   ~ (all_52_15 = e3)
% 200.36/33.06    (23)  op(e2, e2) = all_4_2
% 200.36/33.06    (24)  op(all_4_2, e2) = e1
% 200.36/33.06    (25)  all_58_11 = all_52_29
% 200.36/33.06    (26)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.06    (27)  op(all_10_2, e1) = all_10_1
% 200.36/33.06    (28)  op(e0, e1) = all_52_23
% 200.36/33.06    (29)   ~ (all_52_15 = e0)
% 200.36/33.06    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.06    (31)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 200.36/33.06    (32)  all_58_15 = e0
% 200.36/33.06    (33)  all_56_11 = all_52_29
% 200.36/33.06    (34)   ~ (all_4_0 = e3)
% 200.36/33.06    (35)   ~ (all_52_25 = e0)
% 200.36/33.06    (36)   ~ (all_52_13 = all_10_2)
% 200.36/33.06    (37)  op(e0, e0) = e0
% 200.36/33.06    (38)  all_58_10 = all_52_27
% 200.36/33.06    (39)  all_16_2 = all_10_2
% 200.36/33.06    (40)   ~ (all_52_29 = all_10_2)
% 200.36/33.06    (41)  all_58_7 = all_52_13
% 200.36/33.06    (42)   ~ (all_52_5 = all_52_7)
% 200.36/33.06    (43)  all_58_12 = all_52_7
% 200.36/33.06    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.06    (45)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.06    (46)  all_58_2 = all_52_3
% 200.36/33.06    (47)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.06    (48)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.06    (49)   ~ (all_52_13 = all_4_2)
% 200.36/33.06    (50)  op(e3, e1) = all_52_17
% 200.36/33.06    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.06    (52)   ~ (all_52_9 = all_52_25)
% 200.36/33.06    (53)  all_58_8 = all_10_2
% 200.36/33.06    (54)   ~ (all_52_23 = e0)
% 200.36/33.06    (55)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 200.36/33.06    (56)  all_56_12 = all_52_7
% 200.36/33.06    (57)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.06    (58)  all_58_5 = all_4_0
% 200.36/33.06    (59)   ~ (all_52_25 = all_6_2)
% 200.36/33.06    (60)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.06    (61)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.06    (62)  op(all_4_2, all_4_2) = e2
% 200.36/33.06    (63)   ~ (all_52_9 = all_6_2)
% 200.36/33.06    (64)  op(e3, e3) = all_6_2
% 200.36/33.06    (65)  all_56_3 = all_52_25
% 200.36/33.06    (66)   ~ (all_52_3 = all_52_7)
% 200.36/33.06    (67)  all_56_1 = all_52_9
% 200.36/33.06    (68)   ~ (all_52_15 = all_4_2)
% 200.36/33.06    (69)  all_58_6 = all_52_5
% 200.36/33.06    (70)  op(e3, e2) = all_52_9
% 200.36/33.06    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.06    (72)   ~ (e1 = e0)
% 200.36/33.06    (73)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.06    (74)   ~ (all_52_9 = all_52_17)
% 200.36/33.06    (75)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06    (76)  op(e1, e1) = all_10_2
% 200.36/33.06    (77)  op(all_52_9, all_52_9) = e3
% 200.36/33.06    (78)   ~ (all_52_7 = all_52_23)
% 200.36/33.06    (79)  all_58_3 = all_4_2
% 200.36/33.06    (80)  all_56_13 = all_52_15
% 200.36/33.06    (81)  all_58_4 = all_52_17
% 200.36/33.06    (82)   ~ (all_52_7 = e0)
% 200.36/33.06  
% 200.36/33.06  Begin of proof
% 200.36/33.06  | 
% 200.36/33.06  | BETA: splitting (71) gives:
% 200.36/33.06  | 
% 200.36/33.06  | Case 1:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (83)  all_58_12 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | COMBINE_EQS: (43), (83) imply:
% 200.36/33.06  | |   (84)  all_52_7 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | SIMP: (84) implies:
% 200.36/33.06  | |   (85)  all_52_7 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (66), (85) imply:
% 200.36/33.06  | |   (86)   ~ (all_52_3 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (42), (85) imply:
% 200.36/33.06  | |   (87)   ~ (all_52_5 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (9), (85) imply:
% 200.36/33.06  | |   (88)   ~ (all_52_15 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (78), (85) imply:
% 200.36/33.06  | |   (89)   ~ (all_52_23 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | SIMP: (89) implies:
% 200.36/33.06  | |   (90)   ~ (all_52_23 = e3)
% 200.36/33.06  | | 
% 200.36/33.06  | | REDUCE: (11), (85) imply:
% 200.36/33.06  | |   (91)  op(e3, e3) = all_52_6
% 200.36/33.06  | | 
% 200.36/33.06  | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 200.36/33.06  | |              with (64), (91) gives:
% 200.36/33.06  | |   (92)  all_52_6 = all_6_2
% 200.36/33.06  | | 
% 200.36/33.06  | | BETA: splitting (75) gives:
% 200.36/33.06  | | 
% 200.36/33.06  | | Case 1:
% 200.36/33.06  | | | 
% 200.36/33.06  | | |   (93)  all_58_4 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | COMBINE_EQS: (81), (93) imply:
% 200.36/33.06  | | |   (94)  all_52_17 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | SIMP: (94) implies:
% 200.36/33.06  | | |   (95)  all_52_17 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (74), (95) imply:
% 200.36/33.06  | | |   (96)   ~ (all_52_9 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (12), (95) imply:
% 200.36/33.06  | | |   (97)   ~ (all_52_25 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | SIMP: (97) implies:
% 200.36/33.06  | | |   (98)   ~ (all_52_25 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (15), (95) imply:
% 200.36/33.06  | | |   (99)   ~ (all_10_2 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | SIMP: (99) implies:
% 200.36/33.06  | | |   (100)   ~ (all_10_2 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (2), (95) imply:
% 200.36/33.06  | | |   (101)   ~ (all_4_0 = e3)
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REDUCE: (57), (95) imply:
% 200.36/33.06  | | |   (102)  op(e3, e3) = all_52_16
% 200.36/33.06  | | | 
% 200.36/33.06  | | | REF_CLOSE: (4), (5), (6), (14), (18), (19), (20), (24), (25), (30), (33),
% 200.36/33.06  | | |            (34), (35), (37), (38), (40), (41), (44), (46), (47), (48),
% 200.36/33.06  | | |            (49), (51), (52), (53), (58), (59), (60), (61), (63), (64),
% 200.36/33.06  | | |            (65), (67), (68), (69), (70), (72), (73), (76), (77), (79),
% 200.36/33.06  | | |            (86), (87), (96), (98), (100), (102) are inconsistent by
% 200.36/33.06  | | |            sub-proof #212.
% 200.36/33.06  | | | 
% 200.36/33.06  | | Case 2:
% 200.36/33.06  | | | 
% 200.36/33.06  | | |   (103)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06  | | | 
% 200.36/33.06  | | | BETA: splitting (103) gives:
% 200.36/33.06  | | | 
% 200.36/33.06  | | | Case 1:
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | |   (104)  all_58_5 = e3
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | REF_CLOSE: (34), (58), (104) are inconsistent by sub-proof #215.
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | Case 2:
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | |   (105)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | BETA: splitting (105) gives:
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | | Case 1:
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | |   (106)  all_58_8 = e3
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | COMBINE_EQS: (53), (106) imply:
% 200.36/33.06  | | | | |   (107)  all_10_2 = e3
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | SIMP: (107) implies:
% 200.36/33.06  | | | | |   (108)  all_10_2 = e3
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | COMBINE_EQS: (17), (108) imply:
% 200.36/33.06  | | | | |   (109)  all_26_2 = e3
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | REDUCE: (36), (108) imply:
% 200.36/33.06  | | | | |   (110)   ~ (all_52_13 = e3)
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | REDUCE: (21), (108) imply:
% 200.36/33.06  | | | | |   (111)  op(e3, e3) = all_52_20
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | REDUCE: (27), (108) imply:
% 200.36/33.06  | | | | |   (112)  op(e3, e1) = all_10_1
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | BETA: splitting (31) gives:
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | Case 1:
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | |   (113)   ~ (all_26_2 = e3)
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | REDUCE: (109), (113) imply:
% 200.36/33.06  | | | | | |   (114)  $false
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | CLOSE: (114) is inconsistent.
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | Case 2:
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | |   (115)   ~ (all_26_1 = e0)
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | REDUCE: (16), (115) imply:
% 200.36/33.06  | | | | | |   (116)   ~ (all_10_1 = e0)
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | GROUND_INST: instantiating (4) with all_52_17, all_10_1, e1, e3,
% 200.36/33.06  | | | | | |              simplifying with (50), (112) gives:
% 200.36/33.06  | | | | | |   (117)  all_52_17 = all_10_1
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_20, e3, e3,
% 200.36/33.06  | | | | | |              simplifying with (64), (111) gives:
% 200.36/33.06  | | | | | |   (118)  all_52_20 = all_6_2
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | COMBINE_EQS: (81), (117) imply:
% 200.36/33.06  | | | | | |   (119)  all_58_4 = all_10_1
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | BETA: splitting (3) gives:
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | | Case 1:
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | |   (120)  all_58_4 = e0
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | | COMBINE_EQS: (119), (120) imply:
% 200.36/33.06  | | | | | | |   (121)  all_10_1 = e0
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | | SIMP: (121) implies:
% 200.36/33.06  | | | | | | |   (122)  all_10_1 = e0
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | | REDUCE: (116), (122) imply:
% 200.36/33.06  | | | | | | |   (123)  $false
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | | CLOSE: (123) is inconsistent.
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | Case 2:
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | |   (124)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | | BETA: splitting (61) gives:
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | | Case 1:
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | |   (125)   ~ (all_4_2 = e3)
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | | BETA: splitting (51) gives:
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | | Case 1:
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | |   (126)  all_58_1 = e3
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | | COMBINE_EQS: (5), (126) imply:
% 200.36/33.06  | | | | | | | | |   (127)  all_52_9 = e3
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | | REF_CLOSE: (4), (63), (64), (77), (127) are inconsistent by
% 200.36/33.06  | | | | | | | | |            sub-proof #1337.
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | Case 2:
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | |   (128)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | | REF_CLOSE: (19), (22), (41), (79), (110), (125), (128) are
% 200.36/33.06  | | | | | | | | |            inconsistent by sub-proof #1256.
% 200.36/33.06  | | | | | | | | | 
% 200.36/33.06  | | | | | | | | End of split
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | Case 2:
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | |   (129)   ~ (all_4_0 = e0)
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | | REF_CLOSE: (1), (7), (54), (58), (106), (124), (129) are
% 200.36/33.06  | | | | | | | |            inconsistent by sub-proof #208.
% 200.36/33.06  | | | | | | | | 
% 200.36/33.06  | | | | | | | End of split
% 200.36/33.06  | | | | | | | 
% 200.36/33.06  | | | | | | End of split
% 200.36/33.06  | | | | | | 
% 200.36/33.06  | | | | | End of split
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | Case 2:
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | |   (130)  all_58_14 = e3
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | | REF_CLOSE: (1), (90), (130) are inconsistent by sub-proof #1305.
% 200.36/33.06  | | | | | 
% 200.36/33.06  | | | | End of split
% 200.36/33.06  | | | | 
% 200.36/33.06  | | | End of split
% 200.36/33.06  | | | 
% 200.36/33.06  | | End of split
% 200.36/33.06  | | 
% 200.36/33.06  | Case 2:
% 200.36/33.06  | | 
% 200.36/33.06  | |   (131)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.06  | | 
% 200.36/33.06  | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (13), (19), (22), (23), (26),
% 200.36/33.06  | |            (27), (28), (29), (32), (37), (39), (43), (45), (55), (56), (62),
% 200.36/33.06  | |            (68), (76), (78), (80), (82), (131) are inconsistent by sub-proof
% 200.36/33.06  | |            #648.
% 200.36/33.06  | | 
% 200.36/33.06  | End of split
% 200.36/33.06  | 
% 200.36/33.06  End of proof
% 200.36/33.06  
% 200.36/33.06  Sub-proof #136 shows that the following formulas are inconsistent:
% 200.36/33.06  ----------------------------------------------------------------
% 200.36/33.06    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.06    (2)  all_58_14 = all_52_23
% 200.36/33.06    (3)   ~ (e3 = e1)
% 200.36/33.06    (4)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.06    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.06    (6)   ~ (all_52_5 = all_52_13)
% 200.36/33.06    (7)   ~ (e3 = e0)
% 200.36/33.06    (8)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.06    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.06    (10)   ~ (all_52_7 = all_52_15)
% 200.36/33.06    (11)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.06    (12)  all_16_1 = all_10_1
% 200.36/33.06    (13)  all_58_0 = all_6_2
% 200.36/33.06    (14)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.06    (15)  all_58_13 = all_52_15
% 200.36/33.06    (16)  op(e2, e2) = all_4_2
% 200.36/33.06    (17)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 200.36/33.06    (18)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.06    (19)  op(all_10_2, e1) = all_10_1
% 200.36/33.06    (20)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.06    (21)   ~ (all_52_7 = all_6_2)
% 200.36/33.06    (22)  op(e0, e0) = all_14_2
% 200.36/33.06    (23)  op(e0, e1) = all_52_23
% 200.36/33.06    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.06    (25)  all_58_15 = e0
% 200.36/33.06    (26)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.06    (27)   ~ (e2 = e1)
% 200.36/33.07    (28)  op(e0, e0) = e0
% 200.36/33.07    (29)  all_56_8 = all_52_5
% 200.36/33.07    (30)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.07    (31)  all_16_2 = all_10_2
% 200.36/33.07    (32)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.07    (33)   ~ (all_52_5 = all_52_7)
% 200.36/33.07    (34)  all_58_12 = all_52_7
% 200.36/33.07    (35)   ~ (all_52_7 = all_14_2)
% 200.36/33.07    (36)  all_58_2 = all_52_3
% 200.36/33.07    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.07    (38)   ~ (e2 = e0)
% 200.36/33.07    (39)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.07    (40)  op(e1, e2) = all_52_13
% 200.36/33.07    (41)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.07    (42)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.07    (43)   ~ (all_52_23 = e0)
% 200.36/33.07    (44)   ~ (all_52_5 = all_10_2)
% 200.36/33.07    (45)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 200.36/33.07    (46)  all_56_12 = all_52_7
% 200.36/33.07    (47)  op(e1, all_10_1) = e2
% 200.36/33.07    (48)  op(e3, e3) = all_6_2
% 200.36/33.07    (49)  all_56_14 = all_52_23
% 200.36/33.07    (50)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.07    (51)   ~ (all_52_15 = all_4_2)
% 200.36/33.07    (52)  all_58_6 = all_52_5
% 200.36/33.07    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.07    (54)   ~ (e1 = e0)
% 200.36/33.07    (55)   ~ (e3 = e2)
% 200.36/33.07    (56)  op(e1, e1) = all_10_2
% 200.36/33.07    (57)   ~ (all_52_7 = all_52_23)
% 200.36/33.07    (58)  all_56_13 = all_52_15
% 200.36/33.07    (59)   ~ (all_52_3 = all_4_2)
% 200.36/33.07    (60)   ~ (all_52_7 = e0)
% 200.36/33.07  
% 200.36/33.07  Begin of proof
% 200.36/33.07  | 
% 200.36/33.07  | ALPHA: (8) implies:
% 200.36/33.07  |   (61)  all_52_6 = e0
% 200.36/33.07  |   (62)  all_52_4 = e1
% 200.36/33.07  |   (63)  all_52_2 = e2
% 200.36/33.07  |   (64)  all_52_0 = e3
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (4), (63) imply:
% 200.36/33.07  |   (65)  op(all_52_3, all_52_3) = e2
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (14), (62) imply:
% 200.36/33.07  |   (66)  op(all_52_5, all_52_5) = e1
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (11), (61) imply:
% 200.36/33.07  |   (67)  op(all_52_7, all_52_7) = e0
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (20), (64) imply:
% 200.36/33.07  |   (68)  op(all_6_2, all_6_2) = e3
% 200.36/33.07  | 
% 200.36/33.07  | BETA: splitting (26) gives:
% 200.36/33.07  | 
% 200.36/33.07  | Case 1:
% 200.36/33.07  | | 
% 200.36/33.07  | |   (69)  all_56_13 = e3
% 200.36/33.07  | | 
% 200.36/33.07  | | COMBINE_EQS: (58), (69) imply:
% 200.36/33.07  | |   (70)  all_52_15 = e3
% 200.36/33.07  | | 
% 200.36/33.07  | | SIMP: (70) implies:
% 200.36/33.07  | |   (71)  all_52_15 = e3
% 200.36/33.07  | | 
% 200.36/33.07  | | COMBINE_EQS: (15), (71) imply:
% 200.36/33.07  | |   (72)  all_58_13 = e3
% 200.36/33.07  | | 
% 200.36/33.07  | | REDUCE: (10), (71) imply:
% 200.36/33.07  | |   (73)   ~ (all_52_7 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | REDUCE: (1), (71) imply:
% 200.36/33.07  | |   (74)   ~ (all_52_23 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | SIMP: (74) implies:
% 200.36/33.07  | |   (75)   ~ (all_52_23 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | REDUCE: (51), (71) imply:
% 200.36/33.07  | |   (76)   ~ (all_4_2 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | SIMP: (76) implies:
% 200.36/33.07  | |   (77)   ~ (all_4_2 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | REDUCE: (30), (71) imply:
% 200.36/33.07  | |   (78)  op(e3, e3) = all_52_14
% 200.36/33.07  | | 
% 200.36/33.07  | | GROUND_INST: instantiating (5) with all_6_2, all_52_14, e3, e3, simplifying
% 200.36/33.07  | |              with (48), (78) gives:
% 200.36/33.07  | |   (79)  all_52_14 = all_6_2
% 200.36/33.07  | | 
% 200.36/33.07  | | BETA: splitting (32) gives:
% 200.36/33.07  | | 
% 200.36/33.07  | | Case 1:
% 200.36/33.07  | | | 
% 200.36/33.07  | | |   (80)  all_56_14 = e3
% 200.36/33.07  | | | 
% 200.36/33.07  | | | REF_CLOSE: (49), (75), (80) are inconsistent by sub-proof #1286.
% 200.36/33.07  | | | 
% 200.36/33.07  | | Case 2:
% 200.36/33.07  | | | 
% 200.36/33.07  | | |   (81)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.07  | | | 
% 200.36/33.07  | | | BETA: splitting (9) gives:
% 200.36/33.07  | | | 
% 200.36/33.07  | | | Case 1:
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | |   (82)  all_56_12 = e3
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | | REF_CLOSE: (46), (73), (82) are inconsistent by sub-proof #1383.
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | Case 2:
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | |   (83)   ~ (all_56_12 = e3)
% 200.36/33.07  | | | |   (84)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | | BETA: splitting (39) gives:
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | | Case 1:
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | |   (85)  all_58_12 = e1
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | REF_CLOSE: (2), (5), (6), (18), (19), (21), (23), (25), (27), (29),
% 200.36/33.07  | | | | |            (33), (34), (38), (40), (42), (44), (47), (48), (55), (56),
% 200.36/33.07  | | | | |            (66), (67), (72), (85) are inconsistent by sub-proof #627.
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | Case 2:
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | |   (86)   ~ (all_58_12 = e1)
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | REF_CLOSE: (5), (13), (16), (17), (24), (28), (34), (36), (37), (41),
% 200.36/33.07  | | | | |            (43), (44), (46), (48), (49), (52), (56), (57), (59), (60),
% 200.36/33.07  | | | | |            (65), (66), (67), (68), (73), (77), (81), (84), (86) are
% 200.36/33.07  | | | | |            inconsistent by sub-proof #219.
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | End of split
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | End of split
% 200.36/33.07  | | | 
% 200.36/33.07  | | End of split
% 200.36/33.07  | | 
% 200.36/33.07  | Case 2:
% 200.36/33.07  | | 
% 200.36/33.07  | |   (87)   ~ (all_56_13 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | REDUCE: (58), (87) imply:
% 200.36/33.07  | |   (88)   ~ (all_52_15 = e3)
% 200.36/33.07  | | 
% 200.36/33.07  | | BETA: splitting (53) gives:
% 200.36/33.07  | | 
% 200.36/33.07  | | Case 1:
% 200.36/33.07  | | | 
% 200.36/33.07  | | |   (89)  all_58_12 = e3
% 200.36/33.07  | | | 
% 200.36/33.07  | | | COMBINE_EQS: (34), (89) imply:
% 200.36/33.07  | | |   (90)  all_52_7 = e3
% 200.36/33.07  | | | 
% 200.36/33.07  | | | REF_CLOSE: (5), (13), (16), (21), (22), (24), (34), (35), (36), (37),
% 200.36/33.07  | | |            (44), (48), (52), (53), (56), (59), (65), (66), (67), (68),
% 200.36/33.07  | | |            (90) are inconsistent by sub-proof #1361.
% 200.36/33.07  | | | 
% 200.36/33.07  | | Case 2:
% 200.36/33.07  | | | 
% 200.36/33.07  | | |   (91)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.07  | | | 
% 200.36/33.07  | | | BETA: splitting (91) gives:
% 200.36/33.07  | | | 
% 200.36/33.07  | | | Case 1:
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | |   (92)  all_58_13 = e3
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | | REF_CLOSE: (15), (88), (92) are inconsistent by sub-proof #1360.
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | Case 2:
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | |   (93)  all_58_14 = e3 | all_58_15 = e3
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | | BETA: splitting (93) gives:
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | | Case 1:
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | |   (94)  all_58_14 = e3
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | COMBINE_EQS: (2), (94) imply:
% 200.36/33.07  | | | | |   (95)  all_52_23 = e3
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | SIMP: (95) implies:
% 200.36/33.07  | | | | |   (96)  all_52_23 = e3
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | REDUCE: (57), (96) imply:
% 200.36/33.07  | | | | |   (97)   ~ (all_52_7 = e3)
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | REDUCE: (41), (96) imply:
% 200.36/33.07  | | | | |   (98)  op(e3, e3) = all_52_22
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | REDUCE: (23), (96) imply:
% 200.36/33.07  | | | | |   (99)  op(e0, e1) = e3
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3,
% 200.36/33.07  | | | | |              simplifying with (48), (98) gives:
% 200.36/33.07  | | | | |   (100)  all_52_22 = all_6_2
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | BETA: splitting (9) gives:
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | Case 1:
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | |   (101)  all_56_12 = e3
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | | REF_CLOSE: (46), (97), (101) are inconsistent by sub-proof #1383.
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | Case 2:
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | |   (102)   ~ (all_56_12 = e3)
% 200.36/33.07  | | | | | |   (103)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | | BETA: splitting (39) gives:
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | | Case 1:
% 200.36/33.07  | | | | | | | 
% 200.36/33.07  | | | | | | |   (104)  all_58_12 = e1
% 200.36/33.07  | | | | | | | 
% 200.36/33.07  | | | | | | | REF_CLOSE: (5), (12), (19), (31), (34), (45), (56), (67), (99),
% 200.36/33.07  | | | | | | |            (104) are inconsistent by sub-proof #651.
% 200.36/33.07  | | | | | | | 
% 200.36/33.07  | | | | | | Case 2:
% 200.36/33.07  | | | | | | | 
% 200.36/33.07  | | | | | | |   (105)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.07  | | | | | | | 
% 200.36/33.07  | | | | | | | REF_CLOSE: (3), (5), (7), (10), (13), (15), (16), (17), (18),
% 200.36/33.07  | | | | | | |            (24), (25), (28), (30), (34), (36), (37), (44), (46),
% 200.36/33.07  | | | | | | |            (48), (50), (51), (52), (54), (56), (59), (60), (65),
% 200.36/33.07  | | | | | | |            (66), (67), (68), (94), (97), (103), (105) are
% 200.36/33.07  | | | | | | |            inconsistent by sub-proof #217.
% 200.36/33.07  | | | | | | | 
% 200.36/33.07  | | | | | | End of split
% 200.36/33.07  | | | | | | 
% 200.36/33.07  | | | | | End of split
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | Case 2:
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | |   (106)  all_58_15 = e3
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | | REF_CLOSE: (7), (25), (106) are inconsistent by sub-proof #1350.
% 200.36/33.07  | | | | | 
% 200.36/33.07  | | | | End of split
% 200.36/33.07  | | | | 
% 200.36/33.07  | | | End of split
% 200.36/33.07  | | | 
% 200.36/33.07  | | End of split
% 200.36/33.07  | | 
% 200.36/33.07  | End of split
% 200.36/33.07  | 
% 200.36/33.07  End of proof
% 200.36/33.07  
% 200.36/33.07  Sub-proof #137 shows that the following formulas are inconsistent:
% 200.36/33.07  ----------------------------------------------------------------
% 200.36/33.07    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.07    (2)   ~ (all_52_25 = all_52_27)
% 200.36/33.07    (3)  all_58_14 = all_52_23
% 200.36/33.07    (4)   ~ (e3 = e1)
% 200.36/33.07    (5)   ~ (all_52_17 = all_4_0)
% 200.36/33.07    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.07    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.07    (9)  all_58_1 = all_52_9
% 200.36/33.07    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.07    (11)   ~ (e3 = e0)
% 200.36/33.07    (12)  op(e2, e3) = all_52_3
% 200.36/33.07    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.07    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.07    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.07    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.07    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.07    (18)   ~ (all_52_3 = all_6_2)
% 200.36/33.07    (19)  all_58_0 = all_6_2
% 200.36/33.07    (20)  op(all_14_2, e0) = all_14_1
% 200.36/33.07    (21)  all_56_4 = all_52_3
% 200.36/33.07    (22)   ~ (all_52_17 = all_10_2)
% 200.36/33.07    (23)  op(e3, e0) = all_52_25
% 200.36/33.07    (24)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.07    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.07    (26)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.07    (27)   ~ (all_52_27 = all_52_29)
% 200.36/33.07    (28)  all_58_13 = all_52_15
% 200.36/33.07    (29)  all_58_9 = all_52_25
% 200.36/33.07    (30)   ~ (all_6_1 = e1)
% 200.36/33.07    (31)   ~ (all_52_29 = all_14_2)
% 200.36/33.07    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.07    (33)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.07    (34)  op(e1, e3) = all_52_5
% 200.36/33.07    (35)  op(e2, e2) = all_4_2
% 200.36/33.07    (36)   ~ (all_52_3 = all_52_5)
% 200.36/33.07    (37)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.07    (38)  op(all_4_2, e2) = e1
% 200.36/33.07    (39)  all_58_11 = all_52_29
% 200.36/33.07    (40)  all_56_5 = all_4_2
% 200.36/33.07    (41)   ~ (all_52_25 = all_14_2)
% 200.36/33.07    (42)   ~ (all_52_9 = all_52_15)
% 200.36/33.07    (43)   ~ (all_52_3 = all_52_27)
% 200.36/33.07    (44)  op(all_10_2, e1) = all_10_1
% 200.36/33.07    (45)   ~ (all_10_2 = all_4_0)
% 200.36/33.07    (46)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.07    (47)   ~ (all_52_7 = all_6_2)
% 200.36/33.07    (48)  op(e0, e0) = all_14_2
% 200.36/33.07    (49)  all_56_15 = all_14_2
% 200.36/33.07    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.07    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.07    (52)  all_56_11 = all_52_29
% 200.36/33.07    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.07    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.07    (55)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.07    (56)   ~ (e2 = e1)
% 200.36/33.07    (57)   ~ (all_52_13 = all_10_2)
% 200.36/33.07    (58)   ~ (all_6_0 = e1)
% 200.36/33.07    (59)  all_58_10 = all_52_27
% 200.36/33.07    (60)  all_56_8 = all_52_5
% 200.36/33.07    (61)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.07    (62)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.07    (63)   ~ (all_52_19 = all_52_23)
% 200.36/33.07    (64)   ~ (all_52_25 = all_52_29)
% 200.36/33.07    (65)   ~ (all_52_29 = all_10_2)
% 200.36/33.07    (66)  all_58_7 = all_52_13
% 200.36/33.07    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.07    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.07    (69)   ~ (all_52_5 = all_52_7)
% 200.36/33.07    (70)  all_58_12 = all_52_7
% 200.36/33.07    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.07    (72)   ~ (all_52_7 = all_14_2)
% 200.36/33.07    (73)  all_58_2 = all_52_3
% 200.36/33.07    (74)  all_56_2 = all_52_17
% 200.36/33.07    (75)  all_28_0 = all_4_0
% 200.36/33.07    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.07    (77)  op(e3, all_6_1) = all_6_0
% 200.36/33.07    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.07    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.07    (80)  all_56_7 = all_52_27
% 200.36/33.07    (81)  all_28_2 = all_4_2
% 200.36/33.07    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.07    (83)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.07    (84)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.07    (85)   ~ (all_52_5 = all_52_29)
% 200.36/33.07    (86)   ~ (all_52_15 = all_14_2)
% 200.36/33.07    (87)   ~ (all_52_19 = all_52_27)
% 200.36/33.07    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.07    (89)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.07    (90)   ~ (all_6_0 = e2)
% 200.36/33.07    (91)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.36/33.07            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.36/33.07    (92)   ~ (all_52_13 = all_4_2)
% 200.36/33.07    (93)  op(e3, e1) = all_52_17
% 200.36/33.07    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.07    (95)  op(e0, e3) = all_52_7
% 200.36/33.07    (96)  op(e1, e2) = all_52_13
% 200.36/33.07    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.07    (98)   ~ (all_52_9 = all_52_25)
% 200.36/33.07    (99)  all_58_15 = all_14_2
% 200.36/33.07    (100)   ~ (all_52_19 = all_10_2)
% 200.36/33.07    (101)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.07    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.07    (103)  all_58_8 = all_10_2
% 200.36/33.07    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.07    (105)   ~ (all_52_5 = all_10_2)
% 200.36/33.07    (106)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.07    (107)   ~ (all_52_23 = all_14_2)
% 200.36/33.07    (108)  all_56_12 = all_52_7
% 200.36/33.07    (109)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.07    (110)  all_58_5 = all_4_0
% 200.36/33.07    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.07    (112)   ~ (all_52_25 = all_6_2)
% 200.36/33.07    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.07    (114)   ~ (all_52_9 = all_4_2)
% 200.36/33.07    (115)   ~ (all_52_5 = all_6_2)
% 200.36/33.07    (116)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.07    (117)   ~ (all_52_9 = all_6_2)
% 200.36/33.07    (118)   ~ (all_52_13 = all_52_15)
% 200.36/33.07    (119)  all_56_0 = all_6_2
% 200.36/33.07    (120)  op(all_4_0, all_4_0) = all_52_18
% 200.36/33.07    (121)  op(e3, e3) = all_6_2
% 200.36/33.07    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.07    (123)   ~ (all_52_27 = all_14_2)
% 200.36/33.07    (124)   ~ (all_52_27 = all_4_0)
% 200.36/33.07    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.07    (126)  all_56_14 = all_52_23
% 200.36/33.07    (127)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.36/33.07    (128)  all_56_3 = all_52_25
% 200.36/33.07    (129)  all_28_0 = e3
% 200.36/33.07    (130)   ~ (all_52_3 = all_52_7)
% 200.36/33.07    (131)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.07    (132)  all_58_5 = all_52_19
% 200.36/33.07    (133)  all_56_1 = all_52_9
% 200.36/33.07    (134)   ~ (all_52_15 = all_4_2)
% 200.36/33.07    (135)  op(e0, all_14_1) = e3
% 200.36/33.07    (136)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.07           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.07           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.07           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.07    (137)   ~ (all_52_27 = all_4_2)
% 200.36/33.07    (138)  all_58_6 = all_52_5
% 200.36/33.07    (139)   ~ (all_4_0 = all_4_2)
% 200.36/33.07    (140)  op(e3, e2) = all_52_9
% 200.36/33.07    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.07    (142)   ~ (all_52_17 = all_6_2)
% 200.36/33.07    (143)   ~ (e1 = e0)
% 200.36/33.07    (144)   ~ (e3 = e2)
% 200.36/33.07    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.07    (146)   ~ (all_52_9 = all_52_17)
% 200.36/33.07    (147)   ~ (all_52_3 = all_4_0)
% 200.36/33.07    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.07    (149)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.07    (150)   ~ (all_6_1 = e2)
% 200.36/33.07    (151)  op(e1, e1) = all_10_2
% 200.36/33.07    (152)   ~ (all_52_23 = all_10_2)
% 200.36/33.07    (153)   ~ (all_52_7 = all_52_23)
% 200.36/33.07    (154)   ~ (all_52_17 = all_52_19)
% 200.36/33.07    (155)  all_58_3 = all_4_2
% 200.36/33.07    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.07    (157)  all_56_13 = all_52_15
% 200.36/33.07    (158)   ~ (all_52_3 = all_4_2)
% 200.36/33.07    (159)  all_28_1 = e1
% 200.36/33.07    (160)   ~ (all_52_19 = all_4_2)
% 200.36/33.07    (161)   ~ (all_52_17 = all_52_23)
% 200.36/33.07    (162)  op(all_6_2, e3) = all_6_1
% 200.36/33.07    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.07    (164)   ~ (all_52_13 = all_52_29)
% 200.36/33.07    (165)  all_58_4 = all_52_17
% 200.36/33.07    (166)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.07  
% 200.36/33.07  Begin of proof
% 200.36/33.07  | 
% 200.36/33.07  | COMBINE_EQS: (75), (129) imply:
% 200.36/33.07  |   (167)  all_4_0 = e3
% 200.36/33.07  | 
% 200.36/33.07  | SIMP: (167) implies:
% 200.36/33.07  |   (168)  all_4_0 = e3
% 200.36/33.07  | 
% 200.36/33.07  | COMBINE_EQS: (110), (168) imply:
% 200.36/33.07  |   (169)  all_58_5 = e3
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (147), (168) imply:
% 200.36/33.07  |   (170)   ~ (all_52_3 = e3)
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (5), (168) imply:
% 200.36/33.07  |   (171)   ~ (all_52_17 = e3)
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (124), (168) imply:
% 200.36/33.07  |   (172)   ~ (all_52_27 = e3)
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (45), (168) imply:
% 200.36/33.07  |   (173)   ~ (all_10_2 = e3)
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (139), (168) imply:
% 200.36/33.07  |   (174)   ~ (all_4_2 = e3)
% 200.36/33.07  | 
% 200.36/33.07  | SIMP: (174) implies:
% 200.36/33.07  |   (175)   ~ (all_4_2 = e3)
% 200.36/33.07  | 
% 200.36/33.07  | REDUCE: (120), (168) imply:
% 200.36/33.07  |   (176)  op(e3, e3) = all_52_18
% 200.36/33.07  | 
% 200.36/33.07  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.07  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 200.36/33.07  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 200.36/33.07  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 200.36/33.07  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 200.36/33.07  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 200.36/33.07  |            (70), (71), (72), (73), (74), (76), (77), (78), (79), (80), (81),
% 200.36/33.07  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 200.36/33.07  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 200.36/33.07  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 200.36/33.07  |            (112), (113), (114), (115), (116), (117), (118), (119), (121),
% 200.36/33.07  |            (122), (123), (125), (126), (127), (128), (130), (131), (132),
% 200.36/33.07  |            (133), (134), (135), (136), (137), (138), (139), (140), (141),
% 200.36/33.07  |            (142), (143), (144), (145), (146), (148), (149), (150), (151),
% 200.36/33.07  |            (152), (153), (154), (155), (156), (157), (158), (159), (160),
% 200.36/33.07  |            (161), (162), (163), (164), (165), (166), (169), (170), (171),
% 200.36/33.07  |            (172), (173), (175), (176) are inconsistent by sub-proof #138.
% 200.36/33.07  | 
% 200.36/33.07  End of proof
% 200.36/33.07  
% 200.36/33.07  Sub-proof #138 shows that the following formulas are inconsistent:
% 200.36/33.07  ----------------------------------------------------------------
% 200.36/33.07    (1)  op(e3, e3) = all_52_18
% 200.36/33.07    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.07    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.07    (4)  all_58_14 = all_52_23
% 200.36/33.07    (5)   ~ (e3 = e1)
% 200.36/33.07    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.07    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.07    (9)  all_58_1 = all_52_9
% 200.36/33.07    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.07    (11)   ~ (e3 = e0)
% 200.36/33.07    (12)  op(e2, e3) = all_52_3
% 200.36/33.07    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.07    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.07    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.07    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.07    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.07    (18)   ~ (all_4_2 = e3)
% 200.36/33.07    (19)   ~ (all_52_3 = all_6_2)
% 200.36/33.07    (20)  all_58_0 = all_6_2
% 200.36/33.07    (21)  op(all_14_2, e0) = all_14_1
% 200.36/33.07    (22)  all_56_4 = all_52_3
% 200.36/33.07    (23)   ~ (all_52_17 = all_10_2)
% 200.36/33.07    (24)  op(e3, e0) = all_52_25
% 200.36/33.07    (25)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.07    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.07    (27)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.07    (28)   ~ (all_52_27 = all_52_29)
% 200.36/33.07    (29)  all_58_13 = all_52_15
% 200.36/33.07    (30)  all_58_9 = all_52_25
% 200.36/33.07    (31)   ~ (all_6_1 = e1)
% 200.36/33.07    (32)   ~ (all_52_29 = all_14_2)
% 200.36/33.07    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.07    (34)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.07    (35)  op(e1, e3) = all_52_5
% 200.36/33.07    (36)  op(e2, e2) = all_4_2
% 200.36/33.07    (37)   ~ (all_52_3 = all_52_5)
% 200.36/33.07    (38)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.07    (39)  op(all_4_2, e2) = e1
% 200.36/33.07    (40)  all_58_11 = all_52_29
% 200.36/33.07    (41)   ~ (all_52_3 = e3)
% 200.36/33.07    (42)  all_56_5 = all_4_2
% 200.36/33.07    (43)   ~ (all_52_25 = all_14_2)
% 200.36/33.07    (44)   ~ (all_52_9 = all_52_15)
% 200.36/33.07    (45)   ~ (all_52_3 = all_52_27)
% 200.36/33.07    (46)  op(all_10_2, e1) = all_10_1
% 200.36/33.07    (47)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.07    (48)   ~ (all_52_7 = all_6_2)
% 200.36/33.07    (49)  op(e0, e0) = all_14_2
% 200.36/33.07    (50)  all_56_15 = all_14_2
% 200.36/33.07    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.07    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.07    (53)  all_56_11 = all_52_29
% 200.36/33.07    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.07    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.07    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.07    (57)   ~ (e2 = e1)
% 200.36/33.07    (58)   ~ (all_52_13 = all_10_2)
% 200.36/33.07    (59)   ~ (all_6_0 = e1)
% 200.36/33.07    (60)  all_58_10 = all_52_27
% 200.36/33.07    (61)  all_56_8 = all_52_5
% 200.36/33.07    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.07    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.07    (64)   ~ (all_52_19 = all_52_23)
% 200.36/33.07    (65)   ~ (all_52_25 = all_52_29)
% 200.36/33.07    (66)   ~ (all_52_29 = all_10_2)
% 200.36/33.07    (67)  all_58_7 = all_52_13
% 200.36/33.07    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.08    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.08    (70)   ~ (all_52_5 = all_52_7)
% 200.36/33.08    (71)  all_58_12 = all_52_7
% 200.36/33.08    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.08    (73)   ~ (all_52_7 = all_14_2)
% 200.36/33.08    (74)  all_58_2 = all_52_3
% 200.36/33.08    (75)  all_56_2 = all_52_17
% 200.36/33.08    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.08    (77)  op(e3, all_6_1) = all_6_0
% 200.36/33.08    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.08    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.08    (80)  all_56_7 = all_52_27
% 200.36/33.08    (81)  all_28_2 = all_4_2
% 200.36/33.08    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.08    (83)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.08    (84)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.08    (85)   ~ (all_52_5 = all_52_29)
% 200.36/33.08    (86)   ~ (all_10_2 = e3)
% 200.36/33.08    (87)   ~ (all_52_15 = all_14_2)
% 200.36/33.08    (88)   ~ (all_52_19 = all_52_27)
% 200.36/33.08    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.08    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.08    (91)   ~ (all_52_27 = e3)
% 200.36/33.08    (92)   ~ (all_6_0 = e2)
% 200.36/33.08    (93)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.36/33.08            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.36/33.08    (94)   ~ (all_52_13 = all_4_2)
% 200.36/33.08    (95)  op(e3, e1) = all_52_17
% 200.36/33.08    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.08    (97)  op(e0, e3) = all_52_7
% 200.36/33.08    (98)  op(e1, e2) = all_52_13
% 200.36/33.08    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.08    (100)   ~ (all_52_9 = all_52_25)
% 200.36/33.08    (101)  all_58_15 = all_14_2
% 200.36/33.08    (102)   ~ (all_52_19 = all_10_2)
% 200.36/33.08    (103)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.08    (104)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.08    (105)  all_58_8 = all_10_2
% 200.36/33.08    (106)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.08    (107)   ~ (all_52_5 = all_10_2)
% 200.36/33.08    (108)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.08    (109)   ~ (all_52_23 = all_14_2)
% 200.36/33.08    (110)  all_56_12 = all_52_7
% 200.36/33.08    (111)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.08    (112)  all_58_5 = all_4_0
% 200.36/33.08    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.08    (114)   ~ (all_52_25 = all_6_2)
% 200.36/33.08    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.08    (116)   ~ (all_52_9 = all_4_2)
% 200.36/33.08    (117)   ~ (all_52_5 = all_6_2)
% 200.36/33.08    (118)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.08    (119)   ~ (all_52_9 = all_6_2)
% 200.36/33.08    (120)   ~ (all_52_13 = all_52_15)
% 200.36/33.08    (121)  all_56_0 = all_6_2
% 200.36/33.08    (122)  op(e3, e3) = all_6_2
% 200.36/33.08    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.08    (124)   ~ (all_52_27 = all_14_2)
% 200.36/33.08    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.08    (126)  all_58_5 = e3
% 200.36/33.08    (127)  all_56_14 = all_52_23
% 200.36/33.08    (128)   ~ (all_52_17 = e3)
% 200.36/33.08    (129)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.36/33.08    (130)  all_56_3 = all_52_25
% 200.36/33.08    (131)   ~ (all_52_3 = all_52_7)
% 200.36/33.08    (132)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.08    (133)  all_58_5 = all_52_19
% 200.36/33.08    (134)  all_56_1 = all_52_9
% 200.36/33.08    (135)   ~ (all_52_15 = all_4_2)
% 200.36/33.08    (136)  op(e0, all_14_1) = e3
% 200.36/33.08    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.08           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.08           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.08           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.08    (138)   ~ (all_52_27 = all_4_2)
% 200.36/33.08    (139)  all_58_6 = all_52_5
% 200.36/33.08    (140)   ~ (all_4_0 = all_4_2)
% 200.36/33.08    (141)  op(e3, e2) = all_52_9
% 200.36/33.08    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.08    (143)   ~ (all_52_17 = all_6_2)
% 200.36/33.08    (144)   ~ (e1 = e0)
% 200.36/33.08    (145)   ~ (e3 = e2)
% 200.36/33.08    (146)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.08    (147)   ~ (all_52_9 = all_52_17)
% 200.36/33.08    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.08    (149)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.08    (150)   ~ (all_6_1 = e2)
% 200.36/33.08    (151)  op(e1, e1) = all_10_2
% 200.36/33.08    (152)   ~ (all_52_23 = all_10_2)
% 200.36/33.08    (153)   ~ (all_52_7 = all_52_23)
% 200.36/33.08    (154)   ~ (all_52_17 = all_52_19)
% 200.36/33.08    (155)  all_58_3 = all_4_2
% 200.36/33.08    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.08    (157)  all_56_13 = all_52_15
% 200.36/33.08    (158)   ~ (all_52_3 = all_4_2)
% 200.36/33.08    (159)  all_28_1 = e1
% 200.36/33.08    (160)   ~ (all_52_19 = all_4_2)
% 200.36/33.08    (161)   ~ (all_52_17 = all_52_23)
% 200.36/33.08    (162)  op(all_6_2, e3) = all_6_1
% 200.36/33.08    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.08    (164)   ~ (all_52_13 = all_52_29)
% 200.36/33.08    (165)  all_58_4 = all_52_17
% 200.36/33.08    (166)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.08  
% 200.36/33.08  Begin of proof
% 200.36/33.08  | 
% 200.36/33.08  | BETA: splitting (129) gives:
% 200.36/33.08  | 
% 200.36/33.08  | Case 1:
% 200.36/33.08  | | 
% 200.36/33.08  | |   (167)   ~ (all_28_1 = e1)
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (159), (167) imply:
% 200.36/33.08  | |   (168)  $false
% 200.36/33.08  | | 
% 200.36/33.08  | | CLOSE: (168) is inconsistent.
% 200.36/33.08  | | 
% 200.36/33.08  | Case 2:
% 200.36/33.08  | | 
% 200.36/33.08  | |   (169)   ~ (all_28_2 = e0)
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (81), (169) imply:
% 200.36/33.08  | |   (170)   ~ (all_4_2 = e0)
% 200.36/33.08  | | 
% 200.36/33.08  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 200.36/33.08  | |              with (1), (122) gives:
% 200.36/33.08  | |   (171)  all_52_18 = all_6_2
% 200.36/33.08  | | 
% 200.36/33.08  | | BETA: splitting (93) gives:
% 200.36/33.08  | | 
% 200.36/33.08  | | Case 1:
% 200.36/33.08  | | | 
% 200.36/33.08  | | |   (172)  all_58_15 = e0
% 200.36/33.08  | | | 
% 200.36/33.08  | | | REF_CLOSE: (6), (7), (11), (21), (38), (41), (49), (60), (74), (101),
% 200.36/33.08  | | |            (124), (126), (132), (136), (155), (170), (172) are
% 200.36/33.08  | | |            inconsistent by sub-proof #139.
% 200.36/33.08  | | | 
% 200.36/33.08  | | Case 2:
% 200.36/33.08  | | | 
% 200.36/33.08  | | |   (173)   ~ (all_58_15 = e0)
% 200.36/33.08  | | |   (174)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 200.36/33.08  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 200.36/33.08  | | | 
% 200.36/33.08  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.08  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 200.36/33.08  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 200.36/33.08  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 200.36/33.08  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 200.36/33.08  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 200.36/33.08  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 200.36/33.08  | | |            (75), (76), (77), (78), (79), (80), (82), (83), (84), (85),
% 200.36/33.08  | | |            (86), (87), (88), (89), (90), (91), (92), (94), (95), (96),
% 200.36/33.08  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 200.36/33.08  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 200.36/33.08  | | |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 200.36/33.08  | | |            (124), (125), (126), (127), (128), (130), (131), (132), (133),
% 200.36/33.08  | | |            (134), (135), (137), (138), (139), (140), (141), (142), (143),
% 200.36/33.08  | | |            (144), (145), (146), (147), (148), (149), (150), (151), (152),
% 200.36/33.08  | | |            (153), (154), (155), (156), (157), (158), (160), (161), (162),
% 200.36/33.08  | | |            (163), (164), (165), (166), (170), (171), (173), (174) are
% 200.36/33.08  | | |            inconsistent by sub-proof #146.
% 200.36/33.08  | | | 
% 200.36/33.08  | | End of split
% 200.36/33.08  | | 
% 200.36/33.08  | End of split
% 200.36/33.08  | 
% 200.36/33.08  End of proof
% 200.36/33.08  
% 200.36/33.08  Sub-proof #139 shows that the following formulas are inconsistent:
% 200.36/33.08  ----------------------------------------------------------------
% 200.36/33.08    (1)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.08    (3)   ~ (e3 = e0)
% 200.36/33.08    (4)  op(all_14_2, e0) = all_14_1
% 200.36/33.08    (5)   ~ (all_4_2 = e0)
% 200.36/33.08    (6)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.08    (7)   ~ (all_52_3 = e3)
% 200.36/33.08    (8)  op(e0, e0) = all_14_2
% 200.36/33.08    (9)  all_58_15 = e0
% 200.36/33.08    (10)  all_58_10 = all_52_27
% 200.36/33.08    (11)  all_58_2 = all_52_3
% 200.36/33.08    (12)  all_58_15 = all_14_2
% 200.36/33.08    (13)   ~ (all_52_27 = all_14_2)
% 200.36/33.08    (14)  all_58_5 = e3
% 200.36/33.08    (15)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.08    (16)  op(e0, all_14_1) = e3
% 200.36/33.08    (17)  all_58_3 = all_4_2
% 200.36/33.08  
% 200.36/33.08  Begin of proof
% 200.36/33.08  | 
% 200.36/33.08  | COMBINE_EQS: (9), (12) imply:
% 200.36/33.08  |   (18)  all_14_2 = e0
% 200.36/33.08  | 
% 200.36/33.08  | REDUCE: (13), (18) imply:
% 200.36/33.08  |   (19)   ~ (all_52_27 = e0)
% 200.36/33.08  | 
% 200.36/33.08  | REDUCE: (15), (18) imply:
% 200.36/33.08  |   (20)  op(e0, e0) = all_52_30
% 200.36/33.08  | 
% 200.36/33.08  | REDUCE: (4), (18) imply:
% 200.36/33.08  |   (21)  op(e0, e0) = all_14_1
% 200.36/33.08  | 
% 200.36/33.08  | REDUCE: (8), (18) imply:
% 200.36/33.08  |   (22)  op(e0, e0) = e0
% 200.36/33.08  | 
% 200.36/33.08  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (11), (14), (16), (17), (19),
% 200.36/33.08  |            (20), (21), (22) are inconsistent by sub-proof #140.
% 200.36/33.08  | 
% 200.36/33.08  End of proof
% 200.36/33.08  
% 200.36/33.08  Sub-proof #140 shows that the following formulas are inconsistent:
% 200.36/33.08  ----------------------------------------------------------------
% 200.36/33.08    (1)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.08    (3)   ~ (e3 = e0)
% 200.36/33.08    (4)   ~ (all_4_2 = e0)
% 200.36/33.08    (5)  op(e0, e0) = all_52_30
% 200.36/33.08    (6)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.08    (7)   ~ (all_52_3 = e3)
% 200.36/33.08    (8)  op(e0, e0) = e0
% 200.36/33.08    (9)  all_58_10 = all_52_27
% 200.36/33.08    (10)  all_58_2 = all_52_3
% 200.36/33.08    (11)  op(e0, e0) = all_14_1
% 200.36/33.08    (12)   ~ (all_52_27 = e0)
% 200.36/33.08    (13)  all_58_5 = e3
% 200.36/33.08    (14)  op(e0, all_14_1) = e3
% 200.36/33.08    (15)  all_58_3 = all_4_2
% 200.36/33.08  
% 200.36/33.08  Begin of proof
% 200.36/33.08  | 
% 200.36/33.08  | BETA: splitting (6) gives:
% 200.36/33.08  | 
% 200.36/33.08  | Case 1:
% 200.36/33.08  | | 
% 200.36/33.08  | |   (16)  all_58_2 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | COMBINE_EQS: (10), (16) imply:
% 200.36/33.08  | |   (17)  all_52_3 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | SIMP: (17) implies:
% 200.36/33.08  | |   (18)  all_52_3 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (7), (18) imply:
% 200.36/33.08  | |   (19)   ~ (e3 = e0)
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (1), (18) imply:
% 200.36/33.08  | |   (20)  op(e0, e0) = all_52_2
% 200.36/33.08  | | 
% 200.36/33.08  | | GROUND_INST: instantiating (2) with all_14_1, all_52_30, e0, e0, simplifying
% 200.36/33.08  | |              with (5), (11) gives:
% 200.36/33.08  | |   (21)  all_52_30 = all_14_1
% 200.36/33.08  | | 
% 200.36/33.08  | | GROUND_INST: instantiating (2) with all_52_30, all_52_2, e0, e0, simplifying
% 200.36/33.08  | |              with (5), (20) gives:
% 200.36/33.08  | |   (22)  all_52_2 = all_52_30
% 200.36/33.08  | | 
% 200.36/33.08  | | GROUND_INST: instantiating (2) with e0, all_52_2, e0, e0, simplifying with
% 200.36/33.08  | |              (8), (20) gives:
% 200.36/33.08  | |   (23)  all_52_2 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | COMBINE_EQS: (22), (23) imply:
% 200.36/33.08  | |   (24)  all_52_30 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | SIMP: (24) implies:
% 200.36/33.08  | |   (25)  all_52_30 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | REF_CLOSE: (2), (3), (11), (14), (21), (25) are inconsistent by sub-proof
% 200.36/33.08  | |            #679.
% 200.36/33.08  | | 
% 200.36/33.08  | Case 2:
% 200.36/33.08  | | 
% 200.36/33.08  | |   (26)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.08  | | 
% 200.36/33.08  | | REF_CLOSE: (3), (4), (9), (12), (13), (15), (26) are inconsistent by
% 200.36/33.08  | |            sub-proof #152.
% 200.36/33.08  | | 
% 200.36/33.08  | End of split
% 200.36/33.08  | 
% 200.36/33.08  End of proof
% 200.36/33.08  
% 200.36/33.08  Sub-proof #141 shows that the following formulas are inconsistent:
% 200.36/33.08  ----------------------------------------------------------------
% 200.36/33.08    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.08    (2)   ~ (all_52_25 = all_6_0)
% 200.36/33.08    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.08    (5)   ~ (e3 = e0)
% 200.36/33.08    (6)  op(e2, e3) = all_52_3
% 200.36/33.08    (7)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.08    (8)   ~ (all_52_3 = all_6_2)
% 200.36/33.08    (9)  all_58_0 = all_6_2
% 200.36/33.08    (10)  op(all_14_2, e0) = all_14_1
% 200.36/33.08    (11)  op(e3, e0) = all_52_25
% 200.36/33.08    (12)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.08    (13)  all_58_9 = all_52_25
% 200.36/33.08    (14)   ~ (all_52_29 = all_14_2)
% 200.36/33.08    (15)  all_22_0 = all_6_0
% 200.36/33.08    (16)  op(e1, e3) = all_52_5
% 200.36/33.08    (17)  op(e2, e2) = all_4_2
% 200.36/33.08    (18)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 200.36/33.08    (19)  all_58_11 = all_52_29
% 200.36/33.08    (20)   ~ (all_52_3 = e3)
% 200.36/33.08    (21)   ~ (all_52_25 = all_14_2)
% 200.36/33.08    (22)   ~ (all_52_3 = all_52_27)
% 200.36/33.08    (23)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.08    (24)  op(e0, e0) = all_14_2
% 200.36/33.08    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.08    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.08    (27)   ~ (all_6_0 = e1)
% 200.36/33.08    (28)  all_58_10 = all_52_27
% 200.36/33.08    (29)  op(all_6_2, e3) = e2
% 200.36/33.08    (30)  all_58_12 = all_52_7
% 200.36/33.08    (31)   ~ (all_52_7 = all_14_2)
% 200.36/33.08    (32)  all_52_18 = all_6_2
% 200.36/33.08    (33)  all_58_2 = all_52_3
% 200.36/33.08    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.08    (35)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 200.36/33.08    (36)   ~ (e2 = e0)
% 200.36/33.08    (37)  op(all_6_0, all_6_0) = all_52_8
% 200.36/33.08    (38)   ~ (all_52_5 = all_52_29)
% 200.36/33.08    (39)   ~ (all_52_27 = e3)
% 200.36/33.08    (40)   ~ (all_6_0 = e2)
% 200.36/33.08    (41)  all_58_15 = all_14_2
% 200.36/33.08    (42)   ~ (all_52_5 = all_10_2)
% 200.36/33.08    (43)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.08    (44)   ~ (all_52_25 = all_6_2)
% 200.36/33.08    (45)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.08    (46)  all_56_0 = all_6_2
% 200.36/33.08    (47)  op(e3, e3) = all_6_2
% 200.36/33.08    (48)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.08    (49)  all_56_3 = all_52_25
% 200.36/33.08    (50)   ~ (all_52_3 = all_52_7)
% 200.36/33.08    (51)   ~ (all_6_0 = all_6_2)
% 200.36/33.08    (52)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.08    (53)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.08          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.08          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.08          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.08    (54)  all_58_6 = all_52_5
% 200.36/33.08    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.08    (56)   ~ (e1 = e0)
% 200.36/33.08    (57)   ~ (e3 = e2)
% 200.36/33.08    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.08    (59)  all_56_1 = all_6_0
% 200.36/33.08    (60)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.08    (61)   ~ (all_6_0 = all_4_2)
% 200.36/33.08    (62)  op(e1, e1) = all_10_2
% 200.36/33.08    (63)   ~ (all_52_3 = all_4_2)
% 200.36/33.08    (64)  all_22_2 = all_6_2
% 200.36/33.08    (65)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.08  
% 200.36/33.08  Begin of proof
% 200.36/33.08  | 
% 200.36/33.08  | BETA: splitting (58) gives:
% 200.36/33.08  | 
% 200.36/33.08  | Case 1:
% 200.36/33.08  | | 
% 200.36/33.08  | |   (66)  all_56_1 = e3
% 200.36/33.08  | | 
% 200.36/33.08  | | COMBINE_EQS: (59), (66) imply:
% 200.36/33.08  | |   (67)  all_6_0 = e3
% 200.36/33.08  | | 
% 200.36/33.08  | | SIMP: (67) implies:
% 200.36/33.08  | |   (68)  all_6_0 = e3
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (2), (68) imply:
% 200.36/33.08  | |   (69)   ~ (all_52_25 = e3)
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (51), (68) imply:
% 200.36/33.08  | |   (70)   ~ (all_6_2 = e3)
% 200.36/33.08  | | 
% 200.36/33.08  | | SIMP: (70) implies:
% 200.36/33.08  | |   (71)   ~ (all_6_2 = e3)
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (61), (68) imply:
% 200.36/33.08  | |   (72)   ~ (all_4_2 = e3)
% 200.36/33.08  | | 
% 200.36/33.08  | | SIMP: (72) implies:
% 200.36/33.08  | |   (73)   ~ (all_4_2 = e3)
% 200.36/33.08  | | 
% 200.36/33.08  | | REDUCE: (37), (68) imply:
% 200.36/33.08  | |   (74)  op(e3, e3) = all_52_8
% 200.36/33.08  | | 
% 200.36/33.08  | | GROUND_INST: instantiating (4) with all_6_2, all_52_8, e3, e3, simplifying
% 200.36/33.08  | |              with (47), (74) gives:
% 200.36/33.08  | |   (75)  all_52_8 = all_6_2
% 200.36/33.08  | | 
% 200.36/33.08  | | BETA: splitting (53) gives:
% 200.36/33.08  | | 
% 200.36/33.08  | | Case 1:
% 200.36/33.08  | | | 
% 200.36/33.08  | | |   (76)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.08  | | |         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 200.36/33.08  | | | 
% 200.36/33.08  | | | BETA: splitting (76) gives:
% 200.36/33.08  | | | 
% 200.36/33.08  | | | Case 1:
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | |   (77)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | REF_CLOSE: (3), (4), (7), (9), (12), (17), (23), (24), (25), (30), (31),
% 200.36/33.08  | | | |            (33), (34), (42), (47), (54), (55), (62), (63), (71), (77)
% 200.36/33.08  | | | |            are inconsistent by sub-proof #835.
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | Case 2:
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | |   (78)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | REF_CLOSE: (71), (75), (78) are inconsistent by sub-proof #791.
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | End of split
% 200.36/33.08  | | | 
% 200.36/33.08  | | Case 2:
% 200.36/33.08  | | | 
% 200.36/33.08  | | |   (79)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.08  | | |           e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.36/33.08  | | |           all_52_30 = e0)
% 200.36/33.08  | | | 
% 200.36/33.08  | | | BETA: splitting (79) gives:
% 200.36/33.08  | | | 
% 200.36/33.08  | | | Case 1:
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | |   (80)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.08  | | | |         e0
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | ALPHA: (80) implies:
% 200.36/33.08  | | | |   (81)  all_52_18 = e2
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | COMBINE_EQS: (32), (81) imply:
% 200.36/33.08  | | | |   (82)  all_6_2 = e2
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | SIMP: (82) implies:
% 200.36/33.08  | | | |   (83)  all_6_2 = e2
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | REF_CLOSE: (4), (6), (8), (29), (83) are inconsistent by sub-proof #825.
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | Case 2:
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | |   (84)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.36/33.08  | | | |         e0
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | ALPHA: (84) implies:
% 200.36/33.08  | | | |   (85)  all_52_30 = e0
% 200.36/33.08  | | | |   (86)  all_52_28 = e1
% 200.36/33.08  | | | |   (87)  all_52_24 = e3
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | REDUCE: (65), (87) imply:
% 200.36/33.08  | | | |   (88)  op(all_52_25, all_52_25) = e3
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | REDUCE: (43), (86) imply:
% 200.36/33.08  | | | |   (89)  op(all_52_29, all_52_29) = e1
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | REDUCE: (52), (85) imply:
% 200.36/33.08  | | | |   (90)  op(all_14_2, all_14_2) = e0
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | BETA: splitting (55) gives:
% 200.36/33.08  | | | | 
% 200.36/33.08  | | | | Case 1:
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | |   (91)  all_58_12 = e3
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | COMBINE_EQS: (30), (91) imply:
% 200.36/33.08  | | | | |   (92)  all_52_7 = e3
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | REDUCE: (31), (92) imply:
% 200.36/33.08  | | | | |   (93)   ~ (all_14_2 = e3)
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | SIMP: (93) implies:
% 200.36/33.08  | | | | |   (94)   ~ (all_14_2 = e3)
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | REDUCE: (7), (92) imply:
% 200.36/33.08  | | | | |   (95)  op(e3, e3) = all_52_6
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | BETA: splitting (48) gives:
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | Case 1:
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | |   (96)  all_58_9 = e3
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | REF_CLOSE: (13), (69), (96) are inconsistent by sub-proof #1300.
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | Case 2:
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | |   (97)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | BETA: splitting (97) gives:
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | Case 1:
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | |   (98)  all_58_10 = e3
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | REF_CLOSE: (28), (39), (98) are inconsistent by sub-proof #1301.
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | Case 2:
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | |   (99)  all_58_11 = e3 | all_58_15 = e3
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | BETA: splitting (99) gives:
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | Case 1:
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | |   (100)  all_58_11 = e3
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | COMBINE_EQS: (19), (100) imply:
% 200.36/33.08  | | | | | | | |   (101)  all_52_29 = e3
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | SIMP: (101) implies:
% 200.36/33.08  | | | | | | | |   (102)  all_52_29 = e3
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | REDUCE: (89), (102) imply:
% 200.36/33.08  | | | | | | | |   (103)  op(e3, e3) = e1
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3,
% 200.36/33.08  | | | | | | | |              simplifying with (47), (95) gives:
% 200.36/33.08  | | | | | | | |   (104)  all_52_6 = all_6_2
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | GROUND_INST: instantiating (4) with e1, all_52_6, e3, e3,
% 200.36/33.08  | | | | | | | |              simplifying with (95), (103) gives:
% 200.36/33.08  | | | | | | | |   (105)  all_52_6 = e1
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | COMBINE_EQS: (104), (105) imply:
% 200.36/33.08  | | | | | | | |   (106)  all_6_2 = e1
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (9), (13), (16), (18), (20),
% 200.36/33.08  | | | | | | | |            (22), (24), (28), (29), (33), (36), (54), (56), (88),
% 200.36/33.08  | | | | | | | |            (91), (94), (100), (106) are inconsistent by
% 200.36/33.08  | | | | | | | |            sub-proof #799.
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | Case 2:
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | |   (107)  all_58_15 = e3
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | REF_CLOSE: (41), (94), (107) are inconsistent by sub-proof #197.
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | End of split
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | End of split
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | End of split
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | Case 2:
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | |   (108)   ~ (all_58_12 = e3)
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | REDUCE: (30), (108) imply:
% 200.36/33.08  | | | | |   (109)   ~ (all_52_7 = e3)
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | BETA: splitting (34) gives:
% 200.36/33.08  | | | | | 
% 200.36/33.08  | | | | | Case 1:
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | |   (110)  all_58_0 = e3
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | COMBINE_EQS: (9), (110) imply:
% 200.36/33.08  | | | | | |   (111)  all_6_2 = e3
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | REDUCE: (71), (111) imply:
% 200.36/33.08  | | | | | |   (112)  $false
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | CLOSE: (112) is inconsistent.
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | Case 2:
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | |   (113)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | BETA: splitting (113) gives:
% 200.36/33.08  | | | | | | 
% 200.36/33.08  | | | | | | Case 1:
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | |   (114)  all_58_2 = e3
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | COMBINE_EQS: (33), (114) imply:
% 200.36/33.08  | | | | | | |   (115)  all_52_3 = e3
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | REDUCE: (20), (115) imply:
% 200.36/33.08  | | | | | | |   (116)  $false
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | CLOSE: (116) is inconsistent.
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | Case 2:
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | |   (117)  all_58_6 = e3 | all_58_12 = e3
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | BETA: splitting (117) gives:
% 200.36/33.08  | | | | | | | 
% 200.36/33.08  | | | | | | | Case 1:
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | |   (118)  all_58_6 = e3
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | COMBINE_EQS: (54), (118) imply:
% 200.36/33.08  | | | | | | | |   (119)  all_52_5 = e3
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | REDUCE: (38), (119) imply:
% 200.36/33.08  | | | | | | | |   (120)   ~ (all_52_29 = e3)
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | SIMP: (120) implies:
% 200.36/33.08  | | | | | | | |   (121)   ~ (all_52_29 = e3)
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | REDUCE: (42), (119) imply:
% 200.36/33.08  | | | | | | | |   (122)   ~ (all_10_2 = e3)
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | SIMP: (122) implies:
% 200.36/33.08  | | | | | | | |   (123)   ~ (all_10_2 = e3)
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | REDUCE: (12), (119) imply:
% 200.36/33.08  | | | | | | | |   (124)  op(e3, e3) = all_52_4
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | BETA: splitting (48) gives:
% 200.36/33.08  | | | | | | | | 
% 200.36/33.08  | | | | | | | | Case 1:
% 200.36/33.08  | | | | | | | | | 
% 200.36/33.08  | | | | | | | | |   (125)  all_58_9 = e3
% 200.36/33.08  | | | | | | | | | 
% 200.36/33.08  | | | | | | | | | REF_CLOSE: (13), (69), (125) are inconsistent by sub-proof
% 200.36/33.08  | | | | | | | | |            #1300.
% 200.36/33.08  | | | | | | | | | 
% 200.36/33.08  | | | | | | | | Case 2:
% 200.36/33.08  | | | | | | | | | 
% 200.36/33.08  | | | | | | | | |   (126)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.08  | | | | | | | | | 
% 200.36/33.08  | | | | | | | | | BETA: splitting (126) gives:
% 200.36/33.08  | | | | | | | | | 
% 200.36/33.08  | | | | | | | | | Case 1:
% 200.36/33.08  | | | | | | | | | | 
% 200.36/33.08  | | | | | | | | | |   (127)  all_58_10 = e3
% 200.36/33.08  | | | | | | | | | | 
% 200.36/33.08  | | | | | | | | | | REF_CLOSE: (28), (39), (127) are inconsistent by sub-proof
% 200.36/33.09  | | | | | | | | | |            #1301.
% 200.36/33.09  | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | Case 2:
% 200.36/33.09  | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | |   (128)  all_58_11 = e3 | all_58_15 = e3
% 200.36/33.09  | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | BETA: splitting (128) gives:
% 200.36/33.09  | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | Case 1:
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | |   (129)  all_58_11 = e3
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | REF_CLOSE: (19), (121), (129) are inconsistent by sub-proof
% 200.36/33.09  | | | | | | | | | | |            #1323.
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | Case 2:
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | |   (130)  all_58_15 = e3
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | COMBINE_EQS: (41), (130) imply:
% 200.36/33.09  | | | | | | | | | | |   (131)  all_14_2 = e3
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | SIMP: (131) implies:
% 200.36/33.09  | | | | | | | | | | |   (132)  all_14_2 = e3
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | REDUCE: (90), (132) imply:
% 200.36/33.09  | | | | | | | | | | |   (133)  op(e3, e3) = e0
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | REDUCE: (10), (132) imply:
% 200.36/33.09  | | | | | | | | | | |   (134)  op(e3, e0) = all_14_1
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_25, all_14_1, e0,
% 200.36/33.09  | | | | | | | | | | |              e3, simplifying with (11), (134) gives:
% 200.36/33.09  | | | | | | | | | | |   (135)  all_52_25 = all_14_1
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_4, e3, e3,
% 200.36/33.09  | | | | | | | | | | |              simplifying with (47), (124) gives:
% 200.36/33.09  | | | | | | | | | | |   (136)  all_52_4 = all_6_2
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_52_4, e3, e3,
% 200.36/33.09  | | | | | | | | | | |              simplifying with (124), (133) gives:
% 200.36/33.09  | | | | | | | | | | |   (137)  all_52_4 = e0
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | COMBINE_EQS: (136), (137) imply:
% 200.36/33.09  | | | | | | | | | | |   (138)  all_6_2 = e0
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | SIMP: (138) implies:
% 200.36/33.09  | | | | | | | | | | |   (139)  all_6_2 = e0
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | COMBINE_EQS: (49), (135) imply:
% 200.36/33.09  | | | | | | | | | | |   (140)  all_56_3 = all_14_1
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | COMBINE_EQS: (13), (135) imply:
% 200.36/33.09  | | | | | | | | | | |   (141)  all_58_9 = all_14_1
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | REDUCE: (44), (135), (139) imply:
% 200.36/33.09  | | | | | | | | | | |   (142)   ~ (all_14_1 = e0)
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | REDUCE: (69), (135) imply:
% 200.36/33.09  | | | | | | | | | | |   (143)   ~ (all_14_1 = e3)
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | REDUCE: (88), (135) imply:
% 200.36/33.09  | | | | | | | | | | |   (144)  op(all_14_1, all_14_1) = e3
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | BETA: splitting (45) gives:
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | Case 1:
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | |   (145)  all_56_3 = e3
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | | COMBINE_EQS: (140), (145) imply:
% 200.36/33.09  | | | | | | | | | | | |   (146)  all_14_1 = e3
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | | REDUCE: (143), (146) imply:
% 200.36/33.09  | | | | | | | | | | | |   (147)  $false
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | Case 2:
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | |   (148)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | | REF_CLOSE: (4), (17), (26), (62), (73), (123), (140), (141),
% 200.36/33.09  | | | | | | | | | | | |            (142), (144), (148) are inconsistent by sub-proof
% 200.36/33.09  | | | | | | | | | | | |            #804.
% 200.36/33.09  | | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | | End of split
% 200.36/33.09  | | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | | End of split
% 200.36/33.09  | | | | | | | | | | 
% 200.36/33.09  | | | | | | | | | End of split
% 200.36/33.09  | | | | | | | | | 
% 200.36/33.09  | | | | | | | | End of split
% 200.36/33.09  | | | | | | | | 
% 200.36/33.09  | | | | | | | Case 2:
% 200.36/33.09  | | | | | | | | 
% 200.36/33.09  | | | | | | | |   (149)  all_58_12 = e3
% 200.36/33.09  | | | | | | | | 
% 200.36/33.09  | | | | | | | | COMBINE_EQS: (30), (149) imply:
% 200.36/33.09  | | | | | | | |   (150)  all_52_7 = e3
% 200.36/33.09  | | | | | | | | 
% 200.36/33.09  | | | | | | | | REDUCE: (109), (150) imply:
% 200.36/33.09  | | | | | | | |   (151)  $false
% 200.36/33.09  | | | | | | | | 
% 200.36/33.09  | | | | | | | | CLOSE: (151) is inconsistent.
% 200.36/33.09  | | | | | | | | 
% 200.36/33.09  | | | | | | | End of split
% 200.36/33.09  | | | | | | | 
% 200.36/33.09  | | | | | | End of split
% 200.36/33.09  | | | | | | 
% 200.36/33.09  | | | | | End of split
% 200.36/33.09  | | | | | 
% 200.36/33.09  | | | | End of split
% 200.36/33.09  | | | | 
% 200.36/33.09  | | | End of split
% 200.36/33.09  | | | 
% 200.36/33.09  | | End of split
% 200.36/33.09  | | 
% 200.36/33.09  | Case 2:
% 200.36/33.09  | | 
% 200.36/33.09  | |   (152)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.09  | | 
% 200.36/33.09  | | REF_CLOSE: (4), (6), (8), (15), (23), (27), (29), (35), (40), (46), (47),
% 200.36/33.09  | |            (51), (57), (59), (60), (64), (152) are inconsistent by sub-proof
% 200.36/33.09  | |            #820.
% 200.36/33.09  | | 
% 200.36/33.09  | End of split
% 200.36/33.09  | 
% 200.36/33.09  End of proof
% 200.36/33.09  
% 200.36/33.09  Sub-proof #142 shows that the following formulas are inconsistent:
% 200.36/33.09  ----------------------------------------------------------------
% 200.36/33.09    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.09    (2)   ~ (all_52_25 = all_52_27)
% 200.36/33.09    (3)  all_58_14 = all_52_23
% 200.36/33.09    (4)   ~ (e3 = e1)
% 200.36/33.09    (5)   ~ (all_52_17 = all_4_0)
% 200.36/33.09    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.09    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.09    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.09    (9)  all_58_1 = all_52_9
% 200.36/33.09    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.09    (11)   ~ (e3 = e0)
% 200.36/33.09    (12)  op(e2, e3) = all_52_3
% 200.36/33.09    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.09    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.09    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.09    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.09    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.09    (18)   ~ (all_52_3 = all_6_2)
% 200.36/33.09    (19)  all_58_0 = all_6_2
% 200.36/33.09    (20)  op(all_14_2, e0) = all_14_1
% 200.36/33.09    (21)  all_56_4 = all_52_3
% 200.36/33.09    (22)   ~ (all_52_17 = all_10_2)
% 200.36/33.09    (23)  op(e3, e0) = all_52_25
% 200.36/33.09    (24)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.09    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.09    (26)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.09    (27)   ~ (all_52_27 = all_52_29)
% 200.36/33.09    (28)  all_58_13 = all_52_15
% 200.36/33.09    (29)  op(e0, all_14_1) = e1
% 200.36/33.09    (30)  all_58_9 = all_52_25
% 200.36/33.09    (31)   ~ (all_6_1 = e1)
% 200.36/33.09    (32)   ~ (all_52_29 = all_14_2)
% 200.36/33.09    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.09    (34)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.09    (35)  op(e1, e3) = all_52_5
% 200.36/33.09    (36)  op(e2, e2) = all_4_2
% 200.36/33.09    (37)   ~ (all_52_3 = all_52_5)
% 200.36/33.09    (38)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.09    (39)  op(all_4_2, e2) = e1
% 200.36/33.09    (40)  all_58_11 = all_52_29
% 200.36/33.09    (41)  all_56_5 = all_4_2
% 200.36/33.09    (42)   ~ (all_52_25 = all_14_2)
% 200.36/33.09    (43)   ~ (all_52_9 = all_52_15)
% 200.36/33.09    (44)   ~ (all_52_3 = all_52_27)
% 200.36/33.09    (45)  op(all_10_2, e1) = all_10_1
% 200.36/33.09    (46)   ~ (all_10_2 = all_4_0)
% 200.36/33.09    (47)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.09    (48)   ~ (all_52_7 = all_6_2)
% 200.36/33.09    (49)  op(e0, e0) = all_14_2
% 200.36/33.09    (50)  all_56_15 = all_14_2
% 200.36/33.09    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.09    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.09    (53)  all_56_11 = all_52_29
% 200.36/33.09    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.09    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.09    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.09    (57)   ~ (e2 = e1)
% 200.36/33.09    (58)   ~ (all_52_13 = all_10_2)
% 200.36/33.09    (59)   ~ (all_6_0 = e1)
% 200.36/33.09    (60)  all_58_10 = all_52_27
% 200.36/33.09    (61)  all_56_8 = all_52_5
% 200.36/33.09    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.09    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.09    (64)   ~ (all_52_19 = all_52_23)
% 200.36/33.09    (65)   ~ (all_52_25 = all_52_29)
% 200.36/33.09    (66)   ~ (all_52_29 = all_10_2)
% 200.36/33.09    (67)  all_58_7 = all_52_13
% 200.36/33.09    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.09    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.09    (70)   ~ (all_52_5 = all_52_7)
% 200.36/33.09    (71)  all_58_12 = all_52_7
% 200.36/33.09    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.09    (73)   ~ (all_52_7 = all_14_2)
% 200.36/33.09    (74)  all_58_2 = all_52_3
% 200.36/33.09    (75)  all_56_2 = all_52_17
% 200.36/33.09    (76)  all_28_0 = all_4_0
% 200.36/33.09    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.09    (78)  op(e3, all_6_1) = all_6_0
% 200.36/33.09    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.09    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.09    (81)  all_56_7 = all_52_27
% 200.36/33.09    (82)  all_28_2 = all_4_2
% 200.36/33.09    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.09    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.09    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.09    (86)   ~ (all_52_5 = all_52_29)
% 200.36/33.09    (87)   ~ (all_52_15 = all_14_2)
% 200.36/33.09    (88)   ~ (all_52_19 = all_52_27)
% 200.36/33.09    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.09    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.09    (91)   ~ (all_6_0 = e2)
% 200.36/33.09    (92)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.36/33.09            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.36/33.09    (93)   ~ (all_52_13 = all_4_2)
% 200.36/33.09    (94)  op(e3, e1) = all_52_17
% 200.36/33.09    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.09    (96)  op(e0, e3) = all_52_7
% 200.36/33.09    (97)  op(e1, e2) = all_52_13
% 200.36/33.09    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.09    (99)   ~ (all_52_9 = all_52_25)
% 200.36/33.09    (100)  all_58_15 = all_14_2
% 200.36/33.09    (101)   ~ (all_52_19 = all_10_2)
% 200.36/33.09    (102)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.09    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.09    (104)  all_58_8 = all_10_2
% 200.36/33.09    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.09    (106)   ~ (all_52_5 = all_10_2)
% 200.36/33.09    (107)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.09    (108)   ~ (all_52_23 = all_14_2)
% 200.36/33.09    (109)  all_56_12 = all_52_7
% 200.36/33.09    (110)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.09    (111)  all_58_5 = all_4_0
% 200.36/33.09    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.09    (113)   ~ (all_52_25 = all_6_2)
% 200.36/33.09    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.09    (115)   ~ (all_52_9 = all_4_2)
% 200.36/33.09    (116)   ~ (all_52_5 = all_6_2)
% 200.36/33.09    (117)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.09    (118)   ~ (all_52_9 = all_6_2)
% 200.36/33.09    (119)   ~ (all_52_13 = all_52_15)
% 200.36/33.09    (120)  all_56_0 = all_6_2
% 200.36/33.09    (121)  op(all_4_0, all_4_0) = all_52_18
% 200.36/33.09    (122)  op(e3, e3) = all_6_2
% 200.36/33.09    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.09    (124)   ~ (all_52_27 = all_14_2)
% 200.36/33.09    (125)   ~ (all_52_27 = all_4_0)
% 200.36/33.09    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.09    (127)  all_56_14 = all_52_23
% 200.36/33.09    (128)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.36/33.09    (129)  all_56_3 = all_52_25
% 200.36/33.09    (130)  all_28_0 = e3
% 200.36/33.09    (131)   ~ (all_52_3 = all_52_7)
% 200.36/33.09    (132)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.09    (133)  all_58_5 = all_52_19
% 200.36/33.09    (134)  all_56_1 = all_52_9
% 200.36/33.09    (135)   ~ (all_52_15 = all_4_2)
% 200.36/33.09    (136)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.09           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.09           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.09           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.09    (137)   ~ (all_52_27 = all_4_2)
% 200.36/33.09    (138)  all_58_6 = all_52_5
% 200.36/33.09    (139)   ~ (all_4_0 = all_4_2)
% 200.36/33.09    (140)  op(e3, e2) = all_52_9
% 200.36/33.09    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.09    (142)   ~ (all_52_17 = all_6_2)
% 200.36/33.09    (143)   ~ (e1 = e0)
% 200.36/33.09    (144)   ~ (e3 = e2)
% 200.36/33.09    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.09    (146)   ~ (all_52_9 = all_52_17)
% 200.36/33.09    (147)   ~ (all_52_3 = all_4_0)
% 200.36/33.09    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.09    (149)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.09    (150)   ~ (all_6_1 = e2)
% 200.36/33.09    (151)  op(e1, e1) = all_10_2
% 200.36/33.09    (152)   ~ (all_52_23 = all_10_2)
% 200.36/33.09    (153)   ~ (all_52_7 = all_52_23)
% 200.36/33.09    (154)   ~ (all_52_17 = all_52_19)
% 200.36/33.09    (155)  all_58_3 = all_4_2
% 200.36/33.09    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.09    (157)  all_56_13 = all_52_15
% 200.36/33.09    (158)   ~ (all_52_3 = all_4_2)
% 200.36/33.09    (159)  all_28_1 = e1
% 200.36/33.09    (160)   ~ (all_52_19 = all_4_2)
% 200.36/33.09    (161)   ~ (all_52_17 = all_52_23)
% 200.36/33.09    (162)  op(all_6_2, e3) = all_6_1
% 200.36/33.09    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.09    (164)   ~ (all_52_13 = all_52_29)
% 200.36/33.09    (165)  all_58_4 = all_52_17
% 200.36/33.09    (166)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.09  
% 200.36/33.09  Begin of proof
% 200.36/33.09  | 
% 200.36/33.09  | COMBINE_EQS: (76), (130) imply:
% 200.36/33.09  |   (167)  all_4_0 = e3
% 200.36/33.09  | 
% 200.36/33.09  | SIMP: (167) implies:
% 200.36/33.09  |   (168)  all_4_0 = e3
% 200.36/33.09  | 
% 200.36/33.09  | COMBINE_EQS: (111), (168) imply:
% 200.36/33.09  |   (169)  all_58_5 = e3
% 200.36/33.09  | 
% 200.36/33.09  | REDUCE: (147), (168) imply:
% 200.36/33.09  |   (170)   ~ (all_52_3 = e3)
% 200.36/33.09  | 
% 200.36/33.09  | REDUCE: (5), (168) imply:
% 200.36/33.09  |   (171)   ~ (all_52_17 = e3)
% 200.36/33.09  | 
% 200.36/33.09  | REDUCE: (125), (168) imply:
% 200.36/33.09  |   (172)   ~ (all_52_27 = e3)
% 200.36/33.09  | 
% 200.36/33.09  | REDUCE: (46), (168) imply:
% 200.36/33.09  |   (173)   ~ (all_10_2 = e3)
% 200.36/33.09  | 
% 200.36/33.09  | REDUCE: (139), (168) imply:
% 200.36/33.09  |   (174)   ~ (all_4_2 = e3)
% 200.36/33.09  | 
% 200.36/33.09  | SIMP: (174) implies:
% 200.36/33.09  |   (175)   ~ (all_4_2 = e3)
% 200.36/33.09  | 
% 200.36/33.09  | REDUCE: (121), (168) imply:
% 200.36/33.09  |   (176)  op(e3, e3) = all_52_18
% 200.36/33.09  | 
% 200.36/33.09  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.09  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 200.36/33.09  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 200.36/33.09  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 200.36/33.09  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 200.36/33.09  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 200.36/33.09  |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (80), (81),
% 200.36/33.09  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 200.36/33.09  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 200.36/33.09  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 200.36/33.09  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 200.36/33.09  |            (122), (123), (124), (126), (127), (128), (129), (131), (132),
% 200.36/33.09  |            (133), (134), (135), (136), (137), (138), (139), (140), (141),
% 200.36/33.09  |            (142), (143), (144), (145), (146), (148), (149), (150), (151),
% 200.36/33.09  |            (152), (153), (154), (155), (156), (157), (158), (159), (160),
% 200.36/33.09  |            (161), (162), (163), (164), (165), (166), (169), (170), (171),
% 200.36/33.09  |            (172), (173), (175), (176) are inconsistent by sub-proof #143.
% 200.36/33.09  | 
% 200.36/33.09  End of proof
% 200.36/33.09  
% 200.36/33.09  Sub-proof #143 shows that the following formulas are inconsistent:
% 200.36/33.09  ----------------------------------------------------------------
% 200.36/33.09    (1)  op(e3, e3) = all_52_18
% 200.36/33.09    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.09    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.09    (4)  all_58_14 = all_52_23
% 200.36/33.09    (5)   ~ (e3 = e1)
% 200.36/33.09    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.09    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.09    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.09    (9)  all_58_1 = all_52_9
% 200.36/33.09    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.09    (11)   ~ (e3 = e0)
% 200.36/33.09    (12)  op(e2, e3) = all_52_3
% 200.36/33.09    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.09    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.09    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.09    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.09    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.09    (18)   ~ (all_4_2 = e3)
% 200.36/33.09    (19)   ~ (all_52_3 = all_6_2)
% 200.36/33.09    (20)  all_58_0 = all_6_2
% 200.36/33.09    (21)  op(all_14_2, e0) = all_14_1
% 200.36/33.09    (22)  all_56_4 = all_52_3
% 200.36/33.09    (23)   ~ (all_52_17 = all_10_2)
% 200.36/33.09    (24)  op(e3, e0) = all_52_25
% 200.36/33.09    (25)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.09    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.09    (27)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.09    (28)   ~ (all_52_27 = all_52_29)
% 200.36/33.09    (29)  all_58_13 = all_52_15
% 200.36/33.09    (30)  op(e0, all_14_1) = e1
% 200.36/33.09    (31)  all_58_9 = all_52_25
% 200.36/33.09    (32)   ~ (all_6_1 = e1)
% 200.36/33.09    (33)   ~ (all_52_29 = all_14_2)
% 200.36/33.09    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.09    (35)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.09    (36)  op(e1, e3) = all_52_5
% 200.36/33.09    (37)  op(e2, e2) = all_4_2
% 200.36/33.09    (38)   ~ (all_52_3 = all_52_5)
% 200.36/33.09    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.09    (40)  op(all_4_2, e2) = e1
% 200.36/33.09    (41)  all_58_11 = all_52_29
% 200.36/33.09    (42)   ~ (all_52_3 = e3)
% 200.36/33.09    (43)  all_56_5 = all_4_2
% 200.36/33.09    (44)   ~ (all_52_25 = all_14_2)
% 200.36/33.09    (45)   ~ (all_52_9 = all_52_15)
% 200.36/33.09    (46)   ~ (all_52_3 = all_52_27)
% 200.36/33.09    (47)  op(all_10_2, e1) = all_10_1
% 200.36/33.09    (48)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.09    (49)   ~ (all_52_7 = all_6_2)
% 200.36/33.09    (50)  op(e0, e0) = all_14_2
% 200.36/33.09    (51)  all_56_15 = all_14_2
% 200.36/33.09    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.09    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.09    (54)  all_56_11 = all_52_29
% 200.36/33.09    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.09    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.09    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.09    (58)   ~ (e2 = e1)
% 200.36/33.09    (59)   ~ (all_52_13 = all_10_2)
% 200.36/33.09    (60)   ~ (all_6_0 = e1)
% 200.36/33.09    (61)  all_58_10 = all_52_27
% 200.36/33.09    (62)  all_56_8 = all_52_5
% 200.36/33.09    (63)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.09    (64)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.09    (65)   ~ (all_52_19 = all_52_23)
% 200.36/33.09    (66)   ~ (all_52_25 = all_52_29)
% 200.36/33.09    (67)   ~ (all_52_29 = all_10_2)
% 200.36/33.09    (68)  all_58_7 = all_52_13
% 200.36/33.09    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.09    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.09    (71)   ~ (all_52_5 = all_52_7)
% 200.36/33.09    (72)  all_58_12 = all_52_7
% 200.36/33.09    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.09    (74)   ~ (all_52_7 = all_14_2)
% 200.36/33.09    (75)  all_58_2 = all_52_3
% 200.36/33.09    (76)  all_56_2 = all_52_17
% 200.36/33.09    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.09    (78)  op(e3, all_6_1) = all_6_0
% 200.36/33.09    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.09    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.09    (81)  all_56_7 = all_52_27
% 200.36/33.09    (82)  all_28_2 = all_4_2
% 200.36/33.09    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.09    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.09    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.09    (86)   ~ (all_52_5 = all_52_29)
% 200.36/33.09    (87)   ~ (all_10_2 = e3)
% 200.36/33.09    (88)   ~ (all_52_15 = all_14_2)
% 200.36/33.09    (89)   ~ (all_52_19 = all_52_27)
% 200.36/33.09    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.09    (91)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.09    (92)   ~ (all_52_27 = e3)
% 200.36/33.09    (93)   ~ (all_6_0 = e2)
% 200.36/33.09    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.36/33.09            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.36/33.09    (95)   ~ (all_52_13 = all_4_2)
% 200.36/33.09    (96)  op(e3, e1) = all_52_17
% 200.36/33.09    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.09    (98)  op(e0, e3) = all_52_7
% 200.36/33.09    (99)  op(e1, e2) = all_52_13
% 200.36/33.09    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.09    (101)   ~ (all_52_9 = all_52_25)
% 200.36/33.09    (102)  all_58_15 = all_14_2
% 200.36/33.09    (103)   ~ (all_52_19 = all_10_2)
% 200.36/33.09    (104)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.09    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.09    (106)  all_58_8 = all_10_2
% 200.36/33.09    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.09    (108)   ~ (all_52_5 = all_10_2)
% 200.36/33.09    (109)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.09    (110)   ~ (all_52_23 = all_14_2)
% 200.36/33.09    (111)  all_56_12 = all_52_7
% 200.36/33.09    (112)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.09    (113)  all_58_5 = all_4_0
% 200.36/33.09    (114)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.09    (115)   ~ (all_52_25 = all_6_2)
% 200.36/33.09    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.09    (117)   ~ (all_52_9 = all_4_2)
% 200.36/33.09    (118)   ~ (all_52_5 = all_6_2)
% 200.36/33.09    (119)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.09    (120)   ~ (all_52_9 = all_6_2)
% 200.36/33.09    (121)   ~ (all_52_13 = all_52_15)
% 200.36/33.09    (122)  all_56_0 = all_6_2
% 200.36/33.09    (123)  op(e3, e3) = all_6_2
% 200.36/33.09    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.09    (125)   ~ (all_52_27 = all_14_2)
% 200.36/33.09    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.09    (127)  all_58_5 = e3
% 200.36/33.09    (128)  all_56_14 = all_52_23
% 200.36/33.09    (129)   ~ (all_52_17 = e3)
% 200.36/33.09    (130)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.36/33.09    (131)  all_56_3 = all_52_25
% 200.36/33.09    (132)   ~ (all_52_3 = all_52_7)
% 200.36/33.09    (133)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.09    (134)  all_58_5 = all_52_19
% 200.36/33.09    (135)  all_56_1 = all_52_9
% 200.36/33.09    (136)   ~ (all_52_15 = all_4_2)
% 200.36/33.09    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.09           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.09           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.09           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.09    (138)   ~ (all_52_27 = all_4_2)
% 200.36/33.09    (139)  all_58_6 = all_52_5
% 200.36/33.09    (140)   ~ (all_4_0 = all_4_2)
% 200.36/33.09    (141)  op(e3, e2) = all_52_9
% 200.36/33.09    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.09    (143)   ~ (all_52_17 = all_6_2)
% 200.36/33.09    (144)   ~ (e1 = e0)
% 200.36/33.09    (145)   ~ (e3 = e2)
% 200.36/33.09    (146)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.09    (147)   ~ (all_52_9 = all_52_17)
% 200.36/33.09    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.09    (149)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.09    (150)   ~ (all_6_1 = e2)
% 200.36/33.09    (151)  op(e1, e1) = all_10_2
% 200.36/33.09    (152)   ~ (all_52_23 = all_10_2)
% 200.36/33.10    (153)   ~ (all_52_7 = all_52_23)
% 200.36/33.10    (154)   ~ (all_52_17 = all_52_19)
% 200.36/33.10    (155)  all_58_3 = all_4_2
% 200.36/33.10    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.10    (157)  all_56_13 = all_52_15
% 200.36/33.10    (158)   ~ (all_52_3 = all_4_2)
% 200.36/33.10    (159)  all_28_1 = e1
% 200.36/33.10    (160)   ~ (all_52_19 = all_4_2)
% 200.36/33.10    (161)   ~ (all_52_17 = all_52_23)
% 200.36/33.10    (162)  op(all_6_2, e3) = all_6_1
% 200.36/33.10    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.10    (164)   ~ (all_52_13 = all_52_29)
% 200.36/33.10    (165)  all_58_4 = all_52_17
% 200.36/33.10    (166)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.10  
% 200.36/33.10  Begin of proof
% 200.36/33.10  | 
% 200.36/33.10  | BETA: splitting (130) gives:
% 200.36/33.10  | 
% 200.36/33.10  | Case 1:
% 200.36/33.10  | | 
% 200.36/33.10  | |   (167)   ~ (all_28_1 = e1)
% 200.36/33.10  | | 
% 200.36/33.10  | | REDUCE: (159), (167) imply:
% 200.36/33.10  | |   (168)  $false
% 200.36/33.10  | | 
% 200.36/33.10  | | CLOSE: (168) is inconsistent.
% 200.36/33.10  | | 
% 200.36/33.10  | Case 2:
% 200.36/33.10  | | 
% 200.36/33.10  | |   (169)   ~ (all_28_2 = e0)
% 200.36/33.10  | | 
% 200.36/33.10  | | REDUCE: (82), (169) imply:
% 200.36/33.10  | |   (170)   ~ (all_4_2 = e0)
% 200.36/33.10  | | 
% 200.36/33.10  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 200.36/33.10  | |              with (1), (123) gives:
% 200.36/33.10  | |   (171)  all_52_18 = all_6_2
% 200.36/33.10  | | 
% 200.36/33.10  | | BETA: splitting (94) gives:
% 200.36/33.10  | | 
% 200.36/33.10  | | Case 1:
% 200.36/33.10  | | | 
% 200.36/33.10  | | |   (172)  all_58_15 = e0
% 200.36/33.10  | | | 
% 200.36/33.10  | | | REF_CLOSE: (7), (21), (30), (50), (102), (133), (144), (172) are
% 200.36/33.10  | | |            inconsistent by sub-proof #877.
% 200.36/33.10  | | | 
% 200.36/33.10  | | Case 2:
% 200.36/33.10  | | | 
% 200.36/33.10  | | |   (173)   ~ (all_58_15 = e0)
% 200.36/33.10  | | |   (174)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 200.36/33.10  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 200.36/33.10  | | | 
% 200.36/33.10  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.10  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 200.36/33.10  | | |            (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 200.36/33.10  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 200.36/33.10  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 200.36/33.10  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 200.36/33.10  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 200.36/33.10  | | |            (76), (77), (78), (79), (80), (81), (83), (84), (85), (86),
% 200.36/33.10  | | |            (87), (88), (89), (90), (91), (92), (93), (95), (96), (97),
% 200.36/33.10  | | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 200.36/33.10  | | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 200.36/33.10  | | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 200.36/33.10  | | |            (125), (126), (127), (128), (129), (131), (132), (133), (134),
% 200.36/33.10  | | |            (135), (136), (137), (138), (139), (140), (141), (142), (143),
% 200.36/33.10  | | |            (144), (145), (146), (147), (148), (149), (150), (151), (152),
% 200.36/33.10  | | |            (153), (154), (155), (156), (157), (158), (160), (161), (162),
% 200.36/33.10  | | |            (163), (164), (165), (166), (170), (171), (173), (174) are
% 200.36/33.10  | | |            inconsistent by sub-proof #146.
% 200.36/33.10  | | | 
% 200.36/33.10  | | End of split
% 200.36/33.10  | | 
% 200.36/33.10  | End of split
% 200.36/33.10  | 
% 200.36/33.10  End of proof
% 200.36/33.10  
% 200.36/33.10  Sub-proof #144 shows that the following formulas are inconsistent:
% 200.36/33.10  ----------------------------------------------------------------
% 200.36/33.10    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.10    (2)   ~ (all_52_25 = all_52_27)
% 200.36/33.10    (3)  all_58_14 = all_52_23
% 200.36/33.10    (4)   ~ (e3 = e1)
% 200.36/33.10    (5)   ~ (all_52_17 = all_4_0)
% 200.36/33.10    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.10    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.10    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.10    (9)  all_58_1 = all_52_9
% 200.36/33.10    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.10    (11)   ~ (e3 = e0)
% 200.36/33.10    (12)  op(e2, e3) = all_52_3
% 200.36/33.10    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.10    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.10    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.10    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.10    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.10    (18)   ~ (all_52_3 = all_6_2)
% 200.36/33.10    (19)  all_58_0 = all_6_2
% 200.36/33.10    (20)  op(all_14_2, e0) = all_14_1
% 200.36/33.10    (21)  all_56_4 = all_52_3
% 200.36/33.10    (22)   ~ (all_52_17 = all_10_2)
% 200.36/33.10    (23)  op(e3, e0) = all_52_25
% 200.36/33.10    (24)  op(e0, all_14_1) = all_14_0
% 200.36/33.10    (25)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.10    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.10    (27)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.10    (28)   ~ (all_52_27 = all_52_29)
% 200.36/33.10    (29)  all_58_13 = all_52_15
% 200.36/33.10    (30)  all_58_9 = all_52_25
% 200.36/33.10    (31)   ~ (all_6_1 = e1)
% 200.36/33.10    (32)   ~ (all_52_29 = all_14_2)
% 200.36/33.10    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.10    (34)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.10    (35)  op(e1, e3) = all_52_5
% 200.36/33.10    (36)  op(e2, e2) = all_4_2
% 200.36/33.10    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 200.36/33.10    (38)   ~ (all_52_3 = all_52_5)
% 200.36/33.10    (39)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.10    (40)  op(all_4_2, e2) = e1
% 200.36/33.10    (41)  all_58_11 = all_52_29
% 200.36/33.10    (42)  all_56_5 = all_4_2
% 200.36/33.10    (43)   ~ (all_52_25 = all_14_2)
% 200.36/33.10    (44)   ~ (all_52_9 = all_52_15)
% 200.36/33.10    (45)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.10    (46)   ~ (all_52_3 = all_52_27)
% 200.36/33.10    (47)  op(all_10_2, e1) = all_10_1
% 200.36/33.10    (48)   ~ (all_10_2 = all_4_0)
% 200.36/33.10    (49)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.10    (50)   ~ (all_52_7 = all_6_2)
% 200.36/33.10    (51)  op(e0, e0) = all_14_2
% 200.36/33.10    (52)  all_56_15 = all_14_2
% 200.36/33.10    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.10    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.10    (55)  all_56_11 = all_52_29
% 200.36/33.10    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.10    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.10    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.10    (59)   ~ (e2 = e1)
% 200.36/33.10    (60)   ~ (all_52_13 = all_10_2)
% 200.36/33.10    (61)   ~ (all_6_0 = e1)
% 200.36/33.10    (62)  all_58_10 = all_52_27
% 200.36/33.10    (63)  all_56_8 = all_52_5
% 200.36/33.10    (64)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.10    (65)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.10    (66)   ~ (all_52_19 = all_52_23)
% 200.36/33.10    (67)   ~ (all_52_25 = all_52_29)
% 200.36/33.10    (68)   ~ (all_52_29 = all_10_2)
% 200.36/33.10    (69)  all_58_7 = all_52_13
% 200.36/33.10    (70)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.10    (71)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.10    (72)   ~ (all_52_5 = all_52_7)
% 200.36/33.10    (73)  all_58_12 = all_52_7
% 200.36/33.10    (74)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.10    (75)   ~ (all_52_7 = all_14_2)
% 200.36/33.10    (76)  all_58_2 = all_52_3
% 200.36/33.10    (77)  all_56_2 = all_52_17
% 200.36/33.10    (78)  all_28_0 = all_4_0
% 200.36/33.10    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.10    (80)  op(e3, all_6_1) = all_6_0
% 200.36/33.10    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.10    (82)   ~ (all_14_0 = e3)
% 200.36/33.10    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.10    (84)  all_56_7 = all_52_27
% 200.36/33.10    (85)  all_28_2 = all_4_2
% 200.36/33.10    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.10    (87)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.10    (88)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.10    (89)   ~ (all_52_5 = all_52_29)
% 200.36/33.10    (90)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.10    (91)   ~ (all_52_15 = all_14_2)
% 200.36/33.10    (92)   ~ (all_52_19 = all_52_27)
% 200.36/33.10    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.10    (94)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.10    (95)   ~ (all_6_0 = e2)
% 200.36/33.10    (96)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.36/33.10            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.36/33.10    (97)   ~ (all_52_13 = all_4_2)
% 200.36/33.10    (98)  op(e3, e1) = all_52_17
% 200.36/33.10    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.10    (100)  op(e0, e3) = all_52_7
% 200.36/33.10    (101)  op(e1, e2) = all_52_13
% 200.36/33.10    (102)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.10    (103)   ~ (all_52_9 = all_52_25)
% 200.36/33.10    (104)  all_58_15 = all_14_2
% 200.36/33.10    (105)   ~ (all_52_19 = all_10_2)
% 200.36/33.10    (106)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.10    (107)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.10    (108)  all_58_8 = all_10_2
% 200.36/33.10    (109)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.10    (110)   ~ (all_52_5 = all_10_2)
% 200.36/33.10    (111)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.10    (112)   ~ (all_52_23 = all_14_2)
% 200.36/33.10    (113)  all_56_12 = all_52_7
% 200.36/33.10    (114)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.10    (115)  all_58_5 = all_4_0
% 200.36/33.10    (116)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.10    (117)   ~ (all_52_25 = all_6_2)
% 200.36/33.10    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.10    (119)   ~ (all_52_9 = all_4_2)
% 200.36/33.10    (120)   ~ (all_52_5 = all_6_2)
% 200.36/33.10    (121)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.10    (122)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 200.36/33.10    (123)   ~ (all_52_9 = all_6_2)
% 200.36/33.10    (124)   ~ (all_52_13 = all_52_15)
% 200.36/33.10    (125)  all_56_0 = all_6_2
% 200.36/33.10    (126)  op(all_4_0, all_4_0) = all_52_18
% 200.36/33.10    (127)  op(e3, e3) = all_6_2
% 200.36/33.10    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.10    (129)   ~ (all_52_27 = all_14_2)
% 200.36/33.10    (130)   ~ (all_52_27 = all_4_0)
% 200.36/33.10    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.10    (132)  all_56_14 = all_52_23
% 200.36/33.10    (133)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.36/33.10    (134)  all_56_3 = all_52_25
% 200.36/33.10    (135)  all_28_0 = e3
% 200.36/33.10    (136)   ~ (all_52_3 = all_52_7)
% 200.36/33.10    (137)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.10    (138)  all_58_5 = all_52_19
% 200.36/33.10    (139)  all_56_1 = all_52_9
% 200.36/33.10    (140)   ~ (all_52_15 = all_4_2)
% 200.36/33.10    (141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.10           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.10           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.10           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.10    (142)   ~ (all_52_27 = all_4_2)
% 200.36/33.10    (143)  all_58_6 = all_52_5
% 200.36/33.10    (144)   ~ (all_4_0 = all_4_2)
% 200.36/33.10    (145)  op(e3, e2) = all_52_9
% 200.36/33.10    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.10    (147)   ~ (all_52_17 = all_6_2)
% 200.36/33.10    (148)   ~ (e1 = e0)
% 200.36/33.10    (149)   ~ (e3 = e2)
% 200.36/33.10    (150)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.10    (151)   ~ (all_52_9 = all_52_17)
% 200.36/33.10    (152)   ~ (all_52_3 = all_4_0)
% 200.36/33.10    (153)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.10    (154)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.10    (155)   ~ (all_6_1 = e2)
% 200.36/33.10    (156)  op(e1, e1) = all_10_2
% 200.36/33.10    (157)   ~ (all_52_23 = all_10_2)
% 200.36/33.10    (158)   ~ (all_52_7 = all_52_23)
% 200.36/33.10    (159)   ~ (all_52_17 = all_52_19)
% 200.36/33.10    (160)  all_58_3 = all_4_2
% 200.36/33.10    (161)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.10    (162)  all_56_13 = all_52_15
% 200.36/33.10    (163)   ~ (all_52_3 = all_4_2)
% 200.36/33.10    (164)  all_28_1 = e1
% 200.36/33.10    (165)   ~ (all_52_19 = all_4_2)
% 200.36/33.10    (166)   ~ (all_52_17 = all_52_23)
% 200.36/33.10    (167)  op(all_6_2, e3) = all_6_1
% 200.36/33.10    (168)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.10    (169)   ~ (all_52_13 = all_52_29)
% 200.36/33.10    (170)  all_58_4 = all_52_17
% 200.36/33.10    (171)   ~ (all_14_0 = e1)
% 200.36/33.10    (172)   ~ (all_14_0 = e2)
% 200.36/33.10    (173)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.10  
% 200.36/33.10  Begin of proof
% 200.36/33.10  | 
% 200.36/33.10  | COMBINE_EQS: (78), (135) imply:
% 200.36/33.10  |   (174)  all_4_0 = e3
% 200.36/33.10  | 
% 200.36/33.10  | SIMP: (174) implies:
% 200.36/33.10  |   (175)  all_4_0 = e3
% 200.36/33.10  | 
% 200.36/33.10  | COMBINE_EQS: (115), (175) imply:
% 200.36/33.10  |   (176)  all_58_5 = e3
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (152), (175) imply:
% 200.36/33.10  |   (177)   ~ (all_52_3 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (5), (175) imply:
% 200.36/33.10  |   (178)   ~ (all_52_17 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (13), (175) imply:
% 200.36/33.10  |   (179)   ~ (all_52_23 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (130), (175) imply:
% 200.36/33.10  |   (180)   ~ (all_52_27 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (48), (175) imply:
% 200.36/33.10  |   (181)   ~ (all_10_2 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (144), (175) imply:
% 200.36/33.10  |   (182)   ~ (all_4_2 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | SIMP: (182) implies:
% 200.36/33.10  |   (183)   ~ (all_4_2 = e3)
% 200.36/33.10  | 
% 200.36/33.10  | REDUCE: (126), (175) imply:
% 200.36/33.10  |   (184)  op(e3, e3) = all_52_18
% 200.36/33.10  | 
% 200.36/33.10  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.10  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 200.36/33.10  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 200.36/33.10  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 200.36/33.10  |            (47), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 200.36/33.10  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 200.36/33.10  |            (70), (71), (72), (73), (74), (75), (76), (77), (79), (80), (81),
% 200.36/33.10  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 200.36/33.10  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 200.36/33.10  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 200.36/33.10  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 200.36/33.10  |            (121), (122), (123), (124), (125), (127), (128), (129), (131),
% 200.36/33.10  |            (132), (133), (134), (136), (137), (138), (139), (140), (141),
% 200.36/33.10  |            (142), (143), (144), (145), (146), (147), (148), (149), (150),
% 200.36/33.10  |            (151), (153), (154), (155), (156), (157), (158), (159), (160),
% 200.36/33.10  |            (161), (162), (163), (164), (165), (166), (167), (168), (169),
% 200.36/33.10  |            (170), (171), (172), (173), (176), (177), (178), (179), (180),
% 200.36/33.10  |            (181), (183), (184) are inconsistent by sub-proof #145.
% 200.36/33.10  | 
% 200.36/33.10  End of proof
% 200.36/33.10  
% 200.36/33.10  Sub-proof #145 shows that the following formulas are inconsistent:
% 200.36/33.10  ----------------------------------------------------------------
% 200.36/33.10    (1)  op(e3, e3) = all_52_18
% 200.36/33.10    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.10    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.10    (4)  all_58_14 = all_52_23
% 200.36/33.10    (5)   ~ (e3 = e1)
% 200.36/33.10    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.10    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.10    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.10    (9)  all_58_1 = all_52_9
% 200.36/33.10    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.10    (11)   ~ (e3 = e0)
% 200.36/33.10    (12)  op(e2, e3) = all_52_3
% 200.36/33.10    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.10    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.10    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.10    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.10    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.10    (18)   ~ (all_4_2 = e3)
% 200.36/33.10    (19)   ~ (all_52_3 = all_6_2)
% 200.36/33.10    (20)  all_58_0 = all_6_2
% 200.36/33.10    (21)  op(all_14_2, e0) = all_14_1
% 200.36/33.10    (22)  all_56_4 = all_52_3
% 200.36/33.10    (23)   ~ (all_52_17 = all_10_2)
% 200.36/33.10    (24)  op(e3, e0) = all_52_25
% 200.36/33.10    (25)  op(e0, all_14_1) = all_14_0
% 200.36/33.10    (26)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.10    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.10    (28)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.10    (29)   ~ (all_52_27 = all_52_29)
% 200.36/33.10    (30)  all_58_13 = all_52_15
% 200.36/33.10    (31)  all_58_9 = all_52_25
% 200.36/33.10    (32)   ~ (all_6_1 = e1)
% 200.36/33.10    (33)   ~ (all_52_29 = all_14_2)
% 200.36/33.10    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.10    (35)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.10    (36)  op(e1, e3) = all_52_5
% 200.36/33.10    (37)  op(e2, e2) = all_4_2
% 200.36/33.10    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 200.36/33.10    (39)   ~ (all_52_3 = all_52_5)
% 200.36/33.10    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.10    (41)  op(all_4_2, e2) = e1
% 200.36/33.10    (42)  all_58_11 = all_52_29
% 200.36/33.10    (43)   ~ (all_52_3 = e3)
% 200.36/33.10    (44)  all_56_5 = all_4_2
% 200.36/33.10    (45)   ~ (all_52_25 = all_14_2)
% 200.36/33.10    (46)   ~ (all_52_9 = all_52_15)
% 200.36/33.10    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.10    (48)   ~ (all_52_3 = all_52_27)
% 200.36/33.10    (49)  op(all_10_2, e1) = all_10_1
% 200.36/33.10    (50)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.10    (51)   ~ (all_52_7 = all_6_2)
% 200.36/33.10    (52)  op(e0, e0) = all_14_2
% 200.36/33.10    (53)  all_56_15 = all_14_2
% 200.36/33.10    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.10    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.10    (56)  all_56_11 = all_52_29
% 200.36/33.10    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.10    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.10    (59)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.10    (60)   ~ (e2 = e1)
% 200.36/33.10    (61)   ~ (all_52_13 = all_10_2)
% 200.36/33.10    (62)   ~ (all_6_0 = e1)
% 200.36/33.10    (63)  all_58_10 = all_52_27
% 200.36/33.10    (64)  all_56_8 = all_52_5
% 200.36/33.10    (65)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.10    (66)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.10    (67)   ~ (all_52_19 = all_52_23)
% 200.36/33.10    (68)   ~ (all_52_25 = all_52_29)
% 200.36/33.10    (69)   ~ (all_52_29 = all_10_2)
% 200.36/33.10    (70)  all_58_7 = all_52_13
% 200.36/33.10    (71)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.10    (72)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.10    (73)   ~ (all_52_5 = all_52_7)
% 200.36/33.10    (74)  all_58_12 = all_52_7
% 200.36/33.10    (75)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.10    (76)   ~ (all_52_7 = all_14_2)
% 200.36/33.10    (77)  all_58_2 = all_52_3
% 200.36/33.10    (78)  all_56_2 = all_52_17
% 200.36/33.10    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.10    (80)  op(e3, all_6_1) = all_6_0
% 200.36/33.10    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.10    (82)   ~ (all_14_0 = e3)
% 200.36/33.10    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.10    (84)  all_56_7 = all_52_27
% 200.36/33.10    (85)  all_28_2 = all_4_2
% 200.36/33.10    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.10    (87)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.10    (88)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.10    (89)   ~ (all_52_23 = e3)
% 200.36/33.10    (90)   ~ (all_52_5 = all_52_29)
% 200.36/33.10    (91)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.10    (92)   ~ (all_10_2 = e3)
% 200.36/33.10    (93)   ~ (all_52_15 = all_14_2)
% 200.36/33.10    (94)   ~ (all_52_19 = all_52_27)
% 200.36/33.10    (95)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.10    (96)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.10    (97)   ~ (all_52_27 = e3)
% 200.36/33.10    (98)   ~ (all_6_0 = e2)
% 200.36/33.10    (99)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 200.36/33.10            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 200.36/33.10    (100)   ~ (all_52_13 = all_4_2)
% 200.36/33.10    (101)  op(e3, e1) = all_52_17
% 200.36/33.10    (102)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.10    (103)  op(e0, e3) = all_52_7
% 200.36/33.10    (104)  op(e1, e2) = all_52_13
% 200.36/33.10    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.10    (106)   ~ (all_52_9 = all_52_25)
% 200.36/33.10    (107)  all_58_15 = all_14_2
% 200.36/33.10    (108)   ~ (all_52_19 = all_10_2)
% 200.36/33.10    (109)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.10    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.10    (111)  all_58_8 = all_10_2
% 200.36/33.10    (112)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.10    (113)   ~ (all_52_5 = all_10_2)
% 200.36/33.10    (114)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.10    (115)   ~ (all_52_23 = all_14_2)
% 200.36/33.10    (116)  all_56_12 = all_52_7
% 200.36/33.10    (117)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.10    (118)  all_58_5 = all_4_0
% 200.36/33.10    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.10    (120)   ~ (all_52_25 = all_6_2)
% 200.36/33.10    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.10    (122)   ~ (all_52_9 = all_4_2)
% 200.36/33.10    (123)   ~ (all_52_5 = all_6_2)
% 200.36/33.10    (124)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.10    (125)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 200.36/33.10    (126)   ~ (all_52_9 = all_6_2)
% 200.36/33.10    (127)   ~ (all_52_13 = all_52_15)
% 200.36/33.10    (128)  all_56_0 = all_6_2
% 200.36/33.10    (129)  op(e3, e3) = all_6_2
% 200.36/33.10    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.10    (131)   ~ (all_52_27 = all_14_2)
% 200.36/33.10    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.10    (133)  all_58_5 = e3
% 200.36/33.10    (134)  all_56_14 = all_52_23
% 200.36/33.10    (135)   ~ (all_52_17 = e3)
% 200.36/33.10    (136)   ~ (all_28_1 = e1) |  ~ (all_28_2 = e0)
% 200.36/33.10    (137)  all_56_3 = all_52_25
% 200.36/33.10    (138)   ~ (all_52_3 = all_52_7)
% 200.36/33.10    (139)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.10    (140)  all_58_5 = all_52_19
% 200.36/33.10    (141)  all_56_1 = all_52_9
% 200.36/33.10    (142)   ~ (all_52_15 = all_4_2)
% 200.36/33.11    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.11           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.11           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.11           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.11    (144)   ~ (all_52_27 = all_4_2)
% 200.36/33.11    (145)  all_58_6 = all_52_5
% 200.36/33.11    (146)   ~ (all_4_0 = all_4_2)
% 200.36/33.11    (147)  op(e3, e2) = all_52_9
% 200.36/33.11    (148)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.11    (149)   ~ (all_52_17 = all_6_2)
% 200.36/33.11    (150)   ~ (e1 = e0)
% 200.36/33.11    (151)   ~ (e3 = e2)
% 200.36/33.11    (152)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.11    (153)   ~ (all_52_9 = all_52_17)
% 200.36/33.11    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.11    (155)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.11    (156)   ~ (all_6_1 = e2)
% 200.36/33.11    (157)  op(e1, e1) = all_10_2
% 200.36/33.11    (158)   ~ (all_52_23 = all_10_2)
% 200.36/33.11    (159)   ~ (all_52_7 = all_52_23)
% 200.36/33.11    (160)   ~ (all_52_17 = all_52_19)
% 200.36/33.11    (161)  all_58_3 = all_4_2
% 200.36/33.11    (162)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.11    (163)  all_56_13 = all_52_15
% 200.36/33.11    (164)   ~ (all_52_3 = all_4_2)
% 200.36/33.11    (165)  all_28_1 = e1
% 200.36/33.11    (166)   ~ (all_52_19 = all_4_2)
% 200.36/33.11    (167)   ~ (all_52_17 = all_52_23)
% 200.36/33.11    (168)  op(all_6_2, e3) = all_6_1
% 200.36/33.11    (169)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.11    (170)   ~ (all_52_13 = all_52_29)
% 200.36/33.11    (171)  all_58_4 = all_52_17
% 200.36/33.11    (172)   ~ (all_14_0 = e1)
% 200.36/33.11    (173)   ~ (all_14_0 = e2)
% 200.36/33.11    (174)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.11  
% 200.36/33.11  Begin of proof
% 200.36/33.11  | 
% 200.36/33.11  | BETA: splitting (136) gives:
% 200.36/33.11  | 
% 200.36/33.11  | Case 1:
% 200.36/33.11  | | 
% 200.36/33.11  | |   (175)   ~ (all_28_1 = e1)
% 200.36/33.11  | | 
% 200.36/33.11  | | REDUCE: (165), (175) imply:
% 200.36/33.11  | |   (176)  $false
% 200.36/33.11  | | 
% 200.36/33.11  | | CLOSE: (176) is inconsistent.
% 200.36/33.11  | | 
% 200.36/33.11  | Case 2:
% 200.36/33.11  | | 
% 200.36/33.11  | |   (177)   ~ (all_28_2 = e0)
% 200.36/33.11  | | 
% 200.36/33.11  | | REDUCE: (85), (177) imply:
% 200.36/33.11  | |   (178)   ~ (all_4_2 = e0)
% 200.36/33.11  | | 
% 200.36/33.11  | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3, simplifying
% 200.36/33.11  | |              with (1), (129) gives:
% 200.36/33.11  | |   (179)  all_52_18 = all_6_2
% 200.36/33.11  | | 
% 200.36/33.11  | | BETA: splitting (99) gives:
% 200.36/33.11  | | 
% 200.36/33.11  | | Case 1:
% 200.36/33.11  | | | 
% 200.36/33.11  | | |   (180)  all_58_15 = e0
% 200.36/33.11  | | | 
% 200.36/33.11  | | | COMBINE_EQS: (107), (180) imply:
% 200.36/33.11  | | |   (181)  all_14_2 = e0
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (93), (181) imply:
% 200.36/33.11  | | |   (182)   ~ (all_52_15 = e0)
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (115), (181) imply:
% 200.36/33.11  | | |   (183)   ~ (all_52_23 = e0)
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (45), (181) imply:
% 200.36/33.11  | | |   (184)   ~ (all_52_25 = e0)
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (131), (181) imply:
% 200.36/33.11  | | |   (185)   ~ (all_52_27 = e0)
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (33), (181) imply:
% 200.36/33.11  | | |   (186)   ~ (all_52_29 = e0)
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (139), (181) imply:
% 200.36/33.11  | | |   (187)  op(e0, e0) = all_52_30
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (21), (181) imply:
% 200.36/33.11  | | |   (188)  op(e0, e0) = all_14_1
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REDUCE: (52), (181) imply:
% 200.36/33.11  | | |   (189)  op(e0, e0) = e0
% 200.36/33.11  | | | 
% 200.36/33.11  | | | BETA: splitting (40) gives:
% 200.36/33.11  | | | 
% 200.36/33.11  | | | Case 1:
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | |   (190)  all_58_2 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | COMBINE_EQS: (77), (190) imply:
% 200.36/33.11  | | | |   (191)  all_52_3 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | SIMP: (191) implies:
% 200.36/33.11  | | | |   (192)  all_52_3 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (39), (192) imply:
% 200.36/33.11  | | | |   (193)   ~ (all_52_5 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | SIMP: (193) implies:
% 200.36/33.11  | | | |   (194)   ~ (all_52_5 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (138), (192) imply:
% 200.36/33.11  | | | |   (195)   ~ (all_52_7 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | SIMP: (195) implies:
% 200.36/33.11  | | | |   (196)   ~ (all_52_7 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (48), (192) imply:
% 200.36/33.11  | | | |   (197)   ~ (all_52_27 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (19), (192) imply:
% 200.36/33.11  | | | |   (198)   ~ (all_6_2 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | SIMP: (198) implies:
% 200.36/33.11  | | | |   (199)   ~ (all_6_2 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (6), (192) imply:
% 200.36/33.11  | | | |   (200)  op(e0, e0) = all_52_2
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (12), (192) imply:
% 200.36/33.11  | | | |   (201)  op(e2, e3) = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | GROUND_INST: instantiating (7) with all_14_1, all_52_30, e0, e0,
% 200.36/33.11  | | | |              simplifying with (187), (188) gives:
% 200.36/33.11  | | | |   (202)  all_52_30 = all_14_1
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | GROUND_INST: instantiating (7) with all_52_30, all_52_2, e0, e0,
% 200.36/33.11  | | | |              simplifying with (187), (200) gives:
% 200.36/33.11  | | | |   (203)  all_52_2 = all_52_30
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | GROUND_INST: instantiating (7) with e0, all_52_2, e0, e0, simplifying
% 200.36/33.11  | | | |              with (189), (200) gives:
% 200.36/33.11  | | | |   (204)  all_52_2 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | COMBINE_EQS: (203), (204) imply:
% 200.36/33.11  | | | |   (205)  all_52_30 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | SIMP: (205) implies:
% 200.36/33.11  | | | |   (206)  all_52_30 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | COMBINE_EQS: (202), (206) imply:
% 200.36/33.11  | | | |   (207)  all_14_1 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (25), (207) imply:
% 200.36/33.11  | | | |   (208)  op(e0, e0) = all_14_0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | GROUND_INST: instantiating (7) with e0, all_14_0, e0, e0, simplifying
% 200.36/33.11  | | | |              with (189), (208) gives:
% 200.36/33.11  | | | |   (209)  all_14_0 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (82), (209) imply:
% 200.36/33.11  | | | |   (210)   ~ (e3 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (173), (209) imply:
% 200.36/33.11  | | | |   (211)   ~ (e2 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | SIMP: (211) implies:
% 200.36/33.11  | | | |   (212)   ~ (e2 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REDUCE: (172), (209) imply:
% 200.36/33.11  | | | |   (213)   ~ (e1 = e0)
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | BETA: splitting (143) gives:
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | Case 1:
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | |   (214)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 200.36/33.11  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 200.36/33.11  | | | | |            all_52_14 = e0)
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | | BETA: splitting (214) gives:
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | | Case 1:
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | |   (215)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 200.36/33.11  | | | | | |          e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | ALPHA: (215) implies:
% 200.36/33.11  | | | | | |   (216)  all_52_2 = e2
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | COMBINE_EQS: (204), (216) imply:
% 200.36/33.11  | | | | | |   (217)  e2 = e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (212), (217) imply:
% 200.36/33.11  | | | | | |   (218)  $false
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | CLOSE: (218) is inconsistent.
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | Case 2:
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | |   (219)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 200.36/33.11  | | | | | |          = e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | ALPHA: (219) implies:
% 200.36/33.11  | | | | | |   (220)  all_52_14 = e0
% 200.36/33.11  | | | | | |   (221)  all_52_12 = e1
% 200.36/33.11  | | | | | |   (222)  all_52_8 = e3
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (65), (222) imply:
% 200.36/33.11  | | | | | |   (223)  op(all_52_9, all_52_9) = e3
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (155), (221) imply:
% 200.36/33.11  | | | | | |   (224)  op(all_52_13, all_52_13) = e1
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (66), (220) imply:
% 200.36/33.11  | | | | | |   (225)  op(all_52_15, all_52_15) = e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | BETA: splitting (148) gives:
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | Case 1:
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | |   (226)  all_58_12 = e3
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | COMBINE_EQS: (74), (226) imply:
% 200.36/33.11  | | | | | | |   (227)  all_52_7 = e3
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | SIMP: (227) implies:
% 200.36/33.11  | | | | | | |   (228)  all_52_7 = e3
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | REDUCE: (73), (228) imply:
% 200.36/33.11  | | | | | | |   (229)   ~ (all_52_5 = e3)
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | REDUCE: (15), (228) imply:
% 200.36/33.11  | | | | | | |   (230)   ~ (all_52_15 = e3)
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | SIMP: (230) implies:
% 200.36/33.11  | | | | | | |   (231)   ~ (all_52_15 = e3)
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | REDUCE: (51), (228) imply:
% 200.36/33.11  | | | | | | |   (232)   ~ (all_6_2 = e3)
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | SIMP: (232) implies:
% 200.36/33.11  | | | | | | |   (233)   ~ (all_6_2 = e3)
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | REDUCE: (16), (228) imply:
% 200.36/33.11  | | | | | | |   (234)  op(e3, e3) = all_52_6
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 200.36/33.11  | | | | | | |              simplifying with (129), (234) gives:
% 200.36/33.11  | | | | | | |   (235)  all_52_6 = all_6_2
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | BETA: splitting (154) gives:
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | Case 1:
% 200.36/33.11  | | | | | | | | 
% 200.36/33.11  | | | | | | | |   (236)  all_56_0 = e3
% 200.36/33.11  | | | | | | | | 
% 200.36/33.11  | | | | | | | | REF_CLOSE: (128), (233), (236) are inconsistent by sub-proof
% 200.36/33.11  | | | | | | | |            #598.
% 200.36/33.11  | | | | | | | | 
% 200.36/33.11  | | | | | | | Case 2:
% 200.36/33.11  | | | | | | | | 
% 200.36/33.11  | | | | | | | |   (237)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.11  | | | | | | | | 
% 200.36/33.11  | | | | | | | | REF_CLOSE: (5), (7), (9), (18), (20), (23), (24), (26), (30),
% 200.36/33.11  | | | | | | | |            (31), (36), (42), (58), (59), (60), (61), (62), (64),
% 200.36/33.11  | | | | | | | |            (70), (75), (78), (80), (83), (96), (105), (106),
% 200.36/33.11  | | | | | | | |            (110), (111), (120), (121), (123), (126), (128),
% 200.36/33.11  | | | | | | | |            (129), (132), (137), (141), (145), (150), (152),
% 200.36/33.11  | | | | | | | |            (153), (155), (156), (157), (161), (168), (170),
% 200.36/33.11  | | | | | | | |            (171), (190), (194), (199), (201), (223), (224),
% 200.36/33.11  | | | | | | | |            (226), (229), (231), (233), (237) are inconsistent by
% 200.36/33.11  | | | | | | | |            sub-proof #157.
% 200.36/33.11  | | | | | | | | 
% 200.36/33.11  | | | | | | | End of split
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | Case 2:
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | |   (238)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | | REF_CLOSE: (4), (7), (11), (30), (89), (129), (180), (199), (225),
% 200.36/33.11  | | | | | | |            (238) are inconsistent by sub-proof #156.
% 200.36/33.11  | | | | | | | 
% 200.36/33.11  | | | | | | End of split
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | End of split
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | Case 2:
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | |   (239)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 200.36/33.11  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.36/33.11  | | | | |            all_52_30 = e0)
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | | BETA: splitting (239) gives:
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | | Case 1:
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | |   (240)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 200.36/33.11  | | | | | |          all_52_22 = e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | ALPHA: (240) implies:
% 200.36/33.11  | | | | | |   (241)  all_52_18 = e2
% 200.36/33.11  | | | | | |   (242)  all_52_16 = e3
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | COMBINE_EQS: (179), (241) imply:
% 200.36/33.11  | | | | | |   (243)  all_6_2 = e2
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | COMBINE_EQS: (20), (243) imply:
% 200.36/33.11  | | | | | |   (244)  all_58_0 = e2
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (123), (243) imply:
% 200.36/33.11  | | | | | |   (245)   ~ (all_52_5 = e2)
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (51), (243) imply:
% 200.36/33.11  | | | | | |   (246)   ~ (all_52_7 = e2)
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (149), (243) imply:
% 200.36/33.11  | | | | | |   (247)   ~ (all_52_17 = e2)
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (117), (242) imply:
% 200.36/33.11  | | | | | |   (248)  op(all_52_17, all_52_17) = e3
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (168), (243) imply:
% 200.36/33.11  | | | | | |   (249)  op(e2, e3) = all_6_1
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | GROUND_INST: instantiating (7) with e0, all_6_1, e3, e2, simplifying
% 200.36/33.11  | | | | | |              with (201), (249) gives:
% 200.36/33.11  | | | | | |   (250)  all_6_1 = e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REDUCE: (80), (250) imply:
% 200.36/33.11  | | | | | |   (251)  op(e3, e0) = all_6_0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REF_CLOSE: (7), (9), (14), (16), (24), (31), (34), (45), (52), (58),
% 200.36/33.11  | | | | | |            (62), (64), (73), (76), (78), (88), (92), (110), (113),
% 200.36/33.11  | | | | | |            (116), (121), (132), (135), (137), (157), (171), (194),
% 200.36/33.11  | | | | | |            (196), (200), (244), (245), (246), (247), (248), (251)
% 200.36/33.11  | | | | | |            are inconsistent by sub-proof #154.
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | Case 2:
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | |   (252)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.36/33.11  | | | | | |          all_52_30 = e0
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | | REF_CLOSE: (3), (4), (5), (7), (9), (11), (12), (14), (15), (16),
% 200.36/33.11  | | | | | |            (17), (19), (20), (22), (23), (24), (27), (30), (31),
% 200.36/33.11  | | | | | |            (35), (36), (37), (38), (40), (42), (46), (47), (50),
% 200.36/33.11  | | | | | |            (51), (52), (54), (55), (56), (57), (60), (61), (62),
% 200.36/33.11  | | | | | |            (63), (66), (68), (69), (70), (73), (74), (75), (77),
% 200.36/33.11  | | | | | |            (79), (80), (84), (86), (90), (91), (95), (96), (98),
% 200.36/33.11  | | | | | |            (108), (109), (111), (113), (114), (116), (120), (121),
% 200.36/33.11  | | | | | |            (123), (125), (127), (129), (130), (131), (132), (137),
% 200.36/33.11  | | | | | |            (138), (140), (142), (145), (148), (150), (151), (156),
% 200.36/33.11  | | | | | |            (157), (158), (159), (161), (163), (164), (168), (171),
% 200.36/33.11  | | | | | |            (174), (180), (182), (183), (184), (185), (186), (196),
% 200.36/33.11  | | | | | |            (212), (252) are inconsistent by sub-proof #1203.
% 200.36/33.11  | | | | | | 
% 200.36/33.11  | | | | | End of split
% 200.36/33.11  | | | | | 
% 200.36/33.11  | | | | End of split
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | Case 2:
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | |   (253)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | | REF_CLOSE: (11), (63), (133), (161), (178), (185), (253) are
% 200.36/33.11  | | | |            inconsistent by sub-proof #152.
% 200.36/33.11  | | | | 
% 200.36/33.11  | | | End of split
% 200.36/33.11  | | | 
% 200.36/33.11  | | Case 2:
% 200.36/33.11  | | | 
% 200.36/33.11  | | |   (254)   ~ (all_58_15 = e0)
% 200.36/33.11  | | |   (255)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 200.36/33.11  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 200.36/33.11  | | | 
% 200.36/33.11  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 200.36/33.11  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 200.36/33.11  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 200.36/33.11  | | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 200.36/33.11  | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 200.36/33.11  | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 200.36/33.11  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 200.36/33.11  | | |            (78), (79), (80), (81), (83), (84), (86), (87), (88), (90),
% 200.36/33.11  | | |            (92), (93), (94), (95), (96), (97), (98), (100), (101), (102),
% 200.36/33.11  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 200.36/33.11  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 200.36/33.11  | | |            (121), (122), (123), (124), (126), (127), (128), (129), (130),
% 200.36/33.11  | | |            (131), (132), (133), (134), (135), (137), (138), (139), (140),
% 200.36/33.11  | | |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 200.36/33.11  | | |            (150), (151), (152), (153), (154), (155), (156), (157), (158),
% 200.36/33.11  | | |            (159), (160), (161), (162), (163), (164), (166), (167), (168),
% 200.36/33.11  | | |            (169), (170), (171), (174), (178), (179), (254), (255) are
% 200.36/33.11  | | |            inconsistent by sub-proof #146.
% 200.36/33.11  | | | 
% 200.36/33.11  | | End of split
% 200.36/33.11  | | 
% 200.36/33.11  | End of split
% 200.36/33.11  | 
% 200.36/33.11  End of proof
% 200.36/33.11  
% 200.36/33.11  Sub-proof #146 shows that the following formulas are inconsistent:
% 200.36/33.11  ----------------------------------------------------------------
% 200.36/33.11    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.11    (2)   ~ (all_52_25 = all_52_27)
% 200.36/33.11    (3)  all_58_14 = all_52_23
% 200.36/33.11    (4)   ~ (e3 = e1)
% 200.36/33.11    (5)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.11    (7)   ~ (all_52_5 = all_52_13)
% 200.36/33.11    (8)  all_58_1 = all_52_9
% 200.36/33.11    (9)   ~ (all_52_9 = all_52_13)
% 200.36/33.11    (10)   ~ (e3 = e0)
% 200.36/33.11    (11)  op(e2, e3) = all_52_3
% 200.36/33.11    (12)   ~ (all_52_23 = all_4_0)
% 200.36/33.11    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.11    (14)   ~ (all_52_7 = all_52_15)
% 200.36/33.11    (15)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.11    (16)   ~ (all_52_17 = all_52_25)
% 200.36/33.11    (17)   ~ (all_4_2 = e3)
% 200.36/33.11    (18)   ~ (all_52_3 = all_6_2)
% 200.36/33.11    (19)  all_58_0 = all_6_2
% 200.36/33.11    (20)  all_56_4 = all_52_3
% 200.36/33.11    (21)   ~ (all_52_17 = all_10_2)
% 200.36/33.11    (22)  op(e3, e0) = all_52_25
% 200.36/33.11    (23)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.11    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.11    (25)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.11    (26)   ~ (all_52_27 = all_52_29)
% 200.36/33.11    (27)  all_58_13 = all_52_15
% 200.36/33.11    (28)   ~ (all_4_2 = e0)
% 200.36/33.11    (29)  all_58_9 = all_52_25
% 200.36/33.11    (30)   ~ (all_6_1 = e1)
% 200.36/33.11    (31)   ~ (all_52_29 = all_14_2)
% 200.36/33.11    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.11    (33)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.11    (34)  op(e1, e3) = all_52_5
% 200.36/33.11    (35)  op(e2, e2) = all_4_2
% 200.36/33.11    (36)   ~ (all_52_3 = all_52_5)
% 200.36/33.11    (37)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.11    (38)  op(all_4_2, e2) = e1
% 200.36/33.11    (39)  all_58_11 = all_52_29
% 200.36/33.11    (40)   ~ (all_52_3 = e3)
% 200.36/33.11    (41)  all_56_5 = all_4_2
% 200.36/33.11    (42)   ~ (all_52_25 = all_14_2)
% 200.36/33.11    (43)   ~ (all_52_9 = all_52_15)
% 200.36/33.11    (44)   ~ (all_52_3 = all_52_27)
% 200.36/33.11    (45)  op(all_10_2, e1) = all_10_1
% 200.36/33.11    (46)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.11    (47)   ~ (all_52_7 = all_6_2)
% 200.36/33.11    (48)  op(e0, e0) = all_14_2
% 200.36/33.11    (49)  all_56_15 = all_14_2
% 200.36/33.11    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.11    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.11    (52)   ~ (all_58_15 = e0)
% 200.36/33.11    (53)  all_56_11 = all_52_29
% 200.36/33.11    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.11    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.11    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.11    (57)   ~ (e2 = e1)
% 200.36/33.11    (58)   ~ (all_52_13 = all_10_2)
% 200.36/33.11    (59)   ~ (all_6_0 = e1)
% 200.36/33.11    (60)  all_58_10 = all_52_27
% 200.36/33.11    (61)  all_56_8 = all_52_5
% 200.36/33.11    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.11    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.11    (64)   ~ (all_52_19 = all_52_23)
% 200.36/33.11    (65)   ~ (all_52_25 = all_52_29)
% 200.36/33.11    (66)   ~ (all_52_29 = all_10_2)
% 200.36/33.11    (67)  all_58_7 = all_52_13
% 200.36/33.11    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.11    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.11    (70)   ~ (all_52_5 = all_52_7)
% 200.36/33.11    (71)  all_58_12 = all_52_7
% 200.36/33.11    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.11    (73)   ~ (all_52_7 = all_14_2)
% 200.36/33.11    (74)  all_52_18 = all_6_2
% 200.36/33.11    (75)  all_58_2 = all_52_3
% 200.36/33.11    (76)  all_56_2 = all_52_17
% 200.36/33.11    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.11    (78)  op(e3, all_6_1) = all_6_0
% 200.36/33.11    (79)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.11    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.11    (81)  all_56_7 = all_52_27
% 200.36/33.11    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.11    (83)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.11    (84)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.11    (85)   ~ (all_52_5 = all_52_29)
% 200.36/33.11    (86)   ~ (all_10_2 = e3)
% 200.36/33.11    (87)   ~ (all_52_15 = all_14_2)
% 200.36/33.11    (88)   ~ (all_52_19 = all_52_27)
% 200.36/33.11    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.11    (90)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.11    (91)   ~ (all_52_27 = e3)
% 200.36/33.11    (92)   ~ (all_6_0 = e2)
% 200.36/33.11    (93)   ~ (all_52_13 = all_4_2)
% 200.36/33.11    (94)  op(e3, e1) = all_52_17
% 200.36/33.11    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.11    (96)  op(e0, e3) = all_52_7
% 200.36/33.11    (97)  op(e1, e2) = all_52_13
% 200.36/33.11    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.11    (99)   ~ (all_52_9 = all_52_25)
% 200.36/33.11    (100)  all_58_15 = all_14_2
% 200.36/33.11    (101)   ~ (all_52_19 = all_10_2)
% 200.36/33.11    (102)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.11    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.11    (104)  all_58_8 = all_10_2
% 200.36/33.11    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.11    (106)   ~ (all_52_5 = all_10_2)
% 200.36/33.11    (107)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.11    (108)   ~ (all_52_23 = all_14_2)
% 200.36/33.11    (109)  all_56_12 = all_52_7
% 200.36/33.11    (110)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.11    (111)  all_58_5 = all_4_0
% 200.36/33.11    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.11    (113)   ~ (all_52_25 = all_6_2)
% 200.36/33.11    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.11    (115)   ~ (all_52_9 = all_4_2)
% 200.36/33.11    (116)   ~ (all_52_5 = all_6_2)
% 200.36/33.11    (117)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.11    (118)   ~ (all_52_9 = all_6_2)
% 200.36/33.11    (119)   ~ (all_52_13 = all_52_15)
% 200.36/33.11    (120)  all_56_0 = all_6_2
% 200.36/33.11    (121)  op(e3, e3) = all_6_2
% 200.36/33.11    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.11    (123)   ~ (all_52_27 = all_14_2)
% 200.36/33.11    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.11    (125)  all_58_5 = e3
% 200.36/33.11    (126)  all_56_14 = all_52_23
% 200.36/33.11    (127)   ~ (all_52_17 = e3)
% 200.36/33.11    (128)  all_56_3 = all_52_25
% 200.36/33.11    (129)   ~ (all_52_3 = all_52_7)
% 200.36/33.11    (130)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.11    (131)  all_58_5 = all_52_19
% 200.36/33.11    (132)  all_56_1 = all_52_9
% 200.36/33.11    (133)   ~ (all_52_15 = all_4_2)
% 200.36/33.11    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.11           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.11           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.11           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.11    (135)   ~ (all_52_27 = all_4_2)
% 200.36/33.11    (136)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 200.36/33.11             all_58_13 = e0 | all_58_14 = e0)
% 200.36/33.11    (137)  all_58_6 = all_52_5
% 200.36/33.11    (138)   ~ (all_4_0 = all_4_2)
% 200.36/33.11    (139)  op(e3, e2) = all_52_9
% 200.36/33.11    (140)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.11    (141)   ~ (all_52_17 = all_6_2)
% 200.36/33.11    (142)   ~ (e1 = e0)
% 200.36/33.11    (143)   ~ (e3 = e2)
% 200.36/33.11    (144)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.11    (145)   ~ (all_52_9 = all_52_17)
% 200.36/33.11    (146)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.11    (147)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.11    (148)   ~ (all_6_1 = e2)
% 200.36/33.11    (149)  op(e1, e1) = all_10_2
% 200.36/33.11    (150)   ~ (all_52_23 = all_10_2)
% 200.36/33.11    (151)   ~ (all_52_7 = all_52_23)
% 200.36/33.12    (152)   ~ (all_52_17 = all_52_19)
% 200.36/33.12    (153)  all_58_3 = all_4_2
% 200.36/33.12    (154)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.12    (155)  all_56_13 = all_52_15
% 200.36/33.12    (156)   ~ (all_52_3 = all_4_2)
% 200.36/33.12    (157)   ~ (all_52_19 = all_4_2)
% 200.36/33.12    (158)   ~ (all_52_17 = all_52_23)
% 200.36/33.12    (159)  op(all_6_2, e3) = all_6_1
% 200.36/33.12    (160)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.12    (161)   ~ (all_52_13 = all_52_29)
% 200.36/33.12    (162)  all_58_4 = all_52_17
% 200.36/33.12    (163)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.12  
% 200.36/33.12  Begin of proof
% 200.36/33.12  | 
% 200.36/33.12  | ALPHA: (136) implies:
% 200.36/33.12  |   (164)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.12  |   (165)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.12  | 
% 200.36/33.12  | REDUCE: (52), (100) imply:
% 200.36/33.12  |   (166)   ~ (all_14_2 = e0)
% 200.36/33.12  | 
% 200.36/33.12  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 200.36/33.12  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 200.36/33.12  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 200.36/33.12  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 200.36/33.12  |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 200.36/33.12  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 200.36/33.12  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 200.36/33.12  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 200.36/33.12  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 200.36/33.12  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 200.36/33.12  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 200.36/33.12  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 200.36/33.12  |            (129), (130), (131), (132), (133), (134), (135), (137), (138),
% 200.36/33.12  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 200.36/33.12  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 200.36/33.12  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 200.36/33.12  |            (166) are inconsistent by sub-proof #147.
% 200.36/33.12  | 
% 200.36/33.12  End of proof
% 200.36/33.12  
% 200.36/33.12  Sub-proof #147 shows that the following formulas are inconsistent:
% 200.36/33.12  ----------------------------------------------------------------
% 200.36/33.12    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.12    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.12    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.12    (4)  all_58_14 = all_52_23
% 200.36/33.12    (5)   ~ (e3 = e1)
% 200.36/33.12    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.12    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.12    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.12    (9)  all_58_1 = all_52_9
% 200.36/33.12    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.12    (11)   ~ (e3 = e0)
% 200.36/33.12    (12)  op(e2, e3) = all_52_3
% 200.36/33.12    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.12    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.12    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.12    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.12    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.12    (18)   ~ (all_4_2 = e3)
% 200.36/33.12    (19)   ~ (all_52_3 = all_6_2)
% 200.36/33.12    (20)  all_58_0 = all_6_2
% 200.36/33.12    (21)  all_56_4 = all_52_3
% 200.36/33.12    (22)   ~ (all_52_17 = all_10_2)
% 200.36/33.12    (23)  op(e3, e0) = all_52_25
% 200.36/33.12    (24)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.12    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.12    (26)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.12    (27)   ~ (all_52_27 = all_52_29)
% 200.36/33.12    (28)  all_58_13 = all_52_15
% 200.36/33.12    (29)   ~ (all_4_2 = e0)
% 200.36/33.12    (30)  all_58_9 = all_52_25
% 200.36/33.12    (31)   ~ (all_6_1 = e1)
% 200.36/33.12    (32)   ~ (all_52_29 = all_14_2)
% 200.36/33.12    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.12    (34)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.12    (35)  op(e1, e3) = all_52_5
% 200.36/33.12    (36)  op(e2, e2) = all_4_2
% 200.36/33.12    (37)   ~ (all_52_3 = all_52_5)
% 200.36/33.12    (38)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.12    (39)  op(all_4_2, e2) = e1
% 200.36/33.12    (40)  all_58_11 = all_52_29
% 200.36/33.12    (41)   ~ (all_52_3 = e3)
% 200.36/33.12    (42)  all_56_5 = all_4_2
% 200.36/33.12    (43)   ~ (all_52_25 = all_14_2)
% 200.36/33.12    (44)   ~ (all_52_9 = all_52_15)
% 200.36/33.12    (45)   ~ (all_52_3 = all_52_27)
% 200.36/33.12    (46)  op(all_10_2, e1) = all_10_1
% 200.36/33.12    (47)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.12    (48)   ~ (all_52_7 = all_6_2)
% 200.36/33.12    (49)  op(e0, e0) = all_14_2
% 200.36/33.12    (50)  all_56_15 = all_14_2
% 200.36/33.12    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.12    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.12    (53)  all_56_11 = all_52_29
% 200.36/33.12    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.12    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.12    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.12    (57)   ~ (e2 = e1)
% 200.36/33.12    (58)   ~ (all_52_13 = all_10_2)
% 200.36/33.12    (59)   ~ (all_6_0 = e1)
% 200.36/33.12    (60)  all_58_10 = all_52_27
% 200.36/33.12    (61)  all_56_8 = all_52_5
% 200.36/33.12    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.12    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.12    (64)   ~ (all_52_19 = all_52_23)
% 200.36/33.12    (65)   ~ (all_52_25 = all_52_29)
% 200.36/33.12    (66)   ~ (all_52_29 = all_10_2)
% 200.36/33.12    (67)  all_58_7 = all_52_13
% 200.36/33.12    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.12    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.12    (70)   ~ (all_52_5 = all_52_7)
% 200.36/33.12    (71)  all_58_12 = all_52_7
% 200.36/33.12    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.12    (73)   ~ (all_52_7 = all_14_2)
% 200.36/33.12    (74)   ~ (all_14_2 = e0)
% 200.36/33.12    (75)  all_52_18 = all_6_2
% 200.36/33.12    (76)  all_58_2 = all_52_3
% 200.36/33.12    (77)  all_56_2 = all_52_17
% 200.36/33.12    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.12    (79)  op(e3, all_6_1) = all_6_0
% 200.36/33.12    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.12    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.12    (82)  all_56_7 = all_52_27
% 200.36/33.12    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.12    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.12    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.12    (86)   ~ (all_52_5 = all_52_29)
% 200.36/33.12    (87)   ~ (all_10_2 = e3)
% 200.36/33.12    (88)   ~ (all_52_15 = all_14_2)
% 200.36/33.12    (89)   ~ (all_52_19 = all_52_27)
% 200.36/33.12    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.12    (91)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.12    (92)   ~ (all_52_27 = e3)
% 200.36/33.12    (93)   ~ (all_6_0 = e2)
% 200.36/33.12    (94)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.12    (95)   ~ (all_52_13 = all_4_2)
% 200.36/33.12    (96)  op(e3, e1) = all_52_17
% 200.36/33.12    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.12    (98)  op(e0, e3) = all_52_7
% 200.36/33.12    (99)  op(e1, e2) = all_52_13
% 200.36/33.12    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.12    (101)   ~ (all_52_9 = all_52_25)
% 200.36/33.12    (102)  all_58_15 = all_14_2
% 200.36/33.12    (103)   ~ (all_52_19 = all_10_2)
% 200.36/33.12    (104)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.12    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.12    (106)  all_58_8 = all_10_2
% 200.36/33.12    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.12    (108)   ~ (all_52_5 = all_10_2)
% 200.36/33.12    (109)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.12    (110)   ~ (all_52_23 = all_14_2)
% 200.36/33.12    (111)  all_56_12 = all_52_7
% 200.36/33.12    (112)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.12    (113)  all_58_5 = all_4_0
% 200.36/33.12    (114)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.12    (115)   ~ (all_52_25 = all_6_2)
% 200.36/33.12    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.12    (117)   ~ (all_52_9 = all_4_2)
% 200.36/33.12    (118)   ~ (all_52_5 = all_6_2)
% 200.36/33.12    (119)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.12    (120)   ~ (all_52_9 = all_6_2)
% 200.36/33.12    (121)   ~ (all_52_13 = all_52_15)
% 200.36/33.12    (122)  all_56_0 = all_6_2
% 200.36/33.12    (123)  op(e3, e3) = all_6_2
% 200.36/33.12    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.12    (125)   ~ (all_52_27 = all_14_2)
% 200.36/33.12    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.12    (127)  all_58_5 = e3
% 200.36/33.12    (128)  all_56_14 = all_52_23
% 200.36/33.12    (129)   ~ (all_52_17 = e3)
% 200.36/33.12    (130)  all_56_3 = all_52_25
% 200.36/33.12    (131)   ~ (all_52_3 = all_52_7)
% 200.36/33.12    (132)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.12    (133)  all_58_5 = all_52_19
% 200.36/33.12    (134)  all_56_1 = all_52_9
% 200.36/33.12    (135)   ~ (all_52_15 = all_4_2)
% 200.36/33.12    (136)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.12           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.12           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.12           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.12    (137)   ~ (all_52_27 = all_4_2)
% 200.36/33.12    (138)  all_58_6 = all_52_5
% 200.36/33.12    (139)   ~ (all_4_0 = all_4_2)
% 200.36/33.12    (140)  op(e3, e2) = all_52_9
% 200.36/33.12    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.12    (142)   ~ (all_52_17 = all_6_2)
% 200.36/33.12    (143)   ~ (e1 = e0)
% 200.36/33.12    (144)   ~ (e3 = e2)
% 200.36/33.12    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.12    (146)   ~ (all_52_9 = all_52_17)
% 200.36/33.12    (147)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.12    (148)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.12    (149)   ~ (all_6_1 = e2)
% 200.36/33.12    (150)  op(e1, e1) = all_10_2
% 200.36/33.12    (151)   ~ (all_52_23 = all_10_2)
% 200.36/33.12    (152)   ~ (all_52_7 = all_52_23)
% 200.36/33.12    (153)   ~ (all_52_17 = all_52_19)
% 200.36/33.12    (154)  all_58_3 = all_4_2
% 200.36/33.12    (155)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.12    (156)  all_56_13 = all_52_15
% 200.36/33.12    (157)   ~ (all_52_3 = all_4_2)
% 200.36/33.12    (158)   ~ (all_52_19 = all_4_2)
% 200.36/33.12    (159)   ~ (all_52_17 = all_52_23)
% 200.36/33.12    (160)  op(all_6_2, e3) = all_6_1
% 200.36/33.12    (161)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.12    (162)   ~ (all_52_13 = all_52_29)
% 200.36/33.12    (163)  all_58_4 = all_52_17
% 200.36/33.12    (164)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.12  
% 200.36/33.12  Begin of proof
% 200.36/33.12  | 
% 200.36/33.12  | BETA: splitting (84) gives:
% 200.36/33.12  | 
% 200.36/33.12  | Case 1:
% 200.36/33.12  | | 
% 200.36/33.12  | |   (165)  all_56_5 = e3
% 200.36/33.12  | | 
% 200.36/33.12  | | REF_CLOSE: (18), (42), (165) are inconsistent by sub-proof #1319.
% 200.36/33.12  | | 
% 200.36/33.12  | Case 2:
% 200.36/33.12  | | 
% 200.36/33.12  | |   (166)   ~ (all_56_5 = e3)
% 200.36/33.12  | |   (167)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.12  | | 
% 200.36/33.12  | | BETA: splitting (136) gives:
% 200.36/33.12  | | 
% 200.36/33.12  | | Case 1:
% 200.36/33.12  | | | 
% 200.36/33.12  | | |   (168)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.12  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.36/33.12  | | |            e0)
% 200.36/33.12  | | | 
% 200.36/33.12  | | | BETA: splitting (168) gives:
% 200.36/33.12  | | | 
% 200.36/33.12  | | | Case 1:
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | |   (169)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | ALPHA: (169) implies:
% 200.36/33.12  | | | |   (170)  all_52_2 = e2
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | REDUCE: (6), (170) imply:
% 200.36/33.12  | | | |   (171)  op(all_52_3, all_52_3) = e2
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | REF_CLOSE: (5), (7), (11), (25), (29), (36), (38), (39), (42), (49),
% 200.36/33.12  | | | |            (57), (60), (69), (74), (76), (82), (92), (95), (99), (125),
% 200.36/33.12  | | | |            (127), (137), (143), (154), (157), (161), (167), (171) are
% 200.36/33.12  | | | |            inconsistent by sub-proof #148.
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | Case 2:
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | |   (172)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.36/33.12  | | | |          e0
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | ALPHA: (172) implies:
% 200.36/33.12  | | | |   (173)  all_52_14 = e0
% 200.36/33.12  | | | |   (174)  all_52_12 = e1
% 200.36/33.12  | | | |   (175)  all_52_8 = e3
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | REDUCE: (62), (175) imply:
% 200.36/33.12  | | | |   (176)  op(all_52_9, all_52_9) = e3
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | REDUCE: (148), (174) imply:
% 200.36/33.12  | | | |   (177)  op(all_52_13, all_52_13) = e1
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | REDUCE: (63), (173) imply:
% 200.36/33.12  | | | |   (178)  op(all_52_15, all_52_15) = e0
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | BETA: splitting (38) gives:
% 200.36/33.12  | | | | 
% 200.36/33.12  | | | | Case 1:
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | |   (179)  all_58_2 = e0
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | COMBINE_EQS: (76), (179) imply:
% 200.36/33.12  | | | | |   (180)  all_52_3 = e0
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | SIMP: (180) implies:
% 200.36/33.12  | | | | |   (181)  all_52_3 = e0
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | REDUCE: (37), (181) imply:
% 200.36/33.12  | | | | |   (182)   ~ (all_52_5 = e0)
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | SIMP: (182) implies:
% 200.36/33.12  | | | | |   (183)   ~ (all_52_5 = e0)
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | REDUCE: (19), (181) imply:
% 200.36/33.12  | | | | |   (184)   ~ (all_6_2 = e0)
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | SIMP: (184) implies:
% 200.36/33.12  | | | | |   (185)   ~ (all_6_2 = e0)
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | REDUCE: (41), (181) imply:
% 200.36/33.12  | | | | |   (186)   ~ (e3 = e0)
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | REDUCE: (6), (181) imply:
% 200.36/33.12  | | | | |   (187)  op(e0, e0) = all_52_2
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | REDUCE: (12), (181) imply:
% 200.36/33.12  | | | | |   (188)  op(e2, e3) = e0
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | GROUND_INST: instantiating (7) with all_14_2, all_52_2, e0, e0,
% 200.36/33.12  | | | | |              simplifying with (49), (187) gives:
% 200.36/33.12  | | | | |   (189)  all_52_2 = all_14_2
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | BETA: splitting (147) gives:
% 200.36/33.12  | | | | | 
% 200.36/33.12  | | | | | Case 1:
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | |   (190)  all_56_0 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | COMBINE_EQS: (122), (190) imply:
% 200.36/33.12  | | | | | |   (191)  all_6_2 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | SIMP: (191) implies:
% 200.36/33.12  | | | | | |   (192)  all_6_2 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (118), (192) imply:
% 200.36/33.12  | | | | | |   (193)   ~ (all_52_5 = e3)
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (48), (192) imply:
% 200.36/33.12  | | | | | |   (194)   ~ (all_52_7 = e3)
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (47), (192) imply:
% 200.36/33.12  | | | | | |   (195)  op(e3, e3) = all_52_0
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (160), (192) imply:
% 200.36/33.12  | | | | | |   (196)  op(e3, e3) = all_6_1
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (123), (192) imply:
% 200.36/33.12  | | | | | |   (197)  op(e3, e3) = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | GROUND_INST: instantiating (7) with all_6_1, all_52_0, e3, e3,
% 200.36/33.12  | | | | | |              simplifying with (195), (196) gives:
% 200.36/33.12  | | | | | |   (198)  all_52_0 = all_6_1
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | GROUND_INST: instantiating (7) with e3, all_52_0, e3, e3,
% 200.36/33.12  | | | | | |              simplifying with (195), (197) gives:
% 200.36/33.12  | | | | | |   (199)  all_52_0 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | COMBINE_EQS: (198), (199) imply:
% 200.36/33.12  | | | | | |   (200)  all_6_1 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | SIMP: (200) implies:
% 200.36/33.12  | | | | | |   (201)  all_6_1 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (79), (201) imply:
% 200.36/33.12  | | | | | |   (202)  op(e3, e3) = all_6_0
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | GROUND_INST: instantiating (7) with e3, all_6_0, e3, e3, simplifying
% 200.36/33.12  | | | | | |              with (197), (202) gives:
% 200.36/33.12  | | | | | |   (203)  all_6_0 = e3
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | BETA: splitting (72) gives:
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | Case 1:
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | |   (204)  all_58_6 = e3
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | REF_CLOSE: (138), (193), (204) are inconsistent by sub-proof
% 200.36/33.12  | | | | | | |            #1328.
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | Case 2:
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | |   (205)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | BETA: splitting (141) gives:
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | |   (206)  all_58_12 = e3
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REF_CLOSE: (71), (194), (206) are inconsistent by sub-proof
% 200.36/33.12  | | | | | | | |            #1367.
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | Case 2:
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | |   (207)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | BETA: splitting (107) gives:
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | |   (208)  all_56_15 = e3
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | COMBINE_EQS: (50), (208) imply:
% 200.36/33.12  | | | | | | | | |   (209)  all_14_2 = e3
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | SIMP: (209) implies:
% 200.36/33.12  | | | | | | | | |   (210)  all_14_2 = e3
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | REDUCE: (32), (210) imply:
% 200.36/33.12  | | | | | | | | |   (211)   ~ (all_52_29 = e3)
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | REF_CLOSE: (5), (7), (40), (67), (87), (106), (177), (195),
% 200.36/33.12  | | | | | | | | |            (197), (205), (211) are inconsistent by sub-proof
% 200.36/33.12  | | | | | | | | |            #1139.
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | Case 2:
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | |   (212)   ~ (all_56_15 = e3)
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | REDUCE: (50), (212) imply:
% 200.36/33.12  | | | | | | | | |   (213)   ~ (all_14_2 = e3)
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | BETA: splitting (207) gives:
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | |   (214)  all_58_13 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | COMBINE_EQS: (28), (214) imply:
% 200.36/33.12  | | | | | | | | | |   (215)  all_52_15 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | SIMP: (215) implies:
% 200.36/33.12  | | | | | | | | | |   (216)  all_52_15 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | REDUCE: (178), (216) imply:
% 200.36/33.12  | | | | | | | | | |   (217)  op(e3, e3) = e0
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | REF_CLOSE: (7), (11), (195), (196), (197), (217) are
% 200.36/33.12  | | | | | | | | | |            inconsistent by sub-proof #949.
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | Case 2:
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | |   (218)  all_58_14 = e3 | all_58_15 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (13), (20),
% 200.36/33.12  | | | | | | | | | |            (27), (28), (30), (34), (35), (36), (37), (39),
% 200.36/33.12  | | | | | | | | | |            (40), (42), (49), (51), (57), (60), (61), (67),
% 200.36/33.12  | | | | | | | | | |            (70), (71), (72), (76), (78), (84), (86), (88),
% 200.36/33.12  | | | | | | | | | |            (91), (94), (95), (100), (101), (102), (104),
% 200.36/33.12  | | | | | | | | | |            (105), (106), (108), (113), (118), (119), (120),
% 200.36/33.12  | | | | | | | | | |            (123), (131), (134), (135), (137), (138), (139),
% 200.36/33.12  | | | | | | | | | |            (140), (144), (145), (149), (150), (151), (152),
% 200.36/33.12  | | | | | | | | | |            (154), (157), (160), (176), (177), (178), (213),
% 200.36/33.12  | | | | | | | | | |            (218) are inconsistent by sub-proof #190.
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | End of split
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | End of split
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | End of split
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | End of split
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | Case 2:
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | |   (219)   ~ (all_56_0 = e3)
% 200.36/33.12  | | | | | |   (220)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | REDUCE: (122), (219) imply:
% 200.36/33.12  | | | | | |   (221)   ~ (all_6_2 = e3)
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | BETA: splitting (78) gives:
% 200.36/33.12  | | | | | | 
% 200.36/33.12  | | | | | | Case 1:
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | |   (222)  all_58_0 = e3
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | COMBINE_EQS: (20), (222) imply:
% 200.36/33.12  | | | | | | |   (223)  all_6_2 = e3
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | REDUCE: (221), (223) imply:
% 200.36/33.12  | | | | | | |   (224)  $false
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | CLOSE: (224) is inconsistent.
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | Case 2:
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | |   (225)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | BETA: splitting (14) gives:
% 200.36/33.12  | | | | | | | 
% 200.36/33.12  | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | |   (226)  all_56_12 = e3
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | COMBINE_EQS: (111), (226) imply:
% 200.36/33.12  | | | | | | | |   (227)  all_52_7 = e3
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | COMBINE_EQS: (71), (227) imply:
% 200.36/33.12  | | | | | | | |   (228)  all_58_12 = e3
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REDUCE: (70), (227) imply:
% 200.36/33.12  | | | | | | | |   (229)   ~ (all_52_5 = e3)
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REDUCE: (15), (227) imply:
% 200.36/33.12  | | | | | | | |   (230)   ~ (all_52_15 = e3)
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | SIMP: (230) implies:
% 200.36/33.12  | | | | | | | |   (231)   ~ (all_52_15 = e3)
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REDUCE: (48), (227) imply:
% 200.36/33.12  | | | | | | | |   (232)   ~ (all_6_2 = e3)
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REDUCE: (16), (227) imply:
% 200.36/33.12  | | | | | | | |   (233)  op(e3, e3) = all_52_6
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 200.36/33.12  | | | | | | | |              simplifying with (123), (233) gives:
% 200.36/33.12  | | | | | | | |   (234)  all_52_6 = all_6_2
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REF_CLOSE: (5), (7), (9), (18), (20), (22), (23), (24), (28),
% 200.36/33.12  | | | | | | | |            (30), (35), (40), (55), (56), (57), (58), (59), (61),
% 200.36/33.12  | | | | | | | |            (67), (72), (77), (79), (81), (91), (100), (101),
% 200.36/33.12  | | | | | | | |            (105), (106), (115), (116), (118), (120), (122),
% 200.36/33.12  | | | | | | | |            (123), (126), (130), (134), (138), (143), (145),
% 200.36/33.12  | | | | | | | |            (146), (148), (149), (150), (154), (160), (162),
% 200.36/33.12  | | | | | | | |            (163), (176), (177), (179), (183), (185), (188),
% 200.36/33.12  | | | | | | | |            (220), (221), (228), (229), (231) are inconsistent by
% 200.36/33.12  | | | | | | | |            sub-proof #157.
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | Case 2:
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | |   (235)   ~ (all_56_12 = e3)
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | REDUCE: (111), (235) imply:
% 200.36/33.12  | | | | | | | |   (236)   ~ (all_52_7 = e3)
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | BETA: splitting (225) gives:
% 200.36/33.12  | | | | | | | | 
% 200.36/33.12  | | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | |   (237)  all_58_2 = e3
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | COMBINE_EQS: (179), (237) imply:
% 200.36/33.12  | | | | | | | | |   (238)  e3 = e0
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | REDUCE: (11), (238) imply:
% 200.36/33.12  | | | | | | | | |   (239)  $false
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | CLOSE: (239) is inconsistent.
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | Case 2:
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | |   (240)  all_58_6 = e3 | all_58_12 = e3
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | BETA: splitting (240) gives:
% 200.36/33.12  | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | |   (241)  all_58_6 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | COMBINE_EQS: (138), (241) imply:
% 200.36/33.12  | | | | | | | | | |   (242)  all_52_5 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | SIMP: (242) implies:
% 200.36/33.12  | | | | | | | | | |   (243)  all_52_5 = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | REDUCE: (24), (243) imply:
% 200.36/33.12  | | | | | | | | | |   (244)  op(e3, e3) = all_52_4
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | REDUCE: (35), (243) imply:
% 200.36/33.12  | | | | | | | | | |   (245)  op(e1, e3) = e3
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_4, e3, e3,
% 200.36/33.12  | | | | | | | | | |              simplifying with (123), (244) gives:
% 200.36/33.12  | | | | | | | | | |   (246)  all_52_4 = all_6_2
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | BETA: splitting (81) gives:
% 200.36/33.12  | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | Case 1:
% 200.36/33.12  | | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | |   (247)  all_58_0 = e1
% 200.36/33.12  | | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | | COMBINE_EQS: (20), (247) imply:
% 200.36/33.12  | | | | | | | | | | |   (248)  all_6_2 = e1
% 200.36/33.12  | | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | | REDUCE: (160), (248) imply:
% 200.36/33.12  | | | | | | | | | | |   (249)  op(e1, e3) = all_6_1
% 200.36/33.12  | | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | | REDUCE: (123), (248) imply:
% 200.36/33.12  | | | | | | | | | | |   (250)  op(e3, e3) = e1
% 200.36/33.12  | | | | | | | | | | | 
% 200.36/33.12  | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_6_1, e3, e1,
% 200.36/33.12  | | | | | | | | | | |              simplifying with (245), (249) gives:
% 200.36/33.13  | | | | | | | | | | |   (251)  all_6_1 = e3
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | | REDUCE: (79), (251) imply:
% 200.36/33.13  | | | | | | | | | | |   (252)  op(e3, e3) = all_6_0
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_6_0, e3, e3,
% 200.36/33.13  | | | | | | | | | | |              simplifying with (250), (252) gives:
% 200.36/33.13  | | | | | | | | | | |   (253)  all_6_0 = e1
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | | REDUCE: (59), (253) imply:
% 200.36/33.13  | | | | | | | | | | |   (254)  $false
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | | CLOSE: (254) is inconsistent.
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | Case 2:
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | |   (255)   ~ (all_58_0 = e1)
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | | REDUCE: (20), (255) imply:
% 200.36/33.13  | | | | | | | | | | |   (256)   ~ (all_6_2 = e1)
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | | REF_CLOSE: (7), (9), (14), (15), (18), (28), (31), (48),
% 200.36/33.13  | | | | | | | | | | |            (54), (67), (98), (100), (111), (120), (123),
% 200.36/33.13  | | | | | | | | | | |            (149), (154), (156), (160), (176), (177), (178),
% 200.36/33.13  | | | | | | | | | | |            (256) are inconsistent by sub-proof #892.
% 200.36/33.13  | | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | End of split
% 200.36/33.13  | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | Case 2:
% 200.36/33.13  | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | |   (257)  all_58_12 = e3
% 200.36/33.13  | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | | REF_CLOSE: (71), (236), (257) are inconsistent by sub-proof
% 200.36/33.13  | | | | | | | | | |            #1367.
% 200.36/33.13  | | | | | | | | | | 
% 200.36/33.13  | | | | | | | | | End of split
% 200.36/33.13  | | | | | | | | | 
% 200.36/33.13  | | | | | | | | End of split
% 200.36/33.13  | | | | | | | | 
% 200.36/33.13  | | | | | | | End of split
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | End of split
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | End of split
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | Case 2:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | |   (258)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | REF_CLOSE: (5), (7), (11), (29), (36), (39), (42), (57), (60), (69),
% 200.36/33.13  | | | | |            (76), (95), (99), (127), (137), (143), (154), (157), (161),
% 200.36/33.13  | | | | |            (167), (258) are inconsistent by sub-proof #149.
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | End of split
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | End of split
% 200.36/33.13  | | | 
% 200.36/33.13  | | Case 2:
% 200.36/33.13  | | | 
% 200.36/33.13  | | |   (259)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.13  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.36/33.13  | | |            all_52_30 = e0)
% 200.36/33.13  | | | 
% 200.36/33.13  | | | BETA: splitting (259) gives:
% 200.36/33.13  | | | 
% 200.36/33.13  | | | Case 1:
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | |   (260)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.13  | | | |          e0
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | ALPHA: (260) implies:
% 200.36/33.13  | | | |   (261)  all_52_18 = e2
% 200.36/33.13  | | | |   (262)  all_52_16 = e3
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | COMBINE_EQS: (75), (261) imply:
% 200.36/33.13  | | | |   (263)  all_6_2 = e2
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | SIMP: (263) implies:
% 200.36/33.13  | | | |   (264)  all_6_2 = e2
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | COMBINE_EQS: (20), (264) imply:
% 200.36/33.13  | | | |   (265)  all_58_0 = e2
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (19), (264) imply:
% 200.36/33.13  | | | |   (266)   ~ (all_52_3 = e2)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (118), (264) imply:
% 200.36/33.13  | | | |   (267)   ~ (all_52_5 = e2)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (48), (264) imply:
% 200.36/33.13  | | | |   (268)   ~ (all_52_7 = e2)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (142), (264) imply:
% 200.36/33.13  | | | |   (269)   ~ (all_52_17 = e2)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (112), (262) imply:
% 200.36/33.13  | | | |   (270)  op(all_52_17, all_52_17) = e3
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (160), (264) imply:
% 200.36/33.13  | | | |   (271)  op(e2, e3) = all_6_1
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | GROUND_INST: instantiating (7) with all_52_3, all_6_1, e3, e2,
% 200.36/33.13  | | | |              simplifying with (12), (271) gives:
% 200.36/33.13  | | | |   (272)  all_52_3 = all_6_1
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | COMBINE_EQS: (21), (272) imply:
% 200.36/33.13  | | | |   (273)  all_56_4 = all_6_1
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (37), (272) imply:
% 200.36/33.13  | | | |   (274)   ~ (all_52_5 = all_6_1)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | SIMP: (274) implies:
% 200.36/33.13  | | | |   (275)   ~ (all_52_5 = all_6_1)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (131), (272) imply:
% 200.36/33.13  | | | |   (276)   ~ (all_52_7 = all_6_1)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | SIMP: (276) implies:
% 200.36/33.13  | | | |   (277)   ~ (all_52_7 = all_6_1)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (41), (272) imply:
% 200.36/33.13  | | | |   (278)   ~ (all_6_1 = e3)
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REDUCE: (6), (272) imply:
% 200.36/33.13  | | | |   (279)  op(all_6_1, all_6_1) = all_52_2
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | BETA: splitting (83) gives:
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | Case 1:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | |   (280)  all_56_4 = e3
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | REF_CLOSE: (273), (278), (280) are inconsistent by sub-proof #900.
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | Case 2:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | |   (281)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | BETA: splitting (281) gives:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | Case 1:
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | |   (282)  all_56_4 = e2
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | REF_CLOSE: (149), (273), (282) are inconsistent by sub-proof #1219.
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | Case 2:
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | |   (283)  all_56_4 = e1 | all_56_4 = e0
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | BETA: splitting (283) gives:
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | Case 1:
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | |   (284)  all_56_4 = e1
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | REF_CLOSE: (31), (273), (284) are inconsistent by sub-proof #1218.
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | Case 2:
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | |   (285)  all_56_4 = e0
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | COMBINE_EQS: (273), (285) imply:
% 200.36/33.13  | | | | | | |   (286)  all_6_1 = e0
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | SIMP: (286) implies:
% 200.36/33.13  | | | | | | |   (287)  all_6_1 = e0
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | REDUCE: (275), (287) imply:
% 200.36/33.13  | | | | | | |   (288)   ~ (all_52_5 = e0)
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | REDUCE: (277), (287) imply:
% 200.36/33.13  | | | | | | |   (289)   ~ (all_52_7 = e0)
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | REDUCE: (279), (287) imply:
% 200.36/33.13  | | | | | | |   (290)  op(e0, e0) = all_52_2
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | REDUCE: (79), (287) imply:
% 200.36/33.13  | | | | | | |   (291)  op(e3, e0) = all_6_0
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | | REF_CLOSE: (7), (9), (14), (16), (23), (30), (33), (43), (49),
% 200.36/33.13  | | | | | | |            (55), (59), (61), (70), (73), (77), (85), (87), (105),
% 200.36/33.13  | | | | | | |            (108), (111), (116), (126), (129), (130), (150), (163),
% 200.36/33.13  | | | | | | |            (265), (267), (268), (269), (270), (288), (289), (290),
% 200.36/33.13  | | | | | | |            (291) are inconsistent by sub-proof #154.
% 200.36/33.13  | | | | | | | 
% 200.36/33.13  | | | | | | End of split
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | End of split
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | End of split
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | Case 2:
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | |   (292)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.36/33.13  | | | |          e0
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (12), (14), (15),
% 200.36/33.13  | | | |            (16), (17), (19), (20), (21), (22), (23), (24), (26), (27),
% 200.36/33.13  | | | |            (28), (30), (31), (32), (34), (35), (36), (37), (40), (42),
% 200.36/33.13  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 200.36/33.13  | | | |            (53), (54), (55), (56), (59), (60), (61), (62), (63), (64),
% 200.36/33.13  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 200.36/33.13  | | | |            (76), (77), (78), (79), (80), (81), (83), (84), (86), (88),
% 200.36/33.13  | | | |            (89), (90), (91), (93), (94), (95), (96), (97), (98), (100),
% 200.36/33.13  | | | |            (101), (102), (103), (104), (105), (106), (107), (108),
% 200.36/33.13  | | | |            (109), (110), (111), (112), (114), (115), (116), (117),
% 200.36/33.13  | | | |            (118), (120), (121), (122), (123), (124), (125), (126),
% 200.36/33.13  | | | |            (128), (130), (131), (132), (133), (134), (135), (137),
% 200.36/33.13  | | | |            (138), (141), (142), (144), (145), (147), (148), (149),
% 200.36/33.13  | | | |            (150), (152), (153), (154), (155), (156), (157), (158),
% 200.36/33.13  | | | |            (159), (160), (163), (164), (292) are inconsistent by
% 200.36/33.13  | | | |            sub-proof #1008.
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | End of split
% 200.36/33.13  | | | 
% 200.36/33.13  | | End of split
% 200.36/33.13  | | 
% 200.36/33.13  | End of split
% 200.36/33.13  | 
% 200.36/33.13  End of proof
% 200.36/33.13  
% 200.36/33.13  Sub-proof #148 shows that the following formulas are inconsistent:
% 200.36/33.13  ----------------------------------------------------------------
% 200.36/33.13    (1)   ~ (e3 = e1)
% 200.36/33.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.13    (3)   ~ (e3 = e0)
% 200.36/33.13    (4)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.13    (5)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.13    (6)   ~ (all_4_2 = e0)
% 200.36/33.13    (7)  op(e2, e2) = all_4_2
% 200.36/33.13    (8)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.13    (9)  op(all_4_2, e2) = e1
% 200.36/33.13    (10)  all_56_5 = all_4_2
% 200.36/33.13    (11)  op(e0, e0) = all_14_2
% 200.36/33.13    (12)   ~ (e2 = e1)
% 200.36/33.13    (13)  all_58_10 = all_52_27
% 200.36/33.13    (14)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.13    (15)   ~ (all_14_2 = e0)
% 200.36/33.13    (16)  all_58_2 = all_52_3
% 200.36/33.13    (17)  all_56_7 = all_52_27
% 200.36/33.13    (18)  op(all_52_3, all_52_3) = e2
% 200.36/33.13    (19)   ~ (all_52_27 = e3)
% 200.36/33.13    (20)   ~ (all_52_13 = all_4_2)
% 200.36/33.13    (21)  op(e1, e2) = all_52_13
% 200.36/33.13    (22)   ~ (all_52_27 = all_14_2)
% 200.36/33.13    (23)  all_58_5 = e3
% 200.36/33.13    (24)   ~ (all_52_27 = all_4_2)
% 200.36/33.13    (25)   ~ (e1 = e0)
% 200.36/33.13    (26)  all_58_3 = all_4_2
% 200.36/33.13    (27)   ~ (all_52_3 = all_4_2)
% 200.36/33.13    (28)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.13  
% 200.36/33.13  Begin of proof
% 200.36/33.13  | 
% 200.36/33.13  | BETA: splitting (8) gives:
% 200.36/33.13  | 
% 200.36/33.13  | Case 1:
% 200.36/33.13  | | 
% 200.36/33.13  | |   (29)  all_58_2 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | COMBINE_EQS: (16), (29) imply:
% 200.36/33.13  | |   (30)  all_52_3 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | SIMP: (30) implies:
% 200.36/33.13  | |   (31)  all_52_3 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | REDUCE: (27), (31) imply:
% 200.36/33.13  | |   (32)   ~ (all_4_2 = e0)
% 200.36/33.13  | | 
% 200.36/33.13  | | REDUCE: (18), (31) imply:
% 200.36/33.13  | |   (33)  op(e0, e0) = e2
% 200.36/33.13  | | 
% 200.36/33.13  | | GROUND_INST: instantiating (2) with all_14_2, e2, e0, e0, simplifying with
% 200.36/33.13  | |              (11), (33) gives:
% 200.36/33.13  | |   (34)  all_14_2 = e2
% 200.36/33.13  | | 
% 200.36/33.13  | | REDUCE: (22), (34) imply:
% 200.36/33.13  | |   (35)   ~ (all_52_27 = e2)
% 200.36/33.13  | | 
% 200.36/33.13  | | REDUCE: (15), (34) imply:
% 200.36/33.13  | |   (36)   ~ (e2 = e0)
% 200.36/33.13  | | 
% 200.36/33.13  | | BETA: splitting (4) gives:
% 200.36/33.13  | | 
% 200.36/33.13  | | Case 1:
% 200.36/33.13  | | | 
% 200.36/33.13  | | |   (37)  all_56_7 = e3
% 200.36/33.13  | | | 
% 200.36/33.13  | | | REF_CLOSE: (17), (19), (37) are inconsistent by sub-proof #609.
% 200.36/33.13  | | | 
% 200.36/33.13  | | Case 2:
% 200.36/33.13  | | | 
% 200.36/33.13  | | |   (38)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.13  | | | 
% 200.36/33.13  | | | BETA: splitting (38) gives:
% 200.36/33.13  | | | 
% 200.36/33.13  | | | Case 1:
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | |   (39)  all_56_7 = e2
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | REF_CLOSE: (17), (35), (39) are inconsistent by sub-proof #918.
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | Case 2:
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | |   (40)  all_56_7 = e1 | all_56_7 = e0
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | BETA: splitting (28) gives:
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | | Case 1:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | |   (41)  all_58_2 = e2
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | COMBINE_EQS: (29), (41) imply:
% 200.36/33.13  | | | | |   (42)  e2 = e0
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | REDUCE: (36), (42) imply:
% 200.36/33.13  | | | | |   (43)  $false
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | CLOSE: (43) is inconsistent.
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | Case 2:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | |   (44)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | BETA: splitting (40) gives:
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | | Case 1:
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | |   (45)  all_56_7 = e1
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | COMBINE_EQS: (17), (45) imply:
% 200.36/33.13  | | | | | |   (46)  all_52_27 = e1
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | SIMP: (46) implies:
% 200.36/33.13  | | | | | |   (47)  all_52_27 = e1
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | REDUCE: (24), (47) imply:
% 200.36/33.13  | | | | | |   (48)   ~ (all_4_2 = e1)
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | SIMP: (48) implies:
% 200.36/33.13  | | | | | |   (49)   ~ (all_4_2 = e1)
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | REF_CLOSE: (2), (5), (6), (7), (9), (10), (26), (44), (49) are
% 200.36/33.13  | | | | | |            inconsistent by sub-proof #151.
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | Case 2:
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | |   (50)  all_56_7 = e0
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | COMBINE_EQS: (17), (50) imply:
% 200.36/33.13  | | | | | |   (51)  all_52_27 = e0
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | SIMP: (51) implies:
% 200.36/33.13  | | | | | |   (52)  all_52_27 = e0
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | COMBINE_EQS: (13), (52) imply:
% 200.36/33.13  | | | | | |   (53)  all_58_10 = e0
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (12), (14), (16),
% 200.36/33.13  | | | | | |            (20), (21), (23), (25), (26), (27), (28), (53) are
% 200.36/33.13  | | | | | |            inconsistent by sub-proof #150.
% 200.36/33.13  | | | | | | 
% 200.36/33.13  | | | | | End of split
% 200.36/33.13  | | | | | 
% 200.36/33.13  | | | | End of split
% 200.36/33.13  | | | | 
% 200.36/33.13  | | | End of split
% 200.36/33.13  | | | 
% 200.36/33.13  | | End of split
% 200.36/33.13  | | 
% 200.36/33.13  | Case 2:
% 200.36/33.13  | | 
% 200.36/33.13  | |   (54)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (12), (13), (14), (16),
% 200.36/33.13  | |            (20), (21), (23), (24), (25), (26), (27), (28), (54) are
% 200.36/33.13  | |            inconsistent by sub-proof #149.
% 200.36/33.13  | | 
% 200.36/33.13  | End of split
% 200.36/33.13  | 
% 200.36/33.13  End of proof
% 200.36/33.13  
% 200.36/33.13  Sub-proof #149 shows that the following formulas are inconsistent:
% 200.36/33.13  ----------------------------------------------------------------
% 200.36/33.13    (1)   ~ (e3 = e1)
% 200.36/33.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.13    (3)   ~ (e3 = e0)
% 200.36/33.13    (4)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.13    (5)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.13    (6)   ~ (all_4_2 = e0)
% 200.36/33.13    (7)  op(e2, e2) = all_4_2
% 200.36/33.13    (8)  op(all_4_2, e2) = e1
% 200.36/33.13    (9)  all_56_5 = all_4_2
% 200.36/33.13    (10)   ~ (e2 = e1)
% 200.36/33.13    (11)  all_58_10 = all_52_27
% 200.36/33.13    (12)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.13    (13)  all_58_2 = all_52_3
% 200.36/33.13    (14)   ~ (all_52_13 = all_4_2)
% 200.36/33.13    (15)  op(e1, e2) = all_52_13
% 200.36/33.13    (16)  all_58_5 = e3
% 200.36/33.13    (17)   ~ (all_52_27 = all_4_2)
% 200.36/33.13    (18)   ~ (e1 = e0)
% 200.36/33.13    (19)  all_58_3 = all_4_2
% 200.36/33.13    (20)   ~ (all_52_3 = all_4_2)
% 200.36/33.13    (21)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.13  
% 200.36/33.13  Begin of proof
% 200.36/33.13  | 
% 200.36/33.13  | BETA: splitting (4) gives:
% 200.36/33.13  | 
% 200.36/33.13  | Case 1:
% 200.36/33.13  | | 
% 200.36/33.13  | |   (22)  all_58_3 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | COMBINE_EQS: (19), (22) imply:
% 200.36/33.13  | |   (23)  all_4_2 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | REDUCE: (6), (23) imply:
% 200.36/33.13  | |   (24)  $false
% 200.36/33.13  | | 
% 200.36/33.13  | | CLOSE: (24) is inconsistent.
% 200.36/33.13  | | 
% 200.36/33.13  | Case 2:
% 200.36/33.13  | | 
% 200.36/33.13  | |   (25)  all_58_5 = e0 | all_58_10 = e0
% 200.36/33.13  | | 
% 200.36/33.13  | | BETA: splitting (25) gives:
% 200.36/33.13  | | 
% 200.36/33.13  | | Case 1:
% 200.36/33.13  | | | 
% 200.36/33.13  | | |   (26)  all_58_5 = e0
% 200.36/33.13  | | | 
% 200.36/33.13  | | | REF_CLOSE: (3), (16), (26) are inconsistent by sub-proof #153.
% 200.36/33.13  | | | 
% 200.36/33.13  | | Case 2:
% 200.36/33.13  | | | 
% 200.36/33.13  | | |   (27)  all_58_10 = e0
% 200.36/33.13  | | | 
% 200.36/33.13  | | | COMBINE_EQS: (11), (27) imply:
% 200.36/33.13  | | |   (28)  all_52_27 = e0
% 200.36/33.13  | | | 
% 200.36/33.13  | | | SIMP: (28) implies:
% 200.36/33.13  | | |   (29)  all_52_27 = e0
% 200.36/33.13  | | | 
% 200.36/33.13  | | | REDUCE: (17), (29) imply:
% 200.36/33.13  | | |   (30)   ~ (all_4_2 = e0)
% 200.36/33.13  | | | 
% 200.36/33.13  | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 200.36/33.13  | | |            (15), (16), (18), (19), (20), (21), (27) are inconsistent by
% 200.36/33.13  | | |            sub-proof #150.
% 200.36/33.13  | | | 
% 200.36/33.13  | | End of split
% 200.36/33.13  | | 
% 200.36/33.13  | End of split
% 200.36/33.13  | 
% 200.36/33.13  End of proof
% 200.36/33.13  
% 200.36/33.13  Sub-proof #150 shows that the following formulas are inconsistent:
% 200.36/33.13  ----------------------------------------------------------------
% 200.36/33.13    (1)   ~ (e3 = e1)
% 200.36/33.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.13    (3)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.13    (4)   ~ (all_4_2 = e0)
% 200.36/33.13    (5)  op(e2, e2) = all_4_2
% 200.36/33.13    (6)  op(all_4_2, e2) = e1
% 200.36/33.13    (7)  all_56_5 = all_4_2
% 200.36/33.13    (8)   ~ (e2 = e1)
% 200.36/33.13    (9)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.13    (10)  all_58_2 = all_52_3
% 200.36/33.13    (11)   ~ (all_52_13 = all_4_2)
% 200.36/33.13    (12)  op(e1, e2) = all_52_13
% 200.36/33.13    (13)  all_58_5 = e3
% 200.36/33.13    (14)  all_58_10 = e0
% 200.36/33.13    (15)   ~ (e1 = e0)
% 200.36/33.13    (16)  all_58_3 = all_4_2
% 200.36/33.13    (17)   ~ (all_52_3 = all_4_2)
% 200.36/33.13    (18)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.13  
% 200.36/33.13  Begin of proof
% 200.36/33.13  | 
% 200.36/33.13  | BETA: splitting (9) gives:
% 200.36/33.13  | 
% 200.36/33.13  | Case 1:
% 200.36/33.13  | | 
% 200.36/33.13  | |   (19)  all_58_2 = e1
% 200.36/33.13  | | 
% 200.36/33.13  | | COMBINE_EQS: (10), (19) imply:
% 200.36/33.13  | |   (20)  all_52_3 = e1
% 200.36/33.13  | | 
% 200.36/33.13  | | SIMP: (20) implies:
% 200.36/33.13  | |   (21)  all_52_3 = e1
% 200.36/33.13  | | 
% 200.36/33.13  | | REDUCE: (17), (21) imply:
% 200.36/33.13  | |   (22)   ~ (all_4_2 = e1)
% 200.36/33.13  | | 
% 200.36/33.13  | | SIMP: (22) implies:
% 200.36/33.14  | |   (23)   ~ (all_4_2 = e1)
% 200.36/33.14  | | 
% 200.36/33.14  | | BETA: splitting (18) gives:
% 200.36/33.14  | | 
% 200.36/33.14  | | Case 1:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (24)  all_58_2 = e2
% 200.36/33.14  | | | 
% 200.36/33.14  | | | COMBINE_EQS: (19), (24) imply:
% 200.36/33.14  | | |   (25)  e2 = e1
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (8), (25) imply:
% 200.36/33.14  | | |   (26)  $false
% 200.36/33.14  | | | 
% 200.36/33.14  | | | CLOSE: (26) is inconsistent.
% 200.36/33.14  | | | 
% 200.36/33.14  | | Case 2:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (27)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (16), (23), (27) are inconsistent
% 200.36/33.14  | | |            by sub-proof #151.
% 200.36/33.14  | | | 
% 200.36/33.14  | | End of split
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (28)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.14  | | 
% 200.36/33.14  | | BETA: splitting (28) gives:
% 200.36/33.14  | | 
% 200.36/33.14  | | Case 1:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (29)  all_58_3 = e1
% 200.36/33.14  | | | 
% 200.36/33.14  | | | COMBINE_EQS: (16), (29) imply:
% 200.36/33.14  | | |   (30)  all_4_2 = e1
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (11), (30) imply:
% 200.36/33.14  | | |   (31)   ~ (all_52_13 = e1)
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (6), (30) imply:
% 200.36/33.14  | | |   (32)  op(e1, e2) = e1
% 200.36/33.14  | | | 
% 200.36/33.14  | | | GROUND_INST: instantiating (2) with all_52_13, e1, e2, e1, simplifying
% 200.36/33.14  | | |              with (12), (32) gives:
% 200.36/33.14  | | |   (33)  all_52_13 = e1
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (31), (33) imply:
% 200.36/33.14  | | |   (34)  $false
% 200.36/33.14  | | | 
% 200.36/33.14  | | | CLOSE: (34) is inconsistent.
% 200.36/33.14  | | | 
% 200.36/33.14  | | Case 2:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (35)  all_58_5 = e1 | all_58_10 = e1
% 200.36/33.14  | | | 
% 200.36/33.14  | | | BETA: splitting (35) gives:
% 200.36/33.14  | | | 
% 200.36/33.14  | | | Case 1:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | |   (36)  all_58_5 = e1
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | REF_CLOSE: (1), (13), (36) are inconsistent by sub-proof #391.
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | Case 2:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | |   (37)  all_58_10 = e1
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | COMBINE_EQS: (14), (37) imply:
% 200.36/33.14  | | | |   (38)  e1 = e0
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | REDUCE: (15), (38) imply:
% 200.36/33.14  | | | |   (39)  $false
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | CLOSE: (39) is inconsistent.
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | End of split
% 200.36/33.14  | | | 
% 200.36/33.14  | | End of split
% 200.36/33.14  | | 
% 200.36/33.14  | End of split
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #151 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.14    (2)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.14    (3)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.14    (4)   ~ (all_4_2 = e0)
% 200.36/33.14    (5)  op(e2, e2) = all_4_2
% 200.36/33.14    (6)  op(all_4_2, e2) = e1
% 200.36/33.14    (7)  all_56_5 = all_4_2
% 200.36/33.14    (8)  all_58_3 = all_4_2
% 200.36/33.14    (9)   ~ (all_4_2 = e1)
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | BETA: splitting (2) gives:
% 200.36/33.14  | 
% 200.36/33.14  | Case 1:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (10)  all_58_3 = e2
% 200.36/33.14  | | 
% 200.36/33.14  | | COMBINE_EQS: (8), (10) imply:
% 200.36/33.14  | |   (11)  all_4_2 = e2
% 200.36/33.14  | | 
% 200.36/33.14  | | REDUCE: (6), (11) imply:
% 200.36/33.14  | |   (12)  op(e2, e2) = e1
% 200.36/33.14  | | 
% 200.36/33.14  | | REF_CLOSE: (1), (5), (9), (12) are inconsistent by sub-proof #1193.
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (13)   ~ (all_58_3 = e2)
% 200.36/33.14  | | 
% 200.36/33.14  | | REDUCE: (8), (13) imply:
% 200.36/33.14  | |   (14)   ~ (all_4_2 = e2)
% 200.36/33.14  | | 
% 200.36/33.14  | | REF_CLOSE: (3), (4), (7), (9), (14) are inconsistent by sub-proof #1186.
% 200.36/33.14  | | 
% 200.36/33.14  | End of split
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #152 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)   ~ (e3 = e0)
% 200.36/33.14    (2)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 200.36/33.14    (3)   ~ (all_4_2 = e0)
% 200.36/33.14    (4)  all_58_10 = all_52_27
% 200.36/33.14    (5)   ~ (all_52_27 = e0)
% 200.36/33.14    (6)  all_58_5 = e3
% 200.36/33.14    (7)  all_58_3 = all_4_2
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | BETA: splitting (2) gives:
% 200.36/33.14  | 
% 200.36/33.14  | Case 1:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (8)  all_58_3 = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | COMBINE_EQS: (7), (8) imply:
% 200.36/33.14  | |   (9)  all_4_2 = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | REDUCE: (3), (9) imply:
% 200.36/33.14  | |   (10)  $false
% 200.36/33.14  | | 
% 200.36/33.14  | | CLOSE: (10) is inconsistent.
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (11)  all_58_5 = e0 | all_58_10 = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | BETA: splitting (11) gives:
% 200.36/33.14  | | 
% 200.36/33.14  | | Case 1:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (12)  all_58_5 = e0
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REF_CLOSE: (1), (6), (12) are inconsistent by sub-proof #153.
% 200.36/33.14  | | | 
% 200.36/33.14  | | Case 2:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (13)  all_58_10 = e0
% 200.36/33.14  | | | 
% 200.36/33.14  | | | COMBINE_EQS: (4), (13) imply:
% 200.36/33.14  | | |   (14)  all_52_27 = e0
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (5), (14) imply:
% 200.36/33.14  | | |   (15)  $false
% 200.36/33.14  | | | 
% 200.36/33.14  | | | CLOSE: (15) is inconsistent.
% 200.36/33.14  | | | 
% 200.36/33.14  | | End of split
% 200.36/33.14  | | 
% 200.36/33.14  | End of split
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #153 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)  all_58_5 = e3
% 200.36/33.14    (2)  all_58_5 = e0
% 200.36/33.14    (3)   ~ (e3 = e0)
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | COMBINE_EQS: (1), (2) imply:
% 200.36/33.14  |   (4)  e3 = e0
% 200.36/33.14  | 
% 200.36/33.14  | SIMP: (4) implies:
% 200.36/33.14  |   (5)  e3 = e0
% 200.36/33.14  | 
% 200.36/33.14  | REDUCE: (3), (5) imply:
% 200.36/33.14  |   (6)  $false
% 200.36/33.14  | 
% 200.36/33.14  | CLOSE: (6) is inconsistent.
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #154 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.14    (2)  all_58_1 = all_52_9
% 200.36/33.14    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.14    (4)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.14    (5)  op(e3, e0) = all_52_25
% 200.36/33.14    (6)  all_58_9 = all_52_25
% 200.36/33.14    (7)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 200.36/33.14    (8)  op(e3, e0) = all_6_0
% 200.36/33.14    (9)   ~ (all_52_25 = all_14_2)
% 200.36/33.14    (10)  op(e0, e0) = all_14_2
% 200.36/33.14    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.14    (12)   ~ (all_6_0 = e1)
% 200.36/33.14    (13)  all_56_8 = all_52_5
% 200.36/33.14    (14)   ~ (all_52_5 = all_52_7)
% 200.36/33.14    (15)   ~ (all_52_7 = all_14_2)
% 200.36/33.14    (16)  all_56_2 = all_52_17
% 200.36/33.14    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.14    (18)   ~ (all_10_2 = e3)
% 200.36/33.14    (19)   ~ (all_52_7 = e2)
% 200.36/33.14    (20)   ~ (all_52_5 = e2)
% 200.36/33.14    (21)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.14    (22)  all_58_0 = e2
% 200.36/33.14    (23)   ~ (all_52_5 = all_10_2)
% 200.36/33.14    (24)  all_56_12 = all_52_7
% 200.36/33.14    (25)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.14    (26)   ~ (all_52_5 = e0)
% 200.36/33.14    (27)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.14    (28)   ~ (all_52_17 = e3)
% 200.36/33.14    (29)  all_56_3 = all_52_25
% 200.36/33.14    (30)  op(all_52_17, all_52_17) = e3
% 200.36/33.14    (31)  op(e0, e0) = all_52_2
% 200.36/33.14    (32)  op(e1, e1) = all_10_2
% 200.36/33.14    (33)   ~ (all_52_17 = e2)
% 200.36/33.14    (34)  all_58_4 = all_52_17
% 200.36/33.14    (35)   ~ (all_52_7 = e0)
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | GROUND_INST: instantiating (1) with all_14_2, all_52_2, e0, e0, simplifying
% 200.36/33.14  |              with (10), (31) gives:
% 200.36/33.14  |   (36)  all_52_2 = all_14_2
% 200.36/33.14  | 
% 200.36/33.14  | GROUND_INST: instantiating (1) with all_52_25, all_6_0, e0, e3, simplifying
% 200.36/33.14  |              with (5), (8) gives:
% 200.36/33.14  |   (37)  all_52_25 = all_6_0
% 200.36/33.14  | 
% 200.36/33.14  | COMBINE_EQS: (29), (37) imply:
% 200.36/33.14  |   (38)  all_56_3 = all_6_0
% 200.36/33.14  | 
% 200.36/33.14  | COMBINE_EQS: (6), (37) imply:
% 200.36/33.14  |   (39)  all_58_9 = all_6_0
% 200.36/33.14  | 
% 200.36/33.14  | REDUCE: (9), (37) imply:
% 200.36/33.14  |   (40)   ~ (all_14_2 = all_6_0)
% 200.36/33.14  | 
% 200.36/33.14  | SIMP: (40) implies:
% 200.36/33.14  |   (41)   ~ (all_14_2 = all_6_0)
% 200.36/33.14  | 
% 200.36/33.14  | BETA: splitting (11) gives:
% 200.36/33.14  | 
% 200.36/33.14  | Case 1:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (42)  all_56_2 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | REF_CLOSE: (16), (28), (42) are inconsistent by sub-proof #1327.
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (43)   ~ (all_56_2 = e3)
% 200.36/33.14  | |   (44)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | BETA: splitting (21) gives:
% 200.36/33.14  | | 
% 200.36/33.14  | | Case 1:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (45)  all_56_8 = e3
% 200.36/33.14  | | | 
% 200.36/33.14  | | | COMBINE_EQS: (13), (45) imply:
% 200.36/33.14  | | |   (46)  all_52_5 = e3
% 200.36/33.14  | | | 
% 200.36/33.14  | | | SIMP: (46) implies:
% 200.36/33.14  | | |   (47)  all_52_5 = e3
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (14), (47) imply:
% 200.36/33.14  | | |   (48)   ~ (all_52_7 = e3)
% 200.36/33.14  | | | 
% 200.36/33.14  | | | SIMP: (48) implies:
% 200.36/33.14  | | |   (49)   ~ (all_52_7 = e3)
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (23), (47) imply:
% 200.36/33.14  | | |   (50)   ~ (all_10_2 = e3)
% 200.36/33.14  | | | 
% 200.36/33.14  | | | REDUCE: (20), (47) imply:
% 200.36/33.14  | | |   (51)   ~ (e3 = e2)
% 200.36/33.14  | | | 
% 200.36/33.14  | | | BETA: splitting (3) gives:
% 200.36/33.14  | | | 
% 200.36/33.14  | | | Case 1:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | |   (52)  all_56_12 = e3
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | COMBINE_EQS: (24), (52) imply:
% 200.36/33.14  | | | |   (53)  all_52_7 = e3
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | REDUCE: (49), (53) imply:
% 200.36/33.14  | | | |   (54)  $false
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | CLOSE: (54) is inconsistent.
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | Case 2:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | |   (55)   ~ (all_56_12 = e3)
% 200.36/33.14  | | | |   (56)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | BETA: splitting (56) gives:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | Case 1:
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | |   (57)  all_56_12 = e2
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | COMBINE_EQS: (24), (57) imply:
% 200.36/33.14  | | | | |   (58)  all_52_7 = e2
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | REDUCE: (19), (58) imply:
% 200.36/33.14  | | | | |   (59)  $false
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | CLOSE: (59) is inconsistent.
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | Case 2:
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | |   (60)   ~ (all_56_12 = e2)
% 200.36/33.14  | | | | |   (61)  all_56_12 = e1 | all_56_12 = e0
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | BETA: splitting (61) gives:
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | Case 1:
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | |   (62)  all_56_12 = e1
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | COMBINE_EQS: (24), (62) imply:
% 200.36/33.14  | | | | | |   (63)  all_52_7 = e1
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REDUCE: (49), (63) imply:
% 200.36/33.14  | | | | | |   (64)   ~ (e3 = e1)
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | SIMP: (64) implies:
% 200.36/33.14  | | | | | |   (65)   ~ (e3 = e1)
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REDUCE: (19), (63) imply:
% 200.36/33.14  | | | | | |   (66)   ~ (e2 = e1)
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | SIMP: (66) implies:
% 200.36/33.14  | | | | | |   (67)   ~ (e2 = e1)
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REDUCE: (4), (63) imply:
% 200.36/33.14  | | | | | |   (68)  op(e1, e1) = all_52_6
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | GROUND_INST: instantiating (1) with all_10_2, all_52_6, e1, e1,
% 200.36/33.14  | | | | | |              simplifying with (32), (68) gives:
% 200.36/33.14  | | | | | |   (69)  all_52_6 = all_10_2
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | BETA: splitting (25) gives:
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | Case 1:
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | |   (70)  all_56_3 = e3
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | COMBINE_EQS: (38), (70) imply:
% 200.36/33.14  | | | | | | |   (71)  all_6_0 = e3
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | SIMP: (71) implies:
% 200.36/33.14  | | | | | | |   (72)  all_6_0 = e3
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | REDUCE: (41), (72) imply:
% 200.36/33.14  | | | | | | |   (73)   ~ (all_14_2 = e3)
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | REF_CLOSE: (1), (7), (10), (16), (18), (30), (32), (33), (34),
% 200.36/33.14  | | | | | | |            (44), (73) are inconsistent by sub-proof #1058.
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | Case 2:
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | |   (74)   ~ (all_56_3 = e3)
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | REDUCE: (38), (74) imply:
% 200.36/33.14  | | | | | | |   (75)   ~ (all_6_0 = e3)
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | BETA: splitting (27) gives:
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | | Case 1:
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | |   (76)  all_58_0 = e3
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | | REF_CLOSE: (22), (51), (76) are inconsistent by sub-proof #1235.
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | Case 2:
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | |   (77)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | | BETA: splitting (77) gives:
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | | Case 1:
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | |   (78)  all_58_1 = e3
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | COMBINE_EQS: (2), (78) imply:
% 200.36/33.14  | | | | | | | | |   (79)  all_52_9 = e3
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | BETA: splitting (17) gives:
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | Case 1:
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | |   (80)  all_58_0 = e1
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | COMBINE_EQS: (22), (80) imply:
% 200.36/33.14  | | | | | | | | | |   (81)  e2 = e1
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | REDUCE: (67), (81) imply:
% 200.36/33.14  | | | | | | | | | |   (82)  $false
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | CLOSE: (82) is inconsistent.
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | Case 2:
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | |   (83)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | BETA: splitting (83) gives:
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | Case 1:
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | |   (84)  all_58_1 = e1
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | COMBINE_EQS: (78), (84) imply:
% 200.36/33.14  | | | | | | | | | | |   (85)  e3 = e1
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | REDUCE: (65), (85) imply:
% 200.36/33.14  | | | | | | | | | | |   (86)  $false
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | CLOSE: (86) is inconsistent.
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | Case 2:
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | |   (87)  all_58_4 = e1 | all_58_9 = e1
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | BETA: splitting (87) gives:
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | Case 1:
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | |   (88)  all_58_4 = e1
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | | COMBINE_EQS: (34), (88) imply:
% 200.36/33.14  | | | | | | | | | | | |   (89)  all_52_17 = e1
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | | REDUCE: (30), (89) imply:
% 200.36/33.14  | | | | | | | | | | | |   (90)  op(e1, e1) = e3
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | | REF_CLOSE: (1), (18), (32), (90) are inconsistent by
% 200.36/33.14  | | | | | | | | | | | |            sub-proof #1368.
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | Case 2:
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | |   (91)  all_58_9 = e1
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | | COMBINE_EQS: (39), (91) imply:
% 200.36/33.14  | | | | | | | | | | | |   (92)  all_6_0 = e1
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | | REDUCE: (12), (92) imply:
% 200.36/33.14  | | | | | | | | | | | |   (93)  $false
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | | CLOSE: (93) is inconsistent.
% 200.36/33.14  | | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | | End of split
% 200.36/33.14  | | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | End of split
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | End of split
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | Case 2:
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | |   (94)  all_58_4 = e3 | all_58_9 = e3
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | BETA: splitting (94) gives:
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | Case 1:
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | |   (95)  all_58_4 = e3
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | COMBINE_EQS: (34), (95) imply:
% 200.36/33.14  | | | | | | | | | |   (96)  all_52_17 = e3
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | REDUCE: (28), (96) imply:
% 200.36/33.14  | | | | | | | | | |   (97)  $false
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | CLOSE: (97) is inconsistent.
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | Case 2:
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | |   (98)  all_58_9 = e3
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | COMBINE_EQS: (39), (98) imply:
% 200.36/33.14  | | | | | | | | | |   (99)  all_6_0 = e3
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | REDUCE: (75), (99) imply:
% 200.36/33.14  | | | | | | | | | |   (100)  $false
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | | CLOSE: (100) is inconsistent.
% 200.36/33.14  | | | | | | | | | | 
% 200.36/33.14  | | | | | | | | | End of split
% 200.36/33.14  | | | | | | | | | 
% 200.36/33.14  | | | | | | | | End of split
% 200.36/33.14  | | | | | | | | 
% 200.36/33.14  | | | | | | | End of split
% 200.36/33.14  | | | | | | | 
% 200.36/33.14  | | | | | | End of split
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | Case 2:
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | |   (101)  all_56_12 = e0
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | COMBINE_EQS: (24), (101) imply:
% 200.36/33.14  | | | | | |   (102)  all_52_7 = e0
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REDUCE: (35), (102) imply:
% 200.36/33.14  | | | | | |   (103)  $false
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | CLOSE: (103) is inconsistent.
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | End of split
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | End of split
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | End of split
% 200.36/33.14  | | | 
% 200.36/33.14  | | Case 2:
% 200.36/33.14  | | | 
% 200.36/33.14  | | |   (104)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.14  | | | 
% 200.36/33.14  | | | BETA: splitting (104) gives:
% 200.36/33.14  | | | 
% 200.36/33.14  | | | Case 1:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | |   (105)  all_56_8 = e2
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | REF_CLOSE: (13), (20), (105) are inconsistent by sub-proof #1022.
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | Case 2:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | |   (106)  all_56_8 = e1 | all_56_8 = e0
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | BETA: splitting (106) gives:
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | | Case 1:
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | |   (107)  all_56_8 = e1
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | COMBINE_EQS: (13), (107) imply:
% 200.36/33.14  | | | | |   (108)  all_52_5 = e1
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | SIMP: (108) implies:
% 200.36/33.14  | | | | |   (109)  all_52_5 = e1
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | REDUCE: (14), (109) imply:
% 200.36/33.14  | | | | |   (110)   ~ (all_52_7 = e1)
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | SIMP: (110) implies:
% 200.36/33.14  | | | | |   (111)   ~ (all_52_7 = e1)
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | BETA: splitting (3) gives:
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | Case 1:
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | |   (112)  all_56_12 = e3
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | COMBINE_EQS: (24), (112) imply:
% 200.36/33.14  | | | | | |   (113)  all_52_7 = e3
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REDUCE: (15), (113) imply:
% 200.36/33.14  | | | | | |   (114)   ~ (all_14_2 = e3)
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | SIMP: (114) implies:
% 200.36/33.14  | | | | | |   (115)   ~ (all_14_2 = e3)
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REF_CLOSE: (1), (7), (10), (16), (18), (30), (32), (33), (34), (44),
% 200.36/33.14  | | | | | |            (115) are inconsistent by sub-proof #1058.
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | Case 2:
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | |   (116)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | | REF_CLOSE: (19), (24), (35), (111), (116) are inconsistent by
% 200.36/33.14  | | | | | |            sub-proof #155.
% 200.36/33.14  | | | | | | 
% 200.36/33.14  | | | | | End of split
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | Case 2:
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | |   (117)  all_56_8 = e0
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | | REF_CLOSE: (13), (26), (117) are inconsistent by sub-proof #631.
% 200.36/33.14  | | | | | 
% 200.36/33.14  | | | | End of split
% 200.36/33.14  | | | | 
% 200.36/33.14  | | | End of split
% 200.36/33.14  | | | 
% 200.36/33.14  | | End of split
% 200.36/33.14  | | 
% 200.36/33.14  | End of split
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #155 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.14    (2)   ~ (all_52_7 = e2)
% 200.36/33.14    (3)  all_56_12 = all_52_7
% 200.36/33.14    (4)   ~ (all_52_7 = e1)
% 200.36/33.14    (5)   ~ (all_52_7 = e0)
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | BETA: splitting (1) gives:
% 200.36/33.14  | 
% 200.36/33.14  | Case 1:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (6)  all_56_12 = e2
% 200.36/33.14  | | 
% 200.36/33.14  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1178.
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (7)  all_56_12 = e1 | all_56_12 = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1374.
% 200.36/33.14  | | 
% 200.36/33.14  | End of split
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #156 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)  all_58_14 = all_52_23
% 200.36/33.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.14    (3)   ~ (e3 = e0)
% 200.36/33.14    (4)  op(all_52_15, all_52_15) = e0
% 200.36/33.14    (5)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.14    (6)  all_58_13 = all_52_15
% 200.36/33.14    (7)  all_58_15 = e0
% 200.36/33.14    (8)   ~ (all_6_2 = e0)
% 200.36/33.14    (9)   ~ (all_52_23 = e3)
% 200.36/33.14    (10)  op(e3, e3) = all_6_2
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | BETA: splitting (5) gives:
% 200.36/33.14  | 
% 200.36/33.14  | Case 1:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (11)  all_58_13 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | COMBINE_EQS: (6), (11) imply:
% 200.36/33.14  | |   (12)  all_52_15 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | SIMP: (12) implies:
% 200.36/33.14  | |   (13)  all_52_15 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | REDUCE: (4), (13) imply:
% 200.36/33.14  | |   (14)  op(e3, e3) = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | GROUND_INST: instantiating (2) with all_6_2, e0, e3, e3, simplifying with
% 200.36/33.14  | |              (10), (14) gives:
% 200.36/33.14  | |   (15)  all_6_2 = e0
% 200.36/33.14  | | 
% 200.36/33.14  | | REDUCE: (8), (15) imply:
% 200.36/33.14  | |   (16)  $false
% 200.36/33.14  | | 
% 200.36/33.14  | | CLOSE: (16) is inconsistent.
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (17)  all_58_14 = e3 | all_58_15 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | REF_CLOSE: (1), (3), (7), (9), (17) are inconsistent by sub-proof #983.
% 200.36/33.14  | | 
% 200.36/33.14  | End of split
% 200.36/33.14  | 
% 200.36/33.14  End of proof
% 200.36/33.14  
% 200.36/33.14  Sub-proof #157 shows that the following formulas are inconsistent:
% 200.36/33.14  ----------------------------------------------------------------
% 200.36/33.14    (1)   ~ (e3 = e1)
% 200.36/33.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.14    (3)  all_58_1 = all_52_9
% 200.36/33.14    (4)   ~ (all_4_2 = e3)
% 200.36/33.14    (5)  all_58_0 = all_6_2
% 200.36/33.14    (6)   ~ (all_52_17 = all_10_2)
% 200.36/33.14    (7)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.14    (8)  op(e3, e0) = all_52_25
% 200.36/33.14    (9)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.14    (10)  all_58_13 = all_52_15
% 200.36/33.14    (11)  op(all_52_13, all_52_13) = e1
% 200.36/33.14    (12)  all_58_9 = all_52_25
% 200.36/33.14    (13)   ~ (all_52_15 = e3)
% 200.36/33.14    (14)  op(e1, e3) = all_52_5
% 200.36/33.14    (15)  all_58_11 = all_52_29
% 200.36/33.14    (16)  op(e2, e3) = e0
% 200.36/33.14    (17)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.14    (18)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.14    (19)   ~ (all_6_2 = e3)
% 200.36/33.14    (20)   ~ (e2 = e1)
% 200.36/33.14    (21)   ~ (all_52_13 = all_10_2)
% 200.36/33.14    (22)   ~ (all_6_0 = e1)
% 200.36/33.14    (23)   ~ (all_6_2 = e0)
% 200.36/33.14    (24)  all_56_8 = all_52_5
% 200.36/33.14    (25)  all_58_7 = all_52_13
% 200.36/33.14    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.14    (27)  all_56_2 = all_52_17
% 200.36/33.14    (28)  all_58_2 = e0
% 200.36/33.14    (29)  op(e3, all_6_1) = all_6_0
% 200.36/33.14    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.14    (31)   ~ (all_52_5 = e3)
% 200.36/33.14    (32)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.14    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.14    (34)   ~ (all_52_9 = all_52_25)
% 200.36/33.14    (35)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.14    (36)  all_58_8 = all_10_2
% 200.36/33.14    (37)   ~ (all_52_25 = all_6_2)
% 200.36/33.14    (38)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.14    (39)   ~ (all_52_5 = all_6_2)
% 200.36/33.14    (40)   ~ (all_52_9 = all_6_2)
% 200.36/33.14    (41)  all_56_0 = all_6_2
% 200.36/33.14    (42)   ~ (all_52_5 = e0)
% 200.36/33.14    (43)  op(e3, e3) = all_6_2
% 200.36/33.14    (44)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.14    (45)  all_56_3 = all_52_25
% 200.36/33.14    (46)  all_56_1 = all_52_9
% 200.36/33.14    (47)  all_58_6 = all_52_5
% 200.36/33.14    (48)   ~ (e1 = e0)
% 200.36/33.14    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.14    (50)   ~ (all_52_9 = all_52_17)
% 200.36/33.14    (51)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.14    (52)  all_58_12 = e3
% 200.36/33.14    (53)   ~ (all_6_1 = e2)
% 200.36/33.14    (54)  op(e1, e1) = all_10_2
% 200.36/33.14    (55)  op(all_52_9, all_52_9) = e3
% 200.36/33.14    (56)  all_58_3 = all_4_2
% 200.36/33.14    (57)  op(all_6_2, e3) = all_6_1
% 200.36/33.14    (58)   ~ (all_52_13 = all_52_29)
% 200.36/33.14    (59)  all_58_4 = all_52_17
% 200.36/33.14  
% 200.36/33.14  Begin of proof
% 200.36/33.14  | 
% 200.36/33.14  | BETA: splitting (35) gives:
% 200.36/33.14  | 
% 200.36/33.14  | Case 1:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (60)  all_56_8 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | COMBINE_EQS: (24), (60) imply:
% 200.36/33.14  | |   (61)  all_52_5 = e3
% 200.36/33.14  | | 
% 200.36/33.14  | | REDUCE: (31), (61) imply:
% 200.36/33.14  | |   (62)  $false
% 200.36/33.14  | | 
% 200.36/33.14  | | CLOSE: (62) is inconsistent.
% 200.36/33.14  | | 
% 200.36/33.14  | Case 2:
% 200.36/33.14  | | 
% 200.36/33.14  | |   (63)   ~ (all_56_8 = e3)
% 200.36/33.15  | |   (64)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.15  | | 
% 200.36/33.15  | | BETA: splitting (26) gives:
% 200.36/33.15  | | 
% 200.36/33.15  | | Case 1:
% 200.36/33.15  | | | 
% 200.36/33.15  | | |   (65)  all_58_6 = e3
% 200.36/33.15  | | | 
% 200.36/33.15  | | | COMBINE_EQS: (47), (65) imply:
% 200.36/33.15  | | |   (66)  all_52_5 = e3
% 200.36/33.15  | | | 
% 200.36/33.15  | | | REDUCE: (31), (66) imply:
% 200.36/33.15  | | |   (67)  $false
% 200.36/33.15  | | | 
% 200.36/33.15  | | | CLOSE: (67) is inconsistent.
% 200.36/33.15  | | | 
% 200.36/33.15  | | Case 2:
% 200.36/33.15  | | | 
% 200.36/33.15  | | |   (68)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.15  | | | 
% 200.36/33.15  | | | BETA: splitting (32) gives:
% 200.36/33.15  | | | 
% 200.36/33.15  | | | Case 1:
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | |   (69)  all_58_0 = e2
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | COMBINE_EQS: (5), (69) imply:
% 200.36/33.15  | | | |   (70)  all_6_2 = e2
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (39), (70) imply:
% 200.36/33.15  | | | |   (71)   ~ (all_52_5 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (40), (70) imply:
% 200.36/33.15  | | | |   (72)   ~ (all_52_9 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (37), (70) imply:
% 200.36/33.15  | | | |   (73)   ~ (all_52_25 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (19), (70) imply:
% 200.36/33.15  | | | |   (74)   ~ (e3 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | SIMP: (74) implies:
% 200.36/33.15  | | | |   (75)   ~ (e3 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (57), (70) imply:
% 200.36/33.15  | | | |   (76)  op(e2, e3) = all_6_1
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (43), (70) imply:
% 200.36/33.15  | | | |   (77)  op(e3, e3) = e2
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | BETA: splitting (30) gives:
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | Case 1:
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | |   (78)  all_58_0 = e1
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | COMBINE_EQS: (69), (78) imply:
% 200.36/33.15  | | | | |   (79)  e2 = e1
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | REDUCE: (20), (79) imply:
% 200.36/33.15  | | | | |   (80)  $false
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | CLOSE: (80) is inconsistent.
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | Case 2:
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | |   (81)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | BETA: splitting (81) gives:
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | Case 1:
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | |   (82)  all_58_2 = e1
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | REF_CLOSE: (28), (48), (82) are inconsistent by sub-proof #1129.
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | Case 2:
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | |   (83)  all_58_6 = e1 | all_58_12 = e1
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | BETA: splitting (83) gives:
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | Case 1:
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | |   (84)  all_58_6 = e1
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | COMBINE_EQS: (47), (84) imply:
% 200.36/33.15  | | | | | | |   (85)  all_52_5 = e1
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (71), (85) imply:
% 200.36/33.15  | | | | | | |   (86)   ~ (e2 = e1)
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (9), (85) imply:
% 200.36/33.15  | | | | | | |   (87)  op(e1, e1) = all_52_4
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | GROUND_INST: instantiating (2) with all_10_2, all_52_4, e1, e1,
% 200.36/33.15  | | | | | | |              simplifying with (54), (87) gives:
% 200.36/33.15  | | | | | | |   (88)  all_52_4 = all_10_2
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | GROUND_INST: instantiating (2) with e0, all_6_1, e3, e2,
% 200.36/33.15  | | | | | | |              simplifying with (16), (76) gives:
% 200.36/33.15  | | | | | | |   (89)  all_6_1 = e0
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (29), (89) imply:
% 200.36/33.15  | | | | | | |   (90)  op(e3, e0) = all_6_0
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | GROUND_INST: instantiating (2) with all_52_25, all_6_0, e0, e3,
% 200.36/33.15  | | | | | | |              simplifying with (8), (90) gives:
% 200.36/33.15  | | | | | | |   (91)  all_52_25 = all_6_0
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | COMBINE_EQS: (45), (91) imply:
% 200.36/33.15  | | | | | | |   (92)  all_56_3 = all_6_0
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | COMBINE_EQS: (12), (91) imply:
% 200.36/33.15  | | | | | | |   (93)  all_58_9 = all_6_0
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (34), (91) imply:
% 200.36/33.15  | | | | | | |   (94)   ~ (all_52_9 = all_6_0)
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (73), (91) imply:
% 200.36/33.15  | | | | | | |   (95)   ~ (all_6_0 = e2)
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | BETA: splitting (38) gives:
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | |   (96)  all_56_3 = e3
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | COMBINE_EQS: (92), (96) imply:
% 200.36/33.15  | | | | | | | |   (97)  all_6_0 = e3
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | SIMP: (97) implies:
% 200.36/33.15  | | | | | | | |   (98)  all_6_0 = e3
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | REDUCE: (94), (98) imply:
% 200.36/33.15  | | | | | | | |   (99)   ~ (all_52_9 = e3)
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | BETA: splitting (33) gives:
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | |   (100)  all_58_1 = e3
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | COMBINE_EQS: (3), (100) imply:
% 200.36/33.15  | | | | | | | | |   (101)  all_52_9 = e3
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | REDUCE: (99), (101) imply:
% 200.36/33.15  | | | | | | | | |   (102)  $false
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | CLOSE: (102) is inconsistent.
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | |   (103)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | BETA: splitting (103) gives:
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | |   (104)  all_58_3 = e3
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | COMBINE_EQS: (56), (104) imply:
% 200.36/33.15  | | | | | | | | | |   (105)  all_4_2 = e3
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | REDUCE: (4), (105) imply:
% 200.36/33.15  | | | | | | | | | |   (106)  $false
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | CLOSE: (106) is inconsistent.
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | |   (107)  all_58_7 = e3 | all_58_13 = e3
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | BETA: splitting (107) gives:
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | |   (108)  all_58_7 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | COMBINE_EQS: (25), (108) imply:
% 200.36/33.15  | | | | | | | | | | |   (109)  all_52_13 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (58), (109) imply:
% 200.36/33.15  | | | | | | | | | | |   (110)   ~ (all_52_29 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | SIMP: (110) implies:
% 200.36/33.15  | | | | | | | | | | |   (111)   ~ (all_52_29 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (21), (109) imply:
% 200.36/33.15  | | | | | | | | | | |   (112)   ~ (all_10_2 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | SIMP: (112) implies:
% 200.36/33.15  | | | | | | | | | | |   (113)   ~ (all_10_2 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (11), (109) imply:
% 200.36/33.15  | | | | | | | | | | |   (114)  op(e3, e3) = e1
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REF_CLOSE: (2), (15), (20), (25), (36), (51), (68), (77),
% 200.36/33.15  | | | | | | | | | | |            (111), (113), (114) are inconsistent by sub-proof
% 200.36/33.15  | | | | | | | | | | |            #227.
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | |   (115)  all_58_13 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | COMBINE_EQS: (10), (115) imply:
% 200.36/33.15  | | | | | | | | | | |   (116)  all_52_15 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (13), (116) imply:
% 200.36/33.15  | | | | | | | | | | |   (117)  $false
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | CLOSE: (117) is inconsistent.
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | |   (118)   ~ (all_56_3 = e3)
% 200.36/33.15  | | | | | | | |   (119)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | REDUCE: (92), (118) imply:
% 200.36/33.15  | | | | | | | |   (120)   ~ (all_6_0 = e3)
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | BETA: splitting (119) gives:
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | |   (121)  all_56_3 = e2
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | REF_CLOSE: (92), (95), (121) are inconsistent by sub-proof
% 200.36/33.15  | | | | | | | | |            #1075.
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | |   (122)  all_56_3 = e1 | all_56_3 = e0
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | BETA: splitting (122) gives:
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | |   (123)  all_56_3 = e1
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | REF_CLOSE: (22), (92), (123) are inconsistent by sub-proof
% 200.36/33.15  | | | | | | | | | |            #1074.
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | |   (124)  all_56_3 = e0
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | COMBINE_EQS: (92), (124) imply:
% 200.36/33.15  | | | | | | | | | |   (125)  all_6_0 = e0
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | SIMP: (125) implies:
% 200.36/33.15  | | | | | | | | | |   (126)  all_6_0 = e0
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | COMBINE_EQS: (93), (126) imply:
% 200.36/33.15  | | | | | | | | | |   (127)  all_58_9 = e0
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | REDUCE: (94), (126) imply:
% 200.36/33.15  | | | | | | | | | |   (128)   ~ (all_52_9 = e0)
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | REDUCE: (120), (126) imply:
% 200.36/33.15  | | | | | | | | | |   (129)   ~ (e3 = e0)
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | SIMP: (129) implies:
% 200.36/33.15  | | | | | | | | | |   (130)   ~ (e3 = e0)
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | BETA: splitting (17) gives:
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | |   (131)  all_56_2 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | COMBINE_EQS: (27), (131) imply:
% 200.36/33.15  | | | | | | | | | | |   (132)  all_52_17 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | SIMP: (132) implies:
% 200.36/33.15  | | | | | | | | | | |   (133)  all_52_17 = e3
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (50), (133) imply:
% 200.36/33.15  | | | | | | | | | | |   (134)   ~ (all_52_9 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (6), (133) imply:
% 200.36/33.15  | | | | | | | | | | |   (135)   ~ (all_10_2 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | SIMP: (135) implies:
% 200.36/33.15  | | | | | | | | | | |   (136)   ~ (all_10_2 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | BETA: splitting (49) gives:
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | Case 1:
% 200.36/33.15  | | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | |   (137)  all_56_1 = e3
% 200.36/33.15  | | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | | REF_CLOSE: (46), (134), (137) are inconsistent by sub-proof
% 200.36/33.15  | | | | | | | | | | | |            #1326.
% 200.36/33.15  | | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | |   (138)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.15  | | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | | REF_CLOSE: (2), (3), (18), (46), (54), (55), (72), (128),
% 200.36/33.15  | | | | | | | | | | | |            (136), (138) are inconsistent by sub-proof #896.
% 200.36/33.15  | | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | Case 2:
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | |   (139)   ~ (all_56_2 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REDUCE: (27), (139) imply:
% 200.36/33.15  | | | | | | | | | | |   (140)   ~ (all_52_17 = e3)
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | | REF_CLOSE: (2), (3), (19), (43), (44), (55), (59), (69),
% 200.36/33.15  | | | | | | | | | | |            (75), (127), (130), (140) are inconsistent by
% 200.36/33.15  | | | | | | | | | | |            sub-proof #191.
% 200.36/33.15  | | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | | | 
% 200.36/33.15  | | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | | 
% 200.36/33.15  | | | | | | | | End of split
% 200.36/33.15  | | | | | | | | 
% 200.36/33.15  | | | | | | | End of split
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | Case 2:
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | |   (141)  all_58_12 = e1
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | COMBINE_EQS: (52), (141) imply:
% 200.36/33.15  | | | | | | |   (142)  e3 = e1
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (1), (142) imply:
% 200.36/33.15  | | | | | | |   (143)  $false
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | CLOSE: (143) is inconsistent.
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | End of split
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | End of split
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | End of split
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | Case 2:
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | |   (144)   ~ (all_58_0 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | REDUCE: (5), (144) imply:
% 200.36/33.15  | | | |   (145)   ~ (all_6_2 = e2)
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | BETA: splitting (7) gives:
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | | Case 1:
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | |   (146)  all_56_0 = e2
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | REF_CLOSE: (41), (145), (146) are inconsistent by sub-proof #597.
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | Case 2:
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | |   (147)  all_56_0 = e1 | all_56_0 = e0
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | BETA: splitting (147) gives:
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | | Case 1:
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | |   (148)  all_56_0 = e1
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | COMBINE_EQS: (41), (148) imply:
% 200.36/33.15  | | | | | |   (149)  all_6_2 = e1
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | SIMP: (149) implies:
% 200.36/33.15  | | | | | |   (150)  all_6_2 = e1
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | REDUCE: (39), (150) imply:
% 200.36/33.15  | | | | | |   (151)   ~ (all_52_5 = e1)
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | REDUCE: (57), (150) imply:
% 200.36/33.15  | | | | | |   (152)  op(e1, e3) = all_6_1
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | BETA: splitting (64) gives:
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | Case 1:
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | |   (153)  all_56_8 = e2
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | COMBINE_EQS: (24), (153) imply:
% 200.36/33.15  | | | | | | |   (154)  all_52_5 = e2
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | SIMP: (154) implies:
% 200.36/33.15  | | | | | | |   (155)  all_52_5 = e2
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (14), (155) imply:
% 200.36/33.15  | | | | | | |   (156)  op(e1, e3) = e2
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | GROUND_INST: instantiating (2) with e2, all_6_1, e3, e1,
% 200.36/33.15  | | | | | | |              simplifying with (152), (156) gives:
% 200.36/33.15  | | | | | | |   (157)  all_6_1 = e2
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REDUCE: (53), (157) imply:
% 200.36/33.15  | | | | | | |   (158)  $false
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | CLOSE: (158) is inconsistent.
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | Case 2:
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | |   (159)  all_56_8 = e1 | all_56_8 = e0
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | | REF_CLOSE: (24), (42), (151), (159) are inconsistent by sub-proof
% 200.36/33.15  | | | | | | |            #1020.
% 200.36/33.15  | | | | | | | 
% 200.36/33.15  | | | | | | End of split
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | Case 2:
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | |   (160)  all_56_0 = e0
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | | REF_CLOSE: (23), (41), (160) are inconsistent by sub-proof #570.
% 200.36/33.15  | | | | | | 
% 200.36/33.15  | | | | | End of split
% 200.36/33.15  | | | | | 
% 200.36/33.15  | | | | End of split
% 200.36/33.15  | | | | 
% 200.36/33.15  | | | End of split
% 200.36/33.15  | | | 
% 200.36/33.15  | | End of split
% 200.36/33.15  | | 
% 200.36/33.15  | End of split
% 200.36/33.15  | 
% 200.36/33.15  End of proof
% 200.36/33.15  
% 200.36/33.15  Sub-proof #158 shows that the following formulas are inconsistent:
% 200.36/33.15  ----------------------------------------------------------------
% 200.36/33.15    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.15    (2)   ~ (all_52_25 = all_52_27)
% 200.36/33.15    (3)  all_58_14 = all_52_23
% 200.36/33.15    (4)   ~ (e3 = e1)
% 200.36/33.15    (5)   ~ (all_52_17 = all_4_0)
% 200.36/33.15    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.15    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.15    (8)   ~ (all_52_7 = all_10_0)
% 200.36/33.15    (9)   ~ (all_52_5 = all_52_13)
% 200.36/33.15    (10)  all_58_1 = all_52_9
% 200.36/33.15    (11)   ~ (all_52_9 = all_52_13)
% 200.36/33.15    (12)  op(e2, e3) = all_52_3
% 200.36/33.15    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.15    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.15    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.15    (16)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.15    (17)   ~ (all_52_17 = all_52_25)
% 200.36/33.15    (18)   ~ (all_52_3 = all_6_2)
% 200.36/33.15    (19)  all_58_0 = all_6_2
% 200.36/33.15    (20)  op(all_14_2, e0) = all_14_1
% 200.36/33.15    (21)  all_56_4 = all_52_3
% 200.36/33.15    (22)   ~ (all_52_17 = all_10_2)
% 200.36/33.15    (23)   ~ (all_10_0 = e3)
% 200.36/33.15    (24)  op(e3, e0) = all_52_25
% 200.36/33.15    (25)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.15    (26)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.15    (27)   ~ (all_52_27 = all_52_29)
% 200.36/33.15    (28)  all_58_13 = all_52_15
% 200.36/33.15    (29)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.15    (30)  all_58_9 = all_52_25
% 200.36/33.15    (31)   ~ (all_6_1 = e1)
% 200.36/33.15    (32)   ~ (all_52_29 = all_14_2)
% 200.36/33.15    (33)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.15    (34)  op(e1, e3) = all_52_5
% 200.36/33.15    (35)  op(e2, e2) = all_4_2
% 200.36/33.15    (36)   ~ (all_52_3 = all_52_5)
% 200.36/33.15    (37)  op(all_4_2, e2) = e1
% 200.36/33.15    (38)  all_58_11 = all_52_29
% 200.36/33.15    (39)  all_56_5 = all_4_2
% 200.36/33.15    (40)   ~ (all_52_25 = all_14_2)
% 200.36/33.15    (41)   ~ (all_52_9 = all_52_15)
% 200.36/33.15    (42)   ~ (all_52_3 = all_52_27)
% 200.36/33.15    (43)  op(all_10_2, e1) = all_10_1
% 200.36/33.15    (44)   ~ (all_10_2 = all_4_0)
% 200.36/33.15    (45)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.15    (46)   ~ (all_52_7 = all_6_2)
% 200.36/33.15    (47)  op(e0, e0) = all_14_2
% 200.36/33.15    (48)   ~ (all_10_0 = all_6_2)
% 200.36/33.15    (49)  all_56_15 = all_14_2
% 200.36/33.15    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.15    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.15    (52)   ~ (all_58_15 = e0)
% 200.36/33.15    (53)  all_56_11 = all_52_29
% 200.36/33.15    (54)   ~ (all_10_0 = e2)
% 200.36/33.15    (55)   ~ (all_4_0 = e3)
% 200.36/33.15    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.15    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.15    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.15    (59)   ~ (e2 = e1)
% 200.36/33.15    (60)   ~ (all_52_13 = all_10_2)
% 200.36/33.15    (61)   ~ (all_6_0 = e1)
% 200.36/33.15    (62)  all_58_10 = all_52_27
% 200.36/33.15    (63)  all_56_8 = all_52_5
% 200.36/33.15    (64)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.15    (65)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.15    (66)   ~ (all_52_19 = all_52_23)
% 200.36/33.15    (67)   ~ (all_52_25 = all_52_29)
% 200.36/33.15    (68)   ~ (all_52_29 = all_10_2)
% 200.36/33.15    (69)  op(all_10_2, e1) = e3
% 200.36/33.15    (70)  all_58_7 = all_52_13
% 200.36/33.15    (71)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 200.36/33.15    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.15    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.15    (74)   ~ (all_52_5 = all_52_7)
% 200.36/33.15    (75)  all_58_12 = all_52_7
% 200.36/33.15    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.15    (77)   ~ (all_52_7 = all_14_2)
% 200.36/33.15    (78)  all_30_2 = all_10_2
% 200.36/33.15    (79)  all_58_2 = all_52_3
% 200.36/33.15    (80)  all_56_2 = all_52_17
% 200.36/33.15    (81)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.15    (82)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.15    (83)  op(e3, all_6_1) = all_6_0
% 200.36/33.15    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.15    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.15    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.15    (87)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.15    (88)   ~ (all_52_5 = all_52_29)
% 200.36/33.15    (89)  all_56_8 = all_10_0
% 200.36/33.15    (90)   ~ (all_52_15 = all_14_2)
% 200.36/33.15    (91)   ~ (all_52_19 = all_52_27)
% 200.36/33.15    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.15    (93)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.15    (94)   ~ (all_6_0 = e2)
% 200.36/33.15    (95)   ~ (all_52_13 = all_4_2)
% 200.36/33.15    (96)  op(e3, e1) = all_52_17
% 200.36/33.15    (97)  all_30_0 = all_10_0
% 200.36/33.15    (98)  all_58_6 = all_10_0
% 200.36/33.15    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.15    (100)  op(e0, e3) = all_52_7
% 200.36/33.15    (101)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.15    (102)   ~ (all_52_9 = all_52_25)
% 200.36/33.15    (103)  all_58_15 = all_14_2
% 200.36/33.15    (104)   ~ (all_52_19 = all_10_2)
% 200.36/33.15    (105)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.15    (106)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.15    (107)   ~ (all_10_0 = all_10_2)
% 200.36/33.15    (108)  all_58_8 = all_10_2
% 200.36/33.15    (109)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.15    (110)   ~ (all_52_5 = all_10_2)
% 200.36/33.15    (111)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.15    (112)   ~ (all_52_23 = all_14_2)
% 200.36/33.15    (113)  all_56_12 = all_52_7
% 200.36/33.15    (114)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.15    (115)  all_58_5 = all_4_0
% 200.36/33.15    (116)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.15    (117)   ~ (all_52_25 = all_6_2)
% 200.36/33.15    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.15    (119)   ~ (all_52_9 = all_4_2)
% 200.36/33.15    (120)   ~ (all_52_5 = all_6_2)
% 200.36/33.15    (121)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.15    (122)   ~ (all_52_9 = all_6_2)
% 200.36/33.15    (123)   ~ (all_52_13 = all_52_15)
% 200.36/33.15    (124)  all_56_0 = all_6_2
% 200.36/33.15    (125)  op(e3, e3) = all_6_2
% 200.36/33.15    (126)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.15    (127)   ~ (all_52_27 = all_14_2)
% 200.36/33.15    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.15    (129)  all_56_14 = all_52_23
% 200.36/33.15    (130)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.15    (131)  all_56_3 = all_52_25
% 200.36/33.15    (132)   ~ (all_52_3 = all_52_7)
% 200.36/33.15    (133)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.15    (134)  all_58_5 = all_52_19
% 200.36/33.15    (135)  op(all_10_0, all_10_0) = all_52_4
% 200.36/33.15    (136)  all_56_1 = all_52_9
% 200.36/33.15    (137)   ~ (all_52_15 = all_4_2)
% 200.36/33.15    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.15           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.15           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.15           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.15    (139)   ~ (all_52_27 = all_4_2)
% 200.36/33.15    (140)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 200.36/33.15             all_58_13 = e0 | all_58_14 = e0)
% 200.36/33.15    (141)  all_58_6 = all_52_5
% 200.36/33.15    (142)   ~ (all_4_0 = all_4_2)
% 200.36/33.15    (143)  op(e3, e2) = all_52_9
% 200.36/33.15    (144)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.15    (145)   ~ (all_52_17 = all_6_2)
% 200.36/33.15    (146)   ~ (e3 = e2)
% 200.36/33.15    (147)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.15    (148)   ~ (all_52_9 = all_52_17)
% 200.36/33.15    (149)  all_56_10 = all_10_2
% 200.36/33.15    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.15    (151)   ~ (all_52_3 = all_4_0)
% 200.36/33.15    (152)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.15    (153)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.15    (154)   ~ (all_6_1 = e2)
% 200.36/33.15    (155)  op(e1, e1) = all_10_2
% 200.36/33.15    (156)   ~ (all_52_23 = all_10_2)
% 200.36/33.15    (157)   ~ (all_52_7 = all_52_23)
% 200.36/33.15    (158)   ~ (all_52_17 = all_52_19)
% 200.36/33.15    (159)  all_58_3 = all_4_2
% 200.36/33.15    (160)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.15    (161)  all_56_13 = all_52_15
% 200.36/33.15    (162)   ~ (all_52_3 = all_4_2)
% 200.36/33.15    (163)   ~ (all_52_19 = all_4_2)
% 200.36/33.15    (164)   ~ (all_52_17 = all_52_23)
% 200.36/33.15    (165)  op(all_6_2, e3) = all_6_1
% 200.36/33.15    (166)  all_58_4 = all_52_17
% 200.36/33.15    (167)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.36/33.15    (168)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.15  
% 200.36/33.15  Begin of proof
% 200.36/33.15  | 
% 200.36/33.15  | ALPHA: (140) implies:
% 200.36/33.15  |   (169)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.15  |   (170)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.15  | 
% 200.36/33.15  | REDUCE: (52), (103) imply:
% 200.36/33.15  |   (171)   ~ (all_14_2 = e0)
% 200.36/33.15  | 
% 200.36/33.15  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 200.36/33.15  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 200.36/33.15  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 200.36/33.15  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 200.36/33.15  |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 200.36/33.15  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 200.36/33.15  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 200.36/33.15  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 200.36/33.15  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 200.36/33.15  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 200.36/33.15  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 200.36/33.15  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 200.36/33.15  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 200.36/33.15  |            (138), (139), (141), (142), (143), (144), (145), (146), (147),
% 200.36/33.15  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 200.36/33.15  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 200.36/33.15  |            (166), (167), (168), (169), (170), (171) are inconsistent by
% 200.36/33.15  |            sub-proof #159.
% 200.36/33.15  | 
% 200.36/33.15  End of proof
% 200.36/33.15  
% 200.36/33.15  Sub-proof #159 shows that the following formulas are inconsistent:
% 200.36/33.15  ----------------------------------------------------------------
% 200.36/33.15    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.15    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.15    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.15    (4)  all_58_14 = all_52_23
% 200.36/33.15    (5)   ~ (e3 = e1)
% 200.36/33.15    (6)   ~ (all_52_17 = all_4_0)
% 200.36/33.15    (7)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.15    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.15    (9)   ~ (all_52_7 = all_10_0)
% 200.36/33.15    (10)   ~ (all_52_5 = all_52_13)
% 200.36/33.15    (11)  all_58_1 = all_52_9
% 200.36/33.15    (12)   ~ (all_52_9 = all_52_13)
% 200.36/33.15    (13)  op(e2, e3) = all_52_3
% 200.36/33.15    (14)   ~ (all_52_23 = all_4_0)
% 200.36/33.15    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.15    (16)   ~ (all_52_7 = all_52_15)
% 200.36/33.15    (17)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.15    (18)   ~ (all_52_17 = all_52_25)
% 200.36/33.15    (19)   ~ (all_52_3 = all_6_2)
% 200.36/33.15    (20)  all_58_0 = all_6_2
% 200.36/33.15    (21)  op(all_14_2, e0) = all_14_1
% 200.36/33.15    (22)  all_56_4 = all_52_3
% 200.36/33.15    (23)   ~ (all_52_17 = all_10_2)
% 200.36/33.15    (24)   ~ (all_10_0 = e3)
% 200.36/33.15    (25)  op(e3, e0) = all_52_25
% 200.36/33.15    (26)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.15    (27)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.15    (28)   ~ (all_52_27 = all_52_29)
% 200.36/33.15    (29)  all_58_13 = all_52_15
% 200.36/33.15    (30)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.15    (31)  all_58_9 = all_52_25
% 200.36/33.15    (32)   ~ (all_6_1 = e1)
% 200.36/33.15    (33)   ~ (all_52_29 = all_14_2)
% 200.36/33.15    (34)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.15    (35)  op(e1, e3) = all_52_5
% 200.36/33.15    (36)  op(e2, e2) = all_4_2
% 200.36/33.16    (37)   ~ (all_52_3 = all_52_5)
% 200.36/33.16    (38)  op(all_4_2, e2) = e1
% 200.36/33.16    (39)  all_58_11 = all_52_29
% 200.36/33.16    (40)  all_56_5 = all_4_2
% 200.36/33.16    (41)   ~ (all_52_25 = all_14_2)
% 200.36/33.16    (42)   ~ (all_52_9 = all_52_15)
% 200.36/33.16    (43)   ~ (all_52_3 = all_52_27)
% 200.36/33.16    (44)  op(all_10_2, e1) = all_10_1
% 200.36/33.16    (45)   ~ (all_10_2 = all_4_0)
% 200.36/33.16    (46)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.16    (47)   ~ (all_52_7 = all_6_2)
% 200.36/33.16    (48)  op(e0, e0) = all_14_2
% 200.36/33.16    (49)   ~ (all_10_0 = all_6_2)
% 200.36/33.16    (50)  all_56_15 = all_14_2
% 200.36/33.16    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.16    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.16    (53)  all_56_11 = all_52_29
% 200.36/33.16    (54)   ~ (all_10_0 = e2)
% 200.36/33.16    (55)   ~ (all_4_0 = e3)
% 200.36/33.16    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.16    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.16    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.16    (59)   ~ (e2 = e1)
% 200.36/33.16    (60)   ~ (all_52_13 = all_10_2)
% 200.36/33.16    (61)   ~ (all_6_0 = e1)
% 200.36/33.16    (62)  all_58_10 = all_52_27
% 200.36/33.16    (63)  all_56_8 = all_52_5
% 200.36/33.16    (64)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.16    (65)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.16    (66)   ~ (all_52_19 = all_52_23)
% 200.36/33.16    (67)   ~ (all_52_25 = all_52_29)
% 200.36/33.16    (68)   ~ (all_52_29 = all_10_2)
% 200.36/33.16    (69)  op(all_10_2, e1) = e3
% 200.36/33.16    (70)  all_58_7 = all_52_13
% 200.36/33.16    (71)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 200.36/33.16    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.16    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.16    (74)   ~ (all_52_5 = all_52_7)
% 200.36/33.16    (75)  all_58_12 = all_52_7
% 200.36/33.16    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.16    (77)   ~ (all_52_7 = all_14_2)
% 200.36/33.16    (78)   ~ (all_14_2 = e0)
% 200.36/33.16    (79)  all_30_2 = all_10_2
% 200.36/33.16    (80)  all_58_2 = all_52_3
% 200.36/33.16    (81)  all_56_2 = all_52_17
% 200.36/33.16    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.16    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.16    (84)  op(e3, all_6_1) = all_6_0
% 200.36/33.16    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.16    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.16    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.16    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.16    (89)   ~ (all_52_5 = all_52_29)
% 200.36/33.16    (90)  all_56_8 = all_10_0
% 200.36/33.16    (91)   ~ (all_52_15 = all_14_2)
% 200.36/33.16    (92)   ~ (all_52_19 = all_52_27)
% 200.36/33.16    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.16    (94)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.16    (95)   ~ (all_6_0 = e2)
% 200.36/33.16    (96)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.16    (97)   ~ (all_52_13 = all_4_2)
% 200.36/33.16    (98)  op(e3, e1) = all_52_17
% 200.36/33.16    (99)  all_30_0 = all_10_0
% 200.36/33.16    (100)  all_58_6 = all_10_0
% 200.36/33.16    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.16    (102)  op(e0, e3) = all_52_7
% 200.36/33.16    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.16    (104)   ~ (all_52_9 = all_52_25)
% 200.36/33.16    (105)  all_58_15 = all_14_2
% 200.36/33.16    (106)   ~ (all_52_19 = all_10_2)
% 200.36/33.16    (107)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.16    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.16    (109)   ~ (all_10_0 = all_10_2)
% 200.36/33.16    (110)  all_58_8 = all_10_2
% 200.36/33.16    (111)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.16    (112)   ~ (all_52_5 = all_10_2)
% 200.36/33.16    (113)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.16    (114)   ~ (all_52_23 = all_14_2)
% 200.36/33.16    (115)  all_56_12 = all_52_7
% 200.36/33.16    (116)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.16    (117)  all_58_5 = all_4_0
% 200.36/33.16    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.16    (119)   ~ (all_52_25 = all_6_2)
% 200.36/33.16    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.16    (121)   ~ (all_52_9 = all_4_2)
% 200.36/33.16    (122)   ~ (all_52_5 = all_6_2)
% 200.36/33.16    (123)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.16    (124)   ~ (all_52_9 = all_6_2)
% 200.36/33.16    (125)   ~ (all_52_13 = all_52_15)
% 200.36/33.16    (126)  all_56_0 = all_6_2
% 200.36/33.16    (127)  op(e3, e3) = all_6_2
% 200.36/33.16    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.16    (129)   ~ (all_52_27 = all_14_2)
% 200.36/33.16    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.16    (131)  all_56_14 = all_52_23
% 200.36/33.16    (132)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.16    (133)  all_56_3 = all_52_25
% 200.36/33.16    (134)   ~ (all_52_3 = all_52_7)
% 200.36/33.16    (135)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.16    (136)  all_58_5 = all_52_19
% 200.36/33.16    (137)  op(all_10_0, all_10_0) = all_52_4
% 200.36/33.16    (138)  all_56_1 = all_52_9
% 200.36/33.16    (139)   ~ (all_52_15 = all_4_2)
% 200.36/33.16    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.16           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.16           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.16           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.16    (141)   ~ (all_52_27 = all_4_2)
% 200.36/33.16    (142)  all_58_6 = all_52_5
% 200.36/33.16    (143)   ~ (all_4_0 = all_4_2)
% 200.36/33.16    (144)  op(e3, e2) = all_52_9
% 200.36/33.16    (145)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.16    (146)   ~ (all_52_17 = all_6_2)
% 200.36/33.16    (147)   ~ (e3 = e2)
% 200.36/33.16    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.16    (149)   ~ (all_52_9 = all_52_17)
% 200.36/33.16    (150)  all_56_10 = all_10_2
% 200.36/33.16    (151)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.16    (152)   ~ (all_52_3 = all_4_0)
% 200.36/33.16    (153)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.16    (154)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.16    (155)   ~ (all_6_1 = e2)
% 200.36/33.16    (156)  op(e1, e1) = all_10_2
% 200.36/33.16    (157)   ~ (all_52_23 = all_10_2)
% 200.36/33.16    (158)   ~ (all_52_7 = all_52_23)
% 200.36/33.16    (159)   ~ (all_52_17 = all_52_19)
% 200.36/33.16    (160)  all_58_3 = all_4_2
% 200.36/33.16    (161)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.16    (162)  all_56_13 = all_52_15
% 200.36/33.16    (163)   ~ (all_52_3 = all_4_2)
% 200.36/33.16    (164)   ~ (all_52_19 = all_4_2)
% 200.36/33.16    (165)   ~ (all_52_17 = all_52_23)
% 200.36/33.16    (166)  op(all_6_2, e3) = all_6_1
% 200.36/33.16    (167)  all_58_4 = all_52_17
% 200.36/33.16    (168)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.36/33.16    (169)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.16  
% 200.36/33.16  Begin of proof
% 200.36/33.16  | 
% 200.36/33.16  | BETA: splitting (108) gives:
% 200.36/33.16  | 
% 200.36/33.16  | Case 1:
% 200.36/33.16  | | 
% 200.36/33.16  | |   (170)  all_56_8 = e3
% 200.36/33.16  | | 
% 200.36/33.16  | | REF_CLOSE: (24), (90), (170) are inconsistent by sub-proof #926.
% 200.36/33.16  | | 
% 200.36/33.16  | Case 2:
% 200.36/33.16  | | 
% 200.36/33.16  | |   (171)   ~ (all_56_8 = e3)
% 200.36/33.16  | |   (172)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.16  | | 
% 200.36/33.16  | | BETA: splitting (140) gives:
% 200.36/33.16  | | 
% 200.36/33.16  | | Case 1:
% 200.36/33.16  | | | 
% 200.36/33.16  | | |   (173)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.16  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.36/33.16  | | |            e0)
% 200.36/33.16  | | | 
% 200.36/33.16  | | | BETA: splitting (173) gives:
% 200.36/33.16  | | | 
% 200.36/33.16  | | | Case 1:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | |   (174)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REF_CLOSE: (8), (23), (54), (69), (71), (79), (90), (98), (99), (100),
% 200.36/33.16  | | | |            (109), (118), (137), (150), (156), (168), (172), (174) are
% 200.36/33.16  | | | |            inconsistent by sub-proof #667.
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | Case 2:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | |   (175)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.36/33.16  | | | |          e0
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 200.36/33.16  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (25),
% 200.36/33.16  | | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 200.36/33.16  | | | |            (38), (39), (40), (41), (44), (45), (46), (47), (48), (50),
% 200.36/33.16  | | | |            (51), (55), (56), (57), (59), (60), (61), (62), (63), (64),
% 200.36/33.16  | | | |            (65), (68), (70), (74), (75), (76), (77), (80), (81), (82),
% 200.36/33.16  | | | |            (83), (84), (88), (89), (91), (94), (95), (96), (97), (98),
% 200.36/33.16  | | | |            (102), (103), (104), (105), (107), (108), (110), (111),
% 200.36/33.16  | | | |            (112), (115), (116), (117), (119), (120), (122), (123),
% 200.36/33.16  | | | |            (124), (127), (128), (129), (130), (132), (133), (134),
% 200.36/33.16  | | | |            (135), (138), (139), (141), (142), (143), (144), (145),
% 200.36/33.16  | | | |            (146), (147), (148), (149), (150), (151), (154), (155),
% 200.36/33.16  | | | |            (156), (157), (158), (160), (162), (163), (165), (166),
% 200.36/33.16  | | | |            (167), (168), (169), (175) are inconsistent by sub-proof
% 200.36/33.16  | | | |            #188.
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | End of split
% 200.36/33.16  | | | 
% 200.36/33.16  | | Case 2:
% 200.36/33.16  | | | 
% 200.36/33.16  | | |   (176)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.16  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.36/33.16  | | |            all_52_30 = e0)
% 200.36/33.16  | | | 
% 200.36/33.16  | | | BETA: splitting (176) gives:
% 200.36/33.16  | | | 
% 200.36/33.16  | | | Case 1:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | |   (177)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.16  | | | |          e0
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | ALPHA: (177) implies:
% 200.36/33.16  | | | |   (178)  all_52_22 = e0
% 200.36/33.16  | | | |   (179)  all_52_20 = e1
% 200.36/33.16  | | | |   (180)  all_52_16 = e3
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REDUCE: (116), (180) imply:
% 200.36/33.16  | | | |   (181)  op(all_52_17, all_52_17) = e3
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REDUCE: (107), (178) imply:
% 200.36/33.16  | | | |   (182)  op(all_52_23, all_52_23) = e0
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REDUCE: (30), (179) imply:
% 200.36/33.16  | | | |   (183)  op(all_10_2, all_10_2) = e1
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REF_CLOSE: (2), (4), (7), (8), (9), (11), (13), (14), (15), (17), (19),
% 200.36/33.16  | | | |            (20), (21), (23), (24), (25), (28), (29), (31), (32), (34),
% 200.36/33.16  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 200.36/33.16  | | | |            (47), (48), (49), (50), (51), (54), (55), (56), (57), (59),
% 200.36/33.16  | | | |            (60), (62), (63), (69), (70), (72), (74), (75), (76), (80),
% 200.36/33.16  | | | |            (81), (82), (83), (84), (88), (94), (95), (98), (100), (102),
% 200.36/33.16  | | | |            (103), (105), (106), (108), (110), (111), (114), (115),
% 200.36/33.16  | | | |            (117), (120), (121), (122), (123), (124), (125), (127),
% 200.36/33.16  | | | |            (129), (130), (131), (132), (133), (134), (135), (136),
% 200.36/33.16  | | | |            (139), (141), (142), (143), (144), (145), (146), (147),
% 200.36/33.16  | | | |            (151), (152), (155), (158), (160), (162), (163), (165),
% 200.36/33.16  | | | |            (166), (167), (181), (182), (183) are inconsistent by
% 200.36/33.16  | | | |            sub-proof #160.
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | Case 2:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | |   (184)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.36/33.16  | | | |          e0
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (11), (12), (13), (15), (16),
% 200.36/33.16  | | | |            (17), (18), (19), (20), (22), (23), (25), (26), (27), (28),
% 200.36/33.16  | | | |            (29), (31), (32), (33), (34), (35), (36), (37), (39), (40),
% 200.36/33.16  | | | |            (41), (42), (43), (44), (46), (47), (48), (50), (51), (52),
% 200.36/33.16  | | | |            (53), (56), (57), (58), (61), (62), (63), (64), (65), (66),
% 200.36/33.16  | | | |            (67), (68), (70), (72), (73), (74), (75), (76), (77), (78),
% 200.36/33.16  | | | |            (80), (81), (83), (84), (85), (86), (87), (88), (89), (91),
% 200.36/33.16  | | | |            (92), (93), (94), (95), (96), (97), (98), (101), (102),
% 200.36/33.16  | | | |            (103), (104), (105), (106), (107), (108), (110), (111),
% 200.36/33.16  | | | |            (112), (113), (114), (115), (116), (118), (119), (120),
% 200.36/33.16  | | | |            (121), (122), (124), (125), (126), (127), (128), (129),
% 200.36/33.16  | | | |            (130), (131), (133), (134), (135), (136), (138), (139),
% 200.36/33.16  | | | |            (141), (142), (145), (146), (147), (148), (153), (154),
% 200.36/33.16  | | | |            (155), (156), (158), (159), (160), (161), (162), (163),
% 200.36/33.16  | | | |            (164), (165), (166), (167), (169), (184) are inconsistent by
% 200.36/33.16  | | | |            sub-proof #1008.
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | End of split
% 200.36/33.16  | | | 
% 200.36/33.16  | | End of split
% 200.36/33.16  | | 
% 200.36/33.16  | End of split
% 200.36/33.16  | 
% 200.36/33.16  End of proof
% 200.36/33.16  
% 200.36/33.16  Sub-proof #160 shows that the following formulas are inconsistent:
% 200.36/33.16  ----------------------------------------------------------------
% 200.36/33.16    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.16    (2)  all_58_14 = all_52_23
% 200.36/33.16    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.16    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.16    (5)   ~ (all_52_7 = all_10_0)
% 200.36/33.16    (6)  all_58_1 = all_52_9
% 200.36/33.16    (7)  op(all_52_23, all_52_23) = e0
% 200.36/33.16    (8)  op(e2, e3) = all_52_3
% 200.36/33.16    (9)   ~ (all_52_23 = all_4_0)
% 200.36/33.16    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.16    (11)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.16    (12)   ~ (all_52_3 = all_6_2)
% 200.36/33.16    (13)  all_58_0 = all_6_2
% 200.36/33.16    (14)  op(all_14_2, e0) = all_14_1
% 200.36/33.16    (15)   ~ (all_52_17 = all_10_2)
% 200.36/33.16    (16)   ~ (all_10_0 = e3)
% 200.36/33.16    (17)  op(e3, e0) = all_52_25
% 200.36/33.16    (18)   ~ (all_52_27 = all_52_29)
% 200.36/33.16    (19)  all_58_13 = all_52_15
% 200.36/33.16    (20)  all_58_9 = all_52_25
% 200.36/33.16    (21)   ~ (all_6_1 = e1)
% 200.36/33.16    (22)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.16    (23)  op(e1, e3) = all_52_5
% 200.36/33.16    (24)  op(e2, e2) = all_4_2
% 200.36/33.16    (25)   ~ (all_52_3 = all_52_5)
% 200.36/33.16    (26)  op(all_4_2, e2) = e1
% 200.36/33.16    (27)  all_58_11 = all_52_29
% 200.36/33.16    (28)  all_56_5 = all_4_2
% 200.36/33.16    (29)   ~ (all_52_25 = all_14_2)
% 200.36/33.16    (30)   ~ (all_52_9 = all_52_15)
% 200.36/33.16    (31)   ~ (all_52_3 = all_52_27)
% 200.36/33.16    (32)  op(all_10_2, e1) = all_10_1
% 200.36/33.16    (33)   ~ (all_52_7 = all_6_2)
% 200.36/33.16    (34)  op(e0, e0) = all_14_2
% 200.36/33.16    (35)   ~ (all_10_0 = all_6_2)
% 200.36/33.16    (36)  all_56_15 = all_14_2
% 200.36/33.16    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.16    (38)   ~ (all_10_0 = e2)
% 200.36/33.16    (39)   ~ (all_4_0 = e3)
% 200.36/33.16    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.16    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.16    (42)   ~ (e2 = e1)
% 200.36/33.16    (43)   ~ (all_52_13 = all_10_2)
% 200.36/33.16    (44)  op(all_10_2, all_10_2) = e1
% 200.36/33.16    (45)  all_58_10 = all_52_27
% 200.36/33.16    (46)  all_56_8 = all_52_5
% 200.36/33.16    (47)  op(all_10_2, e1) = e3
% 200.36/33.16    (48)  all_58_7 = all_52_13
% 200.36/33.16    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.16    (50)   ~ (all_52_5 = all_52_7)
% 200.36/33.16    (51)  all_58_12 = all_52_7
% 200.36/33.16    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.16    (53)  all_58_2 = all_52_3
% 200.36/33.16    (54)  all_56_2 = all_52_17
% 200.36/33.16    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.16    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.16    (57)  op(e3, all_6_1) = all_6_0
% 200.36/33.16    (58)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.16    (59)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.16    (60)   ~ (all_6_0 = e2)
% 200.36/33.16    (61)  op(e3, e1) = all_52_17
% 200.36/33.16    (62)  all_58_6 = all_10_0
% 200.36/33.16    (63)  op(e0, e3) = all_52_7
% 200.36/33.16    (64)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.16    (65)  all_58_15 = all_14_2
% 200.36/33.16    (66)   ~ (all_52_19 = all_10_2)
% 200.36/33.16    (67)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.16    (68)  all_58_8 = all_10_2
% 200.36/33.16    (69)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.16    (70)   ~ (all_52_23 = all_14_2)
% 200.36/33.16    (71)  all_56_12 = all_52_7
% 200.36/33.16    (72)  all_58_5 = all_4_0
% 200.36/33.16    (73)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.16    (74)   ~ (all_52_9 = all_4_2)
% 200.36/33.16    (75)   ~ (all_52_5 = all_6_2)
% 200.36/33.16    (76)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.16    (77)   ~ (all_52_9 = all_6_2)
% 200.36/33.16    (78)   ~ (all_52_13 = all_52_15)
% 200.36/33.16    (79)  op(e3, e3) = all_6_2
% 200.36/33.16    (80)   ~ (all_52_27 = all_14_2)
% 200.36/33.16    (81)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.16    (82)  all_56_14 = all_52_23
% 200.36/33.16    (83)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.16    (84)  all_56_3 = all_52_25
% 200.36/33.16    (85)   ~ (all_52_3 = all_52_7)
% 200.36/33.16    (86)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.16    (87)  all_58_5 = all_52_19
% 200.36/33.16    (88)   ~ (all_52_15 = all_4_2)
% 200.36/33.16    (89)   ~ (all_52_27 = all_4_2)
% 200.36/33.16    (90)  op(all_52_17, all_52_17) = e3
% 200.36/33.16    (91)  all_58_6 = all_52_5
% 200.36/33.16    (92)   ~ (all_4_0 = all_4_2)
% 200.36/33.16    (93)  op(e3, e2) = all_52_9
% 200.36/33.16    (94)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.16    (95)   ~ (all_52_17 = all_6_2)
% 200.36/33.16    (96)   ~ (e3 = e2)
% 200.36/33.16    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.16    (98)   ~ (all_52_3 = all_4_0)
% 200.36/33.16    (99)   ~ (all_6_1 = e2)
% 200.36/33.16    (100)   ~ (all_52_7 = all_52_23)
% 200.36/33.16    (101)  all_58_3 = all_4_2
% 200.36/33.16    (102)  all_56_13 = all_52_15
% 200.36/33.16    (103)   ~ (all_52_3 = all_4_2)
% 200.36/33.16    (104)   ~ (all_52_17 = all_52_23)
% 200.36/33.16    (105)  op(all_6_2, e3) = all_6_1
% 200.36/33.16    (106)  all_58_4 = all_52_17
% 200.36/33.16  
% 200.36/33.16  Begin of proof
% 200.36/33.16  | 
% 200.36/33.16  | BETA: splitting (69) gives:
% 200.36/33.16  | 
% 200.36/33.16  | Case 1:
% 200.36/33.16  | | 
% 200.36/33.16  | |   (107)  all_56_15 = e3
% 200.36/33.16  | | 
% 200.36/33.16  | | REF_CLOSE: (2), (3), (4), (6), (11), (12), (13), (14), (17), (19), (20),
% 200.36/33.16  | |            (23), (24), (25), (26), (29), (30), (31), (32), (33), (36), (37),
% 200.36/33.16  | |            (39), (42), (43), (44), (45), (46), (48), (50), (51), (53), (55),
% 200.36/33.16  | |            (56), (57), (59), (60), (61), (64), (66), (67), (68), (70), (72),
% 200.36/33.16  | |            (73), (74), (75), (76), (77), (79), (80), (81), (83), (84), (85),
% 200.36/33.16  | |            (86), (87), (90), (91), (92), (93), (95), (96), (97), (98), (99),
% 200.36/33.16  | |            (101), (103), (105), (106), (107) are inconsistent by sub-proof
% 200.36/33.16  | |            #203.
% 200.36/33.16  | | 
% 200.36/33.16  | Case 2:
% 200.36/33.16  | | 
% 200.36/33.16  | |   (108)   ~ (all_56_15 = e3)
% 200.36/33.16  | | 
% 200.36/33.16  | | REDUCE: (36), (108) imply:
% 200.36/33.16  | |   (109)   ~ (all_14_2 = e3)
% 200.36/33.16  | | 
% 200.36/33.16  | | BETA: splitting (37) gives:
% 200.36/33.16  | | 
% 200.36/33.16  | | Case 1:
% 200.36/33.16  | | | 
% 200.36/33.16  | | |   (110)  all_58_2 = e3
% 200.36/33.16  | | | 
% 200.36/33.16  | | | COMBINE_EQS: (53), (110) imply:
% 200.36/33.16  | | |   (111)  all_52_3 = e3
% 200.36/33.16  | | | 
% 200.36/33.16  | | | SIMP: (111) implies:
% 200.36/33.16  | | |   (112)  all_52_3 = e3
% 200.36/33.16  | | | 
% 200.36/33.16  | | | REDUCE: (12), (112) imply:
% 200.36/33.16  | | |   (113)   ~ (all_6_2 = e3)
% 200.36/33.16  | | | 
% 200.36/33.16  | | | SIMP: (113) implies:
% 200.36/33.16  | | |   (114)   ~ (all_6_2 = e3)
% 200.36/33.16  | | | 
% 200.36/33.16  | | | REDUCE: (98), (112) imply:
% 200.36/33.16  | | |   (115)   ~ (all_4_0 = e3)
% 200.36/33.16  | | | 
% 200.36/33.16  | | | REDUCE: (3), (112) imply:
% 200.36/33.16  | | |   (116)  op(e3, e3) = all_52_2
% 200.36/33.16  | | | 
% 200.36/33.16  | | | REDUCE: (8), (112) imply:
% 200.36/33.16  | | |   (117)  op(e2, e3) = e3
% 200.36/33.16  | | | 
% 200.36/33.16  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_2, e3, e3, simplifying
% 200.36/33.16  | | |              with (79), (116) gives:
% 200.36/33.16  | | |   (118)  all_52_2 = all_6_2
% 200.36/33.16  | | | 
% 200.36/33.16  | | | BETA: splitting (59) gives:
% 200.36/33.16  | | | 
% 200.36/33.16  | | | Case 1:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | |   (119)  all_58_0 = e2
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | REF_CLOSE: (4), (13), (57), (60), (79), (105), (117), (119) are
% 200.36/33.16  | | | |            inconsistent by sub-proof #168.
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | Case 2:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | |   (120)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | BETA: splitting (120) gives:
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | | Case 1:
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | |   (121)  all_58_2 = e2
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | | REF_CLOSE: (96), (110), (121) are inconsistent by sub-proof #1124.
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | Case 2:
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | |   (122)  all_58_6 = e2 | all_58_12 = e2
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | | BETA: splitting (122) gives:
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | | Case 1:
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | |   (123)  all_58_6 = e2
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | REF_CLOSE: (38), (62), (123) are inconsistent by sub-proof #917.
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | Case 2:
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | |   (124)  all_58_12 = e2
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | COMBINE_EQS: (51), (124) imply:
% 200.36/33.16  | | | | | |   (125)  all_52_7 = e2
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | SIMP: (125) implies:
% 200.36/33.16  | | | | | |   (126)  all_52_7 = e2
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | REDUCE: (100), (126) imply:
% 200.36/33.16  | | | | | |   (127)   ~ (all_52_23 = e2)
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | SIMP: (127) implies:
% 200.36/33.16  | | | | | |   (128)   ~ (all_52_23 = e2)
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | REDUCE: (5), (126) imply:
% 200.36/33.16  | | | | | |   (129)   ~ (all_10_0 = e2)
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | BETA: splitting (49) gives:
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | | Case 1:
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | |   (130)  all_56_14 = e3
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | | COMBINE_EQS: (82), (130) imply:
% 200.36/33.16  | | | | | | |   (131)  all_52_23 = e3
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | | SIMP: (131) implies:
% 200.36/33.16  | | | | | | |   (132)  all_52_23 = e3
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | | REDUCE: (104), (132) imply:
% 200.36/33.16  | | | | | | |   (133)   ~ (all_52_17 = e3)
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | | REF_CLOSE: (1), (2), (4), (7), (10), (15), (19), (21), (33), (38),
% 200.36/33.16  | | | | | | |            (39), (40), (47), (61), (62), (63), (65), (68), (71),
% 200.36/33.16  | | | | | | |            (72), (79), (94), (96), (97), (99), (100), (102),
% 200.36/33.16  | | | | | | |            (105), (106), (109), (122), (133) are inconsistent by
% 200.36/33.16  | | | | | | |            sub-proof #164.
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | Case 2:
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | |   (134)   ~ (all_56_14 = e3)
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | | REDUCE: (82), (134) imply:
% 200.36/33.16  | | | | | | |   (135)   ~ (all_52_23 = e3)
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | | REF_CLOSE: (2), (4), (15), (39), (41), (47), (54), (61), (68),
% 200.36/33.16  | | | | | | |            (72), (79), (90), (97), (106), (114), (135) are
% 200.36/33.16  | | | | | | |            inconsistent by sub-proof #163.
% 200.36/33.16  | | | | | | | 
% 200.36/33.16  | | | | | | End of split
% 200.36/33.16  | | | | | | 
% 200.36/33.16  | | | | | End of split
% 200.36/33.16  | | | | | 
% 200.36/33.16  | | | | End of split
% 200.36/33.16  | | | | 
% 200.36/33.16  | | | End of split
% 200.36/33.16  | | | 
% 200.36/33.16  | | Case 2:
% 200.36/33.16  | | | 
% 200.36/33.16  | | |   (136)   ~ (all_58_2 = e3)
% 200.36/33.16  | | |   (137)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.16  | | | 
% 200.36/33.16  | | | REDUCE: (53), (136) imply:
% 200.36/33.16  | | |   (138)   ~ (all_52_3 = e3)
% 200.36/33.16  | | | 
% 200.36/33.16  | | | REF_CLOSE: (2), (4), (7), (10), (11), (13), (15), (16), (18), (19), (21),
% 200.36/33.16  | | |            (22), (24), (27), (28), (32), (33), (34), (35), (39), (41),
% 200.36/33.16  | | |            (44), (45), (47), (48), (51), (52), (53), (54), (56), (58),
% 200.36/33.16  | | |            (61), (62), (63), (65), (66), (68), (71), (72), (78), (79),
% 200.36/33.16  | | |            (80), (87), (88), (89), (90), (94), (95), (97), (99), (100),
% 200.36/33.16  | | |            (101), (105), (106), (109), (137), (138) are inconsistent by
% 200.36/33.16  | | |            sub-proof #161.
% 200.36/33.16  | | | 
% 200.36/33.16  | | End of split
% 200.36/33.16  | | 
% 200.36/33.16  | End of split
% 200.36/33.16  | 
% 200.36/33.16  End of proof
% 200.36/33.16  
% 200.36/33.16  Sub-proof #161 shows that the following formulas are inconsistent:
% 200.36/33.16  ----------------------------------------------------------------
% 200.36/33.16    (1)  all_58_14 = all_52_23
% 200.36/33.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.16    (3)  op(all_52_23, all_52_23) = e0
% 200.36/33.16    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.16    (5)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.17    (6)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.17    (7)  all_58_0 = all_6_2
% 200.36/33.17    (8)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (9)   ~ (all_10_0 = e3)
% 200.36/33.17    (10)   ~ (all_52_27 = all_52_29)
% 200.36/33.17    (11)  all_58_13 = all_52_15
% 200.36/33.17    (12)   ~ (all_6_1 = e1)
% 200.36/33.17    (13)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.17    (14)  op(e2, e2) = all_4_2
% 200.36/33.17    (15)  all_58_11 = all_52_29
% 200.36/33.17    (16)   ~ (all_52_3 = e3)
% 200.36/33.17    (17)  all_56_5 = all_4_2
% 200.36/33.17    (18)  op(all_10_2, e1) = all_10_1
% 200.36/33.17    (19)   ~ (all_52_7 = all_6_2)
% 200.36/33.17    (20)  op(e0, e0) = all_14_2
% 200.36/33.17    (21)   ~ (all_10_0 = all_6_2)
% 200.36/33.17    (22)   ~ (all_4_0 = e3)
% 200.36/33.17    (23)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.17    (24)  op(all_10_2, all_10_2) = e1
% 200.36/33.17    (25)  all_58_10 = all_52_27
% 200.36/33.17    (26)  op(all_10_2, e1) = e3
% 200.36/33.17    (27)  all_58_7 = all_52_13
% 200.36/33.17    (28)  all_58_12 = all_52_7
% 200.36/33.17    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.17    (30)  all_58_2 = all_52_3
% 200.36/33.17    (31)  all_56_2 = all_52_17
% 200.36/33.17    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.17    (33)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.17    (34)  op(e3, e1) = all_52_17
% 200.36/33.17    (35)  all_58_6 = all_10_0
% 200.36/33.17    (36)  op(e0, e3) = all_52_7
% 200.36/33.17    (37)  all_58_15 = all_14_2
% 200.36/33.17    (38)   ~ (all_52_19 = all_10_2)
% 200.36/33.17    (39)  all_58_8 = all_10_2
% 200.36/33.17    (40)  all_56_12 = all_52_7
% 200.36/33.17    (41)  all_58_5 = all_4_0
% 200.36/33.17    (42)   ~ (all_52_13 = all_52_15)
% 200.36/33.17    (43)  op(e3, e3) = all_6_2
% 200.36/33.17    (44)   ~ (all_52_27 = all_14_2)
% 200.36/33.17    (45)  all_58_5 = all_52_19
% 200.36/33.17    (46)   ~ (all_52_15 = all_4_2)
% 200.36/33.17    (47)   ~ (all_52_27 = all_4_2)
% 200.36/33.17    (48)  op(all_52_17, all_52_17) = e3
% 200.36/33.17    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.17    (50)   ~ (all_52_17 = all_6_2)
% 200.36/33.17    (51)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17    (52)   ~ (all_6_1 = e2)
% 200.36/33.17    (53)   ~ (all_52_7 = all_52_23)
% 200.36/33.17    (54)  all_58_3 = all_4_2
% 200.36/33.17    (55)  op(all_6_2, e3) = all_6_1
% 200.36/33.17    (56)  all_58_4 = all_52_17
% 200.36/33.17    (57)   ~ (all_14_2 = e3)
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | BETA: splitting (32) gives:
% 200.36/33.17  | 
% 200.36/33.17  | Case 1:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (58)  all_58_0 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | COMBINE_EQS: (7), (58) imply:
% 200.36/33.17  | |   (59)  all_6_2 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REDUCE: (19), (59) imply:
% 200.36/33.17  | |   (60)   ~ (all_52_7 = e3)
% 200.36/33.17  | | 
% 200.36/33.17  | | REDUCE: (50), (59) imply:
% 200.36/33.17  | |   (61)   ~ (all_52_17 = e3)
% 200.36/33.17  | | 
% 200.36/33.17  | | BETA: splitting (49) gives:
% 200.36/33.17  | | 
% 200.36/33.17  | | Case 1:
% 200.36/33.17  | | | 
% 200.36/33.17  | | |   (62)  all_58_12 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REF_CLOSE: (28), (60), (62) are inconsistent by sub-proof #1367.
% 200.36/33.17  | | | 
% 200.36/33.17  | | Case 2:
% 200.36/33.17  | | | 
% 200.36/33.17  | | |   (63)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | BETA: splitting (23) gives:
% 200.36/33.17  | | | 
% 200.36/33.17  | | | Case 1:
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | |   (64)  all_56_2 = e3
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | | REF_CLOSE: (31), (61), (64) are inconsistent by sub-proof #1327.
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | Case 2:
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | |   (65)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | | BETA: splitting (33) gives:
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | | Case 1:
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | |   (66)  all_56_5 = e3
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | COMBINE_EQS: (17), (66) imply:
% 200.36/33.17  | | | | |   (67)  all_4_2 = e3
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | SIMP: (67) implies:
% 200.36/33.17  | | | | |   (68)  all_4_2 = e3
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | REDUCE: (46), (68) imply:
% 200.36/33.17  | | | | |   (69)   ~ (all_52_15 = e3)
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | REF_CLOSE: (1), (2), (3), (4), (11), (12), (19), (36), (37), (40),
% 200.36/33.17  | | | | |            (43), (52), (53), (55), (57), (63), (69) are inconsistent
% 200.36/33.17  | | | | |            by sub-proof #1045.
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | Case 2:
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | |   (70)   ~ (all_56_5 = e3)
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | REDUCE: (17), (70) imply:
% 200.36/33.17  | | | | |   (71)   ~ (all_4_2 = e3)
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | BETA: splitting (6) gives:
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | | Case 1:
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | |   (72)  all_58_3 = e3
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | | COMBINE_EQS: (54), (72) imply:
% 200.36/33.17  | | | | | |   (73)  all_4_2 = e3
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | | REDUCE: (71), (73) imply:
% 200.36/33.17  | | | | | |   (74)  $false
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | | CLOSE: (74) is inconsistent.
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | Case 2:
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | |   (75)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | | BETA: splitting (75) gives:
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | | Case 1:
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | |   (76)  all_58_5 = e3
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | REF_CLOSE: (22), (41), (76) are inconsistent by sub-proof #215.
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | Case 2:
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | |   (77)  all_58_10 = e3
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | COMBINE_EQS: (25), (77) imply:
% 200.36/33.17  | | | | | | |   (78)  all_52_27 = e3
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | SIMP: (78) implies:
% 200.36/33.17  | | | | | | |   (79)  all_52_27 = e3
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | REDUCE: (10), (79) imply:
% 200.36/33.17  | | | | | | |   (80)   ~ (all_52_29 = e3)
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | SIMP: (80) implies:
% 200.36/33.17  | | | | | | |   (81)   ~ (all_52_29 = e3)
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | REDUCE: (44), (79) imply:
% 200.36/33.17  | | | | | | |   (82)   ~ (all_14_2 = e3)
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | BETA: splitting (29) gives:
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | | Case 1:
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | |   (83)  all_58_6 = e3
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | | REF_CLOSE: (9), (35), (83) are inconsistent by sub-proof #922.
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | Case 2:
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | |   (84)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | | BETA: splitting (84) gives:
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | | Case 1:
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | |   (85)  all_58_7 = e3
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | | COMBINE_EQS: (27), (85) imply:
% 200.36/33.17  | | | | | | | | |   (86)  all_52_13 = e3
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | | REDUCE: (42), (86) imply:
% 200.36/33.17  | | | | | | | | |   (87)   ~ (all_52_15 = e3)
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | | SIMP: (87) implies:
% 200.36/33.17  | | | | | | | | |   (88)   ~ (all_52_15 = e3)
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (11), (12), (19), (36), (37),
% 200.36/33.17  | | | | | | | | |            (40), (43), (52), (53), (55), (57), (63), (88) are
% 200.36/33.17  | | | | | | | | |            inconsistent by sub-proof #1045.
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | Case 2:
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | |   (89)  all_58_8 = e3 | all_58_11 = e3
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | | REF_CLOSE: (2), (13), (14), (15), (18), (20), (24), (25),
% 200.36/33.17  | | | | | | | | |            (31), (34), (38), (39), (43), (44), (45), (47),
% 200.36/33.17  | | | | | | | | |            (48), (50), (65), (75), (81), (89) are inconsistent
% 200.36/33.17  | | | | | | | | |            by sub-proof #233.
% 200.36/33.17  | | | | | | | | | 
% 200.36/33.17  | | | | | | | | End of split
% 200.36/33.17  | | | | | | | | 
% 200.36/33.17  | | | | | | | End of split
% 200.36/33.17  | | | | | | | 
% 200.36/33.17  | | | | | | End of split
% 200.36/33.17  | | | | | | 
% 200.36/33.17  | | | | | End of split
% 200.36/33.17  | | | | | 
% 200.36/33.17  | | | | End of split
% 200.36/33.17  | | | | 
% 200.36/33.17  | | | End of split
% 200.36/33.17  | | | 
% 200.36/33.17  | | End of split
% 200.36/33.17  | | 
% 200.36/33.17  | Case 2:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (90)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (1), (2), (5), (8), (9), (16), (19), (22), (23), (26), (28),
% 200.36/33.17  | |            (30), (31), (34), (35), (39), (41), (43), (48), (51), (53), (56),
% 200.36/33.17  | |            (90) are inconsistent by sub-proof #162.
% 200.36/33.17  | | 
% 200.36/33.17  | End of split
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #162 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)  all_58_14 = all_52_23
% 200.36/33.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (3)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.17    (4)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (5)   ~ (all_10_0 = e3)
% 200.36/33.17    (6)   ~ (all_52_3 = e3)
% 200.36/33.17    (7)   ~ (all_52_7 = all_6_2)
% 200.36/33.17    (8)   ~ (all_4_0 = e3)
% 200.36/33.17    (9)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.17    (10)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.17    (11)  op(all_10_2, e1) = e3
% 200.36/33.17    (12)  all_58_12 = all_52_7
% 200.36/33.17    (13)  all_58_2 = all_52_3
% 200.36/33.17    (14)  all_56_2 = all_52_17
% 200.36/33.17    (15)  op(e3, e1) = all_52_17
% 200.36/33.17    (16)  all_58_6 = all_10_0
% 200.36/33.17    (17)  all_58_8 = all_10_2
% 200.36/33.17    (18)  all_58_5 = all_4_0
% 200.36/33.17    (19)  op(e3, e3) = all_6_2
% 200.36/33.17    (20)  op(all_52_17, all_52_17) = e3
% 200.36/33.17    (21)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17    (22)   ~ (all_52_7 = all_52_23)
% 200.36/33.17    (23)  all_58_4 = all_52_17
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | BETA: splitting (10) gives:
% 200.36/33.17  | 
% 200.36/33.17  | Case 1:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (24)  all_58_2 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (6), (13), (24) are inconsistent by sub-proof #1369.
% 200.36/33.17  | | 
% 200.36/33.17  | Case 2:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (25)  all_58_6 = e3 | all_58_12 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | BETA: splitting (25) gives:
% 200.36/33.17  | | 
% 200.36/33.17  | | Case 1:
% 200.36/33.17  | | | 
% 200.36/33.17  | | |   (26)  all_58_6 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REF_CLOSE: (5), (16), (26) are inconsistent by sub-proof #922.
% 200.36/33.17  | | | 
% 200.36/33.17  | | Case 2:
% 200.36/33.17  | | | 
% 200.36/33.17  | | |   (27)  all_58_12 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | COMBINE_EQS: (12), (27) imply:
% 200.36/33.17  | | |   (28)  all_52_7 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | SIMP: (28) implies:
% 200.36/33.17  | | |   (29)  all_52_7 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REDUCE: (22), (29) imply:
% 200.36/33.17  | | |   (30)   ~ (all_52_23 = e3)
% 200.36/33.17  | | | 
% 200.36/33.17  | | | SIMP: (30) implies:
% 200.36/33.17  | | |   (31)   ~ (all_52_23 = e3)
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REDUCE: (7), (29) imply:
% 200.36/33.17  | | |   (32)   ~ (all_6_2 = e3)
% 200.36/33.17  | | | 
% 200.36/33.17  | | | SIMP: (32) implies:
% 200.36/33.17  | | |   (33)   ~ (all_6_2 = e3)
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REDUCE: (3), (29) imply:
% 200.36/33.17  | | |   (34)  op(e3, e3) = all_52_6
% 200.36/33.17  | | | 
% 200.36/33.17  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_6, e3, e3, simplifying
% 200.36/33.17  | | |              with (19), (34) gives:
% 200.36/33.17  | | |   (35)  all_52_6 = all_6_2
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REF_CLOSE: (1), (2), (4), (8), (9), (11), (14), (15), (17), (18), (19),
% 200.36/33.17  | | |            (20), (21), (23), (31), (33) are inconsistent by sub-proof
% 200.36/33.17  | | |            #163.
% 200.36/33.17  | | | 
% 200.36/33.17  | | End of split
% 200.36/33.17  | | 
% 200.36/33.17  | End of split
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #163 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)  all_58_14 = all_52_23
% 200.36/33.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (4)   ~ (all_4_0 = e3)
% 200.36/33.17    (5)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.17    (6)   ~ (all_6_2 = e3)
% 200.36/33.17    (7)  op(all_10_2, e1) = e3
% 200.36/33.17    (8)  all_56_2 = all_52_17
% 200.36/33.17    (9)   ~ (all_52_23 = e3)
% 200.36/33.17    (10)  op(e3, e1) = all_52_17
% 200.36/33.17    (11)  all_58_8 = all_10_2
% 200.36/33.17    (12)  all_58_5 = all_4_0
% 200.36/33.17    (13)  op(e3, e3) = all_6_2
% 200.36/33.17    (14)  op(all_52_17, all_52_17) = e3
% 200.36/33.17    (15)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17    (16)  all_58_4 = all_52_17
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | BETA: splitting (5) gives:
% 200.36/33.17  | 
% 200.36/33.17  | Case 1:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (17)  all_56_2 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (2), (6), (8), (13), (14), (17) are inconsistent by sub-proof
% 200.36/33.17  | |            #1265.
% 200.36/33.17  | | 
% 200.36/33.17  | Case 2:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (18)   ~ (all_56_2 = e3)
% 200.36/33.17  | | 
% 200.36/33.17  | | REDUCE: (8), (18) imply:
% 200.36/33.17  | |   (19)   ~ (all_52_17 = e3)
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (15), (16), (19)
% 200.36/33.17  | |            are inconsistent by sub-proof #166.
% 200.36/33.17  | | 
% 200.36/33.17  | End of split
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #164 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.17    (2)  all_58_14 = all_52_23
% 200.36/33.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (4)  op(all_52_23, all_52_23) = e0
% 200.36/33.17    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.17    (6)  all_58_6 = e2 | all_58_12 = e2
% 200.36/33.17    (7)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (8)  all_58_13 = all_52_15
% 200.36/33.17    (9)   ~ (all_6_1 = e1)
% 200.36/33.17    (10)   ~ (all_52_7 = all_6_2)
% 200.36/33.17    (11)   ~ (all_10_0 = e2)
% 200.36/33.17    (12)   ~ (all_4_0 = e3)
% 200.36/33.17    (13)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.17    (14)  op(all_10_2, e1) = e3
% 200.36/33.17    (15)  op(e3, e1) = all_52_17
% 200.36/33.17    (16)  all_58_6 = all_10_0
% 200.36/33.17    (17)  op(e0, e3) = all_52_7
% 200.36/33.17    (18)  all_58_15 = all_14_2
% 200.36/33.17    (19)  all_58_8 = all_10_2
% 200.36/33.17    (20)  all_56_12 = all_52_7
% 200.36/33.17    (21)  all_58_5 = all_4_0
% 200.36/33.17    (22)  op(e3, e3) = all_6_2
% 200.36/33.17    (23)   ~ (all_52_17 = e3)
% 200.36/33.17    (24)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.17    (25)   ~ (e3 = e2)
% 200.36/33.17    (26)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17    (27)   ~ (all_6_1 = e2)
% 200.36/33.17    (28)   ~ (all_52_7 = all_52_23)
% 200.36/33.17    (29)  all_56_13 = all_52_15
% 200.36/33.17    (30)  op(all_6_2, e3) = all_6_1
% 200.36/33.17    (31)  all_58_4 = all_52_17
% 200.36/33.17    (32)   ~ (all_14_2 = e3)
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | BETA: splitting (13) gives:
% 200.36/33.17  | 
% 200.36/33.17  | Case 1:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (33)  all_56_13 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (1), (2), (3), (7), (12), (14), (15), (19), (21), (23), (26),
% 200.36/33.17  | |            (29), (31), (33) are inconsistent by sub-proof #165.
% 200.36/33.17  | | 
% 200.36/33.17  | Case 2:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (34)   ~ (all_56_13 = e3)
% 200.36/33.17  | | 
% 200.36/33.17  | | REDUCE: (29), (34) imply:
% 200.36/33.17  | |   (35)   ~ (all_52_15 = e3)
% 200.36/33.17  | | 
% 200.36/33.17  | | BETA: splitting (24) gives:
% 200.36/33.17  | | 
% 200.36/33.17  | | Case 1:
% 200.36/33.17  | | | 
% 200.36/33.17  | | |   (36)  all_58_12 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REF_CLOSE: (6), (11), (16), (25), (36) are inconsistent by sub-proof #889.
% 200.36/33.17  | | | 
% 200.36/33.17  | | Case 2:
% 200.36/33.17  | | | 
% 200.36/33.17  | | |   (37)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.17  | | | 
% 200.36/33.17  | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (17), (18), (20), (22),
% 200.36/33.17  | | |            (27), (28), (30), (32), (35), (37) are inconsistent by
% 200.36/33.17  | | |            sub-proof #1045.
% 200.36/33.17  | | | 
% 200.36/33.17  | | End of split
% 200.36/33.17  | | 
% 200.36/33.17  | End of split
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #165 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.17    (2)  all_58_14 = all_52_23
% 200.36/33.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (4)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (5)  all_56_13 = e3
% 200.36/33.17    (6)   ~ (all_4_0 = e3)
% 200.36/33.17    (7)  op(all_10_2, e1) = e3
% 200.36/33.17    (8)  op(e3, e1) = all_52_17
% 200.36/33.17    (9)  all_58_8 = all_10_2
% 200.36/33.17    (10)  all_58_5 = all_4_0
% 200.36/33.17    (11)   ~ (all_52_17 = e3)
% 200.36/33.17    (12)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17    (13)  all_56_13 = all_52_15
% 200.36/33.17    (14)  all_58_4 = all_52_17
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | COMBINE_EQS: (5), (13) imply:
% 200.36/33.17  |   (15)  all_52_15 = e3
% 200.36/33.17  | 
% 200.36/33.17  | SIMP: (15) implies:
% 200.36/33.17  |   (16)  all_52_15 = e3
% 200.36/33.17  | 
% 200.36/33.17  | REDUCE: (1), (16) imply:
% 200.36/33.17  |   (17)   ~ (all_52_23 = e3)
% 200.36/33.17  | 
% 200.36/33.17  | SIMP: (17) implies:
% 200.36/33.17  |   (18)   ~ (all_52_23 = e3)
% 200.36/33.17  | 
% 200.36/33.17  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14), (18) are
% 200.36/33.17  |            inconsistent by sub-proof #166.
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #166 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)  all_58_14 = all_52_23
% 200.36/33.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (4)   ~ (all_4_0 = e3)
% 200.36/33.17    (5)  op(all_10_2, e1) = e3
% 200.36/33.17    (6)   ~ (all_52_23 = e3)
% 200.36/33.17    (7)  op(e3, e1) = all_52_17
% 200.36/33.17    (8)  all_58_8 = all_10_2
% 200.36/33.17    (9)  all_58_5 = all_4_0
% 200.36/33.17    (10)   ~ (all_52_17 = e3)
% 200.36/33.17    (11)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17    (12)  all_58_4 = all_52_17
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | BETA: splitting (11) gives:
% 200.36/33.17  | 
% 200.36/33.17  | Case 1:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (13)  all_58_4 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | COMBINE_EQS: (12), (13) imply:
% 200.36/33.17  | |   (14)  all_52_17 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REDUCE: (10), (14) imply:
% 200.36/33.17  | |   (15)  $false
% 200.36/33.17  | | 
% 200.36/33.17  | | CLOSE: (15) is inconsistent.
% 200.36/33.17  | | 
% 200.36/33.17  | Case 2:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (16)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (16) are
% 200.36/33.17  | |            inconsistent by sub-proof #167.
% 200.36/33.17  | | 
% 200.36/33.17  | End of split
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #167 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)  all_58_14 = all_52_23
% 200.36/33.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (4)   ~ (all_4_0 = e3)
% 200.36/33.17    (5)  op(all_10_2, e1) = e3
% 200.36/33.17    (6)   ~ (all_52_23 = e3)
% 200.36/33.17    (7)  op(e3, e1) = all_52_17
% 200.36/33.17    (8)  all_58_8 = all_10_2
% 200.36/33.17    (9)  all_58_5 = all_4_0
% 200.36/33.17    (10)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | BETA: splitting (10) gives:
% 200.36/33.17  | 
% 200.36/33.17  | Case 1:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (11)  all_58_5 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | COMBINE_EQS: (9), (11) imply:
% 200.36/33.17  | |   (12)  all_4_0 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REDUCE: (4), (12) imply:
% 200.36/33.17  | |   (13)  $false
% 200.36/33.17  | | 
% 200.36/33.17  | | CLOSE: (13) is inconsistent.
% 200.36/33.17  | | 
% 200.36/33.17  | Case 2:
% 200.36/33.17  | | 
% 200.36/33.17  | |   (14)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.17  | | 
% 200.36/33.17  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (14) are inconsistent by
% 200.36/33.17  | |            sub-proof #899.
% 200.36/33.17  | | 
% 200.36/33.17  | End of split
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #168 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (2)  all_58_0 = all_6_2
% 200.36/33.17    (3)  op(e3, all_6_1) = all_6_0
% 200.36/33.17    (4)   ~ (all_6_0 = e2)
% 200.36/33.17    (5)  op(e2, e3) = e3
% 200.36/33.17    (6)  all_58_0 = e2
% 200.36/33.17    (7)  op(e3, e3) = all_6_2
% 200.36/33.17    (8)  op(all_6_2, e3) = all_6_1
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | COMBINE_EQS: (2), (6) imply:
% 200.36/33.17  |   (9)  all_6_2 = e2
% 200.36/33.17  | 
% 200.36/33.17  | REDUCE: (8), (9) imply:
% 200.36/33.17  |   (10)  op(e2, e3) = all_6_1
% 200.36/33.17  | 
% 200.36/33.17  | REDUCE: (7), (9) imply:
% 200.36/33.17  |   (11)  op(e3, e3) = e2
% 200.36/33.17  | 
% 200.36/33.17  | REF_CLOSE: (1), (3), (4), (5), (10), (11) are inconsistent by sub-proof #169.
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #169 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (2)  op(e3, e3) = e2
% 200.36/33.17    (3)  op(e3, all_6_1) = all_6_0
% 200.36/33.17    (4)  op(e2, e3) = all_6_1
% 200.36/33.17    (5)   ~ (all_6_0 = e2)
% 200.36/33.17    (6)  op(e2, e3) = e3
% 200.36/33.17  
% 200.36/33.17  Begin of proof
% 200.36/33.17  | 
% 200.36/33.17  | GROUND_INST: instantiating (1) with e3, all_6_1, e3, e2, simplifying with (4),
% 200.36/33.17  |              (6) gives:
% 200.36/33.17  |   (7)  all_6_1 = e3
% 200.36/33.17  | 
% 200.36/33.17  | REDUCE: (3), (7) imply:
% 200.36/33.17  |   (8)  op(e3, e3) = all_6_0
% 200.36/33.17  | 
% 200.36/33.17  | GROUND_INST: instantiating (1) with e2, all_6_0, e3, e3, simplifying with (2),
% 200.36/33.17  |              (8) gives:
% 200.36/33.17  |   (9)  all_6_0 = e2
% 200.36/33.17  | 
% 200.36/33.17  | REDUCE: (5), (9) imply:
% 200.36/33.17  |   (10)  $false
% 200.36/33.17  | 
% 200.36/33.17  | CLOSE: (10) is inconsistent.
% 200.36/33.17  | 
% 200.36/33.17  End of proof
% 200.36/33.17  
% 200.36/33.17  Sub-proof #170 shows that the following formulas are inconsistent:
% 200.36/33.17  ----------------------------------------------------------------
% 200.36/33.17    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.17    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.17    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.17    (4)  all_58_14 = all_52_23
% 200.36/33.17    (5)   ~ (e3 = e1)
% 200.36/33.17    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.17    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.17    (8)  all_58_1 = all_52_9
% 200.36/33.17    (9)   ~ (all_52_9 = all_52_13)
% 200.36/33.17    (10)   ~ (e3 = e0)
% 200.36/33.17    (11)  op(e2, e3) = all_52_3
% 200.36/33.17    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.17    (13)   ~ (all_52_7 = all_52_15)
% 200.36/33.17    (14)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.17    (15)   ~ (all_52_17 = all_52_25)
% 200.36/33.17    (16)   ~ (all_52_3 = all_6_2)
% 200.36/33.17    (17)  all_58_0 = all_6_2
% 200.36/33.17    (18)  all_56_4 = all_52_3
% 200.36/33.17    (19)   ~ (all_52_17 = all_10_2)
% 200.36/33.17    (20)   ~ (all_10_0 = e3)
% 200.36/33.17    (21)  all_40_2 = all_10_2
% 200.36/33.17    (22)  op(e3, e0) = all_52_25
% 200.36/33.17    (23)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.17    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.17    (25)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.17    (26)   ~ (all_52_27 = all_52_29)
% 200.36/33.17    (27)  all_58_13 = all_52_15
% 200.36/33.17    (28)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.17    (29)  all_58_9 = all_52_25
% 200.36/33.17    (30)   ~ (all_6_1 = e1)
% 200.36/33.17    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.36/33.17    (32)   ~ (all_52_29 = all_14_2)
% 200.36/33.17    (33)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.17    (34)  op(e1, e3) = all_52_5
% 200.36/33.17    (35)  op(e2, e2) = all_4_2
% 200.36/33.17    (36)  all_58_7 = all_10_0
% 200.36/33.17    (37)   ~ (all_52_3 = all_52_5)
% 200.36/33.17    (38)  op(all_4_2, e2) = e1
% 200.36/33.17    (39)  all_58_11 = all_52_29
% 200.36/33.17    (40)  all_56_5 = all_4_2
% 200.36/33.17    (41)   ~ (all_52_25 = all_14_2)
% 200.36/33.17    (42)   ~ (all_52_9 = all_52_15)
% 200.36/33.17    (43)   ~ (all_52_3 = all_52_27)
% 200.36/33.17    (44)  op(all_10_2, e1) = all_10_1
% 200.36/33.17    (45)   ~ (all_10_2 = all_4_0)
% 200.36/33.17    (46)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.17    (47)   ~ (all_52_7 = all_6_2)
% 200.36/33.17    (48)  op(e0, e0) = all_14_2
% 200.36/33.17    (49)  all_56_15 = all_14_2
% 200.36/33.17    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.17    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.17    (52)  all_56_11 = all_52_29
% 200.36/33.17    (53)   ~ (all_10_0 = e2)
% 200.36/33.17    (54)   ~ (all_4_0 = e3)
% 200.36/33.17    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.18    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.18    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.18    (58)   ~ (e2 = e1)
% 200.36/33.18    (59)   ~ (all_6_0 = e1)
% 200.36/33.18    (60)  all_58_10 = all_52_27
% 200.36/33.18    (61)  all_56_8 = all_52_5
% 200.36/33.18    (62)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.18    (63)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.18    (64)   ~ (all_52_19 = all_52_23)
% 200.36/33.18    (65)  all_56_9 = all_10_0
% 200.36/33.18    (66)   ~ (all_52_25 = all_52_29)
% 200.36/33.18    (67)   ~ (all_52_29 = all_10_2)
% 200.36/33.18    (68)  all_58_7 = all_52_13
% 200.36/33.18    (69)   ~ (all_10_0 = all_4_2)
% 200.36/33.18    (70)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.18    (71)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.18    (72)   ~ (all_52_5 = all_52_7)
% 200.36/33.18    (73)  all_58_12 = all_52_7
% 200.36/33.18    (74)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.18    (75)   ~ (all_52_7 = all_14_2)
% 200.36/33.18    (76)   ~ (all_14_2 = e0)
% 200.36/33.18    (77)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.18    (78)  all_58_2 = all_52_3
% 200.36/33.18    (79)  all_56_2 = all_52_17
% 200.36/33.18    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.18    (81)  op(e3, all_6_1) = all_6_0
% 200.36/33.18    (82)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.18    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.18    (84)  all_56_7 = all_52_27
% 200.36/33.18    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.18    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.18    (87)   ~ (all_52_5 = all_52_29)
% 200.36/33.18    (88)   ~ (all_52_15 = all_14_2)
% 200.36/33.18    (89)   ~ (all_52_19 = all_52_27)
% 200.36/33.18    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.18    (91)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.18    (92)   ~ (all_6_0 = e2)
% 200.36/33.18    (93)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.18    (94)   ~ (all_52_13 = all_4_2)
% 200.36/33.18    (95)  op(e3, e1) = all_52_17
% 200.36/33.18    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.18    (97)  op(e0, e3) = all_52_7
% 200.36/33.18    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.18    (99)   ~ (all_52_9 = all_52_25)
% 200.36/33.18    (100)  all_58_15 = all_14_2
% 200.36/33.18    (101)   ~ (all_52_19 = all_10_2)
% 200.36/33.18    (102)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.18    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.18    (104)  all_58_8 = all_10_2
% 200.36/33.18    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.18    (106)   ~ (all_52_5 = all_10_2)
% 200.36/33.18    (107)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.18    (108)   ~ (all_52_23 = all_14_2)
% 200.36/33.18    (109)  all_56_12 = all_52_7
% 200.36/33.18    (110)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.18    (111)  all_58_5 = all_4_0
% 200.36/33.18    (112)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.18    (113)   ~ (all_52_25 = all_6_2)
% 200.36/33.18    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.18    (115)   ~ (all_52_9 = all_4_2)
% 200.36/33.18    (116)   ~ (all_52_5 = all_6_2)
% 200.36/33.18    (117)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.18    (118)   ~ (all_52_9 = all_6_2)
% 200.36/33.18    (119)   ~ (all_52_13 = all_52_15)
% 200.36/33.18    (120)  all_56_0 = all_6_2
% 200.36/33.18    (121)  op(e3, e3) = all_6_2
% 200.36/33.18    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.18    (123)   ~ (all_52_27 = all_14_2)
% 200.36/33.18    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.18    (125)  all_56_14 = all_52_23
% 200.36/33.18    (126)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.18    (127)  all_40_0 = all_10_0
% 200.36/33.18    (128)  all_56_3 = all_52_25
% 200.36/33.18    (129)   ~ (all_52_3 = all_52_7)
% 200.36/33.18    (130)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.18    (131)  all_58_5 = all_52_19
% 200.36/33.18    (132)  all_56_1 = all_52_9
% 200.36/33.18    (133)   ~ (all_52_15 = all_4_2)
% 200.36/33.18    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.18           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.18           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.18           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.18    (135)   ~ (all_52_27 = all_4_2)
% 200.36/33.18    (136)  all_58_6 = all_52_5
% 200.36/33.18    (137)  op(all_10_2, e1) = e2
% 200.36/33.18    (138)   ~ (all_4_0 = all_4_2)
% 200.36/33.18    (139)  op(e3, e2) = all_52_9
% 200.36/33.18    (140)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.18    (141)   ~ (all_52_17 = all_6_2)
% 200.36/33.18    (142)   ~ (e3 = e2)
% 200.36/33.18    (143)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.18    (144)   ~ (all_52_9 = all_52_17)
% 200.36/33.18    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.18    (146)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.18    (147)   ~ (all_52_3 = all_4_0)
% 200.36/33.18    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.18    (149)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.18    (150)   ~ (all_6_1 = e2)
% 200.36/33.18    (151)  op(e1, e1) = all_10_2
% 200.36/33.18    (152)   ~ (all_52_7 = all_52_23)
% 200.36/33.18    (153)   ~ (all_52_17 = all_52_19)
% 200.36/33.18    (154)   ~ (all_52_5 = all_10_0)
% 200.36/33.18    (155)  all_58_3 = all_4_2
% 200.36/33.18    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.18    (157)  all_56_13 = all_52_15
% 200.36/33.18    (158)   ~ (all_52_3 = all_4_2)
% 200.36/33.18    (159)   ~ (all_52_9 = all_10_0)
% 200.36/33.18    (160)   ~ (all_52_19 = all_4_2)
% 200.36/33.18    (161)   ~ (all_52_17 = all_52_23)
% 200.36/33.18    (162)  op(all_6_2, e3) = all_6_1
% 200.36/33.18    (163)  all_58_4 = all_52_17
% 200.36/33.18    (164)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.18  
% 200.36/33.18  Begin of proof
% 200.36/33.18  | 
% 200.36/33.18  | BETA: splitting (146) gives:
% 200.36/33.18  | 
% 200.36/33.18  | Case 1:
% 200.36/33.18  | | 
% 200.36/33.18  | |   (165)  all_56_9 = e3
% 200.36/33.18  | | 
% 200.36/33.18  | | REF_CLOSE: (20), (65), (165) are inconsistent by sub-proof #1006.
% 200.36/33.18  | | 
% 200.36/33.18  | Case 2:
% 200.36/33.18  | | 
% 200.36/33.18  | |   (166)   ~ (all_56_9 = e3)
% 200.36/33.18  | |   (167)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.18  | | 
% 200.36/33.18  | | BETA: splitting (134) gives:
% 200.36/33.18  | | 
% 200.36/33.18  | | Case 1:
% 200.36/33.18  | | | 
% 200.36/33.18  | | |   (168)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.18  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.36/33.18  | | |            e0)
% 200.36/33.18  | | | 
% 200.36/33.18  | | | BETA: splitting (168) gives:
% 200.36/33.18  | | | 
% 200.36/33.18  | | | Case 1:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | |   (169)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | REF_CLOSE: (1), (4), (6), (7), (8), (12), (13), (14), (16), (17), (19),
% 200.36/33.18  | | | |            (20), (21), (23), (24), (26), (27), (28), (29), (31), (33),
% 200.36/33.18  | | | |            (35), (36), (38), (39), (41), (45), (46), (47), (48), (49),
% 200.36/33.18  | | | |            (50), (53), (54), (58), (60), (61), (65), (69), (73), (74),
% 200.36/33.18  | | | |            (75), (76), (77), (78), (80), (84), (87), (88), (95), (99),
% 200.36/33.18  | | | |            (103), (104), (105), (106), (108), (109), (110), (111),
% 200.36/33.18  | | | |            (116), (118), (121), (123), (124), (126), (127), (130),
% 200.36/33.18  | | | |            (132), (136), (137), (139), (140), (141), (142), (143),
% 200.36/33.18  | | | |            (144), (145), (151), (154), (155), (156), (158), (159),
% 200.36/33.18  | | | |            (163), (167), (169) are inconsistent by sub-proof #171.
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | Case 2:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | |   (170)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 200.36/33.18  | | | |          e0
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | REF_CLOSE: (7), (8), (10), (12), (13), (20), (24), (27), (30), (35),
% 200.36/33.18  | | | |            (36), (38), (47), (50), (53), (54), (60), (62), (63), (78),
% 200.36/33.18  | | | |            (84), (97), (98), (109), (111), (118), (121), (126), (135),
% 200.36/33.18  | | | |            (139), (142), (150), (155), (156), (158), (162), (170) are
% 200.36/33.18  | | | |            inconsistent by sub-proof #182.
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | End of split
% 200.36/33.18  | | | 
% 200.36/33.18  | | Case 2:
% 200.36/33.18  | | | 
% 200.36/33.18  | | |   (171)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.18  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 200.36/33.18  | | |            all_52_30 = e0)
% 200.36/33.18  | | | 
% 200.36/33.18  | | | BETA: splitting (171) gives:
% 200.36/33.18  | | | 
% 200.36/33.18  | | | Case 1:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | |   (172)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 200.36/33.18  | | | |          e0
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | REF_CLOSE: (3), (4), (6), (7), (8), (12), (16), (17), (20), (21), (24),
% 200.36/33.18  | | | |            (26), (27), (28), (29), (30), (33), (35), (36), (37), (38),
% 200.36/33.18  | | | |            (39), (42), (47), (49), (50), (53), (54), (60), (65), (66),
% 200.36/33.18  | | | |            (72), (73), (74), (77), (78), (84), (95), (97), (100), (102),
% 200.36/33.18  | | | |            (104), (105), (108), (109), (110), (111), (116), (117),
% 200.36/33.18  | | | |            (118), (121), (122), (123), (124), (126), (127), (129),
% 200.36/33.18  | | | |            (133), (135), (136), (137), (138), (139), (140), (141),
% 200.36/33.18  | | | |            (145), (147), (150), (152), (155), (158), (159), (162),
% 200.36/33.18  | | | |            (163), (167), (172) are inconsistent by sub-proof #173.
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | Case 2:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | |   (173)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.36/33.18  | | | |          e0
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 200.36/33.18  | | | |            (14), (15), (16), (17), (18), (19), (22), (23), (25), (26),
% 200.36/33.18  | | | |            (27), (29), (30), (32), (33), (34), (35), (37), (39), (40),
% 200.36/33.18  | | | |            (41), (42), (43), (44), (46), (47), (48), (49), (50), (51),
% 200.36/33.18  | | | |            (52), (55), (56), (57), (59), (60), (61), (62), (63), (64),
% 200.36/33.18  | | | |            (66), (67), (68), (70), (71), (72), (73), (74), (75), (76),
% 200.36/33.18  | | | |            (78), (79), (80), (81), (82), (83), (85), (86), (87), (88),
% 200.36/33.18  | | | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 200.36/33.18  | | | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 200.36/33.18  | | | |            (108), (109), (110), (112), (113), (114), (115), (116),
% 200.36/33.18  | | | |            (118), (119), (120), (121), (122), (123), (124), (125),
% 200.36/33.18  | | | |            (128), (129), (130), (131), (132), (133), (135), (136),
% 200.36/33.18  | | | |            (140), (141), (142), (143), (148), (149), (150), (151),
% 200.36/33.18  | | | |            (152), (153), (155), (156), (157), (158), (160), (161),
% 200.36/33.18  | | | |            (162), (163), (164), (173) are inconsistent by sub-proof
% 200.36/33.18  | | | |            #1008.
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | End of split
% 200.36/33.18  | | | 
% 200.36/33.18  | | End of split
% 200.36/33.18  | | 
% 200.36/33.18  | End of split
% 200.36/33.18  | 
% 200.36/33.18  End of proof
% 200.36/33.18  
% 200.36/33.18  Sub-proof #171 shows that the following formulas are inconsistent:
% 200.36/33.18  ----------------------------------------------------------------
% 200.36/33.18    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.18    (2)  all_58_14 = all_52_23
% 200.36/33.18    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.18    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.18    (5)  all_58_1 = all_52_9
% 200.36/33.18    (6)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.18    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.18    (8)   ~ (all_52_7 = all_52_15)
% 200.36/33.18    (9)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.18    (10)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.18    (11)   ~ (all_52_3 = all_6_2)
% 200.36/33.18    (12)  all_58_0 = all_6_2
% 200.36/33.18    (13)   ~ (all_52_17 = all_10_2)
% 200.36/33.18    (14)   ~ (all_10_0 = e3)
% 200.36/33.18    (15)  all_40_2 = all_10_2
% 200.36/33.18    (16)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.18    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.18    (18)   ~ (all_52_27 = all_52_29)
% 200.36/33.18    (19)  all_58_13 = all_52_15
% 200.36/33.18    (20)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.18    (21)  all_58_9 = all_52_25
% 200.36/33.18    (22)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.36/33.18    (23)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.18    (24)  op(e2, e2) = all_4_2
% 200.36/33.18    (25)  all_58_7 = all_10_0
% 200.36/33.18    (26)  op(all_4_2, e2) = e1
% 200.36/33.18    (27)  all_58_11 = all_52_29
% 200.36/33.18    (28)   ~ (all_52_25 = all_14_2)
% 200.36/33.18    (29)   ~ (all_10_2 = all_4_0)
% 200.36/33.18    (30)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.18    (31)   ~ (all_52_7 = all_6_2)
% 200.36/33.18    (32)  op(e0, e0) = all_14_2
% 200.36/33.18    (33)  all_56_15 = all_14_2
% 200.36/33.18    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.18    (35)   ~ (all_10_0 = e2)
% 200.36/33.18    (36)   ~ (all_4_0 = e3)
% 200.36/33.18    (37)   ~ (e2 = e1)
% 200.36/33.18    (38)  all_58_10 = all_52_27
% 200.36/33.18    (39)  all_56_8 = all_52_5
% 200.36/33.18    (40)  all_56_9 = all_10_0
% 200.36/33.18    (41)   ~ (all_10_0 = all_4_2)
% 200.36/33.18    (42)  all_58_12 = all_52_7
% 200.36/33.18    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.18    (44)   ~ (all_52_7 = all_14_2)
% 200.36/33.18    (45)   ~ (all_14_2 = e0)
% 200.36/33.18    (46)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.18    (47)  all_58_2 = all_52_3
% 200.36/33.18    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.18    (49)  all_56_7 = all_52_27
% 200.36/33.18    (50)   ~ (all_52_5 = all_52_29)
% 200.36/33.18    (51)   ~ (all_52_15 = all_14_2)
% 200.36/33.18    (52)  op(e3, e1) = all_52_17
% 200.36/33.18    (53)   ~ (all_52_9 = all_52_25)
% 200.36/33.18    (54)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.18    (55)  all_58_8 = all_10_2
% 200.36/33.18    (56)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.18    (57)   ~ (all_52_5 = all_10_2)
% 200.36/33.18    (58)   ~ (all_52_23 = all_14_2)
% 200.36/33.18    (59)  all_56_12 = all_52_7
% 200.36/33.18    (60)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.18    (61)  all_58_5 = all_4_0
% 200.36/33.18    (62)   ~ (all_52_5 = all_6_2)
% 200.36/33.18    (63)   ~ (all_52_9 = all_6_2)
% 200.36/33.18    (64)  op(e3, e3) = all_6_2
% 200.36/33.18    (65)   ~ (all_52_27 = all_14_2)
% 200.36/33.18    (66)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.18    (67)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.18    (68)  all_40_0 = all_10_0
% 200.36/33.18    (69)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.18    (70)  all_56_1 = all_52_9
% 200.36/33.18    (71)  all_58_6 = all_52_5
% 200.36/33.18    (72)  op(all_10_2, e1) = e2
% 200.36/33.18    (73)  op(e3, e2) = all_52_9
% 200.36/33.18    (74)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.18    (75)   ~ (all_52_17 = all_6_2)
% 200.36/33.18    (76)   ~ (e3 = e2)
% 200.36/33.18    (77)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.18    (78)   ~ (all_52_9 = all_52_17)
% 200.36/33.18    (79)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.18    (80)  op(e1, e1) = all_10_2
% 200.36/33.18    (81)   ~ (all_52_5 = all_10_0)
% 200.36/33.18    (82)  all_58_3 = all_4_2
% 200.36/33.18    (83)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.18    (84)   ~ (all_52_3 = all_4_2)
% 200.36/33.18    (85)   ~ (all_52_9 = all_10_0)
% 200.36/33.18    (86)  all_58_4 = all_52_17
% 200.36/33.18  
% 200.36/33.18  Begin of proof
% 200.36/33.18  | 
% 200.36/33.18  | ALPHA: (6) implies:
% 200.36/33.18  |   (87)  all_52_6 = e0
% 200.36/33.18  |   (88)  all_52_4 = e1
% 200.36/33.18  |   (89)  all_52_2 = e2
% 200.36/33.18  |   (90)  all_52_0 = e3
% 200.36/33.18  | 
% 200.36/33.18  | REDUCE: (3), (89) imply:
% 200.36/33.18  |   (91)  op(all_52_3, all_52_3) = e2
% 200.36/33.18  | 
% 200.36/33.18  | REDUCE: (16), (88) imply:
% 200.36/33.18  |   (92)  op(all_52_5, all_52_5) = e1
% 200.36/33.18  | 
% 200.36/33.18  | REDUCE: (9), (87) imply:
% 200.36/33.18  |   (93)  op(all_52_7, all_52_7) = e0
% 200.36/33.18  | 
% 200.36/33.18  | REDUCE: (30), (90) imply:
% 200.36/33.18  |   (94)  op(all_6_2, all_6_2) = e3
% 200.36/33.18  | 
% 200.36/33.18  | BETA: splitting (56) gives:
% 200.36/33.18  | 
% 200.36/33.18  | Case 1:
% 200.36/33.18  | | 
% 200.36/33.18  | |   (95)  all_56_15 = e3
% 200.36/33.18  | | 
% 200.36/33.18  | | COMBINE_EQS: (33), (95) imply:
% 200.36/33.18  | |   (96)  all_14_2 = e3
% 200.36/33.18  | | 
% 200.36/33.18  | | SIMP: (96) implies:
% 200.36/33.18  | |   (97)  all_14_2 = e3
% 200.36/33.18  | | 
% 200.36/33.18  | | REDUCE: (58), (97) imply:
% 200.36/33.18  | |   (98)   ~ (all_52_23 = e3)
% 200.36/33.18  | | 
% 200.36/33.18  | | REDUCE: (28), (97) imply:
% 200.36/33.18  | |   (99)   ~ (all_52_25 = e3)
% 200.36/33.18  | | 
% 200.36/33.18  | | REDUCE: (65), (97) imply:
% 200.36/33.18  | |   (100)   ~ (all_52_27 = e3)
% 200.36/33.18  | | 
% 200.36/33.18  | | REDUCE: (69), (97) imply:
% 200.36/33.18  | |   (101)  op(e3, e3) = all_52_30
% 200.36/33.18  | | 
% 200.36/33.18  | | GROUND_INST: instantiating (4) with all_6_2, all_52_30, e3, e3, simplifying
% 200.36/33.18  | |              with (64), (101) gives:
% 200.36/33.18  | |   (102)  all_52_30 = all_6_2
% 200.36/33.18  | | 
% 200.36/33.18  | | BETA: splitting (79) gives:
% 200.36/33.18  | | 
% 200.36/33.18  | | Case 1:
% 200.36/33.18  | | | 
% 200.36/33.18  | | |   (103)  all_58_4 = e3
% 200.36/33.18  | | | 
% 200.36/33.18  | | | REF_CLOSE: (4), (12), (24), (32), (34), (42), (44), (47), (48), (57),
% 200.36/33.18  | | |            (64), (71), (74), (75), (80), (84), (86), (91), (92), (93),
% 200.36/33.18  | | |            (94), (103) are inconsistent by sub-proof #591.
% 200.36/33.18  | | | 
% 200.36/33.18  | | Case 2:
% 200.36/33.18  | | | 
% 200.36/33.18  | | |   (104)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.18  | | | 
% 200.36/33.18  | | | BETA: splitting (104) gives:
% 200.36/33.18  | | | 
% 200.36/33.18  | | | Case 1:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | |   (105)  all_58_5 = e3
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | REF_CLOSE: (36), (61), (105) are inconsistent by sub-proof #215.
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | Case 2:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | |   (106)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | BETA: splitting (106) gives:
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | | Case 1:
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | |   (107)  all_58_8 = e3
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | COMBINE_EQS: (55), (107) imply:
% 200.36/33.18  | | | | |   (108)  all_10_2 = e3
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | SIMP: (108) implies:
% 200.36/33.18  | | | | |   (109)  all_10_2 = e3
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | COMBINE_EQS: (15), (109) imply:
% 200.36/33.18  | | | | |   (110)  all_40_2 = e3
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | REDUCE: (13), (109) imply:
% 200.36/33.18  | | | | |   (111)   ~ (all_52_17 = e3)
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | REDUCE: (29), (109) imply:
% 200.36/33.18  | | | | |   (112)   ~ (all_4_0 = e3)
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | REDUCE: (20), (109) imply:
% 200.36/33.18  | | | | |   (113)  op(e3, e3) = all_52_20
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | REDUCE: (72), (109) imply:
% 200.36/33.18  | | | | |   (114)  op(e3, e1) = e2
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | BETA: splitting (46) gives:
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | Case 1:
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | |   (115)   ~ (all_40_2 = e3)
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | | REDUCE: (110), (115) imply:
% 200.36/33.18  | | | | | |   (116)  $false
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | | CLOSE: (116) is inconsistent.
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | Case 2:
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | |   (117)   ~ (all_40_0 = e0)
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | | REDUCE: (68), (117) imply:
% 200.36/33.18  | | | | | |   (118)   ~ (all_10_0 = e0)
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | | BETA: splitting (10) gives:
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | | Case 1:
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | |   (119)  all_56_9 = e2
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | | REF_CLOSE: (35), (40), (119) are inconsistent by sub-proof #991.
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | Case 2:
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | |   (120)  all_56_9 = e1 | all_56_9 = e0
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | | BETA: splitting (120) gives:
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | | Case 1:
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | |   (121)  all_56_9 = e1
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | COMBINE_EQS: (40), (121) imply:
% 200.36/33.18  | | | | | | | |   (122)  all_10_0 = e1
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | SIMP: (122) implies:
% 200.36/33.18  | | | | | | | |   (123)  all_10_0 = e1
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | REDUCE: (85), (123) imply:
% 200.36/33.18  | | | | | | | |   (124)   ~ (all_52_9 = e1)
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | GROUND_INST: instantiating (4) with all_52_17, e2, e1, e3,
% 200.36/33.18  | | | | | | | |              simplifying with (52), (114) gives:
% 200.36/33.18  | | | | | | | |   (125)  all_52_17 = e2
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_20, e3, e3,
% 200.36/33.18  | | | | | | | |              simplifying with (64), (113) gives:
% 200.36/33.18  | | | | | | | |   (126)  all_52_20 = all_6_2
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | REDUCE: (60), (125) imply:
% 200.36/33.18  | | | | | | | |   (127)  op(e2, e2) = all_52_16
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_16, e2, e2,
% 200.36/33.18  | | | | | | | |              simplifying with (24), (127) gives:
% 200.36/33.18  | | | | | | | |   (128)  all_52_16 = all_4_2
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | BETA: splitting (77) gives:
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | Case 1:
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | |   (129)  all_56_1 = e3
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | REF_CLOSE: (4), (12), (24), (32), (34), (42), (44), (47),
% 200.36/33.18  | | | | | | | | |            (48), (57), (63), (64), (70), (71), (74), (80),
% 200.36/33.18  | | | | | | | | |            (84), (91), (92), (93), (94), (129) are
% 200.36/33.18  | | | | | | | | |            inconsistent by sub-proof #527.
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | Case 2:
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | |   (130)   ~ (all_56_1 = e3)
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | REDUCE: (70), (130) imply:
% 200.36/33.18  | | | | | | | | |   (131)   ~ (all_52_9 = e3)
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | BETA: splitting (66) gives:
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | Case 1:
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | |   (132)  all_58_0 = e3
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | COMBINE_EQS: (12), (132) imply:
% 200.36/33.18  | | | | | | | | | |   (133)  all_6_2 = e3
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | REDUCE: (11), (133) imply:
% 200.36/33.18  | | | | | | | | | |   (134)   ~ (all_52_3 = e3)
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | BETA: splitting (34) gives:
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | Case 1:
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | |   (135)  all_58_2 = e3
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | COMBINE_EQS: (47), (135) imply:
% 200.36/33.18  | | | | | | | | | | |   (136)  all_52_3 = e3
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | REDUCE: (134), (136) imply:
% 200.36/33.18  | | | | | | | | | | |   (137)  $false
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | Case 2:
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | |   (138)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | BETA: splitting (138) gives:
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | Case 1:
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | |   (139)  all_58_3 = e3
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | | COMBINE_EQS: (82), (139) imply:
% 200.36/33.18  | | | | | | | | | | | |   (140)  all_4_2 = e3
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | | REDUCE: (26), (140) imply:
% 200.36/33.18  | | | | | | | | | | | |   (141)  op(e3, e2) = e1
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | | REF_CLOSE: (4), (73), (124), (141) are inconsistent by
% 200.36/33.18  | | | | | | | | | | | |            sub-proof #309.
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | Case 2:
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | |   (142)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | | REF_CLOSE: (36), (38), (61), (100), (142) are inconsistent by
% 200.36/33.18  | | | | | | | | | | | |            sub-proof #214.
% 200.36/33.18  | | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | | End of split
% 200.36/33.18  | | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | End of split
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | Case 2:
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | |   (143)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | | REF_CLOSE: (5), (21), (86), (99), (111), (131), (143) are
% 200.36/33.18  | | | | | | | | | |            inconsistent by sub-proof #744.
% 200.36/33.18  | | | | | | | | | | 
% 200.36/33.18  | | | | | | | | | End of split
% 200.36/33.18  | | | | | | | | | 
% 200.36/33.18  | | | | | | | | End of split
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | Case 2:
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | |   (144)  all_56_9 = e0
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | | REF_CLOSE: (40), (118), (144) are inconsistent by sub-proof
% 200.36/33.18  | | | | | | | |            #989.
% 200.36/33.18  | | | | | | | | 
% 200.36/33.18  | | | | | | | End of split
% 200.36/33.18  | | | | | | | 
% 200.36/33.18  | | | | | | End of split
% 200.36/33.18  | | | | | | 
% 200.36/33.18  | | | | | End of split
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | Case 2:
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | |   (145)  all_58_14 = e3
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | | REF_CLOSE: (2), (98), (145) are inconsistent by sub-proof #1305.
% 200.36/33.18  | | | | | 
% 200.36/33.18  | | | | End of split
% 200.36/33.18  | | | | 
% 200.36/33.18  | | | End of split
% 200.36/33.18  | | | 
% 200.36/33.18  | | End of split
% 200.36/33.18  | | 
% 200.36/33.18  | Case 2:
% 200.36/33.18  | | 
% 200.36/33.18  | |   (146)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.18  | | 
% 200.36/33.18  | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (12), (14), (15), (17), (18),
% 200.36/33.18  | |            (19), (20), (21), (22), (23), (24), (25), (26), (27), (31), (32),
% 200.36/33.18  | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 200.36/33.18  | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 200.36/33.18  | |            (55), (57), (59), (60), (61), (62), (63), (64), (67), (68), (70),
% 200.36/33.18  | |            (71), (72), (73), (74), (76), (77), (78), (80), (81), (82), (83),
% 200.36/33.18  | |            (84), (85), (91), (92), (93), (94), (146) are inconsistent by
% 200.36/33.18  | |            sub-proof #172.
% 200.36/33.18  | | 
% 200.36/33.18  | End of split
% 200.36/33.18  | 
% 200.36/33.18  End of proof
% 200.36/33.18  
% 200.36/33.18  Sub-proof #172 shows that the following formulas are inconsistent:
% 200.36/33.18  ----------------------------------------------------------------
% 200.36/33.18    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.18    (3)  op(all_52_7, all_52_7) = e0
% 200.36/33.18    (4)  all_58_1 = all_52_9
% 200.36/33.18    (5)  op(all_52_5, all_52_5) = e1
% 200.36/33.18    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.19    (7)   ~ (all_52_7 = all_52_15)
% 200.36/33.19    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.19    (9)  all_58_0 = all_6_2
% 200.36/33.19    (10)   ~ (all_10_0 = e3)
% 200.36/33.19    (11)  all_40_2 = all_10_2
% 200.36/33.19    (12)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.19    (13)   ~ (all_52_27 = all_52_29)
% 200.36/33.19    (14)  all_58_13 = all_52_15
% 200.36/33.19    (15)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.19    (16)  all_58_9 = all_52_25
% 200.36/33.19    (17)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 200.36/33.19    (18)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.19    (19)  op(e2, e2) = all_4_2
% 200.36/33.19    (20)  all_58_7 = all_10_0
% 200.36/33.19    (21)  op(all_4_2, e2) = e1
% 200.36/33.19    (22)  all_58_11 = all_52_29
% 200.36/33.19    (23)   ~ (all_52_7 = all_6_2)
% 200.36/33.19    (24)  op(e0, e0) = all_14_2
% 200.36/33.19    (25)  all_56_15 = all_14_2
% 200.36/33.19    (26)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.19    (27)   ~ (all_10_0 = e2)
% 200.36/33.19    (28)   ~ (all_4_0 = e3)
% 200.36/33.19    (29)   ~ (e2 = e1)
% 200.36/33.19    (30)  all_58_10 = all_52_27
% 200.36/33.19    (31)  all_56_8 = all_52_5
% 200.36/33.19    (32)  all_56_9 = all_10_0
% 200.36/33.19    (33)   ~ (all_10_0 = all_4_2)
% 200.36/33.19    (34)  op(all_6_2, all_6_2) = e3
% 200.36/33.19    (35)  all_58_12 = all_52_7
% 200.36/33.19    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.19    (37)   ~ (all_52_7 = all_14_2)
% 200.36/33.19    (38)   ~ (all_14_2 = e0)
% 200.36/33.19    (39)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.19    (40)  all_58_2 = all_52_3
% 200.36/33.19    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.19    (42)  all_56_7 = all_52_27
% 200.36/33.19    (43)  op(all_52_3, all_52_3) = e2
% 200.36/33.19    (44)   ~ (all_52_5 = all_52_29)
% 200.36/33.19    (45)   ~ (all_52_15 = all_14_2)
% 200.36/33.19    (46)  op(e3, e1) = all_52_17
% 200.36/33.19    (47)   ~ (all_52_9 = all_52_25)
% 200.36/33.19    (48)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.19    (49)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.19    (50)  all_58_8 = all_10_2
% 200.36/33.19    (51)   ~ (all_52_5 = all_10_2)
% 200.36/33.19    (52)  all_56_12 = all_52_7
% 200.36/33.19    (53)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.19    (54)  all_58_5 = all_4_0
% 200.36/33.19    (55)   ~ (all_52_5 = all_6_2)
% 200.36/33.19    (56)   ~ (all_52_9 = all_6_2)
% 200.36/33.19    (57)  op(e3, e3) = all_6_2
% 200.36/33.19    (58)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.19    (59)  all_40_0 = all_10_0
% 200.36/33.19    (60)  all_56_1 = all_52_9
% 200.36/33.19    (61)  all_58_6 = all_52_5
% 200.36/33.19    (62)  op(all_10_2, e1) = e2
% 200.36/33.19    (63)  op(e3, e2) = all_52_9
% 200.36/33.19    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.19    (65)   ~ (e3 = e2)
% 200.36/33.19    (66)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.19    (67)   ~ (all_52_9 = all_52_17)
% 200.36/33.19    (68)  op(e1, e1) = all_10_2
% 200.36/33.19    (69)   ~ (all_52_5 = all_10_0)
% 200.36/33.19    (70)  all_58_3 = all_4_2
% 200.36/33.19    (71)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.19    (72)   ~ (all_52_3 = all_4_2)
% 200.36/33.19    (73)   ~ (all_52_9 = all_10_0)
% 200.36/33.19  
% 200.36/33.19  Begin of proof
% 200.36/33.19  | 
% 200.36/33.19  | BETA: splitting (12) gives:
% 200.36/33.19  | 
% 200.36/33.19  | Case 1:
% 200.36/33.19  | | 
% 200.36/33.19  | |   (74)  all_56_7 = e3
% 200.36/33.19  | | 
% 200.36/33.19  | | COMBINE_EQS: (42), (74) imply:
% 200.36/33.19  | |   (75)  all_52_27 = e3
% 200.36/33.19  | | 
% 200.36/33.19  | | SIMP: (75) implies:
% 200.36/33.19  | |   (76)  all_52_27 = e3
% 200.36/33.19  | | 
% 200.36/33.19  | | COMBINE_EQS: (30), (76) imply:
% 200.36/33.19  | |   (77)  all_58_10 = e3
% 200.36/33.19  | | 
% 200.36/33.19  | | REDUCE: (13), (76) imply:
% 200.36/33.19  | |   (78)   ~ (all_52_29 = e3)
% 200.36/33.19  | | 
% 200.36/33.19  | | SIMP: (78) implies:
% 200.36/33.19  | |   (79)   ~ (all_52_29 = e3)
% 200.36/33.19  | | 
% 200.36/33.19  | | REDUCE: (18), (76) imply:
% 200.36/33.19  | |   (80)  op(e3, e3) = all_52_26
% 200.36/33.19  | | 
% 200.36/33.19  | | GROUND_INST: instantiating (2) with all_6_2, all_52_26, e3, e3, simplifying
% 200.36/33.19  | |              with (57), (80) gives:
% 200.36/33.19  | |   (81)  all_52_26 = all_6_2
% 200.36/33.19  | | 
% 200.36/33.19  | | BETA: splitting (36) gives:
% 200.36/33.19  | | 
% 200.36/33.19  | | Case 1:
% 200.36/33.19  | | | 
% 200.36/33.19  | | |   (82)  all_58_6 = e3
% 200.36/33.19  | | | 
% 200.36/33.19  | | | REF_CLOSE: (2), (3), (5), (9), (19), (24), (26), (34), (35), (37), (40),
% 200.36/33.19  | | |            (41), (43), (51), (55), (57), (61), (64), (68), (72), (82) are
% 200.36/33.19  | | |            inconsistent by sub-proof #876.
% 200.36/33.19  | | | 
% 200.36/33.19  | | Case 2:
% 200.36/33.19  | | | 
% 200.36/33.19  | | |   (83)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.19  | | | 
% 200.36/33.19  | | | BETA: splitting (83) gives:
% 200.36/33.19  | | | 
% 200.36/33.19  | | | Case 1:
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | |   (84)  all_58_7 = e3
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | COMBINE_EQS: (20), (84) imply:
% 200.36/33.19  | | | |   (85)  all_10_0 = e3
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | REDUCE: (10), (85) imply:
% 200.36/33.19  | | | |   (86)  $false
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | CLOSE: (86) is inconsistent.
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | Case 2:
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | |   (87)  all_58_8 = e3 | all_58_11 = e3
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | BETA: splitting (87) gives:
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | Case 1:
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | |   (88)  all_58_8 = e3
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | COMBINE_EQS: (50), (88) imply:
% 200.36/33.19  | | | | |   (89)  all_10_2 = e3
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | SIMP: (89) implies:
% 200.36/33.19  | | | | |   (90)  all_10_2 = e3
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | COMBINE_EQS: (11), (90) imply:
% 200.36/33.19  | | | | |   (91)  all_40_2 = e3
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | REDUCE: (51), (90) imply:
% 200.36/33.19  | | | | |   (92)   ~ (all_52_5 = e3)
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | REDUCE: (15), (90) imply:
% 200.36/33.19  | | | | |   (93)  op(e3, e3) = all_52_20
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | REDUCE: (62), (90) imply:
% 200.36/33.19  | | | | |   (94)  op(e3, e1) = e2
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | BETA: splitting (39) gives:
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | Case 1:
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | |   (95)   ~ (all_40_2 = e3)
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | REDUCE: (91), (95) imply:
% 200.36/33.19  | | | | | |   (96)  $false
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | CLOSE: (96) is inconsistent.
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | Case 2:
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | |   (97)   ~ (all_40_0 = e0)
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | REDUCE: (59), (97) imply:
% 200.36/33.19  | | | | | |   (98)   ~ (all_10_0 = e0)
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | BETA: splitting (8) gives:
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | Case 1:
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | |   (99)  all_56_9 = e2
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | REF_CLOSE: (27), (32), (99) are inconsistent by sub-proof #991.
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | Case 2:
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | |   (100)  all_56_9 = e1 | all_56_9 = e0
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | BETA: splitting (100) gives:
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | |   (101)  all_56_9 = e1
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | COMBINE_EQS: (32), (101) imply:
% 200.36/33.19  | | | | | | | |   (102)  all_10_0 = e1
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | SIMP: (102) implies:
% 200.36/33.19  | | | | | | | |   (103)  all_10_0 = e1
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | REDUCE: (73), (103) imply:
% 200.36/33.19  | | | | | | | |   (104)   ~ (all_52_9 = e1)
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | REDUCE: (33), (103) imply:
% 200.36/33.19  | | | | | | | |   (105)   ~ (all_4_2 = e1)
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | SIMP: (105) implies:
% 200.36/33.19  | | | | | | | |   (106)   ~ (all_4_2 = e1)
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | GROUND_INST: instantiating (2) with all_52_17, e2, e1, e3,
% 200.36/33.19  | | | | | | | |              simplifying with (46), (94) gives:
% 200.36/33.19  | | | | | | | |   (107)  all_52_17 = e2
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_20, e3, e3,
% 200.36/33.19  | | | | | | | |              simplifying with (57), (93) gives:
% 200.36/33.19  | | | | | | | |   (108)  all_52_20 = all_6_2
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | REDUCE: (67), (107) imply:
% 200.36/33.19  | | | | | | | |   (109)   ~ (all_52_9 = e2)
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | REDUCE: (53), (107) imply:
% 200.36/33.19  | | | | | | | |   (110)  op(e2, e2) = all_52_16
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_16, e2, e2,
% 200.36/33.19  | | | | | | | |              simplifying with (19), (110) gives:
% 200.36/33.19  | | | | | | | |   (111)  all_52_16 = all_4_2
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | BETA: splitting (48) gives:
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | |   (112)  all_56_8 = e3
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | REF_CLOSE: (31), (92), (112) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | | |            #1325.
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | |   (113)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | BETA: splitting (66) gives:
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | |   (114)  all_56_1 = e3
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (19), (24), (26), (34), (35),
% 200.36/33.19  | | | | | | | | | |            (37), (40), (41), (43), (51), (56), (57), (60),
% 200.36/33.19  | | | | | | | | | |            (61), (64), (68), (72), (114) are inconsistent by
% 200.36/33.19  | | | | | | | | | |            sub-proof #527.
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | |   (115)   ~ (all_56_1 = e3)
% 200.36/33.19  | | | | | | | | | |   (116)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | REDUCE: (60), (115) imply:
% 200.36/33.19  | | | | | | | | | |   (117)   ~ (all_52_9 = e3)
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | BETA: splitting (116) gives:
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | |   (118)  all_56_1 = e2
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | REF_CLOSE: (60), (109), (118) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | | | | |            #1194.
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | |   (119)  all_56_1 = e1 | all_56_1 = e0
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | BETA: splitting (119) gives:
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | |   (120)  all_56_1 = e1
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | REF_CLOSE: (60), (104), (120) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | | | | | |            #1061.
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | |   (121)  all_56_1 = e0
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | COMBINE_EQS: (60), (121) imply:
% 200.36/33.19  | | | | | | | | | | | |   (122)  all_52_9 = e0
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | SIMP: (122) implies:
% 200.36/33.19  | | | | | | | | | | | |   (123)  all_52_9 = e0
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | REDUCE: (47), (123) imply:
% 200.36/33.19  | | | | | | | | | | | |   (124)   ~ (all_52_25 = e0)
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | SIMP: (124) implies:
% 200.36/33.19  | | | | | | | | | | | |   (125)   ~ (all_52_25 = e0)
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | REDUCE: (117), (123) imply:
% 200.36/33.19  | | | | | | | | | | | |   (126)   ~ (e3 = e0)
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | SIMP: (126) implies:
% 200.36/33.19  | | | | | | | | | | | |   (127)   ~ (e3 = e0)
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | BETA: splitting (1) gives:
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | |   (128)  all_58_9 = e0
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | REF_CLOSE: (16), (125), (128) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | | | | | | |            #523.
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | |   (129)  all_58_10 = e0 | all_58_11 = e0
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | |   (130)  all_58_10 = e0
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | REF_CLOSE: (77), (127), (130) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | | | | | | | |            #750.
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | |   (131)  all_58_11 = e0
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | COMBINE_EQS: (22), (131) imply:
% 200.36/33.19  | | | | | | | | | | | | | |   (132)  all_52_29 = e0
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | SIMP: (132) implies:
% 200.36/33.19  | | | | | | | | | | | | | |   (133)  all_52_29 = e0
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | REDUCE: (44), (133) imply:
% 200.36/33.19  | | | | | | | | | | | | | |   (134)   ~ (all_52_5 = e0)
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | |   (135)  all_58_6 = e2
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (19), (61), (106), (135) are
% 200.36/33.19  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1192.
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | |   (136)   ~ (all_58_6 = e2)
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | | REDUCE: (61), (136) imply:
% 200.36/33.19  | | | | | | | | | | | | | | |   (137)   ~ (all_52_5 = e2)
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | | REF_CLOSE: (31), (32), (69), (98), (100), (113), (134), (137)
% 200.36/33.19  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #352.
% 200.36/33.19  | | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | |   (138)  all_56_9 = e0
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | REF_CLOSE: (32), (98), (138) are inconsistent by sub-proof #989.
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | End of split
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | End of split
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | End of split
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | Case 2:
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | |   (139)  all_58_11 = e3
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | REF_CLOSE: (22), (79), (139) are inconsistent by sub-proof #1323.
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | End of split
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | End of split
% 200.36/33.19  | | | 
% 200.36/33.19  | | End of split
% 200.36/33.19  | | 
% 200.36/33.19  | Case 2:
% 200.36/33.19  | | 
% 200.36/33.19  | |   (140)   ~ (all_56_7 = e3)
% 200.36/33.19  | | 
% 200.36/33.19  | | REDUCE: (42), (140) imply:
% 200.36/33.19  | |   (141)   ~ (all_52_27 = e3)
% 200.36/33.19  | | 
% 200.36/33.19  | | BETA: splitting (26) gives:
% 200.36/33.19  | | 
% 200.36/33.19  | | Case 1:
% 200.36/33.19  | | | 
% 200.36/33.19  | | |   (142)  all_58_2 = e3
% 200.36/33.19  | | | 
% 200.36/33.19  | | | REF_CLOSE: (2), (19), (34), (40), (43), (57), (72), (142) are inconsistent
% 200.36/33.19  | | |            by sub-proof #1159.
% 200.36/33.19  | | | 
% 200.36/33.19  | | Case 2:
% 200.36/33.19  | | | 
% 200.36/33.19  | | |   (143)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.19  | | | 
% 200.36/33.19  | | | BETA: splitting (143) gives:
% 200.36/33.19  | | | 
% 200.36/33.19  | | | Case 1:
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | |   (144)  all_58_3 = e3
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | COMBINE_EQS: (70), (144) imply:
% 200.36/33.19  | | | |   (145)  all_4_2 = e3
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | REDUCE: (58), (145) imply:
% 200.36/33.19  | | | |   (146)  op(e3, e3) = all_52_10
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | REDUCE: (21), (145) imply:
% 200.36/33.19  | | | |   (147)  op(e3, e2) = e1
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | GROUND_INST: instantiating (2) with all_52_9, e1, e2, e3, simplifying
% 200.36/33.19  | | | |              with (63), (147) gives:
% 200.36/33.19  | | | |   (148)  all_52_9 = e1
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_10, e3, e3,
% 200.36/33.19  | | | |              simplifying with (57), (146) gives:
% 200.36/33.19  | | | |   (149)  all_52_10 = all_6_2
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | COMBINE_EQS: (4), (148) imply:
% 200.36/33.19  | | | |   (150)  all_58_1 = e1
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | BETA: splitting (71) gives:
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | Case 1:
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | |   (151)  all_58_1 = e2
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | REF_CLOSE: (29), (150), (151) are inconsistent by sub-proof #185.
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | Case 2:
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | |   (152)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | BETA: splitting (152) gives:
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | | Case 1:
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | |   (153)  all_58_3 = e2
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | COMBINE_EQS: (144), (153) imply:
% 200.36/33.19  | | | | | |   (154)  e3 = e2
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | REDUCE: (65), (154) imply:
% 200.36/33.19  | | | | | |   (155)  $false
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | CLOSE: (155) is inconsistent.
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | Case 2:
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | |   (156)  all_58_7 = e2 | all_58_13 = e2
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | BETA: splitting (156) gives:
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | | Case 1:
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | |   (157)  all_58_7 = e2
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | COMBINE_EQS: (20), (157) imply:
% 200.36/33.19  | | | | | | |   (158)  all_10_0 = e2
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | REDUCE: (27), (158) imply:
% 200.36/33.19  | | | | | | |   (159)  $false
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | CLOSE: (159) is inconsistent.
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | Case 2:
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | |   (160)  all_58_13 = e2
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | COMBINE_EQS: (14), (160) imply:
% 200.36/33.19  | | | | | | |   (161)  all_52_15 = e2
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | SIMP: (161) implies:
% 200.36/33.19  | | | | | | |   (162)  all_52_15 = e2
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | REDUCE: (7), (162) imply:
% 200.36/33.19  | | | | | | |   (163)   ~ (all_52_7 = e2)
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | REDUCE: (45), (162) imply:
% 200.36/33.19  | | | | | | |   (164)   ~ (all_14_2 = e2)
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | SIMP: (164) implies:
% 200.36/33.19  | | | | | | |   (165)   ~ (all_14_2 = e2)
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | BETA: splitting (49) gives:
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | |   (166)  all_56_15 = e2
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | REF_CLOSE: (25), (165), (166) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | |            #762.
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | |   (167)  all_56_15 = e1 | all_56_15 = e0
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | BETA: splitting (167) gives:
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | | Case 1:
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | |   (168)  all_56_15 = e1
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | COMBINE_EQS: (25), (168) imply:
% 200.36/33.19  | | | | | | | | |   (169)  all_14_2 = e1
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | SIMP: (169) implies:
% 200.36/33.19  | | | | | | | | |   (170)  all_14_2 = e1
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | REDUCE: (37), (170) imply:
% 200.36/33.19  | | | | | | | | |   (171)   ~ (all_52_7 = e1)
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (9), (19), (23), (24), (26),
% 200.36/33.19  | | | | | | | | |            (34), (35), (37), (40), (41), (43), (51), (52),
% 200.36/33.19  | | | | | | | | |            (57), (61), (64), (68), (72), (163), (171) are
% 200.36/33.19  | | | | | | | | |            inconsistent by sub-proof #996.
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | Case 2:
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | |   (172)  all_56_15 = e0
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | | REF_CLOSE: (25), (38), (172) are inconsistent by sub-proof
% 200.36/33.19  | | | | | | | | |            #1162.
% 200.36/33.19  | | | | | | | | | 
% 200.36/33.19  | | | | | | | | End of split
% 200.36/33.19  | | | | | | | | 
% 200.36/33.19  | | | | | | | End of split
% 200.36/33.19  | | | | | | | 
% 200.36/33.19  | | | | | | End of split
% 200.36/33.19  | | | | | | 
% 200.36/33.19  | | | | | End of split
% 200.36/33.19  | | | | | 
% 200.36/33.19  | | | | End of split
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | Case 2:
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | |   (173)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | | REF_CLOSE: (28), (30), (54), (141), (173) are inconsistent by sub-proof
% 200.36/33.19  | | | |            #214.
% 200.36/33.19  | | | | 
% 200.36/33.19  | | | End of split
% 200.36/33.19  | | | 
% 200.36/33.19  | | End of split
% 200.36/33.19  | | 
% 200.36/33.19  | End of split
% 200.36/33.19  | 
% 200.36/33.19  End of proof
% 200.36/33.19  
% 200.36/33.19  Sub-proof #173 shows that the following formulas are inconsistent:
% 200.36/33.19  ----------------------------------------------------------------
% 200.36/33.19    (1)   ~ (all_52_25 = all_52_27)
% 200.36/33.19    (2)  all_58_14 = all_52_23
% 200.36/33.19    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.19    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.19    (5)  all_58_1 = all_52_9
% 200.36/33.19    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.19    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.19    (8)   ~ (all_52_3 = all_6_2)
% 200.36/33.19    (9)  all_58_0 = all_6_2
% 200.36/33.19    (10)   ~ (all_10_0 = e3)
% 200.36/33.19    (11)  all_40_2 = all_10_2
% 200.36/33.19    (12)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.19    (13)   ~ (all_52_27 = all_52_29)
% 200.36/33.19    (14)  all_58_13 = all_52_15
% 200.36/33.19    (15)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.19    (16)  all_58_9 = all_52_25
% 200.36/33.19    (17)   ~ (all_6_1 = e1)
% 200.36/33.19    (18)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.19    (19)  op(e2, e2) = all_4_2
% 200.36/33.19    (20)  all_58_7 = all_10_0
% 200.36/33.19    (21)   ~ (all_52_3 = all_52_5)
% 200.36/33.19    (22)  op(all_4_2, e2) = e1
% 200.36/33.19    (23)  all_58_11 = all_52_29
% 200.36/33.19    (24)   ~ (all_52_9 = all_52_15)
% 200.36/33.19    (25)   ~ (all_52_7 = all_6_2)
% 200.36/33.19    (26)  all_56_15 = all_14_2
% 200.36/33.19    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.19    (28)   ~ (all_10_0 = e2)
% 200.36/33.19    (29)   ~ (all_4_0 = e3)
% 200.36/33.19    (30)  all_58_10 = all_52_27
% 200.36/33.19    (31)  all_56_9 = all_10_0
% 200.36/33.19    (32)   ~ (all_52_25 = all_52_29)
% 200.36/33.19    (33)   ~ (all_52_5 = all_52_7)
% 200.36/33.19    (34)  all_58_12 = all_52_7
% 200.36/33.19    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.19    (36)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.19    (37)  all_58_2 = all_52_3
% 200.36/33.19    (38)  all_56_7 = all_52_27
% 200.36/33.19    (39)  op(e3, e1) = all_52_17
% 200.36/33.19    (40)  op(e0, e3) = all_52_7
% 200.36/33.19    (41)  all_58_15 = all_14_2
% 200.36/33.19    (42)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.19    (43)  all_58_8 = all_10_2
% 200.36/33.19    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.19    (45)   ~ (all_52_23 = all_14_2)
% 200.36/33.19    (46)  all_56_12 = all_52_7
% 200.36/33.19    (47)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.19    (48)  all_58_5 = all_4_0
% 200.36/33.19    (49)   ~ (all_52_5 = all_6_2)
% 200.36/33.19    (50)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.19    (51)   ~ (all_52_9 = all_6_2)
% 200.36/33.19    (52)  op(e3, e3) = all_6_2
% 200.36/33.19    (53)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.19    (54)   ~ (all_52_27 = all_14_2)
% 200.36/33.19    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.19    (56)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.19    (57)  all_40_0 = all_10_0
% 200.36/33.19    (58)   ~ (all_52_3 = all_52_7)
% 200.36/33.19    (59)   ~ (all_52_15 = all_4_2)
% 200.36/33.19    (60)   ~ (all_52_27 = all_4_2)
% 200.36/33.19    (61)  all_58_6 = all_52_5
% 200.36/33.19    (62)  op(all_10_2, e1) = e2
% 200.36/33.19    (63)   ~ (all_4_0 = all_4_2)
% 200.36/33.19    (64)  op(e3, e2) = all_52_9
% 200.36/33.19    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.19    (66)   ~ (all_52_17 = all_6_2)
% 200.36/33.19    (67)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.19    (68)   ~ (all_52_3 = all_4_0)
% 200.36/33.19    (69)   ~ (all_6_1 = e2)
% 200.36/33.19    (70)   ~ (all_52_7 = all_52_23)
% 200.36/33.19    (71)  all_58_3 = all_4_2
% 200.36/33.19    (72)   ~ (all_52_3 = all_4_2)
% 200.36/33.19    (73)   ~ (all_52_9 = all_10_0)
% 200.36/33.19    (74)  op(all_6_2, e3) = all_6_1
% 200.36/33.19    (75)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 200.36/33.19    (76)  all_58_4 = all_52_17
% 200.36/33.19  
% 200.36/33.19  Begin of proof
% 200.36/33.19  | 
% 200.36/33.19  | ALPHA: (75) implies:
% 200.36/33.19  |   (77)  all_52_22 = e0
% 200.36/33.19  |   (78)  all_52_20 = e1
% 200.36/33.19  |   (79)  all_52_16 = e3
% 200.36/33.19  | 
% 200.36/33.19  | REDUCE: (47), (79) imply:
% 200.36/33.19  |   (80)  op(all_52_17, all_52_17) = e3
% 200.36/33.19  | 
% 200.36/33.19  | REDUCE: (42), (77) imply:
% 200.36/33.19  |   (81)  op(all_52_23, all_52_23) = e0
% 200.36/33.19  | 
% 200.36/33.19  | REDUCE: (15), (78) imply:
% 200.36/33.19  |   (82)  op(all_10_2, all_10_2) = e1
% 200.36/33.19  | 
% 200.36/33.19  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 200.36/33.19  |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 200.36/33.19  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 200.36/33.19  |            (36), (37), (38), (39), (40), (41), (43), (44), (45), (46), (48),
% 200.36/33.19  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 200.36/33.19  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 200.36/33.19  |            (71), (72), (73), (74), (76), (80), (81), (82) are inconsistent by
% 200.36/33.19  |            sub-proof #174.
% 200.36/33.19  | 
% 200.36/33.19  End of proof
% 200.36/33.19  
% 200.36/33.19  Sub-proof #174 shows that the following formulas are inconsistent:
% 200.36/33.19  ----------------------------------------------------------------
% 200.36/33.19    (1)   ~ (all_52_25 = all_52_27)
% 200.36/33.19    (2)  all_58_14 = all_52_23
% 200.36/33.19    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.19    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.19    (5)  all_58_1 = all_52_9
% 200.36/33.19    (6)  op(all_52_23, all_52_23) = e0
% 200.36/33.19    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.19    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.19    (9)   ~ (all_52_3 = all_6_2)
% 200.36/33.19    (10)  all_58_0 = all_6_2
% 200.36/33.19    (11)   ~ (all_10_0 = e3)
% 200.36/33.19    (12)  all_40_2 = all_10_2
% 200.36/33.19    (13)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.19    (14)   ~ (all_52_27 = all_52_29)
% 200.36/33.19    (15)  all_58_13 = all_52_15
% 200.36/33.19    (16)  all_58_9 = all_52_25
% 200.36/33.19    (17)   ~ (all_6_1 = e1)
% 200.36/33.19    (18)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.19    (19)  op(e2, e2) = all_4_2
% 200.36/33.19    (20)  all_58_7 = all_10_0
% 200.36/33.19    (21)   ~ (all_52_3 = all_52_5)
% 200.36/33.19    (22)  op(all_4_2, e2) = e1
% 200.36/33.19    (23)  all_58_11 = all_52_29
% 200.36/33.19    (24)   ~ (all_52_9 = all_52_15)
% 200.36/33.19    (25)   ~ (all_52_7 = all_6_2)
% 200.36/33.19    (26)  all_56_15 = all_14_2
% 200.36/33.19    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.19    (28)   ~ (all_10_0 = e2)
% 200.36/33.19    (29)   ~ (all_4_0 = e3)
% 200.36/33.19    (30)  op(all_10_2, all_10_2) = e1
% 200.36/33.19    (31)  all_58_10 = all_52_27
% 200.36/33.19    (32)  all_56_9 = all_10_0
% 200.36/33.19    (33)   ~ (all_52_25 = all_52_29)
% 200.36/33.19    (34)   ~ (all_52_5 = all_52_7)
% 200.36/33.19    (35)  all_58_12 = all_52_7
% 200.36/33.19    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.19    (37)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.19    (38)  all_58_2 = all_52_3
% 200.36/33.19    (39)  all_56_7 = all_52_27
% 200.36/33.19    (40)  op(e3, e1) = all_52_17
% 200.36/33.19    (41)  op(e0, e3) = all_52_7
% 200.36/33.19    (42)  all_58_15 = all_14_2
% 200.36/33.19    (43)  all_58_8 = all_10_2
% 200.36/33.19    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.19    (45)   ~ (all_52_23 = all_14_2)
% 200.36/33.19    (46)  all_56_12 = all_52_7
% 200.36/33.19    (47)  all_58_5 = all_4_0
% 200.36/33.20    (48)   ~ (all_52_5 = all_6_2)
% 200.36/33.20    (49)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.20    (50)   ~ (all_52_9 = all_6_2)
% 200.36/33.20    (51)  op(e3, e3) = all_6_2
% 200.36/33.20    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.20    (53)   ~ (all_52_27 = all_14_2)
% 200.36/33.20    (54)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.20    (55)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.20    (56)  all_40_0 = all_10_0
% 200.36/33.20    (57)   ~ (all_52_3 = all_52_7)
% 200.36/33.20    (58)   ~ (all_52_15 = all_4_2)
% 200.36/33.20    (59)   ~ (all_52_27 = all_4_2)
% 200.36/33.20    (60)  op(all_52_17, all_52_17) = e3
% 200.36/33.20    (61)  all_58_6 = all_52_5
% 200.36/33.20    (62)  op(all_10_2, e1) = e2
% 200.36/33.20    (63)   ~ (all_4_0 = all_4_2)
% 200.36/33.20    (64)  op(e3, e2) = all_52_9
% 200.36/33.20    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.20    (66)   ~ (all_52_17 = all_6_2)
% 200.36/33.20    (67)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.20    (68)   ~ (all_52_3 = all_4_0)
% 200.36/33.20    (69)   ~ (all_6_1 = e2)
% 200.36/33.20    (70)   ~ (all_52_7 = all_52_23)
% 200.36/33.20    (71)  all_58_3 = all_4_2
% 200.36/33.20    (72)   ~ (all_52_3 = all_4_2)
% 200.36/33.20    (73)   ~ (all_52_9 = all_10_0)
% 200.36/33.20    (74)  op(all_6_2, e3) = all_6_1
% 200.36/33.20    (75)  all_58_4 = all_52_17
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | BETA: splitting (44) gives:
% 200.36/33.20  | 
% 200.36/33.20  | Case 1:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (76)  all_56_15 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REF_CLOSE: (2), (4), (8), (12), (19), (22), (26), (27), (28), (29), (30),
% 200.36/33.20  | |            (31), (32), (37), (38), (40), (43), (45), (47), (49), (50), (51),
% 200.36/33.20  | |            (53), (55), (56), (60), (62), (63), (64), (66), (67), (68), (71),
% 200.36/33.20  | |            (72), (75), (76) are inconsistent by sub-proof #180.
% 200.36/33.20  | | 
% 200.36/33.20  | Case 2:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (77)   ~ (all_56_15 = e3)
% 200.36/33.20  | | 
% 200.36/33.20  | | REDUCE: (26), (77) imply:
% 200.36/33.20  | |   (78)   ~ (all_14_2 = e3)
% 200.36/33.20  | | 
% 200.36/33.20  | | BETA: splitting (67) gives:
% 200.36/33.20  | | 
% 200.36/33.20  | | Case 1:
% 200.36/33.20  | | | 
% 200.36/33.20  | | |   (79)  all_58_4 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | COMBINE_EQS: (75), (79) imply:
% 200.36/33.20  | | |   (80)  all_52_17 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | SIMP: (80) implies:
% 200.36/33.20  | | |   (81)  all_52_17 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REF_CLOSE: (4), (51), (60), (66), (81) are inconsistent by sub-proof
% 200.36/33.20  | | |            #1280.
% 200.36/33.20  | | | 
% 200.36/33.20  | | Case 2:
% 200.36/33.20  | | | 
% 200.36/33.20  | | |   (82)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | BETA: splitting (13) gives:
% 200.36/33.20  | | | 
% 200.36/33.20  | | | Case 1:
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | |   (83)  all_56_7 = e3
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | COMBINE_EQS: (39), (83) imply:
% 200.36/33.20  | | | |   (84)  all_52_27 = e3
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | SIMP: (84) implies:
% 200.36/33.20  | | | |   (85)  all_52_27 = e3
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | REDUCE: (1), (85) imply:
% 200.36/33.20  | | | |   (86)   ~ (all_52_25 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | REDUCE: (14), (85) imply:
% 200.36/33.20  | | | |   (87)   ~ (all_52_29 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | SIMP: (87) implies:
% 200.36/33.20  | | | |   (88)   ~ (all_52_29 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | REDUCE: (53), (85) imply:
% 200.36/33.20  | | | |   (89)   ~ (all_14_2 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | REDUCE: (59), (85) imply:
% 200.36/33.20  | | | |   (90)   ~ (all_4_2 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | SIMP: (90) implies:
% 200.36/33.20  | | | |   (91)   ~ (all_4_2 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | REDUCE: (18), (85) imply:
% 200.36/33.20  | | | |   (92)  op(e3, e3) = all_52_26
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_26, e3, e3,
% 200.36/33.20  | | | |              simplifying with (51), (92) gives:
% 200.36/33.20  | | | |   (93)  all_52_26 = all_6_2
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | BETA: splitting (36) gives:
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | Case 1:
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | |   (94)  all_58_6 = e3
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (15), (16), (17), (24),
% 200.36/33.20  | | | | |            (25), (34), (35), (41), (42), (46), (48), (51), (54), (60),
% 200.36/33.20  | | | | |            (61), (65), (66), (69), (70), (74), (75), (78), (86), (94)
% 200.36/33.20  | | | | |            are inconsistent by sub-proof #177.
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | Case 2:
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | |   (95)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REF_CLOSE: (4), (8), (11), (12), (19), (20), (23), (28), (32), (37),
% 200.36/33.20  | | | | |            (40), (43), (56), (60), (62), (88), (91), (95) are
% 200.36/33.20  | | | | |            inconsistent by sub-proof #789.
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | End of split
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | Case 2:
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | |   (96)   ~ (all_56_7 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | REDUCE: (39), (96) imply:
% 200.36/33.20  | | | |   (97)   ~ (all_52_27 = e3)
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | BETA: splitting (27) gives:
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | | Case 1:
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | |   (98)  all_58_2 = e3
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | COMBINE_EQS: (38), (98) imply:
% 200.36/33.20  | | | | |   (99)  all_52_3 = e3
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | SIMP: (99) implies:
% 200.36/33.20  | | | | |   (100)  all_52_3 = e3
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REDUCE: (21), (100) imply:
% 200.36/33.20  | | | | |   (101)   ~ (all_52_5 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | SIMP: (101) implies:
% 200.36/33.20  | | | | |   (102)   ~ (all_52_5 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REDUCE: (57), (100) imply:
% 200.36/33.20  | | | | |   (103)   ~ (all_52_7 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | SIMP: (103) implies:
% 200.36/33.20  | | | | |   (104)   ~ (all_52_7 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REDUCE: (9), (100) imply:
% 200.36/33.20  | | | | |   (105)   ~ (all_6_2 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | SIMP: (105) implies:
% 200.36/33.20  | | | | |   (106)   ~ (all_6_2 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REDUCE: (72), (100) imply:
% 200.36/33.20  | | | | |   (107)   ~ (all_4_2 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | SIMP: (107) implies:
% 200.36/33.20  | | | | |   (108)   ~ (all_4_2 = e3)
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | REDUCE: (3), (100) imply:
% 200.36/33.20  | | | | |   (109)  op(e3, e3) = all_52_2
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_2, e3, e3,
% 200.36/33.20  | | | | |              simplifying with (51), (109) gives:
% 200.36/33.20  | | | | |   (110)  all_52_2 = all_6_2
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | BETA: splitting (52) gives:
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | Case 1:
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | |   (111)  all_58_9 = e3
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | COMBINE_EQS: (16), (111) imply:
% 200.36/33.20  | | | | | |   (112)  all_52_25 = e3
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | SIMP: (112) implies:
% 200.36/33.20  | | | | | |   (113)  all_52_25 = e3
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REDUCE: (33), (113) imply:
% 200.36/33.20  | | | | | |   (114)   ~ (all_52_29 = e3)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | SIMP: (114) implies:
% 200.36/33.20  | | | | | |   (115)   ~ (all_52_29 = e3)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REF_CLOSE: (4), (8), (11), (12), (19), (20), (23), (28), (32), (36),
% 200.36/33.20  | | | | | |            (37), (40), (43), (56), (60), (61), (62), (102), (108),
% 200.36/33.20  | | | | | |            (115) are inconsistent by sub-proof #176.
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | Case 2:
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | |   (116)   ~ (all_58_9 = e3)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REDUCE: (16), (116) imply:
% 200.36/33.20  | | | | | |   (117)   ~ (all_52_25 = e3)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (15), (16), (17), (24),
% 200.36/33.20  | | | | | |            (25), (35), (41), (42), (46), (51), (54), (60), (65),
% 200.36/33.20  | | | | | |            (66), (69), (70), (74), (75), (78), (104), (106), (117)
% 200.36/33.20  | | | | | |            are inconsistent by sub-proof #178.
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | End of split
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | Case 2:
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | |   (118)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | BETA: splitting (118) gives:
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | | Case 1:
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | |   (119)  all_58_3 = e3
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | COMBINE_EQS: (71), (119) imply:
% 200.36/33.20  | | | | | |   (120)  all_4_2 = e3
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REDUCE: (58), (120) imply:
% 200.36/33.20  | | | | | |   (121)   ~ (all_52_15 = e3)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REDUCE: (55), (120) imply:
% 200.36/33.20  | | | | | |   (122)  op(e3, e3) = all_52_10
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REDUCE: (22), (120) imply:
% 200.36/33.20  | | | | | |   (123)  op(e3, e2) = e1
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | GROUND_INST: instantiating (4) with all_52_9, e1, e2, e3,
% 200.36/33.20  | | | | | |              simplifying with (64), (123) gives:
% 200.36/33.20  | | | | | |   (124)  all_52_9 = e1
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_10, e3, e3,
% 200.36/33.20  | | | | | |              simplifying with (51), (122) gives:
% 200.36/33.20  | | | | | |   (125)  all_52_10 = all_6_2
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REDUCE: (73), (124) imply:
% 200.36/33.20  | | | | | |   (126)   ~ (all_10_0 = e1)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | SIMP: (126) implies:
% 200.36/33.20  | | | | | |   (127)   ~ (all_10_0 = e1)
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | BETA: splitting (8) gives:
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | Case 1:
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | |   (128)  all_56_9 = e2
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | | REF_CLOSE: (28), (32), (128) are inconsistent by sub-proof #991.
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | Case 2:
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | |   (129)  all_56_9 = e1 | all_56_9 = e0
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | | BETA: splitting (129) gives:
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | | Case 1:
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | |   (130)  all_56_9 = e1
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | COMBINE_EQS: (32), (130) imply:
% 200.36/33.20  | | | | | | | |   (131)  all_10_0 = e1
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | SIMP: (131) implies:
% 200.36/33.20  | | | | | | | |   (132)  all_10_0 = e1
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | REDUCE: (127), (132) imply:
% 200.36/33.20  | | | | | | | |   (133)  $false
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | CLOSE: (133) is inconsistent.
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | Case 2:
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | |   (134)  all_56_9 = e0
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | COMBINE_EQS: (32), (134) imply:
% 200.36/33.20  | | | | | | | |   (135)  all_10_0 = e0
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | SIMP: (135) implies:
% 200.36/33.20  | | | | | | | |   (136)  all_10_0 = e0
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | COMBINE_EQS: (56), (136) imply:
% 200.36/33.20  | | | | | | | |   (137)  all_40_0 = e0
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | BETA: splitting (37) gives:
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | | Case 1:
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | |   (138)   ~ (all_40_2 = e3)
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | | REDUCE: (12), (138) imply:
% 200.36/33.20  | | | | | | | | |   (139)   ~ (all_10_2 = e3)
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (15), (17), (25), (29), (35),
% 200.36/33.20  | | | | | | | | |            (41), (42), (43), (46), (47), (51), (65), (69),
% 200.36/33.20  | | | | | | | | |            (70), (74), (78), (82), (121), (139) are
% 200.36/33.20  | | | | | | | | |            inconsistent by sub-proof #175.
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | Case 2:
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | |   (140)   ~ (all_40_0 = e0)
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | | REDUCE: (137), (140) imply:
% 200.36/33.20  | | | | | | | | |   (141)  $false
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | | CLOSE: (141) is inconsistent.
% 200.36/33.20  | | | | | | | | | 
% 200.36/33.20  | | | | | | | | End of split
% 200.36/33.20  | | | | | | | | 
% 200.36/33.20  | | | | | | | End of split
% 200.36/33.20  | | | | | | | 
% 200.36/33.20  | | | | | | End of split
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | Case 2:
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | |   (142)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | | REF_CLOSE: (29), (31), (47), (97), (142) are inconsistent by
% 200.36/33.20  | | | | | |            sub-proof #214.
% 200.36/33.20  | | | | | | 
% 200.36/33.20  | | | | | End of split
% 200.36/33.20  | | | | | 
% 200.36/33.20  | | | | End of split
% 200.36/33.20  | | | | 
% 200.36/33.20  | | | End of split
% 200.36/33.20  | | | 
% 200.36/33.20  | | End of split
% 200.36/33.20  | | 
% 200.36/33.20  | End of split
% 200.36/33.20  | 
% 200.36/33.20  End of proof
% 200.36/33.20  
% 200.36/33.20  Sub-proof #175 shows that the following formulas are inconsistent:
% 200.36/33.20  ----------------------------------------------------------------
% 200.36/33.20    (1)  all_58_14 = all_52_23
% 200.36/33.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.20    (3)  op(all_52_23, all_52_23) = e0
% 200.36/33.20    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.20    (5)  all_58_13 = all_52_15
% 200.36/33.20    (6)   ~ (all_6_1 = e1)
% 200.36/33.20    (7)   ~ (all_52_15 = e3)
% 200.36/33.20    (8)   ~ (all_52_7 = all_6_2)
% 200.36/33.20    (9)   ~ (all_4_0 = e3)
% 200.36/33.20    (10)  all_58_12 = all_52_7
% 200.36/33.20    (11)   ~ (all_10_2 = e3)
% 200.36/33.20    (12)  op(e0, e3) = all_52_7
% 200.36/33.20    (13)  all_58_15 = all_14_2
% 200.36/33.20    (14)  all_58_8 = all_10_2
% 200.36/33.20    (15)  all_56_12 = all_52_7
% 200.36/33.20    (16)  all_58_5 = all_4_0
% 200.36/33.20    (17)  op(e3, e3) = all_6_2
% 200.36/33.20    (18)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.20    (19)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.20    (20)   ~ (all_6_1 = e2)
% 200.36/33.20    (21)   ~ (all_52_7 = all_52_23)
% 200.36/33.20    (22)  op(all_6_2, e3) = all_6_1
% 200.36/33.20    (23)   ~ (all_14_2 = e3)
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | BETA: splitting (18) gives:
% 200.36/33.20  | 
% 200.36/33.20  | Case 1:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (24)  all_58_5 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REF_CLOSE: (9), (16), (24) are inconsistent by sub-proof #215.
% 200.36/33.20  | | 
% 200.36/33.20  | Case 2:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (25)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | BETA: splitting (25) gives:
% 200.36/33.20  | | 
% 200.36/33.20  | | Case 1:
% 200.36/33.20  | | | 
% 200.36/33.20  | | |   (26)  all_58_8 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | COMBINE_EQS: (14), (26) imply:
% 200.36/33.20  | | |   (27)  all_10_2 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REDUCE: (11), (27) imply:
% 200.36/33.20  | | |   (28)  $false
% 200.36/33.20  | | | 
% 200.36/33.20  | | | CLOSE: (28) is inconsistent.
% 200.36/33.20  | | | 
% 200.36/33.20  | | Case 2:
% 200.36/33.20  | | | 
% 200.36/33.20  | | |   (29)  all_58_14 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | COMBINE_EQS: (1), (29) imply:
% 200.36/33.20  | | |   (30)  all_52_23 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | SIMP: (30) implies:
% 200.36/33.20  | | |   (31)  all_52_23 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REDUCE: (21), (31) imply:
% 200.36/33.20  | | |   (32)   ~ (all_52_7 = e3)
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (15),
% 200.36/33.20  | | |            (17), (19), (20), (21), (22), (23), (32) are inconsistent by
% 200.36/33.20  | | |            sub-proof #179.
% 200.36/33.20  | | | 
% 200.36/33.20  | | End of split
% 200.36/33.20  | | 
% 200.36/33.20  | End of split
% 200.36/33.20  | 
% 200.36/33.20  End of proof
% 200.36/33.20  
% 200.36/33.20  Sub-proof #176 shows that the following formulas are inconsistent:
% 200.36/33.20  ----------------------------------------------------------------
% 200.36/33.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.20    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.20    (3)   ~ (all_4_2 = e3)
% 200.36/33.20    (4)   ~ (all_10_0 = e3)
% 200.36/33.20    (5)  all_40_2 = all_10_2
% 200.36/33.20    (6)  op(e2, e2) = all_4_2
% 200.36/33.20    (7)  all_58_7 = all_10_0
% 200.36/33.20    (8)  all_58_11 = all_52_29
% 200.36/33.20    (9)   ~ (all_10_0 = e2)
% 200.36/33.20    (10)  all_56_9 = all_10_0
% 200.36/33.20    (11)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.20    (12)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.20    (13)   ~ (all_52_29 = e3)
% 200.36/33.20    (14)   ~ (all_52_5 = e3)
% 200.36/33.20    (15)  op(e3, e1) = all_52_17
% 200.36/33.20    (16)  all_58_8 = all_10_2
% 200.36/33.20    (17)  all_40_0 = all_10_0
% 200.36/33.20    (18)  op(all_52_17, all_52_17) = e3
% 200.36/33.20    (19)  all_58_6 = all_52_5
% 200.36/33.20    (20)  op(all_10_2, e1) = e2
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | BETA: splitting (11) gives:
% 200.36/33.20  | 
% 200.36/33.20  | Case 1:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (21)  all_58_6 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REF_CLOSE: (14), (19), (21) are inconsistent by sub-proof #1328.
% 200.36/33.20  | | 
% 200.36/33.20  | Case 2:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (22)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 200.36/33.20  | |            (15), (16), (17), (18), (20), (22) are inconsistent by sub-proof
% 200.36/33.20  | |            #789.
% 200.36/33.20  | | 
% 200.36/33.20  | End of split
% 200.36/33.20  | 
% 200.36/33.20  End of proof
% 200.36/33.20  
% 200.36/33.20  Sub-proof #177 shows that the following formulas are inconsistent:
% 200.36/33.20  ----------------------------------------------------------------
% 200.36/33.20    (1)  all_58_14 = all_52_23
% 200.36/33.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.20    (3)  all_58_1 = all_52_9
% 200.36/33.20    (4)  op(all_52_23, all_52_23) = e0
% 200.36/33.20    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.20    (6)  all_58_0 = all_6_2
% 200.36/33.20    (7)  all_58_13 = all_52_15
% 200.36/33.20    (8)  all_58_9 = all_52_25
% 200.36/33.20    (9)   ~ (all_6_1 = e1)
% 200.36/33.20    (10)   ~ (all_52_9 = all_52_15)
% 200.36/33.20    (11)   ~ (all_52_7 = all_6_2)
% 200.36/33.20    (12)  all_58_6 = e3
% 200.36/33.20    (13)   ~ (all_52_5 = all_52_7)
% 200.36/33.20    (14)  all_58_12 = all_52_7
% 200.36/33.20    (15)   ~ (all_52_25 = e3)
% 200.36/33.20    (16)  op(e0, e3) = all_52_7
% 200.36/33.20    (17)  all_58_15 = all_14_2
% 200.36/33.20    (18)  all_56_12 = all_52_7
% 200.36/33.20    (19)   ~ (all_52_5 = all_6_2)
% 200.36/33.20    (20)  op(e3, e3) = all_6_2
% 200.36/33.20    (21)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.20    (22)  op(all_52_17, all_52_17) = e3
% 200.36/33.20    (23)  all_58_6 = all_52_5
% 200.36/33.20    (24)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.20    (25)   ~ (all_52_17 = all_6_2)
% 200.36/33.20    (26)   ~ (all_6_1 = e2)
% 200.36/33.20    (27)   ~ (all_52_7 = all_52_23)
% 200.36/33.20    (28)  op(all_6_2, e3) = all_6_1
% 200.36/33.20    (29)  all_58_4 = all_52_17
% 200.36/33.20    (30)   ~ (all_14_2 = e3)
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | COMBINE_EQS: (12), (23) imply:
% 200.36/33.20  |   (31)  all_52_5 = e3
% 200.36/33.20  | 
% 200.36/33.20  | SIMP: (31) implies:
% 200.36/33.20  |   (32)  all_52_5 = e3
% 200.36/33.20  | 
% 200.36/33.20  | REDUCE: (13), (32) imply:
% 200.36/33.20  |   (33)   ~ (all_52_7 = e3)
% 200.36/33.20  | 
% 200.36/33.20  | SIMP: (33) implies:
% 200.36/33.20  |   (34)   ~ (all_52_7 = e3)
% 200.36/33.20  | 
% 200.36/33.20  | REDUCE: (19), (32) imply:
% 200.36/33.20  |   (35)   ~ (all_6_2 = e3)
% 200.36/33.20  | 
% 200.36/33.20  | SIMP: (35) implies:
% 200.36/33.20  |   (36)   ~ (all_6_2 = e3)
% 200.36/33.20  | 
% 200.36/33.20  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14),
% 200.36/33.20  |            (15), (16), (17), (18), (20), (21), (22), (24), (25), (26), (27),
% 200.36/33.20  |            (28), (29), (30), (34), (36) are inconsistent by sub-proof #178.
% 200.36/33.20  | 
% 200.36/33.20  End of proof
% 200.36/33.20  
% 200.36/33.20  Sub-proof #178 shows that the following formulas are inconsistent:
% 200.36/33.20  ----------------------------------------------------------------
% 200.36/33.20    (1)  all_58_14 = all_52_23
% 200.36/33.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.20    (3)  all_58_1 = all_52_9
% 200.36/33.20    (4)  op(all_52_23, all_52_23) = e0
% 200.36/33.20    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.20    (6)  all_58_0 = all_6_2
% 200.36/33.20    (7)  all_58_13 = all_52_15
% 200.36/33.20    (8)  all_58_9 = all_52_25
% 200.36/33.20    (9)   ~ (all_6_1 = e1)
% 200.36/33.20    (10)   ~ (all_52_9 = all_52_15)
% 200.36/33.20    (11)   ~ (all_52_7 = all_6_2)
% 200.36/33.20    (12)   ~ (all_6_2 = e3)
% 200.36/33.20    (13)  all_58_12 = all_52_7
% 200.36/33.20    (14)   ~ (all_52_7 = e3)
% 200.36/33.20    (15)   ~ (all_52_25 = e3)
% 200.36/33.20    (16)  op(e0, e3) = all_52_7
% 200.36/33.20    (17)  all_58_15 = all_14_2
% 200.36/33.20    (18)  all_56_12 = all_52_7
% 200.36/33.20    (19)  op(e3, e3) = all_6_2
% 200.36/33.20    (20)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.20    (21)  op(all_52_17, all_52_17) = e3
% 200.36/33.20    (22)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.20    (23)   ~ (all_52_17 = all_6_2)
% 200.36/33.20    (24)   ~ (all_6_1 = e2)
% 200.36/33.20    (25)   ~ (all_52_7 = all_52_23)
% 200.36/33.20    (26)  op(all_6_2, e3) = all_6_1
% 200.36/33.20    (27)  all_58_4 = all_52_17
% 200.36/33.20    (28)   ~ (all_14_2 = e3)
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | BETA: splitting (20) gives:
% 200.36/33.20  | 
% 200.36/33.20  | Case 1:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (29)  all_58_0 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | COMBINE_EQS: (6), (29) imply:
% 200.36/33.20  | |   (30)  all_6_2 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REDUCE: (12), (30) imply:
% 200.36/33.20  | |   (31)  $false
% 200.36/33.20  | | 
% 200.36/33.20  | | CLOSE: (31) is inconsistent.
% 200.36/33.20  | | 
% 200.36/33.20  | Case 2:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (32)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | BETA: splitting (32) gives:
% 200.36/33.20  | | 
% 200.36/33.20  | | Case 1:
% 200.36/33.20  | | | 
% 200.36/33.20  | | |   (33)  all_58_1 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | COMBINE_EQS: (3), (33) imply:
% 200.36/33.20  | | |   (34)  all_52_9 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REDUCE: (10), (34) imply:
% 200.36/33.20  | | |   (35)   ~ (all_52_15 = e3)
% 200.36/33.20  | | | 
% 200.36/33.20  | | | SIMP: (35) implies:
% 200.36/33.20  | | |   (36)   ~ (all_52_15 = e3)
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (11), (13), (14), (16), (17),
% 200.36/33.20  | | |            (18), (19), (22), (24), (25), (26), (28), (36) are inconsistent
% 200.36/33.20  | | |            by sub-proof #179.
% 200.36/33.20  | | | 
% 200.36/33.20  | | Case 2:
% 200.36/33.20  | | | 
% 200.36/33.20  | | |   (37)  all_58_4 = e3 | all_58_9 = e3
% 200.36/33.20  | | | 
% 200.36/33.20  | | | REF_CLOSE: (2), (8), (15), (19), (21), (23), (27), (37) are inconsistent
% 200.36/33.20  | | |            by sub-proof #1080.
% 200.36/33.20  | | | 
% 200.36/33.20  | | End of split
% 200.36/33.20  | | 
% 200.36/33.20  | End of split
% 200.36/33.20  | 
% 200.36/33.20  End of proof
% 200.36/33.20  
% 200.36/33.20  Sub-proof #179 shows that the following formulas are inconsistent:
% 200.36/33.20  ----------------------------------------------------------------
% 200.36/33.20    (1)  all_58_14 = all_52_23
% 200.36/33.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.20    (3)  op(all_52_23, all_52_23) = e0
% 200.36/33.20    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.20    (5)  all_58_13 = all_52_15
% 200.36/33.20    (6)   ~ (all_6_1 = e1)
% 200.36/33.20    (7)   ~ (all_52_15 = e3)
% 200.36/33.20    (8)   ~ (all_52_7 = all_6_2)
% 200.36/33.20    (9)  all_58_12 = all_52_7
% 200.36/33.20    (10)   ~ (all_52_7 = e3)
% 200.36/33.20    (11)  op(e0, e3) = all_52_7
% 200.36/33.20    (12)  all_58_15 = all_14_2
% 200.36/33.20    (13)  all_56_12 = all_52_7
% 200.36/33.20    (14)  op(e3, e3) = all_6_2
% 200.36/33.20    (15)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.20    (16)   ~ (all_6_1 = e2)
% 200.36/33.20    (17)   ~ (all_52_7 = all_52_23)
% 200.36/33.20    (18)  op(all_6_2, e3) = all_6_1
% 200.36/33.20    (19)   ~ (all_14_2 = e3)
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | BETA: splitting (15) gives:
% 200.36/33.20  | 
% 200.36/33.20  | Case 1:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (20)  all_58_12 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REF_CLOSE: (9), (10), (20) are inconsistent by sub-proof #1367.
% 200.36/33.20  | | 
% 200.36/33.20  | Case 2:
% 200.36/33.20  | | 
% 200.36/33.20  | |   (21)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.20  | | 
% 200.36/33.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 200.36/33.20  | |            (16), (17), (18), (19), (21) are inconsistent by sub-proof #1045.
% 200.36/33.20  | | 
% 200.36/33.20  | End of split
% 200.36/33.20  | 
% 200.36/33.20  End of proof
% 200.36/33.20  
% 200.36/33.20  Sub-proof #180 shows that the following formulas are inconsistent:
% 200.36/33.20  ----------------------------------------------------------------
% 200.36/33.20    (1)  all_58_14 = all_52_23
% 200.36/33.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.20    (3)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.20    (4)  all_40_2 = all_10_2
% 200.36/33.20    (5)  op(e2, e2) = all_4_2
% 200.36/33.20    (6)  op(all_4_2, e2) = e1
% 200.36/33.20    (7)  all_56_15 = all_14_2
% 200.36/33.20    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.20    (9)   ~ (all_10_0 = e2)
% 200.36/33.20    (10)   ~ (all_4_0 = e3)
% 200.36/33.20    (11)  op(all_10_2, all_10_2) = e1
% 200.36/33.20    (12)  all_58_10 = all_52_27
% 200.36/33.20    (13)  all_56_9 = all_10_0
% 200.36/33.20    (14)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.20    (15)  all_58_2 = all_52_3
% 200.36/33.20    (16)  op(e3, e1) = all_52_17
% 200.36/33.20    (17)  all_58_8 = all_10_2
% 200.36/33.20    (18)   ~ (all_52_23 = all_14_2)
% 200.36/33.20    (19)  all_58_5 = all_4_0
% 200.36/33.20    (20)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.20    (21)   ~ (all_52_9 = all_6_2)
% 200.36/33.20    (22)  op(e3, e3) = all_6_2
% 200.36/33.20    (23)  all_56_15 = e3
% 200.36/33.20    (24)   ~ (all_52_27 = all_14_2)
% 200.36/33.20    (25)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.20    (26)  all_40_0 = all_10_0
% 200.36/33.20    (27)  op(all_52_17, all_52_17) = e3
% 200.36/33.20    (28)  op(all_10_2, e1) = e2
% 200.36/33.20    (29)   ~ (all_4_0 = all_4_2)
% 200.36/33.20    (30)  op(e3, e2) = all_52_9
% 200.36/33.20    (31)   ~ (all_52_17 = all_6_2)
% 200.36/33.20    (32)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.20    (33)   ~ (all_52_3 = all_4_0)
% 200.36/33.20    (34)  all_58_3 = all_4_2
% 200.36/33.20    (35)   ~ (all_52_3 = all_4_2)
% 200.36/33.20    (36)  all_58_4 = all_52_17
% 200.36/33.20  
% 200.36/33.20  Begin of proof
% 200.36/33.20  | 
% 200.36/33.20  | COMBINE_EQS: (7), (23) imply:
% 200.36/33.20  |   (37)  all_14_2 = e3
% 200.36/33.20  | 
% 200.36/33.20  | SIMP: (37) implies:
% 200.36/33.20  |   (38)  all_14_2 = e3
% 200.36/33.20  | 
% 200.36/33.20  | REDUCE: (18), (38) imply:
% 200.36/33.21  |   (39)   ~ (all_52_23 = e3)
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (24), (38) imply:
% 200.36/33.21  |   (40)   ~ (all_52_27 = e3)
% 200.36/33.21  | 
% 200.36/33.21  | BETA: splitting (8) gives:
% 200.36/33.21  | 
% 200.36/33.21  | Case 1:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (41)  all_58_2 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | COMBINE_EQS: (15), (41) imply:
% 200.36/33.21  | |   (42)  all_52_3 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | SIMP: (42) implies:
% 200.36/33.21  | |   (43)  all_52_3 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | REDUCE: (33), (43) imply:
% 200.36/33.21  | |   (44)   ~ (all_4_0 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | REDUCE: (35), (43) imply:
% 200.36/33.21  | |   (45)   ~ (all_4_2 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | SIMP: (45) implies:
% 200.36/33.21  | |   (46)   ~ (all_4_2 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (13), (14), (16), (17), (19),
% 200.36/33.21  | |            (22), (26), (27), (28), (31), (32), (36), (39), (46) are
% 200.36/33.21  | |            inconsistent by sub-proof #181.
% 200.36/33.21  | | 
% 200.36/33.21  | Case 2:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (47)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | REF_CLOSE: (1), (2), (5), (6), (10), (11), (12), (17), (19), (20), (21),
% 200.36/33.21  | |            (22), (25), (27), (29), (30), (31), (32), (34), (36), (39), (40),
% 200.36/33.21  | |            (47) are inconsistent by sub-proof #204.
% 200.36/33.21  | | 
% 200.36/33.21  | End of split
% 200.36/33.21  | 
% 200.36/33.21  End of proof
% 200.36/33.21  
% 200.36/33.21  Sub-proof #181 shows that the following formulas are inconsistent:
% 200.36/33.21  ----------------------------------------------------------------
% 200.36/33.21    (1)  all_58_14 = all_52_23
% 200.36/33.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.21    (3)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 200.36/33.21    (4)   ~ (all_4_2 = e3)
% 200.36/33.21    (5)  all_40_2 = all_10_2
% 200.36/33.21    (6)  op(e2, e2) = all_4_2
% 200.36/33.21    (7)   ~ (all_10_0 = e2)
% 200.36/33.21    (8)   ~ (all_4_0 = e3)
% 200.36/33.21    (9)  all_56_9 = all_10_0
% 200.36/33.21    (10)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 200.36/33.21    (11)   ~ (all_52_23 = e3)
% 200.36/33.21    (12)  op(e3, e1) = all_52_17
% 200.36/33.21    (13)  all_58_8 = all_10_2
% 200.36/33.21    (14)  all_58_5 = all_4_0
% 200.36/33.21    (15)  op(e3, e3) = all_6_2
% 200.36/33.21    (16)  all_40_0 = all_10_0
% 200.36/33.21    (17)  op(all_52_17, all_52_17) = e3
% 200.36/33.21    (18)  op(all_10_2, e1) = e2
% 200.36/33.21    (19)   ~ (all_52_17 = all_6_2)
% 200.36/33.21    (20)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.21    (21)  all_58_4 = all_52_17
% 200.36/33.21  
% 200.36/33.21  Begin of proof
% 200.36/33.21  | 
% 200.36/33.21  | BETA: splitting (20) gives:
% 200.36/33.21  | 
% 200.36/33.21  | Case 1:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (22)  all_58_4 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | COMBINE_EQS: (21), (22) imply:
% 200.36/33.21  | |   (23)  all_52_17 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | SIMP: (23) implies:
% 200.36/33.21  | |   (24)  all_52_17 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | REF_CLOSE: (2), (15), (17), (19), (24) are inconsistent by sub-proof #1280.
% 200.36/33.21  | | 
% 200.36/33.21  | Case 2:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (25)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | BETA: splitting (25) gives:
% 200.36/33.21  | | 
% 200.36/33.21  | | Case 1:
% 200.36/33.21  | | | 
% 200.36/33.21  | | |   (26)  all_58_5 = e3
% 200.36/33.21  | | | 
% 200.36/33.21  | | | REF_CLOSE: (8), (14), (26) are inconsistent by sub-proof #215.
% 200.36/33.21  | | | 
% 200.36/33.21  | | Case 2:
% 200.36/33.21  | | | 
% 200.36/33.21  | | |   (27)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.21  | | | 
% 200.36/33.21  | | | BETA: splitting (27) gives:
% 200.36/33.21  | | | 
% 200.36/33.21  | | | Case 1:
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | |   (28)  all_58_8 = e3
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | COMBINE_EQS: (13), (28) imply:
% 200.36/33.21  | | | |   (29)  all_10_2 = e3
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | COMBINE_EQS: (5), (29) imply:
% 200.36/33.21  | | | |   (30)  all_40_2 = e3
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | REDUCE: (18), (29) imply:
% 200.36/33.21  | | | |   (31)  op(e3, e1) = e2
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (12), (16), (17), (30),
% 200.36/33.21  | | | |            (31) are inconsistent by sub-proof #790.
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | Case 2:
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | |   (32)  all_58_14 = e3
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | REF_CLOSE: (1), (11), (32) are inconsistent by sub-proof #1305.
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | End of split
% 200.36/33.21  | | | 
% 200.36/33.21  | | End of split
% 200.36/33.21  | | 
% 200.36/33.21  | End of split
% 200.36/33.21  | 
% 200.36/33.21  End of proof
% 200.36/33.21  
% 200.36/33.21  Sub-proof #182 shows that the following formulas are inconsistent:
% 200.36/33.21  ----------------------------------------------------------------
% 200.36/33.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.21    (2)  all_58_1 = all_52_9
% 200.36/33.21    (3)   ~ (e3 = e0)
% 200.36/33.21    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.21    (5)   ~ (all_52_7 = all_52_15)
% 200.36/33.21    (6)   ~ (all_10_0 = e3)
% 200.36/33.21    (7)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.21    (8)  all_58_13 = all_52_15
% 200.36/33.21    (9)   ~ (all_6_1 = e1)
% 200.36/33.21    (10)  op(e2, e2) = all_4_2
% 200.36/33.21    (11)  all_58_7 = all_10_0
% 200.36/33.21    (12)  op(all_4_2, e2) = e1
% 200.36/33.21    (13)   ~ (all_52_7 = all_6_2)
% 200.36/33.21    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.21    (15)   ~ (all_10_0 = e2)
% 200.36/33.21    (16)   ~ (all_4_0 = e3)
% 200.36/33.21    (17)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 200.36/33.21    (18)  all_58_10 = all_52_27
% 200.36/33.21    (19)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.21    (20)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.21    (21)  all_58_2 = all_52_3
% 200.36/33.21    (22)  all_56_7 = all_52_27
% 200.36/33.21    (23)  op(e0, e3) = all_52_7
% 200.36/33.21    (24)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.21    (25)  all_56_12 = all_52_7
% 200.36/33.21    (26)  all_58_5 = all_4_0
% 200.36/33.21    (27)   ~ (all_52_9 = all_6_2)
% 200.36/33.21    (28)  op(e3, e3) = all_6_2
% 200.36/33.21    (29)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.21    (30)   ~ (all_52_27 = all_4_2)
% 200.36/33.21    (31)  op(e3, e2) = all_52_9
% 200.36/33.21    (32)   ~ (e3 = e2)
% 200.36/33.21    (33)   ~ (all_6_1 = e2)
% 200.36/33.21    (34)  all_58_3 = all_4_2
% 200.36/33.21    (35)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.21    (36)   ~ (all_52_3 = all_4_2)
% 200.36/33.21    (37)  op(all_6_2, e3) = all_6_1
% 200.36/33.21  
% 200.36/33.21  Begin of proof
% 200.36/33.21  | 
% 200.36/33.21  | ALPHA: (17) implies:
% 200.36/33.21  |   (38)  all_52_14 = e0
% 200.36/33.21  |   (39)  all_52_10 = e2
% 200.36/33.21  |   (40)  all_52_8 = e3
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (19), (40) imply:
% 200.36/33.21  |   (41)  op(all_52_9, all_52_9) = e3
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (20), (38) imply:
% 200.36/33.21  |   (42)  op(all_52_15, all_52_15) = e0
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (29), (39) imply:
% 200.36/33.21  |   (43)  op(all_4_2, all_4_2) = e2
% 200.36/33.21  | 
% 200.36/33.21  | BETA: splitting (7) gives:
% 200.36/33.21  | 
% 200.36/33.21  | Case 1:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (44)  all_56_7 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | COMBINE_EQS: (22), (44) imply:
% 200.36/33.21  | |   (45)  all_52_27 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | SIMP: (45) implies:
% 200.36/33.21  | |   (46)  all_52_27 = e3
% 200.36/33.21  | | 
% 200.36/33.21  | | REDUCE: (30), (46) imply:
% 200.36/33.21  | |   (47)   ~ (all_4_2 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | SIMP: (47) implies:
% 200.36/33.21  | |   (48)   ~ (all_4_2 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (13), (23), (24), (25),
% 200.36/33.21  | |            (27), (28), (33), (34), (37), (41), (42), (48) are inconsistent
% 200.36/33.21  | |            by sub-proof #992.
% 200.36/33.21  | | 
% 200.36/33.21  | Case 2:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (49)   ~ (all_56_7 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | REDUCE: (22), (49) imply:
% 200.36/33.21  | |   (50)   ~ (all_52_27 = e3)
% 200.36/33.21  | | 
% 200.36/33.21  | | BETA: splitting (14) gives:
% 200.36/33.21  | | 
% 200.36/33.21  | | Case 1:
% 200.36/33.21  | | | 
% 200.36/33.21  | | |   (51)  all_58_2 = e3
% 200.36/33.21  | | | 
% 200.36/33.21  | | | COMBINE_EQS: (21), (51) imply:
% 200.36/33.21  | | |   (52)  all_52_3 = e3
% 200.36/33.21  | | | 
% 200.36/33.21  | | | SIMP: (52) implies:
% 200.36/33.21  | | |   (53)  all_52_3 = e3
% 200.36/33.21  | | | 
% 200.36/33.21  | | | REDUCE: (36), (53) imply:
% 200.36/33.21  | | |   (54)   ~ (all_4_2 = e3)
% 200.36/33.21  | | | 
% 200.36/33.21  | | | SIMP: (54) implies:
% 200.36/33.21  | | |   (55)   ~ (all_4_2 = e3)
% 200.36/33.21  | | | 
% 200.36/33.21  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (13), (23), (24),
% 200.36/33.21  | | |            (25), (27), (28), (33), (34), (37), (41), (42), (55) are
% 200.36/33.21  | | |            inconsistent by sub-proof #992.
% 200.36/33.21  | | | 
% 200.36/33.21  | | Case 2:
% 200.36/33.21  | | | 
% 200.36/33.21  | | |   (56)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.21  | | | 
% 200.36/33.21  | | | BETA: splitting (56) gives:
% 200.36/33.21  | | | 
% 200.36/33.21  | | | Case 1:
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | |   (57)  all_58_3 = e3
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | REF_CLOSE: (1), (2), (3), (8), (10), (11), (12), (15), (27), (28), (31),
% 200.36/33.21  | | | |            (32), (34), (35), (42), (43), (57) are inconsistent by
% 200.36/33.21  | | | |            sub-proof #183.
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | Case 2:
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | |   (58)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | | REF_CLOSE: (16), (18), (26), (50), (58) are inconsistent by sub-proof
% 200.36/33.21  | | | |            #214.
% 200.36/33.21  | | | | 
% 200.36/33.21  | | | End of split
% 200.36/33.21  | | | 
% 200.36/33.21  | | End of split
% 200.36/33.21  | | 
% 200.36/33.21  | End of split
% 200.36/33.21  | 
% 200.36/33.21  End of proof
% 200.36/33.21  
% 200.36/33.21  Sub-proof #183 shows that the following formulas are inconsistent:
% 200.36/33.21  ----------------------------------------------------------------
% 200.36/33.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.21    (2)  all_58_1 = all_52_9
% 200.36/33.21    (3)   ~ (e3 = e0)
% 200.36/33.21    (4)  op(all_52_15, all_52_15) = e0
% 200.36/33.21    (5)  all_58_3 = e3
% 200.36/33.21    (6)  all_58_13 = all_52_15
% 200.36/33.21    (7)  op(e2, e2) = all_4_2
% 200.36/33.21    (8)  all_58_7 = all_10_0
% 200.36/33.21    (9)  op(all_4_2, e2) = e1
% 200.36/33.21    (10)   ~ (all_10_0 = e2)
% 200.36/33.21    (11)  op(all_4_2, all_4_2) = e2
% 200.36/33.21    (12)   ~ (all_52_9 = all_6_2)
% 200.36/33.21    (13)  op(e3, e3) = all_6_2
% 200.36/33.21    (14)  op(e3, e2) = all_52_9
% 200.36/33.21    (15)   ~ (e3 = e2)
% 200.36/33.21    (16)  all_58_3 = all_4_2
% 200.36/33.21    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.21  
% 200.36/33.21  Begin of proof
% 200.36/33.21  | 
% 200.36/33.21  | COMBINE_EQS: (5), (16) imply:
% 200.36/33.21  |   (18)  all_4_2 = e3
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (11), (18) imply:
% 200.36/33.21  |   (19)  op(e3, e3) = e2
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (9), (18) imply:
% 200.36/33.21  |   (20)  op(e3, e2) = e1
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (7), (18) imply:
% 200.36/33.21  |   (21)  op(e2, e2) = e3
% 200.36/33.21  | 
% 200.36/33.21  | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 200.36/33.21  |              (14), (20) gives:
% 200.36/33.21  |   (22)  all_52_9 = e1
% 200.36/33.21  | 
% 200.36/33.21  | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 200.36/33.21  |              (13), (19) gives:
% 200.36/33.21  |   (23)  all_6_2 = e2
% 200.36/33.21  | 
% 200.36/33.21  | COMBINE_EQS: (2), (22) imply:
% 200.36/33.21  |   (24)  all_58_1 = e1
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (12), (22), (23) imply:
% 200.36/33.21  |   (25)   ~ (e2 = e1)
% 200.36/33.21  | 
% 200.36/33.21  | SIMP: (25) implies:
% 200.36/33.21  |   (26)   ~ (e2 = e1)
% 200.36/33.21  | 
% 200.36/33.21  | BETA: splitting (17) gives:
% 200.36/33.21  | 
% 200.36/33.21  | Case 1:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (27)  all_58_1 = e2
% 200.36/33.21  | | 
% 200.36/33.21  | | REF_CLOSE: (24), (26), (27) are inconsistent by sub-proof #185.
% 200.36/33.21  | | 
% 200.36/33.21  | Case 2:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (28)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.21  | | 
% 200.36/33.21  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (15), (21), (28) are
% 200.36/33.21  | |            inconsistent by sub-proof #184.
% 200.36/33.21  | | 
% 200.36/33.21  | End of split
% 200.36/33.21  | 
% 200.36/33.21  End of proof
% 200.36/33.21  
% 200.36/33.21  Sub-proof #184 shows that the following formulas are inconsistent:
% 200.36/33.21  ----------------------------------------------------------------
% 200.36/33.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.21    (2)   ~ (e3 = e0)
% 200.36/33.21    (3)  op(all_52_15, all_52_15) = e0
% 200.36/33.21    (4)  all_58_3 = e3
% 200.36/33.21    (5)  all_58_13 = all_52_15
% 200.36/33.21    (6)  all_58_7 = all_10_0
% 200.36/33.21    (7)   ~ (all_10_0 = e2)
% 200.36/33.21    (8)  op(e2, e2) = e3
% 200.36/33.21    (9)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.21    (10)   ~ (e3 = e2)
% 200.36/33.21  
% 200.36/33.21  Begin of proof
% 200.36/33.21  | 
% 200.36/33.21  | BETA: splitting (9) gives:
% 200.36/33.21  | 
% 200.36/33.21  | Case 1:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (11)  all_58_3 = e2
% 200.36/33.21  | | 
% 200.36/33.21  | | COMBINE_EQS: (4), (11) imply:
% 200.36/33.21  | |   (12)  e3 = e2
% 200.36/33.21  | | 
% 200.36/33.21  | | REDUCE: (10), (12) imply:
% 200.36/33.21  | |   (13)  $false
% 200.36/33.21  | | 
% 200.36/33.21  | | CLOSE: (13) is inconsistent.
% 200.36/33.21  | | 
% 200.36/33.21  | Case 2:
% 200.36/33.21  | | 
% 200.36/33.21  | |   (14)  all_58_7 = e2 | all_58_13 = e2
% 200.36/33.21  | | 
% 200.36/33.21  | | BETA: splitting (14) gives:
% 200.36/33.21  | | 
% 200.36/33.21  | | Case 1:
% 200.36/33.21  | | | 
% 200.36/33.21  | | |   (15)  all_58_7 = e2
% 200.36/33.21  | | | 
% 200.36/33.21  | | | COMBINE_EQS: (6), (15) imply:
% 200.36/33.21  | | |   (16)  all_10_0 = e2
% 200.36/33.21  | | | 
% 200.36/33.21  | | | REDUCE: (7), (16) imply:
% 200.36/33.21  | | |   (17)  $false
% 200.36/33.21  | | | 
% 200.36/33.21  | | | CLOSE: (17) is inconsistent.
% 200.36/33.21  | | | 
% 200.36/33.21  | | Case 2:
% 200.36/33.21  | | | 
% 200.36/33.21  | | |   (18)  all_58_13 = e2
% 200.36/33.21  | | | 
% 200.36/33.21  | | | COMBINE_EQS: (5), (18) imply:
% 200.36/33.21  | | |   (19)  all_52_15 = e2
% 200.36/33.21  | | | 
% 200.36/33.21  | | | SIMP: (19) implies:
% 200.36/33.21  | | |   (20)  all_52_15 = e2
% 200.36/33.21  | | | 
% 200.36/33.21  | | | REDUCE: (3), (20) imply:
% 200.36/33.21  | | |   (21)  op(e2, e2) = e0
% 200.36/33.21  | | | 
% 200.36/33.21  | | | GROUND_INST: instantiating (1) with e3, e0, e2, e2, simplifying with (8),
% 200.36/33.21  | | |              (21) gives:
% 200.36/33.21  | | |   (22)  e3 = e0
% 200.36/33.21  | | | 
% 200.36/33.21  | | | REDUCE: (2), (22) imply:
% 200.36/33.21  | | |   (23)  $false
% 200.36/33.21  | | | 
% 200.36/33.21  | | | CLOSE: (23) is inconsistent.
% 200.36/33.21  | | | 
% 200.36/33.21  | | End of split
% 200.36/33.21  | | 
% 200.36/33.21  | End of split
% 200.36/33.21  | 
% 200.36/33.21  End of proof
% 200.36/33.21  
% 200.36/33.21  Sub-proof #185 shows that the following formulas are inconsistent:
% 200.36/33.21  ----------------------------------------------------------------
% 200.36/33.21    (1)  all_58_1 = e2
% 200.36/33.21    (2)  all_58_1 = e1
% 200.36/33.21    (3)   ~ (e2 = e1)
% 200.36/33.21  
% 200.36/33.21  Begin of proof
% 200.36/33.21  | 
% 200.36/33.21  | COMBINE_EQS: (1), (2) imply:
% 200.36/33.21  |   (4)  e2 = e1
% 200.36/33.21  | 
% 200.36/33.21  | SIMP: (4) implies:
% 200.36/33.21  |   (5)  e2 = e1
% 200.36/33.21  | 
% 200.36/33.21  | REDUCE: (3), (5) imply:
% 200.36/33.21  |   (6)  $false
% 200.36/33.21  | 
% 200.36/33.21  | CLOSE: (6) is inconsistent.
% 200.36/33.21  | 
% 200.36/33.21  End of proof
% 200.36/33.21  
% 200.36/33.21  Sub-proof #186 shows that the following formulas are inconsistent:
% 200.36/33.21  ----------------------------------------------------------------
% 200.36/33.21    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.21    (2)   ~ (all_52_25 = all_52_27)
% 200.36/33.21    (3)  all_58_14 = all_52_23
% 200.36/33.21    (4)   ~ (e3 = e1)
% 200.36/33.21    (5)   ~ (all_52_17 = all_4_0)
% 200.36/33.21    (6)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.21    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.21    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.21    (9)  all_58_1 = all_52_9
% 200.36/33.21    (10)   ~ (all_52_9 = all_52_13)
% 200.36/33.21    (11)   ~ (e3 = e0)
% 200.36/33.21    (12)  op(e2, e3) = all_52_3
% 200.36/33.21    (13)   ~ (all_52_23 = all_4_0)
% 200.36/33.21    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.21    (15)   ~ (all_52_7 = all_52_15)
% 200.36/33.21    (16)   ~ (all_52_3 = all_52_19)
% 200.36/33.21    (17)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.21    (18)   ~ (all_52_17 = all_52_25)
% 200.36/33.21    (19)   ~ (all_52_3 = all_6_2)
% 200.36/33.21    (20)  all_58_0 = all_6_2
% 200.36/33.21    (21)  op(all_14_2, e0) = all_14_1
% 200.36/33.21    (22)  all_56_4 = all_52_3
% 200.36/33.21    (23)   ~ (all_52_17 = all_10_2)
% 200.36/33.21    (24)  op(e3, e0) = all_52_25
% 200.36/33.21    (25)  op(e0, all_14_1) = all_14_0
% 200.36/33.21    (26)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.21    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.21    (28)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.21    (29)   ~ (all_52_27 = all_52_29)
% 200.36/33.21    (30)  all_58_13 = all_52_15
% 200.36/33.21    (31)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.21    (32)  all_58_9 = all_52_25
% 200.36/33.21    (33)   ~ (all_6_1 = e1)
% 200.36/33.21    (34)   ~ (all_52_29 = all_14_2)
% 200.36/33.21    (35)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.21    (36)  op(e1, e3) = all_52_5
% 200.36/33.21    (37)  op(e2, e2) = all_4_2
% 200.36/33.21    (38)   ~ (all_52_3 = all_52_5)
% 200.36/33.21    (39)  op(all_4_2, e2) = e1
% 200.36/33.21    (40)  all_58_11 = all_52_29
% 200.36/33.21    (41)  all_56_5 = all_4_2
% 200.36/33.21    (42)   ~ (all_52_25 = all_14_2)
% 200.36/33.21    (43)   ~ (all_52_9 = all_52_15)
% 200.36/33.21    (44)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.21    (45)   ~ (all_52_3 = all_52_27)
% 200.36/33.21    (46)  op(all_10_2, e1) = all_10_1
% 200.36/33.21    (47)   ~ (all_10_2 = all_4_0)
% 200.36/33.21    (48)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.21    (49)   ~ (all_52_7 = all_6_2)
% 200.36/33.21    (50)  op(e0, e0) = all_14_2
% 200.36/33.21    (51)  op(e0, e1) = all_52_23
% 200.36/33.21    (52)  all_56_15 = all_14_2
% 200.36/33.21    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.21    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.21    (55)  op(e1, e0) = all_52_29
% 200.36/33.21    (56)   ~ (all_58_15 = e0)
% 200.36/33.21    (57)  all_56_11 = all_52_29
% 200.36/33.21    (58)   ~ (all_4_0 = e3)
% 200.36/33.21    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.21    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.21    (61)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.21    (62)   ~ (e2 = e1)
% 200.36/33.21    (63)   ~ (all_52_13 = all_10_2)
% 200.36/33.21    (64)   ~ (all_6_0 = e1)
% 200.36/33.21    (65)  all_58_10 = all_52_27
% 200.36/33.21    (66)  all_56_8 = all_52_5
% 200.36/33.21    (67)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.21    (68)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.21    (69)   ~ (all_52_19 = all_52_23)
% 200.36/33.21    (70)   ~ (all_52_25 = all_52_29)
% 200.36/33.21    (71)   ~ (all_52_29 = all_10_2)
% 200.36/33.21    (72)  all_58_7 = all_52_13
% 200.36/33.21    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.21    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.21    (75)   ~ (all_52_5 = all_52_7)
% 200.36/33.21    (76)  all_58_12 = all_52_7
% 200.36/33.21    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.21    (78)   ~ (all_52_7 = all_14_2)
% 200.36/33.21    (79)  all_58_2 = all_52_3
% 200.36/33.21    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 200.36/33.21    (81)  all_56_2 = all_52_17
% 200.36/33.21    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.21    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.21    (84)  op(e3, all_6_1) = all_6_0
% 200.36/33.21    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.21    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.21    (87)  all_56_7 = all_52_27
% 200.36/33.21    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.21    (89)   ~ (e2 = e0)
% 200.36/33.21    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.21    (91)   ~ (all_52_5 = all_52_29)
% 200.36/33.21    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.21    (93)  all_56_6 = all_52_19
% 200.36/33.21    (94)   ~ (all_52_15 = all_14_2)
% 200.36/33.21    (95)   ~ (all_52_19 = all_52_27)
% 200.36/33.21    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.21    (97)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.21    (98)   ~ (all_6_0 = e2)
% 200.36/33.21    (99)   ~ (all_52_13 = all_4_2)
% 200.36/33.21    (100)  op(e3, e1) = all_52_17
% 200.36/33.21    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.21    (102)  op(e0, e3) = all_52_7
% 200.36/33.21    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.21    (104)   ~ (all_52_9 = all_52_25)
% 200.36/33.21    (105)  all_58_15 = all_14_2
% 200.36/33.21    (106)   ~ (all_52_19 = all_10_2)
% 200.36/33.21    (107)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.21    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.21    (109)   ~ (all_10_1 = e2)
% 200.36/33.21    (110)  all_58_8 = all_10_2
% 200.36/33.21    (111)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.21    (112)   ~ (all_52_5 = all_10_2)
% 200.36/33.21    (113)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.21    (114)   ~ (all_52_23 = all_14_2)
% 200.36/33.21    (115)  all_56_12 = all_52_7
% 200.36/33.21    (116)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.21    (117)  all_58_5 = all_4_0
% 200.36/33.21    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.21    (119)   ~ (all_52_25 = all_6_2)
% 200.36/33.21    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.21    (121)   ~ (all_52_9 = all_4_2)
% 200.36/33.21    (122)   ~ (all_52_5 = all_6_2)
% 200.36/33.21    (123)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.21    (124)   ~ (all_52_9 = all_6_2)
% 200.36/33.21    (125)   ~ (all_52_13 = all_52_15)
% 200.36/33.21    (126)  all_56_0 = all_6_2
% 200.36/33.21    (127)  op(e3, e3) = all_6_2
% 200.36/33.21    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.21    (129)   ~ (all_52_27 = all_14_2)
% 200.36/33.21    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.21    (131)  all_56_14 = all_52_23
% 200.36/33.21    (132)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.21    (133)  all_56_3 = all_52_25
% 200.36/33.21    (134)   ~ (all_52_3 = all_52_7)
% 200.36/33.21    (135)   ~ (all_10_1 = e3)
% 200.36/33.21    (136)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.21    (137)  all_58_5 = all_52_19
% 200.36/33.21    (138)  all_56_1 = all_52_9
% 200.36/33.21    (139)   ~ (all_52_15 = all_4_2)
% 200.36/33.21    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.21           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.21           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.21           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.21    (141)   ~ (all_52_27 = all_4_2)
% 200.36/33.21    (142)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 200.36/33.21             all_58_13 = e0 | all_58_14 = e0)
% 200.36/33.21    (143)  all_58_6 = all_52_5
% 200.36/33.21    (144)   ~ (all_4_0 = all_4_2)
% 200.36/33.21    (145)  op(e3, e2) = all_52_9
% 200.36/33.21    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.21    (147)   ~ (all_52_17 = all_6_2)
% 200.36/33.21    (148)   ~ (e1 = e0)
% 200.36/33.21    (149)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 200.36/33.21    (150)   ~ (e3 = e2)
% 200.36/33.21    (151)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.21    (152)   ~ (all_52_9 = all_52_17)
% 200.36/33.21    (153)  all_56_10 = all_10_2
% 200.36/33.22    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.22    (155)   ~ (all_52_3 = all_4_0)
% 200.36/33.22    (156)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.22    (157)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.22    (158)   ~ (all_6_1 = e2)
% 200.36/33.22    (159)  op(e1, e1) = all_10_2
% 200.36/33.22    (160)   ~ (all_52_23 = all_10_2)
% 200.36/33.22    (161)   ~ (all_52_7 = all_52_23)
% 200.36/33.22    (162)   ~ (all_52_17 = all_52_19)
% 200.36/33.22    (163)  all_58_3 = all_4_2
% 200.36/33.22    (164)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.22    (165)  all_56_13 = all_52_15
% 200.36/33.22    (166)   ~ (all_52_3 = all_4_2)
% 200.36/33.22    (167)   ~ (all_52_19 = all_4_2)
% 200.36/33.22    (168)   ~ (all_52_17 = all_52_23)
% 200.36/33.22    (169)  op(all_6_2, e3) = all_6_1
% 200.36/33.22    (170)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.22    (171)  all_58_4 = all_52_17
% 200.36/33.22    (172)   ~ (all_14_0 = e2)
% 200.36/33.22    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.36/33.22    (174)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.22  
% 200.36/33.22  Begin of proof
% 200.36/33.22  | 
% 200.36/33.22  | ALPHA: (142) implies:
% 200.36/33.22  |   (175)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.22  |   (176)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.22  | 
% 200.36/33.22  | REDUCE: (56), (105) imply:
% 200.36/33.22  |   (177)   ~ (all_14_2 = e0)
% 200.36/33.22  | 
% 200.36/33.22  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 200.36/33.22  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 200.36/33.22  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 200.36/33.22  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 200.36/33.22  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (57),
% 200.36/33.22  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 200.36/33.22  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 200.36/33.22  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 200.36/33.22  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 200.36/33.22  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 200.36/33.22  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 200.36/33.22  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 200.36/33.22  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 200.36/33.22  |            (138), (139), (140), (141), (143), (144), (145), (146), (147),
% 200.36/33.22  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 200.36/33.22  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 200.36/33.22  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 200.36/33.22  |            (175), (176), (177) are inconsistent by sub-proof #187.
% 200.36/33.22  | 
% 200.36/33.22  End of proof
% 200.36/33.22  
% 200.36/33.22  Sub-proof #187 shows that the following formulas are inconsistent:
% 200.36/33.22  ----------------------------------------------------------------
% 200.36/33.22    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.22    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.22    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.22    (4)  all_58_14 = all_52_23
% 200.36/33.22    (5)   ~ (e3 = e1)
% 200.36/33.22    (6)   ~ (all_52_17 = all_4_0)
% 200.36/33.22    (7)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.22    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.22    (9)   ~ (all_52_5 = all_52_13)
% 200.36/33.22    (10)  all_58_1 = all_52_9
% 200.36/33.22    (11)   ~ (all_52_9 = all_52_13)
% 200.36/33.22    (12)   ~ (e3 = e0)
% 200.36/33.22    (13)  op(e2, e3) = all_52_3
% 200.36/33.22    (14)   ~ (all_52_23 = all_4_0)
% 200.36/33.22    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.22    (16)   ~ (all_52_7 = all_52_15)
% 200.36/33.22    (17)   ~ (all_52_3 = all_52_19)
% 200.36/33.22    (18)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.22    (19)   ~ (all_52_17 = all_52_25)
% 200.36/33.22    (20)   ~ (all_52_3 = all_6_2)
% 200.36/33.22    (21)  all_58_0 = all_6_2
% 200.36/33.22    (22)  op(all_14_2, e0) = all_14_1
% 200.36/33.22    (23)  all_56_4 = all_52_3
% 200.36/33.22    (24)   ~ (all_52_17 = all_10_2)
% 200.36/33.22    (25)  op(e3, e0) = all_52_25
% 200.36/33.22    (26)  op(e0, all_14_1) = all_14_0
% 200.36/33.22    (27)  op(all_52_5, all_52_5) = all_52_4
% 200.36/33.22    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 200.36/33.22    (29)  op(all_52_19, all_52_19) = all_52_18
% 200.36/33.22    (30)   ~ (all_52_27 = all_52_29)
% 200.36/33.22    (31)  all_58_13 = all_52_15
% 200.36/33.22    (32)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.22    (33)  all_58_9 = all_52_25
% 200.36/33.22    (34)   ~ (all_6_1 = e1)
% 200.36/33.22    (35)   ~ (all_52_29 = all_14_2)
% 200.36/33.22    (36)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.22    (37)  op(e1, e3) = all_52_5
% 200.36/33.22    (38)  op(e2, e2) = all_4_2
% 200.36/33.22    (39)   ~ (all_52_3 = all_52_5)
% 200.36/33.22    (40)  op(all_4_2, e2) = e1
% 200.36/33.22    (41)  all_58_11 = all_52_29
% 200.36/33.22    (42)  all_56_5 = all_4_2
% 200.36/33.22    (43)   ~ (all_52_25 = all_14_2)
% 200.36/33.22    (44)   ~ (all_52_9 = all_52_15)
% 200.36/33.22    (45)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.22    (46)   ~ (all_52_3 = all_52_27)
% 200.36/33.22    (47)  op(all_10_2, e1) = all_10_1
% 200.36/33.22    (48)   ~ (all_10_2 = all_4_0)
% 200.36/33.22    (49)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.22    (50)   ~ (all_52_7 = all_6_2)
% 200.36/33.22    (51)  op(e0, e0) = all_14_2
% 200.36/33.22    (52)  op(e0, e1) = all_52_23
% 200.36/33.22    (53)  all_56_15 = all_14_2
% 200.36/33.22    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.22    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 200.36/33.22    (56)  op(e1, e0) = all_52_29
% 200.36/33.22    (57)  all_56_11 = all_52_29
% 200.36/33.22    (58)   ~ (all_4_0 = e3)
% 200.36/33.22    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.22    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.22    (61)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 200.36/33.22    (62)   ~ (e2 = e1)
% 200.36/33.22    (63)   ~ (all_52_13 = all_10_2)
% 200.36/33.22    (64)   ~ (all_6_0 = e1)
% 200.36/33.22    (65)  all_58_10 = all_52_27
% 200.36/33.22    (66)  all_56_8 = all_52_5
% 200.36/33.22    (67)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.22    (68)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.22    (69)   ~ (all_52_19 = all_52_23)
% 200.36/33.22    (70)   ~ (all_52_25 = all_52_29)
% 200.36/33.22    (71)   ~ (all_52_29 = all_10_2)
% 200.36/33.22    (72)  all_58_7 = all_52_13
% 200.36/33.22    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.22    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.22    (75)   ~ (all_52_5 = all_52_7)
% 200.36/33.22    (76)  all_58_12 = all_52_7
% 200.36/33.22    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.22    (78)   ~ (all_52_7 = all_14_2)
% 200.36/33.22    (79)   ~ (all_14_2 = e0)
% 200.36/33.22    (80)  all_58_2 = all_52_3
% 200.36/33.22    (81)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 200.36/33.22    (82)  all_56_2 = all_52_17
% 200.36/33.22    (83)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.22    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.22    (85)  op(e3, all_6_1) = all_6_0
% 200.36/33.22    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 200.36/33.22    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.22    (88)  all_56_7 = all_52_27
% 200.36/33.22    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 200.36/33.22    (90)   ~ (e2 = e0)
% 200.36/33.22    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.22    (92)   ~ (all_52_5 = all_52_29)
% 200.36/33.22    (93)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.22    (94)  all_56_6 = all_52_19
% 200.36/33.22    (95)   ~ (all_52_15 = all_14_2)
% 200.36/33.22    (96)   ~ (all_52_19 = all_52_27)
% 200.36/33.22    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 200.36/33.22    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.22    (99)   ~ (all_6_0 = e2)
% 200.36/33.22    (100)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.22    (101)   ~ (all_52_13 = all_4_2)
% 200.36/33.22    (102)  op(e3, e1) = all_52_17
% 200.36/33.22    (103)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 200.36/33.22    (104)  op(e0, e3) = all_52_7
% 200.36/33.22    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.22    (106)   ~ (all_52_9 = all_52_25)
% 200.36/33.22    (107)  all_58_15 = all_14_2
% 200.36/33.22    (108)   ~ (all_52_19 = all_10_2)
% 200.36/33.22    (109)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.22    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.22    (111)   ~ (all_10_1 = e2)
% 200.36/33.22    (112)  all_58_8 = all_10_2
% 200.36/33.22    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.22    (114)   ~ (all_52_5 = all_10_2)
% 200.36/33.22    (115)  op(all_52_29, all_52_29) = all_52_28
% 200.36/33.22    (116)   ~ (all_52_23 = all_14_2)
% 200.36/33.22    (117)  all_56_12 = all_52_7
% 200.36/33.22    (118)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.22    (119)  all_58_5 = all_4_0
% 200.36/33.22    (120)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 200.36/33.22    (121)   ~ (all_52_25 = all_6_2)
% 200.36/33.22    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.22    (123)   ~ (all_52_9 = all_4_2)
% 200.36/33.22    (124)   ~ (all_52_5 = all_6_2)
% 200.36/33.22    (125)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.22    (126)   ~ (all_52_9 = all_6_2)
% 200.36/33.22    (127)   ~ (all_52_13 = all_52_15)
% 200.36/33.22    (128)  all_56_0 = all_6_2
% 200.36/33.22    (129)  op(e3, e3) = all_6_2
% 200.36/33.22    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.22    (131)   ~ (all_52_27 = all_14_2)
% 200.36/33.22    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.22    (133)  all_56_14 = all_52_23
% 200.36/33.22    (134)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.22    (135)  all_56_3 = all_52_25
% 200.36/33.22    (136)   ~ (all_52_3 = all_52_7)
% 200.36/33.22    (137)   ~ (all_10_1 = e3)
% 200.36/33.22    (138)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.22    (139)  all_58_5 = all_52_19
% 200.36/33.22    (140)  all_56_1 = all_52_9
% 200.36/33.22    (141)   ~ (all_52_15 = all_4_2)
% 200.36/33.22    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.22           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 200.36/33.22           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 200.36/33.22           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 200.36/33.22    (143)   ~ (all_52_27 = all_4_2)
% 200.36/33.22    (144)  all_58_6 = all_52_5
% 200.36/33.22    (145)   ~ (all_4_0 = all_4_2)
% 200.36/33.22    (146)  op(e3, e2) = all_52_9
% 200.36/33.22    (147)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.22    (148)   ~ (all_52_17 = all_6_2)
% 200.36/33.22    (149)   ~ (e1 = e0)
% 200.36/33.22    (150)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 200.36/33.22    (151)   ~ (e3 = e2)
% 200.36/33.22    (152)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.22    (153)   ~ (all_52_9 = all_52_17)
% 200.36/33.22    (154)  all_56_10 = all_10_2
% 200.36/33.22    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.22    (156)   ~ (all_52_3 = all_4_0)
% 200.36/33.22    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 200.36/33.22    (158)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.22    (159)   ~ (all_6_1 = e2)
% 200.36/33.22    (160)  op(e1, e1) = all_10_2
% 200.36/33.22    (161)   ~ (all_52_23 = all_10_2)
% 200.36/33.22    (162)   ~ (all_52_7 = all_52_23)
% 200.36/33.22    (163)   ~ (all_52_17 = all_52_19)
% 200.36/33.22    (164)  all_58_3 = all_4_2
% 200.36/33.22    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 200.36/33.22    (166)  all_56_13 = all_52_15
% 200.36/33.22    (167)   ~ (all_52_3 = all_4_2)
% 200.36/33.22    (168)   ~ (all_52_19 = all_4_2)
% 200.36/33.22    (169)   ~ (all_52_17 = all_52_23)
% 200.36/33.22    (170)  op(all_6_2, e3) = all_6_1
% 200.36/33.22    (171)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 200.36/33.22    (172)  all_58_4 = all_52_17
% 200.36/33.22    (173)   ~ (all_14_0 = e2)
% 200.36/33.22    (174)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.36/33.22    (175)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.22  
% 200.36/33.22  Begin of proof
% 200.36/33.22  | 
% 200.36/33.22  | BETA: splitting (142) gives:
% 200.36/33.22  | 
% 200.36/33.22  | Case 1:
% 200.36/33.22  | | 
% 200.36/33.22  | |   (176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 200.36/33.22  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 200.36/33.22  | | 
% 200.36/33.22  | | BETA: splitting (176) gives:
% 200.36/33.22  | | 
% 200.36/33.22  | | Case 1:
% 200.36/33.22  | | | 
% 200.36/33.22  | | |   (177)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 200.36/33.22  | | | 
% 200.36/33.22  | | | ALPHA: (177) implies:
% 200.36/33.22  | | |   (178)  all_52_6 = e0
% 200.36/33.22  | | |   (179)  all_52_4 = e1
% 200.36/33.22  | | |   (180)  all_52_2 = e2
% 200.36/33.22  | | |   (181)  all_52_0 = e3
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REDUCE: (7), (180) imply:
% 200.36/33.22  | | |   (182)  op(all_52_3, all_52_3) = e2
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REDUCE: (27), (179) imply:
% 200.36/33.22  | | |   (183)  op(all_52_5, all_52_5) = e1
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REDUCE: (18), (178) imply:
% 200.36/33.22  | | |   (184)  op(all_52_7, all_52_7) = e0
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REDUCE: (49), (181) imply:
% 200.36/33.22  | | |   (185)  op(all_6_2, all_6_2) = e3
% 200.36/33.22  | | | 
% 200.36/33.22  | | | BETA: splitting (113) gives:
% 200.36/33.22  | | | 
% 200.36/33.22  | | | Case 1:
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | |   (186)  all_56_15 = e3
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | | REF_CLOSE: (4), (8), (15), (17), (20), (21), (31), (38), (39), (40),
% 200.36/33.22  | | | |            (44), (45), (47), (51), (52), (53), (54), (58), (62), (64),
% 200.36/33.22  | | | |            (65), (66), (67), (69), (73), (74), (76), (78), (79), (80),
% 200.36/33.22  | | | |            (81), (84), (85), (87), (93), (94), (98), (107), (108),
% 200.36/33.22  | | | |            (109), (110), (111), (112), (114), (117), (119), (123),
% 200.36/33.22  | | | |            (124), (125), (129), (131), (132), (133), (134), (137),
% 200.36/33.22  | | | |            (139), (143), (144), (146), (148), (150), (155), (160),
% 200.36/33.22  | | | |            (161), (162), (164), (167), (170), (172), (182), (183),
% 200.36/33.22  | | | |            (184), (185), (186) are inconsistent by sub-proof #198.
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | Case 2:
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | |   (187)   ~ (all_56_15 = e3)
% 200.36/33.22  | | | |   (188)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | | REDUCE: (53), (187) imply:
% 200.36/33.22  | | | |   (189)   ~ (all_14_2 = e3)
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | | BETA: splitting (59) gives:
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | | Case 1:
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | |   (190)  all_56_13 = e3
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | | COMBINE_EQS: (166), (190) imply:
% 200.36/33.22  | | | | |   (191)  all_52_15 = e3
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | | SIMP: (191) implies:
% 200.36/33.22  | | | | |   (192)  all_52_15 = e3
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (12), (15), (16), (17),
% 200.36/33.22  | | | | |            (20), (21), (22), (23), (26), (28), (31), (33), (38), (41),
% 200.36/33.22  | | | | |            (43), (44), (45), (46), (50), (51), (53), (54), (56), (61),
% 200.36/33.22  | | | | |            (67), (68), (73), (76), (78), (79), (80), (81), (84), (88),
% 200.36/33.22  | | | | |            (89), (90), (93), (94), (95), (96), (100), (104), (106),
% 200.36/33.22  | | | | |            (107), (108), (114), (117), (121), (122), (123), (129),
% 200.36/33.22  | | | | |            (130), (132), (133), (135), (136), (138), (139), (140),
% 200.36/33.22  | | | | |            (143), (144), (147), (149), (152), (160), (161), (162),
% 200.36/33.22  | | | | |            (164), (167), (168), (171), (173), (182), (183), (184),
% 200.36/33.22  | | | | |            (185), (188), (192) are inconsistent by sub-proof #661.
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | Case 2:
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | |   (193)   ~ (all_56_13 = e3)
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | | REDUCE: (166), (193) imply:
% 200.36/33.22  | | | | |   (194)   ~ (all_52_15 = e3)
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | | REF_CLOSE: (4), (8), (12), (15), (21), (31), (38), (45), (47), (50),
% 200.36/33.22  | | | | |            (51), (52), (54), (76), (78), (80), (84), (90), (93),
% 200.36/33.22  | | | | |            (100), (107), (114), (117), (129), (137), (141), (144),
% 200.36/33.22  | | | | |            (147), (160), (162), (167), (182), (183), (184), (185),
% 200.36/33.22  | | | | |            (189), (194) are inconsistent by sub-proof #196.
% 200.36/33.22  | | | | | 
% 200.36/33.22  | | | | End of split
% 200.36/33.22  | | | | 
% 200.36/33.22  | | | End of split
% 200.36/33.22  | | | 
% 200.36/33.22  | | Case 2:
% 200.36/33.22  | | | 
% 200.36/33.22  | | |   (195)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14),
% 200.36/33.22  | | |            (15), (16), (18), (19), (20), (21), (22), (24), (25), (30),
% 200.36/33.22  | | |            (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 200.36/33.22  | | |            (41), (42), (43), (47), (48), (49), (50), (51), (53), (54),
% 200.36/33.22  | | |            (58), (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 200.36/33.22  | | |            (71), (72), (75), (76), (77), (78), (80), (82), (83), (84),
% 200.36/33.22  | | |            (85), (91), (92), (95), (98), (99), (100), (101), (102), (104),
% 200.36/33.22  | | |            (105), (106), (107), (109), (110), (112), (113), (114), (117),
% 200.36/33.22  | | |            (118), (119), (121), (122), (124), (125), (126), (129), (130),
% 200.36/33.22  | | |            (131), (132), (134), (135), (136), (138), (140), (141), (143),
% 200.36/33.22  | | |            (144), (145), (146), (147), (148), (151), (152), (153), (154),
% 200.36/33.22  | | |            (155), (158), (159), (160), (161), (162), (164), (166), (167),
% 200.36/33.22  | | |            (169), (170), (172), (174), (175), (195) are inconsistent by
% 200.36/33.22  | | |            sub-proof #188.
% 200.36/33.22  | | | 
% 200.36/33.22  | | End of split
% 200.36/33.22  | | 
% 200.36/33.22  | Case 2:
% 200.36/33.22  | | 
% 200.36/33.22  | |   (196)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 200.36/33.22  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 200.36/33.22  | |            e0)
% 200.36/33.22  | | 
% 200.36/33.22  | | BETA: splitting (196) gives:
% 200.36/33.22  | | 
% 200.36/33.22  | | Case 1:
% 200.36/33.22  | | | 
% 200.36/33.22  | | |   (197)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REF_CLOSE: (2), (4), (7), (8), (10), (15), (18), (20), (21), (22), (24),
% 200.36/33.22  | | |            (25), (31), (32), (33), (34), (37), (38), (39), (40), (43),
% 200.36/33.22  | | |            (44), (46), (47), (50), (51), (53), (54), (58), (59), (60),
% 200.36/33.22  | | |            (62), (63), (65), (66), (72), (75), (76), (78), (80), (82),
% 200.36/33.22  | | |            (83), (84), (85), (95), (98), (99), (102), (104), (105), (107),
% 200.36/33.22  | | |            (108), (109), (110), (111), (112), (113), (116), (117), (118),
% 200.36/33.22  | | |            (119), (122), (123), (124), (125), (126), (129), (131), (132),
% 200.36/33.22  | | |            (134), (135), (136), (138), (139), (144), (145), (146), (147),
% 200.36/33.22  | | |            (148), (151), (155), (156), (159), (162), (164), (166), (167),
% 200.36/33.22  | | |            (170), (172), (197) are inconsistent by sub-proof #200.
% 200.36/33.22  | | | 
% 200.36/33.22  | | Case 2:
% 200.36/33.22  | | | 
% 200.36/33.22  | | |   (198)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 200.36/33.22  | | | 
% 200.36/33.22  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (13), (15), (16),
% 200.36/33.22  | | |            (18), (19), (20), (21), (23), (24), (25), (27), (29), (30),
% 200.36/33.22  | | |            (31), (33), (34), (35), (36), (37), (38), (39), (41), (42),
% 200.36/33.22  | | |            (43), (44), (46), (47), (49), (50), (51), (53), (54), (55),
% 200.36/33.22  | | |            (57), (59), (60), (61), (64), (65), (66), (67), (68), (69),
% 200.36/33.22  | | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 200.36/33.22  | | |            (80), (82), (84), (85), (86), (87), (89), (91), (92), (95),
% 200.36/33.22  | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 200.36/33.22  | | |            (105), (106), (107), (108), (109), (110), (112), (113), (114),
% 200.36/33.22  | | |            (115), (116), (117), (118), (120), (121), (122), (123), (124),
% 200.36/33.22  | | |            (126), (127), (128), (129), (130), (131), (132), (133), (135),
% 200.36/33.22  | | |            (136), (138), (139), (140), (141), (143), (144), (147), (148),
% 200.36/33.22  | | |            (151), (152), (157), (158), (159), (160), (162), (163), (164),
% 200.36/33.22  | | |            (165), (166), (167), (168), (169), (170), (172), (175), (198)
% 200.36/33.22  | | |            are inconsistent by sub-proof #1008.
% 200.36/33.22  | | | 
% 200.36/33.22  | | End of split
% 200.36/33.22  | | 
% 200.36/33.22  | End of split
% 200.36/33.22  | 
% 200.36/33.22  End of proof
% 200.36/33.22  
% 200.36/33.22  Sub-proof #188 shows that the following formulas are inconsistent:
% 200.36/33.22  ----------------------------------------------------------------
% 200.36/33.22    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.22    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.22    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.22    (4)  all_58_14 = all_52_23
% 200.36/33.22    (5)   ~ (e3 = e1)
% 200.36/33.22    (6)   ~ (all_52_17 = all_4_0)
% 200.36/33.22    (7)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.22    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.22    (9)   ~ (all_52_5 = all_52_13)
% 200.36/33.22    (10)  all_58_1 = all_52_9
% 200.36/33.22    (11)   ~ (all_52_9 = all_52_13)
% 200.36/33.22    (12)   ~ (all_52_23 = all_4_0)
% 200.36/33.22    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.22    (14)   ~ (all_52_7 = all_52_15)
% 200.36/33.22    (15)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.22    (16)   ~ (all_52_17 = all_52_25)
% 200.36/33.22    (17)   ~ (all_52_3 = all_6_2)
% 200.36/33.22    (18)  all_58_0 = all_6_2
% 200.36/33.22    (19)  op(all_14_2, e0) = all_14_1
% 200.36/33.22    (20)   ~ (all_52_17 = all_10_2)
% 200.36/33.22    (21)  op(e3, e0) = all_52_25
% 200.36/33.22    (22)   ~ (all_52_27 = all_52_29)
% 200.36/33.22    (23)  all_58_13 = all_52_15
% 200.36/33.22    (24)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.22    (25)  all_58_9 = all_52_25
% 200.36/33.22    (26)   ~ (all_6_1 = e1)
% 200.36/33.22    (27)   ~ (all_52_29 = all_14_2)
% 200.36/33.22    (28)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.22    (29)  op(e1, e3) = all_52_5
% 200.36/33.22    (30)  op(e2, e2) = all_4_2
% 200.36/33.22    (31)   ~ (all_52_3 = all_52_5)
% 200.36/33.22    (32)  op(all_4_2, e2) = e1
% 200.36/33.22    (33)  all_58_11 = all_52_29
% 200.36/33.22    (34)  all_56_5 = all_4_2
% 200.36/33.22    (35)   ~ (all_52_25 = all_14_2)
% 200.36/33.22    (36)  op(all_10_2, e1) = all_10_1
% 200.36/33.22    (37)   ~ (all_10_2 = all_4_0)
% 200.36/33.22    (38)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.22    (39)   ~ (all_52_7 = all_6_2)
% 200.36/33.22    (40)  op(e0, e0) = all_14_2
% 200.36/33.22    (41)  all_56_15 = all_14_2
% 200.36/33.22    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.22    (43)   ~ (all_4_0 = e3)
% 200.36/33.22    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.22    (45)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.22    (46)   ~ (e2 = e1)
% 200.36/33.22    (47)   ~ (all_52_13 = all_10_2)
% 200.36/33.22    (48)   ~ (all_6_0 = e1)
% 200.36/33.22    (49)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 200.36/33.22    (50)  all_58_10 = all_52_27
% 200.36/33.22    (51)  all_56_8 = all_52_5
% 200.36/33.22    (52)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.22    (53)  op(all_52_15, all_52_15) = all_52_14
% 200.36/33.22    (54)   ~ (all_52_29 = all_10_2)
% 200.36/33.22    (55)  all_58_7 = all_52_13
% 200.36/33.22    (56)   ~ (all_52_5 = all_52_7)
% 200.36/33.22    (57)  all_58_12 = all_52_7
% 200.36/33.22    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.22    (59)   ~ (all_52_7 = all_14_2)
% 200.36/33.22    (60)  all_58_2 = all_52_3
% 200.36/33.22    (61)  all_56_2 = all_52_17
% 200.36/33.22    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.22    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.22    (64)  op(e3, all_6_1) = all_6_0
% 200.36/33.22    (65)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.22    (66)   ~ (all_52_5 = all_52_29)
% 200.36/33.22    (67)   ~ (all_52_15 = all_14_2)
% 200.36/33.22    (68)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.22    (69)   ~ (all_6_0 = e2)
% 200.36/33.22    (70)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.22    (71)   ~ (all_52_13 = all_4_2)
% 200.36/33.22    (72)  op(e3, e1) = all_52_17
% 200.36/33.23    (73)  op(e0, e3) = all_52_7
% 200.36/33.23    (74)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.23    (75)   ~ (all_52_9 = all_52_25)
% 200.36/33.23    (76)  all_58_15 = all_14_2
% 200.36/33.23    (77)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.23    (78)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.23    (79)  all_58_8 = all_10_2
% 200.36/33.23    (80)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.23    (81)   ~ (all_52_5 = all_10_2)
% 200.36/33.23    (82)  all_56_12 = all_52_7
% 200.36/33.23    (83)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.23    (84)  all_58_5 = all_4_0
% 200.36/33.23    (85)   ~ (all_52_25 = all_6_2)
% 200.36/33.23    (86)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.23    (87)   ~ (all_52_5 = all_6_2)
% 200.36/33.23    (88)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.23    (89)   ~ (all_52_9 = all_6_2)
% 200.36/33.23    (90)  op(e3, e3) = all_6_2
% 200.36/33.23    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.23    (92)   ~ (all_52_27 = all_14_2)
% 200.36/33.23    (93)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.23    (94)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.23    (95)  all_56_3 = all_52_25
% 200.36/33.23    (96)   ~ (all_52_3 = all_52_7)
% 200.36/33.23    (97)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.23    (98)  all_56_1 = all_52_9
% 200.36/33.23    (99)   ~ (all_52_15 = all_4_2)
% 200.36/33.23    (100)   ~ (all_52_27 = all_4_2)
% 200.36/33.23    (101)  all_58_6 = all_52_5
% 200.36/33.23    (102)   ~ (all_4_0 = all_4_2)
% 200.36/33.23    (103)  op(e3, e2) = all_52_9
% 200.36/33.23    (104)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.23    (105)   ~ (all_52_17 = all_6_2)
% 200.36/33.23    (106)   ~ (e3 = e2)
% 200.36/33.23    (107)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.23    (108)   ~ (all_52_9 = all_52_17)
% 200.36/33.23    (109)  all_56_10 = all_10_2
% 200.36/33.23    (110)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.23    (111)  op(all_52_13, all_52_13) = all_52_12
% 200.36/33.23    (112)   ~ (all_6_1 = e2)
% 200.36/33.23    (113)  op(e1, e1) = all_10_2
% 200.36/33.23    (114)   ~ (all_52_23 = all_10_2)
% 200.36/33.23    (115)   ~ (all_52_7 = all_52_23)
% 200.36/33.23    (116)  all_58_3 = all_4_2
% 200.36/33.23    (117)  all_56_13 = all_52_15
% 200.36/33.23    (118)   ~ (all_52_3 = all_4_2)
% 200.36/33.23    (119)   ~ (all_52_17 = all_52_23)
% 200.36/33.23    (120)  op(all_6_2, e3) = all_6_1
% 200.36/33.23    (121)  all_58_4 = all_52_17
% 200.36/33.23    (122)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.36/33.23    (123)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.23  
% 200.36/33.23  Begin of proof
% 200.36/33.23  | 
% 200.36/33.23  | ALPHA: (49) implies:
% 200.36/33.23  |   (124)  all_52_14 = e0
% 200.36/33.23  |   (125)  all_52_12 = e1
% 200.36/33.23  |   (126)  all_52_10 = e2
% 200.36/33.23  |   (127)  all_52_8 = e3
% 200.36/33.23  | 
% 200.36/33.23  | REDUCE: (52), (127) imply:
% 200.36/33.23  |   (128)  op(all_52_9, all_52_9) = e3
% 200.36/33.23  | 
% 200.36/33.23  | REDUCE: (111), (125) imply:
% 200.36/33.23  |   (129)  op(all_52_13, all_52_13) = e1
% 200.36/33.23  | 
% 200.36/33.23  | REDUCE: (53), (124) imply:
% 200.36/33.23  |   (130)  op(all_52_15, all_52_15) = e0
% 200.36/33.23  | 
% 200.36/33.23  | REDUCE: (94), (126) imply:
% 200.36/33.23  |   (131)  op(all_4_2, all_4_2) = e2
% 200.36/33.23  | 
% 200.36/33.23  | BETA: splitting (80) gives:
% 200.36/33.23  | 
% 200.36/33.23  | Case 1:
% 200.36/33.23  | | 
% 200.36/33.23  | |   (132)  all_56_15 = e3
% 200.36/33.23  | | 
% 200.36/33.23  | | COMBINE_EQS: (41), (132) imply:
% 200.36/33.23  | |   (133)  all_14_2 = e3
% 200.36/33.23  | | 
% 200.36/33.23  | | SIMP: (133) implies:
% 200.36/33.23  | |   (134)  all_14_2 = e3
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (59), (134) imply:
% 200.36/33.23  | |   (135)   ~ (all_52_7 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (35), (134) imply:
% 200.36/33.23  | |   (136)   ~ (all_52_25 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (92), (134) imply:
% 200.36/33.23  | |   (137)   ~ (all_52_27 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (27), (134) imply:
% 200.36/33.23  | |   (138)   ~ (all_52_29 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (97), (134) imply:
% 200.36/33.23  | |   (139)  op(e3, e3) = all_52_30
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (19), (134) imply:
% 200.36/33.23  | |   (140)  op(e3, e0) = all_14_1
% 200.36/33.23  | | 
% 200.36/33.23  | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3, simplifying
% 200.36/33.23  | |              with (21), (140) gives:
% 200.36/33.23  | |   (141)  all_52_25 = all_14_1
% 200.36/33.23  | | 
% 200.36/33.23  | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3, simplifying
% 200.36/33.23  | |              with (90), (139) gives:
% 200.36/33.23  | |   (142)  all_52_30 = all_6_2
% 200.36/33.23  | | 
% 200.36/33.23  | | COMBINE_EQS: (95), (141) imply:
% 200.36/33.23  | |   (143)  all_56_3 = all_14_1
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (75), (141) imply:
% 200.36/33.23  | |   (144)   ~ (all_52_9 = all_14_1)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (16), (141) imply:
% 200.36/33.23  | |   (145)   ~ (all_52_17 = all_14_1)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (85), (141) imply:
% 200.36/33.23  | |   (146)   ~ (all_14_1 = all_6_2)
% 200.36/33.23  | | 
% 200.36/33.23  | | BETA: splitting (42) gives:
% 200.36/33.23  | | 
% 200.36/33.23  | | Case 1:
% 200.36/33.23  | | | 
% 200.36/33.23  | | |   (147)  all_58_2 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | COMBINE_EQS: (60), (147) imply:
% 200.36/33.23  | | |   (148)  all_52_3 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | SIMP: (148) implies:
% 200.36/33.23  | | |   (149)  all_52_3 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (31), (149) imply:
% 200.36/33.23  | | |   (150)   ~ (all_52_5 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | SIMP: (150) implies:
% 200.36/33.23  | | |   (151)   ~ (all_52_5 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (96), (149) imply:
% 200.36/33.23  | | |   (152)   ~ (all_52_7 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (17), (149) imply:
% 200.36/33.23  | | |   (153)   ~ (all_6_2 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | SIMP: (153) implies:
% 200.36/33.23  | | |   (154)   ~ (all_6_2 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (7), (149) imply:
% 200.36/33.23  | | |   (155)  op(e3, e3) = all_52_2
% 200.36/33.23  | | | 
% 200.36/33.23  | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3, simplifying
% 200.36/33.23  | | |              with (90), (155) gives:
% 200.36/33.23  | | |   (156)  all_52_2 = all_6_2
% 200.36/33.23  | | | 
% 200.36/33.23  | | | BETA: splitting (110) gives:
% 200.36/33.23  | | | 
% 200.36/33.23  | | | Case 1:
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | |   (157)  all_58_4 = e3
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | COMBINE_EQS: (121), (157) imply:
% 200.36/33.23  | | | |   (158)  all_52_17 = e3
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | SIMP: (158) implies:
% 200.36/33.23  | | | |   (159)  all_52_17 = e3
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | REDUCE: (145), (159) imply:
% 200.36/33.23  | | | |   (160)   ~ (all_14_1 = e3)
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | SIMP: (160) implies:
% 200.36/33.23  | | | |   (161)   ~ (all_14_1 = e3)
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | REDUCE: (20), (159) imply:
% 200.36/33.23  | | | |   (162)   ~ (all_10_2 = e3)
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | SIMP: (162) implies:
% 200.36/33.23  | | | |   (163)   ~ (all_10_2 = e3)
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | REDUCE: (83), (159) imply:
% 200.36/33.23  | | | |   (164)  op(e3, e3) = all_52_16
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | BETA: splitting (58) gives:
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | Case 1:
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | |   (165)  all_58_6 = e3
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | | REF_CLOSE: (101), (151), (165) are inconsistent by sub-proof #1328.
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | Case 2:
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | |   (166)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | | BETA: splitting (166) gives:
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | | Case 1:
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | |   (167)  all_58_7 = e3
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | COMBINE_EQS: (55), (167) imply:
% 200.36/33.23  | | | | | |   (168)  all_52_13 = e3
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (11), (168) imply:
% 200.36/33.23  | | | | | |   (169)   ~ (all_52_9 = e3)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (129), (168) imply:
% 200.36/33.23  | | | | | |   (170)  op(e3, e3) = e1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_16, e3, e3,
% 200.36/33.23  | | | | | |              simplifying with (90), (164) gives:
% 200.36/33.23  | | | | | |   (171)  all_52_16 = all_6_2
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | GROUND_INST: instantiating (8) with e1, all_52_16, e3, e3,
% 200.36/33.23  | | | | | |              simplifying with (164), (170) gives:
% 200.36/33.23  | | | | | |   (172)  all_52_16 = e1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | COMBINE_EQS: (171), (172) imply:
% 200.36/33.23  | | | | | |   (173)  all_6_2 = e1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | COMBINE_EQS: (18), (173) imply:
% 200.36/33.23  | | | | | |   (174)  all_58_0 = e1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (87), (173) imply:
% 200.36/33.23  | | | | | |   (175)   ~ (all_52_5 = e1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (39), (173) imply:
% 200.36/33.23  | | | | | |   (176)   ~ (all_52_7 = e1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (89), (173) imply:
% 200.36/33.23  | | | | | |   (177)   ~ (all_52_9 = e1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (146), (173) imply:
% 200.36/33.23  | | | | | |   (178)   ~ (all_14_1 = e1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (154), (173) imply:
% 200.36/33.23  | | | | | |   (179)   ~ (e3 = e1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (120), (173) imply:
% 200.36/33.23  | | | | | |   (180)  op(e1, e3) = all_6_1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | GROUND_INST: instantiating (8) with all_52_5, all_6_1, e3, e1,
% 200.36/33.23  | | | | | |              simplifying with (29), (180) gives:
% 200.36/33.23  | | | | | |   (181)  all_52_5 = all_6_1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | COMBINE_EQS: (51), (181) imply:
% 200.36/33.23  | | | | | |   (182)  all_56_8 = all_6_1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | COMBINE_EQS: (101), (181) imply:
% 200.36/33.23  | | | | | |   (183)  all_58_6 = all_6_1
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (56), (181) imply:
% 200.36/33.23  | | | | | |   (184)   ~ (all_52_7 = all_6_1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | SIMP: (184) implies:
% 200.36/33.23  | | | | | |   (185)   ~ (all_52_7 = all_6_1)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REDUCE: (151), (181) imply:
% 200.36/33.23  | | | | | |   (186)   ~ (all_6_1 = e3)
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | BETA: splitting (78) gives:
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | Case 1:
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | |   (187)  all_56_8 = e3
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | | REF_CLOSE: (182), (186), (187) are inconsistent by sub-proof
% 200.36/33.23  | | | | | | |            #1101.
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | Case 2:
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | |   (188)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | | BETA: splitting (68) gives:
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | | Case 1:
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | |   (189)  all_58_0 = e2
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | | REF_CLOSE: (46), (174), (189) are inconsistent by sub-proof
% 200.36/33.23  | | | | | | | |            #1273.
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | Case 2:
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | |   (190)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | | BETA: splitting (190) gives:
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | | Case 1:
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | |   (191)  all_58_2 = e2
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | REF_CLOSE: (106), (147), (191) are inconsistent by sub-proof
% 200.36/33.23  | | | | | | | | |            #1124.
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | Case 2:
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | |   (192)  all_58_6 = e2 | all_58_12 = e2
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | BETA: splitting (192) gives:
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | Case 1:
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | |   (193)  all_58_6 = e2
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | REF_CLOSE: (112), (183), (193) are inconsistent by sub-proof
% 200.36/33.23  | | | | | | | | | |            #1211.
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | Case 2:
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | |   (194)  all_58_12 = e2
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | COMBINE_EQS: (57), (194) imply:
% 200.36/33.23  | | | | | | | | | |   (195)  all_52_7 = e2
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | SIMP: (195) implies:
% 200.36/33.23  | | | | | | | | | |   (196)  all_52_7 = e2
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | REDUCE: (185), (196) imply:
% 200.36/33.23  | | | | | | | | | |   (197)   ~ (all_6_1 = e2)
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | REDUCE: (15), (196) imply:
% 200.36/33.23  | | | | | | | | | |   (198)  op(e2, e2) = all_52_6
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | BETA: splitting (188) gives:
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | Case 1:
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | |   (199)  all_56_8 = e2
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | REF_CLOSE: (112), (182), (199) are inconsistent by sub-proof
% 200.36/33.23  | | | | | | | | | | |            #1321.
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | Case 2:
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | |   (200)  all_56_8 = e1 | all_56_8 = e0
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | BETA: splitting (200) gives:
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | Case 1:
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | |   (201)  all_56_8 = e1
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | REF_CLOSE: (26), (182), (201) are inconsistent by sub-proof
% 200.36/33.23  | | | | | | | | | | | |            #1320.
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | Case 2:
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | |   (202)  all_56_8 = e0
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | COMBINE_EQS: (182), (202) imply:
% 200.36/33.23  | | | | | | | | | | | |   (203)  all_6_1 = e0
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | SIMP: (203) implies:
% 200.36/33.23  | | | | | | | | | | | |   (204)  all_6_1 = e0
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | REDUCE: (64), (204) imply:
% 200.36/33.23  | | | | | | | | | | | |   (205)  op(e3, e0) = all_6_0
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, all_52_6, e2, e2,
% 200.36/33.23  | | | | | | | | | | | |              simplifying with (30), (198) gives:
% 200.36/33.23  | | | | | | | | | | | |   (206)  all_52_6 = all_4_2
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_1, all_6_0, e0, e3,
% 200.36/33.23  | | | | | | | | | | | |              simplifying with (140), (205) gives:
% 200.36/33.23  | | | | | | | | | | | |   (207)  all_14_1 = all_6_0
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | COMBINE_EQS: (143), (207) imply:
% 200.36/33.23  | | | | | | | | | | | |   (208)  all_56_3 = all_6_0
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | REDUCE: (161), (207) imply:
% 200.36/33.23  | | | | | | | | | | | |   (209)   ~ (all_6_0 = e3)
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | BETA: splitting (86) gives:
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | Case 1:
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | |   (210)  all_56_3 = e3
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | | COMBINE_EQS: (208), (210) imply:
% 200.36/33.23  | | | | | | | | | | | | |   (211)  all_6_0 = e3
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | | REDUCE: (209), (211) imply:
% 200.36/33.23  | | | | | | | | | | | | |   (212)  $false
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | Case 2:
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | |   (213)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | | REF_CLOSE: (5), (8), (10), (30), (46), (57), (60), (62),
% 200.36/33.23  | | | | | | | | | | | | |            (63), (69), (98), (101), (107), (118), (128),
% 200.36/33.23  | | | | | | | | | | | | |            (135), (140), (143), (144), (151), (169), (174),
% 200.36/33.23  | | | | | | | | | | | | |            (177), (178), (198), (205), (213) are inconsistent
% 200.36/33.23  | | | | | | | | | | | | |            by sub-proof #1120.
% 200.36/33.23  | | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | | End of split
% 200.36/33.23  | | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | | End of split
% 200.36/33.23  | | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | | End of split
% 200.36/33.23  | | | | | | | | | | 
% 200.36/33.23  | | | | | | | | | End of split
% 200.36/33.23  | | | | | | | | | 
% 200.36/33.23  | | | | | | | | End of split
% 200.36/33.23  | | | | | | | | 
% 200.36/33.23  | | | | | | | End of split
% 200.36/33.23  | | | | | | | 
% 200.36/33.23  | | | | | | End of split
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | Case 2:
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | |   (214)  all_58_8 = e3 | all_58_11 = e3
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | | REF_CLOSE: (33), (79), (138), (163), (214) are inconsistent by
% 200.36/33.23  | | | | | |            sub-proof #1140.
% 200.36/33.23  | | | | | | 
% 200.36/33.23  | | | | | End of split
% 200.36/33.23  | | | | | 
% 200.36/33.23  | | | | End of split
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | Case 2:
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | |   (215)   ~ (all_58_4 = e3)
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | REDUCE: (121), (215) imply:
% 200.36/33.23  | | | |   (216)   ~ (all_52_17 = e3)
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | | REF_CLOSE: (8), (10), (18), (25), (89), (90), (93), (121), (128), (136),
% 200.36/33.23  | | | |            (154), (216) are inconsistent by sub-proof #254.
% 200.36/33.23  | | | | 
% 200.36/33.23  | | | End of split
% 200.36/33.23  | | | 
% 200.36/33.23  | | Case 2:
% 200.36/33.23  | | | 
% 200.36/33.23  | | |   (217)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REF_CLOSE: (8), (18), (30), (32), (43), (50), (57), (58), (60), (63),
% 200.36/33.23  | | |            (81), (84), (90), (101), (103), (106), (113), (116), (118),
% 200.36/33.23  | | |            (128), (131), (135), (137), (217) are inconsistent by sub-proof
% 200.36/33.23  | | |            #194.
% 200.36/33.23  | | | 
% 200.36/33.23  | | End of split
% 200.36/33.23  | | 
% 200.36/33.23  | Case 2:
% 200.36/33.23  | | 
% 200.36/33.23  | |   (218)   ~ (all_56_15 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (41), (218) imply:
% 200.36/33.23  | |   (219)   ~ (all_14_2 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 200.36/33.23  | |            (15), (16), (18), (20), (22), (23), (24), (25), (26), (28), (29),
% 200.36/33.23  | |            (30), (31), (32), (33), (34), (36), (37), (38), (39), (40), (42),
% 200.36/33.23  | |            (43), (44), (45), (46), (47), (48), (50), (51), (54), (55), (56),
% 200.36/33.23  | |            (57), (58), (60), (61), (63), (64), (65), (66), (67), (68), (69),
% 200.36/33.23  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (81),
% 200.36/33.23  | |            (82), (83), (84), (85), (87), (88), (89), (90), (91), (93), (96),
% 200.36/33.23  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 200.36/33.23  | |            (107), (108), (109), (110), (112), (113), (114), (115), (116),
% 200.36/33.23  | |            (117), (118), (119), (120), (121), (122), (123), (128), (129),
% 200.36/33.23  | |            (130), (131), (219) are inconsistent by sub-proof #189.
% 200.36/33.23  | | 
% 200.36/33.23  | End of split
% 200.36/33.23  | 
% 200.36/33.23  End of proof
% 200.36/33.23  
% 200.36/33.23  Sub-proof #189 shows that the following formulas are inconsistent:
% 200.36/33.23  ----------------------------------------------------------------
% 200.36/33.23    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.23    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.23    (3)   ~ (all_52_25 = all_52_27)
% 200.36/33.23    (4)  all_58_14 = all_52_23
% 200.36/33.23    (5)   ~ (e3 = e1)
% 200.36/33.23    (6)   ~ (all_52_17 = all_4_0)
% 200.36/33.23    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.23    (8)   ~ (all_52_5 = all_52_13)
% 200.36/33.23    (9)  all_58_1 = all_52_9
% 200.36/33.23    (10)   ~ (all_52_23 = all_4_0)
% 200.36/33.23    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.23    (12)   ~ (all_52_7 = all_52_15)
% 200.36/33.23    (13)  op(all_52_15, all_52_15) = e0
% 200.36/33.23    (14)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.23    (15)   ~ (all_52_17 = all_52_25)
% 200.36/33.23    (16)  all_58_0 = all_6_2
% 200.36/33.23    (17)   ~ (all_52_17 = all_10_2)
% 200.36/33.23    (18)   ~ (all_52_27 = all_52_29)
% 200.36/33.23    (19)  all_58_13 = all_52_15
% 200.36/33.23    (20)  op(all_52_13, all_52_13) = e1
% 200.36/33.23    (21)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.23    (22)  all_58_9 = all_52_25
% 200.36/33.23    (23)   ~ (all_6_1 = e1)
% 200.36/33.23    (24)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.23    (25)  op(e1, e3) = all_52_5
% 200.36/33.23    (26)  op(e2, e2) = all_4_2
% 200.36/33.23    (27)   ~ (all_52_3 = all_52_5)
% 200.36/33.23    (28)  op(all_4_2, e2) = e1
% 200.36/33.23    (29)  all_58_11 = all_52_29
% 200.36/33.23    (30)  all_56_5 = all_4_2
% 200.36/33.23    (31)  op(all_10_2, e1) = all_10_1
% 200.36/33.23    (32)   ~ (all_10_2 = all_4_0)
% 200.36/33.23    (33)  op(all_6_2, all_6_2) = all_52_0
% 200.36/33.23    (34)   ~ (all_52_7 = all_6_2)
% 200.36/33.23    (35)  op(e0, e0) = all_14_2
% 200.36/33.23    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.23    (37)   ~ (all_4_0 = e3)
% 200.36/33.23    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.23    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.23    (40)   ~ (e2 = e1)
% 200.36/33.23    (41)   ~ (all_52_13 = all_10_2)
% 200.36/33.23    (42)   ~ (all_6_0 = e1)
% 200.36/33.23    (43)  all_58_10 = all_52_27
% 200.36/33.23    (44)  all_56_8 = all_52_5
% 200.36/33.23    (45)   ~ (all_52_29 = all_10_2)
% 200.36/33.23    (46)  all_58_7 = all_52_13
% 200.36/33.23    (47)   ~ (all_52_5 = all_52_7)
% 200.36/33.23    (48)  all_58_12 = all_52_7
% 200.36/33.23    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.23    (50)  all_58_2 = all_52_3
% 200.36/33.23    (51)  all_56_2 = all_52_17
% 200.36/33.23    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.23    (53)  op(e3, all_6_1) = all_6_0
% 200.36/33.23    (54)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.23    (55)   ~ (all_52_5 = all_52_29)
% 200.36/33.23    (56)   ~ (all_52_15 = all_14_2)
% 200.36/33.23    (57)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.23    (58)   ~ (all_6_0 = e2)
% 200.36/33.23    (59)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.23    (60)   ~ (all_52_13 = all_4_2)
% 200.36/33.23    (61)  op(e3, e1) = all_52_17
% 200.36/33.23    (62)  op(e0, e3) = all_52_7
% 200.36/33.23    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.23    (64)   ~ (all_52_9 = all_52_25)
% 200.36/33.23    (65)  all_58_15 = all_14_2
% 200.36/33.23    (66)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.23    (67)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.23    (68)  all_58_8 = all_10_2
% 200.36/33.23    (69)   ~ (all_52_5 = all_10_2)
% 200.36/33.23    (70)  all_56_12 = all_52_7
% 200.36/33.23    (71)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.23    (72)  all_58_5 = all_4_0
% 200.36/33.23    (73)   ~ (all_52_25 = all_6_2)
% 200.36/33.23    (74)   ~ (all_52_5 = all_6_2)
% 200.36/33.23    (75)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.23    (76)  op(all_4_2, all_4_2) = e2
% 200.36/33.23    (77)   ~ (all_52_9 = all_6_2)
% 200.36/33.23    (78)  op(e3, e3) = all_6_2
% 200.36/33.23    (79)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 200.36/33.23    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.23    (81)   ~ (all_52_3 = all_52_7)
% 200.36/33.23    (82)  all_56_1 = all_52_9
% 200.36/33.23    (83)   ~ (all_52_15 = all_4_2)
% 200.36/33.23    (84)   ~ (all_52_27 = all_4_2)
% 200.36/33.23    (85)  all_58_6 = all_52_5
% 200.36/33.23    (86)   ~ (all_4_0 = all_4_2)
% 200.36/33.23    (87)  op(e3, e2) = all_52_9
% 200.36/33.23    (88)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.23    (89)   ~ (all_52_17 = all_6_2)
% 200.36/33.23    (90)   ~ (e3 = e2)
% 200.36/33.23    (91)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.23    (92)   ~ (all_52_9 = all_52_17)
% 200.36/33.23    (93)  all_56_10 = all_10_2
% 200.36/33.23    (94)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.23    (95)   ~ (all_6_1 = e2)
% 200.36/33.23    (96)  op(e1, e1) = all_10_2
% 200.36/33.23    (97)  op(all_52_9, all_52_9) = e3
% 200.36/33.23    (98)   ~ (all_52_23 = all_10_2)
% 200.36/33.23    (99)   ~ (all_52_7 = all_52_23)
% 200.36/33.23    (100)  all_58_3 = all_4_2
% 200.36/33.23    (101)  all_56_13 = all_52_15
% 200.36/33.23    (102)   ~ (all_52_3 = all_4_2)
% 200.36/33.23    (103)   ~ (all_52_17 = all_52_23)
% 200.36/33.23    (104)  op(all_6_2, e3) = all_6_1
% 200.36/33.23    (105)  all_58_4 = all_52_17
% 200.36/33.23    (106)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 200.36/33.23    (107)  op(all_52_25, all_52_25) = all_52_24
% 200.36/33.23    (108)   ~ (all_14_2 = e3)
% 200.36/33.23  
% 200.36/33.23  Begin of proof
% 200.36/33.23  | 
% 200.36/33.23  | BETA: splitting (38) gives:
% 200.36/33.23  | 
% 200.36/33.23  | Case 1:
% 200.36/33.23  | | 
% 200.36/33.23  | |   (109)  all_56_13 = e3
% 200.36/33.23  | | 
% 200.36/33.23  | | COMBINE_EQS: (101), (109) imply:
% 200.36/33.23  | |   (110)  all_52_15 = e3
% 200.36/33.23  | | 
% 200.36/33.23  | | REF_CLOSE: (7), (11), (12), (13), (23), (34), (62), (70), (78), (95), (104),
% 200.36/33.23  | |            (110) are inconsistent by sub-proof #1341.
% 200.36/33.23  | | 
% 200.36/33.23  | Case 2:
% 200.36/33.23  | | 
% 200.36/33.23  | |   (111)   ~ (all_56_13 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | REDUCE: (101), (111) imply:
% 200.36/33.23  | |   (112)   ~ (all_52_15 = e3)
% 200.36/33.23  | | 
% 200.36/33.23  | | BETA: splitting (88) gives:
% 200.36/33.23  | | 
% 200.36/33.23  | | Case 1:
% 200.36/33.23  | | | 
% 200.36/33.23  | | |   (113)  all_58_12 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | COMBINE_EQS: (48), (113) imply:
% 200.36/33.23  | | |   (114)  all_52_7 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | SIMP: (114) implies:
% 200.36/33.23  | | |   (115)  all_52_7 = e3
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (81), (115) imply:
% 200.36/33.23  | | |   (116)   ~ (all_52_3 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (47), (115) imply:
% 200.36/33.23  | | |   (117)   ~ (all_52_5 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (12), (115) imply:
% 200.36/33.23  | | |   (118)   ~ (all_52_15 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (99), (115) imply:
% 200.36/33.23  | | |   (119)   ~ (all_52_23 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | SIMP: (119) implies:
% 200.36/33.23  | | |   (120)   ~ (all_52_23 = e3)
% 200.36/33.23  | | | 
% 200.36/33.23  | | | REDUCE: (14), (115) imply:
% 200.36/33.24  | | |   (121)  op(e3, e3) = all_52_6
% 200.36/33.24  | | | 
% 200.36/33.24  | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3, simplifying
% 200.36/33.24  | | |              with (78), (121) gives:
% 200.36/33.24  | | |   (122)  all_52_6 = all_6_2
% 200.36/33.24  | | | 
% 200.36/33.24  | | | BETA: splitting (94) gives:
% 200.36/33.24  | | | 
% 200.36/33.24  | | | Case 1:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | |   (123)  all_58_4 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | COMBINE_EQS: (105), (123) imply:
% 200.36/33.24  | | | |   (124)  all_52_17 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | SIMP: (124) implies:
% 200.36/33.24  | | | |   (125)  all_52_17 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REDUCE: (92), (125) imply:
% 200.36/33.24  | | | |   (126)   ~ (all_52_9 = e3)
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REDUCE: (17), (125) imply:
% 200.36/33.24  | | | |   (127)   ~ (all_10_2 = e3)
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | SIMP: (127) implies:
% 200.36/33.24  | | | |   (128)   ~ (all_10_2 = e3)
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REDUCE: (6), (125) imply:
% 200.36/33.24  | | | |   (129)   ~ (all_4_0 = e3)
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REDUCE: (71), (125) imply:
% 200.36/33.24  | | | |   (130)  op(e3, e3) = all_52_16
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_16, e3, e3,
% 200.36/33.24  | | | |              simplifying with (78), (130) gives:
% 200.36/33.24  | | | |   (131)  all_52_16 = all_6_2
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | BETA: splitting (36) gives:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | Case 1:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | |   (132)  all_58_2 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | COMBINE_EQS: (50), (132) imply:
% 200.36/33.24  | | | | |   (133)  all_52_3 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | REDUCE: (116), (133) imply:
% 200.36/33.24  | | | | |   (134)  $false
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | CLOSE: (134) is inconsistent.
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | Case 2:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | |   (135)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | REF_CLOSE: (1), (7), (8), (9), (18), (19), (20), (22), (24), (25),
% 200.36/33.24  | | | | |            (26), (28), (29), (30), (37), (43), (44), (46), (49), (54),
% 200.36/33.24  | | | | |            (55), (60), (63), (64), (67), (68), (72), (74), (75), (77),
% 200.36/33.24  | | | | |            (78), (82), (83), (84), (85), (86), (87), (91), (95), (96),
% 200.36/33.24  | | | | |            (97), (100), (104), (117), (126), (128), (135) are
% 200.36/33.24  | | | | |            inconsistent by sub-proof #192.
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | End of split
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | Case 2:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | |   (136)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | BETA: splitting (136) gives:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | Case 1:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | |   (137)  all_58_5 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | REF_CLOSE: (37), (72), (137) are inconsistent by sub-proof #215.
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | Case 2:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | |   (138)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | BETA: splitting (138) gives:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | Case 1:
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | |   (139)  all_58_8 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | COMBINE_EQS: (68), (139) imply:
% 200.36/33.24  | | | | | |   (140)  all_10_2 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | SIMP: (140) implies:
% 200.36/33.24  | | | | | |   (141)  all_10_2 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (17), (141) imply:
% 200.36/33.24  | | | | | |   (142)   ~ (all_52_17 = e3)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (45), (141) imply:
% 200.36/33.24  | | | | | |   (143)   ~ (all_52_29 = e3)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (32), (141) imply:
% 200.36/33.24  | | | | | |   (144)   ~ (all_4_0 = e3)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (21), (141) imply:
% 200.36/33.24  | | | | | |   (145)  op(e3, e3) = all_52_20
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (31), (141) imply:
% 200.36/33.24  | | | | | |   (146)  op(e3, e1) = all_10_1
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | GROUND_INST: instantiating (7) with all_52_17, all_10_1, e1, e3,
% 200.36/33.24  | | | | | |              simplifying with (61), (146) gives:
% 200.36/33.24  | | | | | |   (147)  all_52_17 = all_10_1
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_20, e3, e3,
% 200.36/33.24  | | | | | |              simplifying with (78), (145) gives:
% 200.36/33.24  | | | | | |   (148)  all_52_20 = all_6_2
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | COMBINE_EQS: (51), (147) imply:
% 200.36/33.24  | | | | | |   (149)  all_56_2 = all_10_1
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (92), (147) imply:
% 200.36/33.24  | | | | | |   (150)   ~ (all_52_9 = all_10_1)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (103), (147) imply:
% 200.36/33.24  | | | | | |   (151)   ~ (all_52_23 = all_10_1)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | SIMP: (151) implies:
% 200.36/33.24  | | | | | |   (152)   ~ (all_52_23 = all_10_1)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (15), (147) imply:
% 200.36/33.24  | | | | | |   (153)   ~ (all_52_25 = all_10_1)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | SIMP: (153) implies:
% 200.36/33.24  | | | | | |   (154)   ~ (all_52_25 = all_10_1)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (89), (147) imply:
% 200.36/33.24  | | | | | |   (155)   ~ (all_10_1 = all_6_2)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (142), (147) imply:
% 200.36/33.24  | | | | | |   (156)   ~ (all_10_1 = e3)
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | BETA: splitting (39) gives:
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | Case 1:
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | |   (157)  all_56_2 = e3
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | | REF_CLOSE: (149), (156), (157) are inconsistent by sub-proof
% 200.36/33.24  | | | | | | |            #1029.
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | Case 2:
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | |   (158)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | | BETA: splitting (79) gives:
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | |   (159)  all_58_9 = e3
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | COMBINE_EQS: (22), (159) imply:
% 200.36/33.24  | | | | | | | |   (160)  all_52_25 = e3
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | REDUCE: (3), (160) imply:
% 200.36/33.24  | | | | | | | |   (161)   ~ (all_52_27 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | SIMP: (161) implies:
% 200.36/33.24  | | | | | | | |   (162)   ~ (all_52_27 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | REDUCE: (154), (160) imply:
% 200.36/33.24  | | | | | | | |   (163)   ~ (all_10_1 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | REDUCE: (73), (160) imply:
% 200.36/33.24  | | | | | | | |   (164)   ~ (all_6_2 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | SIMP: (164) implies:
% 200.36/33.24  | | | | | | | |   (165)   ~ (all_6_2 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | REDUCE: (107), (160) imply:
% 200.36/33.24  | | | | | | | |   (166)  op(e3, e3) = all_52_24
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | BETA: splitting (36) gives:
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | |   (167)  all_58_2 = e3
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | REF_CLOSE: (50), (116), (167) are inconsistent by sub-proof
% 200.36/33.24  | | | | | | | | |            #1369.
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | |   (168)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | BETA: splitting (168) gives:
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | |   (169)  all_58_3 = e3
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | COMBINE_EQS: (100), (169) imply:
% 200.36/33.24  | | | | | | | | | |   (170)  all_4_2 = e3
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | REDUCE: (76), (170) imply:
% 200.36/33.24  | | | | | | | | | |   (171)  op(e3, e3) = e2
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | REDUCE: (28), (170) imply:
% 200.36/33.24  | | | | | | | | | |   (172)  op(e3, e2) = e1
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_9, e1, e2, e3,
% 200.36/33.24  | | | | | | | | | |              simplifying with (87), (172) gives:
% 200.36/33.24  | | | | | | | | | |   (173)  all_52_9 = e1
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 200.36/33.24  | | | | | | | | | |              simplifying with (78), (166) gives:
% 200.36/33.24  | | | | | | | | | |   (174)  all_52_24 = all_6_2
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_24, e3, e3,
% 200.36/33.24  | | | | | | | | | |              simplifying with (166), (171) gives:
% 200.36/33.24  | | | | | | | | | |   (175)  all_52_24 = e2
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | COMBINE_EQS: (174), (175) imply:
% 200.36/33.24  | | | | | | | | | |   (176)  all_6_2 = e2
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | SIMP: (176) implies:
% 200.36/33.24  | | | | | | | | | |   (177)  all_6_2 = e2
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | COMBINE_EQS: (16), (177) imply:
% 200.36/33.24  | | | | | | | | | |   (178)  all_58_0 = e2
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | REDUCE: (150), (173) imply:
% 200.36/33.24  | | | | | | | | | |   (179)   ~ (all_10_1 = e1)
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | SIMP: (179) implies:
% 200.36/33.24  | | | | | | | | | |   (180)   ~ (all_10_1 = e1)
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | REDUCE: (155), (177) imply:
% 200.36/33.24  | | | | | | | | | |   (181)   ~ (all_10_1 = e2)
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | REDUCE: (165), (177) imply:
% 200.36/33.24  | | | | | | | | | |   (182)   ~ (e3 = e2)
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | BETA: splitting (158) gives:
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | |   (183)  all_56_2 = e2
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | REF_CLOSE: (149), (181), (183) are inconsistent by sub-proof
% 200.36/33.24  | | | | | | | | | | |            #815.
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | |   (184)  all_56_2 = e1 | all_56_2 = e0
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | BETA: splitting (184) gives:
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | |   (185)  all_56_2 = e1
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | REF_CLOSE: (149), (180), (185) are inconsistent by sub-proof
% 200.36/33.24  | | | | | | | | | | | |            #1025.
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | |   (186)  all_56_2 = e0
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | COMBINE_EQS: (149), (186) imply:
% 200.36/33.24  | | | | | | | | | | | |   (187)  all_10_1 = e0
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | SIMP: (187) implies:
% 200.36/33.24  | | | | | | | | | | | |   (188)  all_10_1 = e0
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | REDUCE: (152), (188) imply:
% 200.36/33.24  | | | | | | | | | | | |   (189)   ~ (all_52_23 = e0)
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | REDUCE: (156), (188) imply:
% 200.36/33.24  | | | | | | | | | | | |   (190)   ~ (e3 = e0)
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | SIMP: (190) implies:
% 200.36/33.24  | | | | | | | | | | | |   (191)   ~ (e3 = e0)
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | BETA: splitting (59) gives:
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | |   (192)  all_58_12 = e0
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | COMBINE_EQS: (113), (192) imply:
% 200.36/33.24  | | | | | | | | | | | | |   (193)  e3 = e0
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | SIMP: (193) implies:
% 200.36/33.24  | | | | | | | | | | | | |   (194)  e3 = e0
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | COMBINE_EQS: (159), (194) imply:
% 200.36/33.24  | | | | | | | | | | | | |   (195)  all_58_9 = e0
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | REF_CLOSE: (7), (9), (78), (80), (90), (97), (105), (142),
% 200.36/33.24  | | | | | | | | | | | | |            (165), (178), (191), (195) are inconsistent by
% 200.36/33.24  | | | | | | | | | | | | |            sub-proof #191.
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | |   (196)  all_58_13 = e0 | all_58_14 = e0
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | BETA: splitting (196) gives:
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | Case 1:
% 200.36/33.24  | | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | |   (197)  all_58_13 = e0
% 200.36/33.24  | | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (19), (35), (56), (197) are
% 200.36/33.24  | | | | | | | | | | | | | |            inconsistent by sub-proof #1100.
% 200.36/33.24  | | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | |   (198)  all_58_14 = e0
% 200.36/33.24  | | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | | REF_CLOSE: (4), (189), (198) are inconsistent by sub-proof
% 200.36/33.24  | | | | | | | | | | | | | |            #1019.
% 200.36/33.24  | | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | | End of split
% 200.36/33.24  | | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | | End of split
% 200.36/33.24  | | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | | End of split
% 200.36/33.24  | | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | End of split
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | |   (199)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | | REF_CLOSE: (37), (43), (72), (162), (199) are inconsistent by
% 200.36/33.24  | | | | | | | | | |            sub-proof #214.
% 200.36/33.24  | | | | | | | | | | 
% 200.36/33.24  | | | | | | | | | End of split
% 200.36/33.24  | | | | | | | | | 
% 200.36/33.24  | | | | | | | | End of split
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | Case 2:
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | |   (200)   ~ (all_58_9 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | REDUCE: (22), (200) imply:
% 200.36/33.24  | | | | | | | |   (201)   ~ (all_52_25 = e3)
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | | REF_CLOSE: (7), (9), (16), (19), (20), (21), (22), (29), (33),
% 200.36/33.24  | | | | | | | |            (41), (42), (46), (49), (53), (58), (63), (68), (74),
% 200.36/33.24  | | | | | | | |            (76), (77), (78), (80), (85), (93), (97), (100),
% 200.36/33.24  | | | | | | | |            (104), (105), (106), (112), (142), (143), (201) are
% 200.36/33.24  | | | | | | | |            inconsistent by sub-proof #1137.
% 200.36/33.24  | | | | | | | | 
% 200.36/33.24  | | | | | | | End of split
% 200.36/33.24  | | | | | | | 
% 200.36/33.24  | | | | | | End of split
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | Case 2:
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | |   (202)  all_58_14 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REF_CLOSE: (4), (120), (202) are inconsistent by sub-proof #1305.
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | End of split
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | End of split
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | End of split
% 200.36/33.24  | | | 
% 200.36/33.24  | | Case 2:
% 200.36/33.24  | | | 
% 200.36/33.24  | | |   (203)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | BETA: splitting (203) gives:
% 200.36/33.24  | | | 
% 200.36/33.24  | | | Case 1:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | |   (204)  all_58_13 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REF_CLOSE: (19), (112), (204) are inconsistent by sub-proof #1360.
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | Case 2:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | |   (205)  all_58_14 = e3 | all_58_15 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (13), (16), (18),
% 200.36/33.24  | | | |            (19), (20), (22), (24), (25), (26), (27), (28), (29), (30),
% 200.36/33.24  | | | |            (35), (36), (40), (43), (44), (46), (47), (48), (49), (50),
% 200.36/33.24  | | | |            (52), (54), (55), (56), (57), (59), (60), (63), (64), (65),
% 200.36/33.24  | | | |            (66), (67), (68), (69), (72), (74), (75), (77), (78), (81),
% 200.36/33.24  | | | |            (82), (83), (84), (85), (86), (87), (90), (91), (95), (96),
% 200.36/33.24  | | | |            (97), (98), (99), (100), (102), (104), (108), (205) are
% 200.36/33.24  | | | |            inconsistent by sub-proof #190.
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | End of split
% 200.36/33.24  | | | 
% 200.36/33.24  | | End of split
% 200.36/33.24  | | 
% 200.36/33.24  | End of split
% 200.36/33.24  | 
% 200.36/33.24  End of proof
% 200.36/33.24  
% 200.36/33.24  Sub-proof #190 shows that the following formulas are inconsistent:
% 200.36/33.24  ----------------------------------------------------------------
% 200.36/33.24    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.24    (2)   ~ (all_52_15 = all_52_23)
% 200.36/33.24    (3)  all_58_14 = all_52_23
% 200.36/33.24    (4)   ~ (e3 = e1)
% 200.36/33.24    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.24    (6)   ~ (all_52_5 = all_52_13)
% 200.36/33.24    (7)  all_58_1 = all_52_9
% 200.36/33.24    (8)   ~ (all_52_23 = all_4_0)
% 200.36/33.24    (9)  op(all_52_15, all_52_15) = e0
% 200.36/33.24    (10)  all_58_0 = all_6_2
% 200.36/33.24    (11)   ~ (all_52_27 = all_52_29)
% 200.36/33.24    (12)  all_58_13 = all_52_15
% 200.36/33.24    (13)  op(all_52_13, all_52_13) = e1
% 200.36/33.24    (14)  all_58_9 = all_52_25
% 200.36/33.24    (15)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.24    (16)  op(e1, e3) = all_52_5
% 200.36/33.24    (17)  op(e2, e2) = all_4_2
% 200.36/33.24    (18)   ~ (all_52_3 = all_52_5)
% 200.36/33.24    (19)  op(all_4_2, e2) = e1
% 200.36/33.24    (20)  all_58_11 = all_52_29
% 200.36/33.24    (21)  all_56_5 = all_4_2
% 200.36/33.24    (22)  op(e0, e0) = all_14_2
% 200.36/33.24    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.24    (24)   ~ (e2 = e1)
% 200.36/33.24    (25)  all_58_10 = all_52_27
% 200.36/33.24    (26)  all_56_8 = all_52_5
% 200.36/33.24    (27)  all_58_7 = all_52_13
% 200.36/33.24    (28)   ~ (all_52_5 = all_52_7)
% 200.36/33.24    (29)  all_58_12 = all_52_7
% 200.36/33.24    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.24    (31)  all_58_2 = all_52_3
% 200.36/33.24    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.24    (33)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.24    (34)   ~ (all_52_5 = all_52_29)
% 200.36/33.24    (35)   ~ (all_52_15 = all_14_2)
% 200.36/33.24    (36)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.24    (37)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.24    (38)   ~ (all_52_13 = all_4_2)
% 200.36/33.24    (39)  all_58_14 = e3 | all_58_15 = e3
% 200.36/33.24    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.24    (41)   ~ (all_52_9 = all_52_25)
% 200.36/33.24    (42)  all_58_15 = all_14_2
% 200.36/33.24    (43)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.24    (44)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.24    (45)  all_58_8 = all_10_2
% 200.36/33.24    (46)   ~ (all_52_5 = all_10_2)
% 200.36/33.24    (47)  all_58_5 = all_4_0
% 200.36/33.24    (48)   ~ (all_52_5 = all_6_2)
% 200.36/33.24    (49)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.24    (50)   ~ (all_52_9 = all_6_2)
% 200.36/33.24    (51)  op(e3, e3) = all_6_2
% 200.36/33.24    (52)   ~ (all_52_3 = all_52_7)
% 200.36/33.24    (53)  all_56_1 = all_52_9
% 200.36/33.24    (54)   ~ (all_52_15 = all_4_2)
% 200.36/33.24    (55)   ~ (all_52_27 = all_4_2)
% 200.36/33.24    (56)  all_58_6 = all_52_5
% 200.36/33.24    (57)   ~ (all_4_0 = all_4_2)
% 200.36/33.24    (58)  op(e3, e2) = all_52_9
% 200.36/33.24    (59)   ~ (e3 = e2)
% 200.36/33.24    (60)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.24    (61)   ~ (all_6_1 = e2)
% 200.36/33.24    (62)  op(e1, e1) = all_10_2
% 200.36/33.24    (63)  op(all_52_9, all_52_9) = e3
% 200.36/33.24    (64)   ~ (all_52_23 = all_10_2)
% 200.36/33.24    (65)   ~ (all_52_7 = all_52_23)
% 200.36/33.24    (66)  all_58_3 = all_4_2
% 200.36/33.24    (67)   ~ (all_52_3 = all_4_2)
% 200.36/33.24    (68)  op(all_6_2, e3) = all_6_1
% 200.36/33.24    (69)   ~ (all_14_2 = e3)
% 200.36/33.24  
% 200.36/33.24  Begin of proof
% 200.36/33.24  | 
% 200.36/33.24  | BETA: splitting (39) gives:
% 200.36/33.24  | 
% 200.36/33.24  | Case 1:
% 200.36/33.24  | | 
% 200.36/33.24  | |   (70)  all_58_14 = e3
% 200.36/33.24  | | 
% 200.36/33.24  | | COMBINE_EQS: (3), (70) imply:
% 200.36/33.24  | |   (71)  all_52_23 = e3
% 200.36/33.24  | | 
% 200.36/33.24  | | SIMP: (71) implies:
% 200.36/33.24  | |   (72)  all_52_23 = e3
% 200.36/33.24  | | 
% 200.36/33.24  | | REDUCE: (65), (72) imply:
% 200.36/33.24  | |   (73)   ~ (all_52_7 = e3)
% 200.36/33.24  | | 
% 200.36/33.24  | | REDUCE: (2), (72) imply:
% 200.36/33.24  | |   (74)   ~ (all_52_15 = e3)
% 200.36/33.24  | | 
% 200.36/33.24  | | REDUCE: (64), (72) imply:
% 200.36/33.24  | |   (75)   ~ (all_10_2 = e3)
% 200.36/33.24  | | 
% 200.36/33.24  | | SIMP: (75) implies:
% 200.36/33.24  | |   (76)   ~ (all_10_2 = e3)
% 200.36/33.24  | | 
% 200.36/33.24  | | REDUCE: (8), (72) imply:
% 200.36/33.24  | |   (77)   ~ (all_4_0 = e3)
% 200.36/33.24  | | 
% 200.36/33.24  | | SIMP: (77) implies:
% 200.36/33.24  | |   (78)   ~ (all_4_0 = e3)
% 200.36/33.24  | | 
% 200.36/33.24  | | REDUCE: (43), (72) imply:
% 200.36/33.24  | |   (79)  op(e3, e3) = all_52_22
% 200.36/33.24  | | 
% 200.36/33.24  | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3, simplifying
% 200.36/33.24  | |              with (51), (79) gives:
% 200.36/33.24  | |   (80)  all_52_22 = all_6_2
% 200.36/33.24  | | 
% 200.36/33.24  | | BETA: splitting (23) gives:
% 200.36/33.24  | | 
% 200.36/33.24  | | Case 1:
% 200.36/33.24  | | | 
% 200.36/33.24  | | |   (81)  all_58_2 = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (12), (13), (16), (18), (22),
% 200.36/33.24  | | |            (24), (26), (27), (28), (29), (31), (32), (35), (36), (37),
% 200.36/33.24  | | |            (40), (44), (48), (50), (51), (52), (56), (59), (61), (63),
% 200.36/33.24  | | |            (66), (67), (68), (70), (74), (81) are inconsistent by
% 200.36/33.24  | | |            sub-proof #1097.
% 200.36/33.24  | | | 
% 200.36/33.24  | | Case 2:
% 200.36/33.24  | | | 
% 200.36/33.24  | | |   (82)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | BETA: splitting (32) gives:
% 200.36/33.24  | | | 
% 200.36/33.24  | | | Case 1:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | |   (83)  all_58_0 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | COMBINE_EQS: (10), (83) imply:
% 200.36/33.24  | | | |   (84)  all_6_2 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REDUCE: (48), (84) imply:
% 200.36/33.24  | | | |   (85)   ~ (all_52_5 = e3)
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REDUCE: (50), (84) imply:
% 200.36/33.24  | | | |   (86)   ~ (all_52_9 = e3)
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | REF_CLOSE: (1), (5), (6), (7), (11), (12), (13), (14), (15), (16), (17),
% 200.36/33.24  | | | |            (19), (20), (21), (25), (26), (27), (30), (33), (34), (38),
% 200.36/33.24  | | | |            (40), (41), (44), (45), (47), (48), (49), (50), (51), (53),
% 200.36/33.24  | | | |            (54), (55), (56), (57), (58), (60), (61), (62), (63), (66),
% 200.36/33.24  | | | |            (68), (76), (78), (82), (85), (86) are inconsistent by
% 200.36/33.24  | | | |            sub-proof #192.
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | Case 2:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | |   (87)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | BETA: splitting (40) gives:
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | | Case 1:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | |   (88)  all_58_1 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | COMBINE_EQS: (7), (88) imply:
% 200.36/33.24  | | | | |   (89)  all_52_9 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | REF_CLOSE: (5), (50), (51), (63), (89) are inconsistent by sub-proof
% 200.36/33.24  | | | | |            #1337.
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | Case 2:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | |   (90)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | BETA: splitting (90) gives:
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | | Case 1:
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | |   (91)  all_58_3 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | COMBINE_EQS: (66), (91) imply:
% 200.36/33.24  | | | | | |   (92)  all_4_2 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (19), (92) imply:
% 200.36/33.24  | | | | | |   (93)  op(e3, e2) = e1
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REDUCE: (17), (92) imply:
% 200.36/33.24  | | | | | |   (94)  op(e2, e2) = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REF_CLOSE: (5), (17), (29), (30), (31), (46), (56), (58), (62),
% 200.36/33.24  | | | | | |            (63), (67), (73), (87), (93), (94) are inconsistent by
% 200.36/33.24  | | | | | |            sub-proof #195.
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | Case 2:
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | |   (95)  all_58_7 = e3 | all_58_13 = e3
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | | REF_CLOSE: (4), (5), (6), (9), (10), (12), (13), (16), (18), (22),
% 200.36/33.24  | | | | | |            (24), (26), (27), (28), (29), (31), (32), (35), (36),
% 200.36/33.24  | | | | | |            (37), (44), (48), (51), (56), (59), (61), (68), (70),
% 200.36/33.24  | | | | | |            (73), (74), (95) are inconsistent by sub-proof #1099.
% 200.36/33.24  | | | | | | 
% 200.36/33.24  | | | | | End of split
% 200.36/33.24  | | | | | 
% 200.36/33.24  | | | | End of split
% 200.36/33.24  | | | | 
% 200.36/33.24  | | | End of split
% 200.36/33.24  | | | 
% 200.36/33.24  | | End of split
% 200.36/33.24  | | 
% 200.36/33.24  | Case 2:
% 200.36/33.24  | | 
% 200.36/33.24  | |   (96)  all_58_15 = e3
% 200.36/33.24  | | 
% 200.36/33.24  | | REF_CLOSE: (42), (69), (96) are inconsistent by sub-proof #197.
% 200.36/33.24  | | 
% 200.36/33.24  | End of split
% 200.36/33.24  | 
% 200.36/33.24  End of proof
% 200.36/33.24  
% 200.36/33.24  Sub-proof #191 shows that the following formulas are inconsistent:
% 200.36/33.24  ----------------------------------------------------------------
% 200.36/33.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.24    (2)  all_58_1 = all_52_9
% 200.36/33.24    (3)   ~ (e3 = e0)
% 200.36/33.24    (4)  all_58_9 = e0
% 200.36/33.24    (5)   ~ (all_6_2 = e3)
% 200.36/33.24    (6)  all_58_0 = e2
% 200.36/33.24    (7)  op(e3, e3) = all_6_2
% 200.36/33.24    (8)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.24    (9)   ~ (all_52_17 = e3)
% 200.36/33.24    (10)   ~ (e3 = e2)
% 200.36/33.24    (11)  op(all_52_9, all_52_9) = e3
% 200.36/33.24    (12)  all_58_4 = all_52_17
% 200.36/33.24  
% 200.36/33.24  Begin of proof
% 200.36/33.24  | 
% 200.36/33.24  | BETA: splitting (8) gives:
% 200.36/33.24  | 
% 200.36/33.24  | Case 1:
% 200.36/33.24  | | 
% 200.36/33.24  | |   (13)  all_58_0 = e3
% 200.36/33.24  | | 
% 200.36/33.24  | | REF_CLOSE: (6), (10), (13) are inconsistent by sub-proof #1235.
% 200.36/33.24  | | 
% 200.36/33.24  | Case 2:
% 200.36/33.24  | | 
% 200.36/33.24  | |   (14)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.24  | | 
% 200.36/33.24  | | BETA: splitting (14) gives:
% 200.36/33.24  | | 
% 200.36/33.24  | | Case 1:
% 200.36/33.24  | | | 
% 200.36/33.24  | | |   (15)  all_58_1 = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | COMBINE_EQS: (2), (15) imply:
% 200.36/33.24  | | |   (16)  all_52_9 = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | REDUCE: (11), (16) imply:
% 200.36/33.24  | | |   (17)  op(e3, e3) = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | REF_CLOSE: (1), (5), (7), (17) are inconsistent by sub-proof #1338.
% 200.36/33.24  | | | 
% 200.36/33.24  | | Case 2:
% 200.36/33.24  | | | 
% 200.36/33.24  | | |   (18)  all_58_4 = e3 | all_58_9 = e3
% 200.36/33.24  | | | 
% 200.36/33.24  | | | REF_CLOSE: (3), (4), (9), (12), (18) are inconsistent by sub-proof #210.
% 200.36/33.24  | | | 
% 200.36/33.24  | | End of split
% 200.36/33.24  | | 
% 200.36/33.24  | End of split
% 200.36/33.24  | 
% 200.36/33.24  End of proof
% 200.36/33.24  
% 200.36/33.24  Sub-proof #192 shows that the following formulas are inconsistent:
% 200.36/33.24  ----------------------------------------------------------------
% 200.36/33.24    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 200.36/33.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.24    (3)   ~ (all_52_5 = all_52_13)
% 200.36/33.24    (4)  all_58_1 = all_52_9
% 200.36/33.24    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.24    (6)   ~ (all_52_27 = all_52_29)
% 200.36/33.24    (7)  all_58_13 = all_52_15
% 200.36/33.24    (8)  op(all_52_13, all_52_13) = e1
% 200.36/33.24    (9)  all_58_9 = all_52_25
% 200.36/33.24    (10)  op(all_52_27, all_52_27) = all_52_26
% 200.36/33.24    (11)  op(e1, e3) = all_52_5
% 200.36/33.24    (12)  op(e2, e2) = all_4_2
% 200.36/33.24    (13)  op(all_4_2, e2) = e1
% 200.36/33.24    (14)  all_58_11 = all_52_29
% 200.36/33.24    (15)  all_56_5 = all_4_2
% 200.36/33.24    (16)   ~ (all_4_0 = e3)
% 200.36/33.24    (17)  all_58_10 = all_52_27
% 200.36/33.24    (18)  all_56_8 = all_52_5
% 200.36/33.24    (19)  all_58_7 = all_52_13
% 200.36/33.24    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.24    (21)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 200.36/33.24    (22)   ~ (all_52_5 = e3)
% 200.36/33.24    (23)   ~ (all_52_5 = all_52_29)
% 200.36/33.24    (24)   ~ (all_10_2 = e3)
% 200.36/33.24    (25)   ~ (all_52_9 = e3)
% 200.36/33.24    (26)   ~ (all_52_13 = all_4_2)
% 200.36/33.24    (27)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.24    (28)   ~ (all_52_9 = all_52_25)
% 200.36/33.24    (29)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.24    (30)  all_58_8 = all_10_2
% 200.36/33.24    (31)  all_58_5 = all_4_0
% 200.36/33.24    (32)   ~ (all_52_5 = all_6_2)
% 200.36/33.24    (33)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.24    (34)   ~ (all_52_9 = all_6_2)
% 200.36/33.24    (35)  op(e3, e3) = all_6_2
% 200.36/33.24    (36)  all_56_1 = all_52_9
% 200.36/33.24    (37)   ~ (all_52_15 = all_4_2)
% 200.36/33.24    (38)   ~ (all_52_27 = all_4_2)
% 200.36/33.24    (39)  all_58_6 = all_52_5
% 200.36/33.24    (40)   ~ (all_4_0 = all_4_2)
% 200.36/33.24    (41)  op(e3, e2) = all_52_9
% 200.36/33.24    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.24    (43)   ~ (all_6_1 = e2)
% 200.36/33.24    (44)  op(e1, e1) = all_10_2
% 200.36/33.24    (45)  op(all_52_9, all_52_9) = e3
% 200.36/33.25    (46)  all_58_3 = all_4_2
% 200.36/33.25    (47)  op(all_6_2, e3) = all_6_1
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.25  | 
% 200.36/33.25  | BETA: splitting (27) gives:
% 200.36/33.25  | 
% 200.36/33.25  | Case 1:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (48)  all_58_1 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | COMBINE_EQS: (4), (48) imply:
% 200.36/33.25  | |   (49)  all_52_9 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (25), (49) imply:
% 200.36/33.25  | |   (50)  $false
% 200.36/33.25  | | 
% 200.36/33.25  | | CLOSE: (50) is inconsistent.
% 200.36/33.25  | | 
% 200.36/33.25  | Case 2:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (51)   ~ (all_58_1 = e3)
% 200.36/33.25  | |   (52)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | BETA: splitting (20) gives:
% 200.36/33.25  | | 
% 200.36/33.25  | | Case 1:
% 200.36/33.25  | | | 
% 200.36/33.25  | | |   (53)  all_58_6 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | COMBINE_EQS: (39), (53) imply:
% 200.36/33.25  | | |   (54)  all_52_5 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | REDUCE: (22), (54) imply:
% 200.36/33.25  | | |   (55)  $false
% 200.36/33.25  | | | 
% 200.36/33.25  | | | CLOSE: (55) is inconsistent.
% 200.36/33.25  | | | 
% 200.36/33.25  | | Case 2:
% 200.36/33.25  | | | 
% 200.36/33.25  | | |   (56)   ~ (all_58_6 = e3)
% 200.36/33.25  | | |   (57)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | BETA: splitting (29) gives:
% 200.36/33.25  | | | 
% 200.36/33.25  | | | Case 1:
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | |   (58)  all_56_8 = e3
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | REF_CLOSE: (18), (22), (58) are inconsistent by sub-proof #1325.
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | Case 2:
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | |   (59)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | BETA: splitting (42) gives:
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | Case 1:
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | |   (60)  all_56_1 = e3
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | | REF_CLOSE: (25), (36), (60) are inconsistent by sub-proof #1326.
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | Case 2:
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | |   (61)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | | BETA: splitting (21) gives:
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | | Case 1:
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | |   (62)  all_56_5 = e3
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | REF_CLOSE: (2), (5), (7), (13), (15), (17), (19), (24), (26), (31),
% 200.36/33.25  | | | | | |            (33), (37), (38), (40), (41), (44), (45), (46), (52),
% 200.36/33.25  | | | | | |            (62) are inconsistent by sub-proof #193.
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | Case 2:
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | |   (63)   ~ (all_56_5 = e3)
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | REDUCE: (15), (63) imply:
% 200.36/33.25  | | | | | |   (64)   ~ (all_4_2 = e3)
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | BETA: splitting (5) gives:
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | Case 1:
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | |   (65)  all_58_3 = e3
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | COMBINE_EQS: (46), (65) imply:
% 200.36/33.25  | | | | | | |   (66)  all_4_2 = e3
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | REDUCE: (64), (66) imply:
% 200.36/33.25  | | | | | | |   (67)  $false
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | CLOSE: (67) is inconsistent.
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | Case 2:
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | |   (68)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | BETA: splitting (68) gives:
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | Case 1:
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | |   (69)  all_58_5 = e3
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | COMBINE_EQS: (31), (69) imply:
% 200.36/33.25  | | | | | | | |   (70)  all_4_0 = e3
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | REDUCE: (16), (70) imply:
% 200.36/33.25  | | | | | | | |   (71)  $false
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | CLOSE: (71) is inconsistent.
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | Case 2:
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | |   (72)  all_58_10 = e3
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | COMBINE_EQS: (17), (72) imply:
% 200.36/33.25  | | | | | | | |   (73)  all_52_27 = e3
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | REDUCE: (6), (73) imply:
% 200.36/33.25  | | | | | | | |   (74)   ~ (all_52_29 = e3)
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | SIMP: (74) implies:
% 200.36/33.25  | | | | | | | |   (75)   ~ (all_52_29 = e3)
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | REDUCE: (10), (73) imply:
% 200.36/33.25  | | | | | | | |   (76)  op(e3, e3) = all_52_26
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | BETA: splitting (57) gives:
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | | Case 1:
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | |   (77)  all_58_7 = e3
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | COMBINE_EQS: (19), (77) imply:
% 200.36/33.25  | | | | | | | | |   (78)  all_52_13 = e3
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (26), (78) imply:
% 200.36/33.25  | | | | | | | | |   (79)   ~ (all_4_2 = e3)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (8), (78) imply:
% 200.36/33.25  | | | | | | | | |   (80)  op(e3, e3) = e1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_26, e3, e3,
% 200.36/33.25  | | | | | | | | |              simplifying with (35), (76) gives:
% 200.36/33.25  | | | | | | | | |   (81)  all_52_26 = all_6_2
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | GROUND_INST: instantiating (2) with e1, all_52_26, e3, e3,
% 200.36/33.25  | | | | | | | | |              simplifying with (76), (80) gives:
% 200.36/33.25  | | | | | | | | |   (82)  all_52_26 = e1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | COMBINE_EQS: (81), (82) imply:
% 200.36/33.25  | | | | | | | | |   (83)  all_6_2 = e1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | SIMP: (83) implies:
% 200.36/33.25  | | | | | | | | |   (84)  all_6_2 = e1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (32), (84) imply:
% 200.36/33.25  | | | | | | | | |   (85)   ~ (all_52_5 = e1)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (34), (84) imply:
% 200.36/33.25  | | | | | | | | |   (86)   ~ (all_52_9 = e1)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (47), (84) imply:
% 200.36/33.25  | | | | | | | | |   (87)  op(e1, e3) = all_6_1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | GROUND_INST: instantiating (2) with all_52_5, all_6_1, e3, e1,
% 200.36/33.25  | | | | | | | | |              simplifying with (11), (87) gives:
% 200.36/33.25  | | | | | | | | |   (88)  all_52_5 = all_6_1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | COMBINE_EQS: (18), (88) imply:
% 200.36/33.25  | | | | | | | | |   (89)  all_56_8 = all_6_1
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (23), (88) imply:
% 200.36/33.25  | | | | | | | | |   (90)   ~ (all_52_29 = all_6_1)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | SIMP: (90) implies:
% 200.36/33.25  | | | | | | | | |   (91)   ~ (all_52_29 = all_6_1)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (22), (88) imply:
% 200.36/33.25  | | | | | | | | |   (92)   ~ (all_6_1 = e3)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REDUCE: (85), (88) imply:
% 200.36/33.25  | | | | | | | | |   (93)   ~ (all_6_1 = e1)
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | BETA: splitting (59) gives:
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | Case 1:
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | |   (94)  all_56_8 = e2
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | REF_CLOSE: (43), (89), (94) are inconsistent by sub-proof
% 200.36/33.25  | | | | | | | | | |            #1321.
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | Case 2:
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | |   (95)  all_56_8 = e1 | all_56_8 = e0
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | BETA: splitting (95) gives:
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | Case 1:
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | |   (96)  all_56_8 = e1
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | REF_CLOSE: (89), (93), (96) are inconsistent by sub-proof
% 200.36/33.25  | | | | | | | | | | |            #1320.
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | Case 2:
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | |   (97)  all_56_8 = e0
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | COMBINE_EQS: (89), (97) imply:
% 200.36/33.25  | | | | | | | | | | |   (98)  all_6_1 = e0
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | SIMP: (98) implies:
% 200.36/33.25  | | | | | | | | | | |   (99)  all_6_1 = e0
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | REDUCE: (91), (99) imply:
% 200.36/33.25  | | | | | | | | | | |   (100)   ~ (all_52_29 = e0)
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | REDUCE: (92), (99) imply:
% 200.36/33.25  | | | | | | | | | | |   (101)   ~ (e3 = e0)
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | SIMP: (101) implies:
% 200.36/33.25  | | | | | | | | | | |   (102)   ~ (e3 = e0)
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | BETA: splitting (1) gives:
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | Case 1:
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | |   (103)  all_58_9 = e0
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | COMBINE_EQS: (9), (103) imply:
% 200.36/33.25  | | | | | | | | | | | |   (104)  all_52_25 = e0
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | SIMP: (104) implies:
% 200.36/33.25  | | | | | | | | | | | |   (105)  all_52_25 = e0
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | REDUCE: (28), (105) imply:
% 200.36/33.25  | | | | | | | | | | | |   (106)   ~ (all_52_9 = e0)
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | REF_CLOSE: (2), (12), (36), (45), (61), (64), (86), (106) are
% 200.36/33.25  | | | | | | | | | | | |            inconsistent by sub-proof #1109.
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | Case 2:
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | |   (107)  all_58_10 = e0 | all_58_11 = e0
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | BETA: splitting (107) gives:
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | Case 1:
% 200.36/33.25  | | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | |   (108)  all_58_10 = e0
% 200.36/33.25  | | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | | REF_CLOSE: (72), (102), (108) are inconsistent by sub-proof
% 200.36/33.25  | | | | | | | | | | | | |            #750.
% 200.36/33.25  | | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | Case 2:
% 200.36/33.25  | | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | |   (109)  all_58_11 = e0
% 200.36/33.25  | | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | | REF_CLOSE: (14), (100), (109) are inconsistent by sub-proof
% 200.36/33.25  | | | | | | | | | | | | |            #1115.
% 200.36/33.25  | | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | | End of split
% 200.36/33.25  | | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | | End of split
% 200.36/33.25  | | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | | End of split
% 200.36/33.25  | | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | End of split
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | Case 2:
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | |   (110)  all_58_8 = e3 | all_58_11 = e3
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | | REF_CLOSE: (14), (24), (30), (75), (110) are inconsistent by
% 200.36/33.25  | | | | | | | | |            sub-proof #1140.
% 200.36/33.25  | | | | | | | | | 
% 200.36/33.25  | | | | | | | | End of split
% 200.36/33.25  | | | | | | | | 
% 200.36/33.25  | | | | | | | End of split
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | End of split
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | End of split
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | End of split
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | End of split
% 200.36/33.25  | | | 
% 200.36/33.25  | | End of split
% 200.36/33.25  | | 
% 200.36/33.25  | End of split
% 200.36/33.25  | 
% 200.36/33.25  End of proof
% 200.36/33.25  
% 200.36/33.25  Sub-proof #193 shows that the following formulas are inconsistent:
% 200.36/33.25  ----------------------------------------------------------------
% 200.36/33.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.25    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.25    (3)  all_58_13 = all_52_15
% 200.36/33.25    (4)  op(all_4_2, e2) = e1
% 200.36/33.25    (5)  all_56_5 = all_4_2
% 200.36/33.25    (6)  all_58_10 = all_52_27
% 200.36/33.25    (7)  all_58_7 = all_52_13
% 200.36/33.25    (8)   ~ (all_10_2 = e3)
% 200.36/33.25    (9)   ~ (all_52_13 = all_4_2)
% 200.36/33.25    (10)  all_58_5 = all_4_0
% 200.36/33.25    (11)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.25    (12)   ~ (all_52_15 = all_4_2)
% 200.36/33.25    (13)   ~ (all_52_27 = all_4_2)
% 200.36/33.25    (14)   ~ (all_4_0 = all_4_2)
% 200.36/33.25    (15)  op(e3, e2) = all_52_9
% 200.36/33.25    (16)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.25    (17)  op(e1, e1) = all_10_2
% 200.36/33.25    (18)  op(all_52_9, all_52_9) = e3
% 200.36/33.25    (19)  all_58_3 = all_4_2
% 200.36/33.25    (20)  all_56_5 = e3
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.25  | 
% 200.36/33.25  | COMBINE_EQS: (5), (20) imply:
% 200.36/33.25  |   (21)  all_4_2 = e3
% 200.36/33.25  | 
% 200.36/33.25  | SIMP: (21) implies:
% 200.36/33.25  |   (22)  all_4_2 = e3
% 200.36/33.25  | 
% 200.36/33.25  | REDUCE: (13), (22) imply:
% 200.36/33.25  |   (23)   ~ (all_52_27 = e3)
% 200.36/33.25  | 
% 200.36/33.25  | REDUCE: (14), (22) imply:
% 200.36/33.25  |   (24)   ~ (all_4_0 = e3)
% 200.36/33.25  | 
% 200.36/33.25  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (15),
% 200.36/33.25  |            (16), (17), (18), (19), (23), (24) are inconsistent by sub-proof
% 200.36/33.25  |            #213.
% 200.36/33.25  | 
% 200.36/33.25  End of proof
% 200.36/33.25  
% 200.36/33.25  Sub-proof #194 shows that the following formulas are inconsistent:
% 200.36/33.25  ----------------------------------------------------------------
% 200.36/33.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.25    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.25    (3)  all_58_0 = all_6_2
% 200.36/33.25    (4)  op(e2, e2) = all_4_2
% 200.36/33.25    (5)  op(all_4_2, e2) = e1
% 200.36/33.25    (6)   ~ (all_4_0 = e3)
% 200.36/33.25    (7)  all_58_10 = all_52_27
% 200.36/33.25    (8)  all_58_12 = all_52_7
% 200.36/33.25    (9)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.25    (10)   ~ (all_52_7 = e3)
% 200.36/33.25    (11)  all_58_2 = all_52_3
% 200.36/33.25    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.25    (13)   ~ (all_52_27 = e3)
% 200.36/33.25    (14)   ~ (all_52_5 = all_10_2)
% 200.36/33.25    (15)  all_58_5 = all_4_0
% 200.36/33.25    (16)  op(all_4_2, all_4_2) = e2
% 200.36/33.25    (17)  op(e3, e3) = all_6_2
% 200.36/33.25    (18)  all_58_6 = all_52_5
% 200.36/33.25    (19)  op(e3, e2) = all_52_9
% 200.36/33.25    (20)   ~ (e3 = e2)
% 200.36/33.25    (21)  op(e1, e1) = all_10_2
% 200.36/33.25    (22)  op(all_52_9, all_52_9) = e3
% 200.36/33.25    (23)  all_58_3 = all_4_2
% 200.36/33.25    (24)   ~ (all_52_3 = all_4_2)
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.25  | 
% 200.36/33.25  | BETA: splitting (2) gives:
% 200.36/33.25  | 
% 200.36/33.25  | Case 1:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (25)  all_58_3 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | COMBINE_EQS: (23), (25) imply:
% 200.36/33.25  | |   (26)  all_4_2 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (16), (26) imply:
% 200.36/33.25  | |   (27)  op(e3, e3) = e2
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (5), (26) imply:
% 200.36/33.25  | |   (28)  op(e3, e2) = e1
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (4), (26) imply:
% 200.36/33.25  | |   (29)  op(e2, e2) = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 200.36/33.25  | |              (19), (28) gives:
% 200.36/33.25  | |   (30)  all_52_9 = e1
% 200.36/33.25  | | 
% 200.36/33.25  | | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 200.36/33.25  | |              (17), (27) gives:
% 200.36/33.25  | |   (31)  all_6_2 = e2
% 200.36/33.25  | | 
% 200.36/33.25  | | COMBINE_EQS: (3), (31) imply:
% 200.36/33.25  | |   (32)  all_58_0 = e2
% 200.36/33.25  | | 
% 200.36/33.25  | | BETA: splitting (12) gives:
% 200.36/33.25  | | 
% 200.36/33.25  | | Case 1:
% 200.36/33.25  | | | 
% 200.36/33.25  | | |   (33)  all_58_0 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | REF_CLOSE: (20), (32), (33) are inconsistent by sub-proof #1235.
% 200.36/33.25  | | | 
% 200.36/33.25  | | Case 2:
% 200.36/33.25  | | | 
% 200.36/33.25  | | |   (34)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | REF_CLOSE: (1), (4), (8), (9), (10), (11), (14), (18), (19), (21), (22),
% 200.36/33.25  | | |            (24), (28), (29), (34) are inconsistent by sub-proof #195.
% 200.36/33.25  | | | 
% 200.36/33.25  | | End of split
% 200.36/33.25  | | 
% 200.36/33.25  | Case 2:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (35)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | REF_CLOSE: (6), (7), (13), (15), (35) are inconsistent by sub-proof #214.
% 200.36/33.25  | | 
% 200.36/33.25  | End of split
% 200.36/33.25  | 
% 200.36/33.25  End of proof
% 200.36/33.25  
% 200.36/33.25  Sub-proof #195 shows that the following formulas are inconsistent:
% 200.36/33.25  ----------------------------------------------------------------
% 200.36/33.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.25    (2)  op(e3, e2) = e1
% 200.36/33.25    (3)  op(e2, e2) = all_4_2
% 200.36/33.25    (4)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.25    (5)  all_58_12 = all_52_7
% 200.36/33.25    (6)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 200.36/33.25    (7)   ~ (all_52_7 = e3)
% 200.36/33.25    (8)  all_58_2 = all_52_3
% 200.36/33.25    (9)   ~ (all_52_5 = all_10_2)
% 200.36/33.25    (10)  op(e2, e2) = e3
% 200.36/33.25    (11)  all_58_6 = all_52_5
% 200.36/33.25    (12)  op(e3, e2) = all_52_9
% 200.36/33.25    (13)  op(e1, e1) = all_10_2
% 200.36/33.25    (14)  op(all_52_9, all_52_9) = e3
% 200.36/33.25    (15)   ~ (all_52_3 = all_4_2)
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.25  | 
% 200.36/33.25  | BETA: splitting (6) gives:
% 200.36/33.25  | 
% 200.36/33.25  | Case 1:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (16)  all_58_6 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | COMBINE_EQS: (11), (16) imply:
% 200.36/33.25  | |   (17)  all_52_5 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | SIMP: (17) implies:
% 200.36/33.25  | |   (18)  all_52_5 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (9), (18) imply:
% 200.36/33.25  | |   (19)   ~ (all_10_2 = e3)
% 200.36/33.25  | | 
% 200.36/33.25  | | SIMP: (19) implies:
% 200.36/33.25  | |   (20)   ~ (all_10_2 = e3)
% 200.36/33.25  | | 
% 200.36/33.25  | | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 200.36/33.25  | |              (2), (12) gives:
% 200.36/33.25  | |   (21)  all_52_9 = e1
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (14), (21) imply:
% 200.36/33.25  | |   (22)  op(e1, e1) = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | REF_CLOSE: (1), (13), (20), (22) are inconsistent by sub-proof #1368.
% 200.36/33.25  | | 
% 200.36/33.25  | Case 2:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (23)   ~ (all_58_6 = e3)
% 200.36/33.25  | | 
% 200.36/33.25  | | REDUCE: (11), (23) imply:
% 200.36/33.25  | |   (24)   ~ (all_52_5 = e3)
% 200.36/33.25  | | 
% 200.36/33.25  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (15), (24) are
% 200.36/33.25  | |            inconsistent by sub-proof #1242.
% 200.36/33.25  | | 
% 200.36/33.25  | End of split
% 200.36/33.25  | 
% 200.36/33.25  End of proof
% 200.36/33.25  
% 200.36/33.25  Sub-proof #196 shows that the following formulas are inconsistent:
% 200.36/33.25  ----------------------------------------------------------------
% 200.36/33.25    (1)  all_58_14 = all_52_23
% 200.36/33.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.25    (3)  op(all_52_7, all_52_7) = e0
% 200.36/33.25    (4)  op(all_52_5, all_52_5) = e1
% 200.36/33.25    (5)   ~ (e3 = e0)
% 200.36/33.25    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.25    (7)  all_58_0 = all_6_2
% 200.36/33.25    (8)  all_58_13 = all_52_15
% 200.36/33.25    (9)   ~ (all_52_15 = e3)
% 200.36/33.25    (10)  op(e2, e2) = all_4_2
% 200.36/33.25    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.25    (12)  op(all_10_2, e1) = all_10_1
% 200.36/33.25    (13)   ~ (all_52_7 = all_6_2)
% 200.36/33.25    (14)  op(e0, e0) = all_14_2
% 200.36/33.25    (15)  op(e0, e1) = all_52_23
% 200.36/33.25    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.25    (17)  op(all_6_2, all_6_2) = e3
% 200.36/33.25    (18)  all_58_12 = all_52_7
% 200.36/33.25    (19)   ~ (all_52_7 = all_14_2)
% 200.36/33.25    (20)  all_58_2 = all_52_3
% 200.36/33.25    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.25    (22)   ~ (e2 = e0)
% 200.36/33.25    (23)  op(all_52_3, all_52_3) = e2
% 200.36/33.25    (24)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.25    (25)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 200.36/33.25    (26)  all_58_15 = all_14_2
% 200.36/33.25    (27)   ~ (all_52_5 = all_10_2)
% 200.36/33.25    (28)  all_56_12 = all_52_7
% 200.36/33.25    (29)  op(e3, e3) = all_6_2
% 200.36/33.25    (30)   ~ (all_10_1 = e3)
% 200.36/33.25    (31)   ~ (all_52_15 = all_4_2)
% 200.36/33.25    (32)  all_58_6 = all_52_5
% 200.36/33.25    (33)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.25    (34)  op(e1, e1) = all_10_2
% 200.36/33.25    (35)   ~ (all_52_7 = all_52_23)
% 200.36/33.25    (36)   ~ (all_52_3 = all_4_2)
% 200.36/33.25    (37)   ~ (all_14_2 = e3)
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.25  | 
% 200.36/33.25  | BETA: splitting (33) gives:
% 200.36/33.25  | 
% 200.36/33.25  | Case 1:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (38)  all_58_12 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | COMBINE_EQS: (18), (38) imply:
% 200.36/33.25  | |   (39)  all_52_7 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | REF_CLOSE: (2), (3), (4), (7), (10), (13), (14), (16), (17), (18), (19),
% 200.36/33.25  | |            (20), (21), (23), (27), (29), (32), (33), (34), (36), (39) are
% 200.36/33.25  | |            inconsistent by sub-proof #1361.
% 200.36/33.25  | | 
% 200.36/33.25  | Case 2:
% 200.36/33.25  | | 
% 200.36/33.25  | |   (40)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.25  | | 
% 200.36/33.25  | | BETA: splitting (40) gives:
% 200.36/33.25  | | 
% 200.36/33.25  | | Case 1:
% 200.36/33.25  | | | 
% 200.36/33.25  | | |   (41)  all_58_13 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | REF_CLOSE: (8), (9), (41) are inconsistent by sub-proof #1360.
% 200.36/33.25  | | | 
% 200.36/33.25  | | Case 2:
% 200.36/33.25  | | | 
% 200.36/33.25  | | |   (42)  all_58_14 = e3 | all_58_15 = e3
% 200.36/33.25  | | | 
% 200.36/33.25  | | | BETA: splitting (42) gives:
% 200.36/33.25  | | | 
% 200.36/33.25  | | | Case 1:
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | |   (43)  all_58_14 = e3
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | COMBINE_EQS: (1), (43) imply:
% 200.36/33.25  | | | |   (44)  all_52_23 = e3
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | SIMP: (44) implies:
% 200.36/33.25  | | | |   (45)  all_52_23 = e3
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | REDUCE: (35), (45) imply:
% 200.36/33.25  | | | |   (46)   ~ (all_52_7 = e3)
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | REDUCE: (15), (45) imply:
% 200.36/33.25  | | | |   (47)  op(e0, e1) = e3
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | BETA: splitting (6) gives:
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | Case 1:
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | |   (48)  all_56_12 = e3
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | | REF_CLOSE: (28), (46), (48) are inconsistent by sub-proof #1383.
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | Case 2:
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | |   (49)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | | BETA: splitting (11) gives:
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | | Case 1:
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | |   (50)  all_58_12 = e2
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | COMBINE_EQS: (18), (50) imply:
% 200.36/33.25  | | | | | |   (51)  all_52_7 = e2
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | REDUCE: (3), (51) imply:
% 200.36/33.25  | | | | | |   (52)  op(e2, e2) = e0
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | REF_CLOSE: (2), (5), (8), (10), (22), (25), (31), (43), (50), (52)
% 200.36/33.25  | | | | | |            are inconsistent by sub-proof #1150.
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | Case 2:
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | |   (53)   ~ (all_58_12 = e2)
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | REDUCE: (18), (53) imply:
% 200.36/33.25  | | | | | |   (54)   ~ (all_52_7 = e2)
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | BETA: splitting (24) gives:
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | | Case 1:
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | |   (55)  all_58_12 = e1
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | REF_CLOSE: (2), (3), (12), (18), (30), (34), (47), (55) are
% 200.36/33.25  | | | | | | |            inconsistent by sub-proof #218.
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | Case 2:
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | |   (56)   ~ (all_58_12 = e1)
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | REDUCE: (18), (56) imply:
% 200.36/33.25  | | | | | | |   (57)   ~ (all_52_7 = e1)
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | | REF_CLOSE: (2), (3), (14), (19), (28), (49), (54), (57) are
% 200.36/33.25  | | | | | | |            inconsistent by sub-proof #1176.
% 200.36/33.25  | | | | | | | 
% 200.36/33.25  | | | | | | End of split
% 200.36/33.25  | | | | | | 
% 200.36/33.25  | | | | | End of split
% 200.36/33.25  | | | | | 
% 200.36/33.25  | | | | End of split
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | Case 2:
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | |   (58)  all_58_15 = e3
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | | REF_CLOSE: (26), (37), (58) are inconsistent by sub-proof #197.
% 200.36/33.25  | | | | 
% 200.36/33.25  | | | End of split
% 200.36/33.25  | | | 
% 200.36/33.25  | | End of split
% 200.36/33.25  | | 
% 200.36/33.25  | End of split
% 200.36/33.25  | 
% 200.36/33.25  End of proof
% 200.36/33.25  
% 200.36/33.25  Sub-proof #197 shows that the following formulas are inconsistent:
% 200.36/33.25  ----------------------------------------------------------------
% 200.36/33.25    (1)  all_58_15 = all_14_2
% 200.36/33.25    (2)  all_58_15 = e3
% 200.36/33.25    (3)   ~ (all_14_2 = e3)
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.25  | 
% 200.36/33.25  | COMBINE_EQS: (1), (2) imply:
% 200.36/33.25  |   (4)  all_14_2 = e3
% 200.36/33.25  | 
% 200.36/33.25  | SIMP: (4) implies:
% 200.36/33.25  |   (5)  all_14_2 = e3
% 200.36/33.25  | 
% 200.36/33.25  | REDUCE: (3), (5) imply:
% 200.36/33.25  |   (6)  $false
% 200.36/33.25  | 
% 200.36/33.25  | CLOSE: (6) is inconsistent.
% 200.36/33.25  | 
% 200.36/33.25  End of proof
% 200.36/33.25  
% 200.36/33.25  Sub-proof #198 shows that the following formulas are inconsistent:
% 200.36/33.25  ----------------------------------------------------------------
% 200.36/33.25    (1)  all_58_14 = all_52_23
% 200.36/33.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.25    (3)  op(all_52_7, all_52_7) = e0
% 200.36/33.25    (4)  op(all_52_5, all_52_5) = e1
% 200.36/33.25    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.25    (6)   ~ (all_52_3 = all_52_19)
% 200.36/33.25    (7)   ~ (all_52_3 = all_6_2)
% 200.36/33.25    (8)  all_58_0 = all_6_2
% 200.36/33.25    (9)  all_58_13 = all_52_15
% 200.36/33.25    (10)  op(e2, e2) = all_4_2
% 200.36/33.25    (11)   ~ (all_52_3 = all_52_5)
% 200.36/33.25    (12)  op(all_4_2, e2) = e1
% 200.36/33.25    (13)   ~ (all_52_9 = all_52_15)
% 200.36/33.25    (14)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.25    (15)  op(all_10_2, e1) = all_10_1
% 200.36/33.25    (16)  op(e0, e0) = all_14_2
% 200.36/33.25    (17)  op(e0, e1) = all_52_23
% 200.36/33.25    (18)  all_56_15 = all_14_2
% 200.36/33.25    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.25    (20)   ~ (all_4_0 = e3)
% 200.36/33.25    (21)   ~ (e2 = e1)
% 200.36/33.25    (22)   ~ (all_6_0 = e1)
% 200.36/33.25    (23)  all_58_10 = all_52_27
% 200.36/33.25    (24)  all_56_8 = all_52_5
% 200.36/33.25    (25)  op(all_52_9, all_52_9) = all_52_8
% 200.36/33.25    (26)   ~ (all_52_19 = all_52_23)
% 200.36/33.25    (27)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 200.36/33.25    (28)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.25    (29)  op(all_6_2, all_6_2) = e3
% 200.36/33.25    (30)  all_58_12 = all_52_7
% 200.36/33.25    (31)   ~ (all_52_7 = all_14_2)
% 200.36/33.25    (32)   ~ (all_14_2 = e0)
% 200.36/33.25    (33)  all_58_2 = all_52_3
% 200.36/33.25    (34)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 200.36/33.25    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.25    (36)  op(e3, all_6_1) = all_6_0
% 200.36/33.25    (37)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.25    (38)  op(all_52_3, all_52_3) = e2
% 200.36/33.25    (39)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.25    (40)  all_56_6 = all_52_19
% 200.36/33.25    (41)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.25    (42)  all_58_15 = all_14_2
% 200.36/33.25    (43)   ~ (all_52_19 = all_10_2)
% 200.36/33.25    (44)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.25    (45)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.25    (46)   ~ (all_10_1 = e2)
% 200.36/33.25    (47)  all_58_8 = all_10_2
% 200.36/33.25    (48)   ~ (all_52_5 = all_10_2)
% 200.36/33.25    (49)  all_56_12 = all_52_7
% 200.36/33.25    (50)  all_58_5 = all_4_0
% 200.36/33.25    (51)   ~ (all_52_9 = all_4_2)
% 200.36/33.25    (52)   ~ (all_52_5 = all_6_2)
% 200.36/33.25    (53)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.25    (54)  op(e3, e3) = all_6_2
% 200.36/33.25    (55)  all_56_15 = e3
% 200.36/33.25    (56)   ~ (all_52_27 = all_14_2)
% 200.36/33.25    (57)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.25    (58)  all_56_14 = all_52_23
% 200.36/33.25    (59)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.25    (60)   ~ (all_10_1 = e3)
% 200.36/33.25    (61)  all_58_5 = all_52_19
% 200.36/33.25    (62)   ~ (all_52_27 = all_4_2)
% 200.36/33.25    (63)  all_58_6 = all_52_5
% 200.36/33.25    (64)  op(e3, e2) = all_52_9
% 200.36/33.25    (65)   ~ (all_52_17 = all_6_2)
% 200.36/33.25    (66)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 200.36/33.25    (67)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.25    (68)  op(e1, e1) = all_10_2
% 200.36/33.25    (69)   ~ (all_52_23 = all_10_2)
% 200.36/33.25    (70)   ~ (all_52_7 = all_52_23)
% 200.36/33.25    (71)  all_58_3 = all_4_2
% 200.36/33.25    (72)   ~ (all_52_3 = all_4_2)
% 200.36/33.25    (73)  op(all_6_2, e3) = all_6_1
% 200.36/33.25    (74)  all_58_4 = all_52_17
% 200.36/33.25  
% 200.36/33.25  Begin of proof
% 200.36/33.26  | 
% 200.36/33.26  | COMBINE_EQS: (18), (55) imply:
% 200.36/33.26  |   (75)  all_14_2 = e3
% 200.36/33.26  | 
% 200.36/33.26  | SIMP: (75) implies:
% 200.36/33.26  |   (76)  all_14_2 = e3
% 200.36/33.26  | 
% 200.36/33.26  | COMBINE_EQS: (42), (76) imply:
% 200.36/33.26  |   (77)  all_58_15 = e3
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (31), (76) imply:
% 200.36/33.26  |   (78)   ~ (all_52_7 = e3)
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (56), (76) imply:
% 200.36/33.26  |   (79)   ~ (all_52_27 = e3)
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (32), (76) imply:
% 200.36/33.26  |   (80)   ~ (e3 = e0)
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (16), (76) imply:
% 200.36/33.26  |   (81)  op(e0, e0) = e3
% 200.36/33.26  | 
% 200.36/33.26  | BETA: splitting (19) gives:
% 200.36/33.26  | 
% 200.36/33.26  | Case 1:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (82)  all_58_2 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | REF_CLOSE: (2), (10), (29), (33), (38), (54), (72), (82) are inconsistent by
% 200.36/33.26  | |            sub-proof #1159.
% 200.36/33.26  | | 
% 200.36/33.26  | Case 2:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (83)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | BETA: splitting (83) gives:
% 200.36/33.26  | | 
% 200.36/33.26  | | Case 1:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (84)  all_58_3 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | COMBINE_EQS: (71), (84) imply:
% 200.36/33.26  | | |   (85)  all_4_2 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (51), (85) imply:
% 200.36/33.26  | | |   (86)   ~ (all_52_9 = e3)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (59), (85) imply:
% 200.36/33.26  | | |   (87)  op(e3, e3) = all_52_10
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (12), (85) imply:
% 200.36/33.26  | | |   (88)  op(e3, e2) = e1
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (10), (85) imply:
% 200.36/33.26  | | |   (89)  op(e2, e2) = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | BETA: splitting (53) gives:
% 200.36/33.26  | | | 
% 200.36/33.26  | | | Case 1:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (90)   ~ (all_4_2 = e3)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REF_CLOSE: (2), (10), (89), (90) are inconsistent by sub-proof #211.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | Case 2:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | GROUND_INST: instantiating (2) with all_52_9, e1, e2, e3, simplifying
% 200.36/33.26  | | | |              with (64), (88) gives:
% 200.36/33.26  | | | |   (91)  all_52_9 = e1
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_10, e3, e3,
% 200.36/33.26  | | | |              simplifying with (54), (87) gives:
% 200.36/33.26  | | | |   (92)  all_52_10 = all_6_2
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (13), (91) imply:
% 200.36/33.26  | | | |   (93)   ~ (all_52_15 = e1)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | SIMP: (93) implies:
% 200.36/33.26  | | | |   (94)   ~ (all_52_15 = e1)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (86), (91) imply:
% 200.36/33.26  | | | |   (95)   ~ (e3 = e1)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | SIMP: (95) implies:
% 200.36/33.26  | | | |   (96)   ~ (e3 = e1)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (25), (91) imply:
% 200.36/33.26  | | | |   (97)  op(e1, e1) = all_52_8
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | GROUND_INST: instantiating (2) with all_10_2, all_52_8, e1, e1,
% 200.36/33.26  | | | |              simplifying with (68), (97) gives:
% 200.36/33.26  | | | |   (98)  all_52_8 = all_10_2
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | BETA: splitting (39) gives:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | Case 1:
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | |   (99)  all_58_12 = e1
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | | COMBINE_EQS: (30), (99) imply:
% 200.36/33.26  | | | | |   (100)  all_52_7 = e1
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | | REF_CLOSE: (2), (3), (15), (17), (27), (46), (58), (60), (68), (69),
% 200.36/33.26  | | | | |            (70), (100) are inconsistent by sub-proof #1379.
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | Case 2:
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | |   (101)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 200.36/33.26  | | | | |            (14), (16), (19), (21), (22), (23), (24), (26), (28), (29),
% 200.36/33.26  | | | | |            (30), (31), (33), (34), (35), (36), (37), (38), (40), (41),
% 200.36/33.26  | | | | |            (43), (44), (45), (47), (48), (49), (52), (54), (57), (61),
% 200.36/33.26  | | | | |            (63), (65), (66), (67), (68), (70), (71), (72), (73), (74),
% 200.36/33.26  | | | | |            (77), (78), (79), (80), (81), (94), (96), (101) are
% 200.36/33.26  | | | | |            inconsistent by sub-proof #199.
% 200.36/33.26  | | | | | 
% 200.36/33.26  | | | | End of split
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | End of split
% 200.36/33.26  | | | 
% 200.36/33.26  | | Case 2:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (102)  all_58_5 = e3 | all_58_10 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REF_CLOSE: (20), (23), (50), (79), (102) are inconsistent by sub-proof
% 200.36/33.26  | | |            #214.
% 200.36/33.26  | | | 
% 200.36/33.26  | | End of split
% 200.36/33.26  | | 
% 200.36/33.26  | End of split
% 200.36/33.26  | 
% 200.36/33.26  End of proof
% 200.36/33.26  
% 200.36/33.26  Sub-proof #199 shows that the following formulas are inconsistent:
% 200.36/33.26  ----------------------------------------------------------------
% 200.36/33.26    (1)   ~ (all_52_15 = e1)
% 200.36/33.26    (2)  all_58_14 = all_52_23
% 200.36/33.26    (3)   ~ (e3 = e1)
% 200.36/33.26    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.26    (5)  op(all_52_7, all_52_7) = e0
% 200.36/33.26    (6)  op(all_52_5, all_52_5) = e1
% 200.36/33.26    (7)   ~ (e3 = e0)
% 200.36/33.26    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.26    (9)   ~ (all_52_3 = all_52_19)
% 200.36/33.26    (10)   ~ (all_52_3 = all_6_2)
% 200.36/33.26    (11)  all_58_0 = all_6_2
% 200.36/33.26    (12)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 200.36/33.26    (13)  all_58_13 = all_52_15
% 200.36/33.26    (14)  op(e2, e2) = all_4_2
% 200.36/33.26    (15)   ~ (all_52_3 = all_52_5)
% 200.36/33.26    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 200.36/33.26    (17)  op(e0, e0) = all_14_2
% 200.36/33.26    (18)  all_58_15 = e3
% 200.36/33.26    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.26    (20)  op(e0, e0) = e3
% 200.36/33.26    (21)   ~ (e2 = e1)
% 200.36/33.26    (22)   ~ (all_6_0 = e1)
% 200.36/33.26    (23)  all_58_10 = all_52_27
% 200.36/33.26    (24)  all_56_8 = all_52_5
% 200.36/33.26    (25)   ~ (all_52_19 = all_52_23)
% 200.36/33.26    (26)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 200.36/33.26    (27)  op(all_6_2, all_6_2) = e3
% 200.36/33.26    (28)  all_58_12 = all_52_7
% 200.36/33.26    (29)   ~ (all_52_7 = e3)
% 200.36/33.26    (30)   ~ (all_52_7 = all_14_2)
% 200.36/33.26    (31)  all_58_2 = all_52_3
% 200.36/33.26    (32)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 200.36/33.26    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.26    (34)  op(e3, all_6_1) = all_6_0
% 200.36/33.26    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 200.36/33.26    (36)  op(all_52_3, all_52_3) = e2
% 200.36/33.26    (37)  all_56_6 = all_52_19
% 200.36/33.26    (38)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.26    (39)   ~ (all_52_27 = e3)
% 200.36/33.26    (40)   ~ (all_52_19 = all_10_2)
% 200.36/33.26    (41)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.26    (42)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.26    (43)  all_58_8 = all_10_2
% 200.36/33.26    (44)   ~ (all_52_5 = all_10_2)
% 200.36/33.26    (45)  all_56_12 = all_52_7
% 200.36/33.26    (46)   ~ (all_52_5 = all_6_2)
% 200.36/33.26    (47)  op(e3, e3) = all_6_2
% 200.36/33.26    (48)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.26    (49)  all_58_5 = all_52_19
% 200.36/33.26    (50)  all_58_6 = all_52_5
% 200.36/33.26    (51)   ~ (all_52_17 = all_6_2)
% 200.36/33.26    (52)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 200.36/33.26    (53)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.26    (54)  op(e1, e1) = all_10_2
% 200.36/33.26    (55)   ~ (all_52_7 = all_52_23)
% 200.36/33.26    (56)  all_58_3 = all_4_2
% 200.36/33.26    (57)   ~ (all_52_3 = all_4_2)
% 200.36/33.26    (58)  op(all_6_2, e3) = all_6_1
% 200.36/33.26    (59)  all_58_4 = all_52_17
% 200.36/33.26  
% 200.36/33.26  Begin of proof
% 200.36/33.26  | 
% 200.36/33.26  | BETA: splitting (12) gives:
% 200.36/33.26  | 
% 200.36/33.26  | Case 1:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (60)  all_58_13 = e1
% 200.36/33.26  | | 
% 200.36/33.26  | | COMBINE_EQS: (13), (60) imply:
% 200.36/33.26  | |   (61)  all_52_15 = e1
% 200.36/33.26  | | 
% 200.36/33.26  | | REDUCE: (1), (61) imply:
% 200.36/33.26  | |   (62)  $false
% 200.36/33.26  | | 
% 200.36/33.26  | | CLOSE: (62) is inconsistent.
% 200.36/33.26  | | 
% 200.36/33.26  | Case 2:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (63)  all_58_14 = e1 | all_58_15 = e1
% 200.36/33.26  | | 
% 200.36/33.26  | | BETA: splitting (63) gives:
% 200.36/33.26  | | 
% 200.36/33.26  | | Case 1:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (64)  all_58_14 = e1
% 200.36/33.26  | | | 
% 200.36/33.26  | | | COMBINE_EQS: (2), (64) imply:
% 200.36/33.26  | | |   (65)  all_52_23 = e1
% 200.36/33.26  | | | 
% 200.36/33.26  | | | SIMP: (65) implies:
% 200.36/33.26  | | |   (66)  all_52_23 = e1
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (55), (66) imply:
% 200.36/33.26  | | |   (67)   ~ (all_52_7 = e1)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (41), (66) imply:
% 200.36/33.26  | | |   (68)  op(e1, e1) = all_52_22
% 200.36/33.26  | | | 
% 200.36/33.26  | | | GROUND_INST: instantiating (4) with all_10_2, all_52_22, e1, e1,
% 200.36/33.26  | | |              simplifying with (54), (68) gives:
% 200.36/33.26  | | |   (69)  all_52_22 = all_10_2
% 200.36/33.26  | | | 
% 200.36/33.26  | | | BETA: splitting (8) gives:
% 200.36/33.26  | | | 
% 200.36/33.26  | | | Case 1:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (70)  all_56_12 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | COMBINE_EQS: (45), (70) imply:
% 200.36/33.26  | | | |   (71)  all_52_7 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (29), (71) imply:
% 200.36/33.26  | | | |   (72)  $false
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | CLOSE: (72) is inconsistent.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | Case 2:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (73)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (14), (15), (16),
% 200.36/33.26  | | | |            (17), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 200.36/33.26  | | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 200.36/33.26  | | | |            (38), (39), (40), (42), (43), (44), (45), (46), (47), (48),
% 200.36/33.26  | | | |            (49), (50), (51), (52), (53), (54), (56), (57), (58), (59),
% 200.36/33.26  | | | |            (67), (73) are inconsistent by sub-proof #691.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | End of split
% 200.36/33.26  | | | 
% 200.36/33.26  | | Case 2:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (74)  all_58_15 = e1
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REF_CLOSE: (3), (18), (74) are inconsistent by sub-proof #586.
% 200.36/33.26  | | | 
% 200.36/33.26  | | End of split
% 200.36/33.26  | | 
% 200.36/33.26  | End of split
% 200.36/33.26  | 
% 200.36/33.26  End of proof
% 200.36/33.26  
% 200.36/33.26  Sub-proof #200 shows that the following formulas are inconsistent:
% 200.36/33.26  ----------------------------------------------------------------
% 200.36/33.26    (1)   ~ (all_52_15 = all_52_23)
% 200.36/33.26    (2)  all_58_14 = all_52_23
% 200.36/33.26    (3)  op(all_52_3, all_52_3) = all_52_2
% 200.36/33.26    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.26    (5)  all_58_1 = all_52_9
% 200.36/33.26    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 200.36/33.26    (7)  op(all_52_7, all_52_7) = all_52_6
% 200.36/33.26    (8)   ~ (all_52_3 = all_6_2)
% 200.36/33.26    (9)  all_58_0 = all_6_2
% 200.36/33.26    (10)  op(all_14_2, e0) = all_14_1
% 200.36/33.26    (11)   ~ (all_52_17 = all_10_2)
% 200.36/33.26    (12)  op(e3, e0) = all_52_25
% 200.36/33.26    (13)  all_58_13 = all_52_15
% 200.36/33.26    (14)  op(all_10_2, all_10_2) = all_52_20
% 200.36/33.26    (15)  all_58_9 = all_52_25
% 200.36/33.26    (16)   ~ (all_6_1 = e1)
% 200.36/33.26    (17)  op(e1, e3) = all_52_5
% 200.36/33.26    (18)  op(e2, e2) = all_4_2
% 200.36/33.26    (19)   ~ (all_52_3 = all_52_5)
% 200.36/33.26    (20)  op(all_4_2, e2) = e1
% 200.36/33.26    (21)   ~ (all_52_25 = all_14_2)
% 200.36/33.26    (22)   ~ (all_52_9 = all_52_15)
% 200.36/33.26    (23)   ~ (all_52_3 = all_52_27)
% 200.36/33.26    (24)  op(all_10_2, e1) = all_10_1
% 200.36/33.26    (25)   ~ (all_52_7 = all_6_2)
% 200.36/33.26    (26)  op(e0, e0) = all_14_2
% 200.36/33.26    (27)  all_56_15 = all_14_2
% 200.36/33.26    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 200.36/33.26    (29)   ~ (all_4_0 = e3)
% 200.36/33.26    (30)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 200.36/33.26    (31)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.26    (32)   ~ (e2 = e1)
% 200.36/33.26    (33)   ~ (all_52_13 = all_10_2)
% 200.36/33.26    (34)  all_58_10 = all_52_27
% 200.36/33.26    (35)  all_56_8 = all_52_5
% 200.36/33.26    (36)  all_58_7 = all_52_13
% 200.36/33.26    (37)   ~ (all_52_5 = all_52_7)
% 200.36/33.26    (38)  all_58_12 = all_52_7
% 200.36/33.26    (39)   ~ (all_52_7 = all_14_2)
% 200.36/33.26    (40)  all_58_2 = all_52_3
% 200.36/33.26    (41)  all_56_2 = all_52_17
% 200.36/33.26    (42)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 200.36/33.26    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 200.36/33.26    (44)  op(e3, all_6_1) = all_6_0
% 200.36/33.26    (45)   ~ (all_52_15 = all_14_2)
% 200.36/33.26    (46)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 200.36/33.26    (47)   ~ (all_6_0 = e2)
% 200.36/33.26    (48)  op(e3, e1) = all_52_17
% 200.36/33.26    (49)  op(e0, e3) = all_52_7
% 200.36/33.26    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 200.36/33.26    (51)  all_58_15 = all_14_2
% 200.36/33.26    (52)   ~ (all_52_19 = all_10_2)
% 200.36/33.26    (53)  op(all_52_23, all_52_23) = all_52_22
% 200.36/33.26    (54)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 200.36/33.26    (55)   ~ (all_10_1 = e2)
% 200.36/33.26    (56)  all_58_8 = all_10_2
% 200.36/33.26    (57)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 200.36/33.26    (58)   ~ (all_52_23 = all_14_2)
% 200.36/33.26    (59)  all_56_12 = all_52_7
% 200.36/33.26    (60)  op(all_52_17, all_52_17) = all_52_16
% 200.36/33.26    (61)  all_58_5 = all_4_0
% 200.36/33.26    (62)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 200.36/33.26    (63)   ~ (all_52_9 = all_4_2)
% 200.36/33.26    (64)   ~ (all_52_5 = all_6_2)
% 200.36/33.26    (65)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 200.36/33.26    (66)   ~ (all_52_9 = all_6_2)
% 200.36/33.26    (67)  op(e3, e3) = all_6_2
% 200.36/33.26    (68)   ~ (all_52_27 = all_14_2)
% 200.36/33.26    (69)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 200.36/33.26    (70)  op(all_4_2, all_4_2) = all_52_10
% 200.36/33.26    (71)  all_56_3 = all_52_25
% 200.36/33.26    (72)   ~ (all_52_3 = all_52_7)
% 200.36/33.26    (73)  op(all_14_2, all_14_2) = all_52_30
% 200.36/33.26    (74)  all_58_5 = all_52_19
% 200.36/33.26    (75)  all_58_6 = all_52_5
% 200.36/33.26    (76)   ~ (all_4_0 = all_4_2)
% 200.36/33.26    (77)  op(e3, e2) = all_52_9
% 200.36/33.26    (78)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.26    (79)   ~ (all_52_17 = all_6_2)
% 200.36/33.26    (80)   ~ (e3 = e2)
% 200.36/33.26    (81)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.26    (82)   ~ (all_52_3 = all_4_0)
% 200.36/33.26    (83)   ~ (all_6_1 = e2)
% 200.36/33.26    (84)   ~ (all_52_7 = all_52_23)
% 200.36/33.26    (85)  all_58_3 = all_4_2
% 200.36/33.26    (86)  all_56_13 = all_52_15
% 200.36/33.26    (87)   ~ (all_52_3 = all_4_2)
% 200.36/33.26    (88)  op(all_6_2, e3) = all_6_1
% 200.36/33.26    (89)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 200.36/33.26    (90)  all_58_4 = all_52_17
% 200.36/33.26  
% 200.36/33.26  Begin of proof
% 200.36/33.26  | 
% 200.36/33.26  | ALPHA: (89) implies:
% 200.36/33.26  |   (91)  all_52_22 = e0
% 200.36/33.26  |   (92)  all_52_20 = e1
% 200.36/33.26  |   (93)  all_52_16 = e3
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (60), (93) imply:
% 200.36/33.26  |   (94)  op(all_52_17, all_52_17) = e3
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (53), (91) imply:
% 200.36/33.26  |   (95)  op(all_52_23, all_52_23) = e0
% 200.36/33.26  | 
% 200.36/33.26  | REDUCE: (14), (92) imply:
% 200.36/33.26  |   (96)  op(all_10_2, all_10_2) = e1
% 200.36/33.26  | 
% 200.36/33.26  | BETA: splitting (57) gives:
% 200.36/33.26  | 
% 200.36/33.26  | Case 1:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (97)  all_56_15 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (15), (17),
% 200.36/33.26  | |            (18), (19), (20), (21), (22), (23), (24), (25), (27), (28), (29),
% 200.36/33.26  | |            (32), (33), (34), (35), (36), (37), (38), (40), (42), (43), (44),
% 200.36/33.26  | |            (46), (47), (48), (50), (52), (54), (56), (58), (61), (62), (63),
% 200.36/33.26  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 200.36/33.26  | |            (75), (76), (77), (79), (80), (81), (82), (83), (85), (87), (88),
% 200.36/33.26  | |            (90), (94), (96), (97) are inconsistent by sub-proof #203.
% 200.36/33.26  | | 
% 200.36/33.26  | Case 2:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (98)   ~ (all_56_15 = e3)
% 200.36/33.26  | | 
% 200.36/33.26  | | REDUCE: (27), (98) imply:
% 200.36/33.26  | |   (99)   ~ (all_14_2 = e3)
% 200.36/33.26  | | 
% 200.36/33.26  | | BETA: splitting (30) gives:
% 200.36/33.26  | | 
% 200.36/33.26  | | Case 1:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (100)  all_56_13 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | COMBINE_EQS: (86), (100) imply:
% 200.36/33.26  | | |   (101)  all_52_15 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | SIMP: (101) implies:
% 200.36/33.26  | | |   (102)  all_52_15 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (1), (102) imply:
% 200.36/33.26  | | |   (103)   ~ (all_52_23 = e3)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | SIMP: (103) implies:
% 200.36/33.26  | | |   (104)   ~ (all_52_23 = e3)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (45), (102) imply:
% 200.36/33.26  | | |   (105)   ~ (all_14_2 = e3)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REF_CLOSE: (2), (4), (11), (24), (26), (29), (31), (41), (48), (55), (56),
% 200.36/33.26  | | |            (61), (67), (79), (81), (90), (94), (96), (99), (104) are
% 200.36/33.26  | | |            inconsistent by sub-proof #201.
% 200.36/33.26  | | | 
% 200.36/33.26  | | Case 2:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (106)   ~ (all_56_13 = e3)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REDUCE: (86), (106) imply:
% 200.36/33.26  | | |   (107)   ~ (all_52_15 = e3)
% 200.36/33.26  | | | 
% 200.36/33.26  | | | BETA: splitting (78) gives:
% 200.36/33.26  | | | 
% 200.36/33.26  | | | Case 1:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (108)  all_58_12 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | COMBINE_EQS: (38), (108) imply:
% 200.36/33.26  | | | |   (109)  all_52_7 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | SIMP: (109) implies:
% 200.36/33.26  | | | |   (110)  all_52_7 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (84), (110) imply:
% 200.36/33.26  | | | |   (111)   ~ (all_52_23 = e3)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | SIMP: (111) implies:
% 200.36/33.26  | | | |   (112)   ~ (all_52_23 = e3)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (39), (110) imply:
% 200.36/33.26  | | | |   (113)   ~ (all_14_2 = e3)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REF_CLOSE: (2), (4), (11), (24), (26), (29), (31), (41), (48), (55),
% 200.36/33.26  | | | |            (56), (61), (67), (79), (81), (90), (94), (96), (99), (112)
% 200.36/33.26  | | | |            are inconsistent by sub-proof #201.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | Case 2:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (114)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REF_CLOSE: (2), (4), (6), (13), (16), (25), (49), (51), (59), (67),
% 200.36/33.26  | | | |            (83), (84), (88), (95), (99), (107), (114) are inconsistent
% 200.36/33.26  | | | |            by sub-proof #1045.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | End of split
% 200.36/33.26  | | | 
% 200.36/33.26  | | End of split
% 200.36/33.26  | | 
% 200.36/33.26  | End of split
% 200.36/33.26  | 
% 200.36/33.26  End of proof
% 200.36/33.26  
% 200.36/33.26  Sub-proof #201 shows that the following formulas are inconsistent:
% 200.36/33.26  ----------------------------------------------------------------
% 200.36/33.26    (1)  all_58_14 = all_52_23
% 200.36/33.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.26    (3)   ~ (all_52_17 = all_10_2)
% 200.36/33.26    (4)  op(all_10_2, e1) = all_10_1
% 200.36/33.26    (5)  op(e0, e0) = all_14_2
% 200.36/33.26    (6)   ~ (all_4_0 = e3)
% 200.36/33.26    (7)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 200.36/33.26    (8)  op(all_10_2, all_10_2) = e1
% 200.36/33.26    (9)  all_56_2 = all_52_17
% 200.36/33.26    (10)   ~ (all_52_23 = e3)
% 200.36/33.26    (11)  op(e3, e1) = all_52_17
% 200.36/33.26    (12)   ~ (all_10_1 = e2)
% 200.36/33.26    (13)  all_58_8 = all_10_2
% 200.36/33.26    (14)  all_58_5 = all_4_0
% 200.36/33.26    (15)  op(e3, e3) = all_6_2
% 200.36/33.26    (16)  op(all_52_17, all_52_17) = e3
% 200.36/33.26    (17)   ~ (all_52_17 = all_6_2)
% 200.36/33.26    (18)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.26    (19)  all_58_4 = all_52_17
% 200.36/33.26    (20)   ~ (all_14_2 = e3)
% 200.36/33.26  
% 200.36/33.26  Begin of proof
% 200.36/33.26  | 
% 200.36/33.26  | BETA: splitting (18) gives:
% 200.36/33.26  | 
% 200.36/33.26  | Case 1:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (21)  all_58_4 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | COMBINE_EQS: (19), (21) imply:
% 200.36/33.26  | |   (22)  all_52_17 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | SIMP: (22) implies:
% 200.36/33.26  | |   (23)  all_52_17 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | REF_CLOSE: (2), (15), (16), (17), (23) are inconsistent by sub-proof #1280.
% 200.36/33.26  | | 
% 200.36/33.26  | Case 2:
% 200.36/33.26  | | 
% 200.36/33.26  | |   (24)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 200.36/33.26  | | 
% 200.36/33.26  | | BETA: splitting (24) gives:
% 200.36/33.26  | | 
% 200.36/33.26  | | Case 1:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (25)  all_58_5 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | REF_CLOSE: (6), (14), (25) are inconsistent by sub-proof #215.
% 200.36/33.26  | | | 
% 200.36/33.26  | | Case 2:
% 200.36/33.26  | | | 
% 200.36/33.26  | | |   (26)  all_58_8 = e3 | all_58_14 = e3
% 200.36/33.26  | | | 
% 200.36/33.26  | | | BETA: splitting (26) gives:
% 200.36/33.26  | | | 
% 200.36/33.26  | | | Case 1:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (27)  all_58_8 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | COMBINE_EQS: (13), (27) imply:
% 200.36/33.26  | | | |   (28)  all_10_2 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (3), (28) imply:
% 200.36/33.26  | | | |   (29)   ~ (all_52_17 = e3)
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (8), (28) imply:
% 200.36/33.26  | | | |   (30)  op(e3, e3) = e1
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REDUCE: (4), (28) imply:
% 200.36/33.26  | | | |   (31)  op(e3, e1) = all_10_1
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REF_CLOSE: (2), (5), (7), (9), (11), (12), (15), (16), (17), (20), (29),
% 200.36/33.26  | | | |            (30), (31) are inconsistent by sub-proof #202.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | Case 2:
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | |   (32)  all_58_14 = e3
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | | REF_CLOSE: (1), (10), (32) are inconsistent by sub-proof #1305.
% 200.36/33.26  | | | | 
% 200.36/33.26  | | | End of split
% 200.36/33.26  | | | 
% 200.36/33.26  | | End of split
% 200.36/33.26  | | 
% 200.36/33.26  | End of split
% 200.36/33.26  | 
% 200.36/33.26  End of proof
% 200.36/33.26  
% 200.36/33.26  Sub-proof #202 shows that the following formulas are inconsistent:
% 200.36/33.26  ----------------------------------------------------------------
% 200.36/33.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 200.36/33.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 200.36/33.26    (2)  op(e0, e0) = all_14_2
% 201.06/33.26    (3)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.06/33.26    (4)  all_56_2 = all_52_17
% 201.06/33.26    (5)  op(e3, e1) = all_10_1
% 201.06/33.26    (6)  op(e3, e1) = all_52_17
% 201.06/33.26    (7)   ~ (all_10_1 = e2)
% 201.06/33.26    (8)  op(e3, e3) = all_6_2
% 201.06/33.26    (9)   ~ (all_52_17 = e3)
% 201.06/33.26    (10)  op(e3, e3) = e1
% 201.06/33.26    (11)  op(all_52_17, all_52_17) = e3
% 201.06/33.26    (12)   ~ (all_52_17 = all_6_2)
% 201.06/33.26    (13)   ~ (all_14_2 = e3)
% 201.06/33.26  
% 201.06/33.26  Begin of proof
% 201.06/33.26  | 
% 201.06/33.26  | GROUND_INST: instantiating (1) with all_52_17, all_10_1, e1, e3, simplifying
% 201.06/33.26  |              with (5), (6) gives:
% 201.06/33.26  |   (14)  all_52_17 = all_10_1
% 201.06/33.26  | 
% 201.06/33.26  | GROUND_INST: instantiating (1) with all_6_2, e1, e3, e3, simplifying with (8),
% 201.06/33.26  |              (10) gives:
% 201.06/33.26  |   (15)  all_6_2 = e1
% 201.06/33.26  | 
% 201.06/33.26  | COMBINE_EQS: (4), (14) imply:
% 201.06/33.26  |   (16)  all_56_2 = all_10_1
% 201.06/33.26  | 
% 201.06/33.26  | REDUCE: (12), (14), (15) imply:
% 201.06/33.26  |   (17)   ~ (all_10_1 = e1)
% 201.06/33.26  | 
% 201.06/33.26  | REDUCE: (9), (14) imply:
% 201.06/33.26  |   (18)   ~ (all_10_1 = e3)
% 201.06/33.26  | 
% 201.06/33.26  | REDUCE: (11), (14) imply:
% 201.06/33.26  |   (19)  op(all_10_1, all_10_1) = e3
% 201.06/33.26  | 
% 201.06/33.26  | BETA: splitting (3) gives:
% 201.06/33.26  | 
% 201.06/33.26  | Case 1:
% 201.06/33.26  | | 
% 201.06/33.26  | |   (20)  all_56_2 = e3
% 201.06/33.26  | | 
% 201.06/33.26  | | REF_CLOSE: (16), (18), (20) are inconsistent by sub-proof #1029.
% 201.06/33.26  | | 
% 201.06/33.26  | Case 2:
% 201.06/33.26  | | 
% 201.06/33.26  | |   (21)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.06/33.26  | | 
% 201.06/33.26  | | REF_CLOSE: (1), (2), (7), (13), (16), (17), (19), (21) are inconsistent by
% 201.06/33.26  | |            sub-proof #445.
% 201.06/33.26  | | 
% 201.06/33.26  | End of split
% 201.06/33.26  | 
% 201.06/33.26  End of proof
% 201.06/33.26  
% 201.06/33.26  Sub-proof #203 shows that the following formulas are inconsistent:
% 201.06/33.26  ----------------------------------------------------------------
% 201.06/33.26    (1)  all_58_14 = all_52_23
% 201.06/33.26    (2)  op(all_52_3, all_52_3) = all_52_2
% 201.06/33.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.27    (4)  all_58_1 = all_52_9
% 201.06/33.27    (5)  op(all_52_7, all_52_7) = all_52_6
% 201.06/33.27    (6)   ~ (all_52_3 = all_6_2)
% 201.06/33.27    (7)  all_58_0 = all_6_2
% 201.06/33.27    (8)  op(all_14_2, e0) = all_14_1
% 201.06/33.27    (9)  op(e3, e0) = all_52_25
% 201.06/33.27    (10)  all_58_13 = all_52_15
% 201.06/33.27    (11)  all_58_9 = all_52_25
% 201.06/33.27    (12)  op(e1, e3) = all_52_5
% 201.06/33.27    (13)  op(e2, e2) = all_4_2
% 201.06/33.27    (14)   ~ (all_52_3 = all_52_5)
% 201.06/33.27    (15)  op(all_4_2, e2) = e1
% 201.06/33.27    (16)   ~ (all_52_25 = all_14_2)
% 201.06/33.27    (17)   ~ (all_52_9 = all_52_15)
% 201.06/33.27    (18)   ~ (all_52_3 = all_52_27)
% 201.06/33.27    (19)  op(all_10_2, e1) = all_10_1
% 201.06/33.27    (20)   ~ (all_52_7 = all_6_2)
% 201.06/33.27    (21)  all_56_15 = all_14_2
% 201.06/33.27    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.27    (23)   ~ (all_4_0 = e3)
% 201.06/33.27    (24)   ~ (e2 = e1)
% 201.06/33.27    (25)   ~ (all_52_13 = all_10_2)
% 201.06/33.27    (26)  op(all_10_2, all_10_2) = e1
% 201.06/33.27    (27)  all_58_10 = all_52_27
% 201.06/33.27    (28)  all_56_8 = all_52_5
% 201.06/33.27    (29)  all_58_7 = all_52_13
% 201.06/33.27    (30)   ~ (all_52_5 = all_52_7)
% 201.06/33.27    (31)  all_58_12 = all_52_7
% 201.06/33.27    (32)  all_58_2 = all_52_3
% 201.06/33.27    (33)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.06/33.27    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.27    (35)  op(e3, all_6_1) = all_6_0
% 201.06/33.27    (36)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.06/33.27    (37)   ~ (all_6_0 = e2)
% 201.06/33.27    (38)  op(e3, e1) = all_52_17
% 201.06/33.27    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.27    (40)   ~ (all_52_19 = all_10_2)
% 201.06/33.27    (41)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.06/33.27    (42)  all_58_8 = all_10_2
% 201.06/33.27    (43)   ~ (all_52_23 = all_14_2)
% 201.06/33.27    (44)  all_58_5 = all_4_0
% 201.06/33.27    (45)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.27    (46)   ~ (all_52_9 = all_4_2)
% 201.06/33.27    (47)   ~ (all_52_5 = all_6_2)
% 201.06/33.27    (48)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 201.06/33.27    (49)   ~ (all_52_9 = all_6_2)
% 201.06/33.27    (50)  op(e3, e3) = all_6_2
% 201.06/33.27    (51)  all_56_15 = e3
% 201.06/33.27    (52)   ~ (all_52_27 = all_14_2)
% 201.06/33.27    (53)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.27    (54)  op(all_4_2, all_4_2) = all_52_10
% 201.06/33.27    (55)  all_56_3 = all_52_25
% 201.06/33.27    (56)   ~ (all_52_3 = all_52_7)
% 201.06/33.27    (57)  op(all_14_2, all_14_2) = all_52_30
% 201.06/33.27    (58)  all_58_5 = all_52_19
% 201.06/33.27    (59)  op(all_52_17, all_52_17) = e3
% 201.06/33.27    (60)  all_58_6 = all_52_5
% 201.06/33.27    (61)   ~ (all_4_0 = all_4_2)
% 201.06/33.27    (62)  op(e3, e2) = all_52_9
% 201.06/33.27    (63)   ~ (all_52_17 = all_6_2)
% 201.06/33.27    (64)   ~ (e3 = e2)
% 201.06/33.27    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27    (66)   ~ (all_52_3 = all_4_0)
% 201.06/33.27    (67)   ~ (all_6_1 = e2)
% 201.06/33.27    (68)  all_58_3 = all_4_2
% 201.06/33.27    (69)   ~ (all_52_3 = all_4_2)
% 201.06/33.27    (70)  op(all_6_2, e3) = all_6_1
% 201.06/33.27    (71)  all_58_4 = all_52_17
% 201.06/33.27  
% 201.06/33.27  Begin of proof
% 201.06/33.27  | 
% 201.06/33.27  | COMBINE_EQS: (21), (51) imply:
% 201.06/33.27  |   (72)  all_14_2 = e3
% 201.06/33.27  | 
% 201.06/33.27  | SIMP: (72) implies:
% 201.06/33.27  |   (73)  all_14_2 = e3
% 201.06/33.27  | 
% 201.06/33.27  | REDUCE: (43), (73) imply:
% 201.06/33.27  |   (74)   ~ (all_52_23 = e3)
% 201.06/33.27  | 
% 201.06/33.27  | REDUCE: (16), (73) imply:
% 201.06/33.27  |   (75)   ~ (all_52_25 = e3)
% 201.06/33.27  | 
% 201.06/33.27  | REDUCE: (52), (73) imply:
% 201.06/33.27  |   (76)   ~ (all_52_27 = e3)
% 201.06/33.27  | 
% 201.06/33.27  | REDUCE: (57), (73) imply:
% 201.06/33.27  |   (77)  op(e3, e3) = all_52_30
% 201.06/33.27  | 
% 201.06/33.27  | REDUCE: (8), (73) imply:
% 201.06/33.27  |   (78)  op(e3, e0) = all_14_1
% 201.06/33.27  | 
% 201.06/33.27  | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 201.06/33.27  |              with (9), (78) gives:
% 201.06/33.27  |   (79)  all_52_25 = all_14_1
% 201.06/33.27  | 
% 201.06/33.27  | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3, simplifying
% 201.06/33.27  |              with (50), (77) gives:
% 201.06/33.27  |   (80)  all_52_30 = all_6_2
% 201.06/33.27  | 
% 201.06/33.27  | COMBINE_EQS: (55), (79) imply:
% 201.06/33.27  |   (81)  all_56_3 = all_14_1
% 201.06/33.27  | 
% 201.06/33.27  | COMBINE_EQS: (11), (79) imply:
% 201.06/33.27  |   (82)  all_58_9 = all_14_1
% 201.06/33.27  | 
% 201.06/33.27  | REDUCE: (75), (79) imply:
% 201.06/33.27  |   (83)   ~ (all_14_1 = e3)
% 201.06/33.27  | 
% 201.06/33.27  | BETA: splitting (45) gives:
% 201.06/33.27  | 
% 201.06/33.27  | Case 1:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (84)  all_56_3 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REF_CLOSE: (81), (83), (84) are inconsistent by sub-proof #1200.
% 201.06/33.27  | | 
% 201.06/33.27  | Case 2:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (85)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.27  | | 
% 201.06/33.27  | | BETA: splitting (22) gives:
% 201.06/33.27  | | 
% 201.06/33.27  | | Case 1:
% 201.06/33.27  | | | 
% 201.06/33.27  | | |   (86)  all_58_2 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | COMBINE_EQS: (32), (86) imply:
% 201.06/33.27  | | |   (87)  all_52_3 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | SIMP: (87) implies:
% 201.06/33.27  | | |   (88)  all_52_3 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (18), (88) imply:
% 201.06/33.27  | | |   (89)   ~ (all_52_27 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (6), (88) imply:
% 201.06/33.27  | | |   (90)   ~ (all_6_2 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | SIMP: (90) implies:
% 201.06/33.27  | | |   (91)   ~ (all_6_2 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (66), (88) imply:
% 201.06/33.27  | | |   (92)   ~ (all_4_0 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (2), (88) imply:
% 201.06/33.27  | | |   (93)  op(e3, e3) = all_52_2
% 201.06/33.27  | | | 
% 201.06/33.27  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_2, e3, e3, simplifying
% 201.06/33.27  | | |              with (50), (93) gives:
% 201.06/33.27  | | |   (94)  all_52_2 = all_6_2
% 201.06/33.27  | | | 
% 201.06/33.27  | | | BETA: splitting (65) gives:
% 201.06/33.27  | | | 
% 201.06/33.27  | | | Case 1:
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | |   (95)  all_58_4 = e3
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | | COMBINE_EQS: (71), (95) imply:
% 201.06/33.27  | | | |   (96)  all_52_17 = e3
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | | REF_CLOSE: (3), (50), (59), (63), (96) are inconsistent by sub-proof
% 201.06/33.27  | | | |            #1280.
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | Case 2:
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | |   (97)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | | BETA: splitting (97) gives:
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | | Case 1:
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | |   (98)  all_58_5 = e3
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | | COMBINE_EQS: (44), (98) imply:
% 201.06/33.27  | | | | |   (99)  all_4_0 = e3
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | | REDUCE: (23), (99) imply:
% 201.06/33.27  | | | | |   (100)  $false
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | | CLOSE: (100) is inconsistent.
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | Case 2:
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | |   (101)  all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13),
% 201.06/33.27  | | | | |            (14), (17), (19), (20), (22), (24), (25), (26), (27), (28),
% 201.06/33.27  | | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 201.06/33.27  | | | | |            (39), (40), (41), (42), (46), (47), (50), (53), (56), (58),
% 201.06/33.27  | | | | |            (59), (60), (63), (64), (67), (68), (69), (70), (71), (74),
% 201.06/33.27  | | | | |            (75), (76), (78), (81), (82), (85), (91), (101) are
% 201.06/33.27  | | | | |            inconsistent by sub-proof #1079.
% 201.06/33.27  | | | | | 
% 201.06/33.27  | | | | End of split
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | End of split
% 201.06/33.27  | | | 
% 201.06/33.27  | | Case 2:
% 201.06/33.27  | | | 
% 201.06/33.27  | | |   (102)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REF_CLOSE: (1), (3), (13), (15), (23), (26), (27), (42), (44), (48), (49),
% 201.06/33.27  | | |            (50), (54), (59), (61), (62), (63), (65), (68), (71), (74),
% 201.06/33.27  | | |            (76), (102) are inconsistent by sub-proof #204.
% 201.06/33.27  | | | 
% 201.06/33.27  | | End of split
% 201.06/33.27  | | 
% 201.06/33.27  | End of split
% 201.06/33.27  | 
% 201.06/33.27  End of proof
% 201.06/33.27  
% 201.06/33.27  Sub-proof #204 shows that the following formulas are inconsistent:
% 201.06/33.27  ----------------------------------------------------------------
% 201.06/33.27    (1)  all_58_14 = all_52_23
% 201.06/33.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.27    (3)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.27    (4)  op(e2, e2) = all_4_2
% 201.06/33.27    (5)  op(all_4_2, e2) = e1
% 201.06/33.27    (6)   ~ (all_4_0 = e3)
% 201.06/33.27    (7)  op(all_10_2, all_10_2) = e1
% 201.06/33.27    (8)  all_58_10 = all_52_27
% 201.06/33.27    (9)   ~ (all_52_23 = e3)
% 201.06/33.27    (10)   ~ (all_52_27 = e3)
% 201.06/33.27    (11)  all_58_8 = all_10_2
% 201.06/33.27    (12)  all_58_5 = all_4_0
% 201.06/33.27    (13)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 201.06/33.27    (14)   ~ (all_52_9 = all_6_2)
% 201.06/33.27    (15)  op(e3, e3) = all_6_2
% 201.06/33.27    (16)  op(all_4_2, all_4_2) = all_52_10
% 201.06/33.27    (17)  op(all_52_17, all_52_17) = e3
% 201.06/33.27    (18)   ~ (all_4_0 = all_4_2)
% 201.06/33.27    (19)  op(e3, e2) = all_52_9
% 201.06/33.27    (20)   ~ (all_52_17 = all_6_2)
% 201.06/33.27    (21)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27    (22)  all_58_3 = all_4_2
% 201.06/33.27    (23)  all_58_4 = all_52_17
% 201.06/33.27  
% 201.06/33.27  Begin of proof
% 201.06/33.27  | 
% 201.06/33.27  | BETA: splitting (3) gives:
% 201.06/33.27  | 
% 201.06/33.27  | Case 1:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (24)  all_58_3 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | COMBINE_EQS: (22), (24) imply:
% 201.06/33.27  | |   (25)  all_4_2 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (16), (25) imply:
% 201.06/33.27  | |   (26)  op(e3, e3) = all_52_10
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (5), (25) imply:
% 201.06/33.27  | |   (27)  op(e3, e2) = e1
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (4), (25) imply:
% 201.06/33.27  | |   (28)  op(e2, e2) = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | BETA: splitting (13) gives:
% 201.06/33.27  | | 
% 201.06/33.27  | | Case 1:
% 201.06/33.27  | | | 
% 201.06/33.27  | | |   (29)   ~ (all_4_2 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REF_CLOSE: (2), (4), (28), (29) are inconsistent by sub-proof #211.
% 201.06/33.27  | | | 
% 201.06/33.27  | | Case 2:
% 201.06/33.27  | | | 
% 201.06/33.27  | | | 
% 201.06/33.27  | | | GROUND_INST: instantiating (2) with all_52_9, e1, e2, e3, simplifying with
% 201.06/33.27  | | |              (19), (27) gives:
% 201.06/33.27  | | |   (30)  all_52_9 = e1
% 201.06/33.27  | | | 
% 201.06/33.27  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_10, e3, e3,
% 201.06/33.27  | | |              simplifying with (15), (26) gives:
% 201.06/33.27  | | |   (31)  all_52_10 = all_6_2
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (14), (30) imply:
% 201.06/33.27  | | |   (32)   ~ (all_6_2 = e1)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | SIMP: (32) implies:
% 201.06/33.27  | | |   (33)   ~ (all_6_2 = e1)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REF_CLOSE: (1), (2), (6), (7), (9), (11), (12), (15), (17), (20), (21),
% 201.06/33.27  | | |            (23), (33) are inconsistent by sub-proof #205.
% 201.06/33.27  | | | 
% 201.06/33.27  | | End of split
% 201.06/33.27  | | 
% 201.06/33.27  | Case 2:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (34)  all_58_5 = e3 | all_58_10 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REF_CLOSE: (6), (8), (10), (12), (34) are inconsistent by sub-proof #214.
% 201.06/33.27  | | 
% 201.06/33.27  | End of split
% 201.06/33.27  | 
% 201.06/33.27  End of proof
% 201.06/33.27  
% 201.06/33.27  Sub-proof #205 shows that the following formulas are inconsistent:
% 201.06/33.27  ----------------------------------------------------------------
% 201.06/33.27    (1)  all_58_14 = all_52_23
% 201.06/33.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.27    (3)   ~ (all_4_0 = e3)
% 201.06/33.27    (4)  op(all_10_2, all_10_2) = e1
% 201.06/33.27    (5)   ~ (all_52_23 = e3)
% 201.06/33.27    (6)  all_58_8 = all_10_2
% 201.06/33.27    (7)  all_58_5 = all_4_0
% 201.06/33.27    (8)  op(e3, e3) = all_6_2
% 201.06/33.27    (9)  op(all_52_17, all_52_17) = e3
% 201.06/33.27    (10)   ~ (all_52_17 = all_6_2)
% 201.06/33.27    (11)   ~ (all_6_2 = e1)
% 201.06/33.27    (12)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27    (13)  all_58_4 = all_52_17
% 201.06/33.27  
% 201.06/33.27  Begin of proof
% 201.06/33.27  | 
% 201.06/33.27  | BETA: splitting (12) gives:
% 201.06/33.27  | 
% 201.06/33.27  | Case 1:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (14)  all_58_4 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | COMBINE_EQS: (13), (14) imply:
% 201.06/33.27  | |   (15)  all_52_17 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | SIMP: (15) implies:
% 201.06/33.27  | |   (16)  all_52_17 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REF_CLOSE: (2), (8), (9), (10), (16) are inconsistent by sub-proof #1280.
% 201.06/33.27  | | 
% 201.06/33.27  | Case 2:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (17)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | BETA: splitting (17) gives:
% 201.06/33.27  | | 
% 201.06/33.27  | | Case 1:
% 201.06/33.27  | | | 
% 201.06/33.27  | | |   (18)  all_58_5 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REF_CLOSE: (3), (7), (18) are inconsistent by sub-proof #215.
% 201.06/33.27  | | | 
% 201.06/33.27  | | Case 2:
% 201.06/33.27  | | | 
% 201.06/33.27  | | |   (19)  all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (11), (19) are inconsistent by
% 201.06/33.27  | | |            sub-proof #283.
% 201.06/33.27  | | | 
% 201.06/33.27  | | End of split
% 201.06/33.27  | | 
% 201.06/33.27  | End of split
% 201.06/33.27  | 
% 201.06/33.27  End of proof
% 201.06/33.27  
% 201.06/33.27  Sub-proof #206 shows that the following formulas are inconsistent:
% 201.06/33.27  ----------------------------------------------------------------
% 201.06/33.27    (1)  all_58_14 = all_52_23
% 201.06/33.27    (2)   ~ (all_52_17 = all_4_0)
% 201.06/33.27    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.06/33.27    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.27    (5)   ~ (all_52_5 = all_52_13)
% 201.06/33.27    (6)  all_58_1 = all_52_9
% 201.06/33.27    (7)   ~ (all_52_9 = all_52_13)
% 201.06/33.27    (8)   ~ (all_52_17 = all_52_25)
% 201.06/33.27    (9)  all_58_0 = all_6_2
% 201.06/33.27    (10)   ~ (all_52_17 = all_10_2)
% 201.06/33.27    (11)   ~ (all_52_27 = all_52_29)
% 201.06/33.27    (12)  all_58_13 = all_52_15
% 201.06/33.27    (13)  op(all_52_13, all_52_13) = e1
% 201.06/33.27    (14)  op(all_10_2, all_10_2) = all_52_20
% 201.06/33.27    (15)  all_58_9 = all_52_25
% 201.06/33.27    (16)   ~ (all_52_15 = e3)
% 201.06/33.27    (17)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.06/33.27    (18)  op(e2, e2) = all_4_2
% 201.06/33.27    (19)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.27    (20)   ~ (all_52_3 = all_52_5)
% 201.06/33.27    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 201.06/33.27    (22)  op(all_4_2, e2) = e1
% 201.06/33.27    (23)  all_58_11 = all_52_29
% 201.06/33.27    (24)   ~ (all_52_3 = e3)
% 201.06/33.27    (25)  op(all_10_2, e1) = all_10_1
% 201.06/33.27    (26)   ~ (all_52_15 = e0)
% 201.06/33.27    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.27    (28)  all_56_11 = all_52_29
% 201.06/33.27    (29)   ~ (all_4_0 = e3)
% 201.06/33.27    (30)   ~ (all_52_25 = e0)
% 201.06/33.27    (31)   ~ (all_6_2 = e3)
% 201.06/33.27    (32)   ~ (all_52_13 = all_10_2)
% 201.06/33.27    (33)  op(e0, e0) = e0
% 201.06/33.27    (34)  all_58_10 = all_52_27
% 201.06/33.27    (35)   ~ (all_52_29 = all_10_2)
% 201.06/33.27    (36)  all_58_7 = all_52_13
% 201.06/33.27    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.27    (38)  all_58_2 = all_52_3
% 201.06/33.27    (39)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.06/33.27    (40)   ~ (all_52_23 = e3)
% 201.06/33.27    (41)   ~ (all_52_5 = e3)
% 201.06/33.27    (42)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.06/33.27    (43)   ~ (all_52_13 = all_4_2)
% 201.06/33.27    (44)  op(e3, e1) = all_52_17
% 201.06/33.27    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.27    (46)   ~ (all_52_9 = all_52_25)
% 201.06/33.27    (47)  all_58_8 = all_10_2
% 201.06/33.27    (48)   ~ (all_52_23 = e0)
% 201.06/33.27    (49)  op(all_52_17, all_52_17) = all_52_16
% 201.06/33.27    (50)  all_58_5 = all_4_0
% 201.06/33.27    (51)   ~ (all_52_25 = all_6_2)
% 201.06/33.27    (52)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.27    (53)   ~ (all_52_9 = all_4_2)
% 201.06/33.27    (54)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 201.06/33.27    (55)   ~ (all_52_9 = all_6_2)
% 201.06/33.27    (56)  op(e3, e3) = all_6_2
% 201.06/33.27    (57)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.27    (58)  all_56_3 = all_52_25
% 201.06/33.27    (59)  all_56_1 = all_52_9
% 201.06/33.27    (60)   ~ (all_52_15 = all_4_2)
% 201.06/33.27    (61)  all_58_6 = all_52_5
% 201.06/33.27    (62)  op(e3, e2) = all_52_9
% 201.06/33.27    (63)   ~ (all_52_17 = all_6_2)
% 201.06/33.27    (64)   ~ (e1 = e0)
% 201.06/33.27    (65)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 201.06/33.27    (66)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.06/33.27    (67)   ~ (all_52_9 = all_52_17)
% 201.06/33.27    (68)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27    (69)  all_58_12 = e3
% 201.06/33.27    (70)  op(e1, e1) = all_10_2
% 201.06/33.27    (71)  op(all_52_9, all_52_9) = e3
% 201.06/33.27    (72)  all_58_3 = all_4_2
% 201.06/33.27    (73)   ~ (all_52_3 = all_4_2)
% 201.06/33.27    (74)  all_58_4 = all_52_17
% 201.06/33.27  
% 201.06/33.27  Begin of proof
% 201.06/33.27  | 
% 201.06/33.27  | BETA: splitting (68) gives:
% 201.06/33.27  | 
% 201.06/33.27  | Case 1:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (75)  all_58_4 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | COMBINE_EQS: (74), (75) imply:
% 201.06/33.27  | |   (76)  all_52_17 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (67), (76) imply:
% 201.06/33.27  | |   (77)   ~ (all_52_9 = e3)
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (8), (76) imply:
% 201.06/33.27  | |   (78)   ~ (all_52_25 = e3)
% 201.06/33.27  | | 
% 201.06/33.27  | | SIMP: (78) implies:
% 201.06/33.27  | |   (79)   ~ (all_52_25 = e3)
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (10), (76) imply:
% 201.06/33.27  | |   (80)   ~ (all_10_2 = e3)
% 201.06/33.27  | | 
% 201.06/33.27  | | SIMP: (80) implies:
% 201.06/33.27  | |   (81)   ~ (all_10_2 = e3)
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (2), (76) imply:
% 201.06/33.27  | |   (82)   ~ (all_4_0 = e3)
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (49), (76) imply:
% 201.06/33.27  | |   (83)  op(e3, e3) = all_52_16
% 201.06/33.27  | | 
% 201.06/33.27  | | REF_CLOSE: (4), (6), (7), (9), (11), (12), (13), (22), (23), (24), (27),
% 201.06/33.27  | |            (28), (29), (30), (33), (34), (35), (36), (37), (38), (39), (41),
% 201.06/33.27  | |            (42), (43), (45), (46), (47), (50), (51), (52), (54), (55), (56),
% 201.06/33.27  | |            (58), (59), (60), (61), (62), (64), (66), (70), (71), (72), (77),
% 201.06/33.27  | |            (79), (81), (83) are inconsistent by sub-proof #212.
% 201.06/33.27  | | 
% 201.06/33.27  | Case 2:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (84)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14), (15),
% 201.06/33.27  | |            (16), (17), (18), (19), (20), (21), (25), (26), (29), (30), (31),
% 201.06/33.27  | |            (32), (33), (36), (38), (40), (44), (45), (47), (48), (50), (53),
% 201.06/33.27  | |            (54), (55), (56), (57), (61), (63), (64), (65), (67), (69), (71),
% 201.06/33.27  | |            (72), (73), (74), (84) are inconsistent by sub-proof #207.
% 201.06/33.27  | | 
% 201.06/33.27  | End of split
% 201.06/33.27  | 
% 201.06/33.27  End of proof
% 201.06/33.27  
% 201.06/33.27  Sub-proof #207 shows that the following formulas are inconsistent:
% 201.06/33.27  ----------------------------------------------------------------
% 201.06/33.27    (1)  all_58_14 = all_52_23
% 201.06/33.27    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.06/33.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.27    (4)   ~ (all_52_5 = all_52_13)
% 201.06/33.27    (5)  all_58_1 = all_52_9
% 201.06/33.27    (6)   ~ (all_52_17 = all_52_25)
% 201.06/33.27    (7)  all_58_0 = all_6_2
% 201.06/33.27    (8)   ~ (all_52_17 = all_10_2)
% 201.06/33.27    (9)  all_58_13 = all_52_15
% 201.06/33.27    (10)  op(all_52_13, all_52_13) = e1
% 201.06/33.27    (11)  op(all_10_2, all_10_2) = all_52_20
% 201.06/33.27    (12)  all_58_9 = all_52_25
% 201.06/33.27    (13)   ~ (all_52_15 = e3)
% 201.06/33.27    (14)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.06/33.27    (15)  op(e2, e2) = all_4_2
% 201.06/33.27    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.27    (17)   ~ (all_52_3 = all_52_5)
% 201.06/33.27    (18)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 201.06/33.27    (19)  op(all_10_2, e1) = all_10_1
% 201.06/33.27    (20)   ~ (all_52_15 = e0)
% 201.06/33.27    (21)   ~ (all_4_0 = e3)
% 201.06/33.27    (22)   ~ (all_52_25 = e0)
% 201.06/33.27    (23)   ~ (all_6_2 = e3)
% 201.06/33.27    (24)   ~ (all_52_13 = all_10_2)
% 201.06/33.27    (25)  op(e0, e0) = e0
% 201.06/33.27    (26)  all_58_7 = all_52_13
% 201.06/33.27    (27)  all_58_2 = all_52_3
% 201.06/33.27    (28)   ~ (all_52_23 = e3)
% 201.06/33.27    (29)  op(e3, e1) = all_52_17
% 201.06/33.27    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.27    (31)  all_58_8 = all_10_2
% 201.06/33.27    (32)   ~ (all_52_23 = e0)
% 201.06/33.27    (33)  all_58_5 = all_4_0
% 201.06/33.27    (34)   ~ (all_52_9 = all_4_2)
% 201.06/33.27    (35)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 201.06/33.27    (36)   ~ (all_52_9 = all_6_2)
% 201.06/33.27    (37)  op(e3, e3) = all_6_2
% 201.06/33.27    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.27    (39)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27    (40)  all_58_6 = all_52_5
% 201.06/33.27    (41)   ~ (all_52_17 = all_6_2)
% 201.06/33.27    (42)   ~ (e1 = e0)
% 201.06/33.27    (43)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 201.06/33.27    (44)   ~ (all_52_9 = all_52_17)
% 201.06/33.27    (45)  all_58_12 = e3
% 201.06/33.27    (46)  op(all_52_9, all_52_9) = e3
% 201.06/33.27    (47)  all_58_3 = all_4_2
% 201.06/33.27    (48)   ~ (all_52_3 = all_4_2)
% 201.06/33.27    (49)  all_58_4 = all_52_17
% 201.06/33.27  
% 201.06/33.27  Begin of proof
% 201.06/33.27  | 
% 201.06/33.27  | BETA: splitting (39) gives:
% 201.06/33.27  | 
% 201.06/33.27  | Case 1:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (50)  all_58_5 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | COMBINE_EQS: (33), (50) imply:
% 201.06/33.27  | |   (51)  all_4_0 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | REDUCE: (21), (51) imply:
% 201.06/33.27  | |   (52)  $false
% 201.06/33.27  | | 
% 201.06/33.27  | | CLOSE: (52) is inconsistent.
% 201.06/33.27  | | 
% 201.06/33.27  | Case 2:
% 201.06/33.27  | | 
% 201.06/33.27  | |   (53)  all_58_8 = e3 | all_58_14 = e3
% 201.06/33.27  | | 
% 201.06/33.27  | | BETA: splitting (53) gives:
% 201.06/33.27  | | 
% 201.06/33.27  | | Case 1:
% 201.06/33.27  | | | 
% 201.06/33.27  | | |   (54)  all_58_8 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | COMBINE_EQS: (31), (54) imply:
% 201.06/33.27  | | |   (55)  all_10_2 = e3
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (24), (55) imply:
% 201.06/33.27  | | |   (56)   ~ (all_52_13 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (8), (55) imply:
% 201.06/33.27  | | |   (57)   ~ (all_52_17 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (11), (55) imply:
% 201.06/33.27  | | |   (58)  op(e3, e3) = all_52_20
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (19), (55) imply:
% 201.06/33.27  | | |   (59)  op(e3, e1) = all_10_1
% 201.06/33.27  | | | 
% 201.06/33.27  | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 201.06/33.27  | | |              simplifying with (29), (59) gives:
% 201.06/33.27  | | |   (60)  all_52_17 = all_10_1
% 201.06/33.27  | | | 
% 201.06/33.27  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_20, e3, e3,
% 201.06/33.27  | | |              simplifying with (37), (58) gives:
% 201.06/33.27  | | |   (61)  all_52_20 = all_6_2
% 201.06/33.27  | | | 
% 201.06/33.27  | | | COMBINE_EQS: (49), (60) imply:
% 201.06/33.27  | | |   (62)  all_58_4 = all_10_1
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (44), (60) imply:
% 201.06/33.27  | | |   (63)   ~ (all_52_9 = all_10_1)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (6), (60) imply:
% 201.06/33.27  | | |   (64)   ~ (all_52_25 = all_10_1)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | SIMP: (64) implies:
% 201.06/33.27  | | |   (65)   ~ (all_52_25 = all_10_1)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (41), (60) imply:
% 201.06/33.27  | | |   (66)   ~ (all_10_1 = all_6_2)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | REDUCE: (57), (60) imply:
% 201.06/33.27  | | |   (67)   ~ (all_10_1 = e3)
% 201.06/33.27  | | | 
% 201.06/33.27  | | | BETA: splitting (30) gives:
% 201.06/33.27  | | | 
% 201.06/33.27  | | | Case 1:
% 201.06/33.27  | | | | 
% 201.06/33.27  | | | |   (68)  all_58_1 = e3
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | COMBINE_EQS: (5), (68) imply:
% 201.06/33.28  | | | |   (69)  all_52_9 = e3
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | REF_CLOSE: (3), (36), (37), (46), (69) are inconsistent by sub-proof
% 201.06/33.28  | | | |            #1337.
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | Case 2:
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | |   (70)   ~ (all_58_1 = e3)
% 201.06/33.28  | | | |   (71)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | REDUCE: (5), (70) imply:
% 201.06/33.28  | | | |   (72)   ~ (all_52_9 = e3)
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | BETA: splitting (38) gives:
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | Case 1:
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | |   (73)  all_58_0 = e3
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | COMBINE_EQS: (7), (73) imply:
% 201.06/33.28  | | | | |   (74)  all_6_2 = e3
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | REDUCE: (23), (74) imply:
% 201.06/33.28  | | | | |   (75)  $false
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | CLOSE: (75) is inconsistent.
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | Case 2:
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | |   (76)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | BETA: splitting (76) gives:
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | Case 1:
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | |   (77)  all_58_1 = e3
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | COMBINE_EQS: (5), (77) imply:
% 201.06/33.28  | | | | | |   (78)  all_52_9 = e3
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | REDUCE: (72), (78) imply:
% 201.06/33.28  | | | | | |   (79)  $false
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | CLOSE: (79) is inconsistent.
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | Case 2:
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | |   (80)  all_58_4 = e3 | all_58_9 = e3
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | BETA: splitting (80) gives:
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | Case 1:
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | |   (81)  all_58_4 = e3
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | COMBINE_EQS: (62), (81) imply:
% 201.06/33.28  | | | | | | |   (82)  all_10_1 = e3
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | REDUCE: (67), (82) imply:
% 201.06/33.28  | | | | | | |   (83)  $false
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | CLOSE: (83) is inconsistent.
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | Case 2:
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | |   (84)  all_58_9 = e3
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | COMBINE_EQS: (12), (84) imply:
% 201.06/33.28  | | | | | | |   (85)  all_52_25 = e3
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | REDUCE: (65), (85) imply:
% 201.06/33.28  | | | | | | |   (86)   ~ (all_10_1 = e3)
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | REDUCE: (22), (85) imply:
% 201.06/33.28  | | | | | | |   (87)   ~ (e3 = e0)
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | BETA: splitting (71) gives:
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | |   (88)  all_58_3 = e3
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | | COMBINE_EQS: (47), (88) imply:
% 201.06/33.28  | | | | | | | |   (89)  all_4_2 = e3
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | | REDUCE: (48), (89) imply:
% 201.06/33.28  | | | | | | | |   (90)   ~ (all_52_3 = e3)
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | | REDUCE: (15), (89) imply:
% 201.06/33.28  | | | | | | | |   (91)  op(e2, e2) = e3
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | | BETA: splitting (35) gives:
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | |   (92)   ~ (all_4_2 = e3)
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | REF_CLOSE: (3), (15), (91), (92) are inconsistent by sub-proof
% 201.06/33.28  | | | | | | | | |            #211.
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | |   (93)   ~ (all_4_0 = e0)
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | BETA: splitting (18) gives:
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | |   (94)  all_58_2 = e0
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | COMBINE_EQS: (27), (94) imply:
% 201.06/33.28  | | | | | | | | | |   (95)  all_52_3 = e0
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | SIMP: (95) implies:
% 201.06/33.28  | | | | | | | | | |   (96)  all_52_3 = e0
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | REDUCE: (17), (96) imply:
% 201.06/33.28  | | | | | | | | | |   (97)   ~ (all_52_5 = e0)
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | SIMP: (97) implies:
% 201.06/33.28  | | | | | | | | | |   (98)   ~ (all_52_5 = e0)
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | REDUCE: (90), (96) imply:
% 201.06/33.28  | | | | | | | | | |   (99)   ~ (e3 = e0)
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | BETA: splitting (43) gives:
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | |   (100)  all_58_6 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | COMBINE_EQS: (40), (100) imply:
% 201.06/33.28  | | | | | | | | | | |   (101)  all_52_5 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | SIMP: (101) implies:
% 201.06/33.28  | | | | | | | | | | |   (102)  all_52_5 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | REDUCE: (98), (102) imply:
% 201.06/33.28  | | | | | | | | | | |   (103)  $false
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | |   (104)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | BETA: splitting (104) gives:
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | |   (105)  all_58_7 = e0
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | COMBINE_EQS: (26), (105) imply:
% 201.06/33.28  | | | | | | | | | | | |   (106)  all_52_13 = e0
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | REDUCE: (10), (106) imply:
% 201.06/33.28  | | | | | | | | | | | |   (107)  op(e0, e0) = e1
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | REF_CLOSE: (3), (25), (42), (107) are inconsistent by
% 201.06/33.28  | | | | | | | | | | | |            sub-proof #221.
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | |   (108)   ~ (all_58_7 = e0)
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | REDUCE: (26), (108) imply:
% 201.06/33.28  | | | | | | | | | | | |   (109)   ~ (all_52_13 = e0)
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | BETA: splitting (14) gives:
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | |   (110)  all_58_1 = e0
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (25), (46), (72), (110) are inconsistent
% 201.06/33.28  | | | | | | | | | | | | |            by sub-proof #1335.
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | |   (111)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | REF_CLOSE: (9), (20), (26), (87), (88), (109), (111) are
% 201.06/33.28  | | | | | | | | | | | | |            inconsistent by sub-proof #1267.
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | |   (112)   ~ (all_58_2 = e0)
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | REDUCE: (27), (112) imply:
% 201.06/33.28  | | | | | | | | | |   (113)   ~ (all_52_3 = e0)
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | BETA: splitting (2) gives:
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | |   (114)  all_58_4 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | COMBINE_EQS: (62), (114) imply:
% 201.06/33.28  | | | | | | | | | | |   (115)  all_10_1 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | SIMP: (115) implies:
% 201.06/33.28  | | | | | | | | | | |   (116)  all_10_1 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | REDUCE: (63), (116) imply:
% 201.06/33.28  | | | | | | | | | | |   (117)   ~ (all_52_9 = e0)
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | REDUCE: (66), (116) imply:
% 201.06/33.28  | | | | | | | | | | |   (118)   ~ (all_6_2 = e0)
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | SIMP: (118) implies:
% 201.06/33.28  | | | | | | | | | | |   (119)   ~ (all_6_2 = e0)
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | REDUCE: (67), (116) imply:
% 201.06/33.28  | | | | | | | | | | |   (120)   ~ (e3 = e0)
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | BETA: splitting (16) gives:
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | |   (121)  all_58_0 = e0
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | COMBINE_EQS: (7), (121) imply:
% 201.06/33.28  | | | | | | | | | | | |   (122)  all_6_2 = e0
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | REDUCE: (119), (122) imply:
% 201.06/33.28  | | | | | | | | | | | |   (123)  $false
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | |   (124)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | BETA: splitting (14) gives:
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | |   (125)  all_58_1 = e0
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | COMBINE_EQS: (5), (125) imply:
% 201.06/33.28  | | | | | | | | | | | | |   (126)  all_52_9 = e0
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | REDUCE: (117), (126) imply:
% 201.06/33.28  | | | | | | | | | | | | |   (127)  $false
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | |   (128)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | |   (129)  all_58_3 = e0
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | COMBINE_EQS: (88), (129) imply:
% 201.06/33.28  | | | | | | | | | | | | | |   (130)  e3 = e0
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | COMBINE_EQS: (84), (130) imply:
% 201.06/33.28  | | | | | | | | | | | | | |   (131)  all_58_9 = e0
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | REF_CLOSE: (49), (57), (80), (87), (131) are inconsistent by
% 201.06/33.28  | | | | | | | | | | | | | |            sub-proof #210.
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | |   (132)   ~ (all_58_3 = e0)
% 201.06/33.28  | | | | | | | | | | | | | |   (133)  all_58_7 = e0 | all_58_13 = e0
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | |   (134)  all_58_2 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | COMBINE_EQS: (27), (134) imply:
% 201.06/33.28  | | | | | | | | | | | | | | |   (135)  all_52_3 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | SIMP: (135) implies:
% 201.06/33.28  | | | | | | | | | | | | | | |   (136)  all_52_3 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | REDUCE: (113), (136) imply:
% 201.06/33.28  | | | | | | | | | | | | | | |   (137)  $false
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | |   (138)  all_58_6 = e0 | all_58_12 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | Case 1:
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | |   (139)  all_58_6 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (139) imply:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (140)  all_52_5 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | SIMP: (140) implies:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (141)  all_52_5 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | REDUCE: (4), (141) imply:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (142)   ~ (all_52_13 = e0)
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | SIMP: (142) implies:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (143)   ~ (all_52_13 = e0)
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (26), (133), (143) are inconsistent by
% 201.06/33.28  | | | | | | | | | | | | | | | |            sub-proof #1268.
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | |   (144)  all_58_12 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (144) imply:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (145)  e3 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | SIMP: (145) implies:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (146)  e3 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (146) imply:
% 201.06/33.28  | | | | | | | | | | | | | | | |   (147)  all_58_9 = e0
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | | REF_CLOSE: (49), (57), (80), (87), (147) are inconsistent by
% 201.06/33.28  | | | | | | | | | | | | | | | |            sub-proof #210.
% 201.06/33.28  | | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | |   (148)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | | REF_CLOSE: (1), (32), (33), (54), (87), (93), (148) are
% 201.06/33.28  | | | | | | | | | | |            inconsistent by sub-proof #208.
% 201.06/33.28  | | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | | 
% 201.06/33.28  | | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | | 
% 201.06/33.28  | | | | | | | | End of split
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | Case 2:
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | |   (149)  all_58_7 = e3 | all_58_13 = e3
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | | REF_CLOSE: (9), (13), (26), (56), (149) are inconsistent by
% 201.06/33.28  | | | | | | | |            sub-proof #1298.
% 201.06/33.28  | | | | | | | | 
% 201.06/33.28  | | | | | | | End of split
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | End of split
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | End of split
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | End of split
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | End of split
% 201.06/33.28  | | | 
% 201.06/33.28  | | Case 2:
% 201.06/33.28  | | | 
% 201.06/33.28  | | |   (150)  all_58_14 = e3
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REF_CLOSE: (1), (28), (150) are inconsistent by sub-proof #1305.
% 201.06/33.28  | | | 
% 201.06/33.28  | | End of split
% 201.06/33.28  | | 
% 201.06/33.28  | End of split
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #208 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)  all_58_14 = all_52_23
% 201.06/33.28    (2)   ~ (e3 = e0)
% 201.06/33.28    (3)  all_58_8 = e3
% 201.06/33.28    (4)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.06/33.28    (5)   ~ (all_52_23 = e0)
% 201.06/33.28    (6)  all_58_5 = all_4_0
% 201.06/33.28    (7)   ~ (all_4_0 = e0)
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | BETA: splitting (4) gives:
% 201.06/33.28  | 
% 201.06/33.28  | Case 1:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (8)  all_58_5 = e0
% 201.06/33.28  | | 
% 201.06/33.28  | | REF_CLOSE: (6), (7), (8) are inconsistent by sub-proof #209.
% 201.06/33.28  | | 
% 201.06/33.28  | Case 2:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (9)  all_58_8 = e0 | all_58_14 = e0
% 201.06/33.28  | | 
% 201.06/33.28  | | BETA: splitting (9) gives:
% 201.06/33.28  | | 
% 201.06/33.28  | | Case 1:
% 201.06/33.28  | | | 
% 201.06/33.28  | | |   (10)  all_58_8 = e0
% 201.06/33.28  | | | 
% 201.06/33.28  | | | COMBINE_EQS: (3), (10) imply:
% 201.06/33.28  | | |   (11)  e3 = e0
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REDUCE: (2), (11) imply:
% 201.06/33.28  | | |   (12)  $false
% 201.06/33.28  | | | 
% 201.06/33.28  | | | CLOSE: (12) is inconsistent.
% 201.06/33.28  | | | 
% 201.06/33.28  | | Case 2:
% 201.06/33.28  | | | 
% 201.06/33.28  | | |   (13)  all_58_14 = e0
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #1019.
% 201.06/33.28  | | | 
% 201.06/33.28  | | End of split
% 201.06/33.28  | | 
% 201.06/33.28  | End of split
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #209 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)  all_58_5 = all_4_0
% 201.06/33.28    (2)  all_58_5 = e0
% 201.06/33.28    (3)   ~ (all_4_0 = e0)
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | COMBINE_EQS: (1), (2) imply:
% 201.06/33.28  |   (4)  all_4_0 = e0
% 201.06/33.28  | 
% 201.06/33.28  | SIMP: (4) implies:
% 201.06/33.28  |   (5)  all_4_0 = e0
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (3), (5) imply:
% 201.06/33.28  |   (6)  $false
% 201.06/33.28  | 
% 201.06/33.28  | CLOSE: (6) is inconsistent.
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #210 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)   ~ (e3 = e0)
% 201.06/33.28    (2)  all_58_9 = e0
% 201.06/33.28    (3)  all_58_4 = e3 | all_58_9 = e3
% 201.06/33.28    (4)   ~ (all_52_17 = e3)
% 201.06/33.28    (5)  all_58_4 = all_52_17
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | BETA: splitting (3) gives:
% 201.06/33.28  | 
% 201.06/33.28  | Case 1:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (6)  all_58_4 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | COMBINE_EQS: (5), (6) imply:
% 201.06/33.28  | |   (7)  all_52_17 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REDUCE: (4), (7) imply:
% 201.06/33.28  | |   (8)  $false
% 201.06/33.28  | | 
% 201.06/33.28  | | CLOSE: (8) is inconsistent.
% 201.06/33.28  | | 
% 201.06/33.28  | Case 2:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (9)  all_58_9 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #841.
% 201.06/33.28  | | 
% 201.06/33.28  | End of split
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #211 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.28    (2)  op(e2, e2) = all_4_2
% 201.06/33.28    (3)  op(e2, e2) = e3
% 201.06/33.28    (4)   ~ (all_4_2 = e3)
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying with (2),
% 201.06/33.28  |              (3) gives:
% 201.06/33.28  |   (5)  all_4_2 = e3
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (4), (5) imply:
% 201.06/33.28  |   (6)  $false
% 201.06/33.28  | 
% 201.06/33.28  | CLOSE: (6) is inconsistent.
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #212 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.28    (2)  all_58_1 = all_52_9
% 201.06/33.28    (3)   ~ (all_52_9 = all_52_13)
% 201.06/33.28    (4)  all_58_0 = all_6_2
% 201.06/33.28    (5)   ~ (all_52_27 = all_52_29)
% 201.06/33.28    (6)  all_58_13 = all_52_15
% 201.06/33.28    (7)  op(all_52_13, all_52_13) = e1
% 201.06/33.28    (8)  op(all_4_2, e2) = e1
% 201.06/33.28    (9)  all_58_11 = all_52_29
% 201.06/33.28    (10)   ~ (all_52_3 = e3)
% 201.06/33.28    (11)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.28    (12)  all_56_11 = all_52_29
% 201.06/33.28    (13)   ~ (all_4_0 = e3)
% 201.06/33.28    (14)   ~ (all_52_25 = e0)
% 201.06/33.28    (15)  op(e0, e0) = e0
% 201.06/33.28    (16)  all_58_10 = all_52_27
% 201.06/33.28    (17)   ~ (all_52_29 = all_10_2)
% 201.06/33.28    (18)  all_58_7 = all_52_13
% 201.06/33.28    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.28    (20)  all_58_2 = all_52_3
% 201.06/33.28    (21)  op(e3, e3) = all_52_16
% 201.06/33.28    (22)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.06/33.28    (23)   ~ (all_52_25 = e3)
% 201.06/33.28    (24)   ~ (all_52_5 = e3)
% 201.06/33.28    (25)   ~ (all_10_2 = e3)
% 201.06/33.28    (26)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.06/33.28    (27)   ~ (all_52_9 = e3)
% 201.06/33.28    (28)   ~ (all_52_13 = all_4_2)
% 201.06/33.28    (29)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.28    (30)   ~ (all_52_9 = all_52_25)
% 201.06/33.28    (31)  all_58_8 = all_10_2
% 201.06/33.28    (32)  all_58_5 = all_4_0
% 201.06/33.28    (33)   ~ (all_52_25 = all_6_2)
% 201.06/33.28    (34)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.28    (35)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 201.06/33.28    (36)   ~ (all_52_9 = all_6_2)
% 201.06/33.28    (37)  op(e3, e3) = all_6_2
% 201.06/33.28    (38)  all_56_3 = all_52_25
% 201.06/33.28    (39)  all_56_1 = all_52_9
% 201.06/33.28    (40)   ~ (all_52_15 = all_4_2)
% 201.06/33.28    (41)  all_58_6 = all_52_5
% 201.06/33.28    (42)  op(e3, e2) = all_52_9
% 201.06/33.28    (43)   ~ (e1 = e0)
% 201.06/33.28    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.06/33.28    (45)  op(e1, e1) = all_10_2
% 201.06/33.28    (46)  op(all_52_9, all_52_9) = e3
% 201.06/33.28    (47)  all_58_3 = all_4_2
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | GROUND_INST: instantiating (1) with all_6_2, all_52_16, e3, e3, simplifying
% 201.06/33.28  |              with (21), (37) gives:
% 201.06/33.28  |   (48)  all_52_16 = all_6_2
% 201.06/33.28  | 
% 201.06/33.28  | BETA: splitting (34) gives:
% 201.06/33.28  | 
% 201.06/33.28  | Case 1:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (49)  all_56_3 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REF_CLOSE: (23), (38), (49) are inconsistent by sub-proof #1339.
% 201.06/33.28  | | 
% 201.06/33.28  | Case 2:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (50)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.28  | | 
% 201.06/33.28  | | BETA: splitting (29) gives:
% 201.06/33.28  | | 
% 201.06/33.28  | | Case 1:
% 201.06/33.28  | | | 
% 201.06/33.28  | | |   (51)  all_58_1 = e3
% 201.06/33.28  | | | 
% 201.06/33.28  | | | COMBINE_EQS: (2), (51) imply:
% 201.06/33.28  | | |   (52)  all_52_9 = e3
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REDUCE: (27), (52) imply:
% 201.06/33.28  | | |   (53)  $false
% 201.06/33.28  | | | 
% 201.06/33.28  | | | CLOSE: (53) is inconsistent.
% 201.06/33.28  | | | 
% 201.06/33.28  | | Case 2:
% 201.06/33.28  | | | 
% 201.06/33.28  | | |   (54)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.28  | | | 
% 201.06/33.28  | | | BETA: splitting (11) gives:
% 201.06/33.28  | | | 
% 201.06/33.28  | | | Case 1:
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | |   (55)  all_58_2 = e3
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | REF_CLOSE: (10), (20), (55) are inconsistent by sub-proof #1369.
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | Case 2:
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | |   (56)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | BETA: splitting (19) gives:
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | | Case 1:
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | |   (57)  all_58_6 = e3
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | REF_CLOSE: (24), (41), (57) are inconsistent by sub-proof #1328.
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | Case 2:
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | |   (58)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | BETA: splitting (26) gives:
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | | Case 1:
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | |   (59)  all_56_11 = e3
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | COMBINE_EQS: (12), (59) imply:
% 201.06/33.28  | | | | | |   (60)  all_52_29 = e3
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | REDUCE: (5), (60) imply:
% 201.06/33.28  | | | | | |   (61)   ~ (all_52_27 = e3)
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | REDUCE: (17), (60) imply:
% 201.06/33.28  | | | | | |   (62)   ~ (all_10_2 = e3)
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | REF_CLOSE: (1), (6), (8), (13), (16), (18), (25), (28), (32), (35),
% 201.06/33.28  | | | | | |            (40), (42), (45), (46), (47), (54), (56), (61) are
% 201.06/33.28  | | | | | |            inconsistent by sub-proof #213.
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | Case 2:
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | |   (63)   ~ (all_56_11 = e3)
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | REDUCE: (12), (63) imply:
% 201.06/33.28  | | | | | |   (64)   ~ (all_52_29 = e3)
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | BETA: splitting (58) gives:
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | | Case 1:
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | |   (65)  all_58_7 = e3
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (14), (15), (18), (21), (22),
% 201.06/33.28  | | | | | | |            (30), (33), (36), (37), (38), (39), (43), (44), (46),
% 201.06/33.28  | | | | | | |            (50), (65) are inconsistent by sub-proof #493.
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | Case 2:
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | |   (66)  all_58_8 = e3 | all_58_11 = e3
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | | REF_CLOSE: (9), (25), (31), (64), (66) are inconsistent by
% 201.06/33.28  | | | | | | |            sub-proof #1140.
% 201.06/33.28  | | | | | | | 
% 201.06/33.28  | | | | | | End of split
% 201.06/33.28  | | | | | | 
% 201.06/33.28  | | | | | End of split
% 201.06/33.28  | | | | | 
% 201.06/33.28  | | | | End of split
% 201.06/33.28  | | | | 
% 201.06/33.28  | | | End of split
% 201.06/33.28  | | | 
% 201.06/33.28  | | End of split
% 201.06/33.28  | | 
% 201.06/33.28  | End of split
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #213 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.28    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.28    (3)  all_58_13 = all_52_15
% 201.06/33.28    (4)  op(all_4_2, e2) = e1
% 201.06/33.28    (5)   ~ (all_4_0 = e3)
% 201.06/33.28    (6)  all_58_10 = all_52_27
% 201.06/33.28    (7)  all_58_7 = all_52_13
% 201.06/33.28    (8)   ~ (all_10_2 = e3)
% 201.06/33.28    (9)   ~ (all_52_27 = e3)
% 201.06/33.28    (10)   ~ (all_52_13 = all_4_2)
% 201.06/33.28    (11)  all_58_5 = all_4_0
% 201.06/33.28    (12)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e3)
% 201.06/33.28    (13)   ~ (all_52_15 = all_4_2)
% 201.06/33.28    (14)  op(e3, e2) = all_52_9
% 201.06/33.28    (15)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.28    (16)  op(e1, e1) = all_10_2
% 201.06/33.28    (17)  op(all_52_9, all_52_9) = e3
% 201.06/33.28    (18)  all_58_3 = all_4_2
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | BETA: splitting (2) gives:
% 201.06/33.28  | 
% 201.06/33.28  | Case 1:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (19)  all_58_3 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | COMBINE_EQS: (18), (19) imply:
% 201.06/33.28  | |   (20)  all_4_2 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REDUCE: (10), (20) imply:
% 201.06/33.28  | |   (21)   ~ (all_52_13 = e3)
% 201.06/33.28  | | 
% 201.06/33.28  | | REDUCE: (13), (20) imply:
% 201.06/33.28  | |   (22)   ~ (all_52_15 = e3)
% 201.06/33.28  | | 
% 201.06/33.28  | | REDUCE: (4), (20) imply:
% 201.06/33.28  | |   (23)  op(e3, e2) = e1
% 201.06/33.28  | | 
% 201.06/33.28  | | BETA: splitting (12) gives:
% 201.06/33.28  | | 
% 201.06/33.28  | | Case 1:
% 201.06/33.28  | | | 
% 201.06/33.28  | | |   (24)   ~ (all_4_2 = e3)
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REF_CLOSE: (3), (7), (15), (18), (21), (22), (24) are inconsistent by
% 201.06/33.28  | | |            sub-proof #1256.
% 201.06/33.28  | | | 
% 201.06/33.28  | | Case 2:
% 201.06/33.28  | | | 
% 201.06/33.28  | | | 
% 201.06/33.28  | | | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 201.06/33.28  | | |              (14), (23) gives:
% 201.06/33.28  | | |   (25)  all_52_9 = e1
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REDUCE: (17), (25) imply:
% 201.06/33.28  | | |   (26)  op(e1, e1) = e3
% 201.06/33.28  | | | 
% 201.06/33.28  | | | REF_CLOSE: (1), (8), (16), (26) are inconsistent by sub-proof #1368.
% 201.06/33.28  | | | 
% 201.06/33.28  | | End of split
% 201.06/33.28  | | 
% 201.06/33.28  | Case 2:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (27)  all_58_5 = e3 | all_58_10 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REF_CLOSE: (5), (6), (9), (11), (27) are inconsistent by sub-proof #214.
% 201.06/33.28  | | 
% 201.06/33.28  | End of split
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #214 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)   ~ (all_4_0 = e3)
% 201.06/33.28    (2)  all_58_10 = all_52_27
% 201.06/33.28    (3)  all_58_5 = e3 | all_58_10 = e3
% 201.06/33.28    (4)   ~ (all_52_27 = e3)
% 201.06/33.28    (5)  all_58_5 = all_4_0
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | BETA: splitting (3) gives:
% 201.06/33.28  | 
% 201.06/33.28  | Case 1:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (6)  all_58_5 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #215.
% 201.06/33.28  | | 
% 201.06/33.28  | Case 2:
% 201.06/33.28  | | 
% 201.06/33.28  | |   (7)  all_58_10 = e3
% 201.06/33.28  | | 
% 201.06/33.28  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1301.
% 201.06/33.28  | | 
% 201.06/33.28  | End of split
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #215 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)  all_58_5 = all_4_0
% 201.06/33.28    (2)  all_58_5 = e3
% 201.06/33.28    (3)   ~ (all_4_0 = e3)
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | COMBINE_EQS: (1), (2) imply:
% 201.06/33.28  |   (4)  all_4_0 = e3
% 201.06/33.28  | 
% 201.06/33.28  | SIMP: (4) implies:
% 201.06/33.28  |   (5)  all_4_0 = e3
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (3), (5) imply:
% 201.06/33.28  |   (6)  $false
% 201.06/33.28  | 
% 201.06/33.28  | CLOSE: (6) is inconsistent.
% 201.06/33.28  | 
% 201.06/33.28  End of proof
% 201.06/33.28  
% 201.06/33.28  Sub-proof #216 shows that the following formulas are inconsistent:
% 201.06/33.28  ----------------------------------------------------------------
% 201.06/33.28    (1)   ~ (all_52_15 = all_52_23)
% 201.06/33.28    (2)  all_58_14 = all_52_23
% 201.06/33.28    (3)   ~ (e3 = e1)
% 201.06/33.28    (4)  op(all_52_3, all_52_3) = all_52_2
% 201.06/33.28    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.28    (6)   ~ (e3 = e0)
% 201.06/33.28    (7)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.06/33.28    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.28    (9)   ~ (all_52_7 = all_52_15)
% 201.06/33.28    (10)  op(all_52_7, all_52_7) = all_52_6
% 201.06/33.28    (11)  all_58_0 = all_6_2
% 201.06/33.28    (12)  op(all_52_5, all_52_5) = all_52_4
% 201.06/33.28    (13)  all_58_13 = all_52_15
% 201.06/33.28    (14)  op(e2, e2) = all_4_2
% 201.06/33.28    (15)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.28    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.06/33.28    (17)  op(all_10_2, e1) = all_10_1
% 201.06/33.28    (18)  op(all_6_2, all_6_2) = all_52_0
% 201.06/33.28    (19)   ~ (all_52_7 = all_6_2)
% 201.06/33.28    (20)  op(e0, e0) = all_14_2
% 201.06/33.28    (21)  op(e0, e1) = all_52_23
% 201.06/33.28    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.28    (23)  all_58_15 = e0
% 201.06/33.28    (24)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.06/33.28    (25)  op(e0, e0) = e0
% 201.06/33.28    (26)  op(all_52_15, all_52_15) = all_52_14
% 201.06/33.28    (27)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.06/33.28    (28)  all_58_12 = all_52_7
% 201.06/33.28    (29)   ~ (all_52_7 = all_14_2)
% 201.06/33.28    (30)  all_58_2 = all_52_3
% 201.06/33.28    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.28    (32)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.06/33.28    (33)  op(all_52_23, all_52_23) = all_52_22
% 201.06/33.28    (34)   ~ (all_10_1 = e2)
% 201.06/33.28    (35)   ~ (all_52_23 = e0)
% 201.06/33.28    (36)   ~ (all_52_5 = all_10_2)
% 201.06/33.28    (37)  all_56_12 = all_52_7
% 201.06/33.28    (38)  op(e3, e3) = all_6_2
% 201.06/33.28    (39)  all_56_14 = all_52_23
% 201.06/33.28    (40)  op(all_4_2, all_4_2) = all_52_10
% 201.06/33.28    (41)   ~ (all_10_1 = e3)
% 201.06/33.28    (42)   ~ (all_52_15 = all_4_2)
% 201.06/33.28    (43)  all_58_6 = all_52_5
% 201.06/33.28    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.06/33.28    (45)   ~ (e1 = e0)
% 201.06/33.28    (46)  op(e1, e1) = all_10_2
% 201.06/33.28    (47)   ~ (all_52_23 = all_10_2)
% 201.06/33.28    (48)   ~ (all_52_7 = all_52_23)
% 201.06/33.28    (49)  all_56_13 = all_52_15
% 201.06/33.28    (50)   ~ (all_52_3 = all_4_2)
% 201.06/33.28    (51)   ~ (all_52_7 = e0)
% 201.06/33.28  
% 201.06/33.28  Begin of proof
% 201.06/33.28  | 
% 201.06/33.28  | ALPHA: (7) implies:
% 201.06/33.28  |   (52)  all_52_6 = e0
% 201.06/33.28  |   (53)  all_52_4 = e1
% 201.06/33.28  |   (54)  all_52_2 = e2
% 201.06/33.28  |   (55)  all_52_0 = e3
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (4), (54) imply:
% 201.06/33.28  |   (56)  op(all_52_3, all_52_3) = e2
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (12), (53) imply:
% 201.06/33.28  |   (57)  op(all_52_5, all_52_5) = e1
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (10), (52) imply:
% 201.06/33.28  |   (58)  op(all_52_7, all_52_7) = e0
% 201.06/33.28  | 
% 201.06/33.28  | REDUCE: (18), (55) imply:
% 201.06/33.28  |   (59)  op(all_6_2, all_6_2) = e3
% 201.06/33.29  | 
% 201.06/33.29  | BETA: splitting (24) gives:
% 201.06/33.29  | 
% 201.06/33.29  | Case 1:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (60)  all_56_13 = e3
% 201.06/33.29  | | 
% 201.06/33.29  | | COMBINE_EQS: (49), (60) imply:
% 201.06/33.29  | |   (61)  all_52_15 = e3
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (9), (61) imply:
% 201.06/33.29  | |   (62)   ~ (all_52_7 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (1), (61) imply:
% 201.06/33.29  | |   (63)   ~ (all_52_23 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | SIMP: (63) implies:
% 201.06/33.29  | |   (64)   ~ (all_52_23 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (42), (61) imply:
% 201.06/33.29  | |   (65)   ~ (all_4_2 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | SIMP: (65) implies:
% 201.06/33.29  | |   (66)   ~ (all_4_2 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (26), (61) imply:
% 201.06/33.29  | |   (67)  op(e3, e3) = all_52_14
% 201.06/33.29  | | 
% 201.06/33.29  | | GROUND_INST: instantiating (5) with all_6_2, all_52_14, e3, e3, simplifying
% 201.06/33.29  | |              with (38), (67) gives:
% 201.06/33.29  | |   (68)  all_52_14 = all_6_2
% 201.06/33.29  | | 
% 201.06/33.29  | | BETA: splitting (27) gives:
% 201.06/33.29  | | 
% 201.06/33.29  | | Case 1:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (69)  all_56_14 = e3
% 201.06/33.29  | | | 
% 201.06/33.29  | | | COMBINE_EQS: (39), (69) imply:
% 201.06/33.29  | | |   (70)  all_52_23 = e3
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (64), (70) imply:
% 201.06/33.29  | | |   (71)  $false
% 201.06/33.29  | | | 
% 201.06/33.29  | | | CLOSE: (71) is inconsistent.
% 201.06/33.29  | | | 
% 201.06/33.29  | | Case 2:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (72)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | BETA: splitting (8) gives:
% 201.06/33.29  | | | 
% 201.06/33.29  | | | Case 1:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (73)  all_56_12 = e3
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REF_CLOSE: (37), (62), (73) are inconsistent by sub-proof #1383.
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | Case 2:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (74)   ~ (all_56_12 = e3)
% 201.06/33.29  | | | |   (75)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | BETA: splitting (32) gives:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | Case 1:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | |   (76)  all_58_12 = e1
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | COMBINE_EQS: (28), (76) imply:
% 201.06/33.29  | | | | |   (77)  all_52_7 = e1
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REF_CLOSE: (5), (17), (21), (27), (34), (39), (41), (46), (47), (48),
% 201.06/33.29  | | | | |            (58), (77) are inconsistent by sub-proof #1379.
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | Case 2:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | |   (78)   ~ (all_58_12 = e1)
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REF_CLOSE: (5), (11), (14), (15), (22), (25), (28), (30), (31), (33),
% 201.06/33.29  | | | | |            (35), (36), (37), (38), (39), (43), (46), (48), (50), (51),
% 201.06/33.29  | | | | |            (56), (57), (58), (59), (62), (66), (72), (75), (78) are
% 201.06/33.29  | | | | |            inconsistent by sub-proof #219.
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | End of split
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | End of split
% 201.06/33.29  | | | 
% 201.06/33.29  | | End of split
% 201.06/33.29  | | 
% 201.06/33.29  | Case 2:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (79)   ~ (all_56_13 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (49), (79) imply:
% 201.06/33.29  | |   (80)   ~ (all_52_15 = e3)
% 201.06/33.29  | | 
% 201.06/33.29  | | BETA: splitting (44) gives:
% 201.06/33.29  | | 
% 201.06/33.29  | | Case 1:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (81)  all_58_12 = e3
% 201.06/33.29  | | | 
% 201.06/33.29  | | | COMBINE_EQS: (28), (81) imply:
% 201.06/33.29  | | |   (82)  all_52_7 = e3
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REF_CLOSE: (5), (11), (14), (19), (20), (22), (28), (29), (30), (31),
% 201.06/33.29  | | |            (36), (38), (43), (44), (46), (50), (56), (57), (58), (59),
% 201.06/33.29  | | |            (82) are inconsistent by sub-proof #1361.
% 201.06/33.29  | | | 
% 201.06/33.29  | | Case 2:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (83)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.06/33.29  | | | 
% 201.06/33.29  | | | BETA: splitting (83) gives:
% 201.06/33.29  | | | 
% 201.06/33.29  | | | Case 1:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (84)  all_58_13 = e3
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REF_CLOSE: (13), (80), (84) are inconsistent by sub-proof #1360.
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | Case 2:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (85)  all_58_14 = e3 | all_58_15 = e3
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | BETA: splitting (85) gives:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | Case 1:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | |   (86)  all_58_14 = e3
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | COMBINE_EQS: (2), (86) imply:
% 201.06/33.29  | | | | |   (87)  all_52_23 = e3
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | SIMP: (87) implies:
% 201.06/33.29  | | | | |   (88)  all_52_23 = e3
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REDUCE: (48), (88) imply:
% 201.06/33.29  | | | | |   (89)   ~ (all_52_7 = e3)
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REDUCE: (33), (88) imply:
% 201.06/33.29  | | | | |   (90)  op(e3, e3) = all_52_22
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REDUCE: (21), (88) imply:
% 201.06/33.29  | | | | |   (91)  op(e0, e1) = e3
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3,
% 201.06/33.29  | | | | |              simplifying with (38), (90) gives:
% 201.06/33.29  | | | | |   (92)  all_52_22 = all_6_2
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | BETA: splitting (8) gives:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | Case 1:
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | |   (93)  all_56_12 = e3
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | | REF_CLOSE: (37), (89), (93) are inconsistent by sub-proof #1383.
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | Case 2:
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | |   (94)   ~ (all_56_12 = e3)
% 201.06/33.29  | | | | | |   (95)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | | BETA: splitting (32) gives:
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | | Case 1:
% 201.06/33.29  | | | | | | | 
% 201.06/33.29  | | | | | | |   (96)  all_58_12 = e1
% 201.06/33.29  | | | | | | | 
% 201.06/33.29  | | | | | | | REF_CLOSE: (5), (17), (28), (41), (46), (58), (91), (96) are
% 201.06/33.29  | | | | | | |            inconsistent by sub-proof #218.
% 201.06/33.29  | | | | | | | 
% 201.06/33.29  | | | | | | Case 2:
% 201.06/33.29  | | | | | | | 
% 201.06/33.29  | | | | | | |   (97)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.06/33.29  | | | | | | | 
% 201.06/33.29  | | | | | | | REF_CLOSE: (3), (5), (6), (9), (11), (13), (14), (15), (16), (22),
% 201.06/33.29  | | | | | | |            (23), (25), (26), (28), (30), (31), (36), (37), (38),
% 201.06/33.29  | | | | | | |            (40), (42), (43), (45), (46), (50), (51), (56), (57),
% 201.06/33.29  | | | | | | |            (58), (59), (86), (89), (95), (97) are inconsistent by
% 201.06/33.29  | | | | | | |            sub-proof #217.
% 201.06/33.29  | | | | | | | 
% 201.06/33.29  | | | | | | End of split
% 201.06/33.29  | | | | | | 
% 201.06/33.29  | | | | | End of split
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | Case 2:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | |   (98)  all_58_15 = e3
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | COMBINE_EQS: (23), (98) imply:
% 201.06/33.29  | | | | |   (99)  e3 = e0
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REDUCE: (6), (99) imply:
% 201.06/33.29  | | | | |   (100)  $false
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | CLOSE: (100) is inconsistent.
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | End of split
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | End of split
% 201.06/33.29  | | | 
% 201.06/33.29  | | End of split
% 201.06/33.29  | | 
% 201.06/33.29  | End of split
% 201.06/33.29  | 
% 201.06/33.29  End of proof
% 201.06/33.29  
% 201.06/33.29  Sub-proof #217 shows that the following formulas are inconsistent:
% 201.06/33.29  ----------------------------------------------------------------
% 201.06/33.29    (1)   ~ (e3 = e1)
% 201.06/33.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.29    (3)  op(all_52_7, all_52_7) = e0
% 201.06/33.29    (4)  op(all_52_5, all_52_5) = e1
% 201.06/33.29    (5)   ~ (e3 = e0)
% 201.06/33.29    (6)   ~ (all_52_7 = all_52_15)
% 201.06/33.29    (7)  all_58_0 = all_6_2
% 201.06/33.29    (8)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.06/33.29    (9)  all_58_13 = all_52_15
% 201.06/33.29    (10)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.29    (11)  op(e2, e2) = all_4_2
% 201.06/33.29    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.29    (13)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.06/33.29    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.29    (15)  all_58_15 = e0
% 201.06/33.29    (16)  op(e0, e0) = e0
% 201.06/33.29    (17)  op(all_52_15, all_52_15) = all_52_14
% 201.06/33.29    (18)  op(all_6_2, all_6_2) = e3
% 201.06/33.29    (19)  all_58_12 = all_52_7
% 201.06/33.29    (20)   ~ (all_52_7 = e3)
% 201.06/33.29    (21)  all_58_2 = all_52_3
% 201.06/33.29    (22)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.29    (23)  op(all_52_3, all_52_3) = e2
% 201.06/33.29    (24)   ~ (all_52_5 = all_10_2)
% 201.06/33.29    (25)  all_56_12 = all_52_7
% 201.06/33.29    (26)  op(e3, e3) = all_6_2
% 201.06/33.29    (27)  op(all_4_2, all_4_2) = all_52_10
% 201.06/33.29    (28)   ~ (all_52_15 = all_4_2)
% 201.06/33.29    (29)  all_58_6 = all_52_5
% 201.06/33.29    (30)   ~ (e1 = e0)
% 201.06/33.29    (31)  op(e1, e1) = all_10_2
% 201.06/33.29    (32)  all_58_14 = e3
% 201.06/33.29    (33)   ~ (all_52_3 = all_4_2)
% 201.06/33.29    (34)   ~ (all_52_7 = e0)
% 201.06/33.29  
% 201.06/33.29  Begin of proof
% 201.06/33.29  | 
% 201.06/33.29  | BETA: splitting (8) gives:
% 201.06/33.29  | 
% 201.06/33.29  | Case 1:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (35)  all_58_13 = e1
% 201.06/33.29  | | 
% 201.06/33.29  | | COMBINE_EQS: (9), (35) imply:
% 201.06/33.29  | |   (36)  all_52_15 = e1
% 201.06/33.29  | | 
% 201.06/33.29  | | SIMP: (36) implies:
% 201.06/33.29  | |   (37)  all_52_15 = e1
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (6), (37) imply:
% 201.06/33.29  | |   (38)   ~ (all_52_7 = e1)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (28), (37) imply:
% 201.06/33.29  | |   (39)   ~ (all_4_2 = e1)
% 201.06/33.29  | | 
% 201.06/33.29  | | SIMP: (39) implies:
% 201.06/33.29  | |   (40)   ~ (all_4_2 = e1)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (17), (37) imply:
% 201.06/33.29  | |   (41)  op(e1, e1) = all_52_14
% 201.06/33.29  | | 
% 201.06/33.29  | | BETA: splitting (13) gives:
% 201.06/33.29  | | 
% 201.06/33.29  | | Case 1:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (42)  all_58_12 = e2
% 201.06/33.29  | | | 
% 201.06/33.29  | | | COMBINE_EQS: (19), (42) imply:
% 201.06/33.29  | | |   (43)  all_52_7 = e2
% 201.06/33.29  | | | 
% 201.06/33.29  | | | SIMP: (43) implies:
% 201.06/33.29  | | |   (44)  all_52_7 = e2
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (34), (44) imply:
% 201.06/33.29  | | |   (45)   ~ (e2 = e0)
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (3), (44) imply:
% 201.06/33.29  | | |   (46)  op(e2, e2) = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | GROUND_INST: instantiating (2) with all_10_2, all_52_14, e1, e1,
% 201.06/33.29  | | |              simplifying with (31), (41) gives:
% 201.06/33.29  | | |   (47)  all_52_14 = all_10_2
% 201.06/33.29  | | | 
% 201.06/33.29  | | | GROUND_INST: instantiating (2) with all_4_2, e0, e2, e2, simplifying with
% 201.06/33.29  | | |              (11), (46) gives:
% 201.06/33.29  | | |   (48)  all_4_2 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (33), (48) imply:
% 201.06/33.29  | | |   (49)   ~ (all_52_3 = e0)
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (40), (48) imply:
% 201.06/33.29  | | |   (50)   ~ (e1 = e0)
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (27), (48) imply:
% 201.06/33.29  | | |   (51)  op(e0, e0) = all_52_10
% 201.06/33.29  | | | 
% 201.06/33.29  | | | GROUND_INST: instantiating (2) with e0, all_52_10, e0, e0, simplifying
% 201.06/33.29  | | |              with (16), (51) gives:
% 201.06/33.29  | | |   (52)  all_52_10 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REF_CLOSE: (2), (4), (5), (7), (11), (12), (14), (16), (18), (19), (20),
% 201.06/33.29  | | |            (21), (22), (23), (24), (26), (29), (30), (31), (33), (42),
% 201.06/33.29  | | |            (45), (49) are inconsistent by sub-proof #220.
% 201.06/33.29  | | | 
% 201.06/33.29  | | Case 2:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (53)   ~ (all_58_12 = e2)
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (19), (53) imply:
% 201.06/33.29  | | |   (54)   ~ (all_52_7 = e2)
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REF_CLOSE: (10), (25), (34), (38), (54) are inconsistent by sub-proof
% 201.06/33.29  | | |            #465.
% 201.06/33.29  | | | 
% 201.06/33.29  | | End of split
% 201.06/33.29  | | 
% 201.06/33.29  | Case 2:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (55)  all_58_14 = e1 | all_58_15 = e1
% 201.06/33.29  | | 
% 201.06/33.29  | | BETA: splitting (55) gives:
% 201.06/33.29  | | 
% 201.06/33.29  | | Case 1:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (56)  all_58_14 = e1
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REF_CLOSE: (1), (32), (56) are inconsistent by sub-proof #814.
% 201.06/33.29  | | | 
% 201.06/33.29  | | Case 2:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (57)  all_58_15 = e1
% 201.06/33.29  | | | 
% 201.06/33.29  | | | COMBINE_EQS: (15), (57) imply:
% 201.06/33.29  | | |   (58)  e1 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (30), (58) imply:
% 201.06/33.29  | | |   (59)  $false
% 201.06/33.29  | | | 
% 201.06/33.29  | | | CLOSE: (59) is inconsistent.
% 201.06/33.29  | | | 
% 201.06/33.29  | | End of split
% 201.06/33.29  | | 
% 201.06/33.29  | End of split
% 201.06/33.29  | 
% 201.06/33.29  End of proof
% 201.06/33.29  
% 201.06/33.29  Sub-proof #218 shows that the following formulas are inconsistent:
% 201.06/33.29  ----------------------------------------------------------------
% 201.06/33.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.29    (2)  op(all_52_7, all_52_7) = e0
% 201.06/33.29    (3)  op(all_10_2, e1) = all_10_1
% 201.06/33.29    (4)  all_58_12 = all_52_7
% 201.06/33.29    (5)   ~ (all_10_1 = e3)
% 201.06/33.29    (6)  op(e1, e1) = all_10_2
% 201.06/33.29    (7)  all_58_12 = e1
% 201.06/33.29    (8)  op(e0, e1) = e3
% 201.06/33.29  
% 201.06/33.29  Begin of proof
% 201.06/33.29  | 
% 201.06/33.29  | COMBINE_EQS: (4), (7) imply:
% 201.06/33.29  |   (9)  all_52_7 = e1
% 201.06/33.29  | 
% 201.06/33.29  | REDUCE: (2), (9) imply:
% 201.06/33.29  |   (10)  op(e1, e1) = e0
% 201.06/33.29  | 
% 201.06/33.29  | REF_CLOSE: (1), (3), (5), (6), (8), (10) are inconsistent by sub-proof #1359.
% 201.06/33.29  | 
% 201.06/33.29  End of proof
% 201.06/33.29  
% 201.06/33.29  Sub-proof #219 shows that the following formulas are inconsistent:
% 201.06/33.29  ----------------------------------------------------------------
% 201.06/33.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.29    (2)  op(all_52_7, all_52_7) = e0
% 201.06/33.29    (3)  op(all_52_5, all_52_5) = e1
% 201.06/33.29    (4)   ~ (all_4_2 = e3)
% 201.06/33.29    (5)  all_58_0 = all_6_2
% 201.06/33.29    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.29    (7)  op(e2, e2) = all_4_2
% 201.06/33.29    (8)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.29    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.29    (10)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.06/33.29    (11)  op(e0, e0) = e0
% 201.06/33.29    (12)  op(all_6_2, all_6_2) = e3
% 201.06/33.29    (13)  all_58_12 = all_52_7
% 201.06/33.29    (14)   ~ (all_52_7 = e3)
% 201.06/33.29    (15)  all_58_2 = all_52_3
% 201.06/33.29    (16)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.29    (17)  op(all_52_3, all_52_3) = e2
% 201.06/33.29    (18)  op(all_52_23, all_52_23) = all_52_22
% 201.06/33.29    (19)   ~ (all_52_23 = e0)
% 201.06/33.29    (20)   ~ (all_52_5 = all_10_2)
% 201.06/33.29    (21)  all_56_12 = all_52_7
% 201.06/33.29    (22)  op(e3, e3) = all_6_2
% 201.06/33.29    (23)  all_56_14 = all_52_23
% 201.06/33.29    (24)  all_58_6 = all_52_5
% 201.06/33.29    (25)  op(e1, e1) = all_10_2
% 201.06/33.29    (26)   ~ (all_52_7 = all_52_23)
% 201.06/33.29    (27)   ~ (all_58_12 = e1)
% 201.06/33.29    (28)   ~ (all_52_3 = all_4_2)
% 201.06/33.29    (29)   ~ (all_52_7 = e0)
% 201.06/33.29  
% 201.06/33.29  Begin of proof
% 201.06/33.29  | 
% 201.06/33.29  | REDUCE: (13), (27) imply:
% 201.06/33.29  |   (30)   ~ (all_52_7 = e1)
% 201.06/33.29  | 
% 201.06/33.29  | BETA: splitting (6) gives:
% 201.06/33.29  | 
% 201.06/33.29  | Case 1:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (31)  all_56_12 = e2
% 201.06/33.29  | | 
% 201.06/33.29  | | COMBINE_EQS: (21), (31) imply:
% 201.06/33.29  | |   (32)  all_52_7 = e2
% 201.06/33.29  | | 
% 201.06/33.29  | | COMBINE_EQS: (13), (32) imply:
% 201.06/33.29  | |   (33)  all_58_12 = e2
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (26), (32) imply:
% 201.06/33.29  | |   (34)   ~ (all_52_23 = e2)
% 201.06/33.29  | | 
% 201.06/33.29  | | SIMP: (34) implies:
% 201.06/33.29  | |   (35)   ~ (all_52_23 = e2)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (29), (32) imply:
% 201.06/33.29  | |   (36)   ~ (e2 = e0)
% 201.06/33.29  | | 
% 201.06/33.29  | | REDUCE: (2), (32) imply:
% 201.06/33.29  | |   (37)  op(e2, e2) = e0
% 201.06/33.29  | | 
% 201.06/33.29  | | BETA: splitting (10) gives:
% 201.06/33.29  | | 
% 201.06/33.29  | | Case 1:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (38)  all_56_14 = e2
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REF_CLOSE: (23), (35), (38) are inconsistent by sub-proof #1285.
% 201.06/33.29  | | | 
% 201.06/33.29  | | Case 2:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (39)  all_56_14 = e1 | all_56_14 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | BETA: splitting (39) gives:
% 201.06/33.29  | | | 
% 201.06/33.29  | | | Case 1:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (40)  all_56_14 = e1
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | COMBINE_EQS: (23), (40) imply:
% 201.06/33.29  | | | |   (41)  all_52_23 = e1
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | SIMP: (41) implies:
% 201.06/33.29  | | | |   (42)  all_52_23 = e1
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REDUCE: (19), (42) imply:
% 201.06/33.29  | | | |   (43)   ~ (e1 = e0)
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REDUCE: (18), (42) imply:
% 201.06/33.29  | | | |   (44)  op(e1, e1) = all_52_22
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | GROUND_INST: instantiating (1) with all_10_2, all_52_22, e1, e1,
% 201.06/33.29  | | | |              simplifying with (25), (44) gives:
% 201.06/33.29  | | | |   (45)  all_52_22 = all_10_2
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e2, simplifying
% 201.06/33.29  | | | |              with (7), (37) gives:
% 201.06/33.29  | | | |   (46)  all_4_2 = e0
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REDUCE: (28), (46) imply:
% 201.06/33.29  | | | |   (47)   ~ (all_52_3 = e0)
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REDUCE: (4), (46) imply:
% 201.06/33.29  | | | |   (48)   ~ (e3 = e0)
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | SIMP: (48) implies:
% 201.06/33.29  | | | |   (49)   ~ (e3 = e0)
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (11), (12), (13), (14), (15),
% 201.06/33.29  | | | |            (16), (17), (20), (22), (24), (25), (28), (33), (36), (43),
% 201.06/33.29  | | | |            (47), (49) are inconsistent by sub-proof #220.
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | Case 2:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (50)  all_56_14 = e0
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REF_CLOSE: (19), (23), (50) are inconsistent by sub-proof #1382.
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | End of split
% 201.06/33.29  | | | 
% 201.06/33.29  | | End of split
% 201.06/33.29  | | 
% 201.06/33.29  | Case 2:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (51)  all_56_12 = e1 | all_56_12 = e0
% 201.06/33.29  | | 
% 201.06/33.29  | | REF_CLOSE: (21), (29), (30), (51) are inconsistent by sub-proof #1374.
% 201.06/33.29  | | 
% 201.06/33.29  | End of split
% 201.06/33.29  | 
% 201.06/33.29  End of proof
% 201.06/33.29  
% 201.06/33.29  Sub-proof #220 shows that the following formulas are inconsistent:
% 201.06/33.29  ----------------------------------------------------------------
% 201.06/33.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.29    (2)  op(all_52_5, all_52_5) = e1
% 201.06/33.29    (3)   ~ (e3 = e0)
% 201.06/33.29    (4)  all_58_0 = all_6_2
% 201.06/33.29    (5)  op(e2, e2) = all_4_2
% 201.06/33.29    (6)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.29    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.29    (8)  op(e0, e0) = e0
% 201.06/33.29    (9)  op(all_6_2, all_6_2) = e3
% 201.06/33.29    (10)  all_58_12 = all_52_7
% 201.06/33.29    (11)   ~ (all_52_7 = e3)
% 201.06/33.29    (12)  all_58_2 = all_52_3
% 201.06/33.29    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.29    (14)   ~ (e2 = e0)
% 201.06/33.29    (15)  op(all_52_3, all_52_3) = e2
% 201.06/33.29    (16)   ~ (all_52_3 = e0)
% 201.06/33.29    (17)   ~ (all_52_5 = all_10_2)
% 201.06/33.29    (18)  op(e3, e3) = all_6_2
% 201.06/33.29    (19)  all_58_12 = e2
% 201.06/33.29    (20)  all_58_6 = all_52_5
% 201.06/33.29    (21)   ~ (e1 = e0)
% 201.06/33.29    (22)  op(e1, e1) = all_10_2
% 201.06/33.29    (23)   ~ (all_52_3 = all_4_2)
% 201.06/33.29  
% 201.06/33.29  Begin of proof
% 201.06/33.29  | 
% 201.06/33.29  | BETA: splitting (13) gives:
% 201.06/33.29  | 
% 201.06/33.29  | Case 1:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (24)  all_58_0 = e3
% 201.06/33.29  | | 
% 201.06/33.29  | | COMBINE_EQS: (4), (24) imply:
% 201.06/33.29  | |   (25)  all_6_2 = e3
% 201.06/33.29  | | 
% 201.06/33.29  | | BETA: splitting (6) gives:
% 201.06/33.29  | | 
% 201.06/33.29  | | Case 1:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (26)  all_58_0 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | COMBINE_EQS: (24), (26) imply:
% 201.06/33.29  | | |   (27)  e3 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | REDUCE: (3), (27) imply:
% 201.06/33.29  | | |   (28)  $false
% 201.06/33.29  | | | 
% 201.06/33.29  | | | CLOSE: (28) is inconsistent.
% 201.06/33.29  | | | 
% 201.06/33.29  | | Case 2:
% 201.06/33.29  | | | 
% 201.06/33.29  | | |   (29)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.29  | | | 
% 201.06/33.29  | | | BETA: splitting (29) gives:
% 201.06/33.29  | | | 
% 201.06/33.29  | | | Case 1:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (30)  all_58_2 = e0
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | COMBINE_EQS: (12), (30) imply:
% 201.06/33.29  | | | |   (31)  all_52_3 = e0
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | REDUCE: (16), (31) imply:
% 201.06/33.29  | | | |   (32)  $false
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | CLOSE: (32) is inconsistent.
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | Case 2:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | |   (33)  all_58_6 = e0 | all_58_12 = e0
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | BETA: splitting (33) gives:
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | | Case 1:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | |   (34)  all_58_6 = e0
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | COMBINE_EQS: (20), (34) imply:
% 201.06/33.29  | | | | |   (35)  all_52_5 = e0
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REDUCE: (2), (35) imply:
% 201.06/33.29  | | | | |   (36)  op(e0, e0) = e1
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REF_CLOSE: (1), (8), (21), (36) are inconsistent by sub-proof #221.
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | Case 2:
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | |   (37)  all_58_12 = e0
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | COMBINE_EQS: (19), (37) imply:
% 201.06/33.29  | | | | |   (38)  e2 = e0
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | REDUCE: (14), (38) imply:
% 201.06/33.29  | | | | |   (39)  $false
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | | CLOSE: (39) is inconsistent.
% 201.06/33.29  | | | | | 
% 201.06/33.29  | | | | End of split
% 201.06/33.29  | | | | 
% 201.06/33.29  | | | End of split
% 201.06/33.29  | | | 
% 201.06/33.29  | | End of split
% 201.06/33.29  | | 
% 201.06/33.29  | Case 2:
% 201.06/33.29  | | 
% 201.06/33.29  | |   (40)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.29  | | 
% 201.06/33.29  | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (11), (12), (15), (17), (18),
% 201.06/33.29  | |            (20), (22), (23), (40) are inconsistent by sub-proof #1364.
% 201.06/33.29  | | 
% 201.06/33.29  | End of split
% 201.06/33.29  | 
% 201.06/33.29  End of proof
% 201.06/33.29  
% 201.06/33.29  Sub-proof #221 shows that the following formulas are inconsistent:
% 201.06/33.29  ----------------------------------------------------------------
% 201.06/33.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.29    (2)  op(e0, e0) = e1
% 201.06/33.29    (3)  op(e0, e0) = e0
% 201.06/33.29    (4)   ~ (e1 = e0)
% 201.06/33.29  
% 201.06/33.29  Begin of proof
% 201.06/33.29  | 
% 201.06/33.29  | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (2), (3)
% 201.06/33.29  |              gives:
% 201.06/33.29  |   (5)  e1 = e0
% 201.06/33.29  | 
% 201.06/33.29  | REDUCE: (4), (5) imply:
% 201.06/33.29  |   (6)  $false
% 201.06/33.29  | 
% 201.06/33.29  | CLOSE: (6) is inconsistent.
% 201.06/33.29  | 
% 201.06/33.29  End of proof
% 201.06/33.29  
% 201.06/33.29  Sub-proof #222 shows that the following formulas are inconsistent:
% 201.06/33.29  ----------------------------------------------------------------
% 201.06/33.29    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.06/33.29    (2)   ~ (all_52_15 = all_52_23)
% 201.06/33.29    (3)   ~ (all_52_25 = all_52_27)
% 201.06/33.29    (4)  all_58_14 = all_52_23
% 201.06/33.29    (5)   ~ (e3 = e1)
% 201.06/33.29    (6)  op(all_52_3, all_52_3) = all_52_2
% 201.06/33.29    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.29    (8)  all_58_1 = all_52_9
% 201.06/33.29    (9)   ~ (e3 = e0)
% 201.06/33.29    (10)  op(all_52_23, all_52_23) = e0
% 201.06/33.29    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.29    (12)   ~ (all_52_7 = all_52_15)
% 201.06/33.29    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.06/33.29    (14)   ~ (all_52_17 = all_52_25)
% 201.06/33.29    (15)  all_58_0 = all_6_2
% 201.06/33.29    (16)  op(all_14_2, e0) = all_14_1
% 201.06/33.29    (17)  all_34_1 = all_14_1
% 201.06/33.29    (18)  op(e3, all_6_1) = e1
% 201.06/33.29    (19)  op(e3, e0) = all_52_25
% 201.06/33.29    (20)  op(all_52_5, all_52_5) = all_52_4
% 201.06/33.29    (21)  all_58_13 = all_52_15
% 201.06/33.29    (22)  op(e0, all_14_1) = e1
% 201.06/33.29    (23)  all_58_9 = all_52_25
% 201.06/33.29    (24)   ~ (all_52_29 = all_14_2)
% 201.06/33.29    (25)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.06/33.29    (26)  op(all_52_27, all_52_27) = all_52_26
% 201.06/33.29    (27)  op(e1, e3) = all_52_5
% 201.06/33.29    (28)  op(e2, e2) = all_4_2
% 201.06/33.29    (29)   ~ (all_52_3 = all_52_5)
% 201.06/33.29    (30)  all_58_11 = all_52_29
% 201.06/33.29    (31)   ~ (all_52_25 = all_14_2)
% 201.06/33.29    (32)   ~ (all_52_9 = all_52_15)
% 201.06/33.29    (33)  op(all_10_2, e1) = all_10_1
% 201.06/33.29    (34)  op(all_6_2, all_6_2) = all_52_0
% 201.06/33.29    (35)   ~ (all_52_7 = all_6_2)
% 201.06/33.29    (36)  op(e0, e0) = all_14_2
% 201.06/33.29    (37)  op(e0, e1) = all_52_23
% 201.06/33.29    (38)  all_56_15 = all_14_2
% 201.06/33.29    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.29    (40)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.06/33.29    (41)  all_56_11 = all_52_29
% 201.06/33.29    (42)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.06/33.29    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.06/33.29    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.06/33.29    (45)  op(e1, all_10_1) = e3
% 201.06/33.29    (46)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.06/33.29    (47)   ~ (e2 = e1)
% 201.06/33.29    (48)   ~ (all_52_13 = all_10_2)
% 201.06/33.29    (49)  op(all_10_2, all_10_2) = e1
% 201.06/33.29    (50)  all_58_10 = all_52_27
% 201.06/33.30    (51)  op(all_52_9, all_52_9) = all_52_8
% 201.06/33.30    (52)  op(all_52_15, all_52_15) = all_52_14
% 201.06/33.30    (53)   ~ (all_52_19 = all_52_23)
% 201.06/33.30    (54)   ~ (all_52_25 = all_52_29)
% 201.06/33.30    (55)   ~ (all_52_29 = all_10_2)
% 201.06/33.30    (56)  all_58_7 = all_52_13
% 201.06/33.30    (57)  op(all_52_19, all_52_19) = e2
% 201.06/33.30    (58)   ~ (all_52_5 = all_52_7)
% 201.06/33.30    (59)  all_58_12 = all_52_7
% 201.06/33.30    (60)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.06/33.30    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.30    (62)   ~ (all_52_7 = all_14_2)
% 201.06/33.30    (63)   ~ (all_14_2 = e0)
% 201.06/33.30    (64)  all_58_2 = all_52_3
% 201.06/33.30    (65)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.06/33.30    (66)  all_56_2 = all_52_17
% 201.06/33.30    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.06/33.30    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.30    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.06/33.30    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.06/33.30    (71)   ~ (e2 = e0)
% 201.06/33.30    (72)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.06/33.30    (73)  all_56_6 = all_52_19
% 201.06/33.30    (74)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.06/33.30    (75)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.06/33.30    (76)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.06/33.30    (77)   ~ (all_52_13 = all_4_2)
% 201.06/33.30    (78)  op(e3, e1) = all_52_17
% 201.06/33.30    (79)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.06/33.30    (80)  op(e0, e3) = all_52_7
% 201.06/33.30    (81)  op(e1, e2) = all_52_13
% 201.06/33.30    (82)   ~ (all_52_9 = all_52_25)
% 201.06/33.30    (83)  all_58_15 = all_14_2
% 201.06/33.30    (84)   ~ (all_52_19 = all_10_2)
% 201.06/33.30    (85)  all_58_8 = all_10_2
% 201.06/33.30    (86)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.30    (87)  all_34_2 = all_14_2
% 201.06/33.30    (88)   ~ (all_52_5 = all_10_2)
% 201.06/33.30    (89)  op(all_52_29, all_52_29) = all_52_28
% 201.06/33.30    (90)   ~ (all_52_23 = all_14_2)
% 201.06/33.30    (91)  all_56_12 = all_52_7
% 201.06/33.30    (92)   ~ (all_52_25 = all_6_2)
% 201.06/33.30    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.30    (94)   ~ (all_52_9 = all_4_2)
% 201.06/33.30    (95)   ~ (all_52_5 = all_6_2)
% 201.06/33.30    (96)   ~ (all_52_9 = all_6_2)
% 201.06/33.30    (97)   ~ (all_52_13 = all_52_15)
% 201.06/33.30    (98)  all_56_0 = all_6_2
% 201.06/33.30    (99)  op(e3, e3) = all_6_2
% 201.06/33.30    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.06/33.30    (101)   ~ (all_52_27 = all_14_2)
% 201.06/33.30    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.30    (103)  all_56_3 = all_52_25
% 201.06/33.30    (104)   ~ (all_52_3 = all_52_7)
% 201.06/33.30    (105)  all_58_5 = all_52_19
% 201.06/33.30    (106)  all_56_1 = all_52_9
% 201.06/33.30    (107)   ~ (all_52_27 = all_4_2)
% 201.06/33.30    (108)  op(all_52_17, all_52_17) = e3
% 201.06/33.30    (109)  all_58_6 = all_52_5
% 201.06/33.30    (110)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.06/33.30    (111)   ~ (all_52_17 = all_6_2)
% 201.06/33.30    (112)   ~ (e1 = e0)
% 201.06/33.30    (113)   ~ (e3 = e2)
% 201.06/33.30    (114)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.06/33.30    (115)   ~ (all_52_9 = all_52_17)
% 201.06/33.30    (116)  all_56_10 = all_10_2
% 201.06/33.30    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.30    (118)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.06/33.30    (119)  op(all_52_13, all_52_13) = all_52_12
% 201.06/33.30    (120)  op(e1, e1) = all_10_2
% 201.06/33.30    (121)   ~ (all_52_23 = all_10_2)
% 201.06/33.30    (122)   ~ (all_52_7 = all_52_23)
% 201.06/33.30    (123)  all_58_3 = all_4_2
% 201.06/33.30    (124)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.06/33.30    (125)  all_56_13 = all_52_15
% 201.06/33.30    (126)   ~ (all_52_3 = all_4_2)
% 201.06/33.30    (127)  op(all_6_2, e3) = all_6_1
% 201.06/33.30    (128)  all_58_4 = all_52_17
% 201.06/33.30    (129)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.06/33.30    (130)  op(all_52_25, all_52_25) = all_52_24
% 201.06/33.30  
% 201.06/33.30  Begin of proof
% 201.06/33.30  | 
% 201.06/33.30  | BETA: splitting (86) gives:
% 201.06/33.30  | 
% 201.06/33.30  | Case 1:
% 201.06/33.30  | | 
% 201.06/33.30  | |   (131)  all_56_15 = e3
% 201.06/33.30  | | 
% 201.06/33.30  | | COMBINE_EQS: (38), (131) imply:
% 201.06/33.30  | |   (132)  all_14_2 = e3
% 201.06/33.30  | | 
% 201.06/33.30  | | REF_CLOSE: (1), (5), (7), (10), (16), (17), (19), (22), (23), (24), (26),
% 201.06/33.30  | |            (30), (31), (36), (37), (40), (41), (42), (49), (50), (54), (55),
% 201.06/33.30  | |            (74), (87), (90), (93), (103), (120), (121), (130), (132) are
% 201.06/33.30  | |            inconsistent by sub-proof #248.
% 201.06/33.30  | | 
% 201.06/33.30  | Case 2:
% 201.06/33.30  | | 
% 201.06/33.30  | |   (133)   ~ (all_56_15 = e3)
% 201.06/33.30  | |   (134)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.30  | | 
% 201.06/33.30  | | REDUCE: (38), (133) imply:
% 201.06/33.30  | |   (135)   ~ (all_14_2 = e3)
% 201.06/33.30  | | 
% 201.06/33.30  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 201.06/33.30  | |            (14), (15), (18), (20), (21), (23), (25), (26), (27), (28), (29),
% 201.06/33.30  | |            (30), (31), (32), (33), (34), (35), (36), (38), (39), (41), (43),
% 201.06/33.30  | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 201.06/33.30  | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 201.06/33.30  | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 201.06/33.30  | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (88), (89),
% 201.06/33.30  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 201.06/33.30  | |            (100), (101), (102), (103), (104), (105), (106), (107), (108),
% 201.06/33.30  | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 201.06/33.30  | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 201.06/33.30  | |            (127), (128), (129), (130), (134), (135) are inconsistent by
% 201.06/33.30  | |            sub-proof #225.
% 201.06/33.30  | | 
% 201.06/33.30  | End of split
% 201.06/33.30  | 
% 201.06/33.30  End of proof
% 201.06/33.30  
% 201.06/33.30  Sub-proof #223 shows that the following formulas are inconsistent:
% 201.06/33.30  ----------------------------------------------------------------
% 201.06/33.30    (1)   ~ (all_52_15 = all_52_23)
% 201.06/33.30    (2)   ~ (all_52_25 = all_52_27)
% 201.06/33.30    (3)  all_58_14 = all_52_23
% 201.06/33.30    (4)   ~ (e3 = e1)
% 201.06/33.30    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.06/33.30    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.30    (7)  all_58_1 = all_52_9
% 201.06/33.30    (8)   ~ (e3 = e0)
% 201.06/33.30    (9)  op(all_52_23, all_52_23) = e0
% 201.06/33.30    (10)   ~ (all_4_0 = e1)
% 201.06/33.30    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.30    (12)   ~ (all_52_7 = all_52_15)
% 201.06/33.30    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.06/33.30    (14)   ~ (all_52_17 = all_52_25)
% 201.06/33.30    (15)  all_58_0 = all_6_2
% 201.06/33.30    (16)  op(e3, all_6_1) = e1
% 201.06/33.30    (17)  op(all_52_5, all_52_5) = all_52_4
% 201.06/33.30    (18)  all_58_13 = all_52_15
% 201.06/33.30    (19)  all_58_9 = all_52_25
% 201.06/33.30    (20)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.06/33.30    (21)  op(all_52_27, all_52_27) = all_52_26
% 201.06/33.30    (22)  op(e1, e3) = all_52_5
% 201.06/33.30    (23)   ~ (all_6_2 = all_4_0)
% 201.06/33.30    (24)  all_32_2 = all_4_2
% 201.06/33.30    (25)  op(e2, e2) = all_4_2
% 201.06/33.30    (26)   ~ (all_52_3 = all_52_5)
% 201.06/33.30    (27)  all_58_11 = all_52_29
% 201.06/33.30    (28)  all_56_5 = all_4_2
% 201.06/33.30    (29)   ~ (all_52_25 = all_14_2)
% 201.06/33.30    (30)   ~ (all_52_9 = all_52_15)
% 201.06/33.30    (31)  op(all_10_2, e1) = all_10_1
% 201.06/33.30    (32)  op(all_6_2, all_6_2) = all_52_0
% 201.06/33.30    (33)   ~ (all_52_7 = all_6_2)
% 201.06/33.30    (34)  all_58_2 = all_4_0
% 201.06/33.30    (35)  op(e0, e0) = all_14_2
% 201.06/33.30    (36)  all_56_15 = all_14_2
% 201.06/33.30    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.30    (38)  op(all_4_2, e2) = e3
% 201.06/33.30    (39)  all_56_11 = all_52_29
% 201.06/33.30    (40)   ~ (all_4_0 = e3)
% 201.06/33.30    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.06/33.30    (42)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.06/33.30    (43)  op(e1, all_10_1) = e3
% 201.06/33.30    (44)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.06/33.30    (45)   ~ (e2 = e1)
% 201.06/33.30    (46)   ~ (all_52_13 = all_10_2)
% 201.06/33.30    (47)  op(all_10_2, all_10_2) = e1
% 201.06/33.30    (48)  all_58_10 = all_52_27
% 201.06/33.30    (49)  op(all_52_9, all_52_9) = all_52_8
% 201.06/33.30    (50)  op(all_52_15, all_52_15) = all_52_14
% 201.06/33.30    (51)   ~ (all_52_19 = all_52_23)
% 201.06/33.30    (52)   ~ (all_52_25 = all_52_29)
% 201.06/33.30    (53)   ~ (all_52_29 = all_10_2)
% 201.06/33.30    (54)  all_58_7 = all_52_13
% 201.06/33.30    (55)  op(all_52_19, all_52_19) = e2
% 201.06/33.30    (56)   ~ (all_52_5 = all_52_7)
% 201.06/33.30    (57)  all_58_12 = all_52_7
% 201.06/33.30    (58)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.06/33.30    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.30    (60)   ~ (all_52_7 = all_14_2)
% 201.06/33.30    (61)   ~ (all_14_2 = e0)
% 201.06/33.30    (62)  all_58_2 = all_52_3
% 201.06/33.30    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.06/33.30    (64)  all_56_2 = all_52_17
% 201.06/33.30    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.06/33.30    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.30    (67)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.06/33.30    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.06/33.30    (69)   ~ (e2 = e0)
% 201.06/33.30    (70)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.06/33.30    (71)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.06/33.30    (72)  all_56_6 = all_52_19
% 201.06/33.30    (73)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.06/33.30    (74)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.06/33.30    (75)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.06/33.30    (76)  all_56_4 = all_4_0
% 201.06/33.30    (77)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.06/33.30    (78)   ~ (all_52_13 = all_4_2)
% 201.06/33.30    (79)  op(e3, e1) = all_52_17
% 201.06/33.30    (80)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.06/33.30    (81)  op(e0, e3) = all_52_7
% 201.06/33.30    (82)  op(e1, e2) = all_52_13
% 201.06/33.30    (83)   ~ (all_52_9 = all_52_25)
% 201.06/33.30    (84)  all_58_15 = all_14_2
% 201.06/33.30    (85)   ~ (all_52_19 = all_10_2)
% 201.06/33.30    (86)  all_58_8 = all_10_2
% 201.06/33.30    (87)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.30    (88)   ~ (all_52_5 = all_10_2)
% 201.06/33.30    (89)  op(all_52_29, all_52_29) = all_52_28
% 201.06/33.30    (90)   ~ (all_52_23 = all_14_2)
% 201.06/33.30    (91)  all_56_12 = all_52_7
% 201.06/33.30    (92)   ~ (all_52_25 = all_6_2)
% 201.06/33.30    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.30    (94)   ~ (all_52_9 = all_4_2)
% 201.06/33.30    (95)   ~ (all_52_5 = all_6_2)
% 201.06/33.30    (96)   ~ (all_52_9 = all_6_2)
% 201.06/33.30    (97)   ~ (all_52_13 = all_52_15)
% 201.06/33.30    (98)  all_56_0 = all_6_2
% 201.06/33.30    (99)  op(e3, e3) = all_6_2
% 201.06/33.30    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.06/33.30    (101)   ~ (all_52_27 = all_14_2)
% 201.06/33.30    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.30    (103)  op(all_4_2, all_4_2) = all_52_10
% 201.06/33.30    (104)  all_32_0 = all_4_0
% 201.06/33.30    (105)  all_56_3 = all_52_25
% 201.06/33.30    (106)   ~ (all_52_3 = all_52_7)
% 201.06/33.30    (107)  all_58_5 = all_52_19
% 201.06/33.30    (108)  all_56_1 = all_52_9
% 201.06/33.30    (109)   ~ (all_52_27 = all_4_2)
% 201.06/33.30    (110)  op(all_52_17, all_52_17) = e3
% 201.06/33.30    (111)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 201.06/33.30    (112)  all_58_6 = all_52_5
% 201.06/33.30    (113)   ~ (all_4_0 = all_4_2)
% 201.06/33.30    (114)  op(e3, e2) = all_52_9
% 201.06/33.30    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.06/33.30    (116)   ~ (all_52_17 = all_6_2)
% 201.06/33.30    (117)   ~ (e1 = e0)
% 201.06/33.30    (118)   ~ (e3 = e2)
% 201.06/33.30    (119)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.06/33.30    (120)   ~ (all_52_9 = all_52_17)
% 201.06/33.30    (121)  all_56_10 = all_10_2
% 201.06/33.30    (122)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.30    (123)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.06/33.30    (124)  op(all_52_13, all_52_13) = all_52_12
% 201.06/33.30    (125)  op(e1, e1) = all_10_2
% 201.06/33.30    (126)   ~ (all_52_23 = all_10_2)
% 201.06/33.30    (127)   ~ (all_52_7 = all_52_23)
% 201.06/33.30    (128)  all_58_3 = all_4_2
% 201.06/33.30    (129)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.06/33.30    (130)  all_56_13 = all_52_15
% 201.06/33.30    (131)   ~ (all_52_3 = all_4_2)
% 201.06/33.30    (132)   ~ (all_52_19 = all_4_2)
% 201.06/33.30    (133)  op(all_6_2, e3) = all_6_1
% 201.06/33.30    (134)  all_58_4 = all_52_17
% 201.06/33.30    (135)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.06/33.30    (136)  op(all_52_25, all_52_25) = all_52_24
% 201.06/33.30  
% 201.06/33.30  Begin of proof
% 201.06/33.30  | 
% 201.06/33.30  | BETA: splitting (87) gives:
% 201.06/33.30  | 
% 201.06/33.30  | Case 1:
% 201.06/33.30  | | 
% 201.06/33.30  | |   (137)  all_56_15 = e3
% 201.06/33.30  | | 
% 201.06/33.30  | | REF_CLOSE: (6), (10), (23), (24), (25), (28), (32), (34), (36), (37), (38),
% 201.06/33.30  | |            (40), (48), (55), (63), (70), (72), (74), (76), (94), (99),
% 201.06/33.30  | |            (101), (103), (104), (107), (111), (113), (114), (128), (132),
% 201.06/33.30  | |            (137) are inconsistent by sub-proof #930.
% 201.06/33.30  | | 
% 201.06/33.30  | Case 2:
% 201.06/33.30  | | 
% 201.06/33.30  | |   (138)   ~ (all_56_15 = e3)
% 201.06/33.30  | |   (139)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.30  | | 
% 201.06/33.30  | | REDUCE: (36), (138) imply:
% 201.06/33.30  | |   (140)   ~ (all_14_2 = e3)
% 201.06/33.30  | | 
% 201.06/33.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 201.06/33.30  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (25), (26),
% 201.06/33.30  | |            (27), (29), (30), (31), (32), (33), (35), (36), (37), (39), (41),
% 201.06/33.30  | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 201.06/33.30  | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 201.06/33.30  | |            (64), (65), (66), (67), (68), (69), (71), (72), (73), (75), (77),
% 201.06/33.30  | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (88), (89),
% 201.06/33.30  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 201.06/33.30  | |            (100), (101), (102), (105), (106), (107), (108), (109), (110),
% 201.06/33.30  | |            (112), (115), (116), (117), (118), (119), (120), (121), (122),
% 201.06/33.30  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 201.06/33.30  | |            (133), (134), (135), (136), (139), (140) are inconsistent by
% 201.06/33.30  | |            sub-proof #225.
% 201.06/33.30  | | 
% 201.06/33.30  | End of split
% 201.06/33.30  | 
% 201.06/33.30  End of proof
% 201.06/33.30  
% 201.06/33.30  Sub-proof #224 shows that the following formulas are inconsistent:
% 201.06/33.30  ----------------------------------------------------------------
% 201.06/33.30    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.06/33.30    (2)   ~ (all_52_15 = all_52_23)
% 201.06/33.30    (3)   ~ (all_52_25 = all_52_27)
% 201.06/33.30    (4)  all_58_14 = all_52_23
% 201.06/33.30    (5)   ~ (e3 = e1)
% 201.06/33.30    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.06/33.30    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.06/33.30    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.30    (9)   ~ (all_52_5 = all_52_13)
% 201.06/33.30    (10)  all_58_1 = all_52_9
% 201.06/33.30    (11)   ~ (all_52_9 = all_52_13)
% 201.06/33.30    (12)   ~ (e3 = e0)
% 201.06/33.30    (13)  op(e2, e3) = all_52_3
% 201.06/33.30    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.30    (15)  op(e0, e2) = all_52_15
% 201.06/33.30    (16)   ~ (all_52_7 = all_52_15)
% 201.06/33.30    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.06/33.30    (18)   ~ (all_52_17 = all_52_25)
% 201.06/33.30    (19)   ~ (all_52_3 = all_6_2)
% 201.06/33.30    (20)  all_58_0 = all_6_2
% 201.06/33.30    (21)  op(all_14_2, e0) = all_14_1
% 201.06/33.30    (22)  all_56_4 = all_52_3
% 201.06/33.30    (23)  op(e3, all_6_1) = e1
% 201.06/33.30    (24)   ~ (all_52_17 = all_10_2)
% 201.06/33.30    (25)  op(e3, e0) = all_52_25
% 201.06/33.30    (26)  op(e0, all_14_1) = all_14_0
% 201.06/33.30    (27)  op(all_52_5, all_52_5) = all_52_4
% 201.06/33.30    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.06/33.30    (29)  op(all_52_19, all_52_19) = all_52_18
% 201.06/33.30    (30)   ~ (all_52_27 = all_52_29)
% 201.06/33.30    (31)  all_58_13 = all_52_15
% 201.06/33.30    (32)  op(all_10_2, all_10_2) = all_52_20
% 201.06/33.30    (33)  all_58_9 = all_52_25
% 201.06/33.30    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.06/33.30    (35)   ~ (all_52_29 = all_14_2)
% 201.06/33.30    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.06/33.30    (37)  op(all_52_27, all_52_27) = all_52_26
% 201.06/33.30    (38)  op(e1, e3) = all_52_5
% 201.06/33.30    (39)  op(e2, e2) = all_4_2
% 201.06/33.30    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.06/33.30    (41)   ~ (all_52_3 = all_52_5)
% 201.06/33.30    (42)  all_58_11 = all_52_29
% 201.06/33.30    (43)  all_56_5 = all_4_2
% 201.06/33.30    (44)   ~ (all_52_25 = all_14_2)
% 201.06/33.30    (45)   ~ (all_52_9 = all_52_15)
% 201.06/33.30    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.06/33.30    (47)   ~ (all_52_3 = all_52_27)
% 201.06/33.30    (48)  op(all_10_2, e1) = all_10_1
% 201.06/33.30    (49)  all_46_2 = all_6_2
% 201.06/33.30    (50)  op(all_6_2, all_6_2) = all_52_0
% 201.06/33.30    (51)   ~ (all_52_7 = all_6_2)
% 201.06/33.30    (52)  op(e0, e0) = all_14_2
% 201.06/33.30    (53)  op(e0, e1) = all_52_23
% 201.06/33.30    (54)  all_56_15 = all_14_2
% 201.06/33.30    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.30    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.06/33.30    (57)  all_56_11 = all_52_29
% 201.06/33.30    (58)   ~ (all_4_1 = e1)
% 201.06/33.30    (59)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.06/33.30    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.06/33.30    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.06/33.30    (62)  op(e1, all_10_1) = e3
% 201.06/33.30    (63)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.06/33.30    (64)  all_56_9 = all_52_13
% 201.06/33.30    (65)   ~ (e2 = e1)
% 201.06/33.30    (66)   ~ (all_52_13 = all_10_2)
% 201.06/33.30    (67)  all_58_10 = all_52_27
% 201.06/33.30    (68)  all_56_8 = all_52_5
% 201.06/33.30    (69)  op(all_52_9, all_52_9) = all_52_8
% 201.06/33.30    (70)  op(all_52_15, all_52_15) = all_52_14
% 201.06/33.30    (71)   ~ (all_52_19 = all_52_23)
% 201.06/33.30    (72)   ~ (all_52_25 = all_52_29)
% 201.06/33.30    (73)   ~ (all_52_29 = all_10_2)
% 201.06/33.30    (74)  all_58_7 = all_52_13
% 201.06/33.30    (75)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.06/33.30    (76)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.06/33.30    (77)   ~ (all_52_5 = all_52_7)
% 201.06/33.30    (78)  all_58_12 = all_52_7
% 201.06/33.30    (79)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.06/33.30    (80)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.30    (81)   ~ (all_52_7 = all_14_2)
% 201.06/33.30    (82)   ~ (all_14_2 = e0)
% 201.06/33.30    (83)  all_58_2 = all_52_3
% 201.06/33.30    (84)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.06/33.30    (85)  all_56_2 = all_52_17
% 201.06/33.30    (86)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.06/33.30    (87)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.30    (88)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.06/33.30    (89)   ~ (all_14_0 = e3)
% 201.06/33.30    (90)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.06/33.30    (91)  all_56_7 = all_52_27
% 201.06/33.30    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.06/33.30    (93)   ~ (e2 = e0)
% 201.06/33.30    (94)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.06/33.30    (95)  op(all_4_2, e2) = all_4_1
% 201.06/33.30    (96)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.06/33.30    (97)   ~ (all_52_5 = all_52_29)
% 201.06/33.30    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.06/33.30    (99)  all_56_6 = all_52_19
% 201.06/33.30    (100)   ~ (all_52_15 = all_14_2)
% 201.06/33.30    (101)   ~ (all_52_19 = all_52_27)
% 201.06/33.30    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.06/33.30    (103)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.06/33.30    (104)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.06/33.30    (105)   ~ (all_52_13 = all_4_2)
% 201.06/33.30    (106)  op(e3, e1) = all_52_17
% 201.06/33.30    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.06/33.30    (108)  op(e0, e3) = all_52_7
% 201.06/33.30    (109)  op(e1, e2) = all_52_13
% 201.06/33.30    (110)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.06/33.30    (111)   ~ (all_52_9 = all_52_25)
% 201.06/33.30    (112)  all_58_15 = all_14_2
% 201.06/33.30    (113)   ~ (all_52_19 = all_10_2)
% 201.06/33.30    (114)  op(all_52_23, all_52_23) = all_52_22
% 201.06/33.30    (115)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.06/33.30    (116)  all_58_8 = all_10_2
% 201.06/33.30    (117)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.30    (118)   ~ (all_52_5 = all_10_2)
% 201.06/33.30    (119)  op(all_52_29, all_52_29) = all_52_28
% 201.06/33.30    (120)   ~ (all_52_23 = all_14_2)
% 201.06/33.30    (121)  all_56_12 = all_52_7
% 201.06/33.30    (122)  op(all_52_17, all_52_17) = all_52_16
% 201.06/33.30    (123)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.06/33.30    (124)   ~ (all_52_25 = all_6_2)
% 201.06/33.30    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.30    (126)   ~ (all_52_9 = all_4_2)
% 201.06/33.30    (127)   ~ (all_52_5 = all_6_2)
% 201.06/33.30    (128)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.06/33.30    (129)   ~ (all_52_9 = all_6_2)
% 201.06/33.30    (130)   ~ (all_52_13 = all_52_15)
% 201.06/33.30    (131)  all_56_0 = all_6_2
% 201.06/33.30    (132)  op(e3, e3) = all_6_2
% 201.06/33.30    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.06/33.30    (134)   ~ (all_52_27 = all_14_2)
% 201.06/33.30    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.30    (136)  all_56_14 = all_52_23
% 201.06/33.30    (137)  op(all_4_2, all_4_2) = all_52_10
% 201.06/33.30    (138)  all_56_3 = all_52_25
% 201.06/33.30    (139)   ~ (all_52_3 = all_52_7)
% 201.06/33.30    (140)  op(all_14_2, all_14_2) = all_52_30
% 201.06/33.30    (141)  all_58_5 = all_52_19
% 201.06/33.30    (142)  all_56_1 = all_52_9
% 201.06/33.30    (143)   ~ (all_52_15 = all_4_2)
% 201.06/33.30    (144)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.06/33.30           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.06/33.30           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.06/33.30           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.06/33.30    (145)   ~ (all_52_27 = all_4_2)
% 201.06/33.30    (146)  all_58_6 = all_52_5
% 201.06/33.30    (147)  op(e3, e2) = all_52_9
% 201.06/33.30    (148)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.06/33.30    (149)   ~ (all_52_17 = all_6_2)
% 201.06/33.30    (150)   ~ (e1 = e0)
% 201.06/33.30    (151)   ~ (e3 = e2)
% 201.06/33.30    (152)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.06/33.30    (153)   ~ (all_52_9 = all_52_17)
% 201.06/33.30    (154)  all_56_10 = all_10_2
% 201.06/33.30    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.30    (156)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.06/33.30    (157)  all_46_1 = all_6_1
% 201.06/33.30    (158)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.06/33.30    (159)  op(all_52_13, all_52_13) = all_52_12
% 201.06/33.30    (160)  op(e1, e1) = all_10_2
% 201.06/33.30    (161)   ~ (all_52_23 = all_10_2)
% 201.06/33.30    (162)   ~ (all_52_7 = all_52_23)
% 201.06/33.30    (163)   ~ (all_52_17 = all_52_19)
% 201.06/33.31    (164)  all_58_3 = all_4_2
% 201.06/33.31    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.06/33.31    (166)  all_56_13 = all_52_15
% 201.06/33.31    (167)   ~ (all_52_3 = all_4_2)
% 201.06/33.31    (168)   ~ (all_52_19 = all_4_2)
% 201.06/33.31    (169)   ~ (all_52_17 = all_52_23)
% 201.06/33.31    (170)  op(all_6_2, e3) = all_6_1
% 201.06/33.31    (171)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.06/33.31    (172)   ~ (all_52_13 = all_52_29)
% 201.06/33.31    (173)  all_58_4 = all_52_17
% 201.06/33.31    (174)   ~ (all_14_0 = e1)
% 201.06/33.31    (175)   ~ (all_14_0 = e2)
% 201.06/33.31    (176)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.06/33.31    (177)  op(all_52_25, all_52_25) = all_52_24
% 201.06/33.31  
% 201.06/33.31  Begin of proof
% 201.06/33.31  | 
% 201.06/33.31  | BETA: splitting (144) gives:
% 201.06/33.31  | 
% 201.06/33.31  | Case 1:
% 201.06/33.31  | | 
% 201.06/33.31  | |   (178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.06/33.31  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 201.06/33.31  | | 
% 201.06/33.31  | | BETA: splitting (178) gives:
% 201.06/33.31  | | 
% 201.06/33.31  | | Case 1:
% 201.06/33.31  | | | 
% 201.06/33.31  | | |   (179)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REF_CLOSE: (5), (7), (8), (17), (20), (23), (27), (39), (50), (51), (52),
% 201.06/33.31  | | |            (55), (78), (81), (83), (87), (118), (132), (135), (146),
% 201.06/33.31  | | |            (148), (160), (167), (170), (179) are inconsistent by sub-proof
% 201.06/33.31  | | |            #302.
% 201.06/33.31  | | | 
% 201.06/33.31  | | Case 2:
% 201.06/33.31  | | | 
% 201.06/33.31  | | |   (180)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 201.06/33.31  | | | 
% 201.06/33.31  | | | ALPHA: (180) implies:
% 201.06/33.31  | | |   (181)  all_52_14 = e0
% 201.06/33.31  | | |   (182)  all_52_12 = e1
% 201.06/33.31  | | |   (183)  all_52_10 = e2
% 201.06/33.31  | | |   (184)  all_52_8 = e3
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (69), (184) imply:
% 201.06/33.31  | | |   (185)  op(all_52_9, all_52_9) = e3
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (159), (182) imply:
% 201.06/33.31  | | |   (186)  op(all_52_13, all_52_13) = e1
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (70), (181) imply:
% 201.06/33.31  | | |   (187)  op(all_52_15, all_52_15) = e0
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (137), (183) imply:
% 201.06/33.31  | | |   (188)  op(all_4_2, all_4_2) = e2
% 201.06/33.31  | | | 
% 201.06/33.31  | | | BETA: splitting (117) gives:
% 201.06/33.31  | | | 
% 201.06/33.31  | | | Case 1:
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | |   (189)  all_56_15 = e3
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | COMBINE_EQS: (54), (189) imply:
% 201.06/33.31  | | | |   (190)  all_14_2 = e3
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | SIMP: (190) implies:
% 201.06/33.31  | | | |   (191)  all_14_2 = e3
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | COMBINE_EQS: (112), (191) imply:
% 201.06/33.31  | | | |   (192)  all_58_15 = e3
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (81), (191) imply:
% 201.06/33.31  | | | |   (193)   ~ (all_52_7 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (100), (191) imply:
% 201.06/33.31  | | | |   (194)   ~ (all_52_15 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (44), (191) imply:
% 201.06/33.31  | | | |   (195)   ~ (all_52_25 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (134), (191) imply:
% 201.06/33.31  | | | |   (196)   ~ (all_52_27 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (35), (191) imply:
% 201.06/33.31  | | | |   (197)   ~ (all_52_29 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (140), (191) imply:
% 201.06/33.31  | | | |   (198)  op(e3, e3) = all_52_30
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (21), (191) imply:
% 201.06/33.31  | | | |   (199)  op(e3, e0) = all_14_1
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (52), (191) imply:
% 201.06/33.31  | | | |   (200)  op(e0, e0) = e3
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 201.06/33.31  | | | |              simplifying with (25), (199) gives:
% 201.06/33.31  | | | |   (201)  all_52_25 = all_14_1
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 201.06/33.31  | | | |              simplifying with (132), (198) gives:
% 201.06/33.31  | | | |   (202)  all_52_30 = all_6_2
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | COMBINE_EQS: (138), (201) imply:
% 201.06/33.31  | | | |   (203)  all_56_3 = all_14_1
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | COMBINE_EQS: (33), (201) imply:
% 201.06/33.31  | | | |   (204)  all_58_9 = all_14_1
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (111), (201) imply:
% 201.06/33.31  | | | |   (205)   ~ (all_52_9 = all_14_1)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (124), (201) imply:
% 201.06/33.31  | | | |   (206)   ~ (all_14_1 = all_6_2)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (195), (201) imply:
% 201.06/33.31  | | | |   (207)   ~ (all_14_1 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (177), (201) imply:
% 201.06/33.31  | | | |   (208)  op(all_14_1, all_14_1) = all_52_24
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | BETA: splitting (60) gives:
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | Case 1:
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | |   (209)  all_56_13 = e3
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | | REF_CLOSE: (166), (194), (209) are inconsistent by sub-proof #1201.
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | Case 2:
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | |   (210)   ~ (all_56_13 = e3)
% 201.06/33.31  | | | | |   (211)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | | BETA: splitting (125) gives:
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | | Case 1:
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | |   (212)  all_56_3 = e3
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | | REF_CLOSE: (203), (207), (212) are inconsistent by sub-proof #1200.
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | Case 2:
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | |   (213)   ~ (all_56_3 = e3)
% 201.06/33.31  | | | | | |   (214)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | | BETA: splitting (98) gives:
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | | Case 1:
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | |   (215)  all_58_12 = e1
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | COMBINE_EQS: (78), (215) imply:
% 201.06/33.31  | | | | | | |   (216)  all_52_7 = e1
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | SIMP: (216) implies:
% 201.06/33.31  | | | | | | |   (217)  all_52_7 = e1
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | REDUCE: (16), (217) imply:
% 201.06/33.31  | | | | | | |   (218)   ~ (all_52_15 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | SIMP: (218) implies:
% 201.06/33.31  | | | | | | |   (219)   ~ (all_52_15 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | REDUCE: (51), (217) imply:
% 201.06/33.31  | | | | | | |   (220)   ~ (all_6_2 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | SIMP: (220) implies:
% 201.06/33.31  | | | | | | |   (221)   ~ (all_6_2 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | REDUCE: (193), (217) imply:
% 201.06/33.31  | | | | | | |   (222)   ~ (e3 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | REDUCE: (17), (217) imply:
% 201.06/33.31  | | | | | | |   (223)  op(e1, e1) = all_52_6
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | GROUND_INST: instantiating (8) with all_10_2, all_52_6, e1, e1,
% 201.06/33.31  | | | | | | |              simplifying with (160), (223) gives:
% 201.06/33.31  | | | | | | |   (224)  all_52_6 = all_10_2
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | REF_CLOSE: (5), (8), (10), (20), (22), (23), (31), (55), (58),
% 201.06/33.31  | | | | | | |            (63), (66), (67), (74), (83), (87), (92), (95), (110),
% 201.06/33.31  | | | | | | |            (129), (132), (135), (141), (147), (160), (163), (164),
% 201.06/33.31  | | | | | | |            (167), (170), (173), (185), (186), (194), (196), (204),
% 201.06/33.31  | | | | | | |            (207), (219), (221) are inconsistent by sub-proof #300.
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | Case 2:
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | |   (225)   ~ (all_58_12 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | REDUCE: (78), (225) imply:
% 201.06/33.31  | | | | | | |   (226)   ~ (all_52_7 = e1)
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | BETA: splitting (128) gives:
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | | Case 1:
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | |   (227)  all_58_9 = e2
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | COMBINE_EQS: (204), (227) imply:
% 201.06/33.31  | | | | | | | |   (228)  all_14_1 = e2
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | SIMP: (228) implies:
% 201.06/33.31  | | | | | | | |   (229)  all_14_1 = e2
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | REDUCE: (26), (229) imply:
% 201.06/33.31  | | | | | | | |   (230)  op(e0, e2) = all_14_0
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | GROUND_INST: instantiating (8) with all_52_15, all_14_0, e2, e0,
% 201.06/33.31  | | | | | | | |              simplifying with (15), (230) gives:
% 201.06/33.31  | | | | | | | |   (231)  all_52_15 = all_14_0
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | COMBINE_EQS: (166), (231) imply:
% 201.06/33.31  | | | | | | | |   (232)  all_56_13 = all_14_0
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | REDUCE: (187), (231) imply:
% 201.06/33.31  | | | | | | | |   (233)  op(all_14_0, all_14_0) = e0
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | BETA: splitting (211) gives:
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | Case 1:
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | |   (234)  all_56_13 = e2
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | REF_CLOSE: (175), (232), (234) are inconsistent by sub-proof
% 201.06/33.31  | | | | | | | | |            #542.
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | Case 2:
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | |   (235)  all_56_13 = e1 | all_56_13 = e0
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | BETA: splitting (235) gives:
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | Case 1:
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | |   (236)  all_56_13 = e1
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | | REF_CLOSE: (174), (232), (236) are inconsistent by sub-proof
% 201.06/33.31  | | | | | | | | | |            #541.
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | Case 2:
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | |   (237)  all_56_13 = e0
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | | COMBINE_EQS: (232), (237) imply:
% 201.06/33.31  | | | | | | | | | |   (238)  all_14_0 = e0
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | | REF_CLOSE: (8), (89), (200), (233), (238) are inconsistent by
% 201.06/33.31  | | | | | | | | | |            sub-proof #285.
% 201.06/33.31  | | | | | | | | | | 
% 201.06/33.31  | | | | | | | | | End of split
% 201.06/33.31  | | | | | | | | | 
% 201.06/33.31  | | | | | | | | End of split
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | Case 2:
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | |   (239)   ~ (all_58_9 = e2)
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | REDUCE: (204), (239) imply:
% 201.06/33.31  | | | | | | | |   (240)   ~ (all_14_1 = e2)
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 201.06/33.31  | | | | | | | |            (19), (20), (23), (24), (26), (27), (31), (33), (39),
% 201.06/33.31  | | | | | | | |            (41), (42), (46), (51), (53), (58), (64), (65), (66),
% 201.06/33.31  | | | | | | | |            (74), (77), (78), (80), (83), (86), (87), (90), (95),
% 201.06/33.31  | | | | | | | |            (96), (105), (110), (116), (121), (122), (126),
% 201.06/33.31  | | | | | | | |            (129), (130), (132), (135), (139), (142), (146),
% 201.06/33.31  | | | | | | | |            (147), (149), (152), (153), (155), (156), (160),
% 201.06/33.31  | | | | | | | |            (164), (167), (170), (173), (175), (185), (186),
% 201.06/33.31  | | | | | | | |            (188), (192), (193), (194), (195), (197), (203),
% 201.06/33.31  | | | | | | | |            (204), (205), (206), (208), (214), (226), (240) are
% 201.06/33.31  | | | | | | | |            inconsistent by sub-proof #299.
% 201.06/33.31  | | | | | | | | 
% 201.06/33.31  | | | | | | | End of split
% 201.06/33.31  | | | | | | | 
% 201.06/33.31  | | | | | | End of split
% 201.06/33.31  | | | | | | 
% 201.06/33.31  | | | | | End of split
% 201.06/33.31  | | | | | 
% 201.06/33.31  | | | | End of split
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | Case 2:
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | |   (241)   ~ (all_56_15 = e3)
% 201.06/33.31  | | | |   (242)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (54), (241) imply:
% 201.06/33.31  | | | |   (243)   ~ (all_14_2 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 201.06/33.31  | | | |            (13), (14), (16), (17), (18), (19), (20), (22), (23), (24),
% 201.06/33.31  | | | |            (27), (28), (31), (32), (33), (34), (35), (36), (38), (39),
% 201.06/33.31  | | | |            (40), (41), (42), (43), (44), (45), (49), (50), (51), (52),
% 201.06/33.31  | | | |            (54), (55), (58), (59), (60), (61), (63), (65), (67), (68),
% 201.06/33.31  | | | |            (71), (72), (74), (77), (78), (79), (80), (81), (83), (84),
% 201.06/33.31  | | | |            (85), (87), (90), (91), (92), (93), (94), (95), (96), (97),
% 201.06/33.31  | | | |            (99), (103), (104), (105), (106), (107), (108), (110), (111),
% 201.06/33.31  | | | |            (112), (114), (115), (116), (119), (120), (121), (122),
% 201.06/33.31  | | | |            (124), (125), (126), (127), (129), (131), (132), (133),
% 201.06/33.31  | | | |            (134), (135), (138), (139), (140), (141), (142), (143),
% 201.06/33.31  | | | |            (145), (146), (147), (148), (149), (150), (151), (152),
% 201.06/33.31  | | | |            (153), (155), (157), (158), (160), (161), (162), (163),
% 201.06/33.31  | | | |            (164), (166), (167), (168), (169), (170), (171), (172),
% 201.06/33.31  | | | |            (173), (177), (185), (186), (187), (188), (242), (243) are
% 201.06/33.31  | | | |            inconsistent by sub-proof #288.
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | End of split
% 201.06/33.31  | | | 
% 201.06/33.31  | | End of split
% 201.06/33.31  | | 
% 201.06/33.31  | Case 2:
% 201.06/33.31  | | 
% 201.06/33.31  | |   (244)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 201.06/33.31  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 201.06/33.31  | |            e0)
% 201.06/33.31  | | 
% 201.06/33.31  | | BETA: splitting (244) gives:
% 201.06/33.31  | | 
% 201.06/33.31  | | Case 1:
% 201.06/33.31  | | | 
% 201.06/33.31  | | |   (245)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 201.06/33.31  | | | 
% 201.06/33.31  | | | ALPHA: (245) implies:
% 201.06/33.31  | | |   (246)  all_52_22 = e0
% 201.06/33.31  | | |   (247)  all_52_20 = e1
% 201.06/33.31  | | |   (248)  all_52_18 = e2
% 201.06/33.31  | | |   (249)  all_52_16 = e3
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (122), (249) imply:
% 201.06/33.31  | | |   (250)  op(all_52_17, all_52_17) = e3
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (29), (248) imply:
% 201.06/33.31  | | |   (251)  op(all_52_19, all_52_19) = e2
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (114), (246) imply:
% 201.06/33.31  | | |   (252)  op(all_52_23, all_52_23) = e0
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REDUCE: (32), (247) imply:
% 201.06/33.31  | | |   (253)  op(all_10_2, all_10_2) = e1
% 201.06/33.31  | | | 
% 201.06/33.31  | | | BETA: splitting (117) gives:
% 201.06/33.31  | | | 
% 201.06/33.31  | | | Case 1:
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | |   (254)  all_56_15 = e3
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REF_CLOSE: (4), (5), (8), (10), (15), (18), (20), (21), (23), (24),
% 201.06/33.31  | | | |            (25), (26), (31), (33), (44), (51), (52), (53), (54), (56),
% 201.06/33.31  | | | |            (61), (69), (71), (75), (78), (85), (87), (89), (98), (112),
% 201.06/33.31  | | | |            (116), (120), (124), (125), (128), (132), (135), (136),
% 201.06/33.31  | | | |            (138), (140), (141), (149), (155), (160), (169), (170),
% 201.06/33.31  | | | |            (173), (174), (175), (177), (250), (251), (252), (253), (254)
% 201.06/33.31  | | | |            are inconsistent by sub-proof #282.
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | Case 2:
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | |   (255)   ~ (all_56_15 = e3)
% 201.06/33.31  | | | |   (256)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REDUCE: (54), (255) imply:
% 201.06/33.31  | | | |   (257)   ~ (all_14_2 = e3)
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (12), (14), (16), (17),
% 201.06/33.31  | | | |            (18), (20), (23), (27), (31), (33), (36), (37), (38), (39),
% 201.06/33.31  | | | |            (41), (42), (44), (45), (48), (50), (51), (52), (54), (55),
% 201.06/33.31  | | | |            (57), (60), (61), (62), (63), (65), (66), (67), (69), (70),
% 201.06/33.31  | | | |            (71), (72), (73), (74), (77), (78), (79), (80), (81), (82),
% 201.06/33.31  | | | |            (83), (84), (85), (86), (87), (88), (90), (93), (96), (99),
% 201.06/33.31  | | | |            (102), (103), (104), (105), (106), (107), (108), (109),
% 201.06/33.31  | | | |            (111), (112), (113), (116), (118), (119), (120), (121),
% 201.06/33.31  | | | |            (124), (125), (126), (127), (129), (130), (131), (132),
% 201.06/33.31  | | | |            (133), (134), (135), (138), (139), (141), (142), (145),
% 201.06/33.31  | | | |            (146), (148), (149), (150), (151), (152), (153), (154),
% 201.06/33.31  | | | |            (155), (158), (159), (160), (161), (162), (164), (165),
% 201.06/33.31  | | | |            (166), (167), (170), (173), (176), (177), (250), (251),
% 201.06/33.31  | | | |            (252), (253), (256), (257) are inconsistent by sub-proof
% 201.06/33.31  | | | |            #225.
% 201.06/33.31  | | | | 
% 201.06/33.31  | | | End of split
% 201.06/33.31  | | | 
% 201.06/33.31  | | Case 2:
% 201.06/33.31  | | | 
% 201.06/33.31  | | |   (258)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.06/33.31  | | | 
% 201.06/33.31  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 201.06/33.31  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 201.06/33.31  | | |            (27), (29), (30), (31), (33), (35), (36), (37), (38), (39),
% 201.06/33.31  | | |            (40), (41), (42), (43), (44), (45), (47), (48), (49), (50),
% 201.06/33.31  | | |            (51), (52), (54), (55), (56), (57), (59), (60), (61), (63),
% 201.06/33.31  | | |            (65), (67), (68), (69), (70), (72), (73), (74), (75), (76),
% 201.06/33.31  | | |            (77), (78), (79), (80), (81), (82), (83), (85), (86), (87),
% 201.06/33.31  | | |            (88), (90), (92), (93), (94), (97), (100), (101), (102), (103),
% 201.06/33.31  | | |            (104), (106), (107), (108), (110), (111), (112), (113), (114),
% 201.06/33.31  | | |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 201.06/33.31  | | |            (124), (125), (126), (127), (129), (130), (131), (132), (133),
% 201.06/33.31  | | |            (134), (135), (136), (138), (139), (140), (141), (142), (143),
% 201.06/33.31  | | |            (145), (146), (147), (148), (149), (150), (151), (152), (157),
% 201.06/33.31  | | |            (158), (159), (160), (161), (162), (163), (164), (165), (166),
% 201.06/33.31  | | |            (167), (168), (169), (170), (171), (173), (177), (258) are
% 201.06/33.31  | | |            inconsistent by sub-proof #271.
% 201.06/33.31  | | | 
% 201.06/33.31  | | End of split
% 201.06/33.31  | | 
% 201.06/33.31  | End of split
% 201.06/33.31  | 
% 201.06/33.31  End of proof
% 201.06/33.31  
% 201.06/33.31  Sub-proof #225 shows that the following formulas are inconsistent:
% 201.06/33.31  ----------------------------------------------------------------
% 201.06/33.31    (1)   ~ (all_52_15 = all_52_23)
% 201.06/33.31    (2)   ~ (all_52_25 = all_52_27)
% 201.06/33.31    (3)  all_58_14 = all_52_23
% 201.06/33.31    (4)   ~ (e3 = e1)
% 201.06/33.31    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.06/33.31    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.06/33.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.06/33.31    (7)  all_58_1 = all_52_9
% 201.06/33.31    (8)   ~ (e3 = e0)
% 201.06/33.31    (9)  op(all_52_23, all_52_23) = e0
% 201.06/33.31    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.06/33.31    (11)   ~ (all_52_7 = all_52_15)
% 201.06/33.31    (12)  op(all_52_7, all_52_7) = all_52_6
% 201.06/33.31    (13)   ~ (all_52_17 = all_52_25)
% 201.06/33.31    (14)  all_58_0 = all_6_2
% 201.06/33.31    (15)  op(e3, all_6_1) = e1
% 201.06/33.31    (16)  op(all_52_5, all_52_5) = all_52_4
% 201.06/33.31    (17)  all_58_13 = all_52_15
% 201.06/33.31    (18)  all_58_9 = all_52_25
% 201.06/33.31    (19)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.06/33.31    (20)  op(all_52_27, all_52_27) = all_52_26
% 201.06/33.31    (21)  op(e1, e3) = all_52_5
% 201.06/33.31    (22)  op(e2, e2) = all_4_2
% 201.06/33.31    (23)   ~ (all_52_3 = all_52_5)
% 201.06/33.31    (24)  all_58_11 = all_52_29
% 201.06/33.31    (25)   ~ (all_52_25 = all_14_2)
% 201.06/33.31    (26)   ~ (all_52_9 = all_52_15)
% 201.06/33.31    (27)  op(all_10_2, e1) = all_10_1
% 201.06/33.31    (28)  op(all_6_2, all_6_2) = all_52_0
% 201.06/33.31    (29)   ~ (all_52_7 = all_6_2)
% 201.06/33.31    (30)  op(e0, e0) = all_14_2
% 201.06/33.31    (31)  all_56_15 = all_14_2
% 201.06/33.31    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.06/33.31    (33)  all_56_11 = all_52_29
% 201.06/33.31    (34)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.06/33.31    (35)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.06/33.31    (36)  op(e1, all_10_1) = e3
% 201.06/33.31    (37)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.06/33.31    (38)   ~ (e2 = e1)
% 201.06/33.31    (39)   ~ (all_52_13 = all_10_2)
% 201.06/33.31    (40)  op(all_10_2, all_10_2) = e1
% 201.06/33.31    (41)  all_58_10 = all_52_27
% 201.06/33.31    (42)  op(all_52_9, all_52_9) = all_52_8
% 201.06/33.31    (43)  op(all_52_15, all_52_15) = all_52_14
% 201.06/33.31    (44)   ~ (all_52_19 = all_52_23)
% 201.06/33.31    (45)   ~ (all_52_25 = all_52_29)
% 201.06/33.31    (46)   ~ (all_52_29 = all_10_2)
% 201.06/33.31    (47)  all_58_7 = all_52_13
% 201.06/33.31    (48)  op(all_52_19, all_52_19) = e2
% 201.06/33.31    (49)   ~ (all_52_5 = all_52_7)
% 201.06/33.31    (50)  all_58_12 = all_52_7
% 201.06/33.31    (51)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.06/33.31    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.06/33.31    (53)   ~ (all_52_7 = all_14_2)
% 201.06/33.31    (54)   ~ (all_14_2 = e0)
% 201.06/33.31    (55)  all_58_2 = all_52_3
% 201.06/33.31    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.06/33.31    (57)  all_56_2 = all_52_17
% 201.06/33.31    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.06/33.31    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.06/33.31    (60)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.06/33.31    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.06/33.31    (62)   ~ (e2 = e0)
% 201.06/33.31    (63)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.06/33.31    (64)  all_56_6 = all_52_19
% 201.06/33.31    (65)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.06/33.31    (66)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.06/33.31    (67)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.06/33.31    (68)   ~ (all_52_13 = all_4_2)
% 201.06/33.31    (69)  op(e3, e1) = all_52_17
% 201.06/33.31    (70)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.06/33.31    (71)  op(e0, e3) = all_52_7
% 201.06/33.31    (72)  op(e1, e2) = all_52_13
% 201.06/33.31    (73)   ~ (all_52_9 = all_52_25)
% 201.06/33.31    (74)  all_58_15 = all_14_2
% 201.06/33.31    (75)   ~ (all_52_19 = all_10_2)
% 201.06/33.31    (76)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.06/33.31    (77)  all_58_8 = all_10_2
% 201.06/33.31    (78)   ~ (all_52_5 = all_10_2)
% 201.06/33.31    (79)  op(all_52_29, all_52_29) = all_52_28
% 201.06/33.31    (80)   ~ (all_52_23 = all_14_2)
% 201.06/33.31    (81)  all_56_12 = all_52_7
% 201.06/33.31    (82)   ~ (all_52_25 = all_6_2)
% 201.06/33.31    (83)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.06/33.31    (84)   ~ (all_52_9 = all_4_2)
% 201.06/33.31    (85)   ~ (all_52_5 = all_6_2)
% 201.06/33.31    (86)   ~ (all_52_9 = all_6_2)
% 201.06/33.31    (87)   ~ (all_52_13 = all_52_15)
% 201.06/33.31    (88)  all_56_0 = all_6_2
% 201.06/33.31    (89)  op(e3, e3) = all_6_2
% 201.06/33.31    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.06/33.31    (91)   ~ (all_52_27 = all_14_2)
% 201.06/33.31    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.06/33.31    (93)  all_56_3 = all_52_25
% 201.06/33.31    (94)   ~ (all_52_3 = all_52_7)
% 201.06/33.31    (95)  all_58_5 = all_52_19
% 201.06/33.31    (96)  all_56_1 = all_52_9
% 201.06/33.31    (97)   ~ (all_52_27 = all_4_2)
% 201.06/33.31    (98)  op(all_52_17, all_52_17) = e3
% 201.06/33.31    (99)  all_58_6 = all_52_5
% 201.06/33.31    (100)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.06/33.31    (101)   ~ (all_52_17 = all_6_2)
% 201.06/33.31    (102)   ~ (e1 = e0)
% 201.06/33.31    (103)   ~ (e3 = e2)
% 201.06/33.31    (104)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.06/33.31    (105)   ~ (all_52_9 = all_52_17)
% 201.06/33.31    (106)  all_56_10 = all_10_2
% 201.06/33.31    (107)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.06/33.31    (108)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.06/33.31    (109)  op(all_52_13, all_52_13) = all_52_12
% 201.06/33.31    (110)  op(e1, e1) = all_10_2
% 201.06/33.31    (111)   ~ (all_52_23 = all_10_2)
% 201.06/33.31    (112)   ~ (all_52_7 = all_52_23)
% 201.06/33.31    (113)  all_58_3 = all_4_2
% 201.06/33.31    (114)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.06/33.31    (115)  all_56_13 = all_52_15
% 201.06/33.31    (116)   ~ (all_52_3 = all_4_2)
% 201.06/33.31    (117)  op(all_6_2, e3) = all_6_1
% 201.06/33.31    (118)  all_58_4 = all_52_17
% 201.06/33.31    (119)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.06/33.31    (120)  op(all_52_25, all_52_25) = all_52_24
% 201.06/33.31    (121)   ~ (all_14_2 = e3)
% 201.06/33.31  
% 201.06/33.31  Begin of proof
% 201.06/33.31  | 
% 201.06/33.31  | BETA: splitting (34) gives:
% 201.06/33.31  | 
% 201.06/33.31  | Case 1:
% 201.06/33.31  | | 
% 201.06/33.31  | |   (122)  all_56_13 = e3
% 201.06/33.31  | | 
% 201.06/33.31  | | COMBINE_EQS: (115), (122) imply:
% 201.06/33.31  | |   (123)  all_52_15 = e3
% 201.06/33.31  | | 
% 201.06/33.31  | | COMBINE_EQS: (17), (123) imply:
% 201.06/33.31  | |   (124)  all_58_13 = e3
% 201.06/33.31  | | 
% 201.06/33.31  | | REDUCE: (11), (123) imply:
% 201.06/33.31  | |   (125)   ~ (all_52_7 = e3)
% 201.06/33.31  | | 
% 201.06/33.31  | | REDUCE: (26), (123) imply:
% 201.06/33.31  | |   (126)   ~ (all_52_9 = e3)
% 201.06/33.31  | | 
% 201.06/33.31  | | REDUCE: (87), (123) imply:
% 201.06/33.31  | |   (127)   ~ (all_52_13 = e3)
% 201.06/33.31  | | 
% 201.06/33.31  | | REDUCE: (1), (123) imply:
% 201.06/33.31  | |   (128)   ~ (all_52_23 = e3)
% 201.06/33.31  | | 
% 201.06/33.31  | | SIMP: (128) implies:
% 201.06/33.31  | |   (129)   ~ (all_52_23 = e3)
% 201.06/33.31  | | 
% 201.06/33.31  | | REDUCE: (43), (123) imply:
% 201.06/33.31  | |   (130)  op(e3, e3) = all_52_14
% 201.06/33.31  | | 
% 201.06/33.31  | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3, simplifying
% 201.06/33.31  | |              with (89), (130) gives:
% 201.06/33.31  | |   (131)  all_52_14 = all_6_2
% 201.06/33.31  | | 
% 201.35/33.32  | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (13), (14), (16), (18), (19), (22),
% 201.35/33.32  | |            (23), (24), (25), (27), (28), (29), (30), (33), (35), (37), (38),
% 201.35/33.32  | |            (40), (42), (45), (46), (47), (48), (50), (52), (55), (57), (58),
% 201.35/33.32  | |            (59), (60), (63), (65), (67), (69), (73), (75), (77), (78), (79),
% 201.35/33.32  | |            (80), (82), (83), (85), (86), (88), (89), (90), (92), (93), (94),
% 201.35/33.32  | |            (95), (96), (98), (99), (101), (103), (104), (105), (107), (108),
% 201.35/33.32  | |            (110), (114), (116), (118), (120), (124), (125), (126), (127),
% 201.35/33.32  | |            (129) are inconsistent by sub-proof #280.
% 201.35/33.32  | | 
% 201.35/33.32  | Case 2:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (132)   ~ (all_56_13 = e3)
% 201.35/33.32  | | 
% 201.35/33.32  | | REDUCE: (115), (132) imply:
% 201.35/33.32  | |   (133)   ~ (all_52_15 = e3)
% 201.35/33.32  | | 
% 201.35/33.32  | | BETA: splitting (100) gives:
% 201.35/33.32  | | 
% 201.35/33.32  | | Case 1:
% 201.35/33.32  | | | 
% 201.35/33.32  | | |   (134)  all_58_12 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | COMBINE_EQS: (50), (134) imply:
% 201.35/33.32  | | |   (135)  all_52_7 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | SIMP: (135) implies:
% 201.35/33.32  | | |   (136)  all_52_7 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (94), (136) imply:
% 201.35/33.32  | | |   (137)   ~ (all_52_3 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (49), (136) imply:
% 201.35/33.32  | | |   (138)   ~ (all_52_5 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (112), (136) imply:
% 201.35/33.32  | | |   (139)   ~ (all_52_23 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | SIMP: (139) implies:
% 201.35/33.32  | | |   (140)   ~ (all_52_23 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (53), (136) imply:
% 201.35/33.32  | | |   (141)   ~ (all_14_2 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (29), (136) imply:
% 201.35/33.32  | | |   (142)   ~ (all_6_2 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | SIMP: (142) implies:
% 201.35/33.32  | | |   (143)   ~ (all_6_2 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (12), (136) imply:
% 201.35/33.32  | | |   (144)  op(e3, e3) = all_52_6
% 201.35/33.32  | | | 
% 201.35/33.32  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 201.35/33.32  | | |              with (89), (144) gives:
% 201.35/33.32  | | |   (145)  all_52_6 = all_6_2
% 201.35/33.32  | | | 
% 201.35/33.32  | | | BETA: splitting (61) gives:
% 201.35/33.32  | | | 
% 201.35/33.32  | | | Case 1:
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | |   (146)  all_58_0 = e1
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | COMBINE_EQS: (14), (146) imply:
% 201.35/33.32  | | | |   (147)  all_6_2 = e1
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REDUCE: (101), (147) imply:
% 201.35/33.32  | | | |   (148)   ~ (all_52_17 = e1)
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REDUCE: (143), (147) imply:
% 201.35/33.32  | | | |   (149)   ~ (e3 = e1)
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REDUCE: (28), (147) imply:
% 201.35/33.32  | | | |   (150)  op(e1, e1) = all_52_0
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REDUCE: (117), (147) imply:
% 201.35/33.32  | | | |   (151)  op(e1, e3) = all_6_1
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REDUCE: (89), (147) imply:
% 201.35/33.32  | | | |   (152)  op(e3, e3) = e1
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_0, e1, e1,
% 201.35/33.32  | | | |              simplifying with (110), (150) gives:
% 201.35/33.32  | | | |   (153)  all_52_0 = all_10_2
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 201.35/33.32  | | | |              simplifying with (21), (151) gives:
% 201.35/33.32  | | | |   (154)  all_52_5 = all_6_1
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | COMBINE_EQS: (99), (154) imply:
% 201.35/33.32  | | | |   (155)  all_58_6 = all_6_1
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REDUCE: (138), (154) imply:
% 201.35/33.32  | | | |   (156)   ~ (all_6_1 = e3)
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | BETA: splitting (83) gives:
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | Case 1:
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | |   (157)  all_56_3 = e3
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | COMBINE_EQS: (93), (157) imply:
% 201.35/33.32  | | | | |   (158)  all_52_25 = e3
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | SIMP: (158) implies:
% 201.35/33.32  | | | | |   (159)  all_52_25 = e3
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | REDUCE: (13), (159) imply:
% 201.35/33.32  | | | | |   (160)   ~ (all_52_17 = e3)
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | REDUCE: (2), (159) imply:
% 201.35/33.32  | | | | |   (161)   ~ (all_52_27 = e3)
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | SIMP: (161) implies:
% 201.35/33.32  | | | | |   (162)   ~ (all_52_27 = e3)
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | REDUCE: (45), (159) imply:
% 201.35/33.32  | | | | |   (163)   ~ (all_52_29 = e3)
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | SIMP: (163) implies:
% 201.35/33.32  | | | | |   (164)   ~ (all_52_29 = e3)
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | REDUCE: (120), (159) imply:
% 201.35/33.32  | | | | |   (165)  op(e3, e3) = all_52_24
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | GROUND_INST: instantiating (6) with e1, all_52_24, e3, e3, simplifying
% 201.35/33.32  | | | | |              with (152), (165) gives:
% 201.35/33.32  | | | | |   (166)  all_52_24 = e1
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | BETA: splitting (35) gives:
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | Case 1:
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | |   (167)  all_56_2 = e3
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | | REF_CLOSE: (57), (160), (167) are inconsistent by sub-proof #1327.
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | Case 2:
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | |   (168)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | | BETA: splitting (32) gives:
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | | Case 1:
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | |   (169)  all_58_2 = e3
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | | REF_CLOSE: (55), (137), (169) are inconsistent by sub-proof #1369.
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | Case 2:
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | |   (170)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | | BETA: splitting (52) gives:
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | | Case 1:
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | |   (171)  all_58_6 = e3
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | | REF_CLOSE: (155), (156), (171) are inconsistent by sub-proof
% 201.35/33.32  | | | | | | | |            #296.
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | Case 2:
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | |   (172)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | | BETA: splitting (56) gives:
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | | Case 1:
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | |   (173)  all_56_6 = e3
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | COMBINE_EQS: (64), (173) imply:
% 201.35/33.32  | | | | | | | | |   (174)  all_52_19 = e3
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | SIMP: (174) implies:
% 201.35/33.32  | | | | | | | | |   (175)  all_52_19 = e3
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | REDUCE: (75), (175) imply:
% 201.35/33.32  | | | | | | | | |   (176)   ~ (all_10_2 = e3)
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | SIMP: (176) implies:
% 201.35/33.32  | | | | | | | | |   (177)   ~ (all_10_2 = e3)
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | REDUCE: (48), (175) imply:
% 201.35/33.32  | | | | | | | | |   (178)  op(e3, e3) = e2
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | REF_CLOSE: (6), (24), (38), (47), (77), (109), (152), (164),
% 201.35/33.32  | | | | | | | | |            (172), (177), (178) are inconsistent by sub-proof
% 201.35/33.32  | | | | | | | | |            #227.
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | Case 2:
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | |   (179)   ~ (all_56_6 = e3)
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | REDUCE: (64), (179) imply:
% 201.35/33.32  | | | | | | | | |   (180)   ~ (all_52_19 = e3)
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | BETA: splitting (170) gives:
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | Case 1:
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | |   (181)  all_58_3 = e3
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | COMBINE_EQS: (113), (181) imply:
% 201.35/33.32  | | | | | | | | | |   (182)  all_4_2 = e3
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | SIMP: (182) implies:
% 201.35/33.32  | | | | | | | | | |   (183)  all_4_2 = e3
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | REDUCE: (68), (183) imply:
% 201.35/33.32  | | | | | | | | | |   (184)   ~ (all_52_13 = e3)
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | BETA: splitting (172) gives:
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | Case 1:
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | |   (185)  all_58_7 = e3
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | COMBINE_EQS: (47), (185) imply:
% 201.35/33.32  | | | | | | | | | | |   (186)  all_52_13 = e3
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | SIMP: (186) implies:
% 201.35/33.32  | | | | | | | | | | |   (187)  all_52_13 = e3
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | REDUCE: (184), (187) imply:
% 201.35/33.32  | | | | | | | | | | |   (188)  $false
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | Case 2:
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | |   (189)  all_58_8 = e3 | all_58_11 = e3
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | BETA: splitting (189) gives:
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | Case 1:
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | |   (190)  all_58_8 = e3
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | COMBINE_EQS: (77), (190) imply:
% 201.35/33.32  | | | | | | | | | | | |   (191)  all_10_2 = e3
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | REDUCE: (27), (191) imply:
% 201.35/33.32  | | | | | | | | | | | |   (192)  op(e3, e1) = all_10_1
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_17, all_10_1, e1,
% 201.35/33.32  | | | | | | | | | | | |              e3, simplifying with (69), (192) gives:
% 201.35/33.32  | | | | | | | | | | | |   (193)  all_52_17 = all_10_1
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | COMBINE_EQS: (57), (193) imply:
% 201.35/33.32  | | | | | | | | | | | |   (194)  all_56_2 = all_10_1
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | COMBINE_EQS: (118), (193) imply:
% 201.35/33.32  | | | | | | | | | | | |   (195)  all_58_4 = all_10_1
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | REDUCE: (148), (193) imply:
% 201.35/33.32  | | | | | | | | | | | |   (196)   ~ (all_10_1 = e1)
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | REDUCE: (98), (193) imply:
% 201.35/33.32  | | | | | | | | | | | |   (197)  op(all_10_1, all_10_1) = e3
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | REF_CLOSE: (6), (30), (36), (70), (72), (121), (168), (184),
% 201.35/33.32  | | | | | | | | | | | |            (194), (195), (196), (197) are inconsistent by
% 201.35/33.32  | | | | | | | | | | | |            sub-proof #226.
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | Case 2:
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | |   (198)  all_58_11 = e3
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | | REF_CLOSE: (24), (164), (198) are inconsistent by sub-proof
% 201.35/33.32  | | | | | | | | | | | |            #1323.
% 201.35/33.32  | | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | | End of split
% 201.35/33.32  | | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | End of split
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | Case 2:
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | |   (199)  all_58_5 = e3 | all_58_10 = e3
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | | REF_CLOSE: (41), (95), (162), (180), (199) are inconsistent
% 201.35/33.32  | | | | | | | | | |            by sub-proof #1132.
% 201.35/33.32  | | | | | | | | | | 
% 201.35/33.32  | | | | | | | | | End of split
% 201.35/33.32  | | | | | | | | | 
% 201.35/33.32  | | | | | | | | End of split
% 201.35/33.32  | | | | | | | | 
% 201.35/33.32  | | | | | | | End of split
% 201.35/33.32  | | | | | | | 
% 201.35/33.32  | | | | | | End of split
% 201.35/33.32  | | | | | | 
% 201.35/33.32  | | | | | End of split
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | Case 2:
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | |   (200)   ~ (all_56_3 = e3)
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (14), (18), (19), (20), (22),
% 201.35/33.32  | | | | |            (27), (30), (32), (35), (38), (40), (41), (42), (44), (48),
% 201.35/33.32  | | | | |            (55), (57), (60), (62), (63), (69), (75), (77), (84), (89),
% 201.35/33.32  | | | | |            (91), (92), (93), (95), (97), (98), (101), (102), (105),
% 201.35/33.32  | | | | |            (106), (107), (110), (113), (118), (119), (121), (137),
% 201.35/33.32  | | | | |            (140), (143), (200) are inconsistent by sub-proof #1046.
% 201.35/33.32  | | | | | 
% 201.35/33.32  | | | | End of split
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | Case 2:
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | |   (201)   ~ (all_58_0 = e1)
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REF_CLOSE: (3), (6), (14), (19), (30), (35), (40), (48), (57), (66),
% 201.35/33.32  | | | |            (77), (89), (95), (98), (101), (106), (107), (110), (118),
% 201.35/33.32  | | | |            (119), (121), (140), (143), (144), (201) are inconsistent by
% 201.35/33.32  | | | |            sub-proof #278.
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | End of split
% 201.35/33.32  | | | 
% 201.35/33.32  | | Case 2:
% 201.35/33.32  | | | 
% 201.35/33.32  | | |   (202)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | BETA: splitting (202) gives:
% 201.35/33.32  | | | 
% 201.35/33.32  | | | Case 1:
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | |   (203)  all_58_13 = e3
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REF_CLOSE: (17), (133), (203) are inconsistent by sub-proof #1360.
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | Case 2:
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | |   (204)  all_58_14 = e3 | all_58_15 = e3
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | | REF_CLOSE: (3), (6), (9), (10), (12), (15), (29), (31), (51), (53),
% 201.35/33.32  | | | |            (54), (69), (71), (74), (76), (81), (89), (98), (110), (111),
% 201.35/33.32  | | | |            (112), (117), (121), (204) are inconsistent by sub-proof
% 201.35/33.32  | | | |            #276.
% 201.35/33.32  | | | | 
% 201.35/33.32  | | | End of split
% 201.35/33.32  | | | 
% 201.35/33.32  | | End of split
% 201.35/33.32  | | 
% 201.35/33.32  | End of split
% 201.35/33.32  | 
% 201.35/33.32  End of proof
% 201.35/33.32  
% 201.35/33.32  Sub-proof #226 shows that the following formulas are inconsistent:
% 201.35/33.32  ----------------------------------------------------------------
% 201.35/33.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.32    (2)   ~ (all_10_1 = e1)
% 201.35/33.32    (3)  all_58_4 = all_10_1
% 201.35/33.32    (4)  op(e0, e0) = all_14_2
% 201.35/33.32    (5)  op(e1, all_10_1) = e3
% 201.35/33.32    (6)  op(all_10_1, all_10_1) = e3
% 201.35/33.32    (7)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.35/33.32    (8)  op(e1, e2) = all_52_13
% 201.35/33.32    (9)  all_56_2 = all_10_1
% 201.35/33.32    (10)   ~ (all_52_13 = e3)
% 201.35/33.32    (11)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.32    (12)   ~ (all_14_2 = e3)
% 201.35/33.32  
% 201.35/33.32  Begin of proof
% 201.35/33.32  | 
% 201.35/33.32  | BETA: splitting (7) gives:
% 201.35/33.32  | 
% 201.35/33.32  | Case 1:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (13)  all_58_4 = e2
% 201.35/33.32  | | 
% 201.35/33.32  | | COMBINE_EQS: (3), (13) imply:
% 201.35/33.32  | |   (14)  all_10_1 = e2
% 201.35/33.32  | | 
% 201.35/33.32  | | REF_CLOSE: (1), (5), (8), (10), (14) are inconsistent by sub-proof #532.
% 201.35/33.32  | | 
% 201.35/33.32  | Case 2:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (15)   ~ (all_58_4 = e2)
% 201.35/33.32  | | 
% 201.35/33.32  | | REDUCE: (3), (15) imply:
% 201.35/33.32  | |   (16)   ~ (all_10_1 = e2)
% 201.35/33.32  | | 
% 201.35/33.32  | | REF_CLOSE: (1), (2), (4), (6), (9), (11), (12), (16) are inconsistent by
% 201.35/33.32  | |            sub-proof #445.
% 201.35/33.32  | | 
% 201.35/33.32  | End of split
% 201.35/33.32  | 
% 201.35/33.32  End of proof
% 201.35/33.32  
% 201.35/33.32  Sub-proof #227 shows that the following formulas are inconsistent:
% 201.35/33.32  ----------------------------------------------------------------
% 201.35/33.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.32    (2)  all_58_11 = all_52_29
% 201.35/33.32    (3)  op(e3, e3) = e2
% 201.35/33.32    (4)   ~ (e2 = e1)
% 201.35/33.32    (5)  all_58_7 = all_52_13
% 201.35/33.32    (6)   ~ (all_52_29 = e3)
% 201.35/33.32    (7)   ~ (all_10_2 = e3)
% 201.35/33.32    (8)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.32    (9)  all_58_8 = all_10_2
% 201.35/33.32    (10)  op(e3, e3) = e1
% 201.35/33.32    (11)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.32  
% 201.35/33.32  Begin of proof
% 201.35/33.32  | 
% 201.35/33.32  | BETA: splitting (8) gives:
% 201.35/33.32  | 
% 201.35/33.32  | Case 1:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (12)  all_58_7 = e3
% 201.35/33.32  | | 
% 201.35/33.32  | | COMBINE_EQS: (5), (12) imply:
% 201.35/33.32  | |   (13)  all_52_13 = e3
% 201.35/33.32  | | 
% 201.35/33.32  | | REDUCE: (11), (13) imply:
% 201.35/33.32  | |   (14)  op(e3, e3) = all_52_12
% 201.35/33.32  | | 
% 201.35/33.32  | | GROUND_INST: instantiating (1) with e1, all_52_12, e3, e3, simplifying with
% 201.35/33.32  | |              (10), (14) gives:
% 201.35/33.32  | |   (15)  all_52_12 = e1
% 201.35/33.32  | | 
% 201.35/33.32  | | GROUND_INST: instantiating (1) with e2, all_52_12, e3, e3, simplifying with
% 201.35/33.32  | |              (3), (14) gives:
% 201.35/33.32  | |   (16)  all_52_12 = e2
% 201.35/33.32  | | 
% 201.35/33.32  | | COMBINE_EQS: (15), (16) imply:
% 201.35/33.32  | |   (17)  e2 = e1
% 201.35/33.32  | | 
% 201.35/33.32  | | SIMP: (17) implies:
% 201.35/33.32  | |   (18)  e2 = e1
% 201.35/33.32  | | 
% 201.35/33.32  | | REDUCE: (4), (18) imply:
% 201.35/33.32  | |   (19)  $false
% 201.35/33.32  | | 
% 201.35/33.32  | | CLOSE: (19) is inconsistent.
% 201.35/33.32  | | 
% 201.35/33.32  | Case 2:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (20)  all_58_8 = e3 | all_58_11 = e3
% 201.35/33.32  | | 
% 201.35/33.32  | | REF_CLOSE: (2), (6), (7), (9), (20) are inconsistent by sub-proof #1140.
% 201.35/33.32  | | 
% 201.35/33.32  | End of split
% 201.35/33.32  | 
% 201.35/33.32  End of proof
% 201.35/33.32  
% 201.35/33.32  Sub-proof #228 shows that the following formulas are inconsistent:
% 201.35/33.32  ----------------------------------------------------------------
% 201.35/33.32    (1)   ~ (all_52_25 = all_52_27)
% 201.35/33.32    (2)  all_58_14 = all_52_23
% 201.35/33.32    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.35/33.32    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.32    (5)   ~ (all_52_5 = all_52_13)
% 201.35/33.32    (6)  all_58_1 = all_52_9
% 201.35/33.32    (7)   ~ (all_52_9 = all_52_13)
% 201.35/33.32    (8)   ~ (e3 = e0)
% 201.35/33.32    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.32    (10)   ~ (all_52_7 = all_52_15)
% 201.35/33.32    (11)  op(all_52_15, all_52_15) = e0
% 201.35/33.32    (12)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.32    (13)   ~ (all_52_17 = all_52_25)
% 201.35/33.32    (14)  all_58_0 = all_6_2
% 201.35/33.32    (15)  op(e3, all_6_1) = e1
% 201.35/33.32    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.32    (17)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.32    (18)  all_58_13 = all_52_15
% 201.35/33.32    (19)  op(all_52_13, all_52_13) = e1
% 201.35/33.32    (20)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.32    (21)  all_58_9 = all_52_25
% 201.35/33.32    (22)  op(e1, e3) = all_52_5
% 201.35/33.32    (23)  op(e2, e2) = all_4_2
% 201.35/33.32    (24)  all_58_11 = all_52_29
% 201.35/33.32    (25)   ~ (all_52_9 = all_52_15)
% 201.35/33.32    (26)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.32    (27)  op(all_10_2, e1) = all_10_1
% 201.35/33.32    (28)   ~ (all_52_7 = all_6_2)
% 201.35/33.32    (29)  op(e0, e1) = all_52_23
% 201.35/33.32    (30)   ~ (all_52_15 = e0)
% 201.35/33.32    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.32    (32)  all_58_15 = e0
% 201.35/33.32    (33)   ~ (all_4_1 = e1)
% 201.35/33.32    (34)   ~ (all_52_25 = e0)
% 201.35/33.32    (35)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.32    (36)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.32    (37)  op(e1, all_10_1) = e3
% 201.35/33.32    (38)  all_56_9 = all_52_13
% 201.35/33.32    (39)   ~ (e2 = e1)
% 201.35/33.32    (40)   ~ (all_52_13 = all_10_2)
% 201.35/33.32    (41)  op(e0, e0) = e0
% 201.35/33.32    (42)  all_58_10 = all_52_27
% 201.35/33.32    (43)   ~ (all_52_25 = all_52_29)
% 201.35/33.32    (44)  all_58_7 = all_52_13
% 201.35/33.32    (45)   ~ (all_52_5 = all_52_7)
% 201.35/33.32    (46)  all_58_12 = all_52_7
% 201.35/33.32    (47)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.32    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.32    (49)  all_58_2 = all_52_3
% 201.35/33.32    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.32    (51)  all_56_2 = all_52_17
% 201.35/33.32    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.32    (53)  all_56_7 = all_52_27
% 201.35/33.32    (54)   ~ (e2 = e0)
% 201.35/33.32    (55)  op(all_4_2, e2) = all_4_1
% 201.35/33.32    (56)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.32    (57)  all_56_6 = all_52_19
% 201.35/33.32    (58)   ~ (all_52_13 = all_4_2)
% 201.35/33.32    (59)  op(e3, e1) = all_52_17
% 201.35/33.32    (60)  op(e0, e3) = all_52_7
% 201.35/33.32    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.32    (62)   ~ (all_52_9 = all_52_25)
% 201.35/33.32    (63)   ~ (all_52_19 = all_10_2)
% 201.35/33.32    (64)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.32    (65)  all_58_8 = all_10_2
% 201.35/33.32    (66)  all_56_12 = all_52_7
% 201.35/33.32    (67)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.32    (68)   ~ (all_52_25 = all_6_2)
% 201.35/33.32    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.32    (70)   ~ (all_52_9 = all_4_2)
% 201.35/33.32    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.35/33.32    (72)  op(all_4_2, all_4_2) = e2
% 201.35/33.32    (73)   ~ (all_52_9 = all_6_2)
% 201.35/33.32    (74)   ~ (all_52_13 = all_52_15)
% 201.35/33.32    (75)  op(e3, e3) = all_6_2
% 201.35/33.32    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.32    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.32    (78)  all_56_3 = all_52_25
% 201.35/33.32    (79)   ~ (all_52_3 = all_52_7)
% 201.35/33.32    (80)  all_58_5 = all_52_19
% 201.35/33.32    (81)  all_56_1 = all_52_9
% 201.35/33.32    (82)   ~ (all_52_15 = all_4_2)
% 201.35/33.32    (83)   ~ (all_52_27 = all_4_2)
% 201.35/33.32    (84)  all_58_6 = all_52_5
% 201.35/33.32    (85)  op(e3, e2) = all_52_9
% 201.35/33.32    (86)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.32    (87)   ~ (all_52_17 = all_6_2)
% 201.35/33.32    (88)   ~ (e1 = e0)
% 201.35/33.32    (89)   ~ (e3 = e2)
% 201.35/33.32    (90)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.32    (91)   ~ (all_52_9 = all_52_17)
% 201.35/33.32    (92)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.32    (93)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.35/33.32    (94)  op(e1, e1) = all_10_2
% 201.35/33.32    (95)  op(all_52_9, all_52_9) = e3
% 201.35/33.32    (96)   ~ (all_52_7 = all_52_23)
% 201.35/33.32    (97)  all_58_3 = all_4_2
% 201.35/33.32    (98)  all_56_13 = all_52_15
% 201.35/33.32    (99)  op(all_6_2, e3) = all_6_1
% 201.35/33.32    (100)   ~ (all_52_13 = all_52_29)
% 201.35/33.32    (101)  all_58_4 = all_52_17
% 201.35/33.32    (102)   ~ (all_52_7 = e0)
% 201.35/33.32    (103)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.32  
% 201.35/33.32  Begin of proof
% 201.35/33.32  | 
% 201.35/33.32  | BETA: splitting (35) gives:
% 201.35/33.32  | 
% 201.35/33.32  | Case 1:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (104)  all_56_13 = e3
% 201.35/33.32  | | 
% 201.35/33.32  | | REF_CLOSE: (2), (4), (9), (10), (11), (15), (18), (23), (25), (26), (28),
% 201.35/33.32  | |            (32), (46), (47), (54), (59), (60), (64), (66), (73), (75), (81),
% 201.35/33.32  | |            (82), (89), (90), (91), (95), (98), (99), (104) are inconsistent
% 201.35/33.32  | |            by sub-proof #321.
% 201.35/33.32  | | 
% 201.35/33.32  | Case 2:
% 201.35/33.32  | | 
% 201.35/33.32  | |   (105)   ~ (all_56_13 = e3)
% 201.35/33.32  | |   (106)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.32  | | 
% 201.35/33.32  | | REDUCE: (98), (105) imply:
% 201.35/33.32  | |   (107)   ~ (all_52_15 = e3)
% 201.35/33.32  | | 
% 201.35/33.32  | | BETA: splitting (86) gives:
% 201.35/33.32  | | 
% 201.35/33.32  | | Case 1:
% 201.35/33.32  | | | 
% 201.35/33.32  | | |   (108)  all_58_12 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | COMBINE_EQS: (46), (108) imply:
% 201.35/33.32  | | |   (109)  all_52_7 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | SIMP: (109) implies:
% 201.35/33.32  | | |   (110)  all_52_7 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (79), (110) imply:
% 201.35/33.32  | | |   (111)   ~ (all_52_3 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (45), (110) imply:
% 201.35/33.32  | | |   (112)   ~ (all_52_5 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (10), (110) imply:
% 201.35/33.32  | | |   (113)   ~ (all_52_15 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (28), (110) imply:
% 201.35/33.32  | | |   (114)   ~ (all_6_2 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | SIMP: (114) implies:
% 201.35/33.32  | | |   (115)   ~ (all_6_2 = e3)
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REDUCE: (12), (110) imply:
% 201.35/33.32  | | |   (116)  op(e3, e3) = all_52_6
% 201.35/33.32  | | | 
% 201.35/33.32  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 201.35/33.32  | | |              with (75), (116) gives:
% 201.35/33.32  | | |   (117)  all_52_6 = all_6_2
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (13), (14), (16), (17), (18),
% 201.35/33.32  | | |            (19), (20), (21), (23), (24), (31), (32), (33), (34), (36),
% 201.35/33.32  | | |            (41), (42), (43), (44), (48), (49), (50), (51), (52), (53),
% 201.35/33.32  | | |            (55), (57), (58), (61), (62), (63), (65), (67), (68), (69),
% 201.35/33.32  | | |            (70), (71), (72), (73), (75), (76), (77), (78), (80), (81),
% 201.35/33.32  | | |            (83), (84), (85), (87), (88), (90), (91), (92), (95), (97),
% 201.35/33.32  | | |            (100), (101), (103), (107), (111), (112), (115) are
% 201.35/33.32  | | |            inconsistent by sub-proof #318.
% 201.35/33.32  | | | 
% 201.35/33.32  | | Case 2:
% 201.35/33.32  | | | 
% 201.35/33.32  | | |   (118)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.32  | | | 
% 201.35/33.32  | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (12), (18), (19), (22),
% 201.35/33.32  | | |            (23), (26), (27), (29), (30), (32), (37), (38), (39), (40),
% 201.35/33.32  | | |            (41), (46), (56), (66), (72), (74), (82), (93), (94), (96),
% 201.35/33.32  | | |            (98), (102), (106), (107), (118) are inconsistent by sub-proof
% 201.35/33.32  | | |            #545.
% 201.35/33.32  | | | 
% 201.35/33.32  | | End of split
% 201.35/33.32  | | 
% 201.35/33.32  | End of split
% 201.35/33.32  | 
% 201.35/33.32  End of proof
% 201.35/33.32  
% 201.35/33.32  Sub-proof #229 shows that the following formulas are inconsistent:
% 201.35/33.32  ----------------------------------------------------------------
% 201.35/33.32    (1)   ~ (all_52_15 = all_52_23)
% 201.35/33.32    (2)   ~ (all_52_25 = all_52_27)
% 201.35/33.32    (3)  all_58_14 = all_52_23
% 201.35/33.32    (4)   ~ (e3 = e1)
% 201.35/33.32    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.32    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.32    (7)   ~ (all_52_5 = all_52_13)
% 201.35/33.32    (8)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 201.35/33.32    (9)  all_58_1 = all_52_9
% 201.35/33.32    (10)   ~ (all_52_9 = all_52_13)
% 201.35/33.32    (11)   ~ (e3 = e0)
% 201.35/33.32    (12)  op(e2, e3) = all_52_3
% 201.35/33.32    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.33    (14)  op(e0, e2) = all_52_15
% 201.35/33.33    (15)   ~ (all_52_7 = all_52_15)
% 201.35/33.33    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.33    (17)   ~ (all_52_17 = all_52_25)
% 201.35/33.33    (18)   ~ (all_52_3 = all_6_2)
% 201.35/33.33    (19)  all_50_1 = all_14_1
% 201.35/33.33    (20)  all_58_0 = all_6_2
% 201.35/33.33    (21)  op(all_14_2, e0) = all_14_1
% 201.35/33.33    (22)  all_56_4 = all_52_3
% 201.35/33.33    (23)  op(e3, all_6_1) = e1
% 201.35/33.33    (24)   ~ (all_52_17 = all_10_2)
% 201.35/33.33    (25)  op(e3, e0) = all_52_25
% 201.35/33.33    (26)  op(all_52_5, all_52_5) = all_52_4
% 201.35/33.33    (27)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.33    (28)   ~ (all_52_27 = all_52_29)
% 201.35/33.33    (29)  all_58_13 = all_52_15
% 201.35/33.33    (30)  all_58_9 = all_52_25
% 201.35/33.33    (31)   ~ (all_52_29 = all_14_2)
% 201.35/33.33    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.35/33.33    (33)  op(e1, e3) = all_52_5
% 201.35/33.33    (34)  op(e2, e2) = all_4_2
% 201.35/33.33    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.35/33.33    (36)   ~ (all_52_3 = all_52_5)
% 201.35/33.33    (37)  all_58_11 = all_52_29
% 201.35/33.33    (38)  all_56_5 = all_4_2
% 201.35/33.33    (39)   ~ (all_52_25 = all_14_2)
% 201.35/33.33    (40)   ~ (all_52_9 = all_52_15)
% 201.35/33.33    (41)   ~ (all_52_3 = all_52_27)
% 201.35/33.33    (42)  op(all_10_2, e1) = all_10_1
% 201.35/33.33    (43)  all_46_2 = all_6_2
% 201.35/33.33    (44)  op(all_6_2, all_6_2) = all_52_0
% 201.35/33.33    (45)   ~ (all_52_7 = all_6_2)
% 201.35/33.33    (46)  op(e0, e0) = all_14_2
% 201.35/33.33    (47)  op(all_52_29, all_52_29) = e1
% 201.35/33.33    (48)  all_56_15 = all_14_2
% 201.35/33.33    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.33    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.35/33.33    (51)  all_56_11 = all_52_29
% 201.35/33.33    (52)   ~ (all_4_1 = e1)
% 201.35/33.33    (53)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.35/33.33    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.33    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.33    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.35/33.33    (57)   ~ (e2 = e1)
% 201.35/33.33    (58)  all_58_10 = all_52_27
% 201.35/33.33    (59)  all_56_8 = all_52_5
% 201.35/33.33    (60)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.33    (61)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.33    (62)   ~ (all_52_25 = all_52_29)
% 201.35/33.33    (63)   ~ (all_52_29 = all_10_2)
% 201.35/33.33    (64)  all_58_7 = all_52_13
% 201.35/33.33    (65)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.33    (66)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.35/33.33    (67)   ~ (all_52_5 = all_52_7)
% 201.35/33.33    (68)  all_58_12 = all_52_7
% 201.35/33.33    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.33    (70)   ~ (all_52_7 = all_14_2)
% 201.35/33.33    (71)   ~ (all_14_2 = e0)
% 201.35/33.33    (72)  all_58_2 = all_52_3
% 201.35/33.33    (73)  all_56_2 = all_52_17
% 201.35/33.33    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.33    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.33    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.35/33.33    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.33    (78)   ~ (e2 = e0)
% 201.35/33.33    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.35/33.33    (80)  op(all_4_2, e2) = all_4_1
% 201.35/33.33    (81)  op(all_52_25, all_52_25) = e3
% 201.35/33.33    (82)   ~ (all_52_5 = all_52_29)
% 201.35/33.33    (83)   ~ (all_52_15 = all_14_2)
% 201.35/33.33    (84)   ~ (all_52_19 = all_52_27)
% 201.35/33.33    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.35/33.33    (86)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.35/33.33    (87)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.35/33.33    (88)  op(e3, e1) = all_52_17
% 201.35/33.33    (89)  op(all_52_27, all_52_27) = e2
% 201.35/33.33    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.35/33.33    (91)  op(e0, e3) = all_52_7
% 201.35/33.33    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.33    (93)   ~ (all_52_9 = all_52_25)
% 201.35/33.33    (94)  all_58_15 = all_14_2
% 201.35/33.33    (95)   ~ (all_52_19 = all_10_2)
% 201.35/33.33    (96)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.33    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.35/33.33    (98)  all_58_8 = all_10_2
% 201.35/33.33    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.35/33.33    (100)   ~ (all_52_5 = all_10_2)
% 201.35/33.33    (101)   ~ (all_52_23 = all_14_2)
% 201.35/33.33    (102)  all_56_12 = all_52_7
% 201.35/33.33    (103)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.33    (104)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.35/33.33    (105)   ~ (all_52_25 = all_6_2)
% 201.35/33.33    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.33    (107)   ~ (all_52_9 = all_4_2)
% 201.35/33.33    (108)   ~ (all_52_5 = all_6_2)
% 201.35/33.33    (109)   ~ (all_52_9 = all_6_2)
% 201.35/33.33    (110)   ~ (all_52_13 = all_52_15)
% 201.35/33.33    (111)  all_56_0 = all_6_2
% 201.35/33.33    (112)  op(e3, e3) = all_6_2
% 201.35/33.33    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.33    (114)   ~ (all_52_27 = all_14_2)
% 201.35/33.33    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.33    (116)  all_56_14 = all_52_23
% 201.35/33.33    (117)  all_56_3 = all_52_25
% 201.35/33.33    (118)  op(e0, all_14_1) = e2
% 201.35/33.33    (119)   ~ (all_52_3 = all_52_7)
% 201.35/33.33    (120)  all_58_5 = all_52_19
% 201.35/33.33    (121)  all_56_1 = all_52_9
% 201.35/33.33    (122)   ~ (all_52_15 = all_4_2)
% 201.35/33.33    (123)   ~ (all_52_27 = all_4_2)
% 201.35/33.33    (124)  all_58_6 = all_52_5
% 201.35/33.33    (125)  op(e3, e2) = all_52_9
% 201.35/33.33    (126)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.33    (127)   ~ (all_52_17 = all_6_2)
% 201.35/33.33    (128)   ~ (e1 = e0)
% 201.35/33.33    (129)  op(all_14_2, all_14_2) = e0
% 201.35/33.33    (130)   ~ (e3 = e2)
% 201.35/33.33    (131)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.33    (132)  all_46_1 = all_6_1
% 201.35/33.33    (133)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.35/33.33    (134)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.33    (135)  op(e1, e1) = all_10_2
% 201.35/33.33    (136)   ~ (all_52_23 = all_10_2)
% 201.35/33.33    (137)   ~ (all_52_7 = all_52_23)
% 201.35/33.33    (138)   ~ (all_52_17 = all_52_19)
% 201.35/33.33    (139)  all_58_3 = all_4_2
% 201.35/33.33    (140)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.35/33.33    (141)  all_56_13 = all_52_15
% 201.35/33.33    (142)   ~ (all_52_3 = all_4_2)
% 201.35/33.33    (143)   ~ (all_52_19 = all_4_2)
% 201.35/33.33    (144)   ~ (all_52_17 = all_52_23)
% 201.35/33.33    (145)  op(all_6_2, e3) = all_6_1
% 201.35/33.33    (146)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.35/33.33    (147)  all_58_4 = all_52_17
% 201.35/33.33    (148)  all_50_2 = all_14_2
% 201.35/33.33  
% 201.35/33.33  Begin of proof
% 201.35/33.33  | 
% 201.35/33.33  | BETA: splitting (99) gives:
% 201.35/33.33  | 
% 201.35/33.33  | Case 1:
% 201.35/33.33  | | 
% 201.35/33.33  | |   (149)  all_56_15 = e3
% 201.35/33.33  | | 
% 201.35/33.33  | | COMBINE_EQS: (48), (149) imply:
% 201.35/33.33  | |   (150)  all_14_2 = e3
% 201.35/33.33  | | 
% 201.35/33.33  | | COMBINE_EQS: (148), (150) imply:
% 201.35/33.33  | |   (151)  all_50_2 = e3
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (70), (150) imply:
% 201.35/33.33  | |   (152)   ~ (all_52_7 = e3)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (83), (150) imply:
% 201.35/33.33  | |   (153)   ~ (all_52_15 = e3)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (39), (150) imply:
% 201.35/33.33  | |   (154)   ~ (all_52_25 = e3)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (129), (150) imply:
% 201.35/33.33  | |   (155)  op(e3, e3) = e0
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (21), (150) imply:
% 201.35/33.33  | |   (156)  op(e3, e0) = all_14_1
% 201.35/33.33  | | 
% 201.35/33.33  | | BETA: splitting (8) gives:
% 201.35/33.33  | | 
% 201.35/33.33  | | Case 1:
% 201.35/33.33  | | | 
% 201.35/33.33  | | |   (157)   ~ (all_50_1 = e1)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (19), (157) imply:
% 201.35/33.33  | | |   (158)   ~ (all_14_1 = e1)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3,
% 201.35/33.33  | | |              simplifying with (25), (156) gives:
% 201.35/33.33  | | |   (159)  all_52_25 = all_14_1
% 201.35/33.33  | | | 
% 201.35/33.33  | | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying with
% 201.35/33.33  | | |              (112), (155) gives:
% 201.35/33.33  | | |   (160)  all_6_2 = e0
% 201.35/33.33  | | | 
% 201.35/33.33  | | | COMBINE_EQS: (117), (159) imply:
% 201.35/33.33  | | |   (161)  all_56_3 = all_14_1
% 201.35/33.33  | | | 
% 201.35/33.33  | | | COMBINE_EQS: (30), (159) imply:
% 201.35/33.33  | | |   (162)  all_58_9 = all_14_1
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (18), (160) imply:
% 201.35/33.33  | | |   (163)   ~ (all_52_3 = e0)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (108), (160) imply:
% 201.35/33.33  | | |   (164)   ~ (all_52_5 = e0)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (45), (160) imply:
% 201.35/33.33  | | |   (165)   ~ (all_52_7 = e0)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (93), (159) imply:
% 201.35/33.33  | | |   (166)   ~ (all_52_9 = all_14_1)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (109), (160) imply:
% 201.35/33.33  | | |   (167)   ~ (all_52_9 = e0)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (105), (159), (160) imply:
% 201.35/33.33  | | |   (168)   ~ (all_14_1 = e0)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (154), (159) imply:
% 201.35/33.33  | | |   (169)   ~ (all_14_1 = e3)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (81), (159) imply:
% 201.35/33.33  | | |   (170)  op(all_14_1, all_14_1) = e3
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (145), (160) imply:
% 201.35/33.33  | | |   (171)  op(e0, e3) = all_6_1
% 201.35/33.33  | | | 
% 201.35/33.33  | | | BETA: splitting (106) gives:
% 201.35/33.33  | | | 
% 201.35/33.33  | | | Case 1:
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | |   (172)  all_56_3 = e3
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | COMBINE_EQS: (161), (172) imply:
% 201.35/33.33  | | | |   (173)  all_14_1 = e3
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | REDUCE: (169), (173) imply:
% 201.35/33.33  | | | |   (174)  $false
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | CLOSE: (174) is inconsistent.
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | Case 2:
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | |   (175)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | BETA: splitting (175) gives:
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | Case 1:
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | |   (176)  all_56_3 = e2
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | COMBINE_EQS: (161), (176) imply:
% 201.35/33.33  | | | | |   (177)  all_14_1 = e2
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (170), (177) imply:
% 201.35/33.33  | | | | |   (178)  op(e2, e2) = e3
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (118), (177) imply:
% 201.35/33.33  | | | | |   (179)  op(e0, e2) = e2
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | GROUND_INST: instantiating (6) with all_52_15, e2, e2, e0, simplifying
% 201.35/33.33  | | | | |              with (14), (179) gives:
% 201.35/33.33  | | | | |   (180)  all_52_15 = e2
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | GROUND_INST: instantiating (6) with all_52_7, all_6_1, e3, e0,
% 201.35/33.33  | | | | |              simplifying with (91), (171) gives:
% 201.35/33.33  | | | | |   (181)  all_52_7 = all_6_1
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | GROUND_INST: instantiating (6) with all_4_2, e3, e2, e2, simplifying
% 201.35/33.33  | | | | |              with (34), (178) gives:
% 201.35/33.33  | | | | |   (182)  all_4_2 = e3
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | COMBINE_EQS: (102), (181) imply:
% 201.35/33.33  | | | | |   (183)  all_56_12 = all_6_1
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (119), (181) imply:
% 201.35/33.33  | | | | |   (184)   ~ (all_52_3 = all_6_1)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (142), (182) imply:
% 201.35/33.33  | | | | |   (185)   ~ (all_52_3 = e3)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (67), (181) imply:
% 201.35/33.33  | | | | |   (186)   ~ (all_52_5 = all_6_1)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (15), (180), (181) imply:
% 201.35/33.33  | | | | |   (187)   ~ (all_6_1 = e2)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (152), (181) imply:
% 201.35/33.33  | | | | |   (188)   ~ (all_6_1 = e3)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (165), (181) imply:
% 201.35/33.33  | | | | |   (189)   ~ (all_6_1 = e0)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (107), (182) imply:
% 201.35/33.33  | | | | |   (190)   ~ (all_52_9 = e3)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | BETA: splitting (13) gives:
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | Case 1:
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | |   (191)  all_56_12 = e3
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | | REF_CLOSE: (183), (188), (191) are inconsistent by sub-proof #1347.
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | Case 2:
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | |   (192)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | | BETA: splitting (192) gives:
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | | Case 1:
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | |   (193)  all_56_12 = e2
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | | REF_CLOSE: (183), (187), (193) are inconsistent by sub-proof
% 201.35/33.33  | | | | | | |            #1346.
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | Case 2:
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | |   (194)  all_56_12 = e1 | all_56_12 = e0
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | | BETA: splitting (194) gives:
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | | Case 1:
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | |   (195)  all_56_12 = e1
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | COMBINE_EQS: (183), (195) imply:
% 201.35/33.33  | | | | | | | |   (196)  all_6_1 = e1
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | SIMP: (196) implies:
% 201.35/33.33  | | | | | | | |   (197)  all_6_1 = e1
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | REDUCE: (184), (197) imply:
% 201.35/33.33  | | | | | | | |   (198)   ~ (all_52_3 = e1)
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | REDUCE: (186), (197) imply:
% 201.35/33.33  | | | | | | | |   (199)   ~ (all_52_5 = e1)
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | BETA: splitting (131) gives:
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | Case 1:
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | |   (200)  all_56_1 = e3
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | COMBINE_EQS: (121), (200) imply:
% 201.35/33.33  | | | | | | | | |   (201)  all_52_9 = e3
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | REDUCE: (190), (201) imply:
% 201.35/33.33  | | | | | | | | |   (202)  $false
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | CLOSE: (202) is inconsistent.
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | Case 2:
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | |   (203)   ~ (all_56_1 = e3)
% 201.35/33.33  | | | | | | | | |   (204)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | BETA: splitting (77) gives:
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | Case 1:
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | |   (205)  all_56_4 = e3
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | | COMBINE_EQS: (22), (205) imply:
% 201.35/33.33  | | | | | | | | | |   (206)  all_52_3 = e3
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | | REDUCE: (185), (206) imply:
% 201.35/33.33  | | | | | | | | | |   (207)  $false
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | | CLOSE: (207) is inconsistent.
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | Case 2:
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | |   (208)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | | REF_CLOSE: (6), (7), (9), (22), (29), (36), (50), (52), (59),
% 201.35/33.33  | | | | | | | | | |            (64), (80), (92), (97), (100), (121), (125),
% 201.35/33.33  | | | | | | | | | |            (135), (139), (153), (161), (162), (163), (164),
% 201.35/33.33  | | | | | | | | | |            (166), (167), (168), (170), (175), (190), (198),
% 201.35/33.33  | | | | | | | | | |            (199), (204), (208) are inconsistent by sub-proof
% 201.35/33.33  | | | | | | | | | |            #558.
% 201.35/33.33  | | | | | | | | | | 
% 201.35/33.33  | | | | | | | | | End of split
% 201.35/33.33  | | | | | | | | | 
% 201.35/33.33  | | | | | | | | End of split
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | Case 2:
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | |   (209)  all_56_12 = e0
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | | REF_CLOSE: (183), (189), (209) are inconsistent by sub-proof
% 201.35/33.33  | | | | | | | |            #1345.
% 201.35/33.33  | | | | | | | | 
% 201.35/33.33  | | | | | | | End of split
% 201.35/33.33  | | | | | | | 
% 201.35/33.33  | | | | | | End of split
% 201.35/33.33  | | | | | | 
% 201.35/33.33  | | | | | End of split
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | Case 2:
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | |   (210)  all_56_3 = e1 | all_56_3 = e0
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REF_CLOSE: (158), (161), (168), (210) are inconsistent by sub-proof
% 201.35/33.33  | | | | |            #806.
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | End of split
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | End of split
% 201.35/33.33  | | | 
% 201.35/33.33  | | Case 2:
% 201.35/33.33  | | | 
% 201.35/33.33  | | |   (211)   ~ (all_50_2 = e3)
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REDUCE: (151), (211) imply:
% 201.35/33.33  | | |   (212)  $false
% 201.35/33.33  | | | 
% 201.35/33.33  | | | CLOSE: (212) is inconsistent.
% 201.35/33.33  | | | 
% 201.35/33.33  | | End of split
% 201.35/33.33  | | 
% 201.35/33.33  | Case 2:
% 201.35/33.33  | | 
% 201.35/33.33  | |   (213)   ~ (all_56_15 = e3)
% 201.35/33.33  | |   (214)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (48), (213) imply:
% 201.35/33.33  | |   (215)   ~ (all_14_2 = e3)
% 201.35/33.33  | | 
% 201.35/33.33  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (15), (16),
% 201.35/33.33  | |            (17), (18), (20), (22), (23), (24), (25), (26), (27), (28), (29),
% 201.35/33.33  | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 201.35/33.33  | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 201.35/33.33  | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 201.35/33.33  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 201.35/33.33  | |            (75), (76), (77), (78), (79), (81), (82), (83), (84), (85), (86),
% 201.35/33.33  | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 201.35/33.33  | |            (98), (100), (101), (103), (104), (105), (106), (107), (108),
% 201.35/33.33  | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 201.35/33.33  | |            (119), (120), (121), (122), (123), (124), (125), (126), (127),
% 201.35/33.33  | |            (128), (129), (130), (131), (132), (133), (134), (135), (136),
% 201.35/33.33  | |            (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 201.35/33.33  | |            (146), (147), (214), (215) are inconsistent by sub-proof #272.
% 201.35/33.33  | | 
% 201.35/33.33  | End of split
% 201.35/33.33  | 
% 201.35/33.33  End of proof
% 201.35/33.33  
% 201.35/33.33  Sub-proof #230 shows that the following formulas are inconsistent:
% 201.35/33.33  ----------------------------------------------------------------
% 201.35/33.33    (1)   ~ (all_52_15 = all_52_23)
% 201.35/33.33    (2)  all_58_14 = all_52_23
% 201.35/33.33    (3)   ~ (e3 = e1)
% 201.35/33.33    (4)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.33    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.33    (6)   ~ (all_52_5 = all_52_13)
% 201.35/33.33    (7)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 201.35/33.33    (8)  all_58_1 = all_52_9
% 201.35/33.33    (9)   ~ (all_52_9 = all_52_13)
% 201.35/33.33    (10)  op(e2, e3) = all_52_3
% 201.35/33.33    (11)  op(e0, e2) = all_52_15
% 201.35/33.33    (12)   ~ (all_52_3 = all_52_19)
% 201.35/33.33    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.33    (14)   ~ (all_52_17 = all_52_25)
% 201.35/33.33    (15)   ~ (all_52_3 = all_6_2)
% 201.35/33.33    (16)  all_50_1 = all_14_1
% 201.35/33.33    (17)  all_58_0 = all_6_2
% 201.35/33.33    (18)  all_56_4 = all_52_3
% 201.35/33.33    (19)  op(e3, all_6_1) = e1
% 201.35/33.33    (20)   ~ (all_52_17 = all_10_2)
% 201.35/33.33    (21)  op(e3, e0) = all_52_25
% 201.35/33.33    (22)  op(all_52_5, all_52_5) = all_52_4
% 201.35/33.33    (23)  all_58_13 = all_52_15
% 201.35/33.33    (24)  all_58_9 = all_52_25
% 201.35/33.33    (25)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.33    (26)  op(e1, e3) = all_52_5
% 201.35/33.33    (27)  op(e2, e2) = all_4_2
% 201.35/33.33    (28)   ~ (all_52_3 = all_52_5)
% 201.35/33.33    (29)  all_58_11 = all_52_29
% 201.35/33.33    (30)   ~ (all_52_9 = all_52_15)
% 201.35/33.33    (31)  op(all_10_2, e1) = all_10_1
% 201.35/33.33    (32)  op(all_6_2, all_6_2) = all_52_0
% 201.35/33.33    (33)   ~ (all_52_7 = all_6_2)
% 201.35/33.33    (34)  op(e0, e0) = all_14_2
% 201.35/33.33    (35)  all_58_15 = e3
% 201.35/33.33    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.33    (37)  all_56_11 = all_52_29
% 201.35/33.33    (38)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.33    (39)   ~ (e2 = e1)
% 201.35/33.33    (40)   ~ (all_52_13 = all_10_2)
% 201.35/33.33    (41)  op(all_10_2, all_10_2) = e1
% 201.35/33.33    (42)  all_58_10 = all_52_27
% 201.35/33.33    (43)  all_56_8 = all_52_5
% 201.35/33.33    (44)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.33    (45)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.33    (46)   ~ (all_52_19 = all_52_23)
% 201.35/33.33    (47)   ~ (all_52_29 = all_10_2)
% 201.35/33.33    (48)  all_58_7 = all_52_13
% 201.35/33.33    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.33    (50)  op(all_52_19, all_52_19) = e2
% 201.35/33.33    (51)   ~ (all_52_5 = all_52_7)
% 201.35/33.33    (52)  all_58_12 = all_52_7
% 201.35/33.33    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.33    (54)   ~ (all_52_7 = e3)
% 201.35/33.33    (55)  all_58_2 = all_52_3
% 201.35/33.33    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.33    (57)  all_56_2 = all_52_17
% 201.35/33.33    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.33    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.33    (60)   ~ (all_52_29 = e3)
% 201.35/33.33    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.35/33.33    (62)   ~ (all_52_25 = e3)
% 201.35/33.33    (63)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.33    (64)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.35/33.33    (65)   ~ (all_52_23 = e3)
% 201.35/33.33    (66)  op(e3, e3) = all_52_30
% 201.35/33.33    (67)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.33    (68)  all_56_6 = all_52_19
% 201.35/33.33    (69)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.35/33.33    (70)   ~ (all_52_27 = e3)
% 201.35/33.33    (71)  all_50_2 = e3
% 201.35/33.33    (72)   ~ (all_52_13 = all_4_2)
% 201.35/33.33    (73)  op(e3, e1) = all_52_17
% 201.35/33.33    (74)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.33    (75)   ~ (all_52_19 = all_10_2)
% 201.35/33.33    (76)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.35/33.33    (77)  all_58_8 = all_10_2
% 201.35/33.33    (78)   ~ (all_52_5 = all_10_2)
% 201.35/33.33    (79)  op(all_52_29, all_52_29) = all_52_28
% 201.35/33.33    (80)   ~ (all_52_25 = all_6_2)
% 201.35/33.33    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.33    (82)   ~ (all_52_9 = all_4_2)
% 201.35/33.33    (83)   ~ (all_52_5 = all_6_2)
% 201.35/33.33    (84)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.35/33.33    (85)   ~ (all_52_9 = all_6_2)
% 201.35/33.33    (86)  op(e3, e3) = all_6_2
% 201.35/33.33    (87)  op(e3, e0) = all_14_1
% 201.35/33.33    (88)   ~ (all_52_27 = all_14_2)
% 201.35/33.33    (89)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.33    (90)  all_56_14 = all_52_23
% 201.35/33.33    (91)  all_56_3 = all_52_25
% 201.35/33.33    (92)  op(e0, all_14_1) = e2
% 201.35/33.33    (93)  all_58_5 = all_52_19
% 201.35/33.33    (94)   ~ (all_52_15 = all_4_2)
% 201.35/33.33    (95)   ~ (all_52_27 = all_4_2)
% 201.35/33.33    (96)  op(all_52_17, all_52_17) = e3
% 201.35/33.33    (97)  all_58_6 = all_52_5
% 201.35/33.33    (98)   ~ (all_52_17 = all_6_2)
% 201.35/33.33    (99)   ~ (e1 = e0)
% 201.35/33.33    (100)   ~ (e3 = e2)
% 201.35/33.33    (101)   ~ (all_52_9 = all_52_17)
% 201.35/33.33    (102)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.33    (103)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.33    (104)  op(e1, e1) = all_10_2
% 201.35/33.33    (105)   ~ (all_52_17 = all_52_19)
% 201.35/33.33    (106)  all_58_3 = all_4_2
% 201.35/33.33    (107)   ~ (all_52_3 = all_4_2)
% 201.35/33.33    (108)   ~ (all_52_17 = all_52_23)
% 201.35/33.33    (109)  op(all_6_2, e3) = all_6_1
% 201.35/33.33    (110)   ~ (all_52_13 = all_52_29)
% 201.35/33.33    (111)  all_58_4 = all_52_17
% 201.35/33.33    (112)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.33  
% 201.35/33.33  Begin of proof
% 201.35/33.33  | 
% 201.35/33.33  | BETA: splitting (7) gives:
% 201.35/33.33  | 
% 201.35/33.33  | Case 1:
% 201.35/33.33  | | 
% 201.35/33.33  | |   (113)   ~ (all_50_1 = e1)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (16), (113) imply:
% 201.35/33.33  | |   (114)   ~ (all_14_1 = e1)
% 201.35/33.33  | | 
% 201.35/33.33  | | GROUND_INST: instantiating (5) with all_52_25, all_14_1, e0, e3, simplifying
% 201.35/33.33  | |              with (21), (87) gives:
% 201.35/33.33  | |   (115)  all_52_25 = all_14_1
% 201.35/33.33  | | 
% 201.35/33.33  | | GROUND_INST: instantiating (5) with all_6_2, all_52_30, e3, e3, simplifying
% 201.35/33.33  | |              with (66), (86) gives:
% 201.35/33.33  | |   (116)  all_52_30 = all_6_2
% 201.35/33.33  | | 
% 201.35/33.33  | | COMBINE_EQS: (91), (115) imply:
% 201.35/33.33  | |   (117)  all_56_3 = all_14_1
% 201.35/33.33  | | 
% 201.35/33.33  | | COMBINE_EQS: (24), (115) imply:
% 201.35/33.33  | |   (118)  all_58_9 = all_14_1
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (14), (115) imply:
% 201.35/33.33  | |   (119)   ~ (all_52_17 = all_14_1)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (80), (115) imply:
% 201.35/33.33  | |   (120)   ~ (all_14_1 = all_6_2)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (62), (115) imply:
% 201.35/33.33  | |   (121)   ~ (all_14_1 = e3)
% 201.35/33.33  | | 
% 201.35/33.33  | | REDUCE: (112), (115) imply:
% 201.35/33.33  | |   (122)  op(all_14_1, all_14_1) = all_52_24
% 201.35/33.33  | | 
% 201.35/33.33  | | BETA: splitting (81) gives:
% 201.35/33.33  | | 
% 201.35/33.33  | | Case 1:
% 201.35/33.33  | | | 
% 201.35/33.33  | | |   (123)  all_56_3 = e3
% 201.35/33.33  | | | 
% 201.35/33.33  | | | REF_CLOSE: (117), (121), (123) are inconsistent by sub-proof #1200.
% 201.35/33.33  | | | 
% 201.35/33.33  | | Case 2:
% 201.35/33.33  | | | 
% 201.35/33.33  | | |   (124)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.33  | | | 
% 201.35/33.33  | | | BETA: splitting (49) gives:
% 201.35/33.33  | | | 
% 201.35/33.33  | | | Case 1:
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | |   (125)  all_56_14 = e3
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | REF_CLOSE: (65), (90), (125) are inconsistent by sub-proof #1286.
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | Case 2:
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | |   (126)   ~ (all_56_14 = e3)
% 201.35/33.33  | | | |   (127)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | BETA: splitting (67) gives:
% 201.35/33.33  | | | | 
% 201.35/33.33  | | | | Case 1:
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | |   (128)  all_58_12 = e1
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | COMBINE_EQS: (52), (128) imply:
% 201.35/33.33  | | | | |   (129)  all_52_7 = e1
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | SIMP: (129) implies:
% 201.35/33.33  | | | | |   (130)  all_52_7 = e1
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (51), (130) imply:
% 201.35/33.33  | | | | |   (131)   ~ (all_52_5 = e1)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (33), (130) imply:
% 201.35/33.33  | | | | |   (132)   ~ (all_6_2 = e1)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | SIMP: (132) implies:
% 201.35/33.33  | | | | |   (133)   ~ (all_6_2 = e1)
% 201.35/33.33  | | | | | 
% 201.35/33.33  | | | | | REDUCE: (13), (130) imply:
% 201.35/33.33  | | | | |   (134)  op(e1, e1) = all_52_6
% 201.35/33.33  | | | | | 
% 201.35/33.34  | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_6, e1, e1,
% 201.35/33.34  | | | | |              simplifying with (104), (134) gives:
% 201.35/33.34  | | | | |   (135)  all_52_6 = all_10_2
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | | BETA: splitting (64) gives:
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | | Case 1:
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | |   (136)  all_58_0 = e1
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | COMBINE_EQS: (17), (136) imply:
% 201.35/33.34  | | | | | |   (137)  all_6_2 = e1
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | REDUCE: (133), (137) imply:
% 201.35/33.34  | | | | | |   (138)  $false
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | CLOSE: (138) is inconsistent.
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | Case 2:
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | |   (139)   ~ (all_58_0 = e1)
% 201.35/33.34  | | | | | |   (140)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | BETA: splitting (76) gives:
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | Case 1:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | |   (141)  all_56_8 = e3
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | COMBINE_EQS: (43), (141) imply:
% 201.35/33.34  | | | | | | |   (142)  all_52_5 = e3
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | SIMP: (142) implies:
% 201.35/33.34  | | | | | | |   (143)  all_52_5 = e3
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | REDUCE: (28), (143) imply:
% 201.35/33.34  | | | | | | |   (144)   ~ (all_52_3 = e3)
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | REDUCE: (6), (143) imply:
% 201.35/33.34  | | | | | | |   (145)   ~ (all_52_13 = e3)
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | SIMP: (145) implies:
% 201.35/33.34  | | | | | | |   (146)   ~ (all_52_13 = e3)
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | REDUCE: (22), (143) imply:
% 201.35/33.34  | | | | | | |   (147)  op(e3, e3) = all_52_4
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 201.35/33.34  | | | | | | |              simplifying with (86), (147) gives:
% 201.35/33.34  | | | | | | |   (148)  all_52_4 = all_6_2
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | BETA: splitting (74) gives:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | |   (149)  all_58_1 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | COMBINE_EQS: (8), (149) imply:
% 201.35/33.34  | | | | | | | |   (150)  all_52_9 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (101), (150) imply:
% 201.35/33.34  | | | | | | | |   (151)   ~ (all_52_17 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (151) implies:
% 201.35/33.34  | | | | | | | |   (152)   ~ (all_52_17 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (82), (150) imply:
% 201.35/33.34  | | | | | | | |   (153)   ~ (all_4_2 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (153) implies:
% 201.35/33.34  | | | | | | | |   (154)   ~ (all_4_2 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | BETA: splitting (102) gives:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | |   (155)  all_58_4 = e3
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REF_CLOSE: (111), (152), (155) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | |            #1302.
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | |   (156)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | BETA: splitting (36) gives:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (157)  all_58_2 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REF_CLOSE: (55), (144), (157) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | |            #1369.
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (158)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | BETA: splitting (158) gives:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (159)  all_58_3 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | COMBINE_EQS: (106), (159) imply:
% 201.35/33.34  | | | | | | | | | | |   (160)  all_4_2 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (154), (160) imply:
% 201.35/33.34  | | | | | | | | | | |   (161)  $false
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (162)  all_58_5 = e3 | all_58_10 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | BETA: splitting (162) gives:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (163)  all_58_5 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | COMBINE_EQS: (93), (163) imply:
% 201.35/33.34  | | | | | | | | | | | |   (164)  all_52_19 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | SIMP: (164) implies:
% 201.35/33.34  | | | | | | | | | | | |   (165)  all_52_19 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (46), (165) imply:
% 201.35/33.34  | | | | | | | | | | | |   (166)   ~ (all_52_23 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (75), (165) imply:
% 201.35/33.34  | | | | | | | | | | | |   (167)   ~ (all_10_2 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | SIMP: (167) implies:
% 201.35/33.34  | | | | | | | | | | | |   (168)   ~ (all_10_2 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | BETA: splitting (140) gives:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (169)  all_58_1 = e1
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (65), (77), (149), (156), (163), (168),
% 201.35/33.34  | | | | | | | | | | | | |            (169) are inconsistent by sub-proof #1050.
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (170)  all_58_4 = e1 | all_58_9 = e1
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | BETA: splitting (170) gives:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | |   (171)  all_58_4 = e1
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REF_CLOSE: (5), (96), (104), (111), (168), (171) are
% 201.35/33.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #1059.
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | |   (172)  all_58_9 = e1
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REF_CLOSE: (114), (118), (172) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | | |            #610.
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (173)  all_58_10 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REF_CLOSE: (42), (70), (173) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | |            #1301.
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | |   (174)   ~ (all_58_1 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (8), (174) imply:
% 201.35/33.34  | | | | | | | |   (175)   ~ (all_52_9 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (17), (24), (29), (32), (37),
% 201.35/33.34  | | | | | | | |            (41), (47), (48), (50), (53), (62), (65), (69), (77),
% 201.35/33.34  | | | | | | | |            (79), (83), (86), (89), (93), (96), (97), (98),
% 201.35/33.34  | | | | | | | |            (100), (102), (111), (146), (175) are inconsistent by
% 201.35/33.34  | | | | | | | |            sub-proof #281.
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | End of split
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | Case 2:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | |   (176)   ~ (all_56_8 = e3)
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | REDUCE: (43), (176) imply:
% 201.35/33.34  | | | | | | |   (177)   ~ (all_52_5 = e3)
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | BETA: splitting (53) gives:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | |   (178)  all_58_6 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REF_CLOSE: (97), (177), (178) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | |            #1328.
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | |   (179)   ~ (all_58_6 = e3)
% 201.35/33.34  | | | | | | | |   (180)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | BETA: splitting (59) gives:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | |   (181)  all_58_0 = e3
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | COMBINE_EQS: (17), (181) imply:
% 201.35/33.34  | | | | | | | | |   (182)  all_6_2 = e3
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (15), (182) imply:
% 201.35/33.34  | | | | | | | | |   (183)   ~ (all_52_3 = e3)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (32), (182) imply:
% 201.35/33.34  | | | | | | | | |   (184)  op(e3, e3) = all_52_0
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (86), (182) imply:
% 201.35/33.34  | | | | | | | | |   (185)  op(e3, e3) = e3
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REF_CLOSE: (3), (5), (29), (36), (41), (42), (48), (50), (55),
% 201.35/33.34  | | | | | | | | |            (60), (70), (72), (75), (77), (93), (100), (103),
% 201.35/33.34  | | | | | | | | |            (106), (110), (180), (183), (184), (185) are
% 201.35/33.34  | | | | | | | | |            inconsistent by sub-proof #1077.
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | |   (186)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | BETA: splitting (186) gives:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (187)  all_58_2 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | COMBINE_EQS: (55), (187) imply:
% 201.35/33.34  | | | | | | | | | |   (188)  all_52_3 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | SIMP: (188) implies:
% 201.35/33.34  | | | | | | | | | |   (189)  all_52_3 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REDUCE: (12), (189) imply:
% 201.35/33.34  | | | | | | | | | |   (190)   ~ (all_52_19 = e3)
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | SIMP: (190) implies:
% 201.35/33.34  | | | | | | | | | |   (191)   ~ (all_52_19 = e3)
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REDUCE: (15), (189) imply:
% 201.35/33.34  | | | | | | | | | |   (192)   ~ (all_6_2 = e3)
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | SIMP: (192) implies:
% 201.35/33.34  | | | | | | | | | |   (193)   ~ (all_6_2 = e3)
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REDUCE: (4), (189) imply:
% 201.35/33.34  | | | | | | | | | |   (194)  op(e3, e3) = all_52_2
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_2, e3, e3,
% 201.35/33.34  | | | | | | | | | |              simplifying with (86), (194) gives:
% 201.35/33.34  | | | | | | | | | |   (195)  all_52_2 = all_6_2
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | BETA: splitting (89) gives:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (196)  all_58_0 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | COMBINE_EQS: (17), (196) imply:
% 201.35/33.34  | | | | | | | | | | |   (197)  all_6_2 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (193), (197) imply:
% 201.35/33.34  | | | | | | | | | | |   (198)  $false
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (199)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | BETA: splitting (74) gives:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (200)  all_58_1 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | COMBINE_EQS: (8), (200) imply:
% 201.35/33.34  | | | | | | | | | | | |   (201)  all_52_9 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (101), (201) imply:
% 201.35/33.34  | | | | | | | | | | | |   (202)   ~ (all_52_17 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | SIMP: (202) implies:
% 201.35/33.34  | | | | | | | | | | | |   (203)   ~ (all_52_17 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | BETA: splitting (102) gives:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (204)  all_58_4 = e3
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | REF_CLOSE: (111), (203), (204) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | |            #1302.
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (205)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | BETA: splitting (205) gives:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | |   (206)  all_58_5 = e3
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REF_CLOSE: (93), (191), (206) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | | |            #1279.
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | |   (207)  all_58_8 = e3 | all_58_14 = e3
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (41), (65), (77), (86), (133), (207) are
% 201.35/33.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #283.
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (208)   ~ (all_58_1 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (8), (208) imply:
% 201.35/33.34  | | | | | | | | | | | |   (209)   ~ (all_52_9 = e3)
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REF_CLOSE: (5), (8), (24), (62), (86), (96), (98), (111),
% 201.35/33.34  | | | | | | | | | | | |            (199), (209) are inconsistent by sub-proof #1072.
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (210)  all_58_6 = e3 | all_58_12 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REF_CLOSE: (52), (54), (97), (177), (210) are inconsistent by
% 201.35/33.34  | | | | | | | | | |            sub-proof #1243.
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | End of split
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | End of split
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | End of split
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | Case 2:
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | |   (211)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | | BETA: splitting (102) gives:
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | | Case 1:
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | |   (212)  all_58_4 = e3
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | COMBINE_EQS: (111), (212) imply:
% 201.35/33.34  | | | | | |   (213)  all_52_17 = e3
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | SIMP: (213) implies:
% 201.35/33.34  | | | | | |   (214)  all_52_17 = e3
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | REF_CLOSE: (5), (86), (96), (98), (214) are inconsistent by
% 201.35/33.34  | | | | | |            sub-proof #1280.
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | Case 2:
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | |   (215)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | BETA: splitting (89) gives:
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | | Case 1:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | |   (216)  all_58_0 = e3
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | COMBINE_EQS: (17), (216) imply:
% 201.35/33.34  | | | | | | |   (217)  all_6_2 = e3
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | REF_CLOSE: (3), (5), (19), (32), (86), (109), (217) are
% 201.35/33.34  | | | | | | |            inconsistent by sub-proof #290.
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | Case 2:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | |   (218)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | BETA: splitting (218) gives:
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | |   (219)  all_58_1 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | COMBINE_EQS: (8), (219) imply:
% 201.35/33.34  | | | | | | | |   (220)  all_52_9 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (9), (220) imply:
% 201.35/33.34  | | | | | | | |   (221)   ~ (all_52_13 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (221) implies:
% 201.35/33.34  | | | | | | | |   (222)   ~ (all_52_13 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (30), (220) imply:
% 201.35/33.34  | | | | | | | |   (223)   ~ (all_52_15 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (223) implies:
% 201.35/33.34  | | | | | | | |   (224)   ~ (all_52_15 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (101), (220) imply:
% 201.35/33.34  | | | | | | | |   (225)   ~ (all_52_17 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (225) implies:
% 201.35/33.34  | | | | | | | |   (226)   ~ (all_52_17 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (85), (220) imply:
% 201.35/33.34  | | | | | | | |   (227)   ~ (all_6_2 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (227) implies:
% 201.35/33.34  | | | | | | | |   (228)   ~ (all_6_2 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (82), (220) imply:
% 201.35/33.34  | | | | | | | |   (229)   ~ (all_4_2 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | SIMP: (229) implies:
% 201.35/33.34  | | | | | | | |   (230)   ~ (all_4_2 = e3)
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REDUCE: (44), (220) imply:
% 201.35/33.34  | | | | | | | |   (231)  op(e3, e3) = all_52_8
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_8, e3, e3,
% 201.35/33.34  | | | | | | | |              simplifying with (86), (231) gives:
% 201.35/33.34  | | | | | | | |   (232)  all_52_8 = all_6_2
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | BETA: splitting (64) gives:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | |   (233)  all_58_0 = e1
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | COMBINE_EQS: (17), (233) imply:
% 201.35/33.34  | | | | | | | | |   (234)  all_6_2 = e1
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (83), (234) imply:
% 201.35/33.34  | | | | | | | | |   (235)   ~ (all_52_5 = e1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (33), (234) imply:
% 201.35/33.34  | | | | | | | | |   (236)   ~ (all_52_7 = e1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (98), (234) imply:
% 201.35/33.34  | | | | | | | | |   (237)   ~ (all_52_17 = e1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (228), (234) imply:
% 201.35/33.34  | | | | | | | | |   (238)   ~ (e3 = e1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (109), (234) imply:
% 201.35/33.34  | | | | | | | | |   (239)  op(e1, e3) = all_6_1
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | GROUND_INST: instantiating (5) with all_52_5, all_6_1, e3, e1,
% 201.35/33.34  | | | | | | | | |              simplifying with (26), (239) gives:
% 201.35/33.34  | | | | | | | | |   (240)  all_52_5 = all_6_1
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | COMBINE_EQS: (97), (240) imply:
% 201.35/33.34  | | | | | | | | |   (241)  all_58_6 = all_6_1
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (78), (240) imply:
% 201.35/33.34  | | | | | | | | |   (242)   ~ (all_10_2 = all_6_1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | SIMP: (242) implies:
% 201.35/33.34  | | | | | | | | |   (243)   ~ (all_10_2 = all_6_1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (235), (240) imply:
% 201.35/33.34  | | | | | | | | |   (244)   ~ (all_6_1 = e1)
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | REDUCE: (22), (240) imply:
% 201.35/33.34  | | | | | | | | |   (245)  op(all_6_1, all_6_1) = all_52_4
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | BETA: splitting (38) gives:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (246)  all_56_2 = e3
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REF_CLOSE: (57), (226), (246) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | |            #1327.
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (247)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | BETA: splitting (53) gives:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (248)  all_58_6 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | COMBINE_EQS: (241), (248) imply:
% 201.35/33.34  | | | | | | | | | | |   (249)  all_6_1 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | SIMP: (249) implies:
% 201.35/33.34  | | | | | | | | | | |   (250)  all_6_1 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (243), (250) imply:
% 201.35/33.34  | | | | | | | | | | |   (251)   ~ (all_10_2 = e3)
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (245), (250) imply:
% 201.35/33.34  | | | | | | | | | | |   (252)  op(e3, e3) = all_52_4
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (10), (12), (15), (17), (18), (39),
% 201.35/33.34  | | | | | | | | | | |            (50), (52), (55), (61), (63), (65), (77), (86),
% 201.35/33.34  | | | | | | | | | | |            (93), (99), (109), (215), (236), (244), (248),
% 201.35/33.34  | | | | | | | | | | |            (251), (252) are inconsistent by sub-proof #1070.
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (253)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | BETA: splitting (253) gives:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (254)  all_58_7 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | COMBINE_EQS: (48), (254) imply:
% 201.35/33.34  | | | | | | | | | | | |   (255)  all_52_13 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (222), (255) imply:
% 201.35/33.34  | | | | | | | | | | | |   (256)  $false
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (257)  all_58_8 = e3 | all_58_11 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | BETA: splitting (59) gives:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (258)  all_58_0 = e3
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | REF_CLOSE: (3), (233), (258) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | |            #1244.
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (259)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | BETA: splitting (259) gives:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | |   (260)  all_58_2 = e3
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | COMBINE_EQS: (55), (260) imply:
% 201.35/33.34  | | | | | | | | | | | | | |   (261)  all_52_3 = e3
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | SIMP: (261) implies:
% 201.35/33.34  | | | | | | | | | | | | | |   (262)  all_52_3 = e3
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REDUCE: (12), (262) imply:
% 201.35/33.34  | | | | | | | | | | | | | |   (263)   ~ (all_52_19 = e3)
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | SIMP: (263) implies:
% 201.35/33.34  | | | | | | | | | | | | | |   (264)   ~ (all_52_19 = e3)
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | |   (265)  all_58_5 = e3
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | REF_CLOSE: (93), (264), (265) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | | | |            #1279.
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | |   (266)  all_58_8 = e3 | all_58_14 = e3
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | |   (267)  all_58_8 = e3
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (267) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (268)  all_10_2 = e3
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | SIMP: (268) implies:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (269)  all_10_2 = e3
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REDUCE: (31), (269) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (270)  op(e3, e1) = all_10_1
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_17, all_10_1, e1,
% 201.35/33.34  | | | | | | | | | | | | | | | |              e3, simplifying with (73), (270) gives:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (271)  all_52_17 = all_10_1
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (271) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (272)  all_56_2 = all_10_1
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REDUCE: (105), (271) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (273)   ~ (all_52_19 = all_10_1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | SIMP: (273) implies:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (274)   ~ (all_52_19 = all_10_1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REDUCE: (108), (271) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (275)   ~ (all_52_23 = all_10_1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | SIMP: (275) implies:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (276)   ~ (all_52_23 = all_10_1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REDUCE: (119), (271) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (277)   ~ (all_14_1 = all_10_1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (278)   ~ (all_14_1 = all_10_1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REDUCE: (226), (271) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (279)   ~ (all_10_1 = e3)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REDUCE: (237), (271) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | |   (280)   ~ (all_10_1 = e1)
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | |   (281)  all_58_0 = e2
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (233), (281) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | | | | | |            #1273.
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | |   (282)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | |   (283)  all_58_9 = e2
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (283) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | | | |   (284)  all_14_1 = e2
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | | REDUCE: (278), (284) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | | | |   (285)   ~ (all_10_1 = e2)
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | | SIMP: (285) implies:
% 201.35/33.34  | | | | | | | | | | | | | | | | | |   (286)   ~ (all_10_1 = e2)
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (11), (27), (38), (46), (50), (56),
% 201.35/33.34  | | | | | | | | | | | | | | | | | |            (68), (90), (92), (94), (114), (117), (122),
% 201.35/33.34  | | | | | | | | | | | | | | | | | |            (124), (127), (264), (272), (274), (276), (278),
% 201.35/33.34  | | | | | | | | | | | | | | | | | |            (279), (280), (286) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | | | | | | |            #332.
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | |   (287)   ~ (all_58_9 = e2)
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | | REDUCE: (118), (287) imply:
% 201.35/33.34  | | | | | | | | | | | | | | | | | |   (288)   ~ (all_14_1 = e2)
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (23), (27), (48), (74), (96), (100), (106),
% 201.35/33.34  | | | | | | | | | | | | | | | | | |            (111), (118), (222), (224), (230), (282), (288)
% 201.35/33.34  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #357.
% 201.35/33.34  | | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | |   (289)  all_58_14 = e3
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (65), (289) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | | | | |            #1305.
% 201.35/33.34  | | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | |   (290)   ~ (all_58_2 = e3)
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REDUCE: (55), (290) imply:
% 201.35/33.34  | | | | | | | | | | | | | |   (291)   ~ (all_52_3 = e3)
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | | REF_CLOSE: (5), (25), (27), (29), (31), (34), (36), (41),
% 201.35/33.34  | | | | | | | | | | | | | |            (42), (55), (57), (60), (73), (75), (77), (86),
% 201.35/33.34  | | | | | | | | | | | | | |            (88), (93), (95), (96), (98), (106), (230), (247),
% 201.35/33.34  | | | | | | | | | | | | | |            (257), (291) are inconsistent by sub-proof #232.
% 201.35/33.34  | | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | |   (292)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | BETA: splitting (292) gives:
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (293)  all_58_1 = e1
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | COMBINE_EQS: (219), (293) imply:
% 201.35/33.34  | | | | | | | | | |   (294)  e3 = e1
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | REDUCE: (3), (294) imply:
% 201.35/33.34  | | | | | | | | | |   (295)  $false
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | CLOSE: (295) is inconsistent.
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | |   (296)  all_58_4 = e1 | all_58_9 = e1
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | BETA: splitting (296) gives:
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (297)  all_58_4 = e1
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | COMBINE_EQS: (111), (297) imply:
% 201.35/33.34  | | | | | | | | | | |   (298)  all_52_17 = e1
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | SIMP: (298) implies:
% 201.35/33.34  | | | | | | | | | | |   (299)  all_52_17 = e1
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (108), (299) imply:
% 201.35/33.34  | | | | | | | | | | |   (300)   ~ (all_52_23 = e1)
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | SIMP: (300) implies:
% 201.35/33.34  | | | | | | | | | | |   (301)   ~ (all_52_23 = e1)
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (98), (299) imply:
% 201.35/33.34  | | | | | | | | | | |   (302)   ~ (all_6_2 = e1)
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | SIMP: (302) implies:
% 201.35/33.34  | | | | | | | | | | |   (303)   ~ (all_6_2 = e1)
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (226), (299) imply:
% 201.35/33.34  | | | | | | | | | | |   (304)   ~ (e3 = e1)
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REDUCE: (96), (299) imply:
% 201.35/33.34  | | | | | | | | | | |   (305)  op(e1, e1) = e3
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | BETA: splitting (211) gives:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (306)  all_58_13 = e1
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | COMBINE_EQS: (23), (306) imply:
% 201.35/33.34  | | | | | | | | | | | |   (307)  all_52_15 = e1
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | SIMP: (307) implies:
% 201.35/33.34  | | | | | | | | | | | |   (308)  all_52_15 = e1
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (45), (308) imply:
% 201.35/33.34  | | | | | | | | | | | |   (309)  op(e1, e1) = all_52_14
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_14, e1,
% 201.35/33.34  | | | | | | | | | | | |              e1, simplifying with (104), (309) gives:
% 201.35/33.34  | | | | | | | | | | | |   (310)  all_52_14 = all_10_2
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | GROUND_INST: instantiating (5) with e3, all_52_14, e1, e1,
% 201.35/33.34  | | | | | | | | | | | |              simplifying with (305), (309) gives:
% 201.35/33.34  | | | | | | | | | | | |   (311)  all_52_14 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | COMBINE_EQS: (310), (311) imply:
% 201.35/33.34  | | | | | | | | | | | |   (312)  all_10_2 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | SIMP: (312) implies:
% 201.35/33.34  | | | | | | | | | | | |   (313)  all_10_2 = e3
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REDUCE: (41), (313) imply:
% 201.35/33.34  | | | | | | | | | | | |   (314)  op(e3, e3) = e1
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | REF_CLOSE: (5), (86), (303), (314) are inconsistent by
% 201.35/33.34  | | | | | | | | | | | |            sub-proof #885.
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | |   (315)  all_58_14 = e1 | all_58_15 = e1
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | BETA: splitting (315) gives:
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 1:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (316)  all_58_14 = e1
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | REF_CLOSE: (2), (301), (316) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | | | |            #231.
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | |   (317)  all_58_15 = e1
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | COMBINE_EQS: (35), (317) imply:
% 201.35/33.34  | | | | | | | | | | | | |   (318)  e3 = e1
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | REDUCE: (3), (318) imply:
% 201.35/33.34  | | | | | | | | | | | | |   (319)  $false
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | | CLOSE: (319) is inconsistent.
% 201.35/33.34  | | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | |   (320)  all_58_9 = e1
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | | REF_CLOSE: (114), (118), (320) are inconsistent by sub-proof
% 201.35/33.34  | | | | | | | | | | |            #610.
% 201.35/33.34  | | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | | 
% 201.35/33.34  | | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | | 
% 201.35/33.34  | | | | | | | | End of split
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | Case 2:
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | |   (321)  all_58_4 = e3 | all_58_9 = e3
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | | REF_CLOSE: (5), (24), (62), (86), (96), (98), (111), (321) are
% 201.35/33.34  | | | | | | | |            inconsistent by sub-proof #1080.
% 201.35/33.34  | | | | | | | | 
% 201.35/33.34  | | | | | | | End of split
% 201.35/33.34  | | | | | | | 
% 201.35/33.34  | | | | | | End of split
% 201.35/33.34  | | | | | | 
% 201.35/33.34  | | | | | End of split
% 201.35/33.34  | | | | | 
% 201.35/33.34  | | | | End of split
% 201.35/33.34  | | | | 
% 201.35/33.34  | | | End of split
% 201.35/33.34  | | | 
% 201.35/33.34  | | End of split
% 201.35/33.34  | | 
% 201.35/33.34  | Case 2:
% 201.35/33.34  | | 
% 201.35/33.34  | |   (322)   ~ (all_50_2 = e3)
% 201.35/33.34  | | 
% 201.35/33.34  | | REDUCE: (71), (322) imply:
% 201.35/33.34  | |   (323)  $false
% 201.35/33.34  | | 
% 201.35/33.34  | | CLOSE: (323) is inconsistent.
% 201.35/33.34  | | 
% 201.35/33.34  | End of split
% 201.35/33.34  | 
% 201.35/33.34  End of proof
% 201.35/33.34  
% 201.35/33.34  Sub-proof #231 shows that the following formulas are inconsistent:
% 201.35/33.34  ----------------------------------------------------------------
% 201.35/33.34    (1)  all_58_14 = all_52_23
% 201.35/33.34    (2)  all_58_14 = e1
% 201.35/33.34    (3)   ~ (all_52_23 = e1)
% 201.35/33.34  
% 201.35/33.34  Begin of proof
% 201.35/33.34  | 
% 201.35/33.34  | COMBINE_EQS: (1), (2) imply:
% 201.35/33.34  |   (4)  all_52_23 = e1
% 201.35/33.34  | 
% 201.35/33.34  | SIMP: (4) implies:
% 201.35/33.34  |   (5)  all_52_23 = e1
% 201.35/33.34  | 
% 201.35/33.34  | REDUCE: (3), (5) imply:
% 201.35/33.34  |   (6)  $false
% 201.35/33.34  | 
% 201.35/33.34  | CLOSE: (6) is inconsistent.
% 201.35/33.34  | 
% 201.35/33.34  End of proof
% 201.35/33.34  
% 201.35/33.34  Sub-proof #232 shows that the following formulas are inconsistent:
% 201.35/33.34  ----------------------------------------------------------------
% 201.35/33.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.34    (2)   ~ (all_4_2 = e3)
% 201.35/33.34    (3)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.34    (4)  op(e2, e2) = all_4_2
% 201.35/33.34    (5)  all_58_11 = all_52_29
% 201.35/33.34    (6)   ~ (all_52_3 = e3)
% 201.35/33.34    (7)  op(all_10_2, e1) = all_10_1
% 201.35/33.34    (8)  op(e0, e0) = all_14_2
% 201.35/33.34    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.34    (10)  op(all_10_2, all_10_2) = e1
% 201.35/33.34    (11)  all_58_10 = all_52_27
% 201.35/33.34    (12)  all_58_8 = e3 | all_58_11 = e3
% 201.35/33.34    (13)  all_58_2 = all_52_3
% 201.35/33.34    (14)  all_56_2 = all_52_17
% 201.35/33.35    (15)   ~ (all_52_29 = e3)
% 201.35/33.35    (16)  op(e3, e1) = all_52_17
% 201.35/33.35    (17)   ~ (all_52_19 = all_10_2)
% 201.35/33.35    (18)  all_58_8 = all_10_2
% 201.35/33.35    (19)  op(e3, e3) = all_6_2
% 201.35/33.35    (20)   ~ (all_52_27 = all_14_2)
% 201.35/33.35    (21)  all_58_5 = all_52_19
% 201.35/33.35    (22)   ~ (all_52_27 = all_4_2)
% 201.35/33.35    (23)  op(all_52_17, all_52_17) = e3
% 201.35/33.35    (24)   ~ (all_52_17 = all_6_2)
% 201.35/33.35    (25)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.35    (26)  all_58_3 = all_4_2
% 201.35/33.35  
% 201.35/33.35  Begin of proof
% 201.35/33.35  | 
% 201.35/33.35  | BETA: splitting (9) gives:
% 201.35/33.35  | 
% 201.35/33.35  | Case 1:
% 201.35/33.35  | | 
% 201.35/33.35  | |   (27)  all_58_2 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | REF_CLOSE: (6), (13), (27) are inconsistent by sub-proof #1369.
% 201.35/33.35  | | 
% 201.35/33.35  | Case 2:
% 201.35/33.35  | | 
% 201.35/33.35  | |   (28)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | BETA: splitting (28) gives:
% 201.35/33.35  | | 
% 201.35/33.35  | | Case 1:
% 201.35/33.35  | | | 
% 201.35/33.35  | | |   (29)  all_58_3 = e3
% 201.35/33.35  | | | 
% 201.35/33.35  | | | COMBINE_EQS: (26), (29) imply:
% 201.35/33.35  | | |   (30)  all_4_2 = e3
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (2), (30) imply:
% 201.35/33.35  | | |   (31)  $false
% 201.35/33.35  | | | 
% 201.35/33.35  | | | CLOSE: (31) is inconsistent.
% 201.35/33.35  | | | 
% 201.35/33.35  | | Case 2:
% 201.35/33.35  | | | 
% 201.35/33.35  | | |   (32)  all_58_5 = e3 | all_58_10 = e3
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (12), (14), (15),
% 201.35/33.35  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 201.35/33.35  | | |            (32) are inconsistent by sub-proof #233.
% 201.35/33.35  | | | 
% 201.35/33.35  | | End of split
% 201.35/33.35  | | 
% 201.35/33.35  | End of split
% 201.35/33.35  | 
% 201.35/33.35  End of proof
% 201.35/33.35  
% 201.35/33.35  Sub-proof #233 shows that the following formulas are inconsistent:
% 201.35/33.35  ----------------------------------------------------------------
% 201.35/33.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.35    (2)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.35    (3)  op(e2, e2) = all_4_2
% 201.35/33.35    (4)  all_58_11 = all_52_29
% 201.35/33.35    (5)  op(all_10_2, e1) = all_10_1
% 201.35/33.35    (6)  op(e0, e0) = all_14_2
% 201.35/33.35    (7)  op(all_10_2, all_10_2) = e1
% 201.35/33.35    (8)  all_58_10 = all_52_27
% 201.35/33.35    (9)  all_58_5 = e3 | all_58_10 = e3
% 201.35/33.35    (10)  all_58_8 = e3 | all_58_11 = e3
% 201.35/33.35    (11)  all_56_2 = all_52_17
% 201.35/33.35    (12)   ~ (all_52_29 = e3)
% 201.35/33.35    (13)  op(e3, e1) = all_52_17
% 201.35/33.35    (14)   ~ (all_52_19 = all_10_2)
% 201.35/33.35    (15)  all_58_8 = all_10_2
% 201.35/33.35    (16)  op(e3, e3) = all_6_2
% 201.35/33.35    (17)   ~ (all_52_27 = all_14_2)
% 201.35/33.35    (18)  all_58_5 = all_52_19
% 201.35/33.35    (19)   ~ (all_52_27 = all_4_2)
% 201.35/33.35    (20)  op(all_52_17, all_52_17) = e3
% 201.35/33.35    (21)   ~ (all_52_17 = all_6_2)
% 201.35/33.35    (22)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.35  
% 201.35/33.35  Begin of proof
% 201.35/33.35  | 
% 201.35/33.35  | BETA: splitting (10) gives:
% 201.35/33.35  | 
% 201.35/33.35  | Case 1:
% 201.35/33.35  | | 
% 201.35/33.35  | |   (23)  all_58_8 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | COMBINE_EQS: (15), (23) imply:
% 201.35/33.35  | |   (24)  all_10_2 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | SIMP: (24) implies:
% 201.35/33.35  | |   (25)  all_10_2 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (14), (25) imply:
% 201.35/33.35  | |   (26)   ~ (all_52_19 = e3)
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (7), (25) imply:
% 201.35/33.35  | |   (27)  op(e3, e3) = e1
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (5), (25) imply:
% 201.35/33.35  | |   (28)  op(e3, e1) = all_10_1
% 201.35/33.35  | | 
% 201.35/33.35  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (11), (13), (16), (17), (18), (19),
% 201.35/33.35  | |            (20), (21), (22), (26), (27), (28) are inconsistent by sub-proof
% 201.35/33.35  | |            #1052.
% 201.35/33.35  | | 
% 201.35/33.35  | Case 2:
% 201.35/33.35  | | 
% 201.35/33.35  | |   (29)  all_58_11 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | REF_CLOSE: (4), (12), (29) are inconsistent by sub-proof #1323.
% 201.35/33.35  | | 
% 201.35/33.35  | End of split
% 201.35/33.35  | 
% 201.35/33.35  End of proof
% 201.35/33.35  
% 201.35/33.35  Sub-proof #234 shows that the following formulas are inconsistent:
% 201.35/33.35  ----------------------------------------------------------------
% 201.35/33.35    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.35/33.35    (2)   ~ (all_52_15 = all_52_23)
% 201.35/33.35    (3)   ~ (all_52_25 = all_52_27)
% 201.35/33.35    (4)  all_58_14 = all_52_23
% 201.35/33.35    (5)   ~ (e3 = e1)
% 201.35/33.35    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.35/33.35    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.35    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.35    (9)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 201.35/33.35    (10)  all_58_1 = all_52_9
% 201.35/33.35    (11)   ~ (all_52_9 = all_52_13)
% 201.35/33.35    (12)   ~ (e3 = e0)
% 201.35/33.35    (13)  op(e2, e3) = all_52_3
% 201.35/33.35    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.35    (15)  op(e0, e2) = all_52_15
% 201.35/33.35    (16)   ~ (all_52_7 = all_52_15)
% 201.35/33.35    (17)  op(all_52_15, all_52_15) = e0
% 201.35/33.35    (18)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.35    (19)   ~ (all_52_17 = all_52_25)
% 201.35/33.35    (20)   ~ (all_52_3 = all_6_2)
% 201.35/33.35    (21)  all_50_1 = all_14_1
% 201.35/33.35    (22)  all_58_0 = all_6_2
% 201.35/33.35    (23)  op(all_14_2, e0) = all_14_1
% 201.35/33.35    (24)  all_56_4 = all_52_3
% 201.35/33.35    (25)  op(e3, all_6_1) = e1
% 201.35/33.35    (26)   ~ (all_52_17 = all_10_2)
% 201.35/33.35    (27)  op(e3, e0) = all_52_25
% 201.35/33.35    (28)  op(all_52_5, all_52_5) = all_52_4
% 201.35/33.35    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.35    (30)  all_58_13 = all_52_15
% 201.35/33.35    (31)  op(all_52_13, all_52_13) = e1
% 201.35/33.35    (32)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.35    (33)  all_58_9 = all_52_25
% 201.35/33.35    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.35/33.35    (35)   ~ (all_52_29 = all_14_2)
% 201.35/33.35    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.35/33.35    (37)  op(e1, e3) = all_52_5
% 201.35/33.35    (38)  op(e2, e2) = all_4_2
% 201.35/33.35    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.35/33.35    (40)   ~ (all_52_3 = all_52_5)
% 201.35/33.35    (41)  all_58_11 = all_52_29
% 201.35/33.35    (42)  all_56_5 = all_4_2
% 201.35/33.35    (43)   ~ (all_52_25 = all_14_2)
% 201.35/33.35    (44)   ~ (all_52_9 = all_52_15)
% 201.35/33.35    (45)  all_46_2 = all_6_2
% 201.35/33.35    (46)  op(all_6_2, all_6_2) = all_52_0
% 201.35/33.35    (47)   ~ (all_52_7 = all_6_2)
% 201.35/33.35    (48)  op(e0, e0) = all_14_2
% 201.35/33.35    (49)  all_56_15 = all_14_2
% 201.35/33.35    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.35    (51)   ~ (all_4_1 = e1)
% 201.35/33.35    (52)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.35/33.35    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.35    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.35    (55)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.35/33.35    (56)   ~ (e2 = e1)
% 201.35/33.35    (57)  all_58_10 = all_52_27
% 201.35/33.35    (58)  all_56_8 = all_52_5
% 201.35/33.35    (59)   ~ (all_52_19 = all_52_23)
% 201.35/33.35    (60)   ~ (all_52_25 = all_52_29)
% 201.35/33.35    (61)  all_58_7 = all_52_13
% 201.35/33.35    (62)   ~ (all_52_5 = all_52_7)
% 201.35/33.35    (63)  all_58_12 = all_52_7
% 201.35/33.35    (64)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.35    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.35    (66)   ~ (all_52_7 = all_14_2)
% 201.35/33.35    (67)  all_58_2 = all_52_3
% 201.35/33.35    (68)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.35    (69)  all_56_2 = all_52_17
% 201.35/33.35    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.35    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.35/33.35    (72)  all_56_7 = all_52_27
% 201.35/33.35    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.35    (74)   ~ (e2 = e0)
% 201.35/33.35    (75)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.35/33.35    (76)  op(all_4_2, e2) = all_4_1
% 201.35/33.35    (77)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.35/33.35    (78)   ~ (all_52_5 = all_52_29)
% 201.35/33.35    (79)  all_56_6 = all_52_19
% 201.35/33.35    (80)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.35/33.35    (81)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.35/33.35    (82)   ~ (all_52_13 = all_4_2)
% 201.35/33.35    (83)  op(e3, e1) = all_52_17
% 201.35/33.35    (84)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.35/33.35    (85)  op(e0, e3) = all_52_7
% 201.35/33.35    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.35    (87)   ~ (all_52_9 = all_52_25)
% 201.35/33.35    (88)  all_58_15 = all_14_2
% 201.35/33.35    (89)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.35    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.35/33.35    (91)  all_58_8 = all_10_2
% 201.35/33.35    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.35/33.35    (93)  op(all_52_29, all_52_29) = all_52_28
% 201.35/33.35    (94)   ~ (all_52_23 = all_14_2)
% 201.35/33.35    (95)  all_56_12 = all_52_7
% 201.35/33.35    (96)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.35    (97)   ~ (all_52_25 = all_6_2)
% 201.35/33.35    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.35    (99)   ~ (all_52_9 = all_4_2)
% 201.35/33.35    (100)   ~ (all_52_5 = all_6_2)
% 201.35/33.35    (101)  op(all_4_2, all_4_2) = e2
% 201.35/33.35    (102)   ~ (all_52_9 = all_6_2)
% 201.35/33.35    (103)  all_56_0 = all_6_2
% 201.35/33.35    (104)  op(e3, e3) = all_6_2
% 201.35/33.35    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.35    (106)   ~ (all_52_27 = all_14_2)
% 201.35/33.35    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.35    (108)  all_56_3 = all_52_25
% 201.35/33.35    (109)  op(e0, all_14_1) = e2
% 201.35/33.35    (110)   ~ (all_52_3 = all_52_7)
% 201.35/33.35    (111)  op(all_14_2, all_14_2) = all_52_30
% 201.35/33.35    (112)  all_58_5 = all_52_19
% 201.35/33.35    (113)  all_56_1 = all_52_9
% 201.35/33.35    (114)   ~ (all_52_15 = all_4_2)
% 201.35/33.35    (115)   ~ (all_52_27 = all_4_2)
% 201.35/33.35    (116)  all_58_6 = all_52_5
% 201.35/33.35    (117)  op(e3, e2) = all_52_9
% 201.35/33.35    (118)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.35    (119)   ~ (all_52_17 = all_6_2)
% 201.35/33.35    (120)   ~ (e1 = e0)
% 201.35/33.35    (121)   ~ (e3 = e2)
% 201.35/33.35    (122)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.35    (123)   ~ (all_52_9 = all_52_17)
% 201.35/33.35    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.35    (125)  all_46_1 = all_6_1
% 201.35/33.35    (126)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.35/33.35    (127)  op(e1, e1) = all_10_2
% 201.35/33.35    (128)  op(all_52_9, all_52_9) = e3
% 201.35/33.35    (129)   ~ (all_52_23 = all_10_2)
% 201.35/33.35    (130)   ~ (all_52_7 = all_52_23)
% 201.35/33.35    (131)   ~ (all_52_17 = all_52_19)
% 201.35/33.35    (132)  all_58_3 = all_4_2
% 201.35/33.35    (133)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.35/33.35    (134)  all_56_13 = all_52_15
% 201.35/33.35    (135)   ~ (all_52_3 = all_4_2)
% 201.35/33.35    (136)   ~ (all_52_19 = all_4_2)
% 201.35/33.35    (137)   ~ (all_52_17 = all_52_23)
% 201.35/33.35    (138)  op(all_6_2, e3) = all_6_1
% 201.35/33.35    (139)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.35/33.35    (140)   ~ (all_52_13 = all_52_29)
% 201.35/33.35    (141)  all_58_4 = all_52_17
% 201.35/33.35    (142)  all_50_2 = all_14_2
% 201.35/33.35    (143)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.35  
% 201.35/33.35  Begin of proof
% 201.35/33.35  | 
% 201.35/33.35  | BETA: splitting (92) gives:
% 201.35/33.35  | 
% 201.35/33.35  | Case 1:
% 201.35/33.35  | | 
% 201.35/33.35  | |   (144)  all_56_15 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | COMBINE_EQS: (49), (144) imply:
% 201.35/33.35  | |   (145)  all_14_2 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | COMBINE_EQS: (142), (145) imply:
% 201.35/33.35  | |   (146)  all_50_2 = e3
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (43), (145) imply:
% 201.35/33.35  | |   (147)   ~ (all_52_25 = e3)
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (106), (145) imply:
% 201.35/33.35  | |   (148)   ~ (all_52_27 = e3)
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (35), (145) imply:
% 201.35/33.35  | |   (149)   ~ (all_52_29 = e3)
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (111), (145) imply:
% 201.35/33.35  | |   (150)  op(e3, e3) = all_52_30
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (23), (145) imply:
% 201.35/33.35  | |   (151)  op(e3, e0) = all_14_1
% 201.35/33.35  | | 
% 201.35/33.35  | | BETA: splitting (9) gives:
% 201.35/33.35  | | 
% 201.35/33.35  | | Case 1:
% 201.35/33.35  | | | 
% 201.35/33.35  | | |   (152)   ~ (all_50_1 = e1)
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (21), (152) imply:
% 201.35/33.35  | | |   (153)   ~ (all_14_1 = e1)
% 201.35/33.35  | | | 
% 201.35/33.35  | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 201.35/33.35  | | |              simplifying with (27), (151) gives:
% 201.35/33.35  | | |   (154)  all_52_25 = all_14_1
% 201.35/33.35  | | | 
% 201.35/33.35  | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 201.35/33.35  | | |              simplifying with (104), (150) gives:
% 201.35/33.35  | | |   (155)  all_52_30 = all_6_2
% 201.35/33.35  | | | 
% 201.35/33.35  | | | COMBINE_EQS: (108), (154) imply:
% 201.35/33.35  | | |   (156)  all_56_3 = all_14_1
% 201.35/33.35  | | | 
% 201.35/33.35  | | | COMBINE_EQS: (33), (154) imply:
% 201.35/33.35  | | |   (157)  all_58_9 = all_14_1
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (87), (154) imply:
% 201.35/33.35  | | |   (158)   ~ (all_52_9 = all_14_1)
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (97), (154) imply:
% 201.35/33.35  | | |   (159)   ~ (all_14_1 = all_6_2)
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (147), (154) imply:
% 201.35/33.35  | | |   (160)   ~ (all_14_1 = e3)
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (143), (154) imply:
% 201.35/33.35  | | |   (161)  op(all_14_1, all_14_1) = all_52_24
% 201.35/33.35  | | | 
% 201.35/33.35  | | | BETA: splitting (98) gives:
% 201.35/33.35  | | | 
% 201.35/33.35  | | | Case 1:
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | |   (162)  all_56_3 = e3
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | | REF_CLOSE: (156), (160), (162) are inconsistent by sub-proof #1200.
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | Case 2:
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | |   (163)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | | BETA: splitting (124) gives:
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | | Case 1:
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | |   (164)  all_58_4 = e3
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | COMBINE_EQS: (141), (164) imply:
% 201.35/33.35  | | | | |   (165)  all_52_17 = e3
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | SIMP: (165) implies:
% 201.35/33.35  | | | | |   (166)  all_52_17 = e3
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | REDUCE: (131), (166) imply:
% 201.35/33.35  | | | | |   (167)   ~ (all_52_19 = e3)
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | SIMP: (167) implies:
% 201.35/33.35  | | | | |   (168)   ~ (all_52_19 = e3)
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | REDUCE: (26), (166) imply:
% 201.35/33.35  | | | | |   (169)   ~ (all_10_2 = e3)
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | SIMP: (169) implies:
% 201.35/33.35  | | | | |   (170)   ~ (all_10_2 = e3)
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | REDUCE: (96), (166) imply:
% 201.35/33.35  | | | | |   (171)  op(e3, e3) = all_52_16
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_16, e3, e3,
% 201.35/33.35  | | | | |              simplifying with (104), (171) gives:
% 201.35/33.35  | | | | |   (172)  all_52_16 = all_6_2
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | BETA: splitting (65) gives:
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | Case 1:
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | |   (173)  all_58_6 = e3
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | COMBINE_EQS: (116), (173) imply:
% 201.35/33.35  | | | | | |   (174)  all_52_5 = e3
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | SIMP: (174) implies:
% 201.35/33.35  | | | | | |   (175)  all_52_5 = e3
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | REDUCE: (40), (175) imply:
% 201.35/33.35  | | | | | |   (176)   ~ (all_52_3 = e3)
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | REDUCE: (62), (175) imply:
% 201.35/33.35  | | | | | |   (177)   ~ (all_52_7 = e3)
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | SIMP: (177) implies:
% 201.35/33.35  | | | | | |   (178)   ~ (all_52_7 = e3)
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | REDUCE: (100), (175) imply:
% 201.35/33.35  | | | | | |   (179)   ~ (all_6_2 = e3)
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | SIMP: (179) implies:
% 201.35/33.35  | | | | | |   (180)   ~ (all_6_2 = e3)
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | REF_CLOSE: (5), (8), (10), (22), (28), (50), (51), (56), (57), (63),
% 201.35/33.35  | | | | | |            (67), (70), (76), (77), (101), (104), (112), (116),
% 201.35/33.35  | | | | | |            (117), (132), (148), (153), (156), (157), (159), (163),
% 201.35/33.35  | | | | | |            (164), (168), (176), (178), (180) are inconsistent by
% 201.35/33.35  | | | | | |            sub-proof #554.
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | Case 2:
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | |   (181)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | BETA: splitting (181) gives:
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | | Case 1:
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | |   (182)  all_58_7 = e3
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | COMBINE_EQS: (61), (182) imply:
% 201.35/33.35  | | | | | | |   (183)  all_52_13 = e3
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | REDUCE: (11), (183) imply:
% 201.35/33.35  | | | | | | |   (184)   ~ (all_52_9 = e3)
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | REDUCE: (82), (183) imply:
% 201.35/33.35  | | | | | | |   (185)   ~ (all_4_2 = e3)
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | SIMP: (185) implies:
% 201.35/33.35  | | | | | | |   (186)   ~ (all_4_2 = e3)
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | REDUCE: (31), (183) imply:
% 201.35/33.35  | | | | | | |   (187)  op(e3, e3) = e1
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | BETA: splitting (50) gives:
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | Case 1:
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | |   (188)  all_58_2 = e3
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | COMBINE_EQS: (67), (188) imply:
% 201.35/33.35  | | | | | | | |   (189)  all_52_3 = e3
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | SIMP: (189) implies:
% 201.35/33.35  | | | | | | | |   (190)  all_52_3 = e3
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | REDUCE: (40), (190) imply:
% 201.35/33.35  | | | | | | | |   (191)   ~ (all_52_5 = e3)
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | SIMP: (191) implies:
% 201.35/33.35  | | | | | | | |   (192)   ~ (all_52_5 = e3)
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | REDUCE: (110), (190) imply:
% 201.35/33.35  | | | | | | | |   (193)   ~ (all_52_7 = e3)
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | SIMP: (193) implies:
% 201.35/33.35  | | | | | | | |   (194)   ~ (all_52_7 = e3)
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | REDUCE: (20), (190) imply:
% 201.35/33.35  | | | | | | | |   (195)   ~ (all_6_2 = e3)
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | SIMP: (195) implies:
% 201.35/33.35  | | | | | | | |   (196)   ~ (all_6_2 = e3)
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | REDUCE: (7), (190) imply:
% 201.35/33.35  | | | | | | | |   (197)  op(e3, e3) = all_52_2
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | REF_CLOSE: (8), (10), (15), (17), (22), (38), (63), (67), (70),
% 201.35/33.35  | | | | | | | |            (99), (102), (104), (109), (113), (116), (122),
% 201.35/33.35  | | | | | | | |            (128), (133), (135), (156), (158), (159), (161),
% 201.35/33.35  | | | | | | | |            (163), (184), (187), (192), (194), (196), (197) are
% 201.35/33.35  | | | | | | | |            inconsistent by sub-proof #235.
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | Case 2:
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | |   (198)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | | REF_CLOSE: (57), (112), (132), (148), (168), (186), (198) are
% 201.35/33.35  | | | | | | | |            inconsistent by sub-proof #1082.
% 201.35/33.35  | | | | | | | | 
% 201.35/33.35  | | | | | | | End of split
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | Case 2:
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | |   (199)  all_58_8 = e3 | all_58_11 = e3
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | | REF_CLOSE: (41), (91), (149), (170), (199) are inconsistent by
% 201.35/33.35  | | | | | | |            sub-proof #1140.
% 201.35/33.35  | | | | | | | 
% 201.35/33.35  | | | | | | End of split
% 201.35/33.35  | | | | | | 
% 201.35/33.35  | | | | | End of split
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | Case 2:
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | |   (200)   ~ (all_58_4 = e3)
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | REDUCE: (141), (200) imply:
% 201.35/33.35  | | | | |   (201)   ~ (all_52_17 = e3)
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | | REF_CLOSE: (5), (8), (10), (22), (25), (33), (46), (102), (104),
% 201.35/33.35  | | | | |            (107), (128), (138), (141), (147), (201) are inconsistent
% 201.35/33.35  | | | | |            by sub-proof #289.
% 201.35/33.35  | | | | | 
% 201.35/33.35  | | | | End of split
% 201.35/33.35  | | | | 
% 201.35/33.35  | | | End of split
% 201.35/33.35  | | | 
% 201.35/33.35  | | Case 2:
% 201.35/33.35  | | | 
% 201.35/33.35  | | |   (202)   ~ (all_50_2 = e3)
% 201.35/33.35  | | | 
% 201.35/33.35  | | | REDUCE: (146), (202) imply:
% 201.35/33.35  | | |   (203)  $false
% 201.35/33.35  | | | 
% 201.35/33.35  | | | CLOSE: (203) is inconsistent.
% 201.35/33.35  | | | 
% 201.35/33.35  | | End of split
% 201.35/33.35  | | 
% 201.35/33.35  | Case 2:
% 201.35/33.35  | | 
% 201.35/33.35  | |   (204)   ~ (all_56_15 = e3)
% 201.35/33.35  | |   (205)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.35/33.35  | | 
% 201.35/33.35  | | REDUCE: (49), (204) imply:
% 201.35/33.35  | |   (206)   ~ (all_14_2 = e3)
% 201.35/33.35  | | 
% 201.35/33.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 201.35/33.35  | |            (14), (16), (17), (18), (19), (20), (22), (24), (25), (26), (28),
% 201.35/33.35  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 201.35/33.35  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 201.35/33.35  | |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 201.35/33.35  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 201.35/33.35  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 201.35/33.35  | |            (84), (85), (86), (87), (88), (89), (90), (91), (93), (94), (95),
% 201.35/33.35  | |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 201.35/33.35  | |            (106), (107), (108), (110), (111), (112), (113), (114), (115),
% 201.35/33.35  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 201.35/33.35  | |            (125), (126), (127), (128), (129), (130), (131), (132), (134),
% 201.35/33.35  | |            (135), (136), (137), (138), (139), (140), (141), (143), (205),
% 201.35/33.35  | |            (206) are inconsistent by sub-proof #288.
% 201.35/33.35  | | 
% 201.35/33.35  | End of split
% 201.35/33.35  | 
% 201.35/33.35  End of proof
% 201.35/33.35  
% 201.35/33.35  Sub-proof #235 shows that the following formulas are inconsistent:
% 201.35/33.35  ----------------------------------------------------------------
% 201.35/33.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.35    (2)  all_58_1 = all_52_9
% 201.35/33.35    (3)  op(e0, e2) = all_52_15
% 201.35/33.35    (4)  op(all_52_15, all_52_15) = e0
% 201.35/33.35    (5)  all_58_0 = all_6_2
% 201.35/33.35    (6)  op(e2, e2) = all_4_2
% 201.35/33.35    (7)  all_56_3 = all_14_1
% 201.35/33.35    (8)   ~ (all_52_9 = all_14_1)
% 201.35/33.35    (9)   ~ (all_6_2 = e3)
% 201.35/33.35    (10)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.35    (11)  all_58_12 = all_52_7
% 201.35/33.35    (12)   ~ (all_52_7 = e3)
% 201.35/33.35    (13)  all_58_2 = all_52_3
% 201.35/33.35    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.35    (15)   ~ (all_14_1 = all_6_2)
% 201.35/33.35    (16)   ~ (all_52_5 = e3)
% 201.35/33.35    (17)   ~ (all_52_9 = e3)
% 201.35/33.35    (18)  op(all_14_1, all_14_1) = all_52_24
% 201.35/33.35    (19)   ~ (all_52_9 = all_4_2)
% 201.35/33.35    (20)  op(e3, e3) = all_52_2
% 201.35/33.35    (21)   ~ (all_52_9 = all_6_2)
% 201.35/33.35    (22)  op(e3, e3) = all_6_2
% 201.35/33.35    (23)  op(e3, e3) = e1
% 201.35/33.35    (24)  op(e0, all_14_1) = e2
% 201.35/33.35    (25)  all_56_1 = all_52_9
% 201.35/33.35    (26)  all_58_6 = all_52_5
% 201.35/33.35    (27)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.35    (28)  op(all_52_9, all_52_9) = e3
% 201.35/33.35    (29)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.35/33.35    (30)   ~ (all_52_3 = all_4_2)
% 201.35/33.35  
% 201.35/33.35  Begin of proof
% 201.35/33.35  | 
% 201.35/33.35  | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3, simplifying
% 201.35/33.35  |              with (20), (22) gives:
% 201.35/33.35  |   (31)  all_52_2 = all_6_2
% 201.35/33.35  | 
% 201.35/33.35  | GROUND_INST: instantiating (1) with e1, all_52_2, e3, e3, simplifying with
% 201.35/33.35  |              (20), (23) gives:
% 201.35/33.35  |   (32)  all_52_2 = e1
% 201.35/33.35  | 
% 201.35/33.35  | COMBINE_EQS: (31), (32) imply:
% 201.35/33.35  |   (33)  all_6_2 = e1
% 201.35/33.35  | 
% 201.35/33.35  | SIMP: (33) implies:
% 201.35/33.35  |   (34)  all_6_2 = e1
% 201.35/33.35  | 
% 201.35/33.35  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.35/33.35  |            (13), (14), (15), (16), (17), (18), (19), (21), (24), (25), (26),
% 201.35/33.35  |            (27), (28), (29), (30), (34) are inconsistent by sub-proof #236.
% 201.35/33.35  | 
% 201.35/33.35  End of proof
% 201.35/33.35  
% 201.35/33.35  Sub-proof #236 shows that the following formulas are inconsistent:
% 201.35/33.35  ----------------------------------------------------------------
% 201.35/33.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.35    (2)  all_58_1 = all_52_9
% 201.35/33.35    (3)  op(e0, e2) = all_52_15
% 201.35/33.35    (4)  op(all_52_15, all_52_15) = e0
% 201.35/33.35    (5)  all_58_0 = all_6_2
% 201.35/33.35    (6)  op(e2, e2) = all_4_2
% 201.35/33.35    (7)  all_56_3 = all_14_1
% 201.35/33.35    (8)   ~ (all_52_9 = all_14_1)
% 201.35/33.35    (9)   ~ (all_6_2 = e3)
% 201.35/33.35    (10)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.35    (11)  all_58_12 = all_52_7
% 201.35/33.35    (12)   ~ (all_52_7 = e3)
% 201.35/33.35    (13)  all_58_2 = all_52_3
% 201.35/33.35    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.35    (15)   ~ (all_14_1 = all_6_2)
% 201.35/33.35    (16)   ~ (all_52_5 = e3)
% 201.35/33.35    (17)   ~ (all_52_9 = e3)
% 201.35/33.35    (18)  op(all_14_1, all_14_1) = all_52_24
% 201.35/33.35    (19)   ~ (all_52_9 = all_4_2)
% 201.35/33.35    (20)   ~ (all_52_9 = all_6_2)
% 201.35/33.35    (21)  op(e0, all_14_1) = e2
% 201.35/33.35    (22)  all_56_1 = all_52_9
% 201.35/33.35    (23)  all_58_6 = all_52_5
% 201.35/33.35    (24)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.35    (25)  all_6_2 = e1
% 201.35/33.35    (26)  op(all_52_9, all_52_9) = e3
% 201.35/33.35    (27)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.35/33.35    (28)   ~ (all_52_3 = all_4_2)
% 201.35/33.35  
% 201.35/33.35  Begin of proof
% 201.35/33.35  | 
% 201.35/33.35  | COMBINE_EQS: (5), (25) imply:
% 201.35/33.35  |   (29)  all_58_0 = e1
% 201.35/33.35  | 
% 201.35/33.35  | REDUCE: (20), (25) imply:
% 201.35/33.35  |   (30)   ~ (all_52_9 = e1)
% 201.35/33.35  | 
% 201.35/33.35  | REDUCE: (15), (25) imply:
% 201.35/33.35  |   (31)   ~ (all_14_1 = e1)
% 201.35/33.35  | 
% 201.35/33.36  | REDUCE: (9), (25) imply:
% 201.35/33.36  |   (32)   ~ (e3 = e1)
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (32) implies:
% 201.35/33.36  |   (33)   ~ (e3 = e1)
% 201.35/33.36  | 
% 201.35/33.36  | BETA: splitting (24) gives:
% 201.35/33.36  | 
% 201.35/33.36  | Case 1:
% 201.35/33.36  | | 
% 201.35/33.36  | |   (34)  all_56_1 = e3
% 201.35/33.36  | | 
% 201.35/33.36  | | REF_CLOSE: (17), (22), (34) are inconsistent by sub-proof #1326.
% 201.35/33.36  | | 
% 201.35/33.36  | Case 2:
% 201.35/33.36  | | 
% 201.35/33.36  | |   (35)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.36  | | 
% 201.35/33.36  | | BETA: splitting (27) gives:
% 201.35/33.36  | | 
% 201.35/33.36  | | Case 1:
% 201.35/33.36  | | | 
% 201.35/33.36  | | |   (36)  all_58_1 = e2
% 201.35/33.36  | | | 
% 201.35/33.36  | | | REF_CLOSE: (1), (2), (6), (11), (12), (13), (14), (16), (23), (26), (28),
% 201.35/33.36  | | |            (29), (33), (36) are inconsistent by sub-proof #1122.
% 201.35/33.36  | | | 
% 201.35/33.36  | | Case 2:
% 201.35/33.36  | | | 
% 201.35/33.36  | | |   (37)   ~ (all_58_1 = e2)
% 201.35/33.36  | | | 
% 201.35/33.36  | | | REDUCE: (2), (37) imply:
% 201.35/33.36  | | |   (38)   ~ (all_52_9 = e2)
% 201.35/33.36  | | | 
% 201.35/33.36  | | | BETA: splitting (35) gives:
% 201.35/33.36  | | | 
% 201.35/33.36  | | | Case 1:
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | |   (39)  all_56_1 = e2
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | | REF_CLOSE: (22), (38), (39) are inconsistent by sub-proof #1194.
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | Case 2:
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | |   (40)  all_56_1 = e1 | all_56_1 = e0
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | | BETA: splitting (40) gives:
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | | Case 1:
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | |   (41)  all_56_1 = e1
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | REF_CLOSE: (22), (30), (41) are inconsistent by sub-proof #1061.
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | Case 2:
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | |   (42)  all_56_1 = e0
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | COMBINE_EQS: (22), (42) imply:
% 201.35/33.36  | | | | |   (43)  all_52_9 = e0
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | SIMP: (43) implies:
% 201.35/33.36  | | | | |   (44)  all_52_9 = e0
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | REDUCE: (8), (44) imply:
% 201.35/33.36  | | | | |   (45)   ~ (all_14_1 = e0)
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | SIMP: (45) implies:
% 201.35/33.36  | | | | |   (46)   ~ (all_14_1 = e0)
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | REDUCE: (19), (44) imply:
% 201.35/33.36  | | | | |   (47)   ~ (all_4_2 = e0)
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | SIMP: (47) implies:
% 201.35/33.36  | | | | |   (48)   ~ (all_4_2 = e0)
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | BETA: splitting (10) gives:
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | | Case 1:
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | |   (49)  all_56_3 = e2
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | COMBINE_EQS: (7), (49) imply:
% 201.35/33.36  | | | | | |   (50)  all_14_1 = e2
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | SIMP: (50) implies:
% 201.35/33.36  | | | | | |   (51)  all_14_1 = e2
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | REDUCE: (18), (51) imply:
% 201.35/33.36  | | | | | |   (52)  op(e2, e2) = all_52_24
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | REDUCE: (21), (51) imply:
% 201.35/33.36  | | | | | |   (53)  op(e0, e2) = e2
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | GROUND_INST: instantiating (1) with all_52_15, e2, e2, e0,
% 201.35/33.36  | | | | | |              simplifying with (3), (53) gives:
% 201.35/33.36  | | | | | |   (54)  all_52_15 = e2
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_24, e2, e2,
% 201.35/33.36  | | | | | |              simplifying with (6), (52) gives:
% 201.35/33.36  | | | | | |   (55)  all_52_24 = all_4_2
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | REDUCE: (4), (54) imply:
% 201.35/33.36  | | | | | |   (56)  op(e2, e2) = e0
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | REF_CLOSE: (1), (6), (48), (56) are inconsistent by sub-proof #1152.
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | Case 2:
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | |   (57)  all_56_3 = e1 | all_56_3 = e0
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | | REF_CLOSE: (7), (31), (46), (57) are inconsistent by sub-proof #806.
% 201.35/33.36  | | | | | | 
% 201.35/33.36  | | | | | End of split
% 201.35/33.36  | | | | | 
% 201.35/33.36  | | | | End of split
% 201.35/33.36  | | | | 
% 201.35/33.36  | | | End of split
% 201.35/33.36  | | | 
% 201.35/33.36  | | End of split
% 201.35/33.36  | | 
% 201.35/33.36  | End of split
% 201.35/33.36  | 
% 201.35/33.36  End of proof
% 201.35/33.36  
% 201.35/33.36  Sub-proof #237 shows that the following formulas are inconsistent:
% 201.35/33.36  ----------------------------------------------------------------
% 201.35/33.36    (1)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.36    (3)  all_58_1 = all_52_9
% 201.35/33.36    (4)   ~ (all_52_9 = all_52_13)
% 201.35/33.36    (5)   ~ (e3 = e0)
% 201.35/33.36    (6)   ~ (all_52_3 = all_6_2)
% 201.35/33.36    (7)  all_58_0 = all_6_2
% 201.35/33.36    (8)  all_26_1 = all_10_1
% 201.35/33.36    (9)  all_26_2 = all_10_2
% 201.35/33.36    (10)  all_58_13 = all_52_15
% 201.35/33.36    (11)  all_58_9 = all_52_25
% 201.35/33.36    (12)  op(e2, e2) = all_4_2
% 201.35/33.36    (13)   ~ (all_52_3 = all_52_5)
% 201.35/33.36    (14)  all_58_11 = all_52_29
% 201.35/33.36    (15)   ~ (all_52_9 = all_52_15)
% 201.35/33.36    (16)  op(all_10_2, e1) = all_10_1
% 201.35/33.36    (17)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 201.35/33.36    (18)   ~ (e2 = e1)
% 201.35/33.36    (19)   ~ (all_52_13 = all_10_2)
% 201.35/33.36    (20)  op(all_10_2, all_10_2) = e1
% 201.35/33.36    (21)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.36    (22)  all_58_7 = all_52_13
% 201.35/33.36    (23)  all_58_12 = all_52_7
% 201.35/33.36    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.36    (25)  all_58_2 = all_52_3
% 201.35/33.36    (26)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.36    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.36    (28)   ~ (all_52_29 = e3)
% 201.35/33.36    (29)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.36    (30)  all_58_9 = all_14_1
% 201.35/33.36    (31)   ~ (all_52_25 = e3)
% 201.35/33.36    (32)   ~ (e2 = e0)
% 201.35/33.36    (33)  op(e3, e1) = all_52_17
% 201.35/33.36    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.36    (35)  all_58_8 = all_10_2
% 201.35/33.36    (36)   ~ (all_52_5 = all_10_2)
% 201.35/33.36    (37)   ~ (all_52_9 = all_4_2)
% 201.35/33.36    (38)   ~ (all_52_9 = all_6_2)
% 201.35/33.36    (39)  op(e3, e3) = all_6_2
% 201.35/33.36    (40)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.36    (41)   ~ (all_52_3 = all_52_7)
% 201.35/33.36    (42)  op(all_52_17, all_52_17) = e3
% 201.35/33.36    (43)  all_58_6 = all_52_5
% 201.35/33.36    (44)   ~ (all_52_17 = all_6_2)
% 201.35/33.36    (45)   ~ (e1 = e0)
% 201.35/33.36    (46)   ~ (e3 = e2)
% 201.35/33.36    (47)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.36    (48)  all_58_3 = all_4_2
% 201.35/33.36    (49)   ~ (all_52_3 = all_4_2)
% 201.35/33.36    (50)  all_58_2 = e3
% 201.35/33.36    (51)  all_58_4 = all_52_17
% 201.35/33.36  
% 201.35/33.36  Begin of proof
% 201.35/33.36  | 
% 201.35/33.36  | COMBINE_EQS: (25), (50) imply:
% 201.35/33.36  |   (52)  all_52_3 = e3
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (52) implies:
% 201.35/33.36  |   (53)  all_52_3 = e3
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (13), (53) imply:
% 201.35/33.36  |   (54)   ~ (all_52_5 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (54) implies:
% 201.35/33.36  |   (55)   ~ (all_52_5 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (41), (53) imply:
% 201.35/33.36  |   (56)   ~ (all_52_7 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (56) implies:
% 201.35/33.36  |   (57)   ~ (all_52_7 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (6), (53) imply:
% 201.35/33.36  |   (58)   ~ (all_6_2 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (58) implies:
% 201.35/33.36  |   (59)   ~ (all_6_2 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (1), (53) imply:
% 201.35/33.36  |   (60)  op(e3, e3) = all_52_2
% 201.35/33.36  | 
% 201.35/33.36  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14), (15),
% 201.35/33.36  |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 201.35/33.36  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 201.35/33.36  |            (38), (39), (40), (42), (43), (44), (45), (46), (47), (48), (49),
% 201.35/33.36  |            (51), (55), (57), (59), (60) are inconsistent by sub-proof #341.
% 201.35/33.36  | 
% 201.35/33.36  End of proof
% 201.35/33.36  
% 201.35/33.36  Sub-proof #238 shows that the following formulas are inconsistent:
% 201.35/33.36  ----------------------------------------------------------------
% 201.35/33.36    (1)   ~ (all_52_25 = all_52_27)
% 201.35/33.36    (2)  all_58_14 = all_52_23
% 201.35/33.36    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.35/33.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.36    (5)  all_58_1 = all_52_9
% 201.35/33.36    (6)   ~ (all_52_9 = all_52_13)
% 201.35/33.36    (7)   ~ (e3 = e0)
% 201.35/33.36    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.36    (9)   ~ (all_52_7 = all_52_15)
% 201.35/33.36    (10)   ~ (all_52_17 = all_52_25)
% 201.35/33.36    (11)  all_16_1 = all_10_1
% 201.35/33.36    (12)  all_58_0 = all_6_2
% 201.35/33.36    (13)  op(e3, all_6_1) = e1
% 201.35/33.36    (14)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.36    (15)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.36    (16)  all_58_13 = all_52_15
% 201.35/33.36    (17)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.36    (18)  all_58_9 = all_52_25
% 201.35/33.36    (19)  op(e2, e2) = all_4_2
% 201.35/33.36    (20)  all_58_11 = all_52_29
% 201.35/33.36    (21)   ~ (all_52_9 = all_52_15)
% 201.35/33.36    (22)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.36    (23)  op(all_10_2, e1) = all_10_1
% 201.35/33.36    (24)   ~ (all_52_7 = all_6_2)
% 201.35/33.36    (25)  op(e0, e1) = all_52_23
% 201.35/33.36    (26)   ~ (all_52_15 = e0)
% 201.35/33.36    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.36    (28)  all_58_15 = e0
% 201.35/33.36    (29)   ~ (all_4_1 = e1)
% 201.35/33.36    (30)   ~ (all_52_25 = e0)
% 201.35/33.36    (31)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.36    (32)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.36    (33)  op(e0, e0) = e0
% 201.35/33.36    (34)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 201.35/33.36    (35)  all_58_10 = all_52_27
% 201.35/33.36    (36)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.36    (37)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.36    (38)   ~ (all_52_25 = all_52_29)
% 201.35/33.36    (39)  all_16_2 = all_10_2
% 201.35/33.36    (40)  all_58_7 = all_52_13
% 201.35/33.36    (41)   ~ (all_52_5 = all_52_7)
% 201.35/33.36    (42)  all_58_12 = all_52_7
% 201.35/33.36    (43)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.36    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.36    (45)  all_58_2 = all_52_3
% 201.35/33.36    (46)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.36    (47)  all_56_2 = all_52_17
% 201.35/33.36    (48)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.36    (49)  all_56_7 = all_52_27
% 201.35/33.36    (50)   ~ (e2 = e0)
% 201.35/33.36    (51)  op(all_4_2, e2) = all_4_1
% 201.35/33.36    (52)  all_56_6 = all_52_19
% 201.35/33.36    (53)   ~ (all_52_13 = all_4_2)
% 201.35/33.36    (54)  op(e3, e1) = all_52_17
% 201.35/33.36    (55)  op(e0, e3) = all_52_7
% 201.35/33.36    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.36    (57)   ~ (all_52_9 = all_52_25)
% 201.35/33.36    (58)   ~ (all_52_19 = all_10_2)
% 201.35/33.36    (59)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.36    (60)  all_58_8 = all_10_2
% 201.35/33.36    (61)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 201.35/33.36    (62)  all_56_12 = all_52_7
% 201.35/33.36    (63)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.36    (64)   ~ (all_52_25 = all_6_2)
% 201.35/33.36    (65)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.36    (66)   ~ (all_52_9 = all_4_2)
% 201.35/33.36    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.35/33.36    (68)   ~ (all_52_9 = all_6_2)
% 201.35/33.36    (69)  op(e3, e3) = all_6_2
% 201.35/33.36    (70)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.36    (71)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.36    (72)  op(all_4_2, all_4_2) = all_52_10
% 201.35/33.36    (73)  all_56_3 = all_52_25
% 201.35/33.36    (74)   ~ (all_52_3 = all_52_7)
% 201.35/33.36    (75)  all_58_5 = all_52_19
% 201.35/33.36    (76)  all_56_1 = all_52_9
% 201.35/33.36    (77)   ~ (all_52_15 = all_4_2)
% 201.35/33.36    (78)   ~ (all_52_27 = all_4_2)
% 201.35/33.36    (79)  all_58_6 = all_52_5
% 201.35/33.36    (80)  op(e3, e2) = all_52_9
% 201.35/33.36    (81)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.36    (82)   ~ (all_52_17 = all_6_2)
% 201.35/33.36    (83)   ~ (e1 = e0)
% 201.35/33.36    (84)   ~ (e3 = e2)
% 201.35/33.36    (85)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.36    (86)   ~ (all_52_9 = all_52_17)
% 201.35/33.36    (87)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.36    (88)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.36    (89)  op(e1, e1) = all_10_2
% 201.35/33.36    (90)   ~ (all_52_7 = all_52_23)
% 201.35/33.36    (91)  all_58_3 = all_4_2
% 201.35/33.36    (92)  all_56_13 = all_52_15
% 201.35/33.36    (93)  op(all_6_2, e3) = all_6_1
% 201.35/33.36    (94)   ~ (all_52_13 = all_52_29)
% 201.35/33.36    (95)  all_58_4 = all_52_17
% 201.35/33.36    (96)   ~ (all_52_7 = e0)
% 201.35/33.36    (97)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.36  
% 201.35/33.36  Begin of proof
% 201.35/33.36  | 
% 201.35/33.36  | ALPHA: (34) implies:
% 201.35/33.36  |   (98)  all_52_14 = e0
% 201.35/33.36  |   (99)  all_52_12 = e1
% 201.35/33.36  |   (100)  all_52_10 = e2
% 201.35/33.36  |   (101)  all_52_8 = e3
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (36), (101) imply:
% 201.35/33.36  |   (102)  op(all_52_9, all_52_9) = e3
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (88), (99) imply:
% 201.35/33.36  |   (103)  op(all_52_13, all_52_13) = e1
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (37), (98) imply:
% 201.35/33.36  |   (104)  op(all_52_15, all_52_15) = e0
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (72), (100) imply:
% 201.35/33.36  |   (105)  op(all_4_2, all_4_2) = e2
% 201.35/33.36  | 
% 201.35/33.36  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.35/33.36  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.35/33.36  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 201.35/33.36  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 201.35/33.36  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 201.35/33.36  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 201.35/33.36  |            (71), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 201.35/33.36  |            (83), (84), (85), (86), (87), (89), (90), (91), (92), (93), (94),
% 201.35/33.36  |            (95), (96), (97), (102), (103), (104), (105) are inconsistent by
% 201.35/33.36  |            sub-proof #239.
% 201.35/33.36  | 
% 201.35/33.36  End of proof
% 201.35/33.36  
% 201.35/33.36  Sub-proof #239 shows that the following formulas are inconsistent:
% 201.35/33.36  ----------------------------------------------------------------
% 201.35/33.36    (1)   ~ (all_52_25 = all_52_27)
% 201.35/33.36    (2)  all_58_14 = all_52_23
% 201.35/33.36    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.35/33.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.36    (5)  all_58_1 = all_52_9
% 201.35/33.36    (6)   ~ (all_52_9 = all_52_13)
% 201.35/33.36    (7)   ~ (e3 = e0)
% 201.35/33.36    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.36    (9)   ~ (all_52_7 = all_52_15)
% 201.35/33.36    (10)  op(all_52_15, all_52_15) = e0
% 201.35/33.36    (11)   ~ (all_52_17 = all_52_25)
% 201.35/33.36    (12)  all_16_1 = all_10_1
% 201.35/33.36    (13)  all_58_0 = all_6_2
% 201.35/33.36    (14)  op(e3, all_6_1) = e1
% 201.35/33.36    (15)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.36    (16)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.36    (17)  all_58_13 = all_52_15
% 201.35/33.36    (18)  op(all_52_13, all_52_13) = e1
% 201.35/33.36    (19)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.36    (20)  all_58_9 = all_52_25
% 201.35/33.36    (21)  op(e2, e2) = all_4_2
% 201.35/33.36    (22)  all_58_11 = all_52_29
% 201.35/33.36    (23)   ~ (all_52_9 = all_52_15)
% 201.35/33.36    (24)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.36    (25)  op(all_10_2, e1) = all_10_1
% 201.35/33.36    (26)   ~ (all_52_7 = all_6_2)
% 201.35/33.36    (27)  op(e0, e1) = all_52_23
% 201.35/33.36    (28)   ~ (all_52_15 = e0)
% 201.35/33.36    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.36    (30)  all_58_15 = e0
% 201.35/33.36    (31)   ~ (all_4_1 = e1)
% 201.35/33.36    (32)   ~ (all_52_25 = e0)
% 201.35/33.36    (33)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.36    (34)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.36    (35)  op(e0, e0) = e0
% 201.35/33.36    (36)  all_58_10 = all_52_27
% 201.35/33.36    (37)   ~ (all_52_25 = all_52_29)
% 201.35/33.36    (38)  all_16_2 = all_10_2
% 201.35/33.36    (39)  all_58_7 = all_52_13
% 201.35/33.36    (40)   ~ (all_52_5 = all_52_7)
% 201.35/33.36    (41)  all_58_12 = all_52_7
% 201.35/33.36    (42)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.36    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.36    (44)  all_58_2 = all_52_3
% 201.35/33.36    (45)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.36    (46)  all_56_2 = all_52_17
% 201.35/33.36    (47)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.36    (48)  all_56_7 = all_52_27
% 201.35/33.36    (49)   ~ (e2 = e0)
% 201.35/33.36    (50)  op(all_4_2, e2) = all_4_1
% 201.35/33.36    (51)  all_56_6 = all_52_19
% 201.35/33.36    (52)   ~ (all_52_13 = all_4_2)
% 201.35/33.36    (53)  op(e3, e1) = all_52_17
% 201.35/33.36    (54)  op(e0, e3) = all_52_7
% 201.35/33.36    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.36    (56)   ~ (all_52_9 = all_52_25)
% 201.35/33.36    (57)   ~ (all_52_19 = all_10_2)
% 201.35/33.36    (58)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.36    (59)  all_58_8 = all_10_2
% 201.35/33.36    (60)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 201.35/33.36    (61)  all_56_12 = all_52_7
% 201.35/33.36    (62)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.36    (63)   ~ (all_52_25 = all_6_2)
% 201.35/33.36    (64)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.36    (65)   ~ (all_52_9 = all_4_2)
% 201.35/33.36    (66)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.35/33.36    (67)  op(all_4_2, all_4_2) = e2
% 201.35/33.36    (68)   ~ (all_52_9 = all_6_2)
% 201.35/33.36    (69)  op(e3, e3) = all_6_2
% 201.35/33.36    (70)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.36    (71)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.36    (72)  all_56_3 = all_52_25
% 201.35/33.36    (73)   ~ (all_52_3 = all_52_7)
% 201.35/33.36    (74)  all_58_5 = all_52_19
% 201.35/33.36    (75)  all_56_1 = all_52_9
% 201.35/33.36    (76)   ~ (all_52_15 = all_4_2)
% 201.35/33.36    (77)   ~ (all_52_27 = all_4_2)
% 201.35/33.36    (78)  all_58_6 = all_52_5
% 201.35/33.36    (79)  op(e3, e2) = all_52_9
% 201.35/33.36    (80)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.36    (81)   ~ (all_52_17 = all_6_2)
% 201.35/33.36    (82)   ~ (e1 = e0)
% 201.35/33.36    (83)   ~ (e3 = e2)
% 201.35/33.36    (84)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.36    (85)   ~ (all_52_9 = all_52_17)
% 201.35/33.36    (86)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.36    (87)  op(e1, e1) = all_10_2
% 201.35/33.36    (88)  op(all_52_9, all_52_9) = e3
% 201.35/33.36    (89)   ~ (all_52_7 = all_52_23)
% 201.35/33.36    (90)  all_58_3 = all_4_2
% 201.35/33.36    (91)  all_56_13 = all_52_15
% 201.35/33.36    (92)  op(all_6_2, e3) = all_6_1
% 201.35/33.36    (93)   ~ (all_52_13 = all_52_29)
% 201.35/33.36    (94)  all_58_4 = all_52_17
% 201.35/33.36    (95)   ~ (all_52_7 = e0)
% 201.35/33.36    (96)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.36  
% 201.35/33.36  Begin of proof
% 201.35/33.36  | 
% 201.35/33.36  | BETA: splitting (33) gives:
% 201.35/33.36  | 
% 201.35/33.36  | Case 1:
% 201.35/33.36  | | 
% 201.35/33.36  | |   (97)  all_56_13 = e3
% 201.35/33.36  | | 
% 201.35/33.36  | | REF_CLOSE: (2), (4), (8), (9), (10), (14), (17), (21), (23), (24), (26),
% 201.35/33.36  | |            (30), (41), (42), (49), (53), (54), (58), (61), (68), (69), (75),
% 201.35/33.36  | |            (76), (83), (84), (85), (88), (91), (92), (97) are inconsistent
% 201.35/33.36  | |            by sub-proof #321.
% 201.35/33.36  | | 
% 201.35/33.36  | Case 2:
% 201.35/33.36  | | 
% 201.35/33.36  | |   (98)   ~ (all_56_13 = e3)
% 201.35/33.36  | |   (99)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.36  | | 
% 201.35/33.36  | | REDUCE: (91), (98) imply:
% 201.35/33.36  | |   (100)   ~ (all_52_15 = e3)
% 201.35/33.36  | | 
% 201.35/33.36  | | BETA: splitting (80) gives:
% 201.35/33.36  | | 
% 201.35/33.36  | | Case 1:
% 201.35/33.36  | | | 
% 201.35/33.36  | | |   (101)  all_58_12 = e3
% 201.35/33.36  | | | 
% 201.35/33.36  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (11), (13), (15), (16), (17),
% 201.35/33.36  | | |            (18), (19), (20), (21), (22), (26), (29), (30), (31), (32),
% 201.35/33.36  | | |            (34), (35), (36), (37), (39), (40), (41), (43), (44), (45),
% 201.35/33.36  | | |            (46), (47), (48), (50), (51), (52), (55), (56), (57), (59),
% 201.35/33.36  | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 201.35/33.36  | | |            (72), (73), (74), (75), (77), (78), (79), (81), (82), (84),
% 201.35/33.36  | | |            (85), (86), (88), (90), (93), (94), (95), (96), (101) are
% 201.35/33.36  | | |            inconsistent by sub-proof #317.
% 201.35/33.36  | | | 
% 201.35/33.36  | | Case 2:
% 201.35/33.36  | | | 
% 201.35/33.36  | | |   (102)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.36  | | | 
% 201.35/33.36  | | | REF_CLOSE: (2), (4), (7), (8), (9), (10), (12), (17), (21), (24), (25),
% 201.35/33.36  | | |            (27), (28), (30), (35), (38), (41), (60), (61), (67), (76),
% 201.35/33.36  | | |            (87), (89), (91), (95), (99), (100), (102) are inconsistent by
% 201.35/33.36  | | |            sub-proof #648.
% 201.35/33.36  | | | 
% 201.35/33.36  | | End of split
% 201.35/33.36  | | 
% 201.35/33.36  | End of split
% 201.35/33.36  | 
% 201.35/33.36  End of proof
% 201.35/33.36  
% 201.35/33.36  Sub-proof #240 shows that the following formulas are inconsistent:
% 201.35/33.36  ----------------------------------------------------------------
% 201.35/33.36    (1)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.36    (3)  op(e2, e3) = all_52_3
% 201.35/33.36    (4)   ~ (all_52_3 = all_52_19)
% 201.35/33.36    (5)   ~ (all_52_3 = all_6_2)
% 201.35/33.36    (6)  all_56_4 = all_52_3
% 201.35/33.36    (7)  op(e3, all_6_1) = e1
% 201.35/33.36    (8)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.36    (9)  all_56_6 = e3
% 201.35/33.36    (10)  all_46_2 = all_6_2
% 201.35/33.36    (11)   ~ (all_52_7 = all_6_2)
% 201.35/33.36    (12)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.35/33.36    (13)  op(all_52_19, all_52_19) = e2
% 201.35/33.36    (14)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.36    (15)  all_56_6 = all_52_19
% 201.35/33.36    (16)  op(e3, e1) = all_52_17
% 201.35/33.36    (17)   ~ (all_52_19 = all_10_2)
% 201.35/33.36    (18)  all_56_12 = all_52_7
% 201.35/33.36    (19)  op(e3, e3) = all_6_2
% 201.35/33.36    (20)   ~ (all_52_3 = all_52_7)
% 201.35/33.36    (21)  op(all_52_17, all_52_17) = e3
% 201.35/33.36    (22)  all_46_1 = all_6_1
% 201.35/33.36    (23)  op(e1, e1) = all_10_2
% 201.35/33.36    (24)  op(all_6_2, e3) = all_6_1
% 201.35/33.36  
% 201.35/33.36  Begin of proof
% 201.35/33.36  | 
% 201.35/33.36  | COMBINE_EQS: (9), (15) imply:
% 201.35/33.36  |   (25)  all_52_19 = e3
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (25) implies:
% 201.35/33.36  |   (26)  all_52_19 = e3
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (4), (26) imply:
% 201.35/33.36  |   (27)   ~ (all_52_3 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (17), (26) imply:
% 201.35/33.36  |   (28)   ~ (all_10_2 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | SIMP: (28) implies:
% 201.35/33.36  |   (29)   ~ (all_10_2 = e3)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (13), (26) imply:
% 201.35/33.36  |   (30)  op(e3, e3) = e2
% 201.35/33.36  | 
% 201.35/33.36  | GROUND_INST: instantiating (2) with all_6_2, e2, e3, e3, simplifying with
% 201.35/33.36  |              (19), (30) gives:
% 201.35/33.36  |   (31)  all_6_2 = e2
% 201.35/33.36  | 
% 201.35/33.36  | COMBINE_EQS: (10), (31) imply:
% 201.35/33.36  |   (32)  all_46_2 = e2
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (5), (31) imply:
% 201.35/33.36  |   (33)   ~ (all_52_3 = e2)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (11), (31) imply:
% 201.35/33.36  |   (34)   ~ (all_52_7 = e2)
% 201.35/33.36  | 
% 201.35/33.36  | REDUCE: (24), (31) imply:
% 201.35/33.36  |   (35)  op(e2, e3) = all_6_1
% 201.35/33.36  | 
% 201.35/33.36  | BETA: splitting (12) gives:
% 201.35/33.36  | 
% 201.35/33.36  | Case 1:
% 201.35/33.36  | | 
% 201.35/33.36  | |   (36)   ~ (all_46_2 = e2)
% 201.35/33.36  | | 
% 201.35/33.36  | | REDUCE: (32), (36) imply:
% 201.35/33.36  | |   (37)  $false
% 201.35/33.36  | | 
% 201.35/33.36  | | CLOSE: (37) is inconsistent.
% 201.35/33.36  | | 
% 201.35/33.36  | Case 2:
% 201.35/33.36  | | 
% 201.35/33.36  | |   (38)   ~ (all_46_1 = e0)
% 201.35/33.36  | | 
% 201.35/33.36  | | REDUCE: (22), (38) imply:
% 201.35/33.36  | |   (39)   ~ (all_6_1 = e0)
% 201.35/33.36  | | 
% 201.35/33.36  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (14), (16), (18), (20), (21), (23),
% 201.35/33.36  | |            (27), (29), (33), (34), (35), (39) are inconsistent by sub-proof
% 201.35/33.37  | |            #241.
% 201.35/33.37  | | 
% 201.35/33.37  | End of split
% 201.35/33.37  | 
% 201.35/33.37  End of proof
% 201.35/33.37  
% 201.35/33.37  Sub-proof #241 shows that the following formulas are inconsistent:
% 201.35/33.37  ----------------------------------------------------------------
% 201.35/33.37    (1)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.37    (3)  op(e2, e3) = all_52_3
% 201.35/33.37    (4)  all_56_4 = all_52_3
% 201.35/33.37    (5)  op(e3, all_6_1) = e1
% 201.35/33.37    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.37    (7)   ~ (all_6_1 = e0)
% 201.35/33.37    (8)   ~ (all_52_3 = e3)
% 201.35/33.37    (9)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.37    (10)  op(e2, e3) = all_6_1
% 201.35/33.37    (11)   ~ (all_10_2 = e3)
% 201.35/33.37    (12)   ~ (all_52_7 = e2)
% 201.35/33.37    (13)  op(e3, e1) = all_52_17
% 201.35/33.37    (14)  all_56_12 = all_52_7
% 201.35/33.37    (15)   ~ (all_52_3 = all_52_7)
% 201.35/33.37    (16)  op(all_52_17, all_52_17) = e3
% 201.35/33.37    (17)  op(e1, e1) = all_10_2
% 201.35/33.37    (18)   ~ (all_52_3 = e2)
% 201.35/33.37  
% 201.35/33.37  Begin of proof
% 201.35/33.37  | 
% 201.35/33.37  | GROUND_INST: instantiating (2) with all_52_3, all_6_1, e3, e2, simplifying
% 201.35/33.37  |              with (3), (10) gives:
% 201.35/33.37  |   (19)  all_52_3 = all_6_1
% 201.35/33.37  | 
% 201.35/33.37  | COMBINE_EQS: (4), (19) imply:
% 201.35/33.37  |   (20)  all_56_4 = all_6_1
% 201.35/33.37  | 
% 201.35/33.37  | REDUCE: (15), (19) imply:
% 201.35/33.37  |   (21)   ~ (all_52_7 = all_6_1)
% 201.35/33.37  | 
% 201.35/33.37  | SIMP: (21) implies:
% 201.35/33.37  |   (22)   ~ (all_52_7 = all_6_1)
% 201.35/33.37  | 
% 201.35/33.37  | REDUCE: (8), (19) imply:
% 201.35/33.37  |   (23)   ~ (all_6_1 = e3)
% 201.35/33.37  | 
% 201.35/33.37  | REDUCE: (18), (19) imply:
% 201.35/33.37  |   (24)   ~ (all_6_1 = e2)
% 201.35/33.37  | 
% 201.35/33.37  | REDUCE: (1), (19) imply:
% 201.35/33.37  |   (25)  op(all_6_1, all_6_1) = all_52_2
% 201.35/33.37  | 
% 201.35/33.37  | BETA: splitting (9) gives:
% 201.35/33.37  | 
% 201.35/33.37  | Case 1:
% 201.35/33.37  | | 
% 201.35/33.37  | |   (26)  all_56_4 = e3
% 201.35/33.37  | | 
% 201.35/33.37  | | COMBINE_EQS: (20), (26) imply:
% 201.35/33.37  | |   (27)  all_6_1 = e3
% 201.35/33.37  | | 
% 201.35/33.37  | | REDUCE: (23), (27) imply:
% 201.35/33.37  | |   (28)  $false
% 201.35/33.37  | | 
% 201.35/33.37  | | CLOSE: (28) is inconsistent.
% 201.35/33.37  | | 
% 201.35/33.37  | Case 2:
% 201.35/33.37  | | 
% 201.35/33.37  | |   (29)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.37  | | 
% 201.35/33.37  | | BETA: splitting (29) gives:
% 201.35/33.37  | | 
% 201.35/33.37  | | Case 1:
% 201.35/33.37  | | | 
% 201.35/33.37  | | |   (30)  all_56_4 = e2
% 201.35/33.37  | | | 
% 201.35/33.37  | | | COMBINE_EQS: (20), (30) imply:
% 201.35/33.37  | | |   (31)  all_6_1 = e2
% 201.35/33.37  | | | 
% 201.35/33.37  | | | REDUCE: (24), (31) imply:
% 201.35/33.37  | | |   (32)  $false
% 201.35/33.37  | | | 
% 201.35/33.37  | | | CLOSE: (32) is inconsistent.
% 201.35/33.37  | | | 
% 201.35/33.37  | | Case 2:
% 201.35/33.37  | | | 
% 201.35/33.37  | | |   (33)  all_56_4 = e1 | all_56_4 = e0
% 201.35/33.37  | | | 
% 201.35/33.37  | | | BETA: splitting (33) gives:
% 201.35/33.37  | | | 
% 201.35/33.37  | | | Case 1:
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | |   (34)  all_56_4 = e1
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | COMBINE_EQS: (20), (34) imply:
% 201.35/33.37  | | | |   (35)  all_6_1 = e1
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | REDUCE: (22), (35) imply:
% 201.35/33.37  | | | |   (36)   ~ (all_52_7 = e1)
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | REDUCE: (25), (35) imply:
% 201.35/33.37  | | | |   (37)  op(e1, e1) = all_52_2
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | REDUCE: (5), (35) imply:
% 201.35/33.37  | | | |   (38)  op(e3, e1) = e1
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | REF_CLOSE: (2), (6), (11), (12), (13), (14), (16), (17), (36), (37),
% 201.35/33.37  | | | |            (38) are inconsistent by sub-proof #266.
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | Case 2:
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | |   (39)  all_56_4 = e0
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | COMBINE_EQS: (20), (39) imply:
% 201.35/33.37  | | | |   (40)  all_6_1 = e0
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | REDUCE: (7), (40) imply:
% 201.35/33.37  | | | |   (41)  $false
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | | CLOSE: (41) is inconsistent.
% 201.35/33.37  | | | | 
% 201.35/33.37  | | | End of split
% 201.35/33.37  | | | 
% 201.35/33.37  | | End of split
% 201.35/33.37  | | 
% 201.35/33.37  | End of split
% 201.35/33.37  | 
% 201.35/33.37  End of proof
% 201.35/33.37  
% 201.35/33.37  Sub-proof #242 shows that the following formulas are inconsistent:
% 201.35/33.37  ----------------------------------------------------------------
% 201.35/33.37    (1)   ~ (all_52_15 = all_52_23)
% 201.35/33.37    (2)   ~ (all_52_25 = all_52_27)
% 201.35/33.37    (3)  all_58_14 = all_52_23
% 201.35/33.37    (4)   ~ (e3 = e1)
% 201.35/33.37    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.35/33.37    (6)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.37    (8)   ~ (all_52_5 = all_52_13)
% 201.35/33.37    (9)  all_58_1 = all_52_9
% 201.35/33.37    (10)   ~ (all_52_9 = all_52_13)
% 201.35/33.37    (11)   ~ (e3 = e0)
% 201.35/33.37    (12)  op(e2, e3) = all_52_3
% 201.35/33.37    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.37    (14)  op(e0, e2) = all_52_15
% 201.35/33.37    (15)   ~ (all_52_7 = all_52_15)
% 201.35/33.37    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.37    (17)   ~ (all_52_17 = all_52_25)
% 201.35/33.37    (18)   ~ (all_52_3 = all_6_2)
% 201.35/33.37    (19)  all_58_0 = all_6_2
% 201.35/33.37    (20)  op(all_14_2, e0) = all_14_1
% 201.35/33.37    (21)  all_56_4 = all_52_3
% 201.35/33.37    (22)  op(e3, all_6_1) = e1
% 201.35/33.37    (23)   ~ (all_52_17 = all_10_2)
% 201.35/33.37    (24)  op(e3, e0) = all_52_25
% 201.35/33.37    (25)  op(e0, all_14_1) = all_14_0
% 201.35/33.37    (26)  op(all_52_5, all_52_5) = all_52_4
% 201.35/33.37    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.37    (28)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.37    (29)   ~ (all_52_27 = all_52_29)
% 201.35/33.37    (30)  all_58_13 = all_52_15
% 201.35/33.37    (31)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.37    (32)  all_58_9 = all_52_25
% 201.35/33.37    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.35/33.37    (34)   ~ (all_52_29 = all_14_2)
% 201.35/33.37    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.35/33.37    (36)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.37    (37)  op(e1, e3) = all_52_5
% 201.35/33.37    (38)  op(e2, e2) = all_4_2
% 201.35/33.37    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.35/33.37    (40)   ~ (all_52_3 = all_52_5)
% 201.35/33.37    (41)  all_58_11 = all_52_29
% 201.35/33.37    (42)  all_56_5 = all_4_2
% 201.35/33.37    (43)   ~ (all_52_25 = all_14_2)
% 201.35/33.37    (44)   ~ (all_52_9 = all_52_15)
% 201.35/33.37    (45)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.37    (46)   ~ (all_52_3 = all_52_27)
% 201.35/33.37    (47)  op(all_10_2, e1) = all_10_1
% 201.35/33.37    (48)  all_46_2 = all_6_2
% 201.35/33.37    (49)  op(all_6_2, all_6_2) = all_52_0
% 201.35/33.37    (50)   ~ (all_52_7 = all_6_2)
% 201.35/33.37    (51)  op(e0, e0) = all_14_2
% 201.35/33.37    (52)  op(e0, e1) = all_52_23
% 201.35/33.37    (53)  all_56_15 = all_14_2
% 201.35/33.37    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.37    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.35/33.37    (56)   ~ (all_58_15 = e0)
% 201.35/33.37    (57)  all_56_11 = all_52_29
% 201.35/33.37    (58)   ~ (all_4_1 = e1)
% 201.35/33.37    (59)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.35/33.37    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.37    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.37    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.35/33.37    (63)  all_56_9 = all_52_13
% 201.35/33.37    (64)   ~ (e2 = e1)
% 201.35/33.37    (65)   ~ (all_52_13 = all_10_2)
% 201.35/33.37    (66)  all_58_10 = all_52_27
% 201.35/33.37    (67)  all_56_8 = all_52_5
% 201.35/33.37    (68)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.37    (69)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.37    (70)   ~ (all_52_19 = all_52_23)
% 201.35/33.37    (71)   ~ (all_52_25 = all_52_29)
% 201.35/33.37    (72)   ~ (all_52_29 = all_10_2)
% 201.35/33.37    (73)  all_58_7 = all_52_13
% 201.35/33.37    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.37    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.35/33.37    (76)   ~ (all_52_5 = all_52_7)
% 201.35/33.37    (77)  all_58_12 = all_52_7
% 201.35/33.37    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.37    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.37    (80)   ~ (all_52_7 = all_14_2)
% 201.35/33.37    (81)  all_58_2 = all_52_3
% 201.35/33.37    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.37    (83)  all_56_2 = all_52_17
% 201.35/33.37    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.37    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.37    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.37    (87)   ~ (all_14_0 = e3)
% 201.35/33.37    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.35/33.37    (89)  all_56_7 = all_52_27
% 201.35/33.37    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.37    (91)   ~ (e2 = e0)
% 201.35/33.37    (92)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.35/33.37    (93)  op(all_4_2, e2) = all_4_1
% 201.35/33.37    (94)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.35/33.37    (95)   ~ (all_52_5 = all_52_29)
% 201.35/33.37    (96)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.37    (97)  all_56_6 = all_52_19
% 201.35/33.37    (98)   ~ (all_52_15 = all_14_2)
% 201.35/33.37    (99)   ~ (all_52_19 = all_52_27)
% 201.35/33.37    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.35/33.37    (101)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.35/33.37    (102)   ~ (all_52_13 = all_4_2)
% 201.35/33.37    (103)  op(e3, e1) = all_52_17
% 201.35/33.37    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.35/33.37    (105)  op(e0, e3) = all_52_7
% 201.35/33.37    (106)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.37    (107)   ~ (all_52_9 = all_52_25)
% 201.35/33.37    (108)  all_58_15 = all_14_2
% 201.35/33.37    (109)   ~ (all_52_19 = all_10_2)
% 201.35/33.37    (110)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.37    (111)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.35/33.37    (112)  all_58_8 = all_10_2
% 201.35/33.37    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.35/33.37    (114)   ~ (all_52_5 = all_10_2)
% 201.35/33.37    (115)  op(all_52_29, all_52_29) = all_52_28
% 201.35/33.37    (116)   ~ (all_52_23 = all_14_2)
% 201.35/33.37    (117)  all_56_12 = all_52_7
% 201.35/33.37    (118)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.37    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.35/33.37    (120)   ~ (all_52_25 = all_6_2)
% 201.35/33.37    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.37    (122)   ~ (all_52_9 = all_4_2)
% 201.35/33.37    (123)   ~ (all_52_5 = all_6_2)
% 201.35/33.37    (124)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.35/33.37    (125)   ~ (all_52_9 = all_6_2)
% 201.35/33.37    (126)   ~ (all_52_13 = all_52_15)
% 201.35/33.37    (127)  all_56_0 = all_6_2
% 201.35/33.37    (128)  op(e3, e3) = all_6_2
% 201.35/33.37    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.37    (130)   ~ (all_52_27 = all_14_2)
% 201.35/33.37    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.37    (132)  all_56_14 = all_52_23
% 201.35/33.37    (133)  op(all_4_2, all_4_2) = all_52_10
% 201.35/33.37    (134)  all_56_3 = all_52_25
% 201.35/33.37    (135)   ~ (all_52_3 = all_52_7)
% 201.35/33.37    (136)  op(all_14_2, all_14_2) = all_52_30
% 201.35/33.37    (137)  all_58_5 = all_52_19
% 201.35/33.37    (138)  all_56_1 = all_52_9
% 201.35/33.37    (139)   ~ (all_52_15 = all_4_2)
% 201.35/33.37    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.35/33.37           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.35/33.37           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.35/33.37           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.35/33.37    (141)   ~ (all_52_27 = all_4_2)
% 201.35/33.37    (142)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 201.35/33.37             all_58_13 = e0 | all_58_14 = e0)
% 201.35/33.37    (143)  all_58_6 = all_52_5
% 201.35/33.37    (144)  op(e3, e2) = all_52_9
% 201.35/33.37    (145)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.37    (146)   ~ (all_52_17 = all_6_2)
% 201.35/33.37    (147)   ~ (e1 = e0)
% 201.35/33.37    (148)   ~ (e3 = e2)
% 201.35/33.37    (149)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.37    (150)   ~ (all_52_9 = all_52_17)
% 201.35/33.37    (151)  all_56_10 = all_10_2
% 201.35/33.37    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.37    (153)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.35/33.37    (154)  all_46_1 = all_6_1
% 201.35/33.37    (155)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.35/33.37    (156)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.37    (157)  op(e1, e1) = all_10_2
% 201.35/33.37    (158)   ~ (all_52_23 = all_10_2)
% 201.35/33.37    (159)   ~ (all_52_7 = all_52_23)
% 201.35/33.37    (160)   ~ (all_52_17 = all_52_19)
% 201.35/33.37    (161)  all_58_3 = all_4_2
% 201.35/33.37    (162)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.35/33.37    (163)  all_56_13 = all_52_15
% 201.35/33.37    (164)   ~ (all_52_3 = all_4_2)
% 201.35/33.37    (165)   ~ (all_52_19 = all_4_2)
% 201.35/33.37    (166)   ~ (all_52_17 = all_52_23)
% 201.35/33.37    (167)  op(all_6_2, e3) = all_6_1
% 201.35/33.37    (168)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.35/33.37    (169)   ~ (all_52_13 = all_52_29)
% 201.35/33.37    (170)  all_58_4 = all_52_17
% 201.35/33.37    (171)   ~ (all_14_0 = e1)
% 201.35/33.37    (172)   ~ (all_14_0 = e2)
% 201.35/33.37    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.35/33.37    (174)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.37  
% 201.35/33.37  Begin of proof
% 201.35/33.37  | 
% 201.35/33.37  | ALPHA: (142) implies:
% 201.35/33.37  |   (175)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.35/33.37  |   (176)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.35/33.37  | 
% 201.35/33.37  | REDUCE: (56), (108) imply:
% 201.35/33.37  |   (177)   ~ (all_14_2 = e0)
% 201.35/33.37  | 
% 201.35/33.37  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.35/33.37  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.35/33.37  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 201.35/33.37  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 201.35/33.37  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (57),
% 201.35/33.37  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 201.35/33.37  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 201.35/33.37  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 201.35/33.37  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 201.35/33.37  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 201.35/33.37  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 201.35/33.37  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 201.35/33.37  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 201.35/33.37  |            (138), (139), (140), (141), (143), (144), (145), (146), (147),
% 201.35/33.37  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 201.35/33.37  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 201.35/33.37  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 201.35/33.37  |            (175), (176), (177) are inconsistent by sub-proof #270.
% 201.35/33.37  | 
% 201.35/33.37  End of proof
% 201.35/33.37  
% 201.35/33.37  Sub-proof #243 shows that the following formulas are inconsistent:
% 201.35/33.37  ----------------------------------------------------------------
% 201.35/33.37    (1)   ~ (all_52_15 = all_52_23)
% 201.35/33.37    (2)   ~ (all_52_25 = all_52_27)
% 201.35/33.37    (3)  all_58_14 = all_52_23
% 201.35/33.37    (4)   ~ (e3 = e1)
% 201.35/33.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.37    (6)  all_58_1 = all_52_9
% 201.35/33.37    (7)   ~ (e3 = e0)
% 201.35/33.37    (8)  op(e2, e3) = all_52_3
% 201.35/33.37    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.37    (10)  op(e0, e2) = all_52_15
% 201.35/33.37    (11)   ~ (all_52_7 = all_52_15)
% 201.35/33.37    (12)   ~ (all_52_3 = all_52_19)
% 201.35/33.37    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.37    (14)   ~ (all_52_17 = all_52_25)
% 201.35/33.37    (15)   ~ (all_52_3 = all_6_2)
% 201.35/33.37    (16)  all_58_0 = all_6_2
% 201.35/33.37    (17)  all_56_4 = all_52_3
% 201.35/33.37    (18)  op(e3, all_6_1) = e1
% 201.35/33.37    (19)   ~ (all_52_17 = all_10_2)
% 201.35/33.37    (20)  op(e3, e0) = all_52_25
% 201.35/33.37    (21)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.37    (22)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.37    (23)  all_58_13 = all_52_15
% 201.35/33.37    (24)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.37    (25)  all_58_9 = all_52_25
% 201.35/33.37    (26)  op(e2, all_4_1) = e3
% 201.35/33.37    (27)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.37    (28)  op(e1, e3) = all_52_5
% 201.35/33.37    (29)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.35/33.37    (30)  op(e2, e2) = all_4_2
% 201.35/33.37    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.35/33.37    (32)  all_58_11 = all_52_29
% 201.35/33.37    (33)   ~ (all_52_9 = all_52_15)
% 201.35/33.37    (34)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.37    (35)   ~ (all_52_3 = all_52_27)
% 201.35/33.37    (36)  op(all_10_2, e1) = all_10_1
% 201.35/33.37    (37)  all_46_2 = all_6_2
% 201.35/33.37    (38)  op(all_6_2, all_6_2) = all_52_0
% 201.35/33.37    (39)   ~ (all_52_7 = all_6_2)
% 201.35/33.37    (40)   ~ (all_52_15 = e0)
% 201.35/33.37    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.37    (42)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.35/33.37    (43)  all_58_15 = e0
% 201.35/33.37    (44)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.35/33.37    (45)   ~ (all_52_25 = e0)
% 201.35/33.37    (46)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.37    (47)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.37    (48)   ~ (e2 = e1)
% 201.35/33.37    (49)   ~ (all_52_13 = all_10_2)
% 201.35/33.37    (50)  op(e0, e0) = e0
% 201.35/33.37    (51)  all_58_10 = all_52_27
% 201.35/33.37    (52)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.37    (53)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.37    (54)   ~ (all_52_19 = all_52_23)
% 201.35/33.37    (55)   ~ (all_52_25 = all_52_29)
% 201.35/33.37    (56)   ~ (all_52_29 = all_10_2)
% 201.35/33.37    (57)  all_58_7 = all_52_13
% 201.35/33.37    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.37    (59)   ~ (all_52_5 = all_52_7)
% 201.35/33.37    (60)  all_58_12 = all_52_7
% 201.35/33.37    (61)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.37    (62)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.37    (63)  all_58_2 = all_52_3
% 201.35/33.37    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.37    (65)  all_56_2 = all_52_17
% 201.35/33.37    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.37    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.37    (68)  all_56_7 = all_52_27
% 201.35/33.37    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.37    (70)   ~ (e2 = e0)
% 201.35/33.37    (71)  op(all_4_2, e2) = all_4_1
% 201.35/33.37    (72)   ~ (all_52_5 = all_52_29)
% 201.35/33.37    (73)   ~ (all_52_29 = e0)
% 201.35/33.37    (74)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.37    (75)  all_56_6 = all_52_19
% 201.35/33.37    (76)   ~ (all_52_19 = all_52_27)
% 201.35/33.37    (77)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.35/33.37    (78)   ~ (all_52_13 = all_4_2)
% 201.35/33.37    (79)  op(e3, e1) = all_52_17
% 201.35/33.37    (80)  op(e0, e3) = all_52_7
% 201.35/33.37    (81)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.37    (82)   ~ (all_52_9 = all_52_25)
% 201.35/33.37    (83)   ~ (all_52_19 = all_10_2)
% 201.35/33.37    (84)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.37    (85)  all_58_8 = all_10_2
% 201.35/33.37    (86)   ~ (all_52_23 = e0)
% 201.35/33.37    (87)  op(all_52_29, all_52_29) = all_52_28
% 201.35/33.37    (88)  all_56_12 = all_52_7
% 201.35/33.37    (89)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.37    (90)   ~ (all_52_25 = all_6_2)
% 201.35/33.37    (91)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.37    (92)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.35/33.37    (93)   ~ (all_52_9 = all_6_2)
% 201.35/33.37    (94)  op(e3, e3) = all_6_2
% 201.35/33.37    (95)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.37    (96)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.37    (97)  all_56_14 = all_52_23
% 201.35/33.37    (98)  op(all_4_2, all_4_2) = all_52_10
% 201.35/33.37    (99)  all_56_3 = all_52_25
% 201.35/33.37    (100)   ~ (all_52_3 = all_52_7)
% 201.35/33.37    (101)  all_58_5 = all_52_19
% 201.35/33.37    (102)  all_56_1 = all_52_9
% 201.35/33.37    (103)   ~ (all_52_15 = all_4_2)
% 201.35/33.37    (104)  all_58_6 = all_52_5
% 201.35/33.37    (105)  op(e3, e2) = all_52_9
% 201.35/33.37    (106)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.37    (107)   ~ (all_52_17 = all_6_2)
% 201.35/33.37    (108)   ~ (e1 = e0)
% 201.35/33.37    (109)   ~ (e3 = e2)
% 201.35/33.37    (110)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.37    (111)   ~ (all_52_9 = all_52_17)
% 201.35/33.37    (112)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.37    (113)  all_46_1 = all_6_1
% 201.35/33.37    (114)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.37    (115)  op(e1, e1) = all_10_2
% 201.35/33.37    (116)   ~ (all_52_23 = all_10_2)
% 201.35/33.37    (117)   ~ (all_52_7 = all_52_23)
% 201.35/33.37    (118)   ~ (all_52_17 = all_52_19)
% 201.35/33.37    (119)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.35/33.37           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.35/33.37    (120)  all_58_3 = all_4_2
% 201.35/33.37    (121)  all_56_13 = all_52_15
% 201.35/33.37    (122)   ~ (all_52_3 = all_4_2)
% 201.35/33.37    (123)   ~ (all_52_19 = all_4_2)
% 201.35/33.37    (124)   ~ (all_52_17 = all_52_23)
% 201.35/33.37    (125)  op(all_6_2, e3) = all_6_1
% 201.35/33.37    (126)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.35/33.37    (127)   ~ (all_52_13 = all_52_29)
% 201.35/33.37    (128)  all_58_4 = all_52_17
% 201.35/33.37    (129)   ~ (all_52_7 = e0)
% 201.35/33.37    (130)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.37  
% 201.35/33.37  Begin of proof
% 201.35/33.37  | 
% 201.35/33.37  | BETA: splitting (119) gives:
% 201.35/33.37  | 
% 201.35/33.37  | Case 1:
% 201.35/33.37  | | 
% 201.35/33.37  | |   (131)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 201.35/33.37  | | 
% 201.35/33.37  | | ALPHA: (131) implies:
% 201.35/33.37  | |   (132)  all_52_22 = e0
% 201.35/33.37  | |   (133)  all_52_20 = e1
% 201.35/33.37  | |   (134)  all_52_18 = e2
% 201.35/33.37  | |   (135)  all_52_16 = e3
% 201.35/33.37  | | 
% 201.35/33.37  | | REDUCE: (89), (135) imply:
% 201.35/33.37  | |   (136)  op(all_52_17, all_52_17) = e3
% 201.35/33.37  | | 
% 201.35/33.37  | | REDUCE: (22), (134) imply:
% 201.35/33.37  | |   (137)  op(all_52_19, all_52_19) = e2
% 201.35/33.37  | | 
% 201.35/33.37  | | REDUCE: (84), (132) imply:
% 201.35/33.37  | |   (138)  op(all_52_23, all_52_23) = e0
% 201.35/33.37  | | 
% 201.35/33.37  | | REDUCE: (24), (133) imply:
% 201.35/33.37  | |   (139)  op(all_10_2, all_10_2) = e1
% 201.35/33.37  | | 
% 201.35/33.37  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 201.35/33.37  | |            (14), (15), (16), (18), (19), (21), (23), (25), (26), (27), (29),
% 201.35/33.37  | |            (30), (32), (34), (36), (39), (41), (43), (45), (46), (47), (48),
% 201.35/33.37  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 201.35/33.37  | |            (60), (61), (62), (63), (64), (65), (66), (68), (70), (71), (74),
% 201.35/33.37  | |            (75), (76), (78), (79), (80), (81), (82), (83), (85), (86), (87),
% 201.35/33.37  | |            (88), (90), (91), (93), (94), (95), (96), (97), (98), (99),
% 201.35/33.37  | |            (100), (101), (102), (104), (105), (106), (107), (109), (110),
% 201.35/33.37  | |            (111), (112), (114), (115), (116), (117), (118), (120), (121),
% 201.35/33.37  | |            (123), (124), (125), (127), (128), (129), (130), (136), (137),
% 201.35/33.37  | |            (138), (139) are inconsistent by sub-proof #244.
% 201.35/33.37  | | 
% 201.35/33.37  | Case 2:
% 201.35/33.37  | | 
% 201.35/33.37  | |   (140)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.35/33.38  | | 
% 201.35/33.38  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (15), (16),
% 201.35/33.38  | |            (17), (18), (19), (20), (21), (23), (25), (27), (28), (30), (31),
% 201.35/33.38  | |            (32), (33), (35), (37), (38), (39), (40), (42), (43), (44), (45),
% 201.35/33.38  | |            (46), (48), (51), (55), (60), (63), (67), (68), (69), (70), (72),
% 201.35/33.38  | |            (73), (74), (77), (84), (86), (87), (88), (90), (91), (92), (93),
% 201.35/33.38  | |            (94), (95), (96), (99), (103), (104), (105), (106), (108), (109),
% 201.35/33.38  | |            (113), (115), (116), (117), (121), (122), (125), (126), (128),
% 201.35/33.38  | |            (129), (130), (140) are inconsistent by sub-proof #304.
% 201.35/33.38  | | 
% 201.35/33.38  | End of split
% 201.35/33.38  | 
% 201.35/33.38  End of proof
% 201.35/33.38  
% 201.35/33.38  Sub-proof #244 shows that the following formulas are inconsistent:
% 201.35/33.38  ----------------------------------------------------------------
% 201.35/33.38    (1)   ~ (all_52_15 = all_52_23)
% 201.35/33.38    (2)   ~ (all_52_25 = all_52_27)
% 201.35/33.38    (3)  all_58_14 = all_52_23
% 201.35/33.38    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.38    (5)  all_58_1 = all_52_9
% 201.35/33.38    (6)   ~ (e3 = e0)
% 201.35/33.38    (7)  op(all_52_23, all_52_23) = e0
% 201.35/33.38    (8)  op(e2, e3) = all_52_3
% 201.35/33.38    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.38    (10)  op(e0, e2) = all_52_15
% 201.35/33.38    (11)   ~ (all_52_7 = all_52_15)
% 201.35/33.38    (12)   ~ (all_52_3 = all_52_19)
% 201.35/33.38    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.38    (14)   ~ (all_52_17 = all_52_25)
% 201.35/33.38    (15)   ~ (all_52_3 = all_6_2)
% 201.35/33.38    (16)  all_58_0 = all_6_2
% 201.35/33.38    (17)  op(e3, all_6_1) = e1
% 201.35/33.38    (18)   ~ (all_52_17 = all_10_2)
% 201.35/33.38    (19)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.38    (20)  all_58_13 = all_52_15
% 201.35/33.38    (21)  all_58_9 = all_52_25
% 201.35/33.38    (22)  op(e2, all_4_1) = e3
% 201.35/33.38    (23)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.38    (24)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.35/33.38    (25)  op(e2, e2) = all_4_2
% 201.35/33.38    (26)  all_58_11 = all_52_29
% 201.35/33.38    (27)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.38    (28)  op(all_10_2, e1) = all_10_1
% 201.35/33.38    (29)   ~ (all_52_7 = all_6_2)
% 201.35/33.38    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.38    (31)  all_58_15 = e0
% 201.35/33.38    (32)   ~ (all_52_25 = e0)
% 201.35/33.38    (33)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.38    (34)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.38    (35)   ~ (e2 = e1)
% 201.35/33.38    (36)   ~ (all_52_13 = all_10_2)
% 201.35/33.38    (37)  op(e0, e0) = e0
% 201.35/33.38    (38)  op(all_10_2, all_10_2) = e1
% 201.35/33.38    (39)  all_58_10 = all_52_27
% 201.35/33.38    (40)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.38    (41)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.38    (42)   ~ (all_52_19 = all_52_23)
% 201.35/33.38    (43)   ~ (all_52_25 = all_52_29)
% 201.35/33.38    (44)   ~ (all_52_29 = all_10_2)
% 201.35/33.38    (45)  all_58_7 = all_52_13
% 201.35/33.38    (46)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.38    (47)  op(all_52_19, all_52_19) = e2
% 201.35/33.38    (48)   ~ (all_52_5 = all_52_7)
% 201.35/33.38    (49)  all_58_12 = all_52_7
% 201.35/33.38    (50)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.38    (51)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.38    (52)  all_58_2 = all_52_3
% 201.35/33.38    (53)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.38    (54)  all_56_2 = all_52_17
% 201.35/33.38    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.38    (56)  all_56_7 = all_52_27
% 201.35/33.38    (57)   ~ (e2 = e0)
% 201.35/33.38    (58)  op(all_4_2, e2) = all_4_1
% 201.35/33.38    (59)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.38    (60)  all_56_6 = all_52_19
% 201.35/33.38    (61)   ~ (all_52_19 = all_52_27)
% 201.35/33.38    (62)   ~ (all_52_13 = all_4_2)
% 201.35/33.38    (63)  op(e3, e1) = all_52_17
% 201.35/33.38    (64)  op(e0, e3) = all_52_7
% 201.35/33.38    (65)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.38    (66)   ~ (all_52_9 = all_52_25)
% 201.35/33.38    (67)   ~ (all_52_19 = all_10_2)
% 201.35/33.38    (68)  all_58_8 = all_10_2
% 201.35/33.38    (69)   ~ (all_52_23 = e0)
% 201.35/33.38    (70)  op(all_52_29, all_52_29) = all_52_28
% 201.35/33.38    (71)  all_56_12 = all_52_7
% 201.35/33.38    (72)   ~ (all_52_25 = all_6_2)
% 201.35/33.38    (73)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.38    (74)   ~ (all_52_9 = all_6_2)
% 201.35/33.38    (75)  op(e3, e3) = all_6_2
% 201.35/33.38    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.38    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.38    (78)  all_56_14 = all_52_23
% 201.35/33.38    (79)  op(all_4_2, all_4_2) = all_52_10
% 201.35/33.38    (80)  all_56_3 = all_52_25
% 201.35/33.38    (81)   ~ (all_52_3 = all_52_7)
% 201.35/33.38    (82)  all_58_5 = all_52_19
% 201.35/33.38    (83)  all_56_1 = all_52_9
% 201.35/33.38    (84)  op(all_52_17, all_52_17) = e3
% 201.35/33.38    (85)  all_58_6 = all_52_5
% 201.35/33.38    (86)  op(e3, e2) = all_52_9
% 201.35/33.38    (87)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.35/33.38    (88)   ~ (all_52_17 = all_6_2)
% 201.35/33.38    (89)   ~ (e3 = e2)
% 201.35/33.38    (90)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.35/33.38    (91)   ~ (all_52_9 = all_52_17)
% 201.35/33.38    (92)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.35/33.38    (93)  op(all_52_13, all_52_13) = all_52_12
% 201.35/33.38    (94)  op(e1, e1) = all_10_2
% 201.35/33.38    (95)   ~ (all_52_23 = all_10_2)
% 201.35/33.38    (96)   ~ (all_52_7 = all_52_23)
% 201.35/33.38    (97)   ~ (all_52_17 = all_52_19)
% 201.35/33.38    (98)  all_58_3 = all_4_2
% 201.35/33.38    (99)  all_56_13 = all_52_15
% 201.35/33.38    (100)   ~ (all_52_19 = all_4_2)
% 201.35/33.38    (101)   ~ (all_52_17 = all_52_23)
% 201.35/33.38    (102)  op(all_6_2, e3) = all_6_1
% 201.35/33.38    (103)   ~ (all_52_13 = all_52_29)
% 201.35/33.38    (104)  all_58_4 = all_52_17
% 201.35/33.38    (105)   ~ (all_52_7 = e0)
% 201.35/33.38    (106)  op(all_52_25, all_52_25) = all_52_24
% 201.35/33.38  
% 201.35/33.38  Begin of proof
% 201.35/33.38  | 
% 201.35/33.38  | BETA: splitting (33) gives:
% 201.35/33.38  | 
% 201.35/33.38  | Case 1:
% 201.35/33.38  | | 
% 201.35/33.38  | |   (107)  all_56_13 = e3
% 201.35/33.38  | | 
% 201.35/33.38  | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (15), (20), (22),
% 201.35/33.38  | |            (25), (27), (31), (34), (35), (37), (38), (41), (42), (46), (49),
% 201.35/33.38  | |            (53), (54), (57), (58), (59), (60), (69), (71), (75), (78), (79),
% 201.35/33.38  | |            (84), (89), (94), (95), (96), (97), (99), (100), (101), (105),
% 201.35/33.38  | |            (107) are inconsistent by sub-proof #765.
% 201.35/33.38  | | 
% 201.35/33.38  | Case 2:
% 201.35/33.38  | | 
% 201.35/33.38  | |   (108)   ~ (all_56_13 = e3)
% 201.35/33.38  | | 
% 201.35/33.38  | | REDUCE: (99), (108) imply:
% 201.35/33.38  | |   (109)   ~ (all_52_15 = e3)
% 201.35/33.38  | | 
% 201.35/33.38  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (13), (14), (16), (17),
% 201.35/33.38  | |            (18), (19), (20), (21), (23), (24), (26), (28), (29), (30), (31),
% 201.35/33.38  | |            (32), (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 201.35/33.38  | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 201.35/33.38  | |            (56), (57), (58), (60), (61), (62), (63), (64), (65), (66), (67),
% 201.35/33.38  | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 201.35/33.38  | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 201.35/33.38  | |            (90), (91), (92), (93), (94), (95), (96), (98), (100), (101),
% 201.35/33.38  | |            (102), (103), (104), (105), (106), (109) are inconsistent by
% 201.35/33.38  | |            sub-proof #313.
% 201.35/33.38  | | 
% 201.35/33.38  | End of split
% 201.35/33.38  | 
% 201.35/33.38  End of proof
% 201.35/33.38  
% 201.35/33.38  Sub-proof #245 shows that the following formulas are inconsistent:
% 201.35/33.38  ----------------------------------------------------------------
% 201.35/33.38    (1)  all_24_0 = e1
% 201.35/33.38    (2)   ~ (all_52_15 = all_52_23)
% 201.35/33.38    (3)   ~ (all_52_25 = all_52_27)
% 201.35/33.38    (4)  all_58_14 = all_52_23
% 201.35/33.38    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.35/33.38    (6)  op(all_52_3, all_52_3) = all_52_2
% 201.35/33.38    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.35/33.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.35/33.38    (8)   ~ (all_52_5 = all_52_13)
% 201.35/33.38    (9)  all_58_1 = all_52_9
% 201.35/33.38    (10)   ~ (all_52_9 = all_52_13)
% 201.35/33.38    (11)   ~ (e3 = e0)
% 201.35/33.38    (12)  op(e2, e3) = all_52_3
% 201.35/33.38    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.35/33.38    (14)   ~ (all_52_7 = all_52_15)
% 201.35/33.38    (15)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.35/33.38    (16)  all_34_0 = all_14_0
% 201.35/33.38    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.35/33.38    (18)   ~ (all_52_17 = all_52_25)
% 201.35/33.38    (19)   ~ (all_52_3 = all_6_2)
% 201.35/33.38    (20)  all_58_0 = all_6_2
% 201.35/33.38    (21)  op(all_14_2, e0) = all_14_1
% 201.35/33.38    (22)  all_46_0 = e1
% 201.35/33.38    (23)  all_34_1 = all_14_1
% 201.35/33.38    (24)  all_56_4 = all_52_3
% 201.35/33.38    (25)  op(e3, all_6_1) = e1
% 201.35/33.38    (26)   ~ (all_52_17 = all_10_2)
% 201.35/33.38    (27)  op(e3, e0) = all_52_25
% 201.35/33.38    (28)  op(e0, all_14_1) = all_14_0
% 201.35/33.38    (29)  op(all_52_5, all_52_5) = all_52_4
% 201.35/33.38    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.35/33.38    (31)  op(all_52_19, all_52_19) = all_52_18
% 201.35/33.38    (32)   ~ (all_52_27 = all_52_29)
% 201.35/33.38    (33)  all_58_13 = all_52_15
% 201.35/33.38    (34)  op(all_10_2, all_10_2) = all_52_20
% 201.35/33.38    (35)  all_58_9 = all_52_25
% 201.35/33.38    (36)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.35/33.38    (37)   ~ (all_52_29 = all_14_2)
% 201.35/33.38    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.35/33.38    (39)  op(all_52_27, all_52_27) = all_52_26
% 201.35/33.38    (40)  op(e1, e3) = all_52_5
% 201.35/33.38    (41)  op(e2, e2) = all_4_2
% 201.35/33.38    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.35/33.38    (43)   ~ (all_52_3 = all_52_5)
% 201.35/33.38    (44)  all_58_11 = all_52_29
% 201.35/33.38    (45)  all_56_5 = all_4_2
% 201.35/33.38    (46)   ~ (all_52_25 = all_14_2)
% 201.35/33.38    (47)   ~ (all_52_9 = all_52_15)
% 201.35/33.38    (48)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.35/33.38    (49)   ~ (all_52_3 = all_52_27)
% 201.35/33.38    (50)  op(all_10_2, e1) = all_10_1
% 201.35/33.38    (51)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.35/33.38    (52)  all_46_2 = all_6_2
% 201.35/33.38    (53)  op(all_6_2, all_6_2) = all_52_0
% 201.35/33.38    (54)   ~ (all_52_7 = all_6_2)
% 201.35/33.38    (55)  op(e0, e0) = all_14_2
% 201.35/33.38    (56)  op(e0, e1) = all_52_23
% 201.35/33.38    (57)  all_56_15 = all_14_2
% 201.35/33.38    (58)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.35/33.38    (59)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.35/33.38    (60)  all_56_11 = all_52_29
% 201.35/33.38    (61)   ~ (all_4_1 = e1)
% 201.35/33.38    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.35/33.38    (63)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.35/33.38    (64)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.35/33.38    (65)  all_56_9 = all_52_13
% 201.35/33.38    (66)   ~ (all_52_13 = all_10_2)
% 201.35/33.38    (67)  all_58_10 = all_52_27
% 201.35/33.38    (68)  all_24_0 = all_14_0
% 201.35/33.38    (69)  all_56_8 = all_52_5
% 201.35/33.38    (70)  op(all_52_9, all_52_9) = all_52_8
% 201.35/33.38    (71)  op(all_52_15, all_52_15) = all_52_14
% 201.35/33.38    (72)   ~ (all_52_19 = all_52_23)
% 201.35/33.38    (73)   ~ (all_52_25 = all_52_29)
% 201.35/33.38    (74)   ~ (all_52_29 = all_10_2)
% 201.35/33.38    (75)  all_58_7 = all_52_13
% 201.35/33.38    (76)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.35/33.38    (77)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.35/33.38    (78)   ~ (all_52_5 = all_52_7)
% 201.35/33.38    (79)  all_58_12 = all_52_7
% 201.35/33.38    (80)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.35/33.38    (81)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.35/33.38    (82)   ~ (all_52_7 = all_14_2)
% 201.35/33.38    (83)  all_58_2 = all_52_3
% 201.35/33.38    (84)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.35/33.38    (85)  all_56_2 = all_52_17
% 201.35/33.38    (86)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.35/33.38    (87)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.35/33.38    (88)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.35/33.38    (89)   ~ (all_14_0 = e3)
% 201.35/33.38    (90)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.35/33.38    (91)  all_56_7 = all_52_27
% 201.35/33.38    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.35/33.38    (93)   ~ (e2 = e0)
% 201.35/33.38    (94)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.35/33.38    (95)  op(all_4_2, e2) = all_4_1
% 201.35/33.38    (96)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.35/33.38    (97)   ~ (all_52_5 = all_52_29)
% 201.35/33.38    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.35/33.38    (99)  all_56_6 = all_52_19
% 201.35/33.38    (100)   ~ (all_52_15 = all_14_2)
% 201.35/33.38    (101)   ~ (all_52_19 = all_52_27)
% 201.35/33.38    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.35/33.38    (103)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.35/33.38    (104)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 201.35/33.38             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 201.35/33.38    (105)   ~ (all_52_13 = all_4_2)
% 201.35/33.38    (106)  op(e3, e1) = all_52_17
% 201.35/33.38    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.35/33.38    (108)  op(e0, e3) = all_52_7
% 201.35/33.38    (109)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.35/33.38    (110)   ~ (all_52_9 = all_52_25)
% 201.35/33.38    (111)  all_58_15 = all_14_2
% 201.35/33.38    (112)   ~ (all_52_19 = all_10_2)
% 201.35/33.38    (113)  op(all_52_23, all_52_23) = all_52_22
% 201.35/33.38    (114)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.35/33.38    (115)  all_58_8 = all_10_2
% 201.35/33.38    (116)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.35/33.38    (117)  all_34_2 = all_14_2
% 201.35/33.38    (118)   ~ (all_52_5 = all_10_2)
% 201.35/33.38    (119)  op(all_52_29, all_52_29) = all_52_28
% 201.35/33.38    (120)   ~ (all_52_23 = all_14_2)
% 201.35/33.38    (121)  all_56_12 = all_52_7
% 201.35/33.38    (122)  op(all_52_17, all_52_17) = all_52_16
% 201.35/33.38    (123)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.35/33.38    (124)   ~ (all_52_25 = all_6_2)
% 201.35/33.38    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.35/33.38    (126)   ~ (all_52_9 = all_4_2)
% 201.35/33.38    (127)   ~ (all_52_5 = all_6_2)
% 201.35/33.38    (128)   ~ (all_52_9 = all_6_2)
% 201.35/33.38    (129)   ~ (all_52_13 = all_52_15)
% 201.35/33.38    (130)  all_56_0 = all_6_2
% 201.35/33.38    (131)  op(e3, e3) = all_6_2
% 201.35/33.38    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.35/33.38    (133)   ~ (all_52_27 = all_14_2)
% 201.35/33.38    (134)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.35/33.38    (135)  all_56_14 = all_52_23
% 201.35/33.38    (136)  op(all_4_2, all_4_2) = all_52_10
% 201.35/33.38    (137)  all_56_3 = all_52_25
% 201.35/33.38    (138)   ~ (all_52_3 = all_52_7)
% 201.35/33.38    (139)  op(all_14_2, all_14_2) = all_52_30
% 201.35/33.38    (140)  all_58_5 = all_52_19
% 201.35/33.38    (141)  all_56_1 = all_52_9
% 201.35/33.38    (142)   ~ (all_52_15 = all_4_2)
% 201.56/33.38    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.38           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.56/33.38           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.56/33.38           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.56/33.38    (144)   ~ (all_52_27 = all_4_2)
% 201.56/33.38    (145)  all_58_6 = all_52_5
% 201.56/33.38    (146)  op(e3, e2) = all_52_9
% 201.56/33.38    (147)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.38    (148)   ~ (all_52_17 = all_6_2)
% 201.56/33.38    (149)   ~ (e1 = e0)
% 201.56/33.38    (150)   ~ (e3 = e2)
% 201.56/33.38    (151)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.38    (152)   ~ (all_52_9 = all_52_17)
% 201.56/33.38    (153)  all_56_10 = all_10_2
% 201.56/33.38    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.38    (155)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.56/33.38    (156)  all_46_1 = all_6_1
% 201.56/33.38    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.38    (158)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.38    (159)  op(e1, e1) = all_10_2
% 201.56/33.38    (160)   ~ (all_52_23 = all_10_2)
% 201.56/33.38    (161)   ~ (all_52_7 = all_52_23)
% 201.56/33.38    (162)   ~ (all_52_17 = all_52_19)
% 201.56/33.38    (163)  all_58_3 = all_4_2
% 201.56/33.38    (164)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.38    (165)  all_56_13 = all_52_15
% 201.56/33.38    (166)   ~ (all_52_3 = all_4_2)
% 201.56/33.38    (167)   ~ (all_52_19 = all_4_2)
% 201.56/33.38    (168)   ~ (all_52_17 = all_52_23)
% 201.56/33.38    (169)  op(all_6_2, e3) = all_6_1
% 201.56/33.38    (170)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.38    (171)   ~ (all_52_13 = all_52_29)
% 201.56/33.38    (172)  all_58_4 = all_52_17
% 201.56/33.38    (173)   ~ (all_14_0 = e2)
% 201.56/33.38    (174)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.56/33.38    (175)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.38  
% 201.56/33.38  Begin of proof
% 201.56/33.38  | 
% 201.56/33.38  | COMBINE_EQS: (1), (68) imply:
% 201.56/33.38  |   (176)  all_14_0 = e1
% 201.56/33.38  | 
% 201.56/33.38  | SIMP: (176) implies:
% 201.56/33.38  |   (177)  all_14_0 = e1
% 201.56/33.38  | 
% 201.56/33.38  | COMBINE_EQS: (16), (177) imply:
% 201.56/33.38  |   (178)  all_34_0 = e1
% 201.56/33.38  | 
% 201.56/33.38  | REDUCE: (89), (177) imply:
% 201.56/33.38  |   (179)   ~ (e3 = e1)
% 201.56/33.38  | 
% 201.56/33.38  | SIMP: (179) implies:
% 201.56/33.38  |   (180)   ~ (e3 = e1)
% 201.56/33.38  | 
% 201.56/33.38  | REDUCE: (173), (177) imply:
% 201.56/33.38  |   (181)   ~ (e2 = e1)
% 201.56/33.38  | 
% 201.56/33.38  | SIMP: (181) implies:
% 201.56/33.38  |   (182)   ~ (e2 = e1)
% 201.56/33.38  | 
% 201.56/33.38  | REDUCE: (28), (177) imply:
% 201.56/33.38  |   (183)  op(e0, all_14_1) = e1
% 201.56/33.38  | 
% 201.56/33.38  | BETA: splitting (51) gives:
% 201.56/33.38  | 
% 201.56/33.38  | Case 1:
% 201.56/33.38  | | 
% 201.56/33.38  | |   (184)   ~ (all_34_0 = e1)
% 201.56/33.38  | | 
% 201.56/33.38  | | REDUCE: (178), (184) imply:
% 201.56/33.38  | |   (185)  $false
% 201.56/33.38  | | 
% 201.56/33.38  | | CLOSE: (185) is inconsistent.
% 201.56/33.38  | | 
% 201.56/33.38  | Case 2:
% 201.56/33.38  | | 
% 201.56/33.38  | |   (186)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.56/33.38  | | 
% 201.56/33.38  | | BETA: splitting (15) gives:
% 201.56/33.38  | | 
% 201.56/33.38  | | Case 1:
% 201.56/33.38  | | | 
% 201.56/33.38  | | |   (187)   ~ (all_46_0 = e1)
% 201.56/33.38  | | | 
% 201.56/33.38  | | | REDUCE: (22), (187) imply:
% 201.56/33.38  | | |   (188)  $false
% 201.56/33.38  | | | 
% 201.56/33.38  | | | CLOSE: (188) is inconsistent.
% 201.56/33.38  | | | 
% 201.56/33.38  | | Case 2:
% 201.56/33.38  | | | 
% 201.56/33.38  | | |   (189)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.38  | | | 
% 201.56/33.38  | | | BETA: splitting (104) gives:
% 201.56/33.38  | | | 
% 201.56/33.38  | | | Case 1:
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | |   (190)  all_58_15 = e0
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | | REF_CLOSE: (7), (21), (55), (111), (139), (149), (183), (190) are
% 201.56/33.38  | | | |            inconsistent by sub-proof #877.
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | Case 2:
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | |   (191)   ~ (all_58_15 = e0)
% 201.56/33.38  | | | |   (192)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 201.56/33.38  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | | ALPHA: (192) implies:
% 201.56/33.38  | | | |   (193)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.38  | | | |   (194)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | | REDUCE: (111), (191) imply:
% 201.56/33.38  | | | |   (195)   ~ (all_14_2 = e0)
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | | BETA: splitting (143) gives:
% 201.56/33.38  | | | | 
% 201.56/33.38  | | | | Case 1:
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | |   (196)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 201.56/33.38  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 201.56/33.38  | | | | |            all_52_14 = e0)
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | | BETA: splitting (196) gives:
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | | Case 1:
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | |   (197)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 201.56/33.38  | | | | | |          e0
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REF_CLOSE: (6), (7), (17), (20), (25), (29), (41), (53), (54), (55),
% 201.56/33.38  | | | | | |            (58), (79), (82), (83), (87), (118), (131), (134), (145),
% 201.56/33.38  | | | | | |            (147), (159), (166), (169), (180), (197) are inconsistent
% 201.56/33.38  | | | | | |            by sub-proof #302.
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | Case 2:
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | |   (198)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 201.56/33.38  | | | | | |          = e0
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | ALPHA: (198) implies:
% 201.56/33.38  | | | | | |   (199)  all_52_14 = e0
% 201.56/33.38  | | | | | |   (200)  all_52_12 = e1
% 201.56/33.38  | | | | | |   (201)  all_52_10 = e2
% 201.56/33.38  | | | | | |   (202)  all_52_8 = e3
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (70), (202) imply:
% 201.56/33.38  | | | | | |   (203)  op(all_52_9, all_52_9) = e3
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (158), (200) imply:
% 201.56/33.38  | | | | | |   (204)  op(all_52_13, all_52_13) = e1
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (71), (199) imply:
% 201.56/33.38  | | | | | |   (205)  op(all_52_15, all_52_15) = e0
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (136), (201) imply:
% 201.56/33.38  | | | | | |   (206)  op(all_4_2, all_4_2) = e2
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.38  | | | | | |            (13), (14), (17), (18), (19), (20), (21), (23), (24),
% 201.56/33.38  | | | | | |            (25), (26), (27), (28), (29), (30), (33), (34), (35),
% 201.56/33.38  | | | | | |            (36), (37), (38), (40), (41), (42), (43), (44), (45),
% 201.56/33.38  | | | | | |            (46), (47), (48), (52), (53), (54), (55), (56), (57),
% 201.56/33.38  | | | | | |            (58), (61), (62), (63), (64), (65), (66), (67), (69),
% 201.56/33.38  | | | | | |            (72), (73), (75), (78), (79), (80), (81), (82), (83),
% 201.56/33.38  | | | | | |            (84), (85), (86), (87), (90), (91), (92), (93), (94),
% 201.56/33.38  | | | | | |            (95), (96), (97), (98), (99), (100), (103), (105), (106),
% 201.56/33.38  | | | | | |            (107), (108), (109), (110), (111), (113), (114), (115),
% 201.56/33.38  | | | | | |            (116), (117), (119), (120), (121), (122), (124), (125),
% 201.56/33.38  | | | | | |            (126), (127), (128), (129), (130), (131), (132), (133),
% 201.56/33.38  | | | | | |            (134), (137), (138), (139), (140), (141), (142), (144),
% 201.56/33.38  | | | | | |            (145), (146), (147), (148), (149), (150), (151), (152),
% 201.56/33.38  | | | | | |            (154), (155), (156), (157), (159), (160), (161), (162),
% 201.56/33.38  | | | | | |            (163), (165), (166), (167), (168), (169), (170), (171),
% 201.56/33.38  | | | | | |            (172), (173), (175), (180), (182), (186), (189), (193),
% 201.56/33.38  | | | | | |            (194), (203), (204), (205), (206) are inconsistent by
% 201.56/33.38  | | | | | |            sub-proof #249.
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | End of split
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | Case 2:
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | |   (207)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 201.56/33.38  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 201.56/33.38  | | | | |            all_52_30 = e0)
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | | BETA: splitting (207) gives:
% 201.56/33.38  | | | | | 
% 201.56/33.38  | | | | | Case 1:
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | |   (208)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 201.56/33.38  | | | | | |          all_52_22 = e0
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | ALPHA: (208) implies:
% 201.56/33.38  | | | | | |   (209)  all_52_22 = e0
% 201.56/33.38  | | | | | |   (210)  all_52_20 = e1
% 201.56/33.38  | | | | | |   (211)  all_52_18 = e2
% 201.56/33.38  | | | | | |   (212)  all_52_16 = e3
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (122), (212) imply:
% 201.56/33.38  | | | | | |   (213)  op(all_52_17, all_52_17) = e3
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (31), (211) imply:
% 201.56/33.38  | | | | | |   (214)  op(all_52_19, all_52_19) = e2
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (113), (209) imply:
% 201.56/33.38  | | | | | |   (215)  op(all_52_23, all_52_23) = e0
% 201.56/33.38  | | | | | | 
% 201.56/33.38  | | | | | | REDUCE: (34), (210) imply:
% 201.56/33.39  | | | | | |   (216)  op(all_10_2, all_10_2) = e1
% 201.56/33.39  | | | | | | 
% 201.56/33.39  | | | | | | BETA: splitting (116) gives:
% 201.56/33.39  | | | | | | 
% 201.56/33.39  | | | | | | Case 1:
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | |   (217)  all_56_15 = e3
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | | COMBINE_EQS: (57), (217) imply:
% 201.56/33.39  | | | | | | |   (218)  all_14_2 = e3
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | | SIMP: (218) implies:
% 201.56/33.39  | | | | | | |   (219)  all_14_2 = e3
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | | REF_CLOSE: (7), (21), (23), (27), (35), (37), (39), (44), (46),
% 201.56/33.39  | | | | | | |            (55), (56), (59), (60), (67), (73), (74), (102), (117),
% 201.56/33.39  | | | | | | |            (120), (125), (137), (159), (160), (175), (180), (183),
% 201.56/33.39  | | | | | | |            (186), (194), (215), (216), (219) are inconsistent by
% 201.56/33.39  | | | | | | |            sub-proof #248.
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | Case 2:
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | |   (220)   ~ (all_56_15 = e3)
% 201.56/33.39  | | | | | | |   (221)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | | REDUCE: (57), (220) imply:
% 201.56/33.39  | | | | | | |   (222)   ~ (all_14_2 = e3)
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (13), (14), (17), (18),
% 201.56/33.39  | | | | | | |            (20), (25), (27), (29), (33), (35), (38), (40), (41),
% 201.56/33.39  | | | | | | |            (42), (43), (44), (46), (47), (50), (53), (54), (55),
% 201.56/33.39  | | | | | | |            (57), (60), (62), (63), (64), (70), (73), (74), (75),
% 201.56/33.39  | | | | | | |            (79), (80), (81), (82), (83), (85), (86), (87), (88),
% 201.56/33.39  | | | | | | |            (90), (93), (96), (102), (103), (106), (108), (110),
% 201.56/33.39  | | | | | | |            (111), (112), (115), (118), (119), (120), (121), (124),
% 201.56/33.39  | | | | | | |            (125), (127), (128), (129), (130), (131), (132), (134),
% 201.56/33.39  | | | | | | |            (137), (138), (140), (141), (145), (146), (147), (148),
% 201.56/33.39  | | | | | | |            (149), (150), (151), (152), (153), (154), (157), (159),
% 201.56/33.39  | | | | | | |            (160), (161), (164), (165), (166), (169), (170), (172),
% 201.56/33.39  | | | | | | |            (174), (175), (180), (182), (193), (195), (213), (214),
% 201.56/33.39  | | | | | | |            (215), (216), (221), (222) are inconsistent by
% 201.56/33.39  | | | | | | |            sub-proof #274.
% 201.56/33.39  | | | | | | | 
% 201.56/33.39  | | | | | | End of split
% 201.56/33.39  | | | | | | 
% 201.56/33.39  | | | | | Case 2:
% 201.56/33.39  | | | | | | 
% 201.56/33.39  | | | | | |   (223)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 201.56/33.39  | | | | | |          all_52_30 = e0
% 201.56/33.39  | | | | | | 
% 201.56/33.39  | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13),
% 201.56/33.39  | | | | | |            (14), (17), (18), (19), (20), (21), (23), (24), (25),
% 201.56/33.39  | | | | | |            (26), (27), (29), (31), (32), (33), (35), (37), (38),
% 201.56/33.39  | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 201.56/33.39  | | | | | |            (49), (50), (52), (53), (54), (55), (56), (57), (58),
% 201.56/33.39  | | | | | |            (59), (60), (62), (63), (64), (67), (69), (70), (71),
% 201.56/33.39  | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 201.56/33.39  | | | | | |            (82), (83), (85), (87), (88), (90), (92), (93), (94),
% 201.56/33.39  | | | | | |            (97), (100), (101), (102), (103), (106), (107), (108),
% 201.56/33.39  | | | | | |            (109), (110), (111), (112), (113), (114), (115), (116),
% 201.56/33.39  | | | | | |            (117), (118), (119), (120), (121), (122), (123), (124),
% 201.56/33.39  | | | | | |            (125), (126), (127), (128), (129), (130), (131), (132),
% 201.56/33.39  | | | | | |            (133), (134), (135), (137), (138), (139), (140), (141),
% 201.56/33.39  | | | | | |            (142), (144), (145), (146), (147), (148), (149), (150),
% 201.56/33.39  | | | | | |            (151), (156), (157), (158), (159), (160), (161), (162),
% 201.56/33.39  | | | | | |            (163), (164), (165), (166), (167), (168), (169), (170),
% 201.56/33.39  | | | | | |            (172), (175), (180), (182), (183), (186), (189), (193),
% 201.56/33.39  | | | | | |            (195), (223) are inconsistent by sub-proof #246.
% 201.56/33.39  | | | | | | 
% 201.56/33.39  | | | | | End of split
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | End of split
% 201.56/33.39  | | | | 
% 201.56/33.39  | | | End of split
% 201.56/33.39  | | | 
% 201.56/33.39  | | End of split
% 201.56/33.39  | | 
% 201.56/33.39  | End of split
% 201.56/33.39  | 
% 201.56/33.39  End of proof
% 201.56/33.39  
% 201.56/33.39  Sub-proof #246 shows that the following formulas are inconsistent:
% 201.56/33.39  ----------------------------------------------------------------
% 201.56/33.39    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.39    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.39    (3)  all_58_14 = all_52_23
% 201.56/33.39    (4)   ~ (e3 = e1)
% 201.56/33.39    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.39    (7)  all_58_1 = all_52_9
% 201.56/33.39    (8)   ~ (all_52_9 = all_52_13)
% 201.56/33.39    (9)   ~ (e3 = e0)
% 201.56/33.39    (10)  op(e2, e3) = all_52_3
% 201.56/33.39    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.39    (12)   ~ (all_52_7 = all_52_15)
% 201.56/33.39    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.39    (14)   ~ (all_52_17 = all_52_25)
% 201.56/33.39    (15)   ~ (all_52_3 = all_6_2)
% 201.56/33.39    (16)  all_58_0 = all_6_2
% 201.56/33.39    (17)  op(all_14_2, e0) = all_14_1
% 201.56/33.39    (18)  all_34_1 = all_14_1
% 201.56/33.39    (19)  all_56_4 = all_52_3
% 201.56/33.39    (20)  op(e3, all_6_1) = e1
% 201.56/33.39    (21)   ~ (all_52_17 = all_10_2)
% 201.56/33.39    (22)  op(e3, e0) = all_52_25
% 201.56/33.39    (23)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.39    (24)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.39    (25)   ~ (all_52_27 = all_52_29)
% 201.56/33.39    (26)  all_58_13 = all_52_15
% 201.56/33.39    (27)  op(e0, all_14_1) = e1
% 201.56/33.39    (28)  all_58_9 = all_52_25
% 201.56/33.39    (29)   ~ (all_52_29 = all_14_2)
% 201.56/33.39    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.39    (31)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.39    (32)  op(e1, e3) = all_52_5
% 201.56/33.39    (33)  op(e2, e2) = all_4_2
% 201.56/33.39    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.39    (35)   ~ (all_52_3 = all_52_5)
% 201.56/33.39    (36)  all_58_11 = all_52_29
% 201.56/33.39    (37)  all_56_5 = all_4_2
% 201.56/33.39    (38)   ~ (all_52_25 = all_14_2)
% 201.56/33.39    (39)   ~ (all_52_9 = all_52_15)
% 201.56/33.39    (40)   ~ (all_52_3 = all_52_27)
% 201.56/33.39    (41)  op(all_10_2, e1) = all_10_1
% 201.56/33.39    (42)  all_46_2 = all_6_2
% 201.56/33.39    (43)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.39    (44)   ~ (all_52_7 = all_6_2)
% 201.56/33.39    (45)  op(e0, e0) = all_14_2
% 201.56/33.39    (46)  op(e0, e1) = all_52_23
% 201.56/33.39    (47)  all_56_15 = all_14_2
% 201.56/33.39    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.39    (49)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.39    (50)  all_56_11 = all_52_29
% 201.56/33.39    (51)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.39    (52)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.56/33.39    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.39    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.39    (55)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.39    (56)   ~ (e2 = e1)
% 201.56/33.39    (57)  all_58_10 = all_52_27
% 201.56/33.39    (58)  all_56_8 = all_52_5
% 201.56/33.39    (59)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.39    (60)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.39    (61)   ~ (all_52_25 = all_52_29)
% 201.56/33.39    (62)   ~ (all_52_29 = all_10_2)
% 201.56/33.39    (63)  all_58_7 = all_52_13
% 201.56/33.39    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.39    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.56/33.39    (66)   ~ (all_52_5 = all_52_7)
% 201.56/33.39    (67)  all_58_12 = all_52_7
% 201.56/33.39    (68)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.39    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.39    (70)   ~ (all_52_7 = all_14_2)
% 201.56/33.39    (71)   ~ (all_14_2 = e0)
% 201.56/33.39    (72)  all_58_2 = all_52_3
% 201.56/33.39    (73)  all_56_2 = all_52_17
% 201.56/33.39    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.39    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.39    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.39    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.39    (78)   ~ (e2 = e0)
% 201.56/33.39    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.39    (80)   ~ (all_52_5 = all_52_29)
% 201.56/33.39    (81)   ~ (all_52_15 = all_14_2)
% 201.56/33.39    (82)   ~ (all_52_19 = all_52_27)
% 201.56/33.39    (83)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.39    (84)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.39    (85)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.39    (86)  op(e3, e1) = all_52_17
% 201.56/33.39    (87)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.39    (88)  op(e0, e3) = all_52_7
% 201.56/33.39    (89)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.39    (90)   ~ (all_52_9 = all_52_25)
% 201.56/33.39    (91)  all_58_15 = all_14_2
% 201.56/33.39    (92)   ~ (all_52_19 = all_10_2)
% 201.56/33.39    (93)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.39    (94)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.39    (95)  all_58_8 = all_10_2
% 201.56/33.39    (96)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.39    (97)  all_34_2 = all_14_2
% 201.56/33.39    (98)   ~ (all_52_5 = all_10_2)
% 201.56/33.39    (99)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.39    (100)   ~ (all_52_23 = all_14_2)
% 201.56/33.39    (101)  all_56_12 = all_52_7
% 201.56/33.39    (102)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.39    (103)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.56/33.39    (104)   ~ (all_52_25 = all_6_2)
% 201.56/33.39    (105)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.39    (106)   ~ (all_52_9 = all_4_2)
% 201.56/33.39    (107)   ~ (all_52_5 = all_6_2)
% 201.56/33.39    (108)   ~ (all_52_9 = all_6_2)
% 201.56/33.39    (109)   ~ (all_52_13 = all_52_15)
% 201.56/33.39    (110)  all_56_0 = all_6_2
% 201.56/33.39    (111)  op(e3, e3) = all_6_2
% 201.56/33.39    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.39    (113)   ~ (all_52_27 = all_14_2)
% 201.56/33.39    (114)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.39    (115)  all_56_14 = all_52_23
% 201.56/33.39    (116)  all_56_3 = all_52_25
% 201.56/33.39    (117)   ~ (all_52_3 = all_52_7)
% 201.56/33.39    (118)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.39    (119)  all_58_5 = all_52_19
% 201.56/33.39    (120)  all_56_1 = all_52_9
% 201.56/33.39    (121)   ~ (all_52_15 = all_4_2)
% 201.56/33.39    (122)   ~ (all_52_27 = all_4_2)
% 201.56/33.39    (123)  all_58_6 = all_52_5
% 201.56/33.39    (124)  op(e3, e2) = all_52_9
% 201.56/33.39    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.39    (126)   ~ (all_52_17 = all_6_2)
% 201.56/33.39    (127)   ~ (e1 = e0)
% 201.56/33.39    (128)   ~ (e3 = e2)
% 201.56/33.39    (129)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.39    (130)  all_46_1 = all_6_1
% 201.56/33.39    (131)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.56/33.39    (132)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.39    (133)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.39    (134)  op(e1, e1) = all_10_2
% 201.56/33.39    (135)   ~ (all_52_23 = all_10_2)
% 201.56/33.39    (136)   ~ (all_52_7 = all_52_23)
% 201.56/33.39    (137)   ~ (all_52_17 = all_52_19)
% 201.56/33.39    (138)  all_58_3 = all_4_2
% 201.56/33.39    (139)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.39    (140)  all_56_13 = all_52_15
% 201.56/33.39    (141)   ~ (all_52_3 = all_4_2)
% 201.56/33.39    (142)   ~ (all_52_19 = all_4_2)
% 201.56/33.39    (143)   ~ (all_52_17 = all_52_23)
% 201.56/33.39    (144)  op(all_6_2, e3) = all_6_1
% 201.56/33.39    (145)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.39    (146)  all_58_4 = all_52_17
% 201.56/33.39    (147)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.39  
% 201.56/33.39  Begin of proof
% 201.56/33.39  | 
% 201.56/33.39  | ALPHA: (131) implies:
% 201.56/33.39  |   (148)  all_52_30 = e0
% 201.56/33.39  |   (149)  all_52_28 = e1
% 201.56/33.39  |   (150)  all_52_26 = e2
% 201.56/33.39  |   (151)  all_52_24 = e3
% 201.56/33.39  | 
% 201.56/33.39  | REDUCE: (147), (151) imply:
% 201.56/33.39  |   (152)  op(all_52_25, all_52_25) = e3
% 201.56/33.39  | 
% 201.56/33.39  | REDUCE: (31), (150) imply:
% 201.56/33.39  |   (153)  op(all_52_27, all_52_27) = e2
% 201.56/33.39  | 
% 201.56/33.39  | REDUCE: (99), (149) imply:
% 201.56/33.39  |   (154)  op(all_52_29, all_52_29) = e1
% 201.56/33.39  | 
% 201.56/33.39  | REDUCE: (118), (148) imply:
% 201.56/33.39  |   (155)  op(all_14_2, all_14_2) = e0
% 201.56/33.39  | 
% 201.56/33.39  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.39  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.56/33.39  |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 201.56/33.39  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 201.56/33.39  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 201.56/33.39  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 201.56/33.39  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 201.56/33.39  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 201.56/33.39  |            (91), (92), (93), (94), (95), (96), (97), (98), (100), (101),
% 201.56/33.39  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 201.56/33.39  |            (111), (112), (113), (114), (115), (116), (117), (119), (120),
% 201.56/33.39  |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 201.56/33.39  |            (130), (132), (133), (134), (135), (136), (137), (138), (139),
% 201.56/33.39  |            (140), (141), (142), (143), (144), (145), (146), (152), (153),
% 201.56/33.39  |            (154), (155) are inconsistent by sub-proof #247.
% 201.56/33.39  | 
% 201.56/33.39  End of proof
% 201.56/33.39  
% 201.56/33.39  Sub-proof #247 shows that the following formulas are inconsistent:
% 201.56/33.39  ----------------------------------------------------------------
% 201.56/33.39    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.39    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.39    (3)  all_58_14 = all_52_23
% 201.56/33.39    (4)   ~ (e3 = e1)
% 201.56/33.39    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.39    (7)  all_58_1 = all_52_9
% 201.56/33.39    (8)   ~ (all_52_9 = all_52_13)
% 201.56/33.39    (9)   ~ (e3 = e0)
% 201.56/33.39    (10)  op(e2, e3) = all_52_3
% 201.56/33.39    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.39    (12)   ~ (all_52_7 = all_52_15)
% 201.56/33.39    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.39    (14)   ~ (all_52_17 = all_52_25)
% 201.56/33.39    (15)   ~ (all_52_3 = all_6_2)
% 201.56/33.39    (16)  all_58_0 = all_6_2
% 201.56/33.39    (17)  op(all_14_2, e0) = all_14_1
% 201.56/33.39    (18)  all_34_1 = all_14_1
% 201.56/33.39    (19)  all_56_4 = all_52_3
% 201.56/33.39    (20)  op(e3, all_6_1) = e1
% 201.56/33.39    (21)   ~ (all_52_17 = all_10_2)
% 201.56/33.39    (22)  op(e3, e0) = all_52_25
% 201.56/33.39    (23)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.39    (24)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.39    (25)   ~ (all_52_27 = all_52_29)
% 201.56/33.39    (26)  all_58_13 = all_52_15
% 201.56/33.39    (27)  op(e0, all_14_1) = e1
% 201.56/33.39    (28)  all_58_9 = all_52_25
% 201.56/33.39    (29)   ~ (all_52_29 = all_14_2)
% 201.56/33.39    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.39    (31)  op(e1, e3) = all_52_5
% 201.56/33.39    (32)  op(e2, e2) = all_4_2
% 201.56/33.39    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.39    (34)   ~ (all_52_3 = all_52_5)
% 201.56/33.39    (35)  all_58_11 = all_52_29
% 201.56/33.39    (36)  all_56_5 = all_4_2
% 201.56/33.39    (37)   ~ (all_52_25 = all_14_2)
% 201.56/33.39    (38)   ~ (all_52_9 = all_52_15)
% 201.56/33.39    (39)   ~ (all_52_3 = all_52_27)
% 201.56/33.39    (40)  op(all_10_2, e1) = all_10_1
% 201.56/33.39    (41)  all_46_2 = all_6_2
% 201.56/33.39    (42)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.39    (43)   ~ (all_52_7 = all_6_2)
% 201.56/33.39    (44)  op(e0, e0) = all_14_2
% 201.56/33.39    (45)  op(all_52_29, all_52_29) = e1
% 201.56/33.39    (46)  op(e0, e1) = all_52_23
% 201.56/33.39    (47)  all_56_15 = all_14_2
% 201.56/33.39    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.39    (49)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.39    (50)  all_56_11 = all_52_29
% 201.56/33.39    (51)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.39    (52)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.56/33.39    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.39    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.39    (55)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.39    (56)   ~ (e2 = e1)
% 201.56/33.39    (57)  all_58_10 = all_52_27
% 201.56/33.39    (58)  all_56_8 = all_52_5
% 201.56/33.39    (59)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.39    (60)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.39    (61)   ~ (all_52_25 = all_52_29)
% 201.56/33.39    (62)   ~ (all_52_29 = all_10_2)
% 201.56/33.39    (63)  all_58_7 = all_52_13
% 201.56/33.39    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.39    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.56/33.39    (66)   ~ (all_52_5 = all_52_7)
% 201.56/33.39    (67)  all_58_12 = all_52_7
% 201.56/33.39    (68)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.39    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.39    (70)   ~ (all_52_7 = all_14_2)
% 201.56/33.39    (71)   ~ (all_14_2 = e0)
% 201.56/33.39    (72)  all_58_2 = all_52_3
% 201.56/33.39    (73)  all_56_2 = all_52_17
% 201.56/33.39    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.39    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.39    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.39    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.39    (78)   ~ (e2 = e0)
% 201.56/33.39    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.39    (80)  op(all_52_25, all_52_25) = e3
% 201.56/33.39    (81)   ~ (all_52_5 = all_52_29)
% 201.56/33.39    (82)   ~ (all_52_15 = all_14_2)
% 201.56/33.39    (83)   ~ (all_52_19 = all_52_27)
% 201.56/33.39    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.39    (85)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.39    (86)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.39    (87)  op(e3, e1) = all_52_17
% 201.56/33.39    (88)  op(all_52_27, all_52_27) = e2
% 201.56/33.39    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.39    (90)  op(e0, e3) = all_52_7
% 201.56/33.39    (91)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.39    (92)   ~ (all_52_9 = all_52_25)
% 201.56/33.39    (93)  all_58_15 = all_14_2
% 201.56/33.39    (94)   ~ (all_52_19 = all_10_2)
% 201.56/33.39    (95)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.39    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.39    (97)  all_58_8 = all_10_2
% 201.56/33.39    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.39    (99)  all_34_2 = all_14_2
% 201.56/33.39    (100)   ~ (all_52_5 = all_10_2)
% 201.56/33.39    (101)   ~ (all_52_23 = all_14_2)
% 201.56/33.39    (102)  all_56_12 = all_52_7
% 201.56/33.39    (103)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.39    (104)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.56/33.39    (105)   ~ (all_52_25 = all_6_2)
% 201.56/33.39    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.39    (107)   ~ (all_52_9 = all_4_2)
% 201.56/33.39    (108)   ~ (all_52_5 = all_6_2)
% 201.56/33.39    (109)   ~ (all_52_9 = all_6_2)
% 201.56/33.39    (110)   ~ (all_52_13 = all_52_15)
% 201.56/33.39    (111)  all_56_0 = all_6_2
% 201.56/33.39    (112)  op(e3, e3) = all_6_2
% 201.56/33.39    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.39    (114)   ~ (all_52_27 = all_14_2)
% 201.56/33.39    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.39    (116)  all_56_14 = all_52_23
% 201.56/33.39    (117)  all_56_3 = all_52_25
% 201.56/33.39    (118)   ~ (all_52_3 = all_52_7)
% 201.56/33.39    (119)  all_58_5 = all_52_19
% 201.56/33.39    (120)  all_56_1 = all_52_9
% 201.56/33.39    (121)   ~ (all_52_15 = all_4_2)
% 201.56/33.39    (122)   ~ (all_52_27 = all_4_2)
% 201.56/33.39    (123)  all_58_6 = all_52_5
% 201.56/33.39    (124)  op(e3, e2) = all_52_9
% 201.56/33.39    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.39    (126)   ~ (all_52_17 = all_6_2)
% 201.56/33.39    (127)   ~ (e1 = e0)
% 201.56/33.39    (128)  op(all_14_2, all_14_2) = e0
% 201.56/33.39    (129)   ~ (e3 = e2)
% 201.56/33.39    (130)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.39    (131)  all_46_1 = all_6_1
% 201.56/33.39    (132)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.39    (133)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.39    (134)  op(e1, e1) = all_10_2
% 201.56/33.39    (135)   ~ (all_52_23 = all_10_2)
% 201.56/33.39    (136)   ~ (all_52_7 = all_52_23)
% 201.56/33.39    (137)   ~ (all_52_17 = all_52_19)
% 201.56/33.39    (138)  all_58_3 = all_4_2
% 201.56/33.39    (139)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.39    (140)  all_56_13 = all_52_15
% 201.56/33.39    (141)   ~ (all_52_3 = all_4_2)
% 201.56/33.39    (142)   ~ (all_52_19 = all_4_2)
% 201.56/33.39    (143)   ~ (all_52_17 = all_52_23)
% 201.56/33.39    (144)  op(all_6_2, e3) = all_6_1
% 201.56/33.39    (145)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.39    (146)  all_58_4 = all_52_17
% 201.56/33.39  
% 201.56/33.39  Begin of proof
% 201.56/33.39  | 
% 201.56/33.39  | BETA: splitting (98) gives:
% 201.56/33.39  | 
% 201.56/33.39  | Case 1:
% 201.56/33.39  | | 
% 201.56/33.39  | |   (147)  all_56_15 = e3
% 201.56/33.39  | | 
% 201.56/33.39  | | COMBINE_EQS: (47), (147) imply:
% 201.56/33.39  | |   (148)  all_14_2 = e3
% 201.56/33.39  | | 
% 201.56/33.39  | | COMBINE_EQS: (99), (148) imply:
% 201.56/33.39  | |   (149)  all_34_2 = e3
% 201.56/33.39  | | 
% 201.56/33.39  | | REDUCE: (70), (148) imply:
% 201.56/33.39  | |   (150)   ~ (all_52_7 = e3)
% 201.56/33.39  | | 
% 201.56/33.39  | | REDUCE: (37), (148) imply:
% 201.56/33.39  | |   (151)   ~ (all_52_25 = e3)
% 201.56/33.39  | | 
% 201.56/33.39  | | REDUCE: (128), (148) imply:
% 201.56/33.39  | |   (152)  op(e3, e3) = e0
% 201.56/33.39  | | 
% 201.56/33.39  | | REDUCE: (17), (148) imply:
% 201.56/33.39  | |   (153)  op(e3, e0) = all_14_1
% 201.56/33.39  | | 
% 201.56/33.39  | | BETA: splitting (52) gives:
% 201.56/33.39  | | 
% 201.56/33.39  | | Case 1:
% 201.56/33.39  | | | 
% 201.56/33.39  | | |   (154)   ~ (all_34_1 = e2)
% 201.56/33.39  | | | 
% 201.56/33.39  | | | REDUCE: (18), (154) imply:
% 201.56/33.39  | | |   (155)   ~ (all_14_1 = e2)
% 201.56/33.39  | | | 
% 201.56/33.39  | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3,
% 201.56/33.39  | | |              simplifying with (22), (153) gives:
% 201.56/33.39  | | |   (156)  all_52_25 = all_14_1
% 201.56/33.39  | | | 
% 201.56/33.39  | | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying with
% 201.56/33.39  | | |              (112), (152) gives:
% 201.56/33.39  | | |   (157)  all_6_2 = e0
% 201.56/33.39  | | | 
% 201.56/33.39  | | | COMBINE_EQS: (117), (156) imply:
% 201.56/33.39  | | |   (158)  all_56_3 = all_14_1
% 201.56/33.39  | | | 
% 201.56/33.39  | | | REDUCE: (43), (157) imply:
% 201.56/33.39  | | |   (159)   ~ (all_52_7 = e0)
% 201.56/33.39  | | | 
% 201.56/33.39  | | | REDUCE: (105), (156), (157) imply:
% 201.56/33.39  | | |   (160)   ~ (all_14_1 = e0)
% 201.56/33.39  | | | 
% 201.56/33.39  | | | REDUCE: (151), (156) imply:
% 201.56/33.39  | | |   (161)   ~ (all_14_1 = e3)
% 201.56/33.39  | | | 
% 201.56/33.39  | | | REDUCE: (144), (157) imply:
% 201.56/33.39  | | |   (162)  op(e0, e3) = all_6_1
% 201.56/33.39  | | | 
% 201.56/33.39  | | | BETA: splitting (68) gives:
% 201.56/33.39  | | | 
% 201.56/33.39  | | | Case 1:
% 201.56/33.39  | | | | 
% 201.56/33.39  | | | |   (163)   ~ (all_6_1 = e2)
% 201.56/33.39  | | | | 
% 201.56/33.39  | | | | BETA: splitting (106) gives:
% 201.56/33.39  | | | | 
% 201.56/33.39  | | | | Case 1:
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | |   (164)  all_56_3 = e3
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | | COMBINE_EQS: (158), (164) imply:
% 201.56/33.39  | | | | |   (165)  all_14_1 = e3
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | | REDUCE: (161), (165) imply:
% 201.56/33.39  | | | | |   (166)  $false
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | | CLOSE: (166) is inconsistent.
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | Case 2:
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | |   (167)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | | BETA: splitting (167) gives:
% 201.56/33.39  | | | | | 
% 201.56/33.39  | | | | | Case 1:
% 201.56/33.39  | | | | | | 
% 201.56/33.40  | | | | | |   (168)  all_56_3 = e2
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | | COMBINE_EQS: (158), (168) imply:
% 201.56/33.40  | | | | | |   (169)  all_14_1 = e2
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | | REDUCE: (155), (169) imply:
% 201.56/33.40  | | | | | |   (170)  $false
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | | CLOSE: (170) is inconsistent.
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | Case 2:
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | |   (171)  all_56_3 = e1 | all_56_3 = e0
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | | BETA: splitting (171) gives:
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | | Case 1:
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | |   (172)  all_56_3 = e1
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | COMBINE_EQS: (158), (172) imply:
% 201.56/33.40  | | | | | | |   (173)  all_14_1 = e1
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | REDUCE: (27), (173) imply:
% 201.56/33.40  | | | | | | |   (174)  op(e0, e1) = e1
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | GROUND_INST: instantiating (6) with all_52_23, e1, e1, e0,
% 201.56/33.40  | | | | | | |              simplifying with (46), (174) gives:
% 201.56/33.40  | | | | | | |   (175)  all_52_23 = e1
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | GROUND_INST: instantiating (6) with all_52_7, all_6_1, e3, e0,
% 201.56/33.40  | | | | | | |              simplifying with (90), (162) gives:
% 201.56/33.40  | | | | | | |   (176)  all_52_7 = all_6_1
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | REDUCE: (136), (175), (176) imply:
% 201.56/33.40  | | | | | | |   (177)   ~ (all_6_1 = e1)
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | REF_CLOSE: (6), (11), (90), (102), (150), (159), (162), (163),
% 201.56/33.40  | | | | | | |            (177) are inconsistent by sub-proof #1343.
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | Case 2:
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | |   (178)  all_56_3 = e0
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | COMBINE_EQS: (158), (178) imply:
% 201.56/33.40  | | | | | | |   (179)  all_14_1 = e0
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | REDUCE: (160), (179) imply:
% 201.56/33.40  | | | | | | |   (180)  $false
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | | CLOSE: (180) is inconsistent.
% 201.56/33.40  | | | | | | | 
% 201.56/33.40  | | | | | | End of split
% 201.56/33.40  | | | | | | 
% 201.56/33.40  | | | | | End of split
% 201.56/33.40  | | | | | 
% 201.56/33.40  | | | | End of split
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | Case 2:
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | |   (181)   ~ (all_6_2 = e0)
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | | REDUCE: (157), (181) imply:
% 201.56/33.40  | | | |   (182)  $false
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | | CLOSE: (182) is inconsistent.
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | End of split
% 201.56/33.40  | | | 
% 201.56/33.40  | | Case 2:
% 201.56/33.40  | | | 
% 201.56/33.40  | | |   (183)   ~ (all_34_2 = e3)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (149), (183) imply:
% 201.56/33.40  | | |   (184)  $false
% 201.56/33.40  | | | 
% 201.56/33.40  | | | CLOSE: (184) is inconsistent.
% 201.56/33.40  | | | 
% 201.56/33.40  | | End of split
% 201.56/33.40  | | 
% 201.56/33.40  | Case 2:
% 201.56/33.40  | | 
% 201.56/33.40  | |   (185)   ~ (all_56_15 = e3)
% 201.56/33.40  | |   (186)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (47), (185) imply:
% 201.56/33.40  | |   (187)   ~ (all_14_2 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 201.56/33.40  | |            (14), (15), (16), (19), (20), (21), (22), (23), (24), (25), (26),
% 201.56/33.40  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 201.56/33.40  | |            (39), (40), (41), (42), (43), (44), (45), (47), (48), (49), (50),
% 201.56/33.40  | |            (51), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 201.56/33.40  | |            (63), (64), (65), (66), (67), (69), (70), (71), (72), (73), (74),
% 201.56/33.40  | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 201.56/33.40  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 201.56/33.40  | |            (97), (100), (101), (103), (104), (105), (106), (107), (108),
% 201.56/33.40  | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 201.56/33.40  | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 201.56/33.40  | |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 201.56/33.40  | |            (136), (137), (138), (139), (140), (141), (142), (143), (144),
% 201.56/33.40  | |            (145), (146), (186), (187) are inconsistent by sub-proof #272.
% 201.56/33.40  | | 
% 201.56/33.40  | End of split
% 201.56/33.40  | 
% 201.56/33.40  End of proof
% 201.56/33.40  
% 201.56/33.40  Sub-proof #248 shows that the following formulas are inconsistent:
% 201.56/33.40  ----------------------------------------------------------------
% 201.56/33.40    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.40    (2)   ~ (e3 = e1)
% 201.56/33.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.40    (4)  op(all_52_23, all_52_23) = e0
% 201.56/33.40    (5)  op(all_14_2, e0) = all_14_1
% 201.56/33.40    (6)  all_34_1 = all_14_1
% 201.56/33.40    (7)  op(e3, e0) = all_52_25
% 201.56/33.40    (8)  op(e0, all_14_1) = e1
% 201.56/33.40    (9)  all_58_9 = all_52_25
% 201.56/33.40    (10)   ~ (all_52_29 = all_14_2)
% 201.56/33.40    (11)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.40    (12)  all_58_11 = all_52_29
% 201.56/33.40    (13)   ~ (all_52_25 = all_14_2)
% 201.56/33.40    (14)  op(e0, e0) = all_14_2
% 201.56/33.40    (15)  op(e0, e1) = all_52_23
% 201.56/33.40    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.40    (17)  all_56_11 = all_52_29
% 201.56/33.40    (18)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.56/33.40    (19)  op(all_10_2, all_10_2) = e1
% 201.56/33.40    (20)  all_58_10 = all_52_27
% 201.56/33.40    (21)   ~ (all_52_25 = all_52_29)
% 201.56/33.40    (22)   ~ (all_52_29 = all_10_2)
% 201.56/33.40    (23)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.40    (24)  all_34_2 = all_14_2
% 201.56/33.40    (25)   ~ (all_52_23 = all_14_2)
% 201.56/33.40    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.40    (27)  all_56_3 = all_52_25
% 201.56/33.40    (28)  op(e1, e1) = all_10_2
% 201.56/33.40    (29)   ~ (all_52_23 = all_10_2)
% 201.56/33.40    (30)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.40    (31)  all_14_2 = e3
% 201.56/33.40  
% 201.56/33.40  Begin of proof
% 201.56/33.40  | 
% 201.56/33.40  | COMBINE_EQS: (24), (31) imply:
% 201.56/33.40  |   (32)  all_34_2 = e3
% 201.56/33.40  | 
% 201.56/33.40  | REDUCE: (25), (31) imply:
% 201.56/33.40  |   (33)   ~ (all_52_23 = e3)
% 201.56/33.40  | 
% 201.56/33.40  | REDUCE: (13), (31) imply:
% 201.56/33.40  |   (34)   ~ (all_52_25 = e3)
% 201.56/33.40  | 
% 201.56/33.40  | REDUCE: (10), (31) imply:
% 201.56/33.40  |   (35)   ~ (all_52_29 = e3)
% 201.56/33.40  | 
% 201.56/33.40  | REDUCE: (5), (31) imply:
% 201.56/33.40  |   (36)  op(e3, e0) = all_14_1
% 201.56/33.40  | 
% 201.56/33.40  | REDUCE: (14), (31) imply:
% 201.56/33.40  |   (37)  op(e0, e0) = e3
% 201.56/33.40  | 
% 201.56/33.40  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (15), (16),
% 201.56/33.40  |            (17), (18), (19), (20), (21), (22), (23), (26), (27), (28), (29),
% 201.56/33.40  |            (30), (32), (33), (34), (35), (36), (37) are inconsistent by
% 201.56/33.40  |            sub-proof #853.
% 201.56/33.40  | 
% 201.56/33.40  End of proof
% 201.56/33.40  
% 201.56/33.40  Sub-proof #249 shows that the following formulas are inconsistent:
% 201.56/33.40  ----------------------------------------------------------------
% 201.56/33.40    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.40    (2)   ~ (all_52_15 = all_52_23)
% 201.56/33.40    (3)   ~ (all_52_25 = all_52_27)
% 201.56/33.40    (4)  all_58_14 = all_52_23
% 201.56/33.40    (5)   ~ (e3 = e1)
% 201.56/33.40    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.40    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.40    (9)   ~ (all_52_5 = all_52_13)
% 201.56/33.40    (10)  all_58_1 = all_52_9
% 201.56/33.40    (11)   ~ (all_52_9 = all_52_13)
% 201.56/33.40    (12)   ~ (e3 = e0)
% 201.56/33.40    (13)  op(e2, e3) = all_52_3
% 201.56/33.40    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.40    (15)   ~ (all_52_7 = all_52_15)
% 201.56/33.40    (16)  op(all_52_15, all_52_15) = e0
% 201.56/33.40    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.40    (18)   ~ (all_52_17 = all_52_25)
% 201.56/33.40    (19)   ~ (all_52_3 = all_6_2)
% 201.56/33.40    (20)  all_58_0 = all_6_2
% 201.56/33.40    (21)  op(all_14_2, e0) = all_14_1
% 201.56/33.40    (22)  all_34_1 = all_14_1
% 201.56/33.40    (23)  all_56_4 = all_52_3
% 201.56/33.40    (24)  op(e3, all_6_1) = e1
% 201.56/33.40    (25)   ~ (all_52_17 = all_10_2)
% 201.56/33.40    (26)  op(e3, e0) = all_52_25
% 201.56/33.40    (27)  op(e0, all_14_1) = all_14_0
% 201.56/33.40    (28)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.40    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.40    (30)  all_58_13 = all_52_15
% 201.56/33.40    (31)  op(all_52_13, all_52_13) = e1
% 201.56/33.40    (32)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.40    (33)  all_58_9 = all_52_25
% 201.56/33.40    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.40    (35)   ~ (all_52_29 = all_14_2)
% 201.56/33.40    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.40    (37)  op(e1, e3) = all_52_5
% 201.56/33.40    (38)  op(e2, e2) = all_4_2
% 201.56/33.40    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.40    (40)   ~ (all_52_3 = all_52_5)
% 201.56/33.40    (41)  all_58_11 = all_52_29
% 201.56/33.40    (42)  all_56_5 = all_4_2
% 201.56/33.40    (43)   ~ (all_52_25 = all_14_2)
% 201.56/33.40    (44)   ~ (all_52_9 = all_52_15)
% 201.56/33.40    (45)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.56/33.40    (46)  all_46_2 = all_6_2
% 201.56/33.40    (47)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.40    (48)   ~ (all_52_7 = all_6_2)
% 201.56/33.40    (49)  op(e0, e0) = all_14_2
% 201.56/33.40    (50)  op(e0, e1) = all_52_23
% 201.56/33.40    (51)  all_56_15 = all_14_2
% 201.56/33.40    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.40    (53)   ~ (all_4_1 = e1)
% 201.56/33.40    (54)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.40    (55)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 201.56/33.40    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.40    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.40    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.40    (59)  all_56_9 = all_52_13
% 201.56/33.40    (60)   ~ (e2 = e1)
% 201.56/33.40    (61)   ~ (all_52_13 = all_10_2)
% 201.56/33.40    (62)  all_58_10 = all_52_27
% 201.56/33.40    (63)  all_56_8 = all_52_5
% 201.56/33.40    (64)   ~ (all_52_19 = all_52_23)
% 201.56/33.40    (65)   ~ (all_52_25 = all_52_29)
% 201.56/33.40    (66)  all_58_7 = all_52_13
% 201.56/33.40    (67)   ~ (all_52_5 = all_52_7)
% 201.56/33.40    (68)  all_58_12 = all_52_7
% 201.56/33.40    (69)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.40    (70)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.40    (71)   ~ (all_52_7 = all_14_2)
% 201.56/33.40    (72)  all_58_2 = all_52_3
% 201.56/33.40    (73)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.40    (74)  all_56_2 = all_52_17
% 201.56/33.40    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.56/33.40    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.40    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.40    (78)  all_56_7 = all_52_27
% 201.56/33.40    (79)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.40    (80)   ~ (e2 = e0)
% 201.56/33.40    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.40    (82)  op(all_4_2, e2) = all_4_1
% 201.56/33.40    (83)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.56/33.40    (84)   ~ (all_52_5 = all_52_29)
% 201.56/33.40    (85)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.56/33.40    (86)  all_56_6 = all_52_19
% 201.56/33.40    (87)   ~ (all_52_15 = all_14_2)
% 201.56/33.40    (88)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.40    (89)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.40    (90)   ~ (all_52_13 = all_4_2)
% 201.56/33.40    (91)  op(e3, e1) = all_52_17
% 201.56/33.40    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.40    (93)  op(e0, e3) = all_52_7
% 201.56/33.40    (94)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.40    (95)   ~ (all_52_9 = all_52_25)
% 201.56/33.40    (96)  all_58_15 = all_14_2
% 201.56/33.40    (97)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.40    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.40    (99)  all_58_8 = all_10_2
% 201.56/33.40    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.40    (101)  all_34_2 = all_14_2
% 201.56/33.40    (102)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.40    (103)   ~ (all_52_23 = all_14_2)
% 201.56/33.40    (104)  all_56_12 = all_52_7
% 201.56/33.40    (105)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.40    (106)   ~ (all_52_25 = all_6_2)
% 201.56/33.40    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.40    (108)   ~ (all_52_9 = all_4_2)
% 201.56/33.40    (109)   ~ (all_52_5 = all_6_2)
% 201.56/33.40    (110)  op(all_4_2, all_4_2) = e2
% 201.56/33.40    (111)   ~ (all_52_9 = all_6_2)
% 201.56/33.40    (112)   ~ (all_52_13 = all_52_15)
% 201.56/33.40    (113)  all_56_0 = all_6_2
% 201.56/33.40    (114)  op(e3, e3) = all_6_2
% 201.56/33.40    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.40    (116)   ~ (all_52_27 = all_14_2)
% 201.56/33.40    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.40    (118)  all_56_3 = all_52_25
% 201.56/33.40    (119)   ~ (all_52_3 = all_52_7)
% 201.56/33.40    (120)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.40    (121)  all_58_5 = all_52_19
% 201.56/33.40    (122)  all_56_1 = all_52_9
% 201.56/33.40    (123)   ~ (all_52_15 = all_4_2)
% 201.56/33.40    (124)   ~ (all_52_27 = all_4_2)
% 201.56/33.40    (125)  all_58_6 = all_52_5
% 201.56/33.40    (126)  op(e3, e2) = all_52_9
% 201.56/33.40    (127)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.40    (128)   ~ (all_52_17 = all_6_2)
% 201.56/33.40    (129)   ~ (e1 = e0)
% 201.56/33.40    (130)   ~ (e3 = e2)
% 201.56/33.40    (131)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.40    (132)   ~ (all_52_9 = all_52_17)
% 201.56/33.40    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.40    (134)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.56/33.40    (135)  all_46_1 = all_6_1
% 201.56/33.40    (136)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.40    (137)  op(e1, e1) = all_10_2
% 201.56/33.40    (138)  op(all_52_9, all_52_9) = e3
% 201.56/33.40    (139)   ~ (all_52_23 = all_10_2)
% 201.56/33.40    (140)   ~ (all_52_7 = all_52_23)
% 201.56/33.40    (141)   ~ (all_52_17 = all_52_19)
% 201.56/33.40    (142)  all_58_3 = all_4_2
% 201.56/33.40    (143)  all_56_13 = all_52_15
% 201.56/33.40    (144)   ~ (all_52_3 = all_4_2)
% 201.56/33.40    (145)   ~ (all_52_19 = all_4_2)
% 201.56/33.40    (146)   ~ (all_52_17 = all_52_23)
% 201.56/33.40    (147)  op(all_6_2, e3) = all_6_1
% 201.56/33.40    (148)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.40    (149)   ~ (all_52_13 = all_52_29)
% 201.56/33.40    (150)  all_58_4 = all_52_17
% 201.56/33.40    (151)   ~ (all_14_0 = e2)
% 201.56/33.40    (152)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.40  
% 201.56/33.40  Begin of proof
% 201.56/33.40  | 
% 201.56/33.40  | BETA: splitting (100) gives:
% 201.56/33.40  | 
% 201.56/33.40  | Case 1:
% 201.56/33.40  | | 
% 201.56/33.40  | |   (153)  all_56_15 = e3
% 201.56/33.40  | | 
% 201.56/33.40  | | COMBINE_EQS: (51), (153) imply:
% 201.56/33.40  | |   (154)  all_14_2 = e3
% 201.56/33.40  | | 
% 201.56/33.40  | | SIMP: (154) implies:
% 201.56/33.40  | |   (155)  all_14_2 = e3
% 201.56/33.40  | | 
% 201.56/33.40  | | COMBINE_EQS: (101), (155) imply:
% 201.56/33.40  | |   (156)  all_34_2 = e3
% 201.56/33.40  | | 
% 201.56/33.40  | | COMBINE_EQS: (96), (155) imply:
% 201.56/33.40  | |   (157)  all_58_15 = e3
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (71), (155) imply:
% 201.56/33.40  | |   (158)   ~ (all_52_7 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (87), (155) imply:
% 201.56/33.40  | |   (159)   ~ (all_52_15 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (43), (155) imply:
% 201.56/33.40  | |   (160)   ~ (all_52_25 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (116), (155) imply:
% 201.56/33.40  | |   (161)   ~ (all_52_27 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (35), (155) imply:
% 201.56/33.40  | |   (162)   ~ (all_52_29 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (120), (155) imply:
% 201.56/33.40  | |   (163)  op(e3, e3) = all_52_30
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (21), (155) imply:
% 201.56/33.40  | |   (164)  op(e3, e0) = all_14_1
% 201.56/33.40  | | 
% 201.56/33.40  | | BETA: splitting (55) gives:
% 201.56/33.40  | | 
% 201.56/33.40  | | Case 1:
% 201.56/33.40  | | | 
% 201.56/33.40  | | |   (165)   ~ (all_34_1 = e2)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (22), (165) imply:
% 201.56/33.40  | | |   (166)   ~ (all_14_1 = e2)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 201.56/33.40  | | |              simplifying with (26), (164) gives:
% 201.56/33.40  | | |   (167)  all_52_25 = all_14_1
% 201.56/33.40  | | | 
% 201.56/33.40  | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 201.56/33.40  | | |              simplifying with (114), (163) gives:
% 201.56/33.40  | | |   (168)  all_52_30 = all_6_2
% 201.56/33.40  | | | 
% 201.56/33.40  | | | COMBINE_EQS: (118), (167) imply:
% 201.56/33.40  | | |   (169)  all_56_3 = all_14_1
% 201.56/33.40  | | | 
% 201.56/33.40  | | | COMBINE_EQS: (33), (167) imply:
% 201.56/33.40  | | |   (170)  all_58_9 = all_14_1
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (95), (167) imply:
% 201.56/33.40  | | |   (171)   ~ (all_52_9 = all_14_1)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (106), (167) imply:
% 201.56/33.40  | | |   (172)   ~ (all_14_1 = all_6_2)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (160), (167) imply:
% 201.56/33.40  | | |   (173)   ~ (all_14_1 = e3)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (152), (167) imply:
% 201.56/33.40  | | |   (174)  op(all_14_1, all_14_1) = all_52_24
% 201.56/33.40  | | | 
% 201.56/33.40  | | | BETA: splitting (107) gives:
% 201.56/33.40  | | | 
% 201.56/33.40  | | | Case 1:
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | |   (175)  all_56_3 = e3
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | | REF_CLOSE: (169), (173), (175) are inconsistent by sub-proof #1200.
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | Case 2:
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | |   (176)   ~ (all_56_3 = e3)
% 201.56/33.40  | | | |   (177)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (13), (14), (15), (19),
% 201.56/33.40  | | | |            (20), (23), (24), (25), (27), (28), (30), (31), (33), (38),
% 201.56/33.40  | | | |            (40), (41), (45), (48), (50), (52), (53), (58), (59), (60),
% 201.56/33.40  | | | |            (61), (62), (66), (67), (68), (70), (72), (75), (76), (77),
% 201.56/33.40  | | | |            (79), (82), (83), (85), (90), (94), (99), (104), (105),
% 201.56/33.40  | | | |            (108), (110), (111), (112), (114), (117), (119), (121),
% 201.56/33.40  | | | |            (122), (125), (126), (128), (131), (132), (133), (134),
% 201.56/33.40  | | | |            (137), (138), (141), (142), (144), (147), (150), (151),
% 201.56/33.40  | | | |            (157), (158), (159), (160), (161), (162), (166), (169),
% 201.56/33.40  | | | |            (170), (171), (172), (173), (174), (177) are inconsistent by
% 201.56/33.40  | | | |            sub-proof #298.
% 201.56/33.40  | | | | 
% 201.56/33.40  | | | End of split
% 201.56/33.40  | | | 
% 201.56/33.40  | | Case 2:
% 201.56/33.40  | | | 
% 201.56/33.40  | | |   (178)   ~ (all_34_2 = e3)
% 201.56/33.40  | | | 
% 201.56/33.40  | | | REDUCE: (156), (178) imply:
% 201.56/33.40  | | |   (179)  $false
% 201.56/33.40  | | | 
% 201.56/33.40  | | | CLOSE: (179) is inconsistent.
% 201.56/33.40  | | | 
% 201.56/33.40  | | End of split
% 201.56/33.40  | | 
% 201.56/33.40  | Case 2:
% 201.56/33.40  | | 
% 201.56/33.40  | |   (180)   ~ (all_56_15 = e3)
% 201.56/33.40  | |   (181)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.40  | | 
% 201.56/33.40  | | REDUCE: (51), (180) imply:
% 201.56/33.40  | |   (182)   ~ (all_14_2 = e3)
% 201.56/33.40  | | 
% 201.56/33.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 201.56/33.40  | |            (14), (15), (16), (17), (18), (19), (20), (23), (24), (25), (28),
% 201.56/33.40  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 201.56/33.40  | |            (40), (41), (42), (43), (44), (46), (47), (48), (49), (51), (52),
% 201.56/33.40  | |            (53), (54), (56), (57), (58), (60), (62), (63), (64), (65), (66),
% 201.56/33.40  | |            (67), (68), (69), (70), (71), (72), (73), (74), (76), (77), (78),
% 201.56/33.40  | |            (79), (80), (81), (82), (83), (84), (86), (88), (89), (90), (91),
% 201.56/33.40  | |            (92), (93), (94), (95), (96), (97), (98), (99), (102), (103),
% 201.56/33.40  | |            (104), (105), (106), (107), (108), (109), (110), (111), (113),
% 201.56/33.40  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 201.56/33.40  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 201.56/33.40  | |            (132), (133), (135), (136), (137), (138), (139), (140), (141),
% 201.56/33.40  | |            (142), (143), (144), (145), (146), (147), (148), (149), (150),
% 201.56/33.40  | |            (152), (181), (182) are inconsistent by sub-proof #288.
% 201.56/33.40  | | 
% 201.56/33.40  | End of split
% 201.56/33.40  | 
% 201.56/33.40  End of proof
% 201.56/33.40  
% 201.56/33.40  Sub-proof #250 shows that the following formulas are inconsistent:
% 201.56/33.40  ----------------------------------------------------------------
% 201.56/33.40    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.40    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.40    (3)  all_58_14 = all_52_23
% 201.56/33.40    (4)   ~ (e3 = e1)
% 201.56/33.40    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.40    (6)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.40    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.40    (8)   ~ (all_52_5 = all_52_13)
% 201.56/33.40    (9)  all_58_1 = all_52_9
% 201.56/33.40    (10)   ~ (all_52_9 = all_52_13)
% 201.56/33.40    (11)   ~ (e3 = e0)
% 201.56/33.40    (12)  op(e2, e3) = all_52_3
% 201.56/33.40    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.40    (14)   ~ (all_52_7 = all_52_15)
% 201.56/33.40    (15)   ~ (all_52_3 = all_52_19)
% 201.56/33.40    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.40    (17)   ~ (all_52_17 = all_52_25)
% 201.56/33.40    (18)   ~ (all_52_3 = all_6_2)
% 201.56/33.40    (19)  all_58_0 = all_6_2
% 201.56/33.40    (20)  op(all_14_2, e0) = all_14_1
% 201.56/33.40    (21)  all_56_4 = all_52_3
% 201.56/33.40    (22)  op(e3, all_6_1) = e1
% 201.56/33.40    (23)   ~ (all_52_17 = all_10_2)
% 201.56/33.40    (24)   ~ (all_10_0 = e3)
% 201.56/33.40    (25)  op(e3, e0) = all_52_25
% 201.56/33.40    (26)  op(e0, all_14_1) = all_14_0
% 201.56/33.40    (27)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.40    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.40    (29)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.40    (30)   ~ (all_52_27 = all_52_29)
% 201.56/33.40    (31)  all_58_13 = all_52_15
% 201.56/33.40    (32)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.40    (33)  all_58_9 = all_52_25
% 201.56/33.40    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.40    (35)   ~ (all_52_29 = all_14_2)
% 201.56/33.40    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.40    (37)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.40    (38)  op(e1, e3) = all_52_5
% 201.56/33.40    (39)  op(e2, e2) = all_4_2
% 201.56/33.40    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.40    (41)   ~ (all_52_3 = all_52_5)
% 201.56/33.40    (42)  all_58_11 = all_52_29
% 201.56/33.40    (43)  all_56_5 = all_4_2
% 201.56/33.40    (44)   ~ (all_52_25 = all_14_2)
% 201.56/33.40    (45)   ~ (all_52_9 = all_52_15)
% 201.56/33.40    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.56/33.40    (47)   ~ (all_52_3 = all_52_27)
% 201.56/33.40    (48)  op(all_10_2, e1) = all_10_1
% 201.56/33.40    (49)  all_46_2 = all_6_2
% 201.56/33.40    (50)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.40    (51)   ~ (all_52_7 = all_6_2)
% 201.56/33.40    (52)  op(e0, e0) = all_14_2
% 201.56/33.40    (53)  op(e0, e1) = all_52_23
% 201.56/33.40    (54)  all_56_15 = all_14_2
% 201.56/33.40    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.40    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.40    (57)   ~ (all_58_15 = e0)
% 201.56/33.40    (58)  all_56_11 = all_52_29
% 201.56/33.40    (59)   ~ (all_10_0 = e2)
% 201.56/33.40    (60)   ~ (all_4_1 = e1)
% 201.56/33.40    (61)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.40    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.40    (63)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.40    (64)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.40    (65)  all_56_9 = all_52_13
% 201.56/33.40    (66)   ~ (e2 = e1)
% 201.56/33.40    (67)   ~ (all_52_13 = all_10_2)
% 201.56/33.40    (68)  all_58_10 = all_52_27
% 201.56/33.40    (69)  all_56_8 = all_52_5
% 201.56/33.40    (70)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.40    (71)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.40    (72)   ~ (all_52_19 = all_52_23)
% 201.56/33.40    (73)   ~ (all_52_25 = all_52_29)
% 201.56/33.40    (74)   ~ (all_52_29 = all_10_2)
% 201.56/33.40    (75)  op(all_10_2, e1) = e3
% 201.56/33.40    (76)  all_58_7 = all_52_13
% 201.56/33.40    (77)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 201.56/33.40    (78)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.40    (79)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.56/33.40    (80)   ~ (all_52_5 = all_52_7)
% 201.56/33.40    (81)  all_58_12 = all_52_7
% 201.56/33.40    (82)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.40    (83)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.40    (84)   ~ (all_52_7 = all_14_2)
% 201.56/33.40    (85)  all_30_2 = all_10_2
% 201.56/33.40    (86)  all_58_2 = all_52_3
% 201.56/33.40    (87)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.40    (88)  all_56_2 = all_52_17
% 201.56/33.40    (89)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.56/33.40    (90)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.40    (91)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.40    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.40    (93)  all_56_7 = all_52_27
% 201.56/33.40    (94)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.41    (95)   ~ (e2 = e0)
% 201.56/33.41    (96)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.41    (97)  op(all_4_2, e2) = all_4_1
% 201.56/33.41    (98)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.56/33.41    (99)   ~ (all_52_5 = all_52_29)
% 201.56/33.41    (100)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.56/33.41    (101)  all_56_6 = all_52_19
% 201.56/33.41    (102)  all_56_8 = all_10_0
% 201.56/33.41    (103)   ~ (all_52_15 = all_14_2)
% 201.56/33.41    (104)   ~ (all_52_19 = all_52_27)
% 201.56/33.41    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.41    (106)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.41    (107)   ~ (all_52_13 = all_4_2)
% 201.56/33.41    (108)  op(e3, e1) = all_52_17
% 201.56/33.41    (109)  all_30_0 = all_10_0
% 201.56/33.41    (110)  all_58_6 = all_10_0
% 201.56/33.41    (111)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.41    (112)  op(e0, e3) = all_52_7
% 201.56/33.41    (113)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.41    (114)   ~ (all_52_9 = all_52_25)
% 201.56/33.41    (115)  all_58_15 = all_14_2
% 201.56/33.41    (116)   ~ (all_52_19 = all_10_2)
% 201.56/33.41    (117)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.41    (118)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.41    (119)   ~ (all_10_0 = all_10_2)
% 201.56/33.41    (120)  all_58_8 = all_10_2
% 201.56/33.41    (121)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.41    (122)   ~ (all_52_5 = all_10_2)
% 201.56/33.41    (123)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.41    (124)   ~ (all_52_23 = all_14_2)
% 201.56/33.41    (125)  all_56_12 = all_52_7
% 201.56/33.41    (126)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.41    (127)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.56/33.41    (128)   ~ (all_52_25 = all_6_2)
% 201.56/33.41    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.41    (130)   ~ (all_52_9 = all_4_2)
% 201.56/33.41    (131)   ~ (all_52_5 = all_6_2)
% 201.56/33.41    (132)   ~ (all_52_9 = all_6_2)
% 201.56/33.41    (133)   ~ (all_52_13 = all_52_15)
% 201.56/33.41    (134)  all_56_0 = all_6_2
% 201.56/33.41    (135)  op(e3, e3) = all_6_2
% 201.56/33.41    (136)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.41    (137)   ~ (all_52_27 = all_14_2)
% 201.56/33.41    (138)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.41    (139)  all_56_14 = all_52_23
% 201.56/33.41    (140)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.41    (141)  all_56_3 = all_52_25
% 201.56/33.41    (142)   ~ (all_52_3 = all_52_7)
% 201.56/33.41    (143)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.41    (144)  all_58_5 = all_52_19
% 201.56/33.41    (145)  op(all_10_0, all_10_0) = all_52_4
% 201.56/33.41    (146)  all_56_1 = all_52_9
% 201.56/33.41    (147)   ~ (all_52_15 = all_4_2)
% 201.56/33.41    (148)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.41           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.56/33.41           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.56/33.41           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.56/33.41    (149)   ~ (all_52_27 = all_4_2)
% 201.56/33.41    (150)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 201.56/33.41             all_58_13 = e0 | all_58_14 = e0)
% 201.56/33.41    (151)  all_58_6 = all_52_5
% 201.56/33.41    (152)  op(e3, e2) = all_52_9
% 201.56/33.41    (153)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.41    (154)   ~ (all_52_17 = all_6_2)
% 201.56/33.41    (155)   ~ (e1 = e0)
% 201.56/33.41    (156)   ~ (e3 = e2)
% 201.56/33.41    (157)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.41    (158)   ~ (all_52_9 = all_52_17)
% 201.56/33.41    (159)  all_56_10 = all_10_2
% 201.56/33.41    (160)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.41    (161)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.56/33.41    (162)  all_46_1 = all_6_1
% 201.56/33.41    (163)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.41    (164)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.41    (165)  op(e1, e1) = all_10_2
% 201.56/33.41    (166)   ~ (all_52_23 = all_10_2)
% 201.56/33.41    (167)   ~ (all_52_7 = all_52_23)
% 201.56/33.41    (168)   ~ (all_52_17 = all_52_19)
% 201.56/33.41    (169)  all_58_3 = all_4_2
% 201.56/33.41    (170)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.41    (171)  all_56_13 = all_52_15
% 201.56/33.41    (172)   ~ (all_52_3 = all_4_2)
% 201.56/33.41    (173)   ~ (all_52_19 = all_4_2)
% 201.56/33.41    (174)   ~ (all_52_17 = all_52_23)
% 201.56/33.41    (175)  op(all_6_2, e3) = all_6_1
% 201.56/33.41    (176)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.41    (177)   ~ (all_52_13 = all_52_29)
% 201.56/33.41    (178)  all_58_4 = all_52_17
% 201.56/33.41    (179)   ~ (all_14_0 = e2)
% 201.56/33.41    (180)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.56/33.41    (181)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.41  
% 201.56/33.41  Begin of proof
% 201.56/33.41  | 
% 201.56/33.41  | ALPHA: (150) implies:
% 201.56/33.41  |   (182)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.41  |   (183)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.41  | 
% 201.56/33.41  | REDUCE: (57), (115) imply:
% 201.56/33.41  |   (184)   ~ (all_14_2 = e0)
% 201.56/33.41  | 
% 201.56/33.41  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.41  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.56/33.41  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 201.56/33.41  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 201.56/33.41  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 201.56/33.41  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 201.56/33.41  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 201.56/33.41  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 201.56/33.41  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 201.56/33.41  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 201.56/33.41  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 201.56/33.41  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 201.56/33.41  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 201.56/33.41  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 201.56/33.41  |            (147), (148), (149), (151), (152), (153), (154), (155), (156),
% 201.56/33.41  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 201.56/33.41  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 201.56/33.41  |            (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 201.56/33.41  |            (184) are inconsistent by sub-proof #251.
% 201.56/33.41  | 
% 201.56/33.41  End of proof
% 201.56/33.41  
% 201.56/33.41  Sub-proof #251 shows that the following formulas are inconsistent:
% 201.56/33.41  ----------------------------------------------------------------
% 201.56/33.41    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.41    (2)   ~ (all_52_15 = all_52_23)
% 201.56/33.41    (3)   ~ (all_52_25 = all_52_27)
% 201.56/33.41    (4)  all_58_14 = all_52_23
% 201.56/33.41    (5)   ~ (e3 = e1)
% 201.56/33.41    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.41    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.41    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.41    (9)   ~ (all_52_5 = all_52_13)
% 201.56/33.41    (10)  all_58_1 = all_52_9
% 201.56/33.41    (11)   ~ (all_52_9 = all_52_13)
% 201.56/33.41    (12)   ~ (e3 = e0)
% 201.56/33.41    (13)  op(e2, e3) = all_52_3
% 201.56/33.41    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.41    (15)   ~ (all_52_7 = all_52_15)
% 201.56/33.41    (16)   ~ (all_52_3 = all_52_19)
% 201.56/33.41    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.41    (18)   ~ (all_52_17 = all_52_25)
% 201.56/33.41    (19)   ~ (all_52_3 = all_6_2)
% 201.56/33.41    (20)  all_58_0 = all_6_2
% 201.56/33.41    (21)  op(all_14_2, e0) = all_14_1
% 201.56/33.41    (22)  all_56_4 = all_52_3
% 201.56/33.41    (23)  op(e3, all_6_1) = e1
% 201.56/33.41    (24)   ~ (all_52_17 = all_10_2)
% 201.56/33.41    (25)   ~ (all_10_0 = e3)
% 201.56/33.41    (26)  op(e3, e0) = all_52_25
% 201.56/33.41    (27)  op(e0, all_14_1) = all_14_0
% 201.56/33.41    (28)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.41    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.41    (30)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.41    (31)   ~ (all_52_27 = all_52_29)
% 201.56/33.41    (32)  all_58_13 = all_52_15
% 201.56/33.41    (33)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.41    (34)  all_58_9 = all_52_25
% 201.56/33.41    (35)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.41    (36)   ~ (all_52_29 = all_14_2)
% 201.56/33.41    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.41    (38)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.41    (39)  op(e1, e3) = all_52_5
% 201.56/33.41    (40)  op(e2, e2) = all_4_2
% 201.56/33.41    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.41    (42)   ~ (all_52_3 = all_52_5)
% 201.56/33.41    (43)  all_58_11 = all_52_29
% 201.56/33.41    (44)  all_56_5 = all_4_2
% 201.56/33.41    (45)   ~ (all_52_25 = all_14_2)
% 201.56/33.41    (46)   ~ (all_52_9 = all_52_15)
% 201.56/33.41    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.56/33.41    (48)   ~ (all_52_3 = all_52_27)
% 201.56/33.41    (49)  op(all_10_2, e1) = all_10_1
% 201.56/33.41    (50)  all_46_2 = all_6_2
% 201.56/33.41    (51)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.41    (52)   ~ (all_52_7 = all_6_2)
% 201.56/33.41    (53)  op(e0, e0) = all_14_2
% 201.56/33.41    (54)  op(e0, e1) = all_52_23
% 201.56/33.41    (55)  all_56_15 = all_14_2
% 201.56/33.41    (56)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.41    (57)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.41    (58)  all_56_11 = all_52_29
% 201.56/33.41    (59)   ~ (all_10_0 = e2)
% 201.56/33.41    (60)   ~ (all_4_1 = e1)
% 201.56/33.41    (61)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.41    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.41    (63)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.41    (64)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.41    (65)  all_56_9 = all_52_13
% 201.56/33.41    (66)   ~ (e2 = e1)
% 201.56/33.41    (67)   ~ (all_52_13 = all_10_2)
% 201.56/33.41    (68)  all_58_10 = all_52_27
% 201.56/33.41    (69)  all_56_8 = all_52_5
% 201.56/33.41    (70)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.41    (71)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.41    (72)   ~ (all_52_19 = all_52_23)
% 201.56/33.41    (73)   ~ (all_52_25 = all_52_29)
% 201.56/33.41    (74)   ~ (all_52_29 = all_10_2)
% 201.56/33.41    (75)  op(all_10_2, e1) = e3
% 201.56/33.41    (76)  all_58_7 = all_52_13
% 201.56/33.41    (77)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 201.56/33.41    (78)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.41    (79)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.56/33.41    (80)   ~ (all_52_5 = all_52_7)
% 201.56/33.41    (81)  all_58_12 = all_52_7
% 201.56/33.41    (82)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.41    (83)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.41    (84)   ~ (all_52_7 = all_14_2)
% 201.56/33.41    (85)   ~ (all_14_2 = e0)
% 201.56/33.41    (86)  all_30_2 = all_10_2
% 201.56/33.41    (87)  all_58_2 = all_52_3
% 201.56/33.41    (88)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.41    (89)  all_56_2 = all_52_17
% 201.56/33.41    (90)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.56/33.41    (91)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.41    (92)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.41    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.41    (94)  all_56_7 = all_52_27
% 201.56/33.41    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.41    (96)   ~ (e2 = e0)
% 201.56/33.41    (97)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.41    (98)  op(all_4_2, e2) = all_4_1
% 201.56/33.41    (99)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.56/33.41    (100)   ~ (all_52_5 = all_52_29)
% 201.56/33.41    (101)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.56/33.41    (102)  all_56_6 = all_52_19
% 201.56/33.41    (103)  all_56_8 = all_10_0
% 201.56/33.41    (104)   ~ (all_52_15 = all_14_2)
% 201.56/33.41    (105)   ~ (all_52_19 = all_52_27)
% 201.56/33.41    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.41    (107)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.41    (108)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.41    (109)   ~ (all_52_13 = all_4_2)
% 201.56/33.41    (110)  op(e3, e1) = all_52_17
% 201.56/33.41    (111)  all_30_0 = all_10_0
% 201.56/33.41    (112)  all_58_6 = all_10_0
% 201.56/33.41    (113)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.41    (114)  op(e0, e3) = all_52_7
% 201.56/33.41    (115)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.41    (116)   ~ (all_52_9 = all_52_25)
% 201.56/33.41    (117)  all_58_15 = all_14_2
% 201.56/33.41    (118)   ~ (all_52_19 = all_10_2)
% 201.56/33.41    (119)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.41    (120)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.41    (121)   ~ (all_10_0 = all_10_2)
% 201.56/33.41    (122)  all_58_8 = all_10_2
% 201.56/33.41    (123)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.41    (124)   ~ (all_52_5 = all_10_2)
% 201.56/33.41    (125)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.41    (126)   ~ (all_52_23 = all_14_2)
% 201.56/33.41    (127)  all_56_12 = all_52_7
% 201.56/33.41    (128)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.41    (129)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.56/33.41    (130)   ~ (all_52_25 = all_6_2)
% 201.56/33.41    (131)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.41    (132)   ~ (all_52_9 = all_4_2)
% 201.56/33.41    (133)   ~ (all_52_5 = all_6_2)
% 201.56/33.41    (134)   ~ (all_52_9 = all_6_2)
% 201.56/33.41    (135)   ~ (all_52_13 = all_52_15)
% 201.56/33.41    (136)  all_56_0 = all_6_2
% 201.56/33.41    (137)  op(e3, e3) = all_6_2
% 201.56/33.41    (138)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.41    (139)   ~ (all_52_27 = all_14_2)
% 201.56/33.41    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.41    (141)  all_56_14 = all_52_23
% 201.56/33.41    (142)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.41    (143)  all_56_3 = all_52_25
% 201.56/33.41    (144)   ~ (all_52_3 = all_52_7)
% 201.56/33.41    (145)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.41    (146)  all_58_5 = all_52_19
% 201.56/33.41    (147)  op(all_10_0, all_10_0) = all_52_4
% 201.56/33.41    (148)  all_56_1 = all_52_9
% 201.56/33.41    (149)   ~ (all_52_15 = all_4_2)
% 201.56/33.41    (150)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.41           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.56/33.41           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.56/33.41           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.56/33.41    (151)   ~ (all_52_27 = all_4_2)
% 201.56/33.41    (152)  all_58_6 = all_52_5
% 201.56/33.41    (153)  op(e3, e2) = all_52_9
% 201.56/33.41    (154)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.41    (155)   ~ (all_52_17 = all_6_2)
% 201.56/33.41    (156)   ~ (e1 = e0)
% 201.56/33.41    (157)   ~ (e3 = e2)
% 201.56/33.41    (158)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.41    (159)   ~ (all_52_9 = all_52_17)
% 201.56/33.41    (160)  all_56_10 = all_10_2
% 201.56/33.41    (161)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.41    (162)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.56/33.41    (163)  all_46_1 = all_6_1
% 201.56/33.41    (164)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.41    (165)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.41    (166)  op(e1, e1) = all_10_2
% 201.56/33.41    (167)   ~ (all_52_23 = all_10_2)
% 201.56/33.41    (168)   ~ (all_52_7 = all_52_23)
% 201.56/33.41    (169)   ~ (all_52_17 = all_52_19)
% 201.56/33.41    (170)  all_58_3 = all_4_2
% 201.56/33.41    (171)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.41    (172)  all_56_13 = all_52_15
% 201.56/33.41    (173)   ~ (all_52_3 = all_4_2)
% 201.56/33.41    (174)   ~ (all_52_19 = all_4_2)
% 201.56/33.41    (175)   ~ (all_52_17 = all_52_23)
% 201.56/33.41    (176)  op(all_6_2, e3) = all_6_1
% 201.56/33.41    (177)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.41    (178)   ~ (all_52_13 = all_52_29)
% 201.56/33.41    (179)  all_58_4 = all_52_17
% 201.56/33.41    (180)   ~ (all_14_0 = e2)
% 201.56/33.41    (181)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.56/33.41    (182)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.41  
% 201.56/33.41  Begin of proof
% 201.56/33.41  | 
% 201.56/33.41  | BETA: splitting (120) gives:
% 201.56/33.41  | 
% 201.56/33.41  | Case 1:
% 201.56/33.41  | | 
% 201.56/33.41  | |   (183)  all_56_8 = e3
% 201.56/33.41  | | 
% 201.56/33.41  | | REF_CLOSE: (25), (103), (183) are inconsistent by sub-proof #926.
% 201.56/33.41  | | 
% 201.56/33.41  | Case 2:
% 201.56/33.41  | | 
% 201.56/33.41  | |   (184)   ~ (all_56_8 = e3)
% 201.56/33.41  | |   (185)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.41  | | 
% 201.56/33.41  | | BETA: splitting (150) gives:
% 201.56/33.41  | | 
% 201.56/33.41  | | Case 1:
% 201.56/33.41  | | | 
% 201.56/33.41  | | |   (186)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.41  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 201.56/33.41  | | |            e0)
% 201.56/33.41  | | | 
% 201.56/33.41  | | | BETA: splitting (186) gives:
% 201.56/33.41  | | | 
% 201.56/33.41  | | | Case 1:
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | |   (187)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REF_CLOSE: (8), (24), (59), (75), (77), (86), (103), (110), (111),
% 201.56/33.41  | | | |            (112), (121), (129), (147), (160), (166), (181), (185), (187)
% 201.56/33.41  | | | |            are inconsistent by sub-proof #667.
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | Case 2:
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | |   (188)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 201.56/33.41  | | | |          e0
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 201.56/33.41  | | | |            (12), (13), (14), (15), (17), (18), (19), (20), (21), (22),
% 201.56/33.41  | | | |            (23), (24), (26), (27), (28), (29), (32), (33), (34), (35),
% 201.56/33.41  | | | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 201.56/33.41  | | | |            (47), (50), (51), (52), (53), (54), (55), (56), (60), (61),
% 201.56/33.41  | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 201.56/33.41  | | | |            (72), (73), (76), (80), (81), (82), (83), (84), (87), (88),
% 201.56/33.41  | | | |            (89), (90), (91), (93), (94), (95), (96), (97), (98), (99),
% 201.56/33.41  | | | |            (100), (101), (102), (104), (107), (108), (109), (110),
% 201.56/33.41  | | | |            (113), (114), (115), (116), (117), (119), (120), (122),
% 201.56/33.41  | | | |            (123), (125), (126), (127), (128), (130), (131), (132),
% 201.56/33.41  | | | |            (133), (134), (135), (136), (137), (138), (139), (140),
% 201.56/33.41  | | | |            (142), (143), (144), (145), (146), (148), (149), (151),
% 201.56/33.41  | | | |            (152), (153), (154), (155), (156), (157), (158), (159),
% 201.56/33.41  | | | |            (161), (162), (163), (164), (165), (166), (167), (168),
% 201.56/33.41  | | | |            (169), (170), (172), (173), (174), (175), (176), (177),
% 201.56/33.41  | | | |            (178), (179), (180), (182), (188) are inconsistent by
% 201.56/33.41  | | | |            sub-proof #286.
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | End of split
% 201.56/33.41  | | | 
% 201.56/33.41  | | Case 2:
% 201.56/33.41  | | | 
% 201.56/33.41  | | |   (189)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 201.56/33.41  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 201.56/33.41  | | |            all_52_30 = e0)
% 201.56/33.41  | | | 
% 201.56/33.41  | | | BETA: splitting (189) gives:
% 201.56/33.41  | | | 
% 201.56/33.41  | | | Case 1:
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | |   (190)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 201.56/33.41  | | | |          e0
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | ALPHA: (190) implies:
% 201.56/33.41  | | | |   (191)  all_52_22 = e0
% 201.56/33.41  | | | |   (192)  all_52_20 = e1
% 201.56/33.41  | | | |   (193)  all_52_18 = e2
% 201.56/33.41  | | | |   (194)  all_52_16 = e3
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REDUCE: (128), (194) imply:
% 201.56/33.41  | | | |   (195)  op(all_52_17, all_52_17) = e3
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REDUCE: (30), (193) imply:
% 201.56/33.41  | | | |   (196)  op(all_52_19, all_52_19) = e2
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REDUCE: (119), (191) imply:
% 201.56/33.41  | | | |   (197)  op(all_52_23, all_52_23) = e0
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REDUCE: (33), (192) imply:
% 201.56/33.41  | | | |   (198)  op(all_10_2, all_10_2) = e1
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | BETA: splitting (123) gives:
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | Case 1:
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | |   (199)  all_56_15 = e3
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | COMBINE_EQS: (55), (199) imply:
% 201.56/33.41  | | | | |   (200)  all_14_2 = e3
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | SIMP: (200) implies:
% 201.56/33.41  | | | | |   (201)  all_14_2 = e3
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | REDUCE: (84), (201) imply:
% 201.56/33.41  | | | | |   (202)   ~ (all_52_7 = e3)
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | REDUCE: (126), (201) imply:
% 201.56/33.41  | | | | |   (203)   ~ (all_52_23 = e3)
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | REDUCE: (45), (201) imply:
% 201.56/33.41  | | | | |   (204)   ~ (all_52_25 = e3)
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | REDUCE: (145), (201) imply:
% 201.56/33.41  | | | | |   (205)  op(e3, e3) = all_52_30
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 201.56/33.41  | | | | |              simplifying with (137), (205) gives:
% 201.56/33.41  | | | | |   (206)  all_52_30 = all_6_2
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | BETA: splitting (91) gives:
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | Case 1:
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | |   (207)  all_58_0 = e3
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | | COMBINE_EQS: (20), (207) imply:
% 201.56/33.41  | | | | | |   (208)  all_6_2 = e3
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | | REF_CLOSE: (5), (8), (23), (137), (176), (208) are inconsistent by
% 201.56/33.41  | | | | | |            sub-proof #310.
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | Case 2:
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | |   (209)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | | REF_CLOSE: (4), (7), (8), (10), (16), (19), (20), (24), (25), (34),
% 201.56/33.41  | | | | | |            (75), (81), (87), (110), (112), (115), (122), (137),
% 201.56/33.41  | | | | | |            (140), (146), (155), (159), (161), (179), (195), (202),
% 201.56/33.41  | | | | | |            (203), (204), (209) are inconsistent by sub-proof #780.
% 201.56/33.41  | | | | | | 
% 201.56/33.41  | | | | | End of split
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | Case 2:
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | |   (210)   ~ (all_56_15 = e3)
% 201.56/33.41  | | | | |   (211)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | REDUCE: (55), (210) imply:
% 201.56/33.41  | | | | |   (212)   ~ (all_14_2 = e3)
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (12), (14), (15), (17),
% 201.56/33.41  | | | | |            (18), (20), (23), (26), (28), (32), (34), (37), (39), (40),
% 201.56/33.41  | | | | |            (41), (42), (43), (45), (46), (49), (51), (52), (53), (55),
% 201.56/33.41  | | | | |            (58), (62), (63), (64), (66), (70), (73), (74), (76), (81),
% 201.56/33.41  | | | | |            (82), (83), (84), (85), (87), (89), (90), (91), (92), (93),
% 201.56/33.41  | | | | |            (96), (99), (106), (107), (108), (110), (114), (116),
% 201.56/33.41  | | | | |            (117), (118), (122), (124), (125), (126), (127), (130),
% 201.56/33.41  | | | | |            (131), (133), (134), (135), (136), (137), (138), (140),
% 201.56/33.41  | | | | |            (143), (144), (146), (148), (152), (153), (154), (155),
% 201.56/33.41  | | | | |            (156), (157), (158), (159), (160), (161), (164), (166),
% 201.56/33.41  | | | | |            (167), (168), (171), (172), (173), (176), (177), (179),
% 201.56/33.41  | | | | |            (181), (182), (195), (196), (197), (198), (211), (212) are
% 201.56/33.41  | | | | |            inconsistent by sub-proof #274.
% 201.56/33.41  | | | | | 
% 201.56/33.41  | | | | End of split
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | Case 2:
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | |   (213)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 201.56/33.41  | | | |          e0
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 201.56/33.41  | | | |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 201.56/33.41  | | | |            (28), (30), (31), (32), (34), (36), (37), (38), (39), (40),
% 201.56/33.41  | | | |            (41), (42), (43), (44), (45), (46), (48), (49), (50), (51),
% 201.56/33.41  | | | |            (52), (53), (55), (56), (57), (58), (61), (62), (63), (64),
% 201.56/33.41  | | | |            (66), (68), (69), (70), (71), (73), (74), (76), (78), (79),
% 201.56/33.41  | | | |            (80), (81), (82), (83), (84), (85), (87), (89), (90), (91),
% 201.56/33.41  | | | |            (92), (93), (95), (96), (97), (100), (104), (105), (106),
% 201.56/33.41  | | | |            (107), (108), (110), (113), (114), (115), (116), (117),
% 201.56/33.41  | | | |            (118), (119), (120), (122), (123), (124), (125), (126),
% 201.56/33.41  | | | |            (127), (128), (129), (130), (131), (132), (133), (134),
% 201.56/33.41  | | | |            (135), (136), (137), (138), (139), (140), (141), (143),
% 201.56/33.41  | | | |            (144), (145), (146), (148), (149), (151), (152), (153),
% 201.56/33.41  | | | |            (154), (155), (156), (157), (158), (163), (164), (165),
% 201.56/33.41  | | | |            (166), (167), (168), (169), (170), (171), (172), (173),
% 201.56/33.41  | | | |            (174), (175), (176), (177), (179), (182), (213) are
% 201.56/33.41  | | | |            inconsistent by sub-proof #271.
% 201.56/33.41  | | | | 
% 201.56/33.41  | | | End of split
% 201.56/33.41  | | | 
% 201.56/33.41  | | End of split
% 201.56/33.41  | | 
% 201.56/33.41  | End of split
% 201.56/33.41  | 
% 201.56/33.41  End of proof
% 201.56/33.41  
% 201.56/33.41  Sub-proof #252 shows that the following formulas are inconsistent:
% 201.56/33.41  ----------------------------------------------------------------
% 201.56/33.41    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.41    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.41    (3)  all_58_14 = all_52_23
% 201.56/33.41    (4)   ~ (e3 = e1)
% 201.56/33.41    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.41    (6)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.41    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.41    (8)  all_58_1 = all_52_9
% 201.56/33.41    (9)   ~ (all_52_9 = all_52_13)
% 201.56/33.41    (10)   ~ (e3 = e0)
% 201.56/33.41    (11)  op(e2, e3) = all_52_3
% 201.56/33.42    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.42    (13)   ~ (all_52_7 = all_52_15)
% 201.56/33.42    (14)   ~ (all_52_3 = all_52_19)
% 201.56/33.42    (15)  op(all_52_15, all_52_15) = e0
% 201.56/33.42    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.42    (17)   ~ (all_52_17 = all_52_25)
% 201.56/33.42    (18)   ~ (all_52_3 = all_6_2)
% 201.56/33.42    (19)  all_58_0 = all_6_2
% 201.56/33.42    (20)  op(e3, all_6_1) = e1
% 201.56/33.42    (21)   ~ (all_52_17 = all_10_2)
% 201.56/33.42    (22)   ~ (all_10_0 = e3)
% 201.56/33.42    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.42    (24)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.42    (25)   ~ (all_52_27 = all_52_29)
% 201.56/33.42    (26)  all_58_13 = all_52_15
% 201.56/33.42    (27)  op(all_52_13, all_52_13) = e1
% 201.56/33.42    (28)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.42    (29)  all_58_9 = all_52_25
% 201.56/33.42    (30)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.42    (31)  op(e2, e2) = all_4_2
% 201.56/33.42    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.42    (33)  all_58_11 = all_52_29
% 201.56/33.42    (34)   ~ (all_52_9 = all_52_15)
% 201.56/33.42    (35)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.56/33.42    (36)   ~ (all_52_3 = all_52_27)
% 201.56/33.42    (37)  all_46_2 = all_6_2
% 201.56/33.42    (38)   ~ (all_52_7 = all_6_2)
% 201.56/33.42    (39)   ~ (all_52_15 = e0)
% 201.56/33.42    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.42    (41)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.42    (42)  all_58_15 = e0
% 201.56/33.42    (43)   ~ (all_10_0 = e2)
% 201.56/33.42    (44)   ~ (all_4_1 = e1)
% 201.56/33.42    (45)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.42    (46)   ~ (all_52_25 = e0)
% 201.56/33.42    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.42    (48)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.42    (49)   ~ (all_52_13 = all_10_2)
% 201.56/33.42    (50)  op(e0, e0) = e0
% 201.56/33.42    (51)  all_58_10 = all_52_27
% 201.56/33.42    (52)   ~ (all_52_25 = all_52_29)
% 201.56/33.42    (53)   ~ (all_52_29 = all_10_2)
% 201.56/33.42    (54)  op(all_10_2, e1) = e3
% 201.56/33.42    (55)  all_58_7 = all_52_13
% 201.56/33.42    (56)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 201.56/33.42    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.42    (58)  all_58_12 = all_52_7
% 201.56/33.42    (59)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.42    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.42    (61)  all_30_2 = all_10_2
% 201.56/33.42    (62)  all_58_2 = all_52_3
% 201.56/33.42    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.42    (64)  all_56_2 = all_52_17
% 201.56/33.42    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.42    (66)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.42    (67)  all_56_7 = all_52_27
% 201.56/33.42    (68)   ~ (e2 = e0)
% 201.56/33.42    (69)  op(all_4_2, e2) = all_4_1
% 201.56/33.42    (70)  all_56_6 = all_52_19
% 201.56/33.42    (71)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.42    (72)   ~ (all_52_13 = all_4_2)
% 201.56/33.42    (73)  op(e3, e1) = all_52_17
% 201.56/33.42    (74)  all_30_0 = all_10_0
% 201.56/33.42    (75)  all_58_6 = all_10_0
% 201.56/33.42    (76)  op(e0, e3) = all_52_7
% 201.56/33.42    (77)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.42    (78)   ~ (all_52_9 = all_52_25)
% 201.56/33.42    (79)   ~ (all_52_19 = all_10_2)
% 201.56/33.42    (80)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.42    (81)   ~ (all_10_0 = all_10_2)
% 201.56/33.42    (82)  all_58_8 = all_10_2
% 201.56/33.42    (83)   ~ (all_52_23 = e0)
% 201.56/33.42    (84)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.42    (85)  all_56_12 = all_52_7
% 201.56/33.42    (86)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.42    (87)   ~ (all_52_25 = all_6_2)
% 201.56/33.42    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.42    (89)   ~ (all_52_9 = all_4_2)
% 201.56/33.42    (90)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.56/33.42    (91)  op(all_4_2, all_4_2) = e2
% 201.56/33.42    (92)   ~ (all_52_9 = all_6_2)
% 201.56/33.42    (93)   ~ (all_52_27 = e0)
% 201.56/33.42    (94)  op(e3, e3) = all_6_2
% 201.56/33.42    (95)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.42    (96)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.42    (97)  all_56_14 = all_52_23
% 201.56/33.42    (98)   ~ (all_52_29 = all_10_0)
% 201.56/33.42    (99)  all_56_3 = all_52_25
% 201.56/33.42    (100)   ~ (all_52_3 = all_52_7)
% 201.56/33.42    (101)  all_58_5 = all_52_19
% 201.56/33.42    (102)  all_56_1 = all_52_9
% 201.56/33.42    (103)   ~ (all_52_15 = all_4_2)
% 201.56/33.42    (104)   ~ (all_52_27 = all_4_2)
% 201.56/33.42    (105)  op(e3, e2) = all_52_9
% 201.56/33.42    (106)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.42    (107)   ~ (all_52_17 = all_6_2)
% 201.56/33.42    (108)   ~ (e1 = e0)
% 201.56/33.42    (109)   ~ (e3 = e2)
% 201.56/33.42    (110)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.42    (111)   ~ (all_52_9 = all_52_17)
% 201.56/33.42    (112)  all_56_10 = all_10_2
% 201.56/33.42    (113)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.42    (114)  all_46_1 = all_6_1
% 201.56/33.42    (115)   ~ (all_52_13 = all_10_0)
% 201.56/33.42    (116)  op(e1, e1) = all_10_2
% 201.56/33.42    (117)  op(all_52_9, all_52_9) = e3
% 201.56/33.42    (118)   ~ (all_52_23 = all_10_2)
% 201.56/33.42    (119)   ~ (all_52_7 = all_52_23)
% 201.56/33.42    (120)  all_58_3 = all_4_2
% 201.56/33.42    (121)  all_56_13 = all_52_15
% 201.56/33.42    (122)   ~ (all_52_17 = all_52_23)
% 201.56/33.42    (123)  op(all_6_2, e3) = all_6_1
% 201.56/33.42    (124)   ~ (all_52_13 = all_52_29)
% 201.56/33.42    (125)  all_58_4 = all_52_17
% 201.56/33.42    (126)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.56/33.42    (127)   ~ (all_52_7 = e0)
% 201.56/33.42    (128)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.42  
% 201.56/33.42  Begin of proof
% 201.56/33.42  | 
% 201.56/33.42  | BETA: splitting (23) gives:
% 201.56/33.42  | 
% 201.56/33.42  | Case 1:
% 201.56/33.42  | | 
% 201.56/33.42  | |   (129)  all_56_7 = e3
% 201.56/33.42  | | 
% 201.56/33.42  | | COMBINE_EQS: (67), (129) imply:
% 201.56/33.42  | |   (130)  all_52_27 = e3
% 201.56/33.42  | | 
% 201.56/33.42  | | SIMP: (130) implies:
% 201.56/33.42  | |   (131)  all_52_27 = e3
% 201.56/33.42  | | 
% 201.56/33.42  | | REDUCE: (36), (131) imply:
% 201.56/33.42  | |   (132)   ~ (all_52_3 = e3)
% 201.56/33.42  | | 
% 201.56/33.42  | | REDUCE: (2), (131) imply:
% 201.56/33.42  | |   (133)   ~ (all_52_25 = e3)
% 201.56/33.42  | | 
% 201.56/33.42  | | REDUCE: (104), (131) imply:
% 201.56/33.42  | |   (134)   ~ (all_4_2 = e3)
% 201.56/33.42  | | 
% 201.56/33.42  | | SIMP: (134) implies:
% 201.56/33.42  | |   (135)   ~ (all_4_2 = e3)
% 201.56/33.42  | | 
% 201.56/33.42  | | REDUCE: (30), (131) imply:
% 201.56/33.42  | |   (136)  op(e3, e3) = all_52_26
% 201.56/33.42  | | 
% 201.56/33.42  | | GROUND_INST: instantiating (7) with all_6_2, all_52_26, e3, e3, simplifying
% 201.56/33.42  | |              with (94), (136) gives:
% 201.56/33.42  | |   (137)  all_52_26 = all_6_2
% 201.56/33.42  | | 
% 201.56/33.42  | | BETA: splitting (65) gives:
% 201.56/33.42  | | 
% 201.56/33.42  | | Case 1:
% 201.56/33.42  | | | 
% 201.56/33.42  | | |   (138)  all_58_0 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | COMBINE_EQS: (19), (138) imply:
% 201.56/33.42  | | |   (139)  all_6_2 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REF_CLOSE: (4), (7), (20), (94), (123), (139) are inconsistent by
% 201.56/33.42  | | |            sub-proof #310.
% 201.56/33.42  | | | 
% 201.56/33.42  | | Case 2:
% 201.56/33.42  | | | 
% 201.56/33.42  | | |   (140)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | BETA: splitting (140) gives:
% 201.56/33.42  | | | 
% 201.56/33.42  | | | Case 1:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | |   (141)  all_58_2 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | REF_CLOSE: (62), (132), (141) are inconsistent by sub-proof #1369.
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | Case 2:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | |   (142)  all_58_6 = e3 | all_58_12 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | BETA: splitting (142) gives:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | Case 1:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | |   (143)  all_58_6 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REF_CLOSE: (22), (75), (143) are inconsistent by sub-proof #922.
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | Case 2:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | |   (144)  all_58_12 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | COMBINE_EQS: (58), (144) imply:
% 201.56/33.42  | | | | |   (145)  all_52_7 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | SIMP: (145) implies:
% 201.56/33.42  | | | | |   (146)  all_52_7 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (13), (146) imply:
% 201.56/33.42  | | | | |   (147)   ~ (all_52_15 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | SIMP: (147) implies:
% 201.56/33.42  | | | | |   (148)   ~ (all_52_15 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (38), (146) imply:
% 201.56/33.42  | | | | |   (149)   ~ (all_6_2 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | SIMP: (149) implies:
% 201.56/33.42  | | | | |   (150)   ~ (all_6_2 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REF_CLOSE: (7), (8), (9), (19), (26), (27), (29), (46), (50), (55),
% 201.56/33.42  | | | | |            (66), (77), (78), (86), (87), (88), (90), (92), (94), (96),
% 201.56/33.42  | | | | |            (99), (102), (108), (110), (117), (120), (125), (133),
% 201.56/33.42  | | | | |            (135), (148), (150) are inconsistent by sub-proof #320.
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | End of split
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | End of split
% 201.56/33.42  | | | 
% 201.56/33.42  | | End of split
% 201.56/33.42  | | 
% 201.56/33.42  | Case 2:
% 201.56/33.42  | | 
% 201.56/33.42  | |   (151)   ~ (all_56_7 = e3)
% 201.56/33.42  | | 
% 201.56/33.42  | | REDUCE: (67), (151) imply:
% 201.56/33.42  | |   (152)   ~ (all_52_27 = e3)
% 201.56/33.42  | | 
% 201.56/33.42  | | BETA: splitting (95) gives:
% 201.56/33.42  | | 
% 201.56/33.42  | | Case 1:
% 201.56/33.42  | | | 
% 201.56/33.42  | | |   (153)  all_58_9 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | COMBINE_EQS: (29), (153) imply:
% 201.56/33.42  | | |   (154)  all_52_25 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | SIMP: (154) implies:
% 201.56/33.42  | | |   (155)  all_52_25 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REDUCE: (78), (155) imply:
% 201.56/33.42  | | |   (156)   ~ (all_52_9 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REDUCE: (17), (155) imply:
% 201.56/33.42  | | |   (157)   ~ (all_52_17 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REDUCE: (2), (155) imply:
% 201.56/33.42  | | |   (158)   ~ (all_52_27 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REDUCE: (52), (155) imply:
% 201.56/33.42  | | |   (159)   ~ (all_52_29 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | SIMP: (159) implies:
% 201.56/33.42  | | |   (160)   ~ (all_52_29 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REDUCE: (87), (155) imply:
% 201.56/33.42  | | |   (161)   ~ (all_6_2 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | SIMP: (161) implies:
% 201.56/33.42  | | |   (162)   ~ (all_6_2 = e3)
% 201.56/33.42  | | | 
% 201.56/33.42  | | | REDUCE: (128), (155) imply:
% 201.56/33.42  | | |   (163)  op(e3, e3) = all_52_24
% 201.56/33.42  | | | 
% 201.56/33.42  | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 201.56/33.42  | | |              simplifying with (94), (163) gives:
% 201.56/33.42  | | |   (164)  all_52_24 = all_6_2
% 201.56/33.42  | | | 
% 201.56/33.42  | | | BETA: splitting (65) gives:
% 201.56/33.42  | | | 
% 201.56/33.42  | | | Case 1:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | |   (165)  all_58_0 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | COMBINE_EQS: (19), (165) imply:
% 201.56/33.42  | | | |   (166)  all_6_2 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | REDUCE: (162), (166) imply:
% 201.56/33.42  | | | |   (167)  $false
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | CLOSE: (167) is inconsistent.
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | Case 2:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | |   (168)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | BETA: splitting (60) gives:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | Case 1:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | |   (169)  all_58_6 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REF_CLOSE: (22), (75), (169) are inconsistent by sub-proof #922.
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | Case 2:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | |   (170)   ~ (all_58_6 = e3)
% 201.56/33.42  | | | | |   (171)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | BETA: splitting (57) gives:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | Case 1:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | |   (172)  all_56_14 = e3
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | COMBINE_EQS: (97), (172) imply:
% 201.56/33.42  | | | | | |   (173)  all_52_23 = e3
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | SIMP: (173) implies:
% 201.56/33.42  | | | | | |   (174)  all_52_23 = e3
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | REDUCE: (119), (174) imply:
% 201.56/33.42  | | | | | |   (175)   ~ (all_52_7 = e3)
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | REDUCE: (118), (174) imply:
% 201.56/33.42  | | | | | |   (176)   ~ (all_10_2 = e3)
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | SIMP: (176) implies:
% 201.56/33.42  | | | | | |   (177)   ~ (all_10_2 = e3)
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | REDUCE: (80), (174) imply:
% 201.56/33.42  | | | | | |   (178)  op(e3, e3) = all_52_22
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | BETA: splitting (171) gives:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | Case 1:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | |   (179)  all_58_7 = e3
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | COMBINE_EQS: (55), (179) imply:
% 201.56/33.42  | | | | | | |   (180)  all_52_13 = e3
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (115), (180) imply:
% 201.56/33.42  | | | | | | |   (181)   ~ (all_10_0 = e3)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (27), (180) imply:
% 201.56/33.42  | | | | | | |   (182)  op(e3, e3) = e1
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | BETA: splitting (168) gives:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (183)  all_58_2 = e3
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | COMBINE_EQS: (62), (183) imply:
% 201.56/33.42  | | | | | | | |   (184)  all_52_3 = e3
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | SIMP: (184) implies:
% 201.56/33.42  | | | | | | | |   (185)  all_52_3 = e3
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REDUCE: (6), (185) imply:
% 201.56/33.42  | | | | | | | |   (186)  op(e3, e3) = all_52_2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_22, e3, e3,
% 201.56/33.42  | | | | | | | |              simplifying with (178), (182) gives:
% 201.56/33.42  | | | | | | | |   (187)  all_52_22 = e1
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_2, e3, e3,
% 201.56/33.42  | | | | | | | |              simplifying with (94), (186) gives:
% 201.56/33.42  | | | | | | | |   (188)  all_52_2 = all_6_2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | GROUND_INST: instantiating (7) with all_52_22, all_52_2, e3, e3,
% 201.56/33.42  | | | | | | | |              simplifying with (178), (186) gives:
% 201.56/33.42  | | | | | | | |   (189)  all_52_2 = all_52_22
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | COMBINE_EQS: (188), (189) imply:
% 201.56/33.42  | | | | | | | |   (190)  all_52_22 = all_6_2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | SIMP: (190) implies:
% 201.56/33.42  | | | | | | | |   (191)  all_52_22 = all_6_2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | COMBINE_EQS: (187), (191) imply:
% 201.56/33.42  | | | | | | | |   (192)  all_6_2 = e1
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | SIMP: (192) implies:
% 201.56/33.42  | | | | | | | |   (193)  all_6_2 = e1
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | COMBINE_EQS: (19), (193) imply:
% 201.56/33.42  | | | | | | | |   (194)  all_58_0 = e1
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | BETA: splitting (32) gives:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | |   (195)  all_58_0 = e0
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | COMBINE_EQS: (194), (195) imply:
% 201.56/33.42  | | | | | | | | |   (196)  e1 = e0
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | REDUCE: (108), (196) imply:
% 201.56/33.42  | | | | | | | | |   (197)  $false
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | CLOSE: (197) is inconsistent.
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | |   (198)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | REF_CLOSE: (7), (10), (54), (56), (58), (61), (74), (75),
% 201.56/33.42  | | | | | | | | |            (81), (112), (116), (126), (127), (177), (183),
% 201.56/33.42  | | | | | | | | |            (198) are inconsistent by sub-proof #375.
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | End of split
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (199)  all_58_6 = e3 | all_58_12 = e3
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REF_CLOSE: (22), (58), (75), (175), (199) are inconsistent by
% 201.56/33.42  | | | | | | | |            sub-proof #921.
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | End of split
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | Case 2:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | |   (200)  all_58_8 = e3 | all_58_11 = e3
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REF_CLOSE: (33), (82), (160), (177), (200) are inconsistent by
% 201.56/33.42  | | | | | | |            sub-proof #1140.
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | End of split
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | Case 2:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | |   (201)   ~ (all_56_14 = e3)
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | REDUCE: (97), (201) imply:
% 201.56/33.42  | | | | | |   (202)   ~ (all_52_23 = e3)
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | BETA: splitting (106) gives:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | Case 1:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | |   (203)  all_58_12 = e3
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | COMBINE_EQS: (58), (203) imply:
% 201.56/33.42  | | | | | | |   (204)  all_52_7 = e3
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | SIMP: (204) implies:
% 201.56/33.42  | | | | | | |   (205)  all_52_7 = e3
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (100), (205) imply:
% 201.56/33.42  | | | | | | |   (206)   ~ (all_52_3 = e3)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (16), (205) imply:
% 201.56/33.42  | | | | | | |   (207)  op(e3, e3) = all_52_6
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 201.56/33.42  | | | | | | |              simplifying with (94), (207) gives:
% 201.56/33.42  | | | | | | |   (208)  all_52_6 = all_6_2
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | BETA: splitting (40) gives:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (209)  all_58_2 = e3
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REF_CLOSE: (62), (206), (209) are inconsistent by sub-proof
% 201.56/33.42  | | | | | | | |            #1369.
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (210)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (19), (24), (27), (28), (31),
% 201.56/33.42  | | | | | | | |            (33), (44), (48), (50), (51), (55), (63), (64), (66),
% 201.56/33.42  | | | | | | | |            (69), (70), (72), (79), (82), (89), (91), (92), (94),
% 201.56/33.42  | | | | | | | |            (101), (102), (105), (107), (108), (110), (111),
% 201.56/33.42  | | | | | | | |            (117), (120), (125), (152), (156), (157), (160),
% 201.56/33.42  | | | | | | | |            (171), (210) are inconsistent by sub-proof #319.
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | End of split
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | Case 2:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | |   (211)   ~ (all_58_12 = e3)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (58), (211) imply:
% 201.56/33.42  | | | | | | |   (212)   ~ (all_52_7 = e3)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REF_CLOSE: (3), (7), (14), (21), (22), (54), (58), (62), (73),
% 201.56/33.42  | | | | | | |            (75), (82), (101), (113), (125), (157), (168), (202),
% 201.56/33.42  | | | | | | |            (212) are inconsistent by sub-proof #779.
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | End of split
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | End of split
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | End of split
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | End of split
% 201.56/33.42  | | | 
% 201.56/33.42  | | Case 2:
% 201.56/33.42  | | | 
% 201.56/33.42  | | |   (213)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.42  | | | 
% 201.56/33.42  | | | BETA: splitting (213) gives:
% 201.56/33.42  | | | 
% 201.56/33.42  | | | Case 1:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | |   (214)  all_58_10 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | REF_CLOSE: (51), (152), (214) are inconsistent by sub-proof #1301.
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | Case 2:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | |   (215)  all_58_11 = e3 | all_58_15 = e3
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | BETA: splitting (215) gives:
% 201.56/33.42  | | | | 
% 201.56/33.42  | | | | Case 1:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | |   (216)  all_58_11 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | COMBINE_EQS: (33), (216) imply:
% 201.56/33.42  | | | | |   (217)  all_52_29 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | SIMP: (217) implies:
% 201.56/33.42  | | | | |   (218)  all_52_29 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (124), (218) imply:
% 201.56/33.42  | | | | |   (219)   ~ (all_52_13 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (52), (218) imply:
% 201.56/33.42  | | | | |   (220)   ~ (all_52_25 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (98), (218) imply:
% 201.56/33.42  | | | | |   (221)   ~ (all_10_0 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (53), (218) imply:
% 201.56/33.42  | | | | |   (222)   ~ (all_10_2 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | SIMP: (222) implies:
% 201.56/33.42  | | | | |   (223)   ~ (all_10_2 = e3)
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REDUCE: (84), (218) imply:
% 201.56/33.42  | | | | |   (224)  op(e3, e3) = all_52_28
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_28, e3, e3,
% 201.56/33.42  | | | | |              simplifying with (94), (224) gives:
% 201.56/33.42  | | | | |   (225)  all_52_28 = all_6_2
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | BETA: splitting (88) gives:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | Case 1:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | |   (226)  all_56_3 = e3
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | REF_CLOSE: (99), (220), (226) are inconsistent by sub-proof #1339.
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | Case 2:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | |   (227)   ~ (all_56_3 = e3)
% 201.56/33.42  | | | | | |   (228)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | BETA: splitting (90) gives:
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | | Case 1:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | |   (229)  all_58_9 = e2
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | COMBINE_EQS: (29), (229) imply:
% 201.56/33.42  | | | | | | |   (230)  all_52_25 = e2
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | SIMP: (230) implies:
% 201.56/33.42  | | | | | | |   (231)  all_52_25 = e2
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (87), (231) imply:
% 201.56/33.42  | | | | | | |   (232)   ~ (all_6_2 = e2)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | SIMP: (232) implies:
% 201.56/33.42  | | | | | | |   (233)   ~ (all_6_2 = e2)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (220), (231) imply:
% 201.56/33.42  | | | | | | |   (234)   ~ (e3 = e2)
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | REDUCE: (128), (231) imply:
% 201.56/33.42  | | | | | | |   (235)  op(e2, e2) = all_52_24
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_24, e2, e2,
% 201.56/33.42  | | | | | | |              simplifying with (31), (235) gives:
% 201.56/33.42  | | | | | | |   (236)  all_52_24 = all_4_2
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | BETA: splitting (71) gives:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (237)  all_58_0 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | COMBINE_EQS: (19), (237) imply:
% 201.56/33.42  | | | | | | | |   (238)  all_6_2 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REDUCE: (233), (238) imply:
% 201.56/33.42  | | | | | | | |   (239)  $false
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | CLOSE: (239) is inconsistent.
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (240)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (12), (13), (15), (16),
% 201.56/33.42  | | | | | | | |            (18), (19), (20), (22), (26), (29), (31), (34), (35),
% 201.56/33.42  | | | | | | | |            (38), (39), (42), (43), (44), (47), (50), (55), (57),
% 201.56/33.42  | | | | | | | |            (58), (59), (62), (65), (69), (73), (75), (76), (77),
% 201.56/33.42  | | | | | | | |            (80), (83), (85), (86), (91), (92), (94), (96), (97),
% 201.56/33.42  | | | | | | | |            (100), (102), (103), (105), (109), (110), (111),
% 201.56/33.42  | | | | | | | |            (113), (117), (119), (120), (121), (122), (123),
% 201.56/33.42  | | | | | | | |            (125), (127), (219), (220), (240) are inconsistent by
% 201.56/33.42  | | | | | | | |            sub-proof #253.
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | End of split
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | Case 2:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | |   (241)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | BETA: splitting (241) gives:
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (242)  all_58_10 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | COMBINE_EQS: (51), (242) imply:
% 201.56/33.42  | | | | | | | |   (243)  all_52_27 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | SIMP: (243) implies:
% 201.56/33.42  | | | | | | | |   (244)  all_52_27 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REDUCE: (2), (244) imply:
% 201.56/33.42  | | | | | | | |   (245)   ~ (all_52_25 = e2)
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REDUCE: (152), (244) imply:
% 201.56/33.42  | | | | | | | |   (246)   ~ (e3 = e2)
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REDUCE: (30), (244) imply:
% 201.56/33.42  | | | | | | | |   (247)  op(e2, e2) = all_52_26
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | BETA: splitting (41) gives:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | |   (248)  all_58_9 = e1
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | COMBINE_EQS: (29), (248) imply:
% 201.56/33.42  | | | | | | | | |   (249)  all_52_25 = e1
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | SIMP: (249) implies:
% 201.56/33.42  | | | | | | | | |   (250)  all_52_25 = e1
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | REDUCE: (220), (250) imply:
% 201.56/33.42  | | | | | | | | |   (251)   ~ (e3 = e1)
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | REDUCE: (128), (250) imply:
% 201.56/33.42  | | | | | | | | |   (252)  op(e1, e1) = all_52_24
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_24, e1,
% 201.56/33.42  | | | | | | | | |              e1, simplifying with (116), (252) gives:
% 201.56/33.42  | | | | | | | | |   (253)  all_52_24 = all_10_2
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_26, e2, e2,
% 201.56/33.42  | | | | | | | | |              simplifying with (31), (247) gives:
% 201.56/33.42  | | | | | | | | |   (254)  all_52_26 = all_4_2
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | BETA: splitting (71) gives:
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | |   (255)  all_58_0 = e2
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | COMBINE_EQS: (19), (255) imply:
% 201.56/33.42  | | | | | | | | | |   (256)  all_6_2 = e2
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | COMBINE_EQS: (37), (256) imply:
% 201.56/33.42  | | | | | | | | | |   (257)  all_46_2 = e2
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | REDUCE: (123), (256) imply:
% 201.56/33.42  | | | | | | | | | |   (258)  op(e2, e3) = all_6_1
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | BETA: splitting (45) gives:
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | |   (259)   ~ (all_46_2 = e2)
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | REDUCE: (257), (259) imply:
% 201.56/33.42  | | | | | | | | | | |   (260)  $false
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | CLOSE: (260) is inconsistent.
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | |   (261)   ~ (all_46_1 = e0)
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | REDUCE: (114), (261) imply:
% 201.56/33.42  | | | | | | | | | | |   (262)   ~ (all_6_1 = e0)
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_3, all_6_1, e3, e2,
% 201.56/33.42  | | | | | | | | | | |              simplifying with (11), (258) gives:
% 201.56/33.42  | | | | | | | | | | |   (263)  all_52_3 = all_6_1
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | COMBINE_EQS: (62), (263) imply:
% 201.56/33.42  | | | | | | | | | | |   (264)  all_58_2 = all_6_1
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | BETA: splitting (32) gives:
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | |   (265)  all_58_0 = e0
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | COMBINE_EQS: (255), (265) imply:
% 201.56/33.42  | | | | | | | | | | | |   (266)  e2 = e0
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | REDUCE: (68), (266) imply:
% 201.56/33.42  | | | | | | | | | | | |   (267)  $false
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | |   (268)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | BETA: splitting (268) gives:
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | Case 1:
% 201.56/33.42  | | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | |   (269)  all_58_2 = e0
% 201.56/33.42  | | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | | REF_CLOSE: (262), (264), (269) are inconsistent by sub-proof
% 201.56/33.42  | | | | | | | | | | | | |            #295.
% 201.56/33.42  | | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | |   (270)  all_58_6 = e0 | all_58_12 = e0
% 201.56/33.42  | | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | | REF_CLOSE: (7), (54), (56), (58), (61), (74), (75), (81),
% 201.56/33.42  | | | | | | | | | | | | |            (112), (116), (126), (127), (223), (270) are
% 201.56/33.42  | | | | | | | | | | | | |            inconsistent by sub-proof #380.
% 201.56/33.42  | | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | | End of split
% 201.56/33.42  | | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | | End of split
% 201.56/33.42  | | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | End of split
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | |   (271)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (12), (13), (15),
% 201.56/33.42  | | | | | | | | | |            (16), (18), (19), (20), (22), (26), (29), (31),
% 201.56/33.42  | | | | | | | | | |            (34), (35), (38), (39), (42), (43), (44), (47),
% 201.56/33.42  | | | | | | | | | |            (50), (55), (57), (58), (59), (62), (65), (69),
% 201.56/33.42  | | | | | | | | | |            (73), (75), (76), (77), (80), (83), (85), (86),
% 201.56/33.42  | | | | | | | | | |            (91), (92), (94), (96), (97), (100), (102), (103),
% 201.56/33.42  | | | | | | | | | |            (105), (109), (110), (111), (113), (117), (119),
% 201.56/33.42  | | | | | | | | | |            (120), (121), (122), (123), (125), (127), (219),
% 201.56/33.42  | | | | | | | | | |            (220), (271) are inconsistent by sub-proof #253.
% 201.56/33.42  | | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | End of split
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | |   (272)   ~ (all_58_9 = e1)
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | REDUCE: (29), (272) imply:
% 201.56/33.42  | | | | | | | | |   (273)   ~ (all_52_25 = e1)
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | | REF_CLOSE: (46), (99), (228), (245), (273) are inconsistent by
% 201.56/33.42  | | | | | | | | |            sub-proof #1215.
% 201.56/33.42  | | | | | | | | | 
% 201.56/33.42  | | | | | | | | End of split
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | Case 2:
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | |   (274)  all_58_11 = e2 | all_58_15 = e2
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | | REF_CLOSE: (42), (68), (109), (216), (274) are inconsistent by
% 201.56/33.42  | | | | | | | |            sub-proof #995.
% 201.56/33.42  | | | | | | | | 
% 201.56/33.42  | | | | | | | End of split
% 201.56/33.42  | | | | | | | 
% 201.56/33.42  | | | | | | End of split
% 201.56/33.42  | | | | | | 
% 201.56/33.42  | | | | | End of split
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | Case 2:
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | |   (275)  all_58_15 = e3
% 201.56/33.42  | | | | | 
% 201.56/33.42  | | | | | REF_CLOSE: (10), (42), (275) are inconsistent by sub-proof #1350.
% 201.56/33.42  | | | | | 
% 201.56/33.43  | | | | End of split
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | End of split
% 201.56/33.43  | | | 
% 201.56/33.43  | | End of split
% 201.56/33.43  | | 
% 201.56/33.43  | End of split
% 201.56/33.43  | 
% 201.56/33.43  End of proof
% 201.56/33.43  
% 201.56/33.43  Sub-proof #253 shows that the following formulas are inconsistent:
% 201.56/33.43  ----------------------------------------------------------------
% 201.56/33.43    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.43    (2)  all_58_14 = all_52_23
% 201.56/33.43    (3)   ~ (e3 = e1)
% 201.56/33.43    (4)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.43    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.43    (6)  all_58_1 = all_52_9
% 201.56/33.43    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.43    (8)   ~ (all_52_7 = all_52_15)
% 201.56/33.43    (9)  op(all_52_15, all_52_15) = e0
% 201.56/33.43    (10)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.43    (11)   ~ (all_52_3 = all_6_2)
% 201.56/33.43    (12)  all_58_0 = all_6_2
% 201.56/33.43    (13)  op(e3, all_6_1) = e1
% 201.56/33.43    (14)   ~ (all_10_0 = e3)
% 201.56/33.43    (15)  all_58_13 = all_52_15
% 201.56/33.43    (16)  all_58_9 = all_52_25
% 201.56/33.43    (17)  op(e2, e2) = all_4_2
% 201.56/33.43    (18)   ~ (all_52_9 = all_52_15)
% 201.56/33.43    (19)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.56/33.43    (20)   ~ (all_52_7 = all_6_2)
% 201.56/33.43    (21)   ~ (all_52_15 = e0)
% 201.56/33.43    (22)  all_58_15 = e0
% 201.56/33.43    (23)   ~ (all_10_0 = e2)
% 201.56/33.43    (24)   ~ (all_4_1 = e1)
% 201.56/33.43    (25)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.43    (26)  op(e0, e0) = e0
% 201.56/33.43    (27)  all_58_7 = all_52_13
% 201.56/33.43    (28)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.43    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.43    (30)  all_58_12 = all_52_7
% 201.56/33.43    (31)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.43    (32)  all_58_2 = all_52_3
% 201.56/33.43    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.43    (34)   ~ (all_52_25 = e3)
% 201.56/33.43    (35)  op(all_4_2, e2) = all_4_1
% 201.56/33.43    (36)  op(e3, e1) = all_52_17
% 201.56/33.43    (37)  all_58_6 = all_10_0
% 201.56/33.43    (38)  op(e0, e3) = all_52_7
% 201.56/33.43    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.43    (40)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.43    (41)   ~ (all_52_23 = e0)
% 201.56/33.43    (42)  all_56_12 = all_52_7
% 201.56/33.43    (43)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.43    (44)  op(all_4_2, all_4_2) = e2
% 201.56/33.43    (45)   ~ (all_52_9 = all_6_2)
% 201.56/33.43    (46)  op(e3, e3) = all_6_2
% 201.56/33.43    (47)   ~ (all_52_13 = e3)
% 201.56/33.43    (48)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.43    (49)  all_56_14 = all_52_23
% 201.56/33.43    (50)   ~ (all_52_3 = all_52_7)
% 201.56/33.43    (51)  all_56_1 = all_52_9
% 201.56/33.43    (52)   ~ (all_52_15 = all_4_2)
% 201.56/33.43    (53)  op(e3, e2) = all_52_9
% 201.56/33.43    (54)   ~ (e3 = e2)
% 201.56/33.43    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.43    (56)   ~ (all_52_9 = all_52_17)
% 201.56/33.43    (57)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.43    (58)  op(all_52_9, all_52_9) = e3
% 201.56/33.43    (59)   ~ (all_52_7 = all_52_23)
% 201.56/33.43    (60)  all_58_3 = all_4_2
% 201.56/33.43    (61)  all_56_13 = all_52_15
% 201.56/33.43    (62)   ~ (all_52_17 = all_52_23)
% 201.56/33.43    (63)  op(all_6_2, e3) = all_6_1
% 201.56/33.43    (64)  all_58_4 = all_52_17
% 201.56/33.43    (65)   ~ (all_52_7 = e0)
% 201.56/33.43  
% 201.56/33.43  Begin of proof
% 201.56/33.43  | 
% 201.56/33.43  | BETA: splitting (7) gives:
% 201.56/33.43  | 
% 201.56/33.43  | Case 1:
% 201.56/33.43  | | 
% 201.56/33.43  | |   (66)  all_56_12 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | COMBINE_EQS: (42), (66) imply:
% 201.56/33.43  | |   (67)  all_52_7 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | SIMP: (67) implies:
% 201.56/33.43  | |   (68)  all_52_7 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | REDUCE: (8), (68) imply:
% 201.56/33.43  | |   (69)   ~ (all_52_15 = e3)
% 201.56/33.43  | | 
% 201.56/33.43  | | SIMP: (69) implies:
% 201.56/33.43  | |   (70)   ~ (all_52_15 = e3)
% 201.56/33.43  | | 
% 201.56/33.43  | | REDUCE: (20), (68) imply:
% 201.56/33.43  | |   (71)   ~ (all_6_2 = e3)
% 201.56/33.43  | | 
% 201.56/33.43  | | SIMP: (71) implies:
% 201.56/33.43  | |   (72)   ~ (all_6_2 = e3)
% 201.56/33.43  | | 
% 201.56/33.43  | | REF_CLOSE: (5), (6), (12), (15), (16), (24), (26), (27), (34), (35), (39),
% 201.56/33.43  | |            (43), (44), (45), (46), (47), (48), (51), (53), (55), (56), (57),
% 201.56/33.43  | |            (58), (60), (64), (70), (72) are inconsistent by sub-proof #1297.
% 201.56/33.43  | | 
% 201.56/33.43  | Case 2:
% 201.56/33.43  | | 
% 201.56/33.43  | |   (73)   ~ (all_56_12 = e3)
% 201.56/33.43  | | 
% 201.56/33.43  | | REDUCE: (42), (73) imply:
% 201.56/33.43  | |   (74)   ~ (all_52_7 = e3)
% 201.56/33.43  | | 
% 201.56/33.43  | | BETA: splitting (33) gives:
% 201.56/33.43  | | 
% 201.56/33.43  | | Case 1:
% 201.56/33.43  | | | 
% 201.56/33.43  | | |   (75)  all_58_0 = e3
% 201.56/33.43  | | | 
% 201.56/33.43  | | | COMBINE_EQS: (12), (75) imply:
% 201.56/33.43  | | |   (76)  all_6_2 = e3
% 201.56/33.43  | | | 
% 201.56/33.43  | | | REF_CLOSE: (3), (5), (13), (46), (63), (76) are inconsistent by sub-proof
% 201.56/33.43  | | |            #310.
% 201.56/33.43  | | | 
% 201.56/33.43  | | Case 2:
% 201.56/33.43  | | | 
% 201.56/33.43  | | |   (77)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.43  | | | 
% 201.56/33.43  | | | BETA: splitting (77) gives:
% 201.56/33.43  | | | 
% 201.56/33.43  | | | Case 1:
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | |   (78)  all_58_2 = e3
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | COMBINE_EQS: (32), (78) imply:
% 201.56/33.43  | | | |   (79)  all_52_3 = e3
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (50), (79) imply:
% 201.56/33.43  | | | |   (80)   ~ (all_52_7 = e3)
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (11), (79) imply:
% 201.56/33.43  | | | |   (81)   ~ (all_6_2 = e3)
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | SIMP: (81) implies:
% 201.56/33.43  | | | |   (82)   ~ (all_6_2 = e3)
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (4), (79) imply:
% 201.56/33.43  | | | |   (83)  op(e3, e3) = all_52_2
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | BETA: splitting (28) gives:
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | Case 1:
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | |   (84)  all_58_2 = e2
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | | REF_CLOSE: (54), (78), (84) are inconsistent by sub-proof #1124.
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | Case 2:
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | |   (85)  all_58_6 = e2 | all_58_12 = e2
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | | BETA: splitting (85) gives:
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | | Case 1:
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | |   (86)  all_58_6 = e2
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | REF_CLOSE: (23), (37), (86) are inconsistent by sub-proof #917.
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | Case 2:
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | |   (87)  all_58_12 = e2
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | COMBINE_EQS: (30), (87) imply:
% 201.56/33.43  | | | | | |   (88)  all_52_7 = e2
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | SIMP: (88) implies:
% 201.56/33.43  | | | | | |   (89)  all_52_7 = e2
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | REDUCE: (8), (89) imply:
% 201.56/33.43  | | | | | |   (90)   ~ (all_52_15 = e2)
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | SIMP: (90) implies:
% 201.56/33.43  | | | | | |   (91)   ~ (all_52_15 = e2)
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | REDUCE: (59), (89) imply:
% 201.56/33.43  | | | | | |   (92)   ~ (all_52_23 = e2)
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | SIMP: (92) implies:
% 201.56/33.43  | | | | | |   (93)   ~ (all_52_23 = e2)
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | REDUCE: (65), (89) imply:
% 201.56/33.43  | | | | | |   (94)   ~ (e2 = e0)
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | REDUCE: (10), (89) imply:
% 201.56/33.43  | | | | | |   (95)  op(e2, e2) = all_52_6
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_6, e2, e2,
% 201.56/33.43  | | | | | |              simplifying with (17), (95) gives:
% 201.56/33.43  | | | | | |   (96)  all_52_6 = all_4_2
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_2, e3, e3,
% 201.56/33.43  | | | | | |              simplifying with (46), (83) gives:
% 201.56/33.43  | | | | | |   (97)  all_52_2 = all_6_2
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | BETA: splitting (29) gives:
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | | Case 1:
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | |   (98)  all_56_14 = e3
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | | COMBINE_EQS: (49), (98) imply:
% 201.56/33.43  | | | | | | |   (99)  all_52_23 = e3
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | | REDUCE: (62), (99) imply:
% 201.56/33.43  | | | | | | |   (100)   ~ (all_52_17 = e3)
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | | REF_CLOSE: (5), (6), (12), (16), (34), (45), (46), (48), (58),
% 201.56/33.43  | | | | | | |            (64), (82), (100) are inconsistent by sub-proof #254.
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | Case 2:
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | |   (101)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | | BETA: splitting (101) gives:
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | | Case 1:
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | |   (102)  all_56_14 = e2
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | | COMBINE_EQS: (49), (102) imply:
% 201.56/33.43  | | | | | | | |   (103)  all_52_23 = e2
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | | REDUCE: (93), (103) imply:
% 201.56/33.43  | | | | | | | |   (104)  $false
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | | CLOSE: (104) is inconsistent.
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | Case 2:
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | |   (105)  all_56_14 = e1 | all_56_14 = e0
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | | BETA: splitting (105) gives:
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | | Case 1:
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | |   (106)  all_56_14 = e1
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | COMBINE_EQS: (49), (106) imply:
% 201.56/33.43  | | | | | | | | |   (107)  all_52_23 = e1
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | REDUCE: (1), (107) imply:
% 201.56/33.43  | | | | | | | | |   (108)   ~ (all_52_15 = e1)
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | BETA: splitting (25) gives:
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | Case 1:
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | |   (109)  all_56_13 = e3
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | COMBINE_EQS: (61), (109) imply:
% 201.56/33.43  | | | | | | | | | |   (110)  all_52_15 = e3
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | SIMP: (110) implies:
% 201.56/33.43  | | | | | | | | | |   (111)  all_52_15 = e3
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | COMBINE_EQS: (15), (111) imply:
% 201.56/33.43  | | | | | | | | | |   (112)  all_58_13 = e3
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | REDUCE: (18), (111) imply:
% 201.56/33.43  | | | | | | | | | |   (113)   ~ (all_52_9 = e3)
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | REDUCE: (52), (111) imply:
% 201.56/33.43  | | | | | | | | | |   (114)   ~ (all_4_2 = e3)
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | SIMP: (114) implies:
% 201.56/33.43  | | | | | | | | | |   (115)   ~ (all_4_2 = e3)
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (13), (17), (19), (20), (22),
% 201.56/33.43  | | | | | | | | | |            (30), (31), (36), (38), (40), (42), (45), (46),
% 201.56/33.43  | | | | | | | | | |            (51), (54), (55), (56), (58), (63), (74), (94),
% 201.56/33.43  | | | | | | | | | |            (111), (112), (113), (115) are inconsistent by
% 201.56/33.43  | | | | | | | | | |            sub-proof #323.
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | Case 2:
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | |   (116)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | | REF_CLOSE: (5), (9), (17), (21), (26), (44), (52), (61),
% 201.56/33.43  | | | | | | | | | |            (108), (116) are inconsistent by sub-proof #886.
% 201.56/33.43  | | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | End of split
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | Case 2:
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | |   (117)  all_56_14 = e0
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | COMBINE_EQS: (49), (117) imply:
% 201.56/33.43  | | | | | | | | |   (118)  all_52_23 = e0
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | REDUCE: (41), (118) imply:
% 201.56/33.43  | | | | | | | | |   (119)  $false
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | | CLOSE: (119) is inconsistent.
% 201.56/33.43  | | | | | | | | | 
% 201.56/33.43  | | | | | | | | End of split
% 201.56/33.43  | | | | | | | | 
% 201.56/33.43  | | | | | | | End of split
% 201.56/33.43  | | | | | | | 
% 201.56/33.43  | | | | | | End of split
% 201.56/33.43  | | | | | | 
% 201.56/33.43  | | | | | End of split
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | End of split
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | Case 2:
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | |   (120)  all_58_6 = e3 | all_58_12 = e3
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REF_CLOSE: (14), (30), (37), (74), (120) are inconsistent by sub-proof
% 201.56/33.43  | | | |            #921.
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | End of split
% 201.56/33.43  | | | 
% 201.56/33.43  | | End of split
% 201.56/33.43  | | 
% 201.56/33.43  | End of split
% 201.56/33.43  | 
% 201.56/33.43  End of proof
% 201.56/33.43  
% 201.56/33.43  Sub-proof #254 shows that the following formulas are inconsistent:
% 201.56/33.43  ----------------------------------------------------------------
% 201.56/33.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.43    (2)  all_58_1 = all_52_9
% 201.56/33.43    (3)  all_58_0 = all_6_2
% 201.56/33.43    (4)  all_58_9 = all_52_25
% 201.56/33.43    (5)   ~ (all_6_2 = e3)
% 201.56/33.43    (6)   ~ (all_52_25 = e3)
% 201.56/33.43    (7)   ~ (all_52_9 = all_6_2)
% 201.56/33.43    (8)  op(e3, e3) = all_6_2
% 201.56/33.43    (9)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.43    (10)   ~ (all_52_17 = e3)
% 201.56/33.43    (11)  op(all_52_9, all_52_9) = e3
% 201.56/33.43    (12)  all_58_4 = all_52_17
% 201.56/33.43  
% 201.56/33.43  Begin of proof
% 201.56/33.43  | 
% 201.56/33.43  | BETA: splitting (9) gives:
% 201.56/33.43  | 
% 201.56/33.43  | Case 1:
% 201.56/33.43  | | 
% 201.56/33.43  | |   (13)  all_58_0 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | COMBINE_EQS: (3), (13) imply:
% 201.56/33.43  | |   (14)  all_6_2 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | REDUCE: (5), (14) imply:
% 201.56/33.43  | |   (15)  $false
% 201.56/33.43  | | 
% 201.56/33.43  | | CLOSE: (15) is inconsistent.
% 201.56/33.43  | | 
% 201.56/33.43  | Case 2:
% 201.56/33.43  | | 
% 201.56/33.43  | |   (16)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (16) are
% 201.56/33.43  | |            inconsistent by sub-proof #1138.
% 201.56/33.43  | | 
% 201.56/33.43  | End of split
% 201.56/33.43  | 
% 201.56/33.43  End of proof
% 201.56/33.43  
% 201.56/33.43  Sub-proof #255 shows that the following formulas are inconsistent:
% 201.56/33.43  ----------------------------------------------------------------
% 201.56/33.43    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.43    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.43    (3)  all_58_14 = all_52_23
% 201.56/33.43    (4)   ~ (e3 = e1)
% 201.56/33.43    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.43    (6)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.43    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.43    (8)   ~ (all_52_5 = all_52_13)
% 201.56/33.43    (9)  all_58_1 = all_52_9
% 201.56/33.43    (10)   ~ (all_52_9 = all_52_13)
% 201.56/33.43    (11)   ~ (e3 = e0)
% 201.56/33.43    (12)  op(e2, e3) = all_52_3
% 201.56/33.43    (13)   ~ (all_4_0 = e1)
% 201.56/33.43    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.43    (15)   ~ (all_52_7 = all_52_15)
% 201.56/33.43    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.43    (17)   ~ (all_52_17 = all_52_25)
% 201.56/33.43    (18)   ~ (all_52_3 = all_6_2)
% 201.56/33.43    (19)  all_58_0 = all_6_2
% 201.56/33.43    (20)  op(all_14_2, e0) = all_14_1
% 201.56/33.43    (21)  all_56_4 = all_52_3
% 201.56/33.43    (22)  op(e3, all_6_1) = e1
% 201.56/33.43    (23)   ~ (all_52_17 = all_10_2)
% 201.56/33.43    (24)  op(e3, e0) = all_52_25
% 201.56/33.43    (25)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.43    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.43    (27)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.43    (28)   ~ (all_52_27 = all_52_29)
% 201.56/33.43    (29)  all_58_13 = all_52_15
% 201.56/33.43    (30)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.43    (31)  all_58_9 = all_52_25
% 201.56/33.43    (32)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.43    (33)   ~ (all_52_29 = all_14_2)
% 201.56/33.43    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.43    (35)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.43    (36)  op(e1, e3) = all_52_5
% 201.56/33.43    (37)   ~ (all_6_2 = all_4_0)
% 201.56/33.43    (38)  all_32_2 = all_4_2
% 201.56/33.43    (39)  op(e2, e2) = all_4_2
% 201.56/33.43    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.43    (41)   ~ (all_52_3 = all_52_5)
% 201.56/33.43    (42)  all_58_11 = all_52_29
% 201.56/33.43    (43)  all_56_5 = all_4_2
% 201.56/33.43    (44)   ~ (all_52_25 = all_14_2)
% 201.56/33.43    (45)   ~ (all_52_9 = all_52_15)
% 201.56/33.43    (46)   ~ (all_52_3 = all_52_27)
% 201.56/33.43    (47)  op(all_10_2, e1) = all_10_1
% 201.56/33.43    (48)  all_46_2 = all_6_2
% 201.56/33.43    (49)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.43    (50)   ~ (all_52_7 = all_6_2)
% 201.56/33.43    (51)  all_58_2 = all_4_0
% 201.56/33.43    (52)  op(e0, e0) = all_14_2
% 201.56/33.43    (53)  all_56_15 = all_14_2
% 201.56/33.43    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.43    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.43    (56)  op(all_4_2, e2) = e3
% 201.56/33.43    (57)   ~ (all_58_15 = e0)
% 201.56/33.43    (58)  all_56_11 = all_52_29
% 201.56/33.43    (59)   ~ (all_4_1 = e1)
% 201.56/33.43    (60)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.43    (61)   ~ (all_4_0 = e3)
% 201.56/33.43    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.43    (63)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.43    (64)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.43    (65)   ~ (e2 = e1)
% 201.56/33.43    (66)  all_58_10 = all_52_27
% 201.56/33.43    (67)  all_56_8 = all_52_5
% 201.56/33.43    (68)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.43    (69)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.43    (70)   ~ (all_52_19 = all_52_23)
% 201.56/33.43    (71)   ~ (all_52_25 = all_52_29)
% 201.56/33.43    (72)   ~ (all_52_29 = all_10_2)
% 201.56/33.43    (73)  all_58_7 = all_52_13
% 201.56/33.43    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.43    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.56/33.43    (76)   ~ (all_52_5 = all_52_7)
% 201.56/33.43    (77)  all_58_12 = all_52_7
% 201.56/33.43    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.43    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.43    (80)   ~ (all_52_7 = all_14_2)
% 201.56/33.43    (81)  all_58_2 = all_52_3
% 201.56/33.43    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.43    (83)  all_56_2 = all_52_17
% 201.56/33.43    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.56/33.43    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.43    (86)  op(all_4_0, all_4_0) = all_52_2
% 201.56/33.43    (87)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.43    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.43    (89)  all_56_7 = all_52_27
% 201.56/33.43    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.43    (91)   ~ (e2 = e0)
% 201.56/33.43    (92)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.43    (93)  op(all_4_2, e2) = all_4_1
% 201.56/33.43    (94)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.56/33.43    (95)   ~ (all_52_5 = all_52_29)
% 201.56/33.43    (96)  all_56_6 = all_52_19
% 201.56/33.43    (97)   ~ (all_52_15 = all_14_2)
% 201.56/33.43    (98)   ~ (all_52_19 = all_52_27)
% 201.56/33.43    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.43    (100)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.43    (101)  all_56_4 = all_4_0
% 201.56/33.43    (102)   ~ (all_52_13 = all_4_2)
% 201.56/33.43    (103)  op(e3, e1) = all_52_17
% 201.56/33.43    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.43    (105)  op(e0, e3) = all_52_7
% 201.56/33.43    (106)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.43    (107)   ~ (all_52_9 = all_52_25)
% 201.56/33.43    (108)  all_58_15 = all_14_2
% 201.56/33.43    (109)   ~ (all_52_19 = all_10_2)
% 201.56/33.43    (110)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.43    (111)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.43    (112)  all_58_8 = all_10_2
% 201.56/33.43    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.43    (114)   ~ (all_52_5 = all_10_2)
% 201.56/33.43    (115)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.43    (116)   ~ (all_52_23 = all_14_2)
% 201.56/33.43    (117)  all_56_12 = all_52_7
% 201.56/33.43    (118)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.43    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.56/33.43    (120)   ~ (all_52_25 = all_6_2)
% 201.56/33.43    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.43    (122)   ~ (all_52_9 = all_4_2)
% 201.56/33.43    (123)   ~ (all_52_5 = all_6_2)
% 201.56/33.43    (124)   ~ (all_52_9 = all_6_2)
% 201.56/33.43    (125)   ~ (all_52_13 = all_52_15)
% 201.56/33.43    (126)  all_56_0 = all_6_2
% 201.56/33.43    (127)  op(e3, e3) = all_6_2
% 201.56/33.43    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.43    (129)   ~ (all_52_27 = all_14_2)
% 201.56/33.43    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.43    (131)  all_56_14 = all_52_23
% 201.56/33.43    (132)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.43    (133)  all_32_0 = all_4_0
% 201.56/33.43    (134)  all_56_3 = all_52_25
% 201.56/33.43    (135)   ~ (all_52_3 = all_52_7)
% 201.56/33.43    (136)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.43    (137)  all_58_5 = all_52_19
% 201.56/33.43    (138)  all_56_1 = all_52_9
% 201.56/33.43    (139)   ~ (all_52_15 = all_4_2)
% 201.56/33.43    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.43           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.56/33.43           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.56/33.43           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.56/33.43    (141)   ~ (all_52_27 = all_4_2)
% 201.56/33.43    (142)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 201.56/33.43             all_58_13 = e0 | all_58_14 = e0)
% 201.56/33.43    (143)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 201.56/33.43    (144)  all_58_6 = all_52_5
% 201.56/33.43    (145)   ~ (all_4_0 = all_4_2)
% 201.56/33.43    (146)  op(e3, e2) = all_52_9
% 201.56/33.43    (147)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.43    (148)   ~ (all_52_17 = all_6_2)
% 201.56/33.43    (149)   ~ (e1 = e0)
% 201.56/33.43    (150)   ~ (e3 = e2)
% 201.56/33.43    (151)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.43    (152)   ~ (all_52_9 = all_52_17)
% 201.56/33.43    (153)  all_56_10 = all_10_2
% 201.56/33.43    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.43    (155)  all_46_1 = all_6_1
% 201.56/33.43    (156)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.43    (157)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.43    (158)  op(e1, e1) = all_10_2
% 201.56/33.43    (159)   ~ (all_52_23 = all_10_2)
% 201.56/33.43    (160)   ~ (all_52_7 = all_52_23)
% 201.56/33.43    (161)   ~ (all_52_17 = all_52_19)
% 201.56/33.43    (162)  all_58_3 = all_4_2
% 201.56/33.43    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.43    (164)  all_56_13 = all_52_15
% 201.56/33.43    (165)   ~ (all_52_3 = all_4_2)
% 201.56/33.43    (166)   ~ (all_52_19 = all_4_2)
% 201.56/33.43    (167)   ~ (all_52_17 = all_52_23)
% 201.56/33.43    (168)  op(all_6_2, e3) = all_6_1
% 201.56/33.43    (169)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.43    (170)   ~ (all_52_13 = all_52_29)
% 201.56/33.43    (171)  all_58_4 = all_52_17
% 201.56/33.43    (172)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.56/33.43    (173)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.43  
% 201.56/33.43  Begin of proof
% 201.56/33.43  | 
% 201.56/33.43  | ALPHA: (142) implies:
% 201.56/33.43  |   (174)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.43  |   (175)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.43  | 
% 201.56/33.43  | REDUCE: (57), (108) imply:
% 201.56/33.43  |   (176)   ~ (all_14_2 = e0)
% 201.56/33.43  | 
% 201.56/33.43  | BETA: splitting (90) gives:
% 201.56/33.43  | 
% 201.56/33.43  | Case 1:
% 201.56/33.43  | | 
% 201.56/33.43  | |   (177)  all_56_4 = e3
% 201.56/33.43  | | 
% 201.56/33.43  | | REF_CLOSE: (61), (101), (177) are inconsistent by sub-proof #980.
% 201.56/33.43  | | 
% 201.56/33.43  | Case 2:
% 201.56/33.43  | | 
% 201.56/33.43  | |   (178)   ~ (all_56_4 = e3)
% 201.56/33.43  | |   (179)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.43  | | 
% 201.56/33.43  | | BETA: splitting (140) gives:
% 201.56/33.43  | | 
% 201.56/33.43  | | Case 1:
% 201.56/33.43  | | | 
% 201.56/33.43  | | |   (180)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.43  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 201.56/33.43  | | |            e0)
% 201.56/33.43  | | | 
% 201.56/33.43  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.43  | | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23),
% 201.56/33.43  | | |            (25), (26), (29), (30), (31), (32), (33), (34), (36), (38),
% 201.56/33.43  | | |            (39), (40), (41), (42), (43), (44), (45), (48), (49), (50),
% 201.56/33.43  | | |            (51), (52), (53), (54), (56), (59), (60), (61), (62), (63),
% 201.56/33.43  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (73), (76),
% 201.56/33.43  | | |            (77), (78), (79), (80), (81), (82), (83), (85), (86), (88),
% 201.56/33.43  | | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (100),
% 201.56/33.43  | | |            (101), (102), (103), (104), (105), (106), (107), (108), (110),
% 201.56/33.43  | | |            (111), (112), (113), (115), (116), (117), (118), (120), (121),
% 201.56/33.43  | | |            (122), (123), (124), (126), (127), (128), (129), (130), (132),
% 201.56/33.43  | | |            (133), (134), (135), (136), (137), (138), (139), (141), (143),
% 201.56/33.43  | | |            (144), (145), (146), (147), (148), (149), (150), (151), (152),
% 201.56/33.43  | | |            (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 201.56/33.43  | | |            (164), (165), (166), (167), (168), (169), (170), (171), (173),
% 201.56/33.43  | | |            (174), (175), (179), (180) are inconsistent by sub-proof #257.
% 201.56/33.43  | | | 
% 201.56/33.43  | | Case 2:
% 201.56/33.43  | | | 
% 201.56/33.43  | | |   (181)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 201.56/33.43  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 201.56/33.43  | | |            all_52_30 = e0)
% 201.56/33.43  | | | 
% 201.56/33.43  | | | BETA: splitting (181) gives:
% 201.56/33.43  | | | 
% 201.56/33.43  | | | Case 1:
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | |   (182)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 201.56/33.43  | | | |          e0
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | ALPHA: (182) implies:
% 201.56/33.43  | | | |   (183)  all_52_22 = e0
% 201.56/33.43  | | | |   (184)  all_52_20 = e1
% 201.56/33.43  | | | |   (185)  all_52_18 = e2
% 201.56/33.43  | | | |   (186)  all_52_16 = e3
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (118), (186) imply:
% 201.56/33.43  | | | |   (187)  op(all_52_17, all_52_17) = e3
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (27), (185) imply:
% 201.56/33.43  | | | |   (188)  op(all_52_19, all_52_19) = e2
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (110), (183) imply:
% 201.56/33.43  | | | |   (189)  op(all_52_23, all_52_23) = e0
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | REDUCE: (30), (184) imply:
% 201.56/33.43  | | | |   (190)  op(all_10_2, all_10_2) = e1
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | BETA: splitting (113) gives:
% 201.56/33.43  | | | | 
% 201.56/33.43  | | | | Case 1:
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | |   (191)  all_56_15 = e3
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | | COMBINE_EQS: (53), (191) imply:
% 201.56/33.43  | | | | |   (192)  all_14_2 = e3
% 201.56/33.43  | | | | | 
% 201.56/33.43  | | | | | REDUCE: (129), (192) imply:
% 201.56/33.43  | | | | |   (193)   ~ (all_52_27 = e3)
% 201.56/33.43  | | | | | 
% 201.56/33.44  | | | | | REF_CLOSE: (7), (13), (37), (38), (39), (43), (49), (51), (54), (56),
% 201.56/33.44  | | | | |            (61), (66), (82), (92), (96), (101), (122), (127), (132),
% 201.56/33.44  | | | | |            (133), (137), (143), (145), (146), (162), (166), (179),
% 201.56/33.44  | | | | |            (188), (193) are inconsistent by sub-proof #944.
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | Case 2:
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | |   (194)   ~ (all_56_15 = e3)
% 201.56/33.44  | | | | |   (195)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | REDUCE: (53), (194) imply:
% 201.56/33.44  | | | | |   (196)   ~ (all_14_2 = e3)
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (14), (15), (16), (17),
% 201.56/33.44  | | | | |            (19), (22), (24), (25), (29), (31), (34), (36), (39), (40),
% 201.56/33.44  | | | | |            (41), (42), (44), (45), (47), (49), (50), (52), (53), (58),
% 201.56/33.44  | | | | |            (62), (63), (64), (65), (68), (71), (72), (73), (77), (78),
% 201.56/33.44  | | | | |            (79), (80), (81), (83), (84), (85), (87), (88), (91), (94),
% 201.56/33.44  | | | | |            (99), (100), (103), (105), (107), (108), (109), (112),
% 201.56/33.44  | | | | |            (114), (115), (116), (117), (120), (121), (123), (124),
% 201.56/33.44  | | | | |            (125), (126), (127), (128), (130), (134), (135), (137),
% 201.56/33.44  | | | | |            (138), (144), (146), (147), (148), (149), (150), (151),
% 201.56/33.44  | | | | |            (152), (153), (154), (156), (158), (159), (160), (163),
% 201.56/33.44  | | | | |            (164), (165), (168), (169), (171), (172), (173), (174),
% 201.56/33.44  | | | | |            (176), (187), (188), (189), (190), (195), (196) are
% 201.56/33.44  | | | | |            inconsistent by sub-proof #274.
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | End of split
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | Case 2:
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | |   (197)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 201.56/33.44  | | | |          e0
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | ALPHA: (197) implies:
% 201.56/33.44  | | | |   (198)  all_52_30 = e0
% 201.56/33.44  | | | |   (199)  all_52_28 = e1
% 201.56/33.44  | | | |   (200)  all_52_26 = e2
% 201.56/33.44  | | | |   (201)  all_52_24 = e3
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REDUCE: (173), (201) imply:
% 201.56/33.44  | | | |   (202)  op(all_52_25, all_52_25) = e3
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REDUCE: (35), (200) imply:
% 201.56/33.44  | | | |   (203)  op(all_52_27, all_52_27) = e2
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REDUCE: (115), (199) imply:
% 201.56/33.44  | | | |   (204)  op(all_52_29, all_52_29) = e1
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REDUCE: (136), (198) imply:
% 201.56/33.44  | | | |   (205)  op(all_14_2, all_14_2) = e0
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.44  | | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.56/33.44  | | | |            (24), (25), (27), (28), (29), (31), (33), (34), (36), (37),
% 201.56/33.44  | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 201.56/33.44  | | | |            (49), (50), (51), (52), (53), (54), (55), (58), (59), (60),
% 201.56/33.44  | | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 201.56/33.44  | | | |            (72), (73), (74), (75), (76), (77), (79), (80), (81), (83),
% 201.56/33.44  | | | |            (85), (86), (87), (88), (90), (91), (92), (93), (95), (97),
% 201.56/33.44  | | | |            (98), (99), (100), (101), (103), (104), (105), (106), (107),
% 201.56/33.44  | | | |            (108), (109), (110), (111), (112), (113), (114), (116),
% 201.56/33.44  | | | |            (118), (119), (120), (121), (122), (123), (124), (125),
% 201.56/33.44  | | | |            (126), (127), (128), (129), (130), (131), (134), (135),
% 201.56/33.44  | | | |            (137), (138), (139), (141), (144), (146), (147), (148),
% 201.56/33.44  | | | |            (149), (150), (151), (155), (156), (157), (158), (159),
% 201.56/33.44  | | | |            (160), (161), (162), (163), (164), (165), (166), (167),
% 201.56/33.44  | | | |            (168), (169), (171), (174), (176), (179), (202), (203),
% 201.56/33.44  | | | |            (204), (205) are inconsistent by sub-proof #256.
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | End of split
% 201.56/33.44  | | | 
% 201.56/33.44  | | End of split
% 201.56/33.44  | | 
% 201.56/33.44  | End of split
% 201.56/33.44  | 
% 201.56/33.44  End of proof
% 201.56/33.44  
% 201.56/33.44  Sub-proof #256 shows that the following formulas are inconsistent:
% 201.56/33.44  ----------------------------------------------------------------
% 201.56/33.44    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.44    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.44    (3)  all_58_14 = all_52_23
% 201.56/33.44    (4)   ~ (e3 = e1)
% 201.56/33.44    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.44    (7)   ~ (all_52_5 = all_52_13)
% 201.56/33.44    (8)  all_58_1 = all_52_9
% 201.56/33.44    (9)   ~ (all_52_9 = all_52_13)
% 201.56/33.44    (10)   ~ (e3 = e0)
% 201.56/33.44    (11)  op(e2, e3) = all_52_3
% 201.56/33.44    (12)   ~ (all_4_0 = e1)
% 201.56/33.44    (13)   ~ (all_52_7 = all_52_15)
% 201.56/33.44    (14)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.44    (15)   ~ (all_52_17 = all_52_25)
% 201.56/33.44    (16)   ~ (all_52_3 = all_6_2)
% 201.56/33.44    (17)  all_58_0 = all_6_2
% 201.56/33.44    (18)  op(all_14_2, e0) = all_14_1
% 201.56/33.44    (19)  all_56_4 = all_52_3
% 201.56/33.44    (20)  op(e3, all_6_1) = e1
% 201.56/33.44    (21)   ~ (all_52_17 = all_10_2)
% 201.56/33.44    (22)  op(e3, e0) = all_52_25
% 201.56/33.44    (23)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.44    (24)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.44    (25)   ~ (all_52_27 = all_52_29)
% 201.56/33.44    (26)  all_58_13 = all_52_15
% 201.56/33.44    (27)  all_58_9 = all_52_25
% 201.56/33.44    (28)   ~ (all_52_29 = all_14_2)
% 201.56/33.44    (29)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.44    (30)  op(e1, e3) = all_52_5
% 201.56/33.44    (31)   ~ (all_6_2 = all_4_0)
% 201.56/33.44    (32)  op(e2, e2) = all_4_2
% 201.56/33.44    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.44    (34)   ~ (all_52_3 = all_52_5)
% 201.56/33.44    (35)  all_58_11 = all_52_29
% 201.56/33.44    (36)  all_56_5 = all_4_2
% 201.56/33.44    (37)   ~ (all_52_25 = all_14_2)
% 201.56/33.44    (38)   ~ (all_52_9 = all_52_15)
% 201.56/33.44    (39)   ~ (all_52_3 = all_52_27)
% 201.56/33.44    (40)  op(all_10_2, e1) = all_10_1
% 201.56/33.44    (41)  all_46_2 = all_6_2
% 201.56/33.44    (42)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.44    (43)   ~ (all_52_7 = all_6_2)
% 201.56/33.44    (44)  all_58_2 = all_4_0
% 201.56/33.44    (45)  op(e0, e0) = all_14_2
% 201.56/33.44    (46)  op(all_52_29, all_52_29) = e1
% 201.56/33.44    (47)  all_56_15 = all_14_2
% 201.56/33.44    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.44    (49)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.56/33.44    (50)  all_56_11 = all_52_29
% 201.56/33.44    (51)   ~ (all_4_1 = e1)
% 201.56/33.44    (52)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.44    (53)   ~ (all_4_0 = e3)
% 201.56/33.44    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.44    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.44    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.44    (57)   ~ (e2 = e1)
% 201.56/33.44    (58)  all_58_10 = all_52_27
% 201.56/33.44    (59)  all_56_8 = all_52_5
% 201.56/33.44    (60)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.44    (61)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.44    (62)   ~ (all_52_25 = all_52_29)
% 201.56/33.44    (63)   ~ (all_52_29 = all_10_2)
% 201.56/33.44    (64)  all_58_7 = all_52_13
% 201.56/33.44    (65)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.56/33.44    (66)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.56/33.44    (67)   ~ (all_52_5 = all_52_7)
% 201.56/33.44    (68)  all_58_12 = all_52_7
% 201.56/33.44    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.44    (70)   ~ (all_52_7 = all_14_2)
% 201.56/33.44    (71)   ~ (all_14_2 = e0)
% 201.56/33.44    (72)  all_58_2 = all_52_3
% 201.56/33.44    (73)  all_56_2 = all_52_17
% 201.56/33.44    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.44    (75)  op(all_4_0, all_4_0) = all_52_2
% 201.56/33.44    (76)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.56/33.44    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.44    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.44    (79)   ~ (e2 = e0)
% 201.56/33.44    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.44    (81)  op(all_4_2, e2) = all_4_1
% 201.56/33.44    (82)  op(all_52_25, all_52_25) = e3
% 201.56/33.44    (83)   ~ (all_52_5 = all_52_29)
% 201.56/33.44    (84)   ~ (all_52_15 = all_14_2)
% 201.56/33.44    (85)   ~ (all_52_19 = all_52_27)
% 201.56/33.44    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.44    (87)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.44    (88)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.44    (89)  all_56_4 = all_4_0
% 201.56/33.44    (90)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.44    (91)  op(e3, e1) = all_52_17
% 201.56/33.44    (92)  op(all_52_27, all_52_27) = e2
% 201.56/33.44    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.44    (94)  op(e0, e3) = all_52_7
% 201.56/33.44    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.44    (96)   ~ (all_52_9 = all_52_25)
% 201.56/33.44    (97)  all_58_15 = all_14_2
% 201.56/33.44    (98)   ~ (all_52_19 = all_10_2)
% 201.56/33.44    (99)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.44    (100)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.44    (101)  all_58_8 = all_10_2
% 201.56/33.44    (102)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.44    (103)   ~ (all_52_5 = all_10_2)
% 201.56/33.44    (104)   ~ (all_52_23 = all_14_2)
% 201.56/33.44    (105)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.44    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.56/33.44    (107)   ~ (all_52_25 = all_6_2)
% 201.56/33.44    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.44    (109)   ~ (all_52_9 = all_4_2)
% 201.56/33.44    (110)   ~ (all_52_5 = all_6_2)
% 201.56/33.44    (111)   ~ (all_52_9 = all_6_2)
% 201.56/33.44    (112)   ~ (all_52_13 = all_52_15)
% 201.56/33.44    (113)  all_56_0 = all_6_2
% 201.56/33.44    (114)  op(e3, e3) = all_6_2
% 201.56/33.44    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.44    (116)   ~ (all_52_27 = all_14_2)
% 201.56/33.44    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.44    (118)  all_56_14 = all_52_23
% 201.56/33.44    (119)  all_56_3 = all_52_25
% 201.56/33.44    (120)   ~ (all_52_3 = all_52_7)
% 201.56/33.44    (121)  all_58_5 = all_52_19
% 201.56/33.44    (122)  all_56_1 = all_52_9
% 201.56/33.44    (123)   ~ (all_52_15 = all_4_2)
% 201.56/33.44    (124)   ~ (all_52_27 = all_4_2)
% 201.56/33.44    (125)  all_58_6 = all_52_5
% 201.56/33.44    (126)  op(e3, e2) = all_52_9
% 201.56/33.44    (127)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.44    (128)   ~ (all_52_17 = all_6_2)
% 201.56/33.44    (129)   ~ (e1 = e0)
% 201.56/33.44    (130)  op(all_14_2, all_14_2) = e0
% 201.56/33.44    (131)   ~ (e3 = e2)
% 201.56/33.44    (132)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.44    (133)  all_46_1 = all_6_1
% 201.56/33.44    (134)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.44    (135)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.44    (136)  op(e1, e1) = all_10_2
% 201.56/33.44    (137)   ~ (all_52_23 = all_10_2)
% 201.56/33.44    (138)   ~ (all_52_7 = all_52_23)
% 201.56/33.44    (139)   ~ (all_52_17 = all_52_19)
% 201.56/33.44    (140)  all_58_3 = all_4_2
% 201.56/33.44    (141)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.56/33.44    (142)  all_56_13 = all_52_15
% 201.56/33.44    (143)   ~ (all_52_3 = all_4_2)
% 201.56/33.44    (144)   ~ (all_52_19 = all_4_2)
% 201.56/33.44    (145)   ~ (all_52_17 = all_52_23)
% 201.56/33.44    (146)  op(all_6_2, e3) = all_6_1
% 201.56/33.44    (147)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.44    (148)  all_58_4 = all_52_17
% 201.56/33.44  
% 201.56/33.44  Begin of proof
% 201.56/33.44  | 
% 201.56/33.44  | BETA: splitting (102) gives:
% 201.56/33.44  | 
% 201.56/33.44  | Case 1:
% 201.56/33.44  | | 
% 201.56/33.44  | |   (149)  all_56_15 = e3
% 201.56/33.44  | | 
% 201.56/33.44  | | COMBINE_EQS: (47), (149) imply:
% 201.56/33.44  | |   (150)  all_14_2 = e3
% 201.56/33.44  | | 
% 201.56/33.44  | | SIMP: (150) implies:
% 201.56/33.44  | |   (151)  all_14_2 = e3
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (70), (151) imply:
% 201.56/33.44  | |   (152)   ~ (all_52_7 = e3)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (84), (151) imply:
% 201.56/33.44  | |   (153)   ~ (all_52_15 = e3)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (37), (151) imply:
% 201.56/33.44  | |   (154)   ~ (all_52_25 = e3)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (130), (151) imply:
% 201.56/33.44  | |   (155)  op(e3, e3) = e0
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (18), (151) imply:
% 201.56/33.44  | |   (156)  op(e3, e0) = all_14_1
% 201.56/33.44  | | 
% 201.56/33.44  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 201.56/33.44  | |              with (22), (156) gives:
% 201.56/33.44  | |   (157)  all_52_25 = all_14_1
% 201.56/33.44  | | 
% 201.56/33.44  | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying with
% 201.56/33.44  | |              (114), (155) gives:
% 201.56/33.44  | |   (158)  all_6_2 = e0
% 201.56/33.44  | | 
% 201.56/33.44  | | COMBINE_EQS: (119), (157) imply:
% 201.56/33.44  | |   (159)  all_56_3 = all_14_1
% 201.56/33.44  | | 
% 201.56/33.44  | | COMBINE_EQS: (27), (157) imply:
% 201.56/33.44  | |   (160)  all_58_9 = all_14_1
% 201.56/33.44  | | 
% 201.56/33.44  | | COMBINE_EQS: (17), (158) imply:
% 201.56/33.44  | |   (161)  all_58_0 = e0
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (110), (158) imply:
% 201.56/33.44  | |   (162)   ~ (all_52_5 = e0)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (96), (157) imply:
% 201.56/33.44  | |   (163)   ~ (all_52_9 = all_14_1)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (111), (158) imply:
% 201.56/33.44  | |   (164)   ~ (all_52_9 = e0)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (107), (157), (158) imply:
% 201.56/33.44  | |   (165)   ~ (all_14_1 = e0)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (154), (157) imply:
% 201.56/33.44  | |   (166)   ~ (all_14_1 = e3)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (31), (158) imply:
% 201.56/33.44  | |   (167)   ~ (all_4_0 = e0)
% 201.56/33.44  | | 
% 201.56/33.44  | | SIMP: (167) implies:
% 201.56/33.44  | |   (168)   ~ (all_4_0 = e0)
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (82), (157) imply:
% 201.56/33.44  | |   (169)  op(all_14_1, all_14_1) = e3
% 201.56/33.44  | | 
% 201.56/33.44  | | BETA: splitting (74) gives:
% 201.56/33.44  | | 
% 201.56/33.44  | | Case 1:
% 201.56/33.44  | | | 
% 201.56/33.44  | | |   (170)  all_58_0 = e3
% 201.56/33.44  | | | 
% 201.56/33.44  | | | REF_CLOSE: (10), (161), (170) are inconsistent by sub-proof #1015.
% 201.56/33.44  | | | 
% 201.56/33.44  | | Case 2:
% 201.56/33.44  | | | 
% 201.56/33.44  | | |   (171)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.44  | | | 
% 201.56/33.44  | | | BETA: splitting (87) gives:
% 201.56/33.44  | | | 
% 201.56/33.44  | | | Case 1:
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | |   (172)  all_56_4 = e2
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | COMBINE_EQS: (89), (172) imply:
% 201.56/33.44  | | | |   (173)  all_4_0 = e2
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | SIMP: (173) implies:
% 201.56/33.44  | | | |   (174)  all_4_0 = e2
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | COMBINE_EQS: (44), (174) imply:
% 201.56/33.44  | | | |   (175)  all_58_2 = e2
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REDUCE: (53), (174) imply:
% 201.56/33.44  | | | |   (176)   ~ (e3 = e2)
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REDUCE: (75), (174) imply:
% 201.56/33.44  | | | |   (177)  op(e2, e2) = all_52_2
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | BETA: splitting (171) gives:
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | Case 1:
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | |   (178)  all_58_2 = e3
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | COMBINE_EQS: (175), (178) imply:
% 201.56/33.44  | | | | |   (179)  e3 = e2
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | REDUCE: (131), (179) imply:
% 201.56/33.44  | | | | |   (180)  $false
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | CLOSE: (180) is inconsistent.
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | Case 2:
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | |   (181)  all_58_6 = e3 | all_58_12 = e3
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | BETA: splitting (181) gives:
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | | Case 1:
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | |   (182)  all_58_6 = e3
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | COMBINE_EQS: (125), (182) imply:
% 201.56/33.44  | | | | | |   (183)  all_52_5 = e3
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | SIMP: (183) implies:
% 201.56/33.44  | | | | | |   (184)  all_52_5 = e3
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | REDUCE: (7), (184) imply:
% 201.56/33.44  | | | | | |   (185)   ~ (all_52_13 = e3)
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | SIMP: (185) implies:
% 201.56/33.44  | | | | | |   (186)   ~ (all_52_13 = e3)
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | REDUCE: (103), (184) imply:
% 201.56/33.44  | | | | | |   (187)   ~ (all_10_2 = e3)
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | SIMP: (187) implies:
% 201.56/33.44  | | | | | |   (188)   ~ (all_10_2 = e3)
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | BETA: splitting (77) gives:
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | Case 1:
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | |   (189)  all_58_0 = e1
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | | REF_CLOSE: (129), (161), (189) are inconsistent by sub-proof #847.
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | Case 2:
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | |   (190)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | | BETA: splitting (190) gives:
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | | Case 1:
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | |   (191)  all_58_2 = e1
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | | REF_CLOSE: (57), (175), (191) are inconsistent by sub-proof
% 201.56/33.44  | | | | | | | |            #1116.
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | Case 2:
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | |   (192)  all_58_6 = e1 | all_58_12 = e1
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | | BETA: splitting (192) gives:
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | | Case 1:
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | |   (193)  all_58_6 = e1
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | REF_CLOSE: (4), (182), (193) are inconsistent by sub-proof
% 201.56/33.44  | | | | | | | | |            #1128.
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | Case 2:
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | |   (194)  all_58_12 = e1
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | COMBINE_EQS: (68), (194) imply:
% 201.56/33.44  | | | | | | | | |   (195)  all_52_7 = e1
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | SIMP: (195) implies:
% 201.56/33.44  | | | | | | | | |   (196)  all_52_7 = e1
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | REDUCE: (14), (196) imply:
% 201.56/33.44  | | | | | | | | |   (197)  op(e1, e1) = all_52_6
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_6, e1, e1,
% 201.56/33.44  | | | | | | | | |              simplifying with (136), (197) gives:
% 201.56/33.44  | | | | | | | | |   (198)  all_52_6 = all_10_2
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | GROUND_INST: instantiating (6) with all_4_2, all_52_2, e2, e2,
% 201.56/33.44  | | | | | | | | |              simplifying with (32), (177) gives:
% 201.56/33.44  | | | | | | | | |   (199)  all_52_2 = all_4_2
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | BETA: splitting (108) gives:
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | Case 1:
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | |   (200)  all_56_3 = e3
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | COMBINE_EQS: (159), (200) imply:
% 201.56/33.44  | | | | | | | | | |   (201)  all_14_1 = e3
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | REDUCE: (166), (201) imply:
% 201.56/33.44  | | | | | | | | | |   (202)  $false
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | CLOSE: (202) is inconsistent.
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | Case 2:
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | |   (203)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | BETA: splitting (117) gives:
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | Case 1:
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | |   (204)  all_58_0 = e3
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | REF_CLOSE: (10), (161), (204) are inconsistent by sub-proof
% 201.56/33.44  | | | | | | | | | | |            #1015.
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | Case 2:
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | |   (205)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | BETA: splitting (205) gives:
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | Case 1:
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | |   (206)  all_58_1 = e3
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | COMBINE_EQS: (8), (206) imply:
% 201.56/33.44  | | | | | | | | | | | |   (207)  all_52_9 = e3
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | REDUCE: (109), (207) imply:
% 201.56/33.44  | | | | | | | | | | | |   (208)   ~ (all_4_2 = e3)
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | SIMP: (208) implies:
% 201.56/33.44  | | | | | | | | | | | |   (209)   ~ (all_4_2 = e3)
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | REF_CLOSE: (6), (32), (49), (136), (159), (160), (165),
% 201.56/33.44  | | | | | | | | | | | |            (169), (188), (203), (209) are inconsistent by
% 201.56/33.44  | | | | | | | | | | | |            sub-proof #804.
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | Case 2:
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | |   (210)   ~ (all_58_1 = e3)
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | REDUCE: (8), (210) imply:
% 201.56/33.44  | | | | | | | | | | | |   (211)   ~ (all_52_9 = e3)
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | BETA: splitting (132) gives:
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | Case 1:
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | |   (212)  all_56_1 = e3
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | | COMBINE_EQS: (122), (212) imply:
% 201.56/33.44  | | | | | | | | | | | | |   (213)  all_52_9 = e3
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | | REDUCE: (211), (213) imply:
% 201.56/33.44  | | | | | | | | | | | | |   (214)  $false
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | | CLOSE: (214) is inconsistent.
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | Case 2:
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | |   (215)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (26), (49), (51), (64), (81), (95),
% 201.56/33.44  | | | | | | | | | | | | |            (122), (126), (136), (140), (153), (159), (160),
% 201.56/33.44  | | | | | | | | | | | | |            (163), (164), (165), (169), (186), (188), (203),
% 201.56/33.44  | | | | | | | | | | | | |            (211), (215) are inconsistent by sub-proof #559.
% 201.56/33.44  | | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | | End of split
% 201.56/33.44  | | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | | End of split
% 201.56/33.44  | | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | | End of split
% 201.56/33.44  | | | | | | | | | | 
% 201.56/33.44  | | | | | | | | | End of split
% 201.56/33.44  | | | | | | | | | 
% 201.56/33.44  | | | | | | | | End of split
% 201.56/33.44  | | | | | | | | 
% 201.56/33.44  | | | | | | | End of split
% 201.56/33.44  | | | | | | | 
% 201.56/33.44  | | | | | | End of split
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | Case 2:
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | |   (216)  all_58_12 = e3
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | | REF_CLOSE: (68), (152), (216) are inconsistent by sub-proof #1367.
% 201.56/33.44  | | | | | | 
% 201.56/33.44  | | | | | End of split
% 201.56/33.44  | | | | | 
% 201.56/33.44  | | | | End of split
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | Case 2:
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | |   (217)  all_56_4 = e1 | all_56_4 = e0
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | | REF_CLOSE: (12), (89), (168), (217) are inconsistent by sub-proof #674.
% 201.56/33.44  | | | | 
% 201.56/33.44  | | | End of split
% 201.56/33.44  | | | 
% 201.56/33.44  | | End of split
% 201.56/33.44  | | 
% 201.56/33.44  | Case 2:
% 201.56/33.44  | | 
% 201.56/33.44  | |   (218)   ~ (all_56_15 = e3)
% 201.56/33.44  | |   (219)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.44  | | 
% 201.56/33.44  | | REDUCE: (47), (218) imply:
% 201.56/33.44  | |   (220)   ~ (all_14_2 = e3)
% 201.56/33.44  | | 
% 201.56/33.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 201.56/33.44  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 201.56/33.44  | |            (27), (28), (29), (30), (32), (33), (34), (35), (36), (37), (38),
% 201.56/33.44  | |            (39), (40), (41), (42), (43), (45), (46), (47), (48), (49), (50),
% 201.56/33.44  | |            (52), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 201.56/33.44  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 201.56/33.44  | |            (76), (77), (78), (79), (80), (82), (83), (84), (85), (86), (88),
% 201.56/33.44  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 201.56/33.44  | |            (100), (101), (103), (104), (105), (106), (107), (108), (109),
% 201.56/33.44  | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 201.56/33.44  | |            (119), (120), (121), (122), (123), (124), (125), (126), (127),
% 201.56/33.44  | |            (128), (129), (130), (131), (132), (133), (134), (135), (136),
% 201.56/33.44  | |            (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 201.56/33.44  | |            (146), (147), (148), (219), (220) are inconsistent by sub-proof
% 201.56/33.44  | |            #272.
% 201.56/33.44  | | 
% 201.56/33.44  | End of split
% 201.56/33.44  | 
% 201.56/33.44  End of proof
% 201.56/33.44  
% 201.56/33.44  Sub-proof #257 shows that the following formulas are inconsistent:
% 201.56/33.44  ----------------------------------------------------------------
% 201.56/33.44    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.44    (2)   ~ (all_52_15 = all_52_23)
% 201.56/33.44    (3)   ~ (all_52_25 = all_52_27)
% 201.56/33.44    (4)  all_58_14 = all_52_23
% 201.56/33.44    (5)   ~ (e3 = e1)
% 201.56/33.44    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.44    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.44    (9)   ~ (all_52_5 = all_52_13)
% 201.56/33.44    (10)  all_58_1 = all_52_9
% 201.56/33.44    (11)   ~ (all_52_9 = all_52_13)
% 201.56/33.44    (12)   ~ (e3 = e0)
% 201.56/33.44    (13)  op(e2, e3) = all_52_3
% 201.56/33.44    (14)   ~ (all_4_0 = e1)
% 201.56/33.44    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.44    (16)   ~ (all_52_7 = all_52_15)
% 201.56/33.44    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.44    (18)   ~ (all_52_17 = all_52_25)
% 201.56/33.44    (19)   ~ (all_52_3 = all_6_2)
% 201.56/33.44    (20)  all_58_0 = all_6_2
% 201.56/33.44    (21)  all_56_4 = all_52_3
% 201.56/33.44    (22)  op(e3, all_6_1) = e1
% 201.56/33.44    (23)   ~ (all_52_17 = all_10_2)
% 201.56/33.44    (24)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.44    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.44    (26)  all_58_13 = all_52_15
% 201.56/33.44    (27)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.44    (28)  all_58_9 = all_52_25
% 201.56/33.44    (29)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.44    (30)   ~ (all_52_29 = all_14_2)
% 201.56/33.44    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.44    (32)  op(e1, e3) = all_52_5
% 201.56/33.44    (33)  all_32_2 = all_4_2
% 201.56/33.44    (34)  op(e2, e2) = all_4_2
% 201.56/33.44    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.44    (36)   ~ (all_52_3 = all_52_5)
% 201.56/33.44    (37)  all_58_11 = all_52_29
% 201.56/33.44    (38)  all_56_5 = all_4_2
% 201.56/33.44    (39)   ~ (all_52_25 = all_14_2)
% 201.56/33.44    (40)   ~ (all_52_9 = all_52_15)
% 201.56/33.44    (41)  all_46_2 = all_6_2
% 201.56/33.44    (42)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.44    (43)   ~ (all_52_7 = all_6_2)
% 201.56/33.44    (44)  all_58_2 = all_4_0
% 201.56/33.44    (45)  op(e0, e0) = all_14_2
% 201.56/33.44    (46)  all_56_15 = all_14_2
% 201.56/33.44    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.44    (48)  op(all_4_2, e2) = e3
% 201.56/33.44    (49)   ~ (all_4_1 = e1)
% 201.56/33.44    (50)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.44    (51)   ~ (all_4_0 = e3)
% 201.56/33.44    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.44    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.44    (54)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.44    (55)   ~ (e2 = e1)
% 201.56/33.44    (56)  all_58_10 = all_52_27
% 201.56/33.44    (57)  all_56_8 = all_52_5
% 201.56/33.44    (58)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.44    (59)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.44    (60)   ~ (all_52_19 = all_52_23)
% 201.56/33.44    (61)   ~ (all_52_25 = all_52_29)
% 201.56/33.44    (62)  all_58_7 = all_52_13
% 201.56/33.44    (63)   ~ (all_52_5 = all_52_7)
% 201.56/33.44    (64)  all_58_12 = all_52_7
% 201.56/33.44    (65)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.44    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.44    (67)   ~ (all_52_7 = all_14_2)
% 201.56/33.44    (68)  all_58_2 = all_52_3
% 201.56/33.44    (69)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.44    (70)  all_56_2 = all_52_17
% 201.56/33.45    (71)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.45    (72)  op(all_4_0, all_4_0) = all_52_2
% 201.56/33.45    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.45    (74)  all_56_7 = all_52_27
% 201.56/33.45    (75)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.45    (76)   ~ (e2 = e0)
% 201.56/33.45    (77)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.45    (78)  op(all_4_2, e2) = all_4_1
% 201.56/33.45    (79)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.56/33.45    (80)   ~ (all_52_5 = all_52_29)
% 201.56/33.45    (81)  all_56_6 = all_52_19
% 201.56/33.45    (82)   ~ (all_52_15 = all_14_2)
% 201.56/33.45    (83)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.45    (84)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.45    (85)  all_56_4 = all_4_0
% 201.56/33.45    (86)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.45    (87)   ~ (all_52_13 = all_4_2)
% 201.56/33.45    (88)  op(e3, e1) = all_52_17
% 201.56/33.45    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.45    (90)  op(e0, e3) = all_52_7
% 201.56/33.45    (91)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.45    (92)   ~ (all_52_9 = all_52_25)
% 201.56/33.45    (93)  all_58_15 = all_14_2
% 201.56/33.45    (94)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.45    (95)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.45    (96)  all_58_8 = all_10_2
% 201.56/33.45    (97)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.45    (98)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.45    (99)   ~ (all_52_23 = all_14_2)
% 201.56/33.45    (100)  all_56_12 = all_52_7
% 201.56/33.45    (101)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.45    (102)   ~ (all_52_25 = all_6_2)
% 201.56/33.45    (103)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.45    (104)   ~ (all_52_9 = all_4_2)
% 201.56/33.45    (105)   ~ (all_52_5 = all_6_2)
% 201.56/33.45    (106)   ~ (all_52_9 = all_6_2)
% 201.56/33.45    (107)  all_56_0 = all_6_2
% 201.56/33.45    (108)  op(e3, e3) = all_6_2
% 201.56/33.45    (109)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.45    (110)   ~ (all_52_27 = all_14_2)
% 201.56/33.45    (111)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.45    (112)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.45    (113)  all_32_0 = all_4_0
% 201.56/33.45    (114)  all_56_3 = all_52_25
% 201.56/33.45    (115)   ~ (all_52_3 = all_52_7)
% 201.56/33.45    (116)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.45    (117)  all_58_5 = all_52_19
% 201.56/33.45    (118)  all_56_1 = all_52_9
% 201.56/33.45    (119)   ~ (all_52_15 = all_4_2)
% 201.56/33.45    (120)   ~ (all_52_27 = all_4_2)
% 201.56/33.45    (121)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 201.56/33.45    (122)  all_58_6 = all_52_5
% 201.56/33.45    (123)   ~ (all_4_0 = all_4_2)
% 201.56/33.45    (124)  op(e3, e2) = all_52_9
% 201.56/33.45    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.45    (126)   ~ (all_52_17 = all_6_2)
% 201.56/33.45    (127)   ~ (e1 = e0)
% 201.56/33.45    (128)   ~ (e3 = e2)
% 201.56/33.45    (129)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.56/33.45           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 201.56/33.45    (130)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.45    (131)   ~ (all_52_9 = all_52_17)
% 201.56/33.45    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.45    (133)  all_46_1 = all_6_1
% 201.56/33.45    (134)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.45    (135)  op(all_52_13, all_52_13) = all_52_12
% 201.56/33.45    (136)  op(e1, e1) = all_10_2
% 201.56/33.45    (137)   ~ (all_52_23 = all_10_2)
% 201.56/33.45    (138)   ~ (all_52_7 = all_52_23)
% 201.56/33.45    (139)   ~ (all_52_17 = all_52_19)
% 201.56/33.45    (140)  all_58_3 = all_4_2
% 201.56/33.45    (141)  all_56_13 = all_52_15
% 201.56/33.45    (142)   ~ (all_52_3 = all_4_2)
% 201.56/33.45    (143)   ~ (all_52_19 = all_4_2)
% 201.56/33.45    (144)   ~ (all_52_17 = all_52_23)
% 201.56/33.45    (145)  op(all_6_2, e3) = all_6_1
% 201.56/33.45    (146)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.45    (147)   ~ (all_52_13 = all_52_29)
% 201.56/33.45    (148)  all_58_4 = all_52_17
% 201.56/33.45    (149)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.45  
% 201.56/33.45  Begin of proof
% 201.56/33.45  | 
% 201.56/33.45  | BETA: splitting (129) gives:
% 201.56/33.45  | 
% 201.56/33.45  | Case 1:
% 201.56/33.45  | | 
% 201.56/33.45  | |   (150)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.56/33.45  | | 
% 201.56/33.45  | | REF_CLOSE: (8), (14), (33), (34), (38), (44), (48), (72), (77), (83), (85),
% 201.56/33.45  | |            (104), (112), (113), (121), (123), (124), (146), (150) are
% 201.56/33.45  | |            inconsistent by sub-proof #970.
% 201.56/33.45  | | 
% 201.56/33.45  | Case 2:
% 201.56/33.45  | | 
% 201.56/33.45  | |   (151)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 201.56/33.45  | | 
% 201.56/33.45  | | ALPHA: (151) implies:
% 201.56/33.45  | |   (152)  all_52_14 = e0
% 201.56/33.45  | |   (153)  all_52_12 = e1
% 201.56/33.45  | |   (154)  all_52_10 = e2
% 201.56/33.45  | |   (155)  all_52_8 = e3
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (58), (155) imply:
% 201.56/33.45  | |   (156)  op(all_52_9, all_52_9) = e3
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (135), (153) imply:
% 201.56/33.45  | |   (157)  op(all_52_13, all_52_13) = e1
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (59), (152) imply:
% 201.56/33.45  | |   (158)  op(all_52_15, all_52_15) = e0
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (112), (154) imply:
% 201.56/33.45  | |   (159)  op(all_4_2, all_4_2) = e2
% 201.56/33.45  | | 
% 201.56/33.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.45  | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 201.56/33.45  | |            (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 201.56/33.45  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 201.56/33.45  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (60),
% 201.56/33.45  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 201.56/33.45  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (84),
% 201.56/33.45  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 201.56/33.45  | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 201.56/33.45  | |            (106), (107), (108), (109), (110), (111), (114), (115), (116),
% 201.56/33.45  | |            (117), (118), (119), (120), (122), (124), (125), (126), (127),
% 201.56/33.45  | |            (128), (130), (131), (132), (133), (134), (136), (137), (138),
% 201.56/33.45  | |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 201.56/33.45  | |            (148), (149), (156), (157), (158), (159) are inconsistent by
% 201.56/33.45  | |            sub-proof #258.
% 201.56/33.45  | | 
% 201.56/33.45  | End of split
% 201.56/33.45  | 
% 201.56/33.45  End of proof
% 201.56/33.45  
% 201.56/33.45  Sub-proof #258 shows that the following formulas are inconsistent:
% 201.56/33.45  ----------------------------------------------------------------
% 201.56/33.45    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.56/33.45    (2)   ~ (all_52_15 = all_52_23)
% 201.56/33.45    (3)   ~ (all_52_25 = all_52_27)
% 201.56/33.45    (4)  all_58_14 = all_52_23
% 201.56/33.45    (5)   ~ (e3 = e1)
% 201.56/33.45    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.56/33.45    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.56/33.45    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.45    (9)   ~ (all_52_5 = all_52_13)
% 201.56/33.45    (10)  all_58_1 = all_52_9
% 201.56/33.45    (11)   ~ (all_52_9 = all_52_13)
% 201.56/33.45    (12)   ~ (e3 = e0)
% 201.56/33.45    (13)  op(e2, e3) = all_52_3
% 201.56/33.45    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.45    (15)   ~ (all_52_7 = all_52_15)
% 201.56/33.45    (16)  op(all_52_15, all_52_15) = e0
% 201.56/33.45    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.45    (18)   ~ (all_52_17 = all_52_25)
% 201.56/33.45    (19)   ~ (all_52_3 = all_6_2)
% 201.56/33.45    (20)  all_58_0 = all_6_2
% 201.56/33.45    (21)  all_56_4 = all_52_3
% 201.56/33.45    (22)  op(e3, all_6_1) = e1
% 201.56/33.45    (23)   ~ (all_52_17 = all_10_2)
% 201.56/33.45    (24)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.45    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.45    (26)  all_58_13 = all_52_15
% 201.56/33.45    (27)  op(all_52_13, all_52_13) = e1
% 201.56/33.45    (28)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.45    (29)  all_58_9 = all_52_25
% 201.56/33.45    (30)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.45    (31)   ~ (all_52_29 = all_14_2)
% 201.56/33.45    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.56/33.45    (33)  op(e1, e3) = all_52_5
% 201.56/33.45    (34)  op(e2, e2) = all_4_2
% 201.56/33.45    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.45    (36)   ~ (all_52_3 = all_52_5)
% 201.56/33.45    (37)  all_58_11 = all_52_29
% 201.56/33.45    (38)  all_56_5 = all_4_2
% 201.56/33.45    (39)   ~ (all_52_25 = all_14_2)
% 201.56/33.45    (40)   ~ (all_52_9 = all_52_15)
% 201.56/33.45    (41)  all_46_2 = all_6_2
% 201.56/33.45    (42)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.45    (43)   ~ (all_52_7 = all_6_2)
% 201.56/33.45    (44)  all_58_2 = all_4_0
% 201.56/33.45    (45)  op(e0, e0) = all_14_2
% 201.56/33.45    (46)  all_56_15 = all_14_2
% 201.56/33.45    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.45    (48)  op(all_4_2, e2) = e3
% 201.56/33.45    (49)   ~ (all_4_1 = e1)
% 201.56/33.45    (50)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.56/33.45    (51)   ~ (all_4_0 = e3)
% 201.56/33.45    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.45    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.45    (54)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.56/33.45    (55)   ~ (e2 = e1)
% 201.56/33.45    (56)  all_58_10 = all_52_27
% 201.56/33.45    (57)  all_56_8 = all_52_5
% 201.56/33.45    (58)   ~ (all_52_19 = all_52_23)
% 201.56/33.45    (59)   ~ (all_52_25 = all_52_29)
% 201.56/33.45    (60)  all_58_7 = all_52_13
% 201.56/33.45    (61)   ~ (all_52_5 = all_52_7)
% 201.56/33.45    (62)  all_58_12 = all_52_7
% 201.56/33.45    (63)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.56/33.45    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.56/33.45    (65)   ~ (all_52_7 = all_14_2)
% 201.56/33.45    (66)  all_58_2 = all_52_3
% 201.56/33.45    (67)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.45    (68)  all_56_2 = all_52_17
% 201.56/33.45    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.45    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.45    (71)  all_56_7 = all_52_27
% 201.56/33.45    (72)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.45    (73)   ~ (e2 = e0)
% 201.56/33.45    (74)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.45    (75)  op(all_4_2, e2) = all_4_1
% 201.56/33.45    (76)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.56/33.45    (77)   ~ (all_52_5 = all_52_29)
% 201.56/33.45    (78)  all_56_6 = all_52_19
% 201.56/33.45    (79)   ~ (all_52_15 = all_14_2)
% 201.56/33.45    (80)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.45    (81)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.56/33.45    (82)   ~ (all_52_13 = all_4_2)
% 201.56/33.45    (83)  op(e3, e1) = all_52_17
% 201.56/33.45    (84)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.56/33.45    (85)  op(e0, e3) = all_52_7
% 201.56/33.45    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.45    (87)   ~ (all_52_9 = all_52_25)
% 201.56/33.45    (88)  all_58_15 = all_14_2
% 201.56/33.45    (89)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.45    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.45    (91)  all_58_8 = all_10_2
% 201.56/33.45    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.45    (93)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.45    (94)   ~ (all_52_23 = all_14_2)
% 201.56/33.45    (95)  all_56_12 = all_52_7
% 201.56/33.45    (96)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.45    (97)   ~ (all_52_25 = all_6_2)
% 201.56/33.45    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.45    (99)   ~ (all_52_9 = all_4_2)
% 201.56/33.45    (100)   ~ (all_52_5 = all_6_2)
% 201.56/33.45    (101)  op(all_4_2, all_4_2) = e2
% 201.56/33.45    (102)   ~ (all_52_9 = all_6_2)
% 201.56/33.45    (103)  all_56_0 = all_6_2
% 201.56/33.45    (104)  op(e3, e3) = all_6_2
% 201.56/33.45    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.56/33.45    (106)   ~ (all_52_27 = all_14_2)
% 201.56/33.45    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.45    (108)  all_56_3 = all_52_25
% 201.56/33.45    (109)   ~ (all_52_3 = all_52_7)
% 201.56/33.45    (110)  op(all_14_2, all_14_2) = all_52_30
% 201.56/33.45    (111)  all_58_5 = all_52_19
% 201.56/33.45    (112)  all_56_1 = all_52_9
% 201.56/33.45    (113)   ~ (all_52_15 = all_4_2)
% 201.56/33.45    (114)   ~ (all_52_27 = all_4_2)
% 201.56/33.45    (115)  all_58_6 = all_52_5
% 201.56/33.45    (116)  op(e3, e2) = all_52_9
% 201.56/33.45    (117)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.45    (118)   ~ (all_52_17 = all_6_2)
% 201.56/33.45    (119)   ~ (e1 = e0)
% 201.56/33.45    (120)   ~ (e3 = e2)
% 201.56/33.45    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.56/33.45    (122)   ~ (all_52_9 = all_52_17)
% 201.56/33.45    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.45    (124)  all_46_1 = all_6_1
% 201.56/33.45    (125)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.56/33.45    (126)  op(e1, e1) = all_10_2
% 201.56/33.45    (127)  op(all_52_9, all_52_9) = e3
% 201.56/33.45    (128)   ~ (all_52_23 = all_10_2)
% 201.56/33.45    (129)   ~ (all_52_7 = all_52_23)
% 201.56/33.45    (130)   ~ (all_52_17 = all_52_19)
% 201.56/33.45    (131)  all_58_3 = all_4_2
% 201.56/33.45    (132)  all_56_13 = all_52_15
% 201.56/33.45    (133)   ~ (all_52_3 = all_4_2)
% 201.56/33.45    (134)   ~ (all_52_19 = all_4_2)
% 201.56/33.45    (135)   ~ (all_52_17 = all_52_23)
% 201.56/33.45    (136)  op(all_6_2, e3) = all_6_1
% 201.56/33.45    (137)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.45    (138)   ~ (all_52_13 = all_52_29)
% 201.56/33.45    (139)  all_58_4 = all_52_17
% 201.56/33.45    (140)  op(all_52_25, all_52_25) = all_52_24
% 201.56/33.45  
% 201.56/33.45  Begin of proof
% 201.56/33.45  | 
% 201.56/33.45  | BETA: splitting (92) gives:
% 201.56/33.45  | 
% 201.56/33.45  | Case 1:
% 201.56/33.45  | | 
% 201.56/33.45  | |   (141)  all_56_15 = e3
% 201.56/33.45  | | 
% 201.56/33.45  | | COMBINE_EQS: (46), (141) imply:
% 201.56/33.45  | |   (142)  all_14_2 = e3
% 201.56/33.45  | | 
% 201.56/33.45  | | SIMP: (142) implies:
% 201.56/33.45  | |   (143)  all_14_2 = e3
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (65), (143) imply:
% 201.56/33.45  | |   (144)   ~ (all_52_7 = e3)
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (79), (143) imply:
% 201.56/33.45  | |   (145)   ~ (all_52_15 = e3)
% 201.56/33.45  | | 
% 201.56/33.45  | | BETA: splitting (69) gives:
% 201.56/33.45  | | 
% 201.56/33.45  | | Case 1:
% 201.56/33.45  | | | 
% 201.56/33.45  | | |   (146)  all_58_0 = e3
% 201.56/33.45  | | | 
% 201.56/33.45  | | | COMBINE_EQS: (20), (146) imply:
% 201.56/33.45  | | |   (147)  all_6_2 = e3
% 201.56/33.45  | | | 
% 201.56/33.45  | | | REF_CLOSE: (5), (8), (22), (104), (136), (147) are inconsistent by
% 201.56/33.45  | | |            sub-proof #310.
% 201.56/33.45  | | | 
% 201.56/33.45  | | Case 2:
% 201.56/33.45  | | | 
% 201.56/33.45  | | |   (148)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.45  | | | 
% 201.56/33.45  | | | REF_CLOSE: (8), (9), (10), (24), (26), (44), (48), (51), (60), (62), (86),
% 201.56/33.45  | | |            (99), (102), (104), (115), (116), (127), (131), (144), (145),
% 201.56/33.45  | | |            (148) are inconsistent by sub-proof #938.
% 201.56/33.45  | | | 
% 201.56/33.45  | | End of split
% 201.56/33.45  | | 
% 201.56/33.45  | Case 2:
% 201.56/33.45  | | 
% 201.56/33.45  | |   (149)   ~ (all_56_15 = e3)
% 201.56/33.45  | |   (150)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.56/33.45  | | 
% 201.56/33.45  | | REDUCE: (46), (149) imply:
% 201.56/33.45  | |   (151)   ~ (all_14_2 = e3)
% 201.56/33.45  | | 
% 201.56/33.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 201.56/33.45  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 201.56/33.45  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 201.56/33.45  | |            (36), (37), (38), (39), (40), (41), (42), (43), (45), (46), (47),
% 201.56/33.45  | |            (49), (50), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 201.56/33.45  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 201.56/33.45  | |            (72), (73), (74), (75), (76), (77), (78), (80), (81), (82), (83),
% 201.56/33.45  | |            (84), (85), (86), (87), (88), (89), (90), (91), (93), (94), (95),
% 201.56/33.45  | |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 201.56/33.45  | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 201.56/33.45  | |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 201.56/33.45  | |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 201.56/33.45  | |            (133), (134), (135), (136), (137), (138), (139), (140), (150),
% 201.56/33.45  | |            (151) are inconsistent by sub-proof #288.
% 201.56/33.45  | | 
% 201.56/33.45  | End of split
% 201.56/33.45  | 
% 201.56/33.45  End of proof
% 201.56/33.45  
% 201.56/33.45  Sub-proof #259 shows that the following formulas are inconsistent:
% 201.56/33.45  ----------------------------------------------------------------
% 201.56/33.45    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.45    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.45    (3)  all_58_14 = all_52_23
% 201.56/33.45    (4)   ~ (e3 = e1)
% 201.56/33.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.45    (6)  all_58_1 = all_52_9
% 201.56/33.45    (7)   ~ (e3 = e0)
% 201.56/33.45    (8)   ~ (all_4_0 = e1)
% 201.56/33.45    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.45    (10)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.45    (11)   ~ (all_52_17 = all_52_25)
% 201.56/33.45    (12)   ~ (all_52_5 = all_4_0)
% 201.56/33.45    (13)  all_58_0 = all_6_2
% 201.56/33.45    (14)  op(e3, all_6_1) = e1
% 201.56/33.45    (15)   ~ (all_52_17 = all_10_2)
% 201.56/33.45    (16)  op(e3, e0) = all_52_25
% 201.56/33.45    (17)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.45    (18)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.45    (19)  op(all_52_19, all_52_19) = all_52_18
% 201.56/33.45    (20)   ~ (all_52_27 = all_52_29)
% 201.56/33.45    (21)  all_58_13 = all_52_15
% 201.56/33.45    (22)  op(all_10_2, all_10_2) = all_52_20
% 201.56/33.45    (23)  all_58_9 = all_52_25
% 201.56/33.45    (24)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.45    (25)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.45    (26)  op(e1, e3) = all_52_5
% 201.56/33.45    (27)   ~ (all_6_2 = all_4_0)
% 201.56/33.45    (28)  all_32_2 = all_4_2
% 201.56/33.45    (29)  op(e2, e2) = all_4_2
% 201.56/33.45    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.45    (31)  all_56_5 = all_4_2
% 201.56/33.45    (32)  op(all_10_2, e1) = all_10_1
% 201.56/33.45    (33)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.45    (34)   ~ (all_52_7 = all_6_2)
% 201.56/33.45    (35)  all_58_2 = all_4_0
% 201.56/33.45    (36)   ~ (all_52_15 = e0)
% 201.56/33.45    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.45    (38)  op(all_4_2, e2) = e3
% 201.56/33.45    (39)  all_58_15 = e0
% 201.56/33.45    (40)  all_56_11 = all_52_29
% 201.56/33.45    (41)   ~ (all_4_0 = e3)
% 201.56/33.45    (42)   ~ (all_52_25 = e0)
% 201.56/33.45    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.45    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.45    (45)   ~ (e2 = e1)
% 201.56/33.45    (46)  op(e0, e0) = e0
% 201.56/33.45    (47)  all_58_10 = all_52_27
% 201.56/33.45    (48)  all_56_8 = all_52_5
% 201.56/33.45    (49)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.45    (50)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.45    (51)   ~ (all_52_5 = all_52_7)
% 201.56/33.45    (52)  all_58_12 = all_52_7
% 201.56/33.45    (53)  all_58_2 = all_52_3
% 201.56/33.45    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.45    (55)  all_56_2 = all_52_17
% 201.56/33.45    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.45    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.45    (58)  all_56_7 = all_52_27
% 201.56/33.45    (59)   ~ (e2 = e0)
% 201.56/33.45    (60)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.45    (61)   ~ (all_52_5 = all_52_29)
% 201.56/33.45    (62)   ~ (all_52_29 = e0)
% 201.56/33.45    (63)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.56/33.45    (64)  all_56_6 = all_52_19
% 201.56/33.45    (65)   ~ (all_52_19 = all_52_27)
% 201.56/33.45    (66)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.45    (67)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.45    (68)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.45    (69)  all_56_4 = all_4_0
% 201.56/33.45    (70)  op(e3, e1) = all_52_17
% 201.56/33.45    (71)  op(e0, e3) = all_52_7
% 201.56/33.45    (72)  op(all_52_23, all_52_23) = all_52_22
% 201.56/33.45    (73)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.45    (74)  all_58_8 = all_10_2
% 201.56/33.45    (75)   ~ (all_52_5 = all_10_2)
% 201.56/33.45    (76)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.45    (77)   ~ (all_52_7 = all_4_0)
% 201.56/33.45    (78)  all_56_12 = all_52_7
% 201.56/33.45    (79)  op(all_52_17, all_52_17) = all_52_16
% 201.56/33.45    (80)   ~ (all_52_25 = all_6_2)
% 201.56/33.45    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.45    (82)   ~ (all_52_9 = all_4_2)
% 201.56/33.45    (83)   ~ (all_52_5 = all_6_2)
% 201.56/33.45    (84)   ~ (all_52_9 = all_6_2)
% 201.56/33.45    (85)  op(e3, e3) = all_6_2
% 201.56/33.45    (86)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.45    (87)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.45    (88)  all_32_0 = all_4_0
% 201.56/33.45    (89)  all_56_3 = all_52_25
% 201.56/33.45    (90)  all_58_5 = all_52_19
% 201.56/33.45    (91)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 201.56/33.45    (92)  all_58_6 = all_52_5
% 201.56/33.45    (93)   ~ (all_4_0 = all_4_2)
% 201.56/33.45    (94)  op(e3, e2) = all_52_9
% 201.56/33.45    (95)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.45    (96)   ~ (all_52_17 = all_6_2)
% 201.56/33.45    (97)   ~ (e1 = e0)
% 201.56/33.45    (98)   ~ (e3 = e2)
% 201.56/33.45    (99)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.45    (100)  op(e1, e1) = all_10_2
% 201.56/33.45    (101)   ~ (all_52_7 = all_52_23)
% 201.56/33.45    (102)  all_58_3 = all_4_2
% 201.56/33.45    (103)  all_56_13 = all_52_15
% 201.56/33.45    (104)   ~ (all_52_19 = all_4_2)
% 201.56/33.45    (105)  op(all_6_2, e3) = all_6_1
% 201.56/33.45    (106)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.45    (107)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 201.56/33.45    (108)  all_58_4 = all_52_17
% 201.56/33.45    (109)   ~ (all_52_7 = e0)
% 201.56/33.45  
% 201.56/33.45  Begin of proof
% 201.56/33.45  | 
% 201.56/33.45  | ALPHA: (107) implies:
% 201.56/33.45  |   (110)  all_52_22 = e0
% 201.56/33.45  |   (111)  all_52_20 = e1
% 201.56/33.45  |   (112)  all_52_18 = e2
% 201.56/33.45  |   (113)  all_52_16 = e3
% 201.56/33.45  | 
% 201.56/33.45  | REDUCE: (79), (113) imply:
% 201.56/33.45  |   (114)  op(all_52_17, all_52_17) = e3
% 201.56/33.45  | 
% 201.56/33.45  | REDUCE: (19), (112) imply:
% 201.56/33.45  |   (115)  op(all_52_19, all_52_19) = e2
% 201.56/33.45  | 
% 201.56/33.45  | REDUCE: (72), (110) imply:
% 201.56/33.45  |   (116)  op(all_52_23, all_52_23) = e0
% 201.56/33.45  | 
% 201.56/33.45  | REDUCE: (22), (111) imply:
% 201.56/33.45  |   (117)  op(all_10_2, all_10_2) = e1
% 201.56/33.45  | 
% 201.56/33.45  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.56/33.45  |            (13), (14), (15), (16), (17), (18), (20), (21), (23), (24), (25),
% 201.56/33.45  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 201.56/33.45  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 201.56/33.45  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 201.56/33.45  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 201.56/33.45  |            (70), (71), (73), (74), (75), (76), (77), (78), (80), (81), (82),
% 201.56/33.45  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 201.56/33.45  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 201.56/33.45  |            (104), (105), (106), (108), (109), (114), (115), (116), (117) are
% 201.56/33.45  |            inconsistent by sub-proof #260.
% 201.56/33.45  | 
% 201.56/33.45  End of proof
% 201.56/33.45  
% 201.56/33.45  Sub-proof #260 shows that the following formulas are inconsistent:
% 201.56/33.45  ----------------------------------------------------------------
% 201.56/33.45    (1)   ~ (all_52_15 = all_52_23)
% 201.56/33.45    (2)   ~ (all_52_25 = all_52_27)
% 201.56/33.45    (3)  all_58_14 = all_52_23
% 201.56/33.45    (4)   ~ (e3 = e1)
% 201.56/33.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.45    (6)  all_58_1 = all_52_9
% 201.56/33.45    (7)   ~ (e3 = e0)
% 201.56/33.45    (8)  op(all_52_23, all_52_23) = e0
% 201.56/33.45    (9)   ~ (all_4_0 = e1)
% 201.56/33.45    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.45    (11)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.45    (12)   ~ (all_52_17 = all_52_25)
% 201.56/33.45    (13)   ~ (all_52_5 = all_4_0)
% 201.56/33.45    (14)  all_58_0 = all_6_2
% 201.56/33.45    (15)  op(e3, all_6_1) = e1
% 201.56/33.45    (16)   ~ (all_52_17 = all_10_2)
% 201.56/33.45    (17)  op(e3, e0) = all_52_25
% 201.56/33.45    (18)  op(all_52_5, all_52_5) = all_52_4
% 201.56/33.45    (19)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.45    (20)   ~ (all_52_27 = all_52_29)
% 201.56/33.45    (21)  all_58_13 = all_52_15
% 201.56/33.45    (22)  all_58_9 = all_52_25
% 201.56/33.45    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.56/33.45    (24)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.45    (25)  op(e1, e3) = all_52_5
% 201.56/33.45    (26)   ~ (all_6_2 = all_4_0)
% 201.56/33.45    (27)  all_32_2 = all_4_2
% 201.56/33.45    (28)  op(e2, e2) = all_4_2
% 201.56/33.45    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.45    (30)  all_56_5 = all_4_2
% 201.56/33.45    (31)  op(all_10_2, e1) = all_10_1
% 201.56/33.45    (32)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.45    (33)   ~ (all_52_7 = all_6_2)
% 201.56/33.45    (34)  all_58_2 = all_4_0
% 201.56/33.45    (35)   ~ (all_52_15 = e0)
% 201.56/33.45    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.45    (37)  op(all_4_2, e2) = e3
% 201.56/33.45    (38)  all_58_15 = e0
% 201.56/33.45    (39)  all_56_11 = all_52_29
% 201.56/33.45    (40)   ~ (all_4_0 = e3)
% 201.56/33.45    (41)   ~ (all_52_25 = e0)
% 201.56/33.45    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.56/33.45    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.45    (44)   ~ (e2 = e1)
% 201.56/33.45    (45)  op(e0, e0) = e0
% 201.56/33.46    (46)  op(all_10_2, all_10_2) = e1
% 201.56/33.46    (47)  all_58_10 = all_52_27
% 201.56/33.46    (48)  all_56_8 = all_52_5
% 201.56/33.46    (49)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.46    (50)  op(all_52_15, all_52_15) = all_52_14
% 201.56/33.46    (51)  op(all_52_19, all_52_19) = e2
% 201.56/33.46    (52)   ~ (all_52_5 = all_52_7)
% 201.56/33.46    (53)  all_58_12 = all_52_7
% 201.56/33.46    (54)  all_58_2 = all_52_3
% 201.56/33.46    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.46    (56)  all_56_2 = all_52_17
% 201.56/33.46    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.46    (58)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.46    (59)  all_56_7 = all_52_27
% 201.56/33.46    (60)   ~ (e2 = e0)
% 201.56/33.46    (61)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.46    (62)   ~ (all_52_5 = all_52_29)
% 201.56/33.46    (63)   ~ (all_52_29 = e0)
% 201.56/33.46    (64)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.56/33.46    (65)  all_56_6 = all_52_19
% 201.56/33.46    (66)   ~ (all_52_19 = all_52_27)
% 201.56/33.46    (67)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.46    (68)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.46    (69)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.46    (70)  all_56_4 = all_4_0
% 201.56/33.46    (71)  op(e3, e1) = all_52_17
% 201.56/33.46    (72)  op(e0, e3) = all_52_7
% 201.56/33.46    (73)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.46    (74)  all_58_8 = all_10_2
% 201.56/33.46    (75)   ~ (all_52_5 = all_10_2)
% 201.56/33.46    (76)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.46    (77)   ~ (all_52_7 = all_4_0)
% 201.56/33.46    (78)  all_56_12 = all_52_7
% 201.56/33.46    (79)   ~ (all_52_25 = all_6_2)
% 201.56/33.46    (80)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.46    (81)   ~ (all_52_9 = all_4_2)
% 201.56/33.46    (82)   ~ (all_52_5 = all_6_2)
% 201.56/33.46    (83)   ~ (all_52_9 = all_6_2)
% 201.56/33.46    (84)  op(e3, e3) = all_6_2
% 201.56/33.46    (85)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.46    (86)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.46    (87)  all_32_0 = all_4_0
% 201.56/33.46    (88)  all_56_3 = all_52_25
% 201.56/33.46    (89)  all_58_5 = all_52_19
% 201.56/33.46    (90)  op(all_52_17, all_52_17) = e3
% 201.56/33.46    (91)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 201.56/33.46    (92)  all_58_6 = all_52_5
% 201.56/33.46    (93)   ~ (all_4_0 = all_4_2)
% 201.56/33.46    (94)  op(e3, e2) = all_52_9
% 201.56/33.46    (95)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.46    (96)   ~ (all_52_17 = all_6_2)
% 201.56/33.46    (97)   ~ (e1 = e0)
% 201.56/33.46    (98)   ~ (e3 = e2)
% 201.56/33.46    (99)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.46    (100)  op(e1, e1) = all_10_2
% 201.56/33.46    (101)   ~ (all_52_7 = all_52_23)
% 201.56/33.46    (102)  all_58_3 = all_4_2
% 201.56/33.46    (103)  all_56_13 = all_52_15
% 201.56/33.46    (104)   ~ (all_52_19 = all_4_2)
% 201.56/33.46    (105)  op(all_6_2, e3) = all_6_1
% 201.56/33.46    (106)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.46    (107)  all_58_4 = all_52_17
% 201.56/33.46    (108)   ~ (all_52_7 = e0)
% 201.56/33.46  
% 201.56/33.46  Begin of proof
% 201.56/33.46  | 
% 201.56/33.46  | BETA: splitting (42) gives:
% 201.56/33.46  | 
% 201.56/33.46  | Case 1:
% 201.56/33.46  | | 
% 201.56/33.46  | |   (109)  all_56_13 = e3
% 201.56/33.46  | | 
% 201.56/33.46  | | COMBINE_EQS: (103), (109) imply:
% 201.56/33.46  | |   (110)  all_52_15 = e3
% 201.56/33.46  | | 
% 201.56/33.46  | | SIMP: (110) implies:
% 201.56/33.46  | |   (111)  all_52_15 = e3
% 201.56/33.46  | | 
% 201.56/33.46  | | REDUCE: (1), (111) imply:
% 201.56/33.46  | |   (112)   ~ (all_52_23 = e3)
% 201.56/33.46  | | 
% 201.56/33.46  | | SIMP: (112) implies:
% 201.56/33.46  | |   (113)   ~ (all_52_23 = e3)
% 201.56/33.46  | | 
% 201.56/33.46  | | REDUCE: (50), (111) imply:
% 201.56/33.46  | |   (114)  op(e3, e3) = all_52_14
% 201.56/33.46  | | 
% 201.56/33.46  | | GROUND_INST: instantiating (5) with all_6_2, all_52_14, e3, e3, simplifying
% 201.56/33.46  | |              with (84), (114) gives:
% 201.56/33.46  | |   (115)  all_52_14 = all_6_2
% 201.56/33.46  | | 
% 201.56/33.46  | | BETA: splitting (57) gives:
% 201.56/33.46  | | 
% 201.56/33.46  | | Case 1:
% 201.56/33.46  | | | 
% 201.56/33.46  | | |   (116)  all_58_0 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | COMBINE_EQS: (14), (116) imply:
% 201.56/33.46  | | |   (117)  all_6_2 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REF_CLOSE: (4), (5), (15), (84), (105), (117) are inconsistent by
% 201.56/33.46  | | |            sub-proof #310.
% 201.56/33.46  | | | 
% 201.56/33.46  | | Case 2:
% 201.56/33.46  | | | 
% 201.56/33.46  | | |   (118)   ~ (all_58_0 = e3)
% 201.56/33.46  | | |   (119)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REDUCE: (14), (118) imply:
% 201.56/33.46  | | |   (120)   ~ (all_6_2 = e3)
% 201.56/33.46  | | | 
% 201.56/33.46  | | | BETA: splitting (119) gives:
% 201.56/33.46  | | | 
% 201.56/33.46  | | | Case 1:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | |   (121)  all_58_2 = e3
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | REF_CLOSE: (34), (40), (121) are inconsistent by sub-proof #948.
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | Case 2:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | |   (122)   ~ (all_58_2 = e3)
% 201.56/33.46  | | | |   (123)  all_58_6 = e3 | all_58_12 = e3
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | BETA: splitting (123) gives:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | Case 1:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | |   (124)  all_58_6 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | COMBINE_EQS: (92), (124) imply:
% 201.56/33.46  | | | | |   (125)  all_52_5 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | SIMP: (125) implies:
% 201.56/33.46  | | | | |   (126)  all_52_5 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (75), (126) imply:
% 201.56/33.46  | | | | |   (127)   ~ (all_10_2 = e3)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | SIMP: (127) implies:
% 201.56/33.46  | | | | |   (128)   ~ (all_10_2 = e3)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (18), (126) imply:
% 201.56/33.46  | | | | |   (129)  op(e3, e3) = all_52_4
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 201.56/33.46  | | | | |              simplifying with (84), (129) gives:
% 201.56/33.46  | | | | |   (130)  all_52_4 = all_6_2
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | BETA: splitting (99) gives:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | Case 1:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | |   (131)  all_58_4 = e3
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | COMBINE_EQS: (107), (131) imply:
% 201.56/33.46  | | | | | |   (132)  all_52_17 = e3
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | SIMP: (132) implies:
% 201.56/33.46  | | | | | |   (133)  all_52_17 = e3
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | REF_CLOSE: (5), (84), (90), (96), (133) are inconsistent by
% 201.56/33.46  | | | | | |            sub-proof #1280.
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | Case 2:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | |   (134)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | BETA: splitting (134) gives:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | Case 1:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | |   (135)  all_58_5 = e3
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | COMBINE_EQS: (89), (135) imply:
% 201.56/33.46  | | | | | | |   (136)  all_52_19 = e3
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REF_CLOSE: (5), (9), (26), (27), (28), (30), (32), (37), (51),
% 201.56/33.46  | | | | | | |            (61), (68), (70), (84), (86), (87), (91), (93), (104),
% 201.56/33.46  | | | | | | |            (136) are inconsistent by sub-proof #946.
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | Case 2:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | |   (137)  all_58_8 = e3 | all_58_14 = e3
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REF_CLOSE: (3), (74), (113), (128), (137) are inconsistent by
% 201.56/33.46  | | | | | | |            sub-proof #1304.
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | End of split
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | End of split
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | Case 2:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | |   (138)  all_58_12 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (12), (13), (14), (15),
% 201.56/33.46  | | | | |            (16), (17), (19), (20), (22), (24), (25), (26), (27), (28),
% 201.56/33.46  | | | | |            (29), (30), (31), (32), (34), (36), (37), (39), (40), (41),
% 201.56/33.46  | | | | |            (43), (44), (45), (46), (47), (49), (51), (54), (55), (56),
% 201.56/33.46  | | | | |            (58), (59), (60), (61), (62), (63), (65), (66), (67), (68),
% 201.56/33.46  | | | | |            (69), (70), (71), (74), (76), (79), (80), (81), (83), (84),
% 201.56/33.46  | | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 201.56/33.46  | | | | |            (96), (97), (98), (99), (102), (104), (105), (106), (107),
% 201.56/33.46  | | | | |            (113), (120), (138) are inconsistent by sub-proof #261.
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | End of split
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | End of split
% 201.56/33.46  | | | 
% 201.56/33.46  | | End of split
% 201.56/33.46  | | 
% 201.56/33.46  | Case 2:
% 201.56/33.46  | | 
% 201.56/33.46  | |   (139)   ~ (all_56_13 = e3)
% 201.56/33.46  | | 
% 201.56/33.46  | | REDUCE: (103), (139) imply:
% 201.56/33.46  | |   (140)   ~ (all_52_15 = e3)
% 201.56/33.46  | | 
% 201.56/33.46  | | BETA: splitting (95) gives:
% 201.56/33.46  | | 
% 201.56/33.46  | | Case 1:
% 201.56/33.46  | | | 
% 201.56/33.46  | | |   (141)  all_58_12 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | COMBINE_EQS: (53), (141) imply:
% 201.56/33.46  | | |   (142)  all_52_7 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | SIMP: (142) implies:
% 201.56/33.46  | | |   (143)  all_52_7 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REDUCE: (101), (143) imply:
% 201.56/33.46  | | |   (144)   ~ (all_52_23 = e3)
% 201.56/33.46  | | | 
% 201.56/33.46  | | | SIMP: (144) implies:
% 201.56/33.46  | | |   (145)   ~ (all_52_23 = e3)
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REDUCE: (33), (143) imply:
% 201.56/33.46  | | |   (146)   ~ (all_6_2 = e3)
% 201.56/33.46  | | | 
% 201.56/33.46  | | | SIMP: (146) implies:
% 201.56/33.46  | | |   (147)   ~ (all_6_2 = e3)
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REDUCE: (77), (143) imply:
% 201.56/33.46  | | |   (148)   ~ (all_4_0 = e3)
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REDUCE: (11), (143) imply:
% 201.56/33.46  | | |   (149)  op(e3, e3) = all_52_6
% 201.56/33.46  | | | 
% 201.56/33.46  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 201.56/33.46  | | |              with (84), (149) gives:
% 201.56/33.46  | | |   (150)  all_52_6 = all_6_2
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (12), (13), (14), (15),
% 201.56/33.46  | | |            (16), (17), (19), (20), (22), (24), (25), (26), (27), (28),
% 201.56/33.46  | | |            (29), (30), (31), (32), (34), (36), (37), (39), (40), (41),
% 201.56/33.46  | | |            (43), (44), (45), (46), (47), (49), (51), (54), (55), (56),
% 201.56/33.46  | | |            (58), (59), (60), (61), (62), (63), (65), (66), (67), (68),
% 201.56/33.46  | | |            (69), (70), (71), (74), (76), (79), (80), (81), (83), (84),
% 201.56/33.46  | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 201.56/33.46  | | |            (96), (97), (98), (99), (102), (104), (105), (106), (107),
% 201.56/33.46  | | |            (141), (145), (147) are inconsistent by sub-proof #261.
% 201.56/33.46  | | | 
% 201.56/33.46  | | Case 2:
% 201.56/33.46  | | | 
% 201.56/33.46  | | |   (151)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.56/33.46  | | | 
% 201.56/33.46  | | | BETA: splitting (151) gives:
% 201.56/33.46  | | | 
% 201.56/33.46  | | | Case 1:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | |   (152)  all_58_13 = e3
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | REF_CLOSE: (21), (140), (152) are inconsistent by sub-proof #1360.
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | Case 2:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | |   (153)  all_58_14 = e3 | all_58_15 = e3
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | BETA: splitting (153) gives:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | Case 1:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | |   (154)  all_58_14 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | COMBINE_EQS: (3), (154) imply:
% 201.56/33.46  | | | | |   (155)  all_52_23 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | SIMP: (155) implies:
% 201.56/33.46  | | | | |   (156)  all_52_23 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (101), (156) imply:
% 201.56/33.46  | | | | |   (157)   ~ (all_52_7 = e3)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (8), (156) imply:
% 201.56/33.46  | | | | |   (158)  op(e3, e3) = e0
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | GROUND_INST: instantiating (5) with all_6_2, e0, e3, e3, simplifying
% 201.56/33.46  | | | | |              with (84), (158) gives:
% 201.56/33.46  | | | | |   (159)  all_6_2 = e0
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (82), (159) imply:
% 201.56/33.46  | | | | |   (160)   ~ (all_52_5 = e0)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (26), (159) imply:
% 201.56/33.46  | | | | |   (161)   ~ (all_4_0 = e0)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | SIMP: (161) implies:
% 201.56/33.46  | | | | |   (162)   ~ (all_4_0 = e0)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (105), (159) imply:
% 201.56/33.46  | | | | |   (163)  op(e0, e3) = all_6_1
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | BETA: splitting (10) gives:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | Case 1:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | |   (164)  all_56_12 = e3
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | REF_CLOSE: (78), (157), (164) are inconsistent by sub-proof #1383.
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | Case 2:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | |   (165)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | BETA: splitting (64) gives:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | Case 1:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | |   (166)  all_58_12 = e1
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | COMBINE_EQS: (53), (166) imply:
% 201.56/33.46  | | | | | | |   (167)  all_52_7 = e1
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | SIMP: (167) implies:
% 201.56/33.46  | | | | | | |   (168)  all_52_7 = e1
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REDUCE: (52), (168) imply:
% 201.56/33.46  | | | | | | |   (169)   ~ (all_52_5 = e1)
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REDUCE: (11), (168) imply:
% 201.56/33.46  | | | | | | |   (170)  op(e1, e1) = all_52_6
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REDUCE: (72), (168) imply:
% 201.56/33.46  | | | | | | |   (171)  op(e0, e3) = e1
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | BETA: splitting (73) gives:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | Case 1:
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | |   (172)  all_56_8 = e3
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | COMBINE_EQS: (48), (172) imply:
% 201.56/33.46  | | | | | | | |   (173)  all_52_5 = e3
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | SIMP: (173) implies:
% 201.56/33.46  | | | | | | | |   (174)  all_52_5 = e3
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | REDUCE: (75), (174) imply:
% 201.56/33.46  | | | | | | | |   (175)   ~ (all_10_2 = e3)
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | SIMP: (175) implies:
% 201.56/33.46  | | | | | | | |   (176)   ~ (all_10_2 = e3)
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | GROUND_INST: instantiating (5) with e1, all_6_1, e3, e0,
% 201.56/33.46  | | | | | | | |              simplifying with (163), (171) gives:
% 201.56/33.46  | | | | | | | |   (177)  all_6_1 = e1
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_6, e1, e1,
% 201.56/33.46  | | | | | | | |              simplifying with (100), (170) gives:
% 201.56/33.46  | | | | | | | |   (178)  all_52_6 = all_10_2
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | REDUCE: (15), (177) imply:
% 201.56/33.46  | | | | | | | |   (179)  op(e3, e1) = e1
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | GROUND_INST: instantiating (5) with all_52_17, e1, e1, e3,
% 201.56/33.46  | | | | | | | |              simplifying with (71), (179) gives:
% 201.56/33.46  | | | | | | | |   (180)  all_52_17 = e1
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | REDUCE: (90), (180) imply:
% 201.56/33.46  | | | | | | | |   (181)  op(e1, e1) = e3
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | REF_CLOSE: (5), (100), (176), (181) are inconsistent by
% 201.56/33.46  | | | | | | | |            sub-proof #1368.
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | Case 2:
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | |   (182)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | | REF_CLOSE: (9), (13), (23), (48), (68), (70), (92), (160),
% 201.56/33.46  | | | | | | | |            (162), (169), (182) are inconsistent by sub-proof
% 201.56/33.46  | | | | | | | |            #672.
% 201.56/33.46  | | | | | | | | 
% 201.56/33.46  | | | | | | | End of split
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | Case 2:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | |   (183)   ~ (all_58_12 = e1)
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REDUCE: (53), (183) imply:
% 201.56/33.46  | | | | | | |   (184)   ~ (all_52_7 = e1)
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REF_CLOSE: (5), (9), (27), (28), (30), (37), (61), (68), (70),
% 201.56/33.46  | | | | | | |            (77), (78), (81), (86), (87), (91), (93), (94), (108),
% 201.56/33.46  | | | | | | |            (165), (184) are inconsistent by sub-proof #966.
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | End of split
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | End of split
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | Case 2:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | |   (185)  all_58_15 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REF_CLOSE: (7), (38), (185) are inconsistent by sub-proof #1350.
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | End of split
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | End of split
% 201.56/33.46  | | | 
% 201.56/33.46  | | End of split
% 201.56/33.46  | | 
% 201.56/33.46  | End of split
% 201.56/33.46  | 
% 201.56/33.46  End of proof
% 201.56/33.46  
% 201.56/33.46  Sub-proof #261 shows that the following formulas are inconsistent:
% 201.56/33.46  ----------------------------------------------------------------
% 201.56/33.46    (1)   ~ (all_52_25 = all_52_27)
% 201.56/33.46    (2)  all_58_14 = all_52_23
% 201.56/33.46    (3)   ~ (e3 = e1)
% 201.56/33.46    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.46    (5)  all_58_1 = all_52_9
% 201.56/33.46    (6)   ~ (e3 = e0)
% 201.56/33.46    (7)   ~ (all_4_0 = e1)
% 201.56/33.46    (8)   ~ (all_52_17 = all_52_25)
% 201.56/33.46    (9)   ~ (all_52_5 = all_4_0)
% 201.56/33.46    (10)  all_58_0 = all_6_2
% 201.56/33.46    (11)  op(e3, all_6_1) = e1
% 201.56/33.46    (12)   ~ (all_52_17 = all_10_2)
% 201.56/33.46    (13)  op(e3, e0) = all_52_25
% 201.56/33.46    (14)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.56/33.46    (15)   ~ (all_52_27 = all_52_29)
% 201.56/33.46    (16)  all_58_9 = all_52_25
% 201.56/33.46    (17)  op(all_52_27, all_52_27) = all_52_26
% 201.56/33.46    (18)  op(e1, e3) = all_52_5
% 201.56/33.46    (19)   ~ (all_6_2 = all_4_0)
% 201.56/33.46    (20)  all_32_2 = all_4_2
% 201.56/33.46    (21)  op(e2, e2) = all_4_2
% 201.56/33.46    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.46    (23)  all_56_5 = all_4_2
% 201.56/33.46    (24)  op(all_10_2, e1) = all_10_1
% 201.56/33.46    (25)  op(all_6_2, all_6_2) = all_52_0
% 201.56/33.46    (26)  all_58_2 = all_4_0
% 201.56/33.46    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.56/33.46    (28)  op(all_4_2, e2) = e3
% 201.56/33.46    (29)  all_56_11 = all_52_29
% 201.56/33.46    (30)   ~ (all_4_0 = e3)
% 201.56/33.46    (31)   ~ (all_52_25 = e0)
% 201.56/33.46    (32)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.56/33.46    (33)   ~ (all_6_2 = e3)
% 201.56/33.46    (34)   ~ (e2 = e1)
% 201.56/33.46    (35)  op(e0, e0) = e0
% 201.56/33.46    (36)  op(all_10_2, all_10_2) = e1
% 201.56/33.46    (37)  all_58_10 = all_52_27
% 201.56/33.46    (38)  op(all_52_9, all_52_9) = all_52_8
% 201.56/33.46    (39)  op(all_52_19, all_52_19) = e2
% 201.56/33.46    (40)  all_58_2 = all_52_3
% 201.56/33.46    (41)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.56/33.46    (42)  all_56_2 = all_52_17
% 201.56/33.46    (43)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.46    (44)  all_56_7 = all_52_27
% 201.56/33.46    (45)   ~ (e2 = e0)
% 201.56/33.46    (46)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.56/33.46    (47)   ~ (all_52_23 = e3)
% 201.56/33.46    (48)   ~ (all_52_5 = all_52_29)
% 201.56/33.46    (49)   ~ (all_52_29 = e0)
% 201.56/33.46    (50)  all_56_6 = all_52_19
% 201.56/33.46    (51)   ~ (all_52_19 = all_52_27)
% 201.56/33.46    (52)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.46    (53)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.56/33.46    (54)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.46    (55)  all_56_4 = all_4_0
% 201.56/33.46    (56)  op(e3, e1) = all_52_17
% 201.56/33.46    (57)  all_58_8 = all_10_2
% 201.56/33.46    (58)  op(all_52_29, all_52_29) = all_52_28
% 201.56/33.46    (59)   ~ (all_52_25 = all_6_2)
% 201.56/33.46    (60)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.56/33.46    (61)   ~ (all_52_9 = all_4_2)
% 201.56/33.46    (62)   ~ (all_52_9 = all_6_2)
% 201.56/33.46    (63)  op(e3, e3) = all_6_2
% 201.56/33.46    (64)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.56/33.46    (65)  op(all_4_2, all_4_2) = all_52_10
% 201.56/33.46    (66)  all_32_0 = all_4_0
% 201.56/33.46    (67)  all_56_3 = all_52_25
% 201.56/33.46    (68)  all_58_5 = all_52_19
% 201.56/33.46    (69)  op(all_52_17, all_52_17) = e3
% 201.56/33.46    (70)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 201.56/33.46    (71)  all_58_6 = all_52_5
% 201.56/33.46    (72)   ~ (all_4_0 = all_4_2)
% 201.56/33.46    (73)  op(e3, e2) = all_52_9
% 201.56/33.46    (74)   ~ (all_52_17 = all_6_2)
% 201.56/33.46    (75)   ~ (e1 = e0)
% 201.56/33.46    (76)   ~ (e3 = e2)
% 201.56/33.46    (77)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.56/33.46    (78)  all_58_12 = e3
% 201.56/33.46    (79)  all_58_3 = all_4_2
% 201.56/33.46    (80)   ~ (all_52_19 = all_4_2)
% 201.56/33.46    (81)  op(all_6_2, e3) = all_6_1
% 201.56/33.46    (82)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.46    (83)  all_58_4 = all_52_17
% 201.56/33.46  
% 201.56/33.46  Begin of proof
% 201.56/33.46  | 
% 201.56/33.46  | BETA: splitting (43) gives:
% 201.56/33.46  | 
% 201.56/33.46  | Case 1:
% 201.56/33.46  | | 
% 201.56/33.46  | |   (84)  all_58_0 = e1
% 201.56/33.46  | | 
% 201.56/33.46  | | REF_CLOSE: (4), (6), (10), (11), (13), (18), (22), (34), (40), (45), (54),
% 201.56/33.46  | |            (59), (62), (71), (73), (75), (76), (78), (81), (82), (84) are
% 201.56/33.46  | |            inconsistent by sub-proof #279.
% 201.56/33.46  | | 
% 201.56/33.46  | Case 2:
% 201.56/33.46  | | 
% 201.56/33.46  | |   (85)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.46  | | 
% 201.56/33.46  | | BETA: splitting (85) gives:
% 201.56/33.46  | | 
% 201.56/33.46  | | Case 1:
% 201.56/33.46  | | | 
% 201.56/33.46  | | |   (86)  all_58_2 = e1
% 201.56/33.46  | | | 
% 201.56/33.46  | | | REF_CLOSE: (7), (26), (86) are inconsistent by sub-proof #967.
% 201.56/33.46  | | | 
% 201.56/33.46  | | Case 2:
% 201.56/33.46  | | | 
% 201.56/33.46  | | |   (87)  all_58_6 = e1 | all_58_12 = e1
% 201.56/33.46  | | | 
% 201.56/33.46  | | | BETA: splitting (87) gives:
% 201.56/33.46  | | | 
% 201.56/33.46  | | | Case 1:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | |   (88)  all_58_6 = e1
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | COMBINE_EQS: (71), (88) imply:
% 201.56/33.46  | | | |   (89)  all_52_5 = e1
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | SIMP: (89) implies:
% 201.56/33.46  | | | |   (90)  all_52_5 = e1
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | REDUCE: (48), (90) imply:
% 201.56/33.46  | | | |   (91)   ~ (all_52_29 = e1)
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | SIMP: (91) implies:
% 201.56/33.46  | | | |   (92)   ~ (all_52_29 = e1)
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | REDUCE: (9), (90) imply:
% 201.56/33.46  | | | |   (93)   ~ (all_4_0 = e1)
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | BETA: splitting (52) gives:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | Case 1:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | |   (94)  all_56_11 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | COMBINE_EQS: (29), (94) imply:
% 201.56/33.46  | | | | |   (95)  all_52_29 = e3
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REDUCE: (15), (95) imply:
% 201.56/33.46  | | | | |   (96)   ~ (all_52_27 = e3)
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | REF_CLOSE: (4), (7), (19), (20), (21), (23), (25), (26), (27), (28),
% 201.56/33.46  | | | | |            (30), (37), (39), (41), (46), (50), (53), (55), (61), (63),
% 201.56/33.46  | | | | |            (65), (66), (68), (70), (72), (73), (79), (80), (96) are
% 201.56/33.46  | | | | |            inconsistent by sub-proof #944.
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | Case 2:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | |   (97)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | BETA: splitting (97) gives:
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | | Case 1:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | |   (98)  all_56_11 = e2
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | COMBINE_EQS: (29), (98) imply:
% 201.56/33.46  | | | | | |   (99)  all_52_29 = e2
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | REDUCE: (58), (99) imply:
% 201.56/33.46  | | | | | |   (100)  op(e2, e2) = all_52_28
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_28, e2, e2,
% 201.56/33.46  | | | | | |              simplifying with (21), (100) gives:
% 201.56/33.46  | | | | | |   (101)  all_52_28 = all_4_2
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | BETA: splitting (14) gives:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | Case 1:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | |   (102)  all_56_7 = e3
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (10), (12), (16), (17), (24),
% 201.56/33.46  | | | | | | |            (31), (32), (33), (35), (36), (38), (42), (44), (47),
% 201.56/33.46  | | | | | | |            (51), (56), (57), (59), (60), (63), (64), (67), (68),
% 201.56/33.46  | | | | | | |            (69), (74), (77), (83), (102) are inconsistent by
% 201.56/33.46  | | | | | | |            sub-proof #1274.
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | Case 2:
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | |   (103)   ~ (all_56_7 = e3)
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REDUCE: (44), (103) imply:
% 201.56/33.46  | | | | | | |   (104)   ~ (all_52_27 = e3)
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | | REF_CLOSE: (4), (7), (19), (20), (21), (23), (25), (26), (27),
% 201.56/33.46  | | | | | | |            (28), (30), (37), (39), (41), (46), (50), (53), (55),
% 201.56/33.46  | | | | | | |            (61), (63), (65), (66), (68), (70), (72), (73), (79),
% 201.56/33.46  | | | | | | |            (80), (104) are inconsistent by sub-proof #944.
% 201.56/33.46  | | | | | | | 
% 201.56/33.46  | | | | | | End of split
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | Case 2:
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | |   (105)  all_56_11 = e1 | all_56_11 = e0
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | | REF_CLOSE: (29), (49), (92), (105) are inconsistent by sub-proof
% 201.56/33.46  | | | | | |            #1001.
% 201.56/33.46  | | | | | | 
% 201.56/33.46  | | | | | End of split
% 201.56/33.46  | | | | | 
% 201.56/33.46  | | | | End of split
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | Case 2:
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | |   (106)  all_58_12 = e1
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | | REF_CLOSE: (3), (78), (106) are inconsistent by sub-proof #894.
% 201.56/33.46  | | | | 
% 201.56/33.46  | | | End of split
% 201.56/33.46  | | | 
% 201.56/33.46  | | End of split
% 201.56/33.46  | | 
% 201.56/33.46  | End of split
% 201.56/33.46  | 
% 201.56/33.46  End of proof
% 201.56/33.46  
% 201.56/33.46  Sub-proof #262 shows that the following formulas are inconsistent:
% 201.56/33.46  ----------------------------------------------------------------
% 201.56/33.46    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.46    (2)  all_58_1 = all_52_9
% 201.56/33.46    (3)   ~ (all_52_7 = all_52_15)
% 201.56/33.46    (4)  op(all_52_7, all_52_7) = all_52_6
% 201.56/33.46    (5)  all_58_0 = all_6_2
% 201.56/33.46    (6)  op(e3, all_6_1) = e1
% 201.56/33.46    (7)  op(e3, e0) = all_52_25
% 201.56/33.46    (8)  all_58_13 = all_52_15
% 201.56/33.46    (9)  op(all_52_13, all_52_13) = e1
% 201.56/33.46    (10)  op(e1, e3) = all_52_5
% 201.56/33.46    (11)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.46    (12)  op(all_4_2, e2) = e3
% 201.56/33.46    (13)  all_56_9 = all_52_13
% 201.56/33.46    (14)   ~ (e2 = e1)
% 201.56/33.46    (15)  all_58_7 = all_52_13
% 201.56/33.46    (16)  all_58_12 = all_52_7
% 201.56/33.46    (17)  all_58_2 = all_52_3
% 201.56/33.46    (18)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.56/33.46    (19)   ~ (e2 = e0)
% 201.56/33.46    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.56/33.46    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.56/33.46    (22)   ~ (all_52_25 = all_6_2)
% 201.56/33.46    (23)   ~ (all_52_9 = all_4_2)
% 201.56/33.46    (24)   ~ (all_52_9 = all_6_2)
% 201.56/33.46    (25)  op(e3, e3) = all_6_2
% 201.56/33.46    (26)  all_58_6 = all_52_5
% 201.56/33.46    (27)  op(e3, e2) = all_52_9
% 201.56/33.46    (28)   ~ (e1 = e0)
% 201.56/33.46    (29)   ~ (e3 = e2)
% 201.56/33.46    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.56/33.46    (31)  all_58_12 = e3
% 201.56/33.46    (32)  op(all_52_9, all_52_9) = e3
% 201.56/33.46    (33)  all_58_3 = all_4_2
% 201.56/33.46    (34)  op(all_6_2, e3) = all_6_1
% 201.56/33.46    (35)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.56/33.46    (36)   ~ (all_52_7 = e0)
% 201.56/33.46  
% 201.56/33.46  Begin of proof
% 201.56/33.46  | 
% 201.56/33.46  | COMBINE_EQS: (16), (31) imply:
% 201.56/33.46  |   (37)  all_52_7 = e3
% 201.56/33.46  | 
% 201.56/33.46  | SIMP: (37) implies:
% 201.56/33.46  |   (38)  all_52_7 = e3
% 201.56/33.46  | 
% 201.56/33.46  | REDUCE: (3), (38) imply:
% 201.56/33.46  |   (39)   ~ (all_52_15 = e3)
% 201.56/33.46  | 
% 201.56/33.46  | SIMP: (39) implies:
% 201.56/33.46  |   (40)   ~ (all_52_15 = e3)
% 201.56/33.46  | 
% 201.56/33.46  | REDUCE: (36), (38) imply:
% 201.56/33.46  |   (41)   ~ (e3 = e0)
% 201.56/33.46  | 
% 201.56/33.46  | REDUCE: (4), (38) imply:
% 201.56/33.46  |   (42)  op(e3, e3) = all_52_6
% 201.56/33.46  | 
% 201.56/33.46  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 201.56/33.46  |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 201.56/33.46  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (40), (41),
% 201.56/33.46  |            (42) are inconsistent by sub-proof #263.
% 201.56/33.46  | 
% 201.56/33.46  End of proof
% 201.56/33.46  
% 201.56/33.46  Sub-proof #263 shows that the following formulas are inconsistent:
% 201.56/33.46  ----------------------------------------------------------------
% 201.56/33.46    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.56/33.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.56/33.46    (2)  all_58_1 = all_52_9
% 201.56/33.46    (3)   ~ (e3 = e0)
% 201.56/33.46    (4)  all_58_0 = all_6_2
% 201.56/33.46    (5)  op(e3, all_6_1) = e1
% 201.56/33.46    (6)  op(e3, e3) = all_52_6
% 201.56/33.46    (7)  op(e3, e0) = all_52_25
% 201.56/33.46    (8)  all_58_13 = all_52_15
% 201.56/33.46    (9)  op(all_52_13, all_52_13) = e1
% 201.56/33.46    (10)   ~ (all_52_15 = e3)
% 201.56/33.46    (11)  op(e1, e3) = all_52_5
% 201.56/33.46    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.56/33.46    (13)  op(all_4_2, e2) = e3
% 201.56/33.46    (14)  all_56_9 = all_52_13
% 201.56/33.46    (15)   ~ (e2 = e1)
% 201.56/33.46    (16)  all_58_7 = all_52_13
% 201.56/33.46    (17)  all_58_2 = all_52_3
% 201.56/33.46    (18)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.76/33.46    (19)   ~ (e2 = e0)
% 201.76/33.46    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.76/33.46    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.76/33.46    (22)   ~ (all_52_25 = all_6_2)
% 201.76/33.46    (23)   ~ (all_52_9 = all_4_2)
% 201.76/33.46    (24)   ~ (all_52_9 = all_6_2)
% 201.76/33.46    (25)  op(e3, e3) = all_6_2
% 201.76/33.46    (26)  all_58_6 = all_52_5
% 201.76/33.47    (27)  op(e3, e2) = all_52_9
% 201.76/33.47    (28)   ~ (e1 = e0)
% 201.76/33.47    (29)   ~ (e3 = e2)
% 201.76/33.47    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.76/33.47    (31)  all_58_12 = e3
% 201.76/33.47    (32)  op(all_52_9, all_52_9) = e3
% 201.76/33.47    (33)  all_58_3 = all_4_2
% 201.76/33.47    (34)  op(all_6_2, e3) = all_6_1
% 201.76/33.47    (35)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.76/33.47  
% 201.76/33.47  Begin of proof
% 201.76/33.47  | 
% 201.76/33.47  | BETA: splitting (18) gives:
% 201.76/33.47  | 
% 201.76/33.47  | Case 1:
% 201.76/33.47  | | 
% 201.76/33.47  | |   (36)  all_58_0 = e1
% 201.76/33.47  | | 
% 201.76/33.47  | | REF_CLOSE: (1), (3), (4), (5), (7), (11), (12), (15), (17), (19), (20),
% 201.76/33.47  | |            (22), (24), (26), (27), (28), (29), (31), (34), (35), (36) are
% 201.76/33.47  | |            inconsistent by sub-proof #279.
% 201.76/33.47  | | 
% 201.76/33.47  | Case 2:
% 201.76/33.47  | | 
% 201.76/33.47  | |   (37)   ~ (all_58_0 = e1)
% 201.76/33.47  | | 
% 201.76/33.47  | | REDUCE: (4), (37) imply:
% 201.76/33.47  | |   (38)   ~ (all_6_2 = e1)
% 201.76/33.47  | | 
% 201.76/33.47  | | REF_CLOSE: (1), (2), (6), (8), (9), (10), (13), (14), (16), (21), (23),
% 201.76/33.47  | |            (24), (25), (27), (30), (32), (33), (38) are inconsistent by
% 201.76/33.47  | |            sub-proof #932.
% 201.76/33.47  | | 
% 201.76/33.47  | End of split
% 201.76/33.47  | 
% 201.76/33.47  End of proof
% 201.76/33.47  
% 201.76/33.47  Sub-proof #264 shows that the following formulas are inconsistent:
% 201.76/33.47  ----------------------------------------------------------------
% 201.76/33.47    (1)   ~ (all_52_15 = all_52_23)
% 201.76/33.47    (2)   ~ (all_52_25 = all_52_27)
% 201.76/33.47    (3)  all_58_14 = all_52_23
% 201.76/33.47    (4)   ~ (e3 = e1)
% 201.76/33.47    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.76/33.47    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.76/33.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.76/33.47    (7)  all_58_1 = all_52_9
% 201.76/33.47    (8)   ~ (all_52_9 = all_52_13)
% 201.76/33.47    (9)   ~ (e3 = e0)
% 201.76/33.47    (10)  op(e2, e3) = all_52_3
% 201.76/33.47    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.76/33.47    (12)   ~ (all_52_7 = all_52_15)
% 201.76/33.47    (13)   ~ (all_52_3 = all_52_19)
% 201.76/33.47    (14)  op(all_52_7, all_52_7) = all_52_6
% 201.76/33.47    (15)   ~ (all_52_17 = all_52_25)
% 201.76/33.47    (16)   ~ (all_52_3 = all_6_2)
% 201.76/33.47    (17)  all_58_0 = all_6_2
% 201.76/33.47    (18)  op(all_14_2, e0) = all_14_1
% 201.76/33.47    (19)  all_56_4 = all_52_3
% 201.76/33.47    (20)  op(e3, all_6_1) = e1
% 201.76/33.47    (21)   ~ (all_52_17 = all_10_2)
% 201.76/33.47    (22)   ~ (all_10_0 = e3)
% 201.76/33.47    (23)  all_40_2 = all_10_2
% 201.76/33.47    (24)  op(e3, e0) = all_52_25
% 201.76/33.47    (25)  op(all_52_5, all_52_5) = all_52_4
% 201.76/33.47    (26)  op(all_52_19, all_52_19) = all_52_18
% 201.76/33.47    (27)   ~ (all_52_27 = all_52_29)
% 201.76/33.47    (28)  all_58_13 = all_52_15
% 201.76/33.47    (29)  op(all_10_2, all_10_2) = all_52_20
% 201.76/33.47    (30)  all_58_9 = all_52_25
% 201.76/33.47    (31)   ~ (all_52_29 = all_14_2)
% 201.76/33.47    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.76/33.47    (33)  op(all_52_27, all_52_27) = all_52_26
% 201.76/33.47    (34)  op(e1, e3) = all_52_5
% 201.76/33.47    (35)  op(e2, e2) = all_4_2
% 201.76/33.47    (36)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.76/33.47    (37)  all_58_7 = all_10_0
% 201.76/33.47    (38)   ~ (all_52_3 = all_52_5)
% 201.76/33.47    (39)  all_58_11 = all_52_29
% 201.76/33.47    (40)  all_56_5 = all_4_2
% 201.76/33.47    (41)   ~ (all_52_25 = all_14_2)
% 201.76/33.47    (42)   ~ (all_52_9 = all_52_15)
% 201.76/33.47    (43)   ~ (all_52_3 = all_52_27)
% 201.76/33.47    (44)  op(all_10_2, e1) = all_10_1
% 201.76/33.47    (45)  all_46_2 = all_6_2
% 201.76/33.47    (46)  op(all_6_2, all_6_2) = all_52_0
% 201.76/33.47    (47)   ~ (all_52_7 = all_6_2)
% 201.76/33.47    (48)  op(e0, e0) = all_14_2
% 201.76/33.47    (49)  all_56_15 = all_14_2
% 201.76/33.47    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.76/33.47    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.76/33.47    (52)   ~ (all_58_15 = e0)
% 201.76/33.47    (53)  all_56_11 = all_52_29
% 201.76/33.47    (54)   ~ (all_10_0 = e2)
% 201.76/33.47    (55)   ~ (all_4_1 = e1)
% 201.76/33.47    (56)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.76/33.47    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.76/33.47    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.76/33.47    (59)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.76/33.47    (60)   ~ (e2 = e1)
% 201.76/33.47    (61)  all_58_10 = all_52_27
% 201.76/33.47    (62)  all_56_8 = all_52_5
% 201.76/33.47    (63)  op(all_52_9, all_52_9) = all_52_8
% 201.76/33.47    (64)  op(all_52_15, all_52_15) = all_52_14
% 201.76/33.47    (65)  all_56_9 = all_10_0
% 201.76/33.47    (66)   ~ (all_52_25 = all_52_29)
% 201.76/33.47    (67)   ~ (all_52_29 = all_10_2)
% 201.76/33.47    (68)  all_58_7 = all_52_13
% 201.76/33.47    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.76/33.47    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.76/33.47    (71)   ~ (all_52_5 = all_52_7)
% 201.76/33.47    (72)  all_58_12 = all_52_7
% 201.76/33.47    (73)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.76/33.47    (74)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.76/33.47    (75)   ~ (all_52_7 = all_14_2)
% 201.76/33.47    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 201.76/33.47    (77)  all_58_2 = all_52_3
% 201.76/33.47    (78)  all_56_2 = all_52_17
% 201.76/33.47    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.76/33.47    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.76/33.47    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.76/33.47    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.76/33.47    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.76/33.47    (84)   ~ (e2 = e0)
% 201.76/33.47    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.76/33.47    (86)  op(all_4_2, e2) = all_4_1
% 201.76/33.47    (87)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.76/33.47    (88)   ~ (all_52_5 = all_52_29)
% 201.76/33.47    (89)   ~ (all_52_15 = all_14_2)
% 201.76/33.47    (90)   ~ (all_52_19 = all_52_27)
% 201.76/33.47    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.76/33.47    (92)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.76/33.47    (93)  op(e3, e1) = all_52_17
% 201.76/33.47    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.76/33.47    (95)  op(e0, e3) = all_52_7
% 201.76/33.47    (96)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.76/33.47    (97)   ~ (all_52_9 = all_52_25)
% 201.76/33.47    (98)  all_58_15 = all_14_2
% 201.76/33.47    (99)   ~ (all_52_19 = all_10_2)
% 201.76/33.47    (100)  op(all_52_23, all_52_23) = all_52_22
% 201.76/33.47    (101)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.76/33.47    (102)   ~ (all_10_0 = all_10_2)
% 201.76/33.47    (103)  all_58_8 = all_10_2
% 201.76/33.47    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.76/33.47    (105)   ~ (all_52_5 = all_10_2)
% 201.76/33.47    (106)  op(all_52_29, all_52_29) = all_52_28
% 201.76/33.47    (107)   ~ (all_52_23 = all_14_2)
% 201.76/33.47    (108)  all_56_12 = all_52_7
% 201.76/33.47    (109)  op(all_52_17, all_52_17) = all_52_16
% 201.76/33.47    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.76/33.47    (111)   ~ (all_52_25 = all_6_2)
% 201.76/33.47    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.76/33.47    (113)   ~ (all_52_9 = all_4_2)
% 201.76/33.47    (114)   ~ (all_52_5 = all_6_2)
% 201.76/33.47    (115)   ~ (all_52_9 = all_6_2)
% 201.76/33.47    (116)   ~ (all_52_13 = all_52_15)
% 201.76/33.47    (117)  all_56_0 = all_6_2
% 201.76/33.47    (118)  op(e3, e3) = all_6_2
% 201.76/33.47    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.76/33.47    (120)   ~ (all_52_27 = all_14_2)
% 201.76/33.47    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.76/33.47    (122)  all_56_14 = all_52_23
% 201.76/33.47    (123)  op(all_4_2, all_4_2) = all_52_10
% 201.76/33.47    (124)  all_40_0 = all_10_0
% 201.76/33.47    (125)  all_56_3 = all_52_25
% 201.76/33.47    (126)   ~ (all_52_3 = all_52_7)
% 201.76/33.47    (127)  op(all_14_2, all_14_2) = all_52_30
% 201.76/33.47    (128)  all_58_5 = all_52_19
% 201.76/33.47    (129)  all_56_1 = all_52_9
% 201.76/33.47    (130)   ~ (all_52_15 = all_4_2)
% 201.76/33.47    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.76/33.47           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.76/33.47           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.76/33.47           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.76/33.47    (132)   ~ (all_52_27 = all_4_2)
% 201.76/33.47    (133)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 201.76/33.47             all_58_13 = e0 | all_58_14 = e0)
% 201.76/33.47    (134)  all_58_6 = all_52_5
% 201.76/33.47    (135)  op(all_10_2, e1) = e2
% 201.76/33.47    (136)  op(e3, e2) = all_52_9
% 201.76/33.47    (137)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.76/33.47    (138)   ~ (all_52_17 = all_6_2)
% 201.76/33.47    (139)   ~ (e1 = e0)
% 201.76/33.47    (140)   ~ (e3 = e2)
% 201.76/33.47    (141)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.76/33.47    (142)   ~ (all_52_9 = all_52_17)
% 201.76/33.47    (143)  all_56_10 = all_10_2
% 201.76/33.47    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.76/33.47    (145)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.76/33.47    (146)  all_46_1 = all_6_1
% 201.76/33.47    (147)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.76/33.47    (148)  op(all_52_13, all_52_13) = all_52_12
% 201.76/33.47    (149)  op(all_10_0, all_10_0) = all_52_12
% 201.76/33.47    (150)  op(e1, e1) = all_10_2
% 201.76/33.47    (151)   ~ (all_52_23 = all_10_2)
% 201.76/33.47    (152)   ~ (all_52_7 = all_52_23)
% 201.76/33.47    (153)   ~ (all_52_17 = all_52_19)
% 201.76/33.47    (154)   ~ (all_52_5 = all_10_0)
% 201.76/33.47    (155)  all_58_3 = all_4_2
% 201.76/33.47    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.76/33.47    (157)  all_56_13 = all_52_15
% 201.76/33.47    (158)   ~ (all_52_3 = all_4_2)
% 201.76/33.47    (159)   ~ (all_52_9 = all_10_0)
% 201.76/33.47    (160)   ~ (all_52_19 = all_4_2)
% 201.76/33.47    (161)   ~ (all_52_17 = all_52_23)
% 201.76/33.47    (162)  op(all_6_2, e3) = all_6_1
% 201.76/33.47    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.76/33.47    (164)  all_58_4 = all_52_17
% 201.76/33.47    (165)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.76/33.47    (166)  op(all_52_25, all_52_25) = all_52_24
% 201.76/33.47  
% 201.76/33.47  Begin of proof
% 201.76/33.47  | 
% 201.76/33.47  | ALPHA: (133) implies:
% 201.76/33.47  |   (167)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.76/33.47  | 
% 201.76/33.47  | REDUCE: (52), (98) imply:
% 201.76/33.47  |   (168)   ~ (all_14_2 = e0)
% 201.76/33.47  | 
% 201.76/33.47  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.76/33.47  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.76/33.47  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 201.76/33.47  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 201.76/33.47  |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 201.76/33.47  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 201.76/33.47  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 201.76/33.47  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 201.76/33.47  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 201.76/33.47  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 201.76/33.47  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 201.76/33.47  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 201.76/33.47  |            (129), (130), (131), (132), (134), (135), (136), (137), (138),
% 201.76/33.47  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 201.76/33.47  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 201.76/33.47  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 201.76/33.47  |            (166), (167), (168) are inconsistent by sub-proof #265.
% 201.76/33.47  | 
% 201.76/33.47  End of proof
% 201.76/33.47  
% 201.76/33.47  Sub-proof #265 shows that the following formulas are inconsistent:
% 201.76/33.47  ----------------------------------------------------------------
% 201.76/33.47    (1)   ~ (all_52_15 = all_52_23)
% 201.76/33.47    (2)   ~ (all_52_25 = all_52_27)
% 201.76/33.47    (3)  all_58_14 = all_52_23
% 201.76/33.47    (4)   ~ (e3 = e1)
% 201.76/33.47    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.76/33.47    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.76/33.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.76/33.47    (7)  all_58_1 = all_52_9
% 201.76/33.47    (8)   ~ (all_52_9 = all_52_13)
% 201.76/33.47    (9)   ~ (e3 = e0)
% 201.76/33.47    (10)  op(e2, e3) = all_52_3
% 201.76/33.47    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.76/33.47    (12)   ~ (all_52_7 = all_52_15)
% 201.76/33.47    (13)   ~ (all_52_3 = all_52_19)
% 201.76/33.47    (14)  op(all_52_7, all_52_7) = all_52_6
% 201.76/33.47    (15)   ~ (all_52_17 = all_52_25)
% 201.76/33.47    (16)   ~ (all_52_3 = all_6_2)
% 201.76/33.47    (17)  all_58_0 = all_6_2
% 201.76/33.47    (18)  op(all_14_2, e0) = all_14_1
% 201.76/33.47    (19)  all_56_4 = all_52_3
% 201.76/33.47    (20)  op(e3, all_6_1) = e1
% 201.76/33.47    (21)   ~ (all_52_17 = all_10_2)
% 201.76/33.47    (22)   ~ (all_10_0 = e3)
% 201.76/33.47    (23)  all_40_2 = all_10_2
% 201.76/33.47    (24)  op(e3, e0) = all_52_25
% 201.76/33.47    (25)  op(all_52_5, all_52_5) = all_52_4
% 201.76/33.47    (26)  op(all_52_19, all_52_19) = all_52_18
% 201.76/33.47    (27)   ~ (all_52_27 = all_52_29)
% 201.76/33.47    (28)  all_58_13 = all_52_15
% 201.76/33.47    (29)  op(all_10_2, all_10_2) = all_52_20
% 201.76/33.47    (30)  all_58_9 = all_52_25
% 201.76/33.47    (31)   ~ (all_52_29 = all_14_2)
% 201.76/33.47    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.76/33.47    (33)  op(all_52_27, all_52_27) = all_52_26
% 201.76/33.47    (34)  op(e1, e3) = all_52_5
% 201.76/33.47    (35)  op(e2, e2) = all_4_2
% 201.76/33.47    (36)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.76/33.47    (37)  all_58_7 = all_10_0
% 201.76/33.47    (38)   ~ (all_52_3 = all_52_5)
% 201.76/33.47    (39)  all_58_11 = all_52_29
% 201.76/33.47    (40)  all_56_5 = all_4_2
% 201.76/33.47    (41)   ~ (all_52_25 = all_14_2)
% 201.76/33.47    (42)   ~ (all_52_9 = all_52_15)
% 201.76/33.47    (43)   ~ (all_52_3 = all_52_27)
% 201.76/33.47    (44)  op(all_10_2, e1) = all_10_1
% 201.76/33.47    (45)  all_46_2 = all_6_2
% 201.76/33.47    (46)  op(all_6_2, all_6_2) = all_52_0
% 201.76/33.47    (47)   ~ (all_52_7 = all_6_2)
% 201.76/33.47    (48)  op(e0, e0) = all_14_2
% 201.76/33.47    (49)  all_56_15 = all_14_2
% 201.76/33.47    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.76/33.47    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.76/33.47    (52)  all_56_11 = all_52_29
% 201.76/33.47    (53)   ~ (all_10_0 = e2)
% 201.76/33.47    (54)   ~ (all_4_1 = e1)
% 201.76/33.47    (55)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.76/33.47    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.76/33.47    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.76/33.47    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.76/33.47    (59)   ~ (e2 = e1)
% 201.76/33.47    (60)  all_58_10 = all_52_27
% 201.76/33.47    (61)  all_56_8 = all_52_5
% 201.76/33.47    (62)  op(all_52_9, all_52_9) = all_52_8
% 201.76/33.47    (63)  op(all_52_15, all_52_15) = all_52_14
% 201.76/33.47    (64)  all_56_9 = all_10_0
% 201.76/33.47    (65)   ~ (all_52_25 = all_52_29)
% 201.76/33.47    (66)   ~ (all_52_29 = all_10_2)
% 201.76/33.47    (67)  all_58_7 = all_52_13
% 201.76/33.47    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.76/33.47    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.76/33.47    (70)   ~ (all_52_5 = all_52_7)
% 201.76/33.47    (71)  all_58_12 = all_52_7
% 201.76/33.47    (72)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.76/33.47    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.76/33.47    (74)   ~ (all_52_7 = all_14_2)
% 201.76/33.47    (75)   ~ (all_14_2 = e0)
% 201.76/33.47    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 201.76/33.47    (77)  all_58_2 = all_52_3
% 201.76/33.47    (78)  all_56_2 = all_52_17
% 201.76/33.47    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.76/33.47    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.76/33.47    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.76/33.47    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.76/33.47    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.76/33.47    (84)   ~ (e2 = e0)
% 201.76/33.47    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.76/33.47    (86)  op(all_4_2, e2) = all_4_1
% 201.76/33.47    (87)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.76/33.47    (88)   ~ (all_52_5 = all_52_29)
% 201.76/33.47    (89)   ~ (all_52_15 = all_14_2)
% 201.76/33.47    (90)   ~ (all_52_19 = all_52_27)
% 201.76/33.47    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.76/33.47    (92)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.76/33.47    (93)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.76/33.47    (94)  op(e3, e1) = all_52_17
% 201.76/33.47    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.76/33.47    (96)  op(e0, e3) = all_52_7
% 201.76/33.47    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.76/33.47    (98)   ~ (all_52_9 = all_52_25)
% 201.76/33.47    (99)  all_58_15 = all_14_2
% 201.76/33.47    (100)   ~ (all_52_19 = all_10_2)
% 201.76/33.47    (101)  op(all_52_23, all_52_23) = all_52_22
% 201.76/33.47    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.76/33.47    (103)   ~ (all_10_0 = all_10_2)
% 201.76/33.47    (104)  all_58_8 = all_10_2
% 201.76/33.47    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.76/33.47    (106)   ~ (all_52_5 = all_10_2)
% 201.76/33.47    (107)  op(all_52_29, all_52_29) = all_52_28
% 201.76/33.47    (108)   ~ (all_52_23 = all_14_2)
% 201.76/33.47    (109)  all_56_12 = all_52_7
% 201.76/33.47    (110)  op(all_52_17, all_52_17) = all_52_16
% 201.76/33.47    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.76/33.47    (112)   ~ (all_52_25 = all_6_2)
% 201.76/33.47    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.76/33.47    (114)   ~ (all_52_9 = all_4_2)
% 201.76/33.47    (115)   ~ (all_52_5 = all_6_2)
% 201.76/33.47    (116)   ~ (all_52_9 = all_6_2)
% 201.76/33.47    (117)   ~ (all_52_13 = all_52_15)
% 201.76/33.47    (118)  all_56_0 = all_6_2
% 201.76/33.47    (119)  op(e3, e3) = all_6_2
% 201.76/33.47    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.76/33.47    (121)   ~ (all_52_27 = all_14_2)
% 201.76/33.47    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.76/33.47    (123)  all_56_14 = all_52_23
% 201.76/33.47    (124)  op(all_4_2, all_4_2) = all_52_10
% 201.76/33.47    (125)  all_40_0 = all_10_0
% 201.76/33.47    (126)  all_56_3 = all_52_25
% 201.76/33.47    (127)   ~ (all_52_3 = all_52_7)
% 201.76/33.47    (128)  op(all_14_2, all_14_2) = all_52_30
% 201.76/33.47    (129)  all_58_5 = all_52_19
% 201.76/33.47    (130)  all_56_1 = all_52_9
% 201.76/33.47    (131)   ~ (all_52_15 = all_4_2)
% 201.76/33.47    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.76/33.47           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.76/33.47           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.76/33.47           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.76/33.47    (133)   ~ (all_52_27 = all_4_2)
% 201.76/33.47    (134)  all_58_6 = all_52_5
% 201.76/33.47    (135)  op(all_10_2, e1) = e2
% 201.76/33.47    (136)  op(e3, e2) = all_52_9
% 201.76/33.47    (137)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.76/33.47    (138)   ~ (all_52_17 = all_6_2)
% 201.76/33.47    (139)   ~ (e1 = e0)
% 201.76/33.47    (140)   ~ (e3 = e2)
% 201.76/33.47    (141)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.76/33.47    (142)   ~ (all_52_9 = all_52_17)
% 201.76/33.47    (143)  all_56_10 = all_10_2
% 201.76/33.47    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.76/33.47    (145)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.76/33.47    (146)  all_46_1 = all_6_1
% 201.76/33.47    (147)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.76/33.47    (148)  op(all_52_13, all_52_13) = all_52_12
% 201.76/33.47    (149)  op(all_10_0, all_10_0) = all_52_12
% 201.76/33.47    (150)  op(e1, e1) = all_10_2
% 201.76/33.47    (151)   ~ (all_52_23 = all_10_2)
% 201.76/33.47    (152)   ~ (all_52_7 = all_52_23)
% 201.76/33.47    (153)   ~ (all_52_17 = all_52_19)
% 201.76/33.47    (154)   ~ (all_52_5 = all_10_0)
% 201.76/33.47    (155)  all_58_3 = all_4_2
% 201.76/33.47    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.76/33.47    (157)  all_56_13 = all_52_15
% 201.76/33.47    (158)   ~ (all_52_3 = all_4_2)
% 201.76/33.47    (159)   ~ (all_52_9 = all_10_0)
% 201.76/33.47    (160)   ~ (all_52_19 = all_4_2)
% 201.76/33.47    (161)   ~ (all_52_17 = all_52_23)
% 201.76/33.47    (162)  op(all_6_2, e3) = all_6_1
% 201.76/33.47    (163)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.76/33.47    (164)  all_58_4 = all_52_17
% 201.76/33.47    (165)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.76/33.47    (166)  op(all_52_25, all_52_25) = all_52_24
% 201.76/33.47  
% 201.76/33.47  Begin of proof
% 201.76/33.47  | 
% 201.76/33.47  | BETA: splitting (145) gives:
% 201.76/33.47  | 
% 201.76/33.47  | Case 1:
% 201.76/33.47  | | 
% 201.76/33.47  | |   (167)  all_56_9 = e3
% 201.76/33.47  | | 
% 201.76/33.47  | | REF_CLOSE: (22), (64), (167) are inconsistent by sub-proof #1006.
% 201.76/33.47  | | 
% 201.76/33.47  | Case 2:
% 201.76/33.47  | | 
% 201.76/33.47  | |   (168)   ~ (all_56_9 = e3)
% 201.76/33.47  | |   (169)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.76/33.47  | | 
% 201.76/33.47  | | BETA: splitting (132) gives:
% 201.76/33.47  | | 
% 201.76/33.47  | | Case 1:
% 201.76/33.47  | | | 
% 201.76/33.47  | | |   (170)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.76/33.47  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 201.76/33.47  | | |            e0)
% 201.76/33.47  | | | 
% 201.76/33.47  | | | BETA: splitting (170) gives:
% 201.76/33.47  | | | 
% 201.76/33.47  | | | Case 1:
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | |   (171)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | REF_CLOSE: (4), (5), (6), (14), (17), (20), (25), (35), (46), (47),
% 201.76/33.47  | | | |            (48), (50), (71), (74), (77), (80), (106), (119), (122),
% 201.76/33.47  | | | |            (134), (137), (150), (158), (162), (171) are inconsistent by
% 201.76/33.47  | | | |            sub-proof #302.
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | Case 2:
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | |   (172)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 201.76/33.47  | | | |          e0
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | ALPHA: (172) implies:
% 201.76/33.47  | | | |   (173)  all_52_14 = e0
% 201.76/33.47  | | | |   (174)  all_52_12 = e1
% 201.76/33.47  | | | |   (175)  all_52_10 = e2
% 201.76/33.47  | | | |   (176)  all_52_8 = e3
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | REDUCE: (62), (176) imply:
% 201.76/33.47  | | | |   (177)  op(all_52_9, all_52_9) = e3
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | REDUCE: (63), (173) imply:
% 201.76/33.47  | | | |   (178)  op(all_52_15, all_52_15) = e0
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | REDUCE: (149), (174) imply:
% 201.76/33.47  | | | |   (179)  op(all_10_0, all_10_0) = e1
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | REDUCE: (124), (175) imply:
% 201.76/33.47  | | | |   (180)  op(all_4_2, all_4_2) = e2
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | BETA: splitting (105) gives:
% 201.76/33.47  | | | | 
% 201.76/33.47  | | | | Case 1:
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | |   (181)  all_56_15 = e3
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | COMBINE_EQS: (49), (181) imply:
% 201.76/33.47  | | | | |   (182)  all_14_2 = e3
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | REDUCE: (89), (182) imply:
% 201.76/33.47  | | | | |   (183)   ~ (all_52_15 = e3)
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | REDUCE: (31), (182) imply:
% 201.76/33.47  | | | | |   (184)   ~ (all_52_29 = e3)
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | REDUCE: (128), (182) imply:
% 201.76/33.47  | | | | |   (185)  op(e3, e3) = all_52_30
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3,
% 201.76/33.47  | | | | |              simplifying with (119), (185) gives:
% 201.76/33.47  | | | | |   (186)  all_52_30 = all_6_2
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | BETA: splitting (73) gives:
% 201.76/33.47  | | | | | 
% 201.76/33.47  | | | | | Case 1:
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | |   (187)  all_58_6 = e3
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | | COMBINE_EQS: (134), (187) imply:
% 201.76/33.47  | | | | | |   (188)  all_52_5 = e3
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | | SIMP: (188) implies:
% 201.76/33.47  | | | | | |   (189)  all_52_5 = e3
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | | REDUCE: (154), (189) imply:
% 201.76/33.47  | | | | | |   (190)   ~ (all_10_0 = e3)
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | | REDUCE: (25), (189) imply:
% 201.76/33.47  | | | | | |   (191)  op(e3, e3) = all_52_4
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_4, e3, e3,
% 201.76/33.47  | | | | | |              simplifying with (119), (191) gives:
% 201.76/33.47  | | | | | |   (192)  all_52_4 = all_6_2
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | | REF_CLOSE: (6), (7), (17), (22), (28), (37), (53), (54), (64), (81),
% 201.76/33.47  | | | | | |            (84), (86), (97), (103), (114), (116), (119), (130),
% 201.76/33.47  | | | | | |            (136), (141), (150), (155), (159), (169), (177), (179),
% 201.76/33.47  | | | | | |            (180), (183) are inconsistent by sub-proof #269.
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | Case 2:
% 201.76/33.47  | | | | | | 
% 201.76/33.47  | | | | | |   (193)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.76/33.47  | | | | | | 
% 201.76/33.48  | | | | | | REF_CLOSE: (6), (22), (23), (37), (39), (53), (64), (76), (103),
% 201.76/33.48  | | | | | |            (104), (125), (150), (169), (179), (184), (193) are
% 201.76/33.48  | | | | | |            inconsistent by sub-proof #986.
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | End of split
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | Case 2:
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | |   (194)   ~ (all_56_15 = e3)
% 201.76/33.48  | | | | |   (195)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (49), (194) imply:
% 201.76/33.48  | | | | |   (196)   ~ (all_14_2 = e3)
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | BETA: splitting (56) gives:
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | Case 1:
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | |   (197)  all_56_13 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | COMBINE_EQS: (157), (197) imply:
% 201.76/33.48  | | | | | |   (198)  all_52_15 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | SIMP: (198) implies:
% 201.76/33.48  | | | | | |   (199)  all_52_15 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | COMBINE_EQS: (28), (199) imply:
% 201.76/33.48  | | | | | |   (200)  all_58_13 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REF_CLOSE: (3), (6), (9), (11), (12), (20), (35), (42), (47), (49),
% 201.76/33.48  | | | | | |            (71), (72), (74), (93), (94), (96), (108), (109), (116),
% 201.76/33.48  | | | | | |            (119), (128), (130), (131), (141), (142), (152), (162),
% 201.76/33.48  | | | | | |            (177), (178), (195), (199), (200) are inconsistent by
% 201.76/33.48  | | | | | |            sub-proof #267.
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | Case 2:
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | |   (201)   ~ (all_56_13 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REDUCE: (157), (201) imply:
% 201.76/33.48  | | | | | |   (202)   ~ (all_52_15 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REF_CLOSE: (6), (7), (22), (28), (37), (48), (54), (86), (97),
% 201.76/33.48  | | | | | |            (114), (116), (119), (130), (136), (141), (155), (177),
% 201.76/33.48  | | | | | |            (180), (196), (202) are inconsistent by sub-proof #431.
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | End of split
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | End of split
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | End of split
% 201.76/33.48  | | | 
% 201.76/33.48  | | Case 2:
% 201.76/33.48  | | | 
% 201.76/33.48  | | |   (203)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 201.76/33.48  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 201.76/33.48  | | |            all_52_30 = e0)
% 201.76/33.48  | | | 
% 201.76/33.48  | | | BETA: splitting (203) gives:
% 201.76/33.48  | | | 
% 201.76/33.48  | | | Case 1:
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | |   (204)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 201.76/33.48  | | | |          e0
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | ALPHA: (204) implies:
% 201.76/33.48  | | | |   (205)  all_52_22 = e0
% 201.76/33.48  | | | |   (206)  all_52_20 = e1
% 201.76/33.48  | | | |   (207)  all_52_18 = e2
% 201.76/33.48  | | | |   (208)  all_52_16 = e3
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | REDUCE: (110), (208) imply:
% 201.76/33.48  | | | |   (209)  op(all_52_17, all_52_17) = e3
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | REDUCE: (26), (207) imply:
% 201.76/33.48  | | | |   (210)  op(all_52_19, all_52_19) = e2
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | REDUCE: (101), (205) imply:
% 201.76/33.48  | | | |   (211)  op(all_52_23, all_52_23) = e0
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | REDUCE: (29), (206) imply:
% 201.76/33.48  | | | |   (212)  op(all_10_2, all_10_2) = e1
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | BETA: splitting (105) gives:
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | Case 1:
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | |   (213)  all_56_15 = e3
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | COMBINE_EQS: (49), (213) imply:
% 201.76/33.48  | | | | |   (214)  all_14_2 = e3
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (74), (214) imply:
% 201.76/33.48  | | | | |   (215)   ~ (all_52_7 = e3)
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (108), (214) imply:
% 201.76/33.48  | | | | |   (216)   ~ (all_52_23 = e3)
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (41), (214) imply:
% 201.76/33.48  | | | | |   (217)   ~ (all_52_25 = e3)
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (31), (214) imply:
% 201.76/33.48  | | | | |   (218)   ~ (all_52_29 = e3)
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (128), (214) imply:
% 201.76/33.48  | | | | |   (219)  op(e3, e3) = all_52_30
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3,
% 201.76/33.48  | | | | |              simplifying with (119), (219) gives:
% 201.76/33.48  | | | | |   (220)  all_52_30 = all_6_2
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | BETA: splitting (73) gives:
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | Case 1:
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | |   (221)  all_58_6 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | COMBINE_EQS: (134), (221) imply:
% 201.76/33.48  | | | | | |   (222)  all_52_5 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | SIMP: (222) implies:
% 201.76/33.48  | | | | | |   (223)  all_52_5 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REDUCE: (70), (223) imply:
% 201.76/33.48  | | | | | |   (224)   ~ (all_52_7 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REDUCE: (106), (223) imply:
% 201.76/33.48  | | | | | |   (225)   ~ (all_10_2 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | SIMP: (225) implies:
% 201.76/33.48  | | | | | |   (226)   ~ (all_10_2 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REDUCE: (115), (223) imply:
% 201.76/33.48  | | | | | |   (227)   ~ (all_6_2 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | SIMP: (227) implies:
% 201.76/33.48  | | | | | |   (228)   ~ (all_6_2 = e3)
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REDUCE: (25), (223) imply:
% 201.76/33.48  | | | | | |   (229)  op(e3, e3) = all_52_4
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_4, e3, e3,
% 201.76/33.48  | | | | | |              simplifying with (119), (229) gives:
% 201.76/33.48  | | | | | |   (230)  all_52_4 = all_6_2
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | BETA: splitting (97) gives:
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | Case 1:
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | |   (231)  all_58_1 = e3
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | COMBINE_EQS: (7), (231) imply:
% 201.76/33.48  | | | | | | |   (232)  all_52_9 = e3
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | REDUCE: (142), (232) imply:
% 201.76/33.48  | | | | | | |   (233)   ~ (all_52_17 = e3)
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | SIMP: (233) implies:
% 201.76/33.48  | | | | | | |   (234)   ~ (all_52_17 = e3)
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | REDUCE: (62), (232) imply:
% 201.76/33.48  | | | | | | |   (235)  op(e3, e3) = all_52_8
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | BETA: splitting (144) gives:
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | |   (236)  all_58_4 = e3
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | | REF_CLOSE: (164), (234), (236) are inconsistent by sub-proof
% 201.76/33.48  | | | | | | | |            #1302.
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | |   (237)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | | BETA: splitting (237) gives:
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | |   (238)  all_58_5 = e3
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | COMBINE_EQS: (129), (238) imply:
% 201.76/33.48  | | | | | | | | |   (239)  all_52_19 = e3
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | SIMP: (239) implies:
% 201.76/33.48  | | | | | | | | |   (240)  all_52_19 = e3
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | REDUCE: (13), (240) imply:
% 201.76/33.48  | | | | | | | | |   (241)   ~ (all_52_3 = e3)
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | REDUCE: (210), (240) imply:
% 201.76/33.48  | | | | | | | | |   (242)  op(e3, e3) = e2
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 201.76/33.48  | | | | | | | | |              simplifying with (119), (235) gives:
% 201.76/33.48  | | | | | | | | |   (243)  all_52_8 = all_6_2
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_52_8, e3, e3,
% 201.76/33.48  | | | | | | | | |              simplifying with (235), (242) gives:
% 201.76/33.48  | | | | | | | | |   (244)  all_52_8 = e2
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | COMBINE_EQS: (243), (244) imply:
% 201.76/33.48  | | | | | | | | |   (245)  all_6_2 = e2
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | SIMP: (245) implies:
% 201.76/33.48  | | | | | | | | |   (246)  all_6_2 = e2
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | COMBINE_EQS: (45), (246) imply:
% 201.76/33.48  | | | | | | | | |   (247)  all_46_2 = e2
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | REDUCE: (16), (246) imply:
% 201.76/33.48  | | | | | | | | |   (248)   ~ (all_52_3 = e2)
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | REDUCE: (47), (246) imply:
% 201.76/33.48  | | | | | | | | |   (249)   ~ (all_52_7 = e2)
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | REDUCE: (162), (246) imply:
% 201.76/33.48  | | | | | | | | |   (250)  op(e2, e3) = all_6_1
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | BETA: splitting (55) gives:
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | |   (251)   ~ (all_46_2 = e2)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | REDUCE: (247), (251) imply:
% 201.76/33.48  | | | | | | | | | |   (252)  $false
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | CLOSE: (252) is inconsistent.
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | |   (253)   ~ (all_46_1 = e0)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | REDUCE: (146), (253) imply:
% 201.76/33.48  | | | | | | | | | |   (254)   ~ (all_6_1 = e0)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_3, all_6_1, e3, e2,
% 201.76/33.48  | | | | | | | | | |              simplifying with (10), (250) gives:
% 201.76/33.48  | | | | | | | | | |   (255)  all_52_3 = all_6_1
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | COMBINE_EQS: (19), (255) imply:
% 201.76/33.48  | | | | | | | | | |   (256)  all_56_4 = all_6_1
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | REDUCE: (127), (255) imply:
% 201.76/33.48  | | | | | | | | | |   (257)   ~ (all_52_7 = all_6_1)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | SIMP: (257) implies:
% 201.76/33.48  | | | | | | | | | |   (258)   ~ (all_52_7 = all_6_1)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | REDUCE: (241), (255) imply:
% 201.76/33.48  | | | | | | | | | |   (259)   ~ (all_6_1 = e3)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | REDUCE: (248), (255) imply:
% 201.76/33.48  | | | | | | | | | |   (260)   ~ (all_6_1 = e2)
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | REDUCE: (5), (255) imply:
% 201.76/33.48  | | | | | | | | | |   (261)  op(all_6_1, all_6_1) = all_52_2
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | BETA: splitting (83) gives:
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | |   (262)  all_56_4 = e3
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | REF_CLOSE: (256), (259), (262) are inconsistent by sub-proof
% 201.76/33.48  | | | | | | | | | | |            #900.
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | |   (263)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | BETA: splitting (263) gives:
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | |   (264)  all_56_4 = e2
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | REF_CLOSE: (256), (260), (264) are inconsistent by sub-proof
% 201.76/33.48  | | | | | | | | | | | |            #1219.
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | |   (265)  all_56_4 = e1 | all_56_4 = e0
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | BETA: splitting (265) gives:
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | |   (266)  all_56_4 = e1
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | COMBINE_EQS: (256), (266) imply:
% 201.76/33.48  | | | | | | | | | | | | |   (267)  all_6_1 = e1
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | SIMP: (267) implies:
% 201.76/33.48  | | | | | | | | | | | | |   (268)  all_6_1 = e1
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | REDUCE: (258), (268) imply:
% 201.76/33.48  | | | | | | | | | | | | |   (269)   ~ (all_52_7 = e1)
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | REDUCE: (261), (268) imply:
% 201.76/33.48  | | | | | | | | | | | | |   (270)  op(e1, e1) = all_52_2
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | REDUCE: (20), (268) imply:
% 201.76/33.48  | | | | | | | | | | | | |   (271)  op(e3, e1) = e1
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | BETA: splitting (11) gives:
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | Case 1:
% 201.76/33.48  | | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | |   (272)  all_56_12 = e3
% 201.76/33.48  | | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | | REF_CLOSE: (109), (215), (272) are inconsistent by sub-proof
% 201.76/33.48  | | | | | | | | | | | | | |            #1383.
% 201.76/33.48  | | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | |   (273)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.76/33.48  | | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | | REF_CLOSE: (6), (94), (109), (150), (209), (226), (249),
% 201.76/33.48  | | | | | | | | | | | | | |            (269), (270), (271), (273) are inconsistent by
% 201.76/33.48  | | | | | | | | | | | | | |            sub-proof #266.
% 201.76/33.48  | | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | End of split
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | |   (274)  all_56_4 = e0
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | | REF_CLOSE: (254), (256), (274) are inconsistent by sub-proof
% 201.76/33.48  | | | | | | | | | | | | |            #1217.
% 201.76/33.48  | | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | | End of split
% 201.76/33.48  | | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | | End of split
% 201.76/33.48  | | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | | End of split
% 201.76/33.48  | | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | End of split
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | Case 2:
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | |   (275)  all_58_8 = e3 | all_58_14 = e3
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | | REF_CLOSE: (3), (104), (216), (226), (275) are inconsistent by
% 201.76/33.48  | | | | | | | | |            sub-proof #1304.
% 201.76/33.48  | | | | | | | | | 
% 201.76/33.48  | | | | | | | | End of split
% 201.76/33.48  | | | | | | | | 
% 201.76/33.48  | | | | | | | End of split
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | Case 2:
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | |   (276)   ~ (all_58_1 = e3)
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | REDUCE: (7), (276) imply:
% 201.76/33.48  | | | | | | |   (277)   ~ (all_52_9 = e3)
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | | REF_CLOSE: (6), (7), (17), (30), (119), (122), (138), (164),
% 201.76/33.48  | | | | | | |            (209), (217), (228), (277) are inconsistent by
% 201.76/33.48  | | | | | | |            sub-proof #1071.
% 201.76/33.48  | | | | | | | 
% 201.76/33.48  | | | | | | End of split
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | Case 2:
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | |   (278)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | | REF_CLOSE: (4), (6), (17), (22), (35), (37), (39), (71), (77), (80),
% 201.76/33.48  | | | | | |            (94), (104), (106), (119), (134), (135), (158), (209),
% 201.76/33.48  | | | | | |            (212), (215), (218), (278) are inconsistent by sub-proof
% 201.76/33.48  | | | | | |            #415.
% 201.76/33.48  | | | | | | 
% 201.76/33.48  | | | | | End of split
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | Case 2:
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | |   (279)   ~ (all_56_15 = e3)
% 201.76/33.48  | | | | |   (280)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REDUCE: (49), (279) imply:
% 201.76/33.48  | | | | |   (281)   ~ (all_14_2 = e3)
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (12), (14), (15),
% 201.76/33.48  | | | | |            (17), (20), (24), (25), (28), (30), (32), (34), (35), (36),
% 201.76/33.48  | | | | |            (38), (39), (41), (42), (44), (46), (47), (48), (49), (52),
% 201.76/33.48  | | | | |            (56), (57), (58), (59), (62), (65), (66), (67), (71), (72),
% 201.76/33.48  | | | | |            (73), (74), (75), (77), (78), (79), (80), (81), (82), (84),
% 201.76/33.48  | | | | |            (87), (91), (92), (93), (94), (96), (98), (99), (100),
% 201.76/33.48  | | | | |            (104), (106), (107), (108), (109), (112), (113), (115),
% 201.76/33.48  | | | | |            (116), (117), (118), (119), (120), (122), (126), (127),
% 201.76/33.48  | | | | |            (129), (130), (134), (136), (137), (138), (139), (140),
% 201.76/33.48  | | | | |            (141), (142), (143), (144), (147), (150), (151), (152),
% 201.76/33.48  | | | | |            (156), (157), (158), (162), (163), (164), (165), (166),
% 201.76/33.48  | | | | |            (209), (210), (211), (212), (280), (281) are inconsistent
% 201.76/33.48  | | | | |            by sub-proof #274.
% 201.76/33.48  | | | | | 
% 201.76/33.48  | | | | End of split
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | Case 2:
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | |   (282)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 201.76/33.48  | | | |          e0
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 201.76/33.48  | | | |            (12), (14), (15), (16), (17), (18), (19), (20), (21), (24),
% 201.76/33.48  | | | |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 201.76/33.48  | | | |            (36), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 201.76/33.48  | | | |            (47), (48), (49), (50), (51), (52), (55), (56), (57), (58),
% 201.76/33.48  | | | |            (59), (60), (61), (62), (63), (65), (66), (67), (68), (69),
% 201.76/33.48  | | | |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (80),
% 201.76/33.48  | | | |            (81), (82), (83), (84), (85), (88), (89), (90), (91), (92),
% 201.76/33.48  | | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 201.76/33.48  | | | |            (102), (104), (105), (106), (107), (108), (109), (110),
% 201.76/33.48  | | | |            (111), (112), (113), (114), (115), (116), (117), (118),
% 201.76/33.48  | | | |            (119), (120), (121), (122), (123), (126), (127), (128),
% 201.76/33.48  | | | |            (129), (130), (131), (133), (134), (136), (137), (138),
% 201.76/33.48  | | | |            (139), (140), (141), (146), (147), (148), (150), (151),
% 201.76/33.48  | | | |            (152), (153), (155), (156), (157), (158), (160), (161),
% 201.76/33.48  | | | |            (162), (163), (164), (166), (282) are inconsistent by
% 201.76/33.48  | | | |            sub-proof #271.
% 201.76/33.48  | | | | 
% 201.76/33.48  | | | End of split
% 201.76/33.48  | | | 
% 201.76/33.48  | | End of split
% 201.76/33.48  | | 
% 201.76/33.48  | End of split
% 201.76/33.48  | 
% 201.76/33.48  End of proof
% 201.76/33.48  
% 201.76/33.48  Sub-proof #266 shows that the following formulas are inconsistent:
% 201.76/33.48  ----------------------------------------------------------------
% 201.76/33.48    (1)  op(e1, e1) = all_52_2
% 201.76/33.48    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.76/33.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.76/33.48    (3)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.76/33.48    (4)  op(e3, e1) = e1
% 201.76/33.48    (5)   ~ (all_10_2 = e3)
% 201.76/33.48    (6)   ~ (all_52_7 = e2)
% 201.76/33.48    (7)  op(e3, e1) = all_52_17
% 201.76/33.48    (8)  all_56_12 = all_52_7
% 201.76/33.48    (9)   ~ (all_52_7 = e1)
% 201.76/33.48    (10)  op(all_52_17, all_52_17) = e3
% 201.76/33.48    (11)  op(e1, e1) = all_10_2
% 201.76/33.48  
% 201.76/33.48  Begin of proof
% 201.76/33.48  | 
% 201.76/33.48  | BETA: splitting (3) gives:
% 201.76/33.48  | 
% 201.76/33.48  | Case 1:
% 201.76/33.48  | | 
% 201.76/33.48  | |   (12)  all_56_12 = e2
% 201.76/33.48  | | 
% 201.76/33.48  | | REF_CLOSE: (6), (8), (12) are inconsistent by sub-proof #1178.
% 201.76/33.48  | | 
% 201.76/33.48  | Case 2:
% 201.76/33.48  | | 
% 201.76/33.48  | |   (13)  all_56_12 = e1 | all_56_12 = e0
% 201.76/33.48  | | 
% 201.76/33.48  | | BETA: splitting (13) gives:
% 201.76/33.48  | | 
% 201.76/33.48  | | Case 1:
% 201.76/33.48  | | | 
% 201.76/33.48  | | |   (14)  all_56_12 = e1
% 201.76/33.48  | | | 
% 201.76/33.48  | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #1376.
% 201.76/33.48  | | | 
% 201.76/33.48  | | Case 2:
% 201.76/33.48  | | | 
% 201.76/33.48  | | | 
% 201.76/33.48  | | | GROUND_INST: instantiating (2) with all_10_2, all_52_2, e1, e1,
% 201.76/33.48  | | |              simplifying with (1), (11) gives:
% 201.76/33.48  | | |   (15)  all_52_2 = all_10_2
% 201.76/33.48  | | | 
% 201.76/33.48  | | | GROUND_INST: instantiating (2) with all_52_17, e1, e1, e3, simplifying
% 201.76/33.48  | | |              with (4), (7) gives:
% 201.76/33.48  | | |   (16)  all_52_17 = e1
% 201.76/33.48  | | | 
% 201.76/33.48  | | | REDUCE: (10), (16) imply:
% 201.80/33.48  | | |   (17)  op(e1, e1) = e3
% 201.80/33.48  | | | 
% 201.80/33.48  | | | REF_CLOSE: (2), (5), (11), (17) are inconsistent by sub-proof #1368.
% 201.80/33.48  | | | 
% 201.80/33.48  | | End of split
% 201.80/33.48  | | 
% 201.80/33.48  | End of split
% 201.80/33.48  | 
% 201.80/33.48  End of proof
% 201.80/33.48  
% 201.80/33.48  Sub-proof #267 shows that the following formulas are inconsistent:
% 201.80/33.48  ----------------------------------------------------------------
% 201.80/33.48    (1)  all_58_14 = all_52_23
% 201.80/33.48    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.48    (3)   ~ (e3 = e0)
% 201.80/33.48    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.80/33.48    (5)   ~ (all_52_7 = all_52_15)
% 201.80/33.48    (6)  op(all_52_15, all_52_15) = e0
% 201.80/33.48    (7)  op(e3, all_6_1) = e1
% 201.80/33.48    (8)  all_58_13 = e3
% 201.80/33.48    (9)  all_52_15 = e3
% 201.80/33.48    (10)  op(e2, e2) = all_4_2
% 201.80/33.48    (11)   ~ (all_52_9 = all_52_15)
% 201.80/33.48    (12)   ~ (all_52_7 = all_6_2)
% 201.80/33.48    (13)  all_56_15 = all_14_2
% 201.80/33.48    (14)  all_58_12 = all_52_7
% 201.80/33.48    (15)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.80/33.48    (16)   ~ (all_52_7 = all_14_2)
% 201.80/33.48    (17)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.80/33.48    (18)  op(e3, e1) = all_52_17
% 201.80/33.48    (19)  op(e0, e3) = all_52_7
% 201.80/33.48    (20)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.80/33.48    (21)   ~ (all_52_23 = all_14_2)
% 201.80/33.48    (22)  all_56_12 = all_52_7
% 201.80/33.48    (23)   ~ (all_52_9 = all_6_2)
% 201.80/33.48    (24)  op(e3, e3) = all_6_2
% 201.80/33.48    (25)  op(all_14_2, all_14_2) = all_52_30
% 201.80/33.48    (26)  all_56_1 = all_52_9
% 201.80/33.48    (27)   ~ (all_52_15 = all_4_2)
% 201.80/33.48    (28)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.48    (29)   ~ (all_52_9 = all_52_17)
% 201.80/33.48    (30)  op(all_52_9, all_52_9) = e3
% 201.80/33.48    (31)   ~ (all_52_7 = all_52_23)
% 201.80/33.48    (32)  op(all_6_2, e3) = all_6_1
% 201.80/33.48  
% 201.80/33.48  Begin of proof
% 201.80/33.48  | 
% 201.80/33.48  | REDUCE: (5), (9) imply:
% 201.80/33.48  |   (33)   ~ (all_52_7 = e3)
% 201.80/33.48  | 
% 201.80/33.48  | REDUCE: (9), (11) imply:
% 201.80/33.48  |   (34)   ~ (all_52_9 = e3)
% 201.80/33.48  | 
% 201.80/33.48  | REDUCE: (9), (27) imply:
% 201.80/33.48  |   (35)   ~ (all_4_2 = e3)
% 201.80/33.48  | 
% 201.80/33.48  | SIMP: (35) implies:
% 201.80/33.48  |   (36)   ~ (all_4_2 = e3)
% 201.80/33.48  | 
% 201.80/33.48  | REDUCE: (6), (9) imply:
% 201.80/33.48  |   (37)  op(e3, e3) = e0
% 201.80/33.48  | 
% 201.80/33.48  | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (12), (13), (14), (15), (16),
% 201.80/33.48  |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (28),
% 201.80/33.48  |            (29), (30), (31), (32), (33), (34), (36), (37) are inconsistent by
% 201.80/33.48  |            sub-proof #297.
% 201.80/33.48  | 
% 201.80/33.48  End of proof
% 201.80/33.48  
% 201.80/33.48  Sub-proof #268 shows that the following formulas are inconsistent:
% 201.80/33.48  ----------------------------------------------------------------
% 201.80/33.48    (1)  all_58_14 = all_52_23
% 201.80/33.48    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.48    (3)  all_58_1 = all_52_9
% 201.80/33.48    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.80/33.48    (5)   ~ (all_52_7 = all_52_15)
% 201.80/33.48    (6)  op(all_52_15, all_52_15) = e0
% 201.80/33.48    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.80/33.48    (8)  all_58_0 = all_6_2
% 201.80/33.48    (9)  op(e3, all_6_1) = e1
% 201.80/33.48    (10)   ~ (all_10_0 = e3)
% 201.80/33.48    (11)  all_58_13 = all_52_15
% 201.80/33.48    (12)  op(all_10_0, all_10_0) = e1
% 201.80/33.48    (13)  op(e2, e2) = all_4_2
% 201.80/33.48    (14)  all_58_7 = all_10_0
% 201.80/33.48    (15)   ~ (all_52_9 = all_52_15)
% 201.80/33.48    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.80/33.48    (17)   ~ (all_52_7 = all_6_2)
% 201.80/33.48    (18)  all_58_15 = e0
% 201.80/33.48    (19)   ~ (all_10_0 = e2)
% 201.80/33.48    (20)   ~ (all_4_1 = e1)
% 201.80/33.48    (21)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.80/33.48    (22)  all_56_9 = all_10_0
% 201.80/33.48    (23)  all_58_12 = all_52_7
% 201.80/33.48    (24)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.80/33.48    (25)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.80/33.48    (26)   ~ (e2 = e0)
% 201.80/33.48    (27)  op(all_4_2, e2) = all_4_1
% 201.80/33.48    (28)  op(e3, e1) = all_52_17
% 201.80/33.48    (29)  op(e0, e3) = all_52_7
% 201.80/33.48    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.48    (31)  op(all_52_23, all_52_23) = all_52_22
% 201.80/33.48    (32)   ~ (all_10_0 = all_10_2)
% 201.80/33.48    (33)  all_56_12 = all_52_7
% 201.80/33.48    (34)   ~ (all_52_9 = all_4_2)
% 201.80/33.48    (35)  op(all_4_2, all_4_2) = e2
% 201.80/33.48    (36)   ~ (all_52_9 = all_6_2)
% 201.80/33.48    (37)  op(e3, e3) = all_6_2
% 201.80/33.48    (38)  all_56_1 = all_52_9
% 201.80/33.48    (39)   ~ (all_52_15 = all_4_2)
% 201.80/33.48    (40)  op(e3, e2) = all_52_9
% 201.80/33.48    (41)   ~ (e3 = e2)
% 201.80/33.48    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.48    (43)   ~ (all_52_9 = all_52_17)
% 201.80/33.48    (44)  op(e1, e1) = all_10_2
% 201.80/33.48    (45)  op(all_52_9, all_52_9) = e3
% 201.80/33.48    (46)  all_58_3 = all_4_2
% 201.80/33.48    (47)  all_56_13 = all_52_15
% 201.80/33.48    (48)   ~ (all_52_9 = all_10_0)
% 201.80/33.48    (49)  op(all_6_2, e3) = all_6_1
% 201.80/33.48  
% 201.80/33.48  Begin of proof
% 201.80/33.48  | 
% 201.80/33.48  | BETA: splitting (21) gives:
% 201.80/33.48  | 
% 201.80/33.48  | Case 1:
% 201.80/33.48  | | 
% 201.80/33.48  | |   (50)  all_56_13 = e3
% 201.80/33.48  | | 
% 201.80/33.48  | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (11), (13), (15), (16), (17), (18),
% 201.80/33.48  | |            (23), (24), (26), (28), (29), (31), (33), (36), (37), (38), (39),
% 201.80/33.48  | |            (41), (42), (43), (45), (47), (49), (50) are inconsistent by
% 201.80/33.48  | |            sub-proof #321.
% 201.80/33.48  | | 
% 201.80/33.48  | Case 2:
% 201.80/33.48  | | 
% 201.80/33.48  | |   (51)   ~ (all_56_13 = e3)
% 201.80/33.48  | | 
% 201.80/33.48  | | REDUCE: (47), (51) imply:
% 201.80/33.48  | |   (52)   ~ (all_52_15 = e3)
% 201.80/33.48  | | 
% 201.80/33.48  | | REF_CLOSE: (2), (3), (7), (8), (10), (11), (12), (14), (19), (20), (22),
% 201.80/33.48  | |            (25), (26), (27), (30), (32), (34), (35), (36), (37), (38), (40),
% 201.80/33.48  | |            (42), (44), (45), (46), (48), (52) are inconsistent by sub-proof
% 201.80/33.48  | |            #269.
% 201.80/33.48  | | 
% 201.80/33.48  | End of split
% 201.80/33.48  | 
% 201.80/33.48  End of proof
% 201.80/33.48  
% 201.80/33.48  Sub-proof #269 shows that the following formulas are inconsistent:
% 201.80/33.48  ----------------------------------------------------------------
% 201.80/33.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.48    (2)  all_58_1 = all_52_9
% 201.80/33.48    (3)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.80/33.48    (4)  all_58_0 = all_6_2
% 201.80/33.48    (5)   ~ (all_10_0 = e3)
% 201.80/33.48    (6)  all_58_13 = all_52_15
% 201.80/33.48    (7)  op(all_10_0, all_10_0) = e1
% 201.80/33.48    (8)   ~ (all_52_15 = e3)
% 201.80/33.48    (9)  all_58_7 = all_10_0
% 201.80/33.48    (10)   ~ (all_10_0 = e2)
% 201.80/33.48    (11)   ~ (all_4_1 = e1)
% 201.80/33.48    (12)  all_56_9 = all_10_0
% 201.80/33.48    (13)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.80/33.48    (14)   ~ (e2 = e0)
% 201.80/33.48    (15)  op(all_4_2, e2) = all_4_1
% 201.80/33.48    (16)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.48    (17)   ~ (all_10_0 = all_10_2)
% 201.80/33.48    (18)   ~ (all_52_9 = all_4_2)
% 201.80/33.48    (19)  op(all_4_2, all_4_2) = e2
% 201.80/33.48    (20)   ~ (all_52_9 = all_6_2)
% 201.80/33.48    (21)  op(e3, e3) = all_6_2
% 201.80/33.48    (22)  all_56_1 = all_52_9
% 201.80/33.48    (23)  op(e3, e2) = all_52_9
% 201.80/33.48    (24)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.48    (25)  op(e1, e1) = all_10_2
% 201.80/33.48    (26)  op(all_52_9, all_52_9) = e3
% 201.80/33.48    (27)  all_58_3 = all_4_2
% 201.80/33.48    (28)   ~ (all_52_9 = all_10_0)
% 201.80/33.48  
% 201.80/33.48  Begin of proof
% 201.80/33.48  | 
% 201.80/33.48  | BETA: splitting (16) gives:
% 201.80/33.48  | 
% 201.80/33.48  | Case 1:
% 201.80/33.48  | | 
% 201.80/33.48  | |   (29)  all_58_1 = e3
% 201.80/33.48  | | 
% 201.80/33.48  | | COMBINE_EQS: (2), (29) imply:
% 201.80/33.48  | |   (30)  all_52_9 = e3
% 201.80/33.48  | | 
% 201.80/33.48  | | REF_CLOSE: (1), (20), (21), (26), (30) are inconsistent by sub-proof #1337.
% 201.80/33.48  | | 
% 201.80/33.48  | Case 2:
% 201.80/33.48  | | 
% 201.80/33.48  | |   (31)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.48  | | 
% 201.80/33.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.80/33.48  | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 201.80/33.48  | |            (25), (27), (28), (31) are inconsistent by sub-proof #716.
% 201.80/33.48  | | 
% 201.80/33.48  | End of split
% 201.80/33.48  | 
% 201.80/33.48  End of proof
% 201.80/33.48  
% 201.80/33.48  Sub-proof #270 shows that the following formulas are inconsistent:
% 201.80/33.48  ----------------------------------------------------------------
% 201.80/33.48    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.80/33.48    (2)   ~ (all_52_15 = all_52_23)
% 201.80/33.48    (3)   ~ (all_52_25 = all_52_27)
% 201.80/33.48    (4)  all_58_14 = all_52_23
% 201.80/33.48    (5)   ~ (e3 = e1)
% 201.80/33.48    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.80/33.48    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.80/33.48    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.48    (9)   ~ (all_52_5 = all_52_13)
% 201.80/33.48    (10)  all_58_1 = all_52_9
% 201.80/33.48    (11)   ~ (all_52_9 = all_52_13)
% 201.80/33.48    (12)   ~ (e3 = e0)
% 201.80/33.48    (13)  op(e2, e3) = all_52_3
% 201.80/33.48    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.80/33.48    (15)  op(e0, e2) = all_52_15
% 201.80/33.48    (16)   ~ (all_52_7 = all_52_15)
% 201.80/33.48    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.80/33.48    (18)   ~ (all_52_17 = all_52_25)
% 201.80/33.48    (19)   ~ (all_52_3 = all_6_2)
% 201.80/33.48    (20)  all_58_0 = all_6_2
% 201.80/33.48    (21)  op(all_14_2, e0) = all_14_1
% 201.80/33.48    (22)  all_56_4 = all_52_3
% 201.80/33.48    (23)  op(e3, all_6_1) = e1
% 201.80/33.48    (24)   ~ (all_52_17 = all_10_2)
% 201.80/33.48    (25)  op(e3, e0) = all_52_25
% 201.80/33.48    (26)  op(e0, all_14_1) = all_14_0
% 201.80/33.48    (27)  op(all_52_5, all_52_5) = all_52_4
% 201.80/33.48    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.80/33.48    (29)  op(all_52_19, all_52_19) = all_52_18
% 201.80/33.48    (30)   ~ (all_52_27 = all_52_29)
% 201.80/33.48    (31)  all_58_13 = all_52_15
% 201.80/33.48    (32)  op(all_10_2, all_10_2) = all_52_20
% 201.80/33.48    (33)  all_58_9 = all_52_25
% 201.80/33.49    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.80/33.49    (35)   ~ (all_52_29 = all_14_2)
% 201.80/33.49    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.80/33.49    (37)  op(all_52_27, all_52_27) = all_52_26
% 201.80/33.49    (38)  op(e1, e3) = all_52_5
% 201.80/33.49    (39)  op(e2, e2) = all_4_2
% 201.80/33.49    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.80/33.49    (41)   ~ (all_52_3 = all_52_5)
% 201.80/33.49    (42)  all_58_11 = all_52_29
% 201.80/33.49    (43)  all_56_5 = all_4_2
% 201.80/33.49    (44)   ~ (all_52_25 = all_14_2)
% 201.80/33.49    (45)   ~ (all_52_9 = all_52_15)
% 201.80/33.49    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.80/33.49    (47)   ~ (all_52_3 = all_52_27)
% 201.80/33.49    (48)  op(all_10_2, e1) = all_10_1
% 201.80/33.49    (49)  all_46_2 = all_6_2
% 201.80/33.49    (50)  op(all_6_2, all_6_2) = all_52_0
% 201.80/33.49    (51)   ~ (all_52_7 = all_6_2)
% 201.80/33.49    (52)  op(e0, e0) = all_14_2
% 201.80/33.49    (53)  op(e0, e1) = all_52_23
% 201.80/33.49    (54)  all_56_15 = all_14_2
% 201.80/33.49    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.80/33.49    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.80/33.49    (57)  all_56_11 = all_52_29
% 201.80/33.49    (58)   ~ (all_4_1 = e1)
% 201.80/33.49    (59)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.80/33.49    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.80/33.49    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.80/33.49    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.80/33.49    (63)  all_56_9 = all_52_13
% 201.80/33.49    (64)   ~ (e2 = e1)
% 201.80/33.49    (65)   ~ (all_52_13 = all_10_2)
% 201.80/33.49    (66)  all_58_10 = all_52_27
% 201.80/33.49    (67)  all_56_8 = all_52_5
% 201.80/33.49    (68)  op(all_52_9, all_52_9) = all_52_8
% 201.80/33.49    (69)  op(all_52_15, all_52_15) = all_52_14
% 201.80/33.49    (70)   ~ (all_52_19 = all_52_23)
% 201.80/33.49    (71)   ~ (all_52_25 = all_52_29)
% 201.80/33.49    (72)   ~ (all_52_29 = all_10_2)
% 201.80/33.49    (73)  all_58_7 = all_52_13
% 201.80/33.49    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.80/33.49    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.80/33.49    (76)   ~ (all_52_5 = all_52_7)
% 201.80/33.49    (77)  all_58_12 = all_52_7
% 201.80/33.49    (78)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.80/33.49    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.80/33.49    (80)   ~ (all_52_7 = all_14_2)
% 201.80/33.49    (81)   ~ (all_14_2 = e0)
% 201.80/33.49    (82)  all_58_2 = all_52_3
% 201.80/33.49    (83)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.80/33.49    (84)  all_56_2 = all_52_17
% 201.80/33.49    (85)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.80/33.49    (86)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.80/33.49    (87)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.80/33.49    (88)   ~ (all_14_0 = e3)
% 201.80/33.49    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.80/33.49    (90)  all_56_7 = all_52_27
% 201.80/33.49    (91)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.80/33.49    (92)   ~ (e2 = e0)
% 201.80/33.49    (93)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.80/33.49    (94)  op(all_4_2, e2) = all_4_1
% 201.80/33.49    (95)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.80/33.49    (96)   ~ (all_52_5 = all_52_29)
% 201.80/33.49    (97)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.80/33.49    (98)  all_56_6 = all_52_19
% 201.80/33.49    (99)   ~ (all_52_15 = all_14_2)
% 201.80/33.49    (100)   ~ (all_52_19 = all_52_27)
% 201.80/33.49    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.80/33.49    (102)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.80/33.49    (103)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.80/33.49    (104)   ~ (all_52_13 = all_4_2)
% 201.80/33.49    (105)  op(e3, e1) = all_52_17
% 201.80/33.49    (106)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.80/33.49    (107)  op(e0, e3) = all_52_7
% 201.80/33.49    (108)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.49    (109)   ~ (all_52_9 = all_52_25)
% 201.80/33.49    (110)  all_58_15 = all_14_2
% 201.80/33.49    (111)   ~ (all_52_19 = all_10_2)
% 201.80/33.49    (112)  op(all_52_23, all_52_23) = all_52_22
% 201.80/33.49    (113)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.80/33.49    (114)  all_58_8 = all_10_2
% 201.80/33.49    (115)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.80/33.49    (116)   ~ (all_52_5 = all_10_2)
% 201.80/33.49    (117)  op(all_52_29, all_52_29) = all_52_28
% 201.80/33.49    (118)   ~ (all_52_23 = all_14_2)
% 201.80/33.49    (119)  all_56_12 = all_52_7
% 201.80/33.49    (120)  op(all_52_17, all_52_17) = all_52_16
% 201.80/33.49    (121)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.80/33.49    (122)   ~ (all_52_25 = all_6_2)
% 201.80/33.49    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.80/33.49    (124)   ~ (all_52_9 = all_4_2)
% 201.80/33.49    (125)   ~ (all_52_5 = all_6_2)
% 201.80/33.49    (126)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.80/33.49    (127)   ~ (all_52_9 = all_6_2)
% 201.80/33.49    (128)   ~ (all_52_13 = all_52_15)
% 201.80/33.49    (129)  all_56_0 = all_6_2
% 201.80/33.49    (130)  op(e3, e3) = all_6_2
% 201.80/33.49    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.80/33.49    (132)   ~ (all_52_27 = all_14_2)
% 201.80/33.49    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.49    (134)  all_56_14 = all_52_23
% 201.80/33.49    (135)  op(all_4_2, all_4_2) = all_52_10
% 201.80/33.49    (136)  all_56_3 = all_52_25
% 201.80/33.49    (137)   ~ (all_52_3 = all_52_7)
% 201.80/33.49    (138)  op(all_14_2, all_14_2) = all_52_30
% 201.80/33.49    (139)  all_58_5 = all_52_19
% 201.80/33.49    (140)  all_56_1 = all_52_9
% 201.80/33.49    (141)   ~ (all_52_15 = all_4_2)
% 201.80/33.49    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.80/33.49           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 201.80/33.49           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.80/33.49           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.80/33.49    (143)   ~ (all_52_27 = all_4_2)
% 201.80/33.49    (144)  all_58_6 = all_52_5
% 201.80/33.49    (145)  op(e3, e2) = all_52_9
% 201.80/33.49    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.80/33.49    (147)   ~ (all_52_17 = all_6_2)
% 201.80/33.49    (148)   ~ (e1 = e0)
% 201.80/33.49    (149)   ~ (e3 = e2)
% 201.80/33.49    (150)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.49    (151)   ~ (all_52_9 = all_52_17)
% 201.80/33.49    (152)  all_56_10 = all_10_2
% 201.80/33.49    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.80/33.49    (154)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.80/33.49    (155)  all_46_1 = all_6_1
% 201.80/33.49    (156)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.80/33.49    (157)  op(all_52_13, all_52_13) = all_52_12
% 201.80/33.49    (158)  op(e1, e1) = all_10_2
% 201.80/33.49    (159)   ~ (all_52_23 = all_10_2)
% 201.80/33.49    (160)   ~ (all_52_7 = all_52_23)
% 201.80/33.49    (161)   ~ (all_52_17 = all_52_19)
% 201.80/33.49    (162)  all_58_3 = all_4_2
% 201.80/33.49    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.80/33.49    (164)  all_56_13 = all_52_15
% 201.80/33.49    (165)   ~ (all_52_3 = all_4_2)
% 201.80/33.49    (166)   ~ (all_52_19 = all_4_2)
% 201.80/33.49    (167)   ~ (all_52_17 = all_52_23)
% 201.80/33.49    (168)  op(all_6_2, e3) = all_6_1
% 201.80/33.49    (169)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.80/33.49    (170)   ~ (all_52_13 = all_52_29)
% 201.80/33.49    (171)  all_58_4 = all_52_17
% 201.80/33.49    (172)   ~ (all_14_0 = e1)
% 201.80/33.49    (173)   ~ (all_14_0 = e2)
% 201.80/33.49    (174)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.80/33.49    (175)  op(all_52_25, all_52_25) = all_52_24
% 201.80/33.49  
% 201.80/33.49  Begin of proof
% 201.80/33.49  | 
% 201.80/33.49  | BETA: splitting (142) gives:
% 201.80/33.49  | 
% 201.80/33.49  | Case 1:
% 201.80/33.49  | | 
% 201.80/33.49  | |   (176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 201.80/33.49  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 201.80/33.49  | | 
% 201.80/33.49  | | BETA: splitting (176) gives:
% 201.80/33.49  | | 
% 201.80/33.49  | | Case 1:
% 201.80/33.49  | | | 
% 201.80/33.49  | | |   (177)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REF_CLOSE: (5), (7), (8), (17), (20), (23), (27), (39), (50), (51), (52),
% 201.80/33.49  | | |            (55), (77), (80), (82), (86), (116), (130), (133), (144),
% 201.80/33.49  | | |            (146), (158), (165), (168), (177) are inconsistent by sub-proof
% 201.80/33.49  | | |            #302.
% 201.80/33.49  | | | 
% 201.80/33.49  | | Case 2:
% 201.80/33.49  | | | 
% 201.80/33.49  | | |   (178)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.80/33.49  | | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.80/33.49  | | |            (24), (25), (26), (27), (28), (31), (32), (33), (34), (35),
% 201.80/33.49  | | |            (36), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 201.80/33.49  | | |            (49), (50), (51), (52), (53), (54), (55), (58), (59), (60),
% 201.80/33.49  | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 201.80/33.49  | | |            (71), (73), (76), (77), (78), (79), (80), (82), (83), (84),
% 201.80/33.49  | | |            (85), (86), (89), (90), (91), (92), (93), (94), (95), (96),
% 201.80/33.49  | | |            (97), (98), (99), (102), (103), (104), (105), (106), (107),
% 201.80/33.49  | | |            (108), (109), (110), (112), (113), (114), (115), (117), (118),
% 201.80/33.49  | | |            (119), (120), (122), (123), (124), (125), (127), (128), (129),
% 201.80/33.49  | | |            (130), (131), (132), (133), (135), (136), (137), (138), (139),
% 201.80/33.49  | | |            (140), (141), (143), (144), (145), (146), (147), (148), (149),
% 201.80/33.49  | | |            (150), (151), (153), (154), (155), (156), (157), (158), (159),
% 201.80/33.49  | | |            (160), (161), (162), (164), (165), (166), (167), (168), (169),
% 201.80/33.49  | | |            (170), (171), (173), (175), (178) are inconsistent by sub-proof
% 201.80/33.49  | | |            #286.
% 201.80/33.49  | | | 
% 201.80/33.49  | | End of split
% 201.80/33.49  | | 
% 201.80/33.49  | Case 2:
% 201.80/33.49  | | 
% 201.80/33.49  | |   (179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 201.80/33.49  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 201.80/33.49  | |            e0)
% 201.80/33.49  | | 
% 201.80/33.49  | | BETA: splitting (179) gives:
% 201.80/33.49  | | 
% 201.80/33.49  | | Case 1:
% 201.80/33.49  | | | 
% 201.80/33.49  | | |   (180)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 201.80/33.49  | | | 
% 201.80/33.49  | | | ALPHA: (180) implies:
% 201.80/33.49  | | |   (181)  all_52_22 = e0
% 201.80/33.49  | | |   (182)  all_52_20 = e1
% 201.80/33.49  | | |   (183)  all_52_18 = e2
% 201.80/33.49  | | |   (184)  all_52_16 = e3
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REDUCE: (120), (184) imply:
% 201.80/33.49  | | |   (185)  op(all_52_17, all_52_17) = e3
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REDUCE: (29), (183) imply:
% 201.80/33.49  | | |   (186)  op(all_52_19, all_52_19) = e2
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REDUCE: (112), (181) imply:
% 201.80/33.49  | | |   (187)  op(all_52_23, all_52_23) = e0
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REDUCE: (32), (182) imply:
% 201.80/33.49  | | |   (188)  op(all_10_2, all_10_2) = e1
% 201.80/33.49  | | | 
% 201.80/33.49  | | | BETA: splitting (115) gives:
% 201.80/33.49  | | | 
% 201.80/33.49  | | | Case 1:
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | |   (189)  all_56_15 = e3
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | | REF_CLOSE: (4), (5), (8), (10), (15), (18), (20), (21), (23), (24),
% 201.80/33.49  | | | |            (25), (26), (31), (33), (44), (51), (52), (53), (54), (56),
% 201.80/33.49  | | | |            (61), (68), (70), (74), (77), (84), (86), (88), (97), (110),
% 201.80/33.49  | | | |            (114), (118), (122), (123), (126), (130), (133), (134),
% 201.80/33.49  | | | |            (136), (138), (139), (147), (153), (158), (167), (168),
% 201.80/33.49  | | | |            (171), (172), (173), (175), (185), (186), (187), (188), (189)
% 201.80/33.49  | | | |            are inconsistent by sub-proof #282.
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | Case 2:
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | |   (190)   ~ (all_56_15 = e3)
% 201.80/33.49  | | | |   (191)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | | REDUCE: (54), (190) imply:
% 201.80/33.49  | | | |   (192)   ~ (all_14_2 = e3)
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (12), (14), (16), (17), (18),
% 201.80/33.49  | | | |            (20), (23), (25), (27), (31), (33), (36), (38), (39), (40),
% 201.80/33.49  | | | |            (41), (42), (44), (45), (48), (50), (51), (52), (54), (57),
% 201.80/33.49  | | | |            (60), (61), (62), (64), (68), (71), (72), (73), (77), (78),
% 201.80/33.49  | | | |            (79), (80), (81), (82), (84), (85), (86), (87), (89), (92),
% 201.80/33.49  | | | |            (95), (101), (102), (103), (105), (107), (109), (110), (111),
% 201.80/33.49  | | | |            (114), (116), (117), (118), (119), (122), (123), (125),
% 201.80/33.49  | | | |            (127), (128), (129), (130), (131), (133), (136), (137),
% 201.80/33.49  | | | |            (139), (140), (144), (145), (146), (147), (148), (149),
% 201.80/33.49  | | | |            (150), (151), (152), (153), (156), (158), (159), (160),
% 201.80/33.49  | | | |            (163), (164), (165), (168), (169), (171), (174), (175),
% 201.80/33.49  | | | |            (185), (186), (187), (188), (191), (192) are inconsistent by
% 201.80/33.49  | | | |            sub-proof #274.
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | End of split
% 201.80/33.49  | | | 
% 201.80/33.49  | | Case 2:
% 201.80/33.49  | | | 
% 201.80/33.49  | | |   (193)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 201.80/33.49  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 201.80/33.49  | | |            (27), (29), (30), (31), (33), (35), (36), (37), (38), (39),
% 201.80/33.49  | | |            (40), (41), (42), (43), (44), (45), (47), (48), (49), (50),
% 201.80/33.49  | | |            (51), (52), (54), (55), (56), (57), (59), (60), (61), (62),
% 201.80/33.49  | | |            (64), (66), (67), (68), (69), (71), (72), (73), (74), (75),
% 201.80/33.49  | | |            (76), (77), (78), (79), (80), (81), (82), (84), (85), (86),
% 201.80/33.49  | | |            (87), (89), (91), (92), (93), (96), (99), (100), (101), (102),
% 201.80/33.49  | | |            (103), (105), (106), (107), (108), (109), (110), (111), (112),
% 201.80/33.49  | | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 201.80/33.49  | | |            (122), (123), (124), (125), (127), (128), (129), (130), (131),
% 201.80/33.49  | | |            (132), (133), (134), (136), (137), (138), (139), (140), (141),
% 201.80/33.49  | | |            (143), (144), (145), (146), (147), (148), (149), (150), (155),
% 201.80/33.49  | | |            (156), (157), (158), (159), (160), (161), (162), (163), (164),
% 201.80/33.49  | | |            (165), (166), (167), (168), (169), (171), (175), (193) are
% 201.80/33.49  | | |            inconsistent by sub-proof #271.
% 201.80/33.49  | | | 
% 201.80/33.49  | | End of split
% 201.80/33.49  | | 
% 201.80/33.49  | End of split
% 201.80/33.49  | 
% 201.80/33.49  End of proof
% 201.80/33.49  
% 201.80/33.49  Sub-proof #271 shows that the following formulas are inconsistent:
% 201.80/33.49  ----------------------------------------------------------------
% 201.80/33.49    (1)   ~ (all_52_15 = all_52_23)
% 201.80/33.49    (2)   ~ (all_52_25 = all_52_27)
% 201.80/33.49    (3)  all_58_14 = all_52_23
% 201.80/33.49    (4)   ~ (e3 = e1)
% 201.80/33.49    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.80/33.49    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.49    (7)  all_58_1 = all_52_9
% 201.80/33.49    (8)   ~ (all_52_9 = all_52_13)
% 201.80/33.49    (9)   ~ (e3 = e0)
% 201.80/33.49    (10)  op(e2, e3) = all_52_3
% 201.80/33.49    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.80/33.49    (12)   ~ (all_52_7 = all_52_15)
% 201.80/33.49    (13)  op(all_52_7, all_52_7) = all_52_6
% 201.80/33.49    (14)   ~ (all_52_17 = all_52_25)
% 201.80/33.49    (15)   ~ (all_52_3 = all_6_2)
% 201.80/33.49    (16)  all_58_0 = all_6_2
% 201.80/33.49    (17)  op(all_14_2, e0) = all_14_1
% 201.80/33.49    (18)  all_56_4 = all_52_3
% 201.80/33.49    (19)  op(e3, all_6_1) = e1
% 201.80/33.49    (20)   ~ (all_52_17 = all_10_2)
% 201.80/33.49    (21)  op(e3, e0) = all_52_25
% 201.80/33.49    (22)  op(all_52_5, all_52_5) = all_52_4
% 201.80/33.49    (23)  op(all_52_19, all_52_19) = all_52_18
% 201.80/33.49    (24)   ~ (all_52_27 = all_52_29)
% 201.80/33.49    (25)  all_58_13 = all_52_15
% 201.80/33.49    (26)  all_58_9 = all_52_25
% 201.80/33.49    (27)   ~ (all_52_29 = all_14_2)
% 201.80/33.49    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.80/33.49    (29)  op(all_52_27, all_52_27) = all_52_26
% 201.80/33.49    (30)  op(e1, e3) = all_52_5
% 201.80/33.49    (31)  op(e2, e2) = all_4_2
% 201.80/33.49    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.80/33.49    (33)   ~ (all_52_3 = all_52_5)
% 201.80/33.49    (34)  all_58_11 = all_52_29
% 201.80/33.49    (35)  all_56_5 = all_4_2
% 201.80/33.49    (36)   ~ (all_52_25 = all_14_2)
% 201.80/33.49    (37)   ~ (all_52_9 = all_52_15)
% 201.80/33.49    (38)   ~ (all_52_3 = all_52_27)
% 201.80/33.49    (39)  op(all_10_2, e1) = all_10_1
% 201.80/33.49    (40)  all_46_2 = all_6_2
% 201.80/33.49    (41)  op(all_6_2, all_6_2) = all_52_0
% 201.80/33.49    (42)   ~ (all_52_7 = all_6_2)
% 201.80/33.49    (43)  op(e0, e0) = all_14_2
% 201.80/33.49    (44)  all_56_15 = all_14_2
% 201.80/33.49    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.80/33.49    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.80/33.49    (47)  all_56_11 = all_52_29
% 201.80/33.49    (48)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.80/33.49    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.80/33.49    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.80/33.49    (51)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.80/33.49    (52)   ~ (e2 = e1)
% 201.80/33.49    (53)  all_58_10 = all_52_27
% 201.80/33.49    (54)  all_56_8 = all_52_5
% 201.80/33.49    (55)  op(all_52_9, all_52_9) = all_52_8
% 201.80/33.49    (56)  op(all_52_15, all_52_15) = all_52_14
% 201.80/33.49    (57)   ~ (all_52_25 = all_52_29)
% 201.80/33.49    (58)   ~ (all_52_29 = all_10_2)
% 201.80/33.49    (59)  all_58_7 = all_52_13
% 201.80/33.49    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.80/33.49    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.80/33.49    (62)   ~ (all_52_5 = all_52_7)
% 201.80/33.49    (63)  all_58_12 = all_52_7
% 201.80/33.49    (64)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.80/33.49    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.80/33.49    (66)   ~ (all_52_7 = all_14_2)
% 201.80/33.49    (67)   ~ (all_14_2 = e0)
% 201.80/33.49    (68)  all_58_2 = all_52_3
% 201.80/33.49    (69)  all_56_2 = all_52_17
% 201.80/33.49    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.80/33.49    (71)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.80/33.49    (72)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.80/33.49    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.80/33.49    (74)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.80/33.49    (75)   ~ (e2 = e0)
% 201.80/33.49    (76)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.80/33.49    (77)   ~ (all_52_5 = all_52_29)
% 201.80/33.49    (78)   ~ (all_52_15 = all_14_2)
% 201.80/33.49    (79)   ~ (all_52_19 = all_52_27)
% 201.80/33.49    (80)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.80/33.49    (81)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.80/33.49    (82)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.80/33.49    (83)  op(e3, e1) = all_52_17
% 201.80/33.49    (84)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.80/33.49    (85)  op(e0, e3) = all_52_7
% 201.80/33.49    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.49    (87)   ~ (all_52_9 = all_52_25)
% 201.80/33.49    (88)  all_58_15 = all_14_2
% 201.80/33.49    (89)   ~ (all_52_19 = all_10_2)
% 201.80/33.49    (90)  op(all_52_23, all_52_23) = all_52_22
% 201.80/33.49    (91)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.80/33.49    (92)  all_58_8 = all_10_2
% 201.80/33.49    (93)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.80/33.49    (94)   ~ (all_52_5 = all_10_2)
% 201.80/33.49    (95)  op(all_52_29, all_52_29) = all_52_28
% 201.80/33.49    (96)   ~ (all_52_23 = all_14_2)
% 201.80/33.49    (97)  all_56_12 = all_52_7
% 201.80/33.49    (98)  op(all_52_17, all_52_17) = all_52_16
% 201.80/33.49    (99)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.80/33.49    (100)   ~ (all_52_25 = all_6_2)
% 201.80/33.49    (101)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.80/33.49    (102)   ~ (all_52_9 = all_4_2)
% 201.80/33.49    (103)   ~ (all_52_5 = all_6_2)
% 201.80/33.49    (104)   ~ (all_52_9 = all_6_2)
% 201.80/33.49    (105)   ~ (all_52_13 = all_52_15)
% 201.80/33.49    (106)  all_56_0 = all_6_2
% 201.80/33.49    (107)  op(e3, e3) = all_6_2
% 201.80/33.49    (108)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.80/33.49    (109)   ~ (all_52_27 = all_14_2)
% 201.80/33.49    (110)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.49    (111)  all_56_14 = all_52_23
% 201.80/33.49    (112)  all_56_3 = all_52_25
% 201.80/33.49    (113)   ~ (all_52_3 = all_52_7)
% 201.80/33.49    (114)  op(all_14_2, all_14_2) = all_52_30
% 201.80/33.49    (115)  all_58_5 = all_52_19
% 201.80/33.49    (116)  all_56_1 = all_52_9
% 201.80/33.49    (117)   ~ (all_52_15 = all_4_2)
% 201.80/33.49    (118)   ~ (all_52_27 = all_4_2)
% 201.80/33.49    (119)  all_58_6 = all_52_5
% 201.80/33.49    (120)  op(e3, e2) = all_52_9
% 201.80/33.49    (121)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.80/33.49    (122)   ~ (all_52_17 = all_6_2)
% 201.80/33.49    (123)   ~ (e1 = e0)
% 201.80/33.49    (124)   ~ (e3 = e2)
% 201.80/33.49    (125)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.49    (126)  all_46_1 = all_6_1
% 201.80/33.49    (127)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.80/33.49    (128)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.80/33.49    (129)  op(all_52_13, all_52_13) = all_52_12
% 201.80/33.49    (130)  op(e1, e1) = all_10_2
% 201.80/33.49    (131)   ~ (all_52_23 = all_10_2)
% 201.80/33.49    (132)   ~ (all_52_7 = all_52_23)
% 201.80/33.49    (133)   ~ (all_52_17 = all_52_19)
% 201.80/33.49    (134)  all_58_3 = all_4_2
% 201.80/33.49    (135)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.80/33.49    (136)  all_56_13 = all_52_15
% 201.80/33.49    (137)   ~ (all_52_3 = all_4_2)
% 201.80/33.49    (138)   ~ (all_52_19 = all_4_2)
% 201.80/33.49    (139)   ~ (all_52_17 = all_52_23)
% 201.80/33.49    (140)  op(all_6_2, e3) = all_6_1
% 201.80/33.49    (141)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.80/33.49    (142)  all_58_4 = all_52_17
% 201.80/33.49    (143)  op(all_52_25, all_52_25) = all_52_24
% 201.80/33.49  
% 201.80/33.49  Begin of proof
% 201.80/33.49  | 
% 201.80/33.49  | ALPHA: (127) implies:
% 201.80/33.49  |   (144)  all_52_30 = e0
% 201.80/33.49  |   (145)  all_52_28 = e1
% 201.80/33.49  |   (146)  all_52_26 = e2
% 201.80/33.49  |   (147)  all_52_24 = e3
% 201.80/33.49  | 
% 201.80/33.49  | REDUCE: (143), (147) imply:
% 201.80/33.49  |   (148)  op(all_52_25, all_52_25) = e3
% 201.80/33.49  | 
% 201.80/33.49  | REDUCE: (29), (146) imply:
% 201.80/33.49  |   (149)  op(all_52_27, all_52_27) = e2
% 201.80/33.49  | 
% 201.80/33.49  | REDUCE: (95), (145) imply:
% 201.80/33.49  |   (150)  op(all_52_29, all_52_29) = e1
% 201.80/33.49  | 
% 201.80/33.49  | REDUCE: (114), (144) imply:
% 201.80/33.49  |   (151)  op(all_14_2, all_14_2) = e0
% 201.80/33.49  | 
% 201.80/33.49  | BETA: splitting (93) gives:
% 201.80/33.49  | 
% 201.80/33.49  | Case 1:
% 201.80/33.49  | | 
% 201.80/33.49  | |   (152)  all_56_15 = e3
% 201.80/33.49  | | 
% 201.80/33.49  | | COMBINE_EQS: (44), (152) imply:
% 201.80/33.49  | |   (153)  all_14_2 = e3
% 201.80/33.49  | | 
% 201.80/33.49  | | SIMP: (153) implies:
% 201.80/33.49  | |   (154)  all_14_2 = e3
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (66), (154) imply:
% 201.80/33.49  | |   (155)   ~ (all_52_7 = e3)
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (36), (154) imply:
% 201.80/33.49  | |   (156)   ~ (all_52_25 = e3)
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (151), (154) imply:
% 201.80/33.49  | |   (157)  op(e3, e3) = e0
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (17), (154) imply:
% 201.80/33.49  | |   (158)  op(e3, e0) = all_14_1
% 201.80/33.49  | | 
% 201.80/33.49  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 201.80/33.49  | |              with (21), (158) gives:
% 201.80/33.49  | |   (159)  all_52_25 = all_14_1
% 201.80/33.49  | | 
% 201.80/33.49  | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying with
% 201.80/33.49  | |              (107), (157) gives:
% 201.80/33.49  | |   (160)  all_6_2 = e0
% 201.80/33.49  | | 
% 201.80/33.49  | | COMBINE_EQS: (26), (159) imply:
% 201.80/33.49  | |   (161)  all_58_9 = all_14_1
% 201.80/33.49  | | 
% 201.80/33.49  | | COMBINE_EQS: (16), (160) imply:
% 201.80/33.49  | |   (162)  all_58_0 = e0
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (42), (160) imply:
% 201.80/33.49  | |   (163)   ~ (all_52_7 = e0)
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (156), (159) imply:
% 201.80/33.49  | |   (164)   ~ (all_14_1 = e3)
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (148), (159) imply:
% 201.80/33.49  | |   (165)  op(all_14_1, all_14_1) = e3
% 201.80/33.49  | | 
% 201.80/33.49  | | REDUCE: (140), (160) imply:
% 201.80/33.49  | |   (166)  op(e0, e3) = all_6_1
% 201.80/33.49  | | 
% 201.80/33.49  | | BETA: splitting (64) gives:
% 201.80/33.49  | | 
% 201.80/33.49  | | Case 1:
% 201.80/33.49  | | | 
% 201.80/33.49  | | |   (167)   ~ (all_6_1 = e2)
% 201.80/33.49  | | | 
% 201.80/33.49  | | | GROUND_INST: instantiating (6) with all_52_7, all_6_1, e3, e0, simplifying
% 201.80/33.49  | | |              with (85), (166) gives:
% 201.80/33.49  | | |   (168)  all_52_7 = all_6_1
% 201.80/33.49  | | | 
% 201.80/33.49  | | | COMBINE_EQS: (97), (168) imply:
% 201.80/33.49  | | |   (169)  all_56_12 = all_6_1
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REDUCE: (155), (168) imply:
% 201.80/33.49  | | |   (170)   ~ (all_6_1 = e3)
% 201.80/33.49  | | | 
% 201.80/33.49  | | | REDUCE: (163), (168) imply:
% 201.80/33.49  | | |   (171)   ~ (all_6_1 = e0)
% 201.80/33.49  | | | 
% 201.80/33.49  | | | BETA: splitting (11) gives:
% 201.80/33.49  | | | 
% 201.80/33.49  | | | Case 1:
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | |   (172)  all_56_12 = e3
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | | REF_CLOSE: (169), (170), (172) are inconsistent by sub-proof #1347.
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | Case 2:
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | |   (173)   ~ (all_56_12 = e3)
% 201.80/33.49  | | | |   (174)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | | BETA: splitting (174) gives:
% 201.80/33.49  | | | | 
% 201.80/33.49  | | | | Case 1:
% 201.80/33.49  | | | | | 
% 201.80/33.49  | | | | |   (175)  all_56_12 = e2
% 201.80/33.49  | | | | | 
% 201.80/33.49  | | | | | REF_CLOSE: (167), (169), (175) are inconsistent by sub-proof #1346.
% 201.80/33.49  | | | | | 
% 201.80/33.49  | | | | Case 2:
% 201.80/33.49  | | | | | 
% 201.80/33.49  | | | | |   (176)   ~ (all_56_12 = e2)
% 201.80/33.49  | | | | |   (177)  all_56_12 = e1 | all_56_12 = e0
% 201.80/33.49  | | | | | 
% 201.80/33.50  | | | | | BETA: splitting (177) gives:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | Case 1:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | |   (178)  all_56_12 = e1
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | COMBINE_EQS: (169), (178) imply:
% 201.80/33.50  | | | | | |   (179)  all_6_1 = e1
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | SIMP: (179) implies:
% 201.80/33.50  | | | | | |   (180)  all_6_1 = e1
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REDUCE: (170), (180) imply:
% 201.80/33.50  | | | | | |   (181)   ~ (e3 = e1)
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REDUCE: (167), (180) imply:
% 201.80/33.50  | | | | | |   (182)   ~ (e2 = e1)
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REDUCE: (19), (180) imply:
% 201.80/33.50  | | | | | |   (183)  op(e3, e1) = e1
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | GROUND_INST: instantiating (6) with all_52_17, e1, e1, e3,
% 201.80/33.50  | | | | | |              simplifying with (83), (183) gives:
% 201.80/33.50  | | | | | |   (184)  all_52_17 = e1
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | COMBINE_EQS: (142), (184) imply:
% 201.80/33.50  | | | | | |   (185)  all_58_4 = e1
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (25), (31), (37), (52), (59),
% 201.80/33.50  | | | | | |            (70), (75), (86), (102), (110), (124), (134), (161),
% 201.80/33.50  | | | | | |            (162), (164), (165), (185) are inconsistent by sub-proof
% 201.80/33.50  | | | | | |            #273.
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | Case 2:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | |   (186)  all_56_12 = e0
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REF_CLOSE: (169), (171), (186) are inconsistent by sub-proof #1345.
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | End of split
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | End of split
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | End of split
% 201.80/33.50  | | | 
% 201.80/33.50  | | Case 2:
% 201.80/33.50  | | | 
% 201.80/33.50  | | |   (187)   ~ (all_6_2 = e0)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (160), (187) imply:
% 201.80/33.50  | | |   (188)  $false
% 201.80/33.50  | | | 
% 201.80/33.50  | | | CLOSE: (188) is inconsistent.
% 201.80/33.50  | | | 
% 201.80/33.50  | | End of split
% 201.80/33.50  | | 
% 201.80/33.50  | Case 2:
% 201.80/33.50  | | 
% 201.80/33.50  | |   (189)   ~ (all_56_15 = e3)
% 201.80/33.50  | |   (190)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (44), (189) imply:
% 201.80/33.50  | |   (191)   ~ (all_14_2 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 201.80/33.50  | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 201.80/33.50  | |            (26), (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 201.80/33.50  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 201.80/33.50  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 201.80/33.50  | |            (60), (61), (62), (63), (65), (66), (67), (68), (69), (71), (72),
% 201.80/33.50  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 201.80/33.50  | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (94), (96),
% 201.80/33.50  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 201.80/33.50  | |            (107), (108), (109), (110), (111), (112), (113), (115), (116),
% 201.80/33.50  | |            (117), (118), (119), (120), (121), (122), (123), (124), (125),
% 201.80/33.50  | |            (126), (128), (129), (130), (131), (132), (133), (134), (135),
% 201.80/33.50  | |            (136), (137), (138), (139), (140), (141), (142), (148), (149),
% 201.80/33.50  | |            (150), (151), (190), (191) are inconsistent by sub-proof #272.
% 201.80/33.50  | | 
% 201.80/33.50  | End of split
% 201.80/33.50  | 
% 201.80/33.50  End of proof
% 201.80/33.50  
% 201.80/33.50  Sub-proof #272 shows that the following formulas are inconsistent:
% 201.80/33.50  ----------------------------------------------------------------
% 201.80/33.50    (1)   ~ (all_52_15 = all_52_23)
% 201.80/33.50    (2)   ~ (all_52_25 = all_52_27)
% 201.80/33.50    (3)  all_58_14 = all_52_23
% 201.80/33.50    (4)   ~ (e3 = e1)
% 201.80/33.50    (5)  op(all_52_3, all_52_3) = all_52_2
% 201.80/33.50    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.50    (7)  all_58_1 = all_52_9
% 201.80/33.50    (8)   ~ (all_52_9 = all_52_13)
% 201.80/33.50    (9)   ~ (e3 = e0)
% 201.80/33.50    (10)  op(e2, e3) = all_52_3
% 201.80/33.50    (11)   ~ (all_52_7 = all_52_15)
% 201.80/33.50    (12)  op(all_52_7, all_52_7) = all_52_6
% 201.80/33.50    (13)   ~ (all_52_17 = all_52_25)
% 201.80/33.50    (14)   ~ (all_52_3 = all_6_2)
% 201.80/33.50    (15)  all_58_0 = all_6_2
% 201.80/33.50    (16)  all_56_4 = all_52_3
% 201.80/33.50    (17)  op(e3, all_6_1) = e1
% 201.80/33.50    (18)   ~ (all_52_17 = all_10_2)
% 201.80/33.50    (19)  op(e3, e0) = all_52_25
% 201.80/33.50    (20)  op(all_52_5, all_52_5) = all_52_4
% 201.80/33.50    (21)  op(all_52_19, all_52_19) = all_52_18
% 201.80/33.50    (22)   ~ (all_52_27 = all_52_29)
% 201.80/33.50    (23)  all_58_13 = all_52_15
% 201.80/33.50    (24)  all_58_9 = all_52_25
% 201.80/33.50    (25)   ~ (all_52_29 = all_14_2)
% 201.80/33.50    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.80/33.50    (27)  op(e1, e3) = all_52_5
% 201.80/33.50    (28)  op(e2, e2) = all_4_2
% 201.80/33.50    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.80/33.50    (30)   ~ (all_52_3 = all_52_5)
% 201.80/33.50    (31)  all_58_11 = all_52_29
% 201.80/33.50    (32)  all_56_5 = all_4_2
% 201.80/33.50    (33)   ~ (all_52_25 = all_14_2)
% 201.80/33.50    (34)   ~ (all_52_9 = all_52_15)
% 201.80/33.50    (35)   ~ (all_52_3 = all_52_27)
% 201.80/33.50    (36)  op(all_10_2, e1) = all_10_1
% 201.80/33.50    (37)  all_46_2 = all_6_2
% 201.80/33.50    (38)  op(all_6_2, all_6_2) = all_52_0
% 201.80/33.50    (39)   ~ (all_52_7 = all_6_2)
% 201.80/33.50    (40)  op(e0, e0) = all_14_2
% 201.80/33.50    (41)  op(all_52_29, all_52_29) = e1
% 201.80/33.50    (42)  all_56_15 = all_14_2
% 201.80/33.50    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.80/33.50    (44)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.80/33.50    (45)  all_56_11 = all_52_29
% 201.80/33.50    (46)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.80/33.50    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.80/33.50    (48)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.80/33.50    (49)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.80/33.50    (50)   ~ (e2 = e1)
% 201.80/33.50    (51)  all_58_10 = all_52_27
% 201.80/33.50    (52)  all_56_8 = all_52_5
% 201.80/33.50    (53)  op(all_52_9, all_52_9) = all_52_8
% 201.80/33.50    (54)  op(all_52_15, all_52_15) = all_52_14
% 201.80/33.50    (55)   ~ (all_52_25 = all_52_29)
% 201.80/33.50    (56)   ~ (all_52_29 = all_10_2)
% 201.80/33.50    (57)  all_58_7 = all_52_13
% 201.80/33.50    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.80/33.50    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 201.80/33.50    (60)   ~ (all_52_5 = all_52_7)
% 201.80/33.50    (61)  all_58_12 = all_52_7
% 201.80/33.50    (62)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.80/33.50    (63)   ~ (all_52_7 = all_14_2)
% 201.80/33.50    (64)   ~ (all_14_2 = e0)
% 201.80/33.50    (65)  all_58_2 = all_52_3
% 201.80/33.50    (66)  all_56_2 = all_52_17
% 201.80/33.50    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.80/33.50    (68)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.80/33.50    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.80/33.50    (70)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.80/33.50    (71)   ~ (e2 = e0)
% 201.80/33.50    (72)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.80/33.50    (73)  op(all_52_25, all_52_25) = e3
% 201.80/33.50    (74)   ~ (all_52_5 = all_52_29)
% 201.80/33.50    (75)   ~ (all_52_15 = all_14_2)
% 201.80/33.50    (76)   ~ (all_52_19 = all_52_27)
% 201.80/33.50    (77)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.80/33.50    (78)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.80/33.50    (79)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.80/33.50    (80)  op(e3, e1) = all_52_17
% 201.80/33.50    (81)  op(all_52_27, all_52_27) = e2
% 201.80/33.50    (82)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.80/33.50    (83)  op(e0, e3) = all_52_7
% 201.80/33.50    (84)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.50    (85)   ~ (all_52_9 = all_52_25)
% 201.80/33.50    (86)  all_58_15 = all_14_2
% 201.80/33.50    (87)   ~ (all_52_19 = all_10_2)
% 201.80/33.50    (88)  op(all_52_23, all_52_23) = all_52_22
% 201.80/33.50    (89)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.80/33.50    (90)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.80/33.50    (91)  all_58_8 = all_10_2
% 201.80/33.50    (92)   ~ (all_52_5 = all_10_2)
% 201.80/33.50    (93)   ~ (all_52_23 = all_14_2)
% 201.80/33.50    (94)  op(all_52_17, all_52_17) = all_52_16
% 201.80/33.50    (95)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 201.80/33.50    (96)   ~ (all_52_25 = all_6_2)
% 201.80/33.50    (97)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.80/33.50    (98)   ~ (all_52_9 = all_4_2)
% 201.80/33.50    (99)   ~ (all_52_5 = all_6_2)
% 201.80/33.50    (100)   ~ (all_52_9 = all_6_2)
% 201.80/33.50    (101)   ~ (all_52_13 = all_52_15)
% 201.80/33.50    (102)  all_56_0 = all_6_2
% 201.80/33.50    (103)  op(e3, e3) = all_6_2
% 201.80/33.50    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.80/33.50    (105)   ~ (all_52_27 = all_14_2)
% 201.80/33.50    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.50    (107)  all_56_14 = all_52_23
% 201.80/33.50    (108)  all_56_3 = all_52_25
% 201.80/33.50    (109)   ~ (all_52_3 = all_52_7)
% 201.80/33.50    (110)  all_58_5 = all_52_19
% 201.80/33.50    (111)  all_56_1 = all_52_9
% 201.80/33.50    (112)   ~ (all_52_15 = all_4_2)
% 201.80/33.50    (113)   ~ (all_52_27 = all_4_2)
% 201.80/33.50    (114)  all_58_6 = all_52_5
% 201.80/33.50    (115)  op(e3, e2) = all_52_9
% 201.80/33.50    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.80/33.50    (117)   ~ (all_52_17 = all_6_2)
% 201.80/33.50    (118)   ~ (e1 = e0)
% 201.80/33.50    (119)  op(all_14_2, all_14_2) = e0
% 201.80/33.50    (120)   ~ (e3 = e2)
% 201.80/33.50    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.50    (122)  all_46_1 = all_6_1
% 201.80/33.50    (123)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.80/33.50    (124)  op(all_52_13, all_52_13) = all_52_12
% 201.80/33.50    (125)  op(e1, e1) = all_10_2
% 201.80/33.50    (126)   ~ (all_52_23 = all_10_2)
% 201.80/33.50    (127)   ~ (all_52_7 = all_52_23)
% 201.80/33.50    (128)   ~ (all_52_17 = all_52_19)
% 201.80/33.50    (129)  all_58_3 = all_4_2
% 201.80/33.50    (130)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.80/33.50    (131)  all_56_13 = all_52_15
% 201.80/33.50    (132)   ~ (all_52_3 = all_4_2)
% 201.80/33.50    (133)   ~ (all_52_19 = all_4_2)
% 201.80/33.50    (134)   ~ (all_52_17 = all_52_23)
% 201.80/33.50    (135)  op(all_6_2, e3) = all_6_1
% 201.80/33.50    (136)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.80/33.50    (137)  all_58_4 = all_52_17
% 201.80/33.50    (138)   ~ (all_14_2 = e3)
% 201.80/33.50  
% 201.80/33.50  Begin of proof
% 201.80/33.50  | 
% 201.80/33.50  | BETA: splitting (47) gives:
% 201.80/33.50  | 
% 201.80/33.50  | Case 1:
% 201.80/33.50  | | 
% 201.80/33.50  | |   (139)  all_56_13 = e3
% 201.80/33.50  | | 
% 201.80/33.50  | | COMBINE_EQS: (131), (139) imply:
% 201.80/33.50  | |   (140)  all_52_15 = e3
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (11), (140) imply:
% 201.80/33.50  | |   (141)   ~ (all_52_7 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (34), (140) imply:
% 201.80/33.50  | |   (142)   ~ (all_52_9 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (101), (140) imply:
% 201.80/33.50  | |   (143)   ~ (all_52_13 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (75), (140) imply:
% 201.80/33.50  | |   (144)   ~ (all_14_2 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (112), (140) imply:
% 201.80/33.50  | |   (145)   ~ (all_4_2 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | SIMP: (145) implies:
% 201.80/33.50  | |   (146)   ~ (all_4_2 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (54), (140) imply:
% 201.80/33.50  | |   (147)  op(e3, e3) = all_52_14
% 201.80/33.50  | | 
% 201.80/33.50  | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3, simplifying
% 201.80/33.50  | |              with (103), (147) gives:
% 201.80/33.50  | |   (148)  all_52_14 = all_6_2
% 201.80/33.50  | | 
% 201.80/33.50  | | BETA: splitting (121) gives:
% 201.80/33.50  | | 
% 201.80/33.50  | | Case 1:
% 201.80/33.50  | | | 
% 201.80/33.50  | | |   (149)  all_56_1 = e3
% 201.80/33.50  | | | 
% 201.80/33.50  | | | COMBINE_EQS: (111), (149) imply:
% 201.80/33.50  | | |   (150)  all_52_9 = e3
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (142), (150) imply:
% 201.80/33.50  | | |   (151)  $false
% 201.80/33.50  | | | 
% 201.80/33.50  | | | CLOSE: (151) is inconsistent.
% 201.80/33.50  | | | 
% 201.80/33.50  | | Case 2:
% 201.80/33.50  | | | 
% 201.80/33.50  | | |   (152)   ~ (all_56_1 = e3)
% 201.80/33.50  | | |   (153)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.80/33.50  | | | 
% 201.80/33.50  | | | BETA: splitting (49) gives:
% 201.80/33.50  | | | 
% 201.80/33.50  | | | Case 1:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | |   (154)  all_58_1 = e1
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | COMBINE_EQS: (7), (154) imply:
% 201.80/33.50  | | | |   (155)  all_52_9 = e1
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | REDUCE: (100), (155) imply:
% 201.80/33.50  | | | |   (156)   ~ (all_6_2 = e1)
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | SIMP: (156) implies:
% 201.80/33.50  | | | |   (157)   ~ (all_6_2 = e1)
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | REDUCE: (53), (155) imply:
% 201.80/33.50  | | | |   (158)  op(e1, e1) = all_52_8
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_8, e1, e1,
% 201.80/33.50  | | | |              simplifying with (125), (158) gives:
% 201.80/33.50  | | | |   (159)  all_52_8 = all_10_2
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | BETA: splitting (97) gives:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | Case 1:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | |   (160)  all_56_3 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | COMBINE_EQS: (108), (160) imply:
% 201.80/33.50  | | | | |   (161)  all_52_25 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REF_CLOSE: (6), (73), (96), (103), (161) are inconsistent by sub-proof
% 201.80/33.50  | | | | |            #1246.
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | Case 2:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | |   (162)   ~ (all_56_3 = e3)
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REDUCE: (108), (162) imply:
% 201.80/33.50  | | | | |   (163)   ~ (all_52_25 = e3)
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | BETA: splitting (104) gives:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | Case 1:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | |   (164)  all_58_9 = e3
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REF_CLOSE: (24), (163), (164) are inconsistent by sub-proof #1300.
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | Case 2:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | |   (165)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | BETA: splitting (106) gives:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | Case 1:
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | |   (166)  all_58_0 = e3
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | COMBINE_EQS: (15), (166) imply:
% 201.80/33.50  | | | | | | |   (167)  all_6_2 = e3
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REDUCE: (14), (167) imply:
% 201.80/33.50  | | | | | | |   (168)   ~ (all_52_3 = e3)
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REDUCE: (99), (167) imply:
% 201.80/33.50  | | | | | | |   (169)   ~ (all_52_5 = e3)
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REDUCE: (38), (167) imply:
% 201.80/33.50  | | | | | | |   (170)  op(e3, e3) = all_52_0
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REDUCE: (103), (167) imply:
% 201.80/33.50  | | | | | | |   (171)  op(e3, e3) = e3
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REF_CLOSE: (2), (4), (6), (7), (13), (15), (18), (24), (31), (40),
% 201.80/33.50  | | | | | | |            (41), (43), (44), (45), (51), (57), (62), (65), (73),
% 201.80/33.50  | | | | | | |            (77), (81), (87), (91), (96), (97), (103), (105),
% 201.80/33.50  | | | | | | |            (106), (108), (110), (114), (120), (125), (129), (137),
% 201.80/33.50  | | | | | | |            (142), (143), (146), (168), (169), (170), (171) are
% 201.80/33.50  | | | | | | |            inconsistent by sub-proof #1227.
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | Case 2:
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | |   (172)   ~ (all_58_0 = e3)
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REDUCE: (15), (172) imply:
% 201.80/33.50  | | | | | | |   (173)   ~ (all_6_2 = e3)
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REF_CLOSE: (2), (6), (7), (13), (15), (18), (20), (24), (30),
% 201.80/33.50  | | | | | | |            (31), (35), (40), (41), (43), (44), (51), (53), (61),
% 201.80/33.50  | | | | | | |            (62), (65), (67), (73), (74), (76), (81), (84), (85),
% 201.80/33.50  | | | | | | |            (86), (92), (96), (97), (103), (104), (105), (106),
% 201.80/33.50  | | | | | | |            (108), (110), (113), (114), (120), (125), (129), (137),
% 201.80/33.50  | | | | | | |            (138), (141), (147), (157), (165), (173) are
% 201.80/33.50  | | | | | | |            inconsistent by sub-proof #1038.
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | End of split
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | End of split
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | End of split
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | Case 2:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | |   (174)   ~ (all_58_1 = e1)
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | REDUCE: (7), (174) imply:
% 201.80/33.50  | | | |   (175)   ~ (all_52_9 = e1)
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | BETA: splitting (106) gives:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | Case 1:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | |   (176)  all_58_0 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | COMBINE_EQS: (15), (176) imply:
% 201.80/33.50  | | | | |   (177)  all_6_2 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REDUCE: (14), (177) imply:
% 201.80/33.50  | | | | |   (178)   ~ (all_52_3 = e3)
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REDUCE: (99), (177) imply:
% 201.80/33.50  | | | | |   (179)   ~ (all_52_5 = e3)
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REDUCE: (38), (177) imply:
% 201.80/33.50  | | | | |   (180)  op(e3, e3) = all_52_0
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REDUCE: (103), (177) imply:
% 201.80/33.50  | | | | |   (181)  op(e3, e3) = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REF_CLOSE: (2), (4), (6), (7), (13), (15), (18), (24), (31), (40),
% 201.80/33.50  | | | | |            (41), (43), (44), (45), (51), (57), (62), (65), (73), (77),
% 201.80/33.50  | | | | |            (81), (87), (91), (96), (97), (103), (105), (106), (108),
% 201.80/33.50  | | | | |            (110), (114), (120), (125), (129), (137), (142), (143),
% 201.80/33.50  | | | | |            (146), (178), (179), (180), (181) are inconsistent by
% 201.80/33.50  | | | | |            sub-proof #1227.
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | Case 2:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | |   (182)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REF_CLOSE: (2), (4), (6), (7), (13), (15), (18), (24), (28), (31),
% 201.80/33.50  | | | | |            (35), (40), (41), (43), (44), (48), (51), (53), (55), (61),
% 201.80/33.50  | | | | |            (65), (66), (67), (73), (74), (81), (85), (86), (94), (96),
% 201.80/33.50  | | | | |            (97), (103), (104), (105), (106), (108), (109), (110),
% 201.80/33.50  | | | | |            (111), (114), (120), (125), (128), (129), (130), (132),
% 201.80/33.50  | | | | |            (137), (138), (142), (146), (153), (175), (182) are
% 201.80/33.50  | | | | |            inconsistent by sub-proof #1035.
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | End of split
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | End of split
% 201.80/33.50  | | | 
% 201.80/33.50  | | End of split
% 201.80/33.50  | | 
% 201.80/33.50  | Case 2:
% 201.80/33.50  | | 
% 201.80/33.50  | |   (183)   ~ (all_56_13 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | REDUCE: (131), (183) imply:
% 201.80/33.50  | |   (184)   ~ (all_52_15 = e3)
% 201.80/33.50  | | 
% 201.80/33.50  | | BETA: splitting (116) gives:
% 201.80/33.50  | | 
% 201.80/33.50  | | Case 1:
% 201.80/33.50  | | | 
% 201.80/33.50  | | |   (185)  all_58_12 = e3
% 201.80/33.50  | | | 
% 201.80/33.50  | | | COMBINE_EQS: (61), (185) imply:
% 201.80/33.50  | | |   (186)  all_52_7 = e3
% 201.80/33.50  | | | 
% 201.80/33.50  | | | SIMP: (186) implies:
% 201.80/33.50  | | |   (187)  all_52_7 = e3
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (109), (187) imply:
% 201.80/33.50  | | |   (188)   ~ (all_52_3 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (60), (187) imply:
% 201.80/33.50  | | |   (189)   ~ (all_52_5 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (127), (187) imply:
% 201.80/33.50  | | |   (190)   ~ (all_52_23 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | SIMP: (190) implies:
% 201.80/33.50  | | |   (191)   ~ (all_52_23 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (63), (187) imply:
% 201.80/33.50  | | |   (192)   ~ (all_14_2 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (39), (187) imply:
% 201.80/33.50  | | |   (193)   ~ (all_6_2 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | SIMP: (193) implies:
% 201.80/33.50  | | |   (194)   ~ (all_6_2 = e3)
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (12), (187) imply:
% 201.80/33.50  | | |   (195)  op(e3, e3) = all_52_6
% 201.80/33.50  | | | 
% 201.80/33.50  | | | REDUCE: (83), (187) imply:
% 201.80/33.50  | | |   (196)  op(e0, e3) = e3
% 201.80/33.50  | | | 
% 201.80/33.50  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 201.80/33.50  | | |              with (103), (195) gives:
% 201.80/33.50  | | |   (197)  all_52_6 = all_6_2
% 201.80/33.50  | | | 
% 201.80/33.50  | | | BETA: splitting (70) gives:
% 201.80/33.50  | | | 
% 201.80/33.50  | | | Case 1:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | |   (198)  all_56_4 = e3
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | REF_CLOSE: (16), (188), (198) are inconsistent by sub-proof #1340.
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | Case 2:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | |   (199)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | BETA: splitting (123) gives:
% 201.80/33.50  | | | | 
% 201.80/33.50  | | | | Case 1:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | |   (200)  all_56_0 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | COMBINE_EQS: (102), (200) imply:
% 201.80/33.50  | | | | |   (201)  all_6_2 = e3
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | REDUCE: (194), (201) imply:
% 201.80/33.50  | | | | |   (202)  $false
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | CLOSE: (202) is inconsistent.
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | Case 2:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | |   (203)   ~ (all_56_0 = e3)
% 201.80/33.50  | | | | |   (204)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | BETA: splitting (58) gives:
% 201.80/33.50  | | | | | 
% 201.80/33.50  | | | | | Case 1:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | |   (205)  all_56_14 = e3
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | REF_CLOSE: (107), (191), (205) are inconsistent by sub-proof #1286.
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | Case 2:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | |   (206)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | BETA: splitting (89) gives:
% 201.80/33.50  | | | | | | 
% 201.80/33.50  | | | | | | Case 1:
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | |   (207)  all_56_8 = e3
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | REF_CLOSE: (52), (189), (207) are inconsistent by sub-proof #1325.
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | Case 2:
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | |   (208)   ~ (all_56_8 = e3)
% 201.80/33.50  | | | | | | |   (209)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | BETA: splitting (69) gives:
% 201.80/33.50  | | | | | | | 
% 201.80/33.50  | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | |   (210)  all_58_0 = e1
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | COMBINE_EQS: (15), (210) imply:
% 201.80/33.50  | | | | | | | |   (211)  all_6_2 = e1
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | REDUCE: (100), (211) imply:
% 201.80/33.50  | | | | | | | |   (212)   ~ (all_52_9 = e1)
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | REDUCE: (96), (211) imply:
% 201.80/33.50  | | | | | | | |   (213)   ~ (all_52_25 = e1)
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | REDUCE: (135), (211) imply:
% 201.80/33.50  | | | | | | | |   (214)  op(e1, e3) = all_6_1
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | REF_CLOSE: (6), (9), (17), (19), (27), (29), (50), (65), (71),
% 201.80/33.50  | | | | | | | |            (78), (114), (115), (118), (120), (136), (185),
% 201.80/33.50  | | | | | | | |            (210), (212), (213), (214) are inconsistent by
% 201.80/33.50  | | | | | | | |            sub-proof #307.
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | |   (215)   ~ (all_58_0 = e1)
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | REDUCE: (15), (215) imply:
% 201.80/33.50  | | | | | | | |   (216)   ~ (all_6_2 = e1)
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | BETA: splitting (106) gives:
% 201.80/33.50  | | | | | | | | 
% 201.80/33.50  | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | |   (217)  all_58_0 = e3
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | COMBINE_EQS: (15), (217) imply:
% 201.80/33.50  | | | | | | | | |   (218)  all_6_2 = e3
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | REDUCE: (194), (218) imply:
% 201.80/33.50  | | | | | | | | |   (219)  $false
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | CLOSE: (219) is inconsistent.
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | |   (220)   ~ (all_58_0 = e3)
% 201.80/33.50  | | | | | | | | |   (221)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | BETA: splitting (78) gives:
% 201.80/33.50  | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | |   (222)  all_58_0 = e2
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | COMBINE_EQS: (15), (222) imply:
% 201.80/33.50  | | | | | | | | | |   (223)  all_6_2 = e2
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | COMBINE_EQS: (37), (223) imply:
% 201.80/33.50  | | | | | | | | | |   (224)  all_46_2 = e2
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | REDUCE: (14), (223) imply:
% 201.80/33.50  | | | | | | | | | |   (225)   ~ (all_52_3 = e2)
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | REDUCE: (96), (223) imply:
% 201.80/33.50  | | | | | | | | | |   (226)   ~ (all_52_25 = e2)
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | REDUCE: (38), (223) imply:
% 201.80/33.50  | | | | | | | | | |   (227)  op(e2, e2) = all_52_0
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | REDUCE: (135), (223) imply:
% 201.80/33.50  | | | | | | | | | |   (228)  op(e2, e3) = all_6_1
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | BETA: splitting (46) gives:
% 201.80/33.50  | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | |   (229)   ~ (all_46_2 = e2)
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | REDUCE: (224), (229) imply:
% 201.80/33.50  | | | | | | | | | | |   (230)  $false
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | |   (231)   ~ (all_46_1 = e0)
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | REDUCE: (122), (231) imply:
% 201.80/33.50  | | | | | | | | | | |   (232)   ~ (all_6_1 = e0)
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_4_2, all_52_0, e2, e2,
% 201.80/33.50  | | | | | | | | | | |              simplifying with (28), (227) gives:
% 201.80/33.50  | | | | | | | | | | |   (233)  all_52_0 = all_4_2
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_3, all_6_1, e3, e2,
% 201.80/33.50  | | | | | | | | | | |              simplifying with (10), (228) gives:
% 201.80/33.50  | | | | | | | | | | |   (234)  all_52_3 = all_6_1
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | COMBINE_EQS: (16), (234) imply:
% 201.80/33.50  | | | | | | | | | | |   (235)  all_56_4 = all_6_1
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | COMBINE_EQS: (65), (234) imply:
% 201.80/33.50  | | | | | | | | | | |   (236)  all_58_2 = all_6_1
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | REDUCE: (30), (234) imply:
% 201.80/33.50  | | | | | | | | | | |   (237)   ~ (all_52_5 = all_6_1)
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | SIMP: (237) implies:
% 201.80/33.50  | | | | | | | | | | |   (238)   ~ (all_52_5 = all_6_1)
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | REDUCE: (225), (234) imply:
% 201.80/33.50  | | | | | | | | | | |   (239)   ~ (all_6_1 = e2)
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | REDUCE: (5), (234) imply:
% 201.80/33.50  | | | | | | | | | | |   (240)  op(all_6_1, all_6_1) = all_52_2
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | BETA: splitting (29) gives:
% 201.80/33.50  | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | |   (241)  all_58_0 = e0
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | COMBINE_EQS: (222), (241) imply:
% 201.80/33.50  | | | | | | | | | | | |   (242)  e2 = e0
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | REDUCE: (71), (242) imply:
% 201.80/33.50  | | | | | | | | | | | |   (243)  $false
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | |   (244)   ~ (all_58_0 = e0)
% 201.80/33.50  | | | | | | | | | | | |   (245)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | BETA: splitting (245) gives:
% 201.80/33.50  | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | |   (246)  all_58_2 = e0
% 201.80/33.50  | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | REF_CLOSE: (232), (236), (246) are inconsistent by sub-proof
% 201.80/33.50  | | | | | | | | | | | | |            #295.
% 201.80/33.50  | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | |   (247)   ~ (all_58_2 = e0)
% 201.80/33.50  | | | | | | | | | | | | |   (248)  all_58_6 = e0 | all_58_12 = e0
% 201.80/33.50  | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 201.80/33.50  | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | |   (249)  all_56_4 = e2
% 201.80/33.50  | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | REF_CLOSE: (235), (239), (249) are inconsistent by sub-proof
% 201.80/33.50  | | | | | | | | | | | | | |            #1219.
% 201.80/33.50  | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | |   (250)  all_56_4 = e1 | all_56_4 = e0
% 201.80/33.50  | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 201.80/33.50  | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | |   (251)  all_56_4 = e1
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | COMBINE_EQS: (235), (251) imply:
% 201.80/33.50  | | | | | | | | | | | | | | |   (252)  all_6_1 = e1
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | SIMP: (252) implies:
% 201.80/33.50  | | | | | | | | | | | | | | |   (253)  all_6_1 = e1
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | REDUCE: (238), (253) imply:
% 201.80/33.50  | | | | | | | | | | | | | | |   (254)   ~ (all_52_5 = e1)
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | REDUCE: (240), (253) imply:
% 201.80/33.50  | | | | | | | | | | | | | | |   (255)  op(e1, e1) = all_52_2
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | REDUCE: (17), (253) imply:
% 201.80/33.50  | | | | | | | | | | | | | | |   (256)  op(e3, e1) = e1
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 201.80/33.50  | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | |   (257)  all_56_8 = e2
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (71), (114), (185), (248), (257) are
% 201.80/33.50  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #294.
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | |   (258)   ~ (all_56_8 = e2)
% 201.80/33.50  | | | | | | | | | | | | | | | |   (259)  all_56_8 = e1 | all_56_8 = e0
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | REDUCE: (52), (258) imply:
% 201.80/33.50  | | | | | | | | | | | | | | | |   (260)   ~ (all_52_5 = e2)
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 201.80/33.50  | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | Case 1:
% 201.80/33.50  | | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | |   (261)  all_56_8 = e1
% 201.80/33.50  | | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (254), (261) are inconsistent by sub-proof
% 201.80/33.50  | | | | | | | | | | | | | | | | |            #707.
% 201.80/33.50  | | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | Case 2:
% 201.80/33.50  | | | | | | | | | | | | | | | | | 
% 201.80/33.50  | | | | | | | | | | | | | | | | |   (262)  all_56_8 = e0
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (262) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (263)  all_52_5 = e0
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | SIMP: (263) implies:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (264)  all_52_5 = e0
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | REDUCE: (189), (264) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (265)   ~ (e3 = e0)
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | REDUCE: (260), (264) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (266)   ~ (e2 = e0)
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | REDUCE: (254), (264) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (267)   ~ (e1 = e0)
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | REDUCE: (20), (264) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (268)  op(e0, e0) = all_52_4
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_14_2, all_52_4, e0, e0,
% 201.80/33.51  | | | | | | | | | | | | | | | | |              simplifying with (40), (268) gives:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (269)  all_52_4 = all_14_2
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_2, e1, e1,
% 201.80/33.51  | | | | | | | | | | | | | | | | |              simplifying with (125), (255) gives:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (270)  all_52_2 = all_10_2
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_17, e1, e1, e3,
% 201.80/33.51  | | | | | | | | | | | | | | | | |              simplifying with (80), (256) gives:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (271)  all_52_17 = e1
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | REDUCE: (94), (271) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (272)  op(e1, e1) = all_52_16
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_16, e1,
% 201.80/33.51  | | | | | | | | | | | | | | | | |              e1, simplifying with (125), (272) gives:
% 201.80/33.51  | | | | | | | | | | | | | | | | |   (273)  all_52_16 = all_10_2
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (274)  all_56_1 = e3
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (274) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (275)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | SIMP: (275) implies:
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (276)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | REDUCE: (85), (276) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (277)   ~ (all_52_25 = e3)
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (278)   ~ (all_52_25 = e3)
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (13),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (15), (18), (21), (22), (23), (24), (25), (28),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (30), (31), (32), (33), (36), (38), (40), (41),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (42), (44), (45), (48), (51), (52), (55), (56),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (57), (59), (62), (64), (65), (66), (68), (71),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (72), (73), (74), (77), (79), (80), (81), (82),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (84), (86), (87), (90), (91), (93), (95), (96),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (97), (98), (99), (103), (104), (105), (106),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (107), (108), (110), (112), (114), (117), (118),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (119), (124), (125), (129), (130), (133), (134),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (135), (137), (138), (185), (189), (194), (195),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (206), (209), (216), (278) are inconsistent by
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            sub-proof #1016.
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (279)   ~ (all_56_1 = e3)
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | REDUCE: (111), (279) imply:
% 201.80/33.51  | | | | | | | | | | | | | | | | | |   (280)   ~ (all_52_9 = e3)
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (13), (18), (24), (40), (44), (48),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (66), (73), (96), (97), (103), (104), (108),
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            (125), (137), (138), (221), (226), (280) are
% 201.80/33.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 201.80/33.51  | | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | |   (281)  all_56_4 = e0
% 201.80/33.51  | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | | REF_CLOSE: (232), (235), (281) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | | | | | | | |            #1217.
% 201.80/33.51  | | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (282)   ~ (all_58_0 = e2)
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REDUCE: (15), (282) imply:
% 201.80/33.51  | | | | | | | | | |   (283)   ~ (all_6_2 = e2)
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REF_CLOSE: (6), (17), (102), (103), (135), (195), (196),
% 201.80/33.51  | | | | | | | | | |            (204), (216), (283) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | | |            #292.
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | End of split
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | End of split
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | End of split
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | End of split
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | End of split
% 201.80/33.51  | | | 
% 201.80/33.51  | | Case 2:
% 201.80/33.51  | | | 
% 201.80/33.51  | | |   (284)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.80/33.51  | | | 
% 201.80/33.51  | | | BETA: splitting (284) gives:
% 201.80/33.51  | | | 
% 201.80/33.51  | | | Case 1:
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | |   (285)  all_58_13 = e3
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | | REF_CLOSE: (23), (184), (285) are inconsistent by sub-proof #1360.
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | Case 2:
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | |   (286)  all_58_14 = e3 | all_58_15 = e3
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | | BETA: splitting (286) gives:
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | | Case 1:
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | |   (287)  all_58_14 = e3
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | COMBINE_EQS: (3), (287) imply:
% 201.80/33.51  | | | | |   (288)  all_52_23 = e3
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | SIMP: (288) implies:
% 201.80/33.51  | | | | |   (289)  all_52_23 = e3
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | REDUCE: (134), (289) imply:
% 201.80/33.51  | | | | |   (290)   ~ (all_52_17 = e3)
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | REDUCE: (93), (289) imply:
% 201.80/33.51  | | | | |   (291)   ~ (all_14_2 = e3)
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | REDUCE: (126), (289) imply:
% 201.80/33.51  | | | | |   (292)   ~ (all_10_2 = e3)
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | SIMP: (292) implies:
% 201.80/33.51  | | | | |   (293)   ~ (all_10_2 = e3)
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | REDUCE: (88), (289) imply:
% 201.80/33.51  | | | | |   (294)  op(e3, e3) = all_52_22
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 201.80/33.51  | | | | |              simplifying with (103), (294) gives:
% 201.80/33.51  | | | | |   (295)  all_52_22 = all_6_2
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | BETA: splitting (48) gives:
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | Case 1:
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | |   (296)  all_56_2 = e3
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | | REF_CLOSE: (66), (290), (296) are inconsistent by sub-proof #1327.
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | Case 2:
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | |   (297)   ~ (all_56_2 = e3)
% 201.80/33.51  | | | | | |   (298)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | | BETA: splitting (26) gives:
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | | Case 1:
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | |   (299)  all_58_4 = e1
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | COMBINE_EQS: (137), (299) imply:
% 201.80/33.51  | | | | | | |   (300)  all_52_17 = e1
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | SIMP: (300) implies:
% 201.80/33.51  | | | | | | |   (301)  all_52_17 = e1
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | REDUCE: (117), (301) imply:
% 201.80/33.51  | | | | | | |   (302)   ~ (all_6_2 = e1)
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | SIMP: (302) implies:
% 201.80/33.51  | | | | | | |   (303)   ~ (all_6_2 = e1)
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | REDUCE: (94), (301) imply:
% 201.80/33.51  | | | | | | |   (304)  op(e1, e1) = all_52_16
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_16, e1, e1,
% 201.80/33.51  | | | | | | |              simplifying with (125), (304) gives:
% 201.80/33.51  | | | | | | |   (305)  all_52_16 = all_10_2
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | BETA: splitting (121) gives:
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | |   (306)  all_56_1 = e3
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | COMBINE_EQS: (111), (306) imply:
% 201.80/33.51  | | | | | | | |   (307)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | SIMP: (307) implies:
% 201.80/33.51  | | | | | | | |   (308)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | REDUCE: (8), (308) imply:
% 201.80/33.51  | | | | | | | |   (309)   ~ (all_52_13 = e3)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | SIMP: (309) implies:
% 201.80/33.51  | | | | | | | |   (310)   ~ (all_52_13 = e3)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | REDUCE: (53), (308) imply:
% 201.80/33.51  | | | | | | | |   (311)  op(e3, e3) = all_52_8
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 201.80/33.51  | | | | | | | |              simplifying with (103), (311) gives:
% 201.80/33.51  | | | | | | | |   (312)  all_52_8 = all_6_2
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | BETA: splitting (62) gives:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (313)  all_58_6 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | COMBINE_EQS: (114), (313) imply:
% 201.80/33.51  | | | | | | | | |   (314)  all_52_5 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | SIMP: (314) implies:
% 201.80/33.51  | | | | | | | | |   (315)  all_52_5 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REF_CLOSE: (2), (6), (7), (13), (15), (18), (20), (24), (30),
% 201.80/33.51  | | | | | | | | |            (31), (40), (43), (44), (51), (53), (65), (73),
% 201.80/33.51  | | | | | | | | |            (74), (76), (81), (84), (85), (86), (92), (96),
% 201.80/33.51  | | | | | | | | |            (97), (103), (104), (105), (106), (108), (110),
% 201.80/33.51  | | | | | | | | |            (113), (120), (125), (129), (137), (138), (315) are
% 201.80/33.51  | | | | | | | | |            inconsistent by sub-proof #797.
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (316)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | BETA: splitting (316) gives:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (317)  all_58_7 = e3
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | COMBINE_EQS: (57), (317) imply:
% 201.80/33.51  | | | | | | | | | |   (318)  all_52_13 = e3
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REDUCE: (310), (318) imply:
% 201.80/33.51  | | | | | | | | | |   (319)  $false
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | CLOSE: (319) is inconsistent.
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (320)  all_58_8 = e3 | all_58_11 = e3
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | BETA: splitting (320) gives:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | |   (321)  all_58_8 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | COMBINE_EQS: (91), (321) imply:
% 201.80/33.51  | | | | | | | | | | |   (322)  all_10_2 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | REDUCE: (293), (322) imply:
% 201.80/33.51  | | | | | | | | | | |   (323)  $false
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | CLOSE: (323) is inconsistent.
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | |   (324)  all_58_11 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | COMBINE_EQS: (31), (324) imply:
% 201.80/33.51  | | | | | | | | | | |   (325)  all_52_29 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | SIMP: (325) implies:
% 201.80/33.51  | | | | | | | | | | |   (326)  all_52_29 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | REDUCE: (41), (326) imply:
% 201.80/33.51  | | | | | | | | | | |   (327)  op(e3, e3) = e1
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | REF_CLOSE: (6), (103), (303), (327) are inconsistent by
% 201.80/33.51  | | | | | | | | | | |            sub-proof #885.
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | |   (328)   ~ (all_56_1 = e3)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | REDUCE: (111), (328) imply:
% 201.80/33.51  | | | | | | | |   (329)   ~ (all_52_9 = e3)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | BETA: splitting (106) gives:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (330)  all_58_0 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | COMBINE_EQS: (15), (330) imply:
% 201.80/33.51  | | | | | | | | |   (331)  all_6_2 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REF_CLOSE: (4), (6), (17), (38), (103), (135), (331) are
% 201.80/33.51  | | | | | | | | |            inconsistent by sub-proof #290.
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (332)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REF_CLOSE: (6), (7), (24), (73), (96), (103), (104), (137),
% 201.80/33.51  | | | | | | | | |            (290), (329), (332) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | |            #1225.
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | End of split
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | Case 2:
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | |   (333)   ~ (all_58_4 = e1)
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | REDUCE: (137), (333) imply:
% 201.80/33.51  | | | | | | |   (334)   ~ (all_52_17 = e1)
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | BETA: splitting (82) gives:
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | |   (335)  all_58_4 = e2
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | COMBINE_EQS: (137), (335) imply:
% 201.80/33.51  | | | | | | | |   (336)  all_52_17 = e2
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | SIMP: (336) implies:
% 201.80/33.51  | | | | | | | |   (337)  all_52_17 = e2
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | REDUCE: (13), (337) imply:
% 201.80/33.51  | | | | | | | |   (338)   ~ (all_52_25 = e2)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | SIMP: (338) implies:
% 201.80/33.51  | | | | | | | |   (339)   ~ (all_52_25 = e2)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | BETA: splitting (121) gives:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (340)  all_56_1 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | COMBINE_EQS: (111), (340) imply:
% 201.80/33.51  | | | | | | | | |   (341)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | SIMP: (341) implies:
% 201.80/33.51  | | | | | | | | |   (342)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REDUCE: (85), (342) imply:
% 201.80/33.51  | | | | | | | | |   (343)   ~ (all_52_25 = e3)
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | SIMP: (343) implies:
% 201.80/33.51  | | | | | | | | |   (344)   ~ (all_52_25 = e3)
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REF_CLOSE: (6), (24), (40), (44), (73), (97), (108), (125),
% 201.80/33.51  | | | | | | | | |            (138), (293), (339), (344) are inconsistent by
% 201.80/33.51  | | | | | | | | |            sub-proof #1231.
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (345)   ~ (all_56_1 = e3)
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REDUCE: (111), (345) imply:
% 201.80/33.51  | | | | | | | | |   (346)   ~ (all_52_9 = e3)
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | BETA: splitting (106) gives:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (347)  all_58_0 = e3
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | COMBINE_EQS: (15), (347) imply:
% 201.80/33.51  | | | | | | | | | |   (348)  all_6_2 = e3
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REDUCE: (96), (348) imply:
% 201.80/33.51  | | | | | | | | | |   (349)   ~ (all_52_25 = e3)
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REF_CLOSE: (6), (24), (40), (44), (73), (97), (108), (125),
% 201.80/33.51  | | | | | | | | | |            (138), (293), (339), (349) are inconsistent by
% 201.80/33.51  | | | | | | | | | |            sub-proof #1231.
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (350)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REF_CLOSE: (6), (7), (24), (73), (96), (103), (104), (137),
% 201.80/33.51  | | | | | | | | | |            (290), (346), (350) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | | |            #1225.
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | |   (351)   ~ (all_58_4 = e2)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | REDUCE: (137), (351) imply:
% 201.80/33.51  | | | | | | | |   (352)   ~ (all_52_17 = e2)
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | BETA: splitting (298) gives:
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (353)  all_56_2 = e2
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | REF_CLOSE: (66), (352), (353) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | |            #1264.
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | |   (354)  all_56_2 = e1 | all_56_2 = e0
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | BETA: splitting (354) gives:
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (355)  all_56_2 = e1
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REF_CLOSE: (66), (334), (355) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | | |            #1263.
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | |   (356)  all_56_2 = e0
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | COMBINE_EQS: (66), (356) imply:
% 201.80/33.51  | | | | | | | | | |   (357)  all_52_17 = e0
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | SIMP: (357) implies:
% 201.80/33.51  | | | | | | | | | |   (358)  all_52_17 = e0
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | REDUCE: (13), (358) imply:
% 201.80/33.51  | | | | | | | | | |   (359)   ~ (all_52_25 = e0)
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | SIMP: (359) implies:
% 201.80/33.51  | | | | | | | | | |   (360)   ~ (all_52_25 = e0)
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | BETA: splitting (97) gives:
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | |   (361)  all_56_3 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | COMBINE_EQS: (108), (361) imply:
% 201.80/33.51  | | | | | | | | | | |   (362)  all_52_25 = e3
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | REF_CLOSE: (6), (73), (96), (103), (362) are inconsistent by
% 201.80/33.51  | | | | | | | | | | |            sub-proof #1246.
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | |   (363)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | BETA: splitting (106) gives:
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | |   (364)  all_58_0 = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | COMBINE_EQS: (15), (364) imply:
% 201.80/33.51  | | | | | | | | | | | |   (365)  all_6_2 = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | REDUCE: (38), (365) imply:
% 201.80/33.51  | | | | | | | | | | | |   (366)  op(e3, e3) = all_52_0
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | REDUCE: (135), (365) imply:
% 201.80/33.51  | | | | | | | | | | | |   (367)  op(e3, e3) = all_6_1
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | REDUCE: (103), (365) imply:
% 201.80/33.51  | | | | | | | | | | | |   (368)  op(e3, e3) = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_1, all_52_0, e3, e3,
% 201.80/33.51  | | | | | | | | | | | |              simplifying with (366), (367) gives:
% 201.80/33.51  | | | | | | | | | | | |   (369)  all_52_0 = all_6_1
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e3, e3,
% 201.80/33.51  | | | | | | | | | | | |              simplifying with (366), (368) gives:
% 201.80/33.51  | | | | | | | | | | | |   (370)  all_52_0 = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | COMBINE_EQS: (369), (370) imply:
% 201.80/33.51  | | | | | | | | | | | |   (371)  all_6_1 = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | SIMP: (371) implies:
% 201.80/33.51  | | | | | | | | | | | |   (372)  all_6_1 = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | REF_CLOSE: (4), (6), (17), (366), (367), (372) are
% 201.80/33.51  | | | | | | | | | | | |            inconsistent by sub-proof #291.
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | |   (373)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | BETA: splitting (373) gives:
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | Case 1:
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | |   (374)  all_58_1 = e3
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | COMBINE_EQS: (7), (374) imply:
% 201.80/33.51  | | | | | | | | | | | | |   (375)  all_52_9 = e3
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | REDUCE: (98), (375) imply:
% 201.80/33.51  | | | | | | | | | | | | |   (376)   ~ (all_4_2 = e3)
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | SIMP: (376) implies:
% 201.80/33.51  | | | | | | | | | | | | |   (377)   ~ (all_4_2 = e3)
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | REF_CLOSE: (6), (24), (28), (44), (73), (108), (125), (293),
% 201.80/33.51  | | | | | | | | | | | | |            (360), (363), (377) are inconsistent by sub-proof
% 201.80/33.51  | | | | | | | | | | | | |            #824.
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | Case 2:
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | |   (378)  all_58_4 = e3 | all_58_9 = e3
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | | REF_CLOSE: (6), (24), (73), (96), (103), (104), (137), (290),
% 201.80/33.51  | | | | | | | | | | | | |            (378) are inconsistent by sub-proof #1226.
% 201.80/33.51  | | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | | 
% 201.80/33.51  | | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | | 
% 201.80/33.51  | | | | | | | | End of split
% 201.80/33.51  | | | | | | | | 
% 201.80/33.51  | | | | | | | End of split
% 201.80/33.51  | | | | | | | 
% 201.80/33.51  | | | | | | End of split
% 201.80/33.51  | | | | | | 
% 201.80/33.51  | | | | | End of split
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | Case 2:
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | |   (379)  all_58_15 = e3
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | COMBINE_EQS: (86), (379) imply:
% 201.80/33.51  | | | | |   (380)  all_14_2 = e3
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | REDUCE: (138), (380) imply:
% 201.80/33.51  | | | | |   (381)  $false
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | | CLOSE: (381) is inconsistent.
% 201.80/33.51  | | | | | 
% 201.80/33.51  | | | | End of split
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | End of split
% 201.80/33.51  | | | 
% 201.80/33.51  | | End of split
% 201.80/33.51  | | 
% 201.80/33.51  | End of split
% 201.80/33.51  | 
% 201.80/33.51  End of proof
% 201.80/33.51  
% 201.80/33.51  Sub-proof #273 shows that the following formulas are inconsistent:
% 201.80/33.51  ----------------------------------------------------------------
% 201.80/33.51    (1)   ~ (e3 = e1)
% 201.80/33.51    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.80/33.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.80/33.51    (3)  all_58_1 = all_52_9
% 201.80/33.51    (4)   ~ (all_52_9 = all_52_13)
% 201.80/33.51    (5)  all_58_4 = e1
% 201.80/33.51    (6)   ~ (e3 = e0)
% 201.80/33.51    (7)   ~ (all_14_1 = e3)
% 201.80/33.51    (8)  all_58_13 = all_52_15
% 201.80/33.51    (9)  op(e2, e2) = all_4_2
% 201.80/33.51    (10)   ~ (all_52_9 = all_52_15)
% 201.80/33.51    (11)   ~ (e2 = e1)
% 201.80/33.51    (12)  all_58_7 = all_52_13
% 201.80/33.51    (13)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.80/33.51    (14)  all_58_9 = all_14_1
% 201.80/33.51    (15)   ~ (e2 = e0)
% 201.80/33.51    (16)  all_58_0 = e0
% 201.80/33.51    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.80/33.51    (18)   ~ (all_52_9 = all_4_2)
% 201.80/33.51    (19)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.51    (20)  op(all_14_1, all_14_1) = e3
% 201.80/33.51    (21)   ~ (e3 = e2)
% 201.80/33.51    (22)  all_58_3 = all_4_2
% 201.80/33.51  
% 201.80/33.51  Begin of proof
% 201.80/33.51  | 
% 201.80/33.51  | BETA: splitting (19) gives:
% 201.80/33.51  | 
% 201.80/33.51  | Case 1:
% 201.80/33.51  | | 
% 201.80/33.51  | |   (23)  all_58_0 = e3
% 201.80/33.51  | | 
% 201.80/33.51  | | REF_CLOSE: (6), (16), (23) are inconsistent by sub-proof #1015.
% 201.80/33.51  | | 
% 201.80/33.51  | Case 2:
% 201.80/33.51  | | 
% 201.80/33.51  | |   (24)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.80/33.51  | | 
% 201.80/33.51  | | BETA: splitting (24) gives:
% 201.80/33.51  | | 
% 201.80/33.51  | | Case 1:
% 201.80/33.51  | | | 
% 201.80/33.51  | | |   (25)  all_58_1 = e3
% 201.80/33.51  | | | 
% 201.80/33.51  | | | COMBINE_EQS: (3), (25) imply:
% 201.80/33.51  | | |   (26)  all_52_9 = e3
% 201.80/33.51  | | | 
% 201.80/33.51  | | | REDUCE: (4), (26) imply:
% 201.80/33.51  | | |   (27)   ~ (all_52_13 = e3)
% 201.80/33.51  | | | 
% 201.80/33.51  | | | SIMP: (27) implies:
% 201.80/33.51  | | |   (28)   ~ (all_52_13 = e3)
% 201.80/33.51  | | | 
% 201.80/33.51  | | | REDUCE: (10), (26) imply:
% 201.80/33.51  | | |   (29)   ~ (all_52_15 = e3)
% 201.80/33.51  | | | 
% 201.80/33.51  | | | SIMP: (29) implies:
% 201.80/33.51  | | |   (30)   ~ (all_52_15 = e3)
% 201.80/33.51  | | | 
% 201.80/33.51  | | | REDUCE: (18), (26) imply:
% 201.80/33.51  | | |   (31)   ~ (all_4_2 = e3)
% 201.80/33.51  | | | 
% 201.80/33.51  | | | SIMP: (31) implies:
% 201.80/33.51  | | |   (32)   ~ (all_4_2 = e3)
% 201.80/33.51  | | | 
% 201.80/33.51  | | | BETA: splitting (13) gives:
% 201.80/33.51  | | | 
% 201.80/33.51  | | | Case 1:
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | |   (33)  all_58_0 = e2
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | | REF_CLOSE: (15), (16), (33) are inconsistent by sub-proof #812.
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | Case 2:
% 201.80/33.51  | | | | 
% 201.80/33.51  | | | |   (34)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.80/33.51  | | | | 
% 201.86/33.51  | | | | REF_CLOSE: (2), (5), (8), (9), (11), (12), (14), (17), (20), (21), (22),
% 201.86/33.51  | | | |            (28), (30), (32), (34) are inconsistent by sub-proof #632.
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | End of split
% 201.86/33.51  | | | 
% 201.86/33.51  | | Case 2:
% 201.86/33.51  | | | 
% 201.86/33.51  | | |   (35)  all_58_4 = e3 | all_58_9 = e3
% 201.86/33.51  | | | 
% 201.86/33.51  | | | BETA: splitting (35) gives:
% 201.86/33.51  | | | 
% 201.86/33.51  | | | Case 1:
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | |   (36)  all_58_4 = e3
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | | REF_CLOSE: (1), (5), (36) are inconsistent by sub-proof #568.
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | Case 2:
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | |   (37)  all_58_9 = e3
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | | COMBINE_EQS: (14), (37) imply:
% 201.86/33.51  | | | |   (38)  all_14_1 = e3
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | | REDUCE: (7), (38) imply:
% 201.86/33.51  | | | |   (39)  $false
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | | CLOSE: (39) is inconsistent.
% 201.86/33.51  | | | | 
% 201.86/33.51  | | | End of split
% 201.86/33.51  | | | 
% 201.86/33.51  | | End of split
% 201.86/33.51  | | 
% 201.86/33.51  | End of split
% 201.86/33.51  | 
% 201.86/33.51  End of proof
% 201.86/33.51  
% 201.86/33.51  Sub-proof #274 shows that the following formulas are inconsistent:
% 201.86/33.51  ----------------------------------------------------------------
% 201.86/33.51    (1)   ~ (all_52_15 = all_52_23)
% 201.86/33.51    (2)  all_58_14 = all_52_23
% 201.86/33.51    (3)   ~ (e3 = e1)
% 201.86/33.51    (4)  op(all_52_3, all_52_3) = all_52_2
% 201.86/33.51    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.51    (6)  all_58_1 = all_52_9
% 201.86/33.51    (7)   ~ (e3 = e0)
% 201.86/33.51    (8)  op(all_52_23, all_52_23) = e0
% 201.86/33.51    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.86/33.51    (10)   ~ (all_52_7 = all_52_15)
% 201.86/33.51    (11)  op(all_52_7, all_52_7) = all_52_6
% 201.86/33.51    (12)   ~ (all_52_17 = all_52_25)
% 201.86/33.51    (13)  all_58_0 = all_6_2
% 201.86/33.51    (14)  op(e3, all_6_1) = e1
% 201.86/33.51    (15)  op(e3, e0) = all_52_25
% 201.86/33.51    (16)  op(all_52_5, all_52_5) = all_52_4
% 201.86/33.51    (17)  all_58_13 = all_52_15
% 201.86/33.51    (18)  all_58_9 = all_52_25
% 201.86/33.51    (19)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.86/33.51    (20)  op(e1, e3) = all_52_5
% 201.86/33.51    (21)  op(e2, e2) = all_4_2
% 201.86/33.51    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.86/33.51    (23)   ~ (all_52_3 = all_52_5)
% 201.86/33.51    (24)  all_58_11 = all_52_29
% 201.86/33.51    (25)   ~ (all_52_25 = all_14_2)
% 201.86/33.51    (26)   ~ (all_52_9 = all_52_15)
% 201.86/33.51    (27)  op(all_10_2, e1) = all_10_1
% 201.86/33.51    (28)  op(all_6_2, all_6_2) = all_52_0
% 201.86/33.51    (29)   ~ (all_52_7 = all_6_2)
% 201.86/33.51    (30)  op(e0, e0) = all_14_2
% 201.86/33.51    (31)  all_56_15 = all_14_2
% 201.86/33.51    (32)  all_56_11 = all_52_29
% 201.86/33.51    (33)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.86/33.51    (34)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.86/33.51    (35)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.86/33.51    (36)   ~ (e2 = e1)
% 201.86/33.51    (37)  op(all_10_2, all_10_2) = e1
% 201.86/33.51    (38)  op(all_52_9, all_52_9) = all_52_8
% 201.86/33.51    (39)   ~ (all_52_25 = all_52_29)
% 201.86/33.51    (40)   ~ (all_52_29 = all_10_2)
% 201.86/33.51    (41)  all_58_7 = all_52_13
% 201.86/33.51    (42)  op(all_52_19, all_52_19) = e2
% 201.86/33.51    (43)  all_58_12 = all_52_7
% 201.86/33.51    (44)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.86/33.51    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.86/33.51    (46)   ~ (all_52_7 = all_14_2)
% 201.86/33.51    (47)   ~ (all_14_2 = e0)
% 201.86/33.51    (48)  all_58_2 = all_52_3
% 201.86/33.51    (49)  all_56_2 = all_52_17
% 201.86/33.51    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.86/33.51    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.86/33.51    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.86/33.51    (53)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.86/33.51    (54)   ~ (e2 = e0)
% 201.86/33.51    (55)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.86/33.51    (56)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.86/33.51    (57)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.86/33.51    (58)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.86/33.51    (59)  op(e3, e1) = all_52_17
% 201.86/33.51    (60)  op(e0, e3) = all_52_7
% 201.86/33.51    (61)   ~ (all_52_9 = all_52_25)
% 201.86/33.51    (62)  all_58_15 = all_14_2
% 201.86/33.51    (63)   ~ (all_52_19 = all_10_2)
% 201.86/33.51    (64)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.86/33.51    (65)  all_58_8 = all_10_2
% 201.86/33.51    (66)   ~ (all_52_5 = all_10_2)
% 201.86/33.51    (67)  op(all_52_29, all_52_29) = all_52_28
% 201.86/33.51    (68)   ~ (all_52_23 = all_14_2)
% 201.86/33.51    (69)  all_56_12 = all_52_7
% 201.86/33.51    (70)   ~ (all_52_25 = all_6_2)
% 201.86/33.51    (71)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.86/33.51    (72)   ~ (all_52_5 = all_6_2)
% 201.86/33.51    (73)   ~ (all_52_9 = all_6_2)
% 201.86/33.51    (74)   ~ (all_52_13 = all_52_15)
% 201.86/33.51    (75)  all_56_0 = all_6_2
% 201.86/33.51    (76)  op(e3, e3) = all_6_2
% 201.86/33.51    (77)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.86/33.51    (78)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.86/33.51    (79)  all_56_3 = all_52_25
% 201.86/33.51    (80)   ~ (all_52_3 = all_52_7)
% 201.86/33.51    (81)  all_58_5 = all_52_19
% 201.86/33.51    (82)  all_56_1 = all_52_9
% 201.86/33.51    (83)  op(all_52_17, all_52_17) = e3
% 201.86/33.51    (84)  all_58_6 = all_52_5
% 201.86/33.51    (85)  op(e3, e2) = all_52_9
% 201.86/33.51    (86)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.86/33.51    (87)   ~ (all_52_17 = all_6_2)
% 201.86/33.51    (88)   ~ (e1 = e0)
% 201.86/33.51    (89)   ~ (e3 = e2)
% 201.86/33.51    (90)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.86/33.51    (91)   ~ (all_52_9 = all_52_17)
% 201.86/33.51    (92)  all_56_10 = all_10_2
% 201.86/33.51    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.86/33.51    (94)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.86/33.51    (95)  op(e1, e1) = all_10_2
% 201.86/33.51    (96)   ~ (all_52_23 = all_10_2)
% 201.86/33.51    (97)   ~ (all_52_7 = all_52_23)
% 201.86/33.51    (98)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.86/33.52    (99)  all_56_13 = all_52_15
% 201.86/33.52    (100)   ~ (all_52_3 = all_4_2)
% 201.86/33.52    (101)  op(all_6_2, e3) = all_6_1
% 201.86/33.52    (102)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.86/33.52    (103)  all_58_4 = all_52_17
% 201.86/33.52    (104)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.86/33.52    (105)  op(all_52_25, all_52_25) = all_52_24
% 201.86/33.52    (106)   ~ (all_14_2 = e3)
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | BETA: splitting (33) gives:
% 201.86/33.52  | 
% 201.86/33.52  | Case 1:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (107)  all_56_13 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (99), (107) imply:
% 201.86/33.52  | |   (108)  all_52_15 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | SIMP: (108) implies:
% 201.86/33.52  | |   (109)  all_52_15 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (17), (109) imply:
% 201.86/33.52  | |   (110)  all_58_13 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (10), (109) imply:
% 201.86/33.52  | |   (111)   ~ (all_52_7 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (26), (109) imply:
% 201.86/33.52  | |   (112)   ~ (all_52_9 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (74), (109) imply:
% 201.86/33.52  | |   (113)   ~ (all_52_13 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (1), (109) imply:
% 201.86/33.52  | |   (114)   ~ (all_52_23 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | SIMP: (114) implies:
% 201.86/33.52  | |   (115)   ~ (all_52_23 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (12), (13), (16), (18), (19), (21),
% 201.86/33.52  | |            (23), (24), (25), (27), (28), (29), (30), (32), (34), (35), (36),
% 201.86/33.52  | |            (37), (38), (39), (40), (41), (42), (43), (45), (48), (49), (50),
% 201.86/33.52  | |            (51), (52), (55), (56), (58), (59), (61), (63), (65), (66), (67),
% 201.86/33.52  | |            (68), (70), (71), (72), (73), (75), (76), (77), (78), (79), (80),
% 201.86/33.52  | |            (81), (82), (83), (84), (87), (89), (90), (91), (93), (94), (95),
% 201.86/33.52  | |            (98), (100), (103), (105), (110), (111), (112), (113), (115) are
% 201.86/33.52  | |            inconsistent by sub-proof #280.
% 201.86/33.52  | | 
% 201.86/33.52  | Case 2:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (116)   ~ (all_56_13 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (99), (116) imply:
% 201.86/33.52  | |   (117)   ~ (all_52_15 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | BETA: splitting (86) gives:
% 201.86/33.52  | | 
% 201.86/33.52  | | Case 1:
% 201.86/33.52  | | | 
% 201.86/33.52  | | |   (118)  all_58_12 = e3
% 201.86/33.52  | | | 
% 201.86/33.52  | | | COMBINE_EQS: (43), (118) imply:
% 201.86/33.52  | | |   (119)  all_52_7 = e3
% 201.86/33.52  | | | 
% 201.86/33.52  | | | SIMP: (119) implies:
% 201.86/33.52  | | |   (120)  all_52_7 = e3
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REDUCE: (97), (120) imply:
% 201.86/33.52  | | |   (121)   ~ (all_52_23 = e3)
% 201.86/33.52  | | | 
% 201.86/33.52  | | | SIMP: (121) implies:
% 201.86/33.52  | | |   (122)   ~ (all_52_23 = e3)
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REDUCE: (46), (120) imply:
% 201.86/33.52  | | |   (123)   ~ (all_14_2 = e3)
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REDUCE: (29), (120) imply:
% 201.86/33.52  | | |   (124)   ~ (all_6_2 = e3)
% 201.86/33.52  | | | 
% 201.86/33.52  | | | SIMP: (124) implies:
% 201.86/33.52  | | |   (125)   ~ (all_6_2 = e3)
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REDUCE: (11), (120) imply:
% 201.86/33.52  | | |   (126)  op(e3, e3) = all_52_6
% 201.86/33.52  | | | 
% 201.86/33.52  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 201.86/33.52  | | |              with (76), (126) gives:
% 201.86/33.52  | | |   (127)  all_52_6 = all_6_2
% 201.86/33.52  | | | 
% 201.86/33.52  | | | BETA: splitting (53) gives:
% 201.86/33.52  | | | 
% 201.86/33.52  | | | Case 1:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | |   (128)  all_58_0 = e1
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | REF_CLOSE: (5), (7), (13), (14), (15), (20), (22), (36), (48), (54),
% 201.86/33.52  | | | |            (57), (70), (73), (84), (85), (88), (89), (101), (102),
% 201.86/33.52  | | | |            (118), (128) are inconsistent by sub-proof #279.
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | Case 2:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | |   (129)   ~ (all_58_0 = e1)
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | REF_CLOSE: (2), (5), (13), (19), (30), (34), (37), (42), (49), (57),
% 201.86/33.52  | | | |            (65), (76), (81), (83), (87), (92), (93), (95), (103), (104),
% 201.86/33.52  | | | |            (106), (122), (125), (126), (129) are inconsistent by
% 201.86/33.52  | | | |            sub-proof #278.
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | End of split
% 201.86/33.52  | | | 
% 201.86/33.52  | | Case 2:
% 201.86/33.52  | | | 
% 201.86/33.52  | | |   (130)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REF_CLOSE: (2), (5), (8), (9), (11), (14), (17), (29), (31), (44), (46),
% 201.86/33.52  | | |            (47), (59), (60), (62), (64), (69), (76), (83), (95), (96),
% 201.86/33.52  | | |            (97), (101), (106), (117), (130) are inconsistent by sub-proof
% 201.86/33.52  | | |            #275.
% 201.86/33.52  | | | 
% 201.86/33.52  | | End of split
% 201.86/33.52  | | 
% 201.86/33.52  | End of split
% 201.86/33.52  | 
% 201.86/33.52  End of proof
% 201.86/33.52  
% 201.86/33.52  Sub-proof #275 shows that the following formulas are inconsistent:
% 201.86/33.52  ----------------------------------------------------------------
% 201.86/33.52    (1)  all_58_14 = all_52_23
% 201.86/33.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.52    (3)  op(all_52_23, all_52_23) = e0
% 201.86/33.52    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.86/33.52    (5)  op(all_52_7, all_52_7) = all_52_6
% 201.86/33.52    (6)  op(e3, all_6_1) = e1
% 201.86/33.52    (7)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.86/33.52    (8)  all_58_13 = all_52_15
% 201.86/33.52    (9)   ~ (all_52_15 = e3)
% 201.86/33.52    (10)   ~ (all_52_7 = all_6_2)
% 201.86/33.52    (11)  all_56_15 = all_14_2
% 201.86/33.52    (12)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.86/33.52    (13)   ~ (all_52_7 = all_14_2)
% 201.86/33.52    (14)   ~ (all_14_2 = e0)
% 201.86/33.52    (15)  op(e3, e1) = all_52_17
% 201.86/33.52    (16)  op(e0, e3) = all_52_7
% 201.86/33.52    (17)  all_58_15 = all_14_2
% 201.86/33.52    (18)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.86/33.52    (19)  all_56_12 = all_52_7
% 201.86/33.52    (20)  op(e3, e3) = all_6_2
% 201.86/33.52    (21)  op(all_52_17, all_52_17) = e3
% 201.86/33.52    (22)  op(e1, e1) = all_10_2
% 201.86/33.52    (23)   ~ (all_52_23 = all_10_2)
% 201.86/33.52    (24)   ~ (all_52_7 = all_52_23)
% 201.86/33.52    (25)  op(all_6_2, e3) = all_6_1
% 201.86/33.52    (26)   ~ (all_14_2 = e3)
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | BETA: splitting (7) gives:
% 201.86/33.52  | 
% 201.86/33.52  | Case 1:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (27)  all_58_13 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REF_CLOSE: (8), (9), (27) are inconsistent by sub-proof #1360.
% 201.86/33.52  | | 
% 201.86/33.52  | Case 2:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (28)  all_58_14 = e3 | all_58_15 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 201.86/33.52  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 201.86/33.52  | |            (28) are inconsistent by sub-proof #276.
% 201.86/33.52  | | 
% 201.86/33.52  | End of split
% 201.86/33.52  | 
% 201.86/33.52  End of proof
% 201.86/33.52  
% 201.86/33.52  Sub-proof #276 shows that the following formulas are inconsistent:
% 201.86/33.52  ----------------------------------------------------------------
% 201.86/33.52    (1)  all_58_14 = all_52_23
% 201.86/33.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.52    (3)  op(all_52_23, all_52_23) = e0
% 201.86/33.52    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.86/33.52    (5)  op(all_52_7, all_52_7) = all_52_6
% 201.86/33.52    (6)  op(e3, all_6_1) = e1
% 201.86/33.52    (7)   ~ (all_52_7 = all_6_2)
% 201.86/33.52    (8)  all_56_15 = all_14_2
% 201.86/33.52    (9)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.86/33.52    (10)   ~ (all_52_7 = all_14_2)
% 201.86/33.52    (11)   ~ (all_14_2 = e0)
% 201.86/33.52    (12)  op(e3, e1) = all_52_17
% 201.86/33.52    (13)  op(e0, e3) = all_52_7
% 201.86/33.52    (14)  all_58_14 = e3 | all_58_15 = e3
% 201.86/33.52    (15)  all_58_15 = all_14_2
% 201.86/33.52    (16)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.86/33.52    (17)  all_56_12 = all_52_7
% 201.86/33.52    (18)  op(e3, e3) = all_6_2
% 201.86/33.52    (19)  op(all_52_17, all_52_17) = e3
% 201.86/33.52    (20)  op(e1, e1) = all_10_2
% 201.86/33.52    (21)   ~ (all_52_23 = all_10_2)
% 201.86/33.52    (22)   ~ (all_52_7 = all_52_23)
% 201.86/33.52    (23)  op(all_6_2, e3) = all_6_1
% 201.86/33.52    (24)   ~ (all_14_2 = e3)
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | BETA: splitting (14) gives:
% 201.86/33.52  | 
% 201.86/33.52  | Case 1:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (25)  all_58_14 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (1), (25) imply:
% 201.86/33.52  | |   (26)  all_52_23 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | SIMP: (26) implies:
% 201.86/33.52  | |   (27)  all_52_23 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (22), (27) imply:
% 201.86/33.52  | |   (28)   ~ (all_52_7 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (21), (27) imply:
% 201.86/33.52  | |   (29)   ~ (all_10_2 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | SIMP: (29) implies:
% 201.86/33.52  | |   (30)   ~ (all_10_2 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (3), (27) imply:
% 201.86/33.52  | |   (31)  op(e3, e3) = e0
% 201.86/33.52  | | 
% 201.86/33.52  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (16),
% 201.86/33.52  | |            (17), (18), (19), (20), (23), (28), (30), (31) are inconsistent
% 201.86/33.52  | |            by sub-proof #277.
% 201.86/33.52  | | 
% 201.86/33.52  | Case 2:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (32)  all_58_15 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (15), (32) imply:
% 201.86/33.52  | |   (33)  all_14_2 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (24), (33) imply:
% 201.86/33.52  | |   (34)  $false
% 201.86/33.52  | | 
% 201.86/33.52  | | CLOSE: (34) is inconsistent.
% 201.86/33.52  | | 
% 201.86/33.52  | End of split
% 201.86/33.52  | 
% 201.86/33.52  End of proof
% 201.86/33.52  
% 201.86/33.52  Sub-proof #277 shows that the following formulas are inconsistent:
% 201.86/33.52  ----------------------------------------------------------------
% 201.86/33.52    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.52    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.86/33.52    (3)  op(all_52_7, all_52_7) = all_52_6
% 201.86/33.52    (4)  op(e3, all_6_1) = e1
% 201.86/33.52    (5)   ~ (all_52_7 = all_6_2)
% 201.86/33.52    (6)  all_56_15 = all_14_2
% 201.86/33.52    (7)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.86/33.52    (8)   ~ (all_52_7 = e3)
% 201.86/33.52    (9)   ~ (all_52_7 = all_14_2)
% 201.86/33.52    (10)   ~ (all_14_2 = e0)
% 201.86/33.52    (11)   ~ (all_10_2 = e3)
% 201.86/33.52    (12)  op(e3, e1) = all_52_17
% 201.86/33.52    (13)  op(e0, e3) = all_52_7
% 201.86/33.52    (14)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.86/33.52    (15)  all_56_12 = all_52_7
% 201.86/33.52    (16)  op(e3, e3) = e0
% 201.86/33.52    (17)  op(e3, e3) = all_6_2
% 201.86/33.52    (18)  op(all_52_17, all_52_17) = e3
% 201.86/33.52    (19)  op(e1, e1) = all_10_2
% 201.86/33.52    (20)  op(all_6_2, e3) = all_6_1
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | GROUND_INST: instantiating (1) with all_6_2, e0, e3, e3, simplifying with
% 201.86/33.52  |              (16), (17) gives:
% 201.86/33.52  |   (21)  all_6_2 = e0
% 201.86/33.52  | 
% 201.86/33.52  | REDUCE: (5), (21) imply:
% 201.86/33.52  |   (22)   ~ (all_52_7 = e0)
% 201.86/33.52  | 
% 201.86/33.52  | REDUCE: (20), (21) imply:
% 201.86/33.52  |   (23)  op(e0, e3) = all_6_1
% 201.86/33.52  | 
% 201.86/33.52  | BETA: splitting (7) gives:
% 201.86/33.52  | 
% 201.86/33.52  | Case 1:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (24)   ~ (all_6_1 = e2)
% 201.86/33.52  | | 
% 201.86/33.52  | | GROUND_INST: instantiating (1) with all_52_7, all_6_1, e3, e0, simplifying
% 201.86/33.52  | |              with (13), (23) gives:
% 201.86/33.52  | |   (25)  all_52_7 = all_6_1
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (15), (25) imply:
% 201.86/33.52  | |   (26)  all_56_12 = all_6_1
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (9), (25) imply:
% 201.86/33.52  | |   (27)   ~ (all_14_2 = all_6_1)
% 201.86/33.52  | | 
% 201.86/33.52  | | SIMP: (27) implies:
% 201.86/33.52  | |   (28)   ~ (all_14_2 = all_6_1)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (8), (25) imply:
% 201.86/33.52  | |   (29)   ~ (all_6_1 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (22), (25) imply:
% 201.86/33.52  | |   (30)   ~ (all_6_1 = e0)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (3), (25) imply:
% 201.86/33.52  | |   (31)  op(all_6_1, all_6_1) = all_52_6
% 201.86/33.52  | | 
% 201.86/33.52  | | BETA: splitting (2) gives:
% 201.86/33.52  | | 
% 201.86/33.52  | | Case 1:
% 201.86/33.52  | | | 
% 201.86/33.52  | | |   (32)  all_56_12 = e3
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REF_CLOSE: (26), (29), (32) are inconsistent by sub-proof #1347.
% 201.86/33.52  | | | 
% 201.86/33.52  | | Case 2:
% 201.86/33.52  | | | 
% 201.86/33.52  | | |   (33)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.86/33.52  | | | 
% 201.86/33.52  | | | BETA: splitting (33) gives:
% 201.86/33.52  | | | 
% 201.86/33.52  | | | Case 1:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | |   (34)  all_56_12 = e2
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | REF_CLOSE: (24), (26), (34) are inconsistent by sub-proof #1346.
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | Case 2:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | |   (35)  all_56_12 = e1 | all_56_12 = e0
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | BETA: splitting (35) gives:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | Case 1:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | |   (36)  all_56_12 = e1
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | COMBINE_EQS: (26), (36) imply:
% 201.86/33.52  | | | | |   (37)  all_6_1 = e1
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | SIMP: (37) implies:
% 201.86/33.52  | | | | |   (38)  all_6_1 = e1
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REDUCE: (28), (38) imply:
% 201.86/33.52  | | | | |   (39)   ~ (all_14_2 = e1)
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REDUCE: (31), (38) imply:
% 201.86/33.52  | | | | |   (40)  op(e1, e1) = all_52_6
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REDUCE: (4), (38) imply:
% 201.86/33.52  | | | | |   (41)  op(e3, e1) = e1
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | BETA: splitting (14) gives:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | Case 1:
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | GROUND_INST: instantiating (1) with all_10_2, all_52_6, e1, e1,
% 201.86/33.52  | | | | | |              simplifying with (19), (40) gives:
% 201.86/33.52  | | | | | |   (42)  all_52_6 = all_10_2
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | REF_CLOSE: (1), (11), (12), (18), (40), (41), (42) are inconsistent
% 201.86/33.52  | | | | | |            by sub-proof #315.
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | Case 2:
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | |   (43)  all_56_15 = e1 | all_56_15 = e0
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | REF_CLOSE: (6), (10), (39), (43) are inconsistent by sub-proof
% 201.86/33.52  | | | | | |            #1161.
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | End of split
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | Case 2:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | |   (44)  all_56_12 = e0
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REF_CLOSE: (26), (30), (44) are inconsistent by sub-proof #1345.
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | End of split
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | End of split
% 201.86/33.52  | | | 
% 201.86/33.52  | | End of split
% 201.86/33.52  | | 
% 201.86/33.52  | Case 2:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (45)   ~ (all_6_2 = e0)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (21), (45) imply:
% 201.86/33.52  | |   (46)  $false
% 201.86/33.52  | | 
% 201.86/33.52  | | CLOSE: (46) is inconsistent.
% 201.86/33.52  | | 
% 201.86/33.52  | End of split
% 201.86/33.52  | 
% 201.86/33.52  End of proof
% 201.86/33.52  
% 201.86/33.52  Sub-proof #278 shows that the following formulas are inconsistent:
% 201.86/33.52  ----------------------------------------------------------------
% 201.86/33.52    (1)  all_58_14 = all_52_23
% 201.86/33.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.52    (3)  all_58_0 = all_6_2
% 201.86/33.52    (4)  op(e3, e3) = all_52_6
% 201.86/33.52    (5)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.86/33.52    (6)  op(e0, e0) = all_14_2
% 201.86/33.52    (7)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.86/33.52    (8)   ~ (all_6_2 = e3)
% 201.86/33.52    (9)  op(all_10_2, all_10_2) = e1
% 201.86/33.52    (10)  op(all_52_19, all_52_19) = e2
% 201.86/33.52    (11)  all_56_2 = all_52_17
% 201.86/33.52    (12)   ~ (all_52_23 = e3)
% 201.86/33.52    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.86/33.52    (14)  all_58_8 = all_10_2
% 201.86/33.52    (15)  op(e3, e3) = all_6_2
% 201.86/33.52    (16)  all_58_5 = all_52_19
% 201.86/33.52    (17)  op(all_52_17, all_52_17) = e3
% 201.86/33.52    (18)   ~ (all_52_17 = all_6_2)
% 201.86/33.52    (19)  all_56_10 = all_10_2
% 201.86/33.52    (20)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.86/33.52    (21)  op(e1, e1) = all_10_2
% 201.86/33.52    (22)   ~ (all_58_0 = e1)
% 201.86/33.52    (23)  all_58_4 = all_52_17
% 201.86/33.52    (24)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 201.86/33.52    (25)   ~ (all_14_2 = e3)
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | REDUCE: (3), (22) imply:
% 201.86/33.52  |   (26)   ~ (all_6_2 = e1)
% 201.86/33.52  | 
% 201.86/33.52  | BETA: splitting (20) gives:
% 201.86/33.52  | 
% 201.86/33.52  | Case 1:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (27)  all_58_4 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (23), (27) imply:
% 201.86/33.52  | |   (28)  all_52_17 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | SIMP: (28) implies:
% 201.86/33.52  | |   (29)  all_52_17 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REF_CLOSE: (2), (15), (17), (18), (29) are inconsistent by sub-proof #1280.
% 201.86/33.52  | | 
% 201.86/33.52  | Case 2:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (30)   ~ (all_58_4 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (23), (30) imply:
% 201.86/33.52  | |   (31)   ~ (all_52_17 = e3)
% 201.86/33.52  | | 
% 201.86/33.52  | | BETA: splitting (7) gives:
% 201.86/33.52  | | 
% 201.86/33.52  | | Case 1:
% 201.86/33.52  | | | 
% 201.86/33.52  | | |   (32)  all_56_2 = e3
% 201.86/33.52  | | | 
% 201.86/33.52  | | | REF_CLOSE: (11), (31), (32) are inconsistent by sub-proof #1327.
% 201.86/33.52  | | | 
% 201.86/33.52  | | Case 2:
% 201.86/33.52  | | | 
% 201.86/33.52  | | |   (33)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.86/33.52  | | | 
% 201.86/33.52  | | | BETA: splitting (13) gives:
% 201.86/33.52  | | | 
% 201.86/33.52  | | | Case 1:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | |   (34)  all_58_0 = e2
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | COMBINE_EQS: (3), (34) imply:
% 201.86/33.52  | | | |   (35)  all_6_2 = e2
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | REDUCE: (18), (35) imply:
% 201.86/33.52  | | | |   (36)   ~ (all_52_17 = e2)
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | BETA: splitting (24) gives:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | Case 1:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | |   (37)  all_56_10 = e3
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REF_CLOSE: (2), (4), (9), (15), (19), (26), (37) are inconsistent by
% 201.86/33.52  | | | | |            sub-proof #397.
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | Case 2:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | |   (38)   ~ (all_56_10 = e3)
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REDUCE: (19), (38) imply:
% 201.86/33.52  | | | | |   (39)   ~ (all_10_2 = e3)
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REF_CLOSE: (2), (5), (6), (11), (17), (21), (23), (25), (33), (36),
% 201.86/33.52  | | | | |            (39) are inconsistent by sub-proof #1058.
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | End of split
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | Case 2:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | |   (40)   ~ (all_58_0 = e2)
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | REDUCE: (3), (40) imply:
% 201.86/33.52  | | | |   (41)   ~ (all_6_2 = e2)
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | BETA: splitting (7) gives:
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | | Case 1:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | |   (42)  all_56_2 = e3
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | REF_CLOSE: (2), (8), (11), (15), (17), (42) are inconsistent by
% 201.86/33.52  | | | | |            sub-proof #1265.
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | Case 2:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | |   (43)   ~ (all_56_2 = e3)
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | BETA: splitting (20) gives:
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | | Case 1:
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | |   (44)  all_58_4 = e3
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | REF_CLOSE: (23), (31), (44) are inconsistent by sub-proof #1302.
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | Case 2:
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | |   (45)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | BETA: splitting (24) gives:
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | | Case 1:
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | |   (46)  all_56_10 = e3
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | | REF_CLOSE: (2), (4), (9), (15), (19), (26), (46) are inconsistent
% 201.86/33.52  | | | | | | |            by sub-proof #397.
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | Case 2:
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | |   (47)   ~ (all_56_10 = e3)
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | | REDUCE: (19), (47) imply:
% 201.86/33.52  | | | | | | |   (48)   ~ (all_10_2 = e3)
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | | BETA: splitting (45) gives:
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | | Case 1:
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | |   (49)  all_58_5 = e3
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | | COMBINE_EQS: (16), (49) imply:
% 201.86/33.52  | | | | | | | |   (50)  all_52_19 = e3
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | | SIMP: (50) implies:
% 201.86/33.52  | | | | | | | |   (51)  all_52_19 = e3
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | | REDUCE: (10), (51) imply:
% 201.86/33.52  | | | | | | | |   (52)  op(e3, e3) = e2
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | | REF_CLOSE: (2), (4), (15), (41), (52) are inconsistent by
% 201.86/33.52  | | | | | | | |            sub-proof #890.
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | Case 2:
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | |   (53)  all_58_8 = e3 | all_58_14 = e3
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | | REF_CLOSE: (1), (12), (14), (48), (53) are inconsistent by
% 201.86/33.52  | | | | | | | |            sub-proof #1304.
% 201.86/33.52  | | | | | | | | 
% 201.86/33.52  | | | | | | | End of split
% 201.86/33.52  | | | | | | | 
% 201.86/33.52  | | | | | | End of split
% 201.86/33.52  | | | | | | 
% 201.86/33.52  | | | | | End of split
% 201.86/33.52  | | | | | 
% 201.86/33.52  | | | | End of split
% 201.86/33.52  | | | | 
% 201.86/33.52  | | | End of split
% 201.86/33.52  | | | 
% 201.86/33.52  | | End of split
% 201.86/33.52  | | 
% 201.86/33.52  | End of split
% 201.86/33.52  | 
% 201.86/33.52  End of proof
% 201.86/33.52  
% 201.86/33.52  Sub-proof #279 shows that the following formulas are inconsistent:
% 201.86/33.52  ----------------------------------------------------------------
% 201.86/33.52    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.52    (2)   ~ (e3 = e0)
% 201.86/33.52    (3)  all_58_0 = all_6_2
% 201.86/33.52    (4)  op(e3, all_6_1) = e1
% 201.86/33.52    (5)  op(e3, e0) = all_52_25
% 201.86/33.52    (6)  op(e1, e3) = all_52_5
% 201.86/33.52    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.86/33.52    (8)   ~ (e2 = e1)
% 201.86/33.52    (9)  all_58_2 = all_52_3
% 201.86/33.52    (10)   ~ (e2 = e0)
% 201.86/33.52    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.86/33.52    (12)   ~ (all_52_25 = all_6_2)
% 201.86/33.52    (13)   ~ (all_52_9 = all_6_2)
% 201.86/33.52    (14)  all_58_6 = all_52_5
% 201.86/33.52    (15)  op(e3, e2) = all_52_9
% 201.86/33.52    (16)   ~ (e1 = e0)
% 201.86/33.52    (17)   ~ (e3 = e2)
% 201.86/33.52    (18)  all_58_12 = e3
% 201.86/33.52    (19)  op(all_6_2, e3) = all_6_1
% 201.86/33.52    (20)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.86/33.52    (21)  all_58_0 = e1
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | COMBINE_EQS: (3), (21) imply:
% 201.86/33.52  |   (22)  all_6_2 = e1
% 201.86/33.52  | 
% 201.86/33.52  | REDUCE: (13), (22) imply:
% 201.86/33.52  |   (23)   ~ (all_52_9 = e1)
% 201.86/33.52  | 
% 201.86/33.52  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 201.86/33.52  |            (15), (16), (17), (18), (19), (20), (21), (22), (23) are
% 201.86/33.52  |            inconsistent by sub-proof #306.
% 201.86/33.52  | 
% 201.86/33.52  End of proof
% 201.86/33.52  
% 201.86/33.52  Sub-proof #280 shows that the following formulas are inconsistent:
% 201.86/33.52  ----------------------------------------------------------------
% 201.86/33.52    (1)  all_58_14 = all_52_23
% 201.86/33.52    (2)   ~ (e3 = e1)
% 201.86/33.52    (3)  op(all_52_3, all_52_3) = all_52_2
% 201.86/33.52    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.52    (5)  all_58_1 = all_52_9
% 201.86/33.52    (6)  op(all_52_23, all_52_23) = e0
% 201.86/33.52    (7)   ~ (all_52_17 = all_52_25)
% 201.86/33.52    (8)  all_58_0 = all_6_2
% 201.86/33.52    (9)  all_58_13 = e3
% 201.86/33.52    (10)  op(all_52_5, all_52_5) = all_52_4
% 201.86/33.52    (11)  all_58_9 = all_52_25
% 201.86/33.52    (12)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.86/33.52    (13)  op(e2, e2) = all_4_2
% 201.86/33.52    (14)   ~ (all_52_3 = all_52_5)
% 201.86/33.52    (15)  all_58_11 = all_52_29
% 201.86/33.52    (16)   ~ (all_52_25 = all_14_2)
% 201.86/33.52    (17)  op(all_10_2, e1) = all_10_1
% 201.86/33.52    (18)  op(all_6_2, all_6_2) = all_52_0
% 201.86/33.52    (19)   ~ (all_52_7 = all_6_2)
% 201.86/33.52    (20)  op(e0, e0) = all_14_2
% 201.86/33.52    (21)  all_56_11 = all_52_29
% 201.86/33.52    (22)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.86/33.52    (23)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.86/33.52    (24)   ~ (e2 = e1)
% 201.86/33.52    (25)  op(all_10_2, all_10_2) = e1
% 201.86/33.52    (26)  op(all_52_9, all_52_9) = all_52_8
% 201.86/33.52    (27)   ~ (all_52_25 = all_52_29)
% 201.86/33.52    (28)   ~ (all_52_29 = all_10_2)
% 201.86/33.52    (29)  all_58_7 = all_52_13
% 201.86/33.52    (30)  op(all_52_19, all_52_19) = e2
% 201.86/33.52    (31)  all_58_12 = all_52_7
% 201.86/33.52    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.86/33.52    (33)   ~ (all_52_7 = e3)
% 201.86/33.52    (34)  all_58_2 = all_52_3
% 201.86/33.52    (35)  all_56_2 = all_52_17
% 201.86/33.52    (36)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.86/33.52    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.86/33.52    (38)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 201.86/33.52    (39)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.86/33.52    (40)   ~ (all_52_23 = e3)
% 201.86/33.52    (41)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.86/33.52    (42)   ~ (all_52_9 = e3)
% 201.86/33.52    (43)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.86/33.52    (44)  op(e3, e1) = all_52_17
% 201.86/33.52    (45)   ~ (all_52_9 = all_52_25)
% 201.86/33.52    (46)   ~ (all_52_19 = all_10_2)
% 201.86/33.52    (47)  all_58_8 = all_10_2
% 201.86/33.52    (48)   ~ (all_52_5 = all_10_2)
% 201.86/33.52    (49)  op(all_52_29, all_52_29) = all_52_28
% 201.86/33.52    (50)   ~ (all_52_23 = all_14_2)
% 201.86/33.52    (51)   ~ (all_52_25 = all_6_2)
% 201.86/33.52    (52)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.86/33.52    (53)   ~ (all_52_5 = all_6_2)
% 201.86/33.52    (54)   ~ (all_52_9 = all_6_2)
% 201.86/33.52    (55)  all_56_0 = all_6_2
% 201.86/33.52    (56)  op(e3, e3) = all_6_2
% 201.86/33.52    (57)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.86/33.52    (58)   ~ (all_52_13 = e3)
% 201.86/33.52    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.86/33.52    (60)  all_56_3 = all_52_25
% 201.86/33.52    (61)   ~ (all_52_3 = all_52_7)
% 201.86/33.52    (62)  all_58_5 = all_52_19
% 201.86/33.52    (63)  all_56_1 = all_52_9
% 201.86/33.52    (64)  op(all_52_17, all_52_17) = e3
% 201.86/33.52    (65)  all_58_6 = all_52_5
% 201.86/33.52    (66)   ~ (all_52_17 = all_6_2)
% 201.86/33.52    (67)   ~ (e3 = e2)
% 201.86/33.52    (68)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.86/33.52    (69)   ~ (all_52_9 = all_52_17)
% 201.86/33.52    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.86/33.52    (71)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.86/33.52    (72)  op(e1, e1) = all_10_2
% 201.86/33.52    (73)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 201.86/33.52    (74)   ~ (all_52_3 = all_4_2)
% 201.86/33.52    (75)  all_58_4 = all_52_17
% 201.86/33.52    (76)  op(all_52_25, all_52_25) = all_52_24
% 201.86/33.52  
% 201.86/33.52  Begin of proof
% 201.86/33.52  | 
% 201.86/33.52  | BETA: splitting (68) gives:
% 201.86/33.52  | 
% 201.86/33.52  | Case 1:
% 201.86/33.52  | | 
% 201.86/33.52  | |   (77)  all_56_1 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | COMBINE_EQS: (63), (77) imply:
% 201.86/33.52  | |   (78)  all_52_9 = e3
% 201.86/33.52  | | 
% 201.86/33.52  | | REDUCE: (42), (78) imply:
% 201.86/33.52  | |   (79)  $false
% 201.86/33.52  | | 
% 201.86/33.52  | | CLOSE: (79) is inconsistent.
% 201.86/33.52  | | 
% 201.86/33.52  | Case 2:
% 201.86/33.52  | | 
% 201.86/33.53  | |   (80)   ~ (all_56_1 = e3)
% 201.86/33.53  | |   (81)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.86/33.53  | | 
% 201.86/33.53  | | BETA: splitting (23) gives:
% 201.86/33.53  | | 
% 201.86/33.53  | | Case 1:
% 201.86/33.53  | | | 
% 201.86/33.53  | | |   (82)  all_58_1 = e1
% 201.86/33.53  | | | 
% 201.86/33.53  | | | COMBINE_EQS: (5), (82) imply:
% 201.86/33.53  | | |   (83)  all_52_9 = e1
% 201.86/33.53  | | | 
% 201.86/33.53  | | | REDUCE: (69), (83) imply:
% 201.86/33.53  | | |   (84)   ~ (all_52_17 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | SIMP: (84) implies:
% 201.86/33.53  | | |   (85)   ~ (all_52_17 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | REDUCE: (54), (83) imply:
% 201.86/33.53  | | |   (86)   ~ (all_6_2 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | SIMP: (86) implies:
% 201.86/33.53  | | |   (87)   ~ (all_6_2 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | REDUCE: (42), (83) imply:
% 201.86/33.53  | | |   (88)   ~ (e3 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | BETA: splitting (52) gives:
% 201.86/33.53  | | | 
% 201.86/33.53  | | | Case 1:
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | |   (89)  all_56_3 = e3
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | COMBINE_EQS: (60), (89) imply:
% 201.86/33.53  | | | |   (90)  all_52_25 = e3
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | SIMP: (90) implies:
% 201.86/33.53  | | | |   (91)  all_52_25 = e3
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (7), (91) imply:
% 201.86/33.53  | | | |   (92)   ~ (all_52_17 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (16), (91) imply:
% 201.86/33.53  | | | |   (93)   ~ (all_14_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | SIMP: (93) implies:
% 201.86/33.53  | | | |   (94)   ~ (all_14_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (51), (91) imply:
% 201.86/33.53  | | | |   (95)   ~ (all_6_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | SIMP: (95) implies:
% 201.86/33.53  | | | |   (96)   ~ (all_6_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REF_CLOSE: (1), (4), (6), (8), (9), (18), (19), (20), (22), (31), (35),
% 201.86/33.53  | | | |            (36), (38), (43), (50), (55), (64), (66), (71), (85), (87),
% 201.86/33.53  | | | |            (92), (94), (96) are inconsistent by sub-proof #1064.
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | Case 2:
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | |   (97)   ~ (all_56_3 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (60), (97) imply:
% 201.86/33.53  | | | |   (98)   ~ (all_52_25 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REF_CLOSE: (1), (2), (4), (5), (8), (11), (15), (18), (21), (25), (28),
% 201.86/33.53  | | | |            (29), (30), (32), (40), (41), (42), (47), (49), (53), (56),
% 201.86/33.53  | | | |            (58), (59), (62), (64), (65), (66), (67), (70), (75), (98)
% 201.86/33.53  | | | |            are inconsistent by sub-proof #281.
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | End of split
% 201.86/33.53  | | | 
% 201.86/33.53  | | Case 2:
% 201.86/33.53  | | | 
% 201.86/33.53  | | |   (99)   ~ (all_58_1 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | REDUCE: (5), (99) imply:
% 201.86/33.53  | | |   (100)   ~ (all_52_9 = e1)
% 201.86/33.53  | | | 
% 201.86/33.53  | | | BETA: splitting (57) gives:
% 201.86/33.53  | | | 
% 201.86/33.53  | | | Case 1:
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | |   (101)  all_58_9 = e3
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | COMBINE_EQS: (11), (101) imply:
% 201.86/33.53  | | | |   (102)  all_52_25 = e3
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | SIMP: (102) implies:
% 201.86/33.53  | | | |   (103)  all_52_25 = e3
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (16), (103) imply:
% 201.86/33.53  | | | |   (104)   ~ (all_14_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | SIMP: (104) implies:
% 201.86/33.53  | | | |   (105)   ~ (all_14_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (51), (103) imply:
% 201.86/33.53  | | | |   (106)   ~ (all_6_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | SIMP: (106) implies:
% 201.86/33.53  | | | |   (107)   ~ (all_6_2 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (76), (103) imply:
% 201.86/33.53  | | | |   (108)  op(e3, e3) = all_52_24
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_24, e3, e3,
% 201.86/33.53  | | | |              simplifying with (56), (108) gives:
% 201.86/33.53  | | | |   (109)  all_52_24 = all_6_2
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | BETA: splitting (37) gives:
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | Case 1:
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | |   (110)  all_58_0 = e3
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | | COMBINE_EQS: (8), (110) imply:
% 201.86/33.53  | | | | |   (111)  all_6_2 = e3
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | | REDUCE: (107), (111) imply:
% 201.86/33.53  | | | | |   (112)  $false
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | | CLOSE: (112) is inconsistent.
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | Case 2:
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | |   (113)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 201.86/33.53  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (22),
% 201.86/33.53  | | | | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34),
% 201.86/33.53  | | | | |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (46),
% 201.86/33.53  | | | | |            (47), (48), (50), (54), (55), (56), (58), (59), (61), (62),
% 201.86/33.53  | | | | |            (63), (64), (65), (66), (67), (69), (70), (71), (72), (73),
% 201.86/33.53  | | | | |            (74), (75), (76), (81), (100), (105), (107), (113) are
% 201.86/33.53  | | | | |            inconsistent by sub-proof #1055.
% 201.86/33.53  | | | | | 
% 201.86/33.53  | | | | End of split
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | Case 2:
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | |   (114)   ~ (all_58_9 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REDUCE: (11), (114) imply:
% 201.86/33.53  | | | |   (115)   ~ (all_52_25 = e3)
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | | REF_CLOSE: (1), (2), (4), (5), (8), (11), (15), (18), (21), (25), (28),
% 201.86/33.53  | | | |            (29), (30), (32), (40), (41), (42), (47), (49), (53), (56),
% 201.86/33.53  | | | |            (58), (59), (62), (64), (65), (66), (67), (70), (75), (115)
% 201.86/33.53  | | | |            are inconsistent by sub-proof #281.
% 201.86/33.53  | | | | 
% 201.86/33.53  | | | End of split
% 201.86/33.53  | | | 
% 201.86/33.53  | | End of split
% 201.86/33.53  | | 
% 201.86/33.53  | End of split
% 201.86/33.53  | 
% 201.86/33.53  End of proof
% 201.86/33.53  
% 201.86/33.53  Sub-proof #281 shows that the following formulas are inconsistent:
% 201.86/33.53  ----------------------------------------------------------------
% 201.86/33.53    (1)  all_58_14 = all_52_23
% 201.86/33.53    (2)   ~ (e3 = e1)
% 201.86/33.53    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.86/33.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.86/33.53    (4)  all_58_1 = all_52_9
% 201.86/33.53    (5)  all_58_0 = all_6_2
% 201.86/33.53    (6)  all_58_9 = all_52_25
% 201.86/33.53    (7)  all_58_11 = all_52_29
% 201.86/33.53    (8)  op(all_6_2, all_6_2) = all_52_0
% 201.86/33.53    (9)  all_56_11 = all_52_29
% 201.86/33.53    (10)  op(all_10_2, all_10_2) = e1
% 201.86/33.53    (11)   ~ (all_52_29 = all_10_2)
% 201.86/33.53    (12)  all_58_7 = all_52_13
% 201.86/33.53    (13)  op(all_52_19, all_52_19) = e2
% 201.86/33.53    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.86/33.53    (15)   ~ (all_52_25 = e3)
% 201.86/33.53    (16)   ~ (all_52_23 = e3)
% 201.86/33.53    (17)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 201.86/33.53    (18)   ~ (all_52_9 = e3)
% 201.86/33.53    (19)  all_58_8 = all_10_2
% 201.86/33.53    (20)  op(all_52_29, all_52_29) = all_52_28
% 201.86/33.53    (21)   ~ (all_52_5 = all_6_2)
% 201.86/33.53    (22)  op(e3, e3) = all_6_2
% 201.86/33.53    (23)   ~ (all_52_13 = e3)
% 201.86/33.53    (24)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.86/33.53    (25)  all_58_5 = all_52_19
% 201.86/33.53    (26)  op(all_52_17, all_52_17) = e3
% 201.86/33.53    (27)  all_58_6 = all_52_5
% 201.86/33.53    (28)   ~ (all_52_17 = all_6_2)
% 201.86/33.53    (29)   ~ (e3 = e2)
% 201.86/33.53    (30)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.86/33.53    (31)  all_58_4 = all_52_17
% 201.86/33.53  
% 201.86/33.53  Begin of proof
% 201.86/33.53  | 
% 201.86/33.53  | BETA: splitting (24) gives:
% 201.86/33.53  | 
% 201.86/33.53  | Case 1:
% 201.86/33.53  | | 
% 201.86/33.53  | |   (32)  all_58_0 = e3
% 201.86/33.53  | | 
% 201.86/33.53  | | COMBINE_EQS: (5), (32) imply:
% 201.86/33.53  | |   (33)  all_6_2 = e3
% 201.86/33.53  | | 
% 201.86/33.53  | | REDUCE: (21), (33) imply:
% 201.86/33.53  | |   (34)   ~ (all_52_5 = e3)
% 201.86/33.53  | | 
% 201.86/33.53  | | REDUCE: (28), (33) imply:
% 201.86/33.53  | |   (35)   ~ (all_52_17 = e3)
% 201.86/33.53  | | 
% 201.86/33.53  | | REDUCE: (8), (33) imply:
% 201.86/33.53  | |   (36)  op(e3, e3) = all_52_0
% 201.86/33.53  | | 
% 201.86/33.53  | | REDUCE: (22), (33) imply:
% 201.86/33.53  | |   (37)  op(e3, e3) = e3
% 201.86/33.53  | | 
% 201.86/33.53  | | REF_CLOSE: (1), (2), (3), (7), (9), (10), (11), (12), (13), (14), (16),
% 201.86/33.53  | |            (17), (19), (20), (23), (25), (27), (29), (30), (31), (34), (35),
% 201.86/33.53  | |            (36), (37) are inconsistent by sub-proof #1063.
% 201.86/33.53  | | 
% 201.86/33.53  | Case 2:
% 201.86/33.53  | | 
% 201.86/33.53  | |   (38)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.86/33.53  | | 
% 201.86/33.53  | | REF_CLOSE: (3), (4), (6), (15), (18), (22), (26), (28), (31), (38) are
% 201.86/33.53  | |            inconsistent by sub-proof #1072.
% 201.86/33.53  | | 
% 201.86/33.53  | End of split
% 201.86/33.53  | 
% 201.86/33.53  End of proof
% 201.86/33.53  
% 201.86/33.53  Sub-proof #282 shows that the following formulas are inconsistent:
% 201.86/33.53  ----------------------------------------------------------------
% 201.89/33.53    (1)  all_58_14 = all_52_23
% 201.89/33.53    (2)   ~ (e3 = e1)
% 201.89/33.53    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.53    (4)  all_58_1 = all_52_9
% 201.89/33.53    (5)  op(all_52_23, all_52_23) = e0
% 201.89/33.53    (6)  op(e0, e2) = all_52_15
% 201.89/33.53    (7)   ~ (all_52_17 = all_52_25)
% 201.89/33.53    (8)  all_58_0 = all_6_2
% 201.89/33.53    (9)  op(all_14_2, e0) = all_14_1
% 201.89/33.53    (10)  op(e3, all_6_1) = e1
% 201.89/33.53    (11)   ~ (all_52_17 = all_10_2)
% 201.89/33.53    (12)  op(e3, e0) = all_52_25
% 201.89/33.53    (13)  op(e0, all_14_1) = all_14_0
% 201.89/33.53    (14)  all_58_13 = all_52_15
% 201.89/33.53    (15)  all_58_9 = all_52_25
% 201.89/33.53    (16)   ~ (all_52_25 = all_14_2)
% 201.89/33.53    (17)   ~ (all_52_7 = all_6_2)
% 201.89/33.53    (18)  op(e0, e0) = all_14_2
% 201.89/33.53    (19)  op(e0, e1) = all_52_23
% 201.89/33.53    (20)  all_56_15 = all_14_2
% 201.89/33.53    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.89/33.53    (22)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.53    (23)  op(all_10_2, all_10_2) = e1
% 201.89/33.53    (24)  op(all_52_9, all_52_9) = all_52_8
% 201.89/33.53    (25)   ~ (all_52_19 = all_52_23)
% 201.89/33.53    (26)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.53    (27)  op(all_52_19, all_52_19) = e2
% 201.89/33.53    (28)  all_58_12 = all_52_7
% 201.89/33.53    (29)  all_56_2 = all_52_17
% 201.89/33.53    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.53    (31)   ~ (all_14_0 = e3)
% 201.89/33.53    (32)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.53    (33)  all_58_15 = all_14_2
% 201.89/33.53    (34)  all_58_8 = all_10_2
% 201.89/33.53    (35)   ~ (all_52_23 = all_14_2)
% 201.89/33.53    (36)   ~ (all_52_25 = all_6_2)
% 201.89/33.53    (37)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.53    (38)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.89/33.53    (39)  op(e3, e3) = all_6_2
% 201.89/33.53    (40)  all_56_15 = e3
% 201.89/33.53    (41)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.53    (42)  all_56_14 = all_52_23
% 201.89/33.53    (43)  all_56_3 = all_52_25
% 201.89/33.53    (44)  op(all_14_2, all_14_2) = all_52_30
% 201.89/33.53    (45)  all_58_5 = all_52_19
% 201.89/33.53    (46)  op(all_52_17, all_52_17) = e3
% 201.89/33.53    (47)   ~ (all_52_17 = all_6_2)
% 201.89/33.53    (48)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.53    (49)  op(e1, e1) = all_10_2
% 201.89/33.53    (50)   ~ (all_52_17 = all_52_23)
% 201.89/33.53    (51)  op(all_6_2, e3) = all_6_1
% 201.89/33.53    (52)  all_58_4 = all_52_17
% 201.89/33.53    (53)   ~ (all_14_0 = e1)
% 201.89/33.53    (54)   ~ (all_14_0 = e2)
% 201.89/33.53    (55)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.53  
% 201.89/33.53  Begin of proof
% 201.89/33.53  | 
% 201.89/33.53  | COMBINE_EQS: (20), (40) imply:
% 201.89/33.53  |   (56)  all_14_2 = e3
% 201.89/33.53  | 
% 201.89/33.53  | SIMP: (56) implies:
% 201.89/33.53  |   (57)  all_14_2 = e3
% 201.89/33.53  | 
% 201.89/33.53  | COMBINE_EQS: (33), (57) imply:
% 201.89/33.53  |   (58)  all_58_15 = e3
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (35), (57) imply:
% 201.89/33.53  |   (59)   ~ (all_52_23 = e3)
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (16), (57) imply:
% 201.89/33.53  |   (60)   ~ (all_52_25 = e3)
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (44), (57) imply:
% 201.89/33.53  |   (61)  op(e3, e3) = all_52_30
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (9), (57) imply:
% 201.89/33.53  |   (62)  op(e3, e0) = all_14_1
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (18), (57) imply:
% 201.89/33.53  |   (63)  op(e0, e0) = e3
% 201.89/33.53  | 
% 201.89/33.53  | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 201.89/33.53  |              with (12), (62) gives:
% 201.89/33.53  |   (64)  all_52_25 = all_14_1
% 201.89/33.53  | 
% 201.89/33.53  | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3, simplifying
% 201.89/33.53  |              with (39), (61) gives:
% 201.89/33.53  |   (65)  all_52_30 = all_6_2
% 201.89/33.53  | 
% 201.89/33.53  | COMBINE_EQS: (43), (64) imply:
% 201.89/33.53  |   (66)  all_56_3 = all_14_1
% 201.89/33.53  | 
% 201.89/33.53  | COMBINE_EQS: (15), (64) imply:
% 201.89/33.53  |   (67)  all_58_9 = all_14_1
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (7), (64) imply:
% 201.89/33.53  |   (68)   ~ (all_52_17 = all_14_1)
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (36), (64) imply:
% 201.89/33.53  |   (69)   ~ (all_14_1 = all_6_2)
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (60), (64) imply:
% 201.89/33.53  |   (70)   ~ (all_14_1 = e3)
% 201.89/33.53  | 
% 201.89/33.53  | REDUCE: (55), (64) imply:
% 201.89/33.53  |   (71)  op(all_14_1, all_14_1) = all_52_24
% 201.89/33.53  | 
% 201.89/33.53  | BETA: splitting (26) gives:
% 201.89/33.53  | 
% 201.89/33.53  | Case 1:
% 201.89/33.53  | | 
% 201.89/33.53  | |   (72)  all_56_14 = e3
% 201.89/33.53  | | 
% 201.89/33.53  | | REF_CLOSE: (42), (59), (72) are inconsistent by sub-proof #1286.
% 201.89/33.53  | | 
% 201.89/33.53  | Case 2:
% 201.89/33.53  | | 
% 201.89/33.53  | |   (73)   ~ (all_56_14 = e3)
% 201.89/33.53  | |   (74)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.53  | | 
% 201.89/33.53  | | BETA: splitting (37) gives:
% 201.89/33.53  | | 
% 201.89/33.53  | | Case 1:
% 201.89/33.53  | | | 
% 201.89/33.53  | | |   (75)  all_56_3 = e3
% 201.89/33.53  | | | 
% 201.89/33.53  | | | REF_CLOSE: (66), (70), (75) are inconsistent by sub-proof #1200.
% 201.89/33.53  | | | 
% 201.89/33.53  | | Case 2:
% 201.89/33.53  | | | 
% 201.89/33.53  | | |   (76)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.53  | | | 
% 201.89/33.53  | | | BETA: splitting (32) gives:
% 201.89/33.53  | | | 
% 201.89/33.53  | | | Case 1:
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | |   (77)  all_58_12 = e1
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | COMBINE_EQS: (28), (77) imply:
% 201.89/33.53  | | | |   (78)  all_52_7 = e1
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | SIMP: (78) implies:
% 201.89/33.53  | | | |   (79)  all_52_7 = e1
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | REDUCE: (17), (79) imply:
% 201.89/33.53  | | | |   (80)   ~ (all_6_2 = e1)
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | SIMP: (80) implies:
% 201.89/33.53  | | | |   (81)   ~ (all_6_2 = e1)
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | BETA: splitting (30) gives:
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | Case 1:
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | |   (82)  all_58_0 = e3
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | COMBINE_EQS: (8), (82) imply:
% 201.89/33.53  | | | | |   (83)  all_6_2 = e3
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | REF_CLOSE: (2), (3), (10), (39), (51), (83) are inconsistent by
% 201.89/33.53  | | | | |            sub-proof #310.
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | Case 2:
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | |   (84)   ~ (all_58_0 = e3)
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | REDUCE: (8), (84) imply:
% 201.89/33.53  | | | | |   (85)   ~ (all_6_2 = e3)
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | BETA: splitting (41) gives:
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | Case 1:
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | |   (86)  all_58_0 = e3
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | COMBINE_EQS: (8), (86) imply:
% 201.89/33.53  | | | | | |   (87)  all_6_2 = e3
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | REDUCE: (85), (87) imply:
% 201.89/33.53  | | | | | |   (88)  $false
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | CLOSE: (88) is inconsistent.
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | Case 2:
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | |   (89)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | BETA: splitting (48) gives:
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | Case 1:
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | |   (90)  all_58_4 = e3
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | COMBINE_EQS: (52), (90) imply:
% 201.89/33.53  | | | | | | |   (91)  all_52_17 = e3
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | SIMP: (91) implies:
% 201.89/33.53  | | | | | | |   (92)  all_52_17 = e3
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | REF_CLOSE: (3), (39), (46), (47), (92) are inconsistent by
% 201.89/33.53  | | | | | | |            sub-proof #1280.
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | Case 2:
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | |   (93)   ~ (all_58_4 = e3)
% 201.89/33.53  | | | | | | |   (94)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | REDUCE: (52), (93) imply:
% 201.89/33.53  | | | | | | |   (95)   ~ (all_52_17 = e3)
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | BETA: splitting (89) gives:
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | Case 1:
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | |   (96)  all_58_1 = e3
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | | COMBINE_EQS: (4), (96) imply:
% 201.89/33.53  | | | | | | | |   (97)  all_52_9 = e3
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | | REDUCE: (24), (97) imply:
% 201.89/33.53  | | | | | | | |   (98)  op(e3, e3) = all_52_8
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | | BETA: splitting (94) gives:
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | | Case 1:
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | |   (99)  all_58_5 = e3
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | COMBINE_EQS: (45), (99) imply:
% 201.89/33.53  | | | | | | | | |   (100)  all_52_19 = e3
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | SIMP: (100) implies:
% 201.89/33.53  | | | | | | | | |   (101)  all_52_19 = e3
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | REDUCE: (25), (101) imply:
% 201.89/33.53  | | | | | | | | |   (102)   ~ (all_52_23 = e3)
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | REDUCE: (27), (101) imply:
% 201.89/33.53  | | | | | | | | |   (103)  op(e3, e3) = e2
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_8, e3, e3,
% 201.89/33.53  | | | | | | | | |              simplifying with (39), (98) gives:
% 201.89/33.53  | | | | | | | | |   (104)  all_52_8 = all_6_2
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_52_8, e3, e3,
% 201.89/33.53  | | | | | | | | |              simplifying with (98), (103) gives:
% 201.89/33.53  | | | | | | | | |   (105)  all_52_8 = e2
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | COMBINE_EQS: (104), (105) imply:
% 201.89/33.53  | | | | | | | | |   (106)  all_6_2 = e2
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | SIMP: (106) implies:
% 201.89/33.53  | | | | | | | | |   (107)  all_6_2 = e2
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | REDUCE: (69), (107) imply:
% 201.89/33.53  | | | | | | | | |   (108)   ~ (all_14_1 = e2)
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | REF_CLOSE: (3), (5), (13), (19), (21), (31), (42), (53), (54),
% 201.89/33.53  | | | | | | | | |            (59), (63), (66), (67), (71), (74), (76), (108) are
% 201.89/33.53  | | | | | | | | |            inconsistent by sub-proof #284.
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | Case 2:
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | |   (109)  all_58_8 = e3 | all_58_14 = e3
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | | REF_CLOSE: (1), (3), (23), (34), (39), (59), (81), (109) are
% 201.89/33.53  | | | | | | | | |            inconsistent by sub-proof #283.
% 201.89/33.53  | | | | | | | | | 
% 201.89/33.53  | | | | | | | | End of split
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | Case 2:
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | |   (110)  all_58_4 = e3 | all_58_9 = e3
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | | REF_CLOSE: (15), (52), (60), (95), (110) are inconsistent by
% 201.89/33.53  | | | | | | | |            sub-proof #1276.
% 201.89/33.53  | | | | | | | | 
% 201.89/33.53  | | | | | | | End of split
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | End of split
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | End of split
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | End of split
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | Case 2:
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | |   (111)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | BETA: splitting (38) gives:
% 201.89/33.53  | | | | 
% 201.89/33.53  | | | | Case 1:
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | |   (112)  all_58_9 = e2
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | COMBINE_EQS: (67), (112) imply:
% 201.89/33.53  | | | | |   (113)  all_14_1 = e2
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | SIMP: (113) implies:
% 201.89/33.53  | | | | |   (114)  all_14_1 = e2
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | REDUCE: (68), (114) imply:
% 201.89/33.53  | | | | |   (115)   ~ (all_52_17 = e2)
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | REDUCE: (13), (114) imply:
% 201.89/33.53  | | | | |   (116)  op(e0, e2) = all_14_0
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | GROUND_INST: instantiating (3) with all_52_15, all_14_0, e2, e0,
% 201.89/33.53  | | | | |              simplifying with (6), (116) gives:
% 201.89/33.53  | | | | |   (117)  all_52_15 = all_14_0
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | COMBINE_EQS: (14), (117) imply:
% 201.89/33.53  | | | | |   (118)  all_58_13 = all_14_0
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | BETA: splitting (111) gives:
% 201.89/33.53  | | | | | 
% 201.89/33.53  | | | | | Case 1:
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | |   (119)  all_58_13 = e1
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | COMBINE_EQS: (118), (119) imply:
% 201.89/33.53  | | | | | |   (120)  all_14_0 = e1
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | SIMP: (120) implies:
% 201.89/33.53  | | | | | |   (121)  all_14_0 = e1
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | REDUCE: (53), (121) imply:
% 201.89/33.53  | | | | | |   (122)  $false
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | CLOSE: (122) is inconsistent.
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | Case 2:
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | |   (123)  all_58_14 = e1 | all_58_15 = e1
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | BETA: splitting (123) gives:
% 201.89/33.53  | | | | | | 
% 201.89/33.53  | | | | | | Case 1:
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | |   (124)  all_58_14 = e1
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | COMBINE_EQS: (1), (124) imply:
% 201.89/33.53  | | | | | | |   (125)  all_52_23 = e1
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | SIMP: (125) implies:
% 201.89/33.53  | | | | | | |   (126)  all_52_23 = e1
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | REDUCE: (50), (126) imply:
% 201.89/33.53  | | | | | | |   (127)   ~ (all_52_17 = e1)
% 201.89/33.53  | | | | | | | 
% 201.89/33.53  | | | | | | | REDUCE: (5), (126) imply:
% 201.89/33.54  | | | | | | |   (128)  op(e1, e1) = e0
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | GROUND_INST: instantiating (3) with all_10_2, e0, e1, e1,
% 201.89/33.54  | | | | | | |              simplifying with (49), (128) gives:
% 201.89/33.54  | | | | | | |   (129)  all_10_2 = e0
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | REDUCE: (11), (129) imply:
% 201.89/33.54  | | | | | | |   (130)   ~ (all_52_17 = e0)
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | BETA: splitting (22) gives:
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | Case 1:
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | |   (131)  all_56_2 = e3
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | | COMBINE_EQS: (29), (131) imply:
% 201.89/33.54  | | | | | | | |   (132)  all_52_17 = e3
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | | REF_CLOSE: (3), (39), (46), (47), (132) are inconsistent by
% 201.89/33.54  | | | | | | | |            sub-proof #1280.
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | Case 2:
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | |   (133)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | | REF_CLOSE: (29), (115), (127), (130), (133) are inconsistent by
% 201.89/33.54  | | | | | | | |            sub-proof #1180.
% 201.89/33.54  | | | | | | | | 
% 201.89/33.54  | | | | | | | End of split
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | Case 2:
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | |   (134)  all_58_15 = e1
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | COMBINE_EQS: (58), (134) imply:
% 201.89/33.54  | | | | | | |   (135)  e3 = e1
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | REDUCE: (2), (135) imply:
% 201.89/33.54  | | | | | | |   (136)  $false
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | | CLOSE: (136) is inconsistent.
% 201.89/33.54  | | | | | | | 
% 201.89/33.54  | | | | | | End of split
% 201.89/33.54  | | | | | | 
% 201.89/33.54  | | | | | End of split
% 201.89/33.54  | | | | | 
% 201.89/33.54  | | | | Case 2:
% 201.89/33.54  | | | | | 
% 201.89/33.54  | | | | |   (137)   ~ (all_58_9 = e2)
% 201.89/33.54  | | | | | 
% 201.89/33.54  | | | | | REDUCE: (67), (137) imply:
% 201.89/33.54  | | | | |   (138)   ~ (all_14_1 = e2)
% 201.89/33.54  | | | | | 
% 201.89/33.54  | | | | | REF_CLOSE: (3), (5), (13), (19), (21), (31), (42), (53), (54), (59),
% 201.89/33.54  | | | | |            (63), (66), (67), (71), (74), (76), (138) are inconsistent
% 201.89/33.54  | | | | |            by sub-proof #284.
% 201.89/33.54  | | | | | 
% 201.89/33.54  | | | | End of split
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | End of split
% 201.89/33.54  | | | 
% 201.89/33.54  | | End of split
% 201.89/33.54  | | 
% 201.89/33.54  | End of split
% 201.89/33.54  | 
% 201.89/33.54  End of proof
% 201.89/33.54  
% 201.89/33.54  Sub-proof #283 shows that the following formulas are inconsistent:
% 201.89/33.54  ----------------------------------------------------------------
% 201.89/33.54    (1)  all_58_14 = all_52_23
% 201.89/33.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.54    (3)  all_58_8 = e3 | all_58_14 = e3
% 201.89/33.54    (4)  op(all_10_2, all_10_2) = e1
% 201.89/33.54    (5)   ~ (all_52_23 = e3)
% 201.89/33.54    (6)  all_58_8 = all_10_2
% 201.89/33.54    (7)  op(e3, e3) = all_6_2
% 201.89/33.54    (8)   ~ (all_6_2 = e1)
% 201.89/33.54  
% 201.89/33.54  Begin of proof
% 201.89/33.54  | 
% 201.89/33.54  | BETA: splitting (3) gives:
% 201.89/33.54  | 
% 201.89/33.54  | Case 1:
% 201.89/33.54  | | 
% 201.89/33.54  | |   (9)  all_58_8 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | COMBINE_EQS: (6), (9) imply:
% 201.89/33.54  | |   (10)  all_10_2 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (4), (10) imply:
% 201.89/33.54  | |   (11)  op(e3, e3) = e1
% 201.89/33.54  | | 
% 201.89/33.54  | | REF_CLOSE: (2), (7), (8), (11) are inconsistent by sub-proof #885.
% 201.89/33.54  | | 
% 201.89/33.54  | Case 2:
% 201.89/33.54  | | 
% 201.89/33.54  | |   (12)  all_58_14 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #1305.
% 201.89/33.54  | | 
% 201.89/33.54  | End of split
% 201.89/33.54  | 
% 201.89/33.54  End of proof
% 201.89/33.54  
% 201.89/33.54  Sub-proof #284 shows that the following formulas are inconsistent:
% 201.89/33.54  ----------------------------------------------------------------
% 201.89/33.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.54    (2)  op(all_52_23, all_52_23) = e0
% 201.89/33.54    (3)   ~ (all_14_1 = e2)
% 201.89/33.54    (4)  op(e0, all_14_1) = all_14_0
% 201.89/33.54    (5)  all_56_3 = all_14_1
% 201.89/33.54    (6)  op(e0, e1) = all_52_23
% 201.89/33.54    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.89/33.54    (8)  op(e0, e0) = e3
% 201.89/33.54    (9)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.54    (10)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.54    (11)   ~ (all_14_0 = e3)
% 201.89/33.54    (12)  all_58_9 = all_14_1
% 201.89/33.54    (13)   ~ (all_52_23 = e3)
% 201.89/33.54    (14)  op(all_14_1, all_14_1) = all_52_24
% 201.89/33.54    (15)  all_56_14 = all_52_23
% 201.89/33.54    (16)   ~ (all_14_0 = e1)
% 201.89/33.54    (17)   ~ (all_14_0 = e2)
% 201.89/33.54  
% 201.89/33.54  Begin of proof
% 201.89/33.54  | 
% 201.89/33.54  | BETA: splitting (7) gives:
% 201.89/33.54  | 
% 201.89/33.54  | Case 1:
% 201.89/33.54  | | 
% 201.89/33.54  | |   (18)  all_58_9 = e1
% 201.89/33.54  | | 
% 201.89/33.54  | | COMBINE_EQS: (12), (18) imply:
% 201.89/33.54  | |   (19)  all_14_1 = e1
% 201.89/33.54  | | 
% 201.89/33.54  | | SIMP: (19) implies:
% 201.89/33.54  | |   (20)  all_14_1 = e1
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (4), (20) imply:
% 201.89/33.54  | |   (21)  op(e0, e1) = all_14_0
% 201.89/33.54  | | 
% 201.89/33.54  | | GROUND_INST: instantiating (1) with all_52_23, all_14_0, e1, e0, simplifying
% 201.89/33.54  | |              with (6), (21) gives:
% 201.89/33.54  | |   (22)  all_52_23 = all_14_0
% 201.89/33.54  | | 
% 201.89/33.54  | | COMBINE_EQS: (15), (22) imply:
% 201.89/33.54  | |   (23)  all_56_14 = all_14_0
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (2), (22) imply:
% 201.89/33.54  | |   (24)  op(all_14_0, all_14_0) = e0
% 201.89/33.54  | | 
% 201.89/33.54  | | BETA: splitting (9) gives:
% 201.89/33.54  | | 
% 201.89/33.54  | | Case 1:
% 201.89/33.54  | | | 
% 201.89/33.54  | | |   (25)  all_56_14 = e2
% 201.89/33.54  | | | 
% 201.89/33.54  | | | REF_CLOSE: (17), (23), (25) are inconsistent by sub-proof #526.
% 201.89/33.54  | | | 
% 201.89/33.54  | | Case 2:
% 201.89/33.54  | | | 
% 201.89/33.54  | | |   (26)  all_56_14 = e1 | all_56_14 = e0
% 201.89/33.54  | | | 
% 201.89/33.54  | | | BETA: splitting (26) gives:
% 201.89/33.54  | | | 
% 201.89/33.54  | | | Case 1:
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | |   (27)  all_56_14 = e1
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | | REF_CLOSE: (16), (23), (27) are inconsistent by sub-proof #525.
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | Case 2:
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | |   (28)  all_56_14 = e0
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | | COMBINE_EQS: (23), (28) imply:
% 201.89/33.54  | | | |   (29)  all_14_0 = e0
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | | REF_CLOSE: (1), (8), (11), (24), (29) are inconsistent by sub-proof
% 201.89/33.54  | | | |            #285.
% 201.89/33.54  | | | | 
% 201.89/33.54  | | | End of split
% 201.89/33.54  | | | 
% 201.89/33.54  | | End of split
% 201.89/33.54  | | 
% 201.89/33.54  | Case 2:
% 201.89/33.54  | | 
% 201.89/33.54  | |   (30)   ~ (all_58_9 = e1)
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (12), (30) imply:
% 201.89/33.54  | |   (31)   ~ (all_14_1 = e1)
% 201.89/33.54  | | 
% 201.89/33.54  | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (14), (31) are inconsistent
% 201.89/33.54  | |            by sub-proof #1181.
% 201.89/33.54  | | 
% 201.89/33.54  | End of split
% 201.89/33.54  | 
% 201.89/33.54  End of proof
% 201.89/33.54  
% 201.89/33.54  Sub-proof #285 shows that the following formulas are inconsistent:
% 201.89/33.54  ----------------------------------------------------------------
% 201.89/33.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.54    (2)  op(e0, e0) = e3
% 201.89/33.54    (3)  all_14_0 = e0
% 201.89/33.54    (4)   ~ (all_14_0 = e3)
% 201.89/33.54    (5)  op(all_14_0, all_14_0) = e0
% 201.89/33.54  
% 201.89/33.54  Begin of proof
% 201.89/33.54  | 
% 201.89/33.54  | SIMP: (3) implies:
% 201.89/33.54  |   (6)  all_14_0 = e0
% 201.89/33.54  | 
% 201.89/33.54  | REDUCE: (4), (6) imply:
% 201.89/33.54  |   (7)   ~ (e3 = e0)
% 201.89/33.54  | 
% 201.89/33.54  | SIMP: (7) implies:
% 201.89/33.54  |   (8)   ~ (e3 = e0)
% 201.89/33.54  | 
% 201.89/33.54  | REDUCE: (5), (6) imply:
% 201.89/33.54  |   (9)  op(e0, e0) = e0
% 201.89/33.54  | 
% 201.89/33.54  | REF_CLOSE: (1), (2), (8), (9) are inconsistent by sub-proof #1336.
% 201.89/33.54  | 
% 201.89/33.54  End of proof
% 201.89/33.54  
% 201.89/33.54  Sub-proof #286 shows that the following formulas are inconsistent:
% 201.89/33.54  ----------------------------------------------------------------
% 201.89/33.54    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.89/33.54    (2)   ~ (all_52_15 = all_52_23)
% 201.89/33.54    (3)   ~ (all_52_25 = all_52_27)
% 201.89/33.54    (4)  all_58_14 = all_52_23
% 201.89/33.54    (5)   ~ (e3 = e1)
% 201.89/33.54    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.89/33.54    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.89/33.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.54    (9)   ~ (all_52_5 = all_52_13)
% 201.89/33.54    (10)  all_58_1 = all_52_9
% 201.89/33.54    (11)   ~ (all_52_9 = all_52_13)
% 201.89/33.54    (12)   ~ (e3 = e0)
% 201.89/33.54    (13)  op(e2, e3) = all_52_3
% 201.89/33.54    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.54    (15)   ~ (all_52_7 = all_52_15)
% 201.89/33.54    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.54    (17)   ~ (all_52_17 = all_52_25)
% 201.89/33.54    (18)   ~ (all_52_3 = all_6_2)
% 201.89/33.54    (19)  all_58_0 = all_6_2
% 201.89/33.54    (20)  op(all_14_2, e0) = all_14_1
% 201.89/33.54    (21)  all_56_4 = all_52_3
% 201.89/33.54    (22)  op(e3, all_6_1) = e1
% 201.89/33.54    (23)   ~ (all_52_17 = all_10_2)
% 201.89/33.54    (24)  op(e3, e0) = all_52_25
% 201.89/33.54    (25)  op(e0, all_14_1) = all_14_0
% 201.89/33.54    (26)  op(all_52_5, all_52_5) = all_52_4
% 201.89/33.54    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.54    (28)  all_58_13 = all_52_15
% 201.89/33.54    (29)  op(all_10_2, all_10_2) = all_52_20
% 201.89/33.54    (30)  all_58_9 = all_52_25
% 201.89/33.54    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.89/33.54    (32)   ~ (all_52_29 = all_14_2)
% 201.89/33.54    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.89/33.54    (34)  op(e1, e3) = all_52_5
% 201.89/33.54    (35)  op(e2, e2) = all_4_2
% 201.89/33.54    (36)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.54    (37)   ~ (all_52_3 = all_52_5)
% 201.89/33.54    (38)  all_58_11 = all_52_29
% 201.89/33.54    (39)  all_56_5 = all_4_2
% 201.89/33.54    (40)   ~ (all_52_25 = all_14_2)
% 201.89/33.54    (41)   ~ (all_52_9 = all_52_15)
% 201.89/33.54    (42)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.89/33.54    (43)  all_46_2 = all_6_2
% 201.89/33.54    (44)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.54    (45)   ~ (all_52_7 = all_6_2)
% 201.89/33.54    (46)  op(e0, e0) = all_14_2
% 201.89/33.54    (47)  op(e0, e1) = all_52_23
% 201.89/33.54    (48)  all_56_15 = all_14_2
% 201.89/33.54    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.54    (50)   ~ (all_4_1 = e1)
% 201.89/33.54    (51)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.89/33.54    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.54    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.54    (54)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.89/33.54    (55)  all_56_9 = all_52_13
% 201.89/33.54    (56)   ~ (e2 = e1)
% 201.89/33.54    (57)   ~ (all_52_13 = all_10_2)
% 201.89/33.54    (58)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 201.89/33.54    (59)  all_58_10 = all_52_27
% 201.89/33.54    (60)  all_56_8 = all_52_5
% 201.89/33.54    (61)  op(all_52_9, all_52_9) = all_52_8
% 201.89/33.54    (62)  op(all_52_15, all_52_15) = all_52_14
% 201.89/33.54    (63)   ~ (all_52_19 = all_52_23)
% 201.89/33.54    (64)   ~ (all_52_25 = all_52_29)
% 201.89/33.54    (65)  all_58_7 = all_52_13
% 201.89/33.54    (66)   ~ (all_52_5 = all_52_7)
% 201.89/33.54    (67)  all_58_12 = all_52_7
% 201.89/33.54    (68)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.54    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.54    (70)   ~ (all_52_7 = all_14_2)
% 201.89/33.54    (71)  all_58_2 = all_52_3
% 201.89/33.54    (72)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.89/33.54    (73)  all_56_2 = all_52_17
% 201.89/33.54    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.54    (75)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.54    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.89/33.54    (77)  all_56_7 = all_52_27
% 201.89/33.54    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.54    (79)   ~ (e2 = e0)
% 201.89/33.54    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.89/33.54    (81)  op(all_4_2, e2) = all_4_1
% 201.89/33.54    (82)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.89/33.54    (83)   ~ (all_52_5 = all_52_29)
% 201.89/33.54    (84)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.54    (85)  all_56_6 = all_52_19
% 201.89/33.54    (86)   ~ (all_52_15 = all_14_2)
% 201.89/33.54    (87)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.54    (88)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.89/33.54    (89)   ~ (all_52_13 = all_4_2)
% 201.89/33.54    (90)  op(e3, e1) = all_52_17
% 201.89/33.54    (91)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.89/33.54    (92)  op(e0, e3) = all_52_7
% 201.89/33.54    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.54    (94)   ~ (all_52_9 = all_52_25)
% 201.89/33.54    (95)  all_58_15 = all_14_2
% 201.89/33.54    (96)  op(all_52_23, all_52_23) = all_52_22
% 201.89/33.54    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.89/33.54    (98)  all_58_8 = all_10_2
% 201.89/33.54    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.89/33.54    (100)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.54    (101)   ~ (all_52_23 = all_14_2)
% 201.89/33.54    (102)  all_56_12 = all_52_7
% 201.89/33.54    (103)  op(all_52_17, all_52_17) = all_52_16
% 201.89/33.54    (104)   ~ (all_52_25 = all_6_2)
% 201.89/33.54    (105)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.54    (106)   ~ (all_52_9 = all_4_2)
% 201.89/33.54    (107)   ~ (all_52_5 = all_6_2)
% 201.89/33.54    (108)   ~ (all_52_9 = all_6_2)
% 201.89/33.54    (109)   ~ (all_52_13 = all_52_15)
% 201.89/33.54    (110)  all_56_0 = all_6_2
% 201.89/33.54    (111)  op(e3, e3) = all_6_2
% 201.89/33.54    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.54    (113)   ~ (all_52_27 = all_14_2)
% 201.89/33.54    (114)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.54    (115)  op(all_4_2, all_4_2) = all_52_10
% 201.89/33.54    (116)  all_56_3 = all_52_25
% 201.89/33.54    (117)   ~ (all_52_3 = all_52_7)
% 201.89/33.54    (118)  op(all_14_2, all_14_2) = all_52_30
% 201.89/33.54    (119)  all_58_5 = all_52_19
% 201.89/33.54    (120)  all_56_1 = all_52_9
% 201.89/33.54    (121)   ~ (all_52_15 = all_4_2)
% 201.89/33.54    (122)   ~ (all_52_27 = all_4_2)
% 201.89/33.54    (123)  all_58_6 = all_52_5
% 201.89/33.54    (124)  op(e3, e2) = all_52_9
% 201.89/33.54    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.54    (126)   ~ (all_52_17 = all_6_2)
% 201.89/33.54    (127)   ~ (e1 = e0)
% 201.89/33.54    (128)   ~ (e3 = e2)
% 201.89/33.54    (129)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.54    (130)   ~ (all_52_9 = all_52_17)
% 201.89/33.54    (131)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.54    (132)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.89/33.54    (133)  all_46_1 = all_6_1
% 201.89/33.54    (134)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.89/33.54    (135)  op(all_52_13, all_52_13) = all_52_12
% 201.89/33.54    (136)  op(e1, e1) = all_10_2
% 201.89/33.54    (137)   ~ (all_52_23 = all_10_2)
% 201.89/33.54    (138)   ~ (all_52_7 = all_52_23)
% 201.89/33.54    (139)   ~ (all_52_17 = all_52_19)
% 201.89/33.54    (140)  all_58_3 = all_4_2
% 201.89/33.54    (141)  all_56_13 = all_52_15
% 201.89/33.54    (142)   ~ (all_52_3 = all_4_2)
% 201.89/33.54    (143)   ~ (all_52_19 = all_4_2)
% 201.89/33.54    (144)   ~ (all_52_17 = all_52_23)
% 201.89/33.54    (145)  op(all_6_2, e3) = all_6_1
% 201.89/33.54    (146)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.54    (147)   ~ (all_52_13 = all_52_29)
% 201.89/33.54    (148)  all_58_4 = all_52_17
% 201.89/33.54    (149)   ~ (all_14_0 = e2)
% 201.89/33.54    (150)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.54  
% 201.89/33.54  Begin of proof
% 201.89/33.54  | 
% 201.89/33.54  | ALPHA: (58) implies:
% 201.89/33.54  |   (151)  all_52_14 = e0
% 201.89/33.54  |   (152)  all_52_12 = e1
% 201.89/33.54  |   (153)  all_52_10 = e2
% 201.89/33.54  |   (154)  all_52_8 = e3
% 201.89/33.54  | 
% 201.89/33.54  | REDUCE: (61), (154) imply:
% 201.89/33.54  |   (155)  op(all_52_9, all_52_9) = e3
% 201.89/33.54  | 
% 201.89/33.54  | REDUCE: (135), (152) imply:
% 201.89/33.54  |   (156)  op(all_52_13, all_52_13) = e1
% 201.89/33.54  | 
% 201.89/33.54  | REDUCE: (62), (151) imply:
% 201.89/33.54  |   (157)  op(all_52_15, all_52_15) = e0
% 201.89/33.54  | 
% 201.89/33.54  | REDUCE: (115), (153) imply:
% 201.89/33.54  |   (158)  op(all_4_2, all_4_2) = e2
% 201.89/33.54  | 
% 201.89/33.54  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.89/33.54  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 201.89/33.54  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 201.89/33.54  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 201.89/33.54  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 201.89/33.54  |            (57), (59), (60), (63), (64), (65), (66), (67), (68), (69), (70),
% 201.89/33.54  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 201.89/33.54  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 201.89/33.54  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 201.89/33.54  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 201.89/33.54  |            (112), (113), (114), (116), (117), (118), (119), (120), (121),
% 201.89/33.54  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 201.89/33.54  |            (131), (132), (133), (134), (136), (137), (138), (139), (140),
% 201.89/33.54  |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 201.89/33.54  |            (150), (155), (156), (157), (158) are inconsistent by sub-proof
% 201.89/33.54  |            #287.
% 201.89/33.54  | 
% 201.89/33.54  End of proof
% 201.89/33.54  
% 201.89/33.54  Sub-proof #287 shows that the following formulas are inconsistent:
% 201.89/33.54  ----------------------------------------------------------------
% 201.89/33.54    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.89/33.54    (2)   ~ (all_52_15 = all_52_23)
% 201.89/33.54    (3)   ~ (all_52_25 = all_52_27)
% 201.89/33.54    (4)  all_58_14 = all_52_23
% 201.89/33.54    (5)   ~ (e3 = e1)
% 201.89/33.54    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.89/33.54    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.89/33.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.54    (9)   ~ (all_52_5 = all_52_13)
% 201.89/33.54    (10)  all_58_1 = all_52_9
% 201.89/33.54    (11)   ~ (all_52_9 = all_52_13)
% 201.89/33.54    (12)   ~ (e3 = e0)
% 201.89/33.54    (13)  op(e2, e3) = all_52_3
% 201.89/33.54    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.54    (15)   ~ (all_52_7 = all_52_15)
% 201.89/33.54    (16)  op(all_52_15, all_52_15) = e0
% 201.89/33.54    (17)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.54    (18)   ~ (all_52_17 = all_52_25)
% 201.89/33.54    (19)   ~ (all_52_3 = all_6_2)
% 201.89/33.54    (20)  all_58_0 = all_6_2
% 201.89/33.54    (21)  op(all_14_2, e0) = all_14_1
% 201.89/33.54    (22)  all_56_4 = all_52_3
% 201.89/33.54    (23)  op(e3, all_6_1) = e1
% 201.89/33.54    (24)   ~ (all_52_17 = all_10_2)
% 201.89/33.54    (25)  op(e3, e0) = all_52_25
% 201.89/33.54    (26)  op(e0, all_14_1) = all_14_0
% 201.89/33.54    (27)  op(all_52_5, all_52_5) = all_52_4
% 201.89/33.54    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.54    (29)  all_58_13 = all_52_15
% 201.89/33.54    (30)  op(all_52_13, all_52_13) = e1
% 201.89/33.54    (31)  op(all_10_2, all_10_2) = all_52_20
% 201.89/33.54    (32)  all_58_9 = all_52_25
% 201.89/33.54    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.89/33.54    (34)   ~ (all_52_29 = all_14_2)
% 201.89/33.54    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.89/33.54    (36)  op(e1, e3) = all_52_5
% 201.89/33.54    (37)  op(e2, e2) = all_4_2
% 201.89/33.54    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.54    (39)   ~ (all_52_3 = all_52_5)
% 201.89/33.54    (40)  all_58_11 = all_52_29
% 201.89/33.54    (41)  all_56_5 = all_4_2
% 201.89/33.54    (42)   ~ (all_52_25 = all_14_2)
% 201.89/33.54    (43)   ~ (all_52_9 = all_52_15)
% 201.89/33.54    (44)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.89/33.54    (45)  all_46_2 = all_6_2
% 201.89/33.54    (46)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.54    (47)   ~ (all_52_7 = all_6_2)
% 201.89/33.54    (48)  op(e0, e0) = all_14_2
% 201.89/33.54    (49)  op(e0, e1) = all_52_23
% 201.89/33.54    (50)  all_56_15 = all_14_2
% 201.89/33.54    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.54    (52)   ~ (all_4_1 = e1)
% 201.89/33.54    (53)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.89/33.54    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.54    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.54    (56)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.89/33.54    (57)  all_56_9 = all_52_13
% 201.89/33.54    (58)   ~ (e2 = e1)
% 201.89/33.54    (59)   ~ (all_52_13 = all_10_2)
% 201.89/33.54    (60)  all_58_10 = all_52_27
% 201.89/33.54    (61)  all_56_8 = all_52_5
% 201.89/33.54    (62)   ~ (all_52_19 = all_52_23)
% 201.89/33.54    (63)   ~ (all_52_25 = all_52_29)
% 201.89/33.54    (64)  all_58_7 = all_52_13
% 201.89/33.54    (65)   ~ (all_52_5 = all_52_7)
% 201.89/33.54    (66)  all_58_12 = all_52_7
% 201.89/33.54    (67)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.54    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.54    (69)   ~ (all_52_7 = all_14_2)
% 201.89/33.54    (70)  all_58_2 = all_52_3
% 201.89/33.54    (71)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.89/33.54    (72)  all_56_2 = all_52_17
% 201.89/33.54    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.54    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.54    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.89/33.54    (76)  all_56_7 = all_52_27
% 201.89/33.54    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.54    (78)   ~ (e2 = e0)
% 201.89/33.54    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.89/33.54    (80)  op(all_4_2, e2) = all_4_1
% 201.89/33.54    (81)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.89/33.54    (82)   ~ (all_52_5 = all_52_29)
% 201.89/33.54    (83)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.54    (84)  all_56_6 = all_52_19
% 201.89/33.54    (85)   ~ (all_52_15 = all_14_2)
% 201.89/33.54    (86)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.54    (87)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.89/33.54    (88)   ~ (all_52_13 = all_4_2)
% 201.89/33.54    (89)  op(e3, e1) = all_52_17
% 201.89/33.54    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.89/33.54    (91)  op(e0, e3) = all_52_7
% 201.89/33.54    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.54    (93)   ~ (all_52_9 = all_52_25)
% 201.89/33.54    (94)  all_58_15 = all_14_2
% 201.89/33.54    (95)  op(all_52_23, all_52_23) = all_52_22
% 201.89/33.54    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.89/33.54    (97)  all_58_8 = all_10_2
% 201.89/33.54    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.89/33.54    (99)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.54    (100)   ~ (all_52_23 = all_14_2)
% 201.89/33.54    (101)  all_56_12 = all_52_7
% 201.89/33.54    (102)  op(all_52_17, all_52_17) = all_52_16
% 201.89/33.54    (103)   ~ (all_52_25 = all_6_2)
% 201.89/33.54    (104)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.54    (105)   ~ (all_52_9 = all_4_2)
% 201.89/33.54    (106)   ~ (all_52_5 = all_6_2)
% 201.89/33.54    (107)  op(all_4_2, all_4_2) = e2
% 201.89/33.54    (108)   ~ (all_52_9 = all_6_2)
% 201.89/33.54    (109)   ~ (all_52_13 = all_52_15)
% 201.89/33.54    (110)  all_56_0 = all_6_2
% 201.89/33.54    (111)  op(e3, e3) = all_6_2
% 201.89/33.54    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.54    (113)   ~ (all_52_27 = all_14_2)
% 201.89/33.54    (114)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.54    (115)  all_56_3 = all_52_25
% 201.89/33.54    (116)   ~ (all_52_3 = all_52_7)
% 201.89/33.54    (117)  op(all_14_2, all_14_2) = all_52_30
% 201.89/33.54    (118)  all_58_5 = all_52_19
% 201.89/33.54    (119)  all_56_1 = all_52_9
% 201.89/33.54    (120)   ~ (all_52_15 = all_4_2)
% 201.89/33.54    (121)   ~ (all_52_27 = all_4_2)
% 201.89/33.54    (122)  all_58_6 = all_52_5
% 201.89/33.54    (123)  op(e3, e2) = all_52_9
% 201.89/33.54    (124)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.54    (125)   ~ (all_52_17 = all_6_2)
% 201.89/33.54    (126)   ~ (e1 = e0)
% 201.89/33.54    (127)   ~ (e3 = e2)
% 201.89/33.54    (128)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.54    (129)   ~ (all_52_9 = all_52_17)
% 201.89/33.54    (130)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.54    (131)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.89/33.54    (132)  all_46_1 = all_6_1
% 201.89/33.54    (133)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.89/33.54    (134)  op(e1, e1) = all_10_2
% 201.89/33.54    (135)  op(all_52_9, all_52_9) = e3
% 201.89/33.54    (136)   ~ (all_52_23 = all_10_2)
% 201.89/33.54    (137)   ~ (all_52_7 = all_52_23)
% 201.89/33.54    (138)   ~ (all_52_17 = all_52_19)
% 201.89/33.54    (139)  all_58_3 = all_4_2
% 201.89/33.54    (140)  all_56_13 = all_52_15
% 201.89/33.54    (141)   ~ (all_52_3 = all_4_2)
% 201.89/33.54    (142)   ~ (all_52_19 = all_4_2)
% 201.89/33.54    (143)   ~ (all_52_17 = all_52_23)
% 201.89/33.54    (144)  op(all_6_2, e3) = all_6_1
% 201.89/33.54    (145)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.54    (146)   ~ (all_52_13 = all_52_29)
% 201.89/33.54    (147)  all_58_4 = all_52_17
% 201.89/33.54    (148)   ~ (all_14_0 = e2)
% 201.89/33.54    (149)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.54  
% 201.89/33.54  Begin of proof
% 201.89/33.54  | 
% 201.89/33.54  | BETA: splitting (98) gives:
% 201.89/33.54  | 
% 201.89/33.54  | Case 1:
% 201.89/33.54  | | 
% 201.89/33.54  | |   (150)  all_56_15 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | COMBINE_EQS: (50), (150) imply:
% 201.89/33.54  | |   (151)  all_14_2 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | SIMP: (151) implies:
% 201.89/33.54  | |   (152)  all_14_2 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | COMBINE_EQS: (94), (152) imply:
% 201.89/33.54  | |   (153)  all_58_15 = e3
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (69), (152) imply:
% 201.89/33.54  | |   (154)   ~ (all_52_7 = e3)
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (85), (152) imply:
% 201.89/33.54  | |   (155)   ~ (all_52_15 = e3)
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (42), (152) imply:
% 201.89/33.54  | |   (156)   ~ (all_52_25 = e3)
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (34), (152) imply:
% 201.89/33.54  | |   (157)   ~ (all_52_29 = e3)
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (117), (152) imply:
% 201.89/33.54  | |   (158)  op(e3, e3) = all_52_30
% 201.89/33.54  | | 
% 201.89/33.54  | | REDUCE: (21), (152) imply:
% 201.89/33.55  | |   (159)  op(e3, e0) = all_14_1
% 201.89/33.55  | | 
% 201.89/33.55  | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3, simplifying
% 201.89/33.55  | |              with (25), (159) gives:
% 201.89/33.55  | |   (160)  all_52_25 = all_14_1
% 201.89/33.55  | | 
% 201.89/33.55  | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3, simplifying
% 201.89/33.55  | |              with (111), (158) gives:
% 201.89/33.55  | |   (161)  all_52_30 = all_6_2
% 201.89/33.55  | | 
% 201.89/33.55  | | COMBINE_EQS: (115), (160) imply:
% 201.89/33.55  | |   (162)  all_56_3 = all_14_1
% 201.89/33.55  | | 
% 201.89/33.55  | | COMBINE_EQS: (32), (160) imply:
% 201.89/33.55  | |   (163)  all_58_9 = all_14_1
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (93), (160) imply:
% 201.89/33.55  | |   (164)   ~ (all_52_9 = all_14_1)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (103), (160) imply:
% 201.89/33.55  | |   (165)   ~ (all_14_1 = all_6_2)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (156), (160) imply:
% 201.89/33.55  | |   (166)   ~ (all_14_1 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (149), (160) imply:
% 201.89/33.55  | |   (167)  op(all_14_1, all_14_1) = all_52_24
% 201.89/33.55  | | 
% 201.89/33.55  | | BETA: splitting (104) gives:
% 201.89/33.55  | | 
% 201.89/33.55  | | Case 1:
% 201.89/33.55  | | | 
% 201.89/33.55  | | |   (168)  all_56_3 = e3
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REF_CLOSE: (162), (166), (168) are inconsistent by sub-proof #1200.
% 201.89/33.55  | | | 
% 201.89/33.55  | | Case 2:
% 201.89/33.55  | | | 
% 201.89/33.55  | | |   (169)   ~ (all_56_3 = e3)
% 201.89/33.55  | | |   (170)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.55  | | | 
% 201.89/33.55  | | | BETA: splitting (131) gives:
% 201.89/33.55  | | | 
% 201.89/33.55  | | | Case 1:
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | |   (171)  all_56_9 = e3
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | COMBINE_EQS: (57), (171) imply:
% 201.89/33.55  | | | |   (172)  all_52_13 = e3
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | SIMP: (172) implies:
% 201.89/33.55  | | | |   (173)  all_52_13 = e3
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | REDUCE: (9), (173) imply:
% 201.89/33.55  | | | |   (174)   ~ (all_52_5 = e3)
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | REDUCE: (30), (173) imply:
% 201.89/33.55  | | | |   (175)  op(e3, e3) = e1
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | GROUND_INST: instantiating (8) with all_6_2, e1, e3, e3, simplifying
% 201.89/33.55  | | | |              with (111), (175) gives:
% 201.89/33.55  | | | |   (176)  all_6_2 = e1
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | REF_CLOSE: (8), (23), (33), (36), (61), (96), (106), (108), (122),
% 201.89/33.55  | | | |            (123), (144), (159), (165), (174), (176) are inconsistent by
% 201.89/33.55  | | | |            sub-proof #301.
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | Case 2:
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | |   (177)   ~ (all_56_9 = e3)
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | REDUCE: (57), (177) imply:
% 201.89/33.55  | | | |   (178)   ~ (all_52_13 = e3)
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | BETA: splitting (92) gives:
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | Case 1:
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | |   (179)  all_58_1 = e3
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | COMBINE_EQS: (10), (179) imply:
% 201.89/33.55  | | | | |   (180)  all_52_9 = e3
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | REF_CLOSE: (8), (108), (111), (135), (180) are inconsistent by
% 201.89/33.55  | | | | |            sub-proof #1337.
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | Case 2:
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | |   (181)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | BETA: splitting (181) gives:
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | Case 1:
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | |   (182)  all_58_3 = e3
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | COMBINE_EQS: (139), (182) imply:
% 201.89/33.55  | | | | | |   (183)  all_4_2 = e3
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | REDUCE: (121), (183) imply:
% 201.89/33.55  | | | | | |   (184)   ~ (all_52_27 = e3)
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | REDUCE: (107), (183) imply:
% 201.89/33.55  | | | | | |   (185)  op(e3, e3) = e2
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | GROUND_INST: instantiating (8) with all_6_2, e2, e3, e3, simplifying
% 201.89/33.55  | | | | | |              with (111), (185) gives:
% 201.89/33.55  | | | | | |   (186)  all_6_2 = e2
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | REDUCE: (165), (186) imply:
% 201.89/33.55  | | | | | |   (187)   ~ (all_14_1 = e2)
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 201.89/33.55  | | | | | |            (19), (20), (22), (23), (24), (26), (27), (29), (30),
% 201.89/33.55  | | | | | |            (32), (37), (39), (40), (44), (47), (49), (51), (52),
% 201.89/33.55  | | | | | |            (56), (57), (58), (59), (60), (64), (65), (66), (68),
% 201.89/33.55  | | | | | |            (70), (73), (74), (75), (77), (80), (81), (83), (88),
% 201.89/33.55  | | | | | |            (92), (97), (101), (102), (105), (107), (108), (109),
% 201.89/33.55  | | | | | |            (111), (114), (116), (118), (119), (122), (123), (125),
% 201.89/33.55  | | | | | |            (128), (129), (130), (131), (134), (135), (138), (139),
% 201.89/33.55  | | | | | |            (141), (144), (147), (148), (153), (154), (155), (156),
% 201.89/33.55  | | | | | |            (157), (162), (163), (164), (165), (166), (167), (170),
% 201.89/33.55  | | | | | |            (184), (187) are inconsistent by sub-proof #298.
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | Case 2:
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | |   (188)  all_58_7 = e3 | all_58_13 = e3
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | REF_CLOSE: (29), (64), (155), (178), (188) are inconsistent by
% 201.89/33.55  | | | | | |            sub-proof #1298.
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | End of split
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | End of split
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | End of split
% 201.89/33.55  | | | 
% 201.89/33.55  | | End of split
% 201.89/33.55  | | 
% 201.89/33.55  | Case 2:
% 201.89/33.55  | | 
% 201.89/33.55  | |   (189)   ~ (all_56_15 = e3)
% 201.89/33.55  | |   (190)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (50), (189) imply:
% 201.89/33.55  | |   (191)   ~ (all_14_2 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 201.89/33.55  | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (27),
% 201.89/33.55  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 201.89/33.55  | |            (39), (40), (41), (42), (43), (45), (46), (47), (48), (50), (51),
% 201.89/33.55  | |            (52), (53), (54), (55), (56), (58), (60), (61), (62), (63), (64),
% 201.89/33.55  | |            (65), (66), (67), (68), (69), (70), (71), (72), (74), (75), (76),
% 201.89/33.55  | |            (77), (78), (79), (80), (81), (82), (84), (86), (87), (88), (89),
% 201.89/33.55  | |            (90), (91), (92), (93), (94), (95), (96), (97), (99), (100),
% 201.89/33.55  | |            (101), (102), (103), (104), (105), (106), (107), (108), (110),
% 201.89/33.55  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 201.89/33.55  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 201.89/33.55  | |            (129), (130), (132), (133), (134), (135), (136), (137), (138),
% 201.89/33.55  | |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 201.89/33.55  | |            (149), (190), (191) are inconsistent by sub-proof #288.
% 201.89/33.55  | | 
% 201.89/33.55  | End of split
% 201.89/33.55  | 
% 201.89/33.55  End of proof
% 201.89/33.55  
% 201.89/33.55  Sub-proof #288 shows that the following formulas are inconsistent:
% 201.89/33.55  ----------------------------------------------------------------
% 201.89/33.55    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 201.89/33.55    (2)   ~ (all_52_15 = all_52_23)
% 201.89/33.55    (3)   ~ (all_52_25 = all_52_27)
% 201.89/33.55    (4)  all_58_14 = all_52_23
% 201.89/33.55    (5)   ~ (e3 = e1)
% 201.89/33.55    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 201.89/33.55    (7)  op(all_52_3, all_52_3) = all_52_2
% 201.89/33.55    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.55    (9)  all_58_1 = all_52_9
% 201.89/33.55    (10)   ~ (all_52_9 = all_52_13)
% 201.89/33.55    (11)   ~ (e3 = e0)
% 201.89/33.55    (12)  op(e2, e3) = all_52_3
% 201.89/33.55    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.55    (14)   ~ (all_52_7 = all_52_15)
% 201.89/33.55    (15)  op(all_52_15, all_52_15) = e0
% 201.89/33.55    (16)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.55    (17)   ~ (all_52_17 = all_52_25)
% 201.89/33.55    (18)   ~ (all_52_3 = all_6_2)
% 201.89/33.55    (19)  all_58_0 = all_6_2
% 201.89/33.55    (20)  all_56_4 = all_52_3
% 201.89/33.55    (21)  op(e3, all_6_1) = e1
% 201.89/33.55    (22)   ~ (all_52_17 = all_10_2)
% 201.89/33.55    (23)  op(all_52_5, all_52_5) = all_52_4
% 201.89/33.55    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.55    (25)  all_58_13 = all_52_15
% 201.89/33.55    (26)  op(all_52_13, all_52_13) = e1
% 201.89/33.55    (27)  op(all_10_2, all_10_2) = all_52_20
% 201.89/33.55    (28)  all_58_9 = all_52_25
% 201.89/33.55    (29)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.89/33.55    (30)   ~ (all_52_29 = all_14_2)
% 201.89/33.55    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 201.89/33.55    (32)  op(e1, e3) = all_52_5
% 201.89/33.55    (33)  op(e2, e2) = all_4_2
% 201.89/33.55    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.55    (35)   ~ (all_52_3 = all_52_5)
% 201.89/33.55    (36)  all_58_11 = all_52_29
% 201.89/33.55    (37)  all_56_5 = all_4_2
% 201.89/33.55    (38)   ~ (all_52_25 = all_14_2)
% 201.89/33.55    (39)   ~ (all_52_9 = all_52_15)
% 201.89/33.55    (40)  all_46_2 = all_6_2
% 201.89/33.55    (41)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.55    (42)   ~ (all_52_7 = all_6_2)
% 201.89/33.55    (43)  op(e0, e0) = all_14_2
% 201.89/33.55    (44)  all_56_15 = all_14_2
% 201.89/33.55    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.55    (46)   ~ (all_4_1 = e1)
% 201.89/33.55    (47)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.89/33.55    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.55    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.55    (50)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.89/33.55    (51)   ~ (e2 = e1)
% 201.89/33.55    (52)  all_58_10 = all_52_27
% 201.89/33.55    (53)  all_56_8 = all_52_5
% 201.89/33.55    (54)   ~ (all_52_19 = all_52_23)
% 201.89/33.55    (55)   ~ (all_52_25 = all_52_29)
% 201.89/33.55    (56)  all_58_7 = all_52_13
% 201.89/33.55    (57)   ~ (all_52_5 = all_52_7)
% 201.89/33.55    (58)  all_58_12 = all_52_7
% 201.89/33.55    (59)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.55    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.55    (61)   ~ (all_52_7 = all_14_2)
% 201.89/33.55    (62)  all_58_2 = all_52_3
% 201.89/33.55    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.89/33.55    (64)  all_56_2 = all_52_17
% 201.89/33.55    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.55    (66)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.89/33.55    (67)  all_56_7 = all_52_27
% 201.89/33.55    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.55    (69)   ~ (e2 = e0)
% 201.89/33.55    (70)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.89/33.55    (71)  op(all_4_2, e2) = all_4_1
% 201.89/33.55    (72)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.89/33.55    (73)   ~ (all_52_5 = all_52_29)
% 201.89/33.55    (74)  all_56_6 = all_52_19
% 201.89/33.55    (75)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.55    (76)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.89/33.55    (77)   ~ (all_52_13 = all_4_2)
% 201.89/33.55    (78)  op(e3, e1) = all_52_17
% 201.89/33.55    (79)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 201.89/33.55    (80)  op(e0, e3) = all_52_7
% 201.89/33.55    (81)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.55    (82)   ~ (all_52_9 = all_52_25)
% 201.89/33.55    (83)  all_58_15 = all_14_2
% 201.89/33.55    (84)  op(all_52_23, all_52_23) = all_52_22
% 201.89/33.55    (85)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.89/33.55    (86)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.89/33.55    (87)  all_58_8 = all_10_2
% 201.89/33.55    (88)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.55    (89)   ~ (all_52_23 = all_14_2)
% 201.89/33.55    (90)  all_56_12 = all_52_7
% 201.89/33.55    (91)  op(all_52_17, all_52_17) = all_52_16
% 201.89/33.55    (92)   ~ (all_52_25 = all_6_2)
% 201.89/33.55    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.55    (94)   ~ (all_52_9 = all_4_2)
% 201.89/33.55    (95)   ~ (all_52_5 = all_6_2)
% 201.89/33.55    (96)  op(all_4_2, all_4_2) = e2
% 201.89/33.55    (97)   ~ (all_52_9 = all_6_2)
% 201.89/33.55    (98)  all_56_0 = all_6_2
% 201.89/33.55    (99)  op(e3, e3) = all_6_2
% 201.89/33.55    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.55    (101)   ~ (all_52_27 = all_14_2)
% 201.89/33.55    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.55    (103)  all_56_3 = all_52_25
% 201.89/33.55    (104)   ~ (all_52_3 = all_52_7)
% 201.89/33.55    (105)  op(all_14_2, all_14_2) = all_52_30
% 201.89/33.55    (106)  all_58_5 = all_52_19
% 201.89/33.55    (107)  all_56_1 = all_52_9
% 201.89/33.55    (108)   ~ (all_52_15 = all_4_2)
% 201.89/33.55    (109)   ~ (all_52_27 = all_4_2)
% 201.89/33.55    (110)  all_58_6 = all_52_5
% 201.89/33.55    (111)  op(e3, e2) = all_52_9
% 201.89/33.55    (112)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.55    (113)   ~ (all_52_17 = all_6_2)
% 201.89/33.55    (114)   ~ (e1 = e0)
% 201.89/33.55    (115)   ~ (e3 = e2)
% 201.89/33.55    (116)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.55    (117)   ~ (all_52_9 = all_52_17)
% 201.89/33.55    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.55    (119)  all_46_1 = all_6_1
% 201.89/33.55    (120)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.89/33.55    (121)  op(e1, e1) = all_10_2
% 201.89/33.55    (122)  op(all_52_9, all_52_9) = e3
% 201.89/33.55    (123)   ~ (all_52_23 = all_10_2)
% 201.89/33.55    (124)   ~ (all_52_7 = all_52_23)
% 201.89/33.55    (125)   ~ (all_52_17 = all_52_19)
% 201.89/33.55    (126)  all_58_3 = all_4_2
% 201.89/33.55    (127)  all_56_13 = all_52_15
% 201.89/33.55    (128)   ~ (all_52_3 = all_4_2)
% 201.89/33.55    (129)   ~ (all_52_19 = all_4_2)
% 201.89/33.55    (130)   ~ (all_52_17 = all_52_23)
% 201.89/33.55    (131)  op(all_6_2, e3) = all_6_1
% 201.89/33.55    (132)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.55    (133)   ~ (all_52_13 = all_52_29)
% 201.89/33.55    (134)  all_58_4 = all_52_17
% 201.89/33.55    (135)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.55    (136)   ~ (all_14_2 = e3)
% 201.89/33.55  
% 201.89/33.55  Begin of proof
% 201.89/33.55  | 
% 201.89/33.55  | BETA: splitting (48) gives:
% 201.89/33.55  | 
% 201.89/33.55  | Case 1:
% 201.89/33.55  | | 
% 201.89/33.55  | |   (137)  all_56_13 = e3
% 201.89/33.55  | | 
% 201.89/33.55  | | COMBINE_EQS: (127), (137) imply:
% 201.89/33.55  | |   (138)  all_52_15 = e3
% 201.89/33.55  | | 
% 201.89/33.55  | | COMBINE_EQS: (25), (138) imply:
% 201.89/33.55  | |   (139)  all_58_13 = e3
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (14), (138) imply:
% 201.89/33.55  | |   (140)   ~ (all_52_7 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (39), (138) imply:
% 201.89/33.55  | |   (141)   ~ (all_52_9 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (108), (138) imply:
% 201.89/33.55  | |   (142)   ~ (all_4_2 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | SIMP: (142) implies:
% 201.89/33.55  | |   (143)   ~ (all_4_2 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (15), (138) imply:
% 201.89/33.55  | |   (144)  op(e3, e3) = e0
% 201.89/33.55  | | 
% 201.89/33.55  | | REF_CLOSE: (4), (8), (11), (13), (21), (33), (42), (44), (58), (59), (61),
% 201.89/33.55  | |            (76), (78), (80), (86), (89), (90), (97), (99), (105), (107),
% 201.89/33.55  | |            (116), (117), (122), (124), (131), (139), (140), (141), (143),
% 201.89/33.55  | |            (144) are inconsistent by sub-proof #297.
% 201.89/33.55  | | 
% 201.89/33.55  | Case 2:
% 201.89/33.55  | | 
% 201.89/33.55  | |   (145)   ~ (all_56_13 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | REDUCE: (127), (145) imply:
% 201.89/33.55  | |   (146)   ~ (all_52_15 = e3)
% 201.89/33.55  | | 
% 201.89/33.55  | | BETA: splitting (112) gives:
% 201.89/33.55  | | 
% 201.89/33.55  | | Case 1:
% 201.89/33.55  | | | 
% 201.89/33.55  | | |   (147)  all_58_12 = e3
% 201.89/33.55  | | | 
% 201.89/33.55  | | | COMBINE_EQS: (58), (147) imply:
% 201.89/33.55  | | |   (148)  all_52_7 = e3
% 201.89/33.55  | | | 
% 201.89/33.55  | | | SIMP: (148) implies:
% 201.89/33.55  | | |   (149)  all_52_7 = e3
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (104), (149) imply:
% 201.89/33.55  | | |   (150)   ~ (all_52_3 = e3)
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (57), (149) imply:
% 201.89/33.55  | | |   (151)   ~ (all_52_5 = e3)
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (14), (149) imply:
% 201.89/33.55  | | |   (152)   ~ (all_52_15 = e3)
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (61), (149) imply:
% 201.89/33.55  | | |   (153)   ~ (all_14_2 = e3)
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (42), (149) imply:
% 201.89/33.55  | | |   (154)   ~ (all_6_2 = e3)
% 201.89/33.55  | | | 
% 201.89/33.55  | | | SIMP: (154) implies:
% 201.89/33.55  | | |   (155)   ~ (all_6_2 = e3)
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (16), (149) imply:
% 201.89/33.55  | | |   (156)  op(e3, e3) = all_52_6
% 201.89/33.55  | | | 
% 201.89/33.55  | | | REDUCE: (80), (149) imply:
% 201.89/33.55  | | |   (157)  op(e0, e3) = e3
% 201.89/33.55  | | | 
% 201.89/33.55  | | | GROUND_INST: instantiating (8) with all_6_2, all_52_6, e3, e3, simplifying
% 201.89/33.55  | | |              with (99), (156) gives:
% 201.89/33.55  | | |   (158)  all_52_6 = all_6_2
% 201.89/33.55  | | | 
% 201.89/33.55  | | | BETA: splitting (68) gives:
% 201.89/33.55  | | | 
% 201.89/33.55  | | | Case 1:
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | |   (159)  all_56_4 = e3
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | REF_CLOSE: (20), (150), (159) are inconsistent by sub-proof #1340.
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | Case 2:
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | |   (160)   ~ (all_56_4 = e3)
% 201.89/33.55  | | | |   (161)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | BETA: splitting (120) gives:
% 201.89/33.55  | | | | 
% 201.89/33.55  | | | | Case 1:
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | |   (162)  all_56_0 = e3
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | COMBINE_EQS: (98), (162) imply:
% 201.89/33.55  | | | | |   (163)  all_6_2 = e3
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | REDUCE: (155), (163) imply:
% 201.89/33.55  | | | | |   (164)  $false
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | CLOSE: (164) is inconsistent.
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | Case 2:
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | |   (165)   ~ (all_56_0 = e3)
% 201.89/33.55  | | | | |   (166)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | BETA: splitting (85) gives:
% 201.89/33.55  | | | | | 
% 201.89/33.55  | | | | | Case 1:
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | |   (167)  all_56_8 = e3
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | REF_CLOSE: (53), (151), (167) are inconsistent by sub-proof #1325.
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | Case 2:
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | |   (168)   ~ (all_56_8 = e3)
% 201.89/33.55  | | | | | |   (169)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | BETA: splitting (66) gives:
% 201.89/33.55  | | | | | | 
% 201.89/33.55  | | | | | | Case 1:
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | |   (170)  all_58_0 = e1
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | COMBINE_EQS: (19), (170) imply:
% 201.89/33.55  | | | | | | |   (171)  all_6_2 = e1
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (95), (171) imply:
% 201.89/33.55  | | | | | | |   (172)   ~ (all_52_5 = e1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (97), (171) imply:
% 201.89/33.55  | | | | | | |   (173)   ~ (all_52_9 = e1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (113), (171) imply:
% 201.89/33.55  | | | | | | |   (174)   ~ (all_52_17 = e1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (155), (171) imply:
% 201.89/33.55  | | | | | | |   (175)   ~ (e3 = e1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (41), (171) imply:
% 201.89/33.55  | | | | | | |   (176)  op(e1, e1) = all_52_0
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (131), (171) imply:
% 201.89/33.55  | | | | | | |   (177)  op(e1, e3) = all_6_1
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | GROUND_INST: instantiating (8) with all_10_2, all_52_0, e1, e1,
% 201.89/33.55  | | | | | | |              simplifying with (121), (176) gives:
% 201.89/33.55  | | | | | | |   (178)  all_52_0 = all_10_2
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | GROUND_INST: instantiating (8) with all_52_5, all_6_1, e3, e1,
% 201.89/33.55  | | | | | | |              simplifying with (32), (177) gives:
% 201.89/33.55  | | | | | | |   (179)  all_52_5 = all_6_1
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | COMBINE_EQS: (53), (179) imply:
% 201.89/33.55  | | | | | | |   (180)  all_56_8 = all_6_1
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | COMBINE_EQS: (110), (179) imply:
% 201.89/33.55  | | | | | | |   (181)  all_58_6 = all_6_1
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (35), (179) imply:
% 201.89/33.55  | | | | | | |   (182)   ~ (all_52_3 = all_6_1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (73), (179) imply:
% 201.89/33.55  | | | | | | |   (183)   ~ (all_52_29 = all_6_1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | SIMP: (183) implies:
% 201.89/33.55  | | | | | | |   (184)   ~ (all_52_29 = all_6_1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (151), (179) imply:
% 201.89/33.55  | | | | | | |   (185)   ~ (all_6_1 = e3)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | REDUCE: (172), (179) imply:
% 201.89/33.55  | | | | | | |   (186)   ~ (all_6_1 = e1)
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | BETA: splitting (75) gives:
% 201.89/33.55  | | | | | | | 
% 201.89/33.55  | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | 
% 201.89/33.55  | | | | | | | |   (187)  all_58_0 = e2
% 201.89/33.55  | | | | | | | | 
% 201.89/33.55  | | | | | | | | REF_CLOSE: (51), (170), (187) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | |            #1273.
% 201.89/33.55  | | | | | | | | 
% 201.89/33.55  | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | 
% 201.89/33.55  | | | | | | | |   (188)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.55  | | | | | | | | 
% 201.89/33.55  | | | | | | | | BETA: splitting (93) gives:
% 201.89/33.55  | | | | | | | | 
% 201.89/33.55  | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | |   (189)  all_56_3 = e3
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | COMBINE_EQS: (103), (189) imply:
% 201.89/33.55  | | | | | | | | |   (190)  all_52_25 = e3
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | SIMP: (190) implies:
% 201.89/33.55  | | | | | | | | |   (191)  all_52_25 = e3
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | COMBINE_EQS: (28), (191) imply:
% 201.89/33.55  | | | | | | | | |   (192)  all_58_9 = e3
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | REDUCE: (82), (191) imply:
% 201.89/33.55  | | | | | | | | |   (193)   ~ (all_52_9 = e3)
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | REDUCE: (17), (191) imply:
% 201.89/33.55  | | | | | | | | |   (194)   ~ (all_52_17 = e3)
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | REDUCE: (3), (191) imply:
% 201.89/33.55  | | | | | | | | |   (195)   ~ (all_52_27 = e3)
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | SIMP: (195) implies:
% 201.89/33.55  | | | | | | | | |   (196)   ~ (all_52_27 = e3)
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | REDUCE: (55), (191) imply:
% 201.89/33.55  | | | | | | | | |   (197)   ~ (all_52_29 = e3)
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | SIMP: (197) implies:
% 201.89/33.55  | | | | | | | | |   (198)   ~ (all_52_29 = e3)
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | BETA: splitting (49) gives:
% 201.89/33.55  | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | |   (199)  all_56_2 = e3
% 201.89/33.55  | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | REF_CLOSE: (64), (194), (199) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | |            #1327.
% 201.89/33.55  | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | |   (200)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.55  | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | BETA: splitting (116) gives:
% 201.89/33.55  | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | |   (201)  all_56_1 = e3
% 201.89/33.55  | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | REF_CLOSE: (107), (193), (201) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | |            #1326.
% 201.89/33.55  | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | |   (202)   ~ (all_56_1 = e3)
% 201.89/33.55  | | | | | | | | | | |   (203)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.55  | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | BETA: splitting (45) gives:
% 201.89/33.55  | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | |   (204)  all_58_2 = e3
% 201.89/33.55  | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | REF_CLOSE: (62), (150), (204) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | | |            #1369.
% 201.89/33.55  | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | |   (205)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.55  | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | BETA: splitting (81) gives:
% 201.89/33.55  | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | |   (206)  all_58_1 = e3
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | COMBINE_EQS: (9), (206) imply:
% 201.89/33.55  | | | | | | | | | | | | |   (207)  all_52_9 = e3
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | REDUCE: (193), (207) imply:
% 201.89/33.55  | | | | | | | | | | | | |   (208)  $false
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | CLOSE: (208) is inconsistent.
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | |   (209)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | BETA: splitting (60) gives:
% 201.89/33.55  | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | |   (210)  all_58_6 = e3
% 201.89/33.55  | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | REF_CLOSE: (181), (185), (210) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | | | | |            #296.
% 201.89/33.55  | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | |   (211)   ~ (all_58_6 = e3)
% 201.89/33.55  | | | | | | | | | | | | | |   (212)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.55  | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 201.89/33.55  | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | |   (213)  all_58_0 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | COMBINE_EQS: (170), (213) imply:
% 201.89/33.55  | | | | | | | | | | | | | | |   (214)  e1 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | REDUCE: (114), (214) imply:
% 201.89/33.55  | | | | | | | | | | | | | | |   (215)  $false
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent.
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | |   (216)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | |   (217)  all_56_6 = e3
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (217) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | |   (218)  all_52_19 = e3
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | SIMP: (218) implies:
% 201.89/33.55  | | | | | | | | | | | | | | | |   (219)  all_52_19 = e3
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | REDUCE: (129), (219) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | |   (220)   ~ (all_4_2 = e3)
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | SIMP: (220) implies:
% 201.89/33.55  | | | | | | | | | | | | | | | |   (221)   ~ (all_4_2 = e3)
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | |   (222)  all_56_5 = e3
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (221), (222) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | | | | | | | |            #1319.
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | |   (223)   ~ (all_56_5 = e3)
% 201.89/33.55  | | | | | | | | | | | | | | | | |   (224)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | |   (225)  all_58_6 = e2
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (225) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | |   (226)  all_6_1 = e2
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | REDUCE: (21), (226) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | |   (227)  op(e3, e2) = e1
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (111), (173), (227) are inconsistent by
% 201.89/33.55  | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | |   (228)   ~ (all_58_6 = e2)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | REDUCE: (181), (228) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | |   (229)   ~ (all_6_1 = e2)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | |   (230)  all_58_2 = e2
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (230) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | |   (231)  all_52_3 = e2
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | REDUCE: (128), (231) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | |   (232)   ~ (all_4_2 = e2)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | SIMP: (232) implies:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | |   (233)   ~ (all_4_2 = e2)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | |   (234)  all_58_2 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (234) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | |   (235)  e2 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (235) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | |   (236)  $false
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | |   (237)  all_58_6 = e0 | all_58_12 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |   (238)  all_58_6 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (238) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |   (239)  all_6_1 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |   (240)  all_6_1 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (240) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |   (241)   ~ (all_52_29 = e0)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (240) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |   (242)   ~ (e3 = e0)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | |   (243)  all_58_9 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (192), (243) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | |            #841.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | |   (244)  all_58_10 = e0 | all_58_11 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_58_10 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (245) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_52_27 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (246) implies:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_52_27 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (247) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |   (248)   ~ (all_4_2 = e0)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |   (249)   ~ (all_4_2 = e0)
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (22), (33), (37), (64), (94), (96),
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |            (107), (117), (121), (122), (134), (174), (200),
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |            (203), (221), (224), (233), (249) are inconsistent
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #936.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_58_11 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (241), (250) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | |            #1115.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |   (251)  all_58_12 = e0
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (147), (251) are inconsistent by sub-proof
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | |            #1212.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | |   (252)  all_58_6 = e2 | all_58_12 = e2
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (147), (181), (229), (252) are inconsistent
% 201.89/33.55  | | | | | | | | | | | | | | | | | | |            by sub-proof #1209.
% 201.89/33.55  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | End of split
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | Case 2:
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | |   (253)   ~ (all_56_6 = e3)
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | REDUCE: (74), (253) imply:
% 201.89/33.55  | | | | | | | | | | | | | | | |   (254)   ~ (all_52_19 = e3)
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 201.89/33.55  | | | | | | | | | | | | | | | | 
% 201.89/33.55  | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.55  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (255)  all_58_3 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (255) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (256)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (257)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | REDUCE: (77), (257) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (258)   ~ (all_52_13 = e3)
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (27), (36), (43), (46), (56), (71),
% 201.89/33.56  | | | | | | | | | | | | | | | | |            (77), (87), (96), (97), (99), (107), (111), (122),
% 201.89/33.56  | | | | | | | | | | | | | | | | |            (126), (136), (146), (198), (203), (209), (212),
% 201.89/33.56  | | | | | | | | | | | | | | | | |            (258) are inconsistent by sub-proof #1112.
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (259)  all_58_5 = e3 | all_58_10 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (106), (196), (254), (259) are inconsistent
% 201.89/33.56  | | | | | | | | | | | | | | | | |            by sub-proof #1132.
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (260)   ~ (all_56_3 = e3)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REDUCE: (103), (260) imply:
% 201.89/33.56  | | | | | | | | |   (261)   ~ (all_52_25 = e3)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | BETA: splitting (102) gives:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (262)  all_58_0 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REF_CLOSE: (5), (170), (262) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | |            #1244.
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (263)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | BETA: splitting (100) gives:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (264)  all_58_9 = e3
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | REF_CLOSE: (28), (261), (264) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | |            #1300.
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (265)   ~ (all_58_9 = e3)
% 201.89/33.56  | | | | | | | | | | |   (266)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | BETA: splitting (49) gives:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (267)  all_56_2 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | COMBINE_EQS: (64), (267) imply:
% 201.89/33.56  | | | | | | | | | | | |   (268)  all_52_17 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | SIMP: (268) implies:
% 201.89/33.56  | | | | | | | | | | | |   (269)  all_52_17 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (125), (269) imply:
% 201.89/33.56  | | | | | | | | | | | |   (270)   ~ (all_52_19 = e3)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | SIMP: (270) implies:
% 201.89/33.56  | | | | | | | | | | | |   (271)   ~ (all_52_19 = e3)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (91), (269) imply:
% 201.89/33.56  | | | | | | | | | | | |   (272)  op(e3, e3) = all_52_16
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | BETA: splitting (45) gives:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (273)  all_58_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | REF_CLOSE: (62), (150), (273) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | |            #1369.
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (274)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (275)  all_56_5 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | COMBINE_EQS: (37), (275) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (276)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | SIMP: (276) implies:
% 201.89/33.56  | | | | | | | | | | | | | |   (277)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (46), (71), (94), (96), (97), (99),
% 201.89/33.56  | | | | | | | | | | | | | |            (107), (111), (116), (122), (136), (272), (277)
% 201.89/33.56  | | | | | | | | | | | | | |            are inconsistent by sub-proof #564.
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (278)   ~ (all_56_5 = e3)
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REDUCE: (37), (278) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (279)   ~ (all_4_2 = e3)
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | |   (280)  all_58_3 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | COMBINE_EQS: (126), (280) imply:
% 201.89/33.56  | | | | | | | | | | | | | | |   (281)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | SIMP: (281) implies:
% 201.89/33.56  | | | | | | | | | | | | | | |   (282)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | REDUCE: (279), (282) imply:
% 201.89/33.56  | | | | | | | | | | | | | | |   (283)  $false
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent.
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | |   (284)  all_58_5 = e3 | all_58_10 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | |   (285)  all_58_5 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | REF_CLOSE: (106), (271), (285) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | | |            #1279.
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | |   (286)  all_58_10 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (286) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | |   (287)  all_52_27 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | SIMP: (287) implies:
% 201.89/33.56  | | | | | | | | | | | | | | | |   (288)  all_52_27 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (289)  all_58_2 = e2
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (289) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (290)  all_52_3 = e2
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | REDUCE: (182), (290) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (291)   ~ (all_6_1 = e2)
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | SIMP: (291) implies:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (292)   ~ (all_6_1 = e2)
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | |   (293)  all_56_8 = e2
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (180), (292), (293) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | | | | |            #1321.
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | |   (294)  all_56_8 = e1 | all_56_8 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |   (295)  all_56_8 = e1
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (180), (186), (295) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |            #1320.
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |   (296)  all_56_8 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (296) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |   (297)  all_6_1 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | SIMP: (297) implies:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |   (298)  all_6_1 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | REDUCE: (184), (298) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |   (299)   ~ (all_52_29 = e0)
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | REDUCE: (185), (298) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | |   (300)   ~ (e3 = e0)
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |   (301)  all_58_9 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (301) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |   (302)  all_52_25 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | SIMP: (302) implies:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |   (303)  all_52_25 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (303) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |   (304)   ~ (all_52_9 = e0)
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (303) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |   (305)  op(e0, e0) = all_52_24
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (24), (25), (28), (30), (33), (36),
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |            (43), (46), (52), (55), (56), (67), (71), (81),
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |            (83), (88), (91), (96), (97), (99), (107), (109),
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |            (111), (116), (117), (118), (122), (126), (133),
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |            (134), (136), (146), (155), (173), (263), (266),
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |            (304), (305) are inconsistent by sub-proof #1106.
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | |   (306)  all_58_10 = e0 | all_58_11 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | |   (307)  all_58_10 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (286), (307) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | |            #750.
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | |   (308)  all_58_11 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (299), (308) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | |            #1115.
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (309)   ~ (all_58_2 = e2)
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | REDUCE: (62), (309) imply:
% 201.89/33.56  | | | | | | | | | | | | | | | | |   (310)   ~ (all_52_3 = e2)
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21), (62), (111), (115), (147), (173),
% 201.89/33.56  | | | | | | | | | | | | | | | | |            (181), (188), (310) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | | | |            #308.
% 201.89/33.56  | | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (311)   ~ (all_56_2 = e3)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (64), (311) imply:
% 201.89/33.56  | | | | | | | | | | | |   (312)   ~ (all_52_17 = e3)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REF_CLOSE: (8), (9), (28), (97), (99), (122), (134), (261),
% 201.89/33.56  | | | | | | | | | | | |            (263), (312) are inconsistent by sub-proof #1138.
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | End of split
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | Case 2:
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | |   (313)   ~ (all_58_0 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | REDUCE: (19), (313) imply:
% 201.89/33.56  | | | | | | |   (314)   ~ (all_6_2 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | BETA: splitting (75) gives:
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | |   (315)  all_58_0 = e2
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | COMBINE_EQS: (19), (315) imply:
% 201.89/33.56  | | | | | | | |   (316)  all_6_2 = e2
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | COMBINE_EQS: (40), (316) imply:
% 201.89/33.56  | | | | | | | |   (317)  all_46_2 = e2
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (18), (316) imply:
% 201.89/33.56  | | | | | | | |   (318)   ~ (all_52_3 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (97), (316) imply:
% 201.89/33.56  | | | | | | | |   (319)   ~ (all_52_9 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (131), (316) imply:
% 201.89/33.56  | | | | | | | |   (320)  op(e2, e3) = all_6_1
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | BETA: splitting (47) gives:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (321)   ~ (all_46_2 = e2)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REDUCE: (317), (321) imply:
% 201.89/33.56  | | | | | | | | |   (322)  $false
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | CLOSE: (322) is inconsistent.
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (323)   ~ (all_46_1 = e0)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REDUCE: (119), (323) imply:
% 201.89/33.56  | | | | | | | | |   (324)   ~ (all_6_1 = e0)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | GROUND_INST: instantiating (8) with all_52_3, all_6_1, e3, e2,
% 201.89/33.56  | | | | | | | | |              simplifying with (12), (320) gives:
% 201.89/33.56  | | | | | | | | |   (325)  all_52_3 = all_6_1
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | COMBINE_EQS: (20), (325) imply:
% 201.89/33.56  | | | | | | | | |   (326)  all_56_4 = all_6_1
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | COMBINE_EQS: (62), (325) imply:
% 201.89/33.56  | | | | | | | | |   (327)  all_58_2 = all_6_1
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REDUCE: (35), (325) imply:
% 201.89/33.56  | | | | | | | | |   (328)   ~ (all_52_5 = all_6_1)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | SIMP: (328) implies:
% 201.89/33.56  | | | | | | | | |   (329)   ~ (all_52_5 = all_6_1)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REDUCE: (318), (325) imply:
% 201.89/33.56  | | | | | | | | |   (330)   ~ (all_6_1 = e2)
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | BETA: splitting (34) gives:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (331)  all_58_0 = e0
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | COMBINE_EQS: (315), (331) imply:
% 201.89/33.56  | | | | | | | | | |   (332)  e2 = e0
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REDUCE: (69), (332) imply:
% 201.89/33.56  | | | | | | | | | |   (333)  $false
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | CLOSE: (333) is inconsistent.
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (334)   ~ (all_58_0 = e0)
% 201.89/33.56  | | | | | | | | | |   (335)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | BETA: splitting (335) gives:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (336)  all_58_2 = e0
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | REF_CLOSE: (324), (327), (336) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | |            #295.
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (337)   ~ (all_58_2 = e0)
% 201.89/33.56  | | | | | | | | | | |   (338)  all_58_6 = e0 | all_58_12 = e0
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | BETA: splitting (161) gives:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (339)  all_56_4 = e2
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REF_CLOSE: (326), (330), (339) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | |            #1219.
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (340)  all_56_4 = e1 | all_56_4 = e0
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | BETA: splitting (340) gives:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (341)  all_56_4 = e1
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | COMBINE_EQS: (326), (341) imply:
% 201.89/33.56  | | | | | | | | | | | | |   (342)  all_6_1 = e1
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | SIMP: (342) implies:
% 201.89/33.56  | | | | | | | | | | | | |   (343)  all_6_1 = e1
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | REDUCE: (329), (343) imply:
% 201.89/33.56  | | | | | | | | | | | | |   (344)   ~ (all_52_5 = e1)
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | REDUCE: (21), (343) imply:
% 201.89/33.56  | | | | | | | | | | | | |   (345)  op(e3, e1) = e1
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | BETA: splitting (169) gives:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (346)  all_56_8 = e2
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REF_CLOSE: (11), (53), (69), (110), (147), (338), (346) are
% 201.89/33.56  | | | | | | | | | | | | | |            inconsistent by sub-proof #294.
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (347)  all_56_8 = e1 | all_56_8 = e0
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | |   (348)  all_56_8 = e1
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | REF_CLOSE: (53), (344), (348) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | | | |            #707.
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | |   (349)  all_56_8 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | COMBINE_EQS: (53), (349) imply:
% 201.89/33.56  | | | | | | | | | | | | | | |   (350)  all_52_5 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | SIMP: (350) implies:
% 201.89/33.56  | | | | | | | | | | | | | | |   (351)  all_52_5 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | REDUCE: (23), (351) imply:
% 201.89/33.56  | | | | | | | | | | | | | | |   (352)  op(e0, e0) = all_52_4
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_4, e0, e0,
% 201.89/33.56  | | | | | | | | | | | | | | |              simplifying with (43), (352) gives:
% 201.89/33.56  | | | | | | | | | | | | | | |   (353)  all_52_4 = all_14_2
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_17, e1, e1, e3,
% 201.89/33.56  | | | | | | | | | | | | | | |              simplifying with (78), (345) gives:
% 201.89/33.56  | | | | | | | | | | | | | | |   (354)  all_52_17 = e1
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | REDUCE: (117), (354) imply:
% 201.89/33.56  | | | | | | | | | | | | | | |   (355)   ~ (all_52_9 = e1)
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | |   (356)  all_56_1 = e3
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (99), (107), (122), (155), (356) are
% 201.89/33.56  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1110.
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | |   (357)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (107), (122), (136), (319), (355),
% 201.89/33.56  | | | | | | | | | | | | | | | |            (357) are inconsistent by sub-proof #293.
% 201.89/33.56  | | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (358)  all_56_4 = e0
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | REF_CLOSE: (324), (326), (358) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | |            #1217.
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | |   (359)   ~ (all_58_0 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (19), (359) imply:
% 201.89/33.56  | | | | | | | |   (360)   ~ (all_6_2 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REF_CLOSE: (8), (21), (98), (99), (131), (156), (157), (166),
% 201.89/33.56  | | | | | | | |            (314), (360) are inconsistent by sub-proof #292.
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | End of split
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | End of split
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | End of split
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | End of split
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | End of split
% 201.89/33.56  | | | 
% 201.89/33.56  | | Case 2:
% 201.89/33.56  | | | 
% 201.89/33.56  | | |   (361)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.56  | | | 
% 201.89/33.56  | | | BETA: splitting (361) gives:
% 201.89/33.56  | | | 
% 201.89/33.56  | | | Case 1:
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | |   (362)  all_58_13 = e3
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | | REF_CLOSE: (25), (146), (362) are inconsistent by sub-proof #1360.
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | Case 2:
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | |   (363)  all_58_14 = e3 | all_58_15 = e3
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | | BETA: splitting (363) gives:
% 201.89/33.56  | | | | 
% 201.89/33.56  | | | | Case 1:
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | |   (364)  all_58_14 = e3
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | COMBINE_EQS: (4), (364) imply:
% 201.89/33.56  | | | | |   (365)  all_52_23 = e3
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | SIMP: (365) implies:
% 201.89/33.56  | | | | |   (366)  all_52_23 = e3
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | REDUCE: (124), (366) imply:
% 201.89/33.56  | | | | |   (367)   ~ (all_52_7 = e3)
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | REDUCE: (130), (366) imply:
% 201.89/33.56  | | | | |   (368)   ~ (all_52_17 = e3)
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | REDUCE: (54), (366) imply:
% 201.89/33.56  | | | | |   (369)   ~ (all_52_19 = e3)
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | REDUCE: (89), (366) imply:
% 201.89/33.56  | | | | |   (370)   ~ (all_14_2 = e3)
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | REDUCE: (123), (366) imply:
% 201.89/33.56  | | | | |   (371)   ~ (all_10_2 = e3)
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | SIMP: (371) implies:
% 201.89/33.56  | | | | |   (372)   ~ (all_10_2 = e3)
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | REDUCE: (84), (366) imply:
% 201.89/33.56  | | | | |   (373)  op(e3, e3) = all_52_22
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_22, e3, e3,
% 201.89/33.56  | | | | |              simplifying with (99), (373) gives:
% 201.89/33.56  | | | | |   (374)  all_52_22 = all_6_2
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | BETA: splitting (49) gives:
% 201.89/33.56  | | | | | 
% 201.89/33.56  | | | | | Case 1:
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | |   (375)  all_56_2 = e3
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | | REF_CLOSE: (64), (368), (375) are inconsistent by sub-proof #1327.
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | Case 2:
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | |   (376)   ~ (all_56_2 = e3)
% 201.89/33.56  | | | | | |   (377)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | | BETA: splitting (31) gives:
% 201.89/33.56  | | | | | | 
% 201.89/33.56  | | | | | | Case 1:
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | |   (378)  all_58_4 = e1
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | COMBINE_EQS: (134), (378) imply:
% 201.89/33.56  | | | | | | |   (379)  all_52_17 = e1
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | SIMP: (379) implies:
% 201.89/33.56  | | | | | | |   (380)  all_52_17 = e1
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | REDUCE: (117), (380) imply:
% 201.89/33.56  | | | | | | |   (381)   ~ (all_52_9 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | REDUCE: (113), (380) imply:
% 201.89/33.56  | | | | | | |   (382)   ~ (all_6_2 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | SIMP: (382) implies:
% 201.89/33.56  | | | | | | |   (383)   ~ (all_6_2 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | REDUCE: (368), (380) imply:
% 201.89/33.56  | | | | | | |   (384)   ~ (e3 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | BETA: splitting (116) gives:
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | |   (385)  all_56_1 = e3
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | COMBINE_EQS: (107), (385) imply:
% 201.89/33.56  | | | | | | | |   (386)  all_52_9 = e3
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | SIMP: (386) implies:
% 201.89/33.56  | | | | | | | |   (387)  all_52_9 = e3
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (39), (387) imply:
% 201.89/33.56  | | | | | | | |   (388)   ~ (all_52_15 = e3)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (94), (387) imply:
% 201.89/33.56  | | | | | | | |   (389)   ~ (all_4_2 = e3)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | SIMP: (389) implies:
% 201.89/33.56  | | | | | | | |   (390)   ~ (all_4_2 = e3)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REF_CLOSE: (8), (9), (25), (26), (56), (81), (97), (99), (122),
% 201.89/33.56  | | | | | | | |            (126), (146), (383), (390) are inconsistent by
% 201.89/33.56  | | | | | | | |            sub-proof #1142.
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | |   (391)   ~ (all_56_1 = e3)
% 201.89/33.56  | | | | | | | |   (392)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (107), (391) imply:
% 201.89/33.56  | | | | | | | |   (393)   ~ (all_52_9 = e3)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | BETA: splitting (81) gives:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (394)  all_58_1 = e3
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | COMBINE_EQS: (9), (394) imply:
% 201.89/33.56  | | | | | | | | |   (395)  all_52_9 = e3
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REDUCE: (393), (395) imply:
% 201.89/33.56  | | | | | | | | |   (396)  $false
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | CLOSE: (396) is inconsistent.
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (397)   ~ (all_58_1 = e3)
% 201.89/33.56  | | | | | | | | |   (398)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | BETA: splitting (102) gives:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (399)  all_58_0 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | COMBINE_EQS: (19), (399) imply:
% 201.89/33.56  | | | | | | | | | |   (400)  all_6_2 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REDUCE: (92), (400) imply:
% 201.89/33.56  | | | | | | | | | |   (401)   ~ (all_52_25 = e3)
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REF_CLOSE: (5), (8), (9), (19), (21), (28), (41), (97), (99),
% 201.89/33.56  | | | | | | | | | |            (102), (122), (131), (134), (368), (401) are
% 201.89/33.56  | | | | | | | | | |            inconsistent by sub-proof #289.
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (402)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | BETA: splitting (402) gives:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (403)  all_58_1 = e3
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | COMBINE_EQS: (9), (403) imply:
% 201.89/33.56  | | | | | | | | | | |   (404)  all_52_9 = e3
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | REDUCE: (393), (404) imply:
% 201.89/33.56  | | | | | | | | | | |   (405)  $false
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | CLOSE: (405) is inconsistent.
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (406)  all_58_4 = e3 | all_58_9 = e3
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | BETA: splitting (406) gives:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (407)  all_58_4 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | COMBINE_EQS: (378), (407) imply:
% 201.89/33.56  | | | | | | | | | | | |   (408)  e3 = e1
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (5), (408) imply:
% 201.89/33.56  | | | | | | | | | | | |   (409)  $false
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | CLOSE: (409) is inconsistent.
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (410)  all_58_9 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | COMBINE_EQS: (28), (410) imply:
% 201.89/33.56  | | | | | | | | | | | |   (411)  all_52_25 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | SIMP: (411) implies:
% 201.89/33.56  | | | | | | | | | | | |   (412)  all_52_25 = e3
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (55), (412) imply:
% 201.89/33.56  | | | | | | | | | | | |   (413)   ~ (all_52_29 = e3)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | SIMP: (413) implies:
% 201.89/33.56  | | | | | | | | | | | |   (414)   ~ (all_52_29 = e3)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (135), (412) imply:
% 201.89/33.56  | | | | | | | | | | | |   (415)  op(e3, e3) = all_52_24
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_24, e3, e3,
% 201.89/33.56  | | | | | | | | | | | |              simplifying with (99), (415) gives:
% 201.89/33.56  | | | | | | | | | | | |   (416)  all_52_24 = all_6_2
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | BETA: splitting (60) gives:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (417)  all_58_6 = e3
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | COMBINE_EQS: (110), (417) imply:
% 201.89/33.56  | | | | | | | | | | | | |   (418)  all_52_5 = e3
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | SIMP: (418) implies:
% 201.89/33.56  | | | | | | | | | | | | |   (419)  all_52_5 = e3
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | REDUCE: (23), (419) imply:
% 201.89/33.56  | | | | | | | | | | | | |   (420)  op(e3, e3) = all_52_4
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | BETA: splitting (398) gives:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (421)  all_58_3 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | COMBINE_EQS: (126), (421) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (422)  all_4_2 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REDUCE: (96), (422) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (423)  op(e3, e3) = e2
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REDUCE: (71), (422) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (424)  op(e3, e2) = all_4_1
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_9, all_4_1, e2, e3,
% 201.89/33.56  | | | | | | | | | | | | | |              simplifying with (111), (424) gives:
% 201.89/33.56  | | | | | | | | | | | | | |   (425)  all_52_9 = all_4_1
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_4, e3, e3,
% 201.89/33.56  | | | | | | | | | | | | | |              simplifying with (99), (420) gives:
% 201.89/33.56  | | | | | | | | | | | | | |   (426)  all_52_4 = all_6_2
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e2, all_52_4, e3, e3,
% 201.89/33.56  | | | | | | | | | | | | | |              simplifying with (420), (423) gives:
% 201.89/33.56  | | | | | | | | | | | | | |   (427)  all_52_4 = e2
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | COMBINE_EQS: (426), (427) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (428)  all_6_2 = e2
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | SIMP: (428) implies:
% 201.89/33.56  | | | | | | | | | | | | | |   (429)  all_6_2 = e2
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | COMBINE_EQS: (107), (425) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (430)  all_56_1 = all_4_1
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REDUCE: (97), (425), (429) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (431)   ~ (all_4_1 = e2)
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REDUCE: (122), (425) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (432)  op(all_4_1, all_4_1) = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (46), (136), (392), (430), (431), (432)
% 201.89/33.56  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1114.
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (433)  all_58_7 = e3 | all_58_13 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (26), (56), (99), (146), (383), (433)
% 201.89/33.56  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1144.
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (434)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | BETA: splitting (434) gives:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (435)  all_58_7 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | COMBINE_EQS: (56), (435) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (436)  all_52_13 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REDUCE: (26), (436) imply:
% 201.89/33.56  | | | | | | | | | | | | | |   (437)  op(e3, e3) = e1
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REF_CLOSE: (8), (99), (383), (437) are inconsistent by
% 201.89/33.56  | | | | | | | | | | | | | |            sub-proof #885.
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | |   (438)  all_58_8 = e3 | all_58_11 = e3
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | | REF_CLOSE: (36), (87), (372), (414), (438) are inconsistent
% 201.89/33.56  | | | | | | | | | | | | | |            by sub-proof #1140.
% 201.89/33.56  | | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | End of split
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | End of split
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | Case 2:
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | |   (439)   ~ (all_58_4 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | REDUCE: (134), (439) imply:
% 201.89/33.56  | | | | | | |   (440)   ~ (all_52_17 = e1)
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | BETA: splitting (79) gives:
% 201.89/33.56  | | | | | | | 
% 201.89/33.56  | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | |   (441)  all_58_4 = e2
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | COMBINE_EQS: (134), (441) imply:
% 201.89/33.56  | | | | | | | |   (442)  all_52_17 = e2
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | SIMP: (442) implies:
% 201.89/33.56  | | | | | | | |   (443)  all_52_17 = e2
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (117), (443) imply:
% 201.89/33.56  | | | | | | | |   (444)   ~ (all_52_9 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | REDUCE: (113), (443) imply:
% 201.89/33.56  | | | | | | | |   (445)   ~ (all_6_2 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | SIMP: (445) implies:
% 201.89/33.56  | | | | | | | |   (446)   ~ (all_6_2 = e2)
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | BETA: splitting (116) gives:
% 201.89/33.56  | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (447)  all_56_1 = e3
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | COMBINE_EQS: (107), (447) imply:
% 201.89/33.56  | | | | | | | | |   (448)  all_52_9 = e3
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | SIMP: (448) implies:
% 201.89/33.56  | | | | | | | | |   (449)  all_52_9 = e3
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | REF_CLOSE: (8), (97), (99), (122), (449) are inconsistent by
% 201.89/33.56  | | | | | | | | |            sub-proof #1337.
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | |   (450)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | BETA: splitting (102) gives:
% 201.89/33.56  | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (451)  all_58_0 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | COMBINE_EQS: (19), (451) imply:
% 201.89/33.56  | | | | | | | | | |   (452)  all_6_2 = e3
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REDUCE: (92), (452) imply:
% 201.89/33.56  | | | | | | | | | |   (453)   ~ (all_52_25 = e3)
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REF_CLOSE: (5), (8), (9), (19), (21), (28), (41), (97), (99),
% 201.89/33.56  | | | | | | | | | |            (102), (122), (131), (134), (368), (453) are
% 201.89/33.56  | | | | | | | | | |            inconsistent by sub-proof #289.
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | |   (454)   ~ (all_58_0 = e3)
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | REDUCE: (19), (454) imply:
% 201.89/33.56  | | | | | | | | | |   (455)   ~ (all_6_2 = e3)
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | BETA: splitting (120) gives:
% 201.89/33.56  | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (456)  all_56_0 = e3
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | REF_CLOSE: (98), (455), (456) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | |            #598.
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | |   (457)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | BETA: splitting (72) gives:
% 201.89/33.56  | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (458)  all_58_0 = e1
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | COMBINE_EQS: (19), (458) imply:
% 201.89/33.56  | | | | | | | | | | | |   (459)  all_6_2 = e1
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (97), (459) imply:
% 201.89/33.56  | | | | | | | | | | | |   (460)   ~ (all_52_9 = e1)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REF_CLOSE: (8), (43), (107), (122), (136), (444), (450),
% 201.89/33.56  | | | | | | | | | | | |            (460) are inconsistent by sub-proof #293.
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | |   (461)   ~ (all_58_0 = e1)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | REDUCE: (19), (461) imply:
% 201.89/33.56  | | | | | | | | | | | |   (462)   ~ (all_6_2 = e1)
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | BETA: splitting (457) gives:
% 201.89/33.56  | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 1:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | |   (463)  all_56_0 = e2
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | | REF_CLOSE: (98), (446), (463) are inconsistent by sub-proof
% 201.89/33.56  | | | | | | | | | | | | |            #597.
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.56  | | | | | | | | | | | | Case 2:
% 201.89/33.56  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | |   (464)  all_56_0 = e1 | all_56_0 = e0
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | BETA: splitting (464) gives:
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | |   (465)  all_56_0 = e1
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | REF_CLOSE: (98), (462), (465) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | | | | | | | |            #596.
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | |   (466)  all_56_0 = e0
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | COMBINE_EQS: (98), (466) imply:
% 201.89/33.57  | | | | | | | | | | | | | |   (467)  all_6_2 = e0
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | SIMP: (467) implies:
% 201.89/33.57  | | | | | | | | | | | | | |   (468)  all_6_2 = e0
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | REDUCE: (97), (468) imply:
% 201.89/33.57  | | | | | | | | | | | | | |   (469)   ~ (all_52_9 = e0)
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (50), (107), (121), (122), (372), (444),
% 201.89/33.57  | | | | | | | | | | | | | |            (450), (469) are inconsistent by sub-proof #896.
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | |   (470)   ~ (all_58_4 = e2)
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | REDUCE: (134), (470) imply:
% 201.89/33.57  | | | | | | | |   (471)   ~ (all_52_17 = e2)
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | BETA: splitting (377) gives:
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | |   (472)  all_56_2 = e2
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | REF_CLOSE: (64), (471), (472) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | | |            #1264.
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | |   (473)   ~ (all_56_2 = e2)
% 201.89/33.57  | | | | | | | | |   (474)  all_56_2 = e1 | all_56_2 = e0
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | BETA: splitting (474) gives:
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | |   (475)  all_56_2 = e1
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | REF_CLOSE: (64), (440), (475) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | | | |            #1263.
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | |   (476)  all_56_2 = e0
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | COMBINE_EQS: (64), (476) imply:
% 201.89/33.57  | | | | | | | | | |   (477)  all_52_17 = e0
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | SIMP: (477) implies:
% 201.89/33.57  | | | | | | | | | |   (478)  all_52_17 = e0
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | REDUCE: (117), (478) imply:
% 201.89/33.57  | | | | | | | | | |   (479)   ~ (all_52_9 = e0)
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | BETA: splitting (93) gives:
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | |   (480)  all_56_3 = e3
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | COMBINE_EQS: (103), (480) imply:
% 201.89/33.57  | | | | | | | | | | |   (481)  all_52_25 = e3
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | SIMP: (481) implies:
% 201.89/33.57  | | | | | | | | | | |   (482)  all_52_25 = e3
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | REDUCE: (82), (482) imply:
% 201.89/33.57  | | | | | | | | | | |   (483)   ~ (all_52_9 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | REDUCE: (3), (482) imply:
% 201.89/33.57  | | | | | | | | | | |   (484)   ~ (all_52_27 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | SIMP: (484) implies:
% 201.89/33.57  | | | | | | | | | | |   (485)   ~ (all_52_27 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | REDUCE: (92), (482) imply:
% 201.89/33.57  | | | | | | | | | | |   (486)   ~ (all_6_2 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | SIMP: (486) implies:
% 201.89/33.57  | | | | | | | | | | |   (487)   ~ (all_6_2 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | REDUCE: (135), (482) imply:
% 201.89/33.57  | | | | | | | | | | |   (488)  op(e3, e3) = all_52_24
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_24, e3, e3,
% 201.89/33.57  | | | | | | | | | | |              simplifying with (99), (488) gives:
% 201.89/33.57  | | | | | | | | | | |   (489)  all_52_24 = all_6_2
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | BETA: splitting (116) gives:
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | |   (490)  all_56_1 = e3
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | REF_CLOSE: (107), (483), (490) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | | | | | |            #1326.
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | |   (491)   ~ (all_56_1 = e3)
% 201.89/33.57  | | | | | | | | | | | |   (492)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | BETA: splitting (60) gives:
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | |   (493)  all_58_6 = e3
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | COMBINE_EQS: (110), (493) imply:
% 201.89/33.57  | | | | | | | | | | | | |   (494)  all_52_5 = e3
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | SIMP: (494) implies:
% 201.89/33.57  | | | | | | | | | | | | |   (495)  all_52_5 = e3
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | REDUCE: (35), (495) imply:
% 201.89/33.57  | | | | | | | | | | | | |   (496)   ~ (all_52_3 = e3)
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | REDUCE: (23), (495) imply:
% 201.89/33.57  | | | | | | | | | | | | |   (497)  op(e3, e3) = all_52_4
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | BETA: splitting (45) gives:
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | |   (498)  all_58_2 = e3
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | REF_CLOSE: (62), (496), (498) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | | | | | | | |            #1369.
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | |   (499)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | BETA: splitting (499) gives:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | |   (500)  all_58_3 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | COMBINE_EQS: (126), (500) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (501)  all_4_2 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REDUCE: (96), (501) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (502)  op(e3, e3) = e2
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REDUCE: (71), (501) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (503)  op(e3, e2) = all_4_1
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_9, all_4_1, e2, e3,
% 201.89/33.57  | | | | | | | | | | | | | | |              simplifying with (111), (503) gives:
% 201.89/33.57  | | | | | | | | | | | | | | |   (504)  all_52_9 = all_4_1
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_4, e3, e3,
% 201.89/33.57  | | | | | | | | | | | | | | |              simplifying with (99), (497) gives:
% 201.89/33.57  | | | | | | | | | | | | | | |   (505)  all_52_4 = all_6_2
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e2, all_52_4, e3, e3,
% 201.89/33.57  | | | | | | | | | | | | | | |              simplifying with (497), (502) gives:
% 201.89/33.57  | | | | | | | | | | | | | | |   (506)  all_52_4 = e2
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | COMBINE_EQS: (505), (506) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (507)  all_6_2 = e2
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | SIMP: (507) implies:
% 201.89/33.57  | | | | | | | | | | | | | | |   (508)  all_6_2 = e2
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | COMBINE_EQS: (107), (504) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (509)  all_56_1 = all_4_1
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REDUCE: (97), (504), (508) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (510)   ~ (all_4_1 = e2)
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REDUCE: (479), (504) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (511)   ~ (all_4_1 = e0)
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REF_CLOSE: (46), (492), (509), (510), (511) are inconsistent
% 201.89/33.57  | | | | | | | | | | | | | | |            by sub-proof #1163.
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | |   (512)  all_58_5 = e3 | all_58_10 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REF_CLOSE: (52), (106), (369), (485), (512) are inconsistent
% 201.89/33.57  | | | | | | | | | | | | | | |            by sub-proof #1132.
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | |   (513)   ~ (all_58_6 = e3)
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | REDUCE: (110), (513) imply:
% 201.89/33.57  | | | | | | | | | | | | |   (514)   ~ (all_52_5 = e3)
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | BETA: splitting (65) gives:
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | |   (515)  all_58_0 = e3
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | COMBINE_EQS: (19), (515) imply:
% 201.89/33.57  | | | | | | | | | | | | | |   (516)  all_6_2 = e3
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | REDUCE: (487), (516) imply:
% 201.89/33.57  | | | | | | | | | | | | | |   (517)  $false
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | CLOSE: (517) is inconsistent.
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | |   (518)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | BETA: splitting (518) gives:
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | |   (519)  all_58_2 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | COMBINE_EQS: (62), (519) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (520)  all_52_3 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | SIMP: (520) implies:
% 201.89/33.57  | | | | | | | | | | | | | | |   (521)  all_52_3 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REDUCE: (128), (521) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (522)   ~ (all_4_2 = e3)
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | SIMP: (522) implies:
% 201.89/33.57  | | | | | | | | | | | | | | |   (523)   ~ (all_4_2 = e3)
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REDUCE: (7), (521) imply:
% 201.89/33.57  | | | | | | | | | | | | | | |   (524)  op(e3, e3) = all_52_2
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | |   (525)  all_58_1 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (525) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | |   (526)  all_52_9 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | REDUCE: (483), (526) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | |   (527)  $false
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | CLOSE: (527) is inconsistent.
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | |   (528)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | BETA: splitting (528) gives:
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | |   (529)  all_58_3 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (529) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | | |   (530)  all_4_2 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | REDUCE: (523), (530) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | | |   (531)  $false
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | CLOSE: (531) is inconsistent.
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | |   (532)  all_58_7 = e3 | all_58_13 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | BETA: splitting (532) gives:
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (533)  all_58_7 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (533) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (534)  all_52_13 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | REDUCE: (26), (534) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (535)  op(e3, e3) = e1
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3,
% 201.89/33.57  | | | | | | | | | | | | | | | | | |              simplifying with (99), (524) gives:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (536)  all_52_2 = all_6_2
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e1, all_52_2, e3, e3,
% 201.89/33.57  | | | | | | | | | | | | | | | | | |              simplifying with (524), (535) gives:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (537)  all_52_2 = e1
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (537) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (538)  all_6_2 = e1
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | SIMP: (538) implies:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (539)  all_6_2 = e1
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | REDUCE: (97), (539) imply:
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (540)   ~ (all_52_9 = e1)
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (33), (64), (107), (116), (117), (122),
% 201.89/33.57  | | | | | | | | | | | | | | | | | |            (134), (377), (440), (471), (483), (523), (540)
% 201.89/33.57  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #736.
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | |   (541)  all_58_13 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (146), (541) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | | | | | | | | | | | |            #1360.
% 201.89/33.57  | | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | |   (542)  all_58_6 = e3 | all_58_12 = e3
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | | REF_CLOSE: (58), (110), (367), (514), (542) are inconsistent
% 201.89/33.57  | | | | | | | | | | | | | | |            by sub-proof #1243.
% 201.89/33.57  | | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | |   (543)   ~ (all_56_3 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | REDUCE: (103), (543) imply:
% 201.89/33.57  | | | | | | | | | | |   (544)   ~ (all_52_25 = e3)
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (19), (21), (28), (41), (97), (99),
% 201.89/33.57  | | | | | | | | | | |            (102), (122), (131), (134), (368), (544) are
% 201.89/33.57  | | | | | | | | | | |            inconsistent by sub-proof #289.
% 201.89/33.57  | | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | | 
% 201.89/33.57  | | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | | 
% 201.89/33.57  | | | | | | | | End of split
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | End of split
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | End of split
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | End of split
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | Case 2:
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | |   (545)  all_58_15 = e3
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | | COMBINE_EQS: (83), (545) imply:
% 201.89/33.57  | | | | |   (546)  all_14_2 = e3
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | | REDUCE: (136), (546) imply:
% 201.89/33.57  | | | | |   (547)  $false
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | | CLOSE: (547) is inconsistent.
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | End of split
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | End of split
% 201.89/33.57  | | | 
% 201.89/33.57  | | End of split
% 201.89/33.57  | | 
% 201.89/33.57  | End of split
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #289 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)   ~ (e3 = e1)
% 201.89/33.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (3)  all_58_1 = all_52_9
% 201.89/33.57    (4)  all_58_0 = all_6_2
% 201.89/33.57    (5)  op(e3, all_6_1) = e1
% 201.89/33.57    (6)  all_58_9 = all_52_25
% 201.89/33.57    (7)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.57    (8)   ~ (all_52_25 = e3)
% 201.89/33.57    (9)   ~ (all_52_9 = all_6_2)
% 201.89/33.57    (10)  op(e3, e3) = all_6_2
% 201.89/33.57    (11)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.57    (12)   ~ (all_52_17 = e3)
% 201.89/33.57    (13)  op(all_52_9, all_52_9) = e3
% 201.89/33.57    (14)  op(all_6_2, e3) = all_6_1
% 201.89/33.57    (15)  all_58_4 = all_52_17
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | BETA: splitting (11) gives:
% 201.89/33.57  | 
% 201.89/33.57  | Case 1:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (16)  all_58_0 = e3
% 201.89/33.57  | | 
% 201.89/33.57  | | COMBINE_EQS: (4), (16) imply:
% 201.89/33.57  | |   (17)  all_6_2 = e3
% 201.89/33.57  | | 
% 201.89/33.57  | | REF_CLOSE: (1), (2), (5), (7), (10), (14), (17) are inconsistent by
% 201.89/33.57  | |            sub-proof #290.
% 201.89/33.57  | | 
% 201.89/33.57  | Case 2:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (18)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.57  | | 
% 201.89/33.57  | | REF_CLOSE: (2), (3), (6), (8), (9), (10), (12), (13), (15), (18) are
% 201.89/33.57  | |            inconsistent by sub-proof #1138.
% 201.89/33.57  | | 
% 201.89/33.57  | End of split
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #290 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)   ~ (e3 = e1)
% 201.89/33.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (3)  op(e3, all_6_1) = e1
% 201.89/33.57    (4)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.57    (5)  all_6_2 = e3
% 201.89/33.57    (6)  op(e3, e3) = all_6_2
% 201.89/33.57    (7)  op(all_6_2, e3) = all_6_1
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (4), (5) imply:
% 201.89/33.57  |   (8)  op(e3, e3) = all_52_0
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (5), (7) imply:
% 201.89/33.57  |   (9)  op(e3, e3) = all_6_1
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (5), (6) imply:
% 201.89/33.57  |   (10)  op(e3, e3) = e3
% 201.89/33.57  | 
% 201.89/33.57  | GROUND_INST: instantiating (2) with all_6_1, all_52_0, e3, e3, simplifying
% 201.89/33.57  |              with (8), (9) gives:
% 201.89/33.57  |   (11)  all_52_0 = all_6_1
% 201.89/33.57  | 
% 201.89/33.57  | GROUND_INST: instantiating (2) with e3, all_52_0, e3, e3, simplifying with
% 201.89/33.57  |              (8), (10) gives:
% 201.89/33.57  |   (12)  all_52_0 = e3
% 201.89/33.57  | 
% 201.89/33.57  | COMBINE_EQS: (11), (12) imply:
% 201.89/33.57  |   (13)  all_6_1 = e3
% 201.89/33.57  | 
% 201.89/33.57  | REF_CLOSE: (1), (2), (3), (8), (9), (13) are inconsistent by sub-proof #291.
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #291 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)   ~ (e3 = e1)
% 201.89/33.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (3)  op(e3, e3) = all_52_0
% 201.89/33.57    (4)  op(e3, all_6_1) = e1
% 201.89/33.57    (5)  all_6_1 = e3
% 201.89/33.57    (6)  op(e3, e3) = all_6_1
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (4), (5) imply:
% 201.89/33.57  |   (7)  op(e3, e3) = e1
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (5), (6) imply:
% 201.89/33.57  |   (8)  op(e3, e3) = e3
% 201.89/33.57  | 
% 201.89/33.57  | REF_CLOSE: (1), (2), (3), (7), (8) are inconsistent by sub-proof #1237.
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #292 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (2)  op(e3, all_6_1) = e1
% 201.89/33.57    (3)  op(e3, e3) = all_52_6
% 201.89/33.57    (4)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 201.89/33.57    (5)   ~ (all_6_2 = e2)
% 201.89/33.57    (6)  op(e0, e3) = e3
% 201.89/33.57    (7)  all_56_0 = all_6_2
% 201.89/33.57    (8)  op(e3, e3) = all_6_2
% 201.89/33.57    (9)   ~ (all_6_2 = e1)
% 201.89/33.57    (10)  op(all_6_2, e3) = all_6_1
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | BETA: splitting (4) gives:
% 201.89/33.57  | 
% 201.89/33.57  | Case 1:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (11)  all_56_0 = e2
% 201.89/33.57  | | 
% 201.89/33.57  | | COMBINE_EQS: (7), (11) imply:
% 201.89/33.57  | |   (12)  all_6_2 = e2
% 201.89/33.57  | | 
% 201.89/33.57  | | REDUCE: (5), (12) imply:
% 201.89/33.57  | |   (13)  $false
% 201.89/33.57  | | 
% 201.89/33.57  | | CLOSE: (13) is inconsistent.
% 201.89/33.57  | | 
% 201.89/33.57  | Case 2:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (14)  all_56_0 = e1 | all_56_0 = e0
% 201.89/33.57  | | 
% 201.89/33.57  | | BETA: splitting (14) gives:
% 201.89/33.57  | | 
% 201.89/33.57  | | Case 1:
% 201.89/33.57  | | | 
% 201.89/33.57  | | |   (15)  all_56_0 = e1
% 201.89/33.57  | | | 
% 201.89/33.57  | | | COMBINE_EQS: (7), (15) imply:
% 201.89/33.57  | | |   (16)  all_6_2 = e1
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REDUCE: (9), (16) imply:
% 201.89/33.57  | | |   (17)  $false
% 201.89/33.57  | | | 
% 201.89/33.57  | | | CLOSE: (17) is inconsistent.
% 201.89/33.57  | | | 
% 201.89/33.57  | | Case 2:
% 201.89/33.57  | | | 
% 201.89/33.57  | | |   (18)  all_56_0 = e0
% 201.89/33.57  | | | 
% 201.89/33.57  | | | COMBINE_EQS: (7), (18) imply:
% 201.89/33.57  | | |   (19)  all_6_2 = e0
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REDUCE: (10), (19) imply:
% 201.89/33.57  | | |   (20)  op(e0, e3) = all_6_1
% 201.89/33.57  | | | 
% 201.89/33.57  | | | GROUND_INST: instantiating (1) with e3, all_6_1, e3, e0, simplifying with
% 201.89/33.57  | | |              (6), (20) gives:
% 201.89/33.57  | | |   (21)  all_6_1 = e3
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REDUCE: (2), (21) imply:
% 201.89/33.57  | | |   (22)  op(e3, e3) = e1
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REF_CLOSE: (1), (3), (8), (9), (22) are inconsistent by sub-proof #1105.
% 201.89/33.57  | | | 
% 201.89/33.57  | | End of split
% 201.89/33.57  | | 
% 201.89/33.57  | End of split
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #293 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (2)  op(e0, e0) = all_14_2
% 201.89/33.57    (3)   ~ (all_52_9 = e2)
% 201.89/33.57    (4)   ~ (all_52_9 = e1)
% 201.89/33.57    (5)  all_56_1 = all_52_9
% 201.89/33.57    (6)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.57    (7)  op(all_52_9, all_52_9) = e3
% 201.89/33.57    (8)   ~ (all_14_2 = e3)
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | BETA: splitting (6) gives:
% 201.89/33.57  | 
% 201.89/33.57  | Case 1:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (9)  all_56_1 = e2
% 201.89/33.57  | | 
% 201.89/33.57  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1194.
% 201.89/33.57  | | 
% 201.89/33.57  | Case 2:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (10)  all_56_1 = e1 | all_56_1 = e0
% 201.89/33.57  | | 
% 201.89/33.57  | | BETA: splitting (10) gives:
% 201.89/33.57  | | 
% 201.89/33.57  | | Case 1:
% 201.89/33.57  | | | 
% 201.89/33.57  | | |   (11)  all_56_1 = e1
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #1061.
% 201.89/33.57  | | | 
% 201.89/33.57  | | Case 2:
% 201.89/33.57  | | | 
% 201.89/33.57  | | |   (12)  all_56_1 = e0
% 201.89/33.57  | | | 
% 201.89/33.57  | | | COMBINE_EQS: (5), (12) imply:
% 201.89/33.57  | | |   (13)  all_52_9 = e0
% 201.89/33.57  | | | 
% 201.89/33.57  | | | SIMP: (13) implies:
% 201.89/33.57  | | |   (14)  all_52_9 = e0
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REDUCE: (7), (14) imply:
% 201.89/33.57  | | |   (15)  op(e0, e0) = e3
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REF_CLOSE: (1), (2), (8), (15) are inconsistent by sub-proof #1372.
% 201.89/33.57  | | | 
% 201.89/33.57  | | End of split
% 201.89/33.57  | | 
% 201.89/33.57  | End of split
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #294 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)   ~ (e3 = e0)
% 201.89/33.57    (2)  all_58_6 = e0 | all_58_12 = e0
% 201.89/33.57    (3)  all_56_8 = all_52_5
% 201.89/33.57    (4)   ~ (e2 = e0)
% 201.89/33.57    (5)  all_58_6 = all_52_5
% 201.89/33.57    (6)  all_56_8 = e2
% 201.89/33.57    (7)  all_58_12 = e3
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | COMBINE_EQS: (3), (6) imply:
% 201.89/33.57  |   (8)  all_52_5 = e2
% 201.89/33.57  | 
% 201.89/33.57  | SIMP: (8) implies:
% 201.89/33.57  |   (9)  all_52_5 = e2
% 201.89/33.57  | 
% 201.89/33.57  | COMBINE_EQS: (5), (9) imply:
% 201.89/33.57  |   (10)  all_58_6 = e2
% 201.89/33.57  | 
% 201.89/33.57  | REF_CLOSE: (1), (2), (4), (7), (10) are inconsistent by sub-proof #383.
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #295 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)  all_58_2 = all_6_1
% 201.89/33.57    (2)  all_58_2 = e0
% 201.89/33.57    (3)   ~ (all_6_1 = e0)
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | COMBINE_EQS: (1), (2) imply:
% 201.89/33.57  |   (4)  all_6_1 = e0
% 201.89/33.57  | 
% 201.89/33.57  | SIMP: (4) implies:
% 201.89/33.57  |   (5)  all_6_1 = e0
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (3), (5) imply:
% 201.89/33.57  |   (6)  $false
% 201.89/33.57  | 
% 201.89/33.57  | CLOSE: (6) is inconsistent.
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #296 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)  all_58_6 = all_6_1
% 201.89/33.57    (2)  all_58_6 = e3
% 201.89/33.57    (3)   ~ (all_6_1 = e3)
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | COMBINE_EQS: (1), (2) imply:
% 201.89/33.57  |   (4)  all_6_1 = e3
% 201.89/33.57  | 
% 201.89/33.57  | SIMP: (4) implies:
% 201.89/33.57  |   (5)  all_6_1 = e3
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (3), (5) imply:
% 201.89/33.57  |   (6)  $false
% 201.89/33.57  | 
% 201.89/33.57  | CLOSE: (6) is inconsistent.
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #297 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)  all_58_14 = all_52_23
% 201.89/33.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (3)   ~ (e3 = e0)
% 201.89/33.57    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.57    (5)   ~ (all_4_2 = e3)
% 201.89/33.57    (6)  op(e3, all_6_1) = e1
% 201.89/33.57    (7)  all_58_13 = e3
% 201.89/33.57    (8)  op(e2, e2) = all_4_2
% 201.89/33.57    (9)   ~ (all_52_7 = all_6_2)
% 201.89/33.57    (10)  all_56_15 = all_14_2
% 201.89/33.57    (11)  all_58_12 = all_52_7
% 201.89/33.57    (12)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.57    (13)   ~ (all_52_7 = e3)
% 201.89/33.57    (14)   ~ (all_52_7 = all_14_2)
% 201.89/33.57    (15)   ~ (all_52_9 = e3)
% 201.89/33.57    (16)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 201.89/33.57    (17)  op(e3, e1) = all_52_17
% 201.89/33.57    (18)  op(e0, e3) = all_52_7
% 201.89/33.57    (19)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 201.89/33.57    (20)   ~ (all_52_23 = all_14_2)
% 201.89/33.57    (21)  all_56_12 = all_52_7
% 201.89/33.57    (22)   ~ (all_52_9 = all_6_2)
% 201.89/33.57    (23)  op(e3, e3) = e0
% 201.89/33.57    (24)  op(e3, e3) = all_6_2
% 201.89/33.57    (25)  op(all_14_2, all_14_2) = all_52_30
% 201.89/33.57    (26)  all_56_1 = all_52_9
% 201.89/33.57    (27)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.57    (28)   ~ (all_52_9 = all_52_17)
% 201.89/33.57    (29)  op(all_52_9, all_52_9) = e3
% 201.89/33.57    (30)   ~ (all_52_7 = all_52_23)
% 201.89/33.57    (31)  op(all_6_2, e3) = all_6_1
% 201.89/33.57  
% 201.89/33.57  Begin of proof
% 201.89/33.57  | 
% 201.89/33.57  | GROUND_INST: instantiating (2) with all_6_2, e0, e3, e3, simplifying with
% 201.89/33.57  |              (23), (24) gives:
% 201.89/33.57  |   (32)  all_6_2 = e0
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (9), (32) imply:
% 201.89/33.57  |   (33)   ~ (all_52_7 = e0)
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (22), (32) imply:
% 201.89/33.57  |   (34)   ~ (all_52_9 = e0)
% 201.89/33.57  | 
% 201.89/33.57  | REDUCE: (31), (32) imply:
% 201.89/33.57  |   (35)  op(e0, e3) = all_6_1
% 201.89/33.57  | 
% 201.89/33.57  | BETA: splitting (16) gives:
% 201.89/33.57  | 
% 201.89/33.57  | Case 1:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (36)  all_58_12 = e0
% 201.89/33.57  | | 
% 201.89/33.57  | | REF_CLOSE: (11), (33), (36) are inconsistent by sub-proof #1067.
% 201.89/33.57  | | 
% 201.89/33.57  | Case 2:
% 201.89/33.57  | | 
% 201.89/33.57  | |   (37)  all_58_13 = e0 | all_58_14 = e0
% 201.89/33.57  | | 
% 201.89/33.57  | | BETA: splitting (12) gives:
% 201.89/33.57  | | 
% 201.89/33.57  | | Case 1:
% 201.89/33.57  | | | 
% 201.89/33.57  | | |   (38)   ~ (all_6_1 = e2)
% 201.89/33.57  | | | 
% 201.89/33.57  | | | BETA: splitting (37) gives:
% 201.89/33.57  | | | 
% 201.89/33.57  | | | Case 1:
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | |   (39)  all_58_13 = e0
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | REF_CLOSE: (3), (7), (39) are inconsistent by sub-proof #1172.
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | Case 2:
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | |   (40)  all_58_14 = e0
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | COMBINE_EQS: (1), (40) imply:
% 201.89/33.57  | | | |   (41)  all_52_23 = e0
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | SIMP: (41) implies:
% 201.89/33.57  | | | |   (42)  all_52_23 = e0
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | REDUCE: (20), (42) imply:
% 201.89/33.57  | | | |   (43)   ~ (all_14_2 = e0)
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | SIMP: (43) implies:
% 201.89/33.57  | | | |   (44)   ~ (all_14_2 = e0)
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | GROUND_INST: instantiating (2) with all_52_7, all_6_1, e3, e0,
% 201.89/33.57  | | | |              simplifying with (18), (35) gives:
% 201.89/33.57  | | | |   (45)  all_52_7 = all_6_1
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | COMBINE_EQS: (21), (45) imply:
% 201.89/33.57  | | | |   (46)  all_56_12 = all_6_1
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | REDUCE: (14), (45) imply:
% 201.89/33.57  | | | |   (47)   ~ (all_14_2 = all_6_1)
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | SIMP: (47) implies:
% 201.89/33.57  | | | |   (48)   ~ (all_14_2 = all_6_1)
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | REDUCE: (13), (45) imply:
% 201.89/33.57  | | | |   (49)   ~ (all_6_1 = e3)
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | REDUCE: (33), (45) imply:
% 201.89/33.57  | | | |   (50)   ~ (all_6_1 = e0)
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | BETA: splitting (4) gives:
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | | Case 1:
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | |   (51)  all_56_12 = e3
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | | REF_CLOSE: (46), (49), (51) are inconsistent by sub-proof #1347.
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | Case 2:
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | |   (52)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | | BETA: splitting (52) gives:
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | | Case 1:
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | |   (53)  all_56_12 = e2
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | | REF_CLOSE: (38), (46), (53) are inconsistent by sub-proof #1346.
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | Case 2:
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | |   (54)  all_56_12 = e1 | all_56_12 = e0
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | | BETA: splitting (54) gives:
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | | Case 1:
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | |   (55)  all_56_12 = e1
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | COMBINE_EQS: (46), (55) imply:
% 201.89/33.57  | | | | | | |   (56)  all_6_1 = e1
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | SIMP: (56) implies:
% 201.89/33.57  | | | | | | |   (57)  all_6_1 = e1
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | REDUCE: (48), (57) imply:
% 201.89/33.57  | | | | | | |   (58)   ~ (all_14_2 = e1)
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | REDUCE: (6), (57) imply:
% 201.89/33.57  | | | | | | |   (59)  op(e3, e1) = e1
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | BETA: splitting (19) gives:
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | Case 1:
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | |   (60)  all_56_15 = e2
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | COMBINE_EQS: (10), (60) imply:
% 201.89/33.57  | | | | | | | |   (61)  all_14_2 = e2
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | SIMP: (61) implies:
% 201.89/33.57  | | | | | | | |   (62)  all_14_2 = e2
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | REDUCE: (25), (62) imply:
% 201.89/33.57  | | | | | | | |   (63)  op(e2, e2) = all_52_30
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_30, e2, e2,
% 201.89/33.57  | | | | | | | |              simplifying with (8), (63) gives:
% 201.89/33.57  | | | | | | | |   (64)  all_52_30 = all_4_2
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | GROUND_INST: instantiating (2) with all_52_17, e1, e1, e3,
% 201.89/33.57  | | | | | | | |              simplifying with (17), (59) gives:
% 201.89/33.57  | | | | | | | |   (65)  all_52_17 = e1
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | REDUCE: (28), (65) imply:
% 201.89/33.57  | | | | | | | |   (66)   ~ (all_52_9 = e1)
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | REF_CLOSE: (2), (5), (8), (15), (26), (27), (29), (34), (66) are
% 201.89/33.57  | | | | | | | |            inconsistent by sub-proof #324.
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | Case 2:
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | |   (67)  all_56_15 = e1 | all_56_15 = e0
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | | REF_CLOSE: (10), (44), (58), (67) are inconsistent by sub-proof
% 201.89/33.57  | | | | | | | |            #1161.
% 201.89/33.57  | | | | | | | | 
% 201.89/33.57  | | | | | | | End of split
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | Case 2:
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | |   (68)  all_56_12 = e0
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | | REF_CLOSE: (46), (50), (68) are inconsistent by sub-proof #1345.
% 201.89/33.57  | | | | | | | 
% 201.89/33.57  | | | | | | End of split
% 201.89/33.57  | | | | | | 
% 201.89/33.57  | | | | | End of split
% 201.89/33.57  | | | | | 
% 201.89/33.57  | | | | End of split
% 201.89/33.57  | | | | 
% 201.89/33.57  | | | End of split
% 201.89/33.57  | | | 
% 201.89/33.57  | | Case 2:
% 201.89/33.57  | | | 
% 201.89/33.57  | | |   (69)   ~ (all_6_2 = e0)
% 201.89/33.57  | | | 
% 201.89/33.57  | | | REDUCE: (32), (69) imply:
% 201.89/33.57  | | |   (70)  $false
% 201.89/33.57  | | | 
% 201.89/33.57  | | | CLOSE: (70) is inconsistent.
% 201.89/33.57  | | | 
% 201.89/33.57  | | End of split
% 201.89/33.57  | | 
% 201.89/33.57  | End of split
% 201.89/33.57  | 
% 201.89/33.57  End of proof
% 201.89/33.57  
% 201.89/33.57  Sub-proof #298 shows that the following formulas are inconsistent:
% 201.89/33.57  ----------------------------------------------------------------
% 201.89/33.57    (1)  all_58_14 = all_52_23
% 201.89/33.57    (2)   ~ (e3 = e1)
% 201.89/33.57    (3)  op(all_52_3, all_52_3) = all_52_2
% 201.89/33.57    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.57    (5)   ~ (all_52_5 = all_52_13)
% 201.89/33.57    (6)  all_58_1 = all_52_9
% 201.89/33.57    (7)   ~ (all_52_9 = all_52_13)
% 201.89/33.57    (8)  op(e2, e3) = all_52_3
% 201.89/33.57    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.57    (10)   ~ (all_52_7 = all_52_15)
% 201.89/33.57    (11)   ~ (all_52_3 = all_6_2)
% 201.89/33.57    (12)   ~ (all_14_1 = e2)
% 201.89/33.57    (13)   ~ (all_14_1 = e3)
% 201.89/33.58    (14)  all_58_0 = all_6_2
% 201.89/33.58    (15)  all_56_4 = all_52_3
% 201.89/33.58    (16)  op(e3, all_6_1) = e1
% 201.89/33.58    (17)   ~ (all_52_17 = all_10_2)
% 201.89/33.58    (18)  op(e0, all_14_1) = all_14_0
% 201.89/33.58    (19)  op(all_52_5, all_52_5) = all_52_4
% 201.89/33.58    (20)  all_58_13 = all_52_15
% 201.89/33.58    (21)  op(all_52_13, all_52_13) = e1
% 201.89/33.58    (22)  all_58_9 = all_52_25
% 201.89/33.58    (23)   ~ (all_52_15 = e3)
% 201.89/33.58    (24)  op(e2, e2) = all_4_2
% 201.89/33.58    (25)   ~ (all_52_3 = all_52_5)
% 201.89/33.58    (26)  all_58_11 = all_52_29
% 201.89/33.58    (27)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.89/33.58    (28)  all_56_3 = all_14_1
% 201.89/33.58    (29)   ~ (all_52_7 = all_6_2)
% 201.89/33.58    (30)  op(e0, e1) = all_52_23
% 201.89/33.58    (31)  all_58_15 = e3
% 201.89/33.58    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.58    (33)   ~ (all_4_1 = e1)
% 201.89/33.58    (34)   ~ (all_52_9 = all_14_1)
% 201.89/33.58    (35)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.89/33.58    (36)  all_56_9 = all_52_13
% 201.89/33.58    (37)   ~ (e2 = e1)
% 201.89/33.58    (38)   ~ (all_52_13 = all_10_2)
% 201.89/33.58    (39)  all_58_10 = all_52_27
% 201.89/33.58    (40)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.58    (41)  all_58_7 = all_52_13
% 201.89/33.58    (42)   ~ (all_52_5 = all_52_7)
% 201.89/33.58    (43)  all_58_12 = all_52_7
% 201.89/33.58    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.58    (45)   ~ (all_52_7 = e3)
% 201.89/33.58    (46)  all_58_2 = all_52_3
% 201.89/33.58    (47)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.58    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.58    (49)   ~ (all_52_29 = e3)
% 201.89/33.58    (50)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.89/33.58    (51)  all_58_9 = all_14_1
% 201.89/33.58    (52)   ~ (all_52_25 = e3)
% 201.89/33.58    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.58    (54)  op(all_4_2, e2) = all_4_1
% 201.89/33.58    (55)   ~ (all_14_1 = all_6_2)
% 201.89/33.58    (56)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.89/33.58    (57)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.58    (58)   ~ (all_52_27 = e3)
% 201.89/33.58    (59)   ~ (all_52_13 = all_4_2)
% 201.89/33.58    (60)  op(all_14_1, all_14_1) = all_52_24
% 201.89/33.58    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.58    (62)  all_58_8 = all_10_2
% 201.89/33.58    (63)  all_56_12 = all_52_7
% 201.89/33.58    (64)  op(all_52_17, all_52_17) = all_52_16
% 201.89/33.58    (65)   ~ (all_52_9 = all_4_2)
% 201.89/33.58    (66)  op(all_4_2, all_4_2) = e2
% 201.89/33.58    (67)   ~ (all_52_9 = all_6_2)
% 201.89/33.58    (68)   ~ (all_52_13 = all_52_15)
% 201.89/33.58    (69)  op(e3, e3) = all_6_2
% 201.89/33.58    (70)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.58    (71)   ~ (all_52_3 = all_52_7)
% 201.89/33.58    (72)  all_58_5 = all_52_19
% 201.89/33.58    (73)  all_56_1 = all_52_9
% 201.89/33.58    (74)  all_58_6 = all_52_5
% 201.89/33.58    (75)  op(e3, e2) = all_52_9
% 201.89/33.58    (76)   ~ (all_52_17 = all_6_2)
% 201.89/33.58    (77)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.58    (78)   ~ (all_52_9 = all_52_17)
% 201.89/33.58    (79)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.58    (80)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.89/33.58    (81)  op(e1, e1) = all_10_2
% 201.89/33.58    (82)  op(all_52_9, all_52_9) = e3
% 201.89/33.58    (83)   ~ (all_52_17 = all_52_19)
% 201.89/33.58    (84)  all_58_3 = all_4_2
% 201.89/33.58    (85)   ~ (all_52_3 = all_4_2)
% 201.89/33.58    (86)  op(all_6_2, e3) = all_6_1
% 201.89/33.58    (87)  all_58_4 = all_52_17
% 201.89/33.58    (88)   ~ (all_14_0 = e2)
% 201.89/33.58  
% 201.89/33.58  Begin of proof
% 201.89/33.58  | 
% 201.89/33.58  | BETA: splitting (57) gives:
% 201.89/33.58  | 
% 201.89/33.58  | Case 1:
% 201.89/33.58  | | 
% 201.89/33.58  | |   (89)  all_58_12 = e1
% 201.89/33.58  | | 
% 201.89/33.58  | | COMBINE_EQS: (43), (89) imply:
% 201.89/33.58  | |   (90)  all_52_7 = e1
% 201.89/33.58  | | 
% 201.89/33.58  | | SIMP: (90) implies:
% 201.89/33.58  | |   (91)  all_52_7 = e1
% 201.89/33.58  | | 
% 201.89/33.58  | | REDUCE: (10), (91) imply:
% 201.89/33.58  | |   (92)   ~ (all_52_15 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | SIMP: (92) implies:
% 201.89/33.58  | |   (93)   ~ (all_52_15 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | REDUCE: (29), (91) imply:
% 201.89/33.58  | |   (94)   ~ (all_6_2 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | SIMP: (94) implies:
% 201.89/33.58  | |   (95)   ~ (all_6_2 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | REDUCE: (45), (91) imply:
% 201.89/33.58  | |   (96)   ~ (e3 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | REF_CLOSE: (2), (4), (6), (13), (14), (15), (16), (20), (21), (23), (32),
% 201.89/33.58  | |            (33), (35), (38), (39), (41), (46), (48), (51), (53), (54), (58),
% 201.89/33.58  | |            (61), (67), (69), (70), (72), (75), (81), (82), (83), (84), (85),
% 201.89/33.58  | |            (86), (87), (93), (95) are inconsistent by sub-proof #300.
% 201.89/33.58  | | 
% 201.89/33.58  | Case 2:
% 201.89/33.58  | | 
% 201.89/33.58  | |   (97)   ~ (all_58_12 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | REDUCE: (43), (97) imply:
% 201.89/33.58  | |   (98)   ~ (all_52_7 = e1)
% 201.89/33.58  | | 
% 201.89/33.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14),
% 201.89/33.58  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 201.89/33.58  | |            (27), (28), (29), (30), (31), (33), (34), (36), (37), (38), (40),
% 201.89/33.58  | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 201.89/33.58  | |            (52), (54), (55), (56), (59), (60), (61), (62), (63), (64), (65),
% 201.89/33.58  | |            (66), (67), (68), (69), (70), (71), (73), (74), (75), (76), (77),
% 201.89/33.58  | |            (78), (79), (80), (81), (82), (84), (85), (86), (87), (88), (98)
% 201.89/33.58  | |            are inconsistent by sub-proof #299.
% 201.89/33.58  | | 
% 201.89/33.58  | End of split
% 201.89/33.58  | 
% 201.89/33.58  End of proof
% 201.89/33.58  
% 201.89/33.58  Sub-proof #299 shows that the following formulas are inconsistent:
% 201.89/33.58  ----------------------------------------------------------------
% 201.89/33.58    (1)  all_58_14 = all_52_23
% 201.89/33.58    (2)   ~ (e3 = e1)
% 201.89/33.58    (3)  op(all_52_3, all_52_3) = all_52_2
% 201.89/33.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.58    (5)   ~ (all_52_5 = all_52_13)
% 201.89/33.58    (6)  all_58_1 = all_52_9
% 201.89/33.58    (7)   ~ (all_52_9 = all_52_13)
% 201.89/33.58    (8)  op(e2, e3) = all_52_3
% 201.89/33.58    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.58    (10)   ~ (all_52_3 = all_6_2)
% 201.89/33.58    (11)   ~ (all_14_1 = e2)
% 201.89/33.58    (12)  all_58_0 = all_6_2
% 201.89/33.58    (13)  op(e3, all_6_1) = e1
% 201.89/33.58    (14)   ~ (all_52_17 = all_10_2)
% 201.89/33.58    (15)  op(e0, all_14_1) = all_14_0
% 201.89/33.58    (16)  op(all_52_5, all_52_5) = all_52_4
% 201.89/33.58    (17)  all_58_13 = all_52_15
% 201.89/33.58    (18)  op(all_52_13, all_52_13) = e1
% 201.89/33.58    (19)  all_58_9 = all_52_25
% 201.89/33.58    (20)   ~ (all_52_15 = e3)
% 201.89/33.58    (21)  op(e2, e2) = all_4_2
% 201.89/33.58    (22)   ~ (all_52_3 = all_52_5)
% 201.89/33.58    (23)  all_58_11 = all_52_29
% 201.89/33.58    (24)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 201.89/33.58    (25)  all_56_3 = all_14_1
% 201.89/33.58    (26)   ~ (all_52_7 = all_6_2)
% 201.89/33.58    (27)  op(e0, e1) = all_52_23
% 201.89/33.58    (28)  all_58_15 = e3
% 201.89/33.58    (29)   ~ (all_4_1 = e1)
% 201.89/33.58    (30)   ~ (all_52_9 = all_14_1)
% 201.89/33.58    (31)  all_56_9 = all_52_13
% 201.89/33.58    (32)   ~ (e2 = e1)
% 201.89/33.58    (33)   ~ (all_52_13 = all_10_2)
% 201.89/33.58    (34)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.58    (35)  all_58_7 = all_52_13
% 201.89/33.58    (36)   ~ (all_52_5 = all_52_7)
% 201.89/33.58    (37)  all_58_12 = all_52_7
% 201.89/33.58    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.58    (39)   ~ (all_52_7 = e3)
% 201.89/33.58    (40)  all_58_2 = all_52_3
% 201.89/33.58    (41)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.58    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.58    (43)   ~ (all_52_29 = e3)
% 201.89/33.58    (44)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.89/33.58    (45)  all_58_9 = all_14_1
% 201.89/33.58    (46)   ~ (all_52_25 = e3)
% 201.89/33.58    (47)  op(all_4_2, e2) = all_4_1
% 201.89/33.58    (48)   ~ (all_14_1 = all_6_2)
% 201.89/33.58    (49)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 201.89/33.58    (50)   ~ (all_52_13 = all_4_2)
% 201.89/33.58    (51)  op(all_14_1, all_14_1) = all_52_24
% 201.89/33.58    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.58    (53)  all_58_8 = all_10_2
% 201.89/33.58    (54)  all_56_12 = all_52_7
% 201.89/33.58    (55)  op(all_52_17, all_52_17) = all_52_16
% 201.89/33.58    (56)   ~ (all_52_9 = all_4_2)
% 201.89/33.58    (57)  op(all_4_2, all_4_2) = e2
% 201.89/33.58    (58)   ~ (all_52_9 = all_6_2)
% 201.89/33.58    (59)   ~ (all_52_13 = all_52_15)
% 201.89/33.58    (60)  op(e3, e3) = all_6_2
% 201.89/33.58    (61)   ~ (all_52_7 = e1)
% 201.89/33.58    (62)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.58    (63)   ~ (all_52_3 = all_52_7)
% 201.89/33.58    (64)  all_56_1 = all_52_9
% 201.89/33.58    (65)  all_58_6 = all_52_5
% 201.89/33.58    (66)  op(e3, e2) = all_52_9
% 201.89/33.58    (67)   ~ (all_52_17 = all_6_2)
% 201.89/33.58    (68)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.58    (69)   ~ (all_52_9 = all_52_17)
% 201.89/33.58    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.58    (71)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 201.89/33.58    (72)  op(e1, e1) = all_10_2
% 201.89/33.58    (73)  op(all_52_9, all_52_9) = e3
% 201.89/33.58    (74)  all_58_3 = all_4_2
% 201.89/33.58    (75)   ~ (all_52_3 = all_4_2)
% 201.89/33.58    (76)  op(all_6_2, e3) = all_6_1
% 201.89/33.58    (77)  all_58_4 = all_52_17
% 201.89/33.58    (78)   ~ (all_14_0 = e2)
% 201.89/33.58  
% 201.89/33.58  Begin of proof
% 201.89/33.58  | 
% 201.89/33.58  | BETA: splitting (42) gives:
% 201.89/33.58  | 
% 201.89/33.58  | Case 1:
% 201.89/33.58  | | 
% 201.89/33.58  | |   (79)  all_58_0 = e3
% 201.89/33.58  | | 
% 201.89/33.58  | | COMBINE_EQS: (12), (79) imply:
% 201.89/33.58  | |   (80)  all_6_2 = e3
% 201.89/33.58  | | 
% 201.89/33.58  | | REF_CLOSE: (2), (4), (13), (60), (76), (80) are inconsistent by sub-proof
% 201.89/33.58  | |            #310.
% 201.89/33.58  | | 
% 201.89/33.58  | Case 2:
% 201.89/33.58  | | 
% 201.89/33.58  | |   (81)   ~ (all_58_0 = e3)
% 201.89/33.58  | |   (82)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.58  | | 
% 201.89/33.58  | | REDUCE: (12), (81) imply:
% 201.89/33.58  | |   (83)   ~ (all_6_2 = e3)
% 201.89/33.58  | | 
% 201.89/33.58  | | BETA: splitting (62) gives:
% 201.89/33.58  | | 
% 201.89/33.58  | | Case 1:
% 201.89/33.58  | | | 
% 201.89/33.58  | | |   (84)  all_58_0 = e3
% 201.89/33.58  | | | 
% 201.89/33.58  | | | COMBINE_EQS: (12), (84) imply:
% 201.89/33.58  | | |   (85)  all_6_2 = e3
% 201.89/33.58  | | | 
% 201.89/33.58  | | | REDUCE: (83), (85) imply:
% 201.89/33.58  | | |   (86)  $false
% 201.89/33.58  | | | 
% 201.89/33.58  | | | CLOSE: (86) is inconsistent.
% 201.89/33.58  | | | 
% 201.89/33.58  | | Case 2:
% 201.89/33.58  | | | 
% 201.89/33.58  | | |   (87)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.58  | | | 
% 201.89/33.58  | | | BETA: splitting (38) gives:
% 201.89/33.58  | | | 
% 201.89/33.58  | | | Case 1:
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | |   (88)  all_58_6 = e3
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | COMBINE_EQS: (65), (88) imply:
% 201.89/33.58  | | | |   (89)  all_52_5 = e3
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | SIMP: (89) implies:
% 201.89/33.58  | | | |   (90)  all_52_5 = e3
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | REDUCE: (36), (90) imply:
% 201.89/33.58  | | | |   (91)   ~ (all_52_7 = e3)
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | REDUCE: (5), (90) imply:
% 201.89/33.58  | | | |   (92)   ~ (all_52_13 = e3)
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | SIMP: (92) implies:
% 201.89/33.58  | | | |   (93)   ~ (all_52_13 = e3)
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | REDUCE: (16), (90) imply:
% 201.89/33.58  | | | |   (94)  op(e3, e3) = all_52_4
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_4, e3, e3,
% 201.89/33.58  | | | |              simplifying with (60), (94) gives:
% 201.89/33.58  | | | |   (95)  all_52_4 = all_6_2
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | BETA: splitting (70) gives:
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | Case 1:
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | |   (96)  all_58_4 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | COMBINE_EQS: (77), (96) imply:
% 201.89/33.58  | | | | |   (97)  all_52_17 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | SIMP: (97) implies:
% 201.89/33.58  | | | | |   (98)  all_52_17 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (69), (98) imply:
% 201.89/33.58  | | | | |   (99)   ~ (all_52_9 = e3)
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (67), (98) imply:
% 201.89/33.58  | | | | |   (100)   ~ (all_6_2 = e3)
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (55), (98) imply:
% 201.89/33.58  | | | | |   (101)  op(e3, e3) = all_52_16
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | BETA: splitting (52) gives:
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | Case 1:
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | |   (102)  all_58_1 = e3
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | COMBINE_EQS: (6), (102) imply:
% 201.89/33.58  | | | | | |   (103)  all_52_9 = e3
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | REDUCE: (99), (103) imply:
% 201.89/33.58  | | | | | |   (104)  $false
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | CLOSE: (104) is inconsistent.
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | Case 2:
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | |   (105)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | BETA: splitting (105) gives:
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | Case 1:
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | |   (106)  all_58_3 = e3
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | COMBINE_EQS: (74), (106) imply:
% 201.89/33.58  | | | | | | |   (107)  all_4_2 = e3
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (75), (107) imply:
% 201.89/33.58  | | | | | | |   (108)   ~ (all_52_3 = e3)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (57), (107) imply:
% 201.89/33.58  | | | | | | |   (109)  op(e3, e3) = e2
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (47), (107) imply:
% 201.89/33.58  | | | | | | |   (110)  op(e3, e2) = all_4_1
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | GROUND_INST: instantiating (4) with all_52_9, all_4_1, e2, e3,
% 201.89/33.58  | | | | | | |              simplifying with (66), (110) gives:
% 201.89/33.58  | | | | | | |   (111)  all_52_9 = all_4_1
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_16, e3, e3,
% 201.89/33.58  | | | | | | |              simplifying with (60), (101) gives:
% 201.89/33.58  | | | | | | |   (112)  all_52_16 = all_6_2
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | GROUND_INST: instantiating (4) with e2, all_52_16, e3, e3,
% 201.89/33.58  | | | | | | |              simplifying with (101), (109) gives:
% 201.89/33.58  | | | | | | |   (113)  all_52_16 = e2
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | COMBINE_EQS: (112), (113) imply:
% 201.89/33.58  | | | | | | |   (114)  all_6_2 = e2
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | SIMP: (114) implies:
% 201.89/33.58  | | | | | | |   (115)  all_6_2 = e2
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | COMBINE_EQS: (64), (111) imply:
% 201.89/33.58  | | | | | | |   (116)  all_56_1 = all_4_1
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | COMBINE_EQS: (6), (111) imply:
% 201.89/33.58  | | | | | | |   (117)  all_58_1 = all_4_1
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | COMBINE_EQS: (12), (115) imply:
% 201.89/33.58  | | | | | | |   (118)  all_58_0 = e2
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (10), (115) imply:
% 201.89/33.58  | | | | | | |   (119)   ~ (all_52_3 = e2)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (26), (115) imply:
% 201.89/33.58  | | | | | | |   (120)   ~ (all_52_7 = e2)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (7), (111) imply:
% 201.89/33.58  | | | | | | |   (121)   ~ (all_52_13 = all_4_1)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | SIMP: (121) implies:
% 201.89/33.58  | | | | | | |   (122)   ~ (all_52_13 = all_4_1)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (30), (111) imply:
% 201.89/33.58  | | | | | | |   (123)   ~ (all_14_1 = all_4_1)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | SIMP: (123) implies:
% 201.89/33.58  | | | | | | |   (124)   ~ (all_14_1 = all_4_1)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (58), (111), (115) imply:
% 201.89/33.58  | | | | | | |   (125)   ~ (all_4_1 = e2)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (99), (111) imply:
% 201.89/33.58  | | | | | | |   (126)   ~ (all_4_1 = e3)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REDUCE: (83), (115) imply:
% 201.89/33.58  | | | | | | |   (127)   ~ (e3 = e2)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | SIMP: (127) implies:
% 201.89/33.58  | | | | | | |   (128)   ~ (e3 = e2)
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | BETA: splitting (44) gives:
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | |   (129)  all_58_0 = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | COMBINE_EQS: (118), (129) imply:
% 201.89/33.58  | | | | | | | |   (130)  e2 = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REDUCE: (32), (130) imply:
% 201.89/33.58  | | | | | | | |   (131)  $false
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | CLOSE: (131) is inconsistent.
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | |   (132)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | BETA: splitting (68) gives:
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | |   (133)  all_56_1 = e3
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | COMBINE_EQS: (116), (133) imply:
% 201.89/33.58  | | | | | | | | |   (134)  all_4_1 = e3
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | REDUCE: (126), (134) imply:
% 201.89/33.58  | | | | | | | | |   (135)  $false
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | CLOSE: (135) is inconsistent.
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | |   (136)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | BETA: splitting (132) gives:
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | |   (137)  all_58_2 = e1
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | COMBINE_EQS: (40), (137) imply:
% 201.89/33.58  | | | | | | | | | |   (138)  all_52_3 = e1
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | SIMP: (138) implies:
% 201.89/33.58  | | | | | | | | | |   (139)  all_52_3 = e1
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REDUCE: (108), (139) imply:
% 201.89/33.58  | | | | | | | | | |   (140)   ~ (e3 = e1)
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REDUCE: (119), (139) imply:
% 201.89/33.58  | | | | | | | | | |   (141)   ~ (e2 = e1)
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REDUCE: (8), (139) imply:
% 201.89/33.58  | | | | | | | | | |   (142)  op(e2, e3) = e1
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (9), (15), (17), (18), (24),
% 201.89/33.58  | | | | | | | | | |            (27), (28), (29), (31), (32), (33), (37), (39),
% 201.89/33.58  | | | | | | | | | |            (45), (49), (51), (54), (59), (63), (71), (72),
% 201.89/33.58  | | | | | | | | | |            (78), (93), (96), (116), (117), (118), (120),
% 201.89/33.58  | | | | | | | | | |            (122), (124), (125), (128), (136), (142) are
% 201.89/33.58  | | | | | | | | | |            inconsistent by sub-proof #567.
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | |   (143)  all_58_6 = e1 | all_58_12 = e1
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REF_CLOSE: (2), (37), (61), (88), (143) are inconsistent by
% 201.89/33.58  | | | | | | | | | |            sub-proof #390.
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | End of split
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | End of split
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | End of split
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | Case 2:
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | |   (144)  all_58_7 = e3 | all_58_13 = e3
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REF_CLOSE: (17), (20), (35), (93), (144) are inconsistent by
% 201.89/33.58  | | | | | | |            sub-proof #1298.
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | End of split
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | End of split
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | Case 2:
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | |   (145)   ~ (all_58_4 = e3)
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (77), (145) imply:
% 201.89/33.58  | | | | |   (146)   ~ (all_52_17 = e3)
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REF_CLOSE: (4), (6), (19), (46), (58), (60), (73), (77), (87), (146)
% 201.89/33.58  | | | | |            are inconsistent by sub-proof #1138.
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | End of split
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | Case 2:
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | |   (147)   ~ (all_58_6 = e3)
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | REDUCE: (65), (147) imply:
% 201.89/33.58  | | | |   (148)   ~ (all_52_5 = e3)
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | BETA: splitting (82) gives:
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | | Case 1:
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | |   (149)  all_58_2 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | COMBINE_EQS: (40), (149) imply:
% 201.89/33.58  | | | | |   (150)  all_52_3 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | SIMP: (150) implies:
% 201.89/33.58  | | | | |   (151)  all_52_3 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (22), (151) imply:
% 201.89/33.58  | | | | |   (152)   ~ (all_52_5 = e3)
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (63), (151) imply:
% 201.89/33.58  | | | | |   (153)   ~ (all_52_7 = e3)
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REDUCE: (3), (151) imply:
% 201.89/33.58  | | | | |   (154)  op(e3, e3) = all_52_2
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_2, e3, e3,
% 201.89/33.58  | | | | |              simplifying with (60), (154) gives:
% 201.89/33.58  | | | | |   (155)  all_52_2 = all_6_2
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | BETA: splitting (70) gives:
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | Case 1:
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | |   (156)  all_58_4 = e3
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | COMBINE_EQS: (77), (156) imply:
% 201.89/33.58  | | | | | |   (157)  all_52_17 = e3
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | SIMP: (157) implies:
% 201.89/33.58  | | | | | |   (158)  all_52_17 = e3
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | REDUCE: (14), (158) imply:
% 201.89/33.58  | | | | | |   (159)   ~ (all_10_2 = e3)
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | SIMP: (159) implies:
% 201.89/33.58  | | | | | |   (160)   ~ (all_10_2 = e3)
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | REDUCE: (67), (158) imply:
% 201.89/33.58  | | | | | |   (161)   ~ (all_6_2 = e3)
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | BETA: splitting (38) gives:
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | Case 1:
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | |   (162)  all_58_6 = e3
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | REF_CLOSE: (65), (148), (162) are inconsistent by sub-proof #1328.
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | Case 2:
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | |   (163)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | BETA: splitting (163) gives:
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | |   (164)  all_58_7 = e3
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | COMBINE_EQS: (35), (164) imply:
% 201.89/33.58  | | | | | | | |   (165)  all_52_13 = e3
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REDUCE: (7), (165) imply:
% 201.89/33.58  | | | | | | | |   (166)   ~ (all_52_9 = e3)
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REDUCE: (18), (165) imply:
% 201.89/33.58  | | | | | | | |   (167)  op(e3, e3) = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | GROUND_INST: instantiating (4) with e1, all_52_2, e3, e3,
% 201.89/33.58  | | | | | | | |              simplifying with (154), (167) gives:
% 201.89/33.58  | | | | | | | |   (168)  all_52_2 = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | COMBINE_EQS: (155), (168) imply:
% 201.89/33.58  | | | | | | | |   (169)  all_6_2 = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | COMBINE_EQS: (12), (169) imply:
% 201.89/33.58  | | | | | | | |   (170)  all_58_0 = e1
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REDUCE: (58), (169) imply:
% 201.89/33.58  | | | | | | | |   (171)   ~ (all_52_9 = e1)
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REDUCE: (48), (169) imply:
% 201.89/33.58  | | | | | | | |   (172)   ~ (all_14_1 = e1)
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REDUCE: (83), (169) imply:
% 201.89/33.58  | | | | | | | |   (173)   ~ (e3 = e1)
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | BETA: splitting (41) gives:
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | |   (174)  all_58_0 = e2
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | REF_CLOSE: (32), (170), (174) are inconsistent by sub-proof
% 201.89/33.58  | | | | | | | | |            #1273.
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | |   (175)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | BETA: splitting (175) gives:
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | |   (176)  all_58_1 = e2
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REF_CLOSE: (2), (4), (6), (21), (37), (39), (40), (42), (65),
% 201.89/33.58  | | | | | | | | | |            (73), (75), (148), (170), (176) are inconsistent
% 201.89/33.58  | | | | | | | | | |            by sub-proof #1122.
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | |   (177)   ~ (all_58_1 = e2)
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | REDUCE: (6), (177) imply:
% 201.89/33.58  | | | | | | | | | |   (178)   ~ (all_52_9 = e2)
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | BETA: splitting (68) gives:
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | |   (179)  all_56_1 = e3
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | COMBINE_EQS: (64), (179) imply:
% 201.89/33.58  | | | | | | | | | | |   (180)  all_52_9 = e3
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | REDUCE: (166), (180) imply:
% 201.89/33.58  | | | | | | | | | | |   (181)  $false
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | |   (182)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | BETA: splitting (34) gives:
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | Case 1:
% 201.89/33.58  | | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | |   (183)  all_56_3 = e2
% 201.89/33.58  | | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | | REF_CLOSE: (11), (25), (183) are inconsistent by sub-proof
% 201.89/33.58  | | | | | | | | | | | |            #1183.
% 201.89/33.58  | | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | |   (184)  all_56_3 = e1 | all_56_3 = e0
% 201.89/33.58  | | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | | REF_CLOSE: (25), (30), (64), (171), (172), (178), (182),
% 201.89/33.58  | | | | | | | | | | | |            (184) are inconsistent by sub-proof #1121.
% 201.89/33.58  | | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | | End of split
% 201.89/33.58  | | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | | End of split
% 201.89/33.58  | | | | | | | | | | 
% 201.89/33.58  | | | | | | | | | End of split
% 201.89/33.58  | | | | | | | | | 
% 201.89/33.58  | | | | | | | | End of split
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | Case 2:
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | |   (185)  all_58_8 = e3 | all_58_11 = e3
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | | REF_CLOSE: (23), (43), (53), (160), (185) are inconsistent by
% 201.89/33.58  | | | | | | | |            sub-proof #1140.
% 201.89/33.58  | | | | | | | | 
% 201.89/33.58  | | | | | | | End of split
% 201.89/33.58  | | | | | | | 
% 201.89/33.58  | | | | | | End of split
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | Case 2:
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | |   (186)   ~ (all_58_4 = e3)
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | REDUCE: (77), (186) imply:
% 201.89/33.58  | | | | | |   (187)   ~ (all_52_17 = e3)
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | | REF_CLOSE: (4), (6), (19), (46), (58), (60), (73), (77), (87), (187)
% 201.89/33.58  | | | | | |            are inconsistent by sub-proof #1138.
% 201.89/33.58  | | | | | | 
% 201.89/33.58  | | | | | End of split
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | Case 2:
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | |   (188)  all_58_6 = e3 | all_58_12 = e3
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | | REF_CLOSE: (37), (39), (65), (148), (188) are inconsistent by
% 201.89/33.58  | | | | |            sub-proof #1243.
% 201.89/33.58  | | | | | 
% 201.89/33.58  | | | | End of split
% 201.89/33.58  | | | | 
% 201.89/33.58  | | | End of split
% 201.89/33.58  | | | 
% 201.89/33.58  | | End of split
% 201.89/33.58  | | 
% 201.89/33.58  | End of split
% 201.89/33.58  | 
% 201.89/33.58  End of proof
% 201.89/33.58  
% 201.89/33.58  Sub-proof #300 shows that the following formulas are inconsistent:
% 201.89/33.58  ----------------------------------------------------------------
% 201.89/33.58    (1)   ~ (all_52_15 = e1)
% 201.89/33.58    (2)   ~ (e3 = e1)
% 201.89/33.58    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.58    (4)  all_58_1 = all_52_9
% 201.89/33.58    (5)   ~ (all_14_1 = e3)
% 201.89/33.58    (6)  all_58_0 = all_6_2
% 201.89/33.58    (7)  all_56_4 = all_52_3
% 201.89/33.58    (8)  op(e3, all_6_1) = e1
% 201.89/33.58    (9)  all_58_13 = all_52_15
% 201.89/33.58    (10)  op(all_52_13, all_52_13) = e1
% 201.89/33.58    (11)   ~ (all_52_15 = e3)
% 201.89/33.58    (12)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.58    (13)   ~ (all_4_1 = e1)
% 201.89/33.58    (14)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 201.89/33.58    (15)   ~ (all_52_13 = all_10_2)
% 201.89/33.58    (16)  all_58_10 = all_52_27
% 201.89/33.58    (17)  all_58_7 = all_52_13
% 201.89/33.58    (18)  all_58_2 = all_52_3
% 201.89/33.58    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.58    (20)  all_58_9 = all_14_1
% 201.89/33.58    (21)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.58    (22)  op(all_4_2, e2) = all_4_1
% 201.89/33.58    (23)   ~ (all_52_27 = e3)
% 201.89/33.58    (24)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.58    (25)   ~ (all_52_9 = all_6_2)
% 201.89/33.58    (26)  op(e3, e3) = all_6_2
% 201.89/33.58    (27)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.58    (28)  all_58_5 = all_52_19
% 201.89/33.58    (29)  op(e3, e2) = all_52_9
% 201.89/33.58    (30)   ~ (all_6_2 = e1)
% 201.89/33.58    (31)  op(e1, e1) = all_10_2
% 201.89/33.58    (32)  op(all_52_9, all_52_9) = e3
% 201.89/33.58    (33)   ~ (all_52_17 = all_52_19)
% 201.89/33.58    (34)  all_58_3 = all_4_2
% 201.89/33.58    (35)   ~ (all_52_3 = all_4_2)
% 201.89/33.58    (36)  op(all_6_2, e3) = all_6_1
% 201.89/33.58    (37)  all_58_4 = all_52_17
% 201.89/33.58  
% 201.89/33.58  Begin of proof
% 201.89/33.58  | 
% 201.89/33.58  | BETA: splitting (21) gives:
% 201.89/33.58  | 
% 201.89/33.58  | Case 1:
% 201.89/33.58  | | 
% 201.89/33.58  | |   (38)  all_56_4 = e3
% 201.89/33.58  | | 
% 201.89/33.58  | | REF_CLOSE: (3), (4), (7), (9), (10), (11), (17), (24), (25), (26), (30),
% 201.89/33.58  | |            (32), (34), (35), (38) are inconsistent by sub-proof #1141.
% 201.89/33.58  | | 
% 201.89/33.58  | Case 2:
% 201.89/33.58  | | 
% 201.89/33.58  | |   (39)   ~ (all_56_4 = e3)
% 201.89/33.58  | | 
% 201.89/33.58  | | REDUCE: (7), (39) imply:
% 201.89/33.58  | |   (40)   ~ (all_52_3 = e3)
% 201.89/33.58  | | 
% 201.89/33.58  | | BETA: splitting (19) gives:
% 201.89/33.58  | | 
% 201.89/33.58  | | Case 1:
% 201.89/33.58  | | | 
% 201.89/33.58  | | |   (41)  all_58_0 = e3
% 201.89/33.58  | | | 
% 201.89/33.58  | | | COMBINE_EQS: (6), (41) imply:
% 201.89/33.58  | | |   (42)  all_6_2 = e3
% 201.89/33.58  | | | 
% 201.89/33.58  | | | REF_CLOSE: (2), (3), (8), (26), (36), (42) are inconsistent by sub-proof
% 201.89/33.58  | | |            #310.
% 201.89/33.58  | | | 
% 201.89/33.58  | | Case 2:
% 201.89/33.58  | | | 
% 201.89/33.58  | | |   (43)   ~ (all_58_0 = e3)
% 201.89/33.58  | | | 
% 201.89/33.58  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (13), (14),
% 201.89/33.58  | | |            (15), (16), (17), (18), (20), (22), (23), (24), (25), (26),
% 201.89/33.58  | | |            (27), (28), (29), (31), (32), (33), (34), (37), (40), (43) are
% 201.89/33.58  | | |            inconsistent by sub-proof #1130.
% 201.89/33.58  | | | 
% 201.89/33.58  | | End of split
% 201.89/33.58  | | 
% 201.89/33.58  | End of split
% 201.89/33.58  | 
% 201.89/33.58  End of proof
% 201.89/33.58  
% 201.89/33.58  Sub-proof #301 shows that the following formulas are inconsistent:
% 201.89/33.58  ----------------------------------------------------------------
% 201.89/33.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.58    (2)  op(e3, all_6_1) = e1
% 201.89/33.58    (3)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 201.89/33.58    (4)  op(e1, e3) = all_52_5
% 201.89/33.58    (5)  all_56_8 = all_52_5
% 201.89/33.58    (6)   ~ (all_14_1 = all_6_2)
% 201.89/33.58    (7)   ~ (all_52_5 = e3)
% 201.89/33.58    (8)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.89/33.58    (9)   ~ (all_52_5 = all_6_2)
% 201.89/33.58    (10)   ~ (all_52_9 = all_6_2)
% 201.89/33.58    (11)  op(e3, e0) = all_14_1
% 201.89/33.58    (12)  all_58_6 = all_52_5
% 201.89/33.58    (13)  op(e3, e2) = all_52_9
% 201.89/33.58    (14)  all_6_2 = e1
% 201.89/33.58    (15)  op(all_6_2, e3) = all_6_1
% 201.89/33.58  
% 201.89/33.58  Begin of proof
% 201.89/33.58  | 
% 201.89/33.58  | REDUCE: (9), (14) imply:
% 201.89/33.59  |   (16)   ~ (all_52_5 = e1)
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (10), (14) imply:
% 201.89/33.59  |   (17)   ~ (all_52_9 = e1)
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (6), (14) imply:
% 201.89/33.59  |   (18)   ~ (all_14_1 = e1)
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (14), (15) imply:
% 201.89/33.59  |   (19)  op(e1, e3) = all_6_1
% 201.89/33.59  | 
% 201.89/33.59  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 201.89/33.59  |              with (4), (19) gives:
% 201.89/33.59  |   (20)  all_52_5 = all_6_1
% 201.89/33.59  | 
% 201.89/33.59  | COMBINE_EQS: (5), (20) imply:
% 201.89/33.59  |   (21)  all_56_8 = all_6_1
% 201.89/33.59  | 
% 201.89/33.59  | COMBINE_EQS: (12), (20) imply:
% 201.89/33.59  |   (22)  all_58_6 = all_6_1
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (7), (20) imply:
% 201.89/33.59  |   (23)   ~ (all_6_1 = e3)
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (16), (20) imply:
% 201.89/33.59  |   (24)   ~ (all_6_1 = e1)
% 201.89/33.59  | 
% 201.89/33.59  | BETA: splitting (8) gives:
% 201.89/33.59  | 
% 201.89/33.59  | Case 1:
% 201.89/33.59  | | 
% 201.89/33.59  | |   (25)  all_56_8 = e3
% 201.89/33.59  | | 
% 201.89/33.59  | | REF_CLOSE: (21), (23), (25) are inconsistent by sub-proof #1101.
% 201.89/33.59  | | 
% 201.89/33.59  | Case 2:
% 201.89/33.59  | | 
% 201.89/33.59  | |   (26)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 201.89/33.59  | | 
% 201.89/33.59  | | BETA: splitting (3) gives:
% 201.89/33.59  | | 
% 201.89/33.59  | | Case 1:
% 201.89/33.59  | | | 
% 201.89/33.59  | | |   (27)  all_58_6 = e2
% 201.89/33.59  | | | 
% 201.89/33.59  | | | COMBINE_EQS: (22), (27) imply:
% 201.89/33.59  | | |   (28)  all_6_1 = e2
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REDUCE: (2), (28) imply:
% 201.89/33.59  | | |   (29)  op(e3, e2) = e1
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REF_CLOSE: (1), (13), (17), (29) are inconsistent by sub-proof #309.
% 201.89/33.59  | | | 
% 201.89/33.59  | | Case 2:
% 201.89/33.59  | | | 
% 201.89/33.59  | | |   (30)   ~ (all_58_6 = e2)
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REDUCE: (22), (30) imply:
% 201.89/33.59  | | |   (31)   ~ (all_6_1 = e2)
% 201.89/33.59  | | | 
% 201.89/33.59  | | | BETA: splitting (26) gives:
% 201.89/33.59  | | | 
% 201.89/33.59  | | | Case 1:
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | |   (32)  all_56_8 = e2
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | | REF_CLOSE: (21), (31), (32) are inconsistent by sub-proof #1321.
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | Case 2:
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | |   (33)  all_56_8 = e1 | all_56_8 = e0
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | | BETA: splitting (33) gives:
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | | Case 1:
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | |   (34)  all_56_8 = e1
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | REF_CLOSE: (21), (24), (34) are inconsistent by sub-proof #1320.
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | Case 2:
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | |   (35)  all_56_8 = e0
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | COMBINE_EQS: (21), (35) imply:
% 201.89/33.59  | | | | |   (36)  all_6_1 = e0
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | SIMP: (36) implies:
% 201.89/33.59  | | | | |   (37)  all_6_1 = e0
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | REDUCE: (2), (37) imply:
% 201.89/33.59  | | | | |   (38)  op(e3, e0) = e1
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | GROUND_INST: instantiating (1) with all_14_1, e1, e0, e3, simplifying
% 201.89/33.59  | | | | |              with (11), (38) gives:
% 201.89/33.59  | | | | |   (39)  all_14_1 = e1
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | REDUCE: (18), (39) imply:
% 201.89/33.59  | | | | |   (40)  $false
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | | CLOSE: (40) is inconsistent.
% 201.89/33.59  | | | | | 
% 201.89/33.59  | | | | End of split
% 201.89/33.59  | | | | 
% 201.89/33.59  | | | End of split
% 201.89/33.59  | | | 
% 201.89/33.59  | | End of split
% 201.89/33.59  | | 
% 201.89/33.59  | End of split
% 201.89/33.59  | 
% 201.89/33.59  End of proof
% 201.89/33.59  
% 201.89/33.59  Sub-proof #302 shows that the following formulas are inconsistent:
% 201.89/33.59  ----------------------------------------------------------------
% 201.89/33.59    (1)   ~ (e3 = e1)
% 201.89/33.59    (2)  op(all_52_3, all_52_3) = all_52_2
% 201.89/33.59    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.59    (4)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 201.89/33.59    (5)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.59    (6)  all_58_0 = all_6_2
% 201.89/33.59    (7)  op(e3, all_6_1) = e1
% 201.89/33.59    (8)  op(all_52_5, all_52_5) = all_52_4
% 201.89/33.59    (9)  op(e2, e2) = all_4_2
% 201.89/33.59    (10)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.59    (11)   ~ (all_52_7 = all_6_2)
% 201.89/33.59    (12)  op(e0, e0) = all_14_2
% 201.89/33.59    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.59    (14)  all_58_12 = all_52_7
% 201.89/33.59    (15)   ~ (all_52_7 = all_14_2)
% 201.89/33.59    (16)  all_58_2 = all_52_3
% 201.89/33.59    (17)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.59    (18)   ~ (all_52_5 = all_10_2)
% 201.89/33.59    (19)  op(e3, e3) = all_6_2
% 201.89/33.59    (20)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.59    (21)  all_58_6 = all_52_5
% 201.89/33.59    (22)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.59    (23)  op(e1, e1) = all_10_2
% 201.89/33.59    (24)   ~ (all_52_3 = all_4_2)
% 201.89/33.59    (25)  op(all_6_2, e3) = all_6_1
% 201.89/33.59  
% 201.89/33.59  Begin of proof
% 201.89/33.59  | 
% 201.89/33.59  | ALPHA: (4) implies:
% 201.89/33.59  |   (26)  all_52_6 = e0
% 201.89/33.59  |   (27)  all_52_4 = e1
% 201.89/33.59  |   (28)  all_52_2 = e2
% 201.89/33.59  |   (29)  all_52_0 = e3
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (2), (28) imply:
% 201.89/33.59  |   (30)  op(all_52_3, all_52_3) = e2
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (8), (27) imply:
% 201.89/33.59  |   (31)  op(all_52_5, all_52_5) = e1
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (5), (26) imply:
% 201.89/33.59  |   (32)  op(all_52_7, all_52_7) = e0
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (10), (29) imply:
% 201.89/33.59  |   (33)  op(all_6_2, all_6_2) = e3
% 201.89/33.59  | 
% 201.89/33.59  | BETA: splitting (22) gives:
% 201.89/33.59  | 
% 201.89/33.59  | Case 1:
% 201.89/33.59  | | 
% 201.89/33.59  | |   (34)  all_58_12 = e3
% 201.89/33.59  | | 
% 201.89/33.59  | | COMBINE_EQS: (14), (34) imply:
% 201.89/33.59  | |   (35)  all_52_7 = e3
% 201.89/33.59  | | 
% 201.89/33.59  | | REF_CLOSE: (3), (6), (9), (11), (12), (13), (14), (15), (16), (17), (18),
% 201.89/33.59  | |            (19), (21), (22), (23), (24), (30), (31), (32), (33), (35) are
% 201.89/33.59  | |            inconsistent by sub-proof #1361.
% 201.89/33.59  | | 
% 201.89/33.59  | Case 2:
% 201.89/33.59  | | 
% 201.89/33.59  | |   (36)   ~ (all_58_12 = e3)
% 201.89/33.59  | | 
% 201.89/33.59  | | REDUCE: (14), (36) imply:
% 201.89/33.59  | |   (37)   ~ (all_52_7 = e3)
% 201.89/33.59  | | 
% 201.89/33.59  | | BETA: splitting (20) gives:
% 201.89/33.59  | | 
% 201.89/33.59  | | Case 1:
% 201.89/33.59  | | | 
% 201.89/33.59  | | |   (38)  all_58_0 = e3
% 201.89/33.59  | | | 
% 201.89/33.59  | | | COMBINE_EQS: (6), (38) imply:
% 201.89/33.59  | | |   (39)  all_6_2 = e3
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REDUCE: (25), (39) imply:
% 201.89/33.59  | | |   (40)  op(e3, e3) = all_6_1
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REDUCE: (19), (39) imply:
% 201.89/33.59  | | |   (41)  op(e3, e3) = e3
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REF_CLOSE: (1), (3), (7), (40), (41) are inconsistent by sub-proof #311.
% 201.89/33.59  | | | 
% 201.89/33.59  | | Case 2:
% 201.89/33.59  | | | 
% 201.89/33.59  | | |   (42)   ~ (all_58_0 = e3)
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REDUCE: (6), (42) imply:
% 201.89/33.59  | | |   (43)   ~ (all_6_2 = e3)
% 201.89/33.59  | | | 
% 201.89/33.59  | | | REF_CLOSE: (3), (6), (9), (13), (14), (16), (17), (18), (19), (21), (23),
% 201.89/33.59  | | |            (24), (30), (31), (33), (37), (43) are inconsistent by
% 201.89/33.59  | | |            sub-proof #1363.
% 201.89/33.59  | | | 
% 201.89/33.59  | | End of split
% 201.89/33.59  | | 
% 201.89/33.59  | End of split
% 201.89/33.59  | 
% 201.89/33.59  End of proof
% 201.89/33.59  
% 201.89/33.59  Sub-proof #303 shows that the following formulas are inconsistent:
% 201.89/33.59  ----------------------------------------------------------------
% 201.89/33.59    (1)   ~ (all_52_15 = all_52_23)
% 201.89/33.59    (2)   ~ (all_52_25 = all_52_27)
% 201.89/33.59    (3)  all_58_14 = all_52_23
% 201.89/33.59    (4)   ~ (e3 = e1)
% 201.89/33.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.59    (6)  all_58_1 = all_52_9
% 201.89/33.59    (7)   ~ (e3 = e0)
% 201.89/33.59    (8)  op(e2, e3) = all_52_3
% 201.89/33.59    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.59    (10)  op(e0, e2) = all_52_15
% 201.89/33.59    (11)   ~ (all_52_7 = all_52_15)
% 201.89/33.59    (12)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.59    (13)   ~ (all_52_17 = all_52_25)
% 201.89/33.59    (14)   ~ (all_52_3 = all_6_2)
% 201.89/33.59    (15)  all_58_0 = all_6_2
% 201.89/33.59    (16)  all_56_4 = all_52_3
% 201.89/33.59    (17)  op(e3, all_6_1) = e1
% 201.89/33.59    (18)   ~ (all_52_17 = all_10_2)
% 201.89/33.59    (19)  op(e3, e0) = all_52_25
% 201.89/33.59    (20)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.59    (21)  op(all_52_19, all_52_19) = all_52_18
% 201.89/33.59    (22)  all_58_13 = all_52_15
% 201.89/33.59    (23)  op(all_10_2, all_10_2) = all_52_20
% 201.89/33.59    (24)  all_58_9 = all_52_25
% 201.89/33.59    (25)  op(all_52_27, all_52_27) = all_52_26
% 201.89/33.59    (26)  op(e1, e3) = all_52_5
% 201.89/33.59    (27)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.89/33.59    (28)  op(e2, e2) = all_4_2
% 201.89/33.59    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.59    (30)   ~ (all_4_1 = e3)
% 201.89/33.59    (31)  all_58_11 = all_52_29
% 201.89/33.59    (32)   ~ (all_52_9 = all_52_15)
% 201.89/33.59    (33)   ~ (all_52_3 = all_52_27)
% 201.89/33.59    (34)  op(all_10_2, e1) = all_10_1
% 201.89/33.59    (35)  all_46_2 = all_6_2
% 201.89/33.59    (36)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.59    (37)   ~ (all_52_7 = all_6_2)
% 201.89/33.59    (38)   ~ (all_52_15 = e0)
% 201.89/33.59    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.59    (40)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.89/33.59    (41)  all_58_15 = e0
% 201.89/33.59    (42)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.89/33.59    (43)   ~ (all_52_25 = e0)
% 201.89/33.59    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.59    (45)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.59    (46)   ~ (e2 = e1)
% 201.89/33.59    (47)   ~ (all_52_13 = all_10_2)
% 201.89/33.59    (48)  op(e0, e0) = e0
% 201.89/33.59    (49)  all_58_10 = all_52_27
% 201.89/33.59    (50)  op(all_52_9, all_52_9) = all_52_8
% 201.89/33.59    (51)   ~ (all_52_19 = all_52_23)
% 201.89/33.59    (52)   ~ (all_52_25 = all_52_29)
% 201.89/33.59    (53)   ~ (all_52_29 = all_10_2)
% 201.89/33.59    (54)  all_58_7 = all_52_13
% 201.89/33.59    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.59    (56)   ~ (all_52_5 = all_52_7)
% 201.89/33.59    (57)  all_58_12 = all_52_7
% 201.89/33.59    (58)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.59    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.59    (60)  all_58_2 = all_52_3
% 201.89/33.59    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.89/33.59    (62)  all_56_2 = all_52_17
% 201.89/33.59    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.59    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.59    (65)  all_56_7 = all_52_27
% 201.89/33.59    (66)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.59    (67)   ~ (e2 = e0)
% 201.89/33.59    (68)  op(all_4_2, e2) = all_4_1
% 201.89/33.59    (69)   ~ (all_52_5 = all_52_29)
% 201.89/33.59    (70)   ~ (all_52_29 = e0)
% 201.89/33.59    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.59    (72)  all_56_6 = all_52_19
% 201.89/33.59    (73)   ~ (all_52_19 = all_52_27)
% 201.89/33.59    (74)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.59    (75)   ~ (all_52_13 = all_4_2)
% 201.89/33.59    (76)  op(e3, e1) = all_52_17
% 201.89/33.59    (77)  op(e0, e3) = all_52_7
% 201.89/33.59    (78)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.59    (79)   ~ (all_52_9 = all_52_25)
% 201.89/33.59    (80)   ~ (all_52_19 = all_10_2)
% 201.89/33.59    (81)  op(all_52_23, all_52_23) = all_52_22
% 201.89/33.59    (82)  all_58_8 = all_10_2
% 201.89/33.59    (83)   ~ (all_52_23 = e0)
% 201.89/33.59    (84)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.59    (85)  all_56_12 = all_52_7
% 201.89/33.59    (86)  op(all_52_17, all_52_17) = all_52_16
% 201.89/33.59    (87)   ~ (all_52_25 = all_6_2)
% 201.89/33.59    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.59    (89)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.89/33.59    (90)   ~ (all_52_9 = all_6_2)
% 201.89/33.59    (91)  op(e3, e3) = all_6_2
% 201.89/33.59    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.59    (93)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.59    (94)  all_56_14 = all_52_23
% 201.89/33.59    (95)  op(all_4_2, all_4_2) = all_52_10
% 201.89/33.59    (96)  all_56_3 = all_52_25
% 201.89/33.59    (97)   ~ (all_52_3 = all_52_7)
% 201.89/33.59    (98)  all_58_5 = all_52_19
% 201.89/33.59    (99)  all_56_1 = all_52_9
% 201.89/33.59    (100)   ~ (all_52_15 = all_4_2)
% 201.89/33.59    (101)  all_58_6 = all_52_5
% 201.89/33.59    (102)  op(e3, e2) = all_52_9
% 201.89/33.59    (103)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.59    (104)   ~ (all_52_17 = all_6_2)
% 201.89/33.59    (105)   ~ (e1 = e0)
% 201.89/33.59    (106)   ~ (e3 = e2)
% 201.89/33.59    (107)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.59    (108)   ~ (all_52_9 = all_52_17)
% 201.89/33.59    (109)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.59    (110)  all_46_1 = all_6_1
% 201.89/33.59    (111)  op(all_52_13, all_52_13) = all_52_12
% 201.89/33.59    (112)  op(e1, e1) = all_10_2
% 201.89/33.59    (113)   ~ (all_52_23 = all_10_2)
% 201.89/33.59    (114)   ~ (all_52_7 = all_52_23)
% 201.89/33.59    (115)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 201.89/33.59           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 201.89/33.59    (116)  all_58_3 = all_4_2
% 201.89/33.59    (117)  all_56_13 = all_52_15
% 201.89/33.59    (118)   ~ (all_52_3 = all_4_2)
% 201.89/33.59    (119)   ~ (all_52_19 = all_4_2)
% 201.89/33.59    (120)   ~ (all_52_17 = all_52_23)
% 201.89/33.59    (121)  op(all_6_2, e3) = all_6_1
% 201.89/33.59    (122)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.59    (123)   ~ (all_52_13 = all_52_29)
% 201.89/33.59    (124)  all_58_4 = all_52_17
% 201.89/33.59    (125)   ~ (all_52_7 = e0)
% 201.89/33.59    (126)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.59  
% 201.89/33.59  Begin of proof
% 201.89/33.59  | 
% 201.89/33.59  | BETA: splitting (115) gives:
% 201.89/33.59  | 
% 201.89/33.59  | Case 1:
% 201.89/33.59  | | 
% 201.89/33.59  | |   (127)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 201.89/33.59  | | 
% 201.89/33.59  | | ALPHA: (127) implies:
% 201.89/33.59  | |   (128)  all_52_22 = e0
% 201.89/33.59  | |   (129)  all_52_20 = e1
% 201.89/33.59  | |   (130)  all_52_18 = e2
% 201.89/33.59  | |   (131)  all_52_16 = e3
% 201.89/33.59  | | 
% 201.89/33.59  | | REDUCE: (86), (131) imply:
% 201.89/33.59  | |   (132)  op(all_52_17, all_52_17) = e3
% 201.89/33.59  | | 
% 201.89/33.59  | | REDUCE: (21), (130) imply:
% 201.89/33.59  | |   (133)  op(all_52_19, all_52_19) = e2
% 201.89/33.59  | | 
% 201.89/33.59  | | REDUCE: (81), (128) imply:
% 201.89/33.59  | |   (134)  op(all_52_23, all_52_23) = e0
% 201.89/33.59  | | 
% 201.89/33.59  | | REDUCE: (23), (129) imply:
% 201.89/33.59  | |   (135)  op(all_10_2, all_10_2) = e1
% 201.89/33.59  | | 
% 201.89/33.59  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (15),
% 201.89/33.59  | |            (17), (18), (20), (22), (24), (25), (27), (28), (30), (31), (34),
% 201.89/33.59  | |            (37), (39), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 201.89/33.59  | |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 201.89/33.59  | |            (62), (63), (65), (67), (68), (71), (72), (73), (75), (76), (77),
% 201.89/33.59  | |            (78), (79), (80), (82), (83), (84), (85), (87), (88), (90), (91),
% 201.89/33.59  | |            (92), (93), (94), (95), (96), (97), (98), (99), (101), (102),
% 201.89/33.59  | |            (103), (104), (106), (107), (108), (109), (111), (112), (113),
% 201.89/33.59  | |            (114), (116), (117), (119), (120), (121), (123), (124), (125),
% 201.89/33.59  | |            (126), (132), (133), (134), (135) are inconsistent by sub-proof
% 201.89/33.59  | |            #312.
% 201.89/33.59  | | 
% 201.89/33.59  | Case 2:
% 201.89/33.59  | | 
% 201.89/33.59  | |   (136)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.89/33.59  | | 
% 201.89/33.59  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 201.89/33.59  | |            (16), (17), (18), (19), (20), (22), (24), (25), (26), (28), (29),
% 201.89/33.59  | |            (31), (32), (33), (35), (36), (37), (38), (40), (41), (42), (43),
% 201.89/33.59  | |            (44), (46), (49), (52), (57), (60), (64), (65), (66), (67), (69),
% 201.89/33.59  | |            (70), (71), (74), (81), (83), (84), (85), (87), (88), (89), (90),
% 201.89/33.59  | |            (91), (92), (93), (96), (100), (101), (102), (103), (105), (106),
% 201.89/33.59  | |            (110), (112), (113), (114), (117), (118), (121), (122), (124),
% 201.89/33.59  | |            (125), (126), (136) are inconsistent by sub-proof #304.
% 201.89/33.59  | | 
% 201.89/33.59  | End of split
% 201.89/33.59  | 
% 201.89/33.59  End of proof
% 201.89/33.59  
% 201.89/33.59  Sub-proof #304 shows that the following formulas are inconsistent:
% 201.89/33.59  ----------------------------------------------------------------
% 201.89/33.59    (1)   ~ (all_52_25 = all_52_27)
% 201.89/33.59    (2)  all_58_14 = all_52_23
% 201.89/33.59    (3)   ~ (e3 = e1)
% 201.89/33.59    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.59    (5)  all_58_1 = all_52_9
% 201.89/33.59    (6)   ~ (e3 = e0)
% 201.89/33.59    (7)  op(e2, e3) = all_52_3
% 201.89/33.59    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.59    (9)   ~ (all_52_7 = all_52_15)
% 201.89/33.59    (10)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.59    (11)   ~ (all_52_3 = all_6_2)
% 201.89/33.59    (12)  all_58_0 = all_6_2
% 201.89/33.59    (13)  all_56_4 = all_52_3
% 201.89/33.59    (14)  op(e3, all_6_1) = e1
% 201.89/33.59    (15)   ~ (all_52_17 = all_10_2)
% 201.89/33.59    (16)  op(e3, e0) = all_52_25
% 201.89/33.59    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.59    (18)  all_58_13 = all_52_15
% 201.89/33.59    (19)  all_58_9 = all_52_25
% 201.89/33.59    (20)  op(all_52_27, all_52_27) = all_52_26
% 201.89/33.59    (21)  op(e1, e3) = all_52_5
% 201.89/33.59    (22)  op(e2, e2) = all_4_2
% 201.89/33.59    (23)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.59    (24)  all_58_11 = all_52_29
% 201.89/33.59    (25)   ~ (all_52_9 = all_52_15)
% 201.89/33.59    (26)   ~ (all_52_3 = all_52_27)
% 201.89/33.59    (27)  all_46_2 = all_6_2
% 201.89/33.59    (28)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.59    (29)   ~ (all_52_7 = all_6_2)
% 201.89/33.59    (30)   ~ (all_52_15 = e0)
% 201.89/33.59    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.89/33.59    (32)  all_58_15 = e0
% 201.89/33.59    (33)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.89/33.59    (34)   ~ (all_52_25 = e0)
% 201.89/33.59    (35)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.59    (36)   ~ (e2 = e1)
% 201.89/33.59    (37)  all_58_10 = all_52_27
% 201.89/33.59    (38)   ~ (all_52_25 = all_52_29)
% 201.89/33.59    (39)  all_58_12 = all_52_7
% 201.89/33.59    (40)  all_58_2 = all_52_3
% 201.89/33.59    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.59    (42)  all_56_7 = all_52_27
% 201.89/33.59    (43)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.59    (44)   ~ (e2 = e0)
% 201.89/33.59    (45)   ~ (all_52_5 = all_52_29)
% 201.89/33.59    (46)   ~ (all_52_29 = e0)
% 201.89/33.59    (47)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.59    (48)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.59    (49)  op(all_52_23, all_52_23) = all_52_22
% 201.89/33.59    (50)   ~ (all_52_23 = e0)
% 201.89/33.59    (51)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.59    (52)  all_56_12 = all_52_7
% 201.89/33.59    (53)   ~ (all_52_25 = all_6_2)
% 201.89/33.59    (54)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.59    (55)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.89/33.59    (56)   ~ (all_52_9 = all_6_2)
% 201.89/33.59    (57)  op(e3, e3) = all_6_2
% 201.89/33.59    (58)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.59    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.59    (60)  all_56_3 = all_52_25
% 201.89/33.59    (61)   ~ (all_52_15 = all_4_2)
% 201.89/33.59    (62)  all_58_6 = all_52_5
% 201.89/33.59    (63)  op(e3, e2) = all_52_9
% 201.89/33.59    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.59    (65)   ~ (e1 = e0)
% 201.89/33.59    (66)   ~ (e3 = e2)
% 201.89/33.59    (67)  all_46_1 = all_6_1
% 201.89/33.59    (68)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 201.89/33.59    (69)  op(e1, e1) = all_10_2
% 201.89/33.59    (70)   ~ (all_52_23 = all_10_2)
% 201.89/33.59    (71)   ~ (all_52_7 = all_52_23)
% 201.89/33.59    (72)  all_56_13 = all_52_15
% 201.89/33.59    (73)   ~ (all_52_3 = all_4_2)
% 201.89/33.59    (74)  op(all_6_2, e3) = all_6_1
% 201.89/33.59    (75)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.59    (76)  all_58_4 = all_52_17
% 201.89/33.59    (77)   ~ (all_52_7 = e0)
% 201.89/33.59    (78)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.59  
% 201.89/33.59  Begin of proof
% 201.89/33.59  | 
% 201.89/33.59  | ALPHA: (68) implies:
% 201.89/33.59  |   (79)  all_52_28 = e1
% 201.89/33.59  |   (80)  all_52_26 = e2
% 201.89/33.59  |   (81)  all_52_24 = e3
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (78), (81) imply:
% 201.89/33.59  |   (82)  op(all_52_25, all_52_25) = e3
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (20), (80) imply:
% 201.89/33.59  |   (83)  op(all_52_27, all_52_27) = e2
% 201.89/33.59  | 
% 201.89/33.59  | REDUCE: (51), (79) imply:
% 201.89/33.59  |   (84)  op(all_52_29, all_52_29) = e1
% 201.89/33.59  | 
% 201.89/33.59  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 201.89/33.59  |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 201.89/33.59  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 201.89/33.59  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 201.89/33.59  |            (47), (48), (49), (50), (52), (53), (54), (55), (56), (57), (58),
% 201.89/33.59  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (69), (70),
% 201.89/33.59  |            (71), (72), (73), (74), (75), (76), (77), (82), (83), (84) are
% 201.89/33.59  |            inconsistent by sub-proof #305.
% 201.89/33.59  | 
% 201.89/33.59  End of proof
% 201.89/33.59  
% 201.89/33.59  Sub-proof #305 shows that the following formulas are inconsistent:
% 201.89/33.59  ----------------------------------------------------------------
% 201.89/33.59    (1)   ~ (all_52_25 = all_52_27)
% 201.89/33.59    (2)  all_58_14 = all_52_23
% 201.89/33.59    (3)   ~ (e3 = e1)
% 201.89/33.59    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.59    (5)  all_58_1 = all_52_9
% 201.89/33.59    (6)   ~ (e3 = e0)
% 201.89/33.59    (7)  op(e2, e3) = all_52_3
% 201.89/33.59    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.59    (9)   ~ (all_52_7 = all_52_15)
% 201.89/33.59    (10)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.59    (11)   ~ (all_52_3 = all_6_2)
% 201.89/33.59    (12)  all_58_0 = all_6_2
% 201.89/33.59    (13)  all_56_4 = all_52_3
% 201.89/33.59    (14)  op(e3, all_6_1) = e1
% 201.89/33.59    (15)   ~ (all_52_17 = all_10_2)
% 201.89/33.59    (16)  op(e3, e0) = all_52_25
% 201.89/33.59    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.59    (18)  all_58_13 = all_52_15
% 201.89/33.59    (19)  all_58_9 = all_52_25
% 201.89/33.59    (20)  op(e1, e3) = all_52_5
% 201.89/33.59    (21)  op(e2, e2) = all_4_2
% 201.89/33.59    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.59    (23)  all_58_11 = all_52_29
% 201.89/33.59    (24)   ~ (all_52_9 = all_52_15)
% 201.89/33.59    (25)   ~ (all_52_3 = all_52_27)
% 201.89/33.59    (26)  all_46_2 = all_6_2
% 201.89/33.59    (27)  op(all_6_2, all_6_2) = all_52_0
% 201.89/33.59    (28)   ~ (all_52_7 = all_6_2)
% 201.89/33.59    (29)  op(all_52_29, all_52_29) = e1
% 201.89/33.59    (30)   ~ (all_52_15 = e0)
% 201.89/33.59    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 201.89/33.59    (32)  all_58_15 = e0
% 201.89/33.59    (33)   ~ (all_46_1 = e0) |  ~ (all_46_2 = e2)
% 201.89/33.59    (34)   ~ (all_52_25 = e0)
% 201.89/33.59    (35)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.59    (36)   ~ (e2 = e1)
% 201.89/33.59    (37)  all_58_10 = all_52_27
% 201.89/33.59    (38)   ~ (all_52_25 = all_52_29)
% 201.89/33.59    (39)  all_58_12 = all_52_7
% 201.89/33.59    (40)  all_58_2 = all_52_3
% 201.89/33.59    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 201.89/33.59    (42)  all_56_7 = all_52_27
% 201.89/33.59    (43)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.59    (44)   ~ (e2 = e0)
% 201.89/33.59    (45)  op(all_52_25, all_52_25) = e3
% 201.89/33.59    (46)   ~ (all_52_5 = all_52_29)
% 201.89/33.59    (47)   ~ (all_52_29 = e0)
% 201.89/33.59    (48)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.59    (49)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.59    (50)  op(all_52_27, all_52_27) = e2
% 201.89/33.59    (51)  op(all_52_23, all_52_23) = all_52_22
% 201.89/33.59    (52)   ~ (all_52_23 = e0)
% 201.89/33.59    (53)  all_56_12 = all_52_7
% 201.89/33.59    (54)   ~ (all_52_25 = all_6_2)
% 201.89/33.59    (55)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.59    (56)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.89/33.59    (57)   ~ (all_52_9 = all_6_2)
% 201.89/33.59    (58)  op(e3, e3) = all_6_2
% 201.89/33.59    (59)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.59    (60)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.59    (61)  all_56_3 = all_52_25
% 201.89/33.59    (62)   ~ (all_52_15 = all_4_2)
% 201.89/33.59    (63)  all_58_6 = all_52_5
% 201.89/33.59    (64)  op(e3, e2) = all_52_9
% 201.89/33.59    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.59    (66)   ~ (e1 = e0)
% 201.89/33.59    (67)   ~ (e3 = e2)
% 201.89/33.59    (68)  all_46_1 = all_6_1
% 201.89/33.59    (69)  op(e1, e1) = all_10_2
% 201.89/33.60    (70)   ~ (all_52_23 = all_10_2)
% 201.89/33.60    (71)   ~ (all_52_7 = all_52_23)
% 201.89/33.60    (72)  all_56_13 = all_52_15
% 201.89/33.60    (73)   ~ (all_52_3 = all_4_2)
% 201.89/33.60    (74)  op(all_6_2, e3) = all_6_1
% 201.89/33.60    (75)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.60    (76)  all_58_4 = all_52_17
% 201.89/33.60    (77)   ~ (all_52_7 = e0)
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | BETA: splitting (35) gives:
% 201.89/33.60  | 
% 201.89/33.60  | Case 1:
% 201.89/33.60  | | 
% 201.89/33.60  | |   (78)  all_56_13 = e3
% 201.89/33.60  | | 
% 201.89/33.60  | | COMBINE_EQS: (72), (78) imply:
% 201.89/33.60  | |   (79)  all_52_15 = e3
% 201.89/33.60  | | 
% 201.89/33.60  | | SIMP: (79) implies:
% 201.89/33.60  | |   (80)  all_52_15 = e3
% 201.89/33.60  | | 
% 201.89/33.60  | | REDUCE: (9), (80) imply:
% 201.89/33.60  | |   (81)   ~ (all_52_7 = e3)
% 201.89/33.60  | | 
% 201.89/33.60  | | REDUCE: (24), (80) imply:
% 201.89/33.60  | |   (82)   ~ (all_52_9 = e3)
% 201.89/33.60  | | 
% 201.89/33.60  | | REDUCE: (62), (80) imply:
% 201.89/33.60  | |   (83)   ~ (all_4_2 = e3)
% 201.89/33.60  | | 
% 201.89/33.60  | | SIMP: (83) implies:
% 201.89/33.60  | |   (84)   ~ (all_4_2 = e3)
% 201.89/33.60  | | 
% 201.89/33.60  | | BETA: splitting (8) gives:
% 201.89/33.60  | | 
% 201.89/33.60  | | Case 1:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (85)  all_56_12 = e3
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REF_CLOSE: (53), (81), (85) are inconsistent by sub-proof #1383.
% 201.89/33.60  | | | 
% 201.89/33.60  | | Case 2:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (86)   ~ (all_56_12 = e3)
% 201.89/33.60  | | |   (87)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.60  | | | 
% 201.89/33.60  | | | BETA: splitting (48) gives:
% 201.89/33.60  | | | 
% 201.89/33.60  | | | Case 1:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | |   (88)  all_58_12 = e1
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | COMBINE_EQS: (39), (88) imply:
% 201.89/33.60  | | | |   (89)  all_52_7 = e1
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | SIMP: (89) implies:
% 201.89/33.60  | | | |   (90)  all_52_7 = e1
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (28), (90) imply:
% 201.89/33.60  | | | |   (91)   ~ (all_6_2 = e1)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | SIMP: (91) implies:
% 201.89/33.60  | | | |   (92)   ~ (all_6_2 = e1)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | BETA: splitting (55) gives:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | Case 1:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (93)  all_56_3 = e3
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | COMBINE_EQS: (61), (93) imply:
% 201.89/33.60  | | | | |   (94)  all_52_25 = e3
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | REF_CLOSE: (4), (45), (54), (58), (94) are inconsistent by sub-proof
% 201.89/33.60  | | | | |            #1246.
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | Case 2:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (95)   ~ (all_56_3 = e3)
% 201.89/33.60  | | | | |   (96)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | REDUCE: (61), (95) imply:
% 201.89/33.60  | | | | |   (97)   ~ (all_52_25 = e3)
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | BETA: splitting (60) gives:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | Case 1:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (98)  all_58_0 = e3
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | COMBINE_EQS: (12), (98) imply:
% 201.89/33.60  | | | | | |   (99)  all_6_2 = e3
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REF_CLOSE: (3), (4), (14), (58), (74), (99) are inconsistent by
% 201.89/33.60  | | | | | |            sub-proof #310.
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | Case 2:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (100)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | BETA: splitting (100) gives:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | Case 1:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | |   (101)  all_58_1 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | COMBINE_EQS: (5), (101) imply:
% 201.89/33.60  | | | | | | |   (102)  all_52_9 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | REDUCE: (82), (102) imply:
% 201.89/33.60  | | | | | | |   (103)  $false
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | CLOSE: (103) is inconsistent.
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | Case 2:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | |   (104)  all_58_4 = e3 | all_58_9 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | BETA: splitting (104) gives:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | Case 1:
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | |   (105)  all_58_4 = e3
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | COMBINE_EQS: (76), (105) imply:
% 201.89/33.60  | | | | | | | |   (106)  all_52_17 = e3
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | SIMP: (106) implies:
% 201.89/33.60  | | | | | | | |   (107)  all_52_17 = e3
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REDUCE: (15), (107) imply:
% 201.89/33.60  | | | | | | | |   (108)   ~ (all_10_2 = e3)
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | SIMP: (108) implies:
% 201.89/33.60  | | | | | | | |   (109)   ~ (all_10_2 = e3)
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REF_CLOSE: (4), (19), (21), (31), (34), (45), (61), (69), (84),
% 201.89/33.60  | | | | | | | |            (96), (109) are inconsistent by sub-proof #824.
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | Case 2:
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | |   (110)  all_58_9 = e3
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REF_CLOSE: (19), (97), (110) are inconsistent by sub-proof
% 201.89/33.60  | | | | | | | |            #1300.
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | End of split
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | End of split
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | End of split
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | End of split
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | Case 2:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | |   (111)   ~ (all_58_12 = e1)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REF_CLOSE: (3), (4), (6), (12), (17), (19), (21), (23), (28), (29),
% 201.89/33.60  | | | |            (32), (34), (37), (38), (39), (40), (41), (42), (45), (46),
% 201.89/33.60  | | | |            (50), (53), (54), (55), (58), (59), (61), (63), (73), (77),
% 201.89/33.60  | | | |            (81), (87), (111) are inconsistent by sub-proof #1222.
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | End of split
% 201.89/33.60  | | | 
% 201.89/33.60  | | End of split
% 201.89/33.60  | | 
% 201.89/33.60  | Case 2:
% 201.89/33.60  | | 
% 201.89/33.60  | |   (112)   ~ (all_56_13 = e3)
% 201.89/33.60  | | 
% 201.89/33.60  | | REDUCE: (72), (112) imply:
% 201.89/33.60  | |   (113)   ~ (all_52_15 = e3)
% 201.89/33.60  | | 
% 201.89/33.60  | | BETA: splitting (65) gives:
% 201.89/33.60  | | 
% 201.89/33.60  | | Case 1:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (114)  all_58_12 = e3
% 201.89/33.60  | | | 
% 201.89/33.60  | | | COMBINE_EQS: (39), (114) imply:
% 201.89/33.60  | | |   (115)  all_52_7 = e3
% 201.89/33.60  | | | 
% 201.89/33.60  | | | SIMP: (115) implies:
% 201.89/33.60  | | |   (116)  all_52_7 = e3
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REDUCE: (28), (116) imply:
% 201.89/33.60  | | |   (117)   ~ (all_6_2 = e3)
% 201.89/33.60  | | | 
% 201.89/33.60  | | | SIMP: (117) implies:
% 201.89/33.60  | | |   (118)   ~ (all_6_2 = e3)
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REDUCE: (10), (116) imply:
% 201.89/33.60  | | |   (119)  op(e3, e3) = all_52_6
% 201.89/33.60  | | | 
% 201.89/33.60  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 201.89/33.60  | | |              with (58), (119) gives:
% 201.89/33.60  | | |   (120)  all_52_6 = all_6_2
% 201.89/33.60  | | | 
% 201.89/33.60  | | | BETA: splitting (17) gives:
% 201.89/33.60  | | | 
% 201.89/33.60  | | | Case 1:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | |   (121)  all_56_7 = e3
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | COMBINE_EQS: (42), (121) imply:
% 201.89/33.60  | | | |   (122)  all_52_27 = e3
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | SIMP: (122) implies:
% 201.89/33.60  | | | |   (123)  all_52_27 = e3
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | COMBINE_EQS: (37), (123) imply:
% 201.89/33.60  | | | |   (124)  all_58_10 = e3
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (25), (123) imply:
% 201.89/33.60  | | | |   (125)   ~ (all_52_3 = e3)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (50), (123) imply:
% 201.89/33.60  | | | |   (126)  op(e3, e3) = e2
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | GROUND_INST: instantiating (4) with all_6_2, e2, e3, e3, simplifying
% 201.89/33.60  | | | |              with (58), (126) gives:
% 201.89/33.60  | | | |   (127)  all_6_2 = e2
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | COMBINE_EQS: (26), (127) imply:
% 201.89/33.60  | | | |   (128)  all_46_2 = e2
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (11), (127) imply:
% 201.89/33.60  | | | |   (129)   ~ (all_52_3 = e2)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (54), (127) imply:
% 201.89/33.60  | | | |   (130)   ~ (all_52_25 = e2)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (118), (127) imply:
% 201.89/33.60  | | | |   (131)   ~ (e3 = e2)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (27), (127) imply:
% 201.89/33.60  | | | |   (132)  op(e2, e2) = all_52_0
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (74), (127) imply:
% 201.89/33.60  | | | |   (133)  op(e2, e3) = all_6_1
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | BETA: splitting (56) gives:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | Case 1:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (134)  all_58_9 = e2
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | REF_CLOSE: (19), (130), (134) are inconsistent by sub-proof #1221.
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | Case 2:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (135)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | BETA: splitting (33) gives:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | Case 1:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (136)   ~ (all_46_2 = e2)
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REDUCE: (128), (136) imply:
% 201.89/33.60  | | | | | |   (137)  $false
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | CLOSE: (137) is inconsistent.
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | Case 2:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (138)   ~ (all_46_1 = e0)
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REDUCE: (68), (138) imply:
% 201.89/33.60  | | | | | |   (139)   ~ (all_6_1 = e0)
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | BETA: splitting (135) gives:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | Case 1:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | |   (140)  all_58_10 = e2
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | REF_CLOSE: (67), (124), (140) are inconsistent by sub-proof #1220.
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | Case 2:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | |   (141)  all_58_11 = e2 | all_58_15 = e2
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | BETA: splitting (141) gives:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | Case 1:
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | |   (142)  all_58_11 = e2
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | COMBINE_EQS: (23), (142) imply:
% 201.89/33.60  | | | | | | | |   (143)  all_52_29 = e2
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | SIMP: (143) implies:
% 201.89/33.60  | | | | | | | |   (144)  all_52_29 = e2
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REDUCE: (29), (144) imply:
% 201.89/33.60  | | | | | | | |   (145)  op(e2, e2) = e1
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_0, e2, e2,
% 201.89/33.60  | | | | | | | |              simplifying with (21), (132) gives:
% 201.89/33.60  | | | | | | | |   (146)  all_52_0 = all_4_2
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | GROUND_INST: instantiating (4) with e1, all_52_0, e2, e2,
% 201.89/33.60  | | | | | | | |              simplifying with (132), (145) gives:
% 201.89/33.60  | | | | | | | |   (147)  all_52_0 = e1
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | GROUND_INST: instantiating (4) with all_52_3, all_6_1, e3, e2,
% 201.89/33.60  | | | | | | | |              simplifying with (7), (133) gives:
% 201.89/33.60  | | | | | | | |   (148)  all_52_3 = all_6_1
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | COMBINE_EQS: (146), (147) imply:
% 201.89/33.60  | | | | | | | |   (149)  all_4_2 = e1
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | SIMP: (149) implies:
% 201.89/33.60  | | | | | | | |   (150)  all_4_2 = e1
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | COMBINE_EQS: (13), (148) imply:
% 201.89/33.60  | | | | | | | |   (151)  all_56_4 = all_6_1
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REDUCE: (73), (148), (150) imply:
% 201.89/33.60  | | | | | | | |   (152)   ~ (all_6_1 = e1)
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REDUCE: (125), (148) imply:
% 201.89/33.60  | | | | | | | |   (153)   ~ (all_6_1 = e3)
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REDUCE: (129), (148) imply:
% 201.89/33.60  | | | | | | | |   (154)   ~ (all_6_1 = e2)
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | BETA: splitting (43) gives:
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | Case 1:
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | |   (155)  all_56_4 = e3
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | | COMBINE_EQS: (151), (155) imply:
% 201.89/33.60  | | | | | | | | |   (156)  all_6_1 = e3
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | | REDUCE: (153), (156) imply:
% 201.89/33.60  | | | | | | | | |   (157)  $false
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | | CLOSE: (157) is inconsistent.
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | Case 2:
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | |   (158)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | | REF_CLOSE: (139), (151), (152), (154), (158) are inconsistent
% 201.89/33.60  | | | | | | | | |            by sub-proof #1216.
% 201.89/33.60  | | | | | | | | | 
% 201.89/33.60  | | | | | | | | End of split
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | Case 2:
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | |   (159)  all_58_15 = e2
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | | REF_CLOSE: (32), (44), (159) are inconsistent by sub-proof
% 201.89/33.60  | | | | | | | |            #1223.
% 201.89/33.60  | | | | | | | | 
% 201.89/33.60  | | | | | | | End of split
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | End of split
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | End of split
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | End of split
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | Case 2:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | |   (160)   ~ (all_56_7 = e3)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (42), (160) imply:
% 201.89/33.60  | | | |   (161)   ~ (all_52_27 = e3)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | BETA: splitting (59) gives:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | Case 1:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (162)  all_58_9 = e3
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | COMBINE_EQS: (19), (162) imply:
% 201.89/33.60  | | | | |   (163)  all_52_25 = e3
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | REF_CLOSE: (4), (45), (54), (58), (163) are inconsistent by sub-proof
% 201.89/33.60  | | | | |            #1246.
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | Case 2:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (164)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | BETA: splitting (164) gives:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | Case 1:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (165)  all_58_10 = e3
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REF_CLOSE: (37), (161), (165) are inconsistent by sub-proof #1301.
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | Case 2:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (166)  all_58_11 = e3 | all_58_15 = e3
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | BETA: splitting (166) gives:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | Case 1:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | |   (167)  all_58_11 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | COMBINE_EQS: (23), (167) imply:
% 201.89/33.60  | | | | | | |   (168)  all_52_29 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | SIMP: (168) implies:
% 201.89/33.60  | | | | | | |   (169)  all_52_29 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | REDUCE: (29), (169) imply:
% 201.89/33.60  | | | | | | |   (170)  op(e3, e3) = e1
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | GROUND_INST: instantiating (4) with all_6_2, e1, e3, e3,
% 201.89/33.60  | | | | | | |              simplifying with (58), (170) gives:
% 201.89/33.60  | | | | | | |   (171)  all_6_2 = e1
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | COMBINE_EQS: (12), (171) imply:
% 201.89/33.60  | | | | | | |   (172)  all_58_0 = e1
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | REDUCE: (57), (171) imply:
% 201.89/33.60  | | | | | | |   (173)   ~ (all_52_9 = e1)
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | REF_CLOSE: (4), (6), (14), (16), (20), (22), (36), (40), (44),
% 201.89/33.60  | | | | | | |            (49), (54), (63), (64), (66), (67), (74), (75), (114),
% 201.89/33.60  | | | | | | |            (171), (172), (173) are inconsistent by sub-proof #306.
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | Case 2:
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | |   (174)  all_58_15 = e3
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | | REF_CLOSE: (6), (32), (174) are inconsistent by sub-proof #1350.
% 201.89/33.60  | | | | | | | 
% 201.89/33.60  | | | | | | End of split
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | End of split
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | End of split
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | End of split
% 201.89/33.60  | | | 
% 201.89/33.60  | | Case 2:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (175)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REF_CLOSE: (1), (2), (3), (4), (6), (12), (18), (19), (21), (23), (29),
% 201.89/33.60  | | |            (31), (32), (34), (37), (38), (39), (40), (41), (45), (46),
% 201.89/33.60  | | |            (50), (51), (52), (54), (55), (58), (59), (61), (63), (69),
% 201.89/33.60  | | |            (70), (71), (73), (113), (175) are inconsistent by sub-proof
% 201.89/33.60  | | |            #1205.
% 201.89/33.60  | | | 
% 201.89/33.60  | | End of split
% 201.89/33.60  | | 
% 201.89/33.60  | End of split
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #306 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (2)   ~ (e3 = e0)
% 201.89/33.60    (3)  op(e3, all_6_1) = e1
% 201.89/33.60    (4)  op(e3, e0) = all_52_25
% 201.89/33.60    (5)  op(e1, e3) = all_52_5
% 201.89/33.60    (6)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.60    (7)   ~ (e2 = e1)
% 201.89/33.60    (8)  all_58_2 = all_52_3
% 201.89/33.60    (9)   ~ (e2 = e0)
% 201.89/33.60    (10)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.60    (11)   ~ (all_52_25 = all_6_2)
% 201.89/33.60    (12)   ~ (all_52_9 = e1)
% 201.89/33.60    (13)  all_58_6 = all_52_5
% 201.89/33.60    (14)  op(e3, e2) = all_52_9
% 201.89/33.60    (15)   ~ (e1 = e0)
% 201.89/33.60    (16)   ~ (e3 = e2)
% 201.89/33.60    (17)  all_6_2 = e1
% 201.89/33.60    (18)  all_58_12 = e3
% 201.89/33.60    (19)  op(all_6_2, e3) = all_6_1
% 201.89/33.60    (20)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.60    (21)  all_58_0 = e1
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (11), (17) imply:
% 201.89/33.60  |   (22)   ~ (all_52_25 = e1)
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (17), (19) imply:
% 201.89/33.60  |   (23)  op(e1, e3) = all_6_1
% 201.89/33.60  | 
% 201.89/33.60  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 201.89/33.60  |            (14), (15), (16), (18), (20), (21), (22), (23) are inconsistent by
% 201.89/33.60  |            sub-proof #307.
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #307 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (2)   ~ (e3 = e0)
% 201.89/33.60    (3)  op(e3, all_6_1) = e1
% 201.89/33.60    (4)  op(e3, e0) = all_52_25
% 201.89/33.60    (5)  op(e1, e3) = all_52_5
% 201.89/33.60    (6)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.60    (7)  op(e1, e3) = all_6_1
% 201.89/33.60    (8)   ~ (e2 = e1)
% 201.89/33.60    (9)  all_58_2 = all_52_3
% 201.89/33.60    (10)   ~ (e2 = e0)
% 201.89/33.60    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.60    (12)   ~ (all_52_25 = e1)
% 201.89/33.60    (13)   ~ (all_52_9 = e1)
% 201.89/33.60    (14)  all_58_6 = all_52_5
% 201.89/33.60    (15)  op(e3, e2) = all_52_9
% 201.89/33.60    (16)   ~ (e1 = e0)
% 201.89/33.60    (17)   ~ (e3 = e2)
% 201.89/33.60    (18)  all_58_12 = e3
% 201.89/33.60    (19)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 201.89/33.60    (20)  all_58_0 = e1
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 201.89/33.60  |              with (5), (7) gives:
% 201.89/33.60  |   (21)  all_52_5 = all_6_1
% 201.89/33.60  | 
% 201.89/33.60  | COMBINE_EQS: (14), (21) imply:
% 201.89/33.60  |   (22)  all_58_6 = all_6_1
% 201.89/33.60  | 
% 201.89/33.60  | BETA: splitting (11) gives:
% 201.89/33.60  | 
% 201.89/33.60  | Case 1:
% 201.89/33.60  | | 
% 201.89/33.60  | |   (23)  all_58_0 = e2
% 201.89/33.60  | | 
% 201.89/33.60  | | REF_CLOSE: (8), (20), (23) are inconsistent by sub-proof #1273.
% 201.89/33.60  | | 
% 201.89/33.60  | Case 2:
% 201.89/33.60  | | 
% 201.89/33.60  | |   (24)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.60  | | 
% 201.89/33.60  | | BETA: splitting (6) gives:
% 201.89/33.60  | | 
% 201.89/33.60  | | Case 1:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (25)  all_58_0 = e0
% 201.89/33.60  | | | 
% 201.89/33.60  | | | COMBINE_EQS: (20), (25) imply:
% 201.89/33.60  | | |   (26)  e1 = e0
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REDUCE: (16), (26) imply:
% 201.89/33.60  | | |   (27)  $false
% 201.89/33.60  | | | 
% 201.89/33.60  | | | CLOSE: (27) is inconsistent.
% 201.89/33.60  | | | 
% 201.89/33.60  | | Case 2:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (28)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 201.89/33.60  | | | 
% 201.89/33.60  | | | BETA: splitting (19) gives:
% 201.89/33.60  | | | 
% 201.89/33.60  | | | Case 1:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | |   (29)  all_58_2 = e2
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | COMBINE_EQS: (9), (29) imply:
% 201.89/33.60  | | | |   (30)  all_52_3 = e2
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | BETA: splitting (28) gives:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | Case 1:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (31)  all_58_2 = e0
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | COMBINE_EQS: (29), (31) imply:
% 201.89/33.60  | | | | |   (32)  e2 = e0
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | REDUCE: (10), (32) imply:
% 201.89/33.60  | | | | |   (33)  $false
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | CLOSE: (33) is inconsistent.
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | Case 2:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | |   (34)  all_58_6 = e0 | all_58_12 = e0
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | BETA: splitting (34) gives:
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | | Case 1:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (35)  all_58_6 = e0
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | COMBINE_EQS: (22), (35) imply:
% 201.89/33.60  | | | | | |   (36)  all_6_1 = e0
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | SIMP: (36) implies:
% 201.89/33.60  | | | | | |   (37)  all_6_1 = e0
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REDUCE: (3), (37) imply:
% 201.89/33.60  | | | | | |   (38)  op(e3, e0) = e1
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | GROUND_INST: instantiating (1) with all_52_25, e1, e0, e3,
% 201.89/33.60  | | | | | |              simplifying with (4), (38) gives:
% 201.89/33.60  | | | | | |   (39)  all_52_25 = e1
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REDUCE: (12), (39) imply:
% 201.89/33.60  | | | | | |   (40)  $false
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | CLOSE: (40) is inconsistent.
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | Case 2:
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | |   (41)  all_58_12 = e0
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | | REF_CLOSE: (2), (18), (41) are inconsistent by sub-proof #1212.
% 201.89/33.60  | | | | | | 
% 201.89/33.60  | | | | | End of split
% 201.89/33.60  | | | | | 
% 201.89/33.60  | | | | End of split
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | Case 2:
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | |   (42)   ~ (all_58_2 = e2)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REDUCE: (9), (42) imply:
% 201.89/33.60  | | | |   (43)   ~ (all_52_3 = e2)
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | | REF_CLOSE: (1), (3), (9), (13), (15), (17), (18), (22), (24), (43) are
% 201.89/33.60  | | | |            inconsistent by sub-proof #308.
% 201.89/33.60  | | | | 
% 201.89/33.60  | | | End of split
% 201.89/33.60  | | | 
% 201.89/33.60  | | End of split
% 201.89/33.60  | | 
% 201.89/33.60  | End of split
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #308 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (2)  op(e3, all_6_1) = e1
% 201.89/33.60    (3)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 201.89/33.60    (4)  all_58_2 = all_52_3
% 201.89/33.60    (5)  all_58_6 = all_6_1
% 201.89/33.60    (6)   ~ (all_52_9 = e1)
% 201.89/33.60    (7)  op(e3, e2) = all_52_9
% 201.89/33.60    (8)   ~ (e3 = e2)
% 201.89/33.60    (9)  all_58_12 = e3
% 201.89/33.60    (10)   ~ (all_52_3 = e2)
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | BETA: splitting (3) gives:
% 201.89/33.60  | 
% 201.89/33.60  | Case 1:
% 201.89/33.60  | | 
% 201.89/33.60  | |   (11)  all_58_2 = e2
% 201.89/33.60  | | 
% 201.89/33.60  | | COMBINE_EQS: (4), (11) imply:
% 201.89/33.60  | |   (12)  all_52_3 = e2
% 201.89/33.60  | | 
% 201.89/33.60  | | REDUCE: (10), (12) imply:
% 201.89/33.60  | |   (13)  $false
% 201.89/33.60  | | 
% 201.89/33.60  | | CLOSE: (13) is inconsistent.
% 201.89/33.60  | | 
% 201.89/33.60  | Case 2:
% 201.89/33.60  | | 
% 201.89/33.60  | |   (14)  all_58_6 = e2 | all_58_12 = e2
% 201.89/33.60  | | 
% 201.89/33.60  | | BETA: splitting (14) gives:
% 201.89/33.60  | | 
% 201.89/33.60  | | Case 1:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (15)  all_58_6 = e2
% 201.89/33.60  | | | 
% 201.89/33.60  | | | COMBINE_EQS: (5), (15) imply:
% 201.89/33.60  | | |   (16)  all_6_1 = e2
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REDUCE: (2), (16) imply:
% 201.89/33.60  | | |   (17)  op(e3, e2) = e1
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REF_CLOSE: (1), (6), (7), (17) are inconsistent by sub-proof #309.
% 201.89/33.60  | | | 
% 201.89/33.60  | | Case 2:
% 201.89/33.60  | | | 
% 201.89/33.60  | | |   (18)  all_58_12 = e2
% 201.89/33.60  | | | 
% 201.89/33.60  | | | COMBINE_EQS: (9), (18) imply:
% 201.89/33.60  | | |   (19)  e3 = e2
% 201.89/33.60  | | | 
% 201.89/33.60  | | | REDUCE: (8), (19) imply:
% 201.89/33.60  | | |   (20)  $false
% 201.89/33.60  | | | 
% 201.89/33.60  | | | CLOSE: (20) is inconsistent.
% 201.89/33.60  | | | 
% 201.89/33.60  | | End of split
% 201.89/33.60  | | 
% 201.89/33.60  | End of split
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #309 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (2)  op(e3, e2) = all_52_9
% 201.89/33.60    (3)  op(e3, e2) = e1
% 201.89/33.60    (4)   ~ (all_52_9 = e1)
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | GROUND_INST: instantiating (1) with all_52_9, e1, e2, e3, simplifying with
% 201.89/33.60  |              (2), (3) gives:
% 201.89/33.60  |   (5)  all_52_9 = e1
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (4), (5) imply:
% 201.89/33.60  |   (6)  $false
% 201.89/33.60  | 
% 201.89/33.60  | CLOSE: (6) is inconsistent.
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #310 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ~ (e3 = e1)
% 201.89/33.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (3)  op(e3, all_6_1) = e1
% 201.89/33.60    (4)  all_6_2 = e3
% 201.89/33.60    (5)  op(e3, e3) = all_6_2
% 201.89/33.60    (6)  op(all_6_2, e3) = all_6_1
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (4), (6) imply:
% 201.89/33.60  |   (7)  op(e3, e3) = all_6_1
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (4), (5) imply:
% 201.89/33.60  |   (8)  op(e3, e3) = e3
% 201.89/33.60  | 
% 201.89/33.60  | REF_CLOSE: (1), (2), (3), (7), (8) are inconsistent by sub-proof #311.
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #311 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ~ (e3 = e1)
% 201.89/33.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (3)  op(e3, all_6_1) = e1
% 201.89/33.60    (4)  op(e3, e3) = all_6_1
% 201.89/33.60    (5)  op(e3, e3) = e3
% 201.89/33.60  
% 201.89/33.60  Begin of proof
% 201.89/33.60  | 
% 201.89/33.60  | GROUND_INST: instantiating (2) with e3, all_6_1, e3, e3, simplifying with (4),
% 201.89/33.60  |              (5) gives:
% 201.89/33.60  |   (6)  all_6_1 = e3
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (3), (6) imply:
% 201.89/33.60  |   (7)  op(e3, e3) = e1
% 201.89/33.60  | 
% 201.89/33.60  | GROUND_INST: instantiating (2) with e3, e1, e3, e3, simplifying with (5), (7)
% 201.89/33.60  |              gives:
% 201.89/33.60  |   (8)  e3 = e1
% 201.89/33.60  | 
% 201.89/33.60  | REDUCE: (1), (8) imply:
% 201.89/33.60  |   (9)  $false
% 201.89/33.60  | 
% 201.89/33.60  | CLOSE: (9) is inconsistent.
% 201.89/33.60  | 
% 201.89/33.60  End of proof
% 201.89/33.60  
% 201.89/33.60  Sub-proof #312 shows that the following formulas are inconsistent:
% 201.89/33.60  ----------------------------------------------------------------
% 201.89/33.60    (1)   ~ (all_52_15 = all_52_23)
% 201.89/33.60    (2)   ~ (all_52_25 = all_52_27)
% 201.89/33.60    (3)  all_58_14 = all_52_23
% 201.89/33.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.60    (5)  all_58_1 = all_52_9
% 201.89/33.60    (6)   ~ (e3 = e0)
% 201.89/33.60    (7)  op(all_52_23, all_52_23) = e0
% 201.89/33.60    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.60    (9)  op(e0, e2) = all_52_15
% 201.89/33.60    (10)   ~ (all_52_7 = all_52_15)
% 201.89/33.60    (11)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.60    (12)   ~ (all_52_17 = all_52_25)
% 201.89/33.60    (13)  all_58_0 = all_6_2
% 201.89/33.60    (14)  op(e3, all_6_1) = e1
% 201.89/33.60    (15)   ~ (all_52_17 = all_10_2)
% 201.89/33.60    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.60    (17)  all_58_13 = all_52_15
% 201.89/33.60    (18)  all_58_9 = all_52_25
% 201.89/33.60    (19)  op(all_52_27, all_52_27) = all_52_26
% 201.89/33.60    (20)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.89/33.60    (21)  op(e2, e2) = all_4_2
% 201.89/33.60    (22)   ~ (all_4_1 = e3)
% 201.89/33.60    (23)  all_58_11 = all_52_29
% 201.89/33.60    (24)  op(all_10_2, e1) = all_10_1
% 201.89/33.60    (25)   ~ (all_52_7 = all_6_2)
% 201.89/33.60    (26)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.60    (27)  all_58_15 = e0
% 201.89/33.60    (28)   ~ (all_52_25 = e0)
% 201.89/33.60    (29)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 201.89/33.60    (30)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.60    (31)   ~ (e2 = e1)
% 201.89/33.60    (32)   ~ (all_52_13 = all_10_2)
% 201.89/33.60    (33)  op(e0, e0) = e0
% 201.89/33.60    (34)  op(all_10_2, all_10_2) = e1
% 201.89/33.60    (35)  all_58_10 = all_52_27
% 201.89/33.60    (36)  op(all_52_9, all_52_9) = all_52_8
% 201.89/33.60    (37)   ~ (all_52_19 = all_52_23)
% 201.89/33.60    (38)   ~ (all_52_25 = all_52_29)
% 201.89/33.60    (39)   ~ (all_52_29 = all_10_2)
% 201.89/33.60    (40)  all_58_7 = all_52_13
% 201.89/33.60    (41)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.60    (42)  op(all_52_19, all_52_19) = e2
% 201.89/33.60    (43)   ~ (all_52_5 = all_52_7)
% 201.89/33.60    (44)  all_58_12 = all_52_7
% 201.89/33.60    (45)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.60    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.60    (47)  all_58_2 = all_52_3
% 201.89/33.60    (48)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.89/33.60    (49)  all_56_2 = all_52_17
% 201.89/33.60    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.60    (51)  all_56_7 = all_52_27
% 201.89/33.60    (52)   ~ (e2 = e0)
% 201.89/33.60    (53)  op(all_4_2, e2) = all_4_1
% 201.89/33.60    (54)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 201.89/33.61    (55)  all_56_6 = all_52_19
% 201.89/33.61    (56)   ~ (all_52_19 = all_52_27)
% 201.89/33.61    (57)   ~ (all_52_13 = all_4_2)
% 201.89/33.61    (58)  op(e3, e1) = all_52_17
% 201.89/33.61    (59)  op(e0, e3) = all_52_7
% 201.89/33.61    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.61    (61)   ~ (all_52_9 = all_52_25)
% 201.89/33.61    (62)   ~ (all_52_19 = all_10_2)
% 201.89/33.61    (63)  all_58_8 = all_10_2
% 201.89/33.61    (64)   ~ (all_52_23 = e0)
% 201.89/33.61    (65)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.61    (66)  all_56_12 = all_52_7
% 201.89/33.61    (67)   ~ (all_52_25 = all_6_2)
% 201.89/33.61    (68)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.61    (69)   ~ (all_52_9 = all_6_2)
% 201.89/33.61    (70)  op(e3, e3) = all_6_2
% 201.89/33.61    (71)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.61    (72)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.61    (73)  all_56_14 = all_52_23
% 201.89/33.61    (74)  op(all_4_2, all_4_2) = all_52_10
% 201.89/33.61    (75)  all_56_3 = all_52_25
% 201.89/33.61    (76)   ~ (all_52_3 = all_52_7)
% 201.89/33.61    (77)  all_58_5 = all_52_19
% 201.89/33.61    (78)  all_56_1 = all_52_9
% 201.89/33.61    (79)  op(all_52_17, all_52_17) = e3
% 201.89/33.61    (80)  all_58_6 = all_52_5
% 201.89/33.61    (81)  op(e3, e2) = all_52_9
% 201.89/33.61    (82)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.61    (83)   ~ (all_52_17 = all_6_2)
% 201.89/33.61    (84)   ~ (e3 = e2)
% 201.89/33.61    (85)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.61    (86)   ~ (all_52_9 = all_52_17)
% 201.89/33.61    (87)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.61    (88)  op(all_52_13, all_52_13) = all_52_12
% 201.89/33.61    (89)  op(e1, e1) = all_10_2
% 201.89/33.61    (90)   ~ (all_52_23 = all_10_2)
% 201.89/33.61    (91)   ~ (all_52_7 = all_52_23)
% 201.89/33.61    (92)  all_58_3 = all_4_2
% 201.89/33.61    (93)  all_56_13 = all_52_15
% 201.89/33.61    (94)   ~ (all_52_19 = all_4_2)
% 201.89/33.61    (95)   ~ (all_52_17 = all_52_23)
% 201.89/33.61    (96)  op(all_6_2, e3) = all_6_1
% 201.89/33.61    (97)   ~ (all_52_13 = all_52_29)
% 201.89/33.61    (98)  all_58_4 = all_52_17
% 201.89/33.61    (99)   ~ (all_52_7 = e0)
% 201.89/33.61    (100)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.61  
% 201.89/33.61  Begin of proof
% 201.89/33.61  | 
% 201.89/33.61  | BETA: splitting (29) gives:
% 201.89/33.61  | 
% 201.89/33.61  | Case 1:
% 201.89/33.61  | | 
% 201.89/33.61  | |   (101)  all_56_13 = e3
% 201.89/33.61  | | 
% 201.89/33.61  | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (21), (22), (33), (34), (41),
% 201.89/33.61  | |            (44), (53), (54), (64), (66), (73), (89), (90), (91), (93), (99),
% 201.89/33.61  | |            (101) are inconsistent by sub-proof #1281.
% 201.89/33.61  | | 
% 201.89/33.61  | Case 2:
% 201.89/33.61  | | 
% 201.89/33.61  | |   (102)   ~ (all_56_13 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (93), (102) imply:
% 201.89/33.61  | |   (103)   ~ (all_52_15 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 201.89/33.61  | |            (15), (16), (17), (18), (19), (20), (23), (24), (25), (26), (27),
% 201.89/33.61  | |            (28), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 201.89/33.61  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 201.89/33.61  | |            (51), (52), (53), (55), (56), (57), (58), (59), (60), (61), (62),
% 201.89/33.61  | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 201.89/33.61  | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 201.89/33.61  | |            (85), (86), (87), (88), (89), (90), (91), (92), (94), (95), (96),
% 201.89/33.61  | |            (97), (98), (99), (100), (103) are inconsistent by sub-proof
% 201.89/33.61  | |            #313.
% 201.89/33.61  | | 
% 201.89/33.61  | End of split
% 201.89/33.61  | 
% 201.89/33.61  End of proof
% 201.89/33.61  
% 201.89/33.61  Sub-proof #313 shows that the following formulas are inconsistent:
% 201.89/33.61  ----------------------------------------------------------------
% 201.89/33.61    (1)   ~ (all_52_25 = all_52_27)
% 201.89/33.61    (2)  all_58_14 = all_52_23
% 201.89/33.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 201.89/33.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 201.89/33.61    (4)  all_58_1 = all_52_9
% 201.89/33.61    (5)   ~ (e3 = e0)
% 201.89/33.61    (6)  op(all_52_23, all_52_23) = e0
% 201.89/33.61    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 201.89/33.61    (8)   ~ (all_52_7 = all_52_15)
% 201.89/33.61    (9)  op(all_52_7, all_52_7) = all_52_6
% 201.89/33.61    (10)   ~ (all_52_17 = all_52_25)
% 201.89/33.61    (11)  all_58_0 = all_6_2
% 201.89/33.61    (12)  op(e3, all_6_1) = e1
% 201.89/33.61    (13)   ~ (all_52_17 = all_10_2)
% 201.89/33.61    (14)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 201.89/33.61    (15)  all_58_13 = all_52_15
% 201.89/33.61    (16)  all_58_9 = all_52_25
% 201.89/33.61    (17)   ~ (all_52_15 = e3)
% 201.89/33.61    (18)  op(all_52_27, all_52_27) = all_52_26
% 201.89/33.61    (19)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 201.89/33.61    (20)  all_58_11 = all_52_29
% 201.89/33.61    (21)  op(all_10_2, e1) = all_10_1
% 201.89/33.61    (22)   ~ (all_52_7 = all_6_2)
% 201.89/33.61    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.61    (24)  all_58_15 = e0
% 201.89/33.61    (25)   ~ (all_52_25 = e0)
% 201.89/33.61    (26)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.61    (27)   ~ (e2 = e1)
% 201.89/33.61    (28)   ~ (all_52_13 = all_10_2)
% 201.89/33.61    (29)  op(e0, e0) = e0
% 201.89/33.61    (30)  op(all_10_2, all_10_2) = e1
% 201.89/33.61    (31)  all_58_10 = all_52_27
% 201.89/33.61    (32)  op(all_52_9, all_52_9) = all_52_8
% 201.89/33.61    (33)   ~ (all_52_19 = all_52_23)
% 201.89/33.61    (34)   ~ (all_52_25 = all_52_29)
% 201.89/33.61    (35)   ~ (all_52_29 = all_10_2)
% 201.89/33.61    (36)  all_58_7 = all_52_13
% 201.89/33.61    (37)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.61    (38)  op(all_52_19, all_52_19) = e2
% 201.89/33.61    (39)   ~ (all_52_5 = all_52_7)
% 201.89/33.61    (40)  all_58_12 = all_52_7
% 201.89/33.61    (41)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 201.89/33.61    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.61    (43)  all_58_2 = all_52_3
% 201.89/33.61    (44)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 201.89/33.61    (45)  all_56_2 = all_52_17
% 201.89/33.61    (46)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 201.89/33.61    (47)  all_56_7 = all_52_27
% 201.89/33.61    (48)   ~ (e2 = e0)
% 201.89/33.61    (49)  op(all_4_2, e2) = all_4_1
% 201.89/33.61    (50)  all_56_6 = all_52_19
% 201.89/33.61    (51)   ~ (all_52_19 = all_52_27)
% 201.89/33.61    (52)   ~ (all_52_13 = all_4_2)
% 201.89/33.61    (53)  op(e3, e1) = all_52_17
% 201.89/33.61    (54)  op(e0, e3) = all_52_7
% 201.89/33.61    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.61    (56)   ~ (all_52_9 = all_52_25)
% 201.89/33.61    (57)   ~ (all_52_19 = all_10_2)
% 201.89/33.61    (58)  all_58_8 = all_10_2
% 201.89/33.61    (59)   ~ (all_52_23 = e0)
% 201.89/33.61    (60)  op(all_52_29, all_52_29) = all_52_28
% 201.89/33.61    (61)  all_56_12 = all_52_7
% 201.89/33.61    (62)   ~ (all_52_25 = all_6_2)
% 201.89/33.61    (63)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 201.89/33.61    (64)   ~ (all_52_9 = all_6_2)
% 201.89/33.61    (65)  op(e3, e3) = all_6_2
% 201.89/33.61    (66)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 201.89/33.61    (67)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 201.89/33.61    (68)  all_56_14 = all_52_23
% 201.89/33.61    (69)  op(all_4_2, all_4_2) = all_52_10
% 201.89/33.61    (70)  all_56_3 = all_52_25
% 201.89/33.61    (71)   ~ (all_52_3 = all_52_7)
% 201.89/33.61    (72)  all_58_5 = all_52_19
% 201.89/33.61    (73)  all_56_1 = all_52_9
% 201.89/33.61    (74)  op(all_52_17, all_52_17) = e3
% 201.89/33.61    (75)  all_58_6 = all_52_5
% 201.89/33.61    (76)  op(e3, e2) = all_52_9
% 201.89/33.61    (77)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 201.89/33.61    (78)   ~ (all_52_17 = all_6_2)
% 201.89/33.61    (79)   ~ (e3 = e2)
% 201.89/33.61    (80)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.61    (81)   ~ (all_52_9 = all_52_17)
% 201.89/33.61    (82)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.61    (83)  op(all_52_13, all_52_13) = all_52_12
% 201.89/33.61    (84)  op(e1, e1) = all_10_2
% 201.89/33.61    (85)   ~ (all_52_23 = all_10_2)
% 201.89/33.61    (86)   ~ (all_52_7 = all_52_23)
% 201.89/33.61    (87)  all_58_3 = all_4_2
% 201.89/33.61    (88)   ~ (all_52_19 = all_4_2)
% 201.89/33.61    (89)   ~ (all_52_17 = all_52_23)
% 201.89/33.61    (90)  op(all_6_2, e3) = all_6_1
% 201.89/33.61    (91)   ~ (all_52_13 = all_52_29)
% 201.89/33.61    (92)  all_58_4 = all_52_17
% 201.89/33.61    (93)   ~ (all_52_7 = e0)
% 201.89/33.61    (94)  op(all_52_25, all_52_25) = all_52_24
% 201.89/33.61  
% 201.89/33.61  Begin of proof
% 201.89/33.61  | 
% 201.89/33.61  | BETA: splitting (77) gives:
% 201.89/33.61  | 
% 201.89/33.61  | Case 1:
% 201.89/33.61  | | 
% 201.89/33.61  | |   (95)  all_58_12 = e3
% 201.89/33.61  | | 
% 201.89/33.61  | | COMBINE_EQS: (40), (95) imply:
% 201.89/33.61  | |   (96)  all_52_7 = e3
% 201.89/33.61  | | 
% 201.89/33.61  | | SIMP: (96) implies:
% 201.89/33.61  | |   (97)  all_52_7 = e3
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (71), (97) imply:
% 201.89/33.61  | |   (98)   ~ (all_52_3 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (39), (97) imply:
% 201.89/33.61  | |   (99)   ~ (all_52_5 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (8), (97) imply:
% 201.89/33.61  | |   (100)   ~ (all_52_15 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (86), (97) imply:
% 201.89/33.61  | |   (101)   ~ (all_52_23 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | SIMP: (101) implies:
% 201.89/33.61  | |   (102)   ~ (all_52_23 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (22), (97) imply:
% 201.89/33.61  | |   (103)   ~ (all_6_2 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | SIMP: (103) implies:
% 201.89/33.61  | |   (104)   ~ (all_6_2 = e3)
% 201.89/33.61  | | 
% 201.89/33.61  | | REDUCE: (9), (97) imply:
% 201.89/33.61  | |   (105)  op(e3, e3) = all_52_6
% 201.89/33.61  | | 
% 201.89/33.61  | | GROUND_INST: instantiating (3) with all_6_2, all_52_6, e3, e3, simplifying
% 201.89/33.61  | |              with (65), (105) gives:
% 201.89/33.61  | |   (106)  all_52_6 = all_6_2
% 201.89/33.61  | | 
% 201.89/33.61  | | BETA: splitting (37) gives:
% 201.89/33.61  | | 
% 201.89/33.61  | | Case 1:
% 201.89/33.61  | | | 
% 201.89/33.61  | | |   (107)  all_56_14 = e3
% 201.89/33.61  | | | 
% 201.89/33.61  | | | REF_CLOSE: (68), (102), (107) are inconsistent by sub-proof #1286.
% 201.89/33.61  | | | 
% 201.89/33.61  | | Case 2:
% 201.89/33.61  | | | 
% 201.89/33.61  | | |   (108)   ~ (all_56_14 = e3)
% 201.89/33.61  | | |   (109)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 201.89/33.61  | | | 
% 201.89/33.61  | | | BETA: splitting (14) gives:
% 201.89/33.61  | | | 
% 201.89/33.61  | | | Case 1:
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | |   (110)  all_56_7 = e3
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | | REF_CLOSE: (1), (2), (3), (4), (10), (11), (13), (16), (18), (21), (25),
% 201.89/33.61  | | | |            (26), (29), (30), (32), (45), (47), (51), (53), (58), (62),
% 201.89/33.61  | | | |            (63), (65), (67), (70), (72), (74), (78), (82), (92), (102),
% 201.89/33.61  | | | |            (104), (110) are inconsistent by sub-proof #1274.
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | Case 2:
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | |   (111)   ~ (all_56_7 = e3)
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | | REDUCE: (47), (111) imply:
% 201.89/33.61  | | | |   (112)   ~ (all_52_27 = e3)
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | | BETA: splitting (23) gives:
% 201.89/33.61  | | | | 
% 201.89/33.61  | | | | Case 1:
% 201.89/33.61  | | | | | 
% 201.89/33.61  | | | | |   (113)  all_58_2 = e3
% 201.89/33.61  | | | | | 
% 201.89/33.61  | | | | | REF_CLOSE: (43), (98), (113) are inconsistent by sub-proof #1369.
% 201.89/33.61  | | | | | 
% 201.89/33.61  | | | | Case 2:
% 201.89/33.61  | | | | | 
% 201.89/33.61  | | | | |   (114)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 201.89/33.61  | | | | | 
% 201.89/33.61  | | | | | BETA: splitting (66) gives:
% 201.89/33.61  | | | | | 
% 201.89/33.61  | | | | | Case 1:
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | |   (115)  all_58_9 = e3
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | COMBINE_EQS: (16), (115) imply:
% 201.89/33.61  | | | | | |   (116)  all_52_25 = e3
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | SIMP: (116) implies:
% 201.89/33.61  | | | | | |   (117)  all_52_25 = e3
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | REDUCE: (56), (117) imply:
% 201.89/33.61  | | | | | |   (118)   ~ (all_52_9 = e3)
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | REDUCE: (10), (117) imply:
% 201.89/33.61  | | | | | |   (119)   ~ (all_52_17 = e3)
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | REDUCE: (1), (117) imply:
% 201.89/33.61  | | | | | |   (120)   ~ (all_52_27 = e3)
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | REDUCE: (34), (117) imply:
% 201.89/33.61  | | | | | |   (121)   ~ (all_52_29 = e3)
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | SIMP: (121) implies:
% 201.89/33.61  | | | | | |   (122)   ~ (all_52_29 = e3)
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | REDUCE: (94), (117) imply:
% 201.89/33.61  | | | | | |   (123)  op(e3, e3) = all_52_24
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_24, e3, e3,
% 201.89/33.61  | | | | | |              simplifying with (65), (123) gives:
% 201.89/33.61  | | | | | |   (124)  all_52_24 = all_6_2
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | BETA: splitting (82) gives:
% 201.89/33.61  | | | | | | 
% 201.89/33.61  | | | | | | Case 1:
% 201.89/33.61  | | | | | | | 
% 201.89/33.61  | | | | | | |   (125)  all_58_4 = e3
% 201.89/33.61  | | | | | | | 
% 201.89/33.61  | | | | | | | REF_CLOSE: (92), (119), (125) are inconsistent by sub-proof #1302.
% 201.89/33.61  | | | | | | | 
% 201.89/33.61  | | | | | | Case 2:
% 201.89/33.61  | | | | | | | 
% 201.89/33.61  | | | | | | |   (126)   ~ (all_58_4 = e3)
% 201.89/33.61  | | | | | | |   (127)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 201.89/33.61  | | | | | | | 
% 201.89/33.61  | | | | | | | BETA: splitting (42) gives:
% 201.89/33.61  | | | | | | | 
% 201.89/33.61  | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | 
% 201.89/33.61  | | | | | | | |   (128)  all_58_6 = e3
% 201.89/33.61  | | | | | | | | 
% 201.89/33.61  | | | | | | | | REF_CLOSE: (75), (99), (128) are inconsistent by sub-proof
% 201.89/33.61  | | | | | | | |            #1328.
% 201.89/33.61  | | | | | | | | 
% 201.89/33.61  | | | | | | | Case 2:
% 201.89/33.61  | | | | | | | | 
% 201.89/33.61  | | | | | | | |   (129)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 201.89/33.61  | | | | | | | | 
% 201.89/33.61  | | | | | | | | BETA: splitting (55) gives:
% 201.89/33.61  | | | | | | | | 
% 201.89/33.61  | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | |   (130)  all_58_1 = e3
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | COMBINE_EQS: (4), (130) imply:
% 201.89/33.61  | | | | | | | | |   (131)  all_52_9 = e3
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | REDUCE: (118), (131) imply:
% 201.89/33.61  | | | | | | | | |   (132)  $false
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | CLOSE: (132) is inconsistent.
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | Case 2:
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | |   (133)   ~ (all_58_1 = e3)
% 201.89/33.61  | | | | | | | | |   (134)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | BETA: splitting (26) gives:
% 201.89/33.61  | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | |   (135)  all_56_2 = e3
% 201.89/33.61  | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | REF_CLOSE: (45), (119), (135) are inconsistent by sub-proof
% 201.89/33.61  | | | | | | | | | |            #1327.
% 201.89/33.61  | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | Case 2:
% 201.89/33.61  | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | |   (136)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 201.89/33.61  | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | BETA: splitting (80) gives:
% 201.89/33.61  | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | |   (137)  all_56_1 = e3
% 201.89/33.61  | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | REF_CLOSE: (73), (118), (137) are inconsistent by sub-proof
% 201.89/33.61  | | | | | | | | | | |            #1326.
% 201.89/33.61  | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | Case 2:
% 201.89/33.61  | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | |   (138)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 201.89/33.61  | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | BETA: splitting (44) gives:
% 201.89/33.61  | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | |   (139)  all_56_6 = e3
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | COMBINE_EQS: (50), (139) imply:
% 201.89/33.61  | | | | | | | | | | | |   (140)  all_52_19 = e3
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | SIMP: (140) implies:
% 201.89/33.61  | | | | | | | | | | | |   (141)  all_52_19 = e3
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | REDUCE: (88), (141) imply:
% 201.89/33.61  | | | | | | | | | | | |   (142)   ~ (all_4_2 = e3)
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | SIMP: (142) implies:
% 201.89/33.61  | | | | | | | | | | | |   (143)   ~ (all_4_2 = e3)
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (15), (17), (19), (26), (28), (29),
% 201.89/33.61  | | | | | | | | | | | |            (36), (38), (45), (57), (58), (64), (65), (72),
% 201.89/33.61  | | | | | | | | | | | |            (73), (74), (78), (81), (83), (84), (87), (102),
% 201.89/33.61  | | | | | | | | | | | |            (104), (127), (134), (136), (138), (143) are
% 201.89/33.61  | | | | | | | | | | | |            inconsistent by sub-proof #1260.
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | Case 2:
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | |   (144)   ~ (all_56_6 = e3)
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | REDUCE: (50), (144) imply:
% 201.89/33.61  | | | | | | | | | | | |   (145)   ~ (all_52_19 = e3)
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | BETA: splitting (114) gives:
% 201.89/33.61  | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | |   (146)  all_58_3 = e3
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | COMBINE_EQS: (87), (146) imply:
% 201.89/33.61  | | | | | | | | | | | | |   (147)  all_4_2 = e3
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | REDUCE: (52), (147) imply:
% 201.89/33.61  | | | | | | | | | | | | |   (148)   ~ (all_52_13 = e3)
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | REDUCE: (69), (147) imply:
% 201.89/33.61  | | | | | | | | | | | | |   (149)  op(e3, e3) = all_52_10
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | REDUCE: (49), (147) imply:
% 201.89/33.61  | | | | | | | | | | | | |   (150)  op(e3, e2) = all_4_1
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 201.89/33.61  | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | |   (151)  all_58_7 = e3
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | COMBINE_EQS: (36), (151) imply:
% 201.89/33.61  | | | | | | | | | | | | | |   (152)  all_52_13 = e3
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | REDUCE: (148), (152) imply:
% 201.89/33.61  | | | | | | | | | | | | | |   (153)  $false
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | Case 2:
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | |   (154)  all_58_8 = e3 | all_58_11 = e3
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 201.89/33.61  | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | |   (155)  all_58_8 = e3
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (58), (155) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (156)  all_10_2 = e3
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | SIMP: (156) implies:
% 201.89/33.61  | | | | | | | | | | | | | | |   (157)  all_10_2 = e3
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (30), (157) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (158)  op(e3, e3) = e1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (21), (157) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (159)  op(e3, e1) = all_10_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1,
% 201.89/33.61  | | | | | | | | | | | | | | |              e3, simplifying with (53), (159) gives:
% 201.89/33.61  | | | | | | | | | | | | | | |   (160)  all_52_17 = all_10_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_9, all_4_1, e2, e3,
% 201.89/33.61  | | | | | | | | | | | | | | |              simplifying with (76), (150) gives:
% 201.89/33.61  | | | | | | | | | | | | | | |   (161)  all_52_9 = all_4_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_10, e3, e3,
% 201.89/33.61  | | | | | | | | | | | | | | |              simplifying with (65), (149) gives:
% 201.89/33.61  | | | | | | | | | | | | | | |   (162)  all_52_10 = all_6_2
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_10, e3, e3,
% 201.89/33.61  | | | | | | | | | | | | | | |              simplifying with (149), (158) gives:
% 201.89/33.61  | | | | | | | | | | | | | | |   (163)  all_52_10 = e1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (164)  all_6_2 = e1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (45), (160) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (165)  all_56_2 = all_10_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (73), (161) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (166)  all_56_1 = all_4_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (92), (160) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (167)  all_58_4 = all_10_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (4), (161) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (168)  all_58_1 = all_4_1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | COMBINE_EQS: (11), (164) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (169)  all_58_0 = e1
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (81), (160), (161) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (170)   ~ (all_10_1 = all_4_1)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | SIMP: (170) implies:
% 201.89/33.61  | | | | | | | | | | | | | | |   (171)   ~ (all_10_1 = all_4_1)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (64), (161), (164) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (172)   ~ (all_4_1 = e1)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (89), (160) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (173)   ~ (all_52_23 = all_10_1)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | SIMP: (173) implies:
% 201.89/33.61  | | | | | | | | | | | | | | |   (174)   ~ (all_52_23 = all_10_1)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (78), (160), (164) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (175)   ~ (all_10_1 = e1)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (119), (160) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (176)   ~ (all_10_1 = e3)
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | REDUCE: (74), (160) imply:
% 201.89/33.61  | | | | | | | | | | | | | | |   (177)  op(all_10_1, all_10_1) = e3
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 201.89/33.61  | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | Case 1:
% 201.89/33.61  | | | | | | | | | | | | | | | | 
% 201.89/33.61  | | | | | | | | | | | | | | | |   (178)  all_58_1 = e0
% 201.89/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (20), (27), (29), (30), (46), (48),
% 202.03/33.61  | | | | | | | | | | | | | | | |            (59), (68), (79), (84), (85), (109), (115), (122),
% 202.03/33.61  | | | | | | | | | | | | | | | |            (154), (155), (167), (169), (174), (178) are
% 202.03/33.61  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1270.
% 202.03/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | Case 2:
% 202.03/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | |   (179)   ~ (all_58_1 = e0)
% 202.03/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | REDUCE: (168), (179) imply:
% 202.03/33.61  | | | | | | | | | | | | | | | |   (180)   ~ (all_4_1 = e0)
% 202.03/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 202.03/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | Case 1:
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | |   (181)  all_56_1 = e2
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (181) imply:
% 202.03/33.61  | | | | | | | | | | | | | | | | |   (182)  all_4_1 = e2
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 202.03/33.61  | | | | | | | | | | | | | | | | |   (183)  all_4_1 = e2
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | | REDUCE: (171), (183) imply:
% 202.03/33.61  | | | | | | | | | | | | | | | | |   (184)   ~ (all_10_1 = e2)
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (26), (29), (165), (175), (176), (177), (184)
% 202.03/33.61  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #483.
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | Case 2:
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | |   (185)  all_56_1 = e1 | all_56_1 = e0
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (172), (180), (185) are inconsistent by
% 202.03/33.61  | | | | | | | | | | | | | | | | |            sub-proof #1164.
% 202.03/33.61  | | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | Case 2:
% 202.03/33.61  | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | |   (186)  all_58_11 = e3
% 202.03/33.61  | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | | REF_CLOSE: (20), (122), (186) are inconsistent by sub-proof
% 202.03/33.61  | | | | | | | | | | | | | | |            #1323.
% 202.03/33.61  | | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | Case 2:
% 202.03/33.61  | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | |   (187)  all_58_5 = e3 | all_58_10 = e3
% 202.03/33.61  | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | | REF_CLOSE: (31), (72), (112), (145), (187) are inconsistent
% 202.03/33.61  | | | | | | | | | | | | |            by sub-proof #1132.
% 202.03/33.61  | | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | | 
% 202.03/33.61  | | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | | 
% 202.03/33.61  | | | | | | | | End of split
% 202.03/33.61  | | | | | | | | 
% 202.03/33.61  | | | | | | | End of split
% 202.03/33.61  | | | | | | | 
% 202.03/33.61  | | | | | | End of split
% 202.03/33.61  | | | | | | 
% 202.03/33.61  | | | | | Case 2:
% 202.03/33.61  | | | | | | 
% 202.03/33.61  | | | | | |   (188)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.61  | | | | | | 
% 202.03/33.61  | | | | | | REF_CLOSE: (2), (3), (4), (5), (10), (15), (17), (20), (24), (25),
% 202.03/33.61  | | | | | |            (26), (29), (31), (32), (34), (35), (36), (38), (45),
% 202.03/33.61  | | | | | |            (55), (58), (60), (62), (63), (64), (65), (70), (72),
% 202.03/33.61  | | | | | |            (74), (78), (82), (87), (88), (91), (92), (102), (112),
% 202.03/33.61  | | | | | |            (188) are inconsistent by sub-proof #1252.
% 202.03/33.61  | | | | | | 
% 202.03/33.61  | | | | | End of split
% 202.03/33.61  | | | | | 
% 202.03/33.61  | | | | End of split
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | End of split
% 202.03/33.61  | | | 
% 202.03/33.61  | | End of split
% 202.03/33.61  | | 
% 202.03/33.61  | Case 2:
% 202.03/33.61  | | 
% 202.03/33.61  | |   (189)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.61  | | 
% 202.03/33.61  | | BETA: splitting (189) gives:
% 202.03/33.61  | | 
% 202.03/33.61  | | Case 1:
% 202.03/33.61  | | | 
% 202.03/33.61  | | |   (190)  all_58_13 = e3
% 202.03/33.61  | | | 
% 202.03/33.61  | | | REF_CLOSE: (15), (17), (190) are inconsistent by sub-proof #1360.
% 202.03/33.61  | | | 
% 202.03/33.61  | | Case 2:
% 202.03/33.61  | | | 
% 202.03/33.61  | | |   (191)  all_58_14 = e3 | all_58_15 = e3
% 202.03/33.61  | | | 
% 202.03/33.61  | | | BETA: splitting (191) gives:
% 202.03/33.61  | | | 
% 202.03/33.61  | | | Case 1:
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | |   (192)  all_58_14 = e3
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | COMBINE_EQS: (2), (192) imply:
% 202.03/33.61  | | | |   (193)  all_52_23 = e3
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | SIMP: (193) implies:
% 202.03/33.61  | | | |   (194)  all_52_23 = e3
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | REDUCE: (86), (194) imply:
% 202.03/33.61  | | | |   (195)   ~ (all_52_7 = e3)
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | REDUCE: (85), (194) imply:
% 202.03/33.61  | | | |   (196)   ~ (all_10_2 = e3)
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | SIMP: (196) implies:
% 202.03/33.61  | | | |   (197)   ~ (all_10_2 = e3)
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | REDUCE: (6), (194) imply:
% 202.03/33.61  | | | |   (198)  op(e3, e3) = e0
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | REF_CLOSE: (3), (7), (9), (12), (22), (41), (53), (54), (61), (65),
% 202.03/33.61  | | | |            (74), (84), (90), (195), (197), (198) are inconsistent by
% 202.03/33.61  | | | |            sub-proof #314.
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | Case 2:
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | |   (199)  all_58_15 = e3
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | REF_CLOSE: (5), (24), (199) are inconsistent by sub-proof #1350.
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | End of split
% 202.03/33.61  | | | 
% 202.03/33.61  | | End of split
% 202.03/33.61  | | 
% 202.03/33.61  | End of split
% 202.03/33.61  | 
% 202.03/33.61  End of proof
% 202.03/33.61  
% 202.03/33.61  Sub-proof #314 shows that the following formulas are inconsistent:
% 202.03/33.61  ----------------------------------------------------------------
% 202.03/33.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.61    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.61    (3)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.61    (4)  op(e3, all_6_1) = e1
% 202.03/33.61    (5)   ~ (all_52_7 = all_6_2)
% 202.03/33.61    (6)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 202.03/33.61    (7)   ~ (all_52_7 = e3)
% 202.03/33.61    (8)   ~ (all_10_2 = e3)
% 202.03/33.61    (9)  op(e3, e1) = all_52_17
% 202.03/33.61    (10)  op(e0, e3) = all_52_7
% 202.03/33.61    (11)  all_56_12 = all_52_7
% 202.03/33.61    (12)  op(e3, e3) = e0
% 202.03/33.61    (13)  op(e3, e3) = all_6_2
% 202.03/33.61    (14)  op(all_52_17, all_52_17) = e3
% 202.03/33.61    (15)  op(e1, e1) = all_10_2
% 202.03/33.61    (16)  op(all_6_2, e3) = all_6_1
% 202.03/33.61  
% 202.03/33.61  Begin of proof
% 202.03/33.61  | 
% 202.03/33.61  | GROUND_INST: instantiating (1) with all_6_2, e0, e3, e3, simplifying with
% 202.03/33.61  |              (12), (13) gives:
% 202.03/33.61  |   (17)  all_6_2 = e0
% 202.03/33.61  | 
% 202.03/33.61  | REDUCE: (5), (17) imply:
% 202.03/33.61  |   (18)   ~ (all_52_7 = e0)
% 202.03/33.61  | 
% 202.03/33.61  | REDUCE: (16), (17) imply:
% 202.03/33.61  |   (19)  op(e0, e3) = all_6_1
% 202.03/33.61  | 
% 202.03/33.61  | BETA: splitting (6) gives:
% 202.03/33.61  | 
% 202.03/33.61  | Case 1:
% 202.03/33.61  | | 
% 202.03/33.61  | |   (20)   ~ (all_6_1 = e2)
% 202.03/33.61  | | 
% 202.03/33.61  | | GROUND_INST: instantiating (1) with all_52_7, all_6_1, e3, e0, simplifying
% 202.03/33.61  | |              with (10), (19) gives:
% 202.03/33.61  | |   (21)  all_52_7 = all_6_1
% 202.03/33.61  | | 
% 202.03/33.61  | | COMBINE_EQS: (11), (21) imply:
% 202.03/33.61  | |   (22)  all_56_12 = all_6_1
% 202.03/33.61  | | 
% 202.03/33.61  | | REDUCE: (7), (21) imply:
% 202.03/33.61  | |   (23)   ~ (all_6_1 = e3)
% 202.03/33.61  | | 
% 202.03/33.61  | | REDUCE: (18), (21) imply:
% 202.03/33.61  | |   (24)   ~ (all_6_1 = e0)
% 202.03/33.61  | | 
% 202.03/33.61  | | REDUCE: (3), (21) imply:
% 202.03/33.61  | |   (25)  op(all_6_1, all_6_1) = all_52_6
% 202.03/33.61  | | 
% 202.03/33.61  | | BETA: splitting (2) gives:
% 202.03/33.61  | | 
% 202.03/33.61  | | Case 1:
% 202.03/33.61  | | | 
% 202.03/33.61  | | |   (26)  all_56_12 = e3
% 202.03/33.61  | | | 
% 202.03/33.61  | | | REF_CLOSE: (22), (23), (26) are inconsistent by sub-proof #1347.
% 202.03/33.61  | | | 
% 202.03/33.61  | | Case 2:
% 202.03/33.61  | | | 
% 202.03/33.61  | | |   (27)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.61  | | | 
% 202.03/33.61  | | | BETA: splitting (27) gives:
% 202.03/33.61  | | | 
% 202.03/33.61  | | | Case 1:
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | |   (28)  all_56_12 = e2
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | REF_CLOSE: (20), (22), (28) are inconsistent by sub-proof #1346.
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | Case 2:
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | |   (29)  all_56_12 = e1 | all_56_12 = e0
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | BETA: splitting (29) gives:
% 202.03/33.61  | | | | 
% 202.03/33.61  | | | | Case 1:
% 202.03/33.61  | | | | | 
% 202.03/33.61  | | | | |   (30)  all_56_12 = e1
% 202.03/33.61  | | | | | 
% 202.03/33.61  | | | | | COMBINE_EQS: (22), (30) imply:
% 202.03/33.61  | | | | |   (31)  all_6_1 = e1
% 202.03/33.61  | | | | | 
% 202.03/33.61  | | | | | SIMP: (31) implies:
% 202.03/33.61  | | | | |   (32)  all_6_1 = e1
% 202.03/33.61  | | | | | 
% 202.03/33.61  | | | | | REDUCE: (25), (32) imply:
% 202.03/33.61  | | | | |   (33)  op(e1, e1) = all_52_6
% 202.03/33.61  | | | | | 
% 202.03/33.61  | | | | | REDUCE: (4), (32) imply:
% 202.03/33.61  | | | | |   (34)  op(e3, e1) = e1
% 202.03/33.61  | | | | | 
% 202.03/33.62  | | | | | GROUND_INST: instantiating (1) with all_10_2, all_52_6, e1, e1,
% 202.03/33.62  | | | | |              simplifying with (15), (33) gives:
% 202.03/33.62  | | | | |   (35)  all_52_6 = all_10_2
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | REF_CLOSE: (1), (8), (9), (14), (33), (34), (35) are inconsistent by
% 202.03/33.62  | | | | |            sub-proof #315.
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | Case 2:
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | |   (36)  all_56_12 = e0
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | REF_CLOSE: (22), (24), (36) are inconsistent by sub-proof #1345.
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | End of split
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | End of split
% 202.03/33.62  | | | 
% 202.03/33.62  | | End of split
% 202.03/33.62  | | 
% 202.03/33.62  | Case 2:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (37)   ~ (all_6_2 = e0)
% 202.03/33.62  | | 
% 202.03/33.62  | | REDUCE: (17), (37) imply:
% 202.03/33.62  | |   (38)  $false
% 202.03/33.62  | | 
% 202.03/33.62  | | CLOSE: (38) is inconsistent.
% 202.03/33.62  | | 
% 202.03/33.62  | End of split
% 202.03/33.62  | 
% 202.03/33.62  End of proof
% 202.03/33.62  
% 202.03/33.62  Sub-proof #315 shows that the following formulas are inconsistent:
% 202.03/33.62  ----------------------------------------------------------------
% 202.03/33.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.62    (2)  all_52_6 = all_10_2
% 202.03/33.62    (3)  op(e1, e1) = all_52_6
% 202.03/33.62    (4)  op(e3, e1) = e1
% 202.03/33.62    (5)   ~ (all_10_2 = e3)
% 202.03/33.62    (6)  op(e3, e1) = all_52_17
% 202.03/33.62    (7)  op(all_52_17, all_52_17) = e3
% 202.03/33.62  
% 202.03/33.62  Begin of proof
% 202.03/33.62  | 
% 202.03/33.62  | GROUND_INST: instantiating (1) with all_52_17, e1, e1, e3, simplifying with
% 202.03/33.62  |              (4), (6) gives:
% 202.03/33.62  |   (8)  all_52_17 = e1
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (7), (8) imply:
% 202.03/33.62  |   (9)  op(e1, e1) = e3
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (2), (3) imply:
% 202.03/33.62  |   (10)  op(e1, e1) = all_10_2
% 202.03/33.62  | 
% 202.03/33.62  | REF_CLOSE: (1), (5), (9), (10) are inconsistent by sub-proof #1368.
% 202.03/33.62  | 
% 202.03/33.62  End of proof
% 202.03/33.62  
% 202.03/33.62  Sub-proof #316 shows that the following formulas are inconsistent:
% 202.03/33.62  ----------------------------------------------------------------
% 202.03/33.62    (1)   ~ (all_52_25 = all_52_27)
% 202.03/33.62    (2)  all_58_14 = all_52_23
% 202.03/33.62    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.03/33.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.62    (5)  all_58_1 = all_52_9
% 202.03/33.62    (6)   ~ (all_52_9 = all_52_13)
% 202.03/33.62    (7)   ~ (e3 = e0)
% 202.03/33.62    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.62    (9)   ~ (all_52_7 = all_52_15)
% 202.03/33.62    (10)  op(all_52_15, all_52_15) = e0
% 202.03/33.62    (11)   ~ (all_52_17 = all_52_25)
% 202.03/33.62    (12)  all_58_0 = all_6_2
% 202.03/33.62    (13)  op(e3, all_6_1) = e1
% 202.03/33.62    (14)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.62    (15)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.62    (16)  all_58_13 = all_52_15
% 202.03/33.62    (17)  op(all_52_13, all_52_13) = e1
% 202.03/33.62    (18)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.62    (19)  all_58_9 = all_52_25
% 202.03/33.62    (20)  op(e2, e2) = all_4_2
% 202.03/33.62    (21)  all_58_11 = all_52_29
% 202.03/33.62    (22)   ~ (all_52_9 = all_52_15)
% 202.03/33.62    (23)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.62    (24)  op(all_10_2, e1) = all_10_1
% 202.03/33.62    (25)   ~ (all_52_7 = all_6_2)
% 202.03/33.62    (26)  op(e0, e1) = all_52_23
% 202.03/33.62    (27)   ~ (all_52_15 = e0)
% 202.03/33.62    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.62    (29)  all_58_15 = e0
% 202.03/33.62    (30)   ~ (all_4_1 = e1)
% 202.03/33.62    (31)   ~ (all_52_25 = e0)
% 202.03/33.62    (32)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.62    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.62    (34)   ~ (e2 = e1)
% 202.03/33.62    (35)  op(e0, e0) = e0
% 202.03/33.62    (36)  all_58_10 = all_52_27
% 202.03/33.62    (37)   ~ (all_52_25 = all_52_29)
% 202.03/33.62    (38)  all_58_7 = all_52_13
% 202.03/33.62    (39)   ~ (all_52_5 = all_52_7)
% 202.03/33.62    (40)  all_58_12 = all_52_7
% 202.03/33.62    (41)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 202.03/33.62    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.62    (43)  all_58_2 = all_52_3
% 202.03/33.62    (44)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.62    (45)  all_56_2 = all_52_17
% 202.03/33.62    (46)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.62    (47)  all_56_7 = all_52_27
% 202.03/33.62    (48)   ~ (e2 = e0)
% 202.03/33.62    (49)  op(all_4_2, e2) = all_4_1
% 202.03/33.62    (50)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.62    (51)  all_56_6 = all_52_19
% 202.03/33.62    (52)   ~ (all_52_13 = all_4_2)
% 202.03/33.62    (53)  op(e3, e1) = all_52_17
% 202.03/33.62    (54)  op(e0, e3) = all_52_7
% 202.03/33.62    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.62    (56)   ~ (all_52_9 = all_52_25)
% 202.03/33.62    (57)   ~ (all_52_19 = all_10_2)
% 202.03/33.62    (58)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.62    (59)  all_58_8 = all_10_2
% 202.03/33.62    (60)  all_56_12 = all_52_7
% 202.03/33.62    (61)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.62    (62)   ~ (all_52_25 = all_6_2)
% 202.03/33.62    (63)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.62    (64)   ~ (all_52_9 = all_4_2)
% 202.03/33.62    (65)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.03/33.62    (66)  op(all_4_2, all_4_2) = e2
% 202.03/33.62    (67)   ~ (all_52_9 = all_6_2)
% 202.03/33.62    (68)  op(e3, e3) = all_6_2
% 202.03/33.62    (69)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.62    (70)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.62    (71)  all_56_3 = all_52_25
% 202.03/33.62    (72)   ~ (all_52_3 = all_52_7)
% 202.03/33.62    (73)   ~ (all_10_1 = e3)
% 202.03/33.62    (74)  all_58_5 = all_52_19
% 202.03/33.62    (75)  all_56_1 = all_52_9
% 202.03/33.62    (76)   ~ (all_52_15 = all_4_2)
% 202.03/33.62    (77)   ~ (all_52_27 = all_4_2)
% 202.03/33.62    (78)  all_58_6 = all_52_5
% 202.03/33.62    (79)  op(e3, e2) = all_52_9
% 202.03/33.62    (80)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.62    (81)   ~ (all_52_17 = all_6_2)
% 202.03/33.62    (82)   ~ (e1 = e0)
% 202.03/33.62    (83)   ~ (e3 = e2)
% 202.03/33.62    (84)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.62    (85)   ~ (all_52_9 = all_52_17)
% 202.03/33.62    (86)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.62    (87)  op(e1, e1) = all_10_2
% 202.03/33.62    (88)  op(all_52_9, all_52_9) = e3
% 202.03/33.62    (89)   ~ (all_52_7 = all_52_23)
% 202.03/33.62    (90)  all_58_3 = all_4_2
% 202.03/33.62    (91)  all_56_13 = all_52_15
% 202.03/33.62    (92)  op(all_6_2, e3) = all_6_1
% 202.03/33.62    (93)   ~ (all_52_13 = all_52_29)
% 202.03/33.62    (94)  all_58_4 = all_52_17
% 202.03/33.62    (95)   ~ (all_52_7 = e0)
% 202.03/33.62    (96)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.62  
% 202.03/33.62  Begin of proof
% 202.03/33.62  | 
% 202.03/33.62  | BETA: splitting (32) gives:
% 202.03/33.62  | 
% 202.03/33.62  | Case 1:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (97)  all_56_13 = e3
% 202.03/33.62  | | 
% 202.03/33.62  | | REF_CLOSE: (2), (4), (8), (9), (10), (13), (16), (20), (22), (23), (25),
% 202.03/33.62  | |            (29), (40), (41), (48), (53), (54), (58), (60), (67), (68), (75),
% 202.03/33.62  | |            (76), (83), (84), (85), (88), (91), (92), (97) are inconsistent
% 202.03/33.62  | |            by sub-proof #321.
% 202.03/33.62  | | 
% 202.03/33.62  | Case 2:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (98)   ~ (all_56_13 = e3)
% 202.03/33.62  | |   (99)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.62  | | 
% 202.03/33.62  | | REDUCE: (91), (98) imply:
% 202.03/33.62  | |   (100)   ~ (all_52_15 = e3)
% 202.03/33.62  | | 
% 202.03/33.62  | | BETA: splitting (80) gives:
% 202.03/33.62  | | 
% 202.03/33.62  | | Case 1:
% 202.03/33.62  | | | 
% 202.03/33.62  | | |   (101)  all_58_12 = e3
% 202.03/33.62  | | | 
% 202.03/33.62  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (11), (12), (14), (15), (16),
% 202.03/33.62  | | |            (17), (18), (19), (20), (21), (25), (28), (29), (30), (31),
% 202.03/33.62  | | |            (33), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 202.03/33.62  | | |            (45), (46), (47), (49), (51), (52), (55), (56), (57), (59),
% 202.03/33.62  | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 202.03/33.62  | | |            (71), (72), (74), (75), (77), (78), (79), (81), (82), (84),
% 202.03/33.62  | | |            (85), (86), (88), (90), (93), (94), (95), (96), (101) are
% 202.03/33.62  | | |            inconsistent by sub-proof #317.
% 202.03/33.62  | | | 
% 202.03/33.62  | | Case 2:
% 202.03/33.62  | | | 
% 202.03/33.62  | | |   (102)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.62  | | | 
% 202.03/33.62  | | | REF_CLOSE: (2), (4), (7), (8), (9), (10), (16), (20), (23), (24), (26),
% 202.03/33.62  | | |            (27), (29), (34), (35), (40), (50), (60), (66), (73), (76),
% 202.03/33.62  | | |            (87), (89), (91), (95), (99), (100), (102) are inconsistent by
% 202.03/33.62  | | |            sub-proof #1288.
% 202.03/33.62  | | | 
% 202.03/33.62  | | End of split
% 202.03/33.62  | | 
% 202.03/33.62  | End of split
% 202.03/33.62  | 
% 202.03/33.62  End of proof
% 202.03/33.62  
% 202.03/33.62  Sub-proof #317 shows that the following formulas are inconsistent:
% 202.03/33.62  ----------------------------------------------------------------
% 202.03/33.62    (1)   ~ (all_52_25 = all_52_27)
% 202.03/33.62    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.03/33.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.62    (4)  all_58_1 = all_52_9
% 202.03/33.62    (5)   ~ (all_52_9 = all_52_13)
% 202.03/33.62    (6)   ~ (all_52_7 = all_52_15)
% 202.03/33.62    (7)   ~ (all_52_17 = all_52_25)
% 202.03/33.62    (8)  all_58_0 = all_6_2
% 202.03/33.62    (9)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.62    (10)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.62    (11)  all_58_13 = all_52_15
% 202.03/33.62    (12)  op(all_52_13, all_52_13) = e1
% 202.03/33.62    (13)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.62    (14)  all_58_9 = all_52_25
% 202.03/33.62    (15)  op(e2, e2) = all_4_2
% 202.03/33.62    (16)  all_58_11 = all_52_29
% 202.03/33.62    (17)   ~ (all_52_7 = all_6_2)
% 202.03/33.62    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.62    (19)  all_58_15 = e0
% 202.03/33.62    (20)   ~ (all_4_1 = e1)
% 202.03/33.62    (21)   ~ (all_52_25 = e0)
% 202.03/33.62    (22)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.62    (23)  op(e0, e0) = e0
% 202.03/33.62    (24)  all_58_10 = all_52_27
% 202.03/33.62    (25)   ~ (all_52_25 = all_52_29)
% 202.03/33.62    (26)  all_58_7 = all_52_13
% 202.03/33.62    (27)   ~ (all_52_5 = all_52_7)
% 202.03/33.62    (28)  all_58_12 = all_52_7
% 202.03/33.62    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.62    (30)  all_58_2 = all_52_3
% 202.03/33.62    (31)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.62    (32)  all_56_2 = all_52_17
% 202.03/33.62    (33)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.62    (34)  all_56_7 = all_52_27
% 202.03/33.62    (35)  op(all_4_2, e2) = all_4_1
% 202.03/33.62    (36)  all_56_6 = all_52_19
% 202.03/33.62    (37)   ~ (all_52_13 = all_4_2)
% 202.03/33.62    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.62    (39)   ~ (all_52_9 = all_52_25)
% 202.03/33.62    (40)   ~ (all_52_19 = all_10_2)
% 202.03/33.62    (41)  all_58_8 = all_10_2
% 202.03/33.62    (42)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.62    (43)   ~ (all_52_25 = all_6_2)
% 202.03/33.62    (44)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.62    (45)   ~ (all_52_9 = all_4_2)
% 202.03/33.62    (46)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.03/33.62    (47)  op(all_4_2, all_4_2) = e2
% 202.03/33.62    (48)   ~ (all_52_9 = all_6_2)
% 202.03/33.62    (49)  op(e3, e3) = all_6_2
% 202.03/33.62    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.62    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.62    (52)  all_56_3 = all_52_25
% 202.03/33.62    (53)   ~ (all_52_3 = all_52_7)
% 202.03/33.62    (54)  all_58_5 = all_52_19
% 202.03/33.62    (55)  all_56_1 = all_52_9
% 202.03/33.62    (56)   ~ (all_52_27 = all_4_2)
% 202.03/33.62    (57)  all_58_6 = all_52_5
% 202.03/33.62    (58)  op(e3, e2) = all_52_9
% 202.03/33.62    (59)   ~ (all_52_17 = all_6_2)
% 202.03/33.62    (60)   ~ (e1 = e0)
% 202.03/33.62    (61)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.62    (62)   ~ (all_52_9 = all_52_17)
% 202.03/33.62    (63)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.62    (64)  all_58_12 = e3
% 202.03/33.62    (65)  op(all_52_9, all_52_9) = e3
% 202.03/33.62    (66)  all_58_3 = all_4_2
% 202.03/33.62    (67)   ~ (all_52_13 = all_52_29)
% 202.03/33.62    (68)  all_58_4 = all_52_17
% 202.03/33.62    (69)   ~ (all_52_7 = e0)
% 202.03/33.62    (70)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.62  
% 202.03/33.62  Begin of proof
% 202.03/33.62  | 
% 202.03/33.62  | COMBINE_EQS: (28), (64) imply:
% 202.03/33.62  |   (71)  all_52_7 = e3
% 202.03/33.62  | 
% 202.03/33.62  | SIMP: (71) implies:
% 202.03/33.62  |   (72)  all_52_7 = e3
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (53), (72) imply:
% 202.03/33.62  |   (73)   ~ (all_52_3 = e3)
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (27), (72) imply:
% 202.03/33.62  |   (74)   ~ (all_52_5 = e3)
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (6), (72) imply:
% 202.03/33.62  |   (75)   ~ (all_52_15 = e3)
% 202.03/33.62  | 
% 202.03/33.62  | SIMP: (75) implies:
% 202.03/33.62  |   (76)   ~ (all_52_15 = e3)
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (17), (72) imply:
% 202.03/33.62  |   (77)   ~ (all_6_2 = e3)
% 202.03/33.62  | 
% 202.03/33.62  | SIMP: (77) implies:
% 202.03/33.62  |   (78)   ~ (all_6_2 = e3)
% 202.03/33.62  | 
% 202.03/33.62  | REDUCE: (69), (72) imply:
% 202.03/33.62  |   (79)   ~ (e3 = e0)
% 202.03/33.62  | 
% 202.03/33.62  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 202.03/33.62  |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 202.03/33.62  |            (26), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 202.03/33.62  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 202.03/33.62  |            (50), (51), (52), (54), (55), (56), (57), (58), (59), (60), (61),
% 202.03/33.62  |            (62), (63), (65), (66), (67), (68), (70), (73), (74), (76), (78),
% 202.03/33.62  |            (79) are inconsistent by sub-proof #318.
% 202.03/33.62  | 
% 202.03/33.62  End of proof
% 202.03/33.62  
% 202.03/33.62  Sub-proof #318 shows that the following formulas are inconsistent:
% 202.03/33.62  ----------------------------------------------------------------
% 202.03/33.62    (1)   ~ (all_52_25 = all_52_27)
% 202.03/33.62    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.03/33.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.62    (4)  all_58_1 = all_52_9
% 202.03/33.62    (5)   ~ (all_52_9 = all_52_13)
% 202.03/33.62    (6)   ~ (e3 = e0)
% 202.03/33.62    (7)   ~ (all_52_17 = all_52_25)
% 202.03/33.62    (8)  all_58_0 = all_6_2
% 202.03/33.62    (9)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.62    (10)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.62    (11)  all_58_13 = all_52_15
% 202.03/33.62    (12)  op(all_52_13, all_52_13) = e1
% 202.03/33.62    (13)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.62    (14)  all_58_9 = all_52_25
% 202.03/33.62    (15)   ~ (all_52_15 = e3)
% 202.03/33.62    (16)  op(e2, e2) = all_4_2
% 202.03/33.62    (17)  all_58_11 = all_52_29
% 202.03/33.62    (18)   ~ (all_52_3 = e3)
% 202.03/33.62    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.62    (20)  all_58_15 = e0
% 202.03/33.62    (21)   ~ (all_4_1 = e1)
% 202.03/33.62    (22)   ~ (all_52_25 = e0)
% 202.03/33.62    (23)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.62    (24)   ~ (all_6_2 = e3)
% 202.03/33.62    (25)  op(e0, e0) = e0
% 202.03/33.62    (26)  all_58_10 = all_52_27
% 202.03/33.62    (27)   ~ (all_52_25 = all_52_29)
% 202.03/33.62    (28)  all_58_7 = all_52_13
% 202.03/33.62    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.62    (30)  all_58_2 = all_52_3
% 202.03/33.62    (31)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.62    (32)  all_56_2 = all_52_17
% 202.03/33.62    (33)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.62    (34)  all_56_7 = all_52_27
% 202.03/33.62    (35)  op(all_4_2, e2) = all_4_1
% 202.03/33.62    (36)   ~ (all_52_5 = e3)
% 202.03/33.62    (37)  all_56_6 = all_52_19
% 202.03/33.62    (38)   ~ (all_52_13 = all_4_2)
% 202.03/33.62    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.62    (40)   ~ (all_52_9 = all_52_25)
% 202.03/33.62    (41)   ~ (all_52_19 = all_10_2)
% 202.03/33.62    (42)  all_58_8 = all_10_2
% 202.03/33.62    (43)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.62    (44)   ~ (all_52_25 = all_6_2)
% 202.03/33.62    (45)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.62    (46)   ~ (all_52_9 = all_4_2)
% 202.03/33.62    (47)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.03/33.62    (48)  op(all_4_2, all_4_2) = e2
% 202.03/33.62    (49)   ~ (all_52_9 = all_6_2)
% 202.03/33.62    (50)  op(e3, e3) = all_6_2
% 202.03/33.62    (51)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.62    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.62    (53)  all_56_3 = all_52_25
% 202.03/33.62    (54)  all_58_5 = all_52_19
% 202.03/33.62    (55)  all_56_1 = all_52_9
% 202.03/33.62    (56)   ~ (all_52_27 = all_4_2)
% 202.03/33.62    (57)  all_58_6 = all_52_5
% 202.03/33.62    (58)  op(e3, e2) = all_52_9
% 202.03/33.62    (59)   ~ (all_52_17 = all_6_2)
% 202.03/33.62    (60)   ~ (e1 = e0)
% 202.03/33.62    (61)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.62    (62)   ~ (all_52_9 = all_52_17)
% 202.03/33.62    (63)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.62    (64)  op(all_52_9, all_52_9) = e3
% 202.03/33.62    (65)  all_58_3 = all_4_2
% 202.03/33.62    (66)   ~ (all_52_13 = all_52_29)
% 202.03/33.62    (67)  all_58_4 = all_52_17
% 202.03/33.62    (68)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.62  
% 202.03/33.62  Begin of proof
% 202.03/33.62  | 
% 202.03/33.62  | BETA: splitting (9) gives:
% 202.03/33.62  | 
% 202.03/33.62  | Case 1:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (69)  all_56_7 = e3
% 202.03/33.62  | | 
% 202.03/33.62  | | COMBINE_EQS: (34), (69) imply:
% 202.03/33.62  | |   (70)  all_52_27 = e3
% 202.03/33.62  | | 
% 202.03/33.62  | | SIMP: (70) implies:
% 202.03/33.62  | |   (71)  all_52_27 = e3
% 202.03/33.62  | | 
% 202.03/33.62  | | REDUCE: (1), (71) imply:
% 202.03/33.62  | |   (72)   ~ (all_52_25 = e3)
% 202.03/33.62  | | 
% 202.03/33.62  | | REDUCE: (56), (71) imply:
% 202.03/33.62  | |   (73)   ~ (all_4_2 = e3)
% 202.03/33.62  | | 
% 202.03/33.62  | | SIMP: (73) implies:
% 202.03/33.62  | |   (74)   ~ (all_4_2 = e3)
% 202.03/33.62  | | 
% 202.03/33.62  | | REF_CLOSE: (3), (4), (5), (8), (11), (12), (14), (15), (22), (24), (25),
% 202.03/33.62  | |            (28), (33), (39), (40), (43), (44), (45), (47), (49), (50), (52),
% 202.03/33.62  | |            (53), (55), (60), (61), (64), (65), (67), (72), (74) are
% 202.03/33.62  | |            inconsistent by sub-proof #320.
% 202.03/33.62  | | 
% 202.03/33.62  | Case 2:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (75)   ~ (all_56_7 = e3)
% 202.03/33.62  | | 
% 202.03/33.62  | | REDUCE: (34), (75) imply:
% 202.03/33.62  | |   (76)   ~ (all_52_27 = e3)
% 202.03/33.62  | | 
% 202.03/33.62  | | BETA: splitting (19) gives:
% 202.03/33.62  | | 
% 202.03/33.62  | | Case 1:
% 202.03/33.62  | | | 
% 202.03/33.62  | | |   (77)  all_58_2 = e3
% 202.03/33.62  | | | 
% 202.03/33.62  | | | REF_CLOSE: (18), (30), (77) are inconsistent by sub-proof #1369.
% 202.03/33.62  | | | 
% 202.03/33.62  | | Case 2:
% 202.03/33.62  | | | 
% 202.03/33.62  | | |   (78)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.62  | | | 
% 202.03/33.62  | | | BETA: splitting (51) gives:
% 202.03/33.62  | | | 
% 202.03/33.62  | | | Case 1:
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | |   (79)  all_58_9 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | COMBINE_EQS: (14), (79) imply:
% 202.03/33.62  | | | |   (80)  all_52_25 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | SIMP: (80) implies:
% 202.03/33.62  | | | |   (81)  all_52_25 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (40), (81) imply:
% 202.03/33.62  | | | |   (82)   ~ (all_52_9 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (7), (81) imply:
% 202.03/33.62  | | | |   (83)   ~ (all_52_17 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (1), (81) imply:
% 202.03/33.62  | | | |   (84)   ~ (all_52_27 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (27), (81) imply:
% 202.03/33.62  | | | |   (85)   ~ (all_52_29 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | SIMP: (85) implies:
% 202.03/33.62  | | | |   (86)   ~ (all_52_29 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (68), (81) imply:
% 202.03/33.62  | | | |   (87)  op(e3, e3) = all_52_24
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_24, e3, e3,
% 202.03/33.62  | | | |              simplifying with (50), (87) gives:
% 202.03/33.62  | | | |   (88)  all_52_24 = all_6_2
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | BETA: splitting (29) gives:
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | Case 1:
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | |   (89)  all_58_6 = e3
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | REF_CLOSE: (36), (57), (89) are inconsistent by sub-proof #1328.
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | Case 2:
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | |   (90)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (12), (13), (16), (17),
% 202.03/33.62  | | | | |            (21), (23), (25), (26), (28), (31), (32), (33), (35), (37),
% 202.03/33.62  | | | | |            (38), (41), (42), (46), (48), (49), (50), (54), (55), (58),
% 202.03/33.62  | | | | |            (59), (60), (61), (62), (64), (65), (67), (76), (78), (82),
% 202.03/33.62  | | | | |            (83), (86), (90) are inconsistent by sub-proof #319.
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | End of split
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | Case 2:
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | |   (91)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REF_CLOSE: (3), (4), (6), (8), (11), (14), (15), (17), (20), (21), (24),
% 202.03/33.62  | | | |            (25), (26), (27), (28), (35), (39), (43), (48), (49), (50),
% 202.03/33.62  | | | |            (52), (55), (58), (61), (62), (63), (64), (65), (66), (67),
% 202.03/33.62  | | | |            (76), (91) are inconsistent by sub-proof #1294.
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | End of split
% 202.03/33.62  | | | 
% 202.03/33.62  | | End of split
% 202.03/33.62  | | 
% 202.03/33.62  | End of split
% 202.03/33.62  | 
% 202.03/33.62  End of proof
% 202.03/33.62  
% 202.03/33.62  Sub-proof #319 shows that the following formulas are inconsistent:
% 202.03/33.62  ----------------------------------------------------------------
% 202.03/33.62    (1)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.03/33.62    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.62    (3)  all_58_1 = all_52_9
% 202.03/33.62    (4)   ~ (all_52_9 = all_52_13)
% 202.03/33.62    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.62    (6)  all_58_0 = all_6_2
% 202.03/33.62    (7)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.62    (8)  op(all_52_13, all_52_13) = e1
% 202.03/33.62    (9)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.62    (10)  op(e2, e2) = all_4_2
% 202.03/33.62    (11)  all_58_11 = all_52_29
% 202.03/33.62    (12)   ~ (all_4_1 = e1)
% 202.03/33.62    (13)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.62    (14)  op(e0, e0) = e0
% 202.03/33.62    (15)  all_58_10 = all_52_27
% 202.03/33.62    (16)  all_58_7 = all_52_13
% 202.03/33.62    (17)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.62    (18)  all_56_2 = all_52_17
% 202.03/33.62    (19)   ~ (all_52_29 = e3)
% 202.03/33.62    (20)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.62    (21)  op(all_4_2, e2) = all_4_1
% 202.03/33.62    (22)  all_56_6 = all_52_19
% 202.03/33.62    (23)   ~ (all_52_27 = e3)
% 202.03/33.62    (24)   ~ (all_52_9 = e3)
% 202.03/33.62    (25)   ~ (all_52_13 = all_4_2)
% 202.03/33.62    (26)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.62    (27)   ~ (all_52_19 = all_10_2)
% 202.03/33.62    (28)  all_58_8 = all_10_2
% 202.03/33.62    (29)   ~ (all_52_9 = all_4_2)
% 202.03/33.62    (30)  op(all_4_2, all_4_2) = e2
% 202.03/33.62    (31)   ~ (all_52_9 = all_6_2)
% 202.03/33.62    (32)  op(e3, e3) = all_6_2
% 202.03/33.62    (33)   ~ (all_52_17 = e3)
% 202.03/33.62    (34)  all_58_5 = all_52_19
% 202.03/33.62    (35)  all_56_1 = all_52_9
% 202.03/33.62    (36)  op(e3, e2) = all_52_9
% 202.03/33.62    (37)   ~ (all_52_17 = all_6_2)
% 202.03/33.62    (38)   ~ (e1 = e0)
% 202.03/33.62    (39)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.62    (40)   ~ (all_52_9 = all_52_17)
% 202.03/33.62    (41)  op(all_52_9, all_52_9) = e3
% 202.03/33.62    (42)  all_58_3 = all_4_2
% 202.03/33.62    (43)  all_58_4 = all_52_17
% 202.03/33.62  
% 202.03/33.62  Begin of proof
% 202.03/33.62  | 
% 202.03/33.62  | BETA: splitting (13) gives:
% 202.03/33.62  | 
% 202.03/33.62  | Case 1:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (44)  all_56_2 = e3
% 202.03/33.62  | | 
% 202.03/33.62  | | REF_CLOSE: (18), (33), (44) are inconsistent by sub-proof #1327.
% 202.03/33.62  | | 
% 202.03/33.62  | Case 2:
% 202.03/33.62  | | 
% 202.03/33.62  | |   (45)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.62  | | 
% 202.03/33.62  | | BETA: splitting (39) gives:
% 202.03/33.62  | | 
% 202.03/33.62  | | Case 1:
% 202.03/33.62  | | | 
% 202.03/33.62  | | |   (46)  all_56_1 = e3
% 202.03/33.62  | | | 
% 202.03/33.62  | | | REF_CLOSE: (24), (35), (46) are inconsistent by sub-proof #1326.
% 202.03/33.62  | | | 
% 202.03/33.62  | | Case 2:
% 202.03/33.62  | | | 
% 202.03/33.62  | | |   (47)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.62  | | | 
% 202.03/33.62  | | | BETA: splitting (17) gives:
% 202.03/33.62  | | | 
% 202.03/33.62  | | | Case 1:
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | |   (48)  all_56_6 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | COMBINE_EQS: (22), (48) imply:
% 202.03/33.62  | | | |   (49)  all_52_19 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | SIMP: (49) implies:
% 202.03/33.62  | | | |   (50)  all_52_19 = e3
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (27), (50) imply:
% 202.03/33.62  | | | |   (51)   ~ (all_10_2 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | SIMP: (51) implies:
% 202.03/33.62  | | | |   (52)   ~ (all_10_2 = e3)
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | REDUCE: (7), (50) imply:
% 202.03/33.62  | | | |   (53)  op(e3, e3) = all_52_18
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | BETA: splitting (26) gives:
% 202.03/33.62  | | | | 
% 202.03/33.62  | | | | Case 1:
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | |   (54)  all_58_7 = e3
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | COMBINE_EQS: (16), (54) imply:
% 202.03/33.62  | | | | |   (55)  all_52_13 = e3
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | REDUCE: (25), (55) imply:
% 202.03/33.62  | | | | |   (56)   ~ (all_4_2 = e3)
% 202.03/33.62  | | | | | 
% 202.03/33.62  | | | | | SIMP: (56) implies:
% 202.03/33.62  | | | | |   (57)   ~ (all_4_2 = e3)
% 202.03/33.62  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (8), (55) imply:
% 202.03/33.63  | | | | |   (58)  op(e3, e3) = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_18, e3, e3,
% 202.03/33.63  | | | | |              simplifying with (32), (53) gives:
% 202.03/33.63  | | | | |   (59)  all_52_18 = all_6_2
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | GROUND_INST: instantiating (2) with e1, all_52_18, e3, e3, simplifying
% 202.03/33.63  | | | | |              with (53), (58) gives:
% 202.03/33.63  | | | | |   (60)  all_52_18 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | COMBINE_EQS: (59), (60) imply:
% 202.03/33.63  | | | | |   (61)  all_6_2 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | SIMP: (61) implies:
% 202.03/33.63  | | | | |   (62)  all_6_2 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | COMBINE_EQS: (6), (62) imply:
% 202.03/33.63  | | | | |   (63)  all_58_0 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (31), (62) imply:
% 202.03/33.63  | | | | |   (64)   ~ (all_52_9 = e1)
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (37), (62) imply:
% 202.03/33.63  | | | | |   (65)   ~ (all_52_17 = e1)
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | BETA: splitting (1) gives:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | Case 1:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | |   (66)  all_58_4 = e0
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | COMBINE_EQS: (43), (66) imply:
% 202.03/33.63  | | | | | |   (67)  all_52_17 = e0
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | REDUCE: (40), (67) imply:
% 202.03/33.63  | | | | | |   (68)   ~ (all_52_9 = e0)
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | REF_CLOSE: (2), (10), (35), (41), (47), (57), (64), (68) are
% 202.03/33.63  | | | | | |            inconsistent by sub-proof #1109.
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | Case 2:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | |   (69)   ~ (all_58_4 = e0)
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | REF_CLOSE: (2), (3), (14), (18), (20), (24), (35), (38), (40), (41),
% 202.03/33.63  | | | | | |            (43), (45), (47), (63), (64), (65), (69) are inconsistent
% 202.03/33.63  | | | | | |            by sub-proof #1306.
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | End of split
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | Case 2:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (70)  all_58_8 = e3 | all_58_11 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REF_CLOSE: (11), (19), (28), (52), (70) are inconsistent by sub-proof
% 202.03/33.63  | | | | |            #1140.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | End of split
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | Case 2:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (71)   ~ (all_56_6 = e3)
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | REDUCE: (22), (71) imply:
% 202.03/33.63  | | | |   (72)   ~ (all_52_19 = e3)
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | BETA: splitting (5) gives:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | Case 1:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (73)  all_58_3 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | COMBINE_EQS: (42), (73) imply:
% 202.03/33.63  | | | | |   (74)  all_4_2 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (25), (74) imply:
% 202.03/33.63  | | | | |   (75)   ~ (all_52_13 = e3)
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (30), (74) imply:
% 202.03/33.63  | | | | |   (76)  op(e3, e3) = e2
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (21), (74) imply:
% 202.03/33.63  | | | | |   (77)  op(e3, e2) = all_4_1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REF_CLOSE: (2), (9), (11), (12), (14), (16), (19), (24), (26), (28),
% 202.03/33.63  | | | | |            (31), (32), (35), (36), (39), (41), (75), (76), (77) are
% 202.03/33.63  | | | | |            inconsistent by sub-proof #1322.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | Case 2:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (78)  all_58_5 = e3 | all_58_10 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REF_CLOSE: (15), (23), (34), (72), (78) are inconsistent by sub-proof
% 202.03/33.63  | | | | |            #1132.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | End of split
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | End of split
% 202.03/33.63  | | | 
% 202.03/33.63  | | End of split
% 202.03/33.63  | | 
% 202.03/33.63  | End of split
% 202.03/33.63  | 
% 202.03/33.63  End of proof
% 202.03/33.63  
% 202.03/33.63  Sub-proof #320 shows that the following formulas are inconsistent:
% 202.03/33.63  ----------------------------------------------------------------
% 202.03/33.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.63    (2)  all_58_1 = all_52_9
% 202.03/33.63    (3)   ~ (all_52_9 = all_52_13)
% 202.03/33.63    (4)   ~ (all_4_2 = e3)
% 202.03/33.63    (5)  all_58_0 = all_6_2
% 202.03/33.63    (6)  all_58_13 = all_52_15
% 202.03/33.63    (7)  op(all_52_13, all_52_13) = e1
% 202.03/33.63    (8)  all_58_9 = all_52_25
% 202.03/33.63    (9)   ~ (all_52_15 = e3)
% 202.03/33.63    (10)   ~ (all_52_25 = e0)
% 202.03/33.63    (11)   ~ (all_6_2 = e3)
% 202.03/33.63    (12)  op(e0, e0) = e0
% 202.03/33.63    (13)  all_58_7 = all_52_13
% 202.03/33.63    (14)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.63    (15)   ~ (all_52_25 = e3)
% 202.03/33.63    (16)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.63    (17)   ~ (all_52_9 = all_52_25)
% 202.03/33.63    (18)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.63    (19)   ~ (all_52_25 = all_6_2)
% 202.03/33.63    (20)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.63    (21)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.03/33.63    (22)   ~ (all_52_9 = all_6_2)
% 202.03/33.63    (23)  op(e3, e3) = all_6_2
% 202.03/33.63    (24)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.63    (25)  all_56_3 = all_52_25
% 202.03/33.63    (26)  all_56_1 = all_52_9
% 202.03/33.63    (27)   ~ (e1 = e0)
% 202.03/33.63    (28)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.63    (29)  op(all_52_9, all_52_9) = e3
% 202.03/33.63    (30)  all_58_3 = all_4_2
% 202.03/33.63    (31)  all_58_4 = all_52_17
% 202.03/33.63  
% 202.03/33.63  Begin of proof
% 202.03/33.63  | 
% 202.03/33.63  | BETA: splitting (20) gives:
% 202.03/33.63  | 
% 202.03/33.63  | Case 1:
% 202.03/33.63  | | 
% 202.03/33.63  | |   (32)  all_56_3 = e3
% 202.03/33.63  | | 
% 202.03/33.63  | | REF_CLOSE: (15), (25), (32) are inconsistent by sub-proof #1339.
% 202.03/33.63  | | 
% 202.03/33.63  | Case 2:
% 202.03/33.63  | | 
% 202.03/33.63  | |   (33)   ~ (all_56_3 = e3)
% 202.03/33.63  | |   (34)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.63  | | 
% 202.03/33.63  | | BETA: splitting (21) gives:
% 202.03/33.63  | | 
% 202.03/33.63  | | Case 1:
% 202.03/33.63  | | | 
% 202.03/33.63  | | |   (35)  all_58_9 = e2
% 202.03/33.63  | | | 
% 202.03/33.63  | | | COMBINE_EQS: (8), (35) imply:
% 202.03/33.63  | | |   (36)  all_52_25 = e2
% 202.03/33.63  | | | 
% 202.03/33.63  | | | SIMP: (36) implies:
% 202.03/33.63  | | |   (37)  all_52_25 = e2
% 202.03/33.63  | | | 
% 202.03/33.63  | | | REDUCE: (17), (37) imply:
% 202.03/33.63  | | |   (38)   ~ (all_52_9 = e2)
% 202.03/33.63  | | | 
% 202.03/33.63  | | | REDUCE: (15), (37) imply:
% 202.03/33.63  | | |   (39)   ~ (e3 = e2)
% 202.03/33.63  | | | 
% 202.03/33.63  | | | SIMP: (39) implies:
% 202.03/33.63  | | |   (40)   ~ (e3 = e2)
% 202.03/33.63  | | | 
% 202.03/33.63  | | | BETA: splitting (16) gives:
% 202.03/33.63  | | | 
% 202.03/33.63  | | | Case 1:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (41)  all_58_1 = e3
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | COMBINE_EQS: (2), (41) imply:
% 202.03/33.63  | | | |   (42)  all_52_9 = e3
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | REF_CLOSE: (1), (22), (23), (29), (42) are inconsistent by sub-proof
% 202.03/33.63  | | | |            #1337.
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | Case 2:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (43)   ~ (all_58_1 = e3)
% 202.03/33.63  | | | |   (44)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | REDUCE: (2), (43) imply:
% 202.03/33.63  | | | |   (45)   ~ (all_52_9 = e3)
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | BETA: splitting (24) gives:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | Case 1:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (46)  all_58_0 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | COMBINE_EQS: (5), (46) imply:
% 202.03/33.63  | | | | |   (47)  all_6_2 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (11), (47) imply:
% 202.03/33.63  | | | | |   (48)  $false
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | CLOSE: (48) is inconsistent.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | Case 2:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (49)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | BETA: splitting (49) gives:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | Case 1:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | |   (50)  all_58_1 = e3
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | COMBINE_EQS: (2), (50) imply:
% 202.03/33.63  | | | | | |   (51)  all_52_9 = e3
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | REDUCE: (45), (51) imply:
% 202.03/33.63  | | | | | |   (52)  $false
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | CLOSE: (52) is inconsistent.
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | Case 2:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | |   (53)  all_58_4 = e3 | all_58_9 = e3
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | BETA: splitting (53) gives:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | Case 1:
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | |   (54)  all_58_4 = e3
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | COMBINE_EQS: (31), (54) imply:
% 202.03/33.63  | | | | | | |   (55)  all_52_17 = e3
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | REDUCE: (18), (55) imply:
% 202.03/33.63  | | | | | | |   (56)  op(e3, e3) = all_52_16
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | BETA: splitting (44) gives:
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | Case 1:
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | |   (57)  all_58_3 = e3
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | COMBINE_EQS: (30), (57) imply:
% 202.03/33.63  | | | | | | | |   (58)  all_4_2 = e3
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | REDUCE: (4), (58) imply:
% 202.03/33.63  | | | | | | | |   (59)  $false
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | CLOSE: (59) is inconsistent.
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | Case 2:
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | |   (60)  all_58_7 = e3 | all_58_13 = e3
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | BETA: splitting (60) gives:
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | Case 1:
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | |   (61)  all_58_7 = e3
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | COMBINE_EQS: (13), (61) imply:
% 202.03/33.63  | | | | | | | | |   (62)  all_52_13 = e3
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | REDUCE: (7), (62) imply:
% 202.03/33.63  | | | | | | | | |   (63)  op(e3, e3) = e1
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | GROUND_INST: instantiating (1) with all_6_2, all_52_16, e3, e3,
% 202.03/33.63  | | | | | | | | |              simplifying with (23), (56) gives:
% 202.03/33.63  | | | | | | | | |   (64)  all_52_16 = all_6_2
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | GROUND_INST: instantiating (1) with e1, all_52_16, e3, e3,
% 202.03/33.63  | | | | | | | | |              simplifying with (56), (63) gives:
% 202.03/33.63  | | | | | | | | |   (65)  all_52_16 = e1
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | COMBINE_EQS: (64), (65) imply:
% 202.03/33.63  | | | | | | | | |   (66)  all_6_2 = e1
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | SIMP: (66) implies:
% 202.03/33.63  | | | | | | | | |   (67)  all_6_2 = e1
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | COMBINE_EQS: (5), (67) imply:
% 202.03/33.63  | | | | | | | | |   (68)  all_58_0 = e1
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | REDUCE: (22), (67) imply:
% 202.03/33.63  | | | | | | | | |   (69)   ~ (all_52_9 = e1)
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | REF_CLOSE: (1), (2), (12), (14), (26), (27), (28), (29), (38),
% 202.03/33.63  | | | | | | | | |            (45), (68), (69) are inconsistent by sub-proof
% 202.03/33.63  | | | | | | | | |            #1331.
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | Case 2:
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | |   (70)  all_58_13 = e3
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | COMBINE_EQS: (6), (70) imply:
% 202.03/33.63  | | | | | | | | |   (71)  all_52_15 = e3
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | REDUCE: (9), (71) imply:
% 202.03/33.63  | | | | | | | | |   (72)  $false
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | | CLOSE: (72) is inconsistent.
% 202.03/33.63  | | | | | | | | | 
% 202.03/33.63  | | | | | | | | End of split
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | End of split
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | Case 2:
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | |   (73)  all_58_9 = e3
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | REF_CLOSE: (35), (40), (73) are inconsistent by sub-proof #840.
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | End of split
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | End of split
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | End of split
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | End of split
% 202.03/33.63  | | | 
% 202.03/33.63  | | Case 2:
% 202.03/33.63  | | | 
% 202.03/33.63  | | |   (74)   ~ (all_58_9 = e2)
% 202.03/33.63  | | | 
% 202.03/33.63  | | | REDUCE: (8), (74) imply:
% 202.03/33.63  | | |   (75)   ~ (all_52_25 = e2)
% 202.03/33.63  | | | 
% 202.03/33.63  | | | BETA: splitting (34) gives:
% 202.03/33.63  | | | 
% 202.03/33.63  | | | Case 1:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (76)  all_56_3 = e2
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | REF_CLOSE: (25), (75), (76) are inconsistent by sub-proof #1259.
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | Case 2:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (77)  all_56_3 = e1 | all_56_3 = e0
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | BETA: splitting (77) gives:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | Case 1:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (78)  all_56_3 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | COMBINE_EQS: (25), (78) imply:
% 202.03/33.63  | | | | |   (79)  all_52_25 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | SIMP: (79) implies:
% 202.03/33.63  | | | | |   (80)  all_52_25 = e1
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REDUCE: (19), (80) imply:
% 202.03/33.63  | | | | |   (81)   ~ (all_6_2 = e1)
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | SIMP: (81) implies:
% 202.03/33.63  | | | | |   (82)   ~ (all_6_2 = e1)
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (13), (16), (22), (23), (29),
% 202.03/33.63  | | | | |            (30), (82) are inconsistent by sub-proof #1142.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | Case 2:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (83)  all_56_3 = e0
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REF_CLOSE: (10), (25), (83) are inconsistent by sub-proof #1258.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | End of split
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | End of split
% 202.03/33.63  | | | 
% 202.03/33.63  | | End of split
% 202.03/33.63  | | 
% 202.03/33.63  | End of split
% 202.03/33.63  | 
% 202.03/33.63  End of proof
% 202.03/33.63  
% 202.03/33.63  Sub-proof #321 shows that the following formulas are inconsistent:
% 202.03/33.63  ----------------------------------------------------------------
% 202.03/33.63    (1)  all_58_14 = all_52_23
% 202.03/33.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.63    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.63    (4)   ~ (all_52_7 = all_52_15)
% 202.03/33.63    (5)  op(all_52_15, all_52_15) = e0
% 202.03/33.63    (6)  op(e3, all_6_1) = e1
% 202.03/33.63    (7)  all_58_13 = all_52_15
% 202.03/33.63    (8)  op(e2, e2) = all_4_2
% 202.03/33.63    (9)  all_56_13 = e3
% 202.03/33.63    (10)   ~ (all_52_9 = all_52_15)
% 202.03/33.63    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.63    (12)   ~ (all_52_7 = all_6_2)
% 202.03/33.63    (13)  all_58_15 = e0
% 202.03/33.63    (14)  all_58_12 = all_52_7
% 202.03/33.63    (15)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 202.03/33.63    (16)   ~ (e2 = e0)
% 202.03/33.63    (17)  op(e3, e1) = all_52_17
% 202.03/33.63    (18)  op(e0, e3) = all_52_7
% 202.03/33.63    (19)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.63    (20)  all_56_12 = all_52_7
% 202.03/33.63    (21)   ~ (all_52_9 = all_6_2)
% 202.03/33.63    (22)  op(e3, e3) = all_6_2
% 202.03/33.63    (23)  all_56_1 = all_52_9
% 202.03/33.63    (24)   ~ (all_52_15 = all_4_2)
% 202.03/33.63    (25)   ~ (e3 = e2)
% 202.03/33.63    (26)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.63    (27)   ~ (all_52_9 = all_52_17)
% 202.03/33.63    (28)  op(all_52_9, all_52_9) = e3
% 202.03/33.63    (29)  all_56_13 = all_52_15
% 202.03/33.63    (30)  op(all_6_2, e3) = all_6_1
% 202.03/33.63  
% 202.03/33.63  Begin of proof
% 202.03/33.63  | 
% 202.03/33.63  | COMBINE_EQS: (9), (29) imply:
% 202.03/33.63  |   (31)  all_52_15 = e3
% 202.03/33.63  | 
% 202.03/33.63  | SIMP: (31) implies:
% 202.03/33.63  |   (32)  all_52_15 = e3
% 202.03/33.63  | 
% 202.03/33.63  | COMBINE_EQS: (7), (32) imply:
% 202.03/33.63  |   (33)  all_58_13 = e3
% 202.03/33.63  | 
% 202.03/33.63  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 202.03/33.63  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 202.03/33.63  |            (26), (27), (28), (30), (32), (33) are inconsistent by sub-proof
% 202.03/33.63  |            #322.
% 202.03/33.63  | 
% 202.03/33.63  End of proof
% 202.03/33.63  
% 202.03/33.63  Sub-proof #322 shows that the following formulas are inconsistent:
% 202.03/33.63  ----------------------------------------------------------------
% 202.03/33.63    (1)  all_58_14 = all_52_23
% 202.03/33.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.63    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.63    (4)   ~ (all_52_7 = all_52_15)
% 202.03/33.63    (5)  op(all_52_15, all_52_15) = e0
% 202.03/33.63    (6)  op(e3, all_6_1) = e1
% 202.03/33.63    (7)  all_58_13 = e3
% 202.03/33.63    (8)  all_52_15 = e3
% 202.03/33.63    (9)  op(e2, e2) = all_4_2
% 202.03/33.63    (10)   ~ (all_52_9 = all_52_15)
% 202.03/33.63    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.63    (12)   ~ (all_52_7 = all_6_2)
% 202.03/33.63    (13)  all_58_15 = e0
% 202.03/33.63    (14)  all_58_12 = all_52_7
% 202.03/33.63    (15)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 202.03/33.63    (16)   ~ (e2 = e0)
% 202.03/33.63    (17)  op(e3, e1) = all_52_17
% 202.03/33.63    (18)  op(e0, e3) = all_52_7
% 202.03/33.63    (19)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.63    (20)  all_56_12 = all_52_7
% 202.03/33.63    (21)   ~ (all_52_9 = all_6_2)
% 202.03/33.63    (22)  op(e3, e3) = all_6_2
% 202.03/33.63    (23)  all_56_1 = all_52_9
% 202.03/33.63    (24)   ~ (all_52_15 = all_4_2)
% 202.03/33.63    (25)   ~ (e3 = e2)
% 202.03/33.63    (26)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.63    (27)   ~ (all_52_9 = all_52_17)
% 202.03/33.63    (28)  op(all_52_9, all_52_9) = e3
% 202.03/33.63    (29)  op(all_6_2, e3) = all_6_1
% 202.03/33.63  
% 202.03/33.63  Begin of proof
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (4), (8) imply:
% 202.03/33.63  |   (30)   ~ (all_52_7 = e3)
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (8), (10) imply:
% 202.03/33.63  |   (31)   ~ (all_52_9 = e3)
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (8), (24) imply:
% 202.03/33.63  |   (32)   ~ (all_4_2 = e3)
% 202.03/33.63  | 
% 202.03/33.63  | SIMP: (32) implies:
% 202.03/33.63  |   (33)   ~ (all_4_2 = e3)
% 202.03/33.63  | 
% 202.03/33.63  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 202.03/33.63  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 202.03/33.63  |            (27), (28), (29), (30), (31), (33) are inconsistent by sub-proof
% 202.03/33.63  |            #323.
% 202.03/33.63  | 
% 202.03/33.63  End of proof
% 202.03/33.63  
% 202.03/33.63  Sub-proof #323 shows that the following formulas are inconsistent:
% 202.03/33.63  ----------------------------------------------------------------
% 202.03/33.63    (1)  all_58_14 = all_52_23
% 202.03/33.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.63    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.63    (4)  op(all_52_15, all_52_15) = e0
% 202.03/33.63    (5)   ~ (all_4_2 = e3)
% 202.03/33.63    (6)  op(e3, all_6_1) = e1
% 202.03/33.63    (7)  all_58_13 = e3
% 202.03/33.63    (8)  all_52_15 = e3
% 202.03/33.63    (9)  op(e2, e2) = all_4_2
% 202.03/33.63    (10)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.63    (11)   ~ (all_52_7 = all_6_2)
% 202.03/33.63    (12)  all_58_15 = e0
% 202.03/33.63    (13)  all_58_12 = all_52_7
% 202.03/33.63    (14)   ~ (all_6_1 = e2) |  ~ (all_6_2 = e0)
% 202.03/33.63    (15)   ~ (all_52_7 = e3)
% 202.03/33.63    (16)   ~ (e2 = e0)
% 202.03/33.63    (17)   ~ (all_52_9 = e3)
% 202.03/33.63    (18)  op(e3, e1) = all_52_17
% 202.03/33.63    (19)  op(e0, e3) = all_52_7
% 202.03/33.63    (20)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.63    (21)  all_56_12 = all_52_7
% 202.03/33.63    (22)   ~ (all_52_9 = all_6_2)
% 202.03/33.63    (23)  op(e3, e3) = all_6_2
% 202.03/33.63    (24)  all_56_1 = all_52_9
% 202.03/33.63    (25)   ~ (e3 = e2)
% 202.03/33.63    (26)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.63    (27)   ~ (all_52_9 = all_52_17)
% 202.03/33.63    (28)  op(all_52_9, all_52_9) = e3
% 202.03/33.63    (29)  op(all_6_2, e3) = all_6_1
% 202.03/33.63  
% 202.03/33.63  Begin of proof
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (4), (8) imply:
% 202.03/33.63  |   (30)  op(e3, e3) = e0
% 202.03/33.63  | 
% 202.03/33.63  | GROUND_INST: instantiating (2) with all_6_2, e0, e3, e3, simplifying with
% 202.03/33.63  |              (23), (30) gives:
% 202.03/33.63  |   (31)  all_6_2 = e0
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (11), (31) imply:
% 202.03/33.63  |   (32)   ~ (all_52_7 = e0)
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (22), (31) imply:
% 202.03/33.63  |   (33)   ~ (all_52_9 = e0)
% 202.03/33.63  | 
% 202.03/33.63  | REDUCE: (29), (31) imply:
% 202.03/33.63  |   (34)  op(e0, e3) = all_6_1
% 202.03/33.63  | 
% 202.03/33.63  | BETA: splitting (14) gives:
% 202.03/33.63  | 
% 202.03/33.63  | Case 1:
% 202.03/33.63  | | 
% 202.03/33.63  | |   (35)   ~ (all_6_1 = e2)
% 202.03/33.63  | | 
% 202.03/33.63  | | GROUND_INST: instantiating (2) with all_52_7, all_6_1, e3, e0, simplifying
% 202.03/33.63  | |              with (19), (34) gives:
% 202.03/33.63  | |   (36)  all_52_7 = all_6_1
% 202.03/33.63  | | 
% 202.03/33.63  | | COMBINE_EQS: (21), (36) imply:
% 202.03/33.63  | |   (37)  all_56_12 = all_6_1
% 202.03/33.63  | | 
% 202.03/33.63  | | COMBINE_EQS: (13), (36) imply:
% 202.03/33.63  | |   (38)  all_58_12 = all_6_1
% 202.03/33.63  | | 
% 202.03/33.63  | | REDUCE: (15), (36) imply:
% 202.03/33.63  | |   (39)   ~ (all_6_1 = e3)
% 202.03/33.63  | | 
% 202.03/33.63  | | REDUCE: (32), (36) imply:
% 202.03/33.63  | |   (40)   ~ (all_6_1 = e0)
% 202.03/33.63  | | 
% 202.03/33.63  | | BETA: splitting (3) gives:
% 202.03/33.63  | | 
% 202.03/33.63  | | Case 1:
% 202.03/33.63  | | | 
% 202.03/33.63  | | |   (41)  all_56_12 = e3
% 202.03/33.63  | | | 
% 202.03/33.63  | | | REF_CLOSE: (37), (39), (41) are inconsistent by sub-proof #1347.
% 202.03/33.63  | | | 
% 202.03/33.63  | | Case 2:
% 202.03/33.63  | | | 
% 202.03/33.63  | | |   (42)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.63  | | | 
% 202.03/33.63  | | | BETA: splitting (10) gives:
% 202.03/33.63  | | | 
% 202.03/33.63  | | | Case 1:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (43)  all_58_12 = e2
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | COMBINE_EQS: (38), (43) imply:
% 202.03/33.63  | | | |   (44)  all_6_1 = e2
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | SIMP: (44) implies:
% 202.03/33.63  | | | |   (45)  all_6_1 = e2
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | REDUCE: (35), (45) imply:
% 202.03/33.63  | | | |   (46)  $false
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | CLOSE: (46) is inconsistent.
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | Case 2:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | |   (47)   ~ (all_58_12 = e2)
% 202.03/33.63  | | | |   (48)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | BETA: splitting (42) gives:
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | | Case 1:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (49)  all_56_12 = e2
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | REF_CLOSE: (35), (37), (49) are inconsistent by sub-proof #1346.
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | Case 2:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | |   (50)  all_56_12 = e1 | all_56_12 = e0
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | BETA: splitting (50) gives:
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | | Case 1:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | |   (51)  all_56_12 = e1
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | COMBINE_EQS: (37), (51) imply:
% 202.03/33.63  | | | | | |   (52)  all_6_1 = e1
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | SIMP: (52) implies:
% 202.03/33.63  | | | | | |   (53)  all_6_1 = e1
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | REDUCE: (6), (53) imply:
% 202.03/33.63  | | | | | |   (54)  op(e3, e1) = e1
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | BETA: splitting (48) gives:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | Case 1:
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | |   (55)  all_58_13 = e2
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | REF_CLOSE: (7), (25), (55) are inconsistent by sub-proof #1248.
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | Case 2:
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | |   (56)  all_58_14 = e2 | all_58_15 = e2
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | BETA: splitting (56) gives:
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | | Case 1:
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | |   (57)  all_58_14 = e2
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | COMBINE_EQS: (1), (57) imply:
% 202.03/33.63  | | | | | | | |   (58)  all_52_23 = e2
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | SIMP: (58) implies:
% 202.03/33.63  | | | | | | | |   (59)  all_52_23 = e2
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | REDUCE: (20), (59) imply:
% 202.03/33.63  | | | | | | | |   (60)  op(e2, e2) = all_52_22
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_22, e2, e2,
% 202.03/33.63  | | | | | | | |              simplifying with (9), (60) gives:
% 202.03/33.63  | | | | | | | |   (61)  all_52_22 = all_4_2
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | GROUND_INST: instantiating (2) with all_52_17, e1, e1, e3,
% 202.03/33.63  | | | | | | | |              simplifying with (18), (54) gives:
% 202.03/33.63  | | | | | | | |   (62)  all_52_17 = e1
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | REDUCE: (27), (62) imply:
% 202.03/33.63  | | | | | | | |   (63)   ~ (all_52_9 = e1)
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | REF_CLOSE: (2), (5), (9), (17), (24), (26), (28), (33), (63) are
% 202.03/33.63  | | | | | | | |            inconsistent by sub-proof #324.
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | Case 2:
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | |   (64)  all_58_15 = e2
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | | REF_CLOSE: (12), (16), (64) are inconsistent by sub-proof #1223.
% 202.03/33.63  | | | | | | | | 
% 202.03/33.63  | | | | | | | End of split
% 202.03/33.63  | | | | | | | 
% 202.03/33.63  | | | | | | End of split
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | Case 2:
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | |   (65)  all_56_12 = e0
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | | REF_CLOSE: (37), (40), (65) are inconsistent by sub-proof #1345.
% 202.03/33.63  | | | | | | 
% 202.03/33.63  | | | | | End of split
% 202.03/33.63  | | | | | 
% 202.03/33.63  | | | | End of split
% 202.03/33.63  | | | | 
% 202.03/33.63  | | | End of split
% 202.03/33.63  | | | 
% 202.03/33.63  | | End of split
% 202.03/33.63  | | 
% 202.03/33.63  | Case 2:
% 202.03/33.63  | | 
% 202.03/33.63  | |   (66)   ~ (all_6_2 = e0)
% 202.03/33.63  | | 
% 202.03/33.63  | | REDUCE: (31), (66) imply:
% 202.03/33.63  | |   (67)  $false
% 202.03/33.63  | | 
% 202.03/33.63  | | CLOSE: (67) is inconsistent.
% 202.03/33.63  | | 
% 202.03/33.63  | End of split
% 202.03/33.63  | 
% 202.03/33.63  End of proof
% 202.03/33.63  
% 202.03/33.63  Sub-proof #324 shows that the following formulas are inconsistent:
% 202.03/33.63  ----------------------------------------------------------------
% 202.03/33.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.63    (2)   ~ (all_4_2 = e3)
% 202.03/33.63    (3)  op(e2, e2) = all_4_2
% 202.03/33.63    (4)   ~ (all_52_9 = e3)
% 202.03/33.63    (5)   ~ (all_52_9 = e1)
% 202.03/33.63    (6)  all_56_1 = all_52_9
% 202.03/33.63    (7)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.63    (8)   ~ (all_52_9 = e0)
% 202.03/33.63    (9)  op(all_52_9, all_52_9) = e3
% 202.03/33.63  
% 202.03/33.63  Begin of proof
% 202.03/33.63  | 
% 202.03/33.63  | BETA: splitting (7) gives:
% 202.03/33.63  | 
% 202.03/33.63  | Case 1:
% 202.03/33.63  | | 
% 202.03/33.63  | |   (10)  all_56_1 = e3
% 202.03/33.63  | | 
% 202.03/33.63  | | COMBINE_EQS: (6), (10) imply:
% 202.03/33.63  | |   (11)  all_52_9 = e3
% 202.03/33.63  | | 
% 202.03/33.63  | | REDUCE: (4), (11) imply:
% 202.03/33.63  | |   (12)  $false
% 202.03/33.63  | | 
% 202.03/33.63  | | CLOSE: (12) is inconsistent.
% 202.03/33.63  | | 
% 202.03/33.63  | Case 2:
% 202.03/33.63  | | 
% 202.03/33.63  | |   (13)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.63  | | 
% 202.03/33.63  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (13) are inconsistent by
% 202.03/33.63  | |            sub-proof #1109.
% 202.03/33.63  | | 
% 202.03/33.63  | End of split
% 202.03/33.63  | 
% 202.03/33.63  End of proof
% 202.03/33.63  
% 202.03/33.63  Sub-proof #325 shows that the following formulas are inconsistent:
% 202.03/33.63  ----------------------------------------------------------------
% 202.03/33.63    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.63    (2)   ~ (all_52_15 = all_52_23)
% 202.03/33.63    (3)   ~ (all_52_25 = all_52_27)
% 202.03/33.63    (4)  all_58_14 = all_52_23
% 202.03/33.63    (5)   ~ (e3 = e1)
% 202.03/33.63    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.63    (8)   ~ (all_52_5 = all_52_13)
% 202.03/33.63    (9)  all_58_1 = all_52_9
% 202.03/33.63    (10)   ~ (all_52_9 = all_52_13)
% 202.03/33.63    (11)   ~ (e3 = e0)
% 202.03/33.63    (12)  op(e2, e3) = all_52_3
% 202.03/33.63    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.63    (14)   ~ (all_52_7 = all_52_15)
% 202.03/33.63    (15)   ~ (all_52_3 = all_52_19)
% 202.03/33.63    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.63    (17)   ~ (all_52_17 = all_52_25)
% 202.03/33.63    (18)   ~ (all_52_3 = all_6_2)
% 202.03/33.63    (19)  all_44_2 = all_6_2
% 202.03/33.63    (20)  all_58_0 = all_6_2
% 202.03/33.63    (21)  op(all_14_2, e0) = all_14_1
% 202.03/33.63    (22)  all_56_4 = all_52_3
% 202.03/33.63    (23)   ~ (all_52_17 = all_10_2)
% 202.03/33.63    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.63    (25)  op(e3, e0) = all_52_25
% 202.03/33.63    (26)  op(e0, all_14_1) = all_14_0
% 202.03/33.63    (27)  op(all_52_5, all_52_5) = all_52_4
% 202.03/33.63    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.63    (29)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.63    (30)   ~ (all_52_27 = all_52_29)
% 202.03/33.63    (31)  all_58_13 = all_52_15
% 202.03/33.63    (32)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.63    (33)  all_58_9 = all_52_25
% 202.03/33.63    (34)   ~ (all_52_29 = all_14_2)
% 202.03/33.63    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.03/33.63    (36)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.63    (37)  op(e1, e3) = all_52_5
% 202.03/33.63    (38)  op(e2, e2) = all_4_2
% 202.03/33.63    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.63    (40)   ~ (all_52_3 = all_52_5)
% 202.03/33.63    (41)  all_58_11 = all_52_29
% 202.03/33.63    (42)  all_56_5 = all_4_2
% 202.03/33.63    (43)   ~ (all_52_25 = all_14_2)
% 202.03/33.63    (44)   ~ (all_52_9 = all_52_15)
% 202.03/33.63    (45)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.63    (46)   ~ (all_52_3 = all_52_27)
% 202.03/33.63    (47)  op(all_10_2, e1) = all_10_1
% 202.03/33.63    (48)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.63    (49)   ~ (all_52_7 = all_6_2)
% 202.03/33.63    (50)  op(e0, e0) = all_14_2
% 202.03/33.63    (51)  op(e0, e1) = all_52_23
% 202.03/33.63    (52)  all_56_15 = all_14_2
% 202.03/33.63    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.63    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.03/33.63    (55)   ~ (all_58_15 = e0)
% 202.03/33.63    (56)  all_56_11 = all_52_29
% 202.03/33.64    (57)   ~ (all_4_1 = e1)
% 202.03/33.64    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.64    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.64    (60)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.03/33.64    (61)  all_56_9 = all_52_13
% 202.03/33.64    (62)   ~ (e2 = e1)
% 202.03/33.64    (63)   ~ (all_52_13 = all_10_2)
% 202.03/33.64    (64)  all_58_10 = all_52_27
% 202.03/33.64    (65)  all_56_8 = all_52_5
% 202.03/33.64    (66)  op(all_52_9, all_52_9) = all_52_8
% 202.03/33.64    (67)  op(all_52_15, all_52_15) = all_52_14
% 202.03/33.64    (68)   ~ (all_52_19 = all_52_23)
% 202.03/33.64    (69)   ~ (all_52_25 = all_52_29)
% 202.03/33.64    (70)   ~ (all_52_29 = all_10_2)
% 202.03/33.64    (71)  all_58_7 = all_52_13
% 202.03/33.64    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.03/33.64    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.64    (74)   ~ (all_52_5 = all_52_7)
% 202.03/33.64    (75)  all_58_12 = all_52_7
% 202.03/33.64    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.64    (77)   ~ (all_52_7 = all_14_2)
% 202.03/33.64    (78)  all_58_2 = all_52_3
% 202.03/33.64    (79)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.64    (80)  all_56_2 = all_52_17
% 202.03/33.64    (81)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.03/33.64    (82)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.64    (83)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.64    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.03/33.64    (85)  all_56_7 = all_52_27
% 202.03/33.64    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.64    (87)   ~ (e2 = e0)
% 202.03/33.64    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.03/33.64    (89)  op(all_4_2, e2) = all_4_1
% 202.03/33.64    (90)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.64    (91)   ~ (all_52_5 = all_52_29)
% 202.03/33.64    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.64    (93)  all_56_6 = all_52_19
% 202.03/33.64    (94)   ~ (all_52_15 = all_14_2)
% 202.03/33.64    (95)   ~ (all_52_19 = all_52_27)
% 202.03/33.64    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.03/33.64    (97)   ~ (all_52_13 = all_4_2)
% 202.03/33.64    (98)  op(e3, e1) = all_52_17
% 202.03/33.64    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.03/33.64    (100)  op(e0, e3) = all_52_7
% 202.03/33.64    (101)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.64    (102)   ~ (all_52_9 = all_52_25)
% 202.03/33.64    (103)  all_58_15 = all_14_2
% 202.03/33.64    (104)   ~ (all_52_19 = all_10_2)
% 202.03/33.64    (105)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.64    (106)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.64    (107)  all_58_8 = all_10_2
% 202.03/33.64    (108)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.03/33.64    (109)   ~ (all_52_5 = all_10_2)
% 202.03/33.64    (110)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.64    (111)   ~ (all_52_23 = all_14_2)
% 202.03/33.64    (112)  all_56_12 = all_52_7
% 202.03/33.64    (113)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.64    (114)  all_8_2 = all_6_2
% 202.03/33.64    (115)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.03/33.64    (116)   ~ (all_52_25 = all_6_2)
% 202.03/33.64    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.64    (118)   ~ (all_52_9 = all_4_2)
% 202.03/33.64    (119)   ~ (all_52_5 = all_6_2)
% 202.03/33.64    (120)   ~ (all_52_9 = all_6_2)
% 202.03/33.64    (121)   ~ (all_52_13 = all_52_15)
% 202.03/33.64    (122)  op(e3, all_6_1) = e2
% 202.03/33.64    (123)  all_56_0 = all_6_2
% 202.03/33.64    (124)  op(e3, e3) = all_6_2
% 202.03/33.64    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.64    (126)   ~ (all_52_27 = all_14_2)
% 202.03/33.64    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.64    (128)  all_56_14 = all_52_23
% 202.03/33.64    (129)  op(all_4_2, all_4_2) = all_52_10
% 202.03/33.64    (130)  all_56_3 = all_52_25
% 202.03/33.64    (131)   ~ (all_52_3 = all_52_7)
% 202.03/33.64    (132)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.64    (133)  all_58_5 = all_52_19
% 202.03/33.64    (134)  all_56_1 = all_52_9
% 202.03/33.64    (135)   ~ (all_52_15 = all_4_2)
% 202.03/33.64    (136)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.03/33.64           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.03/33.64           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.03/33.64           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.03/33.64    (137)   ~ (all_52_27 = all_4_2)
% 202.03/33.64    (138)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 202.03/33.64             all_58_13 = e0 | all_58_14 = e0)
% 202.03/33.64    (139)  all_58_6 = all_52_5
% 202.03/33.64    (140)  op(e3, e2) = all_52_9
% 202.03/33.64    (141)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.64    (142)   ~ (all_52_17 = all_6_2)
% 202.03/33.64    (143)   ~ (e1 = e0)
% 202.03/33.64    (144)   ~ (e3 = e2)
% 202.03/33.64    (145)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.64    (146)  all_44_1 = all_6_1
% 202.03/33.64    (147)   ~ (all_52_9 = all_52_17)
% 202.03/33.64    (148)  all_56_10 = all_10_2
% 202.03/33.64    (149)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.64    (150)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.03/33.64    (151)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.64    (152)  op(all_52_13, all_52_13) = all_52_12
% 202.03/33.64    (153)  op(e1, e1) = all_10_2
% 202.03/33.64    (154)   ~ (all_52_23 = all_10_2)
% 202.03/33.64    (155)   ~ (all_52_7 = all_52_23)
% 202.03/33.64    (156)   ~ (all_52_17 = all_52_19)
% 202.03/33.64    (157)  all_58_3 = all_4_2
% 202.03/33.64    (158)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.03/33.64    (159)  all_56_13 = all_52_15
% 202.03/33.64    (160)   ~ (all_52_3 = all_4_2)
% 202.03/33.64    (161)   ~ (all_52_19 = all_4_2)
% 202.03/33.64    (162)   ~ (all_52_17 = all_52_23)
% 202.03/33.64    (163)  all_8_1 = all_6_1
% 202.03/33.64    (164)  op(all_6_2, e3) = all_6_1
% 202.03/33.64    (165)   ~ (all_52_13 = all_52_29)
% 202.03/33.64    (166)  all_58_4 = all_52_17
% 202.03/33.64    (167)   ~ (all_14_0 = e2)
% 202.03/33.64    (168)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.03/33.64    (169)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.64  
% 202.03/33.64  Begin of proof
% 202.03/33.64  | 
% 202.03/33.64  | ALPHA: (138) implies:
% 202.03/33.64  |   (170)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.03/33.64  |   (171)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.03/33.64  | 
% 202.03/33.64  | REDUCE: (55), (103) imply:
% 202.03/33.64  |   (172)   ~ (all_14_2 = e0)
% 202.03/33.64  | 
% 202.03/33.64  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.03/33.64  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.03/33.64  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.03/33.64  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 202.03/33.64  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 202.03/33.64  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 202.03/33.64  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 202.03/33.64  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 202.03/33.64  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 202.03/33.64  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 202.03/33.64  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 202.03/33.64  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 202.03/33.64  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 202.03/33.64  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 202.03/33.64  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 202.03/33.64  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 202.03/33.64  |            (166), (167), (168), (169), (170), (171), (172) are inconsistent by
% 202.03/33.64  |            sub-proof #327.
% 202.03/33.64  | 
% 202.03/33.64  End of proof
% 202.03/33.64  
% 202.03/33.64  Sub-proof #326 shows that the following formulas are inconsistent:
% 202.03/33.64  ----------------------------------------------------------------
% 202.03/33.64    (1)  all_24_0 = e1
% 202.03/33.64    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.64    (3)   ~ (all_52_15 = all_52_23)
% 202.03/33.64    (4)   ~ (all_52_25 = all_52_27)
% 202.03/33.64    (5)  all_58_14 = all_52_23
% 202.03/33.64    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.64    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.64    (8)   ~ (all_52_5 = all_52_13)
% 202.03/33.64    (9)  all_58_1 = all_52_9
% 202.03/33.64    (10)   ~ (all_52_9 = all_52_13)
% 202.03/33.64    (11)   ~ (e3 = e0)
% 202.03/33.64    (12)  op(e2, e3) = all_52_3
% 202.03/33.64    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.64    (14)   ~ (all_52_7 = all_52_15)
% 202.03/33.64    (15)  all_34_0 = all_14_0
% 202.03/33.64    (16)   ~ (all_52_3 = all_52_19)
% 202.03/33.64    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.64    (18)   ~ (all_52_17 = all_52_25)
% 202.03/33.64    (19)   ~ (all_52_3 = all_6_2)
% 202.03/33.64    (20)  all_44_2 = all_6_2
% 202.03/33.64    (21)  all_58_0 = all_6_2
% 202.03/33.64    (22)  op(all_14_2, e0) = all_14_1
% 202.03/33.64    (23)  all_34_1 = all_14_1
% 202.03/33.64    (24)  all_56_4 = all_52_3
% 202.03/33.64    (25)   ~ (all_52_17 = all_10_2)
% 202.03/33.64    (26)  op(e3, e0) = all_52_25
% 202.03/33.64    (27)  op(e0, all_14_1) = all_14_0
% 202.03/33.64    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.03/33.64    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.64    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.64    (31)   ~ (all_52_27 = all_52_29)
% 202.03/33.64    (32)  all_58_13 = all_52_15
% 202.03/33.64    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.64    (34)  all_58_9 = all_52_25
% 202.03/33.64    (35)   ~ (all_52_29 = all_14_2)
% 202.03/33.64    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.03/33.64    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.64    (38)  op(e1, e3) = all_52_5
% 202.03/33.64    (39)  op(e2, e2) = all_4_2
% 202.03/33.64    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.64    (41)   ~ (all_52_3 = all_52_5)
% 202.03/33.64    (42)  all_58_11 = all_52_29
% 202.03/33.64    (43)  all_56_5 = all_4_2
% 202.03/33.64    (44)   ~ (all_52_25 = all_14_2)
% 202.03/33.64    (45)   ~ (all_52_9 = all_52_15)
% 202.03/33.64    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.64    (47)   ~ (all_52_3 = all_52_27)
% 202.03/33.64    (48)  op(all_10_2, e1) = all_10_1
% 202.03/33.64    (49)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.03/33.64    (50)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.64    (51)   ~ (all_52_7 = all_6_2)
% 202.03/33.64    (52)  op(e0, e0) = all_14_2
% 202.03/33.64    (53)  op(e0, e1) = all_52_23
% 202.03/33.64    (54)  all_56_15 = all_14_2
% 202.03/33.64    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.64    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.03/33.64    (57)  all_56_11 = all_52_29
% 202.03/33.64    (58)   ~ (all_4_1 = e1)
% 202.03/33.64    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.64    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.64    (61)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.03/33.64    (62)  all_56_9 = all_52_13
% 202.03/33.64    (63)   ~ (all_52_13 = all_10_2)
% 202.03/33.64    (64)  all_58_10 = all_52_27
% 202.03/33.64    (65)  all_24_0 = all_14_0
% 202.03/33.64    (66)  all_56_8 = all_52_5
% 202.03/33.64    (67)  op(all_52_9, all_52_9) = all_52_8
% 202.03/33.64    (68)  op(all_52_15, all_52_15) = all_52_14
% 202.03/33.64    (69)   ~ (all_52_19 = all_52_23)
% 202.03/33.64    (70)   ~ (all_52_25 = all_52_29)
% 202.03/33.64    (71)   ~ (all_52_29 = all_10_2)
% 202.03/33.64    (72)  all_58_7 = all_52_13
% 202.03/33.64    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.03/33.64    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.64    (75)   ~ (all_52_5 = all_52_7)
% 202.03/33.64    (76)  all_58_12 = all_52_7
% 202.03/33.64    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.64    (78)   ~ (all_52_7 = all_14_2)
% 202.03/33.64    (79)  all_58_2 = all_52_3
% 202.03/33.64    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.64    (81)  all_56_2 = all_52_17
% 202.03/33.64    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.03/33.64    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.64    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.64    (85)   ~ (all_14_0 = e3)
% 202.03/33.64    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.03/33.64    (87)  all_56_7 = all_52_27
% 202.03/33.64    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.64    (89)   ~ (e2 = e0)
% 202.03/33.64    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.03/33.64    (91)  op(all_4_2, e2) = all_4_1
% 202.03/33.64    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.64    (93)   ~ (all_52_5 = all_52_29)
% 202.03/33.64    (94)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.64    (95)  all_56_6 = all_52_19
% 202.03/33.64    (96)   ~ (all_52_15 = all_14_2)
% 202.03/33.64    (97)   ~ (all_52_19 = all_52_27)
% 202.03/33.64    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.03/33.64    (99)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.03/33.64    (100)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 202.03/33.64             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 202.03/33.64    (101)   ~ (all_52_13 = all_4_2)
% 202.03/33.64    (102)  op(e3, e1) = all_52_17
% 202.03/33.64    (103)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.64    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.03/33.64    (105)  op(e0, e3) = all_52_7
% 202.03/33.64    (106)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.64    (107)   ~ (all_52_9 = all_52_25)
% 202.03/33.64    (108)  all_58_15 = all_14_2
% 202.03/33.64    (109)   ~ (all_52_19 = all_10_2)
% 202.03/33.64    (110)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.64    (111)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.64    (112)  all_58_8 = all_10_2
% 202.03/33.64    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.03/33.64    (114)  all_34_2 = all_14_2
% 202.03/33.64    (115)   ~ (all_52_5 = all_10_2)
% 202.03/33.64    (116)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.64    (117)   ~ (all_52_23 = all_14_2)
% 202.03/33.64    (118)  all_56_12 = all_52_7
% 202.03/33.64    (119)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.64    (120)  all_8_2 = all_6_2
% 202.03/33.64    (121)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.03/33.64    (122)   ~ (all_52_25 = all_6_2)
% 202.03/33.64    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.64    (124)   ~ (all_52_9 = all_4_2)
% 202.03/33.64    (125)   ~ (all_52_5 = all_6_2)
% 202.03/33.64    (126)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.03/33.64    (127)   ~ (all_52_9 = all_6_2)
% 202.03/33.64    (128)   ~ (all_52_13 = all_52_15)
% 202.03/33.64    (129)  op(e3, all_6_1) = e2
% 202.03/33.64    (130)  all_56_0 = all_6_2
% 202.03/33.64    (131)  op(e3, e3) = all_6_2
% 202.03/33.64    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.64    (133)   ~ (all_52_27 = all_14_2)
% 202.03/33.64    (134)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.64    (135)  all_56_14 = all_52_23
% 202.03/33.64    (136)  op(all_4_2, all_4_2) = all_52_10
% 202.03/33.64    (137)  all_56_3 = all_52_25
% 202.03/33.64    (138)   ~ (all_52_3 = all_52_7)
% 202.03/33.64    (139)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.64    (140)  all_58_5 = all_52_19
% 202.03/33.64    (141)  all_56_1 = all_52_9
% 202.03/33.64    (142)   ~ (all_52_15 = all_4_2)
% 202.03/33.64    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.03/33.64           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.03/33.64           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.03/33.64           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.03/33.64    (144)   ~ (all_52_27 = all_4_2)
% 202.03/33.64    (145)  all_58_6 = all_52_5
% 202.03/33.64    (146)  op(e3, e2) = all_52_9
% 202.03/33.64    (147)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.64    (148)   ~ (all_52_17 = all_6_2)
% 202.03/33.64    (149)   ~ (e1 = e0)
% 202.03/33.64    (150)   ~ (e3 = e2)
% 202.03/33.64    (151)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.64    (152)  all_44_1 = all_6_1
% 202.03/33.64    (153)   ~ (all_52_9 = all_52_17)
% 202.03/33.64    (154)  all_56_10 = all_10_2
% 202.03/33.64    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.64    (156)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.03/33.64    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.64    (158)  all_44_0 = e2
% 202.03/33.64    (159)  op(all_52_13, all_52_13) = all_52_12
% 202.03/33.64    (160)  op(e1, e1) = all_10_2
% 202.03/33.64    (161)   ~ (all_52_23 = all_10_2)
% 202.03/33.64    (162)   ~ (all_52_7 = all_52_23)
% 202.03/33.64    (163)   ~ (all_52_17 = all_52_19)
% 202.03/33.64    (164)  all_58_3 = all_4_2
% 202.03/33.64    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.03/33.64    (166)  all_56_13 = all_52_15
% 202.03/33.64    (167)   ~ (all_52_3 = all_4_2)
% 202.03/33.64    (168)   ~ (all_52_19 = all_4_2)
% 202.03/33.64    (169)   ~ (all_52_17 = all_52_23)
% 202.03/33.64    (170)  all_8_1 = all_6_1
% 202.03/33.64    (171)  op(all_6_2, e3) = all_6_1
% 202.03/33.64    (172)   ~ (all_52_13 = all_52_29)
% 202.03/33.64    (173)  all_58_4 = all_52_17
% 202.03/33.64    (174)   ~ (all_14_0 = e2)
% 202.03/33.64    (175)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.03/33.64    (176)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.64  
% 202.03/33.64  Begin of proof
% 202.03/33.64  | 
% 202.03/33.64  | COMBINE_EQS: (1), (65) imply:
% 202.03/33.64  |   (177)  all_14_0 = e1
% 202.03/33.64  | 
% 202.03/33.64  | SIMP: (177) implies:
% 202.03/33.64  |   (178)  all_14_0 = e1
% 202.03/33.64  | 
% 202.03/33.64  | COMBINE_EQS: (15), (178) imply:
% 202.03/33.64  |   (179)  all_34_0 = e1
% 202.03/33.64  | 
% 202.03/33.64  | REDUCE: (85), (178) imply:
% 202.03/33.64  |   (180)   ~ (e3 = e1)
% 202.03/33.64  | 
% 202.03/33.64  | SIMP: (180) implies:
% 202.03/33.64  |   (181)   ~ (e3 = e1)
% 202.03/33.64  | 
% 202.03/33.64  | REDUCE: (174), (178) imply:
% 202.03/33.64  |   (182)   ~ (e2 = e1)
% 202.03/33.64  | 
% 202.03/33.64  | SIMP: (182) implies:
% 202.03/33.64  |   (183)   ~ (e2 = e1)
% 202.03/33.64  | 
% 202.03/33.64  | REDUCE: (27), (178) imply:
% 202.03/33.64  |   (184)  op(e0, all_14_1) = e1
% 202.03/33.64  | 
% 202.03/33.64  | BETA: splitting (49) gives:
% 202.03/33.64  | 
% 202.03/33.64  | Case 1:
% 202.03/33.64  | | 
% 202.03/33.64  | |   (185)   ~ (all_34_0 = e1)
% 202.03/33.64  | | 
% 202.03/33.64  | | REDUCE: (179), (185) imply:
% 202.03/33.64  | |   (186)  $false
% 202.03/33.64  | | 
% 202.03/33.64  | | CLOSE: (186) is inconsistent.
% 202.03/33.64  | | 
% 202.03/33.64  | Case 2:
% 202.03/33.64  | | 
% 202.03/33.64  | |   (187)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.03/33.64  | | 
% 202.03/33.64  | | BETA: splitting (103) gives:
% 202.03/33.64  | | 
% 202.03/33.64  | | Case 1:
% 202.03/33.64  | | | 
% 202.03/33.64  | | |   (188)   ~ (all_44_0 = e2)
% 202.03/33.64  | | | 
% 202.03/33.64  | | | REDUCE: (158), (188) imply:
% 202.03/33.64  | | |   (189)  $false
% 202.03/33.64  | | | 
% 202.03/33.64  | | | CLOSE: (189) is inconsistent.
% 202.03/33.64  | | | 
% 202.03/33.64  | | Case 2:
% 202.03/33.64  | | | 
% 202.03/33.64  | | |   (190)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.64  | | | 
% 202.03/33.64  | | | BETA: splitting (100) gives:
% 202.03/33.64  | | | 
% 202.03/33.64  | | | Case 1:
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | |   (191)  all_58_15 = e0
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | | REF_CLOSE: (7), (22), (52), (108), (139), (149), (184), (191) are
% 202.03/33.64  | | | |            inconsistent by sub-proof #877.
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | Case 2:
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | |   (192)   ~ (all_58_15 = e0)
% 202.03/33.64  | | | |   (193)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 202.03/33.64  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | | ALPHA: (193) implies:
% 202.03/33.64  | | | |   (194)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.03/33.64  | | | |   (195)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | | REDUCE: (108), (192) imply:
% 202.03/33.64  | | | |   (196)   ~ (all_14_2 = e0)
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | | BETA: splitting (143) gives:
% 202.03/33.64  | | | | 
% 202.03/33.64  | | | | Case 1:
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | |   (197)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 202.03/33.64  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 202.03/33.64  | | | | |            all_52_14 = e0)
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | | BETA: splitting (197) gives:
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | | Case 1:
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | |   (198)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 202.03/33.64  | | | | | |          e0
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | REF_CLOSE: (6), (7), (17), (21), (28), (39), (50), (52), (55), (76),
% 202.03/33.64  | | | | | |            (78), (79), (83), (115), (129), (130), (131), (145),
% 202.03/33.64  | | | | | |            (147), (150), (157), (160), (167), (171), (198) are
% 202.03/33.64  | | | | | |            inconsistent by sub-proof #501.
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | Case 2:
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | |   (199)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 202.03/33.64  | | | | | |          = e0
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.03/33.64  | | | | | |            (13), (14), (16), (17), (18), (19), (20), (21), (22),
% 202.03/33.64  | | | | | |            (24), (26), (28), (29), (30), (32), (33), (34), (35),
% 202.03/33.64  | | | | | |            (37), (38), (39), (40), (41), (42), (44), (46), (47),
% 202.03/33.64  | | | | | |            (51), (52), (53), (54), (55), (58), (59), (62), (63),
% 202.03/33.64  | | | | | |            (64), (66), (67), (68), (69), (70), (71), (72), (74),
% 202.03/33.64  | | | | | |            (75), (76), (77), (78), (79), (83), (87), (88), (89),
% 202.03/33.64  | | | | | |            (91), (92), (96), (101), (102), (105), (106), (107),
% 202.03/33.64  | | | | | |            (108), (109), (110), (111), (112), (113), (114), (115),
% 202.03/33.64  | | | | | |            (116), (117), (118), (119), (120), (121), (122), (123),
% 202.03/33.64  | | | | | |            (124), (125), (127), (128), (129), (130), (131), (132),
% 202.03/33.64  | | | | | |            (133), (134), (136), (137), (138), (139), (140), (141),
% 202.03/33.64  | | | | | |            (142), (144), (145), (146), (147), (148), (149), (150),
% 202.03/33.64  | | | | | |            (151), (152), (153), (154), (155), (156), (157), (159),
% 202.03/33.64  | | | | | |            (160), (161), (162), (163), (164), (166), (167), (168),
% 202.03/33.64  | | | | | |            (169), (170), (171), (172), (173), (175), (176), (181),
% 202.03/33.64  | | | | | |            (183), (184), (187), (190), (195), (199) are inconsistent
% 202.03/33.64  | | | | | |            by sub-proof #358.
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | End of split
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | Case 2:
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | |   (200)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 202.03/33.64  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.03/33.64  | | | | |            all_52_30 = e0)
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | | BETA: splitting (200) gives:
% 202.03/33.64  | | | | | 
% 202.03/33.64  | | | | | Case 1:
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | |   (201)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 202.03/33.64  | | | | | |          all_52_22 = e0
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | ALPHA: (201) implies:
% 202.03/33.64  | | | | | |   (202)  all_52_22 = e0
% 202.03/33.64  | | | | | |   (203)  all_52_20 = e1
% 202.03/33.64  | | | | | |   (204)  all_52_18 = e2
% 202.03/33.64  | | | | | |   (205)  all_52_16 = e3
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | REDUCE: (119), (205) imply:
% 202.03/33.64  | | | | | |   (206)  op(all_52_17, all_52_17) = e3
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | REDUCE: (30), (204) imply:
% 202.03/33.64  | | | | | |   (207)  op(all_52_19, all_52_19) = e2
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | REDUCE: (110), (202) imply:
% 202.03/33.64  | | | | | |   (208)  op(all_52_23, all_52_23) = e0
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | REDUCE: (33), (203) imply:
% 202.03/33.64  | | | | | |   (209)  op(all_10_2, all_10_2) = e1
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | BETA: splitting (113) gives:
% 202.03/33.64  | | | | | | 
% 202.03/33.64  | | | | | | Case 1:
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | |   (210)  all_56_15 = e3
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | COMBINE_EQS: (54), (210) imply:
% 202.03/33.64  | | | | | | |   (211)  all_14_2 = e3
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | SIMP: (211) implies:
% 202.03/33.64  | | | | | | |   (212)  all_14_2 = e3
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | COMBINE_EQS: (114), (212) imply:
% 202.03/33.64  | | | | | | |   (213)  all_34_2 = e3
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (78), (212) imply:
% 202.03/33.64  | | | | | | |   (214)   ~ (all_52_7 = e3)
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (117), (212) imply:
% 202.03/33.64  | | | | | | |   (215)   ~ (all_52_23 = e3)
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (44), (212) imply:
% 202.03/33.64  | | | | | | |   (216)   ~ (all_52_25 = e3)
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (35), (212) imply:
% 202.03/33.64  | | | | | | |   (217)   ~ (all_52_29 = e3)
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (139), (212) imply:
% 202.03/33.64  | | | | | | |   (218)  op(e3, e3) = all_52_30
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (22), (212) imply:
% 202.03/33.64  | | | | | | |   (219)  op(e3, e0) = all_14_1
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (12), (16), (19), (21), (23),
% 202.03/33.64  | | | | | | |            (24), (26), (32), (34), (39), (40), (42), (45), (67),
% 202.03/33.64  | | | | | | |            (72), (74), (76), (77), (79), (82), (83), (88), (89),
% 202.03/33.64  | | | | | | |            (99), (102), (106), (112), (115), (122), (124), (127),
% 202.03/33.64  | | | | | | |            (129), (131), (134), (140), (141), (145), (148), (150),
% 202.03/33.64  | | | | | | |            (151), (153), (155), (164), (171), (173), (183), (187),
% 202.03/33.64  | | | | | | |            (206), (207), (209), (213), (214), (215), (216), (217),
% 202.03/33.64  | | | | | | |            (218), (219) are inconsistent by sub-proof #335.
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | Case 2:
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | |   (220)   ~ (all_56_15 = e3)
% 202.03/33.64  | | | | | | | 
% 202.03/33.64  | | | | | | | REDUCE: (54), (220) imply:
% 202.03/33.64  | | | | | | |   (221)   ~ (all_14_2 = e3)
% 202.03/33.64  | | | | | | | 
% 202.03/33.65  | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (13), (14),
% 202.03/33.65  | | | | | | |            (16), (17), (18), (19), (20), (21), (24), (26), (29),
% 202.03/33.65  | | | | | | |            (32), (34), (35), (36), (37), (38), (39), (40), (41),
% 202.03/33.65  | | | | | | |            (42), (44), (45), (48), (50), (51), (52), (55), (59),
% 202.03/33.65  | | | | | | |            (60), (61), (63), (64), (66), (67), (68), (69), (70),
% 202.03/33.65  | | | | | | |            (71), (72), (74), (75), (76), (77), (78), (79), (80),
% 202.03/33.65  | | | | | | |            (81), (82), (83), (84), (86), (87), (88), (89), (92),
% 202.03/33.65  | | | | | | |            (94), (95), (101), (102), (105), (106), (108), (109),
% 202.03/33.65  | | | | | | |            (111), (112), (115), (116), (117), (118), (120), (122),
% 202.03/33.65  | | | | | | |            (123), (124), (125), (127), (128), (129), (130), (131),
% 202.03/33.65  | | | | | | |            (132), (133), (134), (137), (138), (139), (140), (141),
% 202.03/33.65  | | | | | | |            (142), (144), (145), (146), (147), (148), (149), (150),
% 202.03/33.65  | | | | | | |            (151), (152), (153), (154), (155), (157), (159), (160),
% 202.03/33.65  | | | | | | |            (161), (162), (163), (164), (165), (166), (167), (169),
% 202.03/33.65  | | | | | | |            (170), (171), (173), (175), (176), (181), (183), (190),
% 202.03/33.65  | | | | | | |            (194), (206), (207), (208), (209), (221) are
% 202.03/33.65  | | | | | | |            inconsistent by sub-proof #329.
% 202.03/33.65  | | | | | | | 
% 202.03/33.65  | | | | | | End of split
% 202.03/33.65  | | | | | | 
% 202.03/33.65  | | | | | Case 2:
% 202.03/33.65  | | | | | | 
% 202.03/33.65  | | | | | |   (222)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.03/33.65  | | | | | |          all_52_30 = e0
% 202.03/33.65  | | | | | | 
% 202.03/33.65  | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (12), (16),
% 202.03/33.65  | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 202.03/33.65  | | | | | |            (28), (29), (30), (31), (32), (34), (35), (37), (38),
% 202.03/33.65  | | | | | |            (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 202.03/33.65  | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (60),
% 202.03/33.65  | | | | | |            (62), (64), (66), (67), (68), (69), (70), (71), (72),
% 202.03/33.65  | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 202.03/33.65  | | | | | |            (83), (84), (87), (89), (90), (93), (95), (97), (98),
% 202.03/33.65  | | | | | |            (101), (102), (104), (105), (106), (107), (108), (109),
% 202.03/33.65  | | | | | |            (111), (112), (113), (114), (115), (116), (117), (119),
% 202.03/33.65  | | | | | |            (121), (122), (123), (124), (125), (126), (128), (129),
% 202.03/33.65  | | | | | |            (130), (131), (132), (133), (134), (135), (137), (138),
% 202.03/33.65  | | | | | |            (139), (140), (142), (144), (145), (146), (147), (148),
% 202.03/33.65  | | | | | |            (149), (150), (152), (155), (156), (157), (159), (160),
% 202.03/33.65  | | | | | |            (162), (163), (164), (165), (167), (168), (169), (171),
% 202.03/33.65  | | | | | |            (172), (173), (176), (184), (187), (190), (194), (195),
% 202.03/33.65  | | | | | |            (196), (222) are inconsistent by sub-proof #360.
% 202.03/33.65  | | | | | | 
% 202.03/33.65  | | | | | End of split
% 202.03/33.65  | | | | | 
% 202.03/33.65  | | | | End of split
% 202.03/33.65  | | | | 
% 202.03/33.65  | | | End of split
% 202.03/33.65  | | | 
% 202.03/33.65  | | End of split
% 202.03/33.65  | | 
% 202.03/33.65  | End of split
% 202.03/33.65  | 
% 202.03/33.65  End of proof
% 202.03/33.65  
% 202.03/33.65  Sub-proof #327 shows that the following formulas are inconsistent:
% 202.03/33.65  ----------------------------------------------------------------
% 202.03/33.65    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.03/33.65    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.65    (3)   ~ (all_52_15 = all_52_23)
% 202.03/33.65    (4)   ~ (all_52_25 = all_52_27)
% 202.03/33.65    (5)  all_58_14 = all_52_23
% 202.03/33.65    (6)   ~ (e3 = e1)
% 202.03/33.65    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.65    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.65    (9)   ~ (all_52_5 = all_52_13)
% 202.03/33.65    (10)  all_58_1 = all_52_9
% 202.03/33.65    (11)   ~ (all_52_9 = all_52_13)
% 202.03/33.65    (12)   ~ (e3 = e0)
% 202.03/33.65    (13)  op(e2, e3) = all_52_3
% 202.03/33.65    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.65    (15)   ~ (all_52_7 = all_52_15)
% 202.03/33.65    (16)   ~ (all_52_3 = all_52_19)
% 202.03/33.65    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.65    (18)   ~ (all_52_17 = all_52_25)
% 202.03/33.65    (19)   ~ (all_52_3 = all_6_2)
% 202.03/33.65    (20)  all_44_2 = all_6_2
% 202.03/33.65    (21)  all_58_0 = all_6_2
% 202.03/33.65    (22)  op(all_14_2, e0) = all_14_1
% 202.03/33.65    (23)  all_56_4 = all_52_3
% 202.03/33.65    (24)   ~ (all_52_17 = all_10_2)
% 202.03/33.65    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.65    (26)  op(e3, e0) = all_52_25
% 202.03/33.65    (27)  op(e0, all_14_1) = all_14_0
% 202.03/33.65    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.03/33.65    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.65    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.65    (31)   ~ (all_52_27 = all_52_29)
% 202.03/33.65    (32)  all_58_13 = all_52_15
% 202.03/33.65    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.65    (34)  all_58_9 = all_52_25
% 202.03/33.65    (35)   ~ (all_52_29 = all_14_2)
% 202.03/33.65    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.03/33.65    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.65    (38)  op(e1, e3) = all_52_5
% 202.03/33.65    (39)  op(e2, e2) = all_4_2
% 202.03/33.65    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.65    (41)   ~ (all_52_3 = all_52_5)
% 202.03/33.65    (42)  all_58_11 = all_52_29
% 202.03/33.65    (43)  all_56_5 = all_4_2
% 202.03/33.65    (44)   ~ (all_52_25 = all_14_2)
% 202.03/33.65    (45)   ~ (all_52_9 = all_52_15)
% 202.03/33.65    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.65    (47)   ~ (all_52_3 = all_52_27)
% 202.03/33.65    (48)  op(all_10_2, e1) = all_10_1
% 202.03/33.65    (49)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.65    (50)   ~ (all_52_7 = all_6_2)
% 202.03/33.65    (51)  op(e0, e0) = all_14_2
% 202.03/33.65    (52)  op(e0, e1) = all_52_23
% 202.03/33.65    (53)  all_56_15 = all_14_2
% 202.03/33.65    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.65    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.03/33.65    (56)  all_56_11 = all_52_29
% 202.03/33.65    (57)   ~ (all_4_1 = e1)
% 202.03/33.65    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.65    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.65    (60)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.03/33.65    (61)  all_56_9 = all_52_13
% 202.03/33.65    (62)   ~ (e2 = e1)
% 202.03/33.65    (63)   ~ (all_52_13 = all_10_2)
% 202.03/33.65    (64)  all_58_10 = all_52_27
% 202.03/33.65    (65)  all_56_8 = all_52_5
% 202.03/33.65    (66)  op(all_52_9, all_52_9) = all_52_8
% 202.03/33.65    (67)  op(all_52_15, all_52_15) = all_52_14
% 202.03/33.65    (68)   ~ (all_52_19 = all_52_23)
% 202.03/33.65    (69)   ~ (all_52_25 = all_52_29)
% 202.03/33.65    (70)   ~ (all_52_29 = all_10_2)
% 202.03/33.65    (71)  all_58_7 = all_52_13
% 202.03/33.65    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.03/33.65    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.65    (74)   ~ (all_52_5 = all_52_7)
% 202.03/33.65    (75)  all_58_12 = all_52_7
% 202.03/33.65    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.65    (77)   ~ (all_52_7 = all_14_2)
% 202.03/33.65    (78)   ~ (all_14_2 = e0)
% 202.03/33.65    (79)  all_58_2 = all_52_3
% 202.03/33.65    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.65    (81)  all_56_2 = all_52_17
% 202.03/33.65    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.03/33.65    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.65    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.65    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.03/33.65    (86)  all_56_7 = all_52_27
% 202.03/33.65    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.65    (88)   ~ (e2 = e0)
% 202.03/33.65    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.03/33.65    (90)  op(all_4_2, e2) = all_4_1
% 202.03/33.65    (91)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.65    (92)   ~ (all_52_5 = all_52_29)
% 202.03/33.65    (93)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.65    (94)  all_56_6 = all_52_19
% 202.03/33.65    (95)   ~ (all_52_15 = all_14_2)
% 202.03/33.65    (96)   ~ (all_52_19 = all_52_27)
% 202.03/33.65    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.03/33.65    (98)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.03/33.65    (99)   ~ (all_52_13 = all_4_2)
% 202.03/33.65    (100)  op(e3, e1) = all_52_17
% 202.03/33.65    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.03/33.65    (102)  op(e0, e3) = all_52_7
% 202.03/33.65    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.65    (104)   ~ (all_52_9 = all_52_25)
% 202.03/33.65    (105)  all_58_15 = all_14_2
% 202.03/33.65    (106)   ~ (all_52_19 = all_10_2)
% 202.03/33.65    (107)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.65    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.65    (109)  all_58_8 = all_10_2
% 202.03/33.65    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.03/33.65    (111)   ~ (all_52_5 = all_10_2)
% 202.03/33.65    (112)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.65    (113)   ~ (all_52_23 = all_14_2)
% 202.03/33.65    (114)  all_56_12 = all_52_7
% 202.03/33.65    (115)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.65    (116)  all_8_2 = all_6_2
% 202.03/33.65    (117)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.03/33.65    (118)   ~ (all_52_25 = all_6_2)
% 202.03/33.65    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.65    (120)   ~ (all_52_9 = all_4_2)
% 202.03/33.65    (121)   ~ (all_52_5 = all_6_2)
% 202.03/33.65    (122)   ~ (all_52_9 = all_6_2)
% 202.03/33.65    (123)   ~ (all_52_13 = all_52_15)
% 202.03/33.65    (124)  op(e3, all_6_1) = e2
% 202.03/33.65    (125)  all_56_0 = all_6_2
% 202.03/33.65    (126)  op(e3, e3) = all_6_2
% 202.03/33.65    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.65    (128)   ~ (all_52_27 = all_14_2)
% 202.03/33.65    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.65    (130)  all_56_14 = all_52_23
% 202.03/33.65    (131)  op(all_4_2, all_4_2) = all_52_10
% 202.03/33.65    (132)  all_56_3 = all_52_25
% 202.03/33.65    (133)   ~ (all_52_3 = all_52_7)
% 202.03/33.65    (134)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.65    (135)  all_58_5 = all_52_19
% 202.03/33.65    (136)  all_56_1 = all_52_9
% 202.03/33.65    (137)   ~ (all_52_15 = all_4_2)
% 202.03/33.65    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.03/33.65           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.03/33.65           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.03/33.65           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.03/33.65    (139)   ~ (all_52_27 = all_4_2)
% 202.03/33.65    (140)  all_58_6 = all_52_5
% 202.03/33.65    (141)  op(e3, e2) = all_52_9
% 202.03/33.65    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.65    (143)   ~ (all_52_17 = all_6_2)
% 202.03/33.65    (144)   ~ (e1 = e0)
% 202.03/33.65    (145)   ~ (e3 = e2)
% 202.03/33.65    (146)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.65    (147)  all_44_1 = all_6_1
% 202.03/33.65    (148)   ~ (all_52_9 = all_52_17)
% 202.03/33.65    (149)  all_56_10 = all_10_2
% 202.03/33.65    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.65    (151)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.03/33.65    (152)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.65    (153)  op(all_52_13, all_52_13) = all_52_12
% 202.03/33.65    (154)  op(e1, e1) = all_10_2
% 202.03/33.65    (155)   ~ (all_52_23 = all_10_2)
% 202.03/33.65    (156)   ~ (all_52_7 = all_52_23)
% 202.03/33.65    (157)   ~ (all_52_17 = all_52_19)
% 202.03/33.65    (158)  all_58_3 = all_4_2
% 202.03/33.65    (159)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.03/33.65    (160)  all_56_13 = all_52_15
% 202.03/33.65    (161)   ~ (all_52_3 = all_4_2)
% 202.03/33.65    (162)   ~ (all_52_19 = all_4_2)
% 202.03/33.65    (163)   ~ (all_52_17 = all_52_23)
% 202.03/33.65    (164)  all_8_1 = all_6_1
% 202.03/33.65    (165)  op(all_6_2, e3) = all_6_1
% 202.03/33.65    (166)   ~ (all_52_13 = all_52_29)
% 202.03/33.65    (167)  all_58_4 = all_52_17
% 202.03/33.65    (168)   ~ (all_14_0 = e2)
% 202.03/33.65    (169)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.03/33.65    (170)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.65  
% 202.03/33.65  Begin of proof
% 202.03/33.65  | 
% 202.03/33.65  | BETA: splitting (138) gives:
% 202.03/33.65  | 
% 202.03/33.65  | Case 1:
% 202.03/33.65  | | 
% 202.03/33.65  | |   (171)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.03/33.65  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.03/33.65  | | 
% 202.03/33.65  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 202.03/33.65  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 202.03/33.65  | |            (26), (27), (28), (29), (30), (32), (33), (34), (35), (37), (38),
% 202.03/33.65  | |            (39), (40), (41), (42), (44), (46), (47), (49), (50), (51), (52),
% 202.03/33.65  | |            (53), (54), (57), (58), (61), (63), (64), (65), (66), (67), (68),
% 202.03/33.65  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (79), (83),
% 202.03/33.65  | |            (86), (87), (88), (90), (93), (95), (99), (100), (102), (103),
% 202.03/33.65  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 202.03/33.65  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 202.03/33.65  | |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 202.03/33.65  | |            (131), (132), (133), (134), (135), (136), (137), (139), (140),
% 202.03/33.65  | |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 202.03/33.65  | |            (150), (151), (152), (153), (154), (155), (156), (157), (158),
% 202.03/33.65  | |            (160), (161), (162), (163), (164), (165), (166), (167), (168),
% 202.03/33.65  | |            (169), (170), (171) are inconsistent by sub-proof #349.
% 202.03/33.65  | | 
% 202.03/33.65  | Case 2:
% 202.03/33.65  | | 
% 202.03/33.65  | |   (172)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 202.03/33.65  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.03/33.65  | |            e0)
% 202.03/33.65  | | 
% 202.03/33.65  | | BETA: splitting (172) gives:
% 202.03/33.65  | | 
% 202.03/33.65  | | Case 1:
% 202.03/33.65  | | | 
% 202.03/33.65  | | |   (173)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 202.03/33.65  | | | 
% 202.03/33.65  | | | ALPHA: (173) implies:
% 202.03/33.65  | | |   (174)  all_52_22 = e0
% 202.03/33.65  | | |   (175)  all_52_20 = e1
% 202.03/33.65  | | |   (176)  all_52_18 = e2
% 202.03/33.65  | | |   (177)  all_52_16 = e3
% 202.03/33.65  | | | 
% 202.03/33.65  | | | REDUCE: (115), (177) imply:
% 202.03/33.65  | | |   (178)  op(all_52_17, all_52_17) = e3
% 202.03/33.65  | | | 
% 202.03/33.65  | | | REDUCE: (30), (176) imply:
% 202.03/33.65  | | |   (179)  op(all_52_19, all_52_19) = e2
% 202.03/33.65  | | | 
% 202.03/33.65  | | | REDUCE: (107), (174) imply:
% 202.03/33.65  | | |   (180)  op(all_52_23, all_52_23) = e0
% 202.03/33.65  | | | 
% 202.03/33.65  | | | REDUCE: (33), (175) imply:
% 202.03/33.65  | | |   (181)  op(all_10_2, all_10_2) = e1
% 202.03/33.65  | | | 
% 202.03/33.65  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 202.03/33.65  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 202.03/33.65  | | |            (29), (32), (34), (35), (36), (37), (38), (39), (40), (41),
% 202.03/33.65  | | |            (42), (44), (45), (48), (49), (50), (51), (53), (54), (58),
% 202.03/33.65  | | |            (59), (60), (62), (63), (64), (65), (66), (67), (68), (69),
% 202.03/33.65  | | |            (70), (71), (73), (74), (75), (76), (77), (79), (80), (81),
% 202.03/33.65  | | |            (82), (83), (84), (85), (86), (87), (88), (91), (93), (94),
% 202.03/33.65  | | |            (98), (99), (100), (102), (103), (105), (106), (108), (109),
% 202.03/33.65  | | |            (110), (111), (112), (113), (114), (116), (118), (119), (120),
% 202.03/33.65  | | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 202.03/33.65  | | |            (132), (133), (134), (135), (136), (137), (139), (140), (141),
% 202.03/33.65  | | |            (142), (143), (144), (145), (146), (147), (148), (149), (150),
% 202.03/33.65  | | |            (152), (153), (154), (155), (156), (157), (158), (159), (160),
% 202.03/33.65  | | |            (161), (163), (164), (165), (167), (169), (170), (178), (179),
% 202.03/33.65  | | |            (180), (181) are inconsistent by sub-proof #328.
% 202.03/33.65  | | | 
% 202.03/33.65  | | Case 2:
% 202.03/33.65  | | | 
% 202.03/33.65  | | |   (182)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.03/33.65  | | | 
% 202.03/33.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13),
% 202.03/33.65  | | |            (14), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 202.03/33.65  | | |            (28), (29), (30), (31), (32), (34), (35), (37), (38), (39),
% 202.03/33.65  | | |            (40), (41), (42), (43), (44), (47), (48), (49), (50), (51),
% 202.03/33.65  | | |            (53), (54), (55), (56), (59), (64), (65), (66), (69), (70),
% 202.03/33.65  | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 202.03/33.65  | | |            (81), (83), (84), (86), (88), (89), (92), (94), (96), (97),
% 202.03/33.65  | | |            (98), (100), (101), (102), (103), (104), (105), (106), (108),
% 202.03/33.65  | | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 202.03/33.65  | | |            (118), (119), (120), (121), (124), (125), (126), (127), (128),
% 202.03/33.65  | | |            (129), (130), (132), (133), (134), (135), (137), (139), (140),
% 202.03/33.65  | | |            (141), (142), (143), (144), (145), (147), (148), (150), (152),
% 202.03/33.65  | | |            (153), (154), (156), (157), (158), (159), (161), (162), (163),
% 202.03/33.65  | | |            (164), (165), (166), (167), (170), (182) are inconsistent by
% 202.03/33.65  | | |            sub-proof #434.
% 202.03/33.65  | | | 
% 202.03/33.65  | | End of split
% 202.03/33.65  | | 
% 202.03/33.65  | End of split
% 202.03/33.65  | 
% 202.03/33.65  End of proof
% 202.03/33.65  
% 202.03/33.65  Sub-proof #328 shows that the following formulas are inconsistent:
% 202.03/33.65  ----------------------------------------------------------------
% 202.03/33.65    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.65    (2)   ~ (all_52_25 = all_52_27)
% 202.03/33.65    (3)  all_58_14 = all_52_23
% 202.03/33.65    (4)   ~ (e3 = e1)
% 202.03/33.65    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.65    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.65    (7)  all_58_1 = all_52_9
% 202.03/33.65    (8)   ~ (e3 = e0)
% 202.03/33.65    (9)  op(all_52_23, all_52_23) = e0
% 202.03/33.65    (10)  op(e2, e3) = all_52_3
% 202.03/33.65    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.65    (12)   ~ (all_52_7 = all_52_15)
% 202.03/33.65    (13)   ~ (all_52_3 = all_52_19)
% 202.03/33.65    (14)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.65    (15)   ~ (all_52_17 = all_52_25)
% 202.03/33.65    (16)   ~ (all_52_3 = all_6_2)
% 202.03/33.65    (17)  all_44_2 = all_6_2
% 202.03/33.65    (18)  all_58_0 = all_6_2
% 202.03/33.65    (19)  op(all_14_2, e0) = all_14_1
% 202.03/33.65    (20)  all_56_4 = all_52_3
% 202.03/33.65    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.65    (22)  op(e3, e0) = all_52_25
% 202.03/33.65    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.65    (24)  all_58_13 = all_52_15
% 202.03/33.65    (25)  all_58_9 = all_52_25
% 202.03/33.65    (26)   ~ (all_52_29 = all_14_2)
% 202.03/33.65    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.03/33.65    (28)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.65    (29)  op(e1, e3) = all_52_5
% 202.03/33.65    (30)  op(e2, e2) = all_4_2
% 202.03/33.65    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.65    (32)   ~ (all_52_3 = all_52_5)
% 202.03/33.65    (33)  all_58_11 = all_52_29
% 202.03/33.65    (34)   ~ (all_52_25 = all_14_2)
% 202.03/33.65    (35)   ~ (all_52_9 = all_52_15)
% 202.03/33.65    (36)  op(all_10_2, e1) = all_10_1
% 202.03/33.65    (37)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.65    (38)   ~ (all_52_7 = all_6_2)
% 202.03/33.65    (39)  op(e0, e0) = all_14_2
% 202.03/33.65    (40)  all_56_15 = all_14_2
% 202.03/33.65    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.65    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.65    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.65    (44)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.03/33.65    (45)   ~ (e2 = e1)
% 202.03/33.65    (46)   ~ (all_52_13 = all_10_2)
% 202.03/33.65    (47)  op(all_10_2, all_10_2) = e1
% 202.03/33.65    (48)  all_58_10 = all_52_27
% 202.03/33.65    (49)  all_56_8 = all_52_5
% 202.03/33.65    (50)  op(all_52_9, all_52_9) = all_52_8
% 202.03/33.65    (51)  op(all_52_15, all_52_15) = all_52_14
% 202.03/33.65    (52)   ~ (all_52_19 = all_52_23)
% 202.03/33.65    (53)   ~ (all_52_25 = all_52_29)
% 202.03/33.65    (54)   ~ (all_52_29 = all_10_2)
% 202.03/33.65    (55)  all_58_7 = all_52_13
% 202.03/33.65    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.65    (57)  op(all_52_19, all_52_19) = e2
% 202.03/33.65    (58)   ~ (all_52_5 = all_52_7)
% 202.03/33.65    (59)  all_58_12 = all_52_7
% 202.03/33.65    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.65    (61)   ~ (all_52_7 = all_14_2)
% 202.03/33.65    (62)  all_58_2 = all_52_3
% 202.03/33.65    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.65    (64)  all_56_2 = all_52_17
% 202.03/33.65    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.03/33.65    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.65    (67)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.65    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.03/33.65    (69)  all_56_7 = all_52_27
% 202.03/33.65    (70)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.65    (71)   ~ (e2 = e0)
% 202.03/33.65    (72)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.65    (73)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.65    (74)  all_56_6 = all_52_19
% 202.03/33.65    (75)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.03/33.65    (76)   ~ (all_52_13 = all_4_2)
% 202.03/33.65    (77)  op(e3, e1) = all_52_17
% 202.03/33.65    (78)  op(e0, e3) = all_52_7
% 202.03/33.65    (79)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.65    (80)  all_58_15 = all_14_2
% 202.03/33.65    (81)   ~ (all_52_19 = all_10_2)
% 202.03/33.65    (82)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.65    (83)  all_58_8 = all_10_2
% 202.03/33.65    (84)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.03/33.65    (85)   ~ (all_52_5 = all_10_2)
% 202.03/33.65    (86)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.65    (87)   ~ (all_52_23 = all_14_2)
% 202.03/33.65    (88)  all_56_12 = all_52_7
% 202.03/33.65    (89)  all_8_2 = all_6_2
% 202.03/33.65    (90)   ~ (all_52_25 = all_6_2)
% 202.03/33.65    (91)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.65    (92)   ~ (all_52_9 = all_4_2)
% 202.03/33.65    (93)   ~ (all_52_5 = all_6_2)
% 202.03/33.65    (94)   ~ (all_52_9 = all_6_2)
% 202.03/33.65    (95)   ~ (all_52_13 = all_52_15)
% 202.03/33.65    (96)  op(e3, all_6_1) = e2
% 202.03/33.65    (97)  all_56_0 = all_6_2
% 202.03/33.65    (98)  op(e3, e3) = all_6_2
% 202.03/33.65    (99)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.65    (100)   ~ (all_52_27 = all_14_2)
% 202.03/33.65    (101)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.65    (102)  all_56_3 = all_52_25
% 202.03/33.65    (103)   ~ (all_52_3 = all_52_7)
% 202.03/33.65    (104)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.65    (105)  all_58_5 = all_52_19
% 202.03/33.65    (106)  all_56_1 = all_52_9
% 202.03/33.65    (107)   ~ (all_52_15 = all_4_2)
% 202.03/33.65    (108)   ~ (all_52_27 = all_4_2)
% 202.03/33.65    (109)  op(all_52_17, all_52_17) = e3
% 202.03/33.65    (110)  all_58_6 = all_52_5
% 202.03/33.65    (111)  op(e3, e2) = all_52_9
% 202.03/33.65    (112)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.65    (113)   ~ (all_52_17 = all_6_2)
% 202.03/33.65    (114)   ~ (e1 = e0)
% 202.03/33.65    (115)   ~ (e3 = e2)
% 202.03/33.65    (116)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.65    (117)  all_44_1 = all_6_1
% 202.03/33.65    (118)   ~ (all_52_9 = all_52_17)
% 202.03/33.65    (119)  all_56_10 = all_10_2
% 202.03/33.65    (120)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.65    (121)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.65    (122)  op(all_52_13, all_52_13) = all_52_12
% 202.03/33.65    (123)  op(e1, e1) = all_10_2
% 202.03/33.65    (124)   ~ (all_52_23 = all_10_2)
% 202.03/33.65    (125)   ~ (all_52_7 = all_52_23)
% 202.03/33.65    (126)   ~ (all_52_17 = all_52_19)
% 202.03/33.65    (127)  all_58_3 = all_4_2
% 202.03/33.65    (128)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.03/33.65    (129)  all_56_13 = all_52_15
% 202.03/33.65    (130)   ~ (all_52_3 = all_4_2)
% 202.03/33.65    (131)   ~ (all_52_17 = all_52_23)
% 202.03/33.65    (132)  all_8_1 = all_6_1
% 202.03/33.65    (133)  op(all_6_2, e3) = all_6_1
% 202.03/33.65    (134)  all_58_4 = all_52_17
% 202.03/33.65    (135)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.03/33.65    (136)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.65  
% 202.03/33.65  Begin of proof
% 202.03/33.65  | 
% 202.03/33.65  | BETA: splitting (84) gives:
% 202.03/33.65  | 
% 202.03/33.65  | Case 1:
% 202.03/33.65  | | 
% 202.03/33.65  | |   (137)  all_56_15 = e3
% 202.03/33.65  | | 
% 202.03/33.65  | | COMBINE_EQS: (40), (137) imply:
% 202.03/33.65  | |   (138)  all_14_2 = e3
% 202.03/33.65  | | 
% 202.03/33.65  | | SIMP: (138) implies:
% 202.03/33.65  | |   (139)  all_14_2 = e3
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (61), (139) imply:
% 202.03/33.65  | |   (140)   ~ (all_52_7 = e3)
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (87), (139) imply:
% 202.03/33.65  | |   (141)   ~ (all_52_23 = e3)
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (34), (139) imply:
% 202.03/33.65  | |   (142)   ~ (all_52_25 = e3)
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (100), (139) imply:
% 202.03/33.65  | |   (143)   ~ (all_52_27 = e3)
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (104), (139) imply:
% 202.03/33.65  | |   (144)  op(e3, e3) = all_52_30
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (19), (139) imply:
% 202.03/33.65  | |   (145)  op(e3, e0) = all_14_1
% 202.03/33.65  | | 
% 202.03/33.65  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 202.03/33.65  | |              with (22), (145) gives:
% 202.03/33.65  | |   (146)  all_52_25 = all_14_1
% 202.03/33.65  | | 
% 202.03/33.65  | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3, simplifying
% 202.03/33.65  | |              with (98), (144) gives:
% 202.03/33.65  | |   (147)  all_52_30 = all_6_2
% 202.03/33.65  | | 
% 202.03/33.65  | | REDUCE: (90), (146) imply:
% 202.03/33.65  | |   (148)   ~ (all_14_1 = all_6_2)
% 202.03/33.65  | | 
% 202.03/33.66  | | BETA: splitting (11) gives:
% 202.03/33.66  | | 
% 202.03/33.66  | | Case 1:
% 202.03/33.66  | | | 
% 202.03/33.66  | | |   (149)  all_56_12 = e3
% 202.03/33.66  | | | 
% 202.03/33.66  | | | COMBINE_EQS: (88), (149) imply:
% 202.03/33.66  | | |   (150)  all_52_7 = e3
% 202.03/33.66  | | | 
% 202.03/33.66  | | | REDUCE: (140), (150) imply:
% 202.03/33.66  | | |   (151)  $false
% 202.03/33.66  | | | 
% 202.03/33.66  | | | CLOSE: (151) is inconsistent.
% 202.03/33.66  | | | 
% 202.03/33.66  | | Case 2:
% 202.03/33.66  | | | 
% 202.03/33.66  | | |   (152)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.66  | | | 
% 202.03/33.66  | | | BETA: splitting (116) gives:
% 202.03/33.66  | | | 
% 202.03/33.66  | | | Case 1:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | |   (153)  all_56_1 = e3
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | COMBINE_EQS: (106), (153) imply:
% 202.03/33.66  | | | |   (154)  all_52_9 = e3
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | COMBINE_EQS: (7), (154) imply:
% 202.03/33.66  | | | |   (155)  all_58_1 = e3
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (35), (154) imply:
% 202.03/33.66  | | | |   (156)   ~ (all_52_15 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | SIMP: (156) implies:
% 202.03/33.66  | | | |   (157)   ~ (all_52_15 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (118), (154) imply:
% 202.03/33.66  | | | |   (158)   ~ (all_52_17 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | SIMP: (158) implies:
% 202.03/33.66  | | | |   (159)   ~ (all_52_17 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (92), (154) imply:
% 202.03/33.66  | | | |   (160)   ~ (all_4_2 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | SIMP: (160) implies:
% 202.03/33.66  | | | |   (161)   ~ (all_4_2 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (50), (154) imply:
% 202.03/33.66  | | | |   (162)  op(e3, e3) = all_52_8
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (111), (154) imply:
% 202.03/33.66  | | | |   (163)  op(e3, e2) = e3
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 202.03/33.66  | | | |              simplifying with (98), (162) gives:
% 202.03/33.66  | | | |   (164)  all_52_8 = all_6_2
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | BETA: splitting (41) gives:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | Case 1:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | |   (165)  all_58_2 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | COMBINE_EQS: (62), (165) imply:
% 202.03/33.66  | | | | |   (166)  all_52_3 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | SIMP: (166) implies:
% 202.03/33.66  | | | | |   (167)  all_52_3 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (13), (167) imply:
% 202.03/33.66  | | | | |   (168)   ~ (all_52_19 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | SIMP: (168) implies:
% 202.03/33.66  | | | | |   (169)   ~ (all_52_19 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (5), (167) imply:
% 202.03/33.66  | | | | |   (170)  op(e3, e3) = all_52_2
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | BETA: splitting (120) gives:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | Case 1:
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | |   (171)  all_58_4 = e3
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | REF_CLOSE: (134), (159), (171) are inconsistent by sub-proof #1302.
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | Case 2:
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | |   (172)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | BETA: splitting (172) gives:
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | Case 1:
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | |   (173)  all_58_5 = e3
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | REF_CLOSE: (105), (169), (173) are inconsistent by sub-proof
% 202.03/33.66  | | | | | | |            #1279.
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | Case 2:
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | |   (174)  all_58_8 = e3 | all_58_14 = e3
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | BETA: splitting (174) gives:
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | |   (175)  all_58_8 = e3
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | COMBINE_EQS: (83), (175) imply:
% 202.03/33.66  | | | | | | | |   (176)  all_10_2 = e3
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (85), (176) imply:
% 202.03/33.66  | | | | | | | |   (177)   ~ (all_52_5 = e3)
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (46), (176) imply:
% 202.03/33.66  | | | | | | | |   (178)   ~ (all_52_13 = e3)
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (47), (176) imply:
% 202.03/33.66  | | | | | | | |   (179)  op(e3, e3) = e1
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3,
% 202.03/33.66  | | | | | | | |              simplifying with (98), (170) gives:
% 202.03/33.66  | | | | | | | |   (180)  all_52_2 = all_6_2
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | GROUND_INST: instantiating (6) with e1, all_52_2, e3, e3,
% 202.03/33.66  | | | | | | | |              simplifying with (170), (179) gives:
% 202.03/33.66  | | | | | | | |   (181)  all_52_2 = e1
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | COMBINE_EQS: (180), (181) imply:
% 202.03/33.66  | | | | | | | |   (182)  all_6_2 = e1
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | SIMP: (182) implies:
% 202.03/33.66  | | | | | | | |   (183)  all_6_2 = e1
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | COMBINE_EQS: (17), (183) imply:
% 202.03/33.66  | | | | | | | |   (184)  all_44_2 = e1
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (93), (183) imply:
% 202.03/33.66  | | | | | | | |   (185)   ~ (all_52_5 = e1)
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (38), (183) imply:
% 202.03/33.66  | | | | | | | |   (186)   ~ (all_52_7 = e1)
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (133), (183) imply:
% 202.03/33.66  | | | | | | | |   (187)  op(e1, e3) = all_6_1
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | BETA: splitting (21) gives:
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | |   (188)   ~ (all_44_2 = e1)
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | REDUCE: (184), (188) imply:
% 202.03/33.66  | | | | | | | | |   (189)  $false
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | CLOSE: (189) is inconsistent.
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | |   (190)   ~ (all_44_1 = e0)
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | REDUCE: (117), (190) imply:
% 202.03/33.66  | | | | | | | | |   (191)   ~ (all_6_1 = e0)
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | REF_CLOSE: (6), (24), (29), (49), (55), (58), (79), (82),
% 202.03/33.66  | | | | | | | | |            (88), (96), (127), (152), (155), (157), (161),
% 202.03/33.66  | | | | | | | | |            (163), (177), (178), (185), (186), (187), (191) are
% 202.03/33.66  | | | | | | | | |            inconsistent by sub-proof #330.
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | End of split
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | |   (192)  all_58_14 = e3
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REF_CLOSE: (3), (141), (192) are inconsistent by sub-proof
% 202.03/33.66  | | | | | | | |            #1305.
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | End of split
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | End of split
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | End of split
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | Case 2:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | |   (193)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REF_CLOSE: (3), (6), (10), (13), (16), (18), (20), (31), (48), (52),
% 202.03/33.66  | | | | |            (56), (57), (62), (70), (71), (77), (81), (83), (96), (98),
% 202.03/33.66  | | | | |            (105), (113), (120), (126), (127), (133), (134), (143),
% 202.03/33.66  | | | | |            (145), (148), (161), (162), (193) are inconsistent by
% 202.03/33.66  | | | | |            sub-proof #447.
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | End of split
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | Case 2:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | |   (194)   ~ (all_56_1 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (106), (194) imply:
% 202.03/33.66  | | | |   (195)   ~ (all_52_9 = e3)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REF_CLOSE: (6), (7), (18), (25), (96), (98), (101), (109), (113), (115),
% 202.03/33.66  | | | |            (120), (133), (134), (142), (195) are inconsistent by
% 202.03/33.66  | | | |            sub-proof #446.
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | End of split
% 202.03/33.66  | | | 
% 202.03/33.66  | | End of split
% 202.03/33.66  | | 
% 202.03/33.66  | Case 2:
% 202.03/33.66  | | 
% 202.03/33.66  | |   (196)   ~ (all_56_15 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (40), (196) imply:
% 202.03/33.66  | |   (197)   ~ (all_14_2 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.03/33.66  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 202.03/33.66  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 202.03/33.66  | |            (36), (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 202.03/33.66  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 202.03/33.66  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 202.03/33.66  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 202.03/33.66  | |            (81), (82), (83), (85), (86), (87), (88), (89), (90), (91), (92),
% 202.03/33.66  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 202.03/33.66  | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 202.03/33.66  | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 202.03/33.66  | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 202.03/33.66  | |            (130), (131), (132), (133), (134), (135), (136), (197) are
% 202.03/33.66  | |            inconsistent by sub-proof #329.
% 202.03/33.66  | | 
% 202.03/33.66  | End of split
% 202.03/33.66  | 
% 202.03/33.66  End of proof
% 202.03/33.66  
% 202.03/33.66  Sub-proof #329 shows that the following formulas are inconsistent:
% 202.03/33.66  ----------------------------------------------------------------
% 202.03/33.66    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.66    (2)   ~ (all_52_25 = all_52_27)
% 202.03/33.66    (3)  all_58_14 = all_52_23
% 202.03/33.66    (4)   ~ (e3 = e1)
% 202.03/33.66    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.66    (7)  all_58_1 = all_52_9
% 202.03/33.66    (8)   ~ (e3 = e0)
% 202.03/33.66    (9)  op(all_52_23, all_52_23) = e0
% 202.03/33.66    (10)  op(e2, e3) = all_52_3
% 202.03/33.66    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.66    (12)   ~ (all_52_7 = all_52_15)
% 202.03/33.66    (13)   ~ (all_52_3 = all_52_19)
% 202.03/33.66    (14)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.66    (15)   ~ (all_52_17 = all_52_25)
% 202.03/33.66    (16)   ~ (all_52_3 = all_6_2)
% 202.03/33.66    (17)  all_44_2 = all_6_2
% 202.03/33.66    (18)  all_58_0 = all_6_2
% 202.03/33.66    (19)  all_56_4 = all_52_3
% 202.03/33.66    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.66    (21)  op(e3, e0) = all_52_25
% 202.03/33.66    (22)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.66    (23)  all_58_13 = all_52_15
% 202.03/33.66    (24)  all_58_9 = all_52_25
% 202.03/33.66    (25)   ~ (all_52_29 = all_14_2)
% 202.03/33.66    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.03/33.66    (27)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.66    (28)  op(e1, e3) = all_52_5
% 202.03/33.66    (29)  op(e2, e2) = all_4_2
% 202.03/33.66    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.66    (31)   ~ (all_52_3 = all_52_5)
% 202.03/33.66    (32)  all_58_11 = all_52_29
% 202.03/33.66    (33)   ~ (all_52_25 = all_14_2)
% 202.03/33.66    (34)   ~ (all_52_9 = all_52_15)
% 202.03/33.66    (35)  op(all_10_2, e1) = all_10_1
% 202.03/33.66    (36)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.66    (37)   ~ (all_52_7 = all_6_2)
% 202.03/33.66    (38)  op(e0, e0) = all_14_2
% 202.03/33.66    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.66    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.66    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.66    (42)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.03/33.66    (43)   ~ (e2 = e1)
% 202.03/33.66    (44)   ~ (all_52_13 = all_10_2)
% 202.03/33.66    (45)  op(all_10_2, all_10_2) = e1
% 202.03/33.66    (46)  all_58_10 = all_52_27
% 202.03/33.66    (47)  all_56_8 = all_52_5
% 202.03/33.66    (48)  op(all_52_9, all_52_9) = all_52_8
% 202.03/33.66    (49)  op(all_52_15, all_52_15) = all_52_14
% 202.03/33.66    (50)   ~ (all_52_19 = all_52_23)
% 202.03/33.66    (51)   ~ (all_52_25 = all_52_29)
% 202.03/33.66    (52)   ~ (all_52_29 = all_10_2)
% 202.03/33.66    (53)  all_58_7 = all_52_13
% 202.03/33.66    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.66    (55)  op(all_52_19, all_52_19) = e2
% 202.03/33.66    (56)   ~ (all_52_5 = all_52_7)
% 202.03/33.66    (57)  all_58_12 = all_52_7
% 202.03/33.66    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.66    (59)   ~ (all_52_7 = all_14_2)
% 202.03/33.66    (60)  all_58_2 = all_52_3
% 202.03/33.66    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.66    (62)  all_56_2 = all_52_17
% 202.03/33.66    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.03/33.66    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.66    (65)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.66    (66)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.03/33.66    (67)  all_56_7 = all_52_27
% 202.03/33.66    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.66    (69)   ~ (e2 = e0)
% 202.03/33.66    (70)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.66    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.66    (72)  all_56_6 = all_52_19
% 202.03/33.66    (73)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.03/33.66    (74)   ~ (all_52_13 = all_4_2)
% 202.03/33.66    (75)  op(e3, e1) = all_52_17
% 202.03/33.66    (76)  op(e0, e3) = all_52_7
% 202.03/33.66    (77)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.66    (78)  all_58_15 = all_14_2
% 202.03/33.66    (79)   ~ (all_52_19 = all_10_2)
% 202.03/33.66    (80)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.66    (81)  all_58_8 = all_10_2
% 202.03/33.66    (82)   ~ (all_52_5 = all_10_2)
% 202.03/33.66    (83)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.66    (84)   ~ (all_52_23 = all_14_2)
% 202.03/33.66    (85)  all_56_12 = all_52_7
% 202.03/33.66    (86)  all_8_2 = all_6_2
% 202.03/33.66    (87)   ~ (all_52_25 = all_6_2)
% 202.03/33.66    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.66    (89)   ~ (all_52_9 = all_4_2)
% 202.03/33.66    (90)   ~ (all_52_5 = all_6_2)
% 202.03/33.66    (91)   ~ (all_52_9 = all_6_2)
% 202.03/33.66    (92)   ~ (all_52_13 = all_52_15)
% 202.03/33.66    (93)  op(e3, all_6_1) = e2
% 202.03/33.66    (94)  all_56_0 = all_6_2
% 202.03/33.66    (95)  op(e3, e3) = all_6_2
% 202.03/33.66    (96)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.66    (97)   ~ (all_52_27 = all_14_2)
% 202.03/33.66    (98)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.66    (99)  all_56_3 = all_52_25
% 202.03/33.66    (100)   ~ (all_52_3 = all_52_7)
% 202.03/33.66    (101)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.66    (102)  all_58_5 = all_52_19
% 202.03/33.66    (103)  all_56_1 = all_52_9
% 202.03/33.66    (104)   ~ (all_52_15 = all_4_2)
% 202.03/33.66    (105)   ~ (all_52_27 = all_4_2)
% 202.03/33.66    (106)  op(all_52_17, all_52_17) = e3
% 202.03/33.66    (107)  all_58_6 = all_52_5
% 202.03/33.66    (108)  op(e3, e2) = all_52_9
% 202.03/33.66    (109)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.66    (110)   ~ (all_52_17 = all_6_2)
% 202.03/33.66    (111)   ~ (e1 = e0)
% 202.03/33.66    (112)   ~ (e3 = e2)
% 202.03/33.66    (113)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.66    (114)  all_44_1 = all_6_1
% 202.03/33.66    (115)   ~ (all_52_9 = all_52_17)
% 202.03/33.66    (116)  all_56_10 = all_10_2
% 202.03/33.66    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.66    (118)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.66    (119)  op(all_52_13, all_52_13) = all_52_12
% 202.03/33.66    (120)  op(e1, e1) = all_10_2
% 202.03/33.66    (121)   ~ (all_52_23 = all_10_2)
% 202.03/33.66    (122)   ~ (all_52_7 = all_52_23)
% 202.03/33.66    (123)   ~ (all_52_17 = all_52_19)
% 202.03/33.66    (124)  all_58_3 = all_4_2
% 202.03/33.66    (125)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.03/33.66    (126)  all_56_13 = all_52_15
% 202.03/33.66    (127)   ~ (all_52_3 = all_4_2)
% 202.03/33.66    (128)   ~ (all_52_17 = all_52_23)
% 202.03/33.66    (129)  all_8_1 = all_6_1
% 202.03/33.66    (130)  op(all_6_2, e3) = all_6_1
% 202.03/33.66    (131)  all_58_4 = all_52_17
% 202.03/33.66    (132)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.03/33.66    (133)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.66    (134)   ~ (all_14_2 = e3)
% 202.03/33.66  
% 202.03/33.66  Begin of proof
% 202.03/33.66  | 
% 202.03/33.66  | BETA: splitting (40) gives:
% 202.03/33.66  | 
% 202.03/33.66  | Case 1:
% 202.03/33.66  | | 
% 202.03/33.66  | |   (135)  all_56_13 = e3
% 202.03/33.66  | | 
% 202.03/33.66  | | COMBINE_EQS: (126), (135) imply:
% 202.03/33.66  | |   (136)  all_52_15 = e3
% 202.03/33.66  | | 
% 202.03/33.66  | | SIMP: (136) implies:
% 202.03/33.66  | |   (137)  all_52_15 = e3
% 202.03/33.66  | | 
% 202.03/33.66  | | COMBINE_EQS: (23), (137) imply:
% 202.03/33.66  | |   (138)  all_58_13 = e3
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (12), (137) imply:
% 202.03/33.66  | |   (139)   ~ (all_52_7 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (34), (137) imply:
% 202.03/33.66  | |   (140)   ~ (all_52_9 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (92), (137) imply:
% 202.03/33.66  | |   (141)   ~ (all_52_13 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (104), (137) imply:
% 202.03/33.66  | |   (142)   ~ (all_4_2 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | SIMP: (142) implies:
% 202.03/33.66  | |   (143)   ~ (all_4_2 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (49), (137) imply:
% 202.03/33.66  | |   (144)  op(e3, e3) = all_52_14
% 202.03/33.66  | | 
% 202.03/33.66  | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3, simplifying
% 202.03/33.66  | |              with (95), (144) gives:
% 202.03/33.66  | |   (145)  all_52_14 = all_6_2
% 202.03/33.66  | | 
% 202.03/33.66  | | BETA: splitting (113) gives:
% 202.03/33.66  | | 
% 202.03/33.66  | | Case 1:
% 202.03/33.66  | | | 
% 202.03/33.66  | | |   (146)  all_56_1 = e3
% 202.03/33.66  | | | 
% 202.03/33.66  | | | COMBINE_EQS: (103), (146) imply:
% 202.03/33.66  | | |   (147)  all_52_9 = e3
% 202.03/33.66  | | | 
% 202.03/33.66  | | | REDUCE: (140), (147) imply:
% 202.03/33.66  | | |   (148)  $false
% 202.03/33.66  | | | 
% 202.03/33.66  | | | CLOSE: (148) is inconsistent.
% 202.03/33.66  | | | 
% 202.03/33.66  | | Case 2:
% 202.03/33.66  | | | 
% 202.03/33.66  | | |   (149)   ~ (all_56_1 = e3)
% 202.03/33.66  | | |   (150)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.66  | | | 
% 202.03/33.66  | | | BETA: splitting (42) gives:
% 202.03/33.66  | | | 
% 202.03/33.66  | | | Case 1:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | |   (151)  all_58_1 = e1
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | COMBINE_EQS: (7), (151) imply:
% 202.03/33.66  | | | |   (152)  all_52_9 = e1
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (115), (152) imply:
% 202.03/33.66  | | | |   (153)   ~ (all_52_17 = e1)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | SIMP: (153) implies:
% 202.03/33.66  | | | |   (154)   ~ (all_52_17 = e1)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (91), (152) imply:
% 202.03/33.66  | | | |   (155)   ~ (all_6_2 = e1)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | SIMP: (155) implies:
% 202.03/33.66  | | | |   (156)   ~ (all_6_2 = e1)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | BETA: splitting (88) gives:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | Case 1:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | |   (157)  all_56_3 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | COMBINE_EQS: (99), (157) imply:
% 202.03/33.66  | | | | |   (158)  all_52_25 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | SIMP: (158) implies:
% 202.03/33.66  | | | | |   (159)  all_52_25 = e3
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (15), (159) imply:
% 202.03/33.66  | | | | |   (160)   ~ (all_52_17 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (33), (159) imply:
% 202.03/33.66  | | | | |   (161)   ~ (all_14_2 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (87), (159) imply:
% 202.03/33.66  | | | | |   (162)   ~ (all_6_2 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | SIMP: (162) implies:
% 202.03/33.66  | | | | |   (163)   ~ (all_6_2 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REF_CLOSE: (3), (6), (9), (18), (36), (37), (38), (41), (57), (62),
% 202.03/33.66  | | | | |            (63), (65), (73), (84), (94), (106), (110), (118), (134),
% 202.03/33.66  | | | | |            (138), (154), (156), (160), (163) are inconsistent by
% 202.03/33.66  | | | | |            sub-proof #1064.
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | Case 2:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | |   (164)   ~ (all_56_3 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (99), (164) imply:
% 202.03/33.66  | | | | |   (165)   ~ (all_52_25 = e3)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REF_CLOSE: (6), (7), (18), (24), (93), (95), (98), (106), (110),
% 202.03/33.66  | | | | |            (112), (117), (130), (131), (140), (165) are inconsistent
% 202.03/33.66  | | | | |            by sub-proof #446.
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | End of split
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | Case 2:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | |   (166)   ~ (all_58_1 = e1)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | REDUCE: (7), (166) imply:
% 202.03/33.66  | | | |   (167)   ~ (all_52_9 = e1)
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | BETA: splitting (125) gives:
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | | Case 1:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | |   (168)  all_58_1 = e2
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REF_CLOSE: (3), (6), (7), (9), (15), (18), (24), (33), (36), (37),
% 202.03/33.66  | | | | |            (38), (41), (57), (62), (65), (70), (73), (84), (87), (88),
% 202.03/33.66  | | | | |            (91), (93), (94), (95), (98), (99), (106), (110), (115),
% 202.03/33.66  | | | | |            (117), (118), (130), (131), (138), (140), (168) are
% 202.03/33.66  | | | | |            inconsistent by sub-proof #413.
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | Case 2:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | |   (169)   ~ (all_58_1 = e2)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | REDUCE: (7), (169) imply:
% 202.03/33.66  | | | | |   (170)   ~ (all_52_9 = e2)
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | BETA: splitting (150) gives:
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | | Case 1:
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | |   (171)  all_56_1 = e2
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | COMBINE_EQS: (103), (171) imply:
% 202.03/33.66  | | | | | |   (172)  all_52_9 = e2
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | REDUCE: (170), (172) imply:
% 202.03/33.66  | | | | | |   (173)  $false
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | CLOSE: (173) is inconsistent.
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | Case 2:
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | |   (174)   ~ (all_56_1 = e2)
% 202.03/33.66  | | | | | |   (175)  all_56_1 = e1 | all_56_1 = e0
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | BETA: splitting (175) gives:
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | | Case 1:
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | |   (176)  all_56_1 = e1
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | COMBINE_EQS: (103), (176) imply:
% 202.03/33.66  | | | | | | |   (177)  all_52_9 = e1
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | REDUCE: (167), (177) imply:
% 202.03/33.66  | | | | | | |   (178)  $false
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | CLOSE: (178) is inconsistent.
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | Case 2:
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | |   (179)  all_56_1 = e0
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | COMBINE_EQS: (103), (179) imply:
% 202.03/33.66  | | | | | | |   (180)  all_52_9 = e0
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | COMBINE_EQS: (7), (180) imply:
% 202.03/33.66  | | | | | | |   (181)  all_58_1 = e0
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | REDUCE: (140), (180) imply:
% 202.03/33.66  | | | | | | |   (182)   ~ (e3 = e0)
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | REDUCE: (170), (180) imply:
% 202.03/33.66  | | | | | | |   (183)   ~ (e2 = e0)
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | BETA: splitting (41) gives:
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | |   (184)  all_56_2 = e3
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | COMBINE_EQS: (62), (184) imply:
% 202.03/33.66  | | | | | | | |   (185)  all_52_17 = e3
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | SIMP: (185) implies:
% 202.03/33.66  | | | | | | | |   (186)  all_52_17 = e3
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REF_CLOSE: (6), (95), (106), (110), (186) are inconsistent by
% 202.03/33.66  | | | | | | | |            sub-proof #1280.
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | |   (187)   ~ (all_56_2 = e3)
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | REDUCE: (62), (187) imply:
% 202.03/33.66  | | | | | | | |   (188)   ~ (all_52_17 = e3)
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | BETA: splitting (98) gives:
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | |   (189)  all_58_0 = e3
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | COMBINE_EQS: (18), (189) imply:
% 202.03/33.66  | | | | | | | | |   (190)  all_6_2 = e3
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | REF_CLOSE: (6), (93), (95), (112), (130), (190) are
% 202.03/33.66  | | | | | | | | |            inconsistent by sub-proof #502.
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | |   (191)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | BETA: splitting (191) gives:
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | |   (192)  all_58_1 = e3
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | REF_CLOSE: (8), (181), (192) are inconsistent by sub-proof
% 202.03/33.66  | | | | | | | | | |            #1060.
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | |   (193)  all_58_4 = e3 | all_58_9 = e3
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | BETA: splitting (193) gives:
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | |   (194)  all_58_4 = e3
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | REF_CLOSE: (131), (188), (194) are inconsistent by sub-proof
% 202.03/33.66  | | | | | | | | | | |            #1302.
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | |   (195)  all_58_9 = e3
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | COMBINE_EQS: (24), (195) imply:
% 202.03/33.66  | | | | | | | | | | |   (196)  all_52_25 = e3
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | SIMP: (196) implies:
% 202.03/33.66  | | | | | | | | | | |   (197)  all_52_25 = e3
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | REDUCE: (2), (197) imply:
% 202.03/33.66  | | | | | | | | | | |   (198)   ~ (all_52_27 = e3)
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | SIMP: (198) implies:
% 202.03/33.66  | | | | | | | | | | |   (199)   ~ (all_52_27 = e3)
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | REDUCE: (51), (197) imply:
% 202.03/33.66  | | | | | | | | | | |   (200)   ~ (all_52_29 = e3)
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | SIMP: (200) implies:
% 202.03/33.66  | | | | | | | | | | |   (201)   ~ (all_52_29 = e3)
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | REDUCE: (87), (197) imply:
% 202.03/33.66  | | | | | | | | | | |   (202)   ~ (all_6_2 = e3)
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | SIMP: (202) implies:
% 202.03/33.66  | | | | | | | | | | |   (203)   ~ (all_6_2 = e3)
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | REDUCE: (133), (197) imply:
% 202.03/33.66  | | | | | | | | | | |   (204)  op(e3, e3) = all_52_24
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 202.03/33.66  | | | | | | | | | | |              simplifying with (95), (204) gives:
% 202.03/33.66  | | | | | | | | | | |   (205)  all_52_24 = all_6_2
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | BETA: splitting (64) gives:
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | |   (206)  all_58_0 = e3
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | COMBINE_EQS: (18), (206) imply:
% 202.03/33.66  | | | | | | | | | | | |   (207)  all_6_2 = e3
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | REDUCE: (203), (207) imply:
% 202.03/33.66  | | | | | | | | | | | |   (208)  $false
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | CLOSE: (208) is inconsistent.
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | |   (209)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | BETA: splitting (58) gives:
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | Case 1:
% 202.03/33.66  | | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | |   (210)  all_58_6 = e3
% 202.03/33.66  | | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (13), (16), (18), (19), (21),
% 202.03/33.66  | | | | | | | | | | | | |            (24), (30), (31), (39), (46), (54), (55), (56),
% 202.03/33.66  | | | | | | | | | | | | |            (57), (60), (64), (68), (69), (75), (90), (93),
% 202.03/33.66  | | | | | | | | | | | | |            (95), (98), (102), (107), (110), (112), (123),
% 202.03/33.66  | | | | | | | | | | | | |            (124), (130), (131), (140), (143), (199), (210)
% 202.03/33.66  | | | | | | | | | | | | |            are inconsistent by sub-proof #345.
% 202.03/33.66  | | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | Case 2:
% 202.03/33.66  | | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | |   (211)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.66  | | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (18), (29), (31), (32), (35), (43),
% 202.03/33.66  | | | | | | | | | | | | |            (45), (53), (57), (60), (63), (64), (69), (75),
% 202.03/33.66  | | | | | | | | | | | | |            (81), (82), (95), (100), (106), (107), (112),
% 202.03/33.66  | | | | | | | | | | | | |            (127), (131), (139), (141), (181), (195), (201),
% 202.03/33.66  | | | | | | | | | | | | |            (209), (211) are inconsistent by sub-proof #1056.
% 202.03/33.66  | | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | | End of split
% 202.03/33.66  | | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | | End of split
% 202.03/33.66  | | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | | End of split
% 202.03/33.66  | | | | | | | | | | 
% 202.03/33.66  | | | | | | | | | End of split
% 202.03/33.66  | | | | | | | | | 
% 202.03/33.66  | | | | | | | | End of split
% 202.03/33.66  | | | | | | | | 
% 202.03/33.66  | | | | | | | End of split
% 202.03/33.66  | | | | | | | 
% 202.03/33.66  | | | | | | End of split
% 202.03/33.66  | | | | | | 
% 202.03/33.66  | | | | | End of split
% 202.03/33.66  | | | | | 
% 202.03/33.66  | | | | End of split
% 202.03/33.66  | | | | 
% 202.03/33.66  | | | End of split
% 202.03/33.66  | | | 
% 202.03/33.66  | | End of split
% 202.03/33.66  | | 
% 202.03/33.66  | Case 2:
% 202.03/33.66  | | 
% 202.03/33.66  | |   (212)   ~ (all_56_13 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REDUCE: (126), (212) imply:
% 202.03/33.66  | |   (213)   ~ (all_52_15 = e3)
% 202.03/33.66  | | 
% 202.03/33.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.03/33.66  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 202.03/33.66  | |            (25), (26), (27), (28), (29), (30), (32), (35), (37), (38), (39),
% 202.03/33.66  | |            (41), (43), (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 202.03/33.66  | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (65), (66),
% 202.03/33.66  | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 202.03/33.66  | |            (78), (79), (80), (81), (83), (85), (86), (87), (89), (90), (93),
% 202.03/33.66  | |            (95), (96), (97), (98), (100), (101), (102), (103), (105), (106),
% 202.03/33.66  | |            (107), (108), (109), (110), (111), (113), (114), (115), (116),
% 202.03/33.66  | |            (117), (119), (120), (121), (122), (124), (128), (129), (130),
% 202.03/33.66  | |            (131), (132), (133), (134), (213) are inconsistent by sub-proof
% 202.03/33.66  | |            #339.
% 202.03/33.66  | | 
% 202.03/33.66  | End of split
% 202.03/33.66  | 
% 202.03/33.66  End of proof
% 202.03/33.66  
% 202.03/33.66  Sub-proof #330 shows that the following formulas are inconsistent:
% 202.03/33.66  ----------------------------------------------------------------
% 202.03/33.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.66    (2)   ~ (all_4_2 = e3)
% 202.03/33.66    (3)  all_58_13 = all_52_15
% 202.03/33.66    (4)   ~ (all_52_5 = e1)
% 202.03/33.66    (5)   ~ (all_52_15 = e3)
% 202.03/33.66    (6)  op(e1, e3) = all_52_5
% 202.03/33.66    (7)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.66    (8)   ~ (all_6_1 = e0)
% 202.03/33.66    (9)  all_58_1 = e3
% 202.03/33.66    (10)  op(e1, e3) = all_6_1
% 202.03/33.66    (11)  all_56_8 = all_52_5
% 202.03/33.66    (12)  all_58_7 = all_52_13
% 202.03/33.66    (13)   ~ (all_52_5 = all_52_7)
% 202.03/33.66    (14)  op(e3, e2) = e3
% 202.03/33.67    (15)   ~ (all_52_5 = e3)
% 202.03/33.67    (16)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.67    (17)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.67    (18)  all_56_12 = all_52_7
% 202.03/33.67    (19)  op(e3, all_6_1) = e2
% 202.03/33.67    (20)   ~ (all_52_7 = e1)
% 202.03/33.67    (21)   ~ (all_52_13 = e3)
% 202.03/33.67    (22)  all_58_3 = all_4_2
% 202.03/33.67  
% 202.03/33.67  Begin of proof
% 202.03/33.67  | 
% 202.03/33.67  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 202.03/33.67  |              with (6), (10) gives:
% 202.03/33.67  |   (23)  all_52_5 = all_6_1
% 202.03/33.67  | 
% 202.03/33.67  | COMBINE_EQS: (11), (23) imply:
% 202.03/33.67  |   (24)  all_56_8 = all_6_1
% 202.03/33.67  | 
% 202.03/33.67  | REDUCE: (13), (23) imply:
% 202.03/33.67  |   (25)   ~ (all_52_7 = all_6_1)
% 202.03/33.67  | 
% 202.03/33.67  | SIMP: (25) implies:
% 202.03/33.67  |   (26)   ~ (all_52_7 = all_6_1)
% 202.03/33.67  | 
% 202.03/33.67  | REDUCE: (15), (23) imply:
% 202.03/33.67  |   (27)   ~ (all_6_1 = e3)
% 202.03/33.67  | 
% 202.03/33.67  | REDUCE: (4), (23) imply:
% 202.03/33.67  |   (28)   ~ (all_6_1 = e1)
% 202.03/33.67  | 
% 202.03/33.67  | BETA: splitting (17) gives:
% 202.03/33.67  | 
% 202.03/33.67  | Case 1:
% 202.03/33.67  | | 
% 202.03/33.67  | |   (29)  all_56_8 = e3
% 202.03/33.67  | | 
% 202.03/33.67  | | REF_CLOSE: (24), (27), (29) are inconsistent by sub-proof #1101.
% 202.03/33.67  | | 
% 202.03/33.67  | Case 2:
% 202.03/33.67  | | 
% 202.03/33.67  | |   (30)   ~ (all_56_8 = e3)
% 202.03/33.67  | |   (31)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.67  | | 
% 202.03/33.67  | | BETA: splitting (31) gives:
% 202.03/33.67  | | 
% 202.03/33.67  | | Case 1:
% 202.03/33.67  | | | 
% 202.03/33.67  | | |   (32)  all_56_8 = e2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | COMBINE_EQS: (24), (32) imply:
% 202.03/33.67  | | |   (33)  all_6_1 = e2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | SIMP: (33) implies:
% 202.03/33.67  | | |   (34)  all_6_1 = e2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (26), (34) imply:
% 202.03/33.67  | | |   (35)   ~ (all_52_7 = e2)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (27), (34) imply:
% 202.03/33.67  | | |   (36)   ~ (e3 = e2)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | SIMP: (36) implies:
% 202.03/33.67  | | |   (37)   ~ (e3 = e2)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (19), (34) imply:
% 202.03/33.67  | | |   (38)  op(e3, e2) = e2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | BETA: splitting (7) gives:
% 202.03/33.67  | | | 
% 202.03/33.67  | | | Case 1:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | |   (39)  all_56_12 = e2
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REF_CLOSE: (18), (35), (39) are inconsistent by sub-proof #1178.
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | Case 2:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | |   (40)  all_56_12 = e1 | all_56_12 = e0
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | BETA: splitting (40) gives:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | Case 1:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | |   (41)  all_56_12 = e1
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REF_CLOSE: (18), (20), (41) are inconsistent by sub-proof #1376.
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | Case 2:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | GROUND_INST: instantiating (1) with e3, e2, e2, e3, simplifying with
% 202.03/33.67  | | | | |              (14), (38) gives:
% 202.03/33.67  | | | | |   (42)  e3 = e2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (16), (21), (22), (37), (42) are
% 202.03/33.67  | | | | |            inconsistent by sub-proof #1089.
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | End of split
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | End of split
% 202.03/33.67  | | | 
% 202.03/33.67  | | Case 2:
% 202.03/33.67  | | | 
% 202.03/33.67  | | |   (43)  all_56_8 = e1 | all_56_8 = e0
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REF_CLOSE: (8), (24), (28), (43) are inconsistent by sub-proof #495.
% 202.03/33.67  | | | 
% 202.03/33.67  | | End of split
% 202.03/33.67  | | 
% 202.03/33.67  | End of split
% 202.03/33.67  | 
% 202.03/33.67  End of proof
% 202.03/33.67  
% 202.03/33.67  Sub-proof #331 shows that the following formulas are inconsistent:
% 202.03/33.67  ----------------------------------------------------------------
% 202.03/33.67    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.67    (2)   ~ (all_52_15 = all_52_23)
% 202.03/33.67    (3)   ~ (all_52_25 = all_52_27)
% 202.03/33.67    (4)  all_58_14 = all_52_23
% 202.03/33.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.67    (6)   ~ (all_52_5 = all_52_13)
% 202.03/33.67    (7)  all_58_1 = all_52_9
% 202.03/33.67    (8)   ~ (all_52_9 = all_52_13)
% 202.03/33.67    (9)   ~ (e3 = e0)
% 202.03/33.67    (10)  op(e2, e3) = all_52_3
% 202.03/33.67    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.67    (12)   ~ (all_52_7 = all_52_15)
% 202.03/33.67    (13)  op(all_52_15, all_52_15) = e0
% 202.03/33.67    (14)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.67    (15)   ~ (all_52_17 = all_52_25)
% 202.03/33.67    (16)   ~ (all_52_3 = all_6_2)
% 202.03/33.67    (17)  all_44_2 = all_6_2
% 202.03/33.67    (18)  all_58_0 = all_6_2
% 202.03/33.67    (19)  all_56_4 = all_52_3
% 202.03/33.67    (20)   ~ (all_52_17 = all_10_2)
% 202.03/33.67    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.67    (22)  op(e3, e0) = all_52_25
% 202.03/33.67    (23)  op(all_52_5, all_52_5) = all_52_4
% 202.03/33.67    (24)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.67    (25)   ~ (all_52_27 = all_52_29)
% 202.03/33.67    (26)  all_58_13 = all_52_15
% 202.03/33.67    (27)  op(all_52_13, all_52_13) = e1
% 202.03/33.67    (28)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.67    (29)  all_58_9 = all_52_25
% 202.03/33.67    (30)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.67    (31)  op(e1, e3) = all_52_5
% 202.03/33.67    (32)  op(e2, e2) = all_4_2
% 202.03/33.67    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.67    (34)  all_58_11 = all_52_29
% 202.03/33.67    (35)  all_56_5 = all_4_2
% 202.03/33.67    (36)   ~ (all_52_9 = all_52_15)
% 202.03/33.67    (37)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.03/33.67    (38)  op(all_10_2, e1) = all_10_1
% 202.03/33.67    (39)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.67    (40)   ~ (all_52_7 = all_6_2)
% 202.03/33.67    (41)  op(e0, e1) = all_52_23
% 202.03/33.67    (42)   ~ (all_52_15 = e0)
% 202.03/33.67    (43)  all_58_15 = e0
% 202.03/33.67    (44)  all_56_11 = all_52_29
% 202.03/33.67    (45)   ~ (all_4_1 = e1)
% 202.03/33.67    (46)   ~ (all_52_25 = e0)
% 202.03/33.67    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.67    (48)  op(e1, all_10_1) = e3
% 202.03/33.67    (49)  all_56_9 = all_52_13
% 202.03/33.67    (50)   ~ (e2 = e1)
% 202.03/33.67    (51)   ~ (all_52_13 = all_10_2)
% 202.03/33.67    (52)  op(e0, e0) = e0
% 202.03/33.67    (53)  all_58_10 = all_52_27
% 202.03/33.67    (54)  all_56_8 = all_52_5
% 202.03/33.67    (55)   ~ (all_52_25 = all_52_29)
% 202.03/33.67    (56)  all_58_7 = all_52_13
% 202.03/33.67    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.03/33.67    (58)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.67    (59)   ~ (all_52_5 = all_52_7)
% 202.03/33.67    (60)  all_58_12 = all_52_7
% 202.03/33.67    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.67    (62)  all_58_2 = all_52_3
% 202.03/33.67    (63)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.03/33.67    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.67    (65)   ~ (e2 = e0)
% 202.03/33.67    (66)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.03/33.67    (67)  op(all_4_2, e2) = all_4_1
% 202.03/33.67    (68)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.67    (69)   ~ (all_52_5 = all_52_29)
% 202.03/33.67    (70)   ~ (all_52_29 = e0)
% 202.03/33.67    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.03/33.67    (72)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.03/33.67    (73)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.03/33.67    (74)  op(e3, e1) = all_52_17
% 202.03/33.67    (75)  op(e0, e3) = all_52_7
% 202.03/33.67    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.67    (77)   ~ (all_52_9 = all_52_25)
% 202.03/33.67    (78)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.67    (79)  all_58_8 = all_10_2
% 202.03/33.67    (80)   ~ (all_52_23 = e0)
% 202.03/33.67    (81)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.67    (82)  all_56_12 = all_52_7
% 202.03/33.67    (83)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.67    (84)  all_8_2 = all_6_2
% 202.03/33.67    (85)   ~ (all_52_25 = all_6_2)
% 202.03/33.67    (86)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.67    (87)   ~ (all_52_5 = all_6_2)
% 202.03/33.67    (88)  op(all_4_2, all_4_2) = e2
% 202.03/33.67    (89)   ~ (all_52_9 = all_6_2)
% 202.03/33.67    (90)   ~ (all_52_13 = all_52_15)
% 202.03/33.67    (91)  op(e3, all_6_1) = e2
% 202.03/33.67    (92)  all_56_0 = all_6_2
% 202.03/33.67    (93)  op(e3, e3) = all_6_2
% 202.03/33.67    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.67    (95)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.67    (96)  all_56_14 = all_52_23
% 202.03/33.67    (97)  all_56_3 = all_52_25
% 202.03/33.67    (98)   ~ (all_52_3 = all_52_7)
% 202.03/33.67    (99)  all_58_5 = all_52_19
% 202.03/33.67    (100)  all_56_1 = all_52_9
% 202.03/33.67    (101)   ~ (all_52_15 = all_4_2)
% 202.03/33.67    (102)  all_58_6 = all_52_5
% 202.03/33.67    (103)  op(e3, e2) = all_52_9
% 202.03/33.67    (104)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.67    (105)   ~ (all_52_17 = all_6_2)
% 202.03/33.67    (106)   ~ (e1 = e0)
% 202.03/33.67    (107)   ~ (e3 = e2)
% 202.03/33.67    (108)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.67    (109)  all_44_1 = all_6_1
% 202.03/33.67    (110)   ~ (all_52_9 = all_52_17)
% 202.03/33.67    (111)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.67    (112)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.03/33.67    (113)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.67    (114)  op(e1, e1) = all_10_2
% 202.03/33.67    (115)  op(all_52_9, all_52_9) = e3
% 202.03/33.67    (116)   ~ (all_52_23 = all_10_2)
% 202.03/33.67    (117)   ~ (all_52_7 = all_52_23)
% 202.03/33.67    (118)  all_58_3 = all_4_2
% 202.03/33.67    (119)  all_56_13 = all_52_15
% 202.03/33.67    (120)   ~ (all_52_19 = all_4_2)
% 202.03/33.67    (121)  all_8_1 = all_6_1
% 202.03/33.67    (122)  op(all_6_2, e3) = all_6_1
% 202.03/33.67    (123)   ~ (all_52_13 = all_52_29)
% 202.03/33.67    (124)  all_58_4 = all_52_17
% 202.03/33.67    (125)   ~ (all_52_7 = e0)
% 202.03/33.67    (126)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.67  
% 202.03/33.67  Begin of proof
% 202.03/33.67  | 
% 202.03/33.67  | BETA: splitting (47) gives:
% 202.03/33.67  | 
% 202.03/33.67  | Case 1:
% 202.03/33.67  | | 
% 202.03/33.67  | |   (127)  all_56_13 = e3
% 202.03/33.67  | | 
% 202.03/33.67  | | COMBINE_EQS: (119), (127) imply:
% 202.03/33.67  | |   (128)  all_52_15 = e3
% 202.03/33.67  | | 
% 202.03/33.67  | | REF_CLOSE: (1), (2), (5), (11), (12), (13), (14), (32), (40), (57), (75),
% 202.03/33.67  | |            (80), (82), (84), (91), (93), (96), (101), (103), (115), (117),
% 202.03/33.67  | |            (121), (122), (128) are inconsistent by sub-proof #499.
% 202.03/33.67  | | 
% 202.03/33.67  | Case 2:
% 202.03/33.67  | | 
% 202.03/33.67  | |   (129)   ~ (all_56_13 = e3)
% 202.03/33.67  | |   (130)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.67  | | 
% 202.03/33.67  | | REDUCE: (119), (129) imply:
% 202.03/33.67  | |   (131)   ~ (all_52_15 = e3)
% 202.03/33.67  | | 
% 202.03/33.67  | | BETA: splitting (104) gives:
% 202.03/33.67  | | 
% 202.03/33.67  | | Case 1:
% 202.03/33.67  | | | 
% 202.03/33.67  | | |   (132)  all_58_12 = e3
% 202.03/33.67  | | | 
% 202.03/33.67  | | | COMBINE_EQS: (60), (132) imply:
% 202.03/33.67  | | |   (133)  all_52_7 = e3
% 202.03/33.67  | | | 
% 202.03/33.67  | | | SIMP: (133) implies:
% 202.03/33.67  | | |   (134)  all_52_7 = e3
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (59), (134) imply:
% 202.03/33.67  | | |   (135)   ~ (all_52_5 = e3)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (12), (134) imply:
% 202.03/33.67  | | |   (136)   ~ (all_52_15 = e3)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (117), (134) imply:
% 202.03/33.67  | | |   (137)   ~ (all_52_23 = e3)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | SIMP: (137) implies:
% 202.03/33.67  | | |   (138)   ~ (all_52_23 = e3)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (40), (134) imply:
% 202.03/33.67  | | |   (139)   ~ (all_6_2 = e3)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | SIMP: (139) implies:
% 202.03/33.67  | | |   (140)   ~ (all_6_2 = e3)
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (14), (134) imply:
% 202.03/33.67  | | |   (141)  op(e3, e3) = all_52_6
% 202.03/33.67  | | | 
% 202.03/33.67  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 202.03/33.67  | | |              with (93), (141) gives:
% 202.03/33.67  | | |   (142)  all_52_6 = all_6_2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | BETA: splitting (72) gives:
% 202.03/33.67  | | | 
% 202.03/33.67  | | | Case 1:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | |   (143)  all_56_11 = e3
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | COMBINE_EQS: (44), (143) imply:
% 202.03/33.67  | | | |   (144)  all_52_29 = e3
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REF_CLOSE: (5), (7), (18), (26), (29), (45), (52), (55), (56), (67),
% 202.03/33.67  | | | |            (76), (83), (88), (89), (93), (95), (100), (103), (108),
% 202.03/33.67  | | | |            (110), (111), (115), (118), (123), (124), (131), (140), (144)
% 202.03/33.67  | | | |            are inconsistent by sub-proof #1296.
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | Case 2:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | |   (145)   ~ (all_56_11 = e3)
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REDUCE: (44), (145) imply:
% 202.03/33.67  | | | |   (146)   ~ (all_52_29 = e3)
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | BETA: splitting (94) gives:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | Case 1:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | |   (147)  all_58_9 = e3
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | COMBINE_EQS: (29), (147) imply:
% 202.03/33.67  | | | | |   (148)  all_52_25 = e3
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | SIMP: (148) implies:
% 202.03/33.67  | | | | |   (149)  all_52_25 = e3
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (77), (149) imply:
% 202.03/33.67  | | | | |   (150)   ~ (all_52_9 = e3)
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (15), (149) imply:
% 202.03/33.67  | | | | |   (151)   ~ (all_52_17 = e3)
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (126), (149) imply:
% 202.03/33.67  | | | | |   (152)  op(e3, e3) = all_52_24
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 202.03/33.67  | | | | |              simplifying with (93), (152) gives:
% 202.03/33.67  | | | | |   (153)  all_52_24 = all_6_2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | BETA: splitting (111) gives:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | Case 1:
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | |   (154)  all_58_4 = e3
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | | REF_CLOSE: (124), (151), (154) are inconsistent by sub-proof #1302.
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | Case 2:
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | |   (155)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | | BETA: splitting (76) gives:
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | | Case 1:
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | |   (156)  all_58_1 = e3
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | | COMBINE_EQS: (7), (156) imply:
% 202.03/33.67  | | | | | | |   (157)  all_52_9 = e3
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | | REDUCE: (150), (157) imply:
% 202.03/33.67  | | | | | | |   (158)  $false
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | | CLOSE: (158) is inconsistent.
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | Case 2:
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | |   (159)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | | BETA: splitting (78) gives:
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | | Case 1:
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | |   (160)  all_56_8 = e3
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | | REF_CLOSE: (54), (135), (160) are inconsistent by sub-proof
% 202.03/33.67  | | | | | | | |            #1325.
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | Case 2:
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | |   (161)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | | BETA: splitting (66) gives:
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | | Case 1:
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | |   (162)  all_56_5 = e3
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | COMBINE_EQS: (35), (162) imply:
% 202.03/33.67  | | | | | | | | |   (163)  all_4_2 = e3
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | SIMP: (163) implies:
% 202.03/33.67  | | | | | | | | |   (164)  all_4_2 = e3
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | REDUCE: (120), (164) imply:
% 202.03/33.67  | | | | | | | | |   (165)   ~ (all_52_19 = e3)
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | REDUCE: (88), (164) imply:
% 202.03/33.67  | | | | | | | | |   (166)  op(e3, e3) = e2
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | BETA: splitting (155) gives:
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | Case 1:
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | |   (167)  all_58_5 = e3
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | REF_CLOSE: (99), (165), (167) are inconsistent by sub-proof
% 202.03/33.67  | | | | | | | | | |            #1279.
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | Case 2:
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | |   (168)  all_58_8 = e3 | all_58_14 = e3
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | BETA: splitting (168) gives:
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | Case 1:
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | |   (169)  all_58_8 = e3
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | COMBINE_EQS: (79), (169) imply:
% 202.03/33.67  | | | | | | | | | | |   (170)  all_10_2 = e3
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REDUCE: (28), (170) imply:
% 202.03/33.67  | | | | | | | | | | |   (171)  op(e3, e3) = all_52_20
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REDUCE: (38), (170) imply:
% 202.03/33.67  | | | | | | | | | | |   (172)  op(e3, e1) = all_10_1
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_17, all_10_1, e1,
% 202.03/33.67  | | | | | | | | | | |              e3, simplifying with (74), (172) gives:
% 202.03/33.67  | | | | | | | | | | |   (173)  all_52_17 = all_10_1
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_20, e3, e3,
% 202.03/33.67  | | | | | | | | | | |              simplifying with (93), (171) gives:
% 202.03/33.67  | | | | | | | | | | |   (174)  all_52_20 = all_6_2
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_20, e3, e3,
% 202.03/33.67  | | | | | | | | | | |              simplifying with (166), (171) gives:
% 202.03/33.67  | | | | | | | | | | |   (175)  all_52_20 = e2
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | COMBINE_EQS: (174), (175) imply:
% 202.03/33.67  | | | | | | | | | | |   (176)  all_6_2 = e2
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REDUCE: (105), (173), (176) imply:
% 202.03/33.67  | | | | | | | | | | |   (177)   ~ (all_10_1 = e2)
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REDUCE: (151), (173) imply:
% 202.03/33.67  | | | | | | | | | | |   (178)   ~ (all_10_1 = e3)
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REDUCE: (140), (176) imply:
% 202.03/33.67  | | | | | | | | | | |   (179)   ~ (e3 = e2)
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10),
% 202.03/33.67  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 202.03/33.67  | | | | | | | | | | |            (19), (20), (21), (22), (25), (26), (27), (29),
% 202.03/33.67  | | | | | | | | | | |            (30), (31), (32), (33), (34), (36), (37), (38),
% 202.03/33.67  | | | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 202.03/33.67  | | | | | | | | | | |            (47), (50), (52), (53), (54), (55), (56), (57),
% 202.03/33.67  | | | | | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65),
% 202.03/33.67  | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 202.03/33.67  | | | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82),
% 202.03/33.67  | | | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (91),
% 202.03/33.67  | | | | | | | | | | |            (92), (93), (94), (95), (96), (97), (98), (100),
% 202.03/33.67  | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 202.03/33.67  | | | | | | | | | | |            (108), (109), (110), (111), (113), (114), (115),
% 202.03/33.67  | | | | | | | | | | |            (116), (117), (118), (119), (121), (122), (123),
% 202.03/33.67  | | | | | | | | | | |            (124), (125), (126), (177), (178) are inconsistent
% 202.03/33.67  | | | | | | | | | | |            by sub-proof #487.
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | Case 2:
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | |   (180)  all_58_14 = e3
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | | REF_CLOSE: (4), (138), (180) are inconsistent by sub-proof
% 202.03/33.67  | | | | | | | | | | |            #1305.
% 202.03/33.67  | | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | | End of split
% 202.03/33.67  | | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | End of split
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | Case 2:
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | |   (181)   ~ (all_56_5 = e3)
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | REDUCE: (35), (181) imply:
% 202.03/33.67  | | | | | | | | |   (182)   ~ (all_4_2 = e3)
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | | REF_CLOSE: (4), (5), (9), (17), (18), (21), (23), (24), (26),
% 202.03/33.67  | | | | | | | | |            (27), (31), (32), (33), (51), (54), (56), (79),
% 202.03/33.67  | | | | | | | | |            (87), (91), (93), (99), (102), (103), (106), (109),
% 202.03/33.67  | | | | | | | | |            (115), (118), (120), (122), (131), (132), (138),
% 202.03/33.67  | | | | | | | | |            (155), (159), (161), (182) are inconsistent by
% 202.03/33.67  | | | | | | | | |            sub-proof #346.
% 202.03/33.67  | | | | | | | | | 
% 202.03/33.67  | | | | | | | | End of split
% 202.03/33.67  | | | | | | | | 
% 202.03/33.67  | | | | | | | End of split
% 202.03/33.67  | | | | | | | 
% 202.03/33.67  | | | | | | End of split
% 202.03/33.67  | | | | | | 
% 202.03/33.67  | | | | | End of split
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | Case 2:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | |   (183)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REF_CLOSE: (3), (5), (7), (8), (9), (15), (18), (20), (25), (27),
% 202.03/33.67  | | | | |            (29), (30), (34), (43), (46), (52), (53), (56), (61), (63),
% 202.03/33.67  | | | | |            (76), (77), (79), (83), (85), (86), (89), (91), (93), (95),
% 202.03/33.67  | | | | |            (97), (100), (102), (106), (107), (108), (115), (122),
% 202.03/33.67  | | | | |            (124), (135), (140), (146), (183) are inconsistent by
% 202.03/33.67  | | | | |            sub-proof #489.
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | End of split
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | End of split
% 202.03/33.67  | | | 
% 202.03/33.67  | | Case 2:
% 202.03/33.67  | | | 
% 202.03/33.67  | | |   (184)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REF_CLOSE: (4), (5), (6), (9), (11), (12), (13), (14), (26), (27), (31),
% 202.03/33.67  | | |            (32), (37), (38), (41), (42), (43), (48), (49), (50), (51),
% 202.03/33.67  | | |            (52), (60), (71), (82), (88), (90), (101), (112), (114), (117),
% 202.03/33.67  | | |            (119), (125), (130), (131), (184) are inconsistent by sub-proof
% 202.03/33.67  | | |            #545.
% 202.03/33.67  | | | 
% 202.03/33.67  | | End of split
% 202.03/33.67  | | 
% 202.03/33.67  | End of split
% 202.03/33.67  | 
% 202.03/33.67  End of proof
% 202.03/33.67  
% 202.03/33.67  Sub-proof #332 shows that the following formulas are inconsistent:
% 202.03/33.67  ----------------------------------------------------------------
% 202.03/33.67    (1)   ~ (all_52_15 = all_52_23)
% 202.03/33.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.67    (3)  op(e0, e2) = all_52_15
% 202.03/33.67    (4)   ~ (all_10_1 = e1)
% 202.03/33.67    (5)  op(e2, e2) = all_4_2
% 202.03/33.67    (6)  all_56_3 = all_14_1
% 202.03/33.67    (7)   ~ (all_14_1 = all_10_1)
% 202.03/33.67    (8)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.67    (9)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.03/33.67    (10)   ~ (all_52_19 = all_52_23)
% 202.03/33.67    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.67    (12)  op(all_52_19, all_52_19) = e2
% 202.03/33.67    (13)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.03/33.67    (14)   ~ (all_52_19 = e3)
% 202.03/33.67    (15)  all_56_6 = all_52_19
% 202.03/33.67    (16)  op(all_14_1, all_14_1) = all_52_24
% 202.03/33.67    (17)   ~ (all_10_1 = e2)
% 202.03/33.67    (18)   ~ (all_52_23 = all_10_1)
% 202.03/33.67    (19)  all_56_2 = all_10_1
% 202.03/33.67    (20)   ~ (all_14_1 = e1)
% 202.03/33.67    (21)  all_56_14 = all_52_23
% 202.03/33.67    (22)  op(e0, all_14_1) = e2
% 202.03/33.67    (23)   ~ (all_10_1 = e3)
% 202.03/33.67    (24)   ~ (all_52_15 = all_4_2)
% 202.03/33.67    (25)   ~ (all_52_19 = all_10_1)
% 202.03/33.67  
% 202.03/33.67  Begin of proof
% 202.03/33.67  | 
% 202.03/33.67  | BETA: splitting (8) gives:
% 202.03/33.67  | 
% 202.03/33.67  | Case 1:
% 202.03/33.67  | | 
% 202.03/33.67  | |   (26)  all_56_2 = e3
% 202.03/33.67  | | 
% 202.03/33.67  | | COMBINE_EQS: (19), (26) imply:
% 202.03/33.67  | |   (27)  all_10_1 = e3
% 202.03/33.67  | | 
% 202.03/33.67  | | REDUCE: (23), (27) imply:
% 202.03/33.67  | |   (28)  $false
% 202.03/33.67  | | 
% 202.03/33.67  | | CLOSE: (28) is inconsistent.
% 202.03/33.67  | | 
% 202.03/33.67  | Case 2:
% 202.03/33.67  | | 
% 202.03/33.67  | |   (29)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.03/33.67  | | 
% 202.03/33.67  | | BETA: splitting (29) gives:
% 202.03/33.67  | | 
% 202.03/33.67  | | Case 1:
% 202.03/33.67  | | | 
% 202.03/33.67  | | |   (30)  all_56_2 = e2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | COMBINE_EQS: (19), (30) imply:
% 202.03/33.67  | | |   (31)  all_10_1 = e2
% 202.03/33.67  | | | 
% 202.03/33.67  | | | REDUCE: (17), (31) imply:
% 202.03/33.67  | | |   (32)  $false
% 202.03/33.67  | | | 
% 202.03/33.67  | | | CLOSE: (32) is inconsistent.
% 202.03/33.67  | | | 
% 202.03/33.67  | | Case 2:
% 202.03/33.67  | | | 
% 202.03/33.67  | | |   (33)  all_56_2 = e1 | all_56_2 = e0
% 202.03/33.67  | | | 
% 202.03/33.67  | | | BETA: splitting (33) gives:
% 202.03/33.67  | | | 
% 202.03/33.67  | | | Case 1:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | |   (34)  all_56_2 = e1
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | COMBINE_EQS: (19), (34) imply:
% 202.03/33.67  | | | |   (35)  all_10_1 = e1
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REDUCE: (4), (35) imply:
% 202.03/33.67  | | | |   (36)  $false
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | CLOSE: (36) is inconsistent.
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | Case 2:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | |   (37)  all_56_2 = e0
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | COMBINE_EQS: (19), (37) imply:
% 202.03/33.67  | | | |   (38)  all_10_1 = e0
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REDUCE: (25), (38) imply:
% 202.03/33.67  | | | |   (39)   ~ (all_52_19 = e0)
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REDUCE: (18), (38) imply:
% 202.03/33.67  | | | |   (40)   ~ (all_52_23 = e0)
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | REDUCE: (7), (38) imply:
% 202.03/33.67  | | | |   (41)   ~ (all_14_1 = e0)
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | BETA: splitting (11) gives:
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | | Case 1:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | |   (42)  all_56_3 = e2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | COMBINE_EQS: (6), (42) imply:
% 202.03/33.67  | | | | |   (43)  all_14_1 = e2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (16), (43) imply:
% 202.03/33.67  | | | | |   (44)  op(e2, e2) = all_52_24
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (22), (43) imply:
% 202.03/33.67  | | | | |   (45)  op(e0, e2) = e2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | GROUND_INST: instantiating (2) with all_52_15, e2, e2, e0, simplifying
% 202.03/33.67  | | | | |              with (3), (45) gives:
% 202.03/33.67  | | | | |   (46)  all_52_15 = e2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_24, e2, e2,
% 202.03/33.67  | | | | |              simplifying with (5), (44) gives:
% 202.03/33.67  | | | | |   (47)  all_52_24 = all_4_2
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (1), (46) imply:
% 202.03/33.67  | | | | |   (48)   ~ (all_52_23 = e2)
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | SIMP: (48) implies:
% 202.03/33.67  | | | | |   (49)   ~ (all_52_23 = e2)
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REDUCE: (24), (46) imply:
% 202.03/33.67  | | | | |   (50)   ~ (all_4_2 = e2)
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | SIMP: (50) implies:
% 202.03/33.67  | | | | |   (51)   ~ (all_4_2 = e2)
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REF_CLOSE: (2), (5), (9), (10), (12), (13), (14), (15), (21), (39),
% 202.03/33.67  | | | | |            (40), (49), (51) are inconsistent by sub-proof #602.
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | Case 2:
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | |   (52)  all_56_3 = e1 | all_56_3 = e0
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | | REF_CLOSE: (6), (20), (41), (52) are inconsistent by sub-proof #806.
% 202.03/33.67  | | | | | 
% 202.03/33.67  | | | | End of split
% 202.03/33.67  | | | | 
% 202.03/33.67  | | | End of split
% 202.03/33.67  | | | 
% 202.03/33.67  | | End of split
% 202.03/33.67  | | 
% 202.03/33.67  | End of split
% 202.03/33.67  | 
% 202.03/33.67  End of proof
% 202.03/33.67  
% 202.03/33.67  Sub-proof #333 shows that the following formulas are inconsistent:
% 202.03/33.67  ----------------------------------------------------------------
% 202.03/33.67    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.03/33.67    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.67    (3)   ~ (all_52_15 = all_52_23)
% 202.03/33.67    (4)   ~ (all_52_25 = all_52_27)
% 202.03/33.67    (5)  all_58_14 = all_52_23
% 202.03/33.67    (6)   ~ (e3 = e1)
% 202.03/33.67    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.67    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.67    (9)   ~ (all_52_5 = all_52_13)
% 202.03/33.67    (10)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 202.03/33.67    (11)  all_58_1 = all_52_9
% 202.03/33.67    (12)   ~ (e3 = e0)
% 202.03/33.67    (13)  op(e2, e3) = all_52_3
% 202.03/33.67    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.67    (15)   ~ (all_52_7 = all_52_15)
% 202.03/33.67    (16)   ~ (all_52_3 = all_52_19)
% 202.03/33.67    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.67    (18)   ~ (all_52_17 = all_52_25)
% 202.03/33.67    (19)   ~ (all_52_3 = all_6_2)
% 202.03/33.67    (20)  all_50_1 = all_14_1
% 202.03/33.67    (21)  all_44_2 = all_6_2
% 202.03/33.67    (22)  all_58_0 = all_6_2
% 202.03/33.67    (23)  op(all_14_2, e0) = all_14_1
% 202.03/33.67    (24)  all_56_4 = all_52_3
% 202.03/33.67    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.67    (26)  op(e3, e0) = all_52_25
% 202.03/33.67    (27)  op(all_52_5, all_52_5) = all_52_4
% 202.03/33.67    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.67    (29)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.67    (30)  all_58_13 = all_52_15
% 202.03/33.68    (31)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.68    (32)  all_58_9 = all_52_25
% 202.03/33.68    (33)   ~ (all_52_29 = all_14_2)
% 202.03/33.68    (34)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.68    (35)  op(e1, e3) = all_52_5
% 202.03/33.68    (36)  op(e2, e2) = all_4_2
% 202.03/33.68    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.68    (38)   ~ (all_52_3 = all_52_5)
% 202.03/33.68    (39)  all_58_11 = all_52_29
% 202.03/33.68    (40)   ~ (all_52_25 = all_14_2)
% 202.03/33.68    (41)   ~ (all_52_3 = all_52_27)
% 202.03/33.68    (42)  op(all_6_2, all_6_2) = all_52_0
% 202.03/33.68    (43)   ~ (all_52_7 = all_6_2)
% 202.03/33.68    (44)  op(e0, e0) = all_14_2
% 202.03/33.68    (45)  all_56_15 = all_14_2
% 202.03/33.68    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.68    (47)   ~ (all_4_1 = e1)
% 202.03/33.68    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.68    (49)   ~ (e2 = e1)
% 202.03/33.68    (50)   ~ (all_52_13 = all_10_2)
% 202.03/33.68    (51)  all_58_10 = all_52_27
% 202.03/33.68    (52)  all_56_8 = all_52_5
% 202.03/33.68    (53)  op(all_52_9, all_52_9) = all_52_8
% 202.03/33.68    (54)  op(all_52_15, all_52_15) = all_52_14
% 202.03/33.68    (55)   ~ (all_52_19 = all_52_23)
% 202.03/33.68    (56)   ~ (all_52_25 = all_52_29)
% 202.03/33.68    (57)   ~ (all_52_29 = all_10_2)
% 202.03/33.68    (58)  all_58_7 = all_52_13
% 202.03/33.68    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.68    (60)   ~ (all_52_5 = all_52_7)
% 202.03/33.68    (61)  all_58_12 = all_52_7
% 202.03/33.68    (62)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.68    (63)   ~ (all_52_7 = all_14_2)
% 202.03/33.68    (64)  all_58_2 = all_52_3
% 202.03/33.68    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.68    (66)  all_56_7 = all_52_27
% 202.03/33.68    (67)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.68    (68)   ~ (e2 = e0)
% 202.03/33.68    (69)  op(all_4_2, e2) = all_4_1
% 202.03/33.68    (70)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.68    (71)   ~ (all_52_15 = all_14_2)
% 202.03/33.68    (72)   ~ (all_52_13 = all_4_2)
% 202.03/33.68    (73)  op(e3, e1) = all_52_17
% 202.03/33.68    (74)  op(e0, e3) = all_52_7
% 202.03/33.68    (75)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.68    (76)   ~ (all_52_9 = all_52_25)
% 202.03/33.68    (77)  all_58_15 = all_14_2
% 202.03/33.68    (78)   ~ (all_52_19 = all_10_2)
% 202.03/33.68    (79)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.68    (80)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.68    (81)  all_58_8 = all_10_2
% 202.03/33.68    (82)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.03/33.68    (83)   ~ (all_52_5 = all_10_2)
% 202.03/33.68    (84)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.68    (85)   ~ (all_52_23 = all_14_2)
% 202.03/33.68    (86)  all_56_12 = all_52_7
% 202.03/33.68    (87)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.68    (88)  all_8_2 = all_6_2
% 202.03/33.68    (89)   ~ (all_52_25 = all_6_2)
% 202.03/33.68    (90)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.68    (91)   ~ (all_52_9 = all_4_2)
% 202.03/33.68    (92)   ~ (all_52_5 = all_6_2)
% 202.03/33.68    (93)   ~ (all_52_9 = all_6_2)
% 202.03/33.68    (94)  op(e3, all_6_1) = e2
% 202.03/33.68    (95)  all_56_0 = all_6_2
% 202.03/33.68    (96)  op(e3, e3) = all_6_2
% 202.03/33.68    (97)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.68    (98)   ~ (all_52_27 = all_14_2)
% 202.03/33.68    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.68    (100)  op(all_4_2, all_4_2) = all_52_10
% 202.03/33.68    (101)  all_56_3 = all_52_25
% 202.03/33.68    (102)   ~ (all_52_3 = all_52_7)
% 202.03/33.68    (103)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.68    (104)  all_58_5 = all_52_19
% 202.03/33.68    (105)  all_56_1 = all_52_9
% 202.03/33.68    (106)   ~ (all_52_15 = all_4_2)
% 202.03/33.68    (107)   ~ (all_52_27 = all_4_2)
% 202.03/33.68    (108)  all_58_6 = all_52_5
% 202.03/33.68    (109)  op(e3, e2) = all_52_9
% 202.03/33.68    (110)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.68    (111)   ~ (all_52_17 = all_6_2)
% 202.03/33.68    (112)   ~ (e1 = e0)
% 202.03/33.68    (113)   ~ (e3 = e2)
% 202.03/33.68    (114)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.03/33.68           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.03/33.68    (115)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.68    (116)  all_44_1 = all_6_1
% 202.03/33.68    (117)   ~ (all_52_9 = all_52_17)
% 202.03/33.68    (118)  all_56_10 = all_10_2
% 202.03/33.68    (119)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.68    (120)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.68    (121)  op(all_52_13, all_52_13) = all_52_12
% 202.03/33.68    (122)  op(e1, e1) = all_10_2
% 202.03/33.68    (123)   ~ (all_52_23 = all_10_2)
% 202.03/33.68    (124)   ~ (all_52_7 = all_52_23)
% 202.03/33.68    (125)   ~ (all_52_17 = all_52_19)
% 202.03/33.68    (126)  all_58_3 = all_4_2
% 202.03/33.68    (127)  all_56_13 = all_52_15
% 202.03/33.68    (128)   ~ (all_52_3 = all_4_2)
% 202.03/33.68    (129)   ~ (all_52_19 = all_4_2)
% 202.03/33.68    (130)   ~ (all_52_17 = all_52_23)
% 202.03/33.68    (131)  all_8_1 = all_6_1
% 202.03/33.68    (132)  op(all_6_2, e3) = all_6_1
% 202.03/33.68    (133)   ~ (all_52_13 = all_52_29)
% 202.03/33.68    (134)  all_58_4 = all_52_17
% 202.03/33.68    (135)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.03/33.68    (136)  all_50_2 = all_14_2
% 202.03/33.68    (137)  op(all_52_25, all_52_25) = all_52_24
% 202.03/33.68  
% 202.03/33.68  Begin of proof
% 202.03/33.68  | 
% 202.03/33.68  | BETA: splitting (114) gives:
% 202.03/33.68  | 
% 202.03/33.68  | Case 1:
% 202.03/33.68  | | 
% 202.03/33.68  | |   (138)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.03/33.68  | | 
% 202.03/33.68  | | REF_CLOSE: (7), (8), (17), (22), (27), (36), (42), (44), (46), (61), (63),
% 202.03/33.68  | |            (64), (65), (83), (94), (95), (96), (108), (110), (113), (120),
% 202.03/33.68  | |            (122), (128), (132), (138) are inconsistent by sub-proof #501.
% 202.03/33.68  | | 
% 202.03/33.68  | Case 2:
% 202.03/33.68  | | 
% 202.03/33.68  | |   (139)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 202.03/33.68  | | 
% 202.03/33.68  | | ALPHA: (139) implies:
% 202.03/33.68  | |   (140)  all_52_14 = e0
% 202.03/33.68  | |   (141)  all_52_12 = e1
% 202.03/33.68  | |   (142)  all_52_10 = e2
% 202.03/33.68  | |   (143)  all_52_8 = e3
% 202.03/33.68  | | 
% 202.03/33.68  | | REDUCE: (53), (143) imply:
% 202.03/33.68  | |   (144)  op(all_52_9, all_52_9) = e3
% 202.03/33.68  | | 
% 202.03/33.68  | | REDUCE: (121), (141) imply:
% 202.03/33.68  | |   (145)  op(all_52_13, all_52_13) = e1
% 202.03/33.68  | | 
% 202.03/33.68  | | REDUCE: (54), (140) imply:
% 202.03/33.68  | |   (146)  op(all_52_15, all_52_15) = e0
% 202.03/33.68  | | 
% 202.03/33.68  | | REDUCE: (100), (142) imply:
% 202.03/33.68  | |   (147)  op(all_4_2, all_4_2) = e2
% 202.03/33.68  | | 
% 202.03/33.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.03/33.68  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.03/33.68  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.03/33.68  | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 202.03/33.68  | |            (47), (48), (49), (50), (51), (52), (55), (56), (57), (58), (59),
% 202.03/33.68  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 202.03/33.68  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 202.03/33.68  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 202.03/33.68  | |            (93), (94), (95), (96), (97), (98), (99), (101), (102), (103),
% 202.03/33.68  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 202.03/33.68  | |            (113), (115), (116), (117), (118), (119), (120), (123), (124),
% 202.03/33.68  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 202.03/33.68  | |            (134), (135), (136), (137), (144), (145), (146), (147) are
% 202.03/33.68  | |            inconsistent by sub-proof #334.
% 202.03/33.68  | | 
% 202.03/33.68  | End of split
% 202.03/33.68  | 
% 202.03/33.68  End of proof
% 202.03/33.68  
% 202.03/33.68  Sub-proof #334 shows that the following formulas are inconsistent:
% 202.03/33.68  ----------------------------------------------------------------
% 202.03/33.68    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.03/33.68    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.03/33.68    (3)   ~ (all_52_15 = all_52_23)
% 202.03/33.68    (4)   ~ (all_52_25 = all_52_27)
% 202.03/33.68    (5)  all_58_14 = all_52_23
% 202.03/33.68    (6)   ~ (e3 = e1)
% 202.03/33.68    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.03/33.68    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.03/33.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.03/33.68    (9)   ~ (all_52_5 = all_52_13)
% 202.03/33.68    (10)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 202.03/33.68    (11)  all_58_1 = all_52_9
% 202.03/33.68    (12)   ~ (e3 = e0)
% 202.03/33.68    (13)  op(e2, e3) = all_52_3
% 202.03/33.68    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.03/33.68    (15)   ~ (all_52_7 = all_52_15)
% 202.03/33.68    (16)   ~ (all_52_3 = all_52_19)
% 202.03/33.68    (17)  op(all_52_15, all_52_15) = e0
% 202.03/33.68    (18)  op(all_52_7, all_52_7) = all_52_6
% 202.03/33.68    (19)   ~ (all_52_17 = all_52_25)
% 202.03/33.68    (20)   ~ (all_52_3 = all_6_2)
% 202.03/33.68    (21)  all_50_1 = all_14_1
% 202.03/33.68    (22)  all_44_2 = all_6_2
% 202.03/33.68    (23)  all_58_0 = all_6_2
% 202.03/33.68    (24)  op(all_14_2, e0) = all_14_1
% 202.03/33.68    (25)  all_56_4 = all_52_3
% 202.03/33.68    (26)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.03/33.68    (27)  op(e3, e0) = all_52_25
% 202.03/33.68    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.03/33.68    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.03/33.68    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.03/33.68    (31)  all_58_13 = all_52_15
% 202.03/33.68    (32)  op(all_52_13, all_52_13) = e1
% 202.03/33.68    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.03/33.68    (34)  all_58_9 = all_52_25
% 202.03/33.68    (35)   ~ (all_52_29 = all_14_2)
% 202.03/33.68    (36)  op(all_52_27, all_52_27) = all_52_26
% 202.03/33.68    (37)  op(e1, e3) = all_52_5
% 202.03/33.68    (38)  op(e2, e2) = all_4_2
% 202.03/33.68    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.03/33.68    (40)   ~ (all_52_3 = all_52_5)
% 202.03/33.68    (41)  all_58_11 = all_52_29
% 202.03/33.68    (42)   ~ (all_52_25 = all_14_2)
% 202.03/33.68    (43)   ~ (all_52_3 = all_52_27)
% 202.03/33.68    (44)   ~ (all_52_7 = all_6_2)
% 202.03/33.68    (45)  op(e0, e0) = all_14_2
% 202.03/33.68    (46)  all_56_15 = all_14_2
% 202.03/33.68    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.03/33.68    (48)   ~ (all_4_1 = e1)
% 202.03/33.68    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.03/33.68    (50)   ~ (e2 = e1)
% 202.03/33.68    (51)   ~ (all_52_13 = all_10_2)
% 202.03/33.68    (52)  all_58_10 = all_52_27
% 202.03/33.68    (53)  all_56_8 = all_52_5
% 202.03/33.68    (54)   ~ (all_52_19 = all_52_23)
% 202.03/33.68    (55)   ~ (all_52_25 = all_52_29)
% 202.03/33.68    (56)   ~ (all_52_29 = all_10_2)
% 202.03/33.68    (57)  all_58_7 = all_52_13
% 202.03/33.68    (58)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.03/33.68    (59)   ~ (all_52_5 = all_52_7)
% 202.03/33.68    (60)  all_58_12 = all_52_7
% 202.03/33.68    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.03/33.68    (62)   ~ (all_52_7 = all_14_2)
% 202.03/33.68    (63)  all_58_2 = all_52_3
% 202.03/33.68    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.03/33.68    (65)  all_56_7 = all_52_27
% 202.03/33.68    (66)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.03/33.68    (67)   ~ (e2 = e0)
% 202.03/33.68    (68)  op(all_4_2, e2) = all_4_1
% 202.03/33.68    (69)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.03/33.68    (70)   ~ (all_52_15 = all_14_2)
% 202.03/33.68    (71)   ~ (all_52_13 = all_4_2)
% 202.03/33.68    (72)  op(e3, e1) = all_52_17
% 202.03/33.68    (73)  op(e0, e3) = all_52_7
% 202.03/33.68    (74)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.03/33.68    (75)   ~ (all_52_9 = all_52_25)
% 202.03/33.68    (76)  all_58_15 = all_14_2
% 202.03/33.68    (77)   ~ (all_52_19 = all_10_2)
% 202.03/33.68    (78)  op(all_52_23, all_52_23) = all_52_22
% 202.03/33.68    (79)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.03/33.68    (80)  all_58_8 = all_10_2
% 202.03/33.68    (81)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.03/33.68    (82)   ~ (all_52_5 = all_10_2)
% 202.03/33.68    (83)  op(all_52_29, all_52_29) = all_52_28
% 202.03/33.68    (84)   ~ (all_52_23 = all_14_2)
% 202.03/33.68    (85)  all_56_12 = all_52_7
% 202.03/33.68    (86)  op(all_52_17, all_52_17) = all_52_16
% 202.03/33.68    (87)  all_8_2 = all_6_2
% 202.03/33.68    (88)   ~ (all_52_25 = all_6_2)
% 202.03/33.68    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.03/33.68    (90)   ~ (all_52_9 = all_4_2)
% 202.03/33.68    (91)   ~ (all_52_5 = all_6_2)
% 202.03/33.68    (92)  op(all_4_2, all_4_2) = e2
% 202.03/33.68    (93)   ~ (all_52_9 = all_6_2)
% 202.03/33.68    (94)  op(e3, all_6_1) = e2
% 202.03/33.68    (95)  all_56_0 = all_6_2
% 202.03/33.68    (96)  op(e3, e3) = all_6_2
% 202.03/33.68    (97)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.03/33.68    (98)   ~ (all_52_27 = all_14_2)
% 202.03/33.68    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.03/33.68    (100)  all_56_3 = all_52_25
% 202.03/33.68    (101)   ~ (all_52_3 = all_52_7)
% 202.03/33.68    (102)  op(all_14_2, all_14_2) = all_52_30
% 202.03/33.68    (103)  all_58_5 = all_52_19
% 202.03/33.68    (104)  all_56_1 = all_52_9
% 202.03/33.68    (105)   ~ (all_52_15 = all_4_2)
% 202.03/33.68    (106)   ~ (all_52_27 = all_4_2)
% 202.03/33.68    (107)  all_58_6 = all_52_5
% 202.03/33.68    (108)  op(e3, e2) = all_52_9
% 202.03/33.68    (109)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.03/33.68    (110)   ~ (all_52_17 = all_6_2)
% 202.03/33.68    (111)   ~ (e1 = e0)
% 202.03/33.68    (112)   ~ (e3 = e2)
% 202.03/33.68    (113)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.03/33.68    (114)  all_44_1 = all_6_1
% 202.03/33.68    (115)   ~ (all_52_9 = all_52_17)
% 202.03/33.68    (116)  all_56_10 = all_10_2
% 202.03/33.68    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.03/33.68    (118)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.03/33.68    (119)  op(all_52_9, all_52_9) = e3
% 202.03/33.68    (120)   ~ (all_52_23 = all_10_2)
% 202.03/33.68    (121)   ~ (all_52_7 = all_52_23)
% 202.03/33.68    (122)   ~ (all_52_17 = all_52_19)
% 202.03/33.68    (123)  all_58_3 = all_4_2
% 202.03/33.68    (124)  all_56_13 = all_52_15
% 202.11/33.68    (125)   ~ (all_52_3 = all_4_2)
% 202.11/33.68    (126)   ~ (all_52_19 = all_4_2)
% 202.11/33.68    (127)   ~ (all_52_17 = all_52_23)
% 202.11/33.68    (128)  all_8_1 = all_6_1
% 202.11/33.68    (129)  op(all_6_2, e3) = all_6_1
% 202.11/33.68    (130)   ~ (all_52_13 = all_52_29)
% 202.11/33.68    (131)  all_58_4 = all_52_17
% 202.11/33.68    (132)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.68    (133)  all_50_2 = all_14_2
% 202.11/33.68    (134)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.68  
% 202.11/33.68  Begin of proof
% 202.11/33.68  | 
% 202.11/33.68  | BETA: splitting (81) gives:
% 202.11/33.68  | 
% 202.11/33.68  | Case 1:
% 202.11/33.68  | | 
% 202.11/33.68  | |   (135)  all_56_15 = e3
% 202.11/33.68  | | 
% 202.11/33.68  | | COMBINE_EQS: (46), (135) imply:
% 202.11/33.68  | |   (136)  all_14_2 = e3
% 202.11/33.68  | | 
% 202.11/33.68  | | SIMP: (136) implies:
% 202.11/33.68  | |   (137)  all_14_2 = e3
% 202.11/33.68  | | 
% 202.11/33.68  | | COMBINE_EQS: (133), (137) imply:
% 202.11/33.68  | |   (138)  all_50_2 = e3
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (62), (137) imply:
% 202.11/33.68  | |   (139)   ~ (all_52_7 = e3)
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (70), (137) imply:
% 202.11/33.68  | |   (140)   ~ (all_52_15 = e3)
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (42), (137) imply:
% 202.11/33.68  | |   (141)   ~ (all_52_25 = e3)
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (98), (137) imply:
% 202.11/33.68  | |   (142)   ~ (all_52_27 = e3)
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (102), (137) imply:
% 202.11/33.68  | |   (143)  op(e3, e3) = all_52_30
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (24), (137) imply:
% 202.11/33.68  | |   (144)  op(e3, e0) = all_14_1
% 202.11/33.68  | | 
% 202.11/33.68  | | BETA: splitting (10) gives:
% 202.11/33.68  | | 
% 202.11/33.68  | | Case 1:
% 202.11/33.68  | | | 
% 202.11/33.68  | | |   (145)   ~ (all_50_1 = e1)
% 202.11/33.68  | | | 
% 202.11/33.68  | | | REDUCE: (21), (145) imply:
% 202.11/33.68  | | |   (146)   ~ (all_14_1 = e1)
% 202.11/33.68  | | | 
% 202.11/33.68  | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 202.11/33.68  | | |              simplifying with (27), (144) gives:
% 202.11/33.68  | | |   (147)  all_52_25 = all_14_1
% 202.11/33.68  | | | 
% 202.11/33.68  | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 202.11/33.68  | | |              simplifying with (96), (143) gives:
% 202.11/33.68  | | |   (148)  all_52_30 = all_6_2
% 202.11/33.68  | | | 
% 202.11/33.68  | | | COMBINE_EQS: (100), (147) imply:
% 202.11/33.68  | | |   (149)  all_56_3 = all_14_1
% 202.11/33.68  | | | 
% 202.11/33.68  | | | COMBINE_EQS: (34), (147) imply:
% 202.11/33.68  | | |   (150)  all_58_9 = all_14_1
% 202.11/33.68  | | | 
% 202.11/33.68  | | | REDUCE: (88), (147) imply:
% 202.11/33.68  | | |   (151)   ~ (all_14_1 = all_6_2)
% 202.11/33.68  | | | 
% 202.11/33.68  | | | REDUCE: (141), (147) imply:
% 202.11/33.68  | | |   (152)   ~ (all_14_1 = e3)
% 202.11/33.68  | | | 
% 202.11/33.68  | | | BETA: splitting (89) gives:
% 202.11/33.68  | | | 
% 202.11/33.68  | | | Case 1:
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | |   (153)  all_56_3 = e3
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | | REF_CLOSE: (149), (152), (153) are inconsistent by sub-proof #1200.
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | Case 2:
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | |   (154)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | | BETA: splitting (14) gives:
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | | Case 1:
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | |   (155)  all_56_12 = e3
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | | REF_CLOSE: (85), (139), (155) are inconsistent by sub-proof #1383.
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | Case 2:
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | |   (156)   ~ (all_56_12 = e3)
% 202.11/33.68  | | | | |   (157)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | | BETA: splitting (117) gives:
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | | Case 1:
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | |   (158)  all_58_4 = e3
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | COMBINE_EQS: (131), (158) imply:
% 202.11/33.68  | | | | | |   (159)  all_52_17 = e3
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | REDUCE: (115), (159) imply:
% 202.11/33.68  | | | | | |   (160)   ~ (all_52_9 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | REDUCE: (122), (159) imply:
% 202.11/33.68  | | | | | |   (161)   ~ (all_52_19 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | SIMP: (161) implies:
% 202.11/33.68  | | | | | |   (162)   ~ (all_52_19 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | REDUCE: (110), (159) imply:
% 202.11/33.68  | | | | | |   (163)   ~ (all_6_2 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | SIMP: (163) implies:
% 202.11/33.68  | | | | | |   (164)   ~ (all_6_2 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | REDUCE: (86), (159) imply:
% 202.11/33.68  | | | | | |   (165)  op(e3, e3) = all_52_16
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_16, e3, e3,
% 202.11/33.68  | | | | | |              simplifying with (96), (165) gives:
% 202.11/33.68  | | | | | |   (166)  all_52_16 = all_6_2
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | BETA: splitting (47) gives:
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | Case 1:
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | |   (167)  all_58_2 = e3
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | | REF_CLOSE: (7), (8), (9), (11), (22), (26), (28), (31), (32),
% 202.11/33.68  | | | | | | |            (37), (38), (53), (57), (59), (63), (71), (74), (79),
% 202.11/33.68  | | | | | | |            (85), (91), (94), (96), (108), (114), (119), (123),
% 202.11/33.68  | | | | | | |            (125), (129), (140), (157), (160), (167) are
% 202.11/33.68  | | | | | | |            inconsistent by sub-proof #366.
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | Case 2:
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | |   (168)   ~ (all_58_2 = e3)
% 202.11/33.68  | | | | | | |   (169)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | | REDUCE: (63), (168) imply:
% 202.11/33.68  | | | | | | |   (170)   ~ (all_52_3 = e3)
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | | REF_CLOSE: (6), (8), (11), (23), (28), (48), (50), (52), (60),
% 202.11/33.68  | | | | | | |            (63), (64), (68), (69), (92), (96), (103), (107),
% 202.11/33.68  | | | | | | |            (108), (123), (139), (142), (146), (149), (150), (151),
% 202.11/33.68  | | | | | | |            (154), (158), (162), (164), (169), (170) are
% 202.11/33.68  | | | | | | |            inconsistent by sub-proof #555.
% 202.11/33.68  | | | | | | | 
% 202.11/33.68  | | | | | | End of split
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | Case 2:
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | |   (171)   ~ (all_58_4 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | REDUCE: (131), (171) imply:
% 202.11/33.68  | | | | | |   (172)   ~ (all_52_17 = e3)
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | | REF_CLOSE: (8), (11), (23), (34), (93), (94), (96), (99), (112),
% 202.11/33.68  | | | | | |            (119), (129), (131), (141), (172) are inconsistent by
% 202.11/33.68  | | | | | |            sub-proof #492.
% 202.11/33.68  | | | | | | 
% 202.11/33.68  | | | | | End of split
% 202.11/33.68  | | | | | 
% 202.11/33.68  | | | | End of split
% 202.11/33.68  | | | | 
% 202.11/33.68  | | | End of split
% 202.11/33.68  | | | 
% 202.11/33.68  | | Case 2:
% 202.11/33.68  | | | 
% 202.11/33.68  | | |   (173)   ~ (all_50_2 = e3)
% 202.11/33.68  | | | 
% 202.11/33.68  | | | REDUCE: (138), (173) imply:
% 202.11/33.68  | | |   (174)  $false
% 202.11/33.68  | | | 
% 202.11/33.68  | | | CLOSE: (174) is inconsistent.
% 202.11/33.68  | | | 
% 202.11/33.68  | | End of split
% 202.11/33.68  | | 
% 202.11/33.68  | Case 2:
% 202.11/33.68  | | 
% 202.11/33.68  | |   (175)   ~ (all_56_15 = e3)
% 202.11/33.68  | |   (176)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (46), (175) imply:
% 202.11/33.68  | |   (177)   ~ (all_14_2 = e3)
% 202.11/33.68  | | 
% 202.11/33.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 202.11/33.68  | |            (15), (16), (17), (18), (19), (20), (22), (23), (25), (26), (27),
% 202.11/33.68  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 202.11/33.68  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 202.11/33.68  | |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 202.11/33.68  | |            (62), (63), (64), (65), (66), (67), (68), (71), (72), (73), (74),
% 202.11/33.68  | |            (75), (76), (77), (78), (79), (80), (82), (83), (84), (85), (86),
% 202.11/33.68  | |            (87), (89), (90), (91), (92), (93), (94), (95), (96), (97), (99),
% 202.11/33.68  | |            (100), (101), (103), (104), (105), (106), (107), (108), (109),
% 202.11/33.68  | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 202.11/33.68  | |            (119), (120), (121), (123), (124), (125), (126), (127), (128),
% 202.11/33.68  | |            (129), (130), (131), (132), (134), (176), (177) are inconsistent
% 202.11/33.68  | |            by sub-proof #452.
% 202.11/33.68  | | 
% 202.11/33.68  | End of split
% 202.11/33.68  | 
% 202.11/33.68  End of proof
% 202.11/33.68  
% 202.11/33.68  Sub-proof #335 shows that the following formulas are inconsistent:
% 202.11/33.68  ----------------------------------------------------------------
% 202.11/33.68    (1)  all_58_14 = all_52_23
% 202.11/33.68    (2)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.68    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.68    (4)  all_58_1 = all_52_9
% 202.11/33.68    (5)   ~ (all_52_9 = all_52_13)
% 202.11/33.68    (6)  op(e2, e3) = all_52_3
% 202.11/33.68    (7)   ~ (all_52_3 = all_52_19)
% 202.11/33.68    (8)   ~ (all_52_3 = all_6_2)
% 202.11/33.68    (9)  all_58_0 = all_6_2
% 202.11/33.68    (10)  all_34_1 = all_14_1
% 202.11/33.68    (11)  all_56_4 = all_52_3
% 202.11/33.68    (12)  op(e3, e0) = all_52_25
% 202.11/33.68    (13)  all_58_13 = all_52_15
% 202.11/33.68    (14)  all_58_9 = all_52_25
% 202.11/33.68    (15)  op(e2, e2) = all_4_2
% 202.11/33.68    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.68    (17)  all_58_11 = all_52_29
% 202.11/33.68    (18)   ~ (all_52_9 = all_52_15)
% 202.11/33.68    (19)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.11/33.68    (20)   ~ (e2 = e1)
% 202.11/33.68    (21)  op(all_10_2, all_10_2) = e1
% 202.11/33.68    (22)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.68    (23)  all_58_7 = all_52_13
% 202.11/33.68    (24)  all_34_2 = e3
% 202.11/33.68    (25)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.68    (26)  op(all_52_19, all_52_19) = e2
% 202.11/33.68    (27)  all_58_12 = all_52_7
% 202.11/33.68    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.68    (29)   ~ (all_52_7 = e3)
% 202.11/33.68    (30)  all_58_2 = all_52_3
% 202.11/33.68    (31)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.68    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.68    (33)   ~ (all_52_29 = e3)
% 202.11/33.68    (34)   ~ (all_52_25 = e3)
% 202.11/33.68    (35)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.68    (36)   ~ (e2 = e0)
% 202.11/33.68    (37)   ~ (all_52_23 = e3)
% 202.11/33.68    (38)  op(e3, e3) = all_52_30
% 202.11/33.68    (39)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.11/33.68    (40)  op(e3, e1) = all_52_17
% 202.11/33.68    (41)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.68    (42)  all_58_8 = all_10_2
% 202.11/33.68    (43)   ~ (all_52_5 = all_10_2)
% 202.11/33.68    (44)   ~ (all_52_25 = all_6_2)
% 202.11/33.68    (45)   ~ (all_52_9 = all_4_2)
% 202.11/33.68    (46)   ~ (all_52_9 = all_6_2)
% 202.11/33.68    (47)  op(e3, all_6_1) = e2
% 202.11/33.68    (48)  op(e3, e3) = all_6_2
% 202.11/33.68    (49)  op(e3, e0) = all_14_1
% 202.11/33.68    (50)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.68    (51)  all_58_5 = all_52_19
% 202.11/33.68    (52)  all_56_1 = all_52_9
% 202.11/33.68    (53)  op(all_52_17, all_52_17) = e3
% 202.11/33.68    (54)  all_58_6 = all_52_5
% 202.11/33.68    (55)   ~ (all_52_17 = all_6_2)
% 202.11/33.68    (56)   ~ (e3 = e2)
% 202.11/33.68    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.68    (58)   ~ (all_52_9 = all_52_17)
% 202.11/33.68    (59)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.68    (60)  all_58_3 = all_4_2
% 202.11/33.68    (61)  op(all_6_2, e3) = all_6_1
% 202.11/33.68    (62)  all_58_4 = all_52_17
% 202.11/33.68  
% 202.11/33.68  Begin of proof
% 202.11/33.68  | 
% 202.11/33.68  | BETA: splitting (19) gives:
% 202.11/33.68  | 
% 202.11/33.68  | Case 1:
% 202.11/33.68  | | 
% 202.11/33.68  | |   (63)   ~ (all_34_1 = e2)
% 202.11/33.68  | | 
% 202.11/33.68  | | REDUCE: (10), (63) imply:
% 202.11/33.68  | |   (64)   ~ (all_14_1 = e2)
% 202.11/33.68  | | 
% 202.11/33.69  | | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 202.11/33.69  | |              with (12), (49) gives:
% 202.11/33.69  | |   (65)  all_52_25 = all_14_1
% 202.11/33.69  | | 
% 202.11/33.69  | | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3, simplifying
% 202.11/33.69  | |              with (38), (48) gives:
% 202.11/33.69  | |   (66)  all_52_30 = all_6_2
% 202.11/33.69  | | 
% 202.11/33.69  | | COMBINE_EQS: (14), (65) imply:
% 202.11/33.69  | |   (67)  all_58_9 = all_14_1
% 202.11/33.69  | | 
% 202.11/33.69  | | REDUCE: (44), (65) imply:
% 202.11/33.69  | |   (68)   ~ (all_14_1 = all_6_2)
% 202.11/33.69  | | 
% 202.11/33.69  | | BETA: splitting (57) gives:
% 202.11/33.69  | | 
% 202.11/33.69  | | Case 1:
% 202.11/33.69  | | | 
% 202.11/33.69  | | |   (69)  all_56_1 = e3
% 202.11/33.69  | | | 
% 202.11/33.69  | | | COMBINE_EQS: (52), (69) imply:
% 202.11/33.69  | | |   (70)  all_52_9 = e3
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (58), (70) imply:
% 202.11/33.69  | | |   (71)   ~ (all_52_17 = e3)
% 202.11/33.69  | | | 
% 202.11/33.69  | | | SIMP: (71) implies:
% 202.11/33.69  | | |   (72)   ~ (all_52_17 = e3)
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (46), (70) imply:
% 202.11/33.69  | | |   (73)   ~ (all_6_2 = e3)
% 202.11/33.69  | | | 
% 202.11/33.69  | | | SIMP: (73) implies:
% 202.11/33.69  | | |   (74)   ~ (all_6_2 = e3)
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (22), (70) imply:
% 202.11/33.69  | | |   (75)  op(e3, e3) = all_52_8
% 202.11/33.69  | | | 
% 202.11/33.69  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_8, e3, e3, simplifying
% 202.11/33.69  | | |              with (48), (75) gives:
% 202.11/33.69  | | |   (76)  all_52_8 = all_6_2
% 202.11/33.69  | | | 
% 202.11/33.69  | | | BETA: splitting (28) gives:
% 202.11/33.69  | | | 
% 202.11/33.69  | | | Case 1:
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | |   (77)  all_58_6 = e3
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | COMBINE_EQS: (54), (77) imply:
% 202.11/33.69  | | | |   (78)  all_52_5 = e3
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | SIMP: (78) implies:
% 202.11/33.69  | | | |   (79)  all_52_5 = e3
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | REDUCE: (43), (79) imply:
% 202.11/33.69  | | | |   (80)   ~ (all_10_2 = e3)
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | SIMP: (80) implies:
% 202.11/33.69  | | | |   (81)   ~ (all_10_2 = e3)
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (16), (25), (26), (30),
% 202.11/33.69  | | | |            (35), (36), (37), (40), (42), (47), (48), (49), (51), (55),
% 202.11/33.69  | | | |            (59), (61), (62), (68), (72), (75), (81) are inconsistent by
% 202.11/33.69  | | | |            sub-proof #448.
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | Case 2:
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | |   (82)   ~ (all_58_6 = e3)
% 202.11/33.69  | | | |   (83)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | REDUCE: (54), (82) imply:
% 202.11/33.69  | | | |   (84)   ~ (all_52_5 = e3)
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | BETA: splitting (32) gives:
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | | Case 1:
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | |   (85)  all_58_0 = e3
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | | COMBINE_EQS: (9), (85) imply:
% 202.11/33.69  | | | | |   (86)  all_6_2 = e3
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | | REDUCE: (74), (86) imply:
% 202.11/33.69  | | | | |   (87)  $false
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | | CLOSE: (87) is inconsistent.
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | Case 2:
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | |   (88)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | | BETA: splitting (88) gives:
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | | Case 1:
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | |   (89)  all_58_2 = e3
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | | COMBINE_EQS: (30), (89) imply:
% 202.11/33.69  | | | | | |   (90)  all_52_3 = e3
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | | SIMP: (90) implies:
% 202.11/33.69  | | | | | |   (91)  all_52_3 = e3
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | | REDUCE: (2), (91) imply:
% 202.11/33.69  | | | | | |   (92)  op(e3, e3) = all_52_2
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | | REDUCE: (6), (91) imply:
% 202.11/33.69  | | | | | |   (93)  op(e2, e3) = e3
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | | REF_CLOSE: (3), (4), (5), (9), (13), (14), (15), (17), (18), (20),
% 202.11/33.69  | | | | | |            (21), (22), (23), (31), (33), (34), (39), (41), (42),
% 202.11/33.69  | | | | | |            (45), (47), (48), (50), (53), (55), (56), (60), (61),
% 202.11/33.69  | | | | | |            (62), (64), (67), (74), (83), (92), (93) are inconsistent
% 202.11/33.69  | | | | | |            by sub-proof #356.
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | Case 2:
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | |   (94)  all_58_6 = e3 | all_58_12 = e3
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | | REF_CLOSE: (27), (29), (54), (84), (94) are inconsistent by
% 202.11/33.69  | | | | | |            sub-proof #1243.
% 202.11/33.69  | | | | | | 
% 202.11/33.69  | | | | | End of split
% 202.11/33.69  | | | | | 
% 202.11/33.69  | | | | End of split
% 202.11/33.69  | | | | 
% 202.11/33.69  | | | End of split
% 202.11/33.69  | | | 
% 202.11/33.69  | | Case 2:
% 202.11/33.69  | | | 
% 202.11/33.69  | | |   (95)   ~ (all_56_1 = e3)
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (52), (95) imply:
% 202.11/33.69  | | |   (96)   ~ (all_52_9 = e3)
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REF_CLOSE: (3), (4), (9), (14), (34), (47), (48), (50), (53), (55), (56),
% 202.11/33.69  | | |            (59), (61), (62), (96) are inconsistent by sub-proof #446.
% 202.11/33.69  | | | 
% 202.11/33.69  | | End of split
% 202.11/33.69  | | 
% 202.11/33.69  | Case 2:
% 202.11/33.69  | | 
% 202.11/33.69  | |   (97)   ~ (all_34_2 = e3)
% 202.11/33.69  | | 
% 202.11/33.69  | | REDUCE: (24), (97) imply:
% 202.11/33.69  | |   (98)  $false
% 202.11/33.69  | | 
% 202.11/33.69  | | CLOSE: (98) is inconsistent.
% 202.11/33.69  | | 
% 202.11/33.69  | End of split
% 202.11/33.69  | 
% 202.11/33.69  End of proof
% 202.11/33.69  
% 202.11/33.69  Sub-proof #336 shows that the following formulas are inconsistent:
% 202.11/33.69  ----------------------------------------------------------------
% 202.11/33.69    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.11/33.69    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.69    (3)   ~ (all_52_15 = all_52_23)
% 202.11/33.69    (4)   ~ (all_52_25 = all_52_27)
% 202.11/33.69    (5)  all_58_14 = all_52_23
% 202.11/33.69    (6)   ~ (e3 = e1)
% 202.11/33.69    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.69    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.69    (9)   ~ (all_52_5 = all_52_13)
% 202.11/33.69    (10)  all_58_1 = all_52_9
% 202.11/33.69    (11)   ~ (all_52_9 = all_52_13)
% 202.11/33.69    (12)   ~ (e3 = e0)
% 202.11/33.69    (13)  op(e2, e3) = all_52_3
% 202.11/33.69    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.69    (15)   ~ (all_52_7 = all_52_15)
% 202.11/33.69    (16)   ~ (all_52_3 = all_52_19)
% 202.11/33.69    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.69    (18)   ~ (all_52_17 = all_52_25)
% 202.11/33.69    (19)   ~ (all_52_3 = all_6_2)
% 202.11/33.69    (20)  all_44_2 = all_6_2
% 202.11/33.69    (21)  all_58_0 = all_6_2
% 202.11/33.69    (22)  op(all_14_2, e0) = all_14_1
% 202.11/33.69    (23)  all_56_4 = all_52_3
% 202.11/33.69    (24)   ~ (all_52_17 = all_10_2)
% 202.11/33.69    (25)  all_26_1 = all_10_1
% 202.11/33.69    (26)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.69    (27)  op(e3, e0) = all_52_25
% 202.11/33.69    (28)  all_26_2 = all_10_2
% 202.11/33.69    (29)  op(e0, all_14_1) = all_14_0
% 202.11/33.69    (30)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.69    (31)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.69    (32)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.69    (33)   ~ (all_52_27 = all_52_29)
% 202.11/33.69    (34)  all_58_13 = all_52_15
% 202.11/33.69    (35)  op(all_10_2, all_10_2) = all_52_20
% 202.11/33.69    (36)  all_58_9 = all_52_25
% 202.11/33.69    (37)   ~ (all_52_29 = all_14_2)
% 202.11/33.69    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.69    (39)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.69    (40)  op(e1, e3) = all_52_5
% 202.11/33.69    (41)  op(e2, e2) = all_4_2
% 202.11/33.69    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.69    (43)   ~ (all_52_3 = all_52_5)
% 202.11/33.69    (44)  all_58_11 = all_52_29
% 202.11/33.69    (45)  all_56_5 = all_4_2
% 202.11/33.69    (46)   ~ (all_52_25 = all_14_2)
% 202.11/33.69    (47)   ~ (all_52_9 = all_52_15)
% 202.11/33.69    (48)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.11/33.69    (49)   ~ (all_52_3 = all_52_27)
% 202.11/33.69    (50)  op(all_10_2, e1) = all_10_1
% 202.11/33.69    (51)  op(all_6_2, all_6_2) = all_52_0
% 202.11/33.69    (52)   ~ (all_52_7 = all_6_2)
% 202.11/33.69    (53)  op(e0, e0) = all_14_2
% 202.11/33.69    (54)  op(e0, e1) = all_52_23
% 202.11/33.69    (55)  all_56_15 = all_14_2
% 202.11/33.69    (56)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.69    (57)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.11/33.69    (58)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 202.11/33.69    (59)  all_56_11 = all_52_29
% 202.11/33.69    (60)   ~ (all_4_1 = e1)
% 202.11/33.69    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.69    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.69    (63)  all_56_9 = all_52_13
% 202.11/33.69    (64)   ~ (e2 = e1)
% 202.11/33.69    (65)   ~ (all_52_13 = all_10_2)
% 202.11/33.69    (66)  all_58_10 = all_52_27
% 202.11/33.69    (67)  all_56_8 = all_52_5
% 202.11/33.69    (68)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.69    (69)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.69    (70)   ~ (all_52_19 = all_52_23)
% 202.11/33.69    (71)   ~ (all_52_25 = all_52_29)
% 202.11/33.69    (72)   ~ (all_52_29 = all_10_2)
% 202.11/33.69    (73)  all_58_7 = all_52_13
% 202.11/33.69    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.11/33.69    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.69    (76)   ~ (all_52_5 = all_52_7)
% 202.11/33.69    (77)  all_58_12 = all_52_7
% 202.11/33.69    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.69    (79)   ~ (all_52_7 = all_14_2)
% 202.11/33.69    (80)   ~ (all_14_2 = e0)
% 202.11/33.69    (81)  all_58_2 = all_52_3
% 202.11/33.69    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.69    (83)  all_56_2 = all_52_17
% 202.11/33.69    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.69    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.69    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.69    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.11/33.69    (88)  all_56_7 = all_52_27
% 202.11/33.69    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.69    (90)   ~ (e2 = e0)
% 202.11/33.69    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.11/33.69    (92)  op(all_4_2, e2) = all_4_1
% 202.11/33.69    (93)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.69    (94)   ~ (all_52_5 = all_52_29)
% 202.11/33.69    (95)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.69    (96)  all_56_6 = all_52_19
% 202.11/33.69    (97)   ~ (all_52_15 = all_14_2)
% 202.11/33.69    (98)   ~ (all_52_19 = all_52_27)
% 202.11/33.69    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.69    (100)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.69    (101)   ~ (all_52_13 = all_4_2)
% 202.11/33.69    (102)  op(e3, e1) = all_52_17
% 202.11/33.69    (103)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.11/33.69    (104)  op(e0, e3) = all_52_7
% 202.11/33.69    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.69    (106)   ~ (all_52_9 = all_52_25)
% 202.11/33.69    (107)  all_58_15 = all_14_2
% 202.11/33.69    (108)   ~ (all_52_19 = all_10_2)
% 202.11/33.69    (109)  op(all_52_23, all_52_23) = all_52_22
% 202.11/33.69    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.69    (111)  all_58_8 = all_10_2
% 202.11/33.69    (112)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.69    (113)   ~ (all_52_5 = all_10_2)
% 202.11/33.69    (114)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.69    (115)   ~ (all_52_23 = all_14_2)
% 202.11/33.69    (116)  all_56_12 = all_52_7
% 202.11/33.69    (117)  op(all_52_17, all_52_17) = all_52_16
% 202.11/33.69    (118)  all_8_2 = all_6_2
% 202.11/33.69    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.69    (120)   ~ (all_52_25 = all_6_2)
% 202.11/33.69    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.69    (122)   ~ (all_52_9 = all_4_2)
% 202.11/33.69    (123)   ~ (all_52_5 = all_6_2)
% 202.11/33.69    (124)   ~ (all_52_9 = all_6_2)
% 202.11/33.69    (125)   ~ (all_52_13 = all_52_15)
% 202.11/33.69    (126)  op(e3, all_6_1) = e2
% 202.11/33.69    (127)  all_56_0 = all_6_2
% 202.11/33.69    (128)  op(e3, e3) = all_6_2
% 202.11/33.69    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.69    (130)   ~ (all_52_27 = all_14_2)
% 202.11/33.69    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.69    (132)  all_56_14 = all_52_23
% 202.11/33.69    (133)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.69    (134)  all_56_3 = all_52_25
% 202.11/33.69    (135)   ~ (all_52_3 = all_52_7)
% 202.11/33.69    (136)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.69    (137)  all_58_5 = all_52_19
% 202.11/33.69    (138)  all_56_1 = all_52_9
% 202.11/33.69    (139)   ~ (all_52_15 = all_4_2)
% 202.11/33.69    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.69           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.11/33.69           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.11/33.69           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.11/33.69    (141)   ~ (all_52_27 = all_4_2)
% 202.11/33.69    (142)  all_58_6 = all_52_5
% 202.11/33.69    (143)  op(e3, e2) = all_52_9
% 202.11/33.69    (144)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.69    (145)   ~ (all_52_17 = all_6_2)
% 202.11/33.69    (146)   ~ (e1 = e0)
% 202.11/33.69    (147)   ~ (e3 = e2)
% 202.11/33.69    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.69    (149)  all_44_1 = all_6_1
% 202.11/33.69    (150)   ~ (all_52_9 = all_52_17)
% 202.11/33.69    (151)  all_56_10 = all_10_2
% 202.11/33.69    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.69    (153)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.69    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.69    (155)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.69    (156)  op(e1, e1) = all_10_2
% 202.11/33.69    (157)   ~ (all_52_23 = all_10_2)
% 202.11/33.69    (158)   ~ (all_52_7 = all_52_23)
% 202.11/33.69    (159)   ~ (all_52_17 = all_52_19)
% 202.11/33.69    (160)  all_58_3 = all_4_2
% 202.11/33.69    (161)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.11/33.69    (162)  all_56_13 = all_52_15
% 202.11/33.69    (163)   ~ (all_52_3 = all_4_2)
% 202.11/33.69    (164)   ~ (all_52_19 = all_4_2)
% 202.11/33.69    (165)   ~ (all_52_17 = all_52_23)
% 202.11/33.69    (166)  all_8_1 = all_6_1
% 202.11/33.69    (167)  op(all_6_2, e3) = all_6_1
% 202.11/33.69    (168)   ~ (all_52_13 = all_52_29)
% 202.11/33.69    (169)  all_58_4 = all_52_17
% 202.11/33.69    (170)   ~ (all_14_0 = e2)
% 202.11/33.69    (171)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.69    (172)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.69  
% 202.11/33.69  Begin of proof
% 202.11/33.69  | 
% 202.11/33.69  | BETA: splitting (140) gives:
% 202.11/33.69  | 
% 202.11/33.69  | Case 1:
% 202.11/33.69  | | 
% 202.11/33.69  | |   (173)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.69  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.11/33.69  | | 
% 202.11/33.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 202.11/33.69  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 202.11/33.69  | |            (27), (29), (30), (31), (32), (34), (35), (36), (37), (39), (40),
% 202.11/33.69  | |            (41), (42), (43), (44), (46), (48), (49), (51), (52), (53), (54),
% 202.11/33.69  | |            (55), (56), (60), (61), (63), (65), (66), (67), (68), (69), (70),
% 202.11/33.69  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (81), (85),
% 202.11/33.69  | |            (88), (89), (90), (92), (95), (97), (101), (102), (104), (105),
% 202.11/33.69  | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 202.11/33.69  | |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 202.11/33.69  | |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 202.11/33.69  | |            (133), (134), (135), (136), (137), (138), (139), (141), (142),
% 202.11/33.69  | |            (143), (144), (145), (146), (147), (148), (149), (150), (151),
% 202.11/33.69  | |            (152), (153), (154), (155), (156), (157), (158), (159), (160),
% 202.11/33.69  | |            (162), (163), (164), (165), (166), (167), (168), (169), (170),
% 202.11/33.69  | |            (171), (172), (173) are inconsistent by sub-proof #349.
% 202.11/33.69  | | 
% 202.11/33.69  | Case 2:
% 202.11/33.69  | | 
% 202.11/33.69  | |   (174)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 202.11/33.69  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.11/33.69  | |            e0)
% 202.11/33.69  | | 
% 202.11/33.69  | | BETA: splitting (174) gives:
% 202.11/33.69  | | 
% 202.11/33.69  | | Case 1:
% 202.11/33.69  | | | 
% 202.11/33.69  | | |   (175)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 202.11/33.69  | | | 
% 202.11/33.69  | | | ALPHA: (175) implies:
% 202.11/33.69  | | |   (176)  all_52_22 = e0
% 202.11/33.69  | | |   (177)  all_52_20 = e1
% 202.11/33.69  | | |   (178)  all_52_18 = e2
% 202.11/33.69  | | |   (179)  all_52_16 = e3
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (117), (179) imply:
% 202.11/33.69  | | |   (180)  op(all_52_17, all_52_17) = e3
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (32), (178) imply:
% 202.11/33.69  | | |   (181)  op(all_52_19, all_52_19) = e2
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (109), (176) imply:
% 202.11/33.69  | | |   (182)  op(all_52_23, all_52_23) = e0
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REDUCE: (35), (177) imply:
% 202.11/33.69  | | |   (183)  op(all_10_2, all_10_2) = e1
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 202.11/33.69  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 202.11/33.69  | | |            (26), (27), (28), (31), (34), (36), (37), (38), (39), (40),
% 202.11/33.69  | | |            (41), (42), (43), (44), (46), (47), (50), (52), (53), (55),
% 202.11/33.69  | | |            (56), (58), (61), (62), (64), (65), (66), (67), (68), (69),
% 202.11/33.69  | | |            (70), (71), (72), (73), (75), (76), (77), (78), (79), (80),
% 202.11/33.69  | | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 202.11/33.69  | | |            (93), (95), (96), (100), (101), (102), (104), (105), (106),
% 202.11/33.69  | | |            (107), (108), (110), (111), (112), (113), (114), (116), (118),
% 202.11/33.69  | | |            (120), (122), (123), (124), (125), (126), (128), (129), (130),
% 202.11/33.69  | | |            (131), (135), (136), (137), (138), (139), (141), (142), (143),
% 202.11/33.69  | | |            (144), (145), (146), (147), (148), (149), (150), (151), (152),
% 202.11/33.69  | | |            (155), (156), (157), (158), (159), (160), (162), (163), (165),
% 202.11/33.69  | | |            (166), (167), (169), (171), (172), (180), (181), (182), (183)
% 202.11/33.69  | | |            are inconsistent by sub-proof #337.
% 202.11/33.69  | | | 
% 202.11/33.69  | | Case 2:
% 202.11/33.69  | | | 
% 202.11/33.69  | | |   (184)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.11/33.69  | | | 
% 202.11/33.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13),
% 202.11/33.69  | | |            (14), (17), (18), (19), (20), (21), (22), (24), (26), (27),
% 202.11/33.69  | | |            (30), (31), (32), (33), (34), (36), (37), (39), (40), (41),
% 202.11/33.69  | | |            (42), (43), (44), (45), (46), (49), (50), (51), (52), (53),
% 202.11/33.69  | | |            (55), (56), (57), (59), (62), (66), (67), (68), (71), (72),
% 202.11/33.69  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 202.11/33.69  | | |            (83), (85), (86), (88), (90), (91), (94), (96), (98), (99),
% 202.11/33.69  | | |            (100), (102), (103), (104), (105), (106), (107), (108), (110),
% 202.11/33.69  | | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 202.11/33.69  | | |            (120), (121), (122), (123), (126), (127), (128), (129), (130),
% 202.11/33.69  | | |            (131), (132), (134), (135), (136), (137), (139), (141), (142),
% 202.11/33.69  | | |            (143), (144), (145), (146), (147), (149), (150), (152), (154),
% 202.11/33.69  | | |            (155), (156), (158), (159), (160), (161), (163), (164), (165),
% 202.11/33.69  | | |            (166), (167), (168), (169), (172), (184) are inconsistent by
% 202.11/33.69  | | |            sub-proof #434.
% 202.11/33.69  | | | 
% 202.11/33.69  | | End of split
% 202.11/33.69  | | 
% 202.11/33.69  | End of split
% 202.11/33.69  | 
% 202.11/33.69  End of proof
% 202.11/33.69  
% 202.11/33.69  Sub-proof #337 shows that the following formulas are inconsistent:
% 202.11/33.69  ----------------------------------------------------------------
% 202.11/33.69    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.69    (2)   ~ (all_52_25 = all_52_27)
% 202.11/33.69    (3)  all_58_14 = all_52_23
% 202.11/33.69    (4)   ~ (e3 = e1)
% 202.11/33.69    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.69    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.69    (7)  all_58_1 = all_52_9
% 202.11/33.69    (8)   ~ (all_52_9 = all_52_13)
% 202.11/33.69    (9)   ~ (e3 = e0)
% 202.11/33.69    (10)  op(all_52_23, all_52_23) = e0
% 202.11/33.69    (11)  op(e2, e3) = all_52_3
% 202.11/33.69    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.69    (13)   ~ (all_52_7 = all_52_15)
% 202.11/33.69    (14)   ~ (all_52_3 = all_52_19)
% 202.11/33.69    (15)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.69    (16)   ~ (all_52_17 = all_52_25)
% 202.11/33.69    (17)   ~ (all_52_3 = all_6_2)
% 202.11/33.69    (18)  all_44_2 = all_6_2
% 202.11/33.69    (19)  all_58_0 = all_6_2
% 202.11/33.69    (20)  op(all_14_2, e0) = all_14_1
% 202.11/33.69    (21)  all_56_4 = all_52_3
% 202.11/33.69    (22)  all_26_1 = all_10_1
% 202.11/33.69    (23)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.69    (24)  op(e3, e0) = all_52_25
% 202.11/33.69    (25)  all_26_2 = all_10_2
% 202.11/33.69    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.69    (27)  all_58_13 = all_52_15
% 202.11/33.69    (28)  all_58_9 = all_52_25
% 202.11/33.69    (29)   ~ (all_52_29 = all_14_2)
% 202.11/33.69    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.69    (31)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.69    (32)  op(e1, e3) = all_52_5
% 202.11/33.69    (33)  op(e2, e2) = all_4_2
% 202.11/33.69    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.69    (35)   ~ (all_52_3 = all_52_5)
% 202.11/33.69    (36)  all_58_11 = all_52_29
% 202.11/33.69    (37)   ~ (all_52_25 = all_14_2)
% 202.11/33.69    (38)   ~ (all_52_9 = all_52_15)
% 202.11/33.69    (39)  op(all_10_2, e1) = all_10_1
% 202.11/33.69    (40)   ~ (all_52_7 = all_6_2)
% 202.11/33.69    (41)  op(e0, e0) = all_14_2
% 202.11/33.69    (42)  all_56_15 = all_14_2
% 202.11/33.69    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.69    (44)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 202.11/33.69    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.69    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.69    (47)   ~ (e2 = e1)
% 202.11/33.69    (48)   ~ (all_52_13 = all_10_2)
% 202.11/33.69    (49)  op(all_10_2, all_10_2) = e1
% 202.11/33.69    (50)  all_58_10 = all_52_27
% 202.11/33.69    (51)  all_56_8 = all_52_5
% 202.11/33.69    (52)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.69    (53)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.69    (54)   ~ (all_52_19 = all_52_23)
% 202.11/33.69    (55)   ~ (all_52_25 = all_52_29)
% 202.11/33.69    (56)   ~ (all_52_29 = all_10_2)
% 202.11/33.69    (57)  all_58_7 = all_52_13
% 202.11/33.69    (58)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.69    (59)  op(all_52_19, all_52_19) = e2
% 202.11/33.69    (60)   ~ (all_52_5 = all_52_7)
% 202.11/33.69    (61)  all_58_12 = all_52_7
% 202.11/33.69    (62)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.69    (63)   ~ (all_52_7 = all_14_2)
% 202.11/33.69    (64)   ~ (all_14_2 = e0)
% 202.11/33.69    (65)  all_58_2 = all_52_3
% 202.11/33.69    (66)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.69    (67)  all_56_2 = all_52_17
% 202.11/33.69    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.69    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.69    (70)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.69    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.11/33.69    (72)  all_56_7 = all_52_27
% 202.11/33.69    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.69    (74)   ~ (e2 = e0)
% 202.11/33.69    (75)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.69    (76)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.69    (77)  all_56_6 = all_52_19
% 202.11/33.69    (78)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.69    (79)   ~ (all_52_13 = all_4_2)
% 202.11/33.69    (80)  op(e3, e1) = all_52_17
% 202.11/33.69    (81)  op(e0, e3) = all_52_7
% 202.11/33.69    (82)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.69    (83)   ~ (all_52_9 = all_52_25)
% 202.11/33.69    (84)  all_58_15 = all_14_2
% 202.11/33.69    (85)   ~ (all_52_19 = all_10_2)
% 202.11/33.69    (86)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.69    (87)  all_58_8 = all_10_2
% 202.11/33.69    (88)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.69    (89)   ~ (all_52_5 = all_10_2)
% 202.11/33.69    (90)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.69    (91)  all_56_12 = all_52_7
% 202.11/33.69    (92)  all_8_2 = all_6_2
% 202.11/33.69    (93)   ~ (all_52_25 = all_6_2)
% 202.11/33.69    (94)   ~ (all_52_9 = all_4_2)
% 202.11/33.69    (95)   ~ (all_52_5 = all_6_2)
% 202.11/33.69    (96)   ~ (all_52_9 = all_6_2)
% 202.11/33.69    (97)   ~ (all_52_13 = all_52_15)
% 202.11/33.69    (98)  op(e3, all_6_1) = e2
% 202.11/33.69    (99)  op(e3, e3) = all_6_2
% 202.11/33.69    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.69    (101)   ~ (all_52_27 = all_14_2)
% 202.11/33.69    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.69    (103)   ~ (all_52_3 = all_52_7)
% 202.11/33.69    (104)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.69    (105)  all_58_5 = all_52_19
% 202.11/33.69    (106)  all_56_1 = all_52_9
% 202.11/33.69    (107)   ~ (all_52_15 = all_4_2)
% 202.11/33.69    (108)   ~ (all_52_27 = all_4_2)
% 202.11/33.69    (109)  op(all_52_17, all_52_17) = e3
% 202.11/33.69    (110)  all_58_6 = all_52_5
% 202.11/33.69    (111)  op(e3, e2) = all_52_9
% 202.11/33.69    (112)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.69    (113)   ~ (all_52_17 = all_6_2)
% 202.11/33.69    (114)   ~ (e1 = e0)
% 202.11/33.69    (115)   ~ (e3 = e2)
% 202.11/33.69    (116)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.69    (117)  all_44_1 = all_6_1
% 202.11/33.69    (118)   ~ (all_52_9 = all_52_17)
% 202.11/33.69    (119)  all_56_10 = all_10_2
% 202.11/33.69    (120)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.69    (121)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.69    (122)  op(e1, e1) = all_10_2
% 202.11/33.69    (123)   ~ (all_52_23 = all_10_2)
% 202.11/33.69    (124)   ~ (all_52_7 = all_52_23)
% 202.11/33.69    (125)   ~ (all_52_17 = all_52_19)
% 202.11/33.69    (126)  all_58_3 = all_4_2
% 202.11/33.69    (127)  all_56_13 = all_52_15
% 202.11/33.69    (128)   ~ (all_52_3 = all_4_2)
% 202.11/33.69    (129)   ~ (all_52_17 = all_52_23)
% 202.11/33.69    (130)  all_8_1 = all_6_1
% 202.11/33.69    (131)  op(all_6_2, e3) = all_6_1
% 202.11/33.69    (132)  all_58_4 = all_52_17
% 202.11/33.69    (133)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.69    (134)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.69  
% 202.11/33.69  Begin of proof
% 202.11/33.69  | 
% 202.11/33.69  | BETA: splitting (88) gives:
% 202.11/33.69  | 
% 202.11/33.69  | Case 1:
% 202.11/33.69  | | 
% 202.11/33.70  | |   (135)  all_56_15 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | COMBINE_EQS: (42), (135) imply:
% 202.11/33.70  | |   (136)  all_14_2 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (37), (136) imply:
% 202.11/33.70  | |   (137)   ~ (all_52_25 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (101), (136) imply:
% 202.11/33.70  | |   (138)   ~ (all_52_27 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (29), (136) imply:
% 202.11/33.70  | |   (139)   ~ (all_52_29 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (104), (136) imply:
% 202.11/33.70  | |   (140)  op(e3, e3) = all_52_30
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (20), (136) imply:
% 202.11/33.70  | |   (141)  op(e3, e0) = all_14_1
% 202.11/33.70  | | 
% 202.11/33.70  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 202.11/33.70  | |              with (24), (141) gives:
% 202.11/33.70  | |   (142)  all_52_25 = all_14_1
% 202.11/33.70  | | 
% 202.11/33.70  | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3, simplifying
% 202.11/33.70  | |              with (99), (140) gives:
% 202.11/33.70  | |   (143)  all_52_30 = all_6_2
% 202.11/33.70  | | 
% 202.11/33.70  | | COMBINE_EQS: (28), (142) imply:
% 202.11/33.70  | |   (144)  all_58_9 = all_14_1
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (93), (142) imply:
% 202.11/33.70  | |   (145)   ~ (all_14_1 = all_6_2)
% 202.11/33.70  | | 
% 202.11/33.70  | | BETA: splitting (66) gives:
% 202.11/33.70  | | 
% 202.11/33.70  | | Case 1:
% 202.11/33.70  | | | 
% 202.11/33.70  | | |   (146)  all_56_6 = e3
% 202.11/33.70  | | | 
% 202.11/33.70  | | | COMBINE_EQS: (77), (146) imply:
% 202.11/33.70  | | |   (147)  all_52_19 = e3
% 202.11/33.70  | | | 
% 202.11/33.70  | | | SIMP: (147) implies:
% 202.11/33.70  | | |   (148)  all_52_19 = e3
% 202.11/33.70  | | | 
% 202.11/33.70  | | | REDUCE: (54), (148) imply:
% 202.11/33.70  | | |   (149)   ~ (all_52_23 = e3)
% 202.11/33.70  | | | 
% 202.11/33.70  | | | SIMP: (149) implies:
% 202.11/33.70  | | |   (150)   ~ (all_52_23 = e3)
% 202.11/33.70  | | | 
% 202.11/33.70  | | | REDUCE: (85), (148) imply:
% 202.11/33.70  | | |   (151)   ~ (all_10_2 = e3)
% 202.11/33.70  | | | 
% 202.11/33.70  | | | SIMP: (151) implies:
% 202.11/33.70  | | |   (152)   ~ (all_10_2 = e3)
% 202.11/33.70  | | | 
% 202.11/33.70  | | | REF_CLOSE: (3), (6), (7), (11), (14), (17), (19), (21), (28), (34), (52),
% 202.11/33.70  | | |            (58), (59), (65), (73), (74), (80), (82), (87), (98), (99),
% 202.11/33.70  | | |            (102), (105), (109), (113), (115), (118), (120), (131), (132),
% 202.11/33.70  | | |            (137), (141), (145), (150), (152) are inconsistent by sub-proof
% 202.11/33.70  | | |            #416.
% 202.11/33.70  | | | 
% 202.11/33.70  | | Case 2:
% 202.11/33.70  | | | 
% 202.11/33.70  | | |   (153)   ~ (all_56_6 = e3)
% 202.11/33.70  | | | 
% 202.11/33.70  | | | REDUCE: (77), (153) imply:
% 202.11/33.70  | | |   (154)   ~ (all_52_19 = e3)
% 202.11/33.70  | | | 
% 202.11/33.70  | | | BETA: splitting (43) gives:
% 202.11/33.70  | | | 
% 202.11/33.70  | | | Case 1:
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | |   (155)  all_58_2 = e3
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | COMBINE_EQS: (65), (155) imply:
% 202.11/33.70  | | | |   (156)  all_52_3 = e3
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | SIMP: (156) implies:
% 202.11/33.70  | | | |   (157)  all_52_3 = e3
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | REDUCE: (35), (157) imply:
% 202.11/33.70  | | | |   (158)   ~ (all_52_5 = e3)
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | SIMP: (158) implies:
% 202.11/33.70  | | | |   (159)   ~ (all_52_5 = e3)
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | REDUCE: (103), (157) imply:
% 202.11/33.70  | | | |   (160)   ~ (all_52_7 = e3)
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | SIMP: (160) implies:
% 202.11/33.70  | | | |   (161)   ~ (all_52_7 = e3)
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | REDUCE: (17), (157) imply:
% 202.11/33.70  | | | |   (162)   ~ (all_6_2 = e3)
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | SIMP: (162) implies:
% 202.11/33.70  | | | |   (163)   ~ (all_6_2 = e3)
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | REDUCE: (5), (157) imply:
% 202.11/33.70  | | | |   (164)  op(e3, e3) = all_52_2
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | REF_CLOSE: (6), (7), (8), (9), (19), (22), (25), (27), (28), (33), (36),
% 202.11/33.70  | | | |            (38), (39), (44), (47), (48), (49), (52), (57), (61), (62),
% 202.11/33.70  | | | |            (65), (68), (69), (70), (74), (80), (82), (87), (89), (94),
% 202.11/33.70  | | | |            (96), (99), (102), (109), (110), (113), (114), (115), (120),
% 202.11/33.70  | | | |            (126), (128), (132), (137), (139), (144), (159), (161),
% 202.11/33.70  | | | |            (163), (164) are inconsistent by sub-proof #341.
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | Case 2:
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | |   (165)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | BETA: splitting (165) gives:
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | Case 1:
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | |   (166)  all_58_3 = e3
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | COMBINE_EQS: (126), (166) imply:
% 202.11/33.70  | | | | |   (167)  all_4_2 = e3
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REDUCE: (94), (167) imply:
% 202.11/33.70  | | | | |   (168)   ~ (all_52_9 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REF_CLOSE: (6), (7), (19), (28), (98), (99), (102), (109), (113),
% 202.11/33.70  | | | | |            (115), (120), (131), (132), (137), (168) are inconsistent
% 202.11/33.70  | | | | |            by sub-proof #446.
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | Case 2:
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | |   (169)  all_58_5 = e3 | all_58_10 = e3
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REF_CLOSE: (50), (105), (138), (154), (169) are inconsistent by
% 202.11/33.70  | | | | |            sub-proof #1132.
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | End of split
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | End of split
% 202.11/33.70  | | | 
% 202.11/33.70  | | End of split
% 202.11/33.70  | | 
% 202.11/33.70  | Case 2:
% 202.11/33.70  | | 
% 202.11/33.70  | |   (170)   ~ (all_56_15 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (42), (170) imply:
% 202.11/33.70  | |   (171)   ~ (all_14_2 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 202.11/33.70  | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 202.11/33.70  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 202.11/33.70  | |            (38), (39), (40), (41), (43), (44), (45), (46), (47), (48), (49),
% 202.11/33.70  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 202.11/33.70  | |            (61), (62), (63), (65), (66), (67), (68), (69), (70), (71), (72),
% 202.11/33.70  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 202.11/33.70  | |            (84), (85), (86), (87), (90), (91), (92), (93), (94), (95), (97),
% 202.11/33.70  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 202.11/33.70  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 202.11/33.70  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 202.11/33.70  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 202.11/33.70  | |            (134), (171) are inconsistent by sub-proof #338.
% 202.11/33.70  | | 
% 202.11/33.70  | End of split
% 202.11/33.70  | 
% 202.11/33.70  End of proof
% 202.11/33.70  
% 202.11/33.70  Sub-proof #338 shows that the following formulas are inconsistent:
% 202.11/33.70  ----------------------------------------------------------------
% 202.11/33.70    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.70    (2)   ~ (all_52_25 = all_52_27)
% 202.11/33.70    (3)  all_58_14 = all_52_23
% 202.11/33.70    (4)   ~ (e3 = e1)
% 202.11/33.70    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.70    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.70    (7)  all_58_1 = all_52_9
% 202.11/33.70    (8)   ~ (e3 = e0)
% 202.11/33.70    (9)  op(all_52_23, all_52_23) = e0
% 202.11/33.70    (10)  op(e2, e3) = all_52_3
% 202.11/33.70    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.70    (12)   ~ (all_52_7 = all_52_15)
% 202.11/33.70    (13)   ~ (all_52_3 = all_52_19)
% 202.11/33.70    (14)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.70    (15)   ~ (all_52_17 = all_52_25)
% 202.11/33.70    (16)   ~ (all_52_3 = all_6_2)
% 202.11/33.70    (17)  all_44_2 = all_6_2
% 202.11/33.70    (18)  all_58_0 = all_6_2
% 202.11/33.70    (19)  all_56_4 = all_52_3
% 202.11/33.70    (20)  all_26_1 = all_10_1
% 202.11/33.70    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.70    (22)  op(e3, e0) = all_52_25
% 202.11/33.70    (23)  all_26_2 = all_10_2
% 202.11/33.70    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.70    (25)  all_58_13 = all_52_15
% 202.11/33.70    (26)  all_58_9 = all_52_25
% 202.11/33.70    (27)   ~ (all_52_29 = all_14_2)
% 202.11/33.70    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.70    (29)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.70    (30)  op(e1, e3) = all_52_5
% 202.11/33.70    (31)  op(e2, e2) = all_4_2
% 202.11/33.70    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.70    (33)   ~ (all_52_3 = all_52_5)
% 202.11/33.70    (34)  all_58_11 = all_52_29
% 202.11/33.70    (35)   ~ (all_52_9 = all_52_15)
% 202.11/33.70    (36)  op(all_10_2, e1) = all_10_1
% 202.11/33.70    (37)   ~ (all_52_7 = all_6_2)
% 202.11/33.70    (38)  op(e0, e0) = all_14_2
% 202.11/33.70    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.70    (40)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 202.11/33.70    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.70    (42)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.70    (43)   ~ (e2 = e1)
% 202.11/33.70    (44)   ~ (all_52_13 = all_10_2)
% 202.11/33.70    (45)  op(all_10_2, all_10_2) = e1
% 202.11/33.70    (46)  all_58_10 = all_52_27
% 202.11/33.70    (47)  all_56_8 = all_52_5
% 202.11/33.70    (48)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.70    (49)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.70    (50)   ~ (all_52_19 = all_52_23)
% 202.11/33.70    (51)   ~ (all_52_25 = all_52_29)
% 202.11/33.70    (52)   ~ (all_52_29 = all_10_2)
% 202.11/33.70    (53)  all_58_7 = all_52_13
% 202.11/33.70    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.70    (55)  op(all_52_19, all_52_19) = e2
% 202.11/33.70    (56)   ~ (all_52_5 = all_52_7)
% 202.11/33.70    (57)  all_58_12 = all_52_7
% 202.11/33.70    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.70    (59)   ~ (all_52_7 = all_14_2)
% 202.11/33.70    (60)  all_58_2 = all_52_3
% 202.11/33.70    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.70    (62)  all_56_2 = all_52_17
% 202.11/33.70    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.70    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.70    (65)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.70    (66)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.11/33.70    (67)  all_56_7 = all_52_27
% 202.11/33.70    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.70    (69)   ~ (e2 = e0)
% 202.11/33.70    (70)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.70    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.70    (72)  all_56_6 = all_52_19
% 202.11/33.70    (73)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.70    (74)   ~ (all_52_13 = all_4_2)
% 202.11/33.70    (75)  op(e3, e1) = all_52_17
% 202.11/33.70    (76)  op(e0, e3) = all_52_7
% 202.11/33.70    (77)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.70    (78)   ~ (all_52_9 = all_52_25)
% 202.11/33.70    (79)  all_58_15 = all_14_2
% 202.11/33.70    (80)   ~ (all_52_19 = all_10_2)
% 202.11/33.70    (81)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.70    (82)  all_58_8 = all_10_2
% 202.11/33.70    (83)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.70    (84)  all_56_12 = all_52_7
% 202.11/33.70    (85)  all_8_2 = all_6_2
% 202.11/33.70    (86)   ~ (all_52_25 = all_6_2)
% 202.11/33.70    (87)   ~ (all_52_9 = all_4_2)
% 202.11/33.70    (88)   ~ (all_52_5 = all_6_2)
% 202.11/33.70    (89)   ~ (all_52_13 = all_52_15)
% 202.11/33.70    (90)  op(e3, all_6_1) = e2
% 202.11/33.70    (91)  op(e3, e3) = all_6_2
% 202.11/33.70    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.70    (93)   ~ (all_52_27 = all_14_2)
% 202.11/33.70    (94)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.70    (95)   ~ (all_52_3 = all_52_7)
% 202.11/33.70    (96)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.70    (97)  all_58_5 = all_52_19
% 202.11/33.70    (98)  all_56_1 = all_52_9
% 202.11/33.70    (99)   ~ (all_52_15 = all_4_2)
% 202.11/33.70    (100)   ~ (all_52_27 = all_4_2)
% 202.11/33.70    (101)  op(all_52_17, all_52_17) = e3
% 202.11/33.70    (102)  all_58_6 = all_52_5
% 202.11/33.70    (103)  op(e3, e2) = all_52_9
% 202.11/33.70    (104)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.70    (105)   ~ (all_52_17 = all_6_2)
% 202.11/33.70    (106)   ~ (e1 = e0)
% 202.11/33.70    (107)   ~ (e3 = e2)
% 202.11/33.70    (108)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.70    (109)  all_44_1 = all_6_1
% 202.11/33.70    (110)   ~ (all_52_9 = all_52_17)
% 202.11/33.70    (111)  all_56_10 = all_10_2
% 202.11/33.70    (112)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.70    (113)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.70    (114)  op(e1, e1) = all_10_2
% 202.11/33.70    (115)   ~ (all_52_23 = all_10_2)
% 202.11/33.70    (116)   ~ (all_52_7 = all_52_23)
% 202.11/33.70    (117)   ~ (all_52_17 = all_52_19)
% 202.11/33.70    (118)  all_58_3 = all_4_2
% 202.11/33.70    (119)  all_56_13 = all_52_15
% 202.11/33.70    (120)   ~ (all_52_3 = all_4_2)
% 202.11/33.70    (121)   ~ (all_52_17 = all_52_23)
% 202.11/33.70    (122)  all_8_1 = all_6_1
% 202.11/33.70    (123)  op(all_6_2, e3) = all_6_1
% 202.11/33.70    (124)  all_58_4 = all_52_17
% 202.11/33.70    (125)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.70    (126)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.70    (127)   ~ (all_14_2 = e3)
% 202.11/33.70  
% 202.11/33.70  Begin of proof
% 202.11/33.70  | 
% 202.11/33.70  | BETA: splitting (41) gives:
% 202.11/33.70  | 
% 202.11/33.70  | Case 1:
% 202.11/33.70  | | 
% 202.11/33.70  | |   (128)  all_56_13 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | COMBINE_EQS: (119), (128) imply:
% 202.11/33.70  | |   (129)  all_52_15 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | SIMP: (129) implies:
% 202.11/33.70  | |   (130)  all_52_15 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (35), (130) imply:
% 202.11/33.70  | |   (131)   ~ (all_52_9 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (89), (130) imply:
% 202.11/33.70  | |   (132)   ~ (all_52_13 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (99), (130) imply:
% 202.11/33.70  | |   (133)   ~ (all_4_2 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | SIMP: (133) implies:
% 202.11/33.70  | |   (134)   ~ (all_4_2 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (49), (130) imply:
% 202.11/33.70  | |   (135)  op(e3, e3) = all_52_14
% 202.11/33.70  | | 
% 202.11/33.70  | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3, simplifying
% 202.11/33.70  | |              with (91), (135) gives:
% 202.11/33.70  | |   (136)  all_52_14 = all_6_2
% 202.11/33.70  | | 
% 202.11/33.70  | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (13), (16), (18), (19), (20),
% 202.11/33.70  | |            (22), (23), (26), (29), (31), (32), (33), (34), (36), (39), (40),
% 202.11/33.70  | |            (43), (44), (45), (46), (51), (53), (54), (55), (56), (57), (58),
% 202.11/33.70  | |            (60), (63), (64), (65), (68), (69), (75), (78), (80), (82), (88),
% 202.11/33.70  | |            (90), (91), (92), (94), (95), (97), (101), (102), (105), (106),
% 202.11/33.70  | |            (107), (112), (117), (118), (120), (123), (124), (126), (131),
% 202.11/33.70  | |            (132), (134) are inconsistent by sub-proof #343.
% 202.11/33.70  | | 
% 202.11/33.70  | Case 2:
% 202.11/33.70  | | 
% 202.11/33.70  | |   (137)   ~ (all_56_13 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (119), (137) imply:
% 202.11/33.70  | |   (138)   ~ (all_52_15 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.11/33.70  | |            (14), (15), (16), (17), (18), (19), (21), (22), (24), (25), (26),
% 202.11/33.70  | |            (27), (28), (29), (30), (31), (32), (34), (36), (37), (38), (39),
% 202.11/33.70  | |            (42), (43), (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 202.11/33.70  | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (65), (66),
% 202.11/33.70  | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 202.11/33.70  | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (90),
% 202.11/33.70  | |            (91), (92), (93), (94), (95), (96), (97), (98), (100), (101),
% 202.11/33.70  | |            (102), (103), (104), (105), (106), (108), (109), (110), (111),
% 202.11/33.70  | |            (112), (113), (114), (115), (116), (118), (121), (122), (123),
% 202.11/33.70  | |            (124), (125), (126), (127), (138) are inconsistent by sub-proof
% 202.11/33.70  | |            #339.
% 202.11/33.70  | | 
% 202.11/33.70  | End of split
% 202.11/33.70  | 
% 202.11/33.70  End of proof
% 202.11/33.70  
% 202.11/33.70  Sub-proof #339 shows that the following formulas are inconsistent:
% 202.11/33.70  ----------------------------------------------------------------
% 202.11/33.70    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.70    (2)   ~ (all_52_25 = all_52_27)
% 202.11/33.70    (3)  all_58_14 = all_52_23
% 202.11/33.70    (4)   ~ (e3 = e1)
% 202.11/33.70    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.70    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.70    (7)  all_58_1 = all_52_9
% 202.11/33.70    (8)   ~ (e3 = e0)
% 202.11/33.70    (9)  op(all_52_23, all_52_23) = e0
% 202.11/33.70    (10)  op(e2, e3) = all_52_3
% 202.11/33.70    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.70    (12)   ~ (all_52_7 = all_52_15)
% 202.11/33.70    (13)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.70    (14)   ~ (all_52_17 = all_52_25)
% 202.11/33.70    (15)   ~ (all_52_3 = all_6_2)
% 202.11/33.70    (16)  all_44_2 = all_6_2
% 202.11/33.70    (17)  all_58_0 = all_6_2
% 202.11/33.70    (18)  all_56_4 = all_52_3
% 202.11/33.70    (19)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.70    (20)  op(e3, e0) = all_52_25
% 202.11/33.70    (21)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.70    (22)  all_58_13 = all_52_15
% 202.11/33.70    (23)  all_58_9 = all_52_25
% 202.11/33.70    (24)   ~ (all_52_29 = all_14_2)
% 202.11/33.70    (25)   ~ (all_52_15 = e3)
% 202.11/33.70    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.70    (27)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.70    (28)  op(e1, e3) = all_52_5
% 202.11/33.70    (29)  op(e2, e2) = all_4_2
% 202.11/33.70    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.70    (31)  all_58_11 = all_52_29
% 202.11/33.70    (32)  op(all_10_2, e1) = all_10_1
% 202.11/33.70    (33)   ~ (all_52_7 = all_6_2)
% 202.11/33.70    (34)  op(e0, e0) = all_14_2
% 202.11/33.70    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.70    (36)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.70    (37)   ~ (e2 = e1)
% 202.11/33.70    (38)   ~ (all_52_13 = all_10_2)
% 202.11/33.70    (39)  op(all_10_2, all_10_2) = e1
% 202.11/33.70    (40)  all_58_10 = all_52_27
% 202.11/33.70    (41)  all_56_8 = all_52_5
% 202.11/33.70    (42)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.70    (43)   ~ (all_52_19 = all_52_23)
% 202.11/33.70    (44)   ~ (all_52_25 = all_52_29)
% 202.11/33.70    (45)   ~ (all_52_29 = all_10_2)
% 202.11/33.70    (46)  all_58_7 = all_52_13
% 202.11/33.70    (47)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.70    (48)  op(all_52_19, all_52_19) = e2
% 202.11/33.70    (49)   ~ (all_52_5 = all_52_7)
% 202.11/33.70    (50)  all_58_12 = all_52_7
% 202.11/33.70    (51)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.70    (52)   ~ (all_52_7 = all_14_2)
% 202.11/33.70    (53)  all_58_2 = all_52_3
% 202.11/33.70    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.70    (55)  all_56_2 = all_52_17
% 202.11/33.70    (56)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.70    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.11/33.70    (58)  all_56_7 = all_52_27
% 202.11/33.70    (59)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.70    (60)   ~ (e2 = e0)
% 202.11/33.70    (61)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.70    (62)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.70    (63)  all_56_6 = all_52_19
% 202.11/33.70    (64)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.70    (65)   ~ (all_52_13 = all_4_2)
% 202.11/33.70    (66)  op(e3, e1) = all_52_17
% 202.11/33.70    (67)  op(e0, e3) = all_52_7
% 202.11/33.70    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.70    (69)  all_58_15 = all_14_2
% 202.11/33.70    (70)   ~ (all_52_19 = all_10_2)
% 202.11/33.70    (71)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.70    (72)  all_58_8 = all_10_2
% 202.11/33.70    (73)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.70    (74)  all_56_12 = all_52_7
% 202.11/33.70    (75)  all_8_2 = all_6_2
% 202.11/33.70    (76)   ~ (all_52_25 = all_6_2)
% 202.11/33.70    (77)   ~ (all_52_9 = all_4_2)
% 202.11/33.70    (78)   ~ (all_52_5 = all_6_2)
% 202.11/33.70    (79)  op(e3, all_6_1) = e2
% 202.11/33.70    (80)  op(e3, e3) = all_6_2
% 202.11/33.70    (81)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.70    (82)   ~ (all_52_27 = all_14_2)
% 202.11/33.70    (83)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.70    (84)   ~ (all_52_3 = all_52_7)
% 202.11/33.70    (85)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.70    (86)  all_58_5 = all_52_19
% 202.11/33.70    (87)  all_56_1 = all_52_9
% 202.11/33.70    (88)   ~ (all_52_27 = all_4_2)
% 202.11/33.70    (89)  op(all_52_17, all_52_17) = e3
% 202.11/33.70    (90)  all_58_6 = all_52_5
% 202.11/33.70    (91)  op(e3, e2) = all_52_9
% 202.11/33.70    (92)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.70    (93)   ~ (all_52_17 = all_6_2)
% 202.11/33.70    (94)   ~ (e1 = e0)
% 202.11/33.70    (95)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.70    (96)  all_44_1 = all_6_1
% 202.11/33.70    (97)   ~ (all_52_9 = all_52_17)
% 202.11/33.70    (98)  all_56_10 = all_10_2
% 202.11/33.70    (99)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.70    (100)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.70    (101)  op(e1, e1) = all_10_2
% 202.11/33.70    (102)   ~ (all_52_23 = all_10_2)
% 202.11/33.70    (103)   ~ (all_52_7 = all_52_23)
% 202.11/33.70    (104)  all_58_3 = all_4_2
% 202.11/33.70    (105)   ~ (all_52_17 = all_52_23)
% 202.11/33.70    (106)  all_8_1 = all_6_1
% 202.11/33.70    (107)  op(all_6_2, e3) = all_6_1
% 202.11/33.70    (108)  all_58_4 = all_52_17
% 202.11/33.70    (109)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.70    (110)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.70    (111)   ~ (all_14_2 = e3)
% 202.11/33.70  
% 202.11/33.70  Begin of proof
% 202.11/33.70  | 
% 202.11/33.70  | BETA: splitting (92) gives:
% 202.11/33.70  | 
% 202.11/33.70  | Case 1:
% 202.11/33.70  | | 
% 202.11/33.70  | |   (112)  all_58_12 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | COMBINE_EQS: (50), (112) imply:
% 202.11/33.70  | |   (113)  all_52_7 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | SIMP: (113) implies:
% 202.11/33.70  | |   (114)  all_52_7 = e3
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (84), (114) imply:
% 202.11/33.70  | |   (115)   ~ (all_52_3 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (49), (114) imply:
% 202.11/33.70  | |   (116)   ~ (all_52_5 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (103), (114) imply:
% 202.11/33.70  | |   (117)   ~ (all_52_23 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | SIMP: (117) implies:
% 202.11/33.70  | |   (118)   ~ (all_52_23 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (52), (114) imply:
% 202.11/33.70  | |   (119)   ~ (all_14_2 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (33), (114) imply:
% 202.11/33.70  | |   (120)   ~ (all_6_2 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | SIMP: (120) implies:
% 202.11/33.70  | |   (121)   ~ (all_6_2 = e3)
% 202.11/33.70  | | 
% 202.11/33.70  | | REDUCE: (13), (114) imply:
% 202.11/33.70  | |   (122)  op(e3, e3) = all_52_6
% 202.11/33.70  | | 
% 202.11/33.70  | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 202.11/33.70  | |              with (80), (122) gives:
% 202.11/33.70  | |   (123)  all_52_6 = all_6_2
% 202.11/33.70  | | 
% 202.11/33.70  | | BETA: splitting (71) gives:
% 202.11/33.70  | | 
% 202.11/33.70  | | Case 1:
% 202.11/33.70  | | | 
% 202.11/33.70  | | |   (124)  all_56_8 = e3
% 202.11/33.70  | | | 
% 202.11/33.70  | | | REF_CLOSE: (41), (116), (124) are inconsistent by sub-proof #1325.
% 202.11/33.70  | | | 
% 202.11/33.70  | | Case 2:
% 202.11/33.70  | | | 
% 202.11/33.70  | | |   (125)   ~ (all_56_8 = e3)
% 202.11/33.70  | | |   (126)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.70  | | | 
% 202.11/33.70  | | | BETA: splitting (59) gives:
% 202.11/33.70  | | | 
% 202.11/33.70  | | | Case 1:
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | |   (127)  all_56_4 = e3
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | REF_CLOSE: (18), (115), (127) are inconsistent by sub-proof #1340.
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | Case 2:
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | |   (128)   ~ (all_56_4 = e3)
% 202.11/33.70  | | | |   (129)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | BETA: splitting (95) gives:
% 202.11/33.70  | | | | 
% 202.11/33.70  | | | | Case 1:
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | |   (130)  all_56_1 = e3
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | COMBINE_EQS: (87), (130) imply:
% 202.11/33.70  | | | | |   (131)  all_52_9 = e3
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | COMBINE_EQS: (7), (131) imply:
% 202.11/33.70  | | | | |   (132)  all_58_1 = e3
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REDUCE: (97), (131) imply:
% 202.11/33.70  | | | | |   (133)   ~ (all_52_17 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | SIMP: (133) implies:
% 202.11/33.70  | | | | |   (134)   ~ (all_52_17 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REDUCE: (77), (131) imply:
% 202.11/33.70  | | | | |   (135)   ~ (all_4_2 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | SIMP: (135) implies:
% 202.11/33.70  | | | | |   (136)   ~ (all_4_2 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REDUCE: (42), (131) imply:
% 202.11/33.70  | | | | |   (137)  op(e3, e3) = all_52_8
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 202.11/33.70  | | | | |              simplifying with (80), (137) gives:
% 202.11/33.70  | | | | |   (138)  all_52_8 = all_6_2
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REF_CLOSE: (3), (4), (6), (8), (17), (23), (26), (27), (29), (32),
% 202.11/33.70  | | | | |            (34), (35), (36), (37), (39), (40), (43), (48), (53), (55),
% 202.11/33.70  | | | | |            (56), (60), (61), (66), (70), (72), (80), (82), (86), (88),
% 202.11/33.70  | | | | |            (89), (93), (94), (98), (99), (101), (104), (108), (109),
% 202.11/33.70  | | | | |            (111), (115), (118), (132), (134), (136), (137) are
% 202.11/33.70  | | | | |            inconsistent by sub-proof #1047.
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | Case 2:
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | |   (139)   ~ (all_56_1 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | REDUCE: (87), (139) imply:
% 202.11/33.70  | | | | |   (140)   ~ (all_52_9 = e3)
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | BETA: splitting (83) gives:
% 202.11/33.70  | | | | | 
% 202.11/33.70  | | | | | Case 1:
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | |   (141)  all_58_0 = e3
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | | COMBINE_EQS: (17), (141) imply:
% 202.11/33.70  | | | | | |   (142)  all_6_2 = e3
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | | REDUCE: (121), (142) imply:
% 202.11/33.70  | | | | | |   (143)  $false
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | | CLOSE: (143) is inconsistent.
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | Case 2:
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | |   (144)   ~ (all_58_0 = e3)
% 202.11/33.70  | | | | | |   (145)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | | BETA: splitting (57) gives:
% 202.11/33.70  | | | | | | 
% 202.11/33.70  | | | | | | Case 1:
% 202.11/33.70  | | | | | | | 
% 202.11/33.70  | | | | | | |   (146)  all_58_0 = e1
% 202.11/33.70  | | | | | | | 
% 202.11/33.70  | | | | | | | COMBINE_EQS: (17), (146) imply:
% 202.11/33.70  | | | | | | |   (147)  all_6_2 = e1
% 202.11/33.70  | | | | | | | 
% 202.11/33.70  | | | | | | | COMBINE_EQS: (16), (147) imply:
% 202.11/33.70  | | | | | | |   (148)  all_44_2 = e1
% 202.11/33.70  | | | | | | | 
% 202.11/33.70  | | | | | | | REDUCE: (78), (147) imply:
% 202.11/33.70  | | | | | | |   (149)   ~ (all_52_5 = e1)
% 202.11/33.70  | | | | | | | 
% 202.11/33.70  | | | | | | | REDUCE: (93), (147) imply:
% 202.11/33.70  | | | | | | |   (150)   ~ (all_52_17 = e1)
% 202.11/33.70  | | | | | | | 
% 202.11/33.70  | | | | | | | REDUCE: (107), (147) imply:
% 202.11/33.71  | | | | | | |   (151)  op(e1, e3) = all_6_1
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | | BETA: splitting (19) gives:
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | |   (152)   ~ (all_44_2 = e1)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | REDUCE: (148), (152) imply:
% 202.11/33.71  | | | | | | | |   (153)  $false
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | CLOSE: (153) is inconsistent.
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | |   (154)   ~ (all_44_1 = e0)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | REDUCE: (96), (154) imply:
% 202.11/33.71  | | | | | | | |   (155)   ~ (all_6_1 = e0)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 202.11/33.71  | | | | | | | |              simplifying with (28), (151) gives:
% 202.11/33.71  | | | | | | | |   (156)  all_52_5 = all_6_1
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | COMBINE_EQS: (41), (156) imply:
% 202.11/33.71  | | | | | | | |   (157)  all_56_8 = all_6_1
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | COMBINE_EQS: (90), (156) imply:
% 202.11/33.71  | | | | | | | |   (158)  all_58_6 = all_6_1
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | REDUCE: (149), (156) imply:
% 202.11/33.71  | | | | | | | |   (159)   ~ (all_6_1 = e1)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | BETA: splitting (30) gives:
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | |   (160)  all_58_0 = e0
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | COMBINE_EQS: (146), (160) imply:
% 202.11/33.71  | | | | | | | | |   (161)  e1 = e0
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REDUCE: (94), (161) imply:
% 202.11/33.71  | | | | | | | | |   (162)  $false
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | CLOSE: (162) is inconsistent.
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | |   (163)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | BETA: splitting (126) gives:
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | |   (164)  all_56_8 = e2
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | COMBINE_EQS: (157), (164) imply:
% 202.11/33.71  | | | | | | | | | |   (165)  all_6_1 = e2
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | SIMP: (165) implies:
% 202.11/33.71  | | | | | | | | | |   (166)  all_6_1 = e2
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | REDUCE: (79), (166) imply:
% 202.11/33.71  | | | | | | | | | |   (167)  op(e3, e2) = e2
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | BETA: splitting (163) gives:
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | |   (168)  all_58_2 = e0
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | COMBINE_EQS: (53), (168) imply:
% 202.11/33.71  | | | | | | | | | | |   (169)  all_52_3 = e0
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | SIMP: (169) implies:
% 202.11/33.71  | | | | | | | | | | |   (170)  all_52_3 = e0
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | REDUCE: (5), (170) imply:
% 202.11/33.71  | | | | | | | | | | |   (171)  op(e0, e0) = all_52_2
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_14_2, all_52_2, e0, e0,
% 202.11/33.71  | | | | | | | | | | |              simplifying with (34), (171) gives:
% 202.11/33.71  | | | | | | | | | | |   (172)  all_52_2 = all_14_2
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_9, e2, e2, e3,
% 202.11/33.71  | | | | | | | | | | |              simplifying with (91), (167) gives:
% 202.11/33.71  | | | | | | | | | | |   (173)  all_52_9 = e2
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | REDUCE: (97), (173) imply:
% 202.11/33.71  | | | | | | | | | | |   (174)   ~ (all_52_17 = e2)
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | SIMP: (174) implies:
% 202.11/33.71  | | | | | | | | | | |   (175)   ~ (all_52_17 = e2)
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | REF_CLOSE: (6), (34), (36), (55), (80), (89), (111), (121),
% 202.11/33.71  | | | | | | | | | | |            (150), (175) are inconsistent by sub-proof #340.
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | |   (176)  all_58_6 = e0 | all_58_12 = e0
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | REF_CLOSE: (8), (112), (155), (158), (176) are inconsistent
% 202.11/33.71  | | | | | | | | | | |            by sub-proof #485.
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | |   (177)  all_56_8 = e1 | all_56_8 = e0
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | REF_CLOSE: (155), (157), (159), (177) are inconsistent by
% 202.11/33.71  | | | | | | | | | |            sub-proof #495.
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | End of split
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | Case 2:
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | |   (178)   ~ (all_58_0 = e1)
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | | REDUCE: (17), (178) imply:
% 202.11/33.71  | | | | | | |   (179)   ~ (all_6_2 = e1)
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | | BETA: splitting (21) gives:
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | |   (180)  all_56_7 = e3
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | COMBINE_EQS: (58), (180) imply:
% 202.11/33.71  | | | | | | | |   (181)  all_52_27 = e3
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | SIMP: (181) implies:
% 202.11/33.71  | | | | | | | |   (182)  all_52_27 = e3
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | REDUCE: (2), (182) imply:
% 202.11/33.71  | | | | | | | |   (183)   ~ (all_52_25 = e3)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | REF_CLOSE: (6), (7), (23), (80), (89), (93), (108), (140),
% 202.11/33.71  | | | | | | | |            (145), (183) are inconsistent by sub-proof #1072.
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | |   (184)   ~ (all_56_7 = e3)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | REDUCE: (58), (184) imply:
% 202.11/33.71  | | | | | | | |   (185)   ~ (all_52_27 = e3)
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | BETA: splitting (81) gives:
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | |   (186)  all_58_9 = e3
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | COMBINE_EQS: (23), (186) imply:
% 202.11/33.71  | | | | | | | | |   (187)  all_52_25 = e3
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REDUCE: (14), (187) imply:
% 202.11/33.71  | | | | | | | | |   (188)   ~ (all_52_17 = e3)
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REDUCE: (2), (187) imply:
% 202.11/33.71  | | | | | | | | |   (189)   ~ (all_52_27 = e3)
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REDUCE: (44), (187) imply:
% 202.11/33.71  | | | | | | | | |   (190)   ~ (all_52_29 = e3)
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | SIMP: (190) implies:
% 202.11/33.71  | | | | | | | | |   (191)   ~ (all_52_29 = e3)
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REDUCE: (110), (187) imply:
% 202.11/33.71  | | | | | | | | |   (192)  op(e3, e3) = all_52_24
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REDUCE: (20), (187) imply:
% 202.11/33.71  | | | | | | | | |   (193)  op(e3, e0) = e3
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 202.11/33.71  | | | | | | | | |              simplifying with (80), (192) gives:
% 202.11/33.71  | | | | | | | | |   (194)  all_52_24 = all_6_2
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | BETA: splitting (35) gives:
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | |   (195)  all_58_2 = e3
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | REF_CLOSE: (53), (115), (195) are inconsistent by sub-proof
% 202.11/33.71  | | | | | | | | | |            #1369.
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | |   (196)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | BETA: splitting (99) gives:
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | |   (197)  all_58_4 = e3
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | REF_CLOSE: (108), (188), (197) are inconsistent by sub-proof
% 202.11/33.71  | | | | | | | | | | |            #1302.
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | |   (198)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | BETA: splitting (51) gives:
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | |   (199)  all_58_6 = e3
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | REF_CLOSE: (90), (116), (199) are inconsistent by sub-proof
% 202.11/33.71  | | | | | | | | | | | |            #1328.
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | |   (200)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | BETA: splitting (54) gives:
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | |   (201)  all_56_6 = e3
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | COMBINE_EQS: (63), (201) imply:
% 202.11/33.71  | | | | | | | | | | | | |   (202)  all_52_19 = e3
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | SIMP: (202) implies:
% 202.11/33.71  | | | | | | | | | | | | |   (203)  all_52_19 = e3
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | REDUCE: (70), (203) imply:
% 202.11/33.71  | | | | | | | | | | | | |   (204)   ~ (all_10_2 = e3)
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | SIMP: (204) implies:
% 202.11/33.71  | | | | | | | | | | | | |   (205)   ~ (all_10_2 = e3)
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (10), (15), (17), (18), (30), (31),
% 202.11/33.71  | | | | | | | | | | | | |            (38), (46), (47), (48), (53), (60), (66), (72),
% 202.11/33.71  | | | | | | | | | | | | |            (79), (80), (86), (93), (100), (107), (118),
% 202.11/33.71  | | | | | | | | | | | | |            (121), (129), (191), (193), (198), (200), (205)
% 202.11/33.71  | | | | | | | | | | | | |            are inconsistent by sub-proof #440.
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | |   (206)   ~ (all_56_6 = e3)
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | REDUCE: (63), (206) imply:
% 202.11/33.71  | | | | | | | | | | | | |   (207)   ~ (all_52_19 = e3)
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | BETA: splitting (196) gives:
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | Case 1:
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | |   (208)  all_58_3 = e3
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | | COMBINE_EQS: (104), (208) imply:
% 202.11/33.71  | | | | | | | | | | | | | |   (209)  all_4_2 = e3
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | | REDUCE: (65), (209) imply:
% 202.11/33.71  | | | | | | | | | | | | | |   (210)   ~ (all_52_13 = e3)
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | | REF_CLOSE: (6), (31), (39), (46), (72), (80), (98), (109),
% 202.11/33.71  | | | | | | | | | | | | | |            (122), (179), (191), (200), (210) are inconsistent
% 202.11/33.71  | | | | | | | | | | | | | |            by sub-proof #396.
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | |   (211)  all_58_5 = e3 | all_58_10 = e3
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | | REF_CLOSE: (40), (86), (185), (207), (211) are inconsistent
% 202.11/33.71  | | | | | | | | | | | | | |            by sub-proof #1132.
% 202.11/33.71  | | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | Case 2:
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | |   (212)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (17), (23), (24), (26),
% 202.11/33.71  | | | | | | | | |            (31), (34), (37), (40), (42), (43), (44), (45),
% 202.11/33.71  | | | | | | | | |            (48), (56), (60), (61), (68), (69), (70), (72),
% 202.11/33.71  | | | | | | | | |            (73), (80), (86), (89), (93), (94), (97), (99),
% 202.11/33.71  | | | | | | | | |            (101), (108), (111), (118), (145), (185), (212) are
% 202.11/33.71  | | | | | | | | |            inconsistent by sub-proof #443.
% 202.11/33.71  | | | | | | | | | 
% 202.11/33.71  | | | | | | | | End of split
% 202.11/33.71  | | | | | | | | 
% 202.11/33.71  | | | | | | | End of split
% 202.11/33.71  | | | | | | | 
% 202.11/33.71  | | | | | | End of split
% 202.11/33.71  | | | | | | 
% 202.11/33.71  | | | | | End of split
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | End of split
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | End of split
% 202.11/33.71  | | | 
% 202.11/33.71  | | End of split
% 202.11/33.71  | | 
% 202.11/33.71  | Case 2:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (213)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (11), (12), (22), (25), (33), (36),
% 202.11/33.71  | |            (50), (55), (62), (64), (67), (69), (74), (75), (79), (80), (85),
% 202.11/33.71  | |            (89), (91), (93), (94), (97), (101), (102), (103), (105), (106),
% 202.11/33.71  | |            (107), (111), (213) are inconsistent by sub-proof #437.
% 202.11/33.71  | | 
% 202.11/33.71  | End of split
% 202.11/33.71  | 
% 202.11/33.71  End of proof
% 202.11/33.71  
% 202.11/33.71  Sub-proof #340 shows that the following formulas are inconsistent:
% 202.11/33.71  ----------------------------------------------------------------
% 202.11/33.71    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.71    (2)  op(e0, e0) = all_14_2
% 202.11/33.71    (3)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.71    (4)   ~ (all_6_2 = e3)
% 202.11/33.71    (5)  all_56_2 = all_52_17
% 202.11/33.71    (6)  op(e3, e3) = all_6_2
% 202.11/33.71    (7)  op(all_52_17, all_52_17) = e3
% 202.11/33.71    (8)   ~ (all_52_17 = e1)
% 202.11/33.71    (9)   ~ (all_52_17 = e2)
% 202.11/33.71    (10)   ~ (all_14_2 = e3)
% 202.11/33.71  
% 202.11/33.71  Begin of proof
% 202.11/33.71  | 
% 202.11/33.71  | BETA: splitting (3) gives:
% 202.11/33.71  | 
% 202.11/33.71  | Case 1:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (11)  all_56_2 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | REF_CLOSE: (1), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 202.11/33.71  | |            #1265.
% 202.11/33.71  | | 
% 202.11/33.71  | Case 2:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (12)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.71  | | 
% 202.11/33.71  | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (12) are inconsistent by
% 202.11/33.71  | |            sub-proof #1068.
% 202.11/33.71  | | 
% 202.11/33.71  | End of split
% 202.11/33.71  | 
% 202.11/33.71  End of proof
% 202.11/33.71  
% 202.11/33.71  Sub-proof #341 shows that the following formulas are inconsistent:
% 202.11/33.71  ----------------------------------------------------------------
% 202.11/33.71    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.71    (2)  all_58_1 = all_52_9
% 202.11/33.71    (3)   ~ (all_52_9 = all_52_13)
% 202.11/33.71    (4)   ~ (e3 = e0)
% 202.11/33.71    (5)  all_58_0 = all_6_2
% 202.11/33.71    (6)  all_26_1 = all_10_1
% 202.11/33.71    (7)  all_26_2 = all_10_2
% 202.11/33.71    (8)  all_58_13 = all_52_15
% 202.11/33.71    (9)  all_58_9 = all_52_25
% 202.11/33.71    (10)  op(e2, e2) = all_4_2
% 202.11/33.71    (11)  all_58_11 = all_52_29
% 202.11/33.71    (12)   ~ (all_52_9 = all_52_15)
% 202.11/33.71    (13)  op(all_10_2, e1) = all_10_1
% 202.11/33.71    (14)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 202.11/33.71    (15)   ~ (all_6_2 = e3)
% 202.11/33.71    (16)   ~ (e2 = e1)
% 202.11/33.71    (17)   ~ (all_52_13 = all_10_2)
% 202.11/33.71    (18)  op(all_10_2, all_10_2) = e1
% 202.11/33.71    (19)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.71    (20)  all_58_7 = all_52_13
% 202.11/33.71    (21)  all_58_12 = all_52_7
% 202.11/33.71    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.71    (23)   ~ (all_52_7 = e3)
% 202.11/33.71    (24)  all_58_2 = all_52_3
% 202.11/33.71    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.71    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.71    (27)   ~ (all_52_29 = e3)
% 202.11/33.71    (28)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.71    (29)  all_58_9 = all_14_1
% 202.11/33.71    (30)   ~ (all_52_25 = e3)
% 202.11/33.71    (31)   ~ (e2 = e0)
% 202.11/33.71    (32)   ~ (all_52_5 = e3)
% 202.11/33.71    (33)  op(e3, e1) = all_52_17
% 202.11/33.71    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.71    (35)  all_58_8 = all_10_2
% 202.11/33.71    (36)   ~ (all_52_5 = all_10_2)
% 202.11/33.71    (37)   ~ (all_52_9 = all_4_2)
% 202.11/33.71    (38)  op(e3, e3) = all_52_2
% 202.11/33.71    (39)   ~ (all_52_9 = all_6_2)
% 202.11/33.71    (40)  op(e3, e3) = all_6_2
% 202.11/33.71    (41)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.71    (42)  op(all_52_17, all_52_17) = e3
% 202.11/33.71    (43)  all_58_6 = all_52_5
% 202.11/33.71    (44)   ~ (all_52_17 = all_6_2)
% 202.11/33.71    (45)   ~ (e1 = e0)
% 202.11/33.71    (46)   ~ (e3 = e2)
% 202.11/33.71    (47)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.71    (48)  all_58_3 = all_4_2
% 202.11/33.71    (49)   ~ (all_52_3 = all_4_2)
% 202.11/33.71    (50)  all_58_4 = all_52_17
% 202.11/33.71  
% 202.11/33.71  Begin of proof
% 202.11/33.71  | 
% 202.11/33.71  | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3, simplifying
% 202.11/33.71  |              with (38), (40) gives:
% 202.11/33.71  |   (51)  all_52_2 = all_6_2
% 202.11/33.71  | 
% 202.11/33.71  | BETA: splitting (47) gives:
% 202.11/33.71  | 
% 202.11/33.71  | Case 1:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (52)  all_58_4 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | COMBINE_EQS: (50), (52) imply:
% 202.11/33.71  | |   (53)  all_52_17 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | SIMP: (53) implies:
% 202.11/33.71  | |   (54)  all_52_17 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | REF_CLOSE: (1), (40), (42), (44), (54) are inconsistent by sub-proof #1280.
% 202.11/33.71  | | 
% 202.11/33.71  | Case 2:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (55)   ~ (all_58_4 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (50), (55) imply:
% 202.11/33.71  | |   (56)   ~ (all_52_17 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.11/33.71  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.11/33.71  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.11/33.71  | |            (35), (36), (37), (39), (40), (41), (42), (43), (45), (46), (48),
% 202.11/33.71  | |            (49), (50), (56) are inconsistent by sub-proof #636.
% 202.11/33.71  | | 
% 202.11/33.71  | End of split
% 202.11/33.71  | 
% 202.11/33.71  End of proof
% 202.11/33.71  
% 202.11/33.71  Sub-proof #342 shows that the following formulas are inconsistent:
% 202.11/33.71  ----------------------------------------------------------------
% 202.11/33.71    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.71    (2)   ~ (all_52_25 = all_52_27)
% 202.11/33.71    (3)  all_58_14 = all_52_23
% 202.11/33.71    (4)   ~ (e3 = e1)
% 202.11/33.71    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.71    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.71    (7)  all_58_1 = all_52_9
% 202.11/33.71    (8)   ~ (e3 = e0)
% 202.11/33.71    (9)  op(all_52_23, all_52_23) = e0
% 202.11/33.71    (10)  op(e2, e3) = all_52_3
% 202.11/33.71    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.71    (12)   ~ (all_52_7 = all_52_15)
% 202.11/33.71    (13)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.71    (14)   ~ (all_52_17 = all_52_25)
% 202.11/33.71    (15)   ~ (all_52_3 = all_6_2)
% 202.11/33.71    (16)  all_44_2 = all_6_2
% 202.11/33.71    (17)  all_58_0 = all_6_2
% 202.11/33.71    (18)  all_56_4 = all_52_3
% 202.11/33.71    (19)   ~ (all_52_17 = all_10_2)
% 202.11/33.71    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.71    (21)  op(e3, e0) = all_52_25
% 202.11/33.71    (22)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.71    (23)  all_58_13 = all_52_15
% 202.11/33.71    (24)  all_58_9 = all_52_25
% 202.11/33.71    (25)   ~ (all_52_15 = e3)
% 202.11/33.71    (26)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.71    (27)  op(e1, e3) = all_52_5
% 202.11/33.71    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.71    (29)   ~ (all_52_3 = all_52_5)
% 202.11/33.71    (30)  all_58_11 = all_52_29
% 202.11/33.71    (31)  op(all_10_2, e1) = all_10_1
% 202.11/33.71    (32)   ~ (all_52_7 = all_6_2)
% 202.11/33.71    (33)  all_58_15 = e0
% 202.11/33.71    (34)  all_56_11 = all_52_29
% 202.11/33.71    (35)   ~ (all_52_25 = e0)
% 202.11/33.71    (36)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.71    (37)  op(e0, e0) = e0
% 202.11/33.71    (38)  op(all_10_2, all_10_2) = e1
% 202.11/33.71    (39)  all_58_10 = all_52_27
% 202.11/33.71    (40)  all_56_8 = all_52_5
% 202.11/33.71    (41)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.71    (42)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.71    (43)   ~ (all_52_25 = all_52_29)
% 202.11/33.71    (44)   ~ (all_52_29 = all_10_2)
% 202.11/33.71    (45)  all_58_7 = all_52_13
% 202.11/33.71    (46)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.71    (47)  op(all_52_19, all_52_19) = e2
% 202.11/33.71    (48)   ~ (all_52_5 = all_52_7)
% 202.11/33.71    (49)  all_58_12 = all_52_7
% 202.11/33.71    (50)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.71    (51)  all_58_2 = all_52_3
% 202.11/33.71    (52)  all_56_2 = all_52_17
% 202.11/33.71    (53)  all_56_7 = all_52_27
% 202.11/33.71    (54)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.71    (55)   ~ (e2 = e0)
% 202.11/33.71    (56)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.71    (57)   ~ (all_52_5 = all_52_29)
% 202.11/33.71    (58)   ~ (all_52_29 = e0)
% 202.11/33.71    (59)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.71    (60)   ~ (all_52_19 = all_52_27)
% 202.11/33.71    (61)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.71    (62)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.11/33.71    (63)  op(e3, e1) = all_52_17
% 202.11/33.71    (64)  op(e0, e3) = all_52_7
% 202.11/33.71    (65)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.71    (66)  all_58_15 = all_14_2
% 202.11/33.71    (67)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.71    (68)  all_58_8 = all_10_2
% 202.11/33.71    (69)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.71    (70)  all_56_12 = all_52_7
% 202.11/33.71    (71)  all_8_2 = all_6_2
% 202.11/33.71    (72)   ~ (all_52_25 = all_6_2)
% 202.11/33.71    (73)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.71    (74)   ~ (all_52_5 = all_6_2)
% 202.11/33.71    (75)   ~ (all_52_9 = all_6_2)
% 202.11/33.71    (76)  op(e3, all_6_1) = e2
% 202.11/33.71    (77)  all_56_0 = all_6_2
% 202.11/33.71    (78)  op(e3, e3) = all_6_2
% 202.11/33.71    (79)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.71    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.71    (81)  all_56_3 = all_52_25
% 202.11/33.71    (82)   ~ (all_52_3 = all_52_7)
% 202.11/33.71    (83)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.71    (84)  all_58_5 = all_52_19
% 202.11/33.71    (85)  op(all_52_17, all_52_17) = e3
% 202.11/33.71    (86)  all_58_6 = all_52_5
% 202.11/33.71    (87)  op(e3, e2) = all_52_9
% 202.11/33.71    (88)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.71    (89)   ~ (all_52_17 = all_6_2)
% 202.11/33.71    (90)   ~ (e1 = e0)
% 202.11/33.71    (91)  all_44_1 = all_6_1
% 202.11/33.71    (92)   ~ (all_52_9 = all_52_17)
% 202.11/33.71    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.71    (94)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.71    (95)  op(e1, e1) = all_10_2
% 202.11/33.71    (96)   ~ (all_52_23 = all_10_2)
% 202.11/33.71    (97)   ~ (all_52_7 = all_52_23)
% 202.11/33.71    (98)  all_58_3 = all_4_2
% 202.11/33.71    (99)  all_56_13 = all_52_15
% 202.11/33.71    (100)   ~ (all_52_19 = all_4_2)
% 202.11/33.71    (101)   ~ (all_52_17 = all_52_23)
% 202.11/33.71    (102)  all_8_1 = all_6_1
% 202.11/33.71    (103)  op(all_6_2, e3) = all_6_1
% 202.11/33.71    (104)   ~ (all_52_13 = all_52_29)
% 202.11/33.71    (105)  all_58_4 = all_52_17
% 202.11/33.71    (106)   ~ (all_52_7 = e0)
% 202.11/33.71    (107)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.71  
% 202.11/33.71  Begin of proof
% 202.11/33.71  | 
% 202.11/33.71  | BETA: splitting (88) gives:
% 202.11/33.71  | 
% 202.11/33.71  | Case 1:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (108)  all_58_12 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | COMBINE_EQS: (49), (108) imply:
% 202.11/33.71  | |   (109)  all_52_7 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | SIMP: (109) implies:
% 202.11/33.71  | |   (110)  all_52_7 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (82), (110) imply:
% 202.11/33.71  | |   (111)   ~ (all_52_3 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (48), (110) imply:
% 202.11/33.71  | |   (112)   ~ (all_52_5 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (12), (110) imply:
% 202.11/33.71  | |   (113)   ~ (all_52_15 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (97), (110) imply:
% 202.11/33.71  | |   (114)   ~ (all_52_23 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | SIMP: (114) implies:
% 202.11/33.71  | |   (115)   ~ (all_52_23 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (32), (110) imply:
% 202.11/33.71  | |   (116)   ~ (all_6_2 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | SIMP: (116) implies:
% 202.11/33.71  | |   (117)   ~ (all_6_2 = e3)
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (13), (110) imply:
% 202.11/33.71  | |   (118)  op(e3, e3) = all_52_6
% 202.11/33.71  | | 
% 202.11/33.71  | | REDUCE: (64), (110) imply:
% 202.11/33.71  | |   (119)  op(e0, e3) = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 202.11/33.71  | |              with (78), (118) gives:
% 202.11/33.71  | |   (120)  all_52_6 = all_6_2
% 202.11/33.71  | | 
% 202.11/33.71  | | BETA: splitting (22) gives:
% 202.11/33.71  | | 
% 202.11/33.71  | | Case 1:
% 202.11/33.71  | | | 
% 202.11/33.71  | | |   (121)  all_56_7 = e3
% 202.11/33.71  | | | 
% 202.11/33.71  | | | COMBINE_EQS: (53), (121) imply:
% 202.11/33.71  | | |   (122)  all_52_27 = e3
% 202.11/33.71  | | | 
% 202.11/33.71  | | | SIMP: (122) implies:
% 202.11/33.71  | | |   (123)  all_52_27 = e3
% 202.11/33.71  | | | 
% 202.11/33.71  | | | REDUCE: (60), (123) imply:
% 202.11/33.71  | | |   (124)   ~ (all_52_19 = e3)
% 202.11/33.71  | | | 
% 202.11/33.71  | | | REDUCE: (2), (123) imply:
% 202.11/33.71  | | |   (125)   ~ (all_52_25 = e3)
% 202.11/33.71  | | | 
% 202.11/33.71  | | | REDUCE: (26), (123) imply:
% 202.11/33.71  | | |   (126)  op(e3, e3) = all_52_26
% 202.11/33.71  | | | 
% 202.11/33.71  | | | REF_CLOSE: (3), (6), (7), (14), (17), (19), (24), (31), (35), (36), (37),
% 202.11/33.71  | | |            (38), (41), (52), (63), (68), (72), (73), (78), (80), (81),
% 202.11/33.71  | | |            (84), (85), (89), (93), (105), (115), (117), (124), (125),
% 202.11/33.71  | | |            (126) are inconsistent by sub-proof #1275.
% 202.11/33.71  | | | 
% 202.11/33.71  | | Case 2:
% 202.11/33.71  | | | 
% 202.11/33.71  | | |   (127)   ~ (all_56_7 = e3)
% 202.11/33.71  | | | 
% 202.11/33.71  | | | REDUCE: (53), (127) imply:
% 202.11/33.71  | | |   (128)   ~ (all_52_27 = e3)
% 202.11/33.71  | | | 
% 202.11/33.71  | | | BETA: splitting (79) gives:
% 202.11/33.71  | | | 
% 202.11/33.71  | | | Case 1:
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | |   (129)  all_58_9 = e3
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | COMBINE_EQS: (24), (129) imply:
% 202.11/33.71  | | | |   (130)  all_52_25 = e3
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | REDUCE: (14), (130) imply:
% 202.11/33.71  | | | |   (131)   ~ (all_52_17 = e3)
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | REDUCE: (43), (130) imply:
% 202.11/33.71  | | | |   (132)   ~ (all_52_29 = e3)
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | SIMP: (132) implies:
% 202.11/33.71  | | | |   (133)   ~ (all_52_29 = e3)
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | REDUCE: (107), (130) imply:
% 202.11/33.71  | | | |   (134)  op(e3, e3) = all_52_24
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | REDUCE: (21), (130) imply:
% 202.11/33.71  | | | |   (135)  op(e3, e0) = e3
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 202.11/33.71  | | | |              simplifying with (78), (134) gives:
% 202.11/33.71  | | | |   (136)  all_52_24 = all_6_2
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | BETA: splitting (61) gives:
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | Case 1:
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | |   (137)  all_56_11 = e3
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | | REF_CLOSE: (34), (133), (137) are inconsistent by sub-proof #1028.
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | Case 2:
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | |   (138)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | | REF_CLOSE: (1), (5), (6), (8), (10), (15), (16), (17), (18), (20),
% 202.11/33.71  | | | | |            (27), (28), (29), (34), (36), (37), (40), (46), (51), (52),
% 202.11/33.71  | | | | |            (54), (55), (56), (57), (58), (62), (63), (67), (71), (74),
% 202.11/33.71  | | | | |            (76), (77), (78), (85), (86), (87), (89), (90), (91), (92),
% 202.11/33.71  | | | | |            (94), (103), (108), (111), (112), (117), (118), (119),
% 202.11/33.71  | | | | |            (131), (135), (138) are inconsistent by sub-proof #484.
% 202.11/33.71  | | | | | 
% 202.11/33.71  | | | | End of split
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | Case 2:
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | |   (139)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | | REF_CLOSE: (3), (6), (7), (8), (14), (23), (25), (30), (33), (35), (36),
% 202.11/33.71  | | | |            (37), (39), (41), (43), (44), (45), (47), (52), (65), (68),
% 202.11/33.71  | | | |            (69), (72), (73), (75), (78), (81), (84), (85), (89), (93),
% 202.11/33.71  | | | |            (98), (100), (104), (105), (115), (128), (139) are
% 202.11/33.71  | | | |            inconsistent by sub-proof #1252.
% 202.11/33.71  | | | | 
% 202.11/33.71  | | | End of split
% 202.11/33.71  | | | 
% 202.11/33.71  | | End of split
% 202.11/33.71  | | 
% 202.11/33.71  | Case 2:
% 202.11/33.71  | | 
% 202.11/33.71  | |   (140)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.71  | | 
% 202.11/33.71  | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (11), (12), (23), (25), (32), (33),
% 202.11/33.71  | |            (36), (42), (49), (50), (52), (59), (64), (66), (70), (71), (76),
% 202.11/33.71  | |            (78), (83), (85), (87), (89), (90), (92), (95), (96), (97), (99),
% 202.11/33.71  | |            (101), (102), (103), (140) are inconsistent by sub-proof #478.
% 202.11/33.71  | | 
% 202.11/33.71  | End of split
% 202.11/33.71  | 
% 202.11/33.71  End of proof
% 202.11/33.71  
% 202.11/33.71  Sub-proof #343 shows that the following formulas are inconsistent:
% 202.11/33.71  ----------------------------------------------------------------
% 202.11/33.71    (1)   ~ (all_52_25 = all_52_27)
% 202.11/33.71    (2)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.71    (4)  all_58_1 = all_52_9
% 202.11/33.71    (5)   ~ (e3 = e0)
% 202.11/33.71    (6)  op(e2, e3) = all_52_3
% 202.11/33.71    (7)   ~ (all_52_3 = all_52_19)
% 202.11/33.71    (8)   ~ (all_4_2 = e3)
% 202.11/33.71    (9)   ~ (all_52_3 = all_6_2)
% 202.11/33.71    (10)  all_58_0 = all_6_2
% 202.11/33.71    (11)  all_56_4 = all_52_3
% 202.11/33.71    (12)  all_26_1 = all_10_1
% 202.11/33.71    (13)  op(e3, e0) = all_52_25
% 202.11/33.71    (14)  all_26_2 = all_10_2
% 202.11/33.71    (15)  all_58_9 = all_52_25
% 202.11/33.71    (16)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.71    (17)  op(e2, e2) = all_4_2
% 202.11/33.71    (18)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.71    (19)   ~ (all_52_3 = all_52_5)
% 202.11/33.72    (20)  all_58_11 = all_52_29
% 202.11/33.72    (21)  op(all_10_2, e1) = all_10_1
% 202.11/33.72    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.72    (23)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 202.11/33.72    (24)   ~ (e2 = e1)
% 202.11/33.72    (25)   ~ (all_52_13 = all_10_2)
% 202.11/33.72    (26)  op(all_10_2, all_10_2) = e1
% 202.11/33.72    (27)  all_58_10 = all_52_27
% 202.11/33.72    (28)   ~ (all_52_25 = all_52_29)
% 202.11/33.72    (29)  all_58_7 = all_52_13
% 202.11/33.72    (30)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.72    (31)  op(all_52_19, all_52_19) = e2
% 202.11/33.72    (32)   ~ (all_52_5 = all_52_7)
% 202.11/33.72    (33)  all_58_12 = all_52_7
% 202.11/33.72    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.72    (35)  all_58_2 = all_52_3
% 202.11/33.72    (36)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.72    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.72    (38)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.72    (39)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.72    (40)   ~ (e2 = e0)
% 202.11/33.72    (41)   ~ (all_52_9 = e3)
% 202.11/33.72    (42)  op(e3, e1) = all_52_17
% 202.11/33.72    (43)   ~ (all_52_9 = all_52_25)
% 202.11/33.72    (44)   ~ (all_52_19 = all_10_2)
% 202.11/33.72    (45)  all_58_8 = all_10_2
% 202.11/33.72    (46)   ~ (all_52_5 = all_6_2)
% 202.11/33.72    (47)  op(e3, all_6_1) = e2
% 202.11/33.72    (48)  op(e3, e3) = all_6_2
% 202.11/33.72    (49)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.72    (50)   ~ (all_52_13 = e3)
% 202.11/33.72    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.72    (52)   ~ (all_52_3 = all_52_7)
% 202.11/33.72    (53)  all_58_5 = all_52_19
% 202.11/33.72    (54)  op(all_52_17, all_52_17) = e3
% 202.11/33.72    (55)  all_58_6 = all_52_5
% 202.11/33.72    (56)   ~ (all_52_17 = all_6_2)
% 202.11/33.72    (57)   ~ (e1 = e0)
% 202.11/33.72    (58)   ~ (e3 = e2)
% 202.11/33.72    (59)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.72    (60)   ~ (all_52_17 = all_52_19)
% 202.11/33.72    (61)  all_58_3 = all_4_2
% 202.11/33.72    (62)   ~ (all_52_3 = all_4_2)
% 202.11/33.72    (63)  op(all_6_2, e3) = all_6_1
% 202.11/33.72    (64)  all_58_4 = all_52_17
% 202.11/33.72    (65)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.72  
% 202.11/33.72  Begin of proof
% 202.11/33.72  | 
% 202.11/33.72  | BETA: splitting (49) gives:
% 202.11/33.72  | 
% 202.11/33.72  | Case 1:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (66)  all_58_9 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | COMBINE_EQS: (15), (66) imply:
% 202.11/33.72  | |   (67)  all_52_25 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (1), (67) imply:
% 202.11/33.72  | |   (68)   ~ (all_52_27 = e3)
% 202.11/33.72  | | 
% 202.11/33.72  | | SIMP: (68) implies:
% 202.11/33.72  | |   (69)   ~ (all_52_27 = e3)
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (28), (67) imply:
% 202.11/33.72  | |   (70)   ~ (all_52_29 = e3)
% 202.11/33.72  | | 
% 202.11/33.72  | | SIMP: (70) implies:
% 202.11/33.72  | |   (71)   ~ (all_52_29 = e3)
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (65), (67) imply:
% 202.11/33.72  | |   (72)  op(e3, e3) = all_52_24
% 202.11/33.72  | | 
% 202.11/33.72  | | GROUND_INST: instantiating (3) with all_6_2, all_52_24, e3, e3, simplifying
% 202.11/33.72  | |              with (48), (72) gives:
% 202.11/33.72  | |   (73)  all_52_24 = all_6_2
% 202.11/33.72  | | 
% 202.11/33.72  | | BETA: splitting (34) gives:
% 202.11/33.72  | | 
% 202.11/33.72  | | Case 1:
% 202.11/33.72  | | | 
% 202.11/33.72  | | |   (74)  all_58_6 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (13), (15), (18),
% 202.11/33.72  | | |            (19), (22), (27), (30), (31), (32), (33), (35), (37), (39),
% 202.11/33.72  | | |            (40), (41), (42), (46), (47), (48), (51), (53), (55), (56),
% 202.11/33.72  | | |            (58), (60), (61), (63), (64), (69), (74) are inconsistent by
% 202.11/33.72  | | |            sub-proof #345.
% 202.11/33.72  | | | 
% 202.11/33.72  | | Case 2:
% 202.11/33.72  | | | 
% 202.11/33.72  | | |   (75)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (12), (14), (15),
% 202.11/33.72  | | |            (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 202.11/33.72  | | |            (27), (28), (29), (33), (35), (36), (37), (38), (40), (41),
% 202.11/33.72  | | |            (42), (44), (45), (47), (48), (50), (51), (52), (53), (54),
% 202.11/33.72  | | |            (55), (56), (57), (58), (59), (61), (62), (63), (64), (66),
% 202.11/33.72  | | |            (71), (75) are inconsistent by sub-proof #344.
% 202.11/33.72  | | | 
% 202.11/33.72  | | End of split
% 202.11/33.72  | | 
% 202.11/33.72  | Case 2:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (76)   ~ (all_58_9 = e3)
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (15), (76) imply:
% 202.11/33.72  | |   (77)   ~ (all_52_25 = e3)
% 202.11/33.72  | | 
% 202.11/33.72  | | REF_CLOSE: (3), (4), (10), (15), (41), (47), (48), (51), (54), (56), (58),
% 202.11/33.72  | |            (59), (63), (64), (77) are inconsistent by sub-proof #446.
% 202.11/33.72  | | 
% 202.11/33.72  | End of split
% 202.11/33.72  | 
% 202.11/33.72  End of proof
% 202.11/33.72  
% 202.11/33.72  Sub-proof #344 shows that the following formulas are inconsistent:
% 202.11/33.72  ----------------------------------------------------------------
% 202.11/33.72    (1)   ~ (all_52_25 = all_52_27)
% 202.11/33.72    (2)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.72    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.72    (4)  all_58_1 = all_52_9
% 202.11/33.72    (5)   ~ (e3 = e0)
% 202.11/33.72    (6)  all_58_9 = e3
% 202.11/33.72    (7)   ~ (all_4_2 = e3)
% 202.11/33.72    (8)   ~ (all_52_3 = all_6_2)
% 202.11/33.72    (9)  all_58_0 = all_6_2
% 202.11/33.72    (10)  all_26_1 = all_10_1
% 202.11/33.72    (11)  all_26_2 = all_10_2
% 202.11/33.72    (12)  all_58_9 = all_52_25
% 202.11/33.72    (13)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.72    (14)  op(e2, e2) = all_4_2
% 202.11/33.72    (15)   ~ (all_52_3 = all_52_5)
% 202.11/33.72    (16)  all_58_11 = all_52_29
% 202.11/33.72    (17)  op(all_10_2, e1) = all_10_1
% 202.11/33.72    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.72    (19)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 202.11/33.72    (20)   ~ (e2 = e1)
% 202.11/33.72    (21)   ~ (all_52_13 = all_10_2)
% 202.11/33.72    (22)  op(all_10_2, all_10_2) = e1
% 202.11/33.72    (23)  all_58_10 = all_52_27
% 202.11/33.72    (24)   ~ (all_52_25 = all_52_29)
% 202.11/33.72    (25)  all_58_7 = all_52_13
% 202.11/33.72    (26)  all_58_12 = all_52_7
% 202.11/33.72    (27)  all_58_2 = all_52_3
% 202.11/33.72    (28)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.72    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.72    (30)   ~ (all_52_29 = e3)
% 202.11/33.72    (31)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.72    (32)   ~ (e2 = e0)
% 202.11/33.72    (33)   ~ (all_52_9 = e3)
% 202.11/33.72    (34)  op(e3, e1) = all_52_17
% 202.11/33.72    (35)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.72    (36)   ~ (all_52_19 = all_10_2)
% 202.11/33.72    (37)  all_58_8 = all_10_2
% 202.11/33.72    (38)  op(e3, all_6_1) = e2
% 202.11/33.72    (39)  op(e3, e3) = all_6_2
% 202.11/33.72    (40)   ~ (all_52_13 = e3)
% 202.11/33.72    (41)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.72    (42)   ~ (all_52_3 = all_52_7)
% 202.11/33.72    (43)  all_58_5 = all_52_19
% 202.11/33.72    (44)  op(all_52_17, all_52_17) = e3
% 202.11/33.72    (45)  all_58_6 = all_52_5
% 202.11/33.72    (46)   ~ (all_52_17 = all_6_2)
% 202.11/33.72    (47)   ~ (e1 = e0)
% 202.11/33.72    (48)   ~ (e3 = e2)
% 202.11/33.72    (49)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.72    (50)  all_58_3 = all_4_2
% 202.11/33.72    (51)   ~ (all_52_3 = all_4_2)
% 202.11/33.72    (52)  op(all_6_2, e3) = all_6_1
% 202.11/33.72    (53)  all_58_4 = all_52_17
% 202.11/33.72  
% 202.11/33.72  Begin of proof
% 202.11/33.72  | 
% 202.11/33.72  | BETA: splitting (35) gives:
% 202.11/33.72  | 
% 202.11/33.72  | Case 1:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (54)  all_58_7 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | COMBINE_EQS: (25), (54) imply:
% 202.11/33.72  | |   (55)  all_52_13 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (40), (55) imply:
% 202.11/33.72  | |   (56)  $false
% 202.11/33.72  | | 
% 202.11/33.72  | | CLOSE: (56) is inconsistent.
% 202.11/33.72  | | 
% 202.11/33.72  | Case 2:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (57)  all_58_8 = e3 | all_58_11 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | BETA: splitting (57) gives:
% 202.11/33.72  | | 
% 202.11/33.72  | | Case 1:
% 202.11/33.72  | | | 
% 202.11/33.72  | | |   (58)  all_58_8 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | COMBINE_EQS: (37), (58) imply:
% 202.11/33.72  | | |   (59)  all_10_2 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | COMBINE_EQS: (11), (59) imply:
% 202.11/33.72  | | |   (60)  all_26_2 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REDUCE: (36), (59) imply:
% 202.11/33.72  | | |   (61)   ~ (all_52_19 = e3)
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REDUCE: (22), (59) imply:
% 202.11/33.72  | | |   (62)  op(e3, e3) = e1
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REDUCE: (17), (59) imply:
% 202.11/33.72  | | |   (63)  op(e3, e1) = all_10_1
% 202.11/33.72  | | | 
% 202.11/33.72  | | | BETA: splitting (18) gives:
% 202.11/33.72  | | | 
% 202.11/33.72  | | | Case 1:
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | |   (64)  all_58_2 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | COMBINE_EQS: (27), (64) imply:
% 202.11/33.72  | | | |   (65)  all_52_3 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | SIMP: (65) implies:
% 202.11/33.72  | | | |   (66)  all_52_3 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REDUCE: (15), (66) imply:
% 202.11/33.72  | | | |   (67)   ~ (all_52_5 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | SIMP: (67) implies:
% 202.11/33.72  | | | |   (68)   ~ (all_52_5 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REDUCE: (42), (66) imply:
% 202.11/33.72  | | | |   (69)   ~ (all_52_7 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | SIMP: (69) implies:
% 202.11/33.72  | | | |   (70)   ~ (all_52_7 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REDUCE: (8), (66) imply:
% 202.11/33.72  | | | |   (71)   ~ (all_6_2 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | SIMP: (71) implies:
% 202.11/33.72  | | | |   (72)   ~ (all_6_2 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REDUCE: (2), (66) imply:
% 202.11/33.72  | | | |   (73)  op(e3, e3) = all_52_2
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | BETA: splitting (19) gives:
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | Case 1:
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | |   (74)   ~ (all_26_2 = e3)
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | REDUCE: (60), (74) imply:
% 202.11/33.72  | | | | |   (75)  $false
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | CLOSE: (75) is inconsistent.
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | Case 2:
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | |   (76)   ~ (all_26_1 = e0)
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | REDUCE: (10), (76) imply:
% 202.11/33.72  | | | | |   (77)   ~ (all_10_1 = e0)
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 202.11/33.72  | | | | |              simplifying with (34), (63) gives:
% 202.11/33.72  | | | | |   (78)  all_52_17 = all_10_1
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_2, e3, e3,
% 202.11/33.72  | | | | |              simplifying with (39), (73) gives:
% 202.11/33.72  | | | | |   (79)  all_52_2 = all_6_2
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | GROUND_INST: instantiating (3) with e1, all_52_2, e3, e3, simplifying
% 202.11/33.72  | | | | |              with (62), (73) gives:
% 202.11/33.72  | | | | |   (80)  all_52_2 = e1
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | COMBINE_EQS: (79), (80) imply:
% 202.11/33.72  | | | | |   (81)  all_6_2 = e1
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | SIMP: (81) implies:
% 202.11/33.72  | | | | |   (82)  all_6_2 = e1
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | COMBINE_EQS: (53), (78) imply:
% 202.11/33.72  | | | | |   (83)  all_58_4 = all_10_1
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | COMBINE_EQS: (9), (82) imply:
% 202.11/33.72  | | | | |   (84)  all_58_0 = e1
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | REDUCE: (72), (82) imply:
% 202.11/33.72  | | | | |   (85)   ~ (e3 = e1)
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | SIMP: (85) implies:
% 202.11/33.72  | | | | |   (86)   ~ (e3 = e1)
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | BETA: splitting (31) gives:
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | | Case 1:
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | |   (87)  all_58_0 = e0
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | | COMBINE_EQS: (84), (87) imply:
% 202.11/33.72  | | | | | |   (88)  e1 = e0
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | | REDUCE: (47), (88) imply:
% 202.11/33.72  | | | | | |   (89)  $false
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | | CLOSE: (89) is inconsistent.
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | Case 2:
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | |   (90)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | | BETA: splitting (90) gives:
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | | Case 1:
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | |   (91)  all_58_1 = e0
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | | COMBINE_EQS: (4), (91) imply:
% 202.11/33.72  | | | | | | |   (92)  all_52_9 = e0
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | | REF_CLOSE: (3), (6), (9), (14), (20), (26), (27), (28), (29),
% 202.11/33.72  | | | | | | |            (32), (34), (39), (44), (45), (48), (51), (62), (63),
% 202.11/33.72  | | | | | | |            (68), (70), (83), (84), (86), (91) are inconsistent by
% 202.11/33.72  | | | | | | |            sub-proof #1057.
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | Case 2:
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | |   (93)  all_58_4 = e0 | all_58_9 = e0
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | | BETA: splitting (93) gives:
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | | Case 1:
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | |   (94)  all_58_4 = e0
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | | COMBINE_EQS: (83), (94) imply:
% 202.11/33.72  | | | | | | | |   (95)  all_10_1 = e0
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | | REDUCE: (77), (95) imply:
% 202.11/33.72  | | | | | | | |   (96)  $false
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | | CLOSE: (96) is inconsistent.
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | Case 2:
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | |   (97)  all_58_9 = e0
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | | COMBINE_EQS: (6), (97) imply:
% 202.11/33.72  | | | | | | | |   (98)  e3 = e0
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | | COMBINE_EQS: (58), (98) imply:
% 202.11/33.72  | | | | | | | |   (99)  all_58_8 = e0
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | | REF_CLOSE: (3), (4), (5), (9), (12), (16), (24), (25), (33),
% 202.11/33.72  | | | | | | | |            (35), (38), (39), (40), (41), (44), (46), (48), (49),
% 202.11/33.72  | | | | | | | |            (52), (53), (99) are inconsistent by sub-proof #377.
% 202.11/33.72  | | | | | | | | 
% 202.11/33.72  | | | | | | | End of split
% 202.11/33.72  | | | | | | | 
% 202.11/33.72  | | | | | | End of split
% 202.11/33.72  | | | | | | 
% 202.11/33.72  | | | | | End of split
% 202.11/33.72  | | | | | 
% 202.11/33.72  | | | | End of split
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | Case 2:
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | |   (100)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REF_CLOSE: (1), (3), (4), (7), (9), (12), (13), (23), (33), (38), (39),
% 202.11/33.72  | | | |            (41), (43), (44), (46), (48), (49), (50), (52), (53), (61),
% 202.11/33.72  | | | |            (100) are inconsistent by sub-proof #441.
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | End of split
% 202.11/33.72  | | | 
% 202.11/33.72  | | Case 2:
% 202.11/33.72  | | | 
% 202.11/33.72  | | |   (101)  all_58_11 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REF_CLOSE: (16), (30), (101) are inconsistent by sub-proof #1323.
% 202.11/33.72  | | | 
% 202.11/33.72  | | End of split
% 202.11/33.72  | | 
% 202.11/33.72  | End of split
% 202.11/33.72  | 
% 202.11/33.72  End of proof
% 202.11/33.72  
% 202.11/33.72  Sub-proof #345 shows that the following formulas are inconsistent:
% 202.11/33.72  ----------------------------------------------------------------
% 202.11/33.72    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.72    (2)  all_58_1 = all_52_9
% 202.11/33.72    (3)  op(e2, e3) = all_52_3
% 202.11/33.72    (4)   ~ (all_52_3 = all_52_19)
% 202.11/33.72    (5)   ~ (all_4_2 = e3)
% 202.11/33.72    (6)   ~ (all_52_3 = all_6_2)
% 202.11/33.72    (7)  all_58_0 = all_6_2
% 202.11/33.72    (8)  all_56_4 = all_52_3
% 202.11/33.72    (9)  op(e3, e0) = all_52_25
% 202.11/33.72    (10)  all_58_9 = all_52_25
% 202.11/33.72    (11)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.72    (12)   ~ (all_52_3 = all_52_5)
% 202.11/33.72    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.72    (14)  all_58_6 = e3
% 202.11/33.72    (15)  all_58_10 = all_52_27
% 202.11/33.72    (16)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.72    (17)  op(all_52_19, all_52_19) = e2
% 202.11/33.72    (18)   ~ (all_52_5 = all_52_7)
% 202.11/33.72    (19)  all_58_12 = all_52_7
% 202.11/33.72    (20)  all_58_2 = all_52_3
% 202.11/33.72    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.72    (22)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.72    (23)   ~ (e2 = e0)
% 202.11/33.72    (24)   ~ (all_52_27 = e3)
% 202.11/33.72    (25)   ~ (all_52_9 = e3)
% 202.11/33.72    (26)  op(e3, e1) = all_52_17
% 202.11/33.72    (27)   ~ (all_52_5 = all_6_2)
% 202.11/33.72    (28)  op(e3, all_6_1) = e2
% 202.11/33.72    (29)  op(e3, e3) = all_6_2
% 202.11/33.72    (30)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.72    (31)  all_58_5 = all_52_19
% 202.11/33.72    (32)  all_58_6 = all_52_5
% 202.11/33.72    (33)   ~ (all_52_17 = all_6_2)
% 202.11/33.72    (34)   ~ (e3 = e2)
% 202.11/33.72    (35)   ~ (all_52_17 = all_52_19)
% 202.11/33.72    (36)  all_58_3 = all_4_2
% 202.11/33.72    (37)  op(all_6_2, e3) = all_6_1
% 202.11/33.72    (38)  all_58_4 = all_52_17
% 202.11/33.72  
% 202.11/33.72  Begin of proof
% 202.11/33.72  | 
% 202.11/33.72  | COMBINE_EQS: (14), (32) imply:
% 202.11/33.72  |   (39)  all_52_5 = e3
% 202.11/33.72  | 
% 202.11/33.72  | SIMP: (39) implies:
% 202.11/33.72  |   (40)  all_52_5 = e3
% 202.11/33.72  | 
% 202.11/33.72  | REDUCE: (12), (40) imply:
% 202.11/33.72  |   (41)   ~ (all_52_3 = e3)
% 202.11/33.72  | 
% 202.11/33.72  | REDUCE: (18), (40) imply:
% 202.11/33.72  |   (42)   ~ (all_52_7 = e3)
% 202.11/33.72  | 
% 202.11/33.72  | SIMP: (42) implies:
% 202.11/33.72  |   (43)   ~ (all_52_7 = e3)
% 202.11/33.72  | 
% 202.11/33.72  | BETA: splitting (13) gives:
% 202.11/33.72  | 
% 202.11/33.72  | Case 1:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (44)  all_58_2 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | REF_CLOSE: (20), (41), (44) are inconsistent by sub-proof #1369.
% 202.11/33.72  | | 
% 202.11/33.72  | Case 2:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (45)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.11/33.72  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 202.11/33.72  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 202.11/33.72  | |            (38), (43), (45) are inconsistent by sub-proof #353.
% 202.11/33.72  | | 
% 202.11/33.72  | End of split
% 202.11/33.72  | 
% 202.11/33.72  End of proof
% 202.11/33.72  
% 202.11/33.72  Sub-proof #346 shows that the following formulas are inconsistent:
% 202.11/33.72  ----------------------------------------------------------------
% 202.11/33.72    (1)  all_58_14 = all_52_23
% 202.11/33.72    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.72    (3)   ~ (e3 = e0)
% 202.11/33.72    (4)   ~ (all_4_2 = e3)
% 202.11/33.72    (5)  all_44_2 = all_6_2
% 202.11/33.72    (6)  all_58_0 = all_6_2
% 202.11/33.72    (7)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.72    (8)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.72    (9)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.72    (10)  all_58_13 = all_52_15
% 202.11/33.72    (11)  op(all_52_13, all_52_13) = e1
% 202.11/33.72    (12)   ~ (all_52_15 = e3)
% 202.11/33.72    (13)  op(e1, e3) = all_52_5
% 202.11/33.72    (14)  op(e2, e2) = all_4_2
% 202.11/33.72    (15)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.72    (16)   ~ (all_52_13 = all_10_2)
% 202.11/33.72    (17)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.72    (18)  all_56_8 = all_52_5
% 202.11/33.72    (19)  all_58_7 = all_52_13
% 202.11/33.72    (20)   ~ (all_52_23 = e3)
% 202.11/33.72    (21)  all_58_8 = all_10_2
% 202.11/33.72    (22)   ~ (all_52_5 = all_6_2)
% 202.11/33.72    (23)  op(e3, all_6_1) = e2
% 202.11/33.72    (24)  op(e3, e3) = all_6_2
% 202.11/33.72    (25)  all_58_5 = all_52_19
% 202.11/33.72    (26)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.72    (27)  all_58_6 = all_52_5
% 202.11/33.72    (28)  op(e3, e2) = all_52_9
% 202.11/33.72    (29)   ~ (e1 = e0)
% 202.11/33.72    (30)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.72    (31)  all_44_1 = all_6_1
% 202.11/33.72    (32)  all_58_12 = e3
% 202.11/33.72    (33)  op(all_52_9, all_52_9) = e3
% 202.11/33.72    (34)  all_58_3 = all_4_2
% 202.11/33.72    (35)   ~ (all_52_19 = all_4_2)
% 202.11/33.72    (36)  op(all_6_2, e3) = all_6_1
% 202.11/33.72  
% 202.11/33.72  Begin of proof
% 202.11/33.72  | 
% 202.11/33.72  | BETA: splitting (30) gives:
% 202.11/33.72  | 
% 202.11/33.72  | Case 1:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (37)  all_58_3 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | COMBINE_EQS: (34), (37) imply:
% 202.11/33.72  | |   (38)  all_4_2 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (4), (38) imply:
% 202.11/33.72  | |   (39)  $false
% 202.11/33.72  | | 
% 202.11/33.72  | | CLOSE: (39) is inconsistent.
% 202.11/33.72  | | 
% 202.11/33.72  | Case 2:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (40)  all_58_7 = e3 | all_58_13 = e3
% 202.11/33.72  | | 
% 202.11/33.72  | | BETA: splitting (40) gives:
% 202.11/33.72  | | 
% 202.11/33.72  | | Case 1:
% 202.11/33.72  | | | 
% 202.11/33.72  | | |   (41)  all_58_7 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | COMBINE_EQS: (19), (41) imply:
% 202.11/33.72  | | |   (42)  all_52_13 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REDUCE: (16), (42) imply:
% 202.11/33.72  | | |   (43)   ~ (all_10_2 = e3)
% 202.11/33.72  | | | 
% 202.11/33.72  | | | SIMP: (43) implies:
% 202.11/33.72  | | |   (44)   ~ (all_10_2 = e3)
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REDUCE: (11), (42) imply:
% 202.11/33.72  | | |   (45)  op(e3, e3) = e1
% 202.11/33.72  | | | 
% 202.11/33.72  | | | BETA: splitting (26) gives:
% 202.11/33.72  | | | 
% 202.11/33.72  | | | Case 1:
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | |   (46)  all_58_5 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | COMBINE_EQS: (25), (46) imply:
% 202.11/33.72  | | | |   (47)  all_52_19 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | SIMP: (47) implies:
% 202.11/33.72  | | | |   (48)  all_52_19 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REDUCE: (35), (48) imply:
% 202.11/33.72  | | | |   (49)   ~ (all_4_2 = e3)
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REDUCE: (9), (48) imply:
% 202.11/33.72  | | | |   (50)  op(e3, e3) = all_52_18
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (13), (14), (15), (17),
% 202.11/33.72  | | | |            (18), (22), (23), (24), (27), (28), (29), (31), (32), (33),
% 202.11/33.72  | | | |            (36), (45), (50) are inconsistent by sub-proof #347.
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | Case 2:
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | |   (51)  all_58_8 = e3 | all_58_14 = e3
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | | REF_CLOSE: (1), (20), (21), (44), (51) are inconsistent by sub-proof
% 202.11/33.72  | | | |            #1304.
% 202.11/33.72  | | | | 
% 202.11/33.72  | | | End of split
% 202.11/33.72  | | | 
% 202.11/33.72  | | Case 2:
% 202.11/33.72  | | | 
% 202.11/33.72  | | |   (52)  all_58_13 = e3
% 202.11/33.72  | | | 
% 202.11/33.72  | | | REF_CLOSE: (10), (12), (52) are inconsistent by sub-proof #1360.
% 202.11/33.72  | | | 
% 202.11/33.72  | | End of split
% 202.11/33.72  | | 
% 202.11/33.72  | End of split
% 202.11/33.72  | 
% 202.11/33.72  End of proof
% 202.11/33.72  
% 202.11/33.72  Sub-proof #347 shows that the following formulas are inconsistent:
% 202.11/33.72  ----------------------------------------------------------------
% 202.11/33.72    (1)  op(e3, e3) = all_52_18
% 202.11/33.72    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.72    (3)   ~ (e3 = e0)
% 202.11/33.72    (4)   ~ (all_4_2 = e3)
% 202.11/33.72    (5)  all_44_2 = all_6_2
% 202.11/33.72    (6)  all_58_0 = all_6_2
% 202.11/33.72    (7)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.72    (8)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.72    (9)  op(e1, e3) = all_52_5
% 202.11/33.72    (10)  op(e2, e2) = all_4_2
% 202.11/33.72    (11)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.72    (12)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.72    (13)  all_56_8 = all_52_5
% 202.11/33.72    (14)   ~ (all_52_5 = all_6_2)
% 202.11/33.72    (15)  op(e3, all_6_1) = e2
% 202.11/33.72    (16)  op(e3, e3) = all_6_2
% 202.11/33.72    (17)  op(e3, e3) = e1
% 202.11/33.72    (18)  all_58_6 = all_52_5
% 202.11/33.72    (19)  op(e3, e2) = all_52_9
% 202.11/33.72    (20)   ~ (e1 = e0)
% 202.11/33.72    (21)  all_44_1 = all_6_1
% 202.11/33.72    (22)  all_58_12 = e3
% 202.11/33.72    (23)  op(all_52_9, all_52_9) = e3
% 202.11/33.72    (24)  op(all_6_2, e3) = all_6_1
% 202.11/33.72  
% 202.11/33.72  Begin of proof
% 202.11/33.72  | 
% 202.11/33.72  | GROUND_INST: instantiating (2) with all_6_2, all_52_18, e3, e3, simplifying
% 202.11/33.72  |              with (1), (16) gives:
% 202.11/33.72  |   (25)  all_52_18 = all_6_2
% 202.11/33.72  | 
% 202.11/33.72  | GROUND_INST: instantiating (2) with e1, all_52_18, e3, e3, simplifying with
% 202.11/33.72  |              (1), (17) gives:
% 202.11/33.72  |   (26)  all_52_18 = e1
% 202.11/33.72  | 
% 202.11/33.72  | COMBINE_EQS: (25), (26) imply:
% 202.11/33.72  |   (27)  all_6_2 = e1
% 202.11/33.72  | 
% 202.11/33.72  | COMBINE_EQS: (5), (27) imply:
% 202.11/33.72  |   (28)  all_44_2 = e1
% 202.11/33.72  | 
% 202.11/33.72  | COMBINE_EQS: (6), (27) imply:
% 202.11/33.72  |   (29)  all_58_0 = e1
% 202.11/33.72  | 
% 202.11/33.72  | REDUCE: (14), (27) imply:
% 202.11/33.72  |   (30)   ~ (all_52_5 = e1)
% 202.11/33.72  | 
% 202.11/33.72  | REDUCE: (24), (27) imply:
% 202.11/33.72  |   (31)  op(e1, e3) = all_6_1
% 202.11/33.72  | 
% 202.11/33.72  | BETA: splitting (7) gives:
% 202.11/33.72  | 
% 202.11/33.72  | Case 1:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (32)   ~ (all_44_2 = e1)
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (28), (32) imply:
% 202.11/33.72  | |   (33)  $false
% 202.11/33.72  | | 
% 202.11/33.72  | | CLOSE: (33) is inconsistent.
% 202.11/33.72  | | 
% 202.11/33.72  | Case 2:
% 202.11/33.72  | | 
% 202.11/33.72  | |   (34)   ~ (all_44_1 = e0)
% 202.11/33.72  | | 
% 202.11/33.72  | | REDUCE: (21), (34) imply:
% 202.11/33.72  | |   (35)   ~ (all_6_1 = e0)
% 202.11/33.72  | | 
% 202.11/33.72  | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (11), (12), (13), (15), (18),
% 202.11/33.72  | |            (19), (20), (22), (23), (29), (30), (31), (35) are inconsistent
% 202.11/33.72  | |            by sub-proof #459.
% 202.11/33.72  | | 
% 202.11/33.72  | End of split
% 202.11/33.72  | 
% 202.11/33.72  End of proof
% 202.11/33.72  
% 202.11/33.72  Sub-proof #348 shows that the following formulas are inconsistent:
% 202.11/33.72  ----------------------------------------------------------------
% 202.11/33.72    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.72    (2)   ~ (all_52_15 = all_52_23)
% 202.11/33.72    (3)   ~ (all_52_25 = all_52_27)
% 202.11/33.72    (4)  all_58_14 = all_52_23
% 202.11/33.72    (5)   ~ (e3 = e1)
% 202.11/33.72    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.72    (8)   ~ (all_52_7 = all_10_0)
% 202.11/33.72    (9)   ~ (all_52_5 = all_52_13)
% 202.11/33.72    (10)  all_58_1 = all_52_9
% 202.11/33.72    (11)   ~ (all_52_9 = all_52_13)
% 202.11/33.72    (12)   ~ (e3 = e0)
% 202.11/33.72    (13)  op(e2, e3) = all_52_3
% 202.11/33.72    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.72    (15)   ~ (all_52_7 = all_52_15)
% 202.11/33.72    (16)   ~ (all_52_3 = all_52_19)
% 202.11/33.72    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.72    (18)   ~ (all_52_17 = all_52_25)
% 202.11/33.72    (19)   ~ (all_52_3 = all_6_2)
% 202.11/33.72    (20)  all_44_2 = all_6_2
% 202.11/33.72    (21)  all_58_0 = all_6_2
% 202.11/33.72    (22)  op(all_14_2, e0) = all_14_1
% 202.11/33.72    (23)  all_56_4 = all_52_3
% 202.11/33.72    (24)   ~ (all_52_17 = all_10_2)
% 202.11/33.72    (25)   ~ (all_10_0 = e3)
% 202.11/33.72    (26)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.72    (27)  op(e3, e0) = all_52_25
% 202.11/33.72    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.72    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.72    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.72    (31)   ~ (all_52_27 = all_52_29)
% 202.11/33.72    (32)  all_58_13 = all_52_15
% 202.11/33.72    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.11/33.72    (34)  all_58_9 = all_52_25
% 202.11/33.72    (35)   ~ (all_52_29 = all_14_2)
% 202.11/33.72    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.73    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.73    (38)  op(e1, e3) = all_52_5
% 202.11/33.73    (39)  op(e2, e2) = all_4_2
% 202.11/33.73    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.73    (41)   ~ (all_52_3 = all_52_5)
% 202.11/33.73    (42)  all_58_11 = all_52_29
% 202.11/33.73    (43)  all_56_5 = all_4_2
% 202.11/33.73    (44)   ~ (all_52_25 = all_14_2)
% 202.11/33.73    (45)   ~ (all_52_9 = all_52_15)
% 202.11/33.73    (46)   ~ (all_52_3 = all_52_27)
% 202.11/33.73    (47)  op(all_10_2, e1) = all_10_1
% 202.11/33.73    (48)  op(all_6_2, all_6_2) = all_52_0
% 202.11/33.73    (49)   ~ (all_52_7 = all_6_2)
% 202.11/33.73    (50)  op(e0, e0) = all_14_2
% 202.11/33.73    (51)   ~ (all_10_0 = all_6_2)
% 202.11/33.73    (52)  all_56_15 = all_14_2
% 202.11/33.73    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.73    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.11/33.73    (55)   ~ (all_58_15 = e0)
% 202.11/33.73    (56)  all_56_11 = all_52_29
% 202.11/33.73    (57)   ~ (all_10_0 = e2)
% 202.11/33.73    (58)   ~ (all_4_1 = e1)
% 202.11/33.73    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.73    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.73    (61)   ~ (e2 = e1)
% 202.11/33.73    (62)   ~ (all_52_13 = all_10_2)
% 202.11/33.73    (63)  all_58_10 = all_52_27
% 202.11/33.73    (64)  all_56_8 = all_52_5
% 202.11/33.73    (65)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.73    (66)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.73    (67)   ~ (all_52_19 = all_52_23)
% 202.11/33.73    (68)   ~ (all_52_25 = all_52_29)
% 202.11/33.73    (69)   ~ (all_52_29 = all_10_2)
% 202.11/33.73    (70)  op(all_10_2, e1) = e3
% 202.11/33.73    (71)  all_58_7 = all_52_13
% 202.11/33.73    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.11/33.73    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.73    (74)   ~ (all_52_5 = all_52_7)
% 202.11/33.73    (75)  all_58_12 = all_52_7
% 202.11/33.73    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.73    (77)   ~ (all_52_7 = all_14_2)
% 202.11/33.73    (78)  all_58_2 = all_52_3
% 202.11/33.73    (79)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.73    (80)  all_56_2 = all_52_17
% 202.11/33.73    (81)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.73    (82)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.73    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.11/33.73    (84)  all_56_7 = all_52_27
% 202.11/33.73    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.73    (86)   ~ (e2 = e0)
% 202.11/33.73    (87)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.11/33.73    (88)  op(all_4_2, e2) = all_4_1
% 202.11/33.73    (89)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.73    (90)   ~ (all_52_5 = all_52_29)
% 202.11/33.73    (91)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.73    (92)  all_56_6 = all_52_19
% 202.11/33.73    (93)  all_56_8 = all_10_0
% 202.11/33.73    (94)   ~ (all_52_15 = all_14_2)
% 202.11/33.73    (95)   ~ (all_52_19 = all_52_27)
% 202.11/33.73    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.73    (97)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.11/33.73    (98)   ~ (all_52_13 = all_4_2)
% 202.11/33.73    (99)  op(e3, e1) = all_52_17
% 202.11/33.73    (100)  all_58_6 = all_10_0
% 202.11/33.73    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.11/33.73    (102)  op(e0, e3) = all_52_7
% 202.11/33.73    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.73    (104)   ~ (all_52_9 = all_52_25)
% 202.11/33.73    (105)  op(e1, e3) = all_10_0
% 202.11/33.73    (106)  all_58_15 = all_14_2
% 202.11/33.73    (107)   ~ (all_52_19 = all_10_2)
% 202.11/33.73    (108)  op(all_52_23, all_52_23) = all_52_22
% 202.11/33.73    (109)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.73    (110)  all_58_8 = all_10_2
% 202.11/33.73    (111)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.73    (112)   ~ (all_52_5 = all_10_2)
% 202.11/33.73    (113)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.73    (114)   ~ (all_52_23 = all_14_2)
% 202.11/33.73    (115)  all_56_12 = all_52_7
% 202.11/33.73    (116)  op(all_52_17, all_52_17) = all_52_16
% 202.11/33.73    (117)  all_8_2 = all_6_2
% 202.11/33.73    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.73    (119)   ~ (all_52_25 = all_6_2)
% 202.11/33.73    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.73    (121)   ~ (all_52_9 = all_4_2)
% 202.11/33.73    (122)   ~ (all_52_5 = all_6_2)
% 202.11/33.73    (123)   ~ (all_52_9 = all_6_2)
% 202.11/33.73    (124)  op(e3, all_6_1) = e2
% 202.11/33.73    (125)  all_56_0 = all_6_2
% 202.11/33.73    (126)  op(e3, e3) = all_6_2
% 202.11/33.73    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.73    (128)   ~ (all_52_27 = all_14_2)
% 202.11/33.73    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.73    (130)  all_56_14 = all_52_23
% 202.11/33.73    (131)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.73    (132)  all_56_3 = all_52_25
% 202.11/33.73    (133)   ~ (all_52_3 = all_52_7)
% 202.11/33.73    (134)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.73    (135)  all_58_5 = all_52_19
% 202.11/33.73    (136)  op(all_10_0, all_10_0) = all_52_4
% 202.11/33.73    (137)  all_56_1 = all_52_9
% 202.11/33.73    (138)   ~ (all_52_15 = all_4_2)
% 202.11/33.73    (139)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.73           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.11/33.73           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.11/33.73           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.11/33.73    (140)   ~ (all_52_27 = all_4_2)
% 202.11/33.73    (141)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 202.11/33.73             all_58_13 = e0 | all_58_14 = e0)
% 202.11/33.73    (142)  all_58_6 = all_52_5
% 202.11/33.73    (143)  op(e3, e2) = all_52_9
% 202.11/33.73    (144)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.73    (145)   ~ (all_52_17 = all_6_2)
% 202.11/33.73    (146)   ~ (e1 = e0)
% 202.11/33.73    (147)   ~ (e3 = e2)
% 202.11/33.73    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.73    (149)  all_44_1 = all_6_1
% 202.11/33.73    (150)   ~ (all_52_9 = all_52_17)
% 202.11/33.73    (151)  all_56_10 = all_10_2
% 202.11/33.73    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.73    (153)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.73    (154)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.73    (155)  op(e1, e1) = all_10_2
% 202.11/33.73    (156)   ~ (all_52_23 = all_10_2)
% 202.11/33.73    (157)   ~ (all_52_7 = all_52_23)
% 202.11/33.73    (158)   ~ (all_52_17 = all_52_19)
% 202.11/33.73    (159)  all_58_3 = all_4_2
% 202.11/33.73    (160)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.11/33.73    (161)  all_56_13 = all_52_15
% 202.11/33.73    (162)   ~ (all_52_3 = all_4_2)
% 202.11/33.73    (163)   ~ (all_52_19 = all_4_2)
% 202.11/33.73    (164)   ~ (all_52_17 = all_52_23)
% 202.11/33.73    (165)  all_8_1 = all_6_1
% 202.11/33.73    (166)  op(all_6_2, e3) = all_6_1
% 202.11/33.73    (167)   ~ (all_52_13 = all_52_29)
% 202.11/33.73    (168)  all_58_4 = all_52_17
% 202.11/33.73    (169)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.73    (170)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.73  
% 202.11/33.73  Begin of proof
% 202.11/33.73  | 
% 202.11/33.73  | ALPHA: (141) implies:
% 202.11/33.73  |   (171)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.73  |   (172)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.11/33.73  | 
% 202.11/33.73  | REDUCE: (55), (106) imply:
% 202.11/33.73  |   (173)   ~ (all_14_2 = e0)
% 202.11/33.73  | 
% 202.11/33.73  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.11/33.73  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.11/33.73  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.11/33.73  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 202.11/33.73  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 202.11/33.73  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 202.11/33.73  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 202.11/33.73  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 202.11/33.73  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 202.11/33.73  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 202.11/33.73  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 202.11/33.73  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 202.11/33.73  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 202.11/33.73  |            (138), (139), (140), (142), (143), (144), (145), (146), (147),
% 202.11/33.73  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 202.11/33.73  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 202.11/33.73  |            (166), (167), (168), (169), (170), (171), (172), (173) are
% 202.11/33.73  |            inconsistent by sub-proof #368.
% 202.11/33.73  | 
% 202.11/33.73  End of proof
% 202.11/33.73  
% 202.11/33.73  Sub-proof #349 shows that the following formulas are inconsistent:
% 202.11/33.73  ----------------------------------------------------------------
% 202.11/33.73    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.11/33.73    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.73    (3)   ~ (all_52_15 = all_52_23)
% 202.11/33.73    (4)   ~ (all_52_25 = all_52_27)
% 202.11/33.73    (5)  all_58_14 = all_52_23
% 202.11/33.73    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.73    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.73    (8)   ~ (all_52_5 = all_52_13)
% 202.11/33.73    (9)  all_58_1 = all_52_9
% 202.11/33.73    (10)   ~ (all_52_9 = all_52_13)
% 202.11/33.73    (11)   ~ (e3 = e0)
% 202.11/33.73    (12)  op(e2, e3) = all_52_3
% 202.11/33.73    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.73    (14)   ~ (all_52_7 = all_52_15)
% 202.11/33.73    (15)   ~ (all_52_3 = all_52_19)
% 202.11/33.73    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.73    (17)   ~ (all_52_17 = all_52_25)
% 202.11/33.73    (18)   ~ (all_52_3 = all_6_2)
% 202.11/33.73    (19)  all_44_2 = all_6_2
% 202.11/33.73    (20)  all_58_0 = all_6_2
% 202.11/33.73    (21)  op(all_14_2, e0) = all_14_1
% 202.11/33.73    (22)  all_56_4 = all_52_3
% 202.11/33.73    (23)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.73    (24)  op(e3, e0) = all_52_25
% 202.11/33.73    (25)  op(e0, all_14_1) = all_14_0
% 202.11/33.73    (26)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.73    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.73    (28)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.73    (29)  all_58_13 = all_52_15
% 202.11/33.73    (30)  op(all_10_2, all_10_2) = all_52_20
% 202.11/33.73    (31)  all_58_9 = all_52_25
% 202.11/33.73    (32)   ~ (all_52_29 = all_14_2)
% 202.11/33.73    (33)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.73    (34)  op(e1, e3) = all_52_5
% 202.11/33.73    (35)  op(e2, e2) = all_4_2
% 202.11/33.73    (36)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.73    (37)   ~ (all_52_3 = all_52_5)
% 202.11/33.73    (38)  all_58_11 = all_52_29
% 202.11/33.73    (39)   ~ (all_52_25 = all_14_2)
% 202.11/33.73    (40)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.11/33.73    (41)   ~ (all_52_3 = all_52_27)
% 202.11/33.73    (42)  op(all_6_2, all_6_2) = all_52_0
% 202.11/33.73    (43)   ~ (all_52_7 = all_6_2)
% 202.11/33.73    (44)  op(e0, e0) = all_14_2
% 202.11/33.73    (45)  op(e0, e1) = all_52_23
% 202.11/33.73    (46)  all_56_15 = all_14_2
% 202.11/33.73    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.73    (48)   ~ (all_4_1 = e1)
% 202.11/33.73    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.73    (50)  all_56_9 = all_52_13
% 202.11/33.73    (51)   ~ (all_52_13 = all_10_2)
% 202.11/33.73    (52)  all_58_10 = all_52_27
% 202.11/33.73    (53)  all_56_8 = all_52_5
% 202.11/33.73    (54)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.73    (55)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.73    (56)   ~ (all_52_19 = all_52_23)
% 202.11/33.73    (57)   ~ (all_52_25 = all_52_29)
% 202.11/33.73    (58)   ~ (all_52_29 = all_10_2)
% 202.11/33.73    (59)  all_58_7 = all_52_13
% 202.11/33.73    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.11/33.73    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.73    (62)   ~ (all_52_5 = all_52_7)
% 202.11/33.73    (63)  all_58_12 = all_52_7
% 202.11/33.73    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.73    (65)   ~ (all_52_7 = all_14_2)
% 202.11/33.73    (66)  all_58_2 = all_52_3
% 202.11/33.73    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.73    (68)  all_56_7 = all_52_27
% 202.11/33.73    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.73    (70)   ~ (e2 = e0)
% 202.11/33.73    (71)  op(all_4_2, e2) = all_4_1
% 202.11/33.73    (72)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.73    (73)   ~ (all_52_15 = all_14_2)
% 202.11/33.73    (74)   ~ (all_52_13 = all_4_2)
% 202.11/33.73    (75)  op(e3, e1) = all_52_17
% 202.11/33.73    (76)  op(e0, e3) = all_52_7
% 202.11/33.73    (77)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.73    (78)   ~ (all_52_9 = all_52_25)
% 202.11/33.73    (79)  all_58_15 = all_14_2
% 202.11/33.73    (80)   ~ (all_52_19 = all_10_2)
% 202.11/33.73    (81)  op(all_52_23, all_52_23) = all_52_22
% 202.11/33.73    (82)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.73    (83)  all_58_8 = all_10_2
% 202.11/33.73    (84)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.73    (85)   ~ (all_52_5 = all_10_2)
% 202.11/33.73    (86)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.73    (87)   ~ (all_52_23 = all_14_2)
% 202.11/33.73    (88)  all_56_12 = all_52_7
% 202.11/33.73    (89)  op(all_52_17, all_52_17) = all_52_16
% 202.11/33.73    (90)  all_8_2 = all_6_2
% 202.11/33.73    (91)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.73    (92)   ~ (all_52_25 = all_6_2)
% 202.11/33.73    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.73    (94)   ~ (all_52_9 = all_4_2)
% 202.11/33.73    (95)   ~ (all_52_5 = all_6_2)
% 202.11/33.73    (96)   ~ (all_52_9 = all_6_2)
% 202.11/33.73    (97)   ~ (all_52_13 = all_52_15)
% 202.11/33.73    (98)  op(e3, all_6_1) = e2
% 202.11/33.73    (99)  all_56_0 = all_6_2
% 202.11/33.73    (100)  op(e3, e3) = all_6_2
% 202.11/33.73    (101)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.73    (102)   ~ (all_52_27 = all_14_2)
% 202.11/33.73    (103)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.73    (104)  all_56_14 = all_52_23
% 202.11/33.73    (105)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.73    (106)  all_56_3 = all_52_25
% 202.11/33.73    (107)   ~ (all_52_3 = all_52_7)
% 202.11/33.73    (108)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.73    (109)  all_58_5 = all_52_19
% 202.11/33.73    (110)  all_56_1 = all_52_9
% 202.11/33.73    (111)   ~ (all_52_15 = all_4_2)
% 202.11/33.73    (112)   ~ (all_52_27 = all_4_2)
% 202.11/33.73    (113)  all_58_6 = all_52_5
% 202.11/33.73    (114)  op(e3, e2) = all_52_9
% 202.11/33.73    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.73    (116)   ~ (all_52_17 = all_6_2)
% 202.11/33.73    (117)   ~ (e1 = e0)
% 202.11/33.73    (118)   ~ (e3 = e2)
% 202.11/33.73    (119)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.73           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.11/33.73    (120)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.73    (121)  all_44_1 = all_6_1
% 202.11/33.73    (122)   ~ (all_52_9 = all_52_17)
% 202.11/33.73    (123)  all_56_10 = all_10_2
% 202.11/33.73    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.73    (125)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.73    (126)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.73    (127)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.73    (128)  op(e1, e1) = all_10_2
% 202.11/33.73    (129)   ~ (all_52_23 = all_10_2)
% 202.11/33.73    (130)   ~ (all_52_7 = all_52_23)
% 202.11/33.73    (131)   ~ (all_52_17 = all_52_19)
% 202.11/33.73    (132)  all_58_3 = all_4_2
% 202.11/33.73    (133)  all_56_13 = all_52_15
% 202.11/33.73    (134)   ~ (all_52_3 = all_4_2)
% 202.11/33.73    (135)   ~ (all_52_19 = all_4_2)
% 202.11/33.73    (136)   ~ (all_52_17 = all_52_23)
% 202.11/33.73    (137)  all_8_1 = all_6_1
% 202.11/33.73    (138)  op(all_6_2, e3) = all_6_1
% 202.11/33.73    (139)   ~ (all_52_13 = all_52_29)
% 202.11/33.73    (140)  all_58_4 = all_52_17
% 202.11/33.73    (141)   ~ (all_14_0 = e2)
% 202.11/33.73    (142)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.73    (143)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.73  
% 202.11/33.73  Begin of proof
% 202.11/33.73  | 
% 202.11/33.73  | BETA: splitting (119) gives:
% 202.11/33.73  | 
% 202.11/33.73  | Case 1:
% 202.11/33.73  | | 
% 202.11/33.73  | |   (144)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.11/33.73  | | 
% 202.11/33.73  | | REF_CLOSE: (6), (7), (16), (20), (26), (35), (42), (44), (47), (63), (65),
% 202.11/33.73  | |            (66), (67), (85), (98), (99), (100), (113), (115), (118), (126),
% 202.11/33.73  | |            (128), (134), (138), (144) are inconsistent by sub-proof #501.
% 202.11/33.73  | | 
% 202.11/33.73  | Case 2:
% 202.11/33.73  | | 
% 202.11/33.73  | |   (145)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 202.11/33.73  | | 
% 202.11/33.73  | | ALPHA: (145) implies:
% 202.11/33.73  | |   (146)  all_52_14 = e0
% 202.11/33.73  | |   (147)  all_52_12 = e1
% 202.11/33.73  | |   (148)  all_52_10 = e2
% 202.11/33.73  | |   (149)  all_52_8 = e3
% 202.11/33.73  | | 
% 202.11/33.73  | | REDUCE: (54), (149) imply:
% 202.11/33.73  | |   (150)  op(all_52_9, all_52_9) = e3
% 202.11/33.73  | | 
% 202.11/33.73  | | REDUCE: (127), (147) imply:
% 202.11/33.73  | |   (151)  op(all_52_13, all_52_13) = e1
% 202.11/33.73  | | 
% 202.11/33.73  | | REDUCE: (55), (146) imply:
% 202.11/33.73  | |   (152)  op(all_52_15, all_52_15) = e0
% 202.11/33.73  | | 
% 202.11/33.73  | | REDUCE: (105), (148) imply:
% 202.11/33.73  | |   (153)  op(all_4_2, all_4_2) = e2
% 202.11/33.73  | | 
% 202.11/33.73  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.11/33.73  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.11/33.73  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.11/33.73  | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 202.11/33.73  | |            (47), (48), (49), (50), (51), (52), (53), (56), (57), (58), (59),
% 202.11/33.73  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 202.11/33.73  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 202.11/33.73  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 202.11/33.73  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 202.11/33.73  | |            (103), (104), (106), (107), (108), (109), (110), (111), (112),
% 202.11/33.73  | |            (113), (114), (115), (116), (117), (118), (120), (121), (122),
% 202.11/33.73  | |            (123), (124), (125), (126), (128), (129), (130), (131), (132),
% 202.11/33.73  | |            (133), (134), (135), (136), (137), (138), (139), (140), (141),
% 202.11/33.73  | |            (142), (143), (150), (151), (152), (153) are inconsistent by
% 202.11/33.73  | |            sub-proof #451.
% 202.11/33.73  | | 
% 202.11/33.73  | End of split
% 202.11/33.73  | 
% 202.11/33.73  End of proof
% 202.11/33.73  
% 202.11/33.73  Sub-proof #350 shows that the following formulas are inconsistent:
% 202.11/33.73  ----------------------------------------------------------------
% 202.11/33.73    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.73    (2)   ~ (all_52_15 = all_52_23)
% 202.11/33.73    (3)   ~ (all_52_25 = all_52_27)
% 202.11/33.73    (4)  all_58_14 = all_52_23
% 202.11/33.73    (5)   ~ (e3 = e1)
% 202.11/33.73    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.73    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.73    (8)  all_58_1 = all_52_9
% 202.11/33.73    (9)   ~ (all_52_9 = all_52_13)
% 202.11/33.73    (10)   ~ (e3 = e0)
% 202.11/33.73    (11)  op(e2, e3) = all_52_3
% 202.11/33.73    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.73    (13)   ~ (all_52_7 = all_52_15)
% 202.11/33.73    (14)   ~ (all_52_3 = all_52_19)
% 202.11/33.73    (15)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.73    (16)   ~ (all_52_17 = all_52_25)
% 202.11/33.73    (17)   ~ (all_52_3 = all_6_2)
% 202.11/33.73    (18)  all_44_2 = all_6_2
% 202.11/33.73    (19)  all_58_0 = all_6_2
% 202.11/33.73    (20)  op(all_14_2, e0) = all_14_1
% 202.11/33.73    (21)  all_56_4 = all_52_3
% 202.11/33.73    (22)   ~ (all_52_17 = all_10_2)
% 202.11/33.73    (23)   ~ (all_10_0 = e3)
% 202.11/33.73    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.73    (25)  all_40_2 = all_10_2
% 202.11/33.73    (26)  op(e3, e0) = all_52_25
% 202.11/33.73    (27)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.73    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.73    (29)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.73    (30)   ~ (all_52_27 = all_52_29)
% 202.11/33.73    (31)  all_58_13 = all_52_15
% 202.11/33.73    (32)  op(all_10_2, all_10_2) = all_52_20
% 202.11/33.73    (33)  all_58_9 = all_52_25
% 202.11/33.73    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.11/33.73    (35)   ~ (all_52_29 = all_14_2)
% 202.11/33.73    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.73    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.73    (38)  op(e1, e3) = all_52_5
% 202.11/33.73    (39)  op(e2, e2) = all_4_2
% 202.11/33.73    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.73    (41)  all_58_7 = all_10_0
% 202.11/33.73    (42)   ~ (all_52_3 = all_52_5)
% 202.11/33.73    (43)  all_58_11 = all_52_29
% 202.11/33.73    (44)  all_56_5 = all_4_2
% 202.11/33.73    (45)   ~ (all_52_25 = all_14_2)
% 202.11/33.73    (46)   ~ (all_52_9 = all_52_15)
% 202.11/33.73    (47)   ~ (all_52_3 = all_52_27)
% 202.11/33.73    (48)  op(all_10_2, e1) = all_10_1
% 202.11/33.73    (49)  op(all_6_2, all_6_2) = all_52_0
% 202.11/33.73    (50)   ~ (all_52_7 = all_6_2)
% 202.11/33.73    (51)  op(e0, e0) = all_14_2
% 202.11/33.73    (52)  all_56_15 = all_14_2
% 202.11/33.73    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.73    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.11/33.73    (55)   ~ (all_58_15 = e0)
% 202.11/33.73    (56)  all_56_11 = all_52_29
% 202.11/33.73    (57)   ~ (all_10_0 = e2)
% 202.11/33.73    (58)   ~ (all_4_1 = e1)
% 202.11/33.73    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.73    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.73    (61)   ~ (e2 = e1)
% 202.11/33.73    (62)  all_58_10 = all_52_27
% 202.11/33.73    (63)  all_56_8 = all_52_5
% 202.11/33.73    (64)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.73    (65)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.73    (66)   ~ (all_52_19 = all_52_23)
% 202.11/33.73    (67)  all_56_9 = all_10_0
% 202.11/33.73    (68)   ~ (all_52_25 = all_52_29)
% 202.11/33.73    (69)   ~ (all_52_29 = all_10_2)
% 202.11/33.73    (70)  all_58_7 = all_52_13
% 202.11/33.73    (71)   ~ (all_10_0 = all_4_2)
% 202.11/33.73    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.11/33.73    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.73    (74)   ~ (all_52_5 = all_52_7)
% 202.11/33.73    (75)  all_58_12 = all_52_7
% 202.11/33.73    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.73    (77)  op(e2, e1) = all_52_19
% 202.11/33.73    (78)   ~ (all_52_7 = all_14_2)
% 202.11/33.73    (79)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.11/33.73    (80)  all_58_2 = all_52_3
% 202.11/33.73    (81)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.73    (82)  all_56_2 = all_52_17
% 202.11/33.73    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.73    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.73    (85)  all_56_7 = all_52_27
% 202.11/33.73    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.73    (87)   ~ (e2 = e0)
% 202.11/33.73    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.11/33.73    (89)  op(all_4_2, e2) = all_4_1
% 202.11/33.73    (90)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.73    (91)   ~ (all_52_5 = all_52_29)
% 202.11/33.73    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.73    (93)  all_56_6 = all_52_19
% 202.11/33.73    (94)   ~ (all_52_15 = all_14_2)
% 202.11/33.73    (95)   ~ (all_52_19 = all_52_27)
% 202.11/33.73    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.73    (97)  op(e3, e1) = all_52_17
% 202.11/33.73    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.11/33.73    (99)  op(e0, e3) = all_52_7
% 202.11/33.73    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.73    (101)   ~ (all_52_9 = all_52_25)
% 202.11/33.73    (102)  all_58_15 = all_14_2
% 202.11/33.73    (103)   ~ (all_52_19 = all_10_2)
% 202.11/33.73    (104)  op(all_52_23, all_52_23) = all_52_22
% 202.11/33.73    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.73    (106)   ~ (all_10_0 = all_10_2)
% 202.11/33.73    (107)  all_58_8 = all_10_2
% 202.11/33.73    (108)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.73    (109)   ~ (all_52_5 = all_10_2)
% 202.11/33.73    (110)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.73    (111)   ~ (all_52_23 = all_14_2)
% 202.11/33.73    (112)  all_56_12 = all_52_7
% 202.11/33.73    (113)  op(all_52_17, all_52_17) = all_52_16
% 202.11/33.73    (114)  all_8_2 = all_6_2
% 202.11/33.73    (115)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.73    (116)   ~ (all_52_25 = all_6_2)
% 202.11/33.73    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.73    (118)   ~ (all_52_9 = all_4_2)
% 202.11/33.73    (119)   ~ (all_52_5 = all_6_2)
% 202.11/33.73    (120)   ~ (all_52_9 = all_6_2)
% 202.11/33.73    (121)  op(e3, all_6_1) = e2
% 202.11/33.73    (122)  all_56_0 = all_6_2
% 202.11/33.73    (123)  op(e3, e3) = all_6_2
% 202.11/33.73    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.73    (125)   ~ (all_52_27 = all_14_2)
% 202.11/33.73    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.73    (127)  all_56_14 = all_52_23
% 202.11/33.73    (128)   ~ (all_52_29 = all_10_0)
% 202.11/33.73    (129)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.73    (130)  all_40_0 = all_10_0
% 202.11/33.73    (131)  all_56_3 = all_52_25
% 202.11/33.73    (132)   ~ (all_52_3 = all_52_7)
% 202.11/33.73    (133)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.74    (134)  all_58_5 = all_52_19
% 202.11/33.74    (135)  all_56_1 = all_52_9
% 202.11/33.74    (136)   ~ (all_52_15 = all_4_2)
% 202.11/33.74    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.11/33.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.11/33.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.11/33.74    (138)   ~ (all_52_27 = all_4_2)
% 202.11/33.74    (139)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 202.11/33.74             all_58_13 = e0 | all_58_14 = e0)
% 202.11/33.74    (140)  all_58_6 = all_52_5
% 202.11/33.74    (141)  op(all_10_2, e1) = e2
% 202.11/33.74    (142)  op(e3, e2) = all_52_9
% 202.11/33.74    (143)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.74    (144)   ~ (all_52_17 = all_6_2)
% 202.11/33.74    (145)   ~ (e1 = e0)
% 202.11/33.74    (146)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.11/33.74    (147)   ~ (e3 = e2)
% 202.11/33.74    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.74    (149)  all_44_1 = all_6_1
% 202.11/33.74    (150)   ~ (all_52_9 = all_52_17)
% 202.11/33.74    (151)  all_56_10 = all_10_2
% 202.11/33.74    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.74    (153)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.74    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.74    (155)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.74    (156)  op(all_10_0, all_10_0) = all_52_12
% 202.11/33.74    (157)  op(e1, e1) = all_10_2
% 202.11/33.74    (158)   ~ (all_52_23 = all_10_2)
% 202.11/33.74    (159)   ~ (all_52_7 = all_52_23)
% 202.11/33.74    (160)   ~ (all_52_17 = all_52_19)
% 202.11/33.74    (161)   ~ (all_52_5 = all_10_0)
% 202.11/33.74    (162)  all_58_3 = all_4_2
% 202.11/33.74    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.11/33.74    (164)  all_56_13 = all_52_15
% 202.11/33.74    (165)   ~ (all_52_3 = all_4_2)
% 202.11/33.74    (166)   ~ (all_52_9 = all_10_0)
% 202.11/33.74    (167)   ~ (all_52_19 = all_4_2)
% 202.11/33.74    (168)   ~ (all_52_17 = all_52_23)
% 202.11/33.74    (169)  all_8_1 = all_6_1
% 202.11/33.74    (170)  op(all_6_2, e3) = all_6_1
% 202.11/33.74    (171)   ~ (all_52_13 = all_52_29)
% 202.11/33.74    (172)  all_58_4 = all_52_17
% 202.11/33.74    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.74    (174)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.74  
% 202.11/33.74  Begin of proof
% 202.11/33.74  | 
% 202.11/33.74  | ALPHA: (139) implies:
% 202.11/33.74  |   (175)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.74  |   (176)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.11/33.74  | 
% 202.11/33.74  | REDUCE: (55), (102) imply:
% 202.11/33.74  |   (177)   ~ (all_14_2 = e0)
% 202.11/33.74  | 
% 202.11/33.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.11/33.74  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.11/33.74  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.11/33.74  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 202.11/33.74  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 202.11/33.74  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 202.11/33.74  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 202.11/33.74  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 202.11/33.74  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 202.11/33.74  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 202.11/33.74  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 202.11/33.74  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 202.11/33.74  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 202.11/33.74  |            (138), (140), (141), (142), (143), (144), (145), (146), (147),
% 202.11/33.74  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 202.11/33.74  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 202.11/33.74  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 202.11/33.74  |            (175), (176), (177) are inconsistent by sub-proof #351.
% 202.11/33.74  | 
% 202.11/33.74  End of proof
% 202.11/33.74  
% 202.11/33.74  Sub-proof #351 shows that the following formulas are inconsistent:
% 202.11/33.74  ----------------------------------------------------------------
% 202.11/33.74    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.11/33.74    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.74    (3)   ~ (all_52_15 = all_52_23)
% 202.11/33.74    (4)   ~ (all_52_25 = all_52_27)
% 202.11/33.74    (5)  all_58_14 = all_52_23
% 202.11/33.74    (6)   ~ (e3 = e1)
% 202.11/33.74    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.74    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.74    (9)  all_58_1 = all_52_9
% 202.11/33.74    (10)   ~ (all_52_9 = all_52_13)
% 202.11/33.74    (11)   ~ (e3 = e0)
% 202.11/33.74    (12)  op(e2, e3) = all_52_3
% 202.11/33.74    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.74    (14)   ~ (all_52_7 = all_52_15)
% 202.11/33.74    (15)   ~ (all_52_3 = all_52_19)
% 202.11/33.74    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.74    (17)   ~ (all_52_17 = all_52_25)
% 202.11/33.74    (18)   ~ (all_52_3 = all_6_2)
% 202.11/33.74    (19)  all_44_2 = all_6_2
% 202.11/33.74    (20)  all_58_0 = all_6_2
% 202.11/33.74    (21)  op(all_14_2, e0) = all_14_1
% 202.11/33.74    (22)  all_56_4 = all_52_3
% 202.11/33.74    (23)   ~ (all_52_17 = all_10_2)
% 202.11/33.74    (24)   ~ (all_10_0 = e3)
% 202.11/33.74    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.74    (26)  all_40_2 = all_10_2
% 202.11/33.74    (27)  op(e3, e0) = all_52_25
% 202.11/33.74    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.74    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.74    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.74    (31)   ~ (all_52_27 = all_52_29)
% 202.11/33.74    (32)  all_58_13 = all_52_15
% 202.11/33.74    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.11/33.74    (34)  all_58_9 = all_52_25
% 202.11/33.74    (35)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.11/33.74    (36)   ~ (all_52_29 = all_14_2)
% 202.11/33.74    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.74    (38)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.74    (39)  op(e1, e3) = all_52_5
% 202.11/33.74    (40)  op(e2, e2) = all_4_2
% 202.11/33.74    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.74    (42)  all_58_7 = all_10_0
% 202.11/33.74    (43)   ~ (all_52_3 = all_52_5)
% 202.11/33.74    (44)  all_58_11 = all_52_29
% 202.11/33.74    (45)  all_56_5 = all_4_2
% 202.11/33.74    (46)   ~ (all_52_25 = all_14_2)
% 202.11/33.74    (47)   ~ (all_52_9 = all_52_15)
% 202.11/33.74    (48)   ~ (all_52_3 = all_52_27)
% 202.11/33.74    (49)  op(all_10_2, e1) = all_10_1
% 202.11/33.74    (50)  op(all_6_2, all_6_2) = all_52_0
% 202.11/33.74    (51)   ~ (all_52_7 = all_6_2)
% 202.11/33.74    (52)  op(e0, e0) = all_14_2
% 202.11/33.74    (53)  all_56_15 = all_14_2
% 202.11/33.74    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.74    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.11/33.74    (56)  all_56_11 = all_52_29
% 202.11/33.74    (57)   ~ (all_10_0 = e2)
% 202.11/33.74    (58)   ~ (all_4_1 = e1)
% 202.11/33.74    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.74    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.74    (61)   ~ (e2 = e1)
% 202.11/33.74    (62)  all_58_10 = all_52_27
% 202.11/33.74    (63)  all_56_8 = all_52_5
% 202.11/33.74    (64)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.74    (65)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.74    (66)   ~ (all_52_19 = all_52_23)
% 202.11/33.74    (67)  all_56_9 = all_10_0
% 202.11/33.74    (68)   ~ (all_52_25 = all_52_29)
% 202.11/33.74    (69)   ~ (all_52_29 = all_10_2)
% 202.11/33.74    (70)  all_58_7 = all_52_13
% 202.11/33.74    (71)   ~ (all_10_0 = all_4_2)
% 202.11/33.74    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.11/33.74    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.74    (74)   ~ (all_52_5 = all_52_7)
% 202.11/33.74    (75)  all_58_12 = all_52_7
% 202.11/33.74    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.74    (77)  op(e2, e1) = all_52_19
% 202.11/33.74    (78)   ~ (all_52_7 = all_14_2)
% 202.11/33.74    (79)   ~ (all_14_2 = e0)
% 202.11/33.74    (80)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.11/33.74    (81)  all_58_2 = all_52_3
% 202.11/33.74    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.74    (83)  all_56_2 = all_52_17
% 202.11/33.74    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.74    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.74    (86)  all_56_7 = all_52_27
% 202.11/33.74    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.74    (88)   ~ (e2 = e0)
% 202.11/33.74    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.11/33.74    (90)  op(all_4_2, e2) = all_4_1
% 202.11/33.74    (91)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.74    (92)   ~ (all_52_5 = all_52_29)
% 202.11/33.74    (93)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.74    (94)  all_56_6 = all_52_19
% 202.11/33.74    (95)   ~ (all_52_15 = all_14_2)
% 202.11/33.74    (96)   ~ (all_52_19 = all_52_27)
% 202.11/33.74    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.74    (98)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.74    (99)  op(e3, e1) = all_52_17
% 202.11/33.74    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.11/33.74    (101)  op(e0, e3) = all_52_7
% 202.11/33.74    (102)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.74    (103)   ~ (all_52_9 = all_52_25)
% 202.11/33.74    (104)  all_58_15 = all_14_2
% 202.11/33.74    (105)   ~ (all_52_19 = all_10_2)
% 202.11/33.74    (106)  op(all_52_23, all_52_23) = all_52_22
% 202.11/33.74    (107)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.74    (108)   ~ (all_10_0 = all_10_2)
% 202.11/33.74    (109)  all_58_8 = all_10_2
% 202.11/33.74    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.74    (111)   ~ (all_52_5 = all_10_2)
% 202.11/33.74    (112)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.74    (113)   ~ (all_52_23 = all_14_2)
% 202.11/33.74    (114)  all_56_12 = all_52_7
% 202.11/33.74    (115)  op(all_52_17, all_52_17) = all_52_16
% 202.11/33.74    (116)  all_8_2 = all_6_2
% 202.11/33.74    (117)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.74    (118)   ~ (all_52_25 = all_6_2)
% 202.11/33.74    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.74    (120)   ~ (all_52_9 = all_4_2)
% 202.11/33.74    (121)   ~ (all_52_5 = all_6_2)
% 202.11/33.74    (122)   ~ (all_52_9 = all_6_2)
% 202.11/33.74    (123)  op(e3, all_6_1) = e2
% 202.11/33.74    (124)  all_56_0 = all_6_2
% 202.11/33.74    (125)  op(e3, e3) = all_6_2
% 202.11/33.74    (126)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.74    (127)   ~ (all_52_27 = all_14_2)
% 202.11/33.74    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.74    (129)  all_56_14 = all_52_23
% 202.11/33.74    (130)   ~ (all_52_29 = all_10_0)
% 202.11/33.74    (131)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.74    (132)  all_40_0 = all_10_0
% 202.11/33.74    (133)  all_56_3 = all_52_25
% 202.11/33.74    (134)   ~ (all_52_3 = all_52_7)
% 202.11/33.74    (135)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.74    (136)  all_58_5 = all_52_19
% 202.11/33.74    (137)  all_56_1 = all_52_9
% 202.11/33.74    (138)   ~ (all_52_15 = all_4_2)
% 202.11/33.74    (139)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.11/33.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.11/33.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.11/33.74    (140)   ~ (all_52_27 = all_4_2)
% 202.11/33.74    (141)  all_58_6 = all_52_5
% 202.11/33.74    (142)  op(all_10_2, e1) = e2
% 202.11/33.74    (143)  op(e3, e2) = all_52_9
% 202.11/33.74    (144)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.74    (145)   ~ (all_52_17 = all_6_2)
% 202.11/33.74    (146)   ~ (e1 = e0)
% 202.11/33.74    (147)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.11/33.74    (148)   ~ (e3 = e2)
% 202.11/33.74    (149)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.74    (150)  all_44_1 = all_6_1
% 202.11/33.74    (151)   ~ (all_52_9 = all_52_17)
% 202.11/33.74    (152)  all_56_10 = all_10_2
% 202.11/33.74    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.74    (154)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.74    (155)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.74    (156)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.74    (157)  op(all_10_0, all_10_0) = all_52_12
% 202.11/33.74    (158)  op(e1, e1) = all_10_2
% 202.11/33.74    (159)   ~ (all_52_23 = all_10_2)
% 202.11/33.74    (160)   ~ (all_52_7 = all_52_23)
% 202.11/33.74    (161)   ~ (all_52_17 = all_52_19)
% 202.11/33.74    (162)   ~ (all_52_5 = all_10_0)
% 202.11/33.74    (163)  all_58_3 = all_4_2
% 202.11/33.74    (164)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.11/33.74    (165)  all_56_13 = all_52_15
% 202.11/33.74    (166)   ~ (all_52_3 = all_4_2)
% 202.11/33.74    (167)   ~ (all_52_9 = all_10_0)
% 202.11/33.74    (168)   ~ (all_52_19 = all_4_2)
% 202.11/33.74    (169)   ~ (all_52_17 = all_52_23)
% 202.11/33.74    (170)  all_8_1 = all_6_1
% 202.11/33.74    (171)  op(all_6_2, e3) = all_6_1
% 202.11/33.74    (172)   ~ (all_52_13 = all_52_29)
% 202.11/33.74    (173)  all_58_4 = all_52_17
% 202.11/33.74    (174)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.74    (175)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.74  
% 202.11/33.74  Begin of proof
% 202.11/33.74  | 
% 202.11/33.74  | BETA: splitting (154) gives:
% 202.11/33.74  | 
% 202.11/33.74  | Case 1:
% 202.11/33.74  | | 
% 202.11/33.74  | |   (176)  all_56_9 = e3
% 202.11/33.74  | | 
% 202.11/33.74  | | REF_CLOSE: (24), (67), (176) are inconsistent by sub-proof #1006.
% 202.11/33.74  | | 
% 202.11/33.74  | Case 2:
% 202.11/33.74  | | 
% 202.11/33.74  | |   (177)   ~ (all_56_9 = e3)
% 202.11/33.74  | |   (178)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.74  | | 
% 202.11/33.74  | | BETA: splitting (139) gives:
% 202.11/33.74  | | 
% 202.11/33.74  | | Case 1:
% 202.11/33.74  | | | 
% 202.11/33.74  | | |   (179)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.74  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 202.11/33.74  | | |            e0)
% 202.11/33.74  | | | 
% 202.11/33.74  | | | REF_CLOSE: (2), (7), (8), (9), (13), (14), (16), (20), (24), (28), (32),
% 202.11/33.74  | | |            (34), (40), (42), (46), (50), (51), (52), (53), (54), (57),
% 202.11/33.74  | | |            (58), (59), (64), (65), (67), (75), (78), (81), (84), (85),
% 202.11/33.74  | | |            (88), (90), (95), (101), (102), (108), (110), (111), (114),
% 202.11/33.74  | | |            (115), (116), (120), (122), (123), (124), (125), (128), (131),
% 202.11/33.74  | | |            (137), (138), (141), (143), (144), (148), (149), (151), (153),
% 202.11/33.74  | | |            (155), (157), (158), (163), (165), (166), (167), (170), (171),
% 202.11/33.74  | | |            (173), (178), (179) are inconsistent by sub-proof #429.
% 202.11/33.74  | | | 
% 202.11/33.74  | | Case 2:
% 202.11/33.74  | | | 
% 202.11/33.74  | | |   (180)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.11/33.74  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.11/33.74  | | |            all_52_30 = e0)
% 202.11/33.74  | | | 
% 202.11/33.74  | | | BETA: splitting (180) gives:
% 202.11/33.74  | | | 
% 202.11/33.74  | | | Case 1:
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | |   (181)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.11/33.74  | | | |          e0
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | ALPHA: (181) implies:
% 202.11/33.74  | | | |   (182)  all_52_22 = e0
% 202.11/33.74  | | | |   (183)  all_52_20 = e1
% 202.11/33.74  | | | |   (184)  all_52_18 = e2
% 202.11/33.74  | | | |   (185)  all_52_16 = e3
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | REDUCE: (115), (185) imply:
% 202.11/33.74  | | | |   (186)  op(all_52_17, all_52_17) = e3
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | REDUCE: (30), (184) imply:
% 202.11/33.74  | | | |   (187)  op(all_52_19, all_52_19) = e2
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | REDUCE: (106), (182) imply:
% 202.11/33.74  | | | |   (188)  op(all_52_23, all_52_23) = e0
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | REDUCE: (33), (183) imply:
% 202.11/33.74  | | | |   (189)  op(all_10_2, all_10_2) = e1
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | BETA: splitting (110) gives:
% 202.11/33.74  | | | | 
% 202.11/33.74  | | | | Case 1:
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | |   (190)  all_56_15 = e3
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | | COMBINE_EQS: (53), (190) imply:
% 202.11/33.74  | | | | |   (191)  all_14_2 = e3
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (15), (18), (20), (21), (22),
% 202.11/33.74  | | | | |            (24), (27), (28), (34), (36), (40), (41), (42), (44), (46),
% 202.11/33.74  | | | | |            (64), (73), (75), (76), (78), (81), (84), (87), (88), (99),
% 202.11/33.74  | | | | |            (102), (109), (111), (113), (118), (123), (125), (128),
% 202.11/33.74  | | | | |            (135), (136), (141), (142), (145), (148), (151), (153),
% 202.11/33.74  | | | | |            (166), (171), (173), (186), (187), (189), (191) are
% 202.11/33.74  | | | | |            inconsistent by sub-proof #414.
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | Case 2:
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | |   (192)   ~ (all_56_15 = e3)
% 202.11/33.74  | | | | |   (193)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | | REDUCE: (53), (192) imply:
% 202.11/33.74  | | | | |   (194)   ~ (all_14_2 = e3)
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | | BETA: splitting (102) gives:
% 202.11/33.74  | | | | | 
% 202.11/33.74  | | | | | Case 1:
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | |   (195)  all_58_1 = e3
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (13), (14), (16), (20),
% 202.11/33.74  | | | | | |            (26), (32), (34), (36), (37), (40), (42), (44), (47),
% 202.11/33.74  | | | | | |            (51), (52), (56), (57), (60), (61), (64), (66), (67),
% 202.11/33.74  | | | | | |            (69), (74), (75), (76), (80), (83), (85), (88), (91),
% 202.11/33.74  | | | | | |            (93), (97), (98), (99), (101), (104), (105), (109),
% 202.11/33.74  | | | | | |            (114), (116), (120), (123), (125), (132), (135), (136),
% 202.11/33.74  | | | | | |            (141), (142), (143), (144), (145), (146), (151), (153),
% 202.11/33.74  | | | | | |            (158), (159), (160), (167), (169), (170), (171), (173),
% 202.11/33.74  | | | | | |            (178), (186), (187), (188), (194), (195) are inconsistent
% 202.11/33.74  | | | | | |            by sub-proof #409.
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | Case 2:
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | |   (196)   ~ (all_58_1 = e3)
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | | REDUCE: (9), (196) imply:
% 202.11/33.74  | | | | | |   (197)   ~ (all_52_9 = e3)
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | | BETA: splitting (149) gives:
% 202.11/33.74  | | | | | | 
% 202.11/33.74  | | | | | | Case 1:
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | |   (198)  all_56_1 = e3
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | | COMBINE_EQS: (137), (198) imply:
% 202.11/33.74  | | | | | | |   (199)  all_52_9 = e3
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | | REDUCE: (197), (199) imply:
% 202.11/33.74  | | | | | | |   (200)  $false
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | | CLOSE: (200) is inconsistent.
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | Case 2:
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | |   (201)   ~ (all_56_1 = e3)
% 202.11/33.74  | | | | | | |   (202)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | | BETA: splitting (35) gives:
% 202.11/33.74  | | | | | | | 
% 202.11/33.74  | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | |   (203)  all_58_6 = e2
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | COMBINE_EQS: (141), (203) imply:
% 202.11/33.74  | | | | | | | |   (204)  all_52_5 = e2
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | SIMP: (204) implies:
% 202.11/33.74  | | | | | | | |   (205)  all_52_5 = e2
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | REDUCE: (92), (205) imply:
% 202.11/33.74  | | | | | | | |   (206)   ~ (all_52_29 = e2)
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | SIMP: (206) implies:
% 202.11/33.74  | | | | | | | |   (207)   ~ (all_52_29 = e2)
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | REDUCE: (162), (205) imply:
% 202.11/33.74  | | | | | | | |   (208)   ~ (all_10_0 = e2)
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | REDUCE: (28), (205) imply:
% 202.11/33.74  | | | | | | | |   (209)  op(e2, e2) = all_52_4
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, all_52_4, e2, e2,
% 202.11/33.74  | | | | | | | |              simplifying with (40), (209) gives:
% 202.11/33.74  | | | | | | | |   (210)  all_52_4 = all_4_2
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | BETA: splitting (76) gives:
% 202.11/33.74  | | | | | | | | 
% 202.11/33.74  | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | |   (211)  all_58_6 = e3
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | COMBINE_EQS: (203), (211) imply:
% 202.11/33.74  | | | | | | | | |   (212)  e3 = e2
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | REDUCE: (148), (212) imply:
% 202.11/33.74  | | | | | | | | |   (213)  $false
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | CLOSE: (213) is inconsistent.
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | |   (214)   ~ (all_58_6 = e3)
% 202.11/33.74  | | | | | | | | |   (215)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | REDUCE: (203), (214) imply:
% 202.11/33.74  | | | | | | | | |   (216)   ~ (e3 = e2)
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | BETA: splitting (174) gives:
% 202.11/33.74  | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | |   (217)  all_56_10 = e3
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | COMBINE_EQS: (152), (217) imply:
% 202.11/33.74  | | | | | | | | | |   (218)  all_10_2 = e3
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | SIMP: (218) implies:
% 202.11/33.74  | | | | | | | | | |   (219)  all_10_2 = e3
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | COMBINE_EQS: (26), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (220)  all_40_2 = e3
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | COMBINE_EQS: (109), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (221)  all_58_8 = e3
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | REDUCE: (23), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (222)   ~ (all_52_17 = e3)
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | REDUCE: (159), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (223)   ~ (all_52_23 = e3)
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | REDUCE: (69), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (224)   ~ (all_52_29 = e3)
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | REDUCE: (189), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (225)  op(e3, e3) = e1
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | REDUCE: (142), (219) imply:
% 202.11/33.74  | | | | | | | | | |   (226)  op(e3, e1) = e2
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | BETA: splitting (80) gives:
% 202.11/33.74  | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | |   (227)   ~ (all_40_2 = e3)
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | REDUCE: (220), (227) imply:
% 202.11/33.74  | | | | | | | | | | |   (228)  $false
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | |   (229)   ~ (all_40_0 = e0)
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | REDUCE: (132), (229) imply:
% 202.11/33.74  | | | | | | | | | | |   (230)   ~ (all_10_0 = e0)
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | BETA: splitting (147) gives:
% 202.11/33.74  | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | |   (231)  all_58_6 = e0
% 202.11/33.74  | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | REF_CLOSE: (88), (203), (231) are inconsistent by sub-proof
% 202.11/33.74  | | | | | | | | | | | |            #801.
% 202.11/33.74  | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | |   (232)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.11/33.74  | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | BETA: splitting (232) gives:
% 202.11/33.74  | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | |   (233)  all_58_7 = e0
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | COMBINE_EQS: (42), (233) imply:
% 202.11/33.74  | | | | | | | | | | | | |   (234)  all_10_0 = e0
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | REDUCE: (230), (234) imply:
% 202.11/33.74  | | | | | | | | | | | | |   (235)  $false
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | |   (236)  all_58_8 = e0 | all_58_11 = e0
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | BETA: splitting (236) gives:
% 202.11/33.74  | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | |   (237)  all_58_8 = e0
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | COMBINE_EQS: (221), (237) imply:
% 202.11/33.74  | | | | | | | | | | | | | |   (238)  e3 = e0
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | REDUCE: (11), (238) imply:
% 202.11/33.74  | | | | | | | | | | | | | |   (239)  $false
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | |   (240)  all_58_11 = e0
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | COMBINE_EQS: (44), (240) imply:
% 202.11/33.74  | | | | | | | | | | | | | |   (241)  all_52_29 = e0
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | SIMP: (241) implies:
% 202.11/33.74  | | | | | | | | | | | | | |   (242)  all_52_29 = e0
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | REDUCE: (224), (242) imply:
% 202.11/33.74  | | | | | | | | | | | | | |   (243)   ~ (e3 = e0)
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | REDUCE: (207), (242) imply:
% 202.11/33.74  | | | | | | | | | | | | | |   (244)   ~ (e2 = e0)
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | REDUCE: (112), (242) imply:
% 202.11/33.74  | | | | | | | | | | | | | |   (245)  op(e0, e0) = all_52_28
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 202.11/33.74  | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | |   (246)  all_58_6 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | COMBINE_EQS: (203), (246) imply:
% 202.11/33.74  | | | | | | | | | | | | | | |   (247)  e2 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | SIMP: (247) implies:
% 202.11/33.74  | | | | | | | | | | | | | | |   (248)  e2 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | REDUCE: (61), (248) imply:
% 202.11/33.74  | | | | | | | | | | | | | | |   (249)  $false
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent.
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | |   (250)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | |   (251)  all_58_7 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (251) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (252)  all_10_0 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (252) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (253)  all_40_0 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | REDUCE: (71), (252) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (254)   ~ (all_4_2 = e1)
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (255)   ~ (all_4_2 = e1)
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_28, e0,
% 202.11/33.74  | | | | | | | | | | | | | | | |              e0, simplifying with (52), (245) gives:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (256)  all_52_28 = all_14_2
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_17, e2, e1, e3,
% 202.11/33.74  | | | | | | | | | | | | | | | |              simplifying with (99), (226) gives:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (257)  all_52_17 = e2
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, e1, e3, e3,
% 202.11/33.74  | | | | | | | | | | | | | | | |              simplifying with (125), (225) gives:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (258)  all_6_2 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (258) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (259)  all_44_2 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (258) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (260)  all_58_0 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | REDUCE: (151), (257) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (261)   ~ (all_52_9 = e2)
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | REDUCE: (122), (258) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (262)   ~ (all_52_9 = e1)
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | REDUCE: (161), (257) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (263)   ~ (all_52_19 = e2)
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | SIMP: (263) implies:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (264)   ~ (all_52_19 = e2)
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | REDUCE: (186), (257) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | |   (265)  op(e2, e2) = e3
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (9), (11), (12), (13), (14), (15),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (16), (17), (18), (20), (22), (23), (24), (25),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (26), (27), (32), (34), (40), (41), (42), (43),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (44), (46), (47), (51), (52), (53), (57), (60),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (64), (67), (68), (73), (74), (75), (76), (80),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (81), (83), (84), (85), (87), (88), (90), (93),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (95), (98), (99), (101), (103), (104), (109),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (111), (113), (114), (116), (120), (121), (122),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (123), (125), (126), (128), (131), (132), (135),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (136), (137), (138), (141), (142), (143), (144),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (145), (148), (149), (151), (153), (158), (159),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (160), (161), (163), (164), (169), (170), (171),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (173), (175), (178), (186), (187), (188), (189),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (193), (197), (202), (223), (251), (253), (255),
% 202.11/33.74  | | | | | | | | | | | | | | | |            (259), (260), (261), (262), (264), (265) are
% 202.11/33.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #354.
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | |   (266)  all_58_8 = e1 | all_58_11 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | Case 1:
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | |   (267)  all_58_8 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (267) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | | |   (268)  e3 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | | REDUCE: (6), (268) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | | |   (269)  $false
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent.
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | Case 2:
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | |   (270)  all_58_11 = e1
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | | COMBINE_EQS: (240), (270) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | | |   (271)  e1 = e0
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | | REDUCE: (146), (271) imply:
% 202.11/33.74  | | | | | | | | | | | | | | | | |   (272)  $false
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | | CLOSE: (272) is inconsistent.
% 202.11/33.74  | | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | | End of split
% 202.11/33.74  | | | | | | | | | | | | | | | | 
% 202.11/33.74  | | | | | | | | | | | | | | | End of split
% 202.11/33.74  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | |   (273)   ~ (all_56_10 = e3)
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | REDUCE: (152), (273) imply:
% 202.11/33.75  | | | | | | | | | |   (274)   ~ (all_10_2 = e3)
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | BETA: splitting (215) gives:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | |   (275)  all_58_7 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | COMBINE_EQS: (42), (275) imply:
% 202.11/33.75  | | | | | | | | | | |   (276)  all_10_0 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | REDUCE: (24), (276) imply:
% 202.11/33.75  | | | | | | | | | | |   (277)  $false
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | |   (278)  all_58_8 = e3 | all_58_11 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | BETA: splitting (278) gives:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | |   (279)  all_58_8 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REF_CLOSE: (109), (274), (279) are inconsistent by sub-proof
% 202.11/33.75  | | | | | | | | | | | |            #950.
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | |   (280)  all_58_11 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REF_CLOSE: (8), (9), (20), (34), (44), (68), (123), (125),
% 202.11/33.75  | | | | | | | | | | | |            (128), (145), (148), (153), (171), (173), (186),
% 202.11/33.75  | | | | | | | | | | | |            (197), (280) are inconsistent by sub-proof #420.
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | 
% 202.11/33.75  | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | 
% 202.11/33.75  | | | | | | | |   (281)   ~ (all_58_6 = e2)
% 202.11/33.75  | | | | | | | |   (282)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.11/33.75  | | | | | | | | 
% 202.11/33.75  | | | | | | | | REDUCE: (141), (281) imply:
% 202.11/33.75  | | | | | | | |   (283)   ~ (all_52_5 = e2)
% 202.11/33.75  | | | | | | | | 
% 202.11/33.75  | | | | | | | | BETA: splitting (107) gives:
% 202.11/33.75  | | | | | | | | 
% 202.11/33.75  | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | |   (284)  all_56_8 = e3
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | COMBINE_EQS: (63), (284) imply:
% 202.11/33.75  | | | | | | | | |   (285)  all_52_5 = e3
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | SIMP: (285) implies:
% 202.11/33.75  | | | | | | | | |   (286)  all_52_5 = e3
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | REDUCE: (43), (286) imply:
% 202.11/33.75  | | | | | | | | |   (287)   ~ (all_52_3 = e3)
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | REDUCE: (74), (286) imply:
% 202.11/33.75  | | | | | | | | |   (288)   ~ (all_52_7 = e3)
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | SIMP: (288) implies:
% 202.11/33.75  | | | | | | | | |   (289)   ~ (all_52_7 = e3)
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | REDUCE: (28), (286) imply:
% 202.11/33.75  | | | | | | | | |   (290)  op(e3, e3) = all_52_4
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_4, e3, e3,
% 202.11/33.75  | | | | | | | | |              simplifying with (125), (290) gives:
% 202.11/33.75  | | | | | | | | |   (291)  all_52_4 = all_6_2
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | BETA: splitting (126) gives:
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | |   (292)  all_58_9 = e3
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | COMBINE_EQS: (34), (292) imply:
% 202.11/33.75  | | | | | | | | | |   (293)  all_52_25 = e3
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | SIMP: (293) implies:
% 202.11/33.75  | | | | | | | | | |   (294)  all_52_25 = e3
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | REDUCE: (4), (294) imply:
% 202.11/33.75  | | | | | | | | | |   (295)   ~ (all_52_27 = e3)
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | SIMP: (295) implies:
% 202.11/33.75  | | | | | | | | | |   (296)   ~ (all_52_27 = e3)
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | REDUCE: (175), (294) imply:
% 202.11/33.75  | | | | | | | | | |   (297)  op(e3, e3) = all_52_24
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_24, e3, e3,
% 202.11/33.75  | | | | | | | | | |              simplifying with (125), (297) gives:
% 202.11/33.75  | | | | | | | | | |   (298)  all_52_24 = all_6_2
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | BETA: splitting (54) gives:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | |   (299)  all_58_2 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | REF_CLOSE: (81), (287), (299) are inconsistent by sub-proof
% 202.11/33.75  | | | | | | | | | | |            #1369.
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | |   (300)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | BETA: splitting (89) gives:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | |   (301)  all_56_5 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | COMBINE_EQS: (45), (301) imply:
% 202.11/33.75  | | | | | | | | | | | |   (302)  all_4_2 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | SIMP: (302) implies:
% 202.11/33.75  | | | | | | | | | | | |   (303)  all_4_2 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | COMBINE_EQS: (163), (303) imply:
% 202.11/33.75  | | | | | | | | | | | |   (304)  all_58_3 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REDUCE: (138), (303) imply:
% 202.11/33.75  | | | | | | | | | | | |   (305)   ~ (all_52_15 = e3)
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REDUCE: (131), (303) imply:
% 202.11/33.75  | | | | | | | | | | | |   (306)  op(e3, e3) = all_52_10
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REDUCE: (90), (303) imply:
% 202.11/33.75  | | | | | | | | | | | |   (307)  op(e3, e2) = all_4_1
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (13), (14), (16),
% 202.11/33.75  | | | | | | | | | | | |            (20), (23), (24), (26), (32), (34), (42), (44),
% 202.11/33.75  | | | | | | | | | | | |            (46), (47), (51), (52), (53), (57), (60), (64),
% 202.11/33.75  | | | | | | | | | | | |            (67), (68), (74), (75), (76), (80), (83), (93),
% 202.11/33.75  | | | | | | | | | | | |            (95), (98), (99), (101), (103), (104), (109),
% 202.11/33.75  | | | | | | | | | | | |            (113), (114), (116), (122), (123), (125), (126),
% 202.11/33.75  | | | | | | | | | | | |            (128), (132), (135), (137), (141), (142), (143),
% 202.11/33.75  | | | | | | | | | | | |            (144), (145), (146), (148), (149), (151), (153),
% 202.11/33.75  | | | | | | | | | | | |            (158), (159), (160), (164), (169), (170), (171),
% 202.11/33.75  | | | | | | | | | | | |            (173), (175), (178), (186), (188), (189), (193),
% 202.11/33.75  | | | | | | | | | | | |            (197), (304), (305), (306), (307) are inconsistent
% 202.11/33.75  | | | | | | | | | | | |            by sub-proof #408.
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | |   (308)   ~ (all_56_5 = e3)
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REDUCE: (45), (308) imply:
% 202.11/33.75  | | | | | | | | | | | |   (309)   ~ (all_4_2 = e3)
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REF_CLOSE: (8), (9), (12), (15), (18), (20), (22), (27),
% 202.11/33.75  | | | | | | | | | | | |            (34), (41), (43), (62), (73), (75), (81), (84),
% 202.11/33.75  | | | | | | | | | | | |            (87), (88), (99), (121), (123), (125), (128),
% 202.11/33.75  | | | | | | | | | | | |            (136), (141), (145), (148), (161), (163), (171),
% 202.11/33.75  | | | | | | | | | | | |            (173), (187), (197), (289), (296), (300), (309)
% 202.11/33.75  | | | | | | | | | | | |            are inconsistent by sub-proof #353.
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | |   (310)   ~ (all_58_9 = e3)
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | REDUCE: (34), (310) imply:
% 202.11/33.75  | | | | | | | | | |   (311)   ~ (all_52_25 = e3)
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | REF_CLOSE: (8), (9), (20), (34), (123), (125), (128), (145),
% 202.11/33.75  | | | | | | | | | |            (148), (153), (171), (173), (186), (197), (311)
% 202.11/33.75  | | | | | | | | | |            are inconsistent by sub-proof #446.
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | |   (312)   ~ (all_56_8 = e3)
% 202.11/33.75  | | | | | | | | |   (313)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | REDUCE: (63), (312) imply:
% 202.11/33.75  | | | | | | | | |   (314)   ~ (all_52_5 = e3)
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | BETA: splitting (76) gives:
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | |   (315)  all_58_6 = e3
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | REF_CLOSE: (141), (314), (315) are inconsistent by sub-proof
% 202.11/33.75  | | | | | | | | | |            #1328.
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | |   (316)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | BETA: splitting (126) gives:
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | |   (317)  all_58_9 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | COMBINE_EQS: (34), (317) imply:
% 202.11/33.75  | | | | | | | | | | |   (318)  all_52_25 = e3
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | REDUCE: (175), (318) imply:
% 202.11/33.75  | | | | | | | | | | |   (319)  op(e3, e3) = all_52_24
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | BETA: splitting (316) gives:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | |   (320)  all_58_7 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | COMBINE_EQS: (42), (320) imply:
% 202.11/33.75  | | | | | | | | | | | |   (321)  all_10_0 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | REDUCE: (24), (321) imply:
% 202.11/33.75  | | | | | | | | | | | |   (322)  $false
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | CLOSE: (322) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | |   (323)  all_58_8 = e3 | all_58_11 = e3
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | BETA: splitting (323) gives:
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | |   (324)  all_58_8 = e3
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | COMBINE_EQS: (109), (324) imply:
% 202.11/33.75  | | | | | | | | | | | | |   (325)  all_10_2 = e3
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | COMBINE_EQS: (26), (325) imply:
% 202.11/33.75  | | | | | | | | | | | | |   (326)  all_40_2 = e3
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | REDUCE: (23), (325) imply:
% 202.11/33.75  | | | | | | | | | | | | |   (327)   ~ (all_52_17 = e3)
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | REDUCE: (159), (325) imply:
% 202.11/33.75  | | | | | | | | | | | | |   (328)   ~ (all_52_23 = e3)
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | REDUCE: (189), (325) imply:
% 202.11/33.75  | | | | | | | | | | | | |   (329)  op(e3, e3) = e1
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | REDUCE: (142), (325) imply:
% 202.11/33.75  | | | | | | | | | | | | |   (330)  op(e3, e1) = e2
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | BETA: splitting (282) gives:
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | |   (331)  all_58_7 = e2
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | COMBINE_EQS: (42), (331) imply:
% 202.11/33.75  | | | | | | | | | | | | | |   (332)  all_10_0 = e2
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | REDUCE: (57), (332) imply:
% 202.11/33.75  | | | | | | | | | | | | | |   (333)  $false
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | CLOSE: (333) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | |   (334)  all_58_8 = e2 | all_58_11 = e2
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | |   (335)  all_58_8 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | COMBINE_EQS: (324), (335) imply:
% 202.11/33.75  | | | | | | | | | | | | | | |   (336)  e3 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | REDUCE: (148), (336) imply:
% 202.11/33.75  | | | | | | | | | | | | | | |   (337)  $false
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | CLOSE: (337) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | |   (338)  all_58_11 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | COMBINE_EQS: (44), (338) imply:
% 202.11/33.75  | | | | | | | | | | | | | | |   (339)  all_52_29 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | SIMP: (339) implies:
% 202.11/33.75  | | | | | | | | | | | | | | |   (340)  all_52_29 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | REDUCE: (130), (340) imply:
% 202.11/33.75  | | | | | | | | | | | | | | |   (341)   ~ (all_10_0 = e2)
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | REDUCE: (112), (340) imply:
% 202.11/33.75  | | | | | | | | | | | | | | |   (342)  op(e2, e2) = all_52_28
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | |   (343)   ~ (all_40_2 = e3)
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | REDUCE: (326), (343) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | |   (344)  $false
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | CLOSE: (344) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | |   (345)   ~ (all_40_0 = e0)
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | REDUCE: (132), (345) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | |   (346)   ~ (all_10_0 = e0)
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | |   (347)  all_56_9 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (67), (347) are inconsistent by sub-proof
% 202.11/33.75  | | | | | | | | | | | | | | | | |            #991.
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | |   (348)   ~ (all_56_9 = e2)
% 202.11/33.75  | | | | | | | | | | | | | | | | |   (349)  all_56_9 = e1 | all_56_9 = e0
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (350)  all_58_6 = e0
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (350) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (351)  all_52_5 = e0
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | SIMP: (351) implies:
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (352)  all_52_5 = e0
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | REDUCE: (314), (352) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (353)   ~ (e3 = e0)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | REDUCE: (283), (352) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (354)   ~ (e2 = e0)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | |   (355)  all_58_6 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (355) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | |   (356)  e1 = e0
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | REDUCE: (146), (356) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | |   (357)  $false
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | |   (358)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (358) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (359)  all_58_7 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (359) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (360)  all_10_0 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (360) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (361)  all_40_0 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (360) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (362)   ~ (all_4_2 = e1)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | SIMP: (362) implies:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (363)   ~ (all_4_2 = e1)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, all_52_28, e2, e2,
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |              simplifying with (40), (342) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (364)  all_52_28 = all_4_2
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_17, e2, e1, e3,
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |              simplifying with (99), (330) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (365)  all_52_17 = e2
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_24, e3, e3,
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |              simplifying with (125), (319) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (366)  all_52_24 = all_6_2
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e1, all_52_24, e3, e3,
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |              simplifying with (319), (329) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (367)  all_52_24 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (367) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (368)  all_6_2 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (368) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (369)  all_44_2 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (368) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (370)  all_58_0 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (365) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (371)   ~ (all_52_9 = e2)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (368) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (372)   ~ (all_52_9 = e1)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (365) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (373)   ~ (all_52_19 = e2)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | SIMP: (373) implies:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (374)   ~ (all_52_19 = e2)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (327), (365) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (375)   ~ (e3 = e2)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (365) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (376)  op(e2, e2) = e3
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (9), (11), (12), (13), (14), (15),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (16), (17), (18), (20), (22), (23), (24), (25),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (26), (27), (32), (34), (40), (41), (42), (43),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (44), (46), (47), (51), (52), (53), (57), (60),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (64), (67), (68), (73), (74), (75), (76), (80),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (81), (83), (84), (85), (87), (88), (90), (93),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (95), (98), (99), (101), (103), (104), (109),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (111), (113), (114), (116), (120), (121), (122),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (123), (125), (126), (128), (131), (132), (135),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (136), (137), (138), (141), (142), (143), (144),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (145), (148), (149), (151), (153), (158), (159),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (164), (169), (170), (171),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (173), (175), (178), (186), (187), (188), (189),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (193), (197), (202), (328), (359), (361), (363),
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            (369), (370), (371), (372), (374), (376) are
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #354.
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | |   (377)  all_58_8 = e1 | all_58_11 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | |   (378)  all_58_8 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (378) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | |   (379)  e3 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (379) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | |   (380)  $false
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | CLOSE: (380) is inconsistent.
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | |   (381)  all_58_11 = e1
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (61), (77), (105), (109), (142), (334), (381)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #427.
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (382)   ~ (all_58_6 = e0)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | REDUCE: (141), (382) imply:
% 202.11/33.75  | | | | | | | | | | | | | | | | | |   (383)   ~ (all_52_5 = e0)
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (67), (162), (283), (313), (346), (349),
% 202.11/33.75  | | | | | | | | | | | | | | | | | |            (383) are inconsistent by sub-proof #352.
% 202.11/33.75  | | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | |   (384)  all_58_11 = e3
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | | REF_CLOSE: (8), (42), (57), (77), (105), (109), (142), (148),
% 202.11/33.75  | | | | | | | | | | | | |            (282), (384) are inconsistent by sub-proof #997.
% 202.11/33.75  | | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | Case 2:
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | |   (385)   ~ (all_58_9 = e3)
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | REDUCE: (34), (385) imply:
% 202.11/33.75  | | | | | | | | | | |   (386)   ~ (all_52_25 = e3)
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | | REF_CLOSE: (8), (9), (20), (34), (123), (125), (128), (145),
% 202.11/33.75  | | | | | | | | | | |            (148), (153), (171), (173), (186), (197), (386)
% 202.11/33.75  | | | | | | | | | | |            are inconsistent by sub-proof #446.
% 202.11/33.75  | | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | | 
% 202.11/33.75  | | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | | 
% 202.11/33.75  | | | | | | | | End of split
% 202.11/33.75  | | | | | | | | 
% 202.11/33.75  | | | | | | | End of split
% 202.11/33.75  | | | | | | | 
% 202.11/33.75  | | | | | | End of split
% 202.11/33.75  | | | | | | 
% 202.11/33.75  | | | | | End of split
% 202.11/33.75  | | | | | 
% 202.11/33.75  | | | | End of split
% 202.11/33.75  | | | | 
% 202.11/33.75  | | | Case 2:
% 202.11/33.75  | | | | 
% 202.11/33.75  | | | |   (387)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.11/33.75  | | | |          e0
% 202.11/33.75  | | | | 
% 202.11/33.75  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 202.11/33.75  | | | |            (13), (16), (17), (18), (19), (20), (21), (23), (25), (27),
% 202.11/33.75  | | | |            (28), (29), (30), (31), (32), (34), (36), (38), (39), (40),
% 202.11/33.75  | | | |            (41), (43), (44), (45), (46), (48), (49), (50), (51), (52),
% 202.11/33.75  | | | |            (53), (54), (55), (56), (60), (62), (63), (64), (68), (69),
% 202.11/33.75  | | | |            (70), (72), (73), (74), (75), (76), (78), (79), (81), (82),
% 202.11/33.75  | | | |            (83), (84), (85), (86), (88), (89), (92), (94), (96), (97),
% 202.11/33.75  | | | |            (98), (99), (100), (101), (102), (103), (104), (105), (107),
% 202.11/33.75  | | | |            (109), (110), (111), (112), (113), (114), (115), (116),
% 202.11/33.75  | | | |            (117), (118), (119), (120), (121), (123), (124), (125),
% 202.11/33.75  | | | |            (126), (127), (128), (129), (133), (134), (135), (136),
% 202.11/33.75  | | | |            (138), (140), (141), (143), (144), (145), (146), (148),
% 202.11/33.75  | | | |            (150), (151), (153), (155), (156), (158), (160), (161),
% 202.11/33.75  | | | |            (163), (164), (166), (168), (169), (170), (171), (172),
% 202.11/33.75  | | | |            (173), (175), (387) are inconsistent by sub-proof #434.
% 202.11/33.75  | | | | 
% 202.11/33.75  | | | End of split
% 202.11/33.75  | | | 
% 202.11/33.75  | | End of split
% 202.11/33.75  | | 
% 202.11/33.75  | End of split
% 202.11/33.75  | 
% 202.11/33.75  End of proof
% 202.11/33.75  
% 202.11/33.75  Sub-proof #352 shows that the following formulas are inconsistent:
% 202.11/33.75  ----------------------------------------------------------------
% 202.11/33.75    (1)   ~ (all_10_0 = e0)
% 202.11/33.75    (2)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.75    (3)  all_56_8 = all_52_5
% 202.11/33.75    (4)  all_56_9 = all_10_0
% 202.11/33.75    (5)   ~ (all_52_5 = e2)
% 202.11/33.75    (6)  all_56_9 = e1 | all_56_9 = e0
% 202.11/33.75    (7)   ~ (all_52_5 = e0)
% 202.11/33.75    (8)   ~ (all_52_5 = all_10_0)
% 202.11/33.75  
% 202.11/33.75  Begin of proof
% 202.11/33.75  | 
% 202.11/33.75  | BETA: splitting (2) gives:
% 202.11/33.75  | 
% 202.11/33.75  | Case 1:
% 202.11/33.75  | | 
% 202.11/33.75  | |   (9)  all_56_8 = e2
% 202.11/33.75  | | 
% 202.11/33.75  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1022.
% 202.11/33.75  | | 
% 202.11/33.75  | Case 2:
% 202.11/33.75  | | 
% 202.11/33.75  | |   (10)  all_56_8 = e1 | all_56_8 = e0
% 202.11/33.75  | | 
% 202.11/33.75  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10) are inconsistent by sub-proof
% 202.11/33.75  | |            #786.
% 202.11/33.75  | | 
% 202.11/33.75  | End of split
% 202.11/33.75  | 
% 202.11/33.75  End of proof
% 202.11/33.75  
% 202.11/33.75  Sub-proof #353 shows that the following formulas are inconsistent:
% 202.11/33.75  ----------------------------------------------------------------
% 202.11/33.75    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.75    (2)  all_58_1 = all_52_9
% 202.11/33.75    (3)  op(e2, e3) = all_52_3
% 202.11/33.75    (4)   ~ (all_52_3 = all_52_19)
% 202.11/33.75    (5)   ~ (all_4_2 = e3)
% 202.11/33.75    (6)   ~ (all_52_3 = all_6_2)
% 202.11/33.75    (7)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.75    (8)  all_58_0 = all_6_2
% 202.11/33.75    (9)  all_56_4 = all_52_3
% 202.11/33.75    (10)  op(e3, e0) = all_52_25
% 202.11/33.75    (11)  all_58_9 = all_52_25
% 202.11/33.75    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.75    (13)   ~ (all_52_3 = all_52_5)
% 202.11/33.75    (14)  all_58_10 = all_52_27
% 202.11/33.75    (15)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.75    (16)  op(all_52_19, all_52_19) = e2
% 202.11/33.75    (17)  all_58_12 = all_52_7
% 202.11/33.75    (18)   ~ (all_52_7 = e3)
% 202.11/33.75    (19)  all_58_2 = all_52_3
% 202.11/33.75    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.75    (21)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.75    (22)   ~ (e2 = e0)
% 202.11/33.75    (23)   ~ (all_52_27 = e3)
% 202.11/33.75    (24)   ~ (all_52_9 = e3)
% 202.11/33.75    (25)  op(e3, e1) = all_52_17
% 202.11/33.75    (26)   ~ (all_52_5 = all_6_2)
% 202.11/33.75    (27)  op(e3, all_6_1) = e2
% 202.11/33.75    (28)  op(e3, e3) = all_6_2
% 202.11/33.75    (29)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.75    (30)  all_58_5 = all_52_19
% 202.11/33.75    (31)  all_58_6 = all_52_5
% 202.11/33.75    (32)   ~ (all_52_17 = all_6_2)
% 202.11/33.75    (33)   ~ (e3 = e2)
% 202.11/33.75    (34)   ~ (all_52_17 = all_52_19)
% 202.11/33.75    (35)  all_58_3 = all_4_2
% 202.11/33.75    (36)  op(all_6_2, e3) = all_6_1
% 202.11/33.75    (37)  all_58_4 = all_52_17
% 202.11/33.75  
% 202.11/33.75  Begin of proof
% 202.11/33.75  | 
% 202.11/33.75  | BETA: splitting (7) gives:
% 202.11/33.75  | 
% 202.11/33.75  | Case 1:
% 202.11/33.75  | | 
% 202.11/33.75  | |   (38)  all_58_3 = e3
% 202.11/33.75  | | 
% 202.11/33.75  | | COMBINE_EQS: (35), (38) imply:
% 202.11/33.75  | |   (39)  all_4_2 = e3
% 202.11/33.75  | | 
% 202.11/33.75  | | REDUCE: (5), (39) imply:
% 202.11/33.75  | |   (40)  $false
% 202.11/33.75  | | 
% 202.11/33.75  | | CLOSE: (40) is inconsistent.
% 202.11/33.75  | | 
% 202.11/33.75  | Case 2:
% 202.11/33.75  | | 
% 202.11/33.75  | |   (41)  all_58_5 = e3 | all_58_10 = e3
% 202.11/33.75  | | 
% 202.11/33.75  | | BETA: splitting (41) gives:
% 202.11/33.75  | | 
% 202.11/33.75  | | Case 1:
% 202.11/33.75  | | | 
% 202.11/33.75  | | |   (42)  all_58_5 = e3
% 202.11/33.75  | | | 
% 202.11/33.75  | | | COMBINE_EQS: (30), (42) imply:
% 202.11/33.75  | | |   (43)  all_52_19 = e3
% 202.11/33.75  | | | 
% 202.11/33.75  | | | SIMP: (43) implies:
% 202.11/33.75  | | |   (44)  all_52_19 = e3
% 202.11/33.75  | | | 
% 202.11/33.75  | | | REDUCE: (4), (44) imply:
% 202.11/33.75  | | |   (45)   ~ (all_52_3 = e3)
% 202.11/33.75  | | | 
% 202.11/33.75  | | | REDUCE: (34), (44) imply:
% 202.11/33.75  | | |   (46)   ~ (all_52_17 = e3)
% 202.11/33.75  | | | 
% 202.11/33.75  | | | REDUCE: (16), (44) imply:
% 202.11/33.75  | | |   (47)  op(e3, e3) = e2
% 202.11/33.75  | | | 
% 202.11/33.75  | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (15),
% 202.11/33.75  | | |            (17), (18), (19), (20), (21), (22), (24), (25), (26), (27),
% 202.11/33.75  | | |            (28), (29), (31), (32), (33), (36), (37), (45), (46), (47) are
% 202.11/33.75  | | |            inconsistent by sub-proof #454.
% 202.11/33.75  | | | 
% 202.11/33.75  | | Case 2:
% 202.11/33.75  | | | 
% 202.11/33.75  | | |   (48)  all_58_10 = e3
% 202.11/33.75  | | | 
% 202.11/33.75  | | | REF_CLOSE: (14), (23), (48) are inconsistent by sub-proof #1301.
% 202.11/33.75  | | | 
% 202.11/33.75  | | End of split
% 202.11/33.75  | | 
% 202.11/33.75  | End of split
% 202.11/33.75  | 
% 202.11/33.75  End of proof
% 202.11/33.75  
% 202.11/33.75  Sub-proof #354 shows that the following formulas are inconsistent:
% 202.11/33.75  ----------------------------------------------------------------
% 202.11/33.75    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.75    (2)  all_58_14 = all_52_23
% 202.11/33.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.75    (4)  all_58_1 = all_52_9
% 202.11/33.75    (5)   ~ (e3 = e0)
% 202.11/33.75    (6)  op(all_52_23, all_52_23) = e0
% 202.11/33.75    (7)  op(e2, e3) = all_52_3
% 202.11/33.75    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.75    (9)   ~ (all_52_7 = all_52_15)
% 202.11/33.75    (10)   ~ (all_52_3 = all_52_19)
% 202.11/33.75    (11)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.75    (12)   ~ (all_52_17 = all_52_25)
% 202.11/33.75    (13)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.75    (14)   ~ (all_52_3 = all_6_2)
% 202.11/33.75    (15)  all_58_0 = all_6_2
% 202.11/33.75    (16)  all_40_0 = e1
% 202.11/33.75    (17)  all_56_4 = all_52_3
% 202.11/33.75    (18)   ~ (all_52_17 = all_10_2)
% 202.11/33.75    (19)  all_44_2 = e1
% 202.11/33.75    (20)   ~ (all_10_0 = e3)
% 202.11/33.75    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.75    (22)  all_40_2 = all_10_2
% 202.11/33.75    (23)  op(e3, e0) = all_52_25
% 202.11/33.75    (24)  all_58_7 = e1
% 202.11/33.75    (25)  all_58_13 = all_52_15
% 202.11/33.75    (26)  all_58_9 = all_52_25
% 202.11/33.75    (27)  op(e2, e2) = all_4_2
% 202.11/33.75    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.75    (29)  all_58_7 = all_10_0
% 202.11/33.75    (30)   ~ (all_52_3 = all_52_5)
% 202.11/33.75    (31)  all_58_11 = all_52_29
% 202.11/33.75    (32)   ~ (all_52_25 = all_14_2)
% 202.11/33.75    (33)   ~ (all_52_9 = all_52_15)
% 202.11/33.75    (34)   ~ (all_52_7 = all_6_2)
% 202.11/33.75    (35)  op(e0, e0) = all_14_2
% 202.11/33.75    (36)  all_56_15 = all_14_2
% 202.11/33.75    (37)   ~ (all_10_0 = e2)
% 202.11/33.75    (38)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.75    (39)  op(all_10_2, all_10_2) = e1
% 202.11/33.75    (40)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.75    (41)  all_56_9 = all_10_0
% 202.11/33.75    (42)   ~ (all_52_25 = all_52_29)
% 202.11/33.75    (43)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.75    (44)  op(all_52_19, all_52_19) = e2
% 202.11/33.75    (45)   ~ (all_52_5 = all_52_7)
% 202.11/33.75    (46)  all_58_12 = all_52_7
% 202.11/33.75    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.75    (48)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.11/33.75    (49)  all_58_2 = all_52_3
% 202.11/33.75    (50)  all_56_2 = all_52_17
% 202.11/33.75    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.75    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.75    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.75    (54)   ~ (e2 = e0)
% 202.11/33.75    (55)  op(all_4_2, e2) = all_4_1
% 202.11/33.75    (56)   ~ (all_52_23 = e3)
% 202.11/33.75    (57)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.75    (58)   ~ (all_52_15 = all_14_2)
% 202.11/33.75    (59)   ~ (all_52_9 = e3)
% 202.11/33.75    (60)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.75    (61)   ~ (all_52_9 = e2)
% 202.11/33.75    (62)  op(e3, e1) = all_52_17
% 202.11/33.75    (63)  op(e0, e3) = all_52_7
% 202.11/33.75    (64)   ~ (all_52_9 = all_52_25)
% 202.11/33.75    (65)  all_58_15 = all_14_2
% 202.11/33.75    (66)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.75    (67)  all_58_8 = all_10_2
% 202.11/33.75    (68)   ~ (all_52_5 = all_10_2)
% 202.11/33.75    (69)   ~ (all_52_23 = all_14_2)
% 202.11/33.75    (70)  all_56_12 = all_52_7
% 202.11/33.75    (71)  all_8_2 = all_6_2
% 202.11/33.75    (72)   ~ (all_52_9 = all_4_2)
% 202.11/33.75    (73)   ~ (all_52_5 = all_6_2)
% 202.11/33.75    (74)   ~ (all_52_9 = all_6_2)
% 202.11/33.75    (75)  op(e3, all_6_1) = e2
% 202.11/33.75    (76)   ~ (all_52_9 = e1)
% 202.11/33.75    (77)  op(e3, e3) = all_6_2
% 202.11/33.75    (78)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.75    (79)  op(e2, e2) = e3
% 202.11/33.75    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.75    (81)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.75    (82)  all_40_0 = all_10_0
% 202.11/33.76    (83)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.76    (84)  all_58_5 = all_52_19
% 202.11/33.76    (85)  all_56_1 = all_52_9
% 202.11/33.76    (86)   ~ (all_52_15 = all_4_2)
% 202.11/33.76    (87)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.76    (88)  op(all_52_17, all_52_17) = e3
% 202.11/33.76    (89)  all_58_6 = all_52_5
% 202.11/33.76    (90)  op(all_10_2, e1) = e2
% 202.11/33.76    (91)  op(e3, e2) = all_52_9
% 202.11/33.76    (92)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.76    (93)   ~ (all_52_17 = all_6_2)
% 202.11/33.76    (94)   ~ (all_52_19 = e2)
% 202.11/33.76    (95)   ~ (e3 = e2)
% 202.11/33.76    (96)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.76    (97)   ~ (all_52_9 = all_52_17)
% 202.11/33.76    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.76    (99)  op(e1, e1) = all_10_2
% 202.11/33.76    (100)   ~ (all_52_23 = all_10_2)
% 202.11/33.76    (101)   ~ (all_52_7 = all_52_23)
% 202.11/33.76    (102)   ~ (all_52_17 = all_52_19)
% 202.11/33.76    (103)  all_58_3 = all_4_2
% 202.11/33.76    (104)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.11/33.76    (105)   ~ (all_52_17 = all_52_23)
% 202.11/33.76    (106)  all_8_1 = all_6_1
% 202.11/33.76    (107)  op(all_6_2, e3) = all_6_1
% 202.11/33.76    (108)  all_58_0 = e1
% 202.11/33.76    (109)   ~ (all_4_2 = e1)
% 202.11/33.76    (110)  all_58_4 = all_52_17
% 202.11/33.76    (111)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.76  
% 202.11/33.76  Begin of proof
% 202.11/33.76  | 
% 202.11/33.76  | BETA: splitting (52) gives:
% 202.11/33.76  | 
% 202.11/33.76  | Case 1:
% 202.11/33.76  | | 
% 202.11/33.76  | |   (112)  all_58_0 = e0
% 202.11/33.76  | | 
% 202.11/33.76  | | COMBINE_EQS: (108), (112) imply:
% 202.11/33.76  | |   (113)  e1 = e0
% 202.11/33.76  | | 
% 202.11/33.76  | | COMBINE_EQS: (16), (113) imply:
% 202.11/33.76  | |   (114)  all_40_0 = e0
% 202.11/33.76  | | 
% 202.11/33.76  | | COMBINE_EQS: (24), (113) imply:
% 202.11/33.76  | |   (115)  all_58_7 = e0
% 202.11/33.76  | | 
% 202.11/33.76  | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (12), (14), (15), (17), (22),
% 202.11/33.76  | |            (23), (26), (28), (30), (31), (42), (43), (44), (45), (46), (47),
% 202.11/33.76  | |            (48), (49), (51), (53), (54), (56), (59), (62), (67), (68), (73),
% 202.11/33.76  | |            (75), (77), (78), (80), (84), (88), (89), (93), (94), (95), (98),
% 202.11/33.76  | |            (102), (107), (110), (114), (115) are inconsistent by sub-proof
% 202.11/33.76  | |            #411.
% 202.11/33.76  | | 
% 202.11/33.76  | Case 2:
% 202.11/33.76  | | 
% 202.11/33.76  | |   (116)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.76  | | 
% 202.11/33.76  | | BETA: splitting (116) gives:
% 202.11/33.76  | | 
% 202.11/33.76  | | Case 1:
% 202.11/33.76  | | | 
% 202.11/33.76  | | |   (117)  all_58_1 = e0
% 202.11/33.76  | | | 
% 202.11/33.76  | | | COMBINE_EQS: (4), (117) imply:
% 202.11/33.76  | | |   (118)  all_52_9 = e0
% 202.11/33.76  | | | 
% 202.11/33.76  | | | REDUCE: (72), (118) imply:
% 202.11/33.76  | | |   (119)   ~ (all_4_2 = e0)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | SIMP: (119) implies:
% 202.11/33.76  | | |   (120)   ~ (all_4_2 = e0)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | REDUCE: (76), (118) imply:
% 202.11/33.76  | | |   (121)   ~ (e1 = e0)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | SIMP: (121) implies:
% 202.11/33.76  | | |   (122)   ~ (e1 = e0)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | REDUCE: (40), (118) imply:
% 202.11/33.76  | | |   (123)  op(e0, e0) = all_52_8
% 202.11/33.76  | | | 
% 202.11/33.76  | | | BETA: splitting (21) gives:
% 202.11/33.76  | | | 
% 202.11/33.76  | | | Case 1:
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | |   (124)   ~ (all_44_2 = e1)
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REDUCE: (19), (124) imply:
% 202.11/33.76  | | | |   (125)  $false
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | CLOSE: (125) is inconsistent.
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | Case 2:
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_8, e0, e0,
% 202.11/33.76  | | | |              simplifying with (35), (123) gives:
% 202.11/33.76  | | | |   (126)  all_52_8 = all_14_2
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | GROUND_INST: instantiating (3) with all_4_2, e3, e2, e2, simplifying
% 202.11/33.76  | | | |              with (27), (79) gives:
% 202.11/33.76  | | | |   (127)  all_4_2 = e3
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | COMBINE_EQS: (103), (127) imply:
% 202.11/33.76  | | | |   (128)  all_58_3 = e3
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REDUCE: (86), (127) imply:
% 202.11/33.76  | | | |   (129)   ~ (all_52_15 = e3)
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REDUCE: (109), (127) imply:
% 202.11/33.76  | | | |   (130)   ~ (e3 = e1)
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REDUCE: (81), (127) imply:
% 202.11/33.76  | | | |   (131)  op(e3, e3) = all_52_10
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REDUCE: (55), (127) imply:
% 202.11/33.76  | | | |   (132)  op(e3, e2) = all_4_1
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (13), (15),
% 202.11/33.76  | | | |            (18), (20), (22), (25), (26), (29), (31), (32), (33), (34),
% 202.11/33.76  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (45), (46),
% 202.11/33.76  | | | |            (47), (48), (50), (57), (58), (59), (60), (62), (63), (64),
% 202.11/33.76  | | | |            (65), (66), (67), (69), (70), (71), (74), (75), (77), (78),
% 202.11/33.76  | | | |            (80), (82), (83), (85), (88), (89), (90), (91), (92), (93),
% 202.11/33.76  | | | |            (95), (96), (97), (98), (99), (100), (101), (104), (105),
% 202.11/33.76  | | | |            (106), (107), (110), (111), (122), (128), (129), (130),
% 202.11/33.76  | | | |            (131), (132) are inconsistent by sub-proof #408.
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | End of split
% 202.11/33.76  | | | 
% 202.11/33.76  | | Case 2:
% 202.11/33.76  | | | 
% 202.11/33.76  | | |   (133)   ~ (all_58_1 = e0)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | REDUCE: (4), (133) imply:
% 202.11/33.76  | | |   (134)   ~ (all_52_9 = e0)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | REF_CLOSE: (61), (76), (85), (87), (134) are inconsistent by sub-proof
% 202.11/33.76  | | |            #1314.
% 202.11/33.76  | | | 
% 202.11/33.76  | | End of split
% 202.11/33.76  | | 
% 202.11/33.76  | End of split
% 202.11/33.76  | 
% 202.11/33.76  End of proof
% 202.11/33.76  
% 202.11/33.76  Sub-proof #355 shows that the following formulas are inconsistent:
% 202.11/33.76  ----------------------------------------------------------------
% 202.11/33.76    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.11/33.76    (2)   ~ (all_52_15 = all_52_23)
% 202.11/33.76    (3)   ~ (all_52_25 = all_52_27)
% 202.11/33.76    (4)  all_58_14 = all_52_23
% 202.11/33.76    (5)   ~ (e3 = e1)
% 202.11/33.76    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.11/33.76    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.11/33.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.11/33.76    (8)   ~ (all_52_5 = all_52_13)
% 202.11/33.76    (9)  all_58_1 = all_52_9
% 202.11/33.76    (10)   ~ (all_52_9 = all_52_13)
% 202.11/33.76    (11)   ~ (e3 = e0)
% 202.11/33.76    (12)  op(e2, e3) = all_52_3
% 202.11/33.76    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.11/33.76    (14)   ~ (all_52_7 = all_52_15)
% 202.11/33.76    (15)   ~ (all_52_3 = all_52_19)
% 202.11/33.76    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.11/33.76    (17)   ~ (all_52_17 = all_52_25)
% 202.11/33.76    (18)   ~ (all_52_3 = all_6_2)
% 202.11/33.76    (19)  all_44_2 = all_6_2
% 202.11/33.76    (20)  all_58_0 = all_6_2
% 202.11/33.76    (21)  op(all_14_2, e0) = all_14_1
% 202.11/33.76    (22)  all_34_1 = all_14_1
% 202.11/33.76    (23)  all_56_4 = all_52_3
% 202.11/33.76    (24)   ~ (all_52_17 = all_10_2)
% 202.11/33.76    (25)   ~ (all_10_0 = e3)
% 202.11/33.76    (26)  op(e3, e0) = all_52_25
% 202.11/33.76    (27)  op(all_52_5, all_52_5) = all_52_4
% 202.11/33.76    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.11/33.76    (29)  op(all_52_19, all_52_19) = all_52_18
% 202.11/33.76    (30)   ~ (all_52_27 = all_52_29)
% 202.11/33.76    (31)  all_58_13 = all_52_15
% 202.11/33.76    (32)  op(e0, all_14_1) = e1
% 202.11/33.76    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.11/33.76    (34)  all_58_9 = all_52_25
% 202.11/33.76    (35)   ~ (all_52_29 = all_14_2)
% 202.11/33.76    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.11/33.76    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.11/33.76    (38)  op(e1, e3) = all_52_5
% 202.11/33.76    (39)  op(e2, e2) = all_4_2
% 202.11/33.76    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.11/33.76    (41)   ~ (all_52_3 = all_52_5)
% 202.11/33.76    (42)  all_58_11 = all_52_29
% 202.11/33.76    (43)  all_56_5 = all_4_2
% 202.11/33.76    (44)   ~ (all_52_25 = all_14_2)
% 202.11/33.76    (45)   ~ (all_52_9 = all_52_15)
% 202.11/33.76    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.11/33.76    (47)   ~ (all_52_3 = all_52_27)
% 202.11/33.76    (48)  op(all_10_2, e1) = all_10_1
% 202.11/33.76    (49)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.11/33.76    (50)  op(all_6_2, all_6_2) = all_52_0
% 202.11/33.76    (51)   ~ (all_52_7 = all_6_2)
% 202.11/33.76    (52)  op(e0, e0) = all_14_2
% 202.11/33.76    (53)  op(e0, e1) = all_52_23
% 202.11/33.76    (54)  all_56_15 = all_14_2
% 202.11/33.76    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.11/33.76    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.11/33.76    (57)  op(e1, e0) = all_52_29
% 202.11/33.76    (58)  all_56_11 = all_52_29
% 202.11/33.76    (59)   ~ (all_10_0 = e2)
% 202.11/33.76    (60)   ~ (all_4_1 = e1)
% 202.11/33.76    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.11/33.76    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.11/33.76    (63)  all_56_9 = all_52_13
% 202.11/33.76    (64)   ~ (e2 = e1)
% 202.11/33.76    (65)   ~ (all_52_13 = all_10_2)
% 202.11/33.76    (66)  all_58_10 = all_52_27
% 202.11/33.76    (67)  all_56_8 = all_52_5
% 202.11/33.76    (68)  op(all_52_9, all_52_9) = all_52_8
% 202.11/33.76    (69)  op(all_52_15, all_52_15) = all_52_14
% 202.11/33.76    (70)   ~ (all_52_19 = all_52_23)
% 202.11/33.76    (71)   ~ (all_52_25 = all_52_29)
% 202.11/33.76    (72)   ~ (all_52_29 = all_10_2)
% 202.11/33.76    (73)  op(all_10_2, e1) = e3
% 202.11/33.76    (74)  all_58_7 = all_52_13
% 202.11/33.76    (75)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.11/33.76    (76)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.11/33.76    (77)   ~ (all_52_5 = all_52_7)
% 202.11/33.76    (78)  all_58_12 = all_52_7
% 202.11/33.76    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.76    (80)   ~ (all_52_7 = all_14_2)
% 202.11/33.76    (81)  all_58_2 = all_52_3
% 202.11/33.76    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.11/33.76    (83)  all_56_2 = all_52_17
% 202.11/33.76    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.11/33.76    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.76    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.11/33.76    (87)  all_56_7 = all_52_27
% 202.11/33.76    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.11/33.76    (89)   ~ (e2 = e0)
% 202.11/33.76    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.11/33.76    (91)  op(all_4_2, e2) = all_4_1
% 202.11/33.76    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.11/33.76    (93)   ~ (all_52_5 = all_52_29)
% 202.11/33.76    (94)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.11/33.76    (95)  all_56_6 = all_52_19
% 202.11/33.76    (96)   ~ (all_52_15 = all_14_2)
% 202.11/33.76    (97)   ~ (all_52_19 = all_52_27)
% 202.11/33.76    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.11/33.76    (99)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.11/33.76    (100)  all_34_0 = e1
% 202.11/33.76    (101)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 202.11/33.76             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 202.11/33.76    (102)   ~ (all_52_13 = all_4_2)
% 202.11/33.76    (103)  op(e3, e1) = all_52_17
% 202.11/33.76    (104)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.76    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.11/33.76    (106)  op(e0, e3) = all_52_7
% 202.11/33.76    (107)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.11/33.76    (108)   ~ (all_52_9 = all_52_25)
% 202.11/33.76    (109)  op(e1, e3) = all_10_0
% 202.11/33.76    (110)  all_58_15 = all_14_2
% 202.11/33.76    (111)   ~ (all_52_19 = all_10_2)
% 202.11/33.76    (112)  op(all_52_23, all_52_23) = all_52_22
% 202.11/33.76    (113)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.11/33.76    (114)  all_58_8 = all_10_2
% 202.11/33.76    (115)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.76    (116)  all_34_2 = all_14_2
% 202.11/33.76    (117)   ~ (all_52_5 = all_10_2)
% 202.11/33.76    (118)  op(all_52_29, all_52_29) = all_52_28
% 202.11/33.76    (119)   ~ (all_52_23 = all_14_2)
% 202.11/33.76    (120)  all_56_12 = all_52_7
% 202.11/33.76    (121)  op(all_52_17, all_52_17) = all_52_16
% 202.11/33.76    (122)  all_8_2 = all_6_2
% 202.11/33.76    (123)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.11/33.76    (124)   ~ (all_52_25 = all_6_2)
% 202.11/33.76    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.11/33.76    (126)   ~ (all_52_9 = all_4_2)
% 202.11/33.76    (127)   ~ (all_52_5 = all_6_2)
% 202.11/33.76    (128)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.11/33.76    (129)   ~ (all_52_9 = all_6_2)
% 202.11/33.76    (130)   ~ (all_52_13 = all_52_15)
% 202.11/33.76    (131)  op(e3, all_6_1) = e2
% 202.11/33.76    (132)  all_56_0 = all_6_2
% 202.11/33.76    (133)  op(e3, e3) = all_6_2
% 202.11/33.76    (134)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.11/33.76    (135)   ~ (all_52_27 = all_14_2)
% 202.11/33.76    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.11/33.76    (137)  all_56_14 = all_52_23
% 202.11/33.76    (138)  op(all_4_2, all_4_2) = all_52_10
% 202.11/33.76    (139)  all_56_3 = all_52_25
% 202.11/33.76    (140)   ~ (all_52_3 = all_52_7)
% 202.11/33.76    (141)  op(all_14_2, all_14_2) = all_52_30
% 202.11/33.76    (142)  all_58_5 = all_52_19
% 202.11/33.76    (143)  all_56_1 = all_52_9
% 202.11/33.76    (144)   ~ (all_52_15 = all_4_2)
% 202.11/33.76    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.11/33.76           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.11/33.76           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.11/33.76           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.11/33.76    (146)   ~ (all_52_27 = all_4_2)
% 202.11/33.76    (147)  all_58_6 = all_52_5
% 202.11/33.76    (148)  op(e3, e2) = all_52_9
% 202.11/33.76    (149)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.11/33.76    (150)   ~ (all_52_17 = all_6_2)
% 202.11/33.76    (151)   ~ (e1 = e0)
% 202.11/33.76    (152)   ~ (e3 = e2)
% 202.11/33.76    (153)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.11/33.76    (154)  all_44_1 = all_6_1
% 202.11/33.76    (155)   ~ (all_52_9 = all_52_17)
% 202.11/33.76    (156)  all_56_10 = all_10_2
% 202.11/33.76    (157)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.11/33.76    (158)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.11/33.76    (159)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.11/33.76    (160)  all_44_0 = e2
% 202.11/33.76    (161)  op(all_52_13, all_52_13) = all_52_12
% 202.11/33.76    (162)  op(e1, e1) = all_10_2
% 202.11/33.76    (163)   ~ (all_52_23 = all_10_2)
% 202.11/33.76    (164)   ~ (all_52_7 = all_52_23)
% 202.11/33.76    (165)   ~ (all_52_17 = all_52_19)
% 202.11/33.76    (166)  all_58_3 = all_4_2
% 202.11/33.76    (167)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.11/33.76    (168)  all_56_13 = all_52_15
% 202.11/33.76    (169)   ~ (all_52_3 = all_4_2)
% 202.11/33.76    (170)   ~ (all_52_19 = all_4_2)
% 202.11/33.76    (171)   ~ (all_52_17 = all_52_23)
% 202.11/33.76    (172)  all_8_1 = all_6_1
% 202.11/33.76    (173)  op(all_6_2, e3) = all_6_1
% 202.11/33.76    (174)   ~ (all_52_13 = all_52_29)
% 202.11/33.76    (175)  all_58_4 = all_52_17
% 202.11/33.76    (176)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.11/33.76    (177)  op(all_52_25, all_52_25) = all_52_24
% 202.11/33.76  
% 202.11/33.76  Begin of proof
% 202.11/33.76  | 
% 202.11/33.76  | GROUND_INST: instantiating (7) with all_52_5, all_10_0, e3, e1, simplifying
% 202.11/33.76  |              with (38), (109) gives:
% 202.11/33.76  |   (178)  all_52_5 = all_10_0
% 202.11/33.76  | 
% 202.11/33.76  | COMBINE_EQS: (147), (178) imply:
% 202.11/33.76  |   (179)  all_58_6 = all_10_0
% 202.11/33.76  | 
% 202.11/33.76  | REDUCE: (77), (178) imply:
% 202.11/33.76  |   (180)   ~ (all_52_7 = all_10_0)
% 202.11/33.76  | 
% 202.11/33.76  | SIMP: (180) implies:
% 202.11/33.76  |   (181)   ~ (all_52_7 = all_10_0)
% 202.11/33.76  | 
% 202.11/33.76  | BETA: splitting (49) gives:
% 202.11/33.76  | 
% 202.11/33.76  | Case 1:
% 202.11/33.76  | | 
% 202.11/33.76  | |   (182)   ~ (all_34_0 = e1)
% 202.11/33.76  | | 
% 202.11/33.76  | | REDUCE: (100), (182) imply:
% 202.11/33.76  | |   (183)  $false
% 202.11/33.76  | | 
% 202.11/33.76  | | CLOSE: (183) is inconsistent.
% 202.11/33.76  | | 
% 202.11/33.76  | Case 2:
% 202.11/33.76  | | 
% 202.11/33.76  | |   (184)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.11/33.76  | | 
% 202.11/33.76  | | BETA: splitting (104) gives:
% 202.11/33.76  | | 
% 202.11/33.76  | | Case 1:
% 202.11/33.76  | | | 
% 202.11/33.76  | | |   (185)   ~ (all_44_0 = e2)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | REDUCE: (160), (185) imply:
% 202.11/33.76  | | |   (186)  $false
% 202.11/33.76  | | | 
% 202.11/33.76  | | | CLOSE: (186) is inconsistent.
% 202.11/33.76  | | | 
% 202.11/33.76  | | Case 2:
% 202.11/33.76  | | | 
% 202.11/33.76  | | |   (187)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.11/33.76  | | | 
% 202.11/33.76  | | | BETA: splitting (101) gives:
% 202.11/33.76  | | | 
% 202.11/33.76  | | | Case 1:
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | |   (188)  all_58_15 = e0
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REF_CLOSE: (7), (21), (32), (52), (110), (141), (151), (188) are
% 202.11/33.76  | | | |            inconsistent by sub-proof #877.
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | Case 2:
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | |   (189)   ~ (all_58_15 = e0)
% 202.11/33.76  | | | |   (190)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 202.11/33.76  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | ALPHA: (190) implies:
% 202.11/33.76  | | | |   (191)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.11/33.76  | | | |   (192)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | REDUCE: (110), (189) imply:
% 202.11/33.76  | | | |   (193)   ~ (all_14_2 = e0)
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | BETA: splitting (145) gives:
% 202.11/33.76  | | | | 
% 202.11/33.76  | | | | Case 1:
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | |   (194)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 202.11/33.76  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 202.11/33.76  | | | | |            all_52_14 = e0)
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | | BETA: splitting (194) gives:
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | | Case 1:
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | |   (195)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 202.11/33.76  | | | | | |          e0
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | REF_CLOSE: (6), (7), (12), (16), (20), (25), (39), (50), (55), (59),
% 202.11/33.76  | | | | | |            (78), (81), (85), (89), (99), (131), (132), (133), (138),
% 202.11/33.76  | | | | | |            (152), (159), (169), (173), (179), (195) are inconsistent
% 202.11/33.76  | | | | | |            by sub-proof #387.
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | Case 2:
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | |   (196)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 202.11/33.76  | | | | | |          = e0
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 202.11/33.76  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 202.11/33.76  | | | | | |            (21), (23), (26), (27), (28), (29), (31), (32), (33),
% 202.11/33.76  | | | | | |            (34), (35), (37), (38), (39), (40), (41), (42), (44),
% 202.11/33.76  | | | | | |            (46), (47), (51), (52), (53), (54), (55), (60), (61),
% 202.11/33.76  | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 202.11/33.76  | | | | | |            (72), (74), (76), (77), (78), (79), (80), (81), (85),
% 202.11/33.76  | | | | | |            (87), (88), (89), (91), (92), (96), (102), (103), (106),
% 202.11/33.76  | | | | | |            (107), (108), (110), (111), (112), (113), (114), (115),
% 202.11/33.76  | | | | | |            (116), (117), (118), (119), (120), (121), (122), (123),
% 202.11/33.76  | | | | | |            (124), (125), (126), (127), (129), (130), (131), (132),
% 202.11/33.76  | | | | | |            (133), (134), (135), (136), (138), (139), (140), (141),
% 202.11/33.76  | | | | | |            (142), (143), (144), (146), (147), (148), (149), (150),
% 202.11/33.76  | | | | | |            (151), (152), (153), (154), (155), (156), (157), (158),
% 202.11/33.76  | | | | | |            (159), (161), (162), (163), (164), (165), (166), (168),
% 202.11/33.76  | | | | | |            (169), (170), (171), (172), (173), (174), (175), (176),
% 202.11/33.76  | | | | | |            (177), (184), (187), (192), (196) are inconsistent by
% 202.11/33.76  | | | | | |            sub-proof #358.
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | End of split
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | Case 2:
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | |   (197)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 202.11/33.76  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.11/33.76  | | | | |            all_52_30 = e0)
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | | BETA: splitting (197) gives:
% 202.11/33.76  | | | | | 
% 202.11/33.76  | | | | | Case 1:
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | |   (198)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 202.11/33.76  | | | | | |          all_52_22 = e0
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | ALPHA: (198) implies:
% 202.11/33.76  | | | | | |   (199)  all_52_22 = e0
% 202.11/33.76  | | | | | |   (200)  all_52_20 = e1
% 202.11/33.76  | | | | | |   (201)  all_52_18 = e2
% 202.11/33.76  | | | | | |   (202)  all_52_16 = e3
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | REDUCE: (121), (202) imply:
% 202.11/33.76  | | | | | |   (203)  op(all_52_17, all_52_17) = e3
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | REDUCE: (29), (201) imply:
% 202.11/33.76  | | | | | |   (204)  op(all_52_19, all_52_19) = e2
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | REDUCE: (112), (199) imply:
% 202.11/33.76  | | | | | |   (205)  op(all_52_23, all_52_23) = e0
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | REDUCE: (33), (200) imply:
% 202.11/33.76  | | | | | |   (206)  op(all_10_2, all_10_2) = e1
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | BETA: splitting (115) gives:
% 202.11/33.76  | | | | | | 
% 202.11/33.76  | | | | | | Case 1:
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | |   (207)  all_56_15 = e3
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | COMBINE_EQS: (54), (207) imply:
% 202.11/33.76  | | | | | | |   (208)  all_14_2 = e3
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | SIMP: (208) implies:
% 202.11/33.76  | | | | | | |   (209)  all_14_2 = e3
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | COMBINE_EQS: (116), (209) imply:
% 202.11/33.76  | | | | | | |   (210)  all_34_2 = e3
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | REDUCE: (80), (209) imply:
% 202.11/33.76  | | | | | | |   (211)   ~ (all_52_7 = e3)
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | REDUCE: (44), (209) imply:
% 202.11/33.76  | | | | | | |   (212)   ~ (all_52_25 = e3)
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | REDUCE: (35), (209) imply:
% 202.11/33.76  | | | | | | |   (213)   ~ (all_52_29 = e3)
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | REDUCE: (141), (209) imply:
% 202.11/33.76  | | | | | | |   (214)  op(e3, e3) = all_52_30
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | REDUCE: (21), (209) imply:
% 202.11/33.76  | | | | | | |   (215)  op(e3, e0) = all_14_1
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | BETA: splitting (184) gives:
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | |   (216)   ~ (all_34_1 = e2)
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | REDUCE: (22), (216) imply:
% 202.11/33.76  | | | | | | | |   (217)   ~ (all_14_1 = e2)
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3,
% 202.11/33.76  | | | | | | | |              simplifying with (26), (215) gives:
% 202.11/33.76  | | | | | | | |   (218)  all_52_25 = all_14_1
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_30, e3, e3,
% 202.11/33.76  | | | | | | | |              simplifying with (133), (214) gives:
% 202.11/33.76  | | | | | | | |   (219)  all_52_30 = all_6_2
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | COMBINE_EQS: (34), (218) imply:
% 202.11/33.76  | | | | | | | |   (220)  all_58_9 = all_14_1
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | BETA: splitting (79) gives:
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | |   (221)  all_58_6 = e3
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REF_CLOSE: (25), (179), (221) are inconsistent by sub-proof
% 202.11/33.76  | | | | | | | | |            #922.
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | Case 2:
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | |   (222)   ~ (all_58_6 = e3)
% 202.11/33.76  | | | | | | | | |   (223)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | BETA: splitting (85) gives:
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | |   (224)  all_58_0 = e3
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | COMBINE_EQS: (20), (224) imply:
% 202.11/33.76  | | | | | | | | | |   (225)  all_6_2 = e3
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | REF_CLOSE: (7), (131), (133), (152), (173), (225) are
% 202.11/33.76  | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | Case 2:
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | |   (226)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | BETA: splitting (226) gives:
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | |   (227)  all_58_2 = e3
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | COMBINE_EQS: (81), (227) imply:
% 202.11/33.76  | | | | | | | | | | |   (228)  all_52_3 = e3
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | SIMP: (228) implies:
% 202.11/33.76  | | | | | | | | | | |   (229)  all_52_3 = e3
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | REDUCE: (18), (229) imply:
% 202.11/33.76  | | | | | | | | | | |   (230)   ~ (all_6_2 = e3)
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | SIMP: (230) implies:
% 202.11/33.76  | | | | | | | | | | |   (231)   ~ (all_6_2 = e3)
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | REDUCE: (6), (229) imply:
% 202.11/33.76  | | | | | | | | | | |   (232)  op(e3, e3) = all_52_2
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | REDUCE: (12), (229) imply:
% 202.11/33.76  | | | | | | | | | | |   (233)  op(e2, e3) = e3
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (20), (31), (34), (39), (42),
% 202.11/33.76  | | | | | | | | | | |            (45), (64), (68), (74), (84), (99), (107), (114),
% 202.11/33.76  | | | | | | | | | | |            (126), (131), (133), (136), (150), (152), (166),
% 202.11/33.76  | | | | | | | | | | |            (173), (175), (203), (206), (212), (213), (217),
% 202.11/33.76  | | | | | | | | | | |            (220), (223), (231), (232), (233) are inconsistent
% 202.11/33.76  | | | | | | | | | | |            by sub-proof #356.
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | Case 2:
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | |   (234)  all_58_6 = e3 | all_58_12 = e3
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | BETA: splitting (234) gives:
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | |   (235)  all_58_6 = e3
% 202.11/33.76  | | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | | REF_CLOSE: (25), (179), (235) are inconsistent by sub-proof
% 202.11/33.76  | | | | | | | | | | | |            #922.
% 202.11/33.76  | | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | Case 2:
% 202.11/33.76  | | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | |   (236)  all_58_12 = e3
% 202.11/33.76  | | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | | REF_CLOSE: (78), (211), (236) are inconsistent by sub-proof
% 202.11/33.76  | | | | | | | | | | | |            #1367.
% 202.11/33.76  | | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | | End of split
% 202.11/33.76  | | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | | End of split
% 202.11/33.76  | | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | End of split
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | End of split
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | Case 2:
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | |   (237)   ~ (all_34_2 = e3)
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | REDUCE: (210), (237) imply:
% 202.11/33.76  | | | | | | | |   (238)  $false
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | CLOSE: (238) is inconsistent.
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | End of split
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | Case 2:
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | |   (239)   ~ (all_56_15 = e3)
% 202.11/33.76  | | | | | | |   (240)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | REDUCE: (54), (239) imply:
% 202.11/33.76  | | | | | | |   (241)   ~ (all_14_2 = e3)
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | BETA: splitting (79) gives:
% 202.11/33.76  | | | | | | | 
% 202.11/33.76  | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | |   (242)  all_58_6 = e3
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | REF_CLOSE: (25), (179), (242) are inconsistent by sub-proof
% 202.11/33.76  | | | | | | | |            #922.
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | Case 2:
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | |   (243)   ~ (all_58_6 = e3)
% 202.11/33.76  | | | | | | | |   (244)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | BETA: splitting (99) gives:
% 202.11/33.76  | | | | | | | | 
% 202.11/33.76  | | | | | | | | Case 1:
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | |   (245)  all_58_0 = e2
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | COMBINE_EQS: (20), (245) imply:
% 202.11/33.76  | | | | | | | | |   (246)  all_6_2 = e2
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REDUCE: (18), (246) imply:
% 202.11/33.76  | | | | | | | | |   (247)   ~ (all_52_3 = e2)
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REDUCE: (51), (246) imply:
% 202.11/33.76  | | | | | | | | |   (248)   ~ (all_52_7 = e2)
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REDUCE: (150), (246) imply:
% 202.11/33.76  | | | | | | | | |   (249)   ~ (all_52_17 = e2)
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REDUCE: (124), (246) imply:
% 202.11/33.76  | | | | | | | | |   (250)   ~ (all_52_25 = e2)
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REDUCE: (173), (246) imply:
% 202.11/33.76  | | | | | | | | |   (251)  op(e2, e3) = all_6_1
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | REDUCE: (133), (246) imply:
% 202.11/33.76  | | | | | | | | |   (252)  op(e3, e3) = e2
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | GROUND_INST: instantiating (7) with all_52_3, all_6_1, e3, e2,
% 202.11/33.76  | | | | | | | | |              simplifying with (12), (251) gives:
% 202.11/33.76  | | | | | | | | |   (253)  all_52_3 = all_6_1
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | COMBINE_EQS: (23), (253) imply:
% 202.11/33.76  | | | | | | | | |   (254)  all_56_4 = all_6_1
% 202.11/33.76  | | | | | | | | | 
% 202.11/33.76  | | | | | | | | | COMBINE_EQS: (81), (253) imply:
% 202.11/33.76  | | | | | | | | |   (255)  all_58_2 = all_6_1
% 202.11/33.76  | | | | | | | | | 
% 202.21/33.76  | | | | | | | | | REDUCE: (140), (253) imply:
% 202.21/33.76  | | | | | | | | |   (256)   ~ (all_52_7 = all_6_1)
% 202.21/33.76  | | | | | | | | | 
% 202.21/33.76  | | | | | | | | | SIMP: (256) implies:
% 202.21/33.76  | | | | | | | | |   (257)   ~ (all_52_7 = all_6_1)
% 202.21/33.76  | | | | | | | | | 
% 202.21/33.76  | | | | | | | | | REDUCE: (15), (253) imply:
% 202.21/33.76  | | | | | | | | |   (258)   ~ (all_52_19 = all_6_1)
% 202.21/33.76  | | | | | | | | | 
% 202.21/33.76  | | | | | | | | | SIMP: (258) implies:
% 202.21/33.76  | | | | | | | | |   (259)   ~ (all_52_19 = all_6_1)
% 202.21/33.76  | | | | | | | | | 
% 202.21/33.76  | | | | | | | | | REDUCE: (247), (253) imply:
% 202.21/33.77  | | | | | | | | |   (260)   ~ (all_6_1 = e2)
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | BETA: splitting (85) gives:
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | |   (261)  all_58_0 = e3
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | REF_CLOSE: (152), (245), (261) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | |            #1235.
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | |   (262)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | BETA: splitting (88) gives:
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | |   (263)  all_56_4 = e3
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | COMBINE_EQS: (254), (263) imply:
% 202.21/33.77  | | | | | | | | | | |   (264)  all_6_1 = e3
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | SIMP: (264) implies:
% 202.21/33.77  | | | | | | | | | | |   (265)  all_6_1 = e3
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | REDUCE: (257), (265) imply:
% 202.21/33.77  | | | | | | | | | | |   (266)   ~ (all_52_7 = e3)
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | REDUCE: (259), (265) imply:
% 202.21/33.77  | | | | | | | | | | |   (267)   ~ (all_52_19 = e3)
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (11), (13), (14),
% 202.21/33.77  | | | | | | | | | | |            (17), (20), (24), (31), (34), (44), (45), (51),
% 202.21/33.77  | | | | | | | | | | |            (61), (62), (73), (78), (83), (94), (103), (106),
% 202.21/33.77  | | | | | | | | | | |            (107), (110), (114), (120), (122), (131), (133),
% 202.21/33.77  | | | | | | | | | | |            (134), (136), (141), (142), (148), (149), (150),
% 202.21/33.77  | | | | | | | | | | |            (151), (152), (155), (157), (162), (163), (164),
% 202.21/33.77  | | | | | | | | | | |            (168), (171), (172), (173), (175), (191), (203),
% 202.21/33.77  | | | | | | | | | | |            (205), (241), (266), (267) are inconsistent by
% 202.21/33.77  | | | | | | | | | | |            sub-proof #371.
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | |   (268)   ~ (all_56_4 = e3)
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | REDUCE: (254), (268) imply:
% 202.21/33.77  | | | | | | | | | | |   (269)   ~ (all_6_1 = e3)
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | BETA: splitting (262) gives:
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | |   (270)  all_58_2 = e3
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | REF_CLOSE: (255), (269), (270) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | |            #905.
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | |   (271)  all_58_6 = e3 | all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | BETA: splitting (271) gives:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | |   (272)  all_58_6 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REF_CLOSE: (25), (179), (272) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | |            #922.
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | |   (273)  all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | COMBINE_EQS: (78), (273) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (274)  all_52_7 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | SIMP: (274) implies:
% 202.21/33.77  | | | | | | | | | | | | |   (275)  all_52_7 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (164), (275) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (276)   ~ (all_52_23 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | SIMP: (276) implies:
% 202.21/33.77  | | | | | | | | | | | | |   (277)   ~ (all_52_23 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (257), (275) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (278)   ~ (all_6_1 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (16), (275) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (279)  op(e3, e3) = all_52_6
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_6, e3, e3,
% 202.21/33.77  | | | | | | | | | | | | |              simplifying with (252), (279) gives:
% 202.21/33.77  | | | | | | | | | | | | |   (280)  all_52_6 = e2
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | BETA: splitting (153) gives:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (281)  all_56_1 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | COMBINE_EQS: (143), (281) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (282)  all_52_9 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | SIMP: (282) implies:
% 202.21/33.77  | | | | | | | | | | | | | |   (283)  all_52_9 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | COMBINE_EQS: (9), (283) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (284)  all_58_1 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (10), (283) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (285)   ~ (all_52_13 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | SIMP: (285) implies:
% 202.21/33.77  | | | | | | | | | | | | | |   (286)   ~ (all_52_13 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (155), (283) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (287)   ~ (all_52_17 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | SIMP: (287) implies:
% 202.21/33.77  | | | | | | | | | | | | | |   (288)   ~ (all_52_17 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (68), (283) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (289)  op(e3, e3) = all_52_8
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_8, e3, e3,
% 202.21/33.77  | | | | | | | | | | | | | |              simplifying with (252), (289) gives:
% 202.21/33.77  | | | | | | | | | | | | | |   (290)  all_52_8 = e2
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (11), (20), (34), (35), (36), (42),
% 202.21/33.77  | | | | | | | | | | | | | |            (52), (58), (64), (70), (72), (74), (86), (89),
% 202.21/33.77  | | | | | | | | | | | | | |            (92), (98), (111), (114), (133), (142), (151),
% 202.21/33.77  | | | | | | | | | | | | | |            (157), (162), (175), (203), (204), (206), (244),
% 202.21/33.77  | | | | | | | | | | | | | |            (252), (277), (284), (286), (288), (289) are
% 202.21/33.77  | | | | | | | | | | | | | |            inconsistent by sub-proof #829.
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (291)   ~ (all_56_1 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (143), (291) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (292)   ~ (all_52_9 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (293)  all_58_0 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | REF_CLOSE: (152), (245), (293) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | |            #1235.
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (294)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (295)  all_56_3 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (26), (40), (76), (88), (89), (103), (131),
% 202.21/33.77  | | | | | | | | | | | | | | | |            (139), (245), (249), (250), (254), (255), (260),
% 202.21/33.77  | | | | | | | | | | | | | | | |            (269), (295) are inconsistent by sub-proof #384.
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (296)   ~ (all_56_3 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REDUCE: (139), (296) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (297)   ~ (all_52_25 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (34), (133), (150), (175), (203), (292),
% 202.21/33.77  | | | | | | | | | | | | | | | |            (294), (297) are inconsistent by sub-proof #1072.
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | |   (298)   ~ (all_58_0 = e2)
% 202.21/33.77  | | | | | | | | |   (299)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | REDUCE: (20), (298) imply:
% 202.21/33.77  | | | | | | | | |   (300)   ~ (all_6_2 = e2)
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | BETA: splitting (159) gives:
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | |   (301)  all_56_0 = e3
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | COMBINE_EQS: (132), (301) imply:
% 202.21/33.77  | | | | | | | | | |   (302)  all_6_2 = e3
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | REF_CLOSE: (7), (131), (133), (152), (173), (302) are
% 202.21/33.77  | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | |   (303)   ~ (all_56_0 = e3)
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | REDUCE: (132), (303) imply:
% 202.21/33.77  | | | | | | | | | |   (304)   ~ (all_6_2 = e3)
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | BETA: splitting (85) gives:
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | |   (305)  all_58_0 = e3
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | COMBINE_EQS: (20), (305) imply:
% 202.21/33.77  | | | | | | | | | | |   (306)  all_6_2 = e3
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | REDUCE: (304), (306) imply:
% 202.21/33.77  | | | | | | | | | | |   (307)  $false
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | |   (308)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | BETA: splitting (82) gives:
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | |   (309)  all_56_6 = e3
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | COMBINE_EQS: (95), (309) imply:
% 202.21/33.77  | | | | | | | | | | | |   (310)  all_52_19 = e3
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | SIMP: (310) implies:
% 202.21/33.77  | | | | | | | | | | | |   (311)  all_52_19 = e3
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | REDUCE: (15), (311) imply:
% 202.21/33.77  | | | | | | | | | | | |   (312)   ~ (all_52_3 = e3)
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | REDUCE: (204), (311) imply:
% 202.21/33.77  | | | | | | | | | | | |   (313)  op(e3, e3) = e2
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | BETA: splitting (308) gives:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | |   (314)  all_58_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REF_CLOSE: (81), (312), (314) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | |            #1369.
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | |   (315)  all_58_6 = e3 | all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | BETA: splitting (315) gives:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (316)  all_58_6 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REF_CLOSE: (25), (179), (316) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | |            #922.
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (317)  all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | COMBINE_EQS: (78), (317) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (318)  all_52_7 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | SIMP: (318) implies:
% 202.21/33.77  | | | | | | | | | | | | | |   (319)  all_52_7 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (16), (319) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (320)  op(e3, e3) = all_52_6
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REF_CLOSE: (7), (133), (300), (313), (320) are inconsistent
% 202.21/33.77  | | | | | | | | | | | | | |            by sub-proof #890.
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | |   (321)   ~ (all_56_6 = e3)
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | REDUCE: (95), (321) imply:
% 202.21/33.77  | | | | | | | | | | | |   (322)   ~ (all_52_19 = e3)
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | BETA: splitting (125) gives:
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | |   (323)  all_56_3 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | COMBINE_EQS: (139), (323) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (324)  all_52_25 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | SIMP: (324) implies:
% 202.21/33.77  | | | | | | | | | | | | |   (325)  all_52_25 = e3
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (71), (325) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (326)   ~ (all_52_29 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | SIMP: (326) implies:
% 202.21/33.77  | | | | | | | | | | | | |   (327)   ~ (all_52_29 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (44), (325) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (328)   ~ (all_14_2 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (177), (325) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (329)  op(e3, e3) = all_52_24
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 202.21/33.77  | | | | | | | | | | | | |              simplifying with (133), (329) gives:
% 202.21/33.77  | | | | | | | | | | | | |   (330)  all_52_24 = all_6_2
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | BETA: splitting (55) gives:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (331)  all_58_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | COMBINE_EQS: (81), (331) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (332)  all_52_3 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | SIMP: (332) implies:
% 202.21/33.77  | | | | | | | | | | | | | |   (333)  all_52_3 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (140), (333) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (334)   ~ (all_52_7 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | SIMP: (334) implies:
% 202.21/33.77  | | | | | | | | | | | | | |   (335)   ~ (all_52_7 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (6), (333) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (336)  op(e3, e3) = all_52_2
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (337)  all_58_2 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | REF_CLOSE: (152), (331), (337) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | |            #1124.
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (338)  all_58_6 = e2 | all_58_12 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (339)  all_58_6 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (179), (339) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | |            #917.
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (340)  all_58_12 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (340) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (341)  all_52_7 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | SIMP: (341) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (342)  all_52_7 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REDUCE: (80), (342) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (343)   ~ (all_14_2 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | SIMP: (343) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (344)   ~ (all_14_2 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REDUCE: (181), (342) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (345)   ~ (all_10_0 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REDUCE: (335), (342) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | |   (346)   ~ (e3 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (347)  all_56_15 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (344), (347) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | |            #762.
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (348)  all_56_15 = e1 | all_56_15 = e0
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (349)  all_56_15 = e1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (349) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (350)  all_14_2 = e1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | SIMP: (350) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (351)  all_14_2 = e1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | REDUCE: (241), (351) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (352)   ~ (e3 = e1)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | REDUCE: (141), (351) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (353)  op(e1, e1) = all_52_30
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | REDUCE: (21), (351) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (354)  op(e1, e0) = all_14_1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_29, all_14_1, e0,
% 202.21/33.77  | | | | | | | | | | | | | | | | | |              e1, simplifying with (57), (354) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (355)  all_52_29 = all_14_1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_30, e1,
% 202.21/33.77  | | | | | | | | | | | | | | | | | |              e1, simplifying with (162), (353) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (356)  all_52_30 = all_10_2
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_2, e3, e3,
% 202.21/33.77  | | | | | | | | | | | | | | | | | |              simplifying with (133), (336) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (357)  all_52_2 = all_6_2
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (355) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (358)  all_58_11 = all_14_1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | REDUCE: (327), (355) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (359)   ~ (all_14_1 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (360)  all_56_13 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (360) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (361)  all_52_15 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | SIMP: (361) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (362)  all_52_15 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | REDUCE: (130), (362) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (363)   ~ (all_52_13 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (364)  all_58_7 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (364) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (365)  all_52_13 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (365) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (366)  $false
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | CLOSE: (366) is inconsistent.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (367)  all_58_8 = e3 | all_58_11 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (368)  all_58_8 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (368) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (369)  all_10_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24), (73), (103), (369) are inconsistent by
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |            sub-proof #925.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (370)  all_58_11 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (358), (359), (370) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |            #587.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (371)   ~ (all_56_13 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | REDUCE: (168), (371) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (372)   ~ (all_52_15 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (373)  all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (152), (179), (338), (373) are inconsistent
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            by sub-proof #889.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (374)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (11), (13), (14), (31), (51),
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            (62), (78), (83), (94), (106), (110), (120),
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            (122), (131), (133), (141), (148), (150), (151),
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            (155), (162), (163), (164), (171), (172), (173),
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            (191), (203), (205), (241), (372), (374) are
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #437.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (375)  all_56_15 = e0
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (193), (375) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | | |            #1162.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (376)   ~ (all_58_2 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (81), (376) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (377)   ~ (all_52_3 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (378)  all_58_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | REF_CLOSE: (81), (377), (378) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | |            #1369.
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (379)  all_58_6 = e3 | all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (16), (24), (25), (73), (78), (103),
% 202.21/33.77  | | | | | | | | | | | | | | |            (114), (133), (142), (150), (157), (164), (175),
% 202.21/33.77  | | | | | | | | | | | | | | |            (179), (203), (322), (379) are inconsistent by
% 202.21/33.77  | | | | | | | | | | | | | | |            sub-proof #376.
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | |   (380)   ~ (all_56_3 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | REDUCE: (139), (380) imply:
% 202.21/33.77  | | | | | | | | | | | | |   (381)   ~ (all_52_25 = e3)
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (382)  all_58_9 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | COMBINE_EQS: (34), (382) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (383)  all_52_25 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | REDUCE: (381), (383) imply:
% 202.21/33.77  | | | | | | | | | | | | | |   (384)  $false
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | CLOSE: (384) is inconsistent.
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | |   (385)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (386)  all_58_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | COMBINE_EQS: (81), (386) imply:
% 202.21/33.77  | | | | | | | | | | | | | | |   (387)  all_52_3 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | SIMP: (387) implies:
% 202.21/33.77  | | | | | | | | | | | | | | |   (388)  all_52_3 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | REDUCE: (47), (388) imply:
% 202.21/33.77  | | | | | | | | | | | | | | |   (389)   ~ (all_52_27 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | SIMP: (389) implies:
% 202.21/33.77  | | | | | | | | | | | | | | |   (390)   ~ (all_52_27 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (391)  all_58_2 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REF_CLOSE: (152), (386), (391) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | |            #1124.
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (392)  all_58_6 = e2 | all_58_12 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | BETA: splitting (392) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (393)  all_58_6 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (179), (393) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | |            #917.
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (394)  all_58_12 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (394) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (395)  all_52_7 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | SIMP: (395) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (396)  all_52_7 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | REDUCE: (80), (396) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (397)   ~ (all_14_2 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | SIMP: (397) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (398)   ~ (all_14_2 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | REDUCE: (106), (396) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | |   (399)  op(e0, e3) = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | BETA: splitting (385) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (400)  all_58_10 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (390), (400) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | | |            #1301.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | |   (401)  all_58_11 = e3 | all_58_15 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (402)  all_58_11 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (402) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (403)  all_52_29 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | SIMP: (403) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (404)  all_52_29 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | REDUCE: (57), (404) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (405)  op(e1, e0) = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (406)  all_56_15 = e2
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (398), (406) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |            #762.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (407)   ~ (all_56_15 = e2)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | |   (408)  all_56_15 = e1 | all_56_15 = e0
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (408) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (409)  all_56_15 = e1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (409) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (410)  all_14_2 = e1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | SIMP: (410) implies:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (411)  all_14_2 = e1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (411) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (412)   ~ (e2 = e1)
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (411) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (413)  op(e1, e0) = all_14_1
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (32), (64), (399), (405), (413) are
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #859.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |   (414)  all_56_15 = e0
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (193), (414) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | |            #1162.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (415)  all_58_15 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (415) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (416)  all_14_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | REDUCE: (241), (416) imply:
% 202.21/33.77  | | | | | | | | | | | | | | | | | | |   (417)  $false
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | CLOSE: (417) is inconsistent.
% 202.21/33.77  | | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | |   (418)   ~ (all_58_2 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | REDUCE: (81), (418) imply:
% 202.21/33.77  | | | | | | | | | | | | | | |   (419)   ~ (all_52_3 = e3)
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 1:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (420)  all_58_2 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REF_CLOSE: (81), (419), (420) are inconsistent by sub-proof
% 202.21/33.77  | | | | | | | | | | | | | | | |            #1369.
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | Case 2:
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | |   (421)  all_58_6 = e3 | all_58_12 = e3
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (16), (24), (25), (73), (78), (103),
% 202.21/33.77  | | | | | | | | | | | | | | | |            (114), (133), (142), (150), (157), (164), (175),
% 202.21/33.77  | | | | | | | | | | | | | | | |            (179), (203), (322), (421) are inconsistent by
% 202.21/33.77  | | | | | | | | | | | | | | | |            sub-proof #376.
% 202.21/33.77  | | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | | 
% 202.21/33.77  | | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | | 
% 202.21/33.77  | | | | | | | | End of split
% 202.21/33.77  | | | | | | | | 
% 202.21/33.77  | | | | | | | End of split
% 202.21/33.77  | | | | | | | 
% 202.21/33.77  | | | | | | End of split
% 202.21/33.77  | | | | | | 
% 202.21/33.77  | | | | | Case 2:
% 202.21/33.77  | | | | | | 
% 202.21/33.77  | | | | | |   (422)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.21/33.77  | | | | | |          all_52_30 = e0
% 202.21/33.77  | | | | | | 
% 202.21/33.77  | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (15),
% 202.21/33.77  | | | | | |            (16), (17), (18), (19), (20), (21), (22), (24), (26),
% 202.21/33.77  | | | | | |            (27), (28), (29), (30), (31), (32), (34), (35), (37),
% 202.21/33.77  | | | | | |            (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 202.21/33.77  | | | | | |            (48), (50), (51), (52), (53), (54), (55), (56), (58),
% 202.21/33.77  | | | | | |            (62), (63), (66), (67), (68), (69), (70), (71), (72),
% 202.21/33.77  | | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 202.21/33.77  | | | | | |            (83), (85), (86), (87), (89), (90), (93), (95), (97),
% 202.21/33.77  | | | | | |            (98), (102), (103), (105), (106), (107), (108), (110),
% 202.21/33.77  | | | | | |            (111), (113), (114), (115), (116), (117), (118), (119),
% 202.21/33.77  | | | | | |            (121), (123), (124), (125), (126), (127), (128), (130),
% 202.21/33.77  | | | | | |            (131), (132), (133), (134), (135), (136), (137), (139),
% 202.21/33.77  | | | | | |            (140), (141), (142), (144), (146), (147), (148), (149),
% 202.21/33.77  | | | | | |            (150), (151), (152), (154), (157), (158), (159), (161),
% 202.21/33.77  | | | | | |            (162), (164), (165), (166), (167), (169), (170), (171),
% 202.21/33.77  | | | | | |            (173), (174), (175), (177), (184), (187), (191), (192),
% 202.21/33.77  | | | | | |            (193), (422) are inconsistent by sub-proof #360.
% 202.21/33.77  | | | | | | 
% 202.21/33.77  | | | | | End of split
% 202.21/33.77  | | | | | 
% 202.21/33.77  | | | | End of split
% 202.21/33.77  | | | | 
% 202.21/33.77  | | | End of split
% 202.21/33.77  | | | 
% 202.21/33.77  | | End of split
% 202.21/33.77  | | 
% 202.21/33.77  | End of split
% 202.21/33.77  | 
% 202.21/33.77  End of proof
% 202.21/33.77  
% 202.21/33.77  Sub-proof #356 shows that the following formulas are inconsistent:
% 202.21/33.77  ----------------------------------------------------------------
% 202.21/33.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.21/33.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.21/33.77    (2)  all_58_1 = all_52_9
% 202.21/33.77    (3)   ~ (all_52_9 = all_52_13)
% 202.21/33.77    (4)   ~ (all_14_1 = e2)
% 202.21/33.77    (5)  all_58_0 = all_6_2
% 202.21/33.77    (6)  all_58_13 = all_52_15
% 202.21/33.77    (7)  all_58_9 = all_52_25
% 202.21/33.77    (8)  op(e2, e2) = all_4_2
% 202.21/33.77    (9)  all_58_11 = all_52_29
% 202.21/33.77    (10)   ~ (all_52_9 = all_52_15)
% 202.21/33.77    (11)   ~ (all_6_2 = e3)
% 202.21/33.77    (12)   ~ (e2 = e1)
% 202.21/33.77    (13)  op(all_10_2, all_10_2) = e1
% 202.21/33.77    (14)  op(all_52_9, all_52_9) = all_52_8
% 202.21/33.77    (15)  all_58_7 = all_52_13
% 202.21/33.77    (16)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.21/33.77    (17)   ~ (all_52_29 = e3)
% 202.21/33.77    (18)  all_58_9 = all_14_1
% 202.21/33.77    (19)   ~ (all_52_25 = e3)
% 202.21/33.77    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.21/33.77    (21)  op(e2, e3) = e3
% 202.21/33.77    (22)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.21/33.77    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.21/33.77    (24)  all_58_8 = all_10_2
% 202.21/33.77    (25)   ~ (all_52_9 = all_4_2)
% 202.21/33.77    (26)  op(e3, e3) = all_52_2
% 202.21/33.77    (27)  op(e3, all_6_1) = e2
% 202.21/33.77    (28)  op(e3, e3) = all_6_2
% 202.21/33.77    (29)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.21/33.77    (30)  op(all_52_17, all_52_17) = e3
% 202.21/33.77    (31)   ~ (all_52_17 = all_6_2)
% 202.21/33.77    (32)   ~ (e3 = e2)
% 202.21/33.77    (33)  all_58_3 = all_4_2
% 202.21/33.77    (34)  op(all_6_2, e3) = all_6_1
% 202.21/33.77    (35)  all_58_4 = all_52_17
% 202.21/33.77  
% 202.21/33.77  Begin of proof
% 202.21/33.77  | 
% 202.21/33.77  | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3, simplifying
% 202.21/33.77  |              with (26), (28) gives:
% 202.21/33.77  |   (36)  all_52_2 = all_6_2
% 202.21/33.77  | 
% 202.21/33.77  | BETA: splitting (29) gives:
% 202.21/33.77  | 
% 202.21/33.77  | Case 1:
% 202.21/33.77  | | 
% 202.21/33.77  | |   (37)  all_58_0 = e3
% 202.21/33.77  | | 
% 202.21/33.77  | | COMBINE_EQS: (5), (37) imply:
% 202.21/33.77  | |   (38)  all_6_2 = e3
% 202.21/33.77  | | 
% 202.21/33.77  | | REDUCE: (11), (38) imply:
% 202.21/33.77  | |   (39)  $false
% 202.21/33.77  | | 
% 202.21/33.77  | | CLOSE: (39) is inconsistent.
% 202.21/33.77  | | 
% 202.21/33.77  | Case 2:
% 202.21/33.77  | | 
% 202.21/33.77  | |   (40)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.21/33.77  | | 
% 202.21/33.77  | | BETA: splitting (20) gives:
% 202.21/33.77  | | 
% 202.21/33.77  | | Case 1:
% 202.21/33.77  | | | 
% 202.21/33.77  | | |   (41)  all_58_0 = e2
% 202.21/33.77  | | | 
% 202.21/33.77  | | | COMBINE_EQS: (5), (41) imply:
% 202.21/33.77  | | |   (42)  all_6_2 = e2
% 202.21/33.77  | | | 
% 202.21/33.77  | | | REDUCE: (34), (42) imply:
% 202.21/33.77  | | |   (43)  op(e2, e3) = all_6_1
% 202.21/33.77  | | | 
% 202.21/33.78  | | | GROUND_INST: instantiating (1) with e3, all_6_1, e3, e2, simplifying with
% 202.21/33.78  | | |              (21), (43) gives:
% 202.21/33.78  | | |   (44)  all_6_1 = e3
% 202.21/33.78  | | | 
% 202.21/33.78  | | | REDUCE: (27), (44) imply:
% 202.21/33.78  | | |   (45)  op(e3, e3) = e2
% 202.21/33.78  | | | 
% 202.21/33.78  | | | BETA: splitting (23) gives:
% 202.21/33.78  | | | 
% 202.21/33.78  | | | Case 1:
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | |   (46)  all_58_1 = e3
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | COMBINE_EQS: (2), (46) imply:
% 202.21/33.78  | | | |   (47)  all_52_9 = e3
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (3), (47) imply:
% 202.21/33.78  | | | |   (48)   ~ (all_52_13 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | SIMP: (48) implies:
% 202.21/33.78  | | | |   (49)   ~ (all_52_13 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (14), (47) imply:
% 202.21/33.78  | | | |   (50)  op(e3, e3) = all_52_8
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REF_CLOSE: (1), (9), (12), (13), (15), (17), (22), (24), (45), (49),
% 202.21/33.78  | | | |            (50) are inconsistent by sub-proof #830.
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | Case 2:
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | |   (51)   ~ (all_58_1 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (2), (51) imply:
% 202.21/33.78  | | | |   (52)   ~ (all_52_9 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REF_CLOSE: (1), (2), (7), (19), (28), (30), (31), (35), (40), (52) are
% 202.21/33.78  | | | |            inconsistent by sub-proof #1072.
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | End of split
% 202.21/33.78  | | | 
% 202.21/33.78  | | Case 2:
% 202.21/33.78  | | | 
% 202.21/33.78  | | |   (53)   ~ (all_58_0 = e2)
% 202.21/33.78  | | | 
% 202.21/33.78  | | | REDUCE: (5), (53) imply:
% 202.21/33.78  | | |   (54)   ~ (all_6_2 = e2)
% 202.21/33.78  | | | 
% 202.21/33.78  | | | BETA: splitting (23) gives:
% 202.21/33.78  | | | 
% 202.21/33.78  | | | Case 1:
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | |   (55)  all_58_1 = e3
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | COMBINE_EQS: (2), (55) imply:
% 202.21/33.78  | | | |   (56)  all_52_9 = e3
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (3), (56) imply:
% 202.21/33.78  | | | |   (57)   ~ (all_52_13 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | SIMP: (57) implies:
% 202.21/33.78  | | | |   (58)   ~ (all_52_13 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (10), (56) imply:
% 202.21/33.78  | | | |   (59)   ~ (all_52_15 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | SIMP: (59) implies:
% 202.21/33.78  | | | |   (60)   ~ (all_52_15 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (25), (56) imply:
% 202.21/33.78  | | | |   (61)   ~ (all_4_2 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | SIMP: (61) implies:
% 202.21/33.78  | | | |   (62)   ~ (all_4_2 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | BETA: splitting (16) gives:
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | Case 1:
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | |   (63)  all_58_0 = e2
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | | COMBINE_EQS: (5), (63) imply:
% 202.21/33.78  | | | | |   (64)  all_6_2 = e2
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | | REDUCE: (54), (64) imply:
% 202.21/33.78  | | | | |   (65)  $false
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | | CLOSE: (65) is inconsistent.
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | Case 2:
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | |   (66)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | | REF_CLOSE: (1), (4), (6), (8), (15), (18), (23), (30), (32), (33),
% 202.21/33.78  | | | | |            (35), (58), (60), (62), (66) are inconsistent by sub-proof
% 202.21/33.78  | | | | |            #357.
% 202.21/33.78  | | | | | 
% 202.21/33.78  | | | | End of split
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | Case 2:
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | |   (67)   ~ (all_58_1 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REDUCE: (2), (67) imply:
% 202.21/33.78  | | | |   (68)   ~ (all_52_9 = e3)
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | | REF_CLOSE: (1), (2), (7), (19), (28), (30), (31), (35), (40), (68) are
% 202.21/33.78  | | | |            inconsistent by sub-proof #1072.
% 202.21/33.78  | | | | 
% 202.21/33.78  | | | End of split
% 202.21/33.78  | | | 
% 202.21/33.78  | | End of split
% 202.21/33.78  | | 
% 202.21/33.78  | End of split
% 202.21/33.78  | 
% 202.21/33.78  End of proof
% 202.21/33.78  
% 202.21/33.78  Sub-proof #357 shows that the following formulas are inconsistent:
% 202.21/33.78  ----------------------------------------------------------------
% 202.21/33.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.21/33.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.21/33.78    (2)   ~ (all_4_2 = e3)
% 202.21/33.78    (3)   ~ (all_14_1 = e2)
% 202.21/33.78    (4)  all_58_13 = all_52_15
% 202.21/33.78    (5)   ~ (all_52_15 = e3)
% 202.21/33.78    (6)  op(e2, e2) = all_4_2
% 202.21/33.78    (7)  all_58_7 = all_52_13
% 202.21/33.78    (8)  all_58_9 = all_14_1
% 202.21/33.78    (9)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.21/33.78    (10)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.21/33.78    (11)   ~ (all_52_13 = e3)
% 202.21/33.78    (12)  op(all_52_17, all_52_17) = e3
% 202.21/33.78    (13)   ~ (e3 = e2)
% 202.21/33.78    (14)  all_58_3 = all_4_2
% 202.21/33.78    (15)  all_58_4 = all_52_17
% 202.21/33.78  
% 202.21/33.78  Begin of proof
% 202.21/33.78  | 
% 202.21/33.78  | BETA: splitting (9) gives:
% 202.21/33.78  | 
% 202.21/33.78  | Case 1:
% 202.21/33.78  | | 
% 202.21/33.78  | |   (16)  all_58_1 = e2
% 202.21/33.78  | | 
% 202.21/33.78  | | REF_CLOSE: (2), (4), (5), (7), (10), (11), (13), (14), (16) are inconsistent
% 202.21/33.78  | |            by sub-proof #1088.
% 202.21/33.78  | | 
% 202.21/33.78  | Case 2:
% 202.21/33.78  | | 
% 202.21/33.78  | |   (17)  all_58_4 = e2 | all_58_9 = e2
% 202.21/33.78  | | 
% 202.21/33.78  | | BETA: splitting (17) gives:
% 202.21/33.78  | | 
% 202.21/33.78  | | Case 1:
% 202.21/33.78  | | | 
% 202.21/33.78  | | |   (18)  all_58_4 = e2
% 202.21/33.78  | | | 
% 202.21/33.78  | | | REF_CLOSE: (1), (2), (6), (12), (15), (18) are inconsistent by sub-proof
% 202.21/33.78  | | |            #1087.
% 202.21/33.78  | | | 
% 202.21/33.78  | | Case 2:
% 202.21/33.78  | | | 
% 202.21/33.78  | | |   (19)  all_58_9 = e2
% 202.21/33.78  | | | 
% 202.21/33.78  | | | COMBINE_EQS: (8), (19) imply:
% 202.21/33.78  | | |   (20)  all_14_1 = e2
% 202.21/33.78  | | | 
% 202.21/33.78  | | | SIMP: (20) implies:
% 202.21/33.78  | | |   (21)  all_14_1 = e2
% 202.21/33.78  | | | 
% 202.21/33.78  | | | REDUCE: (3), (21) imply:
% 202.21/33.78  | | |   (22)  $false
% 202.21/33.78  | | | 
% 202.21/33.78  | | | CLOSE: (22) is inconsistent.
% 202.21/33.78  | | | 
% 202.21/33.78  | | End of split
% 202.21/33.78  | | 
% 202.21/33.78  | End of split
% 202.21/33.78  | 
% 202.21/33.78  End of proof
% 202.21/33.78  
% 202.21/33.78  Sub-proof #358 shows that the following formulas are inconsistent:
% 202.21/33.78  ----------------------------------------------------------------
% 202.21/33.78    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.21/33.78    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.21/33.78    (3)   ~ (all_52_15 = all_52_23)
% 202.21/33.78    (4)   ~ (all_52_25 = all_52_27)
% 202.21/33.78    (5)  all_58_14 = all_52_23
% 202.21/33.78    (6)   ~ (e3 = e1)
% 202.21/33.78    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.21/33.78    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.21/33.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.21/33.78    (9)   ~ (all_52_5 = all_52_13)
% 202.21/33.78    (10)  all_58_1 = all_52_9
% 202.21/33.78    (11)   ~ (all_52_9 = all_52_13)
% 202.21/33.78    (12)   ~ (e3 = e0)
% 202.21/33.78    (13)  op(e2, e3) = all_52_3
% 202.21/33.78    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.21/33.78    (15)   ~ (all_52_7 = all_52_15)
% 202.21/33.78    (16)   ~ (all_52_3 = all_52_19)
% 202.21/33.78    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.21/33.78    (18)   ~ (all_52_17 = all_52_25)
% 202.21/33.78    (19)   ~ (all_52_3 = all_6_2)
% 202.21/33.78    (20)  all_44_2 = all_6_2
% 202.21/33.78    (21)  all_58_0 = all_6_2
% 202.21/33.78    (22)  op(all_14_2, e0) = all_14_1
% 202.21/33.78    (23)  all_56_4 = all_52_3
% 202.21/33.78    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.21/33.78    (25)  op(e3, e0) = all_52_25
% 202.21/33.78    (26)  op(all_52_5, all_52_5) = all_52_4
% 202.21/33.78    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.21/33.78    (28)  op(all_52_19, all_52_19) = all_52_18
% 202.21/33.78    (29)  all_58_13 = all_52_15
% 202.21/33.78    (30)  op(e0, all_14_1) = e1
% 202.21/33.78    (31)  op(all_10_2, all_10_2) = all_52_20
% 202.21/33.78    (32)  all_58_9 = all_52_25
% 202.21/33.78    (33)   ~ (all_52_29 = all_14_2)
% 202.21/33.78    (34)  op(all_52_27, all_52_27) = all_52_26
% 202.21/33.78    (35)  op(e1, e3) = all_52_5
% 202.21/33.78    (36)  op(e2, e2) = all_4_2
% 202.21/33.78    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.21/33.78    (38)   ~ (all_52_3 = all_52_5)
% 202.21/33.78    (39)  all_58_11 = all_52_29
% 202.21/33.78    (40)   ~ (all_52_25 = all_14_2)
% 202.21/33.78    (41)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.21/33.78    (42)   ~ (all_52_3 = all_52_27)
% 202.21/33.78    (43)   ~ (all_52_7 = all_6_2)
% 202.21/33.78    (44)  op(e0, e0) = all_14_2
% 202.21/33.78    (45)  op(e0, e1) = all_52_23
% 202.21/33.78    (46)  all_56_15 = all_14_2
% 202.21/33.78    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.21/33.78    (48)   ~ (all_4_1 = e1)
% 202.21/33.78    (49)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.21/33.78    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.21/33.78    (51)  all_56_9 = all_52_13
% 202.21/33.78    (52)   ~ (e2 = e1)
% 202.21/33.78    (53)   ~ (all_52_13 = all_10_2)
% 202.21/33.78    (54)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 202.21/33.78    (55)  all_58_10 = all_52_27
% 202.21/33.78    (56)  all_56_8 = all_52_5
% 202.21/33.78    (57)  op(all_52_9, all_52_9) = all_52_8
% 202.21/33.78    (58)  op(all_52_15, all_52_15) = all_52_14
% 202.21/33.78    (59)   ~ (all_52_19 = all_52_23)
% 202.21/33.78    (60)   ~ (all_52_25 = all_52_29)
% 202.21/33.78    (61)   ~ (all_52_29 = all_10_2)
% 202.21/33.78    (62)  all_58_7 = all_52_13
% 202.21/33.78    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.21/33.78    (64)   ~ (all_52_5 = all_52_7)
% 202.21/33.78    (65)  all_58_12 = all_52_7
% 202.21/33.78    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.21/33.78    (67)   ~ (all_52_7 = all_14_2)
% 202.21/33.78    (68)  all_58_2 = all_52_3
% 202.21/33.78    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.21/33.78    (70)  all_56_7 = all_52_27
% 202.21/33.78    (71)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.21/33.78    (72)   ~ (e2 = e0)
% 202.21/33.78    (73)  op(all_4_2, e2) = all_4_1
% 202.21/33.78    (74)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.21/33.78    (75)   ~ (all_52_15 = all_14_2)
% 202.21/33.78    (76)   ~ (all_52_13 = all_4_2)
% 202.21/33.78    (77)  op(e3, e1) = all_52_17
% 202.21/33.78    (78)  op(e0, e3) = all_52_7
% 202.21/33.78    (79)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.21/33.78    (80)   ~ (all_52_9 = all_52_25)
% 202.21/33.78    (81)  all_58_15 = all_14_2
% 202.21/33.78    (82)   ~ (all_52_19 = all_10_2)
% 202.21/33.78    (83)  op(all_52_23, all_52_23) = all_52_22
% 202.21/33.78    (84)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.21/33.78    (85)  all_58_8 = all_10_2
% 202.21/33.78    (86)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.21/33.78    (87)  all_34_2 = all_14_2
% 202.21/33.78    (88)   ~ (all_52_5 = all_10_2)
% 202.21/33.78    (89)  op(all_52_29, all_52_29) = all_52_28
% 202.21/33.78    (90)   ~ (all_52_23 = all_14_2)
% 202.21/33.78    (91)  all_56_12 = all_52_7
% 202.21/33.78    (92)  op(all_52_17, all_52_17) = all_52_16
% 202.21/33.78    (93)  all_8_2 = all_6_2
% 202.21/33.78    (94)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.21/33.78    (95)   ~ (all_52_25 = all_6_2)
% 202.21/33.78    (96)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.21/33.78    (97)   ~ (all_52_9 = all_4_2)
% 202.21/33.78    (98)   ~ (all_52_5 = all_6_2)
% 202.21/33.78    (99)   ~ (all_52_9 = all_6_2)
% 202.21/33.78    (100)   ~ (all_52_13 = all_52_15)
% 202.21/33.78    (101)  op(e3, all_6_1) = e2
% 202.21/33.78    (102)  all_56_0 = all_6_2
% 202.21/33.78    (103)  op(e3, e3) = all_6_2
% 202.21/33.78    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.21/33.78    (105)   ~ (all_52_27 = all_14_2)
% 202.21/33.78    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.21/33.78    (107)  op(all_4_2, all_4_2) = all_52_10
% 202.21/33.78    (108)  all_56_3 = all_52_25
% 202.21/33.78    (109)   ~ (all_52_3 = all_52_7)
% 202.21/33.78    (110)  op(all_14_2, all_14_2) = all_52_30
% 202.21/33.78    (111)  all_58_5 = all_52_19
% 202.21/33.78    (112)  all_56_1 = all_52_9
% 202.21/33.78    (113)   ~ (all_52_15 = all_4_2)
% 202.21/33.78    (114)   ~ (all_52_27 = all_4_2)
% 202.21/33.78    (115)  all_58_6 = all_52_5
% 202.21/33.78    (116)  op(e3, e2) = all_52_9
% 202.21/33.78    (117)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.21/33.78    (118)   ~ (all_52_17 = all_6_2)
% 202.21/33.78    (119)   ~ (e1 = e0)
% 202.21/33.78    (120)   ~ (e3 = e2)
% 202.21/33.78    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.21/33.78    (122)  all_44_1 = all_6_1
% 202.21/33.78    (123)   ~ (all_52_9 = all_52_17)
% 202.21/33.78    (124)  all_56_10 = all_10_2
% 202.21/33.78    (125)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.21/33.78    (126)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.21/33.78    (127)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.21/33.78    (128)  op(all_52_13, all_52_13) = all_52_12
% 202.21/33.78    (129)  op(e1, e1) = all_10_2
% 202.21/33.78    (130)   ~ (all_52_23 = all_10_2)
% 202.21/33.78    (131)   ~ (all_52_7 = all_52_23)
% 202.21/33.78    (132)   ~ (all_52_17 = all_52_19)
% 202.21/33.78    (133)  all_58_3 = all_4_2
% 202.21/33.78    (134)  all_56_13 = all_52_15
% 202.21/33.78    (135)   ~ (all_52_3 = all_4_2)
% 202.21/33.78    (136)   ~ (all_52_19 = all_4_2)
% 202.21/33.78    (137)   ~ (all_52_17 = all_52_23)
% 202.21/33.78    (138)  all_8_1 = all_6_1
% 202.21/33.78    (139)  op(all_6_2, e3) = all_6_1
% 202.21/33.78    (140)   ~ (all_52_13 = all_52_29)
% 202.21/33.78    (141)  all_58_4 = all_52_17
% 202.21/33.78    (142)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.21/33.78    (143)  op(all_52_25, all_52_25) = all_52_24
% 202.21/33.78  
% 202.21/33.78  Begin of proof
% 202.21/33.78  | 
% 202.21/33.78  | ALPHA: (54) implies:
% 202.21/33.78  |   (144)  all_52_14 = e0
% 202.21/33.78  |   (145)  all_52_12 = e1
% 202.21/33.78  |   (146)  all_52_10 = e2
% 202.21/33.78  |   (147)  all_52_8 = e3
% 202.21/33.78  | 
% 202.21/33.78  | REDUCE: (57), (147) imply:
% 202.21/33.78  |   (148)  op(all_52_9, all_52_9) = e3
% 202.21/33.78  | 
% 202.21/33.78  | REDUCE: (128), (145) imply:
% 202.21/33.78  |   (149)  op(all_52_13, all_52_13) = e1
% 202.21/33.78  | 
% 202.21/33.78  | REDUCE: (58), (144) imply:
% 202.21/33.78  |   (150)  op(all_52_15, all_52_15) = e0
% 202.21/33.78  | 
% 202.21/33.78  | REDUCE: (107), (146) imply:
% 202.21/33.78  |   (151)  op(all_4_2, all_4_2) = e2
% 202.21/33.78  | 
% 202.21/33.78  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.21/33.78  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.21/33.78  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 202.21/33.78  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 202.21/33.78  |            (46), (47), (48), (49), (50), (51), (52), (53), (55), (56), (59),
% 202.21/33.78  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 202.21/33.78  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 202.21/33.78  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 202.21/33.78  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 202.21/33.78  |            (103), (104), (105), (106), (108), (109), (110), (111), (112),
% 202.21/33.78  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 202.21/33.78  |            (122), (123), (124), (125), (126), (127), (129), (130), (131),
% 202.21/33.78  |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 202.21/33.78  |            (141), (142), (143), (148), (149), (150), (151) are inconsistent by
% 202.21/33.78  |            sub-proof #365.
% 202.21/33.78  | 
% 202.21/33.78  End of proof
% 202.21/33.78  
% 202.21/33.78  Sub-proof #359 shows that the following formulas are inconsistent:
% 202.21/33.78  ----------------------------------------------------------------
% 202.21/33.78    (1)   ~ (e3 = e1)
% 202.23/33.78    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.78    (3)  all_58_1 = all_52_9
% 202.23/33.78    (4)   ~ (all_10_0 = e3)
% 202.23/33.78    (5)  all_58_13 = all_52_15
% 202.23/33.78    (6)   ~ (all_52_15 = e3)
% 202.23/33.78    (7)  op(e2, e2) = all_4_2
% 202.23/33.78    (8)  all_58_7 = all_10_0
% 202.23/33.78    (9)   ~ (all_4_1 = e1)
% 202.23/33.78    (10)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.78    (11)  op(all_4_2, e2) = all_4_1
% 202.23/33.78    (12)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 202.23/33.78    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.78    (14)   ~ (all_52_9 = all_4_2)
% 202.23/33.78    (15)  all_42_2 = all_4_2
% 202.23/33.78    (16)   ~ (all_52_9 = all_6_2)
% 202.23/33.78    (17)  op(e3, e3) = all_6_2
% 202.23/33.78    (18)  all_56_1 = all_52_9
% 202.23/33.78    (19)  op(e3, e2) = all_52_9
% 202.23/33.78    (20)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.78    (21)  op(e2, all_4_1) = e1
% 202.23/33.78    (22)  all_42_1 = all_4_1
% 202.23/33.78    (23)  op(all_52_9, all_52_9) = e3
% 202.23/33.78    (24)  all_58_3 = all_4_2
% 202.23/33.78  
% 202.23/33.78  Begin of proof
% 202.23/33.78  | 
% 202.23/33.78  | BETA: splitting (13) gives:
% 202.23/33.78  | 
% 202.23/33.78  | Case 1:
% 202.23/33.78  | | 
% 202.23/33.78  | |   (25)  all_58_1 = e3
% 202.23/33.78  | | 
% 202.23/33.78  | | COMBINE_EQS: (3), (25) imply:
% 202.23/33.78  | |   (26)  all_52_9 = e3
% 202.23/33.78  | | 
% 202.23/33.78  | | REF_CLOSE: (2), (16), (17), (23), (26) are inconsistent by sub-proof #1337.
% 202.23/33.78  | | 
% 202.23/33.78  | Case 2:
% 202.23/33.78  | | 
% 202.23/33.78  | |   (27)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.78  | | 
% 202.23/33.78  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 202.23/33.78  | |            (15), (18), (19), (20), (21), (22), (24), (27) are inconsistent
% 202.23/33.78  | |            by sub-proof #607.
% 202.23/33.78  | | 
% 202.23/33.78  | End of split
% 202.23/33.78  | 
% 202.23/33.78  End of proof
% 202.23/33.78  
% 202.23/33.78  Sub-proof #360 shows that the following formulas are inconsistent:
% 202.23/33.78  ----------------------------------------------------------------
% 202.23/33.78    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.78    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.78    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.78    (4)  all_58_14 = all_52_23
% 202.23/33.78    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.78    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.78    (7)  all_58_1 = all_52_9
% 202.23/33.78    (8)   ~ (all_52_9 = all_52_13)
% 202.23/33.78    (9)   ~ (e3 = e0)
% 202.23/33.78    (10)  op(e2, e3) = all_52_3
% 202.23/33.78    (11)   ~ (all_52_3 = all_52_19)
% 202.23/33.78    (12)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.78    (13)   ~ (all_52_17 = all_52_25)
% 202.23/33.78    (14)   ~ (all_52_3 = all_6_2)
% 202.23/33.78    (15)  all_44_2 = all_6_2
% 202.23/33.78    (16)  all_58_0 = all_6_2
% 202.23/33.78    (17)  op(all_14_2, e0) = all_14_1
% 202.23/33.78    (18)  all_34_1 = all_14_1
% 202.23/33.78    (19)   ~ (all_52_17 = all_10_2)
% 202.23/33.78    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.78    (21)  op(e3, e0) = all_52_25
% 202.23/33.78    (22)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.78    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.78    (24)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.78    (25)   ~ (all_52_27 = all_52_29)
% 202.23/33.78    (26)  all_58_13 = all_52_15
% 202.23/33.78    (27)  op(e0, all_14_1) = e1
% 202.23/33.78    (28)  all_58_9 = all_52_25
% 202.23/33.78    (29)   ~ (all_52_29 = all_14_2)
% 202.23/33.78    (30)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.78    (31)  op(e1, e3) = all_52_5
% 202.23/33.78    (32)  op(e2, e2) = all_4_2
% 202.23/33.78    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.78    (34)   ~ (all_52_3 = all_52_5)
% 202.23/33.78    (35)  all_58_11 = all_52_29
% 202.23/33.78    (36)  all_56_5 = all_4_2
% 202.23/33.78    (37)   ~ (all_52_25 = all_14_2)
% 202.23/33.78    (38)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.78    (39)   ~ (all_52_3 = all_52_27)
% 202.23/33.78    (40)  op(all_10_2, e1) = all_10_1
% 202.23/33.78    (41)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.78    (42)   ~ (all_52_7 = all_6_2)
% 202.23/33.78    (43)  op(e0, e0) = all_14_2
% 202.23/33.78    (44)  op(e0, e1) = all_52_23
% 202.23/33.78    (45)  all_56_15 = all_14_2
% 202.23/33.78    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.78    (47)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.78    (48)  all_56_11 = all_52_29
% 202.23/33.78    (49)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.23/33.78    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.78    (51)  all_56_9 = all_52_13
% 202.23/33.78    (52)  all_58_10 = all_52_27
% 202.23/33.78    (53)  all_56_8 = all_52_5
% 202.23/33.78    (54)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.78    (55)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.78    (56)   ~ (all_52_19 = all_52_23)
% 202.23/33.78    (57)   ~ (all_52_25 = all_52_29)
% 202.23/33.78    (58)   ~ (all_52_29 = all_10_2)
% 202.23/33.78    (59)  all_58_7 = all_52_13
% 202.23/33.78    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.78    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.78    (62)   ~ (all_52_5 = all_52_7)
% 202.23/33.78    (63)  all_58_12 = all_52_7
% 202.23/33.78    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.78    (65)   ~ (all_52_7 = all_14_2)
% 202.23/33.78    (66)   ~ (all_14_2 = e0)
% 202.23/33.78    (67)  all_58_2 = all_52_3
% 202.23/33.78    (68)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.78    (69)  all_56_2 = all_52_17
% 202.23/33.78    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.78    (71)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.78    (72)  all_56_7 = all_52_27
% 202.23/33.78    (73)   ~ (e2 = e0)
% 202.23/33.78    (74)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.78    (75)   ~ (all_52_5 = all_52_29)
% 202.23/33.78    (76)  all_56_6 = all_52_19
% 202.23/33.78    (77)   ~ (all_52_19 = all_52_27)
% 202.23/33.78    (78)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.78    (79)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.78    (80)   ~ (all_52_13 = all_4_2)
% 202.23/33.78    (81)  op(e3, e1) = all_52_17
% 202.23/33.78    (82)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.78    (83)  op(e0, e3) = all_52_7
% 202.23/33.78    (84)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.78    (85)   ~ (all_52_9 = all_52_25)
% 202.23/33.78    (86)  all_58_15 = all_14_2
% 202.23/33.78    (87)   ~ (all_52_19 = all_10_2)
% 202.23/33.78    (88)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.78    (89)  all_58_8 = all_10_2
% 202.23/33.78    (90)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.78    (91)  all_34_2 = all_14_2
% 202.23/33.78    (92)   ~ (all_52_5 = all_10_2)
% 202.23/33.78    (93)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.78    (94)   ~ (all_52_23 = all_14_2)
% 202.23/33.78    (95)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.78    (96)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.78    (97)   ~ (all_52_25 = all_6_2)
% 202.23/33.78    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.78    (99)   ~ (all_52_9 = all_4_2)
% 202.23/33.78    (100)   ~ (all_52_5 = all_6_2)
% 202.23/33.78    (101)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.23/33.78    (102)   ~ (all_52_13 = all_52_15)
% 202.23/33.78    (103)  op(e3, all_6_1) = e2
% 202.23/33.78    (104)  all_56_0 = all_6_2
% 202.23/33.78    (105)  op(e3, e3) = all_6_2
% 202.23/33.78    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.78    (107)   ~ (all_52_27 = all_14_2)
% 202.23/33.78    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.78    (109)  all_56_14 = all_52_23
% 202.23/33.78    (110)  all_56_3 = all_52_25
% 202.23/33.78    (111)   ~ (all_52_3 = all_52_7)
% 202.23/33.78    (112)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.78    (113)  all_58_5 = all_52_19
% 202.23/33.78    (114)   ~ (all_52_15 = all_4_2)
% 202.23/33.78    (115)   ~ (all_52_27 = all_4_2)
% 202.23/33.78    (116)  all_58_6 = all_52_5
% 202.23/33.78    (117)  op(e3, e2) = all_52_9
% 202.23/33.78    (118)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.78    (119)   ~ (all_52_17 = all_6_2)
% 202.23/33.78    (120)   ~ (e1 = e0)
% 202.23/33.78    (121)   ~ (e3 = e2)
% 202.23/33.78    (122)  all_44_1 = all_6_1
% 202.23/33.78    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.78    (124)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.78    (125)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.23/33.78    (126)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.78    (127)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.78    (128)  op(e1, e1) = all_10_2
% 202.23/33.78    (129)   ~ (all_52_7 = all_52_23)
% 202.23/33.78    (130)   ~ (all_52_17 = all_52_19)
% 202.23/33.78    (131)  all_58_3 = all_4_2
% 202.23/33.78    (132)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.78    (133)   ~ (all_52_3 = all_4_2)
% 202.23/33.78    (134)   ~ (all_52_19 = all_4_2)
% 202.23/33.78    (135)   ~ (all_52_17 = all_52_23)
% 202.23/33.78    (136)  op(all_6_2, e3) = all_6_1
% 202.23/33.78    (137)   ~ (all_52_13 = all_52_29)
% 202.23/33.78    (138)  all_58_4 = all_52_17
% 202.23/33.78    (139)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.78  
% 202.23/33.78  Begin of proof
% 202.23/33.78  | 
% 202.23/33.78  | ALPHA: (125) implies:
% 202.23/33.78  |   (140)  all_52_30 = e0
% 202.23/33.78  |   (141)  all_52_28 = e1
% 202.23/33.78  |   (142)  all_52_26 = e2
% 202.23/33.78  |   (143)  all_52_24 = e3
% 202.23/33.78  | 
% 202.23/33.78  | REDUCE: (139), (143) imply:
% 202.23/33.78  |   (144)  op(all_52_25, all_52_25) = e3
% 202.23/33.78  | 
% 202.23/33.78  | REDUCE: (30), (142) imply:
% 202.23/33.78  |   (145)  op(all_52_27, all_52_27) = e2
% 202.23/33.78  | 
% 202.23/33.78  | REDUCE: (93), (141) imply:
% 202.23/33.78  |   (146)  op(all_52_29, all_52_29) = e1
% 202.23/33.78  | 
% 202.23/33.78  | REDUCE: (112), (140) imply:
% 202.23/33.78  |   (147)  op(all_14_2, all_14_2) = e0
% 202.23/33.78  | 
% 202.23/33.78  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.23/33.78  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.23/33.78  |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 202.23/33.78  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 202.23/33.78  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 202.23/33.78  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 202.23/33.78  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 202.23/33.78  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 202.23/33.78  |            (91), (92), (94), (95), (96), (97), (98), (99), (100), (101),
% 202.23/33.78  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 202.23/33.78  |            (111), (113), (114), (115), (116), (117), (118), (119), (120),
% 202.23/33.78  |            (121), (122), (123), (124), (126), (127), (128), (129), (130),
% 202.23/33.78  |            (131), (132), (133), (134), (135), (136), (137), (138), (144),
% 202.23/33.78  |            (145), (146), (147) are inconsistent by sub-proof #362.
% 202.23/33.78  | 
% 202.23/33.78  End of proof
% 202.23/33.78  
% 202.23/33.78  Sub-proof #361 shows that the following formulas are inconsistent:
% 202.23/33.78  ----------------------------------------------------------------
% 202.23/33.78    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.78    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.78    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.78    (4)  all_58_14 = all_52_23
% 202.23/33.78    (5)   ~ (e3 = e1)
% 202.23/33.78    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.78    (8)   ~ (all_52_5 = all_52_13)
% 202.23/33.78    (9)  all_58_1 = all_52_9
% 202.23/33.78    (10)   ~ (all_52_9 = all_52_13)
% 202.23/33.78    (11)   ~ (e3 = e0)
% 202.23/33.79    (12)  op(e2, e3) = all_52_3
% 202.23/33.79    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.79    (14)   ~ (all_52_7 = all_52_15)
% 202.23/33.79    (15)   ~ (all_52_3 = all_52_19)
% 202.23/33.79    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.79    (17)   ~ (all_52_17 = all_52_25)
% 202.23/33.79    (18)   ~ (all_52_3 = all_6_2)
% 202.23/33.79    (19)  all_44_2 = all_6_2
% 202.23/33.79    (20)  all_58_0 = all_6_2
% 202.23/33.79    (21)  op(all_14_2, e0) = all_14_1
% 202.23/33.79    (22)  all_34_1 = all_14_1
% 202.23/33.79    (23)  all_56_4 = all_52_3
% 202.23/33.79    (24)   ~ (all_52_17 = all_10_2)
% 202.23/33.79    (25)  op(e3, e0) = all_52_25
% 202.23/33.79    (26)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.79    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.79    (28)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.79    (29)   ~ (all_52_27 = all_52_29)
% 202.23/33.79    (30)  all_58_13 = all_52_15
% 202.23/33.79    (31)  op(e0, all_14_1) = e1
% 202.23/33.79    (32)   ~ (all_40_1 = e2)
% 202.23/33.79    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.23/33.79    (34)  all_58_9 = all_52_25
% 202.23/33.79    (35)   ~ (all_52_29 = all_14_2)
% 202.23/33.79    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.23/33.79    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.79    (38)  op(e1, e3) = all_52_5
% 202.23/33.79    (39)  all_40_1 = all_10_1
% 202.23/33.79    (40)  op(e2, e2) = all_4_2
% 202.23/33.79    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.79    (42)   ~ (all_52_3 = all_52_5)
% 202.23/33.79    (43)  all_58_11 = all_52_29
% 202.23/33.79    (44)  all_56_5 = all_4_2
% 202.23/33.79    (45)   ~ (all_52_25 = all_14_2)
% 202.23/33.79    (46)   ~ (all_52_9 = all_52_15)
% 202.23/33.79    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.79    (48)   ~ (all_52_3 = all_52_27)
% 202.23/33.79    (49)  op(all_10_2, e1) = all_10_1
% 202.23/33.79    (50)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.79    (51)   ~ (all_52_7 = all_6_2)
% 202.23/33.79    (52)  op(e0, e0) = all_14_2
% 202.23/33.79    (53)  op(e0, e1) = all_52_23
% 202.23/33.79    (54)  all_56_15 = all_14_2
% 202.23/33.79    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.79    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.79    (57)  all_56_11 = all_52_29
% 202.23/33.79    (58)   ~ (all_4_1 = e1)
% 202.23/33.79    (59)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.23/33.79    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.79    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.79    (62)  all_56_9 = all_52_13
% 202.23/33.79    (63)   ~ (e2 = e1)
% 202.23/33.79    (64)   ~ (all_52_13 = all_10_2)
% 202.23/33.79    (65)  all_58_10 = all_52_27
% 202.23/33.79    (66)  all_56_8 = all_52_5
% 202.23/33.79    (67)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.79    (68)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.79    (69)   ~ (all_52_19 = all_52_23)
% 202.23/33.79    (70)   ~ (all_52_25 = all_52_29)
% 202.23/33.79    (71)   ~ (all_52_29 = all_10_2)
% 202.23/33.79    (72)  all_58_7 = all_52_13
% 202.23/33.79    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.79    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.79    (75)   ~ (all_52_5 = all_52_7)
% 202.23/33.79    (76)  all_58_12 = all_52_7
% 202.23/33.79    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.79    (78)   ~ (all_52_7 = all_14_2)
% 202.23/33.79    (79)  all_58_2 = all_52_3
% 202.23/33.79    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.79    (81)  all_56_2 = all_52_17
% 202.23/33.79    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.79    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.79    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.79    (85)  all_56_7 = all_52_27
% 202.23/33.79    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.79    (87)   ~ (e2 = e0)
% 202.23/33.79    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.79    (89)  op(all_4_2, e2) = all_4_1
% 202.23/33.79    (90)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.79    (91)   ~ (all_52_5 = all_52_29)
% 202.23/33.79    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.79    (93)  all_56_6 = all_52_19
% 202.23/33.79    (94)   ~ (all_52_15 = all_14_2)
% 202.23/33.79    (95)   ~ (all_52_19 = all_52_27)
% 202.23/33.79    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.79    (97)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 202.23/33.79            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 202.23/33.79    (98)   ~ (all_52_13 = all_4_2)
% 202.23/33.79    (99)  op(e3, e1) = all_52_17
% 202.23/33.79    (100)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.79    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.79    (102)  op(e0, e3) = all_52_7
% 202.23/33.79    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.79    (104)   ~ (all_52_9 = all_52_25)
% 202.23/33.79    (105)  all_58_15 = all_14_2
% 202.23/33.79    (106)   ~ (all_52_19 = all_10_2)
% 202.23/33.79    (107)  op(all_52_23, all_52_23) = all_52_22
% 202.23/33.79    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.79    (109)  all_58_8 = all_10_2
% 202.23/33.79    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.79    (111)  all_34_2 = all_14_2
% 202.23/33.79    (112)   ~ (all_52_5 = all_10_2)
% 202.23/33.79    (113)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.79    (114)   ~ (all_52_23 = all_14_2)
% 202.23/33.79    (115)  all_56_12 = all_52_7
% 202.23/33.79    (116)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.79    (117)  all_8_2 = all_6_2
% 202.23/33.79    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.79    (119)   ~ (all_52_25 = all_6_2)
% 202.23/33.79    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.79    (121)   ~ (all_52_9 = all_4_2)
% 202.23/33.79    (122)   ~ (all_52_5 = all_6_2)
% 202.23/33.79    (123)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.23/33.79    (124)   ~ (all_52_9 = all_6_2)
% 202.23/33.79    (125)   ~ (all_52_13 = all_52_15)
% 202.23/33.79    (126)  op(e3, all_6_1) = e2
% 202.23/33.79    (127)  all_56_0 = all_6_2
% 202.23/33.79    (128)  op(e3, e3) = all_6_2
% 202.23/33.79    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.79    (130)   ~ (all_52_27 = all_14_2)
% 202.23/33.79    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.79    (132)  all_56_14 = all_52_23
% 202.23/33.79    (133)  op(all_4_2, all_4_2) = all_52_10
% 202.23/33.79    (134)  all_56_3 = all_52_25
% 202.23/33.79    (135)   ~ (all_52_3 = all_52_7)
% 202.23/33.79    (136)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.79    (137)  all_58_5 = all_52_19
% 202.23/33.79    (138)  all_56_1 = all_52_9
% 202.23/33.79    (139)   ~ (all_52_15 = all_4_2)
% 202.23/33.79    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.79           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.23/33.79           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.23/33.79           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.23/33.79    (141)   ~ (all_52_27 = all_4_2)
% 202.23/33.79    (142)  all_58_6 = all_52_5
% 202.23/33.79    (143)  op(e3, e2) = all_52_9
% 202.23/33.79    (144)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.79    (145)   ~ (all_52_17 = all_6_2)
% 202.23/33.79    (146)   ~ (e1 = e0)
% 202.23/33.79    (147)   ~ (e3 = e2)
% 202.23/33.79    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.79    (149)  all_44_1 = all_6_1
% 202.23/33.79    (150)   ~ (all_52_9 = all_52_17)
% 202.23/33.79    (151)  all_56_10 = all_10_2
% 202.23/33.79    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.79    (153)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.79    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.79    (155)  all_44_0 = e2
% 202.23/33.79    (156)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.79    (157)  op(e1, e1) = all_10_2
% 202.23/33.79    (158)   ~ (all_52_23 = all_10_2)
% 202.23/33.79    (159)   ~ (all_52_7 = all_52_23)
% 202.23/33.79    (160)   ~ (all_52_17 = all_52_19)
% 202.23/33.79    (161)  all_58_3 = all_4_2
% 202.23/33.79    (162)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.79    (163)  all_56_13 = all_52_15
% 202.23/33.79    (164)   ~ (all_52_3 = all_4_2)
% 202.23/33.79    (165)   ~ (all_52_19 = all_4_2)
% 202.23/33.79    (166)   ~ (all_52_17 = all_52_23)
% 202.23/33.79    (167)  all_8_1 = all_6_1
% 202.23/33.79    (168)  op(all_6_2, e3) = all_6_1
% 202.23/33.79    (169)   ~ (all_52_13 = all_52_29)
% 202.23/33.79    (170)  all_58_4 = all_52_17
% 202.23/33.79    (171)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.79    (172)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.79  
% 202.23/33.79  Begin of proof
% 202.23/33.79  | 
% 202.23/33.79  | REDUCE: (32), (39) imply:
% 202.23/33.79  |   (173)   ~ (all_10_1 = e2)
% 202.23/33.79  | 
% 202.23/33.79  | BETA: splitting (100) gives:
% 202.23/33.79  | 
% 202.23/33.79  | Case 1:
% 202.23/33.79  | | 
% 202.23/33.79  | |   (174)   ~ (all_44_0 = e2)
% 202.23/33.79  | | 
% 202.23/33.79  | | REDUCE: (155), (174) imply:
% 202.23/33.79  | |   (175)  $false
% 202.23/33.79  | | 
% 202.23/33.79  | | CLOSE: (175) is inconsistent.
% 202.23/33.79  | | 
% 202.23/33.79  | Case 2:
% 202.23/33.79  | | 
% 202.23/33.79  | |   (176)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.79  | | 
% 202.23/33.79  | | BETA: splitting (97) gives:
% 202.23/33.79  | | 
% 202.23/33.79  | | Case 1:
% 202.23/33.79  | | | 
% 202.23/33.79  | | |   (177)  all_58_15 = e0
% 202.23/33.79  | | | 
% 202.23/33.79  | | | REF_CLOSE: (7), (21), (31), (52), (105), (136), (146), (177) are
% 202.23/33.79  | | |            inconsistent by sub-proof #877.
% 202.23/33.79  | | | 
% 202.23/33.79  | | Case 2:
% 202.23/33.79  | | | 
% 202.23/33.79  | | |   (178)   ~ (all_58_15 = e0)
% 202.23/33.79  | | |   (179)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 202.23/33.79  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 202.23/33.79  | | | 
% 202.23/33.79  | | | ALPHA: (179) implies:
% 202.23/33.79  | | |   (180)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.79  | | |   (181)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.79  | | | 
% 202.23/33.79  | | | REDUCE: (105), (178) imply:
% 202.23/33.79  | | |   (182)   ~ (all_14_2 = e0)
% 202.23/33.79  | | | 
% 202.23/33.79  | | | BETA: splitting (140) gives:
% 202.23/33.79  | | | 
% 202.23/33.79  | | | Case 1:
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | |   (183)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 202.23/33.79  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 202.23/33.79  | | | |            = e0)
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | | BETA: splitting (183) gives:
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | | Case 1:
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | |   (184)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REF_CLOSE: (6), (7), (16), (20), (26), (40), (50), (52), (55), (76),
% 202.23/33.79  | | | | |            (78), (79), (83), (112), (126), (127), (128), (142), (144),
% 202.23/33.79  | | | | |            (147), (154), (157), (164), (168), (184) are inconsistent
% 202.23/33.79  | | | | |            by sub-proof #501.
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | Case 2:
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | |   (185)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 202.23/33.79  | | | | |          e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | ALPHA: (185) implies:
% 202.23/33.79  | | | | |   (186)  all_52_14 = e0
% 202.23/33.79  | | | | |   (187)  all_52_12 = e1
% 202.23/33.79  | | | | |   (188)  all_52_10 = e2
% 202.23/33.79  | | | | |   (189)  all_52_8 = e3
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (67), (189) imply:
% 202.23/33.79  | | | | |   (190)  op(all_52_9, all_52_9) = e3
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (156), (187) imply:
% 202.23/33.79  | | | | |   (191)  op(all_52_13, all_52_13) = e1
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (68), (186) imply:
% 202.23/33.79  | | | | |   (192)  op(all_52_15, all_52_15) = e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (133), (188) imply:
% 202.23/33.79  | | | | |   (193)  op(all_4_2, all_4_2) = e2
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 202.23/33.79  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 202.23/33.79  | | | | |            (23), (25), (26), (27), (28), (30), (31), (33), (34), (35),
% 202.23/33.79  | | | | |            (37), (38), (40), (41), (42), (43), (45), (47), (48), (51),
% 202.23/33.79  | | | | |            (52), (53), (54), (55), (58), (59), (60), (62), (63), (64),
% 202.23/33.79  | | | | |            (65), (66), (69), (70), (71), (72), (74), (75), (76), (77),
% 202.23/33.79  | | | | |            (78), (79), (83), (85), (86), (87), (89), (90), (94), (98),
% 202.23/33.79  | | | | |            (99), (102), (103), (104), (105), (106), (107), (108),
% 202.23/33.79  | | | | |            (109), (110), (111), (112), (113), (114), (115), (116),
% 202.23/33.79  | | | | |            (117), (118), (119), (120), (121), (122), (124), (125),
% 202.23/33.79  | | | | |            (126), (127), (128), (129), (130), (131), (134), (135),
% 202.23/33.79  | | | | |            (136), (137), (138), (139), (141), (142), (143), (144),
% 202.23/33.79  | | | | |            (145), (146), (147), (148), (149), (150), (151), (152),
% 202.23/33.79  | | | | |            (153), (154), (157), (158), (159), (160), (161), (163),
% 202.23/33.79  | | | | |            (164), (165), (166), (167), (168), (169), (170), (171),
% 202.23/33.79  | | | | |            (172), (176), (181), (190), (191), (192), (193) are
% 202.23/33.79  | | | | |            inconsistent by sub-proof #365.
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | End of split
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | Case 2:
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | |   (194)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.23/33.79  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.23/33.79  | | | |            all_52_30 = e0)
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | | BETA: splitting (194) gives:
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | | Case 1:
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | |   (195)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 202.23/33.79  | | | | |          = e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | ALPHA: (195) implies:
% 202.23/33.79  | | | | |   (196)  all_52_22 = e0
% 202.23/33.79  | | | | |   (197)  all_52_20 = e1
% 202.23/33.79  | | | | |   (198)  all_52_18 = e2
% 202.23/33.79  | | | | |   (199)  all_52_16 = e3
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (116), (199) imply:
% 202.23/33.79  | | | | |   (200)  op(all_52_17, all_52_17) = e3
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (28), (198) imply:
% 202.23/33.79  | | | | |   (201)  op(all_52_19, all_52_19) = e2
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (107), (196) imply:
% 202.23/33.79  | | | | |   (202)  op(all_52_23, all_52_23) = e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (33), (197) imply:
% 202.23/33.79  | | | | |   (203)  op(all_10_2, all_10_2) = e1
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | BETA: splitting (110) gives:
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | Case 1:
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | |   (204)  all_56_15 = e3
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | COMBINE_EQS: (54), (204) imply:
% 202.23/33.79  | | | | | |   (205)  all_14_2 = e3
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | COMBINE_EQS: (111), (205) imply:
% 202.23/33.79  | | | | | |   (206)  all_34_2 = e3
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REDUCE: (78), (205) imply:
% 202.23/33.79  | | | | | |   (207)   ~ (all_52_7 = e3)
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REDUCE: (94), (205) imply:
% 202.23/33.79  | | | | | |   (208)   ~ (all_52_15 = e3)
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REDUCE: (114), (205) imply:
% 202.23/33.79  | | | | | |   (209)   ~ (all_52_23 = e3)
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REDUCE: (136), (205) imply:
% 202.23/33.79  | | | | | |   (210)  op(e3, e3) = all_52_30
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REDUCE: (21), (205) imply:
% 202.23/33.79  | | | | | |   (211)  op(e3, e0) = all_14_1
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | BETA: splitting (59) gives:
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | Case 1:
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | |   (212)   ~ (all_34_1 = e2)
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | REDUCE: (22), (212) imply:
% 202.23/33.79  | | | | | | |   (213)   ~ (all_14_1 = e2)
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3,
% 202.23/33.79  | | | | | | |              simplifying with (25), (211) gives:
% 202.23/33.79  | | | | | | |   (214)  all_52_25 = all_14_1
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_30, e3, e3,
% 202.23/33.79  | | | | | | |              simplifying with (128), (210) gives:
% 202.23/33.79  | | | | | | |   (215)  all_52_30 = all_6_2
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | COMBINE_EQS: (34), (214) imply:
% 202.23/33.79  | | | | | | |   (216)  all_58_9 = all_14_1
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | REDUCE: (119), (214) imply:
% 202.23/33.79  | | | | | | |   (217)   ~ (all_14_1 = all_6_2)
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | REF_CLOSE: (4), (5), (7), (9), (12), (15), (18), (20), (23), (30),
% 202.23/33.79  | | | | | | |            (41), (49), (63), (64), (72), (74), (76), (79), (80),
% 202.23/33.79  | | | | | | |            (82), (83), (86), (87), (93), (99), (103), (109),
% 202.23/33.79  | | | | | | |            (112), (126), (128), (137), (142), (145), (147), (152),
% 202.23/33.79  | | | | | | |            (161), (164), (168), (170), (173), (200), (201), (203),
% 202.23/33.79  | | | | | | |            (207), (208), (209), (211), (213), (216), (217) are
% 202.23/33.79  | | | | | | |            inconsistent by sub-proof #363.
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | Case 2:
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | |   (218)   ~ (all_34_2 = e3)
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | REDUCE: (206), (218) imply:
% 202.23/33.79  | | | | | | |   (219)  $false
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | | CLOSE: (219) is inconsistent.
% 202.23/33.79  | | | | | | | 
% 202.23/33.79  | | | | | | End of split
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | Case 2:
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | |   (220)   ~ (all_56_15 = e3)
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REDUCE: (54), (220) imply:
% 202.23/33.79  | | | | | |   (221)   ~ (all_14_2 = e3)
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 202.23/33.79  | | | | | |            (13), (14), (15), (16), (17), (18), (20), (23), (24),
% 202.23/33.79  | | | | | |            (25), (27), (29), (30), (34), (35), (36), (37), (41),
% 202.23/33.79  | | | | | |            (42), (43), (45), (46), (49), (51), (52), (55), (60),
% 202.23/33.79  | | | | | |            (61), (63), (64), (65), (67), (68), (69), (70), (71),
% 202.23/33.79  | | | | | |            (72), (74), (75), (76), (77), (78), (79), (80), (81),
% 202.23/33.79  | | | | | |            (83), (84), (85), (86), (87), (90), (92), (93), (94),
% 202.23/33.79  | | | | | |            (99), (102), (103), (105), (106), (109), (112), (113),
% 202.23/33.79  | | | | | |            (115), (117), (119), (120), (122), (126), (128), (129),
% 202.23/33.79  | | | | | |            (130), (131), (133), (134), (135), (136), (137), (139),
% 202.23/33.79  | | | | | |            (142), (143), (144), (145), (146), (147), (150), (151),
% 202.23/33.79  | | | | | |            (152), (156), (157), (158), (159), (160), (161), (163),
% 202.23/33.79  | | | | | |            (166), (167), (168), (170), (171), (172), (173), (180),
% 202.23/33.79  | | | | | |            (200), (201), (202), (203), (221) are inconsistent by
% 202.23/33.79  | | | | | |            sub-proof #436.
% 202.23/33.79  | | | | | | 
% 202.23/33.79  | | | | | End of split
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | Case 2:
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | |   (222)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 202.23/33.79  | | | | |          = e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | ALPHA: (222) implies:
% 202.23/33.79  | | | | |   (223)  all_52_30 = e0
% 202.23/33.79  | | | | |   (224)  all_52_28 = e1
% 202.23/33.79  | | | | |   (225)  all_52_26 = e2
% 202.23/33.79  | | | | |   (226)  all_52_24 = e3
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (172), (226) imply:
% 202.23/33.79  | | | | |   (227)  op(all_52_25, all_52_25) = e3
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (37), (225) imply:
% 202.23/33.79  | | | | |   (228)  op(all_52_27, all_52_27) = e2
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (113), (224) imply:
% 202.23/33.79  | | | | |   (229)  op(all_52_29, all_52_29) = e1
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REDUCE: (136), (223) imply:
% 202.23/33.79  | | | | |   (230)  op(all_14_2, all_14_2) = e0
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (15), (16),
% 202.23/33.79  | | | | |            (17), (18), (19), (20), (21), (22), (24), (25), (26), (27),
% 202.23/33.79  | | | | |            (28), (29), (30), (31), (34), (35), (38), (40), (41), (42),
% 202.23/33.79  | | | | |            (43), (44), (45), (47), (48), (49), (50), (51), (52), (53),
% 202.23/33.79  | | | | |            (54), (55), (56), (57), (59), (61), (62), (65), (66), (67),
% 202.23/33.79  | | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 202.23/33.79  | | | | |            (78), (79), (80), (81), (83), (84), (85), (87), (88), (91),
% 202.23/33.79  | | | | |            (93), (95), (96), (98), (99), (101), (102), (103), (104),
% 202.23/33.79  | | | | |            (105), (106), (108), (109), (110), (111), (112), (114),
% 202.23/33.79  | | | | |            (116), (118), (119), (120), (121), (122), (123), (125),
% 202.23/33.79  | | | | |            (126), (127), (128), (129), (130), (131), (132), (134),
% 202.23/33.79  | | | | |            (135), (137), (139), (141), (142), (143), (144), (145),
% 202.23/33.79  | | | | |            (146), (147), (149), (152), (153), (154), (156), (157),
% 202.23/33.79  | | | | |            (159), (160), (161), (162), (164), (165), (166), (168),
% 202.23/33.79  | | | | |            (169), (170), (176), (180), (181), (182), (227), (228),
% 202.23/33.79  | | | | |            (229), (230) are inconsistent by sub-proof #362.
% 202.23/33.79  | | | | | 
% 202.23/33.79  | | | | End of split
% 202.23/33.79  | | | | 
% 202.23/33.79  | | | End of split
% 202.23/33.79  | | | 
% 202.23/33.79  | | End of split
% 202.23/33.79  | | 
% 202.23/33.79  | End of split
% 202.23/33.79  | 
% 202.23/33.79  End of proof
% 202.23/33.79  
% 202.23/33.79  Sub-proof #362 shows that the following formulas are inconsistent:
% 202.23/33.79  ----------------------------------------------------------------
% 202.23/33.79    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.79    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.79    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.79    (4)  all_58_14 = all_52_23
% 202.23/33.79    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.79    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.79    (7)  all_58_1 = all_52_9
% 202.23/33.79    (8)   ~ (all_52_9 = all_52_13)
% 202.23/33.79    (9)   ~ (e3 = e0)
% 202.23/33.79    (10)  op(e2, e3) = all_52_3
% 202.23/33.79    (11)   ~ (all_52_3 = all_52_19)
% 202.23/33.79    (12)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.79    (13)   ~ (all_52_17 = all_52_25)
% 202.23/33.79    (14)   ~ (all_52_3 = all_6_2)
% 202.23/33.79    (15)  all_44_2 = all_6_2
% 202.23/33.79    (16)  all_58_0 = all_6_2
% 202.23/33.79    (17)  op(all_14_2, e0) = all_14_1
% 202.23/33.79    (18)  all_34_1 = all_14_1
% 202.23/33.79    (19)   ~ (all_52_17 = all_10_2)
% 202.23/33.79    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.79    (21)  op(e3, e0) = all_52_25
% 202.23/33.79    (22)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.79    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.79    (24)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.79    (25)   ~ (all_52_27 = all_52_29)
% 202.23/33.79    (26)  all_58_13 = all_52_15
% 202.23/33.79    (27)  op(e0, all_14_1) = e1
% 202.23/33.79    (28)  all_58_9 = all_52_25
% 202.23/33.79    (29)   ~ (all_52_29 = all_14_2)
% 202.23/33.79    (30)  op(e1, e3) = all_52_5
% 202.23/33.79    (31)  op(e2, e2) = all_4_2
% 202.23/33.79    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.79    (33)   ~ (all_52_3 = all_52_5)
% 202.23/33.79    (34)  all_58_11 = all_52_29
% 202.23/33.79    (35)  all_56_5 = all_4_2
% 202.23/33.79    (36)   ~ (all_52_25 = all_14_2)
% 202.23/33.79    (37)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.79    (38)   ~ (all_52_3 = all_52_27)
% 202.23/33.79    (39)  op(all_10_2, e1) = all_10_1
% 202.23/33.79    (40)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.79    (41)   ~ (all_52_7 = all_6_2)
% 202.23/33.79    (42)  op(e0, e0) = all_14_2
% 202.23/33.79    (43)  op(all_52_29, all_52_29) = e1
% 202.23/33.79    (44)  op(e0, e1) = all_52_23
% 202.23/33.79    (45)  all_56_15 = all_14_2
% 202.23/33.79    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.79    (47)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.79    (48)  all_56_11 = all_52_29
% 202.23/33.79    (49)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.23/33.79    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.79    (51)  all_56_9 = all_52_13
% 202.23/33.79    (52)  all_58_10 = all_52_27
% 202.23/33.79    (53)  all_56_8 = all_52_5
% 202.23/33.79    (54)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.79    (55)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.79    (56)   ~ (all_52_19 = all_52_23)
% 202.23/33.79    (57)   ~ (all_52_25 = all_52_29)
% 202.23/33.79    (58)   ~ (all_52_29 = all_10_2)
% 202.23/33.79    (59)  all_58_7 = all_52_13
% 202.23/33.79    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.79    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.79    (62)   ~ (all_52_5 = all_52_7)
% 202.23/33.79    (63)  all_58_12 = all_52_7
% 202.23/33.79    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.79    (65)   ~ (all_52_7 = all_14_2)
% 202.23/33.79    (66)   ~ (all_14_2 = e0)
% 202.23/33.79    (67)  all_58_2 = all_52_3
% 202.23/33.79    (68)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.79    (69)  all_56_2 = all_52_17
% 202.23/33.79    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.79    (71)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.79    (72)  all_56_7 = all_52_27
% 202.23/33.79    (73)   ~ (e2 = e0)
% 202.23/33.79    (74)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.79    (75)  op(all_52_25, all_52_25) = e3
% 202.23/33.79    (76)   ~ (all_52_5 = all_52_29)
% 202.23/33.79    (77)  all_56_6 = all_52_19
% 202.23/33.79    (78)   ~ (all_52_19 = all_52_27)
% 202.23/33.79    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.79    (80)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.79    (81)   ~ (all_52_13 = all_4_2)
% 202.23/33.79    (82)  op(e3, e1) = all_52_17
% 202.23/33.79    (83)  op(all_52_27, all_52_27) = e2
% 202.23/33.79    (84)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.79    (85)  op(e0, e3) = all_52_7
% 202.23/33.79    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.79    (87)   ~ (all_52_9 = all_52_25)
% 202.23/33.79    (88)  all_58_15 = all_14_2
% 202.23/33.79    (89)   ~ (all_52_19 = all_10_2)
% 202.23/33.79    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.79    (91)  all_58_8 = all_10_2
% 202.23/33.79    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.79    (93)  all_34_2 = all_14_2
% 202.23/33.79    (94)   ~ (all_52_5 = all_10_2)
% 202.23/33.79    (95)   ~ (all_52_23 = all_14_2)
% 202.23/33.79    (96)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.79    (97)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.79    (98)   ~ (all_52_25 = all_6_2)
% 202.23/33.79    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.79    (100)   ~ (all_52_9 = all_4_2)
% 202.23/33.79    (101)   ~ (all_52_5 = all_6_2)
% 202.23/33.79    (102)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.23/33.79    (103)   ~ (all_52_13 = all_52_15)
% 202.23/33.79    (104)  op(e3, all_6_1) = e2
% 202.23/33.79    (105)  all_56_0 = all_6_2
% 202.23/33.79    (106)  op(e3, e3) = all_6_2
% 202.23/33.79    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.79    (108)   ~ (all_52_27 = all_14_2)
% 202.23/33.79    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.79    (110)  all_56_14 = all_52_23
% 202.23/33.80    (111)  all_56_3 = all_52_25
% 202.23/33.80    (112)   ~ (all_52_3 = all_52_7)
% 202.23/33.80    (113)  all_58_5 = all_52_19
% 202.23/33.80    (114)   ~ (all_52_15 = all_4_2)
% 202.23/33.80    (115)   ~ (all_52_27 = all_4_2)
% 202.23/33.80    (116)  all_58_6 = all_52_5
% 202.23/33.80    (117)  op(e3, e2) = all_52_9
% 202.23/33.80    (118)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.80    (119)   ~ (all_52_17 = all_6_2)
% 202.23/33.80    (120)   ~ (e1 = e0)
% 202.23/33.80    (121)  op(all_14_2, all_14_2) = e0
% 202.23/33.80    (122)   ~ (e3 = e2)
% 202.23/33.80    (123)  all_44_1 = all_6_1
% 202.23/33.80    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.80    (125)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.80    (126)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.80    (127)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.80    (128)  op(e1, e1) = all_10_2
% 202.23/33.80    (129)   ~ (all_52_7 = all_52_23)
% 202.23/33.80    (130)   ~ (all_52_17 = all_52_19)
% 202.23/33.80    (131)  all_58_3 = all_4_2
% 202.23/33.80    (132)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.80    (133)   ~ (all_52_3 = all_4_2)
% 202.23/33.80    (134)   ~ (all_52_19 = all_4_2)
% 202.23/33.80    (135)   ~ (all_52_17 = all_52_23)
% 202.23/33.80    (136)  op(all_6_2, e3) = all_6_1
% 202.23/33.80    (137)   ~ (all_52_13 = all_52_29)
% 202.23/33.80    (138)  all_58_4 = all_52_17
% 202.23/33.80  
% 202.23/33.80  Begin of proof
% 202.23/33.80  | 
% 202.23/33.80  | BETA: splitting (92) gives:
% 202.23/33.80  | 
% 202.23/33.80  | Case 1:
% 202.23/33.80  | | 
% 202.23/33.80  | |   (139)  all_56_15 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | COMBINE_EQS: (45), (139) imply:
% 202.23/33.80  | |   (140)  all_14_2 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | COMBINE_EQS: (93), (140) imply:
% 202.23/33.80  | |   (141)  all_34_2 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | COMBINE_EQS: (88), (140) imply:
% 202.23/33.80  | |   (142)  all_58_15 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (65), (140) imply:
% 202.23/33.80  | |   (143)   ~ (all_52_7 = e3)
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (36), (140) imply:
% 202.23/33.80  | |   (144)   ~ (all_52_25 = e3)
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (121), (140) imply:
% 202.23/33.80  | |   (145)  op(e3, e3) = e0
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (17), (140) imply:
% 202.23/33.80  | |   (146)  op(e3, e0) = all_14_1
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (42), (140) imply:
% 202.23/33.80  | |   (147)  op(e0, e0) = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | BETA: splitting (49) gives:
% 202.23/33.80  | | 
% 202.23/33.80  | | Case 1:
% 202.23/33.80  | | | 
% 202.23/33.80  | | |   (148)   ~ (all_34_1 = e2)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (18), (148) imply:
% 202.23/33.80  | | |   (149)   ~ (all_14_1 = e2)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3,
% 202.23/33.80  | | |              simplifying with (21), (146) gives:
% 202.23/33.80  | | |   (150)  all_52_25 = all_14_1
% 202.23/33.80  | | | 
% 202.23/33.80  | | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying with
% 202.23/33.80  | | |              (106), (145) gives:
% 202.23/33.80  | | |   (151)  all_6_2 = e0
% 202.23/33.80  | | | 
% 202.23/33.80  | | | COMBINE_EQS: (111), (150) imply:
% 202.23/33.80  | | |   (152)  all_56_3 = all_14_1
% 202.23/33.80  | | | 
% 202.23/33.80  | | | COMBINE_EQS: (28), (150) imply:
% 202.23/33.80  | | |   (153)  all_58_9 = all_14_1
% 202.23/33.80  | | | 
% 202.23/33.80  | | | COMBINE_EQS: (16), (151) imply:
% 202.23/33.80  | | |   (154)  all_58_0 = e0
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (41), (151) imply:
% 202.23/33.80  | | |   (155)   ~ (all_52_7 = e0)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (87), (150) imply:
% 202.23/33.80  | | |   (156)   ~ (all_52_9 = all_14_1)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (119), (151) imply:
% 202.23/33.80  | | |   (157)   ~ (all_52_17 = e0)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (3), (150) imply:
% 202.23/33.80  | | |   (158)   ~ (all_52_27 = all_14_1)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | SIMP: (158) implies:
% 202.23/33.80  | | |   (159)   ~ (all_52_27 = all_14_1)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (98), (150), (151) imply:
% 202.23/33.80  | | |   (160)   ~ (all_14_1 = e0)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (144), (150) imply:
% 202.23/33.80  | | |   (161)   ~ (all_14_1 = e3)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (75), (150) imply:
% 202.23/33.80  | | |   (162)  op(all_14_1, all_14_1) = e3
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (40), (151) imply:
% 202.23/33.80  | | |   (163)  op(e0, e0) = all_52_0
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (136), (151) imply:
% 202.23/33.80  | | |   (164)  op(e0, e3) = all_6_1
% 202.23/33.80  | | | 
% 202.23/33.80  | | | BETA: splitting (99) gives:
% 202.23/33.80  | | | 
% 202.23/33.80  | | | Case 1:
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | |   (165)  all_56_3 = e3
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | | COMBINE_EQS: (152), (165) imply:
% 202.23/33.80  | | | |   (166)  all_14_1 = e3
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | | REDUCE: (161), (166) imply:
% 202.23/33.80  | | | |   (167)  $false
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | | CLOSE: (167) is inconsistent.
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | Case 2:
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | |   (168)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | | BETA: splitting (168) gives:
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | | Case 1:
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | |   (169)  all_56_3 = e2
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | | COMBINE_EQS: (152), (169) imply:
% 202.23/33.80  | | | | |   (170)  all_14_1 = e2
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | | REDUCE: (149), (170) imply:
% 202.23/33.80  | | | | |   (171)  $false
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | | CLOSE: (171) is inconsistent.
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | Case 2:
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | |   (172)   ~ (all_56_3 = e2)
% 202.23/33.80  | | | | |   (173)  all_56_3 = e1 | all_56_3 = e0
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | | BETA: splitting (173) gives:
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | | Case 1:
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | |   (174)  all_56_3 = e1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | COMBINE_EQS: (152), (174) imply:
% 202.23/33.80  | | | | | |   (175)  all_14_1 = e1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | COMBINE_EQS: (153), (175) imply:
% 202.23/33.80  | | | | | |   (176)  all_58_9 = e1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (156), (175) imply:
% 202.23/33.80  | | | | | |   (177)   ~ (all_52_9 = e1)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (159), (175) imply:
% 202.23/33.80  | | | | | |   (178)   ~ (all_52_27 = e1)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (149), (175) imply:
% 202.23/33.80  | | | | | |   (179)   ~ (e2 = e1)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | SIMP: (179) implies:
% 202.23/33.80  | | | | | |   (180)   ~ (e2 = e1)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (162), (175) imply:
% 202.23/33.80  | | | | | |   (181)  op(e1, e1) = e3
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (27), (175) imply:
% 202.23/33.80  | | | | | |   (182)  op(e0, e1) = e1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e0, e0,
% 202.23/33.80  | | | | | |              simplifying with (147), (163) gives:
% 202.23/33.80  | | | | | |   (183)  all_52_0 = e3
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | GROUND_INST: instantiating (6) with all_52_23, e1, e1, e0,
% 202.23/33.80  | | | | | |              simplifying with (44), (182) gives:
% 202.23/33.80  | | | | | |   (184)  all_52_23 = e1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | GROUND_INST: instantiating (6) with all_52_7, all_6_1, e3, e0,
% 202.23/33.80  | | | | | |              simplifying with (85), (164) gives:
% 202.23/33.80  | | | | | |   (185)  all_52_7 = all_6_1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | GROUND_INST: instantiating (6) with all_10_2, e3, e1, e1,
% 202.23/33.80  | | | | | |              simplifying with (128), (181) gives:
% 202.23/33.80  | | | | | |   (186)  all_10_2 = e3
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | COMBINE_EQS: (4), (184) imply:
% 202.23/33.80  | | | | | |   (187)  all_58_14 = e1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | COMBINE_EQS: (63), (185) imply:
% 202.23/33.80  | | | | | |   (188)  all_58_12 = all_6_1
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (94), (186) imply:
% 202.23/33.80  | | | | | |   (189)   ~ (all_52_5 = e3)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (155), (185) imply:
% 202.23/33.80  | | | | | |   (190)   ~ (all_6_1 = e0)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (135), (184) imply:
% 202.23/33.80  | | | | | |   (191)   ~ (all_52_17 = e1)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (19), (186) imply:
% 202.23/33.80  | | | | | |   (192)   ~ (all_52_17 = e3)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (56), (184) imply:
% 202.23/33.80  | | | | | |   (193)   ~ (all_52_19 = e1)
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | BETA: splitting (70) gives:
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | Case 1:
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | |   (194)  all_58_0 = e3
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | | REF_CLOSE: (9), (154), (194) are inconsistent by sub-proof #1015.
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | Case 2:
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | |   (195)   ~ (all_58_0 = e3)
% 202.23/33.80  | | | | | | |   (196)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | | REDUCE: (154), (195) imply:
% 202.23/33.80  | | | | | | |   (197)   ~ (e3 = e0)
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | | BETA: splitting (50) gives:
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | |   (198)  all_56_2 = e3
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | | COMBINE_EQS: (69), (198) imply:
% 202.23/33.80  | | | | | | | |   (199)  all_52_17 = e3
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | | REDUCE: (192), (199) imply:
% 202.23/33.80  | | | | | | | |   (200)  $false
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | | CLOSE: (200) is inconsistent.
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | |   (201)   ~ (all_56_2 = e3)
% 202.23/33.80  | | | | | | | |   (202)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | | BETA: splitting (109) gives:
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | |   (203)  all_58_0 = e3
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | REF_CLOSE: (9), (154), (203) are inconsistent by sub-proof
% 202.23/33.80  | | | | | | | | |            #1015.
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | |   (204)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | BETA: splitting (80) gives:
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | |   (205)  all_58_12 = e0
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | COMBINE_EQS: (188), (205) imply:
% 202.23/33.80  | | | | | | | | | |   (206)  all_6_1 = e0
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | SIMP: (206) implies:
% 202.23/33.80  | | | | | | | | | |   (207)  all_6_1 = e0
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | REDUCE: (190), (207) imply:
% 202.23/33.80  | | | | | | | | | |   (208)  $false
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | CLOSE: (208) is inconsistent.
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | |   (209)  all_58_13 = e0 | all_58_14 = e0
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | BETA: splitting (209) gives:
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | |   (210)  all_58_13 = e0
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | COMBINE_EQS: (26), (210) imply:
% 202.23/33.80  | | | | | | | | | | |   (211)  all_52_15 = e0
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | SIMP: (211) implies:
% 202.23/33.80  | | | | | | | | | | |   (212)  all_52_15 = e0
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | REDUCE: (103), (212) imply:
% 202.23/33.80  | | | | | | | | | | |   (213)   ~ (all_52_13 = e0)
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | REDUCE: (55), (212) imply:
% 202.23/33.80  | | | | | | | | | | |   (214)  op(e0, e0) = all_52_14
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | BETA: splitting (37) gives:
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | |   (215)  all_58_12 = e2
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | COMBINE_EQS: (188), (215) imply:
% 202.23/33.80  | | | | | | | | | | | |   (216)  all_6_1 = e2
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | SIMP: (216) implies:
% 202.23/33.80  | | | | | | | | | | | |   (217)  all_6_1 = e2
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | REDUCE: (104), (217) imply:
% 202.23/33.80  | | | | | | | | | | | |   (218)  op(e3, e2) = e2
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | BETA: splitting (196) gives:
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | |   (219)  all_58_2 = e3
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | COMBINE_EQS: (67), (219) imply:
% 202.23/33.80  | | | | | | | | | | | | |   (220)  all_52_3 = e3
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | REDUCE: (11), (220) imply:
% 202.23/33.80  | | | | | | | | | | | | |   (221)   ~ (all_52_19 = e3)
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | SIMP: (221) implies:
% 202.23/33.80  | | | | | | | | | | | | |   (222)   ~ (all_52_19 = e3)
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | BETA: splitting (86) gives:
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | |   (223)  all_58_1 = e3
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | COMBINE_EQS: (7), (223) imply:
% 202.23/33.80  | | | | | | | | | | | | | |   (224)  all_52_9 = e3
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | REDUCE: (8), (224) imply:
% 202.23/33.80  | | | | | | | | | | | | | |   (225)   ~ (all_52_13 = e3)
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | SIMP: (225) implies:
% 202.23/33.80  | | | | | | | | | | | | | |   (226)   ~ (all_52_13 = e3)
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | REDUCE: (177), (224) imply:
% 202.23/33.80  | | | | | | | | | | | | | |   (227)   ~ (e3 = e1)
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | REDUCE: (117), (224) imply:
% 202.23/33.80  | | | | | | | | | | | | | |   (228)  op(e3, e2) = e3
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | |   (229)  all_58_2 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | COMBINE_EQS: (219), (229) imply:
% 202.23/33.80  | | | | | | | | | | | | | | |   (230)  e3 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | REDUCE: (227), (230) imply:
% 202.23/33.80  | | | | | | | | | | | | | | |   (231)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | |   (232)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | |   (233)  all_58_3 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (233) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | |   (234)  all_4_2 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | REDUCE: (81), (234) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | |   (235)   ~ (all_52_13 = e1)
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | |   (236)  all_56_2 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (236) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | |   (237)  all_52_17 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | REDUCE: (130), (237) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | |   (238)   ~ (all_52_19 = e2)
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | SIMP: (238) implies:
% 202.23/33.80  | | | | | | | | | | | | | | | | |   (239)   ~ (all_52_19 = e2)
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | |   (240)  all_56_6 = e3
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (240) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | |   (241)  all_52_19 = e3
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | REDUCE: (222), (241) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | |   (242)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | |   (243)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | |   (244)  all_56_9 = e3
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (244) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | |   (245)  all_52_13 = e3
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | REDUCE: (226), (245) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | |   (246)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | |   (247)   ~ (all_56_9 = e3)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | |   (248)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |   (249)  all_56_9 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (249) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |   (250)  all_52_13 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (250) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |   (251)   ~ (all_52_29 = e2)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | SIMP: (251) implies:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |   (252)   ~ (all_52_29 = e2)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | REDUCE: (226), (250) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |   (253)   ~ (e3 = e2)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | |   (254)  all_58_9 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (180), (254) are inconsistent by sub-proof
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | |            #1214.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | |   (255)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | |   (256)  all_56_6 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (256) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | |   (257)  all_52_19 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (239), (257) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | |   (258)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | |   (259)  all_56_6 = e1 | all_56_6 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_56_6 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (260) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_52_19 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (261) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (262)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_56_6 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (263) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_52_19 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (264) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (265)   ~ (all_52_27 = e0)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (265) implies:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (266)   ~ (all_52_27 = e0)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (264) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (267)   ~ (e1 = e0)
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (264) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | |   (268)  op(e0, e0) = all_52_18
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_58_10 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (269) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_52_27 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_58_9 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (176), (271) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  e1 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (272) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_58_10 = e0 | all_58_11 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_10 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (275) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  e2 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (276) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_11 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (278) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_52_29 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (279) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  op(e0, e0) = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_18, e0, e0,
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (147), (268) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_52_18 = e3
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_18, all_52_14, e0,
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (214), (268) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_52_14 = all_52_18
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e1, all_52_14, e0, e0,
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (214), (280) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_52_14 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, e3, e2, e3, simplifying
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              with (218), (228) gives:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  e3 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (283) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_52_18 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (285) implies:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_52_18 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (286) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  e3 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (287) implies:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  e3 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (288) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  e2 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (289) imply:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  $false
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_58_11 = e2 | all_58_15 = e2
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (122), (142), (252), (291) are inconsistent
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #633.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |   (292)  all_56_9 = e1 | all_56_9 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (213), (235), (292) are inconsistent by
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | |            sub-proof #1185.
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | |   (293)  all_56_2 = e1 | all_56_2 = e0
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (157), (191), (293) are inconsistent by
% 202.23/33.80  | | | | | | | | | | | | | | | | |            sub-proof #1307.
% 202.23/33.80  | | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | |   (294)  all_58_5 = e1 | all_58_10 = e1
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | | REF_CLOSE: (52), (113), (178), (193), (294) are inconsistent
% 202.23/33.80  | | | | | | | | | | | | | | | |            by sub-proof #869.
% 202.23/33.80  | | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | |   (295)   ~ (all_58_1 = e3)
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | REDUCE: (7), (295) imply:
% 202.23/33.80  | | | | | | | | | | | | | |   (296)   ~ (all_52_9 = e3)
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | | REF_CLOSE: (7), (28), (138), (144), (192), (204), (296) are
% 202.23/33.80  | | | | | | | | | | | | | |            inconsistent by sub-proof #744.
% 202.23/33.80  | | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | |   (297)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | REF_CLOSE: (63), (116), (143), (189), (297) are inconsistent
% 202.23/33.80  | | | | | | | | | | | | |            by sub-proof #1243.
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | |   (298)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | BETA: splitting (298) gives:
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | Case 1:
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | |   (299)  all_58_13 = e2
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | COMBINE_EQS: (210), (299) imply:
% 202.23/33.80  | | | | | | | | | | | | |   (300)  e2 = e0
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | REDUCE: (73), (300) imply:
% 202.23/33.80  | | | | | | | | | | | | |   (301)  $false
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | |   (302)  all_58_14 = e2 | all_58_15 = e2
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | | REF_CLOSE: (122), (142), (180), (187), (302) are inconsistent
% 202.23/33.80  | | | | | | | | | | | | |            by sub-proof #468.
% 202.23/33.80  | | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | Case 2:
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | |   (303)  all_58_14 = e0
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | | REF_CLOSE: (120), (187), (303) are inconsistent by sub-proof
% 202.23/33.80  | | | | | | | | | | |            #761.
% 202.23/33.80  | | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | | 
% 202.23/33.80  | | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | | 
% 202.23/33.80  | | | | | | | | End of split
% 202.23/33.80  | | | | | | | | 
% 202.23/33.80  | | | | | | | End of split
% 202.23/33.80  | | | | | | | 
% 202.23/33.80  | | | | | | End of split
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | Case 2:
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | |   (304)  all_56_3 = e0
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | COMBINE_EQS: (152), (304) imply:
% 202.23/33.80  | | | | | |   (305)  all_14_1 = e0
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | REDUCE: (160), (305) imply:
% 202.23/33.80  | | | | | |   (306)  $false
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | | CLOSE: (306) is inconsistent.
% 202.23/33.80  | | | | | | 
% 202.23/33.80  | | | | | End of split
% 202.23/33.80  | | | | | 
% 202.23/33.80  | | | | End of split
% 202.23/33.80  | | | | 
% 202.23/33.80  | | | End of split
% 202.23/33.80  | | | 
% 202.23/33.80  | | Case 2:
% 202.23/33.80  | | | 
% 202.23/33.80  | | |   (307)   ~ (all_34_2 = e3)
% 202.23/33.80  | | | 
% 202.23/33.80  | | | REDUCE: (141), (307) imply:
% 202.23/33.80  | | |   (308)  $false
% 202.23/33.80  | | | 
% 202.23/33.80  | | | CLOSE: (308) is inconsistent.
% 202.23/33.80  | | | 
% 202.23/33.80  | | End of split
% 202.23/33.80  | | 
% 202.23/33.80  | Case 2:
% 202.23/33.80  | | 
% 202.23/33.80  | |   (309)   ~ (all_56_15 = e3)
% 202.23/33.80  | |   (310)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (45), (309) imply:
% 202.23/33.80  | |   (311)   ~ (all_14_2 = e3)
% 202.23/33.80  | | 
% 202.23/33.80  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 202.23/33.80  | |            (14), (15), (16), (19), (20), (22), (23), (24), (25), (26), (28),
% 202.23/33.80  | |            (29), (30), (31), (32), (33), (34), (35), (36), (38), (39), (40),
% 202.23/33.80  | |            (41), (42), (43), (45), (46), (47), (48), (50), (52), (53), (54),
% 202.23/33.80  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 202.23/33.80  | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 202.23/33.80  | |            (79), (80), (82), (83), (84), (86), (87), (88), (89), (90), (91),
% 202.23/33.80  | |            (94), (95), (96), (97), (98), (99), (100), (101), (104), (105),
% 202.23/33.80  | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 202.23/33.80  | |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 202.23/33.80  | |            (124), (126), (127), (128), (129), (130), (131), (132), (133),
% 202.23/33.80  | |            (134), (135), (136), (137), (138), (310), (311) are inconsistent
% 202.23/33.80  | |            by sub-proof #435.
% 202.23/33.80  | | 
% 202.23/33.80  | End of split
% 202.23/33.80  | 
% 202.23/33.80  End of proof
% 202.23/33.80  
% 202.23/33.80  Sub-proof #363 shows that the following formulas are inconsistent:
% 202.23/33.80  ----------------------------------------------------------------
% 202.23/33.80    (1)  all_58_14 = all_52_23
% 202.23/33.80    (2)   ~ (e3 = e1)
% 202.23/33.80    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.80    (4)  all_58_1 = all_52_9
% 202.23/33.80    (5)  op(e2, e3) = all_52_3
% 202.23/33.80    (6)   ~ (all_52_3 = all_52_19)
% 202.23/33.80    (7)   ~ (all_52_3 = all_6_2)
% 202.23/33.80    (8)   ~ (all_14_1 = e2)
% 202.23/33.80    (9)  all_58_0 = all_6_2
% 202.23/33.80    (10)  all_56_4 = all_52_3
% 202.23/33.80    (11)  all_58_13 = all_52_15
% 202.23/33.80    (12)   ~ (all_52_15 = e3)
% 202.23/33.80    (13)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.80    (14)  op(all_10_2, e1) = all_10_1
% 202.23/33.80    (15)   ~ (e2 = e1)
% 202.23/33.80    (16)   ~ (all_52_13 = all_10_2)
% 202.23/33.80    (17)  op(all_10_2, all_10_2) = e1
% 202.23/33.80    (18)  all_58_7 = all_52_13
% 202.23/33.80    (19)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.80    (20)  op(all_52_19, all_52_19) = e2
% 202.23/33.80    (21)  all_58_12 = all_52_7
% 202.23/33.80    (22)   ~ (all_52_7 = e3)
% 202.23/33.80    (23)  all_58_2 = all_52_3
% 202.23/33.80    (24)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.80    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.80    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.80    (27)  all_58_9 = all_14_1
% 202.23/33.80    (28)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.80    (29)   ~ (e2 = e0)
% 202.23/33.80    (30)   ~ (all_14_1 = all_6_2)
% 202.23/33.80    (31)   ~ (all_52_23 = e3)
% 202.23/33.80    (32)  all_56_6 = all_52_19
% 202.23/33.80    (33)  op(e3, e1) = all_52_17
% 202.23/33.80    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.80    (35)   ~ (all_10_1 = e2)
% 202.23/33.80    (36)  all_58_8 = all_10_2
% 202.23/33.80    (37)   ~ (all_52_5 = all_10_2)
% 202.23/33.80    (38)  op(e3, all_6_1) = e2
% 202.23/33.80    (39)  op(e3, e3) = all_6_2
% 202.23/33.80    (40)  op(e3, e0) = all_14_1
% 202.23/33.80    (41)  all_58_5 = all_52_19
% 202.23/33.80    (42)  op(all_52_17, all_52_17) = e3
% 202.23/33.80    (43)  all_58_6 = all_52_5
% 202.23/33.80    (44)   ~ (all_52_17 = all_6_2)
% 202.23/33.80    (45)   ~ (e3 = e2)
% 202.23/33.80    (46)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.80    (47)  all_58_3 = all_4_2
% 202.23/33.80    (48)   ~ (all_52_3 = all_4_2)
% 202.23/33.80    (49)  op(all_6_2, e3) = all_6_1
% 202.23/33.80    (50)  all_58_4 = all_52_17
% 202.23/33.80  
% 202.23/33.80  Begin of proof
% 202.23/33.80  | 
% 202.23/33.80  | BETA: splitting (24) gives:
% 202.23/33.80  | 
% 202.23/33.80  | Case 1:
% 202.23/33.80  | | 
% 202.23/33.80  | |   (51)  all_56_6 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | COMBINE_EQS: (32), (51) imply:
% 202.23/33.80  | |   (52)  all_52_19 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | SIMP: (52) implies:
% 202.23/33.80  | |   (53)  all_52_19 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (6), (53) imply:
% 202.23/33.80  | |   (54)   ~ (all_52_3 = e3)
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (20), (53) imply:
% 202.23/33.80  | |   (55)  op(e3, e3) = e2
% 202.23/33.80  | | 
% 202.23/33.80  | | GROUND_INST: instantiating (3) with all_6_2, e2, e3, e3, simplifying with
% 202.23/33.80  | |              (39), (55) gives:
% 202.23/33.80  | |   (56)  all_6_2 = e2
% 202.23/33.80  | | 
% 202.23/33.80  | | REF_CLOSE: (3), (5), (7), (9), (10), (13), (19), (23), (28), (29), (30),
% 202.23/33.80  | |            (33), (38), (40), (44), (49), (54), (56) are inconsistent by
% 202.23/33.80  | |            sub-proof #449.
% 202.23/33.80  | | 
% 202.23/33.80  | Case 2:
% 202.23/33.80  | | 
% 202.23/33.80  | |   (57)   ~ (all_56_6 = e3)
% 202.23/33.80  | | 
% 202.23/33.80  | | REDUCE: (32), (57) imply:
% 202.23/33.80  | |   (58)   ~ (all_52_19 = e3)
% 202.23/33.80  | | 
% 202.23/33.80  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (11), (12), (14), (15), (16), (17),
% 202.23/33.80  | |            (18), (21), (22), (23), (25), (26), (27), (31), (33), (34), (35),
% 202.23/33.80  | |            (36), (37), (39), (41), (42), (43), (44), (45), (46), (47), (48),
% 202.23/33.80  | |            (50), (58) are inconsistent by sub-proof #364.
% 202.23/33.80  | | 
% 202.23/33.80  | End of split
% 202.23/33.80  | 
% 202.23/33.80  End of proof
% 202.23/33.80  
% 202.23/33.80  Sub-proof #364 shows that the following formulas are inconsistent:
% 202.23/33.80  ----------------------------------------------------------------
% 202.23/33.80    (1)  all_58_14 = all_52_23
% 202.23/33.80    (2)   ~ (e3 = e1)
% 202.23/33.80    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.80    (4)  all_58_1 = all_52_9
% 202.23/33.80    (5)   ~ (all_14_1 = e2)
% 202.23/33.80    (6)  all_58_0 = all_6_2
% 202.23/33.80    (7)  all_58_13 = all_52_15
% 202.23/33.80    (8)   ~ (all_52_15 = e3)
% 202.23/33.80    (9)  op(all_10_2, e1) = all_10_1
% 202.23/33.80    (10)   ~ (e2 = e1)
% 202.23/33.80    (11)   ~ (all_52_13 = all_10_2)
% 202.23/33.80    (12)  op(all_10_2, all_10_2) = e1
% 202.23/33.80    (13)  all_58_7 = all_52_13
% 202.23/33.80    (14)  all_58_12 = all_52_7
% 202.23/33.80    (15)   ~ (all_52_7 = e3)
% 202.23/33.80    (16)  all_58_2 = all_52_3
% 202.23/33.80    (17)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.80    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.80    (19)  all_58_9 = all_14_1
% 202.23/33.80    (20)   ~ (all_52_23 = e3)
% 202.23/33.80    (21)   ~ (all_52_19 = e3)
% 202.23/33.80    (22)  op(e3, e1) = all_52_17
% 202.23/33.80    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.80    (24)   ~ (all_10_1 = e2)
% 202.23/33.80    (25)  all_58_8 = all_10_2
% 202.23/33.80    (26)   ~ (all_52_5 = all_10_2)
% 202.23/33.80    (27)  op(e3, e3) = all_6_2
% 202.23/33.80    (28)  all_58_5 = all_52_19
% 202.23/33.80    (29)  op(all_52_17, all_52_17) = e3
% 202.23/33.80    (30)  all_58_6 = all_52_5
% 202.23/33.80    (31)   ~ (all_52_17 = all_6_2)
% 202.23/33.80    (32)   ~ (e3 = e2)
% 202.23/33.80    (33)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.80    (34)  all_58_3 = all_4_2
% 202.23/33.80    (35)   ~ (all_52_3 = all_4_2)
% 202.23/33.80    (36)  all_58_4 = all_52_17
% 202.23/33.80  
% 202.23/33.80  Begin of proof
% 202.23/33.80  | 
% 202.23/33.80  | BETA: splitting (33) gives:
% 202.23/33.80  | 
% 202.23/33.80  | Case 1:
% 202.23/33.80  | | 
% 202.23/33.80  | |   (37)  all_58_4 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | COMBINE_EQS: (36), (37) imply:
% 202.23/33.80  | |   (38)  all_52_17 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | SIMP: (38) implies:
% 202.23/33.80  | |   (39)  all_52_17 = e3
% 202.23/33.80  | | 
% 202.23/33.80  | | REF_CLOSE: (3), (27), (29), (31), (39) are inconsistent by sub-proof #1280.
% 202.23/33.80  | | 
% 202.23/33.80  | Case 2:
% 202.23/33.80  | | 
% 202.23/33.81  | |   (40)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.81  | | 
% 202.23/33.81  | | BETA: splitting (40) gives:
% 202.23/33.81  | | 
% 202.23/33.81  | | Case 1:
% 202.23/33.81  | | | 
% 202.23/33.81  | | |   (41)  all_58_5 = e3
% 202.23/33.81  | | | 
% 202.23/33.81  | | | REF_CLOSE: (21), (28), (41) are inconsistent by sub-proof #1279.
% 202.23/33.81  | | | 
% 202.23/33.81  | | Case 2:
% 202.23/33.81  | | | 
% 202.23/33.81  | | |   (42)  all_58_8 = e3 | all_58_14 = e3
% 202.23/33.81  | | | 
% 202.23/33.81  | | | BETA: splitting (42) gives:
% 202.23/33.81  | | | 
% 202.23/33.81  | | | Case 1:
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | |   (43)  all_58_8 = e3
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | COMBINE_EQS: (25), (43) imply:
% 202.23/33.81  | | | |   (44)  all_10_2 = e3
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | REDUCE: (26), (44) imply:
% 202.23/33.81  | | | |   (45)   ~ (all_52_5 = e3)
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | REDUCE: (11), (44) imply:
% 202.23/33.81  | | | |   (46)   ~ (all_52_13 = e3)
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | REDUCE: (12), (44) imply:
% 202.23/33.81  | | | |   (47)  op(e3, e3) = e1
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | REDUCE: (9), (44) imply:
% 202.23/33.81  | | | |   (48)  op(e3, e1) = all_10_1
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 202.23/33.81  | | | |              simplifying with (22), (48) gives:
% 202.23/33.81  | | | |   (49)  all_52_17 = all_10_1
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | GROUND_INST: instantiating (3) with all_6_2, e1, e3, e3, simplifying
% 202.23/33.81  | | | |              with (27), (47) gives:
% 202.23/33.81  | | | |   (50)  all_6_2 = e1
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | COMBINE_EQS: (36), (49) imply:
% 202.23/33.81  | | | |   (51)  all_58_4 = all_10_1
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | COMBINE_EQS: (6), (50) imply:
% 202.23/33.81  | | | |   (52)  all_58_0 = e1
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | BETA: splitting (18) gives:
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | Case 1:
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | |   (53)  all_58_0 = e3
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REF_CLOSE: (2), (52), (53) are inconsistent by sub-proof #1244.
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | Case 2:
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | |   (54)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | BETA: splitting (17) gives:
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | Case 1:
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | |   (55)  all_58_0 = e2
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | REF_CLOSE: (10), (52), (55) are inconsistent by sub-proof #1273.
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | Case 2:
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | |   (56)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | BETA: splitting (54) gives:
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | Case 1:
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | |   (57)  all_58_2 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | COMBINE_EQS: (16), (57) imply:
% 202.23/33.81  | | | | | | |   (58)  all_52_3 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | SIMP: (58) implies:
% 202.23/33.81  | | | | | | |   (59)  all_52_3 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | REDUCE: (35), (59) imply:
% 202.23/33.81  | | | | | | |   (60)   ~ (all_4_2 = e3)
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | SIMP: (60) implies:
% 202.23/33.81  | | | | | | |   (61)   ~ (all_4_2 = e3)
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | BETA: splitting (56) gives:
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | |   (62)  all_58_1 = e2
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | COMBINE_EQS: (4), (62) imply:
% 202.23/33.81  | | | | | | | |   (63)  all_52_9 = e2
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | BETA: splitting (23) gives:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | |   (64)  all_58_1 = e3
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REF_CLOSE: (32), (62), (64) are inconsistent by sub-proof
% 202.23/33.81  | | | | | | | | |            #1090.
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | |   (65)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REF_CLOSE: (7), (8), (13), (34), (46), (61), (65) are
% 202.23/33.81  | | | | | | | | |            inconsistent by sub-proof #1256.
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | |   (66)  all_58_4 = e2 | all_58_9 = e2
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | BETA: splitting (66) gives:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | |   (67)  all_58_4 = e2
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | COMBINE_EQS: (51), (67) imply:
% 202.23/33.81  | | | | | | | | |   (68)  all_10_1 = e2
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REDUCE: (24), (68) imply:
% 202.23/33.81  | | | | | | | | |   (69)  $false
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | CLOSE: (69) is inconsistent.
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | |   (70)  all_58_9 = e2
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | COMBINE_EQS: (19), (70) imply:
% 202.23/33.81  | | | | | | | | |   (71)  all_14_1 = e2
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REDUCE: (5), (71) imply:
% 202.23/33.81  | | | | | | | | |   (72)  $false
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | CLOSE: (72) is inconsistent.
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | End of split
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | Case 2:
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | |   (73)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | REF_CLOSE: (14), (15), (30), (45), (73) are inconsistent by
% 202.23/33.81  | | | | | | |            sub-proof #1243.
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | End of split
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | End of split
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | End of split
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | Case 2:
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | |   (74)  all_58_14 = e3
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | REF_CLOSE: (1), (20), (74) are inconsistent by sub-proof #1305.
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | End of split
% 202.23/33.81  | | | 
% 202.23/33.81  | | End of split
% 202.23/33.81  | | 
% 202.23/33.81  | End of split
% 202.23/33.81  | 
% 202.23/33.81  End of proof
% 202.23/33.81  
% 202.23/33.81  Sub-proof #365 shows that the following formulas are inconsistent:
% 202.23/33.81  ----------------------------------------------------------------
% 202.23/33.81    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.81    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.81    (3)   ~ (all_52_15 = all_52_23)
% 202.23/33.81    (4)   ~ (all_52_25 = all_52_27)
% 202.23/33.81    (5)  all_58_14 = all_52_23
% 202.23/33.81    (6)   ~ (e3 = e1)
% 202.23/33.81    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.81    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.81    (9)   ~ (all_52_5 = all_52_13)
% 202.23/33.81    (10)  all_58_1 = all_52_9
% 202.23/33.81    (11)   ~ (all_52_9 = all_52_13)
% 202.23/33.81    (12)   ~ (e3 = e0)
% 202.23/33.81    (13)  op(e2, e3) = all_52_3
% 202.23/33.81    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.81    (15)   ~ (all_52_7 = all_52_15)
% 202.23/33.81    (16)   ~ (all_52_3 = all_52_19)
% 202.23/33.81    (17)  op(all_52_15, all_52_15) = e0
% 202.23/33.81    (18)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.81    (19)   ~ (all_52_17 = all_52_25)
% 202.23/33.81    (20)   ~ (all_52_3 = all_6_2)
% 202.23/33.81    (21)  all_44_2 = all_6_2
% 202.23/33.81    (22)  all_58_0 = all_6_2
% 202.23/33.81    (23)  op(all_14_2, e0) = all_14_1
% 202.23/33.81    (24)  all_56_4 = all_52_3
% 202.23/33.81    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.81    (26)  op(e3, e0) = all_52_25
% 202.23/33.81    (27)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.81    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.81    (29)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.81    (30)  all_58_13 = all_52_15
% 202.23/33.81    (31)  op(all_52_13, all_52_13) = e1
% 202.23/33.81    (32)  op(e0, all_14_1) = e1
% 202.23/33.81    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.23/33.81    (34)  all_58_9 = all_52_25
% 202.23/33.81    (35)   ~ (all_52_29 = all_14_2)
% 202.23/33.81    (36)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.81    (37)  op(e1, e3) = all_52_5
% 202.23/33.81    (38)  op(e2, e2) = all_4_2
% 202.23/33.81    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.81    (40)   ~ (all_52_3 = all_52_5)
% 202.23/33.81    (41)  all_58_11 = all_52_29
% 202.23/33.81    (42)   ~ (all_52_25 = all_14_2)
% 202.23/33.81    (43)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.81    (44)   ~ (all_52_3 = all_52_27)
% 202.23/33.81    (45)   ~ (all_52_7 = all_6_2)
% 202.23/33.81    (46)  op(e0, e0) = all_14_2
% 202.23/33.81    (47)  op(e0, e1) = all_52_23
% 202.23/33.81    (48)  all_56_15 = all_14_2
% 202.23/33.81    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.81    (50)   ~ (all_4_1 = e1)
% 202.23/33.81    (51)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 202.23/33.81    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.81    (53)  all_56_9 = all_52_13
% 202.23/33.81    (54)   ~ (e2 = e1)
% 202.23/33.81    (55)   ~ (all_52_13 = all_10_2)
% 202.23/33.81    (56)  all_58_10 = all_52_27
% 202.23/33.81    (57)  all_56_8 = all_52_5
% 202.23/33.81    (58)   ~ (all_52_19 = all_52_23)
% 202.23/33.81    (59)   ~ (all_52_25 = all_52_29)
% 202.23/33.81    (60)   ~ (all_52_29 = all_10_2)
% 202.23/33.81    (61)  all_58_7 = all_52_13
% 202.23/33.81    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.81    (63)   ~ (all_52_5 = all_52_7)
% 202.23/33.81    (64)  all_58_12 = all_52_7
% 202.23/33.81    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.81    (66)   ~ (all_52_7 = all_14_2)
% 202.23/33.81    (67)  all_58_2 = all_52_3
% 202.23/33.81    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.81    (69)  all_56_7 = all_52_27
% 202.23/33.81    (70)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.81    (71)   ~ (e2 = e0)
% 202.23/33.81    (72)  op(all_4_2, e2) = all_4_1
% 202.23/33.81    (73)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.81    (74)   ~ (all_52_15 = all_14_2)
% 202.23/33.81    (75)   ~ (all_52_13 = all_4_2)
% 202.23/33.81    (76)  op(e3, e1) = all_52_17
% 202.23/33.81    (77)  op(e0, e3) = all_52_7
% 202.23/33.81    (78)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.81    (79)   ~ (all_52_9 = all_52_25)
% 202.23/33.81    (80)  all_58_15 = all_14_2
% 202.23/33.81    (81)   ~ (all_52_19 = all_10_2)
% 202.23/33.81    (82)  op(all_52_23, all_52_23) = all_52_22
% 202.23/33.81    (83)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.81    (84)  all_58_8 = all_10_2
% 202.23/33.81    (85)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.81    (86)  all_34_2 = all_14_2
% 202.23/33.81    (87)   ~ (all_52_5 = all_10_2)
% 202.23/33.81    (88)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.81    (89)   ~ (all_52_23 = all_14_2)
% 202.23/33.81    (90)  all_56_12 = all_52_7
% 202.23/33.81    (91)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.81    (92)  all_8_2 = all_6_2
% 202.23/33.81    (93)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.81    (94)   ~ (all_52_25 = all_6_2)
% 202.23/33.81    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.81    (96)   ~ (all_52_9 = all_4_2)
% 202.23/33.81    (97)   ~ (all_52_5 = all_6_2)
% 202.23/33.81    (98)  op(all_4_2, all_4_2) = e2
% 202.23/33.81    (99)   ~ (all_52_9 = all_6_2)
% 202.23/33.81    (100)   ~ (all_52_13 = all_52_15)
% 202.23/33.81    (101)  op(e3, all_6_1) = e2
% 202.23/33.81    (102)  all_56_0 = all_6_2
% 202.23/33.81    (103)  op(e3, e3) = all_6_2
% 202.23/33.81    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.81    (105)   ~ (all_52_27 = all_14_2)
% 202.23/33.81    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.81    (107)  all_56_3 = all_52_25
% 202.23/33.81    (108)   ~ (all_52_3 = all_52_7)
% 202.23/33.81    (109)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.81    (110)  all_58_5 = all_52_19
% 202.23/33.81    (111)  all_56_1 = all_52_9
% 202.23/33.81    (112)   ~ (all_52_15 = all_4_2)
% 202.23/33.81    (113)   ~ (all_52_27 = all_4_2)
% 202.23/33.81    (114)  all_58_6 = all_52_5
% 202.23/33.81    (115)  op(e3, e2) = all_52_9
% 202.23/33.81    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.81    (117)   ~ (all_52_17 = all_6_2)
% 202.23/33.81    (118)   ~ (e1 = e0)
% 202.23/33.81    (119)   ~ (e3 = e2)
% 202.23/33.81    (120)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.81    (121)  all_44_1 = all_6_1
% 202.23/33.81    (122)   ~ (all_52_9 = all_52_17)
% 202.23/33.81    (123)  all_56_10 = all_10_2
% 202.23/33.81    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.81    (125)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.81    (126)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.81    (127)  op(e1, e1) = all_10_2
% 202.23/33.81    (128)  op(all_52_9, all_52_9) = e3
% 202.23/33.81    (129)   ~ (all_52_23 = all_10_2)
% 202.23/33.81    (130)   ~ (all_52_7 = all_52_23)
% 202.23/33.81    (131)   ~ (all_52_17 = all_52_19)
% 202.23/33.81    (132)  all_58_3 = all_4_2
% 202.23/33.81    (133)  all_56_13 = all_52_15
% 202.23/33.81    (134)   ~ (all_52_3 = all_4_2)
% 202.23/33.81    (135)   ~ (all_52_19 = all_4_2)
% 202.23/33.81    (136)   ~ (all_52_17 = all_52_23)
% 202.23/33.81    (137)  all_8_1 = all_6_1
% 202.23/33.81    (138)  op(all_6_2, e3) = all_6_1
% 202.23/33.81    (139)   ~ (all_52_13 = all_52_29)
% 202.23/33.81    (140)  all_58_4 = all_52_17
% 202.23/33.81    (141)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.81    (142)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.81  
% 202.23/33.81  Begin of proof
% 202.23/33.81  | 
% 202.23/33.81  | BETA: splitting (85) gives:
% 202.23/33.81  | 
% 202.23/33.81  | Case 1:
% 202.23/33.81  | | 
% 202.23/33.81  | |   (143)  all_56_15 = e3
% 202.23/33.81  | | 
% 202.23/33.81  | | COMBINE_EQS: (48), (143) imply:
% 202.23/33.81  | |   (144)  all_14_2 = e3
% 202.23/33.81  | | 
% 202.23/33.81  | | COMBINE_EQS: (86), (144) imply:
% 202.23/33.81  | |   (145)  all_34_2 = e3
% 202.23/33.81  | | 
% 202.23/33.81  | | COMBINE_EQS: (80), (144) imply:
% 202.23/33.81  | |   (146)  all_58_15 = e3
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (66), (144) imply:
% 202.23/33.81  | |   (147)   ~ (all_52_7 = e3)
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (74), (144) imply:
% 202.23/33.81  | |   (148)   ~ (all_52_15 = e3)
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (42), (144) imply:
% 202.23/33.81  | |   (149)   ~ (all_52_25 = e3)
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (105), (144) imply:
% 202.23/33.81  | |   (150)   ~ (all_52_27 = e3)
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (109), (144) imply:
% 202.23/33.81  | |   (151)  op(e3, e3) = all_52_30
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (23), (144) imply:
% 202.23/33.81  | |   (152)  op(e3, e0) = all_14_1
% 202.23/33.81  | | 
% 202.23/33.81  | | BETA: splitting (51) gives:
% 202.23/33.81  | | 
% 202.23/33.81  | | Case 1:
% 202.23/33.81  | | | 
% 202.23/33.81  | | | 
% 202.23/33.81  | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 202.23/33.81  | | |              simplifying with (26), (152) gives:
% 202.23/33.81  | | |   (153)  all_52_25 = all_14_1
% 202.23/33.81  | | | 
% 202.23/33.81  | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 202.23/33.81  | | |              simplifying with (103), (151) gives:
% 202.23/33.81  | | |   (154)  all_52_30 = all_6_2
% 202.23/33.81  | | | 
% 202.23/33.81  | | | COMBINE_EQS: (34), (153) imply:
% 202.23/33.81  | | |   (155)  all_58_9 = all_14_1
% 202.23/33.81  | | | 
% 202.23/33.81  | | | REDUCE: (79), (153) imply:
% 202.23/33.81  | | |   (156)   ~ (all_52_9 = all_14_1)
% 202.23/33.81  | | | 
% 202.23/33.81  | | | REDUCE: (94), (153) imply:
% 202.23/33.81  | | |   (157)   ~ (all_14_1 = all_6_2)
% 202.23/33.81  | | | 
% 202.23/33.81  | | | REDUCE: (142), (153) imply:
% 202.23/33.81  | | |   (158)  op(all_14_1, all_14_1) = all_52_24
% 202.23/33.81  | | | 
% 202.23/33.81  | | | BETA: splitting (14) gives:
% 202.23/33.81  | | | 
% 202.23/33.81  | | | Case 1:
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | |   (159)  all_56_12 = e3
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | REF_CLOSE: (90), (147), (159) are inconsistent by sub-proof #1383.
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | Case 2:
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | |   (160)   ~ (all_56_12 = e3)
% 202.23/33.81  | | | |   (161)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | BETA: splitting (124) gives:
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | | Case 1:
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | |   (162)  all_58_4 = e3
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | COMBINE_EQS: (140), (162) imply:
% 202.23/33.81  | | | | |   (163)  all_52_17 = e3
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | SIMP: (163) implies:
% 202.23/33.81  | | | | |   (164)  all_52_17 = e3
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REDUCE: (122), (164) imply:
% 202.23/33.81  | | | | |   (165)   ~ (all_52_9 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REDUCE: (131), (164) imply:
% 202.23/33.81  | | | | |   (166)   ~ (all_52_19 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | SIMP: (166) implies:
% 202.23/33.81  | | | | |   (167)   ~ (all_52_19 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REDUCE: (136), (164) imply:
% 202.23/33.81  | | | | |   (168)   ~ (all_52_23 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | SIMP: (168) implies:
% 202.23/33.81  | | | | |   (169)   ~ (all_52_23 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REDUCE: (117), (164) imply:
% 202.23/33.81  | | | | |   (170)   ~ (all_6_2 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | SIMP: (170) implies:
% 202.23/33.81  | | | | |   (171)   ~ (all_6_2 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REDUCE: (91), (164) imply:
% 202.23/33.81  | | | | |   (172)  op(e3, e3) = all_52_16
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_16, e3, e3,
% 202.23/33.81  | | | | |              simplifying with (103), (172) gives:
% 202.23/33.81  | | | | |   (173)  all_52_16 = all_6_2
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | BETA: splitting (49) gives:
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | Case 1:
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | |   (174)  all_58_2 = e3
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | REF_CLOSE: (7), (8), (9), (10), (21), (25), (27), (30), (31), (37),
% 202.23/33.81  | | | | | |            (38), (57), (61), (63), (67), (75), (78), (83), (90),
% 202.23/33.81  | | | | | |            (97), (101), (103), (115), (121), (128), (132), (134),
% 202.23/33.81  | | | | | |            (138), (148), (161), (165), (174) are inconsistent by
% 202.23/33.81  | | | | | |            sub-proof #366.
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | Case 2:
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | |   (175)   ~ (all_58_2 = e3)
% 202.23/33.81  | | | | | |   (176)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | REDUCE: (67), (175) imply:
% 202.23/33.81  | | | | | |   (177)   ~ (all_52_3 = e3)
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | BETA: splitting (68) gives:
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | | Case 1:
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | |   (178)  all_58_0 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | COMBINE_EQS: (22), (178) imply:
% 202.23/33.81  | | | | | | |   (179)  all_6_2 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | REDUCE: (171), (179) imply:
% 202.23/33.81  | | | | | | |   (180)  $false
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | CLOSE: (180) is inconsistent.
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | Case 2:
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | |   (181)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | BETA: splitting (181) gives:
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | |   (182)  all_58_2 = e3
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | REF_CLOSE: (67), (177), (182) are inconsistent by sub-proof
% 202.23/33.81  | | | | | | | |            #1369.
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | |   (183)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | BETA: splitting (176) gives:
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | |   (184)  all_58_3 = e3
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | COMBINE_EQS: (132), (184) imply:
% 202.23/33.81  | | | | | | | | |   (185)  all_4_2 = e3
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REDUCE: (98), (185) imply:
% 202.23/33.81  | | | | | | | | |   (186)  op(e3, e3) = e2
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REDUCE: (72), (185) imply:
% 202.23/33.81  | | | | | | | | |   (187)  op(e3, e2) = all_4_1
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | BETA: splitting (183) gives:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | |   (188)  all_58_6 = e3
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | COMBINE_EQS: (114), (188) imply:
% 202.23/33.81  | | | | | | | | | |   (189)  all_52_5 = e3
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | SIMP: (189) implies:
% 202.23/33.81  | | | | | | | | | |   (190)  all_52_5 = e3
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (9), (190) imply:
% 202.23/33.81  | | | | | | | | | |   (191)   ~ (all_52_13 = e3)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | SIMP: (191) implies:
% 202.23/33.81  | | | | | | | | | |   (192)   ~ (all_52_13 = e3)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (27), (190) imply:
% 202.23/33.81  | | | | | | | | | |   (193)  op(e3, e3) = all_52_4
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_9, all_4_1, e2, e3,
% 202.23/33.81  | | | | | | | | | |              simplifying with (115), (187) gives:
% 202.23/33.81  | | | | | | | | | |   (194)  all_52_9 = all_4_1
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_4, e3, e3,
% 202.23/33.81  | | | | | | | | | |              simplifying with (103), (193) gives:
% 202.23/33.81  | | | | | | | | | |   (195)  all_52_4 = all_6_2
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | GROUND_INST: instantiating (8) with e2, all_52_4, e3, e3,
% 202.23/33.81  | | | | | | | | | |              simplifying with (186), (193) gives:
% 202.23/33.81  | | | | | | | | | |   (196)  all_52_4 = e2
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | COMBINE_EQS: (195), (196) imply:
% 202.23/33.81  | | | | | | | | | |   (197)  all_6_2 = e2
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | SIMP: (197) implies:
% 202.23/33.81  | | | | | | | | | |   (198)  all_6_2 = e2
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | COMBINE_EQS: (111), (194) imply:
% 202.23/33.81  | | | | | | | | | |   (199)  all_56_1 = all_4_1
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | COMBINE_EQS: (10), (194) imply:
% 202.23/33.81  | | | | | | | | | |   (200)  all_58_1 = all_4_1
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | COMBINE_EQS: (22), (198) imply:
% 202.23/33.81  | | | | | | | | | |   (201)  all_58_0 = e2
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (45), (198) imply:
% 202.23/33.81  | | | | | | | | | |   (202)   ~ (all_52_7 = e2)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (11), (194) imply:
% 202.23/33.81  | | | | | | | | | |   (203)   ~ (all_52_13 = all_4_1)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | SIMP: (203) implies:
% 202.23/33.81  | | | | | | | | | |   (204)   ~ (all_52_13 = all_4_1)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (156), (194) imply:
% 202.23/33.81  | | | | | | | | | |   (205)   ~ (all_14_1 = all_4_1)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | SIMP: (205) implies:
% 202.23/33.81  | | | | | | | | | |   (206)   ~ (all_14_1 = all_4_1)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (99), (194), (198) imply:
% 202.23/33.81  | | | | | | | | | |   (207)   ~ (all_4_1 = e2)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (165), (194) imply:
% 202.23/33.81  | | | | | | | | | |   (208)   ~ (all_4_1 = e3)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (157), (198) imply:
% 202.23/33.81  | | | | | | | | | |   (209)   ~ (all_14_1 = e2)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REDUCE: (171), (198) imply:
% 202.23/33.81  | | | | | | | | | |   (210)   ~ (e3 = e2)
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | BETA: splitting (120) gives:
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | |   (211)  all_56_1 = e3
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | COMBINE_EQS: (199), (211) imply:
% 202.23/33.81  | | | | | | | | | | |   (212)  all_4_1 = e3
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | REDUCE: (208), (212) imply:
% 202.23/33.81  | | | | | | | | | | |   (213)  $false
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | |   (214)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | BETA: splitting (214) gives:
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | |   (215)  all_56_1 = e2
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | COMBINE_EQS: (199), (215) imply:
% 202.23/33.81  | | | | | | | | | | | |   (216)  all_4_1 = e2
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | REDUCE: (207), (216) imply:
% 202.23/33.81  | | | | | | | | | | | |   (217)  $false
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | CLOSE: (217) is inconsistent.
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | |   (218)  all_56_1 = e1 | all_56_1 = e0
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | BETA: splitting (73) gives:
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | |   (219)  all_58_0 = e1
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | COMBINE_EQS: (201), (219) imply:
% 202.23/33.81  | | | | | | | | | | | | |   (220)  e2 = e1
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | REDUCE: (54), (220) imply:
% 202.23/33.81  | | | | | | | | | | | | |   (221)  $false
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | |   (222)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | BETA: splitting (222) gives:
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | |   (223)  all_58_1 = e1
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | COMBINE_EQS: (200), (223) imply:
% 202.23/33.81  | | | | | | | | | | | | | |   (224)  all_4_1 = e1
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | REDUCE: (50), (224) imply:
% 202.23/33.81  | | | | | | | | | | | | | |   (225)  $false
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | |   (226)  all_58_4 = e1 | all_58_9 = e1
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | |   (227)  all_58_4 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | COMBINE_EQS: (162), (227) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (228)  e3 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | REDUCE: (6), (228) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (229)  $false
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | |   (230)  all_58_9 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | COMBINE_EQS: (155), (230) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (231)  all_14_1 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | REDUCE: (206), (231) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (232)   ~ (all_4_1 = e1)
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | REDUCE: (209), (231) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (233)   ~ (e2 = e1)
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | REDUCE: (158), (231) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (234)  op(e1, e1) = all_52_24
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | REDUCE: (32), (231) imply:
% 202.23/33.81  | | | | | | | | | | | | | | |   (235)  op(e0, e1) = e1
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | |   (236)  all_56_1 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (236) imply:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (237)  all_4_1 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | REDUCE: (50), (237) imply:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (238)  $false
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | |   (239)  all_56_1 = e0
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (239) imply:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (240)  all_4_1 = e0
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | REDUCE: (204), (240) imply:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (241)   ~ (all_52_13 = e0)
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_23, e1, e1, e0,
% 202.23/33.81  | | | | | | | | | | | | | | | |              simplifying with (47), (235) gives:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (242)  all_52_23 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, all_52_24, e1,
% 202.23/33.81  | | | | | | | | | | | | | | | |              e1, simplifying with (127), (234) gives:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (243)  all_52_24 = all_10_2
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (242) imply:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (244)  all_58_14 = e1
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | REDUCE: (169), (242) imply:
% 202.23/33.81  | | | | | | | | | | | | | | | |   (245)   ~ (e3 = e1)
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.81  | | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | |   (246)  all_58_12 = e2
% 202.23/33.81  | | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (202), (246) are inconsistent by sub-proof
% 202.23/33.81  | | | | | | | | | | | | | | | | |            #506.
% 202.23/33.81  | | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | |   (247)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.81  | | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (30), (31), (53), (54), (55), (61),
% 202.23/33.81  | | | | | | | | | | | | | | | | |            (93), (100), (119), (125), (127), (146), (188),
% 202.23/33.81  | | | | | | | | | | | | | | | | |            (192), (241), (244), (247) are inconsistent by
% 202.23/33.81  | | | | | | | | | | | | | | | | |            sub-proof #467.
% 202.23/33.81  | | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | |   (248)  all_58_12 = e3
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | | REF_CLOSE: (64), (147), (248) are inconsistent by sub-proof
% 202.23/33.81  | | | | | | | | | |            #1367.
% 202.23/33.81  | | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | Case 2:
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | |   (249)  all_58_5 = e3 | all_58_10 = e3
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | | REF_CLOSE: (56), (110), (150), (167), (249) are inconsistent
% 202.23/33.81  | | | | | | | | |            by sub-proof #1132.
% 202.23/33.81  | | | | | | | | | 
% 202.23/33.81  | | | | | | | | End of split
% 202.23/33.81  | | | | | | | | 
% 202.23/33.81  | | | | | | | End of split
% 202.23/33.81  | | | | | | | 
% 202.23/33.81  | | | | | | End of split
% 202.23/33.81  | | | | | | 
% 202.23/33.81  | | | | | End of split
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | Case 2:
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | |   (250)   ~ (all_58_4 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REDUCE: (140), (250) imply:
% 202.23/33.81  | | | | |   (251)   ~ (all_52_17 = e3)
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | | REF_CLOSE: (8), (10), (22), (34), (99), (101), (103), (106), (119),
% 202.23/33.81  | | | | |            (128), (138), (140), (149), (251) are inconsistent by
% 202.23/33.81  | | | | |            sub-proof #492.
% 202.23/33.81  | | | | | 
% 202.23/33.81  | | | | End of split
% 202.23/33.81  | | | | 
% 202.23/33.81  | | | End of split
% 202.23/33.81  | | | 
% 202.23/33.81  | | Case 2:
% 202.23/33.81  | | | 
% 202.23/33.81  | | |   (252)   ~ (all_34_2 = e3)
% 202.23/33.81  | | | 
% 202.23/33.81  | | | REDUCE: (145), (252) imply:
% 202.23/33.81  | | |   (253)  $false
% 202.23/33.81  | | | 
% 202.23/33.81  | | | CLOSE: (253) is inconsistent.
% 202.23/33.81  | | | 
% 202.23/33.81  | | End of split
% 202.23/33.81  | | 
% 202.23/33.81  | Case 2:
% 202.23/33.81  | | 
% 202.23/33.81  | |   (254)   ~ (all_56_15 = e3)
% 202.23/33.81  | |   (255)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.81  | | 
% 202.23/33.81  | | REDUCE: (48), (254) imply:
% 202.23/33.81  | |   (256)   ~ (all_14_2 = e3)
% 202.23/33.81  | | 
% 202.23/33.81  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 202.23/33.81  | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 202.23/33.81  | |            (27), (28), (29), (30), (31), (33), (34), (35), (36), (37), (38),
% 202.23/33.81  | |            (39), (40), (41), (42), (44), (45), (46), (48), (49), (50), (52),
% 202.23/33.81  | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 202.23/33.81  | |            (66), (67), (68), (69), (70), (71), (72), (75), (76), (77), (78),
% 202.23/33.81  | |            (79), (80), (81), (82), (83), (84), (87), (88), (89), (90), (91),
% 202.23/33.81  | |            (92), (95), (96), (97), (98), (99), (101), (102), (103), (104),
% 202.23/33.81  | |            (106), (107), (108), (110), (111), (112), (113), (114), (115),
% 202.23/33.81  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 202.23/33.81  | |            (126), (128), (129), (130), (132), (133), (134), (135), (136),
% 202.23/33.81  | |            (137), (138), (139), (140), (141), (142), (255), (256) are
% 202.23/33.81  | |            inconsistent by sub-proof #452.
% 202.23/33.81  | | 
% 202.23/33.81  | End of split
% 202.23/33.81  | 
% 202.23/33.81  End of proof
% 202.23/33.81  
% 202.23/33.81  Sub-proof #366 shows that the following formulas are inconsistent:
% 202.23/33.81  ----------------------------------------------------------------
% 202.23/33.81    (1)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.81    (3)   ~ (all_52_5 = all_52_13)
% 202.23/33.81    (4)  all_58_1 = all_52_9
% 202.23/33.81    (5)  all_44_2 = all_6_2
% 202.23/33.81    (6)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.81    (7)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.81    (8)  all_58_13 = all_52_15
% 202.23/33.81    (9)  op(all_52_13, all_52_13) = e1
% 202.23/33.81    (10)   ~ (all_52_15 = e3)
% 202.23/33.81    (11)  op(e1, e3) = all_52_5
% 202.23/33.81    (12)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.81    (13)  op(e2, e2) = all_4_2
% 202.23/33.81    (14)  all_56_8 = all_52_5
% 202.23/33.81    (15)  all_58_7 = all_52_13
% 202.23/33.81    (16)   ~ (all_52_5 = all_52_7)
% 202.23/33.81    (17)  all_58_2 = all_52_3
% 202.23/33.81    (18)   ~ (all_52_9 = e3)
% 202.23/33.81    (19)   ~ (all_52_13 = all_4_2)
% 202.23/33.81    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.82    (21)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.82    (22)  all_56_12 = all_52_7
% 202.23/33.82    (23)   ~ (all_52_5 = all_6_2)
% 202.23/33.82    (24)  op(e3, all_6_1) = e2
% 202.23/33.82    (25)  op(e3, e3) = all_6_2
% 202.23/33.82    (26)  op(e3, e2) = all_52_9
% 202.23/33.82    (27)  all_44_1 = all_6_1
% 202.23/33.82    (28)  op(all_52_9, all_52_9) = e3
% 202.23/33.82    (29)  all_58_3 = all_4_2
% 202.23/33.82    (30)   ~ (all_52_3 = all_4_2)
% 202.23/33.82    (31)  op(all_6_2, e3) = all_6_1
% 202.23/33.82    (32)  all_58_2 = e3
% 202.23/33.82  
% 202.23/33.82  Begin of proof
% 202.23/33.82  | 
% 202.23/33.82  | COMBINE_EQS: (17), (32) imply:
% 202.23/33.82  |   (33)  all_52_3 = e3
% 202.23/33.82  | 
% 202.23/33.82  | SIMP: (33) implies:
% 202.23/33.82  |   (34)  all_52_3 = e3
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (30), (34) imply:
% 202.23/33.82  |   (35)   ~ (all_4_2 = e3)
% 202.23/33.82  | 
% 202.23/33.82  | SIMP: (35) implies:
% 202.23/33.82  |   (36)   ~ (all_4_2 = e3)
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (1), (34) imply:
% 202.23/33.82  |   (37)  op(e3, e3) = all_52_2
% 202.23/33.82  | 
% 202.23/33.82  | BETA: splitting (20) gives:
% 202.23/33.82  | 
% 202.23/33.82  | Case 1:
% 202.23/33.82  | | 
% 202.23/33.82  | |   (38)  all_58_1 = e3
% 202.23/33.82  | | 
% 202.23/33.82  | | COMBINE_EQS: (4), (38) imply:
% 202.23/33.82  | |   (39)  all_52_9 = e3
% 202.23/33.82  | | 
% 202.23/33.82  | | REDUCE: (18), (39) imply:
% 202.23/33.82  | |   (40)  $false
% 202.23/33.82  | | 
% 202.23/33.82  | | CLOSE: (40) is inconsistent.
% 202.23/33.82  | | 
% 202.23/33.82  | Case 2:
% 202.23/33.82  | | 
% 202.23/33.82  | |   (41)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.82  | | 
% 202.23/33.82  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 202.23/33.82  | |            (15), (16), (19), (21), (22), (23), (24), (25), (26), (27), (28),
% 202.23/33.82  | |            (29), (31), (36), (37), (41) are inconsistent by sub-proof #462.
% 202.23/33.82  | | 
% 202.23/33.82  | End of split
% 202.23/33.82  | 
% 202.23/33.82  End of proof
% 202.23/33.82  
% 202.23/33.82  Sub-proof #367 shows that the following formulas are inconsistent:
% 202.23/33.82  ----------------------------------------------------------------
% 202.23/33.82    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.82    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.82    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.82    (4)  all_58_14 = all_52_23
% 202.23/33.82    (5)   ~ (e3 = e1)
% 202.23/33.82    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.23/33.82    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.82    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.82    (9)   ~ (all_52_5 = all_52_13)
% 202.23/33.82    (10)  all_58_1 = all_52_9
% 202.23/33.82    (11)   ~ (all_52_9 = all_52_13)
% 202.23/33.82    (12)   ~ (e3 = e0)
% 202.23/33.82    (13)  op(e2, e3) = all_52_3
% 202.23/33.82    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.82    (15)   ~ (all_52_7 = all_52_15)
% 202.23/33.82    (16)   ~ (all_52_3 = all_52_19)
% 202.23/33.82    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.82    (18)   ~ (all_52_17 = all_52_25)
% 202.23/33.82    (19)   ~ (all_52_3 = all_6_2)
% 202.23/33.82    (20)  all_44_2 = all_6_2
% 202.23/33.82    (21)  all_58_0 = all_6_2
% 202.23/33.82    (22)  op(all_14_2, e0) = all_14_1
% 202.23/33.82    (23)  all_56_4 = all_52_3
% 202.23/33.82    (24)   ~ (all_52_17 = all_10_2)
% 202.23/33.82    (25)   ~ (all_10_0 = e3)
% 202.23/33.82    (26)  op(e3, e0) = all_52_25
% 202.23/33.82    (27)  op(e0, all_14_1) = all_14_0
% 202.23/33.82    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.82    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.82    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.82    (31)   ~ (all_52_27 = all_52_29)
% 202.23/33.82    (32)  all_58_13 = all_52_15
% 202.23/33.82    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.23/33.82    (34)  all_58_9 = all_52_25
% 202.23/33.82    (35)   ~ (all_52_29 = all_14_2)
% 202.23/33.82    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.23/33.82    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.82    (38)  op(e1, e3) = all_52_5
% 202.23/33.82    (39)  op(e2, e2) = all_4_2
% 202.23/33.82    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.82    (41)   ~ (all_52_3 = all_52_5)
% 202.23/33.82    (42)  all_58_11 = all_52_29
% 202.23/33.82    (43)  all_56_5 = all_4_2
% 202.23/33.82    (44)   ~ (all_52_25 = all_14_2)
% 202.23/33.82    (45)   ~ (all_52_9 = all_52_15)
% 202.23/33.82    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.82    (47)   ~ (all_52_3 = all_52_27)
% 202.23/33.82    (48)  op(all_10_2, e1) = all_10_1
% 202.23/33.82    (49)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.82    (50)   ~ (all_52_7 = all_6_2)
% 202.23/33.82    (51)  op(e0, e0) = all_14_2
% 202.23/33.82    (52)  all_56_15 = all_14_2
% 202.23/33.82    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.82    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.82    (55)  all_56_11 = all_52_29
% 202.23/33.82    (56)   ~ (all_10_0 = e2)
% 202.23/33.82    (57)   ~ (all_4_1 = e1)
% 202.23/33.82    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.82    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.82    (60)   ~ (e2 = e1)
% 202.23/33.82    (61)   ~ (all_52_13 = all_10_2)
% 202.23/33.82    (62)  op(e1, all_10_1) = all_10_0
% 202.23/33.82    (63)  all_58_10 = all_52_27
% 202.23/33.82    (64)  all_56_8 = all_52_5
% 202.23/33.82    (65)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.82    (66)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.82    (67)   ~ (all_52_19 = all_52_23)
% 202.23/33.82    (68)   ~ (all_52_25 = all_52_29)
% 202.23/33.82    (69)   ~ (all_52_29 = all_10_2)
% 202.23/33.82    (70)  all_58_7 = all_52_13
% 202.23/33.82    (71)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 202.23/33.82    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.82    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.82    (74)   ~ (all_52_5 = all_52_7)
% 202.23/33.82    (75)  all_58_12 = all_52_7
% 202.23/33.82    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.82    (77)   ~ (all_52_7 = all_14_2)
% 202.23/33.82    (78)  all_30_2 = all_10_2
% 202.23/33.82    (79)  all_58_2 = all_52_3
% 202.23/33.82    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.82    (81)  all_56_2 = all_52_17
% 202.23/33.82    (82)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.82    (83)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.82    (84)   ~ (all_14_0 = e3)
% 202.23/33.82    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.82    (86)  all_56_7 = all_52_27
% 202.23/33.82    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.82    (88)   ~ (e2 = e0)
% 202.23/33.82    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.82    (90)  op(all_4_2, e2) = all_4_1
% 202.23/33.82    (91)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.82    (92)   ~ (all_52_5 = all_52_29)
% 202.23/33.82    (93)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.82    (94)  all_56_6 = all_52_19
% 202.23/33.82    (95)   ~ (all_52_15 = all_14_2)
% 202.23/33.82    (96)   ~ (all_52_19 = all_52_27)
% 202.23/33.82    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.82    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.82    (99)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 202.23/33.82            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 202.23/33.82    (100)   ~ (all_52_13 = all_4_2)
% 202.23/33.82    (101)  op(e3, e1) = all_52_17
% 202.23/33.82    (102)  all_30_0 = all_10_0
% 202.23/33.82    (103)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.82    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.82    (105)  op(e0, e3) = all_52_7
% 202.23/33.82    (106)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.82    (107)   ~ (all_52_9 = all_52_25)
% 202.23/33.82    (108)  all_58_15 = all_14_2
% 202.23/33.82    (109)   ~ (all_52_19 = all_10_2)
% 202.23/33.82    (110)  op(all_52_23, all_52_23) = all_52_22
% 202.23/33.82    (111)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.82    (112)  all_58_8 = all_10_2
% 202.23/33.82    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.82    (114)   ~ (all_52_5 = all_10_2)
% 202.23/33.82    (115)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.82    (116)   ~ (all_52_23 = all_14_2)
% 202.23/33.82    (117)  all_56_12 = all_52_7
% 202.23/33.82    (118)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.82    (119)  all_8_2 = all_6_2
% 202.23/33.82    (120)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.82    (121)   ~ (all_52_25 = all_6_2)
% 202.23/33.82    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.82    (123)   ~ (all_52_9 = all_4_2)
% 202.23/33.82    (124)   ~ (all_52_5 = all_6_2)
% 202.23/33.82    (125)   ~ (all_52_9 = all_6_2)
% 202.23/33.82    (126)   ~ (all_52_13 = all_52_15)
% 202.23/33.82    (127)  op(e3, all_6_1) = e2
% 202.23/33.82    (128)  all_56_0 = all_6_2
% 202.23/33.82    (129)  op(e3, e3) = all_6_2
% 202.23/33.82    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.82    (131)   ~ (all_52_27 = all_14_2)
% 202.23/33.82    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.82    (133)  all_56_14 = all_52_23
% 202.23/33.82    (134)  op(all_4_2, all_4_2) = all_52_10
% 202.23/33.82    (135)  all_56_3 = all_52_25
% 202.23/33.82    (136)   ~ (all_52_3 = all_52_7)
% 202.23/33.82    (137)  all_10_1 = e3
% 202.23/33.82    (138)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.82    (139)  all_58_5 = all_52_19
% 202.23/33.82    (140)  all_56_1 = all_52_9
% 202.23/33.82    (141)   ~ (all_52_15 = all_4_2)
% 202.23/33.82    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.82           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.23/33.82           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.23/33.82           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.23/33.82    (143)   ~ (all_52_27 = all_4_2)
% 202.23/33.82    (144)  all_58_6 = all_52_5
% 202.23/33.82    (145)  op(e3, e2) = all_52_9
% 202.23/33.82    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.82    (147)   ~ (all_52_17 = all_6_2)
% 202.23/33.82    (148)   ~ (e1 = e0)
% 202.23/33.82    (149)   ~ (e3 = e2)
% 202.23/33.82    (150)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.82    (151)  all_44_1 = all_6_1
% 202.23/33.82    (152)   ~ (all_52_9 = all_52_17)
% 202.23/33.82    (153)  all_56_10 = all_10_2
% 202.23/33.82    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.82    (155)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.82    (156)  all_44_0 = e2
% 202.23/33.82    (157)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.82    (158)  op(e1, e1) = all_10_2
% 202.23/33.82    (159)   ~ (all_52_23 = all_10_2)
% 202.23/33.82    (160)   ~ (all_52_7 = all_52_23)
% 202.23/33.82    (161)   ~ (all_52_17 = all_52_19)
% 202.23/33.82    (162)  all_58_3 = all_4_2
% 202.23/33.82    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.82    (164)  all_56_13 = all_52_15
% 202.23/33.82    (165)   ~ (all_52_3 = all_4_2)
% 202.23/33.82    (166)   ~ (all_52_19 = all_4_2)
% 202.23/33.82    (167)   ~ (all_52_17 = all_52_23)
% 202.23/33.82    (168)  all_8_1 = all_6_1
% 202.23/33.82    (169)  op(all_6_2, e3) = all_6_1
% 202.23/33.82    (170)   ~ (all_52_13 = all_52_29)
% 202.23/33.82    (171)  all_58_4 = all_52_17
% 202.23/33.82    (172)   ~ (all_14_0 = e1)
% 202.23/33.82    (173)   ~ (all_14_0 = e2)
% 202.23/33.82    (174)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.82    (175)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.82  
% 202.23/33.82  Begin of proof
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (48), (137) imply:
% 202.23/33.82  |   (176)  op(all_10_2, e1) = e3
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (62), (137) imply:
% 202.23/33.82  |   (177)  op(e1, e3) = all_10_0
% 202.23/33.82  | 
% 202.23/33.82  | GROUND_INST: instantiating (8) with all_52_5, all_10_0, e3, e1, simplifying
% 202.23/33.82  |              with (38), (177) gives:
% 202.23/33.82  |   (178)  all_52_5 = all_10_0
% 202.23/33.82  | 
% 202.23/33.82  | COMBINE_EQS: (64), (178) imply:
% 202.23/33.82  |   (179)  all_56_8 = all_10_0
% 202.23/33.82  | 
% 202.23/33.82  | COMBINE_EQS: (144), (178) imply:
% 202.23/33.82  |   (180)  all_58_6 = all_10_0
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (41), (178) imply:
% 202.23/33.82  |   (181)   ~ (all_52_3 = all_10_0)
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (74), (178) imply:
% 202.23/33.82  |   (182)   ~ (all_52_7 = all_10_0)
% 202.23/33.82  | 
% 202.23/33.82  | SIMP: (182) implies:
% 202.23/33.82  |   (183)   ~ (all_52_7 = all_10_0)
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (114), (178) imply:
% 202.23/33.82  |   (184)   ~ (all_10_0 = all_10_2)
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (124), (178) imply:
% 202.23/33.82  |   (185)   ~ (all_10_0 = all_6_2)
% 202.23/33.82  | 
% 202.23/33.82  | REDUCE: (28), (178) imply:
% 202.23/33.82  |   (186)  op(all_10_0, all_10_0) = all_52_4
% 202.23/33.82  | 
% 202.23/33.82  | BETA: splitting (103) gives:
% 202.23/33.82  | 
% 202.23/33.82  | Case 1:
% 202.23/33.82  | | 
% 202.23/33.82  | |   (187)   ~ (all_44_0 = e2)
% 202.23/33.82  | | 
% 202.23/33.82  | | REDUCE: (156), (187) imply:
% 202.23/33.82  | |   (188)  $false
% 202.23/33.82  | | 
% 202.23/33.82  | | CLOSE: (188) is inconsistent.
% 202.23/33.82  | | 
% 202.23/33.82  | Case 2:
% 202.23/33.82  | | 
% 202.23/33.82  | |   (189)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.82  | | 
% 202.23/33.82  | | BETA: splitting (99) gives:
% 202.23/33.82  | | 
% 202.23/33.82  | | Case 1:
% 202.23/33.82  | | | 
% 202.23/33.82  | | |   (190)  all_58_15 = e0
% 202.23/33.82  | | | 
% 202.23/33.82  | | | COMBINE_EQS: (108), (190) imply:
% 202.23/33.82  | | |   (191)  all_14_2 = e0
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (77), (191) imply:
% 202.23/33.82  | | |   (192)   ~ (all_52_7 = e0)
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (95), (191) imply:
% 202.23/33.82  | | |   (193)   ~ (all_52_15 = e0)
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (116), (191) imply:
% 202.23/33.82  | | |   (194)   ~ (all_52_23 = e0)
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (44), (191) imply:
% 202.23/33.82  | | |   (195)   ~ (all_52_25 = e0)
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (138), (191) imply:
% 202.23/33.82  | | |   (196)  op(e0, e0) = all_52_30
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (22), (191) imply:
% 202.23/33.82  | | |   (197)  op(e0, e0) = all_14_1
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (51), (191) imply:
% 202.23/33.82  | | |   (198)  op(e0, e0) = e0
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (13), (14), (15),
% 202.23/33.82  | | |            (17), (18), (19), (20), (21), (23), (24), (25), (26), (27),
% 202.23/33.82  | | |            (30), (32), (34), (35), (37), (38), (39), (40), (41), (42),
% 202.23/33.82  | | |            (45), (46), (49), (50), (51), (53), (54), (56), (58), (59),
% 202.23/33.82  | | |            (60), (63), (64), (65), (66), (67), (68), (70), (71), (72),
% 202.23/33.82  | | |            (73), (74), (75), (76), (78), (79), (80), (81), (82), (83),
% 202.23/33.82  | | |            (84), (85), (87), (92), (93), (94), (98), (101), (102), (105),
% 202.23/33.82  | | |            (107), (108), (110), (111), (112), (115), (117), (118), (119),
% 202.23/33.82  | | |            (121), (122), (124), (125), (126), (127), (128), (129), (130),
% 202.23/33.82  | | |            (131), (132), (133), (134), (135), (136), (138), (139), (140),
% 202.23/33.82  | | |            (141), (142), (144), (145), (146), (147), (149), (150), (151),
% 202.23/33.82  | | |            (152), (153), (154), (155), (158), (159), (160), (161), (162),
% 202.23/33.82  | | |            (164), (165), (166), (167), (168), (169), (171), (172), (173),
% 202.23/33.82  | | |            (174), (175), (176), (177), (179), (180), (181), (183), (184),
% 202.23/33.82  | | |            (185), (186), (189), (190), (192), (193), (194), (195), (196),
% 202.23/33.82  | | |            (197), (198) are inconsistent by sub-proof #374.
% 202.23/33.82  | | | 
% 202.23/33.82  | | Case 2:
% 202.23/33.82  | | | 
% 202.23/33.82  | | |   (199)   ~ (all_58_15 = e0)
% 202.23/33.82  | | |   (200)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 202.23/33.82  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 202.23/33.82  | | | 
% 202.23/33.82  | | | ALPHA: (200) implies:
% 202.23/33.82  | | |   (201)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.82  | | |   (202)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REDUCE: (108), (199) imply:
% 202.23/33.82  | | |   (203)   ~ (all_14_2 = e0)
% 202.23/33.82  | | | 
% 202.23/33.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 202.23/33.82  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.23/33.82  | | |            (24), (25), (26), (28), (29), (30), (31), (32), (33), (34),
% 202.23/33.82  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 202.23/33.82  | | |            (45), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 202.23/33.82  | | |            (56), (57), (58), (59), (60), (61), (63), (64), (65), (66),
% 202.23/33.82  | | |            (67), (68), (69), (70), (72), (73), (74), (75), (76), (77),
% 202.23/33.82  | | |            (79), (80), (81), (82), (83), (85), (86), (87), (88), (89),
% 202.23/33.82  | | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (100),
% 202.23/33.82  | | |            (101), (104), (105), (106), (107), (108), (109), (110), (111),
% 202.23/33.82  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 202.23/33.82  | | |            (121), (122), (123), (124), (125), (127), (128), (129), (130),
% 202.23/33.82  | | |            (131), (132), (133), (134), (135), (136), (138), (139), (140),
% 202.23/33.82  | | |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 202.23/33.82  | | |            (150), (151), (152), (153), (154), (155), (157), (158), (159),
% 202.23/33.82  | | |            (160), (161), (162), (163), (164), (165), (166), (167), (168),
% 202.23/33.82  | | |            (169), (170), (171), (174), (175), (176), (177), (179), (180),
% 202.23/33.82  | | |            (183), (185), (186), (189), (201), (202), (203) are
% 202.23/33.82  | | |            inconsistent by sub-proof #368.
% 202.23/33.82  | | | 
% 202.23/33.82  | | End of split
% 202.23/33.82  | | 
% 202.23/33.82  | End of split
% 202.23/33.82  | 
% 202.23/33.82  End of proof
% 202.23/33.82  
% 202.23/33.82  Sub-proof #368 shows that the following formulas are inconsistent:
% 202.23/33.82  ----------------------------------------------------------------
% 202.23/33.82    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.82    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.82    (3)   ~ (all_52_15 = all_52_23)
% 202.23/33.82    (4)   ~ (all_52_25 = all_52_27)
% 202.23/33.82    (5)  all_58_14 = all_52_23
% 202.23/33.82    (6)   ~ (e3 = e1)
% 202.23/33.82    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.82    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.82    (9)   ~ (all_52_7 = all_10_0)
% 202.23/33.82    (10)   ~ (all_52_5 = all_52_13)
% 202.23/33.82    (11)  all_58_1 = all_52_9
% 202.23/33.82    (12)   ~ (all_52_9 = all_52_13)
% 202.23/33.82    (13)   ~ (e3 = e0)
% 202.23/33.82    (14)  op(e2, e3) = all_52_3
% 202.23/33.82    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.82    (16)   ~ (all_52_7 = all_52_15)
% 202.23/33.82    (17)   ~ (all_52_3 = all_52_19)
% 202.23/33.82    (18)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.82    (19)   ~ (all_52_17 = all_52_25)
% 202.23/33.82    (20)   ~ (all_52_3 = all_6_2)
% 202.23/33.82    (21)  all_44_2 = all_6_2
% 202.23/33.82    (22)  all_58_0 = all_6_2
% 202.23/33.82    (23)  op(all_14_2, e0) = all_14_1
% 202.23/33.82    (24)  all_56_4 = all_52_3
% 202.23/33.82    (25)   ~ (all_52_17 = all_10_2)
% 202.23/33.82    (26)   ~ (all_10_0 = e3)
% 202.23/33.82    (27)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.82    (28)  op(e3, e0) = all_52_25
% 202.23/33.82    (29)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.82    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.82    (31)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.82    (32)   ~ (all_52_27 = all_52_29)
% 202.23/33.82    (33)  all_58_13 = all_52_15
% 202.23/33.82    (34)  op(all_10_2, all_10_2) = all_52_20
% 202.23/33.82    (35)  all_58_9 = all_52_25
% 202.23/33.82    (36)   ~ (all_52_29 = all_14_2)
% 202.23/33.82    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.23/33.82    (38)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.82    (39)  op(e1, e3) = all_52_5
% 202.23/33.82    (40)  op(e2, e2) = all_4_2
% 202.23/33.82    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.82    (42)   ~ (all_52_3 = all_52_5)
% 202.23/33.82    (43)  all_58_11 = all_52_29
% 202.23/33.82    (44)  all_56_5 = all_4_2
% 202.23/33.82    (45)   ~ (all_52_25 = all_14_2)
% 202.23/33.82    (46)   ~ (all_52_9 = all_52_15)
% 202.23/33.82    (47)   ~ (all_52_3 = all_52_27)
% 202.23/33.82    (48)  op(all_10_2, e1) = all_10_1
% 202.23/33.82    (49)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.82    (50)   ~ (all_52_7 = all_6_2)
% 202.23/33.82    (51)  op(e0, e0) = all_14_2
% 202.23/33.82    (52)   ~ (all_10_0 = all_6_2)
% 202.23/33.82    (53)  all_56_15 = all_14_2
% 202.23/33.82    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.82    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.82    (56)  all_56_11 = all_52_29
% 202.23/33.82    (57)   ~ (all_10_0 = e2)
% 202.23/33.82    (58)   ~ (all_4_1 = e1)
% 202.23/33.82    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.82    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.82    (61)   ~ (e2 = e1)
% 202.23/33.82    (62)   ~ (all_52_13 = all_10_2)
% 202.23/33.82    (63)  all_58_10 = all_52_27
% 202.23/33.82    (64)  all_56_8 = all_52_5
% 202.23/33.82    (65)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.82    (66)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.82    (67)   ~ (all_52_19 = all_52_23)
% 202.23/33.82    (68)   ~ (all_52_25 = all_52_29)
% 202.23/33.82    (69)   ~ (all_52_29 = all_10_2)
% 202.23/33.82    (70)  op(all_10_2, e1) = e3
% 202.23/33.82    (71)  all_58_7 = all_52_13
% 202.23/33.82    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.82    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.82    (74)   ~ (all_52_5 = all_52_7)
% 202.23/33.82    (75)  all_58_12 = all_52_7
% 202.23/33.82    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.82    (77)   ~ (all_52_7 = all_14_2)
% 202.23/33.82    (78)   ~ (all_14_2 = e0)
% 202.23/33.82    (79)  all_58_2 = all_52_3
% 202.23/33.82    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.82    (81)  all_56_2 = all_52_17
% 202.23/33.82    (82)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.82    (83)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.82    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.82    (85)  all_56_7 = all_52_27
% 202.23/33.82    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.82    (87)   ~ (e2 = e0)
% 202.23/33.82    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.82    (89)  op(all_4_2, e2) = all_4_1
% 202.23/33.82    (90)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.82    (91)   ~ (all_52_5 = all_52_29)
% 202.23/33.82    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.82    (93)  all_56_6 = all_52_19
% 202.23/33.82    (94)  all_56_8 = all_10_0
% 202.23/33.82    (95)   ~ (all_52_15 = all_14_2)
% 202.23/33.82    (96)   ~ (all_52_19 = all_52_27)
% 202.23/33.82    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.82    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.82    (99)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.82    (100)   ~ (all_52_13 = all_4_2)
% 202.23/33.82    (101)  op(e3, e1) = all_52_17
% 202.23/33.82    (102)  all_58_6 = all_10_0
% 202.23/33.82    (103)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.82    (104)  op(e0, e3) = all_52_7
% 202.23/33.82    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.82    (106)   ~ (all_52_9 = all_52_25)
% 202.23/33.82    (107)  op(e1, e3) = all_10_0
% 202.23/33.82    (108)  all_58_15 = all_14_2
% 202.23/33.82    (109)   ~ (all_52_19 = all_10_2)
% 202.23/33.82    (110)  op(all_52_23, all_52_23) = all_52_22
% 202.23/33.82    (111)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.82    (112)  all_58_8 = all_10_2
% 202.23/33.82    (113)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.82    (114)   ~ (all_52_5 = all_10_2)
% 202.23/33.82    (115)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.82    (116)   ~ (all_52_23 = all_14_2)
% 202.23/33.82    (117)  all_56_12 = all_52_7
% 202.23/33.82    (118)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.82    (119)  all_8_2 = all_6_2
% 202.23/33.82    (120)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.82    (121)   ~ (all_52_25 = all_6_2)
% 202.23/33.82    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.82    (123)   ~ (all_52_9 = all_4_2)
% 202.23/33.82    (124)   ~ (all_52_5 = all_6_2)
% 202.23/33.82    (125)   ~ (all_52_9 = all_6_2)
% 202.23/33.82    (126)  op(e3, all_6_1) = e2
% 202.23/33.82    (127)  all_56_0 = all_6_2
% 202.23/33.82    (128)  op(e3, e3) = all_6_2
% 202.23/33.82    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.82    (130)   ~ (all_52_27 = all_14_2)
% 202.23/33.82    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.82    (132)  all_56_14 = all_52_23
% 202.23/33.82    (133)  op(all_4_2, all_4_2) = all_52_10
% 202.23/33.82    (134)  all_56_3 = all_52_25
% 202.23/33.82    (135)   ~ (all_52_3 = all_52_7)
% 202.23/33.83    (136)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.83    (137)  all_58_5 = all_52_19
% 202.23/33.83    (138)  op(all_10_0, all_10_0) = all_52_4
% 202.23/33.83    (139)  all_56_1 = all_52_9
% 202.23/33.83    (140)   ~ (all_52_15 = all_4_2)
% 202.23/33.83    (141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.83           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.23/33.83           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.23/33.83           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.23/33.83    (142)   ~ (all_52_27 = all_4_2)
% 202.23/33.83    (143)  all_58_6 = all_52_5
% 202.23/33.83    (144)  op(e3, e2) = all_52_9
% 202.23/33.83    (145)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.83    (146)   ~ (all_52_17 = all_6_2)
% 202.23/33.83    (147)   ~ (e1 = e0)
% 202.23/33.83    (148)   ~ (e3 = e2)
% 202.23/33.83    (149)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.83    (150)  all_44_1 = all_6_1
% 202.23/33.83    (151)   ~ (all_52_9 = all_52_17)
% 202.23/33.83    (152)  all_56_10 = all_10_2
% 202.23/33.83    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.83    (154)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.83    (155)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.83    (156)  op(e1, e1) = all_10_2
% 202.23/33.83    (157)   ~ (all_52_23 = all_10_2)
% 202.23/33.83    (158)   ~ (all_52_7 = all_52_23)
% 202.23/33.83    (159)   ~ (all_52_17 = all_52_19)
% 202.23/33.83    (160)  all_58_3 = all_4_2
% 202.23/33.83    (161)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.83    (162)  all_56_13 = all_52_15
% 202.23/33.83    (163)   ~ (all_52_3 = all_4_2)
% 202.23/33.83    (164)   ~ (all_52_19 = all_4_2)
% 202.23/33.83    (165)   ~ (all_52_17 = all_52_23)
% 202.23/33.83    (166)  all_8_1 = all_6_1
% 202.23/33.83    (167)  op(all_6_2, e3) = all_6_1
% 202.23/33.83    (168)   ~ (all_52_13 = all_52_29)
% 202.23/33.83    (169)  all_58_4 = all_52_17
% 202.23/33.83    (170)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.83    (171)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.83  
% 202.23/33.83  Begin of proof
% 202.23/33.83  | 
% 202.23/33.83  | BETA: splitting (111) gives:
% 202.23/33.83  | 
% 202.23/33.83  | Case 1:
% 202.23/33.83  | | 
% 202.23/33.83  | |   (172)  all_56_8 = e3
% 202.23/33.83  | | 
% 202.23/33.83  | | REF_CLOSE: (26), (94), (172) are inconsistent by sub-proof #926.
% 202.23/33.83  | | 
% 202.23/33.83  | Case 2:
% 202.23/33.83  | | 
% 202.23/33.83  | |   (173)   ~ (all_56_8 = e3)
% 202.23/33.83  | |   (174)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.83  | | 
% 202.23/33.83  | | BETA: splitting (141) gives:
% 202.23/33.83  | | 
% 202.23/33.83  | | Case 1:
% 202.23/33.83  | | | 
% 202.23/33.83  | | |   (175)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.83  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 202.23/33.83  | | |            e0)
% 202.23/33.83  | | | 
% 202.23/33.83  | | | BETA: splitting (175) gives:
% 202.23/33.83  | | | 
% 202.23/33.83  | | | Case 1:
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | |   (176)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REF_CLOSE: (7), (8), (14), (18), (22), (26), (40), (49), (54), (57),
% 202.23/33.83  | | | |            (75), (79), (82), (87), (98), (102), (126), (127), (128),
% 202.23/33.83  | | | |            (133), (148), (154), (163), (167), (176) are inconsistent by
% 202.23/33.83  | | | |            sub-proof #387.
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | Case 2:
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | |   (177)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 202.23/33.83  | | | |          e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | ALPHA: (177) implies:
% 202.23/33.83  | | | |   (178)  all_52_14 = e0
% 202.23/33.83  | | | |   (179)  all_52_12 = e1
% 202.23/33.83  | | | |   (180)  all_52_10 = e2
% 202.23/33.83  | | | |   (181)  all_52_8 = e3
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (65), (181) imply:
% 202.23/33.83  | | | |   (182)  op(all_52_9, all_52_9) = e3
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (155), (179) imply:
% 202.23/33.83  | | | |   (183)  op(all_52_13, all_52_13) = e1
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (66), (178) imply:
% 202.23/33.83  | | | |   (184)  op(all_52_15, all_52_15) = e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (133), (180) imply:
% 202.23/33.83  | | | |   (185)  op(all_4_2, all_4_2) = e2
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | BETA: splitting (113) gives:
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | Case 1:
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | |   (186)  all_56_15 = e3
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | COMBINE_EQS: (53), (186) imply:
% 202.23/33.83  | | | | |   (187)  all_14_2 = e3
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (95), (187) imply:
% 202.23/33.83  | | | | |   (188)   ~ (all_52_15 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (45), (187) imply:
% 202.23/33.83  | | | | |   (189)   ~ (all_52_25 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (136), (187) imply:
% 202.23/33.83  | | | | |   (190)  op(e3, e3) = all_52_30
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (23), (187) imply:
% 202.23/33.83  | | | | |   (191)  op(e3, e0) = all_14_1
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 202.23/33.83  | | | | |              simplifying with (28), (191) gives:
% 202.23/33.83  | | | | |   (192)  all_52_25 = all_14_1
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 202.23/33.83  | | | | |              simplifying with (128), (190) gives:
% 202.23/33.83  | | | | |   (193)  all_52_30 = all_6_2
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | COMBINE_EQS: (35), (192) imply:
% 202.23/33.83  | | | | |   (194)  all_58_9 = all_14_1
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (189), (192) imply:
% 202.23/33.83  | | | | |   (195)   ~ (all_14_1 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | BETA: splitting (82) gives:
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | Case 1:
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | |   (196)  all_58_0 = e3
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | COMBINE_EQS: (22), (196) imply:
% 202.23/33.83  | | | | | |   (197)  all_6_2 = e3
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | REF_CLOSE: (8), (126), (128), (148), (167), (197) are inconsistent
% 202.23/33.83  | | | | | |            by sub-proof #502.
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | Case 2:
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | |   (198)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | BETA: splitting (198) gives:
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | Case 1:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | |   (199)  all_58_2 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | COMBINE_EQS: (79), (199) imply:
% 202.23/33.83  | | | | | | |   (200)  all_52_3 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | SIMP: (200) implies:
% 202.23/33.83  | | | | | | |   (201)  all_52_3 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (20), (201) imply:
% 202.23/33.83  | | | | | | |   (202)   ~ (all_6_2 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | SIMP: (202) implies:
% 202.23/33.83  | | | | | | |   (203)   ~ (all_6_2 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (163), (201) imply:
% 202.23/33.83  | | | | | | |   (204)   ~ (all_4_2 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | SIMP: (204) implies:
% 202.23/33.83  | | | | | | |   (205)   ~ (all_4_2 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (7), (201) imply:
% 202.23/33.83  | | | | | | |   (206)  op(e3, e3) = all_52_2
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3,
% 202.23/33.83  | | | | | | |              simplifying with (128), (206) gives:
% 202.23/33.83  | | | | | | |   (207)  all_52_2 = all_6_2
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | BETA: splitting (131) gives:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | |   (208)  all_58_0 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | COMBINE_EQS: (22), (208) imply:
% 202.23/33.83  | | | | | | | |   (209)  all_6_2 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (203), (209) imply:
% 202.23/33.83  | | | | | | | |   (210)  $false
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | CLOSE: (210) is inconsistent.
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | |   (211)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | BETA: splitting (105) gives:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | |   (212)  all_58_1 = e3
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | COMBINE_EQS: (11), (212) imply:
% 202.23/33.83  | | | | | | | | |   (213)  all_52_9 = e3
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | REF_CLOSE: (8), (125), (128), (182), (213) are inconsistent by
% 202.23/33.83  | | | | | | | | |            sub-proof #1337.
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | |   (214)   ~ (all_58_1 = e3)
% 202.23/33.83  | | | | | | | | |   (215)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | REDUCE: (11), (214) imply:
% 202.23/33.83  | | | | | | | | |   (216)   ~ (all_52_9 = e3)
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | BETA: splitting (215) gives:
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | |   (217)  all_58_3 = e3
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | COMBINE_EQS: (160), (217) imply:
% 202.23/33.83  | | | | | | | | | |   (218)  all_4_2 = e3
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | REDUCE: (205), (218) imply:
% 202.23/33.83  | | | | | | | | | |   (219)  $false
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | CLOSE: (219) is inconsistent.
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | |   (220)  all_58_7 = e3 | all_58_13 = e3
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | BETA: splitting (211) gives:
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | |   (221)  all_58_1 = e3
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | COMBINE_EQS: (11), (221) imply:
% 202.23/33.83  | | | | | | | | | | |   (222)  all_52_9 = e3
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | REDUCE: (216), (222) imply:
% 202.23/33.83  | | | | | | | | | | |   (223)  $false
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | |   (224)  all_58_4 = e3 | all_58_9 = e3
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | BETA: splitting (224) gives:
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | |   (225)  all_58_4 = e3
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | COMBINE_EQS: (169), (225) imply:
% 202.23/33.83  | | | | | | | | | | | |   (226)  all_52_17 = e3
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | SIMP: (226) implies:
% 202.23/33.83  | | | | | | | | | | | |   (227)  all_52_17 = e3
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | REDUCE: (118), (227) imply:
% 202.23/33.83  | | | | | | | | | | | |   (228)  op(e3, e3) = all_52_16
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | BETA: splitting (220) gives:
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | |   (229)  all_58_7 = e3
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | COMBINE_EQS: (71), (229) imply:
% 202.23/33.83  | | | | | | | | | | | | |   (230)  all_52_13 = e3
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | REDUCE: (183), (230) imply:
% 202.23/33.83  | | | | | | | | | | | | |   (231)  op(e3, e3) = e1
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_16, e3, e3,
% 202.23/33.83  | | | | | | | | | | | | |              simplifying with (128), (228) gives:
% 202.23/33.83  | | | | | | | | | | | | |   (232)  all_52_16 = all_6_2
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e1, all_52_16, e3, e3,
% 202.23/33.83  | | | | | | | | | | | | |              simplifying with (228), (231) gives:
% 202.23/33.83  | | | | | | | | | | | | |   (233)  all_52_16 = e1
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | COMBINE_EQS: (232), (233) imply:
% 202.23/33.83  | | | | | | | | | | | | |   (234)  all_6_2 = e1
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | REF_CLOSE: (8), (21), (27), (52), (57), (94), (107), (150),
% 202.23/33.83  | | | | | | | | | | | | |            (167), (174), (234) are inconsistent by sub-proof
% 202.23/33.83  | | | | | | | | | | | | |            #378.
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | |   (235)  all_58_13 = e3
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | | REF_CLOSE: (33), (188), (235) are inconsistent by sub-proof
% 202.23/33.83  | | | | | | | | | | | | |            #1360.
% 202.23/33.83  | | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | |   (236)  all_58_9 = e3
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | REF_CLOSE: (194), (195), (236) are inconsistent by sub-proof
% 202.23/33.83  | | | | | | | | | | | |            #1131.
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | End of split
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | Case 2:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | |   (237)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | BETA: splitting (237) gives:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | |   (238)  all_58_6 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REF_CLOSE: (26), (102), (238) are inconsistent by sub-proof
% 202.23/33.83  | | | | | | | |            #922.
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | |   (239)  all_58_12 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | COMBINE_EQS: (75), (239) imply:
% 202.23/33.83  | | | | | | | |   (240)  all_52_7 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | SIMP: (240) implies:
% 202.23/33.83  | | | | | | | |   (241)  all_52_7 = e3
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (16), (241) imply:
% 202.23/33.83  | | | | | | | |   (242)   ~ (all_52_15 = e3)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (77), (241) imply:
% 202.23/33.83  | | | | | | | |   (243)   ~ (all_14_2 = e3)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | SIMP: (243) implies:
% 202.23/33.83  | | | | | | | |   (244)   ~ (all_14_2 = e3)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (13), (14),
% 202.23/33.83  | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 202.23/33.83  | | | | | | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 202.23/33.83  | | | | | | | |            (38), (39), (40), (41), (42), (43), (45), (47), (50),
% 202.23/33.83  | | | | | | | |            (51), (54), (58), (62), (63), (64), (67), (68), (69),
% 202.23/33.83  | | | | | | | |            (71), (73), (74), (75), (76), (77), (79), (82), (85),
% 202.23/33.83  | | | | | | | |            (86), (87), (89), (100), (101), (105), (106), (108),
% 202.23/33.83  | | | | | | | |            (109), (110), (111), (112), (114), (115), (116),
% 202.23/33.83  | | | | | | | |            (117), (118), (122), (123), (124), (125), (126),
% 202.23/33.83  | | | | | | | |            (127), (128), (129), (131), (134), (135), (137),
% 202.23/33.83  | | | | | | | |            (139), (142), (143), (144), (145), (146), (147),
% 202.23/33.83  | | | | | | | |            (148), (149), (150), (151), (152), (153), (154),
% 202.23/33.83  | | | | | | | |            (157), (158), (160), (163), (164), (165), (167),
% 202.23/33.83  | | | | | | | |            (168), (169), (170), (171), (182), (183), (185),
% 202.23/33.83  | | | | | | | |            (188), (244) are inconsistent by sub-proof #453.
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | End of split
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | End of split
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | End of split
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | Case 2:
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | |   (245)   ~ (all_56_15 = e3)
% 202.23/33.83  | | | | |   (246)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (53), (245) imply:
% 202.23/33.83  | | | | |   (247)   ~ (all_14_2 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (13), (14),
% 202.23/33.83  | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (27),
% 202.23/33.83  | | | | |            (28), (29), (30), (31), (33), (34), (35), (36), (38), (39),
% 202.23/33.83  | | | | |            (40), (41), (42), (43), (45), (47), (50), (51), (53), (54),
% 202.23/33.83  | | | | |            (58), (59), (62), (63), (64), (67), (68), (69), (71), (73),
% 202.23/33.83  | | | | |            (74), (75), (76), (77), (79), (82), (85), (86), (87), (89),
% 202.23/33.83  | | | | |            (100), (101), (104), (105), (106), (108), (109), (110),
% 202.23/33.83  | | | | |            (111), (112), (114), (115), (116), (117), (118), (119),
% 202.23/33.83  | | | | |            (122), (123), (124), (125), (126), (127), (128), (129),
% 202.23/33.83  | | | | |            (131), (134), (135), (137), (139), (140), (142), (143),
% 202.23/33.83  | | | | |            (144), (145), (146), (147), (148), (149), (150), (151),
% 202.23/33.83  | | | | |            (152), (153), (154), (157), (158), (160), (162), (163),
% 202.23/33.83  | | | | |            (164), (165), (166), (167), (168), (169), (170), (171),
% 202.23/33.83  | | | | |            (182), (183), (184), (185), (246), (247) are inconsistent
% 202.23/33.83  | | | | |            by sub-proof #452.
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | End of split
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | End of split
% 202.23/33.83  | | | 
% 202.23/33.83  | | Case 2:
% 202.23/33.83  | | | 
% 202.23/33.83  | | |   (248)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.23/33.83  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.23/33.83  | | |            all_52_30 = e0)
% 202.23/33.83  | | | 
% 202.23/33.83  | | | BETA: splitting (248) gives:
% 202.23/33.83  | | | 
% 202.23/33.83  | | | Case 1:
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | |   (249)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.23/33.83  | | | |          e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | ALPHA: (249) implies:
% 202.23/33.83  | | | |   (250)  all_52_22 = e0
% 202.23/33.83  | | | |   (251)  all_52_20 = e1
% 202.23/33.83  | | | |   (252)  all_52_18 = e2
% 202.23/33.83  | | | |   (253)  all_52_16 = e3
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (118), (253) imply:
% 202.23/33.83  | | | |   (254)  op(all_52_17, all_52_17) = e3
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (31), (252) imply:
% 202.23/33.83  | | | |   (255)  op(all_52_19, all_52_19) = e2
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (110), (250) imply:
% 202.23/33.83  | | | |   (256)  op(all_52_23, all_52_23) = e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (34), (251) imply:
% 202.23/33.83  | | | |   (257)  op(all_10_2, all_10_2) = e1
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | BETA: splitting (113) gives:
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | Case 1:
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | |   (258)  all_56_15 = e3
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | COMBINE_EQS: (53), (258) imply:
% 202.23/33.83  | | | | |   (259)  all_14_2 = e3
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (77), (259) imply:
% 202.23/33.83  | | | | |   (260)   ~ (all_52_7 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (116), (259) imply:
% 202.23/33.83  | | | | |   (261)   ~ (all_52_23 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (45), (259) imply:
% 202.23/33.83  | | | | |   (262)   ~ (all_52_25 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (136), (259) imply:
% 202.23/33.83  | | | | |   (263)  op(e3, e3) = all_52_30
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 202.23/33.83  | | | | |              simplifying with (128), (263) gives:
% 202.23/33.83  | | | | |   (264)  all_52_30 = all_6_2
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REF_CLOSE: (5), (7), (8), (11), (17), (20), (22), (25), (26), (35),
% 202.23/33.83  | | | | |            (70), (75), (79), (82), (101), (102), (105), (112), (126),
% 202.23/33.83  | | | | |            (128), (131), (137), (146), (148), (151), (153), (167),
% 202.23/33.83  | | | | |            (169), (254), (260), (261), (262) are inconsistent by
% 202.23/33.83  | | | | |            sub-proof #373.
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | Case 2:
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | |   (265)   ~ (all_56_15 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | REDUCE: (53), (265) imply:
% 202.23/33.83  | | | | |   (266)   ~ (all_14_2 = e3)
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | BETA: splitting (59) gives:
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | | Case 1:
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | |   (267)  all_56_13 = e3
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | COMBINE_EQS: (162), (267) imply:
% 202.23/33.83  | | | | | |   (268)  all_52_15 = e3
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | SIMP: (268) implies:
% 202.23/33.83  | | | | | |   (269)  all_52_15 = e3
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | REDUCE: (16), (269) imply:
% 202.23/33.83  | | | | | |   (270)   ~ (all_52_7 = e3)
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | REDUCE: (95), (269) imply:
% 202.23/33.83  | | | | | |   (271)   ~ (all_14_2 = e3)
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | REDUCE: (66), (269) imply:
% 202.23/33.83  | | | | | |   (272)  op(e3, e3) = all_52_14
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_14, e3, e3,
% 202.23/33.83  | | | | | |              simplifying with (128), (272) gives:
% 202.23/33.83  | | | | | |   (273)  all_52_14 = all_6_2
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | REF_CLOSE: (2), (3), (5), (6), (8), (11), (13), (15), (16), (17),
% 202.23/33.83  | | | | | |            (19), (22), (25), (26), (33), (35), (45), (46), (50),
% 202.23/33.83  | | | | | |            (59), (60), (70), (75), (79), (81), (82), (92), (99),
% 202.23/33.83  | | | | | |            (101), (102), (104), (105), (108), (112), (117), (119),
% 202.23/33.83  | | | | | |            (126), (128), (129), (131), (135), (136), (137), (144),
% 202.23/33.83  | | | | | |            (145), (146), (147), (148), (151), (153), (156), (157),
% 202.23/33.83  | | | | | |            (158), (162), (165), (166), (167), (169), (254), (256),
% 202.23/33.83  | | | | | |            (266), (270) are inconsistent by sub-proof #370.
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | Case 2:
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | |   (274)   ~ (all_56_13 = e3)
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | REDUCE: (162), (274) imply:
% 202.23/33.83  | | | | | |   (275)   ~ (all_52_15 = e3)
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | BETA: splitting (145) gives:
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | | Case 1:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | |   (276)  all_58_12 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | COMBINE_EQS: (75), (276) imply:
% 202.23/33.83  | | | | | | |   (277)  all_52_7 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | SIMP: (277) implies:
% 202.23/33.83  | | | | | | |   (278)  all_52_7 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (135), (278) imply:
% 202.23/33.83  | | | | | | |   (279)   ~ (all_52_3 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (158), (278) imply:
% 202.23/33.83  | | | | | | |   (280)   ~ (all_52_23 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | SIMP: (280) implies:
% 202.23/33.83  | | | | | | |   (281)   ~ (all_52_23 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (9), (278) imply:
% 202.23/33.83  | | | | | | |   (282)   ~ (all_10_0 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (50), (278) imply:
% 202.23/33.83  | | | | | | |   (283)   ~ (all_6_2 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | SIMP: (283) implies:
% 202.23/33.83  | | | | | | |   (284)   ~ (all_6_2 = e3)
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (18), (278) imply:
% 202.23/33.83  | | | | | | |   (285)  op(e3, e3) = all_52_6
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REDUCE: (104), (278) imply:
% 202.23/33.83  | | | | | | |   (286)  op(e0, e3) = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_6, e3, e3,
% 202.23/33.83  | | | | | | |              simplifying with (128), (285) gives:
% 202.23/33.83  | | | | | | |   (287)  all_52_6 = all_6_2
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | BETA: splitting (98) gives:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | |   (288)  all_58_0 = e2
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | COMBINE_EQS: (22), (288) imply:
% 202.23/33.83  | | | | | | | |   (289)  all_6_2 = e2
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (20), (289) imply:
% 202.23/33.83  | | | | | | | |   (290)   ~ (all_52_3 = e2)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (146), (289) imply:
% 202.23/33.83  | | | | | | | |   (291)   ~ (all_52_17 = e2)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (121), (289) imply:
% 202.23/33.83  | | | | | | | |   (292)   ~ (all_52_25 = e2)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (284), (289) imply:
% 202.23/33.83  | | | | | | | |   (293)   ~ (e3 = e2)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (167), (289) imply:
% 202.23/33.83  | | | | | | | |   (294)  op(e2, e3) = all_6_1
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (128), (289) imply:
% 202.23/33.83  | | | | | | | |   (295)  op(e3, e3) = e2
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | GROUND_INST: instantiating (8) with all_52_3, all_6_1, e3, e2,
% 202.23/33.83  | | | | | | | |              simplifying with (14), (294) gives:
% 202.23/33.83  | | | | | | | |   (296)  all_52_3 = all_6_1
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | COMBINE_EQS: (24), (296) imply:
% 202.23/33.83  | | | | | | | |   (297)  all_56_4 = all_6_1
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | COMBINE_EQS: (79), (296) imply:
% 202.23/33.83  | | | | | | | |   (298)  all_58_2 = all_6_1
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (279), (296) imply:
% 202.23/33.83  | | | | | | | |   (299)   ~ (all_6_1 = e3)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REDUCE: (290), (296) imply:
% 202.23/33.83  | | | | | | | |   (300)   ~ (all_6_1 = e2)
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | BETA: splitting (131) gives:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | |   (301)  all_58_0 = e3
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | REF_CLOSE: (148), (288), (301) are inconsistent by sub-proof
% 202.23/33.83  | | | | | | | | |            #1235.
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | |   (302)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | BETA: splitting (122) gives:
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | |   (303)  all_56_3 = e3
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | REF_CLOSE: (8), (28), (41), (73), (86), (87), (101), (126),
% 202.23/33.83  | | | | | | | | | |            (134), (288), (291), (292), (297), (298), (299),
% 202.23/33.83  | | | | | | | | | |            (300), (303) are inconsistent by sub-proof #384.
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | |   (304)   ~ (all_56_3 = e3)
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | REDUCE: (134), (304) imply:
% 202.23/33.83  | | | | | | | | | |   (305)   ~ (all_52_25 = e3)
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | BETA: splitting (302) gives:
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | |   (306)  all_58_1 = e3
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | COMBINE_EQS: (11), (306) imply:
% 202.23/33.83  | | | | | | | | | | |   (307)  all_52_9 = e3
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | REDUCE: (12), (307) imply:
% 202.23/33.83  | | | | | | | | | | |   (308)   ~ (all_52_13 = e3)
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | SIMP: (308) implies:
% 202.23/33.83  | | | | | | | | | | |   (309)   ~ (all_52_13 = e3)
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | REDUCE: (151), (307) imply:
% 202.23/33.83  | | | | | | | | | | |   (310)   ~ (all_52_17 = e3)
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | SIMP: (310) implies:
% 202.23/33.83  | | | | | | | | | | |   (311)   ~ (all_52_17 = e3)
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | REDUCE: (65), (307) imply:
% 202.23/33.83  | | | | | | | | | | |   (312)  op(e3, e3) = all_52_8
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | GROUND_INST: instantiating (8) with e2, all_52_8, e3, e3,
% 202.23/33.83  | | | | | | | | | | |              simplifying with (295), (312) gives:
% 202.23/33.83  | | | | | | | | | | |   (313)  all_52_8 = e2
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | BETA: splitting (76) gives:
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | Case 1:
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | |   (314)  all_58_6 = e3
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | REF_CLOSE: (26), (102), (314) are inconsistent by sub-proof
% 202.23/33.83  | | | | | | | | | | | |            #922.
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | |   (315)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (13), (22), (35), (36), (37), (43),
% 202.23/33.83  | | | | | | | | | | | |            (51), (56), (61), (67), (69), (71), (83), (87),
% 202.23/33.83  | | | | | | | | | | | |            (90), (97), (109), (112), (128), (137), (147),
% 202.23/33.83  | | | | | | | | | | | |            (153), (156), (169), (254), (255), (257), (281),
% 202.23/33.83  | | | | | | | | | | | |            (295), (306), (309), (311), (312), (315) are
% 202.23/33.83  | | | | | | | | | | | |            inconsistent by sub-proof #829.
% 202.23/33.83  | | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | |   (316)  all_58_4 = e3 | all_58_9 = e3
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | | REF_CLOSE: (8), (35), (128), (146), (169), (254), (305),
% 202.23/33.83  | | | | | | | | | | |            (316) are inconsistent by sub-proof #1080.
% 202.23/33.83  | | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | | 
% 202.23/33.83  | | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | | 
% 202.23/33.83  | | | | | | | | End of split
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | Case 2:
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | |   (317)   ~ (all_58_0 = e2)
% 202.23/33.83  | | | | | | | |   (318)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | | REF_CLOSE: (8), (13), (21), (22), (27), (41), (52), (57), (84),
% 202.23/33.83  | | | | | | | |            (87), (94), (102), (107), (126), (127), (128), (147),
% 202.23/33.83  | | | | | | | |            (148), (150), (154), (167), (174), (276), (284),
% 202.23/33.83  | | | | | | | |            (285), (286), (317), (318) are inconsistent by
% 202.23/33.83  | | | | | | | |            sub-proof #381.
% 202.23/33.83  | | | | | | | | 
% 202.23/33.83  | | | | | | | End of split
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | Case 2:
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | |   (319)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | | REF_CLOSE: (2), (5), (6), (8), (13), (15), (16), (33), (50), (60),
% 202.23/33.83  | | | | | | |            (75), (81), (92), (99), (104), (108), (117), (119),
% 202.23/33.83  | | | | | | |            (126), (128), (136), (144), (146), (147), (151), (156),
% 202.23/33.83  | | | | | | |            (157), (158), (165), (166), (167), (254), (256), (266),
% 202.23/33.83  | | | | | | |            (275), (319) are inconsistent by sub-proof #437.
% 202.23/33.83  | | | | | | | 
% 202.23/33.83  | | | | | | End of split
% 202.23/33.83  | | | | | | 
% 202.23/33.83  | | | | | End of split
% 202.23/33.83  | | | | | 
% 202.23/33.83  | | | | End of split
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | Case 2:
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | |   (320)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.23/33.83  | | | |          e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | ALPHA: (320) implies:
% 202.23/33.83  | | | |   (321)  all_52_30 = e0
% 202.23/33.83  | | | |   (322)  all_52_28 = e1
% 202.23/33.83  | | | |   (323)  all_52_26 = e2
% 202.23/33.83  | | | |   (324)  all_52_24 = e3
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (171), (324) imply:
% 202.23/33.83  | | | |   (325)  op(all_52_25, all_52_25) = e3
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (38), (323) imply:
% 202.23/33.83  | | | |   (326)  op(all_52_27, all_52_27) = e2
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (115), (322) imply:
% 202.23/33.83  | | | |   (327)  op(all_52_29, all_52_29) = e1
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REDUCE: (136), (321) imply:
% 202.23/33.83  | | | |   (328)  op(all_14_2, all_14_2) = e0
% 202.23/33.83  | | | | 
% 202.23/33.83  | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 202.23/33.83  | | | |            (15), (18), (19), (20), (21), (22), (23), (25), (26), (27),
% 202.23/33.83  | | | |            (28), (29), (30), (31), (32), (33), (35), (36), (39), (40),
% 202.23/33.83  | | | |            (41), (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 202.23/33.83  | | | |            (52), (53), (54), (55), (56), (57), (60), (62), (63), (64),
% 202.23/33.83  | | | |            (65), (68), (69), (71), (72), (73), (74), (75), (76), (77),
% 202.23/33.83  | | | |            (78), (79), (80), (81), (82), (83), (85), (87), (88), (91),
% 202.23/33.83  | | | |            (93), (94), (95), (96), (97), (99), (101), (102), (103),
% 202.23/33.83  | | | |            (104), (105), (106), (108), (109), (111), (112), (113),
% 202.23/33.83  | | | |            (114), (116), (117), (118), (120), (121), (122), (123),
% 202.23/33.83  | | | |            (124), (126), (127), (128), (129), (130), (131), (132),
% 202.23/33.83  | | | |            (134), (135), (137), (138), (140), (142), (143), (144),
% 202.23/33.83  | | | |            (145), (146), (147), (148), (150), (153), (154), (155),
% 202.23/33.83  | | | |            (156), (158), (159), (160), (161), (163), (164), (165),
% 202.23/33.83  | | | |            (167), (168), (169), (174), (325), (326), (327), (328) are
% 202.23/33.83  | | | |            inconsistent by sub-proof #369.
% 202.23/33.83  | | | | 
% 202.23/33.84  | | | End of split
% 202.23/33.84  | | | 
% 202.23/33.84  | | End of split
% 202.23/33.84  | | 
% 202.23/33.84  | End of split
% 202.23/33.84  | 
% 202.23/33.84  End of proof
% 202.23/33.84  
% 202.23/33.84  Sub-proof #369 shows that the following formulas are inconsistent:
% 202.23/33.84  ----------------------------------------------------------------
% 202.23/33.84    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.84    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.84    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.84    (4)  all_58_14 = all_52_23
% 202.23/33.84    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.84    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.84    (7)   ~ (all_52_7 = all_10_0)
% 202.23/33.84    (8)  all_58_1 = all_52_9
% 202.23/33.84    (9)   ~ (all_52_9 = all_52_13)
% 202.23/33.84    (10)   ~ (e3 = e0)
% 202.23/33.84    (11)  op(e2, e3) = all_52_3
% 202.23/33.84    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.84    (13)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.84    (14)   ~ (all_52_17 = all_52_25)
% 202.23/33.84    (15)   ~ (all_52_3 = all_6_2)
% 202.23/33.84    (16)  all_44_2 = all_6_2
% 202.23/33.84    (17)  all_58_0 = all_6_2
% 202.23/33.84    (18)  op(all_14_2, e0) = all_14_1
% 202.23/33.84    (19)   ~ (all_52_17 = all_10_2)
% 202.23/33.84    (20)   ~ (all_10_0 = e3)
% 202.23/33.84    (21)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.84    (22)  op(e3, e0) = all_52_25
% 202.23/33.84    (23)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.84    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.84    (25)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.84    (26)   ~ (all_52_27 = all_52_29)
% 202.23/33.84    (27)  all_58_13 = all_52_15
% 202.23/33.84    (28)  all_58_9 = all_52_25
% 202.23/33.84    (29)   ~ (all_52_29 = all_14_2)
% 202.23/33.84    (30)  op(e1, e3) = all_52_5
% 202.23/33.84    (31)  op(e2, e2) = all_4_2
% 202.23/33.84    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.84    (33)   ~ (all_52_3 = all_52_5)
% 202.23/33.84    (34)  all_58_11 = all_52_29
% 202.23/33.84    (35)  all_56_5 = all_4_2
% 202.23/33.84    (36)   ~ (all_52_25 = all_14_2)
% 202.23/33.84    (37)   ~ (all_52_3 = all_52_27)
% 202.23/33.84    (38)  op(all_10_2, e1) = all_10_1
% 202.23/33.84    (39)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.84    (40)   ~ (all_52_7 = all_6_2)
% 202.23/33.84    (41)  op(e0, e0) = all_14_2
% 202.23/33.84    (42)   ~ (all_10_0 = all_6_2)
% 202.23/33.84    (43)  op(all_52_29, all_52_29) = e1
% 202.23/33.84    (44)  all_56_15 = all_14_2
% 202.23/33.84    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.84    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.84    (47)  all_56_11 = all_52_29
% 202.23/33.84    (48)   ~ (all_10_0 = e2)
% 202.23/33.84    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.84    (50)   ~ (all_52_13 = all_10_2)
% 202.23/33.84    (51)  all_58_10 = all_52_27
% 202.23/33.84    (52)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.84    (53)  all_56_8 = all_52_5
% 202.23/33.84    (54)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.84    (55)   ~ (all_52_25 = all_52_29)
% 202.23/33.84    (56)   ~ (all_52_29 = all_10_2)
% 202.23/33.84    (57)  all_58_7 = all_52_13
% 202.23/33.84    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.84    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.84    (60)   ~ (all_52_5 = all_52_7)
% 202.23/33.84    (61)  all_58_12 = all_52_7
% 202.23/33.84    (62)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.84    (63)   ~ (all_52_7 = all_14_2)
% 202.23/33.84    (64)   ~ (all_14_2 = e0)
% 202.23/33.84    (65)  all_58_2 = all_52_3
% 202.23/33.84    (66)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.84    (67)  all_56_2 = all_52_17
% 202.23/33.84    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.84    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.84    (70)  all_56_7 = all_52_27
% 202.23/33.84    (71)   ~ (e2 = e0)
% 202.23/33.84    (72)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.84    (73)  op(all_52_25, all_52_25) = e3
% 202.23/33.84    (74)   ~ (all_52_5 = all_52_29)
% 202.23/33.84    (75)  all_56_6 = all_52_19
% 202.23/33.84    (76)  all_56_8 = all_10_0
% 202.23/33.84    (77)   ~ (all_52_15 = all_14_2)
% 202.23/33.84    (78)   ~ (all_52_19 = all_52_27)
% 202.23/33.84    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.84    (80)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.84    (81)  op(e3, e1) = all_52_17
% 202.23/33.84    (82)  op(all_52_27, all_52_27) = e2
% 202.23/33.84    (83)  all_58_6 = all_10_0
% 202.23/33.84    (84)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.84    (85)  op(e0, e3) = all_52_7
% 202.23/33.84    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.84    (87)   ~ (all_52_9 = all_52_25)
% 202.23/33.84    (88)  all_58_15 = all_14_2
% 202.23/33.84    (89)   ~ (all_52_19 = all_10_2)
% 202.23/33.84    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.84    (91)  all_58_8 = all_10_2
% 202.23/33.84    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.84    (93)   ~ (all_52_5 = all_10_2)
% 202.23/33.84    (94)   ~ (all_52_23 = all_14_2)
% 202.23/33.84    (95)  all_56_12 = all_52_7
% 202.23/33.84    (96)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.84    (97)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.84    (98)   ~ (all_52_25 = all_6_2)
% 202.23/33.84    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.84    (100)   ~ (all_52_9 = all_4_2)
% 202.23/33.84    (101)   ~ (all_52_5 = all_6_2)
% 202.23/33.84    (102)  op(e3, all_6_1) = e2
% 202.23/33.84    (103)  all_56_0 = all_6_2
% 202.23/33.84    (104)  op(e3, e3) = all_6_2
% 202.23/33.84    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.84    (106)   ~ (all_52_27 = all_14_2)
% 202.23/33.84    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.84    (108)  all_56_14 = all_52_23
% 202.23/33.84    (109)  all_56_3 = all_52_25
% 202.23/33.84    (110)   ~ (all_52_3 = all_52_7)
% 202.23/33.84    (111)  all_58_5 = all_52_19
% 202.23/33.84    (112)  op(all_10_0, all_10_0) = all_52_4
% 202.23/33.84    (113)   ~ (all_52_15 = all_4_2)
% 202.23/33.84    (114)   ~ (all_52_27 = all_4_2)
% 202.23/33.84    (115)  all_58_6 = all_52_5
% 202.23/33.84    (116)  op(e3, e2) = all_52_9
% 202.23/33.84    (117)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.84    (118)   ~ (all_52_17 = all_6_2)
% 202.23/33.84    (119)   ~ (e1 = e0)
% 202.23/33.84    (120)  op(all_14_2, all_14_2) = e0
% 202.23/33.84    (121)   ~ (e3 = e2)
% 202.23/33.84    (122)  all_44_1 = all_6_1
% 202.23/33.84    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.84    (124)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.84    (125)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.84    (126)  op(e1, e1) = all_10_2
% 202.23/33.84    (127)   ~ (all_52_7 = all_52_23)
% 202.23/33.84    (128)   ~ (all_52_17 = all_52_19)
% 202.23/33.84    (129)  all_58_3 = all_4_2
% 202.23/33.84    (130)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.84    (131)   ~ (all_52_3 = all_4_2)
% 202.23/33.84    (132)   ~ (all_52_19 = all_4_2)
% 202.23/33.84    (133)   ~ (all_52_17 = all_52_23)
% 202.23/33.84    (134)  op(all_6_2, e3) = all_6_1
% 202.23/33.84    (135)   ~ (all_52_13 = all_52_29)
% 202.23/33.84    (136)  all_58_4 = all_52_17
% 202.23/33.84  
% 202.23/33.84  Begin of proof
% 202.23/33.84  | 
% 202.23/33.84  | BETA: splitting (92) gives:
% 202.23/33.84  | 
% 202.23/33.84  | Case 1:
% 202.23/33.84  | | 
% 202.23/33.84  | |   (137)  all_56_15 = e3
% 202.23/33.84  | | 
% 202.23/33.84  | | COMBINE_EQS: (44), (137) imply:
% 202.23/33.84  | |   (138)  all_14_2 = e3
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (77), (138) imply:
% 202.23/33.84  | |   (139)   ~ (all_52_15 = e3)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (36), (138) imply:
% 202.23/33.84  | |   (140)   ~ (all_52_25 = e3)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (120), (138) imply:
% 202.23/33.84  | |   (141)  op(e3, e3) = e0
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (18), (138) imply:
% 202.23/33.84  | |   (142)  op(e3, e0) = all_14_1
% 202.23/33.84  | | 
% 202.23/33.84  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 202.23/33.84  | |              with (22), (142) gives:
% 202.23/33.84  | |   (143)  all_52_25 = all_14_1
% 202.23/33.84  | | 
% 202.23/33.84  | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying with
% 202.23/33.84  | |              (104), (141) gives:
% 202.23/33.84  | |   (144)  all_6_2 = e0
% 202.23/33.84  | | 
% 202.23/33.84  | | COMBINE_EQS: (109), (143) imply:
% 202.23/33.84  | |   (145)  all_56_3 = all_14_1
% 202.23/33.84  | | 
% 202.23/33.84  | | COMBINE_EQS: (28), (143) imply:
% 202.23/33.84  | |   (146)  all_58_9 = all_14_1
% 202.23/33.84  | | 
% 202.23/33.84  | | COMBINE_EQS: (17), (144) imply:
% 202.23/33.84  | |   (147)  all_58_0 = e0
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (40), (144) imply:
% 202.23/33.84  | |   (148)   ~ (all_52_7 = e0)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (87), (143) imply:
% 202.23/33.84  | |   (149)   ~ (all_52_9 = all_14_1)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (98), (143), (144) imply:
% 202.23/33.84  | |   (150)   ~ (all_14_1 = e0)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (140), (143) imply:
% 202.23/33.84  | |   (151)   ~ (all_14_1 = e3)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (42), (144) imply:
% 202.23/33.84  | |   (152)   ~ (all_10_0 = e0)
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (73), (143) imply:
% 202.23/33.84  | |   (153)  op(all_14_1, all_14_1) = e3
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (134), (144) imply:
% 202.23/33.84  | |   (154)  op(e0, e3) = all_6_1
% 202.23/33.84  | | 
% 202.23/33.84  | | BETA: splitting (52) gives:
% 202.23/33.84  | | 
% 202.23/33.84  | | Case 1:
% 202.23/33.84  | | | 
% 202.23/33.84  | | |   (155)  all_56_8 = e2
% 202.23/33.84  | | | 
% 202.23/33.84  | | | REF_CLOSE: (48), (76), (155) are inconsistent by sub-proof #915.
% 202.23/33.84  | | | 
% 202.23/33.84  | | Case 2:
% 202.23/33.84  | | | 
% 202.23/33.84  | | |   (156)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.84  | | | 
% 202.23/33.84  | | | BETA: splitting (68) gives:
% 202.23/33.84  | | | 
% 202.23/33.84  | | | Case 1:
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | |   (157)  all_58_0 = e3
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | | REF_CLOSE: (10), (147), (157) are inconsistent by sub-proof #1015.
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | Case 2:
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | |   (158)   ~ (all_58_0 = e3)
% 202.23/33.84  | | | |   (159)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | | REDUCE: (147), (158) imply:
% 202.23/33.84  | | | |   (160)   ~ (e3 = e0)
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | | BETA: splitting (159) gives:
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | | Case 1:
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | |   (161)  all_58_2 = e3
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | COMBINE_EQS: (65), (161) imply:
% 202.23/33.84  | | | | |   (162)  all_52_3 = e3
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | SIMP: (162) implies:
% 202.23/33.84  | | | | |   (163)  all_52_3 = e3
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | REDUCE: (110), (163) imply:
% 202.23/33.84  | | | | |   (164)   ~ (all_52_7 = e3)
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | SIMP: (164) implies:
% 202.23/33.84  | | | | |   (165)   ~ (all_52_7 = e3)
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | REDUCE: (131), (163) imply:
% 202.23/33.84  | | | | |   (166)   ~ (all_4_2 = e3)
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | SIMP: (166) implies:
% 202.23/33.84  | | | | |   (167)   ~ (all_4_2 = e3)
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | BETA: splitting (156) gives:
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | Case 1:
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | |   (168)  all_56_8 = e1
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | COMBINE_EQS: (76), (168) imply:
% 202.23/33.84  | | | | | |   (169)  all_10_0 = e1
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | SIMP: (169) implies:
% 202.23/33.84  | | | | | |   (170)  all_10_0 = e1
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | REDUCE: (7), (170) imply:
% 202.23/33.84  | | | | | |   (171)   ~ (all_52_7 = e1)
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | REDUCE: (112), (170) imply:
% 202.23/33.84  | | | | | |   (172)  op(e1, e1) = all_52_4
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | BETA: splitting (12) gives:
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | Case 1:
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | |   (173)  all_56_12 = e3
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | REF_CLOSE: (95), (165), (173) are inconsistent by sub-proof #1383.
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | Case 2:
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | |   (174)   ~ (all_56_12 = e3)
% 202.23/33.84  | | | | | | |   (175)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | BETA: splitting (175) gives:
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | Case 1:
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | |   (176)  all_56_12 = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | COMBINE_EQS: (95), (176) imply:
% 202.23/33.84  | | | | | | | |   (177)  all_52_7 = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | SIMP: (177) implies:
% 202.23/33.84  | | | | | | | |   (178)  all_52_7 = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | REDUCE: (165), (178) imply:
% 202.23/33.84  | | | | | | | |   (179)   ~ (e3 = e2)
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | REDUCE: (85), (178) imply:
% 202.23/33.84  | | | | | | | |   (180)  op(e0, e3) = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | GROUND_INST: instantiating (6) with e2, all_6_1, e3, e0,
% 202.23/33.84  | | | | | | | |              simplifying with (154), (180) gives:
% 202.23/33.84  | | | | | | | |   (181)  all_6_1 = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_4, e1, e1,
% 202.23/33.84  | | | | | | | |              simplifying with (126), (172) gives:
% 202.23/33.84  | | | | | | | |   (182)  all_52_4 = all_10_2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | REDUCE: (102), (181) imply:
% 202.23/33.84  | | | | | | | |   (183)  op(e3, e2) = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | GROUND_INST: instantiating (6) with all_52_9, e2, e2, e3,
% 202.23/33.84  | | | | | | | |              simplifying with (116), (183) gives:
% 202.23/33.84  | | | | | | | |   (184)  all_52_9 = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | COMBINE_EQS: (8), (184) imply:
% 202.23/33.84  | | | | | | | |   (185)  all_58_1 = e2
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | REDUCE: (149), (184) imply:
% 202.23/33.84  | | | | | | | |   (186)   ~ (all_14_1 = e2)
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | SIMP: (186) implies:
% 202.23/33.84  | | | | | | | |   (187)   ~ (all_14_1 = e2)
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | BETA: splitting (99) gives:
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | Case 1:
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | |   (188)  all_56_3 = e3
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | COMBINE_EQS: (145), (188) imply:
% 202.23/33.84  | | | | | | | | |   (189)  all_14_1 = e3
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | REDUCE: (151), (189) imply:
% 202.23/33.84  | | | | | | | | |   (190)  $false
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | CLOSE: (190) is inconsistent.
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | Case 2:
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | |   (191)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | BETA: splitting (86) gives:
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | Case 1:
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | |   (192)  all_58_1 = e3
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | REF_CLOSE: (121), (185), (192) are inconsistent by sub-proof
% 202.23/33.84  | | | | | | | | | |            #1090.
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | Case 2:
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | |   (193)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | BETA: splitting (193) gives:
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | Case 1:
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | |   (194)  all_58_3 = e3
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | COMBINE_EQS: (129), (194) imply:
% 202.23/33.84  | | | | | | | | | | |   (195)  all_4_2 = e3
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | REDUCE: (167), (195) imply:
% 202.23/33.84  | | | | | | | | | | |   (196)  $false
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | Case 2:
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | |   (197)  all_58_7 = e3 | all_58_13 = e3
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | BETA: splitting (197) gives:
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | Case 1:
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | |   (198)  all_58_7 = e3
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | | COMBINE_EQS: (57), (198) imply:
% 202.23/33.84  | | | | | | | | | | | |   (199)  all_52_13 = e3
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | | REDUCE: (50), (199) imply:
% 202.23/33.84  | | | | | | | | | | | |   (200)   ~ (all_10_2 = e3)
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | | SIMP: (200) implies:
% 202.23/33.84  | | | | | | | | | | | |   (201)   ~ (all_10_2 = e3)
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | | REF_CLOSE: (6), (46), (126), (145), (146), (150), (153),
% 202.23/33.84  | | | | | | | | | | | |            (187), (191), (201) are inconsistent by sub-proof
% 202.23/33.84  | | | | | | | | | | | |            #560.
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | Case 2:
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | |   (202)  all_58_13 = e3
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | | REF_CLOSE: (27), (139), (202) are inconsistent by sub-proof
% 202.23/33.84  | | | | | | | | | | | |            #1360.
% 202.23/33.84  | | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | | End of split
% 202.23/33.84  | | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | | End of split
% 202.23/33.84  | | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | End of split
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | End of split
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | Case 2:
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | |   (203)  all_56_12 = e1 | all_56_12 = e0
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | BETA: splitting (203) gives:
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | | Case 1:
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | |   (204)  all_56_12 = e1
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | REF_CLOSE: (95), (171), (204) are inconsistent by sub-proof
% 202.23/33.84  | | | | | | | | |            #1376.
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | Case 2:
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | |   (205)  all_56_12 = e0
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | | REF_CLOSE: (95), (148), (205) are inconsistent by sub-proof
% 202.23/33.84  | | | | | | | | |            #1375.
% 202.23/33.84  | | | | | | | | | 
% 202.23/33.84  | | | | | | | | End of split
% 202.23/33.84  | | | | | | | | 
% 202.23/33.84  | | | | | | | End of split
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | End of split
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | Case 2:
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | |   (206)  all_56_8 = e0
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | REF_CLOSE: (76), (152), (206) are inconsistent by sub-proof #883.
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | End of split
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | Case 2:
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | |   (207)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | BETA: splitting (207) gives:
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | | Case 1:
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | |   (208)  all_58_6 = e3
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | REF_CLOSE: (20), (83), (208) are inconsistent by sub-proof #922.
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | Case 2:
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | |   (209)  all_58_12 = e3
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | COMBINE_EQS: (61), (209) imply:
% 202.23/33.84  | | | | | |   (210)  all_52_7 = e3
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | SIMP: (210) implies:
% 202.23/33.84  | | | | | |   (211)  all_52_7 = e3
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | REDUCE: (63), (211) imply:
% 202.23/33.84  | | | | | |   (212)   ~ (all_14_2 = e3)
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | SIMP: (212) implies:
% 202.23/33.84  | | | | | |   (213)   ~ (all_14_2 = e3)
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | REDUCE: (13), (211) imply:
% 202.23/33.84  | | | | | |   (214)  op(e3, e3) = all_52_6
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3,
% 202.23/33.84  | | | | | |              simplifying with (104), (214) gives:
% 202.23/33.84  | | | | | |   (215)  all_52_6 = all_6_2
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | BETA: splitting (92) gives:
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | | Case 1:
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | REDUCE: (138), (213) imply:
% 202.23/33.84  | | | | | | |   (216)  $false
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | CLOSE: (216) is inconsistent.
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | Case 2:
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | |   (217)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 202.23/33.84  | | | | | | |            (13), (14), (15), (16), (17), (19), (21), (23), (24),
% 202.23/33.84  | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 202.23/33.84  | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (43),
% 202.23/33.84  | | | | | | |            (44), (45), (46), (47), (49), (51), (53), (54), (55),
% 202.23/33.84  | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 202.23/33.84  | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 202.23/33.84  | | | | | | |            (74), (75), (78), (79), (80), (81), (82), (84), (86),
% 202.23/33.84  | | | | | | |            (87), (88), (89), (90), (91), (93), (94), (96), (97),
% 202.23/33.84  | | | | | | |            (98), (99), (100), (101), (102), (103), (104), (105),
% 202.23/33.84  | | | | | | |            (106), (107), (108), (109), (110), (111), (113), (114),
% 202.23/33.84  | | | | | | |            (115), (116), (117), (118), (119), (120), (121), (122),
% 202.23/33.84  | | | | | | |            (123), (124), (125), (126), (127), (128), (129), (130),
% 202.23/33.84  | | | | | | |            (131), (132), (133), (134), (135), (136), (213), (217)
% 202.23/33.84  | | | | | | |            are inconsistent by sub-proof #435.
% 202.23/33.84  | | | | | | | 
% 202.23/33.84  | | | | | | End of split
% 202.23/33.84  | | | | | | 
% 202.23/33.84  | | | | | End of split
% 202.23/33.84  | | | | | 
% 202.23/33.84  | | | | End of split
% 202.23/33.84  | | | | 
% 202.23/33.84  | | | End of split
% 202.23/33.84  | | | 
% 202.23/33.84  | | End of split
% 202.23/33.84  | | 
% 202.23/33.84  | Case 2:
% 202.23/33.84  | | 
% 202.23/33.84  | |   (218)   ~ (all_56_15 = e3)
% 202.23/33.84  | |   (219)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.84  | | 
% 202.23/33.84  | | REDUCE: (44), (218) imply:
% 202.23/33.84  | |   (220)   ~ (all_14_2 = e3)
% 202.23/33.84  | | 
% 202.23/33.84  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 202.23/33.84  | |            (15), (16), (17), (19), (21), (23), (24), (25), (26), (27), (28),
% 202.23/33.84  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 202.23/33.84  | |            (40), (41), (43), (44), (45), (46), (47), (49), (51), (53), (54),
% 202.23/33.84  | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 202.23/33.84  | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), (78),
% 202.23/33.84  | |            (79), (80), (81), (82), (84), (86), (87), (88), (89), (90), (91),
% 202.23/33.84  | |            (93), (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 202.23/33.84  | |            (104), (105), (106), (107), (108), (109), (110), (111), (113),
% 202.23/33.84  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 202.23/33.84  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 202.23/33.84  | |            (132), (133), (134), (135), (136), (219), (220) are inconsistent
% 202.23/33.84  | |            by sub-proof #435.
% 202.23/33.84  | | 
% 202.23/33.84  | End of split
% 202.23/33.84  | 
% 202.23/33.84  End of proof
% 202.23/33.84  
% 202.23/33.84  Sub-proof #370 shows that the following formulas are inconsistent:
% 202.23/33.84  ----------------------------------------------------------------
% 202.23/33.84    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.84    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.84    (3)  all_58_14 = all_52_23
% 202.23/33.84    (4)   ~ (e3 = e1)
% 202.23/33.84    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.84    (6)  all_58_1 = all_52_9
% 202.23/33.84    (7)   ~ (e3 = e0)
% 202.23/33.84    (8)  op(all_52_23, all_52_23) = e0
% 202.23/33.84    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.84    (10)   ~ (all_52_7 = all_52_15)
% 202.23/33.84    (11)   ~ (all_52_3 = all_52_19)
% 202.23/33.84    (12)   ~ (all_52_17 = all_52_25)
% 202.23/33.84    (13)  all_58_0 = all_6_2
% 202.23/33.84    (14)   ~ (all_52_17 = all_10_2)
% 202.23/33.84    (15)   ~ (all_10_0 = e3)
% 202.23/33.84    (16)  all_58_13 = all_52_15
% 202.23/33.84    (17)  all_58_9 = all_52_25
% 202.23/33.84    (18)   ~ (all_52_25 = all_14_2)
% 202.23/33.84    (19)   ~ (all_52_9 = all_52_15)
% 202.23/33.84    (20)   ~ (all_52_7 = all_6_2)
% 202.23/33.84    (21)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.84    (22)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.84    (23)  op(all_10_2, e1) = e3
% 202.23/33.84    (24)  all_58_12 = all_52_7
% 202.23/33.84    (25)   ~ (all_52_7 = e3)
% 202.23/33.84    (26)  all_58_2 = all_52_3
% 202.23/33.84    (27)  all_56_2 = all_52_17
% 202.23/33.84    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.84    (29)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.84    (30)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.84    (31)  op(e3, e1) = all_52_17
% 202.23/33.84    (32)  all_58_6 = all_10_0
% 202.23/33.84    (33)  op(e0, e3) = all_52_7
% 202.23/33.84    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.84    (35)  all_58_15 = all_14_2
% 202.23/33.84    (36)  all_58_8 = all_10_2
% 202.23/33.84    (37)  all_56_12 = all_52_7
% 202.23/33.84    (38)  all_8_2 = all_6_2
% 202.23/33.84    (39)  op(e3, all_6_1) = e2
% 202.23/33.84    (40)  op(e3, e3) = all_6_2
% 202.23/33.84    (41)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.84    (42)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.84    (43)   ~ (all_52_3 = all_52_7)
% 202.23/33.84    (44)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.84    (45)  all_58_5 = all_52_19
% 202.23/33.84    (46)  op(all_52_17, all_52_17) = e3
% 202.23/33.84    (47)  op(e3, e2) = all_52_9
% 202.23/33.84    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.84    (49)   ~ (all_52_17 = all_6_2)
% 202.23/33.84    (50)   ~ (e1 = e0)
% 202.23/33.84    (51)   ~ (e3 = e2)
% 202.23/33.84    (52)   ~ (all_52_9 = all_52_17)
% 202.23/33.84    (53)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.84    (54)  op(e1, e1) = all_10_2
% 202.23/33.84    (55)   ~ (all_52_23 = all_10_2)
% 202.23/33.84    (56)   ~ (all_52_7 = all_52_23)
% 202.23/33.84    (57)  all_56_13 = all_52_15
% 202.23/33.84    (58)   ~ (all_52_17 = all_52_23)
% 202.23/33.84    (59)  all_8_1 = all_6_1
% 202.23/33.84    (60)  op(all_6_2, e3) = all_6_1
% 202.23/33.84    (61)  all_58_4 = all_52_17
% 202.23/33.84    (62)   ~ (all_14_2 = e3)
% 202.23/33.84  
% 202.23/33.84  Begin of proof
% 202.23/33.84  | 
% 202.23/33.84  | BETA: splitting (28) gives:
% 202.23/33.84  | 
% 202.23/33.84  | Case 1:
% 202.23/33.84  | | 
% 202.23/33.84  | |   (63)  all_58_0 = e3
% 202.23/33.84  | | 
% 202.23/33.84  | | COMBINE_EQS: (13), (63) imply:
% 202.23/33.84  | |   (64)  all_6_2 = e3
% 202.23/33.84  | | 
% 202.23/33.84  | | REF_CLOSE: (5), (39), (40), (51), (60), (64) are inconsistent by sub-proof
% 202.23/33.84  | |            #502.
% 202.23/33.84  | | 
% 202.23/33.84  | Case 2:
% 202.23/33.84  | | 
% 202.23/33.84  | |   (65)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.84  | | 
% 202.23/33.84  | | BETA: splitting (65) gives:
% 202.23/33.84  | | 
% 202.23/33.84  | | Case 1:
% 202.23/33.84  | | | 
% 202.23/33.84  | | |   (66)  all_58_2 = e3
% 202.23/33.84  | | | 
% 202.23/33.84  | | | COMBINE_EQS: (26), (66) imply:
% 202.23/33.84  | | |   (67)  all_52_3 = e3
% 202.23/33.84  | | | 
% 202.23/33.84  | | | SIMP: (67) implies:
% 202.23/33.84  | | |   (68)  all_52_3 = e3
% 202.23/33.84  | | | 
% 202.23/33.84  | | | REDUCE: (43), (68) imply:
% 202.23/33.84  | | |   (69)   ~ (all_52_7 = e3)
% 202.23/33.84  | | | 
% 202.23/33.84  | | | REDUCE: (11), (68) imply:
% 202.23/33.84  | | |   (70)   ~ (all_52_19 = e3)
% 202.23/33.84  | | | 
% 202.23/33.84  | | | SIMP: (70) implies:
% 202.23/33.84  | | |   (71)   ~ (all_52_19 = e3)
% 202.23/33.84  | | | 
% 202.23/33.84  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 202.23/33.84  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 202.23/33.84  | | |            (25), (27), (29), (30), (31), (33), (34), (35), (36), (37),
% 202.23/33.84  | | |            (38), (39), (40), (41), (42), (44), (45), (46), (47), (48),
% 202.23/33.84  | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 202.23/33.84  | | |            (59), (60), (61), (62), (71) are inconsistent by sub-proof
% 202.23/33.84  | | |            #371.
% 202.23/33.84  | | | 
% 202.23/33.84  | | Case 2:
% 202.23/33.84  | | | 
% 202.23/33.84  | | |   (72)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.84  | | | 
% 202.23/33.84  | | | REF_CLOSE: (15), (24), (25), (32), (72) are inconsistent by sub-proof
% 202.23/33.84  | | |            #921.
% 202.23/33.84  | | | 
% 202.23/33.84  | | End of split
% 202.23/33.84  | | 
% 202.23/33.84  | End of split
% 202.23/33.84  | 
% 202.23/33.84  End of proof
% 202.23/33.84  
% 202.23/33.84  Sub-proof #371 shows that the following formulas are inconsistent:
% 202.23/33.84  ----------------------------------------------------------------
% 202.23/33.84    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.84    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.84    (3)  all_58_14 = all_52_23
% 202.23/33.84    (4)   ~ (e3 = e1)
% 202.23/33.84    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.84    (6)  all_58_1 = all_52_9
% 202.23/33.84    (7)   ~ (e3 = e0)
% 202.23/33.84    (8)  op(all_52_23, all_52_23) = e0
% 202.23/33.84    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.84    (10)   ~ (all_52_7 = all_52_15)
% 202.23/33.84    (11)   ~ (all_52_17 = all_52_25)
% 202.23/33.84    (12)  all_58_0 = all_6_2
% 202.23/33.84    (13)   ~ (all_52_17 = all_10_2)
% 202.23/33.84    (14)  all_58_13 = all_52_15
% 202.23/33.84    (15)  all_58_9 = all_52_25
% 202.23/33.84    (16)   ~ (all_52_25 = all_14_2)
% 202.23/33.84    (17)   ~ (all_52_9 = all_52_15)
% 202.23/33.84    (18)   ~ (all_52_7 = all_6_2)
% 202.23/33.84    (19)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.84    (20)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.84    (21)  op(all_10_2, e1) = e3
% 202.23/33.84    (22)  all_58_12 = all_52_7
% 202.23/33.84    (23)   ~ (all_52_7 = e3)
% 202.23/33.84    (24)  all_56_2 = all_52_17
% 202.23/33.84    (25)   ~ (all_52_19 = e3)
% 202.23/33.84    (26)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.84    (27)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.84    (28)  op(e3, e1) = all_52_17
% 202.23/33.84    (29)  op(e0, e3) = all_52_7
% 202.23/33.84    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.84    (31)  all_58_15 = all_14_2
% 202.23/33.84    (32)  all_58_8 = all_10_2
% 202.23/33.84    (33)  all_56_12 = all_52_7
% 202.23/33.84    (34)  all_8_2 = all_6_2
% 202.23/33.84    (35)  op(e3, all_6_1) = e2
% 202.23/33.84    (36)  op(e3, e3) = all_6_2
% 202.23/33.84    (37)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.84    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.84    (39)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.84    (40)  all_58_5 = all_52_19
% 202.23/33.84    (41)  op(all_52_17, all_52_17) = e3
% 202.23/33.84    (42)  op(e3, e2) = all_52_9
% 202.23/33.84    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.84    (44)   ~ (all_52_17 = all_6_2)
% 202.23/33.84    (45)   ~ (e1 = e0)
% 202.23/33.84    (46)   ~ (e3 = e2)
% 202.23/33.84    (47)   ~ (all_52_9 = all_52_17)
% 202.23/33.84    (48)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.84    (49)  op(e1, e1) = all_10_2
% 202.23/33.84    (50)   ~ (all_52_23 = all_10_2)
% 202.23/33.84    (51)   ~ (all_52_7 = all_52_23)
% 202.23/33.84    (52)  all_56_13 = all_52_15
% 202.23/33.85    (53)   ~ (all_52_17 = all_52_23)
% 202.23/33.85    (54)  all_8_1 = all_6_1
% 202.23/33.85    (55)  op(all_6_2, e3) = all_6_1
% 202.23/33.85    (56)  all_58_4 = all_52_17
% 202.23/33.85    (57)   ~ (all_14_2 = e3)
% 202.23/33.85  
% 202.23/33.85  Begin of proof
% 202.23/33.85  | 
% 202.23/33.85  | BETA: splitting (43) gives:
% 202.23/33.85  | 
% 202.23/33.85  | Case 1:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (58)  all_58_12 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | REF_CLOSE: (22), (23), (58) are inconsistent by sub-proof #1367.
% 202.23/33.85  | | 
% 202.23/33.85  | Case 2:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (59)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | BETA: splitting (37) gives:
% 202.23/33.85  | | 
% 202.23/33.85  | | Case 1:
% 202.23/33.85  | | | 
% 202.23/33.85  | | |   (60)  all_58_9 = e3
% 202.23/33.85  | | | 
% 202.23/33.85  | | | COMBINE_EQS: (15), (60) imply:
% 202.23/33.85  | | |   (61)  all_52_25 = e3
% 202.23/33.85  | | | 
% 202.23/33.85  | | | SIMP: (61) implies:
% 202.23/33.85  | | |   (62)  all_52_25 = e3
% 202.23/33.85  | | | 
% 202.23/33.85  | | | REDUCE: (11), (62) imply:
% 202.23/33.85  | | |   (63)   ~ (all_52_17 = e3)
% 202.23/33.85  | | | 
% 202.23/33.85  | | | REDUCE: (16), (62) imply:
% 202.23/33.85  | | |   (64)   ~ (all_14_2 = e3)
% 202.23/33.85  | | | 
% 202.23/33.85  | | | BETA: splitting (48) gives:
% 202.23/33.85  | | | 
% 202.23/33.85  | | | Case 1:
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | |   (65)  all_58_4 = e3
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | REF_CLOSE: (56), (63), (65) are inconsistent by sub-proof #1302.
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | Case 2:
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | |   (66)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | BETA: splitting (19) gives:
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | Case 1:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | |   (67)  all_56_13 = e3
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | COMBINE_EQS: (52), (67) imply:
% 202.23/33.85  | | | | |   (68)  all_52_15 = e3
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (2), (68) imply:
% 202.23/33.85  | | | | |   (69)   ~ (all_52_23 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | SIMP: (69) implies:
% 202.23/33.85  | | | | |   (70)   ~ (all_52_23 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | BETA: splitting (66) gives:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | Case 1:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | |   (71)  all_58_5 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REF_CLOSE: (25), (40), (71) are inconsistent by sub-proof #1279.
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | Case 2:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | |   (72)  all_58_8 = e3 | all_58_14 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REF_CLOSE: (3), (5), (13), (21), (28), (32), (70), (72) are
% 202.23/33.85  | | | | | |            inconsistent by sub-proof #899.
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | End of split
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | Case 2:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | |   (73)   ~ (all_56_13 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (52), (73) imply:
% 202.23/33.85  | | | | |   (74)   ~ (all_52_15 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (14), (18), (20),
% 202.23/33.85  | | | | |            (22), (24), (26), (27), (29), (31), (33), (34), (35), (36),
% 202.23/33.85  | | | | |            (39), (41), (42), (44), (45), (47), (49), (50), (51), (53),
% 202.23/33.85  | | | | |            (54), (55), (57), (59), (74) are inconsistent by sub-proof
% 202.23/33.85  | | | | |            #437.
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | End of split
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | End of split
% 202.23/33.85  | | | 
% 202.23/33.85  | | Case 2:
% 202.23/33.85  | | | 
% 202.23/33.85  | | |   (75)   ~ (all_58_9 = e3)
% 202.23/33.85  | | | 
% 202.23/33.85  | | | REDUCE: (15), (75) imply:
% 202.23/33.85  | | |   (76)   ~ (all_52_25 = e3)
% 202.23/33.85  | | | 
% 202.23/33.85  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 202.23/33.85  | | |            (17), (18), (20), (22), (24), (26), (27), (29), (30), (31),
% 202.23/33.85  | | |            (33), (34), (35), (36), (38), (39), (41), (42), (44), (45),
% 202.23/33.85  | | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 202.23/33.85  | | |            (57), (59), (76) are inconsistent by sub-proof #372.
% 202.23/33.85  | | | 
% 202.23/33.85  | | End of split
% 202.23/33.85  | | 
% 202.23/33.85  | End of split
% 202.23/33.85  | 
% 202.23/33.85  End of proof
% 202.23/33.85  
% 202.23/33.85  Sub-proof #372 shows that the following formulas are inconsistent:
% 202.23/33.85  ----------------------------------------------------------------
% 202.23/33.85    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.85    (2)  all_58_14 = all_52_23
% 202.23/33.85    (3)   ~ (e3 = e1)
% 202.23/33.85    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.85    (5)  all_58_1 = all_52_9
% 202.23/33.85    (6)   ~ (e3 = e0)
% 202.23/33.85    (7)  op(all_52_23, all_52_23) = e0
% 202.23/33.85    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.85    (9)   ~ (all_52_7 = all_52_15)
% 202.23/33.85    (10)  all_58_0 = all_6_2
% 202.23/33.85    (11)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.85    (12)  all_58_13 = all_52_15
% 202.23/33.85    (13)  all_58_9 = all_52_25
% 202.23/33.85    (14)   ~ (all_52_9 = all_52_15)
% 202.23/33.85    (15)   ~ (all_52_7 = all_6_2)
% 202.23/33.85    (16)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.85    (17)  all_58_12 = all_52_7
% 202.23/33.85    (18)  all_56_2 = all_52_17
% 202.23/33.85    (19)   ~ (all_52_25 = e3)
% 202.23/33.85    (20)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.85    (21)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.85    (22)  op(e0, e3) = all_52_7
% 202.23/33.85    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.85    (24)  all_58_15 = all_14_2
% 202.23/33.85    (25)  all_56_12 = all_52_7
% 202.23/33.85    (26)  all_8_2 = all_6_2
% 202.23/33.85    (27)  op(e3, all_6_1) = e2
% 202.23/33.85    (28)  op(e3, e3) = all_6_2
% 202.23/33.85    (29)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.85    (30)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.85    (31)  op(all_52_17, all_52_17) = e3
% 202.23/33.85    (32)  op(e3, e2) = all_52_9
% 202.23/33.85    (33)   ~ (all_52_17 = all_6_2)
% 202.23/33.85    (34)   ~ (e1 = e0)
% 202.23/33.85    (35)   ~ (e3 = e2)
% 202.23/33.85    (36)   ~ (all_52_9 = all_52_17)
% 202.23/33.85    (37)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.85    (38)  op(e1, e1) = all_10_2
% 202.23/33.85    (39)   ~ (all_52_23 = all_10_2)
% 202.23/33.85    (40)   ~ (all_52_7 = all_52_23)
% 202.23/33.85    (41)   ~ (all_52_17 = all_52_23)
% 202.23/33.85    (42)  all_8_1 = all_6_1
% 202.23/33.85    (43)  op(all_6_2, e3) = all_6_1
% 202.23/33.85    (44)  all_58_4 = all_52_17
% 202.23/33.85    (45)   ~ (all_14_2 = e3)
% 202.23/33.85  
% 202.23/33.85  Begin of proof
% 202.23/33.85  | 
% 202.23/33.85  | BETA: splitting (23) gives:
% 202.23/33.85  | 
% 202.23/33.85  | Case 1:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (46)  all_58_1 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | COMBINE_EQS: (5), (46) imply:
% 202.23/33.85  | |   (47)  all_52_9 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | REDUCE: (14), (47) imply:
% 202.23/33.85  | |   (48)   ~ (all_52_15 = e3)
% 202.23/33.85  | | 
% 202.23/33.85  | | SIMP: (48) implies:
% 202.23/33.85  | |   (49)   ~ (all_52_15 = e3)
% 202.23/33.85  | | 
% 202.23/33.85  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (15), (16),
% 202.23/33.85  | |            (17), (18), (20), (21), (22), (24), (25), (26), (27), (28), (30),
% 202.23/33.85  | |            (31), (32), (33), (34), (36), (38), (39), (40), (41), (42), (43),
% 202.23/33.85  | |            (45), (49) are inconsistent by sub-proof #437.
% 202.23/33.85  | | 
% 202.23/33.85  | Case 2:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (50)   ~ (all_58_1 = e3)
% 202.23/33.85  | | 
% 202.23/33.85  | | REDUCE: (5), (50) imply:
% 202.23/33.85  | |   (51)   ~ (all_52_9 = e3)
% 202.23/33.85  | | 
% 202.23/33.85  | | REF_CLOSE: (4), (5), (10), (13), (19), (27), (28), (29), (31), (33), (35),
% 202.23/33.85  | |            (37), (43), (44), (51) are inconsistent by sub-proof #446.
% 202.23/33.85  | | 
% 202.23/33.85  | End of split
% 202.23/33.85  | 
% 202.23/33.85  End of proof
% 202.23/33.85  
% 202.23/33.85  Sub-proof #373 shows that the following formulas are inconsistent:
% 202.23/33.85  ----------------------------------------------------------------
% 202.23/33.85    (1)  all_58_14 = all_52_23
% 202.23/33.85    (2)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.85    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.85    (4)  all_58_1 = all_52_9
% 202.23/33.85    (5)   ~ (all_52_3 = all_52_19)
% 202.23/33.85    (6)   ~ (all_52_3 = all_6_2)
% 202.23/33.85    (7)  all_58_0 = all_6_2
% 202.23/33.85    (8)   ~ (all_52_17 = all_10_2)
% 202.23/33.85    (9)   ~ (all_10_0 = e3)
% 202.23/33.85    (10)  all_58_9 = all_52_25
% 202.23/33.85    (11)  op(all_10_2, e1) = e3
% 202.23/33.85    (12)  all_58_12 = all_52_7
% 202.23/33.85    (13)   ~ (all_52_7 = e3)
% 202.23/33.85    (14)  all_58_2 = all_52_3
% 202.23/33.85    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.85    (16)   ~ (all_52_25 = e3)
% 202.23/33.85    (17)   ~ (all_52_23 = e3)
% 202.23/33.85    (18)  op(e3, e1) = all_52_17
% 202.23/33.85    (19)  all_58_6 = all_10_0
% 202.23/33.85    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.85    (21)  all_58_8 = all_10_2
% 202.23/33.85    (22)  op(e3, all_6_1) = e2
% 202.23/33.85    (23)  op(e3, e3) = all_6_2
% 202.23/33.85    (24)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.85    (25)  all_58_5 = all_52_19
% 202.23/33.85    (26)  op(all_52_17, all_52_17) = e3
% 202.23/33.85    (27)   ~ (all_52_17 = all_6_2)
% 202.23/33.85    (28)   ~ (e3 = e2)
% 202.23/33.85    (29)   ~ (all_52_9 = all_52_17)
% 202.23/33.85    (30)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.85    (31)  op(all_6_2, e3) = all_6_1
% 202.23/33.85    (32)  all_58_4 = all_52_17
% 202.23/33.85  
% 202.23/33.85  Begin of proof
% 202.23/33.85  | 
% 202.23/33.85  | BETA: splitting (15) gives:
% 202.23/33.85  | 
% 202.23/33.85  | Case 1:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (33)  all_58_0 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | COMBINE_EQS: (7), (33) imply:
% 202.23/33.85  | |   (34)  all_6_2 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | REF_CLOSE: (3), (22), (23), (28), (31), (34) are inconsistent by sub-proof
% 202.23/33.85  | |            #502.
% 202.23/33.85  | | 
% 202.23/33.85  | Case 2:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (35)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.23/33.85  | |            (13), (14), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 202.23/33.85  | |            (26), (27), (29), (30), (32), (35) are inconsistent by sub-proof
% 202.23/33.85  | |            #780.
% 202.23/33.85  | | 
% 202.23/33.85  | End of split
% 202.23/33.85  | 
% 202.23/33.85  End of proof
% 202.23/33.85  
% 202.23/33.85  Sub-proof #374 shows that the following formulas are inconsistent:
% 202.23/33.85  ----------------------------------------------------------------
% 202.23/33.85    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.85    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.85    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.85    (4)  all_58_14 = all_52_23
% 202.23/33.85    (5)   ~ (e3 = e1)
% 202.23/33.85    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.23/33.85    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.85    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.85    (9)   ~ (all_52_7 = all_10_0)
% 202.23/33.85    (10)  all_58_1 = all_52_9
% 202.23/33.85    (11)  op(e2, e3) = all_52_3
% 202.23/33.85    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.85    (13)   ~ (all_52_7 = all_52_15)
% 202.23/33.85    (14)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.85    (15)   ~ (all_52_17 = all_52_25)
% 202.23/33.85    (16)   ~ (all_52_3 = all_6_2)
% 202.23/33.85    (17)  all_44_2 = all_6_2
% 202.23/33.85    (18)  all_58_0 = all_6_2
% 202.23/33.85    (19)  all_56_4 = all_52_3
% 202.23/33.85    (20)   ~ (all_52_17 = all_10_2)
% 202.23/33.85    (21)   ~ (all_10_0 = e3)
% 202.23/33.85    (22)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.85    (23)  op(e3, e0) = all_52_25
% 202.23/33.85    (24)  op(e0, all_14_1) = all_14_0
% 202.23/33.85    (25)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.85    (26)  all_58_13 = all_52_15
% 202.23/33.85    (27)  all_58_9 = all_52_25
% 202.23/33.85    (28)   ~ (all_52_29 = all_14_2)
% 202.23/33.85    (29)  op(e0, e0) = all_52_30
% 202.23/33.85    (30)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.85    (31)  op(e1, e3) = all_52_5
% 202.23/33.85    (32)  op(e2, e2) = all_4_2
% 202.23/33.85    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.85    (34)   ~ (all_52_3 = all_52_5)
% 202.23/33.85    (35)  all_58_11 = all_52_29
% 202.23/33.85    (36)   ~ (all_52_9 = all_52_15)
% 202.23/33.85    (37)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.85    (38)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.85    (39)   ~ (all_52_7 = all_6_2)
% 202.23/33.85    (40)  op(e0, e0) = all_14_2
% 202.23/33.85    (41)   ~ (all_10_0 = all_6_2)
% 202.23/33.85    (42)   ~ (all_52_15 = e0)
% 202.23/33.85    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.85    (44)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.85    (45)  all_58_15 = e0
% 202.23/33.85    (46)   ~ (all_10_0 = e2)
% 202.23/33.85    (47)   ~ (all_52_25 = e0)
% 202.23/33.85    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.85    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.85    (50)   ~ (e2 = e1)
% 202.23/33.85    (51)  op(e0, e0) = e0
% 202.23/33.85    (52)  all_58_10 = all_52_27
% 202.23/33.85    (53)   ~ (all_52_3 = all_10_0)
% 202.23/33.85    (54)  all_56_8 = all_52_5
% 202.23/33.85    (55)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.85    (56)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.85    (57)   ~ (all_52_19 = all_52_23)
% 202.23/33.85    (58)   ~ (all_52_25 = all_52_29)
% 202.23/33.85    (59)  op(all_10_2, e1) = e3
% 202.23/33.85    (60)  all_58_7 = all_52_13
% 202.23/33.85    (61)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 202.23/33.85    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.85    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.85    (64)   ~ (all_52_5 = all_52_7)
% 202.23/33.85    (65)  all_58_12 = all_52_7
% 202.23/33.85    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.85    (67)  all_30_2 = all_10_2
% 202.23/33.85    (68)  all_58_2 = all_52_3
% 202.23/33.85    (69)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.85    (70)  all_56_2 = all_52_17
% 202.23/33.85    (71)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.85    (72)  op(e0, e0) = all_14_1
% 202.23/33.85    (73)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.85    (74)   ~ (all_14_0 = e3)
% 202.23/33.85    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.85    (76)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.85    (77)   ~ (all_52_5 = all_52_29)
% 202.23/33.85    (78)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.85    (79)  all_56_6 = all_52_19
% 202.23/33.85    (80)  all_56_8 = all_10_0
% 202.23/33.85    (81)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.85    (82)  op(e3, e1) = all_52_17
% 202.23/33.85    (83)  all_30_0 = all_10_0
% 202.23/33.85    (84)  all_58_6 = all_10_0
% 202.23/33.85    (85)  op(e0, e3) = all_52_7
% 202.23/33.85    (86)   ~ (all_52_9 = all_52_25)
% 202.23/33.85    (87)  op(e1, e3) = all_10_0
% 202.23/33.85    (88)  all_58_15 = all_14_2
% 202.23/33.85    (89)  op(all_52_23, all_52_23) = all_52_22
% 202.23/33.85    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.85    (91)   ~ (all_10_0 = all_10_2)
% 202.23/33.85    (92)  all_58_8 = all_10_2
% 202.23/33.85    (93)   ~ (all_52_23 = e0)
% 202.23/33.85    (94)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.85    (95)  all_56_12 = all_52_7
% 202.23/33.85    (96)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.85    (97)  all_8_2 = all_6_2
% 202.23/33.85    (98)   ~ (all_52_25 = all_6_2)
% 202.23/33.85    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.85    (100)   ~ (all_52_5 = all_6_2)
% 202.23/33.85    (101)   ~ (all_52_9 = all_6_2)
% 202.23/33.85    (102)   ~ (all_52_13 = all_52_15)
% 202.23/33.85    (103)  op(e3, all_6_1) = e2
% 202.23/33.85    (104)  all_56_0 = all_6_2
% 202.23/33.85    (105)  op(e3, e3) = all_6_2
% 202.23/33.85    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.85    (107)   ~ (all_52_27 = all_14_2)
% 202.23/33.85    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.85    (109)  all_56_14 = all_52_23
% 202.23/33.85    (110)  op(all_4_2, all_4_2) = all_52_10
% 202.23/33.85    (111)  all_56_3 = all_52_25
% 202.23/33.85    (112)   ~ (all_52_3 = all_52_7)
% 202.23/33.85    (113)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.85    (114)  all_58_5 = all_52_19
% 202.23/33.85    (115)  op(all_10_0, all_10_0) = all_52_4
% 202.23/33.85    (116)  all_56_1 = all_52_9
% 202.23/33.85    (117)   ~ (all_52_15 = all_4_2)
% 202.23/33.85    (118)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.85           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.23/33.85           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.23/33.85           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.23/33.85    (119)  all_58_6 = all_52_5
% 202.23/33.85    (120)  op(e3, e2) = all_52_9
% 202.23/33.85    (121)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.85    (122)   ~ (all_52_17 = all_6_2)
% 202.23/33.85    (123)   ~ (e3 = e2)
% 202.23/33.85    (124)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.85    (125)  all_44_1 = all_6_1
% 202.23/33.85    (126)   ~ (all_52_9 = all_52_17)
% 202.23/33.85    (127)  all_56_10 = all_10_2
% 202.23/33.85    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.85    (129)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.85    (130)  op(e1, e1) = all_10_2
% 202.23/33.85    (131)   ~ (all_52_23 = all_10_2)
% 202.23/33.85    (132)   ~ (all_52_7 = all_52_23)
% 202.23/33.85    (133)   ~ (all_52_17 = all_52_19)
% 202.23/33.85    (134)  all_58_3 = all_4_2
% 202.23/33.85    (135)  all_56_13 = all_52_15
% 202.23/33.85    (136)   ~ (all_52_3 = all_4_2)
% 202.23/33.85    (137)   ~ (all_52_19 = all_4_2)
% 202.23/33.85    (138)   ~ (all_52_17 = all_52_23)
% 202.23/33.85    (139)  all_8_1 = all_6_1
% 202.23/33.85    (140)  op(all_6_2, e3) = all_6_1
% 202.23/33.85    (141)  all_58_4 = all_52_17
% 202.23/33.85    (142)   ~ (all_14_0 = e1)
% 202.23/33.85    (143)   ~ (all_14_0 = e2)
% 202.23/33.85    (144)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.85    (145)   ~ (all_52_7 = e0)
% 202.23/33.85    (146)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.85  
% 202.23/33.85  Begin of proof
% 202.23/33.85  | 
% 202.23/33.85  | GROUND_INST: instantiating (8) with all_14_1, all_52_30, e0, e0, simplifying
% 202.23/33.85  |              with (29), (72) gives:
% 202.23/33.85  |   (147)  all_52_30 = all_14_1
% 202.23/33.85  | 
% 202.23/33.85  | GROUND_INST: instantiating (8) with e0, all_52_30, e0, e0, simplifying with
% 202.23/33.85  |              (29), (51) gives:
% 202.23/33.85  |   (148)  all_52_30 = e0
% 202.23/33.85  | 
% 202.23/33.85  | COMBINE_EQS: (147), (148) imply:
% 202.23/33.85  |   (149)  all_14_1 = e0
% 202.23/33.85  | 
% 202.23/33.85  | REDUCE: (24), (149) imply:
% 202.23/33.85  |   (150)  op(e0, e0) = all_14_0
% 202.23/33.85  | 
% 202.23/33.85  | GROUND_INST: instantiating (8) with e0, all_14_0, e0, e0, simplifying with
% 202.23/33.85  |              (51), (150) gives:
% 202.23/33.85  |   (151)  all_14_0 = e0
% 202.23/33.85  | 
% 202.23/33.85  | REDUCE: (74), (151) imply:
% 202.23/33.85  |   (152)   ~ (e3 = e0)
% 202.23/33.85  | 
% 202.23/33.85  | SIMP: (152) implies:
% 202.23/33.85  |   (153)   ~ (e3 = e0)
% 202.23/33.85  | 
% 202.23/33.85  | REDUCE: (143), (151) imply:
% 202.23/33.85  |   (154)   ~ (e2 = e0)
% 202.23/33.85  | 
% 202.23/33.85  | SIMP: (154) implies:
% 202.23/33.85  |   (155)   ~ (e2 = e0)
% 202.23/33.85  | 
% 202.23/33.85  | REDUCE: (142), (151) imply:
% 202.23/33.85  |   (156)   ~ (e1 = e0)
% 202.23/33.85  | 
% 202.23/33.85  | SIMP: (156) implies:
% 202.23/33.85  |   (157)   ~ (e1 = e0)
% 202.23/33.85  | 
% 202.23/33.85  | BETA: splitting (90) gives:
% 202.23/33.85  | 
% 202.23/33.85  | Case 1:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (158)  all_56_8 = e3
% 202.23/33.85  | | 
% 202.23/33.85  | | REF_CLOSE: (21), (80), (158) are inconsistent by sub-proof #926.
% 202.23/33.85  | | 
% 202.23/33.85  | Case 2:
% 202.23/33.85  | | 
% 202.23/33.85  | |   (159)   ~ (all_56_8 = e3)
% 202.23/33.85  | |   (160)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.85  | | 
% 202.23/33.85  | | BETA: splitting (118) gives:
% 202.23/33.85  | | 
% 202.23/33.85  | | Case 1:
% 202.23/33.85  | | | 
% 202.23/33.85  | | |   (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.85  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 202.23/33.85  | | |            e0)
% 202.23/33.85  | | | 
% 202.23/33.85  | | | BETA: splitting (161) gives:
% 202.23/33.85  | | | 
% 202.23/33.85  | | | Case 1:
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | |   (162)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | REF_CLOSE: (7), (8), (11), (14), (18), (21), (32), (38), (43), (46),
% 202.23/33.85  | | | |            (65), (68), (71), (81), (84), (103), (104), (105), (110),
% 202.23/33.85  | | | |            (123), (129), (136), (140), (155), (162) are inconsistent by
% 202.23/33.85  | | | |            sub-proof #387.
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | Case 2:
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | |   (163)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 202.23/33.85  | | | |          e0
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | ALPHA: (163) implies:
% 202.23/33.85  | | | |   (164)  all_52_14 = e0
% 202.23/33.85  | | | |   (165)  all_52_8 = e3
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | REDUCE: (55), (165) imply:
% 202.23/33.85  | | | |   (166)  op(all_52_9, all_52_9) = e3
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | REDUCE: (56), (164) imply:
% 202.23/33.85  | | | |   (167)  op(all_52_15, all_52_15) = e0
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | BETA: splitting (48) gives:
% 202.23/33.85  | | | | 
% 202.23/33.85  | | | | Case 1:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | |   (168)  all_56_13 = e3
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | COMBINE_EQS: (135), (168) imply:
% 202.23/33.85  | | | | |   (169)  all_52_15 = e3
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | SIMP: (169) implies:
% 202.23/33.85  | | | | |   (170)  all_52_15 = e3
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | COMBINE_EQS: (26), (170) imply:
% 202.23/33.85  | | | | |   (171)  all_58_13 = e3
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (13), (170) imply:
% 202.23/33.85  | | | | |   (172)   ~ (all_52_7 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (167), (170) imply:
% 202.23/33.85  | | | | |   (173)  op(e3, e3) = e0
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | GROUND_INST: instantiating (8) with all_6_2, e0, e3, e3, simplifying
% 202.23/33.85  | | | | |              with (105), (173) gives:
% 202.23/33.85  | | | | |   (174)  all_6_2 = e0
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | COMBINE_EQS: (18), (174) imply:
% 202.23/33.85  | | | | |   (175)  all_58_0 = e0
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (41), (174) imply:
% 202.23/33.85  | | | | |   (176)   ~ (all_10_0 = e0)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (140), (174) imply:
% 202.23/33.85  | | | | |   (177)  op(e0, e3) = all_6_1
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | BETA: splitting (71) gives:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | Case 1:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | |   (178)  all_58_0 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REF_CLOSE: (153), (175), (178) are inconsistent by sub-proof #1015.
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | Case 2:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | |   (179)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | BETA: splitting (160) gives:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | Case 1:
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | |   (180)  all_56_8 = e2
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | | REF_CLOSE: (46), (80), (180) are inconsistent by sub-proof #915.
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | Case 2:
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | |   (181)   ~ (all_56_8 = e2)
% 202.23/33.85  | | | | | | |   (182)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | | BETA: splitting (182) gives:
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | | Case 1:
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | |   (183)  all_56_8 = e1
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | COMBINE_EQS: (80), (183) imply:
% 202.23/33.85  | | | | | | | |   (184)  all_10_0 = e1
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | SIMP: (184) implies:
% 202.23/33.85  | | | | | | | |   (185)  all_10_0 = e1
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | REDUCE: (9), (185) imply:
% 202.23/33.85  | | | | | | | |   (186)   ~ (all_52_7 = e1)
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | REDUCE: (21), (185) imply:
% 202.23/33.85  | | | | | | | |   (187)   ~ (e3 = e1)
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | REDUCE: (46), (185) imply:
% 202.23/33.85  | | | | | | | |   (188)   ~ (e2 = e1)
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | BETA: splitting (78) gives:
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | Case 1:
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | |   (189)  all_58_12 = e1
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | REF_CLOSE: (65), (186), (189) are inconsistent by sub-proof
% 202.23/33.85  | | | | | | | | |            #1127.
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | Case 2:
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | |   (190)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | BETA: splitting (190) gives:
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | Case 1:
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | |   (191)  all_58_13 = e1
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | REF_CLOSE: (5), (171), (191) are inconsistent by sub-proof
% 202.23/33.85  | | | | | | | | | |            #770.
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | Case 2:
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | |   (192)  all_58_14 = e1 | all_58_15 = e1
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | BETA: splitting (192) gives:
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | Case 1:
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | |   (193)  all_58_14 = e1
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | BETA: splitting (37) gives:
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | Case 1:
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | |   (194)  all_58_12 = e2
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | | COMBINE_EQS: (65), (194) imply:
% 202.23/33.85  | | | | | | | | | | | |   (195)  all_52_7 = e2
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | | SIMP: (195) implies:
% 202.23/33.85  | | | | | | | | | | | |   (196)  all_52_7 = e2
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | | REDUCE: (14), (196) imply:
% 202.23/33.85  | | | | | | | | | | | |   (197)  op(e2, e2) = all_52_6
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | | REDUCE: (85), (196) imply:
% 202.23/33.85  | | | | | | | | | | | |   (198)  op(e0, e3) = e2
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | | REF_CLOSE: (8), (19), (21), (32), (65), (68), (76), (84),
% 202.23/33.85  | | | | | | | | | | | |            (103), (120), (136), (166), (172), (177), (179),
% 202.23/33.85  | | | | | | | | | | | |            (197), (198) are inconsistent by sub-proof #386.
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | Case 2:
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | |   (199)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | | REF_CLOSE: (45), (50), (123), (155), (171), (193), (199) are
% 202.23/33.85  | | | | | | | | | | | |            inconsistent by sub-proof #385.
% 202.23/33.85  | | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | End of split
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | Case 2:
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | |   (200)  all_58_15 = e1
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | | REF_CLOSE: (45), (157), (200) are inconsistent by sub-proof
% 202.23/33.85  | | | | | | | | | | |            #1207.
% 202.23/33.85  | | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | | End of split
% 202.23/33.85  | | | | | | | | | | 
% 202.23/33.85  | | | | | | | | | End of split
% 202.23/33.85  | | | | | | | | | 
% 202.23/33.85  | | | | | | | | End of split
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | Case 2:
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | |   (201)  all_56_8 = e0
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | | REF_CLOSE: (80), (176), (201) are inconsistent by sub-proof
% 202.23/33.85  | | | | | | | |            #883.
% 202.23/33.85  | | | | | | | | 
% 202.23/33.85  | | | | | | | End of split
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | End of split
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | End of split
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | Case 2:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | |   (202)   ~ (all_56_13 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | REDUCE: (135), (202) imply:
% 202.23/33.85  | | | | |   (203)   ~ (all_52_15 = e3)
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | BETA: splitting (121) gives:
% 202.23/33.85  | | | | | 
% 202.23/33.85  | | | | | Case 1:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | |   (204)  all_58_12 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | COMBINE_EQS: (65), (204) imply:
% 202.23/33.85  | | | | | |   (205)  all_52_7 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | SIMP: (205) implies:
% 202.23/33.85  | | | | | |   (206)  all_52_7 = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REDUCE: (112), (206) imply:
% 202.23/33.85  | | | | | |   (207)   ~ (all_52_3 = e3)
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REDUCE: (39), (206) imply:
% 202.23/33.85  | | | | | |   (208)   ~ (all_6_2 = e3)
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | SIMP: (208) implies:
% 202.23/33.85  | | | | | |   (209)   ~ (all_6_2 = e3)
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REDUCE: (14), (206) imply:
% 202.23/33.85  | | | | | |   (210)  op(e3, e3) = all_52_6
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | REDUCE: (85), (206) imply:
% 202.23/33.85  | | | | | |   (211)  op(e0, e3) = e3
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_6, e3, e3,
% 202.23/33.85  | | | | | |              simplifying with (105), (210) gives:
% 202.23/33.85  | | | | | |   (212)  all_52_6 = all_6_2
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | BETA: splitting (81) gives:
% 202.23/33.85  | | | | | | 
% 202.23/33.85  | | | | | | Case 1:
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | |   (213)  all_58_0 = e2
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | | COMBINE_EQS: (18), (213) imply:
% 202.23/33.85  | | | | | | |   (214)  all_6_2 = e2
% 202.23/33.85  | | | | | | | 
% 202.23/33.85  | | | | | | | REDUCE: (16), (214) imply:
% 202.23/33.86  | | | | | | |   (215)   ~ (all_52_3 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (101), (214) imply:
% 202.23/33.86  | | | | | | |   (216)   ~ (all_52_9 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (122), (214) imply:
% 202.23/33.86  | | | | | | |   (217)   ~ (all_52_17 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (98), (214) imply:
% 202.23/33.86  | | | | | | |   (218)   ~ (all_52_25 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (209), (214) imply:
% 202.23/33.86  | | | | | | |   (219)   ~ (e3 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (140), (214) imply:
% 202.23/33.86  | | | | | | |   (220)  op(e2, e3) = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | GROUND_INST: instantiating (8) with all_52_3, all_6_1, e3, e2,
% 202.23/33.86  | | | | | | |              simplifying with (11), (220) gives:
% 202.23/33.86  | | | | | | |   (221)  all_52_3 = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | COMBINE_EQS: (19), (221) imply:
% 202.23/33.86  | | | | | | |   (222)  all_56_4 = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | COMBINE_EQS: (68), (221) imply:
% 202.23/33.86  | | | | | | |   (223)  all_58_2 = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (207), (221) imply:
% 202.23/33.86  | | | | | | |   (224)   ~ (all_6_1 = e3)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (215), (221) imply:
% 202.23/33.86  | | | | | | |   (225)   ~ (all_6_1 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | BETA: splitting (99) gives:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (226)  all_56_3 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REF_CLOSE: (8), (23), (33), (63), (76), (82), (103), (111),
% 202.23/33.86  | | | | | | | |            (155), (213), (217), (218), (222), (223), (224),
% 202.23/33.86  | | | | | | | |            (225), (226) are inconsistent by sub-proof #384.
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (227)   ~ (all_56_3 = e3)
% 202.23/33.86  | | | | | | | |   (228)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (111), (227) imply:
% 202.23/33.86  | | | | | | | |   (229)   ~ (all_52_25 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | BETA: splitting (228) gives:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (230)  all_56_3 = e2
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | REF_CLOSE: (111), (218), (230) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | |            #1259.
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (231)  all_56_3 = e1 | all_56_3 = e0
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | BETA: splitting (231) gives:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (232)  all_56_3 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | COMBINE_EQS: (111), (232) imply:
% 202.23/33.86  | | | | | | | | | |   (233)  all_52_25 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (233) implies:
% 202.23/33.86  | | | | | | | | | |   (234)  all_52_25 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (86), (234) imply:
% 202.23/33.86  | | | | | | | | | |   (235)   ~ (all_52_9 = e1)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | BETA: splitting (49) gives:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (236)  all_56_2 = e3
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | COMBINE_EQS: (70), (236) imply:
% 202.23/33.86  | | | | | | | | | | |   (237)  all_52_17 = e3
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | SIMP: (237) implies:
% 202.23/33.86  | | | | | | | | | | |   (238)  all_52_17 = e3
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REDUCE: (126), (238) imply:
% 202.23/33.86  | | | | | | | | | | |   (239)   ~ (all_52_9 = e3)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | BETA: splitting (124) gives:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | |   (240)  all_56_1 = e3
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | REF_CLOSE: (116), (239), (240) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | | |            #1326.
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | |   (241)   ~ (all_56_1 = e3)
% 202.23/33.86  | | | | | | | | | | | |   (242)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | BETA: splitting (242) gives:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | |   (243)  all_56_1 = e2
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REF_CLOSE: (116), (216), (243) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | | | |            #1194.
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | |   (244)  all_56_1 = e1 | all_56_1 = e0
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | BETA: splitting (73) gives:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | |   (245)  all_58_0 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | COMBINE_EQS: (213), (245) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (246)  e2 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REDUCE: (155), (246) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (247)  $false
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | |   (248)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (51), (116), (166), (235), (239),
% 202.23/33.86  | | | | | | | | | | | | | |            (244), (248) are inconsistent by sub-proof #1333.
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (249)   ~ (all_56_2 = e3)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REDUCE: (70), (249) imply:
% 202.23/33.86  | | | | | | | | | | |   (250)   ~ (all_52_17 = e3)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REF_CLOSE: (8), (10), (18), (27), (101), (103), (105), (108),
% 202.23/33.86  | | | | | | | | | | |            (123), (140), (141), (166), (229), (250) are
% 202.23/33.86  | | | | | | | | | | |            inconsistent by sub-proof #492.
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (251)  all_56_3 = e0
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REF_CLOSE: (47), (111), (251) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | |            #1258.
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | End of split
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | Case 2:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (252)   ~ (all_58_0 = e2)
% 202.23/33.86  | | | | | | |   (253)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REF_CLOSE: (8), (17), (18), (22), (33), (41), (46), (75), (80),
% 202.23/33.86  | | | | | | |            (84), (87), (103), (104), (105), (123), (125), (129),
% 202.23/33.86  | | | | | | |            (140), (153), (155), (157), (160), (204), (209), (210),
% 202.23/33.86  | | | | | | |            (211), (252), (253) are inconsistent by sub-proof #381.
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | End of split
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | Case 2:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | |   (254)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | BETA: splitting (254) gives:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | Case 1:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (255)  all_58_13 = e3
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REF_CLOSE: (26), (203), (255) are inconsistent by sub-proof #1360.
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | Case 2:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (256)  all_58_14 = e3 | all_58_15 = e3
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | BETA: splitting (256) gives:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (257)  all_58_14 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | COMBINE_EQS: (4), (257) imply:
% 202.23/33.86  | | | | | | | |   (258)  all_52_23 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (258) implies:
% 202.23/33.86  | | | | | | | |   (259)  all_52_23 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (132), (259) imply:
% 202.23/33.86  | | | | | | | |   (260)   ~ (all_52_7 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (131), (259) imply:
% 202.23/33.86  | | | | | | | |   (261)   ~ (all_10_2 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (261) implies:
% 202.23/33.86  | | | | | | | |   (262)   ~ (all_10_2 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (89), (259) imply:
% 202.23/33.86  | | | | | | | |   (263)  op(e3, e3) = all_52_22
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_22, e3, e3,
% 202.23/33.86  | | | | | | | |              simplifying with (105), (263) gives:
% 202.23/33.86  | | | | | | | |   (264)  all_52_22 = all_6_2
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | BETA: splitting (71) gives:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (265)  all_58_0 = e3
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | COMBINE_EQS: (18), (265) imply:
% 202.23/33.86  | | | | | | | | |   (266)  all_6_2 = e3
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | REF_CLOSE: (8), (103), (105), (123), (140), (266) are
% 202.23/33.86  | | | | | | | | |            inconsistent by sub-proof #502.
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (267)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | BETA: splitting (267) gives:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (268)  all_58_2 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | COMBINE_EQS: (68), (268) imply:
% 202.23/33.86  | | | | | | | | | |   (269)  all_52_3 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (269) implies:
% 202.23/33.86  | | | | | | | | | |   (270)  all_52_3 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (112), (270) imply:
% 202.23/33.86  | | | | | | | | | |   (271)   ~ (all_52_7 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (53), (270) imply:
% 202.23/33.86  | | | | | | | | | |   (272)   ~ (all_10_0 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (16), (270) imply:
% 202.23/33.86  | | | | | | | | | |   (273)   ~ (all_6_2 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (273) implies:
% 202.23/33.86  | | | | | | | | | |   (274)   ~ (all_6_2 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | BETA: splitting (81) gives:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (275)  all_58_0 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | COMBINE_EQS: (18), (275) imply:
% 202.23/33.86  | | | | | | | | | | |   (276)  all_6_2 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REF_CLOSE: (8), (33), (59), (61), (65), (67), (83), (84),
% 202.23/33.86  | | | | | | | | | | |            (91), (127), (130), (144), (145), (153), (155),
% 202.23/33.86  | | | | | | | | | | |            (262), (268), (275) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | |            #379.
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (277)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | BETA: splitting (277) gives:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | |   (278)  all_58_2 = e2
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | REF_CLOSE: (123), (268), (278) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | | |            #1124.
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | |   (279)  all_58_6 = e2 | all_58_12 = e2
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | BETA: splitting (279) gives:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | |   (280)  all_58_6 = e2
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REF_CLOSE: (46), (84), (280) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | | | |            #917.
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | |   (281)  all_58_12 = e2
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | COMBINE_EQS: (65), (281) imply:
% 202.23/33.86  | | | | | | | | | | | | |   (282)  all_52_7 = e2
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | SIMP: (282) implies:
% 202.23/33.86  | | | | | | | | | | | | |   (283)  all_52_7 = e2
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REDUCE: (9), (283) imply:
% 202.23/33.86  | | | | | | | | | | | | |   (284)   ~ (all_10_0 = e2)
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REDUCE: (39), (283) imply:
% 202.23/33.86  | | | | | | | | | | | | |   (285)   ~ (all_6_2 = e2)
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | SIMP: (285) implies:
% 202.23/33.86  | | | | | | | | | | | | |   (286)   ~ (all_6_2 = e2)
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REDUCE: (14), (283) imply:
% 202.23/33.86  | | | | | | | | | | | | |   (287)  op(e2, e2) = all_52_6
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REDUCE: (85), (283) imply:
% 202.23/33.86  | | | | | | | | | | | | |   (288)  op(e0, e3) = e2
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | |   (289)  all_58_0 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | COMBINE_EQS: (18), (289) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (290)  all_6_2 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REDUCE: (140), (290) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (291)  op(e0, e3) = all_6_1
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (21), (32), (65), (68), (76), (84),
% 202.23/33.86  | | | | | | | | | | | | | |            (103), (120), (136), (166), (260), (267), (287),
% 202.23/33.86  | | | | | | | | | | | | | |            (288), (291) are inconsistent by sub-proof #386.
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | |   (292)   ~ (all_58_0 = e0)
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REDUCE: (18), (292) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (293)   ~ (all_6_2 = e0)
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | |   (294)  all_56_0 = e3
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | COMBINE_EQS: (104), (294) imply:
% 202.23/33.86  | | | | | | | | | | | | | | |   (295)  all_6_2 = e3
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | REDUCE: (274), (295) imply:
% 202.23/33.86  | | | | | | | | | | | | | | |   (296)  $false
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent.
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | |   (297)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | |   (298)  all_56_0 = e2
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (298) imply:
% 202.23/33.86  | | | | | | | | | | | | | | | |   (299)  all_6_2 = e2
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | REDUCE: (286), (299) imply:
% 202.23/33.86  | | | | | | | | | | | | | | | |   (300)  $false
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent.
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | |   (301)  all_56_0 = e1 | all_56_0 = e0
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | |   (302)  all_56_0 = e1
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (302) imply:
% 202.23/33.86  | | | | | | | | | | | | | | | | |   (303)  all_6_2 = e1
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (22), (41), (46), (80), (87), (125),
% 202.23/33.86  | | | | | | | | | | | | | | | | |            (140), (160), (303) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | | | | | | | |            #378.
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | |   (304)  all_56_0 = e0
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (304) imply:
% 202.23/33.86  | | | | | | | | | | | | | | | | |   (305)  all_6_2 = e0
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | | REDUCE: (293), (305) imply:
% 202.23/33.86  | | | | | | | | | | | | | | | | |   (306)  $false
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | | CLOSE: (306) is inconsistent.
% 202.23/33.86  | | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (307)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REF_CLOSE: (21), (65), (84), (260), (307) are inconsistent by
% 202.23/33.86  | | | | | | | | | |            sub-proof #921.
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (308)  all_58_15 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REF_CLOSE: (45), (153), (308) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | |            #1350.
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | End of split
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | End of split
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | End of split
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | End of split
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | End of split
% 202.23/33.86  | | | 
% 202.23/33.86  | | Case 2:
% 202.23/33.86  | | | 
% 202.23/33.86  | | |   (309)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.23/33.86  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.23/33.86  | | |            all_52_30 = e0)
% 202.23/33.86  | | | 
% 202.23/33.86  | | | BETA: splitting (309) gives:
% 202.23/33.86  | | | 
% 202.23/33.86  | | | Case 1:
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | |   (310)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 202.23/33.86  | | | |          e0
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | | ALPHA: (310) implies:
% 202.23/33.86  | | | |   (311)  all_52_22 = e0
% 202.23/33.86  | | | |   (312)  all_52_16 = e3
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | | REDUCE: (96), (312) imply:
% 202.23/33.86  | | | |   (313)  op(all_52_17, all_52_17) = e3
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | | REDUCE: (89), (311) imply:
% 202.23/33.86  | | | |   (314)  op(all_52_23, all_52_23) = e0
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | | BETA: splitting (48) gives:
% 202.23/33.86  | | | | 
% 202.23/33.86  | | | | Case 1:
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | |   (315)  all_56_13 = e3
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | COMBINE_EQS: (135), (315) imply:
% 202.23/33.86  | | | | |   (316)  all_52_15 = e3
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | SIMP: (316) implies:
% 202.23/33.86  | | | | |   (317)  all_52_15 = e3
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | COMBINE_EQS: (26), (317) imply:
% 202.23/33.86  | | | | |   (318)  all_58_13 = e3
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (13), (317) imply:
% 202.23/33.86  | | | | |   (319)   ~ (all_52_7 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (36), (317) imply:
% 202.23/33.86  | | | | |   (320)   ~ (all_52_9 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (102), (317) imply:
% 202.23/33.86  | | | | |   (321)   ~ (all_52_13 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (2), (317) imply:
% 202.23/33.86  | | | | |   (322)   ~ (all_52_23 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | SIMP: (322) implies:
% 202.23/33.86  | | | | |   (323)   ~ (all_52_23 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (117), (317) imply:
% 202.23/33.86  | | | | |   (324)   ~ (all_4_2 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | SIMP: (324) implies:
% 202.23/33.86  | | | | |   (325)   ~ (all_4_2 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (56), (317) imply:
% 202.23/33.86  | | | | |   (326)  op(e3, e3) = all_52_14
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_14, e3, e3,
% 202.23/33.86  | | | | |              simplifying with (105), (326) gives:
% 202.23/33.86  | | | | |   (327)  all_52_14 = all_6_2
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | BETA: splitting (62) gives:
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | Case 1:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | |   (328)  all_56_14 = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | REF_CLOSE: (109), (323), (328) are inconsistent by sub-proof #1286.
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | Case 2:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | |   (329)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | BETA: splitting (66) gives:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | Case 1:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (330)  all_58_6 = e3
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REF_CLOSE: (21), (84), (330) are inconsistent by sub-proof #922.
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | Case 2:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (331)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | BETA: splitting (78) gives:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (332)  all_58_12 = e1
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | COMBINE_EQS: (65), (332) imply:
% 202.23/33.86  | | | | | | | |   (333)  all_52_7 = e1
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (333) implies:
% 202.23/33.86  | | | | | | | |   (334)  all_52_7 = e1
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (132), (334) imply:
% 202.23/33.86  | | | | | | | |   (335)   ~ (all_52_23 = e1)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (335) implies:
% 202.23/33.86  | | | | | | | |   (336)   ~ (all_52_23 = e1)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (9), (334) imply:
% 202.23/33.86  | | | | | | | |   (337)   ~ (all_10_0 = e1)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (337) implies:
% 202.23/33.86  | | | | | | | |   (338)   ~ (all_10_0 = e1)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | BETA: splitting (160) gives:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (339)  all_56_8 = e2
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | REF_CLOSE: (46), (80), (339) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | |            #915.
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (340)   ~ (all_56_8 = e2)
% 202.23/33.86  | | | | | | | | |   (341)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | BETA: splitting (329) gives:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (342)  all_56_14 = e2
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | COMBINE_EQS: (109), (342) imply:
% 202.23/33.86  | | | | | | | | | |   (343)  all_52_23 = e2
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (343) implies:
% 202.23/33.86  | | | | | | | | | |   (344)  all_52_23 = e2
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | COMBINE_EQS: (4), (344) imply:
% 202.23/33.86  | | | | | | | | | |   (345)  all_58_14 = e2
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (314), (344) imply:
% 202.23/33.86  | | | | | | | | | |   (346)  op(e2, e2) = e0
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | BETA: splitting (341) gives:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (347)  all_56_8 = e1
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REF_CLOSE: (80), (338), (347) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | |            #914.
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (348)  all_56_8 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | COMBINE_EQS: (80), (348) imply:
% 202.23/33.86  | | | | | | | | | | |   (349)  all_10_0 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | SIMP: (349) implies:
% 202.23/33.86  | | | | | | | | | | |   (350)  all_10_0 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REDUCE: (91), (350) imply:
% 202.23/33.86  | | | | | | | | | | |   (351)   ~ (all_10_2 = e0)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | SIMP: (351) implies:
% 202.23/33.86  | | | | | | | | | | |   (352)   ~ (all_10_2 = e0)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REDUCE: (115), (350) imply:
% 202.23/33.86  | | | | | | | | | | |   (353)  op(e0, e0) = all_52_4
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, all_52_4, e0, e0,
% 202.23/33.86  | | | | | | | | | | |              simplifying with (51), (353) gives:
% 202.23/33.86  | | | | | | | | | | |   (354)  all_52_4 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, e0, e2, e2,
% 202.23/33.86  | | | | | | | | | | |              simplifying with (32), (346) gives:
% 202.23/33.86  | | | | | | | | | | |   (355)  all_4_2 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REDUCE: (137), (355) imply:
% 202.23/33.86  | | | | | | | | | | |   (356)   ~ (all_52_19 = e0)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | BETA: splitting (6) gives:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | |   (357)  all_58_4 = e0
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | COMBINE_EQS: (141), (357) imply:
% 202.23/33.86  | | | | | | | | | | | |   (358)  all_52_17 = e0
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | REDUCE: (313), (358) imply:
% 202.23/33.86  | | | | | | | | | | | |   (359)  op(e0, e0) = e3
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | REF_CLOSE: (8), (51), (153), (359) are inconsistent by
% 202.23/33.86  | | | | | | | | | | | |            sub-proof #1336.
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | |   (360)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | BETA: splitting (360) gives:
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | |   (361)  all_58_5 = e0
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | REF_CLOSE: (114), (356), (361) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | | | | |            #754.
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | |   (362)  all_58_8 = e0 | all_58_14 = e0
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | BETA: splitting (362) gives:
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | |   (363)  all_58_8 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | COMBINE_EQS: (92), (363) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (364)  all_10_2 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REDUCE: (352), (364) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (365)  $false
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | CLOSE: (365) is inconsistent.
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | |   (366)  all_58_14 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | COMBINE_EQS: (345), (366) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (367)  e2 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | SIMP: (367) implies:
% 202.23/33.86  | | | | | | | | | | | | | |   (368)  e2 = e0
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | REDUCE: (155), (368) imply:
% 202.23/33.86  | | | | | | | | | | | | | |   (369)  $false
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | | CLOSE: (369) is inconsistent.
% 202.23/33.86  | | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (370)  all_56_14 = e1 | all_56_14 = e0
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REF_CLOSE: (93), (109), (336), (370) are inconsistent by
% 202.23/33.86  | | | | | | | | | |            sub-proof #1381.
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (371)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | BETA: splitting (371) gives:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (372)  all_58_13 = e1
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | REF_CLOSE: (5), (318), (372) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | |            #770.
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (373)  all_58_14 = e1 | all_58_15 = e1
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | BETA: splitting (373) gives:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (374)  all_58_14 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | COMBINE_EQS: (4), (374) imply:
% 202.23/33.86  | | | | | | | | | |   (375)  all_52_23 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (375) implies:
% 202.23/33.86  | | | | | | | | | |   (376)  all_52_23 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (314), (376) imply:
% 202.23/33.86  | | | | | | | | | |   (377)  op(e1, e1) = e0
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | BETA: splitting (37) gives:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (378)  all_58_12 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | COMBINE_EQS: (65), (378) imply:
% 202.23/33.86  | | | | | | | | | | |   (379)  all_52_7 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | SIMP: (379) implies:
% 202.23/33.86  | | | | | | | | | | |   (380)  all_52_7 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REDUCE: (319), (380) imply:
% 202.23/33.86  | | | | | | | | | | |   (381)   ~ (e3 = e2)
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, e0, e1, e1,
% 202.23/33.86  | | | | | | | | | | |              simplifying with (130), (377) gives:
% 202.23/33.86  | | | | | | | | | | |   (382)  all_10_2 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | COMBINE_EQS: (92), (382) imply:
% 202.23/33.86  | | | | | | | | | | |   (383)  all_58_8 = e0
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REF_CLOSE: (8), (10), (18), (27), (35), (58), (60), (103),
% 202.23/33.86  | | | | | | | | | | |            (105), (108), (122), (123), (128), (140), (141),
% 202.23/33.86  | | | | | | | | | | |            (153), (313), (320), (321), (331), (383) are
% 202.23/33.86  | | | | | | | | | | |            inconsistent by sub-proof #377.
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | |   (384)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | | REF_CLOSE: (45), (50), (123), (155), (318), (374), (384) are
% 202.23/33.86  | | | | | | | | | | |            inconsistent by sub-proof #385.
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (385)  all_58_15 = e1
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REF_CLOSE: (45), (157), (385) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | | |            #1207.
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | End of split
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | End of split
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | End of split
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | End of split
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | Case 2:
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | |   (386)   ~ (all_56_13 = e3)
% 202.23/33.86  | | | | |   (387)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | REDUCE: (135), (386) imply:
% 202.23/33.86  | | | | |   (388)   ~ (all_52_15 = e3)
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | BETA: splitting (121) gives:
% 202.23/33.86  | | | | | 
% 202.23/33.86  | | | | | Case 1:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | |   (389)  all_58_12 = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | COMBINE_EQS: (65), (389) imply:
% 202.23/33.86  | | | | | |   (390)  all_52_7 = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | SIMP: (390) implies:
% 202.23/33.86  | | | | | |   (391)  all_52_7 = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | REDUCE: (112), (391) imply:
% 202.23/33.86  | | | | | |   (392)   ~ (all_52_3 = e3)
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | REDUCE: (39), (391) imply:
% 202.23/33.86  | | | | | |   (393)   ~ (all_6_2 = e3)
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | SIMP: (393) implies:
% 202.23/33.86  | | | | | |   (394)   ~ (all_6_2 = e3)
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | REDUCE: (14), (391) imply:
% 202.23/33.86  | | | | | |   (395)  op(e3, e3) = all_52_6
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | REDUCE: (85), (391) imply:
% 202.23/33.86  | | | | | |   (396)  op(e0, e3) = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_6, e3, e3,
% 202.23/33.86  | | | | | |              simplifying with (105), (395) gives:
% 202.23/33.86  | | | | | |   (397)  all_52_6 = all_6_2
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | BETA: splitting (81) gives:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | Case 1:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (398)  all_58_0 = e2
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | COMBINE_EQS: (18), (398) imply:
% 202.23/33.86  | | | | | | |   (399)  all_6_2 = e2
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (16), (399) imply:
% 202.23/33.86  | | | | | | |   (400)   ~ (all_52_3 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (122), (399) imply:
% 202.23/33.86  | | | | | | |   (401)   ~ (all_52_17 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (98), (399) imply:
% 202.23/33.86  | | | | | | |   (402)   ~ (all_52_25 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (140), (399) imply:
% 202.23/33.86  | | | | | | |   (403)  op(e2, e3) = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | GROUND_INST: instantiating (8) with all_52_3, all_6_1, e3, e2,
% 202.23/33.86  | | | | | | |              simplifying with (11), (403) gives:
% 202.23/33.86  | | | | | | |   (404)  all_52_3 = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | COMBINE_EQS: (19), (404) imply:
% 202.23/33.86  | | | | | | |   (405)  all_56_4 = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | COMBINE_EQS: (68), (404) imply:
% 202.23/33.86  | | | | | | |   (406)  all_58_2 = all_6_1
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (392), (404) imply:
% 202.23/33.86  | | | | | | |   (407)   ~ (all_6_1 = e3)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REDUCE: (400), (404) imply:
% 202.23/33.86  | | | | | | |   (408)   ~ (all_6_1 = e2)
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | BETA: splitting (99) gives:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (409)  all_56_3 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REF_CLOSE: (8), (23), (33), (63), (76), (82), (103), (111),
% 202.23/33.86  | | | | | | | |            (155), (398), (401), (402), (405), (406), (407),
% 202.23/33.86  | | | | | | | |            (408), (409) are inconsistent by sub-proof #384.
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (410)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REF_CLOSE: (8), (15), (47), (49), (51), (70), (105), (111),
% 202.23/33.86  | | | | | | | |            (313), (394), (401), (402), (410) are inconsistent by
% 202.23/33.86  | | | | | | | |            sub-proof #1257.
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | End of split
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | Case 2:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (411)   ~ (all_58_0 = e2)
% 202.23/33.86  | | | | | | |   (412)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REF_CLOSE: (8), (17), (18), (22), (33), (41), (46), (75), (80),
% 202.23/33.86  | | | | | | |            (84), (87), (103), (104), (105), (123), (125), (129),
% 202.23/33.86  | | | | | | |            (140), (153), (155), (157), (160), (389), (394), (395),
% 202.23/33.86  | | | | | | |            (396), (411), (412) are inconsistent by sub-proof #381.
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | End of split
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | Case 2:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | |   (413)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | BETA: splitting (413) gives:
% 202.23/33.86  | | | | | | 
% 202.23/33.86  | | | | | | Case 1:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (414)  all_58_13 = e3
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | REF_CLOSE: (26), (388), (414) are inconsistent by sub-proof #1360.
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | Case 2:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | |   (415)  all_58_14 = e3 | all_58_15 = e3
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | BETA: splitting (415) gives:
% 202.23/33.86  | | | | | | | 
% 202.23/33.86  | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | |   (416)  all_58_14 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | COMBINE_EQS: (4), (416) imply:
% 202.23/33.86  | | | | | | | |   (417)  all_52_23 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (417) implies:
% 202.23/33.86  | | | | | | | |   (418)  all_52_23 = e3
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (138), (418) imply:
% 202.23/33.86  | | | | | | | |   (419)   ~ (all_52_17 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (57), (418) imply:
% 202.23/33.86  | | | | | | | |   (420)   ~ (all_52_19 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (131), (418) imply:
% 202.23/33.86  | | | | | | | |   (421)   ~ (all_10_2 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | SIMP: (421) implies:
% 202.23/33.86  | | | | | | | |   (422)   ~ (all_10_2 = e3)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (314), (418) imply:
% 202.23/33.86  | | | | | | | |   (423)  op(e3, e3) = e0
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, e0, e3, e3,
% 202.23/33.86  | | | | | | | |              simplifying with (105), (423) gives:
% 202.23/33.86  | | | | | | | |   (424)  all_6_2 = e0
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | COMBINE_EQS: (97), (424) imply:
% 202.23/33.86  | | | | | | | |   (425)  all_8_2 = e0
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | COMBINE_EQS: (18), (424) imply:
% 202.23/33.86  | | | | | | | |   (426)  all_58_0 = e0
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (122), (424) imply:
% 202.23/33.86  | | | | | | | |   (427)   ~ (all_52_17 = e0)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (41), (424) imply:
% 202.23/33.86  | | | | | | | |   (428)   ~ (all_10_0 = e0)
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | REDUCE: (140), (424) imply:
% 202.23/33.86  | | | | | | | |   (429)  op(e0, e3) = all_6_1
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | BETA: splitting (71) gives:
% 202.23/33.86  | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (430)  all_58_0 = e3
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | REF_CLOSE: (153), (426), (430) are inconsistent by sub-proof
% 202.23/33.86  | | | | | | | | |            #1015.
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | Case 2:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | |   (431)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | BETA: splitting (431) gives:
% 202.23/33.86  | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | |   (432)  all_58_2 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | COMBINE_EQS: (68), (432) imply:
% 202.23/33.86  | | | | | | | | | |   (433)  all_52_3 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (433) implies:
% 202.23/33.86  | | | | | | | | | |   (434)  all_52_3 = e3
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (112), (434) imply:
% 202.23/33.86  | | | | | | | | | |   (435)   ~ (all_52_7 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | SIMP: (435) implies:
% 202.23/33.86  | | | | | | | | | |   (436)   ~ (all_52_7 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | REDUCE: (53), (434) imply:
% 202.23/33.86  | | | | | | | | | |   (437)   ~ (all_10_0 = e3)
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | BETA: splitting (1) gives:
% 202.23/33.86  | | | | | | | | | | 
% 202.23/33.86  | | | | | | | | | | Case 1:
% 202.23/33.86  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | |   (438)   ~ (all_8_1 = e1)
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | REDUCE: (139), (438) imply:
% 202.23/33.87  | | | | | | | | | | |   (439)   ~ (all_6_1 = e1)
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | BETA: splitting (160) gives:
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | |   (440)  all_56_8 = e2
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | REF_CLOSE: (46), (80), (440) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | |            #915.
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | |   (441)   ~ (all_56_8 = e2)
% 202.23/33.87  | | | | | | | | | | | |   (442)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | BETA: splitting (81) gives:
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | |   (443)  all_58_0 = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | REF_CLOSE: (155), (426), (443) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | |            #812.
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | |   (444)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | BETA: splitting (444) gives:
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | |   (445)  all_58_2 = e2
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REF_CLOSE: (123), (432), (445) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | | |            #1124.
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | |   (446)  all_58_6 = e2 | all_58_12 = e2
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | BETA: splitting (446) gives:
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | |   (447)  all_58_6 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | REF_CLOSE: (46), (84), (447) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | | | |            #917.
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | |   (448)  all_58_12 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | COMBINE_EQS: (65), (448) imply:
% 202.23/33.87  | | | | | | | | | | | | | | |   (449)  all_52_7 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | SIMP: (449) implies:
% 202.23/33.87  | | | | | | | | | | | | | | |   (450)  all_52_7 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | REDUCE: (13), (450) imply:
% 202.23/33.87  | | | | | | | | | | | | | | |   (451)   ~ (all_52_15 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | SIMP: (451) implies:
% 202.23/33.87  | | | | | | | | | | | | | | |   (452)   ~ (all_52_15 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | REDUCE: (9), (450) imply:
% 202.23/33.87  | | | | | | | | | | | | | | |   (453)   ~ (all_10_0 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | REDUCE: (85), (450) imply:
% 202.23/33.87  | | | | | | | | | | | | | | |   (454)  op(e0, e3) = e2
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | BETA: splitting (442) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | |   (455)  all_56_8 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (455) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (456)  all_10_0 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | SIMP: (456) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (457)  all_10_0 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | REDUCE: (21), (457) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (458)   ~ (e3 = e1)
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | REDUCE: (46), (457) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (459)   ~ (e2 = e1)
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | REDUCE: (115), (457) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (460)  op(e1, e1) = all_52_4
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (461)  all_58_12 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (448), (461) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | | | | | |            #1198.
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (462)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (463)  all_58_13 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (463) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (464)  all_52_15 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | SIMP: (464) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (465)  all_52_15 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REDUCE: (56), (465) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (466)  op(e1, e1) = all_52_14
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e2, all_6_1, e3, e0,
% 202.23/33.87  | | | | | | | | | | | | | | | | | |              simplifying with (429), (454) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (467)  all_6_1 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, all_52_4, e1, e1,
% 202.23/33.87  | | | | | | | | | | | | | | | | | |              simplifying with (130), (460) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (468)  all_52_4 = all_10_2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_14, all_52_4, e1,
% 202.23/33.87  | | | | | | | | | | | | | | | | | |              e1, simplifying with (460), (466) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (469)  all_52_4 = all_52_14
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (468), (469) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (470)  all_52_14 = all_10_2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | SIMP: (470) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (471)  all_52_14 = all_10_2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REDUCE: (103), (467) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (472)  op(e3, e2) = e2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_9, e2, e2, e3,
% 202.23/33.87  | | | | | | | | | | | | | | | | | |              simplifying with (120), (472) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (473)  all_52_9 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REDUCE: (126), (473) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (474)   ~ (all_52_17 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | SIMP: (474) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (475)   ~ (all_52_17 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (49), (70), (130), (313), (419), (422),
% 202.23/33.87  | | | | | | | | | | | | | | | | | |            (427), (475) are inconsistent by sub-proof #1073.
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (476)   ~ (all_58_13 = e1)
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REDUCE: (26), (476) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (477)   ~ (all_52_15 = e1)
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | BETA: splitting (387) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | |   (478)  all_56_13 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (452), (478) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | | | | | | | |            #1356.
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | |   (479)  all_56_13 = e1 | all_56_13 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |   (480)  all_56_13 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (477), (480) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |            #1355.
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |   (481)  all_56_13 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (481) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |   (482)  all_52_15 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | SIMP: (482) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |   (483)  all_52_15 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (483) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |   (484)  all_58_13 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (49), (65), (70), (78), (85),
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |            (88), (95), (103), (113), (120), (126), (130),
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |            (145), (157), (313), (416), (419), (422), (427),
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |            (429), (436), (439), (484) are inconsistent by
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | |            sub-proof #439.
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | |   (485)  all_56_8 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | REF_CLOSE: (80), (428), (485) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | | | | |            #883.
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | |   (486)   ~ (all_8_2 = e0)
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | REDUCE: (425), (486) imply:
% 202.23/33.87  | | | | | | | | | | |   (487)  $false
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | CLOSE: (487) is inconsistent.
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | |   (488)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REF_CLOSE: (4), (8), (14), (20), (21), (59), (65), (82),
% 202.23/33.87  | | | | | | | | | |            (84), (92), (105), (114), (122), (128), (132),
% 202.23/33.87  | | | | | | | | | |            (141), (313), (420), (488) are inconsistent by
% 202.23/33.87  | | | | | | | | | |            sub-proof #376.
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | |   (489)  all_58_15 = e3
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REF_CLOSE: (45), (153), (489) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | |            #1350.
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | End of split
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | End of split
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | End of split
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | End of split
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | Case 2:
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | |   (490)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.23/33.87  | | | |          e0
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | | ALPHA: (490) implies:
% 202.23/33.87  | | | |   (491)  all_52_28 = e1
% 202.23/33.87  | | | |   (492)  all_52_26 = e2
% 202.23/33.87  | | | |   (493)  all_52_24 = e3
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | | REDUCE: (146), (493) imply:
% 202.23/33.87  | | | |   (494)  op(all_52_25, all_52_25) = e3
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | | REDUCE: (30), (492) imply:
% 202.23/33.87  | | | |   (495)  op(all_52_27, all_52_27) = e2
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | | REDUCE: (94), (491) imply:
% 202.23/33.87  | | | |   (496)  op(all_52_29, all_52_29) = e1
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | | BETA: splitting (48) gives:
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | | Case 1:
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | |   (497)  all_56_13 = e3
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | | REF_CLOSE: (3), (7), (8), (10), (14), (15), (16), (17), (18), (20),
% 202.23/33.87  | | | | |            (22), (25), (27), (28), (31), (33), (34), (35), (36), (40),
% 202.23/33.87  | | | | |            (42), (43), (44), (52), (54), (58), (60), (64), (65), (66),
% 202.23/33.87  | | | | |            (68), (69), (77), (79), (86), (90), (92), (96), (98), (99),
% 202.23/33.87  | | | | |            (100), (102), (103), (105), (106), (107), (108), (111),
% 202.23/33.87  | | | | |            (114), (117), (119), (120), (123), (125), (128), (130),
% 202.23/33.87  | | | | |            (133), (134), (135), (140), (141), (157), (494), (495),
% 202.23/33.87  | | | | |            (496), (497) are inconsistent by sub-proof #473.
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | Case 2:
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | |   (498)   ~ (all_56_13 = e3)
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | | REDUCE: (135), (498) imply:
% 202.23/33.87  | | | | |   (499)   ~ (all_52_15 = e3)
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | | BETA: splitting (121) gives:
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | | Case 1:
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | |   (500)  all_58_12 = e3
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | COMBINE_EQS: (65), (500) imply:
% 202.23/33.87  | | | | | |   (501)  all_52_7 = e3
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | SIMP: (501) implies:
% 202.23/33.87  | | | | | |   (502)  all_52_7 = e3
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | REDUCE: (112), (502) imply:
% 202.23/33.87  | | | | | |   (503)   ~ (all_52_3 = e3)
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | REDUCE: (39), (502) imply:
% 202.23/33.87  | | | | | |   (504)   ~ (all_6_2 = e3)
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | SIMP: (504) implies:
% 202.23/33.87  | | | | | |   (505)   ~ (all_6_2 = e3)
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | REDUCE: (14), (502) imply:
% 202.23/33.87  | | | | | |   (506)  op(e3, e3) = all_52_6
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | REDUCE: (85), (502) imply:
% 202.23/33.87  | | | | | |   (507)  op(e0, e3) = e3
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_6, e3, e3,
% 202.23/33.87  | | | | | |              simplifying with (105), (506) gives:
% 202.23/33.87  | | | | | |   (508)  all_52_6 = all_6_2
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | BETA: splitting (81) gives:
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | Case 1:
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | |   (509)  all_58_0 = e2
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | COMBINE_EQS: (18), (509) imply:
% 202.23/33.87  | | | | | | |   (510)  all_6_2 = e2
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REDUCE: (16), (510) imply:
% 202.23/33.87  | | | | | | |   (511)   ~ (all_52_3 = e2)
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REDUCE: (122), (510) imply:
% 202.23/33.87  | | | | | | |   (512)   ~ (all_52_17 = e2)
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REDUCE: (98), (510) imply:
% 202.23/33.87  | | | | | | |   (513)   ~ (all_52_25 = e2)
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REDUCE: (140), (510) imply:
% 202.23/33.87  | | | | | | |   (514)  op(e2, e3) = all_6_1
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | GROUND_INST: instantiating (8) with all_52_3, all_6_1, e3, e2,
% 202.23/33.87  | | | | | | |              simplifying with (11), (514) gives:
% 202.23/33.87  | | | | | | |   (515)  all_52_3 = all_6_1
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | COMBINE_EQS: (19), (515) imply:
% 202.23/33.87  | | | | | | |   (516)  all_56_4 = all_6_1
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | COMBINE_EQS: (68), (515) imply:
% 202.23/33.87  | | | | | | |   (517)  all_58_2 = all_6_1
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REDUCE: (503), (515) imply:
% 202.23/33.87  | | | | | | |   (518)   ~ (all_6_1 = e3)
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REDUCE: (511), (515) imply:
% 202.23/33.87  | | | | | | |   (519)   ~ (all_6_1 = e2)
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | BETA: splitting (99) gives:
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | |   (520)  all_56_3 = e3
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REF_CLOSE: (8), (23), (33), (63), (76), (82), (103), (111),
% 202.23/33.87  | | | | | | | |            (155), (509), (512), (513), (516), (517), (518),
% 202.23/33.87  | | | | | | | |            (519), (520) are inconsistent by sub-proof #384.
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | |   (521)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | BETA: splitting (521) gives:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | |   (522)  all_56_3 = e2
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | REF_CLOSE: (111), (513), (522) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | |            #1259.
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | |   (523)  all_56_3 = e1 | all_56_3 = e0
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | BETA: splitting (523) gives:
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | |   (524)  all_56_3 = e1
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | COMBINE_EQS: (111), (524) imply:
% 202.23/33.87  | | | | | | | | | |   (525)  all_52_25 = e1
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | SIMP: (525) implies:
% 202.23/33.87  | | | | | | | | | |   (526)  all_52_25 = e1
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REDUCE: (494), (526) imply:
% 202.23/33.87  | | | | | | | | | |   (527)  op(e1, e1) = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, e3, e1, e1,
% 202.23/33.87  | | | | | | | | | |              simplifying with (130), (527) gives:
% 202.23/33.87  | | | | | | | | | |   (528)  all_10_2 = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REF_CLOSE: (8), (20), (59), (82), (528) are inconsistent by
% 202.23/33.87  | | | | | | | | | |            sub-proof #925.
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | |   (529)  all_56_3 = e0
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REF_CLOSE: (47), (111), (529) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | |            #1258.
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | End of split
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | Case 2:
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | |   (530)   ~ (all_58_0 = e2)
% 202.23/33.87  | | | | | | |   (531)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REF_CLOSE: (8), (17), (18), (22), (33), (41), (46), (75), (80),
% 202.23/33.87  | | | | | | |            (84), (87), (103), (104), (105), (123), (125), (129),
% 202.23/33.87  | | | | | | |            (140), (153), (155), (157), (160), (500), (505), (506),
% 202.23/33.87  | | | | | | |            (507), (530), (531) are inconsistent by sub-proof #381.
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | End of split
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | Case 2:
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | |   (532)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | BETA: splitting (532) gives:
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | | Case 1:
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | |   (533)  all_58_13 = e3
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | REF_CLOSE: (26), (499), (533) are inconsistent by sub-proof #1360.
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | Case 2:
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | |   (534)  all_58_14 = e3 | all_58_15 = e3
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | BETA: splitting (534) gives:
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | |   (535)  all_58_14 = e3
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | COMBINE_EQS: (4), (535) imply:
% 202.23/33.87  | | | | | | | |   (536)  all_52_23 = e3
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | SIMP: (536) implies:
% 202.23/33.87  | | | | | | | |   (537)  all_52_23 = e3
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REDUCE: (132), (537) imply:
% 202.23/33.87  | | | | | | | |   (538)   ~ (all_52_7 = e3)
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REDUCE: (138), (537) imply:
% 202.23/33.87  | | | | | | | |   (539)   ~ (all_52_17 = e3)
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REDUCE: (131), (537) imply:
% 202.23/33.87  | | | | | | | |   (540)   ~ (all_10_2 = e3)
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | SIMP: (540) implies:
% 202.23/33.87  | | | | | | | |   (541)   ~ (all_10_2 = e3)
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REDUCE: (89), (537) imply:
% 202.23/33.87  | | | | | | | |   (542)  op(e3, e3) = all_52_22
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_22, e3, e3,
% 202.23/33.87  | | | | | | | |              simplifying with (105), (542) gives:
% 202.23/33.87  | | | | | | | |   (543)  all_52_22 = all_6_2
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | BETA: splitting (71) gives:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | |   (544)  all_58_0 = e3
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | COMBINE_EQS: (18), (544) imply:
% 202.23/33.87  | | | | | | | | |   (545)  all_6_2 = e3
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | REF_CLOSE: (8), (103), (105), (123), (140), (545) are
% 202.23/33.87  | | | | | | | | |            inconsistent by sub-proof #502.
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | |   (546)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | BETA: splitting (546) gives:
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | |   (547)  all_58_2 = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | COMBINE_EQS: (68), (547) imply:
% 202.23/33.87  | | | | | | | | | |   (548)  all_52_3 = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | SIMP: (548) implies:
% 202.23/33.87  | | | | | | | | | |   (549)  all_52_3 = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REDUCE: (16), (549) imply:
% 202.23/33.87  | | | | | | | | | |   (550)   ~ (all_6_2 = e3)
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | SIMP: (550) implies:
% 202.23/33.87  | | | | | | | | | |   (551)   ~ (all_6_2 = e3)
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REDUCE: (7), (549) imply:
% 202.23/33.87  | | | | | | | | | |   (552)  op(e3, e3) = all_52_2
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3,
% 202.23/33.87  | | | | | | | | | |              simplifying with (105), (552) gives:
% 202.23/33.87  | | | | | | | | | |   (553)  all_52_2 = all_6_2
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | BETA: splitting (81) gives:
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | |   (554)  all_58_0 = e2
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | REF_CLOSE: (8), (33), (59), (61), (65), (67), (83), (84),
% 202.23/33.87  | | | | | | | | | | |            (91), (127), (130), (144), (145), (153), (155),
% 202.23/33.87  | | | | | | | | | | |            (541), (547), (554) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | |            #379.
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | |   (555)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | BETA: splitting (555) gives:
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | |   (556)  all_58_2 = e2
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | REF_CLOSE: (123), (547), (556) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | |            #1124.
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | |   (557)  all_58_6 = e2 | all_58_12 = e2
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | BETA: splitting (557) gives:
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | |   (558)  all_58_6 = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | REF_CLOSE: (46), (84), (558) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | | | | | | |            #917.
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | |   (559)  all_58_12 = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | COMBINE_EQS: (65), (559) imply:
% 202.23/33.87  | | | | | | | | | | | | |   (560)  all_52_7 = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | SIMP: (560) implies:
% 202.23/33.87  | | | | | | | | | | | | |   (561)  all_52_7 = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | REDUCE: (85), (561) imply:
% 202.23/33.87  | | | | | | | | | | | | |   (562)  op(e0, e3) = e2
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | |   (563)  all_58_0 = e0
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | COMBINE_EQS: (18), (563) imply:
% 202.23/33.87  | | | | | | | | | | | | | |   (564)  all_6_2 = e0
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REDUCE: (122), (564) imply:
% 202.23/33.87  | | | | | | | | | | | | | |   (565)   ~ (all_52_17 = e0)
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REDUCE: (140), (564) imply:
% 202.23/33.87  | | | | | | | | | | | | | |   (566)  op(e0, e3) = all_6_1
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e2, all_6_1, e3, e0,
% 202.23/33.87  | | | | | | | | | | | | | |              simplifying with (562), (566) gives:
% 202.23/33.87  | | | | | | | | | | | | | |   (567)  all_6_1 = e2
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REDUCE: (103), (567) imply:
% 202.23/33.87  | | | | | | | | | | | | | |   (568)  op(e3, e2) = e2
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_9, e2, e2, e3,
% 202.23/33.87  | | | | | | | | | | | | | |              simplifying with (120), (568) gives:
% 202.23/33.87  | | | | | | | | | | | | | |   (569)  all_52_9 = e2
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REDUCE: (126), (569) imply:
% 202.23/33.87  | | | | | | | | | | | | | |   (570)   ~ (all_52_17 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | SIMP: (570) implies:
% 202.23/33.87  | | | | | | | | | | | | | |   (571)   ~ (all_52_17 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REDUCE: (86), (569) imply:
% 202.23/33.87  | | | | | | | | | | | | | |   (572)   ~ (all_52_25 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | SIMP: (572) implies:
% 202.23/33.87  | | | | | | | | | | | | | |   (573)   ~ (all_52_25 = e2)
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | |   (574)  all_56_2 = e3
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | COMBINE_EQS: (70), (574) imply:
% 202.23/33.87  | | | | | | | | | | | | | | |   (575)  all_52_17 = e3
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | REDUCE: (539), (575) imply:
% 202.23/33.87  | | | | | | | | | | | | | | |   (576)  $false
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | CLOSE: (576) is inconsistent.
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | |   (577)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | BETA: splitting (577) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | |   (578)  all_56_2 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (578) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (579)  all_52_17 = e2
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | REDUCE: (571), (579) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | |   (580)  $false
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | CLOSE: (580) is inconsistent.
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | |   (581)  all_56_2 = e1 | all_56_2 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | BETA: splitting (581) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (582)  all_56_2 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (582) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (583)  all_52_17 = e1
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | REDUCE: (15), (583) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (584)   ~ (all_52_25 = e1)
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | SIMP: (584) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (585)   ~ (all_52_25 = e1)
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (586)  all_56_3 = e3
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (586) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (587)  all_52_25 = e3
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | SIMP: (587) implies:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (588)  all_52_25 = e3
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REDUCE: (494), (588) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (589)  op(e3, e3) = e3
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (105), (551), (589) are inconsistent by
% 202.23/33.87  | | | | | | | | | | | | | | | | | |            sub-proof #1338.
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | |   (590)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (111), (573), (585), (590) are inconsistent
% 202.23/33.87  | | | | | | | | | | | | | | | | | |            by sub-proof #1215.
% 202.23/33.87  | | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (591)  all_56_2 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (591) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (592)  all_52_17 = e0
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | REDUCE: (565), (592) imply:
% 202.23/33.87  | | | | | | | | | | | | | | | | |   (593)  $false
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | | CLOSE: (593) is inconsistent.
% 202.23/33.87  | | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | |   (594)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | | REF_CLOSE: (8), (59), (61), (65), (67), (83), (84), (91),
% 202.23/33.87  | | | | | | | | | | | | | |            (127), (130), (144), (145), (153), (541), (547),
% 202.23/33.87  | | | | | | | | | | | | | |            (594) are inconsistent by sub-proof #375.
% 202.23/33.87  | | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | |   (595)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | | REF_CLOSE: (21), (65), (84), (538), (595) are inconsistent by
% 202.23/33.87  | | | | | | | | | |            sub-proof #921.
% 202.23/33.87  | | | | | | | | | | 
% 202.23/33.87  | | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | | 
% 202.23/33.87  | | | | | | | | End of split
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | Case 2:
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | |   (596)  all_58_15 = e3
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | | REF_CLOSE: (45), (153), (596) are inconsistent by sub-proof
% 202.23/33.87  | | | | | | | |            #1350.
% 202.23/33.87  | | | | | | | | 
% 202.23/33.87  | | | | | | | End of split
% 202.23/33.87  | | | | | | | 
% 202.23/33.87  | | | | | | End of split
% 202.23/33.87  | | | | | | 
% 202.23/33.87  | | | | | End of split
% 202.23/33.87  | | | | | 
% 202.23/33.87  | | | | End of split
% 202.23/33.87  | | | | 
% 202.23/33.87  | | | End of split
% 202.23/33.87  | | | 
% 202.23/33.87  | | End of split
% 202.23/33.87  | | 
% 202.23/33.87  | End of split
% 202.23/33.87  | 
% 202.23/33.87  End of proof
% 202.23/33.87  
% 202.23/33.87  Sub-proof #375 shows that the following formulas are inconsistent:
% 202.23/33.87  ----------------------------------------------------------------
% 202.23/33.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.87    (2)   ~ (e3 = e0)
% 202.23/33.87    (3)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.87    (4)  op(all_10_2, e1) = e3
% 202.23/33.87    (5)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 202.23/33.87    (6)  all_58_12 = all_52_7
% 202.23/33.87    (7)  all_30_2 = all_10_2
% 202.23/33.87    (8)   ~ (all_10_2 = e3)
% 202.23/33.87    (9)  all_30_0 = all_10_0
% 202.23/33.87    (10)  all_58_6 = all_10_0
% 202.23/33.87    (11)   ~ (all_10_0 = all_10_2)
% 202.23/33.87    (12)  all_56_10 = all_10_2
% 202.23/33.87    (13)  op(e1, e1) = all_10_2
% 202.23/33.87    (14)  all_58_2 = e3
% 202.23/33.87    (15)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.87    (16)   ~ (all_52_7 = e0)
% 202.23/33.87  
% 202.23/33.87  Begin of proof
% 202.23/33.87  | 
% 202.23/33.87  | BETA: splitting (3) gives:
% 202.23/33.87  | 
% 202.23/33.87  | Case 1:
% 202.23/33.87  | | 
% 202.23/33.87  | |   (17)  all_58_2 = e0
% 202.23/33.87  | | 
% 202.23/33.87  | | REF_CLOSE: (2), (14), (17) are inconsistent by sub-proof #1123.
% 202.23/33.87  | | 
% 202.23/33.87  | Case 2:
% 202.23/33.87  | | 
% 202.23/33.87  | |   (18)  all_58_6 = e0 | all_58_12 = e0
% 202.23/33.87  | | 
% 202.23/33.87  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15),
% 202.23/33.87  | |            (16), (18) are inconsistent by sub-proof #380.
% 202.23/33.87  | | 
% 202.23/33.87  | End of split
% 202.23/33.87  | 
% 202.23/33.87  End of proof
% 202.23/33.87  
% 202.23/33.87  Sub-proof #376 shows that the following formulas are inconsistent:
% 202.23/33.87  ----------------------------------------------------------------
% 202.23/33.87    (1)  all_58_14 = all_52_23
% 202.23/33.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.87    (3)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.87    (4)   ~ (all_52_17 = all_10_2)
% 202.23/33.87    (5)   ~ (all_10_0 = e3)
% 202.23/33.87    (6)  op(all_10_2, e1) = e3
% 202.23/33.87    (7)  all_58_12 = all_52_7
% 202.23/33.87    (8)   ~ (all_52_19 = e3)
% 202.23/33.87    (9)  op(e3, e1) = all_52_17
% 202.23/33.87    (10)  all_58_6 = all_10_0
% 202.23/33.87    (11)  all_58_8 = all_10_2
% 202.23/33.87    (12)  op(e3, e3) = all_6_2
% 202.23/33.87    (13)  all_58_5 = all_52_19
% 202.23/33.87    (14)  op(all_52_17, all_52_17) = e3
% 202.23/33.87    (15)   ~ (all_52_17 = all_6_2)
% 202.23/33.87    (16)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.87    (17)   ~ (all_52_7 = all_52_23)
% 202.23/33.87    (18)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.87    (19)  all_58_4 = all_52_17
% 202.23/33.87  
% 202.23/33.87  Begin of proof
% 202.23/33.87  | 
% 202.23/33.87  | BETA: splitting (18) gives:
% 202.23/33.87  | 
% 202.23/33.87  | Case 1:
% 202.23/33.87  | | 
% 202.23/33.87  | |   (20)  all_58_6 = e3
% 202.23/33.87  | | 
% 202.23/33.87  | | REF_CLOSE: (5), (10), (20) are inconsistent by sub-proof #922.
% 202.23/33.87  | | 
% 202.23/33.87  | Case 2:
% 202.23/33.87  | | 
% 202.23/33.87  | |   (21)  all_58_12 = e3
% 202.23/33.87  | | 
% 202.23/33.87  | | COMBINE_EQS: (7), (21) imply:
% 202.23/33.87  | |   (22)  all_52_7 = e3
% 202.23/33.87  | | 
% 202.23/33.87  | | SIMP: (22) implies:
% 202.23/33.87  | |   (23)  all_52_7 = e3
% 202.23/33.87  | | 
% 202.23/33.87  | | REDUCE: (17), (23) imply:
% 202.23/33.87  | |   (24)   ~ (all_52_23 = e3)
% 202.23/33.87  | | 
% 202.23/33.87  | | SIMP: (24) implies:
% 202.23/33.87  | |   (25)   ~ (all_52_23 = e3)
% 202.23/33.87  | | 
% 202.23/33.87  | | REDUCE: (3), (23) imply:
% 202.23/33.87  | |   (26)  op(e3, e3) = all_52_6
% 202.23/33.87  | | 
% 202.23/33.87  | | GROUND_INST: instantiating (2) with all_6_2, all_52_6, e3, e3, simplifying
% 202.23/33.87  | |              with (12), (26) gives:
% 202.23/33.87  | |   (27)  all_52_6 = all_6_2
% 202.23/33.87  | | 
% 202.23/33.87  | | BETA: splitting (16) gives:
% 202.23/33.87  | | 
% 202.23/33.87  | | Case 1:
% 202.23/33.87  | | | 
% 202.23/33.87  | | |   (28)  all_58_4 = e3
% 202.23/33.87  | | | 
% 202.23/33.87  | | | COMBINE_EQS: (19), (28) imply:
% 202.23/33.87  | | |   (29)  all_52_17 = e3
% 202.23/33.87  | | | 
% 202.23/33.87  | | | SIMP: (29) implies:
% 202.23/33.87  | | |   (30)  all_52_17 = e3
% 202.23/33.87  | | | 
% 202.23/33.87  | | | REF_CLOSE: (2), (12), (14), (15), (30) are inconsistent by sub-proof
% 202.23/33.87  | | |            #1280.
% 202.23/33.87  | | | 
% 202.23/33.87  | | Case 2:
% 202.23/33.87  | | | 
% 202.23/33.87  | | |   (31)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.87  | | | 
% 202.23/33.87  | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (11), (13), (25), (31) are
% 202.23/33.87  | | |            inconsistent by sub-proof #898.
% 202.23/33.87  | | | 
% 202.23/33.87  | | End of split
% 202.23/33.87  | | 
% 202.23/33.87  | End of split
% 202.23/33.87  | 
% 202.23/33.87  End of proof
% 202.23/33.87  
% 202.23/33.87  Sub-proof #377 shows that the following formulas are inconsistent:
% 202.23/33.87  ----------------------------------------------------------------
% 202.23/33.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.87    (2)  all_58_1 = all_52_9
% 202.23/33.87    (3)   ~ (e3 = e0)
% 202.23/33.87    (4)  all_58_0 = all_6_2
% 202.23/33.87    (5)  all_58_9 = all_52_25
% 202.23/33.87    (6)  all_58_11 = all_52_29
% 202.23/33.87    (7)  all_58_8 = e0
% 202.23/33.87    (8)   ~ (all_52_25 = all_52_29)
% 202.23/33.87    (9)  all_58_7 = all_52_13
% 202.23/33.87    (10)   ~ (all_52_9 = e3)
% 202.23/33.87    (11)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.87    (12)  op(e3, all_6_1) = e2
% 202.23/33.87    (13)  op(e3, e3) = all_6_2
% 202.23/33.87    (14)   ~ (all_52_13 = e3)
% 202.23/33.87    (15)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.87    (16)  op(all_52_17, all_52_17) = e3
% 202.23/33.87    (17)   ~ (all_52_17 = all_6_2)
% 202.23/33.87    (18)   ~ (e3 = e2)
% 202.23/33.87    (19)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.87    (20)  op(all_6_2, e3) = all_6_1
% 202.23/33.87    (21)  all_58_4 = all_52_17
% 202.23/33.87  
% 202.23/33.87  Begin of proof
% 202.23/33.87  | 
% 202.23/33.87  | BETA: splitting (11) gives:
% 202.23/33.87  | 
% 202.23/33.87  | Case 1:
% 202.23/33.87  | | 
% 202.23/33.87  | |   (22)  all_58_7 = e3
% 202.23/33.87  | | 
% 202.23/33.87  | | COMBINE_EQS: (9), (22) imply:
% 202.23/33.87  | |   (23)  all_52_13 = e3
% 202.23/33.87  | | 
% 202.23/33.87  | | REDUCE: (14), (23) imply:
% 202.23/33.87  | |   (24)  $false
% 202.23/33.87  | | 
% 202.23/33.87  | | CLOSE: (24) is inconsistent.
% 202.23/33.87  | | 
% 202.23/33.87  | Case 2:
% 202.23/33.87  | | 
% 202.23/33.87  | |   (25)  all_58_8 = e3 | all_58_11 = e3
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (25) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (26)  all_58_8 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (3), (7), (26) are inconsistent by sub-proof #686.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (27)  all_58_11 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (12), (13), (15), (16),
% 202.23/33.88  | | |            (17), (18), (19), (20), (21), (27) are inconsistent by
% 202.23/33.88  | | |            sub-proof #420.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #378 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)  all_44_2 = all_6_2
% 202.23/33.88    (3)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.88    (4)   ~ (all_10_0 = all_6_2)
% 202.23/33.88    (5)   ~ (all_10_0 = e2)
% 202.23/33.88    (6)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.88    (7)  all_56_8 = all_10_0
% 202.23/33.88    (8)  op(e1, e3) = all_10_0
% 202.23/33.88    (9)  all_6_2 = e1
% 202.23/33.88    (10)  all_44_1 = all_6_1
% 202.23/33.88    (11)  op(all_6_2, e3) = all_6_1
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | COMBINE_EQS: (2), (9) imply:
% 202.23/33.88  |   (12)  all_44_2 = e1
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (4), (9) imply:
% 202.23/33.88  |   (13)   ~ (all_10_0 = e1)
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (9), (11) imply:
% 202.23/33.88  |   (14)  op(e1, e3) = all_6_1
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (6) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (15)  all_56_8 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #915.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (16)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (1), (3), (7), (8), (10), (12), (13), (14), (16) are inconsistent
% 202.23/33.88  | |            by sub-proof #382.
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #379 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)   ~ (e3 = e0)
% 202.23/33.88    (3)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88    (4)  op(all_10_2, e1) = e3
% 202.23/33.88    (5)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 202.23/33.88    (6)  all_58_12 = all_52_7
% 202.23/33.88    (7)  all_30_2 = all_10_2
% 202.23/33.88    (8)   ~ (e2 = e0)
% 202.23/33.88    (9)   ~ (all_10_2 = e3)
% 202.23/33.88    (10)  all_30_0 = all_10_0
% 202.23/33.88    (11)  all_58_6 = all_10_0
% 202.23/33.88    (12)   ~ (all_10_0 = all_10_2)
% 202.23/33.88    (13)  all_58_0 = e2
% 202.23/33.88    (14)  all_56_10 = all_10_2
% 202.23/33.88    (15)  op(e1, e1) = all_10_2
% 202.23/33.88    (16)  all_58_2 = e3
% 202.23/33.88    (17)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.88    (18)   ~ (all_52_7 = e0)
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (3) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (19)  all_58_0 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | COMBINE_EQS: (13), (19) imply:
% 202.23/33.88  | |   (20)  e2 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (8), (20) imply:
% 202.23/33.88  | |   (21)  $false
% 202.23/33.88  | | 
% 202.23/33.88  | | CLOSE: (21) is inconsistent.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (22)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (22) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (23)  all_58_2 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (2), (16), (23) are inconsistent by sub-proof #1123.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (24)  all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12), (14), (15),
% 202.23/33.88  | | |            (17), (18), (24) are inconsistent by sub-proof #380.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #380 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)  all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88    (3)  op(all_10_2, e1) = e3
% 202.23/33.88    (4)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 202.23/33.88    (5)  all_58_12 = all_52_7
% 202.23/33.88    (6)  all_30_2 = all_10_2
% 202.23/33.88    (7)   ~ (all_10_2 = e3)
% 202.23/33.88    (8)  all_30_0 = all_10_0
% 202.23/33.88    (9)  all_58_6 = all_10_0
% 202.23/33.88    (10)   ~ (all_10_0 = all_10_2)
% 202.23/33.88    (11)  all_56_10 = all_10_2
% 202.23/33.88    (12)  op(e1, e1) = all_10_2
% 202.23/33.88    (13)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.88    (14)   ~ (all_52_7 = e0)
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (2) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (15)  all_58_6 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | COMBINE_EQS: (9), (15) imply:
% 202.23/33.88  | |   (16)  all_10_0 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | SIMP: (16) implies:
% 202.23/33.88  | |   (17)  all_10_0 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | COMBINE_EQS: (8), (17) imply:
% 202.23/33.88  | |   (18)  all_30_0 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (10), (17) imply:
% 202.23/33.88  | |   (19)   ~ (all_10_2 = e0)
% 202.23/33.88  | | 
% 202.23/33.88  | | SIMP: (19) implies:
% 202.23/33.88  | |   (20)   ~ (all_10_2 = e0)
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (4) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (21)   ~ (all_30_2 = e2)
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (6), (21) imply:
% 202.23/33.88  | | |   (22)   ~ (all_10_2 = e2)
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (1), (3), (7), (11), (12), (13), (20), (22) are inconsistent by
% 202.23/33.88  | | |            sub-proof #910.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (23)   ~ (all_30_0 = e0)
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (18), (23) imply:
% 202.23/33.88  | | |   (24)  $false
% 202.23/33.88  | | | 
% 202.23/33.88  | | | CLOSE: (24) is inconsistent.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (25)  all_58_12 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (5), (14), (25) are inconsistent by sub-proof #1067.
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #381 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)   ~ (e3 = e0)
% 202.23/33.88    (3)  all_44_2 = all_6_2
% 202.23/33.88    (4)  all_58_0 = all_6_2
% 202.23/33.88    (5)  op(e3, e3) = all_52_6
% 202.23/33.88    (6)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.88    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88    (8)   ~ (all_10_0 = all_6_2)
% 202.23/33.88    (9)   ~ (all_10_0 = e2)
% 202.23/33.88    (10)   ~ (all_6_2 = e3)
% 202.23/33.88    (11)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.88    (12)  op(e0, e3) = e3
% 202.23/33.88    (13)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.88    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.88    (15)   ~ (e2 = e0)
% 202.23/33.88    (16)  all_56_8 = all_10_0
% 202.23/33.88    (17)  all_58_6 = all_10_0
% 202.23/33.88    (18)  op(e1, e3) = all_10_0
% 202.23/33.88    (19)   ~ (all_58_0 = e2)
% 202.23/33.88    (20)  op(e3, all_6_1) = e2
% 202.23/33.88    (21)  all_56_0 = all_6_2
% 202.23/33.88    (22)  op(e3, e3) = all_6_2
% 202.23/33.88    (23)   ~ (e1 = e0)
% 202.23/33.88    (24)   ~ (e3 = e2)
% 202.23/33.88    (25)  all_44_1 = all_6_1
% 202.23/33.88    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.88    (27)  all_58_12 = e3
% 202.23/33.88    (28)  op(all_6_2, e3) = all_6_1
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (4), (19) imply:
% 202.23/33.88  |   (29)   ~ (all_6_2 = e2)
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (13) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (30)  all_58_2 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (26) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (31)  all_56_0 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | COMBINE_EQS: (21), (31) imply:
% 202.23/33.88  | | |   (32)  all_6_2 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (10), (32) imply:
% 202.23/33.88  | | |   (33)  $false
% 202.23/33.88  | | | 
% 202.23/33.88  | | | CLOSE: (33) is inconsistent.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (34)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | BETA: splitting (14) gives:
% 202.23/33.88  | | | 
% 202.23/33.88  | | | Case 1:
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | |   (35)  all_58_0 = e1
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | COMBINE_EQS: (4), (35) imply:
% 202.23/33.88  | | | |   (36)  all_6_2 = e1
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | COMBINE_EQS: (3), (36) imply:
% 202.23/33.88  | | | |   (37)  all_44_2 = e1
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | REDUCE: (8), (36) imply:
% 202.23/33.88  | | | |   (38)   ~ (all_10_0 = e1)
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | REDUCE: (28), (36) imply:
% 202.23/33.88  | | | |   (39)  op(e1, e3) = all_6_1
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | BETA: splitting (7) gives:
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | Case 1:
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | |   (40)  all_58_0 = e0
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | COMBINE_EQS: (35), (40) imply:
% 202.23/33.88  | | | | |   (41)  e1 = e0
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | REDUCE: (23), (41) imply:
% 202.23/33.88  | | | | |   (42)  $false
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | CLOSE: (42) is inconsistent.
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | Case 2:
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | |   (43)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | BETA: splitting (43) gives:
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | Case 1:
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | |   (44)  all_58_2 = e0
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | REF_CLOSE: (15), (30), (44) are inconsistent by sub-proof #1213.
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | Case 2:
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | |   (45)   ~ (all_58_2 = e0)
% 202.23/33.88  | | | | | |   (46)  all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | BETA: splitting (11) gives:
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | Case 1:
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | |   (47)  all_56_8 = e2
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | COMBINE_EQS: (16), (47) imply:
% 202.23/33.88  | | | | | | |   (48)  all_10_0 = e2
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | SIMP: (48) implies:
% 202.23/33.88  | | | | | | |   (49)  all_10_0 = e2
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | COMBINE_EQS: (17), (49) imply:
% 202.23/33.88  | | | | | | |   (50)  all_58_6 = e2
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | REF_CLOSE: (2), (15), (27), (46), (50) are inconsistent by
% 202.23/33.88  | | | | | | |            sub-proof #383.
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | Case 2:
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | |   (51)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (37), (38), (39), (51) are
% 202.23/33.88  | | | | | | |            inconsistent by sub-proof #382.
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | End of split
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | End of split
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | End of split
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | Case 2:
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | |   (52)   ~ (all_58_0 = e1)
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | REDUCE: (4), (52) imply:
% 202.23/33.88  | | | |   (53)   ~ (all_6_2 = e1)
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | BETA: splitting (34) gives:
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | | Case 1:
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | |   (54)  all_56_0 = e2
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | COMBINE_EQS: (21), (54) imply:
% 202.23/33.88  | | | | |   (55)  all_6_2 = e2
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | REDUCE: (29), (55) imply:
% 202.23/33.88  | | | | |   (56)  $false
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | CLOSE: (56) is inconsistent.
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | Case 2:
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | |   (57)   ~ (all_56_0 = e2)
% 202.23/33.88  | | | | |   (58)  all_56_0 = e1 | all_56_0 = e0
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | BETA: splitting (58) gives:
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | | Case 1:
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | |   (59)  all_56_0 = e1
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | COMBINE_EQS: (21), (59) imply:
% 202.23/33.88  | | | | | |   (60)  all_6_2 = e1
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | REDUCE: (53), (60) imply:
% 202.23/33.88  | | | | | |   (61)  $false
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | CLOSE: (61) is inconsistent.
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | Case 2:
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | |   (62)  all_56_0 = e0
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | COMBINE_EQS: (21), (62) imply:
% 202.23/33.88  | | | | | |   (63)  all_6_2 = e0
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | REDUCE: (8), (63) imply:
% 202.23/33.88  | | | | | |   (64)   ~ (all_10_0 = e0)
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | REDUCE: (28), (63) imply:
% 202.23/33.88  | | | | | |   (65)  op(e0, e3) = all_6_1
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | BETA: splitting (11) gives:
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | | Case 1:
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | |   (66)  all_56_8 = e2
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | REF_CLOSE: (9), (16), (66) are inconsistent by sub-proof #915.
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | Case 2:
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | |   (67)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | BETA: splitting (67) gives:
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | | Case 1:
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | | GROUND_INST: instantiating (1) with e3, all_6_1, e3, e0,
% 202.23/33.88  | | | | | | | |              simplifying with (12), (65) gives:
% 202.23/33.88  | | | | | | | |   (68)  all_6_1 = e3
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | | REDUCE: (20), (68) imply:
% 202.23/33.88  | | | | | | | |   (69)  op(e3, e3) = e2
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | | REF_CLOSE: (1), (5), (22), (29), (69) are inconsistent by
% 202.23/33.88  | | | | | | | |            sub-proof #890.
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | Case 2:
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | |   (70)  all_56_8 = e0
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | | REF_CLOSE: (16), (64), (70) are inconsistent by sub-proof #883.
% 202.23/33.88  | | | | | | | | 
% 202.23/33.88  | | | | | | | End of split
% 202.23/33.88  | | | | | | | 
% 202.23/33.88  | | | | | | End of split
% 202.23/33.88  | | | | | | 
% 202.23/33.88  | | | | | End of split
% 202.23/33.88  | | | | | 
% 202.23/33.88  | | | | End of split
% 202.23/33.88  | | | | 
% 202.23/33.88  | | | End of split
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (71)  all_58_6 = e2 | all_58_12 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (9), (17), (24), (27), (71) are inconsistent by sub-proof #889.
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #382 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)  all_44_2 = e1
% 202.23/33.88    (3)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.88    (4)   ~ (all_10_0 = e1)
% 202.23/33.88    (5)  op(e1, e3) = all_6_1
% 202.23/33.88    (6)  all_56_8 = all_10_0
% 202.23/33.88    (7)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.88    (8)  op(e1, e3) = all_10_0
% 202.23/33.88    (9)  all_44_1 = all_6_1
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (3) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (10)   ~ (all_44_2 = e1)
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (2), (10) imply:
% 202.23/33.88  | |   (11)  $false
% 202.23/33.88  | | 
% 202.23/33.88  | | CLOSE: (11) is inconsistent.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (12)   ~ (all_44_1 = e0)
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (9), (12) imply:
% 202.23/33.88  | |   (13)   ~ (all_6_1 = e0)
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (7) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (14)  all_56_8 = e1
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (4), (6), (14) are inconsistent by sub-proof #914.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (15)  all_56_8 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | COMBINE_EQS: (6), (15) imply:
% 202.23/33.88  | | |   (16)  all_10_0 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | SIMP: (16) implies:
% 202.23/33.88  | | |   (17)  all_10_0 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (8), (17) imply:
% 202.23/33.88  | | |   (18)  op(e1, e3) = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | GROUND_INST: instantiating (1) with e0, all_6_1, e3, e1, simplifying with
% 202.23/33.88  | | |              (5), (18) gives:
% 202.23/33.88  | | |   (19)  all_6_1 = e0
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (13), (19) imply:
% 202.23/33.88  | | |   (20)  $false
% 202.23/33.88  | | | 
% 202.23/33.88  | | | CLOSE: (20) is inconsistent.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #383 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)  all_58_6 = e2
% 202.23/33.88    (2)   ~ (e3 = e0)
% 202.23/33.88    (3)  all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88    (4)   ~ (e2 = e0)
% 202.23/33.88    (5)  all_58_12 = e3
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (3) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (6)  all_58_6 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #801.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (7)  all_58_12 = e0
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #1212.
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #384 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)  op(e3, e0) = all_52_25
% 202.23/33.88    (3)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.88    (4)   ~ (all_6_1 = e3)
% 202.23/33.88    (5)  all_56_3 = e3
% 202.23/33.88    (6)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.88    (7)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.88    (8)   ~ (e2 = e0)
% 202.23/33.88    (9)  all_56_4 = all_6_1
% 202.23/33.88    (10)  op(e3, e1) = all_52_17
% 202.23/33.88    (11)  all_58_0 = e2
% 202.23/33.88    (12)   ~ (all_52_25 = e2)
% 202.23/33.88    (13)  op(e3, all_6_1) = e2
% 202.23/33.88    (14)  all_56_3 = all_52_25
% 202.23/33.88    (15)   ~ (all_6_1 = e2)
% 202.23/33.88    (16)   ~ (all_52_17 = e2)
% 202.23/33.88    (17)  all_58_2 = all_6_1
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | COMBINE_EQS: (5), (14) imply:
% 202.23/33.88  |   (18)  all_52_25 = e3
% 202.23/33.88  | 
% 202.23/33.88  | SIMP: (18) implies:
% 202.23/33.88  |   (19)  all_52_25 = e3
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (12), (19) imply:
% 202.23/33.88  |   (20)   ~ (e3 = e2)
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (2), (19) imply:
% 202.23/33.88  |   (21)  op(e3, e0) = e3
% 202.23/33.88  | 
% 202.23/33.88  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13), (15), (16),
% 202.23/33.88  |            (17), (20), (21) are inconsistent by sub-proof #456.
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #385 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)  all_58_13 = e3
% 202.23/33.88    (2)  all_58_15 = e0
% 202.23/33.88    (3)   ~ (e2 = e1)
% 202.23/33.88    (4)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.23/33.88    (5)   ~ (e2 = e0)
% 202.23/33.88    (6)  all_58_14 = e1
% 202.23/33.88    (7)   ~ (e3 = e2)
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (4) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (8)  all_58_13 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #1248.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (9)  all_58_14 = e2 | all_58_15 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (9) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (10)  all_58_14 = e2
% 202.23/33.88  | | | 
% 202.23/33.88  | | | COMBINE_EQS: (6), (10) imply:
% 202.23/33.88  | | |   (11)  e2 = e1
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (3), (11) imply:
% 202.23/33.88  | | |   (12)  $false
% 202.23/33.88  | | | 
% 202.23/33.88  | | | CLOSE: (12) is inconsistent.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (13)  all_58_15 = e2
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #1223.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #386 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (2)  all_56_4 = all_52_3
% 202.23/33.88    (3)   ~ (all_10_0 = e3)
% 202.23/33.88    (4)  op(e2, e2) = all_52_6
% 202.23/33.88    (5)  op(e2, e2) = all_4_2
% 202.23/33.88    (6)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.88    (7)  op(e0, e3) = e2
% 202.23/33.88    (8)  all_58_12 = all_52_7
% 202.23/33.88    (9)   ~ (all_52_7 = e3)
% 202.23/33.88    (10)  all_58_2 = all_52_3
% 202.23/33.88    (11)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.88    (12)  all_58_6 = all_10_0
% 202.23/33.88    (13)  op(e3, all_6_1) = e2
% 202.23/33.88    (14)  op(e3, e2) = all_52_9
% 202.23/33.88    (15)  op(e0, e3) = all_6_1
% 202.23/33.88    (16)  op(all_52_9, all_52_9) = e3
% 202.23/33.88    (17)   ~ (all_52_3 = all_4_2)
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (11) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (18)  all_56_4 = e3
% 202.23/33.88  | | 
% 202.23/33.88  | | COMBINE_EQS: (2), (18) imply:
% 202.23/33.88  | |   (19)  all_52_3 = e3
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (17), (19) imply:
% 202.23/33.88  | |   (20)   ~ (all_4_2 = e3)
% 202.23/33.88  | | 
% 202.23/33.88  | | SIMP: (20) implies:
% 202.23/33.88  | |   (21)   ~ (all_4_2 = e3)
% 202.23/33.88  | | 
% 202.23/33.88  | | GROUND_INST: instantiating (1) with e2, all_6_1, e3, e0, simplifying with
% 202.23/33.88  | |              (7), (15) gives:
% 202.23/33.88  | |   (22)  all_6_1 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | GROUND_INST: instantiating (1) with all_4_2, all_52_6, e2, e2, simplifying
% 202.23/33.88  | |              with (4), (5) gives:
% 202.23/33.88  | |   (23)  all_52_6 = all_4_2
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (13), (22) imply:
% 202.23/33.88  | |   (24)  op(e3, e2) = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | GROUND_INST: instantiating (1) with all_52_9, e2, e2, e3, simplifying with
% 202.23/33.88  | |              (14), (24) gives:
% 202.23/33.88  | |   (25)  all_52_9 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (16), (25) imply:
% 202.23/33.88  | |   (26)  op(e2, e2) = e3
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (1), (5), (21), (26) are inconsistent by sub-proof #1318.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (27)   ~ (all_56_4 = e3)
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (2), (27) imply:
% 202.23/33.88  | |   (28)   ~ (all_52_3 = e3)
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (6) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (29)  all_58_2 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (10), (28), (29) are inconsistent by sub-proof #1369.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (30)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (3), (8), (9), (12), (30) are inconsistent by sub-proof #921.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #387 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (3)  op(e2, e3) = all_52_3
% 202.23/33.88    (4)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.23/33.88    (5)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.88    (6)  all_58_0 = all_6_2
% 202.23/33.88    (7)   ~ (all_10_0 = e3)
% 202.23/33.88    (8)  op(e2, e2) = all_4_2
% 202.23/33.88    (9)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.88    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.88    (11)   ~ (all_10_0 = e2)
% 202.23/33.88    (12)  all_58_12 = all_52_7
% 202.23/33.88    (13)  all_58_2 = all_52_3
% 202.23/33.88    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.88    (15)   ~ (e2 = e0)
% 202.23/33.88    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.88    (17)  all_58_6 = all_10_0
% 202.23/33.88    (18)  op(e3, all_6_1) = e2
% 202.23/33.88    (19)  all_56_0 = all_6_2
% 202.23/33.88    (20)  op(e3, e3) = all_6_2
% 202.23/33.88    (21)  op(all_4_2, all_4_2) = all_52_10
% 202.23/33.88    (22)   ~ (e3 = e2)
% 202.23/33.88    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.88    (24)   ~ (all_52_3 = all_4_2)
% 202.23/33.88    (25)  op(all_6_2, e3) = all_6_1
% 202.23/33.88  
% 202.23/33.88  Begin of proof
% 202.23/33.88  | 
% 202.23/33.88  | ALPHA: (4) implies:
% 202.23/33.88  |   (26)  all_52_6 = e0
% 202.23/33.88  |   (27)  all_52_2 = e2
% 202.23/33.88  |   (28)  all_52_0 = e3
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (1), (27) imply:
% 202.23/33.88  |   (29)  op(all_52_3, all_52_3) = e2
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (5), (26) imply:
% 202.23/33.88  |   (30)  op(all_52_7, all_52_7) = e0
% 202.23/33.88  | 
% 202.23/33.88  | REDUCE: (9), (28) imply:
% 202.23/33.88  |   (31)  op(all_6_2, all_6_2) = e3
% 202.23/33.88  | 
% 202.23/33.88  | BETA: splitting (16) gives:
% 202.23/33.88  | 
% 202.23/33.88  | Case 1:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (32)  all_58_0 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | COMBINE_EQS: (6), (32) imply:
% 202.23/33.88  | |   (33)  all_6_2 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (31), (33) imply:
% 202.23/33.88  | |   (34)  op(e2, e2) = e3
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (25), (33) imply:
% 202.23/33.88  | |   (35)  op(e2, e3) = all_6_1
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (20), (33) imply:
% 202.23/33.88  | |   (36)  op(e3, e3) = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REF_CLOSE: (2), (3), (7), (8), (12), (13), (14), (15), (17), (21), (22),
% 202.23/33.88  | |            (24), (30), (32), (34), (35), (36) are inconsistent by sub-proof
% 202.23/33.88  | |            #904.
% 202.23/33.88  | | 
% 202.23/33.88  | Case 2:
% 202.23/33.88  | | 
% 202.23/33.88  | |   (37)   ~ (all_58_0 = e2)
% 202.23/33.88  | |   (38)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.88  | | 
% 202.23/33.88  | | REDUCE: (6), (37) imply:
% 202.23/33.88  | |   (39)   ~ (all_6_2 = e2)
% 202.23/33.88  | | 
% 202.23/33.88  | | BETA: splitting (23) gives:
% 202.23/33.88  | | 
% 202.23/33.88  | | Case 1:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (40)  all_56_0 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | COMBINE_EQS: (19), (40) imply:
% 202.23/33.88  | | |   (41)  all_6_2 = e3
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (2), (18), (20), (22), (25), (41) are inconsistent by sub-proof
% 202.23/33.88  | | |            #502.
% 202.23/33.88  | | | 
% 202.23/33.88  | | Case 2:
% 202.23/33.88  | | | 
% 202.23/33.88  | | |   (42)   ~ (all_56_0 = e3)
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REDUCE: (19), (42) imply:
% 202.23/33.88  | | |   (43)   ~ (all_6_2 = e3)
% 202.23/33.88  | | | 
% 202.23/33.88  | | | REF_CLOSE: (2), (6), (7), (8), (10), (11), (13), (14), (17), (20), (22),
% 202.23/33.88  | | |            (24), (29), (31), (38), (43) are inconsistent by sub-proof
% 202.23/33.88  | | |            #907.
% 202.23/33.88  | | | 
% 202.23/33.88  | | End of split
% 202.23/33.88  | | 
% 202.23/33.88  | End of split
% 202.23/33.88  | 
% 202.23/33.88  End of proof
% 202.23/33.88  
% 202.23/33.88  Sub-proof #388 shows that the following formulas are inconsistent:
% 202.23/33.88  ----------------------------------------------------------------
% 202.23/33.88    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.23/33.88    (2)   ~ (all_52_15 = all_52_23)
% 202.23/33.88    (3)   ~ (all_52_25 = all_52_27)
% 202.23/33.88    (4)  all_58_14 = all_52_23
% 202.23/33.88    (5)   ~ (e3 = e1)
% 202.23/33.88    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.23/33.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.23/33.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.23/33.88    (8)   ~ (all_52_5 = all_52_13)
% 202.23/33.88    (9)  all_58_1 = all_52_9
% 202.23/33.88    (10)   ~ (all_52_9 = all_52_13)
% 202.23/33.88    (11)   ~ (e3 = e0)
% 202.23/33.88    (12)  op(e2, e3) = all_52_3
% 202.23/33.88    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.88    (14)   ~ (all_52_7 = all_52_15)
% 202.23/33.88    (15)   ~ (all_52_3 = all_52_19)
% 202.23/33.88    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.23/33.88    (17)   ~ (all_52_17 = all_52_25)
% 202.23/33.88    (18)   ~ (all_52_3 = all_6_2)
% 202.23/33.88    (19)  all_44_2 = all_6_2
% 202.23/33.88    (20)  all_58_0 = all_6_2
% 202.23/33.88    (21)  op(all_14_2, e0) = all_14_1
% 202.23/33.88    (22)  all_56_4 = all_52_3
% 202.23/33.88    (23)  all_38_2 = all_4_2
% 202.23/33.88    (24)   ~ (all_52_17 = all_10_2)
% 202.23/33.88    (25)  op(e0, all_14_1) = all_14_0
% 202.23/33.88    (26)  op(all_52_5, all_52_5) = all_52_4
% 202.23/33.89    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.23/33.89    (28)  op(all_52_19, all_52_19) = all_52_18
% 202.23/33.89    (29)   ~ (all_52_27 = all_52_29)
% 202.23/33.89    (30)  all_58_13 = all_52_15
% 202.23/33.89    (31)  op(all_10_2, all_10_2) = all_52_20
% 202.23/33.89    (32)  all_58_9 = all_52_25
% 202.23/33.89    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.23/33.89    (34)   ~ (all_52_29 = all_14_2)
% 202.23/33.89    (35)  op(all_52_27, all_52_27) = all_52_26
% 202.23/33.89    (36)  op(e1, e3) = all_52_5
% 202.23/33.89    (37)  all_32_2 = all_4_2
% 202.23/33.89    (38)  op(e2, e2) = all_4_2
% 202.23/33.89    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.89    (40)   ~ (all_52_3 = all_52_5)
% 202.23/33.89    (41)  all_58_11 = all_52_29
% 202.23/33.89    (42)  all_56_5 = all_4_2
% 202.23/33.89    (43)   ~ (all_52_25 = all_14_2)
% 202.23/33.89    (44)   ~ (all_52_9 = all_52_15)
% 202.23/33.89    (45)   ~ (all_52_3 = all_52_27)
% 202.23/33.89    (46)  op(all_10_2, e1) = all_10_1
% 202.23/33.89    (47)  op(all_6_2, all_6_2) = all_52_0
% 202.23/33.89    (48)   ~ (all_52_7 = all_6_2)
% 202.23/33.89    (49)  op(e0, e0) = all_14_2
% 202.23/33.89    (50)  all_56_15 = all_14_2
% 202.23/33.89    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.89    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.23/33.89    (53)  op(all_4_2, e2) = e3
% 202.23/33.89    (54)  all_56_11 = all_52_29
% 202.23/33.89    (55)   ~ (all_4_0 = e3)
% 202.23/33.89    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.23/33.89    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.89    (58)  all_56_9 = all_52_13
% 202.23/33.89    (59)   ~ (e2 = e1)
% 202.23/33.89    (60)  all_58_10 = all_52_27
% 202.23/33.89    (61)  all_56_8 = all_52_5
% 202.23/33.89    (62)  op(all_52_9, all_52_9) = all_52_8
% 202.23/33.89    (63)  op(all_52_15, all_52_15) = all_52_14
% 202.23/33.89    (64)   ~ (all_52_19 = all_52_23)
% 202.23/33.89    (65)   ~ (all_52_25 = all_52_29)
% 202.23/33.89    (66)   ~ (all_52_29 = all_10_2)
% 202.23/33.89    (67)  all_58_7 = all_52_13
% 202.23/33.89    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.89    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.89    (70)   ~ (all_52_5 = all_52_7)
% 202.23/33.89    (71)  all_58_12 = all_52_7
% 202.23/33.89    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.89    (73)   ~ (all_52_7 = all_14_2)
% 202.23/33.89    (74)  all_38_0 = all_4_0
% 202.23/33.89    (75)  all_58_2 = all_52_3
% 202.23/33.89    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.89    (77)  all_56_2 = all_52_17
% 202.23/33.89    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.89    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.89    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.23/33.89    (81)   ~ (all_14_0 = e3)
% 202.23/33.89    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.89    (83)  all_56_7 = all_52_27
% 202.23/33.89    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.89    (85)   ~ (e2 = e0)
% 202.23/33.89    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.89    (87)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.89    (88)   ~ (all_52_5 = all_52_29)
% 202.23/33.89    (89)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.23/33.89    (90)  all_56_6 = all_52_19
% 202.23/33.89    (91)   ~ (all_52_15 = all_14_2)
% 202.23/33.89    (92)   ~ (all_52_19 = all_52_27)
% 202.23/33.89    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.89    (94)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.23/33.89    (95)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 202.23/33.89            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 202.23/33.89    (96)   ~ (all_52_13 = all_4_2)
% 202.23/33.89    (97)  op(e3, e1) = all_52_17
% 202.23/33.89    (98)   ~ (all_44_0 = e2) |  ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.89    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.89    (100)  op(e0, e3) = all_52_7
% 202.23/33.89    (101)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.89    (102)   ~ (all_52_9 = all_52_25)
% 202.23/33.89    (103)  all_58_15 = all_14_2
% 202.23/33.89    (104)   ~ (all_52_19 = all_10_2)
% 202.23/33.89    (105)  op(all_52_23, all_52_23) = all_52_22
% 202.23/33.89    (106)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.89    (107)  all_58_8 = all_10_2
% 202.23/33.89    (108)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.89    (109)   ~ (all_52_5 = all_10_2)
% 202.23/33.89    (110)  op(all_52_29, all_52_29) = all_52_28
% 202.23/33.89    (111)   ~ (all_52_23 = all_14_2)
% 202.23/33.89    (112)  all_56_12 = all_52_7
% 202.23/33.89    (113)  op(all_52_17, all_52_17) = all_52_16
% 202.23/33.89    (114)  all_8_2 = all_6_2
% 202.23/33.89    (115)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.89    (116)   ~ (all_52_25 = all_6_2)
% 202.23/33.89    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.89    (118)   ~ (all_52_9 = all_4_2)
% 202.23/33.89    (119)   ~ (all_52_5 = all_6_2)
% 202.23/33.89    (120)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.23/33.89    (121)   ~ (all_52_9 = all_6_2)
% 202.23/33.89    (122)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 202.23/33.89    (123)  op(e3, all_6_1) = e2
% 202.23/33.89    (124)  all_56_0 = all_6_2
% 202.23/33.89    (125)  op(e3, e3) = all_6_2
% 202.23/33.89    (126)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.89    (127)   ~ (all_52_27 = all_14_2)
% 202.23/33.89    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.89    (129)  all_56_14 = all_52_23
% 202.23/33.89    (130)  op(all_4_2, all_4_2) = all_52_10
% 202.23/33.89    (131)  all_32_0 = all_4_0
% 202.23/33.89    (132)  all_56_3 = all_52_25
% 202.23/33.89    (133)   ~ (all_52_3 = all_52_7)
% 202.23/33.89    (134)  op(all_14_2, all_14_2) = all_52_30
% 202.23/33.89    (135)  all_58_5 = all_52_19
% 202.23/33.89    (136)  all_56_1 = all_52_9
% 202.23/33.89    (137)   ~ (all_52_15 = all_4_2)
% 202.23/33.89    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.23/33.89           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.23/33.89           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.23/33.89           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.23/33.89    (139)   ~ (all_52_27 = all_4_2)
% 202.23/33.89    (140)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 202.23/33.89    (141)  all_58_6 = all_52_5
% 202.23/33.89    (142)  op(e3, e2) = all_52_9
% 202.23/33.89    (143)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.89    (144)   ~ (all_52_17 = all_6_2)
% 202.23/33.89    (145)   ~ (e1 = e0)
% 202.23/33.89    (146)  op(e2, e3) = all_4_0
% 202.23/33.89    (147)   ~ (e3 = e2)
% 202.23/33.89    (148)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.89    (149)  all_44_1 = all_6_1
% 202.23/33.89    (150)  all_38_1 = e3
% 202.23/33.89    (151)   ~ (all_52_9 = all_52_17)
% 202.23/33.89    (152)  all_56_10 = all_10_2
% 202.23/33.89    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.23/33.89    (154)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.89    (155)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.89    (156)  all_44_0 = e2
% 202.23/33.89    (157)  op(all_52_13, all_52_13) = all_52_12
% 202.23/33.89    (158)  op(e1, e1) = all_10_2
% 202.23/33.89    (159)   ~ (all_52_23 = all_10_2)
% 202.23/33.89    (160)   ~ (all_52_7 = all_52_23)
% 202.23/33.89    (161)   ~ (all_52_17 = all_52_19)
% 202.23/33.89    (162)  all_58_3 = all_4_2
% 202.23/33.89    (163)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.23/33.89    (164)  all_56_13 = all_52_15
% 202.23/33.89    (165)   ~ (all_52_3 = all_4_2)
% 202.23/33.89    (166)   ~ (all_52_19 = all_4_2)
% 202.23/33.89    (167)   ~ (all_52_17 = all_52_23)
% 202.23/33.89    (168)  all_8_1 = all_6_1
% 202.23/33.89    (169)  op(all_6_2, e3) = all_6_1
% 202.23/33.89    (170)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.23/33.89    (171)   ~ (all_52_13 = all_52_29)
% 202.23/33.89    (172)  all_58_4 = all_52_17
% 202.23/33.89    (173)   ~ (all_14_0 = e1)
% 202.23/33.89    (174)   ~ (all_14_0 = e2)
% 202.23/33.89    (175)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.89    (176)  op(all_52_25, all_52_25) = all_52_24
% 202.23/33.89  
% 202.23/33.89  Begin of proof
% 202.23/33.89  | 
% 202.23/33.89  | GROUND_INST: instantiating (7) with all_52_3, all_4_0, e3, e2, simplifying
% 202.23/33.89  |              with (12), (146) gives:
% 202.23/33.89  |   (177)  all_52_3 = all_4_0
% 202.23/33.89  | 
% 202.23/33.89  | COMBINE_EQS: (22), (177) imply:
% 202.23/33.89  |   (178)  all_56_4 = all_4_0
% 202.23/33.89  | 
% 202.23/33.89  | COMBINE_EQS: (75), (177) imply:
% 202.23/33.89  |   (179)  all_58_2 = all_4_0
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (40), (177) imply:
% 202.23/33.89  |   (180)   ~ (all_52_5 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | SIMP: (180) implies:
% 202.23/33.89  |   (181)   ~ (all_52_5 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (133), (177) imply:
% 202.23/33.89  |   (182)   ~ (all_52_7 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | SIMP: (182) implies:
% 202.23/33.89  |   (183)   ~ (all_52_7 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (15), (177) imply:
% 202.23/33.89  |   (184)   ~ (all_52_19 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | SIMP: (184) implies:
% 202.23/33.89  |   (185)   ~ (all_52_19 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (45), (177) imply:
% 202.23/33.89  |   (186)   ~ (all_52_27 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | SIMP: (186) implies:
% 202.23/33.89  |   (187)   ~ (all_52_27 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (18), (177) imply:
% 202.23/33.89  |   (188)   ~ (all_6_2 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | SIMP: (188) implies:
% 202.23/33.89  |   (189)   ~ (all_6_2 = all_4_0)
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (165), (177) imply:
% 202.23/33.89  |   (190)   ~ (all_4_0 = all_4_2)
% 202.23/33.89  | 
% 202.23/33.89  | REDUCE: (6), (177) imply:
% 202.23/33.89  |   (191)  op(all_4_0, all_4_0) = all_52_2
% 202.23/33.89  | 
% 202.23/33.89  | BETA: splitting (122) gives:
% 202.23/33.89  | 
% 202.23/33.89  | Case 1:
% 202.23/33.89  | | 
% 202.23/33.89  | |   (192)   ~ (all_38_0 = e1)
% 202.23/33.89  | | 
% 202.23/33.89  | | REDUCE: (74), (192) imply:
% 202.23/33.89  | |   (193)   ~ (all_4_0 = e1)
% 202.23/33.89  | | 
% 202.23/33.89  | | BETA: splitting (98) gives:
% 202.23/33.89  | | 
% 202.23/33.89  | | Case 1:
% 202.23/33.89  | | | 
% 202.23/33.89  | | |   (194)   ~ (all_44_0 = e2)
% 202.23/33.89  | | | 
% 202.23/33.89  | | | REDUCE: (156), (194) imply:
% 202.23/33.89  | | |   (195)  $false
% 202.23/33.89  | | | 
% 202.23/33.89  | | | CLOSE: (195) is inconsistent.
% 202.23/33.89  | | | 
% 202.23/33.89  | | Case 2:
% 202.23/33.89  | | | 
% 202.23/33.89  | | |   (196)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.23/33.89  | | | 
% 202.23/33.89  | | | BETA: splitting (95) gives:
% 202.23/33.89  | | | 
% 202.23/33.89  | | | Case 1:
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | |   (197)  all_58_15 = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | COMBINE_EQS: (103), (197) imply:
% 202.23/33.89  | | | |   (198)  all_14_2 = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (73), (198) imply:
% 202.23/33.89  | | | |   (199)   ~ (all_52_7 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (91), (198) imply:
% 202.23/33.89  | | | |   (200)   ~ (all_52_15 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (111), (198) imply:
% 202.23/33.89  | | | |   (201)   ~ (all_52_23 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (43), (198) imply:
% 202.23/33.89  | | | |   (202)   ~ (all_52_25 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (127), (198) imply:
% 202.23/33.89  | | | |   (203)   ~ (all_52_27 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (34), (198) imply:
% 202.23/33.89  | | | |   (204)   ~ (all_52_29 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (134), (198) imply:
% 202.23/33.89  | | | |   (205)  op(e0, e0) = all_52_30
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (21), (198) imply:
% 202.23/33.89  | | | |   (206)  op(e0, e0) = all_14_1
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (49), (198) imply:
% 202.23/33.89  | | | |   (207)  op(e0, e0) = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | GROUND_INST: instantiating (7) with all_14_1, all_52_30, e0, e0,
% 202.23/33.89  | | | |              simplifying with (205), (206) gives:
% 202.23/33.89  | | | |   (208)  all_52_30 = all_14_1
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | GROUND_INST: instantiating (7) with e0, all_52_30, e0, e0, simplifying
% 202.23/33.89  | | | |              with (205), (207) gives:
% 202.23/33.89  | | | |   (209)  all_52_30 = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | COMBINE_EQS: (208), (209) imply:
% 202.23/33.89  | | | |   (210)  all_14_1 = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | SIMP: (210) implies:
% 202.23/33.89  | | | |   (211)  all_14_1 = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (25), (211) imply:
% 202.23/33.89  | | | |   (212)  op(e0, e0) = all_14_0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | GROUND_INST: instantiating (7) with e0, all_14_0, e0, e0, simplifying
% 202.23/33.89  | | | |              with (207), (212) gives:
% 202.23/33.89  | | | |   (213)  all_14_0 = e0
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (81), (213) imply:
% 202.23/33.89  | | | |   (214)   ~ (e3 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (174), (213) imply:
% 202.23/33.89  | | | |   (215)   ~ (e2 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | REDUCE: (173), (213) imply:
% 202.23/33.89  | | | |   (216)   ~ (e1 = e0)
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | BETA: splitting (84) gives:
% 202.23/33.89  | | | | 
% 202.23/33.89  | | | | Case 1:
% 202.23/33.89  | | | | | 
% 202.23/33.89  | | | | |   (217)  all_56_4 = e3
% 202.23/33.89  | | | | | 
% 202.23/33.89  | | | | | REF_CLOSE: (55), (178), (217) are inconsistent by sub-proof #980.
% 202.23/33.89  | | | | | 
% 202.23/33.89  | | | | Case 2:
% 202.23/33.89  | | | | | 
% 202.23/33.89  | | | | |   (218)   ~ (all_56_4 = e3)
% 202.23/33.89  | | | | |   (219)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.89  | | | | | 
% 202.23/33.89  | | | | | BETA: splitting (138) gives:
% 202.23/33.89  | | | | | 
% 202.23/33.89  | | | | | Case 1:
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | |   (220)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 202.23/33.89  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 202.23/33.89  | | | | | |            all_52_14 = e0)
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | | BETA: splitting (220) gives:
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | | Case 1:
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | |   (221)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 202.23/33.89  | | | | | | |          = e0
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | ALPHA: (221) implies:
% 202.23/33.89  | | | | | | |   (222)  all_52_6 = e0
% 202.23/33.89  | | | | | | |   (223)  all_52_4 = e1
% 202.23/33.89  | | | | | | |   (224)  all_52_0 = e3
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (26), (223) imply:
% 202.23/33.89  | | | | | | |   (225)  op(all_52_5, all_52_5) = e1
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (16), (222) imply:
% 202.23/33.89  | | | | | | |   (226)  op(all_52_7, all_52_7) = e0
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (47), (224) imply:
% 202.23/33.89  | | | | | | |   (227)  op(all_6_2, all_6_2) = e3
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | BETA: splitting (13) gives:
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | |   (228)  all_56_12 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | COMBINE_EQS: (112), (228) imply:
% 202.23/33.89  | | | | | | | |   (229)  all_52_7 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | SIMP: (229) implies:
% 202.23/33.89  | | | | | | | |   (230)  all_52_7 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | COMBINE_EQS: (71), (230) imply:
% 202.23/33.89  | | | | | | | |   (231)  all_58_12 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (226), (230) imply:
% 202.23/33.89  | | | | | | | |   (232)  op(e3, e3) = e0
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REF_CLOSE: (5), (7), (20), (82), (109), (125), (141), (145),
% 202.23/33.89  | | | | | | | |            (158), (179), (193), (225), (231), (232) are
% 202.23/33.89  | | | | | | | |            inconsistent by sub-proof #845.
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | |   (233)   ~ (all_56_12 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (112), (233) imply:
% 202.23/33.89  | | | | | | | |   (234)   ~ (all_52_7 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REF_CLOSE: (7), (20), (55), (71), (79), (109), (123), (125),
% 202.23/33.89  | | | | | | | |            (141), (147), (158), (169), (179), (225), (227),
% 202.23/33.89  | | | | | | | |            (234) are inconsistent by sub-proof #404.
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | End of split
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | Case 2:
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | |   (235)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 202.23/33.89  | | | | | | |          all_52_14 = e0
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | ALPHA: (235) implies:
% 202.23/33.89  | | | | | | |   (236)  all_52_14 = e0
% 202.23/33.89  | | | | | | |   (237)  all_52_12 = e1
% 202.23/33.89  | | | | | | |   (238)  all_52_8 = e3
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (62), (238) imply:
% 202.23/33.89  | | | | | | |   (239)  op(all_52_9, all_52_9) = e3
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (157), (237) imply:
% 202.23/33.89  | | | | | | |   (240)  op(all_52_13, all_52_13) = e1
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (63), (236) imply:
% 202.23/33.89  | | | | | | |   (241)  op(all_52_15, all_52_15) = e0
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | BETA: splitting (13) gives:
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | |   (242)  all_56_12 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | COMBINE_EQS: (112), (242) imply:
% 202.23/33.89  | | | | | | | |   (243)  all_52_7 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | SIMP: (243) implies:
% 202.23/33.89  | | | | | | | |   (244)  all_52_7 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | COMBINE_EQS: (71), (244) imply:
% 202.23/33.89  | | | | | | | |   (245)  all_58_12 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (14), (244) imply:
% 202.23/33.89  | | | | | | | |   (246)   ~ (all_52_15 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | SIMP: (246) implies:
% 202.23/33.89  | | | | | | | |   (247)   ~ (all_52_15 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (183), (244) imply:
% 202.23/33.89  | | | | | | | |   (248)   ~ (all_4_0 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (16), (244) imply:
% 202.23/33.89  | | | | | | | |   (249)  op(e3, e3) = all_52_6
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 202.23/33.89  | | | | | | | |              simplifying with (125), (249) gives:
% 202.23/33.89  | | | | | | | |   (250)  all_52_6 = all_6_2
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | BETA: splitting (82) gives:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | |   (251)  all_58_0 = e1
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | COMBINE_EQS: (20), (251) imply:
% 202.23/33.89  | | | | | | | | |   (252)  all_6_2 = e1
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | COMBINE_EQS: (19), (252) imply:
% 202.23/33.89  | | | | | | | | |   (253)  all_44_2 = e1
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REDUCE: (169), (252) imply:
% 202.23/33.89  | | | | | | | | |   (254)  op(e1, e3) = all_6_1
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | BETA: splitting (196) gives:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | |   (255)   ~ (all_44_2 = e1)
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REDUCE: (253), (255) imply:
% 202.23/33.89  | | | | | | | | | |   (256)  $false
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | CLOSE: (256) is inconsistent.
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | |   (257)   ~ (all_44_1 = e0)
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REDUCE: (149), (257) imply:
% 202.23/33.89  | | | | | | | | | |   (258)   ~ (all_6_1 = e0)
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_5, all_6_1, e3, e1,
% 202.23/33.89  | | | | | | | | | |              simplifying with (36), (254) gives:
% 202.23/33.89  | | | | | | | | | |   (259)  all_52_5 = all_6_1
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | COMBINE_EQS: (141), (259) imply:
% 202.23/33.89  | | | | | | | | | |   (260)  all_58_6 = all_6_1
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | BETA: splitting (39) gives:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | |   (261)  all_58_0 = e0
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | COMBINE_EQS: (251), (261) imply:
% 202.23/33.89  | | | | | | | | | | |   (262)  e1 = e0
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | REDUCE: (145), (262) imply:
% 202.23/33.89  | | | | | | | | | | |   (263)  $false
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | CLOSE: (263) is inconsistent.
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | |   (264)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | BETA: splitting (264) gives:
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | |   (265)  all_58_2 = e0
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (53), (86), (118), (130),
% 202.23/33.89  | | | | | | | | | | | |            (131), (140), (142), (179), (190), (265) are
% 202.23/33.89  | | | | | | | | | | | |            inconsistent by sub-proof #675.
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | |   (266)  all_58_6 = e0 | all_58_12 = e0
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | REF_CLOSE: (11), (245), (258), (260), (266) are inconsistent
% 202.23/33.89  | | | | | | | | | | | |            by sub-proof #485.
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | End of split
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | End of split
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | End of split
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | |   (267)   ~ (all_58_0 = e1)
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REDUCE: (20), (267) imply:
% 202.23/33.89  | | | | | | | | |   (268)   ~ (all_6_2 = e1)
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REF_CLOSE: (7), (8), (9), (14), (16), (20), (26), (30), (53),
% 202.23/33.89  | | | | | | | | |            (55), (58), (67), (71), (79), (101), (118), (121),
% 202.23/33.89  | | | | | | | | |            (123), (125), (141), (142), (143), (147), (154),
% 202.23/33.89  | | | | | | | | |            (162), (169), (179), (239), (240), (247), (268) are
% 202.23/33.89  | | | | | | | | |            inconsistent by sub-proof #402.
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | End of split
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | |   (269)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | BETA: splitting (82) gives:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | |   (270)  all_58_0 = e1
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | COMBINE_EQS: (20), (270) imply:
% 202.23/33.89  | | | | | | | | |   (271)  all_6_2 = e1
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REDUCE: (48), (271) imply:
% 202.23/33.89  | | | | | | | | |   (272)   ~ (all_52_7 = e1)
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REDUCE: (189), (271) imply:
% 202.23/33.89  | | | | | | | | |   (273)   ~ (all_4_0 = e1)
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (53), (86), (112), (118),
% 202.23/33.89  | | | | | | | | |            (130), (131), (140), (142), (178), (183), (190),
% 202.23/33.89  | | | | | | | | |            (193), (199), (219), (269), (272) are inconsistent
% 202.23/33.89  | | | | | | | | |            by sub-proof #966.
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | |   (274)   ~ (all_58_0 = e1)
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REDUCE: (20), (274) imply:
% 202.23/33.89  | | | | | | | | |   (275)   ~ (all_6_2 = e1)
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | BETA: splitting (56) gives:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | |   (276)  all_56_13 = e3
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | COMBINE_EQS: (164), (276) imply:
% 202.23/33.89  | | | | | | | | | |   (277)  all_52_15 = e3
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REDUCE: (14), (277) imply:
% 202.23/33.89  | | | | | | | | | |   (278)   ~ (all_52_7 = e3)
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REDUCE: (241), (277) imply:
% 202.23/33.89  | | | | | | | | | |   (279)  op(e3, e3) = e0
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REF_CLOSE: (1), (5), (7), (11), (20), (26), (55), (71), (79),
% 202.23/33.89  | | | | | | | | | |            (82), (100), (114), (125), (141), (145), (168),
% 202.23/33.89  | | | | | | | | | |            (169), (178), (179), (189), (193), (219), (278),
% 202.23/33.89  | | | | | | | | | |            (279) are inconsistent by sub-proof #400.
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | |   (280)   ~ (all_56_13 = e3)
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REDUCE: (164), (280) imply:
% 202.23/33.89  | | | | | | | | | |   (281)   ~ (all_52_15 = e3)
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REF_CLOSE: (7), (8), (9), (14), (16), (20), (26), (30), (53),
% 202.23/33.89  | | | | | | | | | |            (55), (58), (67), (71), (79), (101), (118), (121),
% 202.23/33.89  | | | | | | | | | |            (123), (125), (141), (142), (143), (147), (154),
% 202.23/33.89  | | | | | | | | | |            (162), (169), (179), (239), (240), (275), (281)
% 202.23/33.89  | | | | | | | | | |            are inconsistent by sub-proof #402.
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | End of split
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | End of split
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | End of split
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | End of split
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | Case 2:
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | |   (282)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 202.23/33.89  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 202.23/33.89  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | | BETA: splitting (282) gives:
% 202.23/33.89  | | | | | | 
% 202.23/33.89  | | | | | | Case 1:
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | |   (283)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 202.23/33.89  | | | | | | |          all_52_22 = e0
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | ALPHA: (283) implies:
% 202.23/33.89  | | | | | | |   (284)  all_52_22 = e0
% 202.23/33.89  | | | | | | |   (285)  all_52_20 = e1
% 202.23/33.89  | | | | | | |   (286)  all_52_18 = e2
% 202.23/33.89  | | | | | | |   (287)  all_52_16 = e3
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (113), (287) imply:
% 202.23/33.89  | | | | | | |   (288)  op(all_52_17, all_52_17) = e3
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (28), (286) imply:
% 202.23/33.89  | | | | | | |   (289)  op(all_52_19, all_52_19) = e2
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (105), (284) imply:
% 202.23/33.89  | | | | | | |   (290)  op(all_52_23, all_52_23) = e0
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | REDUCE: (31), (285) imply:
% 202.23/33.89  | | | | | | |   (291)  op(all_10_2, all_10_2) = e1
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | BETA: splitting (27) gives:
% 202.23/33.89  | | | | | | | 
% 202.23/33.89  | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | |   (292)  all_56_7 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | COMBINE_EQS: (83), (292) imply:
% 202.23/33.89  | | | | | | | |   (293)  all_52_27 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | SIMP: (293) implies:
% 202.23/33.89  | | | | | | | |   (294)  all_52_27 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | COMBINE_EQS: (60), (294) imply:
% 202.23/33.89  | | | | | | | |   (295)  all_58_10 = e3
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (3), (294) imply:
% 202.23/33.89  | | | | | | | |   (296)   ~ (all_52_25 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (29), (294) imply:
% 202.23/33.89  | | | | | | | |   (297)   ~ (all_52_29 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | SIMP: (297) implies:
% 202.23/33.89  | | | | | | | |   (298)   ~ (all_52_29 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (187), (294) imply:
% 202.23/33.89  | | | | | | | |   (299)   ~ (all_4_0 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (139), (294) imply:
% 202.23/33.89  | | | | | | | |   (300)   ~ (all_4_2 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | SIMP: (300) implies:
% 202.23/33.89  | | | | | | | |   (301)   ~ (all_4_2 = e3)
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | REDUCE: (35), (294) imply:
% 202.23/33.89  | | | | | | | |   (302)  op(e3, e3) = all_52_26
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_26, e3, e3,
% 202.23/33.89  | | | | | | | |              simplifying with (125), (302) gives:
% 202.23/33.89  | | | | | | | |   (303)  all_52_26 = all_6_2
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | BETA: splitting (93) gives:
% 202.23/33.89  | | | | | | | | 
% 202.23/33.89  | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | |   (304)  all_56_11 = e3
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | REF_CLOSE: (54), (298), (304) are inconsistent by sub-proof
% 202.23/33.89  | | | | | | | | |            #1028.
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | |   (305)   ~ (all_56_11 = e3)
% 202.23/33.89  | | | | | | | | |   (306)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | BETA: splitting (117) gives:
% 202.23/33.89  | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | |   (307)  all_56_3 = e3
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | REF_CLOSE: (132), (296), (307) are inconsistent by sub-proof
% 202.23/33.89  | | | | | | | | | |            #1339.
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | |   (308)   ~ (all_56_3 = e3)
% 202.23/33.89  | | | | | | | | | |   (309)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | BETA: splitting (120) gives:
% 202.23/33.89  | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | |   (310)  all_58_9 = e2
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | COMBINE_EQS: (32), (310) imply:
% 202.23/33.89  | | | | | | | | | | |   (311)  all_52_25 = e2
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | SIMP: (311) implies:
% 202.23/33.89  | | | | | | | | | | |   (312)  all_52_25 = e2
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | REDUCE: (65), (312) imply:
% 202.23/33.89  | | | | | | | | | | |   (313)   ~ (all_52_29 = e2)
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | SIMP: (313) implies:
% 202.23/33.89  | | | | | | | | | | |   (314)   ~ (all_52_29 = e2)
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | REDUCE: (116), (312) imply:
% 202.23/33.89  | | | | | | | | | | |   (315)   ~ (all_6_2 = e2)
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | SIMP: (315) implies:
% 202.23/33.89  | | | | | | | | | | |   (316)   ~ (all_6_2 = e2)
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | REDUCE: (176), (312) imply:
% 202.23/33.89  | | | | | | | | | | |   (317)  op(e2, e2) = all_52_24
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | BETA: splitting (306) gives:
% 202.23/33.89  | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | |   (318)  all_56_11 = e2
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | REF_CLOSE: (54), (314), (318) are inconsistent by sub-proof
% 202.23/33.89  | | | | | | | | | | | |            #1024.
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | |   (319)  all_56_11 = e1 | all_56_11 = e0
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | BETA: splitting (319) gives:
% 202.23/33.89  | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | |   (320)  all_56_11 = e1
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | COMBINE_EQS: (54), (320) imply:
% 202.23/33.89  | | | | | | | | | | | | |   (321)  all_52_29 = e1
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | SIMP: (321) implies:
% 202.23/33.89  | | | | | | | | | | | | |   (322)  all_52_29 = e1
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | REDUCE: (88), (322) imply:
% 202.23/33.89  | | | | | | | | | | | | |   (323)   ~ (all_52_5 = e1)
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | REDUCE: (298), (322) imply:
% 202.23/33.89  | | | | | | | | | | | | |   (324)   ~ (e3 = e1)
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_24, e2, e2,
% 202.23/33.89  | | | | | | | | | | | | |              simplifying with (38), (317) gives:
% 202.23/33.89  | | | | | | | | | | | | |   (325)  all_52_24 = all_4_2
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | BETA: splitting (69) gives:
% 202.23/33.89  | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | Case 1:
% 202.23/33.89  | | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | |   (326)  all_58_2 = e1
% 202.23/33.89  | | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | | REF_CLOSE: (179), (193), (326) are inconsistent by sub-proof
% 202.23/33.89  | | | | | | | | | | | | | |            #967.
% 202.23/33.89  | | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | Case 2:
% 202.23/33.89  | | | | | | | | | | | | | | 
% 202.23/33.89  | | | | | | | | | | | | | |   (327)   ~ (all_58_2 = e1)
% 202.23/33.90  | | | | | | | | | | | | | |   (328)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | |   (329)  all_58_0 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (20), (26), (36), (37), (38),
% 202.23/33.90  | | | | | | | | | | | | | | |            (42), (47), (53), (61), (86), (106), (119), (123),
% 202.23/33.90  | | | | | | | | | | | | | | |            (125), (130), (131), (140), (149), (162), (169),
% 202.23/33.90  | | | | | | | | | | | | | | |            (170), (178), (179), (181), (189), (190), (196),
% 202.23/33.90  | | | | | | | | | | | | | | |            (219), (295), (301), (328), (329) are inconsistent
% 202.23/33.90  | | | | | | | | | | | | | | |            by sub-proof #398.
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | |   (330)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | |   (331)  all_58_2 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | REF_CLOSE: (179), (193), (331) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | |            #967.
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | |   (332)  all_58_6 = e1 | all_58_12 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (333)  all_58_6 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (323), (333) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | |            #963.
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (334)  all_58_12 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (334) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (335)  all_52_7 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | SIMP: (335) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (336)  all_52_7 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | REDUCE: (48), (336) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (337)   ~ (all_6_2 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | SIMP: (337) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (338)   ~ (all_6_2 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | REDUCE: (183), (336) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (339)   ~ (all_4_0 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (340)  all_56_0 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (340) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (341)  all_6_2 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | SIMP: (341) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (342)  all_6_2 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (123), (125), (147), (169), (342) are
% 202.23/33.90  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (343)   ~ (all_56_0 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (344)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | REDUCE: (124), (343) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (345)   ~ (all_6_2 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (346)  all_58_0 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (346) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (347)  all_6_2 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REDUCE: (345), (347) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (348)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | CLOSE: (348) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (349)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (350)  all_58_2 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (350) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |            #948.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (351)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (352)  all_58_6 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (352) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (353)  all_52_5 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | SIMP: (353) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (354)  all_52_5 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (354) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (355)  op(e3, e3) = all_52_4
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (356)  all_56_0 = e2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (316), (356) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |            #597.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (357)  all_56_0 = e1 | all_56_0 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_58_0 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (358) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_6_2 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (359) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |   (360)  op(e3, e3) = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (20), (71), (82), (100), (114),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |            (125), (145), (168), (169), (179), (193), (352),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |            (355), (360) are inconsistent by sub-proof #401.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |   (361)   ~ (all_58_0 = e0)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (361) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |   (362)   ~ (all_6_2 = e0)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (338), (357), (362) are inconsistent by
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1066.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (363)  all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (363) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (364)  e3 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (364) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (365)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | |   (366)  all_56_11 = e0
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | REF_CLOSE: (54), (204), (366) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | |            #1002.
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | |   (367)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | BETA: splitting (367) gives:
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | |   (368)  all_58_10 = e2
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | REF_CLOSE: (147), (295), (368) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | |            #1220.
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | |   (369)  all_58_11 = e2 | all_58_15 = e2
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | BETA: splitting (369) gives:
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | |   (370)  all_58_11 = e2
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | COMBINE_EQS: (41), (370) imply:
% 202.23/33.90  | | | | | | | | | | | | |   (371)  all_52_29 = e2
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | SIMP: (371) implies:
% 202.23/33.90  | | | | | | | | | | | | |   (372)  all_52_29 = e2
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | REDUCE: (171), (372) imply:
% 202.23/33.90  | | | | | | | | | | | | |   (373)   ~ (all_52_13 = e2)
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | REDUCE: (65), (372) imply:
% 202.23/33.90  | | | | | | | | | | | | |   (374)   ~ (all_52_25 = e2)
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | REDUCE: (298), (372) imply:
% 202.23/33.90  | | | | | | | | | | | | |   (375)   ~ (e3 = e2)
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | BETA: splitting (52) gives:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | |   (376)  all_58_9 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | COMBINE_EQS: (32), (376) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (377)  all_52_25 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | SIMP: (377) implies:
% 202.23/33.90  | | | | | | | | | | | | | |   (378)  all_52_25 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (116), (378) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (379)   ~ (all_6_2 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | SIMP: (379) implies:
% 202.23/33.90  | | | | | | | | | | | | | |   (380)   ~ (all_6_2 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (296), (378) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (381)   ~ (e3 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | |   (382)  all_58_0 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | COMBINE_EQS: (20), (382) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (383)  all_6_2 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (380), (383) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (384)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | CLOSE: (384) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | |   (385)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | |   (386)  all_56_13 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (386) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | |   (387)  all_52_15 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | REDUCE: (44), (387) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | |   (388)   ~ (all_52_9 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (20), (32), (123), (125), (128), (144),
% 202.23/33.90  | | | | | | | | | | | | | | | |            (147), (153), (169), (172), (288), (296), (388)
% 202.23/33.90  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #446.
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | |   (389)   ~ (all_56_13 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | REDUCE: (164), (389) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | |   (390)   ~ (all_52_15 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (391)  all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (391) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (392)  all_52_7 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | SIMP: (392) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (393)  all_52_7 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | REDUCE: (70), (393) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (394)   ~ (all_52_5 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | REDUCE: (16), (393) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (395)  op(e3, e3) = all_52_6
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | BETA: splitting (385) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (396)  all_58_2 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (193), (396) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | |            #967.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (397)  all_58_6 = e1 | all_58_12 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | BETA: splitting (397) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (398)  all_58_6 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (398) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (399)  all_52_5 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | SIMP: (399) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (400)  all_52_5 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |              simplifying with (125), (395) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (401)  all_52_6 = all_6_2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (402)  all_56_9 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (402) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (403)  all_52_13 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | SIMP: (403) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (404)  all_52_13 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (404) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (405)   ~ (all_52_9 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (20), (32), (123), (125), (128), (144),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |            (147), (153), (169), (172), (288), (296), (405)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #446.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (406)   ~ (all_56_9 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (406) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (407)   ~ (all_52_13 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (408)  all_58_6 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (398), (408) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |            #1128.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (409)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (67), (107), (125), (152), (175),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |            (291), (298), (380), (395), (407), (409) are
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #396.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (410)  all_58_12 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (391), (410) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |            #894.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (411)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (412)  all_58_13 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (390), (412) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | |            #1360.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (413)  all_58_14 = e3 | all_58_15 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | BETA: splitting (413) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (414)  all_58_14 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (414) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (415)  all_52_23 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | SIMP: (415) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (416)  all_52_23 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REDUCE: (160), (416) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (417)   ~ (all_52_7 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REDUCE: (290), (416) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (418)  op(e3, e3) = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (11), (20), (26), (55), (71), (79),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |            (82), (100), (114), (125), (141), (145), (168),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |            (169), (178), (179), (189), (193), (219), (417),
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |            (418) are inconsistent by sub-proof #400.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (419)  all_58_15 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (419) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (420)  e3 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REDUCE: (11), (420) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (421)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | |   (422)   ~ (all_58_9 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (32), (422) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (423)   ~ (all_52_25 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REF_CLOSE: (132), (202), (309), (374), (423) are inconsistent
% 202.23/33.90  | | | | | | | | | | | | | |            by sub-proof #1215.
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | |   (424)  all_58_15 = e2
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | REF_CLOSE: (85), (197), (424) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | |            #1223.
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | |   (425)   ~ (all_56_7 = e3)
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | REDUCE: (83), (425) imply:
% 202.23/33.90  | | | | | | | |   (426)   ~ (all_52_27 = e3)
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (47), (51), (53), (55), (60),
% 202.23/33.90  | | | | | | | |            (76), (86), (90), (118), (125), (130), (131), (135),
% 202.23/33.90  | | | | | | | |            (140), (142), (162), (166), (178), (179), (189),
% 202.23/33.90  | | | | | | | |            (190), (193), (219), (289), (426) are inconsistent by
% 202.23/33.90  | | | | | | | |            sub-proof #944.
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | End of split
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | Case 2:
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | |   (427)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.23/33.90  | | | | | | |          all_52_30 = e0
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | ALPHA: (427) implies:
% 202.23/33.90  | | | | | | |   (428)  all_52_28 = e1
% 202.23/33.90  | | | | | | |   (429)  all_52_26 = e2
% 202.23/33.90  | | | | | | |   (430)  all_52_24 = e3
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REDUCE: (176), (430) imply:
% 202.23/33.90  | | | | | | |   (431)  op(all_52_25, all_52_25) = e3
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REDUCE: (35), (429) imply:
% 202.23/33.90  | | | | | | |   (432)  op(all_52_27, all_52_27) = e2
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REDUCE: (110), (428) imply:
% 202.23/33.90  | | | | | | |   (433)  op(all_52_29, all_52_29) = e1
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REF_CLOSE: (5), (7), (11), (20), (27), (29), (32), (37), (38),
% 202.23/33.90  | | | | | | |            (41), (42), (47), (51), (53), (55), (60), (65), (79),
% 202.23/33.90  | | | | | | |            (83), (86), (116), (117), (118), (125), (126), (130),
% 202.23/33.90  | | | | | | |            (131), (132), (135), (139), (140), (142), (162), (166),
% 202.23/33.90  | | | | | | |            (178), (179), (189), (190), (193), (197), (202), (219),
% 202.23/33.90  | | | | | | |            (431), (432), (433) are inconsistent by sub-proof #941.
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | End of split
% 202.23/33.90  | | | | | | 
% 202.23/33.90  | | | | | End of split
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | End of split
% 202.23/33.90  | | | | 
% 202.23/33.90  | | | Case 2:
% 202.23/33.90  | | | | 
% 202.23/33.90  | | | |   (434)   ~ (all_58_15 = e0)
% 202.23/33.90  | | | |   (435)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 202.23/33.90  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 202.23/33.90  | | | | 
% 202.23/33.90  | | | | ALPHA: (435) implies:
% 202.23/33.90  | | | |   (436)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.23/33.90  | | | |   (437)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.23/33.90  | | | | 
% 202.23/33.90  | | | | REDUCE: (103), (434) imply:
% 202.23/33.90  | | | |   (438)   ~ (all_14_2 = e0)
% 202.23/33.90  | | | | 
% 202.23/33.90  | | | | BETA: splitting (84) gives:
% 202.23/33.90  | | | | 
% 202.23/33.90  | | | | Case 1:
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | |   (439)  all_56_4 = e3
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | | REF_CLOSE: (55), (178), (439) are inconsistent by sub-proof #980.
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | Case 2:
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | |   (440)   ~ (all_56_4 = e3)
% 202.23/33.90  | | | | |   (441)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | | BETA: splitting (138) gives:
% 202.23/33.90  | | | | | 
% 202.23/33.90  | | | | | Case 1:
% 202.23/33.90  | | | | | | 
% 202.23/33.90  | | | | | |   (442)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 202.23/33.90  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 202.23/33.90  | | | | | |            all_52_14 = e0)
% 202.23/33.90  | | | | | | 
% 202.23/33.90  | | | | | | BETA: splitting (442) gives:
% 202.23/33.90  | | | | | | 
% 202.23/33.90  | | | | | | Case 1:
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | |   (443)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 202.23/33.90  | | | | | | |          = e0
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | ALPHA: (443) implies:
% 202.23/33.90  | | | | | | |   (444)  all_52_6 = e0
% 202.23/33.90  | | | | | | |   (445)  all_52_4 = e1
% 202.23/33.90  | | | | | | |   (446)  all_52_0 = e3
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REDUCE: (26), (445) imply:
% 202.23/33.90  | | | | | | |   (447)  op(all_52_5, all_52_5) = e1
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REDUCE: (16), (444) imply:
% 202.23/33.90  | | | | | | |   (448)  op(all_52_7, all_52_7) = e0
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | REDUCE: (47), (446) imply:
% 202.23/33.90  | | | | | | |   (449)  op(all_6_2, all_6_2) = e3
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | BETA: splitting (108) gives:
% 202.23/33.90  | | | | | | | 
% 202.23/33.90  | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | |   (450)  all_56_15 = e3
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | COMBINE_EQS: (50), (450) imply:
% 202.23/33.90  | | | | | | | |   (451)  all_14_2 = e3
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | SIMP: (451) implies:
% 202.23/33.90  | | | | | | | |   (452)  all_14_2 = e3
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | REDUCE: (73), (452) imply:
% 202.23/33.90  | | | | | | | |   (453)   ~ (all_52_7 = e3)
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | REF_CLOSE: (7), (20), (55), (71), (79), (109), (123), (125),
% 202.23/33.90  | | | | | | | |            (141), (147), (158), (169), (179), (447), (449),
% 202.23/33.90  | | | | | | | |            (453) are inconsistent by sub-proof #404.
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | |   (454)   ~ (all_56_15 = e3)
% 202.23/33.90  | | | | | | | |   (455)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | REDUCE: (50), (454) imply:
% 202.23/33.90  | | | | | | | |   (456)   ~ (all_14_2 = e3)
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | BETA: splitting (27) gives:
% 202.23/33.90  | | | | | | | | 
% 202.23/33.90  | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | |   (457)  all_56_7 = e3
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | COMBINE_EQS: (83), (457) imply:
% 202.23/33.90  | | | | | | | | |   (458)  all_52_27 = e3
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | SIMP: (458) implies:
% 202.23/33.90  | | | | | | | | |   (459)  all_52_27 = e3
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | COMBINE_EQS: (60), (459) imply:
% 202.23/33.90  | | | | | | | | |   (460)  all_58_10 = e3
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (92), (459) imply:
% 202.23/33.90  | | | | | | | | |   (461)   ~ (all_52_19 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (3), (459) imply:
% 202.23/33.90  | | | | | | | | |   (462)   ~ (all_52_25 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (29), (459) imply:
% 202.23/33.90  | | | | | | | | |   (463)   ~ (all_52_29 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | SIMP: (463) implies:
% 202.23/33.90  | | | | | | | | |   (464)   ~ (all_52_29 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (127), (459) imply:
% 202.23/33.90  | | | | | | | | |   (465)   ~ (all_14_2 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (187), (459) imply:
% 202.23/33.90  | | | | | | | | |   (466)   ~ (all_4_0 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (139), (459) imply:
% 202.23/33.90  | | | | | | | | |   (467)   ~ (all_4_2 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | SIMP: (467) implies:
% 202.23/33.90  | | | | | | | | |   (468)   ~ (all_4_2 = e3)
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | REDUCE: (35), (459) imply:
% 202.23/33.90  | | | | | | | | |   (469)  op(e3, e3) = all_52_26
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_26, e3, e3,
% 202.23/33.90  | | | | | | | | |              simplifying with (125), (469) gives:
% 202.23/33.90  | | | | | | | | |   (470)  all_52_26 = all_6_2
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | BETA: splitting (93) gives:
% 202.23/33.90  | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | |   (471)  all_56_11 = e3
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | REF_CLOSE: (54), (464), (471) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | |            #1028.
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | |   (472)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | BETA: splitting (117) gives:
% 202.23/33.90  | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | |   (473)  all_56_3 = e3
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | REF_CLOSE: (132), (462), (473) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | |            #1339.
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | |   (474)   ~ (all_56_3 = e3)
% 202.23/33.90  | | | | | | | | | | |   (475)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | BETA: splitting (76) gives:
% 202.23/33.90  | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | |   (476)  all_56_6 = e3
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | REF_CLOSE: (90), (461), (476) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | |            #957.
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | |   (477)   ~ (all_56_6 = e3)
% 202.23/33.90  | | | | | | | | | | | |   (478)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | BETA: splitting (86) gives:
% 202.23/33.90  | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | |   (479)  all_56_5 = e3
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | REF_CLOSE: (42), (468), (479) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | |            #1319.
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | |   (480)   ~ (all_56_5 = e3)
% 202.23/33.90  | | | | | | | | | | | | |   (481)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | BETA: splitting (82) gives:
% 202.23/33.90  | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | |   (482)  all_58_0 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | COMBINE_EQS: (20), (482) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (483)  all_6_2 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | COMBINE_EQS: (19), (483) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (484)  all_44_2 = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (119), (483) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (485)   ~ (all_52_5 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (449), (483) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (486)  op(e1, e1) = e3
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (169), (483) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (487)  op(e1, e3) = all_6_1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | REDUCE: (125), (483) imply:
% 202.23/33.90  | | | | | | | | | | | | | |   (488)  op(e3, e3) = e1
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | |   (489)   ~ (all_44_2 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (484), (489) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (490)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | CLOSE: (490) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | |   (491)   ~ (all_44_1 = e0)
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (149), (491) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (492)   ~ (all_6_1 = e0)
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, e3, e1, e1,
% 202.23/33.90  | | | | | | | | | | | | | | |              simplifying with (158), (486) gives:
% 202.23/33.90  | | | | | | | | | | | | | | |   (493)  all_10_2 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_5, all_6_1, e3, e1,
% 202.23/33.90  | | | | | | | | | | | | | | |              simplifying with (36), (487) gives:
% 202.23/33.90  | | | | | | | | | | | | | | |   (494)  all_52_5 = all_6_1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | COMBINE_EQS: (61), (494) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (495)  all_56_8 = all_6_1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | COMBINE_EQS: (141), (494) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (496)  all_58_6 = all_6_1
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (109), (493), (494) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (497)   ~ (all_6_1 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (485), (494) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (498)   ~ (all_6_1 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (24), (493) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (499)   ~ (all_52_17 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | REDUCE: (31), (493) imply:
% 202.23/33.90  | | | | | | | | | | | | | | |   (500)  op(e3, e3) = all_52_20
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | |   (501)  all_58_0 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (482), (501) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | |            #1244.
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | |   (502)   ~ (all_58_0 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | |   (503)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | REDUCE: (482), (502) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | |   (504)   ~ (e3 = e1)
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (505)  all_58_0 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (482), (505) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | |            #1244.
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | |   (506)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (507)  all_56_8 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (495), (497), (507) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | |            #1101.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (508)   ~ (all_56_8 = e3)
% 202.23/33.90  | | | | | | | | | | | | | | | | | |   (509)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | BETA: splitting (509) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (510)  all_56_8 = e2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (495), (510) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (511)  all_6_1 = e2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | SIMP: (511) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (512)  all_6_1 = e2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (496), (512) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (513)  all_58_6 = e2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REDUCE: (497), (512) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (514)   ~ (e3 = e2)
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (515)  all_58_2 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (515) are inconsistent by sub-proof
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |            #948.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | |   (516)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | BETA: splitting (516) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (517)  all_58_6 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (517) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (518)  e3 = e2
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (518) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (519)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (520)  all_58_12 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (520) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (521)  all_52_7 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | SIMP: (521) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (522)  all_52_7 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (448), (522) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | |   (523)  op(e3, e3) = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (506) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (524)  all_58_1 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (524) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (525)  all_52_9 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (525) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (526)  op(e3, e3) = all_52_8
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_20, e3, e3,
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (488), (500) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (527)  all_52_20 = e1
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_20, all_52_8, e3,
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (500), (526) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (528)  all_52_8 = all_52_20
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, all_52_8, e3, e3,
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (523), (526) gives:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (529)  all_52_8 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (528), (529) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (530)  all_52_20 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | SIMP: (530) implies:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (531)  all_52_20 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (527), (531) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (532)  e1 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (532) imply:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (533)  $false
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (533) is inconsistent.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |   (534)  all_58_4 = e3 | all_58_9 = e3
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (172), (462), (499), (534) are inconsistent
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1276.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |   (535)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (495), (498), (535) are inconsistent by
% 202.23/33.90  | | | | | | | | | | | | | | | | | | |            sub-proof #495.
% 202.23/33.90  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | | End of split
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | Case 2:
% 202.23/33.90  | | | | | | | | | | | | | | 
% 202.23/33.90  | | | | | | | | | | | | | |   (536)   ~ (all_58_0 = e1)
% 202.23/33.91  | | | | | | | | | | | | | |   (537)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.23/33.91  | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | REDUCE: (20), (536) imply:
% 202.23/33.91  | | | | | | | | | | | | | |   (538)   ~ (all_6_2 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 202.23/33.91  | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | |   (539)  all_56_0 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | COMBINE_EQS: (124), (539) imply:
% 202.23/33.91  | | | | | | | | | | | | | | |   (540)  all_6_2 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | REDUCE: (169), (540) imply:
% 202.23/33.91  | | | | | | | | | | | | | | |   (541)  op(e3, e3) = all_6_1
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | REDUCE: (125), (540) imply:
% 202.23/33.91  | | | | | | | | | | | | | | |   (542)  op(e3, e3) = e3
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | REF_CLOSE: (7), (123), (147), (541), (542) are inconsistent
% 202.23/33.91  | | | | | | | | | | | | | | |            by sub-proof #503.
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | |   (543)   ~ (all_56_0 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | |   (544)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | REDUCE: (124), (543) imply:
% 202.23/33.91  | | | | | | | | | | | | | | |   (545)   ~ (all_6_2 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | |   (546)  all_58_0 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (546) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | |   (547)  all_6_2 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | REDUCE: (545), (547) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | |   (548)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | CLOSE: (548) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | |   (549)   ~ (all_58_0 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | |   (550)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | |   (551)  all_58_0 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (551) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | |   (552)  all_6_2 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | REDUCE: (545), (552) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | |   (553)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | CLOSE: (553) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | |   (554)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (555)  all_58_9 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (555) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (556)  all_52_25 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | SIMP: (556) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (557)  all_52_25 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | REDUCE: (65), (557) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (558)   ~ (all_52_29 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | SIMP: (558) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (559)   ~ (all_52_29 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | REDUCE: (43), (557) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (560)   ~ (all_14_2 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | SIMP: (560) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (561)   ~ (all_14_2 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | REDUCE: (116), (557) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (562)   ~ (all_6_2 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | SIMP: (562) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (563)   ~ (all_6_2 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | BETA: splitting (544) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (564)  all_56_0 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (564) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (565)  all_6_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (565) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (566)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | CLOSE: (566) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (567)  all_56_0 = e1 | all_56_0 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (568)  all_56_15 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (561), (568) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |            #762.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (569)  all_56_15 = e1 | all_56_15 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (570)  all_56_15 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (570) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (571)  all_14_2 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | SIMP: (571) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (572)  all_14_2 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (572) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (573)   ~ (all_52_29 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (456), (572) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (574)   ~ (e3 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (572) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (575)  op(e0, e0) = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (576)  all_56_11 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (559), (576) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |            #1024.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (577)  all_56_11 = e1 | all_56_11 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (577) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (578)  all_56_11 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (573), (578) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |            #1023.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (579)  all_56_11 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (579) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (580)  all_52_29 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (580) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (581)  all_52_29 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (581) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (582)  op(e0, e0) = all_52_28
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (567) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (583)  all_56_0 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (583) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (584)  all_6_2 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (584) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (585)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (585) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (586)  all_56_0 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (586) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (587)  all_6_2 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (449), (587) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (588)  op(e0, e0) = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_52_28, e0, e0,
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (582), (588) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (589)  all_52_28 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_28, e0, e0,
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (575), (582) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (590)  all_52_28 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (589), (590) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (591)  e3 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (591) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (592)  e3 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (592) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (593)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (593) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (594)  all_56_15 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (438), (594) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |            #1162.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (595)   ~ (all_58_9 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | REDUCE: (32), (595) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | |   (596)   ~ (all_52_25 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (597)  all_58_4 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (597) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (598)  all_52_17 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | SIMP: (598) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (599)  all_52_17 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | REDUCE: (151), (599) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (600)   ~ (all_52_9 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | REDUCE: (113), (599) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (601)  op(e3, e3) = all_52_16
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_16, e3, e3,
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |              simplifying with (125), (601) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (602)  all_52_16 = all_6_2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (603)  all_58_1 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (603) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (604)  all_52_9 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (600), (604) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (605)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | CLOSE: (605) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (606)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (607)  all_58_2 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (607) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |            #948.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (608)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (608) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (609)  all_58_6 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (609) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (610)  all_52_5 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | SIMP: (610) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (611)  all_52_5 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (611) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (612)   ~ (all_52_13 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | SIMP: (612) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (613)   ~ (all_52_13 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (447), (611) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (614)  op(e3, e3) = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (606) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (615)  all_58_3 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (615) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (616)  all_4_2 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (468), (616) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (617)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (617) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (618)  all_58_7 = e3 | all_58_13 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (619)  all_58_7 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (619) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (620)  all_52_13 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (620) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (621)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (621) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (622)  all_58_13 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (622) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (623)  all_52_15 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (623) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (624)  all_52_15 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (624) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (625)  op(e3, e3) = all_52_14
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (125), (538), (614), (625) are inconsistent
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1247.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (626)  all_58_12 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (109), (141), (158), (179), (193),
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |            (447), (537), (626) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |            #846.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (627)   ~ (all_58_4 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | REDUCE: (172), (627) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | |   (628)   ~ (all_52_17 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (550) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (629)  all_58_1 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (629) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (630)  all_52_9 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (630) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (631)   ~ (all_52_13 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | SIMP: (631) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (632)   ~ (all_52_13 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (630) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (633)   ~ (all_52_17 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (630) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (634)   ~ (all_6_2 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (630) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (635)  op(e3, e3) = all_52_8
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3,
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |              simplifying with (125), (635) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | |   (636)  all_52_8 = all_6_2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (637)  all_58_0 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (637) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (638)  all_6_2 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (638) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (639)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | CLOSE: (639) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | |   (640)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (641)  all_58_0 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (641) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (642)  all_6_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (642) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (643)   ~ (all_52_5 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (642) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (644)   ~ (all_4_0 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | SIMP: (644) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (645)   ~ (all_4_0 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (642) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | |   (646)  op(e3, e3) = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (647)  all_56_4 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (645), (647) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |            #979.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | |   (648)  all_56_4 = e1 | all_56_4 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (648) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (649)  all_56_4 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (193), (649) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |            #978.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (650)  all_56_4 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (650) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (651)  all_4_0 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (651) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (652)  all_4_0 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (652) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (653)  all_32_0 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (652) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (654)  all_58_2 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (652) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (655)   ~ (all_52_7 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (652) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (656)   ~ (all_52_19 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (652) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (657)   ~ (all_4_2 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (657) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (658)   ~ (all_4_2 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (652) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | |   (659)   ~ (e3 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (660)   ~ (all_32_2 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (660) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (661)   ~ (all_4_2 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (662)  all_56_5 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (662) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (663)  all_4_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (663) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (664)  all_4_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (664) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (665)   ~ (all_52_13 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (664) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (666)   ~ (all_52_19 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (667)  all_56_6 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (666), (667) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #956.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (668)   ~ (all_56_6 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (669)  all_56_6 = e1 | all_56_6 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (669) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (670)  all_56_6 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (670) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (671)  all_52_19 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (671) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (672)  all_52_19 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (672) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (673)  all_58_5 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (672) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (674)   ~ (all_52_17 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (672) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (675)   ~ (all_52_23 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (675) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (676)   ~ (all_52_23 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (461), (672) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (677)   ~ (e3 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (666), (672) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (678)   ~ (e2 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (672) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (679)  op(e1, e1) = all_52_18
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (680)  all_56_2 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (680) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (681)  all_52_17 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (628), (681) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (682)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (682) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (683)   ~ (all_56_2 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (684)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (640) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (685)  all_58_1 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (629), (685) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (686)  e3 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (686) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (687)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (687) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (688)  all_58_4 = e1 | all_58_9 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (684) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (689)  all_56_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (689) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (690)  all_52_17 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (690) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (691)  all_58_4 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (20), (32), (34), (41), (43), (49),
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (59), (80), (85), (110), (116), (145),
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (437), (449), (455), (456), (460), (545), (629),
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (688), (691) are inconsistent by sub-proof #393.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (692)  all_56_2 = e1 | all_56_2 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (693)  all_56_2 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (693) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (694)  all_52_17 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (674), (694) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (695)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (695) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (696)  all_56_2 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (696) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (697)  all_52_17 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (697) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (698)   ~ (all_52_23 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (698) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (699)   ~ (all_52_23 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (697) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (700)   ~ (all_52_25 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (700) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (701)   ~ (all_52_25 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (475) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (702)  all_56_3 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (702) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (703)  all_52_25 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (703) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (704)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (704) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (705)  all_56_3 = e1 | all_56_3 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (705) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (706)  all_56_3 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (706) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (707)  all_52_25 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (707) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (708)  all_58_9 = e1
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (707) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (709)   ~ (all_52_29 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (709) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (710)   ~ (all_52_29 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (707) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (711)   ~ (all_14_2 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (711) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (712)   ~ (all_14_2 = e1)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (707) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (713)  op(e1, e1) = all_52_24
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (714)  all_58_9 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (708), (714) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (715)  e1 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (715) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (716)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (716) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (717)  all_58_10 = e0 | all_58_11 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (718)  all_56_15 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (718) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (719)  all_14_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (719) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (720)  all_14_2 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (720) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (721)   ~ (all_52_23 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (720) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (722)   ~ (all_52_29 = e2)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (717) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (723)  all_58_10 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (723) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (724)  e3 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (724) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (725)  $false
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (725) is inconsistent.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (726)  all_58_11 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (726) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (727)  all_52_29 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (727) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (728)  all_52_29 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (728) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (729)   ~ (all_52_13 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (722), (728) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (730)   ~ (e2 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (710), (728) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (731)   ~ (e1 = e0)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (732)  all_56_9 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (632), (732) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #958.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (733)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (734)  all_56_14 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (734) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (735)  all_52_23 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (735) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (736)  all_52_23 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (736) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (737)  all_58_14 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (736) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (738)   ~ (all_10_2 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (738) implies:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (739)   ~ (all_10_2 = e3)
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (736) imply:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  op(e3, e3) = all_52_22
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  all_56_10 = e3
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (152), (739), (741) are inconsistent by sub-proof
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #913.
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  all_58_4 = e2
% 202.23/33.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (20), (34), (41), (49), (50), (80),
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (85), (110), (145), (437), (449), (455), (456),
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (460), (538), (545), (629), (708), (712), (743)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #394.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (744)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (745)  all_58_5 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (673), (745) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (746)  e2 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (746) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (747)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (747) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (748)  all_58_8 = e2 | all_58_14 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (749)  all_58_2 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (654), (749) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (750)  e3 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (750) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (751)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (751) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (752)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (753)  all_58_6 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (753) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (754)  all_52_5 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (754) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (755)  all_52_5 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (447), (755) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (756)  op(e3, e3) = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (757)  all_58_6 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (753), (757) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1128.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (758)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (759)  all_58_7 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (759) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (760)  all_52_13 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (760) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (761)  op(e1, e1) = all_52_12
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (762)  all_58_12 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (762) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (763)  all_52_7 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (763) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (764)  all_52_7 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (448), (764) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (765)  op(e1, e1) = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (742) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (766)  all_56_10 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (766) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (767)  all_10_2 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (767) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (768)  all_10_2 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (768) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (769)  op(e1, e1) = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_24, all_52_18, e1,
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (679), (713) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (770)  all_52_18 = all_52_24
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_18, e1, e1,
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (679), (769) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (771)  all_52_18 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_24, all_52_12, e1,
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (713), (761) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (772)  all_52_12 = all_52_24
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, all_52_12, e1, e1,
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (761), (765) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (773)  all_52_12 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_22, e3, e3,
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (646), (740) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (774)  all_52_22 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_22, e3, e3,
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (740), (756) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (775)  all_52_22 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (772), (773) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (776)  all_52_24 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (776) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (777)  all_52_24 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (770), (771) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (778)  all_52_24 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (778) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (779)  all_52_24 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (774), (775) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (780)  e2 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (780) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (781)  e2 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (777), (779) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  e2 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (781), (782) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  e1 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (783) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (784) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)   ~ (all_56_10 = e2)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (785) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (786)   ~ (all_10_2 = e2)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (748) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  all_58_8 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (787) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  all_10_2 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (786), (788) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (789) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  all_58_14 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (737), (790) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #701.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (791)   ~ (all_58_12 = e1)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (791) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (792)   ~ (all_52_7 = e1)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (71), (145), (537), (654), (753), (792) are
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1126.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)   ~ (all_58_7 = e1)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (793) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)   ~ (all_52_13 = e1)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (665), (729), (733), (794) are inconsistent
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #884.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (795)  all_58_12 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (109), (141), (158), (179), (193),
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (447), (537), (795) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #846.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (796)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (129), (676), (699), (721), (796) are inconsistent
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #960.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (797)  all_56_15 = e1 | all_56_15 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (438), (712), (797) are inconsistent by
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (798)  all_56_3 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (798) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (799)  all_52_25 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (701), (799) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (800)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (800) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (801)  all_56_6 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (656), (801) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #952.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (802)  all_56_5 = e1 | all_56_5 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (802) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (803)  all_56_5 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (661), (803) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1188.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (804)  all_56_5 = e0
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (658), (804) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1313.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (805)   ~ (all_32_0 = e0)
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (653), (805) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (806)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (806) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | |   (807)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (807) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | |   (808)  all_58_1 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (629), (808) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | |   (809)  e3 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (809) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | |   (810)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (810) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | |   (811)  all_58_4 = e2 | all_58_9 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (811) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | |   (812)  all_58_4 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (640) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (813)  all_58_1 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (629), (813) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (814)  e3 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (814) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (815)  $false
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (815) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (816)  all_58_4 = e1 | all_58_9 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (20), (32), (34), (41), (43), (49),
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (59), (80), (85), (110), (116), (145),
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |            (437), (449), (455), (456), (460), (545), (629),
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | |            (812), (816) are inconsistent by sub-proof #393.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | |   (817)  all_58_9 = e2
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (596), (817) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | |            #1221.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | |   (818)  all_58_4 = e3 | all_58_9 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (818) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | |   (819)  all_58_4 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (628), (819) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | |            #1302.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | |   (820)  all_58_9 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (462), (820) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | |            #1300.
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | |   (821)   ~ (all_56_7 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (83), (821) imply:
% 202.23/33.92  | | | | | | | | |   (822)   ~ (all_52_27 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | BETA: splitting (51) gives:
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | |   (823)  all_58_2 = e3
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | REF_CLOSE: (55), (179), (823) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | |            #948.
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | |   (824)   ~ (all_58_2 = e3)
% 202.23/33.92  | | | | | | | | | |   (825)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | BETA: splitting (126) gives:
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | |   (826)  all_58_9 = e3
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | COMBINE_EQS: (32), (826) imply:
% 202.23/33.92  | | | | | | | | | | |   (827)  all_52_25 = e3
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | REDUCE: (3), (827) imply:
% 202.23/33.92  | | | | | | | | | | |   (828)   ~ (all_52_27 = e3)
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | REDUCE: (43), (827) imply:
% 202.23/33.92  | | | | | | | | | | |   (829)   ~ (all_14_2 = e3)
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | REDUCE: (116), (827) imply:
% 202.23/33.92  | | | | | | | | | | |   (830)   ~ (all_6_2 = e3)
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | SIMP: (830) implies:
% 202.23/33.92  | | | | | | | | | | |   (831)   ~ (all_6_2 = e3)
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | REDUCE: (176), (827) imply:
% 202.23/33.92  | | | | | | | | | | |   (832)  op(e3, e3) = all_52_24
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 202.23/33.92  | | | | | | | | | | |              simplifying with (125), (832) gives:
% 202.23/33.92  | | | | | | | | | | |   (833)  all_52_24 = all_6_2
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | |   (834)  all_58_0 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | COMBINE_EQS: (20), (834) imply:
% 202.23/33.92  | | | | | | | | | | | |   (835)  all_6_2 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | REDUCE: (831), (835) imply:
% 202.23/33.92  | | | | | | | | | | | |   (836)  $false
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | CLOSE: (836) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | |   (837)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | BETA: splitting (76) gives:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | |   (838)  all_56_6 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | COMBINE_EQS: (90), (838) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (839)  all_52_19 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | SIMP: (839) implies:
% 202.23/33.92  | | | | | | | | | | | | |   (840)  all_52_19 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (64), (840) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (841)   ~ (all_52_23 = e3)
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | SIMP: (841) implies:
% 202.23/33.92  | | | | | | | | | | | | |   (842)   ~ (all_52_23 = e3)
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (185), (840) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (843)   ~ (all_4_0 = e3)
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (28), (840) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (844)  op(e3, e3) = all_52_18
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3,
% 202.23/33.92  | | | | | | | | | | | | |              simplifying with (125), (844) gives:
% 202.23/33.92  | | | | | | | | | | | | |   (845)  all_52_18 = all_6_2
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | BETA: splitting (72) gives:
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | |   (846)  all_58_6 = e3
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | COMBINE_EQS: (141), (846) imply:
% 202.23/33.92  | | | | | | | | | | | | | |   (847)  all_52_5 = e3
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | SIMP: (847) implies:
% 202.23/33.92  | | | | | | | | | | | | | |   (848)  all_52_5 = e3
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REDUCE: (70), (848) imply:
% 202.23/33.92  | | | | | | | | | | | | | |   (849)   ~ (all_52_7 = e3)
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | SIMP: (849) implies:
% 202.23/33.92  | | | | | | | | | | | | | |   (850)   ~ (all_52_7 = e3)
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REDUCE: (109), (848) imply:
% 202.23/33.92  | | | | | | | | | | | | | |   (851)   ~ (all_10_2 = e3)
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | SIMP: (851) implies:
% 202.23/33.92  | | | | | | | | | | | | | |   (852)   ~ (all_10_2 = e3)
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REDUCE: (447), (848) imply:
% 202.23/33.92  | | | | | | | | | | | | | |   (853)  op(e3, e3) = e1
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | |   (854)  all_58_12 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | REF_CLOSE: (71), (850), (854) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | | | |            #1367.
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | |   (855)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | BETA: splitting (855) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | |   (856)  all_58_13 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (856) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (857)  all_52_15 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | SIMP: (857) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (858)  all_52_15 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | REDUCE: (63), (858) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (859)  op(e3, e3) = all_52_14
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_14, e3, e3,
% 202.23/33.92  | | | | | | | | | | | | | | | |              simplifying with (125), (859) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (860)  all_52_14 = all_6_2
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_14, e3, e3,
% 202.23/33.92  | | | | | | | | | | | | | | | |              simplifying with (853), (859) gives:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (861)  all_52_14 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | COMBINE_EQS: (860), (861) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (862)  all_6_2 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | SIMP: (862) implies:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (863)  all_6_2 = e1
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | REDUCE: (449), (863) imply:
% 202.23/33.92  | | | | | | | | | | | | | | | |   (864)  op(e1, e1) = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (852), (864) are inconsistent by
% 202.23/33.92  | | | | | | | | | | | | | | | |            sub-proof #1368.
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | |   (865)  all_58_14 = e3 | all_58_15 = e3
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (103), (456), (842), (865) are inconsistent
% 202.23/33.92  | | | | | | | | | | | | | | | |            by sub-proof #715.
% 202.23/33.92  | | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | |   (866)   ~ (all_58_6 = e3)
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REDUCE: (141), (866) imply:
% 202.23/33.92  | | | | | | | | | | | | | |   (867)   ~ (all_52_5 = e3)
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (20), (55), (71), (82), (109), (125),
% 202.23/33.92  | | | | | | | | | | | | | |            (141), (145), (158), (179), (193), (447), (448),
% 202.23/33.92  | | | | | | | | | | | | | |            (837), (867) are inconsistent by sub-proof #640.
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | |   (868)   ~ (all_56_6 = e3)
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (90), (868) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (869)   ~ (all_52_19 = e3)
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REF_CLOSE: (7), (53), (60), (118), (135), (142), (162),
% 202.23/33.92  | | | | | | | | | | | | |            (822), (825), (869) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | | |            #945.
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | |   (870)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | BETA: splitting (870) gives:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | |   (871)  all_58_10 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | REF_CLOSE: (60), (822), (871) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | | | |            #1301.
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | |   (872)  all_58_11 = e3 | all_58_15 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | BETA: splitting (872) gives:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | |   (873)  all_58_11 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | COMBINE_EQS: (41), (873) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (874)  all_52_29 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | SIMP: (874) implies:
% 202.23/33.92  | | | | | | | | | | | | |   (875)  all_52_29 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (88), (875) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (876)   ~ (all_52_5 = e3)
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (110), (875) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (877)  op(e3, e3) = all_52_28
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_28, e3, e3,
% 202.23/33.92  | | | | | | | | | | | | |              simplifying with (125), (877) gives:
% 202.23/33.92  | | | | | | | | | | | | |   (878)  all_52_28 = all_6_2
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | |   (879)  all_58_0 = e3
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | COMBINE_EQS: (20), (879) imply:
% 202.23/33.92  | | | | | | | | | | | | | |   (880)  all_6_2 = e3
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REF_CLOSE: (7), (123), (125), (147), (169), (880) are
% 202.23/33.92  | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | |   (881)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (20), (55), (71), (82), (109), (125),
% 202.23/33.92  | | | | | | | | | | | | | |            (141), (145), (158), (179), (193), (447), (448),
% 202.23/33.92  | | | | | | | | | | | | | |            (876), (881) are inconsistent by sub-proof #640.
% 202.23/33.92  | | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | |   (882)  all_58_15 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | COMBINE_EQS: (103), (882) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (883)  all_14_2 = e3
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | REDUCE: (456), (883) imply:
% 202.23/33.92  | | | | | | | | | | | | |   (884)  $false
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | | CLOSE: (884) is inconsistent.
% 202.23/33.92  | | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | End of split
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | End of split
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | Case 2:
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | |   (885)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 202.23/33.92  | | | | | | |          all_52_14 = e0
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | | ALPHA: (885) implies:
% 202.23/33.92  | | | | | | |   (886)  all_52_14 = e0
% 202.23/33.92  | | | | | | |   (887)  all_52_12 = e1
% 202.23/33.92  | | | | | | |   (888)  all_52_8 = e3
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | | REDUCE: (62), (888) imply:
% 202.23/33.92  | | | | | | |   (889)  op(all_52_9, all_52_9) = e3
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | | REDUCE: (157), (887) imply:
% 202.23/33.92  | | | | | | |   (890)  op(all_52_13, all_52_13) = e1
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | | REDUCE: (63), (886) imply:
% 202.23/33.92  | | | | | | |   (891)  op(all_52_15, all_52_15) = e0
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | | BETA: splitting (108) gives:
% 202.23/33.92  | | | | | | | 
% 202.23/33.92  | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | |   (892)  all_56_15 = e3
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | COMBINE_EQS: (50), (892) imply:
% 202.23/33.92  | | | | | | | |   (893)  all_14_2 = e3
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | SIMP: (893) implies:
% 202.23/33.92  | | | | | | | |   (894)  all_14_2 = e3
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | REDUCE: (73), (894) imply:
% 202.23/33.92  | | | | | | | |   (895)   ~ (all_52_7 = e3)
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | REDUCE: (91), (894) imply:
% 202.23/33.92  | | | | | | | |   (896)   ~ (all_52_15 = e3)
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | REF_CLOSE: (7), (8), (9), (20), (26), (30), (53), (55), (67),
% 202.23/33.92  | | | | | | | |            (71), (79), (101), (118), (121), (123), (125), (141),
% 202.23/33.92  | | | | | | | |            (142), (147), (162), (169), (179), (889), (895),
% 202.23/33.92  | | | | | | | |            (896) are inconsistent by sub-proof #403.
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | |   (897)   ~ (all_56_15 = e3)
% 202.23/33.92  | | | | | | | |   (898)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | REDUCE: (50), (897) imply:
% 202.23/33.92  | | | | | | | |   (899)   ~ (all_14_2 = e3)
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | BETA: splitting (27) gives:
% 202.23/33.92  | | | | | | | | 
% 202.23/33.92  | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | |   (900)  all_56_7 = e3
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | COMBINE_EQS: (83), (900) imply:
% 202.23/33.92  | | | | | | | | |   (901)  all_52_27 = e3
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | SIMP: (901) implies:
% 202.23/33.92  | | | | | | | | |   (902)  all_52_27 = e3
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | COMBINE_EQS: (60), (902) imply:
% 202.23/33.92  | | | | | | | | |   (903)  all_58_10 = e3
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (3), (902) imply:
% 202.23/33.92  | | | | | | | | |   (904)   ~ (all_52_25 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (29), (902) imply:
% 202.23/33.92  | | | | | | | | |   (905)   ~ (all_52_29 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | SIMP: (905) implies:
% 202.23/33.92  | | | | | | | | |   (906)   ~ (all_52_29 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (127), (902) imply:
% 202.23/33.92  | | | | | | | | |   (907)   ~ (all_14_2 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (187), (902) imply:
% 202.23/33.92  | | | | | | | | |   (908)   ~ (all_4_0 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (139), (902) imply:
% 202.23/33.92  | | | | | | | | |   (909)   ~ (all_4_2 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | SIMP: (909) implies:
% 202.23/33.92  | | | | | | | | |   (910)   ~ (all_4_2 = e3)
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | REDUCE: (35), (902) imply:
% 202.23/33.92  | | | | | | | | |   (911)  op(e3, e3) = all_52_26
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_26, e3, e3,
% 202.23/33.92  | | | | | | | | |              simplifying with (125), (911) gives:
% 202.23/33.92  | | | | | | | | |   (912)  all_52_26 = all_6_2
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | BETA: splitting (69) gives:
% 202.23/33.92  | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | |   (913)  all_58_2 = e1
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | REF_CLOSE: (179), (193), (913) are inconsistent by sub-proof
% 202.23/33.92  | | | | | | | | | |            #967.
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | |   (914)   ~ (all_58_2 = e1)
% 202.23/33.92  | | | | | | | | | |   (915)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | BETA: splitting (82) gives:
% 202.23/33.92  | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | |   (916)  all_58_0 = e1
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (20), (26), (36), (37), (38),
% 202.23/33.92  | | | | | | | | | | |            (42), (47), (53), (61), (86), (106), (119), (123),
% 202.23/33.92  | | | | | | | | | | |            (125), (130), (131), (140), (149), (162), (169),
% 202.23/33.92  | | | | | | | | | | |            (170), (178), (179), (181), (189), (190), (196),
% 202.23/33.92  | | | | | | | | | | |            (441), (903), (910), (915), (916) are inconsistent
% 202.23/33.92  | | | | | | | | | | |            by sub-proof #398.
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | Case 2:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | |   (917)   ~ (all_58_0 = e1)
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | REDUCE: (20), (917) imply:
% 202.23/33.92  | | | | | | | | | | |   (918)   ~ (all_6_2 = e1)
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | BETA: splitting (155) gives:
% 202.23/33.92  | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | Case 1:
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | |   (919)  all_56_0 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | COMBINE_EQS: (124), (919) imply:
% 202.23/33.92  | | | | | | | | | | | |   (920)  all_6_2 = e3
% 202.23/33.92  | | | | | | | | | | | | 
% 202.23/33.92  | | | | | | | | | | | | REF_CLOSE: (7), (123), (125), (147), (169), (920) are
% 202.23/33.92  | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | |   (921)   ~ (all_56_0 = e3)
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | REDUCE: (124), (921) imply:
% 202.23/33.93  | | | | | | | | | | | |   (922)   ~ (all_6_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | BETA: splitting (128) gives:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | |   (923)  all_58_0 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | COMBINE_EQS: (20), (923) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (924)  all_6_2 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | REDUCE: (922), (924) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (925)  $false
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | CLOSE: (925) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | |   (926)   ~ (all_58_0 = e3)
% 202.23/33.93  | | | | | | | | | | | | |   (927)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | |   (928)  all_58_0 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | COMBINE_EQS: (20), (928) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (929)  all_6_2 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REDUCE: (922), (929) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (930)  $false
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | CLOSE: (930) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | |   (931)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | |   (932)  all_58_4 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | COMBINE_EQS: (172), (932) imply:
% 202.23/33.93  | | | | | | | | | | | | | | |   (933)  all_52_17 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | SIMP: (933) implies:
% 202.23/33.93  | | | | | | | | | | | | | | |   (934)  all_52_17 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | REDUCE: (167), (934) imply:
% 202.23/33.93  | | | | | | | | | | | | | | |   (935)   ~ (all_52_23 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | SIMP: (935) implies:
% 202.23/33.93  | | | | | | | | | | | | | | |   (936)   ~ (all_52_23 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | REDUCE: (24), (934) imply:
% 202.23/33.93  | | | | | | | | | | | | | | |   (937)   ~ (all_10_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | SIMP: (937) implies:
% 202.23/33.93  | | | | | | | | | | | | | | |   (938)   ~ (all_10_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | REDUCE: (113), (934) imply:
% 202.23/33.93  | | | | | | | | | | | | | | |   (939)  op(e3, e3) = all_52_16
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_16, e3, e3,
% 202.23/33.93  | | | | | | | | | | | | | | |              simplifying with (125), (939) gives:
% 202.23/33.93  | | | | | | | | | | | | | | |   (940)  all_52_16 = all_6_2
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | |   (941)  all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (941) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (942)  all_52_7 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | SIMP: (942) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (943)  all_52_7 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | REDUCE: (70), (943) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (944)   ~ (all_52_5 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | REDUCE: (16), (943) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (945)  op(e3, e3) = all_52_6
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (946)  all_58_6 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (944), (946) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | |            #1328.
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (947)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (67), (107), (125), (890), (906),
% 202.23/33.93  | | | | | | | | | | | | | | | | |            (918), (938), (945), (947) are inconsistent by
% 202.23/33.93  | | | | | | | | | | | | | | | | |            sub-proof #1104.
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | |   (948)   ~ (all_58_12 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | |   (949)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | REDUCE: (71), (948) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (950)   ~ (all_52_7 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | BETA: splitting (931) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (951)  all_58_2 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (951) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | |            #948.
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (952)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | BETA: splitting (952) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (953)  all_58_6 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (953) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (954)  all_52_5 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | SIMP: (954) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (955)  all_52_5 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (26), (955) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (956)  op(e3, e3) = all_52_4
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (20), (30), (71), (82), (100),
% 202.23/33.93  | | | | | | | | | | | | | | | | | |            (103), (114), (125), (145), (168), (169), (179),
% 202.23/33.93  | | | | | | | | | | | | | | | | | |            (193), (891), (899), (936), (949), (953), (956)
% 202.23/33.93  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #392.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (957)  all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (950), (957) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | | |            #1367.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | |   (958)   ~ (all_58_4 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | REDUCE: (172), (958) imply:
% 202.23/33.93  | | | | | | | | | | | | | | |   (959)   ~ (all_52_17 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (32), (121), (125), (172), (889), (904),
% 202.23/33.93  | | | | | | | | | | | | | | |            (927), (959) are inconsistent by sub-proof #1138.
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | 
% 202.23/33.93  | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | 
% 202.23/33.93  | | | | | | | | |   (960)   ~ (all_56_7 = e3)
% 202.23/33.93  | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | REDUCE: (83), (960) imply:
% 202.23/33.93  | | | | | | | | |   (961)   ~ (all_52_27 = e3)
% 202.23/33.93  | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | BETA: splitting (51) gives:
% 202.23/33.93  | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | |   (962)  all_58_2 = e3
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | REF_CLOSE: (55), (179), (962) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | |            #948.
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | |   (963)   ~ (all_58_2 = e3)
% 202.23/33.93  | | | | | | | | | |   (964)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | BETA: splitting (126) gives:
% 202.23/33.93  | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | |   (965)  all_58_9 = e3
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | COMBINE_EQS: (32), (965) imply:
% 202.23/33.93  | | | | | | | | | | |   (966)  all_52_25 = e3
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | REDUCE: (102), (966) imply:
% 202.23/33.93  | | | | | | | | | | |   (967)   ~ (all_52_9 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | REDUCE: (3), (966) imply:
% 202.23/33.93  | | | | | | | | | | |   (968)   ~ (all_52_27 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | REDUCE: (65), (966) imply:
% 202.23/33.93  | | | | | | | | | | |   (969)   ~ (all_52_29 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | SIMP: (969) implies:
% 202.23/33.93  | | | | | | | | | | |   (970)   ~ (all_52_29 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | REDUCE: (43), (966) imply:
% 202.23/33.93  | | | | | | | | | | |   (971)   ~ (all_14_2 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | REDUCE: (116), (966) imply:
% 202.23/33.93  | | | | | | | | | | |   (972)   ~ (all_6_2 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | SIMP: (972) implies:
% 202.23/33.93  | | | | | | | | | | |   (973)   ~ (all_6_2 = e3)
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | REDUCE: (176), (966) imply:
% 202.23/33.93  | | | | | | | | | | |   (974)  op(e3, e3) = all_52_24
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 202.23/33.93  | | | | | | | | | | |              simplifying with (125), (974) gives:
% 202.23/33.93  | | | | | | | | | | |   (975)  all_52_24 = all_6_2
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | |   (976)  all_58_0 = e3
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | COMBINE_EQS: (20), (976) imply:
% 202.23/33.93  | | | | | | | | | | | |   (977)  all_6_2 = e3
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | REDUCE: (973), (977) imply:
% 202.23/33.93  | | | | | | | | | | | |   (978)  $false
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | CLOSE: (978) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | |   (979)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | BETA: splitting (148) gives:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | |   (980)  all_56_1 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | COMBINE_EQS: (136), (980) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (981)  all_52_9 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | REDUCE: (967), (981) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (982)  $false
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | CLOSE: (982) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | |   (983)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | |   (984)  all_56_6 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | COMBINE_EQS: (90), (984) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (985)  all_52_19 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | SIMP: (985) implies:
% 202.23/33.93  | | | | | | | | | | | | | |   (986)  all_52_19 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | COMBINE_EQS: (135), (986) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (987)  all_58_5 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REDUCE: (64), (986) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (988)   ~ (all_52_23 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | SIMP: (988) implies:
% 202.23/33.93  | | | | | | | | | | | | | |   (989)   ~ (all_52_23 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REDUCE: (104), (986) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (990)   ~ (all_10_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | SIMP: (990) implies:
% 202.23/33.93  | | | | | | | | | | | | | |   (991)   ~ (all_10_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REDUCE: (185), (986) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (992)   ~ (all_4_0 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REDUCE: (28), (986) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (993)  op(e3, e3) = all_52_18
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3,
% 202.23/33.93  | | | | | | | | | | | | | |              simplifying with (125), (993) gives:
% 202.23/33.93  | | | | | | | | | | | | | |   (994)  all_52_18 = all_6_2
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | |   (995)  all_58_2 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | REF_CLOSE: (179), (193), (995) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | |            #967.
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | |   (996)   ~ (all_58_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | |   (997)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | |   (998)  all_58_6 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (998) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (999)  all_52_5 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | SIMP: (999) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (1000)  all_52_5 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | REDUCE: (70), (1000) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (1001)   ~ (all_52_7 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | SIMP: (1001) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (1002)   ~ (all_52_7 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | REDUCE: (26), (1000) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | |   (1003)  op(e3, e3) = all_52_4
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1004)  all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (1002), (1004) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | |            #1367.
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1005)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (20), (30), (71), (82), (100),
% 202.23/33.93  | | | | | | | | | | | | | | | | |            (103), (114), (125), (145), (168), (169), (179),
% 202.23/33.93  | | | | | | | | | | | | | | | | |            (193), (891), (899), (989), (998), (1003), (1005)
% 202.23/33.93  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #392.
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | |   (1006)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | BETA: splitting (1006) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1007)  all_58_7 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (1007) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1008)  all_52_13 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REDUCE: (8), (1008) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1009)   ~ (all_52_5 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REDUCE: (96), (1008) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1010)   ~ (all_4_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | SIMP: (1010) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1011)   ~ (all_4_2 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REDUCE: (890), (1008) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1012)  op(e3, e3) = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1013)  all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (1013) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1014)  all_52_7 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | SIMP: (1014) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1015)  all_52_7 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (16), (1015) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1016)  op(e3, e3) = all_52_6
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 202.23/33.93  | | | | | | | | | | | | | | | | | |              simplifying with (125), (1016) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1017)  all_52_6 = all_6_2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_6, e3, e3,
% 202.23/33.93  | | | | | | | | | | | | | | | | | |              simplifying with (1012), (1016) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1018)  all_52_6 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1017), (1018) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1019)  all_6_2 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | SIMP: (1019) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1020)  all_6_2 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1021)  all_44_2 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1022)  all_58_0 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (119), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1023)   ~ (all_52_5 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (121), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1024)   ~ (all_52_9 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (189), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1025)   ~ (all_4_0 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (973), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1026)   ~ (e3 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (169), (1020) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1027)  op(e1, e3) = all_6_1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1028)   ~ (all_44_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | REDUCE: (1021), (1028) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1029)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | CLOSE: (1029) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1030)   ~ (all_44_1 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1030) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1031)   ~ (all_6_1 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_5, all_6_1, e3, e1,
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |              simplifying with (36), (1027) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1032)  all_52_5 = all_6_1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (1032) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1033)  all_56_8 = all_6_1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1032) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1034)   ~ (all_6_1 = all_4_0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | REDUCE: (1009), (1032) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1035)   ~ (all_6_1 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | REDUCE: (1023), (1032) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1036)   ~ (all_6_1 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |   (1037)  all_56_8 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1033), (1035), (1037) are inconsistent by
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |            sub-proof #1101.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |   (1038)   ~ (all_56_8 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |   (1039)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | |   (1040)  all_58_0 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1022), (1040) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | |   (1041)  e1 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1041) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | |   (1042)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | CLOSE: (1042) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | |   (1043)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1039) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1044)  all_56_8 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1033), (1044) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1045)  all_6_1 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1045) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1046)  all_6_1 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1034), (1046) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1047)   ~ (all_4_0 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1047) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1048)   ~ (all_4_0 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1035), (1046) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1049)   ~ (e3 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1043) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1050)  all_58_2 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (1050) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1051)  all_4_0 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1051) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1052)  all_4_0 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (1052) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1053)  all_32_0 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (1052) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1054)   ~ (all_52_27 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (1052) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1055)   ~ (all_4_2 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1055) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1056)   ~ (all_4_2 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (1052) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1057)   ~ (e3 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1058)   ~ (all_32_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (1058) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1059)   ~ (all_4_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (997) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (1060)  all_58_3 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (1060) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (1061)  all_4_2 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1059), (1061) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (1062)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1062) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (1063)  all_58_5 = e1 | all_58_10 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1063) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1064)  all_58_5 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (987), (1064) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |            #391.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1065)  all_58_10 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (1065) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1066)  all_52_27 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (1066) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1067)   ~ (all_14_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1067) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1068)   ~ (all_14_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1066) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1069)   ~ (all_4_2 = e1)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1070)  all_56_5 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (1070) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1071)  all_4_2 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1011), (1071) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1072)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1072) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1073)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1074)  all_58_4 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (1074) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1075)  all_52_17 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (1075) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1076)   ~ (all_52_9 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1077)  all_58_9 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (965), (1077) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1078)  e3 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1078) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1079)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1079) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1080)  all_58_10 = e0 | all_58_11 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1080) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1081)  all_58_10 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1065), (1081) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1082)  e1 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1082) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1083)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1083) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1084)  all_58_11 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (1084) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1085)  all_52_29 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1085) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1086)  op(e0, e0) = all_52_28
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (983) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  all_56_1 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (1087) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1088)  all_52_9 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1076), (1088) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1089) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1090)  all_56_1 = e1 | all_56_1 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1090) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1091)  all_56_1 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (1091) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1092)  all_52_9 = e1
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1024), (1092) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1093)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1093) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1094)  all_56_1 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (1094) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1095)  all_52_9 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (889), (1095) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1096)  op(e0, e0) = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (49), (50), (438), (898), (899), (1068),
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1086), (1096) are inconsistent by sub-proof #395.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1097)   ~ (all_58_4 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (1097) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1098)   ~ (all_52_17 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1099)  all_58_0 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (1022), (1099) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1273.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1100)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1100) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1101)  all_58_1 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (1101) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1102)  all_52_9 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1102) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1103)   ~ (all_4_2 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1103) implies:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1104)   ~ (all_4_2 = e2)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (1056), (1059), (1073), (1104) are
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1186.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1105)  all_58_4 = e2 | all_58_9 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1105) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1106)  all_58_4 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (1106) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1107)  all_52_17 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1098), (1107) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1108)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1108) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1109)  all_58_9 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (965), (1109) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1110)  e3 = e2
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1110) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1111)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1111) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1112)   ~ (all_32_0 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1053), (1112) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1113)  $false
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1113) is inconsistent.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1114)   ~ (all_58_2 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (1114) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |   (1115)   ~ (all_4_0 = e0)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (193), (441), (1048), (1115) are
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #673.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |   (1116)  all_56_8 = e1 | all_56_8 = e0
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1031), (1033), (1036), (1116) are inconsistent by
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #495.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1117)   ~ (all_58_12 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | REDUCE: (71), (1117) imply:
% 202.23/33.93  | | | | | | | | | | | | | | | | | |   (1118)   ~ (all_52_7 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | BETA: splitting (979) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1119)  all_58_2 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (1119) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |            #948.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | |   (1120)  all_58_6 = e3 | all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |   (1121)  all_58_6 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (1009), (1121) are inconsistent by
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |   (1122)  all_58_12 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (1118), (1122) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | |            #1367.
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | |   (1123)  all_58_8 = e3 | all_58_11 = e3
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (107), (970), (991), (1123) are inconsistent
% 202.23/33.93  | | | | | | | | | | | | | | | | |            by sub-proof #1140.
% 202.23/33.93  | | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | |   (1124)   ~ (all_56_6 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REDUCE: (90), (1124) imply:
% 202.23/33.93  | | | | | | | | | | | | | |   (1125)   ~ (all_52_19 = e3)
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | REF_CLOSE: (7), (53), (60), (118), (135), (142), (162),
% 202.23/33.93  | | | | | | | | | | | | | |            (961), (964), (1125) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | | | |            #945.
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | End of split
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | |   (1126)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | BETA: splitting (1126) gives:
% 202.23/33.93  | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | |   (1127)  all_58_10 = e3
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | REF_CLOSE: (60), (961), (1127) are inconsistent by sub-proof
% 202.23/33.93  | | | | | | | | | | | |            #1301.
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | Case 2:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | |   (1128)  all_58_11 = e3 | all_58_15 = e3
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | BETA: splitting (1128) gives:
% 202.23/33.93  | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | |   (1129)  all_58_11 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | COMBINE_EQS: (41), (1129) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (1130)  all_52_29 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | SIMP: (1130) implies:
% 202.23/33.93  | | | | | | | | | | | | |   (1131)  all_52_29 = e3
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | REDUCE: (88), (1131) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (1132)   ~ (all_52_5 = e3)
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | REDUCE: (171), (1131) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (1133)   ~ (all_52_13 = e3)
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | REDUCE: (110), (1131) imply:
% 202.23/33.93  | | | | | | | | | | | | |   (1134)  op(e3, e3) = all_52_28
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_28, e3, e3,
% 202.23/33.93  | | | | | | | | | | | | |              simplifying with (125), (1134) gives:
% 202.23/33.93  | | | | | | | | | | | | |   (1135)  all_52_28 = all_6_2
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.23/33.93  | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | Case 1:
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | |   (1136)  all_58_0 = e3
% 202.23/33.93  | | | | | | | | | | | | | | 
% 202.23/33.93  | | | | | | | | | | | | | | COMBINE_EQS: (20), (1136) imply:
% 202.37/33.93  | | | | | | | | | | | | | |   (1137)  all_6_2 = e3
% 202.37/33.93  | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | REF_CLOSE: (7), (123), (125), (147), (169), (1137) are
% 202.37/33.93  | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.37/33.93  | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | Case 2:
% 202.37/33.93  | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | |   (1138)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.37/33.93  | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | BETA: splitting (1138) gives:
% 202.37/33.93  | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | Case 1:
% 202.37/33.93  | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | |   (1139)  all_58_2 = e3
% 202.37/33.93  | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (1139) are inconsistent by sub-proof
% 202.37/33.93  | | | | | | | | | | | | | | |            #948.
% 202.37/33.93  | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | Case 2:
% 202.37/33.93  | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | |   (1140)  all_58_6 = e3 | all_58_12 = e3
% 202.37/33.93  | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | BETA: splitting (1140) gives:
% 202.37/33.93  | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | Case 1:
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1141)  all_58_6 = e3
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | | REF_CLOSE: (141), (1132), (1141) are inconsistent by
% 202.37/33.93  | | | | | | | | | | | | | | | |            sub-proof #1328.
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | Case 2:
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1142)  all_58_12 = e3
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (1142) imply:
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1143)  all_52_7 = e3
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | | SIMP: (1143) implies:
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1144)  all_52_7 = e3
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | | REDUCE: (14), (1144) imply:
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1145)   ~ (all_52_15 = e3)
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | | SIMP: (1145) implies:
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1146)   ~ (all_52_15 = e3)
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.93  | | | | | | | | | | | | | | | | REDUCE: (16), (1144) imply:
% 202.37/33.93  | | | | | | | | | | | | | | | |   (1147)  op(e3, e3) = all_52_6
% 202.37/33.93  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (30), (53), (67), (101), (118), (121),
% 202.37/33.94  | | | | | | | | | | | | | | | |            (125), (142), (162), (889), (1133), (1146), (1147)
% 202.37/33.94  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #933.
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | |   (1148)  all_58_15 = e3
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | COMBINE_EQS: (103), (1148) imply:
% 202.37/33.94  | | | | | | | | | | | | |   (1149)  all_14_2 = e3
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | REDUCE: (899), (1149) imply:
% 202.37/33.94  | | | | | | | | | | | | |   (1150)  $false
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | CLOSE: (1150) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | End of split
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | End of split
% 202.37/33.94  | | | | | | 
% 202.37/33.94  | | | | | Case 2:
% 202.37/33.94  | | | | | | 
% 202.37/33.94  | | | | | |   (1151)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 202.37/33.94  | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 202.37/33.94  | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 202.37/33.94  | | | | | | 
% 202.37/33.94  | | | | | | BETA: splitting (1151) gives:
% 202.37/33.94  | | | | | | 
% 202.37/33.94  | | | | | | Case 1:
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | |   (1152)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 202.37/33.94  | | | | | | |           all_52_22 = e0
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | ALPHA: (1152) implies:
% 202.37/33.94  | | | | | | |   (1153)  all_52_18 = e2
% 202.37/33.94  | | | | | | |   (1154)  all_52_16 = e3
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | REDUCE: (113), (1154) imply:
% 202.37/33.94  | | | | | | |   (1155)  op(all_52_17, all_52_17) = e3
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | REDUCE: (28), (1153) imply:
% 202.37/33.94  | | | | | | |   (1156)  op(all_52_19, all_52_19) = e2
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | BETA: splitting (108) gives:
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | |   (1157)  all_56_15 = e3
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (47), (50), (51), (53), (55),
% 202.37/33.94  | | | | | | | |            (60), (76), (86), (90), (118), (125), (127), (130),
% 202.37/33.94  | | | | | | | |            (131), (135), (140), (142), (162), (166), (178),
% 202.37/33.94  | | | | | | | |            (179), (189), (190), (193), (441), (1156), (1157) are
% 202.37/33.94  | | | | | | | |            inconsistent by sub-proof #930.
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | |   (1158)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | BETA: splitting (27) gives:
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | |   (1159)  all_56_7 = e3
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | COMBINE_EQS: (83), (1159) imply:
% 202.37/33.94  | | | | | | | | |   (1160)  all_52_27 = e3
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | SIMP: (1160) implies:
% 202.37/33.94  | | | | | | | | |   (1161)  all_52_27 = e3
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | COMBINE_EQS: (60), (1161) imply:
% 202.37/33.94  | | | | | | | | |   (1162)  all_58_10 = e3
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REDUCE: (3), (1161) imply:
% 202.37/33.94  | | | | | | | | |   (1163)   ~ (all_52_25 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REDUCE: (127), (1161) imply:
% 202.37/33.94  | | | | | | | | |   (1164)   ~ (all_14_2 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | SIMP: (1164) implies:
% 202.37/33.94  | | | | | | | | |   (1165)   ~ (all_14_2 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REDUCE: (187), (1161) imply:
% 202.37/33.94  | | | | | | | | |   (1166)   ~ (all_4_0 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REDUCE: (139), (1161) imply:
% 202.37/33.94  | | | | | | | | |   (1167)   ~ (all_4_2 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | SIMP: (1167) implies:
% 202.37/33.94  | | | | | | | | |   (1168)   ~ (all_4_2 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REDUCE: (35), (1161) imply:
% 202.37/33.94  | | | | | | | | |   (1169)  op(e3, e3) = all_52_26
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_26, e3, e3,
% 202.37/33.94  | | | | | | | | |              simplifying with (125), (1169) gives:
% 202.37/33.94  | | | | | | | | |   (1170)  all_52_26 = all_6_2
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | BETA: splitting (69) gives:
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | |   (1171)  all_58_2 = e1
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | REF_CLOSE: (179), (193), (1171) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | |            #967.
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | |   (1172)   ~ (all_58_2 = e1)
% 202.37/33.94  | | | | | | | | | |   (1173)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | BETA: splitting (82) gives:
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | |   (1174)  all_58_0 = e1
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | COMBINE_EQS: (20), (1174) imply:
% 202.37/33.94  | | | | | | | | | | |   (1175)  all_6_2 = e1
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | COMBINE_EQS: (19), (1175) imply:
% 202.37/33.94  | | | | | | | | | | |   (1176)  all_44_2 = e1
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | REDUCE: (119), (1175) imply:
% 202.37/33.94  | | | | | | | | | | |   (1177)   ~ (all_52_5 = e1)
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | REDUCE: (189), (1175) imply:
% 202.37/33.94  | | | | | | | | | | |   (1178)   ~ (all_4_0 = e1)
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | REDUCE: (169), (1175) imply:
% 202.37/33.94  | | | | | | | | | | |   (1179)  op(e1, e3) = all_6_1
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | REF_CLOSE: (5), (7), (26), (36), (37), (38), (42), (47),
% 202.37/33.94  | | | | | | | | | | |            (53), (61), (86), (106), (123), (125), (130),
% 202.37/33.94  | | | | | | | | | | |            (131), (140), (149), (162), (170), (178), (179),
% 202.37/33.94  | | | | | | | | | | |            (181), (189), (190), (193), (196), (441), (1162),
% 202.37/33.94  | | | | | | | | | | |            (1168), (1173), (1176), (1177), (1179) are
% 202.37/33.94  | | | | | | | | | | |            inconsistent by sub-proof #399.
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | |   (1180)   ~ (all_58_0 = e1)
% 202.37/33.94  | | | | | | | | | | |   (1181)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | REDUCE: (20), (1180) imply:
% 202.37/33.94  | | | | | | | | | | |   (1182)   ~ (all_6_2 = e1)
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | BETA: splitting (155) gives:
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | |   (1183)  all_56_0 = e3
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | COMBINE_EQS: (124), (1183) imply:
% 202.37/33.94  | | | | | | | | | | | |   (1184)  all_6_2 = e3
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | REF_CLOSE: (7), (123), (125), (147), (169), (1184) are
% 202.37/33.94  | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | |   (1185)   ~ (all_56_0 = e3)
% 202.37/33.94  | | | | | | | | | | | |   (1186)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | REDUCE: (124), (1185) imply:
% 202.37/33.94  | | | | | | | | | | | |   (1187)   ~ (all_6_2 = e3)
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | BETA: splitting (128) gives:
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | |   (1188)  all_58_0 = e3
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | COMBINE_EQS: (20), (1188) imply:
% 202.37/33.94  | | | | | | | | | | | | |   (1189)  all_6_2 = e3
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | REDUCE: (1187), (1189) imply:
% 202.37/33.94  | | | | | | | | | | | | |   (1190)  $false
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | CLOSE: (1190) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | |   (1191)   ~ (all_58_0 = e3)
% 202.37/33.94  | | | | | | | | | | | | |   (1192)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | |   (1193)  all_58_0 = e3
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | COMBINE_EQS: (20), (1193) imply:
% 202.37/33.94  | | | | | | | | | | | | | |   (1194)  all_6_2 = e3
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | REDUCE: (1187), (1194) imply:
% 202.37/33.94  | | | | | | | | | | | | | |   (1195)  $false
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | CLOSE: (1195) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | |   (1196)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | |   (1197)  all_58_9 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | COMBINE_EQS: (32), (1197) imply:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1198)  all_52_25 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | SIMP: (1198) implies:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1199)  all_52_25 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | REDUCE: (43), (1199) imply:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1200)   ~ (all_14_2 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | SIMP: (1200) implies:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1201)   ~ (all_14_2 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | REDUCE: (116), (1199) imply:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1202)   ~ (all_6_2 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | SIMP: (1202) implies:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1203)   ~ (all_6_2 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | REDUCE: (1163), (1199) imply:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1204)   ~ (e3 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | REDUCE: (176), (1199) imply:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1205)  op(e2, e2) = all_52_24
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | BETA: splitting (1186) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1206)  all_56_0 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (1206) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1207)  all_6_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | REDUCE: (1203), (1207) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1208)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | CLOSE: (1208) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1209)   ~ (all_56_0 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1210)  all_56_0 = e1 | all_56_0 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | BETA: splitting (1158) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1211)  all_56_15 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (1201), (1211) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | |            #762.
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1212)   ~ (all_56_15 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1213)  all_56_15 = e1 | all_56_15 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | BETA: splitting (1213) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1214)  all_56_15 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (1214) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1215)  all_14_2 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | SIMP: (1215) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1216)  all_14_2 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | REDUCE: (73), (1216) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1217)   ~ (all_52_7 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | REDUCE: (1165), (1216) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1218)   ~ (e3 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | REDUCE: (1201), (1216) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1219)   ~ (e2 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | BETA: splitting (1181) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |   (1220)  all_58_2 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (193), (1220) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |            #967.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |   (1221)  all_58_6 = e1 | all_58_12 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (1221) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1222)  all_58_6 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (1222) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1223)  all_52_5 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | SIMP: (1223) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1224)  all_52_5 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (1224) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1225)   ~ (all_52_7 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1224) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1226)   ~ (all_6_2 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1224) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1227)   ~ (all_4_0 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1196) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1228)  all_58_2 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (1228) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |            #948.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1229)  all_58_6 = e3 | all_58_12 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1229) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1230)  all_58_6 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (71), (1217), (1221), (1230) are inconsistent
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #390.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1231)  all_58_12 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (1231) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1232)  all_52_7 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1232) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1233)  all_52_7 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (1233) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1234)  op(e0, e3) = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1235)  all_58_0 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (1235) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1236)  all_6_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1203), (1236) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1237)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1237) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1238)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1238) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1239)  all_58_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (1239) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1240)  all_4_0 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1240) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1241)  all_4_0 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (1241) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1242)  op(e2, e2) = all_52_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1210) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1243)  all_56_0 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (1243) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1244)  all_6_2 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1182), (1244) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1245)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1245) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1246)  all_56_0 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (1246) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1247)  all_6_2 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (1247) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1248)  op(e0, e3) = all_6_1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_6_1, e3, e0,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (1234), (1248) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1249)  all_6_1 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_2, e2, e2,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (38), (1242) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1250)  all_52_2 = all_4_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_24, all_52_2, e2,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (1205), (1242) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1251)  all_52_2 = all_52_24
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1250), (1251) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1252)  all_52_24 = all_4_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (1249) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1253)  op(e3, e3) = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (47), (53), (86), (125),
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (140), (178), (189), (190), (193),
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (441), (1168), (1253) are inconsistent by
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #947.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1254)  all_58_6 = e2 | all_58_12 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1254) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1255)  all_58_6 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1222), (1255) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1256)  e2 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (1256) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1257)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1257) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1258)  all_58_12 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (1231), (1258) are inconsistent by
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1210.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1259)  all_58_12 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (1217), (1259) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |            #1127.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1260)  all_56_15 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (438), (1260) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | | |            #1162.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | |   (1261)   ~ (all_58_9 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | REDUCE: (32), (1261) imply:
% 202.37/33.94  | | | | | | | | | | | | | | |   (1262)   ~ (all_52_25 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1263)  all_58_4 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (1263) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1264)  all_52_17 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | SIMP: (1264) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1265)  all_52_17 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (125), (144), (1155), (1265) are inconsistent
% 202.37/33.94  | | | | | | | | | | | | | | | |            by sub-proof #1280.
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1266)   ~ (all_58_4 = e3)
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | REDUCE: (172), (1266) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | |   (1267)   ~ (all_52_17 = e3)
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | BETA: splitting (1192) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1268)  all_58_1 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (1268) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1269)  all_52_9 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | REDUCE: (62), (1269) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1270)  op(e3, e3) = all_52_8
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3,
% 202.37/33.94  | | | | | | | | | | | | | | | | |              simplifying with (125), (1270) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1271)  all_52_8 = all_6_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1272)  all_58_0 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (1272) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1273)  all_6_2 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | REDUCE: (1182), (1273) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1274)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | CLOSE: (1274) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | |   (1275)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |   (1276)  all_58_0 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (1276) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |   (1277)  all_6_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1277) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |   (1278)  op(e3, e3) = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (47), (53), (86), (125),
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |            (130), (131), (140), (178), (189), (190), (193),
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |            (441), (1168), (1278) are inconsistent by
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |            sub-proof #947.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | |   (1279)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (1279) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1280)  all_58_1 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1268), (1280) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1281)  e3 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1281) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1282)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | CLOSE: (1282) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | |   (1283)  all_58_4 = e2 | all_58_9 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1283) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1284)  all_58_4 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (1284) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1285)  all_52_17 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | SIMP: (1285) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1286)  all_52_17 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (1155), (1286) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1287)  op(e2, e2) = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1275) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1288)  all_58_1 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1268), (1288) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1289)  e3 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1289) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1290)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1290) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | |   (1291)  all_58_4 = e1 | all_58_9 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1291) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1292)  all_58_4 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (1284), (1292) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |            #811.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1293)  all_58_9 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (1293) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1294)  all_52_25 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1294) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1295)  all_52_25 = e1
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1295) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1296)   ~ (all_14_2 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1296) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | |   (1297)   ~ (all_14_2 = e1)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1298)  all_58_0 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (1298) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1299)  all_6_2 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (1299) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1300)   ~ (all_4_0 = e0)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1300) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1301)   ~ (all_4_0 = e0)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1158) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1302)  all_56_15 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (1302) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1303)  all_14_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1303) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1304)  all_14_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (1304) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1305)   ~ (all_52_15 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1304) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1306)  op(e2, e2) = all_52_30
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1307)  all_56_4 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (1307) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1308)  all_4_0 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1308) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1309)   ~ (all_52_5 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (1308) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1310)   ~ (all_4_2 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1310) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1311)   ~ (all_4_2 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (1308) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1312)   ~ (e3 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (1308) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1313)  op(e2, e2) = all_52_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1314)  all_58_1 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1268), (1314) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1315)  e3 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1315) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1316)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1316) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1317)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1318)  all_58_6 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (1309), (1318) are inconsistent by
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #540.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1319)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1319) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1320)  all_58_7 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (1320) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1321)  all_52_13 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (1321) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1322)  op(e2, e2) = all_52_12
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_12, e2, e2,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (38), (1322) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1323)  all_52_12 = all_4_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_52_12, e2, e2,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (1287), (1322) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1324)  all_52_12 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_12, all_52_2, e2,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (1313), (1322) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1325)  all_52_2 = all_52_12
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_30, all_52_2, e2,
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (1306), (1313) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1326)  all_52_2 = all_52_30
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1325), (1326) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1327)  all_52_12 = all_52_30
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1327) implies:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1328)  all_52_12 = all_52_30
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1324), (1328) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1329)  all_52_30 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1323), (1328) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1330)  all_52_30 = all_4_2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1329), (1330) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1331)  all_4_2 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1168), (1331) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1332)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1332) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1333)   ~ (all_58_7 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (1333) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1334)   ~ (all_52_13 = e2)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1317) gives:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1335)  all_58_3 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (1335) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1336)  all_4_2 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1311), (1336) imply:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1337)  $false
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1337) is inconsistent.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1338)  all_58_7 = e2 | all_58_13 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (67), (1305), (1334), (1338) are
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #389.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1339)  all_56_4 = e1 | all_56_4 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (193), (1301), (1339) are inconsistent by
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #674.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1340)  all_56_15 = e1 | all_56_15 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (438), (1297), (1340) are inconsistent by
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |   (1341)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (85), (145), (1268), (1284), (1293), (1341)
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1026.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |   (1342)  all_58_9 = e2
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (1262), (1342) are inconsistent by sub-proof
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | |            #1221.
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | |   (1343)  all_58_4 = e3 | all_58_9 = e3
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (172), (1163), (1267), (1343) are
% 202.37/33.94  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1276.
% 202.37/33.94  | | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | Case 2:
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | |   (1344)   ~ (all_56_7 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REDUCE: (83), (1344) imply:
% 202.37/33.94  | | | | | | | | |   (1345)   ~ (all_52_27 = e3)
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | | REF_CLOSE: (7), (37), (38), (42), (47), (51), (53), (55),
% 202.37/33.94  | | | | | | | | |            (60), (76), (86), (90), (118), (125), (130), (131),
% 202.37/33.94  | | | | | | | | |            (135), (140), (142), (162), (166), (178), (179),
% 202.37/33.94  | | | | | | | | |            (189), (190), (193), (441), (1156), (1345) are
% 202.37/33.94  | | | | | | | | |            inconsistent by sub-proof #944.
% 202.37/33.94  | | | | | | | | | 
% 202.37/33.94  | | | | | | | | End of split
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | End of split
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | Case 2:
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | |   (1346)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 202.37/33.94  | | | | | | |           all_52_30 = e0
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | ALPHA: (1346) implies:
% 202.37/33.94  | | | | | | |   (1347)  all_52_30 = e0
% 202.37/33.94  | | | | | | |   (1348)  all_52_28 = e1
% 202.37/33.94  | | | | | | |   (1349)  all_52_26 = e2
% 202.37/33.94  | | | | | | |   (1350)  all_52_24 = e3
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | REDUCE: (176), (1350) imply:
% 202.37/33.94  | | | | | | |   (1351)  op(all_52_25, all_52_25) = e3
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | REDUCE: (35), (1349) imply:
% 202.37/33.94  | | | | | | |   (1352)  op(all_52_27, all_52_27) = e2
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | REDUCE: (110), (1348) imply:
% 202.37/33.94  | | | | | | |   (1353)  op(all_52_29, all_52_29) = e1
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | REDUCE: (134), (1347) imply:
% 202.37/33.94  | | | | | | |   (1354)  op(all_14_2, all_14_2) = e0
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | BETA: splitting (108) gives:
% 202.37/33.94  | | | | | | | 
% 202.37/33.94  | | | | | | | Case 1:
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | |   (1355)  all_56_15 = e3
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | COMBINE_EQS: (50), (1355) imply:
% 202.37/33.94  | | | | | | | |   (1356)  all_14_2 = e3
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | SIMP: (1356) implies:
% 202.37/33.94  | | | | | | | |   (1357)  all_14_2 = e3
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | REDUCE: (73), (1357) imply:
% 202.37/33.94  | | | | | | | |   (1358)   ~ (all_52_7 = e3)
% 202.37/33.94  | | | | | | | | 
% 202.37/33.94  | | | | | | | | REDUCE: (1354), (1357) imply:
% 202.37/33.95  | | | | | | | |   (1359)  op(e3, e3) = e0
% 202.37/33.95  | | | | | | | | 
% 202.37/33.95  | | | | | | | | REF_CLOSE: (1), (5), (7), (11), (20), (26), (55), (71), (79),
% 202.37/33.95  | | | | | | | |            (82), (100), (114), (125), (141), (145), (168),
% 202.37/33.95  | | | | | | | |            (169), (178), (179), (189), (193), (441), (1358),
% 202.37/33.95  | | | | | | | |            (1359) are inconsistent by sub-proof #400.
% 202.37/33.95  | | | | | | | | 
% 202.37/33.95  | | | | | | | Case 2:
% 202.37/33.95  | | | | | | | | 
% 202.37/33.95  | | | | | | | |   (1360)   ~ (all_56_15 = e3)
% 202.37/33.95  | | | | | | | |   (1361)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.37/33.95  | | | | | | | | 
% 202.37/33.95  | | | | | | | | REDUCE: (50), (1360) imply:
% 202.37/33.95  | | | | | | | |   (1362)   ~ (all_14_2 = e3)
% 202.37/33.95  | | | | | | | | 
% 202.37/33.95  | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (16),
% 202.37/33.95  | | | | | | | |            (17), (18), (19), (20), (24), (26), (27), (28), (29),
% 202.37/33.95  | | | | | | | |            (30), (32), (34), (36), (38), (39), (40), (41), (42),
% 202.37/33.95  | | | | | | | |            (43), (45), (46), (47), (48), (49), (50), (51), (52),
% 202.37/33.95  | | | | | | | |            (54), (57), (60), (61), (62), (65), (66), (67), (68),
% 202.37/33.95  | | | | | | | |            (69), (70), (71), (72), (73), (75), (76), (77), (79),
% 202.37/33.95  | | | | | | | |            (80), (83), (85), (86), (88), (90), (92), (93), (97),
% 202.37/33.95  | | | | | | | |            (99), (101), (102), (103), (104), (106), (107),
% 202.37/33.95  | | | | | | | |            (109), (111), (113), (115), (116), (117), (118),
% 202.37/33.95  | | | | | | | |            (119), (123), (124), (125), (126), (127), (128),
% 202.37/33.95  | | | | | | | |            (129), (132), (133), (135), (137), (139), (141),
% 202.37/33.95  | | | | | | | |            (142), (143), (144), (145), (147), (149), (153),
% 202.37/33.95  | | | | | | | |            (155), (157), (158), (160), (161), (162), (163),
% 202.37/33.95  | | | | | | | |            (165), (166), (167), (169), (171), (172), (196),
% 202.37/33.95  | | | | | | | |            (436), (437), (438), (1351), (1352), (1353), (1354),
% 202.37/33.95  | | | | | | | |            (1361), (1362) are inconsistent by sub-proof #435.
% 202.37/33.95  | | | | | | | | 
% 202.37/33.95  | | | | | | | End of split
% 202.37/33.95  | | | | | | | 
% 202.37/33.95  | | | | | | End of split
% 202.37/33.95  | | | | | | 
% 202.37/33.95  | | | | | End of split
% 202.37/33.95  | | | | | 
% 202.37/33.95  | | | | End of split
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | End of split
% 202.37/33.95  | | | 
% 202.37/33.95  | | End of split
% 202.37/33.95  | | 
% 202.37/33.95  | Case 2:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (1363)  all_38_0 = e1
% 202.37/33.95  | |   (1364)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 202.37/33.95  | | 
% 202.37/33.95  | | COMBINE_EQS: (74), (1363) imply:
% 202.37/33.95  | |   (1365)  all_4_0 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (7), (23), (38), (42), (53), (86), (118), (130), (142), (150),
% 202.37/33.95  | |            (190), (1364), (1365) are inconsistent by sub-proof #927.
% 202.37/33.95  | | 
% 202.37/33.95  | End of split
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #389 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)   ~ (all_52_15 = e2)
% 202.37/33.95    (2)  all_58_13 = all_52_15
% 202.37/33.95    (3)  all_58_7 = all_52_13
% 202.37/33.95    (4)  all_58_7 = e2 | all_58_13 = e2
% 202.37/33.95    (5)   ~ (all_52_13 = e2)
% 202.37/33.95  
% 202.37/33.95  Begin of proof
% 202.37/33.95  | 
% 202.37/33.95  | BETA: splitting (4) gives:
% 202.37/33.95  | 
% 202.37/33.95  | Case 1:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (6)  all_58_7 = e2
% 202.37/33.95  | | 
% 202.37/33.95  | | COMBINE_EQS: (3), (6) imply:
% 202.37/33.95  | |   (7)  all_52_13 = e2
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (5), (7) imply:
% 202.37/33.95  | |   (8)  $false
% 202.37/33.95  | | 
% 202.37/33.95  | | CLOSE: (8) is inconsistent.
% 202.37/33.95  | | 
% 202.37/33.95  | Case 2:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (9)  all_58_13 = e2
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #784.
% 202.37/33.95  | | 
% 202.37/33.95  | End of split
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #390 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)   ~ (e3 = e1)
% 202.37/33.95    (2)  all_58_6 = e3
% 202.37/33.95    (3)  all_58_6 = e1 | all_58_12 = e1
% 202.37/33.95    (4)  all_58_12 = all_52_7
% 202.37/33.95    (5)   ~ (all_52_7 = e1)
% 202.37/33.95  
% 202.37/33.95  Begin of proof
% 202.37/33.95  | 
% 202.37/33.95  | BETA: splitting (3) gives:
% 202.37/33.95  | 
% 202.37/33.95  | Case 1:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (6)  all_58_6 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #1128.
% 202.37/33.95  | | 
% 202.37/33.95  | Case 2:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (7)  all_58_12 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1127.
% 202.37/33.95  | | 
% 202.37/33.95  | End of split
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #391 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)  all_58_5 = e3
% 202.37/33.95    (2)  all_58_5 = e1
% 202.37/33.95    (3)   ~ (e3 = e1)
% 202.37/33.95  
% 202.37/33.95  Begin of proof
% 202.37/33.95  | 
% 202.37/33.95  | COMBINE_EQS: (1), (2) imply:
% 202.37/33.95  |   (4)  e3 = e1
% 202.37/33.95  | 
% 202.37/33.95  | SIMP: (4) implies:
% 202.37/33.95  |   (5)  e3 = e1
% 202.37/33.95  | 
% 202.37/33.95  | REDUCE: (3), (5) imply:
% 202.37/33.95  |   (6)  $false
% 202.37/33.95  | 
% 202.37/33.95  | CLOSE: (6) is inconsistent.
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #392 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.37/33.95    (2)  all_58_14 = all_52_23
% 202.37/33.95    (3)   ~ (e3 = e1)
% 202.37/33.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.37/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.37/33.95    (5)   ~ (all_4_0 = e1)
% 202.37/33.95    (6)  op(all_52_15, all_52_15) = e0
% 202.37/33.95    (7)  all_58_0 = all_6_2
% 202.37/33.95    (8)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.37/33.95    (9)  all_58_13 = all_52_15
% 202.37/33.95    (10)  all_58_2 = all_4_0
% 202.37/33.95    (11)  all_58_6 = e3
% 202.37/33.95    (12)  all_58_12 = all_52_7
% 202.37/33.95    (13)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.37/33.95    (14)   ~ (all_52_23 = e3)
% 202.37/33.95    (15)  op(e0, e3) = all_52_7
% 202.37/33.95    (16)  all_58_15 = all_14_2
% 202.37/33.95    (17)  op(e3, e3) = all_52_4
% 202.37/33.95    (18)  all_8_2 = all_6_2
% 202.37/33.95    (19)  op(e3, e3) = all_6_2
% 202.37/33.95    (20)   ~ (e1 = e0)
% 202.37/33.95    (21)  all_8_1 = all_6_1
% 202.37/33.95    (22)  op(all_6_2, e3) = all_6_1
% 202.37/33.95    (23)   ~ (all_14_2 = e3)
% 202.37/33.95  
% 202.37/33.95  Begin of proof
% 202.37/33.95  | 
% 202.37/33.95  | BETA: splitting (8) gives:
% 202.37/33.95  | 
% 202.37/33.95  | Case 1:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (24)  all_58_13 = e3
% 202.37/33.95  | | 
% 202.37/33.95  | | COMBINE_EQS: (9), (24) imply:
% 202.37/33.95  | |   (25)  all_52_15 = e3
% 202.37/33.95  | | 
% 202.37/33.95  | | SIMP: (25) implies:
% 202.37/33.95  | |   (26)  all_52_15 = e3
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (6), (26) imply:
% 202.37/33.95  | |   (27)  op(e3, e3) = e0
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (1), (3), (4), (5), (7), (10), (11), (12), (13), (15), (17),
% 202.37/33.95  | |            (18), (19), (20), (21), (22), (27) are inconsistent by sub-proof
% 202.37/33.95  | |            #401.
% 202.37/33.95  | | 
% 202.37/33.95  | Case 2:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (28)  all_58_14 = e3 | all_58_15 = e3
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (2), (14), (16), (23), (28) are inconsistent by sub-proof #715.
% 202.37/33.95  | | 
% 202.37/33.95  | End of split
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #393 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.37/33.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.37/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.37/33.95    (3)   ~ (e3 = e0)
% 202.37/33.95    (4)  all_58_0 = all_6_2
% 202.37/33.95    (5)  all_58_4 = e2
% 202.37/33.95    (6)  all_58_9 = all_52_25
% 202.37/33.95    (7)   ~ (all_52_29 = all_14_2)
% 202.37/33.95    (8)  all_58_11 = all_52_29
% 202.37/33.95    (9)   ~ (all_52_25 = all_14_2)
% 202.37/33.95    (10)  all_58_1 = e3
% 202.37/33.95    (11)  op(e0, e0) = all_14_2
% 202.37/33.95    (12)  all_56_15 = all_14_2
% 202.37/33.95    (13)   ~ (all_6_2 = e3)
% 202.37/33.95    (14)   ~ (e2 = e1)
% 202.37/33.95    (15)  all_58_4 = e1 | all_58_9 = e1
% 202.37/33.95    (16)  op(all_6_2, all_6_2) = e3
% 202.37/33.95    (17)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.37/33.95    (18)   ~ (e2 = e0)
% 202.37/33.95    (19)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.37/33.95    (20)  op(all_52_29, all_52_29) = all_52_28
% 202.37/33.95    (21)   ~ (all_52_25 = all_6_2)
% 202.37/33.95    (22)  all_58_10 = e3
% 202.37/33.95    (23)   ~ (e1 = e0)
% 202.37/33.95    (24)   ~ (all_14_2 = e3)
% 202.37/33.95  
% 202.37/33.95  Begin of proof
% 202.37/33.95  | 
% 202.37/33.95  | BETA: splitting (15) gives:
% 202.37/33.95  | 
% 202.37/33.95  | Case 1:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (25)  all_58_4 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (5), (14), (25) are inconsistent by sub-proof #811.
% 202.37/33.95  | | 
% 202.37/33.95  | Case 2:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (26)  all_58_9 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | COMBINE_EQS: (6), (26) imply:
% 202.37/33.95  | |   (27)  all_52_25 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | SIMP: (27) implies:
% 202.37/33.95  | |   (28)  all_52_25 = e1
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (9), (28) imply:
% 202.37/33.95  | |   (29)   ~ (all_14_2 = e1)
% 202.37/33.95  | | 
% 202.37/33.95  | | SIMP: (29) implies:
% 202.37/33.95  | |   (30)   ~ (all_14_2 = e1)
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (21), (28) imply:
% 202.37/33.95  | |   (31)   ~ (all_6_2 = e1)
% 202.37/33.95  | | 
% 202.37/33.95  | | SIMP: (31) implies:
% 202.37/33.95  | |   (32)   ~ (all_6_2 = e1)
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (16),
% 202.37/33.95  | |            (17), (18), (19), (20), (22), (23), (24), (26), (30), (32) are
% 202.37/33.95  | |            inconsistent by sub-proof #394.
% 202.37/33.95  | | 
% 202.37/33.95  | End of split
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #394 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.37/33.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.37/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.37/33.95    (3)   ~ (e3 = e0)
% 202.37/33.95    (4)  all_58_0 = all_6_2
% 202.37/33.95    (5)  all_58_4 = e2
% 202.37/33.95    (6)  all_58_9 = e1
% 202.37/33.95    (7)   ~ (all_52_29 = all_14_2)
% 202.37/33.95    (8)  all_58_11 = all_52_29
% 202.37/33.95    (9)  all_58_1 = e3
% 202.37/33.95    (10)  op(e0, e0) = all_14_2
% 202.37/33.95    (11)  all_56_15 = all_14_2
% 202.37/33.95    (12)   ~ (all_6_2 = e3)
% 202.37/33.95    (13)  op(all_6_2, all_6_2) = e3
% 202.37/33.95    (14)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.37/33.95    (15)   ~ (e2 = e0)
% 202.37/33.95    (16)   ~ (all_14_2 = e1)
% 202.37/33.95    (17)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.37/33.95    (18)  op(all_52_29, all_52_29) = all_52_28
% 202.37/33.95    (19)  all_58_10 = e3
% 202.37/33.95    (20)   ~ (e1 = e0)
% 202.37/33.95    (21)   ~ (all_6_2 = e1)
% 202.37/33.95    (22)   ~ (all_14_2 = e3)
% 202.37/33.95  
% 202.37/33.95  Begin of proof
% 202.37/33.95  | 
% 202.37/33.95  | BETA: splitting (14) gives:
% 202.37/33.95  | 
% 202.37/33.95  | Case 1:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (23)  all_58_0 = e0
% 202.37/33.95  | | 
% 202.37/33.95  | | COMBINE_EQS: (4), (23) imply:
% 202.37/33.95  | |   (24)  all_6_2 = e0
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (12), (24) imply:
% 202.37/33.95  | |   (25)   ~ (e3 = e0)
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (21), (24) imply:
% 202.37/33.95  | |   (26)   ~ (e1 = e0)
% 202.37/33.95  | | 
% 202.37/33.95  | | REDUCE: (13), (24) imply:
% 202.37/33.95  | |   (27)  op(e0, e0) = e3
% 202.37/33.95  | | 
% 202.37/33.95  | | BETA: splitting (1) gives:
% 202.37/33.95  | | 
% 202.37/33.95  | | Case 1:
% 202.37/33.95  | | | 
% 202.37/33.95  | | |   (28)  all_58_9 = e0
% 202.37/33.95  | | | 
% 202.37/33.95  | | | COMBINE_EQS: (6), (28) imply:
% 202.37/33.95  | | |   (29)  e1 = e0
% 202.37/33.95  | | | 
% 202.37/33.95  | | | REDUCE: (20), (29) imply:
% 202.37/33.95  | | |   (30)  $false
% 202.37/33.95  | | | 
% 202.37/33.95  | | | CLOSE: (30) is inconsistent.
% 202.37/33.95  | | | 
% 202.37/33.95  | | Case 2:
% 202.37/33.95  | | | 
% 202.37/33.95  | | |   (31)  all_58_10 = e0 | all_58_11 = e0
% 202.37/33.95  | | | 
% 202.37/33.95  | | | BETA: splitting (31) gives:
% 202.37/33.95  | | | 
% 202.37/33.95  | | | Case 1:
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | |   (32)  all_58_10 = e0
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | REF_CLOSE: (3), (19), (32) are inconsistent by sub-proof #750.
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | Case 2:
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | |   (33)  all_58_11 = e0
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | COMBINE_EQS: (8), (33) imply:
% 202.37/33.95  | | | |   (34)  all_52_29 = e0
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | SIMP: (34) implies:
% 202.37/33.95  | | | |   (35)  all_52_29 = e0
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | REDUCE: (7), (35) imply:
% 202.37/33.95  | | | |   (36)   ~ (all_14_2 = e0)
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | SIMP: (36) implies:
% 202.37/33.95  | | | |   (37)   ~ (all_14_2 = e0)
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | REDUCE: (18), (35) imply:
% 202.37/33.95  | | | |   (38)  op(e0, e0) = all_52_28
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | | REF_CLOSE: (2), (10), (11), (16), (17), (22), (27), (37), (38) are
% 202.37/33.95  | | | |            inconsistent by sub-proof #395.
% 202.37/33.95  | | | | 
% 202.37/33.95  | | | End of split
% 202.37/33.95  | | | 
% 202.37/33.95  | | End of split
% 202.37/33.95  | | 
% 202.37/33.95  | Case 2:
% 202.37/33.95  | | 
% 202.37/33.95  | |   (39)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.37/33.95  | | 
% 202.37/33.95  | | REF_CLOSE: (3), (5), (6), (9), (15), (20), (39) are inconsistent by
% 202.37/33.95  | |            sub-proof #1026.
% 202.37/33.95  | | 
% 202.37/33.95  | End of split
% 202.37/33.95  | 
% 202.37/33.95  End of proof
% 202.37/33.95  
% 202.37/33.95  Sub-proof #395 shows that the following formulas are inconsistent:
% 202.37/33.95  ----------------------------------------------------------------
% 202.37/33.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.37/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.37/33.95    (2)  op(e0, e0) = all_52_28
% 202.37/33.95    (3)  op(e0, e0) = all_14_2
% 202.37/33.95    (4)  all_56_15 = all_14_2
% 202.37/33.95    (5)  op(e0, e0) = e3
% 202.47/33.95    (6)   ~ (all_14_2 = e0)
% 202.47/33.95    (7)   ~ (all_14_2 = e1)
% 202.47/33.95    (8)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/33.95    (9)   ~ (all_14_2 = e3)
% 202.47/33.95  
% 202.47/33.95  Begin of proof
% 202.47/33.95  | 
% 202.47/33.95  | BETA: splitting (8) gives:
% 202.47/33.95  | 
% 202.47/33.95  | Case 1:
% 202.47/33.95  | | 
% 202.47/33.95  | |   (10)  all_56_15 = e2
% 202.47/33.95  | | 
% 202.47/33.95  | | COMBINE_EQS: (4), (10) imply:
% 202.47/33.95  | |   (11)  all_14_2 = e2
% 202.47/33.95  | | 
% 202.47/33.95  | | SIMP: (11) implies:
% 202.47/33.95  | |   (12)  all_14_2 = e2
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (9), (12) imply:
% 202.47/33.95  | |   (13)   ~ (e3 = e2)
% 202.47/33.95  | | 
% 202.47/33.95  | | SIMP: (13) implies:
% 202.47/33.95  | |   (14)   ~ (e3 = e2)
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (3), (12) imply:
% 202.47/33.95  | |   (15)  op(e0, e0) = e2
% 202.47/33.95  | | 
% 202.47/33.95  | | REF_CLOSE: (1), (2), (5), (14), (15) are inconsistent by sub-proof #685.
% 202.47/33.95  | | 
% 202.47/33.95  | Case 2:
% 202.47/33.95  | | 
% 202.47/33.95  | |   (16)  all_56_15 = e1 | all_56_15 = e0
% 202.47/33.95  | | 
% 202.47/33.95  | | REF_CLOSE: (4), (6), (7), (16) are inconsistent by sub-proof #1161.
% 202.47/33.95  | | 
% 202.47/33.95  | End of split
% 202.47/33.95  | 
% 202.47/33.95  End of proof
% 202.47/33.95  
% 202.47/33.95  Sub-proof #396 shows that the following formulas are inconsistent:
% 202.47/33.95  ----------------------------------------------------------------
% 202.47/33.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.95    (2)  op(e3, e3) = all_52_6
% 202.47/33.95    (3)  all_58_11 = all_52_29
% 202.47/33.95    (4)  op(all_10_2, all_10_2) = e1
% 202.47/33.95    (5)  all_58_7 = all_52_13
% 202.47/33.95    (6)   ~ (all_52_29 = e3)
% 202.47/33.95    (7)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.95    (8)  all_58_8 = all_10_2
% 202.47/33.95    (9)  op(e3, e3) = all_6_2
% 202.47/33.95    (10)   ~ (all_52_13 = e3)
% 202.47/33.95    (11)   ~ (all_6_2 = e1)
% 202.47/33.95    (12)  all_56_10 = all_10_2
% 202.47/33.95    (13)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.47/33.95  
% 202.47/33.95  Begin of proof
% 202.47/33.95  | 
% 202.47/33.95  | BETA: splitting (7) gives:
% 202.47/33.95  | 
% 202.47/33.95  | Case 1:
% 202.47/33.95  | | 
% 202.47/33.95  | |   (14)  all_58_7 = e3
% 202.47/33.95  | | 
% 202.47/33.95  | | COMBINE_EQS: (5), (14) imply:
% 202.47/33.95  | |   (15)  all_52_13 = e3
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (10), (15) imply:
% 202.47/33.95  | |   (16)  $false
% 202.47/33.95  | | 
% 202.47/33.95  | | CLOSE: (16) is inconsistent.
% 202.47/33.95  | | 
% 202.47/33.95  | Case 2:
% 202.47/33.95  | | 
% 202.47/33.95  | |   (17)  all_58_8 = e3 | all_58_11 = e3
% 202.47/33.95  | | 
% 202.47/33.95  | | BETA: splitting (13) gives:
% 202.47/33.95  | | 
% 202.47/33.95  | | Case 1:
% 202.47/33.95  | | | 
% 202.47/33.95  | | |   (18)  all_56_10 = e3
% 202.47/33.95  | | | 
% 202.47/33.95  | | | REF_CLOSE: (1), (2), (4), (9), (11), (12), (18) are inconsistent by
% 202.47/33.95  | | |            sub-proof #397.
% 202.47/33.95  | | | 
% 202.47/33.95  | | Case 2:
% 202.47/33.95  | | | 
% 202.47/33.95  | | |   (19)   ~ (all_56_10 = e3)
% 202.47/33.95  | | | 
% 202.47/33.95  | | | REDUCE: (12), (19) imply:
% 202.47/33.95  | | |   (20)   ~ (all_10_2 = e3)
% 202.47/33.95  | | | 
% 202.47/33.95  | | | REF_CLOSE: (3), (6), (8), (17), (20) are inconsistent by sub-proof #1140.
% 202.47/33.95  | | | 
% 202.47/33.95  | | End of split
% 202.47/33.95  | | 
% 202.47/33.95  | End of split
% 202.47/33.95  | 
% 202.47/33.95  End of proof
% 202.47/33.95  
% 202.47/33.95  Sub-proof #397 shows that the following formulas are inconsistent:
% 202.47/33.95  ----------------------------------------------------------------
% 202.47/33.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.95    (2)  op(e3, e3) = all_52_6
% 202.47/33.95    (3)  op(all_10_2, all_10_2) = e1
% 202.47/33.95    (4)  all_56_10 = e3
% 202.47/33.95    (5)  op(e3, e3) = all_6_2
% 202.47/33.95    (6)   ~ (all_6_2 = e1)
% 202.47/33.95    (7)  all_56_10 = all_10_2
% 202.47/33.95  
% 202.47/33.95  Begin of proof
% 202.47/33.95  | 
% 202.47/33.95  | COMBINE_EQS: (4), (7) imply:
% 202.47/33.95  |   (8)  all_10_2 = e3
% 202.47/33.95  | 
% 202.47/33.95  | SIMP: (8) implies:
% 202.47/33.95  |   (9)  all_10_2 = e3
% 202.47/33.95  | 
% 202.47/33.95  | REDUCE: (3), (9) imply:
% 202.47/33.95  |   (10)  op(e3, e3) = e1
% 202.47/33.95  | 
% 202.47/33.95  | REF_CLOSE: (1), (2), (5), (6), (10) are inconsistent by sub-proof #1105.
% 202.47/33.95  | 
% 202.47/33.95  End of proof
% 202.47/33.95  
% 202.47/33.95  Sub-proof #398 shows that the following formulas are inconsistent:
% 202.47/33.95  ----------------------------------------------------------------
% 202.47/33.95    (1)   ~ (e3 = e1)
% 202.47/33.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.95    (3)   ~ (all_52_5 = all_4_0)
% 202.47/33.95    (4)   ~ (all_4_2 = e3)
% 202.47/33.95    (5)  all_44_2 = all_6_2
% 202.47/33.95    (6)  all_58_0 = all_6_2
% 202.47/33.95    (7)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.47/33.95    (8)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.95    (9)  op(e1, e3) = all_52_5
% 202.47/33.95    (10)   ~ (all_6_2 = all_4_0)
% 202.47/33.95    (11)  all_32_2 = all_4_2
% 202.47/33.95    (12)  op(e2, e2) = all_4_2
% 202.47/33.95    (13)  all_56_5 = all_4_2
% 202.47/33.95    (14)  op(all_6_2, all_6_2) = all_52_0
% 202.47/33.95    (15)  all_58_2 = all_4_0
% 202.47/33.95    (16)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/33.95    (17)  op(all_4_2, e2) = e3
% 202.47/33.95    (18)  all_56_8 = all_52_5
% 202.47/33.95    (19)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.47/33.95    (20)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.95    (21)  all_56_4 = all_4_0
% 202.47/33.95    (22)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.47/33.95    (23)   ~ (all_52_5 = all_6_2)
% 202.47/33.95    (24)  op(e3, all_6_1) = e2
% 202.47/33.95    (25)  all_58_10 = e3
% 202.47/33.95    (26)  op(e3, e3) = all_6_2
% 202.47/33.95    (27)  op(all_4_2, all_4_2) = all_52_10
% 202.47/33.95    (28)  all_32_0 = all_4_0
% 202.47/33.95    (29)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 202.47/33.95    (30)   ~ (all_4_0 = all_4_2)
% 202.47/33.95    (31)  all_44_1 = all_6_1
% 202.47/33.95    (32)  all_58_3 = all_4_2
% 202.47/33.95    (33)  op(all_6_2, e3) = all_6_1
% 202.47/33.95    (34)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.47/33.95    (35)  all_58_0 = e1
% 202.47/33.95  
% 202.47/33.95  Begin of proof
% 202.47/33.95  | 
% 202.47/33.95  | COMBINE_EQS: (6), (35) imply:
% 202.47/33.95  |   (36)  all_6_2 = e1
% 202.47/33.95  | 
% 202.47/33.95  | COMBINE_EQS: (5), (36) imply:
% 202.47/33.95  |   (37)  all_44_2 = e1
% 202.47/33.95  | 
% 202.47/33.95  | REDUCE: (23), (36) imply:
% 202.47/33.95  |   (38)   ~ (all_52_5 = e1)
% 202.47/33.95  | 
% 202.47/33.95  | REDUCE: (10), (36) imply:
% 202.47/33.95  |   (39)   ~ (all_4_0 = e1)
% 202.47/33.95  | 
% 202.47/33.95  | SIMP: (39) implies:
% 202.47/33.95  |   (40)   ~ (all_4_0 = e1)
% 202.47/33.95  | 
% 202.47/33.95  | REDUCE: (33), (36) imply:
% 202.47/33.95  |   (41)  op(e1, e3) = all_6_1
% 202.47/33.95  | 
% 202.47/33.95  | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 202.47/33.95  |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 202.47/33.95  |            (27), (28), (29), (30), (31), (32), (34), (37), (38), (40), (41)
% 202.47/33.95  |            are inconsistent by sub-proof #399.
% 202.47/33.95  | 
% 202.47/33.95  End of proof
% 202.47/33.95  
% 202.47/33.95  Sub-proof #399 shows that the following formulas are inconsistent:
% 202.47/33.95  ----------------------------------------------------------------
% 202.47/33.95    (1)   ~ (e3 = e1)
% 202.47/33.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.95    (3)   ~ (all_4_0 = e1)
% 202.47/33.95    (4)   ~ (all_52_5 = all_4_0)
% 202.47/33.95    (5)   ~ (all_4_2 = e3)
% 202.47/33.95    (6)  all_44_2 = e1
% 202.47/33.95    (7)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.47/33.95    (8)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.95    (9)   ~ (all_52_5 = e1)
% 202.47/33.95    (10)  op(e1, e3) = all_52_5
% 202.47/33.95    (11)   ~ (all_6_2 = all_4_0)
% 202.47/33.95    (12)  all_32_2 = all_4_2
% 202.47/33.95    (13)  op(e2, e2) = all_4_2
% 202.47/33.95    (14)  all_56_5 = all_4_2
% 202.47/33.95    (15)  op(all_6_2, all_6_2) = all_52_0
% 202.47/33.95    (16)  all_58_2 = all_4_0
% 202.47/33.95    (17)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/33.95    (18)  op(all_4_2, e2) = e3
% 202.47/33.95    (19)  op(e1, e3) = all_6_1
% 202.47/33.95    (20)  all_56_8 = all_52_5
% 202.47/33.95    (21)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.47/33.95    (22)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.95    (23)  all_56_4 = all_4_0
% 202.47/33.95    (24)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.47/33.95    (25)  op(e3, all_6_1) = e2
% 202.47/33.95    (26)  all_58_10 = e3
% 202.47/33.95    (27)  op(e3, e3) = all_6_2
% 202.47/33.95    (28)  op(all_4_2, all_4_2) = all_52_10
% 202.47/33.95    (29)  all_32_0 = all_4_0
% 202.47/33.95    (30)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 202.47/33.95    (31)   ~ (all_4_0 = all_4_2)
% 202.47/33.95    (32)  all_44_1 = all_6_1
% 202.47/33.95    (33)  all_58_3 = all_4_2
% 202.47/33.95    (34)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.47/33.95  
% 202.47/33.95  Begin of proof
% 202.47/33.95  | 
% 202.47/33.95  | BETA: splitting (7) gives:
% 202.47/33.95  | 
% 202.47/33.95  | Case 1:
% 202.47/33.95  | | 
% 202.47/33.95  | |   (35)   ~ (all_44_2 = e1)
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (6), (35) imply:
% 202.47/33.95  | |   (36)  $false
% 202.47/33.95  | | 
% 202.47/33.95  | | CLOSE: (36) is inconsistent.
% 202.47/33.95  | | 
% 202.47/33.95  | Case 2:
% 202.47/33.95  | | 
% 202.47/33.95  | |   (37)   ~ (all_44_1 = e0)
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (32), (37) imply:
% 202.47/33.95  | |   (38)   ~ (all_6_1 = e0)
% 202.47/33.95  | | 
% 202.47/33.95  | | GROUND_INST: instantiating (2) with all_52_5, all_6_1, e3, e1, simplifying
% 202.47/33.95  | |              with (10), (19) gives:
% 202.47/33.95  | |   (39)  all_52_5 = all_6_1
% 202.47/33.95  | | 
% 202.47/33.95  | | COMBINE_EQS: (20), (39) imply:
% 202.47/33.95  | |   (40)  all_56_8 = all_6_1
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (4), (39) imply:
% 202.47/33.95  | |   (41)   ~ (all_6_1 = all_4_0)
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (9), (39) imply:
% 202.47/33.95  | |   (42)   ~ (all_6_1 = e1)
% 202.47/33.95  | | 
% 202.47/33.95  | | REDUCE: (8), (39) imply:
% 202.47/33.95  | |   (43)  op(all_6_1, all_6_1) = all_52_4
% 202.47/33.95  | | 
% 202.47/33.95  | | BETA: splitting (24) gives:
% 202.47/33.95  | | 
% 202.47/33.95  | | Case 1:
% 202.47/33.95  | | | 
% 202.47/33.95  | | |   (44)  all_56_8 = e3
% 202.47/33.95  | | | 
% 202.47/33.95  | | | COMBINE_EQS: (40), (44) imply:
% 202.47/33.95  | | |   (45)  all_6_1 = e3
% 202.47/33.95  | | | 
% 202.47/33.95  | | | SIMP: (45) implies:
% 202.47/33.95  | | |   (46)  all_6_1 = e3
% 202.47/33.95  | | | 
% 202.47/33.95  | | | REDUCE: (25), (46) imply:
% 202.47/33.95  | | |   (47)  op(e3, e3) = e2
% 202.47/33.95  | | | 
% 202.47/33.95  | | | REF_CLOSE: (2), (3), (5), (11), (12), (13), (14), (15), (18), (21), (22),
% 202.47/33.95  | | |            (23), (27), (28), (29), (30), (31), (47) are inconsistent by
% 202.47/33.95  | | |            sub-proof #947.
% 202.47/33.95  | | | 
% 202.47/33.95  | | Case 2:
% 202.47/33.95  | | | 
% 202.47/33.95  | | |   (48)   ~ (all_56_8 = e3)
% 202.47/33.95  | | |   (49)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.47/33.95  | | | 
% 202.47/33.95  | | | REDUCE: (40), (48) imply:
% 202.47/33.95  | | |   (50)   ~ (all_6_1 = e3)
% 202.47/33.95  | | | 
% 202.47/33.95  | | | BETA: splitting (49) gives:
% 202.47/33.95  | | | 
% 202.47/33.95  | | | Case 1:
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | |   (51)  all_56_8 = e2
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | COMBINE_EQS: (40), (51) imply:
% 202.47/33.95  | | | |   (52)  all_6_1 = e2
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | SIMP: (52) implies:
% 202.47/33.95  | | | |   (53)  all_6_1 = e2
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | REDUCE: (41), (53) imply:
% 202.47/33.95  | | | |   (54)   ~ (all_4_0 = e2)
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | SIMP: (54) implies:
% 202.47/33.95  | | | |   (55)   ~ (all_4_0 = e2)
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | REDUCE: (50), (53) imply:
% 202.47/33.95  | | | |   (56)   ~ (e3 = e2)
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | SIMP: (56) implies:
% 202.47/33.95  | | | |   (57)   ~ (e3 = e2)
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | REDUCE: (42), (53) imply:
% 202.47/33.95  | | | |   (58)   ~ (e2 = e1)
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | REDUCE: (43), (53) imply:
% 202.47/33.95  | | | |   (59)  op(e2, e2) = all_52_4
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | BETA: splitting (22) gives:
% 202.47/33.95  | | | | 
% 202.47/33.95  | | | | Case 1:
% 202.47/33.95  | | | | | 
% 202.47/33.95  | | | | |   (60)  all_56_4 = e2
% 202.47/33.95  | | | | | 
% 202.47/33.95  | | | | | REF_CLOSE: (23), (55), (60) are inconsistent by sub-proof #979.
% 202.47/33.95  | | | | | 
% 202.47/33.95  | | | | Case 2:
% 202.47/33.95  | | | | | 
% 202.47/33.95  | | | | |   (61)   ~ (all_56_4 = e2)
% 202.47/33.95  | | | | |   (62)  all_56_4 = e1 | all_56_4 = e0
% 202.47/33.95  | | | | | 
% 202.47/33.95  | | | | | BETA: splitting (62) gives:
% 202.47/33.95  | | | | | 
% 202.47/33.95  | | | | | Case 1:
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | |   (63)  all_56_4 = e1
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | REF_CLOSE: (3), (23), (63) are inconsistent by sub-proof #978.
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | Case 2:
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | |   (64)  all_56_4 = e0
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | COMBINE_EQS: (23), (64) imply:
% 202.47/33.95  | | | | | |   (65)  all_4_0 = e0
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | SIMP: (65) implies:
% 202.47/33.95  | | | | | |   (66)  all_4_0 = e0
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | COMBINE_EQS: (29), (66) imply:
% 202.47/33.95  | | | | | |   (67)  all_32_0 = e0
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | COMBINE_EQS: (16), (66) imply:
% 202.47/33.95  | | | | | |   (68)  all_58_2 = e0
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | REDUCE: (55), (66) imply:
% 202.47/33.95  | | | | | |   (69)   ~ (e2 = e0)
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | SIMP: (69) implies:
% 202.47/33.95  | | | | | |   (70)   ~ (e2 = e0)
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | BETA: splitting (30) gives:
% 202.47/33.95  | | | | | | 
% 202.47/33.95  | | | | | | Case 1:
% 202.47/33.95  | | | | | | | 
% 202.47/33.95  | | | | | | |   (71)   ~ (all_32_2 = e1)
% 202.47/33.95  | | | | | | | 
% 202.47/33.95  | | | | | | | REDUCE: (12), (71) imply:
% 202.47/33.95  | | | | | | |   (72)   ~ (all_4_2 = e1)
% 202.47/33.95  | | | | | | | 
% 202.47/33.95  | | | | | | | BETA: splitting (17) gives:
% 202.47/33.95  | | | | | | | 
% 202.47/33.95  | | | | | | | Case 1:
% 202.47/33.95  | | | | | | | | 
% 202.47/33.96  | | | | | | | |   (73)  all_58_3 = e1
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | | COMBINE_EQS: (33), (73) imply:
% 202.47/33.96  | | | | | | | |   (74)  all_4_2 = e1
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | | REDUCE: (72), (74) imply:
% 202.47/33.96  | | | | | | | |   (75)  $false
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | | CLOSE: (75) is inconsistent.
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | Case 2:
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | |   (76)  all_58_5 = e1 | all_58_10 = e1
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | | BETA: splitting (76) gives:
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | | Case 1:
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | |   (77)  all_58_5 = e1
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | BETA: splitting (34) gives:
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | Case 1:
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | |   (78)  all_58_2 = e2
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | COMBINE_EQS: (68), (78) imply:
% 202.47/33.96  | | | | | | | | | |   (79)  e2 = e0
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | REDUCE: (70), (79) imply:
% 202.47/33.96  | | | | | | | | | |   (80)  $false
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | CLOSE: (80) is inconsistent.
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | Case 2:
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | |   (81)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | BETA: splitting (81) gives:
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | Case 1:
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | |   (82)  all_58_3 = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | COMBINE_EQS: (33), (82) imply:
% 202.47/33.96  | | | | | | | | | | |   (83)  all_4_2 = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | REDUCE: (28), (83) imply:
% 202.47/33.96  | | | | | | | | | | |   (84)  op(e2, e2) = all_52_10
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | REDUCE: (18), (83) imply:
% 202.47/33.96  | | | | | | | | | | |   (85)  op(e2, e2) = e3
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | REDUCE: (13), (83) imply:
% 202.47/33.96  | | | | | | | | | | |   (86)  op(e2, e2) = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | GROUND_INST: instantiating (2) with e2, all_52_10, e2, e2,
% 202.47/33.96  | | | | | | | | | | |              simplifying with (84), (86) gives:
% 202.47/33.96  | | | | | | | | | | |   (87)  all_52_10 = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_10, all_52_4, e2,
% 202.47/33.96  | | | | | | | | | | |              e2, simplifying with (59), (84) gives:
% 202.47/33.96  | | | | | | | | | | |   (88)  all_52_4 = all_52_10
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | GROUND_INST: instantiating (2) with e3, all_52_4, e2, e2,
% 202.47/33.96  | | | | | | | | | | |              simplifying with (59), (85) gives:
% 202.47/33.96  | | | | | | | | | | |   (89)  all_52_4 = e3
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | COMBINE_EQS: (88), (89) imply:
% 202.47/33.96  | | | | | | | | | | |   (90)  all_52_10 = e3
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | SIMP: (90) implies:
% 202.47/33.96  | | | | | | | | | | |   (91)  all_52_10 = e3
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | COMBINE_EQS: (87), (91) imply:
% 202.47/33.96  | | | | | | | | | | |   (92)  e3 = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | SIMP: (92) implies:
% 202.47/33.96  | | | | | | | | | | |   (93)  e3 = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | REDUCE: (57), (93) imply:
% 202.47/33.96  | | | | | | | | | | |   (94)  $false
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | CLOSE: (94) is inconsistent.
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | Case 2:
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | |   (95)  all_58_5 = e2 | all_58_10 = e2
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | | REF_CLOSE: (26), (57), (58), (77), (95) are inconsistent by
% 202.47/33.96  | | | | | | | | | | |            sub-proof #472.
% 202.47/33.96  | | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | | End of split
% 202.47/33.96  | | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | End of split
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | Case 2:
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | |   (96)  all_58_10 = e1
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | | REF_CLOSE: (1), (26), (96) are inconsistent by sub-proof #968.
% 202.47/33.96  | | | | | | | | | 
% 202.47/33.96  | | | | | | | | End of split
% 202.47/33.96  | | | | | | | | 
% 202.47/33.96  | | | | | | | End of split
% 202.47/33.96  | | | | | | | 
% 202.47/33.96  | | | | | | Case 2:
% 202.47/33.96  | | | | | | | 
% 202.47/33.96  | | | | | | |   (97)   ~ (all_32_0 = e0)
% 202.47/33.96  | | | | | | | 
% 202.47/33.96  | | | | | | | REDUCE: (67), (97) imply:
% 202.47/33.96  | | | | | | |   (98)  $false
% 202.47/33.96  | | | | | | | 
% 202.47/33.96  | | | | | | | CLOSE: (98) is inconsistent.
% 202.47/33.96  | | | | | | | 
% 202.47/33.96  | | | | | | End of split
% 202.47/33.96  | | | | | | 
% 202.47/33.96  | | | | | End of split
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | End of split
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | Case 2:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | |   (99)  all_56_8 = e1 | all_56_8 = e0
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | REF_CLOSE: (38), (40), (42), (99) are inconsistent by sub-proof #495.
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | End of split
% 202.47/33.96  | | | 
% 202.47/33.96  | | End of split
% 202.47/33.96  | | 
% 202.47/33.96  | End of split
% 202.47/33.96  | 
% 202.47/33.96  End of proof
% 202.47/33.96  
% 202.47/33.96  Sub-proof #400 shows that the following formulas are inconsistent:
% 202.47/33.96  ----------------------------------------------------------------
% 202.47/33.96    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.96    (2)   ~ (e3 = e1)
% 202.47/33.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.96    (4)   ~ (e3 = e0)
% 202.47/33.96    (5)   ~ (all_4_0 = e1)
% 202.47/33.96    (6)  all_58_0 = all_6_2
% 202.47/33.96    (7)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.96    (8)   ~ (all_6_2 = all_4_0)
% 202.47/33.96    (9)  all_58_2 = all_4_0
% 202.47/33.96    (10)   ~ (all_4_0 = e3)
% 202.47/33.96    (11)  all_58_12 = all_52_7
% 202.47/33.96    (12)   ~ (all_52_7 = e3)
% 202.47/33.96    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/33.96    (15)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.96    (16)  all_56_4 = all_4_0
% 202.47/33.96    (17)  op(e0, e3) = all_52_7
% 202.47/33.96    (18)  all_8_2 = all_6_2
% 202.47/33.96    (19)  op(e3, e3) = e0
% 202.47/33.96    (20)  op(e3, e3) = all_6_2
% 202.47/33.96    (21)  all_58_6 = all_52_5
% 202.47/33.96    (22)   ~ (e1 = e0)
% 202.47/33.96    (23)  all_8_1 = all_6_1
% 202.47/33.96    (24)  op(all_6_2, e3) = all_6_1
% 202.47/33.96  
% 202.47/33.96  Begin of proof
% 202.47/33.96  | 
% 202.47/33.96  | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying with
% 202.47/33.96  |              (19), (20) gives:
% 202.47/33.96  |   (25)  all_6_2 = e0
% 202.47/33.96  | 
% 202.47/33.96  | COMBINE_EQS: (6), (25) imply:
% 202.47/33.96  |   (26)  all_58_0 = e0
% 202.47/33.96  | 
% 202.47/33.96  | REDUCE: (8), (25) imply:
% 202.47/33.96  |   (27)   ~ (all_4_0 = e0)
% 202.47/33.96  | 
% 202.47/33.96  | SIMP: (27) implies:
% 202.47/33.96  |   (28)   ~ (all_4_0 = e0)
% 202.47/33.96  | 
% 202.47/33.96  | BETA: splitting (13) gives:
% 202.47/33.96  | 
% 202.47/33.96  | Case 1:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (29)  all_58_0 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (4), (26), (29) are inconsistent by sub-proof #1015.
% 202.47/33.96  | | 
% 202.47/33.96  | Case 2:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (30)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | BETA: splitting (15) gives:
% 202.47/33.96  | | 
% 202.47/33.96  | | Case 1:
% 202.47/33.96  | | | 
% 202.47/33.96  | | |   (31)  all_56_4 = e2
% 202.47/33.96  | | | 
% 202.47/33.96  | | | COMBINE_EQS: (16), (31) imply:
% 202.47/33.96  | | |   (32)  all_4_0 = e2
% 202.47/33.96  | | | 
% 202.47/33.96  | | | SIMP: (32) implies:
% 202.47/33.96  | | |   (33)  all_4_0 = e2
% 202.47/33.96  | | | 
% 202.47/33.96  | | | COMBINE_EQS: (9), (33) imply:
% 202.47/33.96  | | |   (34)  all_58_2 = e2
% 202.47/33.96  | | | 
% 202.47/33.96  | | | REDUCE: (10), (33) imply:
% 202.47/33.96  | | |   (35)   ~ (e3 = e2)
% 202.47/33.96  | | | 
% 202.47/33.96  | | | SIMP: (35) implies:
% 202.47/33.96  | | |   (36)   ~ (e3 = e2)
% 202.47/33.96  | | | 
% 202.47/33.96  | | | BETA: splitting (30) gives:
% 202.47/33.96  | | | 
% 202.47/33.96  | | | Case 1:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | |   (37)  all_58_2 = e3
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | COMBINE_EQS: (34), (37) imply:
% 202.47/33.96  | | | |   (38)  e3 = e2
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | REDUCE: (36), (38) imply:
% 202.47/33.96  | | | |   (39)  $false
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | CLOSE: (39) is inconsistent.
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | Case 2:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | |   (40)  all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | BETA: splitting (40) gives:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | Case 1:
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | |   (41)  all_58_6 = e3
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | COMBINE_EQS: (21), (41) imply:
% 202.47/33.96  | | | | |   (42)  all_52_5 = e3
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | SIMP: (42) implies:
% 202.47/33.96  | | | | |   (43)  all_52_5 = e3
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | REDUCE: (7), (43) imply:
% 202.47/33.96  | | | | |   (44)  op(e3, e3) = all_52_4
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (11), (14), (17), (18), (19),
% 202.47/33.96  | | | | |            (20), (22), (23), (24), (41), (44) are inconsistent by
% 202.47/33.96  | | | | |            sub-proof #401.
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | Case 2:
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | |   (45)  all_58_12 = e3
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | REF_CLOSE: (11), (12), (45) are inconsistent by sub-proof #1367.
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | End of split
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | End of split
% 202.47/33.96  | | | 
% 202.47/33.96  | | Case 2:
% 202.47/33.96  | | | 
% 202.47/33.96  | | |   (46)  all_56_4 = e1 | all_56_4 = e0
% 202.47/33.96  | | | 
% 202.47/33.96  | | | REF_CLOSE: (5), (16), (28), (46) are inconsistent by sub-proof #674.
% 202.47/33.96  | | | 
% 202.47/33.96  | | End of split
% 202.47/33.96  | | 
% 202.47/33.96  | End of split
% 202.47/33.96  | 
% 202.47/33.96  End of proof
% 202.47/33.96  
% 202.47/33.96  Sub-proof #401 shows that the following formulas are inconsistent:
% 202.47/33.96  ----------------------------------------------------------------
% 202.47/33.96    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.96    (2)   ~ (e3 = e1)
% 202.47/33.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.96    (4)   ~ (all_4_0 = e1)
% 202.47/33.96    (5)  all_58_0 = all_6_2
% 202.47/33.96    (6)  all_58_2 = all_4_0
% 202.47/33.96    (7)  all_58_6 = e3
% 202.47/33.96    (8)  all_58_12 = all_52_7
% 202.47/33.96    (9)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/33.96    (10)  op(e0, e3) = all_52_7
% 202.47/33.96    (11)  op(e3, e3) = all_52_4
% 202.47/33.96    (12)  all_8_2 = all_6_2
% 202.47/33.96    (13)  op(e3, e3) = e0
% 202.47/33.96    (14)  op(e3, e3) = all_6_2
% 202.47/33.96    (15)   ~ (e1 = e0)
% 202.47/33.96    (16)  all_8_1 = all_6_1
% 202.47/33.96    (17)  op(all_6_2, e3) = all_6_1
% 202.47/33.96  
% 202.47/33.96  Begin of proof
% 202.47/33.96  | 
% 202.47/33.96  | GROUND_INST: instantiating (3) with all_6_2, all_52_4, e3, e3, simplifying
% 202.47/33.96  |              with (11), (14) gives:
% 202.47/33.96  |   (18)  all_52_4 = all_6_2
% 202.47/33.96  | 
% 202.47/33.96  | GROUND_INST: instantiating (3) with e0, all_52_4, e3, e3, simplifying with
% 202.47/33.96  |              (11), (13) gives:
% 202.47/33.96  |   (19)  all_52_4 = e0
% 202.47/33.96  | 
% 202.47/33.96  | COMBINE_EQS: (18), (19) imply:
% 202.47/33.96  |   (20)  all_6_2 = e0
% 202.47/33.96  | 
% 202.47/33.96  | SIMP: (20) implies:
% 202.47/33.96  |   (21)  all_6_2 = e0
% 202.47/33.96  | 
% 202.47/33.96  | COMBINE_EQS: (12), (21) imply:
% 202.47/33.96  |   (22)  all_8_2 = e0
% 202.47/33.96  | 
% 202.47/33.96  | COMBINE_EQS: (5), (21) imply:
% 202.47/33.96  |   (23)  all_58_0 = e0
% 202.47/33.96  | 
% 202.47/33.96  | REDUCE: (17), (21) imply:
% 202.47/33.96  |   (24)  op(e0, e3) = all_6_1
% 202.47/33.96  | 
% 202.47/33.96  | BETA: splitting (9) gives:
% 202.47/33.96  | 
% 202.47/33.96  | Case 1:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (25)  all_58_0 = e1
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (15), (23), (25) are inconsistent by sub-proof #847.
% 202.47/33.96  | | 
% 202.47/33.96  | Case 2:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (26)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/33.96  | | 
% 202.47/33.96  | | BETA: splitting (26) gives:
% 202.47/33.96  | | 
% 202.47/33.96  | | Case 1:
% 202.47/33.96  | | | 
% 202.47/33.96  | | |   (27)  all_58_2 = e1
% 202.47/33.96  | | | 
% 202.47/33.96  | | | REF_CLOSE: (4), (6), (27) are inconsistent by sub-proof #967.
% 202.47/33.96  | | | 
% 202.47/33.96  | | Case 2:
% 202.47/33.96  | | | 
% 202.47/33.96  | | |   (28)  all_58_6 = e1 | all_58_12 = e1
% 202.47/33.96  | | | 
% 202.47/33.96  | | | BETA: splitting (1) gives:
% 202.47/33.96  | | | 
% 202.47/33.96  | | | Case 1:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | |   (29)   ~ (all_8_1 = e1)
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | REDUCE: (16), (29) imply:
% 202.47/33.96  | | | |   (30)   ~ (all_6_1 = e1)
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | BETA: splitting (28) gives:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | Case 1:
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | |   (31)  all_58_6 = e1
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | REF_CLOSE: (2), (7), (31) are inconsistent by sub-proof #1128.
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | Case 2:
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | |   (32)  all_58_12 = e1
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | COMBINE_EQS: (8), (32) imply:
% 202.47/33.96  | | | | |   (33)  all_52_7 = e1
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | SIMP: (33) implies:
% 202.47/33.96  | | | | |   (34)  all_52_7 = e1
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | REDUCE: (10), (34) imply:
% 202.47/33.96  | | | | |   (35)  op(e0, e3) = e1
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | | REF_CLOSE: (3), (24), (30), (35) are inconsistent by sub-proof #961.
% 202.47/33.96  | | | | | 
% 202.47/33.96  | | | | End of split
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | Case 2:
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | |   (36)   ~ (all_8_2 = e0)
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | REDUCE: (22), (36) imply:
% 202.47/33.96  | | | |   (37)  $false
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | | CLOSE: (37) is inconsistent.
% 202.47/33.96  | | | | 
% 202.47/33.96  | | | End of split
% 202.47/33.96  | | | 
% 202.47/33.96  | | End of split
% 202.47/33.96  | | 
% 202.47/33.96  | End of split
% 202.47/33.96  | 
% 202.47/33.96  End of proof
% 202.47/33.96  
% 202.47/33.96  Sub-proof #402 shows that the following formulas are inconsistent:
% 202.47/33.96  ----------------------------------------------------------------
% 202.47/33.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.96    (2)   ~ (all_52_5 = all_52_13)
% 202.47/33.96    (3)  all_58_1 = all_52_9
% 202.47/33.96    (4)   ~ (all_52_7 = all_52_15)
% 202.47/33.96    (5)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.96    (6)  all_58_0 = all_6_2
% 202.47/33.96    (7)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.96    (8)  all_58_13 = all_52_15
% 202.47/33.96    (9)  op(all_52_13, all_52_13) = e1
% 202.47/33.96    (10)   ~ (all_52_15 = e3)
% 202.47/33.96    (11)  all_58_2 = all_4_0
% 202.47/33.96    (12)  op(all_4_2, e2) = e3
% 202.47/33.96    (13)   ~ (all_4_0 = e3)
% 202.47/33.96    (14)  all_56_9 = all_52_13
% 202.47/33.96    (15)  all_58_7 = all_52_13
% 202.47/33.96    (16)  all_58_12 = all_52_7
% 202.47/33.96    (17)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.96    (19)   ~ (all_52_9 = all_4_2)
% 202.47/33.96    (20)   ~ (all_52_9 = all_6_2)
% 202.47/33.96    (21)  op(e3, all_6_1) = e2
% 202.47/33.96    (22)  op(e3, e3) = all_6_2
% 202.47/33.96    (23)  all_58_6 = all_52_5
% 202.47/33.96    (24)  op(e3, e2) = all_52_9
% 202.47/33.96    (25)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.96    (26)   ~ (e3 = e2)
% 202.47/33.96    (27)   ~ (all_6_2 = e1)
% 202.47/33.96    (28)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.96    (29)  op(all_52_9, all_52_9) = e3
% 202.47/33.96    (30)  all_58_3 = all_4_2
% 202.47/33.96    (31)  op(all_6_2, e3) = all_6_1
% 202.47/33.96  
% 202.47/33.96  Begin of proof
% 202.47/33.96  | 
% 202.47/33.96  | BETA: splitting (25) gives:
% 202.47/33.96  | 
% 202.47/33.96  | Case 1:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (32)  all_58_12 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | COMBINE_EQS: (16), (32) imply:
% 202.47/33.96  | |   (33)  all_52_7 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | SIMP: (33) implies:
% 202.47/33.96  | |   (34)  all_52_7 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | REDUCE: (4), (34) imply:
% 202.47/33.96  | |   (35)   ~ (all_52_15 = e3)
% 202.47/33.96  | | 
% 202.47/33.96  | | REDUCE: (5), (34) imply:
% 202.47/33.96  | |   (36)  op(e3, e3) = all_52_6
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (1), (3), (8), (9), (10), (12), (14), (15), (18), (19), (20),
% 202.47/33.96  | |            (22), (24), (27), (28), (29), (30), (36) are inconsistent by
% 202.47/33.96  | |            sub-proof #932.
% 202.47/33.96  | | 
% 202.47/33.96  | Case 2:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (37)   ~ (all_58_12 = e3)
% 202.47/33.96  | | 
% 202.47/33.96  | | REDUCE: (16), (37) imply:
% 202.47/33.96  | |   (38)   ~ (all_52_7 = e3)
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (15), (16),
% 202.47/33.96  | |            (17), (18), (19), (20), (21), (22), (23), (24), (26), (29), (30),
% 202.47/33.96  | |            (31), (38) are inconsistent by sub-proof #403.
% 202.47/33.96  | | 
% 202.47/33.96  | End of split
% 202.47/33.96  | 
% 202.47/33.96  End of proof
% 202.47/33.96  
% 202.47/33.96  Sub-proof #403 shows that the following formulas are inconsistent:
% 202.47/33.96  ----------------------------------------------------------------
% 202.47/33.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.96    (2)   ~ (all_52_5 = all_52_13)
% 202.47/33.96    (3)  all_58_1 = all_52_9
% 202.47/33.96    (4)  all_58_0 = all_6_2
% 202.47/33.96    (5)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.96    (6)  all_58_13 = all_52_15
% 202.47/33.96    (7)   ~ (all_52_15 = e3)
% 202.47/33.96    (8)  all_58_2 = all_4_0
% 202.47/33.96    (9)  op(all_4_2, e2) = e3
% 202.47/33.96    (10)   ~ (all_4_0 = e3)
% 202.47/33.96    (11)  all_58_7 = all_52_13
% 202.47/33.96    (12)  all_58_12 = all_52_7
% 202.47/33.96    (13)   ~ (all_52_7 = e3)
% 202.47/33.96    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.96    (16)   ~ (all_52_9 = all_4_2)
% 202.47/33.96    (17)   ~ (all_52_9 = all_6_2)
% 202.47/33.96    (18)  op(e3, all_6_1) = e2
% 202.47/33.96    (19)  op(e3, e3) = all_6_2
% 202.47/33.96    (20)  all_58_6 = all_52_5
% 202.47/33.96    (21)  op(e3, e2) = all_52_9
% 202.47/33.96    (22)   ~ (e3 = e2)
% 202.47/33.96    (23)  op(all_52_9, all_52_9) = e3
% 202.47/33.96    (24)  all_58_3 = all_4_2
% 202.47/33.96    (25)  op(all_6_2, e3) = all_6_1
% 202.47/33.96  
% 202.47/33.96  Begin of proof
% 202.47/33.96  | 
% 202.47/33.96  | BETA: splitting (14) gives:
% 202.47/33.96  | 
% 202.47/33.96  | Case 1:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (26)  all_58_0 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | COMBINE_EQS: (4), (26) imply:
% 202.47/33.96  | |   (27)  all_6_2 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (1), (18), (19), (22), (25), (27) are inconsistent by sub-proof
% 202.47/33.96  | |            #502.
% 202.47/33.96  | | 
% 202.47/33.96  | Case 2:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (28)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 202.47/33.96  | |            (15), (16), (17), (19), (20), (21), (23), (24), (28) are
% 202.47/33.96  | |            inconsistent by sub-proof #938.
% 202.47/33.96  | | 
% 202.47/33.96  | End of split
% 202.47/33.96  | 
% 202.47/33.96  End of proof
% 202.47/33.96  
% 202.47/33.96  Sub-proof #404 shows that the following formulas are inconsistent:
% 202.47/33.96  ----------------------------------------------------------------
% 202.47/33.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.96    (2)  op(all_52_5, all_52_5) = e1
% 202.47/33.96    (3)  all_58_0 = all_6_2
% 202.47/33.96    (4)  all_58_2 = all_4_0
% 202.47/33.96    (5)   ~ (all_4_0 = e3)
% 202.47/33.96    (6)  op(all_6_2, all_6_2) = e3
% 202.47/33.96    (7)  all_58_12 = all_52_7
% 202.47/33.96    (8)   ~ (all_52_7 = e3)
% 202.47/33.96    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96    (10)   ~ (all_52_5 = all_10_2)
% 202.47/33.96    (11)  op(e3, all_6_1) = e2
% 202.47/33.96    (12)  op(e3, e3) = all_6_2
% 202.47/33.96    (13)  all_58_6 = all_52_5
% 202.47/33.96    (14)   ~ (e3 = e2)
% 202.47/33.96    (15)  op(e1, e1) = all_10_2
% 202.47/33.96    (16)  op(all_6_2, e3) = all_6_1
% 202.47/33.96  
% 202.47/33.96  Begin of proof
% 202.47/33.96  | 
% 202.47/33.96  | BETA: splitting (9) gives:
% 202.47/33.96  | 
% 202.47/33.96  | Case 1:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (17)  all_58_0 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | COMBINE_EQS: (3), (17) imply:
% 202.47/33.96  | |   (18)  all_6_2 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | REF_CLOSE: (1), (11), (12), (14), (16), (18) are inconsistent by sub-proof
% 202.47/33.96  | |            #502.
% 202.47/33.96  | | 
% 202.47/33.96  | Case 2:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (19)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | BETA: splitting (19) gives:
% 202.47/33.96  | | 
% 202.47/33.96  | | Case 1:
% 202.47/33.96  | | | 
% 202.47/33.96  | | |   (20)  all_58_2 = e3
% 202.47/33.96  | | | 
% 202.47/33.96  | | | REF_CLOSE: (4), (5), (20) are inconsistent by sub-proof #948.
% 202.47/33.96  | | | 
% 202.47/33.96  | | Case 2:
% 202.47/33.96  | | | 
% 202.47/33.96  | | |   (21)  all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96  | | | 
% 202.47/33.96  | | | REF_CLOSE: (1), (2), (6), (7), (8), (10), (12), (13), (15), (21) are
% 202.47/33.96  | | |            inconsistent by sub-proof #1366.
% 202.47/33.96  | | | 
% 202.47/33.96  | | End of split
% 202.47/33.96  | | 
% 202.47/33.96  | End of split
% 202.47/33.96  | 
% 202.47/33.96  End of proof
% 202.47/33.96  
% 202.47/33.96  Sub-proof #405 shows that the following formulas are inconsistent:
% 202.47/33.96  ----------------------------------------------------------------
% 202.47/33.96    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.96    (2)  all_58_14 = all_52_23
% 202.47/33.96    (3)   ~ (e3 = e1)
% 202.47/33.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.96    (5)  all_58_1 = all_52_9
% 202.47/33.96    (6)   ~ (e3 = e0)
% 202.47/33.96    (7)  op(all_52_23, all_52_23) = e0
% 202.47/33.96    (8)  op(e2, e3) = all_52_3
% 202.47/33.96    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/33.96    (10)   ~ (all_52_7 = all_52_15)
% 202.47/33.96    (11)   ~ (all_52_3 = all_52_19)
% 202.47/33.96    (12)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.96    (13)   ~ (all_52_17 = all_52_25)
% 202.47/33.96    (14)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.96    (15)   ~ (all_52_3 = all_6_2)
% 202.47/33.96    (16)  all_58_0 = all_6_2
% 202.47/33.96    (17)  op(all_14_2, e0) = all_14_1
% 202.47/33.96    (18)  all_56_4 = all_52_3
% 202.47/33.96    (19)   ~ (all_10_0 = e3)
% 202.47/33.96    (20)  all_40_2 = all_10_2
% 202.47/33.96    (21)  op(e3, e0) = all_52_25
% 202.47/33.96    (22)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.96    (23)  all_58_13 = all_52_15
% 202.47/33.96    (24)  all_58_9 = all_52_25
% 202.47/33.96    (25)   ~ (all_52_29 = all_14_2)
% 202.47/33.96    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.47/33.96    (27)  op(e2, e2) = all_4_2
% 202.47/33.96    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/33.96    (29)  all_58_7 = all_10_0
% 202.47/33.96    (30)  all_58_11 = all_52_29
% 202.47/33.96    (31)   ~ (all_52_25 = all_14_2)
% 202.47/33.96    (32)   ~ (all_52_9 = all_52_15)
% 202.47/33.96    (33)  op(all_6_2, all_6_2) = all_52_0
% 202.47/33.96    (34)   ~ (all_52_7 = all_6_2)
% 202.47/33.96    (35)  op(e0, e0) = all_14_2
% 202.47/33.96    (36)  all_56_15 = all_14_2
% 202.47/33.96    (37)  all_56_11 = all_52_29
% 202.47/33.96    (38)   ~ (all_10_0 = e2)
% 202.47/33.96    (39)   ~ (all_4_1 = e1)
% 202.47/33.96    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/33.96    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/33.96    (42)   ~ (e2 = e1)
% 202.47/33.96    (43)  op(all_10_2, all_10_2) = e1
% 202.47/33.96    (44)  op(all_52_9, all_52_9) = all_52_8
% 202.47/33.96    (45)  op(all_52_15, all_52_15) = all_52_14
% 202.47/33.96    (46)   ~ (all_52_19 = all_52_23)
% 202.47/33.96    (47)  all_56_9 = all_10_0
% 202.47/33.96    (48)   ~ (all_52_29 = all_10_2)
% 202.47/33.96    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/33.96    (50)  op(all_52_19, all_52_19) = e2
% 202.47/33.96    (51)   ~ (all_52_5 = all_52_7)
% 202.47/33.96    (52)  all_58_12 = all_52_7
% 202.47/33.96    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.96    (54)   ~ (all_52_7 = all_14_2)
% 202.47/33.96    (55)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.96    (56)  all_58_2 = all_52_3
% 202.47/33.96    (57)  all_56_2 = all_52_17
% 202.47/33.96    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.96    (59)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.47/33.96    (60)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.96    (61)   ~ (e2 = e0)
% 202.47/33.96    (62)  op(all_4_2, e2) = all_4_1
% 202.47/33.96    (63)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.47/33.96    (64)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/33.96    (65)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/33.96    (66)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/33.96    (67)  op(e3, e1) = all_52_17
% 202.47/33.96    (68)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 202.47/33.96    (69)  op(e0, e3) = all_52_7
% 202.47/33.96    (70)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.96    (71)  all_58_15 = all_14_2
% 202.47/33.96    (72)   ~ (all_52_19 = all_10_2)
% 202.47/33.96    (73)  all_58_8 = all_10_2
% 202.47/33.96    (74)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/33.96    (75)   ~ (all_52_5 = all_10_2)
% 202.47/33.96    (76)   ~ (all_52_23 = all_14_2)
% 202.47/33.96    (77)  all_56_12 = all_52_7
% 202.47/33.96    (78)  all_8_2 = all_6_2
% 202.47/33.96    (79)   ~ (all_52_25 = all_6_2)
% 202.47/33.96    (80)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/33.96    (81)   ~ (all_52_9 = all_4_2)
% 202.47/33.96    (82)  all_42_2 = all_4_2
% 202.47/33.96    (83)   ~ (all_52_9 = all_6_2)
% 202.47/33.96    (84)  op(e3, all_6_1) = e2
% 202.47/33.96    (85)  all_56_0 = all_6_2
% 202.47/33.96    (86)  op(e3, e3) = all_6_2
% 202.47/33.96    (87)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.96    (88)  op(all_4_2, all_4_2) = all_52_10
% 202.47/33.96    (89)  all_40_0 = all_10_0
% 202.47/33.96    (90)  all_56_3 = all_52_25
% 202.47/33.96    (91)  op(all_14_2, all_14_2) = all_52_30
% 202.47/33.96    (92)  all_58_5 = all_52_19
% 202.47/33.96    (93)  all_56_1 = all_52_9
% 202.47/33.96    (94)  op(all_52_17, all_52_17) = e3
% 202.47/33.96    (95)  all_58_6 = all_52_5
% 202.47/33.96    (96)  op(all_10_2, e1) = e2
% 202.47/33.96    (97)  op(e3, e2) = all_52_9
% 202.47/33.96    (98)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.96    (99)   ~ (all_52_17 = all_6_2)
% 202.47/33.96    (100)   ~ (e1 = e0)
% 202.47/33.96    (101)   ~ (e3 = e2)
% 202.47/33.96    (102)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/33.96    (103)  op(e2, all_4_1) = e1
% 202.47/33.96    (104)   ~ (all_52_9 = all_52_17)
% 202.47/33.96    (105)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.96    (106)  all_42_1 = all_4_1
% 202.47/33.96    (107)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.47/33.96    (108)  op(e1, e1) = all_10_2
% 202.47/33.96    (109)   ~ (all_52_23 = all_10_2)
% 202.47/33.96    (110)   ~ (all_52_7 = all_52_23)
% 202.47/33.96    (111)  all_58_3 = all_4_2
% 202.47/33.96    (112)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.96    (113)  all_56_13 = all_52_15
% 202.47/33.96    (114)   ~ (all_52_3 = all_4_2)
% 202.47/33.96    (115)   ~ (all_52_9 = all_10_0)
% 202.47/33.96    (116)   ~ (all_52_17 = all_52_23)
% 202.47/33.96    (117)  all_8_1 = all_6_1
% 202.47/33.96    (118)  op(all_6_2, e3) = all_6_1
% 202.47/33.96    (119)  all_58_4 = all_52_17
% 202.47/33.96  
% 202.47/33.96  Begin of proof
% 202.47/33.96  | 
% 202.47/33.96  | BETA: splitting (74) gives:
% 202.47/33.96  | 
% 202.47/33.96  | Case 1:
% 202.47/33.96  | | 
% 202.47/33.96  | |   (120)  all_56_15 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | COMBINE_EQS: (36), (120) imply:
% 202.47/33.96  | |   (121)  all_14_2 = e3
% 202.47/33.96  | | 
% 202.47/33.96  | | SIMP: (121) implies:
% 202.47/33.96  | |   (122)  all_14_2 = e3
% 202.47/33.96  | | 
% 202.47/33.97  | | REF_CLOSE: (2), (3), (4), (5), (8), (11), (15), (16), (17), (18), (19),
% 202.47/33.97  | |            (21), (22), (24), (25), (27), (28), (29), (30), (31), (43), (44),
% 202.47/33.97  | |            (49), (50), (52), (53), (54), (56), (58), (60), (61), (67), (70),
% 202.47/33.97  | |            (73), (75), (76), (79), (84), (86), (87), (91), (92), (94), (95),
% 202.47/33.97  | |            (96), (99), (101), (104), (105), (114), (118), (119), (122) are
% 202.47/33.97  | |            inconsistent by sub-proof #414.
% 202.47/33.97  | | 
% 202.47/33.97  | Case 2:
% 202.47/33.97  | | 
% 202.47/33.97  | |   (123)   ~ (all_56_15 = e3)
% 202.47/33.97  | | 
% 202.47/33.97  | | REDUCE: (36), (123) imply:
% 202.47/33.97  | |   (124)   ~ (all_14_2 = e3)
% 202.47/33.97  | | 
% 202.47/33.97  | | BETA: splitting (40) gives:
% 202.47/33.97  | | 
% 202.47/33.97  | | Case 1:
% 202.47/33.97  | | | 
% 202.47/33.97  | | |   (125)  all_56_13 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | COMBINE_EQS: (113), (125) imply:
% 202.47/33.97  | | |   (126)  all_52_15 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | SIMP: (126) implies:
% 202.47/33.97  | | |   (127)  all_52_15 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | COMBINE_EQS: (23), (127) imply:
% 202.47/33.97  | | |   (128)  all_58_13 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (32), (127) imply:
% 202.47/33.97  | | |   (129)   ~ (all_52_9 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (45), (127) imply:
% 202.47/33.97  | | |   (130)  op(e3, e3) = all_52_14
% 202.47/33.97  | | | 
% 202.47/33.97  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_14, e3, e3,
% 202.47/33.97  | | |              simplifying with (86), (130) gives:
% 202.47/33.97  | | |   (131)  all_52_14 = all_6_2
% 202.47/33.97  | | | 
% 202.47/33.97  | | | BETA: splitting (112) gives:
% 202.47/33.97  | | | 
% 202.47/33.97  | | | Case 1:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | |   (132)  all_58_1 = e2
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REF_CLOSE: (2), (4), (5), (7), (13), (16), (24), (31), (33), (34), (35),
% 202.47/33.97  | | | |            (41), (52), (57), (59), (63), (66), (76), (79), (80), (83),
% 202.47/33.97  | | | |            (84), (85), (86), (87), (90), (94), (99), (104), (105),
% 202.47/33.97  | | | |            (107), (118), (119), (128), (129), (132) are inconsistent by
% 202.47/33.97  | | | |            sub-proof #413.
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | Case 2:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | |   (133)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | BETA: splitting (133) gives:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | Case 1:
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | |   (134)  all_58_3 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | COMBINE_EQS: (111), (134) imply:
% 202.47/33.97  | | | | |   (135)  all_4_2 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (88), (135) imply:
% 202.47/33.97  | | | | |   (136)  op(e2, e2) = all_52_10
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (62), (135) imply:
% 202.47/33.97  | | | | |   (137)  op(e2, e2) = all_4_1
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (27), (135) imply:
% 202.47/33.97  | | | | |   (138)  op(e2, e2) = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | GROUND_INST: instantiating (4) with all_4_1, all_52_10, e2, e2,
% 202.47/33.97  | | | | |              simplifying with (136), (137) gives:
% 202.47/33.97  | | | | |   (139)  all_52_10 = all_4_1
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | GROUND_INST: instantiating (4) with e2, all_52_10, e2, e2, simplifying
% 202.47/33.97  | | | | |              with (136), (138) gives:
% 202.47/33.97  | | | | |   (140)  all_52_10 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | COMBINE_EQS: (139), (140) imply:
% 202.47/33.97  | | | | |   (141)  all_4_1 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | SIMP: (141) implies:
% 202.47/33.97  | | | | |   (142)  all_4_1 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (103), (142) imply:
% 202.47/33.97  | | | | |   (143)  op(e2, e2) = e1
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | GROUND_INST: instantiating (4) with e2, e1, e2, e2, simplifying with
% 202.47/33.97  | | | | |              (138), (143) gives:
% 202.47/33.97  | | | | |   (144)  e2 = e1
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (42), (144) imply:
% 202.47/33.97  | | | | |   (145)  $false
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | CLOSE: (145) is inconsistent.
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | Case 2:
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | |   (146)  all_58_7 = e2 | all_58_13 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REF_CLOSE: (29), (38), (101), (128), (146) are inconsistent by
% 202.47/33.97  | | | | |            sub-proof #721.
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | End of split
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | End of split
% 202.47/33.97  | | | 
% 202.47/33.97  | | Case 2:
% 202.47/33.97  | | | 
% 202.47/33.97  | | |   (147)   ~ (all_56_13 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (113), (147) imply:
% 202.47/33.97  | | |   (148)   ~ (all_52_15 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | BETA: splitting (70) gives:
% 202.47/33.97  | | | 
% 202.47/33.97  | | | Case 1:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | |   (149)  all_58_1 = e3
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | COMBINE_EQS: (5), (149) imply:
% 202.47/33.97  | | | |   (150)  all_52_9 = e3
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REDUCE: (32), (150) imply:
% 202.47/33.97  | | | |   (151)   ~ (all_52_15 = e3)
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REDUCE: (104), (150) imply:
% 202.47/33.97  | | | |   (152)   ~ (all_52_17 = e3)
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | SIMP: (152) implies:
% 202.47/33.97  | | | |   (153)   ~ (all_52_17 = e3)
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REDUCE: (115), (150) imply:
% 202.47/33.97  | | | |   (154)   ~ (all_10_0 = e3)
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REDUCE: (81), (150) imply:
% 202.47/33.97  | | | |   (155)   ~ (all_4_2 = e3)
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | SIMP: (155) implies:
% 202.47/33.97  | | | |   (156)   ~ (all_4_2 = e3)
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REDUCE: (44), (150) imply:
% 202.47/33.97  | | | |   (157)  op(e3, e3) = all_52_8
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (14), (16),
% 202.47/33.97  | | | |            (19), (20), (23), (24), (25), (26), (27), (29), (30), (34),
% 202.47/33.97  | | | |            (35), (37), (38), (41), (42), (46), (47), (48), (50), (51),
% 202.47/33.97  | | | |            (52), (53), (55), (57), (59), (61), (63), (64), (65), (66),
% 202.47/33.97  | | | |            (67), (69), (71), (72), (73), (77), (78), (84), (86), (89),
% 202.47/33.97  | | | |            (91), (92), (94), (95), (96), (97), (98), (99), (100), (104),
% 202.47/33.97  | | | |            (105), (108), (109), (110), (116), (117), (118), (119),
% 202.47/33.97  | | | |            (124), (148), (149), (153), (156), (157) are inconsistent by
% 202.47/33.97  | | | |            sub-proof #410.
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | Case 2:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | |   (158)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REF_CLOSE: (3), (4), (19), (23), (27), (29), (39), (44), (62), (68),
% 202.47/33.97  | | | |            (81), (82), (93), (97), (102), (103), (106), (111), (148),
% 202.47/33.97  | | | |            (158) are inconsistent by sub-proof #607.
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | End of split
% 202.47/33.97  | | | 
% 202.47/33.97  | | End of split
% 202.47/33.97  | | 
% 202.47/33.97  | End of split
% 202.47/33.97  | 
% 202.47/33.97  End of proof
% 202.47/33.97  
% 202.47/33.97  Sub-proof #406 shows that the following formulas are inconsistent:
% 202.47/33.97  ----------------------------------------------------------------
% 202.47/33.97    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.97    (2)   ~ (all_52_15 = all_52_23)
% 202.47/33.97    (3)  all_58_14 = all_52_23
% 202.47/33.97    (4)   ~ (e3 = e1)
% 202.47/33.97    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.47/33.97    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.97    (7)  all_58_1 = all_52_9
% 202.47/33.97    (8)   ~ (e3 = e0)
% 202.47/33.97    (9)  op(all_52_23, all_52_23) = e0
% 202.47/33.97    (10)  op(e2, e3) = all_52_3
% 202.47/33.97    (11)   ~ (all_4_0 = e1)
% 202.47/33.97    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/33.97    (13)   ~ (all_52_7 = all_52_15)
% 202.47/33.97    (14)   ~ (all_52_3 = all_52_19)
% 202.47/33.97    (15)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.97    (16)   ~ (all_52_17 = all_52_25)
% 202.47/33.97    (17)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.97    (18)   ~ (all_52_3 = all_6_2)
% 202.47/33.97    (19)  all_58_0 = all_6_2
% 202.47/33.97    (20)  op(all_14_2, e0) = all_14_1
% 202.47/33.97    (21)  all_56_4 = all_52_3
% 202.47/33.97    (22)   ~ (all_52_17 = all_10_2)
% 202.47/33.97    (23)   ~ (all_10_0 = e3)
% 202.47/33.97    (24)  all_40_2 = all_10_2
% 202.47/33.97    (25)  op(e3, e0) = all_52_25
% 202.47/33.97    (26)  op(all_52_5, all_52_5) = all_52_4
% 202.47/33.97    (27)  all_58_13 = all_52_15
% 202.47/33.97    (28)  all_58_9 = all_52_25
% 202.47/33.97    (29)   ~ (all_52_29 = all_14_2)
% 202.47/33.97    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.47/33.97    (31)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 202.47/33.97    (32)  op(e2, e2) = all_4_2
% 202.47/33.97    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/33.97    (34)  all_58_7 = all_10_0
% 202.47/33.97    (35)   ~ (all_52_3 = all_52_5)
% 202.47/33.97    (36)  all_58_11 = all_52_29
% 202.47/33.97    (37)   ~ (all_52_25 = all_14_2)
% 202.47/33.97    (38)   ~ (all_52_9 = all_52_15)
% 202.47/33.97    (39)   ~ (all_52_3 = all_52_27)
% 202.47/33.97    (40)  op(all_6_2, all_6_2) = all_52_0
% 202.47/33.97    (41)   ~ (all_52_7 = all_6_2)
% 202.47/33.97    (42)  op(e0, e0) = all_14_2
% 202.47/33.97    (43)  all_56_15 = all_14_2
% 202.47/33.97    (44)  op(e2, all_4_1) = all_4_0
% 202.47/33.97    (45)  all_56_11 = all_52_29
% 202.47/33.97    (46)   ~ (all_10_0 = e2)
% 202.47/33.97    (47)   ~ (all_4_0 = e3)
% 202.47/33.97    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/33.97    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/33.97    (50)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.47/33.97    (51)   ~ (e2 = e1)
% 202.47/33.97    (52)  op(all_10_2, all_10_2) = e1
% 202.47/33.97    (53)  all_58_10 = all_52_27
% 202.47/33.97    (54)  op(all_52_9, all_52_9) = all_52_8
% 202.47/33.97    (55)  op(all_52_15, all_52_15) = all_52_14
% 202.47/33.97    (56)   ~ (all_52_19 = all_52_23)
% 202.47/33.97    (57)  all_56_9 = all_10_0
% 202.47/33.97    (58)   ~ (all_52_25 = all_52_29)
% 202.47/33.97    (59)   ~ (all_52_29 = all_10_2)
% 202.47/33.97    (60)   ~ (all_10_0 = all_4_2)
% 202.47/33.97    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/33.97    (62)  op(all_52_19, all_52_19) = e2
% 202.47/33.97    (63)   ~ (all_52_5 = all_52_7)
% 202.47/33.97    (64)  all_58_12 = all_52_7
% 202.47/33.97    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.97    (66)   ~ (all_52_7 = all_14_2)
% 202.47/33.97    (67)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.97    (68)  all_58_2 = all_52_3
% 202.47/33.97    (69)  all_56_2 = all_52_17
% 202.47/33.97    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.97    (71)   ~ (all_52_15 = all_10_0)
% 202.47/33.97    (72)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.47/33.97    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.97    (74)   ~ (e2 = e0)
% 202.47/33.97    (75)  op(all_4_2, e2) = all_4_1
% 202.47/33.97    (76)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.47/33.97    (77)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/33.97    (78)   ~ (all_52_15 = all_14_2)
% 202.47/33.97    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/33.97    (80)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/33.97    (81)  op(e3, e1) = all_52_17
% 202.47/33.97    (82)  op(e0, e3) = all_52_7
% 202.47/33.97    (83)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.97    (84)   ~ (all_52_9 = all_52_25)
% 202.47/33.97    (85)  all_58_15 = all_14_2
% 202.47/33.97    (86)   ~ (all_52_19 = all_10_2)
% 202.47/33.97    (87)  all_58_8 = all_10_2
% 202.47/33.97    (88)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/33.97    (89)   ~ (all_52_5 = all_10_2)
% 202.47/33.97    (90)  op(all_52_29, all_52_29) = all_52_28
% 202.47/33.97    (91)   ~ (all_52_23 = all_14_2)
% 202.47/33.97    (92)  all_56_12 = all_52_7
% 202.47/33.97    (93)  all_8_2 = all_6_2
% 202.47/33.97    (94)   ~ (all_52_25 = all_6_2)
% 202.47/33.97    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/33.97    (96)   ~ (all_52_9 = all_4_2)
% 202.47/33.97    (97)   ~ (all_52_5 = all_6_2)
% 202.47/33.97    (98)   ~ (all_52_9 = all_6_2)
% 202.47/33.97    (99)  op(e3, all_6_1) = e2
% 202.47/33.97    (100)  all_56_0 = all_6_2
% 202.47/33.97    (101)  op(e3, e3) = all_6_2
% 202.47/33.97    (102)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/33.97    (103)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.97    (104)  op(all_4_2, all_4_2) = all_52_10
% 202.47/33.97    (105)  all_40_0 = all_10_0
% 202.47/33.97    (106)  all_56_3 = all_52_25
% 202.47/33.97    (107)  op(all_14_2, all_14_2) = all_52_30
% 202.47/33.97    (108)  all_58_5 = all_52_19
% 202.47/33.97    (109)  all_56_1 = all_52_9
% 202.47/33.97    (110)   ~ (all_52_15 = all_4_2)
% 202.47/33.97    (111)  op(all_52_17, all_52_17) = e3
% 202.47/33.97    (112)  all_58_6 = all_52_5
% 202.47/33.97    (113)  op(all_10_2, e1) = e2
% 202.47/33.97    (114)  op(e3, e2) = all_52_9
% 202.47/33.97    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.97    (116)   ~ (all_52_17 = all_6_2)
% 202.47/33.97    (117)   ~ (e1 = e0)
% 202.47/33.97    (118)   ~ (e3 = e2)
% 202.47/33.97    (119)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/33.97    (120)   ~ (all_52_9 = all_52_17)
% 202.47/33.97    (121)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.97    (122)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.47/33.97    (123)  op(all_10_0, all_10_0) = all_52_12
% 202.47/33.97    (124)  op(e1, e1) = all_10_2
% 202.47/33.97    (125)   ~ (all_52_23 = all_10_2)
% 202.47/33.97    (126)   ~ (all_52_7 = all_52_23)
% 202.47/33.97    (127)   ~ (all_52_17 = all_52_19)
% 202.47/33.97    (128)  all_58_3 = all_4_2
% 202.47/33.97    (129)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.97    (130)  all_56_13 = all_52_15
% 202.47/33.97    (131)   ~ (all_52_3 = all_4_2)
% 202.47/33.97    (132)   ~ (all_52_9 = all_10_0)
% 202.47/33.97    (133)   ~ (all_52_19 = all_4_2)
% 202.47/33.97    (134)   ~ (all_52_17 = all_52_23)
% 202.47/33.97    (135)  all_8_1 = all_6_1
% 202.47/33.97    (136)  op(all_6_2, e3) = all_6_1
% 202.47/33.97    (137)  all_58_4 = all_52_17
% 202.47/33.97    (138)  op(all_52_25, all_52_25) = all_52_24
% 202.47/33.97  
% 202.47/33.97  Begin of proof
% 202.47/33.97  | 
% 202.47/33.97  | BETA: splitting (88) gives:
% 202.47/33.97  | 
% 202.47/33.97  | Case 1:
% 202.47/33.97  | | 
% 202.47/33.97  | |   (139)  all_56_15 = e3
% 202.47/33.97  | | 
% 202.47/33.97  | | COMBINE_EQS: (43), (139) imply:
% 202.47/33.97  | |   (140)  all_14_2 = e3
% 202.47/33.97  | | 
% 202.47/33.97  | | SIMP: (140) implies:
% 202.47/33.97  | |   (141)  all_14_2 = e3
% 202.47/33.97  | | 
% 202.47/33.97  | | REF_CLOSE: (3), (4), (6), (7), (10), (14), (18), (19), (20), (21), (23),
% 202.47/33.97  | |            (25), (26), (28), (29), (32), (33), (34), (36), (37), (52), (54),
% 202.47/33.97  | |            (61), (62), (64), (65), (66), (68), (70), (73), (74), (81), (83),
% 202.47/33.97  | |            (87), (89), (91), (94), (99), (101), (103), (107), (108), (111),
% 202.47/33.97  | |            (112), (113), (116), (118), (120), (121), (131), (136), (137),
% 202.47/33.97  | |            (141) are inconsistent by sub-proof #414.
% 202.47/33.97  | | 
% 202.47/33.97  | Case 2:
% 202.47/33.97  | | 
% 202.47/33.97  | |   (142)   ~ (all_56_15 = e3)
% 202.47/33.97  | |   (143)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/33.97  | | 
% 202.47/33.97  | | REDUCE: (43), (142) imply:
% 202.47/33.97  | |   (144)   ~ (all_14_2 = e3)
% 202.47/33.97  | | 
% 202.47/33.97  | | BETA: splitting (48) gives:
% 202.47/33.97  | | 
% 202.47/33.97  | | Case 1:
% 202.47/33.97  | | | 
% 202.47/33.97  | | |   (145)  all_56_13 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | COMBINE_EQS: (130), (145) imply:
% 202.47/33.97  | | |   (146)  all_52_15 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | SIMP: (146) implies:
% 202.47/33.97  | | |   (147)  all_52_15 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | COMBINE_EQS: (27), (147) imply:
% 202.47/33.97  | | |   (148)  all_58_13 = e3
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (13), (147) imply:
% 202.47/33.97  | | |   (149)   ~ (all_52_7 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (38), (147) imply:
% 202.47/33.97  | | |   (150)   ~ (all_52_9 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (2), (147) imply:
% 202.47/33.97  | | |   (151)   ~ (all_52_23 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | SIMP: (151) implies:
% 202.47/33.97  | | |   (152)   ~ (all_52_23 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (78), (147) imply:
% 202.47/33.97  | | |   (153)   ~ (all_14_2 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (71), (147) imply:
% 202.47/33.97  | | |   (154)   ~ (all_10_0 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (110), (147) imply:
% 202.47/33.97  | | |   (155)   ~ (all_4_2 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | SIMP: (155) implies:
% 202.47/33.97  | | |   (156)   ~ (all_4_2 = e3)
% 202.47/33.97  | | | 
% 202.47/33.97  | | | REDUCE: (55), (147) imply:
% 202.47/33.97  | | |   (157)  op(e3, e3) = all_52_14
% 202.47/33.97  | | | 
% 202.47/33.97  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3,
% 202.47/33.97  | | |              simplifying with (101), (157) gives:
% 202.47/33.97  | | |   (158)  all_52_14 = all_6_2
% 202.47/33.97  | | | 
% 202.47/33.97  | | | BETA: splitting (129) gives:
% 202.47/33.97  | | | 
% 202.47/33.97  | | | Case 1:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | |   (159)  all_58_1 = e2
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | REF_CLOSE: (3), (6), (7), (9), (16), (19), (28), (37), (40), (41), (42),
% 202.47/33.97  | | | |            (49), (64), (69), (72), (76), (80), (91), (94), (95), (98),
% 202.47/33.97  | | | |            (99), (100), (101), (103), (106), (111), (116), (120), (121),
% 202.47/33.97  | | | |            (122), (136), (137), (148), (150), (159) are inconsistent by
% 202.47/33.97  | | | |            sub-proof #413.
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | Case 2:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | |   (160)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | BETA: splitting (160) gives:
% 202.47/33.97  | | | | 
% 202.47/33.97  | | | | Case 1:
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | |   (161)  all_58_3 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | COMBINE_EQS: (128), (161) imply:
% 202.47/33.97  | | | | |   (162)  all_4_2 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (96), (162) imply:
% 202.47/33.97  | | | | |   (163)   ~ (all_52_9 = e2)
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (133), (162) imply:
% 202.47/33.97  | | | | |   (164)   ~ (all_52_19 = e2)
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (104), (162) imply:
% 202.47/33.97  | | | | |   (165)  op(e2, e2) = all_52_10
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (75), (162) imply:
% 202.47/33.97  | | | | |   (166)  op(e2, e2) = all_4_1
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (32), (162) imply:
% 202.47/33.97  | | | | |   (167)  op(e2, e2) = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | GROUND_INST: instantiating (6) with all_4_1, all_52_10, e2, e2,
% 202.47/33.97  | | | | |              simplifying with (165), (166) gives:
% 202.47/33.97  | | | | |   (168)  all_52_10 = all_4_1
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | GROUND_INST: instantiating (6) with e2, all_52_10, e2, e2, simplifying
% 202.47/33.97  | | | | |              with (165), (167) gives:
% 202.47/33.97  | | | | |   (169)  all_52_10 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | COMBINE_EQS: (168), (169) imply:
% 202.47/33.97  | | | | |   (170)  all_4_1 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | SIMP: (170) implies:
% 202.47/33.97  | | | | |   (171)  all_4_1 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (44), (171) imply:
% 202.47/33.97  | | | | |   (172)  op(e2, e2) = all_4_0
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | GROUND_INST: instantiating (6) with e2, all_4_0, e2, e2, simplifying
% 202.47/33.97  | | | | |              with (167), (172) gives:
% 202.47/33.97  | | | | |   (173)  all_4_0 = e2
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | REDUCE: (47), (173) imply:
% 202.47/33.97  | | | | |   (174)   ~ (e3 = e2)
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | BETA: splitting (119) gives:
% 202.47/33.97  | | | | | 
% 202.47/33.97  | | | | | Case 1:
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | |   (175)  all_56_1 = e3
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | | COMBINE_EQS: (109), (175) imply:
% 202.47/33.97  | | | | | |   (176)  all_52_9 = e3
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | | REDUCE: (150), (176) imply:
% 202.47/33.97  | | | | | |   (177)  $false
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | | CLOSE: (177) is inconsistent.
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | Case 2:
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | |   (178)   ~ (all_56_1 = e3)
% 202.47/33.97  | | | | | |   (179)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | | BETA: splitting (50) gives:
% 202.47/33.97  | | | | | | 
% 202.47/33.97  | | | | | | Case 1:
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | |   (180)  all_58_1 = e1
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | | COMBINE_EQS: (7), (180) imply:
% 202.47/33.97  | | | | | | |   (181)  all_52_9 = e1
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | | BETA: splitting (31) gives:
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | |   (182)  all_58_1 = e0
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | COMBINE_EQS: (180), (182) imply:
% 202.47/33.97  | | | | | | | |   (183)  e1 = e0
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | REDUCE: (117), (183) imply:
% 202.47/33.97  | | | | | | | |   (184)  $false
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | CLOSE: (184) is inconsistent.
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | |   (185)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | BETA: splitting (185) gives:
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | |   (186)  all_58_3 = e0
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | COMBINE_EQS: (161), (186) imply:
% 202.47/33.97  | | | | | | | | |   (187)  e2 = e0
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | REDUCE: (74), (187) imply:
% 202.47/33.97  | | | | | | | | |   (188)  $false
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | CLOSE: (188) is inconsistent.
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | |   (189)  all_58_7 = e0 | all_58_13 = e0
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | BETA: splitting (189) gives:
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | |   (190)  all_58_7 = e0
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | COMBINE_EQS: (34), (190) imply:
% 202.47/33.97  | | | | | | | | | |   (191)  all_10_0 = e0
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | COMBINE_EQS: (105), (191) imply:
% 202.47/33.97  | | | | | | | | | |   (192)  all_40_0 = e0
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REDUCE: (23), (191) imply:
% 202.47/33.97  | | | | | | | | | |   (193)   ~ (e3 = e0)
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REDUCE: (46), (191) imply:
% 202.47/33.97  | | | | | | | | | |   (194)   ~ (e2 = e0)
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (14), (16), (18), (19),
% 202.47/33.97  | | | | | | | | | |            (21), (24), (25), (28), (33), (35), (36), (58),
% 202.47/33.97  | | | | | | | | | |            (61), (62), (63), (64), (65), (67), (68), (70),
% 202.47/33.97  | | | | | | | | | |            (73), (74), (81), (87), (89), (97), (99), (101),
% 202.47/33.97  | | | | | | | | | |            (102), (103), (108), (111), (112), (116), (118),
% 202.47/33.97  | | | | | | | | | |            (121), (127), (136), (137), (150), (152), (164),
% 202.47/33.97  | | | | | | | | | |            (190), (192) are inconsistent by sub-proof #411.
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | |   (195)  all_58_13 = e0
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REF_CLOSE: (8), (148), (195) are inconsistent by sub-proof
% 202.47/33.97  | | | | | | | | | |            #1172.
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | End of split
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | End of split
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | End of split
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | Case 2:
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | |   (196)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | | BETA: splitting (196) gives:
% 202.47/33.97  | | | | | | | 
% 202.47/33.97  | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | |   (197)  all_58_3 = e1
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | COMBINE_EQS: (161), (197) imply:
% 202.47/33.97  | | | | | | | |   (198)  e2 = e1
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | REDUCE: (51), (198) imply:
% 202.47/33.97  | | | | | | | |   (199)  $false
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | CLOSE: (199) is inconsistent.
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | |   (200)  all_58_7 = e1 | all_58_13 = e1
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | BETA: splitting (200) gives:
% 202.47/33.97  | | | | | | | | 
% 202.47/33.97  | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | |   (201)  all_58_7 = e1
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | COMBINE_EQS: (34), (201) imply:
% 202.47/33.97  | | | | | | | | |   (202)  all_10_0 = e1
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | REDUCE: (132), (202) imply:
% 202.47/33.97  | | | | | | | | |   (203)   ~ (all_52_9 = e1)
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | REDUCE: (23), (202) imply:
% 202.47/33.97  | | | | | | | | |   (204)   ~ (e3 = e1)
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | REDUCE: (46), (202) imply:
% 202.47/33.97  | | | | | | | | |   (205)   ~ (e2 = e1)
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | REDUCE: (123), (202) imply:
% 202.47/33.97  | | | | | | | | |   (206)  op(e1, e1) = all_52_12
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | BETA: splitting (31) gives:
% 202.47/33.97  | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | |   (207)  all_58_1 = e0
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | COMBINE_EQS: (7), (207) imply:
% 202.47/33.97  | | | | | | | | | |   (208)  all_52_9 = e0
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REDUCE: (150), (208) imply:
% 202.47/33.97  | | | | | | | | | |   (209)   ~ (e3 = e0)
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REDUCE: (163), (208) imply:
% 202.47/33.97  | | | | | | | | | |   (210)   ~ (e2 = e0)
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REDUCE: (203), (208) imply:
% 202.47/33.97  | | | | | | | | | |   (211)   ~ (e1 = e0)
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | REDUCE: (54), (208) imply:
% 202.47/33.97  | | | | | | | | | |   (212)  op(e0, e0) = all_52_8
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | GROUND_INST: instantiating (6) with all_14_2, all_52_8, e0, e0,
% 202.47/33.97  | | | | | | | | | |              simplifying with (42), (212) gives:
% 202.47/33.97  | | | | | | | | | |   (213)  all_52_8 = all_14_2
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_12, e1,
% 202.47/33.97  | | | | | | | | | |              e1, simplifying with (124), (206) gives:
% 202.47/33.97  | | | | | | | | | |   (214)  all_52_12 = all_10_2
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | BETA: splitting (73) gives:
% 202.47/33.97  | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | |   (215)  all_56_4 = e3
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | COMBINE_EQS: (21), (215) imply:
% 202.47/33.97  | | | | | | | | | | |   (216)  all_52_3 = e3
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | SIMP: (216) implies:
% 202.47/33.97  | | | | | | | | | | |   (217)  all_52_3 = e3
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | REDUCE: (35), (217) imply:
% 202.47/33.97  | | | | | | | | | | |   (218)   ~ (all_52_5 = e3)
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | SIMP: (218) implies:
% 202.47/33.97  | | | | | | | | | | |   (219)   ~ (all_52_5 = e3)
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | REDUCE: (39), (217) imply:
% 202.47/33.97  | | | | | | | | | | |   (220)   ~ (all_52_27 = e3)
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | SIMP: (220) implies:
% 202.47/33.97  | | | | | | | | | | |   (221)   ~ (all_52_27 = e3)
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | REDUCE: (18), (217) imply:
% 202.47/33.97  | | | | | | | | | | |   (222)   ~ (all_6_2 = e3)
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | SIMP: (222) implies:
% 202.47/33.97  | | | | | | | | | | |   (223)   ~ (all_6_2 = e3)
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | REDUCE: (5), (217) imply:
% 202.47/33.97  | | | | | | | | | | |   (224)  op(e3, e3) = all_52_2
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3,
% 202.47/33.97  | | | | | | | | | | |              simplifying with (101), (224) gives:
% 202.47/33.97  | | | | | | | | | | |   (225)  all_52_2 = all_6_2
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | BETA: splitting (65) gives:
% 202.47/33.97  | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | |   (226)  all_58_6 = e3
% 202.47/33.97  | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | REF_CLOSE: (112), (219), (226) are inconsistent by sub-proof
% 202.47/33.97  | | | | | | | | | | | |            #1328.
% 202.47/33.97  | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | |   (227)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.97  | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | BETA: splitting (103) gives:
% 202.47/33.97  | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | |   (228)  all_58_0 = e3
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | COMBINE_EQS: (19), (228) imply:
% 202.47/33.97  | | | | | | | | | | | | |   (229)  all_6_2 = e3
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | REDUCE: (223), (229) imply:
% 202.47/33.97  | | | | | | | | | | | | |   (230)  $false
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | |   (231)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | BETA: splitting (102) gives:
% 202.47/33.97  | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | Case 1:
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | |   (232)  all_58_9 = e3
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | | COMBINE_EQS: (28), (232) imply:
% 202.47/33.97  | | | | | | | | | | | | | |   (233)  all_52_25 = e3
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | | SIMP: (233) implies:
% 202.47/33.97  | | | | | | | | | | | | | |   (234)  all_52_25 = e3
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | | REDUCE: (58), (234) imply:
% 202.47/33.97  | | | | | | | | | | | | | |   (235)   ~ (all_52_29 = e3)
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | | SIMP: (235) implies:
% 202.47/33.97  | | | | | | | | | | | | | |   (236)   ~ (all_52_29 = e3)
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (23), (24), (32), (34), (36), (46),
% 202.47/33.97  | | | | | | | | | | | | | |            (57), (67), (81), (87), (105), (111), (113),
% 202.47/33.97  | | | | | | | | | | | | | |            (156), (227), (236) are inconsistent by sub-proof
% 202.47/33.97  | | | | | | | | | | | | | |            #789.
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | Case 2:
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.97  | | | | | | | | | | | | | |   (237)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/33.97  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (19), (28), (29), (30),
% 202.47/33.98  | | | | | | | | | | | | | |            (36), (42), (51), (53), (54), (56), (58), (59),
% 202.47/33.98  | | | | | | | | | | | | | |            (62), (72), (74), (76), (83), (85), (86), (87),
% 202.47/33.98  | | | | | | | | | | | | | |            (90), (101), (108), (111), (116), (117), (120),
% 202.47/33.98  | | | | | | | | | | | | | |            (121), (124), (137), (144), (152), (221), (231),
% 202.47/33.98  | | | | | | | | | | | | | |            (237) are inconsistent by sub-proof #443.
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | |   (238)   ~ (all_56_4 = e3)
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | REDUCE: (21), (238) imply:
% 202.47/33.98  | | | | | | | | | | |   (239)   ~ (all_52_3 = e3)
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | BETA: splitting (70) gives:
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | |   (240)  all_58_0 = e3
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | COMBINE_EQS: (19), (240) imply:
% 202.47/33.98  | | | | | | | | | | | |   (241)  all_6_2 = e3
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | REF_CLOSE: (6), (99), (101), (118), (136), (241) are
% 202.47/33.98  | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | |   (242)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | BETA: splitting (242) gives:
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | |   (243)  all_58_2 = e3
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | REF_CLOSE: (68), (239), (243) are inconsistent by sub-proof
% 202.47/33.98  | | | | | | | | | | | | |            #1369.
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | |   (244)  all_58_6 = e3 | all_58_12 = e3
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | BETA: splitting (244) gives:
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | |   (245)  all_58_6 = e3
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | COMBINE_EQS: (112), (245) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (246)  all_52_5 = e3
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | SIMP: (246) implies:
% 202.47/33.98  | | | | | | | | | | | | | |   (247)  all_52_5 = e3
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (63), (247) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (248)   ~ (all_52_7 = e3)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (89), (247) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (249)   ~ (all_10_2 = e3)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | SIMP: (249) implies:
% 202.47/33.98  | | | | | | | | | | | | | |   (250)   ~ (all_10_2 = e3)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (97), (247) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (251)   ~ (all_6_2 = e3)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | SIMP: (251) implies:
% 202.47/33.98  | | | | | | | | | | | | | |   (252)   ~ (all_6_2 = e3)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (26), (247) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (253)  op(e3, e3) = all_52_4
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_4, e3, e3,
% 202.47/33.98  | | | | | | | | | | | | | |              simplifying with (101), (253) gives:
% 202.47/33.98  | | | | | | | | | | | | | |   (254)  all_52_4 = all_6_2
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (10), (14), (16), (18), (19), (21),
% 202.47/33.98  | | | | | | | | | | | | | |            (25), (28), (33), (35), (61), (62), (64), (68),
% 202.47/33.98  | | | | | | | | | | | | | |            (70), (73), (74), (81), (87), (97), (99), (101),
% 202.47/33.98  | | | | | | | | | | | | | |            (102), (103), (108), (111), (112), (116), (121),
% 202.47/33.98  | | | | | | | | | | | | | |            (127), (136), (137), (149), (150), (152), (164),
% 202.47/33.98  | | | | | | | | | | | | | |            (250), (252) are inconsistent by sub-proof #412.
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | |   (255)  all_58_12 = e3
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REF_CLOSE: (64), (149), (255) are inconsistent by sub-proof
% 202.47/33.98  | | | | | | | | | | | | | |            #1367.
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | |   (256)   ~ (all_58_1 = e0)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | REDUCE: (7), (256) imply:
% 202.47/33.98  | | | | | | | | | |   (257)   ~ (all_52_9 = e0)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | REF_CLOSE: (109), (163), (179), (203), (257) are inconsistent
% 202.47/33.98  | | | | | | | | | |            by sub-proof #1314.
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | |   (258)  all_58_13 = e1
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | REF_CLOSE: (4), (148), (258) are inconsistent by sub-proof
% 202.47/33.98  | | | | | | | | |            #770.
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | End of split
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | End of split
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | End of split
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | End of split
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | Case 2:
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | |   (259)  all_58_7 = e2 | all_58_13 = e2
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | | REF_CLOSE: (34), (46), (118), (148), (259) are inconsistent by
% 202.47/33.98  | | | | |            sub-proof #721.
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | End of split
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | End of split
% 202.47/33.98  | | | 
% 202.47/33.98  | | Case 2:
% 202.47/33.98  | | | 
% 202.47/33.98  | | |   (260)   ~ (all_56_13 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | REDUCE: (130), (260) imply:
% 202.47/33.98  | | |   (261)   ~ (all_52_15 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | BETA: splitting (83) gives:
% 202.47/33.98  | | | 
% 202.47/33.98  | | | Case 1:
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | |   (262)  all_58_1 = e3
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (12), (13), (15), (17),
% 202.47/33.98  | | | |            (19), (24), (27), (28), (29), (30), (32), (34), (36), (38),
% 202.47/33.98  | | | |            (41), (42), (45), (46), (49), (51), (54), (56), (57), (59),
% 202.47/33.98  | | | |            (62), (63), (64), (65), (67), (69), (72), (74), (76), (77),
% 202.47/33.98  | | | |            (79), (80), (81), (82), (85), (86), (87), (92), (93), (96),
% 202.47/33.98  | | | |            (99), (101), (105), (107), (108), (111), (112), (113), (114),
% 202.47/33.98  | | | |            (115), (116), (117), (120), (121), (124), (125), (126),
% 202.47/33.98  | | | |            (132), (134), (135), (136), (137), (144), (262) are
% 202.47/33.98  | | | |            inconsistent by sub-proof #409.
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | Case 2:
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | |   (263)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (12), (13), (15), (17),
% 202.47/33.98  | | | |            (19), (22), (23), (24), (27), (28), (34), (36), (37), (38),
% 202.47/33.98  | | | |            (41), (42), (43), (46), (49), (52), (54), (57), (58), (60),
% 202.47/33.98  | | | |            (63), (64), (65), (67), (69), (75), (77), (78), (80), (81),
% 202.47/33.98  | | | |            (82), (84), (85), (87), (91), (92), (93), (96), (98), (99),
% 202.47/33.98  | | | |            (101), (102), (103), (104), (105), (107), (109), (110),
% 202.47/33.98  | | | |            (111), (112), (113), (114), (115), (116), (117), (118),
% 202.47/33.98  | | | |            (119), (120), (121), (124), (125), (126), (128), (129),
% 202.47/33.98  | | | |            (134), (135), (136), (137), (138), (143), (261), (263) are
% 202.47/33.98  | | | |            inconsistent by sub-proof #407.
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | End of split
% 202.47/33.98  | | | 
% 202.47/33.98  | | End of split
% 202.47/33.98  | | 
% 202.47/33.98  | End of split
% 202.47/33.98  | 
% 202.47/33.98  End of proof
% 202.47/33.98  
% 202.47/33.98  Sub-proof #407 shows that the following formulas are inconsistent:
% 202.47/33.98  ----------------------------------------------------------------
% 202.47/33.98    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.98    (2)  all_58_14 = all_52_23
% 202.47/33.98    (3)   ~ (e3 = e1)
% 202.47/33.98    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.98    (5)  all_58_1 = all_52_9
% 202.47/33.98    (6)   ~ (e3 = e0)
% 202.47/33.98    (7)  op(all_52_23, all_52_23) = e0
% 202.47/33.98    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/33.98    (9)   ~ (all_52_7 = all_52_15)
% 202.47/33.98    (10)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.98    (11)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.98    (12)  all_58_0 = all_6_2
% 202.47/33.98    (13)   ~ (all_52_17 = all_10_2)
% 202.47/33.98    (14)   ~ (all_10_0 = e3)
% 202.47/33.98    (15)  all_40_2 = all_10_2
% 202.47/33.98    (16)  all_58_13 = all_52_15
% 202.47/33.98    (17)  all_58_9 = all_52_25
% 202.47/33.98    (18)   ~ (all_52_15 = e3)
% 202.47/33.98    (19)  all_58_7 = all_10_0
% 202.47/33.98    (20)  all_58_11 = all_52_29
% 202.47/33.98    (21)   ~ (all_52_25 = all_14_2)
% 202.47/33.98    (22)   ~ (all_52_9 = all_52_15)
% 202.47/33.98    (23)   ~ (all_52_7 = all_6_2)
% 202.47/33.98    (24)  op(e0, e0) = all_14_2
% 202.47/33.98    (25)  all_56_15 = all_14_2
% 202.47/33.98    (26)   ~ (all_10_0 = e2)
% 202.47/33.98    (27)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/33.98    (28)  op(all_10_2, all_10_2) = e1
% 202.47/33.98    (29)  op(all_52_9, all_52_9) = all_52_8
% 202.47/33.98    (30)  all_56_9 = all_10_0
% 202.47/33.98    (31)   ~ (all_52_25 = all_52_29)
% 202.47/33.98    (32)   ~ (all_10_0 = all_4_2)
% 202.47/33.98    (33)   ~ (all_52_5 = all_52_7)
% 202.47/33.98    (34)  all_58_12 = all_52_7
% 202.47/33.98    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.98    (36)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.98    (37)  all_56_2 = all_52_17
% 202.47/33.98    (38)  op(all_4_2, e2) = all_4_1
% 202.47/33.98    (39)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/33.98    (40)   ~ (all_52_15 = all_14_2)
% 202.47/33.98    (41)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/33.98    (42)  op(e3, e1) = all_52_17
% 202.47/33.98    (43)  op(e0, e3) = all_52_7
% 202.47/33.98    (44)   ~ (all_52_9 = all_52_25)
% 202.47/33.98    (45)  all_58_15 = all_14_2
% 202.47/33.98    (46)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/33.98    (47)  all_58_8 = all_10_2
% 202.47/33.98    (48)   ~ (all_52_23 = all_14_2)
% 202.47/33.98    (49)  all_56_12 = all_52_7
% 202.47/33.98    (50)  all_8_2 = all_6_2
% 202.47/33.98    (51)   ~ (all_52_9 = all_4_2)
% 202.47/33.98    (52)   ~ (all_52_9 = all_6_2)
% 202.47/33.98    (53)  op(e3, all_6_1) = e2
% 202.47/33.98    (54)  op(e3, e3) = all_6_2
% 202.47/33.98    (55)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/33.98    (56)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.98    (57)  op(all_4_2, all_4_2) = all_52_10
% 202.47/33.98    (58)  all_40_0 = all_10_0
% 202.47/33.98    (59)  op(all_14_2, all_14_2) = all_52_30
% 202.47/33.98    (60)  all_56_1 = all_52_9
% 202.47/33.98    (61)   ~ (all_52_15 = all_4_2)
% 202.47/33.98    (62)  op(all_52_17, all_52_17) = e3
% 202.47/33.98    (63)  all_58_6 = all_52_5
% 202.47/33.98    (64)  op(all_10_2, e1) = e2
% 202.47/33.98    (65)  op(e3, e2) = all_52_9
% 202.47/33.98    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.98    (67)   ~ (all_52_17 = all_6_2)
% 202.47/33.98    (68)   ~ (e1 = e0)
% 202.47/33.98    (69)   ~ (e3 = e2)
% 202.47/33.98    (70)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/33.98    (71)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/33.98    (72)   ~ (all_52_9 = all_52_17)
% 202.47/33.98    (73)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.98    (74)  op(e1, e1) = all_10_2
% 202.47/33.98    (75)   ~ (all_52_23 = all_10_2)
% 202.47/33.98    (76)   ~ (all_52_7 = all_52_23)
% 202.47/33.98    (77)  all_58_3 = all_4_2
% 202.47/33.98    (78)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.98    (79)   ~ (all_52_17 = all_52_23)
% 202.47/33.98    (80)  all_8_1 = all_6_1
% 202.47/33.98    (81)  op(all_6_2, e3) = all_6_1
% 202.47/33.98    (82)  all_58_4 = all_52_17
% 202.47/33.98    (83)  op(all_52_25, all_52_25) = all_52_24
% 202.47/33.98  
% 202.47/33.98  Begin of proof
% 202.47/33.98  | 
% 202.47/33.98  | BETA: splitting (70) gives:
% 202.47/33.98  | 
% 202.47/33.98  | Case 1:
% 202.47/33.98  | | 
% 202.47/33.98  | |   (84)  all_58_3 = e3
% 202.47/33.98  | | 
% 202.47/33.98  | | COMBINE_EQS: (77), (84) imply:
% 202.47/33.98  | |   (85)  all_4_2 = e3
% 202.47/33.98  | | 
% 202.47/33.98  | | REDUCE: (51), (85) imply:
% 202.47/33.98  | |   (86)   ~ (all_52_9 = e3)
% 202.47/33.98  | | 
% 202.47/33.98  | | REDUCE: (57), (85) imply:
% 202.47/33.98  | |   (87)  op(e3, e3) = all_52_10
% 202.47/33.98  | | 
% 202.47/33.98  | | REDUCE: (38), (85) imply:
% 202.47/33.98  | |   (88)  op(e3, e2) = all_4_1
% 202.47/33.98  | | 
% 202.47/33.98  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.47/33.98  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.47/33.98  | |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 202.47/33.98  | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 202.47/33.98  | |            (48), (49), (50), (52), (53), (54), (55), (56), (58), (59), (60),
% 202.47/33.98  | |            (62), (63), (64), (65), (66), (67), (68), (69), (71), (72), (73),
% 202.47/33.98  | |            (74), (75), (76), (78), (79), (80), (81), (82), (83), (84), (86),
% 202.47/33.98  | |            (87), (88) are inconsistent by sub-proof #408.
% 202.47/33.98  | | 
% 202.47/33.98  | Case 2:
% 202.47/33.98  | | 
% 202.47/33.98  | |   (89)  all_58_7 = e3 | all_58_13 = e3
% 202.47/33.98  | | 
% 202.47/33.98  | | REF_CLOSE: (14), (16), (18), (19), (89) are inconsistent by sub-proof #717.
% 202.47/33.98  | | 
% 202.47/33.98  | End of split
% 202.47/33.98  | 
% 202.47/33.98  End of proof
% 202.47/33.98  
% 202.47/33.98  Sub-proof #408 shows that the following formulas are inconsistent:
% 202.47/33.98  ----------------------------------------------------------------
% 202.47/33.98    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.98    (2)  all_58_14 = all_52_23
% 202.47/33.98    (3)   ~ (e3 = e1)
% 202.47/33.98    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.98    (5)  all_58_1 = all_52_9
% 202.47/33.98    (6)   ~ (e3 = e0)
% 202.47/33.98    (7)  op(all_52_23, all_52_23) = e0
% 202.47/33.98    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/33.98    (9)   ~ (all_52_7 = all_52_15)
% 202.47/33.98    (10)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.98    (11)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.98    (12)  all_58_0 = all_6_2
% 202.47/33.98    (13)   ~ (all_52_17 = all_10_2)
% 202.47/33.98    (14)   ~ (all_10_0 = e3)
% 202.47/33.98    (15)  all_40_2 = all_10_2
% 202.47/33.98    (16)  all_58_3 = e3
% 202.47/33.98    (17)  all_58_13 = all_52_15
% 202.47/33.98    (18)  all_58_9 = all_52_25
% 202.47/33.98    (19)   ~ (all_52_15 = e3)
% 202.47/33.98    (20)  all_58_7 = all_10_0
% 202.47/33.98    (21)  all_58_11 = all_52_29
% 202.47/33.98    (22)   ~ (all_52_25 = all_14_2)
% 202.47/33.98    (23)   ~ (all_52_9 = all_52_15)
% 202.47/33.98    (24)   ~ (all_52_7 = all_6_2)
% 202.47/33.98    (25)  op(e0, e0) = all_14_2
% 202.47/33.98    (26)  all_56_15 = all_14_2
% 202.47/33.98    (27)   ~ (all_10_0 = e2)
% 202.47/33.98    (28)  op(e3, e2) = all_4_1
% 202.47/33.98    (29)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/33.98    (30)  op(all_10_2, all_10_2) = e1
% 202.47/33.98    (31)  op(all_52_9, all_52_9) = all_52_8
% 202.47/33.98    (32)  all_56_9 = all_10_0
% 202.47/33.98    (33)   ~ (all_52_25 = all_52_29)
% 202.47/33.98    (34)   ~ (all_52_5 = all_52_7)
% 202.47/33.98    (35)  all_58_12 = all_52_7
% 202.47/33.98    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.98    (37)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.98    (38)  all_56_2 = all_52_17
% 202.47/33.98    (39)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/33.98    (40)  op(e3, e3) = all_52_10
% 202.47/33.98    (41)   ~ (all_52_15 = all_14_2)
% 202.47/33.98    (42)   ~ (all_52_9 = e3)
% 202.47/33.98    (43)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/33.98    (44)  op(e3, e1) = all_52_17
% 202.47/33.98    (45)  op(e0, e3) = all_52_7
% 202.47/33.98    (46)   ~ (all_52_9 = all_52_25)
% 202.47/33.98    (47)  all_58_15 = all_14_2
% 202.47/33.98    (48)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/33.98    (49)  all_58_8 = all_10_2
% 202.47/33.98    (50)   ~ (all_52_23 = all_14_2)
% 202.47/33.98    (51)  all_56_12 = all_52_7
% 202.47/33.98    (52)  all_8_2 = all_6_2
% 202.47/33.98    (53)   ~ (all_52_9 = all_6_2)
% 202.47/33.98    (54)  op(e3, all_6_1) = e2
% 202.47/33.98    (55)  op(e3, e3) = all_6_2
% 202.47/33.98    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/33.98    (57)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.98    (58)  all_40_0 = all_10_0
% 202.47/33.98    (59)  op(all_14_2, all_14_2) = all_52_30
% 202.47/33.98    (60)  all_56_1 = all_52_9
% 202.47/33.98    (61)  op(all_52_17, all_52_17) = e3
% 202.47/33.98    (62)  all_58_6 = all_52_5
% 202.47/33.98    (63)  op(all_10_2, e1) = e2
% 202.47/33.98    (64)  op(e3, e2) = all_52_9
% 202.47/33.98    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.98    (66)   ~ (all_52_17 = all_6_2)
% 202.47/33.98    (67)   ~ (e1 = e0)
% 202.47/33.98    (68)   ~ (e3 = e2)
% 202.47/33.98    (69)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/33.98    (70)   ~ (all_52_9 = all_52_17)
% 202.47/33.98    (71)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.98    (72)  op(e1, e1) = all_10_2
% 202.47/33.98    (73)   ~ (all_52_23 = all_10_2)
% 202.47/33.98    (74)   ~ (all_52_7 = all_52_23)
% 202.47/33.98    (75)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.98    (76)   ~ (all_52_17 = all_52_23)
% 202.47/33.98    (77)  all_8_1 = all_6_1
% 202.47/33.98    (78)  op(all_6_2, e3) = all_6_1
% 202.47/33.98    (79)  all_58_4 = all_52_17
% 202.47/33.98    (80)  op(all_52_25, all_52_25) = all_52_24
% 202.47/33.98  
% 202.47/33.98  Begin of proof
% 202.47/33.98  | 
% 202.47/33.98  | GROUND_INST: instantiating (4) with all_52_9, all_4_1, e2, e3, simplifying
% 202.47/33.98  |              with (28), (64) gives:
% 202.47/33.98  |   (81)  all_52_9 = all_4_1
% 202.47/33.98  | 
% 202.47/33.98  | GROUND_INST: instantiating (4) with all_6_2, all_52_10, e3, e3, simplifying
% 202.47/33.98  |              with (40), (55) gives:
% 202.47/33.98  |   (82)  all_52_10 = all_6_2
% 202.47/33.98  | 
% 202.47/33.98  | COMBINE_EQS: (60), (81) imply:
% 202.47/33.98  |   (83)  all_56_1 = all_4_1
% 202.47/33.98  | 
% 202.47/33.98  | COMBINE_EQS: (5), (81) imply:
% 202.47/33.98  |   (84)  all_58_1 = all_4_1
% 202.47/33.98  | 
% 202.47/33.98  | REDUCE: (23), (81) imply:
% 202.47/33.98  |   (85)   ~ (all_52_15 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | SIMP: (85) implies:
% 202.47/33.98  |   (86)   ~ (all_52_15 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | REDUCE: (70), (81) imply:
% 202.47/33.98  |   (87)   ~ (all_52_17 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | SIMP: (87) implies:
% 202.47/33.98  |   (88)   ~ (all_52_17 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | REDUCE: (46), (81) imply:
% 202.47/33.98  |   (89)   ~ (all_52_25 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | SIMP: (89) implies:
% 202.47/33.98  |   (90)   ~ (all_52_25 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | REDUCE: (53), (81) imply:
% 202.47/33.98  |   (91)   ~ (all_6_2 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | SIMP: (91) implies:
% 202.47/33.98  |   (92)   ~ (all_6_2 = all_4_1)
% 202.47/33.98  | 
% 202.47/33.98  | REDUCE: (42), (81) imply:
% 202.47/33.98  |   (93)   ~ (all_4_1 = e3)
% 202.47/33.98  | 
% 202.47/33.98  | REDUCE: (31), (81) imply:
% 202.47/33.98  |   (94)  op(all_4_1, all_4_1) = all_52_8
% 202.47/33.98  | 
% 202.47/33.98  | BETA: splitting (69) gives:
% 202.47/33.98  | 
% 202.47/33.98  | Case 1:
% 202.47/33.98  | | 
% 202.47/33.98  | |   (95)  all_56_1 = e3
% 202.47/33.98  | | 
% 202.47/33.98  | | COMBINE_EQS: (83), (95) imply:
% 202.47/33.98  | |   (96)  all_4_1 = e3
% 202.47/33.98  | | 
% 202.47/33.98  | | REDUCE: (93), (96) imply:
% 202.47/33.98  | |   (97)  $false
% 202.47/33.98  | | 
% 202.47/33.98  | | CLOSE: (97) is inconsistent.
% 202.47/33.98  | | 
% 202.47/33.98  | Case 2:
% 202.47/33.98  | | 
% 202.47/33.98  | |   (98)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/33.98  | | 
% 202.47/33.98  | | BETA: splitting (56) gives:
% 202.47/33.98  | | 
% 202.47/33.98  | | Case 1:
% 202.47/33.98  | | | 
% 202.47/33.98  | | |   (99)  all_58_9 = e3
% 202.47/33.98  | | | 
% 202.47/33.98  | | | COMBINE_EQS: (18), (99) imply:
% 202.47/33.98  | | |   (100)  all_52_25 = e3
% 202.47/33.98  | | | 
% 202.47/33.98  | | | REDUCE: (33), (100) imply:
% 202.47/33.98  | | |   (101)   ~ (all_52_29 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | SIMP: (101) implies:
% 202.47/33.98  | | |   (102)   ~ (all_52_29 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | REDUCE: (22), (100) imply:
% 202.47/33.98  | | |   (103)   ~ (all_14_2 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | SIMP: (103) implies:
% 202.47/33.98  | | |   (104)   ~ (all_14_2 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | REDUCE: (90), (100) imply:
% 202.47/33.98  | | |   (105)   ~ (all_4_1 = e3)
% 202.47/33.98  | | | 
% 202.47/33.98  | | | REDUCE: (80), (100) imply:
% 202.47/33.98  | | |   (106)  op(e3, e3) = all_52_24
% 202.47/33.98  | | | 
% 202.47/33.98  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_24, e3, e3,
% 202.47/33.98  | | |              simplifying with (55), (106) gives:
% 202.47/33.98  | | |   (107)  all_52_24 = all_6_2
% 202.47/33.98  | | | 
% 202.47/33.98  | | | BETA: splitting (65) gives:
% 202.47/33.98  | | | 
% 202.47/33.98  | | | Case 1:
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | |   (108)  all_58_12 = e3
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | COMBINE_EQS: (35), (108) imply:
% 202.47/33.98  | | | |   (109)  all_52_7 = e3
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | SIMP: (109) implies:
% 202.47/33.98  | | | |   (110)  all_52_7 = e3
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | REDUCE: (34), (110) imply:
% 202.47/33.98  | | | |   (111)   ~ (all_52_5 = e3)
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | REDUCE: (10), (110) imply:
% 202.47/33.98  | | | |   (112)  op(e3, e3) = all_52_6
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | BETA: splitting (36) gives:
% 202.47/33.98  | | | | 
% 202.47/33.98  | | | | Case 1:
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | |   (113)  all_58_6 = e3
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | | REF_CLOSE: (62), (111), (113) are inconsistent by sub-proof #1328.
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | Case 2:
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | |   (114)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | | BETA: splitting (114) gives:
% 202.47/33.98  | | | | | 
% 202.47/33.98  | | | | | Case 1:
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | |   (115)  all_58_7 = e3
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | | COMBINE_EQS: (20), (115) imply:
% 202.47/33.98  | | | | | |   (116)  all_10_0 = e3
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | | REDUCE: (14), (116) imply:
% 202.47/33.98  | | | | | |   (117)  $false
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | | CLOSE: (117) is inconsistent.
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | Case 2:
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | |   (118)  all_58_8 = e3 | all_58_11 = e3
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | | BETA: splitting (118) gives:
% 202.47/33.98  | | | | | | 
% 202.47/33.98  | | | | | | Case 1:
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | |   (119)  all_58_8 = e3
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | COMBINE_EQS: (49), (119) imply:
% 202.47/33.98  | | | | | | |   (120)  all_10_2 = e3
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | COMBINE_EQS: (15), (120) imply:
% 202.47/33.98  | | | | | | |   (121)  all_40_2 = e3
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | REDUCE: (13), (120) imply:
% 202.47/33.98  | | | | | | |   (122)   ~ (all_52_17 = e3)
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | REDUCE: (30), (120) imply:
% 202.47/33.98  | | | | | | |   (123)  op(e3, e3) = e1
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | REDUCE: (63), (120) imply:
% 202.47/33.98  | | | | | | |   (124)  op(e3, e1) = e2
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | BETA: splitting (37) gives:
% 202.47/33.98  | | | | | | | 
% 202.47/33.98  | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | |   (125)   ~ (all_40_2 = e3)
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | | REDUCE: (121), (125) imply:
% 202.47/33.98  | | | | | | | |   (126)  $false
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | | CLOSE: (126) is inconsistent.
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | |   (127)   ~ (all_40_0 = e0)
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | | REDUCE: (58), (127) imply:
% 202.47/33.98  | | | | | | | |   (128)   ~ (all_10_0 = e0)
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | | BETA: splitting (11) gives:
% 202.47/33.98  | | | | | | | | 
% 202.47/33.98  | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | |   (129)  all_56_9 = e2
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | REF_CLOSE: (27), (32), (129) are inconsistent by sub-proof
% 202.47/33.98  | | | | | | | | |            #991.
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | |   (130)  all_56_9 = e1 | all_56_9 = e0
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | BETA: splitting (130) gives:
% 202.47/33.98  | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | |   (131)  all_56_9 = e1
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | COMBINE_EQS: (32), (131) imply:
% 202.47/33.98  | | | | | | | | | |   (132)  all_10_0 = e1
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | SIMP: (132) implies:
% 202.47/33.98  | | | | | | | | | |   (133)  all_10_0 = e1
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | COMBINE_EQS: (20), (133) imply:
% 202.47/33.98  | | | | | | | | | |   (134)  all_58_7 = e1
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_17, e2, e1, e3,
% 202.47/33.98  | | | | | | | | | |              simplifying with (44), (124) gives:
% 202.47/33.98  | | | | | | | | | |   (135)  all_52_17 = e2
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3,
% 202.47/33.98  | | | | | | | | | |              simplifying with (55), (112) gives:
% 202.47/33.98  | | | | | | | | | |   (136)  all_52_6 = all_6_2
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_52_6, e3, e3,
% 202.47/33.98  | | | | | | | | | |              simplifying with (112), (123) gives:
% 202.47/33.98  | | | | | | | | | |   (137)  all_52_6 = e1
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | COMBINE_EQS: (136), (137) imply:
% 202.47/33.98  | | | | | | | | | |   (138)  all_6_2 = e1
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | REDUCE: (66), (135), (138) imply:
% 202.47/33.98  | | | | | | | | | |   (139)   ~ (e2 = e1)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | REDUCE: (88), (135) imply:
% 202.47/33.98  | | | | | | | | | |   (140)   ~ (all_4_1 = e2)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | SIMP: (140) implies:
% 202.47/33.98  | | | | | | | | | |   (141)   ~ (all_4_1 = e2)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | REDUCE: (122), (135) imply:
% 202.47/33.98  | | | | | | | | | |   (142)   ~ (e3 = e2)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | REDUCE: (92), (138) imply:
% 202.47/33.98  | | | | | | | | | |   (143)   ~ (all_4_1 = e1)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | SIMP: (143) implies:
% 202.47/33.98  | | | | | | | | | |   (144)   ~ (all_4_1 = e1)
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | BETA: splitting (75) gives:
% 202.47/33.98  | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | |   (145)  all_58_1 = e2
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | COMBINE_EQS: (84), (145) imply:
% 202.47/33.98  | | | | | | | | | | |   (146)  all_4_1 = e2
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | REDUCE: (141), (146) imply:
% 202.47/33.98  | | | | | | | | | | |   (147)  $false
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | |   (148)   ~ (all_58_1 = e2)
% 202.47/33.98  | | | | | | | | | | |   (149)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | BETA: splitting (149) gives:
% 202.47/33.98  | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | |   (150)  all_58_3 = e2
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | COMBINE_EQS: (16), (150) imply:
% 202.47/33.98  | | | | | | | | | | | |   (151)  e3 = e2
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | REDUCE: (68), (151) imply:
% 202.47/33.98  | | | | | | | | | | | |   (152)  $false
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | |   (153)  all_58_7 = e2 | all_58_13 = e2
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | BETA: splitting (98) gives:
% 202.47/33.98  | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | |   (154)  all_56_1 = e2
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | COMBINE_EQS: (83), (154) imply:
% 202.47/33.98  | | | | | | | | | | | | |   (155)  all_4_1 = e2
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | REDUCE: (141), (155) imply:
% 202.47/33.98  | | | | | | | | | | | | |   (156)  $false
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | |   (157)  all_56_1 = e1 | all_56_1 = e0
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | BETA: splitting (157) gives:
% 202.47/33.98  | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | |   (158)  all_56_1 = e1
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | COMBINE_EQS: (83), (158) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (159)  all_4_1 = e1
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (144), (159) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (160)  $false
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | |   (161)  all_56_1 = e0
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | COMBINE_EQS: (83), (161) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (162)  all_4_1 = e0
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (86), (162) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (163)   ~ (all_52_15 = e0)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (93), (162) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (164)   ~ (e3 = e0)
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | REDUCE: (94), (162) imply:
% 202.47/33.98  | | | | | | | | | | | | | |   (165)  op(e0, e0) = all_52_8
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 202.47/33.98  | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | |   (166)  all_58_12 = e0
% 202.47/33.98  | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | REF_CLOSE: (6), (108), (166) are inconsistent by sub-proof
% 202.47/33.98  | | | | | | | | | | | | | | |            #1212.
% 202.47/33.98  | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | |   (167)  all_58_13 = e0 | all_58_14 = e0
% 202.47/33.98  | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 202.47/33.98  | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | Case 1:
% 202.47/33.98  | | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | |   (168)  all_58_13 = e0
% 202.47/33.98  | | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (163), (168) are inconsistent by sub-proof
% 202.47/33.98  | | | | | | | | | | | | | | | |            #1269.
% 202.47/33.98  | | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | Case 2:
% 202.47/33.98  | | | | | | | | | | | | | | | | 
% 202.47/33.98  | | | | | | | | | | | | | | | |   (169)  all_58_14 = e0
% 202.47/33.98  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (169) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | |   (170)  all_52_23 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | SIMP: (170) implies:
% 202.47/33.99  | | | | | | | | | | | | | | | |   (171)  all_52_23 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | REDUCE: (50), (171) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | |   (172)   ~ (all_14_2 = e0)
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | SIMP: (172) implies:
% 202.47/33.99  | | | | | | | | | | | | | | | |   (173)   ~ (all_14_2 = e0)
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | REDUCE: (7), (171) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | |   (174)  op(e0, e0) = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | Case 1:
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | |   (175)  all_58_7 = e2
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (139), (175) are inconsistent by sub-proof
% 202.47/33.99  | | | | | | | | | | | | | | | | |            #421.
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | Case 2:
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | |   (176)  all_58_13 = e2
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (176) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | | |   (177)  all_52_15 = e2
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | SIMP: (177) implies:
% 202.47/33.99  | | | | | | | | | | | | | | | | |   (178)  all_52_15 = e2
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | REDUCE: (41), (178) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | | |   (179)   ~ (all_14_2 = e2)
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 202.47/33.99  | | | | | | | | | | | | | | | | |   (180)   ~ (all_14_2 = e2)
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | Case 1:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | |   (181)  all_56_15 = e2
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (180), (181) are inconsistent by sub-proof
% 202.47/33.99  | | | | | | | | | | | | | | | | | |            #762.
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | Case 2:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | |   (182)  all_56_15 = e1 | all_56_15 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | Case 1:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (183)  all_56_15 = e1
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (183) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (184)  all_14_2 = e1
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | SIMP: (184) implies:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (185)  all_14_2 = e1
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | REDUCE: (25), (185) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (186)  op(e0, e0) = e1
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_52_8, e0, e0,
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |              simplifying with (165), (186) gives:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (187)  all_52_8 = e1
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_52_8, e0, e0,
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |              simplifying with (165), (174) gives:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (188)  all_52_8 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (188) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (189)  e1 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | SIMP: (189) implies:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (190)  e1 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | REDUCE: (67), (190) imply:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (191)  $false
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | Case 2:
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |   (192)  all_56_15 = e0
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (173), (192) are inconsistent by sub-proof
% 202.47/33.99  | | | | | | | | | | | | | | | | | | |            #1162.
% 202.47/33.99  | | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | Case 2:
% 202.47/33.99  | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | |   (193)  all_56_9 = e0
% 202.47/33.99  | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | | REF_CLOSE: (32), (128), (193) are inconsistent by sub-proof
% 202.47/33.99  | | | | | | | | | |            #989.
% 202.47/33.99  | | | | | | | | | | 
% 202.47/33.99  | | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | | 
% 202.47/33.99  | | | | | | | | End of split
% 202.47/33.99  | | | | | | | | 
% 202.47/33.99  | | | | | | | End of split
% 202.47/33.99  | | | | | | | 
% 202.47/33.99  | | | | | | Case 2:
% 202.47/33.99  | | | | | | | 
% 202.47/33.99  | | | | | | |   (194)  all_58_11 = e3
% 202.47/33.99  | | | | | | | 
% 202.47/33.99  | | | | | | | REF_CLOSE: (21), (102), (194) are inconsistent by sub-proof #1323.
% 202.47/33.99  | | | | | | | 
% 202.47/33.99  | | | | | | End of split
% 202.47/33.99  | | | | | | 
% 202.47/33.99  | | | | | End of split
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | End of split
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | Case 2:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | |   (195)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (17), (19), (24),
% 202.47/33.99  | | | |            (29), (35), (38), (39), (43), (45), (47), (51), (52), (54),
% 202.47/33.99  | | | |            (55), (59), (61), (64), (66), (67), (70), (72), (73), (74),
% 202.47/33.99  | | | |            (76), (77), (78), (104), (195) are inconsistent by sub-proof
% 202.47/33.99  | | | |            #437.
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | End of split
% 202.47/33.99  | | | 
% 202.47/33.99  | | Case 2:
% 202.47/33.99  | | | 
% 202.47/33.99  | | |   (196)   ~ (all_58_9 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REDUCE: (18), (196) imply:
% 202.47/33.99  | | |   (197)   ~ (all_52_25 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REF_CLOSE: (4), (5), (12), (18), (42), (54), (55), (57), (61), (66), (68),
% 202.47/33.99  | | |            (71), (78), (79), (197) are inconsistent by sub-proof #446.
% 202.47/33.99  | | | 
% 202.47/33.99  | | End of split
% 202.47/33.99  | | 
% 202.47/33.99  | End of split
% 202.47/33.99  | 
% 202.47/33.99  End of proof
% 202.47/33.99  
% 202.47/33.99  Sub-proof #409 shows that the following formulas are inconsistent:
% 202.47/33.99  ----------------------------------------------------------------
% 202.47/33.99    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.99    (2)  all_58_14 = all_52_23
% 202.47/33.99    (3)   ~ (e3 = e1)
% 202.47/33.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.99    (5)  all_58_1 = all_52_9
% 202.47/33.99    (6)   ~ (e3 = e0)
% 202.47/33.99    (7)  op(all_52_23, all_52_23) = e0
% 202.47/33.99    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/33.99    (9)   ~ (all_52_7 = all_52_15)
% 202.47/33.99    (10)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.99    (11)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.99    (12)  all_58_0 = all_6_2
% 202.47/33.99    (13)  all_40_2 = all_10_2
% 202.47/33.99    (14)  all_58_13 = all_52_15
% 202.47/33.99    (15)  all_58_9 = all_52_25
% 202.47/33.99    (16)   ~ (all_52_29 = all_14_2)
% 202.47/33.99    (17)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.47/33.99    (18)  op(e2, e2) = all_4_2
% 202.47/33.99    (19)  all_58_7 = all_10_0
% 202.47/33.99    (20)  all_58_11 = all_52_29
% 202.47/33.99    (21)   ~ (all_52_9 = all_52_15)
% 202.47/33.99    (22)  all_58_1 = e3
% 202.47/33.99    (23)   ~ (all_52_7 = all_6_2)
% 202.47/33.99    (24)  op(e0, e0) = all_14_2
% 202.47/33.99    (25)  all_56_11 = all_52_29
% 202.47/33.99    (26)   ~ (all_10_0 = e2)
% 202.47/33.99    (27)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/33.99    (28)   ~ (e2 = e1)
% 202.47/33.99    (29)  op(all_52_9, all_52_9) = all_52_8
% 202.47/33.99    (30)   ~ (all_52_19 = all_52_23)
% 202.47/33.99    (31)  all_56_9 = all_10_0
% 202.47/33.99    (32)   ~ (all_52_29 = all_10_2)
% 202.47/33.99    (33)  op(all_52_19, all_52_19) = e2
% 202.47/33.99    (34)   ~ (all_52_5 = all_52_7)
% 202.47/33.99    (35)  all_58_12 = all_52_7
% 202.47/33.99    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.99    (37)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.99    (38)  all_56_2 = all_52_17
% 202.47/33.99    (39)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.47/33.99    (40)   ~ (e2 = e0)
% 202.47/33.99    (41)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.47/33.99    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/33.99    (43)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/33.99    (44)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/33.99    (45)  op(e3, e1) = all_52_17
% 202.47/33.99    (46)  op(e0, e3) = all_52_7
% 202.47/33.99    (47)  all_58_15 = all_14_2
% 202.47/33.99    (48)   ~ (all_52_19 = all_10_2)
% 202.47/33.99    (49)  all_58_8 = all_10_2
% 202.47/33.99    (50)  all_56_12 = all_52_7
% 202.47/33.99    (51)  all_8_2 = all_6_2
% 202.47/33.99    (52)   ~ (all_52_9 = all_4_2)
% 202.47/33.99    (53)  op(e3, all_6_1) = e2
% 202.47/33.99    (54)  op(e3, e3) = all_6_2
% 202.47/33.99    (55)  all_40_0 = all_10_0
% 202.47/33.99    (56)  op(all_14_2, all_14_2) = all_52_30
% 202.47/33.99    (57)  all_58_5 = all_52_19
% 202.47/33.99    (58)  op(all_52_17, all_52_17) = e3
% 202.47/33.99    (59)  all_58_6 = all_52_5
% 202.47/33.99    (60)  op(all_10_2, e1) = e2
% 202.47/33.99    (61)  op(e3, e2) = all_52_9
% 202.47/33.99    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.99    (63)   ~ (all_52_17 = all_6_2)
% 202.47/33.99    (64)   ~ (e1 = e0)
% 202.47/33.99    (65)   ~ (all_52_9 = all_52_17)
% 202.47/33.99    (66)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.99    (67)  op(e1, e1) = all_10_2
% 202.47/33.99    (68)   ~ (all_52_23 = all_10_2)
% 202.47/33.99    (69)   ~ (all_52_7 = all_52_23)
% 202.47/33.99    (70)   ~ (all_52_9 = all_10_0)
% 202.47/33.99    (71)   ~ (all_52_17 = all_52_23)
% 202.47/33.99    (72)  all_8_1 = all_6_1
% 202.47/33.99    (73)  op(all_6_2, e3) = all_6_1
% 202.47/33.99    (74)  all_58_4 = all_52_17
% 202.47/33.99    (75)   ~ (all_14_2 = e3)
% 202.47/33.99  
% 202.47/33.99  Begin of proof
% 202.47/33.99  | 
% 202.47/33.99  | COMBINE_EQS: (5), (22) imply:
% 202.47/33.99  |   (76)  all_52_9 = e3
% 202.47/33.99  | 
% 202.47/33.99  | REDUCE: (21), (76) imply:
% 202.47/33.99  |   (77)   ~ (all_52_15 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | SIMP: (77) implies:
% 202.47/33.99  |   (78)   ~ (all_52_15 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | REDUCE: (65), (76) imply:
% 202.47/33.99  |   (79)   ~ (all_52_17 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | SIMP: (79) implies:
% 202.47/33.99  |   (80)   ~ (all_52_17 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | REDUCE: (70), (76) imply:
% 202.47/33.99  |   (81)   ~ (all_10_0 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | SIMP: (81) implies:
% 202.47/33.99  |   (82)   ~ (all_10_0 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | REDUCE: (52), (76) imply:
% 202.47/33.99  |   (83)   ~ (all_4_2 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | SIMP: (83) implies:
% 202.47/33.99  |   (84)   ~ (all_4_2 = e3)
% 202.47/33.99  | 
% 202.47/33.99  | REDUCE: (29), (76) imply:
% 202.47/33.99  |   (85)  op(e3, e3) = all_52_8
% 202.47/33.99  | 
% 202.47/33.99  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 202.47/33.99  |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 202.47/33.99  |            (26), (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 202.47/33.99  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 202.47/33.99  |            (49), (50), (51), (53), (54), (55), (56), (57), (58), (59), (60),
% 202.47/33.99  |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (71), (72),
% 202.47/33.99  |            (73), (74), (75), (78), (80), (82), (84), (85) are inconsistent by
% 202.47/33.99  |            sub-proof #410.
% 202.47/33.99  | 
% 202.47/33.99  End of proof
% 202.47/33.99  
% 202.47/33.99  Sub-proof #410 shows that the following formulas are inconsistent:
% 202.47/33.99  ----------------------------------------------------------------
% 202.47/33.99    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/33.99    (2)  all_58_14 = all_52_23
% 202.47/33.99    (3)   ~ (e3 = e1)
% 202.47/33.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.99    (5)   ~ (e3 = e0)
% 202.47/33.99    (6)  op(all_52_23, all_52_23) = e0
% 202.47/33.99    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/33.99    (8)   ~ (all_52_7 = all_52_15)
% 202.47/33.99    (9)  op(all_52_7, all_52_7) = all_52_6
% 202.47/33.99    (10)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/33.99    (11)   ~ (all_4_2 = e3)
% 202.47/33.99    (12)  all_58_0 = all_6_2
% 202.47/33.99    (13)   ~ (all_10_0 = e3)
% 202.47/33.99    (14)  all_40_2 = all_10_2
% 202.47/33.99    (15)  all_58_13 = all_52_15
% 202.47/33.99    (16)  all_58_9 = all_52_25
% 202.47/33.99    (17)   ~ (all_52_29 = all_14_2)
% 202.47/33.99    (18)   ~ (all_52_15 = e3)
% 202.47/33.99    (19)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.47/33.99    (20)  op(e2, e2) = all_4_2
% 202.47/33.99    (21)  all_58_7 = all_10_0
% 202.47/33.99    (22)  all_58_11 = all_52_29
% 202.47/33.99    (23)  all_58_1 = e3
% 202.47/33.99    (24)   ~ (all_52_7 = all_6_2)
% 202.47/33.99    (25)  op(e0, e0) = all_14_2
% 202.47/33.99    (26)  all_56_11 = all_52_29
% 202.47/33.99    (27)   ~ (all_10_0 = e2)
% 202.47/33.99    (28)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/33.99    (29)   ~ (e2 = e1)
% 202.47/33.99    (30)   ~ (all_52_19 = all_52_23)
% 202.47/33.99    (31)  all_56_9 = all_10_0
% 202.47/33.99    (32)   ~ (all_52_29 = all_10_2)
% 202.47/33.99    (33)  op(all_52_19, all_52_19) = e2
% 202.47/33.99    (34)   ~ (all_52_5 = all_52_7)
% 202.47/33.99    (35)  all_58_12 = all_52_7
% 202.47/33.99    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.99    (37)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.99    (38)  all_56_2 = all_52_17
% 202.47/33.99    (39)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.47/33.99    (40)   ~ (e2 = e0)
% 202.47/33.99    (41)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.47/33.99    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/33.99    (43)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/33.99    (44)  op(e3, e3) = all_52_8
% 202.47/33.99    (45)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/33.99    (46)  op(e3, e1) = all_52_17
% 202.47/33.99    (47)  op(e0, e3) = all_52_7
% 202.47/33.99    (48)  all_58_15 = all_14_2
% 202.47/33.99    (49)   ~ (all_52_19 = all_10_2)
% 202.47/33.99    (50)  all_58_8 = all_10_2
% 202.47/33.99    (51)  all_56_12 = all_52_7
% 202.47/33.99    (52)  all_8_2 = all_6_2
% 202.47/33.99    (53)  op(e3, all_6_1) = e2
% 202.47/33.99    (54)  op(e3, e3) = all_6_2
% 202.47/33.99    (55)   ~ (all_52_17 = e3)
% 202.47/33.99    (56)  all_40_0 = all_10_0
% 202.47/33.99    (57)  op(all_14_2, all_14_2) = all_52_30
% 202.47/33.99    (58)  all_58_5 = all_52_19
% 202.47/33.99    (59)  op(all_52_17, all_52_17) = e3
% 202.47/33.99    (60)  all_58_6 = all_52_5
% 202.47/33.99    (61)  op(all_10_2, e1) = e2
% 202.47/33.99    (62)  op(e3, e2) = all_52_9
% 202.47/33.99    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.99    (64)   ~ (all_52_17 = all_6_2)
% 202.47/33.99    (65)   ~ (e1 = e0)
% 202.47/33.99    (66)   ~ (all_52_9 = all_52_17)
% 202.47/33.99    (67)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.99    (68)  op(e1, e1) = all_10_2
% 202.47/33.99    (69)   ~ (all_52_23 = all_10_2)
% 202.47/33.99    (70)   ~ (all_52_7 = all_52_23)
% 202.47/33.99    (71)   ~ (all_52_17 = all_52_23)
% 202.47/33.99    (72)  all_8_1 = all_6_1
% 202.47/33.99    (73)  op(all_6_2, e3) = all_6_1
% 202.47/33.99    (74)  all_58_4 = all_52_17
% 202.47/33.99    (75)   ~ (all_14_2 = e3)
% 202.47/33.99  
% 202.47/33.99  Begin of proof
% 202.47/33.99  | 
% 202.47/33.99  | GROUND_INST: instantiating (4) with all_6_2, all_52_8, e3, e3, simplifying
% 202.47/33.99  |              with (44), (54) gives:
% 202.47/33.99  |   (76)  all_52_8 = all_6_2
% 202.47/33.99  | 
% 202.47/33.99  | BETA: splitting (63) gives:
% 202.47/33.99  | 
% 202.47/33.99  | Case 1:
% 202.47/33.99  | | 
% 202.47/33.99  | |   (77)  all_58_12 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | COMBINE_EQS: (35), (77) imply:
% 202.47/33.99  | |   (78)  all_52_7 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | SIMP: (78) implies:
% 202.47/33.99  | |   (79)  all_52_7 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | REDUCE: (34), (79) imply:
% 202.47/33.99  | |   (80)   ~ (all_52_5 = e3)
% 202.47/33.99  | | 
% 202.47/33.99  | | REDUCE: (70), (79) imply:
% 202.47/33.99  | |   (81)   ~ (all_52_23 = e3)
% 202.47/33.99  | | 
% 202.47/33.99  | | SIMP: (81) implies:
% 202.47/33.99  | |   (82)   ~ (all_52_23 = e3)
% 202.47/33.99  | | 
% 202.47/33.99  | | REDUCE: (9), (79) imply:
% 202.47/33.99  | |   (83)  op(e3, e3) = all_52_6
% 202.47/33.99  | | 
% 202.47/33.99  | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 202.47/33.99  | |              with (54), (83) gives:
% 202.47/33.99  | |   (84)  all_52_6 = all_6_2
% 202.47/33.99  | | 
% 202.47/33.99  | | REF_CLOSE: (2), (3), (4), (5), (10), (11), (12), (13), (14), (16), (17),
% 202.47/33.99  | |            (19), (20), (21), (22), (23), (25), (26), (27), (29), (30), (31),
% 202.47/33.99  | |            (32), (33), (36), (37), (39), (40), (41), (43), (44), (46), (49),
% 202.47/33.99  | |            (50), (54), (55), (56), (58), (59), (60), (61), (65), (67), (68),
% 202.47/33.99  | |            (74), (80), (82) are inconsistent by sub-proof #788.
% 202.47/33.99  | | 
% 202.47/33.99  | Case 2:
% 202.47/33.99  | | 
% 202.47/33.99  | |   (85)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (15), (18), (24), (28),
% 202.47/33.99  | |            (35), (38), (42), (45), (47), (48), (51), (52), (53), (54), (57),
% 202.47/33.99  | |            (59), (62), (64), (65), (66), (68), (69), (70), (71), (72), (73),
% 202.47/33.99  | |            (75), (85) are inconsistent by sub-proof #437.
% 202.47/33.99  | | 
% 202.47/33.99  | End of split
% 202.47/33.99  | 
% 202.47/33.99  End of proof
% 202.47/33.99  
% 202.47/33.99  Sub-proof #411 shows that the following formulas are inconsistent:
% 202.47/33.99  ----------------------------------------------------------------
% 202.47/33.99    (1)  all_58_14 = all_52_23
% 202.47/33.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.99    (3)  all_58_1 = all_52_9
% 202.47/33.99    (4)   ~ (e3 = e0)
% 202.47/33.99    (5)  op(e2, e3) = all_52_3
% 202.47/33.99    (6)   ~ (all_52_3 = all_52_19)
% 202.47/33.99    (7)   ~ (all_52_17 = all_52_25)
% 202.47/33.99    (8)   ~ (all_52_3 = all_6_2)
% 202.47/33.99    (9)  all_58_0 = all_6_2
% 202.47/33.99    (10)  all_56_4 = all_52_3
% 202.47/33.99    (11)  all_40_2 = all_10_2
% 202.47/33.99    (12)  op(e3, e0) = all_52_25
% 202.47/33.99    (13)  all_58_9 = all_52_25
% 202.47/33.99    (14)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/33.99    (15)   ~ (all_52_3 = all_52_5)
% 202.47/33.99    (16)  all_58_11 = all_52_29
% 202.47/33.99    (17)   ~ (all_52_25 = all_52_29)
% 202.47/33.99    (18)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/33.99    (19)  op(all_52_19, all_52_19) = e2
% 202.47/33.99    (20)   ~ (all_52_5 = all_52_7)
% 202.47/33.99    (21)  all_58_12 = all_52_7
% 202.47/33.99    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.99    (23)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/33.99    (24)  all_58_2 = all_52_3
% 202.47/33.99    (25)  all_58_7 = e0
% 202.47/33.99    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.99    (27)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.99    (28)   ~ (e2 = e0)
% 202.47/33.99    (29)   ~ (all_52_23 = e3)
% 202.47/33.99    (30)   ~ (all_52_9 = e3)
% 202.47/33.99    (31)  op(e3, e1) = all_52_17
% 202.47/33.99    (32)  all_58_8 = all_10_2
% 202.47/33.99    (33)   ~ (all_52_5 = all_10_2)
% 202.47/33.99    (34)   ~ (all_52_5 = all_6_2)
% 202.47/33.99    (35)  op(e3, all_6_1) = e2
% 202.47/33.99    (36)  op(e3, e3) = all_6_2
% 202.47/33.99    (37)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/33.99    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.99    (39)  all_58_5 = all_52_19
% 202.47/33.99    (40)  op(all_52_17, all_52_17) = e3
% 202.47/33.99    (41)  all_58_6 = all_52_5
% 202.47/33.99    (42)   ~ (all_52_17 = all_6_2)
% 202.47/33.99    (43)   ~ (all_52_19 = e2)
% 202.47/33.99    (44)   ~ (e3 = e2)
% 202.47/33.99    (45)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.99    (46)   ~ (all_52_17 = all_52_19)
% 202.47/33.99    (47)  op(all_6_2, e3) = all_6_1
% 202.47/33.99    (48)  all_40_0 = e0
% 202.47/33.99    (49)  all_58_4 = all_52_17
% 202.47/33.99  
% 202.47/33.99  Begin of proof
% 202.47/33.99  | 
% 202.47/33.99  | BETA: splitting (23) gives:
% 202.47/33.99  | 
% 202.47/33.99  | Case 1:
% 202.47/33.99  | | 
% 202.47/33.99  | |   (50)   ~ (all_40_2 = e3)
% 202.47/33.99  | | 
% 202.47/33.99  | | REDUCE: (11), (50) imply:
% 202.47/33.99  | |   (51)   ~ (all_10_2 = e3)
% 202.47/33.99  | | 
% 202.47/33.99  | | BETA: splitting (22) gives:
% 202.47/33.99  | | 
% 202.47/33.99  | | Case 1:
% 202.47/33.99  | | | 
% 202.47/33.99  | | |   (52)  all_58_6 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | COMBINE_EQS: (41), (52) imply:
% 202.47/33.99  | | |   (53)  all_52_5 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | SIMP: (53) implies:
% 202.47/33.99  | | |   (54)  all_52_5 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REDUCE: (20), (54) imply:
% 202.47/33.99  | | |   (55)   ~ (all_52_7 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | SIMP: (55) implies:
% 202.47/33.99  | | |   (56)   ~ (all_52_7 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REDUCE: (33), (54) imply:
% 202.47/33.99  | | |   (57)   ~ (all_10_2 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REDUCE: (34), (54) imply:
% 202.47/33.99  | | |   (58)   ~ (all_6_2 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | SIMP: (58) implies:
% 202.47/33.99  | | |   (59)   ~ (all_6_2 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 202.47/33.99  | | |            (15), (18), (19), (21), (24), (26), (27), (28), (29), (30),
% 202.47/33.99  | | |            (31), (32), (34), (35), (36), (37), (38), (39), (40), (41),
% 202.47/33.99  | | |            (42), (43), (45), (46), (47), (49), (51), (56), (59) are
% 202.47/33.99  | | |            inconsistent by sub-proof #412.
% 202.47/33.99  | | | 
% 202.47/33.99  | | Case 2:
% 202.47/33.99  | | | 
% 202.47/33.99  | | |   (60)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | BETA: splitting (60) gives:
% 202.47/33.99  | | | 
% 202.47/33.99  | | | Case 1:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | |   (61)  all_58_7 = e3
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | COMBINE_EQS: (25), (61) imply:
% 202.47/33.99  | | | |   (62)  e3 = e0
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | SIMP: (62) implies:
% 202.47/33.99  | | | |   (63)  e3 = e0
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | REDUCE: (4), (63) imply:
% 202.47/33.99  | | | |   (64)  $false
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | CLOSE: (64) is inconsistent.
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | Case 2:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | |   (65)  all_58_8 = e3 | all_58_11 = e3
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | BETA: splitting (65) gives:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | Case 1:
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | |   (66)  all_58_8 = e3
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | REF_CLOSE: (32), (51), (66) are inconsistent by sub-proof #950.
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | Case 2:
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | |   (67)  all_58_11 = e3
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | REF_CLOSE: (2), (3), (9), (13), (16), (17), (30), (35), (36), (38),
% 202.47/33.99  | | | | |            (40), (42), (44), (45), (47), (49), (67) are inconsistent
% 202.47/33.99  | | | | |            by sub-proof #420.
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | End of split
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | End of split
% 202.47/33.99  | | | 
% 202.47/33.99  | | End of split
% 202.47/33.99  | | 
% 202.47/33.99  | Case 2:
% 202.47/33.99  | | 
% 202.47/33.99  | |   (68)   ~ (all_40_0 = e0)
% 202.47/33.99  | | 
% 202.47/33.99  | | REDUCE: (48), (68) imply:
% 202.47/33.99  | |   (69)  $false
% 202.47/33.99  | | 
% 202.47/33.99  | | CLOSE: (69) is inconsistent.
% 202.47/33.99  | | 
% 202.47/33.99  | End of split
% 202.47/33.99  | 
% 202.47/33.99  End of proof
% 202.47/33.99  
% 202.47/33.99  Sub-proof #412 shows that the following formulas are inconsistent:
% 202.47/33.99  ----------------------------------------------------------------
% 202.47/33.99    (1)  all_58_14 = all_52_23
% 202.47/33.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/33.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/33.99    (3)  all_58_1 = all_52_9
% 202.47/33.99    (4)  op(e2, e3) = all_52_3
% 202.47/33.99    (5)   ~ (all_52_3 = all_52_19)
% 202.47/33.99    (6)   ~ (all_52_17 = all_52_25)
% 202.47/33.99    (7)   ~ (all_52_3 = all_6_2)
% 202.47/33.99    (8)  all_58_0 = all_6_2
% 202.47/33.99    (9)  all_56_4 = all_52_3
% 202.47/33.99    (10)  op(e3, e0) = all_52_25
% 202.47/33.99    (11)  all_58_9 = all_52_25
% 202.47/33.99    (12)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/33.99    (13)   ~ (all_52_3 = all_52_5)
% 202.47/33.99    (14)   ~ (all_6_2 = e3)
% 202.47/33.99    (15)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/33.99    (16)  op(all_52_19, all_52_19) = e2
% 202.47/33.99    (17)  all_58_12 = all_52_7
% 202.47/33.99    (18)   ~ (all_52_7 = e3)
% 202.47/33.99    (19)  all_58_2 = all_52_3
% 202.47/33.99    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/33.99    (21)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/33.99    (22)   ~ (e2 = e0)
% 202.47/33.99    (23)   ~ (all_52_23 = e3)
% 202.47/33.99    (24)   ~ (all_10_2 = e3)
% 202.47/33.99    (25)   ~ (all_52_9 = e3)
% 202.47/33.99    (26)  op(e3, e1) = all_52_17
% 202.47/33.99    (27)  all_58_8 = all_10_2
% 202.47/33.99    (28)   ~ (all_52_5 = all_6_2)
% 202.47/33.99    (29)  op(e3, all_6_1) = e2
% 202.47/33.99    (30)  op(e3, e3) = all_6_2
% 202.47/33.99    (31)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/33.99    (32)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.99    (33)  all_58_5 = all_52_19
% 202.47/33.99    (34)  op(all_52_17, all_52_17) = e3
% 202.47/33.99    (35)  all_58_6 = all_52_5
% 202.47/33.99    (36)   ~ (all_52_17 = all_6_2)
% 202.47/33.99    (37)   ~ (all_52_19 = e2)
% 202.47/33.99    (38)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.99    (39)   ~ (all_52_17 = all_52_19)
% 202.47/33.99    (40)  op(all_6_2, e3) = all_6_1
% 202.47/33.99    (41)  all_58_4 = all_52_17
% 202.47/33.99  
% 202.47/33.99  Begin of proof
% 202.47/33.99  | 
% 202.47/33.99  | BETA: splitting (32) gives:
% 202.47/33.99  | 
% 202.47/33.99  | Case 1:
% 202.47/33.99  | | 
% 202.47/33.99  | |   (42)  all_58_0 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | COMBINE_EQS: (8), (42) imply:
% 202.47/33.99  | |   (43)  all_6_2 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | REDUCE: (14), (43) imply:
% 202.47/33.99  | |   (44)  $false
% 202.47/33.99  | | 
% 202.47/33.99  | | CLOSE: (44) is inconsistent.
% 202.47/33.99  | | 
% 202.47/33.99  | Case 2:
% 202.47/33.99  | | 
% 202.47/33.99  | |   (45)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/33.99  | | 
% 202.47/33.99  | | BETA: splitting (31) gives:
% 202.47/33.99  | | 
% 202.47/33.99  | | Case 1:
% 202.47/33.99  | | | 
% 202.47/33.99  | | |   (46)  all_58_9 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | COMBINE_EQS: (11), (46) imply:
% 202.47/33.99  | | |   (47)  all_52_25 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | SIMP: (47) implies:
% 202.47/33.99  | | |   (48)  all_52_25 = e3
% 202.47/33.99  | | | 
% 202.47/33.99  | | | REDUCE: (6), (48) imply:
% 202.47/33.99  | | |   (49)   ~ (all_52_17 = e3)
% 202.47/33.99  | | | 
% 202.47/33.99  | | | BETA: splitting (38) gives:
% 202.47/33.99  | | | 
% 202.47/33.99  | | | Case 1:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | |   (50)  all_58_4 = e3
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | REF_CLOSE: (41), (49), (50) are inconsistent by sub-proof #1302.
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | Case 2:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | |   (51)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | BETA: splitting (51) gives:
% 202.47/33.99  | | | | 
% 202.47/33.99  | | | | Case 1:
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | |   (52)  all_58_5 = e3
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | COMBINE_EQS: (33), (52) imply:
% 202.47/33.99  | | | | |   (53)  all_52_19 = e3
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | SIMP: (53) implies:
% 202.47/33.99  | | | | |   (54)  all_52_19 = e3
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | REDUCE: (5), (54) imply:
% 202.47/33.99  | | | | |   (55)   ~ (all_52_3 = e3)
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | REDUCE: (37), (54) imply:
% 202.47/33.99  | | | | |   (56)   ~ (e3 = e2)
% 202.47/33.99  | | | | | 
% 202.47/33.99  | | | | | REDUCE: (16), (54) imply:
% 202.47/33.99  | | | | |   (57)  op(e3, e3) = e2
% 202.47/33.99  | | | | | 
% 202.47/34.00  | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (15),
% 202.47/34.00  | | | | |            (17), (18), (19), (20), (21), (22), (25), (26), (28), (29),
% 202.47/34.00  | | | | |            (30), (32), (35), (36), (40), (41), (49), (55), (56), (57)
% 202.47/34.00  | | | | |            are inconsistent by sub-proof #454.
% 202.47/34.00  | | | | | 
% 202.47/34.00  | | | | Case 2:
% 202.47/34.00  | | | | | 
% 202.47/34.00  | | | | |   (58)  all_58_8 = e3 | all_58_14 = e3
% 202.47/34.00  | | | | | 
% 202.47/34.00  | | | | | REF_CLOSE: (1), (23), (24), (27), (58) are inconsistent by sub-proof
% 202.47/34.00  | | | | |            #1304.
% 202.47/34.00  | | | | | 
% 202.47/34.00  | | | | End of split
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | End of split
% 202.47/34.00  | | | 
% 202.47/34.00  | | Case 2:
% 202.47/34.00  | | | 
% 202.47/34.00  | | |   (59)   ~ (all_58_9 = e3)
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REDUCE: (11), (59) imply:
% 202.47/34.00  | | |   (60)   ~ (all_52_25 = e3)
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REF_CLOSE: (2), (3), (11), (25), (30), (34), (36), (41), (45), (60) are
% 202.47/34.00  | | |            inconsistent by sub-proof #1072.
% 202.47/34.00  | | | 
% 202.47/34.00  | | End of split
% 202.47/34.00  | | 
% 202.47/34.00  | End of split
% 202.47/34.00  | 
% 202.47/34.00  End of proof
% 202.47/34.00  
% 202.47/34.00  Sub-proof #413 shows that the following formulas are inconsistent:
% 202.47/34.00  ----------------------------------------------------------------
% 202.47/34.00    (1)  all_58_14 = all_52_23
% 202.47/34.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.00    (3)  all_58_1 = all_52_9
% 202.47/34.00    (4)  op(all_52_23, all_52_23) = e0
% 202.47/34.00    (5)   ~ (all_52_17 = all_52_25)
% 202.47/34.00    (6)  all_58_0 = all_6_2
% 202.47/34.00    (7)  all_58_13 = e3
% 202.47/34.00    (8)  all_58_9 = all_52_25
% 202.47/34.00    (9)   ~ (all_52_25 = all_14_2)
% 202.47/34.00    (10)  op(all_6_2, all_6_2) = all_52_0
% 202.47/34.00    (11)   ~ (all_52_7 = all_6_2)
% 202.47/34.00    (12)  op(e0, e0) = all_14_2
% 202.47/34.00    (13)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/34.00    (14)  all_58_12 = all_52_7
% 202.47/34.00    (15)  all_56_2 = all_52_17
% 202.47/34.00    (16)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.47/34.00    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.47/34.00    (18)   ~ (all_52_9 = e3)
% 202.47/34.00    (19)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.47/34.00    (20)   ~ (all_52_23 = all_14_2)
% 202.47/34.00    (21)   ~ (all_52_25 = all_6_2)
% 202.47/34.00    (22)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/34.00    (23)   ~ (all_52_9 = all_6_2)
% 202.47/34.00    (24)  op(e3, all_6_1) = e2
% 202.47/34.00    (25)  all_56_0 = all_6_2
% 202.47/34.00    (26)  op(e3, e3) = all_6_2
% 202.47/34.00    (27)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.00    (28)  all_56_3 = all_52_25
% 202.47/34.00    (29)  op(all_52_17, all_52_17) = e3
% 202.47/34.00    (30)   ~ (all_52_17 = all_6_2)
% 202.47/34.00    (31)   ~ (all_52_9 = all_52_17)
% 202.47/34.00    (32)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.00    (33)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.47/34.00    (34)  op(all_6_2, e3) = all_6_1
% 202.47/34.00    (35)  all_58_1 = e2
% 202.47/34.00    (36)  all_58_4 = all_52_17
% 202.47/34.00  
% 202.47/34.00  Begin of proof
% 202.47/34.00  | 
% 202.47/34.00  | COMBINE_EQS: (3), (35) imply:
% 202.47/34.00  |   (37)  all_52_9 = e2
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (31), (37) imply:
% 202.47/34.00  |   (38)   ~ (all_52_17 = e2)
% 202.47/34.00  | 
% 202.47/34.00  | SIMP: (38) implies:
% 202.47/34.00  |   (39)   ~ (all_52_17 = e2)
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (23), (37) imply:
% 202.47/34.00  |   (40)   ~ (all_6_2 = e2)
% 202.47/34.00  | 
% 202.47/34.00  | SIMP: (40) implies:
% 202.47/34.00  |   (41)   ~ (all_6_2 = e2)
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (18), (37) imply:
% 202.47/34.00  |   (42)   ~ (e3 = e2)
% 202.47/34.00  | 
% 202.47/34.00  | SIMP: (42) implies:
% 202.47/34.00  |   (43)   ~ (e3 = e2)
% 202.47/34.00  | 
% 202.47/34.00  | BETA: splitting (22) gives:
% 202.47/34.00  | 
% 202.47/34.00  | Case 1:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (44)  all_56_3 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | COMBINE_EQS: (28), (44) imply:
% 202.47/34.00  | |   (45)  all_52_25 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | SIMP: (45) implies:
% 202.47/34.00  | |   (46)  all_52_25 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (5), (46) imply:
% 202.47/34.00  | |   (47)   ~ (all_52_17 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (9), (46) imply:
% 202.47/34.00  | |   (48)   ~ (all_14_2 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | SIMP: (48) implies:
% 202.47/34.00  | |   (49)   ~ (all_14_2 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (21), (46) imply:
% 202.47/34.00  | |   (50)   ~ (all_6_2 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | SIMP: (50) implies:
% 202.47/34.00  | |   (51)   ~ (all_6_2 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | BETA: splitting (33) gives:
% 202.47/34.00  | | 
% 202.47/34.00  | | Case 1:
% 202.47/34.00  | | | 
% 202.47/34.00  | | |   (52)  all_56_0 = e3
% 202.47/34.00  | | | 
% 202.47/34.00  | | | COMBINE_EQS: (25), (52) imply:
% 202.47/34.00  | | |   (53)  all_6_2 = e3
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REDUCE: (51), (53) imply:
% 202.47/34.00  | | |   (54)  $false
% 202.47/34.00  | | | 
% 202.47/34.00  | | | CLOSE: (54) is inconsistent.
% 202.47/34.00  | | | 
% 202.47/34.00  | | Case 2:
% 202.47/34.00  | | | 
% 202.47/34.00  | | |   (55)   ~ (all_56_0 = e3)
% 202.47/34.00  | | |   (56)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.47/34.00  | | | 
% 202.47/34.00  | | | BETA: splitting (13) gives:
% 202.47/34.00  | | | 
% 202.47/34.00  | | | Case 1:
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | |   (57)  all_56_2 = e3
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | | COMBINE_EQS: (15), (57) imply:
% 202.47/34.00  | | | |   (58)  all_52_17 = e3
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | | REDUCE: (47), (58) imply:
% 202.47/34.00  | | | |   (59)  $false
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | | CLOSE: (59) is inconsistent.
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | Case 2:
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | |   (60)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | | REF_CLOSE: (1), (2), (4), (6), (7), (10), (11), (12), (14), (15), (16),
% 202.47/34.00  | | | |            (17), (19), (20), (25), (29), (30), (39), (41), (49), (51),
% 202.47/34.00  | | | |            (56), (60) are inconsistent by sub-proof #1062.
% 202.47/34.00  | | | | 
% 202.47/34.00  | | | End of split
% 202.47/34.00  | | | 
% 202.47/34.00  | | End of split
% 202.47/34.00  | | 
% 202.47/34.00  | Case 2:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (61)   ~ (all_56_3 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (28), (61) imply:
% 202.47/34.00  | |   (62)   ~ (all_52_25 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REF_CLOSE: (2), (3), (6), (8), (18), (24), (26), (27), (29), (30), (32),
% 202.47/34.00  | |            (34), (36), (43), (62) are inconsistent by sub-proof #446.
% 202.47/34.00  | | 
% 202.47/34.00  | End of split
% 202.47/34.00  | 
% 202.47/34.00  End of proof
% 202.47/34.00  
% 202.47/34.00  Sub-proof #414 shows that the following formulas are inconsistent:
% 202.47/34.00  ----------------------------------------------------------------
% 202.47/34.00    (1)  all_58_14 = all_52_23
% 202.47/34.00    (2)   ~ (e3 = e1)
% 202.47/34.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.00    (4)  all_58_1 = all_52_9
% 202.47/34.00    (5)  op(e2, e3) = all_52_3
% 202.47/34.00    (6)   ~ (all_52_3 = all_52_19)
% 202.47/34.00    (7)   ~ (all_52_3 = all_6_2)
% 202.47/34.00    (8)  all_58_0 = all_6_2
% 202.47/34.00    (9)  op(all_14_2, e0) = all_14_1
% 202.47/34.00    (10)  all_56_4 = all_52_3
% 202.47/34.00    (11)   ~ (all_10_0 = e3)
% 202.47/34.00    (12)  op(e3, e0) = all_52_25
% 202.47/34.00    (13)  op(all_52_5, all_52_5) = all_52_4
% 202.47/34.00    (14)  all_58_9 = all_52_25
% 202.47/34.00    (15)   ~ (all_52_29 = all_14_2)
% 202.47/34.00    (16)  op(e2, e2) = all_4_2
% 202.47/34.00    (17)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/34.00    (18)  all_58_7 = all_10_0
% 202.47/34.00    (19)  all_58_11 = all_52_29
% 202.47/34.00    (20)   ~ (all_52_25 = all_14_2)
% 202.47/34.00    (21)  op(all_10_2, all_10_2) = e1
% 202.47/34.00    (22)  op(all_52_9, all_52_9) = all_52_8
% 202.47/34.00    (23)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/34.00    (24)  op(all_52_19, all_52_19) = e2
% 202.47/34.00    (25)  all_58_12 = all_52_7
% 202.47/34.00    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.00    (27)   ~ (all_52_7 = all_14_2)
% 202.47/34.00    (28)  all_58_2 = all_52_3
% 202.47/34.00    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/34.00    (30)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/34.00    (31)   ~ (e2 = e0)
% 202.47/34.00    (32)  op(e3, e1) = all_52_17
% 202.47/34.00    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/34.00    (34)  all_58_8 = all_10_2
% 202.47/34.00    (35)   ~ (all_52_5 = all_10_2)
% 202.47/34.00    (36)   ~ (all_52_23 = all_14_2)
% 202.47/34.00    (37)   ~ (all_52_25 = all_6_2)
% 202.47/34.00    (38)  op(e3, all_6_1) = e2
% 202.47/34.00    (39)  op(e3, e3) = all_6_2
% 202.47/34.00    (40)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.00    (41)  op(all_14_2, all_14_2) = all_52_30
% 202.47/34.00    (42)  all_58_5 = all_52_19
% 202.47/34.00    (43)  op(all_52_17, all_52_17) = e3
% 202.47/34.00    (44)  all_58_6 = all_52_5
% 202.47/34.00    (45)  op(all_10_2, e1) = e2
% 202.47/34.00    (46)   ~ (all_52_17 = all_6_2)
% 202.47/34.00    (47)   ~ (e3 = e2)
% 202.47/34.00    (48)   ~ (all_52_9 = all_52_17)
% 202.47/34.00    (49)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.00    (50)   ~ (all_52_3 = all_4_2)
% 202.47/34.00    (51)  op(all_6_2, e3) = all_6_1
% 202.47/34.00    (52)  all_58_4 = all_52_17
% 202.47/34.00    (53)  all_14_2 = e3
% 202.47/34.00  
% 202.47/34.00  Begin of proof
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (27), (53) imply:
% 202.47/34.00  |   (54)   ~ (all_52_7 = e3)
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (36), (53) imply:
% 202.47/34.00  |   (55)   ~ (all_52_23 = e3)
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (20), (53) imply:
% 202.47/34.00  |   (56)   ~ (all_52_25 = e3)
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (15), (53) imply:
% 202.47/34.00  |   (57)   ~ (all_52_29 = e3)
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (41), (53) imply:
% 202.47/34.00  |   (58)  op(e3, e3) = all_52_30
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (9), (53) imply:
% 202.47/34.00  |   (59)  op(e3, e0) = all_14_1
% 202.47/34.00  | 
% 202.47/34.00  | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 202.47/34.00  |              with (12), (59) gives:
% 202.47/34.00  |   (60)  all_52_25 = all_14_1
% 202.47/34.00  | 
% 202.47/34.00  | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3, simplifying
% 202.47/34.00  |              with (39), (58) gives:
% 202.47/34.00  |   (61)  all_52_30 = all_6_2
% 202.47/34.00  | 
% 202.47/34.00  | REDUCE: (37), (60) imply:
% 202.47/34.00  |   (62)   ~ (all_14_1 = all_6_2)
% 202.47/34.00  | 
% 202.47/34.00  | BETA: splitting (26) gives:
% 202.47/34.00  | 
% 202.47/34.00  | Case 1:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (63)  all_58_6 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | COMBINE_EQS: (44), (63) imply:
% 202.47/34.00  | |   (64)  all_52_5 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | SIMP: (64) implies:
% 202.47/34.00  | |   (65)  all_52_5 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (35), (65) imply:
% 202.47/34.00  | |   (66)   ~ (all_10_2 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | SIMP: (66) implies:
% 202.47/34.00  | |   (67)   ~ (all_10_2 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (13), (65) imply:
% 202.47/34.00  | |   (68)  op(e3, e3) = all_52_4
% 202.47/34.00  | | 
% 202.47/34.00  | | GROUND_INST: instantiating (3) with all_6_2, all_52_4, e3, e3, simplifying
% 202.47/34.00  | |              with (39), (68) gives:
% 202.47/34.00  | |   (69)  all_52_4 = all_6_2
% 202.47/34.00  | | 
% 202.47/34.00  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (14), (17), (22), (23),
% 202.47/34.00  | |            (24), (28), (30), (31), (32), (33), (34), (38), (39), (40), (42),
% 202.47/34.00  | |            (43), (46), (47), (48), (49), (51), (52), (55), (56), (59), (62),
% 202.47/34.00  | |            (67) are inconsistent by sub-proof #416.
% 202.47/34.00  | | 
% 202.47/34.00  | Case 2:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (70)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | REF_CLOSE: (2), (3), (8), (11), (16), (18), (19), (21), (25), (28), (29),
% 202.47/34.00  | |            (32), (34), (35), (39), (43), (44), (45), (50), (54), (57), (70)
% 202.47/34.00  | |            are inconsistent by sub-proof #415.
% 202.47/34.00  | | 
% 202.47/34.00  | End of split
% 202.47/34.00  | 
% 202.47/34.00  End of proof
% 202.47/34.00  
% 202.47/34.00  Sub-proof #415 shows that the following formulas are inconsistent:
% 202.47/34.00  ----------------------------------------------------------------
% 202.47/34.00    (1)   ~ (e3 = e1)
% 202.47/34.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.00    (3)  all_58_0 = all_6_2
% 202.47/34.00    (4)   ~ (all_10_0 = e3)
% 202.47/34.00    (5)  op(e2, e2) = all_4_2
% 202.47/34.00    (6)  all_58_7 = all_10_0
% 202.47/34.00    (7)  all_58_11 = all_52_29
% 202.47/34.00    (8)  op(all_10_2, all_10_2) = e1
% 202.47/34.00    (9)  all_58_12 = all_52_7
% 202.47/34.00    (10)   ~ (all_52_7 = e3)
% 202.47/34.00    (11)  all_58_2 = all_52_3
% 202.47/34.00    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/34.00    (13)   ~ (all_52_29 = e3)
% 202.47/34.00    (14)  op(e3, e1) = all_52_17
% 202.47/34.00    (15)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.00    (16)  all_58_8 = all_10_2
% 202.47/34.00    (17)   ~ (all_52_5 = all_10_2)
% 202.47/34.00    (18)  op(e3, e3) = all_6_2
% 202.47/34.00    (19)  op(all_52_17, all_52_17) = e3
% 202.47/34.00    (20)  all_58_6 = all_52_5
% 202.47/34.00    (21)  op(all_10_2, e1) = e2
% 202.47/34.00    (22)   ~ (all_52_3 = all_4_2)
% 202.47/34.00  
% 202.47/34.00  Begin of proof
% 202.47/34.00  | 
% 202.47/34.00  | BETA: splitting (15) gives:
% 202.47/34.00  | 
% 202.47/34.00  | Case 1:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (23)  all_58_7 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | COMBINE_EQS: (6), (23) imply:
% 202.47/34.00  | |   (24)  all_10_0 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (4), (24) imply:
% 202.47/34.00  | |   (25)  $false
% 202.47/34.00  | | 
% 202.47/34.00  | | CLOSE: (25) is inconsistent.
% 202.47/34.00  | | 
% 202.47/34.00  | Case 2:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (26)  all_58_8 = e3 | all_58_11 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | BETA: splitting (26) gives:
% 202.47/34.00  | | 
% 202.47/34.00  | | Case 1:
% 202.47/34.00  | | | 
% 202.47/34.00  | | |   (27)  all_58_8 = e3
% 202.47/34.00  | | | 
% 202.47/34.00  | | | COMBINE_EQS: (16), (27) imply:
% 202.47/34.00  | | |   (28)  all_10_2 = e3
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REDUCE: (17), (28) imply:
% 202.47/34.00  | | |   (29)   ~ (all_52_5 = e3)
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REDUCE: (8), (28) imply:
% 202.47/34.00  | | |   (30)  op(e3, e3) = e1
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REDUCE: (21), (28) imply:
% 202.47/34.00  | | |   (31)  op(e3, e1) = e2
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REF_CLOSE: (1), (2), (3), (5), (9), (10), (11), (12), (14), (18), (19),
% 202.47/34.00  | | |            (20), (22), (29), (30), (31) are inconsistent by sub-proof
% 202.47/34.00  | | |            #1085.
% 202.47/34.00  | | | 
% 202.47/34.00  | | Case 2:
% 202.47/34.00  | | | 
% 202.47/34.00  | | |   (32)  all_58_11 = e3
% 202.47/34.00  | | | 
% 202.47/34.00  | | | REF_CLOSE: (7), (13), (32) are inconsistent by sub-proof #1323.
% 202.47/34.00  | | | 
% 202.47/34.00  | | End of split
% 202.47/34.00  | | 
% 202.47/34.00  | End of split
% 202.47/34.00  | 
% 202.47/34.00  End of proof
% 202.47/34.00  
% 202.47/34.00  Sub-proof #416 shows that the following formulas are inconsistent:
% 202.47/34.00  ----------------------------------------------------------------
% 202.47/34.00    (1)  all_58_14 = all_52_23
% 202.47/34.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.00    (3)  all_58_1 = all_52_9
% 202.47/34.00    (4)  op(e2, e3) = all_52_3
% 202.47/34.00    (5)   ~ (all_52_3 = all_52_19)
% 202.47/34.00    (6)   ~ (all_52_3 = all_6_2)
% 202.47/34.00    (7)  all_58_0 = all_6_2
% 202.47/34.00    (8)  all_56_4 = all_52_3
% 202.47/34.00    (9)  all_58_9 = all_52_25
% 202.47/34.00    (10)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/34.00    (11)  op(all_52_9, all_52_9) = all_52_8
% 202.47/34.00    (12)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/34.00    (13)  op(all_52_19, all_52_19) = e2
% 202.47/34.00    (14)  all_58_2 = all_52_3
% 202.47/34.00    (15)   ~ (all_52_25 = e3)
% 202.47/34.00    (16)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/34.00    (17)   ~ (e2 = e0)
% 202.47/34.00    (18)   ~ (all_14_1 = all_6_2)
% 202.47/34.00    (19)   ~ (all_52_23 = e3)
% 202.47/34.00    (20)   ~ (all_10_2 = e3)
% 202.47/34.00    (21)  op(e3, e1) = all_52_17
% 202.47/34.00    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/34.00    (23)  all_58_8 = all_10_2
% 202.47/34.00    (24)  op(e3, all_6_1) = e2
% 202.47/34.00    (25)  op(e3, e3) = all_6_2
% 202.47/34.00    (26)  op(e3, e0) = all_14_1
% 202.47/34.00    (27)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.00    (28)  all_58_5 = all_52_19
% 202.47/34.00    (29)  op(all_52_17, all_52_17) = e3
% 202.47/34.00    (30)   ~ (all_52_17 = all_6_2)
% 202.47/34.00    (31)   ~ (e3 = e2)
% 202.47/34.00    (32)   ~ (all_52_9 = all_52_17)
% 202.47/34.00    (33)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.00    (34)  op(all_6_2, e3) = all_6_1
% 202.47/34.00    (35)  all_58_4 = all_52_17
% 202.47/34.00  
% 202.47/34.00  Begin of proof
% 202.47/34.00  | 
% 202.47/34.00  | BETA: splitting (22) gives:
% 202.47/34.00  | 
% 202.47/34.00  | Case 1:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (36)  all_58_1 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | COMBINE_EQS: (3), (36) imply:
% 202.47/34.00  | |   (37)  all_52_9 = e3
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (32), (37) imply:
% 202.47/34.00  | |   (38)   ~ (all_52_17 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | SIMP: (38) implies:
% 202.47/34.00  | |   (39)   ~ (all_52_17 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (11), (37) imply:
% 202.47/34.00  | |   (40)  op(e3, e3) = all_52_8
% 202.47/34.00  | | 
% 202.47/34.00  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (16),
% 202.47/34.00  | |            (17), (18), (19), (20), (21), (23), (24), (25), (26), (28), (30),
% 202.47/34.00  | |            (33), (34), (35), (39), (40) are inconsistent by sub-proof #448.
% 202.47/34.00  | | 
% 202.47/34.00  | Case 2:
% 202.47/34.00  | | 
% 202.47/34.00  | |   (41)   ~ (all_58_1 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REDUCE: (3), (41) imply:
% 202.47/34.00  | |   (42)   ~ (all_52_9 = e3)
% 202.47/34.00  | | 
% 202.47/34.00  | | REF_CLOSE: (2), (3), (7), (9), (15), (24), (25), (27), (29), (30), (31),
% 202.47/34.00  | |            (33), (34), (35), (42) are inconsistent by sub-proof #446.
% 202.47/34.00  | | 
% 202.47/34.00  | End of split
% 202.47/34.00  | 
% 202.47/34.00  End of proof
% 202.47/34.00  
% 202.47/34.00  Sub-proof #417 shows that the following formulas are inconsistent:
% 202.47/34.00  ----------------------------------------------------------------
% 202.47/34.00    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/34.00    (2)   ~ (all_52_15 = all_52_23)
% 202.47/34.00    (3)   ~ (all_52_25 = all_52_27)
% 202.47/34.00    (4)  all_58_14 = all_52_23
% 202.47/34.00    (5)   ~ (e3 = e1)
% 202.47/34.00    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.47/34.00    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.00    (8)   ~ (all_52_5 = all_52_13)
% 202.47/34.00    (9)  all_58_1 = all_52_9
% 202.47/34.00    (10)   ~ (e3 = e0)
% 202.47/34.00    (11)  op(e2, e3) = all_52_3
% 202.47/34.00    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.00    (13)  op(e0, e2) = all_52_15
% 202.47/34.00    (14)   ~ (all_52_7 = all_52_15)
% 202.47/34.00    (15)   ~ (all_52_3 = all_52_19)
% 202.47/34.00    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.47/34.00    (17)   ~ (all_52_17 = all_52_25)
% 202.47/34.00    (18)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/34.00    (19)   ~ (all_52_3 = all_6_2)
% 202.47/34.00    (20)  all_44_2 = all_6_2
% 202.47/34.00    (21)  all_58_0 = all_6_2
% 202.47/34.00    (22)  all_56_4 = all_52_3
% 202.47/34.00    (23)   ~ (all_52_17 = all_10_2)
% 202.47/34.00    (24)   ~ (all_10_0 = e3)
% 202.47/34.00    (25)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.47/34.00    (26)  all_40_2 = all_10_2
% 202.47/34.00    (27)  op(e3, e0) = all_52_25
% 202.47/34.00    (28)  op(all_52_5, all_52_5) = all_52_4
% 202.47/34.00    (29)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.47/34.00    (30)  op(all_52_19, all_52_19) = all_52_18
% 202.47/34.00    (31)   ~ (all_52_27 = all_52_29)
% 202.47/34.00    (32)  all_58_13 = all_52_15
% 202.47/34.00    (33)  op(all_10_2, all_10_2) = all_52_20
% 202.47/34.00    (34)  all_58_9 = all_52_25
% 202.47/34.00    (35)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.00    (36)   ~ (all_52_29 = all_14_2)
% 202.47/34.00    (37)  op(all_52_27, all_52_27) = all_52_26
% 202.47/34.00    (38)  op(e1, e3) = all_52_5
% 202.47/34.00    (39)  op(e2, e2) = all_4_2
% 202.47/34.00    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/34.00    (41)  all_58_7 = all_10_0
% 202.47/34.00    (42)   ~ (all_52_3 = all_52_5)
% 202.47/34.00    (43)   ~ (all_4_1 = e3)
% 202.47/34.00    (44)  all_58_11 = all_52_29
% 202.47/34.00    (45)   ~ (all_52_25 = all_14_2)
% 202.47/34.00    (46)   ~ (all_52_9 = all_52_15)
% 202.47/34.00    (47)   ~ (all_52_3 = all_52_27)
% 202.47/34.00    (48)  op(all_6_2, all_6_2) = all_52_0
% 202.47/34.00    (49)   ~ (all_52_7 = all_6_2)
% 202.47/34.00    (50)  op(e0, e0) = all_14_2
% 202.47/34.00    (51)  all_56_15 = all_14_2
% 202.47/34.00    (52)   ~ (all_52_15 = e0)
% 202.47/34.00    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.47/34.00    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.47/34.00    (55)  all_58_15 = e0
% 202.47/34.00    (56)  all_56_11 = all_52_29
% 202.47/34.00    (57)   ~ (all_10_0 = e2)
% 202.47/34.00    (58)   ~ (all_4_1 = e1)
% 202.47/34.00    (59)   ~ (all_52_25 = e0)
% 202.47/34.00    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/34.00    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/34.00    (62)  all_56_9 = all_52_13
% 202.47/34.00    (63)   ~ (e2 = e1)
% 202.47/34.00    (64)   ~ (all_52_13 = all_10_2)
% 202.47/34.00    (65)  op(e0, e0) = e0
% 202.47/34.00    (66)  all_58_10 = all_52_27
% 202.47/34.00    (67)  all_56_8 = all_52_5
% 202.47/34.00    (68)  op(all_52_9, all_52_9) = all_52_8
% 202.47/34.00    (69)  op(all_52_15, all_52_15) = all_52_14
% 202.47/34.00    (70)  all_56_9 = all_10_0
% 202.47/34.00    (71)   ~ (all_52_25 = all_52_29)
% 202.47/34.00    (72)   ~ (all_52_29 = all_10_2)
% 202.47/34.00    (73)  all_58_7 = all_52_13
% 202.47/34.00    (74)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.47/34.00    (75)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.47/34.00    (76)   ~ (all_52_5 = all_52_7)
% 202.47/34.00    (77)  all_58_12 = all_52_7
% 202.47/34.00    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.00    (79)  op(e2, e1) = all_52_19
% 202.47/34.00    (80)   ~ (all_52_7 = all_14_2)
% 202.47/34.00    (81)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/34.00    (82)  all_58_2 = all_52_3
% 202.47/34.00    (83)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.47/34.00    (84)  all_56_2 = all_52_17
% 202.47/34.00    (85)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.47/34.00    (86)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/34.00    (87)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.47/34.00    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/34.00    (89)  all_56_7 = all_52_27
% 202.47/34.00    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/34.00    (91)   ~ (e2 = e0)
% 202.47/34.00    (92)  op(all_4_2, e2) = all_4_1
% 202.47/34.00    (93)   ~ (all_52_5 = all_52_29)
% 202.47/34.00    (94)   ~ (all_52_29 = e0)
% 202.47/34.00    (95)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/34.00    (96)  all_56_6 = all_52_19
% 202.47/34.00    (97)   ~ (all_52_15 = all_14_2)
% 202.47/34.00    (98)   ~ (all_52_19 = all_52_27)
% 202.47/34.00    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/34.00    (100)   ~ (all_52_13 = all_4_2)
% 202.47/34.00    (101)  op(e3, e1) = all_52_17
% 202.47/34.00    (102)  op(e0, e3) = all_52_7
% 202.47/34.00    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/34.00    (104)   ~ (all_52_9 = all_52_25)
% 202.47/34.00    (105)  all_58_15 = all_14_2
% 202.47/34.00    (106)   ~ (all_52_19 = all_10_2)
% 202.47/34.00    (107)  op(all_52_23, all_52_23) = all_52_22
% 202.47/34.00    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.47/34.00    (109)   ~ (all_10_0 = all_10_2)
% 202.47/34.00    (110)  all_58_8 = all_10_2
% 202.47/34.00    (111)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.47/34.00    (112)   ~ (all_52_23 = e0)
% 202.47/34.00    (113)   ~ (all_52_5 = all_10_2)
% 202.47/34.00    (114)  op(all_52_29, all_52_29) = all_52_28
% 202.47/34.00    (115)  all_56_12 = all_52_7
% 202.47/34.00    (116)  op(all_52_17, all_52_17) = all_52_16
% 202.47/34.00    (117)  all_8_2 = all_6_2
% 202.47/34.00    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.47/34.00    (119)   ~ (all_52_25 = all_6_2)
% 202.47/34.00    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/34.00    (121)   ~ (all_52_9 = all_4_2)
% 202.47/34.00    (122)   ~ (all_52_5 = all_6_2)
% 202.47/34.00    (123)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.47/34.00    (124)   ~ (all_52_9 = all_6_2)
% 202.47/34.00    (125)   ~ (all_52_13 = all_52_15)
% 202.47/34.00    (126)  op(e3, all_6_1) = e2
% 202.47/34.00    (127)   ~ (all_52_27 = e0)
% 202.47/34.00    (128)  all_56_0 = all_6_2
% 202.47/34.00    (129)  op(e3, e3) = all_6_2
% 202.47/34.00    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/34.00    (131)   ~ (all_52_27 = all_14_2)
% 202.47/34.00    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.00    (133)  all_56_14 = all_52_23
% 202.47/34.00    (134)   ~ (all_52_29 = all_10_0)
% 202.47/34.00    (135)  op(all_4_2, all_4_2) = all_52_10
% 202.47/34.00    (136)  all_40_0 = all_10_0
% 202.47/34.00    (137)  all_56_3 = all_52_25
% 202.47/34.00    (138)   ~ (all_52_3 = all_52_7)
% 202.47/34.00    (139)  op(all_14_2, all_14_2) = all_52_30
% 202.47/34.00    (140)  all_58_5 = all_52_19
% 202.47/34.00    (141)  all_56_1 = all_52_9
% 202.47/34.00    (142)   ~ (all_52_15 = all_4_2)
% 202.47/34.00    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.47/34.00           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.47/34.00           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.47/34.00           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.47/34.00    (144)   ~ (all_52_27 = all_4_2)
% 202.47/34.00    (145)  all_58_6 = all_52_5
% 202.47/34.00    (146)  op(all_10_2, e1) = e2
% 202.47/34.00    (147)  op(e3, e2) = all_52_9
% 202.47/34.01    (148)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/34.01    (149)   ~ (all_52_17 = all_6_2)
% 202.47/34.01    (150)   ~ (e1 = e0)
% 202.47/34.01    (151)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.47/34.01    (152)   ~ (e3 = e2)
% 202.47/34.01    (153)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.47/34.01    (154)  all_44_1 = all_6_1
% 202.47/34.01    (155)   ~ (all_52_9 = all_52_17)
% 202.47/34.01    (156)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.01    (157)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/34.01    (158)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.47/34.01    (159)  op(all_10_0, all_10_0) = all_52_12
% 202.47/34.01    (160)  op(e1, e1) = all_10_2
% 202.47/34.01    (161)   ~ (all_52_23 = all_10_2)
% 202.47/34.01    (162)   ~ (all_52_7 = all_52_23)
% 202.47/34.01    (163)   ~ (all_52_17 = all_52_19)
% 202.47/34.01    (164)   ~ (all_52_5 = all_10_0)
% 202.47/34.01    (165)  all_58_3 = all_4_2
% 202.47/34.01    (166)  all_56_13 = all_52_15
% 202.47/34.01    (167)   ~ (all_52_3 = all_4_2)
% 202.47/34.01    (168)   ~ (all_52_9 = all_10_0)
% 202.47/34.01    (169)   ~ (all_52_19 = all_4_2)
% 202.47/34.01    (170)   ~ (all_52_17 = all_52_23)
% 202.47/34.01    (171)  all_8_1 = all_6_1
% 202.47/34.01    (172)  op(all_6_2, e3) = all_6_1
% 202.47/34.01    (173)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.47/34.01    (174)   ~ (all_52_13 = all_52_29)
% 202.47/34.01    (175)  all_58_4 = all_52_17
% 202.47/34.01    (176)   ~ (all_52_7 = e0)
% 202.47/34.01    (177)  op(all_52_25, all_52_25) = all_52_24
% 202.47/34.01  
% 202.47/34.01  Begin of proof
% 202.47/34.01  | 
% 202.47/34.01  | BETA: splitting (143) gives:
% 202.47/34.01  | 
% 202.47/34.01  | Case 1:
% 202.47/34.01  | | 
% 202.47/34.01  | |   (178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.47/34.01  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.47/34.01  | | 
% 202.47/34.01  | | REF_CLOSE: (1), (6), (7), (9), (12), (14), (16), (18), (21), (24), (28),
% 202.47/34.01  | |            (32), (34), (39), (41), (45), (48), (49), (50), (51), (53), (57),
% 202.47/34.01  | |            (58), (60), (68), (69), (70), (77), (80), (82), (86), (87), (91),
% 202.47/34.01  | |            (92), (97), (102), (103), (109), (111), (113), (115), (116),
% 202.47/34.01  | |            (117), (121), (124), (126), (128), (129), (132), (135), (141),
% 202.47/34.01  | |            (142), (145), (147), (148), (152), (153), (155), (156), (158),
% 202.47/34.01  | |            (159), (160), (165), (166), (167), (168), (171), (172), (175),
% 202.47/34.01  | |            (178) are inconsistent by sub-proof #429.
% 202.47/34.01  | | 
% 202.47/34.01  | Case 2:
% 202.47/34.01  | | 
% 202.47/34.01  | |   (179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 202.47/34.01  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.47/34.01  | |            e0)
% 202.47/34.01  | | 
% 202.47/34.01  | | BETA: splitting (179) gives:
% 202.47/34.01  | | 
% 202.47/34.01  | | Case 1:
% 202.47/34.01  | | | 
% 202.47/34.01  | | |   (180)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 202.47/34.01  | | | 
% 202.47/34.01  | | | ALPHA: (180) implies:
% 202.47/34.01  | | |   (181)  all_52_22 = e0
% 202.47/34.01  | | |   (182)  all_52_20 = e1
% 202.47/34.01  | | |   (183)  all_52_18 = e2
% 202.47/34.01  | | |   (184)  all_52_16 = e3
% 202.47/34.01  | | | 
% 202.47/34.01  | | | REDUCE: (116), (184) imply:
% 202.47/34.01  | | |   (185)  op(all_52_17, all_52_17) = e3
% 202.47/34.01  | | | 
% 202.47/34.01  | | | REDUCE: (30), (183) imply:
% 202.47/34.01  | | |   (186)  op(all_52_19, all_52_19) = e2
% 202.47/34.01  | | | 
% 202.47/34.01  | | | REDUCE: (107), (181) imply:
% 202.47/34.01  | | |   (187)  op(all_52_23, all_52_23) = e0
% 202.47/34.01  | | | 
% 202.47/34.01  | | | REDUCE: (33), (182) imply:
% 202.47/34.01  | | |   (188)  op(all_10_2, all_10_2) = e1
% 202.47/34.01  | | | 
% 202.47/34.01  | | | BETA: splitting (29) gives:
% 202.47/34.01  | | | 
% 202.47/34.01  | | | Case 1:
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | |   (189)  all_56_7 = e3
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | COMBINE_EQS: (89), (189) imply:
% 202.47/34.01  | | | |   (190)  all_52_27 = e3
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | SIMP: (190) implies:
% 202.47/34.01  | | | |   (191)  all_52_27 = e3
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | COMBINE_EQS: (66), (191) imply:
% 202.47/34.01  | | | |   (192)  all_58_10 = e3
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REDUCE: (98), (191) imply:
% 202.47/34.01  | | | |   (193)   ~ (all_52_19 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REDUCE: (3), (191) imply:
% 202.47/34.01  | | | |   (194)   ~ (all_52_25 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REDUCE: (31), (191) imply:
% 202.47/34.01  | | | |   (195)   ~ (all_52_29 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | SIMP: (195) implies:
% 202.47/34.01  | | | |   (196)   ~ (all_52_29 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REDUCE: (144), (191) imply:
% 202.47/34.01  | | | |   (197)   ~ (all_4_2 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | SIMP: (197) implies:
% 202.47/34.01  | | | |   (198)   ~ (all_4_2 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REDUCE: (37), (191) imply:
% 202.47/34.01  | | | |   (199)  op(e3, e3) = all_52_26
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REF_CLOSE: (4), (5), (7), (9), (18), (21), (24), (26), (28), (34), (35),
% 202.47/34.01  | | | |            (39), (41), (44), (54), (55), (56), (57), (59), (63), (68),
% 202.47/34.01  | | | |            (70), (71), (78), (79), (81), (85), (93), (94), (99), (101),
% 202.47/34.01  | | | |            (106), (110), (113), (114), (120), (121), (122), (129),
% 202.47/34.01  | | | |            (132), (134), (136), (137), (140), (145), (146), (149),
% 202.47/34.01  | | | |            (150), (152), (156), (175), (185), (187), (192), (193),
% 202.47/34.01  | | | |            (194), (196), (198), (199) are inconsistent by sub-proof
% 202.47/34.01  | | | |            #424.
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | Case 2:
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | |   (200)   ~ (all_56_7 = e3)
% 202.47/34.01  | | | |   (201)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | REDUCE: (89), (200) imply:
% 202.47/34.01  | | | |   (202)   ~ (all_52_27 = e3)
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | BETA: splitting (130) gives:
% 202.47/34.01  | | | | 
% 202.47/34.01  | | | | Case 1:
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | |   (203)  all_58_9 = e3
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | COMBINE_EQS: (34), (203) imply:
% 202.47/34.01  | | | | |   (204)  all_52_25 = e3
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | SIMP: (204) implies:
% 202.47/34.01  | | | | |   (205)  all_52_25 = e3
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | REDUCE: (104), (205) imply:
% 202.47/34.01  | | | | |   (206)   ~ (all_52_9 = e3)
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | REDUCE: (17), (205) imply:
% 202.47/34.01  | | | | |   (207)   ~ (all_52_17 = e3)
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | REDUCE: (3), (205) imply:
% 202.47/34.01  | | | | |   (208)   ~ (all_52_27 = e3)
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | REDUCE: (71), (205) imply:
% 202.47/34.01  | | | | |   (209)   ~ (all_52_29 = e3)
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | SIMP: (209) implies:
% 202.47/34.01  | | | | |   (210)   ~ (all_52_29 = e3)
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | REDUCE: (177), (205) imply:
% 202.47/34.01  | | | | |   (211)  op(e3, e3) = all_52_24
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 202.47/34.01  | | | | |              simplifying with (129), (211) gives:
% 202.47/34.01  | | | | |   (212)  all_52_24 = all_6_2
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | BETA: splitting (99) gives:
% 202.47/34.01  | | | | | 
% 202.47/34.01  | | | | | Case 1:
% 202.47/34.01  | | | | | | 
% 202.47/34.01  | | | | | |   (213)  all_56_11 = e3
% 202.47/34.01  | | | | | | 
% 202.47/34.01  | | | | | | REF_CLOSE: (56), (210), (213) are inconsistent by sub-proof #1028.
% 202.47/34.01  | | | | | | 
% 202.47/34.01  | | | | | Case 2:
% 202.47/34.01  | | | | | | 
% 202.47/34.01  | | | | | |   (214)   ~ (all_56_11 = e3)
% 202.47/34.01  | | | | | |   (215)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/34.01  | | | | | | 
% 202.47/34.01  | | | | | | BETA: splitting (78) gives:
% 202.47/34.01  | | | | | | 
% 202.47/34.01  | | | | | | Case 1:
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | |   (216)  all_58_6 = e3
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | COMBINE_EQS: (145), (216) imply:
% 202.47/34.01  | | | | | | |   (217)  all_52_5 = e3
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | SIMP: (217) implies:
% 202.47/34.01  | | | | | | |   (218)  all_52_5 = e3
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | REDUCE: (42), (218) imply:
% 202.47/34.01  | | | | | | |   (219)   ~ (all_52_3 = e3)
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | REDUCE: (76), (218) imply:
% 202.47/34.01  | | | | | | |   (220)   ~ (all_52_7 = e3)
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | SIMP: (220) implies:
% 202.47/34.01  | | | | | | |   (221)   ~ (all_52_7 = e3)
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | REDUCE: (28), (218) imply:
% 202.47/34.01  | | | | | | |   (222)  op(e3, e3) = all_52_4
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | REDUCE: (38), (218) imply:
% 202.47/34.01  | | | | | | |   (223)  op(e1, e3) = e3
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_4, e3, e3,
% 202.47/34.01  | | | | | | |              simplifying with (129), (222) gives:
% 202.47/34.01  | | | | | | |   (224)  all_52_4 = all_6_2
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | BETA: splitting (12) gives:
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | |   (225)  all_56_12 = e3
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | REF_CLOSE: (115), (221), (225) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | |            #1383.
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | |   (226)   ~ (all_56_12 = e3)
% 202.47/34.01  | | | | | | | |   (227)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | BETA: splitting (90) gives:
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | |   (228)  all_56_4 = e3
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | REF_CLOSE: (22), (219), (228) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | |            #1340.
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | |   (229)   ~ (all_56_4 = e3)
% 202.47/34.01  | | | | | | | | |   (230)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | BETA: splitting (40) gives:
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | |   (231)  all_58_0 = e0
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | COMBINE_EQS: (21), (231) imply:
% 202.47/34.01  | | | | | | | | | |   (232)  all_6_2 = e0
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | COMBINE_EQS: (117), (232) imply:
% 202.47/34.01  | | | | | | | | | |   (233)  all_8_2 = e0
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | REDUCE: (48), (232) imply:
% 202.47/34.01  | | | | | | | | | |   (234)  op(e0, e0) = all_52_0
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | REDUCE: (172), (232) imply:
% 202.47/34.01  | | | | | | | | | |   (235)  op(e0, e3) = all_6_1
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | BETA: splitting (1) gives:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | |   (236)   ~ (all_8_1 = e1)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (171), (236) imply:
% 202.47/34.01  | | | | | | | | | | |   (237)   ~ (all_6_1 = e1)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, all_52_0, e0, e0,
% 202.47/34.01  | | | | | | | | | | |              simplifying with (65), (234) gives:
% 202.47/34.01  | | | | | | | | | | |   (238)  all_52_0 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_7, all_6_1, e3, e0,
% 202.47/34.01  | | | | | | | | | | |              simplifying with (102), (235) gives:
% 202.47/34.01  | | | | | | | | | | |   (239)  all_52_7 = all_6_1
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | COMBINE_EQS: (115), (239) imply:
% 202.47/34.01  | | | | | | | | | | |   (240)  all_56_12 = all_6_1
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (138), (239) imply:
% 202.47/34.01  | | | | | | | | | | |   (241)   ~ (all_52_3 = all_6_1)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (176), (239) imply:
% 202.47/34.01  | | | | | | | | | | |   (242)   ~ (all_6_1 = e0)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | BETA: splitting (227) gives:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (243)  all_56_12 = e2
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | COMBINE_EQS: (240), (243) imply:
% 202.47/34.01  | | | | | | | | | | | |   (244)  all_6_1 = e2
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | SIMP: (244) implies:
% 202.47/34.01  | | | | | | | | | | | |   (245)  all_6_1 = e2
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REDUCE: (241), (245) imply:
% 202.47/34.01  | | | | | | | | | | | |   (246)   ~ (all_52_3 = e2)
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | BETA: splitting (88) gives:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (247)  all_58_0 = e1
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REF_CLOSE: (150), (231), (247) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | |            #847.
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (248)   ~ (all_58_0 = e1)
% 202.47/34.01  | | | | | | | | | | | | |   (249)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REDUCE: (231), (248) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (250)   ~ (e1 = e0)
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | BETA: splitting (230) gives:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | |   (251)  all_56_4 = e2
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | REF_CLOSE: (22), (246), (251) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | |            #1155.
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | |   (252)  all_56_4 = e1 | all_56_4 = e0
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | |   (253)  all_56_4 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | COMBINE_EQS: (22), (253) imply:
% 202.47/34.01  | | | | | | | | | | | | | | |   (254)  all_52_3 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | SIMP: (254) implies:
% 202.47/34.01  | | | | | | | | | | | | | | |   (255)  all_52_3 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | REDUCE: (47), (255) imply:
% 202.47/34.01  | | | | | | | | | | | | | | |   (256)   ~ (all_52_27 = e1)
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | SIMP: (256) implies:
% 202.47/34.01  | | | | | | | | | | | | | | |   (257)   ~ (all_52_27 = e1)
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | |   (258)  all_56_7 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (258) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (259)  all_52_27 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | REDUCE: (31), (259) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (260)   ~ (all_52_29 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | SIMP: (260) implies:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (261)   ~ (all_52_29 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | REDUCE: (202), (259) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (262)   ~ (e3 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (263)  all_56_11 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (261), (263) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | | | | |            #1024.
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (264)  all_56_11 = e1 | all_56_11 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (35), (41), (44), (56), (57), (63), (79),
% 202.47/34.01  | | | | | | | | | | | | | | | | |            (94), (106), (110), (146), (152), (216), (264) are
% 202.47/34.01  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #425.
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | |   (265)  all_56_7 = e1 | all_56_7 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | REF_CLOSE: (89), (127), (257), (265) are inconsistent by
% 202.47/34.01  | | | | | | | | | | | | | | | |            sub-proof #902.
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | |   (266)  all_56_4 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | COMBINE_EQS: (22), (266) imply:
% 202.47/34.01  | | | | | | | | | | | | | | |   (267)  all_52_3 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | SIMP: (267) implies:
% 202.47/34.01  | | | | | | | | | | | | | | |   (268)  all_52_3 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | COMBINE_EQS: (82), (268) imply:
% 202.47/34.01  | | | | | | | | | | | | | | |   (269)  all_58_2 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (12), (13), (14), (16),
% 202.47/34.01  | | | | | | | | | | | | | | |            (32), (39), (43), (49), (52), (60), (61), (65),
% 202.47/34.01  | | | | | | | | | | | | | | |            (69), (74), (77), (84), (92), (95), (102), (105),
% 202.47/34.01  | | | | | | | | | | | | | | |            (112), (115), (117), (126), (129), (133), (139),
% 202.47/34.01  | | | | | | | | | | | | | | |            (147), (149), (150), (155), (160), (161), (162),
% 202.47/34.01  | | | | | | | | | | | | | | |            (166), (170), (171), (172), (176), (185), (187),
% 202.47/34.01  | | | | | | | | | | | | | | |            (188), (216), (221), (249), (269) are inconsistent
% 202.47/34.01  | | | | | | | | | | | | | | |            by sub-proof #422.
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (270)  all_56_12 = e1 | all_56_12 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REF_CLOSE: (237), (240), (242), (270) are inconsistent by
% 202.47/34.01  | | | | | | | | | | | |            sub-proof #1344.
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | |   (271)   ~ (all_8_2 = e0)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (233), (271) imply:
% 202.47/34.01  | | | | | | | | | | |   (272)  $false
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | CLOSE: (272) is inconsistent.
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | |   (273)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | BETA: splitting (273) gives:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | |   (274)  all_58_2 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | COMBINE_EQS: (82), (274) imply:
% 202.47/34.01  | | | | | | | | | | |   (275)  all_52_3 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | SIMP: (275) implies:
% 202.47/34.01  | | | | | | | | | | |   (276)  all_52_3 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (138), (276) imply:
% 202.47/34.01  | | | | | | | | | | |   (277)   ~ (all_52_7 = e0)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (6), (276) imply:
% 202.47/34.01  | | | | | | | | | | |   (278)  op(e0, e0) = all_52_2
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, all_52_2, e0, e0,
% 202.47/34.01  | | | | | | | | | | |              simplifying with (65), (278) gives:
% 202.47/34.01  | | | | | | | | | | |   (279)  all_52_2 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | BETA: splitting (88) gives:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (280)  all_58_0 = e1
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | COMBINE_EQS: (21), (280) imply:
% 202.47/34.01  | | | | | | | | | | | |   (281)  all_6_2 = e1
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | COMBINE_EQS: (20), (281) imply:
% 202.47/34.01  | | | | | | | | | | | |   (282)  all_44_2 = e1
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REDUCE: (172), (281) imply:
% 202.47/34.01  | | | | | | | | | | | |   (283)  op(e1, e3) = all_6_1
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | BETA: splitting (25) gives:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (284)   ~ (all_44_2 = e1)
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REDUCE: (282), (284) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (285)  $false
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_6_1, e3, e1,
% 202.47/34.01  | | | | | | | | | | | | |              simplifying with (223), (283) gives:
% 202.47/34.01  | | | | | | | | | | | | |   (286)  all_6_1 = e3
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REDUCE: (126), (286) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (287)  op(e3, e3) = e2
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (19), (21), (22), (27), (34),
% 202.47/34.01  | | | | | | | | | | | | |            (40), (42), (75), (77), (82), (86), (90), (91),
% 202.47/34.01  | | | | | | | | | | | | |            (101), (122), (126), (129), (132), (145), (149),
% 202.47/34.01  | | | | | | | | | | | | |            (152), (172), (175), (206), (207), (219), (221),
% 202.47/34.01  | | | | | | | | | | | | |            (287) are inconsistent by sub-proof #454.
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (288)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (12), (13), (14), (16),
% 202.47/34.01  | | | | | | | | | | | |            (32), (39), (43), (49), (52), (60), (61), (65),
% 202.47/34.01  | | | | | | | | | | | |            (69), (74), (77), (84), (92), (95), (102), (105),
% 202.47/34.01  | | | | | | | | | | | |            (112), (115), (117), (126), (129), (133), (139),
% 202.47/34.01  | | | | | | | | | | | |            (147), (149), (150), (155), (160), (161), (162),
% 202.47/34.01  | | | | | | | | | | | |            (166), (170), (171), (172), (176), (185), (187),
% 202.47/34.01  | | | | | | | | | | | |            (188), (216), (221), (274), (288) are inconsistent
% 202.47/34.01  | | | | | | | | | | | |            by sub-proof #422.
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | |   (289)  all_58_6 = e0 | all_58_12 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | BETA: splitting (289) gives:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (290)  all_58_6 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REF_CLOSE: (10), (216), (290) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | |            #737.
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (291)  all_58_12 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REF_CLOSE: (77), (176), (291) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | |            #1067.
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | End of split
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | Case 2:
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | |   (292)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | BETA: splitting (292) gives:
% 202.47/34.01  | | | | | | | 
% 202.47/34.01  | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | |   (293)  all_58_7 = e3
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | COMBINE_EQS: (41), (293) imply:
% 202.47/34.01  | | | | | | | |   (294)  all_10_0 = e3
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | REDUCE: (24), (294) imply:
% 202.47/34.01  | | | | | | | |   (295)  $false
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | CLOSE: (295) is inconsistent.
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | |   (296)  all_58_8 = e3 | all_58_11 = e3
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | BETA: splitting (296) gives:
% 202.47/34.01  | | | | | | | | 
% 202.47/34.01  | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | |   (297)  all_58_8 = e3
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | COMBINE_EQS: (110), (297) imply:
% 202.47/34.01  | | | | | | | | |   (298)  all_10_2 = e3
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | COMBINE_EQS: (26), (298) imply:
% 202.47/34.01  | | | | | | | | |   (299)  all_40_2 = e3
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | REDUCE: (161), (298) imply:
% 202.47/34.01  | | | | | | | | |   (300)   ~ (all_52_23 = e3)
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | REDUCE: (146), (298) imply:
% 202.47/34.01  | | | | | | | | |   (301)  op(e3, e1) = e2
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | BETA: splitting (81) gives:
% 202.47/34.01  | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | |   (302)   ~ (all_40_2 = e3)
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | REDUCE: (299), (302) imply:
% 202.47/34.01  | | | | | | | | | |   (303)  $false
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | CLOSE: (303) is inconsistent.
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | |   (304)   ~ (all_40_0 = e0)
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | REDUCE: (136), (304) imply:
% 202.47/34.01  | | | | | | | | | |   (305)   ~ (all_10_0 = e0)
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | BETA: splitting (151) gives:
% 202.47/34.01  | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | |   (306)  all_58_6 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | COMBINE_EQS: (145), (306) imply:
% 202.47/34.01  | | | | | | | | | | |   (307)  all_52_5 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | SIMP: (307) implies:
% 202.47/34.01  | | | | | | | | | | |   (308)  all_52_5 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (93), (308) imply:
% 202.47/34.01  | | | | | | | | | | |   (309)   ~ (all_52_29 = e0)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (164), (308) imply:
% 202.47/34.01  | | | | | | | | | | |   (310)   ~ (all_10_0 = e0)
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | REDUCE: (28), (308) imply:
% 202.47/34.01  | | | | | | | | | | |   (311)  op(e0, e0) = all_52_4
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | BETA: splitting (18) gives:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (312)  all_56_9 = e2
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REF_CLOSE: (57), (70), (312) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | |            #991.
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (313)   ~ (all_56_9 = e2)
% 202.47/34.01  | | | | | | | | | | | |   (314)  all_56_9 = e1 | all_56_9 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | BETA: splitting (314) gives:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (315)  all_56_9 = e1
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | COMBINE_EQS: (70), (315) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (316)  all_10_0 = e1
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | SIMP: (316) implies:
% 202.47/34.01  | | | | | | | | | | | | |   (317)  all_10_0 = e1
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | COMBINE_EQS: (41), (317) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (318)  all_58_7 = e1
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REDUCE: (24), (317) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (319)   ~ (e3 = e1)
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REDUCE: (57), (317) imply:
% 202.47/34.01  | | | | | | | | | | | | |   (320)   ~ (e2 = e1)
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | BETA: splitting (54) gives:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | |   (321)  all_58_9 = e1
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | COMBINE_EQS: (203), (321) imply:
% 202.47/34.01  | | | | | | | | | | | | | |   (322)  e3 = e1
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | REDUCE: (5), (322) imply:
% 202.47/34.01  | | | | | | | | | | | | | |   (323)  $false
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | CLOSE: (323) is inconsistent.
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | |   (324)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, all_52_4, e0, e0,
% 202.47/34.01  | | | | | | | | | | | | | | |              simplifying with (65), (311) gives:
% 202.47/34.01  | | | | | | | | | | | | | | |   (325)  all_52_4 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_17, e2, e1, e3,
% 202.47/34.01  | | | | | | | | | | | | | | |              simplifying with (101), (301) gives:
% 202.47/34.01  | | | | | | | | | | | | | | |   (326)  all_52_17 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | REDUCE: (170), (326) imply:
% 202.47/34.01  | | | | | | | | | | | | | | |   (327)   ~ (all_52_23 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | SIMP: (327) implies:
% 202.47/34.01  | | | | | | | | | | | | | | |   (328)   ~ (all_52_23 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | |   (329)  all_56_14 = e3
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | REF_CLOSE: (133), (300), (329) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | | | |            #1286.
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | |   (330)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (65), (112), (133), (160), (161), (187),
% 202.47/34.01  | | | | | | | | | | | | | | | |            (188), (328), (330) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | | | |            #1284.
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | |   (331)   ~ (all_58_10 = e1)
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | REDUCE: (66), (331) imply:
% 202.47/34.01  | | | | | | | | | | | | | | |   (332)   ~ (all_52_27 = e1)
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | |   (333)  all_56_11 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (333) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (334)  all_52_29 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | SIMP: (334) implies:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (335)  all_52_29 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | REDUCE: (31), (335) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | |   (336)   ~ (all_52_27 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (337)  all_56_7 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (336), (337) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | | | | |            #918.
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (338)  all_56_7 = e1 | all_56_7 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (127), (332), (338) are inconsistent by
% 202.47/34.01  | | | | | | | | | | | | | | | | |            sub-proof #902.
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | |   (339)  all_56_11 = e1 | all_56_11 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (340)  all_58_6 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (340) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (341)  e2 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | REDUCE: (91), (341) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (342)  $false
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | CLOSE: (342) is inconsistent.
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | |   (343)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | |   (344)  all_58_7 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (318), (344) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | | | | | |            #421.
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | |   (345)   ~ (all_58_7 = e2)
% 202.47/34.01  | | | | | | | | | | | | | | | | | |   (346)  all_58_8 = e2 | all_58_11 = e2
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |   (347)  all_56_11 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (347) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |   (348)  all_52_29 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | SIMP: (348) implies:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |   (349)  all_52_29 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (349) imply:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |   (350)  all_58_11 = e1
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (63), (79), (106), (110), (146), (346), (350)
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #427.
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |   (351)  all_56_11 = e0
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (94), (351) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | | | | | | |            #1002.
% 202.47/34.01  | | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (352)  all_56_9 = e0
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REF_CLOSE: (70), (305), (352) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | |            #989.
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | |   (353)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | BETA: splitting (353) gives:
% 202.47/34.01  | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (354)  all_58_7 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | COMBINE_EQS: (41), (354) imply:
% 202.47/34.01  | | | | | | | | | | | |   (355)  all_10_0 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | REDUCE: (305), (355) imply:
% 202.47/34.01  | | | | | | | | | | | |   (356)  $false
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | CLOSE: (356) is inconsistent.
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | |   (357)  all_58_8 = e0 | all_58_11 = e0
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | BETA: splitting (357) gives:
% 202.47/34.01  | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (358)  all_58_8 = e0
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | BETA: splitting (296) gives:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | Case 1:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | REF_CLOSE: (10), (297), (358) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | | |            #686.
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | |   (359)  all_58_11 = e3
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (21), (34), (44), (71), (126), (129),
% 202.47/34.01  | | | | | | | | | | | | | |            (132), (149), (152), (156), (172), (175), (185),
% 202.47/34.01  | | | | | | | | | | | | | |            (206), (359) are inconsistent by sub-proof #420.
% 202.47/34.01  | | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | End of split
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | Case 2:
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | |   (360)  all_58_11 = e0
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | | REF_CLOSE: (44), (94), (360) are inconsistent by sub-proof
% 202.47/34.01  | | | | | | | | | | | | |            #1115.
% 202.47/34.01  | | | | | | | | | | | | | 
% 202.47/34.01  | | | | | | | | | | | | End of split
% 202.47/34.02  | | | | | | | | | | | | 
% 202.47/34.02  | | | | | | | | | | | End of split
% 202.47/34.02  | | | | | | | | | | | 
% 202.47/34.02  | | | | | | | | | | End of split
% 202.47/34.02  | | | | | | | | | | 
% 202.47/34.02  | | | | | | | | | End of split
% 202.47/34.02  | | | | | | | | | 
% 202.47/34.02  | | | | | | | | Case 2:
% 202.47/34.02  | | | | | | | | | 
% 202.47/34.02  | | | | | | | | |   (361)  all_58_11 = e3
% 202.47/34.02  | | | | | | | | | 
% 202.47/34.02  | | | | | | | | | REF_CLOSE: (44), (210), (361) are inconsistent by sub-proof
% 202.47/34.02  | | | | | | | | |            #1323.
% 202.47/34.02  | | | | | | | | | 
% 202.47/34.02  | | | | | | | | End of split
% 202.47/34.02  | | | | | | | | 
% 202.47/34.02  | | | | | | | End of split
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | End of split
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | End of split
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | Case 2:
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | |   (362)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (12), (13), (14), (16),
% 202.47/34.02  | | | | |            (17), (28), (32), (35), (39), (41), (43), (44), (49), (52),
% 202.47/34.02  | | | | |            (55), (57), (59), (60), (61), (65), (66), (68), (69), (71),
% 202.47/34.02  | | | | |            (72), (73), (74), (76), (77), (79), (84), (92), (95),
% 202.47/34.02  | | | | |            (102), (103), (105), (106), (110), (112), (114), (115),
% 202.47/34.02  | | | | |            (117), (119), (120), (124), (126), (129), (133), (137),
% 202.47/34.02  | | | | |            (139), (140), (145), (146), (147), (149), (152), (155),
% 202.47/34.02  | | | | |            (156), (160), (161), (162), (165), (166), (169), (170),
% 202.47/34.02  | | | | |            (171), (172), (174), (175), (176), (185), (186), (187),
% 202.47/34.02  | | | | |            (188), (202), (362) are inconsistent by sub-proof #419.
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | End of split
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | End of split
% 202.47/34.02  | | | 
% 202.47/34.02  | | Case 2:
% 202.47/34.02  | | | 
% 202.47/34.02  | | |   (363)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (15), (16),
% 202.47/34.02  | | |            (17), (19), (20), (21), (22), (23), (25), (27), (30), (32),
% 202.47/34.02  | | |            (34), (36), (37), (38), (39), (40), (42), (44), (46), (47),
% 202.47/34.02  | | |            (48), (49), (50), (52), (53), (54), (55), (56), (59), (60),
% 202.47/34.02  | | |            (62), (64), (66), (67), (71), (73), (76), (77), (78), (82),
% 202.47/34.02  | | |            (83), (86), (90), (91), (93), (94), (96), (99), (100), (104),
% 202.47/34.02  | | |            (106), (107), (108), (110), (112), (113), (114), (116), (118),
% 202.47/34.02  | | |            (119), (120), (122), (123), (125), (126), (129), (130), (131),
% 202.47/34.02  | | |            (132), (137), (140), (142), (145), (147), (148), (150), (151),
% 202.47/34.02  | | |            (152), (154), (156), (157), (160), (161), (162), (163), (165),
% 202.47/34.02  | | |            (166), (167), (169), (172), (173), (174), (175), (176), (177),
% 202.47/34.02  | | |            (363) are inconsistent by sub-proof #418.
% 202.47/34.02  | | | 
% 202.47/34.02  | | End of split
% 202.47/34.02  | | 
% 202.47/34.02  | End of split
% 202.47/34.02  | 
% 202.47/34.02  End of proof
% 202.47/34.02  
% 202.47/34.02  Sub-proof #418 shows that the following formulas are inconsistent:
% 202.47/34.02  ----------------------------------------------------------------
% 202.47/34.02    (1)   ~ (all_52_25 = all_52_27)
% 202.47/34.02    (2)  all_58_14 = all_52_23
% 202.47/34.02    (3)   ~ (e3 = e1)
% 202.47/34.02    (4)  op(all_52_3, all_52_3) = all_52_2
% 202.47/34.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.02    (6)   ~ (all_52_5 = all_52_13)
% 202.47/34.02    (7)  all_58_1 = all_52_9
% 202.47/34.02    (8)   ~ (e3 = e0)
% 202.47/34.02    (9)  op(e2, e3) = all_52_3
% 202.47/34.02    (10)   ~ (all_52_3 = all_52_19)
% 202.47/34.02    (11)  op(all_52_7, all_52_7) = all_52_6
% 202.47/34.02    (12)   ~ (all_52_17 = all_52_25)
% 202.47/34.02    (13)   ~ (all_52_3 = all_6_2)
% 202.47/34.02    (14)  all_44_2 = all_6_2
% 202.47/34.02    (15)  all_58_0 = all_6_2
% 202.47/34.02    (16)  all_56_4 = all_52_3
% 202.47/34.02    (17)   ~ (all_52_17 = all_10_2)
% 202.47/34.02    (18)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.47/34.02    (19)  op(e3, e0) = all_52_25
% 202.47/34.02    (20)  op(all_52_19, all_52_19) = all_52_18
% 202.47/34.02    (21)  all_58_13 = all_52_15
% 202.47/34.02    (22)  all_58_9 = all_52_25
% 202.47/34.02    (23)   ~ (all_52_29 = all_14_2)
% 202.47/34.02    (24)  op(all_52_27, all_52_27) = all_52_26
% 202.47/34.02    (25)  op(e1, e3) = all_52_5
% 202.47/34.02    (26)  op(e2, e2) = all_4_2
% 202.47/34.02    (27)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.47/34.02    (28)   ~ (all_52_3 = all_52_5)
% 202.47/34.02    (29)  all_58_11 = all_52_29
% 202.47/34.02    (30)   ~ (all_52_9 = all_52_15)
% 202.47/34.02    (31)   ~ (all_52_3 = all_52_27)
% 202.47/34.02    (32)  op(all_6_2, all_6_2) = all_52_0
% 202.47/34.02    (33)   ~ (all_52_7 = all_6_2)
% 202.47/34.02    (34)  op(e0, e0) = all_14_2
% 202.47/34.02    (35)   ~ (all_52_15 = e0)
% 202.47/34.02    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.47/34.02    (37)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.47/34.02    (38)  all_58_15 = e0
% 202.47/34.02    (39)  all_56_11 = all_52_29
% 202.47/34.02    (40)   ~ (all_52_25 = e0)
% 202.47/34.02    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/34.02    (42)  all_56_9 = all_52_13
% 202.47/34.02    (43)   ~ (all_52_13 = all_10_2)
% 202.47/34.02    (44)  all_58_10 = all_52_27
% 202.47/34.02    (45)  all_56_8 = all_52_5
% 202.47/34.02    (46)   ~ (all_52_25 = all_52_29)
% 202.47/34.02    (47)  all_58_7 = all_52_13
% 202.47/34.02    (48)   ~ (all_52_5 = all_52_7)
% 202.47/34.02    (49)  all_58_12 = all_52_7
% 202.47/34.02    (50)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.02    (51)  all_58_2 = all_52_3
% 202.47/34.02    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.47/34.02    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.47/34.02    (54)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.47/34.02    (55)   ~ (e2 = e0)
% 202.47/34.02    (56)   ~ (all_52_5 = all_52_29)
% 202.47/34.02    (57)   ~ (all_52_29 = e0)
% 202.47/34.02    (58)  all_56_6 = all_52_19
% 202.47/34.02    (59)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/34.02    (60)   ~ (all_52_13 = all_4_2)
% 202.47/34.02    (61)   ~ (all_52_9 = all_52_25)
% 202.47/34.02    (62)   ~ (all_52_19 = all_10_2)
% 202.47/34.02    (63)  op(all_52_23, all_52_23) = all_52_22
% 202.47/34.02    (64)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.47/34.02    (65)  all_58_8 = all_10_2
% 202.47/34.02    (66)   ~ (all_52_23 = e0)
% 202.47/34.02    (67)   ~ (all_52_5 = all_10_2)
% 202.47/34.02    (68)  op(all_52_29, all_52_29) = all_52_28
% 202.47/34.02    (69)  op(all_52_17, all_52_17) = all_52_16
% 202.47/34.02    (70)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.47/34.02    (71)   ~ (all_52_25 = all_6_2)
% 202.47/34.02    (72)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/34.02    (73)   ~ (all_52_5 = all_6_2)
% 202.47/34.02    (74)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.47/34.02    (75)   ~ (all_52_13 = all_52_15)
% 202.47/34.02    (76)  op(e3, all_6_1) = e2
% 202.47/34.02    (77)  op(e3, e3) = all_6_2
% 202.47/34.02    (78)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/34.02    (79)   ~ (all_52_27 = all_14_2)
% 202.47/34.02    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.02    (81)  all_56_3 = all_52_25
% 202.47/34.02    (82)  all_58_5 = all_52_19
% 202.47/34.02    (83)   ~ (all_52_15 = all_4_2)
% 202.47/34.02    (84)  all_58_6 = all_52_5
% 202.47/34.02    (85)  op(e3, e2) = all_52_9
% 202.47/34.02    (86)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.47/34.02    (87)   ~ (e1 = e0)
% 202.47/34.02    (88)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.47/34.02    (89)   ~ (e3 = e2)
% 202.47/34.02    (90)  all_44_1 = all_6_1
% 202.47/34.02    (91)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.02    (92)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/34.02    (93)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.47/34.02    (94)  op(e1, e1) = all_10_2
% 202.47/34.02    (95)   ~ (all_52_23 = all_10_2)
% 202.47/34.02    (96)   ~ (all_52_7 = all_52_23)
% 202.47/34.02    (97)   ~ (all_52_17 = all_52_19)
% 202.47/34.02    (98)  all_58_3 = all_4_2
% 202.47/34.02    (99)  all_56_13 = all_52_15
% 202.47/34.02    (100)   ~ (all_52_3 = all_4_2)
% 202.47/34.02    (101)   ~ (all_52_19 = all_4_2)
% 202.47/34.02    (102)  op(all_6_2, e3) = all_6_1
% 202.47/34.02    (103)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.47/34.02    (104)   ~ (all_52_13 = all_52_29)
% 202.47/34.02    (105)  all_58_4 = all_52_17
% 202.47/34.02    (106)   ~ (all_52_7 = e0)
% 202.47/34.02    (107)  op(all_52_25, all_52_25) = all_52_24
% 202.47/34.02  
% 202.47/34.02  Begin of proof
% 202.47/34.02  | 
% 202.47/34.02  | ALPHA: (93) implies:
% 202.47/34.02  |   (108)  all_52_28 = e1
% 202.47/34.02  |   (109)  all_52_26 = e2
% 202.47/34.02  |   (110)  all_52_24 = e3
% 202.47/34.02  | 
% 202.47/34.02  | REDUCE: (107), (110) imply:
% 202.47/34.02  |   (111)  op(all_52_25, all_52_25) = e3
% 202.47/34.02  | 
% 202.47/34.02  | REDUCE: (24), (109) imply:
% 202.47/34.02  |   (112)  op(all_52_27, all_52_27) = e2
% 202.47/34.02  | 
% 202.47/34.02  | REDUCE: (68), (108) imply:
% 202.47/34.02  |   (113)  op(all_52_29, all_52_29) = e1
% 202.47/34.02  | 
% 202.47/34.02  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 202.47/34.02  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 202.47/34.02  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 202.47/34.02  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 202.47/34.02  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 202.47/34.02  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (69),
% 202.47/34.02  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 202.47/34.02  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 202.47/34.02  |            (92), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 202.47/34.02  |            (103), (104), (105), (106), (111), (112), (113) are inconsistent by
% 202.47/34.02  |            sub-proof #469.
% 202.47/34.02  | 
% 202.47/34.02  End of proof
% 202.47/34.02  
% 202.47/34.02  Sub-proof #419 shows that the following formulas are inconsistent:
% 202.47/34.02  ----------------------------------------------------------------
% 202.47/34.02    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/34.02    (2)   ~ (all_52_15 = all_52_23)
% 202.47/34.02    (3)  all_58_14 = all_52_23
% 202.47/34.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.02    (5)  all_58_1 = all_52_9
% 202.47/34.02    (6)   ~ (e3 = e0)
% 202.47/34.02    (7)  op(all_52_23, all_52_23) = e0
% 202.47/34.02    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.02    (9)  op(e0, e2) = all_52_15
% 202.47/34.02    (10)   ~ (all_52_7 = all_52_15)
% 202.47/34.02    (11)  op(all_52_7, all_52_7) = all_52_6
% 202.47/34.02    (12)   ~ (all_52_17 = all_52_25)
% 202.47/34.02    (13)  op(all_52_5, all_52_5) = all_52_4
% 202.47/34.02    (14)  all_58_13 = all_52_15
% 202.47/34.02    (15)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.02    (16)  op(e2, e2) = all_4_2
% 202.47/34.02    (17)  all_58_7 = all_10_0
% 202.47/34.02    (18)   ~ (all_4_1 = e3)
% 202.47/34.02    (19)  all_58_11 = all_52_29
% 202.47/34.02    (20)   ~ (all_52_7 = all_6_2)
% 202.47/34.02    (21)   ~ (all_52_15 = e0)
% 202.47/34.02    (22)  all_58_15 = e0
% 202.47/34.02    (23)   ~ (all_10_0 = e2)
% 202.47/34.02    (24)   ~ (all_52_25 = e0)
% 202.47/34.02    (25)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/34.02    (26)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/34.02    (27)  op(e0, e0) = e0
% 202.47/34.02    (28)  op(all_10_2, all_10_2) = e1
% 202.47/34.02    (29)  all_58_10 = all_52_27
% 202.47/34.02    (30)  op(all_52_9, all_52_9) = all_52_8
% 202.47/34.02    (31)  op(all_52_15, all_52_15) = all_52_14
% 202.47/34.02    (32)   ~ (all_52_25 = all_52_29)
% 202.47/34.02    (33)   ~ (all_52_29 = all_10_2)
% 202.47/34.02    (34)  all_58_7 = all_52_13
% 202.47/34.02    (35)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.47/34.02    (36)  op(all_52_19, all_52_19) = e2
% 202.47/34.02    (37)   ~ (all_52_5 = all_52_7)
% 202.47/34.02    (38)  all_58_12 = all_52_7
% 202.47/34.02    (39)  op(e2, e1) = all_52_19
% 202.47/34.02    (40)  all_56_2 = all_52_17
% 202.47/34.02    (41)  op(all_4_2, e2) = all_4_1
% 202.47/34.02    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/34.02    (43)   ~ (all_52_27 = e3)
% 202.47/34.02    (44)  op(e0, e3) = all_52_7
% 202.47/34.02    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.47/34.02    (46)  all_58_15 = all_14_2
% 202.47/34.02    (47)   ~ (all_52_19 = all_10_2)
% 202.47/34.02    (48)  all_58_8 = all_10_2
% 202.47/34.02    (49)   ~ (all_52_23 = e0)
% 202.47/34.02    (50)  op(all_52_29, all_52_29) = all_52_28
% 202.47/34.02    (51)  all_56_12 = all_52_7
% 202.47/34.02    (52)  all_8_2 = all_6_2
% 202.47/34.02    (53)   ~ (all_52_25 = all_6_2)
% 202.47/34.02    (54)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/34.02    (55)   ~ (all_52_9 = all_6_2)
% 202.47/34.02    (56)  op(e3, all_6_1) = e2
% 202.47/34.02    (57)  op(e3, e3) = all_6_2
% 202.47/34.02    (58)  all_56_14 = all_52_23
% 202.47/34.02    (59)  all_56_3 = all_52_25
% 202.47/34.02    (60)  op(all_14_2, all_14_2) = all_52_30
% 202.47/34.02    (61)  all_58_5 = all_52_19
% 202.47/34.02    (62)  op(all_52_17, all_52_17) = e3
% 202.47/34.02    (63)  all_58_6 = all_52_5
% 202.47/34.02    (64)  op(all_10_2, e1) = e2
% 202.47/34.02    (65)  op(e3, e2) = all_52_9
% 202.47/34.02    (66)   ~ (all_52_17 = all_6_2)
% 202.47/34.02    (67)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.47/34.02    (68)   ~ (e3 = e2)
% 202.47/34.02    (69)   ~ (all_52_9 = all_52_17)
% 202.47/34.02    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.02    (71)  op(e1, e1) = all_10_2
% 202.47/34.02    (72)   ~ (all_52_23 = all_10_2)
% 202.47/34.02    (73)   ~ (all_52_7 = all_52_23)
% 202.47/34.02    (74)  all_58_3 = all_4_2
% 202.47/34.02    (75)  all_56_13 = all_52_15
% 202.47/34.02    (76)   ~ (all_52_19 = all_4_2)
% 202.47/34.02    (77)   ~ (all_52_17 = all_52_23)
% 202.47/34.02    (78)  all_8_1 = all_6_1
% 202.47/34.02    (79)  op(all_6_2, e3) = all_6_1
% 202.47/34.02    (80)   ~ (all_52_13 = all_52_29)
% 202.47/34.02    (81)  all_58_4 = all_52_17
% 202.47/34.02    (82)   ~ (all_52_7 = e0)
% 202.47/34.02  
% 202.47/34.02  Begin of proof
% 202.47/34.02  | 
% 202.47/34.02  | BETA: splitting (67) gives:
% 202.47/34.02  | 
% 202.47/34.02  | Case 1:
% 202.47/34.02  | | 
% 202.47/34.02  | |   (83)  all_58_10 = e3
% 202.47/34.02  | | 
% 202.47/34.02  | | REF_CLOSE: (29), (43), (83) are inconsistent by sub-proof #1301.
% 202.47/34.02  | | 
% 202.47/34.02  | Case 2:
% 202.47/34.02  | | 
% 202.47/34.02  | |   (84)  all_58_11 = e3 | all_58_15 = e3
% 202.47/34.02  | | 
% 202.47/34.02  | | BETA: splitting (84) gives:
% 202.47/34.02  | | 
% 202.47/34.02  | | Case 1:
% 202.47/34.02  | | | 
% 202.47/34.02  | | |   (85)  all_58_11 = e3
% 202.47/34.02  | | | 
% 202.47/34.02  | | | COMBINE_EQS: (19), (85) imply:
% 202.47/34.02  | | |   (86)  all_52_29 = e3
% 202.47/34.02  | | | 
% 202.47/34.02  | | | SIMP: (86) implies:
% 202.47/34.02  | | |   (87)  all_52_29 = e3
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REDUCE: (50), (87) imply:
% 202.47/34.02  | | |   (88)  op(e3, e3) = all_52_28
% 202.47/34.02  | | | 
% 202.47/34.02  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_28, e3, e3,
% 202.47/34.02  | | |              simplifying with (57), (88) gives:
% 202.47/34.02  | | |   (89)  all_52_28 = all_6_2
% 202.47/34.02  | | | 
% 202.47/34.02  | | | BETA: splitting (15) gives:
% 202.47/34.02  | | | 
% 202.47/34.02  | | | Case 1:
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | |   (90)  all_58_6 = e2
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | COMBINE_EQS: (63), (90) imply:
% 202.47/34.02  | | | |   (91)  all_52_5 = e2
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | SIMP: (91) implies:
% 202.47/34.02  | | | |   (92)  all_52_5 = e2
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | REDUCE: (37), (92) imply:
% 202.47/34.02  | | | |   (93)   ~ (all_52_7 = e2)
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | SIMP: (93) implies:
% 202.47/34.02  | | | |   (94)   ~ (all_52_7 = e2)
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | REDUCE: (13), (92) imply:
% 202.47/34.02  | | | |   (95)  op(e2, e2) = all_52_4
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_4, e2, e2,
% 202.47/34.02  | | | |              simplifying with (16), (95) gives:
% 202.47/34.02  | | | |   (96)  all_52_4 = all_4_2
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | BETA: splitting (8) gives:
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | Case 1:
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | |   (97)  all_56_12 = e3
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | COMBINE_EQS: (51), (97) imply:
% 202.47/34.02  | | | | |   (98)  all_52_7 = e3
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | REDUCE: (10), (98) imply:
% 202.47/34.02  | | | | |   (99)   ~ (all_52_15 = e3)
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | SIMP: (99) implies:
% 202.47/34.02  | | | | |   (100)   ~ (all_52_15 = e3)
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | REDUCE: (73), (98) imply:
% 202.47/34.02  | | | | |   (101)   ~ (all_52_23 = e3)
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | SIMP: (101) implies:
% 202.47/34.02  | | | | |   (102)   ~ (all_52_23 = e3)
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | REF_CLOSE: (3), (4), (5), (6), (12), (14), (19), (22), (24), (26),
% 202.47/34.02  | | | | |            (27), (30), (32), (33), (34), (36), (40), (45), (48), (50),
% 202.47/34.02  | | | | |            (53), (54), (55), (57), (59), (61), (62), (66), (70), (74),
% 202.47/34.02  | | | | |            (76), (80), (81), (84), (100), (102) are inconsistent by
% 202.47/34.02  | | | | |            sub-proof #1253.
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | Case 2:
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | |   (103)   ~ (all_56_12 = e3)
% 202.47/34.02  | | | | |   (104)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | REDUCE: (51), (103) imply:
% 202.47/34.02  | | | | |   (105)   ~ (all_52_7 = e3)
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | BETA: splitting (104) gives:
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | | Case 1:
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | |   (106)  all_56_12 = e2
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | | COMBINE_EQS: (51), (106) imply:
% 202.47/34.02  | | | | | |   (107)  all_52_7 = e2
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | | REDUCE: (94), (107) imply:
% 202.47/34.02  | | | | | |   (108)  $false
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | | CLOSE: (108) is inconsistent.
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | Case 2:
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | |   (109)  all_56_12 = e1 | all_56_12 = e0
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | | BETA: splitting (109) gives:
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | | Case 1:
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | |   (110)  all_56_12 = e1
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | COMBINE_EQS: (51), (110) imply:
% 202.47/34.02  | | | | | | |   (111)  all_52_7 = e1
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | REDUCE: (10), (111) imply:
% 202.47/34.02  | | | | | | |   (112)   ~ (all_52_15 = e1)
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | SIMP: (112) implies:
% 202.47/34.02  | | | | | | |   (113)   ~ (all_52_15 = e1)
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | REDUCE: (73), (111) imply:
% 202.47/34.02  | | | | | | |   (114)   ~ (all_52_23 = e1)
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | SIMP: (114) implies:
% 202.47/34.02  | | | | | | |   (115)   ~ (all_52_23 = e1)
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | REDUCE: (82), (111) imply:
% 202.47/34.02  | | | | | | |   (116)   ~ (e1 = e0)
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | REDUCE: (11), (111) imply:
% 202.47/34.02  | | | | | | |   (117)  op(e1, e1) = all_52_6
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (14), (16),
% 202.47/34.02  | | | | | | |            (18), (20), (21), (25), (26), (27), (28), (31), (35),
% 202.47/34.02  | | | | | | |            (38), (40), (41), (42), (44), (46), (49), (51), (52),
% 202.47/34.02  | | | | | | |            (56), (57), (58), (60), (62), (65), (66), (69), (71),
% 202.47/34.02  | | | | | | |            (72), (73), (75), (77), (78), (79), (82), (105), (113),
% 202.47/34.02  | | | | | | |            (115), (116), (117) are inconsistent by sub-proof #423.
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | Case 2:
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | |   (118)  all_56_12 = e0
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | COMBINE_EQS: (51), (118) imply:
% 202.47/34.02  | | | | | | |   (119)  all_52_7 = e0
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | REDUCE: (82), (119) imply:
% 202.47/34.02  | | | | | | |   (120)  $false
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | | CLOSE: (120) is inconsistent.
% 202.47/34.02  | | | | | | | 
% 202.47/34.02  | | | | | | End of split
% 202.47/34.02  | | | | | | 
% 202.47/34.02  | | | | | End of split
% 202.47/34.02  | | | | | 
% 202.47/34.02  | | | | End of split
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | Case 2:
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | |   (121)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | | REF_CLOSE: (4), (17), (23), (39), (47), (48), (64), (68), (85), (121)
% 202.47/34.02  | | | |            are inconsistent by sub-proof #997.
% 202.47/34.02  | | | | 
% 202.47/34.02  | | | End of split
% 202.47/34.02  | | | 
% 202.47/34.02  | | Case 2:
% 202.47/34.02  | | | 
% 202.47/34.02  | | |   (122)  all_58_15 = e3
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REF_CLOSE: (6), (22), (122) are inconsistent by sub-proof #1350.
% 202.47/34.02  | | | 
% 202.47/34.02  | | End of split
% 202.47/34.02  | | 
% 202.47/34.02  | End of split
% 202.47/34.02  | 
% 202.47/34.02  End of proof
% 202.47/34.02  
% 202.47/34.02  Sub-proof #420 shows that the following formulas are inconsistent:
% 202.47/34.02  ----------------------------------------------------------------
% 202.47/34.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.02    (2)  all_58_1 = all_52_9
% 202.47/34.02    (3)  all_58_0 = all_6_2
% 202.47/34.02    (4)  all_58_9 = all_52_25
% 202.47/34.02    (5)  all_58_11 = all_52_29
% 202.47/34.02    (6)  all_58_11 = e3
% 202.47/34.02    (7)   ~ (all_52_25 = all_52_29)
% 202.47/34.02    (8)   ~ (all_52_9 = e3)
% 202.47/34.02    (9)  op(e3, all_6_1) = e2
% 202.47/34.02    (10)  op(e3, e3) = all_6_2
% 202.47/34.02    (11)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.02    (12)  op(all_52_17, all_52_17) = e3
% 202.47/34.02    (13)   ~ (all_52_17 = all_6_2)
% 202.47/34.02    (14)   ~ (e3 = e2)
% 202.47/34.02    (15)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.02    (16)  op(all_6_2, e3) = all_6_1
% 202.47/34.02    (17)  all_58_4 = all_52_17
% 202.47/34.02  
% 202.47/34.02  Begin of proof
% 202.47/34.02  | 
% 202.47/34.02  | COMBINE_EQS: (5), (6) imply:
% 202.47/34.02  |   (18)  all_52_29 = e3
% 202.47/34.02  | 
% 202.47/34.02  | SIMP: (18) implies:
% 202.47/34.02  |   (19)  all_52_29 = e3
% 202.47/34.02  | 
% 202.47/34.02  | REDUCE: (7), (19) imply:
% 202.47/34.02  |   (20)   ~ (all_52_25 = e3)
% 202.47/34.02  | 
% 202.47/34.02  | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (13), (14), (15),
% 202.47/34.02  |            (16), (17), (20) are inconsistent by sub-proof #446.
% 202.47/34.02  | 
% 202.47/34.02  End of proof
% 202.47/34.02  
% 202.47/34.02  Sub-proof #421 shows that the following formulas are inconsistent:
% 202.47/34.02  ----------------------------------------------------------------
% 202.47/34.02    (1)  all_58_7 = e2
% 202.47/34.02    (2)  all_58_7 = e1
% 202.47/34.02    (3)   ~ (e2 = e1)
% 202.47/34.02  
% 202.47/34.02  Begin of proof
% 202.47/34.02  | 
% 202.47/34.02  | COMBINE_EQS: (1), (2) imply:
% 202.47/34.02  |   (4)  e2 = e1
% 202.47/34.02  | 
% 202.47/34.02  | SIMP: (4) implies:
% 202.47/34.02  |   (5)  e2 = e1
% 202.47/34.02  | 
% 202.47/34.02  | REDUCE: (3), (5) imply:
% 202.47/34.02  |   (6)  $false
% 202.47/34.02  | 
% 202.47/34.02  | CLOSE: (6) is inconsistent.
% 202.47/34.02  | 
% 202.47/34.02  End of proof
% 202.47/34.02  
% 202.47/34.02  Sub-proof #422 shows that the following formulas are inconsistent:
% 202.47/34.02  ----------------------------------------------------------------
% 202.47/34.02    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/34.02    (2)   ~ (all_52_15 = all_52_23)
% 202.47/34.02    (3)  all_58_14 = all_52_23
% 202.47/34.02    (4)   ~ (e3 = e1)
% 202.47/34.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.02    (6)  op(all_52_23, all_52_23) = e0
% 202.47/34.02    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.02    (8)  op(e0, e2) = all_52_15
% 202.47/34.02    (9)   ~ (all_52_7 = all_52_15)
% 202.47/34.02    (10)  op(all_52_7, all_52_7) = all_52_6
% 202.47/34.02    (11)  all_58_13 = all_52_15
% 202.47/34.02    (12)  op(e2, e2) = all_4_2
% 202.47/34.02    (13)   ~ (all_4_1 = e3)
% 202.47/34.02    (14)   ~ (all_52_7 = all_6_2)
% 202.47/34.02    (15)   ~ (all_52_15 = e0)
% 202.47/34.02    (16)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 202.47/34.02    (17)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/34.02    (18)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/34.02    (19)  all_58_6 = e3
% 202.47/34.02    (20)  op(e0, e0) = e0
% 202.47/34.02    (21)  op(all_10_2, all_10_2) = e1
% 202.47/34.02    (22)  op(all_52_15, all_52_15) = all_52_14
% 202.47/34.02    (23)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.47/34.02    (24)  all_58_12 = all_52_7
% 202.47/34.02    (25)   ~ (all_52_7 = e3)
% 202.47/34.02    (26)  all_56_2 = all_52_17
% 202.47/34.02    (27)  all_58_2 = e0
% 202.47/34.02    (28)  op(all_4_2, e2) = all_4_1
% 202.47/34.02    (29)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/34.02    (30)  op(e0, e3) = all_52_7
% 202.47/34.02    (31)  all_58_15 = all_14_2
% 202.47/34.02    (32)   ~ (all_52_23 = e0)
% 202.47/34.02    (33)  all_56_12 = all_52_7
% 202.47/34.02    (34)  all_8_2 = all_6_2
% 202.47/34.02    (35)  op(e3, all_6_1) = e2
% 202.47/34.02    (36)  op(e3, e3) = all_6_2
% 202.47/34.02    (37)  all_56_14 = all_52_23
% 202.47/34.02    (38)  op(all_14_2, all_14_2) = all_52_30
% 202.47/34.02    (39)  op(all_52_17, all_52_17) = e3
% 202.47/34.02    (40)  op(e3, e2) = all_52_9
% 202.47/34.02    (41)   ~ (all_52_17 = all_6_2)
% 202.47/34.02    (42)   ~ (e1 = e0)
% 202.47/34.02    (43)   ~ (all_52_9 = all_52_17)
% 202.47/34.02    (44)  op(e1, e1) = all_10_2
% 202.47/34.02    (45)   ~ (all_52_23 = all_10_2)
% 202.47/34.02    (46)   ~ (all_52_7 = all_52_23)
% 202.47/34.02    (47)  all_56_13 = all_52_15
% 202.47/34.02    (48)   ~ (all_52_17 = all_52_23)
% 202.47/34.02    (49)  all_8_1 = all_6_1
% 202.47/34.02    (50)  op(all_6_2, e3) = all_6_1
% 202.47/34.02    (51)   ~ (all_52_7 = e0)
% 202.47/34.02  
% 202.47/34.02  Begin of proof
% 202.47/34.02  | 
% 202.47/34.02  | BETA: splitting (16) gives:
% 202.47/34.02  | 
% 202.47/34.02  | Case 1:
% 202.47/34.02  | | 
% 202.47/34.02  | |   (52)  all_58_2 = e1
% 202.47/34.02  | | 
% 202.47/34.02  | | REF_CLOSE: (27), (42), (52) are inconsistent by sub-proof #1129.
% 202.47/34.02  | | 
% 202.47/34.02  | Case 2:
% 202.47/34.02  | | 
% 202.47/34.02  | |   (53)  all_58_6 = e1 | all_58_12 = e1
% 202.47/34.02  | | 
% 202.47/34.02  | | BETA: splitting (53) gives:
% 202.47/34.02  | | 
% 202.47/34.02  | | Case 1:
% 202.47/34.02  | | | 
% 202.47/34.02  | | |   (54)  all_58_6 = e1
% 202.47/34.02  | | | 
% 202.47/34.02  | | | COMBINE_EQS: (19), (54) imply:
% 202.47/34.02  | | |   (55)  e3 = e1
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REDUCE: (4), (55) imply:
% 202.47/34.02  | | |   (56)  $false
% 202.47/34.02  | | | 
% 202.47/34.02  | | | CLOSE: (56) is inconsistent.
% 202.47/34.02  | | | 
% 202.47/34.02  | | Case 2:
% 202.47/34.02  | | | 
% 202.47/34.02  | | |   (57)  all_58_12 = e1
% 202.47/34.02  | | | 
% 202.47/34.02  | | | COMBINE_EQS: (24), (57) imply:
% 202.47/34.02  | | |   (58)  all_52_7 = e1
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REDUCE: (9), (58) imply:
% 202.47/34.02  | | |   (59)   ~ (all_52_15 = e1)
% 202.47/34.02  | | | 
% 202.47/34.02  | | | SIMP: (59) implies:
% 202.47/34.02  | | |   (60)   ~ (all_52_15 = e1)
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REDUCE: (46), (58) imply:
% 202.47/34.02  | | |   (61)   ~ (all_52_23 = e1)
% 202.47/34.02  | | | 
% 202.47/34.02  | | | SIMP: (61) implies:
% 202.47/34.02  | | |   (62)   ~ (all_52_23 = e1)
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REDUCE: (10), (58) imply:
% 202.47/34.02  | | |   (63)  op(e1, e1) = all_52_6
% 202.47/34.02  | | | 
% 202.47/34.02  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 202.47/34.02  | | |            (15), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 202.47/34.02  | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 202.47/34.02  | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 202.47/34.02  | | |            (48), (49), (50), (51), (60), (62), (63) are inconsistent by
% 202.47/34.02  | | |            sub-proof #423.
% 202.47/34.02  | | | 
% 202.47/34.02  | | End of split
% 202.47/34.02  | | 
% 202.47/34.02  | End of split
% 202.47/34.02  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #423 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/34.03    (2)   ~ (all_52_15 = all_52_23)
% 202.47/34.03    (3)   ~ (all_52_15 = e1)
% 202.47/34.03    (4)  all_58_14 = all_52_23
% 202.47/34.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.03    (6)  op(all_52_23, all_52_23) = e0
% 202.47/34.03    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.03    (8)  op(e0, e2) = all_52_15
% 202.47/34.03    (9)   ~ (all_52_7 = all_52_15)
% 202.47/34.03    (10)  all_58_13 = all_52_15
% 202.47/34.03    (11)  op(e2, e2) = all_4_2
% 202.47/34.03    (12)   ~ (all_4_1 = e3)
% 202.47/34.03    (13)   ~ (all_52_7 = all_6_2)
% 202.47/34.03    (14)   ~ (all_52_15 = e0)
% 202.47/34.03    (15)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/34.03    (16)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.47/34.03    (17)  op(e0, e0) = e0
% 202.47/34.03    (18)  op(all_10_2, all_10_2) = e1
% 202.47/34.03    (19)  op(e1, e1) = all_52_6
% 202.47/34.03    (20)  op(all_52_15, all_52_15) = all_52_14
% 202.47/34.03    (21)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.47/34.03    (22)  all_58_12 = all_52_7
% 202.47/34.03    (23)   ~ (all_52_7 = e3)
% 202.47/34.03    (24)  all_56_2 = all_52_17
% 202.47/34.03    (25)  op(all_4_2, e2) = all_4_1
% 202.47/34.03    (26)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.47/34.03    (27)  op(e0, e3) = all_52_7
% 202.47/34.03    (28)   ~ (all_52_23 = e1)
% 202.47/34.03    (29)  all_58_15 = all_14_2
% 202.47/34.03    (30)   ~ (all_52_23 = e0)
% 202.47/34.03    (31)  all_56_12 = all_52_7
% 202.47/34.03    (32)  all_8_2 = all_6_2
% 202.47/34.03    (33)  op(e3, all_6_1) = e2
% 202.47/34.03    (34)  op(e3, e3) = all_6_2
% 202.47/34.03    (35)  all_56_14 = all_52_23
% 202.47/34.03    (36)  op(all_14_2, all_14_2) = all_52_30
% 202.47/34.03    (37)  op(all_52_17, all_52_17) = e3
% 202.47/34.03    (38)  op(e3, e2) = all_52_9
% 202.47/34.03    (39)   ~ (all_52_17 = all_6_2)
% 202.47/34.03    (40)   ~ (e1 = e0)
% 202.47/34.03    (41)   ~ (all_52_9 = all_52_17)
% 202.47/34.03    (42)  op(e1, e1) = all_10_2
% 202.47/34.03    (43)   ~ (all_52_23 = all_10_2)
% 202.47/34.03    (44)   ~ (all_52_7 = all_52_23)
% 202.47/34.03    (45)  all_56_13 = all_52_15
% 202.47/34.03    (46)   ~ (all_52_17 = all_52_23)
% 202.47/34.03    (47)  all_8_1 = all_6_1
% 202.47/34.03    (48)  op(all_6_2, e3) = all_6_1
% 202.47/34.03    (49)   ~ (all_52_7 = e0)
% 202.47/34.03  
% 202.47/34.03  Begin of proof
% 202.47/34.03  | 
% 202.47/34.03  | GROUND_INST: instantiating (5) with all_10_2, all_52_6, e1, e1, simplifying
% 202.47/34.03  |              with (19), (42) gives:
% 202.47/34.03  |   (50)  all_52_6 = all_10_2
% 202.47/34.03  | 
% 202.47/34.03  | BETA: splitting (15) gives:
% 202.47/34.03  | 
% 202.47/34.03  | Case 1:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (51)  all_56_13 = e3
% 202.47/34.03  | | 
% 202.47/34.03  | | COMBINE_EQS: (45), (51) imply:
% 202.47/34.03  | |   (52)  all_52_15 = e3
% 202.47/34.03  | | 
% 202.47/34.03  | | REF_CLOSE: (2), (5), (6), (7), (8), (11), (12), (17), (18), (21), (22),
% 202.47/34.03  | |            (23), (25), (26), (30), (31), (35), (42), (43), (44), (49), (52)
% 202.47/34.03  | |            are inconsistent by sub-proof #1282.
% 202.47/34.03  | | 
% 202.47/34.03  | Case 2:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (53)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.47/34.03  | | 
% 202.47/34.03  | | BETA: splitting (53) gives:
% 202.47/34.03  | | 
% 202.47/34.03  | | Case 1:
% 202.47/34.03  | | | 
% 202.47/34.03  | | |   (54)  all_56_13 = e2
% 202.47/34.03  | | | 
% 202.47/34.03  | | | COMBINE_EQS: (45), (54) imply:
% 202.47/34.03  | | |   (55)  all_52_15 = e2
% 202.47/34.03  | | | 
% 202.47/34.03  | | | REDUCE: (2), (55) imply:
% 202.47/34.03  | | |   (56)   ~ (all_52_23 = e2)
% 202.47/34.03  | | | 
% 202.47/34.03  | | | SIMP: (56) implies:
% 202.47/34.03  | | |   (57)   ~ (all_52_23 = e2)
% 202.47/34.03  | | | 
% 202.47/34.03  | | | BETA: splitting (21) gives:
% 202.47/34.03  | | | 
% 202.47/34.03  | | | Case 1:
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | |   (58)  all_56_14 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | COMBINE_EQS: (35), (58) imply:
% 202.47/34.03  | | | |   (59)  all_52_23 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | COMBINE_EQS: (4), (59) imply:
% 202.47/34.03  | | | |   (60)  all_58_14 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (46), (59) imply:
% 202.47/34.03  | | | |   (61)   ~ (all_52_17 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (43), (59) imply:
% 202.47/34.03  | | | |   (62)   ~ (all_10_2 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | SIMP: (62) implies:
% 202.47/34.03  | | | |   (63)   ~ (all_10_2 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (28), (59) imply:
% 202.47/34.03  | | | |   (64)   ~ (e3 = e1)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (6), (59) imply:
% 202.47/34.03  | | | |   (65)  op(e3, e3) = e0
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REF_CLOSE: (1), (5), (7), (9), (10), (13), (16), (20), (22), (23), (24),
% 202.47/34.03  | | | |            (26), (27), (29), (31), (32), (33), (34), (36), (37), (38),
% 202.47/34.03  | | | |            (39), (40), (41), (42), (45), (47), (48), (53), (60), (61),
% 202.47/34.03  | | | |            (63), (64), (65) are inconsistent by sub-proof #479.
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | Case 2:
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | |   (66)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REF_CLOSE: (28), (30), (35), (57), (66) are inconsistent by sub-proof
% 202.47/34.03  | | | |            #960.
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | End of split
% 202.47/34.03  | | | 
% 202.47/34.03  | | Case 2:
% 202.47/34.03  | | | 
% 202.47/34.03  | | |   (67)  all_56_13 = e1 | all_56_13 = e0
% 202.47/34.03  | | | 
% 202.47/34.03  | | | REF_CLOSE: (3), (14), (45), (67) are inconsistent by sub-proof #959.
% 202.47/34.03  | | | 
% 202.47/34.03  | | End of split
% 202.47/34.03  | | 
% 202.47/34.03  | End of split
% 202.47/34.03  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #424 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)  all_58_14 = all_52_23
% 202.47/34.03    (2)   ~ (e3 = e1)
% 202.47/34.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.03    (4)  all_58_1 = all_52_9
% 202.47/34.03    (5)  op(all_52_23, all_52_23) = e0
% 202.47/34.03    (6)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.47/34.03    (7)   ~ (all_4_2 = e3)
% 202.47/34.03    (8)  all_58_0 = all_6_2
% 202.47/34.03    (9)   ~ (all_10_0 = e3)
% 202.47/34.03    (10)  all_40_2 = all_10_2
% 202.47/34.03    (11)  op(all_52_5, all_52_5) = all_52_4
% 202.47/34.03    (12)  all_58_9 = all_52_25
% 202.47/34.03    (13)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.03    (14)  op(e2, e2) = all_4_2
% 202.47/34.03    (15)  all_58_7 = all_10_0
% 202.47/34.03    (16)  all_58_11 = all_52_29
% 202.47/34.03    (17)  op(e3, e3) = all_52_26
% 202.47/34.03    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.47/34.03    (19)  all_58_15 = e0
% 202.47/34.03    (20)  all_56_11 = all_52_29
% 202.47/34.03    (21)   ~ (all_10_0 = e2)
% 202.47/34.03    (22)   ~ (all_52_25 = e0)
% 202.47/34.03    (23)   ~ (e2 = e1)
% 202.47/34.03    (24)  op(all_52_9, all_52_9) = all_52_8
% 202.47/34.03    (25)  all_56_9 = all_10_0
% 202.47/34.03    (26)   ~ (all_52_25 = all_52_29)
% 202.47/34.03    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.03    (28)  op(e2, e1) = all_52_19
% 202.47/34.03    (29)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 202.47/34.03    (30)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.47/34.03    (31)   ~ (all_52_29 = e3)
% 202.47/34.03    (32)   ~ (all_52_25 = e3)
% 202.47/34.03    (33)   ~ (all_52_19 = e3)
% 202.47/34.03    (34)   ~ (all_52_5 = all_52_29)
% 202.47/34.03    (35)   ~ (all_52_29 = e0)
% 202.47/34.03    (36)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/34.03    (37)  op(e3, e1) = all_52_17
% 202.47/34.03    (38)   ~ (all_52_19 = all_10_2)
% 202.47/34.03    (39)  all_58_8 = all_10_2
% 202.47/34.03    (40)   ~ (all_52_5 = all_10_2)
% 202.47/34.03    (41)  op(all_52_29, all_52_29) = all_52_28
% 202.47/34.03    (42)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/34.03    (43)   ~ (all_52_9 = all_4_2)
% 202.47/34.03    (44)   ~ (all_52_5 = all_6_2)
% 202.47/34.03    (45)  all_58_10 = e3
% 202.47/34.03    (46)  op(e3, e3) = all_6_2
% 202.47/34.03    (47)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.03    (48)   ~ (all_52_29 = all_10_0)
% 202.47/34.03    (49)  all_40_0 = all_10_0
% 202.47/34.03    (50)  all_56_3 = all_52_25
% 202.47/34.03    (51)  all_58_5 = all_52_19
% 202.47/34.03    (52)  op(all_52_17, all_52_17) = e3
% 202.47/34.03    (53)  all_58_6 = all_52_5
% 202.47/34.03    (54)  op(all_10_2, e1) = e2
% 202.47/34.03    (55)   ~ (all_52_17 = all_6_2)
% 202.47/34.03    (56)   ~ (e1 = e0)
% 202.47/34.03    (57)   ~ (e3 = e2)
% 202.47/34.03    (58)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.03    (59)  all_58_4 = all_52_17
% 202.47/34.03  
% 202.47/34.03  Begin of proof
% 202.47/34.03  | 
% 202.47/34.03  | GROUND_INST: instantiating (3) with all_6_2, all_52_26, e3, e3, simplifying
% 202.47/34.03  |              with (17), (46) gives:
% 202.47/34.03  |   (60)  all_52_26 = all_6_2
% 202.47/34.03  | 
% 202.47/34.03  | BETA: splitting (42) gives:
% 202.47/34.03  | 
% 202.47/34.03  | Case 1:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (61)  all_56_3 = e3
% 202.47/34.03  | | 
% 202.47/34.03  | | REF_CLOSE: (32), (50), (61) are inconsistent by sub-proof #1339.
% 202.47/34.03  | | 
% 202.47/34.03  | Case 2:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (62)   ~ (all_56_3 = e3)
% 202.47/34.03  | |   (63)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.47/34.03  | | 
% 202.47/34.03  | | BETA: splitting (36) gives:
% 202.47/34.03  | | 
% 202.47/34.03  | | Case 1:
% 202.47/34.03  | | | 
% 202.47/34.03  | | |   (64)  all_56_11 = e3
% 202.47/34.03  | | | 
% 202.47/34.03  | | | REF_CLOSE: (20), (31), (64) are inconsistent by sub-proof #1028.
% 202.47/34.03  | | | 
% 202.47/34.03  | | Case 2:
% 202.47/34.03  | | | 
% 202.47/34.03  | | |   (65)   ~ (all_56_11 = e3)
% 202.47/34.03  | | |   (66)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.47/34.03  | | | 
% 202.47/34.03  | | | BETA: splitting (27) gives:
% 202.47/34.03  | | | 
% 202.47/34.03  | | | Case 1:
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | |   (67)  all_58_6 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | COMBINE_EQS: (53), (67) imply:
% 202.47/34.03  | | | |   (68)  all_52_5 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | SIMP: (68) implies:
% 202.47/34.03  | | | |   (69)  all_52_5 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (34), (69) imply:
% 202.47/34.03  | | | |   (70)   ~ (all_52_29 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (40), (69) imply:
% 202.47/34.03  | | | |   (71)   ~ (all_10_2 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | SIMP: (71) implies:
% 202.47/34.03  | | | |   (72)   ~ (all_10_2 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (44), (69) imply:
% 202.47/34.03  | | | |   (73)   ~ (all_6_2 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | SIMP: (73) implies:
% 202.47/34.03  | | | |   (74)   ~ (all_6_2 = e3)
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REDUCE: (11), (69) imply:
% 202.47/34.03  | | | |   (75)  op(e3, e3) = all_52_4
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_4, e3, e3,
% 202.47/34.03  | | | |              simplifying with (46), (75) gives:
% 202.47/34.03  | | | |   (76)  all_52_4 = all_6_2
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | BETA: splitting (18) gives:
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | Case 1:
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | |   (77)  all_58_9 = e1
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | COMBINE_EQS: (12), (77) imply:
% 202.47/34.03  | | | | |   (78)  all_52_25 = e1
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | SIMP: (78) implies:
% 202.47/34.03  | | | | |   (79)  all_52_25 = e1
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | REDUCE: (26), (79) imply:
% 202.47/34.03  | | | | |   (80)   ~ (all_52_29 = e1)
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | SIMP: (80) implies:
% 202.47/34.03  | | | | |   (81)   ~ (all_52_29 = e1)
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | BETA: splitting (66) gives:
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | Case 1:
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | |   (82)  all_56_11 = e2
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | COMBINE_EQS: (20), (82) imply:
% 202.47/34.03  | | | | | |   (83)  all_52_29 = e2
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | SIMP: (83) implies:
% 202.47/34.03  | | | | | |   (84)  all_52_29 = e2
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | COMBINE_EQS: (16), (84) imply:
% 202.47/34.03  | | | | | |   (85)  all_58_11 = e2
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | REDUCE: (48), (84) imply:
% 202.47/34.03  | | | | | |   (86)   ~ (all_10_0 = e2)
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | REDUCE: (31), (84) imply:
% 202.47/34.03  | | | | | |   (87)   ~ (e3 = e2)
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | REDUCE: (35), (84) imply:
% 202.47/34.03  | | | | | |   (88)   ~ (e2 = e0)
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | REDUCE: (41), (84) imply:
% 202.47/34.03  | | | | | |   (89)  op(e2, e2) = all_52_28
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_52_28, e2, e2,
% 202.47/34.03  | | | | | |              simplifying with (14), (89) gives:
% 202.47/34.03  | | | | | |   (90)  all_52_28 = all_4_2
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | BETA: splitting (58) gives:
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | Case 1:
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | |   (91)  all_58_4 = e3
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | COMBINE_EQS: (59), (91) imply:
% 202.47/34.03  | | | | | | |   (92)  all_52_17 = e3
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | REF_CLOSE: (3), (46), (52), (55), (92) are inconsistent by
% 202.47/34.03  | | | | | | |            sub-proof #1280.
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | Case 2:
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | |   (93)   ~ (all_58_4 = e3)
% 202.47/34.03  | | | | | | |   (94)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | REDUCE: (59), (93) imply:
% 202.47/34.03  | | | | | | |   (95)   ~ (all_52_17 = e3)
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | BETA: splitting (94) gives:
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | |   (96)  all_58_5 = e3
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | COMBINE_EQS: (51), (96) imply:
% 202.47/34.03  | | | | | | | |   (97)  all_52_19 = e3
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | REDUCE: (33), (97) imply:
% 202.47/34.03  | | | | | | | |   (98)  $false
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | CLOSE: (98) is inconsistent.
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | |   (99)  all_58_8 = e3 | all_58_14 = e3
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | BETA: splitting (47) gives:
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | |   (100)  all_58_0 = e3
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | COMBINE_EQS: (8), (100) imply:
% 202.47/34.03  | | | | | | | | |   (101)  all_6_2 = e3
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | REDUCE: (74), (101) imply:
% 202.47/34.03  | | | | | | | | |   (102)  $false
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | CLOSE: (102) is inconsistent.
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | |   (103)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | BETA: splitting (103) gives:
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | |   (104)  all_58_1 = e3
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | COMBINE_EQS: (4), (104) imply:
% 202.47/34.03  | | | | | | | | | |   (105)  all_52_9 = e3
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | REDUCE: (43), (105) imply:
% 202.47/34.03  | | | | | | | | | |   (106)   ~ (all_4_2 = e3)
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | REDUCE: (24), (105) imply:
% 202.47/34.03  | | | | | | | | | |   (107)  op(e3, e3) = all_52_8
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | BETA: splitting (99) gives:
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | |   (108)  all_58_8 = e3
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | COMBINE_EQS: (39), (108) imply:
% 202.47/34.03  | | | | | | | | | | |   (109)  all_10_2 = e3
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | REDUCE: (72), (109) imply:
% 202.47/34.03  | | | | | | | | | | |   (110)  $false
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | |   (111)  all_58_14 = e3
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | COMBINE_EQS: (1), (111) imply:
% 202.47/34.03  | | | | | | | | | | |   (112)  all_52_23 = e3
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | SIMP: (112) implies:
% 202.47/34.03  | | | | | | | | | | |   (113)  all_52_23 = e3
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | REDUCE: (5), (113) imply:
% 202.47/34.03  | | | | | | | | | | |   (114)  op(e3, e3) = e0
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_8, e3, e3,
% 202.47/34.03  | | | | | | | | | | |              simplifying with (46), (107) gives:
% 202.47/34.03  | | | | | | | | | | |   (115)  all_52_8 = all_6_2
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_52_8, e3, e3,
% 202.47/34.03  | | | | | | | | | | |              simplifying with (107), (114) gives:
% 202.47/34.03  | | | | | | | | | | |   (116)  all_52_8 = e0
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | COMBINE_EQS: (115), (116) imply:
% 202.47/34.03  | | | | | | | | | | |   (117)  all_6_2 = e0
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | SIMP: (117) implies:
% 202.47/34.03  | | | | | | | | | | |   (118)  all_6_2 = e0
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | COMBINE_EQS: (8), (118) imply:
% 202.47/34.03  | | | | | | | | | | |   (119)  all_58_0 = e0
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | BETA: splitting (30) gives:
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | |   (120)  all_58_0 = e2
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | REF_CLOSE: (88), (119), (120) are inconsistent by sub-proof
% 202.47/34.03  | | | | | | | | | | | |            #812.
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | |   (121)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | BETA: splitting (121) gives:
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | |   (122)  all_58_1 = e2
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | COMBINE_EQS: (104), (122) imply:
% 202.47/34.03  | | | | | | | | | | | | |   (123)  e3 = e2
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | REDUCE: (57), (123) imply:
% 202.47/34.03  | | | | | | | | | | | | |   (124)  $false
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | |   (125)   ~ (all_58_1 = e2)
% 202.47/34.03  | | | | | | | | | | | | |   (126)  all_58_4 = e2 | all_58_9 = e2
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | BETA: splitting (126) gives:
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | |   (127)  all_58_4 = e2
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (14), (52), (59), (127) are inconsistent
% 202.47/34.03  | | | | | | | | | | | | | |            by sub-proof #1087.
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | |   (128)  all_58_9 = e2
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | | COMBINE_EQS: (77), (128) imply:
% 202.47/34.03  | | | | | | | | | | | | | |   (129)  e2 = e1
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | | COMBINE_EQS: (85), (129) imply:
% 202.47/34.03  | | | | | | | | | | | | | |   (130)  all_58_11 = e1
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (15), (21), (23), (28), (38), (39),
% 202.47/34.03  | | | | | | | | | | | | | |            (54), (57), (67), (130) are inconsistent by
% 202.47/34.03  | | | | | | | | | | | | | |            sub-proof #426.
% 202.47/34.03  | | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | | End of split
% 202.47/34.03  | | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | | End of split
% 202.47/34.03  | | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | | End of split
% 202.47/34.03  | | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | End of split
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | |   (131)  all_58_4 = e3 | all_58_9 = e3
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | | REF_CLOSE: (12), (32), (59), (95), (131) are inconsistent by
% 202.47/34.03  | | | | | | | | | |            sub-proof #1276.
% 202.47/34.03  | | | | | | | | | | 
% 202.47/34.03  | | | | | | | | | End of split
% 202.47/34.03  | | | | | | | | | 
% 202.47/34.03  | | | | | | | | End of split
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | End of split
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | End of split
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | Case 2:
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | |   (132)  all_56_11 = e1 | all_56_11 = e0
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | REF_CLOSE: (3), (13), (15), (16), (20), (21), (23), (28), (35),
% 202.47/34.03  | | | | | |            (38), (39), (54), (57), (67), (132) are inconsistent by
% 202.47/34.03  | | | | | |            sub-proof #425.
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | End of split
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | Case 2:
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | |   (133)   ~ (all_58_9 = e1)
% 202.47/34.03  | | | | |   (134)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | REDUCE: (12), (133) imply:
% 202.47/34.03  | | | | |   (135)   ~ (all_52_25 = e1)
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | BETA: splitting (134) gives:
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | | Case 1:
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | |   (136)  all_58_10 = e1
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | REF_CLOSE: (2), (45), (136) are inconsistent by sub-proof #968.
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | Case 2:
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | |   (137)  all_58_11 = e1 | all_58_15 = e1
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | BETA: splitting (63) gives:
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | | Case 1:
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | |   (138)  all_56_3 = e2
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | COMBINE_EQS: (50), (138) imply:
% 202.47/34.03  | | | | | | |   (139)  all_52_25 = e2
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | SIMP: (139) implies:
% 202.47/34.03  | | | | | | |   (140)  all_52_25 = e2
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | REDUCE: (26), (140) imply:
% 202.47/34.03  | | | | | | |   (141)   ~ (all_52_29 = e2)
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | SIMP: (141) implies:
% 202.47/34.03  | | | | | | |   (142)   ~ (all_52_29 = e2)
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | REDUCE: (32), (140) imply:
% 202.47/34.03  | | | | | | |   (143)   ~ (e3 = e2)
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | BETA: splitting (137) gives:
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | Case 1:
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | |   (144)  all_58_11 = e1
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | COMBINE_EQS: (16), (144) imply:
% 202.47/34.03  | | | | | | | |   (145)  all_52_29 = e1
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | SIMP: (145) implies:
% 202.47/34.03  | | | | | | | |   (146)  all_52_29 = e1
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | REDUCE: (142), (146) imply:
% 202.47/34.03  | | | | | | | |   (147)   ~ (e2 = e1)
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | REF_CLOSE: (3), (13), (15), (21), (23), (28), (38), (39), (54),
% 202.47/34.03  | | | | | | | |            (57), (67), (144) are inconsistent by sub-proof #426.
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | Case 2:
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | |   (148)  all_58_15 = e1
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | | REF_CLOSE: (19), (56), (148) are inconsistent by sub-proof
% 202.47/34.03  | | | | | | | |            #1207.
% 202.47/34.03  | | | | | | | | 
% 202.47/34.03  | | | | | | | End of split
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | Case 2:
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | |   (149)  all_56_3 = e1 | all_56_3 = e0
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | | REF_CLOSE: (22), (50), (135), (149) are inconsistent by sub-proof
% 202.47/34.03  | | | | | | |            #1330.
% 202.47/34.03  | | | | | | | 
% 202.47/34.03  | | | | | | End of split
% 202.47/34.03  | | | | | | 
% 202.47/34.03  | | | | | End of split
% 202.47/34.03  | | | | | 
% 202.47/34.03  | | | | End of split
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | Case 2:
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | |   (150)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | | REF_CLOSE: (3), (6), (7), (9), (10), (14), (15), (16), (21), (25), (29),
% 202.47/34.03  | | | |            (31), (37), (39), (49), (52), (54), (150) are inconsistent by
% 202.47/34.03  | | | |            sub-proof #789.
% 202.47/34.03  | | | | 
% 202.47/34.03  | | | End of split
% 202.47/34.03  | | | 
% 202.47/34.03  | | End of split
% 202.47/34.03  | | 
% 202.47/34.03  | End of split
% 202.47/34.03  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #425 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.03    (2)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.03    (3)  all_58_7 = all_10_0
% 202.47/34.03    (4)  all_58_11 = all_52_29
% 202.47/34.03    (5)  all_56_11 = all_52_29
% 202.47/34.03    (6)   ~ (all_10_0 = e2)
% 202.47/34.03    (7)  all_58_6 = e3
% 202.47/34.03    (8)   ~ (e2 = e1)
% 202.47/34.03    (9)  op(e2, e1) = all_52_19
% 202.47/34.03    (10)   ~ (all_52_29 = e0)
% 202.47/34.03    (11)   ~ (all_52_19 = all_10_2)
% 202.47/34.03    (12)  all_58_8 = all_10_2
% 202.47/34.03    (13)  all_56_11 = e1 | all_56_11 = e0
% 202.47/34.03    (14)  op(all_10_2, e1) = e2
% 202.47/34.03    (15)   ~ (e3 = e2)
% 202.47/34.03  
% 202.47/34.03  Begin of proof
% 202.47/34.03  | 
% 202.47/34.03  | BETA: splitting (13) gives:
% 202.47/34.03  | 
% 202.47/34.03  | Case 1:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (16)  all_56_11 = e1
% 202.47/34.03  | | 
% 202.47/34.03  | | COMBINE_EQS: (5), (16) imply:
% 202.47/34.03  | |   (17)  all_52_29 = e1
% 202.47/34.03  | | 
% 202.47/34.03  | | SIMP: (17) implies:
% 202.47/34.03  | |   (18)  all_52_29 = e1
% 202.47/34.03  | | 
% 202.47/34.03  | | COMBINE_EQS: (4), (18) imply:
% 202.47/34.03  | |   (19)  all_58_11 = e1
% 202.47/34.03  | | 
% 202.47/34.03  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11), (12), (14), (15), (19)
% 202.47/34.03  | |            are inconsistent by sub-proof #426.
% 202.47/34.03  | | 
% 202.47/34.03  | Case 2:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (20)  all_56_11 = e0
% 202.47/34.03  | | 
% 202.47/34.03  | | REF_CLOSE: (5), (10), (20) are inconsistent by sub-proof #1002.
% 202.47/34.03  | | 
% 202.47/34.03  | End of split
% 202.47/34.03  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #426 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.03    (2)  all_58_11 = e1
% 202.47/34.03    (3)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.03    (4)  all_58_7 = all_10_0
% 202.47/34.03    (5)   ~ (all_10_0 = e2)
% 202.47/34.03    (6)  all_58_6 = e3
% 202.47/34.03    (7)   ~ (e2 = e1)
% 202.47/34.03    (8)  op(e2, e1) = all_52_19
% 202.47/34.03    (9)   ~ (all_52_19 = all_10_2)
% 202.47/34.03    (10)  all_58_8 = all_10_2
% 202.47/34.03    (11)  op(all_10_2, e1) = e2
% 202.47/34.03    (12)   ~ (e3 = e2)
% 202.47/34.03  
% 202.47/34.03  Begin of proof
% 202.47/34.03  | 
% 202.47/34.03  | BETA: splitting (3) gives:
% 202.47/34.03  | 
% 202.47/34.03  | Case 1:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (13)  all_58_6 = e2
% 202.47/34.03  | | 
% 202.47/34.03  | | REF_CLOSE: (6), (12), (13) are inconsistent by sub-proof #428.
% 202.47/34.03  | | 
% 202.47/34.03  | Case 2:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (14)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 202.47/34.03  | | 
% 202.47/34.03  | | BETA: splitting (14) gives:
% 202.47/34.03  | | 
% 202.47/34.03  | | Case 1:
% 202.47/34.03  | | | 
% 202.47/34.03  | | |   (15)  all_58_7 = e2
% 202.47/34.03  | | | 
% 202.47/34.03  | | | COMBINE_EQS: (4), (15) imply:
% 202.47/34.03  | | |   (16)  all_10_0 = e2
% 202.47/34.03  | | | 
% 202.47/34.03  | | | REDUCE: (5), (16) imply:
% 202.47/34.03  | | |   (17)  $false
% 202.47/34.03  | | | 
% 202.47/34.03  | | | CLOSE: (17) is inconsistent.
% 202.47/34.03  | | | 
% 202.47/34.03  | | Case 2:
% 202.47/34.03  | | | 
% 202.47/34.03  | | |   (18)  all_58_8 = e2 | all_58_11 = e2
% 202.47/34.03  | | | 
% 202.47/34.03  | | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (11), (18) are inconsistent by
% 202.47/34.03  | | |            sub-proof #427.
% 202.47/34.03  | | | 
% 202.47/34.03  | | End of split
% 202.47/34.03  | | 
% 202.47/34.03  | End of split
% 202.47/34.03  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #427 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.03    (2)  all_58_11 = e1
% 202.47/34.03    (3)   ~ (e2 = e1)
% 202.47/34.03    (4)  op(e2, e1) = all_52_19
% 202.47/34.03    (5)   ~ (all_52_19 = all_10_2)
% 202.47/34.03    (6)  all_58_8 = all_10_2
% 202.47/34.03    (7)  all_58_8 = e2 | all_58_11 = e2
% 202.47/34.03    (8)  op(all_10_2, e1) = e2
% 202.47/34.03  
% 202.47/34.03  Begin of proof
% 202.47/34.03  | 
% 202.47/34.03  | BETA: splitting (7) gives:
% 202.47/34.03  | 
% 202.47/34.03  | Case 1:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (9)  all_58_8 = e2
% 202.47/34.03  | | 
% 202.47/34.03  | | REF_CLOSE: (1), (4), (5), (6), (8), (9) are inconsistent by sub-proof #999.
% 202.47/34.03  | | 
% 202.47/34.03  | Case 2:
% 202.47/34.03  | | 
% 202.47/34.03  | |   (10)  all_58_11 = e2
% 202.47/34.03  | | 
% 202.47/34.03  | | COMBINE_EQS: (2), (10) imply:
% 202.47/34.03  | |   (11)  e2 = e1
% 202.47/34.03  | | 
% 202.47/34.03  | | REDUCE: (3), (11) imply:
% 202.47/34.03  | |   (12)  $false
% 202.47/34.03  | | 
% 202.47/34.03  | | CLOSE: (12) is inconsistent.
% 202.47/34.03  | | 
% 202.47/34.03  | End of split
% 202.47/34.03  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #428 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)  all_58_6 = e3
% 202.47/34.03    (2)  all_58_6 = e2
% 202.47/34.03    (3)   ~ (e3 = e2)
% 202.47/34.03  
% 202.47/34.03  Begin of proof
% 202.47/34.03  | 
% 202.47/34.03  | COMBINE_EQS: (1), (2) imply:
% 202.47/34.03  |   (4)  e3 = e2
% 202.47/34.03  | 
% 202.47/34.03  | SIMP: (4) implies:
% 202.47/34.03  |   (5)  e3 = e2
% 202.47/34.03  | 
% 202.47/34.03  | REDUCE: (3), (5) imply:
% 202.47/34.03  |   (6)  $false
% 202.47/34.03  | 
% 202.47/34.03  | CLOSE: (6) is inconsistent.
% 202.47/34.03  | 
% 202.47/34.03  End of proof
% 202.47/34.03  
% 202.47/34.03  Sub-proof #429 shows that the following formulas are inconsistent:
% 202.47/34.03  ----------------------------------------------------------------
% 202.47/34.03    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.47/34.03    (2)  op(all_52_3, all_52_3) = all_52_2
% 202.47/34.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.47/34.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.47/34.03    (4)  all_58_1 = all_52_9
% 202.47/34.03    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.47/34.03    (6)   ~ (all_52_7 = all_52_15)
% 202.75/34.03    (7)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.03    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.75/34.03    (9)  all_58_0 = all_6_2
% 202.75/34.03    (10)   ~ (all_10_0 = e3)
% 202.75/34.03    (11)  op(all_52_5, all_52_5) = all_52_4
% 202.75/34.03    (12)  all_58_13 = all_52_15
% 202.75/34.03    (13)  all_58_9 = all_52_25
% 202.75/34.03    (14)  op(e2, e2) = all_4_2
% 202.75/34.03    (15)  all_58_7 = all_10_0
% 202.75/34.03    (16)   ~ (all_52_25 = all_14_2)
% 202.75/34.03    (17)  op(all_6_2, all_6_2) = all_52_0
% 202.75/34.03    (18)   ~ (all_52_7 = all_6_2)
% 202.75/34.03    (19)  op(e0, e0) = all_14_2
% 202.75/34.03    (20)  all_56_15 = all_14_2
% 202.75/34.03    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.03    (22)   ~ (all_10_0 = e2)
% 202.75/34.03    (23)   ~ (all_4_1 = e1)
% 202.75/34.03    (24)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.75/34.03    (25)  op(all_52_9, all_52_9) = all_52_8
% 202.75/34.03    (26)  op(all_52_15, all_52_15) = all_52_14
% 202.75/34.03    (27)  all_56_9 = all_10_0
% 202.75/34.03    (28)  all_58_12 = all_52_7
% 202.75/34.03    (29)   ~ (all_52_7 = all_14_2)
% 202.75/34.03    (30)  all_58_2 = all_52_3
% 202.75/34.03    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.75/34.03    (32)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.75/34.03    (33)   ~ (e2 = e0)
% 202.75/34.03    (34)  op(all_4_2, e2) = all_4_1
% 202.75/34.03    (35)   ~ (all_52_15 = all_14_2)
% 202.75/34.03    (36)  op(e0, e3) = all_52_7
% 202.75/34.04    (37)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04    (38)   ~ (all_10_0 = all_10_2)
% 202.75/34.04    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.04    (40)   ~ (all_52_5 = all_10_2)
% 202.75/34.04    (41)  all_56_12 = all_52_7
% 202.75/34.04    (42)  op(all_52_17, all_52_17) = all_52_16
% 202.75/34.04    (43)  all_8_2 = all_6_2
% 202.75/34.04    (44)   ~ (all_52_9 = all_4_2)
% 202.75/34.04    (45)   ~ (all_52_9 = all_6_2)
% 202.75/34.04    (46)  op(e3, all_6_1) = e2
% 202.75/34.04    (47)  all_56_0 = all_6_2
% 202.75/34.04    (48)  op(e3, e3) = all_6_2
% 202.75/34.04    (49)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.04    (50)  op(all_4_2, all_4_2) = all_52_10
% 202.75/34.04    (51)  all_56_1 = all_52_9
% 202.75/34.04    (52)   ~ (all_52_15 = all_4_2)
% 202.75/34.04    (53)  all_58_6 = all_52_5
% 202.75/34.04    (54)  op(e3, e2) = all_52_9
% 202.75/34.04    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.04    (56)   ~ (e3 = e2)
% 202.75/34.04    (57)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.75/34.04          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.75/34.04    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.75/34.04    (59)   ~ (all_52_9 = all_52_17)
% 202.75/34.04    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.04    (61)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.75/34.04    (62)  op(all_10_0, all_10_0) = all_52_12
% 202.75/34.04    (63)  op(e1, e1) = all_10_2
% 202.75/34.04    (64)  all_58_3 = all_4_2
% 202.75/34.04    (65)  all_56_13 = all_52_15
% 202.75/34.04    (66)   ~ (all_52_3 = all_4_2)
% 202.75/34.04    (67)   ~ (all_52_9 = all_10_0)
% 202.75/34.04    (68)  all_8_1 = all_6_1
% 202.75/34.04    (69)  op(all_6_2, e3) = all_6_1
% 202.75/34.04    (70)  all_58_4 = all_52_17
% 202.75/34.04  
% 202.75/34.04  Begin of proof
% 202.75/34.04  | 
% 202.75/34.04  | BETA: splitting (57) gives:
% 202.75/34.04  | 
% 202.75/34.04  | Case 1:
% 202.75/34.04  | | 
% 202.75/34.04  | |   (71)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.75/34.04  | | 
% 202.75/34.04  | | REF_CLOSE: (2), (3), (7), (9), (11), (14), (17), (19), (21), (28), (29),
% 202.75/34.04  | |            (30), (31), (40), (46), (47), (48), (53), (55), (56), (61), (63),
% 202.75/34.04  | |            (66), (69), (71) are inconsistent by sub-proof #501.
% 202.75/34.04  | | 
% 202.75/34.04  | Case 2:
% 202.75/34.04  | | 
% 202.75/34.04  | |   (72)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 202.75/34.04  | | 
% 202.75/34.04  | | ALPHA: (72) implies:
% 202.75/34.04  | |   (73)  all_52_14 = e0
% 202.75/34.04  | |   (74)  all_52_12 = e1
% 202.75/34.04  | |   (75)  all_52_10 = e2
% 202.75/34.04  | |   (76)  all_52_8 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (25), (76) imply:
% 202.75/34.04  | |   (77)  op(all_52_9, all_52_9) = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (26), (73) imply:
% 202.75/34.04  | |   (78)  op(all_52_15, all_52_15) = e0
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (62), (74) imply:
% 202.75/34.04  | |   (79)  op(all_10_0, all_10_0) = e1
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (50), (75) imply:
% 202.75/34.04  | |   (80)  op(all_4_2, all_4_2) = e2
% 202.75/34.04  | | 
% 202.75/34.04  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 202.75/34.04  | |            (15), (16), (18), (19), (20), (22), (23), (24), (27), (29), (32),
% 202.75/34.04  | |            (33), (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 202.75/34.04  | |            (45), (46), (48), (49), (51), (52), (54), (56), (58), (59), (60),
% 202.75/34.04  | |            (63), (64), (65), (67), (68), (69), (70), (77), (78), (79), (80)
% 202.75/34.04  | |            are inconsistent by sub-proof #430.
% 202.75/34.04  | | 
% 202.75/34.04  | End of split
% 202.75/34.04  | 
% 202.75/34.04  End of proof
% 202.75/34.04  
% 202.75/34.04  Sub-proof #430 shows that the following formulas are inconsistent:
% 202.75/34.04  ----------------------------------------------------------------
% 202.75/34.04    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.04    (3)  all_58_1 = all_52_9
% 202.75/34.04    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.04    (5)   ~ (all_52_7 = all_52_15)
% 202.75/34.04    (6)  op(all_52_15, all_52_15) = e0
% 202.75/34.04    (7)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.04    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.75/34.04    (9)  all_58_0 = all_6_2
% 202.75/34.04    (10)   ~ (all_10_0 = e3)
% 202.75/34.04    (11)  all_58_13 = all_52_15
% 202.75/34.04    (12)  op(all_10_0, all_10_0) = e1
% 202.75/34.04    (13)  all_58_9 = all_52_25
% 202.75/34.04    (14)  op(e2, e2) = all_4_2
% 202.75/34.04    (15)  all_58_7 = all_10_0
% 202.75/34.04    (16)   ~ (all_52_25 = all_14_2)
% 202.75/34.04    (17)   ~ (all_52_7 = all_6_2)
% 202.75/34.04    (18)  op(e0, e0) = all_14_2
% 202.75/34.04    (19)  all_56_15 = all_14_2
% 202.75/34.04    (20)   ~ (all_10_0 = e2)
% 202.75/34.04    (21)   ~ (all_4_1 = e1)
% 202.75/34.04    (22)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.75/34.04    (23)  all_56_9 = all_10_0
% 202.75/34.04    (24)   ~ (all_52_7 = all_14_2)
% 202.75/34.04    (25)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.75/34.04    (26)   ~ (e2 = e0)
% 202.75/34.04    (27)  op(all_4_2, e2) = all_4_1
% 202.75/34.04    (28)   ~ (all_52_15 = all_14_2)
% 202.75/34.04    (29)  op(e0, e3) = all_52_7
% 202.75/34.04    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04    (31)   ~ (all_10_0 = all_10_2)
% 202.75/34.04    (32)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.04    (33)  all_56_12 = all_52_7
% 202.75/34.04    (34)  op(all_52_17, all_52_17) = all_52_16
% 202.75/34.04    (35)  all_8_2 = all_6_2
% 202.75/34.04    (36)   ~ (all_52_9 = all_4_2)
% 202.75/34.04    (37)  op(all_4_2, all_4_2) = e2
% 202.75/34.04    (38)   ~ (all_52_9 = all_6_2)
% 202.75/34.04    (39)  op(e3, all_6_1) = e2
% 202.75/34.04    (40)  op(e3, e3) = all_6_2
% 202.75/34.04    (41)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.04    (42)  all_56_1 = all_52_9
% 202.75/34.04    (43)   ~ (all_52_15 = all_4_2)
% 202.75/34.04    (44)  op(e3, e2) = all_52_9
% 202.75/34.04    (45)   ~ (e3 = e2)
% 202.75/34.04    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.75/34.04    (47)   ~ (all_52_9 = all_52_17)
% 202.75/34.04    (48)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.04    (49)  op(e1, e1) = all_10_2
% 202.75/34.04    (50)  op(all_52_9, all_52_9) = e3
% 202.75/34.04    (51)  all_58_3 = all_4_2
% 202.75/34.04    (52)  all_56_13 = all_52_15
% 202.75/34.04    (53)   ~ (all_52_9 = all_10_0)
% 202.75/34.04    (54)  all_8_1 = all_6_1
% 202.75/34.04    (55)  op(all_6_2, e3) = all_6_1
% 202.75/34.04    (56)  all_58_4 = all_52_17
% 202.75/34.04  
% 202.75/34.04  Begin of proof
% 202.75/34.04  | 
% 202.75/34.04  | BETA: splitting (32) gives:
% 202.75/34.04  | 
% 202.75/34.04  | Case 1:
% 202.75/34.04  | | 
% 202.75/34.04  | |   (57)  all_56_15 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | COMBINE_EQS: (19), (57) imply:
% 202.75/34.04  | |   (58)  all_14_2 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | SIMP: (58) implies:
% 202.75/34.04  | |   (59)  all_14_2 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (28), (59) imply:
% 202.75/34.04  | |   (60)   ~ (all_52_15 = e3)
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (16), (59) imply:
% 202.75/34.04  | |   (61)   ~ (all_52_25 = e3)
% 202.75/34.04  | | 
% 202.75/34.04  | | BETA: splitting (30) gives:
% 202.75/34.04  | | 
% 202.75/34.04  | | Case 1:
% 202.75/34.04  | | | 
% 202.75/34.04  | | |   (62)  all_58_1 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | COMBINE_EQS: (3), (62) imply:
% 202.75/34.04  | | |   (63)  all_52_9 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REF_CLOSE: (2), (38), (40), (50), (63) are inconsistent by sub-proof
% 202.75/34.04  | | |            #1337.
% 202.75/34.04  | | | 
% 202.75/34.04  | | Case 2:
% 202.75/34.04  | | | 
% 202.75/34.04  | | |   (64)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | BETA: splitting (64) gives:
% 202.75/34.04  | | | 
% 202.75/34.04  | | | Case 1:
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | |   (65)  all_58_3 = e3
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | COMBINE_EQS: (51), (65) imply:
% 202.75/34.04  | | | |   (66)  all_4_2 = e3
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | REDUCE: (36), (66) imply:
% 202.75/34.04  | | | |   (67)   ~ (all_52_9 = e3)
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | REDUCE: (37), (66) imply:
% 202.75/34.04  | | | |   (68)  op(e3, e3) = e2
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | REDUCE: (27), (66) imply:
% 202.75/34.04  | | | |   (69)  op(e3, e2) = all_4_1
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | BETA: splitting (48) gives:
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | Case 1:
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | |   (70)  all_58_4 = e3
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | COMBINE_EQS: (56), (70) imply:
% 202.75/34.04  | | | | |   (71)  all_52_17 = e3
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | SIMP: (71) implies:
% 202.75/34.04  | | | | |   (72)  all_52_17 = e3
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | REDUCE: (34), (72) imply:
% 202.75/34.04  | | | | |   (73)  op(e3, e3) = all_52_16
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | GROUND_INST: instantiating (2) with all_52_9, all_4_1, e2, e3,
% 202.75/34.04  | | | | |              simplifying with (44), (69) gives:
% 202.75/34.04  | | | | |   (74)  all_52_9 = all_4_1
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_16, e3, e3,
% 202.75/34.04  | | | | |              simplifying with (40), (73) gives:
% 202.75/34.04  | | | | |   (75)  all_52_16 = all_6_2
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | GROUND_INST: instantiating (2) with e2, all_52_16, e3, e3, simplifying
% 202.75/34.04  | | | | |              with (68), (73) gives:
% 202.75/34.04  | | | | |   (76)  all_52_16 = e2
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | COMBINE_EQS: (75), (76) imply:
% 202.75/34.04  | | | | |   (77)  all_6_2 = e2
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | SIMP: (77) implies:
% 202.75/34.04  | | | | |   (78)  all_6_2 = e2
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | REF_CLOSE: (2), (3), (8), (9), (12), (20), (21), (23), (25), (26),
% 202.75/34.04  | | | | |            (31), (38), (42), (46), (49), (53), (67), (74), (78) are
% 202.75/34.04  | | | | |            inconsistent by sub-proof #718.
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | Case 2:
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | |   (79)   ~ (all_58_4 = e3)
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | REDUCE: (56), (79) imply:
% 202.75/34.04  | | | | |   (80)   ~ (all_52_17 = e3)
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | | REF_CLOSE: (2), (3), (9), (13), (39), (40), (41), (45), (55), (56),
% 202.75/34.04  | | | | |            (61), (67), (80) are inconsistent by sub-proof #476.
% 202.75/34.04  | | | | | 
% 202.75/34.04  | | | | End of split
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | Case 2:
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | |   (81)  all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | | REF_CLOSE: (10), (11), (15), (60), (81) are inconsistent by sub-proof
% 202.75/34.04  | | | |            #717.
% 202.75/34.04  | | | | 
% 202.75/34.04  | | | End of split
% 202.75/34.04  | | | 
% 202.75/34.04  | | End of split
% 202.75/34.04  | | 
% 202.75/34.04  | Case 2:
% 202.75/34.04  | | 
% 202.75/34.04  | |   (82)   ~ (all_56_15 = e3)
% 202.75/34.04  | |   (83)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.04  | | 
% 202.75/34.04  | | REDUCE: (19), (82) imply:
% 202.75/34.04  | |   (84)   ~ (all_14_2 = e3)
% 202.75/34.04  | | 
% 202.75/34.04  | | BETA: splitting (22) gives:
% 202.75/34.04  | | 
% 202.75/34.04  | | Case 1:
% 202.75/34.04  | | | 
% 202.75/34.04  | | |   (85)  all_56_13 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | COMBINE_EQS: (52), (85) imply:
% 202.75/34.04  | | |   (86)  all_52_15 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (14), (17), (19), (24), (29),
% 202.75/34.04  | | |            (33), (35), (39), (40), (43), (44), (50), (54), (55), (83),
% 202.75/34.04  | | |            (86) are inconsistent by sub-proof #432.
% 202.75/34.04  | | | 
% 202.75/34.04  | | Case 2:
% 202.75/34.04  | | | 
% 202.75/34.04  | | |   (87)   ~ (all_56_13 = e3)
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REDUCE: (52), (87) imply:
% 202.75/34.04  | | |   (88)   ~ (all_52_15 = e3)
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REF_CLOSE: (2), (3), (10), (11), (15), (18), (21), (27), (30), (36), (37),
% 202.75/34.04  | | |            (38), (40), (42), (44), (46), (50), (51), (84), (88) are
% 202.75/34.04  | | |            inconsistent by sub-proof #431.
% 202.75/34.04  | | | 
% 202.75/34.04  | | End of split
% 202.75/34.04  | | 
% 202.75/34.04  | End of split
% 202.75/34.04  | 
% 202.75/34.04  End of proof
% 202.75/34.04  
% 202.75/34.04  Sub-proof #431 shows that the following formulas are inconsistent:
% 202.75/34.04  ----------------------------------------------------------------
% 202.75/34.04    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.04    (2)  all_58_1 = all_52_9
% 202.75/34.04    (3)   ~ (all_10_0 = e3)
% 202.75/34.04    (4)  all_58_13 = all_52_15
% 202.75/34.04    (5)   ~ (all_52_15 = e3)
% 202.75/34.04    (6)  all_58_7 = all_10_0
% 202.75/34.04    (7)  op(e0, e0) = all_14_2
% 202.75/34.04    (8)   ~ (all_4_1 = e1)
% 202.75/34.04    (9)  op(all_4_2, e2) = all_4_1
% 202.75/34.04    (10)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04    (11)   ~ (all_52_9 = all_4_2)
% 202.75/34.04    (12)  op(all_4_2, all_4_2) = e2
% 202.75/34.04    (13)   ~ (all_52_9 = all_6_2)
% 202.75/34.04    (14)  op(e3, e3) = all_6_2
% 202.75/34.04    (15)  all_56_1 = all_52_9
% 202.75/34.04    (16)  op(e3, e2) = all_52_9
% 202.75/34.04    (17)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.75/34.04    (18)  op(all_52_9, all_52_9) = e3
% 202.75/34.04    (19)  all_58_3 = all_4_2
% 202.75/34.04    (20)   ~ (all_14_2 = e3)
% 202.75/34.04  
% 202.75/34.04  Begin of proof
% 202.75/34.04  | 
% 202.75/34.04  | BETA: splitting (10) gives:
% 202.75/34.04  | 
% 202.75/34.04  | Case 1:
% 202.75/34.04  | | 
% 202.75/34.04  | |   (21)  all_58_1 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | COMBINE_EQS: (2), (21) imply:
% 202.75/34.04  | |   (22)  all_52_9 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | REF_CLOSE: (1), (13), (14), (18), (22) are inconsistent by sub-proof #1337.
% 202.75/34.04  | | 
% 202.75/34.04  | Case 2:
% 202.75/34.04  | | 
% 202.75/34.04  | |   (23)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04  | | 
% 202.75/34.04  | | BETA: splitting (23) gives:
% 202.75/34.04  | | 
% 202.75/34.04  | | Case 1:
% 202.75/34.04  | | | 
% 202.75/34.04  | | |   (24)  all_58_3 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | COMBINE_EQS: (19), (24) imply:
% 202.75/34.04  | | |   (25)  all_4_2 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REDUCE: (11), (25) imply:
% 202.75/34.04  | | |   (26)   ~ (all_52_9 = e3)
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REDUCE: (12), (25) imply:
% 202.75/34.04  | | |   (27)  op(e3, e3) = e2
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REDUCE: (9), (25) imply:
% 202.75/34.04  | | |   (28)  op(e3, e2) = all_4_1
% 202.75/34.04  | | | 
% 202.75/34.04  | | | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3, simplifying
% 202.75/34.04  | | |              with (16), (28) gives:
% 202.75/34.04  | | |   (29)  all_52_9 = all_4_1
% 202.75/34.04  | | | 
% 202.75/34.04  | | | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 202.75/34.04  | | |              (14), (27) gives:
% 202.75/34.04  | | |   (30)  all_6_2 = e2
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REF_CLOSE: (1), (7), (8), (13), (15), (17), (18), (20), (26), (29), (30)
% 202.75/34.04  | | |            are inconsistent by sub-proof #1096.
% 202.75/34.04  | | | 
% 202.75/34.04  | | Case 2:
% 202.75/34.04  | | | 
% 202.75/34.04  | | |   (31)  all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04  | | | 
% 202.75/34.04  | | | REF_CLOSE: (3), (4), (5), (6), (31) are inconsistent by sub-proof #717.
% 202.75/34.04  | | | 
% 202.75/34.04  | | End of split
% 202.75/34.04  | | 
% 202.75/34.04  | End of split
% 202.75/34.04  | 
% 202.75/34.04  End of proof
% 202.75/34.04  
% 202.75/34.04  Sub-proof #432 shows that the following formulas are inconsistent:
% 202.75/34.04  ----------------------------------------------------------------
% 202.75/34.04    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.04    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.04    (4)   ~ (all_52_7 = all_52_15)
% 202.75/34.04    (5)  op(all_52_15, all_52_15) = e0
% 202.75/34.04    (6)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.04    (7)  op(e2, e2) = all_4_2
% 202.75/34.04    (8)   ~ (all_52_7 = all_6_2)
% 202.75/34.04    (9)  all_52_15 = e3
% 202.75/34.04    (10)  all_56_15 = all_14_2
% 202.75/34.04    (11)   ~ (all_52_7 = all_14_2)
% 202.75/34.04    (12)  op(e0, e3) = all_52_7
% 202.75/34.04    (13)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.04    (14)  all_56_12 = all_52_7
% 202.75/34.04    (15)  all_8_2 = all_6_2
% 202.75/34.04    (16)  op(e3, all_6_1) = e2
% 202.75/34.04    (17)  op(e3, e3) = all_6_2
% 202.75/34.04    (18)   ~ (all_52_15 = all_4_2)
% 202.75/34.04    (19)  op(e3, e2) = all_52_9
% 202.75/34.04    (20)  op(all_52_9, all_52_9) = e3
% 202.75/34.04    (21)  all_8_1 = all_6_1
% 202.75/34.04    (22)  op(all_6_2, e3) = all_6_1
% 202.75/34.04  
% 202.75/34.04  Begin of proof
% 202.75/34.04  | 
% 202.75/34.04  | SIMP: (9) implies:
% 202.75/34.04  |   (23)  all_52_15 = e3
% 202.75/34.04  | 
% 202.75/34.04  | REDUCE: (4), (23) imply:
% 202.75/34.04  |   (24)   ~ (all_52_7 = e3)
% 202.75/34.04  | 
% 202.75/34.04  | REDUCE: (18), (23) imply:
% 202.75/34.04  |   (25)   ~ (all_4_2 = e3)
% 202.75/34.04  | 
% 202.75/34.04  | SIMP: (25) implies:
% 202.75/34.04  |   (26)   ~ (all_4_2 = e3)
% 202.75/34.04  | 
% 202.75/34.04  | REDUCE: (5), (23) imply:
% 202.75/34.04  |   (27)  op(e3, e3) = e0
% 202.75/34.04  | 
% 202.75/34.04  | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 202.75/34.04  |            (16), (17), (19), (20), (21), (22), (24), (26), (27) are
% 202.75/34.04  |            inconsistent by sub-proof #461.
% 202.75/34.04  | 
% 202.75/34.04  End of proof
% 202.75/34.04  
% 202.75/34.04  Sub-proof #433 shows that the following formulas are inconsistent:
% 202.75/34.04  ----------------------------------------------------------------
% 202.75/34.04    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.75/34.04    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.04    (3)   ~ (all_52_15 = all_52_23)
% 202.75/34.04    (4)   ~ (all_52_25 = all_52_27)
% 202.75/34.04    (5)  all_58_14 = all_52_23
% 202.75/34.04    (6)   ~ (e3 = e1)
% 202.75/34.04    (7)  op(all_52_3, all_52_3) = all_52_2
% 202.75/34.04    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.04    (9)   ~ (all_52_5 = all_52_13)
% 202.75/34.04    (10)  all_58_1 = all_52_9
% 202.75/34.04    (11)   ~ (all_52_9 = all_52_13)
% 202.75/34.04    (12)   ~ (e3 = e0)
% 202.75/34.04    (13)  op(e2, e3) = all_52_3
% 202.75/34.04    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.04    (15)  op(e0, e2) = all_52_15
% 202.75/34.04    (16)   ~ (all_52_7 = all_52_15)
% 202.75/34.04    (17)   ~ (all_52_3 = all_52_19)
% 202.75/34.04    (18)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.04    (19)   ~ (all_52_17 = all_52_25)
% 202.75/34.04    (20)   ~ (all_52_3 = all_6_2)
% 202.75/34.04    (21)  all_44_2 = all_6_2
% 202.75/34.04    (22)  all_58_0 = all_6_2
% 202.75/34.04    (23)  op(all_14_2, e0) = all_14_1
% 202.75/34.04    (24)  all_56_4 = all_52_3
% 202.75/34.04    (25)   ~ (all_52_17 = all_10_2)
% 202.75/34.04    (26)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.75/34.04    (27)  op(e3, e0) = all_52_25
% 202.75/34.04    (28)  op(e0, all_14_1) = all_14_0
% 202.75/34.04    (29)  op(all_52_5, all_52_5) = all_52_4
% 202.75/34.04    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.75/34.04    (31)  op(all_52_19, all_52_19) = all_52_18
% 202.75/34.04    (32)   ~ (all_52_27 = all_52_29)
% 202.75/34.04    (33)  all_58_13 = all_52_15
% 202.75/34.04    (34)  op(all_10_2, all_10_2) = all_52_20
% 202.75/34.04    (35)  all_58_9 = all_52_25
% 202.75/34.04    (36)   ~ (all_52_29 = all_14_2)
% 202.75/34.04    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.75/34.04    (38)  op(all_52_27, all_52_27) = all_52_26
% 202.75/34.04    (39)  op(e1, e3) = all_52_5
% 202.75/34.04    (40)  op(e2, e2) = all_4_2
% 202.75/34.04    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.75/34.04    (42)   ~ (all_52_3 = all_52_5)
% 202.75/34.04    (43)  all_58_11 = all_52_29
% 202.75/34.04    (44)  all_56_5 = all_4_2
% 202.75/34.04    (45)   ~ (all_52_25 = all_14_2)
% 202.75/34.04    (46)   ~ (all_52_9 = all_52_15)
% 202.75/34.04    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.75/34.04    (48)   ~ (all_52_3 = all_52_27)
% 202.75/34.04    (49)  op(all_10_2, e1) = all_10_1
% 202.75/34.04    (50)  op(all_6_2, all_6_2) = all_52_0
% 202.75/34.04    (51)   ~ (all_52_7 = all_6_2)
% 202.75/34.04    (52)  op(e0, e0) = all_14_2
% 202.75/34.04    (53)  op(e0, e1) = all_52_23
% 202.75/34.04    (54)  all_56_15 = all_14_2
% 202.75/34.04    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.04    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.75/34.04    (57)  all_56_11 = all_52_29
% 202.75/34.04    (58)   ~ (all_4_1 = e1)
% 202.75/34.04    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.75/34.04    (60)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.04    (61)  all_56_9 = all_52_13
% 202.75/34.04    (62)   ~ (e2 = e1)
% 202.75/34.04    (63)   ~ (all_52_13 = all_10_2)
% 202.75/34.04    (64)  all_58_10 = all_52_27
% 202.75/34.04    (65)  all_56_8 = all_52_5
% 202.75/34.04    (66)  op(all_52_9, all_52_9) = all_52_8
% 202.75/34.04    (67)  op(all_52_15, all_52_15) = all_52_14
% 202.75/34.04    (68)   ~ (all_52_19 = all_52_23)
% 202.75/34.04    (69)   ~ (all_52_25 = all_52_29)
% 202.75/34.04    (70)   ~ (all_52_29 = all_10_2)
% 202.75/34.04    (71)  all_58_7 = all_52_13
% 202.75/34.04    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.75/34.04    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.75/34.04    (74)   ~ (all_52_5 = all_52_7)
% 202.75/34.04    (75)  all_58_12 = all_52_7
% 202.75/34.04    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.75/34.04    (77)   ~ (all_52_7 = all_14_2)
% 202.75/34.04    (78)   ~ (all_14_2 = e0)
% 202.75/34.04    (79)  all_58_2 = all_52_3
% 202.75/34.04    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.75/34.04    (81)  all_56_2 = all_52_17
% 202.75/34.04    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.75/34.04    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.75/34.04    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.75/34.04    (85)  all_56_7 = all_52_27
% 202.75/34.04    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.75/34.04    (87)   ~ (e2 = e0)
% 202.75/34.04    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.75/34.04    (89)  op(all_4_2, e2) = all_4_1
% 202.75/34.04    (90)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.75/34.04    (91)   ~ (all_52_5 = all_52_29)
% 202.75/34.04    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.75/34.04    (93)  all_56_6 = all_52_19
% 202.75/34.04    (94)   ~ (all_52_15 = all_14_2)
% 202.75/34.04    (95)   ~ (all_52_19 = all_52_27)
% 202.75/34.04    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.75/34.04    (97)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.75/34.04    (98)   ~ (all_52_13 = all_4_2)
% 202.75/34.04    (99)  op(e3, e1) = all_52_17
% 202.75/34.04    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.75/34.04    (101)  op(e0, e3) = all_52_7
% 202.75/34.04    (102)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.04    (103)   ~ (all_52_9 = all_52_25)
% 202.75/34.04    (104)  all_58_15 = all_14_2
% 202.75/34.04    (105)   ~ (all_52_19 = all_10_2)
% 202.75/34.04    (106)  op(all_52_23, all_52_23) = all_52_22
% 202.75/34.04    (107)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.75/34.04    (108)   ~ (all_10_1 = e2)
% 202.75/34.04    (109)  all_58_8 = all_10_2
% 202.75/34.04    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.04    (111)   ~ (all_52_5 = all_10_2)
% 202.75/34.04    (112)  op(all_52_29, all_52_29) = all_52_28
% 202.75/34.04    (113)   ~ (all_52_23 = all_14_2)
% 202.75/34.04    (114)  all_56_12 = all_52_7
% 202.75/34.04    (115)  op(all_52_17, all_52_17) = all_52_16
% 202.75/34.04    (116)  all_8_2 = all_6_2
% 202.75/34.04    (117)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.75/34.04    (118)   ~ (all_52_25 = all_6_2)
% 202.75/34.04    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.75/34.04    (120)   ~ (all_52_9 = all_4_2)
% 202.75/34.04    (121)   ~ (all_52_5 = all_6_2)
% 202.75/34.04    (122)   ~ (all_52_9 = all_6_2)
% 202.75/34.04    (123)   ~ (all_52_13 = all_52_15)
% 202.75/34.04    (124)  op(e3, all_6_1) = e2
% 202.75/34.04    (125)  all_56_0 = all_6_2
% 202.75/34.04    (126)  op(e3, e3) = all_6_2
% 202.75/34.04    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.04    (128)   ~ (all_52_27 = all_14_2)
% 202.75/34.04    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.04    (130)  all_56_14 = all_52_23
% 202.75/34.04    (131)  op(all_4_2, all_4_2) = all_52_10
% 202.75/34.04    (132)  all_56_3 = all_52_25
% 202.75/34.04    (133)   ~ (all_52_3 = all_52_7)
% 202.75/34.04    (134)  op(all_14_2, all_14_2) = all_52_30
% 202.75/34.04    (135)  all_58_5 = all_52_19
% 202.75/34.04    (136)  all_56_1 = all_52_9
% 202.75/34.04    (137)   ~ (all_52_15 = all_4_2)
% 202.75/34.04    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.75/34.04           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 202.75/34.04           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 202.75/34.04           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 202.75/34.04    (139)   ~ (all_52_27 = all_4_2)
% 202.75/34.04    (140)  all_58_6 = all_52_5
% 202.75/34.05    (141)  op(e3, e2) = all_52_9
% 202.75/34.05    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.05    (143)   ~ (all_52_17 = all_6_2)
% 202.75/34.05    (144)   ~ (e1 = e0)
% 202.75/34.05    (145)   ~ (e3 = e2)
% 202.75/34.05    (146)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.75/34.05    (147)  all_44_1 = all_6_1
% 202.75/34.05    (148)   ~ (all_52_9 = all_52_17)
% 202.75/34.05    (149)  all_56_10 = all_10_2
% 202.75/34.05    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.05    (151)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.75/34.05    (152)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.75/34.05    (153)  op(all_52_13, all_52_13) = all_52_12
% 202.75/34.05    (154)  op(e1, e1) = all_10_2
% 202.75/34.05    (155)   ~ (all_52_23 = all_10_2)
% 202.75/34.05    (156)   ~ (all_52_7 = all_52_23)
% 202.75/34.05    (157)   ~ (all_52_17 = all_52_19)
% 202.75/34.05    (158)  all_58_3 = all_4_2
% 202.75/34.05    (159)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.75/34.05    (160)  all_56_13 = all_52_15
% 202.75/34.05    (161)   ~ (all_52_3 = all_4_2)
% 202.75/34.05    (162)   ~ (all_52_19 = all_4_2)
% 202.75/34.05    (163)   ~ (all_52_17 = all_52_23)
% 202.75/34.05    (164)  all_8_1 = all_6_1
% 202.75/34.05    (165)  op(all_6_2, e3) = all_6_1
% 202.75/34.05    (166)   ~ (all_52_13 = all_52_29)
% 202.75/34.05    (167)  all_58_4 = all_52_17
% 202.75/34.05    (168)   ~ (all_14_0 = e1)
% 202.75/34.05    (169)   ~ (all_14_0 = e2)
% 202.75/34.05    (170)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.75/34.05    (171)  op(all_52_25, all_52_25) = all_52_24
% 202.75/34.05  
% 202.75/34.05  Begin of proof
% 202.75/34.05  | 
% 202.75/34.05  | BETA: splitting (138) gives:
% 202.75/34.05  | 
% 202.75/34.05  | Case 1:
% 202.75/34.05  | | 
% 202.75/34.05  | |   (172)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 202.75/34.05  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 202.75/34.05  | | 
% 202.75/34.05  | | BETA: splitting (172) gives:
% 202.75/34.05  | | 
% 202.75/34.05  | | Case 1:
% 202.75/34.05  | | | 
% 202.75/34.05  | | |   (173)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REF_CLOSE: (7), (8), (18), (22), (29), (40), (50), (52), (55), (75), (77),
% 202.75/34.05  | | |            (79), (83), (111), (124), (125), (126), (140), (142), (145),
% 202.75/34.05  | | |            (152), (154), (161), (165), (173) are inconsistent by sub-proof
% 202.75/34.05  | | |            #501.
% 202.75/34.05  | | | 
% 202.75/34.05  | | Case 2:
% 202.75/34.05  | | | 
% 202.75/34.05  | | |   (174)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 202.75/34.05  | | | 
% 202.75/34.05  | | | ALPHA: (174) implies:
% 202.75/34.05  | | |   (175)  all_52_14 = e0
% 202.75/34.05  | | |   (176)  all_52_12 = e1
% 202.75/34.05  | | |   (177)  all_52_10 = e2
% 202.75/34.05  | | |   (178)  all_52_8 = e3
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (66), (178) imply:
% 202.75/34.05  | | |   (179)  op(all_52_9, all_52_9) = e3
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (153), (176) imply:
% 202.75/34.05  | | |   (180)  op(all_52_13, all_52_13) = e1
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (67), (175) imply:
% 202.75/34.05  | | |   (181)  op(all_52_15, all_52_15) = e0
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (131), (177) imply:
% 202.75/34.05  | | |   (182)  op(all_4_2, all_4_2) = e2
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 202.75/34.05  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 202.75/34.05  | | |            (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 202.75/34.05  | | |            (38), (39), (40), (41), (42), (43), (45), (47), (48), (51),
% 202.75/34.05  | | |            (52), (53), (54), (55), (58), (59), (61), (63), (64), (65),
% 202.75/34.05  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 202.75/34.05  | | |            (79), (83), (85), (86), (87), (89), (92), (94), (98), (99),
% 202.75/34.05  | | |            (101), (102), (103), (104), (105), (106), (107), (109), (110),
% 202.75/34.05  | | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 202.75/34.05  | | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 202.75/34.05  | | |            (129), (130), (132), (133), (134), (135), (136), (137), (139),
% 202.75/34.05  | | |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 202.75/34.05  | | |            (149), (150), (151), (152), (154), (155), (156), (157), (158),
% 202.75/34.05  | | |            (160), (161), (162), (163), (164), (165), (166), (167), (169),
% 202.75/34.05  | | |            (170), (171), (179), (180), (181), (182) are inconsistent by
% 202.75/34.05  | | |            sub-proof #451.
% 202.75/34.05  | | | 
% 202.75/34.05  | | End of split
% 202.75/34.05  | | 
% 202.75/34.05  | Case 2:
% 202.75/34.05  | | 
% 202.75/34.05  | |   (183)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 202.75/34.05  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 202.75/34.05  | |            e0)
% 202.75/34.05  | | 
% 202.75/34.05  | | BETA: splitting (183) gives:
% 202.75/34.05  | | 
% 202.75/34.05  | | Case 1:
% 202.75/34.05  | | | 
% 202.75/34.05  | | |   (184)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 202.75/34.05  | | | 
% 202.75/34.05  | | | ALPHA: (184) implies:
% 202.75/34.05  | | |   (185)  all_52_22 = e0
% 202.75/34.05  | | |   (186)  all_52_20 = e1
% 202.75/34.05  | | |   (187)  all_52_18 = e2
% 202.75/34.05  | | |   (188)  all_52_16 = e3
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (115), (188) imply:
% 202.75/34.05  | | |   (189)  op(all_52_17, all_52_17) = e3
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (31), (187) imply:
% 202.75/34.05  | | |   (190)  op(all_52_19, all_52_19) = e2
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (106), (185) imply:
% 202.75/34.05  | | |   (191)  op(all_52_23, all_52_23) = e0
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REDUCE: (34), (186) imply:
% 202.75/34.05  | | |   (192)  op(all_10_2, all_10_2) = e1
% 202.75/34.05  | | | 
% 202.75/34.05  | | | BETA: splitting (110) gives:
% 202.75/34.05  | | | 
% 202.75/34.05  | | | Case 1:
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | |   (193)  all_56_15 = e3
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | COMBINE_EQS: (54), (193) imply:
% 202.75/34.05  | | | |   (194)  all_14_2 = e3
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | SIMP: (194) implies:
% 202.75/34.05  | | | |   (195)  all_14_2 = e3
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (77), (195) imply:
% 202.75/34.05  | | | |   (196)   ~ (all_52_7 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (94), (195) imply:
% 202.75/34.05  | | | |   (197)   ~ (all_52_15 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (45), (195) imply:
% 202.75/34.05  | | | |   (198)   ~ (all_52_25 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (128), (195) imply:
% 202.75/34.05  | | | |   (199)   ~ (all_52_27 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (36), (195) imply:
% 202.75/34.05  | | | |   (200)   ~ (all_52_29 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (134), (195) imply:
% 202.75/34.05  | | | |   (201)  op(e3, e3) = all_52_30
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (23), (195) imply:
% 202.75/34.05  | | | |   (202)  op(e3, e0) = all_14_1
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | GROUND_INST: instantiating (8) with all_52_25, all_14_1, e0, e3,
% 202.75/34.05  | | | |              simplifying with (27), (202) gives:
% 202.75/34.05  | | | |   (203)  all_52_25 = all_14_1
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 202.75/34.05  | | | |              simplifying with (126), (201) gives:
% 202.75/34.05  | | | |   (204)  all_52_30 = all_6_2
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | COMBINE_EQS: (35), (203) imply:
% 202.75/34.05  | | | |   (205)  all_58_9 = all_14_1
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (118), (203) imply:
% 202.75/34.05  | | | |   (206)   ~ (all_14_1 = all_6_2)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | BETA: splitting (59) gives:
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | Case 1:
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | |   (207)  all_56_13 = e3
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | | REF_CLOSE: (160), (197), (207) are inconsistent by sub-proof #1201.
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | Case 2:
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | |   (208)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | | BETA: splitting (14) gives:
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | | Case 1:
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | |   (209)  all_56_12 = e3
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | | REF_CLOSE: (114), (196), (209) are inconsistent by sub-proof #1383.
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | Case 2:
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | |   (210)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | | BETA: splitting (146) gives:
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | | Case 1:
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | |   (211)  all_56_1 = e3
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | COMBINE_EQS: (136), (211) imply:
% 202.75/34.05  | | | | | | |   (212)  all_52_9 = e3
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | SIMP: (212) implies:
% 202.75/34.05  | | | | | | |   (213)  all_52_9 = e3
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | REDUCE: (11), (213) imply:
% 202.75/34.05  | | | | | | |   (214)   ~ (all_52_13 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | SIMP: (214) implies:
% 202.75/34.05  | | | | | | |   (215)   ~ (all_52_13 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | REDUCE: (46), (213) imply:
% 202.75/34.05  | | | | | | |   (216)   ~ (all_52_15 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | REDUCE: (120), (213) imply:
% 202.75/34.05  | | | | | | |   (217)   ~ (all_4_2 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | SIMP: (217) implies:
% 202.75/34.05  | | | | | | |   (218)   ~ (all_4_2 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | REDUCE: (66), (213) imply:
% 202.75/34.05  | | | | | | |   (219)  op(e3, e3) = all_52_8
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_8, e3, e3,
% 202.75/34.05  | | | | | | |              simplifying with (126), (219) gives:
% 202.75/34.05  | | | | | | |   (220)  all_52_8 = all_6_2
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | BETA: splitting (55) gives:
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | |   (221)  all_58_2 = e3
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | COMBINE_EQS: (79), (221) imply:
% 202.75/34.05  | | | | | | | |   (222)  all_52_3 = e3
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | SIMP: (222) implies:
% 202.75/34.05  | | | | | | | |   (223)  all_52_3 = e3
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | REDUCE: (42), (223) imply:
% 202.75/34.05  | | | | | | | |   (224)   ~ (all_52_5 = e3)
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | SIMP: (224) implies:
% 202.75/34.05  | | | | | | | |   (225)   ~ (all_52_5 = e3)
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | REDUCE: (7), (223) imply:
% 202.75/34.05  | | | | | | | |   (226)  op(e3, e3) = all_52_2
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | BETA: splitting (76) gives:
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | |   (227)  all_58_6 = e3
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | REF_CLOSE: (140), (225), (227) are inconsistent by sub-proof
% 202.75/34.05  | | | | | | | | |            #1328.
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | |   (228)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | BETA: splitting (228) gives:
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | |   (229)  all_58_7 = e3
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | COMBINE_EQS: (71), (229) imply:
% 202.75/34.05  | | | | | | | | | |   (230)  all_52_13 = e3
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | REDUCE: (215), (230) imply:
% 202.75/34.05  | | | | | | | | | |   (231)  $false
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | CLOSE: (231) is inconsistent.
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | |   (232)  all_58_8 = e3 | all_58_11 = e3
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | BETA: splitting (232) gives:
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | |   (233)  all_58_8 = e3
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | COMBINE_EQS: (109), (233) imply:
% 202.75/34.05  | | | | | | | | | | |   (234)  all_10_2 = e3
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (25), (234) imply:
% 202.75/34.05  | | | | | | | | | | |   (235)   ~ (all_52_17 = e3)
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (192), (234) imply:
% 202.75/34.05  | | | | | | | | | | |   (236)  op(e3, e3) = e1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (49), (234) imply:
% 202.75/34.05  | | | | | | | | | | |   (237)  op(e3, e1) = all_10_1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_17, all_10_1, e1,
% 202.75/34.05  | | | | | | | | | | |              e3, simplifying with (99), (237) gives:
% 202.75/34.05  | | | | | | | | | | |   (238)  all_52_17 = all_10_1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_2, e3, e3,
% 202.75/34.05  | | | | | | | | | | |              simplifying with (126), (226) gives:
% 202.75/34.05  | | | | | | | | | | |   (239)  all_52_2 = all_6_2
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | GROUND_INST: instantiating (8) with e1, all_52_2, e3, e3,
% 202.75/34.05  | | | | | | | | | | |              simplifying with (226), (236) gives:
% 202.75/34.05  | | | | | | | | | | |   (240)  all_52_2 = e1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | COMBINE_EQS: (239), (240) imply:
% 202.75/34.05  | | | | | | | | | | |   (241)  all_6_2 = e1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | SIMP: (241) implies:
% 202.75/34.05  | | | | | | | | | | |   (242)  all_6_2 = e1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | COMBINE_EQS: (21), (242) imply:
% 202.75/34.05  | | | | | | | | | | |   (243)  all_44_2 = e1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | COMBINE_EQS: (81), (238) imply:
% 202.75/34.05  | | | | | | | | | | |   (244)  all_56_2 = all_10_1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | COMBINE_EQS: (167), (238) imply:
% 202.75/34.05  | | | | | | | | | | |   (245)  all_58_4 = all_10_1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | COMBINE_EQS: (22), (242) imply:
% 202.75/34.05  | | | | | | | | | | |   (246)  all_58_0 = e1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (121), (242) imply:
% 202.75/34.05  | | | | | | | | | | |   (247)   ~ (all_52_5 = e1)
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (51), (242) imply:
% 202.75/34.05  | | | | | | | | | | |   (248)   ~ (all_52_7 = e1)
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (143), (238), (242) imply:
% 202.75/34.05  | | | | | | | | | | |   (249)   ~ (all_10_1 = e1)
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (235), (238) imply:
% 202.75/34.05  | | | | | | | | | | |   (250)   ~ (all_10_1 = e3)
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REDUCE: (165), (242) imply:
% 202.75/34.05  | | | | | | | | | | |   (251)  op(e1, e3) = all_6_1
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | BETA: splitting (60) gives:
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | |   (252)  all_56_2 = e3
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | COMBINE_EQS: (244), (252) imply:
% 202.75/34.05  | | | | | | | | | | | |   (253)  all_10_1 = e3
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | REDUCE: (250), (253) imply:
% 202.75/34.05  | | | | | | | | | | | |   (254)  $false
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | CLOSE: (254) is inconsistent.
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | |   (255)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | BETA: splitting (26) gives:
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | |   (256)   ~ (all_44_2 = e1)
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | REDUCE: (243), (256) imply:
% 202.75/34.05  | | | | | | | | | | | | |   (257)  $false
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | CLOSE: (257) is inconsistent.
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | |   (258)   ~ (all_44_1 = e0)
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | REDUCE: (147), (258) imply:
% 202.75/34.05  | | | | | | | | | | | | |   (259)   ~ (all_6_1 = e0)
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | BETA: splitting (82) gives:
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | |   (260)  all_58_0 = e2
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | REF_CLOSE: (62), (246), (260) are inconsistent by sub-proof
% 202.75/34.05  | | | | | | | | | | | | | |            #1273.
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | |   (261)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | |   (262)  all_58_1 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | REF_CLOSE: (33), (71), (102), (145), (158), (197), (215),
% 202.75/34.05  | | | | | | | | | | | | | | |            (218), (262) are inconsistent by sub-proof #1088.
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | |   (263)  all_58_4 = e2 | all_58_9 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | |   (264)  all_56_2 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (264) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | |   (265)  all_10_1 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | REDUCE: (108), (265) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | |   (266)  $false
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent.
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | |   (267)   ~ (all_56_2 = e2)
% 202.75/34.05  | | | | | | | | | | | | | | | |   (268)  all_56_2 = e1 | all_56_2 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (269)  all_56_2 = e1
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (269) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (270)  all_10_1 = e1
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | REDUCE: (249), (270) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (271)  $false
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent.
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (272)  all_56_2 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (272) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (273)  all_10_1 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (273) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (274)  all_58_4 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | REDUCE: (108), (273) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | |   (275)   ~ (e2 = e0)
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (276)  all_58_4 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (276) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (277)  e2 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (278)  e2 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | REDUCE: (87), (278) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (279)  $false
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent.
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (280)  all_58_9 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (280) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (281)  all_14_1 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | REDUCE: (28), (281) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (282)  op(e0, e2) = all_14_0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_15, all_14_0, e2,
% 202.75/34.05  | | | | | | | | | | | | | | | | | |              e0, simplifying with (15), (282) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (283)  all_52_15 = all_14_0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_5, all_6_1, e3, e1,
% 202.75/34.05  | | | | | | | | | | | | | | | | | |              simplifying with (39), (251) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (284)  all_52_5 = all_6_1
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (283) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (285)  all_56_13 = all_14_0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (284) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (286)  all_56_8 = all_6_1
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | REDUCE: (74), (284) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (287)   ~ (all_52_7 = all_6_1)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | SIMP: (287) implies:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (288)   ~ (all_52_7 = all_6_1)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | REDUCE: (225), (284) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (289)   ~ (all_6_1 = e3)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | REDUCE: (247), (284) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (290)   ~ (all_6_1 = e1)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | REDUCE: (16), (283) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | |   (291)   ~ (all_52_7 = all_14_0)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | |   (292)  all_56_8 = e3
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (289), (292) are inconsistent by sub-proof
% 202.75/34.05  | | | | | | | | | | | | | | | | | | |            #1101.
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | |   (293)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | |   (294)  all_56_13 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (285), (294) are inconsistent by sub-proof
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | |            #542.
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | |   (295)  all_56_13 = e1 | all_56_13 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | |   (296)  all_56_13 = e1
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (285), (296) are inconsistent by sub-proof
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | |            #541.
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | |   (297)  all_56_13 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (297) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | |   (298)  all_14_0 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | |   (299)  all_14_0 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (299) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | |   (300)   ~ (all_52_7 = e0)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |   (301)  all_56_8 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (301) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |   (302)  all_6_1 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | SIMP: (302) implies:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |   (303)  all_6_1 = e2
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (288), (303) imply:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |   (304)   ~ (all_52_7 = e2)
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (210), (248), (300), (304) are inconsistent
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #465.
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |   (305)  all_56_8 = e1 | all_56_8 = e0
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (286), (290), (305) are inconsistent by
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #495.
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | |   (306)  all_58_11 = e3
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | | REF_CLOSE: (43), (200), (306) are inconsistent by sub-proof
% 202.75/34.05  | | | | | | | | | | |            #1323.
% 202.75/34.05  | | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | | 
% 202.75/34.05  | | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | | 
% 202.75/34.05  | | | | | | | | End of split
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | Case 2:
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | |   (307)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | | REF_CLOSE: (5), (8), (13), (17), (20), (22), (24), (41), (64),
% 202.75/34.05  | | | | | | | |            (68), (73), (79), (86), (87), (99), (105), (109),
% 202.75/34.05  | | | | | | | |            (124), (126), (135), (143), (150), (157), (158),
% 202.75/34.05  | | | | | | | |            (165), (167), (190), (199), (202), (206), (218),
% 202.75/34.05  | | | | | | | |            (219), (307) are inconsistent by sub-proof #447.
% 202.75/34.05  | | | | | | | | 
% 202.75/34.05  | | | | | | | End of split
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | Case 2:
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | |   (308)   ~ (all_56_1 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | REDUCE: (136), (308) imply:
% 202.75/34.05  | | | | | | |   (309)   ~ (all_52_9 = e3)
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | | REF_CLOSE: (8), (10), (22), (35), (124), (126), (129), (143),
% 202.75/34.05  | | | | | | |            (145), (150), (165), (167), (189), (198), (309) are
% 202.75/34.05  | | | | | | |            inconsistent by sub-proof #446.
% 202.75/34.05  | | | | | | | 
% 202.75/34.05  | | | | | | End of split
% 202.75/34.05  | | | | | | 
% 202.75/34.05  | | | | | End of split
% 202.75/34.05  | | | | | 
% 202.75/34.05  | | | | End of split
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | Case 2:
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | |   (310)   ~ (all_56_15 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REDUCE: (54), (310) imply:
% 202.75/34.05  | | | |   (311)   ~ (all_14_2 = e3)
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 202.75/34.05  | | | |            (14), (16), (17), (18), (19), (20), (22), (24), (25), (27),
% 202.75/34.05  | | | |            (30), (32), (33), (35), (36), (37), (38), (41), (42), (43),
% 202.75/34.05  | | | |            (45), (46), (49), (51), (52), (55), (59), (60), (62), (63),
% 202.75/34.05  | | | |            (64), (66), (67), (68), (69), (70), (71), (73), (74), (75),
% 202.75/34.05  | | | |            (76), (77), (79), (80), (81), (83), (84), (85), (86), (87),
% 202.75/34.05  | | | |            (90), (92), (93), (94), (97), (99), (101), (102), (104),
% 202.75/34.05  | | | |            (105), (108), (109), (111), (112), (114), (116), (118),
% 202.75/34.05  | | | |            (119), (121), (124), (126), (127), (128), (129), (131),
% 202.75/34.05  | | | |            (132), (133), (134), (135), (137), (140), (141), (142),
% 202.75/34.05  | | | |            (143), (144), (145), (148), (149), (150), (153), (154),
% 202.75/34.05  | | | |            (155), (156), (157), (158), (160), (163), (164), (165),
% 202.75/34.05  | | | |            (167), (170), (171), (189), (190), (191), (192), (311) are
% 202.75/34.05  | | | |            inconsistent by sub-proof #436.
% 202.75/34.05  | | | | 
% 202.75/34.05  | | | End of split
% 202.75/34.05  | | | 
% 202.75/34.05  | | Case 2:
% 202.75/34.05  | | | 
% 202.75/34.05  | | |   (312)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.75/34.05  | | | 
% 202.75/34.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13),
% 202.75/34.05  | | |            (14), (18), (19), (20), (21), (22), (23), (25), (26), (27),
% 202.75/34.05  | | |            (29), (30), (31), (32), (33), (35), (36), (38), (39), (40),
% 202.75/34.05  | | |            (41), (42), (43), (44), (45), (48), (49), (50), (51), (52),
% 202.75/34.05  | | |            (54), (55), (56), (57), (60), (64), (65), (66), (69), (70),
% 202.75/34.05  | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 202.75/34.05  | | |            (81), (83), (84), (85), (87), (88), (91), (93), (95), (96),
% 202.75/34.05  | | |            (97), (99), (100), (101), (102), (103), (104), (105), (107),
% 202.75/34.05  | | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 202.75/34.05  | | |            (118), (119), (120), (121), (124), (125), (126), (127), (128),
% 202.75/34.05  | | |            (129), (130), (132), (133), (134), (135), (137), (139), (140),
% 202.75/34.05  | | |            (141), (142), (143), (144), (145), (147), (148), (150), (152),
% 202.75/34.05  | | |            (153), (154), (156), (157), (158), (159), (161), (162), (163),
% 202.75/34.05  | | |            (164), (165), (166), (167), (171), (312) are inconsistent by
% 202.75/34.05  | | |            sub-proof #434.
% 202.75/34.05  | | | 
% 202.75/34.05  | | End of split
% 202.75/34.05  | | 
% 202.75/34.05  | End of split
% 202.75/34.05  | 
% 202.75/34.05  End of proof
% 202.75/34.05  
% 202.75/34.05  Sub-proof #434 shows that the following formulas are inconsistent:
% 202.75/34.05  ----------------------------------------------------------------
% 202.75/34.05    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.75/34.05    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.05    (3)   ~ (all_52_15 = all_52_23)
% 202.75/34.05    (4)   ~ (all_52_25 = all_52_27)
% 202.75/34.05    (5)  all_58_14 = all_52_23
% 202.75/34.05    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.75/34.05    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.05    (8)  all_58_1 = all_52_9
% 202.75/34.05    (9)   ~ (all_52_9 = all_52_13)
% 202.75/34.05    (10)   ~ (e3 = e0)
% 202.75/34.05    (11)  op(e2, e3) = all_52_3
% 202.75/34.05    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.05    (13)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.05    (14)   ~ (all_52_17 = all_52_25)
% 202.75/34.05    (15)   ~ (all_52_3 = all_6_2)
% 202.75/34.05    (16)  all_44_2 = all_6_2
% 202.75/34.05    (17)  all_58_0 = all_6_2
% 202.75/34.05    (18)  op(all_14_2, e0) = all_14_1
% 202.75/34.05    (19)   ~ (all_52_17 = all_10_2)
% 202.75/34.05    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.75/34.05    (21)  op(e3, e0) = all_52_25
% 202.75/34.05    (22)  op(all_52_5, all_52_5) = all_52_4
% 202.75/34.05    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.75/34.05    (24)  op(all_52_19, all_52_19) = all_52_18
% 202.75/34.05    (25)   ~ (all_52_27 = all_52_29)
% 202.75/34.05    (26)  all_58_13 = all_52_15
% 202.75/34.05    (27)  all_58_9 = all_52_25
% 202.75/34.05    (28)   ~ (all_52_29 = all_14_2)
% 202.75/34.05    (29)  op(all_52_27, all_52_27) = all_52_26
% 202.75/34.05    (30)  op(e1, e3) = all_52_5
% 202.75/34.05    (31)  op(e2, e2) = all_4_2
% 202.75/34.05    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.75/34.05    (33)   ~ (all_52_3 = all_52_5)
% 202.75/34.05    (34)  all_58_11 = all_52_29
% 202.75/34.05    (35)  all_56_5 = all_4_2
% 202.75/34.05    (36)   ~ (all_52_25 = all_14_2)
% 202.75/34.05    (37)   ~ (all_52_3 = all_52_27)
% 202.75/34.05    (38)  op(all_10_2, e1) = all_10_1
% 202.75/34.05    (39)  op(all_6_2, all_6_2) = all_52_0
% 202.75/34.05    (40)   ~ (all_52_7 = all_6_2)
% 202.75/34.05    (41)  op(e0, e0) = all_14_2
% 202.75/34.05    (42)  all_56_15 = all_14_2
% 202.75/34.05    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.05    (44)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.75/34.05    (45)  all_56_11 = all_52_29
% 202.75/34.05    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.05    (47)  all_58_10 = all_52_27
% 202.75/34.05    (48)  all_56_8 = all_52_5
% 202.75/34.05    (49)  op(all_52_9, all_52_9) = all_52_8
% 202.75/34.05    (50)   ~ (all_52_25 = all_52_29)
% 202.75/34.05    (51)   ~ (all_52_29 = all_10_2)
% 202.75/34.05    (52)  all_58_7 = all_52_13
% 202.75/34.05    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.75/34.05    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.75/34.05    (55)   ~ (all_52_5 = all_52_7)
% 202.75/34.05    (56)  all_58_12 = all_52_7
% 202.75/34.05    (57)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.75/34.05    (58)   ~ (all_52_7 = all_14_2)
% 202.75/34.05    (59)   ~ (all_14_2 = e0)
% 202.75/34.05    (60)  all_58_2 = all_52_3
% 202.75/34.05    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.75/34.05    (62)  all_56_2 = all_52_17
% 202.75/34.05    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.75/34.05    (64)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.75/34.05    (65)  all_56_7 = all_52_27
% 202.75/34.05    (66)   ~ (e2 = e0)
% 202.75/34.05    (67)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.75/34.05    (68)   ~ (all_52_5 = all_52_29)
% 202.75/34.05    (69)  all_56_6 = all_52_19
% 202.75/34.05    (70)   ~ (all_52_19 = all_52_27)
% 202.75/34.06    (71)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.75/34.06    (72)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.75/34.06    (73)  op(e3, e1) = all_52_17
% 202.75/34.06    (74)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.75/34.06    (75)  op(e0, e3) = all_52_7
% 202.75/34.06    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.06    (77)   ~ (all_52_9 = all_52_25)
% 202.75/34.06    (78)  all_58_15 = all_14_2
% 202.75/34.06    (79)   ~ (all_52_19 = all_10_2)
% 202.75/34.06    (80)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.75/34.06    (81)  all_58_8 = all_10_2
% 202.75/34.06    (82)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.06    (83)   ~ (all_52_5 = all_10_2)
% 202.75/34.06    (84)  op(all_52_29, all_52_29) = all_52_28
% 202.75/34.06    (85)   ~ (all_52_23 = all_14_2)
% 202.75/34.06    (86)  all_56_12 = all_52_7
% 202.75/34.06    (87)  op(all_52_17, all_52_17) = all_52_16
% 202.75/34.06    (88)  all_8_2 = all_6_2
% 202.75/34.06    (89)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.75/34.06    (90)   ~ (all_52_25 = all_6_2)
% 202.75/34.06    (91)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.75/34.06    (92)   ~ (all_52_9 = all_4_2)
% 202.75/34.06    (93)   ~ (all_52_5 = all_6_2)
% 202.75/34.06    (94)  op(e3, all_6_1) = e2
% 202.75/34.06    (95)  all_56_0 = all_6_2
% 202.75/34.06    (96)  op(e3, e3) = all_6_2
% 202.75/34.06    (97)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.06    (98)   ~ (all_52_27 = all_14_2)
% 202.75/34.06    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.06    (100)  all_56_14 = all_52_23
% 202.75/34.06    (101)  all_56_3 = all_52_25
% 202.75/34.06    (102)   ~ (all_52_3 = all_52_7)
% 202.75/34.06    (103)  op(all_14_2, all_14_2) = all_52_30
% 202.75/34.06    (104)  all_58_5 = all_52_19
% 202.75/34.06    (105)   ~ (all_52_15 = all_4_2)
% 202.75/34.06    (106)   ~ (all_52_27 = all_4_2)
% 202.75/34.06    (107)  all_58_6 = all_52_5
% 202.75/34.06    (108)  op(e3, e2) = all_52_9
% 202.75/34.06    (109)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.06    (110)   ~ (all_52_17 = all_6_2)
% 202.75/34.06    (111)   ~ (e1 = e0)
% 202.75/34.06    (112)   ~ (e3 = e2)
% 202.75/34.06    (113)  all_44_1 = all_6_1
% 202.75/34.06    (114)   ~ (all_52_9 = all_52_17)
% 202.75/34.06    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.06    (116)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 202.75/34.06    (117)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.75/34.06    (118)  op(all_52_13, all_52_13) = all_52_12
% 202.75/34.06    (119)  op(e1, e1) = all_10_2
% 202.75/34.06    (120)   ~ (all_52_7 = all_52_23)
% 202.75/34.06    (121)   ~ (all_52_17 = all_52_19)
% 202.75/34.06    (122)  all_58_3 = all_4_2
% 202.75/34.06    (123)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.75/34.06    (124)   ~ (all_52_3 = all_4_2)
% 202.75/34.06    (125)   ~ (all_52_19 = all_4_2)
% 202.75/34.06    (126)   ~ (all_52_17 = all_52_23)
% 202.75/34.06    (127)  all_8_1 = all_6_1
% 202.75/34.06    (128)  op(all_6_2, e3) = all_6_1
% 202.75/34.06    (129)   ~ (all_52_13 = all_52_29)
% 202.75/34.06    (130)  all_58_4 = all_52_17
% 202.75/34.06    (131)  op(all_52_25, all_52_25) = all_52_24
% 202.75/34.06  
% 202.75/34.06  Begin of proof
% 202.75/34.06  | 
% 202.75/34.06  | ALPHA: (116) implies:
% 202.75/34.06  |   (132)  all_52_30 = e0
% 202.75/34.06  |   (133)  all_52_28 = e1
% 202.75/34.06  |   (134)  all_52_26 = e2
% 202.75/34.06  |   (135)  all_52_24 = e3
% 202.75/34.06  | 
% 202.75/34.06  | REDUCE: (131), (135) imply:
% 202.75/34.06  |   (136)  op(all_52_25, all_52_25) = e3
% 202.75/34.06  | 
% 202.75/34.06  | REDUCE: (29), (134) imply:
% 202.75/34.06  |   (137)  op(all_52_27, all_52_27) = e2
% 202.75/34.06  | 
% 202.75/34.06  | REDUCE: (84), (133) imply:
% 202.75/34.06  |   (138)  op(all_52_29, all_52_29) = e1
% 202.75/34.06  | 
% 202.75/34.06  | REDUCE: (103), (132) imply:
% 202.75/34.06  |   (139)  op(all_14_2, all_14_2) = e0
% 202.75/34.06  | 
% 202.75/34.06  | BETA: splitting (82) gives:
% 202.75/34.06  | 
% 202.75/34.06  | Case 1:
% 202.75/34.06  | | 
% 202.75/34.06  | |   (140)  all_56_15 = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | COMBINE_EQS: (42), (140) imply:
% 202.75/34.06  | |   (141)  all_14_2 = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | SIMP: (141) implies:
% 202.75/34.06  | |   (142)  all_14_2 = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (58), (142) imply:
% 202.75/34.06  | |   (143)   ~ (all_52_7 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (36), (142) imply:
% 202.75/34.06  | |   (144)   ~ (all_52_25 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (139), (142) imply:
% 202.75/34.06  | |   (145)  op(e3, e3) = e0
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (18), (142) imply:
% 202.75/34.06  | |   (146)  op(e3, e0) = all_14_1
% 202.75/34.06  | | 
% 202.75/34.06  | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3, simplifying
% 202.75/34.06  | |              with (21), (146) gives:
% 202.75/34.06  | |   (147)  all_52_25 = all_14_1
% 202.75/34.06  | | 
% 202.75/34.06  | | GROUND_INST: instantiating (7) with all_6_2, e0, e3, e3, simplifying with
% 202.75/34.06  | |              (96), (145) gives:
% 202.75/34.06  | |   (148)  all_6_2 = e0
% 202.75/34.06  | | 
% 202.75/34.06  | | COMBINE_EQS: (88), (148) imply:
% 202.75/34.06  | |   (149)  all_8_2 = e0
% 202.75/34.06  | | 
% 202.75/34.06  | | COMBINE_EQS: (101), (147) imply:
% 202.75/34.06  | |   (150)  all_56_3 = all_14_1
% 202.75/34.06  | | 
% 202.75/34.06  | | COMBINE_EQS: (27), (147) imply:
% 202.75/34.06  | |   (151)  all_58_9 = all_14_1
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (40), (148) imply:
% 202.75/34.06  | |   (152)   ~ (all_52_7 = e0)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (77), (147) imply:
% 202.75/34.06  | |   (153)   ~ (all_52_9 = all_14_1)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (14), (147) imply:
% 202.75/34.06  | |   (154)   ~ (all_52_17 = all_14_1)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (110), (148) imply:
% 202.75/34.06  | |   (155)   ~ (all_52_17 = e0)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (90), (147), (148) imply:
% 202.75/34.06  | |   (156)   ~ (all_14_1 = e0)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (144), (147) imply:
% 202.75/34.06  | |   (157)   ~ (all_14_1 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (136), (147) imply:
% 202.75/34.06  | |   (158)  op(all_14_1, all_14_1) = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (128), (148) imply:
% 202.75/34.06  | |   (159)  op(e0, e3) = all_6_1
% 202.75/34.06  | | 
% 202.75/34.06  | | BETA: splitting (2) gives:
% 202.75/34.06  | | 
% 202.75/34.06  | | Case 1:
% 202.75/34.06  | | | 
% 202.75/34.06  | | |   (160)   ~ (all_8_1 = e1)
% 202.75/34.06  | | | 
% 202.75/34.06  | | | REDUCE: (127), (160) imply:
% 202.75/34.06  | | |   (161)   ~ (all_6_1 = e1)
% 202.75/34.06  | | | 
% 202.75/34.06  | | | GROUND_INST: instantiating (7) with all_52_7, all_6_1, e3, e0, simplifying
% 202.75/34.06  | | |              with (75), (159) gives:
% 202.75/34.06  | | |   (162)  all_52_7 = all_6_1
% 202.75/34.06  | | | 
% 202.75/34.06  | | | COMBINE_EQS: (86), (162) imply:
% 202.75/34.06  | | |   (163)  all_56_12 = all_6_1
% 202.75/34.06  | | | 
% 202.75/34.06  | | | REDUCE: (143), (162) imply:
% 202.75/34.06  | | |   (164)   ~ (all_6_1 = e3)
% 202.75/34.06  | | | 
% 202.75/34.06  | | | REDUCE: (152), (162) imply:
% 202.75/34.06  | | |   (165)   ~ (all_6_1 = e0)
% 202.75/34.06  | | | 
% 202.75/34.06  | | | BETA: splitting (12) gives:
% 202.75/34.06  | | | 
% 202.75/34.06  | | | Case 1:
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | |   (166)  all_56_12 = e3
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | | REF_CLOSE: (163), (164), (166) are inconsistent by sub-proof #1347.
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | Case 2:
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | |   (167)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | | BETA: splitting (167) gives:
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | | Case 1:
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | |   (168)  all_56_12 = e2
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | COMBINE_EQS: (163), (168) imply:
% 202.75/34.06  | | | | |   (169)  all_6_1 = e2
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | SIMP: (169) implies:
% 202.75/34.06  | | | | |   (170)  all_6_1 = e2
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | REDUCE: (94), (170) imply:
% 202.75/34.06  | | | | |   (171)  op(e3, e2) = e2
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | GROUND_INST: instantiating (7) with all_52_9, e2, e2, e3, simplifying
% 202.75/34.06  | | | | |              with (108), (171) gives:
% 202.75/34.06  | | | | |   (172)  all_52_9 = e2
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | REDUCE: (114), (172) imply:
% 202.75/34.06  | | | | |   (173)   ~ (all_52_17 = e2)
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | SIMP: (173) implies:
% 202.75/34.06  | | | | |   (174)   ~ (all_52_17 = e2)
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | REDUCE: (153), (172) imply:
% 202.75/34.06  | | | | |   (175)   ~ (all_14_1 = e2)
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | SIMP: (175) implies:
% 202.75/34.06  | | | | |   (176)   ~ (all_14_1 = e2)
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | BETA: splitting (91) gives:
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | Case 1:
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | |   (177)  all_56_3 = e3
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | COMBINE_EQS: (150), (177) imply:
% 202.75/34.06  | | | | | |   (178)  all_14_1 = e3
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | REDUCE: (157), (178) imply:
% 202.75/34.06  | | | | | |   (179)  $false
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | CLOSE: (179) is inconsistent.
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | Case 2:
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | |   (180)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | BETA: splitting (180) gives:
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | Case 1:
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | |   (181)  all_56_3 = e2
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | COMBINE_EQS: (150), (181) imply:
% 202.75/34.06  | | | | | | |   (182)  all_14_1 = e2
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | REDUCE: (176), (182) imply:
% 202.75/34.06  | | | | | | |   (183)  $false
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | CLOSE: (183) is inconsistent.
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | Case 2:
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | |   (184)  all_56_3 = e1 | all_56_3 = e0
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | BETA: splitting (184) gives:
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | Case 1:
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | |   (185)  all_56_3 = e1
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | COMBINE_EQS: (150), (185) imply:
% 202.75/34.06  | | | | | | | |   (186)  all_14_1 = e1
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | REDUCE: (154), (186) imply:
% 202.75/34.06  | | | | | | | |   (187)   ~ (all_52_17 = e1)
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | BETA: splitting (46) gives:
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | Case 1:
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | |   (188)  all_56_2 = e3
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | COMBINE_EQS: (62), (188) imply:
% 202.75/34.06  | | | | | | | | |   (189)  all_52_17 = e3
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | REDUCE: (19), (189) imply:
% 202.75/34.06  | | | | | | | | |   (190)   ~ (all_10_2 = e3)
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | SIMP: (190) implies:
% 202.75/34.06  | | | | | | | | |   (191)   ~ (all_10_2 = e3)
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | REF_CLOSE: (7), (44), (119), (150), (151), (156), (158),
% 202.75/34.06  | | | | | | | | |            (184), (191) are inconsistent by sub-proof #805.
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | Case 2:
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | |   (192)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | REF_CLOSE: (62), (155), (174), (187), (192) are inconsistent
% 202.75/34.06  | | | | | | | | |            by sub-proof #1180.
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | End of split
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | Case 2:
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | |   (193)  all_56_3 = e0
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | COMBINE_EQS: (150), (193) imply:
% 202.75/34.06  | | | | | | | |   (194)  all_14_1 = e0
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | REDUCE: (156), (194) imply:
% 202.75/34.06  | | | | | | | |   (195)  $false
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | CLOSE: (195) is inconsistent.
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | End of split
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | End of split
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | End of split
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | Case 2:
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | |   (196)  all_56_12 = e1 | all_56_12 = e0
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | REF_CLOSE: (161), (163), (165), (196) are inconsistent by sub-proof
% 202.75/34.06  | | | | |            #1344.
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | End of split
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | End of split
% 202.75/34.06  | | | 
% 202.75/34.06  | | Case 2:
% 202.75/34.06  | | | 
% 202.75/34.06  | | |   (197)   ~ (all_8_2 = e0)
% 202.75/34.06  | | | 
% 202.75/34.06  | | | REDUCE: (149), (197) imply:
% 202.75/34.06  | | |   (198)  $false
% 202.75/34.06  | | | 
% 202.75/34.06  | | | CLOSE: (198) is inconsistent.
% 202.75/34.06  | | | 
% 202.75/34.06  | | End of split
% 202.75/34.06  | | 
% 202.75/34.06  | Case 2:
% 202.75/34.06  | | 
% 202.75/34.06  | |   (199)   ~ (all_56_15 = e3)
% 202.75/34.06  | |   (200)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (42), (199) imply:
% 202.75/34.06  | |   (201)   ~ (all_14_2 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 202.75/34.06  | |            (15), (16), (17), (19), (20), (22), (23), (24), (25), (26), (27),
% 202.75/34.06  | |            (28), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 202.75/34.06  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 202.75/34.06  | |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 202.75/34.06  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 202.75/34.06  | |            (73), (74), (76), (77), (78), (79), (80), (81), (83), (85), (87),
% 202.75/34.06  | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 202.75/34.06  | |            (100), (101), (102), (104), (105), (106), (107), (108), (109),
% 202.75/34.06  | |            (110), (111), (112), (113), (115), (117), (118), (119), (120),
% 202.75/34.06  | |            (121), (122), (123), (124), (125), (126), (128), (129), (130),
% 202.75/34.06  | |            (136), (137), (138), (139), (200), (201) are inconsistent by
% 202.75/34.06  | |            sub-proof #435.
% 202.75/34.06  | | 
% 202.75/34.06  | End of split
% 202.75/34.06  | 
% 202.75/34.06  End of proof
% 202.75/34.06  
% 202.75/34.06  Sub-proof #435 shows that the following formulas are inconsistent:
% 202.75/34.06  ----------------------------------------------------------------
% 202.75/34.06    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.75/34.06    (2)   ~ (all_52_15 = all_52_23)
% 202.75/34.06    (3)   ~ (all_52_25 = all_52_27)
% 202.75/34.06    (4)  all_58_14 = all_52_23
% 202.75/34.06    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.75/34.06    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.06    (7)  all_58_1 = all_52_9
% 202.75/34.06    (8)   ~ (all_52_9 = all_52_13)
% 202.75/34.06    (9)   ~ (e3 = e0)
% 202.75/34.06    (10)  op(e2, e3) = all_52_3
% 202.75/34.06    (11)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.06    (12)   ~ (all_52_17 = all_52_25)
% 202.75/34.06    (13)   ~ (all_52_3 = all_6_2)
% 202.75/34.06    (14)  all_44_2 = all_6_2
% 202.75/34.06    (15)  all_58_0 = all_6_2
% 202.75/34.06    (16)   ~ (all_52_17 = all_10_2)
% 202.75/34.06    (17)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.75/34.06    (18)  op(all_52_5, all_52_5) = all_52_4
% 202.75/34.06    (19)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.75/34.06    (20)  op(all_52_19, all_52_19) = all_52_18
% 202.75/34.06    (21)   ~ (all_52_27 = all_52_29)
% 202.75/34.06    (22)  all_58_13 = all_52_15
% 202.75/34.06    (23)  all_58_9 = all_52_25
% 202.75/34.06    (24)   ~ (all_52_29 = all_14_2)
% 202.75/34.06    (25)  op(e1, e3) = all_52_5
% 202.75/34.06    (26)  op(e2, e2) = all_4_2
% 202.75/34.06    (27)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.75/34.06    (28)   ~ (all_52_3 = all_52_5)
% 202.75/34.06    (29)  all_58_11 = all_52_29
% 202.75/34.06    (30)  all_56_5 = all_4_2
% 202.75/34.06    (31)   ~ (all_52_25 = all_14_2)
% 202.75/34.06    (32)   ~ (all_52_3 = all_52_27)
% 202.75/34.06    (33)  op(all_10_2, e1) = all_10_1
% 202.75/34.06    (34)  op(all_6_2, all_6_2) = all_52_0
% 202.75/34.06    (35)   ~ (all_52_7 = all_6_2)
% 202.75/34.06    (36)  op(e0, e0) = all_14_2
% 202.75/34.06    (37)  op(all_52_29, all_52_29) = e1
% 202.75/34.06    (38)  all_56_15 = all_14_2
% 202.75/34.06    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.06    (40)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.75/34.06    (41)  all_56_11 = all_52_29
% 202.75/34.06    (42)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.06    (43)  all_58_10 = all_52_27
% 202.75/34.06    (44)  all_56_8 = all_52_5
% 202.75/34.06    (45)  op(all_52_9, all_52_9) = all_52_8
% 202.75/34.06    (46)   ~ (all_52_25 = all_52_29)
% 202.75/34.06    (47)   ~ (all_52_29 = all_10_2)
% 202.75/34.06    (48)  all_58_7 = all_52_13
% 202.75/34.06    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.75/34.06    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.75/34.06    (51)   ~ (all_52_5 = all_52_7)
% 202.75/34.06    (52)  all_58_12 = all_52_7
% 202.75/34.06    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.75/34.06    (54)   ~ (all_52_7 = all_14_2)
% 202.75/34.06    (55)   ~ (all_14_2 = e0)
% 202.75/34.06    (56)  all_58_2 = all_52_3
% 202.75/34.06    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.75/34.06    (58)  all_56_2 = all_52_17
% 202.75/34.06    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.75/34.06    (60)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.75/34.06    (61)  all_56_7 = all_52_27
% 202.75/34.06    (62)   ~ (e2 = e0)
% 202.75/34.06    (63)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 202.75/34.06    (64)  op(all_52_25, all_52_25) = e3
% 202.75/34.06    (65)   ~ (all_52_5 = all_52_29)
% 202.75/34.06    (66)  all_56_6 = all_52_19
% 202.75/34.06    (67)   ~ (all_52_19 = all_52_27)
% 202.75/34.06    (68)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.75/34.06    (69)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.75/34.06    (70)  op(e3, e1) = all_52_17
% 202.75/34.06    (71)  op(all_52_27, all_52_27) = e2
% 202.75/34.06    (72)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 202.75/34.06    (73)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.06    (74)   ~ (all_52_9 = all_52_25)
% 202.75/34.06    (75)  all_58_15 = all_14_2
% 202.75/34.06    (76)   ~ (all_52_19 = all_10_2)
% 202.75/34.06    (77)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.75/34.06    (78)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.75/34.06    (79)  all_58_8 = all_10_2
% 202.75/34.06    (80)   ~ (all_52_5 = all_10_2)
% 202.75/34.06    (81)   ~ (all_52_23 = all_14_2)
% 202.75/34.06    (82)  op(all_52_17, all_52_17) = all_52_16
% 202.75/34.06    (83)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.75/34.06    (84)   ~ (all_52_25 = all_6_2)
% 202.75/34.06    (85)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.75/34.06    (86)   ~ (all_52_9 = all_4_2)
% 202.75/34.06    (87)   ~ (all_52_5 = all_6_2)
% 202.75/34.06    (88)  op(e3, all_6_1) = e2
% 202.75/34.06    (89)  all_56_0 = all_6_2
% 202.75/34.06    (90)  op(e3, e3) = all_6_2
% 202.75/34.06    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.06    (92)   ~ (all_52_27 = all_14_2)
% 202.75/34.06    (93)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.06    (94)  all_56_14 = all_52_23
% 202.75/34.06    (95)  all_56_3 = all_52_25
% 202.75/34.06    (96)   ~ (all_52_3 = all_52_7)
% 202.75/34.06    (97)  all_58_5 = all_52_19
% 202.75/34.06    (98)   ~ (all_52_15 = all_4_2)
% 202.75/34.06    (99)   ~ (all_52_27 = all_4_2)
% 202.75/34.06    (100)  all_58_6 = all_52_5
% 202.75/34.06    (101)  op(e3, e2) = all_52_9
% 202.75/34.06    (102)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.06    (103)   ~ (all_52_17 = all_6_2)
% 202.75/34.06    (104)   ~ (e1 = e0)
% 202.75/34.06    (105)  op(all_14_2, all_14_2) = e0
% 202.75/34.06    (106)   ~ (e3 = e2)
% 202.75/34.06    (107)  all_44_1 = all_6_1
% 202.75/34.06    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.06    (109)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.75/34.06    (110)  op(all_52_13, all_52_13) = all_52_12
% 202.75/34.06    (111)  op(e1, e1) = all_10_2
% 202.75/34.06    (112)   ~ (all_52_7 = all_52_23)
% 202.75/34.06    (113)   ~ (all_52_17 = all_52_19)
% 202.75/34.06    (114)  all_58_3 = all_4_2
% 202.75/34.06    (115)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 202.75/34.06    (116)   ~ (all_52_3 = all_4_2)
% 202.75/34.06    (117)   ~ (all_52_19 = all_4_2)
% 202.75/34.06    (118)   ~ (all_52_17 = all_52_23)
% 202.75/34.06    (119)  op(all_6_2, e3) = all_6_1
% 202.75/34.06    (120)   ~ (all_52_13 = all_52_29)
% 202.75/34.06    (121)  all_58_4 = all_52_17
% 202.75/34.06    (122)   ~ (all_14_2 = e3)
% 202.75/34.06  
% 202.75/34.06  Begin of proof
% 202.75/34.06  | 
% 202.75/34.06  | BETA: splitting (102) gives:
% 202.75/34.06  | 
% 202.75/34.06  | Case 1:
% 202.75/34.06  | | 
% 202.75/34.06  | |   (123)  all_58_12 = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | COMBINE_EQS: (52), (123) imply:
% 202.75/34.06  | |   (124)  all_52_7 = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | SIMP: (124) implies:
% 202.75/34.06  | |   (125)  all_52_7 = e3
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (96), (125) imply:
% 202.75/34.06  | |   (126)   ~ (all_52_3 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (51), (125) imply:
% 202.75/34.06  | |   (127)   ~ (all_52_5 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (112), (125) imply:
% 202.75/34.06  | |   (128)   ~ (all_52_23 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | SIMP: (128) implies:
% 202.75/34.06  | |   (129)   ~ (all_52_23 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (54), (125) imply:
% 202.75/34.06  | |   (130)   ~ (all_14_2 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (35), (125) imply:
% 202.75/34.06  | |   (131)   ~ (all_6_2 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | SIMP: (131) implies:
% 202.75/34.06  | |   (132)   ~ (all_6_2 = e3)
% 202.75/34.06  | | 
% 202.75/34.06  | | REDUCE: (11), (125) imply:
% 202.75/34.06  | |   (133)  op(e3, e3) = all_52_6
% 202.75/34.06  | | 
% 202.75/34.06  | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 202.75/34.06  | |              with (90), (133) gives:
% 202.75/34.06  | |   (134)  all_52_6 = all_6_2
% 202.75/34.06  | | 
% 202.75/34.06  | | BETA: splitting (49) gives:
% 202.75/34.06  | | 
% 202.75/34.06  | | Case 1:
% 202.75/34.06  | | | 
% 202.75/34.06  | | |   (135)  all_56_14 = e3
% 202.75/34.06  | | | 
% 202.75/34.06  | | | REF_CLOSE: (94), (129), (135) are inconsistent by sub-proof #1286.
% 202.75/34.06  | | | 
% 202.75/34.06  | | Case 2:
% 202.75/34.06  | | | 
% 202.75/34.06  | | |   (136)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.75/34.06  | | | 
% 202.75/34.06  | | | BETA: splitting (77) gives:
% 202.75/34.06  | | | 
% 202.75/34.06  | | | Case 1:
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | |   (137)  all_56_8 = e3
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | | REF_CLOSE: (44), (127), (137) are inconsistent by sub-proof #1325.
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | Case 2:
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | |   (138)   ~ (all_56_8 = e3)
% 202.75/34.06  | | | |   (139)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | | BETA: splitting (85) gives:
% 202.75/34.06  | | | | 
% 202.75/34.06  | | | | Case 1:
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | |   (140)  all_56_3 = e3
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | COMBINE_EQS: (95), (140) imply:
% 202.75/34.06  | | | | |   (141)  all_52_25 = e3
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | REF_CLOSE: (6), (64), (84), (90), (141) are inconsistent by sub-proof
% 202.75/34.06  | | | | |            #1246.
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | Case 2:
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | |   (142)   ~ (all_56_3 = e3)
% 202.75/34.06  | | | | |   (143)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | REDUCE: (95), (142) imply:
% 202.75/34.06  | | | | |   (144)   ~ (all_52_25 = e3)
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | BETA: splitting (91) gives:
% 202.75/34.06  | | | | | 
% 202.75/34.06  | | | | | Case 1:
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | |   (145)  all_58_9 = e3
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | REF_CLOSE: (23), (144), (145) are inconsistent by sub-proof #1300.
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | Case 2:
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | |   (146)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | BETA: splitting (19) gives:
% 202.75/34.06  | | | | | | 
% 202.75/34.06  | | | | | | Case 1:
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | |   (147)  all_56_7 = e3
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | COMBINE_EQS: (61), (147) imply:
% 202.75/34.06  | | | | | | |   (148)  all_52_27 = e3
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | SIMP: (148) implies:
% 202.75/34.06  | | | | | | |   (149)  all_52_27 = e3
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | REDUCE: (21), (149) imply:
% 202.75/34.06  | | | | | | |   (150)   ~ (all_52_29 = e3)
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | SIMP: (150) implies:
% 202.75/34.06  | | | | | | |   (151)   ~ (all_52_29 = e3)
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | REDUCE: (71), (149) imply:
% 202.75/34.06  | | | | | | |   (152)  op(e3, e3) = e2
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (12), (15), (16),
% 202.75/34.06  | | | | | | |            (20), (22), (23), (24), (26), (28), (29), (30), (31),
% 202.75/34.06  | | | | | | |            (33), (34), (36), (38), (40), (41), (42), (44), (46),
% 202.75/34.06  | | | | | | |            (47), (48), (50), (53), (55), (56), (58), (60), (62),
% 202.75/34.06  | | | | | | |            (63), (64), (65), (68), (69), (70), (72), (73), (76),
% 202.75/34.06  | | | | | | |            (78), (79), (81), (83), (84), (85), (86), (87), (90),
% 202.75/34.06  | | | | | | |            (93), (94), (95), (97), (98), (100), (103), (104),
% 202.75/34.06  | | | | | | |            (105), (110), (111), (114), (115), (117), (118), (119),
% 202.75/34.06  | | | | | | |            (121), (122), (123), (127), (132), (136), (139), (143),
% 202.75/34.06  | | | | | | |            (144), (151), (152) are inconsistent by sub-proof
% 202.75/34.06  | | | | | | |            #1018.
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | Case 2:
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | |   (153)   ~ (all_56_7 = e3)
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | REDUCE: (61), (153) imply:
% 202.75/34.06  | | | | | | |   (154)   ~ (all_52_27 = e3)
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | BETA: splitting (146) gives:
% 202.75/34.06  | | | | | | | 
% 202.75/34.06  | | | | | | | Case 1:
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | |   (155)  all_58_10 = e3
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | REF_CLOSE: (43), (154), (155) are inconsistent by sub-proof
% 202.75/34.06  | | | | | | | |            #1301.
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | Case 2:
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | |   (156)  all_58_11 = e3 | all_58_15 = e3
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | BETA: splitting (156) gives:
% 202.75/34.06  | | | | | | | | 
% 202.75/34.06  | | | | | | | | Case 1:
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | |   (157)  all_58_11 = e3
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | COMBINE_EQS: (29), (157) imply:
% 202.75/34.06  | | | | | | | | |   (158)  all_52_29 = e3
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | SIMP: (158) implies:
% 202.75/34.06  | | | | | | | | |   (159)  all_52_29 = e3
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | REDUCE: (37), (159) imply:
% 202.75/34.06  | | | | | | | | |   (160)  op(e3, e3) = e1
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, e1, e3, e3,
% 202.75/34.06  | | | | | | | | |              simplifying with (90), (160) gives:
% 202.75/34.06  | | | | | | | | |   (161)  all_6_2 = e1
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | COMBINE_EQS: (14), (161) imply:
% 202.75/34.06  | | | | | | | | |   (162)  all_44_2 = e1
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | COMBINE_EQS: (15), (161) imply:
% 202.75/34.06  | | | | | | | | |   (163)  all_58_0 = e1
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | REDUCE: (87), (161) imply:
% 202.75/34.06  | | | | | | | | |   (164)   ~ (all_52_5 = e1)
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | REDUCE: (119), (161) imply:
% 202.75/34.06  | | | | | | | | |   (165)  op(e1, e3) = all_6_1
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | BETA: splitting (17) gives:
% 202.75/34.06  | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | Case 1:
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | |   (166)   ~ (all_44_2 = e1)
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | REDUCE: (162), (166) imply:
% 202.75/34.06  | | | | | | | | | |   (167)  $false
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | CLOSE: (167) is inconsistent.
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | Case 2:
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | |   (168)   ~ (all_44_1 = e0)
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | REDUCE: (107), (168) imply:
% 202.75/34.06  | | | | | | | | | |   (169)   ~ (all_6_1 = e0)
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 202.75/34.06  | | | | | | | | | |              simplifying with (25), (165) gives:
% 202.75/34.06  | | | | | | | | | |   (170)  all_52_5 = all_6_1
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | COMBINE_EQS: (44), (170) imply:
% 202.75/34.06  | | | | | | | | | |   (171)  all_56_8 = all_6_1
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | COMBINE_EQS: (100), (170) imply:
% 202.75/34.06  | | | | | | | | | |   (172)  all_58_6 = all_6_1
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | REDUCE: (164), (170) imply:
% 202.75/34.06  | | | | | | | | | |   (173)   ~ (all_6_1 = e1)
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | BETA: splitting (139) gives:
% 202.75/34.06  | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | Case 1:
% 202.75/34.06  | | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | |   (174)  all_56_8 = e2
% 202.75/34.06  | | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | | COMBINE_EQS: (171), (174) imply:
% 202.75/34.06  | | | | | | | | | | |   (175)  all_6_1 = e2
% 202.75/34.06  | | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | | SIMP: (175) implies:
% 202.75/34.06  | | | | | | | | | | |   (176)  all_6_1 = e2
% 202.75/34.06  | | | | | | | | | | | 
% 202.75/34.06  | | | | | | | | | | | COMBINE_EQS: (172), (176) imply:
% 202.75/34.06  | | | | | | | | | | |   (177)  all_58_6 = e2
% 202.75/34.06  | | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (23), (27), (32), (36), (43),
% 202.75/34.07  | | | | | | | | | | |            (56), (62), (64), (104), (122), (123), (126),
% 202.75/34.07  | | | | | | | | | | |            (157), (163), (177) are inconsistent by sub-proof
% 202.75/34.07  | | | | | | | | | | |            #800.
% 202.75/34.07  | | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | |   (178)  all_56_8 = e1 | all_56_8 = e0
% 202.75/34.07  | | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | | REF_CLOSE: (169), (171), (173), (178) are inconsistent by
% 202.75/34.07  | | | | | | | | | | |            sub-proof #495.
% 202.75/34.07  | | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | End of split
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | End of split
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | |   (179)  all_58_15 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | COMBINE_EQS: (75), (179) imply:
% 202.75/34.07  | | | | | | | | |   (180)  all_14_2 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (122), (180) imply:
% 202.75/34.07  | | | | | | | | |   (181)  $false
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | CLOSE: (181) is inconsistent.
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | End of split
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | End of split
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | End of split
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | End of split
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | End of split
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | End of split
% 202.75/34.07  | | | 
% 202.75/34.07  | | End of split
% 202.75/34.07  | | 
% 202.75/34.07  | Case 2:
% 202.75/34.07  | | 
% 202.75/34.07  | |   (182)   ~ (all_58_12 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (52), (182) imply:
% 202.75/34.07  | |   (183)   ~ (all_52_7 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | BETA: splitting (109) gives:
% 202.75/34.07  | | 
% 202.75/34.07  | | Case 1:
% 202.75/34.07  | | | 
% 202.75/34.07  | | |   (184)  all_56_0 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | COMBINE_EQS: (89), (184) imply:
% 202.75/34.07  | | |   (185)  all_6_2 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REF_CLOSE: (6), (88), (90), (106), (119), (185) are inconsistent by
% 202.75/34.07  | | |            sub-proof #502.
% 202.75/34.07  | | | 
% 202.75/34.07  | | Case 2:
% 202.75/34.07  | | | 
% 202.75/34.07  | | |   (186)   ~ (all_56_0 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (89), (186) imply:
% 202.75/34.07  | | |   (187)   ~ (all_6_2 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | BETA: splitting (59) gives:
% 202.75/34.07  | | | 
% 202.75/34.07  | | | Case 1:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | |   (188)  all_58_0 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | COMBINE_EQS: (15), (188) imply:
% 202.75/34.07  | | | |   (189)  all_6_2 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | REDUCE: (187), (189) imply:
% 202.75/34.07  | | | |   (190)  $false
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | CLOSE: (190) is inconsistent.
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | Case 2:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | |   (191)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | BETA: splitting (39) gives:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | Case 1:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | |   (192)  all_58_2 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | COMBINE_EQS: (56), (192) imply:
% 202.75/34.07  | | | | |   (193)  all_52_3 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (193) implies:
% 202.75/34.07  | | | | |   (194)  all_52_3 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (32), (194) imply:
% 202.75/34.07  | | | | |   (195)   ~ (all_52_27 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (195) implies:
% 202.75/34.07  | | | | |   (196)   ~ (all_52_27 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (116), (194) imply:
% 202.75/34.07  | | | | |   (197)   ~ (all_4_2 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (197) implies:
% 202.75/34.07  | | | | |   (198)   ~ (all_4_2 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (5), (194) imply:
% 202.75/34.07  | | | | |   (199)  op(e3, e3) = all_52_2
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3,
% 202.75/34.07  | | | | |              simplifying with (90), (199) gives:
% 202.75/34.07  | | | | |   (200)  all_52_2 = all_6_2
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | BETA: splitting (91) gives:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | Case 1:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (201)  all_58_9 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | COMBINE_EQS: (23), (201) imply:
% 202.75/34.07  | | | | | |   (202)  all_52_25 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | REF_CLOSE: (6), (64), (84), (90), (202) are inconsistent by
% 202.75/34.07  | | | | | |            sub-proof #1246.
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | Case 2:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (203)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | BETA: splitting (203) gives:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | Case 1:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | |   (204)  all_58_10 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | REF_CLOSE: (43), (196), (204) are inconsistent by sub-proof #1301.
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | Case 2:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | |   (205)  all_58_11 = e3 | all_58_15 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | BETA: splitting (205) gives:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | Case 1:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | |   (206)  all_58_11 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | COMBINE_EQS: (29), (206) imply:
% 202.75/34.07  | | | | | | | |   (207)  all_52_29 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | SIMP: (207) implies:
% 202.75/34.07  | | | | | | | |   (208)  all_52_29 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (65), (208) imply:
% 202.75/34.07  | | | | | | | |   (209)   ~ (all_52_5 = e3)
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (120), (208) imply:
% 202.75/34.07  | | | | | | | |   (210)   ~ (all_52_13 = e3)
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (24), (208) imply:
% 202.75/34.07  | | | | | | | |   (211)   ~ (all_14_2 = e3)
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (37), (208) imply:
% 202.75/34.07  | | | | | | | |   (212)  op(e3, e3) = e1
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | BETA: splitting (73) gives:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | Case 1:
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | |   (213)  all_58_1 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | COMBINE_EQS: (7), (213) imply:
% 202.75/34.07  | | | | | | | | |   (214)  all_52_9 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (74), (214) imply:
% 202.75/34.07  | | | | | | | | |   (215)   ~ (all_52_25 = e3)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | SIMP: (215) implies:
% 202.75/34.07  | | | | | | | | |   (216)   ~ (all_52_25 = e3)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (45), (214) imply:
% 202.75/34.07  | | | | | | | | |   (217)  op(e3, e3) = all_52_8
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 202.75/34.07  | | | | | | | | |              simplifying with (90), (217) gives:
% 202.75/34.07  | | | | | | | | |   (218)  all_52_8 = all_6_2
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | GROUND_INST: instantiating (6) with e1, all_52_8, e3, e3,
% 202.75/34.07  | | | | | | | | |              simplifying with (212), (217) gives:
% 202.75/34.07  | | | | | | | | |   (219)  all_52_8 = e1
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | COMBINE_EQS: (218), (219) imply:
% 202.75/34.07  | | | | | | | | |   (220)  all_6_2 = e1
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | SIMP: (220) implies:
% 202.75/34.07  | | | | | | | | |   (221)  all_6_2 = e1
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | COMBINE_EQS: (14), (221) imply:
% 202.75/34.07  | | | | | | | | |   (222)  all_44_2 = e1
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | COMBINE_EQS: (15), (221) imply:
% 202.75/34.07  | | | | | | | | |   (223)  all_58_0 = e1
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (87), (221) imply:
% 202.75/34.07  | | | | | | | | |   (224)   ~ (all_52_5 = e1)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (84), (221) imply:
% 202.75/34.07  | | | | | | | | |   (225)   ~ (all_52_25 = e1)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (119), (221) imply:
% 202.75/34.07  | | | | | | | | |   (226)  op(e1, e3) = all_6_1
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | BETA: splitting (17) gives:
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | Case 1:
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | |   (227)   ~ (all_44_2 = e1)
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | REDUCE: (222), (227) imply:
% 202.75/34.07  | | | | | | | | | |   (228)  $false
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | CLOSE: (228) is inconsistent.
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | |   (229)   ~ (all_44_1 = e0)
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | REDUCE: (107), (229) imply:
% 202.75/34.07  | | | | | | | | | |   (230)   ~ (all_6_1 = e0)
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | | REF_CLOSE: (6), (9), (11), (25), (27), (36), (44), (51),
% 202.75/34.07  | | | | | | | | | |            (52), (64), (74), (77), (85), (88), (95), (100),
% 202.75/34.07  | | | | | | | | | |            (101), (104), (122), (192), (209), (216), (223),
% 202.75/34.07  | | | | | | | | | |            (224), (225), (226), (230) are inconsistent by
% 202.75/34.07  | | | | | | | | | |            sub-proof #475.
% 202.75/34.07  | | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | End of split
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | |   (231)   ~ (all_58_1 = e3)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (7), (231) imply:
% 202.75/34.07  | | | | | | | | |   (232)   ~ (all_52_9 = e3)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REF_CLOSE: (3), (5), (6), (7), (9), (11), (12), (13), (14),
% 202.75/34.07  | | | | | | | | |            (15), (16), (17), (20), (23), (24), (25), (27),
% 202.75/34.07  | | | | | | | | |            (28), (29), (36), (37), (39), (40), (43), (44),
% 202.75/34.07  | | | | | | | | |            (46), (48), (51), (52), (53), (56), (57), (64),
% 202.75/34.07  | | | | | | | | |            (65), (66), (71), (74), (77), (79), (82), (84),
% 202.75/34.07  | | | | | | | | |            (85), (87), (88), (90), (91), (92), (93), (95),
% 202.75/34.07  | | | | | | | | |            (97), (100), (101), (104), (106), (107), (108),
% 202.75/34.07  | | | | | | | | |            (111), (113), (114), (119), (121), (198), (210),
% 202.75/34.07  | | | | | | | | |            (232) are inconsistent by sub-proof #474.
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | End of split
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | |   (233)  all_58_15 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | COMBINE_EQS: (75), (233) imply:
% 202.75/34.07  | | | | | | | |   (234)  all_14_2 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (122), (234) imply:
% 202.75/34.07  | | | | | | | |   (235)  $false
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | CLOSE: (235) is inconsistent.
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | End of split
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | End of split
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | End of split
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | Case 2:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | |   (236)   ~ (all_58_2 = e3)
% 202.75/34.07  | | | | |   (237)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (56), (236) imply:
% 202.75/34.07  | | | | |   (238)   ~ (all_52_3 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | BETA: splitting (191) gives:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | Case 1:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (239)  all_58_2 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | REF_CLOSE: (56), (238), (239) are inconsistent by sub-proof #1369.
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | Case 2:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (240)  all_58_6 = e3 | all_58_12 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | REF_CLOSE: (3), (6), (7), (12), (15), (16), (18), (23), (29), (36),
% 202.75/34.07  | | | | | |            (40), (43), (45), (52), (64), (65), (67), (71), (73),
% 202.75/34.07  | | | | | |            (74), (75), (80), (84), (85), (90), (91), (92), (93),
% 202.75/34.07  | | | | | |            (95), (97), (99), (100), (106), (111), (114), (121),
% 202.75/34.07  | | | | | |            (122), (183), (237), (240) are inconsistent by sub-proof
% 202.75/34.07  | | | | | |            #1011.
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | End of split
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | End of split
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | End of split
% 202.75/34.07  | | | 
% 202.75/34.07  | | End of split
% 202.75/34.07  | | 
% 202.75/34.07  | End of split
% 202.75/34.07  | 
% 202.75/34.07  End of proof
% 202.75/34.07  
% 202.75/34.07  Sub-proof #436 shows that the following formulas are inconsistent:
% 202.75/34.07  ----------------------------------------------------------------
% 202.75/34.07    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.07    (2)   ~ (all_52_15 = all_52_23)
% 202.75/34.07    (3)   ~ (all_52_25 = all_52_27)
% 202.75/34.07    (4)  all_58_14 = all_52_23
% 202.75/34.07    (5)   ~ (e3 = e1)
% 202.75/34.07    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.75/34.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.07    (8)  all_58_1 = all_52_9
% 202.75/34.07    (9)   ~ (all_52_9 = all_52_13)
% 202.75/34.07    (10)   ~ (e3 = e0)
% 202.75/34.07    (11)  op(all_52_23, all_52_23) = e0
% 202.75/34.07    (12)  op(e2, e3) = all_52_3
% 202.75/34.07    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.07    (14)   ~ (all_52_7 = all_52_15)
% 202.75/34.07    (15)   ~ (all_52_3 = all_52_19)
% 202.75/34.07    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.75/34.07    (17)   ~ (all_52_17 = all_52_25)
% 202.75/34.07    (18)   ~ (all_52_3 = all_6_2)
% 202.75/34.07    (19)  all_58_0 = all_6_2
% 202.75/34.07    (20)  all_56_4 = all_52_3
% 202.75/34.07    (21)   ~ (all_52_17 = all_10_2)
% 202.75/34.07    (22)  op(e3, e0) = all_52_25
% 202.75/34.07    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.75/34.07    (24)   ~ (all_52_27 = all_52_29)
% 202.75/34.07    (25)  all_58_13 = all_52_15
% 202.75/34.07    (26)  all_58_9 = all_52_25
% 202.75/34.07    (27)   ~ (all_52_29 = all_14_2)
% 202.75/34.07    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.75/34.07    (29)  op(all_52_27, all_52_27) = all_52_26
% 202.75/34.07    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.75/34.07    (31)   ~ (all_52_3 = all_52_5)
% 202.75/34.07    (32)  all_58_11 = all_52_29
% 202.75/34.07    (33)   ~ (all_52_25 = all_14_2)
% 202.75/34.07    (34)   ~ (all_52_9 = all_52_15)
% 202.75/34.07    (35)  op(all_10_2, e1) = all_10_1
% 202.75/34.07    (36)   ~ (all_52_7 = all_6_2)
% 202.75/34.07    (37)  op(e0, e0) = all_14_2
% 202.75/34.07    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.07    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.75/34.07    (40)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.07    (41)   ~ (e2 = e1)
% 202.75/34.07    (42)   ~ (all_52_13 = all_10_2)
% 202.75/34.07    (43)  op(all_10_2, all_10_2) = e1
% 202.75/34.07    (44)  all_58_10 = all_52_27
% 202.75/34.07    (45)  op(all_52_9, all_52_9) = all_52_8
% 202.75/34.07    (46)  op(all_52_15, all_52_15) = all_52_14
% 202.75/34.07    (47)   ~ (all_52_19 = all_52_23)
% 202.75/34.07    (48)   ~ (all_52_25 = all_52_29)
% 202.75/34.07    (49)   ~ (all_52_29 = all_10_2)
% 202.75/34.07    (50)  all_58_7 = all_52_13
% 202.75/34.07    (51)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.75/34.07    (52)  op(all_52_19, all_52_19) = e2
% 202.75/34.07    (53)   ~ (all_52_5 = all_52_7)
% 202.75/34.07    (54)  all_58_12 = all_52_7
% 202.75/34.07    (55)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.75/34.07    (56)   ~ (all_52_7 = all_14_2)
% 202.75/34.07    (57)  all_58_2 = all_52_3
% 202.75/34.07    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.75/34.07    (59)  all_56_2 = all_52_17
% 202.75/34.07    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.75/34.07    (61)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.75/34.07    (62)  all_56_7 = all_52_27
% 202.75/34.07    (63)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.75/34.07    (64)   ~ (e2 = e0)
% 202.75/34.07    (65)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.75/34.07    (66)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.75/34.07    (67)  all_56_6 = all_52_19
% 202.75/34.07    (68)   ~ (all_52_15 = all_14_2)
% 202.75/34.07    (69)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.75/34.07    (70)  op(e3, e1) = all_52_17
% 202.75/34.07    (71)  op(e0, e3) = all_52_7
% 202.75/34.07    (72)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.75/34.07    (73)  all_58_15 = all_14_2
% 202.75/34.07    (74)   ~ (all_52_19 = all_10_2)
% 202.75/34.07    (75)   ~ (all_10_1 = e2)
% 202.75/34.07    (76)  all_58_8 = all_10_2
% 202.75/34.07    (77)   ~ (all_52_5 = all_10_2)
% 202.75/34.07    (78)  op(all_52_29, all_52_29) = all_52_28
% 202.75/34.07    (79)  all_56_12 = all_52_7
% 202.75/34.07    (80)  all_8_2 = all_6_2
% 202.75/34.07    (81)   ~ (all_52_25 = all_6_2)
% 202.75/34.07    (82)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.75/34.07    (83)   ~ (all_52_5 = all_6_2)
% 202.75/34.07    (84)  op(e3, all_6_1) = e2
% 202.75/34.07    (85)  op(e3, e3) = all_6_2
% 202.75/34.07    (86)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.07    (87)   ~ (all_52_27 = all_14_2)
% 202.75/34.07    (88)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.07    (89)  op(all_4_2, all_4_2) = all_52_10
% 202.75/34.07    (90)  all_56_3 = all_52_25
% 202.75/34.07    (91)   ~ (all_52_3 = all_52_7)
% 202.75/34.07    (92)  op(all_14_2, all_14_2) = all_52_30
% 202.75/34.07    (93)  all_58_5 = all_52_19
% 202.75/34.07    (94)   ~ (all_52_15 = all_4_2)
% 202.75/34.07    (95)  op(all_52_17, all_52_17) = e3
% 202.75/34.07    (96)  all_58_6 = all_52_5
% 202.75/34.07    (97)  op(e3, e2) = all_52_9
% 202.75/34.07    (98)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.07    (99)   ~ (all_52_17 = all_6_2)
% 202.75/34.07    (100)   ~ (e1 = e0)
% 202.75/34.07    (101)   ~ (e3 = e2)
% 202.75/34.07    (102)   ~ (all_52_9 = all_52_17)
% 202.75/34.07    (103)  all_56_10 = all_10_2
% 202.75/34.07    (104)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.07    (105)  op(all_52_13, all_52_13) = all_52_12
% 202.75/34.07    (106)  op(e1, e1) = all_10_2
% 202.75/34.07    (107)   ~ (all_52_23 = all_10_2)
% 202.75/34.07    (108)   ~ (all_52_7 = all_52_23)
% 202.75/34.07    (109)   ~ (all_52_17 = all_52_19)
% 202.75/34.07    (110)  all_58_3 = all_4_2
% 202.75/34.07    (111)  all_56_13 = all_52_15
% 202.75/34.07    (112)   ~ (all_52_17 = all_52_23)
% 202.75/34.07    (113)  all_8_1 = all_6_1
% 202.75/34.07    (114)  op(all_6_2, e3) = all_6_1
% 202.75/34.07    (115)  all_58_4 = all_52_17
% 202.75/34.07    (116)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.75/34.07    (117)  op(all_52_25, all_52_25) = all_52_24
% 202.75/34.07    (118)   ~ (all_14_2 = e3)
% 202.75/34.07  
% 202.75/34.07  Begin of proof
% 202.75/34.07  | 
% 202.75/34.07  | BETA: splitting (39) gives:
% 202.75/34.07  | 
% 202.75/34.07  | Case 1:
% 202.75/34.07  | | 
% 202.75/34.07  | |   (119)  all_56_13 = e3
% 202.75/34.07  | | 
% 202.75/34.07  | | COMBINE_EQS: (111), (119) imply:
% 202.75/34.07  | |   (120)  all_52_15 = e3
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (14), (120) imply:
% 202.75/34.07  | |   (121)   ~ (all_52_7 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (34), (120) imply:
% 202.75/34.07  | |   (122)   ~ (all_52_9 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (2), (120) imply:
% 202.75/34.07  | |   (123)   ~ (all_52_23 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | SIMP: (123) implies:
% 202.75/34.07  | |   (124)   ~ (all_52_23 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (68), (120) imply:
% 202.75/34.07  | |   (125)   ~ (all_14_2 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (94), (120) imply:
% 202.75/34.07  | |   (126)   ~ (all_4_2 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | SIMP: (126) implies:
% 202.75/34.07  | |   (127)   ~ (all_4_2 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (46), (120) imply:
% 202.75/34.07  | |   (128)  op(e3, e3) = all_52_14
% 202.75/34.07  | | 
% 202.75/34.07  | | GROUND_INST: instantiating (7) with all_6_2, all_52_14, e3, e3, simplifying
% 202.75/34.07  | |              with (85), (128) gives:
% 202.75/34.07  | |   (129)  all_52_14 = all_6_2
% 202.75/34.07  | | 
% 202.75/34.07  | | BETA: splitting (58) gives:
% 202.75/34.07  | | 
% 202.75/34.07  | | Case 1:
% 202.75/34.07  | | | 
% 202.75/34.07  | | |   (130)  all_56_6 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | COMBINE_EQS: (67), (130) imply:
% 202.75/34.07  | | |   (131)  all_52_19 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | SIMP: (131) implies:
% 202.75/34.07  | | |   (132)  all_52_19 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (15), (132) imply:
% 202.75/34.07  | | |   (133)   ~ (all_52_3 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (109), (132) imply:
% 202.75/34.07  | | |   (134)   ~ (all_52_17 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (52), (132) imply:
% 202.75/34.07  | | |   (135)  op(e3, e3) = e2
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REF_CLOSE: (7), (8), (12), (18), (19), (20), (22), (26), (30), (31), (51),
% 202.75/34.07  | | |            (54), (57), (60), (63), (64), (70), (83), (84), (85), (88),
% 202.75/34.07  | | |            (96), (99), (101), (114), (115), (121), (122), (133), (134),
% 202.75/34.07  | | |            (135) are inconsistent by sub-proof #454.
% 202.75/34.07  | | | 
% 202.75/34.07  | | Case 2:
% 202.75/34.07  | | | 
% 202.75/34.07  | | |   (136)   ~ (all_56_6 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (67), (136) imply:
% 202.75/34.07  | | |   (137)   ~ (all_52_19 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | BETA: splitting (38) gives:
% 202.75/34.07  | | | 
% 202.75/34.07  | | | Case 1:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | |   (138)  all_58_2 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | COMBINE_EQS: (57), (138) imply:
% 202.75/34.07  | | | |   (139)  all_52_3 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | SIMP: (139) implies:
% 202.75/34.07  | | | |   (140)  all_52_3 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | REDUCE: (15), (140) imply:
% 202.75/34.07  | | | |   (141)   ~ (all_52_19 = e3)
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | REDUCE: (18), (140) imply:
% 202.75/34.07  | | | |   (142)   ~ (all_6_2 = e3)
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | SIMP: (142) implies:
% 202.75/34.07  | | | |   (143)   ~ (all_6_2 = e3)
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | REDUCE: (6), (140) imply:
% 202.75/34.07  | | | |   (144)  op(e3, e3) = all_52_2
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_2, e3, e3,
% 202.75/34.07  | | | |              simplifying with (85), (144) gives:
% 202.75/34.07  | | | |   (145)  all_52_2 = all_6_2
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | BETA: splitting (104) gives:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | Case 1:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | |   (146)  all_58_4 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | COMBINE_EQS: (115), (146) imply:
% 202.75/34.07  | | | | |   (147)  all_52_17 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (147) implies:
% 202.75/34.07  | | | | |   (148)  all_52_17 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REF_CLOSE: (7), (85), (95), (99), (148) are inconsistent by sub-proof
% 202.75/34.07  | | | | |            #1280.
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | Case 2:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | |   (149)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | BETA: splitting (149) gives:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | Case 1:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (150)  all_58_5 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | REF_CLOSE: (93), (137), (150) are inconsistent by sub-proof #1279.
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | Case 2:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (151)  all_58_8 = e3 | all_58_14 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | BETA: splitting (88) gives:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | Case 1:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | |   (152)  all_58_0 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | COMBINE_EQS: (19), (152) imply:
% 202.75/34.07  | | | | | | |   (153)  all_6_2 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | REDUCE: (143), (153) imply:
% 202.75/34.07  | | | | | | |   (154)  $false
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | CLOSE: (154) is inconsistent.
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | Case 2:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | |   (155)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | BETA: splitting (151) gives:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | Case 1:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | |   (156)  all_58_8 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | COMBINE_EQS: (76), (156) imply:
% 202.75/34.07  | | | | | | | |   (157)  all_10_2 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (77), (157) imply:
% 202.75/34.07  | | | | | | | |   (158)   ~ (all_52_5 = e3)
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (43), (157) imply:
% 202.75/34.07  | | | | | | | |   (159)  op(e3, e3) = e1
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REDUCE: (35), (157) imply:
% 202.75/34.07  | | | | | | | |   (160)  op(e3, e1) = all_10_1
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | BETA: splitting (86) gives:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | Case 1:
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | |   (161)  all_58_9 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | COMBINE_EQS: (26), (161) imply:
% 202.75/34.07  | | | | | | | | |   (162)  all_52_25 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | SIMP: (162) implies:
% 202.75/34.07  | | | | | | | | |   (163)  all_52_25 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (17), (163) imply:
% 202.75/34.07  | | | | | | | | |   (164)   ~ (all_52_17 = e3)
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REDUCE: (117), (163) imply:
% 202.75/34.07  | | | | | | | | |   (165)  op(e3, e3) = all_52_24
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REF_CLOSE: (7), (37), (40), (59), (70), (75), (85), (95),
% 202.75/34.07  | | | | | | | | |            (99), (118), (159), (160), (164), (165) are
% 202.75/34.07  | | | | | | | | |            inconsistent by sub-proof #444.
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | |   (166)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (19), (21),
% 202.75/34.07  | | | | | | | | |            (23), (24), (26), (27), (28), (29), (32), (35),
% 202.75/34.07  | | | | | | | | |            (37), (40), (41), (43), (44), (45), (47), (48),
% 202.75/34.07  | | | | | | | | |            (49), (50), (52), (55), (59), (61), (62), (64),
% 202.75/34.07  | | | | | | | | |            (65), (70), (72), (73), (74), (75), (76), (78),
% 202.75/34.07  | | | | | | | | |            (85), (87), (93), (95), (96), (99), (100), (102),
% 202.75/34.07  | | | | | | | | |            (104), (106), (115), (118), (124), (155), (158),
% 202.75/34.07  | | | | | | | | |            (166) are inconsistent by sub-proof #442.
% 202.75/34.07  | | | | | | | | | 
% 202.75/34.07  | | | | | | | | End of split
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | |   (167)  all_58_14 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REF_CLOSE: (4), (124), (167) are inconsistent by sub-proof
% 202.75/34.07  | | | | | | | |            #1305.
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | End of split
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | End of split
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | End of split
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | End of split
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | Case 2:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | |   (168)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | REF_CLOSE: (3), (7), (8), (19), (26), (29), (44), (84), (85), (88),
% 202.75/34.07  | | | |            (93), (95), (99), (101), (104), (110), (114), (115), (122),
% 202.75/34.07  | | | |            (127), (137), (168) are inconsistent by sub-proof #441.
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | End of split
% 202.75/34.07  | | | 
% 202.75/34.07  | | End of split
% 202.75/34.07  | | 
% 202.75/34.07  | Case 2:
% 202.75/34.07  | | 
% 202.75/34.07  | |   (169)   ~ (all_56_13 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | REDUCE: (111), (169) imply:
% 202.75/34.07  | |   (170)   ~ (all_52_15 = e3)
% 202.75/34.07  | | 
% 202.75/34.07  | | BETA: splitting (98) gives:
% 202.75/34.07  | | 
% 202.75/34.07  | | Case 1:
% 202.75/34.07  | | | 
% 202.75/34.07  | | |   (171)  all_58_12 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | COMBINE_EQS: (54), (171) imply:
% 202.75/34.07  | | |   (172)  all_52_7 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | SIMP: (172) implies:
% 202.75/34.07  | | |   (173)  all_52_7 = e3
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (91), (173) imply:
% 202.75/34.07  | | |   (174)   ~ (all_52_3 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (53), (173) imply:
% 202.75/34.07  | | |   (175)   ~ (all_52_5 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (108), (173) imply:
% 202.75/34.07  | | |   (176)   ~ (all_52_23 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | SIMP: (176) implies:
% 202.75/34.07  | | |   (177)   ~ (all_52_23 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (56), (173) imply:
% 202.75/34.07  | | |   (178)   ~ (all_14_2 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (36), (173) imply:
% 202.75/34.07  | | |   (179)   ~ (all_6_2 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | SIMP: (179) implies:
% 202.75/34.07  | | |   (180)   ~ (all_6_2 = e3)
% 202.75/34.07  | | | 
% 202.75/34.07  | | | REDUCE: (16), (173) imply:
% 202.75/34.07  | | |   (181)  op(e3, e3) = all_52_6
% 202.75/34.07  | | | 
% 202.75/34.07  | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3, simplifying
% 202.75/34.07  | | |              with (85), (181) gives:
% 202.75/34.07  | | |   (182)  all_52_6 = all_6_2
% 202.75/34.07  | | | 
% 202.75/34.07  | | | BETA: splitting (63) gives:
% 202.75/34.07  | | | 
% 202.75/34.07  | | | Case 1:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | |   (183)  all_56_4 = e3
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | REF_CLOSE: (20), (174), (183) are inconsistent by sub-proof #1340.
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | Case 2:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | |   (184)   ~ (all_56_4 = e3)
% 202.75/34.07  | | | |   (185)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | BETA: splitting (82) gives:
% 202.75/34.07  | | | | 
% 202.75/34.07  | | | | Case 1:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | |   (186)  all_56_3 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | COMBINE_EQS: (90), (186) imply:
% 202.75/34.07  | | | | |   (187)  all_52_25 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (187) implies:
% 202.75/34.07  | | | | |   (188)  all_52_25 = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (17), (188) imply:
% 202.75/34.07  | | | | |   (189)   ~ (all_52_17 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (3), (188) imply:
% 202.75/34.07  | | | | |   (190)   ~ (all_52_27 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (190) implies:
% 202.75/34.07  | | | | |   (191)   ~ (all_52_27 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (48), (188) imply:
% 202.75/34.07  | | | | |   (192)   ~ (all_52_29 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | SIMP: (192) implies:
% 202.75/34.07  | | | | |   (193)   ~ (all_52_29 = e3)
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (117), (188) imply:
% 202.75/34.07  | | | | |   (194)  op(e3, e3) = all_52_24
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | REDUCE: (22), (188) imply:
% 202.75/34.07  | | | | |   (195)  op(e3, e0) = e3
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 202.75/34.07  | | | | |              simplifying with (85), (194) gives:
% 202.75/34.07  | | | | |   (196)  all_52_24 = all_6_2
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | BETA: splitting (104) gives:
% 202.75/34.07  | | | | | 
% 202.75/34.07  | | | | | Case 1:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (197)  all_58_4 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | REF_CLOSE: (115), (189), (197) are inconsistent by sub-proof #1302.
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | Case 2:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | |   (198)   ~ (all_58_4 = e3)
% 202.75/34.07  | | | | | |   (199)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | BETA: splitting (38) gives:
% 202.75/34.07  | | | | | | 
% 202.75/34.07  | | | | | | Case 1:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | |   (200)  all_58_2 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | REF_CLOSE: (57), (174), (200) are inconsistent by sub-proof #1369.
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | Case 2:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | |   (201)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | BETA: splitting (55) gives:
% 202.75/34.07  | | | | | | | 
% 202.75/34.07  | | | | | | | Case 1:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | |   (202)  all_58_6 = e3
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | | REF_CLOSE: (96), (175), (202) are inconsistent by sub-proof
% 202.75/34.07  | | | | | | | |            #1328.
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | Case 2:
% 202.75/34.07  | | | | | | | | 
% 202.75/34.07  | | | | | | | |   (203)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.75/34.08  | | | | | | | | 
% 202.75/34.08  | | | | | | | | BETA: splitting (40) gives:
% 202.75/34.08  | | | | | | | | 
% 202.75/34.08  | | | | | | | | Case 1:
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | |   (204)  all_56_2 = e3
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | REF_CLOSE: (59), (189), (204) are inconsistent by sub-proof
% 202.75/34.08  | | | | | | | | |            #1327.
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | Case 2:
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | |   (205)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | BETA: splitting (116) gives:
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | Case 1:
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | |   (206)  all_56_10 = e3
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | COMBINE_EQS: (103), (206) imply:
% 202.75/34.08  | | | | | | | | | |   (207)  all_10_2 = e3
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | SIMP: (207) implies:
% 202.75/34.08  | | | | | | | | | |   (208)  all_10_2 = e3
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | REDUCE: (74), (208) imply:
% 202.75/34.08  | | | | | | | | | |   (209)   ~ (all_52_19 = e3)
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | REDUCE: (43), (208) imply:
% 202.75/34.08  | | | | | | | | | |   (210)  op(e3, e3) = e1
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | REDUCE: (35), (208) imply:
% 202.75/34.08  | | | | | | | | | |   (211)  op(e3, e1) = all_10_1
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | BETA: splitting (201) gives:
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | Case 1:
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | |   (212)  all_58_3 = e3
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | COMBINE_EQS: (110), (212) imply:
% 202.75/34.08  | | | | | | | | | | |   (213)  all_4_2 = e3
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | REDUCE: (89), (213) imply:
% 202.75/34.08  | | | | | | | | | | |   (214)  op(e3, e3) = all_52_10
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_17, all_10_1, e1,
% 202.75/34.08  | | | | | | | | | | |              e3, simplifying with (70), (211) gives:
% 202.75/34.08  | | | | | | | | | | |   (215)  all_52_17 = all_10_1
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_10, e3, e3,
% 202.75/34.08  | | | | | | | | | | |              simplifying with (85), (214) gives:
% 202.75/34.08  | | | | | | | | | | |   (216)  all_52_10 = all_6_2
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_10, e3, e3,
% 202.75/34.08  | | | | | | | | | | |              simplifying with (210), (214) gives:
% 202.75/34.08  | | | | | | | | | | |   (217)  all_52_10 = e1
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | COMBINE_EQS: (216), (217) imply:
% 202.75/34.08  | | | | | | | | | | |   (218)  all_6_2 = e1
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | SIMP: (218) implies:
% 202.75/34.08  | | | | | | | | | | |   (219)  all_6_2 = e1
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | COMBINE_EQS: (59), (215) imply:
% 202.75/34.08  | | | | | | | | | | |   (220)  all_56_2 = all_10_1
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | REDUCE: (99), (215), (219) imply:
% 202.75/34.08  | | | | | | | | | | |   (221)   ~ (all_10_1 = e1)
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | REDUCE: (95), (215) imply:
% 202.75/34.08  | | | | | | | | | | |   (222)  op(all_10_1, all_10_1) = e3
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | REF_CLOSE: (7), (37), (75), (118), (205), (220), (221), (222)
% 202.75/34.08  | | | | | | | | | | |            are inconsistent by sub-proof #445.
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | Case 2:
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | |   (223)  all_58_5 = e3 | all_58_10 = e3
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | | REF_CLOSE: (44), (93), (191), (209), (223) are inconsistent
% 202.75/34.08  | | | | | | | | | | |            by sub-proof #1132.
% 202.75/34.08  | | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | End of split
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | Case 2:
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | |   (224)   ~ (all_56_10 = e3)
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | REDUCE: (103), (224) imply:
% 202.75/34.08  | | | | | | | | | |   (225)   ~ (all_10_2 = e3)
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | | REF_CLOSE: (4), (7), (12), (18), (19), (20), (30), (32),
% 202.75/34.08  | | | | | | | | | |            (42), (50), (51), (52), (57), (64), (70), (76),
% 202.75/34.08  | | | | | | | | | |            (84), (85), (93), (99), (105), (114), (177),
% 202.75/34.08  | | | | | | | | | |            (180), (185), (193), (195), (199), (203), (225)
% 202.75/34.08  | | | | | | | | | |            are inconsistent by sub-proof #440.
% 202.75/34.08  | | | | | | | | | | 
% 202.75/34.08  | | | | | | | | | End of split
% 202.75/34.08  | | | | | | | | | 
% 202.75/34.08  | | | | | | | | End of split
% 202.75/34.08  | | | | | | | | 
% 202.75/34.08  | | | | | | | End of split
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | End of split
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | End of split
% 202.75/34.08  | | | | | 
% 202.75/34.08  | | | | Case 2:
% 202.75/34.08  | | | | | 
% 202.75/34.08  | | | | |   (226)   ~ (all_56_3 = e3)
% 202.75/34.08  | | | | | 
% 202.75/34.08  | | | | | REDUCE: (90), (226) imply:
% 202.75/34.08  | | | | |   (227)   ~ (all_52_25 = e3)
% 202.75/34.08  | | | | | 
% 202.75/34.08  | | | | | BETA: splitting (86) gives:
% 202.75/34.08  | | | | | 
% 202.75/34.08  | | | | | Case 1:
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | |   (228)  all_58_9 = e3
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | | REF_CLOSE: (26), (227), (228) are inconsistent by sub-proof #1300.
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | Case 2:
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | |   (229)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | | BETA: splitting (88) gives:
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | | Case 1:
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | |   (230)  all_58_0 = e3
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | | COMBINE_EQS: (19), (230) imply:
% 202.75/34.08  | | | | | | |   (231)  all_6_2 = e3
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | | REDUCE: (180), (231) imply:
% 202.75/34.08  | | | | | | |   (232)  $false
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | | CLOSE: (232) is inconsistent.
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | Case 2:
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | |   (233)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (19), (21), (23),
% 202.75/34.08  | | | | | | |            (24), (26), (27), (28), (29), (32), (35), (37), (40),
% 202.75/34.08  | | | | | | |            (41), (43), (44), (45), (47), (48), (49), (50), (52),
% 202.75/34.08  | | | | | | |            (55), (59), (61), (62), (64), (65), (70), (72), (73),
% 202.75/34.08  | | | | | | |            (74), (75), (76), (78), (85), (87), (93), (95), (96),
% 202.75/34.08  | | | | | | |            (99), (100), (102), (104), (106), (115), (118), (175),
% 202.75/34.08  | | | | | | |            (177), (229), (233) are inconsistent by sub-proof #442.
% 202.75/34.08  | | | | | | | 
% 202.75/34.08  | | | | | | End of split
% 202.75/34.08  | | | | | | 
% 202.75/34.08  | | | | | End of split
% 202.75/34.08  | | | | | 
% 202.75/34.08  | | | | End of split
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | End of split
% 202.75/34.08  | | | 
% 202.75/34.08  | | Case 2:
% 202.75/34.08  | | | 
% 202.75/34.08  | | |   (234)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REF_CLOSE: (1), (4), (5), (7), (10), (11), (13), (14), (25), (36), (40),
% 202.75/34.08  | | |            (54), (59), (66), (69), (71), (73), (79), (80), (84), (85),
% 202.75/34.08  | | |            (92), (95), (97), (99), (100), (102), (106), (107), (108),
% 202.75/34.08  | | |            (112), (113), (114), (118), (170), (234) are inconsistent by
% 202.75/34.08  | | |            sub-proof #437.
% 202.75/34.08  | | | 
% 202.75/34.08  | | End of split
% 202.75/34.08  | | 
% 202.75/34.08  | End of split
% 202.75/34.08  | 
% 202.75/34.08  End of proof
% 202.75/34.08  
% 202.75/34.08  Sub-proof #437 shows that the following formulas are inconsistent:
% 202.75/34.08  ----------------------------------------------------------------
% 202.75/34.08    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.08    (2)  all_58_14 = all_52_23
% 202.75/34.08    (3)   ~ (e3 = e1)
% 202.75/34.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.08    (5)   ~ (e3 = e0)
% 202.75/34.08    (6)  op(all_52_23, all_52_23) = e0
% 202.75/34.08    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.08    (8)   ~ (all_52_7 = all_52_15)
% 202.75/34.08    (9)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.75/34.08    (10)  all_58_13 = all_52_15
% 202.75/34.08    (11)   ~ (all_52_15 = e3)
% 202.75/34.08    (12)   ~ (all_52_7 = all_6_2)
% 202.75/34.08    (13)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.08    (14)  all_58_12 = all_52_7
% 202.75/34.08    (15)  all_56_2 = all_52_17
% 202.75/34.08    (16)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.75/34.08    (17)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.75/34.08    (18)  op(e0, e3) = all_52_7
% 202.75/34.08    (19)  all_58_15 = all_14_2
% 202.75/34.08    (20)  all_56_12 = all_52_7
% 202.75/34.08    (21)  all_8_2 = all_6_2
% 202.75/34.08    (22)  op(e3, all_6_1) = e2
% 202.75/34.08    (23)  op(e3, e3) = all_6_2
% 202.75/34.08    (24)  op(all_14_2, all_14_2) = all_52_30
% 202.75/34.08    (25)  op(all_52_17, all_52_17) = e3
% 202.75/34.08    (26)  op(e3, e2) = all_52_9
% 202.75/34.08    (27)   ~ (all_52_17 = all_6_2)
% 202.75/34.08    (28)   ~ (e1 = e0)
% 202.75/34.08    (29)   ~ (all_52_9 = all_52_17)
% 202.75/34.08    (30)  op(e1, e1) = all_10_2
% 202.75/34.08    (31)   ~ (all_52_23 = all_10_2)
% 202.75/34.08    (32)   ~ (all_52_7 = all_52_23)
% 202.75/34.08    (33)   ~ (all_52_17 = all_52_23)
% 202.75/34.08    (34)  all_8_1 = all_6_1
% 202.75/34.08    (35)  op(all_6_2, e3) = all_6_1
% 202.75/34.08    (36)   ~ (all_14_2 = e3)
% 202.75/34.08  
% 202.75/34.08  Begin of proof
% 202.75/34.08  | 
% 202.75/34.08  | BETA: splitting (9) gives:
% 202.75/34.08  | 
% 202.75/34.08  | Case 1:
% 202.75/34.08  | | 
% 202.75/34.08  | |   (37)  all_58_13 = e3
% 202.75/34.08  | | 
% 202.75/34.08  | | REF_CLOSE: (10), (11), (37) are inconsistent by sub-proof #1360.
% 202.75/34.08  | | 
% 202.75/34.08  | Case 2:
% 202.75/34.08  | | 
% 202.75/34.08  | |   (38)  all_58_14 = e3 | all_58_15 = e3
% 202.75/34.08  | | 
% 202.75/34.08  | | BETA: splitting (38) gives:
% 202.75/34.08  | | 
% 202.75/34.08  | | Case 1:
% 202.75/34.08  | | | 
% 202.75/34.08  | | |   (39)  all_58_14 = e3
% 202.75/34.08  | | | 
% 202.75/34.08  | | | COMBINE_EQS: (2), (39) imply:
% 202.75/34.08  | | |   (40)  all_52_23 = e3
% 202.75/34.08  | | | 
% 202.75/34.08  | | | SIMP: (40) implies:
% 202.75/34.08  | | |   (41)  all_52_23 = e3
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REDUCE: (32), (41) imply:
% 202.75/34.08  | | |   (42)   ~ (all_52_7 = e3)
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REDUCE: (33), (41) imply:
% 202.75/34.08  | | |   (43)   ~ (all_52_17 = e3)
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REDUCE: (31), (41) imply:
% 202.75/34.08  | | |   (44)   ~ (all_10_2 = e3)
% 202.75/34.08  | | | 
% 202.75/34.08  | | | SIMP: (44) implies:
% 202.75/34.08  | | |   (45)   ~ (all_10_2 = e3)
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REDUCE: (6), (41) imply:
% 202.75/34.08  | | |   (46)  op(e3, e3) = e0
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (12), (13), (14), (15),
% 202.75/34.08  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 202.75/34.08  | | |            (26), (27), (28), (29), (30), (34), (35), (39), (42), (43),
% 202.75/34.08  | | |            (45), (46) are inconsistent by sub-proof #438.
% 202.75/34.08  | | | 
% 202.75/34.08  | | Case 2:
% 202.75/34.08  | | | 
% 202.75/34.08  | | |   (47)  all_58_15 = e3
% 202.75/34.08  | | | 
% 202.75/34.08  | | | COMBINE_EQS: (19), (47) imply:
% 202.75/34.08  | | |   (48)  all_14_2 = e3
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REDUCE: (36), (48) imply:
% 202.75/34.08  | | |   (49)  $false
% 202.75/34.08  | | | 
% 202.75/34.08  | | | CLOSE: (49) is inconsistent.
% 202.75/34.08  | | | 
% 202.75/34.08  | | End of split
% 202.75/34.08  | | 
% 202.75/34.08  | End of split
% 202.75/34.08  | 
% 202.75/34.08  End of proof
% 202.75/34.08  
% 202.75/34.08  Sub-proof #438 shows that the following formulas are inconsistent:
% 202.75/34.08  ----------------------------------------------------------------
% 202.75/34.08    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.75/34.08    (2)   ~ (e3 = e1)
% 202.75/34.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.08    (4)   ~ (e3 = e0)
% 202.75/34.08    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.08    (6)   ~ (all_52_7 = all_52_15)
% 202.75/34.08    (7)  all_58_13 = all_52_15
% 202.75/34.08    (8)   ~ (all_52_7 = all_6_2)
% 202.75/34.08    (9)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.08    (10)  all_58_12 = all_52_7
% 202.75/34.08    (11)   ~ (all_52_7 = e3)
% 202.75/34.08    (12)  all_56_2 = all_52_17
% 202.75/34.08    (13)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.75/34.08    (14)   ~ (all_10_2 = e3)
% 202.75/34.08    (15)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 202.75/34.08    (16)  op(e0, e3) = all_52_7
% 202.75/34.08    (17)  all_58_15 = all_14_2
% 202.75/34.08    (18)  all_56_12 = all_52_7
% 202.75/34.08    (19)  all_8_2 = all_6_2
% 202.75/34.08    (20)  op(e3, all_6_1) = e2
% 202.75/34.08    (21)  op(e3, e3) = e0
% 202.75/34.08    (22)  op(e3, e3) = all_6_2
% 202.75/34.08    (23)   ~ (all_52_17 = e3)
% 202.75/34.08    (24)  op(all_14_2, all_14_2) = all_52_30
% 202.75/34.08    (25)  op(all_52_17, all_52_17) = e3
% 202.75/34.08    (26)  op(e3, e2) = all_52_9
% 202.75/34.08    (27)   ~ (all_52_17 = all_6_2)
% 202.75/34.08    (28)   ~ (e1 = e0)
% 202.75/34.08    (29)   ~ (all_52_9 = all_52_17)
% 202.75/34.08    (30)  op(e1, e1) = all_10_2
% 202.75/34.08    (31)  all_58_14 = e3
% 202.75/34.08    (32)  all_8_1 = all_6_1
% 202.75/34.08    (33)  op(all_6_2, e3) = all_6_1
% 202.75/34.08  
% 202.75/34.08  Begin of proof
% 202.75/34.08  | 
% 202.75/34.08  | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying with
% 202.75/34.08  |              (21), (22) gives:
% 202.75/34.08  |   (34)  all_6_2 = e0
% 202.75/34.08  | 
% 202.75/34.08  | COMBINE_EQS: (19), (34) imply:
% 202.75/34.08  |   (35)  all_8_2 = e0
% 202.75/34.08  | 
% 202.75/34.08  | REDUCE: (8), (34) imply:
% 202.75/34.08  |   (36)   ~ (all_52_7 = e0)
% 202.75/34.08  | 
% 202.75/34.08  | REDUCE: (27), (34) imply:
% 202.75/34.08  |   (37)   ~ (all_52_17 = e0)
% 202.75/34.08  | 
% 202.75/34.08  | REDUCE: (33), (34) imply:
% 202.75/34.08  |   (38)  op(e0, e3) = all_6_1
% 202.75/34.08  | 
% 202.75/34.08  | BETA: splitting (1) gives:
% 202.75/34.08  | 
% 202.75/34.08  | Case 1:
% 202.75/34.08  | | 
% 202.75/34.08  | |   (39)   ~ (all_8_1 = e1)
% 202.75/34.08  | | 
% 202.75/34.08  | | REDUCE: (32), (39) imply:
% 202.75/34.08  | |   (40)   ~ (all_6_1 = e1)
% 202.75/34.08  | | 
% 202.75/34.08  | | BETA: splitting (15) gives:
% 202.75/34.08  | | 
% 202.75/34.08  | | Case 1:
% 202.75/34.08  | | | 
% 202.75/34.08  | | |   (41)  all_58_12 = e0
% 202.75/34.08  | | | 
% 202.75/34.08  | | | REF_CLOSE: (10), (36), (41) are inconsistent by sub-proof #1067.
% 202.75/34.08  | | | 
% 202.75/34.08  | | Case 2:
% 202.75/34.08  | | | 
% 202.75/34.08  | | |   (42)  all_58_13 = e0 | all_58_14 = e0
% 202.75/34.08  | | | 
% 202.75/34.08  | | | BETA: splitting (42) gives:
% 202.75/34.08  | | | 
% 202.75/34.08  | | | Case 1:
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | |   (43)  all_58_13 = e0
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | | COMBINE_EQS: (7), (43) imply:
% 202.75/34.08  | | | |   (44)  all_52_15 = e0
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | | SIMP: (44) implies:
% 202.75/34.08  | | | |   (45)  all_52_15 = e0
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | | REF_CLOSE: (2), (3), (5), (9), (10), (11), (12), (13), (14), (16), (17),
% 202.75/34.08  | | | |            (18), (20), (23), (24), (25), (26), (28), (29), (30), (31),
% 202.75/34.08  | | | |            (36), (37), (38), (40), (43) are inconsistent by sub-proof
% 202.75/34.08  | | | |            #439.
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | Case 2:
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | |   (46)  all_58_14 = e0
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | | REF_CLOSE: (4), (31), (46) are inconsistent by sub-proof #1151.
% 202.75/34.08  | | | | 
% 202.75/34.08  | | | End of split
% 202.75/34.08  | | | 
% 202.75/34.08  | | End of split
% 202.75/34.08  | | 
% 202.75/34.08  | Case 2:
% 202.75/34.08  | | 
% 202.75/34.08  | |   (47)   ~ (all_8_2 = e0)
% 202.75/34.08  | | 
% 202.75/34.08  | | REDUCE: (35), (47) imply:
% 202.75/34.08  | |   (48)  $false
% 202.75/34.08  | | 
% 202.75/34.08  | | CLOSE: (48) is inconsistent.
% 202.75/34.08  | | 
% 202.75/34.08  | End of split
% 202.75/34.08  | 
% 202.75/34.08  End of proof
% 202.75/34.08  
% 202.75/34.08  Sub-proof #439 shows that the following formulas are inconsistent:
% 202.75/34.08  ----------------------------------------------------------------
% 202.75/34.08    (1)   ~ (e3 = e1)
% 202.75/34.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.75/34.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.75/34.08    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.75/34.08    (4)   ~ (all_6_1 = e1)
% 202.75/34.08    (5)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.75/34.08    (6)  all_58_12 = all_52_7
% 202.75/34.08    (7)   ~ (all_52_7 = e3)
% 202.75/34.08    (8)  all_56_2 = all_52_17
% 202.90/34.08    (9)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.90/34.08    (10)   ~ (all_10_2 = e3)
% 202.90/34.08    (11)  op(e0, e3) = all_52_7
% 202.90/34.08    (12)  all_58_15 = all_14_2
% 202.90/34.08    (13)  all_56_12 = all_52_7
% 202.90/34.08    (14)  op(e3, all_6_1) = e2
% 202.90/34.08    (15)   ~ (all_52_17 = e3)
% 202.90/34.08    (16)  all_58_13 = e0
% 202.90/34.08    (17)  op(all_14_2, all_14_2) = all_52_30
% 202.90/34.08    (18)  op(all_52_17, all_52_17) = e3
% 202.90/34.08    (19)  op(e3, e2) = all_52_9
% 202.90/34.08    (20)   ~ (e1 = e0)
% 202.90/34.08    (21)  op(e0, e3) = all_6_1
% 202.90/34.08    (22)   ~ (all_52_9 = all_52_17)
% 202.90/34.08    (23)   ~ (all_52_17 = e0)
% 202.90/34.08    (24)  op(e1, e1) = all_10_2
% 202.90/34.08    (25)  all_58_14 = e3
% 202.90/34.08    (26)   ~ (all_52_7 = e0)
% 202.90/34.08  
% 202.90/34.08  Begin of proof
% 202.90/34.08  | 
% 202.90/34.08  | GROUND_INST: instantiating (2) with all_52_7, all_6_1, e3, e0, simplifying
% 202.90/34.08  |              with (11), (21) gives:
% 202.90/34.08  |   (27)  all_52_7 = all_6_1
% 202.90/34.08  | 
% 202.90/34.08  | COMBINE_EQS: (13), (27) imply:
% 202.90/34.08  |   (28)  all_56_12 = all_6_1
% 202.90/34.08  | 
% 202.90/34.08  | COMBINE_EQS: (6), (27) imply:
% 202.90/34.08  |   (29)  all_58_12 = all_6_1
% 202.90/34.08  | 
% 202.90/34.08  | REDUCE: (7), (27) imply:
% 202.90/34.08  |   (30)   ~ (all_6_1 = e3)
% 202.90/34.08  | 
% 202.90/34.08  | REDUCE: (26), (27) imply:
% 202.90/34.08  |   (31)   ~ (all_6_1 = e0)
% 202.90/34.08  | 
% 202.90/34.08  | BETA: splitting (3) gives:
% 202.90/34.08  | 
% 202.90/34.08  | Case 1:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (32)  all_56_12 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | REF_CLOSE: (28), (30), (32) are inconsistent by sub-proof #1347.
% 202.90/34.08  | | 
% 202.90/34.08  | Case 2:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (33)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.08  | | 
% 202.90/34.08  | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (12), (14), (15), (16), (17),
% 202.90/34.08  | |            (18), (19), (20), (22), (23), (24), (25), (28), (29), (31), (33)
% 202.90/34.08  | |            are inconsistent by sub-proof #481.
% 202.90/34.08  | | 
% 202.90/34.08  | End of split
% 202.90/34.08  | 
% 202.90/34.08  End of proof
% 202.90/34.08  
% 202.90/34.08  Sub-proof #440 shows that the following formulas are inconsistent:
% 202.90/34.08  ----------------------------------------------------------------
% 202.90/34.08    (1)  all_58_14 = all_52_23
% 202.90/34.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.08    (3)  op(e2, e3) = all_52_3
% 202.90/34.08    (4)   ~ (all_52_3 = all_6_2)
% 202.90/34.08    (5)  all_58_0 = all_6_2
% 202.90/34.08    (6)  all_56_4 = all_52_3
% 202.90/34.08    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.08    (8)  all_58_11 = all_52_29
% 202.90/34.08    (9)   ~ (all_6_2 = e3)
% 202.90/34.08    (10)   ~ (all_52_13 = all_10_2)
% 202.90/34.08    (11)  all_58_7 = all_52_13
% 202.90/34.08    (12)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.08    (13)  op(all_52_19, all_52_19) = e2
% 202.90/34.08    (14)  all_58_2 = all_52_3
% 202.90/34.08    (15)   ~ (all_52_29 = e3)
% 202.90/34.08    (16)   ~ (e2 = e0)
% 202.90/34.08    (17)   ~ (all_52_23 = e3)
% 202.90/34.08    (18)   ~ (all_10_2 = e3)
% 202.90/34.08    (19)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.08    (20)  op(e3, e1) = all_52_17
% 202.90/34.08    (21)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.08    (22)  op(e3, e0) = e3
% 202.90/34.08    (23)  all_58_8 = all_10_2
% 202.90/34.08    (24)  op(e3, all_6_1) = e2
% 202.90/34.08    (25)  op(e3, e3) = all_6_2
% 202.90/34.08    (26)  all_58_5 = all_52_19
% 202.90/34.08    (27)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.08    (28)   ~ (all_52_17 = all_6_2)
% 202.90/34.08    (29)  op(all_52_13, all_52_13) = all_52_12
% 202.90/34.08    (30)  op(all_6_2, e3) = all_6_1
% 202.90/34.08  
% 202.90/34.08  Begin of proof
% 202.90/34.08  | 
% 202.90/34.08  | BETA: splitting (21) gives:
% 202.90/34.08  | 
% 202.90/34.08  | Case 1:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (31)  all_58_7 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | COMBINE_EQS: (11), (31) imply:
% 202.90/34.08  | |   (32)  all_52_13 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | REDUCE: (10), (32) imply:
% 202.90/34.08  | |   (33)   ~ (all_10_2 = e3)
% 202.90/34.08  | | 
% 202.90/34.08  | | REDUCE: (29), (32) imply:
% 202.90/34.08  | |   (34)  op(e3, e3) = all_52_12
% 202.90/34.08  | | 
% 202.90/34.08  | | BETA: splitting (27) gives:
% 202.90/34.08  | | 
% 202.90/34.08  | | Case 1:
% 202.90/34.08  | | | 
% 202.90/34.08  | | |   (35)  all_58_5 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | COMBINE_EQS: (26), (35) imply:
% 202.90/34.08  | | |   (36)  all_52_19 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | SIMP: (36) implies:
% 202.90/34.08  | | |   (37)  all_52_19 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REDUCE: (13), (37) imply:
% 202.90/34.08  | | |   (38)  op(e3, e3) = e2
% 202.90/34.08  | | | 
% 202.90/34.08  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_12, e3, e3,
% 202.90/34.08  | | |              simplifying with (25), (34) gives:
% 202.90/34.08  | | |   (39)  all_52_12 = all_6_2
% 202.90/34.08  | | | 
% 202.90/34.08  | | | GROUND_INST: instantiating (2) with e2, all_52_12, e3, e3, simplifying
% 202.90/34.08  | | |              with (34), (38) gives:
% 202.90/34.08  | | |   (40)  all_52_12 = e2
% 202.90/34.08  | | | 
% 202.90/34.08  | | | COMBINE_EQS: (39), (40) imply:
% 202.90/34.08  | | |   (41)  all_6_2 = e2
% 202.90/34.08  | | | 
% 202.90/34.08  | | | SIMP: (41) implies:
% 202.90/34.08  | | |   (42)  all_6_2 = e2
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (12), (14), (16), (19),
% 202.90/34.08  | | |            (20), (22), (24), (28), (30), (42) are inconsistent by
% 202.90/34.08  | | |            sub-proof #496.
% 202.90/34.08  | | | 
% 202.90/34.08  | | Case 2:
% 202.90/34.08  | | | 
% 202.90/34.08  | | |   (43)  all_58_8 = e3 | all_58_14 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REF_CLOSE: (1), (17), (18), (23), (43) are inconsistent by sub-proof
% 202.90/34.08  | | |            #1304.
% 202.90/34.08  | | | 
% 202.90/34.08  | | End of split
% 202.90/34.08  | | 
% 202.90/34.08  | Case 2:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (44)  all_58_8 = e3 | all_58_11 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | REF_CLOSE: (8), (15), (18), (23), (44) are inconsistent by sub-proof #1140.
% 202.90/34.08  | | 
% 202.90/34.08  | End of split
% 202.90/34.08  | 
% 202.90/34.08  End of proof
% 202.90/34.08  
% 202.90/34.08  Sub-proof #441 shows that the following formulas are inconsistent:
% 202.90/34.08  ----------------------------------------------------------------
% 202.90/34.08    (1)   ~ (all_52_25 = all_52_27)
% 202.90/34.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.08    (3)  all_58_1 = all_52_9
% 202.90/34.08    (4)   ~ (all_4_2 = e3)
% 202.90/34.08    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.08    (6)  all_58_0 = all_6_2
% 202.90/34.08    (7)  all_58_9 = all_52_25
% 202.90/34.08    (8)  op(all_52_27, all_52_27) = all_52_26
% 202.90/34.08    (9)  all_58_10 = all_52_27
% 202.90/34.08    (10)   ~ (all_52_19 = e3)
% 202.90/34.08    (11)   ~ (all_52_9 = e3)
% 202.90/34.08    (12)  op(e3, all_6_1) = e2
% 202.90/34.08    (13)  op(e3, e3) = all_6_2
% 202.90/34.08    (14)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.08    (15)  all_58_5 = all_52_19
% 202.90/34.08    (16)  op(all_52_17, all_52_17) = e3
% 202.90/34.08    (17)   ~ (all_52_17 = all_6_2)
% 202.90/34.08    (18)   ~ (e3 = e2)
% 202.90/34.08    (19)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.08    (20)  all_58_3 = all_4_2
% 202.90/34.08    (21)  op(all_6_2, e3) = all_6_1
% 202.90/34.08    (22)  all_58_4 = all_52_17
% 202.90/34.08  
% 202.90/34.08  Begin of proof
% 202.90/34.08  | 
% 202.90/34.08  | BETA: splitting (5) gives:
% 202.90/34.08  | 
% 202.90/34.08  | Case 1:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (23)  all_58_3 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | COMBINE_EQS: (20), (23) imply:
% 202.90/34.08  | |   (24)  all_4_2 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | REDUCE: (4), (24) imply:
% 202.90/34.08  | |   (25)  $false
% 202.90/34.08  | | 
% 202.90/34.08  | | CLOSE: (25) is inconsistent.
% 202.90/34.08  | | 
% 202.90/34.08  | Case 2:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (26)  all_58_5 = e3 | all_58_10 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | BETA: splitting (26) gives:
% 202.90/34.08  | | 
% 202.90/34.08  | | Case 1:
% 202.90/34.08  | | | 
% 202.90/34.08  | | |   (27)  all_58_5 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REF_CLOSE: (10), (15), (27) are inconsistent by sub-proof #1279.
% 202.90/34.08  | | | 
% 202.90/34.08  | | Case 2:
% 202.90/34.08  | | | 
% 202.90/34.08  | | |   (28)  all_58_10 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | COMBINE_EQS: (9), (28) imply:
% 202.90/34.08  | | |   (29)  all_52_27 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | SIMP: (29) implies:
% 202.90/34.08  | | |   (30)  all_52_27 = e3
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REDUCE: (1), (30) imply:
% 202.90/34.08  | | |   (31)   ~ (all_52_25 = e3)
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REDUCE: (8), (30) imply:
% 202.90/34.08  | | |   (32)  op(e3, e3) = all_52_26
% 202.90/34.08  | | | 
% 202.90/34.08  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_26, e3, e3,
% 202.90/34.08  | | |              simplifying with (13), (32) gives:
% 202.90/34.08  | | |   (33)  all_52_26 = all_6_2
% 202.90/34.08  | | | 
% 202.90/34.08  | | | REF_CLOSE: (2), (3), (6), (7), (11), (12), (13), (14), (16), (17), (18),
% 202.90/34.08  | | |            (19), (21), (22), (31) are inconsistent by sub-proof #446.
% 202.90/34.08  | | | 
% 202.90/34.08  | | End of split
% 202.90/34.08  | | 
% 202.90/34.08  | End of split
% 202.90/34.08  | 
% 202.90/34.08  End of proof
% 202.90/34.08  
% 202.90/34.08  Sub-proof #442 shows that the following formulas are inconsistent:
% 202.90/34.08  ----------------------------------------------------------------
% 202.90/34.08    (1)   ~ (all_52_25 = all_52_27)
% 202.90/34.08    (2)  all_58_14 = all_52_23
% 202.90/34.08    (3)   ~ (e3 = e1)
% 202.90/34.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.08    (5)  all_58_1 = all_52_9
% 202.90/34.08    (6)   ~ (all_52_9 = all_52_13)
% 202.90/34.08    (7)   ~ (e3 = e0)
% 202.90/34.08    (8)  all_58_0 = all_6_2
% 202.90/34.08    (9)   ~ (all_52_17 = all_10_2)
% 202.90/34.08    (10)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.90/34.08    (11)   ~ (all_52_27 = all_52_29)
% 202.90/34.08    (12)  all_58_9 = all_52_25
% 202.90/34.08    (13)   ~ (all_52_29 = all_14_2)
% 202.90/34.08    (14)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.90/34.08    (15)  op(all_52_27, all_52_27) = all_52_26
% 202.90/34.08    (16)  all_58_11 = all_52_29
% 202.90/34.08    (17)  op(all_10_2, e1) = all_10_1
% 202.90/34.08    (18)  op(e0, e0) = all_14_2
% 202.90/34.08    (19)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.90/34.08    (20)   ~ (e2 = e1)
% 202.90/34.08    (21)  op(all_10_2, all_10_2) = e1
% 202.90/34.08    (22)  all_58_10 = all_52_27
% 202.90/34.08    (23)  op(all_52_9, all_52_9) = all_52_8
% 202.90/34.08    (24)   ~ (all_52_19 = all_52_23)
% 202.90/34.08    (25)   ~ (all_52_25 = all_52_29)
% 202.90/34.08    (26)   ~ (all_52_29 = all_10_2)
% 202.90/34.08    (27)  all_58_7 = all_52_13
% 202.90/34.08    (28)  op(all_52_19, all_52_19) = e2
% 202.90/34.08    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.08    (30)  all_56_2 = all_52_17
% 202.90/34.08    (31)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.90/34.08    (32)  all_56_7 = all_52_27
% 202.90/34.08    (33)   ~ (e2 = e0)
% 202.90/34.08    (34)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.90/34.08    (35)   ~ (all_52_23 = e3)
% 202.90/34.08    (36)   ~ (all_52_5 = e3)
% 202.90/34.08    (37)  op(e3, e1) = all_52_17
% 202.90/34.08    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.08    (39)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.08    (40)  all_58_15 = all_14_2
% 202.90/34.08    (41)   ~ (all_52_19 = all_10_2)
% 202.90/34.08    (42)   ~ (all_10_1 = e2)
% 202.90/34.08    (43)  all_58_8 = all_10_2
% 202.90/34.08    (44)  op(all_52_29, all_52_29) = all_52_28
% 202.90/34.08    (45)  op(e3, e3) = all_6_2
% 202.90/34.08    (46)   ~ (all_52_27 = all_14_2)
% 202.90/34.08    (47)  all_58_5 = all_52_19
% 202.90/34.08    (48)  op(all_52_17, all_52_17) = e3
% 202.90/34.08    (49)  all_58_6 = all_52_5
% 202.90/34.08    (50)   ~ (all_52_17 = all_6_2)
% 202.90/34.08    (51)   ~ (e1 = e0)
% 202.90/34.08    (52)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.08    (53)   ~ (all_52_9 = all_52_17)
% 202.90/34.08    (54)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.08    (55)  op(e1, e1) = all_10_2
% 202.90/34.08    (56)  all_58_4 = all_52_17
% 202.90/34.08    (57)   ~ (all_14_2 = e3)
% 202.90/34.08  
% 202.90/34.08  Begin of proof
% 202.90/34.08  | 
% 202.90/34.08  | BETA: splitting (10) gives:
% 202.90/34.08  | 
% 202.90/34.08  | Case 1:
% 202.90/34.08  | | 
% 202.90/34.08  | |   (58)  all_56_7 = e3
% 202.90/34.08  | | 
% 202.90/34.08  | | COMBINE_EQS: (32), (58) imply:
% 202.90/34.09  | |   (59)  all_52_27 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | SIMP: (59) implies:
% 202.90/34.09  | |   (60)  all_52_27 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (1), (60) imply:
% 202.90/34.09  | |   (61)   ~ (all_52_25 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (11), (60) imply:
% 202.90/34.09  | |   (62)   ~ (all_52_29 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | SIMP: (62) implies:
% 202.90/34.09  | |   (63)   ~ (all_52_29 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (46), (60) imply:
% 202.90/34.09  | |   (64)   ~ (all_14_2 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (15), (60) imply:
% 202.90/34.09  | |   (65)  op(e3, e3) = all_52_26
% 202.90/34.09  | | 
% 202.90/34.09  | | GROUND_INST: instantiating (4) with all_6_2, all_52_26, e3, e3, simplifying
% 202.90/34.09  | |              with (45), (65) gives:
% 202.90/34.09  | |   (66)  all_52_26 = all_6_2
% 202.90/34.09  | | 
% 202.90/34.09  | | BETA: splitting (38) gives:
% 202.90/34.09  | | 
% 202.90/34.09  | | Case 1:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (67)  all_58_1 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | COMBINE_EQS: (5), (67) imply:
% 202.90/34.09  | | |   (68)  all_52_9 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (6), (68) imply:
% 202.90/34.09  | | |   (69)   ~ (all_52_13 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (69) implies:
% 202.90/34.09  | | |   (70)   ~ (all_52_13 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (23), (68) imply:
% 202.90/34.09  | | |   (71)  op(e3, e3) = all_52_8
% 202.90/34.09  | | | 
% 202.90/34.09  | | | BETA: splitting (29) gives:
% 202.90/34.09  | | | 
% 202.90/34.09  | | | Case 1:
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | |   (72)  all_58_6 = e3
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | REF_CLOSE: (36), (49), (72) are inconsistent by sub-proof #1328.
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | Case 2:
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | |   (73)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | BETA: splitting (73) gives:
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | Case 1:
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | |   (74)  all_58_7 = e3
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | | COMBINE_EQS: (27), (74) imply:
% 202.90/34.09  | | | | |   (75)  all_52_13 = e3
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | | REDUCE: (70), (75) imply:
% 202.90/34.09  | | | | |   (76)  $false
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | | CLOSE: (76) is inconsistent.
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | Case 2:
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | |   (77)  all_58_8 = e3 | all_58_11 = e3
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | | BETA: splitting (77) gives:
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | | Case 1:
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | |   (78)  all_58_8 = e3
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | COMBINE_EQS: (43), (78) imply:
% 202.90/34.09  | | | | | |   (79)  all_10_2 = e3
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REDUCE: (9), (79) imply:
% 202.90/34.09  | | | | | |   (80)   ~ (all_52_17 = e3)
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REDUCE: (21), (79) imply:
% 202.90/34.09  | | | | | |   (81)  op(e3, e3) = e1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REDUCE: (17), (79) imply:
% 202.90/34.09  | | | | | |   (82)  op(e3, e1) = all_10_1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | GROUND_INST: instantiating (4) with all_52_17, all_10_1, e1, e3,
% 202.90/34.09  | | | | | |              simplifying with (37), (82) gives:
% 202.90/34.09  | | | | | |   (83)  all_52_17 = all_10_1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_8, e3, e3,
% 202.90/34.09  | | | | | |              simplifying with (45), (71) gives:
% 202.90/34.09  | | | | | |   (84)  all_52_8 = all_6_2
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | GROUND_INST: instantiating (4) with e1, all_52_8, e3, e3,
% 202.90/34.09  | | | | | |              simplifying with (71), (81) gives:
% 202.90/34.09  | | | | | |   (85)  all_52_8 = e1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | COMBINE_EQS: (84), (85) imply:
% 202.90/34.09  | | | | | |   (86)  all_6_2 = e1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | SIMP: (86) implies:
% 202.90/34.09  | | | | | |   (87)  all_6_2 = e1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | COMBINE_EQS: (30), (83) imply:
% 202.90/34.09  | | | | | |   (88)  all_56_2 = all_10_1
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REDUCE: (50), (83), (87) imply:
% 202.90/34.09  | | | | | |   (89)   ~ (all_10_1 = e1)
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REDUCE: (80), (83) imply:
% 202.90/34.09  | | | | | |   (90)   ~ (all_10_1 = e3)
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REDUCE: (48), (83) imply:
% 202.90/34.09  | | | | | |   (91)  op(all_10_1, all_10_1) = e3
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | BETA: splitting (19) gives:
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | Case 1:
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | |   (92)  all_56_2 = e3
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | | COMBINE_EQS: (88), (92) imply:
% 202.90/34.09  | | | | | | |   (93)  all_10_1 = e3
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | | REDUCE: (90), (93) imply:
% 202.90/34.09  | | | | | | |   (94)  $false
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | | CLOSE: (94) is inconsistent.
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | Case 2:
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | |   (95)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | | REF_CLOSE: (4), (18), (42), (57), (88), (89), (91), (95) are
% 202.90/34.09  | | | | | | |            inconsistent by sub-proof #445.
% 202.90/34.09  | | | | | | | 
% 202.90/34.09  | | | | | | End of split
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | Case 2:
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | |   (96)  all_58_11 = e3
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | | REF_CLOSE: (16), (63), (96) are inconsistent by sub-proof #1323.
% 202.90/34.09  | | | | | | 
% 202.90/34.09  | | | | | End of split
% 202.90/34.09  | | | | | 
% 202.90/34.09  | | | | End of split
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | End of split
% 202.90/34.09  | | | 
% 202.90/34.09  | | Case 2:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (97)   ~ (all_58_1 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (5), (97) imply:
% 202.90/34.09  | | |   (98)   ~ (all_52_9 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REF_CLOSE: (4), (5), (12), (39), (45), (48), (50), (56), (61), (98) are
% 202.90/34.09  | | |            inconsistent by sub-proof #1072.
% 202.90/34.09  | | | 
% 202.90/34.09  | | End of split
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (99)   ~ (all_56_7 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (32), (99) imply:
% 202.90/34.09  | |   (100)   ~ (all_52_27 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (12), (13), (14), (16), (18), (20),
% 202.90/34.09  | |            (22), (23), (24), (25), (26), (28), (31), (33), (34), (35), (38),
% 202.90/34.09  | |            (39), (40), (41), (43), (44), (45), (47), (48), (50), (51), (52),
% 202.90/34.09  | |            (53), (54), (55), (56), (57), (100) are inconsistent by sub-proof
% 202.90/34.09  | |            #443.
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #443 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)  all_58_14 = all_52_23
% 202.90/34.09    (2)   ~ (e3 = e1)
% 202.90/34.09    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (4)  all_58_1 = all_52_9
% 202.90/34.09    (5)   ~ (e3 = e0)
% 202.90/34.09    (6)  all_58_0 = all_6_2
% 202.90/34.09    (7)  all_58_9 = all_52_25
% 202.90/34.09    (8)   ~ (all_52_29 = all_14_2)
% 202.90/34.09    (9)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 202.90/34.09    (10)  all_58_11 = all_52_29
% 202.90/34.09    (11)  op(e0, e0) = all_14_2
% 202.90/34.09    (12)   ~ (e2 = e1)
% 202.90/34.09    (13)  all_58_10 = all_52_27
% 202.90/34.09    (14)  op(all_52_9, all_52_9) = all_52_8
% 202.90/34.09    (15)   ~ (all_52_19 = all_52_23)
% 202.90/34.09    (16)   ~ (all_52_25 = all_52_29)
% 202.90/34.09    (17)   ~ (all_52_29 = all_10_2)
% 202.90/34.09    (18)  op(all_52_19, all_52_19) = e2
% 202.90/34.09    (19)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 202.90/34.09    (20)   ~ (e2 = e0)
% 202.90/34.09    (21)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 202.90/34.09    (22)   ~ (all_52_23 = e3)
% 202.90/34.09    (23)   ~ (all_52_27 = e3)
% 202.90/34.09    (24)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.09    (25)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.09    (26)  all_58_15 = all_14_2
% 202.90/34.09    (27)   ~ (all_52_19 = all_10_2)
% 202.90/34.09    (28)  all_58_8 = all_10_2
% 202.90/34.09    (29)  op(all_52_29, all_52_29) = all_52_28
% 202.90/34.09    (30)  op(e3, e3) = all_6_2
% 202.90/34.09    (31)  all_58_5 = all_52_19
% 202.90/34.09    (32)  op(all_52_17, all_52_17) = e3
% 202.90/34.09    (33)   ~ (all_52_17 = all_6_2)
% 202.90/34.09    (34)   ~ (e1 = e0)
% 202.90/34.09    (35)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.09    (36)   ~ (all_52_9 = all_52_17)
% 202.90/34.09    (37)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.09    (38)  op(e1, e1) = all_10_2
% 202.90/34.09    (39)  all_58_4 = all_52_17
% 202.90/34.09    (40)   ~ (all_14_2 = e3)
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | BETA: splitting (35) gives:
% 202.90/34.09  | 
% 202.90/34.09  | Case 1:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (41)  all_58_10 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (13), (23), (41) are inconsistent by sub-proof #1301.
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (42)  all_58_11 = e3 | all_58_15 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | BETA: splitting (42) gives:
% 202.90/34.09  | | 
% 202.90/34.09  | | Case 1:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (43)  all_58_11 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | COMBINE_EQS: (10), (43) imply:
% 202.90/34.09  | | |   (44)  all_52_29 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (44) implies:
% 202.90/34.09  | | |   (45)  all_52_29 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (16), (45) imply:
% 202.90/34.09  | | |   (46)   ~ (all_52_25 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (8), (45) imply:
% 202.90/34.09  | | |   (47)   ~ (all_14_2 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (17), (45) imply:
% 202.90/34.09  | | |   (48)   ~ (all_10_2 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (48) implies:
% 202.90/34.09  | | |   (49)   ~ (all_10_2 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (29), (45) imply:
% 202.90/34.09  | | |   (50)  op(e3, e3) = all_52_28
% 202.90/34.09  | | | 
% 202.90/34.09  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_28, e3, e3,
% 202.90/34.09  | | |              simplifying with (30), (50) gives:
% 202.90/34.09  | | |   (51)  all_52_28 = all_6_2
% 202.90/34.09  | | | 
% 202.90/34.09  | | | BETA: splitting (24) gives:
% 202.90/34.09  | | | 
% 202.90/34.09  | | | Case 1:
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | |   (52)  all_58_1 = e3
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | COMBINE_EQS: (4), (52) imply:
% 202.90/34.09  | | | |   (53)  all_52_9 = e3
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | REDUCE: (36), (53) imply:
% 202.90/34.09  | | | |   (54)   ~ (all_52_17 = e3)
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | SIMP: (54) implies:
% 202.90/34.09  | | | |   (55)   ~ (all_52_17 = e3)
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | REDUCE: (14), (53) imply:
% 202.90/34.09  | | | |   (56)  op(e3, e3) = all_52_8
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (12), (15), (18),
% 202.90/34.09  | | | |            (19), (20), (21), (22), (27), (28), (30), (31), (32), (34),
% 202.90/34.09  | | | |            (37), (38), (39), (40), (49), (52), (55), (56) are
% 202.90/34.09  | | | |            inconsistent by sub-proof #1048.
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | Case 2:
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | |   (57)   ~ (all_58_1 = e3)
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | REDUCE: (4), (57) imply:
% 202.90/34.09  | | | |   (58)   ~ (all_52_9 = e3)
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | | REF_CLOSE: (3), (4), (7), (25), (30), (32), (33), (39), (46), (58) are
% 202.90/34.09  | | | |            inconsistent by sub-proof #1072.
% 202.90/34.09  | | | | 
% 202.90/34.09  | | | End of split
% 202.90/34.09  | | | 
% 202.90/34.09  | | Case 2:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (59)  all_58_15 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | COMBINE_EQS: (26), (59) imply:
% 202.90/34.09  | | |   (60)  all_14_2 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (40), (60) imply:
% 202.90/34.09  | | |   (61)  $false
% 202.90/34.09  | | | 
% 202.90/34.09  | | | CLOSE: (61) is inconsistent.
% 202.90/34.09  | | | 
% 202.90/34.09  | | End of split
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #444 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (2)  op(e0, e0) = all_14_2
% 202.90/34.09    (3)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.90/34.09    (4)  all_56_2 = all_52_17
% 202.90/34.09    (5)  op(e3, e1) = all_10_1
% 202.90/34.09    (6)  op(e3, e1) = all_52_17
% 202.90/34.09    (7)   ~ (all_10_1 = e2)
% 202.90/34.09    (8)  op(e3, e3) = all_6_2
% 202.90/34.09    (9)   ~ (all_52_17 = e3)
% 202.90/34.09    (10)  op(e3, e3) = e1
% 202.90/34.09    (11)  op(e3, e3) = all_52_24
% 202.90/34.09    (12)  op(all_52_17, all_52_17) = e3
% 202.90/34.09    (13)   ~ (all_52_17 = all_6_2)
% 202.90/34.09    (14)   ~ (all_14_2 = e3)
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | GROUND_INST: instantiating (1) with all_52_17, all_10_1, e1, e3, simplifying
% 202.90/34.09  |              with (5), (6) gives:
% 202.90/34.09  |   (15)  all_52_17 = all_10_1
% 202.90/34.09  | 
% 202.90/34.09  | GROUND_INST: instantiating (1) with all_6_2, all_52_24, e3, e3, simplifying
% 202.90/34.09  |              with (8), (11) gives:
% 202.90/34.09  |   (16)  all_52_24 = all_6_2
% 202.90/34.09  | 
% 202.90/34.09  | GROUND_INST: instantiating (1) with e1, all_52_24, e3, e3, simplifying with
% 202.90/34.09  |              (10), (11) gives:
% 202.90/34.09  |   (17)  all_52_24 = e1
% 202.90/34.09  | 
% 202.90/34.09  | COMBINE_EQS: (16), (17) imply:
% 202.90/34.09  |   (18)  all_6_2 = e1
% 202.90/34.09  | 
% 202.90/34.09  | SIMP: (18) implies:
% 202.90/34.09  |   (19)  all_6_2 = e1
% 202.90/34.09  | 
% 202.90/34.09  | COMBINE_EQS: (4), (15) imply:
% 202.90/34.09  |   (20)  all_56_2 = all_10_1
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (13), (15), (19) imply:
% 202.90/34.09  |   (21)   ~ (all_10_1 = e1)
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (9), (15) imply:
% 202.90/34.09  |   (22)   ~ (all_10_1 = e3)
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (12), (15) imply:
% 202.90/34.09  |   (23)  op(all_10_1, all_10_1) = e3
% 202.90/34.09  | 
% 202.90/34.09  | BETA: splitting (3) gives:
% 202.90/34.09  | 
% 202.90/34.09  | Case 1:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (24)  all_56_2 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | COMBINE_EQS: (20), (24) imply:
% 202.90/34.09  | |   (25)  all_10_1 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (22), (25) imply:
% 202.90/34.09  | |   (26)  $false
% 202.90/34.09  | | 
% 202.90/34.09  | | CLOSE: (26) is inconsistent.
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (27)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (1), (2), (7), (14), (20), (21), (23), (27) are inconsistent by
% 202.90/34.09  | |            sub-proof #445.
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #445 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (2)   ~ (all_10_1 = e1)
% 202.90/34.09    (3)  op(e0, e0) = all_14_2
% 202.90/34.09    (4)  op(all_10_1, all_10_1) = e3
% 202.90/34.09    (5)   ~ (all_10_1 = e2)
% 202.90/34.09    (6)  all_56_2 = all_10_1
% 202.90/34.09    (7)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 202.90/34.09    (8)   ~ (all_14_2 = e3)
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | BETA: splitting (7) gives:
% 202.90/34.09  | 
% 202.90/34.09  | Case 1:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (9)  all_56_2 = e2
% 202.90/34.09  | | 
% 202.90/34.09  | | COMBINE_EQS: (6), (9) imply:
% 202.90/34.09  | |   (10)  all_10_1 = e2
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (5), (10) imply:
% 202.90/34.09  | |   (11)  $false
% 202.90/34.09  | | 
% 202.90/34.09  | | CLOSE: (11) is inconsistent.
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (12)  all_56_2 = e1 | all_56_2 = e0
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (12) are inconsistent by sub-proof
% 202.90/34.09  | |            #1053.
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #446 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (2)  all_58_1 = all_52_9
% 202.90/34.09    (3)  all_58_0 = all_6_2
% 202.90/34.09    (4)  all_58_9 = all_52_25
% 202.90/34.09    (5)   ~ (all_52_25 = e3)
% 202.90/34.09    (6)   ~ (all_52_9 = e3)
% 202.90/34.09    (7)  op(e3, all_6_1) = e2
% 202.90/34.09    (8)  op(e3, e3) = all_6_2
% 202.90/34.09    (9)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.09    (10)  op(all_52_17, all_52_17) = e3
% 202.90/34.09    (11)   ~ (all_52_17 = all_6_2)
% 202.90/34.09    (12)   ~ (e3 = e2)
% 202.90/34.09    (13)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.09    (14)  op(all_6_2, e3) = all_6_1
% 202.90/34.09    (15)  all_58_4 = all_52_17
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | BETA: splitting (13) gives:
% 202.90/34.09  | 
% 202.90/34.09  | Case 1:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (16)  all_58_4 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | COMBINE_EQS: (15), (16) imply:
% 202.90/34.09  | |   (17)  all_52_17 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | SIMP: (17) implies:
% 202.90/34.09  | |   (18)  all_52_17 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (1), (8), (10), (11), (18) are inconsistent by sub-proof #1280.
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (19)   ~ (all_58_4 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (15), (19) imply:
% 202.90/34.09  | |   (20)   ~ (all_52_17 = e3)
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (15),
% 202.90/34.09  | |            (20) are inconsistent by sub-proof #476.
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #447 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)  all_58_14 = all_52_23
% 202.90/34.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (3)  op(e2, e3) = all_52_3
% 202.90/34.09    (4)   ~ (all_52_3 = all_52_19)
% 202.90/34.09    (5)   ~ (all_4_2 = e3)
% 202.90/34.09    (6)   ~ (all_52_3 = all_6_2)
% 202.90/34.09    (7)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.09    (8)  all_58_0 = all_6_2
% 202.90/34.09    (9)  all_56_4 = all_52_3
% 202.90/34.09    (10)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.09    (11)  all_58_10 = all_52_27
% 202.90/34.09    (12)   ~ (all_52_19 = all_52_23)
% 202.90/34.09    (13)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.09    (14)  op(all_52_19, all_52_19) = e2
% 202.90/34.09    (15)  all_58_2 = all_52_3
% 202.90/34.09    (16)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.09    (17)   ~ (e2 = e0)
% 202.90/34.09    (18)   ~ (all_14_1 = all_6_2)
% 202.90/34.09    (19)   ~ (all_52_27 = e3)
% 202.90/34.09    (20)  op(e3, e3) = all_52_8
% 202.90/34.09    (21)  op(e3, e1) = all_52_17
% 202.90/34.09    (22)   ~ (all_52_19 = all_10_2)
% 202.90/34.09    (23)  all_58_8 = all_10_2
% 202.90/34.09    (24)  op(e3, all_6_1) = e2
% 202.90/34.09    (25)  op(e3, e3) = all_6_2
% 202.90/34.09    (26)  op(e3, e0) = all_14_1
% 202.90/34.09    (27)  all_58_5 = all_52_19
% 202.90/34.09    (28)   ~ (all_52_17 = all_6_2)
% 202.90/34.09    (29)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.09    (30)   ~ (all_52_17 = all_52_19)
% 202.90/34.09    (31)  all_58_3 = all_4_2
% 202.90/34.09    (32)  op(all_6_2, e3) = all_6_1
% 202.90/34.09    (33)  all_58_4 = all_52_17
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | BETA: splitting (7) gives:
% 202.90/34.09  | 
% 202.90/34.09  | Case 1:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (34)  all_58_3 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | COMBINE_EQS: (31), (34) imply:
% 202.90/34.09  | |   (35)  all_4_2 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | REDUCE: (5), (35) imply:
% 202.90/34.09  | |   (36)  $false
% 202.90/34.09  | | 
% 202.90/34.09  | | CLOSE: (36) is inconsistent.
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (37)  all_58_5 = e3 | all_58_10 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | BETA: splitting (37) gives:
% 202.90/34.09  | | 
% 202.90/34.09  | | Case 1:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (38)  all_58_5 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | COMBINE_EQS: (27), (38) imply:
% 202.90/34.09  | | |   (39)  all_52_19 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (39) implies:
% 202.90/34.09  | | |   (40)  all_52_19 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (30), (40) imply:
% 202.90/34.09  | | |   (41)   ~ (all_52_17 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (12), (40) imply:
% 202.90/34.09  | | |   (42)   ~ (all_52_23 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (42) implies:
% 202.90/34.09  | | |   (43)   ~ (all_52_23 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (22), (40) imply:
% 202.90/34.09  | | |   (44)   ~ (all_10_2 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (44) implies:
% 202.90/34.09  | | |   (45)   ~ (all_10_2 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (13), (14), (15),
% 202.90/34.09  | | |            (16), (17), (18), (20), (21), (23), (24), (25), (26), (27),
% 202.90/34.09  | | |            (28), (29), (32), (33), (41), (43), (45) are inconsistent by
% 202.90/34.09  | | |            sub-proof #448.
% 202.90/34.09  | | | 
% 202.90/34.09  | | Case 2:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (46)  all_58_10 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REF_CLOSE: (11), (19), (46) are inconsistent by sub-proof #1301.
% 202.90/34.09  | | | 
% 202.90/34.09  | | End of split
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #448 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)  all_58_14 = all_52_23
% 202.90/34.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (3)  op(e2, e3) = all_52_3
% 202.90/34.09    (4)   ~ (all_52_3 = all_52_19)
% 202.90/34.09    (5)   ~ (all_52_3 = all_6_2)
% 202.90/34.09    (6)  all_58_0 = all_6_2
% 202.90/34.09    (7)  all_56_4 = all_52_3
% 202.90/34.09    (8)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.09    (9)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.09    (10)  op(all_52_19, all_52_19) = e2
% 202.90/34.09    (11)  all_58_2 = all_52_3
% 202.90/34.09    (12)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.09    (13)   ~ (e2 = e0)
% 202.90/34.09    (14)   ~ (all_14_1 = all_6_2)
% 202.90/34.09    (15)   ~ (all_52_23 = e3)
% 202.90/34.09    (16)   ~ (all_10_2 = e3)
% 202.90/34.09    (17)  op(e3, e3) = all_52_8
% 202.90/34.09    (18)  op(e3, e1) = all_52_17
% 202.90/34.09    (19)  all_58_8 = all_10_2
% 202.90/34.09    (20)  op(e3, all_6_1) = e2
% 202.90/34.09    (21)  op(e3, e3) = all_6_2
% 202.90/34.09    (22)  op(e3, e0) = all_14_1
% 202.90/34.09    (23)   ~ (all_52_17 = e3)
% 202.90/34.09    (24)  all_58_5 = all_52_19
% 202.90/34.09    (25)   ~ (all_52_17 = all_6_2)
% 202.90/34.09    (26)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.09    (27)  op(all_6_2, e3) = all_6_1
% 202.90/34.09    (28)  all_58_4 = all_52_17
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | BETA: splitting (26) gives:
% 202.90/34.09  | 
% 202.90/34.09  | Case 1:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (29)  all_58_4 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | REF_CLOSE: (23), (28), (29) are inconsistent by sub-proof #1302.
% 202.90/34.09  | | 
% 202.90/34.09  | Case 2:
% 202.90/34.09  | | 
% 202.90/34.09  | |   (30)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.09  | | 
% 202.90/34.09  | | BETA: splitting (30) gives:
% 202.90/34.09  | | 
% 202.90/34.09  | | Case 1:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (31)  all_58_5 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | COMBINE_EQS: (24), (31) imply:
% 202.90/34.09  | | |   (32)  all_52_19 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (32) implies:
% 202.90/34.09  | | |   (33)  all_52_19 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (4), (33) imply:
% 202.90/34.09  | | |   (34)   ~ (all_52_3 = e3)
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REDUCE: (10), (33) imply:
% 202.90/34.09  | | |   (35)  op(e3, e3) = e2
% 202.90/34.09  | | | 
% 202.90/34.09  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_8, e3, e3, simplifying
% 202.90/34.09  | | |              with (17), (21) gives:
% 202.90/34.09  | | |   (36)  all_52_8 = all_6_2
% 202.90/34.09  | | | 
% 202.90/34.09  | | | GROUND_INST: instantiating (2) with e2, all_52_8, e3, e3, simplifying with
% 202.90/34.09  | | |              (17), (35) gives:
% 202.90/34.09  | | |   (37)  all_52_8 = e2
% 202.90/34.09  | | | 
% 202.90/34.09  | | | COMBINE_EQS: (36), (37) imply:
% 202.90/34.09  | | |   (38)  all_6_2 = e2
% 202.90/34.09  | | | 
% 202.90/34.09  | | | SIMP: (38) implies:
% 202.90/34.09  | | |   (39)  all_6_2 = e2
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 202.90/34.09  | | |            (18), (20), (22), (25), (27), (34), (39) are inconsistent by
% 202.90/34.09  | | |            sub-proof #449.
% 202.90/34.09  | | | 
% 202.90/34.09  | | Case 2:
% 202.90/34.09  | | | 
% 202.90/34.09  | | |   (40)  all_58_8 = e3 | all_58_14 = e3
% 202.90/34.09  | | | 
% 202.90/34.09  | | | REF_CLOSE: (1), (15), (16), (19), (40) are inconsistent by sub-proof
% 202.90/34.09  | | |            #1304.
% 202.90/34.09  | | | 
% 202.90/34.09  | | End of split
% 202.90/34.09  | | 
% 202.90/34.09  | End of split
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #449 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (2)  op(e2, e3) = all_52_3
% 202.90/34.09    (3)   ~ (all_52_3 = all_6_2)
% 202.90/34.09    (4)  all_58_0 = all_6_2
% 202.90/34.09    (5)  all_56_4 = all_52_3
% 202.90/34.09    (6)  all_6_2 = e2
% 202.90/34.09    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.09    (8)   ~ (all_52_3 = e3)
% 202.90/34.09    (9)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.09    (10)  all_58_2 = all_52_3
% 202.90/34.09    (11)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.09    (12)   ~ (e2 = e0)
% 202.90/34.09    (13)   ~ (all_14_1 = all_6_2)
% 202.90/34.09    (14)  op(e3, e1) = all_52_17
% 202.90/34.09    (15)  op(e3, all_6_1) = e2
% 202.90/34.09    (16)  op(e3, e0) = all_14_1
% 202.90/34.09    (17)   ~ (all_52_17 = all_6_2)
% 202.90/34.09    (18)  op(all_6_2, e3) = all_6_1
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | COMBINE_EQS: (4), (6) imply:
% 202.90/34.09  |   (19)  all_58_0 = e2
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (3), (6) imply:
% 202.90/34.09  |   (20)   ~ (all_52_3 = e2)
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (6), (17) imply:
% 202.90/34.09  |   (21)   ~ (all_52_17 = e2)
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (6), (13) imply:
% 202.90/34.09  |   (22)   ~ (all_14_1 = e2)
% 202.90/34.09  | 
% 202.90/34.09  | REDUCE: (6), (18) imply:
% 202.90/34.09  |   (23)  op(e2, e3) = all_6_1
% 202.90/34.09  | 
% 202.90/34.09  | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 202.90/34.09  |            (19), (20), (21), (22), (23) are inconsistent by sub-proof #450.
% 202.90/34.09  | 
% 202.90/34.09  End of proof
% 202.90/34.09  
% 202.90/34.09  Sub-proof #450 shows that the following formulas are inconsistent:
% 202.90/34.09  ----------------------------------------------------------------
% 202.90/34.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.09    (2)  op(e2, e3) = all_52_3
% 202.90/34.09    (3)   ~ (all_14_1 = e2)
% 202.90/34.09    (4)  all_56_4 = all_52_3
% 202.90/34.09    (5)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.09    (6)   ~ (all_52_3 = e3)
% 202.90/34.09    (7)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.09    (8)  all_58_2 = all_52_3
% 202.90/34.09    (9)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.09    (10)   ~ (e2 = e0)
% 202.90/34.09    (11)  op(e2, e3) = all_6_1
% 202.90/34.09    (12)  op(e3, e1) = all_52_17
% 202.90/34.09    (13)  all_58_0 = e2
% 202.90/34.09    (14)  op(e3, all_6_1) = e2
% 202.90/34.09    (15)  op(e3, e0) = all_14_1
% 202.90/34.09    (16)   ~ (all_52_17 = e2)
% 202.90/34.09    (17)   ~ (all_52_3 = e2)
% 202.90/34.09  
% 202.90/34.09  Begin of proof
% 202.90/34.09  | 
% 202.90/34.09  | GROUND_INST: instantiating (1) with all_52_3, all_6_1, e3, e2, simplifying
% 202.90/34.09  |              with (2), (11) gives:
% 202.90/34.10  |   (18)  all_52_3 = all_6_1
% 202.90/34.10  | 
% 202.90/34.10  | COMBINE_EQS: (4), (18) imply:
% 202.90/34.10  |   (19)  all_56_4 = all_6_1
% 202.90/34.10  | 
% 202.90/34.10  | COMBINE_EQS: (8), (18) imply:
% 202.90/34.10  |   (20)  all_58_2 = all_6_1
% 202.90/34.10  | 
% 202.90/34.10  | REDUCE: (6), (18) imply:
% 202.90/34.10  |   (21)   ~ (all_6_1 = e3)
% 202.90/34.10  | 
% 202.90/34.10  | REDUCE: (17), (18) imply:
% 202.90/34.10  |   (22)   ~ (all_6_1 = e2)
% 202.90/34.10  | 
% 202.90/34.10  | BETA: splitting (9) gives:
% 202.90/34.10  | 
% 202.90/34.10  | Case 1:
% 202.90/34.10  | | 
% 202.90/34.10  | |   (23)  all_56_4 = e3
% 202.90/34.10  | | 
% 202.90/34.10  | | COMBINE_EQS: (19), (23) imply:
% 202.90/34.10  | |   (24)  all_6_1 = e3
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (21), (24) imply:
% 202.90/34.10  | |   (25)  $false
% 202.90/34.10  | | 
% 202.90/34.10  | | CLOSE: (25) is inconsistent.
% 202.90/34.10  | | 
% 202.90/34.10  | Case 2:
% 202.90/34.10  | | 
% 202.90/34.10  | |   (26)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.10  | | 
% 202.90/34.10  | | BETA: splitting (5) gives:
% 202.90/34.10  | | 
% 202.90/34.10  | | Case 1:
% 202.90/34.10  | | | 
% 202.90/34.10  | | |   (27)  all_58_0 = e0
% 202.90/34.10  | | | 
% 202.90/34.10  | | | COMBINE_EQS: (13), (27) imply:
% 202.90/34.10  | | |   (28)  e2 = e0
% 202.90/34.10  | | | 
% 202.90/34.10  | | | REDUCE: (10), (28) imply:
% 202.90/34.10  | | |   (29)  $false
% 202.90/34.10  | | | 
% 202.90/34.10  | | | CLOSE: (29) is inconsistent.
% 202.90/34.10  | | | 
% 202.90/34.10  | | Case 2:
% 202.90/34.10  | | | 
% 202.90/34.10  | | |   (30)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.10  | | | 
% 202.90/34.10  | | | BETA: splitting (7) gives:
% 202.90/34.10  | | | 
% 202.90/34.10  | | | Case 1:
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | |   (31)  all_58_2 = e1
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | | REF_CLOSE: (1), (12), (14), (16), (20), (31) are inconsistent by
% 202.90/34.10  | | | |            sub-proof #498.
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | Case 2:
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | |   (32)   ~ (all_58_2 = e1)
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | | REDUCE: (20), (32) imply:
% 202.90/34.10  | | | |   (33)   ~ (all_6_1 = e1)
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | | REF_CLOSE: (1), (3), (14), (15), (19), (20), (22), (26), (30), (33) are
% 202.90/34.10  | | | |            inconsistent by sub-proof #466.
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | End of split
% 202.90/34.10  | | | 
% 202.90/34.10  | | End of split
% 202.90/34.10  | | 
% 202.90/34.10  | End of split
% 202.90/34.10  | 
% 202.90/34.10  End of proof
% 202.90/34.10  
% 202.90/34.10  Sub-proof #451 shows that the following formulas are inconsistent:
% 202.90/34.10  ----------------------------------------------------------------
% 202.90/34.10    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.90/34.10    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.90/34.10    (3)   ~ (all_52_15 = all_52_23)
% 202.90/34.10    (4)   ~ (all_52_25 = all_52_27)
% 202.90/34.10    (5)  all_58_14 = all_52_23
% 202.90/34.10    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.90/34.10    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.10    (8)   ~ (all_52_5 = all_52_13)
% 202.90/34.10    (9)  all_58_1 = all_52_9
% 202.90/34.10    (10)   ~ (all_52_9 = all_52_13)
% 202.90/34.10    (11)   ~ (e3 = e0)
% 202.90/34.10    (12)  op(e2, e3) = all_52_3
% 202.90/34.10    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.10    (14)   ~ (all_52_7 = all_52_15)
% 202.90/34.10    (15)   ~ (all_52_3 = all_52_19)
% 202.90/34.10    (16)  op(all_52_15, all_52_15) = e0
% 202.90/34.10    (17)  op(all_52_7, all_52_7) = all_52_6
% 202.90/34.10    (18)   ~ (all_52_17 = all_52_25)
% 202.90/34.10    (19)   ~ (all_52_3 = all_6_2)
% 202.90/34.10    (20)  all_44_2 = all_6_2
% 202.90/34.10    (21)  all_58_0 = all_6_2
% 202.90/34.10    (22)  op(all_14_2, e0) = all_14_1
% 202.90/34.10    (23)  all_56_4 = all_52_3
% 202.90/34.10    (24)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.10    (25)  op(e3, e0) = all_52_25
% 202.90/34.10    (26)  op(e0, all_14_1) = all_14_0
% 202.90/34.10    (27)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.10    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.90/34.10    (29)  op(all_52_19, all_52_19) = all_52_18
% 202.90/34.10    (30)  all_58_13 = all_52_15
% 202.90/34.10    (31)  op(all_52_13, all_52_13) = e1
% 202.90/34.10    (32)  op(all_10_2, all_10_2) = all_52_20
% 202.90/34.10    (33)  all_58_9 = all_52_25
% 202.90/34.10    (34)   ~ (all_52_29 = all_14_2)
% 202.90/34.10    (35)  op(all_52_27, all_52_27) = all_52_26
% 202.90/34.10    (36)  op(e1, e3) = all_52_5
% 202.90/34.10    (37)  op(e2, e2) = all_4_2
% 202.90/34.10    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.10    (39)   ~ (all_52_3 = all_52_5)
% 202.90/34.10    (40)  all_58_11 = all_52_29
% 202.90/34.10    (41)   ~ (all_52_25 = all_14_2)
% 202.90/34.10    (42)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.90/34.10    (43)   ~ (all_52_3 = all_52_27)
% 202.90/34.10    (44)   ~ (all_52_7 = all_6_2)
% 202.90/34.10    (45)  op(e0, e0) = all_14_2
% 202.90/34.10    (46)  op(e0, e1) = all_52_23
% 202.90/34.10    (47)  all_56_15 = all_14_2
% 202.90/34.10    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.10    (49)   ~ (all_4_1 = e1)
% 202.90/34.10    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.90/34.10    (51)  all_56_9 = all_52_13
% 202.90/34.10    (52)   ~ (all_52_13 = all_10_2)
% 202.90/34.10    (53)  all_58_10 = all_52_27
% 202.90/34.10    (54)  all_56_8 = all_52_5
% 202.90/34.10    (55)   ~ (all_52_19 = all_52_23)
% 202.90/34.10    (56)   ~ (all_52_25 = all_52_29)
% 202.90/34.10    (57)   ~ (all_52_29 = all_10_2)
% 202.90/34.10    (58)  all_58_7 = all_52_13
% 202.90/34.10    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.90/34.10    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.10    (61)   ~ (all_52_5 = all_52_7)
% 202.90/34.10    (62)  all_58_12 = all_52_7
% 202.90/34.10    (63)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.10    (64)   ~ (all_52_7 = all_14_2)
% 202.90/34.10    (65)  all_58_2 = all_52_3
% 202.90/34.10    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.10    (67)  all_56_7 = all_52_27
% 202.90/34.10    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.10    (69)   ~ (e2 = e0)
% 202.90/34.10    (70)  op(all_4_2, e2) = all_4_1
% 202.90/34.10    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 202.90/34.10    (72)   ~ (all_52_15 = all_14_2)
% 202.90/34.10    (73)   ~ (all_52_13 = all_4_2)
% 202.90/34.10    (74)  op(e3, e1) = all_52_17
% 202.90/34.10    (75)  op(e0, e3) = all_52_7
% 202.90/34.10    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.10    (77)   ~ (all_52_9 = all_52_25)
% 202.90/34.10    (78)  all_58_15 = all_14_2
% 202.90/34.10    (79)   ~ (all_52_19 = all_10_2)
% 202.90/34.10    (80)  op(all_52_23, all_52_23) = all_52_22
% 202.90/34.10    (81)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.10    (82)  all_58_8 = all_10_2
% 202.90/34.10    (83)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.90/34.10    (84)   ~ (all_52_5 = all_10_2)
% 202.90/34.10    (85)  op(all_52_29, all_52_29) = all_52_28
% 202.90/34.10    (86)   ~ (all_52_23 = all_14_2)
% 202.90/34.10    (87)  all_56_12 = all_52_7
% 202.90/34.10    (88)  op(all_52_17, all_52_17) = all_52_16
% 202.90/34.10    (89)  all_8_2 = all_6_2
% 202.90/34.10    (90)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.90/34.10    (91)   ~ (all_52_25 = all_6_2)
% 202.90/34.10    (92)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.90/34.10    (93)   ~ (all_52_9 = all_4_2)
% 202.90/34.10    (94)   ~ (all_52_5 = all_6_2)
% 202.90/34.10    (95)  op(all_4_2, all_4_2) = e2
% 202.90/34.10    (96)   ~ (all_52_9 = all_6_2)
% 202.90/34.10    (97)   ~ (all_52_13 = all_52_15)
% 202.90/34.10    (98)  op(e3, all_6_1) = e2
% 202.90/34.10    (99)  all_56_0 = all_6_2
% 202.90/34.10    (100)  op(e3, e3) = all_6_2
% 202.90/34.10    (101)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.10    (102)   ~ (all_52_27 = all_14_2)
% 202.90/34.10    (103)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.10    (104)  all_56_14 = all_52_23
% 202.90/34.10    (105)  all_56_3 = all_52_25
% 202.90/34.10    (106)   ~ (all_52_3 = all_52_7)
% 202.90/34.10    (107)  op(all_14_2, all_14_2) = all_52_30
% 202.90/34.10    (108)  all_58_5 = all_52_19
% 202.90/34.10    (109)  all_56_1 = all_52_9
% 202.90/34.10    (110)   ~ (all_52_15 = all_4_2)
% 202.90/34.10    (111)   ~ (all_52_27 = all_4_2)
% 202.90/34.10    (112)  all_58_6 = all_52_5
% 202.90/34.10    (113)  op(e3, e2) = all_52_9
% 202.90/34.10    (114)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.90/34.10    (115)   ~ (all_52_17 = all_6_2)
% 202.90/34.10    (116)   ~ (e1 = e0)
% 202.90/34.10    (117)   ~ (e3 = e2)
% 202.90/34.10    (118)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.90/34.10    (119)  all_44_1 = all_6_1
% 202.90/34.10    (120)   ~ (all_52_9 = all_52_17)
% 202.90/34.10    (121)  all_56_10 = all_10_2
% 202.90/34.10    (122)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.10    (123)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.90/34.10    (124)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.90/34.10    (125)  op(e1, e1) = all_10_2
% 202.90/34.10    (126)  op(all_52_9, all_52_9) = e3
% 202.90/34.10    (127)   ~ (all_52_23 = all_10_2)
% 202.90/34.10    (128)   ~ (all_52_7 = all_52_23)
% 202.90/34.10    (129)   ~ (all_52_17 = all_52_19)
% 202.90/34.10    (130)  all_58_3 = all_4_2
% 202.90/34.10    (131)  all_56_13 = all_52_15
% 202.90/34.10    (132)   ~ (all_52_3 = all_4_2)
% 202.90/34.10    (133)   ~ (all_52_19 = all_4_2)
% 202.90/34.10    (134)   ~ (all_52_17 = all_52_23)
% 202.90/34.10    (135)  all_8_1 = all_6_1
% 202.90/34.10    (136)  op(all_6_2, e3) = all_6_1
% 202.90/34.10    (137)   ~ (all_52_13 = all_52_29)
% 202.90/34.10    (138)  all_58_4 = all_52_17
% 202.90/34.10    (139)   ~ (all_14_0 = e2)
% 202.90/34.10    (140)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.90/34.10    (141)  op(all_52_25, all_52_25) = all_52_24
% 202.90/34.10  
% 202.90/34.10  Begin of proof
% 202.90/34.10  | 
% 202.90/34.10  | BETA: splitting (83) gives:
% 202.90/34.10  | 
% 202.90/34.10  | Case 1:
% 202.90/34.10  | | 
% 202.90/34.10  | |   (142)  all_56_15 = e3
% 202.90/34.10  | | 
% 202.90/34.10  | | COMBINE_EQS: (47), (142) imply:
% 202.90/34.10  | |   (143)  all_14_2 = e3
% 202.90/34.10  | | 
% 202.90/34.10  | | SIMP: (143) implies:
% 202.90/34.10  | |   (144)  all_14_2 = e3
% 202.90/34.10  | | 
% 202.90/34.10  | | COMBINE_EQS: (78), (144) imply:
% 202.90/34.10  | |   (145)  all_58_15 = e3
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (64), (144) imply:
% 202.90/34.10  | |   (146)   ~ (all_52_7 = e3)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (72), (144) imply:
% 202.90/34.10  | |   (147)   ~ (all_52_15 = e3)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (86), (144) imply:
% 202.90/34.10  | |   (148)   ~ (all_52_23 = e3)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (41), (144) imply:
% 202.90/34.10  | |   (149)   ~ (all_52_25 = e3)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (102), (144) imply:
% 202.90/34.10  | |   (150)   ~ (all_52_27 = e3)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (107), (144) imply:
% 202.90/34.10  | |   (151)  op(e3, e3) = all_52_30
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (22), (144) imply:
% 202.90/34.10  | |   (152)  op(e3, e0) = all_14_1
% 202.90/34.10  | | 
% 202.90/34.10  | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3, simplifying
% 202.90/34.10  | |              with (25), (152) gives:
% 202.90/34.10  | |   (153)  all_52_25 = all_14_1
% 202.90/34.10  | | 
% 202.90/34.10  | | GROUND_INST: instantiating (7) with all_6_2, all_52_30, e3, e3, simplifying
% 202.90/34.10  | |              with (100), (151) gives:
% 202.90/34.10  | |   (154)  all_52_30 = all_6_2
% 202.90/34.10  | | 
% 202.90/34.10  | | COMBINE_EQS: (105), (153) imply:
% 202.90/34.10  | |   (155)  all_56_3 = all_14_1
% 202.90/34.10  | | 
% 202.90/34.10  | | COMBINE_EQS: (33), (153) imply:
% 202.90/34.10  | |   (156)  all_58_9 = all_14_1
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (77), (153) imply:
% 202.90/34.10  | |   (157)   ~ (all_52_9 = all_14_1)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (18), (153) imply:
% 202.90/34.10  | |   (158)   ~ (all_52_17 = all_14_1)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (91), (153) imply:
% 202.90/34.10  | |   (159)   ~ (all_14_1 = all_6_2)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (149), (153) imply:
% 202.90/34.10  | |   (160)   ~ (all_14_1 = e3)
% 202.90/34.10  | | 
% 202.90/34.10  | | REDUCE: (141), (153) imply:
% 202.90/34.10  | |   (161)  op(all_14_1, all_14_1) = all_52_24
% 202.90/34.10  | | 
% 202.90/34.10  | | BETA: splitting (92) gives:
% 202.90/34.10  | | 
% 202.90/34.10  | | Case 1:
% 202.90/34.10  | | | 
% 202.90/34.10  | | |   (162)  all_56_3 = e3
% 202.90/34.10  | | | 
% 202.90/34.10  | | | REF_CLOSE: (155), (160), (162) are inconsistent by sub-proof #1200.
% 202.90/34.10  | | | 
% 202.90/34.10  | | Case 2:
% 202.90/34.10  | | | 
% 202.90/34.10  | | |   (163)   ~ (all_56_3 = e3)
% 202.90/34.10  | | |   (164)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.90/34.10  | | | 
% 202.90/34.10  | | | BETA: splitting (13) gives:
% 202.90/34.10  | | | 
% 202.90/34.10  | | | Case 1:
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | |   (165)  all_56_12 = e3
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | | REF_CLOSE: (87), (146), (165) are inconsistent by sub-proof #1383.
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | Case 2:
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | |   (166)   ~ (all_56_12 = e3)
% 202.90/34.10  | | | |   (167)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | | BETA: splitting (59) gives:
% 202.90/34.10  | | | | 
% 202.90/34.10  | | | | Case 1:
% 202.90/34.10  | | | | | 
% 202.90/34.10  | | | | |   (168)  all_56_14 = e3
% 202.90/34.10  | | | | | 
% 202.90/34.10  | | | | | REF_CLOSE: (104), (148), (168) are inconsistent by sub-proof #1286.
% 202.90/34.10  | | | | | 
% 202.90/34.10  | | | | Case 2:
% 202.90/34.10  | | | | | 
% 202.90/34.10  | | | | |   (169)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 202.90/34.10  | | | | | 
% 202.90/34.10  | | | | | BETA: splitting (118) gives:
% 202.90/34.10  | | | | | 
% 202.90/34.10  | | | | | Case 1:
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | |   (170)  all_56_1 = e3
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | | COMBINE_EQS: (109), (170) imply:
% 202.90/34.10  | | | | | |   (171)  all_52_9 = e3
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | | SIMP: (171) implies:
% 202.90/34.10  | | | | | |   (172)  all_52_9 = e3
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | | REF_CLOSE: (7), (96), (100), (126), (172) are inconsistent by
% 202.90/34.10  | | | | | |            sub-proof #1337.
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | Case 2:
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | |   (173)   ~ (all_56_1 = e3)
% 202.90/34.10  | | | | | |   (174)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | | REDUCE: (109), (173) imply:
% 202.90/34.10  | | | | | |   (175)   ~ (all_52_9 = e3)
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | | BETA: splitting (103) gives:
% 202.90/34.10  | | | | | | 
% 202.90/34.10  | | | | | | Case 1:
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | |   (176)  all_58_0 = e3
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | | COMBINE_EQS: (21), (176) imply:
% 202.90/34.10  | | | | | | |   (177)  all_6_2 = e3
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | | REF_CLOSE: (7), (98), (100), (117), (136), (177) are inconsistent
% 202.90/34.10  | | | | | | |            by sub-proof #502.
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | Case 2:
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | |   (178)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | | BETA: splitting (178) gives:
% 202.90/34.10  | | | | | | | 
% 202.90/34.10  | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | |   (179)  all_58_1 = e3
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | | COMBINE_EQS: (9), (179) imply:
% 202.90/34.10  | | | | | | | |   (180)  all_52_9 = e3
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | | REDUCE: (175), (180) imply:
% 202.90/34.10  | | | | | | | |   (181)  $false
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | | CLOSE: (181) is inconsistent.
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | |   (182)  all_58_4 = e3 | all_58_9 = e3
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | | BETA: splitting (182) gives:
% 202.90/34.10  | | | | | | | | 
% 202.90/34.10  | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | |   (183)  all_58_4 = e3
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | COMBINE_EQS: (138), (183) imply:
% 202.90/34.10  | | | | | | | | |   (184)  all_52_17 = e3
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | SIMP: (184) implies:
% 202.90/34.10  | | | | | | | | |   (185)  all_52_17 = e3
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | REDUCE: (129), (185) imply:
% 202.90/34.10  | | | | | | | | |   (186)   ~ (all_52_19 = e3)
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | SIMP: (186) implies:
% 202.90/34.10  | | | | | | | | |   (187)   ~ (all_52_19 = e3)
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | REDUCE: (158), (185) imply:
% 202.90/34.10  | | | | | | | | |   (188)   ~ (all_14_1 = e3)
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | REDUCE: (115), (185) imply:
% 202.90/34.10  | | | | | | | | |   (189)   ~ (all_6_2 = e3)
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | SIMP: (189) implies:
% 202.90/34.10  | | | | | | | | |   (190)   ~ (all_6_2 = e3)
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | REDUCE: (88), (185) imply:
% 202.90/34.10  | | | | | | | | |   (191)  op(e3, e3) = all_52_16
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_16, e3, e3,
% 202.90/34.10  | | | | | | | | |              simplifying with (100), (191) gives:
% 202.90/34.10  | | | | | | | | |   (192)  all_52_16 = all_6_2
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | BETA: splitting (76) gives:
% 202.90/34.10  | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | |   (193)  all_58_1 = e3
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | COMBINE_EQS: (9), (193) imply:
% 202.90/34.10  | | | | | | | | | |   (194)  all_52_9 = e3
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | REDUCE: (175), (194) imply:
% 202.90/34.10  | | | | | | | | | |   (195)  $false
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | CLOSE: (195) is inconsistent.
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | |   (196)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | BETA: splitting (63) gives:
% 202.90/34.10  | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | |   (197)  all_58_6 = e3
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | COMBINE_EQS: (112), (197) imply:
% 202.90/34.10  | | | | | | | | | | |   (198)  all_52_5 = e3
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | SIMP: (198) implies:
% 202.90/34.10  | | | | | | | | | | |   (199)  all_52_5 = e3
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | REDUCE: (39), (199) imply:
% 202.90/34.10  | | | | | | | | | | |   (200)   ~ (all_52_3 = e3)
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | REDUCE: (27), (199) imply:
% 202.90/34.10  | | | | | | | | | | |   (201)  op(e3, e3) = all_52_4
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | BETA: splitting (48) gives:
% 202.90/34.10  | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | |   (202)  all_58_2 = e3
% 202.90/34.10  | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | REF_CLOSE: (65), (200), (202) are inconsistent by sub-proof
% 202.90/34.10  | | | | | | | | | | | |            #1369.
% 202.90/34.10  | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | |   (203)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.10  | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | BETA: splitting (203) gives:
% 202.90/34.10  | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | |   (204)  all_58_3 = e3
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | COMBINE_EQS: (130), (204) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (205)  all_4_2 = e3
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (73), (205) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (206)   ~ (all_52_13 = e3)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (95), (205) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (207)  op(e3, e3) = e2
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (70), (205) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (208)  op(e3, e2) = all_4_1
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_9, all_4_1, e2, e3,
% 202.90/34.10  | | | | | | | | | | | | |              simplifying with (113), (208) gives:
% 202.90/34.10  | | | | | | | | | | | | |   (209)  all_52_9 = all_4_1
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_4, e3, e3,
% 202.90/34.10  | | | | | | | | | | | | |              simplifying with (100), (201) gives:
% 202.90/34.10  | | | | | | | | | | | | |   (210)  all_52_4 = all_6_2
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_4, e3, e3,
% 202.90/34.10  | | | | | | | | | | | | |              simplifying with (201), (207) gives:
% 202.90/34.10  | | | | | | | | | | | | |   (211)  all_52_4 = e2
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | COMBINE_EQS: (210), (211) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (212)  all_6_2 = e2
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | SIMP: (212) implies:
% 202.90/34.10  | | | | | | | | | | | | |   (213)  all_6_2 = e2
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | COMBINE_EQS: (109), (209) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (214)  all_56_1 = all_4_1
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | COMBINE_EQS: (21), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (215)  all_58_0 = e2
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (19), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (216)   ~ (all_52_3 = e2)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (44), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (217)   ~ (all_52_7 = e2)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (10), (209) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (218)   ~ (all_52_13 = all_4_1)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | SIMP: (218) implies:
% 202.90/34.10  | | | | | | | | | | | | |   (219)   ~ (all_52_13 = all_4_1)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (157), (209) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (220)   ~ (all_14_1 = all_4_1)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | SIMP: (220) implies:
% 202.90/34.10  | | | | | | | | | | | | |   (221)   ~ (all_14_1 = all_4_1)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (96), (209), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (222)   ~ (all_4_1 = e2)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (159), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (223)   ~ (all_14_1 = e2)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (190), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (224)   ~ (e3 = e2)
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | REDUCE: (136), (213) imply:
% 202.90/34.10  | | | | | | | | | | | | |   (225)  op(e2, e3) = all_6_1
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | BETA: splitting (174) gives:
% 202.90/34.10  | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | |   (226)  all_56_1 = e2
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | COMBINE_EQS: (214), (226) imply:
% 202.90/34.10  | | | | | | | | | | | | | |   (227)  all_4_1 = e2
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | REDUCE: (222), (227) imply:
% 202.90/34.10  | | | | | | | | | | | | | |   (228)  $false
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | |   (229)  all_56_1 = e1 | all_56_1 = e0
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | |   (230)  all_56_1 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | COMBINE_EQS: (214), (230) imply:
% 202.90/34.10  | | | | | | | | | | | | | | |   (231)  all_4_1 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | REDUCE: (49), (231) imply:
% 202.90/34.10  | | | | | | | | | | | | | | |   (232)  $false
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | |   (233)  all_56_1 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | COMBINE_EQS: (214), (233) imply:
% 202.90/34.10  | | | | | | | | | | | | | | |   (234)  all_4_1 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | REDUCE: (219), (234) imply:
% 202.90/34.10  | | | | | | | | | | | | | | |   (235)   ~ (all_52_13 = e0)
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | REDUCE: (221), (234) imply:
% 202.90/34.10  | | | | | | | | | | | | | | |   (236)   ~ (all_14_1 = e0)
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | |   (237)  all_56_3 = e2
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (237) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | |   (238)  all_14_1 = e2
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | REDUCE: (223), (238) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | |   (239)  $false
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | |   (240)   ~ (all_56_3 = e2)
% 202.90/34.10  | | | | | | | | | | | | | | | |   (241)  all_56_3 = e1 | all_56_3 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (242)  all_56_3 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (242) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (243)  all_14_1 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (160), (243) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (244)   ~ (e3 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (245)   ~ (e3 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (223), (243) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (246)   ~ (e2 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | SIMP: (246) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (247)   ~ (e2 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (161), (243) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (248)  op(e1, e1) = all_52_24
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (26), (243) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (249)  op(e0, e1) = all_14_0
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_23, all_14_0, e1,
% 202.90/34.10  | | | | | | | | | | | | | | | | |              e0, simplifying with (46), (249) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (250)  all_52_23 = all_14_0
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_24, e1,
% 202.90/34.10  | | | | | | | | | | | | | | | | |              e1, simplifying with (125), (248) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (251)  all_52_24 = all_10_2
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_3, all_6_1, e3, e2,
% 202.90/34.10  | | | | | | | | | | | | | | | | |              simplifying with (12), (225) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (252)  all_52_3 = all_6_1
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (250) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (253)  all_56_14 = all_14_0
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (252) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (254)  all_56_4 = all_6_1
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (250) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (255)  all_58_14 = all_14_0
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (252) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (256)  all_58_2 = all_6_1
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (106), (252) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (257)   ~ (all_52_7 = all_6_1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | SIMP: (257) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (258)   ~ (all_52_7 = all_6_1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (200), (252) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (259)   ~ (all_6_1 = e3)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (216), (252) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (260)   ~ (all_6_1 = e2)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (128), (250) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (261)   ~ (all_52_7 = all_14_0)
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | |   (262)  all_56_14 = e2
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (253), (262) are inconsistent by sub-proof
% 202.90/34.10  | | | | | | | | | | | | | | | | | |            #526.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | |   (263)   ~ (all_56_14 = e2)
% 202.90/34.10  | | | | | | | | | | | | | | | | | |   (264)  all_56_14 = e1 | all_56_14 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | |   (265)  all_58_12 = e2
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (217), (265) are inconsistent by sub-proof
% 202.90/34.10  | | | | | | | | | | | | | | | | | | |            #506.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | |   (266)   ~ (all_58_12 = e2)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | |   (267)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (268)  all_56_14 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (268) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (269)  all_14_0 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | SIMP: (269) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (270)  all_14_0 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (270) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (271)  all_58_14 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (30), (31), (51), (52), (58), (90), (97),
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |            (117), (123), (125), (145), (197), (206), (235),
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |            (245), (247), (267), (271) are inconsistent by
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |            sub-proof #467.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (272)  all_56_14 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (272) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (273)  all_14_0 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | SIMP: (273) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (274)  all_14_0 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | REDUCE: (261), (274) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (275)   ~ (all_52_7 = e0)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (274) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | |   (276)   ~ (e2 = e0)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | |   (277)  all_58_0 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (277) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | |   (278)  e2 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (278) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | |   (279)  $false
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | |   (280)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (281)  all_58_12 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (281) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (282)  all_52_7 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | SIMP: (282) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (283)  all_52_7 = e1
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (283) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (284)   ~ (all_6_1 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (285)   ~ (all_6_1 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_56_4 = e3
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (286) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_6_1 = e3
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (259), (287) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | |   (288)  $false
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (288) is inconsistent.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (98), (152), (223), (254), (256), (260),
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | |            (280), (285), (289) are inconsistent by sub-proof
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | |            #466.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (290)   ~ (all_58_12 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (290) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |   (291)   ~ (all_52_7 = e1)
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (167), (217), (275), (291) are inconsistent
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #465.
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (292)  all_56_3 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (292) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (293)  all_14_1 = e0
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | REDUCE: (236), (293) imply:
% 202.90/34.10  | | | | | | | | | | | | | | | | |   (294)  $false
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 202.90/34.10  | | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | | End of split
% 202.90/34.10  | | | | | | | | | | | | | | 
% 202.90/34.10  | | | | | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | |   (295)  all_58_5 = e3 | all_58_10 = e3
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | REF_CLOSE: (53), (108), (150), (187), (295) are inconsistent
% 202.90/34.11  | | | | | | | | | | | | |            by sub-proof #1132.
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | |   (296)   ~ (all_58_6 = e3)
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | REDUCE: (112), (296) imply:
% 202.90/34.11  | | | | | | | | | | |   (297)   ~ (all_52_5 = e3)
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | BETA: splitting (66) gives:
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | |   (298)  all_58_0 = e3
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | COMBINE_EQS: (21), (298) imply:
% 202.90/34.11  | | | | | | | | | | | |   (299)  all_6_2 = e3
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (190), (299) imply:
% 202.90/34.11  | | | | | | | | | | | |   (300)  $false
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | CLOSE: (300) is inconsistent.
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | |   (301)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | BETA: splitting (301) gives:
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | |   (302)  all_58_2 = e3
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | COMBINE_EQS: (65), (302) imply:
% 202.90/34.11  | | | | | | | | | | | | |   (303)  all_52_3 = e3
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | SIMP: (303) implies:
% 202.90/34.11  | | | | | | | | | | | | |   (304)  all_52_3 = e3
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | REDUCE: (132), (304) imply:
% 202.90/34.11  | | | | | | | | | | | | |   (305)   ~ (all_4_2 = e3)
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | SIMP: (305) implies:
% 202.90/34.11  | | | | | | | | | | | | |   (306)   ~ (all_4_2 = e3)
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | REDUCE: (6), (304) imply:
% 202.90/34.11  | | | | | | | | | | | | |   (307)  op(e3, e3) = all_52_2
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | REF_CLOSE: (7), (8), (20), (24), (27), (30), (31), (36),
% 202.90/34.11  | | | | | | | | | | | | |            (37), (54), (58), (61), (73), (81), (87), (94),
% 202.90/34.11  | | | | | | | | | | | | |            (98), (100), (113), (119), (126), (130), (136),
% 202.90/34.11  | | | | | | | | | | | | |            (147), (167), (196), (306), (307) are inconsistent
% 202.90/34.11  | | | | | | | | | | | | |            by sub-proof #462.
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | |   (308)  all_58_6 = e3 | all_58_12 = e3
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | REF_CLOSE: (62), (112), (146), (297), (308) are inconsistent
% 202.90/34.11  | | | | | | | | | | | | |            by sub-proof #1243.
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | |   (309)  all_58_9 = e3
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | REF_CLOSE: (156), (160), (309) are inconsistent by sub-proof
% 202.90/34.11  | | | | | | | | |            #1131.
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | End of split
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | End of split
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | End of split
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | End of split
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | End of split
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | End of split
% 202.90/34.11  | | | 
% 202.90/34.11  | | End of split
% 202.90/34.11  | | 
% 202.90/34.11  | Case 2:
% 202.90/34.11  | | 
% 202.90/34.11  | |   (310)   ~ (all_56_15 = e3)
% 202.90/34.11  | |   (311)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (47), (310) imply:
% 202.90/34.11  | |   (312)   ~ (all_14_2 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 202.90/34.11  | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 202.90/34.11  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 202.90/34.11  | |            (38), (39), (40), (41), (43), (44), (45), (47), (48), (49), (50),
% 202.90/34.11  | |            (52), (53), (54), (55), (56), (57), (58), (60), (61), (62), (63),
% 202.90/34.11  | |            (64), (65), (66), (67), (68), (69), (70), (73), (74), (75), (76),
% 202.90/34.11  | |            (77), (78), (79), (80), (81), (82), (84), (85), (86), (87), (88),
% 202.90/34.11  | |            (89), (92), (93), (94), (95), (96), (98), (99), (100), (101),
% 202.90/34.11  | |            (103), (105), (106), (108), (109), (110), (111), (112), (113),
% 202.90/34.11  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 202.90/34.11  | |            (124), (126), (127), (128), (130), (131), (132), (133), (134),
% 202.90/34.11  | |            (135), (136), (137), (138), (140), (141), (311), (312) are
% 202.90/34.11  | |            inconsistent by sub-proof #452.
% 202.90/34.11  | | 
% 202.90/34.11  | End of split
% 202.90/34.11  | 
% 202.90/34.11  End of proof
% 202.90/34.11  
% 202.90/34.11  Sub-proof #452 shows that the following formulas are inconsistent:
% 202.90/34.11  ----------------------------------------------------------------
% 202.90/34.11    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.90/34.11    (2)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.90/34.11    (3)   ~ (all_52_15 = all_52_23)
% 202.90/34.11    (4)   ~ (all_52_25 = all_52_27)
% 202.90/34.11    (5)  all_58_14 = all_52_23
% 202.90/34.11    (6)  op(all_52_3, all_52_3) = all_52_2
% 202.90/34.11    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.11    (8)   ~ (all_52_5 = all_52_13)
% 202.90/34.11    (9)  all_58_1 = all_52_9
% 202.90/34.11    (10)   ~ (e3 = e0)
% 202.90/34.11    (11)  op(e2, e3) = all_52_3
% 202.90/34.11    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.11    (13)   ~ (all_52_7 = all_52_15)
% 202.90/34.11    (14)   ~ (all_52_3 = all_52_19)
% 202.90/34.11    (15)  op(all_52_15, all_52_15) = e0
% 202.90/34.11    (16)  op(all_52_7, all_52_7) = all_52_6
% 202.90/34.11    (17)   ~ (all_52_17 = all_52_25)
% 202.90/34.11    (18)   ~ (all_52_3 = all_6_2)
% 202.90/34.11    (19)  all_44_2 = all_6_2
% 202.90/34.11    (20)  all_58_0 = all_6_2
% 202.90/34.11    (21)  all_56_4 = all_52_3
% 202.90/34.11    (22)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.11    (23)  op(e3, e0) = all_52_25
% 202.90/34.11    (24)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.11    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.90/34.11    (26)  op(all_52_19, all_52_19) = all_52_18
% 202.90/34.11    (27)  all_58_13 = all_52_15
% 202.90/34.11    (28)  op(all_52_13, all_52_13) = e1
% 202.90/34.11    (29)  op(all_10_2, all_10_2) = all_52_20
% 202.90/34.11    (30)  all_58_9 = all_52_25
% 202.90/34.11    (31)   ~ (all_52_29 = all_14_2)
% 202.90/34.11    (32)  op(all_52_27, all_52_27) = all_52_26
% 202.90/34.11    (33)  op(e1, e3) = all_52_5
% 202.90/34.11    (34)  op(e2, e2) = all_4_2
% 202.90/34.11    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.11    (36)   ~ (all_52_3 = all_52_5)
% 202.90/34.11    (37)  all_58_11 = all_52_29
% 202.90/34.11    (38)   ~ (all_52_25 = all_14_2)
% 202.90/34.11    (39)   ~ (all_52_3 = all_52_27)
% 202.90/34.11    (40)   ~ (all_52_7 = all_6_2)
% 202.90/34.11    (41)  op(e0, e0) = all_14_2
% 202.90/34.11    (42)  all_56_15 = all_14_2
% 202.90/34.11    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.11    (44)   ~ (all_4_1 = e1)
% 202.90/34.11    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.90/34.11    (46)   ~ (all_52_13 = all_10_2)
% 202.90/34.11    (47)  all_58_10 = all_52_27
% 202.90/34.11    (48)  all_56_8 = all_52_5
% 202.90/34.11    (49)   ~ (all_52_19 = all_52_23)
% 202.90/34.11    (50)   ~ (all_52_25 = all_52_29)
% 202.90/34.11    (51)   ~ (all_52_29 = all_10_2)
% 202.90/34.11    (52)  all_58_7 = all_52_13
% 202.90/34.11    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.11    (54)   ~ (all_52_5 = all_52_7)
% 202.90/34.11    (55)  all_58_12 = all_52_7
% 202.90/34.11    (56)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.11    (57)   ~ (all_52_7 = all_14_2)
% 202.90/34.11    (58)  all_58_2 = all_52_3
% 202.90/34.11    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.11    (60)  all_56_7 = all_52_27
% 202.90/34.11    (61)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.11    (62)   ~ (e2 = e0)
% 202.90/34.11    (63)  op(all_4_2, e2) = all_4_1
% 202.90/34.11    (64)   ~ (all_52_13 = all_4_2)
% 202.90/34.11    (65)  op(e3, e1) = all_52_17
% 202.90/34.11    (66)  op(e0, e3) = all_52_7
% 202.90/34.11    (67)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.11    (68)   ~ (all_52_9 = all_52_25)
% 202.90/34.11    (69)  all_58_15 = all_14_2
% 202.90/34.11    (70)   ~ (all_52_19 = all_10_2)
% 202.90/34.11    (71)  op(all_52_23, all_52_23) = all_52_22
% 202.90/34.11    (72)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.11    (73)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.90/34.11    (74)  all_58_8 = all_10_2
% 202.90/34.11    (75)   ~ (all_52_5 = all_10_2)
% 202.90/34.11    (76)  op(all_52_29, all_52_29) = all_52_28
% 202.90/34.11    (77)   ~ (all_52_23 = all_14_2)
% 202.90/34.11    (78)  all_56_12 = all_52_7
% 202.90/34.11    (79)  op(all_52_17, all_52_17) = all_52_16
% 202.90/34.11    (80)  all_8_2 = all_6_2
% 202.90/34.11    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.90/34.11    (82)   ~ (all_52_9 = all_4_2)
% 202.90/34.11    (83)   ~ (all_52_5 = all_6_2)
% 202.90/34.11    (84)  op(all_4_2, all_4_2) = e2
% 202.90/34.11    (85)   ~ (all_52_9 = all_6_2)
% 202.90/34.11    (86)  op(e3, all_6_1) = e2
% 202.90/34.11    (87)  all_56_0 = all_6_2
% 202.90/34.11    (88)  op(e3, e3) = all_6_2
% 202.90/34.11    (89)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.11    (90)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.11    (91)  all_56_3 = all_52_25
% 202.90/34.11    (92)   ~ (all_52_3 = all_52_7)
% 202.90/34.11    (93)  all_58_5 = all_52_19
% 202.90/34.11    (94)  all_56_1 = all_52_9
% 202.90/34.11    (95)   ~ (all_52_15 = all_4_2)
% 202.90/34.11    (96)   ~ (all_52_27 = all_4_2)
% 202.90/34.11    (97)  all_58_6 = all_52_5
% 202.90/34.11    (98)  op(e3, e2) = all_52_9
% 202.90/34.11    (99)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.90/34.11    (100)   ~ (all_52_17 = all_6_2)
% 202.90/34.11    (101)   ~ (e1 = e0)
% 202.90/34.11    (102)   ~ (e3 = e2)
% 202.90/34.11    (103)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.90/34.11    (104)  all_44_1 = all_6_1
% 202.90/34.11    (105)   ~ (all_52_9 = all_52_17)
% 202.90/34.11    (106)  all_56_10 = all_10_2
% 202.90/34.11    (107)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.11    (108)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.90/34.11    (109)  op(all_52_9, all_52_9) = e3
% 202.90/34.11    (110)   ~ (all_52_23 = all_10_2)
% 202.90/34.11    (111)   ~ (all_52_7 = all_52_23)
% 202.90/34.11    (112)  all_58_3 = all_4_2
% 202.90/34.11    (113)  all_56_13 = all_52_15
% 202.90/34.11    (114)   ~ (all_52_3 = all_4_2)
% 202.90/34.11    (115)   ~ (all_52_19 = all_4_2)
% 202.90/34.11    (116)   ~ (all_52_17 = all_52_23)
% 202.90/34.11    (117)  all_8_1 = all_6_1
% 202.90/34.11    (118)  op(all_6_2, e3) = all_6_1
% 202.90/34.11    (119)   ~ (all_52_13 = all_52_29)
% 202.90/34.11    (120)  all_58_4 = all_52_17
% 202.90/34.11    (121)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.90/34.11    (122)  op(all_52_25, all_52_25) = all_52_24
% 202.90/34.11    (123)   ~ (all_14_2 = e3)
% 202.90/34.11  
% 202.90/34.11  Begin of proof
% 202.90/34.11  | 
% 202.90/34.11  | BETA: splitting (45) gives:
% 202.90/34.11  | 
% 202.90/34.11  | Case 1:
% 202.90/34.11  | | 
% 202.90/34.11  | |   (124)  all_56_13 = e3
% 202.90/34.11  | | 
% 202.90/34.11  | | COMBINE_EQS: (113), (124) imply:
% 202.90/34.11  | |   (125)  all_52_15 = e3
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (13), (125) imply:
% 202.90/34.11  | |   (126)   ~ (all_52_7 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (95), (125) imply:
% 202.90/34.11  | |   (127)   ~ (all_4_2 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | SIMP: (127) implies:
% 202.90/34.11  | |   (128)   ~ (all_4_2 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (15), (125) imply:
% 202.90/34.11  | |   (129)  op(e3, e3) = e0
% 202.90/34.11  | | 
% 202.90/34.11  | | REF_CLOSE: (2), (7), (12), (16), (34), (40), (42), (57), (66), (73), (78),
% 202.90/34.11  | |            (80), (86), (88), (98), (109), (117), (118), (126), (128), (129)
% 202.90/34.11  | |            are inconsistent by sub-proof #461.
% 202.90/34.11  | | 
% 202.90/34.11  | Case 2:
% 202.90/34.11  | | 
% 202.90/34.11  | |   (130)   ~ (all_56_13 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (113), (130) imply:
% 202.90/34.11  | |   (131)   ~ (all_52_15 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 202.90/34.11  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 202.90/34.11  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 202.90/34.11  | |            (37), (38), (39), (40), (41), (43), (44), (46), (47), (48), (49),
% 202.90/34.11  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 202.90/34.11  | |            (61), (62), (63), (64), (65), (67), (68), (69), (70), (71), (72),
% 202.90/34.11  | |            (74), (75), (76), (77), (78), (79), (81), (82), (83), (84), (85),
% 202.90/34.11  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (96), (97),
% 202.90/34.11  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 202.90/34.11  | |            (107), (108), (109), (110), (111), (112), (114), (115), (116),
% 202.90/34.11  | |            (118), (119), (120), (121), (122), (123), (131) are inconsistent
% 202.90/34.11  | |            by sub-proof #453.
% 202.90/34.11  | | 
% 202.90/34.11  | End of split
% 202.90/34.11  | 
% 202.90/34.11  End of proof
% 202.90/34.11  
% 202.90/34.11  Sub-proof #453 shows that the following formulas are inconsistent:
% 202.90/34.11  ----------------------------------------------------------------
% 202.90/34.11    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 202.90/34.11    (2)   ~ (all_52_15 = all_52_23)
% 202.90/34.11    (3)   ~ (all_52_25 = all_52_27)
% 202.90/34.11    (4)  all_58_14 = all_52_23
% 202.90/34.11    (5)  op(all_52_3, all_52_3) = all_52_2
% 202.90/34.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.11    (7)   ~ (all_52_5 = all_52_13)
% 202.90/34.11    (8)  all_58_1 = all_52_9
% 202.90/34.11    (9)   ~ (e3 = e0)
% 202.90/34.11    (10)  op(e2, e3) = all_52_3
% 202.90/34.11    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.11    (12)   ~ (all_52_7 = all_52_15)
% 202.90/34.11    (13)   ~ (all_52_3 = all_52_19)
% 202.90/34.11    (14)  op(all_52_7, all_52_7) = all_52_6
% 202.90/34.11    (15)   ~ (all_52_17 = all_52_25)
% 202.90/34.11    (16)   ~ (all_52_3 = all_6_2)
% 202.90/34.11    (17)  all_44_2 = all_6_2
% 202.90/34.11    (18)  all_58_0 = all_6_2
% 202.90/34.11    (19)  all_56_4 = all_52_3
% 202.90/34.11    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.11    (21)  op(e3, e0) = all_52_25
% 202.90/34.11    (22)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.11    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 202.90/34.11    (24)  op(all_52_19, all_52_19) = all_52_18
% 202.90/34.11    (25)  all_58_13 = all_52_15
% 202.90/34.11    (26)  op(all_52_13, all_52_13) = e1
% 202.90/34.11    (27)  op(all_10_2, all_10_2) = all_52_20
% 202.90/34.11    (28)  all_58_9 = all_52_25
% 202.90/34.11    (29)   ~ (all_52_29 = all_14_2)
% 202.90/34.11    (30)   ~ (all_52_15 = e3)
% 202.90/34.11    (31)  op(all_52_27, all_52_27) = all_52_26
% 202.90/34.11    (32)  op(e1, e3) = all_52_5
% 202.90/34.11    (33)  op(e2, e2) = all_4_2
% 202.90/34.11    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.11    (35)   ~ (all_52_3 = all_52_5)
% 202.90/34.11    (36)  all_58_11 = all_52_29
% 202.90/34.11    (37)   ~ (all_52_25 = all_14_2)
% 202.90/34.11    (38)   ~ (all_52_3 = all_52_27)
% 202.90/34.11    (39)   ~ (all_52_7 = all_6_2)
% 202.90/34.11    (40)  op(e0, e0) = all_14_2
% 202.90/34.11    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.11    (42)   ~ (all_4_1 = e1)
% 202.90/34.11    (43)   ~ (all_52_13 = all_10_2)
% 202.90/34.11    (44)  all_58_10 = all_52_27
% 202.90/34.11    (45)  all_56_8 = all_52_5
% 202.90/34.11    (46)   ~ (all_52_19 = all_52_23)
% 202.90/34.11    (47)   ~ (all_52_25 = all_52_29)
% 202.90/34.11    (48)   ~ (all_52_29 = all_10_2)
% 202.90/34.11    (49)  all_58_7 = all_52_13
% 202.90/34.11    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.11    (51)   ~ (all_52_5 = all_52_7)
% 202.90/34.11    (52)  all_58_12 = all_52_7
% 202.90/34.11    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.11    (54)   ~ (all_52_7 = all_14_2)
% 202.90/34.11    (55)  all_58_2 = all_52_3
% 202.90/34.11    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.11    (57)  all_56_7 = all_52_27
% 202.90/34.11    (58)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.11    (59)   ~ (e2 = e0)
% 202.90/34.11    (60)  op(all_4_2, e2) = all_4_1
% 202.90/34.11    (61)   ~ (all_52_13 = all_4_2)
% 202.90/34.11    (62)  op(e3, e1) = all_52_17
% 202.90/34.11    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.11    (64)   ~ (all_52_9 = all_52_25)
% 202.90/34.11    (65)  all_58_15 = all_14_2
% 202.90/34.11    (66)   ~ (all_52_19 = all_10_2)
% 202.90/34.11    (67)  op(all_52_23, all_52_23) = all_52_22
% 202.90/34.11    (68)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.11    (69)  all_58_8 = all_10_2
% 202.90/34.11    (70)   ~ (all_52_5 = all_10_2)
% 202.90/34.11    (71)  op(all_52_29, all_52_29) = all_52_28
% 202.90/34.11    (72)   ~ (all_52_23 = all_14_2)
% 202.90/34.11    (73)  all_56_12 = all_52_7
% 202.90/34.11    (74)  op(all_52_17, all_52_17) = all_52_16
% 202.90/34.11    (75)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.90/34.11    (76)   ~ (all_52_9 = all_4_2)
% 202.90/34.11    (77)   ~ (all_52_5 = all_6_2)
% 202.90/34.11    (78)  op(all_4_2, all_4_2) = e2
% 202.90/34.11    (79)   ~ (all_52_9 = all_6_2)
% 202.90/34.11    (80)  op(e3, all_6_1) = e2
% 202.90/34.11    (81)  all_56_0 = all_6_2
% 202.90/34.11    (82)  op(e3, e3) = all_6_2
% 202.90/34.11    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.11    (84)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.11    (85)  all_56_3 = all_52_25
% 202.90/34.11    (86)   ~ (all_52_3 = all_52_7)
% 202.90/34.11    (87)  all_58_5 = all_52_19
% 202.90/34.11    (88)  all_56_1 = all_52_9
% 202.90/34.11    (89)   ~ (all_52_27 = all_4_2)
% 202.90/34.11    (90)  all_58_6 = all_52_5
% 202.90/34.11    (91)  op(e3, e2) = all_52_9
% 202.90/34.11    (92)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.90/34.11    (93)   ~ (all_52_17 = all_6_2)
% 202.90/34.11    (94)   ~ (e1 = e0)
% 202.90/34.11    (95)   ~ (e3 = e2)
% 202.90/34.11    (96)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.90/34.11    (97)  all_44_1 = all_6_1
% 202.90/34.11    (98)   ~ (all_52_9 = all_52_17)
% 202.90/34.11    (99)  all_56_10 = all_10_2
% 202.90/34.11    (100)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.11    (101)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 202.90/34.11    (102)  op(all_52_9, all_52_9) = e3
% 202.90/34.11    (103)   ~ (all_52_23 = all_10_2)
% 202.90/34.11    (104)   ~ (all_52_7 = all_52_23)
% 202.90/34.11    (105)  all_58_3 = all_4_2
% 202.90/34.11    (106)   ~ (all_52_3 = all_4_2)
% 202.90/34.11    (107)   ~ (all_52_19 = all_4_2)
% 202.90/34.11    (108)   ~ (all_52_17 = all_52_23)
% 202.90/34.11    (109)  op(all_6_2, e3) = all_6_1
% 202.90/34.11    (110)   ~ (all_52_13 = all_52_29)
% 202.90/34.11    (111)  all_58_4 = all_52_17
% 202.90/34.11    (112)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.90/34.11    (113)  op(all_52_25, all_52_25) = all_52_24
% 202.90/34.11    (114)   ~ (all_14_2 = e3)
% 202.90/34.11  
% 202.90/34.11  Begin of proof
% 202.90/34.11  | 
% 202.90/34.11  | BETA: splitting (92) gives:
% 202.90/34.11  | 
% 202.90/34.11  | Case 1:
% 202.90/34.11  | | 
% 202.90/34.11  | |   (115)  all_58_12 = e3
% 202.90/34.11  | | 
% 202.90/34.11  | | COMBINE_EQS: (52), (115) imply:
% 202.90/34.11  | |   (116)  all_52_7 = e3
% 202.90/34.11  | | 
% 202.90/34.11  | | SIMP: (116) implies:
% 202.90/34.11  | |   (117)  all_52_7 = e3
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (86), (117) imply:
% 202.90/34.11  | |   (118)   ~ (all_52_3 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (51), (117) imply:
% 202.90/34.11  | |   (119)   ~ (all_52_5 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (12), (117) imply:
% 202.90/34.11  | |   (120)   ~ (all_52_15 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (104), (117) imply:
% 202.90/34.11  | |   (121)   ~ (all_52_23 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | SIMP: (121) implies:
% 202.90/34.11  | |   (122)   ~ (all_52_23 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (54), (117) imply:
% 202.90/34.11  | |   (123)   ~ (all_14_2 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (39), (117) imply:
% 202.90/34.11  | |   (124)   ~ (all_6_2 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | SIMP: (124) implies:
% 202.90/34.11  | |   (125)   ~ (all_6_2 = e3)
% 202.90/34.11  | | 
% 202.90/34.11  | | REDUCE: (14), (117) imply:
% 202.90/34.11  | |   (126)  op(e3, e3) = all_52_6
% 202.90/34.11  | | 
% 202.90/34.11  | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 202.90/34.11  | |              with (82), (126) gives:
% 202.90/34.11  | |   (127)  all_52_6 = all_6_2
% 202.90/34.11  | | 
% 202.90/34.11  | | BETA: splitting (68) gives:
% 202.90/34.11  | | 
% 202.90/34.11  | | Case 1:
% 202.90/34.11  | | | 
% 202.90/34.11  | | |   (128)  all_56_8 = e3
% 202.90/34.11  | | | 
% 202.90/34.11  | | | REF_CLOSE: (45), (119), (128) are inconsistent by sub-proof #1325.
% 202.90/34.11  | | | 
% 202.90/34.11  | | Case 2:
% 202.90/34.11  | | | 
% 202.90/34.11  | | |   (129)   ~ (all_56_8 = e3)
% 202.90/34.11  | | |   (130)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.11  | | | 
% 202.90/34.11  | | | BETA: splitting (75) gives:
% 202.90/34.11  | | | 
% 202.90/34.11  | | | Case 1:
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | |   (131)  all_56_3 = e3
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | COMBINE_EQS: (85), (131) imply:
% 202.90/34.11  | | | |   (132)  all_52_25 = e3
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | SIMP: (132) implies:
% 202.90/34.11  | | | |   (133)  all_52_25 = e3
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | COMBINE_EQS: (28), (133) imply:
% 202.90/34.11  | | | |   (134)  all_58_9 = e3
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | REDUCE: (64), (133) imply:
% 202.90/34.11  | | | |   (135)   ~ (all_52_9 = e3)
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | REDUCE: (15), (133) imply:
% 202.90/34.11  | | | |   (136)   ~ (all_52_17 = e3)
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | REDUCE: (3), (133) imply:
% 202.90/34.11  | | | |   (137)   ~ (all_52_27 = e3)
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | SIMP: (137) implies:
% 202.90/34.11  | | | |   (138)   ~ (all_52_27 = e3)
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | REDUCE: (47), (133) imply:
% 202.90/34.11  | | | |   (139)   ~ (all_52_29 = e3)
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | SIMP: (139) implies:
% 202.90/34.11  | | | |   (140)   ~ (all_52_29 = e3)
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | REDUCE: (113), (133) imply:
% 202.90/34.11  | | | |   (141)  op(e3, e3) = all_52_24
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 202.90/34.11  | | | |              simplifying with (82), (141) gives:
% 202.90/34.11  | | | |   (142)  all_52_24 = all_6_2
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | BETA: splitting (100) gives:
% 202.90/34.11  | | | | 
% 202.90/34.11  | | | | Case 1:
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | |   (143)  all_58_4 = e3
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | | REF_CLOSE: (111), (136), (143) are inconsistent by sub-proof #1302.
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | Case 2:
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | |   (144)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | | BETA: splitting (41) gives:
% 202.90/34.11  | | | | | 
% 202.90/34.11  | | | | | Case 1:
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | |   (145)  all_58_2 = e3
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | | REF_CLOSE: (55), (118), (145) are inconsistent by sub-proof #1369.
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | Case 2:
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | |   (146)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | | BETA: splitting (53) gives:
% 202.90/34.11  | | | | | | 
% 202.90/34.11  | | | | | | Case 1:
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | |   (147)  all_58_6 = e3
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | | REF_CLOSE: (90), (119), (147) are inconsistent by sub-proof #1328.
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | Case 2:
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | |   (148)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | | BETA: splitting (96) gives:
% 202.90/34.11  | | | | | | | 
% 202.90/34.11  | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | |   (149)  all_56_1 = e3
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | | REF_CLOSE: (88), (135), (149) are inconsistent by sub-proof
% 202.90/34.11  | | | | | | | |            #1326.
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | |   (150)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | | BETA: splitting (112) gives:
% 202.90/34.11  | | | | | | | | 
% 202.90/34.11  | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | |   (151)  all_56_10 = e3
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | COMBINE_EQS: (99), (151) imply:
% 202.90/34.11  | | | | | | | | |   (152)  all_10_2 = e3
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | SIMP: (152) implies:
% 202.90/34.11  | | | | | | | | |   (153)  all_10_2 = e3
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | REDUCE: (66), (153) imply:
% 202.90/34.11  | | | | | | | | |   (154)   ~ (all_52_19 = e3)
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | REDUCE: (27), (153) imply:
% 202.90/34.11  | | | | | | | | |   (155)  op(e3, e3) = all_52_20
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | REF_CLOSE: (6), (40), (42), (44), (60), (78), (79), (82),
% 202.90/34.11  | | | | | | | | |            (87), (88), (91), (102), (105), (114), (138),
% 202.90/34.11  | | | | | | | | |            (146), (150), (154), (155) are inconsistent by
% 202.90/34.11  | | | | | | | | |            sub-proof #734.
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | |   (156)   ~ (all_56_10 = e3)
% 202.90/34.11  | | | | | | | | |   (157)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | REDUCE: (99), (156) imply:
% 202.90/34.11  | | | | | | | | |   (158)   ~ (all_10_2 = e3)
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | BETA: splitting (148) gives:
% 202.90/34.11  | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | |   (159)  all_58_7 = e3
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | COMBINE_EQS: (49), (159) imply:
% 202.90/34.11  | | | | | | | | | |   (160)  all_52_13 = e3
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | REDUCE: (43), (160) imply:
% 202.90/34.11  | | | | | | | | | |   (161)   ~ (all_10_2 = e3)
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | REDUCE: (26), (160) imply:
% 202.90/34.11  | | | | | | | | | |   (162)  op(e3, e3) = e1
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | BETA: splitting (144) gives:
% 202.90/34.11  | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | |   (163)  all_58_5 = e3
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | COMBINE_EQS: (87), (163) imply:
% 202.90/34.11  | | | | | | | | | | |   (164)  all_52_19 = e3
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | SIMP: (164) implies:
% 202.90/34.11  | | | | | | | | | | |   (165)  all_52_19 = e3
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | REDUCE: (107), (165) imply:
% 202.90/34.11  | | | | | | | | | | |   (166)   ~ (all_4_2 = e3)
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | SIMP: (166) implies:
% 202.90/34.11  | | | | | | | | | | |   (167)   ~ (all_4_2 = e3)
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | REDUCE: (24), (165) imply:
% 202.90/34.11  | | | | | | | | | | |   (168)  op(e3, e3) = all_52_18
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_18, e3, e3,
% 202.90/34.11  | | | | | | | | | | |              simplifying with (82), (168) gives:
% 202.90/34.11  | | | | | | | | | | |   (169)  all_52_18 = all_6_2
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | GROUND_INST: instantiating (6) with e1, all_52_18, e3, e3,
% 202.90/34.11  | | | | | | | | | | |              simplifying with (162), (168) gives:
% 202.90/34.11  | | | | | | | | | | |   (170)  all_52_18 = e1
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | COMBINE_EQS: (169), (170) imply:
% 202.90/34.11  | | | | | | | | | | |   (171)  all_6_2 = e1
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | COMBINE_EQS: (17), (171) imply:
% 202.90/34.11  | | | | | | | | | | |   (172)  all_44_2 = e1
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | COMBINE_EQS: (18), (171) imply:
% 202.90/34.11  | | | | | | | | | | |   (173)  all_58_0 = e1
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | REDUCE: (77), (171) imply:
% 202.90/34.11  | | | | | | | | | | |   (174)   ~ (all_52_5 = e1)
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | REDUCE: (109), (171) imply:
% 202.90/34.11  | | | | | | | | | | |   (175)  op(e1, e3) = all_6_1
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | BETA: splitting (20) gives:
% 202.90/34.11  | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | |   (176)   ~ (all_44_2 = e1)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (172), (176) imply:
% 202.90/34.11  | | | | | | | | | | | |   (177)  $false
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | Case 2:
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | |   (178)   ~ (all_44_1 = e0)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (97), (178) imply:
% 202.90/34.11  | | | | | | | | | | | |   (179)   ~ (all_6_1 = e0)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 202.90/34.11  | | | | | | | | | | | |              simplifying with (32), (175) gives:
% 202.90/34.11  | | | | | | | | | | | |   (180)  all_52_5 = all_6_1
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | COMBINE_EQS: (45), (180) imply:
% 202.90/34.11  | | | | | | | | | | | |   (181)  all_56_8 = all_6_1
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | COMBINE_EQS: (90), (180) imply:
% 202.90/34.11  | | | | | | | | | | | |   (182)  all_58_6 = all_6_1
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (35), (180) imply:
% 202.90/34.11  | | | | | | | | | | | |   (183)   ~ (all_52_3 = all_6_1)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (70), (180) imply:
% 202.90/34.11  | | | | | | | | | | | |   (184)   ~ (all_10_2 = all_6_1)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | SIMP: (184) implies:
% 202.90/34.11  | | | | | | | | | | | |   (185)   ~ (all_10_2 = all_6_1)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (174), (180) imply:
% 202.90/34.11  | | | | | | | | | | | |   (186)   ~ (all_6_1 = e1)
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | REDUCE: (22), (180) imply:
% 202.90/34.11  | | | | | | | | | | | |   (187)  op(all_6_1, all_6_1) = all_52_4
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | BETA: splitting (34) gives:
% 202.90/34.11  | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | Case 1:
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | |   (188)  all_58_0 = e0
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | COMBINE_EQS: (173), (188) imply:
% 202.90/34.11  | | | | | | | | | | | | |   (189)  e1 = e0
% 202.90/34.11  | | | | | | | | | | | | | 
% 202.90/34.11  | | | | | | | | | | | | | REDUCE: (94), (189) imply:
% 202.90/34.12  | | | | | | | | | | | | |   (190)  $false
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | |   (191)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | BETA: splitting (191) gives:
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | |   (192)  all_58_2 = e0
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | COMBINE_EQS: (55), (192) imply:
% 202.90/34.12  | | | | | | | | | | | | | |   (193)  all_52_3 = e0
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | SIMP: (193) implies:
% 202.90/34.12  | | | | | | | | | | | | | |   (194)  all_52_3 = e0
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | REDUCE: (38), (194) imply:
% 202.90/34.12  | | | | | | | | | | | | | |   (195)   ~ (all_52_27 = e0)
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | SIMP: (195) implies:
% 202.90/34.12  | | | | | | | | | | | | | |   (196)   ~ (all_52_27 = e0)
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | REDUCE: (183), (194) imply:
% 202.90/34.12  | | | | | | | | | | | | | |   (197)   ~ (all_6_1 = e0)
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | REDUCE: (118), (194) imply:
% 202.90/34.12  | | | | | | | | | | | | | |   (198)   ~ (e3 = e0)
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | |   (199)  all_56_8 = e2
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | COMBINE_EQS: (181), (199) imply:
% 202.90/34.12  | | | | | | | | | | | | | | |   (200)  all_6_1 = e2
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | SIMP: (200) implies:
% 202.90/34.12  | | | | | | | | | | | | | | |   (201)  all_6_1 = e2
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | REDUCE: (185), (201) imply:
% 202.90/34.12  | | | | | | | | | | | | | | |   (202)   ~ (all_10_2 = e2)
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | REDUCE: (187), (201) imply:
% 202.90/34.12  | | | | | | | | | | | | | | |   (203)  op(e2, e2) = all_52_4
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | REDUCE: (80), (201) imply:
% 202.90/34.12  | | | | | | | | | | | | | | |   (204)  op(e3, e2) = e2
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | |   (205)  all_58_9 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (205) imply:
% 202.90/34.12  | | | | | | | | | | | | | | | |   (206)  e3 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | REDUCE: (9), (206) imply:
% 202.90/34.12  | | | | | | | | | | | | | | | |   (207)  $false
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | |   (208)  all_58_10 = e0 | all_58_11 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (209)  all_58_10 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (209) imply:
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (210)  all_52_27 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | REDUCE: (196), (210) imply:
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (211)  $false
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (212)  all_58_11 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (212) imply:
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (213)  all_52_29 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | SIMP: (213) implies:
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (214)  all_52_29 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | REDUCE: (48), (214) imply:
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (215)   ~ (all_10_2 = e0)
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 202.90/34.12  | | | | | | | | | | | | | | | | |   (216)   ~ (all_10_2 = e0)
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | |   (217)  all_56_10 = e2
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (202), (217) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | | | | | | | | |            #912.
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | |   (218)  all_56_10 = e1 | all_56_10 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (91), (102), (167), (203), (204) are
% 202.90/34.12  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #464.
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | |   (219)  all_56_10 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (216), (219) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | | | | | | | | | |            #911.
% 202.90/34.12  | | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | |   (220)  all_56_8 = e1 | all_56_8 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | REF_CLOSE: (179), (181), (186), (220) are inconsistent by
% 202.90/34.12  | | | | | | | | | | | | | | |            sub-proof #495.
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | |   (221)  all_58_6 = e0 | all_58_12 = e0
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | |   (222)  all_58_6 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | REF_CLOSE: (179), (182), (222) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | | | | | |            #486.
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | |   (223)  all_58_12 = e0
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | | REF_CLOSE: (9), (115), (223) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | | | | | |            #1212.
% 202.90/34.12  | | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (224)  all_58_8 = e3 | all_58_14 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REF_CLOSE: (4), (69), (122), (158), (224) are inconsistent by
% 202.90/34.12  | | | | | | | | | | |            sub-proof #1304.
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (225)  all_58_8 = e3 | all_58_11 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | REF_CLOSE: (36), (69), (140), (158), (225) are inconsistent
% 202.90/34.12  | | | | | | | | | |            by sub-proof #1140.
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | End of split
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | End of split
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | End of split
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | End of split
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | Case 2:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | |   (226)   ~ (all_56_3 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (85), (226) imply:
% 202.90/34.12  | | | |   (227)   ~ (all_52_25 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | BETA: splitting (83) gives:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | Case 1:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | |   (228)  all_58_9 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | REF_CLOSE: (28), (227), (228) are inconsistent by sub-proof #1300.
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | Case 2:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | |   (229)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | BETA: splitting (84) gives:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | Case 1:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | |   (230)  all_58_0 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | COMBINE_EQS: (18), (230) imply:
% 202.90/34.12  | | | | | |   (231)  all_6_2 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | REDUCE: (125), (231) imply:
% 202.90/34.12  | | | | | |   (232)  $false
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | CLOSE: (232) is inconsistent.
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | Case 2:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | |   (233)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | BETA: splitting (23) gives:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | Case 1:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | |   (234)  all_56_7 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | COMBINE_EQS: (57), (234) imply:
% 202.90/34.12  | | | | | | |   (235)  all_52_27 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | SIMP: (235) implies:
% 202.90/34.12  | | | | | | |   (236)  all_52_27 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REDUCE: (89), (236) imply:
% 202.90/34.12  | | | | | | |   (237)   ~ (all_4_2 = e3)
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | SIMP: (237) implies:
% 202.90/34.12  | | | | | | |   (238)   ~ (all_4_2 = e3)
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REDUCE: (31), (236) imply:
% 202.90/34.12  | | | | | | |   (239)  op(e3, e3) = all_52_26
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_26, e3, e3,
% 202.90/34.12  | | | | | | |              simplifying with (82), (239) gives:
% 202.90/34.12  | | | | | | |   (240)  all_52_26 = all_6_2
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | BETA: splitting (63) gives:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | |   (241)  all_58_1 = e3
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | COMBINE_EQS: (8), (241) imply:
% 202.90/34.12  | | | | | | | |   (242)  all_52_9 = e3
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | REF_CLOSE: (6), (79), (82), (102), (242) are inconsistent by
% 202.90/34.12  | | | | | | | |            sub-proof #1337.
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | |   (243)   ~ (all_58_1 = e3)
% 202.90/34.12  | | | | | | | |   (244)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | REDUCE: (8), (243) imply:
% 202.90/34.12  | | | | | | | |   (245)   ~ (all_52_9 = e3)
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | BETA: splitting (244) gives:
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | |   (246)  all_58_3 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | COMBINE_EQS: (105), (246) imply:
% 202.90/34.12  | | | | | | | | |   (247)  all_4_2 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | REDUCE: (238), (247) imply:
% 202.90/34.12  | | | | | | | | |   (248)  $false
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | CLOSE: (248) is inconsistent.
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | |   (249)  all_58_7 = e3 | all_58_13 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | BETA: splitting (233) gives:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (250)  all_58_1 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | COMBINE_EQS: (8), (250) imply:
% 202.90/34.12  | | | | | | | | | |   (251)  all_52_9 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | REDUCE: (245), (251) imply:
% 202.90/34.12  | | | | | | | | | |   (252)  $false
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | CLOSE: (252) is inconsistent.
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (253)  all_58_4 = e3 | all_58_9 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | BETA: splitting (253) gives:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (254)  all_58_4 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | COMBINE_EQS: (111), (254) imply:
% 202.90/34.12  | | | | | | | | | | |   (255)  all_52_17 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | SIMP: (255) implies:
% 202.90/34.12  | | | | | | | | | | |   (256)  all_52_17 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REDUCE: (74), (256) imply:
% 202.90/34.12  | | | | | | | | | | |   (257)  op(e3, e3) = all_52_16
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | BETA: splitting (249) gives:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | |   (258)  all_58_7 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | COMBINE_EQS: (49), (258) imply:
% 202.90/34.12  | | | | | | | | | | | |   (259)  all_52_13 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REDUCE: (26), (259) imply:
% 202.90/34.12  | | | | | | | | | | | |   (260)  op(e3, e3) = e1
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REF_CLOSE: (6), (9), (17), (18), (20), (22), (32), (33),
% 202.90/34.12  | | | | | | | | | | | |            (34), (45), (77), (80), (82), (90), (91), (94),
% 202.90/34.12  | | | | | | | | | | | |            (97), (102), (109), (115), (130), (238), (257),
% 202.90/34.12  | | | | | | | | | | | |            (260) are inconsistent by sub-proof #458.
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | |   (261)  all_58_13 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REF_CLOSE: (25), (30), (261) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | | |            #1360.
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (262)  all_58_9 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REF_CLOSE: (28), (227), (262) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | |            #1300.
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | End of split
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | Case 2:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | |   (263)   ~ (all_56_7 = e3)
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REDUCE: (57), (263) imply:
% 202.90/34.12  | | | | | | |   (264)   ~ (all_52_27 = e3)
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REF_CLOSE: (6), (8), (25), (28), (29), (30), (36), (40), (42),
% 202.90/34.12  | | | | | | |            (44), (47), (49), (60), (63), (65), (71), (74), (78),
% 202.90/34.12  | | | | | | |            (79), (82), (88), (91), (96), (98), (100), (102),
% 202.90/34.12  | | | | | | |            (105), (110), (111), (114), (229), (233), (264) are
% 202.90/34.12  | | | | | | |            inconsistent by sub-proof #1107.
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | End of split
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | End of split
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | End of split
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | End of split
% 202.90/34.12  | | | 
% 202.90/34.12  | | End of split
% 202.90/34.12  | | 
% 202.90/34.12  | Case 2:
% 202.90/34.12  | | 
% 202.90/34.12  | |   (265)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.90/34.12  | | 
% 202.90/34.12  | | BETA: splitting (265) gives:
% 202.90/34.12  | | 
% 202.90/34.12  | | Case 1:
% 202.90/34.12  | | | 
% 202.90/34.12  | | |   (266)  all_58_13 = e3
% 202.90/34.12  | | | 
% 202.90/34.12  | | | REF_CLOSE: (25), (30), (266) are inconsistent by sub-proof #1360.
% 202.90/34.12  | | | 
% 202.90/34.12  | | Case 2:
% 202.90/34.12  | | | 
% 202.90/34.12  | | |   (267)  all_58_14 = e3 | all_58_15 = e3
% 202.90/34.12  | | | 
% 202.90/34.12  | | | BETA: splitting (267) gives:
% 202.90/34.12  | | | 
% 202.90/34.12  | | | Case 1:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | |   (268)  all_58_14 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | COMBINE_EQS: (4), (268) imply:
% 202.90/34.12  | | | |   (269)  all_52_23 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | SIMP: (269) implies:
% 202.90/34.12  | | | |   (270)  all_52_23 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (104), (270) imply:
% 202.90/34.12  | | | |   (271)   ~ (all_52_7 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (108), (270) imply:
% 202.90/34.12  | | | |   (272)   ~ (all_52_17 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (46), (270) imply:
% 202.90/34.12  | | | |   (273)   ~ (all_52_19 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (72), (270) imply:
% 202.90/34.12  | | | |   (274)   ~ (all_14_2 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (103), (270) imply:
% 202.90/34.12  | | | |   (275)   ~ (all_10_2 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | SIMP: (275) implies:
% 202.90/34.12  | | | |   (276)   ~ (all_10_2 = e3)
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (67), (270) imply:
% 202.90/34.12  | | | |   (277)  op(e3, e3) = all_52_22
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 202.90/34.12  | | | |              simplifying with (82), (277) gives:
% 202.90/34.12  | | | |   (278)  all_52_22 = all_6_2
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | BETA: splitting (11) gives:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | Case 1:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | |   (279)  all_56_12 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | COMBINE_EQS: (73), (279) imply:
% 202.90/34.12  | | | | |   (280)  all_52_7 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | REDUCE: (271), (280) imply:
% 202.90/34.12  | | | | |   (281)  $false
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | CLOSE: (281) is inconsistent.
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | Case 2:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | |   (282)   ~ (all_56_12 = e3)
% 202.90/34.12  | | | | |   (283)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | BETA: splitting (101) gives:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | Case 1:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | |   (284)  all_56_0 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | COMBINE_EQS: (81), (284) imply:
% 202.90/34.12  | | | | | |   (285)  all_6_2 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | REF_CLOSE: (6), (80), (82), (95), (109), (285) are inconsistent by
% 202.90/34.12  | | | | | |            sub-proof #502.
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | Case 2:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | |   (286)   ~ (all_56_0 = e3)
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | REDUCE: (81), (286) imply:
% 202.90/34.12  | | | | | |   (287)   ~ (all_6_2 = e3)
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | BETA: splitting (56) gives:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | Case 1:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | |   (288)  all_58_0 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | COMBINE_EQS: (18), (288) imply:
% 202.90/34.12  | | | | | | |   (289)  all_6_2 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REDUCE: (287), (289) imply:
% 202.90/34.12  | | | | | | |   (290)  $false
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | CLOSE: (290) is inconsistent.
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | Case 2:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | |   (291)   ~ (all_58_0 = e3)
% 202.90/34.12  | | | | | | |   (292)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | BETA: splitting (84) gives:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | |   (293)  all_58_0 = e3
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | COMBINE_EQS: (18), (293) imply:
% 202.90/34.12  | | | | | | | |   (294)  all_6_2 = e3
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | REDUCE: (287), (294) imply:
% 202.90/34.12  | | | | | | | |   (295)  $false
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | CLOSE: (295) is inconsistent.
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | |   (296)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | BETA: splitting (41) gives:
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | |   (297)  all_58_2 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | COMBINE_EQS: (55), (297) imply:
% 202.90/34.12  | | | | | | | | |   (298)  all_52_3 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | SIMP: (298) implies:
% 202.90/34.12  | | | | | | | | |   (299)  all_52_3 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | REDUCE: (35), (299) imply:
% 202.90/34.12  | | | | | | | | |   (300)   ~ (all_52_5 = e3)
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | SIMP: (300) implies:
% 202.90/34.12  | | | | | | | | |   (301)   ~ (all_52_5 = e3)
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | REDUCE: (38), (299) imply:
% 202.90/34.12  | | | | | | | | |   (302)   ~ (all_52_27 = e3)
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | SIMP: (302) implies:
% 202.90/34.12  | | | | | | | | |   (303)   ~ (all_52_27 = e3)
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | REDUCE: (5), (299) imply:
% 202.90/34.12  | | | | | | | | |   (304)  op(e3, e3) = all_52_2
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3,
% 202.90/34.12  | | | | | | | | |              simplifying with (82), (304) gives:
% 202.90/34.12  | | | | | | | | |   (305)  all_52_2 = all_6_2
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | BETA: splitting (83) gives:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (306)  all_58_9 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | COMBINE_EQS: (28), (306) imply:
% 202.90/34.12  | | | | | | | | | |   (307)  all_52_25 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | SIMP: (307) implies:
% 202.90/34.12  | | | | | | | | | |   (308)  all_52_25 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | REDUCE: (47), (308) imply:
% 202.90/34.12  | | | | | | | | | |   (309)   ~ (all_52_29 = e3)
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | SIMP: (309) implies:
% 202.90/34.12  | | | | | | | | | |   (310)   ~ (all_52_29 = e3)
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | REDUCE: (113), (308) imply:
% 202.90/34.12  | | | | | | | | | |   (311)  op(e3, e3) = all_52_24
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | BETA: splitting (53) gives:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (312)  all_58_6 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REF_CLOSE: (90), (301), (312) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | |            #1328.
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (313)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | BETA: splitting (313) gives:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | |   (314)  all_58_7 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | COMBINE_EQS: (49), (314) imply:
% 202.90/34.12  | | | | | | | | | | | |   (315)  all_52_13 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REDUCE: (61), (315) imply:
% 202.90/34.12  | | | | | | | | | | | |   (316)   ~ (all_4_2 = e3)
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | SIMP: (316) implies:
% 202.90/34.12  | | | | | | | | | | | |   (317)   ~ (all_4_2 = e3)
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REDUCE: (26), (315) imply:
% 202.90/34.12  | | | | | | | | | | | |   (318)  op(e3, e3) = e1
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REF_CLOSE: (6), (17), (20), (22), (32), (33), (45), (51),
% 202.90/34.12  | | | | | | | | | | | |            (68), (73), (77), (80), (82), (91), (97), (102),
% 202.90/34.12  | | | | | | | | | | | |            (109), (283), (301), (311), (317), (318) are
% 202.90/34.12  | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | |   (319)  all_58_8 = e3 | all_58_11 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REF_CLOSE: (36), (69), (276), (310), (319) are inconsistent
% 202.90/34.12  | | | | | | | | | | | |            by sub-proof #1140.
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (320)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (29), (30), (36), (40),
% 202.90/34.12  | | | | | | | | | |            (42), (44), (47), (49), (60), (63), (65), (71),
% 202.90/34.12  | | | | | | | | | |            (74), (78), (79), (82), (88), (91), (96), (98),
% 202.90/34.12  | | | | | | | | | |            (100), (102), (105), (110), (111), (114), (296),
% 202.90/34.12  | | | | | | | | | |            (303), (320) are inconsistent by sub-proof #1107.
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | |   (321)   ~ (all_58_2 = e3)
% 202.90/34.12  | | | | | | | | |   (322)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | REDUCE: (55), (321) imply:
% 202.90/34.12  | | | | | | | | |   (323)   ~ (all_52_3 = e3)
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | BETA: splitting (292) gives:
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (324)  all_58_2 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | REF_CLOSE: (55), (323), (324) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | |            #1369.
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | |   (325)  all_58_6 = e3 | all_58_12 = e3
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | BETA: splitting (325) gives:
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (326)  all_58_6 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | COMBINE_EQS: (90), (326) imply:
% 202.90/34.12  | | | | | | | | | | |   (327)  all_52_5 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | SIMP: (327) implies:
% 202.90/34.12  | | | | | | | | | | |   (328)  all_52_5 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REDUCE: (51), (328) imply:
% 202.90/34.12  | | | | | | | | | | |   (329)   ~ (all_52_7 = e3)
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REDUCE: (22), (328) imply:
% 202.90/34.12  | | | | | | | | | | |   (330)  op(e3, e3) = all_52_4
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_4, e3, e3,
% 202.90/34.12  | | | | | | | | | | |              simplifying with (82), (330) gives:
% 202.90/34.12  | | | | | | | | | | |   (331)  all_52_4 = all_6_2
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | BETA: splitting (83) gives:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | |   (332)  all_58_9 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | COMBINE_EQS: (28), (332) imply:
% 202.90/34.12  | | | | | | | | | | | |   (333)  all_52_25 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | SIMP: (333) implies:
% 202.90/34.12  | | | | | | | | | | | |   (334)  all_52_25 = e3
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REDUCE: (3), (334) imply:
% 202.90/34.12  | | | | | | | | | | | |   (335)   ~ (all_52_27 = e3)
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | SIMP: (335) implies:
% 202.90/34.12  | | | | | | | | | | | |   (336)   ~ (all_52_27 = e3)
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | BETA: splitting (322) gives:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | Case 1:
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | |   (337)  all_58_3 = e3
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | COMBINE_EQS: (105), (337) imply:
% 202.90/34.12  | | | | | | | | | | | | |   (338)  all_4_2 = e3
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | REDUCE: (76), (338) imply:
% 202.90/34.12  | | | | | | | | | | | | |   (339)   ~ (all_52_9 = e3)
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | REDUCE: (78), (338) imply:
% 202.90/34.12  | | | | | | | | | | | | |   (340)  op(e3, e3) = e2
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (16), (18), (19), (21), (28),
% 202.90/34.12  | | | | | | | | | | | | |            (34), (35), (50), (52), (55), (56), (58), (59),
% 202.90/34.12  | | | | | | | | | | | | |            (62), (77), (80), (82), (84), (90), (93), (95),
% 202.90/34.12  | | | | | | | | | | | | |            (109), (111), (271), (272), (323), (339), (340)
% 202.90/34.12  | | | | | | | | | | | | |            are inconsistent by sub-proof #454.
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | |   (341)  all_58_5 = e3 | all_58_10 = e3
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | | REF_CLOSE: (44), (87), (273), (336), (341) are inconsistent
% 202.90/34.12  | | | | | | | | | | | | |            by sub-proof #1132.
% 202.90/34.12  | | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | |   (342)   ~ (all_58_9 = e3)
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REDUCE: (28), (342) imply:
% 202.90/34.12  | | | | | | | | | | | |   (343)   ~ (all_52_25 = e3)
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | | REF_CLOSE: (6), (8), (28), (79), (82), (102), (111), (272),
% 202.90/34.12  | | | | | | | | | | | |            (296), (343) are inconsistent by sub-proof #1138.
% 202.90/34.12  | | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | Case 2:
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | |   (344)  all_58_12 = e3
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | | REF_CLOSE: (52), (271), (344) are inconsistent by sub-proof
% 202.90/34.12  | | | | | | | | | | |            #1367.
% 202.90/34.12  | | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | | 
% 202.90/34.12  | | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | | 
% 202.90/34.12  | | | | | | | | End of split
% 202.90/34.12  | | | | | | | | 
% 202.90/34.12  | | | | | | | End of split
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | End of split
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | End of split
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | End of split
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | Case 2:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | |   (345)  all_58_15 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | COMBINE_EQS: (65), (345) imply:
% 202.90/34.12  | | | |   (346)  all_14_2 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REDUCE: (114), (346) imply:
% 202.90/34.12  | | | |   (347)  $false
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | CLOSE: (347) is inconsistent.
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | End of split
% 202.90/34.12  | | | 
% 202.90/34.12  | | End of split
% 202.90/34.12  | | 
% 202.90/34.12  | End of split
% 202.90/34.12  | 
% 202.90/34.12  End of proof
% 202.90/34.12  
% 202.90/34.12  Sub-proof #454 shows that the following formulas are inconsistent:
% 202.90/34.12  ----------------------------------------------------------------
% 202.90/34.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.12    (2)  all_58_1 = all_52_9
% 202.90/34.12    (3)  op(e2, e3) = all_52_3
% 202.90/34.12    (4)   ~ (all_52_3 = all_6_2)
% 202.90/34.12    (5)  all_58_0 = all_6_2
% 202.90/34.12    (6)  all_56_4 = all_52_3
% 202.90/34.12    (7)  op(e3, e0) = all_52_25
% 202.90/34.12    (8)  all_58_9 = all_52_25
% 202.90/34.12    (9)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.12    (10)   ~ (all_52_3 = all_52_5)
% 202.90/34.12    (11)   ~ (all_52_3 = e3)
% 202.90/34.12    (12)  op(e3, e3) = e2
% 202.90/34.12    (13)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.12    (14)  all_58_12 = all_52_7
% 202.90/34.12    (15)   ~ (all_52_7 = e3)
% 202.90/34.12    (16)  all_58_2 = all_52_3
% 202.90/34.12    (17)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.12    (18)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.12    (19)   ~ (e2 = e0)
% 202.90/34.12    (20)   ~ (all_52_9 = e3)
% 202.90/34.12    (21)  op(e3, e1) = all_52_17
% 202.90/34.12    (22)   ~ (all_52_5 = all_6_2)
% 202.90/34.12    (23)  op(e3, all_6_1) = e2
% 202.90/34.12    (24)  op(e3, e3) = all_6_2
% 202.90/34.12    (25)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.12    (26)   ~ (all_52_17 = e3)
% 202.90/34.12    (27)  all_58_6 = all_52_5
% 202.90/34.12    (28)   ~ (all_52_17 = all_6_2)
% 202.90/34.12    (29)   ~ (e3 = e2)
% 202.90/34.12    (30)  op(all_6_2, e3) = all_6_1
% 202.90/34.12    (31)  all_58_4 = all_52_17
% 202.90/34.12  
% 202.90/34.12  Begin of proof
% 202.90/34.12  | 
% 202.90/34.12  | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 202.90/34.12  |              (12), (24) gives:
% 202.90/34.12  |   (32)  all_6_2 = e2
% 202.90/34.12  | 
% 202.90/34.12  | COMBINE_EQS: (5), (32) imply:
% 202.90/34.12  |   (33)  all_58_0 = e2
% 202.90/34.12  | 
% 202.90/34.12  | REDUCE: (4), (32) imply:
% 202.90/34.12  |   (34)   ~ (all_52_3 = e2)
% 202.90/34.12  | 
% 202.90/34.12  | REDUCE: (22), (32) imply:
% 202.90/34.12  |   (35)   ~ (all_52_5 = e2)
% 202.90/34.12  | 
% 202.90/34.12  | REDUCE: (28), (32) imply:
% 202.90/34.12  |   (36)   ~ (all_52_17 = e2)
% 202.90/34.12  | 
% 202.90/34.12  | REDUCE: (30), (32) imply:
% 202.90/34.12  |   (37)  op(e2, e3) = all_6_1
% 202.90/34.12  | 
% 202.90/34.12  | BETA: splitting (17) gives:
% 202.90/34.12  | 
% 202.90/34.12  | Case 1:
% 202.90/34.12  | | 
% 202.90/34.12  | |   (38)  all_58_0 = e3
% 202.90/34.12  | | 
% 202.90/34.12  | | REF_CLOSE: (29), (33), (38) are inconsistent by sub-proof #1235.
% 202.90/34.12  | | 
% 202.90/34.12  | Case 2:
% 202.90/34.12  | | 
% 202.90/34.12  | |   (39)   ~ (all_58_0 = e3)
% 202.90/34.12  | |   (40)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.12  | | 
% 202.90/34.12  | | REDUCE: (33), (39) imply:
% 202.90/34.12  | |   (41)   ~ (e3 = e2)
% 202.90/34.12  | | 
% 202.90/34.12  | | BETA: splitting (40) gives:
% 202.90/34.12  | | 
% 202.90/34.12  | | Case 1:
% 202.90/34.12  | | | 
% 202.90/34.12  | | |   (42)  all_58_2 = e3
% 202.90/34.12  | | | 
% 202.90/34.12  | | | REF_CLOSE: (11), (16), (42) are inconsistent by sub-proof #1369.
% 202.90/34.12  | | | 
% 202.90/34.12  | | Case 2:
% 202.90/34.12  | | | 
% 202.90/34.12  | | |   (43)  all_58_6 = e3 | all_58_12 = e3
% 202.90/34.12  | | | 
% 202.90/34.12  | | | BETA: splitting (25) gives:
% 202.90/34.12  | | | 
% 202.90/34.12  | | | Case 1:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | |   (44)  all_58_0 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | REF_CLOSE: (29), (33), (44) are inconsistent by sub-proof #1235.
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | Case 2:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | |   (45)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | BETA: splitting (45) gives:
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | | Case 1:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | |   (46)  all_58_1 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | COMBINE_EQS: (2), (46) imply:
% 202.90/34.12  | | | | |   (47)  all_52_9 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | REDUCE: (20), (47) imply:
% 202.90/34.12  | | | | |   (48)  $false
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | CLOSE: (48) is inconsistent.
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | Case 2:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | |   (49)  all_58_4 = e3 | all_58_9 = e3
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | BETA: splitting (49) gives:
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | | Case 1:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | |   (50)  all_58_4 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | COMBINE_EQS: (31), (50) imply:
% 202.90/34.12  | | | | | |   (51)  all_52_17 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | REDUCE: (26), (51) imply:
% 202.90/34.12  | | | | | |   (52)  $false
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | CLOSE: (52) is inconsistent.
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | Case 2:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | |   (53)  all_58_9 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | COMBINE_EQS: (8), (53) imply:
% 202.90/34.12  | | | | | |   (54)  all_52_25 = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | REDUCE: (7), (54) imply:
% 202.90/34.12  | | | | | |   (55)  op(e3, e0) = e3
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | BETA: splitting (43) gives:
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | | Case 1:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | |   (56)  all_58_6 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | COMBINE_EQS: (27), (56) imply:
% 202.90/34.12  | | | | | | |   (57)  all_52_5 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | SIMP: (57) implies:
% 202.90/34.12  | | | | | | |   (58)  all_52_5 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REF_CLOSE: (1), (3), (6), (9), (11), (13), (16), (18), (19), (21),
% 202.90/34.12  | | | | | | |            (23), (29), (33), (34), (36), (37), (55) are
% 202.90/34.12  | | | | | | |            inconsistent by sub-proof #455.
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | Case 2:
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | |   (59)  all_58_12 = e3
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | | REF_CLOSE: (14), (15), (59) are inconsistent by sub-proof #1367.
% 202.90/34.12  | | | | | | | 
% 202.90/34.12  | | | | | | End of split
% 202.90/34.12  | | | | | | 
% 202.90/34.12  | | | | | End of split
% 202.90/34.12  | | | | | 
% 202.90/34.12  | | | | End of split
% 202.90/34.12  | | | | 
% 202.90/34.12  | | | End of split
% 202.90/34.12  | | | 
% 202.90/34.12  | | End of split
% 202.90/34.12  | | 
% 202.90/34.12  | End of split
% 202.90/34.12  | 
% 202.90/34.12  End of proof
% 202.90/34.12  
% 202.90/34.12  Sub-proof #455 shows that the following formulas are inconsistent:
% 202.90/34.12  ----------------------------------------------------------------
% 202.90/34.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.12    (2)  op(e2, e3) = all_52_3
% 202.90/34.12    (3)  all_56_4 = all_52_3
% 202.90/34.12    (4)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13    (5)   ~ (all_52_3 = e3)
% 202.90/34.13    (6)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.13    (7)  all_58_2 = all_52_3
% 202.90/34.13    (8)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.13    (9)   ~ (e2 = e0)
% 202.90/34.13    (10)  op(e2, e3) = all_6_1
% 202.90/34.13    (11)  op(e3, e1) = all_52_17
% 202.90/34.13    (12)  op(e3, e0) = e3
% 202.90/34.13    (13)  all_58_0 = e2
% 202.90/34.13    (14)  op(e3, all_6_1) = e2
% 202.90/34.13    (15)   ~ (e3 = e2)
% 202.90/34.13    (16)   ~ (all_52_17 = e2)
% 202.90/34.13    (17)   ~ (all_52_3 = e2)
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with all_52_3, all_6_1, e3, e2, simplifying
% 202.90/34.13  |              with (2), (10) gives:
% 202.90/34.13  |   (18)  all_52_3 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (3), (18) imply:
% 202.90/34.13  |   (19)  all_56_4 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (7), (18) imply:
% 202.90/34.13  |   (20)  all_58_2 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (5), (18) imply:
% 202.90/34.13  |   (21)   ~ (all_6_1 = e3)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (17), (18) imply:
% 202.90/34.13  |   (22)   ~ (all_6_1 = e2)
% 202.90/34.13  | 
% 202.90/34.13  | REF_CLOSE: (1), (4), (6), (8), (9), (11), (12), (13), (14), (15), (16), (19),
% 202.90/34.13  |            (20), (21), (22) are inconsistent by sub-proof #456.
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #456 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13    (3)   ~ (all_6_1 = e3)
% 202.90/34.13    (4)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 202.90/34.13    (5)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.13    (6)   ~ (e2 = e0)
% 202.90/34.13    (7)  all_56_4 = all_6_1
% 202.90/34.13    (8)  op(e3, e1) = all_52_17
% 202.90/34.13    (9)  op(e3, e0) = e3
% 202.90/34.13    (10)  all_58_0 = e2
% 202.90/34.13    (11)  op(e3, all_6_1) = e2
% 202.90/34.13    (12)   ~ (e3 = e2)
% 202.90/34.13    (13)   ~ (all_6_1 = e2)
% 202.90/34.13    (14)   ~ (all_52_17 = e2)
% 202.90/34.13    (15)  all_58_2 = all_6_1
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (5) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (16)  all_56_4 = e3
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (3), (7), (16) are inconsistent by sub-proof #900.
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (17)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 202.90/34.13  | |            (15), (17) are inconsistent by sub-proof #497.
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #457 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)   ~ (all_4_2 = e3)
% 202.90/34.13    (3)  all_44_2 = all_6_2
% 202.90/34.13    (4)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.13    (5)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.13    (6)  op(e1, e3) = all_52_5
% 202.90/34.13    (7)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.13    (8)  op(e2, e2) = all_4_2
% 202.90/34.13    (9)  all_56_8 = all_52_5
% 202.90/34.13    (10)   ~ (all_52_5 = all_52_7)
% 202.90/34.13    (11)   ~ (all_52_5 = e3)
% 202.90/34.13    (12)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13    (13)  all_56_12 = all_52_7
% 202.90/34.13    (14)   ~ (all_52_5 = all_6_2)
% 202.90/34.13    (15)  op(e3, all_6_1) = e2
% 202.90/34.13    (16)  op(e3, e3) = all_6_2
% 202.90/34.13    (17)  op(e3, e3) = e1
% 202.90/34.13    (18)  op(e3, e3) = all_52_24
% 202.90/34.13    (19)  op(e3, e2) = all_52_9
% 202.90/34.13    (20)  all_44_1 = all_6_1
% 202.90/34.13    (21)  op(all_52_9, all_52_9) = e3
% 202.90/34.13    (22)  op(all_6_2, e3) = all_6_1
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with all_6_2, all_52_24, e3, e3, simplifying
% 202.90/34.13  |              with (16), (18) gives:
% 202.90/34.13  |   (23)  all_52_24 = all_6_2
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with e1, all_52_24, e3, e3, simplifying with
% 202.90/34.13  |              (17), (18) gives:
% 202.90/34.13  |   (24)  all_52_24 = e1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (23), (24) imply:
% 202.90/34.13  |   (25)  all_6_2 = e1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (3), (25) imply:
% 202.90/34.13  |   (26)  all_44_2 = e1
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (14), (25) imply:
% 202.90/34.13  |   (27)   ~ (all_52_5 = e1)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (22), (25) imply:
% 202.90/34.13  |   (28)  op(e1, e3) = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (4) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (29)   ~ (all_44_2 = e1)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (26), (29) imply:
% 202.90/34.13  | |   (30)  $false
% 202.90/34.13  | | 
% 202.90/34.13  | | CLOSE: (30) is inconsistent.
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (31)   ~ (all_44_1 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (20), (31) imply:
% 202.90/34.13  | |   (32)   ~ (all_6_1 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15),
% 202.90/34.13  | |            (19), (21), (27), (28), (32) are inconsistent by sub-proof #463.
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #458 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)   ~ (e3 = e0)
% 202.90/34.13    (3)   ~ (all_4_2 = e3)
% 202.90/34.13    (4)  all_44_2 = all_6_2
% 202.90/34.13    (5)  all_58_0 = all_6_2
% 202.90/34.13    (6)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.13    (7)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.13    (8)  op(e1, e3) = all_52_5
% 202.90/34.13    (9)  op(e2, e2) = all_4_2
% 202.90/34.13    (10)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13    (11)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13    (12)  all_56_8 = all_52_5
% 202.90/34.13    (13)  op(e3, e3) = all_52_16
% 202.90/34.13    (14)   ~ (all_52_5 = all_6_2)
% 202.90/34.13    (15)  op(e3, all_6_1) = e2
% 202.90/34.13    (16)  op(e3, e3) = all_6_2
% 202.90/34.13    (17)  op(e3, e3) = e1
% 202.90/34.13    (18)  all_58_6 = all_52_5
% 202.90/34.13    (19)  op(e3, e2) = all_52_9
% 202.90/34.13    (20)   ~ (e1 = e0)
% 202.90/34.13    (21)  all_44_1 = all_6_1
% 202.90/34.13    (22)  all_58_12 = e3
% 202.90/34.13    (23)  op(all_52_9, all_52_9) = e3
% 202.90/34.13    (24)  op(all_6_2, e3) = all_6_1
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with all_6_2, all_52_16, e3, e3, simplifying
% 202.90/34.13  |              with (13), (16) gives:
% 202.90/34.13  |   (25)  all_52_16 = all_6_2
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with e1, all_52_16, e3, e3, simplifying with
% 202.90/34.13  |              (13), (17) gives:
% 202.90/34.13  |   (26)  all_52_16 = e1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (25), (26) imply:
% 202.90/34.13  |   (27)  all_6_2 = e1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (4), (27) imply:
% 202.90/34.13  |   (28)  all_44_2 = e1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (5), (27) imply:
% 202.90/34.13  |   (29)  all_58_0 = e1
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (14), (27) imply:
% 202.90/34.13  |   (30)   ~ (all_52_5 = e1)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (24), (27) imply:
% 202.90/34.13  |   (31)  op(e1, e3) = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (6) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (32)   ~ (all_44_2 = e1)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (28), (32) imply:
% 202.90/34.13  | |   (33)  $false
% 202.90/34.13  | | 
% 202.90/34.13  | | CLOSE: (33) is inconsistent.
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (34)   ~ (all_44_1 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (21), (34) imply:
% 202.90/34.13  | |   (35)   ~ (all_6_1 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (11), (12), (15), (18), (19),
% 202.90/34.13  | |            (20), (22), (23), (29), (30), (31), (35) are inconsistent by
% 202.90/34.13  | |            sub-proof #459.
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #459 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)   ~ (e3 = e0)
% 202.90/34.13    (3)   ~ (all_4_2 = e3)
% 202.90/34.13    (4)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.13    (5)   ~ (all_52_5 = e1)
% 202.90/34.13    (6)  op(e1, e3) = all_52_5
% 202.90/34.13    (7)   ~ (all_6_1 = e0)
% 202.90/34.13    (8)  op(e2, e2) = all_4_2
% 202.90/34.13    (9)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13    (10)  op(e1, e3) = all_6_1
% 202.90/34.13    (11)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13    (12)  all_56_8 = all_52_5
% 202.90/34.13    (13)  op(e3, all_6_1) = e2
% 202.90/34.13    (14)  all_58_6 = all_52_5
% 202.90/34.13    (15)  op(e3, e2) = all_52_9
% 202.90/34.13    (16)   ~ (e1 = e0)
% 202.90/34.13    (17)  all_58_12 = e3
% 202.90/34.13    (18)  op(all_52_9, all_52_9) = e3
% 202.90/34.13    (19)  all_58_0 = e1
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 202.90/34.13  |              with (6), (10) gives:
% 202.90/34.13  |   (20)  all_52_5 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (12), (20) imply:
% 202.90/34.13  |   (21)  all_56_8 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (14), (20) imply:
% 202.90/34.13  |   (22)  all_58_6 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (5), (20) imply:
% 202.90/34.13  |   (23)   ~ (all_6_1 = e1)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (4), (20) imply:
% 202.90/34.13  |   (24)  op(all_6_1, all_6_1) = all_52_4
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (11) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (25)  all_56_8 = e2
% 202.90/34.13  | | 
% 202.90/34.13  | | COMBINE_EQS: (21), (25) imply:
% 202.90/34.13  | |   (26)  all_6_1 = e2
% 202.90/34.13  | | 
% 202.90/34.13  | | SIMP: (26) implies:
% 202.90/34.13  | |   (27)  all_6_1 = e2
% 202.90/34.13  | | 
% 202.90/34.13  | | COMBINE_EQS: (22), (27) imply:
% 202.90/34.13  | |   (28)  all_58_6 = e2
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (7), (27) imply:
% 202.90/34.13  | |   (29)   ~ (e2 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (24), (27) imply:
% 202.90/34.13  | |   (30)  op(e2, e2) = all_52_4
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (13), (27) imply:
% 202.90/34.13  | |   (31)  op(e3, e2) = e2
% 202.90/34.13  | | 
% 202.90/34.13  | | BETA: splitting (9) gives:
% 202.90/34.13  | | 
% 202.90/34.13  | | Case 1:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (32)  all_58_0 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | COMBINE_EQS: (19), (32) imply:
% 202.90/34.13  | | |   (33)  e1 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (16), (33) imply:
% 202.90/34.13  | | |   (34)  $false
% 202.90/34.13  | | | 
% 202.90/34.13  | | | CLOSE: (34) is inconsistent.
% 202.90/34.13  | | | 
% 202.90/34.13  | | Case 2:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (35)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REF_CLOSE: (1), (2), (3), (8), (15), (17), (18), (28), (29), (30), (31),
% 202.90/34.13  | | |            (35) are inconsistent by sub-proof #460.
% 202.90/34.13  | | | 
% 202.90/34.13  | | End of split
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (36)  all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (7), (21), (23), (36) are inconsistent by sub-proof #495.
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #460 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)  all_58_6 = e2
% 202.90/34.13    (3)   ~ (e3 = e0)
% 202.90/34.13    (4)   ~ (all_4_2 = e3)
% 202.90/34.13    (5)  op(e2, e2) = all_4_2
% 202.90/34.13    (6)  op(e3, e2) = e2
% 202.90/34.13    (7)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13    (8)  op(e2, e2) = all_52_4
% 202.90/34.13    (9)   ~ (e2 = e0)
% 202.90/34.13    (10)  op(e3, e2) = all_52_9
% 202.90/34.13    (11)  all_58_12 = e3
% 202.90/34.13    (12)  op(all_52_9, all_52_9) = e3
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (7) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (1), (4), (5), (6), (8), (10), (12) are inconsistent by sub-proof
% 202.90/34.13  | |            #464.
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (13)  all_58_6 = e0 | all_58_12 = e0
% 202.90/34.13  | | 
% 202.90/34.13  | | BETA: splitting (13) gives:
% 202.90/34.13  | | 
% 202.90/34.13  | | Case 1:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (14)  all_58_6 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #801.
% 202.90/34.13  | | | 
% 202.90/34.13  | | Case 2:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (15)  all_58_12 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REF_CLOSE: (3), (11), (15) are inconsistent by sub-proof #1212.
% 202.90/34.13  | | | 
% 202.90/34.13  | | End of split
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #461 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 202.90/34.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.13    (4)  op(all_52_7, all_52_7) = all_52_6
% 202.90/34.13    (5)   ~ (all_4_2 = e3)
% 202.90/34.13    (6)  op(e2, e2) = all_4_2
% 202.90/34.13    (7)   ~ (all_52_7 = all_6_2)
% 202.90/34.13    (8)  all_56_15 = all_14_2
% 202.90/34.13    (9)   ~ (all_52_7 = e3)
% 202.90/34.13    (10)   ~ (all_52_7 = all_14_2)
% 202.90/34.13    (11)  op(e0, e3) = all_52_7
% 202.90/34.13    (12)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 202.90/34.13    (13)  all_56_12 = all_52_7
% 202.90/34.13    (14)  all_8_2 = all_6_2
% 202.90/34.13    (15)  op(e3, all_6_1) = e2
% 202.90/34.13    (16)  op(e3, e3) = e0
% 202.90/34.13    (17)  op(e3, e3) = all_6_2
% 202.90/34.13    (18)  op(e3, e2) = all_52_9
% 202.90/34.13    (19)  op(all_52_9, all_52_9) = e3
% 202.90/34.13    (20)  all_8_1 = all_6_1
% 202.90/34.13    (21)  op(all_6_2, e3) = all_6_1
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (2) with all_6_2, e0, e3, e3, simplifying with
% 202.90/34.13  |              (16), (17) gives:
% 202.90/34.13  |   (22)  all_6_2 = e0
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (14), (22) imply:
% 202.90/34.13  |   (23)  all_8_2 = e0
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (7), (22) imply:
% 202.90/34.13  |   (24)   ~ (all_52_7 = e0)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (21), (22) imply:
% 202.90/34.13  |   (25)  op(e0, e3) = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (1) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (26)   ~ (all_8_1 = e1)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (20), (26) imply:
% 202.90/34.13  | |   (27)   ~ (all_6_1 = e1)
% 202.90/34.13  | | 
% 202.90/34.13  | | GROUND_INST: instantiating (2) with all_52_7, all_6_1, e3, e0, simplifying
% 202.90/34.13  | |              with (11), (25) gives:
% 202.90/34.13  | |   (28)  all_52_7 = all_6_1
% 202.90/34.13  | | 
% 202.90/34.13  | | COMBINE_EQS: (13), (28) imply:
% 202.90/34.13  | |   (29)  all_56_12 = all_6_1
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (10), (28) imply:
% 202.90/34.13  | |   (30)   ~ (all_14_2 = all_6_1)
% 202.90/34.13  | | 
% 202.90/34.13  | | SIMP: (30) implies:
% 202.90/34.13  | |   (31)   ~ (all_14_2 = all_6_1)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (9), (28) imply:
% 202.90/34.13  | |   (32)   ~ (all_6_1 = e3)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (24), (28) imply:
% 202.90/34.13  | |   (33)   ~ (all_6_1 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (4), (28) imply:
% 202.90/34.13  | |   (34)  op(all_6_1, all_6_1) = all_52_6
% 202.90/34.13  | | 
% 202.90/34.13  | | BETA: splitting (3) gives:
% 202.90/34.13  | | 
% 202.90/34.13  | | Case 1:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (35)  all_56_12 = e3
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REF_CLOSE: (29), (32), (35) are inconsistent by sub-proof #1347.
% 202.90/34.13  | | | 
% 202.90/34.13  | | Case 2:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (36)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | BETA: splitting (36) gives:
% 202.90/34.13  | | | 
% 202.90/34.13  | | | Case 1:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | |   (37)  all_56_12 = e2
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | COMBINE_EQS: (29), (37) imply:
% 202.90/34.13  | | | |   (38)  all_6_1 = e2
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | SIMP: (38) implies:
% 202.90/34.13  | | | |   (39)  all_6_1 = e2
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REDUCE: (31), (39) imply:
% 202.90/34.13  | | | |   (40)   ~ (all_14_2 = e2)
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REDUCE: (34), (39) imply:
% 202.90/34.13  | | | |   (41)  op(e2, e2) = all_52_6
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REDUCE: (15), (39) imply:
% 202.90/34.13  | | | |   (42)  op(e3, e2) = e2
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | BETA: splitting (12) gives:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | Case 1:
% 202.90/34.13  | | | | | 
% 202.90/34.13  | | | | |   (43)  all_56_15 = e2
% 202.90/34.13  | | | | | 
% 202.90/34.13  | | | | | REF_CLOSE: (8), (40), (43) are inconsistent by sub-proof #762.
% 202.90/34.13  | | | | | 
% 202.90/34.13  | | | | Case 2:
% 202.90/34.13  | | | | | 
% 202.90/34.13  | | | | | 
% 202.90/34.13  | | | | | REF_CLOSE: (2), (5), (6), (18), (19), (41), (42) are inconsistent by
% 202.90/34.13  | | | | |            sub-proof #500.
% 202.90/34.13  | | | | | 
% 202.90/34.13  | | | | End of split
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | Case 2:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | |   (44)  all_56_12 = e1 | all_56_12 = e0
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REF_CLOSE: (27), (29), (33), (44) are inconsistent by sub-proof #1344.
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | End of split
% 202.90/34.13  | | | 
% 202.90/34.13  | | End of split
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (45)   ~ (all_8_2 = e0)
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (23), (45) imply:
% 202.90/34.13  | |   (46)  $false
% 202.90/34.13  | | 
% 202.90/34.13  | | CLOSE: (46) is inconsistent.
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #462 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)   ~ (all_52_5 = all_52_13)
% 202.90/34.13    (3)   ~ (all_4_2 = e3)
% 202.90/34.13    (4)  all_44_2 = all_6_2
% 202.90/34.13    (5)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.13    (6)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.13    (7)  all_58_13 = all_52_15
% 202.90/34.13    (8)  op(all_52_13, all_52_13) = e1
% 202.90/34.13    (9)   ~ (all_52_15 = e3)
% 202.90/34.13    (10)  op(e1, e3) = all_52_5
% 202.90/34.13    (11)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.13    (12)  op(e2, e2) = all_4_2
% 202.90/34.13    (13)  all_56_8 = all_52_5
% 202.90/34.13    (14)  all_58_7 = all_52_13
% 202.90/34.13    (15)   ~ (all_52_5 = all_52_7)
% 202.90/34.13    (16)   ~ (all_52_13 = all_4_2)
% 202.90/34.13    (17)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13    (18)  all_56_12 = all_52_7
% 202.90/34.13    (19)   ~ (all_52_5 = all_6_2)
% 202.90/34.13    (20)  op(e3, e3) = all_52_2
% 202.90/34.13    (21)  op(e3, all_6_1) = e2
% 202.90/34.13    (22)  op(e3, e3) = all_6_2
% 202.90/34.13    (23)  op(e3, e2) = all_52_9
% 202.90/34.13    (24)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 202.90/34.13    (25)  all_44_1 = all_6_1
% 202.90/34.13    (26)  op(all_52_9, all_52_9) = e3
% 202.90/34.13    (27)  all_58_3 = all_4_2
% 202.90/34.13    (28)  op(all_6_2, e3) = all_6_1
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (24) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (29)  all_58_3 = e3
% 202.90/34.13  | | 
% 202.90/34.13  | | COMBINE_EQS: (27), (29) imply:
% 202.90/34.13  | |   (30)  all_4_2 = e3
% 202.90/34.13  | | 
% 202.90/34.13  | | REDUCE: (3), (30) imply:
% 202.90/34.13  | |   (31)  $false
% 202.90/34.13  | | 
% 202.90/34.13  | | CLOSE: (31) is inconsistent.
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (32)  all_58_7 = e3 | all_58_13 = e3
% 202.90/34.13  | | 
% 202.90/34.13  | | BETA: splitting (32) gives:
% 202.90/34.13  | | 
% 202.90/34.13  | | Case 1:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (33)  all_58_7 = e3
% 202.90/34.13  | | | 
% 202.90/34.13  | | | COMBINE_EQS: (14), (33) imply:
% 202.90/34.13  | | |   (34)  all_52_13 = e3
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (2), (34) imply:
% 202.90/34.13  | | |   (35)   ~ (all_52_5 = e3)
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (16), (34) imply:
% 202.90/34.13  | | |   (36)   ~ (all_4_2 = e3)
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (8), (34) imply:
% 202.90/34.13  | | |   (37)  op(e3, e3) = e1
% 202.90/34.13  | | | 
% 202.90/34.13  | | | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3, simplifying
% 202.90/34.13  | | |              with (20), (22) gives:
% 202.90/34.13  | | |   (38)  all_52_2 = all_6_2
% 202.90/34.13  | | | 
% 202.90/34.13  | | | GROUND_INST: instantiating (1) with e1, all_52_2, e3, e3, simplifying with
% 202.90/34.13  | | |              (20), (37) gives:
% 202.90/34.13  | | |   (39)  all_52_2 = e1
% 202.90/34.13  | | | 
% 202.90/34.13  | | | COMBINE_EQS: (38), (39) imply:
% 202.90/34.13  | | |   (40)  all_6_2 = e1
% 202.90/34.13  | | | 
% 202.90/34.13  | | | COMBINE_EQS: (4), (40) imply:
% 202.90/34.13  | | |   (41)  all_44_2 = e1
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (19), (40) imply:
% 202.90/34.13  | | |   (42)   ~ (all_52_5 = e1)
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (28), (40) imply:
% 202.90/34.13  | | |   (43)  op(e1, e3) = all_6_1
% 202.90/34.13  | | | 
% 202.90/34.13  | | | BETA: splitting (5) gives:
% 202.90/34.13  | | | 
% 202.90/34.13  | | | Case 1:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | |   (44)   ~ (all_44_2 = e1)
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REDUCE: (41), (44) imply:
% 202.90/34.13  | | | |   (45)  $false
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | CLOSE: (45) is inconsistent.
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | Case 2:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | |   (46)   ~ (all_44_1 = e0)
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REDUCE: (25), (46) imply:
% 202.90/34.13  | | | |   (47)   ~ (all_6_1 = e0)
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REF_CLOSE: (1), (3), (6), (10), (11), (12), (13), (15), (17), (18),
% 202.90/34.13  | | | |            (21), (23), (26), (35), (42), (43), (47) are inconsistent by
% 202.90/34.13  | | | |            sub-proof #463.
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | End of split
% 202.90/34.13  | | | 
% 202.90/34.13  | | Case 2:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (48)  all_58_13 = e3
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REF_CLOSE: (7), (9), (48) are inconsistent by sub-proof #1360.
% 202.90/34.13  | | | 
% 202.90/34.13  | | End of split
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #463 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)   ~ (all_4_2 = e3)
% 202.90/34.13    (3)  op(all_52_5, all_52_5) = all_52_4
% 202.90/34.13    (4)   ~ (all_52_5 = e1)
% 202.90/34.13    (5)  op(e1, e3) = all_52_5
% 202.90/34.13    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.13    (7)   ~ (all_6_1 = e0)
% 202.90/34.13    (8)  op(e2, e2) = all_4_2
% 202.90/34.13    (9)  op(e1, e3) = all_6_1
% 202.90/34.13    (10)  all_56_8 = all_52_5
% 202.90/34.13    (11)   ~ (all_52_5 = all_52_7)
% 202.90/34.13    (12)   ~ (all_52_5 = e3)
% 202.90/34.13    (13)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13    (14)  all_56_12 = all_52_7
% 202.90/34.13    (15)  op(e3, all_6_1) = e2
% 202.90/34.13    (16)  op(e3, e2) = all_52_9
% 202.90/34.13    (17)  op(all_52_9, all_52_9) = e3
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 202.90/34.13  |              with (5), (9) gives:
% 202.90/34.13  |   (18)  all_52_5 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | COMBINE_EQS: (10), (18) imply:
% 202.90/34.13  |   (19)  all_56_8 = all_6_1
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (11), (18) imply:
% 202.90/34.13  |   (20)   ~ (all_52_7 = all_6_1)
% 202.90/34.13  | 
% 202.90/34.13  | SIMP: (20) implies:
% 202.90/34.13  |   (21)   ~ (all_52_7 = all_6_1)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (12), (18) imply:
% 202.90/34.13  |   (22)   ~ (all_6_1 = e3)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (4), (18) imply:
% 202.90/34.13  |   (23)   ~ (all_6_1 = e1)
% 202.90/34.13  | 
% 202.90/34.13  | REDUCE: (3), (18) imply:
% 202.90/34.13  |   (24)  op(all_6_1, all_6_1) = all_52_4
% 202.90/34.13  | 
% 202.90/34.13  | BETA: splitting (13) gives:
% 202.90/34.13  | 
% 202.90/34.13  | Case 1:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (25)  all_56_8 = e3
% 202.90/34.13  | | 
% 202.90/34.13  | | REF_CLOSE: (19), (22), (25) are inconsistent by sub-proof #1101.
% 202.90/34.13  | | 
% 202.90/34.13  | Case 2:
% 202.90/34.13  | | 
% 202.90/34.13  | |   (26)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13  | | 
% 202.90/34.13  | | BETA: splitting (26) gives:
% 202.90/34.13  | | 
% 202.90/34.13  | | Case 1:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (27)  all_56_8 = e2
% 202.90/34.13  | | | 
% 202.90/34.13  | | | COMBINE_EQS: (19), (27) imply:
% 202.90/34.13  | | |   (28)  all_6_1 = e2
% 202.90/34.13  | | | 
% 202.90/34.13  | | | SIMP: (28) implies:
% 202.90/34.13  | | |   (29)  all_6_1 = e2
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (21), (29) imply:
% 202.90/34.13  | | |   (30)   ~ (all_52_7 = e2)
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (24), (29) imply:
% 202.90/34.13  | | |   (31)  op(e2, e2) = all_52_4
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REDUCE: (15), (29) imply:
% 202.90/34.13  | | |   (32)  op(e3, e2) = e2
% 202.90/34.13  | | | 
% 202.90/34.13  | | | BETA: splitting (6) gives:
% 202.90/34.13  | | | 
% 202.90/34.13  | | | Case 1:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | |   (33)  all_56_12 = e2
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REF_CLOSE: (14), (30), (33) are inconsistent by sub-proof #1178.
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | Case 2:
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | | REF_CLOSE: (1), (2), (8), (16), (17), (31), (32) are inconsistent by
% 202.90/34.13  | | | |            sub-proof #464.
% 202.90/34.13  | | | | 
% 202.90/34.13  | | | End of split
% 202.90/34.13  | | | 
% 202.90/34.13  | | Case 2:
% 202.90/34.13  | | | 
% 202.90/34.13  | | |   (34)  all_56_8 = e1 | all_56_8 = e0
% 202.90/34.13  | | | 
% 202.90/34.13  | | | REF_CLOSE: (7), (19), (23), (34) are inconsistent by sub-proof #495.
% 202.90/34.13  | | | 
% 202.90/34.13  | | End of split
% 202.90/34.13  | | 
% 202.90/34.13  | End of split
% 202.90/34.13  | 
% 202.90/34.13  End of proof
% 202.90/34.13  
% 202.90/34.13  Sub-proof #464 shows that the following formulas are inconsistent:
% 202.90/34.13  ----------------------------------------------------------------
% 202.90/34.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.13    (2)   ~ (all_4_2 = e3)
% 202.90/34.13    (3)  op(e2, e2) = all_4_2
% 202.90/34.13    (4)  op(e3, e2) = e2
% 202.90/34.13    (5)  op(e2, e2) = all_52_4
% 202.90/34.13    (6)  op(e3, e2) = all_52_9
% 202.90/34.13    (7)  op(all_52_9, all_52_9) = e3
% 202.90/34.13  
% 202.90/34.13  Begin of proof
% 202.90/34.13  | 
% 202.90/34.13  | GROUND_INST: instantiating (1) with all_4_2, all_52_4, e2, e2, simplifying
% 202.90/34.13  |              with (3), (5) gives:
% 202.90/34.13  |   (8)  all_52_4 = all_4_2
% 202.90/34.13  | 
% 202.90/34.14  | GROUND_INST: instantiating (1) with all_52_9, e2, e2, e3, simplifying with
% 202.90/34.14  |              (4), (6) gives:
% 202.90/34.14  |   (9)  all_52_9 = e2
% 202.90/34.14  | 
% 202.90/34.14  | REDUCE: (7), (9) imply:
% 202.90/34.14  |   (10)  op(e2, e2) = e3
% 202.90/34.14  | 
% 202.90/34.14  | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1318.
% 202.90/34.14  | 
% 202.90/34.14  End of proof
% 202.90/34.14  
% 202.90/34.14  Sub-proof #465 shows that the following formulas are inconsistent:
% 202.90/34.14  ----------------------------------------------------------------
% 202.90/34.14    (1)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 202.90/34.14    (2)   ~ (all_52_7 = e2)
% 202.90/34.14    (3)  all_56_12 = all_52_7
% 202.90/34.14    (4)   ~ (all_52_7 = e1)
% 202.90/34.14    (5)   ~ (all_52_7 = e0)
% 202.90/34.14  
% 202.90/34.14  Begin of proof
% 202.90/34.14  | 
% 202.90/34.14  | BETA: splitting (1) gives:
% 202.90/34.14  | 
% 202.90/34.14  | Case 1:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (6)  all_56_12 = e2
% 202.90/34.14  | | 
% 202.90/34.14  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1178.
% 202.90/34.14  | | 
% 202.90/34.14  | Case 2:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (7)  all_56_12 = e1 | all_56_12 = e0
% 202.90/34.14  | | 
% 202.90/34.14  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1374.
% 202.90/34.14  | | 
% 202.90/34.14  | End of split
% 202.90/34.14  | 
% 202.90/34.14  End of proof
% 202.90/34.14  
% 202.90/34.14  Sub-proof #466 shows that the following formulas are inconsistent:
% 202.90/34.14  ----------------------------------------------------------------
% 202.90/34.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.14    (2)   ~ (all_14_1 = e2)
% 202.90/34.14    (3)   ~ (all_6_1 = e1)
% 202.90/34.14    (4)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.14    (5)  all_56_4 = all_6_1
% 202.90/34.14    (6)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.14    (7)  op(e3, all_6_1) = e2
% 202.90/34.14    (8)  op(e3, e0) = all_14_1
% 202.90/34.14    (9)   ~ (all_6_1 = e2)
% 202.90/34.14    (10)  all_58_2 = all_6_1
% 202.90/34.14  
% 202.90/34.14  Begin of proof
% 202.90/34.14  | 
% 202.90/34.14  | BETA: splitting (6) gives:
% 202.90/34.14  | 
% 202.90/34.14  | Case 1:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (11)  all_56_4 = e2
% 202.90/34.14  | | 
% 202.90/34.14  | | REF_CLOSE: (5), (9), (11) are inconsistent by sub-proof #1219.
% 202.90/34.14  | | 
% 202.90/34.14  | Case 2:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (12)  all_56_4 = e1 | all_56_4 = e0
% 202.90/34.14  | | 
% 202.90/34.14  | | BETA: splitting (4) gives:
% 202.90/34.14  | | 
% 202.90/34.14  | | Case 1:
% 202.90/34.14  | | | 
% 202.90/34.14  | | |   (13)  all_58_2 = e0
% 202.90/34.14  | | | 
% 202.90/34.14  | | | COMBINE_EQS: (10), (13) imply:
% 202.90/34.14  | | |   (14)  all_6_1 = e0
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REDUCE: (7), (14) imply:
% 202.90/34.14  | | |   (15)  op(e3, e0) = e2
% 202.90/34.14  | | | 
% 202.90/34.14  | | | GROUND_INST: instantiating (1) with all_14_1, e2, e0, e3, simplifying with
% 202.90/34.14  | | |              (8), (15) gives:
% 202.90/34.14  | | |   (16)  all_14_1 = e2
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REDUCE: (2), (16) imply:
% 202.90/34.14  | | |   (17)  $false
% 202.90/34.14  | | | 
% 202.90/34.14  | | | CLOSE: (17) is inconsistent.
% 202.90/34.14  | | | 
% 202.90/34.14  | | Case 2:
% 202.90/34.14  | | | 
% 202.90/34.14  | | |   (18)   ~ (all_58_2 = e0)
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REDUCE: (10), (18) imply:
% 202.90/34.14  | | |   (19)   ~ (all_6_1 = e0)
% 202.90/34.14  | | | 
% 202.90/34.14  | | | BETA: splitting (12) gives:
% 202.90/34.14  | | | 
% 202.90/34.14  | | | Case 1:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | |   (20)  all_56_4 = e1
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REF_CLOSE: (3), (5), (20) are inconsistent by sub-proof #1218.
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | Case 2:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | |   (21)  all_56_4 = e0
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REF_CLOSE: (5), (19), (21) are inconsistent by sub-proof #1217.
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | End of split
% 202.90/34.14  | | | 
% 202.90/34.14  | | End of split
% 202.90/34.14  | | 
% 202.90/34.14  | End of split
% 202.90/34.14  | 
% 202.90/34.14  End of proof
% 202.90/34.14  
% 202.90/34.14  Sub-proof #467 shows that the following formulas are inconsistent:
% 202.90/34.14  ----------------------------------------------------------------
% 202.90/34.14    (1)   ~ (e3 = e1)
% 202.90/34.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.14    (3)  all_58_13 = all_52_15
% 202.90/34.14    (4)  op(all_52_13, all_52_13) = e1
% 202.90/34.14    (5)  all_58_15 = e3
% 202.90/34.14    (6)  all_58_6 = e3
% 202.90/34.14    (7)  all_56_9 = all_52_13
% 202.90/34.14    (8)   ~ (e2 = e1)
% 202.90/34.14    (9)   ~ (all_52_13 = all_10_2)
% 202.90/34.14    (10)  all_58_7 = all_52_13
% 202.90/34.14    (11)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 202.90/34.14    (12)  all_58_14 = e1
% 202.90/34.14    (13)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.90/34.14    (14)   ~ (all_52_13 = all_52_15)
% 202.90/34.14    (15)   ~ (all_52_13 = e3)
% 202.90/34.14    (16)   ~ (e3 = e2)
% 202.90/34.14    (17)   ~ (all_52_13 = e0)
% 202.90/34.14    (18)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.90/34.14    (19)  op(e1, e1) = all_10_2
% 202.90/34.14  
% 202.90/34.14  Begin of proof
% 202.90/34.14  | 
% 202.90/34.14  | BETA: splitting (13) gives:
% 202.90/34.14  | 
% 202.90/34.14  | Case 1:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (20)  all_58_6 = e1
% 202.90/34.14  | | 
% 202.90/34.14  | | REF_CLOSE: (1), (6), (20) are inconsistent by sub-proof #1128.
% 202.90/34.14  | | 
% 202.90/34.14  | Case 2:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (21)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.90/34.14  | | 
% 202.90/34.14  | | BETA: splitting (21) gives:
% 202.90/34.14  | | 
% 202.90/34.14  | | Case 1:
% 202.90/34.14  | | | 
% 202.90/34.14  | | |   (22)  all_58_7 = e1
% 202.90/34.14  | | | 
% 202.90/34.14  | | | COMBINE_EQS: (10), (22) imply:
% 202.90/34.14  | | |   (23)  all_52_13 = e1
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REF_CLOSE: (2), (4), (9), (19), (23) are inconsistent by sub-proof #1134.
% 202.90/34.14  | | | 
% 202.90/34.14  | | Case 2:
% 202.90/34.14  | | | 
% 202.90/34.14  | | |   (24)   ~ (all_58_7 = e1)
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REDUCE: (10), (24) imply:
% 202.90/34.14  | | |   (25)   ~ (all_52_13 = e1)
% 202.90/34.14  | | | 
% 202.90/34.14  | | | BETA: splitting (18) gives:
% 202.90/34.14  | | | 
% 202.90/34.14  | | | Case 1:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | |   (26)  all_56_9 = e3
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REF_CLOSE: (7), (15), (26) are inconsistent by sub-proof #958.
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | Case 2:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | |   (27)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | BETA: splitting (11) gives:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | Case 1:
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | |   (28)  all_58_13 = e2
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | COMBINE_EQS: (3), (28) imply:
% 202.90/34.14  | | | | |   (29)  all_52_15 = e2
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | SIMP: (29) implies:
% 202.90/34.14  | | | | |   (30)  all_52_15 = e2
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | REDUCE: (14), (30) imply:
% 202.90/34.14  | | | | |   (31)   ~ (all_52_13 = e2)
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | REF_CLOSE: (7), (17), (25), (27), (31) are inconsistent by sub-proof
% 202.90/34.14  | | | | |            #884.
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | Case 2:
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | |   (32)  all_58_14 = e2 | all_58_15 = e2
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | REF_CLOSE: (5), (8), (12), (16), (32) are inconsistent by sub-proof
% 202.90/34.14  | | | | |            #468.
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | End of split
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | End of split
% 202.90/34.14  | | | 
% 202.90/34.14  | | End of split
% 202.90/34.14  | | 
% 202.90/34.14  | End of split
% 202.90/34.14  | 
% 202.90/34.14  End of proof
% 202.90/34.14  
% 202.90/34.14  Sub-proof #468 shows that the following formulas are inconsistent:
% 202.90/34.14  ----------------------------------------------------------------
% 202.90/34.14    (1)  all_58_14 = e2 | all_58_15 = e2
% 202.90/34.14    (2)  all_58_15 = e3
% 202.90/34.14    (3)   ~ (e2 = e1)
% 202.90/34.14    (4)  all_58_14 = e1
% 202.90/34.14    (5)   ~ (e3 = e2)
% 202.90/34.14  
% 202.90/34.14  Begin of proof
% 202.90/34.14  | 
% 202.90/34.14  | BETA: splitting (1) gives:
% 202.90/34.14  | 
% 202.90/34.14  | Case 1:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (6)  all_58_14 = e2
% 202.90/34.14  | | 
% 202.90/34.14  | | COMBINE_EQS: (4), (6) imply:
% 202.90/34.14  | |   (7)  e2 = e1
% 202.90/34.14  | | 
% 202.90/34.14  | | REDUCE: (3), (7) imply:
% 202.90/34.14  | |   (8)  $false
% 202.90/34.14  | | 
% 202.90/34.14  | | CLOSE: (8) is inconsistent.
% 202.90/34.14  | | 
% 202.90/34.14  | Case 2:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (9)  all_58_15 = e2
% 202.90/34.14  | | 
% 202.90/34.14  | | COMBINE_EQS: (2), (9) imply:
% 202.90/34.14  | |   (10)  e3 = e2
% 202.90/34.14  | | 
% 202.90/34.14  | | REDUCE: (5), (10) imply:
% 202.90/34.14  | |   (11)  $false
% 202.90/34.14  | | 
% 202.90/34.14  | | CLOSE: (11) is inconsistent.
% 202.90/34.14  | | 
% 202.90/34.14  | End of split
% 202.90/34.14  | 
% 202.90/34.14  End of proof
% 202.90/34.14  
% 202.90/34.14  Sub-proof #469 shows that the following formulas are inconsistent:
% 202.90/34.14  ----------------------------------------------------------------
% 202.90/34.14    (1)   ~ (all_52_25 = all_52_27)
% 202.90/34.14    (2)  all_58_14 = all_52_23
% 202.90/34.14    (3)   ~ (e3 = e1)
% 202.90/34.14    (4)  op(all_52_3, all_52_3) = all_52_2
% 202.90/34.14    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 202.90/34.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 202.90/34.14    (6)   ~ (all_52_5 = all_52_13)
% 202.90/34.14    (7)  all_58_1 = all_52_9
% 202.90/34.14    (8)   ~ (e3 = e0)
% 202.90/34.14    (9)  op(e2, e3) = all_52_3
% 202.90/34.14    (10)   ~ (all_52_3 = all_52_19)
% 202.90/34.14    (11)  op(all_52_7, all_52_7) = all_52_6
% 202.90/34.14    (12)   ~ (all_52_17 = all_52_25)
% 202.90/34.14    (13)   ~ (all_52_3 = all_6_2)
% 202.90/34.14    (14)  all_44_2 = all_6_2
% 202.90/34.14    (15)  all_58_0 = all_6_2
% 202.90/34.14    (16)  all_56_4 = all_52_3
% 202.90/34.14    (17)   ~ (all_52_17 = all_10_2)
% 202.90/34.14    (18)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 202.90/34.14    (19)  op(e3, e0) = all_52_25
% 202.90/34.14    (20)  op(all_52_19, all_52_19) = all_52_18
% 202.90/34.14    (21)  all_58_13 = all_52_15
% 202.90/34.14    (22)  all_58_9 = all_52_25
% 202.90/34.14    (23)   ~ (all_52_29 = all_14_2)
% 202.90/34.14    (24)  op(e1, e3) = all_52_5
% 202.90/34.14    (25)  op(e2, e2) = all_4_2
% 202.90/34.14    (26)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 202.90/34.14    (27)   ~ (all_52_3 = all_52_5)
% 202.90/34.14    (28)  all_58_11 = all_52_29
% 202.90/34.14    (29)   ~ (all_52_9 = all_52_15)
% 202.90/34.14    (30)   ~ (all_52_3 = all_52_27)
% 202.90/34.14    (31)  op(all_6_2, all_6_2) = all_52_0
% 202.90/34.14    (32)   ~ (all_52_7 = all_6_2)
% 202.90/34.14    (33)  op(e0, e0) = all_14_2
% 202.90/34.14    (34)  op(all_52_29, all_52_29) = e1
% 202.90/34.14    (35)   ~ (all_52_15 = e0)
% 202.90/34.14    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 202.90/34.14    (37)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.90/34.14    (38)  all_58_15 = e0
% 202.90/34.14    (39)  all_56_11 = all_52_29
% 202.90/34.14    (40)   ~ (all_52_25 = e0)
% 202.90/34.14    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 202.90/34.14    (42)  all_56_9 = all_52_13
% 202.90/34.14    (43)   ~ (all_52_13 = all_10_2)
% 202.90/34.14    (44)  all_58_10 = all_52_27
% 202.90/34.14    (45)  all_56_8 = all_52_5
% 202.90/34.14    (46)   ~ (all_52_25 = all_52_29)
% 202.90/34.14    (47)  all_58_7 = all_52_13
% 202.90/34.14    (48)   ~ (all_52_5 = all_52_7)
% 202.90/34.14    (49)  all_58_12 = all_52_7
% 202.90/34.14    (50)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 202.90/34.14    (51)  all_58_2 = all_52_3
% 202.90/34.14    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 202.90/34.14    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 202.90/34.14    (54)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 202.90/34.14    (55)   ~ (e2 = e0)
% 202.90/34.14    (56)  op(all_52_25, all_52_25) = e3
% 202.90/34.14    (57)   ~ (all_52_5 = all_52_29)
% 202.90/34.14    (58)   ~ (all_52_29 = e0)
% 202.90/34.14    (59)  all_56_6 = all_52_19
% 202.90/34.14    (60)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 202.90/34.14    (61)   ~ (all_52_13 = all_4_2)
% 202.90/34.14    (62)  op(all_52_27, all_52_27) = e2
% 202.90/34.14    (63)   ~ (all_52_9 = all_52_25)
% 202.90/34.14    (64)   ~ (all_52_19 = all_10_2)
% 202.90/34.14    (65)  op(all_52_23, all_52_23) = all_52_22
% 202.90/34.14    (66)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 202.90/34.14    (67)  all_58_8 = all_10_2
% 202.90/34.14    (68)   ~ (all_52_23 = e0)
% 202.90/34.14    (69)   ~ (all_52_5 = all_10_2)
% 202.90/34.14    (70)  op(all_52_17, all_52_17) = all_52_16
% 202.90/34.14    (71)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 202.90/34.14    (72)   ~ (all_52_25 = all_6_2)
% 202.90/34.14    (73)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 202.90/34.14    (74)   ~ (all_52_5 = all_6_2)
% 202.90/34.14    (75)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 202.90/34.14    (76)   ~ (all_52_13 = all_52_15)
% 202.90/34.14    (77)  op(e3, all_6_1) = e2
% 202.90/34.14    (78)  op(e3, e3) = all_6_2
% 202.90/34.14    (79)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 202.90/34.14    (80)   ~ (all_52_27 = all_14_2)
% 202.90/34.14    (81)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 202.90/34.14    (82)  all_56_3 = all_52_25
% 202.90/34.14    (83)  all_58_5 = all_52_19
% 202.90/34.14    (84)   ~ (all_52_15 = all_4_2)
% 202.90/34.14    (85)  all_58_6 = all_52_5
% 202.90/34.14    (86)  op(e3, e2) = all_52_9
% 202.90/34.14    (87)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 202.90/34.14    (88)   ~ (e1 = e0)
% 202.90/34.14    (89)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 202.90/34.14    (90)   ~ (e3 = e2)
% 202.90/34.14    (91)  all_44_1 = all_6_1
% 202.90/34.14    (92)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 202.90/34.14    (93)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 202.90/34.14    (94)  op(e1, e1) = all_10_2
% 202.90/34.14    (95)   ~ (all_52_23 = all_10_2)
% 202.90/34.14    (96)   ~ (all_52_7 = all_52_23)
% 202.90/34.14    (97)   ~ (all_52_17 = all_52_19)
% 202.90/34.14    (98)  all_58_3 = all_4_2
% 202.90/34.14    (99)  all_56_13 = all_52_15
% 202.90/34.14    (100)   ~ (all_52_3 = all_4_2)
% 202.90/34.14    (101)   ~ (all_52_19 = all_4_2)
% 202.90/34.14    (102)  op(all_6_2, e3) = all_6_1
% 202.90/34.14    (103)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 202.90/34.14    (104)   ~ (all_52_13 = all_52_29)
% 202.90/34.14    (105)  all_58_4 = all_52_17
% 202.90/34.14    (106)   ~ (all_52_7 = e0)
% 202.90/34.14  
% 202.90/34.14  Begin of proof
% 202.90/34.14  | 
% 202.90/34.14  | BETA: splitting (41) gives:
% 202.90/34.14  | 
% 202.90/34.14  | Case 1:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (107)  all_56_13 = e3
% 202.90/34.14  | | 
% 202.90/34.14  | | REF_CLOSE: (1), (4), (5), (7), (11), (12), (13), (14), (15), (17), (18),
% 202.90/34.14  | |            (20), (22), (23), (24), (26), (27), (28), (29), (33), (34), (35),
% 202.90/34.14  | |            (36), (37), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 202.90/34.14  | |            (56), (57), (59), (62), (63), (66), (67), (70), (72), (73), (74),
% 202.90/34.14  | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 202.90/34.14  | |            (88), (90), (91), (92), (94), (97), (98), (99), (102), (105),
% 202.90/34.14  | |            (107) are inconsistent by sub-proof #473.
% 202.90/34.14  | | 
% 202.90/34.14  | Case 2:
% 202.90/34.14  | | 
% 202.90/34.14  | |   (108)   ~ (all_56_13 = e3)
% 202.90/34.14  | | 
% 202.90/34.14  | | REDUCE: (99), (108) imply:
% 202.90/34.14  | |   (109)   ~ (all_52_15 = e3)
% 202.90/34.14  | | 
% 202.90/34.14  | | BETA: splitting (87) gives:
% 202.90/34.14  | | 
% 202.90/34.14  | | Case 1:
% 202.90/34.14  | | | 
% 202.90/34.14  | | |   (110)  all_58_12 = e3
% 202.90/34.14  | | | 
% 202.90/34.14  | | | COMBINE_EQS: (49), (110) imply:
% 202.90/34.14  | | |   (111)  all_52_7 = e3
% 202.90/34.14  | | | 
% 202.90/34.14  | | | SIMP: (111) implies:
% 202.90/34.14  | | |   (112)  all_52_7 = e3
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REDUCE: (32), (112) imply:
% 202.90/34.14  | | |   (113)   ~ (all_6_2 = e3)
% 202.90/34.14  | | | 
% 202.90/34.14  | | | SIMP: (113) implies:
% 202.90/34.14  | | |   (114)   ~ (all_6_2 = e3)
% 202.90/34.14  | | | 
% 202.90/34.14  | | | REDUCE: (11), (112) imply:
% 202.90/34.14  | | |   (115)  op(e3, e3) = all_52_6
% 202.90/34.14  | | | 
% 202.90/34.14  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 202.90/34.14  | | |              with (78), (115) gives:
% 202.90/34.14  | | |   (116)  all_52_6 = all_6_2
% 202.90/34.14  | | | 
% 202.90/34.14  | | | BETA: splitting (60) gives:
% 202.90/34.14  | | | 
% 202.90/34.14  | | | Case 1:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | |   (117)  all_56_11 = e3
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | COMBINE_EQS: (39), (117) imply:
% 202.90/34.14  | | | |   (118)  all_52_29 = e3
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | SIMP: (118) implies:
% 202.90/34.14  | | | |   (119)  all_52_29 = e3
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | COMBINE_EQS: (28), (119) imply:
% 202.90/34.14  | | | |   (120)  all_58_11 = e3
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (57), (119) imply:
% 202.90/34.14  | | | |   (121)   ~ (all_52_5 = e3)
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (34), (119) imply:
% 202.90/34.14  | | | |   (122)  op(e3, e3) = e1
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | GROUND_INST: instantiating (5) with all_6_2, e1, e3, e3, simplifying
% 202.90/34.14  | | | |              with (78), (122) gives:
% 202.90/34.14  | | | |   (123)  all_6_2 = e1
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | COMBINE_EQS: (14), (123) imply:
% 202.90/34.14  | | | |   (124)  all_44_2 = e1
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (74), (123) imply:
% 202.90/34.14  | | | |   (125)   ~ (all_52_5 = e1)
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (72), (123) imply:
% 202.90/34.14  | | | |   (126)   ~ (all_52_25 = e1)
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (114), (123) imply:
% 202.90/34.14  | | | |   (127)   ~ (e3 = e1)
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (31), (123) imply:
% 202.90/34.14  | | | |   (128)  op(e1, e1) = all_52_0
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | REDUCE: (102), (123) imply:
% 202.90/34.14  | | | |   (129)  op(e1, e3) = all_6_1
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | BETA: splitting (37) gives:
% 202.90/34.14  | | | | 
% 202.90/34.14  | | | | Case 1:
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | |   (130)  all_58_9 = e1
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | REF_CLOSE: (22), (126), (130) are inconsistent by sub-proof #856.
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | Case 2:
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | |   (131)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | BETA: splitting (131) gives:
% 202.90/34.14  | | | | | 
% 202.90/34.14  | | | | | Case 1:
% 202.90/34.14  | | | | | | 
% 202.90/34.14  | | | | | |   (132)  all_58_10 = e1
% 202.90/34.14  | | | | | | 
% 202.90/34.14  | | | | | | COMBINE_EQS: (44), (132) imply:
% 202.90/34.14  | | | | | |   (133)  all_52_27 = e1
% 202.90/34.14  | | | | | | 
% 202.90/34.14  | | | | | | SIMP: (133) implies:
% 202.90/34.14  | | | | | |   (134)  all_52_27 = e1
% 202.90/34.14  | | | | | | 
% 202.90/34.14  | | | | | | REDUCE: (62), (134) imply:
% 202.90/34.14  | | | | | |   (135)  op(e1, e1) = e2
% 202.90/34.14  | | | | | | 
% 202.90/34.14  | | | | | | BETA: splitting (18) gives:
% 202.90/34.14  | | | | | | 
% 202.90/34.14  | | | | | | Case 1:
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | |   (136)   ~ (all_44_2 = e1)
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | REDUCE: (124), (136) imply:
% 202.90/34.14  | | | | | | |   (137)  $false
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | CLOSE: (137) is inconsistent.
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | Case 2:
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | |   (138)   ~ (all_44_1 = e0)
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | REDUCE: (91), (138) imply:
% 202.90/34.14  | | | | | | |   (139)   ~ (all_6_1 = e0)
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_0, e1, e1,
% 202.90/34.14  | | | | | | |              simplifying with (94), (128) gives:
% 202.90/34.14  | | | | | | |   (140)  all_52_0 = all_10_2
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_0, e1, e1,
% 202.90/34.14  | | | | | | |              simplifying with (128), (135) gives:
% 202.90/34.14  | | | | | | |   (141)  all_52_0 = e2
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | GROUND_INST: instantiating (5) with all_52_5, all_6_1, e3, e1,
% 202.90/34.14  | | | | | | |              simplifying with (24), (129) gives:
% 202.90/34.14  | | | | | | |   (142)  all_52_5 = all_6_1
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | COMBINE_EQS: (140), (141) imply:
% 202.90/34.14  | | | | | | |   (143)  all_10_2 = e2
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | SIMP: (143) implies:
% 202.90/34.14  | | | | | | |   (144)  all_10_2 = e2
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | COMBINE_EQS: (45), (142) imply:
% 202.90/34.14  | | | | | | |   (145)  all_56_8 = all_6_1
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | REDUCE: (69), (142), (144) imply:
% 202.90/34.14  | | | | | | |   (146)   ~ (all_6_1 = e2)
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | REDUCE: (121), (142) imply:
% 202.90/34.14  | | | | | | |   (147)   ~ (all_6_1 = e3)
% 202.90/34.14  | | | | | | | 
% 202.90/34.14  | | | | | | | REDUCE: (125), (142) imply:
% 203.09/34.14  | | | | | | |   (148)   ~ (all_6_1 = e1)
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | BETA: splitting (66) gives:
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | Case 1:
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | |   (149)  all_56_8 = e3
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | | REF_CLOSE: (145), (147), (149) are inconsistent by sub-proof
% 203.09/34.14  | | | | | | | |            #1101.
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | Case 2:
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | |   (150)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | | BETA: splitting (150) gives:
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | | Case 1:
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | |   (151)  all_56_8 = e2
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REF_CLOSE: (145), (146), (151) are inconsistent by sub-proof
% 203.09/34.14  | | | | | | | | |            #1321.
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | Case 2:
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | |   (152)  all_56_8 = e1 | all_56_8 = e0
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REF_CLOSE: (139), (145), (148), (152) are inconsistent by
% 203.09/34.14  | | | | | | | | |            sub-proof #495.
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | End of split
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | End of split
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | End of split
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | Case 2:
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | |   (153)  all_58_11 = e1 | all_58_15 = e1
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | REF_CLOSE: (3), (38), (88), (120), (153) are inconsistent by
% 203.09/34.14  | | | | | |            sub-proof #1206.
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | End of split
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | End of split
% 203.09/34.14  | | | | 
% 203.09/34.14  | | | Case 2:
% 203.09/34.14  | | | | 
% 203.09/34.14  | | | |   (154)   ~ (all_56_11 = e3)
% 203.09/34.14  | | | | 
% 203.09/34.14  | | | | REDUCE: (39), (154) imply:
% 203.09/34.14  | | | |   (155)   ~ (all_52_29 = e3)
% 203.09/34.14  | | | | 
% 203.09/34.14  | | | | BETA: splitting (79) gives:
% 203.09/34.14  | | | | 
% 203.09/34.14  | | | | Case 1:
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | |   (156)  all_58_9 = e3
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | | COMBINE_EQS: (22), (156) imply:
% 203.09/34.14  | | | | |   (157)  all_52_25 = e3
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | | REF_CLOSE: (5), (56), (72), (78), (157) are inconsistent by sub-proof
% 203.09/34.14  | | | | |            #1246.
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | Case 2:
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | |   (158)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | | BETA: splitting (158) gives:
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | | Case 1:
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | |   (159)  all_58_10 = e3
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | COMBINE_EQS: (44), (159) imply:
% 203.09/34.14  | | | | | |   (160)  all_52_27 = e3
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | SIMP: (160) implies:
% 203.09/34.14  | | | | | |   (161)  all_52_27 = e3
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | REDUCE: (30), (161) imply:
% 203.09/34.14  | | | | | |   (162)   ~ (all_52_3 = e3)
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | REDUCE: (1), (161) imply:
% 203.09/34.14  | | | | | |   (163)   ~ (all_52_25 = e3)
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | REDUCE: (62), (161) imply:
% 203.09/34.14  | | | | | |   (164)  op(e3, e3) = e2
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | GROUND_INST: instantiating (5) with all_6_2, e2, e3, e3, simplifying
% 203.09/34.14  | | | | | |              with (78), (164) gives:
% 203.09/34.14  | | | | | |   (165)  all_6_2 = e2
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | REDUCE: (72), (165) imply:
% 203.09/34.14  | | | | | |   (166)   ~ (all_52_25 = e2)
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | REDUCE: (102), (165) imply:
% 203.09/34.14  | | | | | |   (167)  op(e2, e3) = all_6_1
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | BETA: splitting (73) gives:
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | Case 1:
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | |   (168)  all_56_3 = e3
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | REF_CLOSE: (82), (163), (168) are inconsistent by sub-proof #1339.
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | Case 2:
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | |   (169)   ~ (all_56_3 = e3)
% 203.09/34.14  | | | | | | |   (170)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | BETA: splitting (170) gives:
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | Case 1:
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | |   (171)  all_56_3 = e2
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | | REF_CLOSE: (82), (166), (171) are inconsistent by sub-proof
% 203.09/34.14  | | | | | | | |            #1259.
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | Case 2:
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | |   (172)  all_56_3 = e1 | all_56_3 = e0
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | | BETA: splitting (37) gives:
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | | Case 1:
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | |   (173)  all_58_9 = e1
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | COMBINE_EQS: (22), (173) imply:
% 203.09/34.14  | | | | | | | | |   (174)  all_52_25 = e1
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | SIMP: (174) implies:
% 203.09/34.14  | | | | | | | | |   (175)  all_52_25 = e1
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REDUCE: (56), (175) imply:
% 203.09/34.14  | | | | | | | | |   (176)  op(e1, e1) = e3
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, e3, e1, e1,
% 203.09/34.14  | | | | | | | | |              simplifying with (94), (176) gives:
% 203.09/34.14  | | | | | | | | |   (177)  all_10_2 = e3
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | GROUND_INST: instantiating (5) with all_52_3, all_6_1, e3, e2,
% 203.09/34.14  | | | | | | | | |              simplifying with (9), (167) gives:
% 203.09/34.14  | | | | | | | | |   (178)  all_52_3 = all_6_1
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | COMBINE_EQS: (16), (178) imply:
% 203.09/34.14  | | | | | | | | |   (179)  all_56_4 = all_6_1
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REDUCE: (162), (178) imply:
% 203.09/34.14  | | | | | | | | |   (180)   ~ (all_6_1 = e3)
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REDUCE: (69), (177) imply:
% 203.09/34.14  | | | | | | | | |   (181)   ~ (all_52_5 = e3)
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | BETA: splitting (54) gives:
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | Case 1:
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | |   (182)  all_56_4 = e3
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | REF_CLOSE: (179), (180), (182) are inconsistent by sub-proof
% 203.09/34.14  | | | | | | | | | |            #900.
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | Case 2:
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | |   (183)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | BETA: splitting (66) gives:
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | Case 1:
% 203.09/34.14  | | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | |   (184)  all_56_8 = e3
% 203.09/34.14  | | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | | REF_CLOSE: (45), (181), (184) are inconsistent by sub-proof
% 203.09/34.14  | | | | | | | | | | |            #1325.
% 203.09/34.14  | | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | Case 2:
% 203.09/34.14  | | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | |   (185)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.09/34.14  | | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (10), (13), (15), (16), (19), (22),
% 203.09/34.14  | | | | | | | | | | |            (25), (26), (27), (28), (31), (34), (38), (40),
% 203.09/34.14  | | | | | | | | | | |            (42), (43), (45), (47), (51), (52), (55), (56),
% 203.09/34.14  | | | | | | | | | | |            (57), (58), (59), (61), (64), (71), (72), (73),
% 203.09/34.14  | | | | | | | | | | |            (75), (77), (78), (82), (83), (85), (89), (93),
% 203.09/34.14  | | | | | | | | | | |            (94), (98), (101), (102), (103), (104), (114),
% 203.09/34.14  | | | | | | | | | | |            (159), (163), (164), (183), (185) are inconsistent
% 203.09/34.14  | | | | | | | | | | |            by sub-proof #470.
% 203.09/34.14  | | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | | End of split
% 203.09/34.14  | | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | End of split
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | Case 2:
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | |   (186)   ~ (all_58_9 = e1)
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REDUCE: (22), (186) imply:
% 203.09/34.14  | | | | | | | | |   (187)   ~ (all_52_25 = e1)
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | | REF_CLOSE: (40), (82), (172), (187) are inconsistent by
% 203.09/34.14  | | | | | | | | |            sub-proof #1330.
% 203.09/34.14  | | | | | | | | | 
% 203.09/34.14  | | | | | | | | End of split
% 203.09/34.14  | | | | | | | | 
% 203.09/34.14  | | | | | | | End of split
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | End of split
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | Case 2:
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | |   (188)  all_58_11 = e3 | all_58_15 = e3
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | BETA: splitting (188) gives:
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | | Case 1:
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | |   (189)  all_58_11 = e3
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | REF_CLOSE: (28), (155), (189) are inconsistent by sub-proof #1323.
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | Case 2:
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | |   (190)  all_58_15 = e3
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | | REF_CLOSE: (8), (38), (190) are inconsistent by sub-proof #1350.
% 203.09/34.14  | | | | | | | 
% 203.09/34.14  | | | | | | End of split
% 203.09/34.14  | | | | | | 
% 203.09/34.14  | | | | | End of split
% 203.09/34.14  | | | | | 
% 203.09/34.14  | | | | End of split
% 203.09/34.14  | | | | 
% 203.09/34.14  | | | End of split
% 203.09/34.14  | | | 
% 203.09/34.14  | | Case 2:
% 203.09/34.14  | | | 
% 203.09/34.14  | | |   (191)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.09/34.14  | | | 
% 203.09/34.14  | | | REF_CLOSE: (1), (2), (3), (5), (8), (15), (21), (22), (25), (28), (34),
% 203.09/34.14  | | |            (37), (38), (40), (44), (46), (49), (51), (53), (56), (57),
% 203.09/34.14  | | |            (62), (65), (68), (72), (73), (78), (79), (82), (85), (94),
% 203.09/34.14  | | |            (95), (96), (100), (109), (191) are inconsistent by sub-proof
% 203.09/34.14  | | |            #1205.
% 203.09/34.14  | | | 
% 203.09/34.14  | | End of split
% 203.09/34.14  | | 
% 203.09/34.14  | End of split
% 203.09/34.14  | 
% 203.09/34.14  End of proof
% 203.09/34.14  
% 203.09/34.14  Sub-proof #470 shows that the following formulas are inconsistent:
% 203.09/34.14  ----------------------------------------------------------------
% 203.09/34.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.09/34.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.09/34.14    (2)   ~ (all_52_5 = all_52_13)
% 203.09/34.14    (3)  op(e2, e3) = all_52_3
% 203.09/34.14    (4)   ~ (all_52_3 = all_52_19)
% 203.09/34.14    (5)   ~ (all_52_3 = all_6_2)
% 203.09/34.14    (6)  all_58_0 = all_6_2
% 203.09/34.14    (7)  all_56_4 = all_52_3
% 203.09/34.14    (8)  op(e3, e0) = all_52_25
% 203.09/34.14    (9)  all_58_9 = all_52_25
% 203.09/34.14    (10)  op(e2, e2) = all_4_2
% 203.09/34.14    (11)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.09/34.14    (12)   ~ (all_52_3 = all_52_5)
% 203.09/34.15    (13)  all_58_11 = all_52_29
% 203.09/34.15    (14)  op(all_6_2, all_6_2) = all_52_0
% 203.09/34.15    (15)  op(all_52_29, all_52_29) = e1
% 203.09/34.15    (16)  op(e3, e3) = e2
% 203.09/34.15    (17)  all_58_15 = e0
% 203.09/34.15    (18)   ~ (all_52_25 = e0)
% 203.09/34.15    (19)   ~ (all_6_2 = e3)
% 203.09/34.15    (20)  all_56_9 = all_52_13
% 203.09/34.15    (21)   ~ (all_52_13 = all_10_2)
% 203.09/34.15    (22)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.09/34.15    (23)  all_56_8 = all_52_5
% 203.09/34.15    (24)  all_58_7 = all_52_13
% 203.09/34.15    (25)  all_58_2 = all_52_3
% 203.09/34.15    (26)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.09/34.15    (27)   ~ (all_52_25 = e3)
% 203.09/34.15    (28)   ~ (e2 = e0)
% 203.09/34.15    (29)  op(all_52_25, all_52_25) = e3
% 203.09/34.15    (30)   ~ (all_52_5 = all_52_29)
% 203.09/34.15    (31)   ~ (all_52_29 = e0)
% 203.09/34.15    (32)  all_56_6 = all_52_19
% 203.09/34.15    (33)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.09/34.15    (34)   ~ (all_52_13 = all_4_2)
% 203.09/34.15    (35)   ~ (all_52_19 = all_10_2)
% 203.09/34.15    (36)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.09/34.15    (37)   ~ (all_52_25 = all_6_2)
% 203.09/34.15    (38)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.09/34.15    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.09/34.15    (40)  op(e3, all_6_1) = e2
% 203.09/34.15    (41)  all_58_10 = e3
% 203.09/34.15    (42)  op(e3, e3) = all_6_2
% 203.09/34.15    (43)  all_56_3 = all_52_25
% 203.09/34.15    (44)  all_58_5 = all_52_19
% 203.09/34.15    (45)  all_58_6 = all_52_5
% 203.09/34.15    (46)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.09/34.15    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.09/34.15    (48)  op(e1, e1) = all_10_2
% 203.09/34.15    (49)  all_58_3 = all_4_2
% 203.09/34.15    (50)   ~ (all_52_19 = all_4_2)
% 203.09/34.15    (51)  op(all_6_2, e3) = all_6_1
% 203.09/34.15    (52)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.09/34.15    (53)   ~ (all_52_13 = all_52_29)
% 203.09/34.15  
% 203.09/34.15  Begin of proof
% 203.09/34.15  | 
% 203.09/34.15  | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 203.09/34.15  |              (16), (42) gives:
% 203.09/34.15  |   (54)  all_6_2 = e2
% 203.09/34.15  | 
% 203.09/34.15  | COMBINE_EQS: (6), (54) imply:
% 203.09/34.15  |   (55)  all_58_0 = e2
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (5), (54) imply:
% 203.09/34.15  |   (56)   ~ (all_52_3 = e2)
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (37), (54) imply:
% 203.09/34.15  |   (57)   ~ (all_52_25 = e2)
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (19), (54) imply:
% 203.09/34.15  |   (58)   ~ (e3 = e2)
% 203.09/34.15  | 
% 203.09/34.15  | SIMP: (58) implies:
% 203.09/34.15  |   (59)   ~ (e3 = e2)
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (14), (54) imply:
% 203.09/34.15  |   (60)  op(e2, e2) = all_52_0
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (51), (54) imply:
% 203.09/34.15  |   (61)  op(e2, e3) = all_6_1
% 203.09/34.15  | 
% 203.09/34.15  | BETA: splitting (38) gives:
% 203.09/34.15  | 
% 203.09/34.15  | Case 1:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (62)  all_56_3 = e3
% 203.09/34.15  | | 
% 203.09/34.15  | | REF_CLOSE: (27), (43), (62) are inconsistent by sub-proof #1339.
% 203.09/34.15  | | 
% 203.09/34.15  | Case 2:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (63)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.09/34.15  | | 
% 203.09/34.15  | | BETA: splitting (39) gives:
% 203.09/34.15  | | 
% 203.09/34.15  | | Case 1:
% 203.09/34.15  | | | 
% 203.09/34.15  | | |   (64)  all_58_9 = e2
% 203.09/34.15  | | | 
% 203.09/34.15  | | | REF_CLOSE: (9), (57), (64) are inconsistent by sub-proof #1221.
% 203.09/34.15  | | | 
% 203.09/34.15  | | Case 2:
% 203.09/34.15  | | | 
% 203.09/34.15  | | |   (65)   ~ (all_58_9 = e2)
% 203.09/34.15  | | |   (66)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.09/34.15  | | | 
% 203.09/34.15  | | | BETA: splitting (63) gives:
% 203.09/34.15  | | | 
% 203.09/34.15  | | | Case 1:
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | |   (67)  all_56_3 = e2
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | | REF_CLOSE: (43), (57), (67) are inconsistent by sub-proof #1259.
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | Case 2:
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | |   (68)  all_56_3 = e1 | all_56_3 = e0
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | | BETA: splitting (68) gives:
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | | Case 1:
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | |   (69)  all_56_3 = e1
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | COMBINE_EQS: (43), (69) imply:
% 203.09/34.15  | | | | |   (70)  all_52_25 = e1
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | SIMP: (70) implies:
% 203.09/34.15  | | | | |   (71)  all_52_25 = e1
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | REDUCE: (29), (71) imply:
% 203.09/34.15  | | | | |   (72)  op(e1, e1) = e3
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | REDUCE: (8), (71) imply:
% 203.09/34.15  | | | | |   (73)  op(e3, e0) = e1
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | BETA: splitting (66) gives:
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | Case 1:
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | |   (74)  all_58_10 = e2
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | | REF_CLOSE: (41), (59), (74) are inconsistent by sub-proof #1220.
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | Case 2:
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | |   (75)  all_58_11 = e2 | all_58_15 = e2
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | | BETA: splitting (75) gives:
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | | Case 1:
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | |   (76)  all_58_11 = e2
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | COMBINE_EQS: (13), (76) imply:
% 203.09/34.15  | | | | | | |   (77)  all_52_29 = e2
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | SIMP: (77) implies:
% 203.09/34.15  | | | | | | |   (78)  all_52_29 = e2
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (30), (78) imply:
% 203.09/34.15  | | | | | | |   (79)   ~ (all_52_5 = e2)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (53), (78) imply:
% 203.09/34.15  | | | | | | |   (80)   ~ (all_52_13 = e2)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (15), (78) imply:
% 203.09/34.15  | | | | | | |   (81)  op(e2, e2) = e1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | GROUND_INST: instantiating (1) with all_10_2, e3, e1, e1,
% 203.09/34.15  | | | | | | |              simplifying with (48), (72) gives:
% 203.09/34.15  | | | | | | |   (82)  all_10_2 = e3
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_0, e2, e2,
% 203.09/34.15  | | | | | | |              simplifying with (10), (60) gives:
% 203.09/34.15  | | | | | | |   (83)  all_52_0 = all_4_2
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | GROUND_INST: instantiating (1) with e1, all_52_0, e2, e2,
% 203.09/34.15  | | | | | | |              simplifying with (60), (81) gives:
% 203.09/34.15  | | | | | | |   (84)  all_52_0 = e1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | GROUND_INST: instantiating (1) with all_52_3, all_6_1, e3, e2,
% 203.09/34.15  | | | | | | |              simplifying with (3), (61) gives:
% 203.09/34.15  | | | | | | |   (85)  all_52_3 = all_6_1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | COMBINE_EQS: (83), (84) imply:
% 203.09/34.15  | | | | | | |   (86)  all_4_2 = e1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | SIMP: (86) implies:
% 203.09/34.15  | | | | | | |   (87)  all_4_2 = e1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | COMBINE_EQS: (7), (85) imply:
% 203.09/34.15  | | | | | | |   (88)  all_56_4 = all_6_1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | COMBINE_EQS: (49), (87) imply:
% 203.09/34.15  | | | | | | |   (89)  all_58_3 = e1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | COMBINE_EQS: (25), (85) imply:
% 203.09/34.15  | | | | | | |   (90)  all_58_2 = all_6_1
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (12), (85) imply:
% 203.09/34.15  | | | | | | |   (91)   ~ (all_52_5 = all_6_1)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | SIMP: (91) implies:
% 203.09/34.15  | | | | | | |   (92)   ~ (all_52_5 = all_6_1)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (4), (85) imply:
% 203.09/34.15  | | | | | | |   (93)   ~ (all_52_19 = all_6_1)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | SIMP: (93) implies:
% 203.09/34.15  | | | | | | |   (94)   ~ (all_52_19 = all_6_1)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (56), (85) imply:
% 203.09/34.15  | | | | | | |   (95)   ~ (all_6_1 = e2)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (21), (82) imply:
% 203.09/34.15  | | | | | | |   (96)   ~ (all_52_13 = e3)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (34), (87) imply:
% 203.09/34.15  | | | | | | |   (97)   ~ (all_52_13 = e1)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (35), (82) imply:
% 203.09/34.15  | | | | | | |   (98)   ~ (all_52_19 = e3)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REDUCE: (50), (87) imply:
% 203.09/34.15  | | | | | | |   (99)   ~ (all_52_19 = e1)
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | BETA: splitting (47) gives:
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | |   (100)  all_56_9 = e3
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | | REF_CLOSE: (20), (96), (100) are inconsistent by sub-proof #958.
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | |   (101)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | | BETA: splitting (52) gives:
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | |   (102)  all_58_2 = e2
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | COMBINE_EQS: (90), (102) imply:
% 203.09/34.15  | | | | | | | | |   (103)  all_6_1 = e2
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | SIMP: (103) implies:
% 203.09/34.15  | | | | | | | | |   (104)  all_6_1 = e2
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | REDUCE: (95), (104) imply:
% 203.09/34.15  | | | | | | | | |   (105)  $false
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | CLOSE: (105) is inconsistent.
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | |   (106)   ~ (all_58_2 = e2)
% 203.09/34.15  | | | | | | | | |   (107)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | BETA: splitting (36) gives:
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | |   (108)  all_58_6 = e1
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | COMBINE_EQS: (45), (108) imply:
% 203.09/34.15  | | | | | | | | | |   (109)  all_52_5 = e1
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | SIMP: (109) implies:
% 203.09/34.15  | | | | | | | | | |   (110)  all_52_5 = e1
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | REDUCE: (2), (110) imply:
% 203.09/34.15  | | | | | | | | | |   (111)   ~ (all_52_13 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | REDUCE: (92), (110) imply:
% 203.09/34.15  | | | | | | | | | |   (112)   ~ (all_6_1 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | SIMP: (112) implies:
% 203.09/34.15  | | | | | | | | | |   (113)   ~ (all_6_1 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | REDUCE: (79), (110) imply:
% 203.09/34.15  | | | | | | | | | |   (114)   ~ (e2 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | SIMP: (114) implies:
% 203.09/34.15  | | | | | | | | | |   (115)   ~ (e2 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | BETA: splitting (11) gives:
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | |   (116)  all_58_0 = e0
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | COMBINE_EQS: (55), (116) imply:
% 203.09/34.15  | | | | | | | | | | |   (117)  e2 = e0
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | REDUCE: (28), (117) imply:
% 203.09/34.15  | | | | | | | | | | |   (118)  $false
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | |   (119)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | BETA: splitting (119) gives:
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | |   (120)  all_58_2 = e0
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | COMBINE_EQS: (90), (120) imply:
% 203.09/34.15  | | | | | | | | | | | |   (121)  all_6_1 = e0
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | REDUCE: (94), (121) imply:
% 203.09/34.15  | | | | | | | | | | | |   (122)   ~ (all_52_19 = e0)
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | REDUCE: (113), (121) imply:
% 203.09/34.15  | | | | | | | | | | | |   (123)   ~ (e1 = e0)
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | SIMP: (123) implies:
% 203.09/34.15  | | | | | | | | | | | |   (124)   ~ (e1 = e0)
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | REDUCE: (40), (121) imply:
% 203.09/34.15  | | | | | | | | | | | |   (125)  op(e3, e0) = e2
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | BETA: splitting (26) gives:
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | |   (126)  all_56_6 = e3
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | COMBINE_EQS: (32), (126) imply:
% 203.09/34.15  | | | | | | | | | | | | |   (127)  all_52_19 = e3
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | REDUCE: (98), (127) imply:
% 203.09/34.15  | | | | | | | | | | | | |   (128)  $false
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | CLOSE: (128) is inconsistent.
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | |   (129)   ~ (all_56_6 = e3)
% 203.09/34.15  | | | | | | | | | | | | |   (130)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | BETA: splitting (101) gives:
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | |   (131)  all_56_9 = e2
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | REF_CLOSE: (20), (80), (131) are inconsistent by sub-proof
% 203.09/34.15  | | | | | | | | | | | | | |            #955.
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | |   (132)  all_56_9 = e1 | all_56_9 = e0
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | |   (133)  all_58_6 = e0
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | COMBINE_EQS: (108), (133) imply:
% 203.09/34.15  | | | | | | | | | | | | | | |   (134)  e1 = e0
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | SIMP: (134) implies:
% 203.09/34.15  | | | | | | | | | | | | | | |   (135)  e1 = e0
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | REDUCE: (124), (135) imply:
% 203.09/34.15  | | | | | | | | | | | | | | |   (136)  $false
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | |   (137)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | |   (138)  all_58_3 = e2
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (138) imply:
% 203.09/34.15  | | | | | | | | | | | | | | | |   (139)  e2 = e1
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | SIMP: (139) implies:
% 203.09/34.15  | | | | | | | | | | | | | | | |   (140)  e2 = e1
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | REDUCE: (115), (140) imply:
% 203.09/34.15  | | | | | | | | | | | | | | | |   (141)  $false
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | |   (142)  all_58_5 = e2 | all_58_10 = e2
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | |   (143)  all_56_6 = e2
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (143) imply:
% 203.09/34.15  | | | | | | | | | | | | | | | | |   (144)  all_52_19 = e2
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (144) imply:
% 203.09/34.15  | | | | | | | | | | | | | | | | |   (145)  all_58_5 = e2
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | Case 1:
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with e1, e2, e0, e3, simplifying
% 203.09/34.15  | | | | | | | | | | | | | | | | | |              with (73), (125) gives:
% 203.09/34.15  | | | | | | | | | | | | | | | | | |   (146)  e2 = e1
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (146) imply:
% 203.09/34.15  | | | | | | | | | | | | | | | | | |   (147)  all_58_5 = e1
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (59), (115), (142), (147) are inconsistent
% 203.09/34.15  | | | | | | | | | | | | | | | | | |            by sub-proof #472.
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | |   (148)   ~ (all_58_7 = e0)
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | | REDUCE: (24), (148) imply:
% 203.09/34.15  | | | | | | | | | | | | | | | | | |   (149)   ~ (all_52_13 = e0)
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (97), (132), (149) are inconsistent by
% 203.09/34.15  | | | | | | | | | | | | | | | | | |            sub-proof #1185.
% 203.09/34.15  | | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | |   (150)  all_56_6 = e1 | all_56_6 = e0
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (99), (122), (150) are inconsistent by
% 203.09/34.15  | | | | | | | | | | | | | | | | |            sub-proof #757.
% 203.09/34.15  | | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | |   (151)   ~ (all_58_2 = e0)
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | REDUCE: (90), (151) imply:
% 203.09/34.15  | | | | | | | | | | | |   (152)   ~ (all_6_1 = e0)
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | | REF_CLOSE: (33), (88), (95), (113), (152) are inconsistent by
% 203.09/34.15  | | | | | | | | | | | |            sub-proof #1216.
% 203.09/34.15  | | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | Case 2:
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | |   (153)   ~ (all_58_6 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | REDUCE: (45), (153) imply:
% 203.09/34.15  | | | | | | | | | |   (154)   ~ (all_52_5 = e1)
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | | REF_CLOSE: (2), (20), (22), (23), (79), (80), (97), (101),
% 203.09/34.15  | | | | | | | | | |            (154) are inconsistent by sub-proof #471.
% 203.09/34.15  | | | | | | | | | | 
% 203.09/34.15  | | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | | 
% 203.09/34.15  | | | | | | | | End of split
% 203.09/34.15  | | | | | | | | 
% 203.09/34.15  | | | | | | | End of split
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | Case 2:
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | |   (155)  all_58_15 = e2
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | | REF_CLOSE: (17), (28), (155) are inconsistent by sub-proof #1223.
% 203.09/34.15  | | | | | | | 
% 203.09/34.15  | | | | | | End of split
% 203.09/34.15  | | | | | | 
% 203.09/34.15  | | | | | End of split
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | Case 2:
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | |   (156)  all_56_3 = e0
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | | REF_CLOSE: (18), (43), (156) are inconsistent by sub-proof #1258.
% 203.09/34.15  | | | | | 
% 203.09/34.15  | | | | End of split
% 203.09/34.15  | | | | 
% 203.09/34.15  | | | End of split
% 203.09/34.15  | | | 
% 203.09/34.15  | | End of split
% 203.09/34.15  | | 
% 203.09/34.15  | End of split
% 203.09/34.15  | 
% 203.09/34.15  End of proof
% 203.09/34.15  
% 203.09/34.15  Sub-proof #471 shows that the following formulas are inconsistent:
% 203.09/34.15  ----------------------------------------------------------------
% 203.09/34.15    (1)   ~ (all_52_5 = all_52_13)
% 203.09/34.15    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.09/34.15    (3)   ~ (all_52_5 = e1)
% 203.09/34.15    (4)  all_56_9 = all_52_13
% 203.09/34.15    (5)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.09/34.15    (6)  all_56_8 = all_52_5
% 203.09/34.15    (7)   ~ (all_52_13 = e1)
% 203.09/34.15    (8)   ~ (all_52_5 = e2)
% 203.09/34.15    (9)   ~ (all_52_13 = e2)
% 203.09/34.15  
% 203.09/34.15  Begin of proof
% 203.09/34.15  | 
% 203.09/34.15  | BETA: splitting (2) gives:
% 203.09/34.15  | 
% 203.09/34.15  | Case 1:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (10)  all_56_9 = e2
% 203.09/34.15  | | 
% 203.09/34.15  | | REF_CLOSE: (4), (9), (10) are inconsistent by sub-proof #955.
% 203.09/34.15  | | 
% 203.09/34.15  | Case 2:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (11)  all_56_9 = e1 | all_56_9 = e0
% 203.09/34.15  | | 
% 203.09/34.15  | | BETA: splitting (11) gives:
% 203.09/34.15  | | 
% 203.09/34.15  | | Case 1:
% 203.09/34.15  | | | 
% 203.09/34.15  | | |   (12)  all_56_9 = e1
% 203.09/34.15  | | | 
% 203.09/34.15  | | | COMBINE_EQS: (4), (12) imply:
% 203.09/34.15  | | |   (13)  all_52_13 = e1
% 203.09/34.15  | | | 
% 203.09/34.15  | | | SIMP: (13) implies:
% 203.09/34.15  | | |   (14)  all_52_13 = e1
% 203.09/34.15  | | | 
% 203.09/34.15  | | | REDUCE: (7), (14) imply:
% 203.09/34.15  | | |   (15)  $false
% 203.09/34.15  | | | 
% 203.09/34.15  | | | CLOSE: (15) is inconsistent.
% 203.09/34.15  | | | 
% 203.09/34.15  | | Case 2:
% 203.09/34.15  | | | 
% 203.09/34.15  | | |   (16)  all_56_9 = e0
% 203.09/34.15  | | | 
% 203.09/34.15  | | | COMBINE_EQS: (4), (16) imply:
% 203.09/34.15  | | |   (17)  all_52_13 = e0
% 203.09/34.15  | | | 
% 203.09/34.15  | | | SIMP: (17) implies:
% 203.09/34.15  | | |   (18)  all_52_13 = e0
% 203.09/34.15  | | | 
% 203.09/34.15  | | | REDUCE: (1), (18) imply:
% 203.09/34.15  | | |   (19)   ~ (all_52_5 = e0)
% 203.09/34.15  | | | 
% 203.09/34.15  | | | REF_CLOSE: (3), (5), (6), (8), (19) are inconsistent by sub-proof #1004.
% 203.09/34.15  | | | 
% 203.09/34.15  | | End of split
% 203.09/34.15  | | 
% 203.09/34.15  | End of split
% 203.09/34.15  | 
% 203.09/34.15  End of proof
% 203.09/34.15  
% 203.09/34.15  Sub-proof #472 shows that the following formulas are inconsistent:
% 203.09/34.15  ----------------------------------------------------------------
% 203.09/34.15    (1)  all_58_5 = e1
% 203.09/34.15    (2)  all_58_5 = e2 | all_58_10 = e2
% 203.09/34.15    (3)   ~ (e2 = e1)
% 203.09/34.15    (4)  all_58_10 = e3
% 203.09/34.15    (5)   ~ (e3 = e2)
% 203.09/34.15  
% 203.09/34.15  Begin of proof
% 203.09/34.15  | 
% 203.09/34.15  | BETA: splitting (2) gives:
% 203.09/34.15  | 
% 203.09/34.15  | Case 1:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (6)  all_58_5 = e2
% 203.09/34.15  | | 
% 203.09/34.15  | | COMBINE_EQS: (1), (6) imply:
% 203.09/34.15  | |   (7)  e2 = e1
% 203.09/34.15  | | 
% 203.09/34.15  | | REDUCE: (3), (7) imply:
% 203.09/34.15  | |   (8)  $false
% 203.09/34.15  | | 
% 203.09/34.15  | | CLOSE: (8) is inconsistent.
% 203.09/34.15  | | 
% 203.09/34.15  | Case 2:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (9)  all_58_10 = e2
% 203.09/34.15  | | 
% 203.09/34.15  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #1220.
% 203.09/34.15  | | 
% 203.09/34.15  | End of split
% 203.09/34.15  | 
% 203.09/34.15  End of proof
% 203.09/34.15  
% 203.09/34.15  Sub-proof #473 shows that the following formulas are inconsistent:
% 203.09/34.15  ----------------------------------------------------------------
% 203.09/34.15    (1)   ~ (all_52_25 = all_52_27)
% 203.09/34.15    (2)  op(all_52_3, all_52_3) = all_52_2
% 203.09/34.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.09/34.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.09/34.15    (4)  all_58_1 = all_52_9
% 203.09/34.15    (5)  op(all_52_7, all_52_7) = all_52_6
% 203.09/34.15    (6)   ~ (all_52_17 = all_52_25)
% 203.09/34.15    (7)   ~ (all_52_3 = all_6_2)
% 203.09/34.15    (8)  all_44_2 = all_6_2
% 203.09/34.15    (9)  all_58_0 = all_6_2
% 203.09/34.15    (10)   ~ (all_52_17 = all_10_2)
% 203.09/34.15    (11)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 203.09/34.15    (12)  op(all_52_19, all_52_19) = all_52_18
% 203.09/34.15    (13)  all_58_9 = all_52_25
% 203.09/34.15    (14)   ~ (all_52_29 = all_14_2)
% 203.09/34.15    (15)  op(e1, e3) = all_52_5
% 203.09/34.15    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.09/34.15    (17)   ~ (all_52_3 = all_52_5)
% 203.09/34.15    (18)  all_58_11 = all_52_29
% 203.09/34.15    (19)  all_56_13 = e3
% 203.09/34.15    (20)   ~ (all_52_9 = all_52_15)
% 203.09/34.15    (21)  op(e0, e0) = all_14_2
% 203.09/34.15    (22)  op(all_52_29, all_52_29) = e1
% 203.09/34.15    (23)   ~ (all_52_15 = e0)
% 203.09/34.15    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.09/34.15    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.09/34.15    (26)  all_58_10 = all_52_27
% 203.09/34.15    (27)  all_56_8 = all_52_5
% 203.09/34.15    (28)   ~ (all_52_25 = all_52_29)
% 203.09/34.15    (29)  all_58_7 = all_52_13
% 203.09/34.15    (30)   ~ (all_52_5 = all_52_7)
% 203.09/34.15    (31)  all_58_12 = all_52_7
% 203.09/34.15    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.09/34.15    (33)  all_58_2 = all_52_3
% 203.09/34.15    (34)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.09/34.15    (35)  op(all_52_25, all_52_25) = e3
% 203.09/34.15    (36)   ~ (all_52_5 = all_52_29)
% 203.09/34.15    (37)  all_56_6 = all_52_19
% 203.09/34.15    (38)  op(all_52_27, all_52_27) = e2
% 203.09/34.15    (39)   ~ (all_52_9 = all_52_25)
% 203.09/34.15    (40)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.09/34.15    (41)  all_58_8 = all_10_2
% 203.09/34.15    (42)  op(all_52_17, all_52_17) = all_52_16
% 203.09/34.15    (43)   ~ (all_52_25 = all_6_2)
% 203.09/34.15    (44)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.09/34.15    (45)   ~ (all_52_5 = all_6_2)
% 203.09/34.15    (46)   ~ (all_52_13 = all_52_15)
% 203.09/34.15    (47)  op(e3, all_6_1) = e2
% 203.09/34.15    (48)  op(e3, e3) = all_6_2
% 203.09/34.15    (49)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.09/34.15    (50)   ~ (all_52_27 = all_14_2)
% 203.09/34.15    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.09/34.15    (52)  all_56_3 = all_52_25
% 203.09/34.15    (53)  all_58_5 = all_52_19
% 203.09/34.15    (54)   ~ (all_52_15 = all_4_2)
% 203.09/34.15    (55)  all_58_6 = all_52_5
% 203.09/34.15    (56)  op(e3, e2) = all_52_9
% 203.09/34.15    (57)   ~ (e1 = e0)
% 203.09/34.15    (58)   ~ (e3 = e2)
% 203.09/34.15    (59)  all_44_1 = all_6_1
% 203.09/34.15    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.09/34.15    (61)  op(e1, e1) = all_10_2
% 203.09/34.15    (62)   ~ (all_52_17 = all_52_19)
% 203.09/34.15    (63)  all_58_3 = all_4_2
% 203.09/34.15    (64)  all_56_13 = all_52_15
% 203.09/34.15    (65)  op(all_6_2, e3) = all_6_1
% 203.09/34.15    (66)  all_58_4 = all_52_17
% 203.09/34.15  
% 203.09/34.15  Begin of proof
% 203.09/34.15  | 
% 203.09/34.15  | COMBINE_EQS: (19), (64) imply:
% 203.09/34.15  |   (67)  all_52_15 = e3
% 203.09/34.15  | 
% 203.09/34.15  | SIMP: (67) implies:
% 203.09/34.15  |   (68)  all_52_15 = e3
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (20), (68) imply:
% 203.09/34.15  |   (69)   ~ (all_52_9 = e3)
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (46), (68) imply:
% 203.09/34.15  |   (70)   ~ (all_52_13 = e3)
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (54), (68) imply:
% 203.09/34.15  |   (71)   ~ (all_4_2 = e3)
% 203.09/34.15  | 
% 203.09/34.15  | SIMP: (71) implies:
% 203.09/34.15  |   (72)   ~ (all_4_2 = e3)
% 203.09/34.15  | 
% 203.09/34.15  | REDUCE: (23), (68) imply:
% 203.09/34.15  |   (73)   ~ (e3 = e0)
% 203.09/34.15  | 
% 203.09/34.15  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.09/34.15  |            (13), (14), (15), (16), (17), (18), (21), (22), (24), (25), (26),
% 203.09/34.15  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 203.09/34.15  |            (38), (39), (40), (41), (42), (43), (44), (45), (47), (48), (49),
% 203.09/34.15  |            (50), (51), (52), (53), (55), (56), (57), (58), (59), (60), (61),
% 203.09/34.15  |            (62), (63), (65), (66), (69), (70), (72), (73) are inconsistent by
% 203.09/34.15  |            sub-proof #474.
% 203.09/34.15  | 
% 203.09/34.15  End of proof
% 203.09/34.15  
% 203.09/34.15  Sub-proof #474 shows that the following formulas are inconsistent:
% 203.09/34.15  ----------------------------------------------------------------
% 203.09/34.15    (1)   ~ (all_52_25 = all_52_27)
% 203.09/34.15    (2)  op(all_52_3, all_52_3) = all_52_2
% 203.09/34.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.09/34.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.09/34.15    (4)  all_58_1 = all_52_9
% 203.09/34.15    (5)   ~ (e3 = e0)
% 203.09/34.15    (6)  op(all_52_7, all_52_7) = all_52_6
% 203.09/34.15    (7)   ~ (all_52_17 = all_52_25)
% 203.09/34.15    (8)   ~ (all_4_2 = e3)
% 203.09/34.15    (9)   ~ (all_52_3 = all_6_2)
% 203.09/34.15    (10)  all_44_2 = all_6_2
% 203.09/34.15    (11)  all_58_0 = all_6_2
% 203.09/34.15    (12)   ~ (all_52_17 = all_10_2)
% 203.09/34.15    (13)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 203.09/34.15    (14)  op(all_52_19, all_52_19) = all_52_18
% 203.09/34.15    (15)  all_58_9 = all_52_25
% 203.09/34.15    (16)   ~ (all_52_29 = all_14_2)
% 203.09/34.15    (17)  op(e1, e3) = all_52_5
% 203.09/34.15    (18)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.09/34.15    (19)   ~ (all_52_3 = all_52_5)
% 203.09/34.15    (20)  all_58_11 = all_52_29
% 203.09/34.15    (21)  op(e0, e0) = all_14_2
% 203.09/34.15    (22)  op(all_52_29, all_52_29) = e1
% 203.09/34.15    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.09/34.15    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.09/34.15    (25)  all_58_10 = all_52_27
% 203.09/34.15    (26)  all_56_8 = all_52_5
% 203.09/34.15    (27)   ~ (all_52_25 = all_52_29)
% 203.09/34.15    (28)  all_58_7 = all_52_13
% 203.09/34.15    (29)   ~ (all_52_5 = all_52_7)
% 203.09/34.15    (30)  all_58_12 = all_52_7
% 203.09/34.15    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.09/34.15    (32)  all_58_2 = all_52_3
% 203.09/34.15    (33)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.09/34.15    (34)  op(all_52_25, all_52_25) = e3
% 203.09/34.15    (35)   ~ (all_52_5 = all_52_29)
% 203.09/34.15    (36)  all_56_6 = all_52_19
% 203.09/34.15    (37)   ~ (all_52_9 = e3)
% 203.09/34.15    (38)  op(all_52_27, all_52_27) = e2
% 203.09/34.15    (39)   ~ (all_52_9 = all_52_25)
% 203.09/34.15    (40)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.09/34.15    (41)  all_58_8 = all_10_2
% 203.09/34.15    (42)  op(all_52_17, all_52_17) = all_52_16
% 203.09/34.15    (43)   ~ (all_52_25 = all_6_2)
% 203.09/34.15    (44)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.09/34.15    (45)   ~ (all_52_5 = all_6_2)
% 203.09/34.15    (46)  op(e3, all_6_1) = e2
% 203.09/34.15    (47)  op(e3, e3) = all_6_2
% 203.09/34.15    (48)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.09/34.15    (49)   ~ (all_52_13 = e3)
% 203.09/34.15    (50)   ~ (all_52_27 = all_14_2)
% 203.09/34.15    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.09/34.15    (52)  all_56_3 = all_52_25
% 203.09/34.15    (53)  all_58_5 = all_52_19
% 203.09/34.15    (54)  all_58_6 = all_52_5
% 203.09/34.15    (55)  op(e3, e2) = all_52_9
% 203.09/34.15    (56)   ~ (e1 = e0)
% 203.09/34.15    (57)   ~ (e3 = e2)
% 203.09/34.15    (58)  all_44_1 = all_6_1
% 203.09/34.15    (59)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.09/34.15    (60)  op(e1, e1) = all_10_2
% 203.09/34.15    (61)   ~ (all_52_17 = all_52_19)
% 203.09/34.15    (62)  all_58_3 = all_4_2
% 203.09/34.15    (63)  op(all_6_2, e3) = all_6_1
% 203.09/34.15    (64)  all_58_4 = all_52_17
% 203.09/34.15  
% 203.09/34.15  Begin of proof
% 203.09/34.15  | 
% 203.09/34.15  | BETA: splitting (33) gives:
% 203.09/34.15  | 
% 203.09/34.15  | Case 1:
% 203.09/34.15  | | 
% 203.09/34.15  | |   (65)  all_56_6 = e3
% 203.09/34.15  | | 
% 203.09/34.15  | | COMBINE_EQS: (36), (65) imply:
% 203.09/34.15  | |   (66)  all_52_19 = e3
% 203.09/34.15  | | 
% 203.09/34.15  | | SIMP: (66) implies:
% 203.09/34.15  | |   (67)  all_52_19 = e3
% 203.09/34.15  | | 
% 203.09/34.15  | | REDUCE: (61), (67) imply:
% 203.09/34.15  | |   (68)   ~ (all_52_17 = e3)
% 203.09/34.15  | | 
% 203.09/34.15  | | REDUCE: (14), (67) imply:
% 203.09/34.15  | |   (69)  op(e3, e3) = all_52_18
% 203.09/34.15  | | 
% 203.09/34.15  | | GROUND_INST: instantiating (3) with all_6_2, all_52_18, e3, e3, simplifying
% 203.09/34.15  | |              with (47), (69) gives:
% 203.09/34.15  | |   (70)  all_52_18 = all_6_2
% 203.09/34.15  | | 
% 203.09/34.15  | | BETA: splitting (48) gives:
% 203.09/34.15  | | 
% 203.09/34.15  | | Case 1:
% 203.09/34.15  | | | 
% 203.09/34.15  | | |   (71)  all_58_9 = e3
% 203.09/34.15  | | | 
% 203.09/34.15  | | | COMBINE_EQS: (15), (71) imply:
% 203.09/34.15  | | |   (72)  all_52_25 = e3
% 203.09/34.15  | | | 
% 203.09/34.15  | | | REF_CLOSE: (3), (34), (43), (47), (72) are inconsistent by sub-proof
% 203.09/34.15  | | |            #1246.
% 203.09/34.15  | | | 
% 203.09/34.15  | | Case 2:
% 203.09/34.15  | | | 
% 203.09/34.16  | | |   (73)   ~ (all_58_9 = e3)
% 203.09/34.16  | | | 
% 203.09/34.16  | | | REDUCE: (15), (73) imply:
% 203.09/34.16  | | |   (74)   ~ (all_52_25 = e3)
% 203.09/34.16  | | | 
% 203.09/34.16  | | | REF_CLOSE: (3), (4), (11), (15), (37), (46), (47), (51), (57), (63), (64),
% 203.09/34.16  | | |            (68), (74) are inconsistent by sub-proof #476.
% 203.09/34.16  | | | 
% 203.09/34.16  | | End of split
% 203.09/34.16  | | 
% 203.09/34.16  | Case 2:
% 203.09/34.16  | | 
% 203.09/34.16  | |   (75)   ~ (all_56_6 = e3)
% 203.09/34.16  | | 
% 203.09/34.16  | | REDUCE: (36), (75) imply:
% 203.09/34.16  | |   (76)   ~ (all_52_19 = e3)
% 203.09/34.16  | | 
% 203.09/34.16  | | BETA: splitting (23) gives:
% 203.09/34.16  | | 
% 203.09/34.16  | | Case 1:
% 203.09/34.16  | | | 
% 203.09/34.16  | | |   (77)  all_58_2 = e3
% 203.09/34.16  | | | 
% 203.09/34.16  | | | COMBINE_EQS: (32), (77) imply:
% 203.09/34.16  | | |   (78)  all_52_3 = e3
% 203.09/34.16  | | | 
% 203.09/34.16  | | | SIMP: (78) implies:
% 203.09/34.16  | | |   (79)  all_52_3 = e3
% 203.09/34.16  | | | 
% 203.09/34.16  | | | REDUCE: (19), (79) imply:
% 203.09/34.16  | | |   (80)   ~ (all_52_5 = e3)
% 203.09/34.16  | | | 
% 203.09/34.16  | | | SIMP: (80) implies:
% 203.09/34.16  | | |   (81)   ~ (all_52_5 = e3)
% 203.09/34.16  | | | 
% 203.09/34.16  | | | REDUCE: (9), (79) imply:
% 203.09/34.16  | | |   (82)   ~ (all_6_2 = e3)
% 203.09/34.16  | | | 
% 203.09/34.16  | | | SIMP: (82) implies:
% 203.09/34.16  | | |   (83)   ~ (all_6_2 = e3)
% 203.09/34.16  | | | 
% 203.09/34.16  | | | REDUCE: (2), (79) imply:
% 203.09/34.16  | | |   (84)  op(e3, e3) = all_52_2
% 203.09/34.16  | | | 
% 203.09/34.16  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_2, e3, e3, simplifying
% 203.09/34.16  | | |              with (47), (84) gives:
% 203.09/34.16  | | |   (85)  all_52_2 = all_6_2
% 203.09/34.16  | | | 
% 203.09/34.16  | | | BETA: splitting (59) gives:
% 203.09/34.16  | | | 
% 203.09/34.16  | | | Case 1:
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | |   (86)  all_58_4 = e3
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | COMBINE_EQS: (64), (86) imply:
% 203.09/34.16  | | | |   (87)  all_52_17 = e3
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | SIMP: (87) implies:
% 203.09/34.16  | | | |   (88)  all_52_17 = e3
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | REDUCE: (12), (88) imply:
% 203.09/34.16  | | | |   (89)   ~ (all_10_2 = e3)
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | SIMP: (89) implies:
% 203.09/34.16  | | | |   (90)   ~ (all_10_2 = e3)
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | REDUCE: (42), (88) imply:
% 203.09/34.16  | | | |   (91)  op(e3, e3) = all_52_16
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | BETA: splitting (31) gives:
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | Case 1:
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | |   (92)  all_58_6 = e3
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | | REF_CLOSE: (54), (81), (92) are inconsistent by sub-proof #1328.
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | Case 2:
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | |   (93)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | | BETA: splitting (93) gives:
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | | Case 1:
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | |   (94)  all_58_7 = e3
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | | COMBINE_EQS: (28), (94) imply:
% 203.09/34.16  | | | | | |   (95)  all_52_13 = e3
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | | REDUCE: (49), (95) imply:
% 203.09/34.16  | | | | | |   (96)  $false
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | | CLOSE: (96) is inconsistent.
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | Case 2:
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | |   (97)  all_58_8 = e3 | all_58_11 = e3
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | | BETA: splitting (97) gives:
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | | Case 1:
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | |   (98)  all_58_8 = e3
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | COMBINE_EQS: (41), (98) imply:
% 203.09/34.16  | | | | | | |   (99)  all_10_2 = e3
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (90), (99) imply:
% 203.09/34.16  | | | | | | |   (100)  $false
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | CLOSE: (100) is inconsistent.
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | Case 2:
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | |   (101)  all_58_11 = e3
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | COMBINE_EQS: (20), (101) imply:
% 203.09/34.16  | | | | | | |   (102)  all_52_29 = e3
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | SIMP: (102) implies:
% 203.09/34.16  | | | | | | |   (103)  all_52_29 = e3
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (27), (103) imply:
% 203.09/34.16  | | | | | | |   (104)   ~ (all_52_25 = e3)
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (16), (103) imply:
% 203.09/34.16  | | | | | | |   (105)   ~ (all_14_2 = e3)
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | SIMP: (105) implies:
% 203.09/34.16  | | | | | | |   (106)   ~ (all_14_2 = e3)
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (22), (103) imply:
% 203.09/34.16  | | | | | | |   (107)  op(e3, e3) = e1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_16, e3, e3,
% 203.09/34.16  | | | | | | |              simplifying with (47), (91) gives:
% 203.09/34.16  | | | | | | |   (108)  all_52_16 = all_6_2
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_16, e3, e3,
% 203.09/34.16  | | | | | | |              simplifying with (91), (107) gives:
% 203.09/34.16  | | | | | | |   (109)  all_52_16 = e1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | COMBINE_EQS: (108), (109) imply:
% 203.09/34.16  | | | | | | |   (110)  all_6_2 = e1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | SIMP: (110) implies:
% 203.09/34.16  | | | | | | |   (111)  all_6_2 = e1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | COMBINE_EQS: (10), (111) imply:
% 203.09/34.16  | | | | | | |   (112)  all_44_2 = e1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | COMBINE_EQS: (11), (111) imply:
% 203.09/34.16  | | | | | | |   (113)  all_58_0 = e1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (45), (111) imply:
% 203.09/34.16  | | | | | | |   (114)   ~ (all_52_5 = e1)
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (43), (111) imply:
% 203.09/34.16  | | | | | | |   (115)   ~ (all_52_25 = e1)
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | REDUCE: (63), (111) imply:
% 203.09/34.16  | | | | | | |   (116)  op(e1, e3) = all_6_1
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | BETA: splitting (13) gives:
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | | Case 1:
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | |   (117)   ~ (all_44_2 = e1)
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | | REDUCE: (112), (117) imply:
% 203.09/34.16  | | | | | | | |   (118)  $false
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | | CLOSE: (118) is inconsistent.
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | Case 2:
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | |   (119)   ~ (all_44_1 = e0)
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | | REDUCE: (58), (119) imply:
% 203.09/34.16  | | | | | | | |   (120)   ~ (all_6_1 = e0)
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | | REF_CLOSE: (3), (5), (6), (17), (18), (21), (26), (29), (30),
% 203.09/34.16  | | | | | | | |            (34), (39), (40), (44), (46), (52), (54), (55), (56),
% 203.09/34.16  | | | | | | | |            (77), (81), (104), (106), (113), (114), (115), (116),
% 203.09/34.16  | | | | | | | |            (120) are inconsistent by sub-proof #475.
% 203.09/34.16  | | | | | | | | 
% 203.09/34.16  | | | | | | | End of split
% 203.09/34.16  | | | | | | | 
% 203.09/34.16  | | | | | | End of split
% 203.09/34.16  | | | | | | 
% 203.09/34.16  | | | | | End of split
% 203.09/34.16  | | | | | 
% 203.09/34.16  | | | | End of split
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | Case 2:
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | |   (121)   ~ (all_58_4 = e3)
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | REDUCE: (64), (121) imply:
% 203.09/34.16  | | | |   (122)   ~ (all_52_17 = e3)
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | | REF_CLOSE: (3), (4), (11), (15), (34), (37), (43), (47), (48), (51),
% 203.09/34.16  | | | |            (64), (83), (122) are inconsistent by sub-proof #1013.
% 203.09/34.16  | | | | 
% 203.09/34.16  | | | End of split
% 203.09/34.16  | | | 
% 203.09/34.16  | | Case 2:
% 203.09/34.16  | | | 
% 203.09/34.16  | | |   (123)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.09/34.16  | | | 
% 203.09/34.16  | | | REF_CLOSE: (1), (3), (4), (7), (8), (11), (12), (15), (21), (24), (25),
% 203.09/34.16  | | |            (34), (37), (38), (43), (44), (47), (50), (51), (52), (53),
% 203.09/34.16  | | |            (57), (60), (62), (64), (76), (123) are inconsistent by
% 203.09/34.16  | | |            sub-proof #1228.
% 203.09/34.16  | | | 
% 203.09/34.16  | | End of split
% 203.09/34.16  | | 
% 203.09/34.16  | End of split
% 203.09/34.16  | 
% 203.09/34.16  End of proof
% 203.09/34.16  
% 203.09/34.16  Sub-proof #475 shows that the following formulas are inconsistent:
% 203.09/34.16  ----------------------------------------------------------------
% 203.09/34.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.09/34.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.09/34.16    (2)   ~ (e3 = e0)
% 203.09/34.16    (3)  op(all_52_7, all_52_7) = all_52_6
% 203.09/34.16    (4)   ~ (all_52_5 = e1)
% 203.09/34.16    (5)  op(e1, e3) = all_52_5
% 203.09/34.16    (6)   ~ (all_6_1 = e0)
% 203.09/34.16    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.09/34.16    (8)  op(e0, e0) = all_14_2
% 203.09/34.16    (9)  op(e1, e3) = all_6_1
% 203.09/34.16    (10)  all_56_8 = all_52_5
% 203.09/34.16    (11)   ~ (all_52_5 = all_52_7)
% 203.13/34.16    (12)  all_58_12 = all_52_7
% 203.13/34.16    (13)   ~ (all_52_25 = e3)
% 203.13/34.16    (14)   ~ (all_52_5 = e3)
% 203.13/34.16    (15)  op(all_52_25, all_52_25) = e3
% 203.13/34.16    (16)   ~ (all_52_9 = all_52_25)
% 203.13/34.16    (17)   ~ (all_52_25 = e1)
% 203.13/34.16    (18)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.16    (19)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.16    (20)  op(e3, all_6_1) = e2
% 203.13/34.16    (21)  all_56_3 = all_52_25
% 203.13/34.16    (22)  all_58_6 = all_52_5
% 203.13/34.16    (23)  op(e3, e2) = all_52_9
% 203.13/34.16    (24)   ~ (e1 = e0)
% 203.13/34.16    (25)  all_58_2 = e3
% 203.13/34.16    (26)  all_58_0 = e1
% 203.13/34.16    (27)   ~ (all_14_2 = e3)
% 203.13/34.16  
% 203.13/34.16  Begin of proof
% 203.13/34.16  | 
% 203.13/34.16  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 203.13/34.16  |              with (5), (9) gives:
% 203.13/34.16  |   (28)  all_52_5 = all_6_1
% 203.13/34.16  | 
% 203.13/34.16  | COMBINE_EQS: (10), (28) imply:
% 203.13/34.16  |   (29)  all_56_8 = all_6_1
% 203.13/34.16  | 
% 203.13/34.16  | COMBINE_EQS: (22), (28) imply:
% 203.13/34.16  |   (30)  all_58_6 = all_6_1
% 203.13/34.16  | 
% 203.13/34.16  | REDUCE: (11), (28) imply:
% 203.13/34.16  |   (31)   ~ (all_52_7 = all_6_1)
% 203.13/34.16  | 
% 203.13/34.16  | SIMP: (31) implies:
% 203.13/34.16  |   (32)   ~ (all_52_7 = all_6_1)
% 203.13/34.16  | 
% 203.13/34.16  | REDUCE: (14), (28) imply:
% 203.13/34.16  |   (33)   ~ (all_6_1 = e3)
% 203.13/34.16  | 
% 203.13/34.16  | REDUCE: (4), (28) imply:
% 203.13/34.16  |   (34)   ~ (all_6_1 = e1)
% 203.13/34.16  | 
% 203.13/34.16  | BETA: splitting (18) gives:
% 203.13/34.16  | 
% 203.13/34.16  | Case 1:
% 203.13/34.16  | | 
% 203.13/34.16  | |   (35)  all_56_8 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | REF_CLOSE: (29), (33), (35) are inconsistent by sub-proof #1101.
% 203.13/34.16  | | 
% 203.13/34.16  | Case 2:
% 203.13/34.16  | | 
% 203.13/34.16  | |   (36)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.16  | | 
% 203.13/34.16  | | BETA: splitting (7) gives:
% 203.13/34.16  | | 
% 203.13/34.16  | | Case 1:
% 203.13/34.16  | | | 
% 203.13/34.16  | | |   (37)  all_58_0 = e0
% 203.13/34.16  | | | 
% 203.13/34.16  | | | COMBINE_EQS: (26), (37) imply:
% 203.13/34.16  | | |   (38)  e1 = e0
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REDUCE: (24), (38) imply:
% 203.13/34.16  | | |   (39)  $false
% 203.13/34.16  | | | 
% 203.13/34.16  | | | CLOSE: (39) is inconsistent.
% 203.13/34.16  | | | 
% 203.13/34.16  | | Case 2:
% 203.13/34.16  | | | 
% 203.13/34.16  | | |   (40)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.16  | | | 
% 203.13/34.16  | | | BETA: splitting (40) gives:
% 203.13/34.16  | | | 
% 203.13/34.16  | | | Case 1:
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | |   (41)  all_58_2 = e0
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | REF_CLOSE: (2), (25), (41) are inconsistent by sub-proof #1123.
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | Case 2:
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | |   (42)  all_58_6 = e0 | all_58_12 = e0
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | BETA: splitting (42) gives:
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | Case 1:
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | |   (43)  all_58_6 = e0
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | REF_CLOSE: (6), (30), (43) are inconsistent by sub-proof #486.
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | Case 2:
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | |   (44)  all_58_12 = e0
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | COMBINE_EQS: (12), (44) imply:
% 203.13/34.16  | | | | |   (45)  all_52_7 = e0
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | SIMP: (45) implies:
% 203.13/34.16  | | | | |   (46)  all_52_7 = e0
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | REDUCE: (32), (46) imply:
% 203.13/34.16  | | | | |   (47)   ~ (all_6_1 = e0)
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | REDUCE: (3), (46) imply:
% 203.13/34.16  | | | | |   (48)  op(e0, e0) = all_52_6
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | BETA: splitting (36) gives:
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | Case 1:
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | |   (49)  all_56_8 = e2
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | COMBINE_EQS: (29), (49) imply:
% 203.13/34.16  | | | | | |   (50)  all_6_1 = e2
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | SIMP: (50) implies:
% 203.13/34.16  | | | | | |   (51)  all_6_1 = e2
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | REDUCE: (20), (51) imply:
% 203.13/34.16  | | | | | |   (52)  op(e3, e2) = e2
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | GROUND_INST: instantiating (1) with all_14_2, all_52_6, e0, e0,
% 203.13/34.16  | | | | | |              simplifying with (8), (48) gives:
% 203.13/34.16  | | | | | |   (53)  all_52_6 = all_14_2
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | GROUND_INST: instantiating (1) with all_52_9, e2, e2, e3,
% 203.13/34.16  | | | | | |              simplifying with (23), (52) gives:
% 203.13/34.16  | | | | | |   (54)  all_52_9 = e2
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | REDUCE: (16), (54) imply:
% 203.13/34.16  | | | | | |   (55)   ~ (all_52_25 = e2)
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | SIMP: (55) implies:
% 203.13/34.16  | | | | | |   (56)   ~ (all_52_25 = e2)
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | BETA: splitting (19) gives:
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | Case 1:
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | |   (57)  all_56_3 = e3
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | COMBINE_EQS: (21), (57) imply:
% 203.13/34.16  | | | | | | |   (58)  all_52_25 = e3
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | REDUCE: (13), (58) imply:
% 203.13/34.16  | | | | | | |   (59)  $false
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | CLOSE: (59) is inconsistent.
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | Case 2:
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | |   (60)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | REF_CLOSE: (1), (8), (15), (17), (21), (27), (56), (60) are
% 203.13/34.16  | | | | | | |            inconsistent by sub-proof #1233.
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | End of split
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | Case 2:
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | |   (61)  all_56_8 = e1 | all_56_8 = e0
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | REF_CLOSE: (6), (29), (34), (61) are inconsistent by sub-proof #495.
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | End of split
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | End of split
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | End of split
% 203.13/34.16  | | | 
% 203.13/34.16  | | End of split
% 203.13/34.16  | | 
% 203.13/34.16  | End of split
% 203.13/34.16  | 
% 203.13/34.16  End of proof
% 203.13/34.16  
% 203.13/34.16  Sub-proof #476 shows that the following formulas are inconsistent:
% 203.13/34.16  ----------------------------------------------------------------
% 203.13/34.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.16    (2)  all_58_1 = all_52_9
% 203.13/34.16    (3)  all_58_0 = all_6_2
% 203.13/34.16    (4)  all_58_9 = all_52_25
% 203.13/34.16    (5)   ~ (all_52_25 = e3)
% 203.13/34.16    (6)   ~ (all_52_9 = e3)
% 203.13/34.16    (7)  op(e3, all_6_1) = e2
% 203.13/34.16    (8)  op(e3, e3) = all_6_2
% 203.13/34.16    (9)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.16    (10)   ~ (all_52_17 = e3)
% 203.13/34.16    (11)   ~ (e3 = e2)
% 203.13/34.16    (12)  op(all_6_2, e3) = all_6_1
% 203.13/34.16    (13)  all_58_4 = all_52_17
% 203.13/34.16  
% 203.13/34.16  Begin of proof
% 203.13/34.16  | 
% 203.13/34.16  | BETA: splitting (9) gives:
% 203.13/34.16  | 
% 203.13/34.16  | Case 1:
% 203.13/34.16  | | 
% 203.13/34.16  | |   (14)  all_58_0 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | COMBINE_EQS: (3), (14) imply:
% 203.13/34.16  | |   (15)  all_6_2 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | REF_CLOSE: (1), (7), (8), (11), (12), (15) are inconsistent by sub-proof
% 203.13/34.16  | |            #502.
% 203.13/34.16  | | 
% 203.13/34.16  | Case 2:
% 203.13/34.16  | | 
% 203.13/34.16  | |   (16)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | REF_CLOSE: (2), (4), (5), (6), (10), (13), (16) are inconsistent by
% 203.13/34.16  | |            sub-proof #744.
% 203.13/34.16  | | 
% 203.13/34.16  | End of split
% 203.13/34.16  | 
% 203.13/34.16  End of proof
% 203.13/34.16  
% 203.13/34.16  Sub-proof #477 shows that the following formulas are inconsistent:
% 203.13/34.16  ----------------------------------------------------------------
% 203.13/34.16    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.16    (2)  all_58_14 = all_52_23
% 203.13/34.16    (3)   ~ (e3 = e1)
% 203.13/34.16    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.13/34.16    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.16    (6)  all_58_1 = all_52_9
% 203.13/34.16    (7)   ~ (all_52_9 = all_52_13)
% 203.13/34.16    (8)   ~ (e3 = e0)
% 203.13/34.16    (9)  op(all_52_23, all_52_23) = e0
% 203.13/34.16    (10)  op(e2, e3) = all_52_3
% 203.13/34.16    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.16    (12)   ~ (all_52_7 = all_52_15)
% 203.13/34.16    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.16    (14)   ~ (all_52_17 = all_52_25)
% 203.13/34.16    (15)   ~ (all_52_3 = all_6_2)
% 203.13/34.16    (16)  all_44_2 = all_6_2
% 203.13/34.16    (17)  all_58_0 = all_6_2
% 203.13/34.16    (18)  all_56_4 = all_52_3
% 203.13/34.16    (19)   ~ (all_52_17 = all_10_2)
% 203.13/34.16    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 203.13/34.16    (21)  op(e3, e0) = all_52_25
% 203.13/34.16    (22)  all_58_13 = all_52_15
% 203.13/34.16    (23)  all_58_9 = all_52_25
% 203.13/34.16    (24)   ~ (all_52_15 = e3)
% 203.13/34.16    (25)  op(e1, e3) = all_52_5
% 203.13/34.16    (26)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.16    (27)   ~ (all_52_3 = all_52_5)
% 203.13/34.16    (28)  all_58_11 = all_52_29
% 203.13/34.16    (29)  op(all_10_2, e1) = all_10_1
% 203.13/34.16    (30)   ~ (all_52_7 = all_6_2)
% 203.13/34.16    (31)  all_58_15 = e0
% 203.13/34.16    (32)  all_56_11 = all_52_29
% 203.13/34.16    (33)   ~ (all_52_25 = e0)
% 203.13/34.16    (34)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.16    (35)  op(e0, e0) = e0
% 203.13/34.16    (36)  op(all_10_2, all_10_2) = e1
% 203.13/34.16    (37)  all_56_8 = all_52_5
% 203.13/34.16    (38)  op(all_52_9, all_52_9) = all_52_8
% 203.13/34.16    (39)  op(all_52_15, all_52_15) = all_52_14
% 203.13/34.16    (40)   ~ (all_52_25 = all_52_29)
% 203.13/34.16    (41)   ~ (all_52_29 = all_10_2)
% 203.13/34.16    (42)  all_58_7 = all_52_13
% 203.13/34.16    (43)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.16    (44)  op(all_52_19, all_52_19) = e2
% 203.13/34.16    (45)   ~ (all_52_5 = all_52_7)
% 203.13/34.16    (46)  all_58_12 = all_52_7
% 203.13/34.16    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.16    (48)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.16    (49)  all_58_2 = all_52_3
% 203.13/34.16    (50)  all_56_2 = all_52_17
% 203.13/34.16    (51)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.16    (52)   ~ (e2 = e0)
% 203.13/34.16    (53)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.13/34.16    (54)   ~ (all_52_5 = all_52_29)
% 203.13/34.16    (55)   ~ (all_52_29 = e0)
% 203.13/34.16    (56)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.16    (57)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.16    (58)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.13/34.16    (59)  op(e3, e1) = all_52_17
% 203.13/34.16    (60)  op(e0, e3) = all_52_7
% 203.13/34.16    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.16    (62)  all_58_15 = all_14_2
% 203.13/34.16    (63)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.16    (64)   ~ (all_10_1 = e2)
% 203.13/34.16    (65)  all_58_8 = all_10_2
% 203.13/34.16    (66)  op(all_52_29, all_52_29) = all_52_28
% 203.13/34.16    (67)  all_56_12 = all_52_7
% 203.13/34.16    (68)  all_8_2 = all_6_2
% 203.13/34.16    (69)   ~ (all_52_25 = all_6_2)
% 203.13/34.16    (70)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.16    (71)   ~ (all_52_5 = all_6_2)
% 203.13/34.16    (72)   ~ (all_52_9 = all_6_2)
% 203.13/34.16    (73)  op(e3, all_6_1) = e2
% 203.13/34.16    (74)  all_56_0 = all_6_2
% 203.13/34.16    (75)  op(e3, e3) = all_6_2
% 203.13/34.16    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.16    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.16    (78)  all_56_3 = all_52_25
% 203.13/34.16    (79)   ~ (all_52_3 = all_52_7)
% 203.13/34.16    (80)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.16    (81)  all_58_5 = all_52_19
% 203.13/34.16    (82)  op(all_52_17, all_52_17) = e3
% 203.13/34.16    (83)  all_58_6 = all_52_5
% 203.13/34.16    (84)  op(e3, e2) = all_52_9
% 203.13/34.16    (85)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.16    (86)   ~ (all_52_17 = all_6_2)
% 203.13/34.16    (87)   ~ (e1 = e0)
% 203.13/34.16    (88)  all_44_1 = all_6_1
% 203.13/34.16    (89)   ~ (all_52_9 = all_52_17)
% 203.13/34.16    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.13/34.16    (91)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.16    (92)  op(e1, e1) = all_10_2
% 203.13/34.16    (93)   ~ (all_52_23 = all_10_2)
% 203.13/34.16    (94)   ~ (all_52_7 = all_52_23)
% 203.13/34.16    (95)  all_58_3 = all_4_2
% 203.13/34.16    (96)  all_56_13 = all_52_15
% 203.13/34.16    (97)   ~ (all_52_19 = all_4_2)
% 203.13/34.16    (98)   ~ (all_52_17 = all_52_23)
% 203.13/34.16    (99)  all_8_1 = all_6_1
% 203.13/34.16    (100)  op(all_6_2, e3) = all_6_1
% 203.13/34.16    (101)   ~ (all_52_13 = all_52_29)
% 203.13/34.16    (102)  all_58_4 = all_52_17
% 203.13/34.16    (103)  op(all_52_25, all_52_25) = all_52_24
% 203.13/34.16  
% 203.13/34.16  Begin of proof
% 203.13/34.16  | 
% 203.13/34.16  | BETA: splitting (85) gives:
% 203.13/34.16  | 
% 203.13/34.16  | Case 1:
% 203.13/34.16  | | 
% 203.13/34.16  | |   (104)  all_58_12 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | COMBINE_EQS: (46), (104) imply:
% 203.13/34.16  | |   (105)  all_52_7 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | SIMP: (105) implies:
% 203.13/34.16  | |   (106)  all_52_7 = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (79), (106) imply:
% 203.13/34.16  | |   (107)   ~ (all_52_3 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (45), (106) imply:
% 203.13/34.16  | |   (108)   ~ (all_52_5 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (12), (106) imply:
% 203.13/34.16  | |   (109)   ~ (all_52_15 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (94), (106) imply:
% 203.13/34.16  | |   (110)   ~ (all_52_23 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | SIMP: (110) implies:
% 203.13/34.16  | |   (111)   ~ (all_52_23 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (30), (106) imply:
% 203.13/34.16  | |   (112)   ~ (all_6_2 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | SIMP: (112) implies:
% 203.13/34.16  | |   (113)   ~ (all_6_2 = e3)
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (13), (106) imply:
% 203.13/34.16  | |   (114)  op(e3, e3) = all_52_6
% 203.13/34.16  | | 
% 203.13/34.16  | | REDUCE: (60), (106) imply:
% 203.13/34.16  | |   (115)  op(e0, e3) = e3
% 203.13/34.16  | | 
% 203.13/34.16  | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 203.13/34.16  | |              with (75), (114) gives:
% 203.13/34.16  | |   (116)  all_52_6 = all_6_2
% 203.13/34.16  | | 
% 203.13/34.16  | | BETA: splitting (57) gives:
% 203.13/34.16  | | 
% 203.13/34.16  | | Case 1:
% 203.13/34.16  | | | 
% 203.13/34.16  | | |   (117)  all_56_11 = e3
% 203.13/34.16  | | | 
% 203.13/34.16  | | | COMBINE_EQS: (32), (117) imply:
% 203.13/34.16  | | |   (118)  all_52_29 = e3
% 203.13/34.16  | | | 
% 203.13/34.16  | | | SIMP: (118) implies:
% 203.13/34.16  | | |   (119)  all_52_29 = e3
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REDUCE: (101), (119) imply:
% 203.13/34.16  | | |   (120)   ~ (all_52_13 = e3)
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REDUCE: (40), (119) imply:
% 203.13/34.16  | | |   (121)   ~ (all_52_25 = e3)
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REDUCE: (41), (119) imply:
% 203.13/34.16  | | |   (122)   ~ (all_10_2 = e3)
% 203.13/34.16  | | | 
% 203.13/34.16  | | | SIMP: (122) implies:
% 203.13/34.16  | | |   (123)   ~ (all_10_2 = e3)
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REDUCE: (66), (119) imply:
% 203.13/34.16  | | |   (124)  op(e3, e3) = all_52_28
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REF_CLOSE: (2), (5), (6), (14), (22), (24), (33), (34), (35), (38), (42),
% 203.13/34.16  | | |            (44), (50), (61), (65), (69), (70), (72), (75), (78), (81),
% 203.13/34.16  | | |            (82), (86), (90), (95), (97), (102), (111), (120), (121),
% 203.13/34.16  | | |            (123), (124) are inconsistent by sub-proof #1254.
% 203.13/34.16  | | | 
% 203.13/34.16  | | Case 2:
% 203.13/34.16  | | | 
% 203.13/34.16  | | |   (125)   ~ (all_56_11 = e3)
% 203.13/34.16  | | |   (126)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.16  | | | 
% 203.13/34.16  | | | REDUCE: (32), (125) imply:
% 203.13/34.16  | | |   (127)   ~ (all_52_29 = e3)
% 203.13/34.16  | | | 
% 203.13/34.16  | | | BETA: splitting (76) gives:
% 203.13/34.16  | | | 
% 203.13/34.16  | | | Case 1:
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | |   (128)  all_58_9 = e3
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | COMBINE_EQS: (23), (128) imply:
% 203.13/34.16  | | | |   (129)  all_52_25 = e3
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | SIMP: (129) implies:
% 203.13/34.16  | | | |   (130)  all_52_25 = e3
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | REDUCE: (14), (130) imply:
% 203.13/34.16  | | | |   (131)   ~ (all_52_17 = e3)
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | REDUCE: (103), (130) imply:
% 203.13/34.16  | | | |   (132)  op(e3, e3) = all_52_24
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | REDUCE: (21), (130) imply:
% 203.13/34.16  | | | |   (133)  op(e3, e0) = e3
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 203.13/34.16  | | | |              simplifying with (75), (132) gives:
% 203.13/34.16  | | | |   (134)  all_52_24 = all_6_2
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | REF_CLOSE: (1), (4), (5), (8), (10), (15), (16), (17), (18), (20), (25),
% 203.13/34.16  | | | |            (26), (27), (32), (34), (35), (37), (43), (49), (50), (51),
% 203.13/34.16  | | | |            (52), (53), (54), (55), (58), (59), (63), (68), (71), (73),
% 203.13/34.16  | | | |            (74), (75), (82), (83), (84), (86), (87), (88), (89), (91),
% 203.13/34.16  | | | |            (100), (104), (107), (108), (113), (114), (115), (126),
% 203.13/34.16  | | | |            (131), (133) are inconsistent by sub-proof #484.
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | Case 2:
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | |   (135)   ~ (all_58_9 = e3)
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | REDUCE: (23), (135) imply:
% 203.13/34.16  | | | |   (136)   ~ (all_52_25 = e3)
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | BETA: splitting (90) gives:
% 203.13/34.16  | | | | 
% 203.13/34.16  | | | | Case 1:
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | |   (137)  all_58_4 = e3
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | COMBINE_EQS: (102), (137) imply:
% 203.13/34.16  | | | | |   (138)  all_52_17 = e3
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | SIMP: (138) implies:
% 203.13/34.16  | | | | |   (139)  all_52_17 = e3
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | REF_CLOSE: (5), (75), (82), (86), (139) are inconsistent by sub-proof
% 203.13/34.16  | | | | |            #1280.
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | Case 2:
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | |   (140)   ~ (all_58_4 = e3)
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | REDUCE: (102), (140) imply:
% 203.13/34.16  | | | | |   (141)   ~ (all_52_17 = e3)
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | BETA: splitting (77) gives:
% 203.13/34.16  | | | | | 
% 203.13/34.16  | | | | | Case 1:
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | |   (142)  all_58_0 = e3
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | COMBINE_EQS: (17), (142) imply:
% 203.13/34.16  | | | | | |   (143)  all_6_2 = e3
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | REDUCE: (113), (143) imply:
% 203.13/34.16  | | | | | |   (144)  $false
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | CLOSE: (144) is inconsistent.
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | Case 2:
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | |   (145)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | BETA: splitting (145) gives:
% 203.13/34.16  | | | | | | 
% 203.13/34.16  | | | | | | Case 1:
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | |   (146)  all_58_1 = e3
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | COMBINE_EQS: (6), (146) imply:
% 203.13/34.16  | | | | | | |   (147)  all_52_9 = e3
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | REDUCE: (7), (147) imply:
% 203.13/34.16  | | | | | | |   (148)   ~ (all_52_13 = e3)
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | SIMP: (148) implies:
% 203.13/34.16  | | | | | | |   (149)   ~ (all_52_13 = e3)
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | REDUCE: (38), (147) imply:
% 203.13/34.16  | | | | | | |   (150)  op(e3, e3) = all_52_8
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | BETA: splitting (47) gives:
% 203.13/34.16  | | | | | | | 
% 203.13/34.16  | | | | | | | Case 1:
% 203.13/34.16  | | | | | | | | 
% 203.13/34.16  | | | | | | | |   (151)  all_58_6 = e3
% 203.13/34.16  | | | | | | | | 
% 203.13/34.16  | | | | | | | | REF_CLOSE: (83), (108), (151) are inconsistent by sub-proof
% 203.13/34.16  | | | | | | | |            #1328.
% 203.13/34.16  | | | | | | | | 
% 203.13/34.16  | | | | | | | Case 2:
% 203.13/34.16  | | | | | | | | 
% 203.13/34.16  | | | | | | | |   (152)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.16  | | | | | | | | 
% 203.13/34.16  | | | | | | | | BETA: splitting (152) gives:
% 203.13/34.16  | | | | | | | | 
% 203.13/34.16  | | | | | | | | Case 1:
% 203.13/34.16  | | | | | | | | | 
% 203.13/34.16  | | | | | | | | |   (153)  all_58_7 = e3
% 203.13/34.16  | | | | | | | | | 
% 203.13/34.16  | | | | | | | | | COMBINE_EQS: (42), (153) imply:
% 203.13/34.16  | | | | | | | | |   (154)  all_52_13 = e3
% 203.13/34.16  | | | | | | | | | 
% 203.13/34.16  | | | | | | | | | REDUCE: (149), (154) imply:
% 203.13/34.16  | | | | | | | | |   (155)  $false
% 203.13/34.16  | | | | | | | | | 
% 203.13/34.16  | | | | | | | | | CLOSE: (155) is inconsistent.
% 203.13/34.16  | | | | | | | | | 
% 203.13/34.17  | | | | | | | | Case 2:
% 203.13/34.17  | | | | | | | | | 
% 203.13/34.17  | | | | | | | | |   (156)  all_58_8 = e3 | all_58_11 = e3
% 203.13/34.17  | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | BETA: splitting (156) gives:
% 203.13/34.17  | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | Case 1:
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | |   (157)  all_58_8 = e3
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | COMBINE_EQS: (65), (157) imply:
% 203.13/34.17  | | | | | | | | | |   (158)  all_10_2 = e3
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | SIMP: (158) implies:
% 203.13/34.17  | | | | | | | | | |   (159)  all_10_2 = e3
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | REDUCE: (36), (159) imply:
% 203.13/34.17  | | | | | | | | | |   (160)  op(e3, e3) = e1
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | REDUCE: (29), (159) imply:
% 203.13/34.17  | | | | | | | | | |   (161)  op(e3, e1) = all_10_1
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_17, all_10_1, e1,
% 203.13/34.17  | | | | | | | | | |              e3, simplifying with (59), (161) gives:
% 203.13/34.17  | | | | | | | | | |   (162)  all_52_17 = all_10_1
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_8, e3, e3,
% 203.13/34.17  | | | | | | | | | |              simplifying with (75), (150) gives:
% 203.13/34.17  | | | | | | | | | |   (163)  all_52_8 = all_6_2
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | GROUND_INST: instantiating (5) with e1, all_52_8, e3, e3,
% 203.13/34.17  | | | | | | | | | |              simplifying with (150), (160) gives:
% 203.13/34.17  | | | | | | | | | |   (164)  all_52_8 = e1
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | COMBINE_EQS: (163), (164) imply:
% 203.13/34.17  | | | | | | | | | |   (165)  all_6_2 = e1
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | SIMP: (165) implies:
% 203.13/34.17  | | | | | | | | | |   (166)  all_6_2 = e1
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | REF_CLOSE: (5), (34), (35), (50), (64), (82), (86), (141),
% 203.13/34.17  | | | | | | | | | |            (162), (166) are inconsistent by sub-proof #482.
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | Case 2:
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | |   (167)  all_58_11 = e3
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | | REF_CLOSE: (28), (127), (167) are inconsistent by sub-proof
% 203.13/34.17  | | | | | | | | | |            #1323.
% 203.13/34.17  | | | | | | | | | | 
% 203.13/34.17  | | | | | | | | | End of split
% 203.13/34.17  | | | | | | | | | 
% 203.13/34.17  | | | | | | | | End of split
% 203.13/34.17  | | | | | | | | 
% 203.13/34.17  | | | | | | | End of split
% 203.13/34.17  | | | | | | | 
% 203.13/34.17  | | | | | | Case 2:
% 203.13/34.17  | | | | | | | 
% 203.13/34.17  | | | | | | |   (168)  all_58_4 = e3 | all_58_9 = e3
% 203.13/34.17  | | | | | | | 
% 203.13/34.17  | | | | | | | REF_CLOSE: (23), (102), (136), (141), (168) are inconsistent by
% 203.13/34.17  | | | | | | |            sub-proof #1276.
% 203.13/34.17  | | | | | | | 
% 203.13/34.17  | | | | | | End of split
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | End of split
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | End of split
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | End of split
% 203.13/34.17  | | | 
% 203.13/34.17  | | End of split
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (169)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.17  | | 
% 203.13/34.17  | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (11), (12), (22), (24), (30), (31),
% 203.13/34.17  | |            (34), (39), (46), (48), (50), (56), (60), (62), (67), (68), (73),
% 203.13/34.17  | |            (75), (80), (82), (84), (86), (87), (89), (92), (93), (94), (96),
% 203.13/34.17  | |            (98), (99), (100), (169) are inconsistent by sub-proof #478.
% 203.13/34.17  | | 
% 203.13/34.17  | End of split
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #478 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.17    (2)  all_58_14 = all_52_23
% 203.13/34.17    (3)   ~ (e3 = e1)
% 203.13/34.17    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (5)   ~ (e3 = e0)
% 203.13/34.17    (6)  op(all_52_23, all_52_23) = e0
% 203.13/34.17    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17    (8)   ~ (all_52_7 = all_52_15)
% 203.13/34.17    (9)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.17    (10)  all_58_13 = all_52_15
% 203.13/34.17    (11)   ~ (all_52_15 = e3)
% 203.13/34.17    (12)   ~ (all_52_7 = all_6_2)
% 203.13/34.17    (13)  all_58_15 = e0
% 203.13/34.17    (14)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (15)  op(all_52_15, all_52_15) = all_52_14
% 203.13/34.17    (16)  all_58_12 = all_52_7
% 203.13/34.17    (17)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.17    (18)  all_56_2 = all_52_17
% 203.13/34.17    (19)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.17    (20)  op(e0, e3) = all_52_7
% 203.13/34.17    (21)  all_58_15 = all_14_2
% 203.13/34.17    (22)  all_56_12 = all_52_7
% 203.13/34.17    (23)  all_8_2 = all_6_2
% 203.13/34.17    (24)  op(e3, all_6_1) = e2
% 203.13/34.17    (25)  op(e3, e3) = all_6_2
% 203.13/34.17    (26)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.17    (27)  op(all_52_17, all_52_17) = e3
% 203.13/34.17    (28)  op(e3, e2) = all_52_9
% 203.13/34.17    (29)   ~ (all_52_17 = all_6_2)
% 203.13/34.17    (30)   ~ (e1 = e0)
% 203.13/34.17    (31)   ~ (all_52_9 = all_52_17)
% 203.13/34.17    (32)  op(e1, e1) = all_10_2
% 203.13/34.17    (33)   ~ (all_52_23 = all_10_2)
% 203.13/34.17    (34)   ~ (all_52_7 = all_52_23)
% 203.13/34.17    (35)  all_56_13 = all_52_15
% 203.13/34.17    (36)   ~ (all_52_17 = all_52_23)
% 203.13/34.17    (37)  all_8_1 = all_6_1
% 203.13/34.17    (38)  op(all_6_2, e3) = all_6_1
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | BETA: splitting (9) gives:
% 203.13/34.17  | 
% 203.13/34.17  | Case 1:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (39)  all_58_13 = e3
% 203.13/34.17  | | 
% 203.13/34.17  | | REF_CLOSE: (10), (11), (39) are inconsistent by sub-proof #1360.
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (40)  all_58_14 = e3 | all_58_15 = e3
% 203.13/34.17  | | 
% 203.13/34.17  | | BETA: splitting (40) gives:
% 203.13/34.17  | | 
% 203.13/34.17  | | Case 1:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (41)  all_58_14 = e3
% 203.13/34.17  | | | 
% 203.13/34.17  | | | COMBINE_EQS: (2), (41) imply:
% 203.13/34.17  | | |   (42)  all_52_23 = e3
% 203.13/34.17  | | | 
% 203.13/34.17  | | | SIMP: (42) implies:
% 203.13/34.17  | | |   (43)  all_52_23 = e3
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REDUCE: (34), (43) imply:
% 203.13/34.17  | | |   (44)   ~ (all_52_7 = e3)
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REDUCE: (36), (43) imply:
% 203.13/34.17  | | |   (45)   ~ (all_52_17 = e3)
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REDUCE: (33), (43) imply:
% 203.13/34.17  | | |   (46)   ~ (all_10_2 = e3)
% 203.13/34.17  | | | 
% 203.13/34.17  | | | SIMP: (46) implies:
% 203.13/34.17  | | |   (47)   ~ (all_10_2 = e3)
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REDUCE: (6), (43) imply:
% 203.13/34.17  | | |   (48)  op(e3, e3) = e0
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (1), (3), (4), (7), (8), (10), (12), (14), (15), (16), (17),
% 203.13/34.17  | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 203.13/34.17  | | |            (28), (29), (30), (31), (32), (35), (37), (38), (41), (44),
% 203.13/34.17  | | |            (45), (47), (48) are inconsistent by sub-proof #479.
% 203.13/34.17  | | | 
% 203.13/34.17  | | Case 2:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (49)  all_58_15 = e3
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (5), (13), (49) are inconsistent by sub-proof #1350.
% 203.13/34.17  | | | 
% 203.13/34.17  | | End of split
% 203.13/34.17  | | 
% 203.13/34.17  | End of split
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #479 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.17    (2)   ~ (e3 = e1)
% 203.13/34.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17    (5)   ~ (all_52_7 = all_52_15)
% 203.13/34.17    (6)  all_58_13 = all_52_15
% 203.13/34.17    (7)   ~ (all_52_7 = all_6_2)
% 203.13/34.17    (8)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (9)  op(all_52_15, all_52_15) = all_52_14
% 203.13/34.17    (10)  all_58_12 = all_52_7
% 203.13/34.17    (11)   ~ (all_52_7 = e3)
% 203.13/34.17    (12)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.17    (13)  all_56_2 = all_52_17
% 203.13/34.17    (14)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.17    (15)   ~ (all_10_2 = e3)
% 203.13/34.17    (16)  op(e0, e3) = all_52_7
% 203.13/34.17    (17)  all_58_15 = all_14_2
% 203.13/34.17    (18)  all_56_12 = all_52_7
% 203.13/34.17    (19)  all_8_2 = all_6_2
% 203.13/34.17    (20)  op(e3, all_6_1) = e2
% 203.13/34.17    (21)  op(e3, e3) = e0
% 203.13/34.17    (22)  op(e3, e3) = all_6_2
% 203.13/34.17    (23)   ~ (all_52_17 = e3)
% 203.13/34.17    (24)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.17    (25)  op(all_52_17, all_52_17) = e3
% 203.13/34.17    (26)  op(e3, e2) = all_52_9
% 203.13/34.17    (27)   ~ (all_52_17 = all_6_2)
% 203.13/34.17    (28)   ~ (e1 = e0)
% 203.13/34.17    (29)   ~ (all_52_9 = all_52_17)
% 203.13/34.17    (30)  op(e1, e1) = all_10_2
% 203.13/34.17    (31)  all_58_14 = e3
% 203.13/34.17    (32)  all_56_13 = all_52_15
% 203.13/34.17    (33)  all_8_1 = all_6_1
% 203.13/34.17    (34)  op(all_6_2, e3) = all_6_1
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying with
% 203.13/34.17  |              (21), (22) gives:
% 203.13/34.17  |   (35)  all_6_2 = e0
% 203.13/34.17  | 
% 203.13/34.17  | COMBINE_EQS: (19), (35) imply:
% 203.13/34.17  |   (36)  all_8_2 = e0
% 203.13/34.17  | 
% 203.13/34.17  | REDUCE: (7), (35) imply:
% 203.13/34.17  |   (37)   ~ (all_52_7 = e0)
% 203.13/34.17  | 
% 203.13/34.17  | REDUCE: (27), (35) imply:
% 203.13/34.17  |   (38)   ~ (all_52_17 = e0)
% 203.13/34.17  | 
% 203.13/34.17  | REDUCE: (34), (35) imply:
% 203.13/34.17  |   (39)  op(e0, e3) = all_6_1
% 203.13/34.17  | 
% 203.13/34.17  | BETA: splitting (1) gives:
% 203.13/34.17  | 
% 203.13/34.17  | Case 1:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (40)   ~ (all_8_1 = e1)
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (33), (40) imply:
% 203.13/34.17  | |   (41)   ~ (all_6_1 = e1)
% 203.13/34.17  | | 
% 203.13/34.17  | | GROUND_INST: instantiating (3) with all_52_7, all_6_1, e3, e0, simplifying
% 203.13/34.17  | |              with (16), (39) gives:
% 203.13/34.17  | |   (42)  all_52_7 = all_6_1
% 203.13/34.17  | | 
% 203.13/34.17  | | COMBINE_EQS: (18), (42) imply:
% 203.13/34.17  | |   (43)  all_56_12 = all_6_1
% 203.13/34.17  | | 
% 203.13/34.17  | | COMBINE_EQS: (10), (42) imply:
% 203.13/34.17  | |   (44)  all_58_12 = all_6_1
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (5), (42) imply:
% 203.13/34.17  | |   (45)   ~ (all_52_15 = all_6_1)
% 203.13/34.17  | | 
% 203.13/34.17  | | SIMP: (45) implies:
% 203.13/34.17  | |   (46)   ~ (all_52_15 = all_6_1)
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (11), (42) imply:
% 203.13/34.17  | |   (47)   ~ (all_6_1 = e3)
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (37), (42) imply:
% 203.13/34.17  | |   (48)   ~ (all_6_1 = e0)
% 203.13/34.17  | | 
% 203.13/34.17  | | BETA: splitting (4) gives:
% 203.13/34.17  | | 
% 203.13/34.17  | | Case 1:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (49)  all_56_12 = e3
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (43), (47), (49) are inconsistent by sub-proof #1347.
% 203.13/34.17  | | | 
% 203.13/34.17  | | Case 2:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (50)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (2), (3), (6), (8), (9), (12), (13), (14), (15), (17), (20),
% 203.13/34.17  | | |            (23), (24), (25), (26), (28), (29), (30), (31), (32), (38),
% 203.13/34.17  | | |            (41), (43), (44), (46), (48), (50) are inconsistent by
% 203.13/34.17  | | |            sub-proof #480.
% 203.13/34.17  | | | 
% 203.13/34.17  | | End of split
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (51)   ~ (all_8_2 = e0)
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (36), (51) imply:
% 203.13/34.17  | |   (52)  $false
% 203.13/34.17  | | 
% 203.13/34.17  | | CLOSE: (52) is inconsistent.
% 203.13/34.17  | | 
% 203.13/34.17  | End of split
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #480 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ~ (e3 = e1)
% 203.13/34.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (3)  all_56_12 = all_6_1
% 203.13/34.17    (4)  all_58_13 = all_52_15
% 203.13/34.17    (5)   ~ (all_6_1 = e1)
% 203.13/34.17    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17    (7)   ~ (all_6_1 = e0)
% 203.13/34.17    (8)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (9)  op(all_52_15, all_52_15) = all_52_14
% 203.13/34.17    (10)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.17    (11)  all_56_2 = all_52_17
% 203.13/34.17    (12)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.17    (13)   ~ (all_10_2 = e3)
% 203.13/34.17    (14)  all_58_15 = all_14_2
% 203.13/34.17    (15)  op(e3, all_6_1) = e2
% 203.13/34.17    (16)   ~ (all_52_15 = all_6_1)
% 203.13/34.17    (17)   ~ (all_52_17 = e3)
% 203.13/34.17    (18)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.17    (19)  op(all_52_17, all_52_17) = e3
% 203.13/34.17    (20)  op(e3, e2) = all_52_9
% 203.13/34.17    (21)   ~ (e1 = e0)
% 203.13/34.17    (22)   ~ (all_52_9 = all_52_17)
% 203.13/34.17    (23)  all_58_12 = all_6_1
% 203.13/34.17    (24)   ~ (all_52_17 = e0)
% 203.13/34.17    (25)  op(e1, e1) = all_10_2
% 203.13/34.17    (26)  all_58_14 = e3
% 203.13/34.17    (27)  all_56_13 = all_52_15
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | BETA: splitting (6) gives:
% 203.13/34.17  | 
% 203.13/34.17  | Case 1:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (28)  all_56_12 = e2
% 203.13/34.17  | | 
% 203.13/34.17  | | COMBINE_EQS: (3), (28) imply:
% 203.13/34.17  | |   (29)  all_6_1 = e2
% 203.13/34.17  | | 
% 203.13/34.17  | | SIMP: (29) implies:
% 203.13/34.17  | |   (30)  all_6_1 = e2
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (16), (30) imply:
% 203.13/34.17  | |   (31)   ~ (all_52_15 = e2)
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (15), (30) imply:
% 203.13/34.17  | |   (32)  op(e3, e2) = e2
% 203.13/34.17  | | 
% 203.13/34.17  | | BETA: splitting (10) gives:
% 203.13/34.17  | | 
% 203.13/34.17  | | Case 1:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (33)  all_56_13 = e2
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (27), (31), (33) are inconsistent by sub-proof #1356.
% 203.13/34.17  | | | 
% 203.13/34.17  | | Case 2:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (34)  all_56_13 = e1 | all_56_13 = e0
% 203.13/34.17  | | | 
% 203.13/34.17  | | | BETA: splitting (34) gives:
% 203.13/34.17  | | | 
% 203.13/34.17  | | | Case 1:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | |   (35)  all_56_13 = e1
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | COMBINE_EQS: (27), (35) imply:
% 203.13/34.17  | | | |   (36)  all_52_15 = e1
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | SIMP: (36) implies:
% 203.13/34.17  | | | |   (37)  all_52_15 = e1
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | REDUCE: (9), (37) imply:
% 203.13/34.17  | | | |   (38)  op(e1, e1) = all_52_14
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | GROUND_INST: instantiating (2) with all_10_2, all_52_14, e1, e1,
% 203.13/34.17  | | | |              simplifying with (25), (38) gives:
% 203.13/34.17  | | | |   (39)  all_52_14 = all_10_2
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | GROUND_INST: instantiating (2) with all_52_9, e2, e2, e3, simplifying
% 203.13/34.17  | | | |              with (20), (32) gives:
% 203.13/34.17  | | | |   (40)  all_52_9 = e2
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | REDUCE: (22), (40) imply:
% 203.13/34.17  | | | |   (41)   ~ (all_52_17 = e2)
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | SIMP: (41) implies:
% 203.13/34.17  | | | |   (42)   ~ (all_52_17 = e2)
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | REF_CLOSE: (2), (8), (11), (13), (17), (19), (24), (25), (42) are
% 203.13/34.17  | | | |            inconsistent by sub-proof #1073.
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | Case 2:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | |   (43)  all_56_13 = e0
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | COMBINE_EQS: (27), (43) imply:
% 203.13/34.17  | | | |   (44)  all_52_15 = e0
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | SIMP: (44) implies:
% 203.13/34.17  | | | |   (45)  all_52_15 = e0
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | COMBINE_EQS: (4), (45) imply:
% 203.13/34.17  | | | |   (46)  all_58_13 = e0
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (12), (13), (14),
% 203.13/34.17  | | | |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 203.13/34.17  | | | |            (26), (46) are inconsistent by sub-proof #481.
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | End of split
% 203.13/34.17  | | | 
% 203.13/34.17  | | End of split
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (47)  all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17  | | 
% 203.13/34.17  | | REF_CLOSE: (3), (5), (7), (47) are inconsistent by sub-proof #1344.
% 203.13/34.17  | | 
% 203.13/34.17  | End of split
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #481 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ~ (e3 = e1)
% 203.13/34.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (3)  all_56_12 = all_6_1
% 203.13/34.17    (4)   ~ (all_6_1 = e1)
% 203.13/34.17    (5)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17    (6)   ~ (all_6_1 = e0)
% 203.13/34.17    (7)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (8)  all_56_2 = all_52_17
% 203.13/34.17    (9)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.17    (10)   ~ (all_10_2 = e3)
% 203.13/34.17    (11)  all_58_15 = all_14_2
% 203.13/34.17    (12)  op(e3, all_6_1) = e2
% 203.13/34.17    (13)   ~ (all_52_17 = e3)
% 203.13/34.17    (14)  all_58_13 = e0
% 203.13/34.17    (15)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.17    (16)  op(all_52_17, all_52_17) = e3
% 203.13/34.17    (17)  op(e3, e2) = all_52_9
% 203.13/34.17    (18)   ~ (e1 = e0)
% 203.13/34.17    (19)   ~ (all_52_9 = all_52_17)
% 203.13/34.17    (20)  all_58_12 = all_6_1
% 203.13/34.17    (21)   ~ (all_52_17 = e0)
% 203.13/34.17    (22)  op(e1, e1) = all_10_2
% 203.13/34.17    (23)  all_58_14 = e3
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | BETA: splitting (9) gives:
% 203.13/34.17  | 
% 203.13/34.17  | Case 1:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (24)  all_58_12 = e1
% 203.13/34.17  | | 
% 203.13/34.17  | | COMBINE_EQS: (20), (24) imply:
% 203.13/34.17  | |   (25)  all_6_1 = e1
% 203.13/34.17  | | 
% 203.13/34.17  | | SIMP: (25) implies:
% 203.13/34.17  | |   (26)  all_6_1 = e1
% 203.13/34.17  | | 
% 203.13/34.17  | | REDUCE: (4), (26) imply:
% 203.13/34.17  | |   (27)  $false
% 203.13/34.17  | | 
% 203.13/34.17  | | CLOSE: (27) is inconsistent.
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (28)   ~ (all_58_12 = e1)
% 203.13/34.17  | |   (29)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.17  | | 
% 203.13/34.17  | | BETA: splitting (5) gives:
% 203.13/34.17  | | 
% 203.13/34.17  | | Case 1:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (30)  all_56_12 = e2
% 203.13/34.17  | | | 
% 203.13/34.17  | | | COMBINE_EQS: (3), (30) imply:
% 203.13/34.17  | | |   (31)  all_6_1 = e2
% 203.13/34.17  | | | 
% 203.13/34.17  | | | SIMP: (31) implies:
% 203.13/34.17  | | |   (32)  all_6_1 = e2
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REDUCE: (12), (32) imply:
% 203.13/34.17  | | |   (33)  op(e3, e2) = e2
% 203.13/34.17  | | | 
% 203.13/34.17  | | | BETA: splitting (29) gives:
% 203.13/34.17  | | | 
% 203.13/34.17  | | | Case 1:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | |   (34)  all_58_13 = e1
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | COMBINE_EQS: (14), (34) imply:
% 203.13/34.17  | | | |   (35)  e1 = e0
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | REDUCE: (18), (35) imply:
% 203.13/34.17  | | | |   (36)  $false
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | CLOSE: (36) is inconsistent.
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | Case 2:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | |   (37)  all_58_14 = e1 | all_58_15 = e1
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | BETA: splitting (37) gives:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | Case 1:
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | |   (38)  all_58_14 = e1
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | REF_CLOSE: (1), (23), (38) are inconsistent by sub-proof #814.
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | Case 2:
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | |   (39)  all_58_15 = e1
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | COMBINE_EQS: (11), (39) imply:
% 203.13/34.17  | | | | |   (40)  all_14_2 = e1
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | REDUCE: (15), (40) imply:
% 203.13/34.17  | | | | |   (41)  op(e1, e1) = all_52_30
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | GROUND_INST: instantiating (2) with all_10_2, all_52_30, e1, e1,
% 203.13/34.17  | | | | |              simplifying with (22), (41) gives:
% 203.13/34.17  | | | | |   (42)  all_52_30 = all_10_2
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | GROUND_INST: instantiating (2) with all_52_9, e2, e2, e3, simplifying
% 203.13/34.17  | | | | |              with (17), (33) gives:
% 203.13/34.17  | | | | |   (43)  all_52_9 = e2
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | REDUCE: (19), (43) imply:
% 203.13/34.17  | | | | |   (44)   ~ (all_52_17 = e2)
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | SIMP: (44) implies:
% 203.13/34.17  | | | | |   (45)   ~ (all_52_17 = e2)
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | REF_CLOSE: (2), (7), (8), (10), (13), (16), (21), (22), (45) are
% 203.13/34.17  | | | | |            inconsistent by sub-proof #1073.
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | End of split
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | End of split
% 203.13/34.17  | | | 
% 203.13/34.17  | | Case 2:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (46)  all_56_12 = e1 | all_56_12 = e0
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (3), (4), (6), (46) are inconsistent by sub-proof #1344.
% 203.13/34.17  | | | 
% 203.13/34.17  | | End of split
% 203.13/34.17  | | 
% 203.13/34.17  | End of split
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #482 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (2)  all_52_17 = all_10_1
% 203.13/34.17    (3)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (4)  op(e0, e0) = e0
% 203.13/34.17    (5)  all_56_2 = all_52_17
% 203.13/34.17    (6)   ~ (all_10_1 = e2)
% 203.13/34.17    (7)   ~ (all_52_17 = e3)
% 203.13/34.17    (8)  op(all_52_17, all_52_17) = e3
% 203.13/34.17    (9)   ~ (all_52_17 = all_6_2)
% 203.13/34.17    (10)  all_6_2 = e1
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | COMBINE_EQS: (2), (5) imply:
% 203.13/34.17  |   (11)  all_56_2 = all_10_1
% 203.13/34.17  | 
% 203.13/34.17  | REDUCE: (2), (9), (10) imply:
% 203.13/34.17  |   (12)   ~ (all_10_1 = e1)
% 203.13/34.17  | 
% 203.13/34.17  | REDUCE: (2), (7) imply:
% 203.13/34.17  |   (13)   ~ (all_10_1 = e3)
% 203.13/34.17  | 
% 203.13/34.17  | REDUCE: (2), (8) imply:
% 203.13/34.17  |   (14)  op(all_10_1, all_10_1) = e3
% 203.13/34.17  | 
% 203.13/34.17  | REF_CLOSE: (1), (3), (4), (6), (11), (12), (13), (14) are inconsistent by
% 203.13/34.17  |            sub-proof #483.
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #483 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (2)   ~ (all_10_1 = e1)
% 203.13/34.17    (3)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (4)  op(e0, e0) = e0
% 203.13/34.17    (5)  op(all_10_1, all_10_1) = e3
% 203.13/34.17    (6)   ~ (all_10_1 = e2)
% 203.13/34.17    (7)  all_56_2 = all_10_1
% 203.13/34.17    (8)   ~ (all_10_1 = e3)
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | BETA: splitting (3) gives:
% 203.13/34.17  | 
% 203.13/34.17  | Case 1:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (9)  all_56_2 = e3
% 203.13/34.17  | | 
% 203.13/34.17  | | REF_CLOSE: (7), (8), (9) are inconsistent by sub-proof #1029.
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (10)   ~ (all_56_2 = e3)
% 203.13/34.17  | |   (11)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17  | | 
% 203.13/34.17  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (11) are inconsistent by
% 203.13/34.17  | |            sub-proof #1278.
% 203.13/34.17  | | 
% 203.13/34.17  | End of split
% 203.13/34.17  | 
% 203.13/34.17  End of proof
% 203.13/34.17  
% 203.13/34.17  Sub-proof #484 shows that the following formulas are inconsistent:
% 203.13/34.17  ----------------------------------------------------------------
% 203.13/34.17    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.17    (2)  op(all_52_3, all_52_3) = all_52_2
% 203.13/34.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.17    (4)   ~ (e3 = e0)
% 203.13/34.17    (5)  op(e2, e3) = all_52_3
% 203.13/34.17    (6)   ~ (all_52_3 = all_6_2)
% 203.13/34.17    (7)  all_44_2 = all_6_2
% 203.13/34.17    (8)  all_58_0 = all_6_2
% 203.13/34.17    (9)  all_56_4 = all_52_3
% 203.13/34.17    (10)  op(e3, e3) = all_52_6
% 203.13/34.17    (11)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 203.13/34.17    (12)  op(e1, e3) = all_52_5
% 203.13/34.17    (13)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.17    (14)   ~ (all_52_3 = all_52_5)
% 203.13/34.17    (15)   ~ (all_52_3 = e3)
% 203.13/34.17    (16)  all_56_11 = all_52_29
% 203.13/34.17    (17)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17    (18)   ~ (all_6_2 = e3)
% 203.13/34.17    (19)  op(e0, e0) = e0
% 203.13/34.17    (20)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.17    (21)  all_56_8 = all_52_5
% 203.13/34.17    (22)  op(e0, e3) = e3
% 203.13/34.17    (23)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.17    (24)  all_58_2 = all_52_3
% 203.13/34.17    (25)  all_56_2 = all_52_17
% 203.13/34.17    (26)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.17    (27)   ~ (e2 = e0)
% 203.13/34.17    (28)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.13/34.17    (29)   ~ (all_52_5 = e3)
% 203.13/34.17    (30)   ~ (all_52_5 = all_52_29)
% 203.13/34.17    (31)   ~ (all_52_29 = e0)
% 203.13/34.17    (32)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.13/34.17    (33)  op(e3, e1) = all_52_17
% 203.13/34.17    (34)  op(e3, e0) = e3
% 203.13/34.17    (35)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.17    (36)  all_8_2 = all_6_2
% 203.13/34.17    (37)   ~ (all_52_5 = all_6_2)
% 203.13/34.17    (38)  op(e3, all_6_1) = e2
% 203.13/34.17    (39)  all_56_0 = all_6_2
% 203.13/34.17    (40)  op(e3, e3) = all_6_2
% 203.13/34.17    (41)   ~ (all_52_17 = e3)
% 203.13/34.17    (42)  op(all_52_17, all_52_17) = e3
% 203.13/34.17    (43)  all_58_6 = all_52_5
% 203.13/34.17    (44)  op(e3, e2) = all_52_9
% 203.13/34.17    (45)   ~ (all_52_17 = all_6_2)
% 203.13/34.17    (46)   ~ (e1 = e0)
% 203.13/34.17    (47)  all_44_1 = all_6_1
% 203.13/34.17    (48)   ~ (all_52_9 = all_52_17)
% 203.13/34.17    (49)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.17    (50)  all_58_12 = e3
% 203.13/34.17    (51)  op(all_6_2, e3) = all_6_1
% 203.13/34.17  
% 203.13/34.17  Begin of proof
% 203.13/34.17  | 
% 203.13/34.17  | BETA: splitting (17) gives:
% 203.13/34.17  | 
% 203.13/34.17  | Case 1:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (52)  all_56_2 = e3
% 203.13/34.17  | | 
% 203.13/34.17  | | REF_CLOSE: (25), (41), (52) are inconsistent by sub-proof #1327.
% 203.13/34.17  | | 
% 203.13/34.17  | Case 2:
% 203.13/34.17  | | 
% 203.13/34.17  | |   (53)   ~ (all_56_2 = e3)
% 203.13/34.17  | |   (54)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.17  | | 
% 203.13/34.17  | | BETA: splitting (49) gives:
% 203.13/34.17  | | 
% 203.13/34.17  | | Case 1:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (55)  all_56_0 = e3
% 203.13/34.17  | | | 
% 203.13/34.17  | | | REF_CLOSE: (18), (39), (55) are inconsistent by sub-proof #598.
% 203.13/34.17  | | | 
% 203.13/34.17  | | Case 2:
% 203.13/34.17  | | | 
% 203.13/34.17  | | |   (56)   ~ (all_56_0 = e3)
% 203.13/34.17  | | |   (57)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.17  | | | 
% 203.13/34.17  | | | BETA: splitting (26) gives:
% 203.13/34.17  | | | 
% 203.13/34.17  | | | Case 1:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | |   (58)  all_56_4 = e3
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | REF_CLOSE: (9), (15), (58) are inconsistent by sub-proof #1340.
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | Case 2:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | |   (59)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | BETA: splitting (35) gives:
% 203.13/34.17  | | | | 
% 203.13/34.17  | | | | Case 1:
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | |   (60)  all_56_8 = e3
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | REF_CLOSE: (21), (29), (60) are inconsistent by sub-proof #1325.
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | Case 2:
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | |   (61)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | BETA: splitting (32) gives:
% 203.13/34.17  | | | | | 
% 203.13/34.17  | | | | | Case 1:
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | |   (62)  all_58_0 = e2
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | | COMBINE_EQS: (8), (62) imply:
% 203.13/34.17  | | | | | |   (63)  all_6_2 = e2
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (13), (18), (23), (24), (27),
% 203.13/34.17  | | | | | |            (33), (34), (38), (45), (51), (59), (63) are inconsistent
% 203.13/34.17  | | | | | |            by sub-proof #496.
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | Case 2:
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | |   (64)   ~ (all_58_0 = e2)
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | | REDUCE: (8), (64) imply:
% 203.13/34.17  | | | | | |   (65)   ~ (all_6_2 = e2)
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | | BETA: splitting (28) gives:
% 203.13/34.17  | | | | | | 
% 203.13/34.17  | | | | | | Case 1:
% 203.13/34.17  | | | | | | | 
% 203.13/34.18  | | | | | | |   (66)  all_58_0 = e1
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | COMBINE_EQS: (8), (66) imply:
% 203.13/34.18  | | | | | | |   (67)  all_6_2 = e1
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | COMBINE_EQS: (7), (67) imply:
% 203.13/34.18  | | | | | | |   (68)  all_44_2 = e1
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | REDUCE: (37), (67) imply:
% 203.13/34.18  | | | | | | |   (69)   ~ (all_52_5 = e1)
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | REDUCE: (45), (67) imply:
% 203.13/34.18  | | | | | | |   (70)   ~ (all_52_17 = e1)
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | REDUCE: (51), (67) imply:
% 203.13/34.18  | | | | | | |   (71)  op(e1, e3) = all_6_1
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | BETA: splitting (11) gives:
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | |   (72)   ~ (all_44_2 = e1)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REDUCE: (68), (72) imply:
% 203.13/34.18  | | | | | | | |   (73)  $false
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | CLOSE: (73) is inconsistent.
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | |   (74)   ~ (all_44_1 = e0)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REDUCE: (47), (74) imply:
% 203.13/34.18  | | | | | | | |   (75)   ~ (all_6_1 = e0)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | GROUND_INST: instantiating (3) with all_52_5, all_6_1, e3, e1,
% 203.13/34.18  | | | | | | | |              simplifying with (12), (71) gives:
% 203.13/34.18  | | | | | | | |   (76)  all_52_5 = all_6_1
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | COMBINE_EQS: (21), (76) imply:
% 203.13/34.18  | | | | | | | |   (77)  all_56_8 = all_6_1
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | COMBINE_EQS: (43), (76) imply:
% 203.13/34.18  | | | | | | | |   (78)  all_58_6 = all_6_1
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REDUCE: (14), (76) imply:
% 203.13/34.18  | | | | | | | |   (79)   ~ (all_52_3 = all_6_1)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REDUCE: (30), (76) imply:
% 203.13/34.18  | | | | | | | |   (80)   ~ (all_52_29 = all_6_1)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | SIMP: (80) implies:
% 203.13/34.18  | | | | | | | |   (81)   ~ (all_52_29 = all_6_1)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REDUCE: (69), (76) imply:
% 203.13/34.18  | | | | | | | |   (82)   ~ (all_6_1 = e1)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | BETA: splitting (13) gives:
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | |   (83)  all_58_0 = e0
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | COMBINE_EQS: (66), (83) imply:
% 203.13/34.18  | | | | | | | | |   (84)  e1 = e0
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | REDUCE: (46), (84) imply:
% 203.13/34.18  | | | | | | | | |   (85)  $false
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | CLOSE: (85) is inconsistent.
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | |   (86)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | BETA: splitting (86) gives:
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | |   (87)  all_58_2 = e0
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | COMBINE_EQS: (24), (87) imply:
% 203.13/34.18  | | | | | | | | | |   (88)  all_52_3 = e0
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | SIMP: (88) implies:
% 203.13/34.18  | | | | | | | | | |   (89)  all_52_3 = e0
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | REDUCE: (79), (89) imply:
% 203.13/34.18  | | | | | | | | | |   (90)   ~ (all_6_1 = e0)
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | REDUCE: (2), (89) imply:
% 203.13/34.18  | | | | | | | | | |   (91)  op(e0, e0) = all_52_2
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | BETA: splitting (61) gives:
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | |   (92)  all_56_8 = e2
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | COMBINE_EQS: (77), (92) imply:
% 203.13/34.18  | | | | | | | | | | |   (93)  all_6_1 = e2
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | SIMP: (93) implies:
% 203.13/34.18  | | | | | | | | | | |   (94)  all_6_1 = e2
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | REDUCE: (81), (94) imply:
% 203.13/34.18  | | | | | | | | | | |   (95)   ~ (all_52_29 = e2)
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | REDUCE: (38), (94) imply:
% 203.13/34.18  | | | | | | | | | | |   (96)  op(e3, e2) = e2
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | BETA: splitting (20) gives:
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | |   (97)  all_56_11 = e2
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | REF_CLOSE: (16), (95), (97) are inconsistent by sub-proof
% 203.13/34.18  | | | | | | | | | | | |            #1024.
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | |   (98)  all_56_11 = e1 | all_56_11 = e0
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | BETA: splitting (98) gives:
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_52_2, e0, e0,
% 203.13/34.18  | | | | | | | | | | | | |              simplifying with (19), (91) gives:
% 203.13/34.18  | | | | | | | | | | | | |   (99)  all_52_2 = e0
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_9, e2, e2, e3,
% 203.13/34.18  | | | | | | | | | | | | |              simplifying with (44), (96) gives:
% 203.13/34.18  | | | | | | | | | | | | |   (100)  all_52_9 = e2
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | REDUCE: (48), (100) imply:
% 203.13/34.18  | | | | | | | | | | | | |   (101)   ~ (all_52_17 = e2)
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | SIMP: (101) implies:
% 203.13/34.18  | | | | | | | | | | | | |   (102)   ~ (all_52_17 = e2)
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | REF_CLOSE: (3), (19), (25), (41), (42), (54), (70), (102) are
% 203.13/34.18  | | | | | | | | | | | | |            inconsistent by sub-proof #1262.
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | |   (103)  all_56_11 = e0
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | | REF_CLOSE: (16), (31), (103) are inconsistent by sub-proof
% 203.13/34.18  | | | | | | | | | | | | |            #1002.
% 203.13/34.18  | | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | | End of split
% 203.13/34.18  | | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | End of split
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | |   (104)  all_56_8 = e1 | all_56_8 = e0
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | | REF_CLOSE: (75), (77), (82), (104) are inconsistent by
% 203.13/34.18  | | | | | | | | | | |            sub-proof #495.
% 203.13/34.18  | | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | End of split
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | |   (105)  all_58_6 = e0 | all_58_12 = e0
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | REF_CLOSE: (4), (50), (75), (78), (105) are inconsistent by
% 203.13/34.18  | | | | | | | | | |            sub-proof #485.
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | End of split
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | End of split
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | End of split
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | Case 2:
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | |   (106)   ~ (all_58_0 = e1)
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | REDUCE: (8), (106) imply:
% 203.13/34.18  | | | | | | |   (107)   ~ (all_6_2 = e1)
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | REF_CLOSE: (1), (3), (10), (22), (36), (38), (39), (40), (51),
% 203.13/34.18  | | | | | | |            (57), (65), (107) are inconsistent by sub-proof #494.
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | End of split
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | End of split
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | End of split
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | End of split
% 203.13/34.18  | | | 
% 203.13/34.18  | | End of split
% 203.13/34.18  | | 
% 203.13/34.18  | End of split
% 203.13/34.18  | 
% 203.13/34.18  End of proof
% 203.13/34.18  
% 203.13/34.18  Sub-proof #485 shows that the following formulas are inconsistent:
% 203.13/34.18  ----------------------------------------------------------------
% 203.13/34.18    (1)   ~ (e3 = e0)
% 203.13/34.18    (2)  all_58_6 = e0 | all_58_12 = e0
% 203.13/34.18    (3)   ~ (all_6_1 = e0)
% 203.13/34.18    (4)  all_58_6 = all_6_1
% 203.13/34.18    (5)  all_58_12 = e3
% 203.13/34.18  
% 203.13/34.18  Begin of proof
% 203.13/34.18  | 
% 203.13/34.18  | BETA: splitting (2) gives:
% 203.13/34.18  | 
% 203.13/34.18  | Case 1:
% 203.13/34.18  | | 
% 203.13/34.18  | |   (6)  all_58_6 = e0
% 203.13/34.18  | | 
% 203.13/34.18  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #486.
% 203.13/34.18  | | 
% 203.13/34.18  | Case 2:
% 203.13/34.18  | | 
% 203.13/34.18  | |   (7)  all_58_12 = e0
% 203.13/34.18  | | 
% 203.13/34.18  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1212.
% 203.13/34.18  | | 
% 203.13/34.18  | End of split
% 203.13/34.18  | 
% 203.13/34.18  End of proof
% 203.13/34.18  
% 203.13/34.18  Sub-proof #486 shows that the following formulas are inconsistent:
% 203.13/34.18  ----------------------------------------------------------------
% 203.13/34.18    (1)  all_58_6 = all_6_1
% 203.13/34.18    (2)  all_58_6 = e0
% 203.13/34.18    (3)   ~ (all_6_1 = e0)
% 203.13/34.18  
% 203.13/34.18  Begin of proof
% 203.13/34.18  | 
% 203.13/34.18  | COMBINE_EQS: (1), (2) imply:
% 203.13/34.18  |   (4)  all_6_1 = e0
% 203.13/34.18  | 
% 203.13/34.18  | SIMP: (4) implies:
% 203.13/34.18  |   (5)  all_6_1 = e0
% 203.13/34.18  | 
% 203.13/34.18  | REDUCE: (3), (5) imply:
% 203.13/34.18  |   (6)  $false
% 203.13/34.18  | 
% 203.13/34.18  | CLOSE: (6) is inconsistent.
% 203.13/34.18  | 
% 203.13/34.18  End of proof
% 203.13/34.18  
% 203.13/34.18  Sub-proof #487 shows that the following formulas are inconsistent:
% 203.13/34.18  ----------------------------------------------------------------
% 203.13/34.18    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.18    (2)   ~ (all_52_15 = all_52_23)
% 203.13/34.18    (3)   ~ (all_52_25 = all_52_27)
% 203.13/34.18    (4)  all_58_14 = all_52_23
% 203.13/34.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.18    (6)  all_58_1 = all_52_9
% 203.13/34.18    (7)   ~ (all_52_9 = all_52_13)
% 203.13/34.18    (8)   ~ (e3 = e0)
% 203.13/34.18    (9)  op(e2, e3) = all_52_3
% 203.13/34.18    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.18    (11)   ~ (all_52_7 = all_52_15)
% 203.13/34.18    (12)  op(all_52_15, all_52_15) = e0
% 203.13/34.18    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.18    (14)   ~ (all_52_17 = all_52_25)
% 203.13/34.18    (15)   ~ (all_52_3 = all_6_2)
% 203.13/34.18    (16)  all_44_2 = all_6_2
% 203.13/34.18    (17)  all_58_0 = all_6_2
% 203.13/34.18    (18)  all_56_4 = all_52_3
% 203.13/34.18    (19)   ~ (all_52_17 = all_10_2)
% 203.13/34.18    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 203.13/34.18    (21)  op(e3, e0) = all_52_25
% 203.13/34.18    (22)   ~ (all_52_27 = all_52_29)
% 203.13/34.18    (23)  all_58_13 = all_52_15
% 203.13/34.18    (24)  op(all_52_13, all_52_13) = e1
% 203.13/34.18    (25)  all_58_9 = all_52_25
% 203.13/34.18    (26)  op(all_52_27, all_52_27) = all_52_26
% 203.13/34.18    (27)  op(e1, e3) = all_52_5
% 203.13/34.18    (28)  op(e2, e2) = all_4_2
% 203.13/34.18    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.18    (30)  all_58_11 = all_52_29
% 203.13/34.18    (31)   ~ (all_52_9 = all_52_15)
% 203.13/34.18    (32)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.13/34.18    (33)  op(all_10_2, e1) = all_10_1
% 203.13/34.18    (34)  op(all_6_2, all_6_2) = all_52_0
% 203.13/34.18    (35)   ~ (all_52_7 = all_6_2)
% 203.13/34.18    (36)  op(e0, e1) = all_52_23
% 203.13/34.18    (37)   ~ (all_52_15 = e0)
% 203.13/34.18    (38)  all_58_15 = e0
% 203.13/34.18    (39)  all_56_11 = all_52_29
% 203.13/34.18    (40)   ~ (all_4_1 = e1)
% 203.13/34.18    (41)   ~ (all_52_25 = e0)
% 203.13/34.18    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.18    (43)   ~ (e2 = e1)
% 203.13/34.18    (44)  op(e0, e0) = e0
% 203.13/34.18    (45)  all_58_10 = all_52_27
% 203.13/34.18    (46)  all_56_8 = all_52_5
% 203.13/34.18    (47)   ~ (all_52_25 = all_52_29)
% 203.13/34.18    (48)  all_58_7 = all_52_13
% 203.13/34.18    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.13/34.18    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.18    (51)   ~ (all_52_5 = all_52_7)
% 203.13/34.18    (52)  all_58_12 = all_52_7
% 203.13/34.18    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.18    (54)  all_58_2 = all_52_3
% 203.13/34.18    (55)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.18    (56)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.18    (57)   ~ (e2 = e0)
% 203.13/34.18    (58)  op(all_4_2, e2) = all_4_1
% 203.13/34.18    (59)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.13/34.18    (60)   ~ (all_52_5 = all_52_29)
% 203.13/34.18    (61)   ~ (all_52_29 = e0)
% 203.13/34.18    (62)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.18    (63)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.18    (64)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.13/34.18    (65)  op(e3, e1) = all_52_17
% 203.13/34.18    (66)  op(e0, e3) = all_52_7
% 203.13/34.18    (67)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.18    (68)   ~ (all_52_9 = all_52_25)
% 203.13/34.18    (69)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.18    (70)   ~ (all_10_1 = e2)
% 203.13/34.18    (71)  all_58_8 = all_10_2
% 203.13/34.18    (72)   ~ (all_52_23 = e0)
% 203.13/34.18    (73)  op(all_52_29, all_52_29) = all_52_28
% 203.13/34.18    (74)  all_56_12 = all_52_7
% 203.13/34.18    (75)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.18    (76)  all_8_2 = all_6_2
% 203.13/34.18    (77)   ~ (all_52_25 = all_6_2)
% 203.13/34.18    (78)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.18    (79)   ~ (all_52_5 = all_6_2)
% 203.13/34.18    (80)  op(all_4_2, all_4_2) = e2
% 203.13/34.18    (81)   ~ (all_52_9 = all_6_2)
% 203.13/34.18    (82)  op(e3, all_6_1) = e2
% 203.13/34.18    (83)  all_56_0 = all_6_2
% 203.13/34.18    (84)  op(e3, e3) = all_6_2
% 203.13/34.18    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.18    (86)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.18    (87)  all_56_14 = all_52_23
% 203.13/34.18    (88)  all_56_3 = all_52_25
% 203.13/34.18    (89)   ~ (all_52_3 = all_52_7)
% 203.13/34.18    (90)   ~ (all_10_1 = e3)
% 203.13/34.18    (91)  all_56_1 = all_52_9
% 203.13/34.18    (92)   ~ (all_52_15 = all_4_2)
% 203.13/34.18    (93)  all_58_6 = all_52_5
% 203.13/34.18    (94)  op(e3, e2) = all_52_9
% 203.13/34.18    (95)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.18    (96)   ~ (all_52_17 = all_6_2)
% 203.13/34.18    (97)   ~ (e1 = e0)
% 203.13/34.18    (98)   ~ (e3 = e2)
% 203.13/34.18    (99)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.18    (100)  all_44_1 = all_6_1
% 203.13/34.18    (101)   ~ (all_52_9 = all_52_17)
% 203.13/34.18    (102)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.13/34.18    (103)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.18    (104)  op(e1, e1) = all_10_2
% 203.13/34.18    (105)  op(all_52_9, all_52_9) = e3
% 203.13/34.18    (106)   ~ (all_52_23 = all_10_2)
% 203.13/34.18    (107)   ~ (all_52_7 = all_52_23)
% 203.13/34.18    (108)  all_58_3 = all_4_2
% 203.13/34.18    (109)  all_56_13 = all_52_15
% 203.13/34.18    (110)  all_8_1 = all_6_1
% 203.13/34.18    (111)  op(all_6_2, e3) = all_6_1
% 203.13/34.18    (112)   ~ (all_52_13 = all_52_29)
% 203.13/34.18    (113)  all_58_4 = all_52_17
% 203.13/34.18    (114)   ~ (all_52_7 = e0)
% 203.13/34.18    (115)  op(all_52_25, all_52_25) = all_52_24
% 203.13/34.18  
% 203.13/34.18  Begin of proof
% 203.13/34.18  | 
% 203.13/34.18  | BETA: splitting (42) gives:
% 203.13/34.18  | 
% 203.13/34.18  | Case 1:
% 203.13/34.18  | | 
% 203.13/34.18  | |   (116)  all_56_13 = e3
% 203.13/34.18  | | 
% 203.13/34.18  | | COMBINE_EQS: (109), (116) imply:
% 203.13/34.18  | |   (117)  all_52_15 = e3
% 203.13/34.18  | | 
% 203.13/34.18  | | REF_CLOSE: (1), (2), (5), (10), (11), (12), (13), (28), (35), (49), (66),
% 203.13/34.18  | |            (72), (74), (76), (82), (84), (87), (92), (94), (105), (107),
% 203.13/34.18  | |            (110), (111), (117) are inconsistent by sub-proof #499.
% 203.13/34.18  | | 
% 203.13/34.18  | Case 2:
% 203.13/34.18  | | 
% 203.13/34.18  | |   (118)   ~ (all_56_13 = e3)
% 203.13/34.18  | |   (119)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (109), (118) imply:
% 203.13/34.18  | |   (120)   ~ (all_52_15 = e3)
% 203.13/34.18  | | 
% 203.13/34.18  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.13/34.18  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.13/34.18  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.13/34.18  | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 203.13/34.18  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.13/34.18  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.13/34.18  | |            (69), (70), (71), (73), (74), (75), (76), (77), (78), (79), (80),
% 203.13/34.18  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 203.13/34.18  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.13/34.18  | |            (102), (103), (104), (105), (106), (107), (108), (109), (111),
% 203.13/34.18  | |            (112), (113), (114), (115), (119), (120) are inconsistent by
% 203.13/34.18  | |            sub-proof #488.
% 203.13/34.18  | | 
% 203.13/34.18  | End of split
% 203.13/34.18  | 
% 203.13/34.18  End of proof
% 203.13/34.18  
% 203.13/34.18  Sub-proof #488 shows that the following formulas are inconsistent:
% 203.13/34.18  ----------------------------------------------------------------
% 203.13/34.18    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.18    (2)   ~ (all_52_15 = all_52_23)
% 203.13/34.18    (3)   ~ (all_52_25 = all_52_27)
% 203.13/34.18    (4)  all_58_14 = all_52_23
% 203.13/34.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.18    (6)  all_58_1 = all_52_9
% 203.13/34.18    (7)   ~ (all_52_9 = all_52_13)
% 203.13/34.18    (8)   ~ (e3 = e0)
% 203.13/34.18    (9)  op(e2, e3) = all_52_3
% 203.13/34.18    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.18    (11)   ~ (all_52_7 = all_52_15)
% 203.13/34.18    (12)  op(all_52_15, all_52_15) = e0
% 203.13/34.18    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.18    (14)   ~ (all_52_17 = all_52_25)
% 203.13/34.18    (15)   ~ (all_52_3 = all_6_2)
% 203.13/34.18    (16)  all_44_2 = all_6_2
% 203.13/34.18    (17)  all_58_0 = all_6_2
% 203.13/34.18    (18)  all_56_4 = all_52_3
% 203.13/34.18    (19)   ~ (all_52_17 = all_10_2)
% 203.13/34.18    (20)   ~ (all_44_1 = e0) |  ~ (all_44_2 = e1)
% 203.13/34.18    (21)  op(e3, e0) = all_52_25
% 203.13/34.18    (22)   ~ (all_52_27 = all_52_29)
% 203.13/34.18    (23)  all_58_13 = all_52_15
% 203.13/34.18    (24)  op(all_52_13, all_52_13) = e1
% 203.13/34.18    (25)  all_58_9 = all_52_25
% 203.13/34.18    (26)   ~ (all_52_15 = e3)
% 203.13/34.18    (27)  op(all_52_27, all_52_27) = all_52_26
% 203.13/34.18    (28)  op(e1, e3) = all_52_5
% 203.13/34.18    (29)  op(e2, e2) = all_4_2
% 203.13/34.18    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.18    (31)  all_58_11 = all_52_29
% 203.13/34.18    (32)   ~ (all_52_9 = all_52_15)
% 203.13/34.18    (33)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.13/34.18    (34)  op(all_10_2, e1) = all_10_1
% 203.13/34.18    (35)  op(all_6_2, all_6_2) = all_52_0
% 203.13/34.18    (36)   ~ (all_52_7 = all_6_2)
% 203.13/34.18    (37)  op(e0, e1) = all_52_23
% 203.13/34.18    (38)   ~ (all_52_15 = e0)
% 203.13/34.18    (39)  all_58_15 = e0
% 203.13/34.18    (40)  all_56_11 = all_52_29
% 203.13/34.18    (41)   ~ (all_4_1 = e1)
% 203.13/34.18    (42)   ~ (all_52_25 = e0)
% 203.13/34.18    (43)   ~ (e2 = e1)
% 203.13/34.18    (44)  op(e0, e0) = e0
% 203.13/34.18    (45)  all_58_10 = all_52_27
% 203.13/34.18    (46)  all_56_8 = all_52_5
% 203.13/34.18    (47)   ~ (all_52_25 = all_52_29)
% 203.13/34.18    (48)  all_58_7 = all_52_13
% 203.13/34.18    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.13/34.18    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.18    (51)   ~ (all_52_5 = all_52_7)
% 203.13/34.18    (52)  all_58_12 = all_52_7
% 203.13/34.18    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.18    (54)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.13/34.18    (55)  all_58_2 = all_52_3
% 203.13/34.18    (56)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.18    (57)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.18    (58)   ~ (e2 = e0)
% 203.13/34.18    (59)  op(all_4_2, e2) = all_4_1
% 203.13/34.18    (60)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.13/34.18    (61)   ~ (all_52_5 = all_52_29)
% 203.13/34.18    (62)   ~ (all_52_29 = e0)
% 203.13/34.18    (63)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.18    (64)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.18    (65)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.13/34.18    (66)  op(e3, e1) = all_52_17
% 203.13/34.18    (67)  op(e0, e3) = all_52_7
% 203.13/34.18    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.18    (69)   ~ (all_52_9 = all_52_25)
% 203.13/34.18    (70)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.18    (71)   ~ (all_10_1 = e2)
% 203.13/34.18    (72)  all_58_8 = all_10_2
% 203.13/34.18    (73)  op(all_52_29, all_52_29) = all_52_28
% 203.13/34.18    (74)  all_56_12 = all_52_7
% 203.13/34.18    (75)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.18    (76)  all_8_2 = all_6_2
% 203.13/34.18    (77)   ~ (all_52_25 = all_6_2)
% 203.13/34.18    (78)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.18    (79)   ~ (all_52_5 = all_6_2)
% 203.13/34.18    (80)  op(all_4_2, all_4_2) = e2
% 203.13/34.18    (81)   ~ (all_52_9 = all_6_2)
% 203.13/34.18    (82)  op(e3, all_6_1) = e2
% 203.13/34.18    (83)  all_56_0 = all_6_2
% 203.13/34.18    (84)  op(e3, e3) = all_6_2
% 203.13/34.18    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.18    (86)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.18    (87)  all_56_14 = all_52_23
% 203.13/34.18    (88)  all_56_3 = all_52_25
% 203.13/34.18    (89)   ~ (all_52_3 = all_52_7)
% 203.13/34.18    (90)   ~ (all_10_1 = e3)
% 203.13/34.18    (91)  all_56_1 = all_52_9
% 203.13/34.18    (92)   ~ (all_52_15 = all_4_2)
% 203.13/34.18    (93)  all_58_6 = all_52_5
% 203.13/34.18    (94)  op(e3, e2) = all_52_9
% 203.13/34.18    (95)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.18    (96)   ~ (all_52_17 = all_6_2)
% 203.13/34.18    (97)   ~ (e1 = e0)
% 203.13/34.18    (98)   ~ (e3 = e2)
% 203.13/34.18    (99)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.18    (100)  all_44_1 = all_6_1
% 203.13/34.18    (101)   ~ (all_52_9 = all_52_17)
% 203.13/34.18    (102)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.13/34.18    (103)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.18    (104)  op(e1, e1) = all_10_2
% 203.13/34.18    (105)  op(all_52_9, all_52_9) = e3
% 203.13/34.18    (106)   ~ (all_52_23 = all_10_2)
% 203.13/34.18    (107)   ~ (all_52_7 = all_52_23)
% 203.13/34.18    (108)  all_58_3 = all_4_2
% 203.13/34.18    (109)  all_56_13 = all_52_15
% 203.13/34.18    (110)  op(all_6_2, e3) = all_6_1
% 203.13/34.18    (111)   ~ (all_52_13 = all_52_29)
% 203.13/34.18    (112)  all_58_4 = all_52_17
% 203.13/34.18    (113)   ~ (all_52_7 = e0)
% 203.13/34.18    (114)  op(all_52_25, all_52_25) = all_52_24
% 203.13/34.18  
% 203.13/34.18  Begin of proof
% 203.13/34.18  | 
% 203.13/34.18  | BETA: splitting (95) gives:
% 203.13/34.18  | 
% 203.13/34.18  | Case 1:
% 203.13/34.18  | | 
% 203.13/34.18  | |   (115)  all_58_12 = e3
% 203.13/34.18  | | 
% 203.13/34.18  | | COMBINE_EQS: (52), (115) imply:
% 203.13/34.18  | |   (116)  all_52_7 = e3
% 203.13/34.18  | | 
% 203.13/34.18  | | SIMP: (116) implies:
% 203.13/34.18  | |   (117)  all_52_7 = e3
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (89), (117) imply:
% 203.13/34.18  | |   (118)   ~ (all_52_3 = e3)
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (51), (117) imply:
% 203.13/34.18  | |   (119)   ~ (all_52_5 = e3)
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (11), (117) imply:
% 203.13/34.18  | |   (120)   ~ (all_52_15 = e3)
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (36), (117) imply:
% 203.13/34.18  | |   (121)   ~ (all_6_2 = e3)
% 203.13/34.18  | | 
% 203.13/34.18  | | SIMP: (121) implies:
% 203.13/34.18  | |   (122)   ~ (all_6_2 = e3)
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (13), (117) imply:
% 203.13/34.18  | |   (123)  op(e3, e3) = all_52_6
% 203.13/34.18  | | 
% 203.13/34.18  | | REDUCE: (67), (117) imply:
% 203.13/34.18  | |   (124)  op(e0, e3) = e3
% 203.13/34.18  | | 
% 203.13/34.18  | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 203.13/34.18  | |              with (84), (123) gives:
% 203.13/34.18  | |   (125)  all_52_6 = all_6_2
% 203.13/34.18  | | 
% 203.13/34.18  | | BETA: splitting (64) gives:
% 203.13/34.18  | | 
% 203.13/34.18  | | Case 1:
% 203.13/34.18  | | | 
% 203.13/34.18  | | |   (126)  all_56_11 = e3
% 203.13/34.18  | | | 
% 203.13/34.18  | | | COMBINE_EQS: (40), (126) imply:
% 203.13/34.18  | | |   (127)  all_52_29 = e3
% 203.13/34.18  | | | 
% 203.13/34.18  | | | SIMP: (127) implies:
% 203.13/34.18  | | |   (128)  all_52_29 = e3
% 203.13/34.18  | | | 
% 203.13/34.18  | | | REDUCE: (111), (128) imply:
% 203.13/34.18  | | |   (129)   ~ (all_52_13 = e3)
% 203.13/34.18  | | | 
% 203.13/34.18  | | | REDUCE: (47), (128) imply:
% 203.13/34.18  | | |   (130)   ~ (all_52_25 = e3)
% 203.13/34.18  | | | 
% 203.13/34.18  | | | REDUCE: (73), (128) imply:
% 203.13/34.18  | | |   (131)  op(e3, e3) = all_52_28
% 203.13/34.18  | | | 
% 203.13/34.18  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_28, e3, e3,
% 203.13/34.18  | | |              simplifying with (84), (131) gives:
% 203.13/34.18  | | |   (132)  all_52_28 = all_6_2
% 203.13/34.18  | | | 
% 203.13/34.18  | | | REF_CLOSE: (5), (6), (17), (23), (25), (26), (41), (44), (48), (59), (68),
% 203.13/34.18  | | |            (75), (80), (81), (84), (86), (91), (94), (99), (101), (102),
% 203.13/34.18  | | |            (105), (108), (112), (122), (129), (130) are inconsistent by
% 203.13/34.18  | | |            sub-proof #1297.
% 203.13/34.18  | | | 
% 203.13/34.18  | | Case 2:
% 203.13/34.18  | | | 
% 203.13/34.18  | | |   (133)   ~ (all_56_11 = e3)
% 203.13/34.18  | | |   (134)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.18  | | | 
% 203.13/34.18  | | | REDUCE: (40), (133) imply:
% 203.13/34.18  | | |   (135)   ~ (all_52_29 = e3)
% 203.13/34.18  | | | 
% 203.13/34.18  | | | BETA: splitting (85) gives:
% 203.13/34.18  | | | 
% 203.13/34.18  | | | Case 1:
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | |   (136)  all_58_9 = e3
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | COMBINE_EQS: (25), (136) imply:
% 203.13/34.18  | | | |   (137)  all_52_25 = e3
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | SIMP: (137) implies:
% 203.13/34.18  | | | |   (138)  all_52_25 = e3
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | REDUCE: (114), (138) imply:
% 203.13/34.18  | | | |   (139)  op(e3, e3) = all_52_24
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | REDUCE: (21), (138) imply:
% 203.13/34.18  | | | |   (140)  op(e3, e0) = e3
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 203.13/34.18  | | | |              simplifying with (84), (139) gives:
% 203.13/34.18  | | | |   (141)  all_52_24 = all_6_2
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | BETA: splitting (103) gives:
% 203.13/34.18  | | | | 
% 203.13/34.18  | | | | Case 1:
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | |   (142)  all_56_0 = e3
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | | REF_CLOSE: (83), (122), (142) are inconsistent by sub-proof #598.
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | Case 2:
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | |   (143)   ~ (all_56_0 = e3)
% 203.13/34.18  | | | | |   (144)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | | BETA: splitting (57) gives:
% 203.13/34.18  | | | | | 
% 203.13/34.18  | | | | | Case 1:
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | |   (145)  all_56_4 = e3
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | | REF_CLOSE: (18), (118), (145) are inconsistent by sub-proof #1340.
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | Case 2:
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | |   (146)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | | BETA: splitting (70) gives:
% 203.13/34.18  | | | | | | 
% 203.13/34.18  | | | | | | Case 1:
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | |   (147)  all_56_8 = e3
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | REF_CLOSE: (46), (119), (147) are inconsistent by sub-proof #1325.
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | Case 2:
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | |   (148)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | BETA: splitting (65) gives:
% 203.13/34.18  | | | | | | | 
% 203.13/34.18  | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | |   (149)  all_58_0 = e2
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | COMBINE_EQS: (17), (149) imply:
% 203.13/34.18  | | | | | | | |   (150)  all_6_2 = e2
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REF_CLOSE: (5), (9), (15), (17), (18), (30), (50), (55), (58),
% 203.13/34.18  | | | | | | | |            (66), (82), (96), (110), (122), (140), (146), (150)
% 203.13/34.18  | | | | | | | |            are inconsistent by sub-proof #496.
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | |   (151)   ~ (all_58_0 = e2)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | REDUCE: (17), (151) imply:
% 203.13/34.18  | | | | | | | |   (152)   ~ (all_6_2 = e2)
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | BETA: splitting (60) gives:
% 203.13/34.18  | | | | | | | | 
% 203.13/34.18  | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | |   (153)  all_58_0 = e1
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | COMBINE_EQS: (17), (153) imply:
% 203.13/34.18  | | | | | | | | |   (154)  all_6_2 = e1
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | COMBINE_EQS: (16), (154) imply:
% 203.13/34.18  | | | | | | | | |   (155)  all_44_2 = e1
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | REDUCE: (79), (154) imply:
% 203.13/34.18  | | | | | | | | |   (156)   ~ (all_52_5 = e1)
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | REDUCE: (35), (154) imply:
% 203.13/34.18  | | | | | | | | |   (157)  op(e1, e1) = all_52_0
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | REDUCE: (110), (154) imply:
% 203.13/34.18  | | | | | | | | |   (158)  op(e1, e3) = all_6_1
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | BETA: splitting (20) gives:
% 203.13/34.18  | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | Case 1:
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | |   (159)   ~ (all_44_2 = e1)
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | REDUCE: (155), (159) imply:
% 203.13/34.18  | | | | | | | | | |   (160)  $false
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | CLOSE: (160) is inconsistent.
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | Case 2:
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | |   (161)   ~ (all_44_1 = e0)
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.18  | | | | | | | | | | REDUCE: (100), (161) imply:
% 203.13/34.18  | | | | | | | | | |   (162)   ~ (all_6_1 = e0)
% 203.13/34.18  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_0, e1, e1,
% 203.13/34.19  | | | | | | | | | |              simplifying with (104), (157) gives:
% 203.13/34.19  | | | | | | | | | |   (163)  all_52_0 = all_10_2
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_5, all_6_1, e3, e1,
% 203.13/34.19  | | | | | | | | | |              simplifying with (28), (158) gives:
% 203.13/34.19  | | | | | | | | | |   (164)  all_52_5 = all_6_1
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | COMBINE_EQS: (46), (164) imply:
% 203.13/34.19  | | | | | | | | | |   (165)  all_56_8 = all_6_1
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | REDUCE: (61), (164) imply:
% 203.13/34.19  | | | | | | | | | |   (166)   ~ (all_52_29 = all_6_1)
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | SIMP: (166) implies:
% 203.13/34.19  | | | | | | | | | |   (167)   ~ (all_52_29 = all_6_1)
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | REDUCE: (156), (164) imply:
% 203.13/34.19  | | | | | | | | | |   (168)   ~ (all_6_1 = e1)
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | BETA: splitting (148) gives:
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | Case 1:
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | |   (169)  all_56_8 = e2
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | COMBINE_EQS: (165), (169) imply:
% 203.13/34.19  | | | | | | | | | | |   (170)  all_6_1 = e2
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | SIMP: (170) implies:
% 203.13/34.19  | | | | | | | | | | |   (171)  all_6_1 = e2
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | REDUCE: (167), (171) imply:
% 203.13/34.19  | | | | | | | | | | |   (172)   ~ (all_52_29 = e2)
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | REDUCE: (82), (171) imply:
% 203.13/34.19  | | | | | | | | | | |   (173)  op(e3, e2) = e2
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | BETA: splitting (134) gives:
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | Case 1:
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | |   (174)  all_56_11 = e2
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | REF_CLOSE: (40), (172), (174) are inconsistent by sub-proof
% 203.13/34.19  | | | | | | | | | | | |            #1024.
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | |   (175)  all_56_11 = e1 | all_56_11 = e0
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | BETA: splitting (175) gives:
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | Case 1:
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | |   (176)  all_56_11 = e1
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | COMBINE_EQS: (40), (176) imply:
% 203.13/34.19  | | | | | | | | | | | | |   (177)  all_52_29 = e1
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | SIMP: (177) implies:
% 203.13/34.19  | | | | | | | | | | | | |   (178)  all_52_29 = e1
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | REDUCE: (73), (178) imply:
% 203.13/34.19  | | | | | | | | | | | | |   (179)  op(e1, e1) = all_52_28
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_28, e1,
% 203.13/34.19  | | | | | | | | | | | | |              e1, simplifying with (104), (179) gives:
% 203.13/34.19  | | | | | | | | | | | | |   (180)  all_52_28 = all_10_2
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_9, e2, e2, e3,
% 203.13/34.19  | | | | | | | | | | | | |              simplifying with (94), (173) gives:
% 203.13/34.19  | | | | | | | | | | | | |   (181)  all_52_9 = e2
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | REDUCE: (32), (181) imply:
% 203.13/34.19  | | | | | | | | | | | | |   (182)   ~ (all_52_15 = e2)
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | SIMP: (182) implies:
% 203.13/34.19  | | | | | | | | | | | | |   (183)   ~ (all_52_15 = e2)
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | BETA: splitting (54) gives:
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | Case 1:
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | |   (184)  all_56_13 = e2
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | REF_CLOSE: (109), (183), (184) are inconsistent by sub-proof
% 203.13/34.19  | | | | | | | | | | | | | |            #1356.
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | |   (185)  all_56_13 = e1 | all_56_13 = e0
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | Case 1:
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | |   (186)  all_56_13 = e1
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | COMBINE_EQS: (109), (186) imply:
% 203.13/34.19  | | | | | | | | | | | | | | |   (187)  all_52_15 = e1
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | SIMP: (187) implies:
% 203.13/34.19  | | | | | | | | | | | | | | |   (188)  all_52_15 = e1
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | REDUCE: (2), (188) imply:
% 203.13/34.19  | | | | | | | | | | | | | | |   (189)   ~ (all_52_23 = e1)
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | SIMP: (189) implies:
% 203.13/34.19  | | | | | | | | | | | | | | |   (190)   ~ (all_52_23 = e1)
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | REDUCE: (12), (188) imply:
% 203.13/34.19  | | | | | | | | | | | | | | |   (191)  op(e1, e1) = e0
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | REF_CLOSE: (5), (34), (37), (49), (71), (87), (90), (104),
% 203.13/34.19  | | | | | | | | | | | | | | |            (106), (190), (191) are inconsistent by sub-proof
% 203.13/34.19  | | | | | | | | | | | | | | |            #1380.
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | |   (192)  all_56_13 = e0
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | | REF_CLOSE: (38), (109), (192) are inconsistent by sub-proof
% 203.13/34.19  | | | | | | | | | | | | | | |            #1354.
% 203.13/34.19  | | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | |   (193)  all_56_11 = e0
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | | REF_CLOSE: (40), (62), (193) are inconsistent by sub-proof
% 203.13/34.19  | | | | | | | | | | | | |            #1002.
% 203.13/34.19  | | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | |   (194)  all_56_8 = e1 | all_56_8 = e0
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | | REF_CLOSE: (162), (165), (168), (194) are inconsistent by
% 203.13/34.19  | | | | | | | | | | |            sub-proof #495.
% 203.13/34.19  | | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | | 
% 203.13/34.19  | | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | | 
% 203.13/34.19  | | | | | | | | |   (195)   ~ (all_58_0 = e1)
% 203.13/34.19  | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | REDUCE: (17), (195) imply:
% 203.13/34.19  | | | | | | | | |   (196)   ~ (all_6_2 = e1)
% 203.13/34.19  | | | | | | | | | 
% 203.13/34.19  | | | | | | | | | REF_CLOSE: (1), (5), (76), (82), (83), (84), (110), (123),
% 203.13/34.19  | | | | | | | | |            (124), (144), (152), (196) are inconsistent by
% 203.13/34.19  | | | | | | | | |            sub-proof #494.
% 203.13/34.19  | | | | | | | | | 
% 203.13/34.19  | | | | | | | | End of split
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | End of split
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | End of split
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | End of split
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | End of split
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | Case 2:
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | |   (197)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | REF_CLOSE: (3), (5), (6), (7), (8), (14), (17), (19), (22), (24), (25),
% 203.13/34.19  | | | |            (27), (31), (39), (42), (44), (45), (48), (53), (56), (68),
% 203.13/34.19  | | | |            (69), (72), (75), (77), (78), (81), (82), (84), (86), (88),
% 203.13/34.19  | | | |            (91), (93), (97), (98), (99), (105), (110), (112), (119),
% 203.13/34.19  | | | |            (122), (135), (197) are inconsistent by sub-proof #489.
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | End of split
% 203.13/34.19  | | | 
% 203.13/34.19  | | End of split
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (198)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (4), (5), (8), (10), (11), (12), (23), (26), (29), (33), (34),
% 203.13/34.19  | |            (37), (38), (39), (43), (44), (52), (54), (63), (74), (80), (90),
% 203.13/34.19  | |            (92), (104), (107), (109), (113), (198) are inconsistent by
% 203.13/34.19  | |            sub-proof #1288.
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #489 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ~ (all_52_25 = all_52_27)
% 203.13/34.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (3)  all_58_1 = all_52_9
% 203.13/34.19    (4)   ~ (all_52_9 = all_52_13)
% 203.13/34.19    (5)   ~ (e3 = e0)
% 203.13/34.19    (6)   ~ (all_52_17 = all_52_25)
% 203.13/34.19    (7)  all_58_0 = all_6_2
% 203.13/34.19    (8)   ~ (all_52_17 = all_10_2)
% 203.13/34.19    (9)   ~ (all_52_27 = all_52_29)
% 203.13/34.19    (10)  op(all_52_13, all_52_13) = e1
% 203.13/34.19    (11)  all_58_9 = all_52_25
% 203.13/34.19    (12)  op(all_52_27, all_52_27) = all_52_26
% 203.13/34.19    (13)  all_58_11 = all_52_29
% 203.13/34.19    (14)  all_58_15 = e0
% 203.13/34.19    (15)   ~ (all_52_25 = e0)
% 203.13/34.19    (16)   ~ (all_6_2 = e3)
% 203.13/34.19    (17)  op(e0, e0) = e0
% 203.13/34.19    (18)  all_58_10 = all_52_27
% 203.13/34.19    (19)  all_58_7 = all_52_13
% 203.13/34.19    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.19    (21)   ~ (all_52_29 = e3)
% 203.13/34.19    (22)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.19    (23)   ~ (all_52_5 = e3)
% 203.13/34.19    (24)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.19    (25)   ~ (all_52_9 = all_52_25)
% 203.13/34.19    (26)  all_58_8 = all_10_2
% 203.13/34.19    (27)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.19    (28)   ~ (all_52_25 = all_6_2)
% 203.13/34.19    (29)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.19    (30)   ~ (all_52_9 = all_6_2)
% 203.13/34.19    (31)  op(e3, all_6_1) = e2
% 203.13/34.19    (32)  op(e3, e3) = all_6_2
% 203.13/34.19    (33)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19    (34)  all_56_3 = all_52_25
% 203.13/34.19    (35)  all_56_1 = all_52_9
% 203.13/34.19    (36)  all_58_6 = all_52_5
% 203.13/34.19    (37)   ~ (e1 = e0)
% 203.13/34.19    (38)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.19    (39)   ~ (e3 = e2)
% 203.13/34.19    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.19    (41)  op(all_52_9, all_52_9) = e3
% 203.13/34.19    (42)  op(all_6_2, e3) = all_6_1
% 203.13/34.19    (43)  all_58_4 = all_52_17
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (38) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (44)  all_58_10 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | COMBINE_EQS: (18), (44) imply:
% 203.13/34.19  | |   (45)  all_52_27 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | SIMP: (45) implies:
% 203.13/34.19  | |   (46)  all_52_27 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REDUCE: (1), (46) imply:
% 203.13/34.19  | |   (47)   ~ (all_52_25 = e3)
% 203.13/34.19  | | 
% 203.13/34.19  | | REDUCE: (9), (46) imply:
% 203.13/34.19  | |   (48)   ~ (all_52_29 = e3)
% 203.13/34.19  | | 
% 203.13/34.19  | | REDUCE: (12), (46) imply:
% 203.13/34.19  | |   (49)  op(e3, e3) = all_52_26
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (13), (15), (16), (17),
% 203.13/34.19  | |            (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 203.13/34.19  | |            (30), (31), (32), (33), (34), (35), (36), (37), (39), (40), (41),
% 203.13/34.19  | |            (42), (43), (47), (49) are inconsistent by sub-proof #490.
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (50)  all_58_11 = e3 | all_58_15 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | BETA: splitting (50) gives:
% 203.13/34.19  | | 
% 203.13/34.19  | | Case 1:
% 203.13/34.19  | | | 
% 203.13/34.19  | | |   (51)  all_58_11 = e3
% 203.13/34.19  | | | 
% 203.13/34.19  | | | REF_CLOSE: (13), (21), (51) are inconsistent by sub-proof #1323.
% 203.13/34.19  | | | 
% 203.13/34.19  | | Case 2:
% 203.13/34.19  | | | 
% 203.13/34.19  | | |   (52)  all_58_15 = e3
% 203.13/34.19  | | | 
% 203.13/34.19  | | | REF_CLOSE: (5), (14), (52) are inconsistent by sub-proof #1350.
% 203.13/34.19  | | | 
% 203.13/34.19  | | End of split
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #490 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (2)  all_58_1 = all_52_9
% 203.13/34.19    (3)   ~ (all_52_9 = all_52_13)
% 203.13/34.19    (4)   ~ (all_52_17 = all_52_25)
% 203.13/34.19    (5)  all_58_0 = all_6_2
% 203.13/34.19    (6)   ~ (all_52_17 = all_10_2)
% 203.13/34.19    (7)  op(all_52_13, all_52_13) = e1
% 203.13/34.19    (8)  all_58_9 = all_52_25
% 203.13/34.19    (9)  all_58_11 = all_52_29
% 203.13/34.19    (10)  op(e3, e3) = all_52_26
% 203.13/34.19    (11)   ~ (all_52_25 = e0)
% 203.13/34.19    (12)   ~ (all_6_2 = e3)
% 203.13/34.19    (13)  op(e0, e0) = e0
% 203.13/34.19    (14)  all_58_7 = all_52_13
% 203.13/34.19    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.19    (16)   ~ (all_52_29 = e3)
% 203.13/34.19    (17)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.19    (18)   ~ (all_52_25 = e3)
% 203.13/34.19    (19)   ~ (all_52_5 = e3)
% 203.13/34.19    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.19    (21)   ~ (all_52_9 = all_52_25)
% 203.13/34.19    (22)  all_58_8 = all_10_2
% 203.13/34.19    (23)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.19    (24)   ~ (all_52_25 = all_6_2)
% 203.13/34.19    (25)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.19    (26)   ~ (all_52_9 = all_6_2)
% 203.13/34.19    (27)  op(e3, all_6_1) = e2
% 203.13/34.19    (28)  op(e3, e3) = all_6_2
% 203.13/34.19    (29)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19    (30)  all_56_3 = all_52_25
% 203.13/34.19    (31)  all_56_1 = all_52_9
% 203.13/34.19    (32)  all_58_6 = all_52_5
% 203.13/34.19    (33)   ~ (e1 = e0)
% 203.13/34.19    (34)   ~ (e3 = e2)
% 203.13/34.19    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.19    (36)  op(all_52_9, all_52_9) = e3
% 203.13/34.19    (37)  op(all_6_2, e3) = all_6_1
% 203.13/34.19    (38)  all_58_4 = all_52_17
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | GROUND_INST: instantiating (1) with all_6_2, all_52_26, e3, e3, simplifying
% 203.13/34.19  |              with (10), (28) gives:
% 203.13/34.19  |   (39)  all_52_26 = all_6_2
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (25) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (40)  all_56_3 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (18), (30), (40) are inconsistent by sub-proof #1339.
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (41)   ~ (all_56_3 = e3)
% 203.13/34.19  | |   (42)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.19  | | 
% 203.13/34.19  | | BETA: splitting (20) gives:
% 203.13/34.19  | | 
% 203.13/34.19  | | Case 1:
% 203.13/34.19  | | | 
% 203.13/34.19  | | |   (43)  all_58_1 = e3
% 203.13/34.19  | | | 
% 203.13/34.19  | | | COMBINE_EQS: (2), (43) imply:
% 203.13/34.19  | | |   (44)  all_52_9 = e3
% 203.13/34.19  | | | 
% 203.13/34.19  | | | REF_CLOSE: (1), (26), (28), (36), (44) are inconsistent by sub-proof
% 203.13/34.19  | | |            #1337.
% 203.13/34.19  | | | 
% 203.13/34.19  | | Case 2:
% 203.13/34.19  | | | 
% 203.13/34.19  | | |   (45)   ~ (all_58_1 = e3)
% 203.13/34.19  | | | 
% 203.13/34.19  | | | REDUCE: (2), (45) imply:
% 203.13/34.19  | | |   (46)   ~ (all_52_9 = e3)
% 203.13/34.19  | | | 
% 203.13/34.19  | | | BETA: splitting (29) gives:
% 203.13/34.19  | | | 
% 203.13/34.19  | | | Case 1:
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | |   (47)  all_58_0 = e3
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | COMBINE_EQS: (5), (47) imply:
% 203.13/34.19  | | | |   (48)  all_6_2 = e3
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | REDUCE: (12), (48) imply:
% 203.13/34.19  | | | |   (49)  $false
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | CLOSE: (49) is inconsistent.
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | Case 2:
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | |   (50)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | BETA: splitting (50) gives:
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | Case 1:
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | |   (51)  all_58_1 = e3
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | | COMBINE_EQS: (2), (51) imply:
% 203.13/34.19  | | | | |   (52)  all_52_9 = e3
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | | REDUCE: (46), (52) imply:
% 203.13/34.19  | | | | |   (53)  $false
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | | CLOSE: (53) is inconsistent.
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | Case 2:
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | |   (54)  all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | | BETA: splitting (54) gives:
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | | Case 1:
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | |   (55)  all_58_4 = e3
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | COMBINE_EQS: (38), (55) imply:
% 203.13/34.19  | | | | | |   (56)  all_52_17 = e3
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | SIMP: (56) implies:
% 203.13/34.19  | | | | | |   (57)  all_52_17 = e3
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | REDUCE: (4), (57) imply:
% 203.13/34.19  | | | | | |   (58)   ~ (all_52_25 = e3)
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | REDUCE: (23), (57) imply:
% 203.13/34.19  | | | | | |   (59)  op(e3, e3) = all_52_16
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | BETA: splitting (15) gives:
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | Case 1:
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | |   (60)  all_58_6 = e3
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | | REF_CLOSE: (19), (32), (60) are inconsistent by sub-proof #1328.
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | Case 2:
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | |   (61)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | | BETA: splitting (61) gives:
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | | Case 1:
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | |   (62)  all_58_7 = e3
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (11), (13), (14), (17),
% 203.13/34.19  | | | | | | | |            (21), (24), (26), (28), (30), (31), (33), (35), (36),
% 203.13/34.19  | | | | | | | |            (42), (59), (62) are inconsistent by sub-proof #493.
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | Case 2:
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | |   (63)  all_58_8 = e3 | all_58_11 = e3
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (16), (18), (22), (26),
% 203.13/34.19  | | | | | | | |            (27), (28), (29), (34), (36), (37), (38), (63) are
% 203.13/34.19  | | | | | | | |            inconsistent by sub-proof #491.
% 203.13/34.19  | | | | | | | | 
% 203.13/34.19  | | | | | | | End of split
% 203.13/34.19  | | | | | | | 
% 203.13/34.19  | | | | | | End of split
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | Case 2:
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | |   (64)  all_58_9 = e3
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | | REF_CLOSE: (8), (18), (64) are inconsistent by sub-proof #1300.
% 203.13/34.19  | | | | | | 
% 203.13/34.19  | | | | | End of split
% 203.13/34.19  | | | | | 
% 203.13/34.19  | | | | End of split
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | End of split
% 203.13/34.19  | | | 
% 203.13/34.19  | | End of split
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #491 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (2)  all_58_1 = all_52_9
% 203.13/34.19    (3)  all_58_0 = all_6_2
% 203.13/34.19    (4)   ~ (all_52_17 = all_10_2)
% 203.13/34.19    (5)  all_58_9 = all_52_25
% 203.13/34.19    (6)  all_58_11 = all_52_29
% 203.13/34.19    (7)  all_58_8 = e3 | all_58_11 = e3
% 203.13/34.19    (8)   ~ (all_52_29 = e3)
% 203.13/34.19    (9)   ~ (all_52_25 = e3)
% 203.13/34.19    (10)  all_58_8 = all_10_2
% 203.13/34.19    (11)   ~ (all_52_9 = all_6_2)
% 203.13/34.19    (12)  op(e3, all_6_1) = e2
% 203.13/34.19    (13)  op(e3, e3) = all_6_2
% 203.13/34.19    (14)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19    (15)   ~ (e3 = e2)
% 203.13/34.19    (16)  op(all_52_9, all_52_9) = e3
% 203.13/34.19    (17)  op(all_6_2, e3) = all_6_1
% 203.13/34.19    (18)  all_58_4 = all_52_17
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (7) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (19)  all_58_8 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | COMBINE_EQS: (10), (19) imply:
% 203.13/34.19  | |   (20)  all_10_2 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REDUCE: (4), (20) imply:
% 203.13/34.19  | |   (21)   ~ (all_52_17 = e3)
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (1), (2), (3), (5), (9), (11), (12), (13), (14), (15), (16),
% 203.13/34.19  | |            (17), (18), (21) are inconsistent by sub-proof #492.
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (22)  all_58_11 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (6), (8), (22) are inconsistent by sub-proof #1323.
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #492 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (2)  all_58_1 = all_52_9
% 203.13/34.19    (3)  all_58_0 = all_6_2
% 203.13/34.19    (4)  all_58_9 = all_52_25
% 203.13/34.19    (5)   ~ (all_52_25 = e3)
% 203.13/34.19    (6)   ~ (all_52_9 = all_6_2)
% 203.13/34.19    (7)  op(e3, all_6_1) = e2
% 203.13/34.19    (8)  op(e3, e3) = all_6_2
% 203.13/34.19    (9)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19    (10)   ~ (all_52_17 = e3)
% 203.13/34.19    (11)   ~ (e3 = e2)
% 203.13/34.19    (12)  op(all_52_9, all_52_9) = e3
% 203.13/34.19    (13)  op(all_6_2, e3) = all_6_1
% 203.13/34.19    (14)  all_58_4 = all_52_17
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (9) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (15)  all_58_0 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | COMBINE_EQS: (3), (15) imply:
% 203.13/34.19  | |   (16)  all_6_2 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (1), (7), (8), (11), (13), (16) are inconsistent by sub-proof
% 203.13/34.19  | |            #502.
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (17)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (12), (14), (17) are
% 203.13/34.19  | |            inconsistent by sub-proof #1138.
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #493 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (2)  all_58_1 = all_52_9
% 203.13/34.19    (3)   ~ (all_52_9 = all_52_13)
% 203.13/34.19    (4)  all_58_0 = all_6_2
% 203.13/34.19    (5)  op(all_52_13, all_52_13) = e1
% 203.13/34.19    (6)   ~ (all_52_25 = e0)
% 203.13/34.19    (7)  op(e0, e0) = e0
% 203.13/34.19    (8)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.19    (9)  all_58_7 = all_52_13
% 203.13/34.19    (10)  op(e3, e3) = all_52_16
% 203.13/34.19    (11)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.19    (12)  all_58_7 = e3
% 203.13/34.19    (13)   ~ (all_52_9 = all_52_25)
% 203.13/34.19    (14)   ~ (all_52_25 = all_6_2)
% 203.13/34.19    (15)   ~ (all_52_9 = all_6_2)
% 203.13/34.19    (16)  op(e3, e3) = all_6_2
% 203.13/34.19    (17)  all_56_3 = all_52_25
% 203.13/34.19    (18)  all_56_1 = all_52_9
% 203.13/34.19    (19)   ~ (e1 = e0)
% 203.13/34.19    (20)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.19    (21)  op(all_52_9, all_52_9) = e3
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | COMBINE_EQS: (9), (12) imply:
% 203.13/34.19  |   (22)  all_52_13 = e3
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (3), (22) imply:
% 203.13/34.19  |   (23)   ~ (all_52_9 = e3)
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (5), (22) imply:
% 203.13/34.19  |   (24)  op(e3, e3) = e1
% 203.13/34.19  | 
% 203.13/34.19  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (13), (14), (15), (16),
% 203.13/34.19  |            (17), (18), (19), (20), (21), (23), (24) are inconsistent by
% 203.13/34.19  |            sub-proof #1329.
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #494 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (3)  op(e3, e3) = all_52_6
% 203.13/34.19    (4)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.19    (5)   ~ (all_6_2 = e2)
% 203.13/34.19    (6)  op(e0, e3) = e3
% 203.13/34.19    (7)  all_8_2 = all_6_2
% 203.13/34.19    (8)  op(e3, all_6_1) = e2
% 203.13/34.19    (9)  all_56_0 = all_6_2
% 203.13/34.19    (10)  op(e3, e3) = all_6_2
% 203.13/34.19    (11)   ~ (all_6_2 = e1)
% 203.13/34.19    (12)  op(all_6_2, e3) = all_6_1
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (4) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (13)  all_56_0 = e2
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #597.
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (14)   ~ (all_56_0 = e2)
% 203.13/34.19  | |   (15)  all_56_0 = e1 | all_56_0 = e0
% 203.13/34.19  | | 
% 203.13/34.19  | | BETA: splitting (15) gives:
% 203.13/34.19  | | 
% 203.13/34.19  | | Case 1:
% 203.13/34.19  | | | 
% 203.13/34.19  | | |   (16)  all_56_0 = e1
% 203.13/34.19  | | | 
% 203.13/34.19  | | | REF_CLOSE: (9), (11), (16) are inconsistent by sub-proof #596.
% 203.13/34.19  | | | 
% 203.13/34.19  | | Case 2:
% 203.13/34.19  | | | 
% 203.13/34.19  | | |   (17)  all_56_0 = e0
% 203.13/34.19  | | | 
% 203.13/34.19  | | | COMBINE_EQS: (9), (17) imply:
% 203.13/34.19  | | |   (18)  all_6_2 = e0
% 203.13/34.19  | | | 
% 203.13/34.19  | | | SIMP: (18) implies:
% 203.13/34.19  | | |   (19)  all_6_2 = e0
% 203.13/34.19  | | | 
% 203.13/34.19  | | | COMBINE_EQS: (7), (19) imply:
% 203.13/34.19  | | |   (20)  all_8_2 = e0
% 203.13/34.19  | | | 
% 203.13/34.19  | | | REDUCE: (12), (19) imply:
% 203.13/34.19  | | |   (21)  op(e0, e3) = all_6_1
% 203.13/34.19  | | | 
% 203.13/34.19  | | | BETA: splitting (1) gives:
% 203.13/34.19  | | | 
% 203.13/34.19  | | | Case 1:
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | GROUND_INST: instantiating (2) with e3, all_6_1, e3, e0, simplifying
% 203.13/34.19  | | | |              with (6), (21) gives:
% 203.13/34.19  | | | |   (22)  all_6_1 = e3
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | REDUCE: (8), (22) imply:
% 203.13/34.19  | | | |   (23)  op(e3, e3) = e2
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | REF_CLOSE: (2), (3), (5), (10), (23) are inconsistent by sub-proof #890.
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | Case 2:
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | |   (24)   ~ (all_8_2 = e0)
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | REDUCE: (20), (24) imply:
% 203.13/34.19  | | | |   (25)  $false
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | | CLOSE: (25) is inconsistent.
% 203.13/34.19  | | | | 
% 203.13/34.19  | | | End of split
% 203.13/34.19  | | | 
% 203.13/34.19  | | End of split
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #495 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)  all_56_8 = e1 | all_56_8 = e0
% 203.13/34.19    (2)  all_56_8 = all_6_1
% 203.13/34.19    (3)   ~ (all_6_1 = e1)
% 203.13/34.19    (4)   ~ (all_6_1 = e0)
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (1) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (5)  all_56_8 = e1
% 203.13/34.19  | | 
% 203.13/34.19  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1320.
% 203.13/34.19  | | 
% 203.13/34.19  | Case 2:
% 203.13/34.19  | | 
% 203.13/34.19  | |   (6)  all_56_8 = e0
% 203.13/34.19  | | 
% 203.13/34.19  | | COMBINE_EQS: (2), (6) imply:
% 203.13/34.19  | |   (7)  all_6_1 = e0
% 203.13/34.19  | | 
% 203.13/34.19  | | SIMP: (7) implies:
% 203.13/34.19  | |   (8)  all_6_1 = e0
% 203.13/34.19  | | 
% 203.13/34.19  | | REDUCE: (4), (8) imply:
% 203.13/34.19  | |   (9)  $false
% 203.13/34.19  | | 
% 203.13/34.19  | | CLOSE: (9) is inconsistent.
% 203.13/34.19  | | 
% 203.13/34.19  | End of split
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #496 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (2)  op(e2, e3) = all_52_3
% 203.13/34.19    (3)   ~ (all_52_3 = all_6_2)
% 203.13/34.19    (4)  all_58_0 = all_6_2
% 203.13/34.19    (5)  all_56_4 = all_52_3
% 203.13/34.19    (6)  all_6_2 = e2
% 203.13/34.19    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.19    (8)   ~ (all_6_2 = e3)
% 203.13/34.19    (9)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.19    (10)  all_58_2 = all_52_3
% 203.13/34.19    (11)   ~ (e2 = e0)
% 203.13/34.19    (12)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.19    (13)  op(e3, e1) = all_52_17
% 203.13/34.19    (14)  op(e3, e0) = e3
% 203.13/34.19    (15)  op(e3, all_6_1) = e2
% 203.13/34.19    (16)   ~ (all_52_17 = all_6_2)
% 203.13/34.19    (17)  op(all_6_2, e3) = all_6_1
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | COMBINE_EQS: (4), (6) imply:
% 203.13/34.19  |   (18)  all_58_0 = e2
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (3), (6) imply:
% 203.13/34.19  |   (19)   ~ (all_52_3 = e2)
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (6), (16) imply:
% 203.13/34.19  |   (20)   ~ (all_52_17 = e2)
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (6), (8) imply:
% 203.13/34.19  |   (21)   ~ (e3 = e2)
% 203.13/34.19  | 
% 203.13/34.19  | SIMP: (21) implies:
% 203.13/34.19  |   (22)   ~ (e3 = e2)
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (6), (17) imply:
% 203.13/34.19  |   (23)  op(e2, e3) = all_6_1
% 203.13/34.19  | 
% 203.13/34.19  | GROUND_INST: instantiating (1) with all_52_3, all_6_1, e3, e2, simplifying
% 203.13/34.19  |              with (2), (23) gives:
% 203.13/34.19  |   (24)  all_52_3 = all_6_1
% 203.13/34.19  | 
% 203.13/34.19  | COMBINE_EQS: (5), (24) imply:
% 203.13/34.19  |   (25)  all_56_4 = all_6_1
% 203.13/34.19  | 
% 203.13/34.19  | COMBINE_EQS: (10), (24) imply:
% 203.13/34.19  |   (26)  all_58_2 = all_6_1
% 203.13/34.19  | 
% 203.13/34.19  | REDUCE: (19), (24) imply:
% 203.13/34.19  |   (27)   ~ (all_6_1 = e2)
% 203.13/34.19  | 
% 203.13/34.19  | REF_CLOSE: (1), (7), (9), (11), (12), (13), (14), (15), (18), (20), (22),
% 203.13/34.19  |            (25), (26), (27) are inconsistent by sub-proof #497.
% 203.13/34.19  | 
% 203.13/34.19  End of proof
% 203.13/34.19  
% 203.13/34.19  Sub-proof #497 shows that the following formulas are inconsistent:
% 203.13/34.19  ----------------------------------------------------------------
% 203.13/34.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.19    (2)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.19    (3)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.19    (4)   ~ (e2 = e0)
% 203.13/34.19    (5)  all_56_4 = all_6_1
% 203.13/34.19    (6)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.19    (7)  op(e3, e1) = all_52_17
% 203.13/34.19    (8)  op(e3, e0) = e3
% 203.13/34.19    (9)  all_58_0 = e2
% 203.13/34.19    (10)  op(e3, all_6_1) = e2
% 203.13/34.19    (11)   ~ (e3 = e2)
% 203.13/34.19    (12)   ~ (all_6_1 = e2)
% 203.13/34.19    (13)   ~ (all_52_17 = e2)
% 203.13/34.19    (14)  all_58_2 = all_6_1
% 203.13/34.19  
% 203.13/34.19  Begin of proof
% 203.13/34.19  | 
% 203.13/34.19  | BETA: splitting (2) gives:
% 203.13/34.19  | 
% 203.13/34.19  | Case 1:
% 203.13/34.19  | | 
% 203.13/34.20  | |   (15)  all_58_0 = e0
% 203.13/34.20  | | 
% 203.13/34.20  | | COMBINE_EQS: (9), (15) imply:
% 203.13/34.20  | |   (16)  e2 = e0
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (4), (16) imply:
% 203.13/34.20  | |   (17)  $false
% 203.13/34.20  | | 
% 203.13/34.20  | | CLOSE: (17) is inconsistent.
% 203.13/34.20  | | 
% 203.13/34.20  | Case 2:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (18)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.20  | | 
% 203.13/34.20  | | BETA: splitting (3) gives:
% 203.13/34.20  | | 
% 203.13/34.20  | | Case 1:
% 203.13/34.20  | | | 
% 203.13/34.20  | | |   (19)  all_58_2 = e1
% 203.13/34.20  | | | 
% 203.13/34.20  | | | REF_CLOSE: (1), (7), (10), (13), (14), (19) are inconsistent by sub-proof
% 203.13/34.20  | | |            #498.
% 203.13/34.20  | | | 
% 203.13/34.20  | | Case 2:
% 203.13/34.20  | | | 
% 203.13/34.20  | | |   (20)   ~ (all_58_2 = e1)
% 203.13/34.20  | | | 
% 203.13/34.20  | | | REDUCE: (14), (20) imply:
% 203.13/34.20  | | |   (21)   ~ (all_6_1 = e1)
% 203.13/34.20  | | | 
% 203.13/34.20  | | | BETA: splitting (18) gives:
% 203.13/34.20  | | | 
% 203.13/34.20  | | | Case 1:
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | |   (22)  all_58_2 = e0
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | COMBINE_EQS: (14), (22) imply:
% 203.13/34.20  | | | |   (23)  all_6_1 = e0
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REDUCE: (10), (23) imply:
% 203.13/34.20  | | | |   (24)  op(e3, e0) = e2
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | GROUND_INST: instantiating (1) with e3, e2, e0, e3, simplifying with
% 203.13/34.20  | | | |              (8), (24) gives:
% 203.13/34.20  | | | |   (25)  e3 = e2
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REDUCE: (11), (25) imply:
% 203.13/34.20  | | | |   (26)  $false
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | CLOSE: (26) is inconsistent.
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | Case 2:
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | |   (27)   ~ (all_58_2 = e0)
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REDUCE: (14), (27) imply:
% 203.13/34.20  | | | |   (28)   ~ (all_6_1 = e0)
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REF_CLOSE: (5), (6), (12), (21), (28) are inconsistent by sub-proof
% 203.13/34.20  | | | |            #1216.
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | End of split
% 203.13/34.20  | | | 
% 203.13/34.20  | | End of split
% 203.13/34.20  | | 
% 203.13/34.20  | End of split
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #498 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (2)  op(e3, e1) = all_52_17
% 203.13/34.20    (3)  all_58_2 = e1
% 203.13/34.20    (4)  op(e3, all_6_1) = e2
% 203.13/34.20    (5)   ~ (all_52_17 = e2)
% 203.13/34.20    (6)  all_58_2 = all_6_1
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | COMBINE_EQS: (3), (6) imply:
% 203.13/34.20  |   (7)  all_6_1 = e1
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (4), (7) imply:
% 203.13/34.20  |   (8)  op(e3, e1) = e2
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (1) with all_52_17, e2, e1, e3, simplifying with
% 203.13/34.20  |              (2), (8) gives:
% 203.13/34.20  |   (9)  all_52_17 = e2
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (5), (9) imply:
% 203.13/34.20  |   (10)  $false
% 203.13/34.20  | 
% 203.13/34.20  | CLOSE: (10) is inconsistent.
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #499 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)   ~ (all_8_1 = e1) |  ~ (all_8_2 = e0)
% 203.13/34.20    (2)   ~ (all_52_15 = all_52_23)
% 203.13/34.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.20    (5)   ~ (all_52_7 = all_52_15)
% 203.13/34.20    (6)  op(all_52_15, all_52_15) = e0
% 203.13/34.20    (7)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.20    (8)  op(e2, e2) = all_4_2
% 203.13/34.20    (9)   ~ (all_52_7 = all_6_2)
% 203.13/34.20    (10)  all_52_15 = e3
% 203.13/34.20    (11)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.13/34.20    (12)  op(e0, e3) = all_52_7
% 203.13/34.20    (13)   ~ (all_52_23 = e0)
% 203.13/34.20    (14)  all_56_12 = all_52_7
% 203.13/34.20    (15)  all_8_2 = all_6_2
% 203.13/34.20    (16)  op(e3, all_6_1) = e2
% 203.13/34.20    (17)  op(e3, e3) = all_6_2
% 203.13/34.20    (18)  all_56_14 = all_52_23
% 203.13/34.20    (19)   ~ (all_52_15 = all_4_2)
% 203.13/34.20    (20)  op(e3, e2) = all_52_9
% 203.13/34.20    (21)  op(all_52_9, all_52_9) = e3
% 203.13/34.20    (22)   ~ (all_52_7 = all_52_23)
% 203.13/34.20    (23)  all_8_1 = all_6_1
% 203.13/34.20    (24)  op(all_6_2, e3) = all_6_1
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (10) implies:
% 203.13/34.20  |   (25)  all_52_15 = e3
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (5), (25) imply:
% 203.13/34.20  |   (26)   ~ (all_52_7 = e3)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (2), (25) imply:
% 203.13/34.20  |   (27)   ~ (all_52_23 = e3)
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (27) implies:
% 203.13/34.20  |   (28)   ~ (all_52_23 = e3)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (19), (25) imply:
% 203.13/34.20  |   (29)   ~ (all_4_2 = e3)
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (29) implies:
% 203.13/34.20  |   (30)   ~ (all_4_2 = e3)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (6), (25) imply:
% 203.13/34.20  |   (31)  op(e3, e3) = e0
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying with
% 203.13/34.20  |              (17), (31) gives:
% 203.13/34.20  |   (32)  all_6_2 = e0
% 203.13/34.20  | 
% 203.13/34.20  | COMBINE_EQS: (15), (32) imply:
% 203.13/34.20  |   (33)  all_8_2 = e0
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (9), (32) imply:
% 203.13/34.20  |   (34)   ~ (all_52_7 = e0)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (24), (32) imply:
% 203.13/34.20  |   (35)  op(e0, e3) = all_6_1
% 203.13/34.20  | 
% 203.13/34.20  | BETA: splitting (1) gives:
% 203.13/34.20  | 
% 203.13/34.20  | Case 1:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (36)   ~ (all_8_1 = e1)
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (23), (36) imply:
% 203.13/34.20  | |   (37)   ~ (all_6_1 = e1)
% 203.13/34.20  | | 
% 203.13/34.20  | | GROUND_INST: instantiating (3) with all_52_7, all_6_1, e3, e0, simplifying
% 203.13/34.20  | |              with (12), (35) gives:
% 203.13/34.20  | |   (38)  all_52_7 = all_6_1
% 203.13/34.20  | | 
% 203.13/34.20  | | COMBINE_EQS: (14), (38) imply:
% 203.13/34.20  | |   (39)  all_56_12 = all_6_1
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (22), (38) imply:
% 203.13/34.20  | |   (40)   ~ (all_52_23 = all_6_1)
% 203.13/34.20  | | 
% 203.13/34.20  | | SIMP: (40) implies:
% 203.13/34.20  | |   (41)   ~ (all_52_23 = all_6_1)
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (26), (38) imply:
% 203.13/34.20  | |   (42)   ~ (all_6_1 = e3)
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (34), (38) imply:
% 203.13/34.20  | |   (43)   ~ (all_6_1 = e0)
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (7), (38) imply:
% 203.13/34.20  | |   (44)  op(all_6_1, all_6_1) = all_52_6
% 203.13/34.20  | | 
% 203.13/34.20  | | BETA: splitting (4) gives:
% 203.13/34.20  | | 
% 203.13/34.20  | | Case 1:
% 203.13/34.20  | | | 
% 203.13/34.20  | | |   (45)  all_56_12 = e3
% 203.13/34.20  | | | 
% 203.13/34.20  | | | REF_CLOSE: (39), (42), (45) are inconsistent by sub-proof #1347.
% 203.13/34.20  | | | 
% 203.13/34.20  | | Case 2:
% 203.13/34.20  | | | 
% 203.13/34.20  | | |   (46)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.20  | | | 
% 203.13/34.20  | | | BETA: splitting (46) gives:
% 203.13/34.20  | | | 
% 203.13/34.20  | | | Case 1:
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | |   (47)  all_56_12 = e2
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | COMBINE_EQS: (39), (47) imply:
% 203.13/34.20  | | | |   (48)  all_6_1 = e2
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | SIMP: (48) implies:
% 203.13/34.20  | | | |   (49)  all_6_1 = e2
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REDUCE: (41), (49) imply:
% 203.13/34.20  | | | |   (50)   ~ (all_52_23 = e2)
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REDUCE: (44), (49) imply:
% 203.13/34.20  | | | |   (51)  op(e2, e2) = all_52_6
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REDUCE: (16), (49) imply:
% 203.13/34.20  | | | |   (52)  op(e3, e2) = e2
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | BETA: splitting (11) gives:
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | Case 1:
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | |   (53)  all_56_14 = e3
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | | REF_CLOSE: (18), (28), (53) are inconsistent by sub-proof #1286.
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | Case 2:
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | |   (54)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | | BETA: splitting (54) gives:
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | | Case 1:
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | |   (55)  all_56_14 = e2
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | | REF_CLOSE: (18), (50), (55) are inconsistent by sub-proof #1285.
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | Case 2:
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | |   (56)  all_56_14 = e1 | all_56_14 = e0
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | | BETA: splitting (56) gives:
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | | Case 1:
% 203.13/34.20  | | | | | | | 
% 203.13/34.20  | | | | | | | 
% 203.13/34.20  | | | | | | | REF_CLOSE: (3), (8), (20), (21), (30), (51), (52) are inconsistent
% 203.13/34.20  | | | | | | |            by sub-proof #500.
% 203.13/34.20  | | | | | | | 
% 203.13/34.20  | | | | | | Case 2:
% 203.13/34.20  | | | | | | | 
% 203.13/34.20  | | | | | | |   (57)  all_56_14 = e0
% 203.13/34.20  | | | | | | | 
% 203.13/34.20  | | | | | | | REF_CLOSE: (13), (18), (57) are inconsistent by sub-proof #1382.
% 203.13/34.20  | | | | | | | 
% 203.13/34.20  | | | | | | End of split
% 203.13/34.20  | | | | | | 
% 203.13/34.20  | | | | | End of split
% 203.13/34.20  | | | | | 
% 203.13/34.20  | | | | End of split
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | Case 2:
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | |   (58)  all_56_12 = e1 | all_56_12 = e0
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | | REF_CLOSE: (37), (39), (43), (58) are inconsistent by sub-proof #1344.
% 203.13/34.20  | | | | 
% 203.13/34.20  | | | End of split
% 203.13/34.20  | | | 
% 203.13/34.20  | | End of split
% 203.13/34.20  | | 
% 203.13/34.20  | Case 2:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (59)   ~ (all_8_2 = e0)
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (33), (59) imply:
% 203.13/34.20  | |   (60)  $false
% 203.13/34.20  | | 
% 203.13/34.20  | | CLOSE: (60) is inconsistent.
% 203.13/34.20  | | 
% 203.13/34.20  | End of split
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #500 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (2)   ~ (all_4_2 = e3)
% 203.13/34.20    (3)  op(e2, e2) = all_52_6
% 203.13/34.20    (4)  op(e2, e2) = all_4_2
% 203.13/34.20    (5)  op(e3, e2) = e2
% 203.13/34.20    (6)  op(e3, e2) = all_52_9
% 203.13/34.20    (7)  op(all_52_9, all_52_9) = e3
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (1) with all_4_2, all_52_6, e2, e2, simplifying
% 203.13/34.20  |              with (3), (4) gives:
% 203.13/34.20  |   (8)  all_52_6 = all_4_2
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (1) with all_52_9, e2, e2, e3, simplifying with
% 203.13/34.20  |              (5), (6) gives:
% 203.13/34.20  |   (9)  all_52_9 = e2
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (7), (9) imply:
% 203.13/34.20  |   (10)  op(e2, e2) = e3
% 203.13/34.20  | 
% 203.13/34.20  | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1318.
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #501 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)  op(all_52_3, all_52_3) = all_52_2
% 203.13/34.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (3)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.13/34.20    (4)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.20    (5)  all_58_0 = all_6_2
% 203.13/34.20    (6)  op(all_52_5, all_52_5) = all_52_4
% 203.13/34.20    (7)  op(e2, e2) = all_4_2
% 203.13/34.20    (8)  op(all_6_2, all_6_2) = all_52_0
% 203.13/34.20    (9)  op(e0, e0) = all_14_2
% 203.13/34.20    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.13/34.20    (11)  all_58_12 = all_52_7
% 203.13/34.20    (12)   ~ (all_52_7 = all_14_2)
% 203.13/34.20    (13)  all_58_2 = all_52_3
% 203.13/34.20    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.13/34.20    (15)   ~ (all_52_5 = all_10_2)
% 203.13/34.20    (16)  op(e3, all_6_1) = e2
% 203.13/34.20    (17)  all_56_0 = all_6_2
% 203.13/34.20    (18)  op(e3, e3) = all_6_2
% 203.13/34.20    (19)  all_58_6 = all_52_5
% 203.13/34.20    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.20    (21)   ~ (e3 = e2)
% 203.13/34.20    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.20    (23)  op(e1, e1) = all_10_2
% 203.13/34.20    (24)   ~ (all_52_3 = all_4_2)
% 203.13/34.20    (25)  op(all_6_2, e3) = all_6_1
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | ALPHA: (3) implies:
% 203.13/34.20  |   (26)  all_52_6 = e0
% 203.13/34.20  |   (27)  all_52_4 = e1
% 203.13/34.20  |   (28)  all_52_2 = e2
% 203.13/34.20  |   (29)  all_52_0 = e3
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (1), (28) imply:
% 203.13/34.20  |   (30)  op(all_52_3, all_52_3) = e2
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (6), (27) imply:
% 203.13/34.20  |   (31)  op(all_52_5, all_52_5) = e1
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (4), (26) imply:
% 203.13/34.20  |   (32)  op(all_52_7, all_52_7) = e0
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (8), (29) imply:
% 203.13/34.20  |   (33)  op(all_6_2, all_6_2) = e3
% 203.13/34.20  | 
% 203.13/34.20  | BETA: splitting (20) gives:
% 203.13/34.20  | 
% 203.13/34.20  | Case 1:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (34)  all_58_12 = e3
% 203.13/34.20  | | 
% 203.13/34.20  | | REF_CLOSE: (2), (9), (11), (12), (18), (32), (33), (34) are inconsistent by
% 203.13/34.20  | |            sub-proof #1371.
% 203.13/34.20  | | 
% 203.13/34.20  | Case 2:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (35)   ~ (all_58_12 = e3)
% 203.13/34.20  | | 
% 203.13/34.20  | | REDUCE: (11), (35) imply:
% 203.13/34.20  | |   (36)   ~ (all_52_7 = e3)
% 203.13/34.20  | | 
% 203.13/34.20  | | BETA: splitting (22) gives:
% 203.13/34.20  | | 
% 203.13/34.20  | | Case 1:
% 203.13/34.20  | | | 
% 203.13/34.20  | | |   (37)  all_56_0 = e3
% 203.13/34.20  | | | 
% 203.13/34.20  | | | COMBINE_EQS: (17), (37) imply:
% 203.13/34.20  | | |   (38)  all_6_2 = e3
% 203.13/34.20  | | | 
% 203.13/34.20  | | | REF_CLOSE: (2), (16), (18), (21), (25), (38) are inconsistent by sub-proof
% 203.13/34.20  | | |            #502.
% 203.13/34.20  | | | 
% 203.13/34.20  | | Case 2:
% 203.13/34.20  | | | 
% 203.13/34.20  | | |   (39)   ~ (all_56_0 = e3)
% 203.13/34.20  | | | 
% 203.13/34.20  | | | REDUCE: (17), (39) imply:
% 203.13/34.20  | | |   (40)   ~ (all_6_2 = e3)
% 203.13/34.20  | | | 
% 203.13/34.20  | | | REF_CLOSE: (2), (5), (7), (10), (11), (13), (14), (15), (18), (19), (23),
% 203.13/34.20  | | |            (24), (30), (31), (33), (36), (40) are inconsistent by
% 203.13/34.20  | | |            sub-proof #1363.
% 203.13/34.20  | | | 
% 203.13/34.20  | | End of split
% 203.13/34.20  | | 
% 203.13/34.20  | End of split
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #502 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (2)  all_6_2 = e3
% 203.13/34.20    (3)  op(e3, all_6_1) = e2
% 203.13/34.20    (4)  op(e3, e3) = all_6_2
% 203.13/34.20    (5)   ~ (e3 = e2)
% 203.13/34.20    (6)  op(all_6_2, e3) = all_6_1
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (2), (6) imply:
% 203.13/34.20  |   (7)  op(e3, e3) = all_6_1
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (2), (4) imply:
% 203.13/34.20  |   (8)  op(e3, e3) = e3
% 203.13/34.20  | 
% 203.13/34.20  | REF_CLOSE: (1), (3), (5), (7), (8) are inconsistent by sub-proof #503.
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #503 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (2)  op(e3, e3) = all_6_1
% 203.13/34.20    (3)  op(e3, e3) = e3
% 203.13/34.20    (4)  op(e3, all_6_1) = e2
% 203.13/34.20    (5)   ~ (e3 = e2)
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (1) with e3, all_6_1, e3, e3, simplifying with (2),
% 203.13/34.20  |              (3) gives:
% 203.13/34.20  |   (6)  all_6_1 = e3
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (4), (6) imply:
% 203.13/34.20  |   (7)  op(e3, e3) = e2
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (1) with e3, e2, e3, e3, simplifying with (3), (7)
% 203.13/34.20  |              gives:
% 203.13/34.20  |   (8)  e3 = e2
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (5), (8) imply:
% 203.13/34.20  |   (9)  $false
% 203.13/34.20  | 
% 203.13/34.20  | CLOSE: (9) is inconsistent.
% 203.13/34.20  | 
% 203.13/34.20  End of proof
% 203.13/34.20  
% 203.13/34.20  Sub-proof #504 shows that the following formulas are inconsistent:
% 203.13/34.20  ----------------------------------------------------------------
% 203.13/34.20    (1)   ~ (all_52_15 = all_52_23)
% 203.13/34.20    (2)   ~ (all_52_25 = all_52_27)
% 203.13/34.20    (3)  all_58_14 = all_52_23
% 203.13/34.20    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.13/34.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.20    (6)  all_58_1 = all_52_9
% 203.13/34.20    (7)   ~ (all_52_9 = all_52_13)
% 203.13/34.20    (8)   ~ (e3 = e0)
% 203.13/34.20    (9)  op(e2, e3) = all_52_3
% 203.13/34.20    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.20    (11)   ~ (all_52_3 = all_52_19)
% 203.13/34.20    (12)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.20    (13)   ~ (all_52_17 = all_52_25)
% 203.13/34.20    (14)   ~ (all_52_3 = all_6_2)
% 203.13/34.20    (15)  all_58_0 = all_6_2
% 203.13/34.20    (16)  op(all_14_2, e0) = all_14_1
% 203.13/34.20    (17)  all_56_4 = all_52_3
% 203.13/34.20    (18)   ~ (all_52_17 = all_10_2)
% 203.13/34.20    (19)  op(e3, e0) = all_52_25
% 203.13/34.20    (20)  op(all_52_5, all_52_5) = all_52_4
% 203.13/34.20    (21)  op(all_52_19, all_52_19) = all_52_18
% 203.13/34.20    (22)   ~ (all_52_27 = all_52_29)
% 203.13/34.20    (23)  all_58_13 = all_52_15
% 203.13/34.20    (24)  op(all_10_2, all_10_2) = all_52_20
% 203.13/34.20    (25)  all_58_9 = all_52_25
% 203.13/34.20    (26)   ~ (all_6_1 = e1)
% 203.13/34.20    (27)   ~ (all_52_29 = all_14_2)
% 203.13/34.20    (28)  all_22_0 = all_6_0
% 203.13/34.20    (29)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.13/34.20    (30)  op(all_52_27, all_52_27) = all_52_26
% 203.13/34.20    (31)  op(e1, e3) = all_52_5
% 203.13/34.20    (32)  op(e2, e2) = all_4_2
% 203.13/34.20    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.20    (34)   ~ (all_52_3 = all_52_5)
% 203.13/34.20    (35)  all_58_11 = all_52_29
% 203.13/34.20    (36)  all_56_5 = all_4_2
% 203.13/34.20    (37)   ~ (all_52_25 = all_14_2)
% 203.13/34.20    (38)   ~ (all_52_9 = all_52_15)
% 203.13/34.20    (39)   ~ (all_52_3 = all_52_27)
% 203.13/34.20    (40)  op(all_10_2, e1) = all_10_1
% 203.13/34.20    (41)  op(all_6_2, all_6_2) = all_52_0
% 203.13/34.20    (42)   ~ (all_52_7 = all_6_2)
% 203.13/34.20    (43)  op(e0, e0) = all_14_2
% 203.13/34.20    (44)  all_56_15 = all_14_2
% 203.13/34.20    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.13/34.20    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.13/34.20    (47)  op(e1, e0) = all_52_29
% 203.13/34.20    (48)  all_56_11 = all_52_29
% 203.13/34.20    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.20    (50)  op(e1, all_10_1) = e3
% 203.13/34.20    (51)   ~ (all_52_13 = all_10_2)
% 203.13/34.20    (52)   ~ (all_6_0 = e1)
% 203.13/34.20    (53)  all_58_10 = all_52_27
% 203.13/34.20    (54)  all_56_8 = all_52_5
% 203.13/34.20    (55)  op(all_52_9, all_52_9) = all_52_8
% 203.13/34.20    (56)   ~ (all_52_19 = all_52_23)
% 203.13/34.20    (57)   ~ (all_52_25 = all_52_29)
% 203.13/34.20    (58)   ~ (all_52_29 = all_10_2)
% 203.13/34.20    (59)  all_58_7 = all_52_13
% 203.13/34.20    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.13/34.20    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.20    (62)   ~ (all_52_5 = all_52_7)
% 203.13/34.20    (63)  all_58_12 = all_52_7
% 203.13/34.20    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.20    (65)   ~ (all_52_7 = all_14_2)
% 203.13/34.20    (66)  all_58_2 = all_52_3
% 203.13/34.20    (67)  all_56_2 = all_52_17
% 203.13/34.20    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.13/34.20    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.13/34.20    (70)  op(e3, all_6_1) = all_6_0
% 203.13/34.20    (71)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.20    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.13/34.20    (73)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.13/34.20    (74)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.20    (75)   ~ (e2 = e0)
% 203.13/34.20    (76)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.13/34.20    (77)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.13/34.20    (78)   ~ (all_52_5 = all_52_29)
% 203.13/34.20    (79)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.20    (80)   ~ (all_52_15 = all_14_2)
% 203.13/34.20    (81)   ~ (all_52_19 = all_52_27)
% 203.13/34.20    (82)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.20    (83)   ~ (all_6_0 = e2)
% 203.13/34.20    (84)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.13/34.20            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.13/34.20    (85)  op(e3, e1) = all_52_17
% 203.13/34.20    (86)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.13/34.20    (87)  op(e0, e3) = all_52_7
% 203.13/34.20    (88)  op(e1, e2) = all_52_13
% 203.13/34.20    (89)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.20    (90)   ~ (all_52_9 = all_52_25)
% 203.13/34.20    (91)  all_58_15 = all_14_2
% 203.13/34.20    (92)   ~ (all_52_19 = all_10_2)
% 203.13/34.20    (93)  op(all_52_23, all_52_23) = all_52_22
% 203.13/34.20    (94)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.20    (95)  all_58_8 = all_10_2
% 203.13/34.20    (96)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.13/34.20    (97)   ~ (all_52_5 = all_10_2)
% 203.13/34.20    (98)  op(all_52_29, all_52_29) = all_52_28
% 203.13/34.20    (99)   ~ (all_52_23 = all_14_2)
% 203.13/34.20    (100)  all_56_12 = all_52_7
% 203.13/34.20    (101)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.20    (102)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.13/34.20    (103)   ~ (all_52_25 = all_6_2)
% 203.13/34.20    (104)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.20    (105)   ~ (all_52_9 = all_4_2)
% 203.13/34.20    (106)   ~ (all_52_5 = all_6_2)
% 203.13/34.20    (107)   ~ (all_52_9 = all_6_2)
% 203.13/34.20    (108)  all_56_0 = all_6_2
% 203.13/34.20    (109)  op(e3, e3) = all_6_2
% 203.13/34.20    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.20    (111)   ~ (all_52_27 = all_14_2)
% 203.13/34.20    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.20    (113)  all_56_14 = all_52_23
% 203.13/34.20    (114)  all_56_3 = all_52_25
% 203.13/34.20    (115)  op(e0, all_14_1) = e2
% 203.13/34.20    (116)   ~ (all_52_3 = all_52_7)
% 203.13/34.20    (117)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.20    (118)  all_58_5 = all_52_19
% 203.13/34.20    (119)  all_56_1 = all_52_9
% 203.13/34.20    (120)   ~ (all_52_15 = all_4_2)
% 203.13/34.20    (121)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.13/34.20           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.13/34.20           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.13/34.20           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.13/34.20    (122)   ~ (all_52_27 = all_4_2)
% 203.13/34.20    (123)  all_58_6 = all_52_5
% 203.13/34.20    (124)  op(e3, e2) = all_52_9
% 203.13/34.20    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.20    (126)   ~ (all_52_17 = all_6_2)
% 203.13/34.20    (127)   ~ (e1 = e0)
% 203.13/34.20    (128)   ~ (e3 = e2)
% 203.13/34.20    (129)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.20    (130)   ~ (all_52_9 = all_52_17)
% 203.13/34.20    (131)  all_56_10 = all_10_2
% 203.13/34.20    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.13/34.20    (133)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.20    (134)  op(all_52_13, all_52_13) = all_52_12
% 203.13/34.20    (135)  all_6_1 = e2
% 203.13/34.20    (136)  op(e1, e1) = all_10_2
% 203.13/34.20    (137)   ~ (all_52_23 = all_10_2)
% 203.13/34.20    (138)   ~ (all_52_7 = all_52_23)
% 203.13/34.20    (139)   ~ (all_52_17 = all_52_19)
% 203.13/34.20    (140)  all_58_3 = all_4_2
% 203.13/34.20    (141)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.13/34.20    (142)   ~ (all_52_3 = all_4_2)
% 203.13/34.20    (143)   ~ (all_52_19 = all_4_2)
% 203.13/34.20    (144)   ~ (all_52_17 = all_52_23)
% 203.13/34.20    (145)  op(all_6_2, e3) = all_6_1
% 203.13/34.20    (146)  all_22_2 = all_6_2
% 203.13/34.20    (147)  all_58_4 = all_52_17
% 203.13/34.20    (148)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.13/34.20    (149)  op(all_52_25, all_52_25) = all_52_24
% 203.13/34.20  
% 203.13/34.20  Begin of proof
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (26), (135) imply:
% 203.13/34.20  |   (150)   ~ (e2 = e1)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (135), (145) imply:
% 203.13/34.20  |   (151)  op(all_6_2, e3) = e2
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (70), (135) imply:
% 203.13/34.20  |   (152)  op(e3, e2) = all_6_0
% 203.13/34.20  | 
% 203.13/34.20  | GROUND_INST: instantiating (5) with all_52_9, all_6_0, e2, e3, simplifying
% 203.13/34.20  |              with (124), (152) gives:
% 203.13/34.20  |   (153)  all_52_9 = all_6_0
% 203.13/34.20  | 
% 203.13/34.20  | COMBINE_EQS: (119), (153) imply:
% 203.13/34.20  |   (154)  all_56_1 = all_6_0
% 203.13/34.20  | 
% 203.13/34.20  | COMBINE_EQS: (6), (153) imply:
% 203.13/34.20  |   (155)  all_58_1 = all_6_0
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (7), (153) imply:
% 203.13/34.20  |   (156)   ~ (all_52_13 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (156) implies:
% 203.13/34.20  |   (157)   ~ (all_52_13 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (38), (153) imply:
% 203.13/34.20  |   (158)   ~ (all_52_15 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (158) implies:
% 203.13/34.20  |   (159)   ~ (all_52_15 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (130), (153) imply:
% 203.13/34.20  |   (160)   ~ (all_52_17 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (160) implies:
% 203.13/34.20  |   (161)   ~ (all_52_17 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (90), (153) imply:
% 203.13/34.20  |   (162)   ~ (all_52_25 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | SIMP: (162) implies:
% 203.13/34.20  |   (163)   ~ (all_52_25 = all_6_0)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (107), (153) imply:
% 203.13/34.20  |   (164)   ~ (all_6_0 = all_6_2)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (105), (153) imply:
% 203.13/34.20  |   (165)   ~ (all_6_0 = all_4_2)
% 203.13/34.20  | 
% 203.13/34.20  | REDUCE: (55), (153) imply:
% 203.13/34.20  |   (166)  op(all_6_0, all_6_0) = all_52_8
% 203.13/34.20  | 
% 203.13/34.20  | BETA: splitting (84) gives:
% 203.13/34.20  | 
% 203.13/34.20  | Case 1:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (167)  all_58_15 = e0
% 203.13/34.20  | | 
% 203.13/34.20  | | REF_CLOSE: (5), (16), (43), (75), (91), (115), (117), (167) are inconsistent
% 203.13/34.20  | |            by sub-proof #612.
% 203.13/34.20  | | 
% 203.13/34.20  | Case 2:
% 203.13/34.20  | | 
% 203.13/34.20  | |   (168)   ~ (all_58_15 = e0)
% 203.13/34.20  | |   (169)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 203.13/34.20  | |            | all_58_13 = e0 | all_58_14 = e0)
% 203.13/34.20  | | 
% 203.13/34.21  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.13/34.21  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.13/34.21  | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.13/34.21  | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 203.13/34.21  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 203.13/34.21  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 203.13/34.21  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 203.13/34.21  | |            (82), (83), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 203.13/34.21  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.13/34.21  | |            (104), (105), (106), (108), (109), (110), (111), (112), (113),
% 203.13/34.21  | |            (114), (116), (117), (118), (120), (121), (122), (123), (125),
% 203.13/34.21  | |            (126), (127), (128), (129), (131), (132), (133), (134), (136),
% 203.13/34.21  | |            (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 203.13/34.21  | |            (146), (147), (148), (149), (150), (151), (154), (155), (157),
% 203.13/34.21  | |            (159), (161), (163), (164), (165), (166), (168), (169) are
% 203.13/34.21  | |            inconsistent by sub-proof #505.
% 203.13/34.21  | | 
% 203.13/34.21  | End of split
% 203.13/34.21  | 
% 203.13/34.21  End of proof
% 203.13/34.21  
% 203.13/34.21  Sub-proof #505 shows that the following formulas are inconsistent:
% 203.13/34.21  ----------------------------------------------------------------
% 203.13/34.21    (1)   ~ (all_52_15 = all_52_23)
% 203.13/34.21    (2)   ~ (all_52_25 = all_6_0)
% 203.13/34.21    (3)   ~ (all_52_25 = all_52_27)
% 203.13/34.21    (4)  all_58_14 = all_52_23
% 203.13/34.21    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.13/34.21    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.21    (7)  all_58_1 = all_52_9
% 203.13/34.21    (8)   ~ (all_52_9 = all_52_13)
% 203.13/34.21    (9)   ~ (e3 = e0)
% 203.13/34.21    (10)  op(e2, e3) = all_52_3
% 203.13/34.21    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.21    (12)   ~ (all_52_3 = all_52_19)
% 203.13/34.21    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.13/34.21    (14)   ~ (all_52_17 = all_52_25)
% 203.13/34.21    (15)   ~ (all_52_3 = all_6_2)
% 203.13/34.21    (16)  all_58_0 = all_6_2
% 203.13/34.21    (17)  op(all_14_2, e0) = all_14_1
% 203.13/34.21    (18)  all_56_4 = all_52_3
% 203.13/34.21    (19)   ~ (all_52_17 = all_10_2)
% 203.13/34.21    (20)  op(e3, e0) = all_52_25
% 203.13/34.21    (21)  op(all_52_5, all_52_5) = all_52_4
% 203.13/34.21    (22)  op(all_52_19, all_52_19) = all_52_18
% 203.13/34.21    (23)   ~ (all_52_27 = all_52_29)
% 203.13/34.21    (24)  all_58_13 = all_52_15
% 203.13/34.21    (25)  op(all_10_2, all_10_2) = all_52_20
% 203.13/34.21    (26)  all_58_9 = all_52_25
% 203.13/34.21    (27)   ~ (all_52_29 = all_14_2)
% 203.13/34.21    (28)  all_22_0 = all_6_0
% 203.13/34.21    (29)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.13/34.21    (30)   ~ (all_52_17 = all_6_0)
% 203.13/34.21    (31)  op(all_52_27, all_52_27) = all_52_26
% 203.13/34.21    (32)  op(e1, e3) = all_52_5
% 203.13/34.21    (33)  op(e2, e2) = all_4_2
% 203.13/34.21    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.13/34.21    (35)   ~ (all_52_3 = all_52_5)
% 203.13/34.21    (36)  all_58_11 = all_52_29
% 203.13/34.21    (37)  all_56_5 = all_4_2
% 203.13/34.21    (38)   ~ (all_52_25 = all_14_2)
% 203.13/34.21    (39)   ~ (all_52_3 = all_52_27)
% 203.13/34.21    (40)  op(all_10_2, e1) = all_10_1
% 203.13/34.21    (41)  op(all_6_2, all_6_2) = all_52_0
% 203.13/34.21    (42)   ~ (all_52_7 = all_6_2)
% 203.13/34.21    (43)  op(e0, e0) = all_14_2
% 203.13/34.21    (44)  all_56_15 = all_14_2
% 203.13/34.21    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.13/34.21    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.13/34.21    (47)  op(e1, e0) = all_52_29
% 203.13/34.21    (48)   ~ (all_58_15 = e0)
% 203.13/34.21    (49)  all_56_11 = all_52_29
% 203.13/34.21    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.21    (51)  op(e1, all_10_1) = e3
% 203.13/34.21    (52)   ~ (e2 = e1)
% 203.13/34.21    (53)   ~ (all_52_13 = all_10_2)
% 203.13/34.21    (54)   ~ (all_6_0 = e1)
% 203.13/34.21    (55)  all_58_10 = all_52_27
% 203.13/34.21    (56)  all_56_8 = all_52_5
% 203.13/34.21    (57)  op(all_52_9, all_52_9) = all_52_8
% 203.13/34.21    (58)   ~ (all_52_19 = all_52_23)
% 203.13/34.21    (59)   ~ (all_52_25 = all_52_29)
% 203.13/34.21    (60)  op(all_6_2, e3) = e2
% 203.13/34.21    (61)   ~ (all_52_29 = all_10_2)
% 203.13/34.21    (62)  all_58_7 = all_52_13
% 203.13/34.21    (63)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.13/34.21    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.21    (65)  all_58_1 = all_6_0
% 203.13/34.21    (66)   ~ (all_52_5 = all_52_7)
% 203.13/34.21    (67)  all_58_12 = all_52_7
% 203.13/34.21    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.21    (69)   ~ (all_52_7 = all_14_2)
% 203.13/34.21    (70)  all_58_2 = all_52_3
% 203.13/34.21    (71)  all_56_2 = all_52_17
% 203.13/34.21    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.13/34.21    (73)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.13/34.21    (74)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.13/34.21    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.13/34.21    (76)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.13/34.21    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.21    (78)   ~ (e2 = e0)
% 203.13/34.21    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.13/34.21    (80)  op(all_6_0, all_6_0) = all_52_8
% 203.13/34.21    (81)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.13/34.21    (82)   ~ (all_52_5 = all_52_29)
% 203.13/34.21    (83)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.21    (84)   ~ (all_52_15 = all_14_2)
% 203.13/34.21    (85)   ~ (all_52_13 = all_6_0)
% 203.13/34.21    (86)   ~ (all_52_19 = all_52_27)
% 203.13/34.21    (87)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.21    (88)   ~ (all_6_0 = e2)
% 203.13/34.21    (89)  op(e3, e1) = all_52_17
% 203.13/34.21    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.13/34.21    (91)  op(e0, e3) = all_52_7
% 203.13/34.21    (92)  op(e1, e2) = all_52_13
% 203.13/34.21    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.13/34.21    (94)   ~ (all_52_9 = all_52_25)
% 203.13/34.21    (95)  all_58_15 = all_14_2
% 203.13/34.21    (96)   ~ (all_52_19 = all_10_2)
% 203.13/34.21    (97)  op(all_52_23, all_52_23) = all_52_22
% 203.13/34.21    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.21    (99)  all_58_8 = all_10_2
% 203.13/34.21    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.13/34.21    (101)   ~ (all_52_5 = all_10_2)
% 203.13/34.21    (102)  op(all_52_29, all_52_29) = all_52_28
% 203.13/34.21    (103)   ~ (all_52_23 = all_14_2)
% 203.13/34.21    (104)  all_56_12 = all_52_7
% 203.13/34.21    (105)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.21    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.13/34.21    (107)   ~ (all_52_25 = all_6_2)
% 203.13/34.21    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.13/34.21    (109)   ~ (all_52_9 = all_4_2)
% 203.13/34.21    (110)   ~ (all_52_5 = all_6_2)
% 203.13/34.21    (111)  all_56_0 = all_6_2
% 203.13/34.21    (112)  op(e3, e3) = all_6_2
% 203.13/34.21    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.21    (114)   ~ (all_52_15 = all_6_0)
% 203.13/34.21    (115)   ~ (all_52_27 = all_14_2)
% 203.13/34.21    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.13/34.21    (117)  all_56_14 = all_52_23
% 203.13/34.21    (118)  all_56_3 = all_52_25
% 203.13/34.21    (119)   ~ (all_52_3 = all_52_7)
% 203.13/34.21    (120)   ~ (all_6_0 = all_6_2)
% 203.13/34.21    (121)  op(all_14_2, all_14_2) = all_52_30
% 203.13/34.21    (122)  all_58_5 = all_52_19
% 203.13/34.21    (123)   ~ (all_52_15 = all_4_2)
% 203.13/34.21    (124)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.13/34.21           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.13/34.21           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.13/34.21           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.13/34.21    (125)   ~ (all_52_27 = all_4_2)
% 203.13/34.21    (126)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 203.13/34.21             all_58_13 = e0 | all_58_14 = e0)
% 203.13/34.21    (127)  all_58_6 = all_52_5
% 203.13/34.21    (128)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.13/34.21    (129)   ~ (all_52_17 = all_6_2)
% 203.13/34.21    (130)   ~ (e1 = e0)
% 203.13/34.21    (131)   ~ (e3 = e2)
% 203.13/34.21    (132)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.13/34.21    (133)  all_56_10 = all_10_2
% 203.13/34.21    (134)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.13/34.21    (135)  all_56_1 = all_6_0
% 203.13/34.21    (136)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.13/34.21    (137)  op(all_52_13, all_52_13) = all_52_12
% 203.13/34.21    (138)   ~ (all_6_0 = all_4_2)
% 203.13/34.21    (139)  op(e1, e1) = all_10_2
% 203.13/34.21    (140)   ~ (all_52_23 = all_10_2)
% 203.13/34.21    (141)   ~ (all_52_7 = all_52_23)
% 203.13/34.21    (142)   ~ (all_52_17 = all_52_19)
% 203.13/34.21    (143)  all_58_3 = all_4_2
% 203.13/34.21    (144)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.13/34.21    (145)   ~ (all_52_3 = all_4_2)
% 203.13/34.21    (146)   ~ (all_52_19 = all_4_2)
% 203.13/34.21    (147)   ~ (all_52_17 = all_52_23)
% 203.13/34.21    (148)  op(all_6_2, e3) = all_6_1
% 203.13/34.21    (149)  all_22_2 = all_6_2
% 203.13/34.21    (150)  all_58_4 = all_52_17
% 203.13/34.21    (151)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.13/34.21    (152)  op(all_52_25, all_52_25) = all_52_24
% 203.13/34.21  
% 203.13/34.21  Begin of proof
% 203.13/34.21  | 
% 203.13/34.21  | ALPHA: (126) implies:
% 203.13/34.21  |   (153)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.13/34.21  |   (154)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.13/34.21  | 
% 203.13/34.21  | REDUCE: (48), (95) imply:
% 203.13/34.21  |   (155)   ~ (all_14_2 = e0)
% 203.13/34.21  | 
% 203.13/34.21  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.13/34.21  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.13/34.21  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.13/34.21  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 203.13/34.21  |            (46), (47), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.13/34.21  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.13/34.21  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.13/34.21  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 203.13/34.21  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.13/34.21  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.13/34.21  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 203.13/34.21  |            (120), (121), (122), (123), (124), (125), (127), (128), (129),
% 203.13/34.21  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 203.13/34.21  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 203.13/34.21  |            (148), (149), (150), (151), (152), (153), (154), (155) are
% 203.13/34.21  |            inconsistent by sub-proof #509.
% 203.13/34.21  | 
% 203.13/34.21  End of proof
% 203.13/34.21  
% 203.13/34.21  Sub-proof #506 shows that the following formulas are inconsistent:
% 203.13/34.21  ----------------------------------------------------------------
% 203.13/34.21    (1)  all_58_12 = all_52_7
% 203.13/34.21    (2)  all_58_12 = e2
% 203.13/34.21    (3)   ~ (all_52_7 = e2)
% 203.13/34.21  
% 203.13/34.21  Begin of proof
% 203.13/34.21  | 
% 203.13/34.21  | COMBINE_EQS: (1), (2) imply:
% 203.13/34.21  |   (4)  all_52_7 = e2
% 203.13/34.21  | 
% 203.13/34.21  | SIMP: (4) implies:
% 203.13/34.21  |   (5)  all_52_7 = e2
% 203.13/34.21  | 
% 203.13/34.21  | REDUCE: (3), (5) imply:
% 203.13/34.21  |   (6)  $false
% 203.13/34.21  | 
% 203.13/34.21  | CLOSE: (6) is inconsistent.
% 203.13/34.21  | 
% 203.13/34.21  End of proof
% 203.13/34.21  
% 203.13/34.21  Sub-proof #507 shows that the following formulas are inconsistent:
% 203.13/34.21  ----------------------------------------------------------------
% 203.13/34.21    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.13/34.21    (2)   ~ (all_52_15 = all_52_23)
% 203.13/34.21    (3)  all_58_14 = all_52_23
% 203.13/34.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.13/34.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.13/34.21    (5)   ~ (all_52_5 = all_52_13)
% 203.13/34.21    (6)  op(all_52_7, all_52_7) = e0
% 203.13/34.21    (7)  all_58_1 = all_52_9
% 203.13/34.21    (8)   ~ (all_52_9 = all_52_13)
% 203.13/34.21    (9)  op(all_52_5, all_52_5) = e1
% 203.13/34.21    (10)   ~ (e3 = e0)
% 203.13/34.21    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.13/34.21    (12)   ~ (all_52_7 = all_52_15)
% 203.13/34.21    (13)   ~ (all_52_3 = all_52_19)
% 203.13/34.21    (14)   ~ (all_52_17 = all_52_25)
% 203.13/34.21    (15)   ~ (all_52_3 = all_6_2)
% 203.13/34.21    (16)  all_58_0 = all_6_2
% 203.13/34.21    (17)  op(all_14_2, e0) = all_14_1
% 203.13/34.21    (18)  all_56_4 = all_52_3
% 203.13/34.21    (19)  op(e0, all_14_1) = all_14_0
% 203.13/34.21    (20)  op(all_52_19, all_52_19) = all_52_18
% 203.13/34.21    (21)   ~ (all_52_27 = all_52_29)
% 203.13/34.21    (22)  all_58_13 = all_52_15
% 203.13/34.21    (23)  op(all_10_2, all_10_2) = all_52_20
% 203.13/34.21    (24)  all_58_9 = all_52_25
% 203.13/34.21    (25)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.13/34.21    (26)   ~ (all_52_29 = all_14_2)
% 203.13/34.21    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.13/34.21    (28)  op(all_52_27, all_52_27) = all_52_26
% 203.13/34.21    (29)  op(e2, e2) = all_4_2
% 203.13/34.21    (30)  all_58_11 = all_52_29
% 203.13/34.21    (31)  all_56_5 = all_4_2
% 203.13/34.21    (32)   ~ (all_52_25 = all_14_2)
% 203.13/34.21    (33)  all_56_13 = e3
% 203.13/34.21    (34)   ~ (all_52_9 = all_52_15)
% 203.13/34.21    (35)   ~ (all_52_3 = all_52_27)
% 203.13/34.21    (36)  op(all_10_2, e1) = all_10_1
% 203.13/34.21    (37)   ~ (all_52_7 = all_6_2)
% 203.13/34.21    (38)  op(e0, e0) = all_14_2
% 203.13/34.21    (39)  all_56_15 = all_14_2
% 203.13/34.21    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.13/34.21    (41)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.13/34.21    (42)  op(e1, e0) = all_52_29
% 203.13/34.21    (43)  all_56_11 = all_52_29
% 203.13/34.21    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.13/34.21    (45)  op(e1, all_10_1) = e3
% 203.13/34.21    (46)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.13/34.21    (47)  all_56_9 = all_52_13
% 203.13/34.21    (48)   ~ (e2 = e1)
% 203.13/34.21    (49)   ~ (all_52_13 = all_10_2)
% 203.13/34.21    (50)   ~ (all_6_0 = e1)
% 203.13/34.21    (51)  all_58_10 = all_52_27
% 203.13/34.21    (52)  all_56_8 = all_52_5
% 203.13/34.21    (53)  op(all_52_9, all_52_9) = all_52_8
% 203.13/34.21    (54)   ~ (all_52_19 = all_52_23)
% 203.13/34.21    (55)   ~ (all_52_29 = all_10_2)
% 203.13/34.21    (56)  all_58_7 = all_52_13
% 203.13/34.21    (57)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.13/34.21    (58)  op(all_6_2, all_6_2) = e3
% 203.13/34.21    (59)   ~ (all_52_5 = all_52_7)
% 203.13/34.21    (60)  all_58_12 = all_52_7
% 203.13/34.21    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.13/34.21    (62)   ~ (all_52_7 = all_14_2)
% 203.13/34.21    (63)   ~ (all_14_2 = e0)
% 203.13/34.21    (64)  all_58_2 = all_52_3
% 203.13/34.21    (65)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.13/34.21    (66)  all_56_2 = all_52_17
% 203.13/34.21    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.13/34.21    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.13/34.21    (69)  op(e3, all_6_1) = all_6_0
% 203.13/34.21    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.13/34.21    (71)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.13/34.21    (72)   ~ (e2 = e0)
% 203.13/34.21    (73)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.13/34.21    (74)  op(all_52_3, all_52_3) = e2
% 203.13/34.21    (75)   ~ (all_52_5 = all_52_29)
% 203.13/34.21    (76)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.13/34.21    (77)  all_56_6 = all_52_19
% 203.13/34.21    (78)   ~ (all_52_15 = all_14_2)
% 203.13/34.21    (79)   ~ (all_52_19 = all_52_27)
% 203.13/34.21    (80)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.13/34.21    (81)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.13/34.21    (82)   ~ (all_6_0 = e2)
% 203.13/34.21    (83)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.13/34.21    (84)   ~ (all_52_13 = all_4_2)
% 203.13/34.21    (85)  op(e3, e1) = all_52_17
% 203.13/34.21    (86)  op(e0, e3) = all_52_7
% 203.13/34.21    (87)  op(e1, e2) = all_52_13
% 203.13/34.21    (88)   ~ (all_52_9 = all_52_25)
% 203.13/34.21    (89)  all_58_15 = all_14_2
% 203.13/34.21    (90)   ~ (all_52_19 = all_10_2)
% 203.13/34.21    (91)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.13/34.21    (92)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.13/34.21    (93)  all_58_8 = all_10_2
% 203.13/34.21    (94)   ~ (all_52_5 = all_10_2)
% 203.13/34.21    (95)  op(all_52_29, all_52_29) = all_52_28
% 203.13/34.21    (96)  all_56_12 = all_52_7
% 203.13/34.21    (97)  op(all_52_17, all_52_17) = all_52_16
% 203.13/34.21    (98)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.13/34.21    (99)   ~ (all_52_25 = all_6_2)
% 203.13/34.21    (100)   ~ (all_52_9 = all_4_2)
% 203.13/34.21    (101)   ~ (all_52_5 = all_6_2)
% 203.13/34.21    (102)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.13/34.21    (103)   ~ (all_52_9 = all_6_2)
% 203.13/34.21    (104)   ~ (all_52_13 = all_52_15)
% 203.13/34.21    (105)  all_56_0 = all_6_2
% 203.13/34.21    (106)  op(e3, e3) = all_6_2
% 203.13/34.21    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.13/34.21    (108)   ~ (all_52_27 = all_14_2)
% 203.13/34.21    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.21    (110)  op(all_4_2, all_4_2) = all_52_10
% 203.30/34.21    (111)   ~ (all_52_3 = all_52_7)
% 203.30/34.21    (112)  op(all_14_2, all_14_2) = all_52_30
% 203.30/34.21    (113)  all_58_5 = all_52_19
% 203.30/34.21    (114)  all_56_1 = all_52_9
% 203.30/34.21    (115)   ~ (all_52_15 = all_4_2)
% 203.30/34.21    (116)   ~ (all_52_27 = all_4_2)
% 203.30/34.21    (117)  all_58_6 = all_52_5
% 203.30/34.21    (118)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.30/34.21    (119)   ~ (all_52_17 = all_6_2)
% 203.30/34.21    (120)   ~ (e1 = e0)
% 203.30/34.21    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.30/34.21    (122)   ~ (all_52_9 = all_52_17)
% 203.30/34.21    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.30/34.21    (124)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.30/34.21    (125)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.30/34.21    (126)  op(all_52_13, all_52_13) = all_52_12
% 203.30/34.21    (127)  op(e1, e1) = all_10_2
% 203.30/34.21    (128)   ~ (all_52_23 = all_10_2)
% 203.30/34.21    (129)  all_58_3 = all_4_2
% 203.30/34.21    (130)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.21    (131)  all_56_13 = all_52_15
% 203.30/34.21    (132)   ~ (all_52_3 = all_4_2)
% 203.30/34.21    (133)  op(all_6_2, e3) = all_6_1
% 203.30/34.21    (134)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.30/34.21    (135)   ~ (all_52_13 = all_52_29)
% 203.30/34.21    (136)  all_58_4 = all_52_17
% 203.30/34.21    (137)   ~ (all_14_0 = e2)
% 203.30/34.21  
% 203.30/34.21  Begin of proof
% 203.30/34.21  | 
% 203.30/34.21  | COMBINE_EQS: (33), (131) imply:
% 203.30/34.21  |   (138)  all_52_15 = e3
% 203.30/34.21  | 
% 203.30/34.21  | SIMP: (138) implies:
% 203.30/34.21  |   (139)  all_52_15 = e3
% 203.30/34.21  | 
% 203.30/34.21  | COMBINE_EQS: (22), (139) imply:
% 203.30/34.21  |   (140)  all_58_13 = e3
% 203.30/34.21  | 
% 203.30/34.21  | REDUCE: (12), (139) imply:
% 203.30/34.21  |   (141)   ~ (all_52_7 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | REDUCE: (34), (139) imply:
% 203.30/34.21  |   (142)   ~ (all_52_9 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | REDUCE: (104), (139) imply:
% 203.30/34.21  |   (143)   ~ (all_52_13 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | REDUCE: (2), (139) imply:
% 203.30/34.21  |   (144)   ~ (all_52_23 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | SIMP: (144) implies:
% 203.30/34.21  |   (145)   ~ (all_52_23 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | REDUCE: (78), (139) imply:
% 203.30/34.21  |   (146)   ~ (all_14_2 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | SIMP: (146) implies:
% 203.30/34.21  |   (147)   ~ (all_14_2 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | REDUCE: (115), (139) imply:
% 203.30/34.21  |   (148)   ~ (all_4_2 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | SIMP: (148) implies:
% 203.30/34.21  |   (149)   ~ (all_4_2 = e3)
% 203.30/34.21  | 
% 203.30/34.21  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 203.30/34.21  |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 203.30/34.21  |            (27), (28), (29), (30), (31), (32), (35), (36), (37), (38), (39),
% 203.30/34.21  |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 203.30/34.21  |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 203.30/34.21  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 203.30/34.21  |            (73), (74), (75), (76), (77), (79), (80), (81), (82), (83), (84),
% 203.30/34.21  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 203.30/34.21  |            (96), (97), (98), (99), (100), (101), (102), (103), (105), (106),
% 203.30/34.21  |            (107), (108), (109), (110), (111), (112), (113), (114), (116),
% 203.30/34.21  |            (117), (118), (119), (120), (121), (122), (123), (124), (125),
% 203.30/34.21  |            (126), (127), (128), (129), (130), (132), (133), (134), (135),
% 203.30/34.21  |            (136), (137), (140), (141), (142), (143), (145), (147), (149) are
% 203.30/34.21  |            inconsistent by sub-proof #519.
% 203.30/34.21  | 
% 203.30/34.21  End of proof
% 203.30/34.21  
% 203.30/34.21  Sub-proof #508 shows that the following formulas are inconsistent:
% 203.30/34.21  ----------------------------------------------------------------
% 203.30/34.21    (1)   ~ (all_52_15 = all_52_23)
% 203.30/34.21    (2)   ~ (all_52_25 = all_52_27)
% 203.30/34.21    (3)  all_58_14 = all_52_23
% 203.30/34.21    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.30/34.21    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.21    (6)  all_58_1 = all_52_9
% 203.30/34.21    (7)   ~ (all_52_9 = all_52_13)
% 203.30/34.21    (8)   ~ (e3 = e0)
% 203.30/34.21    (9)  op(e2, e3) = all_52_3
% 203.30/34.21    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.21    (11)   ~ (all_52_3 = all_52_19)
% 203.30/34.21    (12)  op(all_52_7, all_52_7) = all_52_6
% 203.30/34.21    (13)   ~ (all_52_17 = all_52_25)
% 203.30/34.21    (14)   ~ (all_52_3 = all_6_2)
% 203.30/34.21    (15)  all_58_0 = all_6_2
% 203.30/34.21    (16)  op(all_14_2, e0) = all_14_1
% 203.30/34.21    (17)  all_56_4 = all_52_3
% 203.30/34.21    (18)   ~ (all_52_17 = all_10_2)
% 203.30/34.21    (19)  op(e3, e0) = all_52_25
% 203.30/34.21    (20)  op(all_52_5, all_52_5) = all_52_4
% 203.30/34.21    (21)  op(all_52_19, all_52_19) = all_52_18
% 203.30/34.21    (22)   ~ (all_52_27 = all_52_29)
% 203.30/34.21    (23)  all_58_13 = all_52_15
% 203.30/34.21    (24)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.21    (25)  all_58_9 = all_52_25
% 203.30/34.21    (26)   ~ (all_6_1 = e1)
% 203.30/34.21    (27)   ~ (all_52_29 = all_14_2)
% 203.30/34.21    (28)  all_22_0 = all_6_0
% 203.30/34.21    (29)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.30/34.21    (30)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.21    (31)  op(e1, e3) = all_52_5
% 203.30/34.21    (32)  op(e2, e2) = all_4_2
% 203.30/34.21    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.30/34.21    (34)   ~ (all_52_3 = all_52_5)
% 203.30/34.21    (35)  all_58_11 = all_52_29
% 203.30/34.21    (36)  all_56_5 = all_4_2
% 203.30/34.21    (37)   ~ (all_52_25 = all_14_2)
% 203.30/34.21    (38)   ~ (all_52_9 = all_52_15)
% 203.30/34.21    (39)   ~ (all_52_3 = all_52_27)
% 203.30/34.21    (40)  op(all_10_2, e1) = all_10_1
% 203.30/34.21    (41)  op(all_6_2, all_6_2) = all_52_0
% 203.30/34.21    (42)   ~ (all_52_7 = all_6_2)
% 203.30/34.21    (43)  op(e0, e0) = all_14_2
% 203.30/34.21    (44)  all_56_15 = all_14_2
% 203.30/34.21    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.21    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.30/34.21    (47)  op(e1, e0) = all_52_29
% 203.30/34.21    (48)  all_56_11 = all_52_29
% 203.30/34.21    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.30/34.21    (50)  op(e1, all_10_1) = e3
% 203.30/34.21    (51)   ~ (all_52_13 = all_10_2)
% 203.30/34.21    (52)   ~ (all_6_0 = e1)
% 203.30/34.21    (53)  all_58_10 = all_52_27
% 203.30/34.21    (54)  all_56_8 = all_52_5
% 203.30/34.21    (55)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.21    (56)   ~ (all_52_19 = all_52_23)
% 203.30/34.21    (57)   ~ (all_52_25 = all_52_29)
% 203.30/34.21    (58)   ~ (all_52_29 = all_10_2)
% 203.30/34.21    (59)  all_58_7 = all_52_13
% 203.30/34.21    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.21    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.30/34.21    (62)   ~ (all_52_5 = all_52_7)
% 203.30/34.21    (63)  all_58_12 = all_52_7
% 203.30/34.21    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.21    (65)   ~ (all_52_7 = all_14_2)
% 203.30/34.21    (66)  all_58_2 = all_52_3
% 203.30/34.21    (67)  all_56_2 = all_52_17
% 203.30/34.21    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.30/34.21    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.21    (70)  op(e3, all_6_1) = all_6_0
% 203.30/34.21    (71)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.30/34.21    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.30/34.21    (73)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.30/34.21    (74)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.21    (75)   ~ (e2 = e0)
% 203.30/34.21    (76)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.30/34.22    (77)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.30/34.22    (78)   ~ (all_52_5 = all_52_29)
% 203.30/34.22    (79)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.22    (80)   ~ (all_52_15 = all_14_2)
% 203.30/34.22    (81)   ~ (all_52_19 = all_52_27)
% 203.30/34.22    (82)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.30/34.22    (83)   ~ (all_6_0 = e2)
% 203.30/34.22    (84)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.30/34.22            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.30/34.22    (85)  op(e3, e1) = all_52_17
% 203.30/34.22    (86)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.30/34.22    (87)  op(e0, e3) = all_52_7
% 203.30/34.22    (88)  op(e1, e2) = all_52_13
% 203.30/34.22    (89)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.30/34.22    (90)   ~ (all_52_9 = all_52_25)
% 203.30/34.22    (91)  all_58_15 = all_14_2
% 203.30/34.22    (92)   ~ (all_52_19 = all_10_2)
% 203.30/34.22    (93)  op(all_52_23, all_52_23) = all_52_22
% 203.30/34.22    (94)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.22    (95)  all_58_8 = all_10_2
% 203.30/34.22    (96)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.30/34.22    (97)   ~ (all_52_5 = all_10_2)
% 203.30/34.22    (98)  op(all_52_29, all_52_29) = all_52_28
% 203.30/34.22    (99)   ~ (all_52_23 = all_14_2)
% 203.30/34.22    (100)  all_56_12 = all_52_7
% 203.30/34.22    (101)  op(all_52_17, all_52_17) = all_52_16
% 203.30/34.22    (102)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.30/34.22    (103)   ~ (all_52_25 = all_6_2)
% 203.30/34.22    (104)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.30/34.22    (105)   ~ (all_52_9 = all_4_2)
% 203.30/34.22    (106)   ~ (all_52_5 = all_6_2)
% 203.30/34.22    (107)   ~ (all_52_9 = all_6_2)
% 203.30/34.22    (108)  all_56_0 = all_6_2
% 203.30/34.22    (109)  op(e3, e3) = all_6_2
% 203.30/34.22    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.30/34.22    (111)   ~ (all_52_27 = all_14_2)
% 203.30/34.22    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.22    (113)  all_56_14 = all_52_23
% 203.30/34.22    (114)  all_56_3 = all_52_25
% 203.30/34.22    (115)   ~ (all_52_3 = all_52_7)
% 203.30/34.22    (116)  op(all_14_2, all_14_2) = all_52_30
% 203.30/34.22    (117)  all_58_5 = all_52_19
% 203.30/34.22    (118)  all_56_1 = all_52_9
% 203.30/34.22    (119)   ~ (all_52_15 = all_4_2)
% 203.30/34.22    (120)  op(e0, all_14_1) = e3
% 203.30/34.22    (121)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.30/34.22           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.30/34.22           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.30/34.22           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.30/34.22    (122)   ~ (all_52_27 = all_4_2)
% 203.30/34.22    (123)  all_58_6 = all_52_5
% 203.30/34.22    (124)  op(e3, e2) = all_52_9
% 203.30/34.22    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.30/34.22    (126)   ~ (all_52_17 = all_6_2)
% 203.30/34.22    (127)   ~ (e1 = e0)
% 203.30/34.22    (128)   ~ (e3 = e2)
% 203.30/34.22    (129)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.30/34.22    (130)   ~ (all_52_9 = all_52_17)
% 203.30/34.22    (131)  all_56_10 = all_10_2
% 203.30/34.22    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.30/34.22    (133)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.30/34.22    (134)  op(all_52_13, all_52_13) = all_52_12
% 203.30/34.22    (135)  all_6_1 = e2
% 203.30/34.22    (136)  op(e1, e1) = all_10_2
% 203.30/34.22    (137)   ~ (all_52_23 = all_10_2)
% 203.30/34.22    (138)   ~ (all_52_7 = all_52_23)
% 203.30/34.22    (139)   ~ (all_52_17 = all_52_19)
% 203.30/34.22    (140)  all_58_3 = all_4_2
% 203.30/34.22    (141)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.22    (142)   ~ (all_52_3 = all_4_2)
% 203.30/34.22    (143)   ~ (all_52_19 = all_4_2)
% 203.30/34.22    (144)   ~ (all_52_17 = all_52_23)
% 203.30/34.22    (145)  op(all_6_2, e3) = all_6_1
% 203.30/34.22    (146)  all_22_2 = all_6_2
% 203.30/34.22    (147)  all_58_4 = all_52_17
% 203.30/34.22    (148)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.30/34.22    (149)  op(all_52_25, all_52_25) = all_52_24
% 203.30/34.22  
% 203.30/34.22  Begin of proof
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (26), (135) imply:
% 203.30/34.22  |   (150)   ~ (e2 = e1)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (135), (145) imply:
% 203.30/34.22  |   (151)  op(all_6_2, e3) = e2
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (70), (135) imply:
% 203.30/34.22  |   (152)  op(e3, e2) = all_6_0
% 203.30/34.22  | 
% 203.30/34.22  | GROUND_INST: instantiating (5) with all_52_9, all_6_0, e2, e3, simplifying
% 203.30/34.22  |              with (124), (152) gives:
% 203.30/34.22  |   (153)  all_52_9 = all_6_0
% 203.30/34.22  | 
% 203.30/34.22  | COMBINE_EQS: (118), (153) imply:
% 203.30/34.22  |   (154)  all_56_1 = all_6_0
% 203.30/34.22  | 
% 203.30/34.22  | COMBINE_EQS: (6), (153) imply:
% 203.30/34.22  |   (155)  all_58_1 = all_6_0
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (7), (153) imply:
% 203.30/34.22  |   (156)   ~ (all_52_13 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | SIMP: (156) implies:
% 203.30/34.22  |   (157)   ~ (all_52_13 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (38), (153) imply:
% 203.30/34.22  |   (158)   ~ (all_52_15 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | SIMP: (158) implies:
% 203.30/34.22  |   (159)   ~ (all_52_15 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (130), (153) imply:
% 203.30/34.22  |   (160)   ~ (all_52_17 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | SIMP: (160) implies:
% 203.30/34.22  |   (161)   ~ (all_52_17 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (90), (153) imply:
% 203.30/34.22  |   (162)   ~ (all_52_25 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | SIMP: (162) implies:
% 203.30/34.22  |   (163)   ~ (all_52_25 = all_6_0)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (107), (153) imply:
% 203.30/34.22  |   (164)   ~ (all_6_0 = all_6_2)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (105), (153) imply:
% 203.30/34.22  |   (165)   ~ (all_6_0 = all_4_2)
% 203.30/34.22  | 
% 203.30/34.22  | REDUCE: (55), (153) imply:
% 203.30/34.22  |   (166)  op(all_6_0, all_6_0) = all_52_8
% 203.30/34.22  | 
% 203.30/34.22  | BETA: splitting (84) gives:
% 203.30/34.22  | 
% 203.30/34.22  | Case 1:
% 203.30/34.22  | | 
% 203.30/34.22  | |   (167)  all_58_15 = e0
% 203.30/34.22  | | 
% 203.30/34.22  | | REF_CLOSE: (5), (8), (16), (43), (91), (116), (120), (167) are inconsistent
% 203.30/34.22  | |            by sub-proof #678.
% 203.30/34.22  | | 
% 203.30/34.22  | Case 2:
% 203.30/34.22  | | 
% 203.30/34.22  | |   (168)   ~ (all_58_15 = e0)
% 203.30/34.22  | |   (169)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 203.30/34.22  | |            | all_58_13 = e0 | all_58_14 = e0)
% 203.30/34.22  | | 
% 203.30/34.22  | | ALPHA: (169) implies:
% 203.30/34.22  | |   (170)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.30/34.22  | |   (171)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (91), (168) imply:
% 203.30/34.22  | |   (172)   ~ (all_14_2 = e0)
% 203.30/34.22  | | 
% 203.30/34.22  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.30/34.22  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.30/34.22  | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.30/34.22  | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 203.30/34.22  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 203.30/34.22  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 203.30/34.22  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 203.30/34.22  | |            (82), (83), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 203.30/34.22  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.30/34.22  | |            (104), (105), (106), (108), (109), (110), (111), (112), (113),
% 203.30/34.22  | |            (114), (115), (116), (117), (119), (121), (122), (123), (125),
% 203.30/34.22  | |            (126), (127), (128), (129), (131), (132), (133), (134), (136),
% 203.30/34.22  | |            (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 203.30/34.22  | |            (146), (147), (148), (149), (150), (151), (154), (155), (157),
% 203.30/34.22  | |            (159), (161), (163), (164), (165), (166), (170), (171), (172) are
% 203.30/34.22  | |            inconsistent by sub-proof #509.
% 203.30/34.22  | | 
% 203.30/34.22  | End of split
% 203.30/34.22  | 
% 203.30/34.22  End of proof
% 203.30/34.22  
% 203.30/34.22  Sub-proof #509 shows that the following formulas are inconsistent:
% 203.30/34.22  ----------------------------------------------------------------
% 203.30/34.22    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.30/34.22    (2)   ~ (all_52_15 = all_52_23)
% 203.30/34.22    (3)   ~ (all_52_25 = all_6_0)
% 203.30/34.22    (4)   ~ (all_52_25 = all_52_27)
% 203.30/34.22    (5)  all_58_14 = all_52_23
% 203.30/34.22    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.30/34.22    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.22    (8)  all_58_1 = all_52_9
% 203.30/34.22    (9)   ~ (all_52_9 = all_52_13)
% 203.30/34.22    (10)   ~ (e3 = e0)
% 203.30/34.22    (11)  op(e2, e3) = all_52_3
% 203.30/34.22    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.22    (13)   ~ (all_52_3 = all_52_19)
% 203.30/34.22    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.30/34.22    (15)   ~ (all_52_17 = all_52_25)
% 203.30/34.22    (16)   ~ (all_52_3 = all_6_2)
% 203.30/34.22    (17)  all_58_0 = all_6_2
% 203.30/34.22    (18)  op(all_14_2, e0) = all_14_1
% 203.30/34.22    (19)  all_56_4 = all_52_3
% 203.30/34.22    (20)   ~ (all_52_17 = all_10_2)
% 203.30/34.22    (21)  op(e3, e0) = all_52_25
% 203.30/34.22    (22)  op(all_52_5, all_52_5) = all_52_4
% 203.30/34.22    (23)  op(all_52_19, all_52_19) = all_52_18
% 203.30/34.22    (24)   ~ (all_52_27 = all_52_29)
% 203.30/34.22    (25)  all_58_13 = all_52_15
% 203.30/34.22    (26)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.22    (27)  all_58_9 = all_52_25
% 203.30/34.22    (28)   ~ (all_52_29 = all_14_2)
% 203.30/34.22    (29)  all_22_0 = all_6_0
% 203.30/34.22    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.30/34.22    (31)   ~ (all_52_17 = all_6_0)
% 203.30/34.22    (32)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.22    (33)  op(e1, e3) = all_52_5
% 203.30/34.22    (34)  op(e2, e2) = all_4_2
% 203.30/34.22    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.30/34.22    (36)   ~ (all_52_3 = all_52_5)
% 203.30/34.22    (37)  all_58_11 = all_52_29
% 203.30/34.22    (38)  all_56_5 = all_4_2
% 203.30/34.22    (39)   ~ (all_52_25 = all_14_2)
% 203.30/34.22    (40)   ~ (all_52_3 = all_52_27)
% 203.30/34.22    (41)  op(all_10_2, e1) = all_10_1
% 203.30/34.22    (42)  op(all_6_2, all_6_2) = all_52_0
% 203.30/34.22    (43)   ~ (all_52_7 = all_6_2)
% 203.30/34.22    (44)  op(e0, e0) = all_14_2
% 203.30/34.22    (45)  all_56_15 = all_14_2
% 203.30/34.22    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.22    (47)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.30/34.22    (48)  op(e1, e0) = all_52_29
% 203.30/34.22    (49)  all_56_11 = all_52_29
% 203.30/34.22    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.30/34.22    (51)  op(e1, all_10_1) = e3
% 203.30/34.22    (52)   ~ (e2 = e1)
% 203.30/34.22    (53)   ~ (all_52_13 = all_10_2)
% 203.30/34.22    (54)   ~ (all_6_0 = e1)
% 203.30/34.22    (55)  all_58_10 = all_52_27
% 203.30/34.22    (56)  all_56_8 = all_52_5
% 203.30/34.22    (57)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.22    (58)   ~ (all_52_19 = all_52_23)
% 203.30/34.22    (59)   ~ (all_52_25 = all_52_29)
% 203.30/34.22    (60)  op(all_6_2, e3) = e2
% 203.30/34.22    (61)   ~ (all_52_29 = all_10_2)
% 203.30/34.22    (62)  all_58_7 = all_52_13
% 203.30/34.22    (63)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.22    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.30/34.22    (65)  all_58_1 = all_6_0
% 203.30/34.22    (66)   ~ (all_52_5 = all_52_7)
% 203.30/34.22    (67)  all_58_12 = all_52_7
% 203.30/34.22    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.22    (69)   ~ (all_52_7 = all_14_2)
% 203.30/34.22    (70)   ~ (all_14_2 = e0)
% 203.30/34.22    (71)  all_58_2 = all_52_3
% 203.30/34.22    (72)  all_56_2 = all_52_17
% 203.30/34.22    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.30/34.22    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.22    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.30/34.22    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.30/34.22    (77)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.30/34.22    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.22    (79)   ~ (e2 = e0)
% 203.30/34.22    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.30/34.22    (81)  op(all_6_0, all_6_0) = all_52_8
% 203.30/34.22    (82)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.30/34.22    (83)   ~ (all_52_5 = all_52_29)
% 203.30/34.22    (84)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.22    (85)   ~ (all_52_15 = all_14_2)
% 203.30/34.22    (86)   ~ (all_52_13 = all_6_0)
% 203.30/34.22    (87)   ~ (all_52_19 = all_52_27)
% 203.30/34.22    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.30/34.22    (89)   ~ (all_6_0 = e2)
% 203.30/34.22    (90)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.30/34.22    (91)  op(e3, e1) = all_52_17
% 203.30/34.22    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.30/34.22    (93)  op(e0, e3) = all_52_7
% 203.30/34.22    (94)  op(e1, e2) = all_52_13
% 203.30/34.22    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.30/34.22    (96)   ~ (all_52_9 = all_52_25)
% 203.30/34.22    (97)  all_58_15 = all_14_2
% 203.30/34.22    (98)   ~ (all_52_19 = all_10_2)
% 203.30/34.22    (99)  op(all_52_23, all_52_23) = all_52_22
% 203.30/34.22    (100)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.22    (101)  all_58_8 = all_10_2
% 203.30/34.22    (102)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.30/34.22    (103)   ~ (all_52_5 = all_10_2)
% 203.30/34.22    (104)  op(all_52_29, all_52_29) = all_52_28
% 203.30/34.22    (105)   ~ (all_52_23 = all_14_2)
% 203.30/34.22    (106)  all_56_12 = all_52_7
% 203.30/34.22    (107)  op(all_52_17, all_52_17) = all_52_16
% 203.30/34.22    (108)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.30/34.22    (109)   ~ (all_52_25 = all_6_2)
% 203.30/34.22    (110)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.30/34.22    (111)   ~ (all_52_9 = all_4_2)
% 203.30/34.22    (112)   ~ (all_52_5 = all_6_2)
% 203.30/34.22    (113)  all_56_0 = all_6_2
% 203.30/34.22    (114)  op(e3, e3) = all_6_2
% 203.30/34.22    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.30/34.22    (116)   ~ (all_52_15 = all_6_0)
% 203.30/34.22    (117)   ~ (all_52_27 = all_14_2)
% 203.30/34.22    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.22    (119)  all_56_14 = all_52_23
% 203.30/34.22    (120)  all_56_3 = all_52_25
% 203.30/34.22    (121)   ~ (all_52_3 = all_52_7)
% 203.30/34.22    (122)   ~ (all_6_0 = all_6_2)
% 203.30/34.22    (123)  op(all_14_2, all_14_2) = all_52_30
% 203.30/34.22    (124)  all_58_5 = all_52_19
% 203.30/34.22    (125)   ~ (all_52_15 = all_4_2)
% 203.30/34.22    (126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.30/34.22           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.30/34.22           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.30/34.22           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.30/34.22    (127)   ~ (all_52_27 = all_4_2)
% 203.30/34.22    (128)  all_58_6 = all_52_5
% 203.30/34.22    (129)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.30/34.22    (130)   ~ (all_52_17 = all_6_2)
% 203.30/34.22    (131)   ~ (e1 = e0)
% 203.30/34.22    (132)   ~ (e3 = e2)
% 203.30/34.22    (133)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.30/34.22    (134)  all_56_10 = all_10_2
% 203.30/34.22    (135)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.30/34.22    (136)  all_56_1 = all_6_0
% 203.30/34.22    (137)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.30/34.22    (138)  op(all_52_13, all_52_13) = all_52_12
% 203.30/34.22    (139)   ~ (all_6_0 = all_4_2)
% 203.30/34.22    (140)  op(e1, e1) = all_10_2
% 203.30/34.22    (141)   ~ (all_52_23 = all_10_2)
% 203.30/34.22    (142)   ~ (all_52_7 = all_52_23)
% 203.30/34.22    (143)   ~ (all_52_17 = all_52_19)
% 203.30/34.22    (144)  all_58_3 = all_4_2
% 203.30/34.22    (145)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.22    (146)   ~ (all_52_3 = all_4_2)
% 203.30/34.22    (147)   ~ (all_52_19 = all_4_2)
% 203.30/34.22    (148)   ~ (all_52_17 = all_52_23)
% 203.30/34.22    (149)  op(all_6_2, e3) = all_6_1
% 203.30/34.22    (150)  all_22_2 = all_6_2
% 203.30/34.22    (151)  all_58_4 = all_52_17
% 203.30/34.22    (152)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.30/34.22    (153)  op(all_52_25, all_52_25) = all_52_24
% 203.30/34.22  
% 203.30/34.22  Begin of proof
% 203.30/34.22  | 
% 203.30/34.22  | BETA: splitting (133) gives:
% 203.30/34.22  | 
% 203.30/34.22  | Case 1:
% 203.30/34.22  | | 
% 203.30/34.22  | |   (154)  all_56_1 = e3
% 203.30/34.22  | | 
% 203.30/34.22  | | COMBINE_EQS: (136), (154) imply:
% 203.30/34.22  | |   (155)  all_6_0 = e3
% 203.30/34.22  | | 
% 203.30/34.22  | | COMBINE_EQS: (65), (155) imply:
% 203.30/34.22  | |   (156)  all_58_1 = e3
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (86), (155) imply:
% 203.30/34.22  | |   (157)   ~ (all_52_13 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (116), (155) imply:
% 203.30/34.22  | |   (158)   ~ (all_52_15 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (31), (155) imply:
% 203.30/34.22  | |   (159)   ~ (all_52_17 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (3), (155) imply:
% 203.30/34.22  | |   (160)   ~ (all_52_25 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (122), (155) imply:
% 203.30/34.22  | |   (161)   ~ (all_6_2 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | SIMP: (161) implies:
% 203.30/34.22  | |   (162)   ~ (all_6_2 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (139), (155) imply:
% 203.30/34.22  | |   (163)   ~ (all_4_2 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | SIMP: (163) implies:
% 203.30/34.22  | |   (164)   ~ (all_4_2 = e3)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (54), (155) imply:
% 203.30/34.22  | |   (165)   ~ (e3 = e1)
% 203.30/34.22  | | 
% 203.30/34.22  | | REDUCE: (81), (155) imply:
% 203.30/34.22  | |   (166)  op(e3, e3) = all_52_8
% 203.30/34.22  | | 
% 203.30/34.22  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 203.30/34.22  | |              with (114), (166) gives:
% 203.30/34.22  | |   (167)  all_52_8 = all_6_2
% 203.30/34.22  | | 
% 203.30/34.22  | | BETA: splitting (126) gives:
% 203.30/34.22  | | 
% 203.30/34.22  | | Case 1:
% 203.30/34.22  | | | 
% 203.30/34.22  | | |   (168)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.30/34.22  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.30/34.22  | | |            e0)
% 203.30/34.22  | | | 
% 203.30/34.22  | | | BETA: splitting (168) gives:
% 203.30/34.22  | | | 
% 203.30/34.22  | | | Case 1:
% 203.30/34.22  | | | | 
% 203.30/34.22  | | | |   (169)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.30/34.22  | | | | 
% 203.30/34.22  | | | | REF_CLOSE: (6), (7), (14), (17), (22), (34), (42), (44), (46), (67),
% 203.30/34.22  | | | |            (69), (71), (74), (103), (114), (128), (129), (140), (146),
% 203.30/34.22  | | | |            (162), (169) are inconsistent by sub-proof #835.
% 203.30/34.22  | | | | 
% 203.30/34.22  | | | Case 2:
% 203.30/34.22  | | | | 
% 203.30/34.22  | | | |   (170)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.30/34.22  | | | |          e0
% 203.30/34.22  | | | | 
% 203.30/34.22  | | | | REF_CLOSE: (162), (167), (170) are inconsistent by sub-proof #834.
% 203.30/34.22  | | | | 
% 203.30/34.22  | | | End of split
% 203.30/34.22  | | | 
% 203.30/34.22  | | Case 2:
% 203.30/34.22  | | | 
% 203.30/34.22  | | |   (171)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.30/34.22  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.30/34.22  | | |            all_52_30 = e0)
% 203.30/34.22  | | | 
% 203.30/34.22  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.30/34.22  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.30/34.22  | | |            (24), (25), (26), (27), (28), (30), (32), (33), (34), (35),
% 203.30/34.22  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 203.30/34.22  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (55), (56),
% 203.30/34.22  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (66), (67),
% 203.30/34.22  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (78),
% 203.30/34.22  | | |            (79), (80), (82), (83), (84), (85), (87), (88), (90), (91),
% 203.30/34.22  | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.30/34.22  | | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.30/34.22  | | |            (111), (112), (114), (115), (117), (118), (119), (120), (121),
% 203.30/34.22  | | |            (123), (124), (125), (127), (128), (129), (130), (131), (132),
% 203.30/34.22  | | |            (134), (135), (138), (140), (141), (142), (143), (144), (145),
% 203.30/34.22  | | |            (146), (147), (148), (149), (151), (152), (153), (156), (157),
% 203.30/34.22  | | |            (158), (159), (160), (162), (164), (165), (166), (171) are
% 203.30/34.22  | | |            inconsistent by sub-proof #513.
% 203.30/34.22  | | | 
% 203.30/34.22  | | End of split
% 203.30/34.22  | | 
% 203.30/34.22  | Case 2:
% 203.30/34.22  | | 
% 203.30/34.22  | |   (172)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.30/34.22  | | 
% 203.30/34.22  | | REF_CLOSE: (7), (11), (16), (29), (42), (54), (60), (77), (89), (113),
% 203.30/34.22  | |            (114), (122), (132), (136), (137), (150), (172) are inconsistent
% 203.30/34.22  | |            by sub-proof #820.
% 203.30/34.22  | | 
% 203.30/34.22  | End of split
% 203.30/34.22  | 
% 203.30/34.22  End of proof
% 203.30/34.22  
% 203.30/34.22  Sub-proof #510 shows that the following formulas are inconsistent:
% 203.30/34.22  ----------------------------------------------------------------
% 203.30/34.22    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.30/34.22    (2)   ~ (all_52_15 = all_52_23)
% 203.30/34.22    (3)   ~ (all_52_25 = all_52_27)
% 203.30/34.22    (4)  all_58_14 = all_52_23
% 203.30/34.22    (5)   ~ (e3 = e1)
% 203.30/34.22    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.30/34.22    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.22    (8)   ~ (all_52_5 = all_52_13)
% 203.30/34.22    (9)  all_58_1 = all_52_9
% 203.30/34.22    (10)   ~ (all_52_9 = all_52_13)
% 203.30/34.22    (11)   ~ (e3 = e0)
% 203.30/34.22    (12)  op(e2, e3) = all_52_3
% 203.30/34.22    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.22    (14)  op(e0, e2) = all_52_15
% 203.30/34.22    (15)   ~ (all_52_7 = all_52_15)
% 203.30/34.22    (16)   ~ (all_52_3 = all_52_19)
% 203.30/34.22    (17)  op(all_52_7, all_52_7) = all_52_6
% 203.30/34.22    (18)   ~ (all_52_17 = all_52_25)
% 203.30/34.22    (19)   ~ (all_52_3 = all_6_2)
% 203.30/34.22    (20)  all_58_0 = all_6_2
% 203.30/34.22    (21)  op(all_14_2, e0) = all_14_1
% 203.30/34.22    (22)  all_56_4 = all_52_3
% 203.30/34.22    (23)   ~ (all_52_17 = all_10_2)
% 203.30/34.22    (24)  op(e3, e0) = all_52_25
% 203.30/34.22    (25)  op(all_52_5, all_52_5) = all_52_4
% 203.30/34.22    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.30/34.22    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.30/34.22    (28)   ~ (all_52_27 = all_52_29)
% 203.30/34.22    (29)  all_58_13 = all_52_15
% 203.30/34.22    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.22    (31)  all_58_9 = all_52_25
% 203.30/34.22    (32)   ~ (all_6_1 = e1)
% 203.30/34.22    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.30/34.22    (34)   ~ (all_52_29 = all_14_2)
% 203.30/34.22    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.30/34.22    (36)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.22    (37)  op(e1, e3) = all_52_5
% 203.30/34.22    (38)  op(e2, e2) = all_4_2
% 203.30/34.22    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.30/34.22    (40)   ~ (all_52_3 = all_52_5)
% 203.30/34.22    (41)   ~ (all_4_1 = e3)
% 203.30/34.22    (42)  all_58_11 = all_52_29
% 203.30/34.22    (43)  all_56_5 = all_4_2
% 203.30/34.22    (44)   ~ (all_52_25 = all_14_2)
% 203.30/34.22    (45)   ~ (all_52_9 = all_52_15)
% 203.30/34.22    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.30/34.22    (47)   ~ (all_52_3 = all_52_27)
% 203.30/34.23    (48)  op(all_10_2, e1) = all_10_1
% 203.30/34.23    (49)  op(all_6_2, all_6_2) = all_52_0
% 203.30/34.23    (50)   ~ (all_52_7 = all_6_2)
% 203.30/34.23    (51)  op(e0, e0) = all_14_2
% 203.30/34.23    (52)  op(e0, e1) = all_52_23
% 203.30/34.23    (53)  all_56_15 = all_14_2
% 203.30/34.23    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.23    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.30/34.23    (56)  op(e2, all_4_1) = all_4_0
% 203.30/34.23    (57)  all_56_11 = all_52_29
% 203.30/34.23    (58)   ~ (all_4_1 = e1)
% 203.30/34.23    (59)   ~ (all_4_0 = e3)
% 203.30/34.23    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.30/34.23    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.30/34.23    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.30/34.23    (63)  all_56_9 = all_52_13
% 203.30/34.23    (64)   ~ (e2 = e1)
% 203.30/34.23    (65)   ~ (all_52_13 = all_10_2)
% 203.30/34.23    (66)   ~ (all_6_0 = e1)
% 203.30/34.23    (67)  all_58_10 = all_52_27
% 203.30/34.23    (68)  all_56_8 = all_52_5
% 203.30/34.23    (69)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.23    (70)  op(all_52_15, all_52_15) = all_52_14
% 203.30/34.23    (71)   ~ (all_52_19 = all_52_23)
% 203.30/34.23    (72)   ~ (all_52_25 = all_52_29)
% 203.30/34.23    (73)   ~ (all_52_29 = all_10_2)
% 203.30/34.23    (74)  all_58_7 = all_52_13
% 203.30/34.23    (75)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.23    (76)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.30/34.23    (77)  all_36_2 = all_10_2
% 203.30/34.23    (78)  all_36_1 = all_10_1
% 203.30/34.23    (79)   ~ (all_52_5 = all_52_7)
% 203.30/34.23    (80)  all_58_12 = all_52_7
% 203.30/34.23    (81)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.23    (82)   ~ (all_52_7 = all_14_2)
% 203.30/34.23    (83)   ~ (all_14_2 = e0)
% 203.30/34.23    (84)  all_58_2 = all_52_3
% 203.30/34.23    (85)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.30/34.23    (86)  all_56_2 = all_52_17
% 203.30/34.23    (87)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.30/34.23    (88)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.23    (89)  op(e3, all_6_1) = all_6_0
% 203.30/34.23    (90)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.30/34.23    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.30/34.23    (92)  all_56_7 = all_52_27
% 203.30/34.23    (93)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.23    (94)   ~ (e2 = e0)
% 203.30/34.23    (95)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.30/34.23    (96)  op(all_4_2, e2) = all_4_1
% 203.30/34.23    (97)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.30/34.23    (98)   ~ (all_52_5 = all_52_29)
% 203.30/34.23    (99)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.23    (100)  all_56_6 = all_52_19
% 203.30/34.23    (101)   ~ (all_52_15 = all_14_2)
% 203.30/34.23    (102)   ~ (all_52_19 = all_52_27)
% 203.30/34.23    (103)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.30/34.23    (104)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.30/34.23    (105)   ~ (all_6_0 = e2)
% 203.30/34.23    (106)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.30/34.23    (107)   ~ (all_52_13 = all_4_2)
% 203.30/34.23    (108)  op(e3, e1) = all_52_17
% 203.30/34.23    (109)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.30/34.23    (110)  op(e0, e3) = all_52_7
% 203.30/34.23    (111)  op(e1, e2) = all_52_13
% 203.30/34.23    (112)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.30/34.23    (113)   ~ (all_52_9 = all_52_25)
% 203.30/34.23    (114)  all_58_15 = all_14_2
% 203.30/34.23    (115)   ~ (all_52_19 = all_10_2)
% 203.30/34.23    (116)  op(all_52_23, all_52_23) = all_52_22
% 203.30/34.23    (117)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.23    (118)  all_58_8 = all_10_2
% 203.30/34.23    (119)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.30/34.23    (120)   ~ (all_52_5 = all_10_2)
% 203.30/34.23    (121)  op(all_52_29, all_52_29) = all_52_28
% 203.30/34.23    (122)   ~ (all_52_23 = all_14_2)
% 203.30/34.23    (123)  all_56_12 = all_52_7
% 203.30/34.23    (124)  op(all_52_17, all_52_17) = all_52_16
% 203.30/34.23    (125)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.30/34.23    (126)   ~ (all_52_25 = all_6_2)
% 203.30/34.23    (127)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.30/34.23    (128)   ~ (all_52_9 = all_4_2)
% 203.30/34.23    (129)   ~ (all_52_5 = all_6_2)
% 203.30/34.23    (130)   ~ (all_52_9 = all_6_2)
% 203.30/34.23    (131)   ~ (all_52_13 = all_52_15)
% 203.30/34.23    (132)  all_56_0 = all_6_2
% 203.30/34.23    (133)  op(e3, e3) = all_6_2
% 203.30/34.23    (134)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.30/34.23    (135)   ~ (all_52_27 = all_14_2)
% 203.30/34.23    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.23    (137)  all_56_14 = all_52_23
% 203.30/34.23    (138)  op(all_4_2, all_4_2) = all_52_10
% 203.30/34.23    (139)  all_56_3 = all_52_25
% 203.30/34.23    (140)   ~ (all_52_3 = all_52_7)
% 203.30/34.23    (141)  op(all_14_2, all_14_2) = all_52_30
% 203.30/34.23    (142)  all_58_5 = all_52_19
% 203.30/34.23    (143)  all_56_1 = all_52_9
% 203.30/34.23    (144)   ~ (all_52_15 = all_4_2)
% 203.30/34.23    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.30/34.23           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.30/34.23           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.30/34.23           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.30/34.23    (146)   ~ (all_52_27 = all_4_2)
% 203.30/34.23    (147)  all_58_6 = all_52_5
% 203.30/34.23    (148)  op(e3, e2) = all_52_9
% 203.30/34.23    (149)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.30/34.23    (150)   ~ (all_52_17 = all_6_2)
% 203.30/34.23    (151)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.30/34.23    (152)   ~ (e1 = e0)
% 203.30/34.23    (153)   ~ (e3 = e2)
% 203.30/34.23    (154)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.30/34.23    (155)   ~ (all_10_1 = e0) |  ~ (all_10_2 = e2)
% 203.30/34.23    (156)   ~ (all_52_9 = all_52_17)
% 203.30/34.23    (157)  all_56_10 = all_10_2
% 203.30/34.23    (158)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.30/34.23    (159)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.30/34.23    (160)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.30/34.23    (161)  op(all_52_13, all_52_13) = all_52_12
% 203.30/34.23    (162)   ~ (all_6_1 = e2)
% 203.30/34.23    (163)  op(e1, e1) = all_10_2
% 203.30/34.23    (164)   ~ (all_52_23 = all_10_2)
% 203.30/34.23    (165)   ~ (all_52_7 = all_52_23)
% 203.30/34.23    (166)   ~ (all_52_17 = all_52_19)
% 203.30/34.23    (167)  all_58_3 = all_4_2
% 203.30/34.23    (168)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.23    (169)  all_56_13 = all_52_15
% 203.30/34.23    (170)   ~ (all_52_3 = all_4_2)
% 203.30/34.23    (171)   ~ (all_52_19 = all_4_2)
% 203.30/34.23    (172)   ~ (all_52_17 = all_52_23)
% 203.30/34.23    (173)  op(all_6_2, e3) = all_6_1
% 203.30/34.23    (174)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.30/34.23    (175)   ~ (all_52_13 = all_52_29)
% 203.30/34.23    (176)  all_58_4 = all_52_17
% 203.30/34.23    (177)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.30/34.23    (178)  op(all_52_25, all_52_25) = all_52_24
% 203.30/34.23  
% 203.30/34.23  Begin of proof
% 203.30/34.23  | 
% 203.30/34.23  | BETA: splitting (145) gives:
% 203.30/34.23  | 
% 203.30/34.23  | Case 1:
% 203.30/34.23  | | 
% 203.30/34.23  | |   (179)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.30/34.23  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 203.30/34.23  | | 
% 203.30/34.23  | | BETA: splitting (179) gives:
% 203.30/34.23  | | 
% 203.30/34.23  | | Case 1:
% 203.30/34.23  | | | 
% 203.30/34.23  | | |   (180)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.30/34.23  | | | 
% 203.30/34.23  | | | ALPHA: (180) implies:
% 203.30/34.23  | | |   (181)  all_52_6 = e0
% 203.30/34.23  | | |   (182)  all_52_4 = e1
% 203.30/34.23  | | |   (183)  all_52_2 = e2
% 203.30/34.23  | | |   (184)  all_52_0 = e3
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REDUCE: (6), (183) imply:
% 203.30/34.23  | | |   (185)  op(all_52_3, all_52_3) = e2
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REDUCE: (25), (182) imply:
% 203.30/34.23  | | |   (186)  op(all_52_5, all_52_5) = e1
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REDUCE: (17), (181) imply:
% 203.30/34.23  | | |   (187)  op(all_52_7, all_52_7) = e0
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REDUCE: (49), (184) imply:
% 203.30/34.23  | | |   (188)  op(all_6_2, all_6_2) = e3
% 203.30/34.23  | | | 
% 203.30/34.23  | | | BETA: splitting (119) gives:
% 203.30/34.23  | | | 
% 203.30/34.23  | | | Case 1:
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | |   (189)  all_56_15 = e3
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | | REF_CLOSE: (7), (9), (10), (13), (14), (15), (16), (19), (20), (22),
% 203.30/34.23  | | | |            (26), (28), (29), (30), (33), (34), (36), (38), (40), (42),
% 203.30/34.23  | | | |            (46), (47), (48), (50), (51), (52), (53), (54), (58), (60),
% 203.30/34.23  | | | |            (67), (68), (69), (74), (75), (77), (78), (79), (80), (81),
% 203.30/34.23  | | | |            (82), (83), (84), (85), (88), (89), (92), (93), (96), (99),
% 203.30/34.23  | | | |            (100), (101), (102), (104), (105), (115), (117), (118),
% 203.30/34.23  | | | |            (120), (122), (123), (125), (128), (129), (133), (135),
% 203.30/34.23  | | | |            (136), (137), (140), (141), (142), (144), (146), (147),
% 203.30/34.23  | | | |            (151), (155), (163), (164), (165), (167), (168), (169),
% 203.30/34.23  | | | |            (170), (173), (174), (185), (186), (187), (188), (189) are
% 203.30/34.23  | | | |            inconsistent by sub-proof #511.
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | Case 2:
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | |   (190)   ~ (all_56_15 = e3)
% 203.30/34.23  | | | |   (191)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | | REDUCE: (53), (190) imply:
% 203.30/34.23  | | | |   (192)   ~ (all_14_2 = e3)
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | | REF_CLOSE: (2), (4), (7), (9), (11), (13), (14), (15), (19), (20), (22),
% 203.30/34.23  | | | |            (29), (38), (40), (41), (43), (45), (46), (50), (51), (53),
% 203.30/34.23  | | | |            (54), (56), (58), (59), (60), (64), (69), (74), (76), (80),
% 203.30/34.23  | | | |            (82), (83), (84), (88), (93), (94), (95), (96), (99), (101),
% 203.30/34.23  | | | |            (104), (106), (111), (112), (114), (116), (120), (123),
% 203.30/34.23  | | | |            (128), (130), (133), (140), (141), (143), (144), (147),
% 203.30/34.23  | | | |            (148), (149), (152), (153), (154), (161), (163), (164),
% 203.30/34.23  | | | |            (165), (167), (168), (169), (170), (174), (185), (186),
% 203.30/34.23  | | | |            (187), (188), (191), (192) are inconsistent by sub-proof
% 203.30/34.23  | | | |            #1145.
% 203.30/34.23  | | | | 
% 203.30/34.23  | | | End of split
% 203.30/34.23  | | | 
% 203.30/34.23  | | Case 2:
% 203.30/34.23  | | | 
% 203.30/34.23  | | |   (193)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 203.30/34.23  | | |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 203.30/34.23  | | |            (26), (27), (28), (29), (30), (31), (32), (34), (36), (37),
% 203.30/34.23  | | |            (38), (39), (40), (41), (42), (43), (44), (47), (49), (50),
% 203.30/34.23  | | |            (51), (53), (54), (57), (58), (60), (62), (63), (64), (65),
% 203.30/34.23  | | |            (66), (67), (68), (69), (70), (71), (72), (74), (76), (79),
% 203.30/34.23  | | |            (80), (81), (82), (83), (84), (87), (88), (89), (91), (92),
% 203.30/34.23  | | |            (93), (94), (95), (96), (98), (99), (101), (103), (104), (105),
% 203.30/34.23  | | |            (106), (107), (110), (111), (112), (113), (114), (116), (117),
% 203.30/34.23  | | |            (118), (119), (121), (122), (123), (124), (126), (127), (128),
% 203.30/34.23  | | |            (129), (130), (133), (134), (135), (136), (138), (139), (140),
% 203.30/34.23  | | |            (141), (142), (143), (146), (147), (148), (149), (150), (152),
% 203.30/34.23  | | |            (153), (154), (156), (157), (158), (159), (161), (162), (163),
% 203.30/34.23  | | |            (165), (166), (167), (169), (170), (171), (172), (173), (175),
% 203.30/34.23  | | |            (176), (177), (178), (193) are inconsistent by sub-proof #1091.
% 203.30/34.23  | | | 
% 203.30/34.23  | | End of split
% 203.30/34.23  | | 
% 203.30/34.23  | Case 2:
% 203.30/34.23  | | 
% 203.30/34.23  | |   (194)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 203.30/34.23  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.30/34.23  | |            e0)
% 203.30/34.23  | | 
% 203.30/34.23  | | BETA: splitting (194) gives:
% 203.30/34.23  | | 
% 203.30/34.23  | | Case 1:
% 203.30/34.23  | | | 
% 203.30/34.23  | | |   (195)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 203.30/34.23  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 203.30/34.23  | | |            (27), (29), (30), (31), (32), (34), (35), (36), (37), (38),
% 203.30/34.23  | | |            (40), (42), (44), (45), (47), (48), (49), (50), (51), (53),
% 203.30/34.23  | | |            (54), (57), (60), (61), (62), (63), (64), (65), (66), (67),
% 203.30/34.23  | | |            (68), (69), (71), (72), (73), (74), (79), (80), (81), (82),
% 203.30/34.23  | | |            (84), (85), (86), (87), (88), (89), (90), (91), (93), (94),
% 203.30/34.23  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 203.30/34.23  | | |            (106), (107), (108), (110), (112), (113), (114), (115), (116),
% 203.30/34.23  | | |            (117), (118), (119), (120), (121), (122), (123), (124), (126),
% 203.30/34.23  | | |            (127), (128), (129), (130), (131), (132), (133), (135), (136),
% 203.30/34.23  | | |            (138), (139), (140), (141), (142), (143), (146), (147), (149),
% 203.30/34.23  | | |            (150), (152), (153), (154), (156), (157), (158), (159), (160),
% 203.30/34.23  | | |            (161), (162), (163), (165), (166), (167), (168), (169), (170),
% 203.30/34.23  | | |            (173), (175), (176), (177), (178), (195) are inconsistent by
% 203.30/34.23  | | |            sub-proof #1042.
% 203.30/34.23  | | | 
% 203.30/34.23  | | Case 2:
% 203.30/34.23  | | | 
% 203.30/34.23  | | |   (196)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 203.30/34.23  | | | 
% 203.30/34.23  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (15),
% 203.30/34.23  | | |            (17), (18), (19), (20), (22), (23), (24), (25), (27), (28),
% 203.30/34.23  | | |            (29), (31), (32), (34), (36), (37), (38), (40), (42), (43),
% 203.30/34.23  | | |            (44), (45), (47), (48), (49), (50), (51), (53), (54), (55),
% 203.30/34.23  | | |            (57), (60), (61), (62), (66), (67), (68), (69), (70), (71),
% 203.30/34.23  | | |            (72), (73), (74), (75), (76), (79), (80), (81), (82), (83),
% 203.30/34.23  | | |            (84), (86), (88), (89), (90), (91), (93), (95), (98), (101),
% 203.30/34.23  | | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.30/34.23  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 203.30/34.23  | | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 203.30/34.23  | | |            (130), (131), (132), (133), (134), (135), (136), (137), (139),
% 203.30/34.23  | | |            (140), (141), (142), (143), (144), (146), (147), (149), (150),
% 203.30/34.23  | | |            (153), (154), (160), (161), (162), (163), (165), (166), (167),
% 203.30/34.23  | | |            (168), (169), (170), (171), (172), (173), (176), (178), (196)
% 203.30/34.23  | | |            are inconsistent by sub-proof #1008.
% 203.30/34.23  | | | 
% 203.30/34.23  | | End of split
% 203.30/34.23  | | 
% 203.30/34.23  | End of split
% 203.30/34.23  | 
% 203.30/34.23  End of proof
% 203.30/34.23  
% 203.30/34.23  Sub-proof #511 shows that the following formulas are inconsistent:
% 203.30/34.23  ----------------------------------------------------------------
% 203.30/34.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.23    (2)  op(all_52_7, all_52_7) = e0
% 203.30/34.23    (3)  all_58_1 = all_52_9
% 203.30/34.23    (4)   ~ (all_52_9 = all_52_13)
% 203.30/34.23    (5)  op(all_52_5, all_52_5) = e1
% 203.30/34.23    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.23    (7)  op(e0, e2) = all_52_15
% 203.30/34.23    (8)   ~ (all_52_7 = all_52_15)
% 203.30/34.23    (9)   ~ (all_52_3 = all_52_19)
% 203.30/34.23    (10)   ~ (all_52_3 = all_6_2)
% 203.30/34.23    (11)  all_58_0 = all_6_2
% 203.30/34.23    (12)  all_56_4 = all_52_3
% 203.30/34.23    (13)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.30/34.23    (14)   ~ (all_52_27 = all_52_29)
% 203.30/34.23    (15)  all_58_13 = all_52_15
% 203.30/34.23    (16)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.23    (17)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.30/34.23    (18)   ~ (all_52_29 = all_14_2)
% 203.30/34.23    (19)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.23    (20)  op(e2, e2) = all_4_2
% 203.30/34.23    (21)   ~ (all_52_3 = all_52_5)
% 203.30/34.23    (22)  all_58_11 = all_52_29
% 203.30/34.23    (23)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.30/34.23    (24)   ~ (all_52_3 = all_52_27)
% 203.30/34.23    (25)  op(all_10_2, e1) = all_10_1
% 203.30/34.23    (26)   ~ (all_52_7 = all_6_2)
% 203.30/34.23    (27)  op(e0, e0) = all_14_2
% 203.30/34.23    (28)  op(e0, e1) = all_52_23
% 203.30/34.23    (29)  all_56_15 = all_14_2
% 203.30/34.23    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.23    (31)   ~ (all_4_1 = e1)
% 203.30/34.23    (32)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.30/34.23    (33)  all_58_10 = all_52_27
% 203.30/34.23    (34)  all_56_8 = all_52_5
% 203.30/34.23    (35)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.23    (36)  all_58_7 = all_52_13
% 203.30/34.23    (37)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.23    (38)  all_36_2 = all_10_2
% 203.30/34.23    (39)  all_36_1 = all_10_1
% 203.30/34.23    (40)  op(all_6_2, all_6_2) = e3
% 203.30/34.23    (41)   ~ (all_52_5 = all_52_7)
% 203.30/34.23    (42)  all_58_12 = all_52_7
% 203.30/34.23    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.23    (44)   ~ (all_52_7 = all_14_2)
% 203.30/34.23    (45)   ~ (all_14_2 = e0)
% 203.30/34.23    (46)  all_58_2 = all_52_3
% 203.30/34.23    (47)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.30/34.23    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.23    (49)  op(e3, all_6_1) = all_6_0
% 203.30/34.23    (50)  all_56_7 = all_52_27
% 203.30/34.23    (51)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.23    (52)  op(all_4_2, e2) = all_4_1
% 203.30/34.23    (53)  op(all_52_3, all_52_3) = e2
% 203.30/34.23    (54)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.23    (55)  all_56_6 = all_52_19
% 203.30/34.23    (56)   ~ (all_52_15 = all_14_2)
% 203.30/34.23    (57)   ~ (all_52_19 = all_52_27)
% 203.30/34.23    (58)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.30/34.23    (59)   ~ (all_6_0 = e2)
% 203.30/34.23    (60)   ~ (all_52_19 = all_10_2)
% 203.30/34.23    (61)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.23    (62)  all_58_8 = all_10_2
% 203.30/34.23    (63)   ~ (all_52_5 = all_10_2)
% 203.30/34.23    (64)   ~ (all_52_23 = all_14_2)
% 203.30/34.23    (65)  all_56_12 = all_52_7
% 203.30/34.23    (66)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.30/34.23    (67)   ~ (all_52_9 = all_4_2)
% 203.30/34.23    (68)   ~ (all_52_5 = all_6_2)
% 203.30/34.23    (69)  op(e3, e3) = all_6_2
% 203.30/34.23    (70)  all_56_15 = e3
% 203.30/34.23    (71)   ~ (all_52_27 = all_14_2)
% 203.30/34.23    (72)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.23    (73)  all_56_14 = all_52_23
% 203.30/34.23    (74)   ~ (all_52_3 = all_52_7)
% 203.30/34.23    (75)  op(all_14_2, all_14_2) = all_52_30
% 203.30/34.23    (76)  all_58_5 = all_52_19
% 203.30/34.23    (77)   ~ (all_52_15 = all_4_2)
% 203.30/34.23    (78)   ~ (all_52_27 = all_4_2)
% 203.30/34.23    (79)  all_58_6 = all_52_5
% 203.30/34.23    (80)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.30/34.23    (81)   ~ (all_10_1 = e0) |  ~ (all_10_2 = e2)
% 203.30/34.23    (82)  op(e1, e1) = all_10_2
% 203.30/34.23    (83)   ~ (all_52_23 = all_10_2)
% 203.30/34.23    (84)   ~ (all_52_7 = all_52_23)
% 203.30/34.23    (85)  all_58_3 = all_4_2
% 203.30/34.23    (86)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.23    (87)  all_56_13 = all_52_15
% 203.30/34.23    (88)   ~ (all_52_3 = all_4_2)
% 203.30/34.23    (89)  op(all_6_2, e3) = all_6_1
% 203.30/34.23    (90)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.30/34.23  
% 203.30/34.23  Begin of proof
% 203.30/34.23  | 
% 203.30/34.23  | COMBINE_EQS: (29), (70) imply:
% 203.30/34.23  |   (91)  all_14_2 = e3
% 203.30/34.23  | 
% 203.30/34.23  | SIMP: (91) implies:
% 203.30/34.23  |   (92)  all_14_2 = e3
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (44), (92) imply:
% 203.30/34.23  |   (93)   ~ (all_52_7 = e3)
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (56), (92) imply:
% 203.30/34.23  |   (94)   ~ (all_52_15 = e3)
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (64), (92) imply:
% 203.30/34.23  |   (95)   ~ (all_52_23 = e3)
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (71), (92) imply:
% 203.30/34.23  |   (96)   ~ (all_52_27 = e3)
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (18), (92) imply:
% 203.30/34.23  |   (97)   ~ (all_52_29 = e3)
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (45), (92) imply:
% 203.30/34.23  |   (98)   ~ (e3 = e0)
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (75), (92) imply:
% 203.30/34.23  |   (99)  op(e3, e3) = all_52_30
% 203.30/34.23  | 
% 203.30/34.23  | REDUCE: (27), (92) imply:
% 203.30/34.23  |   (100)  op(e0, e0) = e3
% 203.30/34.23  | 
% 203.30/34.23  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.30/34.23  |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 203.30/34.23  |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 203.30/34.23  |            (37), (38), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 203.30/34.23  |            (49), (50), (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 203.30/34.23  |            (61), (62), (63), (65), (66), (67), (68), (69), (72), (73), (74),
% 203.30/34.23  |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 203.30/34.23  |            (87), (88), (89), (90), (93), (94), (95), (96), (97), (98), (99),
% 203.30/34.23  |            (100) are inconsistent by sub-proof #512.
% 203.30/34.23  | 
% 203.30/34.23  End of proof
% 203.30/34.23  
% 203.30/34.23  Sub-proof #512 shows that the following formulas are inconsistent:
% 203.30/34.23  ----------------------------------------------------------------
% 203.30/34.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.23    (2)  op(all_52_7, all_52_7) = e0
% 203.30/34.23    (3)  all_58_1 = all_52_9
% 203.30/34.23    (4)   ~ (all_52_9 = all_52_13)
% 203.30/34.23    (5)  op(all_52_5, all_52_5) = e1
% 203.30/34.23    (6)   ~ (e3 = e0)
% 203.30/34.23    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.23    (8)  op(e0, e2) = all_52_15
% 203.30/34.23    (9)   ~ (all_52_7 = all_52_15)
% 203.30/34.23    (10)   ~ (all_52_3 = all_52_19)
% 203.30/34.23    (11)   ~ (all_52_3 = all_6_2)
% 203.30/34.23    (12)  all_58_0 = all_6_2
% 203.30/34.23    (13)  all_56_4 = all_52_3
% 203.30/34.23    (14)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.30/34.23    (15)   ~ (all_52_27 = all_52_29)
% 203.30/34.23    (16)  all_58_13 = all_52_15
% 203.30/34.23    (17)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.23    (18)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.30/34.23    (19)   ~ (all_52_15 = e3)
% 203.30/34.23    (20)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.23    (21)  op(e2, e2) = all_4_2
% 203.30/34.23    (22)   ~ (all_52_3 = all_52_5)
% 203.30/34.23    (23)  all_58_11 = all_52_29
% 203.30/34.23    (24)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.30/34.23    (25)   ~ (all_52_3 = all_52_27)
% 203.30/34.23    (26)  op(all_10_2, e1) = all_10_1
% 203.30/34.23    (27)   ~ (all_52_7 = all_6_2)
% 203.30/34.23    (28)  op(e0, e0) = all_14_2
% 203.30/34.23    (29)  op(e0, e1) = all_52_23
% 203.30/34.23    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.23    (31)   ~ (all_4_1 = e1)
% 203.30/34.23    (32)  op(e0, e0) = e3
% 203.30/34.23    (33)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.30/34.23    (34)  all_58_10 = all_52_27
% 203.30/34.23    (35)  all_56_8 = all_52_5
% 203.30/34.23    (36)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.23    (37)  all_58_7 = all_52_13
% 203.30/34.23    (38)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.23    (39)  all_36_2 = all_10_2
% 203.30/34.23    (40)  all_36_1 = all_10_1
% 203.30/34.23    (41)  op(all_6_2, all_6_2) = e3
% 203.30/34.23    (42)   ~ (all_52_5 = all_52_7)
% 203.30/34.23    (43)  all_58_12 = all_52_7
% 203.30/34.23    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.23    (45)   ~ (all_52_7 = e3)
% 203.30/34.23    (46)   ~ (all_52_7 = all_14_2)
% 203.30/34.23    (47)  all_58_2 = all_52_3
% 203.30/34.23    (48)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.30/34.23    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.23    (50)   ~ (all_52_29 = e3)
% 203.30/34.23    (51)  op(e3, all_6_1) = all_6_0
% 203.30/34.23    (52)  all_56_7 = all_52_27
% 203.30/34.23    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.23    (54)  op(all_4_2, e2) = all_4_1
% 203.30/34.23    (55)   ~ (all_52_23 = e3)
% 203.30/34.23    (56)  op(all_52_3, all_52_3) = e2
% 203.30/34.23    (57)  op(e3, e3) = all_52_30
% 203.30/34.23    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.23    (59)  all_56_6 = all_52_19
% 203.30/34.23    (60)   ~ (all_52_19 = all_52_27)
% 203.30/34.23    (61)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.30/34.23    (62)   ~ (all_52_27 = e3)
% 203.30/34.23    (63)   ~ (all_6_0 = e2)
% 203.30/34.23    (64)   ~ (all_52_19 = all_10_2)
% 203.30/34.23    (65)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.23    (66)  all_58_8 = all_10_2
% 203.30/34.23    (67)   ~ (all_52_5 = all_10_2)
% 203.30/34.23    (68)  all_56_12 = all_52_7
% 203.30/34.23    (69)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.30/34.23    (70)   ~ (all_52_9 = all_4_2)
% 203.30/34.23    (71)   ~ (all_52_5 = all_6_2)
% 203.30/34.23    (72)  op(e3, e3) = all_6_2
% 203.30/34.23    (73)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.23    (74)  all_56_14 = all_52_23
% 203.30/34.23    (75)   ~ (all_52_3 = all_52_7)
% 203.30/34.23    (76)  all_58_5 = all_52_19
% 203.30/34.23    (77)   ~ (all_52_15 = all_4_2)
% 203.30/34.23    (78)   ~ (all_52_27 = all_4_2)
% 203.30/34.23    (79)  all_58_6 = all_52_5
% 203.30/34.23    (80)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.30/34.23    (81)   ~ (all_10_1 = e0) |  ~ (all_10_2 = e2)
% 203.30/34.23    (82)  op(e1, e1) = all_10_2
% 203.30/34.23    (83)   ~ (all_52_23 = all_10_2)
% 203.30/34.23    (84)   ~ (all_52_7 = all_52_23)
% 203.30/34.23    (85)  all_58_3 = all_4_2
% 203.30/34.24    (86)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.24    (87)  all_56_13 = all_52_15
% 203.30/34.24    (88)   ~ (all_52_3 = all_4_2)
% 203.30/34.24    (89)  op(all_6_2, e3) = all_6_1
% 203.30/34.24    (90)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.30/34.24  
% 203.30/34.24  Begin of proof
% 203.30/34.24  | 
% 203.30/34.24  | GROUND_INST: instantiating (1) with all_6_2, all_52_30, e3, e3, simplifying
% 203.30/34.24  |              with (57), (72) gives:
% 203.30/34.24  |   (91)  all_52_30 = all_6_2
% 203.30/34.24  | 
% 203.30/34.24  | BETA: splitting (33) gives:
% 203.30/34.24  | 
% 203.30/34.24  | Case 1:
% 203.30/34.24  | | 
% 203.30/34.24  | |   (92)  all_56_13 = e3
% 203.30/34.24  | | 
% 203.30/34.24  | | REF_CLOSE: (19), (87), (92) are inconsistent by sub-proof #1201.
% 203.30/34.24  | | 
% 203.30/34.24  | Case 2:
% 203.30/34.24  | | 
% 203.30/34.24  | |   (93)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.30/34.24  | | 
% 203.30/34.24  | | BETA: splitting (38) gives:
% 203.30/34.24  | | 
% 203.30/34.24  | | Case 1:
% 203.30/34.24  | | | 
% 203.30/34.24  | | |   (94)  all_56_14 = e3
% 203.30/34.24  | | | 
% 203.30/34.24  | | | REF_CLOSE: (55), (74), (94) are inconsistent by sub-proof #1286.
% 203.30/34.24  | | | 
% 203.30/34.24  | | Case 2:
% 203.30/34.24  | | | 
% 203.30/34.24  | | |   (95)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.24  | | | 
% 203.30/34.24  | | | BETA: splitting (14) gives:
% 203.30/34.24  | | | 
% 203.30/34.24  | | | Case 1:
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | |   (96)  all_56_7 = e3
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | | REF_CLOSE: (52), (62), (96) are inconsistent by sub-proof #609.
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | Case 2:
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | |   (97)   ~ (all_56_7 = e3)
% 203.30/34.24  | | | |   (98)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | | BETA: splitting (7) gives:
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | | Case 1:
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | |   (99)  all_56_12 = e3
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | | REF_CLOSE: (45), (68), (99) are inconsistent by sub-proof #1383.
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | Case 2:
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | |   (100)   ~ (all_56_12 = e3)
% 203.30/34.24  | | | | |   (101)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | | BETA: splitting (73) gives:
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | | Case 1:
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | |   (102)  all_58_0 = e3
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | COMBINE_EQS: (12), (102) imply:
% 203.30/34.24  | | | | | |   (103)  all_6_2 = e3
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (11), (103) imply:
% 203.30/34.24  | | | | | |   (104)   ~ (all_52_3 = e3)
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (71), (103) imply:
% 203.30/34.24  | | | | | |   (105)   ~ (all_52_5 = e3)
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (89), (103) imply:
% 203.30/34.24  | | | | | |   (106)  op(e3, e3) = all_6_1
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (72), (103) imply:
% 203.30/34.24  | | | | | |   (107)  op(e3, e3) = e3
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | GROUND_INST: instantiating (1) with e3, all_6_1, e3, e3, simplifying
% 203.30/34.24  | | | | | |              with (106), (107) gives:
% 203.30/34.24  | | | | | |   (108)  all_6_1 = e3
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (51), (108) imply:
% 203.30/34.24  | | | | | |   (109)  op(e3, e3) = all_6_0
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | GROUND_INST: instantiating (1) with e3, all_6_0, e3, e3, simplifying
% 203.30/34.24  | | | | | |              with (107), (109) gives:
% 203.30/34.24  | | | | | |   (110)  all_6_0 = e3
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (63), (110) imply:
% 203.30/34.24  | | | | | |   (111)   ~ (e3 = e2)
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | BETA: splitting (30) gives:
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | Case 1:
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | |   (112)  all_58_2 = e3
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | | REF_CLOSE: (47), (104), (112) are inconsistent by sub-proof #1369.
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | Case 2:
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | |   (113)   ~ (all_58_2 = e3)
% 203.30/34.24  | | | | | | |   (114)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | | BETA: splitting (44) gives:
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | |   (115)  all_58_6 = e3
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | | REF_CLOSE: (79), (105), (115) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | |            #1328.
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | |   (116)   ~ (all_58_6 = e3)
% 203.30/34.24  | | | | | | | |   (117)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | | BETA: splitting (53) gives:
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | |   (118)  all_56_4 = e3
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | REF_CLOSE: (13), (104), (118) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | |            #1340.
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | |   (119)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | BETA: splitting (65) gives:
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | |   (120)  all_56_8 = e3
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | REF_CLOSE: (35), (105), (120) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | |            #1325.
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | |   (121)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | BETA: splitting (58) gives:
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | |   (122)  all_58_12 = e1
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | REF_CLOSE: (1), (2), (26), (29), (39), (40), (43), (74),
% 203.30/34.24  | | | | | | | | | | |            (80), (82), (83), (84), (95), (122) are
% 203.30/34.24  | | | | | | | | | | |            inconsistent by sub-proof #543.
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | |   (123)   ~ (all_58_12 = e1)
% 203.30/34.24  | | | | | | | | | | |   (124)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | REDUCE: (43), (123) imply:
% 203.30/34.24  | | | | | | | | | | |   (125)   ~ (all_52_7 = e1)
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | BETA: splitting (48) gives:
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | |   (126)  all_56_6 = e3
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | COMBINE_EQS: (59), (126) imply:
% 203.30/34.24  | | | | | | | | | | | |   (127)  all_52_19 = e3
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | SIMP: (127) implies:
% 203.30/34.24  | | | | | | | | | | | |   (128)  all_52_19 = e3
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | COMBINE_EQS: (76), (128) imply:
% 203.30/34.24  | | | | | | | | | | | |   (129)  all_58_5 = e3
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | REDUCE: (60), (128) imply:
% 203.30/34.24  | | | | | | | | | | | |   (130)   ~ (all_52_27 = e3)
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | REDUCE: (64), (128) imply:
% 203.30/34.24  | | | | | | | | | | | |   (131)   ~ (all_10_2 = e3)
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | SIMP: (131) implies:
% 203.30/34.24  | | | | | | | | | | | |   (132)   ~ (all_10_2 = e3)
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | BETA: splitting (117) gives:
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | |   (133)  all_58_7 = e3
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | COMBINE_EQS: (37), (133) imply:
% 203.30/34.24  | | | | | | | | | | | | |   (134)  all_52_13 = e3
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | REDUCE: (4), (134) imply:
% 203.30/34.24  | | | | | | | | | | | | |   (135)   ~ (all_52_9 = e3)
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | BETA: splitting (18) gives:
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | |   (136)  all_58_6 = e2
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | COMBINE_EQS: (79), (136) imply:
% 203.30/34.24  | | | | | | | | | | | | | |   (137)  all_52_5 = e2
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | SIMP: (137) implies:
% 203.30/34.24  | | | | | | | | | | | | | |   (138)  all_52_5 = e2
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | REDUCE: (42), (138) imply:
% 203.30/34.24  | | | | | | | | | | | | | |   (139)   ~ (all_52_7 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | SIMP: (139) implies:
% 203.30/34.24  | | | | | | | | | | | | | |   (140)   ~ (all_52_7 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (28), (46), (68), (101), (125), (140)
% 203.30/34.24  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1176.
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | |   (141)   ~ (all_58_6 = e2)
% 203.30/34.24  | | | | | | | | | | | | | |   (142)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | REDUCE: (79), (141) imply:
% 203.30/34.24  | | | | | | | | | | | | | |   (143)   ~ (all_52_5 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | |   (144)  all_58_0 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | COMBINE_EQS: (102), (144) imply:
% 203.30/34.24  | | | | | | | | | | | | | | |   (145)  e3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | REDUCE: (111), (145) imply:
% 203.30/34.24  | | | | | | | | | | | | | | |   (146)  $false
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | |   (147)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | |   (148)  all_58_1 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (148) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | |   (149)  all_52_9 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | REDUCE: (70), (149) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | |   (150)   ~ (all_4_2 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | SIMP: (150) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | |   (151)   ~ (all_4_2 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | REDUCE: (135), (149) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | |   (152)   ~ (e3 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | REDUCE: (36), (149) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | |   (153)  op(e2, e2) = all_52_8
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_8, e2, e2,
% 203.30/34.24  | | | | | | | | | | | | | | | |              simplifying with (21), (153) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | |   (154)  all_52_8 = all_4_2
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (155)  all_58_2 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (155) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (156)  all_52_3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | SIMP: (156) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (157)  all_52_3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (21), (56), (88), (157) are inconsistent by
% 203.30/34.24  | | | | | | | | | | | | | | | | |            sub-proof #1157.
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (158)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | |   (159)  all_58_3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (159) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | |   (160)  all_4_2 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | REDUCE: (151), (160) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | |   (161)  $false
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | |   (162)  all_58_5 = e2 | all_58_10 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (163)  all_58_5 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (129), (163) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |            #625.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (164)  all_58_10 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (164) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (165)  all_52_27 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | SIMP: (165) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (166)  all_52_27 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REDUCE: (25), (166) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (167)   ~ (all_52_3 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REDUCE: (15), (166) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (168)   ~ (all_52_29 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | SIMP: (168) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (169)   ~ (all_52_29 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REDUCE: (20), (166) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (170)  op(e2, e2) = all_52_26
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (171)  all_58_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (171) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (172)  e3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (172) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (173)  $false
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (174)  all_58_8 = e2 | all_58_11 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (175)  all_58_8 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (175) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (176)  all_10_2 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (177)  all_10_2 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (177) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (178)  op(e2, e2) = all_52_20
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (179)  all_58_12 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (179) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (180)  all_52_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | SIMP: (180) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (181)  all_52_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (181) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (182)   ~ (all_52_15 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_52_15 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (181) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (184)  op(e2, e2) = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (185)   ~ (all_10_2 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (185) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (186)  $false
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (186) is inconsistent.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_26, e2, e2,
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (21), (170) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_52_26 = all_4_2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_52_26, all_52_20, e2,
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (170), (178) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_52_20 = all_52_26
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with e0, all_52_20, e2, e2,
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (178), (184) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_52_20 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (189) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_52_26 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_52_26 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (191) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_4_2 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (192) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (193)   ~ (all_52_15 = e0)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (16), (21), (31), (54), (87), (93),
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |            (124), (183), (184), (193) are inconsistent by
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1352.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (194)   ~ (all_58_12 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (194) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (195)   ~ (all_52_7 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (13), (21), (43), (47), (68), (75),
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |            (79), (88), (101), (119), (125), (147), (167),
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |            (195) are inconsistent by sub-proof #1148.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (196)  all_58_11 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (169), (196) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |            #1189.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | |   (197)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (198)  all_58_6 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (198) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (199)  all_52_5 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | SIMP: (199) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (200)  all_52_5 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (67), (82), (200) are inconsistent by
% 203.30/34.24  | | | | | | | | | | | | | | | | |            sub-proof #871.
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (201)   ~ (all_58_6 = e1)
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | REDUCE: (79), (201) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | |   (202)   ~ (all_52_5 = e1)
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | |   (203)  all_56_8 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (143), (203) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | |            #1022.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | |   (204)  all_56_8 = e1 | all_56_8 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (205)  all_56_8 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (202), (205) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |            #707.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (206)  all_56_8 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (206) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (207)  all_52_5 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (208)  all_52_5 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REDUCE: (22), (208) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (209)   ~ (all_52_3 = e0)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REDUCE: (42), (208) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (210)   ~ (all_52_7 = e0)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (211)   ~ (all_52_7 = e0)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | REDUCE: (5), (208) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | |   (212)  op(e0, e0) = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (213)  all_56_12 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (213) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (214)  all_52_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (215)  all_52_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (215) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (216)   ~ (all_52_3 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (215) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_52_15 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | SIMP: (217) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (218)   ~ (all_52_15 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (215) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (219)   ~ (e3 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (220)  all_56_4 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (216), (220) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |            #1155.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | |   (221)  all_56_4 = e1 | all_56_4 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (222)  all_58_3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (222) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (223)  all_4_2 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (223) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (224)   ~ (all_52_27 = e2)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_56_4 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (225) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_52_3 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_52_3 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (227) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (228)   ~ (all_52_27 = e1)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (229)   ~ (all_52_27 = e1)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (227) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (230)   ~ (e3 = e1)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (231)   ~ (e3 = e1)
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_56_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (224), (232) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_56_7 = e1 | all_56_7 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_56_7 = e1
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (229), (234) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | |            #903.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_56_7 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (235) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_52_27 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (20), (32), (212), (231), (236) are
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_56_4 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (209), (237) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |            #1309.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | |   (238)  all_58_7 = e2 | all_58_13 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_58_7 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (239) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (240)  e3 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (240) imply:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (241)  $false
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_58_13 = e2
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (218), (242) are inconsistent by sub-proof
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | |            #784.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |   (243)  all_56_12 = e1 | all_56_12 = e0
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (125), (211), (243) are inconsistent by
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | |            sub-proof #1374.
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | |   (244)  all_58_8 = e3 | all_58_11 = e3
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | | REF_CLOSE: (23), (50), (66), (132), (244) are inconsistent by
% 203.30/34.24  | | | | | | | | | | | | |            sub-proof #1140.
% 203.30/34.24  | | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | Case 2:
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | |   (245)   ~ (all_56_6 = e3)
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | REDUCE: (59), (245) imply:
% 203.30/34.24  | | | | | | | | | | | |   (246)   ~ (all_52_19 = e3)
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | | REF_CLOSE: (1), (2), (6), (21), (24), (28), (34), (43), (46),
% 203.30/34.24  | | | | | | | | | | | |            (62), (68), (76), (85), (101), (114), (125), (246)
% 203.30/34.24  | | | | | | | | | | | |            are inconsistent by sub-proof #692.
% 203.30/34.24  | | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | | 
% 203.30/34.24  | | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | | 
% 203.30/34.24  | | | | | | | | End of split
% 203.30/34.24  | | | | | | | | 
% 203.30/34.24  | | | | | | | End of split
% 203.30/34.24  | | | | | | | 
% 203.30/34.24  | | | | | | End of split
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | Case 2:
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | |   (247)   ~ (all_58_0 = e3)
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REDUCE: (12), (247) imply:
% 203.30/34.24  | | | | | |   (248)   ~ (all_6_2 = e3)
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | | REF_CLOSE: (1), (5), (12), (21), (30), (41), (43), (45), (47), (49),
% 203.30/34.24  | | | | | |            (56), (67), (72), (79), (82), (88), (248) are
% 203.30/34.24  | | | | | |            inconsistent by sub-proof #1363.
% 203.30/34.24  | | | | | | 
% 203.30/34.24  | | | | | End of split
% 203.30/34.24  | | | | | 
% 203.30/34.24  | | | | End of split
% 203.30/34.24  | | | | 
% 203.30/34.24  | | | End of split
% 203.30/34.24  | | | 
% 203.30/34.24  | | End of split
% 203.30/34.24  | | 
% 203.30/34.24  | End of split
% 203.30/34.24  | 
% 203.30/34.24  End of proof
% 203.30/34.24  
% 203.30/34.24  Sub-proof #513 shows that the following formulas are inconsistent:
% 203.30/34.24  ----------------------------------------------------------------
% 203.30/34.24    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.30/34.24    (2)   ~ (all_52_15 = all_52_23)
% 203.30/34.24    (3)   ~ (all_52_25 = all_52_27)
% 203.30/34.24    (4)  all_58_14 = all_52_23
% 203.30/34.24    (5)   ~ (e3 = e1)
% 203.30/34.24    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.30/34.24    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.24    (8)  all_58_1 = all_52_9
% 203.30/34.24    (9)   ~ (all_52_9 = all_52_13)
% 203.30/34.24    (10)   ~ (e3 = e0)
% 203.30/34.24    (11)  op(e2, e3) = all_52_3
% 203.30/34.24    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.24    (13)   ~ (all_52_3 = all_52_19)
% 203.30/34.24    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.30/34.24    (15)   ~ (all_52_17 = all_52_25)
% 203.30/34.24    (16)   ~ (all_4_2 = e3)
% 203.30/34.24    (17)   ~ (all_52_3 = all_6_2)
% 203.30/34.24    (18)  all_58_0 = all_6_2
% 203.30/34.24    (19)  op(all_14_2, e0) = all_14_1
% 203.30/34.24    (20)  all_56_4 = all_52_3
% 203.30/34.24    (21)   ~ (all_52_17 = all_10_2)
% 203.30/34.24    (22)  op(e3, e0) = all_52_25
% 203.30/34.24    (23)  op(all_52_5, all_52_5) = all_52_4
% 203.30/34.24    (24)  op(all_52_19, all_52_19) = all_52_18
% 203.30/34.24    (25)   ~ (all_52_27 = all_52_29)
% 203.30/34.24    (26)  all_58_13 = all_52_15
% 203.30/34.24    (27)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.24    (28)  all_58_9 = all_52_25
% 203.30/34.24    (29)   ~ (all_52_29 = all_14_2)
% 203.30/34.24    (30)   ~ (all_52_15 = e3)
% 203.30/34.24    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.30/34.24    (32)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.24    (33)  op(e1, e3) = all_52_5
% 203.30/34.24    (34)  op(e2, e2) = all_4_2
% 203.30/34.24    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.30/34.24    (36)   ~ (all_52_3 = all_52_5)
% 203.30/34.24    (37)  all_58_11 = all_52_29
% 203.30/34.24    (38)  all_56_5 = all_4_2
% 203.30/34.24    (39)   ~ (all_52_25 = all_14_2)
% 203.30/34.24    (40)   ~ (all_52_3 = all_52_27)
% 203.30/34.24    (41)  op(all_10_2, e1) = all_10_1
% 203.30/34.24    (42)  all_58_1 = e3
% 203.30/34.24    (43)  op(all_6_2, all_6_2) = all_52_0
% 203.30/34.24    (44)   ~ (all_52_7 = all_6_2)
% 203.30/34.24    (45)  op(e0, e0) = all_14_2
% 203.30/34.24    (46)  all_56_15 = all_14_2
% 203.30/34.24    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.24    (48)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.30/34.24    (49)  op(e1, e0) = all_52_29
% 203.30/34.24    (50)  all_56_11 = all_52_29
% 203.30/34.24    (51)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.30/34.24    (52)  op(e1, all_10_1) = e3
% 203.30/34.24    (53)   ~ (all_6_2 = e3)
% 203.30/34.24    (54)   ~ (e2 = e1)
% 203.30/34.24    (55)   ~ (all_52_13 = all_10_2)
% 203.30/34.24    (56)  all_58_10 = all_52_27
% 203.30/34.24    (57)  all_56_8 = all_52_5
% 203.30/34.24    (58)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.24    (59)   ~ (all_52_19 = all_52_23)
% 203.30/34.24    (60)   ~ (all_52_25 = all_52_29)
% 203.30/34.24    (61)  op(all_6_2, e3) = e2
% 203.30/34.24    (62)   ~ (all_52_29 = all_10_2)
% 203.30/34.24    (63)  all_58_7 = all_52_13
% 203.30/34.24    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.30/34.24    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.30/34.24    (66)   ~ (all_52_5 = all_52_7)
% 203.30/34.24    (67)  all_58_12 = all_52_7
% 203.30/34.24    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.30/34.24    (69)   ~ (all_52_7 = all_14_2)
% 203.30/34.24    (70)   ~ (all_14_2 = e0)
% 203.30/34.24    (71)  all_58_2 = all_52_3
% 203.30/34.24    (72)  all_56_2 = all_52_17
% 203.30/34.24    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.30/34.24    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.24    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.30/34.24    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.30/34.24    (77)   ~ (all_52_25 = e3)
% 203.30/34.24    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.30/34.24    (79)   ~ (e2 = e0)
% 203.30/34.24    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.30/34.24    (81)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.30/34.24    (82)   ~ (all_52_5 = all_52_29)
% 203.30/34.24    (83)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.24    (84)   ~ (all_52_15 = all_14_2)
% 203.30/34.24    (85)   ~ (all_52_19 = all_52_27)
% 203.30/34.24    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.30/34.24    (87)  op(e3, e3) = all_52_8
% 203.30/34.24    (88)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.30/34.24    (89)  op(e3, e1) = all_52_17
% 203.30/34.24    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.30/34.24    (91)  op(e0, e3) = all_52_7
% 203.30/34.24    (92)  op(e1, e2) = all_52_13
% 203.30/34.24    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.30/34.24    (94)   ~ (all_52_9 = all_52_25)
% 203.30/34.24    (95)  all_58_15 = all_14_2
% 203.30/34.24    (96)   ~ (all_52_19 = all_10_2)
% 203.30/34.24    (97)  op(all_52_23, all_52_23) = all_52_22
% 203.30/34.24    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.30/34.24    (99)  all_58_8 = all_10_2
% 203.30/34.24    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.30/34.24    (101)   ~ (all_52_5 = all_10_2)
% 203.30/34.24    (102)  op(all_52_29, all_52_29) = all_52_28
% 203.30/34.24    (103)   ~ (all_52_23 = all_14_2)
% 203.30/34.24    (104)  all_56_12 = all_52_7
% 203.30/34.24    (105)  op(all_52_17, all_52_17) = all_52_16
% 203.30/34.24    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.30/34.24    (107)   ~ (all_52_25 = all_6_2)
% 203.30/34.24    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.30/34.24    (109)   ~ (all_52_9 = all_4_2)
% 203.30/34.24    (110)   ~ (all_52_5 = all_6_2)
% 203.30/34.24    (111)  op(e3, e3) = all_6_2
% 203.30/34.24    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.30/34.24    (113)   ~ (all_52_13 = e3)
% 203.30/34.24    (114)   ~ (all_52_27 = all_14_2)
% 203.30/34.24    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.30/34.24    (116)  all_56_14 = all_52_23
% 203.30/34.24    (117)   ~ (all_52_17 = e3)
% 203.30/34.24    (118)  all_56_3 = all_52_25
% 203.30/34.24    (119)   ~ (all_52_3 = all_52_7)
% 203.30/34.24    (120)  op(all_14_2, all_14_2) = all_52_30
% 203.30/34.25    (121)  all_58_5 = all_52_19
% 203.30/34.25    (122)   ~ (all_52_15 = all_4_2)
% 203.30/34.25    (123)   ~ (all_52_27 = all_4_2)
% 203.30/34.25    (124)  all_58_6 = all_52_5
% 203.30/34.25    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.30/34.25    (126)   ~ (all_52_17 = all_6_2)
% 203.30/34.25    (127)   ~ (e1 = e0)
% 203.30/34.25    (128)   ~ (e3 = e2)
% 203.30/34.25    (129)  all_56_10 = all_10_2
% 203.30/34.25    (130)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.30/34.25    (131)  op(all_52_13, all_52_13) = all_52_12
% 203.30/34.25    (132)  op(e1, e1) = all_10_2
% 203.30/34.25    (133)   ~ (all_52_23 = all_10_2)
% 203.30/34.25    (134)   ~ (all_52_7 = all_52_23)
% 203.30/34.25    (135)   ~ (all_52_17 = all_52_19)
% 203.30/34.25    (136)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.30/34.25           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.30/34.25    (137)  all_58_3 = all_4_2
% 203.30/34.25    (138)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.30/34.25    (139)   ~ (all_52_3 = all_4_2)
% 203.30/34.25    (140)   ~ (all_52_19 = all_4_2)
% 203.30/34.25    (141)   ~ (all_52_17 = all_52_23)
% 203.30/34.25    (142)  op(all_6_2, e3) = all_6_1
% 203.30/34.25    (143)  all_58_4 = all_52_17
% 203.30/34.25    (144)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.30/34.25    (145)  op(all_52_25, all_52_25) = all_52_24
% 203.30/34.25  
% 203.30/34.25  Begin of proof
% 203.30/34.25  | 
% 203.30/34.25  | BETA: splitting (136) gives:
% 203.30/34.25  | 
% 203.30/34.25  | Case 1:
% 203.30/34.25  | | 
% 203.30/34.25  | |   (146)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 203.30/34.25  | | 
% 203.30/34.25  | | ALPHA: (146) implies:
% 203.30/34.25  | |   (147)  all_52_22 = e0
% 203.30/34.25  | |   (148)  all_52_20 = e1
% 203.30/34.25  | |   (149)  all_52_18 = e2
% 203.30/34.25  | |   (150)  all_52_16 = e3
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (105), (150) imply:
% 203.30/34.25  | |   (151)  op(all_52_17, all_52_17) = e3
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (24), (149) imply:
% 203.30/34.25  | |   (152)  op(all_52_19, all_52_19) = e2
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (97), (147) imply:
% 203.30/34.25  | |   (153)  op(all_52_23, all_52_23) = e0
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (27), (148) imply:
% 203.30/34.25  | |   (154)  op(all_10_2, all_10_2) = e1
% 203.30/34.25  | | 
% 203.30/34.25  | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (13), (15), (16), (17), (18),
% 203.30/34.25  | |            (23), (26), (28), (29), (30), (31), (32), (33), (34), (37), (39),
% 203.30/34.25  | |            (41), (42), (44), (45), (46), (47), (49), (50), (51), (52), (53),
% 203.30/34.25  | |            (54), (55), (56), (59), (61), (62), (63), (67), (68), (69), (70),
% 203.30/34.25  | |            (71), (72), (73), (74), (75), (77), (79), (81), (83), (84), (86),
% 203.30/34.25  | |            (87), (88), (89), (91), (93), (95), (96), (99), (100), (101),
% 203.30/34.25  | |            (103), (107), (108), (110), (111), (113), (114), (117), (118),
% 203.30/34.25  | |            (119), (120), (121), (123), (124), (125), (126), (127), (129),
% 203.30/34.25  | |            (130), (132), (133), (134), (135), (137), (139), (141), (143),
% 203.30/34.25  | |            (144), (151), (152), (153), (154) are inconsistent by sub-proof
% 203.30/34.25  | |            #533.
% 203.30/34.25  | | 
% 203.30/34.25  | Case 2:
% 203.30/34.25  | | 
% 203.30/34.25  | |   (155)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 203.30/34.25  | | 
% 203.30/34.25  | | ALPHA: (155) implies:
% 203.30/34.25  | |   (156)  all_52_30 = e0
% 203.30/34.25  | |   (157)  all_52_28 = e1
% 203.30/34.25  | |   (158)  all_52_26 = e2
% 203.30/34.25  | |   (159)  all_52_24 = e3
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (145), (159) imply:
% 203.30/34.25  | |   (160)  op(all_52_25, all_52_25) = e3
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (32), (158) imply:
% 203.30/34.25  | |   (161)  op(all_52_27, all_52_27) = e2
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (102), (157) imply:
% 203.30/34.25  | |   (162)  op(all_52_29, all_52_29) = e1
% 203.30/34.25  | | 
% 203.30/34.25  | | REDUCE: (120), (156) imply:
% 203.30/34.25  | |   (163)  op(all_14_2, all_14_2) = e0
% 203.30/34.25  | | 
% 203.30/34.25  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.30/34.25  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.30/34.25  | |            (24), (25), (26), (28), (29), (30), (33), (34), (35), (36), (37),
% 203.30/34.25  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 203.30/34.25  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (60), (61),
% 203.30/34.25  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 203.30/34.25  | |            (73), (74), (75), (76), (77), (78), (79), (80), (82), (84), (85),
% 203.30/34.25  | |            (86), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 203.30/34.25  | |            (98), (99), (100), (101), (103), (104), (106), (107), (108),
% 203.30/34.25  | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 203.30/34.25  | |            (118), (119), (121), (122), (123), (124), (125), (126), (127),
% 203.30/34.25  | |            (128), (131), (132), (133), (134), (137), (138), (139), (140),
% 203.30/34.25  | |            (141), (142), (143), (160), (161), (162), (163) are inconsistent
% 203.30/34.25  | |            by sub-proof #531.
% 203.30/34.25  | | 
% 203.30/34.25  | End of split
% 203.30/34.25  | 
% 203.30/34.25  End of proof
% 203.30/34.25  
% 203.30/34.25  Sub-proof #514 shows that the following formulas are inconsistent:
% 203.30/34.25  ----------------------------------------------------------------
% 203.30/34.25    (1)  all_58_14 = all_52_23
% 203.30/34.25    (2)   ~ (e3 = e1)
% 203.30/34.25    (3)  op(all_52_3, all_52_3) = all_52_2
% 203.30/34.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.25    (5)   ~ (e3 = e0)
% 203.30/34.25    (6)  op(e2, e3) = all_52_3
% 203.30/34.25    (7)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.30/34.25    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.25    (9)  op(e0, e2) = all_52_15
% 203.30/34.25    (10)   ~ (all_52_7 = all_52_15)
% 203.30/34.25    (11)  op(all_52_7, all_52_7) = all_52_6
% 203.30/34.25    (12)  all_58_0 = all_6_2
% 203.30/34.25    (13)  op(all_52_5, all_52_5) = all_52_4
% 203.30/34.25    (14)  all_58_13 = all_52_15
% 203.30/34.25    (15)  op(e2, all_4_1) = e3
% 203.30/34.25    (16)  op(e1, e3) = all_52_5
% 203.30/34.25    (17)  op(e2, e2) = all_4_2
% 203.30/34.25    (18)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.30/34.25    (19)  op(all_10_2, e1) = all_10_1
% 203.30/34.25    (20)  op(all_6_2, all_6_2) = all_52_0
% 203.30/34.25    (21)   ~ (all_52_7 = all_6_2)
% 203.30/34.25    (22)  op(e0, e0) = all_14_2
% 203.30/34.25    (23)  op(e0, e1) = all_52_23
% 203.30/34.25    (24)   ~ (all_52_15 = e0)
% 203.30/34.25    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.25    (26)  all_58_15 = e0
% 203.30/34.25    (27)   ~ (all_4_1 = e1)
% 203.30/34.25    (28)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.30/34.25    (29)  op(e1, all_10_1) = e3
% 203.30/34.25    (30)   ~ (e2 = e1)
% 203.30/34.25    (31)  op(all_52_15, all_52_15) = all_52_14
% 203.30/34.25    (32)  all_36_2 = all_10_2
% 203.30/34.25    (33)  all_36_1 = all_10_1
% 203.30/34.25    (34)  all_58_12 = all_52_7
% 203.30/34.25    (35)   ~ (all_52_7 = all_14_2)
% 203.30/34.25    (36)  all_58_2 = all_52_3
% 203.30/34.25    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.30/34.25    (38)   ~ (e2 = e0)
% 203.30/34.25    (39)  op(all_4_2, e2) = all_4_1
% 203.30/34.25    (40)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.30/34.25    (41)  op(all_52_23, all_52_23) = all_52_22
% 203.30/34.25    (42)   ~ (all_52_5 = all_10_2)
% 203.30/34.25    (43)  all_56_12 = all_52_7
% 203.30/34.25    (44)  op(e3, e3) = all_6_2
% 203.30/34.25    (45)  all_58_6 = all_52_5
% 203.30/34.25    (46)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.30/34.25    (47)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.30/34.25    (48)   ~ (e1 = e0)
% 203.30/34.25    (49)   ~ (e3 = e2)
% 203.30/34.25    (50)  op(e1, e1) = all_10_2
% 203.30/34.25    (51)   ~ (all_52_7 = all_52_23)
% 203.30/34.25    (52)  all_56_13 = all_52_15
% 203.30/34.25    (53)   ~ (all_52_3 = all_4_2)
% 203.30/34.25    (54)   ~ (all_52_7 = e0)
% 203.30/34.25  
% 203.30/34.25  Begin of proof
% 203.30/34.25  | 
% 203.30/34.25  | ALPHA: (7) implies:
% 203.30/34.25  |   (55)  all_52_6 = e0
% 203.30/34.25  |   (56)  all_52_4 = e1
% 203.30/34.25  |   (57)  all_52_2 = e2
% 203.30/34.25  |   (58)  all_52_0 = e3
% 203.30/34.25  | 
% 203.30/34.25  | REDUCE: (3), (57) imply:
% 203.30/34.25  |   (59)  op(all_52_3, all_52_3) = e2
% 203.30/34.25  | 
% 203.30/34.25  | REDUCE: (13), (56) imply:
% 203.30/34.25  |   (60)  op(all_52_5, all_52_5) = e1
% 203.30/34.25  | 
% 203.30/34.25  | REDUCE: (11), (55) imply:
% 203.30/34.25  |   (61)  op(all_52_7, all_52_7) = e0
% 203.30/34.25  | 
% 203.30/34.25  | REDUCE: (20), (58) imply:
% 203.30/34.25  |   (62)  op(all_6_2, all_6_2) = e3
% 203.30/34.25  | 
% 203.30/34.25  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (12), (14), (15), (16),
% 203.30/34.25  |            (17), (18), (19), (21), (22), (23), (24), (25), (26), (27), (28),
% 203.30/34.25  |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 203.30/34.25  |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 203.30/34.25  |            (51), (52), (53), (54), (59), (60), (61), (62) are inconsistent by
% 203.30/34.25  |            sub-proof #528.
% 203.30/34.25  | 
% 203.30/34.25  End of proof
% 203.30/34.25  
% 203.30/34.25  Sub-proof #515 shows that the following formulas are inconsistent:
% 203.30/34.25  ----------------------------------------------------------------
% 203.30/34.25    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.30/34.25    (2)   ~ (all_52_15 = all_52_23)
% 203.30/34.25    (3)   ~ (all_52_25 = all_52_27)
% 203.30/34.25    (4)  all_58_14 = all_52_23
% 203.30/34.25    (5)   ~ (e3 = e1)
% 203.30/34.25    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.30/34.25    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.30/34.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.30/34.25    (8)   ~ (all_52_5 = all_52_13)
% 203.30/34.25    (9)  op(all_52_7, all_52_7) = e0
% 203.30/34.25    (10)  all_58_1 = all_52_9
% 203.30/34.25    (11)   ~ (all_52_9 = all_52_13)
% 203.30/34.25    (12)  op(all_52_5, all_52_5) = e1
% 203.30/34.25    (13)   ~ (e3 = e0)
% 203.30/34.25    (14)  all_24_1 = all_14_1
% 203.30/34.25    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.30/34.25    (16)  op(e0, e2) = all_52_15
% 203.30/34.25    (17)   ~ (all_52_7 = all_52_15)
% 203.30/34.25    (18)   ~ (all_52_3 = all_52_19)
% 203.30/34.25    (19)   ~ (all_52_17 = all_52_25)
% 203.30/34.25    (20)   ~ (all_52_3 = all_6_2)
% 203.30/34.25    (21)  all_58_0 = all_6_2
% 203.30/34.25    (22)  op(all_14_2, e0) = all_14_1
% 203.30/34.25    (23)  all_34_1 = all_14_1
% 203.30/34.25    (24)  all_56_4 = all_52_3
% 203.30/34.25    (25)  op(e3, e0) = all_52_25
% 203.30/34.25    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.30/34.25    (27)  all_58_13 = all_52_15
% 203.30/34.25    (28)  op(e0, all_14_1) = e1
% 203.30/34.25    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.30/34.25    (30)  all_58_9 = all_52_25
% 203.30/34.25    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.30/34.25    (32)   ~ (all_52_29 = all_14_2)
% 203.30/34.25    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.30/34.25    (34)  op(e2, all_4_1) = e3
% 203.30/34.25    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.30/34.25    (36)  op(e2, e2) = all_4_2
% 203.30/34.25    (37)   ~ (all_52_3 = all_52_5)
% 203.30/34.25    (38)  all_58_11 = all_52_29
% 203.30/34.25    (39)  all_56_5 = all_4_2
% 203.30/34.25    (40)   ~ (all_52_25 = all_14_2)
% 203.30/34.25    (41)   ~ (all_52_9 = all_52_15)
% 203.30/34.25    (42)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.30/34.25    (43)   ~ (all_52_3 = all_52_27)
% 203.30/34.25    (44)  op(all_10_2, e1) = all_10_1
% 203.30/34.25    (45)   ~ (all_52_7 = all_6_2)
% 203.30/34.25    (46)  op(e0, e0) = all_14_2
% 203.30/34.25    (47)  op(e0, e1) = all_52_23
% 203.30/34.25    (48)  all_56_15 = all_14_2
% 203.30/34.25    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.30/34.25    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.30/34.25    (51)  op(e1, e0) = all_52_29
% 203.30/34.25    (52)  all_56_11 = all_52_29
% 203.30/34.25    (53)   ~ (all_4_1 = e1)
% 203.30/34.25    (54)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 203.30/34.25    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.30/34.25    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.30/34.25    (57)  op(e1, all_10_1) = e3
% 203.30/34.25    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.30/34.25    (59)  all_56_9 = all_52_13
% 203.30/34.25    (60)   ~ (e2 = e1)
% 203.30/34.25    (61)   ~ (all_52_13 = all_10_2)
% 203.30/34.25    (62)   ~ (all_6_0 = e1)
% 203.30/34.25    (63)  all_58_10 = all_52_27
% 203.30/34.25    (64)  all_56_8 = all_52_5
% 203.30/34.25    (65)  op(all_52_9, all_52_9) = all_52_8
% 203.30/34.25    (66)  op(all_52_15, all_52_15) = all_52_14
% 203.30/34.25    (67)   ~ (all_52_19 = all_52_23)
% 203.30/34.25    (68)   ~ (all_52_25 = all_52_29)
% 203.30/34.25    (69)   ~ (all_52_29 = all_10_2)
% 203.30/34.25    (70)  all_58_7 = all_52_13
% 203.30/34.25    (71)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.30/34.25    (72)  op(all_6_2, all_6_2) = e3
% 203.30/34.25    (73)   ~ (all_52_5 = all_52_7)
% 203.30/34.25    (74)  all_58_12 = all_52_7
% 203.37/34.25    (75)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.25    (76)   ~ (all_52_7 = all_14_2)
% 203.37/34.25    (77)   ~ (all_14_2 = e0)
% 203.37/34.25    (78)  all_58_2 = all_52_3
% 203.37/34.25    (79)  all_56_2 = all_52_17
% 203.37/34.25    (80)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.25    (81)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.25    (82)  op(e3, all_6_1) = all_6_0
% 203.37/34.25    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.25    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.37/34.25    (85)   ~ (e2 = e0)
% 203.37/34.25    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.25    (87)  op(all_4_2, e2) = all_4_1
% 203.37/34.25    (88)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.37/34.25    (89)  op(all_52_3, all_52_3) = e2
% 203.37/34.25    (90)   ~ (all_52_5 = all_52_29)
% 203.37/34.25    (91)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.25    (92)   ~ (all_52_15 = all_14_2)
% 203.37/34.25    (93)   ~ (all_52_19 = all_52_27)
% 203.37/34.25    (94)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.25    (95)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.37/34.25    (96)   ~ (all_6_0 = e2)
% 203.37/34.25    (97)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.25    (98)   ~ (all_52_13 = all_4_2)
% 203.37/34.25    (99)  op(e3, e1) = all_52_17
% 203.37/34.25    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.37/34.25    (101)  op(e0, e3) = all_52_7
% 203.37/34.25    (102)  op(e1, e2) = all_52_13
% 203.37/34.25    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.25    (104)   ~ (all_52_9 = all_52_25)
% 203.37/34.25    (105)  all_58_15 = all_14_2
% 203.37/34.25    (106)   ~ (all_52_19 = all_10_2)
% 203.37/34.25    (107)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.25    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.25    (109)  all_58_8 = all_10_2
% 203.37/34.25    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.25    (111)  all_34_2 = all_14_2
% 203.37/34.25    (112)   ~ (all_52_5 = all_10_2)
% 203.37/34.25    (113)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.25    (114)   ~ (all_52_23 = all_14_2)
% 203.37/34.25    (115)  all_56_12 = all_52_7
% 203.37/34.25    (116)  op(all_52_17, all_52_17) = all_52_16
% 203.37/34.25    (117)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.25    (118)   ~ (all_52_25 = all_6_2)
% 203.37/34.25    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.25    (120)   ~ (all_52_9 = all_4_2)
% 203.37/34.25    (121)   ~ (all_52_5 = all_6_2)
% 203.37/34.25    (122)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.25    (123)   ~ (all_52_9 = all_6_2)
% 203.37/34.25    (124)  all_24_2 = all_14_2
% 203.37/34.25    (125)   ~ (all_52_13 = all_52_15)
% 203.37/34.25    (126)  op(e3, e3) = all_6_2
% 203.37/34.25    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.25    (128)   ~ (all_52_27 = all_14_2)
% 203.37/34.25    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.37/34.25    (130)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.25    (131)  all_56_3 = all_52_25
% 203.37/34.25    (132)   ~ (all_52_3 = all_52_7)
% 203.37/34.25    (133)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.25    (134)  all_58_5 = all_52_19
% 203.37/34.25    (135)  all_56_1 = all_52_9
% 203.37/34.25    (136)   ~ (all_52_15 = all_4_2)
% 203.37/34.25    (137)   ~ (all_52_27 = all_4_2)
% 203.37/34.25    (138)  all_58_6 = all_52_5
% 203.37/34.25    (139)  op(e3, e2) = all_52_9
% 203.37/34.25    (140)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.25    (141)   ~ (all_52_17 = all_6_2)
% 203.37/34.25    (142)   ~ (e1 = e0)
% 203.37/34.25    (143)  op(e2, e0) = all_52_27
% 203.37/34.25    (144)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.37/34.25    (145)   ~ (e3 = e2)
% 203.37/34.25    (146)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.25    (147)   ~ (all_52_9 = all_52_17)
% 203.37/34.25    (148)  all_56_10 = all_10_2
% 203.37/34.25    (149)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.25    (150)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.25    (151)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 203.37/34.25    (152)  op(all_52_13, all_52_13) = all_52_12
% 203.37/34.25    (153)  op(e1, e1) = all_10_2
% 203.37/34.25    (154)   ~ (all_52_23 = all_10_2)
% 203.37/34.25    (155)   ~ (all_52_7 = all_52_23)
% 203.37/34.25    (156)   ~ (all_52_17 = all_52_19)
% 203.37/34.25    (157)  all_58_3 = all_4_2
% 203.37/34.25    (158)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.25    (159)  all_56_13 = all_52_15
% 203.37/34.25    (160)   ~ (all_52_3 = all_4_2)
% 203.37/34.25    (161)   ~ (all_52_19 = all_4_2)
% 203.37/34.25    (162)   ~ (all_52_17 = all_52_23)
% 203.37/34.25    (163)  op(all_6_2, e3) = all_6_1
% 203.37/34.25    (164)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.37/34.25    (165)   ~ (all_52_13 = all_52_29)
% 203.37/34.25    (166)  all_58_4 = all_52_17
% 203.37/34.25    (167)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.37/34.25    (168)  op(all_52_25, all_52_25) = all_52_24
% 203.37/34.25  
% 203.37/34.25  Begin of proof
% 203.37/34.25  | 
% 203.37/34.25  | BETA: splitting (110) gives:
% 203.37/34.25  | 
% 203.37/34.25  | Case 1:
% 203.37/34.25  | | 
% 203.37/34.25  | |   (169)  all_56_15 = e3
% 203.37/34.25  | | 
% 203.37/34.25  | | COMBINE_EQS: (48), (169) imply:
% 203.37/34.25  | |   (170)  all_14_2 = e3
% 203.37/34.25  | | 
% 203.37/34.25  | | REF_CLOSE: (3), (5), (7), (9), (12), (21), (22), (23), (25), (28), (30),
% 203.37/34.25  | |            (32), (36), (37), (38), (40), (46), (47), (49), (50), (54), (63),
% 203.37/34.25  | |            (67), (68), (70), (71), (72), (74), (75), (76), (78), (81), (89),
% 203.37/34.25  | |            (98), (107), (109), (111), (112), (114), (117), (119), (121),
% 203.37/34.25  | |            (126), (131), (133), (134), (138), (140), (145), (152), (153),
% 203.37/34.25  | |            (154), (157), (160), (168), (170) are inconsistent by sub-proof
% 203.37/34.25  | |            #713.
% 203.37/34.25  | | 
% 203.37/34.25  | Case 2:
% 203.37/34.25  | | 
% 203.37/34.25  | |   (171)   ~ (all_56_15 = e3)
% 203.37/34.25  | |   (172)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.25  | | 
% 203.37/34.25  | | REDUCE: (48), (171) imply:
% 203.37/34.25  | |   (173)   ~ (all_14_2 = e3)
% 203.37/34.25  | | 
% 203.37/34.25  | | BETA: splitting (55) gives:
% 203.37/34.25  | | 
% 203.37/34.25  | | Case 1:
% 203.37/34.25  | | | 
% 203.37/34.25  | | |   (174)  all_56_13 = e3
% 203.37/34.25  | | | 
% 203.37/34.25  | | | COMBINE_EQS: (159), (174) imply:
% 203.37/34.25  | | |   (175)  all_52_15 = e3
% 203.37/34.25  | | | 
% 203.37/34.25  | | | COMBINE_EQS: (27), (175) imply:
% 203.37/34.25  | | |   (176)  all_58_13 = e3
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (17), (175) imply:
% 203.37/34.25  | | |   (177)   ~ (all_52_7 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (41), (175) imply:
% 203.37/34.25  | | |   (178)   ~ (all_52_9 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (125), (175) imply:
% 203.37/34.25  | | |   (179)   ~ (all_52_13 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (2), (175) imply:
% 203.37/34.25  | | |   (180)   ~ (all_52_23 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | SIMP: (180) implies:
% 203.37/34.25  | | |   (181)   ~ (all_52_23 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (92), (175) imply:
% 203.37/34.25  | | |   (182)   ~ (all_14_2 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (136), (175) imply:
% 203.37/34.25  | | |   (183)   ~ (all_4_2 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | SIMP: (183) implies:
% 203.37/34.25  | | |   (184)   ~ (all_4_2 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (66), (175) imply:
% 203.37/34.25  | | |   (185)  op(e3, e3) = all_52_14
% 203.37/34.25  | | | 
% 203.37/34.25  | | | GROUND_INST: instantiating (7) with all_6_2, all_52_14, e3, e3,
% 203.37/34.25  | | |              simplifying with (126), (185) gives:
% 203.37/34.25  | | |   (186)  all_52_14 = all_6_2
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 203.37/34.25  | | |            (16), (18), (19), (21), (22), (26), (28), (29), (30), (31),
% 203.37/34.25  | | |            (32), (33), (35), (36), (38), (39), (40), (43), (44), (46),
% 203.37/34.25  | | |            (48), (49), (50), (51), (52), (56), (57), (58), (59), (60),
% 203.37/34.25  | | |            (61), (62), (63), (64), (65), (67), (69), (70), (71), (72),
% 203.37/34.25  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 203.37/34.25  | | |            (83), (85), (86), (88), (89), (90), (91), (92), (93), (94),
% 203.37/34.25  | | |            (95), (96), (97), (98), (99), (101), (102), (104), (105),
% 203.37/34.25  | | |            (106), (107), (108), (109), (112), (113), (115), (116), (117),
% 203.37/34.25  | | |            (118), (120), (121), (122), (123), (124), (126), (127), (128),
% 203.37/34.25  | | |            (129), (130), (133), (134), (135), (137), (138), (141), (142),
% 203.37/34.25  | | |            (143), (144), (146), (147), (148), (149), (150), (151), (153),
% 203.37/34.25  | | |            (154), (157), (158), (160), (161), (163), (165), (166), (167),
% 203.37/34.25  | | |            (172), (173), (176), (177), (178), (179), (181), (184) are
% 203.37/34.25  | | |            inconsistent by sub-proof #516.
% 203.37/34.25  | | | 
% 203.37/34.25  | | Case 2:
% 203.37/34.25  | | | 
% 203.37/34.25  | | |   (187)   ~ (all_56_13 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REDUCE: (159), (187) imply:
% 203.37/34.25  | | |   (188)   ~ (all_52_15 = e3)
% 203.37/34.25  | | | 
% 203.37/34.25  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.37/34.25  | | |            (14), (15), (18), (19), (20), (21), (22), (24), (27), (29),
% 203.37/34.25  | | |            (30), (31), (32), (34), (36), (38), (39), (40), (41), (42),
% 203.37/34.25  | | |            (43), (44), (45), (46), (48), (49), (53), (56), (59), (61),
% 203.37/34.25  | | |            (63), (64), (65), (68), (70), (71), (72), (73), (74), (75),
% 203.37/34.25  | | |            (76), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 203.37/34.25  | | |            (87), (89), (96), (97), (98), (100), (103), (104), (105),
% 203.37/34.25  | | |            (107), (108), (109), (112), (114), (115), (116), (117), (118),
% 203.37/34.25  | | |            (121), (123), (124), (126), (127), (128), (132), (133), (134),
% 203.37/34.25  | | |            (135), (136), (137), (138), (139), (140), (141), (143), (146),
% 203.37/34.25  | | |            (147), (150), (151), (153), (154), (155), (156), (157), (158),
% 203.37/34.25  | | |            (160), (162), (163), (164), (165), (166), (172), (173), (188)
% 203.37/34.25  | | |            are inconsistent by sub-proof #698.
% 203.37/34.25  | | | 
% 203.37/34.25  | | End of split
% 203.37/34.25  | | 
% 203.37/34.25  | End of split
% 203.37/34.25  | 
% 203.37/34.25  End of proof
% 203.37/34.25  
% 203.37/34.25  Sub-proof #516 shows that the following formulas are inconsistent:
% 203.37/34.25  ----------------------------------------------------------------
% 203.37/34.25    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.37/34.25    (2)  all_58_14 = all_52_23
% 203.37/34.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.25    (4)   ~ (all_52_5 = all_52_13)
% 203.37/34.25    (5)  op(all_52_7, all_52_7) = e0
% 203.37/34.25    (6)  all_58_1 = all_52_9
% 203.37/34.25    (7)   ~ (all_52_9 = all_52_13)
% 203.37/34.25    (8)  op(all_52_5, all_52_5) = e1
% 203.37/34.25    (9)   ~ (e3 = e0)
% 203.37/34.25    (10)  all_24_1 = all_14_1
% 203.37/34.25    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.25    (12)  op(e0, e2) = all_52_15
% 203.37/34.25    (13)   ~ (all_52_3 = all_52_19)
% 203.37/34.25    (14)   ~ (all_52_17 = all_52_25)
% 203.37/34.25    (15)   ~ (all_4_2 = e3)
% 203.37/34.25    (16)  all_58_0 = all_6_2
% 203.37/34.25    (17)  op(all_14_2, e0) = all_14_1
% 203.37/34.25    (18)  all_58_13 = e3
% 203.37/34.25    (19)  op(all_52_19, all_52_19) = all_52_18
% 203.37/34.25    (20)  op(e0, all_14_1) = e1
% 203.37/34.25    (21)  op(all_10_2, all_10_2) = all_52_20
% 203.37/34.25    (22)  all_58_9 = all_52_25
% 203.37/34.25    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.37/34.25    (24)   ~ (all_52_29 = all_14_2)
% 203.37/34.25    (25)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.37/34.25    (26)  op(all_52_27, all_52_27) = all_52_26
% 203.37/34.25    (27)  op(e2, e2) = all_4_2
% 203.37/34.25    (28)  all_58_11 = all_52_29
% 203.37/34.25    (29)  all_56_5 = all_4_2
% 203.37/34.25    (30)   ~ (all_52_25 = all_14_2)
% 203.37/34.25    (31)   ~ (all_52_3 = all_52_27)
% 203.37/34.25    (32)  op(all_10_2, e1) = all_10_1
% 203.37/34.25    (33)  op(e0, e0) = all_14_2
% 203.37/34.25    (34)  all_56_15 = all_14_2
% 203.37/34.25    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.25    (36)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.37/34.25    (37)  op(e1, e0) = all_52_29
% 203.37/34.25    (38)  all_56_11 = all_52_29
% 203.37/34.25    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.25    (40)  op(e1, all_10_1) = e3
% 203.37/34.25    (41)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.37/34.25    (42)  all_56_9 = all_52_13
% 203.37/34.25    (43)   ~ (e2 = e1)
% 203.37/34.25    (44)   ~ (all_52_13 = all_10_2)
% 203.37/34.25    (45)   ~ (all_6_0 = e1)
% 203.37/34.25    (46)  all_58_10 = all_52_27
% 203.37/34.25    (47)  all_56_8 = all_52_5
% 203.37/34.25    (48)  op(all_52_9, all_52_9) = all_52_8
% 203.37/34.25    (49)   ~ (all_52_19 = all_52_23)
% 203.37/34.25    (50)   ~ (all_52_29 = all_10_2)
% 203.37/34.25    (51)  all_58_7 = all_52_13
% 203.37/34.25    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.37/34.25    (53)  op(all_6_2, all_6_2) = e3
% 203.37/34.25    (54)   ~ (all_52_5 = all_52_7)
% 203.37/34.25    (55)  all_58_12 = all_52_7
% 203.37/34.25    (56)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.25    (57)   ~ (all_52_7 = e3)
% 203.37/34.25    (58)   ~ (all_52_7 = all_14_2)
% 203.37/34.25    (59)   ~ (all_14_2 = e0)
% 203.37/34.25    (60)  all_58_2 = all_52_3
% 203.37/34.25    (61)  all_56_2 = all_52_17
% 203.37/34.26    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.26    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.26    (64)  op(e3, all_6_1) = all_6_0
% 203.37/34.26    (65)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.26    (66)   ~ (e2 = e0)
% 203.37/34.26    (67)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.26    (68)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.37/34.26    (69)   ~ (all_52_23 = e3)
% 203.37/34.26    (70)  op(all_52_3, all_52_3) = e2
% 203.37/34.26    (71)   ~ (all_52_5 = all_52_29)
% 203.37/34.26    (72)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.26    (73)   ~ (all_52_15 = all_14_2)
% 203.37/34.26    (74)   ~ (all_52_19 = all_52_27)
% 203.37/34.26    (75)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.26    (76)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.37/34.26    (77)   ~ (all_6_0 = e2)
% 203.37/34.26    (78)   ~ (all_52_9 = e3)
% 203.37/34.26    (79)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.26    (80)   ~ (all_52_13 = all_4_2)
% 203.37/34.26    (81)  op(e3, e1) = all_52_17
% 203.37/34.26    (82)  op(e0, e3) = all_52_7
% 203.37/34.26    (83)  op(e1, e2) = all_52_13
% 203.37/34.26    (84)   ~ (all_52_9 = all_52_25)
% 203.37/34.26    (85)  all_58_15 = all_14_2
% 203.37/34.26    (86)   ~ (all_52_19 = all_10_2)
% 203.37/34.26    (87)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.26    (88)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.26    (89)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.26    (90)  all_58_8 = all_10_2
% 203.37/34.26    (91)   ~ (all_52_5 = all_10_2)
% 203.37/34.26    (92)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.26    (93)  all_56_12 = all_52_7
% 203.37/34.26    (94)  op(all_52_17, all_52_17) = all_52_16
% 203.37/34.26    (95)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.26    (96)   ~ (all_52_25 = all_6_2)
% 203.37/34.26    (97)   ~ (all_52_9 = all_4_2)
% 203.37/34.26    (98)   ~ (all_52_5 = all_6_2)
% 203.37/34.26    (99)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.26    (100)   ~ (all_52_9 = all_6_2)
% 203.37/34.26    (101)  all_24_2 = all_14_2
% 203.37/34.26    (102)  op(e3, e3) = all_6_2
% 203.37/34.26    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.26    (104)   ~ (all_52_13 = e3)
% 203.37/34.26    (105)   ~ (all_52_27 = all_14_2)
% 203.37/34.26    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.37/34.26    (107)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.26    (108)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.26    (109)  all_58_5 = all_52_19
% 203.37/34.26    (110)  all_56_1 = all_52_9
% 203.37/34.26    (111)   ~ (all_52_27 = all_4_2)
% 203.37/34.26    (112)  all_58_6 = all_52_5
% 203.37/34.26    (113)   ~ (all_52_17 = all_6_2)
% 203.37/34.26    (114)   ~ (e1 = e0)
% 203.37/34.26    (115)  op(e2, e0) = all_52_27
% 203.37/34.26    (116)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.37/34.26    (117)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.26    (118)   ~ (all_52_9 = all_52_17)
% 203.37/34.26    (119)  all_56_10 = all_10_2
% 203.37/34.26    (120)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.26    (121)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.26    (122)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 203.37/34.26    (123)  op(e1, e1) = all_10_2
% 203.37/34.26    (124)   ~ (all_52_23 = all_10_2)
% 203.37/34.26    (125)  all_58_3 = all_4_2
% 203.37/34.26    (126)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.26    (127)   ~ (all_52_3 = all_4_2)
% 203.37/34.26    (128)   ~ (all_52_19 = all_4_2)
% 203.37/34.26    (129)  op(all_6_2, e3) = all_6_1
% 203.37/34.26    (130)   ~ (all_52_13 = all_52_29)
% 203.37/34.26    (131)  all_58_4 = all_52_17
% 203.37/34.26    (132)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.37/34.26    (133)   ~ (all_14_2 = e3)
% 203.37/34.26  
% 203.37/34.26  Begin of proof
% 203.37/34.26  | 
% 203.37/34.26  | BETA: splitting (67) gives:
% 203.37/34.26  | 
% 203.37/34.26  | Case 1:
% 203.37/34.26  | | 
% 203.37/34.26  | |   (134)  all_56_5 = e3
% 203.37/34.26  | | 
% 203.37/34.26  | | REF_CLOSE: (15), (29), (134) are inconsistent by sub-proof #1319.
% 203.37/34.26  | | 
% 203.37/34.26  | Case 2:
% 203.37/34.26  | | 
% 203.37/34.26  | |   (135)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.26  | | 
% 203.37/34.26  | | BETA: splitting (117) gives:
% 203.37/34.26  | | 
% 203.37/34.26  | | Case 1:
% 203.37/34.26  | | | 
% 203.37/34.26  | | |   (136)  all_56_1 = e3
% 203.37/34.26  | | | 
% 203.37/34.26  | | | COMBINE_EQS: (110), (136) imply:
% 203.37/34.26  | | |   (137)  all_52_9 = e3
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (78), (137) imply:
% 203.37/34.26  | | |   (138)  $false
% 203.37/34.26  | | | 
% 203.37/34.26  | | | CLOSE: (138) is inconsistent.
% 203.37/34.26  | | | 
% 203.37/34.26  | | Case 2:
% 203.37/34.26  | | | 
% 203.37/34.26  | | |   (139)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.26  | | | 
% 203.37/34.26  | | | BETA: splitting (121) gives:
% 203.37/34.26  | | | 
% 203.37/34.26  | | | Case 1:
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | |   (140)  all_56_9 = e3
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | | REF_CLOSE: (42), (104), (140) are inconsistent by sub-proof #958.
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | Case 2:
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | |   (141)   ~ (all_56_9 = e3)
% 203.37/34.26  | | | |   (142)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | | BETA: splitting (11) gives:
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | | Case 1:
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | |   (143)  all_56_12 = e3
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | | COMBINE_EQS: (93), (143) imply:
% 203.37/34.26  | | | | |   (144)  all_52_7 = e3
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | | REDUCE: (57), (144) imply:
% 203.37/34.26  | | | | |   (145)  $false
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | | CLOSE: (145) is inconsistent.
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | Case 2:
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | |   (146)   ~ (all_56_12 = e3)
% 203.37/34.26  | | | | |   (147)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | | BETA: splitting (41) gives:
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | | Case 1:
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | |   (148)  all_58_1 = e1
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (13), (16), (18),
% 203.37/34.26  | | | | | |            (19), (21), (22), (25), (27), (28), (31), (32), (35),
% 203.37/34.26  | | | | | |            (36), (38), (39), (43), (45), (46), (49), (50), (51),
% 203.37/34.26  | | | | | |            (52), (53), (55), (56), (57), (60), (61), (63), (64),
% 203.37/34.26  | | | | | |            (65), (66), (69), (70), (71), (72), (74), (75), (76),
% 203.37/34.26  | | | | | |            (77), (79), (81), (84), (85), (86), (90), (91), (95),
% 203.37/34.26  | | | | | |            (96), (97), (98), (102), (103), (104), (105), (106),
% 203.37/34.26  | | | | | |            (108), (109), (112), (113), (114), (118), (120), (123),
% 203.37/34.26  | | | | | |            (124), (125), (127), (129), (131), (133), (148) are
% 203.37/34.26  | | | | | |            inconsistent by sub-proof #708.
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | Case 2:
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | |   (149)   ~ (all_58_1 = e1)
% 203.37/34.26  | | | | | |   (150)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | | REDUCE: (6), (149) imply:
% 203.37/34.26  | | | | | |   (151)   ~ (all_52_9 = e1)
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | | BETA: splitting (103) gives:
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | | Case 1:
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | |   (152)  all_58_9 = e3
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | | REF_CLOSE: (3), (8), (16), (22), (27), (35), (53), (55), (57),
% 203.37/34.26  | | | | | | |            (60), (63), (70), (91), (96), (102), (112), (123),
% 203.37/34.26  | | | | | | |            (127), (152) are inconsistent by sub-proof #660.
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | Case 2:
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | |   (153)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | | BETA: splitting (106) gives:
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | |   (154)  all_58_0 = e3
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | COMBINE_EQS: (16), (154) imply:
% 203.37/34.26  | | | | | | | |   (155)  all_6_2 = e3
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (98), (155) imply:
% 203.37/34.26  | | | | | | | |   (156)   ~ (all_52_5 = e3)
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (113), (155) imply:
% 203.37/34.26  | | | | | | | |   (157)   ~ (all_52_17 = e3)
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (129), (155) imply:
% 203.37/34.26  | | | | | | | |   (158)  op(e3, e3) = all_6_1
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (102), (155) imply:
% 203.37/34.26  | | | | | | | |   (159)  op(e3, e3) = e3
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_1, e3, e3,
% 203.37/34.26  | | | | | | | |              simplifying with (158), (159) gives:
% 203.37/34.26  | | | | | | | |   (160)  all_6_1 = e3
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (64), (160) imply:
% 203.37/34.26  | | | | | | | |   (161)  op(e3, e3) = all_6_0
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3,
% 203.37/34.26  | | | | | | | |              simplifying with (159), (161) gives:
% 203.37/34.26  | | | | | | | |   (162)  all_6_0 = e3
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (77), (162) imply:
% 203.37/34.26  | | | | | | | |   (163)   ~ (e3 = e2)
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (45), (162) imply:
% 203.37/34.26  | | | | | | | |   (164)   ~ (e3 = e1)
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | BETA: splitting (120) gives:
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | |   (165)  all_58_4 = e3
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | REF_CLOSE: (131), (157), (165) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | |            #1302.
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | |   (166)   ~ (all_58_4 = e3)
% 203.37/34.26  | | | | | | | | |   (167)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | BETA: splitting (68) gives:
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | |   (168)  all_58_0 = e1
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | COMBINE_EQS: (154), (168) imply:
% 203.37/34.26  | | | | | | | | | |   (169)  e3 = e1
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | REDUCE: (164), (169) imply:
% 203.37/34.26  | | | | | | | | | |   (170)  $false
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | CLOSE: (170) is inconsistent.
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | |   (171)   ~ (all_58_0 = e1)
% 203.37/34.26  | | | | | | | | | |   (172)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | BETA: splitting (88) gives:
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | |   (173)  all_56_8 = e3
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | REF_CLOSE: (47), (156), (173) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | | | |            #1325.
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | |   (174)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | BETA: splitting (39) gives:
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | |   (175)  all_56_2 = e3
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | REF_CLOSE: (61), (157), (175) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | | | | |            #1327.
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | |   (176)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | BETA: splitting (65) gives:
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | |   (177)  all_58_0 = e1
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | COMBINE_EQS: (154), (177) imply:
% 203.37/34.26  | | | | | | | | | | | | |   (178)  e3 = e1
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | REDUCE: (164), (178) imply:
% 203.37/34.26  | | | | | | | | | | | | |   (179)  $false
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | |   (180)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | BETA: splitting (132) gives:
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | |   (181)  all_56_10 = e3
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | COMBINE_EQS: (119), (181) imply:
% 203.37/34.26  | | | | | | | | | | | | | |   (182)  all_10_2 = e3
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | SIMP: (182) implies:
% 203.37/34.26  | | | | | | | | | | | | | |   (183)  all_10_2 = e3
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | REDUCE: (50), (183) imply:
% 203.37/34.26  | | | | | | | | | | | | | |   (184)   ~ (all_52_29 = e3)
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | REDUCE: (32), (183) imply:
% 203.37/34.26  | | | | | | | | | | | | | |   (185)  op(e3, e1) = all_10_1
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | |   (186)  all_58_10 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | COMBINE_EQS: (46), (186) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (187)  all_52_27 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | SIMP: (187) implies:
% 203.37/34.26  | | | | | | | | | | | | | | |   (188)  all_52_27 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REDUCE: (74), (188) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (189)   ~ (all_52_19 = e3)
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REDUCE: (111), (188) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (190)   ~ (all_4_2 = e3)
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REDUCE: (115), (188) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (191)  op(e2, e0) = e3
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1,
% 203.37/34.26  | | | | | | | | | | | | | | |              e3, simplifying with (81), (185) gives:
% 203.37/34.26  | | | | | | | | | | | | | | |   (192)  all_52_17 = all_10_1
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | COMBINE_EQS: (61), (192) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (193)  all_56_2 = all_10_1
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | COMBINE_EQS: (131), (192) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (194)  all_58_4 = all_10_1
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REDUCE: (118), (192) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (195)   ~ (all_52_9 = all_10_1)
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REDUCE: (14), (192) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (196)   ~ (all_52_25 = all_10_1)
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | SIMP: (196) implies:
% 203.37/34.26  | | | | | | | | | | | | | | |   (197)   ~ (all_52_25 = all_10_1)
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REDUCE: (94), (192) imply:
% 203.37/34.26  | | | | | | | | | | | | | | |   (198)  op(all_10_1, all_10_1) = all_52_16
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | |   (199)  all_58_1 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (199) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (200)  all_52_9 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | REDUCE: (7), (200) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (201)   ~ (all_52_13 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | SIMP: (201) implies:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (202)   ~ (all_52_13 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | REDUCE: (84), (200) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (203)   ~ (all_52_25 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | SIMP: (203) implies:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (204)   ~ (all_52_25 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | REDUCE: (78), (200) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (205)   ~ (e3 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | |   (206)  all_58_5 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (189), (206) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | | | | | | | | | |            #1279.
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | |   (207)  all_58_8 = e3 | all_58_14 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | |   (208)  all_58_8 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | |   (209)  all_58_9 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (209) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | |   (210)  all_52_25 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | REDUCE: (204), (210) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | |   (211)  $false
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | |   (212)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | |   (213)  all_58_6 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (213) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | |   (214)  all_52_5 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (214) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | |   (215)   ~ (all_52_29 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | |   (216)   ~ (all_52_29 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |   (217)  all_58_10 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (186), (217) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |            #1220.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |   (218)  all_58_11 = e2 | all_58_15 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (219)  all_58_11 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (216), (219) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |            #1189.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (220)  all_58_15 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (220) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (221)  all_14_2 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | SIMP: (221) implies:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (222)  all_14_2 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (222) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (223)  all_24_2 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (222) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (224)  op(e2, e0) = all_14_1
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (122), (191), (223), (224) are
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #843.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | |   (225)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |   (226)  all_58_7 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (226) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |   (227)  all_52_13 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (227) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |   (228)  $false
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | |   (229)  all_58_8 = e2 | all_58_11 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (230)  all_58_8 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (230) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (231)  e3 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (231) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (232)  $false
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (233)  all_58_11 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (233) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (234)  all_52_29 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (234) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (235)   ~ (all_14_2 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (236)   ~ (all_14_2 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (234) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | |   (237)  op(e1, e0) = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_56_15 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (238) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_14_2 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (239) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | |   (240)  $false
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_56_15 = e1 | all_56_15 = e0
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_56_15 = e1
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (242) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_14_2 = e1
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (243) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (244)   ~ (all_52_15 = e1)
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (243) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (245)  op(e1, e0) = all_14_1
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_14_1, e0, e1,
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (237), (245) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_14_1 = e2
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (246) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (247)  op(e0, e2) = e1
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_15, e1, e2, e0,
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (12), (247) gives:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_52_15 = e1
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (244), (248) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (249)  $false
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_56_15 = e0
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (250) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_14_2 = e0
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (251) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | |   (252)  $false
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | |   (253)  all_58_14 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (69), (253) are inconsistent by sub-proof
% 203.37/34.26  | | | | | | | | | | | | | | | | | |            #1305.
% 203.37/34.26  | | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | |   (254)   ~ (all_58_1 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | REDUCE: (6), (254) imply:
% 203.37/34.26  | | | | | | | | | | | | | | | |   (255)   ~ (all_52_9 = e2)
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (15), (22), (24),
% 203.37/34.26  | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (34), (40), (42), (47),
% 203.37/34.26  | | | | | | | | | | | | | | | |            (48), (54), (58), (62), (71), (78), (80), (83),
% 203.37/34.26  | | | | | | | | | | | | | | | |            (84), (89), (92), (93), (95), (97), (99), (104),
% 203.37/34.26  | | | | | | | | | | | | | | | |            (107), (108), (110), (112), (130), (135), (139),
% 203.37/34.26  | | | | | | | | | | | | | | | |            (142), (147), (151), (154), (163), (174), (176),
% 203.37/34.26  | | | | | | | | | | | | | | | |            (186), (193), (194), (195), (197), (198), (255)
% 203.37/34.26  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #517.
% 203.37/34.26  | | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | |   (256)  all_58_11 = e3 | all_58_15 = e3
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | | REF_CLOSE: (28), (85), (133), (184), (256) are inconsistent
% 203.37/34.26  | | | | | | | | | | | | | | |            by sub-proof #1103.
% 203.37/34.26  | | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | |   (257)   ~ (all_56_10 = e3)
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | REDUCE: (119), (257) imply:
% 203.37/34.26  | | | | | | | | | | | | | |   (258)   ~ (all_10_2 = e3)
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (13), (14), (17),
% 203.37/34.26  | | | | | | | | | | | | | |            (18), (20), (21), (22), (23), (25), (26), (27),
% 203.37/34.26  | | | | | | | | | | | | | |            (28), (30), (31), (32), (33), (34), (36), (37),
% 203.37/34.26  | | | | | | | | | | | | | |            (43), (46), (47), (49), (50), (51), (54), (55),
% 203.37/34.26  | | | | | | | | | | | | | |            (58), (59), (60), (69), (70), (71), (74), (79),
% 203.37/34.26  | | | | | | | | | | | | | |            (80), (82), (85), (87), (89), (90), (91), (93),
% 203.37/34.26  | | | | | | | | | | | | | |            (94), (95), (108), (109), (111), (112), (114),
% 203.37/34.26  | | | | | | | | | | | | | |            (115), (116), (123), (125), (128), (131), (133),
% 203.37/34.26  | | | | | | | | | | | | | |            (147), (150), (151), (153), (167), (172), (174),
% 203.37/34.26  | | | | | | | | | | | | | |            (180), (258) are inconsistent by sub-proof #706.
% 203.37/34.26  | | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | | 
% 203.37/34.26  | | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | | 
% 203.37/34.26  | | | | | | | | End of split
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | Case 2:
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | |   (259)   ~ (all_58_0 = e3)
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REDUCE: (16), (259) imply:
% 203.37/34.26  | | | | | | | |   (260)   ~ (all_6_2 = e3)
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | | REF_CLOSE: (3), (8), (16), (27), (35), (53), (55), (57), (60),
% 203.37/34.26  | | | | | | | |            (63), (70), (91), (102), (112), (123), (127), (260)
% 203.37/34.26  | | | | | | | |            are inconsistent by sub-proof #1363.
% 203.37/34.26  | | | | | | | | 
% 203.37/34.26  | | | | | | | End of split
% 203.37/34.26  | | | | | | | 
% 203.37/34.26  | | | | | | End of split
% 203.37/34.26  | | | | | | 
% 203.37/34.26  | | | | | End of split
% 203.37/34.26  | | | | | 
% 203.37/34.26  | | | | End of split
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | End of split
% 203.37/34.26  | | | 
% 203.37/34.26  | | End of split
% 203.37/34.26  | | 
% 203.37/34.26  | End of split
% 203.37/34.26  | 
% 203.37/34.26  End of proof
% 203.37/34.26  
% 203.37/34.26  Sub-proof #517 shows that the following formulas are inconsistent:
% 203.37/34.26  ----------------------------------------------------------------
% 203.37/34.26    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.37/34.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.26    (3)   ~ (all_52_5 = all_52_13)
% 203.37/34.26    (4)  op(all_10_1, all_10_1) = all_52_16
% 203.37/34.26    (5)  op(all_52_7, all_52_7) = e0
% 203.37/34.26    (6)  all_58_1 = all_52_9
% 203.37/34.26    (7)  op(all_52_5, all_52_5) = e1
% 203.37/34.26    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.26    (9)   ~ (all_4_2 = e3)
% 203.37/34.26    (10)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.26    (11)  all_58_9 = all_52_25
% 203.37/34.26    (12)   ~ (all_52_29 = all_14_2)
% 203.37/34.26    (13)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.26    (14)  all_58_11 = all_52_29
% 203.37/34.26    (15)  all_56_5 = all_4_2
% 203.37/34.26    (16)   ~ (all_52_25 = all_14_2)
% 203.37/34.26    (17)  all_58_4 = all_10_1
% 203.37/34.26    (18)  op(e0, e0) = all_14_2
% 203.37/34.26    (19)  all_56_15 = all_14_2
% 203.37/34.26    (20)  op(e1, all_10_1) = e3
% 203.37/34.26    (21)   ~ (all_52_25 = all_10_1)
% 203.37/34.26    (22)  all_56_9 = all_52_13
% 203.37/34.26    (23)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.26    (24)  all_56_8 = all_52_5
% 203.37/34.26    (25)  op(all_52_9, all_52_9) = all_52_8
% 203.37/34.26    (26)   ~ (all_52_5 = all_52_7)
% 203.37/34.26    (27)   ~ (all_52_7 = all_14_2)
% 203.37/34.26    (28)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.26    (29)   ~ (all_52_5 = all_52_29)
% 203.37/34.26    (30)   ~ (all_52_9 = e3)
% 203.37/34.26    (31)   ~ (all_52_13 = all_4_2)
% 203.37/34.26    (32)  all_58_0 = e3
% 203.37/34.26    (33)   ~ (all_52_9 = e2)
% 203.37/34.26    (34)  op(e1, e2) = all_52_13
% 203.37/34.26    (35)   ~ (all_52_9 = all_52_25)
% 203.37/34.26    (36)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.26    (37)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.26    (38)  all_56_12 = all_52_7
% 203.37/34.26    (39)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.26    (40)   ~ (all_52_9 = all_4_2)
% 203.37/34.26    (41)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.26    (42)  all_56_2 = all_10_1
% 203.37/34.26    (43)   ~ (all_52_9 = e1)
% 203.37/34.26    (44)  all_58_10 = e3
% 203.37/34.26    (45)   ~ (all_52_13 = e3)
% 203.37/34.26    (46)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.26    (47)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.26    (48)  all_56_1 = all_52_9
% 203.37/34.26    (49)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.26    (50)  all_58_6 = all_52_5
% 203.37/34.26    (51)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.26    (52)   ~ (e3 = e2)
% 203.37/34.26    (53)   ~ (all_52_13 = all_52_29)
% 203.37/34.26    (54)   ~ (all_52_9 = all_10_1)
% 203.37/34.26  
% 203.37/34.26  Begin of proof
% 203.37/34.26  | 
% 203.37/34.26  | BETA: splitting (49) gives:
% 203.37/34.26  | 
% 203.37/34.26  | Case 1:
% 203.37/34.26  | | 
% 203.37/34.26  | |   (55)  all_56_1 = e2
% 203.37/34.26  | | 
% 203.37/34.26  | | REF_CLOSE: (33), (48), (55) are inconsistent by sub-proof #1194.
% 203.37/34.26  | | 
% 203.37/34.26  | Case 2:
% 203.37/34.26  | | 
% 203.37/34.26  | |   (56)   ~ (all_56_1 = e2)
% 203.37/34.26  | |   (57)  all_56_1 = e1 | all_56_1 = e0
% 203.37/34.26  | | 
% 203.37/34.26  | | BETA: splitting (57) gives:
% 203.37/34.26  | | 
% 203.37/34.26  | | Case 1:
% 203.37/34.26  | | | 
% 203.37/34.26  | | |   (58)  all_56_1 = e1
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REF_CLOSE: (43), (48), (58) are inconsistent by sub-proof #1061.
% 203.37/34.26  | | | 
% 203.37/34.26  | | Case 2:
% 203.37/34.26  | | | 
% 203.37/34.26  | | |   (59)  all_56_1 = e0
% 203.37/34.26  | | | 
% 203.37/34.26  | | | COMBINE_EQS: (48), (59) imply:
% 203.37/34.26  | | |   (60)  all_52_9 = e0
% 203.37/34.26  | | | 
% 203.37/34.26  | | | SIMP: (60) implies:
% 203.37/34.26  | | |   (61)  all_52_9 = e0
% 203.37/34.26  | | | 
% 203.37/34.26  | | | COMBINE_EQS: (6), (61) imply:
% 203.37/34.26  | | |   (62)  all_58_1 = e0
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (35), (61) imply:
% 203.37/34.26  | | |   (63)   ~ (all_52_25 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | SIMP: (63) implies:
% 203.37/34.26  | | |   (64)   ~ (all_52_25 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (54), (61) imply:
% 203.37/34.26  | | |   (65)   ~ (all_10_1 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | SIMP: (65) implies:
% 203.37/34.26  | | |   (66)   ~ (all_10_1 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (40), (61) imply:
% 203.37/34.26  | | |   (67)   ~ (all_4_2 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | SIMP: (67) implies:
% 203.37/34.26  | | |   (68)   ~ (all_4_2 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (30), (61) imply:
% 203.37/34.26  | | |   (69)   ~ (e3 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | SIMP: (69) implies:
% 203.37/34.26  | | |   (70)   ~ (e3 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (33), (61) imply:
% 203.37/34.26  | | |   (71)   ~ (e2 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | SIMP: (71) implies:
% 203.37/34.26  | | |   (72)   ~ (e2 = e0)
% 203.37/34.26  | | | 
% 203.37/34.26  | | | REDUCE: (25), (61) imply:
% 203.37/34.26  | | |   (73)  op(e0, e0) = all_52_8
% 203.37/34.26  | | | 
% 203.37/34.26  | | | BETA: splitting (1) gives:
% 203.37/34.26  | | | 
% 203.37/34.26  | | | Case 1:
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | |   (74)  all_58_9 = e0
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | | REF_CLOSE: (11), (64), (74) are inconsistent by sub-proof #523.
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | Case 2:
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | |   (75)  all_58_10 = e0 | all_58_11 = e0
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 203.37/34.26  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.37/34.26  | | | |            (24), (26), (27), (28), (29), (31), (32), (34), (36), (37),
% 203.37/34.26  | | | |            (38), (39), (41), (42), (44), (45), (46), (47), (50), (51),
% 203.37/34.26  | | | |            (52), (53), (62), (66), (68), (70), (72), (73), (75) are
% 203.37/34.26  | | | |            inconsistent by sub-proof #520.
% 203.37/34.26  | | | | 
% 203.37/34.26  | | | End of split
% 203.37/34.26  | | | 
% 203.37/34.26  | | End of split
% 203.37/34.26  | | 
% 203.37/34.26  | End of split
% 203.37/34.26  | 
% 203.37/34.26  End of proof
% 203.37/34.26  
% 203.37/34.26  Sub-proof #518 shows that the following formulas are inconsistent:
% 203.37/34.26  ----------------------------------------------------------------
% 203.37/34.26    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.37/34.26    (2)   ~ (all_52_15 = all_52_23)
% 203.37/34.26    (3)   ~ (all_52_25 = all_52_27)
% 203.37/34.26    (4)  all_58_14 = all_52_23
% 203.37/34.26    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.37/34.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.27    (7)   ~ (all_52_5 = all_52_13)
% 203.37/34.27    (8)  op(all_52_7, all_52_7) = e0
% 203.37/34.27    (9)  all_58_1 = all_52_9
% 203.37/34.27    (10)   ~ (all_52_9 = all_52_13)
% 203.37/34.27    (11)  op(all_52_5, all_52_5) = e1
% 203.37/34.27    (12)   ~ (e3 = e0)
% 203.37/34.27    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.27    (14)  op(e0, e2) = all_52_15
% 203.37/34.27    (15)   ~ (all_52_7 = all_52_15)
% 203.37/34.27    (16)   ~ (all_52_3 = all_52_19)
% 203.37/34.27    (17)   ~ (all_52_17 = all_52_25)
% 203.37/34.27    (18)   ~ (all_52_3 = all_6_2)
% 203.37/34.27    (19)  all_58_0 = all_6_2
% 203.37/34.27    (20)  op(all_14_2, e0) = all_14_1
% 203.37/34.27    (21)  all_56_4 = all_52_3
% 203.37/34.27    (22)   ~ (all_52_17 = all_10_2)
% 203.37/34.27    (23)  op(e3, e0) = all_52_25
% 203.37/34.27    (24)  op(e0, all_14_1) = all_14_0
% 203.37/34.27    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.37/34.27    (26)   ~ (all_52_27 = all_52_29)
% 203.37/34.27    (27)  all_58_13 = all_52_15
% 203.37/34.27    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.37/34.27    (29)  all_58_9 = all_52_25
% 203.37/34.27    (30)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.37/34.27    (31)   ~ (all_52_29 = all_14_2)
% 203.37/34.27    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.37/34.27    (33)  op(e2, all_4_1) = e3
% 203.37/34.27    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.37/34.27    (35)  op(e2, e2) = all_4_2
% 203.37/34.27    (36)  all_58_11 = all_52_29
% 203.37/34.27    (37)  all_56_5 = all_4_2
% 203.37/34.27    (38)   ~ (all_52_25 = all_14_2)
% 203.37/34.27    (39)   ~ (all_52_9 = all_52_15)
% 203.37/34.27    (40)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.37/34.27    (41)   ~ (all_52_3 = all_52_27)
% 203.37/34.27    (42)  op(all_10_2, e1) = all_10_1
% 203.37/34.27    (43)   ~ (all_52_7 = all_6_2)
% 203.37/34.27    (44)  op(e0, e0) = all_14_2
% 203.37/34.27    (45)  op(e0, e1) = all_52_23
% 203.37/34.27    (46)  all_56_15 = all_14_2
% 203.37/34.27    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.27    (48)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.37/34.27    (49)  op(e1, e0) = all_52_29
% 203.37/34.27    (50)  all_56_11 = all_52_29
% 203.37/34.27    (51)   ~ (all_4_1 = e1)
% 203.37/34.27    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.27    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.27    (54)  op(e1, all_10_1) = e3
% 203.37/34.27    (55)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.37/34.27    (56)  all_56_9 = all_52_13
% 203.37/34.27    (57)   ~ (e2 = e1)
% 203.37/34.27    (58)   ~ (all_52_13 = all_10_2)
% 203.37/34.27    (59)   ~ (all_6_0 = e1)
% 203.37/34.27    (60)  all_58_10 = all_52_27
% 203.37/34.27    (61)  all_56_8 = all_52_5
% 203.37/34.27    (62)  op(all_52_9, all_52_9) = all_52_8
% 203.37/34.27    (63)  op(all_52_15, all_52_15) = all_52_14
% 203.37/34.27    (64)   ~ (all_52_19 = all_52_23)
% 203.37/34.27    (65)   ~ (all_52_25 = all_52_29)
% 203.37/34.27    (66)   ~ (all_52_29 = all_10_2)
% 203.37/34.27    (67)  all_58_7 = all_52_13
% 203.37/34.27    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.37/34.27    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.37/34.27    (70)  all_36_2 = all_10_2
% 203.37/34.27    (71)  all_36_1 = all_10_1
% 203.37/34.27    (72)  op(all_6_2, all_6_2) = e3
% 203.37/34.27    (73)   ~ (all_52_5 = all_52_7)
% 203.37/34.27    (74)  all_58_12 = all_52_7
% 203.37/34.27    (75)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.27    (76)   ~ (all_52_7 = all_14_2)
% 203.37/34.27    (77)   ~ (all_14_2 = e0)
% 203.37/34.27    (78)  all_58_2 = all_52_3
% 203.37/34.27    (79)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.37/34.27    (80)  all_56_2 = all_52_17
% 203.37/34.27    (81)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.27    (82)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.27    (83)  op(e3, all_6_1) = all_6_0
% 203.37/34.27    (84)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.37/34.27    (85)   ~ (all_14_0 = e3)
% 203.37/34.27    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.27    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.37/34.27    (88)   ~ (e2 = e0)
% 203.37/34.27    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.27    (90)  op(all_4_2, e2) = all_4_1
% 203.37/34.27    (91)  op(all_52_3, all_52_3) = e2
% 203.37/34.27    (92)   ~ (all_52_5 = all_52_29)
% 203.37/34.27    (93)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.27    (94)  all_56_6 = all_52_19
% 203.37/34.27    (95)   ~ (all_52_15 = all_14_2)
% 203.37/34.27    (96)   ~ (all_52_19 = all_52_27)
% 203.37/34.27    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.27    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.37/34.27    (99)   ~ (all_6_0 = e2)
% 203.37/34.27    (100)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.27    (101)   ~ (all_52_13 = all_4_2)
% 203.37/34.27    (102)  op(e3, e1) = all_52_17
% 203.37/34.27    (103)  op(e0, e3) = all_52_7
% 203.37/34.27    (104)  op(e1, e2) = all_52_13
% 203.37/34.27    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.27    (106)   ~ (all_52_9 = all_52_25)
% 203.37/34.27    (107)  all_58_15 = all_14_2
% 203.37/34.27    (108)   ~ (all_52_19 = all_10_2)
% 203.37/34.27    (109)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.27    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.27    (111)  all_58_8 = all_10_2
% 203.37/34.27    (112)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.27    (113)   ~ (all_52_5 = all_10_2)
% 203.37/34.27    (114)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.27    (115)   ~ (all_52_23 = all_14_2)
% 203.37/34.27    (116)  all_56_12 = all_52_7
% 203.37/34.27    (117)  op(all_52_17, all_52_17) = all_52_16
% 203.37/34.27    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.27    (119)   ~ (all_52_25 = all_6_2)
% 203.37/34.27    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.27    (121)   ~ (all_52_9 = all_4_2)
% 203.37/34.27    (122)   ~ (all_52_5 = all_6_2)
% 203.37/34.27    (123)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.27    (124)   ~ (all_52_9 = all_6_2)
% 203.37/34.27    (125)   ~ (all_52_13 = all_52_15)
% 203.37/34.27    (126)  all_56_0 = all_6_2
% 203.37/34.27    (127)  op(e3, e3) = all_6_2
% 203.37/34.27    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.27    (129)   ~ (all_52_27 = all_14_2)
% 203.37/34.27    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.37/34.27    (131)  all_56_14 = all_52_23
% 203.37/34.27    (132)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.27    (133)  all_56_3 = all_52_25
% 203.37/34.27    (134)   ~ (all_52_3 = all_52_7)
% 203.37/34.27    (135)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.27    (136)  all_58_5 = all_52_19
% 203.37/34.27    (137)  all_56_1 = all_52_9
% 203.37/34.27    (138)   ~ (all_52_15 = all_4_2)
% 203.37/34.27    (139)   ~ (all_52_27 = all_4_2)
% 203.37/34.27    (140)  all_58_6 = all_52_5
% 203.37/34.27    (141)  op(e3, e2) = all_52_9
% 203.37/34.27    (142)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.27    (143)   ~ (all_52_17 = all_6_2)
% 203.37/34.27    (144)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.37/34.27    (145)   ~ (e1 = e0)
% 203.37/34.27    (146)  op(e2, e0) = all_52_27
% 203.37/34.27    (147)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.27    (148)   ~ (all_52_9 = all_52_17)
% 203.37/34.27    (149)  all_56_10 = all_10_2
% 203.37/34.27    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.27    (151)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.27    (152)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.37/34.27    (153)  op(all_52_13, all_52_13) = all_52_12
% 203.37/34.27    (154)  op(e1, e1) = all_10_2
% 203.37/34.27    (155)   ~ (all_52_23 = all_10_2)
% 203.37/34.27    (156)   ~ (all_52_7 = all_52_23)
% 203.37/34.27    (157)  all_58_3 = all_4_2
% 203.37/34.27    (158)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.27    (159)  all_56_13 = all_52_15
% 203.37/34.27    (160)   ~ (all_52_3 = all_4_2)
% 203.37/34.27    (161)   ~ (all_52_19 = all_4_2)
% 203.37/34.27    (162)   ~ (all_52_17 = all_52_23)
% 203.37/34.27    (163)  op(all_6_2, e3) = all_6_1
% 203.37/34.27    (164)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.37/34.27    (165)   ~ (all_52_13 = all_52_29)
% 203.37/34.27    (166)  all_58_4 = all_52_17
% 203.37/34.27    (167)   ~ (all_14_0 = e1)
% 203.37/34.27    (168)   ~ (all_14_0 = e2)
% 203.37/34.27    (169)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.37/34.27    (170)  op(all_52_25, all_52_25) = all_52_24
% 203.37/34.27  
% 203.37/34.27  Begin of proof
% 203.37/34.27  | 
% 203.37/34.27  | BETA: splitting (112) gives:
% 203.37/34.27  | 
% 203.37/34.27  | Case 1:
% 203.37/34.27  | | 
% 203.37/34.27  | |   (171)  all_56_15 = e3
% 203.37/34.27  | | 
% 203.37/34.27  | | COMBINE_EQS: (46), (171) imply:
% 203.37/34.27  | |   (172)  all_14_2 = e3
% 203.37/34.27  | | 
% 203.37/34.27  | | SIMP: (172) implies:
% 203.37/34.27  | |   (173)  all_14_2 = e3
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (95), (173) imply:
% 203.37/34.27  | |   (174)   ~ (all_52_15 = e3)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (115), (173) imply:
% 203.37/34.27  | |   (175)   ~ (all_52_23 = e3)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (38), (173) imply:
% 203.37/34.27  | |   (176)   ~ (all_52_25 = e3)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (129), (173) imply:
% 203.37/34.27  | |   (177)   ~ (all_52_27 = e3)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (31), (173) imply:
% 203.37/34.27  | |   (178)   ~ (all_52_29 = e3)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (135), (173) imply:
% 203.37/34.27  | |   (179)  op(e3, e3) = all_52_30
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (20), (173) imply:
% 203.37/34.27  | |   (180)  op(e3, e0) = all_14_1
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (44), (173) imply:
% 203.37/34.27  | |   (181)  op(e0, e0) = e3
% 203.37/34.27  | | 
% 203.37/34.27  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 203.37/34.27  | |              with (23), (180) gives:
% 203.37/34.27  | |   (182)  all_52_25 = all_14_1
% 203.37/34.27  | | 
% 203.37/34.27  | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3, simplifying
% 203.37/34.27  | |              with (127), (179) gives:
% 203.37/34.27  | |   (183)  all_52_30 = all_6_2
% 203.37/34.27  | | 
% 203.37/34.27  | | COMBINE_EQS: (133), (182) imply:
% 203.37/34.27  | |   (184)  all_56_3 = all_14_1
% 203.37/34.27  | | 
% 203.37/34.27  | | COMBINE_EQS: (29), (182) imply:
% 203.37/34.27  | |   (185)  all_58_9 = all_14_1
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (106), (182) imply:
% 203.37/34.27  | |   (186)   ~ (all_52_9 = all_14_1)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (17), (182) imply:
% 203.37/34.27  | |   (187)   ~ (all_52_17 = all_14_1)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (3), (182) imply:
% 203.37/34.27  | |   (188)   ~ (all_52_27 = all_14_1)
% 203.37/34.27  | | 
% 203.37/34.27  | | SIMP: (188) implies:
% 203.37/34.27  | |   (189)   ~ (all_52_27 = all_14_1)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (65), (182) imply:
% 203.37/34.27  | |   (190)   ~ (all_52_29 = all_14_1)
% 203.37/34.27  | | 
% 203.37/34.27  | | SIMP: (190) implies:
% 203.37/34.27  | |   (191)   ~ (all_52_29 = all_14_1)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (119), (182) imply:
% 203.37/34.27  | |   (192)   ~ (all_14_1 = all_6_2)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (176), (182) imply:
% 203.37/34.27  | |   (193)   ~ (all_14_1 = e3)
% 203.37/34.27  | | 
% 203.37/34.27  | | REDUCE: (170), (182) imply:
% 203.37/34.27  | |   (194)  op(all_14_1, all_14_1) = all_52_24
% 203.37/34.27  | | 
% 203.37/34.27  | | BETA: splitting (52) gives:
% 203.37/34.27  | | 
% 203.37/34.27  | | Case 1:
% 203.37/34.27  | | | 
% 203.37/34.27  | | |   (195)  all_56_13 = e3
% 203.37/34.27  | | | 
% 203.37/34.27  | | | REF_CLOSE: (159), (174), (195) are inconsistent by sub-proof #1201.
% 203.37/34.27  | | | 
% 203.37/34.27  | | Case 2:
% 203.37/34.27  | | | 
% 203.37/34.27  | | |   (196)   ~ (all_56_13 = e3)
% 203.37/34.27  | | |   (197)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.27  | | | 
% 203.37/34.27  | | | BETA: splitting (68) gives:
% 203.37/34.27  | | | 
% 203.37/34.27  | | | Case 1:
% 203.37/34.27  | | | | 
% 203.37/34.27  | | | |   (198)  all_56_14 = e3
% 203.37/34.27  | | | | 
% 203.37/34.27  | | | | REF_CLOSE: (131), (175), (198) are inconsistent by sub-proof #1286.
% 203.37/34.27  | | | | 
% 203.37/34.27  | | | Case 2:
% 203.37/34.27  | | | | 
% 203.37/34.27  | | | |   (199)   ~ (all_56_14 = e3)
% 203.37/34.27  | | | |   (200)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.37/34.27  | | | | 
% 203.37/34.27  | | | | BETA: splitting (120) gives:
% 203.37/34.27  | | | | 
% 203.37/34.27  | | | | Case 1:
% 203.37/34.27  | | | | | 
% 203.37/34.27  | | | | |   (201)  all_56_3 = e3
% 203.37/34.27  | | | | | 
% 203.37/34.27  | | | | | REF_CLOSE: (184), (193), (201) are inconsistent by sub-proof #1200.
% 203.37/34.27  | | | | | 
% 203.37/34.27  | | | | Case 2:
% 203.37/34.27  | | | | | 
% 203.37/34.27  | | | | |   (202)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.27  | | | | | 
% 203.37/34.27  | | | | | BETA: splitting (147) gives:
% 203.37/34.27  | | | | | 
% 203.37/34.27  | | | | | Case 1:
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | |   (203)  all_56_1 = e3
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | | REF_CLOSE: (6), (8), (11), (19), (35), (44), (47), (72), (74), (76),
% 203.37/34.27  | | | | | |            (78), (82), (91), (113), (124), (127), (137), (140),
% 203.37/34.27  | | | | | |            (142), (154), (160), (203) are inconsistent by sub-proof
% 203.37/34.27  | | | | | |            #527.
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | Case 2:
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | |   (204)   ~ (all_56_1 = e3)
% 203.37/34.27  | | | | | |   (205)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | | REDUCE: (137), (204) imply:
% 203.37/34.27  | | | | | |   (206)   ~ (all_52_9 = e3)
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | | BETA: splitting (105) gives:
% 203.37/34.27  | | | | | | 
% 203.37/34.27  | | | | | | Case 1:
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | |   (207)  all_58_1 = e3
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | | COMBINE_EQS: (9), (207) imply:
% 203.37/34.27  | | | | | | |   (208)  all_52_9 = e3
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | | REDUCE: (206), (208) imply:
% 203.37/34.27  | | | | | | |   (209)  $false
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | | CLOSE: (209) is inconsistent.
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | Case 2:
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | |   (210)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | | BETA: splitting (130) gives:
% 203.37/34.27  | | | | | | | 
% 203.37/34.27  | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | |   (211)  all_58_0 = e3
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | COMBINE_EQS: (19), (211) imply:
% 203.37/34.27  | | | | | | | |   (212)  all_6_2 = e3
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | REDUCE: (18), (212) imply:
% 203.37/34.27  | | | | | | | |   (213)   ~ (all_52_3 = e3)
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | REDUCE: (122), (212) imply:
% 203.37/34.27  | | | | | | | |   (214)   ~ (all_52_5 = e3)
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | REDUCE: (43), (212) imply:
% 203.37/34.27  | | | | | | | |   (215)   ~ (all_52_7 = e3)
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | REDUCE: (143), (212) imply:
% 203.37/34.27  | | | | | | | |   (216)   ~ (all_52_17 = e3)
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | BETA: splitting (150) gives:
% 203.37/34.27  | | | | | | | | 
% 203.37/34.27  | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | 
% 203.37/34.27  | | | | | | | | |   (217)  all_58_4 = e3
% 203.37/34.27  | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | REF_CLOSE: (166), (216), (217) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | |            #1302.
% 203.37/34.27  | | | | | | | | | 
% 203.37/34.27  | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | 
% 203.37/34.27  | | | | | | | | |   (218)   ~ (all_58_4 = e3)
% 203.37/34.27  | | | | | | | | |   (219)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.27  | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | BETA: splitting (47) gives:
% 203.37/34.27  | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | |   (220)  all_58_2 = e3
% 203.37/34.27  | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | REF_CLOSE: (78), (213), (220) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | | |            #1369.
% 203.37/34.27  | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | |   (221)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.27  | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | BETA: splitting (75) gives:
% 203.37/34.27  | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | |   (222)  all_58_6 = e3
% 203.37/34.27  | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | REF_CLOSE: (140), (214), (222) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | | | |            #1328.
% 203.37/34.27  | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | |   (223)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.27  | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | BETA: splitting (53) gives:
% 203.37/34.27  | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | |   (224)  all_56_2 = e3
% 203.37/34.27  | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | REF_CLOSE: (80), (216), (224) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | | | | |            #1327.
% 203.37/34.27  | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | |   (225)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.27  | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | BETA: splitting (48) gives:
% 203.37/34.27  | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | |   (226)  all_58_9 = e1
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | COMBINE_EQS: (185), (226) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (227)  all_14_1 = e1
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | SIMP: (227) implies:
% 203.37/34.27  | | | | | | | | | | | | |   (228)  all_14_1 = e1
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | REDUCE: (187), (228) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (229)   ~ (all_52_17 = e1)
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | REDUCE: (193), (228) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (230)   ~ (e3 = e1)
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | SIMP: (230) implies:
% 203.37/34.27  | | | | | | | | | | | | |   (231)   ~ (e3 = e1)
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | REDUCE: (194), (228) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (232)  op(e1, e1) = all_52_24
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | REDUCE: (24), (228) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (233)  op(e0, e1) = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_23, all_14_0, e1,
% 203.37/34.27  | | | | | | | | | | | | |              e0, simplifying with (45), (233) gives:
% 203.37/34.27  | | | | | | | | | | | | |   (234)  all_52_23 = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_24, e1,
% 203.37/34.27  | | | | | | | | | | | | |              e1, simplifying with (154), (232) gives:
% 203.37/34.27  | | | | | | | | | | | | |   (235)  all_52_24 = all_10_2
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | COMBINE_EQS: (131), (234) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (236)  all_56_14 = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | COMBINE_EQS: (4), (234) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (237)  all_58_14 = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | REDUCE: (162), (234) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (238)   ~ (all_52_17 = all_14_0)
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | BETA: splitting (200) gives:
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | |   (239)  all_56_14 = e2
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | REF_CLOSE: (168), (236), (239) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | | | | | | |            #526.
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | |   (240)  all_56_14 = e1 | all_56_14 = e0
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | |   (241)  all_56_14 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REF_CLOSE: (167), (236), (241) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | | | | | | | |            #525.
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | |   (242)  all_56_14 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | COMBINE_EQS: (236), (242) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (243)  all_14_0 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | SIMP: (243) implies:
% 203.37/34.27  | | | | | | | | | | | | | | |   (244)  all_14_0 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | COMBINE_EQS: (237), (244) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (245)  all_58_14 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REDUCE: (238), (244) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (246)   ~ (all_52_17 = e0)
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REDUCE: (167), (244) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (247)   ~ (e1 = e0)
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | |   (248)  all_56_2 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (248) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | |   (249)  all_52_17 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (249) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | |   (250)  all_58_4 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | REDUCE: (102), (249) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | |   (251)  op(e3, e1) = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (252)  all_56_6 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (252) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (253)  all_52_19 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | SIMP: (253) implies:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (254)  all_52_19 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | REDUCE: (108), (254) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (255)   ~ (all_10_2 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | SIMP: (255) implies:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (256)   ~ (all_10_2 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (257)  all_58_4 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (257) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (258)  e2 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | REDUCE: (57), (258) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (259)  $false
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (260)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |   (261)  all_58_5 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (111), (175), (219), (231), (256), (261) are
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1051.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |   (262)  all_58_8 = e1 | all_58_14 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (263)  all_58_8 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (263) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (264)  all_10_2 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (264) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (265)  op(e1, e1) = all_52_20
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (264) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (266)  op(e1, e1) = all_10_1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (264) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (267)  op(e1, e1) = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_1, all_52_20, e1,
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (265), (266) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (268)  all_52_20 = all_10_1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (54), (154), (256), (265), (267), (268) are
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #524.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (269)  all_58_14 = e1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (269) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (270)  e1 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (270) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (271)  $false
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (272)   ~ (all_56_6 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | REDUCE: (94), (272) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (273)   ~ (all_52_19 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (274)  all_58_3 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (274) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (275)  all_4_2 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | REDUCE: (101), (275) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (276)   ~ (all_52_13 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |   (277)  all_58_7 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (277) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |   (278)  all_52_13 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | REDUCE: (276), (278) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |   (279)  $false
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | |   (280)  all_58_8 = e3 | all_58_11 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (281)  all_58_8 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (281) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (282)  all_10_2 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (282) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (283)  op(e3, e1) = all_10_1
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_10_1, e1, e3,
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |              simplifying with (251), (283) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (284)  all_10_1 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (54), (104), (276), (284) are inconsistent by
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |            sub-proof #532.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (285)  all_58_11 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (285) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (286)  all_52_29 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (178), (286) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | |   (287)  $false
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | |   (288)  all_58_5 = e3 | all_58_10 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (136), (177), (273), (288) are inconsistent
% 203.37/34.27  | | | | | | | | | | | | | | | | | |            by sub-proof #1132.
% 203.37/34.27  | | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | |   (289)  all_56_2 = e1 | all_56_2 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | REF_CLOSE: (80), (229), (246), (289) are inconsistent by
% 203.37/34.27  | | | | | | | | | | | | | | | |            sub-proof #1307.
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | |   (290)   ~ (all_58_9 = e1)
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | REDUCE: (185), (290) imply:
% 203.37/34.27  | | | | | | | | | | | | |   (291)   ~ (all_14_1 = e1)
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | BETA: splitting (169) gives:
% 203.37/34.27  | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | |   (292)  all_56_10 = e3
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | COMBINE_EQS: (149), (292) imply:
% 203.37/34.27  | | | | | | | | | | | | | |   (293)  all_10_2 = e3
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | SIMP: (293) implies:
% 203.37/34.27  | | | | | | | | | | | | | |   (294)  all_10_2 = e3
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | REDUCE: (58), (294) imply:
% 203.37/34.27  | | | | | | | | | | | | | |   (295)   ~ (all_52_13 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | |   (296)  all_58_3 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | COMBINE_EQS: (157), (296) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (297)  all_4_2 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REDUCE: (90), (297) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (298)  op(e3, e2) = all_4_1
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_9, all_4_1, e2, e3,
% 203.37/34.27  | | | | | | | | | | | | | | |              simplifying with (141), (298) gives:
% 203.37/34.27  | | | | | | | | | | | | | | |   (299)  all_52_9 = all_4_1
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REDUCE: (206), (299) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (300)   ~ (all_4_1 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (11), (12), (13), (14), (15),
% 203.37/34.27  | | | | | | | | | | | | | | |            (18), (19), (22), (24), (27), (28), (30), (35),
% 203.37/34.27  | | | | | | | | | | | | | | |            (36), (39), (40), (42), (43), (44), (45), (47),
% 203.37/34.27  | | | | | | | | | | | | | | |            (48), (51), (55), (58), (59), (60), (64), (67),
% 203.37/34.27  | | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (78),
% 203.37/34.27  | | | | | | | | | | | | | | |            (82), (83), (84), (85), (88), (90), (91), (93),
% 203.37/34.27  | | | | | | | | | | | | | | |            (101), (104), (105), (108), (111), (113), (116),
% 203.37/34.27  | | | | | | | | | | | | | | |            (120), (122), (123), (124), (127), (130), (131),
% 203.37/34.27  | | | | | | | | | | | | | | |            (132), (136), (138), (140), (143), (144), (145),
% 203.37/34.27  | | | | | | | | | | | | | | |            (149), (150), (154), (155), (156), (157), (158),
% 203.37/34.27  | | | | | | | | | | | | | | |            (159), (160), (163), (164), (166), (169), (174),
% 203.37/34.27  | | | | | | | | | | | | | | |            (177), (178), (181), (184), (185), (186), (189),
% 203.37/34.27  | | | | | | | | | | | | | | |            (191), (192), (193), (194), (197), (200), (215),
% 203.37/34.27  | | | | | | | | | | | | | | |            (300) are inconsistent by sub-proof #538.
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | |   (301)  all_58_7 = e3 | all_58_13 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REF_CLOSE: (27), (67), (174), (295), (301) are inconsistent
% 203.37/34.27  | | | | | | | | | | | | | | |            by sub-proof #1298.
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | End of split
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | |   (302)   ~ (all_56_10 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | REDUCE: (149), (302) imply:
% 203.37/34.27  | | | | | | | | | | | | | |   (303)   ~ (all_10_2 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 203.37/34.27  | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | |   (304)  all_58_5 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | COMBINE_EQS: (136), (304) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (305)  all_52_19 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | SIMP: (305) implies:
% 203.37/34.27  | | | | | | | | | | | | | | |   (306)  all_52_19 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | REDUCE: (161), (306) imply:
% 203.37/34.27  | | | | | | | | | | | | | | |   (307)   ~ (all_4_2 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | SIMP: (307) implies:
% 203.37/34.27  | | | | | | | | | | | | | | |   (308)   ~ (all_4_2 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | |   (309)  all_56_5 = e3
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | REF_CLOSE: (37), (308), (309) are inconsistent by sub-proof
% 203.37/34.27  | | | | | | | | | | | | | | | |            #1319.
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | Case 2:
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | |   (310)   ~ (all_56_5 = e3)
% 203.37/34.27  | | | | | | | | | | | | | | | |   (311)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (312)  all_58_9 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (312) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (313)  all_14_1 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | SIMP: (313) implies:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (314)  all_14_1 = e2
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | REDUCE: (186), (314) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (315)   ~ (all_52_9 = e2)
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | REDUCE: (194), (314) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (316)  op(e2, e2) = all_52_24
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | REDUCE: (24), (314) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (317)  op(e0, e2) = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_15, all_14_0, e2,
% 203.37/34.27  | | | | | | | | | | | | | | | | |              e0, simplifying with (14), (317) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (318)  all_52_15 = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_4_2, all_52_24, e2, e2,
% 203.37/34.27  | | | | | | | | | | | | | | | | |              simplifying with (35), (316) gives:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (319)  all_52_24 = all_4_2
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (318) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (320)  all_56_13 = all_14_0
% 203.37/34.27  | | | | | | | | | | | | | | | | | 
% 203.37/34.27  | | | | | | | | | | | | | | | | | REDUCE: (39), (318) imply:
% 203.37/34.27  | | | | | | | | | | | | | | | | |   (321)   ~ (all_52_9 = all_14_0)
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | REDUCE: (138), (318) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | |   (322)   ~ (all_14_0 = all_4_2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | |   (323)  all_58_1 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (323) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | |   (324)  all_52_9 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | REDUCE: (315), (324) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | |   (325)  $false
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | |   (326)   ~ (all_58_1 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | |   (327)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | |   (328)  all_56_13 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (328) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | |   (329)  all_14_0 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | REDUCE: (168), (329) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | |   (330)  $false
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | |   (331)  all_56_13 = e1 | all_56_13 = e0
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (332)  all_56_13 = e1
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (332) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (333)  all_14_0 = e1
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (333) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (334)  $false
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (335)  all_56_13 = e0
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (335) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (336)  all_14_0 = e0
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (321), (336) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (337)   ~ (all_52_9 = e0)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (336) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (338)   ~ (all_4_2 = e0)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | |   (339)   ~ (all_4_2 = e0)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (340)  all_58_3 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (340) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (341)  all_4_2 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (308), (341) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (342)   ~ (e3 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | SIMP: (342) implies:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (343)   ~ (e3 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (341) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (344)  op(e2, e2) = all_52_10
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (341) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (345)  op(e2, e2) = all_4_1
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (341) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (346)  op(e2, e2) = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | |   (347)  all_56_1 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (347) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | |   (348)  all_52_9 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (315), (348) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | |   (349)  $false
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (349) is inconsistent.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | |   (350)  all_56_1 = e1 | all_56_1 = e0
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_4_1, all_52_10, e2, e2,
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (344), (345) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_52_10 = all_4_1
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_52_10, e2, e2,
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (344), (346) gives:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |   (352)  all_52_10 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (352) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |   (353)  all_4_1 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (353) implies:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_4_1 = e2
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (343), (344), (345), (354) are
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #722.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |   (355)   ~ (all_58_1 = e1)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (355) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |   (356)   ~ (all_52_9 = e1)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (337), (350), (356) are inconsistent by
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1334.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (357)   ~ (all_58_3 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (357) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |   (358)   ~ (all_4_2 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (121), (137), (205), (311), (315), (337),
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | |            (339), (358) are inconsistent by sub-proof #1311.
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | |   (359)   ~ (all_58_9 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | REDUCE: (185), (359) imply:
% 203.37/34.28  | | | | | | | | | | | | | | | | |   (360)   ~ (all_14_1 = e2)
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (24), (85), (181), (184), (194), (202),
% 203.37/34.28  | | | | | | | | | | | | | | | | |            (291), (360) are inconsistent by sub-proof #1181.
% 203.37/34.28  | | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | |   (361)  all_58_8 = e3 | all_58_14 = e3
% 203.37/34.28  | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | | REF_CLOSE: (4), (111), (175), (303), (361) are inconsistent
% 203.37/34.28  | | | | | | | | | | | | | | |            by sub-proof #1304.
% 203.37/34.28  | | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | |   (362)   ~ (all_58_0 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (19), (362) imply:
% 203.37/34.28  | | | | | | | |   (363)   ~ (all_6_2 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REF_CLOSE: (6), (8), (11), (19), (35), (44), (47), (72), (74),
% 203.37/34.28  | | | | | | | |            (76), (78), (82), (91), (113), (127), (140), (142),
% 203.37/34.28  | | | | | | | |            (154), (160), (363) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | |            #1362.
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | End of split
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | End of split
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | End of split
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | End of split
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | End of split
% 203.37/34.28  | | | 
% 203.37/34.28  | | End of split
% 203.37/34.28  | | 
% 203.37/34.28  | Case 2:
% 203.37/34.28  | | 
% 203.37/34.28  | |   (364)   ~ (all_56_15 = e3)
% 203.37/34.28  | |   (365)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.28  | | 
% 203.37/34.28  | | REDUCE: (46), (364) imply:
% 203.37/34.28  | |   (366)   ~ (all_14_2 = e3)
% 203.37/34.28  | | 
% 203.37/34.28  | | BETA: splitting (52) gives:
% 203.37/34.28  | | 
% 203.37/34.28  | | Case 1:
% 203.37/34.28  | | | 
% 203.37/34.28  | | |   (367)  all_56_13 = e3
% 203.37/34.28  | | | 
% 203.37/34.28  | | | COMBINE_EQS: (159), (367) imply:
% 203.37/34.28  | | |   (368)  all_52_15 = e3
% 203.37/34.28  | | | 
% 203.37/34.28  | | | SIMP: (368) implies:
% 203.37/34.28  | | |   (369)  all_52_15 = e3
% 203.37/34.28  | | | 
% 203.37/34.28  | | | COMBINE_EQS: (27), (369) imply:
% 203.37/34.28  | | |   (370)  all_58_13 = e3
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (15), (369) imply:
% 203.37/34.28  | | |   (371)   ~ (all_52_7 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (39), (369) imply:
% 203.37/34.28  | | |   (372)   ~ (all_52_9 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (125), (369) imply:
% 203.37/34.28  | | |   (373)   ~ (all_52_13 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (2), (369) imply:
% 203.37/34.28  | | |   (374)   ~ (all_52_23 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | SIMP: (374) implies:
% 203.37/34.28  | | |   (375)   ~ (all_52_23 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (95), (369) imply:
% 203.37/34.28  | | |   (376)   ~ (all_14_2 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (138), (369) imply:
% 203.37/34.28  | | |   (377)   ~ (all_4_2 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | SIMP: (377) implies:
% 203.37/34.28  | | |   (378)   ~ (all_4_2 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (63), (369) imply:
% 203.37/34.28  | | |   (379)  op(e3, e3) = all_52_14
% 203.37/34.28  | | | 
% 203.37/34.28  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_14, e3, e3,
% 203.37/34.28  | | |              simplifying with (127), (379) gives:
% 203.37/34.28  | | |   (380)  all_52_14 = all_6_2
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (12), (13), (16),
% 203.37/34.28  | | |            (17), (18), (19), (20), (21), (24), (25), (26), (28), (29),
% 203.37/34.28  | | |            (30), (31), (32), (34), (35), (36), (37), (38), (41), (42),
% 203.37/34.28  | | |            (43), (44), (46), (47), (48), (49), (50), (53), (54), (55),
% 203.37/34.28  | | |            (56), (57), (58), (59), (60), (61), (62), (64), (66), (67),
% 203.37/34.28  | | |            (69), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 203.37/34.28  | | |            (81), (82), (83), (86), (87), (88), (89), (91), (92), (93),
% 203.37/34.28  | | |            (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.37/34.28  | | |            (104), (106), (107), (108), (110), (111), (113), (114), (116),
% 203.37/34.28  | | |            (117), (118), (119), (121), (122), (123), (124), (126), (127),
% 203.37/34.28  | | |            (128), (129), (130), (132), (134), (135), (136), (137), (139),
% 203.37/34.28  | | |            (140), (142), (143), (145), (147), (148), (150), (151), (152),
% 203.37/34.28  | | |            (153), (154), (155), (157), (158), (160), (163), (164), (165),
% 203.37/34.28  | | |            (166), (168), (365), (366), (370), (371), (372), (373), (375),
% 203.37/34.28  | | |            (378) are inconsistent by sub-proof #519.
% 203.37/34.28  | | | 
% 203.37/34.28  | | Case 2:
% 203.37/34.28  | | | 
% 203.37/34.28  | | |   (381)   ~ (all_56_13 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REDUCE: (159), (381) imply:
% 203.37/34.28  | | |   (382)   ~ (all_52_15 = e3)
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.37/34.28  | | |            (13), (16), (17), (19), (20), (21), (22), (24), (27), (28),
% 203.37/34.28  | | |            (29), (30), (31), (33), (34), (35), (36), (38), (40), (41),
% 203.37/34.28  | | |            (42), (43), (44), (46), (47), (50), (51), (53), (56), (57),
% 203.37/34.28  | | |            (58), (59), (60), (61), (62), (65), (67), (69), (72), (74),
% 203.37/34.28  | | |            (75), (76), (77), (78), (80), (81), (82), (83), (86), (87),
% 203.37/34.28  | | |            (88), (90), (91), (92), (93), (97), (101), (103), (105), (106),
% 203.37/34.28  | | |            (107), (108), (109), (110), (111), (113), (114), (115), (116),
% 203.37/34.28  | | |            (118), (119), (121), (122), (124), (127), (128), (129), (130),
% 203.37/34.28  | | |            (134), (135), (136), (137), (139), (140), (141), (142), (146),
% 203.37/34.28  | | |            (147), (148), (151), (153), (154), (155), (156), (157), (160),
% 203.37/34.28  | | |            (162), (163), (164), (165), (166), (167), (365), (366), (382)
% 203.37/34.28  | | |            are inconsistent by sub-proof #742.
% 203.37/34.28  | | | 
% 203.37/34.28  | | End of split
% 203.37/34.28  | | 
% 203.37/34.28  | End of split
% 203.37/34.28  | 
% 203.37/34.28  End of proof
% 203.37/34.28  
% 203.37/34.28  Sub-proof #519 shows that the following formulas are inconsistent:
% 203.37/34.28  ----------------------------------------------------------------
% 203.37/34.28    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.37/34.28    (2)  all_58_14 = all_52_23
% 203.37/34.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.28    (4)   ~ (all_52_5 = all_52_13)
% 203.37/34.28    (5)  op(all_52_7, all_52_7) = e0
% 203.37/34.28    (6)  all_58_1 = all_52_9
% 203.37/34.28    (7)   ~ (all_52_9 = all_52_13)
% 203.37/34.28    (8)  op(all_52_5, all_52_5) = e1
% 203.37/34.28    (9)   ~ (e3 = e0)
% 203.37/34.28    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.28    (11)   ~ (all_52_3 = all_52_19)
% 203.37/34.28    (12)   ~ (all_52_17 = all_52_25)
% 203.37/34.28    (13)   ~ (all_4_2 = e3)
% 203.37/34.28    (14)   ~ (all_52_3 = all_6_2)
% 203.37/34.28    (15)  all_58_0 = all_6_2
% 203.37/34.28    (16)  op(all_14_2, e0) = all_14_1
% 203.37/34.28    (17)  all_56_4 = all_52_3
% 203.37/34.28    (18)  all_58_13 = e3
% 203.37/34.28    (19)  op(e0, all_14_1) = all_14_0
% 203.37/34.28    (20)  op(all_52_19, all_52_19) = all_52_18
% 203.37/34.28    (21)   ~ (all_52_27 = all_52_29)
% 203.37/34.28    (22)  op(all_10_2, all_10_2) = all_52_20
% 203.37/34.28    (23)  all_58_9 = all_52_25
% 203.37/34.28    (24)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.37/34.28    (25)   ~ (all_52_29 = all_14_2)
% 203.37/34.28    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.37/34.28    (27)  op(all_52_27, all_52_27) = all_52_26
% 203.37/34.28    (28)  op(e2, e2) = all_4_2
% 203.37/34.28    (29)  all_58_11 = all_52_29
% 203.37/34.28    (30)  all_56_5 = all_4_2
% 203.37/34.28    (31)   ~ (all_52_25 = all_14_2)
% 203.37/34.28    (32)   ~ (all_52_3 = all_52_27)
% 203.37/34.28    (33)  op(all_10_2, e1) = all_10_1
% 203.37/34.28    (34)   ~ (all_52_7 = all_6_2)
% 203.37/34.28    (35)  op(e0, e0) = all_14_2
% 203.37/34.28    (36)  all_56_15 = all_14_2
% 203.37/34.28    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.28    (38)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.37/34.28    (39)  op(e1, e0) = all_52_29
% 203.37/34.28    (40)  all_56_11 = all_52_29
% 203.37/34.28    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.28    (42)  op(e1, all_10_1) = e3
% 203.37/34.28    (43)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.37/34.28    (44)  all_56_9 = all_52_13
% 203.37/34.28    (45)   ~ (e2 = e1)
% 203.37/34.28    (46)   ~ (all_52_13 = all_10_2)
% 203.37/34.28    (47)   ~ (all_6_0 = e1)
% 203.37/34.28    (48)  all_58_10 = all_52_27
% 203.37/34.28    (49)  all_56_8 = all_52_5
% 203.37/34.28    (50)  op(all_52_9, all_52_9) = all_52_8
% 203.37/34.28    (51)   ~ (all_52_19 = all_52_23)
% 203.37/34.28    (52)   ~ (all_52_29 = all_10_2)
% 203.37/34.28    (53)  all_58_7 = all_52_13
% 203.37/34.28    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.37/34.28    (55)  op(all_6_2, all_6_2) = e3
% 203.37/34.28    (56)   ~ (all_52_5 = all_52_7)
% 203.37/34.28    (57)  all_58_12 = all_52_7
% 203.37/34.28    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.28    (59)   ~ (all_52_7 = e3)
% 203.37/34.28    (60)   ~ (all_52_7 = all_14_2)
% 203.37/34.28    (61)   ~ (all_14_2 = e0)
% 203.37/34.28    (62)  all_58_2 = all_52_3
% 203.37/34.28    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.37/34.28    (64)  all_56_2 = all_52_17
% 203.37/34.28    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.28    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.28    (67)  op(e3, all_6_1) = all_6_0
% 203.37/34.28    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.28    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.37/34.28    (70)   ~ (e2 = e0)
% 203.37/34.28    (71)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.28    (72)   ~ (all_52_23 = e3)
% 203.37/34.28    (73)  op(all_52_3, all_52_3) = e2
% 203.37/34.28    (74)   ~ (all_52_5 = all_52_29)
% 203.37/34.28    (75)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.28    (76)  all_56_6 = all_52_19
% 203.37/34.28    (77)   ~ (all_52_19 = all_52_27)
% 203.37/34.28    (78)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.28    (79)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.37/34.28    (80)   ~ (all_6_0 = e2)
% 203.37/34.28    (81)   ~ (all_52_9 = e3)
% 203.37/34.28    (82)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.28    (83)   ~ (all_52_13 = all_4_2)
% 203.37/34.28    (84)  op(e3, e1) = all_52_17
% 203.37/34.28    (85)  op(e0, e3) = all_52_7
% 203.37/34.28    (86)  op(e1, e2) = all_52_13
% 203.37/34.28    (87)   ~ (all_52_9 = all_52_25)
% 203.37/34.28    (88)  all_58_15 = all_14_2
% 203.37/34.28    (89)   ~ (all_52_19 = all_10_2)
% 203.37/34.28    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.28    (91)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.28    (92)  all_58_8 = all_10_2
% 203.37/34.28    (93)   ~ (all_52_5 = all_10_2)
% 203.37/34.28    (94)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.28    (95)  all_56_12 = all_52_7
% 203.37/34.28    (96)  op(all_52_17, all_52_17) = all_52_16
% 203.37/34.28    (97)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.28    (98)   ~ (all_52_25 = all_6_2)
% 203.37/34.28    (99)   ~ (all_52_9 = all_4_2)
% 203.37/34.28    (100)   ~ (all_52_5 = all_6_2)
% 203.37/34.28    (101)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.28    (102)   ~ (all_52_9 = all_6_2)
% 203.37/34.28    (103)  all_56_0 = all_6_2
% 203.37/34.28    (104)  op(e3, e3) = all_6_2
% 203.37/34.28    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.28    (106)   ~ (all_52_13 = e3)
% 203.37/34.28    (107)   ~ (all_52_27 = all_14_2)
% 203.37/34.28    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.37/34.28    (109)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.28    (110)   ~ (all_52_3 = all_52_7)
% 203.37/34.28    (111)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.28    (112)  all_58_5 = all_52_19
% 203.37/34.28    (113)  all_56_1 = all_52_9
% 203.37/34.28    (114)   ~ (all_52_27 = all_4_2)
% 203.37/34.28    (115)  all_58_6 = all_52_5
% 203.37/34.28    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.28    (117)   ~ (all_52_17 = all_6_2)
% 203.37/34.28    (118)   ~ (e1 = e0)
% 203.37/34.28    (119)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.28    (120)   ~ (all_52_9 = all_52_17)
% 203.37/34.28    (121)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.28    (122)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.28    (123)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.37/34.28    (124)  op(all_52_13, all_52_13) = all_52_12
% 203.37/34.28    (125)  op(e1, e1) = all_10_2
% 203.37/34.28    (126)   ~ (all_52_23 = all_10_2)
% 203.37/34.28    (127)  all_58_3 = all_4_2
% 203.37/34.28    (128)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.28    (129)   ~ (all_52_3 = all_4_2)
% 203.37/34.28    (130)  op(all_6_2, e3) = all_6_1
% 203.37/34.28    (131)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.37/34.28    (132)   ~ (all_52_13 = all_52_29)
% 203.37/34.28    (133)  all_58_4 = all_52_17
% 203.37/34.28    (134)   ~ (all_14_0 = e2)
% 203.37/34.28    (135)   ~ (all_14_2 = e3)
% 203.37/34.28  
% 203.37/34.28  Begin of proof
% 203.37/34.28  | 
% 203.37/34.28  | BETA: splitting (71) gives:
% 203.37/34.28  | 
% 203.37/34.28  | Case 1:
% 203.37/34.28  | | 
% 203.37/34.28  | |   (136)  all_56_5 = e3
% 203.37/34.28  | | 
% 203.37/34.28  | | REF_CLOSE: (13), (30), (136) are inconsistent by sub-proof #1319.
% 203.37/34.28  | | 
% 203.37/34.28  | Case 2:
% 203.37/34.28  | | 
% 203.37/34.28  | |   (137)   ~ (all_56_5 = e3)
% 203.37/34.28  | |   (138)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.28  | | 
% 203.37/34.28  | | BETA: splitting (119) gives:
% 203.37/34.28  | | 
% 203.37/34.28  | | Case 1:
% 203.37/34.28  | | | 
% 203.37/34.28  | | |   (139)  all_56_1 = e3
% 203.37/34.28  | | | 
% 203.37/34.28  | | | REF_CLOSE: (81), (113), (139) are inconsistent by sub-proof #1326.
% 203.37/34.28  | | | 
% 203.37/34.28  | | Case 2:
% 203.37/34.28  | | | 
% 203.37/34.28  | | |   (140)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.28  | | | 
% 203.37/34.28  | | | BETA: splitting (122) gives:
% 203.37/34.28  | | | 
% 203.37/34.28  | | | Case 1:
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | |   (141)  all_56_9 = e3
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | | REF_CLOSE: (44), (106), (141) are inconsistent by sub-proof #958.
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | Case 2:
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | |   (142)   ~ (all_56_9 = e3)
% 203.37/34.28  | | | |   (143)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | | BETA: splitting (10) gives:
% 203.37/34.28  | | | | 
% 203.37/34.28  | | | | Case 1:
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | |   (144)  all_56_12 = e3
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | | REF_CLOSE: (59), (95), (144) are inconsistent by sub-proof #1383.
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | Case 2:
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | |   (145)   ~ (all_56_12 = e3)
% 203.37/34.28  | | | | |   (146)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | | BETA: splitting (43) gives:
% 203.37/34.28  | | | | | 
% 203.37/34.28  | | | | | Case 1:
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | |   (147)  all_58_1 = e1
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (15), (18),
% 203.37/34.28  | | | | | |            (20), (22), (23), (26), (28), (29), (32), (33), (37),
% 203.37/34.28  | | | | | |            (38), (40), (41), (45), (47), (48), (51), (52), (53),
% 203.37/34.28  | | | | | |            (54), (55), (57), (58), (59), (62), (64), (66), (67),
% 203.37/34.28  | | | | | |            (68), (70), (72), (73), (74), (75), (77), (78), (79),
% 203.37/34.28  | | | | | |            (80), (82), (84), (87), (88), (89), (92), (93), (97),
% 203.37/34.28  | | | | | |            (98), (99), (100), (104), (105), (106), (107), (108),
% 203.37/34.28  | | | | | |            (111), (112), (115), (117), (118), (120), (121), (125),
% 203.37/34.28  | | | | | |            (126), (127), (129), (130), (133), (135), (147) are
% 203.37/34.28  | | | | | |            inconsistent by sub-proof #708.
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | Case 2:
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | |   (148)   ~ (all_58_1 = e1)
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | | REDUCE: (6), (148) imply:
% 203.37/34.28  | | | | | |   (149)   ~ (all_52_9 = e1)
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | | BETA: splitting (128) gives:
% 203.37/34.28  | | | | | | 
% 203.37/34.28  | | | | | | Case 1:
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | |   (150)  all_58_1 = e2
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | COMBINE_EQS: (6), (150) imply:
% 203.37/34.28  | | | | | | |   (151)  all_52_9 = e2
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | REDUCE: (87), (151) imply:
% 203.37/34.28  | | | | | | |   (152)   ~ (all_52_25 = e2)
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | SIMP: (152) implies:
% 203.37/34.28  | | | | | | |   (153)   ~ (all_52_25 = e2)
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | REDUCE: (99), (151) imply:
% 203.37/34.28  | | | | | | |   (154)   ~ (all_4_2 = e2)
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | SIMP: (154) implies:
% 203.37/34.28  | | | | | | |   (155)   ~ (all_4_2 = e2)
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | REDUCE: (50), (151) imply:
% 203.37/34.28  | | | | | | |   (156)  op(e2, e2) = all_52_8
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_52_8, e2, e2,
% 203.37/34.28  | | | | | | |              simplifying with (28), (156) gives:
% 203.37/34.28  | | | | | | |   (157)  all_52_8 = all_4_2
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | BETA: splitting (108) gives:
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | |   (158)  all_58_0 = e3
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | COMBINE_EQS: (15), (158) imply:
% 203.37/34.28  | | | | | | | |   (159)  all_6_2 = e3
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (14), (159) imply:
% 203.37/34.28  | | | | | | | |   (160)   ~ (all_52_3 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (100), (159) imply:
% 203.37/34.28  | | | | | | | |   (161)   ~ (all_52_5 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (98), (159) imply:
% 203.37/34.28  | | | | | | | |   (162)   ~ (all_52_25 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (130), (159) imply:
% 203.37/34.28  | | | | | | | |   (163)  op(e3, e3) = all_6_1
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (104), (159) imply:
% 203.37/34.28  | | | | | | | |   (164)  op(e3, e3) = e3
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_1, e3, e3,
% 203.37/34.28  | | | | | | | |              simplifying with (163), (164) gives:
% 203.37/34.28  | | | | | | | |   (165)  all_6_1 = e3
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (67), (165) imply:
% 203.37/34.28  | | | | | | | |   (166)  op(e3, e3) = all_6_0
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3,
% 203.37/34.28  | | | | | | | |              simplifying with (164), (166) gives:
% 203.37/34.28  | | | | | | | |   (167)  all_6_0 = e3
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (80), (167) imply:
% 203.37/34.28  | | | | | | | |   (168)   ~ (e3 = e2)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | BETA: splitting (58) gives:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | |   (169)  all_58_6 = e3
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REF_CLOSE: (115), (161), (169) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | | |            #1328.
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | |   (170)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | BETA: splitting (105) gives:
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | |   (171)  all_58_9 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REF_CLOSE: (23), (162), (171) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | | | |            #1300.
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | |   (172)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | BETA: splitting (37) gives:
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | |   (173)  all_58_2 = e3
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | REF_CLOSE: (62), (160), (173) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | | | | |            #1369.
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | |   (174)   ~ (all_58_2 = e3)
% 203.37/34.28  | | | | | | | | | | |   (175)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (9), (11), (13), (15), (16),
% 203.37/34.28  | | | | | | | | | | |            (17), (18), (19), (20), (21), (23), (24), (28),
% 203.37/34.28  | | | | | | | | | | |            (29), (35), (36), (37), (39), (44), (46), (48),
% 203.37/34.28  | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 203.37/34.28  | | | | | | | | | | |            (60), (61), (62), (63), (66), (69), (73), (75),
% 203.37/34.28  | | | | | | | | | | |            (76), (77), (79), (82), (83), (85), (88), (89),
% 203.37/34.28  | | | | | | | | | | |            (91), (92), (93), (94), (95), (100), (101), (104),
% 203.37/34.28  | | | | | | | | | | |            (106), (107), (110), (112), (115), (116), (118),
% 203.37/34.28  | | | | | | | | | | |            (124), (125), (126), (127), (129), (131), (132),
% 203.37/34.28  | | | | | | | | | | |            (134), (135), (143), (146), (153), (155), (158),
% 203.37/34.28  | | | | | | | | | | |            (160), (168), (170), (172), (175) are inconsistent
% 203.37/34.28  | | | | | | | | | | |            by sub-proof #622.
% 203.37/34.28  | | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | End of split
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | |   (176)   ~ (all_58_0 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REDUCE: (15), (176) imply:
% 203.37/34.28  | | | | | | | |   (177)   ~ (all_6_2 = e3)
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REF_CLOSE: (3), (5), (8), (15), (28), (35), (37), (55), (57),
% 203.37/34.28  | | | | | | | |            (60), (62), (66), (73), (93), (104), (115), (116),
% 203.37/34.28  | | | | | | | |            (125), (129), (177) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | |            #1362.
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | End of split
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | Case 2:
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | |   (178)   ~ (all_58_1 = e2)
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | REDUCE: (6), (178) imply:
% 203.37/34.28  | | | | | | |   (179)   ~ (all_52_9 = e2)
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | BETA: splitting (140) gives:
% 203.37/34.28  | | | | | | | 
% 203.37/34.28  | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | |   (180)  all_56_1 = e2
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | REF_CLOSE: (113), (179), (180) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | |            #1194.
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | |   (181)   ~ (all_56_1 = e2)
% 203.37/34.28  | | | | | | | |   (182)  all_56_1 = e1 | all_56_1 = e0
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | BETA: splitting (182) gives:
% 203.37/34.28  | | | | | | | | 
% 203.37/34.28  | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | |   (183)  all_56_1 = e1
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REF_CLOSE: (113), (149), (183) are inconsistent by sub-proof
% 203.37/34.28  | | | | | | | | |            #1061.
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | Case 2:
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | |   (184)  all_56_1 = e0
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | COMBINE_EQS: (113), (184) imply:
% 203.37/34.28  | | | | | | | | |   (185)  all_52_9 = e0
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | SIMP: (185) implies:
% 203.37/34.28  | | | | | | | | |   (186)  all_52_9 = e0
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | COMBINE_EQS: (6), (186) imply:
% 203.37/34.28  | | | | | | | | |   (187)  all_58_1 = e0
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (120), (186) imply:
% 203.37/34.28  | | | | | | | | |   (188)   ~ (all_52_17 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | SIMP: (188) implies:
% 203.37/34.28  | | | | | | | | |   (189)   ~ (all_52_17 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (87), (186) imply:
% 203.37/34.28  | | | | | | | | |   (190)   ~ (all_52_25 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | SIMP: (190) implies:
% 203.37/34.28  | | | | | | | | |   (191)   ~ (all_52_25 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (102), (186) imply:
% 203.37/34.28  | | | | | | | | |   (192)   ~ (all_6_2 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | SIMP: (192) implies:
% 203.37/34.28  | | | | | | | | |   (193)   ~ (all_6_2 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (99), (186) imply:
% 203.37/34.28  | | | | | | | | |   (194)   ~ (all_4_2 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | SIMP: (194) implies:
% 203.37/34.28  | | | | | | | | |   (195)   ~ (all_4_2 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (179), (186) imply:
% 203.37/34.28  | | | | | | | | |   (196)   ~ (e2 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (149), (186) imply:
% 203.37/34.28  | | | | | | | | |   (197)   ~ (e1 = e0)
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | REDUCE: (50), (186) imply:
% 203.37/34.28  | | | | | | | | |   (198)  op(e0, e0) = all_52_8
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_8, e0, e0,
% 203.37/34.28  | | | | | | | | |              simplifying with (35), (198) gives:
% 203.37/34.28  | | | | | | | | |   (199)  all_52_8 = all_14_2
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | BETA: splitting (123) gives:
% 203.37/34.28  | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | Case 1:
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | |   (200)  all_56_0 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | COMBINE_EQS: (103), (200) imply:
% 203.37/34.28  | | | | | | | | | |   (201)  all_6_2 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | SIMP: (201) implies:
% 203.37/34.28  | | | | | | | | | |   (202)  all_6_2 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | COMBINE_EQS: (15), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (203)  all_58_0 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (14), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (204)   ~ (all_52_3 = e3)
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (100), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (205)   ~ (all_52_5 = e3)
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (117), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (206)   ~ (all_52_17 = e3)
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (98), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (207)   ~ (all_52_25 = e3)
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (130), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (208)  op(e3, e3) = all_6_1
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (104), (202) imply:
% 203.37/34.28  | | | | | | | | | |   (209)  op(e3, e3) = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_1, e3, e3,
% 203.37/34.28  | | | | | | | | | |              simplifying with (208), (209) gives:
% 203.37/34.28  | | | | | | | | | |   (210)  all_6_1 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | REDUCE: (67), (210) imply:
% 203.37/34.28  | | | | | | | | | |   (211)  op(e3, e3) = all_6_0
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.28  | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3,
% 203.37/34.28  | | | | | | | | | |              simplifying with (209), (211) gives:
% 203.37/34.28  | | | | | | | | | |   (212)  all_6_0 = e3
% 203.37/34.28  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REDUCE: (80), (212) imply:
% 203.37/34.29  | | | | | | | | | |   (213)   ~ (e3 = e2)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | BETA: splitting (41) gives:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | |   (214)  all_56_2 = e3
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | REF_CLOSE: (64), (206), (214) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | |            #1327.
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | |   (215)   ~ (all_56_2 = e3)
% 203.37/34.29  | | | | | | | | | | |   (216)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | BETA: splitting (105) gives:
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | |   (217)  all_58_9 = e3
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | REF_CLOSE: (23), (207), (217) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | |            #1300.
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | |   (218)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | BETA: splitting (121) gives:
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | |   (219)  all_58_4 = e3
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | REF_CLOSE: (133), (206), (219) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | |            #1302.
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | |   (220)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | |   (221)  all_58_2 = e3
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | REF_CLOSE: (62), (204), (221) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | |            #1369.
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | |   (222)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | |   (223)  all_56_8 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | REF_CLOSE: (49), (205), (223) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | |            #1325.
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | |   (224)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | |   (225)  all_56_6 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (225) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | |   (226)  all_52_19 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | |   (227)  all_52_19 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | REDUCE: (77), (227) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | |   (228)   ~ (all_52_27 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | |   (229)   ~ (all_52_27 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | |   (230)  all_58_10 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (229), (230) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | |            #1301.
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | |   (231)  all_58_11 = e3 | all_58_15 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (232)  all_58_11 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (232) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (233)  all_52_29 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | SIMP: (233) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (234)  all_52_29 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | REDUCE: (39), (234) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (235)  op(e1, e0) = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (236)  all_58_9 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (191), (236) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |            #523.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (237)  all_58_10 = e0 | all_58_11 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (238)  all_58_10 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (238) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (239)  all_52_27 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (240)  all_52_27 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (240) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (241)   ~ (all_14_2 = e0)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (229), (240) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (242)   ~ (e3 = e0)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (240) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (243)  op(e0, e0) = all_52_26
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_26, e0,
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (35), (243) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (244)  all_52_26 = all_14_2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |   (245)  all_58_9 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (245) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |   (246)  all_52_25 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (246) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |   (247)   ~ (all_14_2 = e2)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (16), (19), (35), (36), (60), (61),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |            (85), (91), (95), (134), (146), (235), (247) are
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #759.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |   (248)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (249)  all_58_10 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (70), (232), (237), (249) are inconsistent by
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #522.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (250)  all_58_11 = e2 | all_58_15 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_58_11 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (213), (232), (251) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | |            #998.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_15 = e2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (18), (35), (57), (60), (75),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | |            (82), (88), (95), (118), (125), (126), (146),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | |            (252) are inconsistent by sub-proof #621.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (253)  all_58_11 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (232), (253) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |            #863.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (254)  all_58_15 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (254) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (255)  all_14_2 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | REDUCE: (135), (255) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (256)  $false
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | |   (257)   ~ (all_56_6 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | REDUCE: (76), (257) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | |   (258)   ~ (all_52_19 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | |   (259)  all_58_5 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (258), (259) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | |            #1279.
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | |   (260)  all_58_8 = e3 | all_58_14 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (261)  all_58_3 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (261) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (262)  all_4_2 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | REDUCE: (13), (262) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (263)  $false
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | |   (264)  all_58_5 = e3 | all_58_10 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (265)  all_58_8 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (265) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (266)  all_10_2 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (267)  all_10_2 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | REDUCE: (33), (267) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (268)  op(e3, e1) = all_10_1
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (269)  all_58_5 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (258), (269) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |            #1279.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (270)  all_58_10 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (270) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (271)  all_52_27 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (272)  all_52_27 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (272) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (273)   ~ (all_52_29 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | SIMP: (273) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (274)   ~ (all_52_29 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (272) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | |   (275)   ~ (all_4_2 = e3)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |   (276)  all_58_9 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (191), (276) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |            #523.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | |   (277)  all_58_10 = e0 | all_58_11 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_10 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (270), (278) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            #750.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (279)  all_58_11 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (279) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (280)  all_52_29 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | SIMP: (280) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (281)  all_52_29 = e0
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (281) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (282)   ~ (e3 = e0)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (281) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (283)  op(e0, e0) = all_52_28
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_28, e0,
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (35), (283) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (284)  all_52_28 = all_14_2
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1,
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (84), (268) gives:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (285)  all_52_17 = all_10_1
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (285) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (286)  all_56_2 = all_10_1
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (285) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (287)  all_58_4 = all_10_1
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (285) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (288)   ~ (all_52_25 = all_10_1)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (289)   ~ (all_52_25 = all_10_1)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (285) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (290)   ~ (all_10_1 = e0)
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (285) imply:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |   (291)  op(all_10_1, all_10_1) = all_52_16
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (8), (9), (13), (23), (25), (29),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            (30), (31), (35), (36), (42), (44), (49), (56),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            (60), (65), (70), (74), (83), (86), (91), (94),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            (95), (97), (101), (106), (109), (111), (115),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            (132), (138), (143), (146), (187), (195), (198),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            (203), (213), (216), (224), (270), (277), (286),
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            (287), (289), (290), (291) are inconsistent by
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #520.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |   (292)  all_58_14 = e3
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (72), (292) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | | | | | | | | |            #1305.
% 203.37/34.29  | | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | |   (293)   ~ (all_56_0 = e3)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REDUCE: (103), (293) imply:
% 203.37/34.29  | | | | | | | | | |   (294)   ~ (all_6_2 = e3)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REF_CLOSE: (3), (5), (8), (15), (28), (35), (37), (55), (57),
% 203.37/34.29  | | | | | | | | | |            (60), (62), (66), (73), (93), (104), (115), (116),
% 203.37/34.29  | | | | | | | | | |            (125), (129), (294) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | |            #1362.
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | End of split
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | End of split
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | End of split
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | End of split
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | End of split
% 203.37/34.29  | | | 
% 203.37/34.29  | | End of split
% 203.37/34.29  | | 
% 203.37/34.29  | End of split
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #520 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.29    (2)   ~ (all_52_5 = all_52_13)
% 203.37/34.29    (3)  all_58_1 = e0
% 203.37/34.29    (4)  op(all_10_1, all_10_1) = all_52_16
% 203.37/34.29    (5)  op(all_52_7, all_52_7) = e0
% 203.37/34.29    (6)  op(all_52_5, all_52_5) = e1
% 203.37/34.29    (7)   ~ (e3 = e0)
% 203.37/34.29    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.37/34.29    (9)   ~ (all_4_2 = e3)
% 203.37/34.29    (10)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.29    (11)   ~ (all_4_2 = e0)
% 203.37/34.29    (12)  all_58_9 = all_52_25
% 203.37/34.29    (13)   ~ (all_52_29 = all_14_2)
% 203.37/34.29    (14)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.29    (15)  all_58_11 = all_52_29
% 203.37/34.29    (16)  all_56_5 = all_4_2
% 203.37/34.29    (17)   ~ (all_52_25 = all_14_2)
% 203.37/34.29    (18)  all_58_4 = all_10_1
% 203.37/34.29    (19)  op(e0, e0) = all_14_2
% 203.37/34.29    (20)  all_56_15 = all_14_2
% 203.37/34.29    (21)  op(e1, all_10_1) = e3
% 203.37/34.29    (22)   ~ (all_52_25 = all_10_1)
% 203.37/34.29    (23)  all_56_9 = all_52_13
% 203.37/34.29    (24)   ~ (all_10_1 = e0)
% 203.37/34.29    (25)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.29    (26)  all_56_8 = all_52_5
% 203.37/34.29    (27)   ~ (all_52_5 = all_52_7)
% 203.37/34.29    (28)   ~ (all_52_7 = all_14_2)
% 203.37/34.29    (29)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.29    (30)   ~ (e2 = e0)
% 203.37/34.29    (31)   ~ (all_52_5 = all_52_29)
% 203.37/34.29    (32)  all_58_10 = e0 | all_58_11 = e0
% 203.37/34.29    (33)   ~ (all_52_13 = all_4_2)
% 203.37/34.29    (34)  all_58_0 = e3
% 203.37/34.29    (35)  op(e1, e2) = all_52_13
% 203.37/34.29    (36)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.29    (37)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.29    (38)  all_56_12 = all_52_7
% 203.37/34.29    (39)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.29    (40)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.29    (41)  all_56_2 = all_10_1
% 203.37/34.29    (42)  all_58_10 = e3
% 203.37/34.29    (43)   ~ (all_52_13 = e3)
% 203.37/34.29    (44)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.29    (45)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.29    (46)  all_58_6 = all_52_5
% 203.37/34.29    (47)  op(e0, e0) = all_52_8
% 203.37/34.29    (48)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.29    (49)   ~ (e3 = e2)
% 203.37/34.29    (50)   ~ (all_52_13 = all_52_29)
% 203.37/34.29  
% 203.37/34.29  Begin of proof
% 203.37/34.29  | 
% 203.37/34.29  | BETA: splitting (32) gives:
% 203.37/34.29  | 
% 203.37/34.29  | Case 1:
% 203.37/34.29  | | 
% 203.37/34.29  | |   (51)  all_58_10 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | REF_CLOSE: (7), (42), (51) are inconsistent by sub-proof #750.
% 203.37/34.29  | | 
% 203.37/34.29  | Case 2:
% 203.37/34.29  | | 
% 203.37/34.29  | |   (52)  all_58_11 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | COMBINE_EQS: (15), (52) imply:
% 203.37/34.29  | |   (53)  all_52_29 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | SIMP: (53) implies:
% 203.37/34.29  | |   (54)  all_52_29 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | REDUCE: (31), (54) imply:
% 203.37/34.29  | |   (55)   ~ (all_52_5 = e0)
% 203.37/34.29  | | 
% 203.37/34.29  | | REDUCE: (50), (54) imply:
% 203.37/34.29  | |   (56)   ~ (all_52_13 = e0)
% 203.37/34.29  | | 
% 203.37/34.29  | | REDUCE: (13), (54) imply:
% 203.37/34.29  | |   (57)   ~ (all_14_2 = e0)
% 203.37/34.29  | | 
% 203.37/34.29  | | SIMP: (57) implies:
% 203.37/34.29  | |   (58)   ~ (all_14_2 = e0)
% 203.37/34.29  | | 
% 203.37/34.29  | | REDUCE: (37), (54) imply:
% 203.37/34.29  | |   (59)  op(e0, e0) = all_52_28
% 203.37/34.29  | | 
% 203.37/34.29  | | GROUND_INST: instantiating (1) with all_14_2, all_52_8, e0, e0, simplifying
% 203.37/34.29  | |              with (19), (47) gives:
% 203.37/34.29  | |   (60)  all_52_8 = all_14_2
% 203.37/34.29  | | 
% 203.37/34.29  | | GROUND_INST: instantiating (1) with all_52_28, all_52_8, e0, e0, simplifying
% 203.37/34.29  | |              with (47), (59) gives:
% 203.37/34.29  | |   (61)  all_52_8 = all_52_28
% 203.37/34.29  | | 
% 203.37/34.29  | | COMBINE_EQS: (60), (61) imply:
% 203.37/34.29  | |   (62)  all_52_28 = all_14_2
% 203.37/34.29  | | 
% 203.37/34.29  | | BETA: splitting (29) gives:
% 203.37/34.29  | | 
% 203.37/34.29  | | Case 1:
% 203.37/34.29  | | | 
% 203.37/34.29  | | |   (63)  all_58_0 = e2
% 203.37/34.29  | | | 
% 203.37/34.29  | | | COMBINE_EQS: (34), (63) imply:
% 203.37/34.29  | | |   (64)  e3 = e2
% 203.37/34.29  | | | 
% 203.37/34.29  | | | REDUCE: (49), (64) imply:
% 203.37/34.29  | | |   (65)  $false
% 203.37/34.29  | | | 
% 203.37/34.29  | | | CLOSE: (65) is inconsistent.
% 203.37/34.29  | | | 
% 203.37/34.29  | | Case 2:
% 203.37/34.29  | | | 
% 203.37/34.29  | | |   (66)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.29  | | | 
% 203.37/34.29  | | | BETA: splitting (40) gives:
% 203.37/34.29  | | | 
% 203.37/34.29  | | | Case 1:
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | |   (67)  all_58_9 = e2
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | COMBINE_EQS: (12), (67) imply:
% 203.37/34.29  | | | |   (68)  all_52_25 = e2
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | REDUCE: (17), (68) imply:
% 203.37/34.29  | | | |   (69)   ~ (all_14_2 = e2)
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | SIMP: (69) implies:
% 203.37/34.29  | | | |   (70)   ~ (all_14_2 = e2)
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | REDUCE: (22), (68) imply:
% 203.37/34.29  | | | |   (71)   ~ (all_10_1 = e2)
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | SIMP: (71) implies:
% 203.37/34.29  | | | |   (72)   ~ (all_10_1 = e2)
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | BETA: splitting (36) gives:
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | Case 1:
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | |   (73)  all_56_15 = e2
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | | REF_CLOSE: (20), (70), (73) are inconsistent by sub-proof #762.
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | Case 2:
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | |   (74)  all_56_15 = e1 | all_56_15 = e0
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | | BETA: splitting (48) gives:
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | | Case 1:
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | |   (75)  all_56_2 = e2
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | | REF_CLOSE: (41), (72), (75) are inconsistent by sub-proof #815.
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | Case 2:
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | |   (76)  all_56_2 = e1 | all_56_2 = e0
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | | BETA: splitting (76) gives:
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | | Case 1:
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | |   (77)  all_56_2 = e1
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | COMBINE_EQS: (41), (77) imply:
% 203.37/34.29  | | | | | | |   (78)  all_10_1 = e1
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | SIMP: (78) implies:
% 203.37/34.29  | | | | | | |   (79)  all_10_1 = e1
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | REDUCE: (4), (79) imply:
% 203.37/34.29  | | | | | | |   (80)  op(e1, e1) = all_52_16
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | REDUCE: (21), (79) imply:
% 203.37/34.29  | | | | | | |   (81)  op(e1, e1) = e3
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | BETA: splitting (74) gives:
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | |   (82)  all_56_15 = e1
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | COMBINE_EQS: (20), (82) imply:
% 203.37/34.29  | | | | | | | |   (83)  all_14_2 = e1
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | REDUCE: (28), (83) imply:
% 203.37/34.29  | | | | | | | |   (84)   ~ (all_52_7 = e1)
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | REDUCE: (45), (83) imply:
% 203.37/34.29  | | | | | | | |   (85)  op(e1, e1) = all_52_30
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | GROUND_INST: instantiating (1) with e3, all_52_16, e1, e1,
% 203.37/34.29  | | | | | | | |              simplifying with (80), (81) gives:
% 203.37/34.29  | | | | | | | |   (86)  all_52_16 = e3
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | GROUND_INST: instantiating (1) with all_52_30, all_52_16, e1,
% 203.37/34.29  | | | | | | | |              e1, simplifying with (80), (85) gives:
% 203.37/34.29  | | | | | | | |   (87)  all_52_16 = all_52_30
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | COMBINE_EQS: (86), (87) imply:
% 203.37/34.29  | | | | | | | |   (88)  all_52_30 = e3
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | BETA: splitting (39) gives:
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | |   (89)  all_58_6 = e1
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | COMBINE_EQS: (46), (89) imply:
% 203.37/34.29  | | | | | | | | |   (90)  all_52_5 = e1
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | REDUCE: (2), (90) imply:
% 203.37/34.29  | | | | | | | | |   (91)   ~ (all_52_13 = e1)
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | SIMP: (91) implies:
% 203.37/34.29  | | | | | | | | |   (92)   ~ (all_52_13 = e1)
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | REDUCE: (6), (90) imply:
% 203.37/34.29  | | | | | | | | |   (93)  op(e1, e1) = e1
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | BETA: splitting (8) gives:
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | |   (94)  all_56_9 = e2
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | COMBINE_EQS: (23), (94) imply:
% 203.37/34.29  | | | | | | | | | |   (95)  all_52_13 = e2
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | SIMP: (95) implies:
% 203.37/34.29  | | | | | | | | | |   (96)  all_52_13 = e2
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REDUCE: (33), (96) imply:
% 203.37/34.29  | | | | | | | | | |   (97)   ~ (all_4_2 = e2)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | SIMP: (97) implies:
% 203.37/34.29  | | | | | | | | | |   (98)   ~ (all_4_2 = e2)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | BETA: splitting (10) gives:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | |   (99)  all_56_5 = e2
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | REF_CLOSE: (16), (98), (99) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | |            #1315.
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | |   (100)  all_56_5 = e1 | all_56_5 = e0
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | BETA: splitting (100) gives:
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | |   (101)  all_56_5 = e1
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | COMBINE_EQS: (16), (101) imply:
% 203.37/34.29  | | | | | | | | | | | |   (102)  all_4_2 = e1
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | SIMP: (102) implies:
% 203.37/34.29  | | | | | | | | | | | |   (103)  all_4_2 = e1
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | REDUCE: (9), (103) imply:
% 203.37/34.29  | | | | | | | | | | | |   (104)   ~ (e3 = e1)
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | SIMP: (104) implies:
% 203.37/34.29  | | | | | | | | | | | |   (105)   ~ (e3 = e1)
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | REDUCE: (44), (103) imply:
% 203.37/34.29  | | | | | | | | | | | |   (106)  op(e1, e1) = all_52_10
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | GROUND_INST: instantiating (1) with e3, all_52_10, e1, e1,
% 203.37/34.29  | | | | | | | | | | | |              simplifying with (81), (106) gives:
% 203.37/34.29  | | | | | | | | | | | |   (107)  all_52_10 = e3
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | GROUND_INST: instantiating (1) with e1, all_52_10, e1, e1,
% 203.37/34.29  | | | | | | | | | | | |              simplifying with (93), (106) gives:
% 203.37/34.29  | | | | | | | | | | | |   (108)  all_52_10 = e1
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | COMBINE_EQS: (107), (108) imply:
% 203.37/34.29  | | | | | | | | | | | |   (109)  e3 = e1
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | REDUCE: (105), (109) imply:
% 203.37/34.29  | | | | | | | | | | | |   (110)  $false
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | |   (111)  all_56_5 = e0
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | | REF_CLOSE: (11), (16), (111) are inconsistent by sub-proof
% 203.37/34.29  | | | | | | | | | | | |            #1313.
% 203.37/34.29  | | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | |   (112)  all_56_9 = e1 | all_56_9 = e0
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REF_CLOSE: (23), (56), (92), (112) are inconsistent by
% 203.37/34.29  | | | | | | | | | |            sub-proof #1185.
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | |   (113)   ~ (all_58_6 = e1)
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | REDUCE: (46), (113) imply:
% 203.37/34.29  | | | | | | | | |   (114)   ~ (all_52_5 = e1)
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | BETA: splitting (25) gives:
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | Case 1:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | |   (115)  all_56_8 = e2
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | COMBINE_EQS: (26), (115) imply:
% 203.37/34.29  | | | | | | | | | |   (116)  all_52_5 = e2
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REDUCE: (27), (116) imply:
% 203.37/34.29  | | | | | | | | | |   (117)   ~ (all_52_7 = e2)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | SIMP: (117) implies:
% 203.37/34.29  | | | | | | | | | |   (118)   ~ (all_52_7 = e2)
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REF_CLOSE: (1), (5), (14), (19), (28), (38), (84), (118) are
% 203.37/34.29  | | | | | | | | | |            inconsistent by sub-proof #1176.
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | |   (119)  all_56_8 = e1 | all_56_8 = e0
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | | REF_CLOSE: (26), (55), (114), (119) are inconsistent by
% 203.37/34.29  | | | | | | | | | |            sub-proof #1020.
% 203.37/34.29  | | | | | | | | | | 
% 203.37/34.29  | | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | | 
% 203.37/34.29  | | | | | | | | End of split
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | Case 2:
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | |   (120)  all_56_15 = e0
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | COMBINE_EQS: (20), (120) imply:
% 203.37/34.29  | | | | | | | |   (121)  all_14_2 = e0
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | REDUCE: (58), (121) imply:
% 203.37/34.29  | | | | | | | |   (122)  $false
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | | CLOSE: (122) is inconsistent.
% 203.37/34.29  | | | | | | | | 
% 203.37/34.29  | | | | | | | End of split
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | Case 2:
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | |   (123)  all_56_2 = e0
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | | REF_CLOSE: (24), (41), (123) are inconsistent by sub-proof #809.
% 203.37/34.29  | | | | | | | 
% 203.37/34.29  | | | | | | End of split
% 203.37/34.29  | | | | | | 
% 203.37/34.29  | | | | | End of split
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | End of split
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | Case 2:
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | |   (124)   ~ (all_58_9 = e2)
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | REDUCE: (12), (124) imply:
% 203.37/34.29  | | | |   (125)   ~ (all_52_25 = e2)
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | BETA: splitting (66) gives:
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | | Case 1:
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | |   (126)  all_58_1 = e2
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | | REF_CLOSE: (3), (30), (126) are inconsistent by sub-proof #1272.
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | Case 2:
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | |   (127)  all_58_4 = e2 | all_58_9 = e2
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | | REF_CLOSE: (1), (12), (18), (21), (35), (43), (125), (127) are
% 203.37/34.29  | | | | |            inconsistent by sub-proof #521.
% 203.37/34.29  | | | | | 
% 203.37/34.29  | | | | End of split
% 203.37/34.29  | | | | 
% 203.37/34.29  | | | End of split
% 203.37/34.29  | | | 
% 203.37/34.29  | | End of split
% 203.37/34.29  | | 
% 203.37/34.29  | End of split
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #521 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.29    (2)  all_58_9 = all_52_25
% 203.37/34.29    (3)  all_58_4 = all_10_1
% 203.37/34.29    (4)  op(e1, all_10_1) = e3
% 203.37/34.29    (5)  op(e1, e2) = all_52_13
% 203.37/34.29    (6)  all_58_4 = e2 | all_58_9 = e2
% 203.37/34.29    (7)   ~ (all_52_25 = e2)
% 203.37/34.29    (8)   ~ (all_52_13 = e3)
% 203.37/34.29  
% 203.37/34.29  Begin of proof
% 203.37/34.29  | 
% 203.37/34.29  | BETA: splitting (6) gives:
% 203.37/34.29  | 
% 203.37/34.29  | Case 1:
% 203.37/34.29  | | 
% 203.37/34.29  | |   (9)  all_58_4 = e2
% 203.37/34.29  | | 
% 203.37/34.29  | | COMBINE_EQS: (3), (9) imply:
% 203.37/34.29  | |   (10)  all_10_1 = e2
% 203.37/34.29  | | 
% 203.37/34.29  | | REF_CLOSE: (1), (4), (5), (8), (10) are inconsistent by sub-proof #532.
% 203.37/34.29  | | 
% 203.37/34.29  | Case 2:
% 203.37/34.29  | | 
% 203.37/34.29  | |   (11)  all_58_9 = e2
% 203.37/34.29  | | 
% 203.37/34.29  | | COMBINE_EQS: (2), (11) imply:
% 203.37/34.29  | |   (12)  all_52_25 = e2
% 203.37/34.29  | | 
% 203.37/34.29  | | REDUCE: (7), (12) imply:
% 203.37/34.29  | |   (13)  $false
% 203.37/34.29  | | 
% 203.37/34.29  | | CLOSE: (13) is inconsistent.
% 203.37/34.29  | | 
% 203.37/34.29  | End of split
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #522 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.29    (1)   ~ (e3 = e0)
% 203.37/34.29    (2)  all_58_10 = e2
% 203.37/34.29    (3)  all_58_11 = e3
% 203.37/34.29    (4)   ~ (e2 = e0)
% 203.37/34.29    (5)  all_58_10 = e0 | all_58_11 = e0
% 203.37/34.29  
% 203.37/34.29  Begin of proof
% 203.37/34.29  | 
% 203.37/34.29  | BETA: splitting (5) gives:
% 203.37/34.29  | 
% 203.37/34.29  | Case 1:
% 203.37/34.29  | | 
% 203.37/34.29  | |   (6)  all_58_10 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | COMBINE_EQS: (2), (6) imply:
% 203.37/34.29  | |   (7)  e2 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | SIMP: (7) implies:
% 203.37/34.29  | |   (8)  e2 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | REDUCE: (4), (8) imply:
% 203.37/34.29  | |   (9)  $false
% 203.37/34.29  | | 
% 203.37/34.29  | | CLOSE: (9) is inconsistent.
% 203.37/34.29  | | 
% 203.37/34.29  | Case 2:
% 203.37/34.29  | | 
% 203.37/34.29  | |   (10)  all_58_11 = e0
% 203.37/34.29  | | 
% 203.37/34.29  | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #863.
% 203.37/34.29  | | 
% 203.37/34.29  | End of split
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #523 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.29    (1)  all_58_9 = all_52_25
% 203.37/34.29    (2)  all_58_9 = e0
% 203.37/34.29    (3)   ~ (all_52_25 = e0)
% 203.37/34.29  
% 203.37/34.29  Begin of proof
% 203.37/34.29  | 
% 203.37/34.29  | COMBINE_EQS: (1), (2) imply:
% 203.37/34.29  |   (4)  all_52_25 = e0
% 203.37/34.29  | 
% 203.37/34.29  | SIMP: (4) implies:
% 203.37/34.29  |   (5)  all_52_25 = e0
% 203.37/34.29  | 
% 203.37/34.29  | REDUCE: (3), (5) imply:
% 203.37/34.29  |   (6)  $false
% 203.37/34.29  | 
% 203.37/34.29  | CLOSE: (6) is inconsistent.
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #524 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.29    (2)  all_52_20 = all_10_1
% 203.37/34.29    (3)  op(e1, all_10_1) = e3
% 203.37/34.29    (4)  op(e1, e1) = e1
% 203.37/34.29    (5)   ~ (all_10_2 = e3)
% 203.37/34.29    (6)  op(e1, e1) = all_52_20
% 203.37/34.29    (7)  op(e1, e1) = all_10_2
% 203.37/34.29  
% 203.37/34.29  Begin of proof
% 203.37/34.29  | 
% 203.37/34.29  | GROUND_INST: instantiating (1) with e1, all_52_20, e1, e1, simplifying with
% 203.37/34.29  |              (4), (6) gives:
% 203.37/34.29  |   (8)  all_52_20 = e1
% 203.37/34.29  | 
% 203.37/34.29  | COMBINE_EQS: (2), (8) imply:
% 203.37/34.29  |   (9)  all_10_1 = e1
% 203.37/34.29  | 
% 203.37/34.29  | SIMP: (9) implies:
% 203.37/34.29  |   (10)  all_10_1 = e1
% 203.37/34.29  | 
% 203.37/34.29  | REDUCE: (3), (10) imply:
% 203.37/34.29  |   (11)  op(e1, e1) = e3
% 203.37/34.29  | 
% 203.37/34.29  | REF_CLOSE: (1), (5), (7), (11) are inconsistent by sub-proof #1368.
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #525 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.29    (1)  all_56_14 = all_14_0
% 203.37/34.29    (2)  all_56_14 = e1
% 203.37/34.29    (3)   ~ (all_14_0 = e1)
% 203.37/34.29  
% 203.37/34.29  Begin of proof
% 203.37/34.29  | 
% 203.37/34.29  | COMBINE_EQS: (1), (2) imply:
% 203.37/34.29  |   (4)  all_14_0 = e1
% 203.37/34.29  | 
% 203.37/34.29  | SIMP: (4) implies:
% 203.37/34.29  |   (5)  all_14_0 = e1
% 203.37/34.29  | 
% 203.37/34.29  | REDUCE: (3), (5) imply:
% 203.37/34.29  |   (6)  $false
% 203.37/34.29  | 
% 203.37/34.29  | CLOSE: (6) is inconsistent.
% 203.37/34.29  | 
% 203.37/34.29  End of proof
% 203.37/34.29  
% 203.37/34.29  Sub-proof #526 shows that the following formulas are inconsistent:
% 203.37/34.29  ----------------------------------------------------------------
% 203.37/34.30    (1)  all_56_14 = all_14_0
% 203.37/34.30    (2)  all_56_14 = e2
% 203.37/34.30    (3)   ~ (all_14_0 = e2)
% 203.37/34.30  
% 203.37/34.30  Begin of proof
% 203.37/34.30  | 
% 203.37/34.30  | COMBINE_EQS: (1), (2) imply:
% 203.37/34.30  |   (4)  all_14_0 = e2
% 203.37/34.30  | 
% 203.37/34.30  | SIMP: (4) implies:
% 203.37/34.30  |   (5)  all_14_0 = e2
% 203.37/34.30  | 
% 203.37/34.30  | REDUCE: (3), (5) imply:
% 203.37/34.30  |   (6)  $false
% 203.37/34.30  | 
% 203.37/34.30  | CLOSE: (6) is inconsistent.
% 203.37/34.30  | 
% 203.37/34.30  End of proof
% 203.37/34.30  
% 203.37/34.30  Sub-proof #527 shows that the following formulas are inconsistent:
% 203.37/34.30  ----------------------------------------------------------------
% 203.37/34.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.30    (2)  op(all_52_7, all_52_7) = e0
% 203.37/34.30    (3)  op(all_52_5, all_52_5) = e1
% 203.37/34.30    (4)  all_58_0 = all_6_2
% 203.37/34.30    (5)  op(e2, e2) = all_4_2
% 203.37/34.30    (6)  op(e0, e0) = all_14_2
% 203.37/34.30    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.30    (8)  op(all_6_2, all_6_2) = e3
% 203.37/34.30    (9)  all_58_12 = all_52_7
% 203.37/34.30    (10)   ~ (all_52_7 = all_14_2)
% 203.37/34.30    (11)  all_58_2 = all_52_3
% 203.37/34.30    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.30    (13)  op(all_52_3, all_52_3) = e2
% 203.37/34.30    (14)   ~ (all_52_5 = all_10_2)
% 203.37/34.30    (15)   ~ (all_52_9 = all_6_2)
% 203.37/34.30    (16)  op(e3, e3) = all_6_2
% 203.37/34.30    (17)  all_56_1 = all_52_9
% 203.37/34.30    (18)  all_58_6 = all_52_5
% 203.37/34.30    (19)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.30    (20)  all_56_1 = e3
% 203.37/34.30    (21)  op(e1, e1) = all_10_2
% 203.37/34.30    (22)   ~ (all_52_3 = all_4_2)
% 203.37/34.30  
% 203.37/34.30  Begin of proof
% 203.37/34.30  | 
% 203.37/34.30  | COMBINE_EQS: (17), (20) imply:
% 203.37/34.30  |   (23)  all_52_9 = e3
% 203.37/34.30  | 
% 203.37/34.30  | SIMP: (23) implies:
% 203.37/34.30  |   (24)  all_52_9 = e3
% 203.37/34.30  | 
% 203.37/34.30  | REDUCE: (15), (24) imply:
% 203.37/34.30  |   (25)   ~ (all_6_2 = e3)
% 203.37/34.30  | 
% 203.37/34.30  | SIMP: (25) implies:
% 203.37/34.30  |   (26)   ~ (all_6_2 = e3)
% 203.37/34.30  | 
% 203.37/34.30  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.37/34.30  |            (13), (14), (16), (18), (19), (21), (22), (26) are inconsistent by
% 203.37/34.30  |            sub-proof #1362.
% 203.37/34.30  | 
% 203.37/34.30  End of proof
% 203.37/34.30  
% 203.37/34.30  Sub-proof #528 shows that the following formulas are inconsistent:
% 203.37/34.30  ----------------------------------------------------------------
% 203.37/34.30    (1)  all_58_14 = all_52_23
% 203.37/34.30    (2)   ~ (e3 = e1)
% 203.37/34.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.30    (4)  op(all_52_7, all_52_7) = e0
% 203.37/34.30    (5)  op(all_52_5, all_52_5) = e1
% 203.37/34.30    (6)   ~ (e3 = e0)
% 203.37/34.30    (7)  op(e2, e3) = all_52_3
% 203.37/34.30    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.30    (9)  op(e0, e2) = all_52_15
% 203.37/34.30    (10)   ~ (all_52_7 = all_52_15)
% 203.37/34.30    (11)  all_58_0 = all_6_2
% 203.37/34.30    (12)  all_58_13 = all_52_15
% 203.37/34.30    (13)  op(e2, all_4_1) = e3
% 203.37/34.30    (14)  op(e1, e3) = all_52_5
% 203.37/34.30    (15)  op(e2, e2) = all_4_2
% 203.37/34.30    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.37/34.30    (17)  op(all_10_2, e1) = all_10_1
% 203.37/34.30    (18)   ~ (all_52_7 = all_6_2)
% 203.37/34.30    (19)  op(e0, e0) = all_14_2
% 203.37/34.30    (20)  op(e0, e1) = all_52_23
% 203.37/34.30    (21)   ~ (all_52_15 = e0)
% 203.37/34.30    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.30    (23)  all_58_15 = e0
% 203.37/34.30    (24)   ~ (all_4_1 = e1)
% 203.37/34.30    (25)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.30    (26)  op(e1, all_10_1) = e3
% 203.37/34.30    (27)   ~ (e2 = e1)
% 203.37/34.30    (28)  op(all_52_15, all_52_15) = all_52_14
% 203.37/34.30    (29)  all_36_2 = all_10_2
% 203.37/34.30    (30)  all_36_1 = all_10_1
% 203.37/34.30    (31)  op(all_6_2, all_6_2) = e3
% 203.37/34.30    (32)  all_58_12 = all_52_7
% 203.37/34.30    (33)   ~ (all_52_7 = all_14_2)
% 203.37/34.30    (34)  all_58_2 = all_52_3
% 203.37/34.30    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.30    (36)   ~ (e2 = e0)
% 203.37/34.30    (37)  op(all_4_2, e2) = all_4_1
% 203.37/34.30    (38)  op(all_52_3, all_52_3) = e2
% 203.37/34.30    (39)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.30    (40)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.30    (41)   ~ (all_52_5 = all_10_2)
% 203.37/34.30    (42)  all_56_12 = all_52_7
% 203.37/34.30    (43)  op(e3, e3) = all_6_2
% 203.37/34.30    (44)  all_58_6 = all_52_5
% 203.37/34.30    (45)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.30    (46)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.37/34.30    (47)   ~ (e1 = e0)
% 203.37/34.30    (48)   ~ (e3 = e2)
% 203.37/34.30    (49)  op(e1, e1) = all_10_2
% 203.37/34.30    (50)   ~ (all_52_7 = all_52_23)
% 203.37/34.30    (51)  all_56_13 = all_52_15
% 203.37/34.30    (52)   ~ (all_52_3 = all_4_2)
% 203.37/34.30    (53)   ~ (all_52_7 = e0)
% 203.37/34.30  
% 203.37/34.30  Begin of proof
% 203.37/34.30  | 
% 203.37/34.30  | BETA: splitting (25) gives:
% 203.37/34.30  | 
% 203.37/34.30  | Case 1:
% 203.37/34.30  | | 
% 203.37/34.30  | |   (54)  all_56_13 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | COMBINE_EQS: (51), (54) imply:
% 203.37/34.30  | |   (55)  all_52_15 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | SIMP: (55) implies:
% 203.37/34.30  | |   (56)  all_52_15 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | COMBINE_EQS: (12), (56) imply:
% 203.37/34.30  | |   (57)  all_58_13 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (10), (56) imply:
% 203.37/34.30  | |   (58)   ~ (all_52_7 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (28), (56) imply:
% 203.37/34.30  | |   (59)  op(e3, e3) = all_52_14
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (9), (56) imply:
% 203.37/34.30  | |   (60)  op(e0, e2) = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | GROUND_INST: instantiating (3) with all_6_2, all_52_14, e3, e3, simplifying
% 203.37/34.30  | |              with (43), (59) gives:
% 203.37/34.30  | |   (61)  all_52_14 = all_6_2
% 203.37/34.30  | | 
% 203.37/34.30  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (13), (15), (16), (17), (18), (20),
% 203.37/34.30  | |            (23), (27), (29), (30), (32), (36), (37), (38), (39), (42), (43),
% 203.37/34.30  | |            (46), (47), (48), (49), (53), (57), (58), (60) are inconsistent
% 203.37/34.30  | |            by sub-proof #529.
% 203.37/34.30  | | 
% 203.37/34.30  | Case 2:
% 203.37/34.30  | | 
% 203.37/34.30  | |   (62)   ~ (all_56_13 = e3)
% 203.37/34.30  | |   (63)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (51), (62) imply:
% 203.37/34.30  | |   (64)   ~ (all_52_15 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 203.37/34.30  | |            (17), (18), (19), (20), (21), (22), (23), (24), (26), (29), (31),
% 203.37/34.30  | |            (32), (33), (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 203.37/34.30  | |            (44), (45), (46), (49), (50), (51), (52), (53), (63), (64) are
% 203.37/34.30  | |            inconsistent by sub-proof #548.
% 203.37/34.30  | | 
% 203.37/34.30  | End of split
% 203.37/34.30  | 
% 203.37/34.30  End of proof
% 203.37/34.30  
% 203.37/34.30  Sub-proof #529 shows that the following formulas are inconsistent:
% 203.37/34.30  ----------------------------------------------------------------
% 203.37/34.30    (1)  all_58_14 = all_52_23
% 203.37/34.30    (2)   ~ (e3 = e1)
% 203.37/34.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.30    (4)  op(all_52_7, all_52_7) = e0
% 203.37/34.30    (5)  op(e2, e3) = all_52_3
% 203.37/34.30    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.30    (7)  all_58_13 = e3
% 203.37/34.30    (8)  op(e0, e2) = e3
% 203.37/34.30    (9)  op(e2, all_4_1) = e3
% 203.37/34.30    (10)  op(e2, e2) = all_4_2
% 203.37/34.30    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.37/34.30    (12)  op(all_10_2, e1) = all_10_1
% 203.37/34.30    (13)   ~ (all_52_7 = all_6_2)
% 203.37/34.30    (14)  op(e0, e1) = all_52_23
% 203.37/34.30    (15)  all_58_15 = e0
% 203.37/34.30    (16)   ~ (e2 = e1)
% 203.37/34.30    (17)  all_36_2 = all_10_2
% 203.37/34.30    (18)  all_36_1 = all_10_1
% 203.37/34.30    (19)  all_58_12 = all_52_7
% 203.37/34.30    (20)   ~ (all_52_7 = e3)
% 203.37/34.30    (21)   ~ (e2 = e0)
% 203.37/34.30    (22)  op(all_4_2, e2) = all_4_1
% 203.37/34.30    (23)  op(all_52_3, all_52_3) = e2
% 203.37/34.30    (24)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.30    (25)  all_56_12 = all_52_7
% 203.37/34.30    (26)  op(e3, e3) = all_6_2
% 203.37/34.30    (27)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.37/34.30    (28)   ~ (e1 = e0)
% 203.37/34.30    (29)   ~ (e3 = e2)
% 203.37/34.30    (30)  op(e1, e1) = all_10_2
% 203.37/34.30    (31)   ~ (all_52_7 = e0)
% 203.37/34.30  
% 203.37/34.30  Begin of proof
% 203.37/34.30  | 
% 203.37/34.30  | BETA: splitting (6) gives:
% 203.37/34.30  | 
% 203.37/34.30  | Case 1:
% 203.37/34.30  | | 
% 203.37/34.30  | |   (32)  all_56_12 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | REF_CLOSE: (20), (25), (32) are inconsistent by sub-proof #1383.
% 203.37/34.30  | | 
% 203.37/34.30  | Case 2:
% 203.37/34.30  | | 
% 203.37/34.30  | |   (33)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.30  | | 
% 203.37/34.30  | | BETA: splitting (24) gives:
% 203.37/34.30  | | 
% 203.37/34.30  | | Case 1:
% 203.37/34.30  | | | 
% 203.37/34.30  | | |   (34)  all_58_12 = e1
% 203.37/34.30  | | | 
% 203.37/34.30  | | | COMBINE_EQS: (19), (34) imply:
% 203.37/34.30  | | |   (35)  all_52_7 = e1
% 203.37/34.30  | | | 
% 203.37/34.30  | | | SIMP: (35) implies:
% 203.37/34.30  | | |   (36)  all_52_7 = e1
% 203.37/34.30  | | | 
% 203.37/34.30  | | | REDUCE: (4), (36) imply:
% 203.37/34.30  | | |   (37)  op(e1, e1) = e0
% 203.37/34.30  | | | 
% 203.37/34.30  | | | REF_CLOSE: (1), (3), (7), (11), (12), (14), (15), (16), (17), (18), (21),
% 203.37/34.30  | | |            (27), (29), (30), (34), (37) are inconsistent by sub-proof
% 203.37/34.30  | | |            #550.
% 203.37/34.30  | | | 
% 203.37/34.30  | | Case 2:
% 203.37/34.30  | | | 
% 203.37/34.30  | | |   (38)   ~ (all_58_12 = e1)
% 203.37/34.30  | | |   (39)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.30  | | | 
% 203.37/34.30  | | | REDUCE: (19), (38) imply:
% 203.37/34.30  | | |   (40)   ~ (all_52_7 = e1)
% 203.37/34.30  | | | 
% 203.37/34.30  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (13), (15), (22),
% 203.37/34.30  | | |            (23), (25), (26), (28), (31), (33), (39), (40) are inconsistent
% 203.37/34.30  | | |            by sub-proof #768.
% 203.37/34.30  | | | 
% 203.37/34.30  | | End of split
% 203.37/34.30  | | 
% 203.37/34.30  | End of split
% 203.37/34.30  | 
% 203.37/34.30  End of proof
% 203.37/34.30  
% 203.37/34.30  Sub-proof #530 shows that the following formulas are inconsistent:
% 203.37/34.30  ----------------------------------------------------------------
% 203.37/34.30    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.37/34.30    (2)   ~ (all_52_15 = all_52_23)
% 203.37/34.30    (3)   ~ (all_52_25 = all_6_0)
% 203.37/34.30    (4)   ~ (all_52_25 = all_52_27)
% 203.37/34.30    (5)  all_58_14 = all_52_23
% 203.37/34.30    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.37/34.30    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.30    (8)  all_58_1 = all_52_9
% 203.37/34.30    (9)   ~ (all_52_9 = all_52_13)
% 203.37/34.30    (10)   ~ (e3 = e0)
% 203.37/34.30    (11)  op(e2, e3) = all_52_3
% 203.37/34.30    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.30    (13)  op(e0, e2) = all_52_15
% 203.37/34.30    (14)   ~ (all_52_7 = all_52_15)
% 203.37/34.30    (15)   ~ (all_52_3 = all_52_19)
% 203.37/34.30    (16)  op(all_52_7, all_52_7) = all_52_6
% 203.37/34.30    (17)   ~ (all_52_17 = all_52_25)
% 203.37/34.30    (18)   ~ (all_52_3 = all_6_2)
% 203.37/34.30    (19)  all_58_0 = all_6_2
% 203.37/34.30    (20)  op(all_14_2, e0) = all_14_1
% 203.37/34.30    (21)  all_56_4 = all_52_3
% 203.37/34.30    (22)   ~ (all_52_17 = all_10_2)
% 203.37/34.30    (23)  op(e3, e0) = all_52_25
% 203.37/34.30    (24)  op(e0, all_14_1) = all_14_0
% 203.37/34.30    (25)  op(all_52_5, all_52_5) = all_52_4
% 203.37/34.30    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.37/34.30    (27)   ~ (all_52_27 = all_52_29)
% 203.37/34.30    (28)  all_58_13 = all_52_15
% 203.37/34.30    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.37/34.30    (30)  all_58_9 = all_52_25
% 203.37/34.30    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.37/34.30    (32)   ~ (all_52_29 = all_14_2)
% 203.37/34.30    (33)  all_22_0 = all_6_0
% 203.37/34.30    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.37/34.30    (35)   ~ (all_52_17 = all_6_0)
% 203.37/34.30    (36)  op(all_52_27, all_52_27) = all_52_26
% 203.37/34.30    (37)  op(e1, e3) = all_52_5
% 203.37/34.30    (38)  op(e2, e2) = all_4_2
% 203.37/34.30    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.37/34.30    (40)   ~ (all_52_3 = all_52_5)
% 203.37/34.30    (41)   ~ (all_4_1 = e3)
% 203.37/34.30    (42)  all_58_11 = all_52_29
% 203.37/34.30    (43)  all_56_5 = all_4_2
% 203.37/34.30    (44)   ~ (all_52_25 = all_14_2)
% 203.37/34.30    (45)   ~ (all_52_9 = all_52_15)
% 203.37/34.30    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.37/34.30    (47)   ~ (all_52_3 = all_52_27)
% 203.37/34.30    (48)  op(all_10_2, e1) = all_10_1
% 203.37/34.30    (49)  op(all_6_2, all_6_2) = all_52_0
% 203.37/34.30    (50)   ~ (all_52_7 = all_6_2)
% 203.37/34.30    (51)  op(e0, e0) = all_14_2
% 203.37/34.30    (52)  op(e0, e1) = all_52_23
% 203.37/34.30    (53)  all_56_15 = all_14_2
% 203.37/34.30    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.30    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.37/34.30    (56)  op(e2, all_4_1) = all_4_0
% 203.37/34.30    (57)  op(e1, e0) = all_52_29
% 203.37/34.30    (58)  all_56_11 = all_52_29
% 203.37/34.30    (59)   ~ (all_4_1 = e1)
% 203.37/34.30    (60)   ~ (all_4_0 = e3)
% 203.37/34.30    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.30    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.30    (63)  op(e1, all_10_1) = e3
% 203.37/34.30    (64)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.37/34.30    (65)   ~ (e2 = e1)
% 203.37/34.30    (66)   ~ (all_52_13 = all_10_2)
% 203.37/34.30    (67)   ~ (all_6_0 = e1)
% 203.37/34.30    (68)  all_58_10 = all_52_27
% 203.37/34.30    (69)  all_56_8 = all_52_5
% 203.37/34.30    (70)  op(all_52_9, all_52_9) = all_52_8
% 203.37/34.30    (71)   ~ (all_52_19 = all_52_23)
% 203.37/34.30    (72)   ~ (all_52_25 = all_52_29)
% 203.37/34.30    (73)  op(all_6_2, e3) = e2
% 203.37/34.30    (74)   ~ (all_52_29 = all_10_2)
% 203.37/34.30    (75)  all_58_7 = all_52_13
% 203.37/34.30    (76)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.37/34.30    (77)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.37/34.30    (78)  all_58_1 = all_6_0
% 203.37/34.30    (79)  all_36_2 = all_10_2
% 203.37/34.30    (80)  all_36_1 = all_10_1
% 203.37/34.30    (81)   ~ (all_52_5 = all_52_7)
% 203.37/34.30    (82)  all_58_12 = all_52_7
% 203.37/34.30    (83)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.30    (84)   ~ (all_52_7 = all_14_2)
% 203.37/34.30    (85)   ~ (all_14_2 = e0)
% 203.37/34.30    (86)  all_58_2 = all_52_3
% 203.37/34.30    (87)  all_56_2 = all_52_17
% 203.37/34.30    (88)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.30    (89)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.30    (90)  op(e3, all_6_1) = all_6_0
% 203.37/34.30    (91)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.37/34.30    (92)   ~ (all_14_0 = e3)
% 203.37/34.30    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.30    (94)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.37/34.30    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.37/34.30    (96)   ~ (e2 = e0)
% 203.37/34.30    (97)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.30    (98)  op(all_4_2, e2) = all_4_1
% 203.37/34.30    (99)  op(all_6_0, all_6_0) = all_52_8
% 203.37/34.30    (100)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.37/34.30    (101)   ~ (all_52_5 = all_52_29)
% 203.37/34.30    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.30    (103)   ~ (all_52_15 = all_14_2)
% 203.37/34.30    (104)   ~ (all_52_13 = all_6_0)
% 203.37/34.30    (105)   ~ (all_52_19 = all_52_27)
% 203.37/34.30    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.30    (107)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.37/34.30    (108)   ~ (all_6_0 = e2)
% 203.37/34.30    (109)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.30    (110)   ~ (all_52_13 = all_4_2)
% 203.37/34.30    (111)  op(e3, e1) = all_52_17
% 203.37/34.30    (112)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.37/34.30    (113)  op(e0, e3) = all_52_7
% 203.37/34.30    (114)  op(e1, e2) = all_52_13
% 203.37/34.30    (115)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.30    (116)   ~ (all_52_9 = all_52_25)
% 203.37/34.30    (117)  all_58_15 = all_14_2
% 203.37/34.30    (118)   ~ (all_52_19 = all_10_2)
% 203.37/34.30    (119)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.30    (120)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.30    (121)  all_58_8 = all_10_2
% 203.37/34.30    (122)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.30    (123)   ~ (all_52_5 = all_10_2)
% 203.37/34.30    (124)  op(all_52_29, all_52_29) = all_52_28
% 203.37/34.30    (125)   ~ (all_52_23 = all_14_2)
% 203.37/34.30    (126)  all_56_12 = all_52_7
% 203.37/34.30    (127)  op(all_52_17, all_52_17) = all_52_16
% 203.37/34.30    (128)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.30    (129)   ~ (all_52_25 = all_6_2)
% 203.37/34.30    (130)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.30    (131)   ~ (all_52_9 = all_4_2)
% 203.37/34.30    (132)   ~ (all_52_5 = all_6_2)
% 203.37/34.30    (133)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.37/34.30    (134)   ~ (all_52_9 = all_6_2)
% 203.37/34.30    (135)  all_56_0 = all_6_2
% 203.37/34.30    (136)  op(e3, e3) = all_6_2
% 203.37/34.30    (137)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.30    (138)   ~ (all_52_15 = all_6_0)
% 203.37/34.30    (139)   ~ (all_52_27 = all_14_2)
% 203.37/34.30    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.37/34.30    (141)  all_56_14 = all_52_23
% 203.37/34.30    (142)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.30    (143)  all_56_3 = all_52_25
% 203.37/34.30    (144)   ~ (all_52_3 = all_52_7)
% 203.37/34.30    (145)   ~ (all_6_0 = all_6_2)
% 203.37/34.30    (146)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.30    (147)  all_58_5 = all_52_19
% 203.37/34.30    (148)  all_56_1 = all_52_9
% 203.37/34.30    (149)   ~ (all_52_15 = all_4_2)
% 203.37/34.30    (150)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.37/34.30           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.37/34.30           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.37/34.30           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.37/34.30    (151)   ~ (all_52_27 = all_4_2)
% 203.37/34.30    (152)  all_58_6 = all_52_5
% 203.37/34.30    (153)  op(e3, e2) = all_52_9
% 203.37/34.30    (154)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.30    (155)   ~ (all_52_17 = all_6_2)
% 203.37/34.30    (156)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.37/34.30    (157)   ~ (e1 = e0)
% 203.37/34.30    (158)   ~ (e3 = e2)
% 203.37/34.30    (159)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.30    (160)  all_56_10 = all_10_2
% 203.37/34.30    (161)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.30    (162)  all_56_1 = all_6_0
% 203.37/34.30    (163)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.37/34.30    (164)  op(all_52_13, all_52_13) = all_52_12
% 203.37/34.30    (165)   ~ (all_6_0 = all_4_2)
% 203.37/34.30    (166)  op(e1, e1) = all_10_2
% 203.37/34.30    (167)   ~ (all_52_23 = all_10_2)
% 203.37/34.30    (168)   ~ (all_52_7 = all_52_23)
% 203.37/34.30    (169)   ~ (all_52_17 = all_52_19)
% 203.37/34.30    (170)  all_58_3 = all_4_2
% 203.37/34.30    (171)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.30    (172)  all_56_13 = all_52_15
% 203.37/34.30    (173)   ~ (all_52_3 = all_4_2)
% 203.37/34.30    (174)   ~ (all_52_19 = all_4_2)
% 203.37/34.30    (175)   ~ (all_52_17 = all_52_23)
% 203.37/34.30    (176)  op(all_6_2, e3) = all_6_1
% 203.37/34.30    (177)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.37/34.30    (178)  all_22_2 = all_6_2
% 203.37/34.30    (179)  all_58_4 = all_52_17
% 203.37/34.30    (180)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.37/34.30    (181)  op(all_52_25, all_52_25) = all_52_24
% 203.37/34.30  
% 203.37/34.30  Begin of proof
% 203.37/34.30  | 
% 203.37/34.30  | BETA: splitting (159) gives:
% 203.37/34.30  | 
% 203.37/34.30  | Case 1:
% 203.37/34.30  | | 
% 203.37/34.30  | |   (182)  all_56_1 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | COMBINE_EQS: (162), (182) imply:
% 203.37/34.30  | |   (183)  all_6_0 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | SIMP: (183) implies:
% 203.37/34.30  | |   (184)  all_6_0 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | COMBINE_EQS: (78), (184) imply:
% 203.37/34.30  | |   (185)  all_58_1 = e3
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (104), (184) imply:
% 203.37/34.30  | |   (186)   ~ (all_52_13 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (138), (184) imply:
% 203.37/34.30  | |   (187)   ~ (all_52_15 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (35), (184) imply:
% 203.37/34.30  | |   (188)   ~ (all_52_17 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (3), (184) imply:
% 203.37/34.30  | |   (189)   ~ (all_52_25 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (145), (184) imply:
% 203.37/34.30  | |   (190)   ~ (all_6_2 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | SIMP: (190) implies:
% 203.37/34.30  | |   (191)   ~ (all_6_2 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (165), (184) imply:
% 203.37/34.30  | |   (192)   ~ (all_4_2 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | SIMP: (192) implies:
% 203.37/34.30  | |   (193)   ~ (all_4_2 = e3)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (67), (184) imply:
% 203.37/34.30  | |   (194)   ~ (e3 = e1)
% 203.37/34.30  | | 
% 203.37/34.30  | | REDUCE: (99), (184) imply:
% 203.37/34.30  | |   (195)  op(e3, e3) = all_52_8
% 203.37/34.30  | | 
% 203.37/34.30  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 203.37/34.30  | |              with (136), (195) gives:
% 203.37/34.30  | |   (196)  all_52_8 = all_6_2
% 203.37/34.30  | | 
% 203.37/34.30  | | BETA: splitting (150) gives:
% 203.37/34.30  | | 
% 203.37/34.30  | | Case 1:
% 203.37/34.30  | | | 
% 203.37/34.30  | | |   (197)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.37/34.30  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.37/34.30  | | |            e0)
% 203.37/34.30  | | | 
% 203.37/34.30  | | | BETA: splitting (197) gives:
% 203.37/34.30  | | | 
% 203.37/34.30  | | | Case 1:
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | |   (198)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | ALPHA: (198) implies:
% 203.37/34.30  | | | |   (199)  all_52_6 = e0
% 203.37/34.30  | | | |   (200)  all_52_4 = e1
% 203.37/34.30  | | | |   (201)  all_52_2 = e2
% 203.37/34.30  | | | |   (202)  all_52_0 = e3
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (6), (201) imply:
% 203.37/34.30  | | | |   (203)  op(all_52_3, all_52_3) = e2
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (25), (200) imply:
% 203.37/34.30  | | | |   (204)  op(all_52_5, all_52_5) = e1
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (16), (199) imply:
% 203.37/34.30  | | | |   (205)  op(all_52_7, all_52_7) = e0
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (49), (202) imply:
% 203.37/34.30  | | | |   (206)  op(all_6_2, all_6_2) = e3
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (12), (13), (14), (18), (19),
% 203.37/34.30  | | | |            (20), (21), (22), (23), (24), (28), (29), (30), (31), (32),
% 203.37/34.30  | | | |            (38), (40), (41), (42), (43), (44), (45), (46), (48), (50),
% 203.37/34.30  | | | |            (51), (52), (53), (54), (55), (56), (59), (60), (61), (64),
% 203.37/34.30  | | | |            (65), (66), (67), (68), (70), (71), (72), (75), (76), (77),
% 203.37/34.30  | | | |            (79), (80), (81), (82), (83), (84), (85), (86), (89), (90),
% 203.37/34.30  | | | |            (91), (92), (95), (96), (97), (98), (102), (103), (107),
% 203.37/34.30  | | | |            (109), (110), (114), (115), (116), (117), (118), (119),
% 203.37/34.30  | | | |            (121), (122), (123), (125), (126), (129), (130), (131),
% 203.37/34.30  | | | |            (132), (133), (134), (136), (139), (140), (141), (142),
% 203.37/34.30  | | | |            (143), (144), (146), (147), (148), (149), (152), (153),
% 203.37/34.30  | | | |            (154), (155), (156), (157), (158), (159), (160), (161),
% 203.37/34.30  | | | |            (164), (166), (167), (168), (170), (171), (172), (173),
% 203.37/34.30  | | | |            (176), (177), (179), (180), (181), (203), (204), (205), (206)
% 203.37/34.30  | | | |            are inconsistent by sub-proof #537.
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | Case 2:
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | |   (207)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.37/34.30  | | | |          e0
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REF_CLOSE: (191), (196), (207) are inconsistent by sub-proof #791.
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | End of split
% 203.37/34.30  | | | 
% 203.37/34.30  | | Case 2:
% 203.37/34.30  | | | 
% 203.37/34.30  | | |   (208)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.37/34.30  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.37/34.30  | | |            all_52_30 = e0)
% 203.37/34.30  | | | 
% 203.37/34.30  | | | BETA: splitting (208) gives:
% 203.37/34.30  | | | 
% 203.37/34.30  | | | Case 1:
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | |   (209)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.37/34.30  | | | |          e0
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | ALPHA: (209) implies:
% 203.37/34.30  | | | |   (210)  all_52_22 = e0
% 203.37/34.30  | | | |   (211)  all_52_20 = e1
% 203.37/34.30  | | | |   (212)  all_52_18 = e2
% 203.37/34.30  | | | |   (213)  all_52_16 = e3
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (127), (213) imply:
% 203.37/34.30  | | | |   (214)  op(all_52_17, all_52_17) = e3
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (26), (212) imply:
% 203.37/34.30  | | | |   (215)  op(all_52_19, all_52_19) = e2
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (119), (210) imply:
% 203.37/34.30  | | | |   (216)  op(all_52_23, all_52_23) = e0
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REDUCE: (29), (211) imply:
% 203.37/34.30  | | | |   (217)  op(all_10_2, all_10_2) = e1
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | | REF_CLOSE: (5), (6), (7), (10), (11), (15), (17), (18), (19), (25),
% 203.37/34.30  | | | |            (28), (30), (32), (34), (36), (37), (38), (42), (44), (48),
% 203.37/34.30  | | | |            (50), (51), (53), (54), (57), (58), (62), (63), (65), (66),
% 203.37/34.30  | | | |            (68), (71), (73), (74), (75), (82), (83), (84), (85), (86),
% 203.37/34.30  | | | |            (87), (88), (89), (91), (96), (100), (102), (103), (106),
% 203.37/34.30  | | | |            (109), (111), (113), (115), (117), (118), (121), (122),
% 203.37/34.30  | | | |            (123), (125), (129), (130), (132), (136), (139), (143),
% 203.37/34.30  | | | |            (144), (146), (147), (151), (152), (154), (155), (157),
% 203.37/34.30  | | | |            (160), (161), (166), (167), (168), (169), (170), (173),
% 203.37/34.30  | | | |            (175), (179), (180), (185), (186), (187), (188), (189),
% 203.37/34.30  | | | |            (191), (193), (194), (195), (214), (215), (216), (217) are
% 203.37/34.30  | | | |            inconsistent by sub-proof #533.
% 203.37/34.30  | | | | 
% 203.37/34.30  | | | Case 2:
% 203.37/34.30  | | | | 
% 203.37/34.31  | | | |   (218)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.37/34.31  | | | |          e0
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | | ALPHA: (218) implies:
% 203.37/34.31  | | | |   (219)  all_52_30 = e0
% 203.37/34.31  | | | |   (220)  all_52_28 = e1
% 203.37/34.31  | | | |   (221)  all_52_26 = e2
% 203.37/34.31  | | | |   (222)  all_52_24 = e3
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | | REDUCE: (181), (222) imply:
% 203.37/34.31  | | | |   (223)  op(all_52_25, all_52_25) = e3
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | | REDUCE: (36), (221) imply:
% 203.37/34.31  | | | |   (224)  op(all_52_27, all_52_27) = e2
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | | REDUCE: (124), (220) imply:
% 203.37/34.31  | | | |   (225)  op(all_52_29, all_52_29) = e1
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | | REDUCE: (146), (219) imply:
% 203.37/34.31  | | | |   (226)  op(all_14_2, all_14_2) = e0
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.37/34.31  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 203.37/34.31  | | | |            (26), (27), (28), (30), (32), (37), (38), (39), (40), (42),
% 203.37/34.31  | | | |            (43), (44), (47), (48), (49), (50), (51), (53), (54), (55),
% 203.37/34.31  | | | |            (58), (62), (63), (65), (66), (68), (69), (70), (72), (73),
% 203.37/34.31  | | | |            (74), (75), (76), (77), (81), (82), (83), (84), (85), (86),
% 203.37/34.31  | | | |            (87), (88), (89), (91), (93), (95), (96), (97), (101), (103),
% 203.37/34.31  | | | |            (105), (106), (109), (111), (112), (113), (114), (115),
% 203.37/34.31  | | | |            (116), (117), (118), (119), (120), (121), (122), (123),
% 203.37/34.31  | | | |            (125), (126), (128), (129), (130), (131), (132), (136),
% 203.37/34.31  | | | |            (137), (139), (140), (141), (143), (144), (147), (149),
% 203.37/34.31  | | | |            (151), (152), (154), (155), (157), (158), (164), (166),
% 203.37/34.31  | | | |            (167), (168), (170), (171), (173), (174), (175), (176),
% 203.37/34.31  | | | |            (179), (185), (186), (187), (188), (189), (191), (193),
% 203.37/34.31  | | | |            (194), (223), (224), (225), (226) are inconsistent by
% 203.37/34.31  | | | |            sub-proof #531.
% 203.37/34.31  | | | | 
% 203.37/34.31  | | | End of split
% 203.37/34.31  | | | 
% 203.37/34.31  | | End of split
% 203.37/34.31  | | 
% 203.37/34.31  | Case 2:
% 203.37/34.31  | | 
% 203.37/34.31  | |   (227)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.37/34.31  | | 
% 203.37/34.31  | | REF_CLOSE: (7), (11), (18), (33), (49), (67), (73), (94), (108), (135),
% 203.37/34.31  | |            (136), (145), (158), (162), (163), (178), (227) are inconsistent
% 203.37/34.31  | |            by sub-proof #820.
% 203.37/34.31  | | 
% 203.37/34.31  | End of split
% 203.37/34.31  | 
% 203.37/34.31  End of proof
% 203.37/34.31  
% 203.37/34.31  Sub-proof #531 shows that the following formulas are inconsistent:
% 203.37/34.31  ----------------------------------------------------------------
% 203.37/34.31    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.37/34.31    (2)   ~ (all_52_15 = all_52_23)
% 203.37/34.31    (3)   ~ (all_52_25 = all_52_27)
% 203.37/34.31    (4)  all_58_14 = all_52_23
% 203.37/34.31    (5)   ~ (e3 = e1)
% 203.37/34.31    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.37/34.31    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.31    (8)  all_58_1 = all_52_9
% 203.37/34.31    (9)   ~ (all_52_9 = all_52_13)
% 203.37/34.31    (10)   ~ (e3 = e0)
% 203.37/34.31    (11)  op(e2, e3) = all_52_3
% 203.37/34.31    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.31    (13)   ~ (all_52_3 = all_52_19)
% 203.37/34.31    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.37/34.31    (15)   ~ (all_52_17 = all_52_25)
% 203.37/34.31    (16)   ~ (all_4_2 = e3)
% 203.37/34.31    (17)   ~ (all_52_3 = all_6_2)
% 203.37/34.31    (18)  all_58_0 = all_6_2
% 203.37/34.31    (19)  op(all_14_2, e0) = all_14_1
% 203.37/34.31    (20)  all_56_4 = all_52_3
% 203.37/34.31    (21)   ~ (all_52_17 = all_10_2)
% 203.37/34.31    (22)  op(e3, e0) = all_52_25
% 203.37/34.31    (23)  op(all_52_5, all_52_5) = all_52_4
% 203.37/34.31    (24)  op(all_52_19, all_52_19) = all_52_18
% 203.37/34.31    (25)   ~ (all_52_27 = all_52_29)
% 203.37/34.31    (26)  all_58_13 = all_52_15
% 203.37/34.31    (27)  all_58_9 = all_52_25
% 203.37/34.31    (28)   ~ (all_52_29 = all_14_2)
% 203.37/34.31    (29)   ~ (all_52_15 = e3)
% 203.37/34.31    (30)  op(e1, e3) = all_52_5
% 203.37/34.31    (31)  op(e2, e2) = all_4_2
% 203.37/34.31    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.37/34.31    (33)   ~ (all_52_3 = all_52_5)
% 203.37/34.31    (34)  all_58_11 = all_52_29
% 203.37/34.31    (35)  all_56_5 = all_4_2
% 203.37/34.31    (36)   ~ (all_52_25 = all_14_2)
% 203.37/34.31    (37)   ~ (all_52_3 = all_52_27)
% 203.37/34.31    (38)  op(all_10_2, e1) = all_10_1
% 203.37/34.31    (39)  all_58_1 = e3
% 203.37/34.31    (40)  op(all_6_2, all_6_2) = all_52_0
% 203.37/34.31    (41)   ~ (all_52_7 = all_6_2)
% 203.37/34.31    (42)  op(e0, e0) = all_14_2
% 203.37/34.31    (43)  op(all_52_29, all_52_29) = e1
% 203.37/34.31    (44)  all_56_15 = all_14_2
% 203.37/34.31    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.31    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.37/34.31    (47)  all_56_11 = all_52_29
% 203.37/34.31    (48)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.31    (49)  op(e1, all_10_1) = e3
% 203.37/34.31    (50)   ~ (all_6_2 = e3)
% 203.37/34.31    (51)   ~ (e2 = e1)
% 203.37/34.31    (52)   ~ (all_52_13 = all_10_2)
% 203.37/34.31    (53)  all_58_10 = all_52_27
% 203.37/34.31    (54)  all_56_8 = all_52_5
% 203.37/34.31    (55)  op(all_52_9, all_52_9) = all_52_8
% 203.37/34.31    (56)   ~ (all_52_25 = all_52_29)
% 203.37/34.31    (57)  op(all_6_2, e3) = e2
% 203.37/34.31    (58)   ~ (all_52_29 = all_10_2)
% 203.37/34.31    (59)  all_58_7 = all_52_13
% 203.37/34.31    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.37/34.31    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.37/34.31    (62)   ~ (all_52_5 = all_52_7)
% 203.37/34.31    (63)  all_58_12 = all_52_7
% 203.37/34.31    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.31    (65)   ~ (all_52_7 = all_14_2)
% 203.37/34.31    (66)   ~ (all_14_2 = e0)
% 203.37/34.31    (67)  all_58_2 = all_52_3
% 203.37/34.31    (68)  all_56_2 = all_52_17
% 203.37/34.31    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.31    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.31    (71)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.37/34.31    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.31    (73)   ~ (all_52_25 = e3)
% 203.37/34.31    (74)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.37/34.31    (75)   ~ (e2 = e0)
% 203.37/34.31    (76)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.31    (77)  op(all_52_25, all_52_25) = e3
% 203.37/34.31    (78)   ~ (all_52_5 = all_52_29)
% 203.37/34.31    (79)   ~ (all_52_15 = all_14_2)
% 203.37/34.31    (80)   ~ (all_52_19 = all_52_27)
% 203.37/34.31    (81)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.31    (82)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.31    (83)  op(e3, e1) = all_52_17
% 203.37/34.31    (84)  op(all_52_27, all_52_27) = e2
% 203.37/34.31    (85)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.37/34.31    (86)  op(e0, e3) = all_52_7
% 203.37/34.31    (87)  op(e1, e2) = all_52_13
% 203.37/34.31    (88)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.31    (89)   ~ (all_52_9 = all_52_25)
% 203.37/34.31    (90)  all_58_15 = all_14_2
% 203.37/34.31    (91)   ~ (all_52_19 = all_10_2)
% 203.37/34.31    (92)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.31    (93)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.37/34.31    (94)  all_58_8 = all_10_2
% 203.37/34.31    (95)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.31    (96)   ~ (all_52_5 = all_10_2)
% 203.37/34.31    (97)   ~ (all_52_23 = all_14_2)
% 203.37/34.31    (98)  all_56_12 = all_52_7
% 203.37/34.31    (99)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.37/34.31    (100)   ~ (all_52_25 = all_6_2)
% 203.37/34.31    (101)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.31    (102)   ~ (all_52_9 = all_4_2)
% 203.37/34.31    (103)   ~ (all_52_5 = all_6_2)
% 203.37/34.31    (104)  op(e3, e3) = all_6_2
% 203.37/34.31    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.37/34.31    (106)   ~ (all_52_13 = e3)
% 203.37/34.31    (107)   ~ (all_52_27 = all_14_2)
% 203.37/34.31    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.37/34.31    (109)  all_56_14 = all_52_23
% 203.37/34.31    (110)   ~ (all_52_17 = e3)
% 203.37/34.31    (111)  all_56_3 = all_52_25
% 203.37/34.31    (112)   ~ (all_52_3 = all_52_7)
% 203.37/34.31    (113)  all_58_5 = all_52_19
% 203.37/34.31    (114)   ~ (all_52_15 = all_4_2)
% 203.37/34.31    (115)   ~ (all_52_27 = all_4_2)
% 203.37/34.31    (116)  all_58_6 = all_52_5
% 203.37/34.31    (117)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.31    (118)   ~ (all_52_17 = all_6_2)
% 203.37/34.31    (119)   ~ (e1 = e0)
% 203.37/34.31    (120)  op(all_14_2, all_14_2) = e0
% 203.37/34.31    (121)   ~ (e3 = e2)
% 203.37/34.31    (122)  op(all_52_13, all_52_13) = all_52_12
% 203.37/34.31    (123)  op(e1, e1) = all_10_2
% 203.37/34.31    (124)   ~ (all_52_23 = all_10_2)
% 203.37/34.31    (125)   ~ (all_52_7 = all_52_23)
% 203.37/34.31    (126)  all_58_3 = all_4_2
% 203.37/34.31    (127)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.37/34.31    (128)   ~ (all_52_3 = all_4_2)
% 203.37/34.31    (129)   ~ (all_52_19 = all_4_2)
% 203.37/34.31    (130)   ~ (all_52_17 = all_52_23)
% 203.37/34.31    (131)  op(all_6_2, e3) = all_6_1
% 203.37/34.31    (132)  all_58_4 = all_52_17
% 203.37/34.31  
% 203.37/34.31  Begin of proof
% 203.37/34.31  | 
% 203.37/34.31  | BETA: splitting (95) gives:
% 203.37/34.31  | 
% 203.37/34.31  | Case 1:
% 203.37/34.31  | | 
% 203.37/34.31  | |   (133)  all_56_15 = e3
% 203.37/34.31  | | 
% 203.37/34.31  | | COMBINE_EQS: (44), (133) imply:
% 203.37/34.31  | |   (134)  all_14_2 = e3
% 203.37/34.31  | | 
% 203.37/34.31  | | SIMP: (134) implies:
% 203.37/34.31  | |   (135)  all_14_2 = e3
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (65), (135) imply:
% 203.37/34.31  | |   (136)   ~ (all_52_7 = e3)
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (28), (135) imply:
% 203.37/34.31  | |   (137)   ~ (all_52_29 = e3)
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (120), (135) imply:
% 203.37/34.31  | |   (138)  op(e3, e3) = e0
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (19), (135) imply:
% 203.37/34.31  | |   (139)  op(e3, e0) = all_14_1
% 203.37/34.31  | | 
% 203.37/34.31  | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3, simplifying
% 203.37/34.31  | |              with (22), (139) gives:
% 203.37/34.31  | |   (140)  all_52_25 = all_14_1
% 203.37/34.31  | | 
% 203.37/34.31  | | GROUND_INST: instantiating (7) with all_6_2, e0, e3, e3, simplifying with
% 203.37/34.31  | |              (104), (138) gives:
% 203.37/34.31  | |   (141)  all_6_2 = e0
% 203.37/34.31  | | 
% 203.37/34.31  | | COMBINE_EQS: (111), (140) imply:
% 203.37/34.31  | |   (142)  all_56_3 = all_14_1
% 203.37/34.31  | | 
% 203.37/34.31  | | COMBINE_EQS: (27), (140) imply:
% 203.37/34.31  | |   (143)  all_58_9 = all_14_1
% 203.37/34.31  | | 
% 203.37/34.31  | | COMBINE_EQS: (18), (141) imply:
% 203.37/34.31  | |   (144)  all_58_0 = e0
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (41), (141) imply:
% 203.37/34.31  | |   (145)   ~ (all_52_7 = e0)
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (118), (141) imply:
% 203.37/34.31  | |   (146)   ~ (all_52_17 = e0)
% 203.37/34.31  | | 
% 203.37/34.31  | | REDUCE: (100), (140), (141) imply:
% 203.37/34.31  | |   (147)   ~ (all_14_1 = e0)
% 203.37/34.31  | | 
% 203.37/34.32  | | REDUCE: (73), (140) imply:
% 203.37/34.32  | |   (148)   ~ (all_14_1 = e3)
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (50), (141) imply:
% 203.37/34.32  | |   (149)   ~ (e3 = e0)
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (77), (140) imply:
% 203.37/34.32  | |   (150)  op(all_14_1, all_14_1) = e3
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (57), (141) imply:
% 203.37/34.32  | |   (151)  op(e0, e3) = e2
% 203.37/34.32  | | 
% 203.37/34.32  | | GROUND_INST: instantiating (7) with all_52_7, e2, e3, e0, simplifying with
% 203.37/34.32  | |              (86), (151) gives:
% 203.37/34.32  | |   (152)  all_52_7 = e2
% 203.37/34.32  | | 
% 203.37/34.32  | | COMBINE_EQS: (63), (152) imply:
% 203.37/34.32  | |   (153)  all_58_12 = e2
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (112), (152) imply:
% 203.37/34.32  | |   (154)   ~ (all_52_3 = e2)
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (136), (152) imply:
% 203.37/34.32  | |   (155)   ~ (e3 = e2)
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (14), (152) imply:
% 203.37/34.32  | |   (156)  op(e2, e2) = all_52_6
% 203.37/34.32  | | 
% 203.37/34.32  | | GROUND_INST: instantiating (7) with all_4_2, all_52_6, e2, e2, simplifying
% 203.37/34.32  | |              with (31), (156) gives:
% 203.37/34.32  | |   (157)  all_52_6 = all_4_2
% 203.37/34.32  | | 
% 203.37/34.32  | | BETA: splitting (101) gives:
% 203.37/34.32  | | 
% 203.37/34.32  | | Case 1:
% 203.37/34.32  | | | 
% 203.37/34.32  | | |   (158)  all_56_3 = e3
% 203.37/34.32  | | | 
% 203.37/34.32  | | | REF_CLOSE: (142), (148), (158) are inconsistent by sub-proof #1200.
% 203.37/34.32  | | | 
% 203.37/34.32  | | Case 2:
% 203.37/34.32  | | | 
% 203.37/34.32  | | |   (159)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.32  | | | 
% 203.37/34.32  | | | BETA: splitting (48) gives:
% 203.37/34.32  | | | 
% 203.37/34.32  | | | Case 1:
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | |   (160)  all_56_2 = e3
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | | REF_CLOSE: (68), (110), (160) are inconsistent by sub-proof #1327.
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | Case 2:
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | |   (161)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | | BETA: splitting (74) gives:
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | | Case 1:
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | |   (162)  all_56_4 = e3
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | COMBINE_EQS: (20), (162) imply:
% 203.37/34.32  | | | | |   (163)  all_52_3 = e3
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | SIMP: (163) implies:
% 203.37/34.32  | | | | |   (164)  all_52_3 = e3
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | COMBINE_EQS: (67), (164) imply:
% 203.37/34.32  | | | | |   (165)  all_58_2 = e3
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | REDUCE: (33), (164) imply:
% 203.37/34.32  | | | | |   (166)   ~ (all_52_5 = e3)
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | SIMP: (166) implies:
% 203.37/34.32  | | | | |   (167)   ~ (all_52_5 = e3)
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | REDUCE: (128), (164) imply:
% 203.37/34.32  | | | | |   (168)   ~ (all_4_2 = e3)
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | BETA: splitting (64) gives:
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | Case 1:
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | |   (169)  all_58_6 = e3
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | | REF_CLOSE: (116), (167), (169) are inconsistent by sub-proof #1328.
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | Case 2:
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | |   (170)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | | BETA: splitting (170) gives:
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | | Case 1:
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | |   (171)  all_58_7 = e3
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | | COMBINE_EQS: (59), (171) imply:
% 203.37/34.32  | | | | | | |   (172)  all_52_13 = e3
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | | REDUCE: (106), (172) imply:
% 203.37/34.32  | | | | | | |   (173)  $false
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | | CLOSE: (173) is inconsistent.
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | Case 2:
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | |   (174)  all_58_8 = e3 | all_58_11 = e3
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | | BETA: splitting (174) gives:
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | | Case 1:
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | |   (175)  all_58_8 = e3
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | | COMBINE_EQS: (94), (175) imply:
% 203.37/34.32  | | | | | | | |   (176)  all_10_2 = e3
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | | SIMP: (176) implies:
% 203.37/34.32  | | | | | | | |   (177)  all_10_2 = e3
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | | REDUCE: (38), (177) imply:
% 203.37/34.32  | | | | | | | |   (178)  op(e3, e1) = all_10_1
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | | BETA: splitting (72) gives:
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | | Case 1:
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | |   (179)  all_58_0 = e1
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | REF_CLOSE: (119), (144), (179) are inconsistent by sub-proof
% 203.37/34.32  | | | | | | | | |            #847.
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | Case 2:
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | |   (180)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | BETA: splitting (180) gives:
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | Case 1:
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | |   (181)  all_58_2 = e1
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | COMBINE_EQS: (165), (181) imply:
% 203.37/34.32  | | | | | | | | | |   (182)  e3 = e1
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | SIMP: (182) implies:
% 203.37/34.32  | | | | | | | | | |   (183)  e3 = e1
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | REDUCE: (5), (183) imply:
% 203.37/34.32  | | | | | | | | | |   (184)  $false
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | CLOSE: (184) is inconsistent.
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | Case 2:
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | |   (185)  all_58_6 = e1 | all_58_12 = e1
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | BETA: splitting (185) gives:
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | Case 1:
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_17, all_10_1, e1,
% 203.37/34.32  | | | | | | | | | | |              e3, simplifying with (83), (178) gives:
% 203.37/34.32  | | | | | | | | | | |   (186)  all_52_17 = all_10_1
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | COMBINE_EQS: (68), (186) imply:
% 203.37/34.32  | | | | | | | | | | |   (187)  all_56_2 = all_10_1
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | COMBINE_EQS: (132), (186) imply:
% 203.37/34.32  | | | | | | | | | | |   (188)  all_58_4 = all_10_1
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | REDUCE: (146), (186) imply:
% 203.37/34.32  | | | | | | | | | | |   (189)   ~ (all_10_1 = e0)
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | BETA: splitting (85) gives:
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | Case 1:
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | |   (190)  all_58_4 = e2
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | | COMBINE_EQS: (188), (190) imply:
% 203.37/34.32  | | | | | | | | | | | |   (191)  all_10_1 = e2
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | | REF_CLOSE: (7), (49), (87), (106), (191) are inconsistent by
% 203.37/34.32  | | | | | | | | | | | |            sub-proof #532.
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | Case 2:
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | |   (192)   ~ (all_58_4 = e2)
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | | REDUCE: (188), (192) imply:
% 203.37/34.32  | | | | | | | | | | | |   (193)   ~ (all_10_1 = e2)
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | | REF_CLOSE: (7), (16), (26), (29), (31), (59), (69), (75),
% 203.37/34.32  | | | | | | | | | | | |            (88), (106), (121), (126), (143), (144), (150),
% 203.37/34.32  | | | | | | | | | | | |            (161), (187), (188), (189), (193) are inconsistent
% 203.37/34.32  | | | | | | | | | | | |            by sub-proof #807.
% 203.37/34.32  | | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | End of split
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | Case 2:
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | |   (194)  all_58_12 = e1
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | | REF_CLOSE: (51), (153), (194) are inconsistent by sub-proof
% 203.37/34.32  | | | | | | | | | | |            #1198.
% 203.37/34.32  | | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | | End of split
% 203.37/34.32  | | | | | | | | | | 
% 203.37/34.32  | | | | | | | | | End of split
% 203.37/34.32  | | | | | | | | | 
% 203.37/34.32  | | | | | | | | End of split
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | Case 2:
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | |   (195)  all_58_11 = e3
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | | REF_CLOSE: (34), (137), (195) are inconsistent by sub-proof
% 203.37/34.32  | | | | | | | |            #1323.
% 203.37/34.32  | | | | | | | | 
% 203.37/34.32  | | | | | | | End of split
% 203.37/34.32  | | | | | | | 
% 203.37/34.32  | | | | | | End of split
% 203.37/34.32  | | | | | | 
% 203.37/34.32  | | | | | End of split
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | Case 2:
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | |   (196)   ~ (all_56_4 = e3)
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | REDUCE: (20), (196) imply:
% 203.37/34.32  | | | | |   (197)   ~ (all_52_3 = e3)
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | REF_CLOSE: (7), (10), (16), (26), (29), (31), (39), (46), (59), (67),
% 203.37/34.32  | | | | |            (70), (88), (96), (106), (116), (121), (123), (126), (142),
% 203.37/34.32  | | | | |            (143), (144), (147), (150), (153), (159), (197) are
% 203.37/34.32  | | | | |            inconsistent by sub-proof #803.
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | End of split
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | End of split
% 203.37/34.32  | | | 
% 203.37/34.32  | | End of split
% 203.37/34.32  | | 
% 203.37/34.32  | Case 2:
% 203.37/34.32  | | 
% 203.37/34.32  | |   (198)   ~ (all_56_15 = e3)
% 203.37/34.32  | |   (199)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (44), (198) imply:
% 203.37/34.32  | |   (200)   ~ (all_14_2 = e3)
% 203.37/34.32  | | 
% 203.37/34.32  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.37/34.32  | |            (14), (15), (16), (17), (18), (21), (23), (24), (25), (26), (27),
% 203.37/34.32  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 203.37/34.32  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (50), (53),
% 203.37/34.32  | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 203.37/34.32  | |            (65), (66), (67), (68), (70), (71), (73), (75), (76), (77), (78),
% 203.37/34.32  | |            (80), (81), (82), (83), (84), (85), (88), (89), (90), (91), (92),
% 203.37/34.32  | |            (93), (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.37/34.32  | |            (104), (105), (106), (107), (108), (109), (111), (112), (113),
% 203.37/34.32  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 203.37/34.32  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 203.37/34.32  | |            (132), (199), (200) are inconsistent by sub-proof #795.
% 203.37/34.32  | | 
% 203.37/34.32  | End of split
% 203.37/34.32  | 
% 203.37/34.32  End of proof
% 203.37/34.32  
% 203.37/34.32  Sub-proof #532 shows that the following formulas are inconsistent:
% 203.37/34.32  ----------------------------------------------------------------
% 203.37/34.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.32    (2)  op(e1, all_10_1) = e3
% 203.37/34.32    (3)  op(e1, e2) = all_52_13
% 203.37/34.32    (4)  all_10_1 = e2
% 203.37/34.32    (5)   ~ (all_52_13 = e3)
% 203.37/34.32  
% 203.37/34.32  Begin of proof
% 203.37/34.32  | 
% 203.37/34.32  | REDUCE: (2), (4) imply:
% 203.37/34.32  |   (6)  op(e1, e2) = e3
% 203.37/34.32  | 
% 203.37/34.32  | GROUND_INST: instantiating (1) with all_52_13, e3, e2, e1, simplifying with
% 203.37/34.32  |              (3), (6) gives:
% 203.37/34.32  |   (7)  all_52_13 = e3
% 203.37/34.32  | 
% 203.37/34.32  | REDUCE: (5), (7) imply:
% 203.37/34.32  |   (8)  $false
% 203.37/34.32  | 
% 203.37/34.32  | CLOSE: (8) is inconsistent.
% 203.37/34.32  | 
% 203.37/34.32  End of proof
% 203.37/34.32  
% 203.37/34.32  Sub-proof #533 shows that the following formulas are inconsistent:
% 203.37/34.32  ----------------------------------------------------------------
% 203.37/34.32    (1)  all_58_14 = all_52_23
% 203.37/34.32    (2)   ~ (e3 = e1)
% 203.37/34.32    (3)  op(all_52_3, all_52_3) = all_52_2
% 203.37/34.32    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.32    (5)   ~ (e3 = e0)
% 203.37/34.32    (6)  op(all_52_23, all_52_23) = e0
% 203.37/34.32    (7)  op(e2, e3) = all_52_3
% 203.37/34.32    (8)   ~ (all_52_3 = all_52_19)
% 203.37/34.32    (9)   ~ (all_52_17 = all_52_25)
% 203.37/34.32    (10)   ~ (all_4_2 = e3)
% 203.37/34.32    (11)   ~ (all_52_3 = all_6_2)
% 203.37/34.32    (12)  all_58_0 = all_6_2
% 203.37/34.32    (13)  op(all_52_5, all_52_5) = all_52_4
% 203.37/34.32    (14)  all_58_13 = all_52_15
% 203.37/34.32    (15)  all_58_9 = all_52_25
% 203.37/34.32    (16)   ~ (all_52_29 = all_14_2)
% 203.37/34.32    (17)   ~ (all_52_15 = e3)
% 203.37/34.32    (18)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.37/34.32    (19)  op(all_52_27, all_52_27) = all_52_26
% 203.37/34.32    (20)  op(e1, e3) = all_52_5
% 203.37/34.32    (21)  op(e2, e2) = all_4_2
% 203.37/34.32    (22)  all_58_11 = all_52_29
% 203.37/34.32    (23)   ~ (all_52_25 = all_14_2)
% 203.37/34.32    (24)  op(all_10_2, e1) = all_10_1
% 203.37/34.32    (25)  all_58_1 = e3
% 203.37/34.32    (26)   ~ (all_52_7 = all_6_2)
% 203.37/34.32    (27)  op(e0, e0) = all_14_2
% 203.37/34.32    (28)  all_56_15 = all_14_2
% 203.37/34.32    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.32    (30)  op(e1, e0) = all_52_29
% 203.37/34.32    (31)  all_56_11 = all_52_29
% 203.37/34.32    (32)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.37/34.32    (33)  op(e1, all_10_1) = e3
% 203.37/34.32    (34)   ~ (all_6_2 = e3)
% 203.37/34.32    (35)   ~ (e2 = e1)
% 203.37/34.32    (36)   ~ (all_52_13 = all_10_2)
% 203.37/34.32    (37)  op(all_10_2, all_10_2) = e1
% 203.37/34.32    (38)  all_58_10 = all_52_27
% 203.37/34.32    (39)   ~ (all_52_19 = all_52_23)
% 203.37/34.32    (40)  op(all_6_2, e3) = e2
% 203.37/34.32    (41)   ~ (all_52_29 = all_10_2)
% 203.37/34.32    (42)  all_58_7 = all_52_13
% 203.37/34.32    (43)  op(all_52_19, all_52_19) = e2
% 203.37/34.32    (44)  all_58_12 = all_52_7
% 203.37/34.32    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.37/34.32    (46)   ~ (all_52_7 = all_14_2)
% 203.37/34.32    (47)   ~ (all_14_2 = e0)
% 203.37/34.32    (48)  all_58_2 = all_52_3
% 203.37/34.32    (49)  all_56_2 = all_52_17
% 203.37/34.32    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.32    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.32    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.37/34.32    (53)   ~ (all_52_25 = e3)
% 203.37/34.32    (54)   ~ (e2 = e0)
% 203.37/34.32    (55)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.37/34.32    (56)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.32    (57)   ~ (all_52_15 = all_14_2)
% 203.37/34.32    (58)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.37/34.32    (59)  op(e3, e3) = all_52_8
% 203.37/34.32    (60)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.37/34.32    (61)  op(e3, e1) = all_52_17
% 203.37/34.32    (62)  op(e0, e3) = all_52_7
% 203.37/34.32    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.32    (64)  all_58_15 = all_14_2
% 203.37/34.32    (65)   ~ (all_52_19 = all_10_2)
% 203.37/34.32    (66)  all_58_8 = all_10_2
% 203.37/34.32    (67)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.37/34.32    (68)   ~ (all_52_5 = all_10_2)
% 203.37/34.32    (69)   ~ (all_52_23 = all_14_2)
% 203.37/34.32    (70)   ~ (all_52_25 = all_6_2)
% 203.37/34.32    (71)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.37/34.32    (72)   ~ (all_52_5 = all_6_2)
% 203.37/34.32    (73)  op(e3, e3) = all_6_2
% 203.37/34.32    (74)   ~ (all_52_13 = e3)
% 203.37/34.32    (75)   ~ (all_52_27 = all_14_2)
% 203.37/34.32    (76)   ~ (all_52_17 = e3)
% 203.37/34.32    (77)  all_56_3 = all_52_25
% 203.37/34.32    (78)   ~ (all_52_3 = all_52_7)
% 203.37/34.32    (79)  op(all_14_2, all_14_2) = all_52_30
% 203.37/34.32    (80)  all_58_5 = all_52_19
% 203.37/34.32    (81)   ~ (all_52_27 = all_4_2)
% 203.37/34.32    (82)  op(all_52_17, all_52_17) = e3
% 203.37/34.32    (83)  all_58_6 = all_52_5
% 203.37/34.32    (84)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.32    (85)   ~ (all_52_17 = all_6_2)
% 203.37/34.32    (86)   ~ (e1 = e0)
% 203.37/34.32    (87)  all_56_10 = all_10_2
% 203.37/34.32    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.32    (89)  op(e1, e1) = all_10_2
% 203.37/34.32    (90)   ~ (all_52_23 = all_10_2)
% 203.37/34.32    (91)   ~ (all_52_7 = all_52_23)
% 203.37/34.32    (92)   ~ (all_52_17 = all_52_19)
% 203.37/34.32    (93)  all_58_3 = all_4_2
% 203.37/34.32    (94)   ~ (all_52_3 = all_4_2)
% 203.37/34.32    (95)   ~ (all_52_17 = all_52_23)
% 203.37/34.32    (96)  all_58_4 = all_52_17
% 203.37/34.32    (97)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.37/34.32  
% 203.37/34.32  Begin of proof
% 203.37/34.32  | 
% 203.37/34.32  | BETA: splitting (67) gives:
% 203.37/34.32  | 
% 203.37/34.32  | Case 1:
% 203.37/34.32  | | 
% 203.37/34.32  | |   (98)  all_56_15 = e3
% 203.37/34.32  | | 
% 203.37/34.32  | | COMBINE_EQS: (28), (98) imply:
% 203.37/34.32  | |   (99)  all_14_2 = e3
% 203.37/34.32  | | 
% 203.37/34.32  | | SIMP: (99) implies:
% 203.37/34.32  | |   (100)  all_14_2 = e3
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (69), (100) imply:
% 203.37/34.32  | |   (101)   ~ (all_52_23 = e3)
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (75), (100) imply:
% 203.37/34.32  | |   (102)   ~ (all_52_27 = e3)
% 203.37/34.32  | | 
% 203.37/34.32  | | REDUCE: (79), (100) imply:
% 203.37/34.32  | |   (103)  op(e3, e3) = all_52_30
% 203.37/34.32  | | 
% 203.37/34.32  | | GROUND_INST: instantiating (4) with all_6_2, all_52_30, e3, e3, simplifying
% 203.37/34.32  | |              with (73), (103) gives:
% 203.37/34.32  | |   (104)  all_52_30 = all_6_2
% 203.37/34.32  | | 
% 203.37/34.32  | | BETA: splitting (29) gives:
% 203.37/34.32  | | 
% 203.37/34.32  | | Case 1:
% 203.37/34.32  | | | 
% 203.37/34.32  | | |   (105)  all_58_2 = e3
% 203.37/34.32  | | | 
% 203.37/34.32  | | | COMBINE_EQS: (48), (105) imply:
% 203.37/34.32  | | |   (106)  all_52_3 = e3
% 203.37/34.32  | | | 
% 203.37/34.32  | | | SIMP: (106) implies:
% 203.37/34.32  | | |   (107)  all_52_3 = e3
% 203.37/34.32  | | | 
% 203.37/34.32  | | | REDUCE: (78), (107) imply:
% 203.37/34.32  | | |   (108)   ~ (all_52_7 = e3)
% 203.37/34.32  | | | 
% 203.37/34.32  | | | SIMP: (108) implies:
% 203.37/34.32  | | |   (109)   ~ (all_52_7 = e3)
% 203.37/34.32  | | | 
% 203.37/34.32  | | | REDUCE: (8), (107) imply:
% 203.37/34.32  | | |   (110)   ~ (all_52_19 = e3)
% 203.37/34.32  | | | 
% 203.37/34.32  | | | SIMP: (110) implies:
% 203.37/34.32  | | |   (111)   ~ (all_52_19 = e3)
% 203.37/34.32  | | | 
% 203.37/34.32  | | | REDUCE: (11), (107) imply:
% 203.37/34.32  | | |   (112)   ~ (all_6_2 = e3)
% 203.37/34.32  | | | 
% 203.37/34.32  | | | REDUCE: (94), (107) imply:
% 203.37/34.32  | | |   (113)   ~ (all_4_2 = e3)
% 203.37/34.32  | | | 
% 203.37/34.32  | | | REDUCE: (3), (107) imply:
% 203.37/34.32  | | |   (114)  op(e3, e3) = all_52_2
% 203.37/34.32  | | | 
% 203.37/34.32  | | | BETA: splitting (88) gives:
% 203.37/34.32  | | | 
% 203.37/34.32  | | | Case 1:
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | |   (115)  all_58_4 = e3
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | | REF_CLOSE: (76), (96), (115) are inconsistent by sub-proof #1302.
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | Case 2:
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | |   (116)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | | BETA: splitting (116) gives:
% 203.37/34.32  | | | | 
% 203.37/34.32  | | | | Case 1:
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | |   (117)  all_58_5 = e3
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | | REF_CLOSE: (80), (111), (117) are inconsistent by sub-proof #1279.
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | Case 2:
% 203.37/34.32  | | | | | 
% 203.37/34.32  | | | | |   (118)  all_58_8 = e3 | all_58_14 = e3
% 203.37/34.32  | | | | | 
% 203.37/34.33  | | | | | BETA: splitting (118) gives:
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | Case 1:
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | |   (119)  all_58_8 = e3
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | COMBINE_EQS: (66), (119) imply:
% 203.37/34.33  | | | | | |   (120)  all_10_2 = e3
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | SIMP: (120) implies:
% 203.37/34.33  | | | | | |   (121)  all_10_2 = e3
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (68), (121) imply:
% 203.37/34.33  | | | | | |   (122)   ~ (all_52_5 = e3)
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (41), (121) imply:
% 203.37/34.33  | | | | | |   (123)   ~ (all_52_29 = e3)
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (37), (121) imply:
% 203.37/34.33  | | | | | |   (124)  op(e3, e3) = e1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (24), (121) imply:
% 203.37/34.33  | | | | | |   (125)  op(e3, e1) = all_10_1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | GROUND_INST: instantiating (4) with all_52_17, all_10_1, e1, e3,
% 203.37/34.33  | | | | | |              simplifying with (61), (125) gives:
% 203.37/34.33  | | | | | |   (126)  all_52_17 = all_10_1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_2, e3, e3,
% 203.37/34.33  | | | | | |              simplifying with (73), (114) gives:
% 203.37/34.33  | | | | | |   (127)  all_52_2 = all_6_2
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | GROUND_INST: instantiating (4) with e1, all_52_2, e3, e3,
% 203.37/34.33  | | | | | |              simplifying with (114), (124) gives:
% 203.37/34.33  | | | | | |   (128)  all_52_2 = e1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | COMBINE_EQS: (127), (128) imply:
% 203.37/34.33  | | | | | |   (129)  all_6_2 = e1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | SIMP: (129) implies:
% 203.37/34.33  | | | | | |   (130)  all_6_2 = e1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | COMBINE_EQS: (96), (126) imply:
% 203.37/34.33  | | | | | |   (131)  all_58_4 = all_10_1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | COMBINE_EQS: (12), (130) imply:
% 203.37/34.33  | | | | | |   (132)  all_58_0 = e1
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (72), (130) imply:
% 203.37/34.33  | | | | | |   (133)   ~ (all_52_5 = e1)
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (34), (130) imply:
% 203.37/34.33  | | | | | |   (134)   ~ (e3 = e1)
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (40), (130) imply:
% 203.37/34.33  | | | | | |   (135)  op(e1, e3) = e2
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | GROUND_INST: instantiating (4) with all_52_5, e2, e3, e1,
% 203.37/34.33  | | | | | |              simplifying with (20), (135) gives:
% 203.37/34.33  | | | | | |   (136)  all_52_5 = e2
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REDUCE: (122), (136) imply:
% 203.37/34.33  | | | | | |   (137)   ~ (e3 = e2)
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | SIMP: (137) implies:
% 203.37/34.33  | | | | | |   (138)   ~ (e3 = e2)
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (14), (17), (21), (25), (30),
% 203.37/34.33  | | | | | |            (33), (35), (42), (44), (48), (50), (51), (52), (54),
% 203.37/34.33  | | | | | |            (61), (63), (73), (74), (82), (83), (86), (93), (94),
% 203.37/34.33  | | | | | |            (109), (122), (123), (124), (125), (131), (132), (138)
% 203.37/34.33  | | | | | |            are inconsistent by sub-proof #534.
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | Case 2:
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | |   (139)  all_58_14 = e3
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | | REF_CLOSE: (1), (101), (139) are inconsistent by sub-proof #1305.
% 203.37/34.33  | | | | | | 
% 203.37/34.33  | | | | | End of split
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | End of split
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | End of split
% 203.37/34.33  | | | 
% 203.37/34.33  | | Case 2:
% 203.37/34.33  | | | 
% 203.37/34.33  | | |   (140)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.33  | | | 
% 203.37/34.33  | | | REF_CLOSE: (1), (2), (4), (5), (7), (10), (11), (12), (13), (15), (16),
% 203.37/34.33  | | |            (18), (22), (25), (27), (31), (35), (37), (38), (39), (40),
% 203.37/34.33  | | |            (41), (42), (43), (45), (52), (54), (55), (58), (59), (65),
% 203.37/34.33  | | |            (66), (73), (74), (80), (82), (83), (86), (88), (89), (92),
% 203.37/34.33  | | |            (93), (96), (102), (140) are inconsistent by sub-proof #828.
% 203.37/34.33  | | | 
% 203.37/34.33  | | End of split
% 203.37/34.33  | | 
% 203.37/34.33  | Case 2:
% 203.37/34.33  | | 
% 203.37/34.33  | |   (141)   ~ (all_56_15 = e3)
% 203.37/34.33  | | 
% 203.37/34.33  | | REDUCE: (28), (141) imply:
% 203.37/34.33  | |   (142)   ~ (all_14_2 = e3)
% 203.37/34.33  | | 
% 203.37/34.33  | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (12), (14), (15), (17), (18),
% 203.37/34.33  | |            (19), (21), (23), (24), (25), (26), (27), (29), (32), (34), (35),
% 203.37/34.33  | |            (37), (38), (39), (40), (43), (44), (46), (48), (49), (52), (53),
% 203.37/34.33  | |            (54), (55), (56), (59), (60), (61), (62), (64), (65), (66), (70),
% 203.37/34.33  | |            (71), (73), (75), (76), (77), (78), (80), (81), (82), (84), (85),
% 203.37/34.33  | |            (86), (87), (88), (89), (90), (91), (93), (95), (96), (97), (142)
% 203.37/34.33  | |            are inconsistent by sub-proof #813.
% 203.37/34.33  | | 
% 203.37/34.33  | End of split
% 203.37/34.33  | 
% 203.37/34.33  End of proof
% 203.37/34.33  
% 203.37/34.33  Sub-proof #534 shows that the following formulas are inconsistent:
% 203.37/34.33  ----------------------------------------------------------------
% 203.37/34.33    (1)   ~ (e3 = e1)
% 203.37/34.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.33    (3)   ~ (e3 = e0)
% 203.37/34.33    (4)   ~ (all_4_2 = e3)
% 203.37/34.33    (5)  all_58_0 = all_6_2
% 203.37/34.33    (6)  all_58_13 = all_52_15
% 203.37/34.33    (7)   ~ (all_52_15 = e3)
% 203.37/34.33    (8)  op(e2, e2) = all_4_2
% 203.37/34.33    (9)  all_58_4 = all_10_1
% 203.37/34.33    (10)  all_58_1 = e3
% 203.37/34.33    (11)  op(e1, e0) = all_52_29
% 203.37/34.33    (12)  op(e1, all_10_1) = e3
% 203.37/34.33    (13)   ~ (e2 = e1)
% 203.37/34.33    (14)  all_58_7 = all_52_13
% 203.37/34.33    (15)  all_58_12 = all_52_7
% 203.37/34.33    (16)   ~ (all_52_7 = e3)
% 203.37/34.33    (17)  all_58_2 = all_52_3
% 203.37/34.33    (18)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.33    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.33    (20)   ~ (all_52_29 = e3)
% 203.37/34.33    (21)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.37/34.33    (22)  op(e3, e1) = all_10_1
% 203.37/34.33    (23)   ~ (e2 = e0)
% 203.37/34.33    (24)   ~ (all_52_5 = e3)
% 203.37/34.33    (25)  op(e3, e1) = all_52_17
% 203.37/34.33    (26)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.33    (27)  op(e3, e3) = all_6_2
% 203.37/34.33    (28)   ~ (all_52_13 = e3)
% 203.37/34.33    (29)  op(e3, e3) = e1
% 203.37/34.33    (30)  op(all_52_17, all_52_17) = e3
% 203.37/34.33    (31)  all_58_6 = all_52_5
% 203.37/34.33    (32)   ~ (e1 = e0)
% 203.37/34.33    (33)   ~ (e3 = e2)
% 203.37/34.33    (34)  all_58_3 = all_4_2
% 203.37/34.33    (35)   ~ (all_52_3 = all_4_2)
% 203.37/34.33    (36)  all_58_0 = e1
% 203.37/34.33  
% 203.37/34.33  Begin of proof
% 203.37/34.33  | 
% 203.37/34.33  | BETA: splitting (18) gives:
% 203.37/34.33  | 
% 203.37/34.33  | Case 1:
% 203.37/34.33  | | 
% 203.37/34.33  | |   (37)  all_58_0 = e2
% 203.37/34.33  | | 
% 203.37/34.33  | | REF_CLOSE: (13), (36), (37) are inconsistent by sub-proof #1273.
% 203.37/34.33  | | 
% 203.37/34.33  | Case 2:
% 203.37/34.33  | | 
% 203.37/34.33  | |   (38)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.37/34.33  | | 
% 203.37/34.33  | | BETA: splitting (21) gives:
% 203.37/34.33  | | 
% 203.37/34.33  | | Case 1:
% 203.37/34.33  | | | 
% 203.37/34.33  | | |   (39)  all_58_0 = e0
% 203.37/34.33  | | | 
% 203.37/34.33  | | | COMBINE_EQS: (36), (39) imply:
% 203.37/34.33  | | |   (40)  e1 = e0
% 203.37/34.33  | | | 
% 203.37/34.33  | | | REDUCE: (32), (40) imply:
% 203.37/34.33  | | |   (41)  $false
% 203.37/34.33  | | | 
% 203.37/34.33  | | | CLOSE: (41) is inconsistent.
% 203.37/34.33  | | | 
% 203.37/34.33  | | Case 2:
% 203.37/34.33  | | | 
% 203.37/34.33  | | |   (42)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.37/34.33  | | | 
% 203.37/34.33  | | | BETA: splitting (42) gives:
% 203.37/34.33  | | | 
% 203.37/34.33  | | | Case 1:
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | |   (43)  all_58_1 = e0
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | | COMBINE_EQS: (10), (43) imply:
% 203.37/34.33  | | | |   (44)  e3 = e0
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | | REDUCE: (3), (44) imply:
% 203.37/34.33  | | | |   (45)  $false
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | | CLOSE: (45) is inconsistent.
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | Case 2:
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | |   (46)  all_58_4 = e0 | all_58_9 = e0
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | | BETA: splitting (46) gives:
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | | Case 1:
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | |   (47)  all_58_4 = e0
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | COMBINE_EQS: (9), (47) imply:
% 203.37/34.33  | | | | |   (48)  all_10_1 = e0
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | REDUCE: (12), (48) imply:
% 203.37/34.33  | | | | |   (49)  op(e1, e0) = e3
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | GROUND_INST: instantiating (2) with all_52_29, e3, e0, e1, simplifying
% 203.37/34.33  | | | | |              with (11), (49) gives:
% 203.37/34.33  | | | | |   (50)  all_52_29 = e3
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | REDUCE: (20), (50) imply:
% 203.37/34.33  | | | | |   (51)  $false
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | CLOSE: (51) is inconsistent.
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | Case 2:
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | |   (52)  all_58_9 = e0
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (14), (15), (16),
% 203.37/34.33  | | | | |            (17), (19), (22), (23), (24), (25), (26), (27), (28), (29),
% 203.37/34.33  | | | | |            (30), (31), (33), (34), (35), (38), (52) are inconsistent
% 203.37/34.33  | | | | |            by sub-proof #1083.
% 203.37/34.33  | | | | | 
% 203.37/34.33  | | | | End of split
% 203.37/34.33  | | | | 
% 203.37/34.33  | | | End of split
% 203.37/34.33  | | | 
% 203.37/34.33  | | End of split
% 203.37/34.33  | | 
% 203.37/34.33  | End of split
% 203.37/34.33  | 
% 203.37/34.33  End of proof
% 203.37/34.33  
% 203.37/34.33  Sub-proof #535 shows that the following formulas are inconsistent:
% 203.37/34.33  ----------------------------------------------------------------
% 203.37/34.33    (1)  all_58_14 = all_52_23
% 203.37/34.33    (2)  op(all_52_3, all_52_3) = all_52_2
% 203.37/34.33    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.33    (4)   ~ (e3 = e0)
% 203.37/34.33    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.37/34.33    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.33    (7)  op(e0, e2) = all_52_15
% 203.37/34.33    (8)   ~ (all_52_7 = all_52_15)
% 203.37/34.33    (9)  op(all_52_7, all_52_7) = all_52_6
% 203.37/34.33    (10)  all_58_0 = all_6_2
% 203.37/34.33    (11)  op(all_52_5, all_52_5) = all_52_4
% 203.37/34.33    (12)  all_58_13 = all_52_15
% 203.37/34.33    (13)  op(e1, e3) = all_52_5
% 203.37/34.33    (14)  op(e2, e2) = all_4_2
% 203.37/34.33    (15)   ~ (all_4_1 = e3)
% 203.37/34.33    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.37/34.33    (17)  op(all_10_2, e1) = all_10_1
% 203.37/34.33    (18)  op(all_6_2, all_6_2) = all_52_0
% 203.37/34.33    (19)   ~ (all_52_7 = all_6_2)
% 203.37/34.33    (20)  op(e0, e0) = all_14_2
% 203.37/34.33    (21)  op(e0, e1) = all_52_23
% 203.37/34.33    (22)   ~ (all_52_15 = e0)
% 203.37/34.33    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.37/34.33    (24)  all_58_15 = e0
% 203.37/34.33    (25)   ~ (all_4_1 = e1)
% 203.37/34.33    (26)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.33    (27)  op(e1, all_10_1) = e3
% 203.37/34.33    (28)   ~ (e2 = e1)
% 203.37/34.33    (29)  all_36_2 = all_10_2
% 203.37/34.33    (30)  all_36_1 = all_10_1
% 203.37/34.33    (31)  all_58_12 = all_52_7
% 203.37/34.33    (32)   ~ (all_52_7 = all_14_2)
% 203.37/34.33    (33)  all_58_2 = all_52_3
% 203.37/34.33    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.37/34.33    (35)   ~ (e2 = e0)
% 203.37/34.33    (36)  op(all_4_2, e2) = all_4_1
% 203.37/34.33    (37)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.37/34.33    (38)  op(all_52_23, all_52_23) = all_52_22
% 203.37/34.33    (39)   ~ (all_52_5 = all_10_2)
% 203.37/34.33    (40)  all_56_12 = all_52_7
% 203.37/34.33    (41)  op(e3, e3) = all_6_2
% 203.37/34.33    (42)  all_58_6 = all_52_5
% 203.37/34.33    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.37/34.33    (44)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.37/34.33    (45)   ~ (e3 = e2)
% 203.37/34.33    (46)  op(e1, e1) = all_10_2
% 203.37/34.33    (47)   ~ (all_52_7 = all_52_23)
% 203.37/34.33    (48)  all_56_13 = all_52_15
% 203.37/34.33    (49)   ~ (all_52_3 = all_4_2)
% 203.37/34.33    (50)   ~ (all_52_7 = e0)
% 203.37/34.33  
% 203.37/34.33  Begin of proof
% 203.37/34.33  | 
% 203.37/34.33  | ALPHA: (5) implies:
% 203.37/34.33  |   (51)  all_52_6 = e0
% 203.37/34.33  |   (52)  all_52_4 = e1
% 203.37/34.33  |   (53)  all_52_2 = e2
% 203.37/34.33  |   (54)  all_52_0 = e3
% 203.37/34.33  | 
% 203.37/34.33  | REDUCE: (2), (53) imply:
% 203.37/34.33  |   (55)  op(all_52_3, all_52_3) = e2
% 203.37/34.33  | 
% 203.37/34.33  | REDUCE: (11), (52) imply:
% 203.37/34.33  |   (56)  op(all_52_5, all_52_5) = e1
% 203.37/34.33  | 
% 203.37/34.33  | REDUCE: (9), (51) imply:
% 203.37/34.33  |   (57)  op(all_52_7, all_52_7) = e0
% 203.37/34.33  | 
% 203.37/34.33  | REDUCE: (18), (54) imply:
% 203.37/34.33  |   (58)  op(all_6_2, all_6_2) = e3
% 203.37/34.33  | 
% 203.37/34.33  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (12), (13), (14), (15), (16),
% 203.37/34.33  |            (17), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 203.37/34.33  |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 203.37/34.33  |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 203.37/34.33  |            (55), (56), (57), (58) are inconsistent by sub-proof #547.
% 203.37/34.33  | 
% 203.37/34.33  End of proof
% 203.37/34.33  
% 203.37/34.33  Sub-proof #536 shows that the following formulas are inconsistent:
% 203.37/34.33  ----------------------------------------------------------------
% 203.37/34.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.37/34.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.37/34.33    (2)  all_58_1 = all_52_9
% 203.37/34.33    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.37/34.33    (4)   ~ (all_52_7 = all_52_15)
% 203.37/34.33    (5)  op(all_52_15, all_52_15) = e0
% 203.37/34.33    (6)   ~ (all_4_2 = e3)
% 203.37/34.33    (7)  all_58_0 = all_6_2
% 203.37/34.33    (8)   ~ (all_6_2 = e2)
% 203.37/34.33    (9)  all_58_13 = all_52_15
% 203.37/34.33    (10)  op(all_52_13, all_52_13) = e1
% 203.37/34.33    (11)   ~ (all_6_1 = e1)
% 203.37/34.33    (12)  op(e1, e3) = all_52_5
% 203.37/34.33    (13)   ~ (all_6_2 = all_4_0)
% 203.37/34.33    (14)  all_32_2 = all_4_2
% 203.37/34.33    (15)  op(e2, e2) = all_4_2
% 203.37/34.33    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.37/34.33    (17)  all_56_5 = all_4_2
% 203.37/34.33    (18)   ~ (all_52_7 = all_6_2)
% 203.37/34.33    (19)  op(all_4_2, e2) = e3
% 203.37/34.33    (20)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.37/34.33    (21)  all_58_7 = all_52_13
% 203.37/34.33    (22)  all_58_12 = all_52_7
% 203.37/34.33    (23)  op(e3, all_6_1) = all_6_0
% 203.37/34.33    (24)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.37/34.33    (25)   ~ (e2 = e0)
% 203.37/34.33    (26)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.37/34.33    (27)  op(e3, e0) = e2
% 203.37/34.33    (28)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.37/34.33    (29)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.37/34.33    (30)  all_56_4 = all_4_0
% 203.37/34.33    (31)   ~ (all_6_0 = e2)
% 203.37/34.33    (32)  op(e0, e3) = all_52_7
% 203.37/34.33    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.37/34.33    (34)   ~ (all_52_7 = all_4_0)
% 203.37/34.33    (35)  all_56_12 = all_52_7
% 203.37/34.33    (36)   ~ (all_52_9 = all_4_2)
% 203.37/34.33    (37)   ~ (all_52_9 = all_6_2)
% 203.37/34.33    (38)  op(e3, e3) = all_6_2
% 203.37/34.33    (39)  op(all_4_2, all_4_2) = all_52_10
% 203.37/34.33    (40)  all_32_0 = all_4_0
% 203.37/34.33    (41)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.37/34.33    (42)  all_58_6 = all_52_5
% 203.37/34.33    (43)   ~ (all_4_0 = all_4_2)
% 203.37/34.33    (44)  op(e3, e2) = all_52_9
% 203.37/34.33    (45)   ~ (e1 = e0)
% 203.47/34.33    (46)   ~ (e3 = e2)
% 203.47/34.33    (47)   ~ (all_6_1 = e2)
% 203.47/34.33    (48)  op(all_52_9, all_52_9) = e3
% 203.47/34.33    (49)  all_58_3 = all_4_2
% 203.47/34.33    (50)  all_56_13 = all_52_15
% 203.47/34.33    (51)  op(all_6_2, e3) = all_6_1
% 203.47/34.33    (52)   ~ (all_52_7 = e0)
% 203.47/34.33  
% 203.47/34.33  Begin of proof
% 203.47/34.33  | 
% 203.47/34.33  | BETA: splitting (24) gives:
% 203.47/34.33  | 
% 203.47/34.33  | Case 1:
% 203.47/34.33  | | 
% 203.47/34.33  | |   (53)  all_58_0 = e1
% 203.47/34.33  | | 
% 203.47/34.33  | | COMBINE_EQS: (7), (53) imply:
% 203.47/34.33  | |   (54)  all_6_2 = e1
% 203.47/34.33  | | 
% 203.47/34.33  | | REDUCE: (18), (54) imply:
% 203.47/34.33  | |   (55)   ~ (all_52_7 = e1)
% 203.47/34.33  | | 
% 203.47/34.33  | | REDUCE: (13), (54) imply:
% 203.47/34.33  | |   (56)   ~ (all_4_0 = e1)
% 203.47/34.33  | | 
% 203.47/34.33  | | SIMP: (56) implies:
% 203.47/34.33  | |   (57)   ~ (all_4_0 = e1)
% 203.47/34.33  | | 
% 203.47/34.33  | | REDUCE: (8), (54) imply:
% 203.47/34.33  | |   (58)   ~ (e2 = e1)
% 203.47/34.33  | | 
% 203.47/34.33  | | SIMP: (58) implies:
% 203.47/34.33  | |   (59)   ~ (e2 = e1)
% 203.47/34.33  | | 
% 203.47/34.33  | | REDUCE: (51), (54) imply:
% 203.47/34.33  | |   (60)  op(e1, e3) = all_6_1
% 203.47/34.33  | | 
% 203.47/34.34  | | REF_CLOSE: (1), (3), (12), (14), (15), (16), (17), (19), (22), (23), (25),
% 203.47/34.34  | |            (26), (27), (28), (29), (30), (31), (34), (35), (36), (39), (40),
% 203.47/34.34  | |            (41), (42), (43), (44), (45), (46), (47), (52), (53), (55), (57),
% 203.47/34.34  | |            (59), (60) are inconsistent by sub-proof #965.
% 203.47/34.34  | | 
% 203.47/34.34  | Case 2:
% 203.47/34.34  | | 
% 203.47/34.34  | |   (61)   ~ (all_58_0 = e1)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (7), (61) imply:
% 203.47/34.34  | |   (62)   ~ (all_6_2 = e1)
% 203.47/34.34  | | 
% 203.47/34.34  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (18), (20), (21),
% 203.47/34.34  | |            (32), (33), (35), (37), (38), (47), (48), (49), (50), (51), (62)
% 203.47/34.34  | |            are inconsistent by sub-proof #892.
% 203.47/34.34  | | 
% 203.47/34.34  | End of split
% 203.47/34.34  | 
% 203.47/34.34  End of proof
% 203.47/34.34  
% 203.47/34.34  Sub-proof #537 shows that the following formulas are inconsistent:
% 203.47/34.34  ----------------------------------------------------------------
% 203.47/34.34    (1)   ~ (all_52_15 = all_52_23)
% 203.47/34.34    (2)   ~ (all_52_25 = all_52_27)
% 203.47/34.34    (3)  all_58_14 = all_52_23
% 203.47/34.34    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.34    (5)  op(all_52_7, all_52_7) = e0
% 203.47/34.34    (6)  all_58_1 = all_52_9
% 203.47/34.34    (7)  op(all_52_5, all_52_5) = e1
% 203.47/34.34    (8)   ~ (e3 = e0)
% 203.47/34.34    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.34    (10)  op(e0, e2) = all_52_15
% 203.47/34.34    (11)   ~ (all_52_7 = all_52_15)
% 203.47/34.34    (12)   ~ (all_52_3 = all_6_2)
% 203.47/34.34    (13)  all_58_0 = all_6_2
% 203.47/34.34    (14)  op(all_14_2, e0) = all_14_1
% 203.47/34.34    (15)  all_56_4 = all_52_3
% 203.47/34.34    (16)   ~ (all_52_17 = all_10_2)
% 203.47/34.34    (17)  op(e3, e0) = all_52_25
% 203.47/34.34    (18)  op(e0, all_14_1) = all_14_0
% 203.47/34.34    (19)  all_58_13 = all_52_15
% 203.47/34.34    (20)  op(all_10_2, all_10_2) = all_52_20
% 203.47/34.34    (21)  all_58_9 = all_52_25
% 203.47/34.34    (22)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.47/34.34    (23)   ~ (all_52_29 = all_14_2)
% 203.47/34.34    (24)  op(e2, e2) = all_4_2
% 203.47/34.34    (25)   ~ (all_52_3 = all_52_5)
% 203.47/34.34    (26)   ~ (all_4_1 = e3)
% 203.47/34.34    (27)  all_58_11 = all_52_29
% 203.47/34.34    (28)  all_56_5 = all_4_2
% 203.47/34.34    (29)   ~ (all_52_25 = all_14_2)
% 203.47/34.34    (30)   ~ (all_52_9 = all_52_15)
% 203.47/34.34    (31)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.34    (32)  op(all_10_2, e1) = all_10_1
% 203.47/34.34    (33)   ~ (all_52_7 = all_6_2)
% 203.47/34.34    (34)  op(e0, e0) = all_14_2
% 203.47/34.34    (35)  op(e0, e1) = all_52_23
% 203.47/34.34    (36)  all_56_15 = all_14_2
% 203.47/34.34    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.47/34.34    (38)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.47/34.34    (39)  op(e2, all_4_1) = all_4_0
% 203.47/34.34    (40)   ~ (all_4_1 = e1)
% 203.47/34.34    (41)   ~ (all_4_0 = e3)
% 203.47/34.34    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.34    (43)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.47/34.34    (44)   ~ (e2 = e1)
% 203.47/34.34    (45)   ~ (all_52_13 = all_10_2)
% 203.47/34.34    (46)   ~ (all_6_0 = e1)
% 203.47/34.34    (47)  all_58_10 = all_52_27
% 203.47/34.34    (48)  op(all_52_9, all_52_9) = all_52_8
% 203.47/34.34    (49)   ~ (all_52_19 = all_52_23)
% 203.47/34.34    (50)   ~ (all_52_25 = all_52_29)
% 203.47/34.34    (51)  all_58_7 = all_52_13
% 203.47/34.34    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.47/34.34    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.47/34.34    (54)  all_36_2 = all_10_2
% 203.47/34.34    (55)  all_36_1 = all_10_1
% 203.47/34.34    (56)  op(all_6_2, all_6_2) = e3
% 203.47/34.34    (57)   ~ (all_52_5 = all_52_7)
% 203.47/34.34    (58)  all_58_12 = all_52_7
% 203.47/34.34    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.47/34.34    (60)   ~ (all_52_7 = all_14_2)
% 203.47/34.34    (61)   ~ (all_14_2 = e0)
% 203.47/34.34    (62)  all_58_2 = all_52_3
% 203.47/34.34    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.47/34.34    (64)  op(e3, all_6_1) = all_6_0
% 203.47/34.34    (65)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.47/34.34    (66)   ~ (all_14_0 = e3)
% 203.47/34.34    (67)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.47/34.34    (68)   ~ (e2 = e0)
% 203.47/34.34    (69)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.47/34.34    (70)  op(all_4_2, e2) = all_4_1
% 203.47/34.34    (71)  op(all_52_3, all_52_3) = e2
% 203.47/34.34    (72)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.34    (73)   ~ (all_52_15 = all_14_2)
% 203.47/34.34    (74)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.47/34.34    (75)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.47/34.34    (76)   ~ (all_52_13 = all_4_2)
% 203.47/34.34    (77)  op(e1, e2) = all_52_13
% 203.47/34.34    (78)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.47/34.34    (79)   ~ (all_52_9 = all_52_25)
% 203.47/34.34    (80)  all_58_15 = all_14_2
% 203.47/34.34    (81)   ~ (all_52_19 = all_10_2)
% 203.47/34.34    (82)  op(all_52_23, all_52_23) = all_52_22
% 203.47/34.34    (83)  all_58_8 = all_10_2
% 203.47/34.34    (84)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.47/34.34    (85)   ~ (all_52_5 = all_10_2)
% 203.47/34.34    (86)   ~ (all_52_23 = all_14_2)
% 203.47/34.34    (87)  all_56_12 = all_52_7
% 203.47/34.34    (88)   ~ (all_52_25 = all_6_2)
% 203.47/34.34    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.47/34.34    (90)   ~ (all_52_9 = all_4_2)
% 203.47/34.34    (91)   ~ (all_52_5 = all_6_2)
% 203.47/34.34    (92)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.47/34.34    (93)   ~ (all_52_9 = all_6_2)
% 203.47/34.34    (94)  op(e3, e3) = all_6_2
% 203.47/34.34    (95)   ~ (all_52_27 = all_14_2)
% 203.47/34.34    (96)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.47/34.34    (97)  all_56_14 = all_52_23
% 203.47/34.34    (98)  op(all_4_2, all_4_2) = all_52_10
% 203.47/34.34    (99)  all_56_3 = all_52_25
% 203.47/34.34    (100)   ~ (all_52_3 = all_52_7)
% 203.47/34.34    (101)  op(all_14_2, all_14_2) = all_52_30
% 203.47/34.34    (102)  all_58_5 = all_52_19
% 203.47/34.34    (103)  all_56_1 = all_52_9
% 203.47/34.34    (104)   ~ (all_52_15 = all_4_2)
% 203.47/34.34    (105)  all_58_6 = all_52_5
% 203.47/34.34    (106)  op(e3, e2) = all_52_9
% 203.47/34.34    (107)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.34    (108)   ~ (all_52_17 = all_6_2)
% 203.47/34.34    (109)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.34    (110)   ~ (e1 = e0)
% 203.47/34.34    (111)   ~ (e3 = e2)
% 203.47/34.34    (112)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.47/34.34    (113)  all_56_10 = all_10_2
% 203.47/34.34    (114)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.47/34.34    (115)  op(all_52_13, all_52_13) = all_52_12
% 203.47/34.34    (116)  op(e1, e1) = all_10_2
% 203.47/34.34    (117)   ~ (all_52_23 = all_10_2)
% 203.47/34.34    (118)   ~ (all_52_7 = all_52_23)
% 203.47/34.34    (119)  all_58_3 = all_4_2
% 203.47/34.34    (120)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.47/34.34    (121)  all_56_13 = all_52_15
% 203.47/34.34    (122)   ~ (all_52_3 = all_4_2)
% 203.47/34.34    (123)  op(all_6_2, e3) = all_6_1
% 203.47/34.34    (124)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.47/34.34    (125)  all_58_4 = all_52_17
% 203.47/34.34    (126)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.47/34.34    (127)  op(all_52_25, all_52_25) = all_52_24
% 203.47/34.34  
% 203.47/34.34  Begin of proof
% 203.47/34.34  | 
% 203.47/34.34  | BETA: splitting (84) gives:
% 203.47/34.34  | 
% 203.47/34.34  | Case 1:
% 203.47/34.34  | | 
% 203.47/34.34  | |   (128)  all_56_15 = e3
% 203.47/34.34  | | 
% 203.47/34.34  | | COMBINE_EQS: (36), (128) imply:
% 203.47/34.34  | |   (129)  all_14_2 = e3
% 203.47/34.34  | | 
% 203.47/34.34  | | SIMP: (129) implies:
% 203.47/34.34  | |   (130)  all_14_2 = e3
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (60), (130) imply:
% 203.47/34.34  | |   (131)   ~ (all_52_7 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (73), (130) imply:
% 203.47/34.34  | |   (132)   ~ (all_52_15 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (86), (130) imply:
% 203.47/34.34  | |   (133)   ~ (all_52_23 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (29), (130) imply:
% 203.47/34.34  | |   (134)   ~ (all_52_25 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (95), (130) imply:
% 203.47/34.34  | |   (135)   ~ (all_52_27 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (23), (130) imply:
% 203.47/34.34  | |   (136)   ~ (all_52_29 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (101), (130) imply:
% 203.47/34.34  | |   (137)  op(e3, e3) = all_52_30
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (14), (130) imply:
% 203.47/34.34  | |   (138)  op(e3, e0) = all_14_1
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (34), (130) imply:
% 203.47/34.34  | |   (139)  op(e0, e0) = e3
% 203.47/34.34  | | 
% 203.47/34.34  | | GROUND_INST: instantiating (4) with all_52_25, all_14_1, e0, e3, simplifying
% 203.47/34.34  | |              with (17), (138) gives:
% 203.47/34.34  | |   (140)  all_52_25 = all_14_1
% 203.47/34.34  | | 
% 203.47/34.34  | | GROUND_INST: instantiating (4) with all_6_2, all_52_30, e3, e3, simplifying
% 203.47/34.34  | |              with (94), (137) gives:
% 203.47/34.34  | |   (141)  all_52_30 = all_6_2
% 203.47/34.34  | | 
% 203.47/34.34  | | COMBINE_EQS: (99), (140) imply:
% 203.47/34.34  | |   (142)  all_56_3 = all_14_1
% 203.47/34.34  | | 
% 203.47/34.34  | | COMBINE_EQS: (21), (140) imply:
% 203.47/34.34  | |   (143)  all_58_9 = all_14_1
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (79), (140) imply:
% 203.47/34.34  | |   (144)   ~ (all_52_9 = all_14_1)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (2), (140) imply:
% 203.47/34.34  | |   (145)   ~ (all_52_27 = all_14_1)
% 203.47/34.34  | | 
% 203.47/34.34  | | SIMP: (145) implies:
% 203.47/34.34  | |   (146)   ~ (all_52_27 = all_14_1)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (50), (140) imply:
% 203.47/34.34  | |   (147)   ~ (all_52_29 = all_14_1)
% 203.47/34.34  | | 
% 203.47/34.34  | | SIMP: (147) implies:
% 203.47/34.34  | |   (148)   ~ (all_52_29 = all_14_1)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (88), (140) imply:
% 203.47/34.34  | |   (149)   ~ (all_14_1 = all_6_2)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (134), (140) imply:
% 203.47/34.34  | |   (150)   ~ (all_14_1 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (127), (140) imply:
% 203.47/34.34  | |   (151)  op(all_14_1, all_14_1) = all_52_24
% 203.47/34.34  | | 
% 203.47/34.34  | | BETA: splitting (42) gives:
% 203.47/34.34  | | 
% 203.47/34.34  | | Case 1:
% 203.47/34.34  | | | 
% 203.47/34.34  | | |   (152)  all_56_13 = e3
% 203.47/34.34  | | | 
% 203.47/34.34  | | | REF_CLOSE: (121), (132), (152) are inconsistent by sub-proof #1201.
% 203.47/34.34  | | | 
% 203.47/34.34  | | Case 2:
% 203.47/34.34  | | | 
% 203.47/34.34  | | |   (153)   ~ (all_56_13 = e3)
% 203.47/34.34  | | |   (154)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.34  | | | 
% 203.47/34.34  | | | BETA: splitting (52) gives:
% 203.47/34.34  | | | 
% 203.47/34.34  | | | Case 1:
% 203.47/34.34  | | | | 
% 203.47/34.34  | | | |   (155)  all_56_14 = e3
% 203.47/34.34  | | | | 
% 203.47/34.34  | | | | REF_CLOSE: (97), (133), (155) are inconsistent by sub-proof #1286.
% 203.47/34.34  | | | | 
% 203.47/34.34  | | | Case 2:
% 203.47/34.34  | | | | 
% 203.47/34.34  | | | |   (156)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.47/34.34  | | | | 
% 203.47/34.34  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.47/34.34  | | | |            (16), (18), (19), (20), (22), (24), (26), (27), (30), (31),
% 203.47/34.34  | | | |            (32), (33), (34), (35), (37), (38), (40), (43), (45), (46),
% 203.47/34.34  | | | |            (47), (49), (51), (54), (55), (56), (57), (58), (59), (60),
% 203.47/34.34  | | | |            (62), (63), (64), (65), (66), (68), (70), (71), (72), (76),
% 203.47/34.34  | | | |            (77), (78), (81), (83), (85), (87), (89), (91), (92), (93),
% 203.47/34.34  | | | |            (94), (96), (97), (98), (102), (104), (105), (108), (109),
% 203.47/34.34  | | | |            (110), (113), (114), (116), (117), (118), (119), (120),
% 203.47/34.34  | | | |            (121), (122), (123), (124), (125), (126), (131), (132),
% 203.47/34.34  | | | |            (135), (136), (139), (142), (143), (144), (146), (148),
% 203.47/34.34  | | | |            (149), (150), (151), (154), (156) are inconsistent by
% 203.47/34.34  | | | |            sub-proof #538.
% 203.47/34.34  | | | | 
% 203.47/34.34  | | | End of split
% 203.47/34.34  | | | 
% 203.47/34.34  | | End of split
% 203.47/34.34  | | 
% 203.47/34.34  | Case 2:
% 203.47/34.34  | | 
% 203.47/34.34  | |   (157)   ~ (all_56_15 = e3)
% 203.47/34.34  | |   (158)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.47/34.34  | | 
% 203.47/34.34  | | REDUCE: (36), (157) imply:
% 203.47/34.34  | |   (159)   ~ (all_14_2 = e3)
% 203.47/34.34  | | 
% 203.47/34.34  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.47/34.34  | |            (15), (19), (24), (25), (26), (28), (30), (31), (33), (34), (36),
% 203.47/34.34  | |            (37), (39), (40), (41), (42), (44), (48), (51), (53), (56), (58),
% 203.47/34.34  | |            (60), (61), (62), (63), (67), (68), (69), (70), (71), (72), (73),
% 203.47/34.34  | |            (74), (75), (77), (78), (80), (82), (85), (87), (90), (93), (94),
% 203.47/34.34  | |            (100), (101), (103), (104), (105), (106), (107), (110), (111),
% 203.47/34.34  | |            (112), (115), (116), (117), (118), (119), (120), (121), (122),
% 203.47/34.34  | |            (124), (158), (159) are inconsistent by sub-proof #1145.
% 203.47/34.34  | | 
% 203.47/34.34  | End of split
% 203.47/34.34  | 
% 203.47/34.34  End of proof
% 203.47/34.34  
% 203.47/34.34  Sub-proof #538 shows that the following formulas are inconsistent:
% 203.47/34.34  ----------------------------------------------------------------
% 203.47/34.34    (1)  all_58_14 = all_52_23
% 203.47/34.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.34    (3)  op(all_52_7, all_52_7) = e0
% 203.47/34.34    (4)  all_58_1 = all_52_9
% 203.47/34.34    (5)  op(all_52_5, all_52_5) = e1
% 203.47/34.34    (6)   ~ (e3 = e0)
% 203.47/34.34    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.34    (8)  op(e0, e2) = all_52_15
% 203.47/34.34    (9)   ~ (all_52_7 = all_52_15)
% 203.47/34.34    (10)   ~ (all_52_3 = all_6_2)
% 203.47/34.34    (11)   ~ (all_14_1 = e3)
% 203.47/34.34    (12)  all_58_0 = all_6_2
% 203.47/34.34    (13)   ~ (all_52_17 = all_10_2)
% 203.47/34.34    (14)  op(e0, all_14_1) = all_14_0
% 203.47/34.34    (15)  all_58_13 = all_52_15
% 203.47/34.34    (16)  op(all_10_2, all_10_2) = all_52_20
% 203.47/34.34    (17)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.47/34.34    (18)   ~ (all_52_15 = e3)
% 203.47/34.34    (19)  op(e2, e2) = all_4_2
% 203.47/34.34    (20)   ~ (all_4_1 = e3)
% 203.47/34.34    (21)  all_58_11 = all_52_29
% 203.47/34.34    (22)   ~ (all_52_9 = all_52_15)
% 203.47/34.34    (23)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.34    (24)  op(all_10_2, e1) = all_10_1
% 203.47/34.34    (25)  all_56_3 = all_14_1
% 203.47/34.34    (26)   ~ (all_52_7 = all_6_2)
% 203.47/34.34    (27)  op(e0, e0) = all_14_2
% 203.47/34.34    (28)  op(e0, e1) = all_52_23
% 203.47/34.34    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.47/34.34    (30)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.47/34.34    (31)   ~ (all_52_29 = all_14_1)
% 203.47/34.34    (32)   ~ (all_4_1 = e1)
% 203.47/34.34    (33)  op(e0, e0) = e3
% 203.47/34.34    (34)   ~ (all_52_9 = all_14_1)
% 203.47/34.34    (35)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.47/34.34    (36)   ~ (all_52_13 = all_10_2)
% 203.47/34.34    (37)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.47/34.34    (38)   ~ (all_6_0 = e1)
% 203.47/34.34    (39)  all_58_10 = all_52_27
% 203.47/34.34    (40)   ~ (all_52_19 = all_52_23)
% 203.47/34.34    (41)  all_58_7 = all_52_13
% 203.47/34.34    (42)  all_36_2 = all_10_2
% 203.47/34.34    (43)  all_36_1 = all_10_1
% 203.47/34.34    (44)  op(all_6_2, all_6_2) = e3
% 203.47/34.34    (45)   ~ (all_52_5 = all_52_7)
% 203.47/34.34    (46)  all_58_12 = all_52_7
% 203.47/34.34    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.47/34.34    (48)   ~ (all_52_7 = e3)
% 203.47/34.34    (49)   ~ (all_52_7 = all_14_2)
% 203.47/34.34    (50)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.34    (51)  all_58_2 = all_52_3
% 203.47/34.34    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.47/34.34    (53)   ~ (all_52_29 = e3)
% 203.47/34.34    (54)  op(e3, all_6_1) = all_6_0
% 203.47/34.34    (55)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.47/34.34    (56)   ~ (all_14_0 = e3)
% 203.47/34.34    (57)  all_58_9 = all_14_1
% 203.47/34.34    (58)   ~ (e2 = e0)
% 203.47/34.34    (59)  op(all_4_2, e2) = all_4_1
% 203.47/34.34    (60)   ~ (all_14_1 = all_6_2)
% 203.47/34.34    (61)  op(all_52_3, all_52_3) = e2
% 203.47/34.34    (62)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.34    (63)   ~ (all_52_27 = e3)
% 203.47/34.34    (64)   ~ (all_52_13 = all_4_2)
% 203.47/34.34    (65)  op(all_14_1, all_14_1) = all_52_24
% 203.47/34.34    (66)  op(e1, e2) = all_52_13
% 203.47/34.34    (67)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.47/34.34    (68)   ~ (all_52_19 = all_10_2)
% 203.47/34.34    (69)  all_58_8 = all_10_2
% 203.47/34.34    (70)   ~ (all_52_5 = all_10_2)
% 203.47/34.34    (71)  all_56_12 = all_52_7
% 203.47/34.34    (72)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.47/34.34    (73)   ~ (all_52_5 = all_6_2)
% 203.47/34.34    (74)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.47/34.34    (75)   ~ (all_52_9 = all_6_2)
% 203.47/34.34    (76)   ~ (all_52_27 = all_14_1)
% 203.47/34.35    (77)  op(e3, e3) = all_6_2
% 203.47/34.35    (78)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.47/34.35    (79)  all_56_14 = all_52_23
% 203.47/34.35    (80)  op(all_4_2, all_4_2) = all_52_10
% 203.47/34.35    (81)  all_58_5 = all_52_19
% 203.47/34.35    (82)   ~ (all_52_15 = all_4_2)
% 203.47/34.35    (83)  all_58_6 = all_52_5
% 203.47/34.35    (84)   ~ (all_52_17 = all_6_2)
% 203.47/34.35    (85)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.35    (86)   ~ (e1 = e0)
% 203.47/34.35    (87)  all_56_10 = all_10_2
% 203.47/34.35    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.47/34.35    (89)  op(e1, e1) = all_10_2
% 203.47/34.35    (90)   ~ (all_52_23 = all_10_2)
% 203.47/34.35    (91)   ~ (all_52_7 = all_52_23)
% 203.47/34.35    (92)  all_58_3 = all_4_2
% 203.47/34.35    (93)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.47/34.35    (94)  all_56_13 = all_52_15
% 203.47/34.35    (95)   ~ (all_52_3 = all_4_2)
% 203.47/34.35    (96)  op(all_6_2, e3) = all_6_1
% 203.47/34.35    (97)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.47/34.35    (98)  all_58_4 = all_52_17
% 203.47/34.35    (99)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.47/34.35  
% 203.47/34.35  Begin of proof
% 203.47/34.35  | 
% 203.47/34.35  | BETA: splitting (72) gives:
% 203.47/34.35  | 
% 203.47/34.35  | Case 1:
% 203.47/34.35  | | 
% 203.47/34.35  | |   (100)  all_56_3 = e3
% 203.47/34.35  | | 
% 203.47/34.35  | | REF_CLOSE: (11), (25), (100) are inconsistent by sub-proof #1200.
% 203.47/34.35  | | 
% 203.47/34.35  | Case 2:
% 203.47/34.35  | | 
% 203.47/34.35  | |   (101)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.47/34.35  | | 
% 203.47/34.35  | | BETA: splitting (7) gives:
% 203.47/34.35  | | 
% 203.47/34.35  | | Case 1:
% 203.47/34.35  | | | 
% 203.47/34.35  | | |   (102)  all_56_12 = e3
% 203.47/34.35  | | | 
% 203.47/34.35  | | | REF_CLOSE: (48), (71), (102) are inconsistent by sub-proof #1383.
% 203.47/34.35  | | | 
% 203.47/34.35  | | Case 2:
% 203.47/34.35  | | | 
% 203.47/34.35  | | |   (103)   ~ (all_56_12 = e3)
% 203.47/34.35  | | |   (104)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.35  | | | 
% 203.47/34.35  | | | BETA: splitting (62) gives:
% 203.47/34.35  | | | 
% 203.47/34.35  | | | Case 1:
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | |   (105)  all_58_12 = e1
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | | REF_CLOSE: (2), (3), (24), (28), (37), (42), (43), (46), (79), (85),
% 203.47/34.35  | | | |            (89), (90), (91), (105) are inconsistent by sub-proof #543.
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | Case 2:
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | |   (106)   ~ (all_58_12 = e1)
% 203.47/34.35  | | | |   (107)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | | REDUCE: (46), (106) imply:
% 203.47/34.35  | | | |   (108)   ~ (all_52_7 = e1)
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | | BETA: splitting (88) gives:
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | | Case 1:
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | |   (109)  all_58_4 = e3
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | | COMBINE_EQS: (98), (109) imply:
% 203.47/34.35  | | | | |   (110)  all_52_17 = e3
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | | REF_CLOSE: (2), (5), (12), (19), (29), (44), (46), (48), (51), (52),
% 203.47/34.35  | | | | |            (61), (70), (77), (83), (84), (89), (95), (110) are
% 203.47/34.35  | | | | |            inconsistent by sub-proof #1199.
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | Case 2:
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | |   (111)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | | BETA: splitting (78) gives:
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | | Case 1:
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | |   (112)  all_58_0 = e3
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | COMBINE_EQS: (12), (112) imply:
% 203.47/34.35  | | | | | |   (113)  all_6_2 = e3
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (10), (113) imply:
% 203.47/34.35  | | | | | |   (114)   ~ (all_52_3 = e3)
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (73), (113) imply:
% 203.47/34.35  | | | | | |   (115)   ~ (all_52_5 = e3)
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (75), (113) imply:
% 203.47/34.35  | | | | | |   (116)   ~ (all_52_9 = e3)
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (96), (113) imply:
% 203.47/34.35  | | | | | |   (117)  op(e3, e3) = all_6_1
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (77), (113) imply:
% 203.47/34.35  | | | | | |   (118)  op(e3, e3) = e3
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | GROUND_INST: instantiating (2) with e3, all_6_1, e3, e3, simplifying
% 203.47/34.35  | | | | | |              with (117), (118) gives:
% 203.47/34.35  | | | | | |   (119)  all_6_1 = e3
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (54), (119) imply:
% 203.47/34.35  | | | | | |   (120)  op(e3, e3) = all_6_0
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | GROUND_INST: instantiating (2) with e3, all_6_0, e3, e3, simplifying
% 203.47/34.35  | | | | | |              with (118), (120) gives:
% 203.47/34.35  | | | | | |   (121)  all_6_0 = e3
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (38), (121) imply:
% 203.47/34.35  | | | | | |   (122)   ~ (e3 = e1)
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | BETA: splitting (47) gives:
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | Case 1:
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | |   (123)  all_58_6 = e3
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | | REF_CLOSE: (83), (115), (123) are inconsistent by sub-proof #1328.
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | Case 2:
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | |   (124)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | | BETA: splitting (29) gives:
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | |   (125)  all_58_2 = e3
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | | REF_CLOSE: (51), (114), (125) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | |            #1369.
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | |   (126)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | | BETA: splitting (67) gives:
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | |   (127)  all_58_1 = e3
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | COMBINE_EQS: (4), (127) imply:
% 203.47/34.35  | | | | | | | | |   (128)  all_52_9 = e3
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | REDUCE: (116), (128) imply:
% 203.47/34.35  | | | | | | | | |   (129)  $false
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | CLOSE: (129) is inconsistent.
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | |   (130)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | BETA: splitting (99) gives:
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | |   (131)  all_56_10 = e3
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | COMBINE_EQS: (87), (131) imply:
% 203.47/34.35  | | | | | | | | | |   (132)  all_10_2 = e3
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | REDUCE: (36), (132) imply:
% 203.47/34.35  | | | | | | | | | |   (133)   ~ (all_52_13 = e3)
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | BETA: splitting (130) gives:
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | |   (134)  all_58_3 = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | COMBINE_EQS: (92), (134) imply:
% 203.47/34.35  | | | | | | | | | | |   (135)  all_4_2 = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | REDUCE: (19), (135) imply:
% 203.47/34.35  | | | | | | | | | | |   (136)  op(e2, e2) = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (23), (27), (46), (49), (71),
% 203.47/34.35  | | | | | | | | | | |            (104), (108), (136) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | |            #1160.
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | |   (137)  all_58_7 = e3 | all_58_13 = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | REF_CLOSE: (15), (18), (41), (133), (137) are inconsistent by
% 203.47/34.35  | | | | | | | | | | |            sub-proof #1298.
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | |   (138)   ~ (all_56_10 = e3)
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | REDUCE: (87), (138) imply:
% 203.47/34.35  | | | | | | | | | |   (139)   ~ (all_10_2 = e3)
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | BETA: splitting (124) gives:
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | |   (140)  all_58_7 = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | COMBINE_EQS: (41), (140) imply:
% 203.47/34.35  | | | | | | | | | | |   (141)  all_52_13 = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | REDUCE: (64), (141) imply:
% 203.47/34.35  | | | | | | | | | | |   (142)   ~ (all_4_2 = e3)
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | SIMP: (142) implies:
% 203.47/34.35  | | | | | | | | | | |   (143)   ~ (all_4_2 = e3)
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | REDUCE: (66), (141) imply:
% 203.47/34.35  | | | | | | | | | | |   (144)  op(e1, e2) = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | BETA: splitting (126) gives:
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | |   (145)  all_58_3 = e3
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | COMBINE_EQS: (92), (145) imply:
% 203.47/34.35  | | | | | | | | | | | |   (146)  all_4_2 = e3
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | REDUCE: (143), (146) imply:
% 203.47/34.35  | | | | | | | | | | | |   (147)  $false
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | |   (148)  all_58_5 = e3 | all_58_10 = e3
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | BETA: splitting (148) gives:
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | |   (149)  all_58_5 = e3
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | COMBINE_EQS: (81), (149) imply:
% 203.47/34.35  | | | | | | | | | | | | |   (150)  all_52_19 = e3
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | SIMP: (150) implies:
% 203.47/34.35  | | | | | | | | | | | | |   (151)  all_52_19 = e3
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | REDUCE: (40), (151) imply:
% 203.47/34.35  | | | | | | | | | | | | |   (152)   ~ (all_52_23 = e3)
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | SIMP: (152) implies:
% 203.47/34.35  | | | | | | | | | | | | |   (153)   ~ (all_52_23 = e3)
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | REDUCE: (68), (151) imply:
% 203.47/34.35  | | | | | | | | | | | | |   (154)   ~ (all_10_2 = e3)
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | BETA: splitting (74) gives:
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | |   (155)  all_58_9 = e2
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | COMBINE_EQS: (57), (155) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (156)  all_14_1 = e2
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (34), (156) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (157)   ~ (all_52_9 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (76), (156) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (158)   ~ (all_52_27 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (31), (156) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (159)   ~ (all_52_29 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (11), (156) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (160)   ~ (e3 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | SIMP: (160) implies:
% 203.47/34.35  | | | | | | | | | | | | | |   (161)   ~ (e3 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (65), (156) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (162)  op(e2, e2) = all_52_24
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (14), (156) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (163)  op(e0, e2) = all_14_0
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_15, all_14_0, e2,
% 203.47/34.35  | | | | | | | | | | | | | |              e0, simplifying with (8), (163) gives:
% 203.47/34.35  | | | | | | | | | | | | | |   (164)  all_52_15 = all_14_0
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_24, e2, e2,
% 203.47/34.35  | | | | | | | | | | | | | |              simplifying with (19), (162) gives:
% 203.47/34.35  | | | | | | | | | | | | | |   (165)  all_52_24 = all_4_2
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | COMBINE_EQS: (94), (164) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (166)  all_56_13 = all_14_0
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (9), (164) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (167)   ~ (all_52_7 = all_14_0)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (22), (164) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (168)   ~ (all_52_9 = all_14_0)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (82), (164) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (169)   ~ (all_14_0 = all_4_2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | |   (170)  all_58_1 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | COMBINE_EQS: (4), (170) imply:
% 203.47/34.35  | | | | | | | | | | | | | | |   (171)  all_52_9 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | REDUCE: (157), (171) imply:
% 203.47/34.35  | | | | | | | | | | | | | | |   (172)  $false
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | |   (173)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | |   (174)  all_58_3 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (174) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | |   (175)  all_4_2 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | REDUCE: (169), (175) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | |   (176)   ~ (all_14_0 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | REDUCE: (80), (175) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | |   (177)  op(e2, e2) = all_52_10
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | REDUCE: (59), (175) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | |   (178)  op(e2, e2) = all_4_1
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | REDUCE: (19), (175) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | |   (179)  op(e2, e2) = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (180)  all_58_1 = e1
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (180) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (181)  all_52_9 = e1
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | REDUCE: (168), (181) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (182)   ~ (all_14_0 = e1)
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (183)   ~ (all_14_0 = e1)
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (184)  all_58_0 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (184) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (185)  e3 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | REDUCE: (6), (185) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (186)  $false
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | CLOSE: (186) is inconsistent.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (187)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |   (188)  all_58_1 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (188) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |   (189)  e1 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | REDUCE: (86), (189) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |   (190)  $false
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |   (191)  all_58_4 = e0 | all_58_9 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |   (192)  all_58_4 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (192) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |   (193)  all_52_17 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |   (194)  all_52_17 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (194) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |   (195)   ~ (all_10_2 = e0)
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | SIMP: (195) implies:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |   (196)   ~ (all_10_2 = e0)
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | |   (197)  all_56_13 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (176), (197) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | |            #542.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | |   (198)  all_56_13 = e1 | all_56_13 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | |   (199)  all_56_13 = e1
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (183), (199) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | |            #541.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_13 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (200) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | |   (201)  all_14_0 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | SIMP: (201) implies:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | |   (202)  all_14_0 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (202) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | |   (203)   ~ (all_52_7 = e0)
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_56_12 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (204) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_52_7 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_52_7 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (206) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |   (207)   ~ (all_52_5 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (206) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |   (208)  op(e2, e2) = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_58_6 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (207), (209) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | |            #540.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_58_7 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (211) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  e3 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (212) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  $false
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_58_8 = e2 | all_58_11 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_58_8 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (215) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_10_2 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (216) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  op(e2, e2) = all_52_20
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (58), (177), (178), (179), (208), (217) are
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1191.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_58_11 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (159), (218) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1189.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_56_12 = e1 | all_56_12 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (108), (203), (219) are inconsistent by
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1374.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |   (220)  all_58_9 = e0
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (155), (220) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | |            #1084.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (221)   ~ (all_58_1 = e1)
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | REDUCE: (4), (221) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (222)   ~ (all_52_9 = e1)
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (15), (19), (20),
% 203.47/34.35  | | | | | | | | | | | | | | | | |            (23), (27), (32), (35), (46), (49), (59), (69),
% 203.47/34.35  | | | | | | | | | | | | | | | | |            (71), (92), (104), (107), (111), (122), (139),
% 203.47/34.35  | | | | | | | | | | | | | | | | |            (140), (144), (149), (153), (222) are inconsistent
% 203.47/34.35  | | | | | | | | | | | | | | | | |            by sub-proof #645.
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | |   (223)   ~ (all_58_3 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | REDUCE: (92), (223) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | |   (224)   ~ (all_4_2 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (225)  all_58_2 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (225) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (226)  all_52_3 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (227)  all_52_3 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (19), (61), (95), (227) are inconsistent by
% 203.47/34.35  | | | | | | | | | | | | | | | | |            sub-proof #1157.
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | |   (228)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (229)  all_58_3 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (229) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (230)  all_4_2 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | REDUCE: (224), (230) imply:
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (231)  $false
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | |   (232)  all_58_5 = e2 | all_58_10 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | Case 1:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |   (233)  all_58_5 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (233) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |            #625.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |   (234)  all_58_10 = e2
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (158), (234) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | | | | | | | |            #539.
% 203.47/34.35  | | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | |   (235)   ~ (all_58_9 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REDUCE: (57), (235) imply:
% 203.47/34.35  | | | | | | | | | | | | | |   (236)   ~ (all_14_1 = e2)
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (11), (14), (15),
% 203.47/34.35  | | | | | | | | | | | | | |            (19), (20), (23), (25), (27), (30), (32), (33),
% 203.47/34.35  | | | | | | | | | | | | | |            (34), (35), (46), (49), (56), (57), (59), (65),
% 203.47/34.35  | | | | | | | | | | | | | |            (69), (71), (92), (101), (104), (107), (111),
% 203.47/34.35  | | | | | | | | | | | | | |            (139), (140), (144), (149), (153), (236) are
% 203.47/34.35  | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 203.47/34.35  | | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | |   (237)  all_58_10 = e3
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | | REF_CLOSE: (39), (63), (237) are inconsistent by sub-proof
% 203.47/34.35  | | | | | | | | | | | | |            #1301.
% 203.47/34.35  | | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | Case 2:
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | |   (238)  all_58_8 = e3 | all_58_11 = e3
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | | REF_CLOSE: (21), (53), (69), (139), (238) are inconsistent by
% 203.47/34.35  | | | | | | | | | | |            sub-proof #1140.
% 203.47/34.35  | | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | | 
% 203.47/34.35  | | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | | 
% 203.47/34.35  | | | | | | | | End of split
% 203.47/34.35  | | | | | | | | 
% 203.47/34.35  | | | | | | | End of split
% 203.47/34.35  | | | | | | | 
% 203.47/34.35  | | | | | | End of split
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | Case 2:
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | |   (239)   ~ (all_58_0 = e3)
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REDUCE: (12), (239) imply:
% 203.47/34.35  | | | | | |   (240)   ~ (all_6_2 = e3)
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | | REF_CLOSE: (2), (5), (12), (19), (29), (44), (46), (48), (51), (52),
% 203.47/34.35  | | | | | |            (61), (70), (77), (83), (89), (95), (240) are
% 203.47/34.35  | | | | | |            inconsistent by sub-proof #1363.
% 203.47/34.35  | | | | | | 
% 203.47/34.35  | | | | | End of split
% 203.47/34.35  | | | | | 
% 203.47/34.35  | | | | End of split
% 203.47/34.35  | | | | 
% 203.47/34.35  | | | End of split
% 203.47/34.35  | | | 
% 203.47/34.35  | | End of split
% 203.47/34.35  | | 
% 203.47/34.35  | End of split
% 203.47/34.35  | 
% 203.47/34.35  End of proof
% 203.47/34.35  
% 203.47/34.35  Sub-proof #539 shows that the following formulas are inconsistent:
% 203.47/34.35  ----------------------------------------------------------------
% 203.47/34.35    (1)  all_58_10 = all_52_27
% 203.47/34.35    (2)  all_58_10 = e2
% 203.47/34.35    (3)   ~ (all_52_27 = e2)
% 203.47/34.35  
% 203.47/34.35  Begin of proof
% 203.47/34.35  | 
% 203.47/34.35  | COMBINE_EQS: (1), (2) imply:
% 203.47/34.35  |   (4)  all_52_27 = e2
% 203.47/34.35  | 
% 203.47/34.35  | SIMP: (4) implies:
% 203.47/34.35  |   (5)  all_52_27 = e2
% 203.47/34.35  | 
% 203.47/34.35  | REDUCE: (3), (5) imply:
% 203.47/34.35  |   (6)  $false
% 203.47/34.35  | 
% 203.47/34.35  | CLOSE: (6) is inconsistent.
% 203.47/34.35  | 
% 203.47/34.35  End of proof
% 203.47/34.35  
% 203.47/34.35  Sub-proof #540 shows that the following formulas are inconsistent:
% 203.47/34.35  ----------------------------------------------------------------
% 203.47/34.35    (1)  all_58_6 = all_52_5
% 203.47/34.35    (2)  all_58_6 = e2
% 203.47/34.36    (3)   ~ (all_52_5 = e2)
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | COMBINE_EQS: (1), (2) imply:
% 203.47/34.36  |   (4)  all_52_5 = e2
% 203.47/34.36  | 
% 203.47/34.36  | SIMP: (4) implies:
% 203.47/34.36  |   (5)  all_52_5 = e2
% 203.47/34.36  | 
% 203.47/34.36  | REDUCE: (3), (5) imply:
% 203.47/34.36  |   (6)  $false
% 203.47/34.36  | 
% 203.47/34.36  | CLOSE: (6) is inconsistent.
% 203.47/34.36  | 
% 203.47/34.36  End of proof
% 203.47/34.36  
% 203.47/34.36  Sub-proof #541 shows that the following formulas are inconsistent:
% 203.47/34.36  ----------------------------------------------------------------
% 203.47/34.36    (1)  all_56_13 = all_14_0
% 203.47/34.36    (2)  all_56_13 = e1
% 203.47/34.36    (3)   ~ (all_14_0 = e1)
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | COMBINE_EQS: (1), (2) imply:
% 203.47/34.36  |   (4)  all_14_0 = e1
% 203.47/34.36  | 
% 203.47/34.36  | SIMP: (4) implies:
% 203.47/34.36  |   (5)  all_14_0 = e1
% 203.47/34.36  | 
% 203.47/34.36  | REDUCE: (3), (5) imply:
% 203.47/34.36  |   (6)  $false
% 203.47/34.36  | 
% 203.47/34.36  | CLOSE: (6) is inconsistent.
% 203.47/34.36  | 
% 203.47/34.36  End of proof
% 203.47/34.36  
% 203.47/34.36  Sub-proof #542 shows that the following formulas are inconsistent:
% 203.47/34.36  ----------------------------------------------------------------
% 203.47/34.36    (1)  all_56_13 = all_14_0
% 203.47/34.36    (2)  all_56_13 = e2
% 203.47/34.36    (3)   ~ (all_14_0 = e2)
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | COMBINE_EQS: (1), (2) imply:
% 203.47/34.36  |   (4)  all_14_0 = e2
% 203.47/34.36  | 
% 203.47/34.36  | SIMP: (4) implies:
% 203.47/34.36  |   (5)  all_14_0 = e2
% 203.47/34.36  | 
% 203.47/34.36  | REDUCE: (3), (5) imply:
% 203.47/34.36  |   (6)  $false
% 203.47/34.36  | 
% 203.47/34.36  | CLOSE: (6) is inconsistent.
% 203.47/34.36  | 
% 203.47/34.36  End of proof
% 203.47/34.36  
% 203.47/34.36  Sub-proof #543 shows that the following formulas are inconsistent:
% 203.47/34.36  ----------------------------------------------------------------
% 203.47/34.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.36    (2)  op(all_52_7, all_52_7) = e0
% 203.47/34.36    (3)  op(all_10_2, e1) = all_10_1
% 203.47/34.36    (4)  op(e0, e1) = all_52_23
% 203.47/34.36    (5)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.47/34.36    (6)  all_36_2 = all_10_2
% 203.47/34.36    (7)  all_36_1 = all_10_1
% 203.47/34.36    (8)  all_58_12 = all_52_7
% 203.47/34.36    (9)  all_56_14 = all_52_23
% 203.47/34.36    (10)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.36    (11)  op(e1, e1) = all_10_2
% 203.47/34.36    (12)   ~ (all_52_23 = all_10_2)
% 203.47/34.36    (13)   ~ (all_52_7 = all_52_23)
% 203.47/34.36    (14)  all_58_12 = e1
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | COMBINE_EQS: (8), (14) imply:
% 203.47/34.36  |   (15)  all_52_7 = e1
% 203.47/34.36  | 
% 203.47/34.36  | SIMP: (15) implies:
% 203.47/34.36  |   (16)  all_52_7 = e1
% 203.47/34.36  | 
% 203.47/34.36  | REDUCE: (13), (16) imply:
% 203.47/34.36  |   (17)   ~ (all_52_23 = e1)
% 203.47/34.36  | 
% 203.47/34.36  | SIMP: (17) implies:
% 203.47/34.36  |   (18)   ~ (all_52_23 = e1)
% 203.47/34.36  | 
% 203.47/34.36  | REDUCE: (2), (16) imply:
% 203.47/34.36  |   (19)  op(e1, e1) = e0
% 203.47/34.36  | 
% 203.47/34.36  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 203.47/34.36  |              (11), (19) gives:
% 203.47/34.36  |   (20)  all_10_2 = e0
% 203.47/34.36  | 
% 203.47/34.36  | REDUCE: (12), (20) imply:
% 203.47/34.36  |   (21)   ~ (all_52_23 = e0)
% 203.47/34.36  | 
% 203.47/34.36  | BETA: splitting (5) gives:
% 203.47/34.36  | 
% 203.47/34.36  | Case 1:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (22)  all_56_14 = e2
% 203.47/34.36  | | 
% 203.47/34.36  | | COMBINE_EQS: (9), (22) imply:
% 203.47/34.36  | |   (23)  all_52_23 = e2
% 203.47/34.36  | | 
% 203.47/34.36  | | SIMP: (23) implies:
% 203.47/34.36  | |   (24)  all_52_23 = e2
% 203.47/34.36  | | 
% 203.47/34.36  | | REDUCE: (4), (24) imply:
% 203.47/34.36  | |   (25)  op(e0, e1) = e2
% 203.47/34.36  | | 
% 203.47/34.36  | | REF_CLOSE: (1), (3), (6), (7), (10), (11), (19), (25) are inconsistent by
% 203.47/34.36  | |            sub-proof #551.
% 203.47/34.36  | | 
% 203.47/34.36  | Case 2:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (26)  all_56_14 = e1 | all_56_14 = e0
% 203.47/34.36  | | 
% 203.47/34.36  | | REF_CLOSE: (9), (18), (21), (26) are inconsistent by sub-proof #1381.
% 203.47/34.36  | | 
% 203.47/34.36  | End of split
% 203.47/34.36  | 
% 203.47/34.36  End of proof
% 203.47/34.36  
% 203.47/34.36  Sub-proof #544 shows that the following formulas are inconsistent:
% 203.47/34.36  ----------------------------------------------------------------
% 203.47/34.36    (1)   ~ (all_52_25 = all_52_27)
% 203.47/34.36    (2)  all_58_14 = all_52_23
% 203.47/34.36    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.47/34.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.36    (5)   ~ (all_52_5 = all_52_13)
% 203.47/34.36    (6)  all_58_1 = all_52_9
% 203.47/34.36    (7)   ~ (all_52_9 = all_52_13)
% 203.47/34.36    (8)   ~ (e3 = e0)
% 203.47/34.36    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.36    (10)   ~ (all_52_7 = all_52_15)
% 203.47/34.36    (11)  op(all_52_15, all_52_15) = e0
% 203.47/34.36    (12)  op(all_52_7, all_52_7) = all_52_6
% 203.47/34.36    (13)   ~ (all_52_17 = all_52_25)
% 203.47/34.36    (14)   ~ (all_52_3 = all_6_2)
% 203.47/34.36    (15)  all_58_0 = all_6_2
% 203.47/34.36    (16)  all_56_4 = all_52_3
% 203.47/34.36    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.47/34.36    (18)  op(all_52_19, all_52_19) = all_52_18
% 203.47/34.36    (19)  all_58_13 = all_52_15
% 203.47/34.36    (20)  op(all_52_13, all_52_13) = e1
% 203.47/34.36    (21)  op(all_10_2, all_10_2) = all_52_20
% 203.47/34.36    (22)  all_58_9 = all_52_25
% 203.47/34.36    (23)   ~ (all_6_1 = e1)
% 203.47/34.36    (24)  op(all_52_27, all_52_27) = all_52_26
% 203.47/34.36    (25)  op(e1, e3) = all_52_5
% 203.47/34.36    (26)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 203.47/34.36    (27)  op(e2, e2) = all_4_2
% 203.47/34.36    (28)   ~ (all_52_3 = all_52_5)
% 203.47/34.36    (29)  all_58_11 = all_52_29
% 203.47/34.36    (30)  all_56_5 = all_4_2
% 203.47/34.36    (31)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.36    (32)  op(all_10_2, e1) = all_10_1
% 203.47/34.36    (33)   ~ (all_52_7 = all_6_2)
% 203.47/34.36    (34)  op(e0, e1) = all_52_23
% 203.47/34.36    (35)   ~ (all_52_15 = e0)
% 203.47/34.36    (36)  all_58_15 = e0
% 203.47/34.36    (37)   ~ (all_4_1 = e1)
% 203.47/34.36    (38)   ~ (all_52_25 = e0)
% 203.47/34.36    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.36    (40)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.47/34.36    (41)  op(e1, all_10_1) = e3
% 203.47/34.36    (42)  all_56_9 = all_52_13
% 203.47/34.36    (43)   ~ (e2 = e1)
% 203.47/34.36    (44)   ~ (all_52_13 = all_10_2)
% 203.47/34.36    (45)  op(e0, e0) = e0
% 203.47/34.36    (46)  all_58_10 = all_52_27
% 203.47/34.36    (47)  all_56_8 = all_52_5
% 203.47/34.36    (48)   ~ (all_52_25 = all_52_29)
% 203.47/34.36    (49)  all_58_7 = all_52_13
% 203.47/34.36    (50)   ~ (all_52_5 = all_52_7)
% 203.47/34.36    (51)  all_58_12 = all_52_7
% 203.47/34.36    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.47/34.36    (53)  all_56_2 = all_52_17
% 203.47/34.36    (54)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.47/34.36    (55)  all_56_7 = all_52_27
% 203.47/34.36    (56)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.47/34.36    (57)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.47/34.36    (58)  op(all_4_2, e2) = all_4_1
% 203.47/34.36    (59)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.36    (60)   ~ (all_52_13 = all_4_2)
% 203.47/34.36    (61)  op(e0, e3) = all_52_7
% 203.47/34.36    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.47/34.36    (63)   ~ (all_52_9 = all_52_25)
% 203.47/34.36    (64)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.47/34.36    (65)  all_58_8 = all_10_2
% 203.47/34.36    (66)  all_56_12 = all_52_7
% 203.47/34.36    (67)  op(all_52_17, all_52_17) = all_52_16
% 203.47/34.36    (68)   ~ (all_52_25 = all_6_2)
% 203.47/34.36    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.47/34.36    (70)   ~ (all_52_9 = all_4_2)
% 203.47/34.36    (71)   ~ (all_52_5 = all_6_2)
% 203.47/34.36    (72)  op(all_4_2, all_4_2) = e2
% 203.47/34.36    (73)   ~ (all_52_9 = all_6_2)
% 203.47/34.36    (74)   ~ (all_52_13 = all_52_15)
% 203.47/34.36    (75)  op(e3, e3) = all_6_2
% 203.47/34.36    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.47/34.36    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.47/34.36    (78)  all_56_3 = all_52_25
% 203.47/34.36    (79)   ~ (all_52_3 = all_52_7)
% 203.47/34.36    (80)  all_58_5 = all_52_19
% 203.47/34.36    (81)  all_56_1 = all_52_9
% 203.47/34.36    (82)   ~ (all_52_15 = all_4_2)
% 203.47/34.36    (83)   ~ (all_52_27 = all_4_2)
% 203.47/34.36    (84)  all_58_6 = all_52_5
% 203.47/34.36    (85)  op(e3, e2) = all_52_9
% 203.47/34.36    (86)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.36    (87)   ~ (all_52_17 = all_6_2)
% 203.47/34.36    (88)   ~ (e1 = e0)
% 203.47/34.36    (89)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.47/34.36    (90)   ~ (all_52_9 = all_52_17)
% 203.47/34.36    (91)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.47/34.36    (92)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.47/34.36    (93)   ~ (all_6_1 = e2)
% 203.47/34.36    (94)  op(e1, e1) = all_10_2
% 203.47/34.36    (95)  op(all_52_9, all_52_9) = e3
% 203.47/34.36    (96)   ~ (all_52_7 = all_52_23)
% 203.47/34.36    (97)  all_58_3 = all_4_2
% 203.47/34.36    (98)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.47/34.36    (99)  all_56_13 = all_52_15
% 203.47/34.36    (100)   ~ (all_52_3 = all_4_2)
% 203.47/34.36    (101)   ~ (all_52_19 = all_4_2)
% 203.47/34.36    (102)  op(all_6_2, e3) = all_6_1
% 203.47/34.36    (103)   ~ (all_52_13 = all_52_29)
% 203.47/34.36    (104)  all_58_4 = all_52_17
% 203.47/34.36    (105)   ~ (all_52_7 = e0)
% 203.47/34.36    (106)  op(all_52_25, all_52_25) = all_52_24
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | BETA: splitting (39) gives:
% 203.47/34.36  | 
% 203.47/34.36  | Case 1:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (107)  all_56_13 = e3
% 203.47/34.36  | | 
% 203.47/34.36  | | COMBINE_EQS: (99), (107) imply:
% 203.47/34.36  | |   (108)  all_52_15 = e3
% 203.47/34.36  | | 
% 203.47/34.36  | | REF_CLOSE: (4), (9), (10), (11), (23), (33), (61), (66), (75), (93), (102),
% 203.47/34.36  | |            (108) are inconsistent by sub-proof #1341.
% 203.47/34.36  | | 
% 203.47/34.36  | Case 2:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (109)   ~ (all_56_13 = e3)
% 203.47/34.36  | |   (110)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.36  | | 
% 203.47/34.36  | | REDUCE: (99), (109) imply:
% 203.47/34.36  | |   (111)   ~ (all_52_15 = e3)
% 203.47/34.36  | | 
% 203.47/34.36  | | BETA: splitting (86) gives:
% 203.47/34.36  | | 
% 203.47/34.36  | | Case 1:
% 203.47/34.36  | | | 
% 203.47/34.36  | | |   (112)  all_58_12 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | COMBINE_EQS: (51), (112) imply:
% 203.47/34.36  | | |   (113)  all_52_7 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | SIMP: (113) implies:
% 203.47/34.36  | | |   (114)  all_52_7 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (79), (114) imply:
% 203.47/34.36  | | |   (115)   ~ (all_52_3 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (50), (114) imply:
% 203.47/34.36  | | |   (116)   ~ (all_52_5 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (10), (114) imply:
% 203.47/34.36  | | |   (117)   ~ (all_52_15 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (96), (114) imply:
% 203.47/34.36  | | |   (118)   ~ (all_52_23 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | SIMP: (118) implies:
% 203.47/34.36  | | |   (119)   ~ (all_52_23 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (33), (114) imply:
% 203.47/34.36  | | |   (120)   ~ (all_6_2 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | SIMP: (120) implies:
% 203.47/34.36  | | |   (121)   ~ (all_6_2 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (12), (114) imply:
% 203.47/34.36  | | |   (122)  op(e3, e3) = all_52_6
% 203.47/34.36  | | | 
% 203.47/34.36  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 203.47/34.36  | | |              with (75), (122) gives:
% 203.47/34.36  | | |   (123)  all_52_6 = all_6_2
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13), (14), (15), (16),
% 203.47/34.36  | | |            (17), (18), (19), (20), (21), (22), (24), (25), (26), (27),
% 203.47/34.36  | | |            (28), (29), (30), (36), (37), (38), (40), (44), (45), (46),
% 203.47/34.36  | | |            (47), (48), (49), (52), (53), (54), (55), (56), (57), (58),
% 203.47/34.36  | | |            (60), (62), (63), (64), (65), (67), (68), (69), (70), (71),
% 203.47/34.36  | | |            (72), (73), (74), (75), (76), (77), (78), (80), (81), (83),
% 203.47/34.36  | | |            (84), (85), (87), (88), (89), (90), (91), (93), (95), (97),
% 203.47/34.36  | | |            (98), (100), (101), (102), (103), (104), (106), (111), (115),
% 203.47/34.36  | | |            (116), (119), (121) are inconsistent by sub-proof #1293.
% 203.47/34.36  | | | 
% 203.47/34.36  | | Case 2:
% 203.47/34.36  | | | 
% 203.47/34.36  | | |   (124)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (12), (19), (20), (25),
% 203.47/34.36  | | |            (27), (31), (32), (34), (35), (36), (41), (42), (43), (44),
% 203.47/34.36  | | |            (45), (51), (59), (66), (72), (74), (82), (92), (94), (96),
% 203.47/34.36  | | |            (99), (105), (110), (111), (124) are inconsistent by sub-proof
% 203.47/34.36  | | |            #545.
% 203.47/34.36  | | | 
% 203.47/34.36  | | End of split
% 203.47/34.36  | | 
% 203.47/34.36  | End of split
% 203.47/34.36  | 
% 203.47/34.36  End of proof
% 203.47/34.36  
% 203.47/34.36  Sub-proof #545 shows that the following formulas are inconsistent:
% 203.47/34.36  ----------------------------------------------------------------
% 203.47/34.36    (1)  all_58_14 = all_52_23
% 203.47/34.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.36    (3)   ~ (all_52_5 = all_52_13)
% 203.47/34.36    (4)   ~ (e3 = e0)
% 203.47/34.36    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.36    (6)   ~ (all_52_7 = all_52_15)
% 203.47/34.36    (7)  op(all_52_15, all_52_15) = e0
% 203.47/34.36    (8)  op(all_52_7, all_52_7) = all_52_6
% 203.47/34.36    (9)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.36    (10)  all_58_13 = all_52_15
% 203.47/34.36    (11)  op(all_52_13, all_52_13) = e1
% 203.47/34.36    (12)   ~ (all_52_15 = e3)
% 203.47/34.36    (13)  op(e1, e3) = all_52_5
% 203.47/34.36    (14)  op(e2, e2) = all_4_2
% 203.47/34.36    (15)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.36    (16)  op(all_10_2, e1) = all_10_1
% 203.47/34.36    (17)  op(e0, e1) = all_52_23
% 203.47/34.36    (18)   ~ (all_52_15 = e0)
% 203.47/34.36    (19)  all_58_15 = e0
% 203.47/34.36    (20)  op(e1, all_10_1) = e3
% 203.47/34.36    (21)  all_56_9 = all_52_13
% 203.47/34.36    (22)   ~ (e2 = e1)
% 203.47/34.36    (23)   ~ (all_52_13 = all_10_2)
% 203.47/34.36    (24)  op(e0, e0) = e0
% 203.47/34.36    (25)  all_58_12 = all_52_7
% 203.47/34.36    (26)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.36    (27)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.36    (28)  all_56_12 = all_52_7
% 203.47/34.36    (29)  op(all_4_2, all_4_2) = e2
% 203.47/34.36    (30)   ~ (all_52_13 = all_52_15)
% 203.47/34.36    (31)   ~ (all_52_15 = all_4_2)
% 203.47/34.36    (32)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.47/34.36    (33)  op(e1, e1) = all_10_2
% 203.47/34.36    (34)   ~ (all_52_7 = all_52_23)
% 203.47/34.36    (35)  all_56_13 = all_52_15
% 203.47/34.36    (36)   ~ (all_52_7 = e0)
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | BETA: splitting (9) gives:
% 203.47/34.36  | 
% 203.47/34.36  | Case 1:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (37)  all_58_13 = e3
% 203.47/34.36  | | 
% 203.47/34.36  | | REF_CLOSE: (10), (12), (37) are inconsistent by sub-proof #1360.
% 203.47/34.36  | | 
% 203.47/34.36  | Case 2:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (38)  all_58_14 = e3 | all_58_15 = e3
% 203.47/34.36  | | 
% 203.47/34.36  | | BETA: splitting (38) gives:
% 203.47/34.36  | | 
% 203.47/34.36  | | Case 1:
% 203.47/34.36  | | | 
% 203.47/34.36  | | |   (39)  all_58_14 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | COMBINE_EQS: (1), (39) imply:
% 203.47/34.36  | | |   (40)  all_52_23 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | SIMP: (40) implies:
% 203.47/34.36  | | |   (41)  all_52_23 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (34), (41) imply:
% 203.47/34.36  | | |   (42)   ~ (all_52_7 = e3)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (17), (41) imply:
% 203.47/34.36  | | |   (43)  op(e0, e1) = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (13), (14), (15),
% 203.47/34.36  | | |            (16), (18), (20), (21), (22), (23), (24), (25), (26), (27),
% 203.47/34.36  | | |            (28), (29), (30), (31), (32), (33), (35), (36), (42), (43) are
% 203.47/34.36  | | |            inconsistent by sub-proof #546.
% 203.47/34.36  | | | 
% 203.47/34.36  | | Case 2:
% 203.47/34.36  | | | 
% 203.47/34.36  | | |   (44)  all_58_15 = e3
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REF_CLOSE: (4), (19), (44) are inconsistent by sub-proof #1350.
% 203.47/34.36  | | | 
% 203.47/34.36  | | End of split
% 203.47/34.36  | | 
% 203.47/34.36  | End of split
% 203.47/34.36  | 
% 203.47/34.36  End of proof
% 203.47/34.36  
% 203.47/34.36  Sub-proof #546 shows that the following formulas are inconsistent:
% 203.47/34.36  ----------------------------------------------------------------
% 203.47/34.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.36    (2)   ~ (all_52_5 = all_52_13)
% 203.47/34.36    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.36    (4)   ~ (all_52_7 = all_52_15)
% 203.47/34.36    (5)  op(all_52_15, all_52_15) = e0
% 203.47/34.36    (6)  op(all_52_7, all_52_7) = all_52_6
% 203.47/34.36    (7)  all_58_13 = all_52_15
% 203.47/34.36    (8)  op(all_52_13, all_52_13) = e1
% 203.47/34.36    (9)  op(e1, e3) = all_52_5
% 203.47/34.36    (10)  op(e2, e2) = all_4_2
% 203.47/34.36    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.36    (12)  op(all_10_2, e1) = all_10_1
% 203.47/34.36    (13)   ~ (all_52_15 = e0)
% 203.47/34.36    (14)  op(e1, all_10_1) = e3
% 203.47/34.36    (15)  all_56_9 = all_52_13
% 203.47/34.36    (16)   ~ (e2 = e1)
% 203.47/34.36    (17)   ~ (all_52_13 = all_10_2)
% 203.47/34.36    (18)  op(e0, e0) = e0
% 203.47/34.36    (19)  all_58_12 = all_52_7
% 203.47/34.36    (20)   ~ (all_52_7 = e3)
% 203.47/34.36    (21)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.36    (22)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.36    (23)  all_56_12 = all_52_7
% 203.47/34.36    (24)  op(all_4_2, all_4_2) = e2
% 203.47/34.36    (25)   ~ (all_52_13 = all_52_15)
% 203.47/34.36    (26)   ~ (all_52_15 = all_4_2)
% 203.47/34.36    (27)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.47/34.36    (28)  op(e1, e1) = all_10_2
% 203.47/34.36    (29)  all_56_13 = all_52_15
% 203.47/34.36    (30)  op(e0, e1) = e3
% 203.47/34.36    (31)   ~ (all_52_7 = e0)
% 203.47/34.36  
% 203.47/34.36  Begin of proof
% 203.47/34.36  | 
% 203.47/34.36  | BETA: splitting (3) gives:
% 203.47/34.36  | 
% 203.47/34.36  | Case 1:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (32)  all_56_12 = e3
% 203.47/34.36  | | 
% 203.47/34.36  | | REF_CLOSE: (20), (23), (32) are inconsistent by sub-proof #1383.
% 203.47/34.36  | | 
% 203.47/34.36  | Case 2:
% 203.47/34.36  | | 
% 203.47/34.36  | |   (33)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.36  | | 
% 203.47/34.36  | | BETA: splitting (22) gives:
% 203.47/34.36  | | 
% 203.47/34.36  | | Case 1:
% 203.47/34.36  | | | 
% 203.47/34.36  | | |   (34)  all_58_12 = e1
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REF_CLOSE: (1), (4), (5), (7), (10), (11), (13), (16), (18), (19), (21),
% 203.47/34.36  | | |            (24), (26), (29), (34) are inconsistent by sub-proof #888.
% 203.47/34.36  | | | 
% 203.47/34.36  | | Case 2:
% 203.47/34.36  | | | 
% 203.47/34.36  | | |   (35)   ~ (all_58_12 = e1)
% 203.47/34.36  | | |   (36)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.36  | | | 
% 203.47/34.36  | | | REDUCE: (19), (35) imply:
% 203.47/34.36  | | |   (37)   ~ (all_52_7 = e1)
% 203.47/34.36  | | | 
% 203.47/34.36  | | | BETA: splitting (33) gives:
% 203.47/34.36  | | | 
% 203.47/34.36  | | | Case 1:
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | |   (38)  all_56_12 = e2
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | COMBINE_EQS: (23), (38) imply:
% 203.47/34.36  | | | |   (39)  all_52_7 = e2
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | SIMP: (39) implies:
% 203.47/34.36  | | | |   (40)  all_52_7 = e2
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | REDUCE: (4), (40) imply:
% 203.47/34.36  | | | |   (41)   ~ (all_52_15 = e2)
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | SIMP: (41) implies:
% 203.47/34.36  | | | |   (42)   ~ (all_52_15 = e2)
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | REDUCE: (6), (40) imply:
% 203.47/34.36  | | | |   (43)  op(e2, e2) = all_52_6
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | BETA: splitting (36) gives:
% 203.47/34.36  | | | | 
% 203.47/34.36  | | | | Case 1:
% 203.47/34.36  | | | | | 
% 203.47/34.36  | | | | |   (44)  all_58_13 = e1
% 203.47/34.36  | | | | | 
% 203.47/34.36  | | | | | COMBINE_EQS: (7), (44) imply:
% 203.47/34.36  | | | | |   (45)  all_52_15 = e1
% 203.47/34.36  | | | | | 
% 203.47/34.36  | | | | | SIMP: (45) implies:
% 203.47/34.36  | | | | |   (46)  all_52_15 = e1
% 203.47/34.36  | | | | | 
% 203.47/34.36  | | | | | REDUCE: (25), (46) imply:
% 203.47/34.36  | | | | |   (47)   ~ (all_52_13 = e1)
% 203.47/34.36  | | | | | 
% 203.47/34.36  | | | | | REDUCE: (26), (46) imply:
% 203.47/34.36  | | | | |   (48)   ~ (all_4_2 = e1)
% 203.47/34.36  | | | | | 
% 203.47/34.36  | | | | | SIMP: (48) implies:
% 203.47/34.36  | | | | |   (49)   ~ (all_4_2 = e1)
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REDUCE: (5), (46) imply:
% 203.47/34.37  | | | | |   (50)  op(e1, e1) = e0
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying
% 203.47/34.37  | | | | |              with (28), (50) gives:
% 203.47/34.37  | | | | |   (51)  all_10_2 = e0
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_6, e2, e2,
% 203.47/34.37  | | | | |              simplifying with (10), (43) gives:
% 203.47/34.37  | | | | |   (52)  all_52_6 = all_4_2
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REDUCE: (17), (51) imply:
% 203.47/34.37  | | | | |   (53)   ~ (all_52_13 = e0)
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REDUCE: (12), (51) imply:
% 203.47/34.37  | | | | |   (54)  op(e0, e1) = all_10_1
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | GROUND_INST: instantiating (1) with e3, all_10_1, e1, e0, simplifying
% 203.47/34.37  | | | | |              with (30), (54) gives:
% 203.47/34.37  | | | | |   (55)  all_10_1 = e3
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REDUCE: (14), (55) imply:
% 203.47/34.37  | | | | |   (56)  op(e1, e3) = e3
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | GROUND_INST: instantiating (1) with all_52_5, e3, e3, e1, simplifying
% 203.47/34.37  | | | | |              with (9), (56) gives:
% 203.47/34.37  | | | | |   (57)  all_52_5 = e3
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REDUCE: (2), (57) imply:
% 203.47/34.37  | | | | |   (58)   ~ (all_52_13 = e3)
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | SIMP: (58) implies:
% 203.47/34.37  | | | | |   (59)   ~ (all_52_13 = e3)
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REF_CLOSE: (1), (8), (10), (15), (27), (47), (49), (53), (59) are
% 203.47/34.37  | | | | |            inconsistent by sub-proof #887.
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | Case 2:
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | |   (60)   ~ (all_58_13 = e1)
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REDUCE: (7), (60) imply:
% 203.47/34.37  | | | | |   (61)   ~ (all_52_15 = e1)
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REF_CLOSE: (13), (21), (29), (42), (61) are inconsistent by sub-proof
% 203.47/34.37  | | | | |            #1353.
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | End of split
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | Case 2:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (62)  all_56_12 = e1 | all_56_12 = e0
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REF_CLOSE: (23), (31), (37), (62) are inconsistent by sub-proof #1374.
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | End of split
% 203.47/34.37  | | | 
% 203.47/34.37  | | End of split
% 203.47/34.37  | | 
% 203.47/34.37  | End of split
% 203.47/34.37  | 
% 203.47/34.37  End of proof
% 203.47/34.37  
% 203.47/34.37  Sub-proof #547 shows that the following formulas are inconsistent:
% 203.47/34.37  ----------------------------------------------------------------
% 203.47/34.37    (1)  all_58_14 = all_52_23
% 203.47/34.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.37    (3)  op(all_52_7, all_52_7) = e0
% 203.47/34.37    (4)  op(all_52_5, all_52_5) = e1
% 203.47/34.37    (5)   ~ (e3 = e0)
% 203.47/34.37    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.37    (7)  op(e0, e2) = all_52_15
% 203.47/34.37    (8)   ~ (all_52_7 = all_52_15)
% 203.47/34.37    (9)  all_58_0 = all_6_2
% 203.47/34.37    (10)  all_58_13 = all_52_15
% 203.47/34.37    (11)  op(e1, e3) = all_52_5
% 203.47/34.37    (12)  op(e2, e2) = all_4_2
% 203.47/34.37    (13)   ~ (all_4_1 = e3)
% 203.47/34.37    (14)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.37    (15)  op(all_10_2, e1) = all_10_1
% 203.47/34.37    (16)   ~ (all_52_7 = all_6_2)
% 203.47/34.37    (17)  op(e0, e0) = all_14_2
% 203.47/34.37    (18)  op(e0, e1) = all_52_23
% 203.47/34.37    (19)   ~ (all_52_15 = e0)
% 203.47/34.37    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.47/34.37    (21)  all_58_15 = e0
% 203.47/34.37    (22)   ~ (all_4_1 = e1)
% 203.47/34.37    (23)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.37    (24)  op(e1, all_10_1) = e3
% 203.47/34.37    (25)   ~ (e2 = e1)
% 203.47/34.37    (26)  all_36_2 = all_10_2
% 203.47/34.37    (27)  all_36_1 = all_10_1
% 203.47/34.37    (28)  op(all_6_2, all_6_2) = e3
% 203.47/34.37    (29)  all_58_12 = all_52_7
% 203.47/34.37    (30)   ~ (all_52_7 = all_14_2)
% 203.47/34.37    (31)  all_58_2 = all_52_3
% 203.47/34.37    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.47/34.37    (33)   ~ (e2 = e0)
% 203.47/34.37    (34)  op(all_4_2, e2) = all_4_1
% 203.47/34.37    (35)  op(all_52_3, all_52_3) = e2
% 203.47/34.37    (36)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.37    (37)  op(all_52_23, all_52_23) = all_52_22
% 203.47/34.37    (38)   ~ (all_52_5 = all_10_2)
% 203.47/34.37    (39)  all_56_12 = all_52_7
% 203.47/34.37    (40)  op(e3, e3) = all_6_2
% 203.47/34.37    (41)  all_58_6 = all_52_5
% 203.47/34.37    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.37    (43)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.37    (44)   ~ (e3 = e2)
% 203.47/34.37    (45)  op(e1, e1) = all_10_2
% 203.47/34.37    (46)   ~ (all_52_7 = all_52_23)
% 203.47/34.37    (47)  all_56_13 = all_52_15
% 203.47/34.37    (48)   ~ (all_52_3 = all_4_2)
% 203.47/34.37    (49)   ~ (all_52_7 = e0)
% 203.47/34.37  
% 203.47/34.37  Begin of proof
% 203.47/34.37  | 
% 203.47/34.37  | BETA: splitting (23) gives:
% 203.47/34.37  | 
% 203.47/34.37  | Case 1:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (50)  all_56_13 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | COMBINE_EQS: (47), (50) imply:
% 203.47/34.37  | |   (51)  all_52_15 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | SIMP: (51) implies:
% 203.47/34.37  | |   (52)  all_52_15 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | COMBINE_EQS: (10), (52) imply:
% 203.47/34.37  | |   (53)  all_58_13 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (8), (52) imply:
% 203.47/34.37  | |   (54)   ~ (all_52_7 = e3)
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (7), (52) imply:
% 203.47/34.37  | |   (55)  op(e0, e2) = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | BETA: splitting (6) gives:
% 203.47/34.37  | | 
% 203.47/34.37  | | Case 1:
% 203.47/34.37  | | | 
% 203.47/34.37  | | |   (56)  all_56_12 = e3
% 203.47/34.37  | | | 
% 203.47/34.37  | | | REF_CLOSE: (39), (54), (56) are inconsistent by sub-proof #1383.
% 203.47/34.37  | | | 
% 203.47/34.37  | | Case 2:
% 203.47/34.37  | | | 
% 203.47/34.37  | | |   (57)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.37  | | | 
% 203.47/34.37  | | | BETA: splitting (36) gives:
% 203.47/34.37  | | | 
% 203.47/34.37  | | | Case 1:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (58)  all_58_12 = e1
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | COMBINE_EQS: (29), (58) imply:
% 203.47/34.37  | | | |   (59)  all_52_7 = e1
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | SIMP: (59) implies:
% 203.47/34.37  | | | |   (60)  all_52_7 = e1
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REDUCE: (3), (60) imply:
% 203.47/34.37  | | | |   (61)  op(e1, e1) = e0
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REF_CLOSE: (1), (2), (14), (15), (18), (21), (25), (26), (27), (33),
% 203.47/34.37  | | | |            (43), (44), (45), (53), (58), (61) are inconsistent by
% 203.47/34.37  | | | |            sub-proof #550.
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | Case 2:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (62)   ~ (all_58_12 = e1)
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REDUCE: (29), (62) imply:
% 203.47/34.37  | | | |   (63)   ~ (all_52_7 = e1)
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REF_CLOSE: (2), (3), (12), (13), (34), (39), (49), (55), (57), (63) are
% 203.47/34.37  | | | |            inconsistent by sub-proof #1373.
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | End of split
% 203.47/34.37  | | | 
% 203.47/34.37  | | End of split
% 203.47/34.37  | | 
% 203.47/34.37  | Case 2:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (64)   ~ (all_56_13 = e3)
% 203.47/34.37  | |   (65)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (47), (64) imply:
% 203.47/34.37  | |   (66)   ~ (all_52_15 = e3)
% 203.47/34.37  | | 
% 203.47/34.37  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.47/34.37  | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (26), (28),
% 203.47/34.37  | |            (29), (30), (31), (32), (34), (35), (36), (37), (38), (39), (40),
% 203.47/34.37  | |            (41), (42), (43), (45), (46), (47), (48), (49), (65), (66) are
% 203.47/34.37  | |            inconsistent by sub-proof #548.
% 203.47/34.37  | | 
% 203.47/34.37  | End of split
% 203.47/34.37  | 
% 203.47/34.37  End of proof
% 203.47/34.37  
% 203.47/34.37  Sub-proof #548 shows that the following formulas are inconsistent:
% 203.47/34.37  ----------------------------------------------------------------
% 203.47/34.37    (1)  all_58_14 = all_52_23
% 203.47/34.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.37    (3)  op(all_52_7, all_52_7) = e0
% 203.47/34.37    (4)  op(all_52_5, all_52_5) = e1
% 203.47/34.37    (5)   ~ (e3 = e0)
% 203.47/34.37    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.37    (7)  op(e0, e2) = all_52_15
% 203.47/34.37    (8)   ~ (all_52_7 = all_52_15)
% 203.47/34.37    (9)  all_58_0 = all_6_2
% 203.47/34.37    (10)  all_58_13 = all_52_15
% 203.47/34.37    (11)   ~ (all_52_15 = e3)
% 203.47/34.37    (12)  op(e1, e3) = all_52_5
% 203.47/34.37    (13)  op(e2, e2) = all_4_2
% 203.47/34.37    (14)  op(all_10_2, e1) = all_10_1
% 203.47/34.37    (15)   ~ (all_52_7 = all_6_2)
% 203.47/34.37    (16)  op(e0, e0) = all_14_2
% 203.47/34.37    (17)  op(e0, e1) = all_52_23
% 203.47/34.37    (18)   ~ (all_52_15 = e0)
% 203.47/34.37    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.47/34.37    (20)  all_58_15 = e0
% 203.47/34.37    (21)   ~ (all_4_1 = e1)
% 203.47/34.37    (22)  op(e1, all_10_1) = e3
% 203.47/34.37    (23)  all_36_2 = all_10_2
% 203.47/34.37    (24)  op(all_6_2, all_6_2) = e3
% 203.47/34.37    (25)  all_58_12 = all_52_7
% 203.47/34.37    (26)   ~ (all_52_7 = all_14_2)
% 203.47/34.37    (27)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.47/34.37    (28)  all_58_2 = all_52_3
% 203.47/34.37    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.47/34.37    (30)  op(all_4_2, e2) = all_4_1
% 203.47/34.37    (31)  op(all_52_3, all_52_3) = e2
% 203.47/34.37    (32)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.37    (33)  op(all_52_23, all_52_23) = all_52_22
% 203.47/34.37    (34)   ~ (all_52_5 = all_10_2)
% 203.47/34.37    (35)  all_56_12 = all_52_7
% 203.47/34.37    (36)  op(e3, e3) = all_6_2
% 203.47/34.37    (37)  all_58_6 = all_52_5
% 203.47/34.37    (38)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.37    (39)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.37    (40)  op(e1, e1) = all_10_2
% 203.47/34.37    (41)   ~ (all_52_7 = all_52_23)
% 203.47/34.37    (42)  all_56_13 = all_52_15
% 203.47/34.37    (43)   ~ (all_52_3 = all_4_2)
% 203.47/34.37    (44)   ~ (all_52_7 = e0)
% 203.47/34.37  
% 203.47/34.37  Begin of proof
% 203.47/34.37  | 
% 203.47/34.37  | BETA: splitting (38) gives:
% 203.47/34.37  | 
% 203.47/34.37  | Case 1:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (45)  all_58_12 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | COMBINE_EQS: (25), (45) imply:
% 203.47/34.37  | |   (46)  all_52_7 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | REF_CLOSE: (2), (3), (4), (9), (13), (15), (16), (19), (24), (25), (26),
% 203.47/34.37  | |            (28), (29), (31), (34), (36), (37), (38), (40), (43), (46) are
% 203.47/34.37  | |            inconsistent by sub-proof #1361.
% 203.47/34.37  | | 
% 203.47/34.37  | Case 2:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (47)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | BETA: splitting (47) gives:
% 203.47/34.37  | | 
% 203.47/34.37  | | Case 1:
% 203.47/34.37  | | | 
% 203.47/34.37  | | |   (48)  all_58_13 = e3
% 203.47/34.37  | | | 
% 203.47/34.37  | | | REF_CLOSE: (10), (11), (48) are inconsistent by sub-proof #1360.
% 203.47/34.37  | | | 
% 203.47/34.37  | | Case 2:
% 203.47/34.37  | | | 
% 203.47/34.37  | | |   (49)  all_58_14 = e3 | all_58_15 = e3
% 203.47/34.37  | | | 
% 203.47/34.37  | | | BETA: splitting (49) gives:
% 203.47/34.37  | | | 
% 203.47/34.37  | | | Case 1:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (50)  all_58_14 = e3
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | COMBINE_EQS: (1), (50) imply:
% 203.47/34.37  | | | |   (51)  all_52_23 = e3
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | SIMP: (51) implies:
% 203.47/34.37  | | | |   (52)  all_52_23 = e3
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REDUCE: (41), (52) imply:
% 203.47/34.37  | | | |   (53)   ~ (all_52_7 = e3)
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REDUCE: (33), (52) imply:
% 203.47/34.37  | | | |   (54)  op(e3, e3) = all_52_22
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REDUCE: (17), (52) imply:
% 203.47/34.37  | | | |   (55)  op(e0, e1) = e3
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_22, e3, e3,
% 203.47/34.37  | | | |              simplifying with (36), (54) gives:
% 203.47/34.37  | | | |   (56)  all_52_22 = all_6_2
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | BETA: splitting (6) gives:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | Case 1:
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | |   (57)  all_56_12 = e3
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | REF_CLOSE: (35), (53), (57) are inconsistent by sub-proof #1383.
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | Case 2:
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | |   (58)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | BETA: splitting (32) gives:
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | | Case 1:
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | |   (59)  all_58_12 = e1
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | | REF_CLOSE: (2), (3), (4), (12), (14), (15), (22), (23), (25), (36),
% 203.47/34.37  | | | | | |            (39), (40), (55), (59) are inconsistent by sub-proof
% 203.47/34.37  | | | | | |            #549.
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | Case 2:
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | |   (60)   ~ (all_58_12 = e1)
% 203.47/34.37  | | | | | |   (61)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | | REDUCE: (25), (60) imply:
% 203.47/34.37  | | | | | |   (62)   ~ (all_52_7 = e1)
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (13), (18), (21), (27), (30),
% 203.47/34.37  | | | | | |            (35), (42), (44), (58), (61), (62) are inconsistent by
% 203.47/34.37  | | | | | |            sub-proof #1351.
% 203.47/34.37  | | | | | | 
% 203.47/34.37  | | | | | End of split
% 203.47/34.37  | | | | | 
% 203.47/34.37  | | | | End of split
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | Case 2:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (63)  all_58_15 = e3
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REF_CLOSE: (5), (20), (63) are inconsistent by sub-proof #1350.
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | End of split
% 203.47/34.37  | | | 
% 203.47/34.37  | | End of split
% 203.47/34.37  | | 
% 203.47/34.37  | End of split
% 203.47/34.37  | 
% 203.47/34.37  End of proof
% 203.47/34.37  
% 203.47/34.37  Sub-proof #549 shows that the following formulas are inconsistent:
% 203.47/34.37  ----------------------------------------------------------------
% 203.47/34.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.37    (2)  op(all_52_7, all_52_7) = e0
% 203.47/34.37    (3)  op(all_52_5, all_52_5) = e1
% 203.47/34.37    (4)  op(e1, e3) = all_52_5
% 203.47/34.37    (5)  op(all_10_2, e1) = all_10_1
% 203.47/34.37    (6)   ~ (all_52_7 = all_6_2)
% 203.47/34.37    (7)  op(e1, all_10_1) = e3
% 203.47/34.37    (8)  all_36_2 = all_10_2
% 203.47/34.37    (9)  all_58_12 = all_52_7
% 203.47/34.37    (10)  op(e3, e3) = all_6_2
% 203.47/34.37    (11)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.37    (12)  op(e1, e1) = all_10_2
% 203.47/34.37    (13)  all_58_12 = e1
% 203.47/34.37    (14)  op(e0, e1) = e3
% 203.47/34.37  
% 203.47/34.37  Begin of proof
% 203.47/34.37  | 
% 203.47/34.37  | COMBINE_EQS: (9), (13) imply:
% 203.47/34.37  |   (15)  all_52_7 = e1
% 203.47/34.37  | 
% 203.47/34.37  | SIMP: (15) implies:
% 203.47/34.37  |   (16)  all_52_7 = e1
% 203.47/34.37  | 
% 203.47/34.37  | REDUCE: (6), (16) imply:
% 203.47/34.37  |   (17)   ~ (all_6_2 = e1)
% 203.47/34.37  | 
% 203.47/34.37  | SIMP: (17) implies:
% 203.47/34.37  |   (18)   ~ (all_6_2 = e1)
% 203.47/34.37  | 
% 203.47/34.37  | REDUCE: (2), (16) imply:
% 203.47/34.37  |   (19)  op(e1, e1) = e0
% 203.47/34.37  | 
% 203.47/34.37  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 203.47/34.37  |              (12), (19) gives:
% 203.47/34.37  |   (20)  all_10_2 = e0
% 203.47/34.37  | 
% 203.47/34.37  | COMBINE_EQS: (8), (20) imply:
% 203.47/34.37  |   (21)  all_36_2 = e0
% 203.47/34.37  | 
% 203.47/34.37  | REDUCE: (5), (20) imply:
% 203.47/34.37  |   (22)  op(e0, e1) = all_10_1
% 203.47/34.37  | 
% 203.47/34.37  | BETA: splitting (11) gives:
% 203.47/34.37  | 
% 203.47/34.37  | Case 1:
% 203.47/34.37  | | 
% 203.47/34.37  | | 
% 203.47/34.37  | | GROUND_INST: instantiating (1) with e3, all_10_1, e1, e0, simplifying with
% 203.47/34.37  | |              (14), (22) gives:
% 203.47/34.37  | |   (23)  all_10_1 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (7), (23) imply:
% 203.47/34.37  | |   (24)  op(e1, e3) = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | GROUND_INST: instantiating (1) with all_52_5, e3, e3, e1, simplifying with
% 203.47/34.37  | |              (4), (24) gives:
% 203.47/34.37  | |   (25)  all_52_5 = e3
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (3), (25) imply:
% 203.47/34.37  | |   (26)  op(e3, e3) = e1
% 203.47/34.37  | | 
% 203.47/34.37  | | REF_CLOSE: (1), (10), (18), (26) are inconsistent by sub-proof #885.
% 203.47/34.37  | | 
% 203.47/34.37  | Case 2:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (27)   ~ (all_36_2 = e0)
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (21), (27) imply:
% 203.47/34.37  | |   (28)  $false
% 203.47/34.37  | | 
% 203.47/34.37  | | CLOSE: (28) is inconsistent.
% 203.47/34.37  | | 
% 203.47/34.37  | End of split
% 203.47/34.37  | 
% 203.47/34.37  End of proof
% 203.47/34.37  
% 203.47/34.37  Sub-proof #550 shows that the following formulas are inconsistent:
% 203.47/34.37  ----------------------------------------------------------------
% 203.47/34.37    (1)  all_58_14 = all_52_23
% 203.47/34.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.37    (3)  all_58_13 = e3
% 203.47/34.37    (4)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.37    (5)  op(all_10_2, e1) = all_10_1
% 203.47/34.37    (6)  op(e0, e1) = all_52_23
% 203.47/34.37    (7)  op(e1, e1) = e0
% 203.47/34.37    (8)  all_58_15 = e0
% 203.47/34.37    (9)   ~ (e2 = e1)
% 203.47/34.37    (10)  all_36_2 = all_10_2
% 203.47/34.37    (11)  all_36_1 = all_10_1
% 203.47/34.37    (12)   ~ (e2 = e0)
% 203.47/34.37    (13)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.37    (14)   ~ (e3 = e2)
% 203.47/34.37    (15)  op(e1, e1) = all_10_2
% 203.47/34.37    (16)  all_58_12 = e1
% 203.47/34.37  
% 203.47/34.37  Begin of proof
% 203.47/34.37  | 
% 203.47/34.37  | BETA: splitting (4) gives:
% 203.47/34.37  | 
% 203.47/34.37  | Case 1:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (17)  all_58_12 = e2
% 203.47/34.37  | | 
% 203.47/34.37  | | COMBINE_EQS: (16), (17) imply:
% 203.47/34.37  | |   (18)  e2 = e1
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (9), (18) imply:
% 203.47/34.37  | |   (19)  $false
% 203.47/34.37  | | 
% 203.47/34.37  | | CLOSE: (19) is inconsistent.
% 203.47/34.37  | | 
% 203.47/34.37  | Case 2:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (20)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.37  | | 
% 203.47/34.37  | | BETA: splitting (20) gives:
% 203.47/34.37  | | 
% 203.47/34.37  | | Case 1:
% 203.47/34.37  | | | 
% 203.47/34.37  | | |   (21)  all_58_13 = e2
% 203.47/34.37  | | | 
% 203.47/34.37  | | | REF_CLOSE: (3), (14), (21) are inconsistent by sub-proof #1248.
% 203.47/34.37  | | | 
% 203.47/34.37  | | Case 2:
% 203.47/34.37  | | | 
% 203.47/34.37  | | |   (22)  all_58_14 = e2 | all_58_15 = e2
% 203.47/34.37  | | | 
% 203.47/34.37  | | | BETA: splitting (22) gives:
% 203.47/34.37  | | | 
% 203.47/34.37  | | | Case 1:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (23)  all_58_14 = e2
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | COMBINE_EQS: (1), (23) imply:
% 203.47/34.37  | | | |   (24)  all_52_23 = e2
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | SIMP: (24) implies:
% 203.47/34.37  | | | |   (25)  all_52_23 = e2
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REDUCE: (6), (25) imply:
% 203.47/34.37  | | | |   (26)  op(e0, e1) = e2
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REF_CLOSE: (2), (5), (7), (10), (11), (13), (15), (26) are inconsistent
% 203.47/34.37  | | | |            by sub-proof #551.
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | Case 2:
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | |   (27)  all_58_15 = e2
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | | REF_CLOSE: (8), (12), (27) are inconsistent by sub-proof #1223.
% 203.47/34.37  | | | | 
% 203.47/34.37  | | | End of split
% 203.47/34.37  | | | 
% 203.47/34.37  | | End of split
% 203.47/34.37  | | 
% 203.47/34.37  | End of split
% 203.47/34.37  | 
% 203.47/34.37  End of proof
% 203.47/34.37  
% 203.47/34.37  Sub-proof #551 shows that the following formulas are inconsistent:
% 203.47/34.37  ----------------------------------------------------------------
% 203.47/34.37    (1)  op(e0, e1) = e2
% 203.47/34.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.37    (3)  op(all_10_2, e1) = all_10_1
% 203.47/34.37    (4)  op(e1, e1) = e0
% 203.47/34.37    (5)  all_36_2 = all_10_2
% 203.47/34.37    (6)  all_36_1 = all_10_1
% 203.47/34.37    (7)   ~ (all_36_1 = e2) |  ~ (all_36_2 = e0)
% 203.47/34.37    (8)  op(e1, e1) = all_10_2
% 203.47/34.37  
% 203.47/34.37  Begin of proof
% 203.47/34.37  | 
% 203.47/34.37  | GROUND_INST: instantiating (2) with all_10_2, e0, e1, e1, simplifying with
% 203.47/34.37  |              (4), (8) gives:
% 203.47/34.37  |   (9)  all_10_2 = e0
% 203.47/34.37  | 
% 203.47/34.37  | COMBINE_EQS: (5), (9) imply:
% 203.47/34.37  |   (10)  all_36_2 = e0
% 203.47/34.37  | 
% 203.47/34.37  | REDUCE: (3), (9) imply:
% 203.47/34.37  |   (11)  op(e0, e1) = all_10_1
% 203.47/34.37  | 
% 203.47/34.37  | BETA: splitting (7) gives:
% 203.47/34.37  | 
% 203.47/34.37  | Case 1:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (12)   ~ (all_36_1 = e2)
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (6), (12) imply:
% 203.47/34.37  | |   (13)   ~ (all_10_1 = e2)
% 203.47/34.37  | | 
% 203.47/34.37  | | GROUND_INST: instantiating (2) with e2, all_10_1, e1, e0, simplifying with
% 203.47/34.37  | |              (1), (11) gives:
% 203.47/34.37  | |   (14)  all_10_1 = e2
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (13), (14) imply:
% 203.47/34.37  | |   (15)  $false
% 203.47/34.37  | | 
% 203.47/34.37  | | CLOSE: (15) is inconsistent.
% 203.47/34.37  | | 
% 203.47/34.37  | Case 2:
% 203.47/34.37  | | 
% 203.47/34.37  | |   (16)   ~ (all_36_2 = e0)
% 203.47/34.37  | | 
% 203.47/34.37  | | REDUCE: (10), (16) imply:
% 203.47/34.37  | |   (17)  $false
% 203.47/34.37  | | 
% 203.47/34.37  | | CLOSE: (17) is inconsistent.
% 203.47/34.37  | | 
% 203.47/34.37  | End of split
% 203.47/34.37  | 
% 203.47/34.37  End of proof
% 203.47/34.37  
% 203.47/34.37  Sub-proof #552 shows that the following formulas are inconsistent:
% 203.47/34.37  ----------------------------------------------------------------
% 203.47/34.37    (1)   ~ (all_52_15 = all_52_23)
% 203.47/34.37    (2)   ~ (all_52_25 = all_52_27)
% 203.47/34.37    (3)  all_58_14 = all_52_23
% 203.47/34.37    (4)   ~ (e3 = e1)
% 203.47/34.37    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.47/34.37    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.47/34.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.47/34.37    (7)   ~ (all_52_5 = all_52_13)
% 203.47/34.37    (8)  all_58_1 = all_52_9
% 203.47/34.37    (9)   ~ (all_52_9 = all_52_13)
% 203.47/34.37    (10)   ~ (e3 = e0)
% 203.47/34.37    (11)  op(e2, e3) = all_52_3
% 203.47/34.37    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.47/34.37    (13)   ~ (all_52_7 = all_52_15)
% 203.47/34.37    (14)  all_18_0 = all_14_0
% 203.47/34.37    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.47/34.37    (16)   ~ (all_52_17 = all_52_25)
% 203.47/34.37    (17)   ~ (all_52_3 = all_6_2)
% 203.47/34.37    (18)  all_50_1 = all_14_1
% 203.47/34.37    (19)  all_58_0 = all_6_2
% 203.47/34.37    (20)  op(all_14_2, e0) = all_14_1
% 203.47/34.37    (21)  all_56_4 = all_52_3
% 203.47/34.37    (22)   ~ (all_52_17 = all_10_2)
% 203.47/34.38    (23)  op(all_6_2, e3) = e1
% 203.47/34.38    (24)  op(e3, e0) = all_52_25
% 203.47/34.38    (25)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 203.47/34.38    (26)  op(e0, all_14_1) = all_14_0
% 203.47/34.38    (27)  op(all_52_5, all_52_5) = all_52_4
% 203.47/34.38    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.47/34.38    (29)   ~ (all_52_27 = all_52_29)
% 203.47/34.38    (30)  all_58_13 = all_52_15
% 203.47/34.38    (31)  all_58_9 = all_52_25
% 203.47/34.38    (32)   ~ (all_52_29 = all_14_2)
% 203.47/34.38    (33)  op(all_52_27, all_52_27) = all_52_26
% 203.47/34.38    (34)  op(e1, e3) = all_52_5
% 203.47/34.38    (35)  op(e2, e2) = all_4_2
% 203.47/34.38    (36)  all_12_0 = all_6_0
% 203.47/34.38    (37)   ~ (all_52_3 = all_52_5)
% 203.47/34.38    (38)  all_58_11 = all_52_29
% 203.47/34.38    (39)   ~ (all_52_25 = all_14_2)
% 203.47/34.38    (40)   ~ (all_52_9 = all_52_15)
% 203.47/34.38    (41)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.47/34.38    (42)  op(all_6_2, all_6_2) = all_52_0
% 203.47/34.38    (43)   ~ (all_52_7 = all_6_2)
% 203.47/34.38    (44)  op(e0, e0) = all_14_2
% 203.47/34.38    (45)  op(e0, e1) = all_52_23
% 203.47/34.38    (46)  all_56_15 = all_14_2
% 203.47/34.38    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.47/34.38    (48)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.47/34.38    (49)   ~ (all_4_1 = e1)
% 203.47/34.38    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.47/34.38    (51)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.47/34.38    (52)  all_56_9 = all_52_13
% 203.47/34.38    (53)   ~ (e2 = e1)
% 203.47/34.38    (54)   ~ (all_52_13 = all_10_2)
% 203.47/34.38    (55)   ~ (all_6_0 = e1)
% 203.47/34.38    (56)  all_12_2 = all_6_2
% 203.47/34.38    (57)  all_58_10 = all_52_27
% 203.47/34.38    (58)  all_56_8 = all_52_5
% 203.47/34.38    (59)  op(all_52_9, all_52_9) = all_52_8
% 203.47/34.38    (60)  op(all_52_15, all_52_15) = all_52_14
% 203.47/34.38    (61)   ~ (all_52_25 = all_52_29)
% 203.47/34.38    (62)  all_58_7 = all_52_13
% 203.47/34.38    (63)  all_50_0 = all_14_0
% 203.47/34.38    (64)   ~ (all_52_5 = all_52_7)
% 203.47/34.38    (65)  all_58_12 = all_52_7
% 203.47/34.38    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.47/34.38    (67)   ~ (all_52_7 = all_14_2)
% 203.47/34.38    (68)  all_58_2 = all_52_3
% 203.47/34.38    (69)  all_56_2 = all_52_17
% 203.47/34.38    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.47/34.38    (71)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.47/34.38    (72)  all_56_7 = all_52_27
% 203.47/34.38    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.47/34.38    (74)   ~ (e2 = e0)
% 203.47/34.38    (75)  op(all_4_2, e2) = all_4_1
% 203.47/34.38    (76)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.47/34.38    (77)   ~ (all_14_0 = e2) |  ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 203.47/34.38    (78)   ~ (all_52_5 = all_52_29)
% 203.47/34.38    (79)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 203.47/34.38    (80)   ~ (all_52_15 = all_14_2)
% 203.47/34.38    (81)   ~ (all_52_19 = all_52_27)
% 203.47/34.38    (82)   ~ (all_6_0 = e2)
% 203.47/34.38    (83)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.47/34.38            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.47/34.38    (84)   ~ (all_52_13 = all_4_2)
% 203.47/34.38    (85)  op(e3, e1) = all_52_17
% 203.47/34.38    (86)  op(e0, e3) = all_52_7
% 203.47/34.38    (87)  op(e3, e1) = all_6_0
% 203.47/34.38    (88)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.47/34.38    (89)   ~ (all_52_9 = all_52_25)
% 203.47/34.38    (90)  all_58_15 = all_14_2
% 203.47/34.38    (91)  op(all_52_23, all_52_23) = all_52_22
% 203.47/34.38    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.47/34.38    (93)  all_58_8 = all_10_2
% 203.47/34.38    (94)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.47/34.38    (95)   ~ (all_52_5 = all_10_2)
% 203.47/34.38    (96)  op(all_52_29, all_52_29) = all_52_28
% 203.47/34.38    (97)   ~ (all_52_23 = all_14_2)
% 203.47/34.38    (98)  all_56_12 = all_52_7
% 203.47/34.38    (99)  op(all_52_17, all_52_17) = all_52_16
% 203.47/34.38    (100)   ~ (all_52_25 = all_6_2)
% 203.47/34.38    (101)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.47/34.38    (102)   ~ (all_52_9 = all_4_2)
% 203.47/34.38    (103)   ~ (all_52_5 = all_6_2)
% 203.47/34.38    (104)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.47/34.38    (105)   ~ (all_52_9 = all_6_2)
% 203.47/34.38    (106)   ~ (all_52_13 = all_52_15)
% 203.47/34.38    (107)  all_56_0 = all_6_2
% 203.47/34.38    (108)   ~ (all_18_0 = e3) |  ~ (all_18_1 = e2) |  ~ (all_18_2 = e1)
% 203.47/34.38    (109)  op(e3, e3) = all_6_2
% 203.47/34.38    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.47/34.38    (111)   ~ (all_52_27 = all_14_2)
% 203.47/34.38    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.47/34.38    (113)  op(all_4_2, all_4_2) = all_52_10
% 203.47/34.38    (114)  all_56_3 = all_52_25
% 203.47/34.38    (115)   ~ (all_52_3 = all_52_7)
% 203.47/34.38    (116)  op(all_14_2, all_14_2) = all_52_30
% 203.47/34.38    (117)  all_58_5 = all_52_19
% 203.47/34.38    (118)  all_56_1 = all_52_9
% 203.47/34.38    (119)   ~ (all_52_15 = all_4_2)
% 203.47/34.38    (120)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.47/34.38           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.47/34.38           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.47/34.38           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.47/34.38    (121)  all_58_6 = all_52_5
% 203.47/34.38    (122)  op(e3, e2) = all_52_9
% 203.47/34.38    (123)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.47/34.38    (124)   ~ (all_52_17 = all_6_2)
% 203.47/34.38    (125)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.47/34.38    (126)   ~ (all_52_9 = all_52_17)
% 203.47/34.38    (127)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.47/34.38    (128)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.47/34.38    (129)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.47/34.38    (130)  op(all_52_13, all_52_13) = all_52_12
% 203.47/34.38    (131)  op(e1, e1) = all_10_2
% 203.47/34.38    (132)   ~ (all_52_17 = all_52_19)
% 203.47/34.38    (133)  all_58_3 = all_4_2
% 203.47/34.38    (134)   ~ (all_52_3 = all_4_2)
% 203.47/34.38    (135)   ~ (all_52_17 = all_52_23)
% 203.47/34.38    (136)   ~ (all_52_13 = all_52_29)
% 203.47/34.38    (137)  all_58_4 = all_52_17
% 203.47/34.38    (138)  all_50_2 = all_14_2
% 203.47/34.38    (139)  op(all_52_25, all_52_25) = all_52_24
% 203.47/34.38  
% 203.47/34.38  Begin of proof
% 203.47/34.38  | 
% 203.47/34.38  | GROUND_INST: instantiating (6) with all_52_17, all_6_0, e1, e3, simplifying
% 203.47/34.38  |              with (85), (87) gives:
% 203.47/34.38  |   (140)  all_52_17 = all_6_0
% 203.47/34.38  | 
% 203.47/34.38  | COMBINE_EQS: (69), (140) imply:
% 203.47/34.38  |   (141)  all_56_2 = all_6_0
% 203.47/34.38  | 
% 203.47/34.38  | COMBINE_EQS: (137), (140) imply:
% 203.47/34.38  |   (142)  all_58_4 = all_6_0
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (126), (140) imply:
% 203.47/34.38  |   (143)   ~ (all_52_9 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (132), (140) imply:
% 203.47/34.38  |   (144)   ~ (all_52_19 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | SIMP: (144) implies:
% 203.47/34.38  |   (145)   ~ (all_52_19 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (135), (140) imply:
% 203.47/34.38  |   (146)   ~ (all_52_23 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | SIMP: (146) implies:
% 203.47/34.38  |   (147)   ~ (all_52_23 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (16), (140) imply:
% 203.47/34.38  |   (148)   ~ (all_52_25 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | SIMP: (148) implies:
% 203.47/34.38  |   (149)   ~ (all_52_25 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (22), (140) imply:
% 203.47/34.38  |   (150)   ~ (all_10_2 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | SIMP: (150) implies:
% 203.47/34.38  |   (151)   ~ (all_10_2 = all_6_0)
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (124), (140) imply:
% 203.47/34.38  |   (152)   ~ (all_6_0 = all_6_2)
% 203.47/34.38  | 
% 203.47/34.38  | REDUCE: (99), (140) imply:
% 203.47/34.38  |   (153)  op(all_6_0, all_6_0) = all_52_16
% 203.47/34.38  | 
% 203.47/34.38  | BETA: splitting (77) gives:
% 203.47/34.38  | 
% 203.47/34.38  | Case 1:
% 203.47/34.38  | | 
% 203.47/34.38  | |   (154)   ~ (all_14_0 = e2)
% 203.47/34.38  | | 
% 203.47/34.38  | | BETA: splitting (108) gives:
% 203.47/34.38  | | 
% 203.47/34.38  | | Case 1:
% 203.47/34.38  | | | 
% 203.47/34.38  | | |   (155)   ~ (all_18_0 = e3)
% 203.47/34.38  | | | 
% 203.47/34.38  | | | REDUCE: (14), (155) imply:
% 203.47/34.38  | | |   (156)   ~ (all_14_0 = e3)
% 203.47/34.38  | | | 
% 203.47/34.38  | | | BETA: splitting (83) gives:
% 203.47/34.38  | | | 
% 203.47/34.38  | | | Case 1:
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | |   (157)  all_58_15 = e0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | COMBINE_EQS: (90), (157) imply:
% 203.47/34.38  | | | |   (158)  all_14_2 = e0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (67), (158) imply:
% 203.47/34.38  | | | |   (159)   ~ (all_52_7 = e0)
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (97), (158) imply:
% 203.47/34.38  | | | |   (160)   ~ (all_52_23 = e0)
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (39), (158) imply:
% 203.47/34.38  | | | |   (161)   ~ (all_52_25 = e0)
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (116), (158) imply:
% 203.47/34.38  | | | |   (162)  op(e0, e0) = all_52_30
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (20), (158) imply:
% 203.47/34.38  | | | |   (163)  op(e0, e0) = all_14_1
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (44), (158) imply:
% 203.47/34.38  | | | |   (164)  op(e0, e0) = e0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | GROUND_INST: instantiating (6) with all_14_1, all_52_30, e0, e0,
% 203.47/34.38  | | | |              simplifying with (162), (163) gives:
% 203.47/34.38  | | | |   (165)  all_52_30 = all_14_1
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | GROUND_INST: instantiating (6) with e0, all_52_30, e0, e0, simplifying
% 203.47/34.38  | | | |              with (162), (164) gives:
% 203.47/34.38  | | | |   (166)  all_52_30 = e0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | COMBINE_EQS: (165), (166) imply:
% 203.47/34.38  | | | |   (167)  all_14_1 = e0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (26), (167) imply:
% 203.47/34.38  | | | |   (168)  op(e0, e0) = all_14_0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | GROUND_INST: instantiating (6) with e0, all_14_0, e0, e0, simplifying
% 203.47/34.38  | | | |              with (164), (168) gives:
% 203.47/34.38  | | | |   (169)  all_14_0 = e0
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (156), (169) imply:
% 203.47/34.38  | | | |   (170)   ~ (e3 = e0)
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | REDUCE: (154), (169) imply:
% 203.47/34.38  | | | |   (171)   ~ (e2 = e0)
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | BETA: splitting (50) gives:
% 203.47/34.38  | | | | 
% 203.47/34.38  | | | | Case 1:
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | |   (172)  all_56_2 = e3
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | COMBINE_EQS: (141), (172) imply:
% 203.47/34.38  | | | | |   (173)  all_6_0 = e3
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | SIMP: (173) implies:
% 203.47/34.38  | | | | |   (174)  all_6_0 = e3
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | COMBINE_EQS: (142), (174) imply:
% 203.47/34.38  | | | | |   (175)  all_58_4 = e3
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (143), (174) imply:
% 203.47/34.38  | | | | |   (176)   ~ (all_52_9 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (145), (174) imply:
% 203.47/34.38  | | | | |   (177)   ~ (all_52_19 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (147), (174) imply:
% 203.47/34.38  | | | | |   (178)   ~ (all_52_23 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (149), (174) imply:
% 203.47/34.38  | | | | |   (179)   ~ (all_52_25 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (151), (174) imply:
% 203.47/34.38  | | | | |   (180)   ~ (all_10_2 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (152), (174) imply:
% 203.47/34.38  | | | | |   (181)   ~ (all_6_2 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | SIMP: (181) implies:
% 203.47/34.38  | | | | |   (182)   ~ (all_6_2 = e3)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (82), (174) imply:
% 203.47/34.38  | | | | |   (183)   ~ (e3 = e2)
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | REDUCE: (153), (174) imply:
% 203.47/34.38  | | | | |   (184)  op(e3, e3) = all_52_16
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_16, e3, e3,
% 203.47/34.38  | | | | |              simplifying with (109), (184) gives:
% 203.47/34.38  | | | | |   (185)  all_52_16 = all_6_2
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | BETA: splitting (120) gives:
% 203.47/34.38  | | | | | 
% 203.47/34.38  | | | | | Case 1:
% 203.47/34.38  | | | | | | 
% 203.47/34.38  | | | | | |   (186)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 203.47/34.38  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 203.47/34.38  | | | | | |            all_52_14 = e0)
% 203.47/34.38  | | | | | | 
% 203.47/34.38  | | | | | | BETA: splitting (186) gives:
% 203.47/34.38  | | | | | | 
% 203.47/34.38  | | | | | | Case 1:
% 203.47/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | |   (187)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 203.53/34.38  | | | | | | |          = e0
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REF_CLOSE: (5), (6), (15), (19), (27), (35), (42), (44), (47),
% 203.53/34.38  | | | | | | |            (65), (67), (68), (71), (95), (109), (121), (123),
% 203.53/34.38  | | | | | | |            (131), (134), (182), (187) are inconsistent by
% 203.53/34.38  | | | | | | |            sub-proof #835.
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | Case 2:
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | |   (188)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 203.53/34.38  | | | | | | |          all_52_14 = e0
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | ALPHA: (188) implies:
% 203.53/34.38  | | | | | | |   (189)  all_52_14 = e0
% 203.53/34.38  | | | | | | |   (190)  all_52_12 = e1
% 203.53/34.38  | | | | | | |   (191)  all_52_10 = e2
% 203.53/34.38  | | | | | | |   (192)  all_52_8 = e3
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (59), (192) imply:
% 203.53/34.38  | | | | | | |   (193)  op(all_52_9, all_52_9) = e3
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (130), (190) imply:
% 203.53/34.38  | | | | | | |   (194)  op(all_52_13, all_52_13) = e1
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (60), (189) imply:
% 203.53/34.38  | | | | | | |   (195)  op(all_52_15, all_52_15) = e0
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (113), (191) imply:
% 203.53/34.38  | | | | | | |   (196)  op(all_4_2, all_4_2) = e2
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | BETA: splitting (123) gives:
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | |   (197)  all_58_12 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | COMBINE_EQS: (65), (197) imply:
% 203.53/34.38  | | | | | | | |   (198)  all_52_7 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | SIMP: (198) implies:
% 203.53/34.38  | | | | | | | |   (199)  all_52_7 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (115), (199) imply:
% 203.53/34.38  | | | | | | | |   (200)   ~ (all_52_3 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (64), (199) imply:
% 203.53/34.38  | | | | | | | |   (201)   ~ (all_52_5 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (13), (199) imply:
% 203.53/34.38  | | | | | | | |   (202)   ~ (all_52_15 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | SIMP: (202) implies:
% 203.53/34.38  | | | | | | | |   (203)   ~ (all_52_15 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (15), (199) imply:
% 203.53/34.38  | | | | | | | |   (204)  op(e3, e3) = all_52_6
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3,
% 203.53/34.38  | | | | | | | |              simplifying with (109), (204) gives:
% 203.53/34.38  | | | | | | | |   (205)  all_52_6 = all_6_2
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | BETA: splitting (66) gives:
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | |   (206)  all_58_6 = e3
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | REF_CLOSE: (121), (201), (206) are inconsistent by sub-proof
% 203.53/34.38  | | | | | | | | |            #1328.
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | |   (207)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | BETA: splitting (110) gives:
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | |   (208)  all_58_9 = e3
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | REF_CLOSE: (31), (179), (208) are inconsistent by sub-proof
% 203.53/34.38  | | | | | | | | | |            #1300.
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | |   (209)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | BETA: splitting (47) gives:
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | |   (210)  all_58_2 = e3
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | REF_CLOSE: (68), (200), (210) are inconsistent by sub-proof
% 203.53/34.38  | | | | | | | | | | |            #1369.
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | |   (211)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | BETA: splitting (28) gives:
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | |   (212)  all_56_7 = e3
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | COMBINE_EQS: (72), (212) imply:
% 203.53/34.38  | | | | | | | | | | | |   (213)  all_52_27 = e3
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | REDUCE: (29), (213) imply:
% 203.53/34.38  | | | | | | | | | | | |   (214)   ~ (all_52_29 = e3)
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | SIMP: (214) implies:
% 203.53/34.38  | | | | | | | | | | | |   (215)   ~ (all_52_29 = e3)
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | BETA: splitting (207) gives:
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | |   (216)  all_58_7 = e3
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | COMBINE_EQS: (62), (216) imply:
% 203.53/34.38  | | | | | | | | | | | | |   (217)  all_52_13 = e3
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | REDUCE: (84), (217) imply:
% 203.53/34.38  | | | | | | | | | | | | |   (218)   ~ (all_4_2 = e3)
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | SIMP: (218) implies:
% 203.53/34.38  | | | | | | | | | | | | |   (219)   ~ (all_4_2 = e3)
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | REDUCE: (194), (217) imply:
% 203.53/34.38  | | | | | | | | | | | | |   (220)  op(e3, e3) = e1
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | REF_CLOSE: (6), (23), (33), (34), (57), (103), (109), (117),
% 203.53/34.38  | | | | | | | | | | | | |            (133), (177), (211), (219), (220) are inconsistent
% 203.53/34.38  | | | | | | | | | | | | |            by sub-proof #576.
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | |   (221)  all_58_8 = e3 | all_58_11 = e3
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | REF_CLOSE: (38), (93), (180), (215), (221) are inconsistent
% 203.53/34.38  | | | | | | | | | | | | |            by sub-proof #1140.
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | End of split
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | |   (222)   ~ (all_56_7 = e3)
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | REDUCE: (72), (222) imply:
% 203.53/34.38  | | | | | | | | | | | |   (223)   ~ (all_52_27 = e3)
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | BETA: splitting (209) gives:
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | |   (224)  all_58_10 = e3
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | REF_CLOSE: (57), (223), (224) are inconsistent by sub-proof
% 203.53/34.38  | | | | | | | | | | | | |            #1301.
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | |   (225)  all_58_11 = e3 | all_58_15 = e3
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (19), (30), (31), (38), (49),
% 203.53/34.38  | | | | | | | | | | | | |            (61), (62), (75), (88), (99), (105), (109), (112),
% 203.53/34.38  | | | | | | | | | | | | |            (118), (122), (125), (126), (127), (133), (136),
% 203.53/34.38  | | | | | | | | | | | | |            (137), (157), (164), (182), (193), (196), (203),
% 203.53/34.38  | | | | | | | | | | | | |            (225) are inconsistent by sub-proof #1295.
% 203.53/34.38  | | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | | End of split
% 203.53/34.38  | | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | | End of split
% 203.53/34.38  | | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | | End of split
% 203.53/34.38  | | | | | | | | | | 
% 203.53/34.38  | | | | | | | | | End of split
% 203.53/34.38  | | | | | | | | | 
% 203.53/34.38  | | | | | | | | End of split
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | |   (226)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (15), (19), (23), (30),
% 203.53/34.38  | | | | | | | |            (31), (35), (40), (41), (51), (53), (65), (70), (74),
% 203.53/34.38  | | | | | | | |            (86), (89), (91), (104), (105), (109), (118), (119),
% 203.53/34.38  | | | | | | | |            (125), (131), (157), (160), (175), (178), (180),
% 203.53/34.38  | | | | | | | |            (183), (193), (195), (226) are inconsistent by
% 203.53/34.38  | | | | | | | |            sub-proof #574.
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | End of split
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | End of split
% 203.53/34.38  | | | | | | 
% 203.53/34.38  | | | | | Case 2:
% 203.53/34.38  | | | | | | 
% 203.53/34.38  | | | | | |   (227)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 203.53/34.38  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 203.53/34.38  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 203.53/34.38  | | | | | | 
% 203.53/34.38  | | | | | | BETA: splitting (227) gives:
% 203.53/34.38  | | | | | | 
% 203.53/34.38  | | | | | | Case 1:
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | |   (228)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 203.53/34.38  | | | | | | |          all_52_22 = e0
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REF_CLOSE: (182), (185), (228) are inconsistent by sub-proof #573.
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | Case 2:
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | |   (229)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.53/34.38  | | | | | | |          all_52_30 = e0
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | ALPHA: (229) implies:
% 203.53/34.38  | | | | | | |   (230)  all_52_28 = e1
% 203.53/34.38  | | | | | | |   (231)  all_52_26 = e2
% 203.53/34.38  | | | | | | |   (232)  all_52_24 = e3
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (139), (232) imply:
% 203.53/34.38  | | | | | | |   (233)  op(all_52_25, all_52_25) = e3
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (33), (231) imply:
% 203.53/34.38  | | | | | | |   (234)  op(all_52_27, all_52_27) = e2
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | REDUCE: (96), (230) imply:
% 203.53/34.38  | | | | | | |   (235)  op(all_52_29, all_52_29) = e1
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | BETA: splitting (123) gives:
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | | Case 1:
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | |   (236)  all_58_12 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | COMBINE_EQS: (65), (236) imply:
% 203.53/34.38  | | | | | | | |   (237)  all_52_7 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | SIMP: (237) implies:
% 203.53/34.38  | | | | | | | |   (238)  all_52_7 = e3
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (115), (238) imply:
% 203.53/34.38  | | | | | | | |   (239)   ~ (all_52_3 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (64), (238) imply:
% 203.53/34.38  | | | | | | | |   (240)   ~ (all_52_5 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (13), (238) imply:
% 203.53/34.38  | | | | | | | |   (241)   ~ (all_52_15 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | SIMP: (241) implies:
% 203.53/34.38  | | | | | | | |   (242)   ~ (all_52_15 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REF_CLOSE: (2), (6), (8), (9), (16), (19), (22), (23), (30),
% 203.53/34.38  | | | | | | | |            (31), (34), (38), (44), (47), (48), (52), (57), (62),
% 203.53/34.38  | | | | | | | |            (66), (68), (84), (88), (93), (100), (101), (103),
% 203.53/34.38  | | | | | | | |            (109), (111), (112), (113), (114), (117), (121),
% 203.53/34.38  | | | | | | | |            (128), (131), (133), (137), (176), (177), (180),
% 203.53/34.38  | | | | | | | |            (183), (233), (234), (235), (239), (240), (242) are
% 203.53/34.38  | | | | | | | |            inconsistent by sub-proof #571.
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | Case 2:
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | |   (243)   ~ (all_58_12 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REDUCE: (65), (243) imply:
% 203.53/34.38  | | | | | | | |   (244)   ~ (all_52_7 = e3)
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (19), (31), (35), (38), (48),
% 203.53/34.38  | | | | | | | |            (57), (61), (65), (68), (71), (78), (100), (101),
% 203.53/34.38  | | | | | | | |            (109), (110), (114), (121), (131), (134), (157),
% 203.53/34.38  | | | | | | | |            (161), (180), (233), (234), (235), (244) are
% 203.53/34.38  | | | | | | | |            inconsistent by sub-proof #1238.
% 203.53/34.38  | | | | | | | | 
% 203.53/34.38  | | | | | | | End of split
% 203.53/34.38  | | | | | | | 
% 203.53/34.38  | | | | | | End of split
% 203.53/34.38  | | | | | | 
% 203.53/34.38  | | | | | End of split
% 203.53/34.38  | | | | | 
% 203.53/34.38  | | | | Case 2:
% 203.53/34.38  | | | | | 
% 203.53/34.38  | | | | |   (245)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.53/34.38  | | | | | 
% 203.53/34.38  | | | | | REF_CLOSE: (4), (6), (23), (34), (36), (42), (55), (56), (79), (82),
% 203.53/34.38  | | | | |            (103), (107), (109), (129), (141), (152), (245) are
% 203.53/34.38  | | | | |            inconsistent by sub-proof #569.
% 203.53/34.38  | | | | | 
% 203.53/34.38  | | | | End of split
% 203.53/34.38  | | | | 
% 203.53/34.38  | | | Case 2:
% 203.53/34.38  | | | | 
% 203.53/34.38  | | | |   (246)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.53/34.38  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.53/34.38  | | | | 
% 203.53/34.38  | | | | ALPHA: (246) implies:
% 203.53/34.38  | | | |   (247)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.53/34.38  | | | | 
% 203.53/34.39  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 203.53/34.39  | | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (26),
% 203.53/34.39  | | | |            (27), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 203.53/34.39  | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 203.53/34.39  | | | |            (49), (50), (52), (53), (54), (55), (56), (57), (58), (59),
% 203.53/34.39  | | | |            (60), (62), (64), (65), (66), (67), (68), (70), (71), (73),
% 203.53/34.39  | | | |            (75), (76), (79), (80), (82), (84), (86), (88), (89), (90),
% 203.53/34.39  | | | |            (92), (93), (94), (95), (96), (97), (98), (100), (101),
% 203.53/34.39  | | | |            (102), (103), (105), (106), (107), (109), (111), (112),
% 203.53/34.39  | | | |            (113), (114), (115), (116), (117), (118), (119), (120),
% 203.53/34.39  | | | |            (121), (122), (123), (125), (128), (129), (130), (131),
% 203.53/34.39  | | | |            (133), (134), (137), (139), (141), (142), (143), (145),
% 203.53/34.39  | | | |            (147), (151), (152), (153), (154), (247) are inconsistent by
% 203.53/34.39  | | | |            sub-proof #556.
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | End of split
% 203.53/34.39  | | | 
% 203.53/34.39  | | Case 2:
% 203.53/34.39  | | | 
% 203.53/34.39  | | |   (248)  all_18_0 = e3
% 203.53/34.39  | | | 
% 203.53/34.39  | | | COMBINE_EQS: (14), (248) imply:
% 203.53/34.39  | | |   (249)  all_14_0 = e3
% 203.53/34.39  | | | 
% 203.53/34.39  | | | REDUCE: (26), (249) imply:
% 203.53/34.39  | | |   (250)  op(e0, all_14_1) = e3
% 203.53/34.39  | | | 
% 203.53/34.39  | | | BETA: splitting (83) gives:
% 203.53/34.39  | | | 
% 203.53/34.39  | | | Case 1:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | |   (251)  all_58_15 = e0
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | REF_CLOSE: (6), (10), (20), (44), (90), (116), (250), (251) are
% 203.53/34.39  | | | |            inconsistent by sub-proof #678.
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | Case 2:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | |   (252)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.53/34.39  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | ALPHA: (252) implies:
% 203.53/34.39  | | | |   (253)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 203.53/34.39  | | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (26),
% 203.53/34.39  | | | |            (27), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 203.53/34.39  | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 203.53/34.39  | | | |            (49), (50), (52), (53), (54), (55), (56), (57), (58), (59),
% 203.53/34.39  | | | |            (60), (62), (64), (65), (66), (67), (68), (70), (71), (73),
% 203.53/34.39  | | | |            (75), (76), (79), (80), (82), (84), (86), (88), (89), (90),
% 203.53/34.39  | | | |            (92), (93), (94), (95), (96), (97), (98), (100), (101),
% 203.53/34.39  | | | |            (102), (103), (105), (106), (107), (109), (111), (112),
% 203.53/34.39  | | | |            (113), (114), (115), (116), (117), (118), (119), (120),
% 203.53/34.39  | | | |            (121), (122), (123), (125), (128), (129), (130), (131),
% 203.53/34.39  | | | |            (133), (134), (137), (139), (141), (142), (143), (145),
% 203.53/34.39  | | | |            (147), (151), (152), (153), (154), (253) are inconsistent by
% 203.53/34.39  | | | |            sub-proof #556.
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | End of split
% 203.53/34.39  | | | 
% 203.53/34.39  | | End of split
% 203.53/34.39  | | 
% 203.53/34.39  | Case 2:
% 203.53/34.39  | | 
% 203.53/34.39  | |   (254)  all_14_0 = e2
% 203.53/34.39  | | 
% 203.53/34.39  | | COMBINE_EQS: (63), (254) imply:
% 203.53/34.39  | |   (255)  all_50_0 = e2
% 203.53/34.39  | | 
% 203.53/34.39  | | REDUCE: (26), (254) imply:
% 203.53/34.39  | |   (256)  op(e0, all_14_1) = e2
% 203.53/34.39  | | 
% 203.53/34.39  | | BETA: splitting (25) gives:
% 203.53/34.39  | | 
% 203.53/34.39  | | Case 1:
% 203.53/34.39  | | | 
% 203.53/34.39  | | |   (257)   ~ (all_50_0 = e2)
% 203.53/34.39  | | | 
% 203.53/34.39  | | | REDUCE: (255), (257) imply:
% 203.53/34.39  | | |   (258)  $false
% 203.53/34.39  | | | 
% 203.53/34.39  | | | CLOSE: (258) is inconsistent.
% 203.53/34.39  | | | 
% 203.53/34.39  | | Case 2:
% 203.53/34.39  | | | 
% 203.53/34.39  | | |   (259)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 203.53/34.39  | | | 
% 203.53/34.39  | | | BETA: splitting (83) gives:
% 203.53/34.39  | | | 
% 203.53/34.39  | | | Case 1:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | |   (260)  all_58_15 = e0
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | REF_CLOSE: (6), (20), (44), (74), (90), (116), (256), (260) are
% 203.53/34.39  | | | |            inconsistent by sub-proof #612.
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | Case 2:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | |   (261)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.53/34.39  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | ALPHA: (261) implies:
% 203.53/34.39  | | | |   (262)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | BETA: splitting (50) gives:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | Case 1:
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | |   (263)  all_56_2 = e3
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | COMBINE_EQS: (141), (263) imply:
% 203.53/34.39  | | | | |   (264)  all_6_0 = e3
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | COMBINE_EQS: (142), (264) imply:
% 203.53/34.39  | | | | |   (265)  all_58_4 = e3
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (143), (264) imply:
% 203.53/34.39  | | | | |   (266)   ~ (all_52_9 = e3)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (145), (264) imply:
% 203.53/34.39  | | | | |   (267)   ~ (all_52_19 = e3)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (147), (264) imply:
% 203.53/34.39  | | | | |   (268)   ~ (all_52_23 = e3)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (151), (264) imply:
% 203.53/34.39  | | | | |   (269)   ~ (all_10_2 = e3)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (152), (264) imply:
% 203.53/34.39  | | | | |   (270)   ~ (all_6_2 = e3)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | SIMP: (270) implies:
% 203.53/34.39  | | | | |   (271)   ~ (all_6_2 = e3)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (82), (264) imply:
% 203.53/34.39  | | | | |   (272)   ~ (e3 = e2)
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (153), (264) imply:
% 203.53/34.39  | | | | |   (273)  op(e3, e3) = all_52_16
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_16, e3, e3,
% 203.53/34.39  | | | | |              simplifying with (109), (273) gives:
% 203.53/34.39  | | | | |   (274)  all_52_16 = all_6_2
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | BETA: splitting (120) gives:
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | Case 1:
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | |   (275)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 203.53/34.39  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 203.53/34.39  | | | | | |            all_52_14 = e0)
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | | BETA: splitting (275) gives:
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | | Case 1:
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | |   (276)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 203.53/34.39  | | | | | | |          = e0
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REF_CLOSE: (5), (6), (15), (19), (27), (35), (42), (44), (47),
% 203.53/34.39  | | | | | | |            (65), (67), (68), (71), (95), (109), (121), (123),
% 203.53/34.39  | | | | | | |            (131), (134), (271), (276) are inconsistent by
% 203.53/34.39  | | | | | | |            sub-proof #835.
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | Case 2:
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | |   (277)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 203.53/34.39  | | | | | | |          all_52_14 = e0
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | ALPHA: (277) implies:
% 203.53/34.39  | | | | | | |   (278)  all_52_14 = e0
% 203.53/34.39  | | | | | | |   (279)  all_52_12 = e1
% 203.53/34.39  | | | | | | |   (280)  all_52_10 = e2
% 203.53/34.39  | | | | | | |   (281)  all_52_8 = e3
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (59), (281) imply:
% 203.53/34.39  | | | | | | |   (282)  op(all_52_9, all_52_9) = e3
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (130), (279) imply:
% 203.53/34.39  | | | | | | |   (283)  op(all_52_13, all_52_13) = e1
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (60), (278) imply:
% 203.53/34.39  | | | | | | |   (284)  op(all_52_15, all_52_15) = e0
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (113), (280) imply:
% 203.53/34.39  | | | | | | |   (285)  op(all_4_2, all_4_2) = e2
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | BETA: splitting (94) gives:
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | Case 1:
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | |   (286)  all_56_15 = e3
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | COMBINE_EQS: (46), (286) imply:
% 203.53/34.39  | | | | | | | |   (287)  all_14_2 = e3
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | SIMP: (287) implies:
% 203.53/34.39  | | | | | | | |   (288)  all_14_2 = e3
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | COMBINE_EQS: (138), (288) imply:
% 203.53/34.39  | | | | | | | |   (289)  all_50_2 = e3
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (67), (288) imply:
% 203.53/34.39  | | | | | | | |   (290)   ~ (all_52_7 = e3)
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (39), (288) imply:
% 203.53/34.39  | | | | | | | |   (291)   ~ (all_52_25 = e3)
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (111), (288) imply:
% 203.53/34.39  | | | | | | | |   (292)   ~ (all_52_27 = e3)
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (32), (288) imply:
% 203.53/34.39  | | | | | | | |   (293)   ~ (all_52_29 = e3)
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (116), (288) imply:
% 203.53/34.39  | | | | | | | |   (294)  op(e3, e3) = all_52_30
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (20), (288) imply:
% 203.53/34.39  | | | | | | | |   (295)  op(e3, e0) = all_14_1
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | BETA: splitting (259) gives:
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | Case 1:
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | |   (296)   ~ (all_50_1 = e1)
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | REDUCE: (18), (296) imply:
% 203.53/34.39  | | | | | | | | |   (297)   ~ (all_14_1 = e1)
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0,
% 203.53/34.39  | | | | | | | | |              e3, simplifying with (24), (295) gives:
% 203.53/34.39  | | | | | | | | |   (298)  all_52_25 = all_14_1
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3,
% 203.53/34.39  | | | | | | | | |              simplifying with (109), (294) gives:
% 203.53/34.39  | | | | | | | | |   (299)  all_52_30 = all_6_2
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | COMBINE_EQS: (114), (298) imply:
% 203.53/34.39  | | | | | | | | |   (300)  all_56_3 = all_14_1
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | COMBINE_EQS: (31), (298) imply:
% 203.53/34.39  | | | | | | | | |   (301)  all_58_9 = all_14_1
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | REDUCE: (100), (298) imply:
% 203.53/34.39  | | | | | | | | |   (302)   ~ (all_14_1 = all_6_2)
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | REDUCE: (291), (298) imply:
% 203.53/34.39  | | | | | | | | |   (303)   ~ (all_14_1 = e3)
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | BETA: splitting (101) gives:
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | Case 1:
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | |   (304)  all_56_3 = e3
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | REF_CLOSE: (300), (303), (304) are inconsistent by sub-proof
% 203.53/34.39  | | | | | | | | | |            #1200.
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | Case 2:
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | |   (305)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | BETA: splitting (66) gives:
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | Case 1:
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | |   (306)  all_58_6 = e3
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | | COMBINE_EQS: (121), (306) imply:
% 203.53/34.39  | | | | | | | | | | |   (307)  all_52_5 = e3
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | | SIMP: (307) implies:
% 203.53/34.39  | | | | | | | | | | |   (308)  all_52_5 = e3
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | | REDUCE: (37), (308) imply:
% 203.53/34.39  | | | | | | | | | | |   (309)   ~ (all_52_3 = e3)
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | | REDUCE: (64), (308) imply:
% 203.53/34.39  | | | | | | | | | | |   (310)   ~ (all_52_7 = e3)
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (19), (27), (47), (49), (53), (57),
% 203.53/34.39  | | | | | | | | | | |            (65), (68), (71), (75), (76), (109), (117), (121),
% 203.53/34.39  | | | | | | | | | | |            (122), (133), (265), (267), (271), (285), (290),
% 203.53/34.39  | | | | | | | | | | |            (292), (297), (300), (301), (302), (305), (309)
% 203.53/34.39  | | | | | | | | | | |            are inconsistent by sub-proof #554.
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | Case 2:
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | |   (311)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (19), (23), (34), (38), (62), (65),
% 203.53/34.39  | | | | | | | | | | |            (68), (71), (93), (103), (109), (121), (269),
% 203.53/34.39  | | | | | | | | | | |            (271), (283), (290), (293), (311) are inconsistent
% 203.53/34.39  | | | | | | | | | | |            by sub-proof #565.
% 203.53/34.39  | | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | | End of split
% 203.53/34.39  | | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | End of split
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | Case 2:
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | |   (312)   ~ (all_50_2 = e3)
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | REDUCE: (289), (312) imply:
% 203.53/34.39  | | | | | | | | |   (313)  $false
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | | CLOSE: (313) is inconsistent.
% 203.53/34.39  | | | | | | | | | 
% 203.53/34.39  | | | | | | | | End of split
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | Case 2:
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | |   (314)   ~ (all_56_15 = e3)
% 203.53/34.39  | | | | | | | |   (315)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REDUCE: (46), (314) imply:
% 203.53/34.39  | | | | | | | |   (316)   ~ (all_14_2 = e3)
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | | REF_CLOSE: (3), (6), (8), (13), (15), (19), (23), (30), (31),
% 203.53/34.39  | | | | | | | |            (33), (34), (35), (39), (43), (44), (46), (47), (49),
% 203.53/34.39  | | | | | | | |            (52), (57), (62), (65), (67), (68), (70), (75), (80),
% 203.53/34.39  | | | | | | | |            (84), (86), (88), (90), (97), (102), (103), (105),
% 203.53/34.39  | | | | | | | |            (109), (115), (117), (118), (119), (122), (123),
% 203.53/34.39  | | | | | | | |            (125), (128), (133), (262), (265), (266), (267),
% 203.53/34.39  | | | | | | | |            (268), (271), (273), (282), (283), (284), (285),
% 203.53/34.39  | | | | | | | |            (315), (316) are inconsistent by sub-proof #562.
% 203.53/34.39  | | | | | | | | 
% 203.53/34.39  | | | | | | | End of split
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | End of split
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | Case 2:
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | |   (317)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 203.53/34.39  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 203.53/34.39  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | | BETA: splitting (317) gives:
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | | Case 1:
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | |   (318)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 203.53/34.39  | | | | | | |          all_52_22 = e0
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REF_CLOSE: (271), (274), (318) are inconsistent by sub-proof #553.
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | Case 2:
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | |   (319)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.53/34.39  | | | | | | |          all_52_30 = e0
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | ALPHA: (319) implies:
% 203.53/34.39  | | | | | | |   (320)  all_52_30 = e0
% 203.53/34.39  | | | | | | |   (321)  all_52_28 = e1
% 203.53/34.39  | | | | | | |   (322)  all_52_26 = e2
% 203.53/34.39  | | | | | | |   (323)  all_52_24 = e3
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (139), (323) imply:
% 203.53/34.39  | | | | | | |   (324)  op(all_52_25, all_52_25) = e3
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (33), (322) imply:
% 203.53/34.39  | | | | | | |   (325)  op(all_52_27, all_52_27) = e2
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (96), (321) imply:
% 203.53/34.39  | | | | | | |   (326)  op(all_52_29, all_52_29) = e1
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REDUCE: (116), (320) imply:
% 203.53/34.39  | | | | | | |   (327)  op(all_14_2, all_14_2) = e0
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (13), (15), (16),
% 203.53/34.39  | | | | | | |            (17), (19), (20), (21), (22), (23), (24), (30), (31),
% 203.53/34.39  | | | | | | |            (34), (35), (37), (38), (39), (40), (44), (46), (47),
% 203.53/34.39  | | | | | | |            (48), (49), (52), (57), (58), (60), (62), (64), (65),
% 203.53/34.39  | | | | | | |            (66), (68), (73), (75), (80), (84), (86), (88), (89),
% 203.53/34.39  | | | | | | |            (90), (92), (93), (94), (95), (100), (101), (103),
% 203.53/34.39  | | | | | | |            (105), (106), (109), (111), (112), (113), (114), (115),
% 203.53/34.39  | | | | | | |            (117), (118), (119), (121), (122), (123), (125), (128),
% 203.53/34.39  | | | | | | |            (131), (133), (134), (137), (266), (267), (268), (269),
% 203.53/34.39  | | | | | | |            (272), (324), (325), (326), (327) are inconsistent by
% 203.53/34.39  | | | | | | |            sub-proof #557.
% 203.53/34.39  | | | | | | | 
% 203.53/34.39  | | | | | | End of split
% 203.53/34.39  | | | | | | 
% 203.53/34.39  | | | | | End of split
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | Case 2:
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | |   (328)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REF_CLOSE: (4), (6), (23), (34), (36), (42), (55), (56), (79), (82),
% 203.53/34.39  | | | | |            (103), (107), (109), (129), (141), (152), (328) are
% 203.53/34.39  | | | | |            inconsistent by sub-proof #569.
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | End of split
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | End of split
% 203.53/34.39  | | | 
% 203.53/34.39  | | End of split
% 203.53/34.39  | | 
% 203.53/34.39  | End of split
% 203.53/34.39  | 
% 203.53/34.39  End of proof
% 203.53/34.39  
% 203.53/34.39  Sub-proof #553 shows that the following formulas are inconsistent:
% 203.53/34.39  ----------------------------------------------------------------
% 203.53/34.39    (1)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 203.53/34.39    (2)  all_52_16 = all_6_2
% 203.53/34.39    (3)   ~ (all_6_2 = e3)
% 203.53/34.39  
% 203.53/34.39  Begin of proof
% 203.53/34.39  | 
% 203.53/34.39  | ALPHA: (1) implies:
% 203.53/34.39  |   (4)  all_52_16 = e3
% 203.53/34.39  | 
% 203.53/34.39  | COMBINE_EQS: (2), (4) imply:
% 203.53/34.39  |   (5)  all_6_2 = e3
% 203.53/34.39  | 
% 203.53/34.39  | REDUCE: (3), (5) imply:
% 203.53/34.39  |   (6)  $false
% 203.53/34.39  | 
% 203.53/34.39  | CLOSE: (6) is inconsistent.
% 203.53/34.39  | 
% 203.53/34.39  End of proof
% 203.53/34.39  
% 203.53/34.39  Sub-proof #554 shows that the following formulas are inconsistent:
% 203.53/34.39  ----------------------------------------------------------------
% 203.53/34.39    (1)   ~ (e3 = e1)
% 203.53/34.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.39    (3)  all_58_1 = all_52_9
% 203.53/34.39    (4)  all_58_0 = all_6_2
% 203.53/34.39    (5)  op(all_52_5, all_52_5) = all_52_4
% 203.53/34.39    (6)   ~ (all_52_3 = e3)
% 203.53/34.39    (7)  all_56_3 = all_14_1
% 203.53/34.39    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.39    (9)   ~ (all_4_1 = e1)
% 203.53/34.39    (10)   ~ (all_6_2 = e3)
% 203.53/34.39    (11)   ~ (e2 = e1)
% 203.53/34.39    (12)  all_58_10 = all_52_27
% 203.53/34.39    (13)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.39    (14)  all_58_12 = all_52_7
% 203.53/34.39    (15)   ~ (all_52_7 = e3)
% 203.53/34.39    (16)  all_58_2 = all_52_3
% 203.53/34.39    (17)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.39    (18)  all_58_4 = e3
% 203.53/34.39    (19)  all_58_9 = all_14_1
% 203.53/34.39    (20)  op(all_4_2, e2) = all_4_1
% 203.53/34.39    (21)   ~ (all_14_1 = all_6_2)
% 203.53/34.39    (22)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.53/34.39    (23)   ~ (all_52_19 = e3)
% 203.53/34.39    (24)   ~ (all_52_27 = e3)
% 203.53/34.39    (25)  op(all_4_2, all_4_2) = e2
% 203.53/34.39    (26)   ~ (all_14_1 = e1)
% 203.53/34.39    (27)  op(e3, e3) = all_6_2
% 203.53/34.39    (28)  all_58_5 = all_52_19
% 203.53/34.39    (29)  all_58_6 = all_52_5
% 203.53/34.39    (30)  op(e3, e2) = all_52_9
% 203.53/34.39    (31)  all_58_3 = all_4_2
% 203.53/34.39  
% 203.53/34.39  Begin of proof
% 203.53/34.39  | 
% 203.53/34.39  | BETA: splitting (8) gives:
% 203.53/34.39  | 
% 203.53/34.39  | Case 1:
% 203.53/34.39  | | 
% 203.53/34.39  | |   (32)  all_58_2 = e3
% 203.53/34.39  | | 
% 203.53/34.39  | | REF_CLOSE: (6), (16), (32) are inconsistent by sub-proof #1369.
% 203.53/34.39  | | 
% 203.53/34.39  | Case 2:
% 203.53/34.39  | | 
% 203.53/34.39  | |   (33)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.39  | | 
% 203.53/34.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 203.53/34.39  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 203.53/34.39  | |            (25), (26), (27), (28), (29), (30), (31), (33) are inconsistent
% 203.53/34.39  | |            by sub-proof #555.
% 203.53/34.39  | | 
% 203.53/34.39  | End of split
% 203.53/34.39  | 
% 203.53/34.39  End of proof
% 203.53/34.39  
% 203.53/34.39  Sub-proof #555 shows that the following formulas are inconsistent:
% 203.53/34.39  ----------------------------------------------------------------
% 203.53/34.39    (1)   ~ (e3 = e1)
% 203.53/34.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.39    (3)  all_58_1 = all_52_9
% 203.53/34.39    (4)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.39    (5)  all_58_0 = all_6_2
% 203.53/34.39    (6)  op(all_52_5, all_52_5) = all_52_4
% 203.53/34.39    (7)   ~ (all_52_3 = e3)
% 203.53/34.39    (8)  all_56_3 = all_14_1
% 203.53/34.39    (9)   ~ (all_4_1 = e1)
% 203.53/34.39    (10)   ~ (all_6_2 = e3)
% 203.53/34.39    (11)   ~ (e2 = e1)
% 203.53/34.39    (12)  all_58_10 = all_52_27
% 203.53/34.39    (13)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.39    (14)  all_58_12 = all_52_7
% 203.53/34.39    (15)   ~ (all_52_7 = e3)
% 203.53/34.39    (16)  all_58_2 = all_52_3
% 203.53/34.39    (17)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.39    (18)  all_58_4 = e3
% 203.53/34.39    (19)  all_58_9 = all_14_1
% 203.53/34.39    (20)  op(all_4_2, e2) = all_4_1
% 203.53/34.39    (21)   ~ (all_14_1 = all_6_2)
% 203.53/34.39    (22)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.53/34.39    (23)   ~ (all_52_19 = e3)
% 203.53/34.39    (24)   ~ (all_52_27 = e3)
% 203.53/34.39    (25)  op(all_4_2, all_4_2) = e2
% 203.53/34.39    (26)   ~ (all_14_1 = e1)
% 203.53/34.39    (27)  op(e3, e3) = all_6_2
% 203.53/34.39    (28)  all_58_5 = all_52_19
% 203.53/34.39    (29)  all_58_6 = all_52_5
% 203.53/34.39    (30)  op(e3, e2) = all_52_9
% 203.53/34.39    (31)  all_58_3 = all_4_2
% 203.53/34.39  
% 203.53/34.39  Begin of proof
% 203.53/34.39  | 
% 203.53/34.39  | BETA: splitting (17) gives:
% 203.53/34.39  | 
% 203.53/34.39  | Case 1:
% 203.53/34.39  | | 
% 203.53/34.39  | |   (32)  all_58_0 = e3
% 203.53/34.39  | | 
% 203.53/34.39  | | COMBINE_EQS: (5), (32) imply:
% 203.53/34.39  | |   (33)  all_6_2 = e3
% 203.53/34.39  | | 
% 203.53/34.39  | | REDUCE: (10), (33) imply:
% 203.53/34.39  | |   (34)  $false
% 203.53/34.39  | | 
% 203.53/34.39  | | CLOSE: (34) is inconsistent.
% 203.53/34.39  | | 
% 203.53/34.39  | Case 2:
% 203.53/34.39  | | 
% 203.53/34.39  | |   (35)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.39  | | 
% 203.53/34.39  | | BETA: splitting (35) gives:
% 203.53/34.39  | | 
% 203.53/34.39  | | Case 1:
% 203.53/34.39  | | | 
% 203.53/34.39  | | |   (36)  all_58_2 = e3
% 203.53/34.39  | | | 
% 203.53/34.39  | | | REF_CLOSE: (7), (16), (36) are inconsistent by sub-proof #1369.
% 203.53/34.39  | | | 
% 203.53/34.39  | | Case 2:
% 203.53/34.39  | | | 
% 203.53/34.39  | | |   (37)  all_58_6 = e3 | all_58_12 = e3
% 203.53/34.39  | | | 
% 203.53/34.39  | | | BETA: splitting (37) gives:
% 203.53/34.39  | | | 
% 203.53/34.39  | | | Case 1:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | |   (38)  all_58_6 = e3
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | COMBINE_EQS: (29), (38) imply:
% 203.53/34.39  | | | |   (39)  all_52_5 = e3
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | SIMP: (39) implies:
% 203.53/34.39  | | | |   (40)  all_52_5 = e3
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | REDUCE: (6), (40) imply:
% 203.53/34.39  | | | |   (41)  op(e3, e3) = all_52_4
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | BETA: splitting (4) gives:
% 203.53/34.39  | | | | 
% 203.53/34.39  | | | | Case 1:
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | |   (42)  all_58_3 = e3
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | COMBINE_EQS: (31), (42) imply:
% 203.53/34.39  | | | | |   (43)  all_4_2 = e3
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (25), (43) imply:
% 203.53/34.39  | | | | |   (44)  op(e3, e3) = e2
% 203.53/34.39  | | | | | 
% 203.53/34.39  | | | | | REDUCE: (20), (43) imply:
% 203.53/34.39  | | | | |   (45)  op(e3, e2) = all_4_1
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | GROUND_INST: instantiating (2) with all_52_9, all_4_1, e2, e3,
% 203.53/34.40  | | | | |              simplifying with (30), (45) gives:
% 203.53/34.40  | | | | |   (46)  all_52_9 = all_4_1
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_4, e3, e3,
% 203.53/34.40  | | | | |              simplifying with (27), (41) gives:
% 203.53/34.40  | | | | |   (47)  all_52_4 = all_6_2
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | GROUND_INST: instantiating (2) with e2, all_52_4, e3, e3, simplifying
% 203.53/34.40  | | | | |              with (41), (44) gives:
% 203.53/34.40  | | | | |   (48)  all_52_4 = e2
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | COMBINE_EQS: (47), (48) imply:
% 203.53/34.40  | | | | |   (49)  all_6_2 = e2
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | SIMP: (49) implies:
% 203.53/34.40  | | | | |   (50)  all_6_2 = e2
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | COMBINE_EQS: (3), (46) imply:
% 203.53/34.40  | | | | |   (51)  all_58_1 = all_4_1
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | COMBINE_EQS: (5), (50) imply:
% 203.53/34.40  | | | | |   (52)  all_58_0 = e2
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (21), (50) imply:
% 203.53/34.40  | | | | |   (53)   ~ (all_14_1 = e2)
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | BETA: splitting (22) gives:
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | Case 1:
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | |   (54)  all_58_0 = e1
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | COMBINE_EQS: (52), (54) imply:
% 203.53/34.40  | | | | | |   (55)  e2 = e1
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | REDUCE: (11), (55) imply:
% 203.53/34.40  | | | | | |   (56)  $false
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | CLOSE: (56) is inconsistent.
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | Case 2:
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | |   (57)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | BETA: splitting (13) gives:
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | Case 1:
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | |   (58)  all_56_3 = e2
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | COMBINE_EQS: (8), (58) imply:
% 203.53/34.40  | | | | | | |   (59)  all_14_1 = e2
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | REDUCE: (53), (59) imply:
% 203.53/34.40  | | | | | | |   (60)  $false
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | CLOSE: (60) is inconsistent.
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | Case 2:
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | |   (61)  all_56_3 = e1 | all_56_3 = e0
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | BETA: splitting (61) gives:
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | Case 1:
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | |   (62)  all_56_3 = e1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (8), (62) imply:
% 203.53/34.40  | | | | | | | |   (63)  all_14_1 = e1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (26), (63) imply:
% 203.53/34.40  | | | | | | | |   (64)  $false
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | CLOSE: (64) is inconsistent.
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | Case 2:
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | |   (65)  all_56_3 = e0
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (8), (65) imply:
% 203.53/34.40  | | | | | | | |   (66)  all_14_1 = e0
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (19), (66) imply:
% 203.53/34.40  | | | | | | | |   (67)  all_58_9 = e0
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (26), (66) imply:
% 203.53/34.40  | | | | | | | |   (68)   ~ (e1 = e0)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | SIMP: (68) implies:
% 203.53/34.40  | | | | | | | |   (69)   ~ (e1 = e0)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | BETA: splitting (57) gives:
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | Case 1:
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | |   (70)  all_58_1 = e1
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | COMBINE_EQS: (51), (70) imply:
% 203.53/34.40  | | | | | | | | |   (71)  all_4_1 = e1
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | REDUCE: (9), (71) imply:
% 203.53/34.40  | | | | | | | | |   (72)  $false
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | CLOSE: (72) is inconsistent.
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | Case 2:
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | |   (73)  all_58_4 = e1 | all_58_9 = e1
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | BETA: splitting (73) gives:
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | Case 1:
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | |   (74)  all_58_4 = e1
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | | COMBINE_EQS: (18), (74) imply:
% 203.53/34.40  | | | | | | | | | |   (75)  e3 = e1
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | | REDUCE: (1), (75) imply:
% 203.53/34.40  | | | | | | | | | |   (76)  $false
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | | CLOSE: (76) is inconsistent.
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | Case 2:
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | |   (77)  all_58_9 = e1
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | | REF_CLOSE: (67), (69), (77) are inconsistent by sub-proof
% 203.53/34.40  | | | | | | | | | |            #865.
% 203.53/34.40  | | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | End of split
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | End of split
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | End of split
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | End of split
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | End of split
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | Case 2:
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | |   (78)  all_58_5 = e3 | all_58_10 = e3
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REF_CLOSE: (12), (23), (24), (28), (78) are inconsistent by sub-proof
% 203.53/34.40  | | | | |            #1132.
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | End of split
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | Case 2:
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | |   (79)  all_58_12 = e3
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REF_CLOSE: (14), (15), (79) are inconsistent by sub-proof #1367.
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | End of split
% 203.53/34.40  | | | 
% 203.53/34.40  | | End of split
% 203.53/34.40  | | 
% 203.53/34.40  | End of split
% 203.53/34.40  | 
% 203.53/34.40  End of proof
% 203.53/34.40  
% 203.53/34.40  Sub-proof #556 shows that the following formulas are inconsistent:
% 203.53/34.40  ----------------------------------------------------------------
% 203.53/34.40    (1)   ~ (all_52_25 = all_52_27)
% 203.53/34.40    (2)  all_58_14 = all_52_23
% 203.53/34.40    (3)   ~ (e3 = e1)
% 203.53/34.40    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.53/34.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.40    (6)   ~ (all_52_5 = all_52_13)
% 203.53/34.40    (7)  all_58_1 = all_52_9
% 203.53/34.40    (8)   ~ (all_52_9 = all_52_13)
% 203.53/34.40    (9)  op(e2, e3) = all_52_3
% 203.53/34.40    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.53/34.40    (11)   ~ (all_52_7 = all_52_15)
% 203.53/34.40    (12)  op(all_52_7, all_52_7) = all_52_6
% 203.53/34.40    (13)   ~ (all_52_17 = all_52_25)
% 203.53/34.40    (14)   ~ (all_52_3 = all_6_2)
% 203.53/34.40    (15)  all_58_0 = all_6_2
% 203.53/34.40    (16)  op(all_14_2, e0) = all_14_1
% 203.53/34.40    (17)  all_56_4 = all_52_3
% 203.53/34.40    (18)   ~ (all_52_17 = all_10_2)
% 203.53/34.40    (19)  op(all_6_0, all_6_0) = all_52_16
% 203.53/34.40    (20)  op(all_6_2, e3) = e1
% 203.53/34.40    (21)  op(e3, e0) = all_52_25
% 203.53/34.40    (22)  op(e0, all_14_1) = all_14_0
% 203.53/34.40    (23)  op(all_52_5, all_52_5) = all_52_4
% 203.53/34.40    (24)   ~ (all_10_2 = all_6_0)
% 203.53/34.40    (25)  all_58_13 = all_52_15
% 203.53/34.40    (26)  all_58_9 = all_52_25
% 203.53/34.40    (27)   ~ (all_52_29 = all_14_2)
% 203.53/34.40    (28)  op(all_52_27, all_52_27) = all_52_26
% 203.53/34.40    (29)  op(e1, e3) = all_52_5
% 203.53/34.40    (30)  op(e2, e2) = all_4_2
% 203.53/34.40    (31)  all_12_0 = all_6_0
% 203.53/34.40    (32)   ~ (all_52_3 = all_52_5)
% 203.53/34.40    (33)  all_58_11 = all_52_29
% 203.53/34.40    (34)   ~ (all_52_25 = all_14_2)
% 203.53/34.40    (35)   ~ (all_52_9 = all_52_15)
% 203.53/34.40    (36)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.53/34.40    (37)  op(all_6_2, all_6_2) = all_52_0
% 203.53/34.40    (38)   ~ (all_52_7 = all_6_2)
% 203.53/34.40    (39)  op(e0, e0) = all_14_2
% 203.53/34.40    (40)  op(e0, e1) = all_52_23
% 203.53/34.40    (41)  all_56_2 = all_6_0
% 203.53/34.40    (42)  all_56_15 = all_14_2
% 203.53/34.40    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.40    (44)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.40    (45)   ~ (all_4_1 = e1)
% 203.53/34.40    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.53/34.40    (47)  all_58_4 = all_6_0
% 203.53/34.40    (48)  all_56_9 = all_52_13
% 203.53/34.40    (49)   ~ (e2 = e1)
% 203.53/34.40    (50)   ~ (all_52_13 = all_10_2)
% 203.53/34.40    (51)   ~ (all_6_0 = e1)
% 203.53/34.40    (52)  all_12_2 = all_6_2
% 203.53/34.40    (53)  all_58_10 = all_52_27
% 203.53/34.40    (54)   ~ (all_52_19 = all_6_0)
% 203.53/34.40    (55)  all_56_8 = all_52_5
% 203.53/34.40    (56)  op(all_52_9, all_52_9) = all_52_8
% 203.53/34.40    (57)  op(all_52_15, all_52_15) = all_52_14
% 203.53/34.40    (58)  all_58_7 = all_52_13
% 203.53/34.40    (59)   ~ (all_52_5 = all_52_7)
% 203.53/34.40    (60)  all_58_12 = all_52_7
% 203.53/34.40    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.40    (62)   ~ (all_52_7 = all_14_2)
% 203.53/34.40    (63)  all_58_2 = all_52_3
% 203.53/34.40    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.40    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.40    (66)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.53/34.40    (67)  op(all_4_2, e2) = all_4_1
% 203.53/34.40    (68)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.53/34.40    (69)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 203.53/34.40    (70)   ~ (all_52_15 = all_14_2)
% 203.53/34.40    (71)   ~ (all_6_0 = e2)
% 203.53/34.40    (72)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.53/34.40    (73)   ~ (all_52_13 = all_4_2)
% 203.53/34.40    (74)  op(e0, e3) = all_52_7
% 203.53/34.40    (75)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.40    (76)   ~ (all_52_9 = all_52_25)
% 203.53/34.40    (77)  all_58_15 = all_14_2
% 203.53/34.40    (78)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.53/34.40    (79)   ~ (all_52_23 = all_6_0)
% 203.53/34.40    (80)  all_58_8 = all_10_2
% 203.53/34.40    (81)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.40    (82)   ~ (all_52_9 = all_6_0)
% 203.53/34.40    (83)   ~ (all_52_5 = all_10_2)
% 203.53/34.40    (84)  op(all_52_29, all_52_29) = all_52_28
% 203.53/34.40    (85)   ~ (all_52_23 = all_14_2)
% 203.53/34.40    (86)  all_56_12 = all_52_7
% 203.53/34.40    (87)   ~ (all_52_25 = all_6_2)
% 203.53/34.40    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.40    (89)   ~ (all_52_9 = all_4_2)
% 203.53/34.40    (90)   ~ (all_52_5 = all_6_2)
% 203.53/34.40    (91)   ~ (all_52_9 = all_6_2)
% 203.53/34.40    (92)   ~ (all_52_13 = all_52_15)
% 203.53/34.40    (93)  all_56_0 = all_6_2
% 203.53/34.40    (94)  op(e3, e3) = all_6_2
% 203.53/34.40    (95)   ~ (all_52_27 = all_14_2)
% 203.53/34.40    (96)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.53/34.40    (97)  op(all_4_2, all_4_2) = all_52_10
% 203.53/34.40    (98)  all_56_3 = all_52_25
% 203.53/34.40    (99)   ~ (all_52_3 = all_52_7)
% 203.53/34.40    (100)   ~ (all_6_0 = all_6_2)
% 203.53/34.40    (101)  op(all_14_2, all_14_2) = all_52_30
% 203.53/34.40    (102)  all_58_5 = all_52_19
% 203.53/34.40    (103)  all_56_1 = all_52_9
% 203.53/34.40    (104)   ~ (all_52_15 = all_4_2)
% 203.53/34.40    (105)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.53/34.40           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.53/34.40           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.53/34.40           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.53/34.40    (106)  all_58_6 = all_52_5
% 203.53/34.40    (107)  op(e3, e2) = all_52_9
% 203.53/34.40    (108)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.40    (109)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.40    (110)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.40    (111)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.53/34.40    (112)  op(all_52_13, all_52_13) = all_52_12
% 203.53/34.40    (113)  op(e1, e1) = all_10_2
% 203.53/34.40    (114)  all_58_3 = all_4_2
% 203.53/34.40    (115)   ~ (all_52_3 = all_4_2)
% 203.53/34.40    (116)  all_58_4 = all_52_17
% 203.53/34.40    (117)   ~ (all_14_0 = e2)
% 203.53/34.40    (118)  op(all_52_25, all_52_25) = all_52_24
% 203.53/34.40  
% 203.53/34.40  Begin of proof
% 203.53/34.40  | 
% 203.53/34.40  | BETA: splitting (46) gives:
% 203.53/34.40  | 
% 203.53/34.40  | Case 1:
% 203.53/34.40  | | 
% 203.53/34.40  | |   (119)  all_56_2 = e3
% 203.53/34.40  | | 
% 203.53/34.40  | | COMBINE_EQS: (41), (119) imply:
% 203.53/34.40  | |   (120)  all_6_0 = e3
% 203.53/34.40  | | 
% 203.53/34.40  | | SIMP: (120) implies:
% 203.53/34.40  | |   (121)  all_6_0 = e3
% 203.53/34.40  | | 
% 203.53/34.40  | | COMBINE_EQS: (47), (121) imply:
% 203.53/34.40  | |   (122)  all_58_4 = e3
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (82), (121) imply:
% 203.53/34.40  | |   (123)   ~ (all_52_9 = e3)
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (54), (121) imply:
% 203.53/34.40  | |   (124)   ~ (all_52_19 = e3)
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (79), (121) imply:
% 203.53/34.40  | |   (125)   ~ (all_52_23 = e3)
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (24), (121) imply:
% 203.53/34.40  | |   (126)   ~ (all_10_2 = e3)
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (100), (121) imply:
% 203.53/34.40  | |   (127)   ~ (all_6_2 = e3)
% 203.53/34.40  | | 
% 203.53/34.40  | | SIMP: (127) implies:
% 203.53/34.40  | |   (128)   ~ (all_6_2 = e3)
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (71), (121) imply:
% 203.53/34.40  | |   (129)   ~ (e3 = e2)
% 203.53/34.40  | | 
% 203.53/34.40  | | REDUCE: (19), (121) imply:
% 203.53/34.40  | |   (130)  op(e3, e3) = all_52_16
% 203.53/34.40  | | 
% 203.53/34.40  | | GROUND_INST: instantiating (5) with all_6_2, all_52_16, e3, e3, simplifying
% 203.53/34.40  | |              with (94), (130) gives:
% 203.53/34.40  | |   (131)  all_52_16 = all_6_2
% 203.53/34.40  | | 
% 203.53/34.40  | | BETA: splitting (105) gives:
% 203.53/34.40  | | 
% 203.53/34.40  | | Case 1:
% 203.53/34.40  | | | 
% 203.53/34.40  | | |   (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.53/34.40  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.53/34.40  | | |            e0)
% 203.53/34.40  | | | 
% 203.53/34.40  | | | BETA: splitting (132) gives:
% 203.53/34.40  | | | 
% 203.53/34.40  | | | Case 1:
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | |   (133)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REF_CLOSE: (4), (5), (12), (15), (23), (30), (37), (39), (43), (60),
% 203.53/34.40  | | | |            (62), (63), (65), (83), (94), (106), (108), (113), (115),
% 203.53/34.40  | | | |            (128), (133) are inconsistent by sub-proof #835.
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | Case 2:
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | |   (134)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.53/34.40  | | | |          e0
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | ALPHA: (134) implies:
% 203.53/34.40  | | | |   (135)  all_52_14 = e0
% 203.53/34.40  | | | |   (136)  all_52_12 = e1
% 203.53/34.40  | | | |   (137)  all_52_10 = e2
% 203.53/34.40  | | | |   (138)  all_52_8 = e3
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (56), (138) imply:
% 203.53/34.40  | | | |   (139)  op(all_52_9, all_52_9) = e3
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (112), (136) imply:
% 203.53/34.40  | | | |   (140)  op(all_52_13, all_52_13) = e1
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (57), (135) imply:
% 203.53/34.40  | | | |   (141)  op(all_52_15, all_52_15) = e0
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (97), (137) imply:
% 203.53/34.40  | | | |   (142)  op(all_4_2, all_4_2) = e2
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | BETA: splitting (81) gives:
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | Case 1:
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | |   (143)  all_56_15 = e3
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | COMBINE_EQS: (42), (143) imply:
% 203.53/34.40  | | | | |   (144)  all_14_2 = e3
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | SIMP: (144) implies:
% 203.53/34.40  | | | | |   (145)  all_14_2 = e3
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | COMBINE_EQS: (77), (145) imply:
% 203.53/34.40  | | | | |   (146)  all_58_15 = e3
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (62), (145) imply:
% 203.53/34.40  | | | | |   (147)   ~ (all_52_7 = e3)
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (95), (145) imply:
% 203.53/34.40  | | | | |   (148)   ~ (all_52_27 = e3)
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (27), (145) imply:
% 203.53/34.40  | | | | |   (149)   ~ (all_52_29 = e3)
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (101), (145) imply:
% 203.53/34.40  | | | | |   (150)  op(e3, e3) = all_52_30
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (16), (145) imply:
% 203.53/34.40  | | | | |   (151)  op(e3, e0) = all_14_1
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | GROUND_INST: instantiating (5) with all_52_25, all_14_1, e0, e3,
% 203.53/34.40  | | | | |              simplifying with (21), (151) gives:
% 203.53/34.40  | | | | |   (152)  all_52_25 = all_14_1
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_30, e3, e3,
% 203.53/34.40  | | | | |              simplifying with (94), (150) gives:
% 203.53/34.40  | | | | |   (153)  all_52_30 = all_6_2
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | COMBINE_EQS: (26), (152) imply:
% 203.53/34.40  | | | | |   (154)  all_58_9 = all_14_1
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (76), (152) imply:
% 203.53/34.40  | | | | |   (155)   ~ (all_52_9 = all_14_1)
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (118), (152) imply:
% 203.53/34.40  | | | | |   (156)  op(all_14_1, all_14_1) = all_52_24
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | BETA: splitting (61) gives:
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | Case 1:
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | |   (157)  all_58_6 = e3
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | COMBINE_EQS: (106), (157) imply:
% 203.53/34.40  | | | | | |   (158)  all_52_5 = e3
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | SIMP: (158) implies:
% 203.53/34.40  | | | | | |   (159)  all_52_5 = e3
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | REDUCE: (32), (159) imply:
% 203.53/34.40  | | | | | |   (160)   ~ (all_52_3 = e3)
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | REDUCE: (59), (159) imply:
% 203.53/34.40  | | | | | |   (161)   ~ (all_52_7 = e3)
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | REDUCE: (23), (159) imply:
% 203.53/34.40  | | | | | |   (162)  op(e3, e3) = all_52_4
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | BETA: splitting (43) gives:
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | Case 1:
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | |   (163)  all_58_2 = e3
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | REF_CLOSE: (63), (160), (163) are inconsistent by sub-proof #1369.
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | Case 2:
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | |   (164)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | BETA: splitting (164) gives:
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | | Case 1:
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | |   (165)  all_58_3 = e3
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (114), (165) imply:
% 203.53/34.40  | | | | | | | |   (166)  all_4_2 = e3
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (73), (166) imply:
% 203.53/34.40  | | | | | | | |   (167)   ~ (all_52_13 = e3)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (142), (166) imply:
% 203.53/34.40  | | | | | | | |   (168)  op(e3, e3) = e2
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (67), (166) imply:
% 203.53/34.40  | | | | | | | |   (169)  op(e3, e2) = all_4_1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | GROUND_INST: instantiating (5) with all_52_9, all_4_1, e2, e3,
% 203.53/34.40  | | | | | | | |              simplifying with (107), (169) gives:
% 203.53/34.40  | | | | | | | |   (170)  all_52_9 = all_4_1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 203.53/34.40  | | | | | | | |              simplifying with (94), (162) gives:
% 203.53/34.40  | | | | | | | |   (171)  all_52_4 = all_6_2
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_4, e3, e3,
% 203.53/34.40  | | | | | | | |              simplifying with (162), (168) gives:
% 203.53/34.40  | | | | | | | |   (172)  all_52_4 = e2
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (171), (172) imply:
% 203.53/34.40  | | | | | | | |   (173)  all_6_2 = e2
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | SIMP: (173) implies:
% 203.53/34.40  | | | | | | | |   (174)  all_6_2 = e2
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (103), (170) imply:
% 203.53/34.40  | | | | | | | |   (175)  all_56_1 = all_4_1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (7), (170) imply:
% 203.53/34.40  | | | | | | | |   (176)  all_58_1 = all_4_1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | COMBINE_EQS: (15), (174) imply:
% 203.53/34.40  | | | | | | | |   (177)  all_58_0 = e2
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (38), (174) imply:
% 203.53/34.40  | | | | | | | |   (178)   ~ (all_52_7 = e2)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (8), (170) imply:
% 203.53/34.40  | | | | | | | |   (179)   ~ (all_52_13 = all_4_1)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | SIMP: (179) implies:
% 203.53/34.40  | | | | | | | |   (180)   ~ (all_52_13 = all_4_1)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (155), (170) imply:
% 203.53/34.40  | | | | | | | |   (181)   ~ (all_14_1 = all_4_1)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | SIMP: (181) implies:
% 203.53/34.40  | | | | | | | |   (182)   ~ (all_14_1 = all_4_1)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (91), (170), (174) imply:
% 203.53/34.40  | | | | | | | |   (183)   ~ (all_4_1 = e2)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (123), (170) imply:
% 203.53/34.40  | | | | | | | |   (184)   ~ (all_4_1 = e3)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (128), (174) imply:
% 203.53/34.40  | | | | | | | |   (185)   ~ (e3 = e2)
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REDUCE: (20), (174) imply:
% 203.53/34.40  | | | | | | | |   (186)  op(e2, e3) = e1
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | BETA: splitting (109) gives:
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | Case 1:
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | |   (187)  all_56_1 = e3
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | COMBINE_EQS: (175), (187) imply:
% 203.53/34.40  | | | | | | | | |   (188)  all_4_1 = e3
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | REDUCE: (184), (188) imply:
% 203.53/34.40  | | | | | | | | |   (189)  $false
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | CLOSE: (189) is inconsistent.
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | Case 2:
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | |   (190)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (10), (22), (25), (36), (40),
% 203.53/34.40  | | | | | | | | |            (45), (48), (49), (50), (60), (68), (86), (92),
% 203.53/34.40  | | | | | | | | |            (99), (110), (113), (117), (122), (129), (140),
% 203.53/34.40  | | | | | | | | |            (146), (147), (154), (156), (167), (175), (176),
% 203.53/34.40  | | | | | | | | |            (177), (178), (180), (182), (183), (186), (190) are
% 203.53/34.40  | | | | | | | | |            inconsistent by sub-proof #567.
% 203.53/34.40  | | | | | | | | | 
% 203.53/34.40  | | | | | | | | End of split
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | Case 2:
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | |   (191)  all_58_5 = e3 | all_58_10 = e3
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | | REF_CLOSE: (53), (102), (124), (148), (191) are inconsistent by
% 203.53/34.40  | | | | | | | |            sub-proof #1132.
% 203.53/34.40  | | | | | | | | 
% 203.53/34.40  | | | | | | | End of split
% 203.53/34.40  | | | | | | | 
% 203.53/34.40  | | | | | | End of split
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | Case 2:
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | |   (192)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | | REF_CLOSE: (4), (5), (6), (15), (20), (29), (33), (58), (60), (63),
% 203.53/34.40  | | | | | |            (65), (80), (90), (94), (106), (126), (128), (140),
% 203.53/34.40  | | | | | |            (147), (149), (192) are inconsistent by sub-proof #565.
% 203.53/34.40  | | | | | | 
% 203.53/34.40  | | | | | End of split
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | Case 2:
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | |   (193)   ~ (all_56_15 = e3)
% 203.53/34.40  | | | | |   (194)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REDUCE: (42), (193) imply:
% 203.53/34.40  | | | | |   (195)   ~ (all_14_2 = e3)
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | | REF_CLOSE: (2), (5), (7), (11), (12), (15), (20), (25), (26), (28),
% 203.53/34.40  | | | | |            (29), (30), (34), (38), (39), (42), (43), (45), (48), (53),
% 203.53/34.40  | | | | |            (58), (60), (62), (63), (64), (67), (70), (72), (73), (74),
% 203.53/34.40  | | | | |            (75), (77), (85), (89), (90), (91), (94), (99), (102),
% 203.53/34.40  | | | | |            (103), (104), (107), (108), (109), (110), (114), (122),
% 203.53/34.40  | | | | |            (123), (124), (125), (128), (130), (139), (140), (141),
% 203.53/34.40  | | | | |            (142), (194), (195) are inconsistent by sub-proof #562.
% 203.53/34.40  | | | | | 
% 203.53/34.40  | | | | End of split
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | End of split
% 203.53/34.40  | | | 
% 203.53/34.40  | | Case 2:
% 203.53/34.40  | | | 
% 203.53/34.40  | | |   (196)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.53/34.40  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.53/34.40  | | |            all_52_30 = e0)
% 203.53/34.40  | | | 
% 203.53/34.40  | | | BETA: splitting (196) gives:
% 203.53/34.40  | | | 
% 203.53/34.40  | | | Case 1:
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | |   (197)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.53/34.40  | | | |          e0
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REF_CLOSE: (128), (131), (197) are inconsistent by sub-proof #573.
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | Case 2:
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | |   (198)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.53/34.40  | | | |          e0
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | ALPHA: (198) implies:
% 203.53/34.40  | | | |   (199)  all_52_30 = e0
% 203.53/34.40  | | | |   (200)  all_52_28 = e1
% 203.53/34.40  | | | |   (201)  all_52_26 = e2
% 203.53/34.40  | | | |   (202)  all_52_24 = e3
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (118), (202) imply:
% 203.53/34.40  | | | |   (203)  op(all_52_25, all_52_25) = e3
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (28), (201) imply:
% 203.53/34.40  | | | |   (204)  op(all_52_27, all_52_27) = e2
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (84), (200) imply:
% 203.53/34.40  | | | |   (205)  op(all_52_29, all_52_29) = e1
% 203.53/34.40  | | | | 
% 203.53/34.40  | | | | REDUCE: (101), (199) imply:
% 203.53/34.40  | | | |   (206)  op(all_14_2, all_14_2) = e0
% 203.53/34.40  | | | | 
% 203.53/34.41  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 203.53/34.41  | | | |            (15), (16), (17), (18), (20), (21), (25), (26), (29), (30),
% 203.53/34.41  | | | |            (32), (33), (34), (35), (39), (42), (43), (44), (45), (48),
% 203.53/34.41  | | | |            (53), (55), (57), (58), (59), (60), (61), (63), (66), (67),
% 203.53/34.41  | | | |            (70), (73), (74), (75), (76), (77), (78), (80), (81), (83),
% 203.53/34.41  | | | |            (87), (88), (90), (91), (92), (94), (95), (96), (97), (98),
% 203.53/34.41  | | | |            (99), (102), (103), (104), (106), (107), (108), (109), (110),
% 203.53/34.41  | | | |            (113), (114), (115), (116), (123), (124), (125), (126),
% 203.53/34.41  | | | |            (129), (203), (204), (205), (206) are inconsistent by
% 203.53/34.41  | | | |            sub-proof #557.
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | End of split
% 203.53/34.41  | | | 
% 203.53/34.41  | | End of split
% 203.53/34.41  | | 
% 203.53/34.41  | Case 2:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (207)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.53/34.41  | | 
% 203.53/34.41  | | REF_CLOSE: (3), (5), (20), (29), (31), (37), (41), (51), (52), (69), (71),
% 203.53/34.41  | |            (90), (93), (94), (100), (111), (207) are inconsistent by
% 203.53/34.41  | |            sub-proof #569.
% 203.53/34.41  | | 
% 203.53/34.41  | End of split
% 203.53/34.41  | 
% 203.53/34.41  End of proof
% 203.53/34.41  
% 203.53/34.41  Sub-proof #557 shows that the following formulas are inconsistent:
% 203.53/34.41  ----------------------------------------------------------------
% 203.53/34.41    (1)   ~ (all_52_25 = all_52_27)
% 203.53/34.41    (2)  all_58_14 = all_52_23
% 203.53/34.41    (3)  op(all_52_3, all_52_3) = all_52_2
% 203.53/34.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.41    (5)   ~ (all_52_5 = all_52_13)
% 203.53/34.41    (6)  all_58_1 = all_52_9
% 203.53/34.41    (7)   ~ (all_52_9 = all_52_13)
% 203.53/34.41    (8)   ~ (all_52_7 = all_52_15)
% 203.53/34.41    (9)  op(all_52_7, all_52_7) = all_52_6
% 203.53/34.41    (10)   ~ (all_52_17 = all_52_25)
% 203.53/34.41    (11)   ~ (all_52_3 = all_6_2)
% 203.53/34.41    (12)  all_58_0 = all_6_2
% 203.53/34.41    (13)  op(all_14_2, e0) = all_14_1
% 203.53/34.41    (14)  all_56_4 = all_52_3
% 203.53/34.41    (15)   ~ (all_52_17 = all_10_2)
% 203.53/34.41    (16)  op(all_6_2, e3) = e1
% 203.53/34.41    (17)  op(e3, e0) = all_52_25
% 203.53/34.41    (18)  all_58_13 = all_52_15
% 203.53/34.41    (19)  all_58_9 = all_52_25
% 203.53/34.41    (20)  op(e1, e3) = all_52_5
% 203.53/34.41    (21)  op(e2, e2) = all_4_2
% 203.53/34.41    (22)   ~ (all_52_3 = all_52_5)
% 203.53/34.41    (23)  all_58_11 = all_52_29
% 203.53/34.41    (24)   ~ (all_52_25 = all_14_2)
% 203.53/34.41    (25)   ~ (all_52_9 = all_52_15)
% 203.53/34.41    (26)  op(e0, e0) = all_14_2
% 203.53/34.41    (27)  op(all_52_29, all_52_29) = e1
% 203.53/34.41    (28)  all_56_15 = all_14_2
% 203.53/34.41    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.41    (30)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.41    (31)   ~ (all_4_1 = e1)
% 203.53/34.41    (32)  all_56_9 = all_52_13
% 203.53/34.41    (33)  all_58_10 = all_52_27
% 203.53/34.41    (34)  all_56_8 = all_52_5
% 203.53/34.41    (35)  op(all_52_15, all_52_15) = all_52_14
% 203.53/34.41    (36)  all_58_7 = all_52_13
% 203.53/34.41    (37)   ~ (all_52_5 = all_52_7)
% 203.53/34.41    (38)  all_58_12 = all_52_7
% 203.53/34.41    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.41    (40)  all_58_2 = all_52_3
% 203.53/34.41    (41)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.53/34.41    (42)  op(all_4_2, e2) = all_4_1
% 203.53/34.41    (43)   ~ (all_52_23 = e3)
% 203.53/34.41    (44)   ~ (all_52_19 = e3)
% 203.53/34.41    (45)  op(all_52_25, all_52_25) = e3
% 203.53/34.41    (46)   ~ (all_10_2 = e3)
% 203.53/34.41    (47)   ~ (all_52_15 = all_14_2)
% 203.53/34.41    (48)   ~ (all_52_9 = e3)
% 203.53/34.41    (49)   ~ (all_52_13 = all_4_2)
% 203.53/34.41    (50)  op(all_52_27, all_52_27) = e2
% 203.53/34.41    (51)  op(e0, e3) = all_52_7
% 203.53/34.41    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.41    (53)   ~ (all_52_9 = all_52_25)
% 203.53/34.41    (54)  all_58_15 = all_14_2
% 203.53/34.41    (55)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.53/34.41    (56)  all_58_8 = all_10_2
% 203.53/34.41    (57)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.41    (58)   ~ (all_52_5 = all_10_2)
% 203.53/34.41    (59)   ~ (all_52_25 = all_6_2)
% 203.53/34.41    (60)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.41    (61)   ~ (all_52_5 = all_6_2)
% 203.53/34.41    (62)   ~ (all_52_9 = all_6_2)
% 203.53/34.41    (63)   ~ (all_52_13 = all_52_15)
% 203.53/34.41    (64)  op(e3, e3) = all_6_2
% 203.53/34.41    (65)   ~ (all_52_27 = all_14_2)
% 203.53/34.41    (66)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.53/34.41    (67)  op(all_4_2, all_4_2) = all_52_10
% 203.53/34.41    (68)  all_56_3 = all_52_25
% 203.53/34.41    (69)   ~ (all_52_3 = all_52_7)
% 203.53/34.41    (70)  all_58_5 = all_52_19
% 203.53/34.41    (71)  all_56_1 = all_52_9
% 203.53/34.41    (72)   ~ (all_52_15 = all_4_2)
% 203.53/34.41    (73)  all_58_6 = all_52_5
% 203.53/34.41    (74)  op(e3, e2) = all_52_9
% 203.53/34.41    (75)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.41    (76)  op(all_14_2, all_14_2) = e0
% 203.53/34.41    (77)   ~ (e3 = e2)
% 203.53/34.41    (78)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.41    (79)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.41    (80)  op(e1, e1) = all_10_2
% 203.53/34.41    (81)  all_58_3 = all_4_2
% 203.53/34.41    (82)   ~ (all_52_3 = all_4_2)
% 203.53/34.41    (83)  all_58_4 = all_52_17
% 203.53/34.41  
% 203.53/34.41  Begin of proof
% 203.53/34.41  | 
% 203.53/34.41  | BETA: splitting (57) gives:
% 203.53/34.41  | 
% 203.53/34.41  | Case 1:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (84)  all_56_15 = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | COMBINE_EQS: (28), (84) imply:
% 203.53/34.41  | |   (85)  all_14_2 = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | SIMP: (85) implies:
% 203.53/34.41  | |   (86)  all_14_2 = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (47), (86) imply:
% 203.53/34.41  | |   (87)   ~ (all_52_15 = e3)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (24), (86) imply:
% 203.53/34.41  | |   (88)   ~ (all_52_25 = e3)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (76), (86) imply:
% 203.53/34.41  | |   (89)  op(e3, e3) = e0
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (13), (86) imply:
% 203.53/34.41  | |   (90)  op(e3, e0) = all_14_1
% 203.53/34.41  | | 
% 203.53/34.41  | | GROUND_INST: instantiating (4) with all_52_25, all_14_1, e0, e3, simplifying
% 203.53/34.41  | |              with (17), (90) gives:
% 203.53/34.41  | |   (91)  all_52_25 = all_14_1
% 203.53/34.41  | | 
% 203.53/34.41  | | GROUND_INST: instantiating (4) with all_6_2, e0, e3, e3, simplifying with
% 203.53/34.41  | |              (64), (89) gives:
% 203.53/34.41  | |   (92)  all_6_2 = e0
% 203.53/34.41  | | 
% 203.53/34.41  | | COMBINE_EQS: (68), (91) imply:
% 203.53/34.41  | |   (93)  all_56_3 = all_14_1
% 203.53/34.41  | | 
% 203.53/34.41  | | COMBINE_EQS: (19), (91) imply:
% 203.53/34.41  | |   (94)  all_58_9 = all_14_1
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (11), (92) imply:
% 203.53/34.41  | |   (95)   ~ (all_52_3 = e0)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (61), (92) imply:
% 203.53/34.41  | |   (96)   ~ (all_52_5 = e0)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (53), (91) imply:
% 203.53/34.41  | |   (97)   ~ (all_52_9 = all_14_1)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (62), (92) imply:
% 203.53/34.41  | |   (98)   ~ (all_52_9 = e0)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (59), (91), (92) imply:
% 203.53/34.41  | |   (99)   ~ (all_14_1 = e0)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (88), (91) imply:
% 203.53/34.41  | |   (100)   ~ (all_14_1 = e3)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (45), (91) imply:
% 203.53/34.41  | |   (101)  op(all_14_1, all_14_1) = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (16), (92) imply:
% 203.53/34.41  | |   (102)  op(e0, e3) = e1
% 203.53/34.41  | | 
% 203.53/34.41  | | GROUND_INST: instantiating (4) with all_52_7, e1, e3, e0, simplifying with
% 203.53/34.41  | |              (51), (102) gives:
% 203.53/34.41  | |   (103)  all_52_7 = e1
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (69), (103) imply:
% 203.53/34.41  | |   (104)   ~ (all_52_3 = e1)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (37), (103) imply:
% 203.53/34.41  | |   (105)   ~ (all_52_5 = e1)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (9), (103) imply:
% 203.53/34.41  | |   (106)  op(e1, e1) = all_52_6
% 203.53/34.41  | | 
% 203.53/34.41  | | GROUND_INST: instantiating (4) with all_10_2, all_52_6, e1, e1, simplifying
% 203.53/34.41  | |              with (80), (106) gives:
% 203.53/34.41  | |   (107)  all_52_6 = all_10_2
% 203.53/34.41  | | 
% 203.53/34.41  | | BETA: splitting (78) gives:
% 203.53/34.41  | | 
% 203.53/34.41  | | Case 1:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (108)  all_56_1 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (48), (71), (108) are inconsistent by sub-proof #1326.
% 203.53/34.41  | | | 
% 203.53/34.41  | | Case 2:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (109)   ~ (all_56_1 = e3)
% 203.53/34.41  | | |   (110)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.41  | | | 
% 203.53/34.41  | | | BETA: splitting (60) gives:
% 203.53/34.41  | | | 
% 203.53/34.41  | | | Case 1:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | |   (111)  all_56_3 = e3
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REF_CLOSE: (93), (100), (111) are inconsistent by sub-proof #1200.
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | Case 2:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | |   (112)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | BETA: splitting (41) gives:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | Case 1:
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | |   (113)  all_56_4 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | COMBINE_EQS: (14), (113) imply:
% 203.53/34.41  | | | | |   (114)  all_52_3 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | SIMP: (114) implies:
% 203.53/34.41  | | | | |   (115)  all_52_3 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | REF_CLOSE: (4), (21), (30), (46), (80), (82), (93), (94), (99), (101),
% 203.53/34.41  | | | | |            (112), (115) are inconsistent by sub-proof #561.
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | Case 2:
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | |   (116)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | REF_CLOSE: (4), (5), (6), (14), (18), (22), (30), (31), (34), (36),
% 203.53/34.41  | | | | |            (42), (48), (52), (55), (58), (71), (74), (80), (81), (87),
% 203.53/34.41  | | | | |            (93), (94), (95), (96), (97), (98), (99), (101), (104),
% 203.53/34.41  | | | | |            (105), (110), (112), (116) are inconsistent by sub-proof
% 203.53/34.41  | | | | |            #558.
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | End of split
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | End of split
% 203.53/34.41  | | | 
% 203.53/34.41  | | End of split
% 203.53/34.41  | | 
% 203.53/34.41  | Case 2:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (117)   ~ (all_56_15 = e3)
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (28), (117) imply:
% 203.53/34.41  | |   (118)   ~ (all_14_2 = e3)
% 203.53/34.41  | | 
% 203.53/34.41  | | BETA: splitting (75) gives:
% 203.53/34.41  | | 
% 203.53/34.41  | | Case 1:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (119)  all_58_12 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | COMBINE_EQS: (38), (119) imply:
% 203.53/34.41  | | |   (120)  all_52_7 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | SIMP: (120) implies:
% 203.53/34.41  | | |   (121)  all_52_7 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (69), (121) imply:
% 203.53/34.41  | | |   (122)   ~ (all_52_3 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (37), (121) imply:
% 203.53/34.41  | | |   (123)   ~ (all_52_5 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (8), (121) imply:
% 203.53/34.41  | | |   (124)   ~ (all_52_15 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | SIMP: (124) implies:
% 203.53/34.41  | | |   (125)   ~ (all_52_15 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (9), (121) imply:
% 203.53/34.41  | | |   (126)  op(e3, e3) = all_52_6
% 203.53/34.41  | | | 
% 203.53/34.41  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 203.53/34.41  | | |              with (64), (126) gives:
% 203.53/34.41  | | |   (127)  all_52_6 = all_6_2
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (1), (4), (6), (7), (10), (12), (15), (16), (18), (19), (20),
% 203.53/34.41  | | |            (23), (26), (27), (29), (30), (32), (33), (36), (39), (40),
% 203.53/34.41  | | |            (44), (45), (46), (48), (49), (50), (52), (56), (59), (60),
% 203.53/34.41  | | |            (61), (64), (65), (66), (67), (68), (70), (73), (77), (79),
% 203.53/34.41  | | |            (80), (81), (83), (122), (123), (125) are inconsistent by
% 203.53/34.41  | | |            sub-proof #571.
% 203.53/34.41  | | | 
% 203.53/34.41  | | Case 2:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (128)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | BETA: splitting (128) gives:
% 203.53/34.41  | | | 
% 203.53/34.41  | | | Case 1:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | |   (129)  all_58_13 = e3
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | COMBINE_EQS: (18), (129) imply:
% 203.53/34.41  | | | |   (130)  all_52_15 = e3
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | SIMP: (130) implies:
% 203.53/34.41  | | | |   (131)  all_52_15 = e3
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REDUCE: (63), (131) imply:
% 203.53/34.41  | | | |   (132)   ~ (all_52_13 = e3)
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REDUCE: (72), (131) imply:
% 203.53/34.41  | | | |   (133)   ~ (all_4_2 = e3)
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | SIMP: (133) implies:
% 203.53/34.41  | | | |   (134)   ~ (all_4_2 = e3)
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REDUCE: (35), (131) imply:
% 203.53/34.41  | | | |   (135)  op(e3, e3) = all_52_14
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_14, e3, e3,
% 203.53/34.41  | | | |              simplifying with (64), (135) gives:
% 203.53/34.41  | | | |   (136)  all_52_14 = all_6_2
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | BETA: splitting (29) gives:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | Case 1:
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | |   (137)  all_58_2 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | COMBINE_EQS: (40), (137) imply:
% 203.53/34.41  | | | | |   (138)  all_52_3 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | SIMP: (138) implies:
% 203.53/34.41  | | | | |   (139)  all_52_3 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | REDUCE: (22), (139) imply:
% 203.53/34.41  | | | | |   (140)   ~ (all_52_5 = e3)
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | SIMP: (140) implies:
% 203.53/34.41  | | | | |   (141)   ~ (all_52_5 = e3)
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | REDUCE: (3), (139) imply:
% 203.53/34.41  | | | | |   (142)  op(e3, e3) = all_52_2
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | BETA: splitting (39) gives:
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | Case 1:
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | |   (143)  all_58_6 = e3
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | | REF_CLOSE: (73), (141), (143) are inconsistent by sub-proof #1328.
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | Case 2:
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | |   (144)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | | BETA: splitting (144) gives:
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | | Case 1:
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | |   (145)  all_58_7 = e3
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | | COMBINE_EQS: (36), (145) imply:
% 203.53/34.41  | | | | | | |   (146)  all_52_13 = e3
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | | REDUCE: (132), (146) imply:
% 203.53/34.41  | | | | | | |   (147)  $false
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | | CLOSE: (147) is inconsistent.
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | Case 2:
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | |   (148)  all_58_8 = e3 | all_58_11 = e3
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | | BETA: splitting (148) gives:
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | | Case 1:
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | |   (149)  all_58_8 = e3
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | | REF_CLOSE: (46), (56), (149) are inconsistent by sub-proof #950.
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | Case 2:
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | |   (150)  all_58_11 = e3
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | | COMBINE_EQS: (23), (150) imply:
% 203.53/34.41  | | | | | | | |   (151)  all_52_29 = e3
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | | SIMP: (151) implies:
% 203.53/34.41  | | | | | | | |   (152)  all_52_29 = e3
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | | REDUCE: (27), (152) imply:
% 203.53/34.41  | | | | | | | |   (153)  op(e3, e3) = e1
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | | REF_CLOSE: (4), (16), (20), (61), (64), (142), (153) are
% 203.53/34.41  | | | | | | | |            inconsistent by sub-proof #566.
% 203.53/34.41  | | | | | | | | 
% 203.53/34.41  | | | | | | | End of split
% 203.53/34.41  | | | | | | | 
% 203.53/34.41  | | | | | | End of split
% 203.53/34.41  | | | | | | 
% 203.53/34.41  | | | | | End of split
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | Case 2:
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | |   (154)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | | REF_CLOSE: (1), (4), (6), (10), (12), (15), (19), (26), (30), (33),
% 203.53/34.41  | | | | |            (44), (45), (48), (50), (59), (60), (64), (65), (66), (68),
% 203.53/34.41  | | | | |            (70), (77), (80), (81), (83), (134), (154) are inconsistent
% 203.53/34.41  | | | | |            by sub-proof #1228.
% 203.53/34.41  | | | | | 
% 203.53/34.41  | | | | End of split
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | Case 2:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | |   (155)  all_58_14 = e3 | all_58_15 = e3
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REF_CLOSE: (2), (43), (54), (118), (155) are inconsistent by sub-proof
% 203.53/34.41  | | | |            #715.
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | End of split
% 203.53/34.41  | | | 
% 203.53/34.41  | | End of split
% 203.53/34.41  | | 
% 203.53/34.41  | End of split
% 203.53/34.41  | 
% 203.53/34.41  End of proof
% 203.53/34.41  
% 203.53/34.41  Sub-proof #558 shows that the following formulas are inconsistent:
% 203.53/34.41  ----------------------------------------------------------------
% 203.53/34.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.41    (2)   ~ (all_52_5 = all_52_13)
% 203.53/34.41    (3)  all_58_1 = all_52_9
% 203.53/34.41    (4)  all_56_4 = all_52_3
% 203.53/34.41    (5)  all_58_13 = all_52_15
% 203.53/34.41    (6)   ~ (all_52_5 = e1)
% 203.53/34.41    (7)   ~ (all_52_15 = e3)
% 203.53/34.41    (8)   ~ (all_52_3 = all_52_5)
% 203.53/34.41    (9)  all_56_3 = all_14_1
% 203.53/34.41    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.41    (11)   ~ (all_4_1 = e1)
% 203.53/34.41    (12)   ~ (all_52_9 = all_14_1)
% 203.53/34.41    (13)   ~ (all_52_3 = e1)
% 203.53/34.41    (14)  all_56_8 = all_52_5
% 203.53/34.41    (15)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.41    (16)  all_58_7 = all_52_13
% 203.53/34.41    (17)  all_58_9 = all_14_1
% 203.53/34.41    (18)  op(all_4_2, e2) = all_4_1
% 203.53/34.41    (19)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.53/34.41    (20)   ~ (all_52_3 = e0)
% 203.53/34.41    (21)   ~ (all_52_9 = e3)
% 203.53/34.41    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.41    (23)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.53/34.41    (24)   ~ (all_52_5 = all_10_2)
% 203.53/34.41    (25)   ~ (all_52_5 = e0)
% 203.53/34.41    (26)  all_56_1 = all_52_9
% 203.53/34.41    (27)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.41    (28)  op(e3, e2) = all_52_9
% 203.53/34.41    (29)  op(all_14_1, all_14_1) = e3
% 203.53/34.41    (30)   ~ (all_14_1 = e0)
% 203.53/34.41    (31)  op(e1, e1) = all_10_2
% 203.53/34.41    (32)   ~ (all_52_9 = e0)
% 203.53/34.41    (33)  all_58_3 = all_4_2
% 203.53/34.41  
% 203.53/34.41  Begin of proof
% 203.53/34.41  | 
% 203.53/34.41  | BETA: splitting (19) gives:
% 203.53/34.41  | 
% 203.53/34.41  | Case 1:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (34)  all_56_4 = e2
% 203.53/34.41  | | 
% 203.53/34.41  | | COMBINE_EQS: (4), (34) imply:
% 203.53/34.41  | |   (35)  all_52_3 = e2
% 203.53/34.41  | | 
% 203.53/34.41  | | SIMP: (35) implies:
% 203.53/34.41  | |   (36)  all_52_3 = e2
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (8), (36) imply:
% 203.53/34.41  | |   (37)   ~ (all_52_5 = e2)
% 203.53/34.41  | | 
% 203.53/34.41  | | SIMP: (37) implies:
% 203.53/34.41  | |   (38)   ~ (all_52_5 = e2)
% 203.53/34.41  | | 
% 203.53/34.41  | | BETA: splitting (23) gives:
% 203.53/34.41  | | 
% 203.53/34.41  | | Case 1:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (39)  all_56_8 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | COMBINE_EQS: (14), (39) imply:
% 203.53/34.41  | | |   (40)  all_52_5 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (2), (40) imply:
% 203.53/34.41  | | |   (41)   ~ (all_52_13 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | SIMP: (41) implies:
% 203.53/34.41  | | |   (42)   ~ (all_52_13 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (24), (40) imply:
% 203.53/34.41  | | |   (43)   ~ (all_10_2 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | SIMP: (43) implies:
% 203.53/34.41  | | |   (44)   ~ (all_10_2 = e3)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (15), (16), (17),
% 203.53/34.41  | | |            (18), (21), (22), (26), (27), (28), (29), (30), (31), (32),
% 203.53/34.41  | | |            (33), (42), (44) are inconsistent by sub-proof #559.
% 203.53/34.41  | | | 
% 203.53/34.41  | | Case 2:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (45)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (6), (14), (25), (38), (45) are inconsistent by sub-proof
% 203.53/34.41  | | |            #1004.
% 203.53/34.41  | | | 
% 203.53/34.41  | | End of split
% 203.53/34.41  | | 
% 203.53/34.41  | Case 2:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (46)  all_56_4 = e1 | all_56_4 = e0
% 203.53/34.41  | | 
% 203.53/34.41  | | BETA: splitting (46) gives:
% 203.53/34.41  | | 
% 203.53/34.41  | | Case 1:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (47)  all_56_4 = e1
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (4), (13), (47) are inconsistent by sub-proof #1310.
% 203.53/34.41  | | | 
% 203.53/34.41  | | Case 2:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (48)  all_56_4 = e0
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (4), (20), (48) are inconsistent by sub-proof #1309.
% 203.53/34.41  | | | 
% 203.53/34.41  | | End of split
% 203.53/34.41  | | 
% 203.53/34.41  | End of split
% 203.53/34.41  | 
% 203.53/34.41  End of proof
% 203.53/34.41  
% 203.53/34.41  Sub-proof #559 shows that the following formulas are inconsistent:
% 203.53/34.41  ----------------------------------------------------------------
% 203.53/34.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.41    (2)  all_58_1 = all_52_9
% 203.53/34.41    (3)  all_58_13 = all_52_15
% 203.53/34.41    (4)   ~ (all_52_15 = e3)
% 203.53/34.41    (5)  all_56_3 = all_14_1
% 203.53/34.41    (6)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.41    (7)   ~ (all_4_1 = e1)
% 203.53/34.41    (8)   ~ (all_52_9 = all_14_1)
% 203.53/34.41    (9)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.41    (10)  all_58_7 = all_52_13
% 203.53/34.41    (11)  all_58_9 = all_14_1
% 203.53/34.41    (12)  op(all_4_2, e2) = all_4_1
% 203.53/34.41    (13)   ~ (all_10_2 = e3)
% 203.53/34.41    (14)   ~ (all_52_9 = e3)
% 203.53/34.41    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.41    (16)   ~ (all_52_13 = e3)
% 203.53/34.41    (17)  all_56_1 = all_52_9
% 203.53/34.41    (18)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.41    (19)  op(e3, e2) = all_52_9
% 203.53/34.41    (20)  op(all_14_1, all_14_1) = e3
% 203.53/34.41    (21)   ~ (all_14_1 = e0)
% 203.53/34.41    (22)  op(e1, e1) = all_10_2
% 203.53/34.41    (23)   ~ (all_52_9 = e0)
% 203.53/34.41    (24)  all_58_3 = all_4_2
% 203.53/34.41  
% 203.53/34.41  Begin of proof
% 203.53/34.41  | 
% 203.53/34.41  | BETA: splitting (15) gives:
% 203.53/34.41  | 
% 203.53/34.41  | Case 1:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (25)  all_58_1 = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | COMBINE_EQS: (2), (25) imply:
% 203.53/34.41  | |   (26)  all_52_9 = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (14), (26) imply:
% 203.53/34.41  | |   (27)  $false
% 203.53/34.41  | | 
% 203.53/34.41  | | CLOSE: (27) is inconsistent.
% 203.53/34.41  | | 
% 203.53/34.41  | Case 2:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (28)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.41  | | 
% 203.53/34.41  | | BETA: splitting (28) gives:
% 203.53/34.41  | | 
% 203.53/34.41  | | Case 1:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (29)  all_58_3 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | COMBINE_EQS: (24), (29) imply:
% 203.53/34.41  | | |   (30)  all_4_2 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (12), (30) imply:
% 203.53/34.41  | | |   (31)  op(e3, e2) = all_4_1
% 203.53/34.41  | | | 
% 203.53/34.41  | | | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3, simplifying
% 203.53/34.41  | | |              with (19), (31) gives:
% 203.53/34.41  | | |   (32)  all_52_9 = all_4_1
% 203.53/34.41  | | | 
% 203.53/34.41  | | | COMBINE_EQS: (17), (32) imply:
% 203.53/34.41  | | |   (33)  all_56_1 = all_4_1
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (8), (32) imply:
% 203.53/34.41  | | |   (34)   ~ (all_14_1 = all_4_1)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | SIMP: (34) implies:
% 203.53/34.41  | | |   (35)   ~ (all_14_1 = all_4_1)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REDUCE: (23), (32) imply:
% 203.53/34.41  | | |   (36)   ~ (all_4_1 = e0)
% 203.53/34.41  | | | 
% 203.53/34.41  | | | BETA: splitting (18) gives:
% 203.53/34.41  | | | 
% 203.53/34.41  | | | Case 1:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | |   (37)  all_56_1 = e2
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | COMBINE_EQS: (33), (37) imply:
% 203.53/34.41  | | | |   (38)  all_4_1 = e2
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REDUCE: (35), (38) imply:
% 203.53/34.41  | | | |   (39)   ~ (all_14_1 = e2)
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REF_CLOSE: (1), (5), (6), (9), (11), (13), (20), (21), (22), (39) are
% 203.53/34.41  | | | |            inconsistent by sub-proof #560.
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | Case 2:
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | |   (40)  all_56_1 = e1 | all_56_1 = e0
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | | REF_CLOSE: (7), (33), (36), (40) are inconsistent by sub-proof #1164.
% 203.53/34.41  | | | | 
% 203.53/34.41  | | | End of split
% 203.53/34.41  | | | 
% 203.53/34.41  | | Case 2:
% 203.53/34.41  | | | 
% 203.53/34.41  | | |   (41)  all_58_7 = e3 | all_58_13 = e3
% 203.53/34.41  | | | 
% 203.53/34.41  | | | REF_CLOSE: (3), (4), (10), (16), (41) are inconsistent by sub-proof #1298.
% 203.53/34.41  | | | 
% 203.53/34.41  | | End of split
% 203.53/34.41  | | 
% 203.53/34.41  | End of split
% 203.53/34.41  | 
% 203.53/34.41  End of proof
% 203.53/34.41  
% 203.53/34.41  Sub-proof #560 shows that the following formulas are inconsistent:
% 203.53/34.41  ----------------------------------------------------------------
% 203.53/34.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.41    (2)   ~ (all_14_1 = e2)
% 203.53/34.41    (3)  all_56_3 = all_14_1
% 203.53/34.41    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.41    (5)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.41    (6)  all_58_9 = all_14_1
% 203.53/34.41    (7)   ~ (all_10_2 = e3)
% 203.53/34.41    (8)  op(all_14_1, all_14_1) = e3
% 203.53/34.41    (9)   ~ (all_14_1 = e0)
% 203.53/34.41    (10)  op(e1, e1) = all_10_2
% 203.53/34.41  
% 203.53/34.41  Begin of proof
% 203.53/34.41  | 
% 203.53/34.41  | BETA: splitting (5) gives:
% 203.53/34.41  | 
% 203.53/34.41  | Case 1:
% 203.53/34.41  | | 
% 203.53/34.41  | |   (11)  all_56_3 = e2
% 203.53/34.41  | | 
% 203.53/34.41  | | COMBINE_EQS: (3), (11) imply:
% 203.53/34.41  | |   (12)  all_14_1 = e2
% 203.53/34.41  | | 
% 203.53/34.41  | | REDUCE: (2), (12) imply:
% 203.53/34.42  | |   (13)  $false
% 203.53/34.42  | | 
% 203.53/34.42  | | CLOSE: (13) is inconsistent.
% 203.53/34.42  | | 
% 203.53/34.42  | Case 2:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (14)  all_56_3 = e1 | all_56_3 = e0
% 203.53/34.42  | | 
% 203.53/34.42  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (14) are inconsistent by
% 203.53/34.42  | |            sub-proof #805.
% 203.53/34.42  | | 
% 203.53/34.42  | End of split
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #561 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (2)  op(e2, e2) = all_4_2
% 203.53/34.42    (3)  all_52_3 = e3
% 203.53/34.42    (4)  all_56_3 = all_14_1
% 203.53/34.42    (5)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.42    (6)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.42    (7)  all_58_9 = all_14_1
% 203.53/34.42    (8)   ~ (all_10_2 = e3)
% 203.53/34.42    (9)  op(all_14_1, all_14_1) = e3
% 203.53/34.42    (10)   ~ (all_14_1 = e0)
% 203.53/34.42    (11)  op(e1, e1) = all_10_2
% 203.53/34.42    (12)   ~ (all_52_3 = all_4_2)
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | REDUCE: (3), (12) imply:
% 203.53/34.42  |   (13)   ~ (all_4_2 = e3)
% 203.53/34.42  | 
% 203.53/34.42  | SIMP: (13) implies:
% 203.53/34.42  |   (14)   ~ (all_4_2 = e3)
% 203.53/34.42  | 
% 203.53/34.42  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (14) are
% 203.53/34.42  |            inconsistent by sub-proof #804.
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #562 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)  all_58_14 = all_52_23
% 203.53/34.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (3)  all_58_1 = all_52_9
% 203.53/34.42    (4)   ~ (all_52_7 = all_52_15)
% 203.53/34.42    (5)  op(all_52_15, all_52_15) = e0
% 203.53/34.42    (6)  op(all_52_7, all_52_7) = all_52_6
% 203.53/34.42    (7)  all_58_0 = all_6_2
% 203.53/34.42    (8)  op(all_6_2, e3) = e1
% 203.53/34.42    (9)  all_58_13 = all_52_15
% 203.53/34.42    (10)  op(all_52_13, all_52_13) = e1
% 203.53/34.42    (11)  all_58_9 = all_52_25
% 203.53/34.42    (12)  op(all_52_27, all_52_27) = all_52_26
% 203.53/34.42    (13)  op(e1, e3) = all_52_5
% 203.53/34.42    (14)  op(e2, e2) = all_4_2
% 203.53/34.42    (15)   ~ (all_52_25 = all_14_2)
% 203.53/34.42    (16)   ~ (all_52_7 = all_6_2)
% 203.53/34.42    (17)  op(e0, e0) = all_14_2
% 203.53/34.42    (18)  all_56_15 = all_14_2
% 203.53/34.42    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.42    (20)   ~ (all_4_1 = e1)
% 203.53/34.42    (21)   ~ (all_6_2 = e3)
% 203.53/34.42    (22)  all_56_9 = all_52_13
% 203.53/34.42    (23)  all_58_10 = all_52_27
% 203.53/34.42    (24)  all_58_7 = all_52_13
% 203.53/34.42    (25)  all_58_12 = all_52_7
% 203.53/34.42    (26)   ~ (all_52_7 = all_14_2)
% 203.53/34.42    (27)  all_58_2 = all_52_3
% 203.53/34.42    (28)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.42    (29)  op(e3, e3) = all_52_16
% 203.53/34.42    (30)  all_58_4 = e3
% 203.53/34.42    (31)  op(all_4_2, e2) = all_4_1
% 203.53/34.42    (32)   ~ (all_52_23 = e3)
% 203.53/34.42    (33)   ~ (all_52_19 = e3)
% 203.53/34.42    (34)   ~ (all_52_15 = all_14_2)
% 203.53/34.42    (35)   ~ (all_52_9 = e3)
% 203.53/34.42    (36)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.53/34.42    (37)   ~ (all_52_13 = all_4_2)
% 203.53/34.42    (38)  op(e0, e3) = all_52_7
% 203.53/34.42    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.42    (40)  all_58_15 = all_14_2
% 203.53/34.42    (41)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.42    (42)   ~ (all_52_23 = all_14_2)
% 203.53/34.42    (43)   ~ (all_52_9 = all_4_2)
% 203.53/34.42    (44)   ~ (all_52_5 = all_6_2)
% 203.53/34.42    (45)  op(all_4_2, all_4_2) = e2
% 203.53/34.42    (46)   ~ (all_52_9 = all_6_2)
% 203.53/34.42    (47)  op(e3, e3) = all_6_2
% 203.53/34.42    (48)   ~ (all_52_3 = all_52_7)
% 203.53/34.42    (49)  all_58_5 = all_52_19
% 203.53/34.42    (50)  all_56_1 = all_52_9
% 203.53/34.42    (51)   ~ (all_52_15 = all_4_2)
% 203.53/34.42    (52)  op(e3, e2) = all_52_9
% 203.53/34.42    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.42    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.42    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.42    (56)  op(all_52_9, all_52_9) = e3
% 203.53/34.42    (57)  all_58_3 = all_4_2
% 203.53/34.42    (58)   ~ (all_14_2 = e3)
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | BETA: splitting (53) gives:
% 203.53/34.42  | 
% 203.53/34.42  | Case 1:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (59)  all_58_12 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | COMBINE_EQS: (25), (59) imply:
% 203.53/34.42  | |   (60)  all_52_7 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | SIMP: (60) implies:
% 203.53/34.42  | |   (61)  all_52_7 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (48), (61) imply:
% 203.53/34.42  | |   (62)   ~ (all_52_3 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (4), (61) imply:
% 203.53/34.42  | |   (63)   ~ (all_52_15 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | SIMP: (63) implies:
% 203.53/34.42  | |   (64)   ~ (all_52_15 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (26), (61) imply:
% 203.53/34.42  | |   (65)   ~ (all_14_2 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (6), (61) imply:
% 203.53/34.42  | |   (66)  op(e3, e3) = all_52_6
% 203.53/34.42  | | 
% 203.53/34.42  | | GROUND_INST: instantiating (2) with all_6_2, all_52_6, e3, e3, simplifying
% 203.53/34.42  | |              with (47), (66) gives:
% 203.53/34.42  | |   (67)  all_52_6 = all_6_2
% 203.53/34.42  | | 
% 203.53/34.42  | | BETA: splitting (19) gives:
% 203.53/34.42  | | 
% 203.53/34.42  | | Case 1:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (68)  all_58_2 = e3
% 203.53/34.42  | | | 
% 203.53/34.42  | | | REF_CLOSE: (27), (62), (68) are inconsistent by sub-proof #1369.
% 203.53/34.42  | | | 
% 203.53/34.42  | | Case 2:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (69)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.42  | | | 
% 203.53/34.42  | | | BETA: splitting (39) gives:
% 203.53/34.42  | | | 
% 203.53/34.42  | | | Case 1:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (70)  all_58_1 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | COMBINE_EQS: (3), (70) imply:
% 203.53/34.42  | | | |   (71)  all_52_9 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REDUCE: (35), (71) imply:
% 203.53/34.42  | | | |   (72)  $false
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | CLOSE: (72) is inconsistent.
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | Case 2:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (73)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | BETA: splitting (55) gives:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | Case 1:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | |   (74)  all_56_9 = e3
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | COMBINE_EQS: (22), (74) imply:
% 203.53/34.42  | | | | |   (75)  all_52_13 = e3
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | SIMP: (75) implies:
% 203.53/34.42  | | | | |   (76)  all_52_13 = e3
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (37), (76) imply:
% 203.53/34.42  | | | | |   (77)   ~ (all_4_2 = e3)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | SIMP: (77) implies:
% 203.53/34.42  | | | | |   (78)   ~ (all_4_2 = e3)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (10), (76) imply:
% 203.53/34.42  | | | | |   (79)  op(e3, e3) = e1
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REF_CLOSE: (2), (8), (12), (13), (23), (33), (44), (47), (49), (57),
% 203.53/34.42  | | | | |            (69), (78), (79) are inconsistent by sub-proof #576.
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | Case 2:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | |   (80)   ~ (all_56_9 = e3)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (22), (80) imply:
% 203.53/34.42  | | | | |   (81)   ~ (all_52_13 = e3)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | BETA: splitting (73) gives:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | Case 1:
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | |   (82)  all_58_3 = e3
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | | COMBINE_EQS: (57), (82) imply:
% 203.53/34.42  | | | | | |   (83)  all_4_2 = e3
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | | REF_CLOSE: (2), (17), (20), (29), (31), (43), (45), (46), (47),
% 203.53/34.42  | | | | | |            (50), (52), (54), (56), (58), (83) are inconsistent by
% 203.53/34.42  | | | | | |            sub-proof #564.
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | Case 2:
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | |   (84)  all_58_7 = e3 | all_58_13 = e3
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | | REF_CLOSE: (9), (24), (64), (81), (84) are inconsistent by sub-proof
% 203.53/34.42  | | | | | |            #1298.
% 203.53/34.42  | | | | | | 
% 203.53/34.42  | | | | | End of split
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | End of split
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | End of split
% 203.53/34.42  | | | 
% 203.53/34.42  | | End of split
% 203.53/34.42  | | 
% 203.53/34.42  | Case 2:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (85)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (14), (15), (16), (18),
% 203.53/34.42  | |            (21), (25), (26), (28), (30), (32), (34), (36), (38), (40), (41),
% 203.53/34.42  | |            (42), (47), (51), (56), (58), (85) are inconsistent by sub-proof
% 203.53/34.42  | |            #563.
% 203.53/34.42  | | 
% 203.53/34.42  | End of split
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #563 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)  all_58_14 = all_52_23
% 203.53/34.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (3)  all_58_1 = all_52_9
% 203.53/34.42    (4)  op(all_52_15, all_52_15) = e0
% 203.53/34.42    (5)  all_58_0 = all_6_2
% 203.53/34.42    (6)  op(all_6_2, e3) = e1
% 203.53/34.42    (7)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.42    (8)  all_58_13 = all_52_15
% 203.53/34.42    (9)  all_58_9 = all_52_25
% 203.53/34.42    (10)  op(e2, e2) = all_4_2
% 203.53/34.42    (11)   ~ (all_52_25 = all_14_2)
% 203.53/34.42    (12)   ~ (all_52_7 = all_6_2)
% 203.53/34.42    (13)  all_56_15 = all_14_2
% 203.53/34.42    (14)   ~ (all_6_2 = e3)
% 203.53/34.42    (15)  all_58_12 = all_52_7
% 203.53/34.42    (16)   ~ (all_52_7 = all_14_2)
% 203.53/34.42    (17)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.42    (18)  all_58_4 = e3
% 203.53/34.42    (19)   ~ (all_52_23 = e3)
% 203.53/34.42    (20)   ~ (all_52_15 = all_14_2)
% 203.53/34.42    (21)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.53/34.42    (22)  op(e0, e3) = all_52_7
% 203.53/34.42    (23)  all_58_15 = all_14_2
% 203.53/34.42    (24)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.42    (25)   ~ (all_52_23 = all_14_2)
% 203.53/34.42    (26)  op(e3, e3) = all_6_2
% 203.53/34.42    (27)   ~ (all_52_15 = all_4_2)
% 203.53/34.42    (28)  op(all_52_9, all_52_9) = e3
% 203.53/34.42    (29)   ~ (all_14_2 = e3)
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | BETA: splitting (7) gives:
% 203.53/34.42  | 
% 203.53/34.42  | Case 1:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (30)  all_58_13 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | COMBINE_EQS: (8), (30) imply:
% 203.53/34.42  | |   (31)  all_52_15 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | SIMP: (31) implies:
% 203.53/34.42  | |   (32)  all_52_15 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (20), (32) imply:
% 203.53/34.42  | |   (33)   ~ (all_14_2 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (27), (32) imply:
% 203.53/34.42  | |   (34)   ~ (all_4_2 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | SIMP: (34) implies:
% 203.53/34.42  | |   (35)   ~ (all_4_2 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (4), (32) imply:
% 203.53/34.42  | |   (36)  op(e3, e3) = e0
% 203.53/34.42  | | 
% 203.53/34.42  | | GROUND_INST: instantiating (2) with all_6_2, e0, e3, e3, simplifying with
% 203.53/34.42  | |              (26), (36) gives:
% 203.53/34.42  | |   (37)  all_6_2 = e0
% 203.53/34.42  | | 
% 203.53/34.42  | | COMBINE_EQS: (5), (37) imply:
% 203.53/34.42  | |   (38)  all_58_0 = e0
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (12), (37) imply:
% 203.53/34.42  | |   (39)   ~ (all_52_7 = e0)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (14), (37) imply:
% 203.53/34.42  | |   (40)   ~ (e3 = e0)
% 203.53/34.42  | | 
% 203.53/34.42  | | SIMP: (40) implies:
% 203.53/34.42  | |   (41)   ~ (e3 = e0)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (6), (37) imply:
% 203.53/34.42  | |   (42)  op(e0, e3) = e1
% 203.53/34.42  | | 
% 203.53/34.42  | | BETA: splitting (21) gives:
% 203.53/34.42  | | 
% 203.53/34.42  | | Case 1:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (43)  all_58_12 = e0
% 203.53/34.42  | | | 
% 203.53/34.42  | | | REF_CLOSE: (15), (39), (43) are inconsistent by sub-proof #1067.
% 203.53/34.42  | | | 
% 203.53/34.42  | | Case 2:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (44)  all_58_13 = e0 | all_58_14 = e0
% 203.53/34.42  | | | 
% 203.53/34.42  | | | BETA: splitting (44) gives:
% 203.53/34.42  | | | 
% 203.53/34.42  | | | Case 1:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (45)  all_58_13 = e0
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REF_CLOSE: (30), (41), (45) are inconsistent by sub-proof #1172.
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | Case 2:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (46)  all_58_14 = e0
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | COMBINE_EQS: (1), (46) imply:
% 203.53/34.42  | | | |   (47)  all_52_23 = e0
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | SIMP: (47) implies:
% 203.53/34.42  | | | |   (48)  all_52_23 = e0
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REDUCE: (25), (48) imply:
% 203.53/34.42  | | | |   (49)   ~ (all_14_2 = e0)
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | SIMP: (49) implies:
% 203.53/34.42  | | | |   (50)   ~ (all_14_2 = e0)
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | GROUND_INST: instantiating (2) with all_52_7, e1, e3, e0, simplifying
% 203.53/34.42  | | | |              with (22), (42) gives:
% 203.53/34.42  | | | |   (51)  all_52_7 = e1
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REDUCE: (16), (51) imply:
% 203.53/34.42  | | | |   (52)   ~ (all_14_2 = e1)
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | SIMP: (52) implies:
% 203.53/34.42  | | | |   (53)   ~ (all_14_2 = e1)
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | BETA: splitting (24) gives:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | Case 1:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | |   (54)  all_56_15 = e2
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | COMBINE_EQS: (13), (54) imply:
% 203.53/34.42  | | | | |   (55)  all_14_2 = e2
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (11), (55) imply:
% 203.53/34.42  | | | | |   (56)   ~ (all_52_25 = e2)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (29), (55) imply:
% 203.53/34.42  | | | | |   (57)   ~ (e3 = e2)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | SIMP: (57) implies:
% 203.53/34.42  | | | | |   (58)   ~ (e3 = e2)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (50), (55) imply:
% 203.53/34.42  | | | | |   (59)   ~ (e2 = e0)
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REF_CLOSE: (2), (3), (9), (10), (17), (18), (28), (35), (38), (56),
% 203.53/34.42  | | | | |            (58), (59) are inconsistent by sub-proof #575.
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | Case 2:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | |   (60)  all_56_15 = e1 | all_56_15 = e0
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REF_CLOSE: (13), (50), (53), (60) are inconsistent by sub-proof #1161.
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | End of split
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | End of split
% 203.53/34.42  | | | 
% 203.53/34.42  | | End of split
% 203.53/34.42  | | 
% 203.53/34.42  | Case 2:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (61)  all_58_14 = e3 | all_58_15 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | REF_CLOSE: (1), (19), (23), (29), (61) are inconsistent by sub-proof #715.
% 203.53/34.42  | | 
% 203.53/34.42  | End of split
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #564 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (2)  all_4_2 = e3
% 203.53/34.42    (3)  op(e0, e0) = all_14_2
% 203.53/34.42    (4)   ~ (all_4_1 = e1)
% 203.53/34.42    (5)  op(e3, e3) = all_52_16
% 203.53/34.42    (6)  op(all_4_2, e2) = all_4_1
% 203.53/34.42    (7)   ~ (all_52_9 = all_4_2)
% 203.53/34.42    (8)  op(all_4_2, all_4_2) = e2
% 203.53/34.42    (9)   ~ (all_52_9 = all_6_2)
% 203.53/34.42    (10)  op(e3, e3) = all_6_2
% 203.53/34.42    (11)  all_56_1 = all_52_9
% 203.53/34.42    (12)  op(e3, e2) = all_52_9
% 203.53/34.42    (13)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.42    (14)  op(all_52_9, all_52_9) = e3
% 203.53/34.42    (15)   ~ (all_14_2 = e3)
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | REDUCE: (2), (7) imply:
% 203.53/34.42  |   (16)   ~ (all_52_9 = e3)
% 203.53/34.42  | 
% 203.53/34.42  | REDUCE: (2), (8) imply:
% 203.53/34.42  |   (17)  op(e3, e3) = e2
% 203.53/34.42  | 
% 203.53/34.42  | REDUCE: (2), (6) imply:
% 203.53/34.42  |   (18)  op(e3, e2) = all_4_1
% 203.53/34.42  | 
% 203.53/34.42  | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (12), (13), (14), (15), (16),
% 203.53/34.42  |            (17), (18) are inconsistent by sub-proof #1108.
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #565 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)  op(all_52_3, all_52_3) = all_52_2
% 203.53/34.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (3)   ~ (all_52_5 = all_52_13)
% 203.53/34.42    (4)  all_58_0 = all_6_2
% 203.53/34.42    (5)  op(all_6_2, e3) = e1
% 203.53/34.42    (6)  op(all_52_13, all_52_13) = e1
% 203.53/34.42    (7)  op(e1, e3) = all_52_5
% 203.53/34.42    (8)  all_58_11 = all_52_29
% 203.53/34.42    (9)   ~ (all_6_2 = e3)
% 203.53/34.42    (10)  all_58_7 = all_52_13
% 203.53/34.42    (11)  all_58_12 = all_52_7
% 203.53/34.42    (12)   ~ (all_52_7 = e3)
% 203.53/34.42    (13)  all_58_2 = all_52_3
% 203.53/34.42    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.42    (15)   ~ (all_52_29 = e3)
% 203.53/34.42    (16)   ~ (all_10_2 = e3)
% 203.53/34.42    (17)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.42    (18)  all_58_8 = all_10_2
% 203.53/34.42    (19)   ~ (all_52_5 = all_6_2)
% 203.53/34.42    (20)  op(e3, e3) = all_6_2
% 203.53/34.42    (21)  all_58_6 = all_52_5
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | BETA: splitting (17) gives:
% 203.53/34.42  | 
% 203.53/34.42  | Case 1:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (22)  all_58_7 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | COMBINE_EQS: (10), (22) imply:
% 203.53/34.42  | |   (23)  all_52_13 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (3), (23) imply:
% 203.53/34.42  | |   (24)   ~ (all_52_5 = e3)
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (6), (23) imply:
% 203.53/34.42  | |   (25)  op(e3, e3) = e1
% 203.53/34.42  | | 
% 203.53/34.42  | | BETA: splitting (14) gives:
% 203.53/34.42  | | 
% 203.53/34.42  | | Case 1:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (26)  all_58_0 = e3
% 203.53/34.42  | | | 
% 203.53/34.42  | | | COMBINE_EQS: (4), (26) imply:
% 203.53/34.42  | | |   (27)  all_6_2 = e3
% 203.53/34.42  | | | 
% 203.53/34.42  | | | REDUCE: (9), (27) imply:
% 203.53/34.42  | | |   (28)  $false
% 203.53/34.42  | | | 
% 203.53/34.42  | | | CLOSE: (28) is inconsistent.
% 203.53/34.42  | | | 
% 203.53/34.42  | | Case 2:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (29)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.42  | | | 
% 203.53/34.42  | | | BETA: splitting (29) gives:
% 203.53/34.42  | | | 
% 203.53/34.42  | | | Case 1:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (30)  all_58_2 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | COMBINE_EQS: (13), (30) imply:
% 203.53/34.42  | | | |   (31)  all_52_3 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | SIMP: (31) implies:
% 203.53/34.42  | | | |   (32)  all_52_3 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REDUCE: (1), (32) imply:
% 203.53/34.42  | | | |   (33)  op(e3, e3) = all_52_2
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REF_CLOSE: (2), (5), (7), (19), (20), (25), (33) are inconsistent by
% 203.53/34.42  | | | |            sub-proof #566.
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | Case 2:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (34)  all_58_6 = e3 | all_58_12 = e3
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REF_CLOSE: (11), (12), (21), (24), (34) are inconsistent by sub-proof
% 203.53/34.42  | | | |            #1243.
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | End of split
% 203.53/34.42  | | | 
% 203.53/34.42  | | End of split
% 203.53/34.42  | | 
% 203.53/34.42  | Case 2:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (35)  all_58_8 = e3 | all_58_11 = e3
% 203.53/34.42  | | 
% 203.53/34.42  | | REF_CLOSE: (8), (15), (16), (18), (35) are inconsistent by sub-proof #1140.
% 203.53/34.42  | | 
% 203.53/34.42  | End of split
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #566 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (2)  op(all_6_2, e3) = e1
% 203.53/34.42    (3)  op(e1, e3) = all_52_5
% 203.53/34.42    (4)   ~ (all_52_5 = all_6_2)
% 203.53/34.42    (5)  op(e3, e3) = all_52_2
% 203.53/34.42    (6)  op(e3, e3) = all_6_2
% 203.53/34.42    (7)  op(e3, e3) = e1
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3, simplifying
% 203.53/34.42  |              with (5), (6) gives:
% 203.53/34.42  |   (8)  all_52_2 = all_6_2
% 203.53/34.42  | 
% 203.53/34.42  | GROUND_INST: instantiating (1) with e1, all_52_2, e3, e3, simplifying with
% 203.53/34.42  |              (5), (7) gives:
% 203.53/34.42  |   (9)  all_52_2 = e1
% 203.53/34.42  | 
% 203.53/34.42  | COMBINE_EQS: (8), (9) imply:
% 203.53/34.42  |   (10)  all_6_2 = e1
% 203.53/34.42  | 
% 203.53/34.42  | SIMP: (10) implies:
% 203.53/34.42  |   (11)  all_6_2 = e1
% 203.53/34.42  | 
% 203.53/34.42  | REF_CLOSE: (1), (2), (3), (4), (11) are inconsistent by sub-proof #578.
% 203.53/34.42  | 
% 203.53/34.42  End of proof
% 203.53/34.42  
% 203.53/34.42  Sub-proof #567 shows that the following formulas are inconsistent:
% 203.53/34.42  ----------------------------------------------------------------
% 203.53/34.42    (1)  all_58_14 = all_52_23
% 203.53/34.42    (2)   ~ (e3 = e1)
% 203.53/34.42    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.42    (4)  op(e2, e3) = all_52_3
% 203.53/34.42    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.53/34.42    (6)  op(e0, all_14_1) = all_14_0
% 203.53/34.42    (7)  all_58_13 = all_52_15
% 203.53/34.42    (8)  op(all_52_13, all_52_13) = e1
% 203.53/34.42    (9)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.53/34.42    (10)  all_56_1 = all_4_1
% 203.53/34.42    (11)  op(e0, e1) = all_52_23
% 203.53/34.42    (12)  all_58_15 = e3
% 203.53/34.42    (13)   ~ (all_4_1 = e1)
% 203.53/34.42    (14)  all_56_9 = all_52_13
% 203.53/34.42    (15)   ~ (e2 = e1)
% 203.53/34.42    (16)   ~ (all_4_1 = e2)
% 203.53/34.42    (17)   ~ (all_52_13 = all_10_2)
% 203.53/34.42    (18)  op(e2, e3) = e1
% 203.53/34.42    (19)  all_58_1 = all_4_1
% 203.53/34.42    (20)  all_58_12 = all_52_7
% 203.53/34.42    (21)   ~ (all_52_7 = e3)
% 203.53/34.42    (22)  all_58_4 = e3
% 203.53/34.42    (23)  all_58_9 = all_14_1
% 203.53/34.42    (24)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.53/34.42    (25)   ~ (all_14_1 = all_4_1)
% 203.53/34.42    (26)   ~ (all_52_7 = e2)
% 203.53/34.42    (27)  op(all_14_1, all_14_1) = all_52_24
% 203.53/34.42    (28)   ~ (all_52_13 = all_4_1)
% 203.53/34.42    (29)  all_58_0 = e2
% 203.53/34.42    (30)  all_56_12 = all_52_7
% 203.53/34.42    (31)   ~ (all_52_13 = all_52_15)
% 203.53/34.42    (32)   ~ (all_52_13 = e3)
% 203.53/34.42    (33)   ~ (all_52_3 = all_52_7)
% 203.53/34.42    (34)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.42    (35)   ~ (e3 = e2)
% 203.53/34.42    (36)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.42    (37)  op(e1, e1) = all_10_2
% 203.53/34.42    (38)   ~ (all_14_0 = e2)
% 203.53/34.42  
% 203.53/34.42  Begin of proof
% 203.53/34.42  | 
% 203.53/34.42  | BETA: splitting (34) gives:
% 203.53/34.42  | 
% 203.53/34.42  | Case 1:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (39)  all_56_1 = e2
% 203.53/34.42  | | 
% 203.53/34.42  | | COMBINE_EQS: (10), (39) imply:
% 203.53/34.42  | |   (40)  all_4_1 = e2
% 203.53/34.42  | | 
% 203.53/34.42  | | REDUCE: (16), (40) imply:
% 203.53/34.42  | |   (41)  $false
% 203.53/34.42  | | 
% 203.53/34.42  | | CLOSE: (41) is inconsistent.
% 203.53/34.42  | | 
% 203.53/34.42  | Case 2:
% 203.53/34.42  | | 
% 203.53/34.42  | |   (42)  all_56_1 = e1 | all_56_1 = e0
% 203.53/34.42  | | 
% 203.53/34.42  | | BETA: splitting (24) gives:
% 203.53/34.42  | | 
% 203.53/34.42  | | Case 1:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (43)  all_58_0 = e1
% 203.53/34.42  | | | 
% 203.53/34.42  | | | COMBINE_EQS: (29), (43) imply:
% 203.53/34.42  | | |   (44)  e2 = e1
% 203.53/34.42  | | | 
% 203.53/34.42  | | | REDUCE: (15), (44) imply:
% 203.53/34.42  | | |   (45)  $false
% 203.53/34.42  | | | 
% 203.53/34.42  | | | CLOSE: (45) is inconsistent.
% 203.53/34.42  | | | 
% 203.53/34.42  | | Case 2:
% 203.53/34.42  | | | 
% 203.53/34.42  | | |   (46)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.53/34.42  | | | 
% 203.53/34.42  | | | BETA: splitting (46) gives:
% 203.53/34.42  | | | 
% 203.53/34.42  | | | Case 1:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (47)  all_58_1 = e1
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | COMBINE_EQS: (19), (47) imply:
% 203.53/34.42  | | | |   (48)  all_4_1 = e1
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | REDUCE: (13), (48) imply:
% 203.53/34.42  | | | |   (49)  $false
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | CLOSE: (49) is inconsistent.
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | Case 2:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | |   (50)  all_58_4 = e1 | all_58_9 = e1
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | BETA: splitting (50) gives:
% 203.53/34.42  | | | | 
% 203.53/34.42  | | | | Case 1:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | |   (51)  all_58_4 = e1
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REF_CLOSE: (2), (22), (51) are inconsistent by sub-proof #568.
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | Case 2:
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | |   (52)  all_58_9 = e1
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | COMBINE_EQS: (23), (52) imply:
% 203.53/34.42  | | | | |   (53)  all_14_1 = e1
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | SIMP: (53) implies:
% 203.53/34.42  | | | | |   (54)  all_14_1 = e1
% 203.53/34.42  | | | | | 
% 203.53/34.42  | | | | | REDUCE: (25), (54) imply:
% 203.53/34.42  | | | | |   (55)   ~ (all_4_1 = e1)
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (27), (54) imply:
% 203.53/34.43  | | | | |   (56)  op(e1, e1) = all_52_24
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (6), (54) imply:
% 203.53/34.43  | | | | |   (57)  op(e0, e1) = all_14_0
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | BETA: splitting (42) gives:
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | Case 1:
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | |   (58)  all_56_1 = e1
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | COMBINE_EQS: (10), (58) imply:
% 203.53/34.43  | | | | | |   (59)  all_4_1 = e1
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | REDUCE: (13), (59) imply:
% 203.53/34.43  | | | | | |   (60)  $false
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | CLOSE: (60) is inconsistent.
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | Case 2:
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | |   (61)  all_56_1 = e0
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | COMBINE_EQS: (10), (61) imply:
% 203.53/34.43  | | | | | |   (62)  all_4_1 = e0
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | REDUCE: (28), (62) imply:
% 203.53/34.43  | | | | | |   (63)   ~ (all_52_13 = e0)
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | GROUND_INST: instantiating (3) with all_52_23, all_14_0, e1, e0,
% 203.53/34.43  | | | | | |              simplifying with (11), (57) gives:
% 203.53/34.43  | | | | | |   (64)  all_52_23 = all_14_0
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_24, e1, e1,
% 203.53/34.43  | | | | | |              simplifying with (37), (56) gives:
% 203.53/34.43  | | | | | |   (65)  all_52_24 = all_10_2
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | GROUND_INST: instantiating (3) with all_52_3, e1, e3, e2,
% 203.53/34.43  | | | | | |              simplifying with (4), (18) gives:
% 203.53/34.43  | | | | | |   (66)  all_52_3 = e1
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | COMBINE_EQS: (1), (64) imply:
% 203.53/34.43  | | | | | |   (67)  all_58_14 = all_14_0
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | REDUCE: (33), (66) imply:
% 203.53/34.43  | | | | | |   (68)   ~ (all_52_7 = e1)
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | SIMP: (68) implies:
% 203.53/34.43  | | | | | |   (69)   ~ (all_52_7 = e1)
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | BETA: splitting (5) gives:
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | Case 1:
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | |   (70)  all_56_12 = e3
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | REF_CLOSE: (21), (30), (70) are inconsistent by sub-proof #1383.
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | Case 2:
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | |   (71)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | BETA: splitting (71) gives:
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | |   (72)  all_56_12 = e2
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | | REF_CLOSE: (26), (30), (72) are inconsistent by sub-proof #1178.
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | |   (73)   ~ (all_56_12 = e2)
% 203.53/34.43  | | | | | | | |   (74)  all_56_12 = e1 | all_56_12 = e0
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | | BETA: splitting (74) gives:
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | |   (75)  all_56_12 = e1
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | REF_CLOSE: (30), (69), (75) are inconsistent by sub-proof
% 203.53/34.43  | | | | | | | | |            #1376.
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | |   (76)  all_56_12 = e0
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | COMBINE_EQS: (30), (76) imply:
% 203.53/34.43  | | | | | | | | |   (77)  all_52_7 = e0
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | SIMP: (77) implies:
% 203.53/34.43  | | | | | | | | |   (78)  all_52_7 = e0
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | COMBINE_EQS: (20), (78) imply:
% 203.53/34.43  | | | | | | | | |   (79)  all_58_12 = e0
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | REDUCE: (26), (78) imply:
% 203.53/34.43  | | | | | | | | |   (80)   ~ (e2 = e0)
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | SIMP: (80) implies:
% 203.53/34.43  | | | | | | | | |   (81)   ~ (e2 = e0)
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | BETA: splitting (9) gives:
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | |   (82)  all_58_12 = e2
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | COMBINE_EQS: (79), (82) imply:
% 203.53/34.43  | | | | | | | | | |   (83)  e2 = e0
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | REDUCE: (81), (83) imply:
% 203.53/34.43  | | | | | | | | | |   (84)  $false
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | CLOSE: (84) is inconsistent.
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | |   (85)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | BETA: splitting (85) gives:
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | |   (86)  all_58_13 = e2
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | COMBINE_EQS: (7), (86) imply:
% 203.53/34.43  | | | | | | | | | | |   (87)  all_52_15 = e2
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | SIMP: (87) implies:
% 203.53/34.43  | | | | | | | | | | |   (88)  all_52_15 = e2
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | REDUCE: (31), (88) imply:
% 203.53/34.43  | | | | | | | | | | |   (89)   ~ (all_52_13 = e2)
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | BETA: splitting (36) gives:
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | |   (90)  all_56_9 = e3
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | REF_CLOSE: (14), (32), (90) are inconsistent by sub-proof
% 203.53/34.43  | | | | | | | | | | | |            #958.
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | |   (91)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | BETA: splitting (91) gives:
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | |   (92)  all_56_9 = e2
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | REF_CLOSE: (14), (89), (92) are inconsistent by sub-proof
% 203.53/34.43  | | | | | | | | | | | | |            #955.
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | |   (93)  all_56_9 = e1 | all_56_9 = e0
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | BETA: splitting (93) gives:
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | |   (94)  all_56_9 = e1
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | | COMBINE_EQS: (14), (94) imply:
% 203.53/34.43  | | | | | | | | | | | | | |   (95)  all_52_13 = e1
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | | SIMP: (95) implies:
% 203.53/34.43  | | | | | | | | | | | | | |   (96)  all_52_13 = e1
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (17), (37), (96) are inconsistent by
% 203.53/34.43  | | | | | | | | | | | | | |            sub-proof #1134.
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | |   (97)  all_56_9 = e0
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | | REF_CLOSE: (14), (63), (97) are inconsistent by sub-proof
% 203.53/34.43  | | | | | | | | | | | | | |            #953.
% 203.53/34.43  | | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | |   (98)  all_58_14 = e2 | all_58_15 = e2
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | BETA: splitting (98) gives:
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | Case 1:
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | |   (99)  all_58_14 = e2
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | COMBINE_EQS: (67), (99) imply:
% 203.53/34.43  | | | | | | | | | | | |   (100)  all_14_0 = e2
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | SIMP: (100) implies:
% 203.53/34.43  | | | | | | | | | | | |   (101)  all_14_0 = e2
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | REDUCE: (38), (101) imply:
% 203.53/34.43  | | | | | | | | | | | |   (102)  $false
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | Case 2:
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | |   (103)  all_58_15 = e2
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | COMBINE_EQS: (12), (103) imply:
% 203.53/34.43  | | | | | | | | | | | |   (104)  e3 = e2
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | REDUCE: (35), (104) imply:
% 203.53/34.43  | | | | | | | | | | | |   (105)  $false
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | | CLOSE: (105) is inconsistent.
% 203.53/34.43  | | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | | | 
% 203.53/34.43  | | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | | 
% 203.53/34.43  | | | | | | | | End of split
% 203.53/34.43  | | | | | | | | 
% 203.53/34.43  | | | | | | | End of split
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | End of split
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | End of split
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | End of split
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | End of split
% 203.53/34.43  | | | 
% 203.53/34.43  | | End of split
% 203.53/34.43  | | 
% 203.53/34.43  | End of split
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #568 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)  all_58_4 = e3
% 203.53/34.43    (2)  all_58_4 = e1
% 203.53/34.43    (3)   ~ (e3 = e1)
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | COMBINE_EQS: (1), (2) imply:
% 203.53/34.43  |   (4)  e3 = e1
% 203.53/34.43  | 
% 203.53/34.43  | SIMP: (4) implies:
% 203.53/34.43  |   (5)  e3 = e1
% 203.53/34.43  | 
% 203.53/34.43  | REDUCE: (3), (5) imply:
% 203.53/34.43  |   (6)  $false
% 203.53/34.43  | 
% 203.53/34.43  | CLOSE: (6) is inconsistent.
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #569 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)   ~ (e3 = e1)
% 203.53/34.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.43    (3)  op(all_6_2, e3) = e1
% 203.53/34.43    (4)  op(e1, e3) = all_52_5
% 203.53/34.43    (5)  all_12_0 = all_6_0
% 203.53/34.43    (6)  op(all_6_2, all_6_2) = all_52_0
% 203.53/34.43    (7)  all_56_2 = all_6_0
% 203.53/34.43    (8)   ~ (all_6_0 = e1)
% 203.53/34.43    (9)  all_12_2 = all_6_2
% 203.53/34.43    (10)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e2)
% 203.53/34.43    (11)   ~ (all_6_0 = e2)
% 203.53/34.43    (12)   ~ (all_52_5 = all_6_2)
% 203.53/34.43    (13)  all_56_0 = all_6_2
% 203.53/34.43    (14)  op(e3, e3) = all_6_2
% 203.53/34.43    (15)   ~ (all_6_0 = all_6_2)
% 203.53/34.43    (16)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.53/34.43    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | BETA: splitting (16) gives:
% 203.53/34.43  | 
% 203.53/34.43  | Case 1:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (18)  all_56_2 = e2
% 203.53/34.43  | | 
% 203.53/34.43  | | COMBINE_EQS: (7), (18) imply:
% 203.53/34.43  | |   (19)  all_6_0 = e2
% 203.53/34.43  | | 
% 203.53/34.43  | | SIMP: (19) implies:
% 203.53/34.43  | |   (20)  all_6_0 = e2
% 203.53/34.43  | | 
% 203.53/34.43  | | REDUCE: (11), (20) imply:
% 203.53/34.43  | |   (21)  $false
% 203.53/34.43  | | 
% 203.53/34.43  | | CLOSE: (21) is inconsistent.
% 203.53/34.43  | | 
% 203.53/34.43  | Case 2:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (22)  all_56_2 = e1 | all_56_2 = e0
% 203.53/34.43  | | 
% 203.53/34.43  | | BETA: splitting (22) gives:
% 203.53/34.43  | | 
% 203.53/34.43  | | Case 1:
% 203.53/34.43  | | | 
% 203.53/34.43  | | |   (23)  all_56_2 = e1
% 203.53/34.43  | | | 
% 203.53/34.43  | | | COMBINE_EQS: (7), (23) imply:
% 203.53/34.43  | | |   (24)  all_6_0 = e1
% 203.53/34.43  | | | 
% 203.53/34.43  | | | SIMP: (24) implies:
% 203.53/34.43  | | |   (25)  all_6_0 = e1
% 203.53/34.43  | | | 
% 203.53/34.43  | | | REDUCE: (8), (25) imply:
% 203.53/34.43  | | |   (26)  $false
% 203.53/34.43  | | | 
% 203.53/34.43  | | | CLOSE: (26) is inconsistent.
% 203.53/34.43  | | | 
% 203.53/34.43  | | Case 2:
% 203.53/34.43  | | | 
% 203.53/34.43  | | |   (27)  all_56_2 = e0
% 203.53/34.43  | | | 
% 203.53/34.43  | | | COMBINE_EQS: (7), (27) imply:
% 203.53/34.43  | | |   (28)  all_6_0 = e0
% 203.53/34.43  | | | 
% 203.53/34.43  | | | SIMP: (28) implies:
% 203.53/34.43  | | |   (29)  all_6_0 = e0
% 203.53/34.43  | | | 
% 203.53/34.43  | | | COMBINE_EQS: (5), (29) imply:
% 203.53/34.43  | | |   (30)  all_12_0 = e0
% 203.53/34.43  | | | 
% 203.53/34.43  | | | REDUCE: (15), (29) imply:
% 203.53/34.43  | | |   (31)   ~ (all_6_2 = e0)
% 203.53/34.43  | | | 
% 203.53/34.43  | | | SIMP: (31) implies:
% 203.53/34.43  | | |   (32)   ~ (all_6_2 = e0)
% 203.53/34.43  | | | 
% 203.53/34.43  | | | BETA: splitting (10) gives:
% 203.53/34.43  | | | 
% 203.53/34.43  | | | Case 1:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | |   (33)   ~ (all_12_2 = e2)
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | REDUCE: (9), (33) imply:
% 203.53/34.43  | | | |   (34)   ~ (all_6_2 = e2)
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | BETA: splitting (17) gives:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | Case 1:
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | |   (35)  all_56_0 = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | COMBINE_EQS: (13), (35) imply:
% 203.53/34.43  | | | | |   (36)  all_6_2 = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | SIMP: (36) implies:
% 203.53/34.43  | | | | |   (37)  all_6_2 = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (6), (37) imply:
% 203.53/34.43  | | | | |   (38)  op(e3, e3) = all_52_0
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (3), (37) imply:
% 203.53/34.43  | | | | |   (39)  op(e3, e3) = e1
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (14), (37) imply:
% 203.53/34.43  | | | | |   (40)  op(e3, e3) = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REF_CLOSE: (1), (2), (38), (39), (40) are inconsistent by sub-proof
% 203.53/34.43  | | | | |            #1237.
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | Case 2:
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | |   (41)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | BETA: splitting (41) gives:
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | Case 1:
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | |   (42)  all_56_0 = e2
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | REF_CLOSE: (13), (34), (42) are inconsistent by sub-proof #597.
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | Case 2:
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | |   (43)  all_56_0 = e1 | all_56_0 = e0
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | BETA: splitting (43) gives:
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | | Case 1:
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | |   (44)  all_56_0 = e1
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | COMBINE_EQS: (13), (44) imply:
% 203.53/34.43  | | | | | | |   (45)  all_6_2 = e1
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | SIMP: (45) implies:
% 203.53/34.43  | | | | | | |   (46)  all_6_2 = e1
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | REDUCE: (12), (46) imply:
% 203.53/34.43  | | | | | | |   (47)   ~ (all_52_5 = e1)
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | REDUCE: (3), (46) imply:
% 203.53/34.43  | | | | | | |   (48)  op(e1, e3) = e1
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | GROUND_INST: instantiating (2) with all_52_5, e1, e3, e1,
% 203.53/34.43  | | | | | | |              simplifying with (4), (48) gives:
% 203.53/34.43  | | | | | | |   (49)  all_52_5 = e1
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | REDUCE: (47), (49) imply:
% 203.53/34.43  | | | | | | |   (50)  $false
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | CLOSE: (50) is inconsistent.
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | Case 2:
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | |   (51)  all_56_0 = e0
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | | REF_CLOSE: (13), (32), (51) are inconsistent by sub-proof #570.
% 203.53/34.43  | | | | | | | 
% 203.53/34.43  | | | | | | End of split
% 203.53/34.43  | | | | | | 
% 203.53/34.43  | | | | | End of split
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | End of split
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | Case 2:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | |   (52)   ~ (all_12_0 = e0)
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | REDUCE: (30), (52) imply:
% 203.53/34.43  | | | |   (53)  $false
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | CLOSE: (53) is inconsistent.
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | End of split
% 203.53/34.43  | | | 
% 203.53/34.43  | | End of split
% 203.53/34.43  | | 
% 203.53/34.43  | End of split
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #570 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)  all_56_0 = all_6_2
% 203.53/34.43    (2)  all_56_0 = e0
% 203.53/34.43    (3)   ~ (all_6_2 = e0)
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | COMBINE_EQS: (1), (2) imply:
% 203.53/34.43  |   (4)  all_6_2 = e0
% 203.53/34.43  | 
% 203.53/34.43  | SIMP: (4) implies:
% 203.53/34.43  |   (5)  all_6_2 = e0
% 203.53/34.43  | 
% 203.53/34.43  | REDUCE: (3), (5) imply:
% 203.53/34.43  |   (6)  $false
% 203.53/34.43  | 
% 203.53/34.43  | CLOSE: (6) is inconsistent.
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #571 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)   ~ (all_52_25 = all_52_27)
% 203.53/34.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.43    (3)  all_58_1 = all_52_9
% 203.53/34.43    (4)   ~ (all_52_9 = all_52_13)
% 203.53/34.43    (5)   ~ (all_52_17 = all_52_25)
% 203.53/34.43    (6)  all_58_0 = all_6_2
% 203.53/34.43    (7)   ~ (all_52_17 = all_10_2)
% 203.53/34.43    (8)  op(all_6_2, e3) = e1
% 203.53/34.43    (9)  all_58_13 = all_52_15
% 203.53/34.43    (10)  all_58_9 = all_52_25
% 203.53/34.43    (11)   ~ (all_52_15 = e3)
% 203.53/34.43    (12)  op(e1, e3) = all_52_5
% 203.53/34.43    (13)  all_58_11 = all_52_29
% 203.53/34.43    (14)   ~ (all_52_3 = e3)
% 203.53/34.43    (15)  op(e0, e0) = all_14_2
% 203.53/34.43    (16)  op(all_52_29, all_52_29) = e1
% 203.53/34.43    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.43    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.53/34.43    (19)  all_56_9 = all_52_13
% 203.53/34.43    (20)  all_58_10 = all_52_27
% 203.53/34.43    (21)  all_58_7 = all_52_13
% 203.53/34.43    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.43    (23)  all_58_2 = all_52_3
% 203.53/34.43    (24)   ~ (all_52_19 = e3)
% 203.53/34.43    (25)   ~ (all_52_5 = e3)
% 203.53/34.43    (26)  op(all_52_25, all_52_25) = e3
% 203.53/34.43    (27)   ~ (all_10_2 = e3)
% 203.53/34.43    (28)   ~ (all_52_9 = e3)
% 203.53/34.43    (29)   ~ (all_52_13 = all_4_2)
% 203.53/34.43    (30)  op(all_52_27, all_52_27) = e2
% 203.53/34.43    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.43    (32)  all_58_8 = all_10_2
% 203.53/34.43    (33)   ~ (all_52_25 = all_6_2)
% 203.53/34.43    (34)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.53/34.43    (35)   ~ (all_52_5 = all_6_2)
% 203.53/34.43    (36)  op(e3, e3) = all_6_2
% 203.53/34.43    (37)   ~ (all_52_27 = all_14_2)
% 203.53/34.43    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.53/34.43    (39)  op(all_4_2, all_4_2) = all_52_10
% 203.53/34.43    (40)  all_56_3 = all_52_25
% 203.53/34.43    (41)  all_58_5 = all_52_19
% 203.53/34.43    (42)  all_58_6 = all_52_5
% 203.53/34.43    (43)   ~ (e3 = e2)
% 203.53/34.43    (44)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.43    (45)  op(e1, e1) = all_10_2
% 203.53/34.43    (46)  all_58_3 = all_4_2
% 203.53/34.43    (47)  all_58_4 = all_52_17
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | BETA: splitting (22) gives:
% 203.53/34.43  | 
% 203.53/34.43  | Case 1:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (48)  all_58_6 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | REF_CLOSE: (25), (42), (48) are inconsistent by sub-proof #1328.
% 203.53/34.43  | | 
% 203.53/34.43  | Case 2:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (49)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | BETA: splitting (17) gives:
% 203.53/34.43  | | 
% 203.53/34.43  | | Case 1:
% 203.53/34.43  | | | 
% 203.53/34.43  | | |   (50)  all_58_2 = e3
% 203.53/34.43  | | | 
% 203.53/34.43  | | | REF_CLOSE: (14), (23), (50) are inconsistent by sub-proof #1369.
% 203.53/34.43  | | | 
% 203.53/34.43  | | Case 2:
% 203.53/34.43  | | | 
% 203.53/34.43  | | |   (51)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.43  | | | 
% 203.53/34.43  | | | BETA: splitting (31) gives:
% 203.53/34.43  | | | 
% 203.53/34.43  | | | Case 1:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | |   (52)  all_58_1 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | COMBINE_EQS: (3), (52) imply:
% 203.53/34.43  | | | |   (53)  all_52_9 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | REDUCE: (28), (53) imply:
% 203.53/34.43  | | | |   (54)  $false
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | CLOSE: (54) is inconsistent.
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | Case 2:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | |   (55)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | BETA: splitting (44) gives:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | Case 1:
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | |   (56)  all_56_9 = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | COMBINE_EQS: (19), (56) imply:
% 203.53/34.43  | | | | |   (57)  all_52_13 = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | SIMP: (57) implies:
% 203.53/34.43  | | | | |   (58)  all_52_13 = e3
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (29), (58) imply:
% 203.53/34.43  | | | | |   (59)   ~ (all_4_2 = e3)
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | SIMP: (59) implies:
% 203.53/34.43  | | | | |   (60)   ~ (all_4_2 = e3)
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (15), (18), (20), (24),
% 203.53/34.43  | | | | |            (26), (28), (30), (33), (34), (36), (37), (38), (40), (41),
% 203.53/34.43  | | | | |            (43), (45), (46), (47), (51), (60) are inconsistent by
% 203.53/34.43  | | | | |            sub-proof #1228.
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | Case 2:
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | |   (61)   ~ (all_56_9 = e3)
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REDUCE: (19), (61) imply:
% 203.53/34.43  | | | | |   (62)   ~ (all_52_13 = e3)
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | | REF_CLOSE: (2), (8), (9), (11), (12), (13), (16), (21), (27), (32),
% 203.53/34.43  | | | | |            (35), (36), (39), (46), (49), (55), (62) are inconsistent
% 203.53/34.43  | | | | |            by sub-proof #572.
% 203.53/34.43  | | | | | 
% 203.53/34.43  | | | | End of split
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | End of split
% 203.53/34.43  | | | 
% 203.53/34.43  | | End of split
% 203.53/34.43  | | 
% 203.53/34.43  | End of split
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #572 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.43    (2)  op(all_6_2, e3) = e1
% 203.53/34.43    (3)  all_58_13 = all_52_15
% 203.53/34.43    (4)   ~ (all_52_15 = e3)
% 203.53/34.43    (5)  op(e1, e3) = all_52_5
% 203.53/34.43    (6)  all_58_11 = all_52_29
% 203.53/34.43    (7)  op(all_52_29, all_52_29) = e1
% 203.53/34.43    (8)  all_58_7 = all_52_13
% 203.53/34.43    (9)   ~ (all_10_2 = e3)
% 203.53/34.43    (10)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.43    (11)  all_58_8 = all_10_2
% 203.53/34.43    (12)   ~ (all_52_5 = all_6_2)
% 203.53/34.43    (13)  op(e3, e3) = all_6_2
% 203.53/34.43    (14)   ~ (all_52_13 = e3)
% 203.53/34.43    (15)  op(all_4_2, all_4_2) = all_52_10
% 203.53/34.43    (16)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.53/34.43    (17)  all_58_3 = all_4_2
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | BETA: splitting (10) gives:
% 203.53/34.43  | 
% 203.53/34.43  | Case 1:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (18)  all_58_7 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | COMBINE_EQS: (8), (18) imply:
% 203.53/34.43  | |   (19)  all_52_13 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | REDUCE: (14), (19) imply:
% 203.53/34.43  | |   (20)  $false
% 203.53/34.43  | | 
% 203.53/34.43  | | CLOSE: (20) is inconsistent.
% 203.53/34.43  | | 
% 203.53/34.43  | Case 2:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (21)   ~ (all_58_7 = e3)
% 203.53/34.43  | |   (22)  all_58_8 = e3 | all_58_11 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | BETA: splitting (16) gives:
% 203.53/34.43  | | 
% 203.53/34.43  | | Case 1:
% 203.53/34.43  | | | 
% 203.53/34.43  | | |   (23)  all_58_3 = e3
% 203.53/34.43  | | | 
% 203.53/34.43  | | | COMBINE_EQS: (17), (23) imply:
% 203.53/34.43  | | |   (24)  all_4_2 = e3
% 203.53/34.43  | | | 
% 203.53/34.43  | | | REDUCE: (15), (24) imply:
% 203.53/34.43  | | |   (25)  op(e3, e3) = all_52_10
% 203.53/34.43  | | | 
% 203.53/34.43  | | | BETA: splitting (22) gives:
% 203.53/34.43  | | | 
% 203.53/34.43  | | | Case 1:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | |   (26)  all_58_8 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | REF_CLOSE: (9), (11), (26) are inconsistent by sub-proof #950.
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | Case 2:
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | |   (27)  all_58_11 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | COMBINE_EQS: (6), (27) imply:
% 203.53/34.43  | | | |   (28)  all_52_29 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | SIMP: (28) implies:
% 203.53/34.43  | | | |   (29)  all_52_29 = e3
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | REDUCE: (7), (29) imply:
% 203.53/34.43  | | | |   (30)  op(e3, e3) = e1
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | GROUND_INST: instantiating (1) with all_6_2, all_52_10, e3, e3,
% 203.53/34.43  | | | |              simplifying with (13), (25) gives:
% 203.53/34.43  | | | |   (31)  all_52_10 = all_6_2
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | GROUND_INST: instantiating (1) with e1, all_52_10, e3, e3, simplifying
% 203.53/34.43  | | | |              with (25), (30) gives:
% 203.53/34.43  | | | |   (32)  all_52_10 = e1
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | COMBINE_EQS: (31), (32) imply:
% 203.53/34.43  | | | |   (33)  all_6_2 = e1
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | SIMP: (33) implies:
% 203.53/34.43  | | | |   (34)  all_6_2 = e1
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | | REF_CLOSE: (1), (2), (5), (12), (34) are inconsistent by sub-proof #578.
% 203.53/34.43  | | | | 
% 203.53/34.43  | | | End of split
% 203.53/34.43  | | | 
% 203.53/34.43  | | Case 2:
% 203.53/34.43  | | | 
% 203.53/34.43  | | |   (35)  all_58_7 = e3 | all_58_13 = e3
% 203.53/34.43  | | | 
% 203.53/34.43  | | | REF_CLOSE: (3), (4), (8), (14), (35) are inconsistent by sub-proof #1298.
% 203.53/34.43  | | | 
% 203.53/34.43  | | End of split
% 203.53/34.43  | | 
% 203.53/34.43  | End of split
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #573 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 203.53/34.43    (2)  all_52_16 = all_6_2
% 203.53/34.43    (3)   ~ (all_6_2 = e3)
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | ALPHA: (1) implies:
% 203.53/34.43  |   (4)  all_52_16 = e3
% 203.53/34.43  | 
% 203.53/34.43  | COMBINE_EQS: (2), (4) imply:
% 203.53/34.43  |   (5)  all_6_2 = e3
% 203.53/34.43  | 
% 203.53/34.43  | SIMP: (5) implies:
% 203.53/34.43  |   (6)  all_6_2 = e3
% 203.53/34.43  | 
% 203.53/34.43  | REDUCE: (3), (6) imply:
% 203.53/34.43  |   (7)  $false
% 203.53/34.43  | 
% 203.53/34.43  | CLOSE: (7) is inconsistent.
% 203.53/34.43  | 
% 203.53/34.43  End of proof
% 203.53/34.43  
% 203.53/34.43  Sub-proof #574 shows that the following formulas are inconsistent:
% 203.53/34.43  ----------------------------------------------------------------
% 203.53/34.43    (1)   ~ (all_52_15 = all_52_23)
% 203.53/34.43    (2)  all_58_14 = all_52_23
% 203.53/34.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.43    (4)  all_58_1 = all_52_9
% 203.53/34.43    (5)   ~ (e3 = e0)
% 203.53/34.43    (6)  op(all_52_15, all_52_15) = e0
% 203.53/34.43    (7)  op(all_52_7, all_52_7) = all_52_6
% 203.53/34.43    (8)  all_58_0 = all_6_2
% 203.53/34.43    (9)  op(all_6_2, e3) = e1
% 203.53/34.43    (10)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.43    (11)  all_58_13 = all_52_15
% 203.53/34.43    (12)  all_58_9 = all_52_25
% 203.53/34.43    (13)  op(e2, e2) = all_4_2
% 203.53/34.43    (14)   ~ (all_52_9 = all_52_15)
% 203.53/34.43    (15)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.53/34.43    (16)  all_58_15 = e0
% 203.53/34.43    (17)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.53/34.43    (18)   ~ (e2 = e1)
% 203.53/34.43    (19)  all_58_12 = all_52_7
% 203.53/34.43    (20)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.43    (21)  all_58_4 = e3
% 203.53/34.43    (22)   ~ (e2 = e0)
% 203.53/34.43    (23)   ~ (all_52_23 = e3)
% 203.53/34.43    (24)   ~ (all_10_2 = e3)
% 203.53/34.43    (25)  op(e0, e3) = all_52_7
% 203.53/34.43    (26)   ~ (all_52_9 = all_52_25)
% 203.53/34.43    (27)  op(all_52_23, all_52_23) = all_52_22
% 203.53/34.43    (28)   ~ (all_52_23 = e0)
% 203.53/34.43    (29)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.53/34.43    (30)   ~ (all_52_9 = all_6_2)
% 203.53/34.43    (31)  op(e3, e3) = all_6_2
% 203.53/34.43    (32)  all_56_1 = all_52_9
% 203.53/34.43    (33)   ~ (all_52_15 = all_4_2)
% 203.53/34.43    (34)   ~ (e3 = e2)
% 203.53/34.43    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.43    (36)  op(e1, e1) = all_10_2
% 203.53/34.43    (37)  op(all_52_9, all_52_9) = e3
% 203.53/34.43  
% 203.53/34.43  Begin of proof
% 203.53/34.43  | 
% 203.53/34.43  | BETA: splitting (10) gives:
% 203.53/34.43  | 
% 203.53/34.43  | Case 1:
% 203.53/34.43  | | 
% 203.53/34.43  | |   (38)  all_58_13 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | COMBINE_EQS: (11), (38) imply:
% 203.53/34.43  | |   (39)  all_52_15 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | SIMP: (39) implies:
% 203.53/34.43  | |   (40)  all_52_15 = e3
% 203.53/34.43  | | 
% 203.53/34.43  | | REDUCE: (14), (40) imply:
% 203.53/34.43  | |   (41)   ~ (all_52_9 = e3)
% 203.53/34.43  | | 
% 203.53/34.43  | | REDUCE: (1), (40) imply:
% 203.53/34.43  | |   (42)   ~ (all_52_23 = e3)
% 203.53/34.43  | | 
% 203.53/34.43  | | REDUCE: (33), (40) imply:
% 203.53/34.43  | |   (43)   ~ (all_4_2 = e3)
% 203.53/34.43  | | 
% 203.53/34.43  | | SIMP: (43) implies:
% 203.53/34.43  | |   (44)   ~ (all_4_2 = e3)
% 203.53/34.43  | | 
% 203.53/34.43  | | REDUCE: (6), (40) imply:
% 203.53/34.43  | |   (45)  op(e3, e3) = e0
% 203.53/34.43  | | 
% 203.53/34.44  | | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying with
% 203.53/34.44  | |              (31), (45) gives:
% 203.53/34.44  | |   (46)  all_6_2 = e0
% 203.53/34.44  | | 
% 203.53/34.44  | | COMBINE_EQS: (8), (46) imply:
% 203.53/34.44  | |   (47)  all_58_0 = e0
% 203.53/34.44  | | 
% 203.53/34.44  | | REDUCE: (30), (46) imply:
% 203.53/34.44  | |   (48)   ~ (all_52_9 = e0)
% 203.53/34.44  | | 
% 203.53/34.44  | | REDUCE: (9), (46) imply:
% 203.53/34.44  | |   (49)  op(e0, e3) = e1
% 203.53/34.44  | | 
% 203.53/34.44  | | GROUND_INST: instantiating (3) with all_52_7, e1, e3, e0, simplifying with
% 203.53/34.44  | |              (25), (49) gives:
% 203.53/34.44  | |   (50)  all_52_7 = e1
% 203.53/34.44  | | 
% 203.53/34.44  | | COMBINE_EQS: (19), (50) imply:
% 203.53/34.44  | |   (51)  all_58_12 = e1
% 203.53/34.44  | | 
% 203.53/34.44  | | REDUCE: (7), (50) imply:
% 203.53/34.44  | |   (52)  op(e1, e1) = all_52_6
% 203.53/34.44  | | 
% 203.53/34.44  | | BETA: splitting (15) gives:
% 203.53/34.44  | | 
% 203.53/34.44  | | Case 1:
% 203.53/34.44  | | | 
% 203.53/34.44  | | |   (53)  all_58_12 = e2
% 203.53/34.44  | | | 
% 203.53/34.44  | | | COMBINE_EQS: (51), (53) imply:
% 203.53/34.44  | | |   (54)  e2 = e1
% 203.53/34.44  | | | 
% 203.53/34.44  | | | REDUCE: (18), (54) imply:
% 203.53/34.44  | | |   (55)  $false
% 203.53/34.44  | | | 
% 203.53/34.44  | | | CLOSE: (55) is inconsistent.
% 203.53/34.44  | | | 
% 203.53/34.44  | | Case 2:
% 203.53/34.44  | | | 
% 203.53/34.44  | | |   (56)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.53/34.44  | | | 
% 203.53/34.44  | | | BETA: splitting (56) gives:
% 203.53/34.44  | | | 
% 203.53/34.44  | | | Case 1:
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | |   (57)  all_58_13 = e2
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | REF_CLOSE: (34), (38), (57) are inconsistent by sub-proof #1248.
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | Case 2:
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | |   (58)  all_58_14 = e2 | all_58_15 = e2
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | BETA: splitting (58) gives:
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | Case 1:
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | |   (59)  all_58_14 = e2
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | COMBINE_EQS: (2), (59) imply:
% 203.53/34.44  | | | | |   (60)  all_52_23 = e2
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | SIMP: (60) implies:
% 203.53/34.44  | | | | |   (61)  all_52_23 = e2
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | REDUCE: (23), (61) imply:
% 203.53/34.44  | | | | |   (62)   ~ (e3 = e2)
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | REDUCE: (27), (61) imply:
% 203.53/34.44  | | | | |   (63)  op(e2, e2) = all_52_22
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_6, e1, e1,
% 203.53/34.44  | | | | |              simplifying with (36), (52) gives:
% 203.53/34.44  | | | | |   (64)  all_52_6 = all_10_2
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | GROUND_INST: instantiating (3) with all_4_2, all_52_22, e2, e2,
% 203.53/34.44  | | | | |              simplifying with (13), (63) gives:
% 203.53/34.44  | | | | |   (65)  all_52_22 = all_4_2
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | BETA: splitting (35) gives:
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | Case 1:
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | |   (66)  all_56_1 = e3
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | | REF_CLOSE: (32), (41), (66) are inconsistent by sub-proof #1326.
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | Case 2:
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | |   (67)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | | BETA: splitting (29) gives:
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | | Case 1:
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | |   (68)  all_58_9 = e2
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | | COMBINE_EQS: (12), (68) imply:
% 203.53/34.44  | | | | | | |   (69)  all_52_25 = e2
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | | REDUCE: (26), (69) imply:
% 203.53/34.44  | | | | | | |   (70)   ~ (all_52_9 = e2)
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | | REF_CLOSE: (3), (4), (17), (24), (32), (36), (37), (48), (67),
% 203.53/34.44  | | | | | | |            (70) are inconsistent by sub-proof #896.
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | Case 2:
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | |   (71)   ~ (all_58_9 = e2)
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | | REDUCE: (12), (71) imply:
% 203.53/34.44  | | | | | | |   (72)   ~ (all_52_25 = e2)
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | | REF_CLOSE: (3), (4), (12), (13), (20), (21), (22), (34), (37),
% 203.53/34.44  | | | | | | |            (44), (47), (72) are inconsistent by sub-proof #575.
% 203.53/34.44  | | | | | | | 
% 203.53/34.44  | | | | | | End of split
% 203.53/34.44  | | | | | | 
% 203.53/34.44  | | | | | End of split
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | Case 2:
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | |   (73)  all_58_15 = e2
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | | REF_CLOSE: (16), (22), (73) are inconsistent by sub-proof #1223.
% 203.53/34.44  | | | | | 
% 203.53/34.44  | | | | End of split
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | End of split
% 203.53/34.44  | | | 
% 203.53/34.44  | | End of split
% 203.53/34.44  | | 
% 203.53/34.44  | Case 2:
% 203.53/34.44  | | 
% 203.53/34.44  | |   (74)  all_58_14 = e3 | all_58_15 = e3
% 203.53/34.44  | | 
% 203.53/34.44  | | REF_CLOSE: (2), (5), (16), (23), (74) are inconsistent by sub-proof #983.
% 203.53/34.44  | | 
% 203.53/34.44  | End of split
% 203.53/34.44  | 
% 203.53/34.44  End of proof
% 203.53/34.44  
% 203.53/34.44  Sub-proof #575 shows that the following formulas are inconsistent:
% 203.53/34.44  ----------------------------------------------------------------
% 203.53/34.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.44    (2)  all_58_1 = all_52_9
% 203.53/34.44    (3)   ~ (all_4_2 = e3)
% 203.53/34.44    (4)  all_58_9 = all_52_25
% 203.53/34.44    (5)  op(e2, e2) = all_4_2
% 203.53/34.44    (6)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.44    (7)  all_58_4 = e3
% 203.53/34.44    (8)   ~ (e2 = e0)
% 203.53/34.44    (9)  all_58_0 = e0
% 203.53/34.44    (10)   ~ (all_52_25 = e2)
% 203.53/34.44    (11)   ~ (e3 = e2)
% 203.53/34.44    (12)  op(all_52_9, all_52_9) = e3
% 203.53/34.44  
% 203.53/34.44  Begin of proof
% 203.53/34.44  | 
% 203.53/34.44  | BETA: splitting (6) gives:
% 203.53/34.44  | 
% 203.53/34.44  | Case 1:
% 203.53/34.44  | | 
% 203.53/34.44  | |   (13)  all_58_0 = e2
% 203.53/34.44  | | 
% 203.53/34.44  | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #812.
% 203.53/34.44  | | 
% 203.53/34.44  | Case 2:
% 203.53/34.44  | | 
% 203.53/34.44  | |   (14)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.44  | | 
% 203.53/34.44  | | BETA: splitting (14) gives:
% 203.53/34.44  | | 
% 203.53/34.44  | | Case 1:
% 203.53/34.44  | | | 
% 203.53/34.44  | | |   (15)  all_58_1 = e2
% 203.53/34.44  | | | 
% 203.53/34.44  | | | COMBINE_EQS: (2), (15) imply:
% 203.53/34.44  | | |   (16)  all_52_9 = e2
% 203.53/34.44  | | | 
% 203.53/34.44  | | | REDUCE: (12), (16) imply:
% 203.53/34.44  | | |   (17)  op(e2, e2) = e3
% 203.53/34.44  | | | 
% 203.53/34.44  | | | REF_CLOSE: (1), (3), (5), (17) are inconsistent by sub-proof #1318.
% 203.53/34.44  | | | 
% 203.53/34.44  | | Case 2:
% 203.53/34.44  | | | 
% 203.53/34.44  | | |   (18)  all_58_4 = e2 | all_58_9 = e2
% 203.53/34.44  | | | 
% 203.53/34.44  | | | BETA: splitting (18) gives:
% 203.53/34.44  | | | 
% 203.53/34.44  | | | Case 1:
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | |   (19)  all_58_4 = e2
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | COMBINE_EQS: (7), (19) imply:
% 203.53/34.44  | | | |   (20)  e3 = e2
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | REDUCE: (11), (20) imply:
% 203.53/34.44  | | | |   (21)  $false
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | CLOSE: (21) is inconsistent.
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | Case 2:
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | |   (22)  all_58_9 = e2
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | COMBINE_EQS: (4), (22) imply:
% 203.53/34.44  | | | |   (23)  all_52_25 = e2
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | REDUCE: (10), (23) imply:
% 203.53/34.44  | | | |   (24)  $false
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | | CLOSE: (24) is inconsistent.
% 203.53/34.44  | | | | 
% 203.53/34.44  | | | End of split
% 203.53/34.44  | | | 
% 203.53/34.44  | | End of split
% 203.53/34.44  | | 
% 203.53/34.44  | End of split
% 203.53/34.44  | 
% 203.53/34.44  End of proof
% 203.53/34.44  
% 203.53/34.44  Sub-proof #576 shows that the following formulas are inconsistent:
% 203.53/34.44  ----------------------------------------------------------------
% 203.53/34.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.44    (2)   ~ (all_4_2 = e3)
% 203.53/34.44    (3)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.44    (4)  op(all_6_2, e3) = e1
% 203.53/34.44    (5)  op(all_52_27, all_52_27) = all_52_26
% 203.53/34.44    (6)  op(e1, e3) = all_52_5
% 203.53/34.44    (7)  all_58_10 = all_52_27
% 203.53/34.44    (8)   ~ (all_52_19 = e3)
% 203.53/34.44    (9)   ~ (all_52_5 = all_6_2)
% 203.53/34.44    (10)  op(e3, e3) = all_6_2
% 203.53/34.44    (11)  op(e3, e3) = e1
% 203.53/34.44    (12)  all_58_5 = all_52_19
% 203.53/34.44    (13)  all_58_3 = all_4_2
% 203.53/34.44  
% 203.53/34.44  Begin of proof
% 203.53/34.44  | 
% 203.53/34.44  | BETA: splitting (3) gives:
% 203.53/34.44  | 
% 203.53/34.44  | Case 1:
% 203.53/34.44  | | 
% 203.53/34.44  | |   (14)  all_58_3 = e3
% 203.53/34.44  | | 
% 203.53/34.44  | | COMBINE_EQS: (13), (14) imply:
% 203.53/34.44  | |   (15)  all_4_2 = e3
% 203.53/34.44  | | 
% 203.53/34.44  | | REDUCE: (2), (15) imply:
% 203.53/34.44  | |   (16)  $false
% 203.53/34.44  | | 
% 203.53/34.44  | | CLOSE: (16) is inconsistent.
% 203.53/34.44  | | 
% 203.53/34.44  | Case 2:
% 203.53/34.44  | | 
% 203.53/34.44  | |   (17)  all_58_5 = e3 | all_58_10 = e3
% 203.53/34.44  | | 
% 203.53/34.44  | | BETA: splitting (17) gives:
% 203.53/34.44  | | 
% 203.53/34.44  | | Case 1:
% 203.53/34.44  | | | 
% 203.53/34.44  | | |   (18)  all_58_5 = e3
% 203.53/34.44  | | | 
% 203.53/34.44  | | | REF_CLOSE: (8), (12), (18) are inconsistent by sub-proof #1279.
% 203.53/34.44  | | | 
% 203.53/34.44  | | Case 2:
% 203.53/34.44  | | | 
% 203.53/34.44  | | |   (19)  all_58_10 = e3
% 203.53/34.44  | | | 
% 203.53/34.44  | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (19) are inconsistent
% 203.53/34.44  | | |            by sub-proof #577.
% 203.53/34.44  | | | 
% 203.53/34.44  | | End of split
% 203.53/34.44  | | 
% 203.53/34.44  | End of split
% 203.53/34.44  | 
% 203.53/34.44  End of proof
% 203.53/34.44  
% 203.53/34.44  Sub-proof #577 shows that the following formulas are inconsistent:
% 203.53/34.44  ----------------------------------------------------------------
% 203.53/34.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.44    (2)  op(all_6_2, e3) = e1
% 203.53/34.44    (3)  op(all_52_27, all_52_27) = all_52_26
% 203.53/34.44    (4)  op(e1, e3) = all_52_5
% 203.53/34.44    (5)  all_58_10 = all_52_27
% 203.53/34.44    (6)   ~ (all_52_5 = all_6_2)
% 203.53/34.44    (7)  all_58_10 = e3
% 203.53/34.44    (8)  op(e3, e3) = all_6_2
% 203.53/34.44    (9)  op(e3, e3) = e1
% 203.53/34.44  
% 203.53/34.44  Begin of proof
% 203.53/34.44  | 
% 203.53/34.44  | COMBINE_EQS: (5), (7) imply:
% 203.53/34.44  |   (10)  all_52_27 = e3
% 203.53/34.44  | 
% 203.53/34.44  | SIMP: (10) implies:
% 203.53/34.44  |   (11)  all_52_27 = e3
% 203.53/34.44  | 
% 203.53/34.44  | REDUCE: (3), (11) imply:
% 203.53/34.44  |   (12)  op(e3, e3) = all_52_26
% 203.53/34.44  | 
% 203.53/34.44  | GROUND_INST: instantiating (1) with all_6_2, all_52_26, e3, e3, simplifying
% 203.53/34.44  |              with (8), (12) gives:
% 203.53/34.44  |   (13)  all_52_26 = all_6_2
% 203.53/34.44  | 
% 203.53/34.44  | GROUND_INST: instantiating (1) with e1, all_52_26, e3, e3, simplifying with
% 203.53/34.44  |              (9), (12) gives:
% 203.53/34.44  |   (14)  all_52_26 = e1
% 203.53/34.44  | 
% 203.53/34.44  | COMBINE_EQS: (13), (14) imply:
% 203.53/34.44  |   (15)  all_6_2 = e1
% 203.53/34.44  | 
% 203.53/34.44  | SIMP: (15) implies:
% 203.53/34.44  |   (16)  all_6_2 = e1
% 203.53/34.44  | 
% 203.53/34.44  | REF_CLOSE: (1), (2), (4), (6), (16) are inconsistent by sub-proof #578.
% 203.53/34.44  | 
% 203.53/34.44  End of proof
% 203.53/34.44  
% 203.53/34.44  Sub-proof #578 shows that the following formulas are inconsistent:
% 203.53/34.44  ----------------------------------------------------------------
% 203.53/34.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.44    (2)  op(all_6_2, e3) = e1
% 203.53/34.44    (3)  op(e1, e3) = all_52_5
% 203.53/34.44    (4)   ~ (all_52_5 = all_6_2)
% 203.53/34.44    (5)  all_6_2 = e1
% 203.53/34.44  
% 203.53/34.44  Begin of proof
% 203.53/34.44  | 
% 203.53/34.44  | REDUCE: (4), (5) imply:
% 203.53/34.44  |   (6)   ~ (all_52_5 = e1)
% 203.53/34.44  | 
% 203.53/34.44  | REDUCE: (2), (5) imply:
% 203.53/34.44  |   (7)  op(e1, e3) = e1
% 203.53/34.44  | 
% 203.53/34.44  | GROUND_INST: instantiating (1) with all_52_5, e1, e3, e1, simplifying with
% 203.53/34.44  |              (3), (7) gives:
% 203.53/34.44  |   (8)  all_52_5 = e1
% 203.53/34.44  | 
% 203.53/34.44  | REDUCE: (6), (8) imply:
% 203.53/34.44  |   (9)  $false
% 203.53/34.44  | 
% 203.53/34.44  | CLOSE: (9) is inconsistent.
% 203.53/34.44  | 
% 203.53/34.44  End of proof
% 203.53/34.44  
% 203.53/34.44  Sub-proof #579 shows that the following formulas are inconsistent:
% 203.53/34.44  ----------------------------------------------------------------
% 203.53/34.44    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.53/34.44    (2)  all_58_14 = all_52_23
% 203.53/34.44    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.53/34.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.53/34.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.53/34.44    (5)   ~ (all_52_5 = all_52_13)
% 203.53/34.44    (6)  op(all_52_7, all_52_7) = e0
% 203.53/34.44    (7)  all_58_1 = all_52_9
% 203.53/34.44    (8)   ~ (all_52_9 = all_52_13)
% 203.53/34.44    (9)  op(all_52_5, all_52_5) = e1
% 203.53/34.44    (10)   ~ (e3 = e0)
% 203.53/34.44    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.53/34.44    (12)   ~ (all_52_3 = all_52_19)
% 203.53/34.44    (13)   ~ (all_52_17 = all_52_25)
% 203.53/34.44    (14)   ~ (all_52_3 = all_6_2)
% 203.53/34.44    (15)  all_58_0 = all_6_2
% 203.53/34.44    (16)  op(all_14_2, e0) = all_14_1
% 203.53/34.44    (17)  all_56_4 = all_52_3
% 203.53/34.44    (18)   ~ (all_52_17 = all_10_2)
% 203.53/34.44    (19)   ~ (all_52_27 = all_52_29)
% 203.53/34.44    (20)  all_58_13 = all_52_15
% 203.53/34.44    (21)  op(all_10_2, all_10_2) = all_52_20
% 203.53/34.44    (22)  all_58_9 = all_52_25
% 203.53/34.44    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.53/34.44    (24)   ~ (all_52_29 = all_14_2)
% 203.53/34.44    (25)   ~ (all_52_15 = e3)
% 203.53/34.44    (26)  op(e2, all_4_1) = e3
% 203.53/34.44    (27)  op(e2, e2) = all_4_2
% 203.53/34.44    (28)  all_58_11 = all_52_29
% 203.53/34.44    (29)  all_56_5 = all_4_2
% 203.53/34.44    (30)   ~ (all_52_25 = all_14_2)
% 203.53/34.44    (31)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.53/34.44    (32)   ~ (all_52_3 = all_52_27)
% 203.53/34.44    (33)  op(all_10_2, e1) = all_10_1
% 203.53/34.44    (34)   ~ (all_52_7 = all_6_2)
% 203.53/34.44    (35)  op(e0, e0) = all_14_2
% 203.53/34.44    (36)  all_56_15 = all_14_2
% 203.53/34.44    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.53/34.44    (38)   ~ (all_4_1 = e1)
% 203.53/34.44    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.53/34.44    (40)  all_56_9 = all_52_13
% 203.53/34.44    (41)   ~ (e2 = e1)
% 203.53/34.44    (42)   ~ (all_52_13 = all_10_2)
% 203.53/34.44    (43)   ~ (all_6_0 = e1)
% 203.53/34.44    (44)  all_58_10 = all_52_27
% 203.53/34.44    (45)  all_56_8 = all_52_5
% 203.53/34.44    (46)  op(all_52_9, all_52_9) = all_52_8
% 203.53/34.44    (47)   ~ (all_52_19 = all_52_23)
% 203.53/34.44    (48)   ~ (all_52_25 = all_52_29)
% 203.53/34.44    (49)  all_58_7 = all_52_13
% 203.53/34.44    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.53/34.44    (51)  op(all_6_2, all_6_2) = e3
% 203.53/34.44    (52)  all_58_12 = all_52_7
% 203.53/34.44    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.53/34.44    (54)   ~ (all_52_7 = all_14_2)
% 203.53/34.44    (55)   ~ (all_14_2 = e0)
% 203.53/34.44    (56)  all_58_2 = all_52_3
% 203.53/34.44    (57)  all_56_2 = all_52_17
% 203.53/34.44    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.53/34.44    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.53/34.44    (60)  op(e3, all_6_1) = all_6_0
% 203.53/34.44    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.53/34.44    (62)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.53/34.44    (63)   ~ (e2 = e0)
% 203.53/34.44    (64)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.53/34.44    (65)  op(all_4_2, e2) = all_4_1
% 203.53/34.44    (66)  op(all_52_3, all_52_3) = e2
% 203.53/34.44    (67)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.53/34.44    (68)   ~ (all_52_13 = all_4_2)
% 203.53/34.44    (69)  op(e0, e3) = all_52_7
% 203.53/34.44    (70)   ~ (all_52_9 = all_52_25)
% 203.53/34.44    (71)  all_58_15 = all_14_2
% 203.53/34.44    (72)   ~ (all_52_19 = all_10_2)
% 203.53/34.44    (73)  op(all_52_23, all_52_23) = all_52_22
% 203.53/34.44    (74)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.53/34.44    (75)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.53/34.44    (76)  all_58_8 = all_10_2
% 203.53/34.44    (77)   ~ (all_52_5 = all_10_2)
% 203.53/34.44    (78)  all_56_12 = all_52_7
% 203.53/34.44    (79)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.53/34.44    (80)   ~ (all_52_9 = all_4_2)
% 203.53/34.44    (81)   ~ (all_52_5 = all_6_2)
% 203.53/34.44    (82)   ~ (all_52_9 = all_6_2)
% 203.53/34.44    (83)  op(e3, e3) = all_6_2
% 203.53/34.44    (84)   ~ (all_52_27 = all_14_2)
% 203.53/34.44    (85)  op(e0, all_14_1) = e2
% 203.53/34.44    (86)   ~ (all_52_3 = all_52_7)
% 203.53/34.44    (87)  op(all_14_2, all_14_2) = all_52_30
% 203.53/34.44    (88)  all_58_5 = all_52_19
% 203.53/34.44    (89)  all_56_1 = all_52_9
% 203.53/34.44    (90)  all_58_6 = all_52_5
% 203.53/34.44    (91)  op(e3, e2) = all_52_9
% 203.53/34.44    (92)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.53/34.44    (93)   ~ (all_52_17 = all_6_2)
% 203.53/34.44    (94)  op(e2, e0) = all_52_27
% 203.53/34.44    (95)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.53/34.44    (96)   ~ (all_52_9 = all_52_17)
% 203.53/34.44    (97)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.53/34.44    (98)  op(e1, e1) = all_10_2
% 203.53/34.44    (99)   ~ (all_52_23 = all_10_2)
% 203.53/34.44    (100)   ~ (all_52_7 = all_52_23)
% 203.53/34.44    (101)  all_58_3 = all_4_2
% 203.53/34.44    (102)   ~ (all_52_3 = all_4_2)
% 203.53/34.44    (103)   ~ (all_52_17 = all_52_23)
% 203.53/34.44    (104)  op(all_6_2, e3) = all_6_1
% 203.53/34.44    (105)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.53/34.44    (106)   ~ (all_52_13 = all_52_29)
% 203.53/34.44    (107)  all_58_4 = all_52_17
% 203.53/34.44    (108)   ~ (all_14_2 = e3)
% 203.53/34.44  
% 203.53/34.44  Begin of proof
% 203.53/34.44  | 
% 203.53/34.44  | BETA: splitting (92) gives:
% 203.53/34.44  | 
% 203.53/34.44  | Case 1:
% 203.53/34.44  | | 
% 203.53/34.44  | |   (109)  all_58_12 = e3
% 203.53/34.44  | | 
% 203.53/34.44  | | COMBINE_EQS: (52), (109) imply:
% 203.53/34.44  | |   (110)  all_52_7 = e3
% 203.53/34.44  | | 
% 203.53/34.44  | | REF_CLOSE: (4), (6), (9), (15), (27), (34), (35), (37), (51), (52), (54),
% 203.53/34.44  | |            (56), (59), (66), (77), (83), (90), (92), (98), (102), (110) are
% 203.53/34.44  | |            inconsistent by sub-proof #1361.
% 203.53/34.44  | | 
% 203.53/34.44  | Case 2:
% 203.53/34.44  | | 
% 203.62/34.44  | |   (111)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.44  | | 
% 203.62/34.44  | | BETA: splitting (111) gives:
% 203.62/34.44  | | 
% 203.62/34.44  | | Case 1:
% 203.62/34.44  | | | 
% 203.62/34.44  | | |   (112)  all_58_13 = e3
% 203.62/34.44  | | | 
% 203.62/34.44  | | | REF_CLOSE: (20), (25), (112) are inconsistent by sub-proof #1360.
% 203.62/34.44  | | | 
% 203.62/34.44  | | Case 2:
% 203.62/34.44  | | | 
% 203.62/34.44  | | |   (113)  all_58_14 = e3 | all_58_15 = e3
% 203.62/34.44  | | | 
% 203.62/34.44  | | | BETA: splitting (113) gives:
% 203.62/34.44  | | | 
% 203.62/34.44  | | | Case 1:
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | |   (114)  all_58_14 = e3
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | COMBINE_EQS: (2), (114) imply:
% 203.62/34.44  | | | |   (115)  all_52_23 = e3
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | SIMP: (115) implies:
% 203.62/34.44  | | | |   (116)  all_52_23 = e3
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | REDUCE: (100), (116) imply:
% 203.62/34.44  | | | |   (117)   ~ (all_52_7 = e3)
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | REDUCE: (103), (116) imply:
% 203.62/34.44  | | | |   (118)   ~ (all_52_17 = e3)
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | REDUCE: (47), (116) imply:
% 203.62/34.44  | | | |   (119)   ~ (all_52_19 = e3)
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | REDUCE: (99), (116) imply:
% 203.62/34.44  | | | |   (120)   ~ (all_10_2 = e3)
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | SIMP: (120) implies:
% 203.62/34.44  | | | |   (121)   ~ (all_10_2 = e3)
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | REDUCE: (73), (116) imply:
% 203.62/34.44  | | | |   (122)  op(e3, e3) = all_52_22
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_22, e3, e3,
% 203.62/34.44  | | | |              simplifying with (83), (122) gives:
% 203.62/34.44  | | | |   (123)  all_52_22 = all_6_2
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | BETA: splitting (11) gives:
% 203.62/34.44  | | | | 
% 203.62/34.44  | | | | Case 1:
% 203.62/34.44  | | | | | 
% 203.62/34.44  | | | | |   (124)  all_56_12 = e3
% 203.62/34.44  | | | | | 
% 203.62/34.44  | | | | | REF_CLOSE: (78), (117), (124) are inconsistent by sub-proof #1383.
% 203.62/34.44  | | | | | 
% 203.62/34.44  | | | | Case 2:
% 203.62/34.44  | | | | | 
% 203.62/34.44  | | | | |   (125)   ~ (all_56_12 = e3)
% 203.62/34.44  | | | | |   (126)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.44  | | | | | 
% 203.62/34.44  | | | | | BETA: splitting (39) gives:
% 203.62/34.44  | | | | | 
% 203.62/34.44  | | | | | Case 1:
% 203.62/34.44  | | | | | | 
% 203.62/34.44  | | | | | |   (127)  all_56_2 = e3
% 203.62/34.44  | | | | | | 
% 203.62/34.44  | | | | | | REF_CLOSE: (57), (118), (127) are inconsistent by sub-proof #1327.
% 203.62/34.44  | | | | | | 
% 203.62/34.44  | | | | | Case 2:
% 203.62/34.44  | | | | | | 
% 203.62/34.44  | | | | | |   (128)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.44  | | | | | | 
% 203.62/34.44  | | | | | | BETA: splitting (59) gives:
% 203.62/34.44  | | | | | | 
% 203.62/34.44  | | | | | | Case 1:
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | |   (129)  all_58_0 = e3
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | COMBINE_EQS: (15), (129) imply:
% 203.62/34.44  | | | | | | |   (130)  all_6_2 = e3
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (14), (130) imply:
% 203.62/34.44  | | | | | | |   (131)   ~ (all_52_3 = e3)
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (81), (130) imply:
% 203.62/34.44  | | | | | | |   (132)   ~ (all_52_5 = e3)
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (82), (130) imply:
% 203.62/34.44  | | | | | | |   (133)   ~ (all_52_9 = e3)
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (104), (130) imply:
% 203.62/34.44  | | | | | | |   (134)  op(e3, e3) = all_6_1
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (83), (130) imply:
% 203.62/34.44  | | | | | | |   (135)  op(e3, e3) = e3
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | GROUND_INST: instantiating (4) with e3, all_6_1, e3, e3,
% 203.62/34.44  | | | | | | |              simplifying with (134), (135) gives:
% 203.62/34.44  | | | | | | |   (136)  all_6_1 = e3
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (60), (136) imply:
% 203.62/34.44  | | | | | | |   (137)  op(e3, e3) = all_6_0
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | GROUND_INST: instantiating (4) with e3, all_6_0, e3, e3,
% 203.62/34.44  | | | | | | |              simplifying with (135), (137) gives:
% 203.62/34.44  | | | | | | |   (138)  all_6_0 = e3
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | REDUCE: (43), (138) imply:
% 203.62/34.44  | | | | | | |   (139)   ~ (e3 = e1)
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | BETA: splitting (37) gives:
% 203.62/34.44  | | | | | | | 
% 203.62/34.44  | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | 
% 203.62/34.44  | | | | | | | |   (140)  all_58_2 = e3
% 203.62/34.44  | | | | | | | | 
% 203.62/34.44  | | | | | | | | REF_CLOSE: (56), (131), (140) are inconsistent by sub-proof
% 203.62/34.44  | | | | | | | |            #1369.
% 203.62/34.44  | | | | | | | | 
% 203.62/34.44  | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | 
% 203.62/34.44  | | | | | | | |   (141)   ~ (all_58_2 = e3)
% 203.62/34.44  | | | | | | | |   (142)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.44  | | | | | | | | 
% 203.62/34.44  | | | | | | | | BETA: splitting (53) gives:
% 203.62/34.44  | | | | | | | | 
% 203.62/34.44  | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | 
% 203.62/34.44  | | | | | | | | |   (143)  all_58_6 = e3
% 203.62/34.44  | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | REF_CLOSE: (90), (132), (143) are inconsistent by sub-proof
% 203.62/34.44  | | | | | | | | |            #1328.
% 203.62/34.44  | | | | | | | | | 
% 203.62/34.44  | | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | | 
% 203.62/34.44  | | | | | | | | |   (144)   ~ (all_58_6 = e3)
% 203.62/34.44  | | | | | | | | |   (145)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.44  | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | BETA: splitting (74) gives:
% 203.62/34.44  | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | |   (146)  all_56_8 = e3
% 203.62/34.44  | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | REF_CLOSE: (45), (132), (146) are inconsistent by sub-proof
% 203.62/34.44  | | | | | | | | | |            #1325.
% 203.62/34.44  | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | |   (147)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.44  | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | BETA: splitting (95) gives:
% 203.62/34.44  | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | |   (148)  all_56_1 = e3
% 203.62/34.44  | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | REF_CLOSE: (89), (133), (148) are inconsistent by sub-proof
% 203.62/34.44  | | | | | | | | | | |            #1326.
% 203.62/34.44  | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | |   (149)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.44  | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | BETA: splitting (62) gives:
% 203.62/34.44  | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | |   (150)  all_56_4 = e3
% 203.62/34.44  | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | REF_CLOSE: (17), (131), (150) are inconsistent by sub-proof
% 203.62/34.44  | | | | | | | | | | | |            #1340.
% 203.62/34.44  | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | |   (151)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.44  | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | BETA: splitting (64) gives:
% 203.62/34.44  | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | |   (152)  all_56_5 = e3
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12),
% 203.62/34.44  | | | | | | | | | | | | |            (13), (17), (22), (23), (26), (27), (28), (29),
% 203.62/34.44  | | | | | | | | | | | | |            (31), (32), (35), (38), (40), (42), (44), (45),
% 203.62/34.44  | | | | | | | | | | | | |            (46), (48), (49), (50), (52), (54), (56), (57),
% 203.62/34.44  | | | | | | | | | | | | |            (65), (66), (68), (70), (76), (77), (78), (86),
% 203.62/34.44  | | | | | | | | | | | | |            (88), (89), (90), (91), (96), (97), (102), (105),
% 203.62/34.44  | | | | | | | | | | | | |            (106), (107), (114), (118), (121), (126), (128),
% 203.62/34.44  | | | | | | | | | | | | |            (145), (147), (149), (151), (152) are inconsistent
% 203.62/34.44  | | | | | | | | | | | | |            by sub-proof #703.
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | |   (153)   ~ (all_56_5 = e3)
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | REDUCE: (29), (153) imply:
% 203.62/34.44  | | | | | | | | | | | | |   (154)   ~ (all_4_2 = e3)
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | BETA: splitting (142) gives:
% 203.62/34.44  | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | |   (155)  all_58_3 = e3
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | COMBINE_EQS: (101), (155) imply:
% 203.62/34.44  | | | | | | | | | | | | | |   (156)  all_4_2 = e3
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | REDUCE: (154), (156) imply:
% 203.62/34.44  | | | | | | | | | | | | | |   (157)  $false
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | Case 2:
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | |   (158)  all_58_5 = e3 | all_58_10 = e3
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 203.62/34.44  | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | Case 1:
% 203.62/34.44  | | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | |   (159)  all_58_5 = e3
% 203.62/34.44  | | | | | | | | | | | | | | | 
% 203.62/34.44  | | | | | | | | | | | | | | | REF_CLOSE: (88), (119), (159) are inconsistent by sub-proof
% 203.62/34.45  | | | | | | | | | | | | | | |            #1279.
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | Case 2:
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | |   (160)  all_58_10 = e3
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | COMBINE_EQS: (44), (160) imply:
% 203.62/34.45  | | | | | | | | | | | | | | |   (161)  all_52_27 = e3
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | SIMP: (161) implies:
% 203.62/34.45  | | | | | | | | | | | | | | |   (162)  all_52_27 = e3
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | REDUCE: (19), (162) imply:
% 203.62/34.45  | | | | | | | | | | | | | | |   (163)   ~ (all_52_29 = e3)
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | SIMP: (163) implies:
% 203.62/34.45  | | | | | | | | | | | | | | |   (164)   ~ (all_52_29 = e3)
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | REDUCE: (84), (162) imply:
% 203.62/34.45  | | | | | | | | | | | | | | |   (165)   ~ (all_14_2 = e3)
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | REDUCE: (94), (162) imply:
% 203.62/34.45  | | | | | | | | | | | | | | |   (166)  op(e2, e0) = e3
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (9), (10), (16), (18), (21), (22),
% 203.62/34.45  | | | | | | | | | | | | | | |            (24), (28), (30), (33), (36), (41), (42), (49),
% 203.62/34.45  | | | | | | | | | | | | | | |            (52), (54), (55), (56), (58), (61), (63), (66),
% 203.62/34.45  | | | | | | | | | | | | | | |            (67), (68), (69), (72), (75), (76), (77), (79),
% 203.62/34.45  | | | | | | | | | | | | | | |            (80), (85), (87), (88), (90), (98), (101), (105),
% 203.62/34.45  | | | | | | | | | | | | | | |            (107), (108), (121), (129), (139), (145), (160),
% 203.62/34.45  | | | | | | | | | | | | | | |            (164), (166) are inconsistent by sub-proof #580.
% 203.62/34.45  | | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | End of split
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | End of split
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | Case 2:
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | |   (167)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | | REF_CLOSE: (4), (9), (27), (37), (51), (52), (56), (66), (77),
% 203.62/34.45  | | | | | | |            (83), (90), (98), (102), (117), (167) are inconsistent
% 203.62/34.45  | | | | | | |            by sub-proof #1364.
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | End of split
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | End of split
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | End of split
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | Case 2:
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | |   (168)  all_58_15 = e3
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | COMBINE_EQS: (71), (168) imply:
% 203.62/34.45  | | | |   (169)  all_14_2 = e3
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | REDUCE: (108), (169) imply:
% 203.62/34.45  | | | |   (170)  $false
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | CLOSE: (170) is inconsistent.
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | End of split
% 203.62/34.45  | | | 
% 203.62/34.45  | | End of split
% 203.62/34.45  | | 
% 203.62/34.45  | End of split
% 203.62/34.45  | 
% 203.62/34.45  End of proof
% 203.62/34.45  
% 203.62/34.45  Sub-proof #580 shows that the following formulas are inconsistent:
% 203.62/34.45  ----------------------------------------------------------------
% 203.62/34.45    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.45    (2)   ~ (e3 = e1)
% 203.62/34.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.45    (4)  all_58_1 = all_52_9
% 203.62/34.45    (5)  op(all_52_5, all_52_5) = e1
% 203.62/34.45    (6)   ~ (e3 = e0)
% 203.62/34.45    (7)  op(all_14_2, e0) = all_14_1
% 203.62/34.45    (8)   ~ (all_52_17 = all_10_2)
% 203.62/34.45    (9)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.45    (10)  all_58_9 = all_52_25
% 203.62/34.45    (11)   ~ (all_52_29 = all_14_2)
% 203.62/34.45    (12)  all_58_11 = all_52_29
% 203.62/34.45    (13)   ~ (all_52_25 = all_14_2)
% 203.62/34.45    (14)  op(all_10_2, e1) = all_10_1
% 203.62/34.45    (15)  all_56_15 = all_14_2
% 203.62/34.45    (16)   ~ (e2 = e1)
% 203.62/34.45    (17)   ~ (all_52_13 = all_10_2)
% 203.62/34.45    (18)  all_58_7 = all_52_13
% 203.62/34.45    (19)  all_58_12 = all_52_7
% 203.62/34.45    (20)   ~ (all_52_7 = all_14_2)
% 203.62/34.45    (21)   ~ (all_14_2 = e0)
% 203.62/34.45    (22)  all_58_2 = all_52_3
% 203.62/34.45    (23)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.45    (24)   ~ (all_52_29 = e3)
% 203.62/34.45    (25)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.45    (26)   ~ (e2 = e0)
% 203.62/34.45    (27)  op(all_52_3, all_52_3) = e2
% 203.62/34.45    (28)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.45    (29)   ~ (all_10_2 = e3)
% 203.62/34.45    (30)   ~ (all_52_13 = all_4_2)
% 203.62/34.45    (31)  all_58_0 = e3
% 203.62/34.45    (32)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.45    (33)  op(e0, e3) = all_52_7
% 203.62/34.45    (34)   ~ (all_52_19 = all_10_2)
% 203.62/34.45    (35)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.45    (36)  all_58_8 = all_10_2
% 203.62/34.45    (37)   ~ (all_52_5 = all_10_2)
% 203.62/34.45    (38)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.45    (39)   ~ (all_52_9 = all_4_2)
% 203.62/34.45    (40)  all_58_10 = e3
% 203.62/34.45    (41)  op(e2, e0) = e3
% 203.62/34.45    (42)  op(e0, all_14_1) = e2
% 203.62/34.45    (43)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.45    (44)  all_58_5 = all_52_19
% 203.62/34.45    (45)  all_58_6 = all_52_5
% 203.62/34.45    (46)  op(e1, e1) = all_10_2
% 203.62/34.45    (47)  all_58_3 = all_4_2
% 203.62/34.45    (48)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.62/34.45    (49)  all_58_4 = all_52_17
% 203.62/34.45    (50)   ~ (all_14_2 = e3)
% 203.62/34.45  
% 203.62/34.45  Begin of proof
% 203.62/34.45  | 
% 203.62/34.45  | BETA: splitting (32) gives:
% 203.62/34.45  | 
% 203.62/34.45  | Case 1:
% 203.62/34.45  | | 
% 203.62/34.45  | |   (51)  all_58_7 = e3
% 203.62/34.45  | | 
% 203.62/34.45  | | COMBINE_EQS: (18), (51) imply:
% 203.62/34.45  | |   (52)  all_52_13 = e3
% 203.62/34.45  | | 
% 203.62/34.45  | | REDUCE: (17), (52) imply:
% 203.62/34.45  | |   (53)   ~ (all_10_2 = e3)
% 203.62/34.45  | | 
% 203.62/34.45  | | REDUCE: (30), (52) imply:
% 203.62/34.45  | |   (54)   ~ (all_4_2 = e3)
% 203.62/34.45  | | 
% 203.62/34.45  | | SIMP: (54) implies:
% 203.62/34.45  | |   (55)   ~ (all_4_2 = e3)
% 203.62/34.45  | | 
% 203.62/34.45  | | BETA: splitting (28) gives:
% 203.62/34.45  | | 
% 203.62/34.45  | | Case 1:
% 203.62/34.45  | | | 
% 203.62/34.45  | | |   (56)  all_58_12 = e1
% 203.62/34.45  | | | 
% 203.62/34.45  | | | COMBINE_EQS: (19), (56) imply:
% 203.62/34.45  | | |   (57)  all_52_7 = e1
% 203.62/34.45  | | | 
% 203.62/34.45  | | | SIMP: (57) implies:
% 203.62/34.45  | | |   (58)  all_52_7 = e1
% 203.62/34.45  | | | 
% 203.62/34.45  | | | REDUCE: (20), (58) imply:
% 203.62/34.45  | | |   (59)   ~ (all_14_2 = e1)
% 203.62/34.45  | | | 
% 203.62/34.45  | | | SIMP: (59) implies:
% 203.62/34.45  | | |   (60)   ~ (all_14_2 = e1)
% 203.62/34.45  | | | 
% 203.62/34.45  | | | REDUCE: (33), (58) imply:
% 203.62/34.45  | | |   (61)  op(e0, e3) = e1
% 203.62/34.45  | | | 
% 203.62/34.45  | | | BETA: splitting (35) gives:
% 203.62/34.45  | | | 
% 203.62/34.45  | | | Case 1:
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | |   (62)  all_56_15 = e2
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | COMBINE_EQS: (15), (62) imply:
% 203.62/34.45  | | | |   (63)  all_14_2 = e2
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | SIMP: (63) implies:
% 203.62/34.45  | | | |   (64)  all_14_2 = e2
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | REDUCE: (7), (64) imply:
% 203.62/34.45  | | | |   (65)  op(e2, e0) = all_14_1
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | GROUND_INST: instantiating (3) with e3, all_14_1, e0, e2, simplifying
% 203.62/34.45  | | | |              with (41), (65) gives:
% 203.62/34.45  | | | |   (66)  all_14_1 = e3
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | REDUCE: (42), (66) imply:
% 203.62/34.45  | | | |   (67)  op(e0, e3) = e2
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | REF_CLOSE: (3), (16), (61), (67) are inconsistent by sub-proof #635.
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | Case 2:
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | |   (68)  all_56_15 = e1 | all_56_15 = e0
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | REF_CLOSE: (15), (21), (60), (68) are inconsistent by sub-proof #1161.
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | End of split
% 203.62/34.45  | | | 
% 203.62/34.45  | | Case 2:
% 203.62/34.45  | | | 
% 203.62/34.45  | | |   (69)   ~ (all_58_12 = e1)
% 203.62/34.45  | | | 
% 203.62/34.45  | | | REDUCE: (19), (69) imply:
% 203.62/34.45  | | |   (70)   ~ (all_52_7 = e1)
% 203.62/34.45  | | | 
% 203.62/34.45  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 203.62/34.45  | | |            (14), (15), (16), (19), (20), (22), (23), (25), (26), (27),
% 203.62/34.45  | | |            (29), (31), (34), (35), (36), (37), (38), (39), (40), (43),
% 203.62/34.45  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (55), (70) are
% 203.62/34.45  | | |            inconsistent by sub-proof #659.
% 203.62/34.45  | | | 
% 203.62/34.45  | | End of split
% 203.62/34.45  | | 
% 203.62/34.45  | Case 2:
% 203.62/34.45  | | 
% 203.62/34.45  | |   (71)  all_58_8 = e3 | all_58_11 = e3
% 203.62/34.45  | | 
% 203.62/34.45  | | REF_CLOSE: (12), (24), (29), (36), (71) are inconsistent by sub-proof #1140.
% 203.62/34.45  | | 
% 203.62/34.45  | End of split
% 203.62/34.45  | 
% 203.62/34.45  End of proof
% 203.62/34.45  
% 203.62/34.45  Sub-proof #581 shows that the following formulas are inconsistent:
% 203.62/34.45  ----------------------------------------------------------------
% 203.62/34.45    (1)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 203.62/34.45    (2)  all_58_14 = all_52_23
% 203.62/34.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.45    (4)  op(all_52_7, all_52_7) = e0
% 203.62/34.45    (5)  all_58_1 = all_52_9
% 203.62/34.45    (6)   ~ (all_52_9 = all_52_13)
% 203.62/34.45    (7)  op(all_52_5, all_52_5) = e1
% 203.62/34.45    (8)   ~ (e3 = e0)
% 203.62/34.45    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.45    (10)   ~ (all_52_3 = all_52_19)
% 203.62/34.45    (11)   ~ (all_4_2 = e3)
% 203.62/34.45    (12)   ~ (all_52_3 = all_6_2)
% 203.62/34.45    (13)  all_58_0 = all_6_2
% 203.62/34.45    (14)  op(all_14_2, e0) = all_14_1
% 203.62/34.45    (15)  all_56_4 = all_52_3
% 203.62/34.45    (16)  all_58_13 = e3
% 203.62/34.45    (17)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.45    (18)   ~ (all_52_27 = all_52_29)
% 203.62/34.45    (19)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.45    (20)  all_58_9 = all_52_25
% 203.62/34.45    (21)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.62/34.45    (22)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.45    (23)  op(e2, e2) = all_4_2
% 203.62/34.45    (24)  all_58_11 = all_52_29
% 203.62/34.45    (25)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.45    (26)   ~ (all_52_3 = all_52_27)
% 203.62/34.45    (27)  op(all_10_2, e1) = all_10_1
% 203.62/34.45    (28)   ~ (all_52_7 = all_6_2)
% 203.62/34.45    (29)  op(e0, e0) = all_14_2
% 203.62/34.45    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.45    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.45    (32)  op(e1, e0) = all_52_29
% 203.62/34.45    (33)  all_56_11 = all_52_29
% 203.62/34.45    (34)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.62/34.45    (35)  all_56_9 = all_52_13
% 203.62/34.45    (36)   ~ (e2 = e1)
% 203.62/34.45    (37)   ~ (all_52_13 = all_10_2)
% 203.62/34.45    (38)   ~ (all_6_0 = e1)
% 203.62/34.45    (39)  all_58_10 = all_52_27
% 203.62/34.45    (40)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.45    (41)   ~ (all_52_19 = all_52_23)
% 203.62/34.45    (42)   ~ (all_52_29 = all_10_2)
% 203.62/34.45    (43)  all_58_7 = all_52_13
% 203.62/34.45    (44)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.45    (45)  op(all_6_2, all_6_2) = e3
% 203.62/34.45    (46)   ~ (all_52_5 = all_52_7)
% 203.62/34.45    (47)  all_58_12 = all_52_7
% 203.62/34.45    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.45    (49)   ~ (all_52_7 = e3)
% 203.62/34.45    (50)   ~ (all_52_7 = all_14_2)
% 203.62/34.45    (51)  all_58_2 = all_52_3
% 203.62/34.45    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.45    (53)  op(e3, all_6_1) = all_6_0
% 203.62/34.45    (54)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.45    (55)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.45    (56)   ~ (e2 = e0)
% 203.62/34.45    (57)   ~ (all_52_23 = e3)
% 203.62/34.45    (58)  op(all_52_3, all_52_3) = e2
% 203.62/34.45    (59)   ~ (all_52_5 = all_52_29)
% 203.62/34.45    (60)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.45    (61)   ~ (all_52_19 = all_52_27)
% 203.62/34.45    (62)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.45    (63)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.45    (64)   ~ (all_6_0 = e2)
% 203.62/34.45    (65)   ~ (all_52_9 = e3)
% 203.62/34.45    (66)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.45    (67)   ~ (all_52_13 = all_4_2)
% 203.62/34.45    (68)  op(e3, e1) = all_52_17
% 203.62/34.45    (69)   ~ (all_52_9 = all_52_25)
% 203.62/34.45    (70)  all_58_15 = all_14_2
% 203.62/34.45    (71)   ~ (all_52_19 = all_10_2)
% 203.62/34.45    (72)  all_58_8 = all_10_2
% 203.62/34.45    (73)   ~ (all_52_5 = all_10_2)
% 203.62/34.45    (74)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.45    (75)  all_56_12 = all_52_7
% 203.62/34.45    (76)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.45    (77)   ~ (all_52_25 = all_6_2)
% 203.62/34.45    (78)   ~ (all_52_9 = all_4_2)
% 203.62/34.45    (79)   ~ (all_52_5 = all_6_2)
% 203.62/34.45    (80)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.45    (81)   ~ (all_52_9 = all_6_2)
% 203.62/34.45    (82)  op(e3, e3) = all_6_2
% 203.62/34.45    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.45    (84)   ~ (all_52_13 = e3)
% 203.62/34.45    (85)   ~ (all_52_27 = all_14_2)
% 203.62/34.45    (86)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.45    (87)   ~ (all_52_3 = all_52_7)
% 203.62/34.45    (88)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.45    (89)  all_58_5 = all_52_19
% 203.62/34.45    (90)  all_56_1 = all_52_9
% 203.62/34.45    (91)  all_58_6 = all_52_5
% 203.62/34.45    (92)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.45    (93)   ~ (all_52_17 = all_6_2)
% 203.62/34.45    (94)   ~ (e1 = e0)
% 203.62/34.45    (95)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.45    (96)   ~ (all_52_9 = all_52_17)
% 203.62/34.45    (97)  all_56_10 = all_10_2
% 203.62/34.45    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.45    (99)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.45    (100)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.45    (101)  op(e1, e1) = all_10_2
% 203.62/34.45    (102)   ~ (all_52_23 = all_10_2)
% 203.62/34.45    (103)  all_58_3 = all_4_2
% 203.62/34.45    (104)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.45    (105)   ~ (all_52_3 = all_4_2)
% 203.62/34.45    (106)  op(all_6_2, e3) = all_6_1
% 203.62/34.45    (107)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.62/34.45    (108)   ~ (all_52_13 = all_52_29)
% 203.62/34.45    (109)  all_58_4 = all_52_17
% 203.62/34.45    (110)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.45    (111)   ~ (all_14_2 = e3)
% 203.62/34.45  
% 203.62/34.45  Begin of proof
% 203.62/34.45  | 
% 203.62/34.45  | BETA: splitting (95) gives:
% 203.62/34.45  | 
% 203.62/34.45  | Case 1:
% 203.62/34.45  | | 
% 203.62/34.45  | |   (112)  all_56_1 = e3
% 203.62/34.45  | | 
% 203.62/34.45  | | COMBINE_EQS: (90), (112) imply:
% 203.62/34.45  | |   (113)  all_52_9 = e3
% 203.62/34.45  | | 
% 203.62/34.45  | | REDUCE: (65), (113) imply:
% 203.62/34.45  | |   (114)  $false
% 203.62/34.45  | | 
% 203.62/34.45  | | CLOSE: (114) is inconsistent.
% 203.62/34.45  | | 
% 203.62/34.45  | Case 2:
% 203.62/34.45  | | 
% 203.62/34.45  | |   (115)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.45  | | 
% 203.62/34.45  | | BETA: splitting (9) gives:
% 203.62/34.45  | | 
% 203.62/34.45  | | Case 1:
% 203.62/34.45  | | | 
% 203.62/34.45  | | |   (116)  all_56_12 = e3
% 203.62/34.45  | | | 
% 203.62/34.45  | | | COMBINE_EQS: (75), (116) imply:
% 203.62/34.45  | | |   (117)  all_52_7 = e3
% 203.62/34.45  | | | 
% 203.62/34.45  | | | REDUCE: (49), (117) imply:
% 203.62/34.45  | | |   (118)  $false
% 203.62/34.45  | | | 
% 203.62/34.45  | | | CLOSE: (118) is inconsistent.
% 203.62/34.45  | | | 
% 203.62/34.45  | | Case 2:
% 203.62/34.45  | | | 
% 203.62/34.45  | | |   (119)   ~ (all_56_12 = e3)
% 203.62/34.45  | | |   (120)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.45  | | | 
% 203.62/34.45  | | | BETA: splitting (99) gives:
% 203.62/34.45  | | | 
% 203.62/34.45  | | | Case 1:
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | |   (121)  all_56_9 = e3
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | REF_CLOSE: (35), (84), (121) are inconsistent by sub-proof #958.
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | Case 2:
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | |   (122)   ~ (all_56_9 = e3)
% 203.62/34.45  | | | |   (123)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | BETA: splitting (98) gives:
% 203.62/34.45  | | | | 
% 203.62/34.45  | | | | Case 1:
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | |   (124)  all_58_4 = e3
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | | COMBINE_EQS: (109), (124) imply:
% 203.62/34.45  | | | | |   (125)  all_52_17 = e3
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | | REF_CLOSE: (3), (7), (13), (23), (30), (45), (47), (49), (51), (52),
% 203.62/34.45  | | | | |            (58), (73), (82), (91), (93), (101), (105), (125) are
% 203.62/34.45  | | | | |            inconsistent by sub-proof #1199.
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | Case 2:
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | |   (126)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | | BETA: splitting (86) gives:
% 203.62/34.45  | | | | | 
% 203.62/34.45  | | | | | Case 1:
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | |   (127)  all_58_0 = e3
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | COMBINE_EQS: (13), (127) imply:
% 203.62/34.45  | | | | | |   (128)  all_6_2 = e3
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (12), (128) imply:
% 203.62/34.45  | | | | | |   (129)   ~ (all_52_3 = e3)
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (79), (128) imply:
% 203.62/34.45  | | | | | |   (130)   ~ (all_52_5 = e3)
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (77), (128) imply:
% 203.62/34.45  | | | | | |   (131)   ~ (all_52_25 = e3)
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (106), (128) imply:
% 203.62/34.45  | | | | | |   (132)  op(e3, e3) = all_6_1
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (82), (128) imply:
% 203.62/34.45  | | | | | |   (133)  op(e3, e3) = e3
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | GROUND_INST: instantiating (3) with e3, all_6_1, e3, e3, simplifying
% 203.62/34.45  | | | | | |              with (132), (133) gives:
% 203.62/34.45  | | | | | |   (134)  all_6_1 = e3
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (53), (134) imply:
% 203.62/34.45  | | | | | |   (135)  op(e3, e3) = all_6_0
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3, simplifying
% 203.62/34.45  | | | | | |              with (133), (135) gives:
% 203.62/34.45  | | | | | |   (136)  all_6_0 = e3
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | REDUCE: (64), (136) imply:
% 203.62/34.45  | | | | | |   (137)   ~ (e3 = e2)
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | BETA: splitting (48) gives:
% 203.62/34.45  | | | | | | 
% 203.62/34.45  | | | | | | Case 1:
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | |   (138)  all_58_6 = e3
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | | REF_CLOSE: (91), (130), (138) are inconsistent by sub-proof #1328.
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | Case 2:
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | |   (139)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | | BETA: splitting (83) gives:
% 203.62/34.45  | | | | | | | 
% 203.62/34.45  | | | | | | | Case 1:
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | |   (140)  all_58_9 = e3
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | | REF_CLOSE: (20), (131), (140) are inconsistent by sub-proof
% 203.62/34.45  | | | | | | | |            #1300.
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | Case 2:
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | |   (141)   ~ (all_58_9 = e3)
% 203.62/34.45  | | | | | | | |   (142)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | | BETA: splitting (30) gives:
% 203.62/34.45  | | | | | | | | 
% 203.62/34.45  | | | | | | | | Case 1:
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | |   (143)  all_58_2 = e3
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | REF_CLOSE: (51), (129), (143) are inconsistent by sub-proof
% 203.62/34.45  | | | | | | | | |            #1369.
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | Case 2:
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | |   (144)   ~ (all_58_2 = e3)
% 203.62/34.45  | | | | | | | | |   (145)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | BETA: splitting (55) gives:
% 203.62/34.45  | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | Case 1:
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | |   (146)  all_56_4 = e3
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | REF_CLOSE: (15), (129), (146) are inconsistent by sub-proof
% 203.62/34.45  | | | | | | | | | |            #1340.
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | Case 2:
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | |   (147)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | BETA: splitting (34) gives:
% 203.62/34.45  | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | Case 1:
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | |   (148)  all_58_1 = e1
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | COMBINE_EQS: (5), (148) imply:
% 203.62/34.45  | | | | | | | | | | |   (149)  all_52_9 = e1
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REDUCE: (6), (149) imply:
% 203.62/34.45  | | | | | | | | | | |   (150)   ~ (all_52_13 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | SIMP: (150) implies:
% 203.62/34.45  | | | | | | | | | | |   (151)   ~ (all_52_13 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REDUCE: (96), (149) imply:
% 203.62/34.45  | | | | | | | | | | |   (152)   ~ (all_52_17 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | SIMP: (152) implies:
% 203.62/34.45  | | | | | | | | | | |   (153)   ~ (all_52_17 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REDUCE: (69), (149) imply:
% 203.62/34.45  | | | | | | | | | | |   (154)   ~ (all_52_25 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | SIMP: (154) implies:
% 203.62/34.45  | | | | | | | | | | |   (155)   ~ (all_52_25 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REDUCE: (78), (149) imply:
% 203.62/34.45  | | | | | | | | | | |   (156)   ~ (all_4_2 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | SIMP: (156) implies:
% 203.62/34.45  | | | | | | | | | | |   (157)   ~ (all_4_2 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REDUCE: (65), (149) imply:
% 203.62/34.45  | | | | | | | | | | |   (158)   ~ (e3 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | SIMP: (158) implies:
% 203.62/34.45  | | | | | | | | | | |   (159)   ~ (e3 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (10), (16), (17), (19),
% 203.62/34.45  | | | | | | | | | | |            (20), (22), (23), (24), (26), (27), (31), (33),
% 203.62/34.45  | | | | | | | | | | |            (36), (39), (41), (42), (43), (44), (47), (51),
% 203.62/34.45  | | | | | | | | | | |            (54), (56), (57), (58), (59), (60), (61), (62),
% 203.62/34.45  | | | | | | | | | | |            (63), (66), (68), (70), (71), (72), (73), (76),
% 203.62/34.45  | | | | | | | | | | |            (83), (84), (85), (88), (89), (91), (94), (101),
% 203.62/34.45  | | | | | | | | | | |            (102), (103), (105), (109), (111), (126), (127),
% 203.62/34.45  | | | | | | | | | | |            (131), (137), (139), (151), (153), (155), (157),
% 203.62/34.45  | | | | | | | | | | |            (159) are inconsistent by sub-proof #709.
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | Case 2:
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | |   (160)   ~ (all_58_1 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | REDUCE: (5), (160) imply:
% 203.62/34.45  | | | | | | | | | | |   (161)   ~ (all_52_9 = e1)
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | BETA: splitting (104) gives:
% 203.62/34.45  | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | Case 1:
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | |   (162)  all_58_1 = e2
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | COMBINE_EQS: (5), (162) imply:
% 203.62/34.45  | | | | | | | | | | | |   (163)  all_52_9 = e2
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | REDUCE: (69), (163) imply:
% 203.62/34.45  | | | | | | | | | | | |   (164)   ~ (all_52_25 = e2)
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | SIMP: (164) implies:
% 203.62/34.45  | | | | | | | | | | | |   (165)   ~ (all_52_25 = e2)
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | REDUCE: (78), (163) imply:
% 203.62/34.45  | | | | | | | | | | | |   (166)   ~ (all_4_2 = e2)
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | SIMP: (166) implies:
% 203.62/34.45  | | | | | | | | | | | |   (167)   ~ (all_4_2 = e2)
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | REDUCE: (65), (163) imply:
% 203.62/34.45  | | | | | | | | | | | |   (168)   ~ (e3 = e2)
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | REDUCE: (40), (163) imply:
% 203.62/34.45  | | | | | | | | | | | |   (169)  op(e2, e2) = all_52_8
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_52_8, e2, e2,
% 203.62/34.45  | | | | | | | | | | | |              simplifying with (23), (169) gives:
% 203.62/34.45  | | | | | | | | | | | |   (170)  all_52_8 = all_4_2
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | BETA: splitting (110) gives:
% 203.62/34.45  | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | Case 1:
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | |   (171)  all_56_10 = e3
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | COMBINE_EQS: (97), (171) imply:
% 203.62/34.45  | | | | | | | | | | | | |   (172)  all_10_2 = e3
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | SIMP: (172) implies:
% 203.62/34.45  | | | | | | | | | | | | |   (173)  all_10_2 = e3
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | REDUCE: (71), (173) imply:
% 203.62/34.45  | | | | | | | | | | | | |   (174)   ~ (all_52_19 = e3)
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (10), (11), (13), (15),
% 203.62/34.45  | | | | | | | | | | | | |            (16), (17), (18), (20), (21), (23), (24), (29),
% 203.62/34.45  | | | | | | | | | | | | |            (30), (35), (37), (39), (42), (43), (44), (45),
% 203.62/34.45  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (58),
% 203.62/34.45  | | | | | | | | | | | | |            (60), (63), (66), (67), (70), (71), (72), (73),
% 203.62/34.45  | | | | | | | | | | | | |            (74), (75), (79), (80), (82), (84), (87), (89),
% 203.62/34.45  | | | | | | | | | | | | |            (91), (92), (94), (100), (101), (102), (103),
% 203.62/34.45  | | | | | | | | | | | | |            (105), (107), (108), (120), (123), (127), (137),
% 203.62/34.45  | | | | | | | | | | | | |            (139), (145), (147), (165), (167), (174) are
% 203.62/34.45  | | | | | | | | | | | | |            inconsistent by sub-proof #623.
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.45  | | | | | | | | | | | | Case 2:
% 203.62/34.45  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | |   (175)   ~ (all_56_10 = e3)
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | REDUCE: (97), (175) imply:
% 203.62/34.46  | | | | | | | | | | | | |   (176)   ~ (all_10_2 = e3)
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | BETA: splitting (126) gives:
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | Case 1:
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | |   (177)  all_58_5 = e3
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | COMBINE_EQS: (89), (177) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (178)  all_52_19 = e3
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | SIMP: (178) implies:
% 203.62/34.46  | | | | | | | | | | | | | |   (179)  all_52_19 = e3
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (41), (179) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (180)   ~ (all_52_23 = e3)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (61), (179) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (181)   ~ (all_52_27 = e3)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | SIMP: (181) implies:
% 203.62/34.46  | | | | | | | | | | | | | |   (182)   ~ (all_52_27 = e3)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (13), (14), (16),
% 203.62/34.46  | | | | | | | | | | | | | |            (17), (23), (24), (25), (29), (30), (32), (36),
% 203.62/34.46  | | | | | | | | | | | | | |            (38), (39), (41), (42), (45), (47), (50), (51),
% 203.62/34.46  | | | | | | | | | | | | | |            (52), (53), (56), (57), (58), (60), (66), (70),
% 203.62/34.46  | | | | | | | | | | | | | |            (71), (72), (73), (74), (75), (82), (86), (89),
% 203.62/34.46  | | | | | | | | | | | | | |            (91), (92), (93), (94), (98), (101), (102), (105),
% 203.62/34.46  | | | | | | | | | | | | | |            (106), (109), (111), (120), (142), (182) are
% 203.62/34.46  | | | | | | | | | | | | | |            inconsistent by sub-proof #589.
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | Case 2:
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | |   (183)  all_58_8 = e3 | all_58_14 = e3
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REF_CLOSE: (2), (57), (72), (176), (183) are inconsistent by
% 203.62/34.46  | | | | | | | | | | | | | |            sub-proof #1304.
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | Case 2:
% 203.62/34.46  | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | |   (184)   ~ (all_58_1 = e2)
% 203.62/34.46  | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | REDUCE: (5), (184) imply:
% 203.62/34.46  | | | | | | | | | | | |   (185)   ~ (all_52_9 = e2)
% 203.62/34.46  | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | BETA: splitting (115) gives:
% 203.62/34.46  | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | Case 1:
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | |   (186)  all_56_1 = e2
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | COMBINE_EQS: (90), (186) imply:
% 203.62/34.46  | | | | | | | | | | | | |   (187)  all_52_9 = e2
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | REDUCE: (185), (187) imply:
% 203.62/34.46  | | | | | | | | | | | | |   (188)  $false
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | Case 2:
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | |   (189)  all_56_1 = e1 | all_56_1 = e0
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | Case 1:
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | |   (190)  all_56_1 = e1
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | COMBINE_EQS: (90), (190) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (191)  all_52_9 = e1
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (161), (191) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (192)  $false
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | CLOSE: (192) is inconsistent.
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | Case 2:
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | |   (193)  all_56_1 = e0
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | COMBINE_EQS: (90), (193) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (194)  all_52_9 = e0
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (78), (194) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (195)   ~ (all_4_2 = e0)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | SIMP: (195) implies:
% 203.62/34.46  | | | | | | | | | | | | | |   (196)   ~ (all_4_2 = e0)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (65), (194) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (197)   ~ (e3 = e0)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (161), (194) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (198)   ~ (e1 = e0)
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | REDUCE: (40), (194) imply:
% 203.62/34.46  | | | | | | | | | | | | | |   (199)  op(e0, e0) = all_52_8
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_8, e0, e0,
% 203.62/34.46  | | | | | | | | | | | | | |              simplifying with (29), (199) gives:
% 203.62/34.46  | | | | | | | | | | | | | |   (200)  all_52_8 = all_14_2
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | Case 1:
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | |   (201)  all_58_12 = e2
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | | COMBINE_EQS: (47), (201) imply:
% 203.62/34.46  | | | | | | | | | | | | | | |   (202)  all_52_7 = e2
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | | SIMP: (202) implies:
% 203.62/34.46  | | | | | | | | | | | | | | |   (203)  all_52_7 = e2
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | | REDUCE: (4), (203) imply:
% 203.62/34.46  | | | | | | | | | | | | | | |   (204)  op(e2, e2) = e0
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | | REF_CLOSE: (3), (23), (196), (204) are inconsistent by
% 203.62/34.46  | | | | | | | | | | | | | | |            sub-proof #1152.
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | Case 2:
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | |   (205)   ~ (all_58_12 = e2)
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | | REDUCE: (47), (205) imply:
% 203.62/34.46  | | | | | | | | | | | | | | |   (206)   ~ (all_52_7 = e2)
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (16), (29), (47), (50), (60),
% 203.62/34.46  | | | | | | | | | | | | | | |            (66), (75), (94), (101), (102), (120), (206) are
% 203.62/34.46  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 203.62/34.46  | | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | | 
% 203.62/34.46  | | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | | 
% 203.62/34.46  | | | | | | | | End of split
% 203.62/34.46  | | | | | | | | 
% 203.62/34.46  | | | | | | | End of split
% 203.62/34.46  | | | | | | | 
% 203.62/34.46  | | | | | | End of split
% 203.62/34.46  | | | | | | 
% 203.62/34.46  | | | | | Case 2:
% 203.62/34.46  | | | | | | 
% 203.62/34.46  | | | | | |   (207)   ~ (all_58_0 = e3)
% 203.62/34.46  | | | | | | 
% 203.62/34.46  | | | | | | REDUCE: (13), (207) imply:
% 203.62/34.46  | | | | | |   (208)   ~ (all_6_2 = e3)
% 203.62/34.46  | | | | | | 
% 203.62/34.46  | | | | | | REF_CLOSE: (3), (7), (13), (23), (30), (45), (47), (49), (51), (52),
% 203.62/34.46  | | | | | |            (58), (73), (82), (91), (101), (105), (208) are
% 203.62/34.46  | | | | | |            inconsistent by sub-proof #1363.
% 203.62/34.46  | | | | | | 
% 203.62/34.46  | | | | | End of split
% 203.62/34.46  | | | | | 
% 203.62/34.46  | | | | End of split
% 203.62/34.46  | | | | 
% 203.62/34.46  | | | End of split
% 203.62/34.46  | | | 
% 203.62/34.46  | | End of split
% 203.62/34.46  | | 
% 203.62/34.46  | End of split
% 203.62/34.46  | 
% 203.62/34.46  End of proof
% 203.62/34.46  
% 203.62/34.46  Sub-proof #582 shows that the following formulas are inconsistent:
% 203.62/34.46  ----------------------------------------------------------------
% 203.62/34.46    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.46    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.46    (3)  all_58_14 = all_52_23
% 203.62/34.46    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.46    (5)  all_22_1 = e2
% 203.62/34.46    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.46    (7)   ~ (all_52_5 = all_52_13)
% 203.62/34.46    (8)  all_58_1 = all_52_9
% 203.62/34.46    (9)   ~ (all_52_9 = all_52_13)
% 203.62/34.46    (10)   ~ (e3 = e0)
% 203.62/34.46    (11)  op(e2, e3) = all_52_3
% 203.62/34.46    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.46    (13)   ~ (all_52_3 = all_52_19)
% 203.62/34.46    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.46    (15)   ~ (all_52_17 = all_52_25)
% 203.62/34.46    (16)   ~ (all_52_3 = all_6_2)
% 203.62/34.46    (17)  all_58_0 = all_6_2
% 203.62/34.46    (18)  op(all_14_2, e0) = all_14_1
% 203.62/34.46    (19)  all_56_4 = all_52_3
% 203.62/34.46    (20)   ~ (all_52_17 = all_10_2)
% 203.62/34.46    (21)  all_26_1 = all_10_1
% 203.62/34.46    (22)  op(e3, e0) = all_52_25
% 203.62/34.46    (23)  all_26_2 = all_10_2
% 203.62/34.46    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.46    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.46    (26)   ~ (all_52_27 = all_52_29)
% 203.62/34.46    (27)  all_58_13 = all_52_15
% 203.62/34.46    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.46    (29)  all_58_9 = all_52_25
% 203.62/34.46    (30)   ~ (all_6_1 = e1)
% 203.62/34.46    (31)   ~ (all_52_29 = all_14_2)
% 203.62/34.46    (32)  all_22_0 = all_6_0
% 203.62/34.46    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.46    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.46    (35)  op(e1, e3) = all_52_5
% 203.62/34.46    (36)  op(e2, e2) = all_4_2
% 203.62/34.46    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.46    (38)   ~ (all_52_3 = all_52_5)
% 203.62/34.46    (39)  all_58_11 = all_52_29
% 203.62/34.46    (40)  all_56_5 = all_4_2
% 203.62/34.46    (41)   ~ (all_52_25 = all_14_2)
% 203.62/34.46    (42)   ~ (all_52_9 = all_52_15)
% 203.62/34.46    (43)   ~ (all_52_3 = all_52_27)
% 203.62/34.46    (44)  op(all_10_2, e1) = all_10_1
% 203.62/34.46    (45)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.46    (46)   ~ (all_52_7 = all_6_2)
% 203.62/34.46    (47)  op(e0, e0) = all_14_2
% 203.62/34.46    (48)  all_56_15 = all_14_2
% 203.62/34.46    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.46    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.46    (51)  all_56_11 = all_52_29
% 203.62/34.46    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.46    (53)   ~ (all_52_13 = all_10_2)
% 203.62/34.46    (54)   ~ (all_6_0 = e1)
% 203.62/34.46    (55)  all_58_10 = all_52_27
% 203.62/34.46    (56)  all_56_8 = all_52_5
% 203.62/34.46    (57)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.46    (58)   ~ (all_52_19 = all_52_23)
% 203.62/34.46    (59)   ~ (all_52_25 = all_52_29)
% 203.62/34.46    (60)   ~ (all_52_29 = all_10_2)
% 203.62/34.46    (61)  all_58_7 = all_52_13
% 203.62/34.46    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.46    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.46    (64)   ~ (all_52_5 = all_52_7)
% 203.62/34.46    (65)  all_58_12 = all_52_7
% 203.62/34.46    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.46    (67)   ~ (all_52_7 = all_14_2)
% 203.62/34.46    (68)  all_58_2 = all_52_3
% 203.62/34.46    (69)  all_56_2 = all_52_17
% 203.62/34.46    (70)  all_22_1 = all_6_1
% 203.62/34.46    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.46    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.46    (73)  op(e3, all_6_1) = all_6_0
% 203.62/34.46    (74)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.46    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.46    (76)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.46    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.46    (78)   ~ (e2 = e0)
% 203.62/34.46    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.46    (80)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.46    (81)   ~ (all_52_5 = all_52_29)
% 203.62/34.46    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.46    (83)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.46    (84)   ~ (all_52_15 = all_14_2)
% 203.62/34.46    (85)   ~ (all_52_19 = all_52_27)
% 203.62/34.46    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.46    (87)   ~ (all_6_0 = e2)
% 203.62/34.46    (88)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.46            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.46    (89)  op(e3, e1) = all_52_17
% 203.62/34.46    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.46    (91)  op(e0, e3) = all_52_7
% 203.62/34.46    (92)  op(e1, e2) = all_52_13
% 203.62/34.46    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.46    (94)   ~ (all_52_9 = all_52_25)
% 203.62/34.46    (95)  all_58_15 = all_14_2
% 203.62/34.46    (96)   ~ (all_52_19 = all_10_2)
% 203.62/34.46    (97)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.46    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.46    (99)  all_58_8 = all_10_2
% 203.62/34.46    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.46    (101)   ~ (all_52_5 = all_10_2)
% 203.62/34.46    (102)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.46    (103)   ~ (all_52_23 = all_14_2)
% 203.62/34.46    (104)  all_56_12 = all_52_7
% 203.62/34.46    (105)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.46    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.46    (107)   ~ (all_52_25 = all_6_2)
% 203.62/34.46    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.46    (109)   ~ (all_52_9 = all_4_2)
% 203.62/34.46    (110)   ~ (all_52_5 = all_6_2)
% 203.62/34.46    (111)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.46    (112)   ~ (all_52_9 = all_6_2)
% 203.62/34.46    (113)  op(e1, all_10_1) = e2
% 203.62/34.46    (114)  all_56_0 = all_6_2
% 203.62/34.46    (115)  op(e3, e3) = all_6_2
% 203.62/34.46    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.46    (117)   ~ (all_52_27 = all_14_2)
% 203.62/34.46    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.46    (119)  all_56_14 = all_52_23
% 203.62/34.46    (120)  all_56_3 = all_52_25
% 203.62/34.46    (121)  op(e0, all_14_1) = e2
% 203.62/34.46    (122)   ~ (all_52_3 = all_52_7)
% 203.62/34.46    (123)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.46    (124)  all_58_5 = all_52_19
% 203.62/34.46    (125)  all_56_1 = all_52_9
% 203.62/34.46    (126)   ~ (all_52_15 = all_4_2)
% 203.62/34.46    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.46           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.46           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.46           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.46    (128)   ~ (all_52_27 = all_4_2)
% 203.62/34.46    (129)  all_58_6 = all_52_5
% 203.62/34.46    (130)  op(e3, e2) = all_52_9
% 203.62/34.46    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.46    (132)   ~ (all_52_17 = all_6_2)
% 203.62/34.46    (133)   ~ (e1 = e0)
% 203.62/34.46    (134)   ~ (e3 = e2)
% 203.62/34.46    (135)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.46    (136)  all_26_0 = e2
% 203.62/34.46    (137)   ~ (all_52_9 = all_52_17)
% 203.62/34.46    (138)  all_56_10 = all_10_2
% 203.62/34.46    (139)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.46    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.46    (141)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.46    (142)  op(e1, e1) = all_10_2
% 203.62/34.46    (143)   ~ (all_52_23 = all_10_2)
% 203.62/34.46    (144)   ~ (all_52_7 = all_52_23)
% 203.62/34.46    (145)   ~ (all_52_17 = all_52_19)
% 203.62/34.46    (146)  all_58_3 = all_4_2
% 203.62/34.46    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.46    (148)   ~ (all_52_3 = all_4_2)
% 203.62/34.46    (149)   ~ (all_52_19 = all_4_2)
% 203.62/34.46    (150)   ~ (all_52_17 = all_52_23)
% 203.62/34.46    (151)  op(all_6_2, e3) = all_6_1
% 203.62/34.46    (152)   ~ (all_52_13 = all_52_29)
% 203.62/34.46    (153)  all_22_2 = all_6_2
% 203.62/34.46    (154)  all_58_4 = all_52_17
% 203.62/34.46    (155)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.46    (156)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.46  
% 203.62/34.46  Begin of proof
% 203.62/34.46  | 
% 203.62/34.46  | COMBINE_EQS: (5), (70) imply:
% 203.62/34.46  |   (157)  all_6_1 = e2
% 203.62/34.46  | 
% 203.62/34.46  | SIMP: (157) implies:
% 203.62/34.46  |   (158)  all_6_1 = e2
% 203.62/34.46  | 
% 203.62/34.46  | REDUCE: (30), (158) imply:
% 203.62/34.46  |   (159)   ~ (e2 = e1)
% 203.62/34.46  | 
% 203.62/34.46  | REDUCE: (151), (158) imply:
% 203.62/34.46  |   (160)  op(all_6_2, e3) = e2
% 203.62/34.46  | 
% 203.62/34.46  | REDUCE: (73), (158) imply:
% 203.62/34.46  |   (161)  op(e3, e2) = all_6_0
% 203.62/34.46  | 
% 203.62/34.46  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.62/34.46  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 203.62/34.46  |            (25), (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 203.62/34.46  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 203.62/34.46  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 203.62/34.46  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 203.62/34.46  |            (71), (72), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 203.62/34.46  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 203.62/34.46  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.62/34.46  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 203.62/34.46  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 203.62/34.46  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 203.62/34.46  |            (131), (132), (133), (134), (135), (136), (137), (138), (139),
% 203.62/34.46  |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 203.62/34.46  |            (149), (150), (151), (152), (153), (154), (155), (156), (159),
% 203.62/34.46  |            (160), (161) are inconsistent by sub-proof #583.
% 203.62/34.46  | 
% 203.62/34.46  End of proof
% 203.62/34.46  
% 203.62/34.46  Sub-proof #583 shows that the following formulas are inconsistent:
% 203.62/34.46  ----------------------------------------------------------------
% 203.62/34.46    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.46    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.46    (3)  all_58_14 = all_52_23
% 203.62/34.46    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.46    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.46    (6)   ~ (all_52_5 = all_52_13)
% 203.62/34.46    (7)  all_58_1 = all_52_9
% 203.62/34.46    (8)   ~ (all_52_9 = all_52_13)
% 203.62/34.46    (9)   ~ (e3 = e0)
% 203.62/34.46    (10)  op(e2, e3) = all_52_3
% 203.62/34.46    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.46    (12)   ~ (all_52_3 = all_52_19)
% 203.62/34.46    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.46    (14)   ~ (all_52_17 = all_52_25)
% 203.62/34.46    (15)   ~ (all_52_3 = all_6_2)
% 203.62/34.46    (16)  all_58_0 = all_6_2
% 203.62/34.46    (17)  op(all_14_2, e0) = all_14_1
% 203.62/34.46    (18)  all_56_4 = all_52_3
% 203.62/34.46    (19)   ~ (all_52_17 = all_10_2)
% 203.62/34.46    (20)  all_26_1 = all_10_1
% 203.62/34.46    (21)  op(e3, e0) = all_52_25
% 203.62/34.46    (22)  all_26_2 = all_10_2
% 203.62/34.46    (23)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.46    (24)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.46    (25)   ~ (all_52_27 = all_52_29)
% 203.62/34.46    (26)  all_58_13 = all_52_15
% 203.62/34.46    (27)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.46    (28)  all_58_9 = all_52_25
% 203.62/34.46    (29)   ~ (all_52_29 = all_14_2)
% 203.62/34.46    (30)  all_22_0 = all_6_0
% 203.62/34.46    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.46    (32)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.46    (33)  op(e1, e3) = all_52_5
% 203.62/34.46    (34)  op(e2, e2) = all_4_2
% 203.62/34.46    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.46    (36)   ~ (all_52_3 = all_52_5)
% 203.62/34.46    (37)  all_58_11 = all_52_29
% 203.62/34.46    (38)  all_56_5 = all_4_2
% 203.62/34.46    (39)   ~ (all_52_25 = all_14_2)
% 203.62/34.46    (40)   ~ (all_52_9 = all_52_15)
% 203.62/34.46    (41)   ~ (all_52_3 = all_52_27)
% 203.62/34.46    (42)  op(all_10_2, e1) = all_10_1
% 203.62/34.46    (43)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.46    (44)   ~ (all_52_7 = all_6_2)
% 203.62/34.46    (45)  op(e0, e0) = all_14_2
% 203.62/34.46    (46)  all_56_15 = all_14_2
% 203.62/34.46    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.46    (48)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.46    (49)  all_56_11 = all_52_29
% 203.62/34.46    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.46    (51)   ~ (e2 = e1)
% 203.62/34.46    (52)   ~ (all_52_13 = all_10_2)
% 203.62/34.46    (53)   ~ (all_6_0 = e1)
% 203.62/34.46    (54)  all_58_10 = all_52_27
% 203.62/34.46    (55)  all_56_8 = all_52_5
% 203.62/34.46    (56)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.46    (57)   ~ (all_52_19 = all_52_23)
% 203.62/34.46    (58)   ~ (all_52_25 = all_52_29)
% 203.62/34.46    (59)  op(all_6_2, e3) = e2
% 203.62/34.46    (60)   ~ (all_52_29 = all_10_2)
% 203.62/34.46    (61)  all_58_7 = all_52_13
% 203.62/34.46    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.46    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.46    (64)   ~ (all_52_5 = all_52_7)
% 203.62/34.46    (65)  all_58_12 = all_52_7
% 203.62/34.46    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.46    (67)   ~ (all_52_7 = all_14_2)
% 203.62/34.46    (68)  all_58_2 = all_52_3
% 203.62/34.46    (69)  all_56_2 = all_52_17
% 203.62/34.46    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.46    (71)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.46    (72)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.46    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.46    (74)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.46    (75)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.46    (76)   ~ (e2 = e0)
% 203.62/34.46    (77)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.46    (78)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.46    (79)   ~ (all_52_5 = all_52_29)
% 203.62/34.46    (80)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.46    (81)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.46    (82)   ~ (all_52_15 = all_14_2)
% 203.62/34.46    (83)   ~ (all_52_19 = all_52_27)
% 203.62/34.46    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.46    (85)   ~ (all_6_0 = e2)
% 203.62/34.46    (86)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.46            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.46    (87)  op(e3, e1) = all_52_17
% 203.62/34.46    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.46    (89)  op(e0, e3) = all_52_7
% 203.62/34.46    (90)  op(e1, e2) = all_52_13
% 203.62/34.46    (91)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.46    (92)   ~ (all_52_9 = all_52_25)
% 203.62/34.46    (93)  all_58_15 = all_14_2
% 203.62/34.46    (94)   ~ (all_52_19 = all_10_2)
% 203.62/34.46    (95)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.46    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.46    (97)  all_58_8 = all_10_2
% 203.62/34.46    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.46    (99)   ~ (all_52_5 = all_10_2)
% 203.62/34.46    (100)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.46    (101)   ~ (all_52_23 = all_14_2)
% 203.62/34.46    (102)  all_56_12 = all_52_7
% 203.62/34.46    (103)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.46    (104)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.46    (105)  op(e3, e2) = all_6_0
% 203.62/34.46    (106)   ~ (all_52_25 = all_6_2)
% 203.62/34.46    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.46    (108)   ~ (all_52_9 = all_4_2)
% 203.62/34.46    (109)   ~ (all_52_5 = all_6_2)
% 203.62/34.46    (110)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.46    (111)   ~ (all_52_9 = all_6_2)
% 203.62/34.46    (112)  op(e1, all_10_1) = e2
% 203.62/34.46    (113)  all_56_0 = all_6_2
% 203.62/34.46    (114)  op(e3, e3) = all_6_2
% 203.62/34.46    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.46    (116)   ~ (all_52_27 = all_14_2)
% 203.62/34.46    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.46    (118)  all_56_14 = all_52_23
% 203.62/34.46    (119)  all_56_3 = all_52_25
% 203.62/34.46    (120)  op(e0, all_14_1) = e2
% 203.62/34.46    (121)   ~ (all_52_3 = all_52_7)
% 203.62/34.46    (122)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.46    (123)  all_58_5 = all_52_19
% 203.62/34.46    (124)  all_56_1 = all_52_9
% 203.62/34.46    (125)   ~ (all_52_15 = all_4_2)
% 203.62/34.47    (126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.47           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.47           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.47           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.47    (127)   ~ (all_52_27 = all_4_2)
% 203.62/34.47    (128)  all_58_6 = all_52_5
% 203.62/34.47    (129)  op(e3, e2) = all_52_9
% 203.62/34.47    (130)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.47    (131)   ~ (all_52_17 = all_6_2)
% 203.62/34.47    (132)   ~ (e1 = e0)
% 203.62/34.47    (133)   ~ (e3 = e2)
% 203.62/34.47    (134)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.47    (135)  all_26_0 = e2
% 203.62/34.47    (136)   ~ (all_52_9 = all_52_17)
% 203.62/34.47    (137)  all_56_10 = all_10_2
% 203.62/34.47    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.47    (139)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.47    (140)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.47    (141)  op(e1, e1) = all_10_2
% 203.62/34.47    (142)   ~ (all_52_23 = all_10_2)
% 203.62/34.47    (143)   ~ (all_52_7 = all_52_23)
% 203.62/34.47    (144)   ~ (all_52_17 = all_52_19)
% 203.62/34.47    (145)  all_58_3 = all_4_2
% 203.62/34.47    (146)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.47    (147)   ~ (all_52_3 = all_4_2)
% 203.62/34.47    (148)   ~ (all_52_19 = all_4_2)
% 203.62/34.47    (149)   ~ (all_52_17 = all_52_23)
% 203.62/34.47    (150)  op(all_6_2, e3) = all_6_1
% 203.62/34.47    (151)   ~ (all_52_13 = all_52_29)
% 203.62/34.47    (152)  all_22_2 = all_6_2
% 203.62/34.47    (153)  all_58_4 = all_52_17
% 203.62/34.47    (154)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.47    (155)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.47  
% 203.62/34.47  Begin of proof
% 203.62/34.47  | 
% 203.62/34.47  | GROUND_INST: instantiating (5) with all_52_9, all_6_0, e2, e3, simplifying
% 203.62/34.47  |              with (105), (129) gives:
% 203.62/34.47  |   (156)  all_52_9 = all_6_0
% 203.62/34.47  | 
% 203.62/34.47  | COMBINE_EQS: (124), (156) imply:
% 203.62/34.47  |   (157)  all_56_1 = all_6_0
% 203.62/34.47  | 
% 203.62/34.47  | COMBINE_EQS: (7), (156) imply:
% 203.62/34.47  |   (158)  all_58_1 = all_6_0
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (8), (156) imply:
% 203.62/34.47  |   (159)   ~ (all_52_13 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (159) implies:
% 203.62/34.47  |   (160)   ~ (all_52_13 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (40), (156) imply:
% 203.62/34.47  |   (161)   ~ (all_52_15 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (161) implies:
% 203.62/34.47  |   (162)   ~ (all_52_15 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (136), (156) imply:
% 203.62/34.47  |   (163)   ~ (all_52_17 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (163) implies:
% 203.62/34.47  |   (164)   ~ (all_52_17 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (92), (156) imply:
% 203.62/34.47  |   (165)   ~ (all_52_25 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (165) implies:
% 203.62/34.47  |   (166)   ~ (all_52_25 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (111), (156) imply:
% 203.62/34.47  |   (167)   ~ (all_6_0 = all_6_2)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (108), (156) imply:
% 203.62/34.47  |   (168)   ~ (all_6_0 = all_4_2)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (56), (156) imply:
% 203.62/34.47  |   (169)  op(all_6_0, all_6_0) = all_52_8
% 203.62/34.47  | 
% 203.62/34.47  | BETA: splitting (81) gives:
% 203.62/34.47  | 
% 203.62/34.47  | Case 1:
% 203.62/34.47  | | 
% 203.62/34.47  | |   (170)   ~ (all_26_0 = e2)
% 203.62/34.47  | | 
% 203.62/34.47  | | REDUCE: (135), (170) imply:
% 203.62/34.47  | |   (171)  $false
% 203.62/34.47  | | 
% 203.62/34.47  | | CLOSE: (171) is inconsistent.
% 203.62/34.47  | | 
% 203.62/34.47  | Case 2:
% 203.62/34.47  | | 
% 203.62/34.47  | |   (172)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.47  | | 
% 203.62/34.47  | | BETA: splitting (86) gives:
% 203.62/34.47  | | 
% 203.62/34.47  | | Case 1:
% 203.62/34.47  | | | 
% 203.62/34.47  | | |   (173)  all_58_15 = e0
% 203.62/34.47  | | | 
% 203.62/34.47  | | | REF_CLOSE: (5), (17), (45), (76), (93), (120), (122), (173) are
% 203.62/34.47  | | |            inconsistent by sub-proof #612.
% 203.62/34.47  | | | 
% 203.62/34.47  | | Case 2:
% 203.62/34.47  | | | 
% 203.62/34.47  | | |   (174)   ~ (all_58_15 = e0)
% 203.62/34.47  | | |   (175)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 203.62/34.47  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.47  | | | 
% 203.62/34.47  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.47  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 203.62/34.47  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 203.62/34.47  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 203.62/34.47  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 203.62/34.47  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 203.62/34.47  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 203.62/34.47  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (82), (83),
% 203.62/34.47  | | |            (84), (85), (87), (88), (89), (90), (91), (92), (93), (94),
% 203.62/34.47  | | |            (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.62/34.47  | | |            (104), (106), (107), (108), (109), (110), (111), (112), (113),
% 203.62/34.47  | | |            (114), (115), (116), (117), (118), (119), (121), (122), (123),
% 203.62/34.47  | | |            (125), (126), (127), (128), (130), (131), (132), (133), (134),
% 203.62/34.47  | | |            (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 203.62/34.47  | | |            (146), (147), (148), (149), (150), (151), (152), (153), (154),
% 203.62/34.47  | | |            (155), (157), (158), (160), (162), (164), (166), (167), (168),
% 203.62/34.47  | | |            (169), (172), (174), (175) are inconsistent by sub-proof #629.
% 203.62/34.47  | | | 
% 203.62/34.47  | | End of split
% 203.62/34.47  | | 
% 203.62/34.47  | End of split
% 203.62/34.47  | 
% 203.62/34.47  End of proof
% 203.62/34.47  
% 203.62/34.47  Sub-proof #584 shows that the following formulas are inconsistent:
% 203.62/34.47  ----------------------------------------------------------------
% 203.62/34.47    (1)  all_58_14 = all_52_23
% 203.62/34.47    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.47    (3)   ~ (all_52_5 = all_52_13)
% 203.62/34.47    (4)  op(all_52_7, all_52_7) = e0
% 203.62/34.47    (5)  op(all_52_5, all_52_5) = e1
% 203.62/34.47    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.47    (7)   ~ (all_52_3 = all_52_19)
% 203.62/34.47    (8)   ~ (all_52_3 = all_6_2)
% 203.62/34.47    (9)  all_58_0 = all_6_2
% 203.62/34.47    (10)  op(e2, e2) = all_4_2
% 203.62/34.47    (11)   ~ (all_52_3 = all_52_5)
% 203.62/34.47    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.47    (13)  op(all_10_2, e1) = all_10_1
% 203.62/34.47    (14)   ~ (all_52_7 = all_6_2)
% 203.62/34.47    (15)  op(e0, e0) = all_14_2
% 203.62/34.47    (16)  op(e0, e1) = all_52_23
% 203.62/34.47    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.47    (18)   ~ (e2 = e1)
% 203.62/34.47    (19)   ~ (all_6_0 = e1)
% 203.62/34.47    (20)  all_58_10 = all_52_27
% 203.62/34.47    (21)  all_56_8 = all_52_5
% 203.62/34.47    (22)   ~ (all_52_19 = all_52_23)
% 203.62/34.47    (23)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.47    (24)  op(all_6_2, all_6_2) = e3
% 203.62/34.47    (25)   ~ (all_52_5 = all_52_7)
% 203.62/34.47    (26)  all_58_12 = all_52_7
% 203.62/34.47    (27)   ~ (all_52_7 = all_14_2)
% 203.62/34.47    (28)   ~ (all_14_2 = e0)
% 203.62/34.47    (29)  all_58_2 = all_52_3
% 203.62/34.47    (30)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.47    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.47    (32)  op(e3, all_6_1) = all_6_0
% 203.62/34.47    (33)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.47    (34)   ~ (e2 = e0)
% 203.62/34.47    (35)  op(all_52_3, all_52_3) = e2
% 203.62/34.47    (36)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.47    (37)  all_56_6 = all_52_19
% 203.62/34.47    (38)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.47    (39)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.47    (40)  op(e1, e2) = all_52_13
% 203.62/34.47    (41)  all_58_15 = all_14_2
% 203.62/34.47    (42)   ~ (all_52_19 = all_10_2)
% 203.62/34.47    (43)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.47    (44)  all_58_8 = all_10_2
% 203.62/34.47    (45)   ~ (all_52_5 = all_10_2)
% 203.62/34.47    (46)  all_56_12 = all_52_7
% 203.62/34.47    (47)   ~ (all_52_5 = all_6_2)
% 203.62/34.47    (48)  op(e1, all_10_1) = e2
% 203.62/34.47    (49)  op(e3, e3) = all_6_2
% 203.62/34.47    (50)   ~ (all_52_27 = all_14_2)
% 203.62/34.47    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.47    (52)  all_58_5 = all_52_19
% 203.62/34.47    (53)  all_58_6 = all_52_5
% 203.62/34.47    (54)   ~ (all_52_17 = all_6_2)
% 203.62/34.47    (55)   ~ (e1 = e0)
% 203.62/34.47    (56)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.62/34.47    (57)   ~ (e3 = e2)
% 203.62/34.47    (58)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.47    (59)  op(e1, e1) = all_10_2
% 203.62/34.47    (60)   ~ (all_52_23 = all_10_2)
% 203.62/34.47    (61)  all_58_3 = all_4_2
% 203.62/34.47    (62)   ~ (all_52_3 = all_4_2)
% 203.62/34.47    (63)  op(all_6_2, e3) = all_6_1
% 203.62/34.47    (64)  all_58_4 = all_52_17
% 203.62/34.47    (65)  all_14_2 = e3
% 203.62/34.47  
% 203.62/34.47  Begin of proof
% 203.62/34.47  | 
% 203.62/34.47  | COMBINE_EQS: (41), (65) imply:
% 203.62/34.47  |   (66)  all_58_15 = e3
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (27), (65) imply:
% 203.62/34.47  |   (67)   ~ (all_52_7 = e3)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (50), (65) imply:
% 203.62/34.47  |   (68)   ~ (all_52_27 = e3)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (28), (65) imply:
% 203.62/34.47  |   (69)   ~ (e3 = e0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (15), (65) imply:
% 203.62/34.47  |   (70)  op(e0, e0) = e3
% 203.62/34.47  | 
% 203.62/34.47  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.47  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.62/34.47  |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34), (35),
% 203.62/34.47  |            (36), (37), (38), (39), (40), (42), (43), (44), (45), (46), (47),
% 203.62/34.47  |            (48), (49), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 203.62/34.47  |            (60), (61), (62), (63), (64), (66), (67), (68), (69), (70) are
% 203.62/34.47  |            inconsistent by sub-proof #616.
% 203.62/34.47  | 
% 203.62/34.47  End of proof
% 203.62/34.47  
% 203.62/34.47  Sub-proof #585 shows that the following formulas are inconsistent:
% 203.62/34.47  ----------------------------------------------------------------
% 203.62/34.47    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.47    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.47    (3)  all_58_14 = all_52_23
% 203.62/34.47    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.47    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.47    (6)   ~ (all_52_5 = all_52_13)
% 203.62/34.47    (7)  all_58_1 = all_52_9
% 203.62/34.47    (8)   ~ (all_52_9 = all_52_13)
% 203.62/34.47    (9)   ~ (e3 = e0)
% 203.62/34.47    (10)  op(e2, e3) = all_52_3
% 203.62/34.47    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.47    (12)  op(e0, e2) = all_52_15
% 203.62/34.47    (13)   ~ (all_52_7 = all_52_15)
% 203.62/34.47    (14)   ~ (all_52_3 = all_52_19)
% 203.62/34.47    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.47    (16)   ~ (all_52_17 = all_52_25)
% 203.62/34.47    (17)   ~ (all_52_3 = all_6_2)
% 203.62/34.47    (18)  all_58_0 = all_6_2
% 203.62/34.47    (19)  op(all_14_2, e0) = all_14_1
% 203.62/34.47    (20)  all_56_4 = all_52_3
% 203.62/34.47    (21)   ~ (all_52_17 = all_10_2)
% 203.62/34.47    (22)   ~ (all_10_0 = e3)
% 203.62/34.47    (23)  all_40_2 = all_10_2
% 203.62/34.47    (24)  op(e3, e0) = all_52_25
% 203.62/34.47    (25)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 203.62/34.47    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.47    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.47    (28)   ~ (all_52_27 = all_52_29)
% 203.62/34.47    (29)  all_58_13 = all_52_15
% 203.62/34.47    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.47    (31)  all_58_9 = all_52_25
% 203.62/34.47    (32)   ~ (all_52_29 = all_14_2)
% 203.62/34.47    (33)  all_22_0 = all_6_0
% 203.62/34.47    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.47    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.47    (36)  op(e1, e3) = all_52_5
% 203.62/34.47    (37)  all_40_1 = all_10_1
% 203.62/34.47    (38)  op(e2, e2) = all_4_2
% 203.62/34.47    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.47    (40)   ~ (all_52_3 = all_52_5)
% 203.62/34.47    (41)  all_58_11 = all_52_29
% 203.62/34.47    (42)  all_56_5 = all_4_2
% 203.62/34.47    (43)   ~ (all_52_25 = all_14_2)
% 203.62/34.47    (44)   ~ (all_52_9 = all_52_15)
% 203.62/34.47    (45)   ~ (all_52_3 = all_52_27)
% 203.62/34.47    (46)  op(all_10_2, e1) = all_10_1
% 203.62/34.47    (47)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.47    (48)   ~ (all_52_7 = all_6_2)
% 203.62/34.47    (49)  op(e0, e0) = all_14_2
% 203.62/34.47    (50)  all_56_15 = all_14_2
% 203.62/34.47    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.47    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.47    (53)  all_56_11 = all_52_29
% 203.62/34.47    (54)   ~ (all_10_0 = e2)
% 203.62/34.47    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.47    (56)  all_56_9 = all_52_13
% 203.62/34.47    (57)   ~ (e2 = e1)
% 203.62/34.47    (58)   ~ (all_52_13 = all_10_2)
% 203.62/34.47    (59)   ~ (all_6_0 = e1)
% 203.62/34.47    (60)  op(e1, all_10_1) = all_10_0
% 203.62/34.47    (61)  all_58_10 = all_52_27
% 203.62/34.47    (62)  all_56_8 = all_52_5
% 203.62/34.47    (63)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.47    (64)   ~ (all_52_19 = all_52_23)
% 203.62/34.47    (65)   ~ (all_52_25 = all_52_29)
% 203.62/34.47    (66)  op(all_6_2, e3) = e2
% 203.62/34.47    (67)   ~ (all_52_29 = all_10_2)
% 203.62/34.47    (68)  all_58_7 = all_52_13
% 203.62/34.47    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.47    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.47    (71)   ~ (all_52_5 = all_52_7)
% 203.62/34.47    (72)  all_58_12 = all_52_7
% 203.62/34.47    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.47    (74)   ~ (all_52_7 = all_14_2)
% 203.62/34.47    (75)  all_58_2 = all_52_3
% 203.62/34.47    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.47    (77)  all_56_2 = all_52_17
% 203.62/34.47    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.47    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.47    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.47    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.47    (82)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.47    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.47    (84)   ~ (e2 = e0)
% 203.62/34.47    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.47    (86)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.47    (87)   ~ (all_52_5 = all_52_29)
% 203.62/34.47    (88)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.47    (89)  all_56_6 = all_52_19
% 203.62/34.47    (90)   ~ (all_52_15 = all_14_2)
% 203.62/34.47    (91)   ~ (all_52_19 = all_52_27)
% 203.62/34.47    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.47    (93)   ~ (all_6_0 = e2)
% 203.62/34.47    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.47            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.47    (95)  op(e3, e1) = all_52_17
% 203.62/34.47    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.47    (97)  op(e0, e3) = all_52_7
% 203.62/34.47    (98)  op(e1, e2) = all_52_13
% 203.62/34.47    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.47    (100)   ~ (all_52_9 = all_52_25)
% 203.62/34.47    (101)  all_58_15 = all_14_2
% 203.62/34.47    (102)   ~ (all_52_19 = all_10_2)
% 203.62/34.47    (103)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.47    (104)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3)
% 203.62/34.47    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.47    (106)  all_58_8 = all_10_2
% 203.62/34.47    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.47    (108)   ~ (all_52_5 = all_10_2)
% 203.62/34.47    (109)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.47    (110)   ~ (all_52_23 = all_14_2)
% 203.62/34.47    (111)  all_56_12 = all_52_7
% 203.62/34.47    (112)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.47    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.47    (114)  op(e3, e2) = all_6_0
% 203.62/34.47    (115)   ~ (all_52_25 = all_6_2)
% 203.62/34.47    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.47    (117)   ~ (all_52_9 = all_4_2)
% 203.62/34.47    (118)   ~ (all_52_5 = all_6_2)
% 203.62/34.47    (119)   ~ (all_52_9 = all_6_2)
% 203.62/34.47    (120)  all_56_0 = all_6_2
% 203.62/34.47    (121)  op(e3, e3) = all_6_2
% 203.62/34.47    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.47    (123)   ~ (all_52_27 = all_14_2)
% 203.62/34.47    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.47    (125)  all_56_14 = all_52_23
% 203.62/34.47    (126)  all_40_0 = all_10_0
% 203.62/34.47    (127)  all_56_3 = all_52_25
% 203.62/34.47    (128)  op(e0, all_14_1) = e2
% 203.62/34.47    (129)   ~ (all_52_3 = all_52_7)
% 203.62/34.47    (130)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.47    (131)  all_58_5 = all_52_19
% 203.62/34.47    (132)  all_56_1 = all_52_9
% 203.62/34.47    (133)   ~ (all_52_15 = all_4_2)
% 203.62/34.47    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.47           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.47           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.47           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.47    (135)   ~ (all_52_27 = all_4_2)
% 203.62/34.47    (136)  all_58_6 = all_52_5
% 203.62/34.47    (137)  op(e3, e2) = all_52_9
% 203.62/34.47    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.47    (139)   ~ (all_52_17 = all_6_2)
% 203.62/34.47    (140)  all_30_1 = all_10_1
% 203.62/34.47    (141)   ~ (e1 = e0)
% 203.62/34.47    (142)  all_50_0 = e2
% 203.62/34.47    (143)   ~ (e3 = e2)
% 203.62/34.47    (144)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.47    (145)   ~ (all_52_9 = all_52_17)
% 203.62/34.47    (146)  all_56_10 = all_10_2
% 203.62/34.47    (147)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.47    (148)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2)
% 203.62/34.47    (149)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.47    (150)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.47    (151)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.47    (152)  op(e1, e1) = all_10_2
% 203.62/34.47    (153)   ~ (all_52_23 = all_10_2)
% 203.62/34.47    (154)   ~ (all_52_7 = all_52_23)
% 203.62/34.47    (155)   ~ (all_52_17 = all_52_19)
% 203.62/34.47    (156)  all_58_3 = all_4_2
% 203.62/34.47    (157)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.47    (158)   ~ (all_52_3 = all_4_2)
% 203.62/34.47    (159)   ~ (all_52_19 = all_4_2)
% 203.62/34.47    (160)   ~ (all_52_17 = all_52_23)
% 203.62/34.47    (161)  op(all_6_2, e3) = all_6_1
% 203.62/34.47    (162)  all_22_2 = all_6_2
% 203.62/34.47    (163)  all_58_4 = all_52_17
% 203.62/34.47    (164)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.47    (165)  all_50_2 = all_14_2
% 203.62/34.47    (166)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.47  
% 203.62/34.47  Begin of proof
% 203.62/34.47  | 
% 203.62/34.47  | GROUND_INST: instantiating (5) with all_52_9, all_6_0, e2, e3, simplifying
% 203.62/34.47  |              with (114), (137) gives:
% 203.62/34.47  |   (167)  all_52_9 = all_6_0
% 203.62/34.47  | 
% 203.62/34.47  | COMBINE_EQS: (132), (167) imply:
% 203.62/34.47  |   (168)  all_56_1 = all_6_0
% 203.62/34.47  | 
% 203.62/34.47  | COMBINE_EQS: (7), (167) imply:
% 203.62/34.47  |   (169)  all_58_1 = all_6_0
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (8), (167) imply:
% 203.62/34.47  |   (170)   ~ (all_52_13 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (170) implies:
% 203.62/34.47  |   (171)   ~ (all_52_13 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (44), (167) imply:
% 203.62/34.47  |   (172)   ~ (all_52_15 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (172) implies:
% 203.62/34.47  |   (173)   ~ (all_52_15 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (145), (167) imply:
% 203.62/34.47  |   (174)   ~ (all_52_17 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (174) implies:
% 203.62/34.47  |   (175)   ~ (all_52_17 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (100), (167) imply:
% 203.62/34.47  |   (176)   ~ (all_52_25 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | SIMP: (176) implies:
% 203.62/34.47  |   (177)   ~ (all_52_25 = all_6_0)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (119), (167) imply:
% 203.62/34.47  |   (178)   ~ (all_6_0 = all_6_2)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (117), (167) imply:
% 203.62/34.47  |   (179)   ~ (all_6_0 = all_4_2)
% 203.62/34.47  | 
% 203.62/34.47  | REDUCE: (63), (167) imply:
% 203.62/34.47  |   (180)  op(all_6_0, all_6_0) = all_52_8
% 203.62/34.47  | 
% 203.62/34.47  | BETA: splitting (148) gives:
% 203.62/34.47  | 
% 203.62/34.47  | Case 1:
% 203.62/34.47  | | 
% 203.62/34.47  | |   (181)   ~ (all_30_1 = e3)
% 203.62/34.47  | | 
% 203.62/34.47  | | REDUCE: (140), (181) imply:
% 203.62/34.47  | |   (182)   ~ (all_10_1 = e3)
% 203.62/34.47  | | 
% 203.62/34.47  | | BETA: splitting (104) gives:
% 203.62/34.47  | | 
% 203.62/34.47  | | Case 1:
% 203.62/34.47  | | | 
% 203.62/34.47  | | |   (183)   ~ (all_40_1 = e2)
% 203.62/34.47  | | | 
% 203.62/34.47  | | | REDUCE: (37), (183) imply:
% 203.62/34.47  | | |   (184)   ~ (all_10_1 = e2)
% 203.62/34.47  | | | 
% 203.62/34.47  | | | BETA: splitting (25) gives:
% 203.62/34.47  | | | 
% 203.62/34.47  | | | Case 1:
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | |   (185)   ~ (all_50_0 = e2)
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | | REDUCE: (142), (185) imply:
% 203.62/34.47  | | | |   (186)  $false
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | | CLOSE: (186) is inconsistent.
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | Case 2:
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | |   (187)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | | BETA: splitting (94) gives:
% 203.62/34.47  | | | | 
% 203.62/34.47  | | | | Case 1:
% 203.62/34.47  | | | | | 
% 203.62/34.47  | | | | |   (188)  all_58_15 = e0
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | REF_CLOSE: (5), (19), (49), (84), (101), (128), (130), (188) are
% 203.62/34.48  | | | | |            inconsistent by sub-proof #612.
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | Case 2:
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | |   (189)   ~ (all_58_15 = e0)
% 203.62/34.48  | | | | |   (190)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.48  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | ALPHA: (190) implies:
% 203.62/34.48  | | | | |   (191)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.48  | | | | |   (192)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | REDUCE: (101), (189) imply:
% 203.62/34.48  | | | | |   (193)   ~ (all_14_2 = e0)
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | BETA: splitting (144) gives:
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | Case 1:
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | |   (194)  all_56_1 = e3
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | COMBINE_EQS: (168), (194) imply:
% 203.62/34.48  | | | | | |   (195)  all_6_0 = e3
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | COMBINE_EQS: (169), (195) imply:
% 203.62/34.48  | | | | | |   (196)  all_58_1 = e3
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (171), (195) imply:
% 203.62/34.48  | | | | | |   (197)   ~ (all_52_13 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (173), (195) imply:
% 203.62/34.48  | | | | | |   (198)   ~ (all_52_15 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (175), (195) imply:
% 203.62/34.48  | | | | | |   (199)   ~ (all_52_17 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (177), (195) imply:
% 203.62/34.48  | | | | | |   (200)   ~ (all_52_25 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (178), (195) imply:
% 203.62/34.48  | | | | | |   (201)   ~ (all_6_2 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | SIMP: (201) implies:
% 203.62/34.48  | | | | | |   (202)   ~ (all_6_2 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (179), (195) imply:
% 203.62/34.48  | | | | | |   (203)   ~ (all_4_2 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | SIMP: (203) implies:
% 203.62/34.48  | | | | | |   (204)   ~ (all_4_2 = e3)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (59), (195) imply:
% 203.62/34.48  | | | | | |   (205)   ~ (e3 = e1)
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (180), (195) imply:
% 203.62/34.48  | | | | | |   (206)  op(e3, e3) = all_52_8
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_8, e3, e3,
% 203.62/34.48  | | | | | |              simplifying with (121), (206) gives:
% 203.62/34.48  | | | | | |   (207)  all_52_8 = all_6_2
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | BETA: splitting (134) gives:
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | Case 1:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | |   (208)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 203.62/34.48  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 203.62/34.48  | | | | | | |            e1 & all_52_14 = e0)
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | BETA: splitting (208) gives:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | |   (209)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 203.62/34.48  | | | | | | | |          all_52_6 = e0
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REF_CLOSE: (4), (5), (15), (18), (26), (38), (47), (49), (51),
% 203.62/34.48  | | | | | | | |            (72), (74), (75), (79), (108), (121), (136), (138),
% 203.62/34.48  | | | | | | | |            (152), (158), (202), (209) are inconsistent by
% 203.62/34.48  | | | | | | | |            sub-proof #835.
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | |   (210)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 203.62/34.48  | | | | | | | |          all_52_14 = e0
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REF_CLOSE: (202), (207), (210) are inconsistent by sub-proof
% 203.62/34.48  | | | | | | | |            #834.
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | End of split
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | Case 2:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | |   (211)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 203.62/34.48  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 203.62/34.48  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | BETA: splitting (211) gives:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | |   (212)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 203.62/34.48  | | | | | | | |          all_52_22 = e0
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | ALPHA: (212) implies:
% 203.62/34.48  | | | | | | | |   (213)  all_52_22 = e0
% 203.62/34.48  | | | | | | | |   (214)  all_52_20 = e1
% 203.62/34.48  | | | | | | | |   (215)  all_52_18 = e2
% 203.62/34.48  | | | | | | | |   (216)  all_52_16 = e3
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REDUCE: (112), (216) imply:
% 203.62/34.48  | | | | | | | |   (217)  op(all_52_17, all_52_17) = e3
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REDUCE: (27), (215) imply:
% 203.62/34.48  | | | | | | | |   (218)  op(all_52_19, all_52_19) = e2
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REDUCE: (103), (213) imply:
% 203.62/34.48  | | | | | | | |   (219)  op(all_52_23, all_52_23) = e0
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REDUCE: (30), (214) imply:
% 203.62/34.48  | | | | | | | |   (220)  op(all_10_2, all_10_2) = e1
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (12), (16), (17),
% 203.62/34.48  | | | | | | | |            (18), (19), (21), (24), (26), (29), (31), (32), (34),
% 203.62/34.48  | | | | | | | |            (35), (38), (40), (41), (43), (46), (48), (49), (50),
% 203.62/34.48  | | | | | | | |            (51), (55), (57), (58), (61), (64), (66), (68), (69),
% 203.62/34.48  | | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 203.62/34.48  | | | | | | | |            (84), (86), (88), (89), (90), (95), (97), (99),
% 203.62/34.48  | | | | | | | |            (101), (102), (106), (107), (115), (116), (121),
% 203.62/34.48  | | | | | | | |            (123), (125), (127), (128), (129), (130), (131),
% 203.62/34.48  | | | | | | | |            (133), (135), (136), (138), (139), (141), (143),
% 203.62/34.48  | | | | | | | |            (146), (147), (152), (153), (154), (155), (156),
% 203.62/34.48  | | | | | | | |            (158), (160), (163), (164), (165), (166), (184),
% 203.62/34.48  | | | | | | | |            (187), (191), (196), (197), (198), (199), (200),
% 203.62/34.48  | | | | | | | |            (202), (204), (205), (206), (217), (218), (219),
% 203.62/34.48  | | | | | | | |            (220) are inconsistent by sub-proof #601.
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | |   (221)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.62/34.48  | | | | | | | |          all_52_30 = e0
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 203.62/34.48  | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (24),
% 203.62/34.48  | | | | | | | |            (26), (27), (28), (29), (31), (32), (35), (36), (38),
% 203.62/34.48  | | | | | | | |            (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 203.62/34.48  | | | | | | | |            (49), (50), (51), (52), (53), (55), (57), (58), (61),
% 203.62/34.48  | | | | | | | |            (62), (63), (65), (66), (67), (68), (69), (70), (71),
% 203.62/34.48  | | | | | | | |            (72), (73), (74), (75), (77), (78), (79), (80), (81),
% 203.62/34.48  | | | | | | | |            (83), (84), (85), (87), (90), (91), (92), (95), (96),
% 203.62/34.48  | | | | | | | |            (97), (99), (100), (101), (102), (103), (105), (106),
% 203.62/34.48  | | | | | | | |            (107), (108), (109), (110), (111), (113), (115),
% 203.62/34.48  | | | | | | | |            (116), (117), (118), (121), (122), (123), (124),
% 203.62/34.48  | | | | | | | |            (125), (127), (129), (130), (131), (133), (135),
% 203.62/34.48  | | | | | | | |            (136), (138), (139), (141), (143), (151), (152),
% 203.62/34.48  | | | | | | | |            (153), (154), (156), (157), (158), (159), (160),
% 203.62/34.48  | | | | | | | |            (161), (163), (166), (184), (191), (192), (193),
% 203.62/34.48  | | | | | | | |            (196), (197), (198), (199), (200), (202), (204),
% 203.62/34.48  | | | | | | | |            (205), (221) are inconsistent by sub-proof #600.
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | End of split
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | End of split
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | Case 2:
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | |   (222)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REF_CLOSE: (5), (10), (17), (33), (47), (59), (66), (82), (93),
% 203.62/34.48  | | | | | |            (120), (121), (143), (150), (162), (168), (178), (222)
% 203.62/34.48  | | | | | |            are inconsistent by sub-proof #820.
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | End of split
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | End of split
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | End of split
% 203.62/34.48  | | | 
% 203.62/34.48  | | Case 2:
% 203.62/34.48  | | | 
% 203.62/34.48  | | |   (223)  all_40_1 = e2
% 203.62/34.48  | | |   (224)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.62/34.48  | | | 
% 203.62/34.48  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 203.62/34.48  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 203.62/34.48  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.62/34.48  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (45), (46),
% 203.62/34.48  | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 203.62/34.48  | | |            (57), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 203.62/34.48  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (77), (79),
% 203.62/34.48  | | |            (80), (82), (83), (84), (85), (86), (87), (88), (91), (92),
% 203.62/34.48  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 203.62/34.48  | | |            (103), (105), (106), (107), (108), (109), (110), (111), (112),
% 203.62/34.48  | | |            (113), (115), (116), (117), (118), (120), (121), (122), (123),
% 203.62/34.48  | | |            (124), (125), (126), (127), (128), (129), (130), (131), (133),
% 203.62/34.48  | | |            (134), (135), (136), (138), (139), (141), (144), (146), (147),
% 203.62/34.48  | | |            (149), (150), (151), (152), (153), (154), (156), (157), (158),
% 203.62/34.48  | | |            (159), (160), (161), (162), (163), (164), (166), (168), (169),
% 203.62/34.48  | | |            (171), (173), (175), (177), (178), (179), (180), (182), (223),
% 203.62/34.48  | | |            (224) are inconsistent by sub-proof #599.
% 203.62/34.48  | | | 
% 203.62/34.48  | | End of split
% 203.62/34.48  | | 
% 203.62/34.48  | Case 2:
% 203.62/34.48  | | 
% 203.62/34.48  | |   (225)  all_30_1 = e3
% 203.62/34.48  | | 
% 203.62/34.48  | | COMBINE_EQS: (140), (225) imply:
% 203.62/34.48  | |   (226)  all_10_1 = e3
% 203.62/34.48  | | 
% 203.62/34.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15),
% 203.62/34.48  | |            (16), (17), (18), (19), (21), (22), (26), (27), (28), (29), (30),
% 203.62/34.48  | |            (31), (32), (33), (34), (35), (36), (38), (39), (40), (41), (42),
% 203.62/34.48  | |            (43), (45), (46), (47), (48), (49), (50), (51), (52), (53), (55),
% 203.62/34.48  | |            (57), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.62/34.48  | |            (69), (70), (71), (72), (73), (74), (75), (77), (79), (80), (82),
% 203.62/34.48  | |            (84), (85), (86), (87), (88), (91), (92), (93), (94), (95), (96),
% 203.62/34.48  | |            (97), (99), (100), (101), (102), (103), (105), (106), (107),
% 203.62/34.48  | |            (108), (109), (110), (111), (112), (113), (115), (116), (117),
% 203.62/34.48  | |            (118), (120), (121), (122), (123), (124), (125), (127), (128),
% 203.62/34.48  | |            (129), (130), (131), (133), (134), (135), (136), (138), (139),
% 203.62/34.48  | |            (141), (143), (144), (145), (146), (147), (150), (151), (152),
% 203.62/34.48  | |            (153), (154), (156), (157), (158), (159), (160), (161), (162),
% 203.62/34.48  | |            (163), (164), (166), (168), (169), (171), (173), (175), (177),
% 203.62/34.48  | |            (178), (179), (180), (226) are inconsistent by sub-proof #592.
% 203.62/34.48  | | 
% 203.62/34.48  | End of split
% 203.62/34.48  | 
% 203.62/34.48  End of proof
% 203.62/34.48  
% 203.62/34.48  Sub-proof #586 shows that the following formulas are inconsistent:
% 203.62/34.48  ----------------------------------------------------------------
% 203.62/34.48    (1)  all_58_15 = e3
% 203.62/34.48    (2)  all_58_15 = e1
% 203.62/34.48    (3)   ~ (e3 = e1)
% 203.62/34.48  
% 203.62/34.48  Begin of proof
% 203.62/34.48  | 
% 203.62/34.48  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.48  |   (4)  e3 = e1
% 203.62/34.48  | 
% 203.62/34.48  | SIMP: (4) implies:
% 203.62/34.48  |   (5)  e3 = e1
% 203.62/34.48  | 
% 203.62/34.48  | REDUCE: (3), (5) imply:
% 203.62/34.48  |   (6)  $false
% 203.62/34.48  | 
% 203.62/34.48  | CLOSE: (6) is inconsistent.
% 203.62/34.48  | 
% 203.62/34.48  End of proof
% 203.62/34.48  
% 203.62/34.48  Sub-proof #587 shows that the following formulas are inconsistent:
% 203.62/34.48  ----------------------------------------------------------------
% 203.62/34.48    (1)  all_58_11 = all_14_1
% 203.62/34.48    (2)  all_58_11 = e3
% 203.62/34.48    (3)   ~ (all_14_1 = e3)
% 203.62/34.48  
% 203.62/34.48  Begin of proof
% 203.62/34.48  | 
% 203.62/34.48  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.48  |   (4)  all_14_1 = e3
% 203.62/34.48  | 
% 203.62/34.48  | SIMP: (4) implies:
% 203.62/34.48  |   (5)  all_14_1 = e3
% 203.62/34.48  | 
% 203.62/34.48  | REDUCE: (3), (5) imply:
% 203.62/34.48  |   (6)  $false
% 203.62/34.48  | 
% 203.62/34.48  | CLOSE: (6) is inconsistent.
% 203.62/34.48  | 
% 203.62/34.48  End of proof
% 203.62/34.48  
% 203.62/34.48  Sub-proof #588 shows that the following formulas are inconsistent:
% 203.62/34.48  ----------------------------------------------------------------
% 203.62/34.48    (1)   ~ (all_52_25 = all_52_27)
% 203.62/34.48    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.48    (3)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 203.62/34.48    (4)  op(all_52_7, all_52_7) = e0
% 203.62/34.48    (5)  op(all_52_5, all_52_5) = e1
% 203.62/34.48    (6)   ~ (all_52_17 = all_52_25)
% 203.62/34.48    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.48    (8)  all_50_1 = all_14_1
% 203.62/34.48    (9)  all_58_0 = all_6_2
% 203.62/34.48    (10)   ~ (all_52_17 = all_10_2)
% 203.62/34.48    (11)   ~ (all_10_0 = e3)
% 203.62/34.48    (12)  all_40_2 = all_10_2
% 203.62/34.48    (13)  op(e3, e0) = all_52_25
% 203.62/34.48    (14)  all_58_9 = all_52_25
% 203.62/34.48    (15)  op(e2, e2) = all_4_2
% 203.62/34.48    (16)  all_58_7 = all_10_0
% 203.62/34.48    (17)  all_58_11 = all_52_29
% 203.62/34.48    (18)  op(e0, e0) = all_14_2
% 203.62/34.48    (19)  all_58_15 = e3
% 203.62/34.48    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.48    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.48    (22)   ~ (all_10_0 = e2)
% 203.62/34.48    (23)  op(e0, e0) = e3
% 203.62/34.48    (24)  all_58_10 = all_52_27
% 203.62/34.48    (25)  all_56_9 = all_10_0
% 203.62/34.48    (26)  op(all_6_2, all_6_2) = e3
% 203.62/34.48    (27)  all_58_12 = all_52_7
% 203.62/34.48    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.48    (29)   ~ (all_52_7 = all_14_2)
% 203.62/34.48    (30)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.62/34.48    (31)  all_58_2 = all_52_3
% 203.62/34.48    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.48    (33)   ~ (all_52_29 = e3)
% 203.62/34.48    (34)   ~ (all_52_25 = e3)
% 203.62/34.48    (35)  op(all_52_3, all_52_3) = e2
% 203.62/34.48    (36)  op(e3, e3) = all_52_30
% 203.62/34.48    (37)  all_50_2 = e3
% 203.62/34.48    (38)  op(e3, e1) = all_52_17
% 203.62/34.48    (39)   ~ (all_10_0 = all_10_2)
% 203.62/34.48    (40)  all_58_8 = all_10_2
% 203.62/34.48    (41)   ~ (all_52_5 = all_10_2)
% 203.62/34.48    (42)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.48    (43)   ~ (all_52_5 = all_6_2)
% 203.62/34.48    (44)  op(e3, e3) = all_6_2
% 203.62/34.48    (45)  op(e3, e0) = all_14_1
% 203.62/34.48    (46)   ~ (all_52_29 = all_10_0)
% 203.62/34.48    (47)  all_40_0 = all_10_0
% 203.62/34.48    (48)  all_56_3 = all_52_25
% 203.62/34.48    (49)  op(e0, all_14_1) = e2
% 203.62/34.48    (50)  all_58_6 = all_52_5
% 203.62/34.48    (51)  op(all_10_2, e1) = e2
% 203.62/34.48    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.48    (53)  op(e1, e1) = all_10_2
% 203.62/34.48    (54)   ~ (all_52_3 = all_4_2)
% 203.62/34.48    (55)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.48  
% 203.62/34.48  Begin of proof
% 203.62/34.48  | 
% 203.62/34.48  | BETA: splitting (3) gives:
% 203.62/34.48  | 
% 203.62/34.48  | Case 1:
% 203.62/34.48  | | 
% 203.62/34.48  | |   (56)   ~ (all_50_1 = e1)
% 203.62/34.48  | | 
% 203.62/34.48  | | REDUCE: (8), (56) imply:
% 203.62/34.48  | |   (57)   ~ (all_14_1 = e1)
% 203.62/34.48  | | 
% 203.62/34.48  | | GROUND_INST: instantiating (2) with all_52_25, all_14_1, e0, e3, simplifying
% 203.62/34.48  | |              with (13), (45) gives:
% 203.62/34.48  | |   (58)  all_52_25 = all_14_1
% 203.62/34.48  | | 
% 203.62/34.48  | | GROUND_INST: instantiating (2) with all_6_2, all_52_30, e3, e3, simplifying
% 203.62/34.48  | |              with (36), (44) gives:
% 203.62/34.48  | |   (59)  all_52_30 = all_6_2
% 203.62/34.48  | | 
% 203.62/34.48  | | COMBINE_EQS: (48), (58) imply:
% 203.62/34.48  | |   (60)  all_56_3 = all_14_1
% 203.62/34.48  | | 
% 203.62/34.48  | | COMBINE_EQS: (14), (58) imply:
% 203.62/34.48  | |   (61)  all_58_9 = all_14_1
% 203.62/34.48  | | 
% 203.62/34.48  | | REDUCE: (6), (58) imply:
% 203.62/34.48  | |   (62)   ~ (all_52_17 = all_14_1)
% 203.62/34.48  | | 
% 203.62/34.48  | | REDUCE: (1), (58) imply:
% 203.62/34.48  | |   (63)   ~ (all_52_27 = all_14_1)
% 203.62/34.48  | | 
% 203.62/34.48  | | SIMP: (63) implies:
% 203.62/34.48  | |   (64)   ~ (all_52_27 = all_14_1)
% 203.62/34.48  | | 
% 203.62/34.48  | | REDUCE: (34), (58) imply:
% 203.62/34.48  | |   (65)   ~ (all_14_1 = e3)
% 203.62/34.48  | | 
% 203.62/34.48  | | REDUCE: (55), (58) imply:
% 203.62/34.48  | |   (66)  op(all_14_1, all_14_1) = all_52_24
% 203.62/34.48  | | 
% 203.62/34.48  | | BETA: splitting (42) gives:
% 203.62/34.48  | | 
% 203.62/34.48  | | Case 1:
% 203.62/34.48  | | | 
% 203.62/34.48  | | |   (67)  all_56_3 = e3
% 203.62/34.48  | | | 
% 203.62/34.48  | | | REF_CLOSE: (60), (65), (67) are inconsistent by sub-proof #1200.
% 203.62/34.48  | | | 
% 203.62/34.48  | | Case 2:
% 203.62/34.48  | | | 
% 203.62/34.48  | | |   (68)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.48  | | | 
% 203.62/34.48  | | | BETA: splitting (21) gives:
% 203.62/34.48  | | | 
% 203.62/34.48  | | | Case 1:
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | |   (69)  all_58_9 = e1
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | | REF_CLOSE: (57), (61), (69) are inconsistent by sub-proof #610.
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | Case 2:
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | |   (70)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | | BETA: splitting (28) gives:
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | | Case 1:
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | |   (71)  all_58_6 = e3
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | REF_CLOSE: (2), (4), (5), (9), (15), (18), (20), (26), (27), (29),
% 203.62/34.48  | | | | |            (31), (32), (35), (41), (43), (44), (50), (52), (53), (54),
% 203.62/34.48  | | | | |            (71) are inconsistent by sub-proof #876.
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | Case 2:
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | |   (72)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | BETA: splitting (72) gives:
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | | Case 1:
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | |   (73)  all_58_7 = e3
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | COMBINE_EQS: (16), (73) imply:
% 203.62/34.48  | | | | | |   (74)  all_10_0 = e3
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | REDUCE: (11), (74) imply:
% 203.62/34.48  | | | | | |   (75)  $false
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | CLOSE: (75) is inconsistent.
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | Case 2:
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | |   (76)  all_58_8 = e3 | all_58_11 = e3
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | BETA: splitting (76) gives:
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | | Case 1:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | |   (77)  all_58_8 = e3
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | COMBINE_EQS: (40), (77) imply:
% 203.62/34.48  | | | | | | |   (78)  all_10_2 = e3
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | COMBINE_EQS: (12), (78) imply:
% 203.62/34.48  | | | | | | |   (79)  all_40_2 = e3
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | REDUCE: (10), (78) imply:
% 203.62/34.48  | | | | | | |   (80)   ~ (all_52_17 = e3)
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | REDUCE: (51), (78) imply:
% 203.62/34.48  | | | | | | |   (81)  op(e3, e1) = e2
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | BETA: splitting (30) gives:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | |   (82)   ~ (all_40_2 = e3)
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REDUCE: (79), (82) imply:
% 203.62/34.48  | | | | | | | |   (83)  $false
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | CLOSE: (83) is inconsistent.
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | |   (84)   ~ (all_40_0 = e0)
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | REDUCE: (47), (84) imply:
% 203.62/34.48  | | | | | | | |   (85)   ~ (all_10_0 = e0)
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | BETA: splitting (7) gives:
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | |   (86)  all_56_9 = e2
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | REF_CLOSE: (22), (25), (86) are inconsistent by sub-proof
% 203.62/34.48  | | | | | | | | |            #991.
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | |   (87)  all_56_9 = e1 | all_56_9 = e0
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | BETA: splitting (87) gives:
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | |   (88)  all_56_9 = e1
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | COMBINE_EQS: (25), (88) imply:
% 203.62/34.48  | | | | | | | | | |   (89)  all_10_0 = e1
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | SIMP: (89) implies:
% 203.62/34.48  | | | | | | | | | |   (90)  all_10_0 = e1
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | REDUCE: (46), (90) imply:
% 203.62/34.48  | | | | | | | | | |   (91)   ~ (all_52_29 = e1)
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | REDUCE: (11), (90) imply:
% 203.62/34.48  | | | | | | | | | |   (92)   ~ (e3 = e1)
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | SIMP: (92) implies:
% 203.62/34.48  | | | | | | | | | |   (93)   ~ (e3 = e1)
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | BETA: splitting (70) gives:
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | |   (94)  all_58_10 = e1
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | COMBINE_EQS: (24), (94) imply:
% 203.62/34.48  | | | | | | | | | | |   (95)  all_52_27 = e1
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | SIMP: (95) implies:
% 203.62/34.48  | | | | | | | | | | |   (96)  all_52_27 = e1
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | REDUCE: (64), (96) imply:
% 203.62/34.48  | | | | | | | | | | |   (97)   ~ (all_14_1 = e1)
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_17, e2, e1, e3,
% 203.62/34.48  | | | | | | | | | | |              simplifying with (38), (81) gives:
% 203.62/34.48  | | | | | | | | | | |   (98)  all_52_17 = e2
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | REDUCE: (62), (98) imply:
% 203.62/34.48  | | | | | | | | | | |   (99)   ~ (all_14_1 = e2)
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | SIMP: (99) implies:
% 203.62/34.48  | | | | | | | | | | |   (100)   ~ (all_14_1 = e2)
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | REDUCE: (80), (98) imply:
% 203.62/34.48  | | | | | | | | | | |   (101)   ~ (e3 = e2)
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | SIMP: (101) implies:
% 203.62/34.48  | | | | | | | | | | |   (102)   ~ (e3 = e2)
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | REF_CLOSE: (2), (23), (49), (57), (60), (66), (68), (100),
% 203.62/34.48  | | | | | | | | | | |            (102) are inconsistent by sub-proof #611.
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | |   (103)  all_58_11 = e1 | all_58_15 = e1
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | BETA: splitting (103) gives:
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | Case 1:
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | |   (104)  all_58_11 = e1
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | | REF_CLOSE: (17), (91), (104) are inconsistent by sub-proof
% 203.62/34.48  | | | | | | | | | | | |            #873.
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | |   (105)  all_58_15 = e1
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | | COMBINE_EQS: (19), (105) imply:
% 203.62/34.48  | | | | | | | | | | | |   (106)  e3 = e1
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | | REDUCE: (93), (106) imply:
% 203.62/34.48  | | | | | | | | | | | |   (107)  $false
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | | CLOSE: (107) is inconsistent.
% 203.62/34.48  | | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | | End of split
% 203.62/34.48  | | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | End of split
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | Case 2:
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | |   (108)  all_56_9 = e0
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | | REF_CLOSE: (25), (85), (108) are inconsistent by sub-proof
% 203.62/34.48  | | | | | | | | | |            #989.
% 203.62/34.48  | | | | | | | | | | 
% 203.62/34.48  | | | | | | | | | End of split
% 203.62/34.48  | | | | | | | | | 
% 203.62/34.48  | | | | | | | | End of split
% 203.62/34.48  | | | | | | | | 
% 203.62/34.48  | | | | | | | End of split
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | Case 2:
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | |   (109)  all_58_11 = e3
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | | REF_CLOSE: (17), (33), (109) are inconsistent by sub-proof #1323.
% 203.62/34.48  | | | | | | | 
% 203.62/34.48  | | | | | | End of split
% 203.62/34.48  | | | | | | 
% 203.62/34.48  | | | | | End of split
% 203.62/34.48  | | | | | 
% 203.62/34.48  | | | | End of split
% 203.62/34.48  | | | | 
% 203.62/34.48  | | | End of split
% 203.62/34.48  | | | 
% 203.62/34.48  | | End of split
% 203.62/34.48  | | 
% 203.62/34.48  | Case 2:
% 203.62/34.48  | | 
% 203.62/34.48  | |   (110)   ~ (all_50_2 = e3)
% 203.62/34.48  | | 
% 203.62/34.48  | | REDUCE: (37), (110) imply:
% 203.62/34.48  | |   (111)  $false
% 203.62/34.48  | | 
% 203.62/34.48  | | CLOSE: (111) is inconsistent.
% 203.62/34.48  | | 
% 203.62/34.48  | End of split
% 203.62/34.48  | 
% 203.62/34.48  End of proof
% 203.62/34.48  
% 203.62/34.48  Sub-proof #589 shows that the following formulas are inconsistent:
% 203.62/34.48  ----------------------------------------------------------------
% 203.62/34.48    (1)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 203.62/34.48    (2)  all_58_14 = all_52_23
% 203.62/34.48    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.48    (4)  op(all_52_7, all_52_7) = e0
% 203.62/34.48    (5)  op(all_52_5, all_52_5) = e1
% 203.62/34.48    (6)   ~ (e3 = e0)
% 203.62/34.48    (7)  all_58_0 = all_6_2
% 203.62/34.48    (8)  op(all_14_2, e0) = all_14_1
% 203.62/34.48    (9)  all_58_13 = e3
% 203.62/34.48    (10)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.49    (11)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.49    (12)  op(e2, e2) = all_4_2
% 203.62/34.49    (13)  all_58_11 = all_52_29
% 203.62/34.49    (14)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.49    (15)  op(e0, e0) = all_14_2
% 203.62/34.49    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.49    (17)  op(e1, e0) = all_52_29
% 203.62/34.49    (18)   ~ (e2 = e1)
% 203.62/34.49    (19)   ~ (all_6_0 = e1)
% 203.62/34.49    (20)  all_58_10 = all_52_27
% 203.62/34.49    (21)   ~ (all_52_19 = all_52_23)
% 203.62/34.49    (22)   ~ (all_52_29 = all_10_2)
% 203.62/34.49    (23)  op(all_6_2, all_6_2) = e3
% 203.62/34.49    (24)  all_58_12 = all_52_7
% 203.62/34.49    (25)   ~ (all_52_7 = all_14_2)
% 203.62/34.49    (26)  all_58_2 = all_52_3
% 203.62/34.49    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.49    (28)  op(e3, all_6_1) = all_6_0
% 203.62/34.49    (29)   ~ (e2 = e0)
% 203.62/34.49    (30)   ~ (all_52_23 = e3)
% 203.62/34.49    (31)  op(all_52_3, all_52_3) = e2
% 203.62/34.49    (32)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.49    (33)   ~ (all_52_27 = e3)
% 203.62/34.49    (34)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.49    (35)  all_58_15 = all_14_2
% 203.62/34.49    (36)   ~ (all_52_19 = all_10_2)
% 203.62/34.49    (37)  all_58_8 = all_10_2
% 203.62/34.49    (38)   ~ (all_52_5 = all_10_2)
% 203.62/34.49    (39)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.49    (40)  all_56_12 = all_52_7
% 203.62/34.49    (41)  op(e3, e3) = all_6_2
% 203.62/34.49    (42)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.49    (43)  all_58_5 = all_52_19
% 203.62/34.49    (44)  all_58_6 = all_52_5
% 203.62/34.49    (45)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.49    (46)   ~ (all_52_17 = all_6_2)
% 203.62/34.49    (47)   ~ (e1 = e0)
% 203.62/34.49    (48)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.49    (49)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.49    (50)  op(e1, e1) = all_10_2
% 203.62/34.49    (51)   ~ (all_52_23 = all_10_2)
% 203.62/34.49    (52)   ~ (all_52_3 = all_4_2)
% 203.62/34.49    (53)  op(all_6_2, e3) = all_6_1
% 203.62/34.49    (54)  all_58_4 = all_52_17
% 203.62/34.49    (55)   ~ (all_14_2 = e3)
% 203.62/34.49  
% 203.62/34.49  Begin of proof
% 203.62/34.49  | 
% 203.62/34.49  | BETA: splitting (48) gives:
% 203.62/34.49  | 
% 203.62/34.49  | Case 1:
% 203.62/34.49  | | 
% 203.62/34.49  | |   (56)  all_58_10 = e3
% 203.62/34.49  | | 
% 203.62/34.49  | | REF_CLOSE: (20), (33), (56) are inconsistent by sub-proof #1301.
% 203.62/34.49  | | 
% 203.62/34.49  | Case 2:
% 203.62/34.49  | | 
% 203.62/34.49  | |   (57)  all_58_11 = e3 | all_58_15 = e3
% 203.62/34.49  | | 
% 203.62/34.49  | | BETA: splitting (57) gives:
% 203.62/34.49  | | 
% 203.62/34.49  | | Case 1:
% 203.62/34.49  | | | 
% 203.62/34.49  | | |   (58)  all_58_11 = e3
% 203.62/34.49  | | | 
% 203.62/34.49  | | | COMBINE_EQS: (13), (58) imply:
% 203.62/34.49  | | |   (59)  all_52_29 = e3
% 203.62/34.49  | | | 
% 203.62/34.49  | | | SIMP: (59) implies:
% 203.62/34.49  | | |   (60)  all_52_29 = e3
% 203.62/34.49  | | | 
% 203.62/34.49  | | | REDUCE: (22), (60) imply:
% 203.62/34.49  | | |   (61)   ~ (all_10_2 = e3)
% 203.62/34.49  | | | 
% 203.62/34.49  | | | SIMP: (61) implies:
% 203.62/34.49  | | |   (62)   ~ (all_10_2 = e3)
% 203.62/34.49  | | | 
% 203.62/34.49  | | | REDUCE: (39), (60) imply:
% 203.62/34.49  | | |   (63)  op(e3, e3) = all_52_28
% 203.62/34.49  | | | 
% 203.62/34.49  | | | REDUCE: (17), (60) imply:
% 203.62/34.49  | | |   (64)  op(e1, e0) = e3
% 203.62/34.49  | | | 
% 203.62/34.49  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_28, e3, e3,
% 203.62/34.49  | | |              simplifying with (41), (63) gives:
% 203.62/34.49  | | |   (65)  all_52_28 = all_6_2
% 203.62/34.49  | | | 
% 203.62/34.49  | | | BETA: splitting (42) gives:
% 203.62/34.49  | | | 
% 203.62/34.49  | | | Case 1:
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | |   (66)  all_58_0 = e3
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | COMBINE_EQS: (7), (66) imply:
% 203.62/34.49  | | | |   (67)  all_6_2 = e3
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | REDUCE: (46), (67) imply:
% 203.62/34.49  | | | |   (68)   ~ (all_52_17 = e3)
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | REDUCE: (53), (67) imply:
% 203.62/34.49  | | | |   (69)  op(e3, e3) = all_6_1
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | REDUCE: (41), (67) imply:
% 203.62/34.49  | | | |   (70)  op(e3, e3) = e3
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | BETA: splitting (49) gives:
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | Case 1:
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | |   (71)  all_58_4 = e3
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | | REF_CLOSE: (54), (68), (71) are inconsistent by sub-proof #1302.
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | Case 2:
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | |   (72)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | | BETA: splitting (72) gives:
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | | Case 1:
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | |   (73)  all_58_5 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | COMBINE_EQS: (43), (73) imply:
% 203.62/34.49  | | | | | |   (74)  all_52_19 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | SIMP: (74) implies:
% 203.62/34.49  | | | | | |   (75)  all_52_19 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | REDUCE: (21), (75) imply:
% 203.62/34.49  | | | | | |   (76)   ~ (all_52_23 = e3)
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | REDUCE: (10), (75) imply:
% 203.62/34.49  | | | | | |   (77)  op(e3, e3) = all_52_18
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | GROUND_INST: instantiating (3) with all_6_1, all_52_18, e3, e3,
% 203.62/34.49  | | | | | |              simplifying with (69), (77) gives:
% 203.62/34.49  | | | | | |   (78)  all_52_18 = all_6_1
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | GROUND_INST: instantiating (3) with e3, all_52_18, e3, e3,
% 203.62/34.49  | | | | | |              simplifying with (70), (77) gives:
% 203.62/34.49  | | | | | |   (79)  all_52_18 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | COMBINE_EQS: (78), (79) imply:
% 203.62/34.49  | | | | | |   (80)  all_6_1 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | SIMP: (80) implies:
% 203.62/34.49  | | | | | |   (81)  all_6_1 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | REDUCE: (28), (81) imply:
% 203.62/34.49  | | | | | |   (82)  op(e3, e3) = all_6_0
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3, simplifying
% 203.62/34.49  | | | | | |              with (70), (82) gives:
% 203.62/34.49  | | | | | |   (83)  all_6_0 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | REDUCE: (19), (83) imply:
% 203.62/34.49  | | | | | |   (84)   ~ (e3 = e1)
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | BETA: splitting (14) gives:
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | Case 1:
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | |   (85)  all_58_12 = e2
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | | COMBINE_EQS: (24), (85) imply:
% 203.62/34.49  | | | | | | |   (86)  all_52_7 = e2
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | | BETA: splitting (34) gives:
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | | Case 1:
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | |   (87)  all_58_12 = e0
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | | REF_CLOSE: (29), (85), (87) are inconsistent by sub-proof #1153.
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | Case 2:
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | |   (88)  all_58_13 = e0 | all_58_14 = e0
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | | BETA: splitting (32) gives:
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | | Case 1:
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | |   (89)  all_58_12 = e1
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | REF_CLOSE: (18), (85), (89) are inconsistent by sub-proof
% 203.62/34.49  | | | | | | | | |            #1198.
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | Case 2:
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | |   (90)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | BETA: splitting (90) gives:
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | Case 1:
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | |   (91)  all_58_13 = e1
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | COMBINE_EQS: (9), (91) imply:
% 203.62/34.49  | | | | | | | | | |   (92)  e3 = e1
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | REF_CLOSE: (2), (30), (37), (62), (72), (73), (84), (92) are
% 203.62/34.49  | | | | | | | | | |            inconsistent by sub-proof #712.
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | Case 2:
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | |   (93)  all_58_14 = e1 | all_58_15 = e1
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | BETA: splitting (93) gives:
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | Case 1:
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | |   (94)  all_58_14 = e1
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | | REF_CLOSE: (6), (9), (47), (88), (94) are inconsistent by
% 203.62/34.49  | | | | | | | | | | |            sub-proof #710.
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | Case 2:
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | |   (95)  all_58_15 = e1
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | | COMBINE_EQS: (35), (95) imply:
% 203.62/34.49  | | | | | | | | | | |   (96)  all_14_2 = e1
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | | SIMP: (96) implies:
% 203.62/34.49  | | | | | | | | | | |   (97)  all_14_2 = e1
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | | REDUCE: (8), (97) imply:
% 203.62/34.49  | | | | | | | | | | |   (98)  op(e1, e0) = all_14_1
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | | REF_CLOSE: (1), (3), (64), (97), (98) are inconsistent by
% 203.62/34.49  | | | | | | | | | | |            sub-proof #590.
% 203.62/34.49  | | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | | End of split
% 203.62/34.49  | | | | | | | | | | 
% 203.62/34.49  | | | | | | | | | End of split
% 203.62/34.49  | | | | | | | | | 
% 203.62/34.49  | | | | | | | | End of split
% 203.62/34.49  | | | | | | | | 
% 203.62/34.49  | | | | | | | End of split
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | Case 2:
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | |   (99)   ~ (all_58_12 = e2)
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | | REDUCE: (24), (99) imply:
% 203.62/34.49  | | | | | | |   (100)   ~ (all_52_7 = e2)
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | | REF_CLOSE: (2), (3), (4), (6), (9), (11), (15), (24), (25), (32),
% 203.62/34.49  | | | | | | |            (34), (40), (47), (50), (51), (100) are inconsistent by
% 203.62/34.49  | | | | | | |            sub-proof #1169.
% 203.62/34.49  | | | | | | | 
% 203.62/34.49  | | | | | | End of split
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | Case 2:
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | |   (101)  all_58_8 = e3 | all_58_14 = e3
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | | REF_CLOSE: (2), (30), (37), (62), (101) are inconsistent by
% 203.62/34.49  | | | | | |            sub-proof #1304.
% 203.62/34.49  | | | | | | 
% 203.62/34.49  | | | | | End of split
% 203.62/34.49  | | | | | 
% 203.62/34.49  | | | | End of split
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | Case 2:
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | |   (102)   ~ (all_58_0 = e3)
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | REDUCE: (7), (102) imply:
% 203.62/34.49  | | | |   (103)   ~ (all_6_2 = e3)
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | | REF_CLOSE: (3), (4), (5), (7), (12), (15), (16), (23), (24), (25), (26),
% 203.62/34.49  | | | |            (27), (31), (38), (41), (44), (45), (50), (52), (103) are
% 203.62/34.49  | | | |            inconsistent by sub-proof #1362.
% 203.62/34.49  | | | | 
% 203.62/34.49  | | | End of split
% 203.62/34.49  | | | 
% 203.62/34.49  | | Case 2:
% 203.62/34.49  | | | 
% 203.62/34.49  | | |   (104)  all_58_15 = e3
% 203.62/34.49  | | | 
% 203.62/34.49  | | | COMBINE_EQS: (35), (104) imply:
% 203.62/34.49  | | |   (105)  all_14_2 = e3
% 203.62/34.49  | | | 
% 203.62/34.49  | | | REDUCE: (55), (105) imply:
% 203.62/34.49  | | |   (106)  $false
% 203.62/34.49  | | | 
% 203.62/34.49  | | | CLOSE: (106) is inconsistent.
% 203.62/34.49  | | | 
% 203.62/34.49  | | End of split
% 203.62/34.49  | | 
% 203.62/34.49  | End of split
% 203.62/34.49  | 
% 203.62/34.49  End of proof
% 203.62/34.49  
% 203.62/34.49  Sub-proof #590 shows that the following formulas are inconsistent:
% 203.62/34.49  ----------------------------------------------------------------
% 203.62/34.49    (1)   ~ (all_14_1 = e3) |  ~ (all_14_2 = e1)
% 203.62/34.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.49    (3)  op(e1, e0) = all_14_1
% 203.62/34.49    (4)  all_14_2 = e1
% 203.62/34.49    (5)  op(e1, e0) = e3
% 203.62/34.49  
% 203.62/34.49  Begin of proof
% 203.62/34.49  | 
% 203.62/34.49  | BETA: splitting (1) gives:
% 203.62/34.49  | 
% 203.62/34.49  | Case 1:
% 203.62/34.49  | | 
% 203.62/34.49  | |   (6)   ~ (all_14_1 = e3)
% 203.62/34.49  | | 
% 203.62/34.49  | | GROUND_INST: instantiating (2) with e3, all_14_1, e0, e1, simplifying with
% 203.62/34.49  | |              (3), (5) gives:
% 203.62/34.49  | |   (7)  all_14_1 = e3
% 203.62/34.49  | | 
% 203.62/34.49  | | REDUCE: (6), (7) imply:
% 203.62/34.49  | |   (8)  $false
% 203.62/34.49  | | 
% 203.62/34.49  | | CLOSE: (8) is inconsistent.
% 203.62/34.49  | | 
% 203.62/34.49  | Case 2:
% 203.62/34.49  | | 
% 203.62/34.49  | |   (9)   ~ (all_14_2 = e1)
% 203.62/34.49  | | 
% 203.62/34.49  | | REDUCE: (4), (9) imply:
% 203.62/34.49  | |   (10)  $false
% 203.62/34.49  | | 
% 203.62/34.49  | | CLOSE: (10) is inconsistent.
% 203.62/34.49  | | 
% 203.62/34.49  | End of split
% 203.62/34.49  | 
% 203.62/34.49  End of proof
% 203.62/34.49  
% 203.62/34.49  Sub-proof #591 shows that the following formulas are inconsistent:
% 203.62/34.49  ----------------------------------------------------------------
% 203.62/34.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.49    (2)  op(all_52_7, all_52_7) = e0
% 203.62/34.49    (3)  op(all_52_5, all_52_5) = e1
% 203.62/34.49    (4)  all_58_0 = all_6_2
% 203.62/34.49    (5)  op(e2, e2) = all_4_2
% 203.62/34.49    (6)  op(e0, e0) = all_14_2
% 203.62/34.49    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.49    (8)  op(all_6_2, all_6_2) = e3
% 203.62/34.49    (9)  all_58_12 = all_52_7
% 203.62/34.49    (10)   ~ (all_52_7 = all_14_2)
% 203.62/34.49    (11)  all_58_2 = all_52_3
% 203.62/34.49    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.49    (13)  all_58_4 = e3
% 203.62/34.49    (14)  op(all_52_3, all_52_3) = e2
% 203.62/34.49    (15)   ~ (all_52_5 = all_10_2)
% 203.62/34.49    (16)  op(e3, e3) = all_6_2
% 203.62/34.49    (17)  all_58_6 = all_52_5
% 203.62/34.49    (18)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.49    (19)   ~ (all_52_17 = all_6_2)
% 203.62/34.49    (20)  op(e1, e1) = all_10_2
% 203.62/34.49    (21)   ~ (all_52_3 = all_4_2)
% 203.62/34.49    (22)  all_58_4 = all_52_17
% 203.62/34.49  
% 203.62/34.49  Begin of proof
% 203.62/34.49  | 
% 203.62/34.49  | COMBINE_EQS: (13), (22) imply:
% 203.62/34.49  |   (23)  all_52_17 = e3
% 203.62/34.49  | 
% 203.62/34.49  | SIMP: (23) implies:
% 203.62/34.49  |   (24)  all_52_17 = e3
% 203.62/34.49  | 
% 203.62/34.49  | REDUCE: (19), (24) imply:
% 203.62/34.49  |   (25)   ~ (all_6_2 = e3)
% 203.62/34.49  | 
% 203.62/34.49  | SIMP: (25) implies:
% 203.62/34.49  |   (26)   ~ (all_6_2 = e3)
% 203.62/34.49  | 
% 203.62/34.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.49  |            (14), (15), (16), (17), (18), (20), (21), (26) are inconsistent by
% 203.62/34.49  |            sub-proof #1362.
% 203.62/34.49  | 
% 203.62/34.49  End of proof
% 203.62/34.49  
% 203.62/34.49  Sub-proof #592 shows that the following formulas are inconsistent:
% 203.62/34.49  ----------------------------------------------------------------
% 203.62/34.49    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.49    (2)   ~ (all_52_25 = all_6_0)
% 203.62/34.49    (3)   ~ (all_52_25 = all_52_27)
% 203.62/34.49    (4)  all_58_14 = all_52_23
% 203.62/34.49    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.49    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.49    (7)  all_58_1 = all_52_9
% 203.62/34.49    (8)   ~ (all_52_9 = all_52_13)
% 203.62/34.49    (9)   ~ (e3 = e0)
% 203.62/34.49    (10)  op(e2, e3) = all_52_3
% 203.62/34.49    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.49    (12)   ~ (all_52_3 = all_52_19)
% 203.62/34.49    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.49    (14)   ~ (all_52_17 = all_52_25)
% 203.62/34.49    (15)   ~ (all_52_3 = all_6_2)
% 203.62/34.49    (16)  all_58_0 = all_6_2
% 203.62/34.49    (17)  op(all_14_2, e0) = all_14_1
% 203.62/34.49    (18)   ~ (all_52_17 = all_10_2)
% 203.62/34.49    (19)   ~ (all_10_0 = e3)
% 203.62/34.49    (20)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.49    (21)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.49    (22)   ~ (all_52_27 = all_52_29)
% 203.62/34.49    (23)  all_58_13 = all_52_15
% 203.62/34.49    (24)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.49    (25)  all_58_9 = all_52_25
% 203.62/34.49    (26)   ~ (all_52_29 = all_14_2)
% 203.62/34.49    (27)  all_22_0 = all_6_0
% 203.62/34.49    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.49    (29)   ~ (all_52_17 = all_6_0)
% 203.62/34.49    (30)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.49    (31)  op(e1, e3) = all_52_5
% 203.62/34.49    (32)  op(e2, e2) = all_4_2
% 203.62/34.49    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.49    (34)   ~ (all_52_3 = all_52_5)
% 203.62/34.49    (35)  all_58_11 = all_52_29
% 203.62/34.49    (36)  all_56_5 = all_4_2
% 203.62/34.49    (37)   ~ (all_52_25 = all_14_2)
% 203.62/34.49    (38)   ~ (all_52_3 = all_52_27)
% 203.62/34.49    (39)  op(all_10_2, e1) = all_10_1
% 203.62/34.49    (40)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.49    (41)   ~ (all_52_7 = all_6_2)
% 203.62/34.49    (42)  op(e0, e0) = all_14_2
% 203.62/34.49    (43)  all_56_15 = all_14_2
% 203.62/34.49    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.49    (45)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.49    (46)  all_56_11 = all_52_29
% 203.62/34.49    (47)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.49    (48)   ~ (e2 = e1)
% 203.62/34.49    (49)   ~ (all_6_0 = e1)
% 203.62/34.49    (50)  op(e1, all_10_1) = all_10_0
% 203.62/34.49    (51)  all_58_10 = all_52_27
% 203.62/34.49    (52)  all_56_8 = all_52_5
% 203.62/34.49    (53)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.49    (54)   ~ (all_52_19 = all_52_23)
% 203.62/34.49    (55)   ~ (all_52_25 = all_52_29)
% 203.62/34.49    (56)  op(all_6_2, e3) = e2
% 203.62/34.49    (57)   ~ (all_52_29 = all_10_2)
% 203.62/34.49    (58)  all_58_7 = all_52_13
% 203.62/34.49    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.49    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.49    (61)  all_58_1 = all_6_0
% 203.62/34.49    (62)   ~ (all_52_5 = all_52_7)
% 203.62/34.49    (63)  all_58_12 = all_52_7
% 203.62/34.49    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.49    (65)   ~ (all_52_7 = all_14_2)
% 203.62/34.49    (66)  all_58_2 = all_52_3
% 203.62/34.49    (67)  all_56_2 = all_52_17
% 203.62/34.49    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.49    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.49    (70)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.49    (71)   ~ (e2 = e0)
% 203.62/34.49    (72)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.49    (73)  op(all_6_0, all_6_0) = all_52_8
% 203.62/34.49    (74)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.49    (75)   ~ (all_52_5 = all_52_29)
% 203.62/34.49    (76)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.49    (77)   ~ (all_52_13 = all_6_0)
% 203.62/34.49    (78)   ~ (all_52_19 = all_52_27)
% 203.62/34.49    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.49    (80)   ~ (all_6_0 = e2)
% 203.62/34.49    (81)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.49            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.49    (82)  op(e3, e1) = all_52_17
% 203.62/34.49    (83)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.49    (84)  op(e0, e3) = all_52_7
% 203.62/34.49    (85)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.49    (86)   ~ (all_52_9 = all_52_25)
% 203.62/34.49    (87)  all_58_15 = all_14_2
% 203.62/34.49    (88)   ~ (all_52_19 = all_10_2)
% 203.62/34.49    (89)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.49    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.49    (91)  all_58_8 = all_10_2
% 203.62/34.49    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.49    (93)   ~ (all_52_5 = all_10_2)
% 203.62/34.49    (94)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.49    (95)   ~ (all_52_23 = all_14_2)
% 203.62/34.49    (96)  all_56_12 = all_52_7
% 203.62/34.49    (97)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.49    (98)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.49    (99)   ~ (all_52_25 = all_6_2)
% 203.62/34.49    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.49    (101)   ~ (all_52_9 = all_4_2)
% 203.62/34.49    (102)   ~ (all_52_5 = all_6_2)
% 203.62/34.49    (103)  all_56_0 = all_6_2
% 203.62/34.49    (104)  op(e3, e3) = all_6_2
% 203.62/34.49    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.49    (106)   ~ (all_52_15 = all_6_0)
% 203.62/34.49    (107)   ~ (all_52_27 = all_14_2)
% 203.62/34.49    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.49    (109)  all_56_14 = all_52_23
% 203.62/34.49    (110)  all_56_3 = all_52_25
% 203.62/34.49    (111)  op(e0, all_14_1) = e2
% 203.62/34.49    (112)   ~ (all_52_3 = all_52_7)
% 203.62/34.49    (113)   ~ (all_6_0 = all_6_2)
% 203.62/34.49    (114)  all_10_1 = e3
% 203.62/34.49    (115)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.49    (116)  all_58_5 = all_52_19
% 203.62/34.49    (117)   ~ (all_52_15 = all_4_2)
% 203.62/34.49    (118)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.49           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.49           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.49           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.49    (119)   ~ (all_52_27 = all_4_2)
% 203.62/34.49    (120)  all_58_6 = all_52_5
% 203.62/34.49    (121)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.49    (122)   ~ (all_52_17 = all_6_2)
% 203.62/34.49    (123)   ~ (e1 = e0)
% 203.62/34.49    (124)   ~ (e3 = e2)
% 203.62/34.49    (125)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.49    (126)   ~ (all_52_9 = all_52_17)
% 203.62/34.49    (127)  all_56_10 = all_10_2
% 203.62/34.49    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.49    (129)  all_56_1 = all_6_0
% 203.62/34.49    (130)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.49    (131)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.49    (132)   ~ (all_6_0 = all_4_2)
% 203.62/34.49    (133)  op(e1, e1) = all_10_2
% 203.62/34.49    (134)   ~ (all_52_23 = all_10_2)
% 203.62/34.49    (135)   ~ (all_52_7 = all_52_23)
% 203.62/34.49    (136)  all_58_3 = all_4_2
% 203.62/34.49    (137)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.49    (138)   ~ (all_52_3 = all_4_2)
% 203.62/34.49    (139)   ~ (all_52_19 = all_4_2)
% 203.62/34.49    (140)   ~ (all_52_17 = all_52_23)
% 203.62/34.49    (141)  op(all_6_2, e3) = all_6_1
% 203.62/34.49    (142)  all_22_2 = all_6_2
% 203.62/34.49    (143)  all_58_4 = all_52_17
% 203.62/34.49    (144)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.49    (145)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.49  
% 203.62/34.49  Begin of proof
% 203.62/34.49  | 
% 203.62/34.49  | REDUCE: (39), (114) imply:
% 203.62/34.49  |   (146)  op(all_10_2, e1) = e3
% 203.62/34.49  | 
% 203.62/34.49  | REDUCE: (50), (114) imply:
% 203.62/34.49  |   (147)  op(e1, e3) = all_10_0
% 203.62/34.49  | 
% 203.62/34.49  | GROUND_INST: instantiating (6) with all_52_5, all_10_0, e3, e1, simplifying
% 203.62/34.49  |              with (31), (147) gives:
% 203.62/34.49  |   (148)  all_52_5 = all_10_0
% 203.62/34.49  | 
% 203.62/34.49  | COMBINE_EQS: (120), (148) imply:
% 203.62/34.49  |   (149)  all_58_6 = all_10_0
% 203.62/34.49  | 
% 203.62/34.49  | BETA: splitting (81) gives:
% 203.62/34.49  | 
% 203.62/34.49  | Case 1:
% 203.62/34.49  | | 
% 203.62/34.49  | |   (150)  all_58_15 = e0
% 203.62/34.49  | | 
% 203.62/34.49  | | REF_CLOSE: (6), (17), (42), (71), (87), (111), (115), (150) are inconsistent
% 203.62/34.49  | |            by sub-proof #612.
% 203.62/34.49  | | 
% 203.62/34.49  | Case 2:
% 203.62/34.49  | | 
% 203.62/34.49  | |   (151)   ~ (all_58_15 = e0)
% 203.62/34.49  | |   (152)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 203.62/34.49  | |            | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.49  | | 
% 203.62/34.49  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.49  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 203.62/34.49  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.62/34.49  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 203.62/34.49  | |            (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 203.62/34.49  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 203.62/34.49  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 203.62/34.49  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 203.62/34.49  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 203.62/34.49  | |            (103), (104), (105), (106), (107), (108), (109), (110), (112),
% 203.62/34.49  | |            (113), (115), (116), (117), (118), (119), (120), (121), (122),
% 203.62/34.49  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 203.62/34.49  | |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 203.62/34.49  | |            (141), (142), (143), (144), (145), (146), (149), (151), (152) are
% 203.62/34.49  | |            inconsistent by sub-proof #773.
% 203.62/34.49  | | 
% 203.62/34.49  | End of split
% 203.62/34.49  | 
% 203.62/34.49  End of proof
% 203.62/34.49  
% 203.62/34.49  Sub-proof #593 shows that the following formulas are inconsistent:
% 203.62/34.49  ----------------------------------------------------------------
% 203.62/34.49    (1)   ~ (all_52_25 = all_6_0)
% 203.62/34.49    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.49    (3)  all_58_14 = all_52_23
% 203.62/34.49    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.50    (5)  all_58_1 = all_52_9
% 203.62/34.50    (6)  op(e2, e3) = all_52_3
% 203.62/34.50    (7)   ~ (all_52_7 = all_52_15)
% 203.62/34.50    (8)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.50    (9)   ~ (all_52_17 = all_52_25)
% 203.62/34.50    (10)   ~ (all_52_3 = all_6_2)
% 203.62/34.50    (11)  all_58_0 = all_6_2
% 203.62/34.50    (12)  all_56_4 = all_52_3
% 203.62/34.50    (13)  all_38_2 = all_4_2
% 203.62/34.50    (14)   ~ (all_52_17 = all_10_2)
% 203.62/34.50    (15)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.50    (16)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.50    (17)  all_58_13 = all_52_15
% 203.62/34.50    (18)  all_58_9 = all_52_25
% 203.62/34.50    (19)  all_22_0 = all_6_0
% 203.62/34.50    (20)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.50    (21)  op(e1, e3) = all_52_5
% 203.62/34.50    (22)  all_32_2 = all_4_2
% 203.62/34.50    (23)  op(e2, e2) = all_4_2
% 203.62/34.50    (24)   ~ (all_52_3 = all_52_5)
% 203.62/34.50    (25)  all_4_1 = e3
% 203.62/34.50    (26)  all_58_11 = all_52_29
% 203.62/34.50    (27)  all_56_5 = all_4_2
% 203.62/34.50    (28)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.50    (29)   ~ (all_52_7 = all_6_2)
% 203.62/34.50    (30)  op(e0, e0) = all_14_2
% 203.62/34.50    (31)  all_56_15 = all_14_2
% 203.62/34.50    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.50    (33)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.50    (34)  op(e2, all_4_1) = all_4_0
% 203.62/34.50    (35)   ~ (all_4_0 = e3)
% 203.62/34.50    (36)   ~ (e2 = e1)
% 203.62/34.50    (37)   ~ (all_6_0 = e1)
% 203.62/34.50    (38)  all_58_10 = all_52_27
% 203.62/34.50    (39)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.50    (40)  op(all_6_2, e3) = e2
% 203.62/34.50    (41)  all_58_7 = all_52_13
% 203.62/34.50    (42)  all_58_1 = all_6_0
% 203.62/34.50    (43)  all_58_12 = all_52_7
% 203.62/34.50    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.50    (45)   ~ (all_52_7 = all_14_2)
% 203.62/34.50    (46)  all_38_0 = all_4_0
% 203.62/34.50    (47)  all_58_2 = all_52_3
% 203.62/34.50    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.50    (49)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.50    (50)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.50    (51)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.50    (52)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.50    (53)  op(all_4_2, e2) = all_4_1
% 203.62/34.50    (54)  op(all_6_0, all_6_0) = all_52_8
% 203.62/34.50    (55)   ~ (all_52_5 = all_52_29)
% 203.62/34.50    (56)  all_38_1 = all_4_1
% 203.62/34.50    (57)   ~ (all_52_13 = all_6_0)
% 203.62/34.50    (58)   ~ (all_52_19 = all_52_27)
% 203.62/34.50    (59)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.50    (60)   ~ (all_6_0 = e2)
% 203.62/34.50    (61)  op(e0, e3) = all_52_7
% 203.62/34.50    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.50    (63)   ~ (all_52_9 = all_52_25)
% 203.62/34.50    (64)  all_58_15 = all_14_2
% 203.62/34.50    (65)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.50    (66)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.50    (67)   ~ (all_52_5 = all_10_2)
% 203.62/34.50    (68)   ~ (all_52_25 = all_6_2)
% 203.62/34.50    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.50    (70)   ~ (all_52_9 = all_4_2)
% 203.62/34.50    (71)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 203.62/34.50    (72)  all_56_0 = all_6_2
% 203.62/34.50    (73)  op(e3, e3) = all_6_2
% 203.62/34.50    (74)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.50    (75)   ~ (all_52_15 = all_6_0)
% 203.62/34.50    (76)   ~ (all_52_27 = all_14_2)
% 203.62/34.50    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.50    (78)  op(all_4_2, all_4_2) = all_52_10
% 203.62/34.50    (79)  all_32_0 = all_4_0
% 203.62/34.50    (80)  all_56_3 = all_52_25
% 203.62/34.50    (81)   ~ (all_52_3 = all_52_7)
% 203.62/34.50    (82)   ~ (all_6_0 = all_6_2)
% 203.62/34.50    (83)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.50    (84)  all_58_5 = all_52_19
% 203.62/34.50    (85)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.50          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.50          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.50          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.50    (86)   ~ (all_52_27 = all_4_2)
% 203.62/34.50    (87)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.62/34.50    (88)  all_58_6 = all_52_5
% 203.62/34.50    (89)  op(e3, e2) = all_52_9
% 203.62/34.50    (90)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.50    (91)   ~ (e1 = e0)
% 203.62/34.50    (92)   ~ (e3 = e2)
% 203.62/34.50    (93)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.50    (94)  all_56_1 = all_6_0
% 203.62/34.50    (95)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.50    (96)   ~ (all_6_0 = all_4_2)
% 203.62/34.50    (97)  op(e1, e1) = all_10_2
% 203.62/34.50    (98)  all_58_3 = all_4_2
% 203.62/34.50    (99)   ~ (all_52_3 = all_4_2)
% 203.62/34.50    (100)   ~ (all_52_19 = all_4_2)
% 203.62/34.50    (101)  all_22_2 = all_6_2
% 203.62/34.50    (102)  all_58_4 = all_52_17
% 203.62/34.50    (103)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.50  
% 203.62/34.50  Begin of proof
% 203.62/34.50  | 
% 203.62/34.50  | COMBINE_EQS: (25), (56) imply:
% 203.62/34.50  |   (104)  all_38_1 = e3
% 203.62/34.50  | 
% 203.62/34.50  | REDUCE: (25), (53) imply:
% 203.62/34.50  |   (105)  op(all_4_2, e2) = e3
% 203.62/34.50  | 
% 203.62/34.50  | REDUCE: (25), (34) imply:
% 203.62/34.50  |   (106)  op(e2, e3) = all_4_0
% 203.62/34.50  | 
% 203.62/34.50  | GROUND_INST: instantiating (4) with all_52_3, all_4_0, e3, e2, simplifying
% 203.62/34.50  |              with (6), (106) gives:
% 203.62/34.50  |   (107)  all_52_3 = all_4_0
% 203.62/34.50  | 
% 203.62/34.50  | COMBINE_EQS: (12), (107) imply:
% 203.62/34.50  |   (108)  all_56_4 = all_4_0
% 203.62/34.50  | 
% 203.62/34.50  | COMBINE_EQS: (47), (107) imply:
% 203.62/34.50  |   (109)  all_58_2 = all_4_0
% 203.62/34.50  | 
% 203.62/34.50  | REDUCE: (24), (107) imply:
% 203.62/34.50  |   (110)   ~ (all_52_5 = all_4_0)
% 203.62/34.50  | 
% 203.62/34.50  | SIMP: (110) implies:
% 203.62/34.50  |   (111)   ~ (all_52_5 = all_4_0)
% 203.62/34.50  | 
% 203.62/34.50  | REDUCE: (81), (107) imply:
% 203.62/34.50  |   (112)   ~ (all_52_7 = all_4_0)
% 203.62/34.50  | 
% 203.62/34.50  | SIMP: (112) implies:
% 203.62/34.50  |   (113)   ~ (all_52_7 = all_4_0)
% 203.62/34.50  | 
% 203.62/34.50  | REDUCE: (10), (107) imply:
% 203.62/34.50  |   (114)   ~ (all_6_2 = all_4_0)
% 203.62/34.50  | 
% 203.62/34.50  | SIMP: (114) implies:
% 203.62/34.50  |   (115)   ~ (all_6_2 = all_4_0)
% 203.62/34.50  | 
% 203.62/34.50  | REDUCE: (99), (107) imply:
% 203.62/34.50  |   (116)   ~ (all_4_0 = all_4_2)
% 203.62/34.50  | 
% 203.62/34.50  | BETA: splitting (71) gives:
% 203.62/34.50  | 
% 203.62/34.50  | Case 1:
% 203.62/34.50  | | 
% 203.62/34.50  | |   (117)   ~ (all_38_0 = e1)
% 203.62/34.50  | | 
% 203.62/34.50  | | REDUCE: (46), (117) imply:
% 203.62/34.50  | |   (118)   ~ (all_4_0 = e1)
% 203.62/34.50  | | 
% 203.62/34.50  | | BETA: splitting (93) gives:
% 203.62/34.50  | | 
% 203.62/34.50  | | Case 1:
% 203.62/34.50  | | | 
% 203.62/34.50  | | |   (119)  all_56_1 = e3
% 203.62/34.50  | | | 
% 203.62/34.50  | | | COMBINE_EQS: (94), (119) imply:
% 203.62/34.50  | | |   (120)  all_6_0 = e3
% 203.62/34.50  | | | 
% 203.62/34.50  | | | COMBINE_EQS: (42), (120) imply:
% 203.62/34.50  | | |   (121)  all_58_1 = e3
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (57), (120) imply:
% 203.62/34.50  | | |   (122)   ~ (all_52_13 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (75), (120) imply:
% 203.62/34.50  | | |   (123)   ~ (all_52_15 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (1), (120) imply:
% 203.62/34.50  | | |   (124)   ~ (all_52_25 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (82), (120) imply:
% 203.62/34.50  | | |   (125)   ~ (all_6_2 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | SIMP: (125) implies:
% 203.62/34.50  | | |   (126)   ~ (all_6_2 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (96), (120) imply:
% 203.62/34.50  | | |   (127)   ~ (all_4_2 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | SIMP: (127) implies:
% 203.62/34.50  | | |   (128)   ~ (all_4_2 = e3)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (37), (120) imply:
% 203.62/34.50  | | |   (129)   ~ (e3 = e1)
% 203.62/34.50  | | | 
% 203.62/34.50  | | | REDUCE: (54), (120) imply:
% 203.62/34.50  | | |   (130)  op(e3, e3) = all_52_8
% 203.62/34.50  | | | 
% 203.62/34.50  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_8, e3, e3, simplifying
% 203.62/34.50  | | |              with (73), (130) gives:
% 203.62/34.50  | | |   (131)  all_52_8 = all_6_2
% 203.62/34.50  | | | 
% 203.62/34.50  | | | BETA: splitting (85) gives:
% 203.62/34.50  | | | 
% 203.62/34.50  | | | Case 1:
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | |   (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 203.62/34.50  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 203.62/34.50  | | | |            = e0)
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | | BETA: splitting (132) gives:
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | | Case 1:
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | |   (133)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | ALPHA: (133) implies:
% 203.62/34.50  | | | | |   (134)  all_52_6 = e0
% 203.62/34.50  | | | | |   (135)  all_52_4 = e1
% 203.62/34.50  | | | | |   (136)  all_52_0 = e3
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (15), (135) imply:
% 203.62/34.50  | | | | |   (137)  op(all_52_5, all_52_5) = e1
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (8), (134) imply:
% 203.62/34.50  | | | | |   (138)  op(all_52_7, all_52_7) = e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (28), (136) imply:
% 203.62/34.50  | | | | |   (139)  op(all_6_2, all_6_2) = e3
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REF_CLOSE: (4), (11), (35), (43), (48), (49), (67), (73), (88), (90),
% 203.62/34.50  | | | | |            (91), (97), (109), (118), (126), (129), (137), (138), (139)
% 203.62/34.50  | | | | |            are inconsistent by sub-proof #641.
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | Case 2:
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | |   (140)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.62/34.50  | | | | |          e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REF_CLOSE: (126), (131), (140) are inconsistent by sub-proof #834.
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | End of split
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | Case 2:
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | |   (141)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.62/34.50  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.62/34.50  | | | |            all_52_30 = e0)
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | | BETA: splitting (141) gives:
% 203.62/34.50  | | | | 
% 203.62/34.50  | | | | Case 1:
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | |   (142)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 203.62/34.50  | | | | |          = e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | ALPHA: (142) implies:
% 203.62/34.50  | | | | |   (143)  all_52_22 = e0
% 203.62/34.50  | | | | |   (144)  all_52_18 = e2
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (16), (144) imply:
% 203.62/34.50  | | | | |   (145)  op(all_52_19, all_52_19) = e2
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (65), (143) imply:
% 203.62/34.50  | | | | |   (146)  op(all_52_23, all_52_23) = e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | BETA: splitting (51) gives:
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | Case 1:
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | |   (147)  all_56_4 = e3
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | | REF_CLOSE: (35), (108), (147) are inconsistent by sub-proof #980.
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | Case 2:
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | |   (148)   ~ (all_56_4 = e3)
% 203.62/34.50  | | | | | |   (149)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | | BETA: splitting (48) gives:
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | | Case 1:
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | |   (150)  all_58_0 = e3
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | COMBINE_EQS: (11), (150) imply:
% 203.62/34.50  | | | | | | |   (151)  all_6_2 = e3
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | REDUCE: (126), (151) imply:
% 203.62/34.50  | | | | | | |   (152)  $false
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | CLOSE: (152) is inconsistent.
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | Case 2:
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | |   (153)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | BETA: splitting (32) gives:
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | |   (154)  all_58_2 = e3
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | | REF_CLOSE: (35), (109), (154) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | |            #948.
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | |   (155)   ~ (all_58_2 = e3)
% 203.62/34.50  | | | | | | | |   (156)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | | BETA: splitting (66) gives:
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | |   (157)  all_56_15 = e3
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | COMBINE_EQS: (31), (157) imply:
% 203.62/34.50  | | | | | | | | |   (158)  all_14_2 = e3
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | SIMP: (158) implies:
% 203.62/34.50  | | | | | | | | |   (159)  all_14_2 = e3
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | REDUCE: (76), (159) imply:
% 203.62/34.50  | | | | | | | | |   (160)   ~ (all_52_27 = e3)
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | BETA: splitting (156) gives:
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | |   (161)  all_58_3 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | COMBINE_EQS: (98), (161) imply:
% 203.62/34.50  | | | | | | | | | |   (162)  all_4_2 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | REDUCE: (128), (162) imply:
% 203.62/34.50  | | | | | | | | | |   (163)  $false
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | CLOSE: (163) is inconsistent.
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | |   (164)  all_58_5 = e3 | all_58_10 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | BETA: splitting (164) gives:
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | |   (165)  all_58_5 = e3
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | COMBINE_EQS: (84), (165) imply:
% 203.62/34.50  | | | | | | | | | | |   (166)  all_52_19 = e3
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | REF_CLOSE: (4), (22), (23), (27), (28), (52), (73), (78),
% 203.62/34.50  | | | | | | | | | | |            (79), (87), (100), (105), (108), (115), (116),
% 203.62/34.50  | | | | | | | | | | |            (118), (145), (149), (166) are inconsistent by
% 203.62/34.50  | | | | | | | | | | |            sub-proof #946.
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | |   (167)  all_58_10 = e3
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | REF_CLOSE: (38), (160), (167) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | |            #1301.
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | |   (168)   ~ (all_56_15 = e3)
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | REDUCE: (31), (168) imply:
% 203.62/34.50  | | | | | | | | |   (169)   ~ (all_14_2 = e3)
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | BETA: splitting (90) gives:
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | |   (170)  all_58_12 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | COMBINE_EQS: (43), (170) imply:
% 203.62/34.50  | | | | | | | | | |   (171)  all_52_7 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | SIMP: (171) implies:
% 203.62/34.50  | | | | | | | | | |   (172)  all_52_7 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | REDUCE: (7), (172) imply:
% 203.62/34.50  | | | | | | | | | |   (173)   ~ (all_52_15 = e3)
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | REDUCE: (113), (172) imply:
% 203.62/34.50  | | | | | | | | | |   (174)   ~ (all_4_0 = e3)
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | REDUCE: (61), (172) imply:
% 203.62/34.50  | | | | | | | | | |   (175)  op(e0, e3) = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | REF_CLOSE: (4), (11), (17), (21), (22), (23), (27), (28),
% 203.62/34.50  | | | | | | | | | |            (35), (40), (41), (49), (52), (59), (62), (70),
% 203.62/34.50  | | | | | | | | | |            (72), (73), (78), (79), (87), (89), (95), (98),
% 203.62/34.50  | | | | | | | | | |            (105), (108), (111), (115), (116), (118), (121),
% 203.62/34.50  | | | | | | | | | |            (122), (123), (126), (128), (149), (175) are
% 203.62/34.50  | | | | | | | | | |            inconsistent by sub-proof #595.
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | |   (176)   ~ (all_58_12 = e3)
% 203.62/34.50  | | | | | | | | | |   (177)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | REDUCE: (43), (176) imply:
% 203.62/34.50  | | | | | | | | | |   (178)   ~ (all_52_7 = e3)
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | BETA: splitting (153) gives:
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | |   (179)  all_58_2 = e3
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | REF_CLOSE: (35), (109), (179) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | |            #948.
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | |   (180)  all_58_6 = e3 | all_58_12 = e3
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | BETA: splitting (177) gives:
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | |   (181)  all_58_13 = e3
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | REF_CLOSE: (17), (123), (181) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | | |            #1360.
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | |   (182)  all_58_14 = e3 | all_58_15 = e3
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | BETA: splitting (180) gives:
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | |   (183)  all_58_6 = e3
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | COMBINE_EQS: (88), (183) imply:
% 203.62/34.50  | | | | | | | | | | | | |   (184)  all_52_5 = e3
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | SIMP: (184) implies:
% 203.62/34.50  | | | | | | | | | | | | |   (185)  all_52_5 = e3
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | REDUCE: (55), (185) imply:
% 203.62/34.50  | | | | | | | | | | | | |   (186)   ~ (all_52_29 = e3)
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | SIMP: (186) implies:
% 203.62/34.50  | | | | | | | | | | | | |   (187)   ~ (all_52_29 = e3)
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | REDUCE: (15), (185) imply:
% 203.62/34.50  | | | | | | | | | | | | |   (188)  op(e3, e3) = all_52_4
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | BETA: splitting (74) gives:
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | |   (189)  all_58_9 = e3
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | REF_CLOSE: (18), (124), (189) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | | | | |            #1300.
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | |   (190)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | |   (191)  all_58_10 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | COMBINE_EQS: (38), (191) imply:
% 203.62/34.50  | | | | | | | | | | | | | | |   (192)  all_52_27 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | SIMP: (192) implies:
% 203.62/34.50  | | | | | | | | | | | | | | |   (193)  all_52_27 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | REDUCE: (76), (193) imply:
% 203.62/34.50  | | | | | | | | | | | | | | |   (194)   ~ (all_14_2 = e3)
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | REDUCE: (20), (193) imply:
% 203.62/34.50  | | | | | | | | | | | | | | |   (195)  op(e3, e3) = all_52_26
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | |   (196)  all_58_14 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (196) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (197)  all_52_23 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (198)  all_52_23 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | REDUCE: (146), (198) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (199)  op(e3, e3) = e0
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_52_26, e3, e3,
% 203.62/34.50  | | | | | | | | | | | | | | | |              simplifying with (195), (199) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (200)  all_52_26 = e0
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_4, e3, e3,
% 203.62/34.50  | | | | | | | | | | | | | | | |              simplifying with (73), (188) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (201)  all_52_4 = all_6_2
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_26, all_52_4, e3,
% 203.62/34.50  | | | | | | | | | | | | | | | |              e3, simplifying with (188), (195) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (202)  all_52_4 = all_52_26
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (203)  all_52_26 = all_6_2
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | SIMP: (203) implies:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (204)  all_52_26 = all_6_2
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (204) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (205)  all_6_2 = e0
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (206)  all_6_2 = e0
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (206) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (207)  all_58_0 = e0
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | REDUCE: (115), (206) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (208)   ~ (all_4_0 = e0)
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | SIMP: (208) implies:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (209)   ~ (all_4_0 = e0)
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | REDUCE: (40), (206) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (210)  op(e0, e3) = e2
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | |   (211)  all_56_4 = e2
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (211) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | | |   (212)  all_4_0 = e2
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 203.62/34.50  | | | | | | | | | | | | | | | | |   (213)  all_4_0 = e2
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (213) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | | |   (214)  all_58_2 = e2
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | REDUCE: (113), (213) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | | |   (215)   ~ (all_52_7 = e2)
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | |   (216)  all_58_0 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (207), (216) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | | | | | | | | |            #847.
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | |   (217)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | |   (218)  all_58_2 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (214), (218) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | | | | | | | | | |            #1116.
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | |   (219)  all_58_6 = e1 | all_58_12 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |   (220)  all_58_6 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (129), (183), (220) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |            #1128.
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |   (221)  all_58_12 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (221) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |   (222)  all_52_7 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |   (223)  all_52_7 = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (223) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |   (224)   ~ (e2 = e1)
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (223) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |   (225)  op(e0, e3) = e1
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (210), (225) are inconsistent by
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | |            sub-proof #635.
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | |   (226)  all_56_4 = e1 | all_56_4 = e0
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (118), (209), (226) are inconsistent by
% 203.62/34.50  | | | | | | | | | | | | | | | | |            sub-proof #674.
% 203.62/34.50  | | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | |   (227)  all_58_15 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (227) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (228)  all_14_2 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | REDUCE: (169), (228) imply:
% 203.62/34.50  | | | | | | | | | | | | | | | |   (229)  $false
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 203.62/34.50  | | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | |   (230)  all_58_11 = e3 | all_58_15 = e3
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | | REF_CLOSE: (26), (64), (169), (187), (230) are inconsistent
% 203.62/34.50  | | | | | | | | | | | | | | |            by sub-proof #1103.
% 203.62/34.50  | | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | |   (231)  all_58_12 = e3
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | | REF_CLOSE: (43), (178), (231) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | | | | | | |            #1367.
% 203.62/34.50  | | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | End of split
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | End of split
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | End of split
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | End of split
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | Case 2:
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | |   (232)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 203.62/34.50  | | | | |          = e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | ALPHA: (232) implies:
% 203.62/34.50  | | | | |   (233)  all_52_30 = e0
% 203.62/34.50  | | | | |   (234)  all_52_26 = e2
% 203.62/34.50  | | | | |   (235)  all_52_24 = e3
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (103), (235) imply:
% 203.62/34.50  | | | | |   (236)  op(all_52_25, all_52_25) = e3
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (20), (234) imply:
% 203.62/34.50  | | | | |   (237)  op(all_52_27, all_52_27) = e2
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | REDUCE: (83), (233) imply:
% 203.62/34.50  | | | | |   (238)  op(all_14_2, all_14_2) = e0
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | BETA: splitting (51) gives:
% 203.62/34.50  | | | | | 
% 203.62/34.50  | | | | | Case 1:
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | |   (239)  all_56_4 = e3
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | | REF_CLOSE: (35), (108), (239) are inconsistent by sub-proof #980.
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | Case 2:
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | |   (240)   ~ (all_56_4 = e3)
% 203.62/34.50  | | | | | |   (241)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | | BETA: splitting (48) gives:
% 203.62/34.50  | | | | | | 
% 203.62/34.50  | | | | | | Case 1:
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | |   (242)  all_58_0 = e3
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | COMBINE_EQS: (11), (242) imply:
% 203.62/34.50  | | | | | | |   (243)  all_6_2 = e3
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | REDUCE: (126), (243) imply:
% 203.62/34.50  | | | | | | |   (244)  $false
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | CLOSE: (244) is inconsistent.
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | Case 2:
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | |   (245)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | BETA: splitting (32) gives:
% 203.62/34.50  | | | | | | | 
% 203.62/34.50  | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | |   (246)  all_58_2 = e3
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | | REF_CLOSE: (35), (109), (246) are inconsistent by sub-proof
% 203.62/34.50  | | | | | | | |            #948.
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | Case 2:
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | |   (247)   ~ (all_58_2 = e3)
% 203.62/34.50  | | | | | | | |   (248)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | | BETA: splitting (66) gives:
% 203.62/34.50  | | | | | | | | 
% 203.62/34.50  | | | | | | | | Case 1:
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | |   (249)  all_56_15 = e3
% 203.62/34.50  | | | | | | | | | 
% 203.62/34.50  | | | | | | | | | COMBINE_EQS: (31), (249) imply:
% 203.62/34.51  | | | | | | | | |   (250)  all_14_2 = e3
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | SIMP: (250) implies:
% 203.62/34.51  | | | | | | | | |   (251)  all_14_2 = e3
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REDUCE: (45), (251) imply:
% 203.62/34.51  | | | | | | | | |   (252)   ~ (all_52_7 = e3)
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REDUCE: (76), (251) imply:
% 203.62/34.51  | | | | | | | | |   (253)   ~ (all_52_27 = e3)
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REDUCE: (238), (251) imply:
% 203.62/34.51  | | | | | | | | |   (254)  op(e3, e3) = e0
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | BETA: splitting (248) gives:
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | |   (255)  all_58_3 = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | COMBINE_EQS: (98), (255) imply:
% 203.62/34.51  | | | | | | | | | |   (256)  all_4_2 = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REDUCE: (128), (256) imply:
% 203.62/34.51  | | | | | | | | | |   (257)  $false
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | CLOSE: (257) is inconsistent.
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | |   (258)  all_58_5 = e3 | all_58_10 = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | BETA: splitting (245) gives:
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | |   (259)  all_58_2 = e3
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | REF_CLOSE: (35), (109), (259) are inconsistent by sub-proof
% 203.62/34.51  | | | | | | | | | | |            #948.
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | |   (260)  all_58_6 = e3 | all_58_12 = e3
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | BETA: splitting (258) gives:
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | |   (261)  all_58_5 = e3
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | COMBINE_EQS: (84), (261) imply:
% 203.62/34.51  | | | | | | | | | | | |   (262)  all_52_19 = e3
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | SIMP: (262) implies:
% 203.62/34.51  | | | | | | | | | | | |   (263)  all_52_19 = e3
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | REDUCE: (16), (263) imply:
% 203.62/34.51  | | | | | | | | | | | |   (264)  op(e3, e3) = all_52_18
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | BETA: splitting (44) gives:
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | |   (265)  all_58_6 = e3
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | COMBINE_EQS: (88), (265) imply:
% 203.62/34.51  | | | | | | | | | | | | |   (266)  all_52_5 = e3
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | SIMP: (266) implies:
% 203.62/34.51  | | | | | | | | | | | | |   (267)  all_52_5 = e3
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | REDUCE: (15), (267) imply:
% 203.62/34.51  | | | | | | | | | | | | |   (268)  op(e3, e3) = all_52_4
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_18, e3, e3,
% 203.62/34.51  | | | | | | | | | | | | |              simplifying with (73), (264) gives:
% 203.62/34.51  | | | | | | | | | | | | |   (269)  all_52_18 = all_6_2
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_18, all_52_4, e3,
% 203.62/34.51  | | | | | | | | | | | | |              e3, simplifying with (264), (268) gives:
% 203.62/34.51  | | | | | | | | | | | | |   (270)  all_52_4 = all_52_18
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_52_4, e3, e3,
% 203.62/34.51  | | | | | | | | | | | | |              simplifying with (254), (268) gives:
% 203.62/34.51  | | | | | | | | | | | | |   (271)  all_52_4 = e0
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | COMBINE_EQS: (270), (271) imply:
% 203.62/34.51  | | | | | | | | | | | | |   (272)  all_52_18 = e0
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | SIMP: (272) implies:
% 203.62/34.51  | | | | | | | | | | | | |   (273)  all_52_18 = e0
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | COMBINE_EQS: (269), (273) imply:
% 203.62/34.51  | | | | | | | | | | | | |   (274)  all_6_2 = e0
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | SIMP: (274) implies:
% 203.62/34.51  | | | | | | | | | | | | |   (275)  all_6_2 = e0
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | COMBINE_EQS: (11), (275) imply:
% 203.62/34.51  | | | | | | | | | | | | |   (276)  all_58_0 = e0
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | REDUCE: (40), (275) imply:
% 203.62/34.51  | | | | | | | | | | | | |   (277)  op(e0, e3) = e2
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | |   (278)  all_58_0 = e1
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | REF_CLOSE: (91), (276), (278) are inconsistent by sub-proof
% 203.62/34.51  | | | | | | | | | | | | | |            #847.
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | |   (279)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | |   (280)  all_58_2 = e1
% 203.62/34.51  | | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | | REF_CLOSE: (109), (118), (280) are inconsistent by sub-proof
% 203.62/34.51  | | | | | | | | | | | | | | |            #967.
% 203.62/34.51  | | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | |   (281)  all_58_6 = e1 | all_58_12 = e1
% 203.62/34.51  | | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (43), (61), (129), (265), (277), (281)
% 203.62/34.51  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #634.
% 203.62/34.51  | | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | |   (282)   ~ (all_58_6 = e3)
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | | REF_CLOSE: (43), (88), (252), (260), (282) are inconsistent
% 203.62/34.51  | | | | | | | | | | | | |            by sub-proof #594.
% 203.62/34.51  | | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | |   (283)  all_58_10 = e3
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | | REF_CLOSE: (38), (253), (283) are inconsistent by sub-proof
% 203.62/34.51  | | | | | | | | | | | |            #1301.
% 203.62/34.51  | | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | |   (284)   ~ (all_56_15 = e3)
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REDUCE: (31), (284) imply:
% 203.62/34.51  | | | | | | | | |   (285)   ~ (all_14_2 = e3)
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | BETA: splitting (90) gives:
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | |   (286)  all_58_12 = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | COMBINE_EQS: (43), (286) imply:
% 203.62/34.51  | | | | | | | | | |   (287)  all_52_7 = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | SIMP: (287) implies:
% 203.62/34.51  | | | | | | | | | |   (288)  all_52_7 = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REDUCE: (7), (288) imply:
% 203.62/34.51  | | | | | | | | | |   (289)   ~ (all_52_15 = e3)
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REDUCE: (113), (288) imply:
% 203.62/34.51  | | | | | | | | | |   (290)   ~ (all_4_0 = e3)
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REDUCE: (8), (288) imply:
% 203.62/34.51  | | | | | | | | | |   (291)  op(e3, e3) = all_52_6
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REDUCE: (61), (288) imply:
% 203.62/34.51  | | | | | | | | | |   (292)  op(e0, e3) = e3
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3,
% 203.62/34.51  | | | | | | | | | |              simplifying with (73), (291) gives:
% 203.62/34.51  | | | | | | | | | |   (293)  all_52_6 = all_6_2
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REF_CLOSE: (4), (11), (17), (21), (22), (23), (27), (28),
% 203.62/34.51  | | | | | | | | | |            (35), (40), (41), (49), (52), (59), (62), (70),
% 203.62/34.51  | | | | | | | | | |            (72), (73), (78), (79), (87), (89), (95), (98),
% 203.62/34.51  | | | | | | | | | |            (105), (108), (111), (115), (116), (118), (121),
% 203.62/34.51  | | | | | | | | | |            (122), (123), (126), (128), (241), (292) are
% 203.62/34.51  | | | | | | | | | |            inconsistent by sub-proof #595.
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | |   (294)   ~ (all_58_12 = e3)
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | REDUCE: (43), (294) imply:
% 203.62/34.51  | | | | | | | | | |   (295)   ~ (all_52_7 = e3)
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | BETA: splitting (245) gives:
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | |   (296)  all_58_2 = e3
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | REF_CLOSE: (35), (109), (296) are inconsistent by sub-proof
% 203.62/34.51  | | | | | | | | | | |            #948.
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | |   (297)  all_58_6 = e3 | all_58_12 = e3
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (11), (14), (15), (18), (26),
% 203.62/34.51  | | | | | | | | | | |            (30), (33), (38), (39), (43), (55), (58), (62),
% 203.62/34.51  | | | | | | | | | | |            (63), (64), (67), (68), (69), (73), (74), (76),
% 203.62/34.51  | | | | | | | | | | |            (77), (80), (84), (86), (88), (92), (97), (98),
% 203.62/34.51  | | | | | | | | | | |            (102), (236), (237), (248), (285), (295), (297)
% 203.62/34.51  | | | | | | | | | | |            are inconsistent by sub-proof #1011.
% 203.62/34.51  | | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | End of split
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | End of split
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | End of split
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | End of split
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | End of split
% 203.62/34.51  | | | 
% 203.62/34.51  | | Case 2:
% 203.62/34.51  | | | 
% 203.62/34.51  | | |   (298)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.51  | | | 
% 203.62/34.51  | | | BETA: splitting (298) gives:
% 203.62/34.51  | | | 
% 203.62/34.51  | | | Case 1:
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | |   (299)  all_56_1 = e2
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | COMBINE_EQS: (94), (299) imply:
% 203.62/34.51  | | | |   (300)  all_6_0 = e2
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | REDUCE: (60), (300) imply:
% 203.62/34.51  | | | |   (301)  $false
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | CLOSE: (301) is inconsistent.
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | Case 2:
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | |   (302)  all_56_1 = e1 | all_56_1 = e0
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | BETA: splitting (302) gives:
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | Case 1:
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | |   (303)  all_56_1 = e1
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | COMBINE_EQS: (94), (303) imply:
% 203.62/34.51  | | | | |   (304)  all_6_0 = e1
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | REDUCE: (37), (304) imply:
% 203.62/34.51  | | | | |   (305)  $false
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | CLOSE: (305) is inconsistent.
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | Case 2:
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | |   (306)  all_56_1 = e0
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | COMBINE_EQS: (94), (306) imply:
% 203.62/34.51  | | | | |   (307)  all_6_0 = e0
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | COMBINE_EQS: (19), (307) imply:
% 203.62/34.51  | | | | |   (308)  all_22_0 = e0
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | REDUCE: (82), (307) imply:
% 203.62/34.51  | | | | |   (309)   ~ (all_6_2 = e0)
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | SIMP: (309) implies:
% 203.62/34.51  | | | | |   (310)   ~ (all_6_2 = e0)
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | BETA: splitting (50) gives:
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | Case 1:
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | |   (311)   ~ (all_22_2 = e1)
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | REDUCE: (101), (311) imply:
% 203.62/34.51  | | | | | |   (312)   ~ (all_6_2 = e1)
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | BETA: splitting (51) gives:
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | Case 1:
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | |   (313)  all_56_4 = e3
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | REF_CLOSE: (35), (108), (313) are inconsistent by sub-proof #980.
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | Case 2:
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | |   (314)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | BETA: splitting (95) gives:
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | |   (315)  all_56_0 = e3
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | COMBINE_EQS: (72), (315) imply:
% 203.62/34.51  | | | | | | | |   (316)  all_6_2 = e3
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | SIMP: (316) implies:
% 203.62/34.51  | | | | | | | |   (317)  all_6_2 = e3
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | REDUCE: (28), (317) imply:
% 203.62/34.51  | | | | | | | |   (318)  op(e3, e3) = all_52_0
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | REDUCE: (40), (317) imply:
% 203.62/34.51  | | | | | | | |   (319)  op(e3, e3) = e2
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | REDUCE: (73), (317) imply:
% 203.62/34.51  | | | | | | | |   (320)  op(e3, e3) = e3
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | REF_CLOSE: (4), (92), (318), (319), (320) are inconsistent by
% 203.62/34.51  | | | | | | | |            sub-proof #821.
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | |   (321)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | BETA: splitting (321) gives:
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | | Case 1:
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | |   (322)  all_56_0 = e2
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | COMBINE_EQS: (72), (322) imply:
% 203.62/34.51  | | | | | | | | |   (323)  all_6_2 = e2
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | SIMP: (323) implies:
% 203.62/34.51  | | | | | | | | |   (324)  all_6_2 = e2
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REDUCE: (115), (324) imply:
% 203.62/34.51  | | | | | | | | |   (325)   ~ (all_4_0 = e2)
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | SIMP: (325) implies:
% 203.62/34.51  | | | | | | | | |   (326)   ~ (all_4_0 = e2)
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REF_CLOSE: (4), (22), (23), (27), (52), (70), (78), (79),
% 203.62/34.51  | | | | | | | | |            (87), (89), (105), (108), (116), (118), (314),
% 203.62/34.51  | | | | | | | | |            (326) are inconsistent by sub-proof #971.
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | Case 2:
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | |   (327)  all_56_0 = e1 | all_56_0 = e0
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | | REF_CLOSE: (72), (310), (312), (327) are inconsistent by
% 203.62/34.51  | | | | | | | | |            sub-proof #1066.
% 203.62/34.51  | | | | | | | | | 
% 203.62/34.51  | | | | | | | | End of split
% 203.62/34.51  | | | | | | | | 
% 203.62/34.51  | | | | | | | End of split
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | End of split
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | Case 2:
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | |   (328)   ~ (all_22_0 = e0)
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | REDUCE: (308), (328) imply:
% 203.62/34.51  | | | | | |   (329)  $false
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | CLOSE: (329) is inconsistent.
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | End of split
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | End of split
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | End of split
% 203.62/34.51  | | | 
% 203.62/34.51  | | End of split
% 203.62/34.51  | | 
% 203.62/34.51  | Case 2:
% 203.62/34.51  | | 
% 203.62/34.51  | |   (330)  all_38_0 = e1
% 203.62/34.51  | |   (331)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 203.62/34.51  | | 
% 203.62/34.51  | | COMBINE_EQS: (46), (330) imply:
% 203.62/34.51  | |   (332)  all_4_0 = e1
% 203.62/34.51  | | 
% 203.62/34.51  | | REF_CLOSE: (4), (13), (23), (27), (52), (70), (78), (89), (104), (105),
% 203.62/34.51  | |            (116), (331), (332) are inconsistent by sub-proof #927.
% 203.62/34.51  | | 
% 203.62/34.51  | End of split
% 203.62/34.51  | 
% 203.62/34.51  End of proof
% 203.62/34.51  
% 203.62/34.51  Sub-proof #594 shows that the following formulas are inconsistent:
% 203.62/34.51  ----------------------------------------------------------------
% 203.62/34.51    (1)   ~ (all_58_6 = e3)
% 203.62/34.51    (2)  all_58_12 = all_52_7
% 203.62/34.51    (3)   ~ (all_52_7 = e3)
% 203.62/34.51    (4)  all_58_6 = all_52_5
% 203.62/34.51    (5)  all_58_6 = e3 | all_58_12 = e3
% 203.62/34.51  
% 203.62/34.51  Begin of proof
% 203.62/34.51  | 
% 203.62/34.51  | REDUCE: (1), (4) imply:
% 203.62/34.51  |   (6)   ~ (all_52_5 = e3)
% 203.62/34.51  | 
% 203.62/34.51  | BETA: splitting (5) gives:
% 203.62/34.51  | 
% 203.62/34.51  | Case 1:
% 203.62/34.51  | | 
% 203.62/34.51  | |   (7)  all_58_6 = e3
% 203.62/34.51  | | 
% 203.62/34.51  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1328.
% 203.62/34.51  | | 
% 203.62/34.51  | Case 2:
% 203.62/34.51  | | 
% 203.62/34.51  | |   (8)  all_58_12 = e3
% 203.62/34.51  | | 
% 203.62/34.51  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #1367.
% 203.62/34.51  | | 
% 203.62/34.51  | End of split
% 203.62/34.51  | 
% 203.62/34.51  End of proof
% 203.62/34.51  
% 203.62/34.51  Sub-proof #595 shows that the following formulas are inconsistent:
% 203.62/34.51  ----------------------------------------------------------------
% 203.62/34.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.51    (2)   ~ (all_4_0 = e1)
% 203.62/34.51    (3)   ~ (all_52_5 = all_4_0)
% 203.62/34.51    (4)   ~ (all_4_2 = e3)
% 203.62/34.51    (5)  all_58_0 = all_6_2
% 203.62/34.51    (6)  all_58_13 = all_52_15
% 203.62/34.51    (7)   ~ (all_52_15 = e3)
% 203.62/34.51    (8)  op(e1, e3) = all_52_5
% 203.62/34.51    (9)   ~ (all_6_2 = all_4_0)
% 203.62/34.51    (10)  all_32_2 = all_4_2
% 203.62/34.51    (11)  op(e2, e2) = all_4_2
% 203.62/34.51    (12)  all_56_5 = all_4_2
% 203.62/34.51    (13)  all_58_1 = e3
% 203.62/34.51    (14)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.51    (15)  op(all_4_2, e2) = e3
% 203.62/34.51    (16)   ~ (all_4_0 = e3)
% 203.62/34.51    (17)   ~ (all_6_2 = e3)
% 203.62/34.51    (18)  op(all_6_2, e3) = e2
% 203.62/34.51    (19)  all_58_7 = all_52_13
% 203.62/34.51    (20)  op(e0, e3) = e3
% 203.62/34.51    (21)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.51    (22)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.51    (23)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.51    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.51    (25)  all_56_4 = all_4_0
% 203.62/34.51    (26)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.51    (27)   ~ (all_52_9 = all_4_2)
% 203.62/34.51    (28)  all_56_0 = all_6_2
% 203.62/34.51    (29)  op(e3, e3) = all_6_2
% 203.62/34.51    (30)   ~ (all_52_13 = e3)
% 203.62/34.51    (31)  op(all_4_2, all_4_2) = all_52_10
% 203.62/34.51    (32)  all_32_0 = all_4_0
% 203.62/34.51    (33)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.62/34.51    (34)   ~ (all_4_0 = all_4_2)
% 203.62/34.51    (35)  op(e3, e2) = all_52_9
% 203.62/34.51    (36)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.51    (37)  all_58_3 = all_4_2
% 203.62/34.51  
% 203.62/34.51  Begin of proof
% 203.62/34.51  | 
% 203.62/34.51  | BETA: splitting (21) gives:
% 203.62/34.51  | 
% 203.62/34.51  | Case 1:
% 203.62/34.51  | | 
% 203.62/34.51  | |   (38)  all_58_0 = e1
% 203.62/34.51  | | 
% 203.62/34.51  | | COMBINE_EQS: (5), (38) imply:
% 203.62/34.51  | |   (39)  all_6_2 = e1
% 203.62/34.51  | | 
% 203.62/34.51  | | REDUCE: (9), (39) imply:
% 203.62/34.51  | |   (40)   ~ (all_4_0 = e1)
% 203.62/34.51  | | 
% 203.62/34.51  | | REDUCE: (18), (39) imply:
% 203.62/34.51  | |   (41)  op(e1, e3) = e2
% 203.62/34.51  | | 
% 203.62/34.51  | | GROUND_INST: instantiating (1) with all_52_5, e2, e3, e1, simplifying with
% 203.62/34.51  | |              (8), (41) gives:
% 203.62/34.51  | |   (42)  all_52_5 = e2
% 203.62/34.51  | | 
% 203.62/34.51  | | REDUCE: (3), (42) imply:
% 203.62/34.51  | |   (43)   ~ (all_4_0 = e2)
% 203.62/34.51  | | 
% 203.62/34.51  | | SIMP: (43) implies:
% 203.62/34.51  | |   (44)   ~ (all_4_0 = e2)
% 203.62/34.51  | | 
% 203.62/34.51  | | REF_CLOSE: (1), (2), (10), (11), (12), (15), (22), (23), (25), (27), (31),
% 203.62/34.51  | |            (32), (33), (34), (35), (44) are inconsistent by sub-proof #971.
% 203.62/34.51  | | 
% 203.62/34.51  | Case 2:
% 203.62/34.51  | | 
% 203.62/34.51  | |   (45)   ~ (all_58_0 = e1)
% 203.62/34.51  | | 
% 203.62/34.51  | | REDUCE: (5), (45) imply:
% 203.62/34.51  | |   (46)   ~ (all_6_2 = e1)
% 203.62/34.51  | | 
% 203.62/34.51  | | BETA: splitting (36) gives:
% 203.62/34.51  | | 
% 203.62/34.51  | | Case 1:
% 203.62/34.51  | | | 
% 203.62/34.51  | | |   (47)  all_56_0 = e3
% 203.62/34.51  | | | 
% 203.62/34.51  | | | REF_CLOSE: (17), (28), (47) are inconsistent by sub-proof #598.
% 203.62/34.51  | | | 
% 203.62/34.51  | | Case 2:
% 203.62/34.51  | | | 
% 203.62/34.51  | | |   (48)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.51  | | | 
% 203.62/34.51  | | | BETA: splitting (24) gives:
% 203.62/34.51  | | | 
% 203.62/34.51  | | | Case 1:
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | |   (49)  all_58_0 = e2
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | COMBINE_EQS: (5), (49) imply:
% 203.62/34.51  | | | |   (50)  all_6_2 = e2
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | REDUCE: (29), (50) imply:
% 203.62/34.51  | | | |   (51)  op(e3, e3) = e2
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | REF_CLOSE: (1), (2), (4), (9), (10), (11), (12), (14), (15), (22), (23),
% 203.62/34.51  | | | |            (25), (29), (31), (32), (33), (34), (51) are inconsistent by
% 203.62/34.51  | | | |            sub-proof #947.
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | Case 2:
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | |   (52)   ~ (all_58_0 = e2)
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | REDUCE: (5), (52) imply:
% 203.62/34.51  | | | |   (53)   ~ (all_6_2 = e2)
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | BETA: splitting (48) gives:
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | | Case 1:
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | |   (54)  all_56_0 = e2
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | REF_CLOSE: (28), (53), (54) are inconsistent by sub-proof #597.
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | Case 2:
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | |   (55)  all_56_0 = e1 | all_56_0 = e0
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | BETA: splitting (55) gives:
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | | Case 1:
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | |   (56)  all_56_0 = e1
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | REF_CLOSE: (28), (46), (56) are inconsistent by sub-proof #596.
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | Case 2:
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | |   (57)  all_56_0 = e0
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | COMBINE_EQS: (28), (57) imply:
% 203.62/34.51  | | | | | |   (58)  all_6_2 = e0
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | SIMP: (58) implies:
% 203.62/34.51  | | | | | |   (59)  all_6_2 = e0
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | REDUCE: (9), (59) imply:
% 203.62/34.51  | | | | | |   (60)   ~ (all_4_0 = e0)
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | SIMP: (60) implies:
% 203.62/34.51  | | | | | |   (61)   ~ (all_4_0 = e0)
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | REDUCE: (18), (59) imply:
% 203.62/34.51  | | | | | |   (62)  op(e0, e3) = e2
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | BETA: splitting (23) gives:
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | | Case 1:
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | |   (63)  all_56_4 = e2
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | COMBINE_EQS: (25), (63) imply:
% 203.62/34.51  | | | | | | |   (64)  all_4_0 = e2
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | SIMP: (64) implies:
% 203.62/34.51  | | | | | | |   (65)  all_4_0 = e2
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | REDUCE: (16), (65) imply:
% 203.62/34.51  | | | | | | |   (66)   ~ (e3 = e2)
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | SIMP: (66) implies:
% 203.62/34.51  | | | | | | |   (67)   ~ (e3 = e2)
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | GROUND_INST: instantiating (1) with e3, e2, e3, e0, simplifying
% 203.62/34.51  | | | | | | |              with (20), (62) gives:
% 203.62/34.51  | | | | | | |   (68)  e3 = e2
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | REF_CLOSE: (4), (6), (7), (13), (19), (26), (30), (37), (67), (68)
% 203.62/34.51  | | | | | | |            are inconsistent by sub-proof #1089.
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | Case 2:
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | |   (69)  all_56_4 = e1 | all_56_4 = e0
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | | REF_CLOSE: (2), (25), (61), (69) are inconsistent by sub-proof
% 203.62/34.51  | | | | | | |            #674.
% 203.62/34.51  | | | | | | | 
% 203.62/34.51  | | | | | | End of split
% 203.62/34.51  | | | | | | 
% 203.62/34.51  | | | | | End of split
% 203.62/34.51  | | | | | 
% 203.62/34.51  | | | | End of split
% 203.62/34.51  | | | | 
% 203.62/34.51  | | | End of split
% 203.62/34.51  | | | 
% 203.62/34.51  | | End of split
% 203.62/34.51  | | 
% 203.62/34.51  | End of split
% 203.62/34.51  | 
% 203.62/34.51  End of proof
% 203.62/34.51  
% 203.62/34.51  Sub-proof #596 shows that the following formulas are inconsistent:
% 203.62/34.51  ----------------------------------------------------------------
% 203.62/34.51    (1)  all_56_0 = all_6_2
% 203.62/34.51    (2)  all_56_0 = e1
% 203.62/34.51    (3)   ~ (all_6_2 = e1)
% 203.62/34.51  
% 203.62/34.51  Begin of proof
% 203.62/34.51  | 
% 203.62/34.51  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.51  |   (4)  all_6_2 = e1
% 203.62/34.51  | 
% 203.62/34.51  | SIMP: (4) implies:
% 203.62/34.51  |   (5)  all_6_2 = e1
% 203.62/34.51  | 
% 203.62/34.51  | REDUCE: (3), (5) imply:
% 203.62/34.51  |   (6)  $false
% 203.62/34.51  | 
% 203.62/34.51  | CLOSE: (6) is inconsistent.
% 203.62/34.51  | 
% 203.62/34.51  End of proof
% 203.62/34.51  
% 203.62/34.51  Sub-proof #597 shows that the following formulas are inconsistent:
% 203.62/34.51  ----------------------------------------------------------------
% 203.62/34.51    (1)  all_56_0 = all_6_2
% 203.62/34.51    (2)  all_56_0 = e2
% 203.62/34.51    (3)   ~ (all_6_2 = e2)
% 203.62/34.51  
% 203.62/34.51  Begin of proof
% 203.62/34.51  | 
% 203.62/34.51  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.51  |   (4)  all_6_2 = e2
% 203.62/34.51  | 
% 203.62/34.51  | SIMP: (4) implies:
% 203.62/34.51  |   (5)  all_6_2 = e2
% 203.62/34.51  | 
% 203.62/34.51  | REDUCE: (3), (5) imply:
% 203.62/34.51  |   (6)  $false
% 203.62/34.51  | 
% 203.62/34.51  | CLOSE: (6) is inconsistent.
% 203.62/34.51  | 
% 203.62/34.51  End of proof
% 203.62/34.51  
% 203.62/34.51  Sub-proof #598 shows that the following formulas are inconsistent:
% 203.62/34.51  ----------------------------------------------------------------
% 203.62/34.51    (1)  all_56_0 = all_6_2
% 203.62/34.51    (2)  all_56_0 = e3
% 203.62/34.51    (3)   ~ (all_6_2 = e3)
% 203.62/34.51  
% 203.62/34.51  Begin of proof
% 203.62/34.51  | 
% 203.62/34.51  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.51  |   (4)  all_6_2 = e3
% 203.62/34.51  | 
% 203.62/34.51  | SIMP: (4) implies:
% 203.62/34.51  |   (5)  all_6_2 = e3
% 203.62/34.51  | 
% 203.62/34.51  | REDUCE: (3), (5) imply:
% 203.62/34.51  |   (6)  $false
% 203.62/34.51  | 
% 203.62/34.51  | CLOSE: (6) is inconsistent.
% 203.62/34.51  | 
% 203.62/34.51  End of proof
% 203.62/34.51  
% 203.62/34.51  Sub-proof #599 shows that the following formulas are inconsistent:
% 203.62/34.51  ----------------------------------------------------------------
% 203.62/34.51    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.51    (2)   ~ (all_52_25 = all_6_0)
% 203.62/34.51    (3)   ~ (all_52_25 = all_52_27)
% 203.62/34.51    (4)  all_58_14 = all_52_23
% 203.62/34.51    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.51    (7)   ~ (all_52_5 = all_52_13)
% 203.62/34.51    (8)  all_58_1 = all_52_9
% 203.62/34.51    (9)   ~ (all_52_9 = all_52_13)
% 203.62/34.51    (10)   ~ (e3 = e0)
% 203.62/34.51    (11)  op(e2, e3) = all_52_3
% 203.62/34.51    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.51    (13)   ~ (all_52_7 = all_52_15)
% 203.62/34.51    (14)   ~ (all_52_3 = all_52_19)
% 203.62/34.51    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.51    (16)   ~ (all_52_17 = all_52_25)
% 203.62/34.51    (17)   ~ (all_52_3 = all_6_2)
% 203.62/34.51    (18)  all_58_0 = all_6_2
% 203.62/34.51    (19)  op(all_14_2, e0) = all_14_1
% 203.62/34.51    (20)  all_56_4 = all_52_3
% 203.62/34.51    (21)   ~ (all_52_17 = all_10_2)
% 203.62/34.51    (22)  all_40_2 = all_10_2
% 203.62/34.51    (23)  op(e3, e0) = all_52_25
% 203.62/34.51    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.51    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.51    (26)   ~ (all_52_27 = all_52_29)
% 203.62/34.51    (27)  all_58_13 = all_52_15
% 203.62/34.51    (28)  all_40_1 = e2
% 203.62/34.51    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.51    (30)  all_58_9 = all_52_25
% 203.62/34.51    (31)   ~ (all_52_29 = all_14_2)
% 203.62/34.51    (32)  all_22_0 = all_6_0
% 203.62/34.51    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.51    (34)   ~ (all_52_17 = all_6_0)
% 203.62/34.51    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.51    (36)  op(e1, e3) = all_52_5
% 203.62/34.51    (37)  all_40_1 = all_10_1
% 203.62/34.51    (38)  op(e2, e2) = all_4_2
% 203.62/34.51    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.51    (40)   ~ (all_52_3 = all_52_5)
% 203.62/34.51    (41)  all_58_11 = all_52_29
% 203.62/34.51    (42)  all_56_5 = all_4_2
% 203.62/34.51    (43)   ~ (all_52_25 = all_14_2)
% 203.62/34.51    (44)   ~ (all_52_3 = all_52_27)
% 203.62/34.51    (45)  op(all_10_2, e1) = all_10_1
% 203.62/34.51    (46)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.51    (47)   ~ (all_52_7 = all_6_2)
% 203.62/34.51    (48)  op(e0, e0) = all_14_2
% 203.62/34.51    (49)  all_56_15 = all_14_2
% 203.62/34.51    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.51    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.51    (52)  all_56_11 = all_52_29
% 203.62/34.51    (53)   ~ (all_10_0 = e2)
% 203.62/34.51    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.51    (55)  all_56_9 = all_52_13
% 203.62/34.51    (56)   ~ (e2 = e1)
% 203.62/34.51    (57)   ~ (all_6_0 = e1)
% 203.62/34.51    (58)  op(e1, all_10_1) = all_10_0
% 203.62/34.51    (59)  all_58_10 = all_52_27
% 203.62/34.51    (60)  all_56_8 = all_52_5
% 203.62/34.51    (61)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.51    (62)   ~ (all_52_19 = all_52_23)
% 203.62/34.51    (63)   ~ (all_52_25 = all_52_29)
% 203.62/34.51    (64)  op(all_6_2, e3) = e2
% 203.62/34.51    (65)   ~ (all_52_29 = all_10_2)
% 203.62/34.51    (66)  all_58_7 = all_52_13
% 203.62/34.51    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.51    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.52    (69)  all_58_1 = all_6_0
% 203.62/34.52    (70)   ~ (all_52_5 = all_52_7)
% 203.62/34.52    (71)  all_58_12 = all_52_7
% 203.62/34.52    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.52    (73)   ~ (all_52_7 = all_14_2)
% 203.62/34.52    (74)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.62/34.52    (75)  all_58_2 = all_52_3
% 203.62/34.52    (76)  all_56_2 = all_52_17
% 203.62/34.52    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.52    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.52    (79)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.52    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.52    (81)   ~ (e2 = e0)
% 203.62/34.52    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.52    (83)  op(all_6_0, all_6_0) = all_52_8
% 203.62/34.52    (84)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.52    (85)   ~ (all_52_5 = all_52_29)
% 203.62/34.52    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.52    (87)   ~ (all_52_13 = all_6_0)
% 203.62/34.52    (88)   ~ (all_52_19 = all_52_27)
% 203.62/34.52    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.52    (90)   ~ (all_6_0 = e2)
% 203.62/34.52    (91)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.52            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.52    (92)  op(e3, e1) = all_52_17
% 203.62/34.52    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.52    (94)  op(e0, e3) = all_52_7
% 203.62/34.52    (95)  op(e1, e2) = all_52_13
% 203.62/34.52    (96)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.52    (97)   ~ (all_52_9 = all_52_25)
% 203.62/34.52    (98)  all_58_15 = all_14_2
% 203.62/34.52    (99)   ~ (all_52_19 = all_10_2)
% 203.62/34.52    (100)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.52    (101)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.52    (102)  all_58_8 = all_10_2
% 203.62/34.52    (103)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.52    (104)   ~ (all_52_5 = all_10_2)
% 203.62/34.52    (105)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.52    (106)   ~ (all_52_23 = all_14_2)
% 203.62/34.52    (107)  all_56_12 = all_52_7
% 203.62/34.52    (108)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.52    (109)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.52    (110)   ~ (all_52_25 = all_6_2)
% 203.62/34.52    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.52    (112)   ~ (all_52_9 = all_4_2)
% 203.62/34.52    (113)   ~ (all_52_5 = all_6_2)
% 203.62/34.52    (114)  all_56_0 = all_6_2
% 203.62/34.52    (115)  op(e3, e3) = all_6_2
% 203.62/34.52    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.52    (117)   ~ (all_52_15 = all_6_0)
% 203.62/34.52    (118)   ~ (all_52_27 = all_14_2)
% 203.62/34.52    (119)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.52    (120)  all_56_14 = all_52_23
% 203.62/34.52    (121)  all_40_0 = all_10_0
% 203.62/34.52    (122)  all_56_3 = all_52_25
% 203.62/34.52    (123)  op(e0, all_14_1) = e2
% 203.62/34.52    (124)   ~ (all_52_3 = all_52_7)
% 203.62/34.52    (125)   ~ (all_6_0 = all_6_2)
% 203.62/34.52    (126)   ~ (all_10_1 = e3)
% 203.62/34.52    (127)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.52    (128)  all_58_5 = all_52_19
% 203.62/34.52    (129)   ~ (all_52_15 = all_4_2)
% 203.62/34.52    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.52           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.52           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.52           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.52    (131)   ~ (all_52_27 = all_4_2)
% 203.62/34.52    (132)  all_58_6 = all_52_5
% 203.62/34.52    (133)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.52    (134)   ~ (all_52_17 = all_6_2)
% 203.62/34.52    (135)   ~ (e1 = e0)
% 203.62/34.52    (136)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.52    (137)  all_56_10 = all_10_2
% 203.62/34.52    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.52    (139)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.52    (140)  all_56_1 = all_6_0
% 203.62/34.52    (141)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.52    (142)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.52    (143)   ~ (all_6_0 = all_4_2)
% 203.62/34.52    (144)  op(e1, e1) = all_10_2
% 203.62/34.52    (145)   ~ (all_52_23 = all_10_2)
% 203.62/34.52    (146)   ~ (all_52_7 = all_52_23)
% 203.62/34.52    (147)  all_58_3 = all_4_2
% 203.62/34.52    (148)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.52    (149)   ~ (all_52_3 = all_4_2)
% 203.62/34.52    (150)   ~ (all_52_19 = all_4_2)
% 203.62/34.52    (151)   ~ (all_52_17 = all_52_23)
% 203.62/34.52    (152)  op(all_6_2, e3) = all_6_1
% 203.62/34.52    (153)  all_22_2 = all_6_2
% 203.62/34.52    (154)  all_58_4 = all_52_17
% 203.62/34.52    (155)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.52    (156)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.52  
% 203.62/34.52  Begin of proof
% 203.62/34.52  | 
% 203.62/34.52  | COMBINE_EQS: (28), (37) imply:
% 203.62/34.52  |   (157)  all_10_1 = e2
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (126), (157) imply:
% 203.62/34.52  |   (158)   ~ (e3 = e2)
% 203.62/34.52  | 
% 203.62/34.52  | SIMP: (158) implies:
% 203.62/34.52  |   (159)   ~ (e3 = e2)
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (45), (157) imply:
% 203.62/34.52  |   (160)  op(all_10_2, e1) = e2
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (58), (157) imply:
% 203.62/34.52  |   (161)  op(e1, e2) = all_10_0
% 203.62/34.52  | 
% 203.62/34.52  | GROUND_INST: instantiating (6) with all_52_13, all_10_0, e2, e1, simplifying
% 203.62/34.52  |              with (95), (161) gives:
% 203.62/34.52  |   (162)  all_52_13 = all_10_0
% 203.62/34.52  | 
% 203.62/34.52  | COMBINE_EQS: (55), (162) imply:
% 203.62/34.52  |   (163)  all_56_9 = all_10_0
% 203.62/34.52  | 
% 203.62/34.52  | COMBINE_EQS: (66), (162) imply:
% 203.62/34.52  |   (164)  all_58_7 = all_10_0
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (7), (162) imply:
% 203.62/34.52  |   (165)   ~ (all_52_5 = all_10_0)
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (87), (162) imply:
% 203.62/34.52  |   (166)   ~ (all_10_0 = all_6_0)
% 203.62/34.52  | 
% 203.62/34.52  | BETA: splitting (91) gives:
% 203.62/34.52  | 
% 203.62/34.52  | Case 1:
% 203.62/34.52  | | 
% 203.62/34.52  | |   (167)  all_58_15 = e0
% 203.62/34.52  | | 
% 203.62/34.52  | | REF_CLOSE: (6), (19), (48), (81), (98), (123), (127), (167) are inconsistent
% 203.62/34.52  | |            by sub-proof #612.
% 203.62/34.52  | | 
% 203.62/34.52  | Case 2:
% 203.62/34.52  | | 
% 203.62/34.52  | |   (168)   ~ (all_58_15 = e0)
% 203.62/34.52  | |   (169)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 203.62/34.52  | |            | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.52  | | 
% 203.62/34.52  | | ALPHA: (169) implies:
% 203.62/34.52  | |   (170)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.52  | |   (171)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.52  | | 
% 203.62/34.52  | | REDUCE: (98), (168) imply:
% 203.62/34.52  | |   (172)   ~ (all_14_2 = e0)
% 203.62/34.52  | | 
% 203.62/34.52  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 203.62/34.52  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 203.62/34.52  | |            (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 203.62/34.52  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 203.62/34.52  | |            (49), (50), (51), (52), (53), (54), (56), (57), (59), (60), (61),
% 203.62/34.52  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 203.62/34.52  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 203.62/34.52  | |            (84), (85), (86), (88), (89), (90), (92), (93), (94), (96), (97),
% 203.62/34.52  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 203.62/34.52  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 203.62/34.52  | |            (116), (117), (118), (119), (120), (121), (122), (124), (125),
% 203.62/34.52  | |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 203.62/34.52  | |            (136), (137), (138), (139), (140), (141), (142), (143), (144),
% 203.62/34.52  | |            (145), (146), (147), (148), (149), (150), (151), (152), (153),
% 203.62/34.52  | |            (154), (155), (156), (159), (160), (163), (164), (165), (166),
% 203.62/34.52  | |            (170), (171), (172) are inconsistent by sub-proof #664.
% 203.62/34.52  | | 
% 203.62/34.52  | End of split
% 203.62/34.52  | 
% 203.62/34.52  End of proof
% 203.62/34.52  
% 203.62/34.52  Sub-proof #600 shows that the following formulas are inconsistent:
% 203.62/34.52  ----------------------------------------------------------------
% 203.62/34.52    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.52    (2)   ~ (all_52_15 = all_52_23)
% 203.62/34.52    (3)   ~ (all_52_25 = all_52_27)
% 203.62/34.52    (4)  all_58_14 = all_52_23
% 203.62/34.52    (5)   ~ (e3 = e1)
% 203.62/34.52    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.52    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.52    (8)  all_58_1 = all_52_9
% 203.62/34.52    (9)   ~ (all_52_9 = all_52_13)
% 203.62/34.52    (10)   ~ (e3 = e0)
% 203.62/34.52    (11)  op(e2, e3) = all_52_3
% 203.62/34.52    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.52    (13)   ~ (all_52_3 = all_52_19)
% 203.62/34.52    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.52    (15)   ~ (all_52_17 = all_52_25)
% 203.62/34.52    (16)   ~ (all_4_2 = e3)
% 203.62/34.52    (17)   ~ (all_52_3 = all_6_2)
% 203.62/34.52    (18)  all_58_0 = all_6_2
% 203.62/34.52    (19)  op(all_14_2, e0) = all_14_1
% 203.62/34.52    (20)  all_56_4 = all_52_3
% 203.62/34.52    (21)   ~ (all_52_17 = all_10_2)
% 203.62/34.52    (22)  op(e3, e0) = all_52_25
% 203.62/34.52    (23)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.52    (24)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.52    (25)   ~ (all_52_27 = all_52_29)
% 203.62/34.52    (26)  all_58_13 = all_52_15
% 203.62/34.52    (27)  all_58_9 = all_52_25
% 203.62/34.52    (28)   ~ (all_52_29 = all_14_2)
% 203.62/34.52    (29)   ~ (all_52_15 = e3)
% 203.62/34.52    (30)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.52    (31)  op(e1, e3) = all_52_5
% 203.62/34.52    (32)  op(e2, e2) = all_4_2
% 203.62/34.52    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.52    (34)   ~ (all_52_3 = all_52_5)
% 203.62/34.52    (35)  all_58_11 = all_52_29
% 203.62/34.52    (36)  all_56_5 = all_4_2
% 203.62/34.52    (37)   ~ (all_52_25 = all_14_2)
% 203.62/34.52    (38)   ~ (all_52_3 = all_52_27)
% 203.62/34.52    (39)  op(all_10_2, e1) = all_10_1
% 203.62/34.52    (40)  all_58_1 = e3
% 203.62/34.52    (41)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.52    (42)   ~ (all_52_7 = all_6_2)
% 203.62/34.52    (43)  op(e0, e0) = all_14_2
% 203.62/34.52    (44)  all_56_15 = all_14_2
% 203.62/34.52    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.52    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.52    (47)  all_56_11 = all_52_29
% 203.62/34.52    (48)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.52    (49)   ~ (all_6_2 = e3)
% 203.62/34.52    (50)   ~ (e2 = e1)
% 203.62/34.52    (51)   ~ (all_52_13 = all_10_2)
% 203.62/34.52    (52)  all_58_10 = all_52_27
% 203.62/34.52    (53)  all_56_8 = all_52_5
% 203.62/34.52    (54)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.52    (55)   ~ (all_52_25 = all_52_29)
% 203.62/34.52    (56)  op(all_6_2, e3) = e2
% 203.62/34.52    (57)   ~ (all_52_29 = all_10_2)
% 203.62/34.52    (58)  all_58_7 = all_52_13
% 203.62/34.52    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.52    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.52    (61)   ~ (all_52_5 = all_52_7)
% 203.62/34.52    (62)  all_58_12 = all_52_7
% 203.62/34.52    (63)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.52    (64)   ~ (all_52_7 = all_14_2)
% 203.62/34.52    (65)   ~ (all_14_2 = e0)
% 203.62/34.52    (66)  all_58_2 = all_52_3
% 203.62/34.52    (67)  all_56_2 = all_52_17
% 203.62/34.52    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.52    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.52    (70)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.52    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.52    (72)   ~ (all_52_25 = e3)
% 203.62/34.52    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.52    (74)   ~ (e2 = e0)
% 203.62/34.52    (75)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.52    (76)   ~ (all_52_5 = all_52_29)
% 203.62/34.52    (77)   ~ (all_52_15 = all_14_2)
% 203.62/34.52    (78)   ~ (all_52_19 = all_52_27)
% 203.62/34.52    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.52    (80)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.52    (81)  op(e3, e1) = all_52_17
% 203.62/34.52    (82)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.52    (83)  op(e0, e3) = all_52_7
% 203.62/34.52    (84)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.52    (85)   ~ (all_52_9 = all_52_25)
% 203.62/34.52    (86)  all_58_15 = all_14_2
% 203.62/34.52    (87)   ~ (all_52_19 = all_10_2)
% 203.62/34.52    (88)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.52    (89)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.52    (90)   ~ (all_10_1 = e2)
% 203.62/34.52    (91)  all_58_8 = all_10_2
% 203.62/34.52    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.52    (93)   ~ (all_52_5 = all_10_2)
% 203.62/34.52    (94)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.52    (95)   ~ (all_52_23 = all_14_2)
% 203.62/34.52    (96)  all_56_12 = all_52_7
% 203.62/34.52    (97)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.52    (98)   ~ (all_52_25 = all_6_2)
% 203.62/34.52    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.52    (100)   ~ (all_52_9 = all_4_2)
% 203.62/34.52    (101)   ~ (all_52_5 = all_6_2)
% 203.62/34.52    (102)  op(e3, e3) = all_6_2
% 203.62/34.52    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.52    (104)   ~ (all_52_13 = e3)
% 203.62/34.52    (105)   ~ (all_52_27 = all_14_2)
% 203.62/34.52    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.52    (107)  all_56_14 = all_52_23
% 203.62/34.52    (108)   ~ (all_52_17 = e3)
% 203.62/34.52    (109)  all_56_3 = all_52_25
% 203.62/34.52    (110)   ~ (all_52_3 = all_52_7)
% 203.62/34.52    (111)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.52    (112)  all_58_5 = all_52_19
% 203.62/34.52    (113)   ~ (all_52_15 = all_4_2)
% 203.62/34.52    (114)   ~ (all_52_27 = all_4_2)
% 203.62/34.52    (115)  all_58_6 = all_52_5
% 203.62/34.52    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.52    (117)   ~ (all_52_17 = all_6_2)
% 203.62/34.52    (118)   ~ (e1 = e0)
% 203.62/34.52    (119)   ~ (e3 = e2)
% 203.62/34.52    (120)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 203.62/34.52    (121)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.52    (122)  op(e1, e1) = all_10_2
% 203.62/34.52    (123)   ~ (all_52_23 = all_10_2)
% 203.62/34.52    (124)   ~ (all_52_7 = all_52_23)
% 203.62/34.52    (125)  all_58_3 = all_4_2
% 203.62/34.52    (126)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.52    (127)   ~ (all_52_3 = all_4_2)
% 203.62/34.52    (128)   ~ (all_52_19 = all_4_2)
% 203.62/34.52    (129)   ~ (all_52_17 = all_52_23)
% 203.62/34.52    (130)  op(all_6_2, e3) = all_6_1
% 203.62/34.52    (131)  all_58_4 = all_52_17
% 203.62/34.52    (132)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.52  
% 203.62/34.52  Begin of proof
% 203.62/34.52  | 
% 203.62/34.52  | ALPHA: (120) implies:
% 203.62/34.52  |   (133)  all_52_30 = e0
% 203.62/34.52  |   (134)  all_52_28 = e1
% 203.62/34.52  |   (135)  all_52_26 = e2
% 203.62/34.52  |   (136)  all_52_24 = e3
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (132), (136) imply:
% 203.62/34.52  |   (137)  op(all_52_25, all_52_25) = e3
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (30), (135) imply:
% 203.62/34.52  |   (138)  op(all_52_27, all_52_27) = e2
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (94), (134) imply:
% 203.62/34.52  |   (139)  op(all_52_29, all_52_29) = e1
% 203.62/34.52  | 
% 203.62/34.52  | REDUCE: (111), (133) imply:
% 203.62/34.52  |   (140)  op(all_14_2, all_14_2) = e0
% 203.62/34.52  | 
% 203.62/34.52  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.52  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.62/34.52  |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 203.62/34.52  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 203.62/34.52  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.62/34.52  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.62/34.52  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.62/34.52  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 203.62/34.52  |            (91), (92), (93), (95), (96), (97), (98), (99), (100), (101),
% 203.62/34.52  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.62/34.52  |            (112), (113), (114), (115), (116), (117), (118), (119), (121),
% 203.62/34.52  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 203.62/34.52  |            (131), (137), (138), (139), (140) are inconsistent by sub-proof
% 203.62/34.52  |            #794.
% 203.62/34.52  | 
% 203.62/34.52  End of proof
% 203.62/34.52  
% 203.62/34.52  Sub-proof #601 shows that the following formulas are inconsistent:
% 203.62/34.52  ----------------------------------------------------------------
% 203.62/34.52    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.52    (2)  all_58_14 = all_52_23
% 203.62/34.52    (3)   ~ (e3 = e1)
% 203.62/34.52    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.52    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.52    (6)   ~ (all_50_1 = e1) |  ~ (all_50_2 = e3)
% 203.62/34.52    (7)   ~ (e3 = e0)
% 203.62/34.52    (8)  op(all_52_23, all_52_23) = e0
% 203.62/34.52    (9)  op(e2, e3) = all_52_3
% 203.62/34.52    (10)  op(e0, e2) = all_52_15
% 203.62/34.52    (11)   ~ (all_52_17 = all_52_25)
% 203.62/34.52    (12)   ~ (all_4_2 = e3)
% 203.62/34.52    (13)   ~ (all_52_3 = all_6_2)
% 203.62/34.52    (14)  all_58_0 = all_6_2
% 203.62/34.52    (15)  op(all_14_2, e0) = all_14_1
% 203.62/34.52    (16)   ~ (all_52_17 = all_10_2)
% 203.62/34.52    (17)  op(e3, e0) = all_52_25
% 203.62/34.52    (18)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.52    (19)  all_58_13 = all_52_15
% 203.62/34.52    (20)  all_58_9 = all_52_25
% 203.62/34.52    (21)   ~ (all_52_29 = all_14_2)
% 203.62/34.52    (22)   ~ (all_52_15 = e3)
% 203.62/34.52    (23)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.52    (24)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.52    (25)  op(e2, e2) = all_4_2
% 203.62/34.52    (26)   ~ (all_52_3 = all_52_5)
% 203.62/34.52    (27)  all_58_11 = all_52_29
% 203.62/34.52    (28)   ~ (all_52_25 = all_14_2)
% 203.62/34.52    (29)  op(all_10_2, e1) = all_10_1
% 203.62/34.52    (30)  all_58_1 = e3
% 203.62/34.52    (31)   ~ (all_52_7 = all_6_2)
% 203.62/34.52    (32)  op(e0, e0) = all_14_2
% 203.62/34.52    (33)  all_56_15 = all_14_2
% 203.62/34.52    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.52    (35)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.52    (36)   ~ (all_6_2 = e3)
% 203.62/34.52    (37)   ~ (e2 = e1)
% 203.62/34.52    (38)   ~ (all_52_13 = all_10_2)
% 203.62/34.52    (39)  op(all_10_2, all_10_2) = e1
% 203.62/34.52    (40)  all_58_10 = all_52_27
% 203.62/34.52    (41)   ~ (all_52_19 = all_52_23)
% 203.62/34.52    (42)  op(all_6_2, e3) = e2
% 203.62/34.52    (43)  all_58_7 = all_52_13
% 203.62/34.52    (44)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.52    (45)  op(all_52_19, all_52_19) = e2
% 203.62/34.52    (46)  all_58_12 = all_52_7
% 203.62/34.52    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.52    (48)   ~ (all_52_7 = all_14_2)
% 203.62/34.52    (49)  all_58_2 = all_52_3
% 203.62/34.52    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.52    (51)  all_56_2 = all_52_17
% 203.62/34.52    (52)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.52    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.52    (54)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.52    (55)   ~ (all_52_25 = e3)
% 203.62/34.52    (56)   ~ (e2 = e0)
% 203.62/34.52    (57)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.52    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.52    (59)  all_56_6 = all_52_19
% 203.62/34.52    (60)   ~ (all_52_15 = all_14_2)
% 203.62/34.52    (61)  op(e3, e3) = all_52_8
% 203.62/34.52    (62)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.52    (63)  op(e3, e1) = all_52_17
% 203.62/34.52    (64)  op(e0, e3) = all_52_7
% 203.62/34.52    (65)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.52    (66)  all_58_15 = all_14_2
% 203.62/34.52    (67)   ~ (all_52_19 = all_10_2)
% 203.62/34.52    (68)   ~ (all_10_1 = e2)
% 203.62/34.52    (69)  all_58_8 = all_10_2
% 203.62/34.52    (70)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.52    (71)   ~ (all_52_25 = all_6_2)
% 203.62/34.52    (72)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.52    (73)  op(e3, e3) = all_6_2
% 203.62/34.52    (74)   ~ (all_52_13 = e3)
% 203.62/34.52    (75)   ~ (all_52_27 = all_14_2)
% 203.62/34.52    (76)  all_56_14 = all_52_23
% 203.62/34.52    (77)   ~ (all_52_17 = e3)
% 203.62/34.52    (78)  all_56_3 = all_52_25
% 203.62/34.52    (79)  op(e0, all_14_1) = e2
% 203.62/34.52    (80)   ~ (all_52_3 = all_52_7)
% 203.62/34.52    (81)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.52    (82)  all_58_5 = all_52_19
% 203.62/34.52    (83)   ~ (all_52_15 = all_4_2)
% 203.62/34.52    (84)   ~ (all_52_27 = all_4_2)
% 203.62/34.52    (85)  op(all_52_17, all_52_17) = e3
% 203.62/34.52    (86)  all_58_6 = all_52_5
% 203.62/34.53    (87)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.53    (88)   ~ (all_52_17 = all_6_2)
% 203.62/34.53    (89)   ~ (e1 = e0)
% 203.62/34.53    (90)   ~ (e3 = e2)
% 203.62/34.53    (91)  all_56_10 = all_10_2
% 203.62/34.53    (92)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.53    (93)  op(e1, e1) = all_10_2
% 203.62/34.53    (94)   ~ (all_52_23 = all_10_2)
% 203.62/34.53    (95)   ~ (all_52_7 = all_52_23)
% 203.62/34.53    (96)   ~ (all_52_17 = all_52_19)
% 203.62/34.53    (97)  all_58_3 = all_4_2
% 203.62/34.53    (98)   ~ (all_52_3 = all_4_2)
% 203.62/34.53    (99)   ~ (all_52_17 = all_52_23)
% 203.62/34.53    (100)  all_58_4 = all_52_17
% 203.62/34.53    (101)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.53    (102)  all_50_2 = all_14_2
% 203.62/34.53    (103)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.53  
% 203.62/34.53  Begin of proof
% 203.62/34.53  | 
% 203.62/34.53  | BETA: splitting (70) gives:
% 203.62/34.53  | 
% 203.62/34.53  | Case 1:
% 203.62/34.53  | | 
% 203.62/34.53  | |   (104)  all_56_15 = e3
% 203.62/34.53  | | 
% 203.62/34.53  | | COMBINE_EQS: (33), (104) imply:
% 203.62/34.53  | |   (105)  all_14_2 = e3
% 203.62/34.53  | | 
% 203.62/34.53  | | SIMP: (105) implies:
% 203.62/34.53  | |   (106)  all_14_2 = e3
% 203.62/34.53  | | 
% 203.62/34.53  | | COMBINE_EQS: (102), (106) imply:
% 203.62/34.53  | |   (107)  all_50_2 = e3
% 203.62/34.53  | | 
% 203.62/34.53  | | REDUCE: (48), (106) imply:
% 203.62/34.53  | |   (108)   ~ (all_52_7 = e3)
% 203.62/34.53  | | 
% 203.62/34.53  | | REDUCE: (75), (106) imply:
% 203.62/34.53  | |   (109)   ~ (all_52_27 = e3)
% 203.62/34.53  | | 
% 203.62/34.53  | | REDUCE: (21), (106) imply:
% 203.62/34.53  | |   (110)   ~ (all_52_29 = e3)
% 203.62/34.53  | | 
% 203.62/34.53  | | REDUCE: (81), (106) imply:
% 203.62/34.53  | |   (111)  op(e3, e3) = all_52_30
% 203.62/34.53  | | 
% 203.62/34.53  | | REDUCE: (15), (106) imply:
% 203.62/34.53  | |   (112)  op(e3, e0) = all_14_1
% 203.62/34.53  | | 
% 203.62/34.53  | | BETA: splitting (6) gives:
% 203.62/34.53  | | 
% 203.62/34.53  | | Case 1:
% 203.62/34.53  | | | 
% 203.62/34.53  | | | 
% 203.62/34.53  | | | GROUND_INST: instantiating (5) with all_52_25, all_14_1, e0, e3,
% 203.62/34.53  | | |              simplifying with (17), (112) gives:
% 203.62/34.53  | | |   (113)  all_52_25 = all_14_1
% 203.62/34.53  | | | 
% 203.62/34.53  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_30, e3, e3,
% 203.62/34.53  | | |              simplifying with (73), (111) gives:
% 203.62/34.53  | | |   (114)  all_52_30 = all_6_2
% 203.62/34.53  | | | 
% 203.62/34.53  | | | COMBINE_EQS: (20), (113) imply:
% 203.62/34.53  | | |   (115)  all_58_9 = all_14_1
% 203.62/34.53  | | | 
% 203.62/34.53  | | | REDUCE: (103), (113) imply:
% 203.62/34.53  | | |   (116)  op(all_14_1, all_14_1) = all_52_24
% 203.62/34.53  | | | 
% 203.62/34.53  | | | BETA: splitting (47) gives:
% 203.62/34.53  | | | 
% 203.62/34.53  | | | Case 1:
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | |   (117)  all_58_6 = e3
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | COMBINE_EQS: (86), (117) imply:
% 203.62/34.53  | | | |   (118)  all_52_5 = e3
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | REDUCE: (26), (118) imply:
% 203.62/34.53  | | | |   (119)   ~ (all_52_3 = e3)
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | REDUCE: (18), (118) imply:
% 203.62/34.53  | | | |   (120)  op(e3, e3) = all_52_4
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | REF_CLOSE: (5), (9), (12), (13), (34), (40), (42), (45), (49), (73),
% 203.62/34.53  | | | |            (82), (97), (109), (119), (120) are inconsistent by sub-proof
% 203.62/34.53  | | | |            #816.
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | Case 2:
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | |   (121)   ~ (all_58_6 = e3)
% 203.62/34.53  | | | |   (122)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | REDUCE: (86), (121) imply:
% 203.62/34.53  | | | |   (123)   ~ (all_52_5 = e3)
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | BETA: splitting (122) gives:
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | Case 1:
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | |   (124)  all_58_7 = e3
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | COMBINE_EQS: (43), (124) imply:
% 203.62/34.53  | | | | |   (125)  all_52_13 = e3
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | REDUCE: (74), (125) imply:
% 203.62/34.53  | | | | |   (126)  $false
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | CLOSE: (126) is inconsistent.
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | Case 2:
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | |   (127)  all_58_8 = e3 | all_58_11 = e3
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | BETA: splitting (53) gives:
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | Case 1:
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | |   (128)  all_58_0 = e3
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | | COMBINE_EQS: (14), (128) imply:
% 203.62/34.53  | | | | | |   (129)  all_6_2 = e3
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | | REDUCE: (36), (129) imply:
% 203.62/34.53  | | | | | |   (130)  $false
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | | CLOSE: (130) is inconsistent.
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | Case 2:
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | |   (131)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | | BETA: splitting (131) gives:
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | | Case 1:
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | |   (132)  all_58_2 = e3
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | | COMBINE_EQS: (49), (132) imply:
% 203.62/34.53  | | | | | | |   (133)  all_52_3 = e3
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | | REDUCE: (98), (133) imply:
% 203.62/34.53  | | | | | | |   (134)   ~ (all_4_2 = e3)
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | | REDUCE: (4), (133) imply:
% 203.62/34.53  | | | | | | |   (135)  op(e3, e3) = all_52_2
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | | BETA: splitting (127) gives:
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | |   (136)  all_58_8 = e3
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | COMBINE_EQS: (69), (136) imply:
% 203.62/34.53  | | | | | | | |   (137)  all_10_2 = e3
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | SIMP: (137) implies:
% 203.62/34.53  | | | | | | | |   (138)  all_10_2 = e3
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (67), (138) imply:
% 203.62/34.53  | | | | | | | |   (139)   ~ (all_52_19 = e3)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (94), (138) imply:
% 203.62/34.53  | | | | | | | |   (140)   ~ (all_52_23 = e3)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (39), (138) imply:
% 203.62/34.53  | | | | | | | |   (141)  op(e3, e3) = e1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (29), (138) imply:
% 203.62/34.53  | | | | | | | |   (142)  op(e3, e1) = all_10_1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | GROUND_INST: instantiating (5) with all_52_17, all_10_1, e1, e3,
% 203.62/34.53  | | | | | | | |              simplifying with (63), (142) gives:
% 203.62/34.53  | | | | | | | |   (143)  all_52_17 = all_10_1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_2, e3, e3,
% 203.62/34.53  | | | | | | | |              simplifying with (73), (135) gives:
% 203.62/34.53  | | | | | | | |   (144)  all_52_2 = all_6_2
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | GROUND_INST: instantiating (5) with e1, all_52_2, e3, e3,
% 203.62/34.53  | | | | | | | |              simplifying with (135), (141) gives:
% 203.62/34.53  | | | | | | | |   (145)  all_52_2 = e1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | COMBINE_EQS: (144), (145) imply:
% 203.62/34.53  | | | | | | | |   (146)  all_6_2 = e1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | SIMP: (146) implies:
% 203.62/34.53  | | | | | | | |   (147)  all_6_2 = e1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | COMBINE_EQS: (51), (143) imply:
% 203.62/34.53  | | | | | | | |   (148)  all_56_2 = all_10_1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | COMBINE_EQS: (100), (143) imply:
% 203.62/34.53  | | | | | | | |   (149)  all_58_4 = all_10_1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | COMBINE_EQS: (14), (147) imply:
% 203.62/34.53  | | | | | | | |   (150)  all_58_0 = e1
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (96), (143) imply:
% 203.62/34.53  | | | | | | | |   (151)   ~ (all_52_19 = all_10_1)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | SIMP: (151) implies:
% 203.62/34.53  | | | | | | | |   (152)   ~ (all_52_19 = all_10_1)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (99), (143) imply:
% 203.62/34.53  | | | | | | | |   (153)   ~ (all_52_23 = all_10_1)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | SIMP: (153) implies:
% 203.62/34.53  | | | | | | | |   (154)   ~ (all_52_23 = all_10_1)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (88), (143), (147) imply:
% 203.62/34.53  | | | | | | | |   (155)   ~ (all_10_1 = e1)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REDUCE: (77), (143) imply:
% 203.62/34.53  | | | | | | | |   (156)   ~ (all_10_1 = e3)
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | BETA: splitting (52) gives:
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | |   (157)  all_58_0 = e2
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | REF_CLOSE: (37), (150), (157) are inconsistent by sub-proof
% 203.62/34.53  | | | | | | | | |            #1273.
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | |   (158)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | BETA: splitting (35) gives:
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | |   (159)  all_56_2 = e3
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | REF_CLOSE: (148), (156), (159) are inconsistent by sub-proof
% 203.62/34.53  | | | | | | | | | |            #1029.
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | |   (160)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | BETA: splitting (160) gives:
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | |   (161)  all_56_2 = e2
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | REF_CLOSE: (68), (148), (161) are inconsistent by sub-proof
% 203.62/34.53  | | | | | | | | | | |            #815.
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | |   (162)   ~ (all_56_2 = e2)
% 203.62/34.53  | | | | | | | | | | |   (163)  all_56_2 = e1 | all_56_2 = e0
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | BETA: splitting (163) gives:
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | |   (164)  all_56_2 = e1
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | REF_CLOSE: (148), (155), (164) are inconsistent by sub-proof
% 203.62/34.53  | | | | | | | | | | | |            #1025.
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | |   (165)  all_56_2 = e0
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | COMBINE_EQS: (148), (165) imply:
% 203.62/34.53  | | | | | | | | | | | |   (166)  all_10_1 = e0
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | SIMP: (166) implies:
% 203.62/34.53  | | | | | | | | | | | |   (167)  all_10_1 = e0
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | COMBINE_EQS: (149), (167) imply:
% 203.62/34.53  | | | | | | | | | | | |   (168)  all_58_4 = e0
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | REDUCE: (152), (167) imply:
% 203.62/34.53  | | | | | | | | | | | |   (169)   ~ (all_52_19 = e0)
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | REDUCE: (154), (167) imply:
% 203.62/34.53  | | | | | | | | | | | |   (170)   ~ (all_52_23 = e0)
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | REDUCE: (68), (167) imply:
% 203.62/34.53  | | | | | | | | | | | |   (171)   ~ (e2 = e0)
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | BETA: splitting (158) gives:
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | |   (172)  all_58_1 = e2
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | REF_CLOSE: (12), (19), (22), (43), (65), (74), (90), (97),
% 203.62/34.53  | | | | | | | | | | | | |            (172) are inconsistent by sub-proof #1088.
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | |   (173)  all_58_4 = e2 | all_58_9 = e2
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | BETA: splitting (173) gives:
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | |   (174)  all_58_4 = e2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | COMBINE_EQS: (168), (174) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (175)  e2 = e0
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | REDUCE: (56), (175) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (176)  $false
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | |   (177)  all_58_9 = e2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | COMBINE_EQS: (115), (177) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (178)  all_14_1 = e2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | SIMP: (178) implies:
% 203.62/34.53  | | | | | | | | | | | | | |   (179)  all_14_1 = e2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | REDUCE: (116), (179) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (180)  op(e2, e2) = all_52_24
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | REDUCE: (79), (179) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (181)  op(e0, e2) = e2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_15, e2, e2, e0,
% 203.62/34.53  | | | | | | | | | | | | | |              simplifying with (10), (181) gives:
% 203.62/34.53  | | | | | | | | | | | | | |   (182)  all_52_15 = e2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_24, e2, e2,
% 203.62/34.53  | | | | | | | | | | | | | |              simplifying with (25), (180) gives:
% 203.62/34.53  | | | | | | | | | | | | | |   (183)  all_52_24 = all_4_2
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | REDUCE: (1), (182) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (184)   ~ (all_52_23 = e2)
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | SIMP: (184) implies:
% 203.62/34.53  | | | | | | | | | | | | | |   (185)   ~ (all_52_23 = e2)
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | REDUCE: (83), (182) imply:
% 203.62/34.53  | | | | | | | | | | | | | |   (186)   ~ (all_4_2 = e2)
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | SIMP: (186) implies:
% 203.62/34.53  | | | | | | | | | | | | | |   (187)   ~ (all_4_2 = e2)
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | Case 1:
% 203.62/34.53  | | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | |   (188)  all_56_14 = e3
% 203.62/34.53  | | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | | REF_CLOSE: (76), (140), (188) are inconsistent by sub-proof
% 203.62/34.53  | | | | | | | | | | | | | | |            #1286.
% 203.62/34.53  | | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | |   (189)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.53  | | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | | REF_CLOSE: (5), (25), (41), (45), (50), (59), (76), (139),
% 203.62/34.53  | | | | | | | | | | | | | | |            (169), (170), (185), (187), (189) are inconsistent
% 203.62/34.53  | | | | | | | | | | | | | | |            by sub-proof #602.
% 203.62/34.53  | | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | | | 
% 203.62/34.53  | | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | | 
% 203.62/34.53  | | | | | | | | End of split
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | Case 2:
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | |   (190)  all_58_11 = e3
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | | REF_CLOSE: (27), (110), (190) are inconsistent by sub-proof
% 203.62/34.53  | | | | | | | |            #1323.
% 203.62/34.53  | | | | | | | | 
% 203.62/34.53  | | | | | | | End of split
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | Case 2:
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | |   (191)  all_58_6 = e3 | all_58_12 = e3
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | | REF_CLOSE: (46), (86), (108), (123), (191) are inconsistent by
% 203.62/34.53  | | | | | | |            sub-proof #1243.
% 203.62/34.53  | | | | | | | 
% 203.62/34.53  | | | | | | End of split
% 203.62/34.53  | | | | | | 
% 203.62/34.53  | | | | | End of split
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | End of split
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | End of split
% 203.62/34.53  | | | 
% 203.62/34.53  | | Case 2:
% 203.62/34.53  | | | 
% 203.62/34.53  | | |   (192)   ~ (all_50_2 = e3)
% 203.62/34.53  | | | 
% 203.62/34.53  | | | REDUCE: (107), (192) imply:
% 203.62/34.53  | | |   (193)  $false
% 203.62/34.53  | | | 
% 203.62/34.53  | | | CLOSE: (193) is inconsistent.
% 203.62/34.53  | | | 
% 203.62/34.53  | | End of split
% 203.62/34.53  | | 
% 203.62/34.53  | Case 2:
% 203.62/34.53  | | 
% 203.62/34.53  | |   (194)   ~ (all_56_15 = e3)
% 203.62/34.53  | | 
% 203.62/34.53  | | REDUCE: (33), (194) imply:
% 203.62/34.53  | |   (195)   ~ (all_14_2 = e3)
% 203.62/34.53  | | 
% 203.62/34.53  | | REF_CLOSE: (2), (3), (5), (7), (8), (11), (12), (14), (19), (20), (22),
% 203.62/34.53  | |            (23), (24), (25), (28), (29), (30), (31), (32), (34), (35), (36),
% 203.62/34.53  | |            (37), (39), (40), (41), (42), (45), (46), (48), (49), (51), (54),
% 203.62/34.53  | |            (55), (56), (57), (58), (61), (62), (63), (64), (66), (67), (69),
% 203.62/34.53  | |            (71), (72), (73), (75), (77), (78), (80), (82), (84), (85), (87),
% 203.62/34.53  | |            (88), (89), (91), (92), (93), (94), (95), (97), (99), (100),
% 203.62/34.53  | |            (101), (195) are inconsistent by sub-proof #813.
% 203.62/34.53  | | 
% 203.62/34.53  | End of split
% 203.62/34.53  | 
% 203.62/34.53  End of proof
% 203.62/34.53  
% 203.62/34.53  Sub-proof #602 shows that the following formulas are inconsistent:
% 203.62/34.53  ----------------------------------------------------------------
% 203.62/34.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.53    (2)  op(e2, e2) = all_4_2
% 203.62/34.53    (3)   ~ (all_52_19 = e0)
% 203.62/34.53    (4)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.53    (5)   ~ (all_52_19 = all_52_23)
% 203.62/34.53    (6)   ~ (all_52_23 = e2)
% 203.62/34.53    (7)  op(all_52_19, all_52_19) = e2
% 203.62/34.53    (8)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.53    (9)   ~ (all_52_19 = e3)
% 203.62/34.53    (10)  all_56_6 = all_52_19
% 203.62/34.53    (11)   ~ (all_52_23 = e0)
% 203.62/34.53    (12)   ~ (all_4_2 = e2)
% 203.62/34.53    (13)  all_56_14 = all_52_23
% 203.62/34.53  
% 203.62/34.53  Begin of proof
% 203.62/34.53  | 
% 203.62/34.53  | BETA: splitting (4) gives:
% 203.62/34.53  | 
% 203.62/34.53  | Case 1:
% 203.62/34.53  | | 
% 203.62/34.53  | |   (14)  all_56_14 = e2
% 203.62/34.53  | | 
% 203.62/34.53  | | REF_CLOSE: (6), (13), (14) are inconsistent by sub-proof #1285.
% 203.62/34.53  | | 
% 203.62/34.53  | Case 2:
% 203.62/34.53  | | 
% 203.62/34.53  | |   (15)  all_56_14 = e1 | all_56_14 = e0
% 203.62/34.53  | | 
% 203.62/34.53  | | BETA: splitting (15) gives:
% 203.62/34.53  | | 
% 203.62/34.53  | | Case 1:
% 203.62/34.53  | | | 
% 203.62/34.53  | | |   (16)  all_56_14 = e1
% 203.62/34.53  | | | 
% 203.62/34.53  | | | COMBINE_EQS: (13), (16) imply:
% 203.62/34.53  | | |   (17)  all_52_23 = e1
% 203.62/34.53  | | | 
% 203.62/34.53  | | | SIMP: (17) implies:
% 203.62/34.53  | | |   (18)  all_52_23 = e1
% 203.62/34.53  | | | 
% 203.62/34.53  | | | REDUCE: (5), (18) imply:
% 203.62/34.53  | | |   (19)   ~ (all_52_19 = e1)
% 203.62/34.53  | | | 
% 203.62/34.53  | | | BETA: splitting (8) gives:
% 203.62/34.53  | | | 
% 203.62/34.53  | | | Case 1:
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | |   (20)  all_56_6 = e3
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | REF_CLOSE: (9), (10), (20) are inconsistent by sub-proof #957.
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | Case 2:
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | |   (21)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | BETA: splitting (21) gives:
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | | Case 1:
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | |   (22)  all_56_6 = e2
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | COMBINE_EQS: (10), (22) imply:
% 203.62/34.53  | | | | |   (23)  all_52_19 = e2
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | SIMP: (23) implies:
% 203.62/34.53  | | | | |   (24)  all_52_19 = e2
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | REDUCE: (7), (24) imply:
% 203.62/34.53  | | | | |   (25)  op(e2, e2) = e2
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | REF_CLOSE: (1), (2), (12), (25) are inconsistent by sub-proof #1158.
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | Case 2:
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | |   (26)  all_56_6 = e1 | all_56_6 = e0
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | | REF_CLOSE: (3), (10), (19), (26) are inconsistent by sub-proof #757.
% 203.62/34.53  | | | | | 
% 203.62/34.53  | | | | End of split
% 203.62/34.53  | | | | 
% 203.62/34.53  | | | End of split
% 203.62/34.53  | | | 
% 203.62/34.53  | | Case 2:
% 203.62/34.53  | | | 
% 203.62/34.53  | | |   (27)  all_56_14 = e0
% 203.62/34.53  | | | 
% 203.62/34.53  | | | REF_CLOSE: (11), (13), (27) are inconsistent by sub-proof #1382.
% 203.62/34.53  | | | 
% 203.62/34.53  | | End of split
% 203.62/34.53  | | 
% 203.62/34.53  | End of split
% 203.62/34.53  | 
% 203.62/34.53  End of proof
% 203.62/34.53  
% 203.62/34.53  Sub-proof #603 shows that the following formulas are inconsistent:
% 203.62/34.53  ----------------------------------------------------------------
% 203.62/34.53    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.53    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.53    (3)  all_58_14 = all_52_23
% 203.62/34.53    (4)   ~ (e3 = e1)
% 203.62/34.53    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.62/34.53    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.53    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.53    (8)   ~ (all_52_5 = all_52_13)
% 203.62/34.53    (9)  all_58_1 = all_52_9
% 203.62/34.53    (10)   ~ (all_52_9 = all_52_13)
% 203.62/34.53    (11)   ~ (e3 = e0)
% 203.62/34.53    (12)  op(e2, e3) = all_52_3
% 203.62/34.53    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.53    (14)   ~ (all_52_7 = all_52_15)
% 203.62/34.53    (15)   ~ (all_52_3 = all_52_19)
% 203.62/34.53    (16)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.53    (17)   ~ (all_52_17 = all_52_25)
% 203.62/34.53    (18)   ~ (all_52_3 = all_6_2)
% 203.62/34.53    (19)  all_58_0 = all_6_2
% 203.62/34.53    (20)  op(all_14_2, e0) = all_14_1
% 203.62/34.53    (21)  all_56_4 = all_52_3
% 203.62/34.53    (22)   ~ (all_52_17 = all_10_2)
% 203.62/34.53    (23)   ~ (all_10_0 = e3)
% 203.62/34.53    (24)  all_30_1 = e3
% 203.62/34.53    (25)  op(e3, e0) = all_52_25
% 203.62/34.53    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.53    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.62/34.53    (28)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.53    (29)   ~ (all_52_27 = all_52_29)
% 203.62/34.53    (30)  all_58_13 = all_52_15
% 203.62/34.53    (31)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.53    (32)  all_58_9 = all_52_25
% 203.62/34.53    (33)   ~ (all_6_1 = e1)
% 203.62/34.53    (34)   ~ (all_52_29 = all_14_2)
% 203.62/34.53    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.53    (36)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.53    (37)  op(e1, e3) = all_52_5
% 203.62/34.53    (38)  op(e2, e2) = all_4_2
% 203.62/34.53    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.53    (40)   ~ (all_52_3 = all_52_5)
% 203.62/34.53    (41)  all_58_11 = all_52_29
% 203.62/34.53    (42)  all_56_5 = all_4_2
% 203.62/34.53    (43)   ~ (all_52_25 = all_14_2)
% 203.62/34.53    (44)   ~ (all_52_9 = all_52_15)
% 203.62/34.53    (45)   ~ (all_52_3 = all_52_27)
% 203.62/34.53    (46)  op(all_10_2, e1) = all_10_1
% 203.62/34.53    (47)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.53    (48)   ~ (all_52_7 = all_6_2)
% 203.62/34.53    (49)  op(e0, e0) = all_14_2
% 203.62/34.53    (50)  all_56_15 = all_14_2
% 203.62/34.53    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.53    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.53    (53)  all_56_11 = all_52_29
% 203.62/34.53    (54)   ~ (all_10_0 = e2)
% 203.62/34.53    (55)   ~ (all_4_1 = e1)
% 203.62/34.53    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.62/34.53    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.53    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.62/34.53    (59)  all_56_9 = all_52_13
% 203.62/34.53    (60)   ~ (e2 = e1)
% 203.62/34.53    (61)   ~ (all_52_13 = all_10_2)
% 203.62/34.53    (62)   ~ (all_6_0 = e1)
% 203.62/34.53    (63)  op(e1, all_10_1) = all_10_0
% 203.62/34.53    (64)  all_58_10 = all_52_27
% 203.62/34.53    (65)  all_56_8 = all_52_5
% 203.62/34.53    (66)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.53    (67)  op(all_52_15, all_52_15) = all_52_14
% 203.62/34.53    (68)   ~ (all_52_19 = all_52_23)
% 203.62/34.53    (69)   ~ (all_52_25 = all_52_29)
% 203.62/34.53    (70)   ~ (all_52_29 = all_10_2)
% 203.62/34.53    (71)  all_58_7 = all_52_13
% 203.62/34.53    (72)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 203.62/34.53    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.53    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.53    (75)   ~ (all_52_5 = all_52_7)
% 203.62/34.53    (76)  all_58_12 = all_52_7
% 203.62/34.53    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.53    (78)   ~ (all_52_7 = all_14_2)
% 203.62/34.53    (79)  all_30_2 = all_10_2
% 203.62/34.53    (80)  all_58_2 = all_52_3
% 203.62/34.53    (81)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.53    (82)  all_56_2 = all_52_17
% 203.62/34.53    (83)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.53    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.53    (85)  op(e3, all_6_1) = all_6_0
% 203.62/34.53    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.53    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.53    (88)  all_56_7 = all_52_27
% 203.62/34.53    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.53    (90)   ~ (e2 = e0)
% 203.62/34.53    (91)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.53    (92)  op(all_4_2, e2) = all_4_1
% 203.62/34.53    (93)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.53    (94)   ~ (all_52_5 = all_52_29)
% 203.62/34.53    (95)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.53    (96)  all_56_6 = all_52_19
% 203.62/34.53    (97)   ~ (all_52_15 = all_14_2)
% 203.62/34.53    (98)   ~ (all_52_19 = all_52_27)
% 203.62/34.53    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.53    (100)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.53    (101)   ~ (all_6_0 = e2)
% 203.62/34.53    (102)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.53             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.53    (103)   ~ (all_52_13 = all_4_2)
% 203.62/34.53    (104)  op(e3, e1) = all_52_17
% 203.62/34.53    (105)  all_30_0 = all_10_0
% 203.62/34.53    (106)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.53    (107)  op(e0, e3) = all_52_7
% 203.62/34.53    (108)  op(e1, e2) = all_52_13
% 203.62/34.53    (109)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.53    (110)   ~ (all_52_9 = all_52_25)
% 203.62/34.53    (111)  all_58_15 = all_14_2
% 203.62/34.53    (112)   ~ (all_52_19 = all_10_2)
% 203.62/34.53    (113)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.53    (114)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.53    (115)  all_58_8 = all_10_2
% 203.62/34.53    (116)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.53    (117)   ~ (all_52_5 = all_10_2)
% 203.62/34.53    (118)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.53    (119)   ~ (all_52_23 = all_14_2)
% 203.62/34.53    (120)  all_56_12 = all_52_7
% 203.62/34.53    (121)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.53    (122)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.53    (123)   ~ (all_52_25 = all_6_2)
% 203.62/34.53    (124)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.53    (125)   ~ (all_52_9 = all_4_2)
% 203.62/34.53    (126)   ~ (all_52_5 = all_6_2)
% 203.62/34.53    (127)   ~ (all_52_9 = all_6_2)
% 203.62/34.53    (128)   ~ (all_52_13 = all_52_15)
% 203.62/34.53    (129)  all_56_0 = all_6_2
% 203.62/34.53    (130)  op(e3, e3) = all_6_2
% 203.62/34.53    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.53    (132)   ~ (all_52_27 = all_14_2)
% 203.62/34.53    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.53    (134)  all_56_14 = all_52_23
% 203.62/34.53    (135)  op(all_4_2, all_4_2) = all_52_10
% 203.62/34.53    (136)  all_56_3 = all_52_25
% 203.62/34.53    (137)  op(e0, all_14_1) = e2
% 203.62/34.53    (138)   ~ (all_52_3 = all_52_7)
% 203.62/34.53    (139)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.53    (140)  all_58_5 = all_52_19
% 203.62/34.53    (141)  all_56_1 = all_52_9
% 203.62/34.53    (142)   ~ (all_52_15 = all_4_2)
% 203.62/34.54    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.54           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.54           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.54           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.54    (144)   ~ (all_52_27 = all_4_2)
% 203.62/34.54    (145)  all_58_6 = all_52_5
% 203.62/34.54    (146)  op(e3, e2) = all_52_9
% 203.62/34.54    (147)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.54    (148)   ~ (all_52_17 = all_6_2)
% 203.62/34.54    (149)  all_30_1 = all_10_1
% 203.62/34.54    (150)   ~ (e1 = e0)
% 203.62/34.54    (151)   ~ (e3 = e2)
% 203.62/34.54    (152)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.54    (153)   ~ (all_52_9 = all_52_17)
% 203.62/34.54    (154)  all_56_10 = all_10_2
% 203.62/34.54    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.54    (156)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.54    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.54    (158)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.54    (159)   ~ (all_6_1 = e2)
% 203.62/34.54    (160)  op(e1, e1) = all_10_2
% 203.62/34.54    (161)   ~ (all_52_23 = all_10_2)
% 203.62/34.54    (162)   ~ (all_52_7 = all_52_23)
% 203.62/34.54    (163)   ~ (all_52_17 = all_52_19)
% 203.62/34.54    (164)  all_58_3 = all_4_2
% 203.62/34.54    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.54    (166)  all_56_13 = all_52_15
% 203.62/34.54    (167)   ~ (all_52_3 = all_4_2)
% 203.62/34.54    (168)   ~ (all_52_19 = all_4_2)
% 203.62/34.54    (169)   ~ (all_52_17 = all_52_23)
% 203.62/34.54    (170)  op(all_6_2, e3) = all_6_1
% 203.62/34.54    (171)   ~ (all_52_13 = all_52_29)
% 203.62/34.54    (172)  all_58_4 = all_52_17
% 203.62/34.54    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.54    (174)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.54  
% 203.62/34.54  Begin of proof
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (24), (149) imply:
% 203.62/34.54  |   (175)  all_10_1 = e3
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (46), (175) imply:
% 203.62/34.54  |   (176)  op(all_10_2, e1) = e3
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (63), (175) imply:
% 203.62/34.54  |   (177)  op(e1, e3) = all_10_0
% 203.62/34.54  | 
% 203.62/34.54  | GROUND_INST: instantiating (7) with all_52_5, all_10_0, e3, e1, simplifying
% 203.62/34.54  |              with (37), (177) gives:
% 203.62/34.54  |   (178)  all_52_5 = all_10_0
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (65), (178) imply:
% 203.62/34.54  |   (179)  all_56_8 = all_10_0
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (145), (178) imply:
% 203.62/34.54  |   (180)  all_58_6 = all_10_0
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (117), (178) imply:
% 203.62/34.54  |   (181)   ~ (all_10_0 = all_10_2)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (26), (178) imply:
% 203.62/34.54  |   (182)  op(all_10_0, all_10_0) = all_52_4
% 203.62/34.54  | 
% 203.62/34.54  | BETA: splitting (102) gives:
% 203.62/34.54  | 
% 203.62/34.54  | Case 1:
% 203.62/34.54  | | 
% 203.62/34.54  | |   (183)  all_58_15 = e0
% 203.62/34.54  | | 
% 203.62/34.54  | | REF_CLOSE: (7), (20), (49), (90), (111), (137), (139), (183) are
% 203.62/34.54  | |            inconsistent by sub-proof #612.
% 203.62/34.54  | | 
% 203.62/34.54  | Case 2:
% 203.62/34.54  | | 
% 203.62/34.54  | |   (184)   ~ (all_58_15 = e0)
% 203.62/34.54  | |   (185)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 203.62/34.54  | |            | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.54  | | 
% 203.62/34.54  | | ALPHA: (185) implies:
% 203.62/34.54  | |   (186)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.54  | |   (187)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.54  | | 
% 203.62/34.54  | | REDUCE: (111), (184) imply:
% 203.62/34.54  | |   (188)   ~ (all_14_2 = e0)
% 203.62/34.54  | | 
% 203.62/34.54  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.54  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.62/34.54  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.62/34.54  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 203.62/34.54  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.62/34.54  | |            (58), (59), (60), (61), (62), (64), (65), (66), (67), (68), (69),
% 203.62/34.54  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 203.62/34.54  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 203.62/34.54  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.62/34.54  | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 203.62/34.54  | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 203.62/34.54  | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 203.62/34.54  | |            (130), (131), (132), (133), (134), (135), (136), (138), (139),
% 203.62/34.54  | |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 203.62/34.54  | |            (150), (151), (152), (153), (154), (155), (156), (157), (158),
% 203.62/34.54  | |            (159), (160), (161), (162), (163), (164), (165), (166), (167),
% 203.62/34.54  | |            (168), (169), (170), (171), (172), (173), (174), (176), (179),
% 203.62/34.54  | |            (180), (181), (182), (186), (187), (188) are inconsistent by
% 203.62/34.54  | |            sub-proof #666.
% 203.62/34.54  | | 
% 203.62/34.54  | End of split
% 203.62/34.54  | 
% 203.62/34.54  End of proof
% 203.62/34.54  
% 203.62/34.54  Sub-proof #604 shows that the following formulas are inconsistent:
% 203.62/34.54  ----------------------------------------------------------------
% 203.62/34.54    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.54    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.54    (3)  all_58_14 = all_52_23
% 203.62/34.54    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.62/34.54    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.54    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.54    (7)   ~ (all_52_5 = all_52_13)
% 203.62/34.54    (8)  all_58_1 = all_52_9
% 203.62/34.54    (9)   ~ (all_52_9 = all_52_13)
% 203.62/34.54    (10)   ~ (e3 = e0)
% 203.62/34.54    (11)  op(e2, e3) = all_52_3
% 203.62/34.54    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.54    (13)   ~ (all_52_7 = all_52_15)
% 203.62/34.54    (14)   ~ (all_52_3 = all_52_19)
% 203.62/34.54    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.54    (16)   ~ (all_52_17 = all_52_25)
% 203.62/34.54    (17)   ~ (all_52_3 = all_6_2)
% 203.62/34.54    (18)  all_58_0 = all_6_2
% 203.62/34.54    (19)  op(all_14_2, e0) = all_14_1
% 203.62/34.54    (20)  all_56_4 = all_52_3
% 203.62/34.54    (21)  all_38_2 = all_4_2
% 203.62/34.54    (22)   ~ (all_52_17 = all_10_2)
% 203.62/34.54    (23)  op(e3, e0) = all_52_25
% 203.62/34.54    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.54    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.54    (26)   ~ (all_52_27 = all_52_29)
% 203.62/34.54    (27)  all_58_13 = all_52_15
% 203.62/34.54    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.54    (29)  all_58_9 = all_52_25
% 203.62/34.54    (30)   ~ (all_6_1 = e1)
% 203.62/34.54    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.62/34.54    (32)   ~ (all_52_29 = all_14_2)
% 203.62/34.54    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.54    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.54    (35)  op(e1, e3) = all_52_5
% 203.62/34.54    (36)  all_32_2 = all_4_2
% 203.62/34.54    (37)  op(e2, e2) = all_4_2
% 203.62/34.54    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.54    (39)   ~ (all_52_3 = all_52_5)
% 203.62/34.54    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 203.62/34.54    (41)  all_4_1 = e3
% 203.62/34.54    (42)  all_58_11 = all_52_29
% 203.62/34.54    (43)  all_56_5 = all_4_2
% 203.62/34.54    (44)   ~ (all_52_25 = all_14_2)
% 203.62/34.54    (45)   ~ (all_52_9 = all_52_15)
% 203.62/34.54    (46)   ~ (all_52_3 = all_52_27)
% 203.62/34.54    (47)  op(all_10_2, e1) = all_10_1
% 203.62/34.54    (48)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.54    (49)   ~ (all_52_7 = all_6_2)
% 203.62/34.54    (50)  op(e0, e0) = all_14_2
% 203.62/34.54    (51)  all_56_15 = all_14_2
% 203.62/34.54    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.54    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.54    (54)  op(e2, all_4_1) = all_4_0
% 203.62/34.54    (55)  all_56_11 = all_52_29
% 203.62/34.54    (56)   ~ (all_4_1 = e1)
% 203.62/34.54    (57)   ~ (all_4_0 = e3)
% 203.62/34.54    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.62/34.54    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.54    (60)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.62/34.54    (61)  all_56_9 = all_52_13
% 203.62/34.54    (62)   ~ (e2 = e1)
% 203.62/34.54    (63)   ~ (all_52_13 = all_10_2)
% 203.62/34.54    (64)   ~ (all_6_0 = e1)
% 203.62/34.54    (65)  all_58_10 = all_52_27
% 203.62/34.54    (66)  all_56_8 = all_52_5
% 203.62/34.54    (67)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.54    (68)  op(all_52_15, all_52_15) = all_52_14
% 203.62/34.54    (69)   ~ (all_52_19 = all_52_23)
% 203.62/34.54    (70)   ~ (all_52_25 = all_52_29)
% 203.62/34.54    (71)   ~ (all_52_29 = all_10_2)
% 203.62/34.54    (72)  all_58_7 = all_52_13
% 203.62/34.54    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.54    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.54    (75)   ~ (all_52_5 = all_52_7)
% 203.62/34.54    (76)  all_58_12 = all_52_7
% 203.62/34.54    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.54    (78)   ~ (all_52_7 = all_14_2)
% 203.62/34.54    (79)  all_38_0 = all_4_0
% 203.62/34.54    (80)  all_58_2 = all_52_3
% 203.62/34.54    (81)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.54    (82)  all_56_2 = all_52_17
% 203.62/34.54    (83)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.54    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.54    (85)  op(e3, all_6_1) = all_6_0
% 203.62/34.54    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.54    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.54    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.54    (89)   ~ (e2 = e0)
% 203.62/34.54    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.54    (91)  op(all_4_2, e2) = all_4_1
% 203.62/34.54    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.54    (93)   ~ (all_52_5 = all_52_29)
% 203.62/34.54    (94)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.54    (95)  all_56_6 = all_52_19
% 203.62/34.54    (96)  all_38_1 = all_4_1
% 203.62/34.54    (97)   ~ (all_52_15 = all_14_2)
% 203.62/34.54    (98)   ~ (all_52_19 = all_52_27)
% 203.62/34.54    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.54    (100)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.54    (101)   ~ (all_6_0 = e2)
% 203.62/34.54    (102)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.54             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.54    (103)   ~ (all_52_13 = all_4_2)
% 203.62/34.54    (104)  op(e3, e1) = all_52_17
% 203.62/34.54    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.54    (106)  op(e0, e3) = all_52_7
% 203.62/34.54    (107)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.54    (108)   ~ (all_52_9 = all_52_25)
% 203.62/34.54    (109)  all_58_15 = all_14_2
% 203.62/34.54    (110)   ~ (all_52_19 = all_10_2)
% 203.62/34.54    (111)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.54    (112)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.54    (113)  all_58_8 = all_10_2
% 203.62/34.54    (114)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.54    (115)   ~ (all_52_5 = all_10_2)
% 203.62/34.54    (116)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.54    (117)   ~ (all_52_23 = all_14_2)
% 203.62/34.54    (118)  all_56_12 = all_52_7
% 203.62/34.54    (119)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.54    (120)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.54    (121)   ~ (all_52_25 = all_6_2)
% 203.62/34.54    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.54    (123)   ~ (all_52_9 = all_4_2)
% 203.62/34.54    (124)   ~ (all_52_5 = all_6_2)
% 203.62/34.54    (125)   ~ (all_52_9 = all_6_2)
% 203.62/34.54    (126)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 203.62/34.54    (127)   ~ (all_52_13 = all_52_15)
% 203.62/34.54    (128)  all_56_0 = all_6_2
% 203.62/34.54    (129)  op(e3, e3) = all_6_2
% 203.62/34.54    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.54    (131)   ~ (all_52_27 = all_14_2)
% 203.62/34.54    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.54    (133)  all_56_14 = all_52_23
% 203.62/34.54    (134)  op(all_4_2, all_4_2) = all_52_10
% 203.62/34.54    (135)  all_32_0 = all_4_0
% 203.62/34.54    (136)  all_56_3 = all_52_25
% 203.62/34.54    (137)  op(e0, all_14_1) = e2
% 203.62/34.54    (138)   ~ (all_52_3 = all_52_7)
% 203.62/34.54    (139)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.54    (140)  all_58_5 = all_52_19
% 203.62/34.54    (141)  all_56_1 = all_52_9
% 203.62/34.54    (142)   ~ (all_52_15 = all_4_2)
% 203.62/34.54    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.54           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.54           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.54           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.54    (144)   ~ (all_52_27 = all_4_2)
% 203.62/34.54    (145)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.62/34.54    (146)  all_58_6 = all_52_5
% 203.62/34.54    (147)  op(e3, e2) = all_52_9
% 203.62/34.54    (148)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.54    (149)   ~ (all_52_17 = all_6_2)
% 203.62/34.54    (150)   ~ (e1 = e0)
% 203.62/34.54    (151)   ~ (e3 = e2)
% 203.62/34.54    (152)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.54    (153)   ~ (all_52_9 = all_52_17)
% 203.62/34.54    (154)  all_56_10 = all_10_2
% 203.62/34.54    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.54    (156)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.54    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.54    (158)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.54    (159)   ~ (all_6_1 = e2)
% 203.62/34.54    (160)  op(e1, e1) = all_10_2
% 203.62/34.54    (161)   ~ (all_52_23 = all_10_2)
% 203.62/34.54    (162)   ~ (all_52_7 = all_52_23)
% 203.62/34.54    (163)   ~ (all_52_17 = all_52_19)
% 203.62/34.54    (164)  all_58_3 = all_4_2
% 203.62/34.54    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.54    (166)  all_56_13 = all_52_15
% 203.62/34.54    (167)   ~ (all_52_3 = all_4_2)
% 203.62/34.54    (168)   ~ (all_52_19 = all_4_2)
% 203.62/34.54    (169)   ~ (all_52_17 = all_52_23)
% 203.62/34.54    (170)  op(all_6_2, e3) = all_6_1
% 203.62/34.54    (171)  all_58_4 = all_52_17
% 203.62/34.54    (172)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.54    (173)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.54  
% 203.62/34.54  Begin of proof
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (41), (96) imply:
% 203.62/34.54  |   (174)  all_38_1 = e3
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (41), (56) imply:
% 203.62/34.54  |   (175)   ~ (e3 = e1)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (41), (91) imply:
% 203.62/34.54  |   (176)  op(all_4_2, e2) = e3
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (41), (54) imply:
% 203.62/34.54  |   (177)  op(e2, e3) = all_4_0
% 203.62/34.54  | 
% 203.62/34.54  | GROUND_INST: instantiating (6) with all_52_3, all_4_0, e3, e2, simplifying
% 203.62/34.54  |              with (11), (177) gives:
% 203.62/34.54  |   (178)  all_52_3 = all_4_0
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (20), (178) imply:
% 203.62/34.54  |   (179)  all_56_4 = all_4_0
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (80), (178) imply:
% 203.62/34.54  |   (180)  all_58_2 = all_4_0
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (39), (178) imply:
% 203.62/34.54  |   (181)   ~ (all_52_5 = all_4_0)
% 203.62/34.54  | 
% 203.62/34.54  | SIMP: (181) implies:
% 203.62/34.54  |   (182)   ~ (all_52_5 = all_4_0)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (138), (178) imply:
% 203.62/34.54  |   (183)   ~ (all_52_7 = all_4_0)
% 203.62/34.54  | 
% 203.62/34.54  | SIMP: (183) implies:
% 203.62/34.54  |   (184)   ~ (all_52_7 = all_4_0)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (17), (178) imply:
% 203.62/34.54  |   (185)   ~ (all_6_2 = all_4_0)
% 203.62/34.54  | 
% 203.62/34.54  | SIMP: (185) implies:
% 203.62/34.54  |   (186)   ~ (all_6_2 = all_4_0)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (167), (178) imply:
% 203.62/34.54  |   (187)   ~ (all_4_0 = all_4_2)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (5), (178) imply:
% 203.62/34.54  |   (188)  op(all_4_0, all_4_0) = all_52_2
% 203.62/34.54  | 
% 203.62/34.54  | BETA: splitting (126) gives:
% 203.62/34.54  | 
% 203.62/34.54  | Case 1:
% 203.62/34.54  | | 
% 203.62/34.54  | |   (189)   ~ (all_38_0 = e1)
% 203.62/34.54  | | 
% 203.62/34.54  | | REDUCE: (79), (189) imply:
% 203.62/34.54  | |   (190)   ~ (all_4_0 = e1)
% 203.62/34.54  | | 
% 203.62/34.54  | | BETA: splitting (102) gives:
% 203.62/34.54  | | 
% 203.62/34.54  | | Case 1:
% 203.62/34.54  | | | 
% 203.62/34.54  | | |   (191)  all_58_15 = e0
% 203.62/34.54  | | | 
% 203.62/34.54  | | | REF_CLOSE: (6), (19), (50), (89), (109), (137), (139), (191) are
% 203.62/34.54  | | |            inconsistent by sub-proof #612.
% 203.62/34.54  | | | 
% 203.62/34.54  | | Case 2:
% 203.62/34.54  | | | 
% 203.62/34.54  | | |   (192)   ~ (all_58_15 = e0)
% 203.62/34.54  | | |   (193)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 203.62/34.54  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.54  | | | 
% 203.62/34.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.54  | | |            (13), (14), (15), (16), (17), (18), (20), (22), (23), (24),
% 203.62/34.54  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.62/34.54  | | |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (45),
% 203.62/34.54  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (55), (56),
% 203.62/34.54  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 203.62/34.54  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 203.62/34.54  | | |            (77), (78), (80), (81), (82), (83), (84), (85), (86), (87),
% 203.62/34.54  | | |            (88), (89), (90), (91), (92), (93), (94), (95), (97), (98),
% 203.62/34.54  | | |            (99), (100), (101), (103), (104), (105), (106), (107), (108),
% 203.62/34.54  | | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 203.62/34.54  | | |            (118), (119), (120), (121), (122), (123), (124), (125), (127),
% 203.62/34.54  | | |            (128), (129), (130), (131), (132), (133), (134), (135), (136),
% 203.62/34.54  | | |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 203.62/34.54  | | |            (147), (148), (149), (150), (151), (152), (153), (154), (155),
% 203.62/34.54  | | |            (156), (157), (158), (159), (160), (161), (162), (163), (164),
% 203.62/34.54  | | |            (165), (166), (167), (168), (169), (170), (171), (172), (173),
% 203.62/34.54  | | |            (175), (176), (179), (180), (182), (184), (186), (187), (188),
% 203.62/34.54  | | |            (190), (192), (193) are inconsistent by sub-proof #669.
% 203.62/34.54  | | | 
% 203.62/34.54  | | End of split
% 203.62/34.54  | | 
% 203.62/34.54  | Case 2:
% 203.62/34.54  | | 
% 203.62/34.54  | |   (194)  all_38_0 = e1
% 203.62/34.54  | |   (195)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 203.62/34.54  | | 
% 203.62/34.54  | | COMBINE_EQS: (79), (194) imply:
% 203.62/34.54  | |   (196)  all_4_0 = e1
% 203.62/34.54  | | 
% 203.62/34.54  | | REF_CLOSE: (6), (21), (37), (43), (90), (123), (134), (147), (174), (176),
% 203.62/34.54  | |            (187), (195), (196) are inconsistent by sub-proof #927.
% 203.62/34.54  | | 
% 203.62/34.54  | End of split
% 203.62/34.54  | 
% 203.62/34.54  End of proof
% 203.62/34.54  
% 203.62/34.54  Sub-proof #605 shows that the following formulas are inconsistent:
% 203.62/34.54  ----------------------------------------------------------------
% 203.62/34.54    (1)   ~ (e3 = e1)
% 203.62/34.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.54    (3)  all_58_1 = all_52_9
% 203.62/34.54    (4)  all_58_13 = all_52_15
% 203.62/34.54    (5)  op(e2, e2) = all_4_2
% 203.62/34.54    (6)  all_56_5 = all_4_2
% 203.62/34.54    (7)   ~ (all_4_1 = e1)
% 203.62/34.54    (8)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.54    (9)  all_58_7 = all_52_13
% 203.62/34.54    (10)  op(all_4_2, e2) = all_4_1
% 203.62/34.54    (11)   ~ (all_52_13 = all_4_2)
% 203.62/34.54    (12)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 203.62/34.54    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.54    (14)   ~ (all_52_9 = all_4_2)
% 203.62/34.54    (15)  all_42_2 = all_4_2
% 203.62/34.54    (16)  all_56_1 = all_52_9
% 203.62/34.54    (17)   ~ (all_52_15 = all_4_2)
% 203.62/34.54    (18)  op(e3, e2) = all_52_9
% 203.62/34.54    (19)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.54    (20)  op(e2, all_4_1) = e1
% 203.62/34.54    (21)  all_42_1 = all_4_1
% 203.62/34.54    (22)  all_58_3 = all_4_2
% 203.62/34.54    (23)  all_56_5 = e3
% 203.62/34.54  
% 203.62/34.54  Begin of proof
% 203.62/34.54  | 
% 203.62/34.54  | COMBINE_EQS: (6), (23) imply:
% 203.62/34.54  |   (24)  all_4_2 = e3
% 203.62/34.54  | 
% 203.62/34.54  | SIMP: (24) implies:
% 203.62/34.54  |   (25)  all_4_2 = e3
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (14), (25) imply:
% 203.62/34.54  |   (26)   ~ (all_52_9 = e3)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (11), (25) imply:
% 203.62/34.54  |   (27)   ~ (all_52_13 = e3)
% 203.62/34.54  | 
% 203.62/34.54  | REDUCE: (17), (25) imply:
% 203.62/34.54  |   (28)   ~ (all_52_15 = e3)
% 203.62/34.54  | 
% 203.62/34.54  | BETA: splitting (13) gives:
% 203.62/34.54  | 
% 203.62/34.54  | Case 1:
% 203.62/34.54  | | 
% 203.62/34.54  | |   (29)  all_58_1 = e3
% 203.62/34.54  | | 
% 203.62/34.54  | | COMBINE_EQS: (3), (29) imply:
% 203.62/34.54  | |   (30)  all_52_9 = e3
% 203.62/34.54  | | 
% 203.62/34.54  | | REDUCE: (26), (30) imply:
% 203.62/34.54  | |   (31)  $false
% 203.62/34.54  | | 
% 203.62/34.54  | | CLOSE: (31) is inconsistent.
% 203.62/34.54  | | 
% 203.62/34.54  | Case 2:
% 203.62/34.54  | | 
% 203.62/34.54  | |   (32)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.54  | | 
% 203.62/34.54  | | BETA: splitting (32) gives:
% 203.62/34.54  | | 
% 203.62/34.54  | | Case 1:
% 203.62/34.54  | | | 
% 203.62/34.54  | | |   (33)  all_58_3 = e3
% 203.62/34.54  | | | 
% 203.62/34.55  | | | REF_CLOSE: (1), (2), (5), (7), (8), (10), (12), (14), (15), (16), (18),
% 203.62/34.55  | | |            (19), (20), (21), (22), (33) are inconsistent by sub-proof
% 203.62/34.55  | | |            #606.
% 203.62/34.55  | | | 
% 203.62/34.55  | | Case 2:
% 203.62/34.55  | | | 
% 203.62/34.55  | | |   (34)  all_58_7 = e3 | all_58_13 = e3
% 203.62/34.55  | | | 
% 203.62/34.55  | | | REF_CLOSE: (4), (9), (27), (28), (34) are inconsistent by sub-proof #1298.
% 203.62/34.55  | | | 
% 203.62/34.55  | | End of split
% 203.62/34.55  | | 
% 203.62/34.55  | End of split
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #606 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)   ~ (e3 = e1)
% 203.62/34.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.55    (3)  all_58_3 = e3
% 203.62/34.55    (4)  op(e2, e2) = all_4_2
% 203.62/34.55    (5)   ~ (all_4_1 = e1)
% 203.62/34.55    (6)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.55    (7)  op(all_4_2, e2) = all_4_1
% 203.62/34.55    (8)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 203.62/34.55    (9)   ~ (all_52_9 = all_4_2)
% 203.62/34.55    (10)  all_42_2 = all_4_2
% 203.62/34.55    (11)  all_56_1 = all_52_9
% 203.62/34.55    (12)  op(e3, e2) = all_52_9
% 203.62/34.55    (13)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.55    (14)  op(e2, all_4_1) = e1
% 203.62/34.55    (15)  all_42_1 = all_4_1
% 203.62/34.55    (16)  all_58_3 = all_4_2
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (3), (16) imply:
% 203.62/34.55  |   (17)  all_4_2 = e3
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (10), (17) imply:
% 203.62/34.55  |   (18)  all_42_2 = e3
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (9), (17) imply:
% 203.62/34.55  |   (19)   ~ (all_52_9 = e3)
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (7), (17) imply:
% 203.62/34.55  |   (20)  op(e3, e2) = all_4_1
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (4), (17) imply:
% 203.62/34.55  |   (21)  op(e2, e2) = e3
% 203.62/34.55  | 
% 203.62/34.55  | REF_CLOSE: (1), (2), (5), (6), (8), (11), (12), (13), (14), (15), (18), (19),
% 203.62/34.55  |            (20), (21) are inconsistent by sub-proof #608.
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #607 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)   ~ (e3 = e1)
% 203.62/34.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.55    (3)   ~ (all_10_0 = e3)
% 203.62/34.55    (4)  all_58_13 = all_52_15
% 203.62/34.55    (5)   ~ (all_52_15 = e3)
% 203.62/34.55    (6)  op(e2, e2) = all_4_2
% 203.62/34.55    (7)  all_58_7 = all_10_0
% 203.62/34.55    (8)   ~ (all_4_1 = e1)
% 203.62/34.55    (9)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.55    (10)  op(all_4_2, e2) = all_4_1
% 203.62/34.55    (11)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 203.62/34.55    (12)   ~ (all_52_9 = all_4_2)
% 203.62/34.55    (13)  all_42_2 = all_4_2
% 203.62/34.55    (14)  all_56_1 = all_52_9
% 203.62/34.55    (15)  op(e3, e2) = all_52_9
% 203.62/34.55    (16)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.55    (17)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.55    (18)  op(e2, all_4_1) = e1
% 203.62/34.55    (19)  all_42_1 = all_4_1
% 203.62/34.55    (20)  all_58_3 = all_4_2
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | BETA: splitting (16) gives:
% 203.62/34.55  | 
% 203.62/34.55  | Case 1:
% 203.62/34.55  | | 
% 203.62/34.55  | |   (21)  all_58_3 = e3
% 203.62/34.55  | | 
% 203.62/34.55  | | COMBINE_EQS: (20), (21) imply:
% 203.62/34.55  | |   (22)  all_4_2 = e3
% 203.62/34.55  | | 
% 203.62/34.55  | | COMBINE_EQS: (13), (22) imply:
% 203.62/34.55  | |   (23)  all_42_2 = e3
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (12), (22) imply:
% 203.62/34.55  | |   (24)   ~ (all_52_9 = e3)
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (10), (22) imply:
% 203.62/34.55  | |   (25)  op(e3, e2) = all_4_1
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (6), (22) imply:
% 203.62/34.55  | |   (26)  op(e2, e2) = e3
% 203.62/34.55  | | 
% 203.62/34.55  | | REF_CLOSE: (1), (2), (8), (9), (11), (14), (15), (17), (18), (19), (23),
% 203.62/34.55  | |            (24), (25), (26) are inconsistent by sub-proof #608.
% 203.62/34.55  | | 
% 203.62/34.55  | Case 2:
% 203.62/34.55  | | 
% 203.62/34.55  | |   (27)  all_58_7 = e3 | all_58_13 = e3
% 203.62/34.55  | | 
% 203.62/34.55  | | REF_CLOSE: (3), (4), (5), (7), (27) are inconsistent by sub-proof #717.
% 203.62/34.55  | | 
% 203.62/34.55  | End of split
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #608 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)   ~ (e3 = e1)
% 203.62/34.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.55    (3)  all_42_2 = e3
% 203.62/34.55    (4)   ~ (all_4_1 = e1)
% 203.62/34.55    (5)  op(e3, e2) = all_4_1
% 203.62/34.55    (6)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.55    (7)   ~ (all_52_9 = e3)
% 203.62/34.55    (8)   ~ (all_42_1 = e0) |  ~ (all_42_2 = e3)
% 203.62/34.55    (9)  op(e2, e2) = e3
% 203.62/34.55    (10)  all_56_1 = all_52_9
% 203.62/34.55    (11)  op(e3, e2) = all_52_9
% 203.62/34.55    (12)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.55    (13)  op(e2, all_4_1) = e1
% 203.62/34.55    (14)  all_42_1 = all_4_1
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | BETA: splitting (8) gives:
% 203.62/34.55  | 
% 203.62/34.55  | Case 1:
% 203.62/34.55  | | 
% 203.62/34.55  | |   (15)   ~ (all_42_2 = e3)
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (3), (15) imply:
% 203.62/34.55  | |   (16)  $false
% 203.62/34.55  | | 
% 203.62/34.55  | | CLOSE: (16) is inconsistent.
% 203.62/34.55  | | 
% 203.62/34.55  | Case 2:
% 203.62/34.55  | | 
% 203.62/34.55  | |   (17)   ~ (all_42_1 = e0)
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (14), (17) imply:
% 203.62/34.55  | |   (18)   ~ (all_4_1 = e0)
% 203.62/34.55  | | 
% 203.62/34.55  | | GROUND_INST: instantiating (2) with all_52_9, all_4_1, e2, e3, simplifying
% 203.62/34.55  | |              with (5), (11) gives:
% 203.62/34.55  | |   (19)  all_52_9 = all_4_1
% 203.62/34.55  | | 
% 203.62/34.55  | | COMBINE_EQS: (10), (19) imply:
% 203.62/34.55  | |   (20)  all_56_1 = all_4_1
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (7), (19) imply:
% 203.62/34.55  | |   (21)   ~ (all_4_1 = e3)
% 203.62/34.55  | | 
% 203.62/34.55  | | REDUCE: (6), (19) imply:
% 203.62/34.55  | |   (22)  op(all_4_1, all_4_1) = all_52_8
% 203.62/34.55  | | 
% 203.62/34.55  | | BETA: splitting (12) gives:
% 203.62/34.55  | | 
% 203.62/34.55  | | Case 1:
% 203.62/34.55  | | | 
% 203.62/34.55  | | |   (23)  all_56_1 = e3
% 203.62/34.55  | | | 
% 203.62/34.55  | | | COMBINE_EQS: (20), (23) imply:
% 203.62/34.55  | | |   (24)  all_4_1 = e3
% 203.62/34.55  | | | 
% 203.62/34.55  | | | REDUCE: (21), (24) imply:
% 203.62/34.55  | | |   (25)  $false
% 203.62/34.55  | | | 
% 203.62/34.55  | | | CLOSE: (25) is inconsistent.
% 203.62/34.55  | | | 
% 203.62/34.55  | | Case 2:
% 203.62/34.55  | | | 
% 203.62/34.55  | | |   (26)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.55  | | | 
% 203.62/34.55  | | | BETA: splitting (26) gives:
% 203.62/34.55  | | | 
% 203.62/34.55  | | | Case 1:
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | |   (27)  all_56_1 = e2
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | | COMBINE_EQS: (20), (27) imply:
% 203.62/34.55  | | | |   (28)  all_4_1 = e2
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | | REDUCE: (22), (28) imply:
% 203.62/34.55  | | | |   (29)  op(e2, e2) = all_52_8
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | | REDUCE: (13), (28) imply:
% 203.62/34.55  | | | |   (30)  op(e2, e2) = e1
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | | REF_CLOSE: (1), (2), (9), (29), (30) are inconsistent by sub-proof #753.
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | Case 2:
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | |   (31)  all_56_1 = e1 | all_56_1 = e0
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | | REF_CLOSE: (4), (18), (20), (31) are inconsistent by sub-proof #1164.
% 203.62/34.55  | | | | 
% 203.62/34.55  | | | End of split
% 203.62/34.55  | | | 
% 203.62/34.55  | | End of split
% 203.62/34.55  | | 
% 203.62/34.55  | End of split
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #609 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)  all_56_7 = all_52_27
% 203.62/34.55    (2)  all_56_7 = e3
% 203.62/34.55    (3)   ~ (all_52_27 = e3)
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.55  |   (4)  all_52_27 = e3
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (4) implies:
% 203.62/34.55  |   (5)  all_52_27 = e3
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (3), (5) imply:
% 203.62/34.55  |   (6)  $false
% 203.62/34.55  | 
% 203.62/34.55  | CLOSE: (6) is inconsistent.
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #610 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)  all_58_9 = all_14_1
% 203.62/34.55    (2)  all_58_9 = e1
% 203.62/34.55    (3)   ~ (all_14_1 = e1)
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (1), (2) imply:
% 203.62/34.55  |   (4)  all_14_1 = e1
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (4) implies:
% 203.62/34.55  |   (5)  all_14_1 = e1
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (3), (5) imply:
% 203.62/34.55  |   (6)  $false
% 203.62/34.55  | 
% 203.62/34.55  | CLOSE: (6) is inconsistent.
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #611 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.55    (2)   ~ (all_14_1 = e2)
% 203.62/34.55    (3)  all_56_3 = all_14_1
% 203.62/34.55    (4)  op(e0, e0) = e3
% 203.62/34.55    (5)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.55    (6)  op(all_14_1, all_14_1) = all_52_24
% 203.62/34.55    (7)   ~ (all_14_1 = e1)
% 203.62/34.55    (8)  op(e0, all_14_1) = e2
% 203.62/34.55    (9)   ~ (e3 = e2)
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | BETA: splitting (5) gives:
% 203.62/34.55  | 
% 203.62/34.55  | Case 1:
% 203.62/34.55  | | 
% 203.62/34.55  | |   (10)  all_56_3 = e2
% 203.62/34.55  | | 
% 203.62/34.55  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #1183.
% 203.62/34.55  | | 
% 203.62/34.55  | Case 2:
% 203.62/34.55  | | 
% 203.62/34.55  | |   (11)  all_56_3 = e1 | all_56_3 = e0
% 203.62/34.55  | | 
% 203.62/34.55  | | BETA: splitting (11) gives:
% 203.62/34.55  | | 
% 203.62/34.55  | | Case 1:
% 203.62/34.55  | | | 
% 203.62/34.55  | | |   (12)  all_56_3 = e1
% 203.62/34.55  | | | 
% 203.62/34.55  | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #1182.
% 203.62/34.55  | | | 
% 203.62/34.55  | | Case 2:
% 203.62/34.55  | | | 
% 203.62/34.55  | | |   (13)  all_56_3 = e0
% 203.62/34.55  | | | 
% 203.62/34.55  | | | COMBINE_EQS: (3), (13) imply:
% 203.62/34.55  | | |   (14)  all_14_1 = e0
% 203.62/34.55  | | | 
% 203.62/34.55  | | | SIMP: (14) implies:
% 203.62/34.55  | | |   (15)  all_14_1 = e0
% 203.62/34.55  | | | 
% 203.62/34.55  | | | REDUCE: (6), (15) imply:
% 203.62/34.55  | | |   (16)  op(e0, e0) = all_52_24
% 203.62/34.55  | | | 
% 203.62/34.55  | | | REDUCE: (8), (15) imply:
% 203.62/34.55  | | |   (17)  op(e0, e0) = e2
% 203.62/34.55  | | | 
% 203.62/34.55  | | | GROUND_INST: instantiating (1) with e3, all_52_24, e0, e0, simplifying
% 203.62/34.55  | | |              with (4), (16) gives:
% 203.62/34.55  | | |   (18)  all_52_24 = e3
% 203.62/34.55  | | | 
% 203.62/34.55  | | | GROUND_INST: instantiating (1) with e2, all_52_24, e0, e0, simplifying
% 203.62/34.55  | | |              with (16), (17) gives:
% 203.62/34.55  | | |   (19)  all_52_24 = e2
% 203.62/34.55  | | | 
% 203.62/34.55  | | | COMBINE_EQS: (18), (19) imply:
% 203.62/34.55  | | |   (20)  e3 = e2
% 203.62/34.55  | | | 
% 203.62/34.55  | | | REDUCE: (9), (20) imply:
% 203.62/34.55  | | |   (21)  $false
% 203.62/34.55  | | | 
% 203.62/34.55  | | | CLOSE: (21) is inconsistent.
% 203.62/34.55  | | | 
% 203.62/34.55  | | End of split
% 203.62/34.55  | | 
% 203.62/34.55  | End of split
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #612 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.55    (2)  op(all_14_2, e0) = all_14_1
% 203.62/34.55    (3)  op(e0, e0) = all_14_2
% 203.62/34.55    (4)  all_58_15 = e0
% 203.62/34.55    (5)   ~ (e2 = e0)
% 203.62/34.55    (6)  all_58_15 = all_14_2
% 203.62/34.55    (7)  op(e0, all_14_1) = e2
% 203.62/34.55    (8)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (4), (6) imply:
% 203.62/34.55  |   (9)  all_14_2 = e0
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (8), (9) imply:
% 203.62/34.55  |   (10)  op(e0, e0) = all_52_30
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (2), (9) imply:
% 203.62/34.55  |   (11)  op(e0, e0) = all_14_1
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (3), (9) imply:
% 203.62/34.55  |   (12)  op(e0, e0) = e0
% 203.62/34.55  | 
% 203.62/34.55  | GROUND_INST: instantiating (1) with all_14_1, all_52_30, e0, e0, simplifying
% 203.62/34.55  |              with (10), (11) gives:
% 203.62/34.55  |   (13)  all_52_30 = all_14_1
% 203.62/34.55  | 
% 203.62/34.55  | GROUND_INST: instantiating (1) with e0, all_52_30, e0, e0, simplifying with
% 203.62/34.55  |              (10), (12) gives:
% 203.62/34.55  |   (14)  all_52_30 = e0
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (13), (14) imply:
% 203.62/34.55  |   (15)  all_14_1 = e0
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (15) implies:
% 203.62/34.55  |   (16)  all_14_1 = e0
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (7), (16) imply:
% 203.62/34.55  |   (17)  op(e0, e0) = e2
% 203.62/34.55  | 
% 203.62/34.55  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (12),
% 203.62/34.55  |              (17) gives:
% 203.62/34.55  |   (18)  e2 = e0
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (5), (18) imply:
% 203.62/34.55  |   (19)  $false
% 203.62/34.55  | 
% 203.62/34.55  | CLOSE: (19) is inconsistent.
% 203.62/34.55  | 
% 203.62/34.55  End of proof
% 203.62/34.55  
% 203.62/34.55  Sub-proof #613 shows that the following formulas are inconsistent:
% 203.62/34.55  ----------------------------------------------------------------
% 203.62/34.55    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.55    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.55    (3)  all_58_14 = all_52_23
% 203.62/34.55    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.55    (5)  all_22_1 = e2
% 203.62/34.55    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.55    (7)   ~ (all_52_5 = all_52_13)
% 203.62/34.55    (8)  all_58_1 = all_52_9
% 203.62/34.55    (9)   ~ (all_52_9 = all_52_13)
% 203.62/34.55    (10)   ~ (e3 = e0)
% 203.62/34.55    (11)  op(e2, e3) = all_52_3
% 203.62/34.55    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.55    (13)   ~ (all_52_3 = all_52_19)
% 203.62/34.55    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.55    (15)   ~ (all_52_17 = all_52_25)
% 203.62/34.55    (16)   ~ (all_52_3 = all_6_2)
% 203.62/34.55    (17)  all_58_0 = all_6_2
% 203.62/34.55    (18)  op(all_14_2, e0) = all_14_1
% 203.62/34.55    (19)  all_56_4 = all_52_3
% 203.62/34.55    (20)   ~ (all_52_17 = all_10_2)
% 203.62/34.55    (21)  all_26_1 = all_10_1
% 203.62/34.55    (22)  op(e3, e0) = all_52_25
% 203.62/34.55    (23)  all_26_2 = all_10_2
% 203.62/34.55    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.55    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.55    (26)   ~ (all_52_27 = all_52_29)
% 203.62/34.55    (27)  all_58_13 = all_52_15
% 203.62/34.55    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.55    (29)  all_58_9 = all_52_25
% 203.62/34.55    (30)   ~ (all_6_1 = e1)
% 203.62/34.55    (31)   ~ (all_52_29 = all_14_2)
% 203.62/34.55    (32)  all_22_0 = all_6_0
% 203.62/34.55    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.55    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.55    (35)  op(e1, e3) = all_52_5
% 203.62/34.55    (36)  op(e2, e2) = all_4_2
% 203.62/34.55    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.55    (38)   ~ (all_52_3 = all_52_5)
% 203.62/34.55    (39)  all_58_11 = all_52_29
% 203.62/34.55    (40)  all_56_5 = all_4_2
% 203.62/34.55    (41)   ~ (all_52_25 = all_14_2)
% 203.62/34.55    (42)   ~ (all_52_9 = all_52_15)
% 203.62/34.55    (43)   ~ (all_52_3 = all_52_27)
% 203.62/34.55    (44)  op(all_10_2, e1) = all_10_1
% 203.62/34.55    (45)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.55    (46)   ~ (all_52_7 = all_6_2)
% 203.62/34.55    (47)  op(e0, e0) = all_14_2
% 203.62/34.55    (48)  all_56_15 = all_14_2
% 203.62/34.55    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.55    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.55    (51)  all_56_11 = all_52_29
% 203.62/34.55    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.55    (53)   ~ (all_52_13 = all_10_2)
% 203.62/34.55    (54)   ~ (all_6_0 = e1)
% 203.62/34.55    (55)  all_58_10 = all_52_27
% 203.62/34.55    (56)  all_56_8 = all_52_5
% 203.62/34.55    (57)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.55    (58)   ~ (all_52_19 = all_52_23)
% 203.62/34.55    (59)   ~ (all_52_25 = all_52_29)
% 203.62/34.55    (60)   ~ (all_52_29 = all_10_2)
% 203.62/34.55    (61)  all_58_7 = all_52_13
% 203.62/34.55    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.55    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.55    (64)   ~ (all_52_5 = all_52_7)
% 203.62/34.55    (65)  all_58_12 = all_52_7
% 203.62/34.55    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.55    (67)   ~ (all_52_7 = all_14_2)
% 203.62/34.55    (68)  all_58_2 = all_52_3
% 203.62/34.55    (69)  all_56_2 = all_52_17
% 203.62/34.55    (70)  all_22_1 = all_6_1
% 203.62/34.55    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.55    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.55    (73)  op(e3, all_6_1) = all_6_0
% 203.62/34.55    (74)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.55    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.55    (76)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.55    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.55    (78)   ~ (e2 = e0)
% 203.62/34.55    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.55    (80)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.55    (81)   ~ (all_52_5 = all_52_29)
% 203.62/34.55    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.55    (83)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.55    (84)   ~ (all_52_15 = all_14_2)
% 203.62/34.55    (85)   ~ (all_52_19 = all_52_27)
% 203.62/34.55    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.55    (87)   ~ (all_6_0 = e2)
% 203.62/34.55    (88)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.55            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.55    (89)  op(e3, e1) = all_52_17
% 203.62/34.55    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.55    (91)  op(e0, e3) = all_52_7
% 203.62/34.55    (92)  op(e1, e2) = all_52_13
% 203.62/34.55    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.55    (94)   ~ (all_52_9 = all_52_25)
% 203.62/34.55    (95)  all_58_15 = all_14_2
% 203.62/34.55    (96)   ~ (all_52_19 = all_10_2)
% 203.62/34.55    (97)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.55    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.55    (99)  all_58_8 = all_10_2
% 203.62/34.55    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.55    (101)   ~ (all_52_5 = all_10_2)
% 203.62/34.55    (102)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.55    (103)   ~ (all_52_23 = all_14_2)
% 203.62/34.55    (104)  all_56_12 = all_52_7
% 203.62/34.55    (105)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.55    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.55    (107)   ~ (all_52_25 = all_6_2)
% 203.62/34.55    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.55    (109)   ~ (all_52_9 = all_4_2)
% 203.62/34.55    (110)   ~ (all_52_5 = all_6_2)
% 203.62/34.55    (111)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.55    (112)   ~ (all_52_9 = all_6_2)
% 203.62/34.55    (113)  op(e1, all_10_1) = e2
% 203.62/34.55    (114)  all_56_0 = all_6_2
% 203.62/34.55    (115)  op(e3, e3) = all_6_2
% 203.62/34.55    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.55    (117)   ~ (all_52_27 = all_14_2)
% 203.62/34.55    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.55    (119)  all_56_14 = all_52_23
% 203.62/34.55    (120)  all_56_3 = all_52_25
% 203.62/34.55    (121)   ~ (all_52_3 = all_52_7)
% 203.62/34.55    (122)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.55    (123)  all_58_5 = all_52_19
% 203.62/34.55    (124)  all_56_1 = all_52_9
% 203.62/34.55    (125)   ~ (all_52_15 = all_4_2)
% 203.62/34.55    (126)  op(e0, all_14_1) = e3
% 203.62/34.55    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.55           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.55           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.55           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.55    (128)   ~ (all_52_27 = all_4_2)
% 203.62/34.55    (129)  all_58_6 = all_52_5
% 203.62/34.55    (130)  op(e3, e2) = all_52_9
% 203.62/34.55    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.55    (132)   ~ (all_52_17 = all_6_2)
% 203.62/34.55    (133)   ~ (e1 = e0)
% 203.62/34.55    (134)   ~ (e3 = e2)
% 203.62/34.55    (135)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.55    (136)  all_26_0 = e2
% 203.62/34.55    (137)   ~ (all_52_9 = all_52_17)
% 203.62/34.55    (138)  all_56_10 = all_10_2
% 203.62/34.55    (139)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.55    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.55    (141)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.55    (142)  op(e1, e1) = all_10_2
% 203.62/34.55    (143)   ~ (all_52_23 = all_10_2)
% 203.62/34.55    (144)   ~ (all_52_7 = all_52_23)
% 203.62/34.55    (145)   ~ (all_52_17 = all_52_19)
% 203.62/34.55    (146)  all_58_3 = all_4_2
% 203.62/34.55    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.55    (148)   ~ (all_52_3 = all_4_2)
% 203.62/34.55    (149)   ~ (all_52_19 = all_4_2)
% 203.62/34.55    (150)   ~ (all_52_17 = all_52_23)
% 203.62/34.55    (151)  op(all_6_2, e3) = all_6_1
% 203.62/34.55    (152)   ~ (all_52_13 = all_52_29)
% 203.62/34.55    (153)  all_22_2 = all_6_2
% 203.62/34.55    (154)  all_58_4 = all_52_17
% 203.62/34.55    (155)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.55    (156)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.55  
% 203.62/34.55  Begin of proof
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (5), (70) imply:
% 203.62/34.55  |   (157)  all_6_1 = e2
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (157) implies:
% 203.62/34.55  |   (158)  all_6_1 = e2
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (30), (158) imply:
% 203.62/34.55  |   (159)   ~ (e2 = e1)
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (151), (158) imply:
% 203.62/34.55  |   (160)  op(all_6_2, e3) = e2
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (73), (158) imply:
% 203.62/34.55  |   (161)  op(e3, e2) = all_6_0
% 203.62/34.55  | 
% 203.62/34.55  | GROUND_INST: instantiating (6) with all_52_9, all_6_0, e2, e3, simplifying
% 203.62/34.55  |              with (130), (161) gives:
% 203.62/34.55  |   (162)  all_52_9 = all_6_0
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (124), (162) imply:
% 203.62/34.55  |   (163)  all_56_1 = all_6_0
% 203.62/34.55  | 
% 203.62/34.55  | COMBINE_EQS: (8), (162) imply:
% 203.62/34.55  |   (164)  all_58_1 = all_6_0
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (9), (162) imply:
% 203.62/34.55  |   (165)   ~ (all_52_13 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (165) implies:
% 203.62/34.55  |   (166)   ~ (all_52_13 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (42), (162) imply:
% 203.62/34.55  |   (167)   ~ (all_52_15 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (167) implies:
% 203.62/34.55  |   (168)   ~ (all_52_15 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (137), (162) imply:
% 203.62/34.55  |   (169)   ~ (all_52_17 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (169) implies:
% 203.62/34.55  |   (170)   ~ (all_52_17 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | REDUCE: (94), (162) imply:
% 203.62/34.55  |   (171)   ~ (all_52_25 = all_6_0)
% 203.62/34.55  | 
% 203.62/34.55  | SIMP: (171) implies:
% 203.62/34.55  |   (172)   ~ (all_52_25 = all_6_0)
% 203.62/34.56  | 
% 203.62/34.56  | REDUCE: (112), (162) imply:
% 203.62/34.56  |   (173)   ~ (all_6_0 = all_6_2)
% 203.62/34.56  | 
% 203.62/34.56  | REDUCE: (109), (162) imply:
% 203.62/34.56  |   (174)   ~ (all_6_0 = all_4_2)
% 203.62/34.56  | 
% 203.62/34.56  | REDUCE: (57), (162) imply:
% 203.62/34.56  |   (175)  op(all_6_0, all_6_0) = all_52_8
% 203.62/34.56  | 
% 203.62/34.56  | BETA: splitting (83) gives:
% 203.62/34.56  | 
% 203.62/34.56  | Case 1:
% 203.62/34.56  | | 
% 203.62/34.56  | |   (176)   ~ (all_26_0 = e2)
% 203.62/34.56  | | 
% 203.62/34.56  | | REDUCE: (136), (176) imply:
% 203.62/34.56  | |   (177)  $false
% 203.62/34.56  | | 
% 203.62/34.56  | | CLOSE: (177) is inconsistent.
% 203.62/34.56  | | 
% 203.62/34.56  | Case 2:
% 203.62/34.56  | | 
% 203.62/34.56  | |   (178)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.56  | | 
% 203.62/34.56  | | BETA: splitting (88) gives:
% 203.62/34.56  | | 
% 203.62/34.56  | | Case 1:
% 203.62/34.56  | | | 
% 203.62/34.56  | | |   (179)  all_58_15 = e0
% 203.62/34.56  | | | 
% 203.62/34.56  | | | REF_CLOSE: (6), (10), (18), (47), (95), (122), (126), (179) are
% 203.62/34.56  | | |            inconsistent by sub-proof #678.
% 203.62/34.56  | | | 
% 203.62/34.56  | | Case 2:
% 203.62/34.56  | | | 
% 203.62/34.56  | | |   (180)   ~ (all_58_15 = e0)
% 203.62/34.56  | | |   (181)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 203.62/34.56  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.62/34.56  | | | 
% 203.62/34.56  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.62/34.56  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.62/34.56  | | |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34),
% 203.62/34.56  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 203.62/34.56  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 203.62/34.56  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 203.62/34.56  | | |            (65), (66), (67), (68), (69), (71), (72), (74), (75), (76),
% 203.62/34.56  | | |            (77), (78), (79), (80), (81), (82), (84), (85), (86), (87),
% 203.62/34.56  | | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 203.62/34.56  | | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 203.62/34.56  | | |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 203.62/34.56  | | |            (117), (118), (119), (120), (121), (122), (123), (125), (127),
% 203.62/34.56  | | |            (128), (129), (131), (132), (133), (134), (135), (138), (139),
% 203.62/34.56  | | |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 203.62/34.56  | | |            (149), (150), (151), (152), (153), (154), (155), (156), (159),
% 203.62/34.56  | | |            (160), (163), (164), (166), (168), (170), (172), (173), (174),
% 203.62/34.56  | | |            (175), (178), (180), (181) are inconsistent by sub-proof #629.
% 203.62/34.56  | | | 
% 203.62/34.56  | | End of split
% 203.62/34.56  | | 
% 203.62/34.56  | End of split
% 203.62/34.56  | 
% 203.62/34.56  End of proof
% 203.62/34.56  
% 203.62/34.56  Sub-proof #614 shows that the following formulas are inconsistent:
% 203.62/34.56  ----------------------------------------------------------------
% 203.62/34.56    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.56    (2)   ~ (all_52_15 = all_52_23)
% 203.62/34.56    (3)   ~ (all_52_25 = all_52_27)
% 203.62/34.56    (4)  all_58_14 = all_52_23
% 203.62/34.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.56    (6)   ~ (all_52_5 = all_52_13)
% 203.62/34.56    (7)  op(all_52_7, all_52_7) = e0
% 203.62/34.56    (8)  all_58_1 = all_52_9
% 203.62/34.56    (9)  op(all_52_5, all_52_5) = e1
% 203.62/34.56    (10)   ~ (e3 = e0)
% 203.62/34.56    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.56    (12)   ~ (all_52_7 = all_52_15)
% 203.62/34.56    (13)   ~ (all_52_3 = all_52_19)
% 203.62/34.56    (14)   ~ (all_52_17 = all_52_25)
% 203.62/34.56    (15)  all_16_1 = all_10_1
% 203.62/34.56    (16)   ~ (all_52_3 = all_6_2)
% 203.62/34.56    (17)  all_58_0 = all_6_2
% 203.62/34.56    (18)  op(all_14_2, e0) = all_14_1
% 203.62/34.56    (19)  all_56_4 = all_52_3
% 203.62/34.56    (20)  all_26_1 = all_10_1
% 203.62/34.56    (21)  all_26_2 = all_10_2
% 203.62/34.56    (22)  op(e0, all_14_1) = all_14_0
% 203.62/34.56    (23)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.56    (24)   ~ (all_52_27 = all_52_29)
% 203.62/34.56    (25)  all_58_13 = all_52_15
% 203.62/34.56    (26)  all_58_9 = all_52_25
% 203.62/34.56    (27)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.62/34.56    (28)  op(e2, e2) = all_4_2
% 203.62/34.56    (29)   ~ (all_52_3 = all_52_5)
% 203.62/34.56    (30)  all_58_11 = all_52_29
% 203.62/34.56    (31)   ~ (all_52_25 = all_14_2)
% 203.62/34.56    (32)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.56    (33)   ~ (all_52_3 = all_52_27)
% 203.62/34.56    (34)  op(all_10_2, e1) = all_10_1
% 203.62/34.56    (35)   ~ (all_52_7 = all_6_2)
% 203.62/34.56    (36)  op(e0, e0) = all_14_2
% 203.62/34.56    (37)  op(e0, e1) = all_52_23
% 203.62/34.56    (38)  all_56_15 = all_14_2
% 203.62/34.56    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.56    (40)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.56    (41)  op(e1, e0) = all_52_29
% 203.62/34.56    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.62/34.56    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.56    (44)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.62/34.56    (45)  all_56_9 = all_52_13
% 203.62/34.56    (46)   ~ (e2 = e1)
% 203.62/34.56    (47)   ~ (all_52_13 = all_10_2)
% 203.62/34.56    (48)   ~ (all_6_0 = e1)
% 203.62/34.56    (49)  all_58_10 = all_52_27
% 203.62/34.56    (50)  all_56_8 = all_52_5
% 203.62/34.56    (51)   ~ (all_52_19 = all_52_23)
% 203.62/34.56    (52)  all_16_2 = all_10_2
% 203.62/34.56    (53)   ~ (all_52_29 = all_10_2)
% 203.62/34.56    (54)  all_58_7 = all_52_13
% 203.62/34.56    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.56    (56)  op(all_6_2, all_6_2) = e3
% 203.62/34.56    (57)   ~ (all_52_5 = all_52_7)
% 203.62/34.56    (58)  all_58_12 = all_52_7
% 203.62/34.56    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.56    (60)   ~ (all_52_7 = all_14_2)
% 203.62/34.56    (61)   ~ (all_14_2 = e0)
% 203.62/34.56    (62)  all_58_2 = all_52_3
% 203.62/34.56    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.56    (64)  all_56_2 = all_52_17
% 203.62/34.56    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.56    (66)  op(e3, all_6_1) = all_6_0
% 203.62/34.56    (67)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.56    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.56    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.56    (70)   ~ (e2 = e0)
% 203.62/34.56    (71)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.56    (72)  op(all_52_3, all_52_3) = e2
% 203.62/34.56    (73)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.56    (74)  all_56_6 = all_52_19
% 203.62/34.56    (75)   ~ (all_52_15 = all_14_2)
% 203.62/34.56    (76)   ~ (all_52_19 = all_52_27)
% 203.62/34.56    (77)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.56    (78)   ~ (all_6_0 = e2)
% 203.62/34.56    (79)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.56    (80)   ~ (all_52_13 = all_4_2)
% 203.62/34.56    (81)  op(e3, e1) = all_52_17
% 203.62/34.56    (82)  op(e0, e3) = all_52_7
% 203.62/34.56    (83)  op(e1, e2) = all_52_13
% 203.62/34.56    (84)   ~ (all_52_9 = all_52_25)
% 203.62/34.56    (85)  all_58_15 = all_14_2
% 203.62/34.56    (86)   ~ (all_52_19 = all_10_2)
% 203.62/34.56    (87)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.56    (88)  all_58_8 = all_10_2
% 203.62/34.56    (89)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.56    (90)   ~ (all_52_5 = all_10_2)
% 203.62/34.56    (91)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.62/34.56    (92)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.56    (93)  all_56_12 = all_52_7
% 203.62/34.56    (94)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.56    (95)   ~ (all_52_25 = all_6_2)
% 203.62/34.56    (96)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.56    (97)   ~ (all_52_5 = all_6_2)
% 203.62/34.56    (98)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.56    (99)   ~ (all_52_13 = all_52_15)
% 203.62/34.56    (100)  op(e1, all_10_1) = e2
% 203.62/34.56    (101)  op(e3, e3) = all_6_2
% 203.62/34.56    (102)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.56    (103)   ~ (all_52_27 = all_14_2)
% 203.62/34.56    (104)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.56    (105)  all_56_3 = all_52_25
% 203.62/34.56    (106)   ~ (all_52_3 = all_52_7)
% 203.62/34.56    (107)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.56    (108)  all_58_5 = all_52_19
% 203.62/34.56    (109)   ~ (all_52_15 = all_4_2)
% 203.62/34.56    (110)   ~ (all_52_27 = all_4_2)
% 203.62/34.56    (111)  all_58_6 = all_52_5
% 203.62/34.56    (112)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.56    (113)   ~ (all_52_17 = all_6_2)
% 203.62/34.56    (114)   ~ (e1 = e0)
% 203.62/34.56    (115)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.62/34.56    (116)   ~ (e3 = e2)
% 203.62/34.56    (117)   ~ (all_52_9 = all_52_17)
% 203.62/34.56    (118)  all_56_10 = all_10_2
% 203.62/34.56    (119)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.56    (120)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.56    (121)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.56    (122)  op(e1, e1) = all_10_2
% 203.62/34.56    (123)   ~ (all_52_23 = all_10_2)
% 203.62/34.56    (124)   ~ (all_52_7 = all_52_23)
% 203.62/34.56    (125)  all_58_3 = all_4_2
% 203.62/34.56    (126)  all_56_13 = all_52_15
% 203.62/34.56    (127)   ~ (all_52_3 = all_4_2)
% 203.62/34.56    (128)  op(all_6_2, e3) = all_6_1
% 203.62/34.56    (129)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.62/34.56    (130)   ~ (all_52_13 = all_52_29)
% 203.62/34.56    (131)  all_58_4 = all_52_17
% 203.62/34.56    (132)   ~ (all_14_0 = e2)
% 203.62/34.56    (133)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.56    (134)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.56  
% 203.62/34.56  Begin of proof
% 203.62/34.56  | 
% 203.62/34.56  | BETA: splitting (89) gives:
% 203.62/34.56  | 
% 203.62/34.56  | Case 1:
% 203.62/34.56  | | 
% 203.62/34.56  | |   (135)  all_56_15 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | COMBINE_EQS: (38), (135) imply:
% 203.62/34.56  | |   (136)  all_14_2 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | SIMP: (136) implies:
% 203.62/34.56  | |   (137)  all_14_2 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | COMBINE_EQS: (85), (137) imply:
% 203.62/34.56  | |   (138)  all_58_15 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | REDUCE: (60), (137) imply:
% 203.62/34.56  | |   (139)   ~ (all_52_7 = e3)
% 203.62/34.56  | | 
% 203.62/34.56  | | REDUCE: (103), (137) imply:
% 203.62/34.56  | |   (140)   ~ (all_52_27 = e3)
% 203.62/34.56  | | 
% 203.62/34.56  | | REDUCE: (107), (137) imply:
% 203.62/34.56  | |   (141)  op(e3, e3) = all_52_30
% 203.62/34.56  | | 
% 203.62/34.56  | | REDUCE: (36), (137) imply:
% 203.62/34.56  | |   (142)  op(e0, e0) = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | GROUND_INST: instantiating (5) with all_6_2, all_52_30, e3, e3, simplifying
% 203.62/34.56  | |              with (101), (141) gives:
% 203.62/34.56  | |   (143)  all_52_30 = all_6_2
% 203.62/34.56  | | 
% 203.62/34.56  | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (11), (13), (16), (17), (28),
% 203.62/34.56  | |            (29), (32), (34), (35), (36), (37), (39), (46), (48), (49), (50),
% 203.62/34.56  | |            (51), (55), (56), (57), (58), (60), (62), (63), (65), (66), (68),
% 203.62/34.56  | |            (70), (72), (73), (74), (77), (79), (83), (86), (87), (88), (90),
% 203.62/34.56  | |            (93), (97), (100), (101), (104), (108), (111), (113), (114),
% 203.62/34.56  | |            (115), (116), (119), (122), (123), (125), (127), (128), (131),
% 203.62/34.56  | |            (138), (139), (140), (142) are inconsistent by sub-proof #616.
% 203.62/34.56  | | 
% 203.62/34.56  | Case 2:
% 203.62/34.56  | | 
% 203.62/34.56  | |   (144)   ~ (all_56_15 = e3)
% 203.62/34.56  | |   (145)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.56  | | 
% 203.62/34.56  | | REDUCE: (38), (144) imply:
% 203.62/34.56  | |   (146)   ~ (all_14_2 = e3)
% 203.62/34.56  | | 
% 203.62/34.56  | | BETA: splitting (42) gives:
% 203.62/34.56  | | 
% 203.62/34.56  | | Case 1:
% 203.62/34.56  | | | 
% 203.62/34.56  | | |   (147)  all_56_13 = e3
% 203.62/34.56  | | | 
% 203.62/34.56  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 203.62/34.56  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 203.62/34.56  | | |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 203.62/34.56  | | |            (36), (38), (39), (40), (41), (43), (44), (45), (46), (47),
% 203.62/34.56  | | |            (48), (49), (53), (54), (55), (56), (57), (58), (59), (60),
% 203.62/34.56  | | |            (61), (62), (63), (64), (65), (66), (67), (69), (70), (71),
% 203.62/34.56  | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 203.62/34.56  | | |            (82), (83), (84), (85), (86), (88), (90), (92), (93), (94),
% 203.62/34.56  | | |            (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 203.62/34.56  | | |            (105), (106), (108), (110), (111), (112), (113), (114), (117),
% 203.62/34.56  | | |            (118), (119), (120), (121), (122), (123), (125), (126), (127),
% 203.62/34.56  | | |            (128), (129), (130), (131), (132), (133), (134), (145), (147)
% 203.62/34.56  | | |            are inconsistent by sub-proof #619.
% 203.62/34.56  | | | 
% 203.62/34.56  | | Case 2:
% 203.62/34.56  | | | 
% 203.62/34.56  | | |   (148)   ~ (all_56_13 = e3)
% 203.62/34.56  | | | 
% 203.62/34.56  | | | REDUCE: (126), (148) imply:
% 203.62/34.56  | | |   (149)   ~ (all_52_15 = e3)
% 203.62/34.56  | | | 
% 203.62/34.56  | | | REF_CLOSE: (4), (5), (7), (9), (10), (11), (15), (17), (25), (28), (32),
% 203.62/34.56  | | |            (34), (35), (36), (37), (39), (52), (56), (58), (60), (62),
% 203.62/34.56  | | |            (65), (70), (72), (73), (79), (85), (90), (91), (93), (101),
% 203.62/34.56  | | |            (109), (111), (112), (122), (124), (127), (146), (149) are
% 203.62/34.56  | | |            inconsistent by sub-proof #615.
% 203.62/34.56  | | | 
% 203.62/34.56  | | End of split
% 203.62/34.56  | | 
% 203.62/34.56  | End of split
% 203.62/34.56  | 
% 203.62/34.56  End of proof
% 203.62/34.56  
% 203.62/34.56  Sub-proof #615 shows that the following formulas are inconsistent:
% 203.62/34.56  ----------------------------------------------------------------
% 203.62/34.56    (1)  all_58_14 = all_52_23
% 203.62/34.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.56    (3)  op(all_52_7, all_52_7) = e0
% 203.62/34.56    (4)  op(all_52_5, all_52_5) = e1
% 203.62/34.56    (5)   ~ (e3 = e0)
% 203.62/34.56    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.56    (7)  all_16_1 = all_10_1
% 203.62/34.56    (8)  all_58_0 = all_6_2
% 203.62/34.56    (9)  all_58_13 = all_52_15
% 203.62/34.56    (10)   ~ (all_52_15 = e3)
% 203.62/34.56    (11)  op(e2, e2) = all_4_2
% 203.62/34.56    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.56    (13)  op(all_10_2, e1) = all_10_1
% 203.62/34.56    (14)   ~ (all_52_7 = all_6_2)
% 203.62/34.56    (15)  op(e0, e0) = all_14_2
% 203.62/34.56    (16)  op(e0, e1) = all_52_23
% 203.62/34.56    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.56    (18)  all_16_2 = all_10_2
% 203.62/34.56    (19)  op(all_6_2, all_6_2) = e3
% 203.62/34.56    (20)  all_58_12 = all_52_7
% 203.62/34.56    (21)   ~ (all_52_7 = all_14_2)
% 203.62/34.56    (22)  all_58_2 = all_52_3
% 203.62/34.56    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.56    (24)   ~ (e2 = e0)
% 203.62/34.56    (25)  op(all_52_3, all_52_3) = e2
% 203.62/34.56    (26)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.56    (27)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.56    (28)  all_58_15 = all_14_2
% 203.62/34.56    (29)   ~ (all_52_5 = all_10_2)
% 203.62/34.56    (30)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.62/34.56    (31)  all_56_12 = all_52_7
% 203.62/34.56    (32)  op(e3, e3) = all_6_2
% 203.62/34.56    (33)   ~ (all_52_15 = all_4_2)
% 203.62/34.56    (34)  all_58_6 = all_52_5
% 203.62/34.56    (35)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.56    (36)  op(e1, e1) = all_10_2
% 203.62/34.56    (37)   ~ (all_52_7 = all_52_23)
% 203.62/34.56    (38)   ~ (all_52_3 = all_4_2)
% 203.62/34.56    (39)   ~ (all_14_2 = e3)
% 203.62/34.56  
% 203.62/34.56  Begin of proof
% 203.62/34.56  | 
% 203.62/34.56  | BETA: splitting (35) gives:
% 203.62/34.56  | 
% 203.62/34.56  | Case 1:
% 203.62/34.56  | | 
% 203.62/34.56  | |   (40)  all_58_12 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | COMBINE_EQS: (20), (40) imply:
% 203.62/34.56  | |   (41)  all_52_7 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | REF_CLOSE: (2), (3), (4), (8), (11), (14), (15), (17), (19), (20), (21),
% 203.62/34.56  | |            (22), (23), (25), (29), (32), (34), (35), (36), (38), (41) are
% 203.62/34.56  | |            inconsistent by sub-proof #1361.
% 203.62/34.56  | | 
% 203.62/34.56  | Case 2:
% 203.62/34.56  | | 
% 203.62/34.56  | |   (42)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.56  | | 
% 203.62/34.56  | | BETA: splitting (42) gives:
% 203.62/34.56  | | 
% 203.62/34.56  | | Case 1:
% 203.62/34.56  | | | 
% 203.62/34.56  | | |   (43)  all_58_13 = e3
% 203.62/34.56  | | | 
% 203.62/34.56  | | | REF_CLOSE: (9), (10), (43) are inconsistent by sub-proof #1360.
% 203.62/34.56  | | | 
% 203.62/34.56  | | Case 2:
% 203.62/34.56  | | | 
% 203.62/34.56  | | |   (44)  all_58_14 = e3 | all_58_15 = e3
% 203.62/34.56  | | | 
% 203.62/34.56  | | | BETA: splitting (44) gives:
% 203.62/34.56  | | | 
% 203.62/34.56  | | | Case 1:
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | |   (45)  all_58_14 = e3
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | COMBINE_EQS: (1), (45) imply:
% 203.62/34.56  | | | |   (46)  all_52_23 = e3
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | SIMP: (46) implies:
% 203.62/34.56  | | | |   (47)  all_52_23 = e3
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | REDUCE: (37), (47) imply:
% 203.62/34.56  | | | |   (48)   ~ (all_52_7 = e3)
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | REDUCE: (16), (47) imply:
% 203.62/34.56  | | | |   (49)  op(e0, e1) = e3
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | BETA: splitting (6) gives:
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | Case 1:
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | |   (50)  all_56_12 = e3
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | | REF_CLOSE: (31), (48), (50) are inconsistent by sub-proof #1383.
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | Case 2:
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | |   (51)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | | BETA: splitting (12) gives:
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | | Case 1:
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | |   (52)  all_58_12 = e2
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | | REF_CLOSE: (2), (3), (5), (9), (11), (20), (24), (27), (33), (45),
% 203.62/34.56  | | | | | |            (52) are inconsistent by sub-proof #702.
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | Case 2:
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | |   (53)   ~ (all_58_12 = e2)
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | | REDUCE: (20), (53) imply:
% 203.62/34.56  | | | | | |   (54)   ~ (all_52_7 = e2)
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | | BETA: splitting (26) gives:
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | | Case 1:
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | |   (55)  all_58_12 = e1
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | | REF_CLOSE: (2), (3), (7), (13), (18), (20), (30), (36), (49), (55)
% 203.62/34.56  | | | | | | |            are inconsistent by sub-proof #651.
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | Case 2:
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | |   (56)   ~ (all_58_12 = e1)
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | | REDUCE: (20), (56) imply:
% 203.62/34.56  | | | | | | |   (57)   ~ (all_52_7 = e1)
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | | REF_CLOSE: (2), (3), (15), (21), (31), (51), (54), (57) are
% 203.62/34.56  | | | | | | |            inconsistent by sub-proof #1176.
% 203.62/34.56  | | | | | | | 
% 203.62/34.56  | | | | | | End of split
% 203.62/34.56  | | | | | | 
% 203.62/34.56  | | | | | End of split
% 203.62/34.56  | | | | | 
% 203.62/34.56  | | | | End of split
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | Case 2:
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | |   (58)  all_58_15 = e3
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | COMBINE_EQS: (28), (58) imply:
% 203.62/34.56  | | | |   (59)  all_14_2 = e3
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | REDUCE: (39), (59) imply:
% 203.62/34.56  | | | |   (60)  $false
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | | CLOSE: (60) is inconsistent.
% 203.62/34.56  | | | | 
% 203.62/34.56  | | | End of split
% 203.62/34.56  | | | 
% 203.62/34.56  | | End of split
% 203.62/34.56  | | 
% 203.62/34.56  | End of split
% 203.62/34.56  | 
% 203.62/34.56  End of proof
% 203.62/34.56  
% 203.62/34.56  Sub-proof #616 shows that the following formulas are inconsistent:
% 203.62/34.56  ----------------------------------------------------------------
% 203.62/34.56    (1)  all_58_14 = all_52_23
% 203.62/34.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.56    (3)   ~ (all_52_5 = all_52_13)
% 203.62/34.56    (4)  op(all_52_7, all_52_7) = e0
% 203.62/34.56    (5)  op(all_52_5, all_52_5) = e1
% 203.62/34.56    (6)   ~ (e3 = e0)
% 203.62/34.56    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.56    (8)   ~ (all_52_3 = all_52_19)
% 203.62/34.56    (9)   ~ (all_52_3 = all_6_2)
% 203.62/34.56    (10)  all_58_0 = all_6_2
% 203.62/34.56    (11)  op(e2, e2) = all_4_2
% 203.62/34.56    (12)   ~ (all_52_3 = all_52_5)
% 203.62/34.56    (13)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.56    (14)  op(all_10_2, e1) = all_10_1
% 203.62/34.56    (15)   ~ (all_52_7 = all_6_2)
% 203.62/34.56    (16)  op(e0, e0) = all_14_2
% 203.62/34.56    (17)  op(e0, e1) = all_52_23
% 203.62/34.56    (18)  all_58_15 = e3
% 203.62/34.56    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.56    (20)  op(e0, e0) = e3
% 203.62/34.56    (21)   ~ (e2 = e1)
% 203.62/34.56    (22)   ~ (all_6_0 = e1)
% 203.62/34.56    (23)  all_58_10 = all_52_27
% 203.62/34.56    (24)  all_56_8 = all_52_5
% 203.62/34.56    (25)   ~ (all_52_19 = all_52_23)
% 203.62/34.56    (26)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.56    (27)  op(all_6_2, all_6_2) = e3
% 203.62/34.56    (28)   ~ (all_52_5 = all_52_7)
% 203.62/34.56    (29)  all_58_12 = all_52_7
% 203.62/34.56    (30)   ~ (all_52_7 = e3)
% 203.62/34.56    (31)   ~ (all_52_7 = all_14_2)
% 203.62/34.56    (32)  all_58_2 = all_52_3
% 203.62/34.56    (33)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.56    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.56    (35)  op(e3, all_6_1) = all_6_0
% 203.62/34.56    (36)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.56    (37)   ~ (e2 = e0)
% 203.62/34.56    (38)  op(all_52_3, all_52_3) = e2
% 203.62/34.56    (39)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.56    (40)  all_56_6 = all_52_19
% 203.62/34.56    (41)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.56    (42)   ~ (all_52_27 = e3)
% 203.62/34.56    (43)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.56    (44)  op(e1, e2) = all_52_13
% 203.62/34.56    (45)   ~ (all_52_19 = all_10_2)
% 203.62/34.56    (46)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.56    (47)  all_58_8 = all_10_2
% 203.62/34.56    (48)   ~ (all_52_5 = all_10_2)
% 203.62/34.56    (49)  all_56_12 = all_52_7
% 203.62/34.56    (50)   ~ (all_52_5 = all_6_2)
% 203.62/34.56    (51)  op(e1, all_10_1) = e2
% 203.62/34.56    (52)  op(e3, e3) = all_6_2
% 203.62/34.56    (53)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.56    (54)  all_58_5 = all_52_19
% 203.62/34.56    (55)  all_58_6 = all_52_5
% 203.62/34.56    (56)   ~ (all_52_17 = all_6_2)
% 203.62/34.56    (57)   ~ (e1 = e0)
% 203.62/34.56    (58)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.62/34.56    (59)   ~ (e3 = e2)
% 203.62/34.56    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.56    (61)  op(e1, e1) = all_10_2
% 203.62/34.57    (62)   ~ (all_52_23 = all_10_2)
% 203.62/34.57    (63)  all_58_3 = all_4_2
% 203.62/34.57    (64)   ~ (all_52_3 = all_4_2)
% 203.62/34.57    (65)  op(all_6_2, e3) = all_6_1
% 203.62/34.57    (66)  all_58_4 = all_52_17
% 203.62/34.57  
% 203.62/34.57  Begin of proof
% 203.62/34.57  | 
% 203.62/34.57  | BETA: splitting (7) gives:
% 203.62/34.57  | 
% 203.62/34.57  | Case 1:
% 203.62/34.57  | | 
% 203.62/34.57  | |   (67)  all_56_12 = e3
% 203.62/34.57  | | 
% 203.62/34.57  | | COMBINE_EQS: (49), (67) imply:
% 203.62/34.57  | |   (68)  all_52_7 = e3
% 203.62/34.57  | | 
% 203.62/34.57  | | REDUCE: (30), (68) imply:
% 203.62/34.57  | |   (69)  $false
% 203.62/34.57  | | 
% 203.62/34.57  | | CLOSE: (69) is inconsistent.
% 203.62/34.57  | | 
% 203.62/34.57  | Case 2:
% 203.62/34.57  | | 
% 203.62/34.57  | |   (70)   ~ (all_56_12 = e3)
% 203.62/34.57  | |   (71)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.57  | | 
% 203.62/34.57  | | BETA: splitting (39) gives:
% 203.62/34.57  | | 
% 203.62/34.57  | | Case 1:
% 203.62/34.57  | | | 
% 203.62/34.57  | | |   (72)  all_58_12 = e1
% 203.62/34.57  | | | 
% 203.62/34.57  | | | COMBINE_EQS: (29), (72) imply:
% 203.62/34.57  | | |   (73)  all_52_7 = e1
% 203.62/34.57  | | | 
% 203.62/34.57  | | | SIMP: (73) implies:
% 203.62/34.57  | | |   (74)  all_52_7 = e1
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (28), (74) imply:
% 203.62/34.57  | | |   (75)   ~ (all_52_5 = e1)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (15), (74) imply:
% 203.62/34.57  | | |   (76)   ~ (all_6_2 = e1)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | SIMP: (76) implies:
% 203.62/34.57  | | |   (77)   ~ (all_6_2 = e1)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (4), (74) imply:
% 203.62/34.57  | | |   (78)  op(e1, e1) = e0
% 203.62/34.57  | | | 
% 203.62/34.57  | | | GROUND_INST: instantiating (2) with all_10_2, e0, e1, e1, simplifying with
% 203.62/34.57  | | |              (61), (78) gives:
% 203.62/34.57  | | |   (79)  all_10_2 = e0
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (48), (79) imply:
% 203.62/34.57  | | |   (80)   ~ (all_52_5 = e0)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (62), (79) imply:
% 203.62/34.57  | | |   (81)   ~ (all_52_23 = e0)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (14), (79) imply:
% 203.62/34.57  | | |   (82)  op(e0, e1) = all_10_1
% 203.62/34.57  | | | 
% 203.62/34.57  | | | BETA: splitting (43) gives:
% 203.62/34.57  | | | 
% 203.62/34.57  | | | Case 1:
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | |   (83)  all_58_12 = e0
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | | REF_CLOSE: (57), (72), (83) are inconsistent by sub-proof #1173.
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | Case 2:
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | |   (84)  all_58_13 = e0 | all_58_14 = e0
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | | BETA: splitting (84) gives:
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | | Case 1:
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | |   (85)  all_58_13 = e0
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | | BETA: splitting (13) gives:
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | | Case 1:
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | |   (86)  all_58_12 = e2
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | | COMBINE_EQS: (72), (86) imply:
% 203.62/34.57  | | | | | |   (87)  e2 = e1
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | | REDUCE: (21), (87) imply:
% 203.62/34.57  | | | | | |   (88)  $false
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | | CLOSE: (88) is inconsistent.
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | Case 2:
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | |   (89)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | | BETA: splitting (89) gives:
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | | Case 1:
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | |   (90)  all_58_13 = e2
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | | COMBINE_EQS: (85), (90) imply:
% 203.62/34.57  | | | | | | |   (91)  e2 = e0
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | | REDUCE: (37), (91) imply:
% 203.62/34.57  | | | | | | |   (92)  $false
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | | CLOSE: (92) is inconsistent.
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | Case 2:
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | |   (93)  all_58_14 = e2 | all_58_15 = e2
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | | BETA: splitting (93) gives:
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | | Case 1:
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | |   (94)  all_58_14 = e2
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | COMBINE_EQS: (1), (94) imply:
% 203.62/34.57  | | | | | | | |   (95)  all_52_23 = e2
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | SIMP: (95) implies:
% 203.62/34.57  | | | | | | | |   (96)  all_52_23 = e2
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | REDUCE: (17), (96) imply:
% 203.62/34.57  | | | | | | | |   (97)  op(e0, e1) = e2
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | REF_CLOSE: (2), (3), (5), (24), (44), (46), (51), (52), (75),
% 203.62/34.57  | | | | | | | |            (77), (80), (82), (97) are inconsistent by sub-proof
% 203.62/34.57  | | | | | | | |            #654.
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | Case 2:
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | |   (98)  all_58_15 = e2
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | COMBINE_EQS: (18), (98) imply:
% 203.62/34.57  | | | | | | | |   (99)  e3 = e2
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | REDUCE: (59), (99) imply:
% 203.62/34.57  | | | | | | | |   (100)  $false
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | | CLOSE: (100) is inconsistent.
% 203.62/34.57  | | | | | | | | 
% 203.62/34.57  | | | | | | | End of split
% 203.62/34.57  | | | | | | | 
% 203.62/34.57  | | | | | | End of split
% 203.62/34.57  | | | | | | 
% 203.62/34.57  | | | | | End of split
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | Case 2:
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | |   (101)  all_58_14 = e0
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | | REF_CLOSE: (1), (81), (101) are inconsistent by sub-proof #1019.
% 203.62/34.57  | | | | | 
% 203.62/34.57  | | | | End of split
% 203.62/34.57  | | | | 
% 203.62/34.57  | | | End of split
% 203.62/34.57  | | | 
% 203.62/34.57  | | Case 2:
% 203.62/34.57  | | | 
% 203.62/34.57  | | |   (102)   ~ (all_58_12 = e1)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REDUCE: (29), (102) imply:
% 203.62/34.57  | | |   (103)   ~ (all_52_7 = e1)
% 203.62/34.57  | | | 
% 203.62/34.57  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 203.62/34.57  | | |            (16), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 203.62/34.57  | | |            (29), (30), (31), (32), (33), (34), (35), (36), (38), (40),
% 203.62/34.57  | | |            (41), (42), (45), (46), (47), (48), (49), (50), (52), (53),
% 203.62/34.57  | | |            (54), (55), (56), (58), (60), (61), (63), (64), (65), (66),
% 203.62/34.57  | | |            (71), (103) are inconsistent by sub-proof #691.
% 203.62/34.57  | | | 
% 203.62/34.57  | | End of split
% 203.62/34.57  | | 
% 203.62/34.57  | End of split
% 203.62/34.57  | 
% 203.62/34.57  End of proof
% 203.62/34.57  
% 203.62/34.57  Sub-proof #617 shows that the following formulas are inconsistent:
% 203.62/34.57  ----------------------------------------------------------------
% 203.62/34.57    (1)   ~ (all_52_15 = all_52_23)
% 203.62/34.57    (2)   ~ (all_52_25 = all_52_27)
% 203.62/34.57    (3)  all_58_14 = all_52_23
% 203.62/34.57    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.57    (6)   ~ (all_52_5 = all_52_13)
% 203.62/34.57    (7)  all_58_1 = all_52_9
% 203.62/34.57    (8)   ~ (all_52_9 = all_52_13)
% 203.62/34.57    (9)   ~ (e3 = e0)
% 203.62/34.57    (10)  op(e2, e3) = all_52_3
% 203.62/34.57    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.57    (12)   ~ (all_52_3 = all_52_19)
% 203.62/34.57    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.57    (14)   ~ (all_52_17 = all_52_25)
% 203.62/34.57    (15)   ~ (all_52_3 = all_6_2)
% 203.62/34.57    (16)  all_58_0 = all_6_2
% 203.62/34.57    (17)  op(all_14_2, e0) = all_14_1
% 203.62/34.57    (18)  all_56_4 = all_52_3
% 203.62/34.57    (19)   ~ (all_52_17 = all_10_2)
% 203.62/34.57    (20)  all_26_1 = all_10_1
% 203.62/34.57    (21)  op(e3, e0) = all_52_25
% 203.62/34.57    (22)  all_26_2 = all_10_2
% 203.62/34.57    (23)  op(e0, all_14_1) = all_14_0
% 203.62/34.57    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.57    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.62/34.57    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.57    (27)   ~ (all_52_27 = all_52_29)
% 203.62/34.57    (28)  all_58_13 = all_52_15
% 203.62/34.57    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.57    (30)  all_58_9 = all_52_25
% 203.62/34.57    (31)   ~ (all_6_1 = e1)
% 203.62/34.57    (32)   ~ (all_52_29 = all_14_2)
% 203.62/34.57    (33)  all_22_0 = all_6_0
% 203.62/34.57    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.62/34.57    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.57    (36)  op(e1, e3) = all_52_5
% 203.62/34.57    (37)  op(e2, e2) = all_4_2
% 203.62/34.57    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.57    (39)   ~ (all_52_3 = all_52_5)
% 203.62/34.57    (40)  all_58_11 = all_52_29
% 203.62/34.57    (41)  all_56_5 = all_4_2
% 203.62/34.57    (42)   ~ (all_52_25 = all_14_2)
% 203.62/34.57    (43)   ~ (all_52_9 = all_52_15)
% 203.62/34.57    (44)   ~ (all_52_3 = all_52_27)
% 203.62/34.57    (45)  op(all_10_2, e1) = all_10_1
% 203.62/34.57    (46)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.57    (47)   ~ (all_52_7 = all_6_2)
% 203.62/34.57    (48)  op(e0, e0) = all_14_2
% 203.62/34.57    (49)  all_56_15 = all_14_2
% 203.62/34.57    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.57    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.62/34.57    (52)  all_56_11 = all_52_29
% 203.62/34.57    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.62/34.57    (54)   ~ (all_52_13 = all_10_2)
% 203.62/34.57    (55)   ~ (all_6_0 = e1)
% 203.62/34.57    (56)  all_58_10 = all_52_27
% 203.62/34.57    (57)  all_24_0 = all_14_0
% 203.62/34.57    (58)  all_56_8 = all_52_5
% 203.62/34.57    (59)  op(all_52_9, all_52_9) = all_52_8
% 203.62/34.57    (60)   ~ (all_52_19 = all_52_23)
% 203.62/34.57    (61)   ~ (all_52_25 = all_52_29)
% 203.62/34.57    (62)   ~ (all_52_29 = all_10_2)
% 203.62/34.57    (63)  all_58_7 = all_52_13
% 203.62/34.57    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.62/34.57    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.57    (66)   ~ (all_52_5 = all_52_7)
% 203.62/34.57    (67)  all_58_12 = all_52_7
% 203.62/34.57    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.57    (69)   ~ (all_52_7 = all_14_2)
% 203.62/34.57    (70)  all_58_2 = all_52_3
% 203.62/34.57    (71)  all_56_2 = all_52_17
% 203.62/34.57    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.57    (73)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.57    (74)  op(e3, all_6_1) = all_6_0
% 203.62/34.57    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.62/34.57    (76)   ~ (all_14_0 = e3)
% 203.62/34.57    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.57    (78)  all_56_7 = all_52_27
% 203.62/34.57    (79)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.62/34.57    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.57    (81)   ~ (e2 = e0)
% 203.62/34.57    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.57    (83)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.62/34.57    (84)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 203.62/34.57    (85)   ~ (all_52_5 = all_52_29)
% 203.62/34.57    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.57    (87)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.62/34.57    (88)   ~ (all_52_15 = all_14_2)
% 203.62/34.57    (89)   ~ (all_52_19 = all_52_27)
% 203.62/34.57    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.57    (91)   ~ (all_6_0 = e2)
% 203.62/34.57    (92)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.62/34.57            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.62/34.57    (93)  op(e3, e1) = all_52_17
% 203.62/34.57    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.62/34.57    (95)  op(e0, e3) = all_52_7
% 203.62/34.57    (96)  op(e1, e2) = all_52_13
% 203.62/34.57    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.57    (98)   ~ (all_52_9 = all_52_25)
% 203.62/34.57    (99)  all_58_15 = all_14_2
% 203.62/34.57    (100)   ~ (all_52_19 = all_10_2)
% 203.62/34.57    (101)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.57    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.57    (103)  all_58_8 = all_10_2
% 203.62/34.57    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.57    (105)   ~ (all_52_5 = all_10_2)
% 203.62/34.57    (106)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.57    (107)   ~ (all_52_23 = all_14_2)
% 203.62/34.57    (108)  all_56_12 = all_52_7
% 203.62/34.57    (109)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.57    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.62/34.57    (111)   ~ (all_52_25 = all_6_2)
% 203.62/34.57    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.57    (113)   ~ (all_52_9 = all_4_2)
% 203.62/34.57    (114)   ~ (all_52_5 = all_6_2)
% 203.62/34.57    (115)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.57    (116)   ~ (all_52_9 = all_6_2)
% 203.62/34.57    (117)  op(e1, all_10_1) = e2
% 203.62/34.57    (118)  all_56_0 = all_6_2
% 203.62/34.57    (119)  op(e3, e3) = all_6_2
% 203.62/34.57    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.57    (121)   ~ (all_52_27 = all_14_2)
% 203.62/34.57    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.57    (123)  all_56_14 = all_52_23
% 203.62/34.57    (124)  all_56_3 = all_52_25
% 203.62/34.57    (125)   ~ (all_52_3 = all_52_7)
% 203.62/34.57    (126)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.57    (127)  all_58_5 = all_52_19
% 203.62/34.57    (128)  all_56_1 = all_52_9
% 203.62/34.57    (129)   ~ (all_52_15 = all_4_2)
% 203.62/34.57    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.62/34.57           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.62/34.57           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.62/34.57           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.62/34.57    (131)   ~ (all_52_27 = all_4_2)
% 203.62/34.57    (132)  all_58_6 = all_52_5
% 203.62/34.57    (133)  op(e3, e2) = all_52_9
% 203.62/34.57    (134)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.57    (135)   ~ (all_52_17 = all_6_2)
% 203.62/34.57    (136)   ~ (e1 = e0)
% 203.62/34.57    (137)   ~ (e3 = e2)
% 203.62/34.57    (138)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.57    (139)  all_26_0 = e2
% 203.62/34.57    (140)   ~ (all_52_9 = all_52_17)
% 203.62/34.57    (141)  all_56_10 = all_10_2
% 203.62/34.57    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.57    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.62/34.57    (144)  op(all_52_13, all_52_13) = all_52_12
% 203.62/34.57    (145)  all_6_1 = e2
% 203.62/34.57    (146)  op(e1, e1) = all_10_2
% 203.62/34.57    (147)   ~ (all_52_23 = all_10_2)
% 203.62/34.57    (148)   ~ (all_52_7 = all_52_23)
% 203.62/34.57    (149)   ~ (all_52_17 = all_52_19)
% 203.62/34.57    (150)  all_58_3 = all_4_2
% 203.62/34.57    (151)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.62/34.57    (152)   ~ (all_52_3 = all_4_2)
% 203.62/34.57    (153)   ~ (all_52_19 = all_4_2)
% 203.62/34.57    (154)   ~ (all_52_17 = all_52_23)
% 203.62/34.57    (155)  op(all_6_2, e3) = all_6_1
% 203.62/34.57    (156)   ~ (all_52_13 = all_52_29)
% 203.62/34.57    (157)  all_22_2 = all_6_2
% 203.62/34.57    (158)  all_58_4 = all_52_17
% 203.62/34.57    (159)   ~ (all_14_0 = e2)
% 203.62/34.57    (160)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.57    (161)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.57  
% 203.62/34.57  Begin of proof
% 203.62/34.57  | 
% 203.62/34.57  | REDUCE: (31), (145) imply:
% 203.62/34.57  |   (162)   ~ (e2 = e1)
% 203.62/34.57  | 
% 203.62/34.57  | REDUCE: (145), (155) imply:
% 203.62/34.57  |   (163)  op(all_6_2, e3) = e2
% 203.62/34.57  | 
% 203.62/34.57  | REDUCE: (74), (145) imply:
% 203.62/34.57  |   (164)  op(e3, e2) = all_6_0
% 203.62/34.57  | 
% 203.62/34.57  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.62/34.57  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.62/34.57  |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 203.62/34.57  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 203.62/34.57  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.62/34.57  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.62/34.57  |            (69), (70), (71), (72), (73), (75), (76), (77), (78), (79), (80),
% 203.62/34.57  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 203.62/34.57  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.62/34.57  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.62/34.57  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 203.62/34.57  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 203.62/34.57  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 203.62/34.57  |            (138), (139), (140), (141), (142), (143), (144), (146), (147),
% 203.62/34.57  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 203.62/34.57  |            (157), (158), (159), (160), (161), (162), (163), (164) are
% 203.62/34.57  |            inconsistent by sub-proof #628.
% 203.62/34.57  | 
% 203.62/34.57  End of proof
% 203.62/34.57  
% 203.62/34.57  Sub-proof #618 shows that the following formulas are inconsistent:
% 203.62/34.57  ----------------------------------------------------------------
% 203.62/34.57    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.62/34.57    (2)   ~ (all_52_15 = all_52_23)
% 203.62/34.57    (3)   ~ (all_52_25 = all_52_27)
% 203.62/34.57    (4)  all_58_14 = all_52_23
% 203.62/34.57    (5)   ~ (e3 = e1)
% 203.62/34.57    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.62/34.57    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.62/34.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.62/34.57    (8)   ~ (all_52_5 = all_52_13)
% 203.62/34.57    (9)  all_58_1 = all_52_9
% 203.62/34.57    (10)   ~ (all_52_9 = all_52_13)
% 203.62/34.57    (11)   ~ (e3 = e0)
% 203.62/34.57    (12)  op(e2, e3) = all_52_3
% 203.62/34.57    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.62/34.57    (14)   ~ (all_52_7 = all_52_15)
% 203.62/34.57    (15)  op(all_52_15, all_52_15) = e0
% 203.62/34.57    (16)  op(all_52_7, all_52_7) = all_52_6
% 203.62/34.57    (17)   ~ (all_52_17 = all_52_25)
% 203.62/34.57    (18)   ~ (all_52_3 = all_6_2)
% 203.62/34.57    (19)  all_58_0 = all_6_2
% 203.62/34.57    (20)  op(all_14_2, e0) = all_14_1
% 203.62/34.57    (21)  all_56_4 = all_52_3
% 203.62/34.57    (22)   ~ (all_52_17 = all_10_2)
% 203.62/34.57    (23)  op(e3, e0) = all_52_25
% 203.62/34.57    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.62/34.57    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.62/34.57    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.62/34.57    (27)   ~ (all_52_27 = all_52_29)
% 203.62/34.57    (28)  all_58_13 = all_52_15
% 203.62/34.57    (29)  op(all_52_13, all_52_13) = e1
% 203.62/34.57    (30)  op(e0, all_14_1) = e1
% 203.62/34.57    (31)  op(all_10_2, all_10_2) = all_52_20
% 203.62/34.57    (32)  all_58_9 = all_52_25
% 203.62/34.57    (33)   ~ (all_6_1 = e1)
% 203.62/34.57    (34)   ~ (all_52_29 = all_14_2)
% 203.62/34.57    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.62/34.57    (36)  op(e1, e3) = all_52_5
% 203.62/34.57    (37)  op(e2, e2) = all_4_2
% 203.62/34.57    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.62/34.57    (39)   ~ (all_52_3 = all_52_5)
% 203.62/34.57    (40)  all_58_11 = all_52_29
% 203.62/34.57    (41)  all_56_5 = all_4_2
% 203.62/34.57    (42)   ~ (all_52_25 = all_14_2)
% 203.62/34.57    (43)   ~ (all_52_3 = all_52_27)
% 203.62/34.57    (44)  op(all_6_2, all_6_2) = all_52_0
% 203.62/34.57    (45)   ~ (all_52_7 = all_6_2)
% 203.62/34.57    (46)  op(e0, e0) = all_14_2
% 203.62/34.57    (47)  all_56_15 = all_14_2
% 203.62/34.57    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.62/34.57    (49)  all_56_11 = all_52_29
% 203.62/34.57    (50)   ~ (all_4_1 = e1)
% 203.62/34.57    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.62/34.57    (52)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.62/34.57    (53)  all_56_9 = all_52_13
% 203.62/34.57    (54)   ~ (e2 = e1)
% 203.62/34.57    (55)   ~ (all_52_13 = all_10_2)
% 203.62/34.57    (56)   ~ (all_6_0 = e1)
% 203.62/34.57    (57)  all_58_10 = all_52_27
% 203.62/34.57    (58)  all_56_8 = all_52_5
% 203.62/34.57    (59)   ~ (all_52_19 = all_52_23)
% 203.62/34.57    (60)   ~ (all_52_25 = all_52_29)
% 203.62/34.57    (61)   ~ (all_52_29 = all_10_2)
% 203.62/34.57    (62)  all_58_7 = all_52_13
% 203.62/34.57    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.62/34.57    (64)   ~ (all_52_5 = all_52_7)
% 203.62/34.57    (65)  all_58_12 = all_52_7
% 203.62/34.57    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.62/34.57    (67)   ~ (all_52_7 = all_14_2)
% 203.62/34.57    (68)   ~ (all_14_2 = e0)
% 203.62/34.57    (69)  all_58_2 = all_52_3
% 203.62/34.57    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.62/34.57    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.62/34.57    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.62/34.57    (73)  op(e3, all_6_1) = all_6_0
% 203.62/34.57    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.62/34.57    (75)  all_56_7 = all_52_27
% 203.62/34.57    (76)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.57    (77)   ~ (e2 = e0)
% 203.62/34.57    (78)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.62/34.57    (79)  op(all_4_2, e2) = all_4_1
% 203.62/34.57    (80)   ~ (all_52_5 = all_52_29)
% 203.62/34.57    (81)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.62/34.57    (82)  all_56_6 = all_52_19
% 203.62/34.57    (83)   ~ (all_52_15 = all_14_2)
% 203.62/34.57    (84)   ~ (all_52_19 = all_52_27)
% 203.62/34.57    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.62/34.57    (86)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.57    (87)   ~ (all_6_0 = e2)
% 203.62/34.57    (88)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.62/34.57    (89)   ~ (all_52_13 = all_4_2)
% 203.62/34.57    (90)  op(e0, e3) = all_52_7
% 203.62/34.57    (91)  op(e1, e2) = all_52_13
% 203.62/34.57    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.57    (93)   ~ (all_52_9 = all_52_25)
% 203.62/34.57    (94)  all_58_15 = all_14_2
% 203.62/34.57    (95)   ~ (all_52_19 = all_10_2)
% 203.62/34.57    (96)  op(all_52_23, all_52_23) = all_52_22
% 203.62/34.57    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.57    (98)  all_58_8 = all_10_2
% 203.62/34.57    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.62/34.57    (100)   ~ (all_52_5 = all_10_2)
% 203.62/34.57    (101)  op(all_52_29, all_52_29) = all_52_28
% 203.62/34.57    (102)   ~ (all_52_23 = all_14_2)
% 203.62/34.57    (103)  all_56_12 = all_52_7
% 203.62/34.57    (104)  op(all_52_17, all_52_17) = all_52_16
% 203.62/34.57    (105)   ~ (all_52_25 = all_6_2)
% 203.62/34.57    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.62/34.57    (107)   ~ (all_52_9 = all_4_2)
% 203.62/34.57    (108)   ~ (all_52_5 = all_6_2)
% 203.62/34.57    (109)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.62/34.57    (110)  op(all_4_2, all_4_2) = e2
% 203.62/34.57    (111)   ~ (all_52_9 = all_6_2)
% 203.62/34.57    (112)   ~ (all_52_13 = all_52_15)
% 203.62/34.57    (113)  op(e3, e3) = all_6_2
% 203.62/34.57    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.62/34.57    (115)   ~ (all_52_27 = all_14_2)
% 203.62/34.57    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.57    (117)  all_56_3 = all_52_25
% 203.62/34.57    (118)   ~ (all_52_3 = all_52_7)
% 203.62/34.57    (119)  op(all_14_2, all_14_2) = all_52_30
% 203.62/34.57    (120)  all_58_5 = all_52_19
% 203.62/34.57    (121)  all_56_1 = all_52_9
% 203.62/34.57    (122)   ~ (all_52_15 = all_4_2)
% 203.62/34.57    (123)   ~ (all_52_27 = all_4_2)
% 203.62/34.57    (124)  all_58_6 = all_52_5
% 203.62/34.57    (125)  op(e3, e2) = all_52_9
% 203.62/34.58    (126)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.62/34.58    (127)   ~ (all_52_17 = all_6_2)
% 203.62/34.58    (128)   ~ (e1 = e0)
% 203.62/34.58    (129)  op(e2, e0) = all_52_27
% 203.62/34.58    (130)   ~ (e3 = e2)
% 203.62/34.58    (131)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.62/34.58    (132)   ~ (all_52_9 = all_52_17)
% 203.62/34.58    (133)  all_56_10 = all_10_2
% 203.62/34.58    (134)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.62/34.58    (135)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.62/34.58    (136)   ~ (all_6_1 = e2)
% 203.62/34.58    (137)  op(e1, e1) = all_10_2
% 203.62/34.58    (138)  op(all_52_9, all_52_9) = e3
% 203.62/34.58    (139)   ~ (all_52_23 = all_10_2)
% 203.62/34.58    (140)   ~ (all_52_7 = all_52_23)
% 203.62/34.58    (141)   ~ (all_52_17 = all_52_19)
% 203.62/34.58    (142)  all_58_3 = all_4_2
% 203.62/34.58    (143)  all_56_13 = all_52_15
% 203.62/34.58    (144)   ~ (all_52_3 = all_4_2)
% 203.62/34.58    (145)   ~ (all_52_19 = all_4_2)
% 203.62/34.58    (146)   ~ (all_52_17 = all_52_23)
% 203.62/34.58    (147)  op(all_6_2, e3) = all_6_1
% 203.62/34.58    (148)   ~ (all_52_13 = all_52_29)
% 203.62/34.58    (149)  all_58_4 = all_52_17
% 203.62/34.58    (150)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.62/34.58    (151)  op(all_52_25, all_52_25) = all_52_24
% 203.62/34.58  
% 203.62/34.58  Begin of proof
% 203.62/34.58  | 
% 203.62/34.58  | BETA: splitting (99) gives:
% 203.62/34.58  | 
% 203.62/34.58  | Case 1:
% 203.62/34.58  | | 
% 203.62/34.58  | |   (152)  all_56_15 = e3
% 203.62/34.58  | | 
% 203.62/34.58  | | COMBINE_EQS: (47), (152) imply:
% 203.62/34.58  | |   (153)  all_14_2 = e3
% 203.62/34.58  | | 
% 203.62/34.58  | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (14), (16), (18), (19),
% 203.62/34.58  | |            (20), (21), (23), (24), (28), (29), (31), (32), (33), (34), (36),
% 203.62/34.58  | |            (37), (38), (39), (40), (42), (44), (45), (48), (50), (52), (54),
% 203.62/34.58  | |            (55), (56), (57), (62), (65), (66), (67), (68), (69), (71), (72),
% 203.62/34.58  | |            (73), (74), (76), (77), (79), (81), (83), (86), (87), (92), (93),
% 203.62/34.58  | |            (98), (104), (105), (106), (108), (110), (111), (113), (115),
% 203.62/34.58  | |            (116), (117), (118), (119), (120), (121), (124), (125), (127),
% 203.62/34.58  | |            (128), (130), (131), (132), (133), (134), (136), (137), (138),
% 203.62/34.58  | |            (141), (142), (144), (147), (149), (150), (153) are inconsistent
% 203.62/34.58  | |            by sub-proof #1117.
% 203.62/34.58  | | 
% 203.62/34.58  | Case 2:
% 203.62/34.58  | | 
% 203.62/34.58  | |   (154)   ~ (all_56_15 = e3)
% 203.62/34.58  | | 
% 203.62/34.58  | | REDUCE: (47), (154) imply:
% 203.62/34.58  | |   (155)   ~ (all_14_2 = e3)
% 203.62/34.58  | | 
% 203.62/34.58  | | BETA: splitting (51) gives:
% 203.62/34.58  | | 
% 203.62/34.58  | | Case 1:
% 203.62/34.58  | | | 
% 203.62/34.58  | | |   (156)  all_56_13 = e3
% 203.62/34.58  | | | 
% 203.62/34.58  | | | REF_CLOSE: (7), (13), (14), (15), (33), (45), (90), (103), (113), (136),
% 203.62/34.58  | | |            (143), (147), (156) are inconsistent by sub-proof #893.
% 203.62/34.58  | | | 
% 203.62/34.58  | | Case 2:
% 203.62/34.58  | | | 
% 203.62/34.58  | | |   (157)   ~ (all_56_13 = e3)
% 203.62/34.58  | | | 
% 203.62/34.58  | | | REDUCE: (143), (157) imply:
% 203.62/34.58  | | |   (158)   ~ (all_52_15 = e3)
% 203.62/34.58  | | | 
% 203.62/34.58  | | | BETA: splitting (126) gives:
% 203.62/34.58  | | | 
% 203.62/34.58  | | | Case 1:
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | |   (159)  all_58_12 = e3
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | COMBINE_EQS: (65), (159) imply:
% 203.62/34.58  | | | |   (160)  all_52_7 = e3
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | SIMP: (160) implies:
% 203.62/34.58  | | | |   (161)  all_52_7 = e3
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (118), (161) imply:
% 203.62/34.58  | | | |   (162)   ~ (all_52_3 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (64), (161) imply:
% 203.62/34.58  | | | |   (163)   ~ (all_52_5 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (14), (161) imply:
% 203.62/34.58  | | | |   (164)   ~ (all_52_15 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (140), (161) imply:
% 203.62/34.58  | | | |   (165)   ~ (all_52_23 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | SIMP: (165) implies:
% 203.62/34.58  | | | |   (166)   ~ (all_52_23 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (67), (161) imply:
% 203.62/34.58  | | | |   (167)   ~ (all_14_2 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (45), (161) imply:
% 203.62/34.58  | | | |   (168)   ~ (all_6_2 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | SIMP: (168) implies:
% 203.62/34.58  | | | |   (169)   ~ (all_6_2 = e3)
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | REDUCE: (16), (161) imply:
% 203.62/34.58  | | | |   (170)  op(e3, e3) = all_52_6
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 203.62/34.58  | | | |              simplifying with (113), (170) gives:
% 203.62/34.58  | | | |   (171)  all_52_6 = all_6_2
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | BETA: splitting (76) gives:
% 203.62/34.58  | | | | 
% 203.62/34.58  | | | | Case 1:
% 203.62/34.58  | | | | | 
% 203.62/34.58  | | | | |   (172)  all_56_4 = e3
% 203.62/34.58  | | | | | 
% 203.62/34.58  | | | | | REF_CLOSE: (21), (162), (172) are inconsistent by sub-proof #1340.
% 203.62/34.58  | | | | | 
% 203.62/34.58  | | | | Case 2:
% 203.62/34.58  | | | | | 
% 203.62/34.58  | | | | |   (173)   ~ (all_56_4 = e3)
% 203.62/34.58  | | | | |   (174)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.62/34.58  | | | | | 
% 203.62/34.58  | | | | | BETA: splitting (97) gives:
% 203.62/34.58  | | | | | 
% 203.62/34.58  | | | | | Case 1:
% 203.62/34.58  | | | | | | 
% 203.62/34.58  | | | | | |   (175)  all_56_8 = e3
% 203.62/34.58  | | | | | | 
% 203.62/34.58  | | | | | | REF_CLOSE: (58), (163), (175) are inconsistent by sub-proof #1325.
% 203.62/34.58  | | | | | | 
% 203.62/34.58  | | | | | Case 2:
% 203.62/34.58  | | | | | | 
% 203.62/34.58  | | | | | |   (176)   ~ (all_56_8 = e3)
% 203.62/34.58  | | | | | |   (177)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.62/34.58  | | | | | | 
% 203.62/34.58  | | | | | | BETA: splitting (70) gives:
% 203.62/34.58  | | | | | | 
% 203.62/34.58  | | | | | | Case 1:
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | |   (178)  all_56_6 = e3
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | COMBINE_EQS: (82), (178) imply:
% 203.62/34.58  | | | | | | |   (179)  all_52_19 = e3
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | SIMP: (179) implies:
% 203.62/34.58  | | | | | | |   (180)  all_52_19 = e3
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | REDUCE: (84), (180) imply:
% 203.62/34.58  | | | | | | |   (181)   ~ (all_52_27 = e3)
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | SIMP: (181) implies:
% 203.62/34.58  | | | | | | |   (182)   ~ (all_52_27 = e3)
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | REDUCE: (145), (180) imply:
% 203.62/34.58  | | | | | | |   (183)   ~ (all_4_2 = e3)
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | SIMP: (183) implies:
% 203.62/34.58  | | | | | | |   (184)   ~ (all_4_2 = e3)
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | REDUCE: (26), (180) imply:
% 203.62/34.58  | | | | | | |   (185)  op(e3, e3) = all_52_18
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_18, e3, e3,
% 203.62/34.58  | | | | | | |              simplifying with (113), (185) gives:
% 203.62/34.58  | | | | | | |   (186)  all_52_18 = all_6_2
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | BETA: splitting (92) gives:
% 203.62/34.58  | | | | | | | 
% 203.62/34.58  | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | |   (187)  all_58_1 = e3
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | | COMBINE_EQS: (9), (187) imply:
% 203.62/34.58  | | | | | | | |   (188)  all_52_9 = e3
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | | REF_CLOSE: (7), (111), (113), (138), (188) are inconsistent by
% 203.62/34.58  | | | | | | | |            sub-proof #1337.
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | Case 2:
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | |   (189)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | | BETA: splitting (189) gives:
% 203.62/34.58  | | | | | | | | 
% 203.62/34.58  | | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | |   (190)  all_58_3 = e3
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | COMBINE_EQS: (142), (190) imply:
% 203.62/34.58  | | | | | | | | |   (191)  all_4_2 = e3
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | REDUCE: (184), (191) imply:
% 203.62/34.58  | | | | | | | | |   (192)  $false
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | CLOSE: (192) is inconsistent.
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | Case 2:
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | |   (193)  all_58_7 = e3 | all_58_13 = e3
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | BETA: splitting (116) gives:
% 203.62/34.58  | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | |   (194)  all_58_0 = e3
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | COMBINE_EQS: (19), (194) imply:
% 203.62/34.58  | | | | | | | | | |   (195)  all_6_2 = e3
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | REDUCE: (169), (195) imply:
% 203.62/34.58  | | | | | | | | | |   (196)  $false
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | CLOSE: (196) is inconsistent.
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | Case 2:
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | |   (197)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | BETA: splitting (193) gives:
% 203.62/34.58  | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | |   (198)  all_58_7 = e3
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | COMBINE_EQS: (62), (198) imply:
% 203.62/34.58  | | | | | | | | | | |   (199)  all_52_13 = e3
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | REDUCE: (55), (199) imply:
% 203.62/34.58  | | | | | | | | | | |   (200)   ~ (all_10_2 = e3)
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | SIMP: (200) implies:
% 203.62/34.58  | | | | | | | | | | |   (201)   ~ (all_10_2 = e3)
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | REDUCE: (29), (199) imply:
% 203.62/34.58  | | | | | | | | | | |   (202)  op(e3, e3) = e1
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | BETA: splitting (114) gives:
% 203.62/34.58  | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | |   (203)  all_58_9 = e3
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | COMBINE_EQS: (32), (203) imply:
% 203.62/34.58  | | | | | | | | | | | |   (204)  all_52_25 = e3
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | SIMP: (204) implies:
% 203.62/34.58  | | | | | | | | | | | |   (205)  all_52_25 = e3
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (60), (205) imply:
% 203.62/34.58  | | | | | | | | | | | |   (206)   ~ (all_52_29 = e3)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | SIMP: (206) implies:
% 203.62/34.58  | | | | | | | | | | | |   (207)   ~ (all_52_29 = e3)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (151), (205) imply:
% 203.62/34.58  | | | | | | | | | | | |   (208)  op(e3, e3) = all_52_24
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 203.62/34.58  | | | | | | | | | | | |              simplifying with (113), (208) gives:
% 203.62/34.58  | | | | | | | | | | | |   (209)  all_52_24 = all_6_2
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_24, e3, e3,
% 203.62/34.58  | | | | | | | | | | | |              simplifying with (202), (208) gives:
% 203.62/34.58  | | | | | | | | | | | |   (210)  all_52_24 = e1
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | COMBINE_EQS: (209), (210) imply:
% 203.62/34.58  | | | | | | | | | | | |   (211)  all_6_2 = e1
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | COMBINE_EQS: (19), (211) imply:
% 203.62/34.58  | | | | | | | | | | | |   (212)  all_58_0 = e1
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (18), (211) imply:
% 203.62/34.58  | | | | | | | | | | | |   (213)   ~ (all_52_3 = e1)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (44), (211) imply:
% 203.62/34.58  | | | | | | | | | | | |   (214)  op(e1, e1) = all_52_0
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (147), (211) imply:
% 203.62/34.58  | | | | | | | | | | | |   (215)  op(e1, e3) = all_6_1
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_0, e1, e1,
% 203.62/34.58  | | | | | | | | | | | |              simplifying with (137), (214) gives:
% 203.62/34.58  | | | | | | | | | | | |   (216)  all_52_0 = all_10_2
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_5, all_6_1, e3, e1,
% 203.62/34.58  | | | | | | | | | | | |              simplifying with (36), (215) gives:
% 203.62/34.58  | | | | | | | | | | | |   (217)  all_52_5 = all_6_1
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | COMBINE_EQS: (124), (217) imply:
% 203.62/34.58  | | | | | | | | | | | |   (218)  all_58_6 = all_6_1
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (80), (217) imply:
% 203.62/34.58  | | | | | | | | | | | |   (219)   ~ (all_52_29 = all_6_1)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | SIMP: (219) implies:
% 203.62/34.58  | | | | | | | | | | | |   (220)   ~ (all_52_29 = all_6_1)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (100), (217) imply:
% 203.62/34.58  | | | | | | | | | | | |   (221)   ~ (all_10_2 = all_6_1)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | SIMP: (221) implies:
% 203.62/34.58  | | | | | | | | | | | |   (222)   ~ (all_10_2 = all_6_1)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | REDUCE: (163), (217) imply:
% 203.62/34.58  | | | | | | | | | | | |   (223)   ~ (all_6_1 = e3)
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | BETA: splitting (86) gives:
% 203.62/34.58  | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | |   (224)  all_58_0 = e2
% 203.62/34.58  | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | REF_CLOSE: (54), (212), (224) are inconsistent by sub-proof
% 203.62/34.58  | | | | | | | | | | | | |            #1273.
% 203.62/34.58  | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | Case 2:
% 203.62/34.58  | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | |   (225)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.62/34.58  | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | BETA: splitting (225) gives:
% 203.62/34.58  | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | Case 1:
% 203.62/34.58  | | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | |   (226)  all_58_2 = e2
% 203.62/34.58  | | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | | COMBINE_EQS: (69), (226) imply:
% 203.62/34.58  | | | | | | | | | | | | | |   (227)  all_52_3 = e2
% 203.62/34.58  | | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | | SIMP: (227) implies:
% 203.62/34.58  | | | | | | | | | | | | | |   (228)  all_52_3 = e2
% 203.62/34.58  | | | | | | | | | | | | | | 
% 203.62/34.58  | | | | | | | | | | | | | | REDUCE: (144), (228) imply:
% 203.72/34.58  | | | | | | | | | | | | | |   (229)   ~ (all_4_2 = e2)
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | SIMP: (229) implies:
% 203.72/34.58  | | | | | | | | | | | | | |   (230)   ~ (all_4_2 = e2)
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | |   (231)  all_58_0 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | COMBINE_EQS: (212), (231) imply:
% 203.72/34.58  | | | | | | | | | | | | | | |   (232)  e1 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | REDUCE: (128), (232) imply:
% 203.72/34.58  | | | | | | | | | | | | | | |   (233)  $false
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | |   (234)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | |   (235)  all_58_2 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | REF_CLOSE: (77), (226), (235) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | | | | | | |            #1213.
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | |   (236)  all_58_6 = e0 | all_58_12 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (237)  all_58_6 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (237) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (238)  all_6_1 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | SIMP: (238) implies:
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (239)  all_6_1 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | REDUCE: (220), (239) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (240)   ~ (all_52_29 = e0)
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | REDUCE: (222), (239) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (241)   ~ (all_10_2 = e0)
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | REDUCE: (223), (239) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (242)   ~ (e3 = e0)
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | |   (243)  all_58_9 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (243) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | |   (244)  e3 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | REDUCE: (11), (244) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | |   (245)  $false
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | |   (246)  all_58_10 = e0 | all_58_11 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (247)  all_58_10 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (247) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (248)  all_52_27 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | REDUCE: (27), (248) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (249)   ~ (all_52_29 = e0)
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | REDUCE: (123), (248) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (250)   ~ (all_4_2 = e0)
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | SIMP: (250) implies:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (251)   ~ (all_4_2 = e0)
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | REDUCE: (35), (248) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (252)  op(e0, e0) = all_52_26
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | REDUCE: (129), (248) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (253)  op(e2, e0) = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | |   (254)  all_56_5 = e3
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (254) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | |   (255)  all_4_2 = e3
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (255) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | |   (256)  $false
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | |   (257)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | |   (258)  all_56_5 = e2
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (258) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | |   (259)  all_4_2 = e2
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | REDUCE: (230), (259) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | |   (260)  $false
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | |   (261)  all_56_5 = e1 | all_56_5 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | |   (262)  all_58_2 = e1
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (226), (262) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | |            #1116.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | |   (263)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_58_3 = e1
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (264) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_4_2 = e1
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (265) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | |   (266)  op(e1, e1) = e2
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_56_11 = e3
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (207), (267) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | |            #1028.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20), (30), (34), (40), (46), (49), (61),
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | |            (94), (109), (137), (201), (203), (240), (241),
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | |            (247), (252), (253), (266), (268) are inconsistent
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #839.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_58_3 = e1)
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (269) imply:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | |   (270)   ~ (all_4_2 = e1)
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (251), (261), (270) are inconsistent by
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1021.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |   (271)  all_58_11 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (240), (271) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | | | | | | | | | |            #1115.
% 203.72/34.58  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | |   (272)  all_58_12 = e0
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (159), (272) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | | | | | | | |            #1212.
% 203.72/34.58  | | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | |   (273)  all_58_6 = e2 | all_58_12 = e2
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | | REF_CLOSE: (130), (136), (159), (218), (273) are inconsistent
% 203.72/34.58  | | | | | | | | | | | | | |            by sub-proof #1209.
% 203.72/34.58  | | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | |   (274)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.58  | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | | REF_CLOSE: (7), (9), (28), (32), (34), (40), (46), (50),
% 203.72/34.58  | | | | | | | | | | | |            (57), (60), (62), (79), (92), (94), (101), (104),
% 203.72/34.58  | | | | | | | | | | | |            (110), (111), (113), (121), (125), (131), (132),
% 203.72/34.58  | | | | | | | | | | | |            (134), (138), (142), (148), (149), (155), (158),
% 203.72/34.58  | | | | | | | | | | | |            (182), (197), (274) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | | |            #1107.
% 203.72/34.58  | | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | Case 2:
% 203.72/34.58  | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | |   (275)  all_58_13 = e3
% 203.72/34.58  | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | | REF_CLOSE: (28), (158), (275) are inconsistent by sub-proof
% 203.72/34.58  | | | | | | | | | | |            #1360.
% 203.72/34.58  | | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | | 
% 203.72/34.58  | | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | | 
% 203.72/34.58  | | | | | | | | End of split
% 203.72/34.58  | | | | | | | | 
% 203.72/34.58  | | | | | | | End of split
% 203.72/34.58  | | | | | | | 
% 203.72/34.58  | | | | | | Case 2:
% 203.72/34.58  | | | | | | | 
% 203.72/34.58  | | | | | | |   (276)   ~ (all_56_6 = e3)
% 203.72/34.58  | | | | | | | 
% 203.72/34.58  | | | | | | | REDUCE: (82), (276) imply:
% 203.72/34.58  | | | | | | |   (277)   ~ (all_52_19 = e3)
% 203.72/34.58  | | | | | | | 
% 203.72/34.58  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (17), (18), (19),
% 203.72/34.58  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 203.72/34.58  | | | | | | |            (31), (32), (34), (35), (36), (37), (39), (40), (41),
% 203.72/34.58  | | | | | | |            (42), (43), (46), (48), (49), (50), (53), (54), (55),
% 203.72/34.58  | | | | | | |            (57), (58), (60), (62), (63), (66), (69), (73), (74),
% 203.72/34.58  | | | | | | |            (75), (78), (79), (80), (85), (86), (87), (89), (91),
% 203.72/34.58  | | | | | | |            (92), (93), (94), (95), (98), (100), (101), (104),
% 203.72/34.58  | | | | | | |            (105), (106), (107), (108), (110), (111), (113), (114),
% 203.72/34.58  | | | | | | |            (116), (117), (120), (121), (122), (123), (124), (125),
% 203.72/34.58  | | | | | | |            (127), (130), (131), (132), (134), (135), (136), (138),
% 203.72/34.58  | | | | | | |            (139), (142), (144), (145), (147), (148), (149), (151),
% 203.72/34.58  | | | | | | |            (155), (158), (159), (162), (163), (166), (169), (170),
% 203.72/34.58  | | | | | | |            (174), (177), (277) are inconsistent by sub-proof #738.
% 203.72/34.58  | | | | | | | 
% 203.72/34.58  | | | | | | End of split
% 203.72/34.58  | | | | | | 
% 203.72/34.58  | | | | | End of split
% 203.72/34.58  | | | | | 
% 203.72/34.58  | | | | End of split
% 203.72/34.58  | | | | 
% 203.72/34.58  | | | Case 2:
% 203.72/34.58  | | | | 
% 203.72/34.58  | | | |   (278)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.58  | | | | 
% 203.72/34.58  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (15), (19), (24), (28),
% 203.72/34.58  | | | |            (29), (32), (36), (37), (39), (40), (42), (44), (45), (46),
% 203.72/34.58  | | | |            (48), (50), (54), (56), (57), (58), (59), (62), (64), (65),
% 203.72/34.58  | | | |            (66), (69), (72), (73), (79), (83), (86), (87), (88), (92),
% 203.72/34.58  | | | |            (94), (96), (97), (101), (102), (105), (107), (108), (110),
% 203.72/34.58  | | | |            (111), (113), (114), (116), (118), (120), (121), (123),
% 203.72/34.58  | | | |            (124), (125), (130), (131), (136), (138), (140), (142),
% 203.72/34.58  | | | |            (144), (146), (147), (149), (151), (155), (158), (278) are
% 203.72/34.58  | | | |            inconsistent by sub-proof #1094.
% 203.72/34.58  | | | | 
% 203.72/34.58  | | | End of split
% 203.72/34.58  | | | 
% 203.72/34.58  | | End of split
% 203.72/34.58  | | 
% 203.72/34.58  | End of split
% 203.72/34.58  | 
% 203.72/34.58  End of proof
% 203.72/34.58  
% 203.72/34.58  Sub-proof #619 shows that the following formulas are inconsistent:
% 203.72/34.58  ----------------------------------------------------------------
% 203.72/34.58    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.72/34.58    (2)   ~ (all_52_15 = all_52_23)
% 203.72/34.58    (3)   ~ (all_52_25 = all_52_27)
% 203.72/34.58    (4)  all_58_14 = all_52_23
% 203.72/34.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.58    (6)  op(all_52_7, all_52_7) = e0
% 203.72/34.58    (7)  all_58_1 = all_52_9
% 203.72/34.58    (8)  op(all_52_5, all_52_5) = e1
% 203.72/34.58    (9)   ~ (e3 = e0)
% 203.72/34.58    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.58    (11)   ~ (all_52_7 = all_52_15)
% 203.72/34.58    (12)   ~ (all_52_3 = all_52_19)
% 203.72/34.58    (13)   ~ (all_52_17 = all_52_25)
% 203.72/34.58    (14)   ~ (all_52_3 = all_6_2)
% 203.72/34.58    (15)  all_58_0 = all_6_2
% 203.72/34.58    (16)  op(all_14_2, e0) = all_14_1
% 203.72/34.58    (17)  all_56_4 = all_52_3
% 203.72/34.58    (18)  all_26_1 = all_10_1
% 203.72/34.58    (19)  all_26_2 = all_10_2
% 203.72/34.58    (20)  op(e0, all_14_1) = all_14_0
% 203.72/34.58    (21)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.58    (22)   ~ (all_52_27 = all_52_29)
% 203.72/34.58    (23)  all_58_13 = all_52_15
% 203.72/34.58    (24)  all_58_9 = all_52_25
% 203.72/34.58    (25)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.72/34.58    (26)  op(e2, e2) = all_4_2
% 203.72/34.58    (27)  all_58_11 = all_52_29
% 203.72/34.58    (28)   ~ (all_52_25 = all_14_2)
% 203.72/34.58    (29)  all_56_13 = e3
% 203.72/34.58    (30)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.72/34.58    (31)   ~ (all_52_3 = all_52_27)
% 203.72/34.58    (32)  op(all_10_2, e1) = all_10_1
% 203.72/34.58    (33)   ~ (all_52_7 = all_6_2)
% 203.72/34.58    (34)  op(e0, e0) = all_14_2
% 203.72/34.58    (35)  all_56_15 = all_14_2
% 203.72/34.58    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.58    (37)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.58    (38)  op(e1, e0) = all_52_29
% 203.72/34.58    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.58    (40)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.72/34.58    (41)  all_56_9 = all_52_13
% 203.72/34.58    (42)   ~ (e2 = e1)
% 203.72/34.58    (43)   ~ (all_52_13 = all_10_2)
% 203.72/34.58    (44)   ~ (all_6_0 = e1)
% 203.72/34.58    (45)  all_58_10 = all_52_27
% 203.72/34.58    (46)   ~ (all_52_29 = all_10_2)
% 203.72/34.58    (47)  all_58_7 = all_52_13
% 203.72/34.58    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.58    (49)  op(all_6_2, all_6_2) = e3
% 203.72/34.58    (50)   ~ (all_52_5 = all_52_7)
% 203.72/34.58    (51)  all_58_12 = all_52_7
% 203.72/34.58    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.58    (53)   ~ (all_52_7 = all_14_2)
% 203.72/34.58    (54)   ~ (all_14_2 = e0)
% 203.72/34.58    (55)  all_58_2 = all_52_3
% 203.72/34.58    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.72/34.58    (57)  all_56_2 = all_52_17
% 203.72/34.58    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.58    (59)  op(e3, all_6_1) = all_6_0
% 203.72/34.58    (60)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.72/34.58    (61)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.59    (62)   ~ (e2 = e0)
% 203.72/34.59    (63)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.72/34.59    (64)  op(all_52_3, all_52_3) = e2
% 203.72/34.59    (65)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.59    (66)  all_56_6 = all_52_19
% 203.72/34.59    (67)   ~ (all_52_15 = all_14_2)
% 203.72/34.59    (68)   ~ (all_52_19 = all_52_27)
% 203.72/34.59    (69)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.72/34.59    (70)   ~ (all_6_0 = e2)
% 203.72/34.59    (71)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.59    (72)   ~ (all_52_13 = all_4_2)
% 203.72/34.59    (73)  op(e3, e1) = all_52_17
% 203.72/34.59    (74)  op(e0, e3) = all_52_7
% 203.72/34.59    (75)  op(e1, e2) = all_52_13
% 203.72/34.59    (76)   ~ (all_52_9 = all_52_25)
% 203.72/34.59    (77)  all_58_15 = all_14_2
% 203.72/34.59    (78)   ~ (all_52_19 = all_10_2)
% 203.72/34.59    (79)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.72/34.59    (80)  all_58_8 = all_10_2
% 203.72/34.59    (81)   ~ (all_52_5 = all_10_2)
% 203.72/34.59    (82)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.59    (83)  all_56_12 = all_52_7
% 203.72/34.59    (84)  op(all_52_17, all_52_17) = all_52_16
% 203.72/34.59    (85)   ~ (all_52_25 = all_6_2)
% 203.72/34.59    (86)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.59    (87)   ~ (all_52_5 = all_6_2)
% 203.72/34.59    (88)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.59    (89)   ~ (all_52_13 = all_52_15)
% 203.72/34.59    (90)  op(e1, all_10_1) = e2
% 203.72/34.59    (91)  op(e3, e3) = all_6_2
% 203.72/34.59    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.59    (93)   ~ (all_52_27 = all_14_2)
% 203.72/34.59    (94)  all_56_3 = all_52_25
% 203.72/34.59    (95)   ~ (all_52_3 = all_52_7)
% 203.72/34.59    (96)  all_58_5 = all_52_19
% 203.72/34.59    (97)   ~ (all_52_27 = all_4_2)
% 203.72/34.59    (98)  all_58_6 = all_52_5
% 203.72/34.59    (99)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.59    (100)   ~ (all_52_17 = all_6_2)
% 203.72/34.59    (101)   ~ (e1 = e0)
% 203.72/34.59    (102)   ~ (all_52_9 = all_52_17)
% 203.72/34.59    (103)  all_56_10 = all_10_2
% 203.72/34.59    (104)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.72/34.59    (105)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.72/34.59    (106)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.59    (107)  op(e1, e1) = all_10_2
% 203.72/34.59    (108)   ~ (all_52_23 = all_10_2)
% 203.72/34.59    (109)  all_58_3 = all_4_2
% 203.72/34.59    (110)  all_56_13 = all_52_15
% 203.72/34.59    (111)   ~ (all_52_3 = all_4_2)
% 203.72/34.59    (112)  op(all_6_2, e3) = all_6_1
% 203.72/34.59    (113)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.72/34.59    (114)   ~ (all_52_13 = all_52_29)
% 203.72/34.59    (115)  all_58_4 = all_52_17
% 203.72/34.59    (116)   ~ (all_14_0 = e2)
% 203.72/34.59    (117)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.72/34.59    (118)  op(all_52_25, all_52_25) = all_52_24
% 203.72/34.59  
% 203.72/34.59  Begin of proof
% 203.72/34.59  | 
% 203.72/34.59  | COMBINE_EQS: (29), (110) imply:
% 203.72/34.59  |   (119)  all_52_15 = e3
% 203.72/34.59  | 
% 203.72/34.59  | SIMP: (119) implies:
% 203.72/34.59  |   (120)  all_52_15 = e3
% 203.72/34.59  | 
% 203.72/34.59  | COMBINE_EQS: (23), (120) imply:
% 203.72/34.59  |   (121)  all_58_13 = e3
% 203.72/34.59  | 
% 203.72/34.59  | REDUCE: (11), (120) imply:
% 203.72/34.59  |   (122)   ~ (all_52_7 = e3)
% 203.72/34.59  | 
% 203.72/34.59  | REDUCE: (89), (120) imply:
% 203.72/34.59  |   (123)   ~ (all_52_13 = e3)
% 203.72/34.59  | 
% 203.72/34.59  | REDUCE: (2), (120) imply:
% 203.72/34.59  |   (124)   ~ (all_52_23 = e3)
% 203.72/34.59  | 
% 203.72/34.59  | SIMP: (124) implies:
% 203.72/34.59  |   (125)   ~ (all_52_23 = e3)
% 203.72/34.59  | 
% 203.72/34.59  | REDUCE: (67), (120) imply:
% 203.72/34.59  |   (126)   ~ (all_14_2 = e3)
% 203.72/34.59  | 
% 203.72/34.59  | SIMP: (126) implies:
% 203.72/34.59  |   (127)   ~ (all_14_2 = e3)
% 203.72/34.59  | 
% 203.72/34.59  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 203.72/34.59  |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 203.72/34.59  |            (27), (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 203.72/34.59  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 203.72/34.59  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 203.72/34.59  |            (61), (62), (63), (64), (65), (66), (68), (69), (70), (71), (72),
% 203.72/34.59  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 203.72/34.59  |            (84), (85), (86), (87), (88), (90), (91), (92), (93), (94), (95),
% 203.72/34.59  |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 203.72/34.59  |            (106), (107), (108), (109), (111), (112), (113), (114), (115),
% 203.72/34.59  |            (116), (117), (118), (121), (122), (123), (125), (127) are
% 203.72/34.59  |            inconsistent by sub-proof #620.
% 203.72/34.59  | 
% 203.72/34.59  End of proof
% 203.72/34.59  
% 203.72/34.59  Sub-proof #620 shows that the following formulas are inconsistent:
% 203.72/34.59  ----------------------------------------------------------------
% 203.72/34.59    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.72/34.59    (2)   ~ (all_52_25 = all_52_27)
% 203.72/34.59    (3)  all_58_14 = all_52_23
% 203.72/34.59    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.59    (5)  op(all_52_7, all_52_7) = e0
% 203.72/34.59    (6)  all_58_1 = all_52_9
% 203.72/34.59    (7)  op(all_52_5, all_52_5) = e1
% 203.72/34.59    (8)   ~ (e3 = e0)
% 203.72/34.59    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.59    (10)   ~ (all_52_3 = all_52_19)
% 203.72/34.59    (11)   ~ (all_52_17 = all_52_25)
% 203.72/34.59    (12)   ~ (all_52_3 = all_6_2)
% 203.72/34.59    (13)  all_58_0 = all_6_2
% 203.72/34.59    (14)  op(all_14_2, e0) = all_14_1
% 203.72/34.59    (15)  all_56_4 = all_52_3
% 203.72/34.59    (16)  all_26_1 = all_10_1
% 203.72/34.59    (17)  all_26_2 = all_10_2
% 203.72/34.59    (18)  all_58_13 = e3
% 203.72/34.59    (19)  op(e0, all_14_1) = all_14_0
% 203.72/34.59    (20)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.59    (21)   ~ (all_52_27 = all_52_29)
% 203.72/34.59    (22)  all_58_9 = all_52_25
% 203.72/34.59    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.72/34.59    (24)  op(e2, e2) = all_4_2
% 203.72/34.59    (25)  all_58_11 = all_52_29
% 203.72/34.59    (26)   ~ (all_52_25 = all_14_2)
% 203.72/34.59    (27)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.72/34.59    (28)   ~ (all_52_3 = all_52_27)
% 203.72/34.59    (29)  op(all_10_2, e1) = all_10_1
% 203.72/34.59    (30)   ~ (all_52_7 = all_6_2)
% 203.72/34.59    (31)  op(e0, e0) = all_14_2
% 203.72/34.59    (32)  all_56_15 = all_14_2
% 203.72/34.59    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.59    (34)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.59    (35)  op(e1, e0) = all_52_29
% 203.72/34.59    (36)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.59    (37)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.72/34.59    (38)  all_56_9 = all_52_13
% 203.72/34.59    (39)   ~ (e2 = e1)
% 203.72/34.59    (40)   ~ (all_52_13 = all_10_2)
% 203.72/34.59    (41)   ~ (all_6_0 = e1)
% 203.72/34.59    (42)  all_58_10 = all_52_27
% 203.72/34.59    (43)   ~ (all_52_29 = all_10_2)
% 203.72/34.59    (44)  all_58_7 = all_52_13
% 203.72/34.59    (45)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.59    (46)  op(all_6_2, all_6_2) = e3
% 203.72/34.59    (47)   ~ (all_52_5 = all_52_7)
% 203.72/34.59    (48)  all_58_12 = all_52_7
% 203.72/34.59    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.59    (50)   ~ (all_52_7 = e3)
% 203.72/34.59    (51)   ~ (all_52_7 = all_14_2)
% 203.72/34.59    (52)   ~ (all_14_2 = e0)
% 203.72/34.59    (53)  all_58_2 = all_52_3
% 203.72/34.59    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.72/34.59    (55)  all_56_2 = all_52_17
% 203.72/34.59    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.59    (57)  op(e3, all_6_1) = all_6_0
% 203.72/34.59    (58)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.72/34.59    (59)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.59    (60)   ~ (e2 = e0)
% 203.72/34.59    (61)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.72/34.59    (62)   ~ (all_52_23 = e3)
% 203.72/34.59    (63)  op(all_52_3, all_52_3) = e2
% 203.72/34.59    (64)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.59    (65)  all_56_6 = all_52_19
% 203.72/34.59    (66)   ~ (all_52_19 = all_52_27)
% 203.72/34.59    (67)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.72/34.59    (68)   ~ (all_6_0 = e2)
% 203.72/34.59    (69)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.59    (70)   ~ (all_52_13 = all_4_2)
% 203.72/34.59    (71)  op(e3, e1) = all_52_17
% 203.72/34.59    (72)  op(e0, e3) = all_52_7
% 203.72/34.59    (73)  op(e1, e2) = all_52_13
% 203.72/34.59    (74)   ~ (all_52_9 = all_52_25)
% 203.72/34.59    (75)  all_58_15 = all_14_2
% 203.72/34.59    (76)   ~ (all_52_19 = all_10_2)
% 203.72/34.59    (77)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.72/34.59    (78)  all_58_8 = all_10_2
% 203.72/34.59    (79)   ~ (all_52_5 = all_10_2)
% 203.72/34.59    (80)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.59    (81)  all_56_12 = all_52_7
% 203.72/34.59    (82)  op(all_52_17, all_52_17) = all_52_16
% 203.72/34.59    (83)   ~ (all_52_25 = all_6_2)
% 203.72/34.59    (84)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.59    (85)   ~ (all_52_5 = all_6_2)
% 203.72/34.59    (86)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.59    (87)  op(e1, all_10_1) = e2
% 203.72/34.59    (88)  op(e3, e3) = all_6_2
% 203.72/34.59    (89)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.59    (90)   ~ (all_52_13 = e3)
% 203.72/34.59    (91)   ~ (all_52_27 = all_14_2)
% 203.72/34.59    (92)  all_56_3 = all_52_25
% 203.72/34.59    (93)   ~ (all_52_3 = all_52_7)
% 203.72/34.59    (94)  all_58_5 = all_52_19
% 203.72/34.59    (95)   ~ (all_52_27 = all_4_2)
% 203.72/34.59    (96)  all_58_6 = all_52_5
% 203.72/34.59    (97)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.59    (98)   ~ (all_52_17 = all_6_2)
% 203.72/34.59    (99)   ~ (e1 = e0)
% 203.72/34.59    (100)   ~ (all_52_9 = all_52_17)
% 203.72/34.59    (101)  all_56_10 = all_10_2
% 203.72/34.59    (102)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.72/34.59    (103)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.72/34.59    (104)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.59    (105)  op(e1, e1) = all_10_2
% 203.72/34.59    (106)   ~ (all_52_23 = all_10_2)
% 203.72/34.59    (107)  all_58_3 = all_4_2
% 203.72/34.59    (108)   ~ (all_52_3 = all_4_2)
% 203.72/34.59    (109)  op(all_6_2, e3) = all_6_1
% 203.72/34.59    (110)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.72/34.59    (111)   ~ (all_52_13 = all_52_29)
% 203.72/34.59    (112)  all_58_4 = all_52_17
% 203.72/34.59    (113)   ~ (all_14_0 = e2)
% 203.72/34.59    (114)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.72/34.59    (115)  op(all_52_25, all_52_25) = all_52_24
% 203.72/34.59    (116)   ~ (all_14_2 = e3)
% 203.72/34.59  
% 203.72/34.59  Begin of proof
% 203.72/34.59  | 
% 203.72/34.59  | BETA: splitting (9) gives:
% 203.72/34.59  | 
% 203.72/34.59  | Case 1:
% 203.72/34.59  | | 
% 203.72/34.59  | |   (117)  all_56_12 = e3
% 203.72/34.59  | | 
% 203.72/34.59  | | COMBINE_EQS: (81), (117) imply:
% 203.72/34.59  | |   (118)  all_52_7 = e3
% 203.72/34.59  | | 
% 203.72/34.59  | | REDUCE: (50), (118) imply:
% 203.72/34.59  | |   (119)  $false
% 203.72/34.59  | | 
% 203.72/34.59  | | CLOSE: (119) is inconsistent.
% 203.72/34.59  | | 
% 203.72/34.59  | Case 2:
% 203.72/34.59  | | 
% 203.72/34.59  | |   (120)   ~ (all_56_12 = e3)
% 203.72/34.59  | |   (121)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.59  | | 
% 203.72/34.59  | | BETA: splitting (103) gives:
% 203.72/34.59  | | 
% 203.72/34.59  | | Case 1:
% 203.72/34.59  | | | 
% 203.72/34.59  | | |   (122)  all_56_9 = e3
% 203.72/34.59  | | | 
% 203.72/34.59  | | | REF_CLOSE: (38), (90), (122) are inconsistent by sub-proof #958.
% 203.72/34.59  | | | 
% 203.72/34.59  | | Case 2:
% 203.72/34.59  | | | 
% 203.72/34.59  | | |   (123)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.72/34.59  | | | 
% 203.72/34.59  | | | BETA: splitting (56) gives:
% 203.72/34.59  | | | 
% 203.72/34.59  | | | Case 1:
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | |   (124)  all_58_0 = e3
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | COMBINE_EQS: (13), (124) imply:
% 203.72/34.59  | | | |   (125)  all_6_2 = e3
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (12), (125) imply:
% 203.72/34.59  | | | |   (126)   ~ (all_52_3 = e3)
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (85), (125) imply:
% 203.72/34.59  | | | |   (127)   ~ (all_52_5 = e3)
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (98), (125) imply:
% 203.72/34.59  | | | |   (128)   ~ (all_52_17 = e3)
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (83), (125) imply:
% 203.72/34.59  | | | |   (129)   ~ (all_52_25 = e3)
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (109), (125) imply:
% 203.72/34.59  | | | |   (130)  op(e3, e3) = all_6_1
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (88), (125) imply:
% 203.72/34.59  | | | |   (131)  op(e3, e3) = e3
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | GROUND_INST: instantiating (4) with e3, all_6_1, e3, e3, simplifying
% 203.72/34.59  | | | |              with (130), (131) gives:
% 203.72/34.59  | | | |   (132)  all_6_1 = e3
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (57), (132) imply:
% 203.72/34.59  | | | |   (133)  op(e3, e3) = all_6_0
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | GROUND_INST: instantiating (4) with e3, all_6_0, e3, e3, simplifying
% 203.72/34.59  | | | |              with (131), (133) gives:
% 203.72/34.59  | | | |   (134)  all_6_0 = e3
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (68), (134) imply:
% 203.72/34.59  | | | |   (135)   ~ (e3 = e2)
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | REDUCE: (41), (134) imply:
% 203.72/34.59  | | | |   (136)   ~ (e3 = e1)
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | BETA: splitting (33) gives:
% 203.72/34.59  | | | | 
% 203.72/34.59  | | | | Case 1:
% 203.72/34.59  | | | | | 
% 203.72/34.59  | | | | |   (137)  all_58_2 = e3
% 203.72/34.59  | | | | | 
% 203.72/34.59  | | | | | REF_CLOSE: (53), (126), (137) are inconsistent by sub-proof #1369.
% 203.72/34.59  | | | | | 
% 203.72/34.59  | | | | Case 2:
% 203.72/34.59  | | | | | 
% 203.72/34.59  | | | | |   (138)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.59  | | | | | 
% 203.72/34.59  | | | | | BETA: splitting (89) gives:
% 203.72/34.59  | | | | | 
% 203.72/34.59  | | | | | Case 1:
% 203.72/34.59  | | | | | | 
% 203.72/34.59  | | | | | |   (139)  all_58_9 = e3
% 203.72/34.59  | | | | | | 
% 203.72/34.59  | | | | | | REF_CLOSE: (22), (129), (139) are inconsistent by sub-proof #1300.
% 203.72/34.59  | | | | | | 
% 203.72/34.59  | | | | | Case 2:
% 203.72/34.59  | | | | | | 
% 203.72/34.59  | | | | | |   (140)   ~ (all_58_9 = e3)
% 203.72/34.59  | | | | | |   (141)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.59  | | | | | | 
% 203.72/34.59  | | | | | | BETA: splitting (102) gives:
% 203.72/34.59  | | | | | | 
% 203.72/34.59  | | | | | | Case 1:
% 203.72/34.59  | | | | | | | 
% 203.72/34.59  | | | | | | |   (142)  all_58_4 = e3
% 203.72/34.59  | | | | | | | 
% 203.72/34.59  | | | | | | | REF_CLOSE: (112), (128), (142) are inconsistent by sub-proof
% 203.72/34.59  | | | | | | |            #1302.
% 203.72/34.59  | | | | | | | 
% 203.72/34.59  | | | | | | Case 2:
% 203.72/34.59  | | | | | | | 
% 203.72/34.59  | | | | | | |   (143)   ~ (all_58_4 = e3)
% 203.72/34.59  | | | | | | |   (144)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.72/34.59  | | | | | | | 
% 203.72/34.59  | | | | | | | BETA: splitting (49) gives:
% 203.72/34.59  | | | | | | | 
% 203.72/34.59  | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | 
% 203.72/34.59  | | | | | | | |   (145)  all_58_6 = e3
% 203.72/34.59  | | | | | | | | 
% 203.72/34.59  | | | | | | | | REF_CLOSE: (96), (127), (145) are inconsistent by sub-proof
% 203.72/34.59  | | | | | | | |            #1328.
% 203.72/34.59  | | | | | | | | 
% 203.72/34.59  | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | 
% 203.72/34.59  | | | | | | | |   (146)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.59  | | | | | | | | 
% 203.72/34.59  | | | | | | | | BETA: splitting (36) gives:
% 203.72/34.59  | | | | | | | | 
% 203.72/34.59  | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | 
% 203.72/34.59  | | | | | | | | |   (147)  all_56_2 = e3
% 203.72/34.59  | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | REF_CLOSE: (55), (128), (147) are inconsistent by sub-proof
% 203.72/34.59  | | | | | | | | |            #1327.
% 203.72/34.59  | | | | | | | | | 
% 203.72/34.59  | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | 
% 203.72/34.59  | | | | | | | | |   (148)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.59  | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | BETA: splitting (84) gives:
% 203.72/34.59  | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | |   (149)  all_56_3 = e3
% 203.72/34.59  | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | REF_CLOSE: (92), (129), (149) are inconsistent by sub-proof
% 203.72/34.59  | | | | | | | | | |            #1339.
% 203.72/34.59  | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | |   (150)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.59  | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | BETA: splitting (114) gives:
% 203.72/34.59  | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | |   (151)  all_56_10 = e3
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | COMBINE_EQS: (101), (151) imply:
% 203.72/34.59  | | | | | | | | | | |   (152)  all_10_2 = e3
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | SIMP: (152) implies:
% 203.72/34.59  | | | | | | | | | | |   (153)  all_10_2 = e3
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | COMBINE_EQS: (17), (153) imply:
% 203.72/34.59  | | | | | | | | | | |   (154)  all_26_2 = e3
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | REDUCE: (43), (153) imply:
% 203.72/34.59  | | | | | | | | | | |   (155)   ~ (all_52_29 = e3)
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | REDUCE: (29), (153) imply:
% 203.72/34.59  | | | | | | | | | | |   (156)  op(e3, e1) = all_10_1
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | REDUCE: (105), (153) imply:
% 203.72/34.59  | | | | | | | | | | |   (157)  op(e1, e1) = e3
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | BETA: splitting (34) gives:
% 203.72/34.59  | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | |   (158)   ~ (all_26_2 = e3)
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | REDUCE: (154), (158) imply:
% 203.72/34.59  | | | | | | | | | | | |   (159)  $false
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | |   (160)   ~ (all_26_1 = e0)
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | REDUCE: (16), (160) imply:
% 203.72/34.59  | | | | | | | | | | | |   (161)   ~ (all_10_1 = e0)
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | BETA: splitting (141) gives:
% 203.72/34.59  | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | |   (162)  all_58_10 = e3
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | COMBINE_EQS: (42), (162) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (163)  all_52_27 = e3
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | SIMP: (163) implies:
% 203.72/34.59  | | | | | | | | | | | | |   (164)  all_52_27 = e3
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | REDUCE: (91), (164) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (165)   ~ (all_14_2 = e3)
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | REDUCE: (95), (164) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (166)   ~ (all_4_2 = e3)
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | SIMP: (166) implies:
% 203.72/34.59  | | | | | | | | | | | | |   (167)   ~ (all_4_2 = e3)
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_17, all_10_1, e1,
% 203.72/34.59  | | | | | | | | | | | | |              e3, simplifying with (71), (156) gives:
% 203.72/34.59  | | | | | | | | | | | | |   (168)  all_52_17 = all_10_1
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | COMBINE_EQS: (55), (168) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (169)  all_56_2 = all_10_1
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | COMBINE_EQS: (112), (168) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (170)  all_58_4 = all_10_1
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | REDUCE: (100), (168) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (171)   ~ (all_52_9 = all_10_1)
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | REDUCE: (11), (168) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (172)   ~ (all_52_25 = all_10_1)
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | SIMP: (172) implies:
% 203.72/34.59  | | | | | | | | | | | | |   (173)   ~ (all_52_25 = all_10_1)
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | REDUCE: (82), (168) imply:
% 203.72/34.59  | | | | | | | | | | | | |   (174)  op(all_10_1, all_10_1) = all_52_16
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | BETA: splitting (58) gives:
% 203.72/34.59  | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | |   (175)  all_58_0 = e0
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | COMBINE_EQS: (124), (175) imply:
% 203.72/34.59  | | | | | | | | | | | | | |   (176)  e3 = e0
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | REDUCE: (8), (176) imply:
% 203.72/34.59  | | | | | | | | | | | | | |   (177)  $false
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | |   (178)   ~ (all_58_0 = e0)
% 203.72/34.59  | | | | | | | | | | | | | |   (179)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 203.72/34.59  | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | |   (180)  all_58_0 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | COMBINE_EQS: (124), (180) imply:
% 203.72/34.59  | | | | | | | | | | | | | | |   (181)  e3 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | REDUCE: (136), (181) imply:
% 203.72/34.59  | | | | | | | | | | | | | | |   (182)  $false
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | |   (183)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | |   (184)  all_58_1 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (184) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | |   (185)  all_52_9 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | REDUCE: (74), (185) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | |   (186)   ~ (all_52_25 = e1)
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | SIMP: (186) implies:
% 203.72/34.59  | | | | | | | | | | | | | | | |   (187)   ~ (all_52_25 = e1)
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | REDUCE: (171), (185) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | |   (188)   ~ (all_10_1 = e1)
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 203.72/34.59  | | | | | | | | | | | | | | | |   (189)   ~ (all_10_1 = e1)
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | |   (190)  all_58_1 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (190) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | |   (191)  e1 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | REDUCE: (99), (191) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | |   (192)  $false
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent.
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | |   (193)   ~ (all_58_1 = e0)
% 203.72/34.59  | | | | | | | | | | | | | | | | |   (194)  all_58_4 = e0 | all_58_9 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (195)  all_56_2 = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (195) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (196)  all_10_1 = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (197)  all_10_1 = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (197) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (198)  all_58_4 = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | REDUCE: (173), (197) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (199)   ~ (all_52_25 = e2)
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | REDUCE: (174), (197) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (200)  op(e2, e2) = all_52_16
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | REDUCE: (87), (197) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | |   (201)  op(e1, e2) = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | |   (202)  all_56_3 = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (199), (202) are inconsistent by sub-proof
% 203.72/34.59  | | | | | | | | | | | | | | | | | | |            #1259.
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | |   (203)   ~ (all_56_3 = e2)
% 203.72/34.59  | | | | | | | | | | | | | | | | | | |   (204)  all_56_3 = e1 | all_56_3 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (205)  all_56_3 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (205) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (206)  all_52_25 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | SIMP: (206) implies:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (207)  all_52_25 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (207) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (208)  all_58_9 = e1
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (99), (194), (198), (208) are inconsistent
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1027.
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (209)  all_56_3 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (209) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (210)  all_52_25 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (211)  all_52_25 = e0
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (211) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (212)   ~ (all_14_2 = e0)
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (211) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (213)   ~ (e3 = e0)
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (211) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (214)   ~ (e1 = e0)
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (211) imply:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (215)  op(e0, e0) = all_52_24
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_14_2, all_52_24, e0,
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (31), (215) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (216)  all_52_24 = all_14_2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, e2, e2, e1,
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |              simplifying with (73), (201) gives:
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | |   (217)  all_52_13 = e2
% 203.72/34.59  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_16, e2, e2,
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |              simplifying with (24), (200) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (218)  all_52_16 = all_4_2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (217) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (219)   ~ (all_4_2 = e2)
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (220)   ~ (all_4_2 = e2)
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (217) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (221)   ~ (e3 = e2)
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (10), (13), (14), (15),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (21), (22), (23), (24), (25),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (31), (32), (33), (35), (38), (40), (42), (43),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (52), (53), (54), (56), (59), (63), (64), (65),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (66), (67), (69), (70), (72), (75), (76), (77),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (78), (79), (80), (81), (85), (86), (88), (90),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (91), (93), (94), (96), (97), (99), (104), (105),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (111), (113), (116),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (121), (123), (124), (126), (135), (138), (141),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            (146), (167), (199), (220) are inconsistent by
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |            sub-proof #622.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (222)  all_56_2 = e1 | all_56_2 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |   (223)  all_56_2 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (189), (223) are inconsistent by sub-proof
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |            #1025.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |   (224)  all_56_2 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (224) are inconsistent by sub-proof
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |            #809.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | |   (225)   ~ (all_58_1 = e1)
% 203.72/34.60  | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | REDUCE: (6), (225) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | |   (226)   ~ (all_52_9 = e1)
% 203.72/34.60  | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | |   (227)  all_58_1 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (227) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | |   (228)  all_52_9 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | REDUCE: (226), (228) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | |   (229)  $false
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | |   (230)  all_58_4 = e1 | all_58_9 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (231)  all_58_4 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (231) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (232)  all_10_1 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | REDUCE: (174), (232) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (233)  op(e1, e1) = all_52_16
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | REDUCE: (87), (232) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (234)  op(e1, e1) = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e3, all_52_16, e1, e1,
% 203.72/34.60  | | | | | | | | | | | | | | | | | |              simplifying with (157), (233) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (235)  all_52_16 = e3
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e2, all_52_16, e1, e1,
% 203.72/34.60  | | | | | | | | | | | | | | | | | |              simplifying with (233), (234) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (236)  all_52_16 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (235), (236) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (237)  e3 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | SIMP: (237) implies:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (238)  e3 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | REDUCE: (135), (238) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (239)  $false
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | |   (240)  all_58_9 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |   (241)  all_58_9 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (240), (241) are inconsistent by sub-proof
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |            #865.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |   (242)   ~ (all_58_9 = e0)
% 203.72/34.60  | | | | | | | | | | | | | | | | | | |   (243)  all_58_10 = e0 | all_58_11 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (244)  all_58_9 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (240), (244) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (245)  e2 = e1
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (245) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (246)  $false
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | |   (247)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | |   (248)  all_58_10 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (162), (248) are inconsistent by sub-proof
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | |            #1220.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | |   (249)  all_58_11 = e2 | all_58_15 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | |   (250)  all_58_11 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_58_10 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (251) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | |   (252)  e3 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (252) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | |   (253)  $false
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_58_11 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (254) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | |   (255)  e2 = e0
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (255) imply:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | |   (256)  $false
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | |   (257)  all_58_15 = e2
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (8), (18), (31), (48), (51), (64),
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | |            (69), (75), (81), (99), (105), (106), (121), (257)
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #621.
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | |   (258)  all_58_11 = e3 | all_58_15 = e3
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | REF_CLOSE: (25), (75), (116), (155), (258) are inconsistent
% 203.72/34.60  | | | | | | | | | | | | |            by sub-proof #1103.
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | |   (259)   ~ (all_56_10 = e3)
% 203.72/34.60  | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | REDUCE: (101), (259) imply:
% 203.72/34.60  | | | | | | | | | | |   (260)   ~ (all_10_2 = e3)
% 203.72/34.60  | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | BETA: splitting (144) gives:
% 203.72/34.60  | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | |   (261)  all_58_5 = e3
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | COMBINE_EQS: (94), (261) imply:
% 203.72/34.60  | | | | | | | | | | | |   (262)  all_52_19 = e3
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | SIMP: (262) implies:
% 203.72/34.60  | | | | | | | | | | | |   (263)  all_52_19 = e3
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | REDUCE: (66), (263) imply:
% 203.72/34.60  | | | | | | | | | | | |   (264)   ~ (all_52_27 = e3)
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | SIMP: (264) implies:
% 203.72/34.60  | | | | | | | | | | | |   (265)   ~ (all_52_27 = e3)
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | BETA: splitting (141) gives:
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | |   (266)  all_58_10 = e3
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | REF_CLOSE: (42), (265), (266) are inconsistent by sub-proof
% 203.72/34.60  | | | | | | | | | | | | |            #1301.
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | |   (267)  all_58_11 = e3 | all_58_15 = e3
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (8), (14), (18), (19), (25), (27),
% 203.72/34.60  | | | | | | | | | | | | |            (31), (32), (35), (48), (51), (52), (64), (69),
% 203.72/34.60  | | | | | | | | | | | | |            (72), (75), (77), (81), (99), (105), (106), (113),
% 203.72/34.60  | | | | | | | | | | | | |            (116), (121), (267) are inconsistent by sub-proof
% 203.72/34.60  | | | | | | | | | | | | |            #758.
% 203.72/34.60  | | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | |   (268)  all_58_8 = e3 | all_58_14 = e3
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | | REF_CLOSE: (3), (62), (78), (260), (268) are inconsistent by
% 203.72/34.60  | | | | | | | | | | | |            sub-proof #1304.
% 203.72/34.60  | | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | | 
% 203.72/34.60  | | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | | 
% 203.72/34.60  | | | | | | | | End of split
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | End of split
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | End of split
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | End of split
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | End of split
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | Case 2:
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | |   (269)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | | REF_CLOSE: (4), (7), (24), (33), (46), (48), (50), (53), (63), (79),
% 203.72/34.60  | | | |            (88), (96), (105), (108), (269) are inconsistent by sub-proof
% 203.72/34.60  | | | |            #1364.
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | End of split
% 203.72/34.60  | | | 
% 203.72/34.60  | | End of split
% 203.72/34.60  | | 
% 203.72/34.60  | End of split
% 203.72/34.60  | 
% 203.72/34.60  End of proof
% 203.72/34.60  
% 203.72/34.60  Sub-proof #621 shows that the following formulas are inconsistent:
% 203.72/34.60  ----------------------------------------------------------------
% 203.72/34.60    (1)  all_58_14 = all_52_23
% 203.72/34.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.60    (3)  op(all_52_7, all_52_7) = e0
% 203.72/34.60    (4)   ~ (e3 = e0)
% 203.72/34.60    (5)  all_58_13 = e3
% 203.72/34.60    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.60    (7)  op(e0, e0) = all_14_2
% 203.72/34.60    (8)  all_58_12 = all_52_7
% 203.72/34.60    (9)   ~ (all_52_7 = all_14_2)
% 203.72/34.60    (10)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.60    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.60    (12)  all_58_15 = all_14_2
% 203.72/34.60    (13)  all_56_12 = all_52_7
% 203.72/34.60    (14)   ~ (e1 = e0)
% 203.72/34.60    (15)  op(e1, e1) = all_10_2
% 203.72/34.60    (16)  all_58_15 = e2
% 203.72/34.60    (17)   ~ (all_52_23 = all_10_2)
% 203.72/34.60  
% 203.72/34.60  Begin of proof
% 203.72/34.60  | 
% 203.72/34.60  | COMBINE_EQS: (12), (16) imply:
% 203.72/34.60  |   (18)  all_14_2 = e2
% 203.72/34.60  | 
% 203.72/34.60  | SIMP: (18) implies:
% 203.72/34.60  |   (19)  all_14_2 = e2
% 203.72/34.60  | 
% 203.72/34.60  | REDUCE: (9), (19) imply:
% 203.72/34.60  |   (20)   ~ (all_52_7 = e2)
% 203.72/34.60  | 
% 203.72/34.60  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 203.72/34.60  |            (14), (15), (17), (20) are inconsistent by sub-proof #1169.
% 203.72/34.60  | 
% 203.72/34.60  End of proof
% 203.72/34.60  
% 203.72/34.60  Sub-proof #622 shows that the following formulas are inconsistent:
% 203.72/34.60  ----------------------------------------------------------------
% 203.72/34.60    (1)  all_58_14 = all_52_23
% 203.72/34.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.60    (3)  op(all_52_7, all_52_7) = e0
% 203.72/34.60    (4)  op(all_52_5, all_52_5) = e1
% 203.72/34.60    (5)   ~ (e3 = e0)
% 203.72/34.60    (6)   ~ (all_52_3 = all_52_19)
% 203.72/34.60    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.72/34.60    (8)   ~ (all_4_2 = e3)
% 203.72/34.60    (9)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.60    (10)  all_58_0 = all_6_2
% 203.72/34.60    (11)  op(all_14_2, e0) = all_14_1
% 203.72/34.60    (12)  all_56_4 = all_52_3
% 203.72/34.60    (13)  all_58_13 = e3
% 203.72/34.60    (14)  op(e0, all_14_1) = all_14_0
% 203.72/34.60    (15)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.60    (16)   ~ (all_52_27 = all_52_29)
% 203.72/34.60    (17)  all_58_9 = all_52_25
% 203.72/34.60    (18)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.72/34.60    (19)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.60    (20)  op(e2, e2) = all_4_2
% 203.72/34.60    (21)  all_58_11 = all_52_29
% 203.72/34.60    (22)   ~ (all_52_3 = e3)
% 203.72/34.60    (23)  op(e0, e0) = all_14_2
% 203.72/34.60    (24)  all_56_15 = all_14_2
% 203.72/34.60    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.60    (26)  op(e1, e0) = all_52_29
% 203.72/34.60    (27)  all_56_9 = all_52_13
% 203.72/34.60    (28)   ~ (all_52_13 = all_10_2)
% 203.72/34.60    (29)  all_58_10 = all_52_27
% 203.72/34.60    (30)   ~ (all_52_29 = all_10_2)
% 203.72/34.60    (31)  all_58_7 = all_52_13
% 203.72/34.60    (32)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.60    (33)  op(all_6_2, all_6_2) = e3
% 203.72/34.60    (34)   ~ (all_52_5 = all_52_7)
% 203.72/34.60    (35)  all_58_12 = all_52_7
% 203.72/34.60    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.60    (37)   ~ (all_52_7 = e3)
% 203.72/34.60    (38)   ~ (all_52_7 = all_14_2)
% 203.72/34.60    (39)   ~ (all_14_2 = e0)
% 203.72/34.60    (40)  all_58_2 = all_52_3
% 203.72/34.60    (41)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.72/34.60    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.60    (43)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.60    (44)  op(all_52_3, all_52_3) = e2
% 203.72/34.60    (45)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.60    (46)  all_56_6 = all_52_19
% 203.72/34.60    (47)   ~ (all_52_19 = all_52_27)
% 203.72/34.60    (48)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.72/34.60    (49)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.60    (50)   ~ (all_52_13 = all_4_2)
% 203.72/34.60    (51)  all_58_0 = e3
% 203.72/34.60    (52)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.60    (53)  op(e0, e3) = all_52_7
% 203.72/34.60    (54)  all_58_15 = all_14_2
% 203.72/34.60    (55)   ~ (all_52_19 = all_10_2)
% 203.72/34.60    (56)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.72/34.60    (57)  all_58_8 = all_10_2
% 203.72/34.60    (58)   ~ (all_52_5 = all_10_2)
% 203.72/34.60    (59)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.60    (60)  all_56_12 = all_52_7
% 203.72/34.60    (61)   ~ (all_52_25 = e2)
% 203.72/34.60    (62)   ~ (all_52_5 = all_6_2)
% 203.72/34.60    (63)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.60    (64)  op(e3, e3) = all_6_2
% 203.72/34.60    (65)   ~ (all_4_2 = e2)
% 203.72/34.60    (66)   ~ (all_52_13 = e3)
% 203.72/34.60    (67)   ~ (all_52_27 = all_14_2)
% 203.72/34.60    (68)   ~ (all_52_3 = all_52_7)
% 203.72/34.60    (69)  all_58_5 = all_52_19
% 203.72/34.60    (70)  all_58_6 = all_52_5
% 203.72/34.60    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.60    (72)   ~ (e1 = e0)
% 203.72/34.60    (73)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.60    (74)   ~ (e3 = e2)
% 203.72/34.60    (75)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.60    (76)  op(e1, e1) = all_10_2
% 203.72/34.60    (77)   ~ (all_52_23 = all_10_2)
% 203.72/34.60    (78)  all_58_3 = all_4_2
% 203.72/34.60    (79)   ~ (all_52_3 = all_4_2)
% 203.72/34.60    (80)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.72/34.60    (81)   ~ (all_52_13 = all_52_29)
% 203.72/34.60    (82)   ~ (all_14_0 = e2)
% 203.72/34.60    (83)   ~ (all_14_2 = e3)
% 203.72/34.60  
% 203.72/34.60  Begin of proof
% 203.72/34.60  | 
% 203.72/34.60  | BETA: splitting (43) gives:
% 203.72/34.60  | 
% 203.72/34.60  | Case 1:
% 203.72/34.60  | | 
% 203.72/34.60  | |   (84)  all_56_4 = e3
% 203.72/34.60  | | 
% 203.72/34.60  | | REF_CLOSE: (12), (22), (84) are inconsistent by sub-proof #1340.
% 203.72/34.60  | | 
% 203.72/34.60  | Case 2:
% 203.72/34.60  | | 
% 203.72/34.60  | |   (85)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.60  | | 
% 203.72/34.60  | | BETA: splitting (41) gives:
% 203.72/34.60  | | 
% 203.72/34.60  | | Case 1:
% 203.72/34.60  | | | 
% 203.72/34.60  | | |   (86)  all_56_6 = e3
% 203.72/34.60  | | | 
% 203.72/34.60  | | | COMBINE_EQS: (46), (86) imply:
% 203.72/34.60  | | |   (87)  all_52_19 = e3
% 203.72/34.60  | | | 
% 203.72/34.60  | | | SIMP: (87) implies:
% 203.72/34.60  | | |   (88)  all_52_19 = e3
% 203.72/34.60  | | | 
% 203.72/34.60  | | | COMBINE_EQS: (69), (88) imply:
% 203.72/34.60  | | |   (89)  all_58_5 = e3
% 203.72/34.60  | | | 
% 203.72/34.60  | | | REDUCE: (47), (88) imply:
% 203.72/34.60  | | |   (90)   ~ (all_52_27 = e3)
% 203.72/34.60  | | | 
% 203.72/34.60  | | | SIMP: (90) implies:
% 203.72/34.60  | | |   (91)   ~ (all_52_27 = e3)
% 203.72/34.60  | | | 
% 203.72/34.60  | | | BETA: splitting (73) gives:
% 203.72/34.60  | | | 
% 203.72/34.60  | | | Case 1:
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | |   (92)  all_58_10 = e3
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | | REF_CLOSE: (29), (91), (92) are inconsistent by sub-proof #1301.
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | Case 2:
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | |   (93)  all_58_11 = e3 | all_58_15 = e3
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | | BETA: splitting (93) gives:
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | | Case 1:
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | |   (94)  all_58_11 = e3
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | COMBINE_EQS: (21), (94) imply:
% 203.72/34.60  | | | | |   (95)  all_52_29 = e3
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | SIMP: (95) implies:
% 203.72/34.60  | | | | |   (96)  all_52_29 = e3
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | REDUCE: (26), (96) imply:
% 203.72/34.60  | | | | |   (97)  op(e1, e0) = e3
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | BETA: splitting (80) gives:
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | Case 1:
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | |   (98)  all_58_2 = e2
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | | COMBINE_EQS: (40), (98) imply:
% 203.72/34.60  | | | | | |   (99)  all_52_3 = e2
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | | SIMP: (99) implies:
% 203.72/34.60  | | | | | |   (100)  all_52_3 = e2
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | | REF_CLOSE: (2), (20), (44), (79), (100) are inconsistent by
% 203.72/34.60  | | | | | |            sub-proof #1157.
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | Case 2:
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | |   (101)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | | BETA: splitting (101) gives:
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | | Case 1:
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | |   (102)  all_58_3 = e2
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | | COMBINE_EQS: (78), (102) imply:
% 203.72/34.60  | | | | | | |   (103)  all_4_2 = e2
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | | REDUCE: (65), (103) imply:
% 203.72/34.60  | | | | | | |   (104)  $false
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | | CLOSE: (104) is inconsistent.
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | Case 2:
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | |   (105)  all_58_5 = e2 | all_58_10 = e2
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | | BETA: splitting (105) gives:
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | | Case 1:
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | |   (106)  all_58_5 = e2
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | | REF_CLOSE: (74), (89), (106) are inconsistent by sub-proof #625.
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | Case 2:
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | |   (107)  all_58_10 = e2
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | | COMBINE_EQS: (29), (107) imply:
% 203.72/34.60  | | | | | | | |   (108)  all_52_27 = e2
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | | SIMP: (108) implies:
% 203.72/34.60  | | | | | | | |   (109)  all_52_27 = e2
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | | REDUCE: (67), (109) imply:
% 203.72/34.60  | | | | | | | |   (110)   ~ (all_14_2 = e2)
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | | REF_CLOSE: (2), (3), (11), (14), (19), (23), (24), (38), (39),
% 203.72/34.60  | | | | | | | |            (53), (56), (60), (82), (97), (110) are inconsistent
% 203.72/34.60  | | | | | | | |            by sub-proof #759.
% 203.72/34.60  | | | | | | | | 
% 203.72/34.60  | | | | | | | End of split
% 203.72/34.60  | | | | | | | 
% 203.72/34.60  | | | | | | End of split
% 203.72/34.60  | | | | | | 
% 203.72/34.60  | | | | | End of split
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | Case 2:
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | |   (111)  all_58_15 = e3
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | COMBINE_EQS: (54), (111) imply:
% 203.72/34.60  | | | | |   (112)  all_14_2 = e3
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | REDUCE: (83), (112) imply:
% 203.72/34.60  | | | | |   (113)  $false
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | | CLOSE: (113) is inconsistent.
% 203.72/34.60  | | | | | 
% 203.72/34.60  | | | | End of split
% 203.72/34.60  | | | | 
% 203.72/34.60  | | | End of split
% 203.72/34.60  | | | 
% 203.72/34.60  | | Case 2:
% 203.72/34.60  | | | 
% 203.72/34.60  | | |   (114)   ~ (all_56_6 = e3)
% 203.72/34.60  | | | 
% 203.72/34.60  | | | REDUCE: (46), (114) imply:
% 203.72/34.60  | | |   (115)   ~ (all_52_19 = e3)
% 203.72/34.60  | | | 
% 203.72/34.60  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 203.72/34.60  | | |            (15), (16), (17), (18), (19), (20), (21), (23), (25), (27),
% 203.72/34.60  | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 203.72/34.60  | | |            (38), (40), (42), (44), (45), (48), (49), (50), (51), (52),
% 203.72/34.60  | | |            (54), (55), (57), (58), (59), (60), (61), (62), (63), (64),
% 203.72/34.60  | | |            (65), (66), (68), (69), (70), (71), (72), (74), (75), (76),
% 203.72/34.60  | | |            (77), (78), (79), (80), (81), (85), (115) are inconsistent by
% 203.72/34.60  | | |            sub-proof #623.
% 203.72/34.60  | | | 
% 203.72/34.60  | | End of split
% 203.72/34.60  | | 
% 203.72/34.60  | End of split
% 203.72/34.60  | 
% 203.72/34.60  End of proof
% 203.72/34.60  
% 203.72/34.60  Sub-proof #623 shows that the following formulas are inconsistent:
% 203.72/34.60  ----------------------------------------------------------------
% 203.72/34.60    (1)  all_58_14 = all_52_23
% 203.72/34.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.60    (3)  op(all_52_7, all_52_7) = e0
% 203.72/34.60    (4)  op(all_52_5, all_52_5) = e1
% 203.72/34.60    (5)   ~ (e3 = e0)
% 203.72/34.60    (6)   ~ (all_52_3 = all_52_19)
% 203.72/34.60    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.72/34.60    (8)   ~ (all_4_2 = e3)
% 203.72/34.60    (9)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.60    (10)  all_58_0 = all_6_2
% 203.72/34.60    (11)  all_56_4 = all_52_3
% 203.72/34.60    (12)  all_58_13 = e3
% 203.72/34.60    (13)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.60    (14)   ~ (all_52_27 = all_52_29)
% 203.72/34.60    (15)  all_58_9 = all_52_25
% 203.72/34.60    (16)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.72/34.60    (17)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.60    (18)  op(e2, e2) = all_4_2
% 203.72/34.60    (19)  all_58_11 = all_52_29
% 203.72/34.60    (20)  op(e0, e0) = all_14_2
% 203.72/34.60    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.60    (22)  all_56_9 = all_52_13
% 203.72/34.60    (23)   ~ (all_52_13 = all_10_2)
% 203.72/34.60    (24)  all_58_10 = all_52_27
% 203.72/34.60    (25)   ~ (all_52_29 = all_10_2)
% 203.72/34.60    (26)  all_58_7 = all_52_13
% 203.72/34.60    (27)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.60    (28)  op(all_6_2, all_6_2) = e3
% 203.72/34.60    (29)   ~ (all_52_5 = all_52_7)
% 203.72/34.60    (30)  all_58_12 = all_52_7
% 203.72/34.60    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.60    (32)   ~ (all_52_7 = e3)
% 203.72/34.60    (33)   ~ (all_52_7 = all_14_2)
% 203.72/34.60    (34)  all_58_2 = all_52_3
% 203.72/34.60    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.60    (36)   ~ (all_52_19 = e3)
% 203.72/34.60    (37)  op(all_52_3, all_52_3) = e2
% 203.72/34.60    (38)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.60    (39)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.60    (40)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.72/34.60    (41)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.60    (42)   ~ (all_52_13 = all_4_2)
% 203.72/34.60    (43)  all_58_0 = e3
% 203.72/34.60    (44)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.60    (45)  all_58_15 = all_14_2
% 203.72/34.60    (46)   ~ (all_52_19 = all_10_2)
% 203.72/34.60    (47)  all_58_8 = all_10_2
% 203.72/34.60    (48)   ~ (all_52_5 = all_10_2)
% 203.72/34.60    (49)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.60    (50)  all_56_12 = all_52_7
% 203.72/34.60    (51)   ~ (all_52_25 = e2)
% 203.72/34.60    (52)   ~ (all_52_5 = all_6_2)
% 203.72/34.60    (53)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.60    (54)  op(e3, e3) = all_6_2
% 203.72/34.60    (55)   ~ (all_4_2 = e2)
% 203.72/34.60    (56)   ~ (all_52_13 = e3)
% 203.72/34.60    (57)   ~ (all_52_3 = all_52_7)
% 203.72/34.60    (58)  all_58_5 = all_52_19
% 203.72/34.60    (59)  all_58_6 = all_52_5
% 203.72/34.60    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.60    (61)   ~ (e1 = e0)
% 203.72/34.60    (62)   ~ (e3 = e2)
% 203.72/34.60    (63)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.60    (64)  op(e1, e1) = all_10_2
% 203.72/34.60    (65)   ~ (all_52_23 = all_10_2)
% 203.72/34.60    (66)  all_58_3 = all_4_2
% 203.72/34.60    (67)   ~ (all_52_3 = all_4_2)
% 203.72/34.60    (68)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.72/34.60    (69)   ~ (all_52_13 = all_52_29)
% 203.72/34.60  
% 203.72/34.60  Begin of proof
% 203.72/34.60  | 
% 203.72/34.60  | BETA: splitting (9) gives:
% 203.72/34.61  | 
% 203.72/34.61  | Case 1:
% 203.72/34.61  | | 
% 203.72/34.61  | |   (70)  all_58_3 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | COMBINE_EQS: (66), (70) imply:
% 203.72/34.61  | |   (71)  all_4_2 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | REDUCE: (8), (71) imply:
% 203.72/34.61  | |   (72)  $false
% 203.72/34.61  | | 
% 203.72/34.61  | | CLOSE: (72) is inconsistent.
% 203.72/34.61  | | 
% 203.72/34.61  | Case 2:
% 203.72/34.61  | | 
% 203.72/34.61  | |   (73)  all_58_5 = e3 | all_58_10 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 203.72/34.61  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 203.72/34.61  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 203.72/34.61  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 203.72/34.61  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 203.72/34.61  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 203.72/34.61  | |            (73) are inconsistent by sub-proof #624.
% 203.72/34.61  | | 
% 203.72/34.61  | End of split
% 203.72/34.61  | 
% 203.72/34.61  End of proof
% 203.72/34.61  
% 203.72/34.61  Sub-proof #624 shows that the following formulas are inconsistent:
% 203.72/34.61  ----------------------------------------------------------------
% 203.72/34.61    (1)  all_58_14 = all_52_23
% 203.72/34.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.61    (3)  op(all_52_7, all_52_7) = e0
% 203.72/34.61    (4)  op(all_52_5, all_52_5) = e1
% 203.72/34.61    (5)   ~ (e3 = e0)
% 203.72/34.61    (6)   ~ (all_52_3 = all_52_19)
% 203.72/34.61    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.72/34.61    (8)  all_58_0 = all_6_2
% 203.72/34.61    (9)  all_56_4 = all_52_3
% 203.72/34.61    (10)  all_58_13 = e3
% 203.72/34.61    (11)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.61    (12)   ~ (all_52_27 = all_52_29)
% 203.72/34.61    (13)  all_58_9 = all_52_25
% 203.72/34.61    (14)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.72/34.61    (15)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.61    (16)  op(e2, e2) = all_4_2
% 203.72/34.61    (17)  all_58_11 = all_52_29
% 203.72/34.61    (18)  op(e0, e0) = all_14_2
% 203.72/34.61    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.61    (20)  all_56_9 = all_52_13
% 203.72/34.61    (21)   ~ (all_52_13 = all_10_2)
% 203.72/34.61    (22)  all_58_10 = all_52_27
% 203.72/34.61    (23)   ~ (all_52_29 = all_10_2)
% 203.72/34.61    (24)  all_58_7 = all_52_13
% 203.72/34.61    (25)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.61    (26)  op(all_6_2, all_6_2) = e3
% 203.72/34.61    (27)   ~ (all_52_5 = all_52_7)
% 203.72/34.61    (28)  all_58_12 = all_52_7
% 203.72/34.61    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.61    (30)  all_58_5 = e3 | all_58_10 = e3
% 203.72/34.61    (31)   ~ (all_52_7 = e3)
% 203.72/34.61    (32)   ~ (all_52_7 = all_14_2)
% 203.72/34.61    (33)  all_58_2 = all_52_3
% 203.72/34.61    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.61    (35)   ~ (all_52_19 = e3)
% 203.72/34.61    (36)  op(all_52_3, all_52_3) = e2
% 203.72/34.61    (37)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.61    (38)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.61    (39)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.72/34.61    (40)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.61    (41)   ~ (all_52_13 = all_4_2)
% 203.72/34.61    (42)  all_58_0 = e3
% 203.72/34.61    (43)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.61    (44)  all_58_15 = all_14_2
% 203.72/34.61    (45)   ~ (all_52_19 = all_10_2)
% 203.72/34.61    (46)  all_58_8 = all_10_2
% 203.72/34.61    (47)   ~ (all_52_5 = all_10_2)
% 203.72/34.61    (48)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.61    (49)  all_56_12 = all_52_7
% 203.72/34.61    (50)   ~ (all_52_25 = e2)
% 203.72/34.61    (51)   ~ (all_52_5 = all_6_2)
% 203.72/34.61    (52)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.61    (53)  op(e3, e3) = all_6_2
% 203.72/34.61    (54)   ~ (all_4_2 = e2)
% 203.72/34.61    (55)   ~ (all_52_13 = e3)
% 203.72/34.61    (56)   ~ (all_52_3 = all_52_7)
% 203.72/34.61    (57)  all_58_5 = all_52_19
% 203.72/34.61    (58)  all_58_6 = all_52_5
% 203.72/34.61    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.61    (60)   ~ (e1 = e0)
% 203.72/34.61    (61)   ~ (e3 = e2)
% 203.72/34.61    (62)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.61    (63)  op(e1, e1) = all_10_2
% 203.72/34.61    (64)   ~ (all_52_23 = all_10_2)
% 203.72/34.61    (65)  all_58_3 = all_4_2
% 203.72/34.61    (66)   ~ (all_52_3 = all_4_2)
% 203.72/34.61    (67)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.72/34.61    (68)   ~ (all_52_13 = all_52_29)
% 203.72/34.61  
% 203.72/34.61  Begin of proof
% 203.72/34.61  | 
% 203.72/34.61  | BETA: splitting (30) gives:
% 203.72/34.61  | 
% 203.72/34.61  | Case 1:
% 203.72/34.61  | | 
% 203.72/34.61  | |   (69)  all_58_5 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | REF_CLOSE: (35), (57), (69) are inconsistent by sub-proof #1279.
% 203.72/34.61  | | 
% 203.72/34.61  | Case 2:
% 203.72/34.61  | | 
% 203.72/34.61  | |   (70)  all_58_10 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | COMBINE_EQS: (22), (70) imply:
% 203.72/34.61  | |   (71)  all_52_27 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | SIMP: (71) implies:
% 203.72/34.61  | |   (72)  all_52_27 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | REDUCE: (12), (72) imply:
% 203.72/34.61  | |   (73)   ~ (all_52_29 = e3)
% 203.72/34.61  | | 
% 203.72/34.61  | | SIMP: (73) implies:
% 203.72/34.61  | |   (74)   ~ (all_52_29 = e3)
% 203.72/34.61  | | 
% 203.72/34.61  | | BETA: splitting (43) gives:
% 203.72/34.61  | | 
% 203.72/34.61  | | Case 1:
% 203.72/34.61  | | | 
% 203.72/34.61  | | |   (75)  all_58_7 = e3
% 203.72/34.61  | | | 
% 203.72/34.61  | | | COMBINE_EQS: (24), (75) imply:
% 203.72/34.61  | | |   (76)  all_52_13 = e3
% 203.72/34.61  | | | 
% 203.72/34.61  | | | REDUCE: (55), (76) imply:
% 203.72/34.61  | | |   (77)  $false
% 203.72/34.61  | | | 
% 203.72/34.61  | | | CLOSE: (77) is inconsistent.
% 203.72/34.61  | | | 
% 203.72/34.61  | | Case 2:
% 203.72/34.61  | | | 
% 203.72/34.61  | | |   (78)  all_58_8 = e3 | all_58_11 = e3
% 203.72/34.61  | | | 
% 203.72/34.61  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 203.72/34.61  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 203.72/34.61  | | |            (25), (26), (27), (28), (29), (31), (32), (33), (34), (36),
% 203.72/34.61  | | |            (37), (38), (39), (40), (41), (42), (44), (45), (46), (47),
% 203.72/34.61  | | |            (48), (49), (50), (51), (52), (53), (54), (56), (57), (58),
% 203.72/34.61  | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.72/34.61  | | |            (70), (74), (78) are inconsistent by sub-proof #723.
% 203.72/34.61  | | | 
% 203.72/34.61  | | End of split
% 203.72/34.61  | | 
% 203.72/34.61  | End of split
% 203.72/34.61  | 
% 203.72/34.61  End of proof
% 203.72/34.61  
% 203.72/34.61  Sub-proof #625 shows that the following formulas are inconsistent:
% 203.72/34.61  ----------------------------------------------------------------
% 203.72/34.61    (1)  all_58_5 = e3
% 203.72/34.61    (2)  all_58_5 = e2
% 203.72/34.61    (3)   ~ (e3 = e2)
% 203.72/34.61  
% 203.72/34.61  Begin of proof
% 203.72/34.61  | 
% 203.72/34.61  | COMBINE_EQS: (1), (2) imply:
% 203.72/34.61  |   (4)  e3 = e2
% 203.72/34.61  | 
% 203.72/34.61  | SIMP: (4) implies:
% 203.72/34.61  |   (5)  e3 = e2
% 203.72/34.61  | 
% 203.72/34.61  | REDUCE: (3), (5) imply:
% 203.72/34.61  |   (6)  $false
% 203.72/34.61  | 
% 203.72/34.61  | CLOSE: (6) is inconsistent.
% 203.72/34.61  | 
% 203.72/34.61  End of proof
% 203.72/34.61  
% 203.72/34.61  Sub-proof #626 shows that the following formulas are inconsistent:
% 203.72/34.61  ----------------------------------------------------------------
% 203.72/34.61    (1)  all_58_14 = all_52_23
% 203.72/34.61    (2)   ~ (e3 = e1)
% 203.72/34.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.61    (4)   ~ (all_52_5 = all_52_13)
% 203.72/34.61    (5)  op(all_52_7, all_52_7) = e0
% 203.72/34.61    (6)  op(all_52_5, all_52_5) = e1
% 203.72/34.61    (7)   ~ (e3 = e0)
% 203.72/34.61    (8)  op(e2, e3) = all_52_3
% 203.72/34.61    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.61    (10)  op(e0, e2) = all_52_15
% 203.72/34.61    (11)   ~ (all_52_7 = all_52_15)
% 203.72/34.61    (12)  all_16_1 = all_10_1
% 203.72/34.61    (13)  all_58_0 = all_6_2
% 203.72/34.61    (14)  all_58_13 = all_52_15
% 203.72/34.61    (15)  op(e2, all_4_1) = e3
% 203.72/34.61    (16)  op(e2, e2) = all_4_2
% 203.72/34.61    (17)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.72/34.61    (18)  op(all_10_2, e1) = all_10_1
% 203.72/34.61    (19)   ~ (all_52_7 = all_6_2)
% 203.72/34.61    (20)  op(e0, e0) = all_14_2
% 203.72/34.61    (21)  op(e0, e1) = all_52_23
% 203.72/34.61    (22)   ~ (all_52_15 = e0)
% 203.72/34.61    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.61    (24)  all_58_15 = e0
% 203.72/34.61    (25)   ~ (all_4_1 = e1)
% 203.72/34.61    (26)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.72/34.61    (27)   ~ (e2 = e1)
% 203.72/34.61    (28)  all_56_8 = all_52_5
% 203.72/34.61    (29)  op(all_52_15, all_52_15) = all_52_14
% 203.72/34.61    (30)  all_16_2 = all_10_2
% 203.72/34.61    (31)  op(all_6_2, all_6_2) = e3
% 203.72/34.61    (32)   ~ (all_52_5 = all_52_7)
% 203.72/34.61    (33)  all_58_12 = all_52_7
% 203.72/34.61    (34)   ~ (all_52_7 = all_14_2)
% 203.72/34.61    (35)  all_58_2 = all_52_3
% 203.72/34.61    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.61    (37)   ~ (e2 = e0)
% 203.72/34.61    (38)  op(all_4_2, e2) = all_4_1
% 203.72/34.61    (39)  op(all_52_3, all_52_3) = e2
% 203.72/34.61    (40)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.61    (41)  op(e1, e2) = all_52_13
% 203.72/34.61    (42)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.72/34.61    (43)   ~ (all_52_5 = all_10_2)
% 203.72/34.61    (44)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.72/34.61    (45)  all_56_12 = all_52_7
% 203.72/34.61    (46)  op(e1, all_10_1) = e2
% 203.72/34.61    (47)  op(e3, e3) = all_6_2
% 203.72/34.61    (48)  all_58_6 = all_52_5
% 203.72/34.61    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.61    (50)   ~ (e1 = e0)
% 203.72/34.61    (51)   ~ (e3 = e2)
% 203.72/34.61    (52)  op(e1, e1) = all_10_2
% 203.72/34.61    (53)   ~ (all_52_7 = all_52_23)
% 203.72/34.61    (54)  all_56_13 = all_52_15
% 203.72/34.61    (55)   ~ (all_52_3 = all_4_2)
% 203.72/34.61    (56)   ~ (all_52_7 = e0)
% 203.72/34.61  
% 203.72/34.61  Begin of proof
% 203.72/34.61  | 
% 203.72/34.61  | BETA: splitting (26) gives:
% 203.72/34.61  | 
% 203.72/34.61  | Case 1:
% 203.72/34.61  | | 
% 203.72/34.61  | |   (57)  all_56_13 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | COMBINE_EQS: (54), (57) imply:
% 203.72/34.61  | |   (58)  all_52_15 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | SIMP: (58) implies:
% 203.72/34.61  | |   (59)  all_52_15 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | COMBINE_EQS: (14), (59) imply:
% 203.72/34.61  | |   (60)  all_58_13 = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | REDUCE: (11), (59) imply:
% 203.72/34.61  | |   (61)   ~ (all_52_7 = e3)
% 203.72/34.61  | | 
% 203.72/34.61  | | REDUCE: (29), (59) imply:
% 203.72/34.61  | |   (62)  op(e3, e3) = all_52_14
% 203.72/34.61  | | 
% 203.72/34.61  | | REDUCE: (10), (59) imply:
% 203.72/34.61  | |   (63)  op(e0, e2) = e3
% 203.72/34.61  | | 
% 203.72/34.61  | | GROUND_INST: instantiating (3) with all_6_2, all_52_14, e3, e3, simplifying
% 203.72/34.61  | |              with (47), (62) gives:
% 203.72/34.61  | |   (64)  all_52_14 = all_6_2
% 203.72/34.61  | | 
% 203.72/34.61  | | BETA: splitting (9) gives:
% 203.72/34.61  | | 
% 203.72/34.61  | | Case 1:
% 203.72/34.61  | | | 
% 203.72/34.61  | | |   (65)  all_56_12 = e3
% 203.72/34.61  | | | 
% 203.72/34.61  | | | REF_CLOSE: (45), (61), (65) are inconsistent by sub-proof #1383.
% 203.72/34.61  | | | 
% 203.72/34.61  | | Case 2:
% 203.72/34.61  | | | 
% 203.72/34.61  | | |   (66)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.61  | | | 
% 203.72/34.61  | | | BETA: splitting (40) gives:
% 203.72/34.61  | | | 
% 203.72/34.61  | | | Case 1:
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | |   (67)  all_58_12 = e1
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (17), (18), (19), (21), (24), (27),
% 203.72/34.61  | | | |            (28), (32), (33), (37), (41), (42), (43), (46), (47), (51),
% 203.72/34.61  | | | |            (52), (60), (67) are inconsistent by sub-proof #627.
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | Case 2:
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | |   (68)   ~ (all_58_12 = e1)
% 203.72/34.61  | | | |   (69)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | | REDUCE: (33), (68) imply:
% 203.72/34.61  | | | |   (70)   ~ (all_52_7 = e1)
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | | REF_CLOSE: (2), (3), (5), (8), (15), (16), (19), (24), (38), (39), (45),
% 203.72/34.61  | | | |            (47), (50), (56), (60), (63), (66), (69), (70) are
% 203.72/34.61  | | | |            inconsistent by sub-proof #768.
% 203.72/34.61  | | | | 
% 203.72/34.61  | | | End of split
% 203.72/34.61  | | | 
% 203.72/34.61  | | End of split
% 203.72/34.61  | | 
% 203.72/34.61  | Case 2:
% 203.72/34.61  | | 
% 203.72/34.61  | |   (71)   ~ (all_56_13 = e3)
% 203.72/34.61  | |   (72)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.72/34.61  | | 
% 203.72/34.61  | | REDUCE: (54), (71) imply:
% 203.72/34.61  | |   (73)   ~ (all_52_15 = e3)
% 203.72/34.61  | | 
% 203.72/34.61  | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14), (16),
% 203.72/34.61  | |            (18), (19), (20), (21), (22), (23), (24), (25), (30), (31), (33),
% 203.72/34.61  | |            (34), (35), (36), (38), (39), (40), (43), (44), (45), (47), (48),
% 203.72/34.61  | |            (49), (52), (53), (54), (55), (56), (72), (73) are inconsistent
% 203.72/34.61  | |            by sub-proof #650.
% 203.72/34.61  | | 
% 203.72/34.61  | End of split
% 203.72/34.61  | 
% 203.72/34.61  End of proof
% 203.72/34.61  
% 203.72/34.61  Sub-proof #627 shows that the following formulas are inconsistent:
% 203.72/34.61  ----------------------------------------------------------------
% 203.72/34.61    (1)  all_58_14 = all_52_23
% 203.72/34.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.61    (3)   ~ (all_52_5 = all_52_13)
% 203.72/34.61    (4)  op(all_52_7, all_52_7) = e0
% 203.72/34.61    (5)  op(all_52_5, all_52_5) = e1
% 203.72/34.61    (6)  all_58_13 = e3
% 203.72/34.61    (7)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.72/34.61    (8)  op(all_10_2, e1) = all_10_1
% 203.72/34.61    (9)   ~ (all_52_7 = all_6_2)
% 203.72/34.61    (10)  op(e0, e1) = all_52_23
% 203.72/34.61    (11)  all_58_15 = e0
% 203.72/34.61    (12)   ~ (e2 = e1)
% 203.72/34.61    (13)  all_56_8 = all_52_5
% 203.72/34.61    (14)   ~ (all_52_5 = all_52_7)
% 203.72/34.61    (15)  all_58_12 = all_52_7
% 203.72/34.61    (16)   ~ (e2 = e0)
% 203.72/34.61    (17)  op(e1, e2) = all_52_13
% 203.72/34.61    (18)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.72/34.61    (19)   ~ (all_52_5 = all_10_2)
% 203.72/34.61    (20)  op(e1, all_10_1) = e2
% 203.72/34.61    (21)  op(e3, e3) = all_6_2
% 203.72/34.61    (22)   ~ (e3 = e2)
% 203.72/34.61    (23)  op(e1, e1) = all_10_2
% 203.72/34.61    (24)  all_58_12 = e1
% 203.72/34.61  
% 203.72/34.61  Begin of proof
% 203.72/34.61  | 
% 203.72/34.61  | COMBINE_EQS: (15), (24) imply:
% 203.72/34.61  |   (25)  all_52_7 = e1
% 203.72/34.61  | 
% 203.72/34.61  | SIMP: (25) implies:
% 203.72/34.61  |   (26)  all_52_7 = e1
% 203.72/34.61  | 
% 203.72/34.61  | REDUCE: (14), (26) imply:
% 203.72/34.61  |   (27)   ~ (all_52_5 = e1)
% 203.72/34.61  | 
% 203.72/34.61  | REDUCE: (9), (26) imply:
% 203.72/34.61  |   (28)   ~ (all_6_2 = e1)
% 203.72/34.61  | 
% 203.72/34.61  | SIMP: (28) implies:
% 203.72/34.61  |   (29)   ~ (all_6_2 = e1)
% 203.72/34.61  | 
% 203.72/34.61  | REDUCE: (4), (26) imply:
% 203.72/34.61  |   (30)  op(e1, e1) = e0
% 203.72/34.61  | 
% 203.72/34.61  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (16),
% 203.72/34.61  |            (17), (18), (19), (20), (21), (22), (23), (24), (27), (29), (30)
% 203.72/34.61  |            are inconsistent by sub-proof #653.
% 203.72/34.61  | 
% 203.72/34.61  End of proof
% 203.72/34.61  
% 203.72/34.61  Sub-proof #628 shows that the following formulas are inconsistent:
% 203.72/34.61  ----------------------------------------------------------------
% 203.72/34.61    (1)   ~ (all_52_15 = all_52_23)
% 203.72/34.61    (2)   ~ (all_52_25 = all_52_27)
% 203.72/34.61    (3)  all_58_14 = all_52_23
% 203.72/34.61    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.72/34.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.61    (6)   ~ (all_52_5 = all_52_13)
% 203.72/34.61    (7)  all_58_1 = all_52_9
% 203.72/34.61    (8)   ~ (all_52_9 = all_52_13)
% 203.72/34.61    (9)   ~ (e3 = e0)
% 203.72/34.61    (10)  op(e2, e3) = all_52_3
% 203.72/34.61    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.61    (12)   ~ (all_52_3 = all_52_19)
% 203.72/34.61    (13)  op(all_52_7, all_52_7) = all_52_6
% 203.72/34.61    (14)   ~ (all_52_17 = all_52_25)
% 203.72/34.61    (15)   ~ (all_52_3 = all_6_2)
% 203.72/34.61    (16)  all_58_0 = all_6_2
% 203.72/34.61    (17)  op(all_14_2, e0) = all_14_1
% 203.72/34.61    (18)  all_56_4 = all_52_3
% 203.72/34.61    (19)   ~ (all_52_17 = all_10_2)
% 203.72/34.61    (20)  all_26_1 = all_10_1
% 203.72/34.61    (21)  op(e3, e0) = all_52_25
% 203.72/34.61    (22)  all_26_2 = all_10_2
% 203.72/34.61    (23)  op(e0, all_14_1) = all_14_0
% 203.72/34.61    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.72/34.61    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.72/34.61    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.61    (27)   ~ (all_52_27 = all_52_29)
% 203.72/34.61    (28)  all_58_13 = all_52_15
% 203.72/34.61    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.72/34.61    (30)  all_58_9 = all_52_25
% 203.72/34.61    (31)   ~ (all_52_29 = all_14_2)
% 203.72/34.61    (32)  all_22_0 = all_6_0
% 203.72/34.61    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.72/34.61    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.72/34.61    (35)  op(e1, e3) = all_52_5
% 203.72/34.61    (36)  op(e2, e2) = all_4_2
% 203.72/34.61    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.72/34.61    (38)   ~ (all_52_3 = all_52_5)
% 203.72/34.61    (39)  all_58_11 = all_52_29
% 203.72/34.61    (40)  all_56_5 = all_4_2
% 203.72/34.61    (41)   ~ (all_52_25 = all_14_2)
% 203.72/34.61    (42)   ~ (all_52_9 = all_52_15)
% 203.72/34.61    (43)   ~ (all_52_3 = all_52_27)
% 203.72/34.61    (44)  op(all_10_2, e1) = all_10_1
% 203.72/34.61    (45)  op(all_6_2, all_6_2) = all_52_0
% 203.72/34.61    (46)   ~ (all_52_7 = all_6_2)
% 203.72/34.61    (47)  op(e0, e0) = all_14_2
% 203.72/34.61    (48)  all_56_15 = all_14_2
% 203.72/34.61    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.61    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.72/34.61    (51)  all_56_11 = all_52_29
% 203.72/34.61    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.61    (53)   ~ (e2 = e1)
% 203.72/34.61    (54)   ~ (all_52_13 = all_10_2)
% 203.72/34.61    (55)   ~ (all_6_0 = e1)
% 203.72/34.61    (56)  all_58_10 = all_52_27
% 203.72/34.61    (57)  all_24_0 = all_14_0
% 203.72/34.61    (58)  all_56_8 = all_52_5
% 203.72/34.61    (59)  op(all_52_9, all_52_9) = all_52_8
% 203.72/34.61    (60)   ~ (all_52_19 = all_52_23)
% 203.72/34.61    (61)   ~ (all_52_25 = all_52_29)
% 203.72/34.61    (62)  op(all_6_2, e3) = e2
% 203.72/34.61    (63)   ~ (all_52_29 = all_10_2)
% 203.72/34.61    (64)  all_58_7 = all_52_13
% 203.72/34.61    (65)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.72/34.61    (66)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.61    (67)   ~ (all_52_5 = all_52_7)
% 203.72/34.61    (68)  all_58_12 = all_52_7
% 203.72/34.61    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.61    (70)   ~ (all_52_7 = all_14_2)
% 203.72/34.61    (71)  all_58_2 = all_52_3
% 203.72/34.61    (72)  all_56_2 = all_52_17
% 203.72/34.61    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.72/34.61    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.61    (75)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.72/34.61    (76)   ~ (all_14_0 = e3)
% 203.72/34.61    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.72/34.61    (78)  all_56_7 = all_52_27
% 203.72/34.61    (79)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.72/34.61    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.61    (81)   ~ (e2 = e0)
% 203.72/34.61    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.72/34.61    (83)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.72/34.61    (84)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 203.72/34.61    (85)   ~ (all_52_5 = all_52_29)
% 203.72/34.61    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.61    (87)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.61    (88)   ~ (all_52_15 = all_14_2)
% 203.72/34.61    (89)   ~ (all_52_19 = all_52_27)
% 203.72/34.61    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.72/34.61    (91)   ~ (all_6_0 = e2)
% 203.72/34.61    (92)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.72/34.61            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.72/34.61    (93)  op(e3, e1) = all_52_17
% 203.72/34.61    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.72/34.61    (95)  op(e0, e3) = all_52_7
% 203.72/34.61    (96)  op(e1, e2) = all_52_13
% 203.72/34.61    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.72/34.61    (98)   ~ (all_52_9 = all_52_25)
% 203.72/34.61    (99)  all_58_15 = all_14_2
% 203.72/34.61    (100)   ~ (all_52_19 = all_10_2)
% 203.72/34.61    (101)  op(all_52_23, all_52_23) = all_52_22
% 203.72/34.61    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.72/34.61    (103)  all_58_8 = all_10_2
% 203.72/34.61    (104)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.72/34.61    (105)   ~ (all_52_5 = all_10_2)
% 203.72/34.61    (106)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.61    (107)   ~ (all_52_23 = all_14_2)
% 203.72/34.61    (108)  all_56_12 = all_52_7
% 203.72/34.61    (109)  op(all_52_17, all_52_17) = all_52_16
% 203.72/34.61    (110)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.72/34.61    (111)  op(e3, e2) = all_6_0
% 203.72/34.61    (112)   ~ (all_52_25 = all_6_2)
% 203.72/34.61    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.61    (114)   ~ (all_52_9 = all_4_2)
% 203.72/34.61    (115)   ~ (all_52_5 = all_6_2)
% 203.72/34.61    (116)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.61    (117)   ~ (all_52_9 = all_6_2)
% 203.72/34.61    (118)  op(e1, all_10_1) = e2
% 203.72/34.61    (119)  all_56_0 = all_6_2
% 203.72/34.61    (120)  op(e3, e3) = all_6_2
% 203.72/34.61    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.61    (122)   ~ (all_52_27 = all_14_2)
% 203.72/34.61    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.72/34.61    (124)  all_56_14 = all_52_23
% 203.72/34.61    (125)  all_56_3 = all_52_25
% 203.72/34.61    (126)   ~ (all_52_3 = all_52_7)
% 203.72/34.61    (127)  op(all_14_2, all_14_2) = all_52_30
% 203.72/34.61    (128)  all_58_5 = all_52_19
% 203.72/34.61    (129)  all_56_1 = all_52_9
% 203.72/34.61    (130)   ~ (all_52_15 = all_4_2)
% 203.72/34.62    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.72/34.62           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.72/34.62           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.72/34.62           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.72/34.62    (132)   ~ (all_52_27 = all_4_2)
% 203.72/34.62    (133)  all_58_6 = all_52_5
% 203.72/34.62    (134)  op(e3, e2) = all_52_9
% 203.72/34.62    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.62    (136)   ~ (all_52_17 = all_6_2)
% 203.72/34.62    (137)   ~ (e1 = e0)
% 203.72/34.62    (138)   ~ (e3 = e2)
% 203.72/34.62    (139)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.72/34.62    (140)  all_26_0 = e2
% 203.72/34.62    (141)   ~ (all_52_9 = all_52_17)
% 203.72/34.62    (142)  all_56_10 = all_10_2
% 203.72/34.62    (143)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.72/34.62    (144)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.72/34.62    (145)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.62    (146)  op(e1, e1) = all_10_2
% 203.72/34.62    (147)   ~ (all_52_23 = all_10_2)
% 203.72/34.62    (148)   ~ (all_52_7 = all_52_23)
% 203.72/34.62    (149)   ~ (all_52_17 = all_52_19)
% 203.72/34.62    (150)  all_58_3 = all_4_2
% 203.72/34.62    (151)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.72/34.62    (152)   ~ (all_52_3 = all_4_2)
% 203.72/34.62    (153)   ~ (all_52_19 = all_4_2)
% 203.72/34.62    (154)   ~ (all_52_17 = all_52_23)
% 203.72/34.62    (155)  op(all_6_2, e3) = all_6_1
% 203.72/34.62    (156)   ~ (all_52_13 = all_52_29)
% 203.72/34.62    (157)  all_22_2 = all_6_2
% 203.72/34.62    (158)  all_58_4 = all_52_17
% 203.72/34.62    (159)   ~ (all_14_0 = e2)
% 203.72/34.62    (160)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.72/34.62    (161)  op(all_52_25, all_52_25) = all_52_24
% 203.72/34.62  
% 203.72/34.62  Begin of proof
% 203.72/34.62  | 
% 203.72/34.62  | GROUND_INST: instantiating (5) with all_52_9, all_6_0, e2, e3, simplifying
% 203.72/34.62  |              with (111), (134) gives:
% 203.72/34.62  |   (162)  all_52_9 = all_6_0
% 203.72/34.62  | 
% 203.72/34.62  | COMBINE_EQS: (129), (162) imply:
% 203.72/34.62  |   (163)  all_56_1 = all_6_0
% 203.72/34.62  | 
% 203.72/34.62  | COMBINE_EQS: (7), (162) imply:
% 203.72/34.62  |   (164)  all_58_1 = all_6_0
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (8), (162) imply:
% 203.72/34.62  |   (165)   ~ (all_52_13 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | SIMP: (165) implies:
% 203.72/34.62  |   (166)   ~ (all_52_13 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (42), (162) imply:
% 203.72/34.62  |   (167)   ~ (all_52_15 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | SIMP: (167) implies:
% 203.72/34.62  |   (168)   ~ (all_52_15 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (141), (162) imply:
% 203.72/34.62  |   (169)   ~ (all_52_17 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | SIMP: (169) implies:
% 203.72/34.62  |   (170)   ~ (all_52_17 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (98), (162) imply:
% 203.72/34.62  |   (171)   ~ (all_52_25 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | SIMP: (171) implies:
% 203.72/34.62  |   (172)   ~ (all_52_25 = all_6_0)
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (117), (162) imply:
% 203.72/34.62  |   (173)   ~ (all_6_0 = all_6_2)
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (114), (162) imply:
% 203.72/34.62  |   (174)   ~ (all_6_0 = all_4_2)
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (59), (162) imply:
% 203.72/34.62  |   (175)  op(all_6_0, all_6_0) = all_52_8
% 203.72/34.62  | 
% 203.72/34.62  | BETA: splitting (84) gives:
% 203.72/34.62  | 
% 203.72/34.62  | Case 1:
% 203.72/34.62  | | 
% 203.72/34.62  | |   (176)   ~ (all_24_0 = e1)
% 203.72/34.62  | | 
% 203.72/34.62  | | REDUCE: (57), (176) imply:
% 203.72/34.62  | |   (177)   ~ (all_14_0 = e1)
% 203.72/34.62  | | 
% 203.72/34.62  | | BETA: splitting (87) gives:
% 203.72/34.62  | | 
% 203.72/34.62  | | Case 1:
% 203.72/34.62  | | | 
% 203.72/34.62  | | |   (178)   ~ (all_26_0 = e2)
% 203.72/34.62  | | | 
% 203.72/34.62  | | | REDUCE: (140), (178) imply:
% 203.72/34.62  | | |   (179)  $false
% 203.72/34.62  | | | 
% 203.72/34.62  | | | CLOSE: (179) is inconsistent.
% 203.72/34.62  | | | 
% 203.72/34.62  | | Case 2:
% 203.72/34.62  | | | 
% 203.72/34.62  | | |   (180)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.62  | | | 
% 203.72/34.62  | | | BETA: splitting (92) gives:
% 203.72/34.62  | | | 
% 203.72/34.62  | | | Case 1:
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | |   (181)  all_58_15 = e0
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | COMBINE_EQS: (99), (181) imply:
% 203.72/34.62  | | | |   (182)  all_14_2 = e0
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (70), (182) imply:
% 203.72/34.62  | | | |   (183)   ~ (all_52_7 = e0)
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (107), (182) imply:
% 203.72/34.62  | | | |   (184)   ~ (all_52_23 = e0)
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (41), (182) imply:
% 203.72/34.62  | | | |   (185)   ~ (all_52_25 = e0)
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (127), (182) imply:
% 203.72/34.62  | | | |   (186)  op(e0, e0) = all_52_30
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (17), (182) imply:
% 203.72/34.62  | | | |   (187)  op(e0, e0) = all_14_1
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (47), (182) imply:
% 203.72/34.62  | | | |   (188)  op(e0, e0) = e0
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (13), (14), (15), (16),
% 203.72/34.62  | | | |            (19), (23), (24), (25), (26), (28), (29), (30), (31), (32),
% 203.72/34.62  | | | |            (33), (34), (36), (39), (44), (45), (47), (49), (50), (51),
% 203.72/34.62  | | | |            (52), (53), (55), (56), (59), (60), (61), (62), (63), (64),
% 203.72/34.62  | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (78),
% 203.72/34.62  | | | |            (79), (83), (85), (89), (90), (91), (93), (95), (97), (100),
% 203.72/34.62  | | | |            (101), (103), (105), (106), (109), (112), (113), (117),
% 203.72/34.62  | | | |            (119), (120), (121), (125), (126), (128), (131), (133),
% 203.72/34.62  | | | |            (135), (136), (138), (139), (143), (144), (146), (147),
% 203.72/34.62  | | | |            (148), (149), (150), (152), (153), (154), (157), (158),
% 203.72/34.62  | | | |            (159), (161), (163), (164), (166), (168), (170), (172),
% 203.72/34.62  | | | |            (173), (174), (175), (177), (181), (183), (184), (185),
% 203.72/34.62  | | | |            (186), (187), (188) are inconsistent by sub-proof #819.
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | Case 2:
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | |   (189)   ~ (all_58_15 = e0)
% 203.72/34.62  | | | |   (190)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.72/34.62  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | ALPHA: (190) implies:
% 203.72/34.62  | | | |   (191)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.62  | | | |   (192)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REDUCE: (99), (189) imply:
% 203.72/34.62  | | | |   (193)   ~ (all_14_2 = e0)
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 203.72/34.62  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 203.72/34.62  | | | |            (22), (24), (26), (27), (28), (29), (30), (31), (32), (33),
% 203.72/34.62  | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 203.72/34.62  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 203.72/34.62  | | | |            (54), (55), (56), (58), (59), (60), (61), (62), (63), (64),
% 203.72/34.62  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 203.72/34.62  | | | |            (75), (77), (79), (80), (81), (82), (83), (85), (86), (88),
% 203.72/34.62  | | | |            (89), (90), (91), (93), (94), (95), (96), (97), (98), (99),
% 203.72/34.62  | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 203.72/34.62  | | | |            (108), (109), (110), (112), (113), (114), (115), (116),
% 203.72/34.62  | | | |            (117), (118), (119), (120), (121), (122), (123), (124),
% 203.72/34.62  | | | |            (125), (126), (127), (128), (130), (131), (132), (133),
% 203.72/34.62  | | | |            (135), (136), (137), (138), (139), (142), (143), (144),
% 203.72/34.62  | | | |            (145), (146), (147), (148), (149), (150), (151), (152),
% 203.72/34.62  | | | |            (153), (154), (155), (156), (157), (158), (160), (161),
% 203.72/34.62  | | | |            (163), (164), (166), (168), (170), (172), (173), (174),
% 203.72/34.62  | | | |            (175), (180), (191), (192), (193) are inconsistent by
% 203.72/34.62  | | | |            sub-proof #630.
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | End of split
% 203.72/34.62  | | | 
% 203.72/34.62  | | End of split
% 203.72/34.62  | | 
% 203.72/34.62  | Case 2:
% 203.72/34.62  | | 
% 203.72/34.62  | |   (194)  all_24_0 = e1
% 203.72/34.62  | | 
% 203.72/34.62  | | COMBINE_EQS: (57), (194) imply:
% 203.72/34.62  | |   (195)  all_14_0 = e1
% 203.72/34.62  | | 
% 203.72/34.62  | | SIMP: (195) implies:
% 203.72/34.62  | |   (196)  all_14_0 = e1
% 203.72/34.62  | | 
% 203.72/34.62  | | REDUCE: (159), (196) imply:
% 203.72/34.62  | |   (197)   ~ (e2 = e1)
% 203.72/34.62  | | 
% 203.72/34.62  | | REDUCE: (23), (196) imply:
% 203.72/34.62  | |   (198)  op(e0, all_14_1) = e1
% 203.72/34.62  | | 
% 203.72/34.62  | | BETA: splitting (87) gives:
% 203.72/34.62  | | 
% 203.72/34.62  | | Case 1:
% 203.72/34.62  | | | 
% 203.72/34.62  | | |   (199)   ~ (all_26_0 = e2)
% 203.72/34.62  | | | 
% 203.72/34.62  | | | REDUCE: (140), (199) imply:
% 203.72/34.62  | | |   (200)  $false
% 203.72/34.62  | | | 
% 203.72/34.62  | | | CLOSE: (200) is inconsistent.
% 203.72/34.62  | | | 
% 203.72/34.62  | | Case 2:
% 203.72/34.62  | | | 
% 203.72/34.62  | | |   (201)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.62  | | | 
% 203.72/34.62  | | | BETA: splitting (92) gives:
% 203.72/34.62  | | | 
% 203.72/34.62  | | | Case 1:
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | |   (202)  all_58_15 = e0
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REF_CLOSE: (5), (17), (47), (99), (127), (137), (198), (202) are
% 203.72/34.62  | | | |            inconsistent by sub-proof #877.
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | Case 2:
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | |   (203)   ~ (all_58_15 = e0)
% 203.72/34.62  | | | |   (204)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.72/34.62  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 203.72/34.62  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 203.72/34.62  | | | |            (22), (24), (26), (27), (28), (29), (30), (31), (32), (33),
% 203.72/34.62  | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 203.72/34.62  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 203.72/34.62  | | | |            (54), (55), (56), (58), (59), (60), (61), (62), (63), (64),
% 203.72/34.62  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 203.72/34.62  | | | |            (75), (77), (79), (80), (81), (82), (83), (85), (86), (88),
% 203.72/34.62  | | | |            (89), (90), (91), (93), (94), (95), (96), (97), (98), (99),
% 203.72/34.62  | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 203.72/34.62  | | | |            (108), (109), (110), (112), (113), (114), (115), (116),
% 203.72/34.62  | | | |            (117), (118), (119), (120), (121), (122), (123), (124),
% 203.72/34.62  | | | |            (125), (126), (127), (128), (130), (131), (132), (133),
% 203.72/34.62  | | | |            (135), (136), (137), (138), (139), (142), (143), (144),
% 203.72/34.62  | | | |            (145), (146), (147), (148), (149), (150), (151), (152),
% 203.72/34.62  | | | |            (153), (154), (155), (156), (157), (158), (160), (161),
% 203.72/34.62  | | | |            (163), (164), (166), (168), (170), (172), (173), (174),
% 203.72/34.62  | | | |            (175), (201), (203), (204) are inconsistent by sub-proof
% 203.72/34.62  | | | |            #629.
% 203.72/34.62  | | | | 
% 203.72/34.62  | | | End of split
% 203.72/34.62  | | | 
% 203.72/34.62  | | End of split
% 203.72/34.62  | | 
% 203.72/34.62  | End of split
% 203.72/34.62  | 
% 203.72/34.62  End of proof
% 203.72/34.62  
% 203.72/34.62  Sub-proof #629 shows that the following formulas are inconsistent:
% 203.72/34.62  ----------------------------------------------------------------
% 203.72/34.62    (1)   ~ (all_52_15 = all_52_23)
% 203.72/34.62    (2)   ~ (all_52_25 = all_6_0)
% 203.72/34.62    (3)   ~ (all_52_25 = all_52_27)
% 203.72/34.62    (4)  all_58_14 = all_52_23
% 203.72/34.62    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.72/34.62    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.62    (7)   ~ (all_52_5 = all_52_13)
% 203.72/34.62    (8)  all_58_1 = all_52_9
% 203.72/34.62    (9)   ~ (all_52_9 = all_52_13)
% 203.72/34.62    (10)   ~ (e3 = e0)
% 203.72/34.62    (11)  op(e2, e3) = all_52_3
% 203.72/34.62    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.62    (13)   ~ (all_52_3 = all_52_19)
% 203.72/34.62    (14)  op(all_52_7, all_52_7) = all_52_6
% 203.72/34.62    (15)   ~ (all_52_17 = all_52_25)
% 203.72/34.62    (16)   ~ (all_52_3 = all_6_2)
% 203.72/34.62    (17)  all_58_0 = all_6_2
% 203.72/34.62    (18)  op(all_14_2, e0) = all_14_1
% 203.72/34.62    (19)  all_56_4 = all_52_3
% 203.72/34.62    (20)   ~ (all_52_17 = all_10_2)
% 203.72/34.62    (21)  all_26_1 = all_10_1
% 203.72/34.62    (22)  op(e3, e0) = all_52_25
% 203.72/34.62    (23)  all_26_2 = all_10_2
% 203.72/34.62    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.72/34.62    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.62    (26)   ~ (all_52_27 = all_52_29)
% 203.72/34.62    (27)  all_58_13 = all_52_15
% 203.72/34.62    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.72/34.62    (29)  all_58_9 = all_52_25
% 203.72/34.62    (30)   ~ (all_52_29 = all_14_2)
% 203.72/34.62    (31)  all_22_0 = all_6_0
% 203.72/34.62    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.72/34.62    (33)   ~ (all_52_17 = all_6_0)
% 203.72/34.62    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.72/34.62    (35)  op(e1, e3) = all_52_5
% 203.72/34.62    (36)  op(e2, e2) = all_4_2
% 203.72/34.62    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.72/34.62    (38)   ~ (all_52_3 = all_52_5)
% 203.72/34.62    (39)  all_58_11 = all_52_29
% 203.72/34.62    (40)  all_56_5 = all_4_2
% 203.72/34.62    (41)   ~ (all_52_25 = all_14_2)
% 203.72/34.62    (42)   ~ (all_52_9 = all_52_15)
% 203.72/34.62    (43)   ~ (all_52_3 = all_52_27)
% 203.72/34.62    (44)  op(all_10_2, e1) = all_10_1
% 203.72/34.62    (45)  op(all_6_2, all_6_2) = all_52_0
% 203.72/34.62    (46)   ~ (all_52_7 = all_6_2)
% 203.72/34.62    (47)  op(e0, e0) = all_14_2
% 203.72/34.62    (48)  all_56_15 = all_14_2
% 203.72/34.62    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.62    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.72/34.62    (51)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.62    (52)   ~ (all_58_15 = e0)
% 203.72/34.62    (53)  all_56_11 = all_52_29
% 203.72/34.62    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.62    (55)   ~ (e2 = e1)
% 203.72/34.62    (56)   ~ (all_52_13 = all_10_2)
% 203.72/34.62    (57)   ~ (all_6_0 = e1)
% 203.72/34.62    (58)  all_58_10 = all_52_27
% 203.72/34.62    (59)  all_56_8 = all_52_5
% 203.72/34.62    (60)  op(all_52_9, all_52_9) = all_52_8
% 203.72/34.62    (61)   ~ (all_52_19 = all_52_23)
% 203.72/34.62    (62)   ~ (all_52_25 = all_52_29)
% 203.72/34.62    (63)  op(all_6_2, e3) = e2
% 203.72/34.62    (64)   ~ (all_52_29 = all_10_2)
% 203.72/34.62    (65)  all_58_7 = all_52_13
% 203.72/34.62    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.72/34.62    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.62    (68)  all_58_1 = all_6_0
% 203.72/34.62    (69)   ~ (all_52_5 = all_52_7)
% 203.72/34.62    (70)  all_58_12 = all_52_7
% 203.72/34.62    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.62    (72)   ~ (all_52_7 = all_14_2)
% 203.72/34.62    (73)  all_58_2 = all_52_3
% 203.72/34.62    (74)  all_56_2 = all_52_17
% 203.72/34.62    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.72/34.62    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.62    (77)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.72/34.62    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.72/34.62    (79)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.72/34.62    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.62    (81)   ~ (e2 = e0)
% 203.72/34.62    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.72/34.62    (83)  op(all_6_0, all_6_0) = all_52_8
% 203.72/34.62    (84)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.72/34.62    (85)   ~ (all_52_5 = all_52_29)
% 203.72/34.62    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.62    (87)   ~ (all_52_15 = all_14_2)
% 203.72/34.62    (88)   ~ (all_52_13 = all_6_0)
% 203.72/34.62    (89)   ~ (all_52_19 = all_52_27)
% 203.72/34.62    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.72/34.62    (91)   ~ (all_6_0 = e2)
% 203.72/34.62    (92)  op(e3, e1) = all_52_17
% 203.72/34.62    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.72/34.62    (94)  op(e0, e3) = all_52_7
% 203.72/34.62    (95)  op(e1, e2) = all_52_13
% 203.72/34.62    (96)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.72/34.62    (97)   ~ (all_52_9 = all_52_25)
% 203.72/34.62    (98)  all_58_15 = all_14_2
% 203.72/34.62    (99)   ~ (all_52_19 = all_10_2)
% 203.72/34.62    (100)  op(all_52_23, all_52_23) = all_52_22
% 203.72/34.62    (101)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.72/34.62    (102)  all_58_8 = all_10_2
% 203.72/34.62    (103)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.72/34.62    (104)   ~ (all_52_5 = all_10_2)
% 203.72/34.62    (105)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.62    (106)   ~ (all_52_23 = all_14_2)
% 203.72/34.62    (107)  all_56_12 = all_52_7
% 203.72/34.62    (108)  op(all_52_17, all_52_17) = all_52_16
% 203.72/34.62    (109)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.72/34.62    (110)   ~ (all_52_25 = all_6_2)
% 203.72/34.62    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.62    (112)   ~ (all_52_9 = all_4_2)
% 203.72/34.62    (113)   ~ (all_52_5 = all_6_2)
% 203.72/34.62    (114)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.62    (115)   ~ (all_52_9 = all_6_2)
% 203.72/34.62    (116)  op(e1, all_10_1) = e2
% 203.72/34.62    (117)  all_56_0 = all_6_2
% 203.72/34.62    (118)  op(e3, e3) = all_6_2
% 203.72/34.62    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.62    (120)   ~ (all_52_15 = all_6_0)
% 203.72/34.62    (121)   ~ (all_52_27 = all_14_2)
% 203.72/34.62    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.72/34.62    (123)  all_56_14 = all_52_23
% 203.72/34.62    (124)  all_56_3 = all_52_25
% 203.72/34.62    (125)   ~ (all_52_3 = all_52_7)
% 203.72/34.62    (126)   ~ (all_6_0 = all_6_2)
% 203.72/34.62    (127)  op(all_14_2, all_14_2) = all_52_30
% 203.72/34.62    (128)  all_58_5 = all_52_19
% 203.72/34.62    (129)   ~ (all_52_15 = all_4_2)
% 203.72/34.62    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.72/34.62           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.72/34.62           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.72/34.62           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.72/34.62    (131)   ~ (all_52_27 = all_4_2)
% 203.72/34.62    (132)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 203.72/34.62             all_58_13 = e0 | all_58_14 = e0)
% 203.72/34.62    (133)  all_58_6 = all_52_5
% 203.72/34.62    (134)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.62    (135)   ~ (all_52_17 = all_6_2)
% 203.72/34.62    (136)   ~ (e1 = e0)
% 203.72/34.62    (137)   ~ (e3 = e2)
% 203.72/34.62    (138)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.72/34.62    (139)  all_56_10 = all_10_2
% 203.72/34.62    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.72/34.62    (141)  all_56_1 = all_6_0
% 203.72/34.62    (142)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.72/34.62    (143)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.62    (144)   ~ (all_6_0 = all_4_2)
% 203.72/34.62    (145)  op(e1, e1) = all_10_2
% 203.72/34.62    (146)   ~ (all_52_23 = all_10_2)
% 203.72/34.62    (147)   ~ (all_52_7 = all_52_23)
% 203.72/34.62    (148)   ~ (all_52_17 = all_52_19)
% 203.72/34.62    (149)  all_58_3 = all_4_2
% 203.72/34.62    (150)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.72/34.62    (151)   ~ (all_52_3 = all_4_2)
% 203.72/34.62    (152)   ~ (all_52_19 = all_4_2)
% 203.72/34.62    (153)   ~ (all_52_17 = all_52_23)
% 203.72/34.62    (154)  op(all_6_2, e3) = all_6_1
% 203.72/34.62    (155)   ~ (all_52_13 = all_52_29)
% 203.72/34.62    (156)  all_22_2 = all_6_2
% 203.72/34.62    (157)  all_58_4 = all_52_17
% 203.72/34.62    (158)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.72/34.62    (159)  op(all_52_25, all_52_25) = all_52_24
% 203.72/34.62  
% 203.72/34.62  Begin of proof
% 203.72/34.62  | 
% 203.72/34.62  | ALPHA: (132) implies:
% 203.72/34.62  |   (160)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.62  |   (161)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.72/34.62  | 
% 203.72/34.62  | REDUCE: (52), (98) imply:
% 203.72/34.62  |   (162)   ~ (all_14_2 = e0)
% 203.72/34.62  | 
% 203.72/34.62  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.72/34.62  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.72/34.62  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.72/34.62  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 203.72/34.62  |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 203.72/34.62  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.72/34.62  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.72/34.62  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 203.72/34.62  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.72/34.62  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.72/34.62  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 203.72/34.62  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 203.72/34.62  |            (129), (130), (131), (133), (134), (135), (136), (137), (138),
% 203.72/34.62  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 203.72/34.62  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 203.72/34.62  |            (157), (158), (159), (160), (161), (162) are inconsistent by
% 203.72/34.62  |            sub-proof #630.
% 203.72/34.62  | 
% 203.72/34.62  End of proof
% 203.72/34.62  
% 203.72/34.62  Sub-proof #630 shows that the following formulas are inconsistent:
% 203.72/34.62  ----------------------------------------------------------------
% 203.72/34.62    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.72/34.62    (2)   ~ (all_52_15 = all_52_23)
% 203.72/34.62    (3)   ~ (all_52_25 = all_6_0)
% 203.72/34.62    (4)   ~ (all_52_25 = all_52_27)
% 203.72/34.62    (5)  all_58_14 = all_52_23
% 203.72/34.62    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.72/34.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.72/34.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.72/34.63    (8)   ~ (all_52_5 = all_52_13)
% 203.72/34.63    (9)  all_58_1 = all_52_9
% 203.72/34.63    (10)   ~ (all_52_9 = all_52_13)
% 203.72/34.63    (11)   ~ (e3 = e0)
% 203.72/34.63    (12)  op(e2, e3) = all_52_3
% 203.72/34.63    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.72/34.63    (14)   ~ (all_52_3 = all_52_19)
% 203.72/34.63    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.72/34.63    (16)   ~ (all_52_17 = all_52_25)
% 203.72/34.63    (17)   ~ (all_52_3 = all_6_2)
% 203.72/34.63    (18)  all_58_0 = all_6_2
% 203.72/34.63    (19)  op(all_14_2, e0) = all_14_1
% 203.72/34.63    (20)  all_56_4 = all_52_3
% 203.72/34.63    (21)   ~ (all_52_17 = all_10_2)
% 203.72/34.63    (22)  all_26_1 = all_10_1
% 203.72/34.63    (23)  op(e3, e0) = all_52_25
% 203.72/34.63    (24)  all_26_2 = all_10_2
% 203.72/34.63    (25)  op(all_52_5, all_52_5) = all_52_4
% 203.72/34.63    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.72/34.63    (27)   ~ (all_52_27 = all_52_29)
% 203.72/34.63    (28)  all_58_13 = all_52_15
% 203.72/34.63    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.72/34.63    (30)  all_58_9 = all_52_25
% 203.72/34.63    (31)   ~ (all_52_29 = all_14_2)
% 203.72/34.63    (32)  all_22_0 = all_6_0
% 203.72/34.63    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.72/34.63    (34)   ~ (all_52_17 = all_6_0)
% 203.72/34.63    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.72/34.63    (36)  op(e1, e3) = all_52_5
% 203.72/34.63    (37)  op(e2, e2) = all_4_2
% 203.72/34.63    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.72/34.63    (39)   ~ (all_52_3 = all_52_5)
% 203.72/34.63    (40)  all_58_11 = all_52_29
% 203.72/34.63    (41)  all_56_5 = all_4_2
% 203.72/34.63    (42)   ~ (all_52_25 = all_14_2)
% 203.72/34.63    (43)   ~ (all_52_9 = all_52_15)
% 203.72/34.63    (44)   ~ (all_52_3 = all_52_27)
% 203.72/34.63    (45)  op(all_10_2, e1) = all_10_1
% 203.72/34.63    (46)  op(all_6_2, all_6_2) = all_52_0
% 203.72/34.63    (47)   ~ (all_52_7 = all_6_2)
% 203.72/34.63    (48)  op(e0, e0) = all_14_2
% 203.72/34.63    (49)  all_56_15 = all_14_2
% 203.72/34.63    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.63    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.72/34.63    (52)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.72/34.63    (53)  all_56_11 = all_52_29
% 203.72/34.63    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.63    (55)   ~ (e2 = e1)
% 203.72/34.63    (56)   ~ (all_52_13 = all_10_2)
% 203.72/34.63    (57)   ~ (all_6_0 = e1)
% 203.72/34.63    (58)  all_58_10 = all_52_27
% 203.72/34.63    (59)  all_56_8 = all_52_5
% 203.72/34.63    (60)  op(all_52_9, all_52_9) = all_52_8
% 203.72/34.63    (61)   ~ (all_52_19 = all_52_23)
% 203.72/34.63    (62)   ~ (all_52_25 = all_52_29)
% 203.72/34.63    (63)  op(all_6_2, e3) = e2
% 203.72/34.63    (64)   ~ (all_52_29 = all_10_2)
% 203.72/34.63    (65)  all_58_7 = all_52_13
% 203.72/34.63    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.72/34.63    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.72/34.63    (68)  all_58_1 = all_6_0
% 203.72/34.63    (69)   ~ (all_52_5 = all_52_7)
% 203.72/34.63    (70)  all_58_12 = all_52_7
% 203.72/34.63    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.72/34.63    (72)   ~ (all_52_7 = all_14_2)
% 203.72/34.63    (73)   ~ (all_14_2 = e0)
% 203.72/34.63    (74)  all_58_2 = all_52_3
% 203.72/34.63    (75)  all_56_2 = all_52_17
% 203.72/34.63    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.72/34.63    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.72/34.63    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.72/34.63    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.72/34.63    (80)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.72/34.63    (81)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.72/34.63    (82)   ~ (e2 = e0)
% 203.72/34.63    (83)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.72/34.63    (84)  op(all_6_0, all_6_0) = all_52_8
% 203.72/34.63    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.72/34.63    (86)   ~ (all_52_5 = all_52_29)
% 203.72/34.63    (87)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.72/34.63    (88)   ~ (all_52_15 = all_14_2)
% 203.72/34.63    (89)   ~ (all_52_13 = all_6_0)
% 203.72/34.63    (90)   ~ (all_52_19 = all_52_27)
% 203.72/34.63    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.72/34.63    (92)   ~ (all_6_0 = e2)
% 203.72/34.63    (93)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.72/34.63    (94)  op(e3, e1) = all_52_17
% 203.72/34.63    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.72/34.63    (96)  op(e0, e3) = all_52_7
% 203.72/34.63    (97)  op(e1, e2) = all_52_13
% 203.72/34.63    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.72/34.63    (99)   ~ (all_52_9 = all_52_25)
% 203.72/34.63    (100)  all_58_15 = all_14_2
% 203.72/34.63    (101)   ~ (all_52_19 = all_10_2)
% 203.72/34.63    (102)  op(all_52_23, all_52_23) = all_52_22
% 203.72/34.63    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.72/34.63    (104)  all_58_8 = all_10_2
% 203.72/34.63    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.72/34.63    (106)   ~ (all_52_5 = all_10_2)
% 203.72/34.63    (107)  op(all_52_29, all_52_29) = all_52_28
% 203.72/34.63    (108)   ~ (all_52_23 = all_14_2)
% 203.72/34.63    (109)  all_56_12 = all_52_7
% 203.72/34.63    (110)  op(all_52_17, all_52_17) = all_52_16
% 203.72/34.63    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.72/34.63    (112)   ~ (all_52_25 = all_6_2)
% 203.72/34.63    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.63    (114)   ~ (all_52_9 = all_4_2)
% 203.72/34.63    (115)   ~ (all_52_5 = all_6_2)
% 203.72/34.63    (116)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.72/34.63    (117)   ~ (all_52_9 = all_6_2)
% 203.72/34.63    (118)  op(e1, all_10_1) = e2
% 203.72/34.63    (119)  all_56_0 = all_6_2
% 203.72/34.63    (120)  op(e3, e3) = all_6_2
% 203.72/34.63    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.72/34.63    (122)   ~ (all_52_15 = all_6_0)
% 203.72/34.63    (123)   ~ (all_52_27 = all_14_2)
% 203.72/34.63    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.72/34.63    (125)  all_56_14 = all_52_23
% 203.72/34.63    (126)  all_56_3 = all_52_25
% 203.72/34.63    (127)   ~ (all_52_3 = all_52_7)
% 203.72/34.63    (128)   ~ (all_6_0 = all_6_2)
% 203.72/34.63    (129)  op(all_14_2, all_14_2) = all_52_30
% 203.72/34.63    (130)  all_58_5 = all_52_19
% 203.72/34.63    (131)   ~ (all_52_15 = all_4_2)
% 203.72/34.63    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.72/34.63           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.72/34.63           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.72/34.63           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.72/34.63    (133)   ~ (all_52_27 = all_4_2)
% 203.72/34.63    (134)  all_58_6 = all_52_5
% 203.72/34.63    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.72/34.63    (136)   ~ (all_52_17 = all_6_2)
% 203.72/34.63    (137)   ~ (e1 = e0)
% 203.72/34.63    (138)   ~ (e3 = e2)
% 203.72/34.63    (139)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.72/34.63    (140)  all_56_10 = all_10_2
% 203.72/34.63    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.72/34.63    (142)  all_56_1 = all_6_0
% 203.72/34.63    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.72/34.63    (144)  op(all_52_13, all_52_13) = all_52_12
% 203.72/34.63    (145)   ~ (all_6_0 = all_4_2)
% 203.72/34.63    (146)  op(e1, e1) = all_10_2
% 203.72/34.63    (147)   ~ (all_52_23 = all_10_2)
% 203.72/34.63    (148)   ~ (all_52_7 = all_52_23)
% 203.72/34.63    (149)   ~ (all_52_17 = all_52_19)
% 203.72/34.63    (150)  all_58_3 = all_4_2
% 203.72/34.63    (151)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.72/34.63    (152)   ~ (all_52_3 = all_4_2)
% 203.72/34.63    (153)   ~ (all_52_19 = all_4_2)
% 203.72/34.63    (154)   ~ (all_52_17 = all_52_23)
% 203.72/34.63    (155)  op(all_6_2, e3) = all_6_1
% 203.72/34.63    (156)   ~ (all_52_13 = all_52_29)
% 203.72/34.63    (157)  all_22_2 = all_6_2
% 203.72/34.63    (158)  all_58_4 = all_52_17
% 203.72/34.63    (159)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.72/34.63    (160)  op(all_52_25, all_52_25) = all_52_24
% 203.72/34.63  
% 203.72/34.63  Begin of proof
% 203.72/34.63  | 
% 203.72/34.63  | BETA: splitting (139) gives:
% 203.72/34.63  | 
% 203.72/34.63  | Case 1:
% 203.72/34.63  | | 
% 203.72/34.63  | |   (161)  all_56_1 = e3
% 203.72/34.63  | | 
% 203.72/34.63  | | COMBINE_EQS: (142), (161) imply:
% 203.72/34.63  | |   (162)  all_6_0 = e3
% 203.72/34.63  | | 
% 203.72/34.63  | | COMBINE_EQS: (68), (162) imply:
% 203.72/34.63  | |   (163)  all_58_1 = e3
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (89), (162) imply:
% 203.72/34.63  | |   (164)   ~ (all_52_13 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (122), (162) imply:
% 203.72/34.63  | |   (165)   ~ (all_52_15 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (34), (162) imply:
% 203.72/34.63  | |   (166)   ~ (all_52_17 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (3), (162) imply:
% 203.72/34.63  | |   (167)   ~ (all_52_25 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (128), (162) imply:
% 203.72/34.63  | |   (168)   ~ (all_6_2 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | SIMP: (168) implies:
% 203.72/34.63  | |   (169)   ~ (all_6_2 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (145), (162) imply:
% 203.72/34.63  | |   (170)   ~ (all_4_2 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | SIMP: (170) implies:
% 203.72/34.63  | |   (171)   ~ (all_4_2 = e3)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (57), (162) imply:
% 203.72/34.63  | |   (172)   ~ (e3 = e1)
% 203.72/34.63  | | 
% 203.72/34.63  | | REDUCE: (84), (162) imply:
% 203.72/34.63  | |   (173)  op(e3, e3) = all_52_8
% 203.72/34.63  | | 
% 203.72/34.63  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 203.72/34.63  | |              with (120), (173) gives:
% 203.72/34.63  | |   (174)  all_52_8 = all_6_2
% 203.72/34.63  | | 
% 203.72/34.63  | | BETA: splitting (132) gives:
% 203.72/34.63  | | 
% 203.72/34.63  | | Case 1:
% 203.72/34.63  | | | 
% 203.72/34.63  | | |   (175)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.72/34.63  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.72/34.63  | | |            e0)
% 203.72/34.63  | | | 
% 203.72/34.63  | | | BETA: splitting (175) gives:
% 203.72/34.63  | | | 
% 203.72/34.63  | | | Case 1:
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | |   (176)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REF_CLOSE: (6), (7), (15), (18), (25), (37), (46), (48), (50), (70),
% 203.72/34.63  | | | |            (72), (74), (77), (106), (120), (134), (135), (146), (152),
% 203.72/34.63  | | | |            (169), (176) are inconsistent by sub-proof #835.
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | Case 2:
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | |   (177)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.72/34.63  | | | |          e0
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REF_CLOSE: (169), (174), (177) are inconsistent by sub-proof #834.
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | End of split
% 203.72/34.63  | | | 
% 203.72/34.63  | | Case 2:
% 203.72/34.63  | | | 
% 203.72/34.63  | | |   (178)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.72/34.63  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.72/34.63  | | |            all_52_30 = e0)
% 203.72/34.63  | | | 
% 203.72/34.63  | | | BETA: splitting (178) gives:
% 203.72/34.63  | | | 
% 203.72/34.63  | | | Case 1:
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | |   (179)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.72/34.63  | | | |          e0
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | ALPHA: (179) implies:
% 203.72/34.63  | | | |   (180)  all_52_22 = e0
% 203.72/34.63  | | | |   (181)  all_52_20 = e1
% 203.72/34.63  | | | |   (182)  all_52_18 = e2
% 203.72/34.63  | | | |   (183)  all_52_16 = e3
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (110), (183) imply:
% 203.72/34.63  | | | |   (184)  op(all_52_17, all_52_17) = e3
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (26), (182) imply:
% 203.72/34.63  | | | |   (185)  op(all_52_19, all_52_19) = e2
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (102), (180) imply:
% 203.72/34.63  | | | |   (186)  op(all_52_23, all_52_23) = e0
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (29), (181) imply:
% 203.72/34.63  | | | |   (187)  op(all_10_2, all_10_2) = e1
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | BETA: splitting (105) gives:
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | Case 1:
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | |   (188)  all_56_15 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (49), (188) imply:
% 203.72/34.63  | | | | |   (189)  all_14_2 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | SIMP: (189) implies:
% 203.72/34.63  | | | | |   (190)  all_14_2 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (123), (190) imply:
% 203.72/34.63  | | | | |   (191)   ~ (all_52_27 = e3)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (31), (190) imply:
% 203.72/34.63  | | | | |   (192)   ~ (all_52_29 = e3)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (129), (190) imply:
% 203.72/34.63  | | | | |   (193)  op(e3, e3) = all_52_30
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (19), (190) imply:
% 203.72/34.63  | | | | |   (194)  op(e3, e0) = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3,
% 203.72/34.63  | | | | |              simplifying with (23), (194) gives:
% 203.72/34.63  | | | | |   (195)  all_52_25 = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_30, e3, e3,
% 203.72/34.63  | | | | |              simplifying with (120), (193) gives:
% 203.72/34.63  | | | | |   (196)  all_52_30 = all_6_2
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (30), (195) imply:
% 203.72/34.63  | | | | |   (197)  all_58_9 = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | BETA: splitting (50) gives:
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | Case 1:
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | |   (198)  all_58_2 = e3
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | COMBINE_EQS: (74), (198) imply:
% 203.72/34.63  | | | | | |   (199)  all_52_3 = e3
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | SIMP: (199) implies:
% 203.72/34.63  | | | | | |   (200)  all_52_3 = e3
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | REDUCE: (39), (200) imply:
% 203.72/34.63  | | | | | |   (201)   ~ (all_52_5 = e3)
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | SIMP: (201) implies:
% 203.72/34.63  | | | | | |   (202)   ~ (all_52_5 = e3)
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | REDUCE: (127), (200) imply:
% 203.72/34.63  | | | | | |   (203)   ~ (all_52_7 = e3)
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | SIMP: (203) implies:
% 203.72/34.63  | | | | | |   (204)   ~ (all_52_7 = e3)
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | REF_CLOSE: (7), (9), (10), (11), (18), (22), (24), (28), (30), (37),
% 203.72/34.63  | | | | | |            (40), (43), (45), (52), (55), (56), (60), (65), (70),
% 203.72/34.63  | | | | | |            (71), (74), (76), (77), (78), (82), (94), (98), (104),
% 203.72/34.63  | | | | | |            (106), (114), (117), (120), (124), (134), (137), (138),
% 203.72/34.63  | | | | | |            (150), (152), (158), (166), (167), (169), (184), (187),
% 203.72/34.63  | | | | | |            (192), (197), (202), (204) are inconsistent by sub-proof
% 203.72/34.63  | | | | | |            #636.
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | Case 2:
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | |   (205)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | REF_CLOSE: (5), (7), (11), (12), (17), (18), (25), (30), (31), (33),
% 203.72/34.63  | | | | | |            (40), (48), (53), (55), (58), (61), (63), (64), (65),
% 203.72/34.63  | | | | | |            (71), (78), (82), (85), (91), (101), (104), (120), (130),
% 203.72/34.63  | | | | | |            (134), (137), (141), (146), (149), (150), (158), (163),
% 203.72/34.63  | | | | | |            (164), (171), (172), (173), (184), (185), (187), (191),
% 203.72/34.63  | | | | | |            (205) are inconsistent by sub-proof #828.
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | End of split
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | Case 2:
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | |   (206)   ~ (all_56_15 = e3)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (49), (206) imply:
% 203.72/34.63  | | | | |   (207)   ~ (all_14_2 = e3)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REF_CLOSE: (5), (7), (11), (16), (18), (28), (30), (33), (35), (37),
% 203.72/34.63  | | | | |            (42), (45), (47), (48), (50), (54), (55), (58), (61), (63),
% 203.72/34.63  | | | | |            (70), (72), (74), (75), (78), (82), (85), (87), (93), (94),
% 203.72/34.63  | | | | |            (96), (100), (101), (104), (112), (113), (120), (123),
% 203.72/34.63  | | | | |            (126), (127), (130), (133), (135), (136), (137), (140),
% 203.72/34.63  | | | | |            (141), (146), (147), (148), (150), (154), (158), (159),
% 203.72/34.63  | | | | |            (163), (165), (166), (167), (169), (171), (172), (173),
% 203.72/34.63  | | | | |            (184), (185), (186), (187), (207) are inconsistent by
% 203.72/34.63  | | | | |            sub-proof #813.
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | End of split
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | Case 2:
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | |   (208)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.72/34.63  | | | |          e0
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | ALPHA: (208) implies:
% 203.72/34.63  | | | |   (209)  all_52_30 = e0
% 203.72/34.63  | | | |   (210)  all_52_28 = e1
% 203.72/34.63  | | | |   (211)  all_52_26 = e2
% 203.72/34.63  | | | |   (212)  all_52_24 = e3
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (160), (212) imply:
% 203.72/34.63  | | | |   (213)  op(all_52_25, all_52_25) = e3
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (35), (211) imply:
% 203.72/34.63  | | | |   (214)  op(all_52_27, all_52_27) = e2
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (107), (210) imply:
% 203.72/34.63  | | | |   (215)  op(all_52_29, all_52_29) = e1
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | REDUCE: (129), (209) imply:
% 203.72/34.63  | | | |   (216)  op(all_14_2, all_14_2) = e0
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | BETA: splitting (105) gives:
% 203.72/34.63  | | | | 
% 203.72/34.63  | | | | Case 1:
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | |   (217)  all_56_15 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (49), (217) imply:
% 203.72/34.63  | | | | |   (218)  all_14_2 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | SIMP: (218) implies:
% 203.72/34.63  | | | | |   (219)  all_14_2 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (100), (219) imply:
% 203.72/34.63  | | | | |   (220)  all_58_15 = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (108), (219) imply:
% 203.72/34.63  | | | | |   (221)   ~ (all_52_23 = e3)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (216), (219) imply:
% 203.72/34.63  | | | | |   (222)  op(e3, e3) = e0
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (19), (219) imply:
% 203.72/34.63  | | | | |   (223)  op(e3, e0) = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3,
% 203.72/34.63  | | | | |              simplifying with (23), (223) gives:
% 203.72/34.63  | | | | |   (224)  all_52_25 = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | GROUND_INST: instantiating (7) with all_6_2, e0, e3, e3, simplifying
% 203.72/34.63  | | | | |              with (120), (222) gives:
% 203.72/34.63  | | | | |   (225)  all_6_2 = e0
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (126), (224) imply:
% 203.72/34.63  | | | | |   (226)  all_56_3 = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (30), (224) imply:
% 203.72/34.63  | | | | |   (227)  all_58_9 = all_14_1
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (18), (225) imply:
% 203.72/34.63  | | | | |   (228)  all_58_0 = e0
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (17), (225) imply:
% 203.72/34.63  | | | | |   (229)   ~ (all_52_3 = e0)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (115), (225) imply:
% 203.72/34.63  | | | | |   (230)   ~ (all_52_5 = e0)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (47), (225) imply:
% 203.72/34.63  | | | | |   (231)   ~ (all_52_7 = e0)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (136), (225) imply:
% 203.72/34.63  | | | | |   (232)   ~ (all_52_17 = e0)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (112), (224), (225) imply:
% 203.72/34.63  | | | | |   (233)   ~ (all_14_1 = e0)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (167), (224) imply:
% 203.72/34.63  | | | | |   (234)   ~ (all_14_1 = e3)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (213), (224) imply:
% 203.72/34.63  | | | | |   (235)  op(all_14_1, all_14_1) = e3
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (63), (225) imply:
% 203.72/34.63  | | | | |   (236)  op(e0, e3) = e2
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | GROUND_INST: instantiating (7) with all_52_7, e2, e3, e0, simplifying
% 203.72/34.63  | | | | |              with (96), (236) gives:
% 203.72/34.63  | | | | |   (237)  all_52_7 = e2
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | COMBINE_EQS: (70), (237) imply:
% 203.72/34.63  | | | | |   (238)  all_58_12 = e2
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (127), (237) imply:
% 203.72/34.63  | | | | |   (239)   ~ (all_52_3 = e2)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (69), (237) imply:
% 203.72/34.63  | | | | |   (240)   ~ (all_52_5 = e2)
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | REDUCE: (15), (237) imply:
% 203.72/34.63  | | | | |   (241)  op(e2, e2) = all_52_6
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_6, e2, e2,
% 203.72/34.63  | | | | |              simplifying with (37), (241) gives:
% 203.72/34.63  | | | | |   (242)  all_52_6 = all_4_2
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | BETA: splitting (54) gives:
% 203.72/34.63  | | | | | 
% 203.72/34.63  | | | | | Case 1:
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | |   (243)  all_56_2 = e3
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | REF_CLOSE: (75), (166), (243) are inconsistent by sub-proof #1327.
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | Case 2:
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | |   (244)   ~ (all_56_2 = e3)
% 203.72/34.63  | | | | | |   (245)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | BETA: splitting (103) gives:
% 203.72/34.63  | | | | | | 
% 203.72/34.63  | | | | | | Case 1:
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | |   (246)  all_56_8 = e3
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | COMBINE_EQS: (59), (246) imply:
% 203.72/34.63  | | | | | | |   (247)  all_52_5 = e3
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | SIMP: (247) implies:
% 203.72/34.63  | | | | | | |   (248)  all_52_5 = e3
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | COMBINE_EQS: (134), (248) imply:
% 203.72/34.63  | | | | | | |   (249)  all_58_6 = e3
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | REDUCE: (39), (248) imply:
% 203.72/34.63  | | | | | | |   (250)   ~ (all_52_3 = e3)
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | REDUCE: (8), (248) imply:
% 203.72/34.63  | | | | | | |   (251)   ~ (all_52_13 = e3)
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | BETA: splitting (79) gives:
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | Case 1:
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | |   (252)  all_58_0 = e1
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | | REF_CLOSE: (137), (228), (252) are inconsistent by sub-proof
% 203.72/34.63  | | | | | | | |            #847.
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | Case 2:
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | |   (253)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | | BETA: splitting (253) gives:
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | | Case 1:
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | |   (254)  all_58_2 = e1
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | COMBINE_EQS: (74), (254) imply:
% 203.72/34.63  | | | | | | | | |   (255)  all_52_3 = e1
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | SIMP: (255) implies:
% 203.72/34.63  | | | | | | | | |   (256)  all_52_3 = e1
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | REDUCE: (6), (256) imply:
% 203.72/34.63  | | | | | | | | |   (257)  op(e1, e1) = all_52_2
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_2, e1, e1,
% 203.72/34.63  | | | | | | | | |              simplifying with (146), (257) gives:
% 203.72/34.63  | | | | | | | | |   (258)  all_52_2 = all_10_2
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | BETA: splitting (113) gives:
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | Case 1:
% 203.72/34.63  | | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | |   (259)  all_56_3 = e3
% 203.72/34.63  | | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | | REF_CLOSE: (226), (234), (259) are inconsistent by sub-proof
% 203.72/34.63  | | | | | | | | | |            #1200.
% 203.72/34.63  | | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | Case 2:
% 203.72/34.63  | | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | |   (260)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.72/34.63  | | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | | REF_CLOSE: (7), (11), (28), (37), (51), (65), (74), (77),
% 203.72/34.63  | | | | | | | | | |            (98), (106), (134), (138), (146), (150), (163),
% 203.72/34.63  | | | | | | | | | |            (164), (165), (171), (226), (227), (228), (233),
% 203.72/34.63  | | | | | | | | | |            (235), (238), (250), (260) are inconsistent by
% 203.72/34.63  | | | | | | | | | |            sub-proof #803.
% 203.72/34.63  | | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | End of split
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | Case 2:
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | |   (261)  all_58_6 = e1 | all_58_12 = e1
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | | REF_CLOSE: (7), (55), (70), (96), (172), (236), (249), (261)
% 203.72/34.63  | | | | | | | | |            are inconsistent by sub-proof #634.
% 203.72/34.63  | | | | | | | | | 
% 203.72/34.63  | | | | | | | | End of split
% 203.72/34.63  | | | | | | | | 
% 203.72/34.63  | | | | | | | End of split
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | Case 2:
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | |   (262)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | BETA: splitting (262) gives:
% 203.72/34.63  | | | | | | | 
% 203.72/34.63  | | | | | | | Case 1:
% 203.72/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | |   (263)  all_56_8 = e2
% 203.81/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | | REF_CLOSE: (59), (240), (263) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | |            #1022.
% 203.81/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | |   (264)   ~ (all_56_8 = e2)
% 203.81/34.64  | | | | | | | |   (265)  all_56_8 = e1 | all_56_8 = e0
% 203.81/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | | BETA: splitting (265) gives:
% 203.81/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | |   (266)  all_56_8 = e1
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | COMBINE_EQS: (59), (266) imply:
% 203.81/34.64  | | | | | | | | |   (267)  all_52_5 = e1
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | SIMP: (267) implies:
% 203.81/34.64  | | | | | | | | |   (268)  all_52_5 = e1
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | REDUCE: (39), (268) imply:
% 203.81/34.64  | | | | | | | | |   (269)   ~ (all_52_3 = e1)
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | REDUCE: (8), (268) imply:
% 203.81/34.64  | | | | | | | | |   (270)   ~ (all_52_13 = e1)
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | SIMP: (270) implies:
% 203.81/34.64  | | | | | | | | |   (271)   ~ (all_52_13 = e1)
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | REDUCE: (106), (268) imply:
% 203.81/34.64  | | | | | | | | |   (272)   ~ (all_10_2 = e1)
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | SIMP: (272) implies:
% 203.81/34.64  | | | | | | | | |   (273)   ~ (all_10_2 = e1)
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | REDUCE: (240), (268) imply:
% 203.81/34.64  | | | | | | | | |   (274)   ~ (e2 = e1)
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | BETA: splitting (81) gives:
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | |   (275)  all_56_4 = e3
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | COMBINE_EQS: (20), (275) imply:
% 203.81/34.64  | | | | | | | | | |   (276)  all_52_3 = e3
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | SIMP: (276) implies:
% 203.81/34.64  | | | | | | | | | |   (277)  all_52_3 = e3
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | REDUCE: (14), (277) imply:
% 203.81/34.64  | | | | | | | | | |   (278)   ~ (all_52_19 = e3)
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | SIMP: (278) implies:
% 203.81/34.64  | | | | | | | | | |   (279)   ~ (all_52_19 = e3)
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | BETA: splitting (141) gives:
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | |   (280)  all_58_4 = e3
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | REF_CLOSE: (158), (166), (280) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | | | | |            #1302.
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | |   (281)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | BETA: splitting (281) gives:
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | |   (282)  all_58_5 = e3
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | REF_CLOSE: (130), (279), (282) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | | | | | |            #1279.
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | |   (283)  all_58_8 = e3 | all_58_14 = e3
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | BETA: splitting (283) gives:
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | |   (284)  all_58_8 = e3
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | COMBINE_EQS: (104), (284) imply:
% 203.81/34.64  | | | | | | | | | | | | |   (285)  all_10_2 = e3
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | SIMP: (285) implies:
% 203.81/34.64  | | | | | | | | | | | | |   (286)  all_10_2 = e3
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | COMBINE_EQS: (24), (286) imply:
% 203.81/34.64  | | | | | | | | | | | | |   (287)  all_26_2 = e3
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | REDUCE: (45), (286) imply:
% 203.81/34.64  | | | | | | | | | | | | |   (288)  op(e3, e1) = all_10_1
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | BETA: splitting (52) gives:
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | |   (289)   ~ (all_26_2 = e3)
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | REDUCE: (287), (289) imply:
% 203.81/34.64  | | | | | | | | | | | | | |   (290)  $false
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | CLOSE: (290) is inconsistent.
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_17, all_10_1, e1,
% 203.81/34.64  | | | | | | | | | | | | | |              e3, simplifying with (94), (288) gives:
% 203.81/34.64  | | | | | | | | | | | | | |   (291)  all_52_17 = all_10_1
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | COMBINE_EQS: (75), (291) imply:
% 203.81/34.64  | | | | | | | | | | | | | |   (292)  all_56_2 = all_10_1
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | COMBINE_EQS: (158), (291) imply:
% 203.81/34.64  | | | | | | | | | | | | | |   (293)  all_58_4 = all_10_1
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | REDUCE: (232), (291) imply:
% 203.81/34.64  | | | | | | | | | | | | | |   (294)   ~ (all_10_1 = e0)
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | REDUCE: (110), (291) imply:
% 203.81/34.64  | | | | | | | | | | | | | |   (295)  op(all_10_1, all_10_1) = all_52_16
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | |   (296)  all_58_0 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | REF_CLOSE: (82), (228), (296) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | | | | | | | | |            #812.
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | |   (297)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | |   (298)  all_58_9 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (298) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | |   (299)  all_14_1 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | |   (300)  all_58_1 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (65), (98), (138), (150), (164), (165),
% 203.81/34.64  | | | | | | | | | | | | | | | | |            (171), (300) are inconsistent by sub-proof #1088.
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | |   (301)  all_58_4 = e2 | all_58_9 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (302)  all_56_2 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (302) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (303)  all_10_1 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | SIMP: (303) implies:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (304)  all_10_1 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (293), (304) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (305)  all_58_4 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REDUCE: (295), (304) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (306)  op(e2, e2) = all_52_16
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REDUCE: (118), (304) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (307)  op(e1, e2) = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_13, e2, e2, e1,
% 203.81/34.64  | | | | | | | | | | | | | | | | | |              simplifying with (97), (307) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (308)  all_52_13 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_16, e2, e2,
% 203.81/34.64  | | | | | | | | | | | | | | | | | |              simplifying with (37), (306) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (309)  all_52_16 = all_4_2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REDUCE: (156), (308) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (310)   ~ (all_52_29 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | SIMP: (310) implies:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (311)   ~ (all_52_29 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REDUCE: (164), (308) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (312)   ~ (e3 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (313)  all_58_9 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (313) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (314)  e2 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | SIMP: (314) implies:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (315)  e2 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (315) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (316)  all_58_4 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (55), (171), (227), (235), (301), (316)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #810.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (317)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (318)  all_58_10 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (318) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (319)  all_52_27 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | SIMP: (319) implies:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (320)  all_52_27 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (320) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (321)   ~ (all_4_2 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (322)   ~ (all_4_2 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (320) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (323)  op(e2, e2) = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (322), (323) are inconsistent by
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |            sub-proof #1158.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |   (324)  all_58_11 = e2 | all_58_15 = e2
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (138), (220), (311), (324) are inconsistent
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | |            by sub-proof #633.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (325)   ~ (all_56_2 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (326)  all_56_2 = e1 | all_56_2 = e0
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REDUCE: (292), (325) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (327)   ~ (all_10_1 = e2)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (171), (227), (235), (292), (293),
% 203.81/34.64  | | | | | | | | | | | | | | | | | |            (294), (301), (326), (327) are inconsistent by
% 203.81/34.64  | | | | | | | | | | | | | | | | | |            sub-proof #808.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | |   (328)   ~ (all_58_9 = e1)
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | REDUCE: (227), (328) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | |   (329)   ~ (all_14_1 = e1)
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | |   (330)  all_58_0 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (228), (330) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | | | | | | | | | | |            #847.
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | |   (331)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (332)  all_58_1 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (332) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (333)  e3 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | REDUCE: (172), (333) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (334)  $false
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | |   (335)  all_58_4 = e1 | all_58_9 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | Case 1:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (336)  all_58_4 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (293), (336) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (337)  all_10_1 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (28), (37), (55), (65), (98), (138), (150),
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |            (164), (165), (171), (227), (235), (297), (336)
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #632.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (338)  all_58_9 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (338) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (339)  all_14_1 = e1
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | REDUCE: (329), (339) imply:
% 203.81/34.64  | | | | | | | | | | | | | | | | | | |   (340)  $false
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent.
% 203.81/34.64  | | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | |   (341)  all_58_14 = e3
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | | REF_CLOSE: (5), (221), (341) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | | | | | | |            #1305.
% 203.81/34.64  | | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | |   (342)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | | REF_CLOSE: (20), (229), (239), (269), (342) are inconsistent
% 203.81/34.64  | | | | | | | | | |            by sub-proof #724.
% 203.81/34.64  | | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | Case 2:
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | |   (343)  all_56_8 = e0
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | | REF_CLOSE: (59), (230), (343) are inconsistent by sub-proof
% 203.81/34.64  | | | | | | | | |            #631.
% 203.81/34.64  | | | | | | | | | 
% 203.81/34.64  | | | | | | | | End of split
% 203.81/34.64  | | | | | | | | 
% 203.81/34.64  | | | | | | | End of split
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | End of split
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | End of split
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | Case 2:
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | |   (344)   ~ (all_56_15 = e3)
% 203.81/34.64  | | | | |   (345)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | REDUCE: (49), (344) imply:
% 203.81/34.64  | | | | |   (346)   ~ (all_14_2 = e3)
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 203.81/34.64  | | | | |            (14), (15), (16), (17), (18), (21), (25), (26), (27), (28),
% 203.81/34.64  | | | | |            (30), (31), (36), (37), (38), (39), (40), (41), (42), (44),
% 203.81/34.64  | | | | |            (45), (46), (47), (48), (49), (50), (51), (53), (54), (58),
% 203.81/34.64  | | | | |            (59), (60), (62), (63), (64), (65), (66), (67), (69), (70),
% 203.81/34.64  | | | | |            (71), (72), (73), (74), (75), (77), (78), (82), (83), (86),
% 203.81/34.64  | | | | |            (90), (91), (93), (94), (95), (98), (99), (100), (101),
% 203.81/34.64  | | | | |            (102), (103), (104), (106), (108), (109), (111), (112),
% 203.81/34.64  | | | | |            (113), (114), (115), (120), (121), (123), (124), (125),
% 203.81/34.64  | | | | |            (126), (127), (130), (131), (133), (134), (135), (136),
% 203.81/34.64  | | | | |            (137), (138), (144), (146), (147), (148), (150), (151),
% 203.81/34.64  | | | | |            (152), (153), (154), (155), (158), (164), (165), (167),
% 203.81/34.64  | | | | |            (169), (171), (213), (214), (215), (216), (345), (346) are
% 203.81/34.64  | | | | |            inconsistent by sub-proof #795.
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | End of split
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | End of split
% 203.81/34.64  | | | 
% 203.81/34.64  | | End of split
% 203.81/34.64  | | 
% 203.81/34.64  | Case 2:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (347)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.81/34.64  | | 
% 203.81/34.64  | | REF_CLOSE: (7), (12), (17), (32), (46), (57), (63), (80), (92), (119),
% 203.81/34.64  | |            (120), (128), (138), (142), (143), (157), (347) are inconsistent
% 203.81/34.64  | |            by sub-proof #820.
% 203.81/34.64  | | 
% 203.81/34.64  | End of split
% 203.81/34.64  | 
% 203.81/34.64  End of proof
% 203.81/34.64  
% 203.81/34.64  Sub-proof #631 shows that the following formulas are inconsistent:
% 203.81/34.64  ----------------------------------------------------------------
% 203.81/34.64    (1)  all_56_8 = all_52_5
% 203.81/34.64    (2)  all_56_8 = e0
% 203.81/34.64    (3)   ~ (all_52_5 = e0)
% 203.81/34.64  
% 203.81/34.64  Begin of proof
% 203.81/34.64  | 
% 203.81/34.64  | COMBINE_EQS: (1), (2) imply:
% 203.81/34.64  |   (4)  all_52_5 = e0
% 203.81/34.64  | 
% 203.81/34.64  | SIMP: (4) implies:
% 203.81/34.64  |   (5)  all_52_5 = e0
% 203.81/34.64  | 
% 203.81/34.64  | REDUCE: (3), (5) imply:
% 203.81/34.64  |   (6)  $false
% 203.81/34.64  | 
% 203.81/34.64  | CLOSE: (6) is inconsistent.
% 203.81/34.64  | 
% 203.81/34.64  End of proof
% 203.81/34.64  
% 203.81/34.64  Sub-proof #632 shows that the following formulas are inconsistent:
% 203.81/34.64  ----------------------------------------------------------------
% 203.81/34.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.64    (2)  all_58_4 = e1
% 203.81/34.64    (3)   ~ (all_4_2 = e3)
% 203.81/34.64    (4)  all_58_13 = all_52_15
% 203.81/34.64    (5)   ~ (all_52_15 = e3)
% 203.81/34.64    (6)  op(e2, e2) = all_4_2
% 203.81/34.64    (7)   ~ (e2 = e1)
% 203.81/34.64    (8)  all_58_7 = all_52_13
% 203.81/34.64    (9)  all_58_9 = all_14_1
% 203.81/34.64    (10)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.81/34.64    (11)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.81/34.64    (12)   ~ (all_52_13 = e3)
% 203.81/34.64    (13)  op(all_14_1, all_14_1) = e3
% 203.81/34.64    (14)   ~ (e3 = e2)
% 203.81/34.64    (15)  all_58_3 = all_4_2
% 203.81/34.64  
% 203.81/34.64  Begin of proof
% 203.81/34.64  | 
% 203.81/34.64  | BETA: splitting (10) gives:
% 203.81/34.64  | 
% 203.81/34.64  | Case 1:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (16)  all_58_1 = e2
% 203.81/34.64  | | 
% 203.81/34.64  | | REF_CLOSE: (3), (4), (5), (8), (11), (12), (14), (15), (16) are inconsistent
% 203.81/34.64  | |            by sub-proof #1088.
% 203.81/34.64  | | 
% 203.81/34.64  | Case 2:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (17)  all_58_4 = e2 | all_58_9 = e2
% 203.81/34.64  | | 
% 203.81/34.64  | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (13), (17) are inconsistent by
% 203.81/34.64  | |            sub-proof #810.
% 203.81/34.64  | | 
% 203.81/34.64  | End of split
% 203.81/34.64  | 
% 203.81/34.64  End of proof
% 203.81/34.64  
% 203.81/34.64  Sub-proof #633 shows that the following formulas are inconsistent:
% 203.81/34.64  ----------------------------------------------------------------
% 203.81/34.64    (1)  all_58_11 = all_52_29
% 203.81/34.64    (2)   ~ (all_52_29 = e2)
% 203.81/34.64    (3)  all_58_15 = e3
% 203.81/34.64    (4)  all_58_11 = e2 | all_58_15 = e2
% 203.81/34.64    (5)   ~ (e3 = e2)
% 203.81/34.64  
% 203.81/34.64  Begin of proof
% 203.81/34.64  | 
% 203.81/34.64  | BETA: splitting (4) gives:
% 203.81/34.64  | 
% 203.81/34.64  | Case 1:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (6)  all_58_11 = e2
% 203.81/34.64  | | 
% 203.81/34.64  | | COMBINE_EQS: (1), (6) imply:
% 203.81/34.64  | |   (7)  all_52_29 = e2
% 203.81/34.64  | | 
% 203.81/34.64  | | REDUCE: (2), (7) imply:
% 203.81/34.64  | |   (8)  $false
% 203.81/34.64  | | 
% 203.81/34.64  | | CLOSE: (8) is inconsistent.
% 203.81/34.64  | | 
% 203.81/34.64  | Case 2:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (9)  all_58_15 = e2
% 203.81/34.64  | | 
% 203.81/34.64  | | COMBINE_EQS: (3), (9) imply:
% 203.81/34.64  | |   (10)  e3 = e2
% 203.81/34.64  | | 
% 203.81/34.64  | | REDUCE: (5), (10) imply:
% 203.81/34.64  | |   (11)  $false
% 203.81/34.64  | | 
% 203.81/34.64  | | CLOSE: (11) is inconsistent.
% 203.81/34.64  | | 
% 203.81/34.64  | End of split
% 203.81/34.64  | 
% 203.81/34.64  End of proof
% 203.81/34.64  
% 203.81/34.64  Sub-proof #634 shows that the following formulas are inconsistent:
% 203.81/34.64  ----------------------------------------------------------------
% 203.81/34.64    (1)   ~ (e3 = e1)
% 203.81/34.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.64    (3)  all_58_6 = e3
% 203.81/34.64    (4)  all_58_6 = e1 | all_58_12 = e1
% 203.81/34.64    (5)   ~ (e2 = e1)
% 203.81/34.64    (6)  op(e0, e3) = e2
% 203.81/34.64    (7)  all_58_12 = all_52_7
% 203.81/34.64    (8)  op(e0, e3) = all_52_7
% 203.81/34.64  
% 203.81/34.64  Begin of proof
% 203.81/34.64  | 
% 203.81/34.64  | BETA: splitting (4) gives:
% 203.81/34.64  | 
% 203.81/34.64  | Case 1:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (9)  all_58_6 = e1
% 203.81/34.64  | | 
% 203.81/34.64  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1128.
% 203.81/34.64  | | 
% 203.81/34.64  | Case 2:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (10)  all_58_12 = e1
% 203.81/34.64  | | 
% 203.81/34.64  | | COMBINE_EQS: (7), (10) imply:
% 203.81/34.64  | |   (11)  all_52_7 = e1
% 203.81/34.64  | | 
% 203.81/34.64  | | SIMP: (11) implies:
% 203.81/34.64  | |   (12)  all_52_7 = e1
% 203.81/34.64  | | 
% 203.81/34.64  | | REDUCE: (8), (12) imply:
% 203.81/34.64  | |   (13)  op(e0, e3) = e1
% 203.81/34.64  | | 
% 203.81/34.64  | | REF_CLOSE: (2), (5), (6), (13) are inconsistent by sub-proof #635.
% 203.81/34.64  | | 
% 203.81/34.64  | End of split
% 203.81/34.64  | 
% 203.81/34.64  End of proof
% 203.81/34.64  
% 203.81/34.64  Sub-proof #635 shows that the following formulas are inconsistent:
% 203.81/34.64  ----------------------------------------------------------------
% 203.81/34.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.64    (2)  op(e0, e3) = e2
% 203.81/34.64    (3)  op(e0, e3) = e1
% 203.81/34.64    (4)   ~ (e2 = e1)
% 203.81/34.64  
% 203.81/34.64  Begin of proof
% 203.81/34.64  | 
% 203.81/34.64  | GROUND_INST: instantiating (1) with e1, e2, e3, e0, simplifying with (2), (3)
% 203.81/34.64  |              gives:
% 203.81/34.64  |   (5)  e2 = e1
% 203.81/34.64  | 
% 203.81/34.64  | REDUCE: (4), (5) imply:
% 203.81/34.64  |   (6)  $false
% 203.81/34.64  | 
% 203.81/34.64  | CLOSE: (6) is inconsistent.
% 203.81/34.64  | 
% 203.81/34.64  End of proof
% 203.81/34.64  
% 203.81/34.64  Sub-proof #636 shows that the following formulas are inconsistent:
% 203.81/34.64  ----------------------------------------------------------------
% 203.81/34.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.64    (2)  all_58_1 = all_52_9
% 203.81/34.64    (3)   ~ (all_52_9 = all_52_13)
% 203.81/34.64    (4)   ~ (e3 = e0)
% 203.81/34.64    (5)  all_58_0 = all_6_2
% 203.81/34.64    (6)  all_26_1 = all_10_1
% 203.81/34.64    (7)  all_26_2 = all_10_2
% 203.81/34.64    (8)  all_58_13 = all_52_15
% 203.81/34.64    (9)  all_58_9 = all_52_25
% 203.81/34.64    (10)  op(e2, e2) = all_4_2
% 203.81/34.64    (11)  all_58_11 = all_52_29
% 203.81/34.64    (12)   ~ (all_52_9 = all_52_15)
% 203.81/34.64    (13)  op(all_10_2, e1) = all_10_1
% 203.81/34.64    (14)   ~ (all_26_1 = e0) |  ~ (all_26_2 = e3)
% 203.81/34.64    (15)   ~ (all_6_2 = e3)
% 203.81/34.64    (16)   ~ (e2 = e1)
% 203.81/34.64    (17)   ~ (all_52_13 = all_10_2)
% 203.81/34.64    (18)  op(all_10_2, all_10_2) = e1
% 203.81/34.64    (19)  op(all_52_9, all_52_9) = all_52_8
% 203.81/34.64    (20)  all_58_7 = all_52_13
% 203.81/34.64    (21)  all_58_12 = all_52_7
% 203.81/34.64    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.81/34.64    (23)   ~ (all_52_7 = e3)
% 203.81/34.64    (24)  all_58_2 = all_52_3
% 203.81/34.64    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.81/34.64    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.81/34.64    (27)   ~ (all_52_29 = e3)
% 203.81/34.64    (28)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.81/34.64    (29)  all_58_9 = all_14_1
% 203.81/34.64    (30)   ~ (all_52_25 = e3)
% 203.81/34.64    (31)   ~ (e2 = e0)
% 203.81/34.64    (32)   ~ (all_52_5 = e3)
% 203.81/34.64    (33)  op(e3, e1) = all_52_17
% 203.81/34.64    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.81/34.64    (35)  all_58_8 = all_10_2
% 203.81/34.64    (36)   ~ (all_52_5 = all_10_2)
% 203.81/34.64    (37)   ~ (all_52_9 = all_4_2)
% 203.81/34.64    (38)   ~ (all_52_9 = all_6_2)
% 203.81/34.64    (39)  op(e3, e3) = all_6_2
% 203.81/34.64    (40)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.81/34.64    (41)   ~ (all_52_17 = e3)
% 203.81/34.64    (42)  op(all_52_17, all_52_17) = e3
% 203.81/34.64    (43)  all_58_6 = all_52_5
% 203.81/34.64    (44)   ~ (e1 = e0)
% 203.81/34.64    (45)   ~ (e3 = e2)
% 203.81/34.64    (46)  all_58_3 = all_4_2
% 203.81/34.64    (47)   ~ (all_52_3 = all_4_2)
% 203.81/34.64    (48)  all_58_4 = all_52_17
% 203.81/34.64  
% 203.81/34.64  Begin of proof
% 203.81/34.64  | 
% 203.81/34.64  | BETA: splitting (40) gives:
% 203.81/34.64  | 
% 203.81/34.64  | Case 1:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (49)  all_58_0 = e3
% 203.81/34.64  | | 
% 203.81/34.64  | | COMBINE_EQS: (5), (49) imply:
% 203.81/34.64  | |   (50)  all_6_2 = e3
% 203.81/34.64  | | 
% 203.81/34.64  | | REDUCE: (15), (50) imply:
% 203.81/34.64  | |   (51)  $false
% 203.81/34.64  | | 
% 203.81/34.64  | | CLOSE: (51) is inconsistent.
% 203.81/34.64  | | 
% 203.81/34.64  | Case 2:
% 203.81/34.64  | | 
% 203.81/34.64  | |   (52)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.81/34.64  | | 
% 203.81/34.64  | | BETA: splitting (52) gives:
% 203.81/34.64  | | 
% 203.81/34.64  | | Case 1:
% 203.81/34.64  | | | 
% 203.81/34.64  | | |   (53)  all_58_1 = e3
% 203.81/34.64  | | | 
% 203.81/34.64  | | | COMBINE_EQS: (2), (53) imply:
% 203.81/34.64  | | |   (54)  all_52_9 = e3
% 203.81/34.64  | | | 
% 203.81/34.64  | | | REDUCE: (3), (54) imply:
% 203.81/34.64  | | |   (55)   ~ (all_52_13 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | SIMP: (55) implies:
% 203.81/34.64  | | |   (56)   ~ (all_52_13 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | REDUCE: (12), (54) imply:
% 203.81/34.64  | | |   (57)   ~ (all_52_15 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | SIMP: (57) implies:
% 203.81/34.64  | | |   (58)   ~ (all_52_15 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | REDUCE: (38), (54) imply:
% 203.81/34.64  | | |   (59)   ~ (all_6_2 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | REDUCE: (37), (54) imply:
% 203.81/34.64  | | |   (60)   ~ (all_4_2 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | SIMP: (60) implies:
% 203.81/34.64  | | |   (61)   ~ (all_4_2 = e3)
% 203.81/34.64  | | | 
% 203.81/34.64  | | | REDUCE: (19), (54) imply:
% 203.81/34.64  | | |   (62)  op(e3, e3) = all_52_8
% 203.81/34.64  | | | 
% 203.81/34.64  | | | BETA: splitting (22) gives:
% 203.81/34.64  | | | 
% 203.81/34.64  | | | Case 1:
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | |   (63)  all_58_6 = e3
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | | REF_CLOSE: (32), (43), (63) are inconsistent by sub-proof #1328.
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | Case 2:
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | |   (64)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | | BETA: splitting (64) gives:
% 203.81/34.64  | | | | 
% 203.81/34.64  | | | | Case 1:
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | |   (65)  all_58_7 = e3
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | COMBINE_EQS: (20), (65) imply:
% 203.81/34.64  | | | | |   (66)  all_52_13 = e3
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | REDUCE: (56), (66) imply:
% 203.81/34.64  | | | | |   (67)  $false
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | CLOSE: (67) is inconsistent.
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | Case 2:
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | |   (68)  all_58_8 = e3 | all_58_11 = e3
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | BETA: splitting (68) gives:
% 203.81/34.64  | | | | | 
% 203.81/34.64  | | | | | Case 1:
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | |   (69)  all_58_8 = e3
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | | COMBINE_EQS: (35), (69) imply:
% 203.81/34.64  | | | | | |   (70)  all_10_2 = e3
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | | COMBINE_EQS: (7), (70) imply:
% 203.81/34.64  | | | | | |   (71)  all_26_2 = e3
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | | REDUCE: (18), (70) imply:
% 203.81/34.64  | | | | | |   (72)  op(e3, e3) = e1
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | | REDUCE: (13), (70) imply:
% 203.81/34.64  | | | | | |   (73)  op(e3, e1) = all_10_1
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | | BETA: splitting (14) gives:
% 203.81/34.64  | | | | | | 
% 203.81/34.64  | | | | | | Case 1:
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | |   (74)   ~ (all_26_2 = e3)
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | | REDUCE: (71), (74) imply:
% 203.81/34.64  | | | | | | |   (75)  $false
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | | CLOSE: (75) is inconsistent.
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | Case 2:
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | |   (76)   ~ (all_26_1 = e0)
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | | REDUCE: (6), (76) imply:
% 203.81/34.64  | | | | | | |   (77)   ~ (all_10_1 = e0)
% 203.81/34.64  | | | | | | | 
% 203.81/34.64  | | | | | | | GROUND_INST: instantiating (1) with all_52_17, all_10_1, e1, e3,
% 203.81/34.64  | | | | | | |              simplifying with (33), (73) gives:
% 203.81/34.64  | | | | | | |   (78)  all_52_17 = all_10_1
% 203.81/34.64  | | | | | | | 
% 203.81/34.65  | | | | | | | GROUND_INST: instantiating (1) with all_6_2, all_52_8, e3, e3,
% 203.81/34.65  | | | | | | |              simplifying with (39), (62) gives:
% 203.81/34.65  | | | | | | |   (79)  all_52_8 = all_6_2
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | GROUND_INST: instantiating (1) with e1, all_52_8, e3, e3,
% 203.81/34.65  | | | | | | |              simplifying with (62), (72) gives:
% 203.81/34.65  | | | | | | |   (80)  all_52_8 = e1
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | COMBINE_EQS: (79), (80) imply:
% 203.81/34.65  | | | | | | |   (81)  all_6_2 = e1
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | SIMP: (81) implies:
% 203.81/34.65  | | | | | | |   (82)  all_6_2 = e1
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | COMBINE_EQS: (48), (78) imply:
% 203.81/34.65  | | | | | | |   (83)  all_58_4 = all_10_1
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | COMBINE_EQS: (5), (82) imply:
% 203.81/34.65  | | | | | | |   (84)  all_58_0 = e1
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | REDUCE: (15), (82) imply:
% 203.81/34.65  | | | | | | |   (85)   ~ (e3 = e1)
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | SIMP: (85) implies:
% 203.81/34.65  | | | | | | |   (86)   ~ (e3 = e1)
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | BETA: splitting (28) gives:
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | |   (87)  all_58_0 = e0
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | COMBINE_EQS: (84), (87) imply:
% 203.81/34.65  | | | | | | | |   (88)  e1 = e0
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | REDUCE: (44), (88) imply:
% 203.81/34.65  | | | | | | | |   (89)  $false
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | CLOSE: (89) is inconsistent.
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | |   (90)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | BETA: splitting (90) gives:
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | |   (91)  all_58_1 = e0
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | COMBINE_EQS: (53), (91) imply:
% 203.81/34.65  | | | | | | | | |   (92)  e3 = e0
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | REDUCE: (4), (92) imply:
% 203.81/34.65  | | | | | | | | |   (93)  $false
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | CLOSE: (93) is inconsistent.
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | |   (94)  all_58_4 = e0 | all_58_9 = e0
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | BETA: splitting (94) gives:
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | |   (95)  all_58_4 = e0
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | COMBINE_EQS: (83), (95) imply:
% 203.81/34.65  | | | | | | | | | |   (96)  all_10_1 = e0
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | REDUCE: (77), (96) imply:
% 203.81/34.65  | | | | | | | | | |   (97)  $false
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | CLOSE: (97) is inconsistent.
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | |   (98)  all_58_9 = e0
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | COMBINE_EQS: (29), (98) imply:
% 203.81/34.65  | | | | | | | | | |   (99)  all_14_1 = e0
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | BETA: splitting (25) gives:
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | |   (100)  all_58_0 = e2
% 203.81/34.65  | | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | | REF_CLOSE: (16), (84), (100) are inconsistent by sub-proof
% 203.81/34.65  | | | | | | | | | | |            #1273.
% 203.81/34.65  | | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | |   (101)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.81/34.65  | | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | | REF_CLOSE: (1), (5), (8), (10), (20), (21), (23), (24), (26),
% 203.81/34.65  | | | | | | | | | | |            (31), (32), (33), (34), (39), (42), (43), (45),
% 203.81/34.65  | | | | | | | | | | |            (46), (47), (56), (58), (61), (72), (73), (83),
% 203.81/34.65  | | | | | | | | | | |            (86), (98), (101) are inconsistent by sub-proof
% 203.81/34.65  | | | | | | | | | | |            #1083.
% 203.81/34.65  | | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | End of split
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | End of split
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | End of split
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | End of split
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | End of split
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | Case 2:
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | |   (102)  all_58_11 = e3
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | | REF_CLOSE: (11), (27), (102) are inconsistent by sub-proof #1323.
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | End of split
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | End of split
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | End of split
% 203.81/34.65  | | | 
% 203.81/34.65  | | Case 2:
% 203.81/34.65  | | | 
% 203.81/34.65  | | |   (103)  all_58_4 = e3 | all_58_9 = e3
% 203.81/34.65  | | | 
% 203.81/34.65  | | | REF_CLOSE: (9), (30), (41), (48), (103) are inconsistent by sub-proof
% 203.81/34.65  | | |            #1276.
% 203.81/34.65  | | | 
% 203.81/34.65  | | End of split
% 203.81/34.65  | | 
% 203.81/34.65  | End of split
% 203.81/34.65  | 
% 203.81/34.65  End of proof
% 203.81/34.65  
% 203.81/34.65  Sub-proof #637 shows that the following formulas are inconsistent:
% 203.81/34.65  ----------------------------------------------------------------
% 203.81/34.65    (1)   ~ (all_52_25 = all_52_27)
% 203.81/34.65    (2)  all_58_14 = all_52_23
% 203.81/34.65    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.81/34.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.65    (5)   ~ (all_52_5 = all_52_13)
% 203.81/34.65    (6)  all_58_1 = all_52_9
% 203.81/34.65    (7)   ~ (all_52_9 = all_52_13)
% 203.81/34.65    (8)   ~ (e3 = e0)
% 203.81/34.65    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.65    (10)   ~ (all_52_7 = all_52_15)
% 203.81/34.65    (11)   ~ (all_52_17 = all_52_25)
% 203.81/34.65    (12)  all_16_1 = all_10_1
% 203.81/34.65    (13)   ~ (all_52_3 = all_6_2)
% 203.81/34.65    (14)  all_58_0 = all_6_2
% 203.81/34.65    (15)  all_56_4 = all_52_3
% 203.81/34.65    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.81/34.65    (17)  op(all_52_19, all_52_19) = all_52_18
% 203.81/34.65    (18)  all_58_13 = all_52_15
% 203.81/34.65    (19)  op(all_10_2, all_10_2) = all_52_20
% 203.81/34.65    (20)  all_58_9 = all_52_25
% 203.81/34.65    (21)   ~ (all_6_1 = e1)
% 203.81/34.65    (22)  op(all_52_27, all_52_27) = all_52_26
% 203.81/34.65    (23)  op(e1, e3) = all_52_5
% 203.81/34.65    (24)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 203.81/34.65    (25)  op(e2, e2) = all_4_2
% 203.81/34.65    (26)   ~ (all_52_3 = all_52_5)
% 203.81/34.65    (27)  all_58_11 = all_52_29
% 203.81/34.65    (28)  all_56_5 = all_4_2
% 203.81/34.65    (29)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.81/34.65    (30)  op(all_10_2, e1) = all_10_1
% 203.81/34.65    (31)   ~ (all_52_7 = all_6_2)
% 203.81/34.65    (32)  op(e0, e1) = all_52_23
% 203.81/34.65    (33)   ~ (all_52_15 = e0)
% 203.81/34.65    (34)  all_58_15 = e0
% 203.81/34.65    (35)   ~ (all_4_1 = e1)
% 203.81/34.65    (36)   ~ (all_52_25 = e0)
% 203.81/34.65    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.81/34.65    (38)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.81/34.65    (39)   ~ (all_52_13 = all_10_2)
% 203.81/34.65    (40)  op(e0, e0) = e0
% 203.81/34.65    (41)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 203.81/34.65    (42)  all_58_10 = all_52_27
% 203.81/34.65    (43)  all_56_8 = all_52_5
% 203.81/34.65    (44)  op(all_52_9, all_52_9) = all_52_8
% 203.81/34.65    (45)  op(all_52_15, all_52_15) = all_52_14
% 203.81/34.65    (46)   ~ (all_52_25 = all_52_29)
% 203.81/34.65    (47)  all_16_2 = all_10_2
% 203.81/34.65    (48)  all_58_7 = all_52_13
% 203.81/34.65    (49)   ~ (all_52_5 = all_52_7)
% 203.81/34.65    (50)  all_58_12 = all_52_7
% 203.81/34.65    (51)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.81/34.65    (52)  all_56_2 = all_52_17
% 203.81/34.65    (53)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.81/34.65    (54)  all_56_7 = all_52_27
% 203.81/34.65    (55)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.65    (56)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.81/34.65    (57)  op(all_4_2, e2) = all_4_1
% 203.81/34.65    (58)   ~ (all_52_13 = all_4_2)
% 203.81/34.65    (59)  op(e0, e3) = all_52_7
% 203.81/34.65    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.81/34.65    (61)   ~ (all_52_9 = all_52_25)
% 203.81/34.65    (62)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.81/34.65    (63)  all_58_8 = all_10_2
% 203.81/34.65    (64)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.81/34.65    (65)  all_56_12 = all_52_7
% 203.81/34.65    (66)  op(all_52_17, all_52_17) = all_52_16
% 203.81/34.65    (67)   ~ (all_52_25 = all_6_2)
% 203.81/34.65    (68)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.65    (69)   ~ (all_52_9 = all_4_2)
% 203.81/34.65    (70)   ~ (all_52_5 = all_6_2)
% 203.81/34.65    (71)   ~ (all_52_9 = all_6_2)
% 203.81/34.65    (72)   ~ (all_52_13 = all_52_15)
% 203.81/34.65    (73)  op(e3, e3) = all_6_2
% 203.81/34.65    (74)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.81/34.65    (75)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.81/34.65    (76)  op(all_4_2, all_4_2) = all_52_10
% 203.81/34.65    (77)  all_56_3 = all_52_25
% 203.81/34.65    (78)   ~ (all_52_3 = all_52_7)
% 203.81/34.65    (79)  all_58_5 = all_52_19
% 203.81/34.65    (80)  all_56_1 = all_52_9
% 203.81/34.65    (81)   ~ (all_52_15 = all_4_2)
% 203.81/34.65    (82)   ~ (all_52_27 = all_4_2)
% 203.81/34.65    (83)  all_58_6 = all_52_5
% 203.81/34.65    (84)  op(e3, e2) = all_52_9
% 203.81/34.65    (85)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.81/34.65    (86)   ~ (all_52_17 = all_6_2)
% 203.81/34.65    (87)   ~ (e1 = e0)
% 203.81/34.65    (88)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.81/34.65    (89)   ~ (all_52_9 = all_52_17)
% 203.81/34.65    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.81/34.65    (91)  op(all_52_13, all_52_13) = all_52_12
% 203.81/34.65    (92)   ~ (all_6_1 = e2)
% 203.81/34.65    (93)  op(e1, e1) = all_10_2
% 203.81/34.65    (94)   ~ (all_52_7 = all_52_23)
% 203.81/34.65    (95)  all_58_3 = all_4_2
% 203.81/34.65    (96)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.81/34.65    (97)  all_56_13 = all_52_15
% 203.81/34.65    (98)   ~ (all_52_3 = all_4_2)
% 203.81/34.65    (99)   ~ (all_52_19 = all_4_2)
% 203.81/34.65    (100)  op(all_6_2, e3) = all_6_1
% 203.81/34.65    (101)   ~ (all_52_13 = all_52_29)
% 203.81/34.65    (102)  all_58_4 = all_52_17
% 203.81/34.65    (103)   ~ (all_52_7 = e0)
% 203.81/34.65    (104)  op(all_52_25, all_52_25) = all_52_24
% 203.81/34.65  
% 203.81/34.65  Begin of proof
% 203.81/34.65  | 
% 203.81/34.65  | ALPHA: (41) implies:
% 203.81/34.65  |   (105)  all_52_14 = e0
% 203.81/34.65  |   (106)  all_52_12 = e1
% 203.81/34.65  |   (107)  all_52_10 = e2
% 203.81/34.65  |   (108)  all_52_8 = e3
% 203.81/34.65  | 
% 203.81/34.65  | REDUCE: (44), (108) imply:
% 203.81/34.65  |   (109)  op(all_52_9, all_52_9) = e3
% 203.81/34.65  | 
% 203.81/34.65  | REDUCE: (91), (106) imply:
% 203.81/34.65  |   (110)  op(all_52_13, all_52_13) = e1
% 203.81/34.65  | 
% 203.81/34.65  | REDUCE: (45), (105) imply:
% 203.81/34.65  |   (111)  op(all_52_15, all_52_15) = e0
% 203.81/34.65  | 
% 203.81/34.65  | REDUCE: (76), (107) imply:
% 203.81/34.65  |   (112)  op(all_4_2, all_4_2) = e2
% 203.81/34.65  | 
% 203.81/34.65  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.81/34.65  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.81/34.65  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.81/34.65  |            (35), (36), (37), (38), (39), (40), (42), (43), (46), (47), (48),
% 203.81/34.65  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 203.81/34.65  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 203.81/34.65  |            (71), (72), (73), (74), (75), (77), (78), (79), (80), (81), (82),
% 203.81/34.65  |            (83), (84), (85), (86), (87), (88), (89), (90), (92), (93), (94),
% 203.81/34.65  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 203.81/34.65  |            (109), (110), (111), (112) are inconsistent by sub-proof #647.
% 203.81/34.65  | 
% 203.81/34.65  End of proof
% 203.81/34.65  
% 203.81/34.65  Sub-proof #638 shows that the following formulas are inconsistent:
% 203.81/34.65  ----------------------------------------------------------------
% 203.81/34.65    (1)   ~ (all_52_25 = all_52_27)
% 203.81/34.65    (2)   ~ (e3 = e1)
% 203.81/34.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.65    (4)  op(all_52_7, all_52_7) = e0
% 203.81/34.65    (5)  op(all_52_5, all_52_5) = e1
% 203.81/34.65    (6)   ~ (e3 = e0)
% 203.81/34.65    (7)   ~ (all_4_0 = e1)
% 203.81/34.65    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.65    (9)   ~ (all_52_5 = all_4_0)
% 203.81/34.65    (10)  all_58_0 = all_6_2
% 203.81/34.65    (11)  op(e3, e0) = all_52_25
% 203.81/34.65    (12)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.81/34.65    (13)   ~ (all_52_27 = all_52_29)
% 203.81/34.65    (14)  all_58_9 = all_52_25
% 203.81/34.65    (15)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.81/34.65    (16)  op(all_52_27, all_52_27) = all_52_26
% 203.81/34.65    (17)  op(e1, e3) = all_52_5
% 203.81/34.65    (18)   ~ (all_6_2 = all_4_0)
% 203.81/34.65    (19)  all_32_2 = all_4_2
% 203.81/34.65    (20)  op(e2, e2) = all_4_2
% 203.81/34.65    (21)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.81/34.65    (22)  all_58_11 = all_52_29
% 203.81/34.65    (23)  all_56_5 = all_4_2
% 203.81/34.65    (24)   ~ (all_52_7 = all_6_2)
% 203.81/34.65    (25)  all_58_2 = all_4_0
% 203.81/34.65    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.81/34.65    (27)  op(all_4_2, e2) = e3
% 203.81/34.65    (28)  all_58_15 = e0
% 203.81/34.65    (29)   ~ (all_4_0 = e3)
% 203.81/34.65    (30)   ~ (all_52_25 = e0)
% 203.81/34.65    (31)   ~ (e2 = e1)
% 203.81/34.65    (32)  all_58_10 = all_52_27
% 203.81/34.65    (33)  all_56_8 = all_52_5
% 203.81/34.65    (34)   ~ (all_52_25 = all_52_29)
% 203.81/34.65    (35)  op(all_6_2, all_6_2) = e3
% 203.81/34.65    (36)   ~ (all_52_5 = all_52_7)
% 203.81/34.65    (37)  all_58_12 = all_52_7
% 203.81/34.65    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.81/34.65    (39)  op(e3, all_6_1) = all_6_0
% 203.81/34.65    (40)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.65    (41)  all_56_7 = all_52_27
% 203.81/34.65    (42)   ~ (e2 = e0)
% 203.81/34.65    (43)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.81/34.65    (44)   ~ (all_52_5 = all_52_29)
% 203.81/34.65    (45)   ~ (all_52_29 = e0)
% 203.81/34.65    (46)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.81/34.65    (47)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.65    (48)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.81/34.65    (49)  all_56_4 = all_4_0
% 203.81/34.65    (50)   ~ (all_6_0 = e2)
% 203.81/34.65    (51)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.81/34.65    (52)   ~ (all_52_5 = all_10_2)
% 203.81/34.65    (53)  op(all_52_29, all_52_29) = all_52_28
% 203.81/34.65    (54)   ~ (all_52_7 = all_4_0)
% 203.81/34.65    (55)  all_56_12 = all_52_7
% 203.81/34.65    (56)   ~ (all_52_25 = all_6_2)
% 203.81/34.65    (57)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.65    (58)   ~ (all_52_9 = all_4_2)
% 203.81/34.65    (59)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.81/34.65    (60)   ~ (all_52_27 = e0)
% 203.81/34.65    (61)  op(e3, e3) = all_6_2
% 203.81/34.65    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.81/34.65    (63)   ~ (all_52_27 = all_4_0)
% 203.81/34.65    (64)  op(all_4_2, all_4_2) = all_52_10
% 203.81/34.65    (65)  all_32_0 = all_4_0
% 203.81/34.65    (66)  all_56_3 = all_52_25
% 203.81/34.65    (67)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.81/34.65    (68)  all_58_6 = all_52_5
% 203.81/34.65    (69)   ~ (all_4_0 = all_4_2)
% 203.81/34.65    (70)  op(e3, e2) = all_52_9
% 203.81/34.65    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.81/34.65    (72)   ~ (e1 = e0)
% 203.81/34.65    (73)   ~ (e3 = e2)
% 203.81/34.65    (74)   ~ (all_6_1 = e2)
% 203.81/34.65    (75)  op(e1, e1) = all_10_2
% 203.81/34.65    (76)  op(all_6_2, e3) = all_6_1
% 203.81/34.65    (77)   ~ (all_52_7 = e0)
% 203.81/34.65    (78)  op(all_52_25, all_52_25) = all_52_24
% 203.81/34.65  
% 203.81/34.65  Begin of proof
% 203.81/34.65  | 
% 203.81/34.65  | BETA: splitting (12) gives:
% 203.81/34.65  | 
% 203.81/34.65  | Case 1:
% 203.81/34.65  | | 
% 203.81/34.65  | |   (79)  all_56_7 = e3
% 203.81/34.65  | | 
% 203.81/34.65  | | COMBINE_EQS: (41), (79) imply:
% 203.81/34.65  | |   (80)  all_52_27 = e3
% 203.81/34.65  | | 
% 203.81/34.65  | | SIMP: (80) implies:
% 203.81/34.65  | |   (81)  all_52_27 = e3
% 203.81/34.65  | | 
% 203.81/34.65  | | COMBINE_EQS: (32), (81) imply:
% 203.81/34.65  | |   (82)  all_58_10 = e3
% 203.81/34.65  | | 
% 203.81/34.65  | | REDUCE: (1), (81) imply:
% 203.81/34.65  | |   (83)   ~ (all_52_25 = e3)
% 203.81/34.65  | | 
% 203.81/34.65  | | REDUCE: (16), (81) imply:
% 203.81/34.65  | |   (84)  op(e3, e3) = all_52_26
% 203.81/34.65  | | 
% 203.81/34.65  | | GROUND_INST: instantiating (3) with all_6_2, all_52_26, e3, e3, simplifying
% 203.81/34.65  | |              with (61), (84) gives:
% 203.81/34.65  | |   (85)  all_52_26 = all_6_2
% 203.81/34.65  | | 
% 203.81/34.65  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15), (17),
% 203.81/34.65  | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 203.81/34.65  | |            (30), (31), (33), (34), (36), (37), (39), (40), (42), (43), (44),
% 203.81/34.65  | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 203.81/34.65  | |            (56), (57), (58), (59), (61), (64), (65), (66), (67), (68), (69),
% 203.81/34.65  | |            (70), (72), (73), (74), (75), (76), (77), (78), (82), (83) are
% 203.81/34.65  | |            inconsistent by sub-proof #642.
% 203.81/34.65  | | 
% 203.81/34.65  | Case 2:
% 203.81/34.65  | | 
% 203.81/34.65  | |   (86)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.81/34.65  | | 
% 203.81/34.65  | | BETA: splitting (62) gives:
% 203.81/34.65  | | 
% 203.81/34.65  | | Case 1:
% 203.81/34.65  | | | 
% 203.81/34.65  | | |   (87)  all_58_9 = e3
% 203.81/34.65  | | | 
% 203.81/34.65  | | | COMBINE_EQS: (14), (87) imply:
% 203.81/34.65  | | |   (88)  all_52_25 = e3
% 203.81/34.65  | | | 
% 203.81/34.65  | | | SIMP: (88) implies:
% 203.81/34.65  | | |   (89)  all_52_25 = e3
% 203.81/34.65  | | | 
% 203.81/34.65  | | | REDUCE: (56), (89) imply:
% 203.81/34.65  | | |   (90)   ~ (all_6_2 = e3)
% 203.81/34.65  | | | 
% 203.81/34.65  | | | SIMP: (90) implies:
% 203.81/34.65  | | |   (91)   ~ (all_6_2 = e3)
% 203.81/34.65  | | | 
% 203.81/34.65  | | | REDUCE: (78), (89) imply:
% 203.81/34.65  | | |   (92)  op(e3, e3) = all_52_24
% 203.81/34.65  | | | 
% 203.81/34.65  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_24, e3, e3,
% 203.81/34.65  | | |              simplifying with (61), (92) gives:
% 203.81/34.65  | | |   (93)  all_52_24 = all_6_2
% 203.81/34.65  | | | 
% 203.81/34.65  | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (25), (29), (35), (37), (38),
% 203.81/34.65  | | |            (40), (52), (61), (68), (71), (72), (75), (91) are inconsistent
% 203.81/34.65  | | |            by sub-proof #641.
% 203.81/34.65  | | | 
% 203.81/34.65  | | Case 2:
% 203.81/34.65  | | | 
% 203.81/34.65  | | |   (94)   ~ (all_58_9 = e3)
% 203.81/34.65  | | |   (95)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.81/34.65  | | | 
% 203.81/34.65  | | | REDUCE: (14), (94) imply:
% 203.81/34.65  | | |   (96)   ~ (all_52_25 = e3)
% 203.81/34.65  | | | 
% 203.81/34.65  | | | BETA: splitting (95) gives:
% 203.81/34.65  | | | 
% 203.81/34.65  | | | Case 1:
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | |   (97)  all_58_10 = e3
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15),
% 203.81/34.65  | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 203.81/34.65  | | | |            (27), (28), (30), (31), (33), (34), (36), (37), (39), (40),
% 203.81/34.65  | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 203.81/34.65  | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (61), (64),
% 203.81/34.65  | | | |            (65), (66), (67), (68), (69), (70), (72), (73), (74), (75),
% 203.81/34.65  | | | |            (76), (77), (78), (96), (97) are inconsistent by sub-proof
% 203.81/34.65  | | | |            #642.
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | Case 2:
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | |   (98)  all_58_11 = e3 | all_58_15 = e3
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | | BETA: splitting (98) gives:
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | | Case 1:
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | |   (99)  all_58_11 = e3
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | COMBINE_EQS: (22), (99) imply:
% 203.81/34.65  | | | | |   (100)  all_52_29 = e3
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | SIMP: (100) implies:
% 203.81/34.65  | | | | |   (101)  all_52_29 = e3
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | REDUCE: (44), (101) imply:
% 203.81/34.65  | | | | |   (102)   ~ (all_52_5 = e3)
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | REDUCE: (13), (101) imply:
% 203.81/34.65  | | | | |   (103)   ~ (all_52_27 = e3)
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | REDUCE: (53), (101) imply:
% 203.81/34.65  | | | | |   (104)  op(e3, e3) = all_52_28
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_28, e3, e3,
% 203.81/34.65  | | | | |              simplifying with (61), (104) gives:
% 203.81/34.65  | | | | |   (105)  all_52_28 = all_6_2
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | BETA: splitting (57) gives:
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | Case 1:
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | |   (106)  all_56_3 = e3
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | | REF_CLOSE: (66), (96), (106) are inconsistent by sub-proof #1339.
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | Case 2:
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | |   (107)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | | BETA: splitting (59) gives:
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | | Case 1:
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | |   (108)  all_58_9 = e2
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | COMBINE_EQS: (14), (108) imply:
% 203.81/34.65  | | | | | | |   (109)  all_52_25 = e2
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | SIMP: (109) implies:
% 203.81/34.65  | | | | | | |   (110)  all_52_25 = e2
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | REDUCE: (78), (110) imply:
% 203.81/34.65  | | | | | | |   (111)  op(e2, e2) = all_52_24
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | BETA: splitting (26) gives:
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | |   (112)  all_58_9 = e1
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | REF_CLOSE: (31), (108), (112) are inconsistent by sub-proof
% 203.81/34.65  | | | | | | | |            #1214.
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | |   (113)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | BETA: splitting (113) gives:
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | |   (114)  all_58_10 = e1
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | COMBINE_EQS: (32), (114) imply:
% 203.81/34.65  | | | | | | | | |   (115)  all_52_27 = e1
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | SIMP: (115) implies:
% 203.81/34.65  | | | | | | | | |   (116)  all_52_27 = e1
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | REDUCE: (63), (116) imply:
% 203.81/34.65  | | | | | | | | |   (117)   ~ (all_4_0 = e1)
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | REDUCE: (103), (116) imply:
% 203.81/34.65  | | | | | | | | |   (118)   ~ (e3 = e1)
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | REDUCE: (16), (116) imply:
% 203.81/34.65  | | | | | | | | |   (119)  op(e1, e1) = all_52_26
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_26, e1,
% 203.81/34.65  | | | | | | | | |              e1, simplifying with (75), (119) gives:
% 203.81/34.65  | | | | | | | | |   (120)  all_52_26 = all_10_2
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_52_24, e2, e2,
% 203.81/34.65  | | | | | | | | |              simplifying with (20), (111) gives:
% 203.81/34.65  | | | | | | | | |   (121)  all_52_24 = all_4_2
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | BETA: splitting (38) gives:
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | Case 1:
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | |   (122)  all_58_0 = e3
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (15), (19),
% 203.81/34.65  | | | | | | | | | |            (20), (21), (23), (25), (27), (33), (36), (37),
% 203.81/34.65  | | | | | | | | | |            (40), (43), (46), (47), (49), (51), (52), (54),
% 203.81/34.65  | | | | | | | | | |            (58), (64), (65), (67), (68), (69), (70), (75),
% 203.81/34.65  | | | | | | | | | |            (102), (122) are inconsistent by sub-proof #671.
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | |   (123)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (25), (29), (37),
% 203.81/34.65  | | | | | | | | | |            (40), (52), (61), (68), (72), (75), (102), (123)
% 203.81/34.65  | | | | | | | | | |            are inconsistent by sub-proof #640.
% 203.81/34.65  | | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | End of split
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | Case 2:
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | |   (124)  all_58_11 = e1 | all_58_15 = e1
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | | REF_CLOSE: (2), (28), (72), (99), (124) are inconsistent by
% 203.81/34.65  | | | | | | | | |            sub-proof #1206.
% 203.81/34.65  | | | | | | | | | 
% 203.81/34.65  | | | | | | | | End of split
% 203.81/34.65  | | | | | | | | 
% 203.81/34.65  | | | | | | | End of split
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | Case 2:
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | |   (125)   ~ (all_58_9 = e2)
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | REDUCE: (14), (125) imply:
% 203.81/34.65  | | | | | | |   (126)   ~ (all_52_25 = e2)
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | | REF_CLOSE: (1), (3), (7), (19), (20), (23), (27), (30), (41),
% 203.81/34.65  | | | | | | |            (43), (47), (49), (58), (60), (63), (64), (65), (66),
% 203.81/34.65  | | | | | | |            (67), (69), (70), (86), (107), (126) are inconsistent
% 203.81/34.65  | | | | | | |            by sub-proof #639.
% 203.81/34.65  | | | | | | | 
% 203.81/34.65  | | | | | | End of split
% 203.81/34.65  | | | | | | 
% 203.81/34.65  | | | | | End of split
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | Case 2:
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | |   (127)  all_58_15 = e3
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | | REF_CLOSE: (6), (28), (127) are inconsistent by sub-proof #1350.
% 203.81/34.65  | | | | | 
% 203.81/34.65  | | | | End of split
% 203.81/34.65  | | | | 
% 203.81/34.65  | | | End of split
% 203.81/34.65  | | | 
% 203.81/34.65  | | End of split
% 203.81/34.65  | | 
% 203.81/34.65  | End of split
% 203.81/34.65  | 
% 203.81/34.65  End of proof
% 203.81/34.65  
% 203.81/34.65  Sub-proof #639 shows that the following formulas are inconsistent:
% 203.81/34.65  ----------------------------------------------------------------
% 203.81/34.65    (1)   ~ (all_52_25 = all_52_27)
% 203.81/34.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.65    (3)   ~ (all_4_0 = e1)
% 203.81/34.66    (4)  all_32_2 = all_4_2
% 203.81/34.66    (5)  op(e2, e2) = all_4_2
% 203.81/34.66    (6)  all_56_5 = all_4_2
% 203.81/34.66    (7)  op(all_4_2, e2) = e3
% 203.81/34.66    (8)   ~ (all_52_25 = e0)
% 203.81/34.66    (9)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.66    (10)  all_56_7 = all_52_27
% 203.81/34.66    (11)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.81/34.66    (12)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.66    (13)  all_56_4 = all_4_0
% 203.81/34.66    (14)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.81/34.66    (15)   ~ (all_52_25 = e2)
% 203.81/34.66    (16)   ~ (all_52_9 = all_4_2)
% 203.81/34.66    (17)   ~ (all_52_27 = e0)
% 203.81/34.66    (18)   ~ (all_52_27 = all_4_0)
% 203.81/34.66    (19)  op(all_4_2, all_4_2) = all_52_10
% 203.81/34.66    (20)  all_32_0 = all_4_0
% 203.81/34.66    (21)  all_56_3 = all_52_25
% 203.81/34.66    (22)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.81/34.66    (23)   ~ (all_4_0 = all_4_2)
% 203.81/34.66    (24)  op(e3, e2) = all_52_9
% 203.81/34.66  
% 203.81/34.66  Begin of proof
% 203.81/34.66  | 
% 203.81/34.66  | BETA: splitting (9) gives:
% 203.81/34.66  | 
% 203.81/34.66  | Case 1:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (25)  all_56_3 = e2
% 203.81/34.66  | | 
% 203.81/34.66  | | REF_CLOSE: (15), (21), (25) are inconsistent by sub-proof #1259.
% 203.81/34.66  | | 
% 203.81/34.66  | Case 2:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (26)  all_56_3 = e1 | all_56_3 = e0
% 203.81/34.66  | | 
% 203.81/34.66  | | BETA: splitting (26) gives:
% 203.81/34.66  | | 
% 203.81/34.66  | | Case 1:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (27)  all_56_3 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | COMBINE_EQS: (21), (27) imply:
% 203.81/34.66  | | |   (28)  all_52_25 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (28) implies:
% 203.81/34.66  | | |   (29)  all_52_25 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (1), (29) imply:
% 203.81/34.66  | | |   (30)   ~ (all_52_27 = e1)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (30) implies:
% 203.81/34.66  | | |   (31)   ~ (all_52_27 = e1)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | BETA: splitting (14) gives:
% 203.81/34.66  | | | 
% 203.81/34.66  | | | Case 1:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (32)  all_56_7 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | COMBINE_EQS: (10), (32) imply:
% 203.81/34.66  | | | |   (33)  all_52_27 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | SIMP: (33) implies:
% 203.81/34.66  | | | |   (34)  all_52_27 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REDUCE: (18), (34) imply:
% 203.81/34.66  | | | |   (35)   ~ (all_4_0 = e2)
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | SIMP: (35) implies:
% 203.81/34.66  | | | |   (36)   ~ (all_4_0 = e2)
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (12), (13), (16), (19),
% 203.81/34.66  | | | |            (20), (22), (23), (24), (36) are inconsistent by sub-proof
% 203.81/34.66  | | | |            #971.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | Case 2:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (37)  all_56_7 = e1 | all_56_7 = e0
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (10), (17), (31), (37) are inconsistent by sub-proof #902.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | End of split
% 203.81/34.66  | | | 
% 203.81/34.66  | | Case 2:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (38)  all_56_3 = e0
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REF_CLOSE: (8), (21), (38) are inconsistent by sub-proof #1258.
% 203.81/34.66  | | | 
% 203.81/34.66  | | End of split
% 203.81/34.66  | | 
% 203.81/34.66  | End of split
% 203.81/34.66  | 
% 203.81/34.66  End of proof
% 203.81/34.66  
% 203.81/34.66  Sub-proof #640 shows that the following formulas are inconsistent:
% 203.81/34.66  ----------------------------------------------------------------
% 203.81/34.66    (1)   ~ (e3 = e1)
% 203.81/34.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.66    (3)  op(all_52_7, all_52_7) = e0
% 203.81/34.66    (4)  op(all_52_5, all_52_5) = e1
% 203.81/34.66    (5)   ~ (all_4_0 = e1)
% 203.81/34.66    (6)  all_58_0 = all_6_2
% 203.81/34.66    (7)  all_58_2 = all_4_0
% 203.81/34.66    (8)   ~ (all_4_0 = e3)
% 203.81/34.66    (9)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.81/34.66    (10)  all_58_12 = all_52_7
% 203.81/34.66    (11)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66    (12)   ~ (all_52_5 = e3)
% 203.81/34.66    (13)   ~ (all_52_5 = all_10_2)
% 203.81/34.66    (14)  op(e3, e3) = all_6_2
% 203.81/34.66    (15)  all_58_6 = all_52_5
% 203.81/34.66    (16)   ~ (e1 = e0)
% 203.81/34.66    (17)  op(e1, e1) = all_10_2
% 203.81/34.66  
% 203.81/34.66  Begin of proof
% 203.81/34.66  | 
% 203.81/34.66  | BETA: splitting (9) gives:
% 203.81/34.66  | 
% 203.81/34.66  | Case 1:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (18)  all_58_2 = e3
% 203.81/34.66  | | 
% 203.81/34.66  | | REF_CLOSE: (7), (8), (18) are inconsistent by sub-proof #948.
% 203.81/34.66  | | 
% 203.81/34.66  | Case 2:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (19)  all_58_6 = e3 | all_58_12 = e3
% 203.81/34.66  | | 
% 203.81/34.66  | | BETA: splitting (19) gives:
% 203.81/34.66  | | 
% 203.81/34.66  | | Case 1:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (20)  all_58_6 = e3
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REF_CLOSE: (12), (15), (20) are inconsistent by sub-proof #1328.
% 203.81/34.66  | | | 
% 203.81/34.66  | | Case 2:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (21)  all_58_12 = e3
% 203.81/34.66  | | | 
% 203.81/34.66  | | | COMBINE_EQS: (10), (21) imply:
% 203.81/34.66  | | |   (22)  all_52_7 = e3
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (22) implies:
% 203.81/34.66  | | |   (23)  all_52_7 = e3
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (3), (23) imply:
% 203.81/34.66  | | |   (24)  op(e3, e3) = e0
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (11), (13), (14), (15), (16),
% 203.81/34.66  | | |            (17), (21), (24) are inconsistent by sub-proof #845.
% 203.81/34.66  | | | 
% 203.81/34.66  | | End of split
% 203.81/34.66  | | 
% 203.81/34.66  | End of split
% 203.81/34.66  | 
% 203.81/34.66  End of proof
% 203.81/34.66  
% 203.81/34.66  Sub-proof #641 shows that the following formulas are inconsistent:
% 203.81/34.66  ----------------------------------------------------------------
% 203.81/34.66    (1)   ~ (e3 = e1)
% 203.81/34.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.66    (3)  op(all_52_7, all_52_7) = e0
% 203.81/34.66    (4)  op(all_52_5, all_52_5) = e1
% 203.81/34.66    (5)   ~ (all_4_0 = e1)
% 203.81/34.66    (6)  all_58_0 = all_6_2
% 203.81/34.66    (7)  all_58_2 = all_4_0
% 203.81/34.66    (8)   ~ (all_4_0 = e3)
% 203.81/34.66    (9)   ~ (all_6_2 = e3)
% 203.81/34.66    (10)  op(all_6_2, all_6_2) = e3
% 203.81/34.66    (11)  all_58_12 = all_52_7
% 203.81/34.66    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.81/34.66    (13)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66    (14)   ~ (all_52_5 = all_10_2)
% 203.81/34.66    (15)  op(e3, e3) = all_6_2
% 203.81/34.66    (16)  all_58_6 = all_52_5
% 203.81/34.66    (17)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.81/34.66    (18)   ~ (e1 = e0)
% 203.81/34.66    (19)  op(e1, e1) = all_10_2
% 203.81/34.66  
% 203.81/34.66  Begin of proof
% 203.81/34.66  | 
% 203.81/34.66  | BETA: splitting (12) gives:
% 203.81/34.66  | 
% 203.81/34.66  | Case 1:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (20)  all_58_0 = e3
% 203.81/34.66  | | 
% 203.81/34.66  | | COMBINE_EQS: (6), (20) imply:
% 203.81/34.66  | |   (21)  all_6_2 = e3
% 203.81/34.66  | | 
% 203.81/34.66  | | REDUCE: (9), (21) imply:
% 203.81/34.66  | |   (22)  $false
% 203.81/34.66  | | 
% 203.81/34.66  | | CLOSE: (22) is inconsistent.
% 203.81/34.66  | | 
% 203.81/34.66  | Case 2:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (23)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.81/34.66  | | 
% 203.81/34.66  | | BETA: splitting (17) gives:
% 203.81/34.66  | | 
% 203.81/34.66  | | Case 1:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (24)  all_58_12 = e3
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (13), (14), (15),
% 203.81/34.66  | | |            (16), (18), (19), (24) are inconsistent by sub-proof #844.
% 203.81/34.66  | | | 
% 203.81/34.66  | | Case 2:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (25)   ~ (all_58_12 = e3)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (11), (25) imply:
% 203.81/34.66  | | |   (26)   ~ (all_52_7 = e3)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | BETA: splitting (23) gives:
% 203.81/34.66  | | | 
% 203.81/34.66  | | | Case 1:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (27)  all_58_2 = e3
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (7), (8), (27) are inconsistent by sub-proof #948.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | Case 2:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (28)  all_58_6 = e3 | all_58_12 = e3
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (2), (4), (10), (11), (14), (15), (16), (19), (26), (28) are
% 203.81/34.66  | | | |            inconsistent by sub-proof #1366.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | End of split
% 203.81/34.66  | | | 
% 203.81/34.66  | | End of split
% 203.81/34.66  | | 
% 203.81/34.66  | End of split
% 203.81/34.66  | 
% 203.81/34.66  End of proof
% 203.81/34.66  
% 203.81/34.66  Sub-proof #642 shows that the following formulas are inconsistent:
% 203.81/34.66  ----------------------------------------------------------------
% 203.81/34.66    (1)   ~ (e3 = e1)
% 203.81/34.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.66    (3)  op(all_52_7, all_52_7) = e0
% 203.81/34.66    (4)  op(all_52_5, all_52_5) = e1
% 203.81/34.66    (5)   ~ (all_4_0 = e1)
% 203.81/34.66    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.66    (7)   ~ (all_52_5 = all_4_0)
% 203.81/34.66    (8)  all_58_0 = all_6_2
% 203.81/34.66    (9)  op(e3, e0) = all_52_25
% 203.81/34.66    (10)  all_58_9 = all_52_25
% 203.81/34.66    (11)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.81/34.66    (12)  op(e1, e3) = all_52_5
% 203.81/34.66    (13)   ~ (all_6_2 = all_4_0)
% 203.81/34.66    (14)  all_32_2 = all_4_2
% 203.81/34.66    (15)  op(e2, e2) = all_4_2
% 203.81/34.66    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.81/34.66    (17)  all_58_11 = all_52_29
% 203.81/34.66    (18)  all_56_5 = all_4_2
% 203.81/34.66    (19)   ~ (all_52_7 = all_6_2)
% 203.81/34.66    (20)  all_58_2 = all_4_0
% 203.81/34.66    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.81/34.66    (22)  op(all_4_2, e2) = e3
% 203.81/34.66    (23)  all_58_15 = e0
% 203.81/34.66    (24)   ~ (all_52_25 = e0)
% 203.81/34.66    (25)   ~ (e2 = e1)
% 203.81/34.66    (26)  all_56_8 = all_52_5
% 203.81/34.66    (27)   ~ (all_52_25 = all_52_29)
% 203.81/34.66    (28)   ~ (all_52_5 = all_52_7)
% 203.81/34.66    (29)  all_58_12 = all_52_7
% 203.81/34.66    (30)  op(e3, all_6_1) = all_6_0
% 203.81/34.66    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66    (32)   ~ (all_52_25 = e3)
% 203.81/34.66    (33)   ~ (e2 = e0)
% 203.81/34.66    (34)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.81/34.66    (35)   ~ (all_52_5 = all_52_29)
% 203.81/34.66    (36)   ~ (all_52_29 = e0)
% 203.81/34.66    (37)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.81/34.66    (38)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.66    (39)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.81/34.66    (40)  all_56_4 = all_4_0
% 203.81/34.66    (41)   ~ (all_6_0 = e2)
% 203.81/34.66    (42)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.81/34.66    (43)   ~ (all_52_5 = all_10_2)
% 203.81/34.66    (44)  op(all_52_29, all_52_29) = all_52_28
% 203.81/34.66    (45)   ~ (all_52_7 = all_4_0)
% 203.81/34.66    (46)  all_56_12 = all_52_7
% 203.81/34.66    (47)   ~ (all_52_25 = all_6_2)
% 203.81/34.66    (48)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.66    (49)   ~ (all_52_9 = all_4_2)
% 203.81/34.66    (50)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.81/34.66    (51)  all_58_10 = e3
% 203.81/34.66    (52)  op(e3, e3) = all_6_2
% 203.81/34.66    (53)  op(all_4_2, all_4_2) = all_52_10
% 203.81/34.66    (54)  all_32_0 = all_4_0
% 203.81/34.66    (55)  all_56_3 = all_52_25
% 203.81/34.66    (56)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.81/34.66    (57)  all_58_6 = all_52_5
% 203.81/34.66    (58)   ~ (all_4_0 = all_4_2)
% 203.81/34.66    (59)  op(e3, e2) = all_52_9
% 203.81/34.66    (60)   ~ (e1 = e0)
% 203.81/34.66    (61)   ~ (e3 = e2)
% 203.81/34.66    (62)   ~ (all_6_1 = e2)
% 203.81/34.66    (63)  op(e1, e1) = all_10_2
% 203.81/34.66    (64)  op(all_6_2, e3) = all_6_1
% 203.81/34.66    (65)   ~ (all_52_7 = e0)
% 203.81/34.66    (66)  op(all_52_25, all_52_25) = all_52_24
% 203.81/34.66  
% 203.81/34.66  Begin of proof
% 203.81/34.66  | 
% 203.81/34.66  | BETA: splitting (48) gives:
% 203.81/34.66  | 
% 203.81/34.66  | Case 1:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (67)  all_56_3 = e3
% 203.81/34.66  | | 
% 203.81/34.66  | | REF_CLOSE: (32), (55), (67) are inconsistent by sub-proof #1339.
% 203.81/34.66  | | 
% 203.81/34.66  | Case 2:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (68)   ~ (all_56_3 = e3)
% 203.81/34.66  | |   (69)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.66  | | 
% 203.81/34.66  | | BETA: splitting (50) gives:
% 203.81/34.66  | | 
% 203.81/34.66  | | Case 1:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (70)  all_58_9 = e2
% 203.81/34.66  | | | 
% 203.81/34.66  | | | COMBINE_EQS: (10), (70) imply:
% 203.81/34.66  | | |   (71)  all_52_25 = e2
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (71) implies:
% 203.81/34.66  | | |   (72)  all_52_25 = e2
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (47), (72) imply:
% 203.81/34.66  | | |   (73)   ~ (all_6_2 = e2)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (73) implies:
% 203.81/34.66  | | |   (74)   ~ (all_6_2 = e2)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (32), (72) imply:
% 203.81/34.66  | | |   (75)   ~ (e3 = e2)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (66), (72) imply:
% 203.81/34.66  | | |   (76)  op(e2, e2) = all_52_24
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (9), (72) imply:
% 203.81/34.66  | | |   (77)  op(e3, e0) = e2
% 203.81/34.66  | | | 
% 203.81/34.66  | | | BETA: splitting (21) gives:
% 203.81/34.66  | | | 
% 203.81/34.66  | | | Case 1:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (78)  all_58_9 = e1
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (25), (70), (78) are inconsistent by sub-proof #1214.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | Case 2:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (79)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | BETA: splitting (79) gives:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | Case 1:
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | |   (80)  all_58_10 = e1
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | REF_CLOSE: (1), (51), (80) are inconsistent by sub-proof #968.
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | Case 2:
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | |   (81)  all_58_11 = e1 | all_58_15 = e1
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | BETA: splitting (81) gives:
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | Case 1:
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | |   (82)  all_58_11 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | COMBINE_EQS: (17), (82) imply:
% 203.81/34.66  | | | | | |   (83)  all_52_29 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | SIMP: (83) implies:
% 203.81/34.66  | | | | | |   (84)  all_52_29 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REDUCE: (35), (84) imply:
% 203.81/34.66  | | | | | |   (85)   ~ (all_52_5 = e1)
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REDUCE: (44), (84) imply:
% 203.81/34.66  | | | | | |   (86)  op(e1, e1) = all_52_28
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | GROUND_INST: instantiating (2) with all_10_2, all_52_28, e1, e1,
% 203.81/34.66  | | | | | |              simplifying with (63), (86) gives:
% 203.81/34.66  | | | | | |   (87)  all_52_28 = all_10_2
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_24, e2, e2,
% 203.81/34.66  | | | | | |              simplifying with (15), (76) gives:
% 203.81/34.66  | | | | | |   (88)  all_52_24 = all_4_2
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | BETA: splitting (31) gives:
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | Case 1:
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | |   (89)  all_58_0 = e1
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | REF_CLOSE: (2), (6), (8), (12), (13), (14), (15), (16), (18),
% 203.81/34.66  | | | | | | |            (19), (22), (29), (30), (33), (34), (38), (39), (40),
% 203.81/34.66  | | | | | | |            (41), (45), (46), (49), (53), (54), (56), (57), (58),
% 203.81/34.66  | | | | | | |            (59), (60), (61), (62), (64), (65), (74), (77), (89)
% 203.81/34.66  | | | | | | |            are inconsistent by sub-proof #964.
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | Case 2:
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | |   (90)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (11), (14), (15), (18), (19),
% 203.81/34.66  | | | | | | |            (20), (22), (26), (28), (29), (34), (38), (40), (42),
% 203.81/34.66  | | | | | | |            (43), (45), (49), (52), (53), (54), (56), (57), (58),
% 203.81/34.66  | | | | | | |            (59), (63), (85), (90) are inconsistent by sub-proof
% 203.81/34.66  | | | | | | |            #643.
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | End of split
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | Case 2:
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | |   (91)  all_58_15 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REF_CLOSE: (23), (60), (91) are inconsistent by sub-proof #1207.
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | End of split
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | End of split
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | End of split
% 203.81/34.66  | | | 
% 203.81/34.66  | | Case 2:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (92)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 203.81/34.66  | | | 
% 203.81/34.66  | | | BETA: splitting (92) gives:
% 203.81/34.66  | | | 
% 203.81/34.66  | | | Case 1:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (93)  all_58_10 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (51), (61), (93) are inconsistent by sub-proof #1220.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | Case 2:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (94)  all_58_11 = e2 | all_58_15 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | BETA: splitting (94) gives:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | Case 1:
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | |   (95)  all_58_11 = e2
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | COMBINE_EQS: (17), (95) imply:
% 203.81/34.66  | | | | |   (96)  all_52_29 = e2
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | SIMP: (96) implies:
% 203.81/34.66  | | | | |   (97)  all_52_29 = e2
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | REDUCE: (27), (97) imply:
% 203.81/34.66  | | | | |   (98)   ~ (all_52_25 = e2)
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | REDUCE: (44), (97) imply:
% 203.81/34.66  | | | | |   (99)  op(e2, e2) = all_52_28
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | BETA: splitting (21) gives:
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | Case 1:
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | |   (100)  all_58_9 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | COMBINE_EQS: (10), (100) imply:
% 203.81/34.66  | | | | | |   (101)  all_52_25 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | SIMP: (101) implies:
% 203.81/34.66  | | | | | |   (102)  all_52_25 = e1
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REDUCE: (47), (102) imply:
% 203.81/34.66  | | | | | |   (103)   ~ (all_6_2 = e1)
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | SIMP: (103) implies:
% 203.81/34.66  | | | | | |   (104)   ~ (all_6_2 = e1)
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REDUCE: (32), (102) imply:
% 203.81/34.66  | | | | | |   (105)   ~ (e3 = e1)
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REDUCE: (66), (102) imply:
% 203.81/34.66  | | | | | |   (106)  op(e1, e1) = all_52_24
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | GROUND_INST: instantiating (2) with all_10_2, all_52_24, e1, e1,
% 203.81/34.66  | | | | | |              simplifying with (63), (106) gives:
% 203.81/34.66  | | | | | |   (107)  all_52_24 = all_10_2
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_28, e2, e2,
% 203.81/34.66  | | | | | |              simplifying with (15), (99) gives:
% 203.81/34.66  | | | | | |   (108)  all_52_28 = all_4_2
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | BETA: splitting (31) gives:
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | Case 1:
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | |   (109)  all_58_0 = e1
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | COMBINE_EQS: (8), (109) imply:
% 203.81/34.66  | | | | | | |   (110)  all_6_2 = e1
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | REDUCE: (104), (110) imply:
% 203.81/34.66  | | | | | | |   (111)  $false
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | CLOSE: (111) is inconsistent.
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | Case 2:
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | |   (112)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | BETA: splitting (6) gives:
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | | Case 1:
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | |   (113)  all_56_12 = e3
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | | COMBINE_EQS: (46), (113) imply:
% 203.81/34.66  | | | | | | | |   (114)  all_52_7 = e3
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | | SIMP: (114) implies:
% 203.81/34.66  | | | | | | | |   (115)  all_52_7 = e3
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | | COMBINE_EQS: (29), (115) imply:
% 203.81/34.66  | | | | | | | |   (116)  all_58_12 = e3
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (20), (43), (57), (63), (112),
% 203.81/34.66  | | | | | | | |            (116) are inconsistent by sub-proof #846.
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | Case 2:
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | |   (117)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | | BETA: splitting (37) gives:
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | | Case 1:
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | |   (118)  all_58_12 = e1
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | COMBINE_EQS: (29), (118) imply:
% 203.81/34.66  | | | | | | | | |   (119)  all_52_7 = e1
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | SIMP: (119) implies:
% 203.81/34.66  | | | | | | | | |   (120)  all_52_7 = e1
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | REDUCE: (28), (120) imply:
% 203.81/34.66  | | | | | | | | |   (121)   ~ (all_52_5 = e1)
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | REDUCE: (45), (120) imply:
% 203.81/34.66  | | | | | | | | |   (122)   ~ (all_4_0 = e1)
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (11), (14), (15), (18),
% 203.81/34.66  | | | | | | | | |            (19), (20), (22), (26), (28), (29), (34), (38),
% 203.81/34.66  | | | | | | | | |            (40), (42), (43), (45), (49), (52), (53), (54),
% 203.81/34.66  | | | | | | | | |            (56), (57), (58), (59), (63), (112), (121) are
% 203.81/34.66  | | | | | | | | |            inconsistent by sub-proof #643.
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | Case 2:
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | |   (123)   ~ (all_58_12 = e1)
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | REDUCE: (29), (123) imply:
% 203.81/34.66  | | | | | | | | |   (124)   ~ (all_52_7 = e1)
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | | REF_CLOSE: (2), (5), (14), (15), (18), (22), (34), (38), (40),
% 203.81/34.66  | | | | | | | | |            (45), (46), (49), (53), (54), (56), (58), (59),
% 203.81/34.66  | | | | | | | | |            (65), (117), (124) are inconsistent by sub-proof
% 203.81/34.66  | | | | | | | | |            #966.
% 203.81/34.66  | | | | | | | | | 
% 203.81/34.66  | | | | | | | | End of split
% 203.81/34.66  | | | | | | | | 
% 203.81/34.66  | | | | | | | End of split
% 203.81/34.66  | | | | | | | 
% 203.81/34.66  | | | | | | End of split
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | Case 2:
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | |   (125)   ~ (all_58_9 = e1)
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REDUCE: (10), (125) imply:
% 203.81/34.66  | | | | | |   (126)   ~ (all_52_25 = e1)
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | | REF_CLOSE: (24), (55), (69), (98), (126) are inconsistent by
% 203.81/34.66  | | | | | |            sub-proof #1215.
% 203.81/34.66  | | | | | | 
% 203.81/34.66  | | | | | End of split
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | Case 2:
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | |   (127)  all_58_15 = e2
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | | REF_CLOSE: (23), (33), (127) are inconsistent by sub-proof #1223.
% 203.81/34.66  | | | | | 
% 203.81/34.66  | | | | End of split
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | End of split
% 203.81/34.66  | | | 
% 203.81/34.66  | | End of split
% 203.81/34.66  | | 
% 203.81/34.66  | End of split
% 203.81/34.66  | 
% 203.81/34.66  End of proof
% 203.81/34.66  
% 203.81/34.66  Sub-proof #643 shows that the following formulas are inconsistent:
% 203.81/34.66  ----------------------------------------------------------------
% 203.81/34.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.66    (2)  op(all_52_7, all_52_7) = e0
% 203.81/34.66    (3)  op(all_52_5, all_52_5) = e1
% 203.81/34.66    (4)   ~ (all_4_0 = e1)
% 203.81/34.66    (5)   ~ (all_52_5 = all_4_0)
% 203.81/34.66    (6)   ~ (all_52_5 = e1)
% 203.81/34.66    (7)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.81/34.66    (8)  all_32_2 = all_4_2
% 203.81/34.66    (9)  op(e2, e2) = all_4_2
% 203.81/34.66    (10)  all_56_5 = all_4_2
% 203.81/34.66    (11)   ~ (all_52_7 = all_6_2)
% 203.81/34.66    (12)  all_58_2 = all_4_0
% 203.81/34.66    (13)  op(all_4_2, e2) = e3
% 203.81/34.66    (14)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66    (15)  all_56_8 = all_52_5
% 203.81/34.66    (16)   ~ (all_52_5 = all_52_7)
% 203.81/34.66    (17)  all_58_12 = all_52_7
% 203.81/34.66    (18)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.81/34.66    (19)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.66    (20)  all_56_4 = all_4_0
% 203.81/34.66    (21)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.81/34.66    (22)   ~ (all_52_5 = all_10_2)
% 203.81/34.66    (23)   ~ (all_52_7 = all_4_0)
% 203.81/34.66    (24)   ~ (all_52_9 = all_4_2)
% 203.81/34.66    (25)  op(e3, e3) = all_6_2
% 203.81/34.66    (26)  op(all_4_2, all_4_2) = all_52_10
% 203.81/34.66    (27)  all_32_0 = all_4_0
% 203.81/34.66    (28)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.81/34.66    (29)  all_58_6 = all_52_5
% 203.81/34.66    (30)   ~ (all_4_0 = all_4_2)
% 203.81/34.66    (31)  op(e3, e2) = all_52_9
% 203.81/34.66    (32)  op(e1, e1) = all_10_2
% 203.81/34.66  
% 203.81/34.66  Begin of proof
% 203.81/34.66  | 
% 203.81/34.66  | BETA: splitting (14) gives:
% 203.81/34.66  | 
% 203.81/34.66  | Case 1:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (33)  all_58_2 = e1
% 203.81/34.66  | | 
% 203.81/34.66  | | REF_CLOSE: (4), (12), (33) are inconsistent by sub-proof #967.
% 203.81/34.66  | | 
% 203.81/34.66  | Case 2:
% 203.81/34.66  | | 
% 203.81/34.66  | |   (34)  all_58_6 = e1 | all_58_12 = e1
% 203.81/34.66  | | 
% 203.81/34.66  | | BETA: splitting (34) gives:
% 203.81/34.66  | | 
% 203.81/34.66  | | Case 1:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (35)  all_58_6 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REF_CLOSE: (6), (29), (35) are inconsistent by sub-proof #963.
% 203.81/34.66  | | | 
% 203.81/34.66  | | Case 2:
% 203.81/34.66  | | | 
% 203.81/34.66  | | |   (36)  all_58_12 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | COMBINE_EQS: (17), (36) imply:
% 203.81/34.66  | | |   (37)  all_52_7 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (37) implies:
% 203.81/34.66  | | |   (38)  all_52_7 = e1
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (11), (38) imply:
% 203.81/34.66  | | |   (39)   ~ (all_6_2 = e1)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | SIMP: (39) implies:
% 203.81/34.66  | | |   (40)   ~ (all_6_2 = e1)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (23), (38) imply:
% 203.81/34.66  | | |   (41)   ~ (all_4_0 = e1)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (2), (38) imply:
% 203.81/34.66  | | |   (42)  op(e1, e1) = e0
% 203.81/34.66  | | | 
% 203.81/34.66  | | | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 203.81/34.66  | | |              (32), (42) gives:
% 203.81/34.66  | | |   (43)  all_10_2 = e0
% 203.81/34.66  | | | 
% 203.81/34.66  | | | REDUCE: (22), (43) imply:
% 203.81/34.66  | | |   (44)   ~ (all_52_5 = e0)
% 203.81/34.66  | | | 
% 203.81/34.66  | | | BETA: splitting (7) gives:
% 203.81/34.66  | | | 
% 203.81/34.66  | | | Case 1:
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | |   (45)  all_58_6 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | COMBINE_EQS: (29), (45) imply:
% 203.81/34.66  | | | |   (46)  all_52_5 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | SIMP: (46) implies:
% 203.81/34.66  | | | |   (47)  all_52_5 = e2
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REDUCE: (5), (47) imply:
% 203.81/34.66  | | | |   (48)   ~ (all_4_0 = e2)
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | SIMP: (48) implies:
% 203.81/34.66  | | | |   (49)   ~ (all_4_0 = e2)
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | | REF_CLOSE: (1), (4), (8), (9), (10), (13), (18), (19), (20), (24), (26),
% 203.81/34.66  | | | |            (27), (28), (30), (31), (49) are inconsistent by sub-proof
% 203.81/34.66  | | | |            #971.
% 203.81/34.66  | | | | 
% 203.81/34.66  | | | Case 2:
% 203.81/34.66  | | | | 
% 203.81/34.67  | | | |   (50)   ~ (all_58_6 = e2)
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | REDUCE: (29), (50) imply:
% 203.81/34.67  | | | |   (51)   ~ (all_52_5 = e2)
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | REF_CLOSE: (1), (3), (6), (15), (21), (25), (40), (44), (51) are
% 203.81/34.67  | | | |            inconsistent by sub-proof #655.
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | End of split
% 203.81/34.67  | | | 
% 203.81/34.67  | | End of split
% 203.81/34.67  | | 
% 203.81/34.67  | End of split
% 203.81/34.67  | 
% 203.81/34.67  End of proof
% 203.81/34.67  
% 203.81/34.67  Sub-proof #644 shows that the following formulas are inconsistent:
% 203.81/34.67  ----------------------------------------------------------------
% 203.81/34.67    (1)  all_58_14 = all_52_23
% 203.81/34.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.67    (3)  op(all_52_7, all_52_7) = e0
% 203.81/34.67    (4)  all_58_1 = all_52_9
% 203.81/34.67    (5)  op(e0, e2) = all_52_15
% 203.81/34.67    (6)   ~ (all_52_7 = all_52_15)
% 203.81/34.67    (7)   ~ (all_14_1 = e2)
% 203.81/34.67    (8)   ~ (all_14_1 = e3)
% 203.81/34.67    (9)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.81/34.67    (10)  op(e0, all_14_1) = all_14_0
% 203.81/34.67    (11)  all_58_13 = all_52_15
% 203.81/34.67    (12)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.67    (13)  op(e2, e2) = all_4_2
% 203.81/34.67    (14)   ~ (all_4_1 = e3)
% 203.81/34.67    (15)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.81/34.67    (16)  all_56_3 = all_14_1
% 203.81/34.67    (17)  op(e0, e0) = all_14_2
% 203.81/34.67    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.81/34.67    (19)   ~ (all_4_1 = e1)
% 203.81/34.67    (20)  op(e0, e0) = e3
% 203.81/34.67    (21)   ~ (all_52_9 = all_14_1)
% 203.81/34.67    (22)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.81/34.67    (23)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.67    (24)  all_58_12 = all_52_7
% 203.81/34.67    (25)   ~ (all_52_7 = all_14_2)
% 203.81/34.67    (26)  op(e1, e2) = e3
% 203.81/34.67    (27)   ~ (all_14_0 = e3)
% 203.81/34.67    (28)  all_58_9 = all_14_1
% 203.81/34.67    (29)  all_58_7 = e3
% 203.81/34.67    (30)  op(all_4_2, e2) = all_4_1
% 203.81/34.67    (31)   ~ (all_52_23 = e3)
% 203.81/34.67    (32)   ~ (all_10_2 = e3)
% 203.81/34.67    (33)  op(all_14_1, all_14_1) = all_52_24
% 203.81/34.67    (34)  all_58_8 = all_10_2
% 203.81/34.67    (35)  all_56_12 = all_52_7
% 203.81/34.67    (36)  all_58_5 = e3
% 203.81/34.67    (37)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.81/34.67    (38)  all_58_3 = all_4_2
% 203.81/34.67  
% 203.81/34.67  Begin of proof
% 203.81/34.67  | 
% 203.81/34.67  | BETA: splitting (18) gives:
% 203.81/34.67  | 
% 203.81/34.67  | Case 1:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (39)  all_58_9 = e1
% 203.81/34.67  | | 
% 203.81/34.67  | | COMBINE_EQS: (28), (39) imply:
% 203.81/34.67  | |   (40)  all_14_1 = e1
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (21), (40) imply:
% 203.81/34.67  | |   (41)   ~ (all_52_9 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (8), (40) imply:
% 203.81/34.67  | |   (42)   ~ (e3 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | SIMP: (42) implies:
% 203.81/34.67  | |   (43)   ~ (e3 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (12), (13), (14), (15),
% 203.81/34.67  | |            (17), (19), (22), (24), (25), (26), (29), (30), (31), (32), (34),
% 203.81/34.67  | |            (35), (36), (37), (38), (41), (43) are inconsistent by sub-proof
% 203.81/34.67  | |            #645.
% 203.81/34.67  | | 
% 203.81/34.67  | Case 2:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (44)   ~ (all_58_9 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (28), (44) imply:
% 203.81/34.67  | |   (45)   ~ (all_14_1 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (2), (7), (10), (16), (20), (23), (27), (33), (45) are
% 203.81/34.67  | |            inconsistent by sub-proof #1181.
% 203.81/34.67  | | 
% 203.81/34.67  | End of split
% 203.81/34.67  | 
% 203.81/34.67  End of proof
% 203.81/34.67  
% 203.81/34.67  Sub-proof #645 shows that the following formulas are inconsistent:
% 203.81/34.67  ----------------------------------------------------------------
% 203.81/34.67    (1)  all_58_14 = all_52_23
% 203.81/34.67    (2)   ~ (e3 = e1)
% 203.81/34.67    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.67    (4)  op(all_52_7, all_52_7) = e0
% 203.81/34.67    (5)  all_58_1 = all_52_9
% 203.81/34.67    (6)  op(e0, e2) = all_52_15
% 203.81/34.67    (7)   ~ (all_52_7 = all_52_15)
% 203.81/34.67    (8)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.81/34.67    (9)  all_58_13 = all_52_15
% 203.81/34.67    (10)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.67    (11)  op(e2, e2) = all_4_2
% 203.81/34.67    (12)   ~ (all_4_1 = e3)
% 203.81/34.67    (13)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.81/34.67    (14)  op(e0, e0) = all_14_2
% 203.81/34.67    (15)   ~ (all_4_1 = e1)
% 203.81/34.67    (16)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.81/34.67    (17)  all_58_12 = all_52_7
% 203.81/34.67    (18)   ~ (all_52_7 = all_14_2)
% 203.81/34.67    (19)  op(e1, e2) = e3
% 203.81/34.67    (20)  all_58_7 = e3
% 203.81/34.67    (21)  op(all_4_2, e2) = all_4_1
% 203.81/34.67    (22)   ~ (all_52_23 = e3)
% 203.81/34.67    (23)   ~ (all_10_2 = e3)
% 203.81/34.67    (24)  all_58_8 = all_10_2
% 203.81/34.67    (25)  all_56_12 = all_52_7
% 203.81/34.67    (26)   ~ (all_52_9 = e1)
% 203.81/34.67    (27)  all_58_5 = e3
% 203.81/34.67    (28)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.81/34.67    (29)  all_58_3 = all_4_2
% 203.81/34.67  
% 203.81/34.67  Begin of proof
% 203.81/34.67  | 
% 203.81/34.67  | BETA: splitting (8) gives:
% 203.81/34.67  | 
% 203.81/34.67  | Case 1:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (30)  all_58_13 = e1
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (13), (14), (15), (17),
% 203.81/34.67  | |            (18), (21), (25), (30) are inconsistent by sub-proof #646.
% 203.81/34.67  | | 
% 203.81/34.67  | Case 2:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (31)   ~ (all_58_13 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (9), (31) imply:
% 203.81/34.67  | |   (32)   ~ (all_52_15 = e1)
% 203.81/34.67  | | 
% 203.81/34.67  | | BETA: splitting (16) gives:
% 203.81/34.67  | | 
% 203.81/34.67  | | Case 1:
% 203.81/34.67  | | | 
% 203.81/34.67  | | |   (33)  all_58_1 = e1
% 203.81/34.67  | | | 
% 203.81/34.67  | | | COMBINE_EQS: (5), (33) imply:
% 203.81/34.67  | | |   (34)  all_52_9 = e1
% 203.81/34.67  | | | 
% 203.81/34.67  | | | REDUCE: (26), (34) imply:
% 203.81/34.67  | | |   (35)  $false
% 203.81/34.67  | | | 
% 203.81/34.67  | | | CLOSE: (35) is inconsistent.
% 203.81/34.67  | | | 
% 203.81/34.67  | | Case 2:
% 203.81/34.67  | | | 
% 203.81/34.67  | | |   (36)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.81/34.67  | | | 
% 203.81/34.67  | | | BETA: splitting (36) gives:
% 203.81/34.67  | | | 
% 203.81/34.67  | | | Case 1:
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | |   (37)  all_58_3 = e1
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | COMBINE_EQS: (29), (37) imply:
% 203.81/34.67  | | | |   (38)  all_4_2 = e1
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | REDUCE: (21), (38) imply:
% 203.81/34.67  | | | |   (39)  op(e1, e2) = all_4_1
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | GROUND_INST: instantiating (3) with e3, all_4_1, e2, e1, simplifying
% 203.81/34.67  | | | |              with (19), (39) gives:
% 203.81/34.67  | | | |   (40)  all_4_1 = e3
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | REDUCE: (12), (40) imply:
% 203.81/34.67  | | | |   (41)  $false
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | CLOSE: (41) is inconsistent.
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | Case 2:
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | |   (42)  all_58_7 = e1 | all_58_13 = e1
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | BETA: splitting (42) gives:
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | Case 1:
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | |   (43)  all_58_7 = e1
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | COMBINE_EQS: (20), (43) imply:
% 203.81/34.67  | | | | |   (44)  e3 = e1
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | COMBINE_EQS: (27), (44) imply:
% 203.81/34.67  | | | | |   (45)  all_58_5 = e1
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | REF_CLOSE: (1), (2), (22), (23), (24), (28), (45) are inconsistent by
% 203.81/34.67  | | | | |            sub-proof #1051.
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | Case 2:
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | |   (46)  all_58_13 = e1
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | REF_CLOSE: (9), (32), (46) are inconsistent by sub-proof #1133.
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | End of split
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | End of split
% 203.81/34.67  | | | 
% 203.81/34.67  | | End of split
% 203.81/34.67  | | 
% 203.81/34.67  | End of split
% 203.81/34.67  | 
% 203.81/34.67  End of proof
% 203.81/34.67  
% 203.81/34.67  Sub-proof #646 shows that the following formulas are inconsistent:
% 203.81/34.67  ----------------------------------------------------------------
% 203.81/34.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.67    (2)  op(all_52_7, all_52_7) = e0
% 203.81/34.67    (3)  op(e0, e2) = all_52_15
% 203.81/34.67    (4)   ~ (all_52_7 = all_52_15)
% 203.81/34.67    (5)  all_58_13 = all_52_15
% 203.81/34.67    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.67    (7)  op(e2, e2) = all_4_2
% 203.81/34.67    (8)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.81/34.67    (9)  op(e0, e0) = all_14_2
% 203.81/34.67    (10)   ~ (all_4_1 = e1)
% 203.81/34.67    (11)  all_58_12 = all_52_7
% 203.81/34.67    (12)  all_58_13 = e1
% 203.81/34.67    (13)   ~ (all_52_7 = all_14_2)
% 203.81/34.67    (14)  op(all_4_2, e2) = all_4_1
% 203.81/34.67    (15)  all_56_12 = all_52_7
% 203.81/34.67  
% 203.81/34.67  Begin of proof
% 203.81/34.67  | 
% 203.81/34.67  | COMBINE_EQS: (5), (12) imply:
% 203.81/34.67  |   (16)  all_52_15 = e1
% 203.81/34.67  | 
% 203.81/34.67  | SIMP: (16) implies:
% 203.81/34.67  |   (17)  all_52_15 = e1
% 203.81/34.67  | 
% 203.81/34.67  | REDUCE: (4), (17) imply:
% 203.81/34.67  |   (18)   ~ (all_52_7 = e1)
% 203.81/34.67  | 
% 203.81/34.67  | REDUCE: (3), (17) imply:
% 203.81/34.67  |   (19)  op(e0, e2) = e1
% 203.81/34.67  | 
% 203.81/34.67  | BETA: splitting (8) gives:
% 203.81/34.67  | 
% 203.81/34.67  | Case 1:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (20)  all_58_12 = e2
% 203.81/34.67  | | 
% 203.81/34.67  | | COMBINE_EQS: (11), (20) imply:
% 203.81/34.67  | |   (21)  all_52_7 = e2
% 203.81/34.67  | | 
% 203.81/34.67  | | SIMP: (21) implies:
% 203.81/34.67  | |   (22)  all_52_7 = e2
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (2), (22) imply:
% 203.81/34.67  | |   (23)  op(e2, e2) = e0
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (1), (7), (10), (14), (19), (23) are inconsistent by sub-proof
% 203.81/34.67  | |            #1357.
% 203.81/34.67  | | 
% 203.81/34.67  | Case 2:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (24)   ~ (all_58_12 = e2)
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (11), (24) imply:
% 203.81/34.67  | |   (25)   ~ (all_52_7 = e2)
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (1), (2), (6), (9), (13), (15), (18), (25) are inconsistent by
% 203.81/34.67  | |            sub-proof #1176.
% 203.81/34.67  | | 
% 203.81/34.67  | End of split
% 203.81/34.67  | 
% 203.81/34.67  End of proof
% 203.81/34.67  
% 203.81/34.67  Sub-proof #647 shows that the following formulas are inconsistent:
% 203.81/34.67  ----------------------------------------------------------------
% 203.81/34.67    (1)   ~ (all_52_25 = all_52_27)
% 203.81/34.67    (2)  all_58_14 = all_52_23
% 203.81/34.67    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.81/34.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.67    (5)   ~ (all_52_5 = all_52_13)
% 203.81/34.67    (6)  all_58_1 = all_52_9
% 203.81/34.67    (7)   ~ (all_52_9 = all_52_13)
% 203.81/34.67    (8)   ~ (e3 = e0)
% 203.81/34.67    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.67    (10)   ~ (all_52_7 = all_52_15)
% 203.81/34.67    (11)  op(all_52_15, all_52_15) = e0
% 203.81/34.67    (12)   ~ (all_52_17 = all_52_25)
% 203.81/34.67    (13)  all_16_1 = all_10_1
% 203.81/34.67    (14)   ~ (all_52_3 = all_6_2)
% 203.81/34.67    (15)  all_58_0 = all_6_2
% 203.81/34.67    (16)  all_56_4 = all_52_3
% 203.81/34.67    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.81/34.67    (18)  op(all_52_19, all_52_19) = all_52_18
% 203.81/34.67    (19)  all_58_13 = all_52_15
% 203.81/34.67    (20)  op(all_52_13, all_52_13) = e1
% 203.81/34.67    (21)  op(all_10_2, all_10_2) = all_52_20
% 203.81/34.67    (22)  all_58_9 = all_52_25
% 203.81/34.67    (23)   ~ (all_6_1 = e1)
% 203.81/34.67    (24)  op(all_52_27, all_52_27) = all_52_26
% 203.81/34.67    (25)  op(e1, e3) = all_52_5
% 203.81/34.67    (26)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 203.81/34.67    (27)  op(e2, e2) = all_4_2
% 203.81/34.67    (28)   ~ (all_52_3 = all_52_5)
% 203.81/34.67    (29)  all_58_11 = all_52_29
% 203.81/34.67    (30)  all_56_5 = all_4_2
% 203.81/34.67    (31)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.81/34.67    (32)  op(all_10_2, e1) = all_10_1
% 203.81/34.67    (33)   ~ (all_52_7 = all_6_2)
% 203.81/34.67    (34)  op(e0, e1) = all_52_23
% 203.81/34.67    (35)   ~ (all_52_15 = e0)
% 203.81/34.67    (36)  all_58_15 = e0
% 203.81/34.67    (37)   ~ (all_4_1 = e1)
% 203.81/34.67    (38)   ~ (all_52_25 = e0)
% 203.81/34.67    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.81/34.67    (40)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.81/34.67    (41)   ~ (all_52_13 = all_10_2)
% 203.81/34.67    (42)  op(e0, e0) = e0
% 203.81/34.67    (43)  all_58_10 = all_52_27
% 203.81/34.67    (44)  all_56_8 = all_52_5
% 203.81/34.67    (45)   ~ (all_52_25 = all_52_29)
% 203.81/34.67    (46)  all_16_2 = all_10_2
% 203.81/34.67    (47)  all_58_7 = all_52_13
% 203.81/34.67    (48)   ~ (all_52_5 = all_52_7)
% 203.81/34.67    (49)  all_58_12 = all_52_7
% 203.81/34.67    (50)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.81/34.67    (51)  all_56_2 = all_52_17
% 203.81/34.67    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.81/34.67    (53)  all_56_7 = all_52_27
% 203.81/34.67    (54)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.81/34.67    (55)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.81/34.67    (56)  op(all_4_2, e2) = all_4_1
% 203.81/34.67    (57)   ~ (all_52_13 = all_4_2)
% 203.81/34.67    (58)  op(e0, e3) = all_52_7
% 203.81/34.67    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.81/34.67    (60)   ~ (all_52_9 = all_52_25)
% 203.81/34.67    (61)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.81/34.67    (62)  all_58_8 = all_10_2
% 203.81/34.67    (63)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.81/34.67    (64)  all_56_12 = all_52_7
% 203.81/34.67    (65)  op(all_52_17, all_52_17) = all_52_16
% 203.81/34.67    (66)   ~ (all_52_25 = all_6_2)
% 203.81/34.67    (67)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.81/34.67    (68)   ~ (all_52_9 = all_4_2)
% 203.81/34.67    (69)   ~ (all_52_5 = all_6_2)
% 203.81/34.67    (70)  op(all_4_2, all_4_2) = e2
% 203.81/34.67    (71)   ~ (all_52_9 = all_6_2)
% 203.81/34.67    (72)   ~ (all_52_13 = all_52_15)
% 203.81/34.67    (73)  op(e3, e3) = all_6_2
% 203.81/34.67    (74)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.81/34.67    (75)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.81/34.67    (76)  all_56_3 = all_52_25
% 203.81/34.67    (77)   ~ (all_52_3 = all_52_7)
% 203.81/34.67    (78)  all_58_5 = all_52_19
% 203.81/34.67    (79)  all_56_1 = all_52_9
% 203.81/34.67    (80)   ~ (all_52_15 = all_4_2)
% 203.81/34.67    (81)   ~ (all_52_27 = all_4_2)
% 203.81/34.67    (82)  all_58_6 = all_52_5
% 203.81/34.67    (83)  op(e3, e2) = all_52_9
% 203.81/34.67    (84)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.81/34.67    (85)   ~ (all_52_17 = all_6_2)
% 203.81/34.67    (86)   ~ (e1 = e0)
% 203.81/34.67    (87)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.81/34.67    (88)   ~ (all_52_9 = all_52_17)
% 203.81/34.67    (89)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.81/34.67    (90)   ~ (all_6_1 = e2)
% 203.81/34.67    (91)  op(e1, e1) = all_10_2
% 203.81/34.67    (92)  op(all_52_9, all_52_9) = e3
% 203.81/34.67    (93)   ~ (all_52_7 = all_52_23)
% 203.81/34.67    (94)  all_58_3 = all_4_2
% 203.81/34.67    (95)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.81/34.67    (96)  all_56_13 = all_52_15
% 203.81/34.67    (97)   ~ (all_52_3 = all_4_2)
% 203.81/34.67    (98)   ~ (all_52_19 = all_4_2)
% 203.81/34.67    (99)  op(all_6_2, e3) = all_6_1
% 203.81/34.67    (100)   ~ (all_52_13 = all_52_29)
% 203.81/34.67    (101)  all_58_4 = all_52_17
% 203.81/34.67    (102)   ~ (all_52_7 = e0)
% 203.81/34.67    (103)  op(all_52_25, all_52_25) = all_52_24
% 203.81/34.67  
% 203.81/34.67  Begin of proof
% 203.81/34.67  | 
% 203.81/34.67  | BETA: splitting (39) gives:
% 203.81/34.67  | 
% 203.81/34.67  | Case 1:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (104)  all_56_13 = e3
% 203.81/34.67  | | 
% 203.81/34.67  | | COMBINE_EQS: (96), (104) imply:
% 203.81/34.67  | |   (105)  all_52_15 = e3
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (4), (9), (10), (11), (23), (33), (58), (64), (73), (90), (99),
% 203.81/34.67  | |            (105) are inconsistent by sub-proof #1341.
% 203.81/34.67  | | 
% 203.81/34.67  | Case 2:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (106)   ~ (all_56_13 = e3)
% 203.81/34.67  | |   (107)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.81/34.67  | | 
% 203.81/34.67  | | REDUCE: (96), (106) imply:
% 203.81/34.67  | |   (108)   ~ (all_52_15 = e3)
% 203.81/34.67  | | 
% 203.81/34.67  | | BETA: splitting (84) gives:
% 203.81/34.67  | | 
% 203.81/34.67  | | Case 1:
% 203.81/34.67  | | | 
% 203.81/34.67  | | |   (109)  all_58_12 = e3
% 203.81/34.67  | | | 
% 203.81/34.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12), (14), (15),
% 203.81/34.67  | | |            (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 203.81/34.67  | | |            (27), (28), (29), (30), (33), (36), (37), (38), (40), (41),
% 203.81/34.67  | | |            (42), (43), (44), (45), (47), (48), (49), (50), (51), (52),
% 203.81/34.67  | | |            (53), (54), (55), (56), (57), (59), (60), (61), (62), (65),
% 203.81/34.67  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 203.81/34.67  | | |            (76), (77), (78), (79), (81), (82), (83), (85), (86), (87),
% 203.81/34.67  | | |            (88), (89), (90), (92), (93), (94), (95), (97), (98), (99),
% 203.81/34.67  | | |            (100), (101), (102), (103), (109) are inconsistent by sub-proof
% 203.81/34.67  | | |            #1292.
% 203.81/34.67  | | | 
% 203.81/34.67  | | Case 2:
% 203.81/34.67  | | | 
% 203.81/34.67  | | |   (110)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.81/34.67  | | | 
% 203.81/34.67  | | | REF_CLOSE: (2), (4), (8), (9), (10), (11), (13), (19), (27), (31), (32),
% 203.81/34.67  | | |            (34), (35), (36), (42), (46), (49), (63), (64), (70), (80),
% 203.81/34.67  | | |            (91), (93), (96), (102), (107), (108), (110) are inconsistent
% 203.81/34.67  | | |            by sub-proof #648.
% 203.81/34.67  | | | 
% 203.81/34.67  | | End of split
% 203.81/34.67  | | 
% 203.81/34.67  | End of split
% 203.81/34.67  | 
% 203.81/34.67  End of proof
% 203.81/34.67  
% 203.81/34.67  Sub-proof #648 shows that the following formulas are inconsistent:
% 203.81/34.67  ----------------------------------------------------------------
% 203.81/34.67    (1)  all_58_14 = all_52_23
% 203.81/34.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.81/34.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.81/34.67    (3)   ~ (e3 = e0)
% 203.81/34.67    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.67    (5)   ~ (all_52_7 = all_52_15)
% 203.81/34.67    (6)  op(all_52_15, all_52_15) = e0
% 203.81/34.67    (7)  all_16_1 = all_10_1
% 203.81/34.67    (8)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.81/34.67    (9)  all_58_13 = all_52_15
% 203.81/34.67    (10)   ~ (all_52_15 = e3)
% 203.81/34.67    (11)  op(e2, e2) = all_4_2
% 203.81/34.67    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.81/34.67    (13)  op(all_10_2, e1) = all_10_1
% 203.81/34.67    (14)  op(e0, e1) = all_52_23
% 203.81/34.67    (15)   ~ (all_52_15 = e0)
% 203.81/34.67    (16)  all_58_15 = e0
% 203.81/34.67    (17)  op(e0, e0) = e0
% 203.81/34.67    (18)  all_16_2 = all_10_2
% 203.81/34.67    (19)  all_58_12 = all_52_7
% 203.81/34.67    (20)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.81/34.67    (21)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.81/34.67    (22)  all_56_12 = all_52_7
% 203.81/34.67    (23)  op(all_4_2, all_4_2) = e2
% 203.81/34.67    (24)   ~ (all_52_15 = all_4_2)
% 203.81/34.67    (25)  op(e1, e1) = all_10_2
% 203.81/34.67    (26)   ~ (all_52_7 = all_52_23)
% 203.81/34.67    (27)  all_56_13 = all_52_15
% 203.81/34.67    (28)   ~ (all_52_7 = e0)
% 203.81/34.67  
% 203.81/34.67  Begin of proof
% 203.81/34.67  | 
% 203.81/34.67  | BETA: splitting (8) gives:
% 203.81/34.67  | 
% 203.81/34.67  | Case 1:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (29)  all_58_13 = e3
% 203.81/34.67  | | 
% 203.81/34.67  | | REF_CLOSE: (9), (10), (29) are inconsistent by sub-proof #1360.
% 203.81/34.67  | | 
% 203.81/34.67  | Case 2:
% 203.81/34.67  | | 
% 203.81/34.67  | |   (30)  all_58_14 = e3 | all_58_15 = e3
% 203.81/34.67  | | 
% 203.81/34.67  | | BETA: splitting (30) gives:
% 203.81/34.67  | | 
% 203.81/34.67  | | Case 1:
% 203.81/34.67  | | | 
% 203.81/34.67  | | |   (31)  all_58_14 = e3
% 203.81/34.67  | | | 
% 203.81/34.67  | | | COMBINE_EQS: (1), (31) imply:
% 203.81/34.67  | | |   (32)  all_52_23 = e3
% 203.81/34.67  | | | 
% 203.81/34.67  | | | SIMP: (32) implies:
% 203.81/34.67  | | |   (33)  all_52_23 = e3
% 203.81/34.67  | | | 
% 203.81/34.67  | | | REDUCE: (26), (33) imply:
% 203.81/34.67  | | |   (34)   ~ (all_52_7 = e3)
% 203.81/34.67  | | | 
% 203.81/34.67  | | | REDUCE: (14), (33) imply:
% 203.81/34.67  | | |   (35)  op(e0, e1) = e3
% 203.81/34.67  | | | 
% 203.81/34.67  | | | BETA: splitting (4) gives:
% 203.81/34.67  | | | 
% 203.81/34.67  | | | Case 1:
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | |   (36)  all_56_12 = e3
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | REF_CLOSE: (22), (34), (36) are inconsistent by sub-proof #1383.
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | Case 2:
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | |   (37)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | BETA: splitting (12) gives:
% 203.81/34.67  | | | | 
% 203.81/34.67  | | | | Case 1:
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | |   (38)  all_58_12 = e2
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | COMBINE_EQS: (19), (38) imply:
% 203.81/34.67  | | | | |   (39)  all_52_7 = e2
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | SIMP: (39) implies:
% 203.81/34.67  | | | | |   (40)  all_52_7 = e2
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | REDUCE: (5), (40) imply:
% 203.81/34.67  | | | | |   (41)   ~ (all_52_15 = e2)
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | SIMP: (41) implies:
% 203.81/34.67  | | | | |   (42)   ~ (all_52_15 = e2)
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | BETA: splitting (20) gives:
% 203.81/34.67  | | | | | 
% 203.81/34.67  | | | | | Case 1:
% 203.81/34.67  | | | | | | 
% 203.81/34.67  | | | | | |   (43)  all_56_13 = e2
% 203.81/34.67  | | | | | | 
% 203.81/34.67  | | | | | | REF_CLOSE: (27), (42), (43) are inconsistent by sub-proof #1356.
% 203.81/34.67  | | | | | | 
% 203.81/34.67  | | | | | Case 2:
% 203.81/34.67  | | | | | | 
% 203.81/34.67  | | | | | |   (44)  all_56_13 = e1 | all_56_13 = e0
% 203.81/34.67  | | | | | | 
% 203.81/34.67  | | | | | | BETA: splitting (44) gives:
% 203.81/34.67  | | | | | | 
% 203.81/34.67  | | | | | | Case 1:
% 203.81/34.67  | | | | | | | 
% 203.81/34.67  | | | | | | |   (45)  all_56_13 = e1
% 203.81/34.67  | | | | | | | 
% 203.81/34.67  | | | | | | | COMBINE_EQS: (27), (45) imply:
% 203.81/34.67  | | | | | | |   (46)  all_52_15 = e1
% 203.81/34.67  | | | | | | | 
% 203.81/34.67  | | | | | | | SIMP: (46) implies:
% 203.81/34.67  | | | | | | |   (47)  all_52_15 = e1
% 203.81/34.67  | | | | | | | 
% 203.81/34.67  | | | | | | | REDUCE: (6), (47) imply:
% 203.81/34.67  | | | | | | |   (48)  op(e1, e1) = e0
% 203.81/34.67  | | | | | | | 
% 203.86/34.67  | | | | | | | REF_CLOSE: (2), (7), (13), (18), (21), (25), (35), (48) are
% 203.86/34.67  | | | | | | |            inconsistent by sub-proof #652.
% 203.86/34.67  | | | | | | | 
% 203.86/34.67  | | | | | | Case 2:
% 203.86/34.67  | | | | | | | 
% 203.86/34.67  | | | | | | |   (49)  all_56_13 = e0
% 203.86/34.67  | | | | | | | 
% 203.86/34.67  | | | | | | | REF_CLOSE: (15), (27), (49) are inconsistent by sub-proof #1354.
% 203.86/34.67  | | | | | | | 
% 203.86/34.67  | | | | | | End of split
% 203.86/34.67  | | | | | | 
% 203.86/34.67  | | | | | End of split
% 203.86/34.67  | | | | | 
% 203.86/34.67  | | | | Case 2:
% 203.86/34.67  | | | | | 
% 203.86/34.67  | | | | |   (50)   ~ (all_58_12 = e2)
% 203.86/34.67  | | | | |   (51)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.67  | | | | | 
% 203.86/34.67  | | | | | REDUCE: (19), (50) imply:
% 203.86/34.67  | | | | |   (52)   ~ (all_52_7 = e2)
% 203.86/34.67  | | | | | 
% 203.86/34.67  | | | | | REF_CLOSE: (2), (5), (6), (9), (11), (15), (17), (20), (22), (23),
% 203.86/34.67  | | | | |            (24), (27), (28), (37), (51), (52) are inconsistent by
% 203.86/34.67  | | | | |            sub-proof #882.
% 203.86/34.67  | | | | | 
% 203.86/34.67  | | | | End of split
% 203.86/34.67  | | | | 
% 203.86/34.67  | | | End of split
% 203.86/34.67  | | | 
% 203.86/34.67  | | Case 2:
% 203.86/34.67  | | | 
% 203.86/34.67  | | |   (53)  all_58_15 = e3
% 203.86/34.67  | | | 
% 203.86/34.67  | | | REF_CLOSE: (3), (16), (53) are inconsistent by sub-proof #1350.
% 203.86/34.67  | | | 
% 203.86/34.67  | | End of split
% 203.86/34.67  | | 
% 203.86/34.67  | End of split
% 203.86/34.67  | 
% 203.86/34.67  End of proof
% 203.86/34.67  
% 203.86/34.67  Sub-proof #649 shows that the following formulas are inconsistent:
% 203.86/34.67  ----------------------------------------------------------------
% 203.86/34.67    (1)  all_58_14 = all_52_23
% 203.86/34.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.67    (3)   ~ (all_52_5 = all_52_13)
% 203.86/34.67    (4)  op(all_52_7, all_52_7) = e0
% 203.86/34.67    (5)  op(all_52_5, all_52_5) = e1
% 203.86/34.67    (6)   ~ (e3 = e0)
% 203.86/34.67    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.67    (8)  op(e0, e2) = all_52_15
% 203.86/34.67    (9)   ~ (all_52_7 = all_52_15)
% 203.86/34.67    (10)  all_16_1 = all_10_1
% 203.86/34.67    (11)  all_58_0 = all_6_2
% 203.86/34.67    (12)  all_58_13 = all_52_15
% 203.86/34.67    (13)  op(e2, e2) = all_4_2
% 203.86/34.67    (14)   ~ (all_4_1 = e3)
% 203.86/34.67    (15)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.67    (16)  op(all_10_2, e1) = all_10_1
% 203.86/34.67    (17)   ~ (all_52_7 = all_6_2)
% 203.86/34.68    (18)  op(e0, e0) = all_14_2
% 203.86/34.68    (19)  op(e0, e1) = all_52_23
% 203.86/34.68    (20)   ~ (all_52_15 = e0)
% 203.86/34.68    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.68    (22)  all_58_15 = e0
% 203.86/34.68    (23)   ~ (all_4_1 = e1)
% 203.86/34.68    (24)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.68    (25)   ~ (e2 = e1)
% 203.86/34.68    (26)  all_56_8 = all_52_5
% 203.86/34.68    (27)  op(all_52_15, all_52_15) = all_52_14
% 203.86/34.68    (28)  all_16_2 = all_10_2
% 203.86/34.68    (29)  op(all_6_2, all_6_2) = e3
% 203.86/34.68    (30)   ~ (all_52_5 = all_52_7)
% 203.86/34.68    (31)  all_58_12 = all_52_7
% 203.86/34.68    (32)   ~ (all_52_7 = all_14_2)
% 203.86/34.68    (33)  all_58_2 = all_52_3
% 203.86/34.68    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.68    (35)   ~ (e2 = e0)
% 203.86/34.68    (36)  op(all_4_2, e2) = all_4_1
% 203.86/34.68    (37)  op(all_52_3, all_52_3) = e2
% 203.86/34.68    (38)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.68    (39)  op(e1, e2) = all_52_13
% 203.86/34.68    (40)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.68    (41)   ~ (all_52_5 = all_10_2)
% 203.86/34.68    (42)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.86/34.68    (43)  all_56_12 = all_52_7
% 203.86/34.68    (44)  op(e1, all_10_1) = e2
% 203.86/34.68    (45)  op(e3, e3) = all_6_2
% 203.86/34.68    (46)  all_58_6 = all_52_5
% 203.86/34.68    (47)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.68    (48)   ~ (e3 = e2)
% 203.86/34.68    (49)  op(e1, e1) = all_10_2
% 203.86/34.68    (50)   ~ (all_52_7 = all_52_23)
% 203.86/34.68    (51)  all_56_13 = all_52_15
% 203.86/34.68    (52)   ~ (all_52_3 = all_4_2)
% 203.86/34.68    (53)   ~ (all_52_7 = e0)
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | BETA: splitting (24) gives:
% 203.86/34.68  | 
% 203.86/34.68  | Case 1:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (54)  all_56_13 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | COMBINE_EQS: (51), (54) imply:
% 203.86/34.68  | |   (55)  all_52_15 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | SIMP: (55) implies:
% 203.86/34.68  | |   (56)  all_52_15 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | COMBINE_EQS: (12), (56) imply:
% 203.86/34.68  | |   (57)  all_58_13 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (9), (56) imply:
% 203.86/34.68  | |   (58)   ~ (all_52_7 = e3)
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (27), (56) imply:
% 203.86/34.68  | |   (59)  op(e3, e3) = all_52_14
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (8), (56) imply:
% 203.86/34.68  | |   (60)  op(e0, e2) = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | GROUND_INST: instantiating (2) with all_6_2, all_52_14, e3, e3, simplifying
% 203.86/34.68  | |              with (45), (59) gives:
% 203.86/34.68  | |   (61)  all_52_14 = all_6_2
% 203.86/34.68  | | 
% 203.86/34.68  | | BETA: splitting (7) gives:
% 203.86/34.68  | | 
% 203.86/34.68  | | Case 1:
% 203.86/34.68  | | | 
% 203.86/34.68  | | |   (62)  all_56_12 = e3
% 203.86/34.68  | | | 
% 203.86/34.68  | | | REF_CLOSE: (43), (58), (62) are inconsistent by sub-proof #1383.
% 203.86/34.68  | | | 
% 203.86/34.68  | | Case 2:
% 203.86/34.68  | | | 
% 203.86/34.68  | | |   (63)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.68  | | | 
% 203.86/34.68  | | | BETA: splitting (38) gives:
% 203.86/34.68  | | | 
% 203.86/34.68  | | | Case 1:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | |   (64)  all_58_12 = e1
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | COMBINE_EQS: (31), (64) imply:
% 203.86/34.68  | | | |   (65)  all_52_7 = e1
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | SIMP: (65) implies:
% 203.86/34.68  | | | |   (66)  all_52_7 = e1
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (30), (66) imply:
% 203.86/34.68  | | | |   (67)   ~ (all_52_5 = e1)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (17), (66) imply:
% 203.86/34.68  | | | |   (68)   ~ (all_6_2 = e1)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | SIMP: (68) implies:
% 203.86/34.68  | | | |   (69)   ~ (all_6_2 = e1)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (4), (66) imply:
% 203.86/34.68  | | | |   (70)  op(e1, e1) = e0
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REF_CLOSE: (1), (2), (3), (5), (15), (16), (19), (22), (25), (26), (35),
% 203.86/34.68  | | | |            (39), (40), (41), (44), (45), (48), (49), (57), (64), (67),
% 203.86/34.68  | | | |            (69), (70) are inconsistent by sub-proof #653.
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | Case 2:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | |   (71)   ~ (all_58_12 = e1)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (31), (71) imply:
% 203.86/34.68  | | | |   (72)   ~ (all_52_7 = e1)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REF_CLOSE: (2), (4), (13), (14), (36), (43), (53), (60), (63), (72) are
% 203.86/34.68  | | | |            inconsistent by sub-proof #1373.
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | End of split
% 203.86/34.68  | | | 
% 203.86/34.68  | | End of split
% 203.86/34.68  | | 
% 203.86/34.68  | Case 2:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (73)   ~ (all_56_13 = e3)
% 203.86/34.68  | |   (74)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (51), (73) imply:
% 203.86/34.68  | |   (75)   ~ (all_52_15 = e3)
% 203.86/34.68  | | 
% 203.86/34.68  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.86/34.68  | |            (16), (17), (18), (19), (20), (21), (22), (23), (28), (29), (31),
% 203.86/34.68  | |            (32), (33), (34), (36), (37), (38), (41), (42), (43), (45), (46),
% 203.86/34.68  | |            (47), (49), (50), (51), (52), (53), (74), (75) are inconsistent
% 203.86/34.68  | |            by sub-proof #650.
% 203.86/34.68  | | 
% 203.86/34.68  | End of split
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #650 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)  all_58_14 = all_52_23
% 203.86/34.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (3)  op(all_52_7, all_52_7) = e0
% 203.86/34.68    (4)  op(all_52_5, all_52_5) = e1
% 203.86/34.68    (5)   ~ (e3 = e0)
% 203.86/34.68    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.68    (7)  op(e0, e2) = all_52_15
% 203.86/34.68    (8)   ~ (all_52_7 = all_52_15)
% 203.86/34.68    (9)  all_16_1 = all_10_1
% 203.86/34.68    (10)  all_58_0 = all_6_2
% 203.86/34.68    (11)  all_58_13 = all_52_15
% 203.86/34.68    (12)   ~ (all_52_15 = e3)
% 203.86/34.68    (13)  op(e2, e2) = all_4_2
% 203.86/34.68    (14)  op(all_10_2, e1) = all_10_1
% 203.86/34.68    (15)   ~ (all_52_7 = all_6_2)
% 203.86/34.68    (16)  op(e0, e0) = all_14_2
% 203.86/34.68    (17)  op(e0, e1) = all_52_23
% 203.86/34.68    (18)   ~ (all_52_15 = e0)
% 203.86/34.68    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.68    (20)  all_58_15 = e0
% 203.86/34.68    (21)   ~ (all_4_1 = e1)
% 203.86/34.68    (22)  all_16_2 = all_10_2
% 203.86/34.68    (23)  op(all_6_2, all_6_2) = e3
% 203.86/34.68    (24)  all_58_12 = all_52_7
% 203.86/34.68    (25)   ~ (all_52_7 = all_14_2)
% 203.86/34.68    (26)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.68    (27)  all_58_2 = all_52_3
% 203.86/34.68    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.68    (29)  op(all_4_2, e2) = all_4_1
% 203.86/34.68    (30)  op(all_52_3, all_52_3) = e2
% 203.86/34.68    (31)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.68    (32)   ~ (all_52_5 = all_10_2)
% 203.86/34.68    (33)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.86/34.68    (34)  all_56_12 = all_52_7
% 203.86/34.68    (35)  op(e3, e3) = all_6_2
% 203.86/34.68    (36)  all_58_6 = all_52_5
% 203.86/34.68    (37)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.68    (38)  op(e1, e1) = all_10_2
% 203.86/34.68    (39)   ~ (all_52_7 = all_52_23)
% 203.86/34.68    (40)  all_56_13 = all_52_15
% 203.86/34.68    (41)   ~ (all_52_3 = all_4_2)
% 203.86/34.68    (42)   ~ (all_52_7 = e0)
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | BETA: splitting (37) gives:
% 203.86/34.68  | 
% 203.86/34.68  | Case 1:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (43)  all_58_12 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | COMBINE_EQS: (24), (43) imply:
% 203.86/34.68  | |   (44)  all_52_7 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | REF_CLOSE: (2), (3), (4), (10), (13), (15), (16), (19), (23), (24), (25),
% 203.86/34.68  | |            (27), (28), (30), (32), (35), (36), (37), (38), (41), (44) are
% 203.86/34.68  | |            inconsistent by sub-proof #1361.
% 203.86/34.68  | | 
% 203.86/34.68  | Case 2:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (45)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | BETA: splitting (45) gives:
% 203.86/34.68  | | 
% 203.86/34.68  | | Case 1:
% 203.86/34.68  | | | 
% 203.86/34.68  | | |   (46)  all_58_13 = e3
% 203.86/34.68  | | | 
% 203.86/34.68  | | | REF_CLOSE: (11), (12), (46) are inconsistent by sub-proof #1360.
% 203.86/34.68  | | | 
% 203.86/34.68  | | Case 2:
% 203.86/34.68  | | | 
% 203.86/34.68  | | |   (47)  all_58_14 = e3 | all_58_15 = e3
% 203.86/34.68  | | | 
% 203.86/34.68  | | | BETA: splitting (47) gives:
% 203.86/34.68  | | | 
% 203.86/34.68  | | | Case 1:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | |   (48)  all_58_14 = e3
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | COMBINE_EQS: (1), (48) imply:
% 203.86/34.68  | | | |   (49)  all_52_23 = e3
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | SIMP: (49) implies:
% 203.86/34.68  | | | |   (50)  all_52_23 = e3
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (39), (50) imply:
% 203.86/34.68  | | | |   (51)   ~ (all_52_7 = e3)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (17), (50) imply:
% 203.86/34.68  | | | |   (52)  op(e0, e1) = e3
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | BETA: splitting (6) gives:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | Case 1:
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | |   (53)  all_56_12 = e3
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | | REF_CLOSE: (34), (51), (53) are inconsistent by sub-proof #1383.
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | Case 2:
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | |   (54)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | | BETA: splitting (31) gives:
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | | Case 1:
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | |   (55)  all_58_12 = e1
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | | REF_CLOSE: (2), (3), (9), (14), (22), (24), (33), (38), (52), (55)
% 203.86/34.68  | | | | | |            are inconsistent by sub-proof #651.
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | Case 2:
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | |   (56)   ~ (all_58_12 = e1)
% 203.86/34.68  | | | | | |   (57)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | | REDUCE: (24), (56) imply:
% 203.86/34.68  | | | | | |   (58)   ~ (all_52_7 = e1)
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | | REF_CLOSE: (2), (3), (7), (8), (11), (13), (18), (21), (26), (29),
% 203.86/34.68  | | | | | |            (34), (40), (42), (54), (57), (58) are inconsistent by
% 203.86/34.68  | | | | | |            sub-proof #1351.
% 203.86/34.68  | | | | | | 
% 203.86/34.68  | | | | | End of split
% 203.86/34.68  | | | | | 
% 203.86/34.68  | | | | End of split
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | Case 2:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | |   (59)  all_58_15 = e3
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REF_CLOSE: (5), (20), (59) are inconsistent by sub-proof #1350.
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | End of split
% 203.86/34.68  | | | 
% 203.86/34.68  | | End of split
% 203.86/34.68  | | 
% 203.86/34.68  | End of split
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #651 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (2)  op(all_52_7, all_52_7) = e0
% 203.86/34.68    (3)  all_16_1 = all_10_1
% 203.86/34.68    (4)  op(all_10_2, e1) = all_10_1
% 203.86/34.68    (5)  all_16_2 = all_10_2
% 203.86/34.68    (6)  all_58_12 = all_52_7
% 203.86/34.68    (7)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.86/34.68    (8)  op(e1, e1) = all_10_2
% 203.86/34.68    (9)  all_58_12 = e1
% 203.86/34.68    (10)  op(e0, e1) = e3
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | COMBINE_EQS: (6), (9) imply:
% 203.86/34.68  |   (11)  all_52_7 = e1
% 203.86/34.68  | 
% 203.86/34.68  | SIMP: (11) implies:
% 203.86/34.68  |   (12)  all_52_7 = e1
% 203.86/34.68  | 
% 203.86/34.68  | REDUCE: (2), (12) imply:
% 203.86/34.68  |   (13)  op(e1, e1) = e0
% 203.86/34.68  | 
% 203.86/34.68  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (13) are inconsistent by
% 203.86/34.68  |            sub-proof #652.
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #652 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (2)  all_16_1 = all_10_1
% 203.86/34.68    (3)  op(all_10_2, e1) = all_10_1
% 203.86/34.68    (4)  op(e1, e1) = e0
% 203.86/34.68    (5)  all_16_2 = all_10_2
% 203.86/34.68    (6)   ~ (all_16_1 = e3) |  ~ (all_16_2 = e0)
% 203.86/34.68    (7)  op(e1, e1) = all_10_2
% 203.86/34.68    (8)  op(e0, e1) = e3
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 203.86/34.68  |              (4), (7) gives:
% 203.86/34.68  |   (9)  all_10_2 = e0
% 203.86/34.68  | 
% 203.86/34.68  | COMBINE_EQS: (5), (9) imply:
% 203.86/34.68  |   (10)  all_16_2 = e0
% 203.86/34.68  | 
% 203.86/34.68  | BETA: splitting (6) gives:
% 203.86/34.68  | 
% 203.86/34.68  | Case 1:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (11)   ~ (all_16_1 = e3)
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (2), (11) imply:
% 203.86/34.68  | |   (12)   ~ (all_10_1 = e3)
% 203.86/34.68  | | 
% 203.86/34.68  | | REF_CLOSE: (1), (3), (4), (7), (8), (12) are inconsistent by sub-proof
% 203.86/34.68  | |            #1359.
% 203.86/34.68  | | 
% 203.86/34.68  | Case 2:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (13)   ~ (all_16_2 = e0)
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (10), (13) imply:
% 203.86/34.68  | |   (14)  $false
% 203.86/34.68  | | 
% 203.86/34.68  | | CLOSE: (14) is inconsistent.
% 203.86/34.68  | | 
% 203.86/34.68  | End of split
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #653 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)  all_58_14 = all_52_23
% 203.86/34.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (3)   ~ (all_52_5 = all_52_13)
% 203.86/34.68    (4)  op(all_52_5, all_52_5) = e1
% 203.86/34.68    (5)  all_58_13 = e3
% 203.86/34.68    (6)   ~ (all_52_5 = e1)
% 203.86/34.68    (7)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.68    (8)  op(all_10_2, e1) = all_10_1
% 203.86/34.68    (9)  op(e0, e1) = all_52_23
% 203.86/34.68    (10)  op(e1, e1) = e0
% 203.86/34.68    (11)  all_58_15 = e0
% 203.86/34.68    (12)   ~ (e2 = e1)
% 203.86/34.68    (13)  all_56_8 = all_52_5
% 203.86/34.68    (14)   ~ (e2 = e0)
% 203.86/34.68    (15)  op(e1, e2) = all_52_13
% 203.86/34.68    (16)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.68    (17)   ~ (all_52_5 = all_10_2)
% 203.86/34.68    (18)  op(e1, all_10_1) = e2
% 203.86/34.68    (19)  op(e3, e3) = all_6_2
% 203.86/34.68    (20)   ~ (e3 = e2)
% 203.86/34.68    (21)   ~ (all_6_2 = e1)
% 203.86/34.68    (22)  op(e1, e1) = all_10_2
% 203.86/34.68    (23)  all_58_12 = e1
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | BETA: splitting (7) gives:
% 203.86/34.68  | 
% 203.86/34.68  | Case 1:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (24)  all_58_12 = e2
% 203.86/34.68  | | 
% 203.86/34.68  | | COMBINE_EQS: (23), (24) imply:
% 203.86/34.68  | |   (25)  e2 = e1
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (12), (25) imply:
% 203.86/34.68  | |   (26)  $false
% 203.86/34.68  | | 
% 203.86/34.68  | | CLOSE: (26) is inconsistent.
% 203.86/34.68  | | 
% 203.86/34.68  | Case 2:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (27)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.68  | | 
% 203.86/34.68  | | BETA: splitting (27) gives:
% 203.86/34.68  | | 
% 203.86/34.68  | | Case 1:
% 203.86/34.68  | | | 
% 203.86/34.68  | | |   (28)  all_58_13 = e2
% 203.86/34.68  | | | 
% 203.86/34.68  | | | REF_CLOSE: (5), (20), (28) are inconsistent by sub-proof #1248.
% 203.86/34.68  | | | 
% 203.86/34.68  | | Case 2:
% 203.86/34.68  | | | 
% 203.86/34.68  | | |   (29)  all_58_14 = e2 | all_58_15 = e2
% 203.86/34.68  | | | 
% 203.86/34.68  | | | BETA: splitting (29) gives:
% 203.86/34.68  | | | 
% 203.86/34.68  | | | Case 1:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | |   (30)  all_58_14 = e2
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | COMBINE_EQS: (1), (30) imply:
% 203.86/34.68  | | | |   (31)  all_52_23 = e2
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | SIMP: (31) implies:
% 203.86/34.68  | | | |   (32)  all_52_23 = e2
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (9), (32) imply:
% 203.86/34.68  | | | |   (33)  op(e0, e1) = e2
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | GROUND_INST: instantiating (2) with all_10_2, e0, e1, e1, simplifying
% 203.86/34.68  | | | |              with (10), (22) gives:
% 203.86/34.68  | | | |   (34)  all_10_2 = e0
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (17), (34) imply:
% 203.86/34.68  | | | |   (35)   ~ (all_52_5 = e0)
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REDUCE: (8), (34) imply:
% 203.86/34.68  | | | |   (36)  op(e0, e1) = all_10_1
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REF_CLOSE: (2), (3), (4), (6), (13), (15), (16), (18), (19), (21), (33),
% 203.86/34.68  | | | |            (35), (36) are inconsistent by sub-proof #654.
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | Case 2:
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | |   (37)  all_58_15 = e2
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | | REF_CLOSE: (11), (14), (37) are inconsistent by sub-proof #1223.
% 203.86/34.68  | | | | 
% 203.86/34.68  | | | End of split
% 203.86/34.68  | | | 
% 203.86/34.68  | | End of split
% 203.86/34.68  | | 
% 203.86/34.68  | End of split
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #654 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)  op(e0, e1) = e2
% 203.86/34.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (3)   ~ (all_52_5 = all_52_13)
% 203.86/34.68    (4)  op(all_52_5, all_52_5) = e1
% 203.86/34.68    (5)   ~ (all_52_5 = e1)
% 203.86/34.68    (6)  all_56_8 = all_52_5
% 203.86/34.68    (7)  op(e1, e2) = all_52_13
% 203.86/34.68    (8)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.68    (9)  op(e1, all_10_1) = e2
% 203.86/34.68    (10)   ~ (all_52_5 = e0)
% 203.86/34.68    (11)  op(e3, e3) = all_6_2
% 203.86/34.68    (12)   ~ (all_6_2 = e1)
% 203.86/34.68    (13)  op(e0, e1) = all_10_1
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | GROUND_INST: instantiating (2) with e2, all_10_1, e1, e0, simplifying with
% 203.86/34.68  |              (1), (13) gives:
% 203.86/34.68  |   (14)  all_10_1 = e2
% 203.86/34.68  | 
% 203.86/34.68  | REDUCE: (9), (14) imply:
% 203.86/34.68  |   (15)  op(e1, e2) = e2
% 203.86/34.68  | 
% 203.86/34.68  | GROUND_INST: instantiating (2) with all_52_13, e2, e2, e1, simplifying with
% 203.86/34.68  |              (7), (15) gives:
% 203.86/34.68  |   (16)  all_52_13 = e2
% 203.86/34.68  | 
% 203.86/34.68  | REDUCE: (3), (16) imply:
% 203.86/34.68  |   (17)   ~ (all_52_5 = e2)
% 203.86/34.68  | 
% 203.86/34.68  | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (17) are inconsistent by
% 203.86/34.68  |            sub-proof #655.
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #655 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (2)  op(all_52_5, all_52_5) = e1
% 203.86/34.68    (3)   ~ (all_52_5 = e1)
% 203.86/34.68    (4)  all_56_8 = all_52_5
% 203.86/34.68    (5)   ~ (all_52_5 = e2)
% 203.86/34.68    (6)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.68    (7)   ~ (all_52_5 = e0)
% 203.86/34.68    (8)  op(e3, e3) = all_6_2
% 203.86/34.68    (9)   ~ (all_6_2 = e1)
% 203.86/34.68  
% 203.86/34.68  Begin of proof
% 203.86/34.68  | 
% 203.86/34.68  | BETA: splitting (6) gives:
% 203.86/34.68  | 
% 203.86/34.68  | Case 1:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (10)  all_56_8 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | COMBINE_EQS: (4), (10) imply:
% 203.86/34.68  | |   (11)  all_52_5 = e3
% 203.86/34.68  | | 
% 203.86/34.68  | | REDUCE: (2), (11) imply:
% 203.86/34.68  | |   (12)  op(e3, e3) = e1
% 203.86/34.68  | | 
% 203.86/34.68  | | REF_CLOSE: (1), (8), (9), (12) are inconsistent by sub-proof #885.
% 203.86/34.68  | | 
% 203.86/34.68  | Case 2:
% 203.86/34.68  | | 
% 203.86/34.68  | |   (13)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.68  | | 
% 203.86/34.68  | | REF_CLOSE: (3), (4), (5), (7), (13) are inconsistent by sub-proof #1004.
% 203.86/34.68  | | 
% 203.86/34.68  | End of split
% 203.86/34.68  | 
% 203.86/34.68  End of proof
% 203.86/34.68  
% 203.86/34.68  Sub-proof #656 shows that the following formulas are inconsistent:
% 203.86/34.68  ----------------------------------------------------------------
% 203.86/34.68    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.68    (2)   ~ (all_52_15 = all_52_23)
% 203.86/34.68    (3)   ~ (all_52_25 = all_52_27)
% 203.86/34.68    (4)  all_58_14 = all_52_23
% 203.86/34.68    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.86/34.68    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.68    (7)   ~ (all_52_5 = all_52_13)
% 203.86/34.68    (8)  op(all_52_7, all_52_7) = e0
% 203.86/34.68    (9)  all_58_1 = all_52_9
% 203.86/34.68    (10)   ~ (all_52_9 = all_52_13)
% 203.86/34.68    (11)  op(all_52_5, all_52_5) = e1
% 203.86/34.68    (12)   ~ (e3 = e0)
% 203.86/34.68    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.68    (14)   ~ (all_52_7 = all_52_15)
% 203.86/34.68    (15)   ~ (all_52_3 = all_52_19)
% 203.86/34.68    (16)   ~ (all_52_17 = all_52_25)
% 203.86/34.68    (17)   ~ (all_52_3 = all_6_2)
% 203.86/34.68    (18)  all_58_0 = all_6_2
% 203.86/34.68    (19)  op(all_14_2, e0) = all_14_1
% 203.86/34.68    (20)  all_56_4 = all_52_3
% 203.86/34.68    (21)   ~ (all_52_17 = all_10_2)
% 203.86/34.68    (22)  op(e0, all_14_1) = all_14_0
% 203.86/34.68    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.86/34.68    (24)  all_58_13 = all_52_15
% 203.86/34.68    (25)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.68    (26)  all_58_9 = all_52_25
% 203.86/34.68    (27)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.86/34.68    (28)   ~ (all_52_29 = all_14_2)
% 203.86/34.68    (29)  op(e2, all_4_1) = e3
% 203.86/34.68    (30)  op(e2, e2) = all_4_2
% 203.86/34.68    (31)  all_58_11 = all_52_29
% 203.86/34.68    (32)   ~ (all_52_25 = all_14_2)
% 203.86/34.68    (33)   ~ (all_52_9 = all_52_15)
% 203.86/34.68    (34)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.68    (35)   ~ (all_52_3 = all_52_27)
% 203.86/34.68    (36)  op(all_10_2, e1) = all_10_1
% 203.86/34.68    (37)   ~ (all_52_7 = all_6_2)
% 203.86/34.68    (38)  op(e0, e0) = all_14_2
% 203.86/34.68    (39)  op(e0, e1) = all_52_23
% 203.86/34.68    (40)  all_56_15 = all_14_2
% 203.86/34.68    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.68    (42)  op(e1, e0) = all_52_29
% 203.86/34.68    (43)   ~ (all_4_1 = e1)
% 203.86/34.68    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.68    (45)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.68    (46)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.86/34.68    (47)  all_56_9 = all_52_13
% 203.86/34.68    (48)   ~ (e2 = e1)
% 203.86/34.68    (49)   ~ (all_52_13 = all_10_2)
% 203.86/34.68    (50)   ~ (all_6_0 = e1)
% 203.86/34.68    (51)  all_58_10 = all_52_27
% 203.86/34.68    (52)  all_56_8 = all_52_5
% 203.86/34.68    (53)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.68    (54)  op(all_52_15, all_52_15) = all_52_14
% 203.86/34.68    (55)  all_58_7 = all_52_13
% 203.86/34.68    (56)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.68    (57)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.68    (58)  op(all_6_2, all_6_2) = e3
% 203.86/34.68    (59)  all_58_12 = all_52_7
% 203.86/34.68    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.68    (61)   ~ (all_52_7 = all_14_2)
% 203.86/34.68    (62)   ~ (all_14_2 = e0)
% 203.86/34.68    (63)  all_58_2 = all_52_3
% 203.86/34.68    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.68    (65)  all_56_2 = all_52_17
% 203.86/34.68    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.68    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.68    (68)  op(e3, all_6_1) = all_6_0
% 203.86/34.68    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.68    (70)  all_56_7 = all_52_27
% 203.86/34.69    (71)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.69    (72)   ~ (e2 = e0)
% 203.86/34.69    (73)  op(all_4_2, e2) = all_4_1
% 203.86/34.69    (74)  op(all_52_3, all_52_3) = e2
% 203.86/34.69    (75)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.69    (76)  all_56_6 = all_52_19
% 203.86/34.69    (77)   ~ (all_52_15 = all_14_2)
% 203.86/34.69    (78)   ~ (all_52_19 = all_52_27)
% 203.86/34.69    (79)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.86/34.69    (80)   ~ (all_52_13 = all_4_2)
% 203.86/34.69    (81)  op(e0, e3) = all_52_7
% 203.86/34.69    (82)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.69    (83)   ~ (all_52_9 = all_52_25)
% 203.86/34.69    (84)  all_58_15 = all_14_2
% 203.86/34.69    (85)   ~ (all_52_19 = all_10_2)
% 203.86/34.69    (86)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.69    (87)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.69    (88)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.69    (89)  all_58_8 = all_10_2
% 203.86/34.69    (90)   ~ (all_52_5 = all_10_2)
% 203.86/34.69    (91)   ~ (all_52_23 = all_14_2)
% 203.86/34.69    (92)  all_56_12 = all_52_7
% 203.86/34.69    (93)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.69    (94)   ~ (all_52_25 = all_6_2)
% 203.86/34.69    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.69    (96)   ~ (all_52_9 = all_4_2)
% 203.86/34.69    (97)   ~ (all_52_5 = all_6_2)
% 203.86/34.69    (98)   ~ (all_52_9 = all_6_2)
% 203.86/34.69    (99)  op(e3, e3) = all_6_2
% 203.86/34.69    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.69    (101)   ~ (all_52_27 = all_14_2)
% 203.86/34.69    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.69    (103)  all_56_14 = all_52_23
% 203.86/34.69    (104)  all_56_3 = all_52_25
% 203.86/34.69    (105)   ~ (all_52_3 = all_52_7)
% 203.86/34.69    (106)   ~ (all_10_1 = e3)
% 203.86/34.69    (107)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.69    (108)  all_58_5 = all_52_19
% 203.86/34.69    (109)  all_56_1 = all_52_9
% 203.86/34.69    (110)   ~ (all_52_27 = all_4_2)
% 203.86/34.69    (111)  all_58_6 = all_52_5
% 203.86/34.69    (112)  op(e3, e2) = all_52_9
% 203.86/34.69    (113)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.69    (114)   ~ (all_52_17 = all_6_2)
% 203.86/34.69    (115)   ~ (e1 = e0)
% 203.86/34.69    (116)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.69    (117)   ~ (all_52_9 = all_52_17)
% 203.86/34.69    (118)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.69    (119)  op(e1, e1) = all_10_2
% 203.86/34.69    (120)   ~ (all_52_23 = all_10_2)
% 203.86/34.69    (121)   ~ (all_52_7 = all_52_23)
% 203.86/34.69    (122)  all_58_3 = all_4_2
% 203.86/34.69    (123)  all_56_13 = all_52_15
% 203.86/34.69    (124)   ~ (all_52_3 = all_4_2)
% 203.86/34.69    (125)   ~ (all_52_19 = all_4_2)
% 203.86/34.69    (126)   ~ (all_52_17 = all_52_23)
% 203.86/34.69    (127)  op(all_6_2, e3) = all_6_1
% 203.86/34.69    (128)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.86/34.69    (129)   ~ (all_52_13 = all_52_29)
% 203.86/34.69    (130)  all_58_4 = all_52_17
% 203.86/34.69    (131)   ~ (all_14_0 = e2)
% 203.86/34.69    (132)   ~ (all_14_2 = e3)
% 203.86/34.69  
% 203.86/34.69  Begin of proof
% 203.86/34.69  | 
% 203.86/34.69  | BETA: splitting (44) gives:
% 203.86/34.69  | 
% 203.86/34.69  | Case 1:
% 203.86/34.69  | | 
% 203.86/34.69  | |   (133)  all_56_13 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | COMBINE_EQS: (123), (133) imply:
% 203.86/34.69  | |   (134)  all_52_15 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (12), (13), (14), (15),
% 203.86/34.69  | |            (17), (18), (19), (20), (22), (23), (24), (26), (30), (31), (32),
% 203.86/34.69  | |            (33), (34), (35), (37), (38), (40), (41), (42), (46), (53), (54),
% 203.86/34.69  | |            (56), (58), (59), (61), (62), (63), (64), (67), (70), (71), (72),
% 203.86/34.69  | |            (74), (75), (76), (77), (78), (79), (81), (83), (84), (85), (88),
% 203.86/34.69  | |            (90), (92), (94), (95), (96), (99), (100), (102), (103), (104),
% 203.86/34.69  | |            (105), (107), (108), (109), (110), (111), (113), (115), (116),
% 203.86/34.69  | |            (119), (120), (121), (122), (124), (125), (128), (131), (134) are
% 203.86/34.69  | |            inconsistent by sub-proof #661.
% 203.86/34.69  | | 
% 203.86/34.69  | Case 2:
% 203.86/34.69  | | 
% 203.86/34.69  | |   (135)   ~ (all_56_13 = e3)
% 203.86/34.69  | | 
% 203.86/34.69  | | REDUCE: (123), (135) imply:
% 203.86/34.69  | |   (136)   ~ (all_52_15 = e3)
% 203.86/34.69  | | 
% 203.86/34.69  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.86/34.69  | |            (15), (16), (18), (20), (21), (24), (25), (26), (27), (28), (29),
% 203.86/34.69  | |            (30), (31), (32), (34), (35), (36), (37), (38), (39), (40), (41),
% 203.86/34.69  | |            (43), (45), (47), (48), (49), (50), (51), (52), (53), (55), (57),
% 203.86/34.69  | |            (58), (59), (60), (61), (63), (65), (66), (67), (68), (69), (71),
% 203.86/34.69  | |            (72), (73), (74), (75), (80), (82), (83), (84), (85), (86), (87),
% 203.86/34.69  | |            (88), (89), (90), (91), (92), (93), (94), (96), (97), (98), (99),
% 203.86/34.69  | |            (100), (101), (102), (105), (106), (107), (108), (109), (110),
% 203.86/34.69  | |            (111), (112), (113), (114), (116), (117), (118), (119), (120),
% 203.86/34.69  | |            (121), (122), (124), (126), (127), (128), (129), (130), (132),
% 203.86/34.69  | |            (136) are inconsistent by sub-proof #657.
% 203.86/34.69  | | 
% 203.86/34.69  | End of split
% 203.86/34.69  | 
% 203.86/34.69  End of proof
% 203.86/34.69  
% 203.86/34.69  Sub-proof #657 shows that the following formulas are inconsistent:
% 203.86/34.69  ----------------------------------------------------------------
% 203.86/34.69    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.69    (2)   ~ (all_52_15 = all_52_23)
% 203.86/34.69    (3)  all_58_14 = all_52_23
% 203.86/34.69    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.86/34.69    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.69    (6)   ~ (all_52_5 = all_52_13)
% 203.86/34.69    (7)  op(all_52_7, all_52_7) = e0
% 203.86/34.69    (8)  all_58_1 = all_52_9
% 203.86/34.69    (9)   ~ (all_52_9 = all_52_13)
% 203.86/34.69    (10)  op(all_52_5, all_52_5) = e1
% 203.86/34.69    (11)   ~ (e3 = e0)
% 203.86/34.69    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.69    (13)   ~ (all_52_3 = all_52_19)
% 203.86/34.69    (14)   ~ (all_52_17 = all_52_25)
% 203.86/34.69    (15)  all_58_0 = all_6_2
% 203.86/34.69    (16)  all_56_4 = all_52_3
% 203.86/34.69    (17)   ~ (all_52_17 = all_10_2)
% 203.86/34.69    (18)  all_58_13 = all_52_15
% 203.86/34.69    (19)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.69    (20)  all_58_9 = all_52_25
% 203.86/34.69    (21)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.86/34.69    (22)   ~ (all_52_29 = all_14_2)
% 203.86/34.69    (23)   ~ (all_52_15 = e3)
% 203.86/34.69    (24)  op(e2, all_4_1) = e3
% 203.86/34.69    (25)  op(e2, e2) = all_4_2
% 203.86/34.69    (26)  all_58_11 = all_52_29
% 203.86/34.69    (27)   ~ (all_52_25 = all_14_2)
% 203.86/34.69    (28)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.69    (29)   ~ (all_52_3 = all_52_27)
% 203.86/34.69    (30)  op(all_10_2, e1) = all_10_1
% 203.86/34.69    (31)   ~ (all_52_7 = all_6_2)
% 203.86/34.69    (32)  op(e0, e0) = all_14_2
% 203.86/34.69    (33)  op(e0, e1) = all_52_23
% 203.86/34.69    (34)  all_56_15 = all_14_2
% 203.86/34.69    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.69    (36)   ~ (all_4_1 = e1)
% 203.86/34.69    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.69    (38)  all_56_9 = all_52_13
% 203.86/34.69    (39)   ~ (e2 = e1)
% 203.86/34.69    (40)   ~ (all_52_13 = all_10_2)
% 203.86/34.69    (41)   ~ (all_6_0 = e1)
% 203.86/34.69    (42)  all_58_10 = all_52_27
% 203.86/34.69    (43)  all_56_8 = all_52_5
% 203.86/34.69    (44)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.69    (45)  all_58_7 = all_52_13
% 203.86/34.69    (46)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.69    (47)  op(all_6_2, all_6_2) = e3
% 203.86/34.69    (48)  all_58_12 = all_52_7
% 203.86/34.69    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.69    (50)   ~ (all_52_7 = all_14_2)
% 203.86/34.69    (51)  all_58_2 = all_52_3
% 203.86/34.69    (52)  all_56_2 = all_52_17
% 203.86/34.69    (53)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.69    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.69    (55)  op(e3, all_6_1) = all_6_0
% 203.86/34.69    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.69    (57)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.69    (58)   ~ (e2 = e0)
% 203.86/34.69    (59)  op(all_4_2, e2) = all_4_1
% 203.86/34.69    (60)  op(all_52_3, all_52_3) = e2
% 203.86/34.69    (61)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.69    (62)   ~ (all_52_13 = all_4_2)
% 203.86/34.69    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.69    (64)   ~ (all_52_9 = all_52_25)
% 203.86/34.69    (65)  all_58_15 = all_14_2
% 203.86/34.69    (66)   ~ (all_52_19 = all_10_2)
% 203.86/34.69    (67)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.69    (68)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.69    (69)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.69    (70)  all_58_8 = all_10_2
% 203.86/34.69    (71)   ~ (all_52_5 = all_10_2)
% 203.86/34.69    (72)   ~ (all_52_23 = all_14_2)
% 203.86/34.69    (73)  all_56_12 = all_52_7
% 203.86/34.69    (74)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.69    (75)   ~ (all_52_25 = all_6_2)
% 203.86/34.69    (76)   ~ (all_52_9 = all_4_2)
% 203.86/34.69    (77)   ~ (all_52_5 = all_6_2)
% 203.86/34.69    (78)   ~ (all_52_9 = all_6_2)
% 203.86/34.69    (79)  op(e3, e3) = all_6_2
% 203.86/34.69    (80)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.69    (81)   ~ (all_52_27 = all_14_2)
% 203.86/34.69    (82)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.69    (83)   ~ (all_52_3 = all_52_7)
% 203.86/34.69    (84)   ~ (all_10_1 = e3)
% 203.86/34.69    (85)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.69    (86)  all_58_5 = all_52_19
% 203.86/34.69    (87)  all_56_1 = all_52_9
% 203.86/34.69    (88)   ~ (all_52_27 = all_4_2)
% 203.86/34.69    (89)  all_58_6 = all_52_5
% 203.86/34.69    (90)  op(e3, e2) = all_52_9
% 203.86/34.69    (91)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.69    (92)   ~ (all_52_17 = all_6_2)
% 203.86/34.69    (93)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.69    (94)   ~ (all_52_9 = all_52_17)
% 203.86/34.69    (95)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.69    (96)  op(e1, e1) = all_10_2
% 203.86/34.69    (97)   ~ (all_52_23 = all_10_2)
% 203.86/34.69    (98)   ~ (all_52_7 = all_52_23)
% 203.86/34.69    (99)  all_58_3 = all_4_2
% 203.86/34.69    (100)   ~ (all_52_3 = all_4_2)
% 203.86/34.69    (101)   ~ (all_52_17 = all_52_23)
% 203.86/34.69    (102)  op(all_6_2, e3) = all_6_1
% 203.86/34.69    (103)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.86/34.69    (104)   ~ (all_52_13 = all_52_29)
% 203.86/34.69    (105)  all_58_4 = all_52_17
% 203.86/34.69    (106)   ~ (all_14_2 = e3)
% 203.86/34.69  
% 203.86/34.69  Begin of proof
% 203.86/34.69  | 
% 203.86/34.69  | BETA: splitting (91) gives:
% 203.86/34.69  | 
% 203.86/34.69  | Case 1:
% 203.86/34.69  | | 
% 203.86/34.69  | |   (107)  all_58_12 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | COMBINE_EQS: (48), (107) imply:
% 203.86/34.69  | |   (108)  all_52_7 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | REF_CLOSE: (5), (7), (10), (15), (25), (31), (32), (35), (47), (48), (50),
% 203.86/34.69  | |            (51), (54), (60), (71), (79), (89), (91), (96), (100), (108) are
% 203.86/34.69  | |            inconsistent by sub-proof #1361.
% 203.86/34.69  | | 
% 203.86/34.69  | Case 2:
% 203.86/34.69  | | 
% 203.86/34.69  | |   (109)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.86/34.69  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.86/34.69  | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 203.86/34.69  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 203.86/34.69  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.86/34.69  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.86/34.69  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.86/34.69  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 203.86/34.69  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.86/34.69  | |            (102), (103), (104), (105), (106), (109) are inconsistent by
% 203.86/34.69  | |            sub-proof #658.
% 203.86/34.69  | | 
% 203.86/34.69  | End of split
% 203.86/34.69  | 
% 203.86/34.69  End of proof
% 203.86/34.69  
% 203.86/34.69  Sub-proof #658 shows that the following formulas are inconsistent:
% 203.86/34.69  ----------------------------------------------------------------
% 203.86/34.69    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.69    (2)   ~ (all_52_15 = all_52_23)
% 203.86/34.69    (3)  all_58_14 = all_52_23
% 203.86/34.69    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.86/34.69    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.69    (6)   ~ (all_52_5 = all_52_13)
% 203.86/34.69    (7)  op(all_52_7, all_52_7) = e0
% 203.86/34.69    (8)  all_58_1 = all_52_9
% 203.86/34.69    (9)   ~ (all_52_9 = all_52_13)
% 203.86/34.69    (10)  op(all_52_5, all_52_5) = e1
% 203.86/34.69    (11)   ~ (e3 = e0)
% 203.86/34.69    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.69    (13)   ~ (all_52_3 = all_52_19)
% 203.86/34.69    (14)   ~ (all_52_17 = all_52_25)
% 203.86/34.69    (15)  all_58_0 = all_6_2
% 203.86/34.69    (16)  all_56_4 = all_52_3
% 203.86/34.69    (17)   ~ (all_52_17 = all_10_2)
% 203.86/34.69    (18)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.69    (19)  all_58_13 = all_52_15
% 203.86/34.69    (20)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.69    (21)  all_58_9 = all_52_25
% 203.86/34.69    (22)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.86/34.69    (23)   ~ (all_52_29 = all_14_2)
% 203.86/34.69    (24)   ~ (all_52_15 = e3)
% 203.86/34.69    (25)  op(e2, all_4_1) = e3
% 203.86/34.69    (26)  op(e2, e2) = all_4_2
% 203.86/34.69    (27)  all_58_11 = all_52_29
% 203.86/34.69    (28)   ~ (all_52_25 = all_14_2)
% 203.86/34.69    (29)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.69    (30)   ~ (all_52_3 = all_52_27)
% 203.86/34.69    (31)  op(all_10_2, e1) = all_10_1
% 203.86/34.69    (32)  op(e0, e0) = all_14_2
% 203.86/34.69    (33)  op(e0, e1) = all_52_23
% 203.86/34.69    (34)  all_56_15 = all_14_2
% 203.86/34.69    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.69    (36)   ~ (all_4_1 = e1)
% 203.86/34.69    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.69    (38)  all_56_9 = all_52_13
% 203.86/34.69    (39)   ~ (e2 = e1)
% 203.86/34.69    (40)   ~ (all_52_13 = all_10_2)
% 203.86/34.69    (41)   ~ (all_6_0 = e1)
% 203.86/34.69    (42)  all_58_10 = all_52_27
% 203.86/34.69    (43)  all_56_8 = all_52_5
% 203.86/34.69    (44)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.69    (45)  all_58_7 = all_52_13
% 203.86/34.69    (46)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.69    (47)  op(all_6_2, all_6_2) = e3
% 203.86/34.69    (48)  all_58_12 = all_52_7
% 203.86/34.69    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.69    (50)   ~ (all_52_7 = all_14_2)
% 203.86/34.69    (51)  all_58_2 = all_52_3
% 203.86/34.69    (52)  all_56_2 = all_52_17
% 203.86/34.69    (53)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.69    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.69    (55)  op(e3, all_6_1) = all_6_0
% 203.86/34.69    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.69    (57)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.69    (58)   ~ (e2 = e0)
% 203.86/34.69    (59)  op(all_4_2, e2) = all_4_1
% 203.86/34.69    (60)  op(all_52_3, all_52_3) = e2
% 203.86/34.69    (61)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.69    (62)   ~ (all_52_13 = all_4_2)
% 203.86/34.69    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.69    (64)   ~ (all_52_9 = all_52_25)
% 203.86/34.69    (65)  all_58_15 = all_14_2
% 203.86/34.69    (66)   ~ (all_52_19 = all_10_2)
% 203.86/34.69    (67)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.69    (68)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.69    (69)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.69    (70)  all_58_8 = all_10_2
% 203.86/34.69    (71)   ~ (all_52_5 = all_10_2)
% 203.86/34.69    (72)   ~ (all_52_23 = all_14_2)
% 203.86/34.69    (73)  all_56_12 = all_52_7
% 203.86/34.69    (74)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.69    (75)   ~ (all_52_25 = all_6_2)
% 203.86/34.69    (76)   ~ (all_52_9 = all_4_2)
% 203.86/34.69    (77)   ~ (all_52_5 = all_6_2)
% 203.86/34.69    (78)   ~ (all_52_9 = all_6_2)
% 203.86/34.69    (79)  op(e3, e3) = all_6_2
% 203.86/34.69    (80)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.69    (81)   ~ (all_52_27 = all_14_2)
% 203.86/34.69    (82)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.69    (83)   ~ (all_52_3 = all_52_7)
% 203.86/34.69    (84)   ~ (all_10_1 = e3)
% 203.86/34.69    (85)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.69    (86)  all_58_5 = all_52_19
% 203.86/34.69    (87)  all_56_1 = all_52_9
% 203.86/34.69    (88)   ~ (all_52_27 = all_4_2)
% 203.86/34.69    (89)  all_58_6 = all_52_5
% 203.86/34.69    (90)  op(e3, e2) = all_52_9
% 203.86/34.69    (91)   ~ (all_52_17 = all_6_2)
% 203.86/34.69    (92)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.69    (93)   ~ (all_52_9 = all_52_17)
% 203.86/34.69    (94)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.69    (95)  op(e1, e1) = all_10_2
% 203.86/34.69    (96)   ~ (all_52_23 = all_10_2)
% 203.86/34.69    (97)   ~ (all_52_7 = all_52_23)
% 203.86/34.69    (98)  all_58_3 = all_4_2
% 203.86/34.69    (99)   ~ (all_52_3 = all_4_2)
% 203.86/34.69    (100)   ~ (all_52_17 = all_52_23)
% 203.86/34.69    (101)  op(all_6_2, e3) = all_6_1
% 203.86/34.69    (102)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.86/34.69    (103)   ~ (all_52_13 = all_52_29)
% 203.86/34.69    (104)  all_58_4 = all_52_17
% 203.86/34.69    (105)   ~ (all_14_2 = e3)
% 203.86/34.69  
% 203.86/34.69  Begin of proof
% 203.86/34.69  | 
% 203.86/34.69  | BETA: splitting (18) gives:
% 203.86/34.69  | 
% 203.86/34.69  | Case 1:
% 203.86/34.69  | | 
% 203.86/34.69  | |   (106)  all_58_13 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | REF_CLOSE: (19), (24), (106) are inconsistent by sub-proof #1360.
% 203.86/34.69  | | 
% 203.86/34.69  | Case 2:
% 203.86/34.69  | | 
% 203.86/34.69  | |   (107)  all_58_14 = e3 | all_58_15 = e3
% 203.86/34.69  | | 
% 203.86/34.69  | | BETA: splitting (107) gives:
% 203.86/34.69  | | 
% 203.86/34.69  | | Case 1:
% 203.86/34.69  | | | 
% 203.86/34.69  | | |   (108)  all_58_14 = e3
% 203.86/34.69  | | | 
% 203.86/34.69  | | | COMBINE_EQS: (3), (108) imply:
% 203.86/34.69  | | |   (109)  all_52_23 = e3
% 203.86/34.69  | | | 
% 203.86/34.69  | | | SIMP: (109) implies:
% 203.86/34.69  | | |   (110)  all_52_23 = e3
% 203.86/34.69  | | | 
% 203.86/34.69  | | | REDUCE: (97), (110) imply:
% 203.86/34.69  | | |   (111)   ~ (all_52_7 = e3)
% 203.86/34.69  | | | 
% 203.86/34.69  | | | REDUCE: (100), (110) imply:
% 203.86/34.69  | | |   (112)   ~ (all_52_17 = e3)
% 203.86/34.69  | | | 
% 203.86/34.69  | | | REDUCE: (72), (110) imply:
% 203.86/34.69  | | |   (113)   ~ (all_14_2 = e3)
% 203.86/34.69  | | | 
% 203.86/34.69  | | | REDUCE: (96), (110) imply:
% 203.86/34.69  | | |   (114)   ~ (all_10_2 = e3)
% 203.86/34.69  | | | 
% 203.86/34.69  | | | SIMP: (114) implies:
% 203.86/34.69  | | |   (115)   ~ (all_10_2 = e3)
% 203.86/34.69  | | | 
% 203.86/34.69  | | | REDUCE: (67), (110) imply:
% 203.86/34.69  | | |   (116)  op(e3, e3) = all_52_22
% 203.86/34.69  | | | 
% 203.86/34.69  | | | REDUCE: (33), (110) imply:
% 203.86/34.69  | | |   (117)  op(e0, e1) = e3
% 203.86/34.69  | | | 
% 203.86/34.69  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3,
% 203.86/34.69  | | |              simplifying with (79), (116) gives:
% 203.86/34.69  | | |   (118)  all_52_22 = all_6_2
% 203.86/34.69  | | | 
% 203.86/34.69  | | | BETA: splitting (12) gives:
% 203.86/34.69  | | | 
% 203.86/34.69  | | | Case 1:
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | |   (119)  all_56_12 = e3
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | | COMBINE_EQS: (73), (119) imply:
% 203.86/34.69  | | | |   (120)  all_52_7 = e3
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | | REDUCE: (111), (120) imply:
% 203.86/34.69  | | | |   (121)  $false
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | | CLOSE: (121) is inconsistent.
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | Case 2:
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | |   (122)   ~ (all_56_12 = e3)
% 203.86/34.69  | | | |   (123)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | | BETA: splitting (37) gives:
% 203.86/34.69  | | | | 
% 203.86/34.69  | | | | Case 1:
% 203.86/34.69  | | | | | 
% 203.86/34.69  | | | | |   (124)  all_56_2 = e3
% 203.86/34.69  | | | | | 
% 203.86/34.69  | | | | | REF_CLOSE: (52), (112), (124) are inconsistent by sub-proof #1327.
% 203.86/34.69  | | | | | 
% 203.86/34.69  | | | | Case 2:
% 203.86/34.69  | | | | | 
% 203.86/34.69  | | | | |   (125)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.69  | | | | | 
% 203.86/34.69  | | | | | BETA: splitting (80) gives:
% 203.86/34.69  | | | | | 
% 203.86/34.69  | | | | | Case 1:
% 203.86/34.69  | | | | | | 
% 203.86/34.69  | | | | | |   (126)  all_58_9 = e3
% 203.86/34.69  | | | | | | 
% 203.86/34.69  | | | | | | REF_CLOSE: (5), (10), (15), (21), (26), (35), (47), (48), (51),
% 203.86/34.69  | | | | | |            (54), (60), (71), (75), (79), (89), (95), (99), (111),
% 203.86/34.69  | | | | | |            (126) are inconsistent by sub-proof #660.
% 203.86/34.69  | | | | | | 
% 203.86/34.69  | | | | | Case 2:
% 203.86/34.69  | | | | | | 
% 203.86/34.69  | | | | | |   (127)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.69  | | | | | | 
% 203.86/34.69  | | | | | | BETA: splitting (82) gives:
% 203.86/34.69  | | | | | | 
% 203.86/34.69  | | | | | | Case 1:
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | |   (128)  all_58_0 = e3
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | COMBINE_EQS: (15), (128) imply:
% 203.86/34.69  | | | | | | |   (129)  all_6_2 = e3
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (77), (129) imply:
% 203.86/34.69  | | | | | | |   (130)   ~ (all_52_5 = e3)
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (78), (129) imply:
% 203.86/34.69  | | | | | | |   (131)   ~ (all_52_9 = e3)
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (75), (129) imply:
% 203.86/34.69  | | | | | | |   (132)   ~ (all_52_25 = e3)
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (101), (129) imply:
% 203.86/34.69  | | | | | | |   (133)  op(e3, e3) = all_6_1
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (79), (129) imply:
% 203.86/34.69  | | | | | | |   (134)  op(e3, e3) = e3
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | GROUND_INST: instantiating (5) with e3, all_6_1, e3, e3,
% 203.86/34.69  | | | | | | |              simplifying with (133), (134) gives:
% 203.86/34.69  | | | | | | |   (135)  all_6_1 = e3
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (55), (135) imply:
% 203.86/34.69  | | | | | | |   (136)  op(e3, e3) = all_6_0
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | GROUND_INST: instantiating (5) with e3, all_6_0, e3, e3,
% 203.86/34.69  | | | | | | |              simplifying with (134), (136) gives:
% 203.86/34.69  | | | | | | |   (137)  all_6_0 = e3
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | REDUCE: (41), (137) imply:
% 203.86/34.69  | | | | | | |   (138)   ~ (e3 = e1)
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | BETA: splitting (49) gives:
% 203.86/34.69  | | | | | | | 
% 203.86/34.69  | | | | | | | Case 1:
% 203.86/34.69  | | | | | | | | 
% 203.86/34.69  | | | | | | | |   (139)  all_58_6 = e3
% 203.86/34.69  | | | | | | | | 
% 203.86/34.69  | | | | | | | | REF_CLOSE: (89), (130), (139) are inconsistent by sub-proof
% 203.86/34.69  | | | | | | | |            #1328.
% 203.86/34.69  | | | | | | | | 
% 203.86/34.69  | | | | | | | Case 2:
% 203.86/34.69  | | | | | | | | 
% 203.86/34.69  | | | | | | | |   (140)   ~ (all_58_6 = e3)
% 203.86/34.69  | | | | | | | |   (141)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.69  | | | | | | | | 
% 203.86/34.69  | | | | | | | | BETA: splitting (63) gives:
% 203.86/34.69  | | | | | | | | 
% 203.86/34.69  | | | | | | | | Case 1:
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | |   (142)  all_58_1 = e3
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | COMBINE_EQS: (8), (142) imply:
% 203.86/34.69  | | | | | | | | |   (143)  all_52_9 = e3
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | REDUCE: (131), (143) imply:
% 203.86/34.69  | | | | | | | | |   (144)  $false
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | CLOSE: (144) is inconsistent.
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | Case 2:
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | |   (145)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | BETA: splitting (94) gives:
% 203.86/34.69  | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | Case 1:
% 203.86/34.69  | | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | |   (146)  all_56_9 = e3
% 203.86/34.69  | | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | | COMBINE_EQS: (38), (146) imply:
% 203.86/34.69  | | | | | | | | | |   (147)  all_52_13 = e3
% 203.86/34.69  | | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | | SIMP: (147) implies:
% 203.86/34.69  | | | | | | | | | |   (148)  all_52_13 = e3
% 203.86/34.69  | | | | | | | | | | 
% 203.86/34.69  | | | | | | | | | | COMBINE_EQS: (45), (148) imply:
% 203.86/34.69  | | | | | | | | | |   (149)  all_58_7 = e3
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | REDUCE: (103), (148) imply:
% 203.86/34.70  | | | | | | | | | |   (150)   ~ (all_52_29 = e3)
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | SIMP: (150) implies:
% 203.86/34.70  | | | | | | | | | |   (151)   ~ (all_52_29 = e3)
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | BETA: splitting (127) gives:
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | Case 1:
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | |   (152)  all_58_10 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | COMBINE_EQS: (42), (152) imply:
% 203.86/34.70  | | | | | | | | | | |   (153)  all_52_27 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | SIMP: (153) implies:
% 203.86/34.70  | | | | | | | | | | |   (154)  all_52_27 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | REDUCE: (88), (154) imply:
% 203.86/34.70  | | | | | | | | | | |   (155)   ~ (all_4_2 = e3)
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | SIMP: (155) implies:
% 203.86/34.70  | | | | | | | | | | |   (156)   ~ (all_4_2 = e3)
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | BETA: splitting (61) gives:
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | Case 1:
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | |   (157)  all_58_12 = e1
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | REF_CLOSE: (5), (7), (31), (48), (84), (95), (117), (157) are
% 203.86/34.70  | | | | | | | | | | | |            inconsistent by sub-proof #1358.
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | Case 2:
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | |   (158)   ~ (all_58_12 = e1)
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | REDUCE: (48), (158) imply:
% 203.86/34.70  | | | | | | | | | | | |   (159)   ~ (all_52_7 = e1)
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | REF_CLOSE: (1), (5), (8), (10), (11), (17), (20), (21), (23),
% 203.86/34.70  | | | | | | | | | | | |            (27), (28), (31), (34), (39), (48), (50), (51),
% 203.86/34.70  | | | | | | | | | | | |            (53), (56), (58), (60), (66), (69), (70), (71),
% 203.86/34.70  | | | | | | | | | | | |            (74), (76), (85), (86), (89), (95), (98), (102),
% 203.86/34.70  | | | | | | | | | | | |            (104), (105), (115), (128), (138), (149), (152),
% 203.86/34.70  | | | | | | | | | | | |            (156), (159) are inconsistent by sub-proof #659.
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | End of split
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | Case 2:
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | |   (160)  all_58_11 = e3 | all_58_15 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | REF_CLOSE: (27), (65), (105), (151), (160) are inconsistent
% 203.86/34.70  | | | | | | | | | | |            by sub-proof #1103.
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | End of split
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | Case 2:
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | |   (161)   ~ (all_56_9 = e3)
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | REDUCE: (38), (161) imply:
% 203.86/34.70  | | | | | | | | | |   (162)   ~ (all_52_13 = e3)
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | BETA: splitting (141) gives:
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | Case 1:
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | |   (163)  all_58_7 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | COMBINE_EQS: (45), (163) imply:
% 203.86/34.70  | | | | | | | | | | |   (164)  all_52_13 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | REDUCE: (162), (164) imply:
% 203.86/34.70  | | | | | | | | | | |   (165)  $false
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | Case 2:
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | |   (166)   ~ (all_58_7 = e3)
% 203.86/34.70  | | | | | | | | | | |   (167)  all_58_8 = e3 | all_58_11 = e3
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | BETA: splitting (167) gives:
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | Case 1:
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | |   (168)  all_58_8 = e3
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | COMBINE_EQS: (70), (168) imply:
% 203.86/34.70  | | | | | | | | | | | |   (169)  all_10_2 = e3
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | REDUCE: (115), (169) imply:
% 203.86/34.70  | | | | | | | | | | | |   (170)  $false
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | Case 2:
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | |   (171)  all_58_11 = e3
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (13),
% 203.86/34.70  | | | | | | | | | | | |            (14), (16), (19), (21), (22), (24), (25), (26),
% 203.86/34.70  | | | | | | | | | | | |            (29), (30), (32), (36), (38), (40), (42), (43),
% 203.86/34.70  | | | | | | | | | | | |            (44), (45), (46), (48), (50), (51), (52), (57),
% 203.86/34.70  | | | | | | | | | | | |            (59), (60), (62), (64), (68), (70), (71), (73),
% 203.86/34.70  | | | | | | | | | | | |            (76), (83), (86), (87), (89), (90), (92), (93),
% 203.86/34.70  | | | | | | | | | | | |            (94), (98), (99), (102), (104), (108), (112),
% 203.86/34.70  | | | | | | | | | | | |            (123), (125), (130), (132), (145), (162), (171)
% 203.86/34.70  | | | | | | | | | | | |            are inconsistent by sub-proof #751.
% 203.86/34.70  | | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | | End of split
% 203.86/34.70  | | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | | End of split
% 203.86/34.70  | | | | | | | | | | 
% 203.86/34.70  | | | | | | | | | End of split
% 203.86/34.70  | | | | | | | | | 
% 203.86/34.70  | | | | | | | | End of split
% 203.86/34.70  | | | | | | | | 
% 203.86/34.70  | | | | | | | End of split
% 203.86/34.70  | | | | | | | 
% 203.86/34.70  | | | | | | Case 2:
% 203.86/34.70  | | | | | | | 
% 203.86/34.70  | | | | | | |   (172)   ~ (all_58_0 = e3)
% 203.86/34.70  | | | | | | | 
% 203.86/34.70  | | | | | | | REDUCE: (15), (172) imply:
% 203.86/34.70  | | | | | | |   (173)   ~ (all_6_2 = e3)
% 203.86/34.70  | | | | | | | 
% 203.86/34.70  | | | | | | | REF_CLOSE: (5), (10), (15), (26), (35), (47), (48), (51), (54),
% 203.86/34.70  | | | | | | |            (60), (71), (79), (89), (95), (99), (111), (173) are
% 203.86/34.70  | | | | | | |            inconsistent by sub-proof #1363.
% 203.86/34.70  | | | | | | | 
% 203.86/34.70  | | | | | | End of split
% 203.86/34.70  | | | | | | 
% 203.86/34.70  | | | | | End of split
% 203.86/34.70  | | | | | 
% 203.86/34.70  | | | | End of split
% 203.86/34.70  | | | | 
% 203.86/34.70  | | | End of split
% 203.86/34.70  | | | 
% 203.86/34.70  | | Case 2:
% 203.86/34.70  | | | 
% 203.86/34.70  | | |   (174)  all_58_15 = e3
% 203.86/34.70  | | | 
% 203.86/34.70  | | | COMBINE_EQS: (65), (174) imply:
% 203.86/34.70  | | |   (175)  all_14_2 = e3
% 203.86/34.70  | | | 
% 203.86/34.70  | | | REDUCE: (105), (175) imply:
% 203.86/34.70  | | |   (176)  $false
% 203.86/34.70  | | | 
% 203.86/34.70  | | | CLOSE: (176) is inconsistent.
% 203.86/34.70  | | | 
% 203.86/34.70  | | End of split
% 203.86/34.70  | | 
% 203.86/34.70  | End of split
% 203.86/34.70  | 
% 203.86/34.70  End of proof
% 203.86/34.70  
% 203.86/34.70  Sub-proof #659 shows that the following formulas are inconsistent:
% 203.86/34.70  ----------------------------------------------------------------
% 203.86/34.70    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.70    (2)   ~ (e3 = e1)
% 203.86/34.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.70    (4)  all_58_1 = all_52_9
% 203.86/34.70    (5)  op(all_52_5, all_52_5) = e1
% 203.86/34.70    (6)   ~ (e3 = e0)
% 203.86/34.70    (7)   ~ (all_4_2 = e3)
% 203.86/34.70    (8)   ~ (all_52_17 = all_10_2)
% 203.86/34.70    (9)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.70    (10)  all_58_9 = all_52_25
% 203.86/34.70    (11)   ~ (all_52_29 = all_14_2)
% 203.86/34.70    (12)  all_58_11 = all_52_29
% 203.86/34.70    (13)   ~ (all_52_25 = all_14_2)
% 203.86/34.70    (14)  op(all_10_2, e1) = all_10_1
% 203.86/34.70    (15)  all_56_15 = all_14_2
% 203.86/34.70    (16)   ~ (e2 = e1)
% 203.86/34.70    (17)  all_58_12 = all_52_7
% 203.86/34.70    (18)   ~ (all_52_7 = all_14_2)
% 203.86/34.70    (19)  all_58_2 = all_52_3
% 203.86/34.70    (20)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.70    (21)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.70    (22)  all_58_7 = e3
% 203.86/34.70    (23)   ~ (e2 = e0)
% 203.86/34.70    (24)  op(all_52_3, all_52_3) = e2
% 203.86/34.70    (25)   ~ (all_10_2 = e3)
% 203.86/34.70    (26)  all_58_0 = e3
% 203.86/34.70    (27)   ~ (all_52_19 = all_10_2)
% 203.86/34.70    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.70    (29)  all_58_8 = all_10_2
% 203.86/34.70    (30)   ~ (all_52_5 = all_10_2)
% 203.86/34.70    (31)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.70    (32)   ~ (all_52_9 = all_4_2)
% 203.86/34.70    (33)  all_58_10 = e3
% 203.86/34.70    (34)   ~ (all_52_7 = e1)
% 203.86/34.70    (35)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.70    (36)  all_58_5 = all_52_19
% 203.86/34.70    (37)  all_58_6 = all_52_5
% 203.86/34.70    (38)  op(e1, e1) = all_10_2
% 203.86/34.70    (39)  all_58_3 = all_4_2
% 203.86/34.70    (40)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.86/34.70    (41)  all_58_4 = all_52_17
% 203.86/34.70    (42)   ~ (all_14_2 = e3)
% 203.86/34.70  
% 203.86/34.70  Begin of proof
% 203.86/34.70  | 
% 203.86/34.70  | BETA: splitting (21) gives:
% 203.86/34.70  | 
% 203.86/34.70  | Case 1:
% 203.86/34.70  | | 
% 203.86/34.70  | |   (43)  all_58_0 = e1
% 203.86/34.70  | | 
% 203.86/34.70  | | COMBINE_EQS: (26), (43) imply:
% 203.86/34.70  | |   (44)  e3 = e1
% 203.86/34.70  | | 
% 203.86/34.70  | | REDUCE: (2), (44) imply:
% 203.86/34.70  | |   (45)  $false
% 203.86/34.70  | | 
% 203.86/34.70  | | CLOSE: (45) is inconsistent.
% 203.86/34.70  | | 
% 203.86/34.70  | Case 2:
% 203.86/34.70  | | 
% 203.86/34.70  | |   (46)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.70  | | 
% 203.86/34.70  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.86/34.70  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 203.86/34.70  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.86/34.70  | |            (36), (37), (38), (39), (40), (41), (42), (46) are inconsistent
% 203.86/34.70  | |            by sub-proof #745.
% 203.86/34.70  | | 
% 203.86/34.70  | End of split
% 203.86/34.70  | 
% 203.86/34.70  End of proof
% 203.86/34.70  
% 203.86/34.70  Sub-proof #660 shows that the following formulas are inconsistent:
% 203.86/34.70  ----------------------------------------------------------------
% 203.86/34.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.70    (2)  op(all_52_5, all_52_5) = e1
% 203.86/34.70    (3)  all_58_9 = e3
% 203.86/34.70    (4)  all_58_0 = all_6_2
% 203.86/34.70    (5)  all_58_9 = all_52_25
% 203.86/34.70    (6)  op(e2, e2) = all_4_2
% 203.86/34.70    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.70    (8)  op(all_6_2, all_6_2) = e3
% 203.86/34.70    (9)  all_58_12 = all_52_7
% 203.86/34.70    (10)   ~ (all_52_7 = e3)
% 203.86/34.70    (11)  all_58_2 = all_52_3
% 203.86/34.70    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.70    (13)  op(all_52_3, all_52_3) = e2
% 203.86/34.70    (14)   ~ (all_52_5 = all_10_2)
% 203.86/34.70    (15)   ~ (all_52_25 = all_6_2)
% 203.86/34.70    (16)  op(e3, e3) = all_6_2
% 203.86/34.70    (17)  all_58_6 = all_52_5
% 203.86/34.70    (18)  op(e1, e1) = all_10_2
% 203.86/34.70    (19)   ~ (all_52_3 = all_4_2)
% 203.86/34.70  
% 203.86/34.70  Begin of proof
% 203.86/34.70  | 
% 203.86/34.70  | COMBINE_EQS: (3), (5) imply:
% 203.86/34.70  |   (20)  all_52_25 = e3
% 203.86/34.70  | 
% 203.86/34.70  | SIMP: (20) implies:
% 203.86/34.70  |   (21)  all_52_25 = e3
% 203.86/34.70  | 
% 203.86/34.70  | REDUCE: (15), (21) imply:
% 203.86/34.70  |   (22)   ~ (all_6_2 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | SIMP: (22) implies:
% 203.86/34.70  |   (23)   ~ (all_6_2 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 203.86/34.70  |            (16), (17), (18), (19), (23) are inconsistent by sub-proof #1363.
% 203.86/34.70  | 
% 203.86/34.70  End of proof
% 203.86/34.70  
% 203.86/34.70  Sub-proof #661 shows that the following formulas are inconsistent:
% 203.86/34.70  ----------------------------------------------------------------
% 203.86/34.70    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.70    (2)   ~ (all_52_15 = all_52_23)
% 203.86/34.70    (3)   ~ (all_52_25 = all_52_27)
% 203.86/34.70    (4)  all_58_14 = all_52_23
% 203.86/34.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.70    (6)  op(all_52_7, all_52_7) = e0
% 203.86/34.70    (7)  all_58_1 = all_52_9
% 203.86/34.70    (8)  op(all_52_5, all_52_5) = e1
% 203.86/34.70    (9)   ~ (e3 = e0)
% 203.86/34.70    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.70    (11)   ~ (all_52_7 = all_52_15)
% 203.86/34.70    (12)   ~ (all_52_3 = all_52_19)
% 203.86/34.70    (13)   ~ (all_52_3 = all_6_2)
% 203.86/34.70    (14)  all_58_0 = all_6_2
% 203.86/34.70    (15)  op(all_14_2, e0) = all_14_1
% 203.86/34.70    (16)  all_56_4 = all_52_3
% 203.86/34.70    (17)  op(e0, all_14_1) = all_14_0
% 203.86/34.70    (18)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.86/34.70    (19)  all_58_13 = all_52_15
% 203.86/34.70    (20)  all_58_9 = all_52_25
% 203.86/34.70    (21)  all_52_15 = e3
% 203.86/34.70    (22)  op(e2, e2) = all_4_2
% 203.86/34.70    (23)  all_58_11 = all_52_29
% 203.86/34.70    (24)   ~ (all_52_25 = all_14_2)
% 203.86/34.70    (25)   ~ (all_52_9 = all_52_15)
% 203.86/34.70    (26)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.86/34.70    (27)   ~ (all_52_3 = all_52_27)
% 203.86/34.70    (28)   ~ (all_52_7 = all_6_2)
% 203.86/34.70    (29)  op(e0, e0) = all_14_2
% 203.86/34.70    (30)  all_56_15 = all_14_2
% 203.86/34.70    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.70    (32)  op(e1, e0) = all_52_29
% 203.86/34.70    (33)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.86/34.70    (34)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.70    (35)  op(all_52_15, all_52_15) = all_52_14
% 203.86/34.70    (36)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.70    (37)  op(all_6_2, all_6_2) = e3
% 203.86/34.70    (38)  all_58_12 = all_52_7
% 203.86/34.70    (39)   ~ (all_52_7 = all_14_2)
% 203.86/34.70    (40)   ~ (all_14_2 = e0)
% 203.86/34.70    (41)  all_58_2 = all_52_3
% 203.86/34.70    (42)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.70    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.70    (44)  all_56_7 = all_52_27
% 203.86/34.70    (45)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.70    (46)   ~ (e2 = e0)
% 203.86/34.70    (47)  op(all_52_3, all_52_3) = e2
% 203.86/34.70    (48)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.70    (49)  all_56_6 = all_52_19
% 203.86/34.70    (50)   ~ (all_52_15 = all_14_2)
% 203.86/34.70    (51)   ~ (all_52_19 = all_52_27)
% 203.86/34.70    (52)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.86/34.70    (53)  op(e0, e3) = all_52_7
% 203.86/34.70    (54)   ~ (all_52_9 = all_52_25)
% 203.86/34.70    (55)  all_58_15 = all_14_2
% 203.86/34.70    (56)   ~ (all_52_19 = all_10_2)
% 203.86/34.70    (57)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.70    (58)   ~ (all_52_5 = all_10_2)
% 203.86/34.70    (59)  all_56_12 = all_52_7
% 203.86/34.70    (60)   ~ (all_52_25 = all_6_2)
% 203.86/34.70    (61)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.70    (62)   ~ (all_52_9 = all_4_2)
% 203.86/34.70    (63)  op(e3, e3) = all_6_2
% 203.86/34.70    (64)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.70    (65)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.70    (66)  all_56_14 = all_52_23
% 203.86/34.70    (67)  all_56_3 = all_52_25
% 203.86/34.70    (68)   ~ (all_52_3 = all_52_7)
% 203.86/34.70    (69)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.70    (70)  all_58_5 = all_52_19
% 203.86/34.70    (71)  all_56_1 = all_52_9
% 203.86/34.70    (72)   ~ (all_52_27 = all_4_2)
% 203.86/34.70    (73)  all_58_6 = all_52_5
% 203.86/34.70    (74)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.70    (75)   ~ (e1 = e0)
% 203.86/34.70    (76)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.70    (77)  op(e1, e1) = all_10_2
% 203.86/34.70    (78)   ~ (all_52_23 = all_10_2)
% 203.86/34.70    (79)   ~ (all_52_7 = all_52_23)
% 203.86/34.70    (80)  all_58_3 = all_4_2
% 203.86/34.70    (81)   ~ (all_52_3 = all_4_2)
% 203.86/34.70    (82)   ~ (all_52_19 = all_4_2)
% 203.86/34.70    (83)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.86/34.70    (84)   ~ (all_14_0 = e2)
% 203.86/34.70  
% 203.86/34.70  Begin of proof
% 203.86/34.70  | 
% 203.86/34.70  | COMBINE_EQS: (19), (21) imply:
% 203.86/34.70  |   (85)  all_58_13 = e3
% 203.86/34.70  | 
% 203.86/34.70  | REDUCE: (11), (21) imply:
% 203.86/34.70  |   (86)   ~ (all_52_7 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | REDUCE: (21), (25) imply:
% 203.86/34.70  |   (87)   ~ (all_52_9 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | REDUCE: (2), (21) imply:
% 203.86/34.70  |   (88)   ~ (all_52_23 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | SIMP: (88) implies:
% 203.86/34.70  |   (89)   ~ (all_52_23 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | REDUCE: (21), (50) imply:
% 203.86/34.70  |   (90)   ~ (all_14_2 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | SIMP: (90) implies:
% 203.86/34.70  |   (91)   ~ (all_14_2 = e3)
% 203.86/34.70  | 
% 203.86/34.70  | REDUCE: (21), (35) imply:
% 203.86/34.70  |   (92)  op(e3, e3) = all_52_14
% 203.86/34.70  | 
% 203.86/34.70  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 203.86/34.70  |            (15), (16), (17), (18), (20), (22), (23), (24), (26), (27), (28),
% 203.86/34.70  |            (29), (30), (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 203.86/34.70  |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (51), (52),
% 203.86/34.70  |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 203.86/34.70  |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 203.86/34.70  |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 203.86/34.70  |            (86), (87), (89), (91), (92) are inconsistent by sub-proof #755.
% 203.86/34.70  | 
% 203.86/34.70  End of proof
% 203.86/34.70  
% 203.86/34.70  Sub-proof #662 shows that the following formulas are inconsistent:
% 203.86/34.70  ----------------------------------------------------------------
% 203.86/34.70    (1)   ~ (all_52_15 = all_52_23)
% 203.86/34.70    (2)   ~ (all_52_25 = all_52_27)
% 203.86/34.70    (3)  all_58_14 = all_52_23
% 203.86/34.70    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.86/34.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.70    (6)   ~ (all_52_5 = all_52_13)
% 203.86/34.70    (7)  all_58_1 = all_52_9
% 203.86/34.70    (8)   ~ (all_52_9 = all_52_13)
% 203.86/34.70    (9)   ~ (e3 = e0)
% 203.86/34.70    (10)  op(e2, e3) = all_52_3
% 203.86/34.70    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.70    (12)  op(e0, e2) = all_52_15
% 203.86/34.70    (13)   ~ (all_52_7 = all_52_15)
% 203.86/34.70    (14)   ~ (all_52_3 = all_52_19)
% 203.86/34.70    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.86/34.70    (16)   ~ (all_52_17 = all_52_25)
% 203.86/34.70    (17)   ~ (all_52_3 = all_6_2)
% 203.86/34.70    (18)  all_58_0 = all_6_2
% 203.86/34.70    (19)  op(all_14_2, e0) = all_14_1
% 203.86/34.70    (20)  all_56_4 = all_52_3
% 203.86/34.70    (21)   ~ (all_52_17 = all_10_2)
% 203.86/34.70    (22)   ~ (all_10_0 = e3)
% 203.86/34.70    (23)  all_40_2 = all_10_2
% 203.86/34.70    (24)  op(e3, e0) = all_52_25
% 203.86/34.70    (25)  op(e0, all_14_1) = all_14_0
% 203.86/34.70    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.86/34.70    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.86/34.70    (28)   ~ (all_52_27 = all_52_29)
% 203.86/34.70    (29)  all_58_13 = all_52_15
% 203.86/34.70    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.70    (31)  all_58_9 = all_52_25
% 203.86/34.70    (32)   ~ (all_6_1 = e1)
% 203.86/34.70    (33)   ~ (all_52_29 = all_14_2)
% 203.86/34.70    (34)  all_22_0 = all_6_0
% 203.86/34.70    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.86/34.70    (36)  op(all_52_27, all_52_27) = all_52_26
% 203.86/34.70    (37)  op(e1, e3) = all_52_5
% 203.86/34.70    (38)  all_40_1 = all_10_1
% 203.86/34.70    (39)  op(e2, e2) = all_4_2
% 203.86/34.70    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.86/34.70    (41)   ~ (all_52_3 = all_52_5)
% 203.86/34.70    (42)  all_58_11 = all_52_29
% 203.86/34.70    (43)  all_56_5 = all_4_2
% 203.86/34.70    (44)   ~ (all_52_25 = all_14_2)
% 203.86/34.70    (45)   ~ (all_52_9 = all_52_15)
% 203.86/34.70    (46)   ~ (all_52_3 = all_52_27)
% 203.86/34.70    (47)  op(all_10_2, e1) = all_10_1
% 203.86/34.70    (48)  op(all_6_2, all_6_2) = all_52_0
% 203.86/34.70    (49)   ~ (all_52_7 = all_6_2)
% 203.86/34.70    (50)  op(e0, e0) = all_14_2
% 203.86/34.70    (51)  all_56_15 = all_14_2
% 203.86/34.70    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.70    (53)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.86/34.70    (54)  all_56_11 = all_52_29
% 203.86/34.70    (55)   ~ (all_10_0 = e2)
% 203.86/34.70    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.70    (57)  all_56_9 = all_52_13
% 203.86/34.70    (58)   ~ (all_52_13 = all_10_2)
% 203.86/34.70    (59)   ~ (all_6_0 = e1)
% 203.86/34.70    (60)  op(e1, all_10_1) = all_10_0
% 203.86/34.70    (61)  all_58_10 = all_52_27
% 203.86/34.70    (62)  all_56_8 = all_52_5
% 203.86/34.70    (63)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.70    (64)   ~ (all_52_19 = all_52_23)
% 203.86/34.70    (65)   ~ (all_52_25 = all_52_29)
% 203.86/34.70    (66)   ~ (all_52_29 = all_10_2)
% 203.86/34.70    (67)  all_58_7 = all_52_13
% 203.86/34.70    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.70    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.70    (70)   ~ (all_52_5 = all_52_7)
% 203.86/34.70    (71)  all_58_12 = all_52_7
% 203.86/34.70    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.70    (73)   ~ (all_52_7 = all_14_2)
% 203.86/34.70    (74)  all_58_2 = all_52_3
% 203.86/34.70    (75)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.70    (76)  all_56_2 = all_52_17
% 203.86/34.70    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.70    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.70    (79)  op(e3, all_6_1) = all_6_0
% 203.86/34.70    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.86/34.70    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.70    (82)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.86/34.70    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.70    (84)   ~ (e2 = e0)
% 203.86/34.70    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.86/34.70    (86)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.86/34.70    (87)   ~ (all_52_5 = all_52_29)
% 203.86/34.70    (88)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.70    (89)  all_56_6 = all_52_19
% 203.86/34.70    (90)   ~ (all_52_15 = all_14_2)
% 203.86/34.70    (91)   ~ (all_52_19 = all_52_27)
% 203.86/34.70    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.86/34.70    (93)   ~ (all_6_0 = e2)
% 203.86/34.70    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.86/34.70            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.86/34.70    (95)  op(e3, e1) = all_52_17
% 203.86/34.70    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.86/34.70    (97)  op(e0, e3) = all_52_7
% 203.86/34.70    (98)  op(e1, e2) = all_52_13
% 203.86/34.70    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.70    (100)   ~ (all_52_9 = all_52_25)
% 203.86/34.70    (101)  all_58_15 = all_14_2
% 203.86/34.70    (102)   ~ (all_52_19 = all_10_2)
% 203.86/34.70    (103)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.70    (104)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3)
% 203.86/34.70    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.70    (106)  all_58_8 = all_10_2
% 203.86/34.70    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.70    (108)   ~ (all_52_5 = all_10_2)
% 203.86/34.70    (109)  op(all_52_29, all_52_29) = all_52_28
% 203.86/34.70    (110)   ~ (all_52_23 = all_14_2)
% 203.86/34.70    (111)  all_56_12 = all_52_7
% 203.86/34.70    (112)  op(all_52_17, all_52_17) = all_52_16
% 203.86/34.70    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.70    (114)   ~ (all_52_25 = all_6_2)
% 203.86/34.70    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.70    (116)   ~ (all_52_9 = all_4_2)
% 203.86/34.70    (117)   ~ (all_52_5 = all_6_2)
% 203.86/34.70    (118)   ~ (all_52_9 = all_6_2)
% 203.86/34.70    (119)  all_56_0 = all_6_2
% 203.86/34.70    (120)  op(e3, e3) = all_6_2
% 203.86/34.71    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.71    (122)   ~ (all_52_27 = all_14_2)
% 203.86/34.71    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.71    (124)  all_56_14 = all_52_23
% 203.86/34.71    (125)  all_40_0 = all_10_0
% 203.86/34.71    (126)  all_56_3 = all_52_25
% 203.86/34.71    (127)   ~ (all_52_3 = all_52_7)
% 203.86/34.71    (128)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.71    (129)  all_58_5 = all_52_19
% 203.86/34.71    (130)  all_56_1 = all_52_9
% 203.86/34.71    (131)   ~ (all_52_15 = all_4_2)
% 203.86/34.71    (132)  op(e0, all_14_1) = e3
% 203.86/34.71    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.71           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.86/34.71           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.86/34.71           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.86/34.71    (134)   ~ (all_52_27 = all_4_2)
% 203.86/34.71    (135)  all_58_6 = all_52_5
% 203.86/34.71    (136)  op(e3, e2) = all_52_9
% 203.86/34.71    (137)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.71    (138)   ~ (all_52_17 = all_6_2)
% 203.86/34.71    (139)  all_30_1 = all_10_1
% 203.86/34.71    (140)   ~ (e1 = e0)
% 203.86/34.71    (141)   ~ (e3 = e2)
% 203.86/34.71    (142)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.71    (143)   ~ (all_52_9 = all_52_17)
% 203.86/34.71    (144)  all_56_10 = all_10_2
% 203.86/34.71    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.86/34.71    (146)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2)
% 203.86/34.71    (147)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.71    (148)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.86/34.71    (149)  op(all_52_13, all_52_13) = all_52_12
% 203.86/34.71    (150)  all_6_1 = e2
% 203.86/34.71    (151)  op(e1, e1) = all_10_2
% 203.86/34.71    (152)   ~ (all_52_23 = all_10_2)
% 203.86/34.71    (153)   ~ (all_52_7 = all_52_23)
% 203.86/34.71    (154)   ~ (all_52_17 = all_52_19)
% 203.86/34.71    (155)  all_58_3 = all_4_2
% 203.86/34.71    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.86/34.71    (157)   ~ (all_52_3 = all_4_2)
% 203.86/34.71    (158)   ~ (all_52_19 = all_4_2)
% 203.86/34.71    (159)   ~ (all_52_17 = all_52_23)
% 203.86/34.71    (160)  op(all_6_2, e3) = all_6_1
% 203.86/34.71    (161)  all_22_2 = all_6_2
% 203.86/34.71    (162)  all_58_4 = all_52_17
% 203.86/34.71    (163)   ~ (all_14_0 = e2)
% 203.86/34.71    (164)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.86/34.71    (165)  op(all_52_25, all_52_25) = all_52_24
% 203.86/34.71  
% 203.86/34.71  Begin of proof
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (32), (150) imply:
% 203.86/34.71  |   (166)   ~ (e2 = e1)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (150), (160) imply:
% 203.86/34.71  |   (167)  op(all_6_2, e3) = e2
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (79), (150) imply:
% 203.86/34.71  |   (168)  op(e3, e2) = all_6_0
% 203.86/34.71  | 
% 203.86/34.71  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.86/34.71  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.86/34.71  |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 203.86/34.71  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 203.86/34.71  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 203.86/34.71  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.86/34.71  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (80),
% 203.86/34.71  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 203.86/34.71  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.86/34.71  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.86/34.71  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 203.86/34.71  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 203.86/34.71  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 203.86/34.71  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 203.86/34.71  |            (147), (148), (149), (151), (152), (153), (154), (155), (156),
% 203.86/34.71  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 203.86/34.71  |            (166), (167), (168) are inconsistent by sub-proof #663.
% 203.86/34.71  | 
% 203.86/34.71  End of proof
% 203.86/34.71  
% 203.86/34.71  Sub-proof #663 shows that the following formulas are inconsistent:
% 203.86/34.71  ----------------------------------------------------------------
% 203.86/34.71    (1)   ~ (all_52_15 = all_52_23)
% 203.86/34.71    (2)   ~ (all_52_25 = all_52_27)
% 203.86/34.71    (3)  all_58_14 = all_52_23
% 203.86/34.71    (4)  op(all_52_3, all_52_3) = all_52_2
% 203.86/34.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.71    (6)   ~ (all_52_5 = all_52_13)
% 203.86/34.71    (7)  all_58_1 = all_52_9
% 203.86/34.71    (8)   ~ (all_52_9 = all_52_13)
% 203.86/34.71    (9)   ~ (e3 = e0)
% 203.86/34.71    (10)  op(e2, e3) = all_52_3
% 203.86/34.71    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.71    (12)  op(e0, e2) = all_52_15
% 203.86/34.71    (13)   ~ (all_52_7 = all_52_15)
% 203.86/34.71    (14)   ~ (all_52_3 = all_52_19)
% 203.86/34.71    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.86/34.71    (16)   ~ (all_52_17 = all_52_25)
% 203.86/34.71    (17)   ~ (all_52_3 = all_6_2)
% 203.86/34.71    (18)  all_58_0 = all_6_2
% 203.86/34.71    (19)  op(all_14_2, e0) = all_14_1
% 203.86/34.71    (20)  all_56_4 = all_52_3
% 203.86/34.71    (21)   ~ (all_52_17 = all_10_2)
% 203.86/34.71    (22)   ~ (all_10_0 = e3)
% 203.86/34.71    (23)  all_40_2 = all_10_2
% 203.86/34.71    (24)  op(e3, e0) = all_52_25
% 203.86/34.71    (25)  op(e0, all_14_1) = all_14_0
% 203.86/34.71    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.86/34.71    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.86/34.71    (28)   ~ (all_52_27 = all_52_29)
% 203.86/34.71    (29)  all_58_13 = all_52_15
% 203.86/34.71    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.71    (31)  all_58_9 = all_52_25
% 203.86/34.71    (32)   ~ (all_52_29 = all_14_2)
% 203.86/34.71    (33)  all_22_0 = all_6_0
% 203.86/34.71    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.86/34.71    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.86/34.71    (36)  op(e1, e3) = all_52_5
% 203.86/34.71    (37)  all_40_1 = all_10_1
% 203.86/34.71    (38)  op(e2, e2) = all_4_2
% 203.86/34.71    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.86/34.71    (40)   ~ (all_52_3 = all_52_5)
% 203.86/34.71    (41)  all_58_11 = all_52_29
% 203.86/34.71    (42)  all_56_5 = all_4_2
% 203.86/34.71    (43)   ~ (all_52_25 = all_14_2)
% 203.86/34.71    (44)   ~ (all_52_9 = all_52_15)
% 203.86/34.71    (45)   ~ (all_52_3 = all_52_27)
% 203.86/34.71    (46)  op(all_10_2, e1) = all_10_1
% 203.86/34.71    (47)  op(all_6_2, all_6_2) = all_52_0
% 203.86/34.71    (48)   ~ (all_52_7 = all_6_2)
% 203.86/34.71    (49)  op(e0, e0) = all_14_2
% 203.86/34.71    (50)  all_56_15 = all_14_2
% 203.86/34.71    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.71    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.86/34.71    (53)  all_56_11 = all_52_29
% 203.86/34.71    (54)   ~ (all_10_0 = e2)
% 203.86/34.71    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.71    (56)  all_56_9 = all_52_13
% 203.86/34.71    (57)   ~ (e2 = e1)
% 203.86/34.71    (58)   ~ (all_52_13 = all_10_2)
% 203.86/34.71    (59)   ~ (all_6_0 = e1)
% 203.86/34.71    (60)  op(e1, all_10_1) = all_10_0
% 203.86/34.71    (61)  all_58_10 = all_52_27
% 203.86/34.71    (62)  all_56_8 = all_52_5
% 203.86/34.71    (63)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.71    (64)   ~ (all_52_19 = all_52_23)
% 203.86/34.71    (65)   ~ (all_52_25 = all_52_29)
% 203.86/34.71    (66)  op(all_6_2, e3) = e2
% 203.86/34.71    (67)   ~ (all_52_29 = all_10_2)
% 203.86/34.71    (68)  all_58_7 = all_52_13
% 203.86/34.71    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.71    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.71    (71)   ~ (all_52_5 = all_52_7)
% 203.86/34.71    (72)  all_58_12 = all_52_7
% 203.86/34.71    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.71    (74)   ~ (all_52_7 = all_14_2)
% 203.86/34.71    (75)  all_58_2 = all_52_3
% 203.86/34.71    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.71    (77)  all_56_2 = all_52_17
% 203.86/34.71    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.71    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.71    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.86/34.71    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.71    (82)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.86/34.71    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.71    (84)   ~ (e2 = e0)
% 203.86/34.71    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.86/34.71    (86)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.86/34.71    (87)   ~ (all_52_5 = all_52_29)
% 203.86/34.71    (88)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.71    (89)  all_56_6 = all_52_19
% 203.86/34.71    (90)   ~ (all_52_15 = all_14_2)
% 203.86/34.71    (91)   ~ (all_52_19 = all_52_27)
% 203.86/34.71    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.86/34.71    (93)   ~ (all_6_0 = e2)
% 203.86/34.71    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.86/34.71            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.86/34.71    (95)  op(e3, e1) = all_52_17
% 203.86/34.71    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.86/34.71    (97)  op(e0, e3) = all_52_7
% 203.86/34.71    (98)  op(e1, e2) = all_52_13
% 203.86/34.71    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.71    (100)   ~ (all_52_9 = all_52_25)
% 203.86/34.71    (101)  all_58_15 = all_14_2
% 203.86/34.71    (102)   ~ (all_52_19 = all_10_2)
% 203.86/34.71    (103)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.71    (104)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3)
% 203.86/34.71    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.71    (106)  all_58_8 = all_10_2
% 203.86/34.71    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.71    (108)   ~ (all_52_5 = all_10_2)
% 203.86/34.71    (109)  op(all_52_29, all_52_29) = all_52_28
% 203.86/34.71    (110)   ~ (all_52_23 = all_14_2)
% 203.86/34.71    (111)  all_56_12 = all_52_7
% 203.86/34.71    (112)  op(all_52_17, all_52_17) = all_52_16
% 203.86/34.71    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.71    (114)  op(e3, e2) = all_6_0
% 203.86/34.71    (115)   ~ (all_52_25 = all_6_2)
% 203.86/34.71    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.71    (117)   ~ (all_52_9 = all_4_2)
% 203.86/34.71    (118)   ~ (all_52_5 = all_6_2)
% 203.86/34.71    (119)   ~ (all_52_9 = all_6_2)
% 203.86/34.71    (120)  all_56_0 = all_6_2
% 203.86/34.71    (121)  op(e3, e3) = all_6_2
% 203.86/34.71    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.71    (123)   ~ (all_52_27 = all_14_2)
% 203.86/34.71    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.71    (125)  all_56_14 = all_52_23
% 203.86/34.71    (126)  all_40_0 = all_10_0
% 203.86/34.71    (127)  all_56_3 = all_52_25
% 203.86/34.71    (128)   ~ (all_52_3 = all_52_7)
% 203.86/34.71    (129)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.71    (130)  all_58_5 = all_52_19
% 203.86/34.71    (131)  all_56_1 = all_52_9
% 203.86/34.71    (132)   ~ (all_52_15 = all_4_2)
% 203.86/34.71    (133)  op(e0, all_14_1) = e3
% 203.86/34.71    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.71           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.86/34.71           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.86/34.71           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.86/34.71    (135)   ~ (all_52_27 = all_4_2)
% 203.86/34.71    (136)  all_58_6 = all_52_5
% 203.86/34.71    (137)  op(e3, e2) = all_52_9
% 203.86/34.71    (138)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.71    (139)   ~ (all_52_17 = all_6_2)
% 203.86/34.71    (140)  all_30_1 = all_10_1
% 203.86/34.71    (141)   ~ (e1 = e0)
% 203.86/34.71    (142)   ~ (e3 = e2)
% 203.86/34.71    (143)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.71    (144)   ~ (all_52_9 = all_52_17)
% 203.86/34.71    (145)  all_56_10 = all_10_2
% 203.86/34.71    (146)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.86/34.71    (147)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2)
% 203.86/34.71    (148)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.71    (149)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.86/34.71    (150)  op(all_52_13, all_52_13) = all_52_12
% 203.86/34.71    (151)  op(e1, e1) = all_10_2
% 203.86/34.71    (152)   ~ (all_52_23 = all_10_2)
% 203.86/34.71    (153)   ~ (all_52_7 = all_52_23)
% 203.86/34.71    (154)   ~ (all_52_17 = all_52_19)
% 203.86/34.71    (155)  all_58_3 = all_4_2
% 203.86/34.71    (156)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.86/34.71    (157)   ~ (all_52_3 = all_4_2)
% 203.86/34.71    (158)   ~ (all_52_19 = all_4_2)
% 203.86/34.71    (159)   ~ (all_52_17 = all_52_23)
% 203.86/34.71    (160)  op(all_6_2, e3) = all_6_1
% 203.86/34.71    (161)  all_22_2 = all_6_2
% 203.86/34.71    (162)  all_58_4 = all_52_17
% 203.86/34.71    (163)   ~ (all_14_0 = e2)
% 203.86/34.71    (164)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.86/34.71    (165)  op(all_52_25, all_52_25) = all_52_24
% 203.86/34.71  
% 203.86/34.71  Begin of proof
% 203.86/34.71  | 
% 203.86/34.71  | GROUND_INST: instantiating (5) with all_52_9, all_6_0, e2, e3, simplifying
% 203.86/34.71  |              with (114), (137) gives:
% 203.86/34.71  |   (166)  all_52_9 = all_6_0
% 203.86/34.71  | 
% 203.86/34.71  | COMBINE_EQS: (131), (166) imply:
% 203.86/34.71  |   (167)  all_56_1 = all_6_0
% 203.86/34.71  | 
% 203.86/34.71  | COMBINE_EQS: (7), (166) imply:
% 203.86/34.71  |   (168)  all_58_1 = all_6_0
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (8), (166) imply:
% 203.86/34.71  |   (169)   ~ (all_52_13 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | SIMP: (169) implies:
% 203.86/34.71  |   (170)   ~ (all_52_13 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (44), (166) imply:
% 203.86/34.71  |   (171)   ~ (all_52_15 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | SIMP: (171) implies:
% 203.86/34.71  |   (172)   ~ (all_52_15 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (144), (166) imply:
% 203.86/34.71  |   (173)   ~ (all_52_17 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | SIMP: (173) implies:
% 203.86/34.71  |   (174)   ~ (all_52_17 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (100), (166) imply:
% 203.86/34.71  |   (175)   ~ (all_52_25 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | SIMP: (175) implies:
% 203.86/34.71  |   (176)   ~ (all_52_25 = all_6_0)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (119), (166) imply:
% 203.86/34.71  |   (177)   ~ (all_6_0 = all_6_2)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (117), (166) imply:
% 203.86/34.71  |   (178)   ~ (all_6_0 = all_4_2)
% 203.86/34.71  | 
% 203.86/34.71  | REDUCE: (63), (166) imply:
% 203.86/34.71  |   (179)  op(all_6_0, all_6_0) = all_52_8
% 203.86/34.71  | 
% 203.86/34.71  | BETA: splitting (147) gives:
% 203.86/34.71  | 
% 203.86/34.71  | Case 1:
% 203.86/34.71  | | 
% 203.86/34.71  | |   (180)   ~ (all_30_1 = e3)
% 203.86/34.71  | | 
% 203.86/34.71  | | REDUCE: (140), (180) imply:
% 203.86/34.71  | |   (181)   ~ (all_10_1 = e3)
% 203.86/34.71  | | 
% 203.86/34.71  | | BETA: splitting (104) gives:
% 203.86/34.71  | | 
% 203.86/34.71  | | Case 1:
% 203.86/34.71  | | | 
% 203.86/34.71  | | |   (182)   ~ (all_40_1 = e2)
% 203.86/34.71  | | | 
% 203.86/34.71  | | | REDUCE: (37), (182) imply:
% 203.86/34.71  | | |   (183)   ~ (all_10_1 = e2)
% 203.86/34.71  | | | 
% 203.86/34.71  | | | BETA: splitting (94) gives:
% 203.86/34.71  | | | 
% 203.86/34.71  | | | Case 1:
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | |   (184)  all_58_15 = e0
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | | REF_CLOSE: (5), (9), (19), (49), (101), (129), (133), (184) are
% 203.86/34.71  | | | |            inconsistent by sub-proof #693.
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | Case 2:
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | |   (185)   ~ (all_58_15 = e0)
% 203.86/34.71  | | | |   (186)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.86/34.71  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 203.86/34.71  | | | |            (12), (14), (15), (16), (17), (18), (19), (20), (21), (24),
% 203.86/34.71  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.86/34.71  | | | |            (35), (36), (38), (39), (40), (41), (42), (43), (45), (46),
% 203.86/34.71  | | | |            (47), (48), (49), (50), (51), (52), (53), (55), (57), (58),
% 203.86/34.71  | | | |            (59), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 203.86/34.71  | | | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.86/34.71  | | | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 203.86/34.71  | | | |            (90), (91), (92), (93), (95), (96), (97), (99), (100), (101),
% 203.86/34.71  | | | |            (102), (103), (105), (106), (107), (108), (109), (110),
% 203.86/34.71  | | | |            (111), (112), (113), (115), (116), (117), (118), (120),
% 203.86/34.71  | | | |            (121), (122), (123), (124), (125), (127), (128), (129),
% 203.86/34.71  | | | |            (130), (132), (134), (135), (136), (138), (139), (141),
% 203.86/34.71  | | | |            (142), (143), (145), (146), (149), (150), (151), (152),
% 203.86/34.71  | | | |            (153), (154), (155), (156), (157), (158), (159), (160),
% 203.86/34.71  | | | |            (161), (162), (163), (164), (165), (167), (168), (170),
% 203.86/34.71  | | | |            (172), (174), (176), (177), (178), (179), (183), (185), (186)
% 203.86/34.71  | | | |            are inconsistent by sub-proof #775.
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | End of split
% 203.86/34.71  | | | 
% 203.86/34.71  | | Case 2:
% 203.86/34.71  | | | 
% 203.86/34.71  | | |   (187)  all_40_1 = e2
% 203.86/34.71  | | |   (188)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.86/34.71  | | | 
% 203.86/34.71  | | | COMBINE_EQS: (37), (187) imply:
% 203.86/34.71  | | |   (189)  all_10_1 = e2
% 203.86/34.71  | | | 
% 203.86/34.71  | | | SIMP: (189) implies:
% 203.86/34.71  | | |   (190)  all_10_1 = e2
% 203.86/34.71  | | | 
% 203.86/34.71  | | | REDUCE: (181), (190) imply:
% 203.86/34.71  | | |   (191)   ~ (e3 = e2)
% 203.86/34.71  | | | 
% 203.86/34.71  | | | REDUCE: (46), (190) imply:
% 203.86/34.71  | | |   (192)  op(all_10_2, e1) = e2
% 203.86/34.71  | | | 
% 203.86/34.71  | | | REDUCE: (60), (190) imply:
% 203.86/34.71  | | |   (193)  op(e1, e2) = all_10_0
% 203.86/34.71  | | | 
% 203.86/34.71  | | | GROUND_INST: instantiating (5) with all_52_13, all_10_0, e2, e1,
% 203.86/34.71  | | |              simplifying with (98), (193) gives:
% 203.86/34.71  | | |   (194)  all_52_13 = all_10_0
% 203.86/34.71  | | | 
% 203.86/34.71  | | | COMBINE_EQS: (56), (194) imply:
% 203.86/34.71  | | |   (195)  all_56_9 = all_10_0
% 203.86/34.71  | | | 
% 203.86/34.71  | | | COMBINE_EQS: (68), (194) imply:
% 203.86/34.71  | | |   (196)  all_58_7 = all_10_0
% 203.86/34.71  | | | 
% 203.86/34.71  | | | REDUCE: (6), (194) imply:
% 203.86/34.71  | | |   (197)   ~ (all_52_5 = all_10_0)
% 203.86/34.71  | | | 
% 203.86/34.71  | | | REDUCE: (170), (194) imply:
% 203.86/34.71  | | |   (198)   ~ (all_10_0 = all_6_0)
% 203.86/34.71  | | | 
% 203.86/34.71  | | | BETA: splitting (94) gives:
% 203.86/34.71  | | | 
% 203.86/34.71  | | | Case 1:
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | |   (199)  all_58_15 = e0
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | | REF_CLOSE: (5), (9), (19), (49), (101), (129), (133), (199) are
% 203.86/34.71  | | | |            inconsistent by sub-proof #678.
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | Case 2:
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | |   (200)   ~ (all_58_15 = e0)
% 203.86/34.71  | | | |   (201)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 203.86/34.71  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | | ALPHA: (201) implies:
% 203.86/34.71  | | | |   (202)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.86/34.71  | | | |   (203)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | | REDUCE: (101), (200) imply:
% 203.86/34.71  | | | |   (204)   ~ (all_14_2 = e0)
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13),
% 203.86/34.71  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 203.86/34.71  | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 203.86/34.71  | | | |            (36), (38), (39), (40), (41), (42), (43), (45), (46), (47),
% 203.86/34.71  | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (57), (59),
% 203.86/34.71  | | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 203.86/34.71  | | | |            (71), (72), (73), (74), (75), (77), (79), (80), (82), (83),
% 203.86/34.71  | | | |            (84), (85), (86), (87), (88), (91), (92), (93), (95), (96),
% 203.86/34.71  | | | |            (97), (99), (100), (101), (102), (103), (105), (106), (107),
% 203.86/34.71  | | | |            (108), (109), (110), (111), (112), (113), (115), (116),
% 203.86/34.71  | | | |            (117), (118), (120), (121), (122), (123), (124), (125),
% 203.86/34.71  | | | |            (126), (127), (128), (129), (130), (132), (134), (135),
% 203.86/34.71  | | | |            (136), (138), (139), (141), (142), (143), (145), (146),
% 203.86/34.71  | | | |            (148), (149), (150), (151), (152), (153), (155), (156),
% 203.86/34.71  | | | |            (157), (158), (159), (160), (161), (162), (164), (165),
% 203.86/34.71  | | | |            (167), (168), (172), (174), (176), (177), (178), (179),
% 203.86/34.71  | | | |            (188), (192), (195), (196), (197), (198), (202), (203), (204)
% 203.86/34.71  | | | |            are inconsistent by sub-proof #664.
% 203.86/34.71  | | | | 
% 203.86/34.71  | | | End of split
% 203.86/34.71  | | | 
% 203.86/34.71  | | End of split
% 203.86/34.71  | | 
% 203.86/34.71  | Case 2:
% 203.86/34.71  | | 
% 203.86/34.71  | |   (205)  all_30_1 = e3
% 203.86/34.71  | | 
% 203.86/34.71  | | COMBINE_EQS: (140), (205) imply:
% 203.86/34.71  | |   (206)  all_10_1 = e3
% 203.86/34.71  | | 
% 203.86/34.71  | | SIMP: (206) implies:
% 203.86/34.71  | |   (207)  all_10_1 = e3
% 203.86/34.71  | | 
% 203.86/34.71  | | REDUCE: (46), (207) imply:
% 203.86/34.71  | |   (208)  op(all_10_2, e1) = e3
% 203.86/34.71  | | 
% 203.86/34.71  | | REDUCE: (60), (207) imply:
% 203.86/34.71  | |   (209)  op(e1, e3) = all_10_0
% 203.86/34.71  | | 
% 203.86/34.71  | | GROUND_INST: instantiating (5) with all_52_5, all_10_0, e3, e1, simplifying
% 203.86/34.71  | |              with (36), (209) gives:
% 203.86/34.71  | |   (210)  all_52_5 = all_10_0
% 203.86/34.71  | | 
% 203.86/34.71  | | COMBINE_EQS: (136), (210) imply:
% 203.86/34.71  | |   (211)  all_58_6 = all_10_0
% 203.86/34.71  | | 
% 203.86/34.71  | | BETA: splitting (94) gives:
% 203.86/34.71  | | 
% 203.86/34.71  | | Case 1:
% 203.86/34.71  | | | 
% 203.86/34.71  | | |   (212)  all_58_15 = e0
% 203.86/34.71  | | | 
% 203.86/34.72  | | | REF_CLOSE: (5), (9), (19), (49), (101), (129), (133), (212) are
% 203.86/34.72  | | |            inconsistent by sub-proof #678.
% 203.86/34.72  | | | 
% 203.86/34.72  | | Case 2:
% 203.86/34.72  | | | 
% 203.86/34.72  | | |   (213)   ~ (all_58_15 = e0)
% 203.86/34.72  | | |   (214)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 203.86/34.72  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.86/34.72  | | | 
% 203.86/34.72  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15),
% 203.86/34.72  | | |            (16), (17), (18), (21), (22), (26), (27), (28), (29), (30),
% 203.86/34.72  | | |            (31), (32), (33), (34), (35), (36), (38), (39), (40), (41),
% 203.86/34.72  | | |            (42), (43), (45), (46), (47), (48), (49), (50), (51), (52),
% 203.86/34.72  | | |            (53), (55), (57), (59), (61), (62), (63), (64), (65), (66),
% 203.86/34.72  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (77),
% 203.86/34.72  | | |            (79), (80), (82), (84), (85), (86), (87), (88), (91), (92),
% 203.86/34.72  | | |            (93), (95), (96), (97), (99), (100), (101), (102), (103),
% 203.86/34.72  | | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 203.86/34.72  | | |            (115), (116), (117), (118), (120), (121), (122), (123), (124),
% 203.86/34.72  | | |            (125), (127), (128), (129), (130), (132), (134), (135), (136),
% 203.86/34.72  | | |            (138), (139), (141), (142), (143), (144), (145), (146), (149),
% 203.86/34.72  | | |            (150), (151), (152), (153), (155), (156), (157), (158), (159),
% 203.86/34.72  | | |            (160), (161), (162), (164), (165), (167), (168), (170), (172),
% 203.86/34.72  | | |            (174), (176), (177), (178), (179), (208), (211), (213), (214)
% 203.86/34.72  | | |            are inconsistent by sub-proof #773.
% 203.86/34.72  | | | 
% 203.86/34.72  | | End of split
% 203.86/34.72  | | 
% 203.86/34.72  | End of split
% 203.86/34.72  | 
% 203.86/34.72  End of proof
% 203.86/34.72  
% 203.86/34.72  Sub-proof #664 shows that the following formulas are inconsistent:
% 203.86/34.72  ----------------------------------------------------------------
% 203.86/34.72    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.72    (2)   ~ (all_52_15 = all_52_23)
% 203.86/34.72    (3)   ~ (all_52_25 = all_6_0)
% 203.86/34.72    (4)   ~ (all_52_25 = all_52_27)
% 203.86/34.72    (5)  all_58_14 = all_52_23
% 203.86/34.72    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.86/34.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.72    (8)  all_58_1 = all_52_9
% 203.86/34.72    (9)   ~ (all_52_9 = all_52_13)
% 203.86/34.72    (10)   ~ (e3 = e0)
% 203.86/34.72    (11)  op(e2, e3) = all_52_3
% 203.86/34.72    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.72    (13)   ~ (all_52_7 = all_52_15)
% 203.86/34.72    (14)   ~ (all_52_3 = all_52_19)
% 203.86/34.72    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.86/34.72    (16)   ~ (all_52_17 = all_52_25)
% 203.86/34.72    (17)   ~ (all_52_3 = all_6_2)
% 203.86/34.72    (18)  all_58_0 = all_6_2
% 203.86/34.72    (19)  op(all_14_2, e0) = all_14_1
% 203.86/34.72    (20)  all_56_4 = all_52_3
% 203.86/34.72    (21)   ~ (all_52_17 = all_10_2)
% 203.86/34.72    (22)  all_40_2 = all_10_2
% 203.86/34.72    (23)  op(e3, e0) = all_52_25
% 203.86/34.72    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.86/34.72    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.86/34.72    (26)   ~ (all_52_27 = all_52_29)
% 203.86/34.72    (27)  all_58_13 = all_52_15
% 203.86/34.72    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.72    (29)  all_58_9 = all_52_25
% 203.86/34.72    (30)   ~ (all_52_29 = all_14_2)
% 203.86/34.72    (31)  all_22_0 = all_6_0
% 203.86/34.72    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.86/34.72    (33)   ~ (all_52_17 = all_6_0)
% 203.86/34.72    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.86/34.72    (35)  op(e1, e3) = all_52_5
% 203.86/34.72    (36)  op(e2, e2) = all_4_2
% 203.86/34.72    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.86/34.72    (38)  all_58_7 = all_10_0
% 203.86/34.72    (39)   ~ (all_52_3 = all_52_5)
% 203.86/34.72    (40)  all_58_11 = all_52_29
% 203.86/34.72    (41)  all_56_5 = all_4_2
% 203.86/34.72    (42)   ~ (all_52_25 = all_14_2)
% 203.86/34.72    (43)   ~ (all_52_3 = all_52_27)
% 203.86/34.72    (44)  op(all_10_2, e1) = all_10_1
% 203.86/34.72    (45)  op(all_6_2, all_6_2) = all_52_0
% 203.86/34.72    (46)   ~ (all_52_7 = all_6_2)
% 203.86/34.72    (47)  op(e0, e0) = all_14_2
% 203.86/34.72    (48)  all_56_15 = all_14_2
% 203.86/34.72    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.72    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.86/34.72    (51)  all_56_11 = all_52_29
% 203.86/34.72    (52)   ~ (all_10_0 = e2)
% 203.86/34.72    (53)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.72    (54)   ~ (e2 = e1)
% 203.86/34.72    (55)   ~ (all_6_0 = e1)
% 203.86/34.72    (56)  all_58_10 = all_52_27
% 203.86/34.72    (57)  all_56_8 = all_52_5
% 203.86/34.72    (58)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.72    (59)   ~ (all_52_19 = all_52_23)
% 203.86/34.72    (60)  all_56_9 = all_10_0
% 203.86/34.72    (61)   ~ (all_52_25 = all_52_29)
% 203.86/34.72    (62)  op(all_6_2, e3) = e2
% 203.86/34.72    (63)   ~ (all_52_29 = all_10_2)
% 203.86/34.72    (64)  all_58_7 = all_52_13
% 203.86/34.72    (65)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.72    (66)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.72    (67)  all_58_1 = all_6_0
% 203.86/34.72    (68)   ~ (all_52_5 = all_52_7)
% 203.86/34.72    (69)  all_58_12 = all_52_7
% 203.86/34.72    (70)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.72    (71)   ~ (all_52_7 = all_14_2)
% 203.86/34.72    (72)   ~ (all_14_2 = e0)
% 203.86/34.72    (73)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.86/34.72    (74)  all_58_2 = all_52_3
% 203.86/34.72    (75)  all_56_2 = all_52_17
% 203.86/34.72    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.72    (77)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.86/34.72    (78)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 203.86/34.72    (79)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.72    (80)   ~ (e2 = e0)
% 203.86/34.72    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.86/34.72    (82)  op(all_6_0, all_6_0) = all_52_8
% 203.86/34.72    (83)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.86/34.72    (84)   ~ (all_52_5 = all_52_29)
% 203.86/34.72    (85)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.72    (86)   ~ (all_52_19 = all_52_27)
% 203.86/34.72    (87)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.86/34.72    (88)   ~ (all_6_0 = e2)
% 203.86/34.72    (89)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.86/34.72    (90)  op(e3, e1) = all_52_17
% 203.86/34.72    (91)   ~ (all_10_0 = all_6_0)
% 203.86/34.72    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.86/34.72    (93)  op(e0, e3) = all_52_7
% 203.86/34.72    (94)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.72    (95)   ~ (all_52_9 = all_52_25)
% 203.86/34.72    (96)  all_58_15 = all_14_2
% 203.86/34.72    (97)   ~ (all_52_19 = all_10_2)
% 203.86/34.72    (98)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.72    (99)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.72    (100)  all_58_8 = all_10_2
% 203.86/34.72    (101)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.72    (102)   ~ (all_52_5 = all_10_2)
% 203.86/34.72    (103)  op(all_52_29, all_52_29) = all_52_28
% 203.86/34.72    (104)   ~ (all_52_23 = all_14_2)
% 203.86/34.72    (105)  all_56_12 = all_52_7
% 203.86/34.72    (106)  op(all_52_17, all_52_17) = all_52_16
% 203.86/34.72    (107)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.72    (108)   ~ (all_52_25 = all_6_2)
% 203.86/34.72    (109)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.72    (110)   ~ (all_52_9 = all_4_2)
% 203.86/34.72    (111)   ~ (all_52_5 = all_6_2)
% 203.86/34.72    (112)  all_56_0 = all_6_2
% 203.86/34.72    (113)  op(e3, e3) = all_6_2
% 203.86/34.72    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.72    (115)   ~ (all_52_15 = all_6_0)
% 203.86/34.72    (116)   ~ (all_52_27 = all_14_2)
% 203.86/34.72    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.72    (118)  all_56_14 = all_52_23
% 203.86/34.72    (119)  all_40_0 = all_10_0
% 203.86/34.72    (120)  all_56_3 = all_52_25
% 203.86/34.72    (121)   ~ (all_52_3 = all_52_7)
% 203.86/34.72    (122)   ~ (all_6_0 = all_6_2)
% 203.86/34.72    (123)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.72    (124)  all_58_5 = all_52_19
% 203.86/34.72    (125)   ~ (all_52_15 = all_4_2)
% 203.86/34.72    (126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.72           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.86/34.72           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.86/34.72           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.86/34.72    (127)   ~ (all_52_27 = all_4_2)
% 203.86/34.72    (128)  all_58_6 = all_52_5
% 203.86/34.72    (129)  op(all_10_2, e1) = e2
% 203.86/34.72    (130)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.72    (131)   ~ (all_52_17 = all_6_2)
% 203.86/34.72    (132)   ~ (e1 = e0)
% 203.86/34.72    (133)   ~ (e3 = e2)
% 203.86/34.72    (134)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.72    (135)  all_56_10 = all_10_2
% 203.86/34.72    (136)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.86/34.72    (137)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.72    (138)  all_56_1 = all_6_0
% 203.86/34.72    (139)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.86/34.72    (140)  op(all_52_13, all_52_13) = all_52_12
% 203.86/34.72    (141)   ~ (all_6_0 = all_4_2)
% 203.86/34.72    (142)  op(e1, e1) = all_10_2
% 203.86/34.72    (143)   ~ (all_52_23 = all_10_2)
% 203.86/34.72    (144)   ~ (all_52_7 = all_52_23)
% 203.86/34.72    (145)   ~ (all_52_5 = all_10_0)
% 203.86/34.72    (146)  all_58_3 = all_4_2
% 203.86/34.72    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.86/34.72    (148)   ~ (all_52_3 = all_4_2)
% 203.86/34.72    (149)   ~ (all_52_19 = all_4_2)
% 203.86/34.72    (150)   ~ (all_52_17 = all_52_23)
% 203.86/34.72    (151)  op(all_6_2, e3) = all_6_1
% 203.86/34.72    (152)  all_22_2 = all_6_2
% 203.86/34.72    (153)  all_58_4 = all_52_17
% 203.86/34.72    (154)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.86/34.72    (155)  op(all_52_25, all_52_25) = all_52_24
% 203.86/34.72  
% 203.86/34.72  Begin of proof
% 203.86/34.72  | 
% 203.86/34.72  | BETA: splitting (134) gives:
% 203.86/34.72  | 
% 203.86/34.72  | Case 1:
% 203.86/34.72  | | 
% 203.86/34.72  | |   (156)  all_56_1 = e3
% 203.86/34.72  | | 
% 203.86/34.72  | | COMBINE_EQS: (138), (156) imply:
% 203.86/34.72  | |   (157)  all_6_0 = e3
% 203.86/34.72  | | 
% 203.86/34.72  | | COMBINE_EQS: (67), (157) imply:
% 203.86/34.72  | |   (158)  all_58_1 = e3
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (115), (157) imply:
% 203.86/34.72  | |   (159)   ~ (all_52_15 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (33), (157) imply:
% 203.86/34.72  | |   (160)   ~ (all_52_17 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (3), (157) imply:
% 203.86/34.72  | |   (161)   ~ (all_52_25 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (91), (157) imply:
% 203.86/34.72  | |   (162)   ~ (all_10_0 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (122), (157) imply:
% 203.86/34.72  | |   (163)   ~ (all_6_2 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | SIMP: (163) implies:
% 203.86/34.72  | |   (164)   ~ (all_6_2 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (141), (157) imply:
% 203.86/34.72  | |   (165)   ~ (all_4_2 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | SIMP: (165) implies:
% 203.86/34.72  | |   (166)   ~ (all_4_2 = e3)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (55), (157) imply:
% 203.86/34.72  | |   (167)   ~ (e3 = e1)
% 203.86/34.72  | | 
% 203.86/34.72  | | REDUCE: (82), (157) imply:
% 203.86/34.72  | |   (168)  op(e3, e3) = all_52_8
% 203.86/34.72  | | 
% 203.86/34.72  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 203.86/34.72  | |              with (113), (168) gives:
% 203.86/34.72  | |   (169)  all_52_8 = all_6_2
% 203.86/34.72  | | 
% 203.86/34.72  | | BETA: splitting (126) gives:
% 203.86/34.72  | | 
% 203.86/34.72  | | Case 1:
% 203.86/34.72  | | | 
% 203.86/34.72  | | |   (170)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.72  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.86/34.72  | | |            e0)
% 203.86/34.72  | | | 
% 203.86/34.72  | | | BETA: splitting (170) gives:
% 203.86/34.72  | | | 
% 203.86/34.72  | | | Case 1:
% 203.86/34.72  | | | | 
% 203.86/34.72  | | | |   (171)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.86/34.72  | | | | 
% 203.86/34.72  | | | | REF_CLOSE: (6), (7), (15), (18), (24), (36), (45), (47), (49), (69),
% 203.86/34.72  | | | |            (71), (74), (76), (102), (113), (128), (130), (142), (148),
% 203.86/34.72  | | | |            (164), (171) are inconsistent by sub-proof #835.
% 203.86/34.72  | | | | 
% 203.86/34.72  | | | Case 2:
% 203.86/34.72  | | | | 
% 203.86/34.72  | | | |   (172)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.86/34.72  | | | |          e0
% 203.86/34.72  | | | | 
% 203.86/34.72  | | | | REF_CLOSE: (164), (169), (172) are inconsistent by sub-proof #834.
% 203.86/34.72  | | | | 
% 203.86/34.72  | | | End of split
% 203.86/34.72  | | | 
% 203.86/34.72  | | Case 2:
% 203.86/34.72  | | | 
% 203.86/34.72  | | |   (173)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.86/34.72  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.86/34.72  | | |            all_52_30 = e0)
% 203.86/34.72  | | | 
% 203.86/34.72  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 203.86/34.72  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.86/34.72  | | |            (24), (25), (26), (27), (28), (29), (30), (32), (34), (35),
% 203.86/34.72  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 203.86/34.72  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56),
% 203.86/34.72  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 203.86/34.72  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 203.86/34.72  | | |            (79), (80), (81), (83), (84), (85), (86), (87), (89), (90),
% 203.86/34.72  | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.86/34.72  | | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.86/34.72  | | |            (111), (113), (114), (116), (117), (118), (119), (120), (121),
% 203.86/34.72  | | |            (123), (124), (125), (127), (128), (129), (130), (131), (132),
% 203.86/34.72  | | |            (133), (135), (136), (137), (140), (142), (143), (144), (145),
% 203.86/34.72  | | |            (146), (147), (148), (149), (150), (151), (153), (154), (155),
% 203.86/34.72  | | |            (158), (159), (160), (161), (162), (164), (166), (167), (168),
% 203.86/34.72  | | |            (173) are inconsistent by sub-proof #694.
% 203.86/34.72  | | | 
% 203.86/34.72  | | End of split
% 203.86/34.72  | | 
% 203.86/34.72  | Case 2:
% 203.86/34.72  | | 
% 203.86/34.72  | |   (174)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.72  | | 
% 203.86/34.72  | | REF_CLOSE: (7), (11), (17), (31), (45), (55), (62), (78), (88), (112),
% 203.86/34.72  | |            (113), (122), (133), (138), (139), (152), (174) are inconsistent
% 203.86/34.72  | |            by sub-proof #820.
% 203.86/34.72  | | 
% 203.86/34.72  | End of split
% 203.86/34.72  | 
% 203.86/34.72  End of proof
% 203.86/34.72  
% 203.86/34.72  Sub-proof #665 shows that the following formulas are inconsistent:
% 203.86/34.72  ----------------------------------------------------------------
% 203.86/34.72    (1)   ~ (all_52_15 = all_52_23)
% 203.86/34.72    (2)   ~ (all_52_25 = all_52_27)
% 203.86/34.72    (3)  all_58_14 = all_52_23
% 203.86/34.72    (4)   ~ (e3 = e1)
% 203.86/34.72    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.86/34.72    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.86/34.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.72    (8)   ~ (all_52_5 = all_52_13)
% 203.86/34.72    (9)  all_58_1 = all_52_9
% 203.86/34.72    (10)   ~ (all_52_9 = all_52_13)
% 203.86/34.72    (11)   ~ (e3 = e0)
% 203.86/34.72    (12)  op(e2, e3) = all_52_3
% 203.86/34.72    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.72    (14)   ~ (all_52_7 = all_52_15)
% 203.86/34.72    (15)   ~ (all_52_3 = all_52_19)
% 203.86/34.72    (16)  op(all_52_7, all_52_7) = all_52_6
% 203.86/34.72    (17)   ~ (all_52_17 = all_52_25)
% 203.86/34.72    (18)   ~ (all_52_3 = all_6_2)
% 203.86/34.72    (19)  all_58_0 = all_6_2
% 203.86/34.72    (20)  op(all_14_2, e0) = all_14_1
% 203.86/34.72    (21)  all_56_4 = all_52_3
% 203.86/34.72    (22)   ~ (all_52_17 = all_10_2)
% 203.86/34.72    (23)   ~ (all_10_0 = e3)
% 203.86/34.72    (24)  op(e3, e0) = all_52_25
% 203.86/34.72    (25)  op(all_52_5, all_52_5) = all_52_4
% 203.86/34.72    (26)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.86/34.72    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.86/34.72    (28)   ~ (all_52_27 = all_52_29)
% 203.86/34.72    (29)  all_58_13 = all_52_15
% 203.86/34.72    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.72    (31)  all_58_9 = all_52_25
% 203.86/34.72    (32)   ~ (all_6_1 = e1)
% 203.86/34.72    (33)   ~ (all_52_29 = all_14_2)
% 203.86/34.72    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.86/34.72    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.86/34.72    (36)  op(e1, e3) = all_52_5
% 203.86/34.72    (37)  op(e2, e2) = all_4_2
% 203.86/34.72    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.86/34.72    (39)   ~ (all_52_3 = all_52_5)
% 203.86/34.72    (40)  all_58_11 = all_52_29
% 203.86/34.72    (41)  all_56_5 = all_4_2
% 203.86/34.72    (42)   ~ (all_52_25 = all_14_2)
% 203.86/34.72    (43)   ~ (all_52_9 = all_52_15)
% 203.86/34.72    (44)   ~ (all_52_3 = all_52_27)
% 203.86/34.72    (45)  op(all_10_2, e1) = all_10_1
% 203.86/34.72    (46)  op(all_6_2, all_6_2) = all_52_0
% 203.86/34.72    (47)   ~ (all_52_7 = all_6_2)
% 203.86/34.72    (48)  op(e0, e0) = all_14_2
% 203.86/34.72    (49)  all_56_15 = all_14_2
% 203.86/34.72    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.72    (51)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.86/34.72    (52)  all_56_11 = all_52_29
% 203.86/34.72    (53)   ~ (all_10_0 = e2)
% 203.86/34.72    (54)   ~ (all_4_1 = e1)
% 203.86/34.72    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.72    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.72    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.86/34.72    (58)  all_56_9 = all_52_13
% 203.86/34.72    (59)   ~ (e2 = e1)
% 203.86/34.72    (60)   ~ (all_52_13 = all_10_2)
% 203.86/34.72    (61)   ~ (all_6_0 = e1)
% 203.86/34.72    (62)  op(e1, all_10_1) = all_10_0
% 203.86/34.72    (63)  all_58_10 = all_52_27
% 203.86/34.72    (64)  all_56_8 = all_52_5
% 203.86/34.72    (65)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.72    (66)  op(all_52_15, all_52_15) = all_52_14
% 203.86/34.72    (67)   ~ (all_52_19 = all_52_23)
% 203.86/34.72    (68)   ~ (all_52_25 = all_52_29)
% 203.86/34.72    (69)   ~ (all_52_29 = all_10_2)
% 203.86/34.72    (70)  all_58_7 = all_52_13
% 203.86/34.72    (71)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 203.86/34.72    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.72    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.72    (74)   ~ (all_52_5 = all_52_7)
% 203.86/34.72    (75)  all_58_12 = all_52_7
% 203.86/34.72    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.72    (77)   ~ (all_52_7 = all_14_2)
% 203.86/34.72    (78)  all_30_2 = all_10_2
% 203.86/34.72    (79)  all_58_2 = all_52_3
% 203.86/34.72    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.72    (81)  all_56_2 = all_52_17
% 203.86/34.72    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.72    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.72    (84)  op(e3, all_6_1) = all_6_0
% 203.86/34.72    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.86/34.72    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.72    (87)  all_56_7 = all_52_27
% 203.86/34.72    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.72    (89)   ~ (e2 = e0)
% 203.86/34.72    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.86/34.72    (91)  op(all_4_2, e2) = all_4_1
% 203.86/34.72    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.86/34.72    (93)   ~ (all_52_5 = all_52_29)
% 203.86/34.72    (94)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.72    (95)  all_56_6 = all_52_19
% 203.86/34.72    (96)   ~ (all_52_15 = all_14_2)
% 203.86/34.72    (97)   ~ (all_52_19 = all_52_27)
% 203.86/34.72    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.86/34.72    (99)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.86/34.72    (100)   ~ (all_6_0 = e2)
% 203.86/34.72    (101)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.86/34.72             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.86/34.72    (102)   ~ (all_52_13 = all_4_2)
% 203.86/34.72    (103)  op(e3, e1) = all_52_17
% 203.86/34.72    (104)  all_30_0 = all_10_0
% 203.86/34.72    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.86/34.72    (106)  op(e0, e3) = all_52_7
% 203.86/34.72    (107)  op(e1, e2) = all_52_13
% 203.86/34.72    (108)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.72    (109)   ~ (all_52_9 = all_52_25)
% 203.86/34.72    (110)  all_58_15 = all_14_2
% 203.86/34.72    (111)   ~ (all_52_19 = all_10_2)
% 203.86/34.72    (112)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.72    (113)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.72    (114)  all_58_8 = all_10_2
% 203.86/34.72    (115)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.72    (116)   ~ (all_52_5 = all_10_2)
% 203.86/34.72    (117)  op(all_52_29, all_52_29) = all_52_28
% 203.86/34.72    (118)   ~ (all_52_23 = all_14_2)
% 203.86/34.72    (119)  all_56_12 = all_52_7
% 203.86/34.72    (120)  op(all_52_17, all_52_17) = all_52_16
% 203.86/34.72    (121)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.72    (122)   ~ (all_52_25 = all_6_2)
% 203.86/34.72    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.72    (124)   ~ (all_52_9 = all_4_2)
% 203.86/34.72    (125)   ~ (all_52_5 = all_6_2)
% 203.86/34.72    (126)   ~ (all_52_9 = all_6_2)
% 203.86/34.73    (127)   ~ (all_52_13 = all_52_15)
% 203.86/34.73    (128)  all_56_0 = all_6_2
% 203.86/34.73    (129)  op(e3, e3) = all_6_2
% 203.86/34.73    (130)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.73    (131)   ~ (all_52_27 = all_14_2)
% 203.86/34.73    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.73    (133)  all_56_14 = all_52_23
% 203.86/34.73    (134)  op(all_4_2, all_4_2) = all_52_10
% 203.86/34.73    (135)  all_56_3 = all_52_25
% 203.86/34.73    (136)   ~ (all_52_3 = all_52_7)
% 203.86/34.73    (137)  all_10_1 = e3
% 203.86/34.73    (138)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.73    (139)  all_58_5 = all_52_19
% 203.86/34.73    (140)  all_56_1 = all_52_9
% 203.86/34.73    (141)   ~ (all_52_15 = all_4_2)
% 203.86/34.73    (142)  op(e0, all_14_1) = e3
% 203.86/34.73    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.73           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.86/34.73           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.86/34.73           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.86/34.73    (144)   ~ (all_52_27 = all_4_2)
% 203.86/34.73    (145)  all_58_6 = all_52_5
% 203.86/34.73    (146)  op(e3, e2) = all_52_9
% 203.86/34.73    (147)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.73    (148)   ~ (all_52_17 = all_6_2)
% 203.86/34.73    (149)   ~ (e1 = e0)
% 203.86/34.73    (150)   ~ (e3 = e2)
% 203.86/34.73    (151)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.73    (152)   ~ (all_52_9 = all_52_17)
% 203.86/34.73    (153)  all_56_10 = all_10_2
% 203.86/34.73    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.86/34.73    (155)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.73    (156)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.86/34.73    (157)  op(all_52_13, all_52_13) = all_52_12
% 203.86/34.73    (158)   ~ (all_6_1 = e2)
% 203.86/34.73    (159)  op(e1, e1) = all_10_2
% 203.86/34.73    (160)   ~ (all_52_23 = all_10_2)
% 203.86/34.73    (161)   ~ (all_52_7 = all_52_23)
% 203.86/34.73    (162)   ~ (all_52_17 = all_52_19)
% 203.86/34.73    (163)  all_58_3 = all_4_2
% 203.86/34.73    (164)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.86/34.73    (165)  all_56_13 = all_52_15
% 203.86/34.73    (166)   ~ (all_52_3 = all_4_2)
% 203.86/34.73    (167)   ~ (all_52_19 = all_4_2)
% 203.86/34.73    (168)   ~ (all_52_17 = all_52_23)
% 203.86/34.73    (169)  op(all_6_2, e3) = all_6_1
% 203.86/34.73    (170)   ~ (all_52_13 = all_52_29)
% 203.86/34.73    (171)  all_58_4 = all_52_17
% 203.86/34.73    (172)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.86/34.73    (173)  op(all_52_25, all_52_25) = all_52_24
% 203.86/34.73  
% 203.86/34.73  Begin of proof
% 203.86/34.73  | 
% 203.86/34.73  | REDUCE: (45), (137) imply:
% 203.86/34.73  |   (174)  op(all_10_2, e1) = e3
% 203.86/34.73  | 
% 203.86/34.73  | REDUCE: (62), (137) imply:
% 203.86/34.73  |   (175)  op(e1, e3) = all_10_0
% 203.86/34.73  | 
% 203.86/34.73  | GROUND_INST: instantiating (7) with all_52_5, all_10_0, e3, e1, simplifying
% 203.86/34.73  |              with (36), (175) gives:
% 203.86/34.73  |   (176)  all_52_5 = all_10_0
% 203.86/34.73  | 
% 203.86/34.73  | COMBINE_EQS: (64), (176) imply:
% 203.86/34.73  |   (177)  all_56_8 = all_10_0
% 203.86/34.73  | 
% 203.86/34.73  | COMBINE_EQS: (145), (176) imply:
% 203.86/34.73  |   (178)  all_58_6 = all_10_0
% 203.86/34.73  | 
% 203.86/34.73  | REDUCE: (116), (176) imply:
% 203.86/34.73  |   (179)   ~ (all_10_0 = all_10_2)
% 203.86/34.73  | 
% 203.86/34.73  | REDUCE: (25), (176) imply:
% 203.86/34.73  |   (180)  op(all_10_0, all_10_0) = all_52_4
% 203.86/34.73  | 
% 203.86/34.73  | BETA: splitting (101) gives:
% 203.86/34.73  | 
% 203.86/34.73  | Case 1:
% 203.86/34.73  | | 
% 203.86/34.73  | |   (181)  all_58_15 = e0
% 203.86/34.73  | | 
% 203.86/34.73  | | REF_CLOSE: (7), (11), (20), (48), (110), (138), (142), (181) are
% 203.86/34.73  | |            inconsistent by sub-proof #693.
% 203.86/34.73  | | 
% 203.86/34.73  | Case 2:
% 203.86/34.73  | | 
% 203.86/34.73  | |   (182)   ~ (all_58_15 = e0)
% 203.86/34.73  | |   (183)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 203.86/34.73  | |            | all_58_13 = e0 | all_58_14 = e0)
% 203.86/34.73  | | 
% 203.86/34.73  | | ALPHA: (183) implies:
% 203.86/34.73  | |   (184)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.86/34.73  | |   (185)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.73  | | 
% 203.86/34.73  | | REDUCE: (110), (182) imply:
% 203.86/34.73  | |   (186)   ~ (all_14_2 = e0)
% 203.86/34.73  | | 
% 203.86/34.73  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.86/34.73  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.86/34.73  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.86/34.73  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 203.86/34.73  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 203.86/34.73  | |            (57), (58), (59), (60), (61), (63), (64), (65), (66), (67), (68),
% 203.86/34.73  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.86/34.73  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 203.86/34.73  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 203.86/34.73  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.86/34.73  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 203.86/34.73  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 203.86/34.73  | |            (129), (130), (131), (132), (133), (134), (135), (136), (138),
% 203.86/34.73  | |            (139), (140), (141), (143), (144), (145), (146), (147), (148),
% 203.86/34.73  | |            (149), (150), (151), (152), (153), (154), (155), (156), (157),
% 203.86/34.73  | |            (158), (159), (160), (161), (162), (163), (164), (165), (166),
% 203.86/34.73  | |            (167), (168), (169), (170), (171), (172), (173), (174), (177),
% 203.86/34.73  | |            (178), (179), (180), (184), (185), (186) are inconsistent by
% 203.86/34.73  | |            sub-proof #666.
% 203.86/34.73  | | 
% 203.86/34.73  | End of split
% 203.86/34.73  | 
% 203.86/34.73  End of proof
% 203.86/34.73  
% 203.86/34.73  Sub-proof #666 shows that the following formulas are inconsistent:
% 203.86/34.73  ----------------------------------------------------------------
% 203.86/34.73    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.86/34.73    (2)   ~ (all_52_15 = all_52_23)
% 203.86/34.73    (3)   ~ (all_52_25 = all_52_27)
% 203.86/34.73    (4)  all_58_14 = all_52_23
% 203.86/34.73    (5)   ~ (e3 = e1)
% 203.86/34.73    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.86/34.73    (7)  op(all_52_3, all_52_3) = all_52_2
% 203.86/34.73    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.73    (9)   ~ (all_52_5 = all_52_13)
% 203.86/34.73    (10)  all_58_1 = all_52_9
% 203.86/34.73    (11)   ~ (all_52_9 = all_52_13)
% 203.86/34.73    (12)   ~ (e3 = e0)
% 203.86/34.73    (13)  op(e2, e3) = all_52_3
% 203.86/34.73    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.73    (15)   ~ (all_52_7 = all_52_15)
% 203.86/34.73    (16)   ~ (all_52_3 = all_52_19)
% 203.86/34.73    (17)  op(all_52_7, all_52_7) = all_52_6
% 203.86/34.73    (18)   ~ (all_52_17 = all_52_25)
% 203.86/34.73    (19)   ~ (all_52_3 = all_6_2)
% 203.86/34.73    (20)  all_58_0 = all_6_2
% 203.86/34.73    (21)  op(all_14_2, e0) = all_14_1
% 203.86/34.73    (22)  all_56_4 = all_52_3
% 203.86/34.73    (23)   ~ (all_52_17 = all_10_2)
% 203.86/34.73    (24)   ~ (all_10_0 = e3)
% 203.86/34.73    (25)  op(e3, e0) = all_52_25
% 203.86/34.73    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.86/34.73    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.86/34.73    (28)  op(all_52_19, all_52_19) = all_52_18
% 203.86/34.73    (29)   ~ (all_52_27 = all_52_29)
% 203.86/34.73    (30)  all_58_13 = all_52_15
% 203.86/34.73    (31)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.73    (32)  all_58_9 = all_52_25
% 203.86/34.73    (33)   ~ (all_6_1 = e1)
% 203.86/34.73    (34)   ~ (all_52_29 = all_14_2)
% 203.86/34.73    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.86/34.73    (36)  op(all_52_27, all_52_27) = all_52_26
% 203.86/34.73    (37)  op(e1, e3) = all_52_5
% 203.86/34.73    (38)  op(e2, e2) = all_4_2
% 203.86/34.73    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.86/34.73    (40)   ~ (all_52_3 = all_52_5)
% 203.86/34.73    (41)  all_58_11 = all_52_29
% 203.86/34.73    (42)  all_56_5 = all_4_2
% 203.86/34.73    (43)   ~ (all_52_25 = all_14_2)
% 203.86/34.73    (44)   ~ (all_52_9 = all_52_15)
% 203.86/34.73    (45)   ~ (all_52_3 = all_52_27)
% 203.86/34.73    (46)  op(all_10_2, e1) = all_10_1
% 203.86/34.73    (47)  op(all_6_2, all_6_2) = all_52_0
% 203.86/34.73    (48)   ~ (all_52_7 = all_6_2)
% 203.86/34.73    (49)  op(e0, e0) = all_14_2
% 203.86/34.73    (50)  all_56_15 = all_14_2
% 203.86/34.73    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.73    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.86/34.73    (53)  all_56_11 = all_52_29
% 203.86/34.73    (54)   ~ (all_10_0 = e2)
% 203.86/34.73    (55)   ~ (all_4_1 = e1)
% 203.86/34.73    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.73    (57)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.73    (58)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.86/34.73    (59)  all_56_9 = all_52_13
% 203.86/34.73    (60)   ~ (e2 = e1)
% 203.86/34.73    (61)   ~ (all_52_13 = all_10_2)
% 203.86/34.73    (62)   ~ (all_6_0 = e1)
% 203.86/34.73    (63)  all_58_10 = all_52_27
% 203.86/34.73    (64)  all_56_8 = all_52_5
% 203.86/34.73    (65)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.73    (66)  op(all_52_15, all_52_15) = all_52_14
% 203.86/34.73    (67)   ~ (all_52_19 = all_52_23)
% 203.86/34.73    (68)   ~ (all_52_25 = all_52_29)
% 203.86/34.73    (69)   ~ (all_52_29 = all_10_2)
% 203.86/34.73    (70)  op(all_10_2, e1) = e3
% 203.86/34.73    (71)  all_58_7 = all_52_13
% 203.86/34.73    (72)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 203.86/34.73    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.73    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.73    (75)   ~ (all_52_5 = all_52_7)
% 203.86/34.73    (76)  all_58_12 = all_52_7
% 203.86/34.73    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.73    (78)   ~ (all_52_7 = all_14_2)
% 203.86/34.73    (79)   ~ (all_14_2 = e0)
% 203.86/34.73    (80)  all_30_2 = all_10_2
% 203.86/34.73    (81)  all_58_2 = all_52_3
% 203.86/34.73    (82)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.73    (83)  all_56_2 = all_52_17
% 203.86/34.73    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.73    (85)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.73    (86)  op(e3, all_6_1) = all_6_0
% 203.86/34.73    (87)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.86/34.73    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.73    (89)  all_56_7 = all_52_27
% 203.86/34.73    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.73    (91)   ~ (e2 = e0)
% 203.86/34.73    (92)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.86/34.73    (93)  op(all_4_2, e2) = all_4_1
% 203.86/34.73    (94)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.86/34.73    (95)   ~ (all_52_5 = all_52_29)
% 203.86/34.73    (96)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.86/34.73    (97)  all_56_6 = all_52_19
% 203.86/34.73    (98)  all_56_8 = all_10_0
% 203.86/34.73    (99)   ~ (all_52_15 = all_14_2)
% 203.86/34.73    (100)   ~ (all_52_19 = all_52_27)
% 203.86/34.73    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.86/34.73    (102)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.86/34.73    (103)   ~ (all_6_0 = e2)
% 203.86/34.73    (104)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.86/34.73    (105)   ~ (all_52_13 = all_4_2)
% 203.86/34.73    (106)  op(e3, e1) = all_52_17
% 203.86/34.73    (107)  all_30_0 = all_10_0
% 203.86/34.73    (108)  all_58_6 = all_10_0
% 203.86/34.73    (109)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.86/34.73    (110)  op(e0, e3) = all_52_7
% 203.86/34.73    (111)  op(e1, e2) = all_52_13
% 203.86/34.73    (112)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.86/34.73    (113)   ~ (all_52_9 = all_52_25)
% 203.86/34.73    (114)  all_58_15 = all_14_2
% 203.86/34.73    (115)   ~ (all_52_19 = all_10_2)
% 203.86/34.73    (116)  op(all_52_23, all_52_23) = all_52_22
% 203.86/34.73    (117)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.73    (118)   ~ (all_10_0 = all_10_2)
% 203.86/34.73    (119)  all_58_8 = all_10_2
% 203.86/34.73    (120)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.86/34.73    (121)   ~ (all_52_5 = all_10_2)
% 203.86/34.73    (122)  op(all_52_29, all_52_29) = all_52_28
% 203.86/34.73    (123)   ~ (all_52_23 = all_14_2)
% 203.86/34.73    (124)  all_56_12 = all_52_7
% 203.86/34.73    (125)  op(all_52_17, all_52_17) = all_52_16
% 203.86/34.73    (126)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.73    (127)   ~ (all_52_25 = all_6_2)
% 203.86/34.73    (128)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.86/34.73    (129)   ~ (all_52_9 = all_4_2)
% 203.86/34.73    (130)   ~ (all_52_5 = all_6_2)
% 203.86/34.73    (131)   ~ (all_52_9 = all_6_2)
% 203.86/34.73    (132)   ~ (all_52_13 = all_52_15)
% 203.86/34.73    (133)  all_56_0 = all_6_2
% 203.86/34.73    (134)  op(e3, e3) = all_6_2
% 203.86/34.73    (135)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.86/34.73    (136)   ~ (all_52_27 = all_14_2)
% 203.86/34.73    (137)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.86/34.73    (138)  all_56_14 = all_52_23
% 203.86/34.73    (139)  op(all_4_2, all_4_2) = all_52_10
% 203.86/34.73    (140)  all_56_3 = all_52_25
% 203.86/34.73    (141)   ~ (all_52_3 = all_52_7)
% 203.86/34.73    (142)  op(all_14_2, all_14_2) = all_52_30
% 203.86/34.73    (143)  all_58_5 = all_52_19
% 203.86/34.73    (144)  op(all_10_0, all_10_0) = all_52_4
% 203.86/34.73    (145)  all_56_1 = all_52_9
% 203.86/34.73    (146)   ~ (all_52_15 = all_4_2)
% 203.86/34.73    (147)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.73           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.86/34.73           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.86/34.73           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.86/34.73    (148)   ~ (all_52_27 = all_4_2)
% 203.86/34.73    (149)  all_58_6 = all_52_5
% 203.86/34.73    (150)  op(e3, e2) = all_52_9
% 203.86/34.73    (151)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.86/34.73    (152)   ~ (all_52_17 = all_6_2)
% 203.86/34.73    (153)   ~ (e1 = e0)
% 203.86/34.73    (154)   ~ (e3 = e2)
% 203.86/34.73    (155)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.86/34.73    (156)   ~ (all_52_9 = all_52_17)
% 203.86/34.73    (157)  all_56_10 = all_10_2
% 203.86/34.73    (158)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.86/34.73    (159)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.86/34.73    (160)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.86/34.73    (161)  op(all_52_13, all_52_13) = all_52_12
% 203.86/34.73    (162)   ~ (all_6_1 = e2)
% 203.86/34.73    (163)  op(e1, e1) = all_10_2
% 203.86/34.73    (164)   ~ (all_52_23 = all_10_2)
% 203.86/34.73    (165)   ~ (all_52_7 = all_52_23)
% 203.86/34.73    (166)   ~ (all_52_17 = all_52_19)
% 203.86/34.73    (167)  all_58_3 = all_4_2
% 203.86/34.73    (168)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.86/34.73    (169)  all_56_13 = all_52_15
% 203.86/34.73    (170)   ~ (all_52_3 = all_4_2)
% 203.86/34.73    (171)   ~ (all_52_19 = all_4_2)
% 203.86/34.73    (172)   ~ (all_52_17 = all_52_23)
% 203.86/34.73    (173)  op(all_6_2, e3) = all_6_1
% 203.86/34.73    (174)   ~ (all_52_13 = all_52_29)
% 203.86/34.73    (175)  all_58_4 = all_52_17
% 203.86/34.73    (176)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.86/34.73    (177)  op(all_52_25, all_52_25) = all_52_24
% 203.86/34.73  
% 203.86/34.73  Begin of proof
% 203.86/34.73  | 
% 203.86/34.73  | BETA: splitting (117) gives:
% 203.86/34.73  | 
% 203.86/34.73  | Case 1:
% 203.86/34.73  | | 
% 203.86/34.73  | |   (178)  all_56_8 = e3
% 203.86/34.73  | | 
% 203.86/34.73  | | REF_CLOSE: (24), (98), (178) are inconsistent by sub-proof #926.
% 203.86/34.73  | | 
% 203.86/34.73  | Case 2:
% 203.86/34.73  | | 
% 203.86/34.73  | |   (179)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.73  | | 
% 203.86/34.73  | | BETA: splitting (147) gives:
% 203.86/34.73  | | 
% 203.86/34.73  | | Case 1:
% 203.86/34.73  | | | 
% 203.86/34.73  | | |   (180)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.86/34.73  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.86/34.73  | | |            e0)
% 203.86/34.73  | | | 
% 203.86/34.73  | | | BETA: splitting (180) gives:
% 203.86/34.73  | | | 
% 203.86/34.73  | | | Case 1:
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | |   (181)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | | REF_CLOSE: (8), (23), (54), (70), (72), (80), (98), (106), (107), (108),
% 203.86/34.73  | | | |            (118), (126), (144), (157), (163), (176), (179), (181) are
% 203.86/34.73  | | | |            inconsistent by sub-proof #667.
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | Case 2:
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | |   (182)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.86/34.73  | | | |          e0
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 203.86/34.73  | | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 203.86/34.73  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.86/34.73  | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (45), (47),
% 203.86/34.73  | | | |            (48), (49), (50), (51), (53), (55), (56), (57), (58), (59),
% 203.86/34.73  | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (71),
% 203.86/34.73  | | | |            (74), (75), (76), (77), (78), (79), (81), (82), (83), (84),
% 203.86/34.73  | | | |            (85), (86), (88), (89), (90), (91), (92), (93), (95), (96),
% 203.86/34.73  | | | |            (97), (99), (100), (101), (102), (103), (104), (105), (110),
% 203.86/34.73  | | | |            (111), (112), (113), (114), (115), (116), (117), (119),
% 203.86/34.73  | | | |            (120), (121), (122), (123), (124), (125), (127), (128),
% 203.86/34.73  | | | |            (129), (130), (131), (133), (134), (135), (136), (137),
% 203.86/34.73  | | | |            (139), (140), (141), (142), (143), (145), (146), (148),
% 203.86/34.73  | | | |            (149), (150), (151), (152), (153), (154), (155), (156),
% 203.86/34.73  | | | |            (157), (158), (159), (160), (161), (162), (163), (164),
% 203.86/34.73  | | | |            (165), (166), (167), (169), (170), (171), (172), (173),
% 203.86/34.73  | | | |            (174), (175), (176), (177), (182) are inconsistent by
% 203.86/34.73  | | | |            sub-proof #731.
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | End of split
% 203.86/34.73  | | | 
% 203.86/34.73  | | Case 2:
% 203.86/34.73  | | | 
% 203.86/34.73  | | |   (183)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.86/34.73  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.86/34.73  | | |            all_52_30 = e0)
% 203.86/34.73  | | | 
% 203.86/34.73  | | | BETA: splitting (183) gives:
% 203.86/34.73  | | | 
% 203.86/34.73  | | | Case 1:
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | |   (184)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.86/34.73  | | | |          e0
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 203.86/34.73  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (25), (26),
% 203.86/34.73  | | | |            (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 203.86/34.73  | | | |            (40), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 203.86/34.73  | | | |            (51), (53), (56), (57), (58), (59), (60), (61), (62), (63),
% 203.86/34.73  | | | |            (64), (65), (67), (68), (69), (71), (75), (76), (77), (78),
% 203.86/34.73  | | | |            (81), (82), (83), (84), (85), (86), (87), (88), (90), (91),
% 203.86/34.73  | | | |            (94), (95), (96), (97), (99), (100), (101), (102), (103),
% 203.86/34.73  | | | |            (104), (105), (106), (110), (112), (113), (114), (115),
% 203.86/34.73  | | | |            (116), (117), (119), (120), (121), (122), (123), (124),
% 203.86/34.73  | | | |            (125), (127), (128), (129), (130), (131), (132), (133),
% 203.86/34.73  | | | |            (134), (136), (137), (139), (140), (141), (142), (143),
% 203.86/34.73  | | | |            (145), (148), (149), (151), (152), (153), (154), (155),
% 203.86/34.73  | | | |            (156), (157), (158), (159), (160), (161), (162), (163),
% 203.86/34.73  | | | |            (165), (166), (167), (168), (169), (170), (173), (174),
% 203.86/34.73  | | | |            (175), (176), (177), (184) are inconsistent by sub-proof
% 203.86/34.73  | | | |            #1042.
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | Case 2:
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | |   (185)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.86/34.73  | | | |          e0
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (13), (14), (15),
% 203.86/34.73  | | | |            (17), (18), (19), (20), (22), (23), (25), (26), (28), (29),
% 203.86/34.73  | | | |            (30), (32), (33), (34), (36), (37), (38), (40), (41), (42),
% 203.86/34.73  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 203.86/34.73  | | | |            (53), (56), (57), (58), (62), (63), (64), (65), (66), (67),
% 203.86/34.73  | | | |            (68), (69), (71), (73), (74), (75), (76), (77), (78), (79),
% 203.86/34.73  | | | |            (81), (83), (85), (86), (87), (88), (90), (92), (95), (99),
% 203.86/34.73  | | | |            (100), (101), (102), (103), (104), (105), (106), (109),
% 203.86/34.73  | | | |            (110), (112), (113), (114), (115), (116), (117), (119),
% 203.86/34.73  | | | |            (120), (121), (122), (123), (124), (125), (126), (127),
% 203.86/34.73  | | | |            (128), (129), (130), (131), (132), (133), (134), (135),
% 203.86/34.73  | | | |            (136), (137), (138), (140), (141), (142), (143), (145),
% 203.86/34.73  | | | |            (146), (148), (149), (151), (152), (154), (155), (160),
% 203.86/34.73  | | | |            (161), (162), (163), (165), (166), (167), (168), (169),
% 203.86/34.73  | | | |            (170), (171), (172), (173), (175), (177), (185) are
% 203.86/34.73  | | | |            inconsistent by sub-proof #1008.
% 203.86/34.73  | | | | 
% 203.86/34.73  | | | End of split
% 203.86/34.73  | | | 
% 203.86/34.73  | | End of split
% 203.86/34.73  | | 
% 203.86/34.73  | End of split
% 203.86/34.73  | 
% 203.86/34.73  End of proof
% 203.86/34.73  
% 203.86/34.73  Sub-proof #667 shows that the following formulas are inconsistent:
% 203.86/34.73  ----------------------------------------------------------------
% 203.86/34.73    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.73    (2)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.86/34.73    (3)   ~ (all_52_17 = all_10_2)
% 203.86/34.73    (4)   ~ (all_10_0 = e2)
% 203.86/34.73    (5)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.86/34.73    (6)  op(all_10_2, e1) = e3
% 203.86/34.73    (7)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 203.86/34.73    (8)  all_30_2 = all_10_2
% 203.86/34.73    (9)  all_56_8 = all_10_0
% 203.86/34.73    (10)  op(e3, e1) = all_52_17
% 203.86/34.73    (11)  all_30_0 = all_10_0
% 203.86/34.73    (12)  all_58_6 = all_10_0
% 203.86/34.73    (13)   ~ (all_10_0 = all_10_2)
% 203.86/34.73    (14)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.86/34.73    (15)  op(all_10_0, all_10_0) = all_52_4
% 203.86/34.73    (16)  all_56_10 = all_10_2
% 203.86/34.73    (17)  op(e1, e1) = all_10_2
% 203.86/34.73    (18)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.86/34.73  
% 203.86/34.73  Begin of proof
% 203.86/34.73  | 
% 203.86/34.73  | ALPHA: (2) implies:
% 203.86/34.73  |   (19)  all_52_4 = e1
% 203.86/34.73  | 
% 203.86/34.73  | REDUCE: (15), (19) imply:
% 203.86/34.73  |   (20)  op(all_10_0, all_10_0) = e1
% 203.86/34.73  | 
% 203.86/34.73  | BETA: splitting (14) gives:
% 203.86/34.73  | 
% 203.86/34.73  | Case 1:
% 203.86/34.73  | | 
% 203.86/34.73  | |   (21)  all_58_6 = e1
% 203.86/34.73  | | 
% 203.86/34.73  | | COMBINE_EQS: (12), (21) imply:
% 203.86/34.73  | |   (22)  all_10_0 = e1
% 203.86/34.73  | | 
% 203.86/34.73  | | REF_CLOSE: (1), (13), (17), (20), (22) are inconsistent by sub-proof #990.
% 203.86/34.73  | | 
% 203.86/34.73  | Case 2:
% 203.86/34.73  | | 
% 203.86/34.73  | |   (23)   ~ (all_58_6 = e1)
% 203.86/34.73  | | 
% 203.86/34.73  | | REDUCE: (12), (23) imply:
% 203.86/34.73  | |   (24)   ~ (all_10_0 = e1)
% 203.86/34.73  | | 
% 203.86/34.73  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (16),
% 203.86/34.73  | |            (17), (18), (24) are inconsistent by sub-proof #909.
% 203.86/34.73  | | 
% 203.86/34.73  | End of split
% 203.86/34.73  | 
% 203.86/34.73  End of proof
% 203.86/34.73  
% 203.86/34.73  Sub-proof #668 shows that the following formulas are inconsistent:
% 203.86/34.73  ----------------------------------------------------------------
% 203.86/34.73    (1)   ~ (all_52_15 = all_52_23)
% 203.86/34.73    (2)   ~ (all_52_25 = all_52_27)
% 203.86/34.73    (3)  all_58_14 = all_52_23
% 203.86/34.73    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.86/34.73    (5)  op(all_52_3, all_52_3) = all_52_2
% 203.86/34.74    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.86/34.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.86/34.74    (7)   ~ (all_52_5 = all_52_13)
% 203.86/34.74    (8)  all_58_1 = all_52_9
% 203.86/34.74    (9)   ~ (all_52_9 = all_52_13)
% 203.86/34.74    (10)   ~ (e3 = e0)
% 203.86/34.74    (11)  op(e2, e3) = all_52_3
% 203.86/34.74    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.86/34.74    (13)   ~ (all_52_7 = all_52_15)
% 203.86/34.74    (14)   ~ (all_52_3 = all_52_19)
% 203.86/34.74    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.86/34.74    (16)   ~ (all_52_17 = all_52_25)
% 203.86/34.74    (17)   ~ (all_52_3 = all_6_2)
% 203.86/34.74    (18)  all_58_0 = all_6_2
% 203.86/34.74    (19)  op(all_14_2, e0) = all_14_1
% 203.86/34.74    (20)  all_56_4 = all_52_3
% 203.86/34.74    (21)  all_38_2 = all_4_2
% 203.86/34.74    (22)   ~ (all_52_17 = all_10_2)
% 203.86/34.74    (23)  op(e3, e0) = all_52_25
% 203.86/34.74    (24)  op(all_52_5, all_52_5) = all_52_4
% 203.86/34.74    (25)  op(all_52_19, all_52_19) = all_52_18
% 203.86/34.74    (26)   ~ (all_52_27 = all_52_29)
% 203.86/34.74    (27)  all_58_13 = all_52_15
% 203.86/34.74    (28)  op(all_10_2, all_10_2) = all_52_20
% 203.86/34.74    (29)  all_58_9 = all_52_25
% 203.86/34.74    (30)   ~ (all_6_1 = e1)
% 203.86/34.74    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.86/34.74    (32)   ~ (all_52_29 = all_14_2)
% 203.86/34.74    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.86/34.74    (34)  op(all_52_27, all_52_27) = all_52_26
% 203.86/34.74    (35)  op(e1, e3) = all_52_5
% 203.86/34.74    (36)  all_32_2 = all_4_2
% 203.86/34.74    (37)  op(e2, e2) = all_4_2
% 203.86/34.74    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.86/34.74    (39)   ~ (all_52_3 = all_52_5)
% 203.86/34.74    (40)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 203.86/34.74    (41)  all_58_11 = all_52_29
% 203.86/34.74    (42)  all_56_5 = all_4_2
% 203.86/34.74    (43)   ~ (all_52_25 = all_14_2)
% 203.86/34.74    (44)   ~ (all_52_9 = all_52_15)
% 203.86/34.74    (45)   ~ (all_52_3 = all_52_27)
% 203.86/34.74    (46)  op(all_10_2, e1) = all_10_1
% 203.86/34.74    (47)  op(all_6_2, all_6_2) = all_52_0
% 203.86/34.74    (48)   ~ (all_52_7 = all_6_2)
% 203.86/34.74    (49)  op(e0, e0) = all_14_2
% 203.86/34.74    (50)  all_56_15 = all_14_2
% 203.86/34.74    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.86/34.74    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.86/34.74    (53)  op(e2, all_4_1) = all_4_0
% 203.86/34.74    (54)  all_56_11 = all_52_29
% 203.86/34.74    (55)   ~ (all_4_1 = e1)
% 203.86/34.74    (56)   ~ (all_4_0 = e3)
% 203.86/34.74    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.86/34.74    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.86/34.74    (59)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.86/34.74    (60)  all_56_9 = all_52_13
% 203.86/34.74    (61)   ~ (e2 = e1)
% 203.86/34.74    (62)   ~ (all_52_13 = all_10_2)
% 203.86/34.74    (63)   ~ (all_6_0 = e1)
% 203.86/34.74    (64)  all_58_10 = all_52_27
% 203.86/34.74    (65)  all_56_8 = all_52_5
% 203.86/34.74    (66)  op(all_52_9, all_52_9) = all_52_8
% 203.86/34.74    (67)  op(all_52_15, all_52_15) = all_52_14
% 203.86/34.74    (68)   ~ (all_52_19 = all_52_23)
% 203.86/34.74    (69)   ~ (all_52_25 = all_52_29)
% 203.86/34.74    (70)   ~ (all_52_29 = all_10_2)
% 203.86/34.74    (71)  all_58_7 = all_52_13
% 203.86/34.74    (72)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.86/34.74    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.86/34.74    (74)   ~ (all_52_5 = all_52_7)
% 203.86/34.74    (75)  all_58_12 = all_52_7
% 203.86/34.74    (76)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.86/34.74    (77)   ~ (all_52_7 = all_14_2)
% 203.86/34.74    (78)  all_38_0 = all_4_0
% 203.86/34.74    (79)  all_58_2 = all_52_3
% 203.86/34.74    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.86/34.74    (81)  all_56_2 = all_52_17
% 203.86/34.74    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.86/34.74    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.86/34.74    (84)  all_32_1 = e3
% 203.86/34.74    (85)  op(e3, all_6_1) = all_6_0
% 203.86/34.74    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.86/34.74    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.86/34.74    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.86/34.74    (89)   ~ (e2 = e0)
% 203.86/34.74    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.92/34.74    (91)  op(all_4_2, e2) = all_4_1
% 203.92/34.74    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.92/34.74    (93)   ~ (all_52_5 = all_52_29)
% 203.92/34.74    (94)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.92/34.74    (95)  all_56_6 = all_52_19
% 203.92/34.74    (96)  all_38_1 = all_4_1
% 203.92/34.74    (97)   ~ (all_52_15 = all_14_2)
% 203.92/34.74    (98)   ~ (all_52_19 = all_52_27)
% 203.92/34.74    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.92/34.74    (100)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.92/34.74    (101)   ~ (all_6_0 = e2)
% 203.92/34.74    (102)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 203.92/34.74             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 203.92/34.74    (103)   ~ (all_52_13 = all_4_2)
% 203.92/34.74    (104)  op(e3, e1) = all_52_17
% 203.92/34.74    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.92/34.74    (106)  op(e0, e3) = all_52_7
% 203.92/34.74    (107)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.92/34.74    (108)   ~ (all_52_9 = all_52_25)
% 203.92/34.74    (109)  all_58_15 = all_14_2
% 203.92/34.74    (110)   ~ (all_52_19 = all_10_2)
% 203.92/34.74    (111)  op(all_52_23, all_52_23) = all_52_22
% 203.92/34.74    (112)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.92/34.74    (113)  all_58_8 = all_10_2
% 203.92/34.74    (114)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.92/34.74    (115)   ~ (all_52_5 = all_10_2)
% 203.92/34.74    (116)  op(all_52_29, all_52_29) = all_52_28
% 203.92/34.74    (117)   ~ (all_52_23 = all_14_2)
% 203.92/34.74    (118)  all_56_12 = all_52_7
% 203.92/34.74    (119)  op(all_52_17, all_52_17) = all_52_16
% 203.92/34.74    (120)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.92/34.74    (121)   ~ (all_52_25 = all_6_2)
% 203.92/34.74    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.92/34.74    (123)   ~ (all_52_9 = all_4_2)
% 203.92/34.74    (124)   ~ (all_52_5 = all_6_2)
% 203.92/34.74    (125)  all_32_1 = all_4_1
% 203.92/34.74    (126)   ~ (all_52_9 = all_6_2)
% 203.92/34.74    (127)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 203.92/34.74    (128)   ~ (all_52_13 = all_52_15)
% 203.92/34.74    (129)  all_56_0 = all_6_2
% 203.92/34.74    (130)  op(e3, e3) = all_6_2
% 203.92/34.74    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.92/34.74    (132)   ~ (all_52_27 = all_14_2)
% 203.92/34.74    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.92/34.74    (134)  all_56_14 = all_52_23
% 203.92/34.74    (135)  op(all_4_2, all_4_2) = all_52_10
% 203.92/34.74    (136)  all_32_0 = all_4_0
% 203.92/34.74    (137)  all_56_3 = all_52_25
% 203.92/34.74    (138)   ~ (all_52_3 = all_52_7)
% 203.92/34.74    (139)  op(all_14_2, all_14_2) = all_52_30
% 203.92/34.74    (140)  all_58_5 = all_52_19
% 203.92/34.74    (141)  all_56_1 = all_52_9
% 203.92/34.74    (142)   ~ (all_52_15 = all_4_2)
% 203.92/34.74    (143)  op(e0, all_14_1) = e3
% 203.92/34.74    (144)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.92/34.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.92/34.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.92/34.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.92/34.74    (145)   ~ (all_52_27 = all_4_2)
% 203.92/34.74    (146)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.92/34.74    (147)  all_58_6 = all_52_5
% 203.92/34.74    (148)  op(e3, e2) = all_52_9
% 203.92/34.74    (149)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.92/34.74    (150)   ~ (all_52_17 = all_6_2)
% 203.92/34.74    (151)   ~ (e1 = e0)
% 203.92/34.74    (152)   ~ (e3 = e2)
% 203.92/34.74    (153)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.92/34.74    (154)   ~ (all_52_9 = all_52_17)
% 203.92/34.74    (155)  all_56_10 = all_10_2
% 203.92/34.74    (156)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.92/34.74    (157)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.92/34.74    (158)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.92/34.74    (159)  op(all_52_13, all_52_13) = all_52_12
% 203.92/34.74    (160)   ~ (all_6_1 = e2)
% 203.92/34.74    (161)  op(e1, e1) = all_10_2
% 203.92/34.74    (162)   ~ (all_52_23 = all_10_2)
% 203.92/34.74    (163)   ~ (all_52_7 = all_52_23)
% 203.92/34.74    (164)   ~ (all_52_17 = all_52_19)
% 203.92/34.74    (165)  all_58_3 = all_4_2
% 203.92/34.74    (166)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.92/34.74    (167)  all_56_13 = all_52_15
% 203.92/34.74    (168)   ~ (all_52_3 = all_4_2)
% 203.92/34.74    (169)   ~ (all_52_19 = all_4_2)
% 203.92/34.74    (170)   ~ (all_52_17 = all_52_23)
% 203.92/34.74    (171)  op(all_6_2, e3) = all_6_1
% 203.92/34.74    (172)  all_58_4 = all_52_17
% 203.92/34.74    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.92/34.74    (174)  op(all_52_25, all_52_25) = all_52_24
% 203.92/34.74  
% 203.92/34.74  Begin of proof
% 203.92/34.74  | 
% 203.92/34.74  | COMBINE_EQS: (84), (125) imply:
% 203.92/34.74  |   (175)  all_4_1 = e3
% 203.92/34.74  | 
% 203.92/34.74  | COMBINE_EQS: (96), (175) imply:
% 203.92/34.74  |   (176)  all_38_1 = e3
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (55), (175) imply:
% 203.92/34.74  |   (177)   ~ (e3 = e1)
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (91), (175) imply:
% 203.92/34.74  |   (178)  op(all_4_2, e2) = e3
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (53), (175) imply:
% 203.92/34.74  |   (179)  op(e2, e3) = all_4_0
% 203.92/34.74  | 
% 203.92/34.74  | GROUND_INST: instantiating (6) with all_52_3, all_4_0, e3, e2, simplifying
% 203.92/34.74  |              with (11), (179) gives:
% 203.92/34.74  |   (180)  all_52_3 = all_4_0
% 203.92/34.74  | 
% 203.92/34.74  | COMBINE_EQS: (20), (180) imply:
% 203.92/34.74  |   (181)  all_56_4 = all_4_0
% 203.92/34.74  | 
% 203.92/34.74  | COMBINE_EQS: (79), (180) imply:
% 203.92/34.74  |   (182)  all_58_2 = all_4_0
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (39), (180) imply:
% 203.92/34.74  |   (183)   ~ (all_52_5 = all_4_0)
% 203.92/34.74  | 
% 203.92/34.74  | SIMP: (183) implies:
% 203.92/34.74  |   (184)   ~ (all_52_5 = all_4_0)
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (138), (180) imply:
% 203.92/34.74  |   (185)   ~ (all_52_7 = all_4_0)
% 203.92/34.74  | 
% 203.92/34.74  | SIMP: (185) implies:
% 203.92/34.74  |   (186)   ~ (all_52_7 = all_4_0)
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (17), (180) imply:
% 203.92/34.74  |   (187)   ~ (all_6_2 = all_4_0)
% 203.92/34.74  | 
% 203.92/34.74  | SIMP: (187) implies:
% 203.92/34.74  |   (188)   ~ (all_6_2 = all_4_0)
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (168), (180) imply:
% 203.92/34.74  |   (189)   ~ (all_4_0 = all_4_2)
% 203.92/34.74  | 
% 203.92/34.74  | REDUCE: (5), (180) imply:
% 203.92/34.74  |   (190)  op(all_4_0, all_4_0) = all_52_2
% 203.92/34.74  | 
% 203.92/34.74  | BETA: splitting (127) gives:
% 203.92/34.74  | 
% 203.92/34.74  | Case 1:
% 203.92/34.74  | | 
% 203.92/34.74  | |   (191)   ~ (all_38_0 = e1)
% 203.92/34.74  | | 
% 203.92/34.74  | | REDUCE: (78), (191) imply:
% 203.92/34.74  | |   (192)   ~ (all_4_0 = e1)
% 203.92/34.74  | | 
% 203.92/34.74  | | BETA: splitting (102) gives:
% 203.92/34.74  | | 
% 203.92/34.74  | | Case 1:
% 203.92/34.74  | | | 
% 203.92/34.74  | | |   (193)  all_58_15 = e0
% 203.92/34.74  | | | 
% 203.92/34.74  | | | REF_CLOSE: (6), (10), (19), (49), (109), (139), (143), (193) are
% 203.92/34.74  | | |            inconsistent by sub-proof #693.
% 203.92/34.74  | | | 
% 203.92/34.74  | | Case 2:
% 203.92/34.74  | | | 
% 203.92/34.74  | | |   (194)   ~ (all_58_15 = e0)
% 203.92/34.74  | | |   (195)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 203.92/34.74  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 203.92/34.74  | | | 
% 203.92/34.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.92/34.74  | | |            (13), (14), (15), (16), (17), (18), (20), (22), (23), (24),
% 203.92/34.74  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.92/34.74  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 203.92/34.74  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (54), (55),
% 203.92/34.74  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 203.92/34.74  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 203.92/34.74  | | |            (76), (77), (79), (80), (81), (82), (83), (85), (86), (87),
% 203.92/34.74  | | |            (88), (89), (90), (91), (92), (93), (94), (95), (97), (98),
% 203.92/34.74  | | |            (99), (100), (101), (103), (104), (105), (106), (107), (108),
% 203.92/34.74  | | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 203.92/34.74  | | |            (118), (119), (120), (121), (122), (123), (124), (126), (128),
% 203.92/34.74  | | |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 203.92/34.74  | | |            (138), (139), (140), (141), (142), (144), (145), (146), (147),
% 203.92/34.74  | | |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 203.92/34.74  | | |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 203.92/34.74  | | |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 203.92/34.74  | | |            (177), (178), (181), (182), (184), (186), (188), (189), (190),
% 203.92/34.74  | | |            (192), (194), (195) are inconsistent by sub-proof #669.
% 203.92/34.74  | | | 
% 203.92/34.74  | | End of split
% 203.92/34.74  | | 
% 203.92/34.74  | Case 2:
% 203.92/34.74  | | 
% 203.92/34.74  | |   (196)  all_38_0 = e1
% 203.92/34.74  | |   (197)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 203.92/34.74  | | 
% 203.92/34.74  | | COMBINE_EQS: (78), (196) imply:
% 203.92/34.74  | |   (198)  all_4_0 = e1
% 203.92/34.74  | | 
% 203.92/34.74  | | REF_CLOSE: (6), (21), (37), (42), (90), (123), (135), (148), (176), (178),
% 203.92/34.74  | |            (189), (197), (198) are inconsistent by sub-proof #927.
% 203.92/34.74  | | 
% 203.92/34.74  | End of split
% 203.92/34.74  | 
% 203.92/34.74  End of proof
% 203.92/34.74  
% 203.92/34.74  Sub-proof #669 shows that the following formulas are inconsistent:
% 203.92/34.74  ----------------------------------------------------------------
% 203.92/34.74    (1)   ~ (all_52_15 = all_52_23)
% 203.92/34.74    (2)   ~ (all_52_25 = all_52_27)
% 203.92/34.74    (3)  all_58_14 = all_52_23
% 203.92/34.74    (4)   ~ (e3 = e1)
% 203.92/34.74    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.92/34.74    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.92/34.74    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.92/34.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.92/34.74    (8)   ~ (all_52_5 = all_52_13)
% 203.92/34.74    (9)  all_58_1 = all_52_9
% 203.92/34.74    (10)   ~ (all_52_9 = all_52_13)
% 203.92/34.74    (11)   ~ (e3 = e0)
% 203.92/34.74    (12)  op(e2, e3) = all_52_3
% 203.92/34.74    (13)   ~ (all_4_0 = e1)
% 203.92/34.74    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.92/34.74    (15)   ~ (all_52_7 = all_52_15)
% 203.92/34.74    (16)   ~ (all_52_3 = all_52_19)
% 203.92/34.74    (17)  op(all_52_7, all_52_7) = all_52_6
% 203.92/34.74    (18)   ~ (all_52_17 = all_52_25)
% 203.92/34.74    (19)   ~ (all_52_5 = all_4_0)
% 203.92/34.74    (20)   ~ (all_52_3 = all_6_2)
% 203.92/34.74    (21)  all_58_0 = all_6_2
% 203.92/34.74    (22)  all_56_4 = all_52_3
% 203.92/34.74    (23)   ~ (all_52_17 = all_10_2)
% 203.92/34.74    (24)  op(e3, e0) = all_52_25
% 203.92/34.74    (25)  op(all_52_5, all_52_5) = all_52_4
% 203.92/34.74    (26)  op(all_52_19, all_52_19) = all_52_18
% 203.92/34.74    (27)   ~ (all_52_27 = all_52_29)
% 203.92/34.74    (28)  all_58_13 = all_52_15
% 203.92/34.74    (29)  op(all_10_2, all_10_2) = all_52_20
% 203.92/34.74    (30)  all_58_9 = all_52_25
% 203.92/34.74    (31)   ~ (all_6_1 = e1)
% 203.92/34.74    (32)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.92/34.74    (33)   ~ (all_52_29 = all_14_2)
% 203.92/34.74    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.92/34.74    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.92/34.74    (36)  op(e1, e3) = all_52_5
% 203.92/34.74    (37)   ~ (all_6_2 = all_4_0)
% 203.92/34.74    (38)  all_32_2 = all_4_2
% 203.92/34.74    (39)  op(e2, e2) = all_4_2
% 203.92/34.74    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.92/34.74    (41)   ~ (all_52_3 = all_52_5)
% 203.92/34.74    (42)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 203.92/34.74    (43)  all_58_11 = all_52_29
% 203.92/34.74    (44)  all_56_5 = all_4_2
% 203.92/34.74    (45)   ~ (all_52_25 = all_14_2)
% 203.92/34.74    (46)   ~ (all_52_9 = all_52_15)
% 203.92/34.74    (47)   ~ (all_52_3 = all_52_27)
% 203.92/34.74    (48)  op(all_10_2, e1) = all_10_1
% 203.92/34.74    (49)  op(all_6_2, all_6_2) = all_52_0
% 203.92/34.74    (50)   ~ (all_52_7 = all_6_2)
% 203.92/34.74    (51)  all_58_2 = all_4_0
% 203.92/34.74    (52)  op(e0, e0) = all_14_2
% 203.92/34.74    (53)  all_56_15 = all_14_2
% 203.92/34.74    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.92/34.74    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.92/34.74    (56)  op(all_4_2, e2) = e3
% 203.92/34.74    (57)   ~ (all_58_15 = e0)
% 203.92/34.74    (58)  all_56_11 = all_52_29
% 203.92/34.74    (59)   ~ (all_4_1 = e1)
% 203.92/34.74    (60)   ~ (all_4_0 = e3)
% 203.92/34.74    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.92/34.74    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.92/34.74    (63)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.92/34.74    (64)  all_56_9 = all_52_13
% 203.92/34.74    (65)   ~ (e2 = e1)
% 203.92/34.74    (66)   ~ (all_52_13 = all_10_2)
% 203.92/34.74    (67)   ~ (all_6_0 = e1)
% 203.92/34.74    (68)  all_58_10 = all_52_27
% 203.92/34.74    (69)  all_56_8 = all_52_5
% 203.92/34.74    (70)  op(all_52_9, all_52_9) = all_52_8
% 203.92/34.74    (71)  op(all_52_15, all_52_15) = all_52_14
% 203.92/34.74    (72)   ~ (all_52_19 = all_52_23)
% 203.92/34.74    (73)   ~ (all_52_25 = all_52_29)
% 203.92/34.74    (74)   ~ (all_52_29 = all_10_2)
% 203.92/34.74    (75)  all_58_7 = all_52_13
% 203.92/34.74    (76)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.92/34.74    (77)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.92/34.74    (78)   ~ (all_52_5 = all_52_7)
% 203.92/34.74    (79)  all_58_12 = all_52_7
% 203.92/34.74    (80)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.92/34.74    (81)   ~ (all_52_7 = all_14_2)
% 203.92/34.74    (82)  all_58_2 = all_52_3
% 203.92/34.74    (83)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.92/34.74    (84)  all_56_2 = all_52_17
% 203.92/34.74    (85)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.92/34.74    (86)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.92/34.74    (87)  op(all_4_0, all_4_0) = all_52_2
% 203.92/34.74    (88)  op(e3, all_6_1) = all_6_0
% 203.92/34.74    (89)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.92/34.74    (90)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.92/34.74    (91)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.92/34.74    (92)   ~ (e2 = e0)
% 203.92/34.74    (93)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.92/34.74    (94)  op(all_4_2, e2) = all_4_1
% 203.92/34.74    (95)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.92/34.74    (96)   ~ (all_52_5 = all_52_29)
% 203.92/34.74    (97)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.92/34.74    (98)  all_56_6 = all_52_19
% 203.92/34.74    (99)   ~ (all_52_15 = all_14_2)
% 203.92/34.74    (100)   ~ (all_52_19 = all_52_27)
% 203.92/34.74    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.92/34.74    (102)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.92/34.74    (103)  all_56_4 = all_4_0
% 203.92/34.74    (104)   ~ (all_6_0 = e2)
% 203.92/34.74    (105)   ~ (all_52_13 = all_4_2)
% 203.92/34.74    (106)  op(e3, e1) = all_52_17
% 203.92/34.74    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.92/34.74    (108)  op(e0, e3) = all_52_7
% 203.92/34.74    (109)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.92/34.74    (110)   ~ (all_52_9 = all_52_25)
% 203.92/34.74    (111)  all_58_15 = all_14_2
% 203.92/34.74    (112)   ~ (all_52_19 = all_10_2)
% 203.92/34.74    (113)  op(all_52_23, all_52_23) = all_52_22
% 203.92/34.74    (114)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.92/34.74    (115)  all_58_8 = all_10_2
% 203.92/34.74    (116)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.92/34.74    (117)   ~ (all_52_5 = all_10_2)
% 203.92/34.74    (118)  op(all_52_29, all_52_29) = all_52_28
% 203.92/34.74    (119)   ~ (all_52_7 = all_4_0)
% 203.92/34.74    (120)   ~ (all_52_23 = all_14_2)
% 203.92/34.74    (121)  all_56_12 = all_52_7
% 203.92/34.74    (122)  op(all_52_17, all_52_17) = all_52_16
% 203.92/34.74    (123)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.92/34.74    (124)   ~ (all_52_25 = all_6_2)
% 203.92/34.74    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.92/34.74    (126)   ~ (all_52_9 = all_4_2)
% 203.92/34.74    (127)   ~ (all_52_5 = all_6_2)
% 203.92/34.74    (128)   ~ (all_52_9 = all_6_2)
% 203.92/34.74    (129)   ~ (all_52_13 = all_52_15)
% 203.92/34.74    (130)  all_56_0 = all_6_2
% 203.92/34.74    (131)  op(e3, e3) = all_6_2
% 203.92/34.74    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.92/34.74    (133)   ~ (all_52_27 = all_14_2)
% 203.92/34.74    (134)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.92/34.74    (135)  all_56_14 = all_52_23
% 203.92/34.74    (136)  op(all_4_2, all_4_2) = all_52_10
% 203.92/34.74    (137)  all_32_0 = all_4_0
% 203.92/34.74    (138)  all_56_3 = all_52_25
% 203.92/34.74    (139)   ~ (all_52_3 = all_52_7)
% 203.92/34.74    (140)  op(all_14_2, all_14_2) = all_52_30
% 203.92/34.74    (141)  all_58_5 = all_52_19
% 203.92/34.74    (142)  all_56_1 = all_52_9
% 203.92/34.74    (143)   ~ (all_52_15 = all_4_2)
% 203.92/34.75    (144)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.92/34.75           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.92/34.75           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.92/34.75           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.92/34.75    (145)   ~ (all_52_27 = all_4_2)
% 203.92/34.75    (146)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 203.92/34.75             all_58_13 = e0 | all_58_14 = e0)
% 203.92/34.75    (147)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.92/34.75    (148)  all_58_6 = all_52_5
% 203.92/34.75    (149)   ~ (all_4_0 = all_4_2)
% 203.92/34.75    (150)  op(e3, e2) = all_52_9
% 203.92/34.75    (151)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.92/34.75    (152)   ~ (all_52_17 = all_6_2)
% 203.92/34.75    (153)   ~ (e1 = e0)
% 203.92/34.75    (154)   ~ (e3 = e2)
% 203.92/34.75    (155)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.92/34.75    (156)   ~ (all_52_9 = all_52_17)
% 203.92/34.75    (157)  all_56_10 = all_10_2
% 203.92/34.75    (158)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.92/34.75    (159)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.92/34.75    (160)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.92/34.75    (161)  op(all_52_13, all_52_13) = all_52_12
% 203.92/34.75    (162)   ~ (all_6_1 = e2)
% 203.92/34.75    (163)  op(e1, e1) = all_10_2
% 203.92/34.75    (164)   ~ (all_52_23 = all_10_2)
% 203.92/34.75    (165)   ~ (all_52_7 = all_52_23)
% 203.92/34.75    (166)   ~ (all_52_17 = all_52_19)
% 203.92/34.75    (167)  all_58_3 = all_4_2
% 203.92/34.75    (168)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.92/34.75    (169)  all_56_13 = all_52_15
% 203.92/34.75    (170)   ~ (all_52_3 = all_4_2)
% 203.92/34.75    (171)   ~ (all_52_19 = all_4_2)
% 203.92/34.75    (172)   ~ (all_52_17 = all_52_23)
% 203.92/34.75    (173)  op(all_6_2, e3) = all_6_1
% 203.92/34.75    (174)  all_58_4 = all_52_17
% 203.92/34.75    (175)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.92/34.75    (176)  op(all_52_25, all_52_25) = all_52_24
% 203.92/34.75  
% 203.92/34.75  Begin of proof
% 203.92/34.75  | 
% 203.92/34.75  | ALPHA: (146) implies:
% 203.92/34.75  |   (177)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.92/34.75  |   (178)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.92/34.75  | 
% 203.92/34.75  | REDUCE: (57), (111) imply:
% 203.92/34.75  |   (179)   ~ (all_14_2 = e0)
% 203.92/34.75  | 
% 203.92/34.75  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.92/34.75  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 203.92/34.75  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 203.92/34.75  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 203.92/34.75  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 203.92/34.75  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 203.92/34.75  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 203.92/34.75  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 203.92/34.75  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 203.92/34.75  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 203.92/34.75  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 203.92/34.75  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 203.92/34.75  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 203.92/34.75  |            (138), (139), (140), (141), (142), (143), (144), (145), (147),
% 203.92/34.75  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 203.92/34.75  |            (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 203.92/34.75  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 203.92/34.75  |            (175), (176), (177), (178), (179) are inconsistent by sub-proof
% 203.92/34.75  |            #670.
% 203.92/34.75  | 
% 203.92/34.75  End of proof
% 203.92/34.75  
% 203.92/34.75  Sub-proof #670 shows that the following formulas are inconsistent:
% 203.92/34.75  ----------------------------------------------------------------
% 203.92/34.75    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.92/34.75    (2)   ~ (all_52_15 = all_52_23)
% 203.92/34.75    (3)   ~ (all_52_25 = all_52_27)
% 203.92/34.75    (4)  all_58_14 = all_52_23
% 203.92/34.75    (5)   ~ (e3 = e1)
% 203.92/34.75    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.92/34.75    (7)  op(all_52_3, all_52_3) = all_52_2
% 203.92/34.75    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.92/34.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.92/34.75    (9)   ~ (all_52_5 = all_52_13)
% 203.92/34.75    (10)  all_58_1 = all_52_9
% 203.92/34.75    (11)   ~ (all_52_9 = all_52_13)
% 203.92/34.75    (12)   ~ (e3 = e0)
% 203.92/34.75    (13)  op(e2, e3) = all_52_3
% 203.92/34.75    (14)   ~ (all_4_0 = e1)
% 203.92/34.75    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.92/34.75    (16)   ~ (all_52_7 = all_52_15)
% 203.92/34.75    (17)   ~ (all_52_3 = all_52_19)
% 203.92/34.75    (18)  op(all_52_7, all_52_7) = all_52_6
% 203.92/34.75    (19)   ~ (all_52_17 = all_52_25)
% 203.92/34.75    (20)   ~ (all_52_5 = all_4_0)
% 203.92/34.75    (21)   ~ (all_52_3 = all_6_2)
% 203.92/34.75    (22)  all_58_0 = all_6_2
% 203.92/34.75    (23)  all_56_4 = all_52_3
% 203.92/34.75    (24)   ~ (all_52_17 = all_10_2)
% 203.92/34.75    (25)  op(e3, e0) = all_52_25
% 203.92/34.75    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.92/34.75    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.92/34.75    (28)   ~ (all_52_27 = all_52_29)
% 203.92/34.75    (29)  all_58_13 = all_52_15
% 203.92/34.75    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.92/34.75    (31)  all_58_9 = all_52_25
% 203.92/34.75    (32)   ~ (all_6_1 = e1)
% 203.92/34.75    (33)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.92/34.75    (34)   ~ (all_52_29 = all_14_2)
% 203.92/34.75    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.92/34.75    (36)  op(all_52_27, all_52_27) = all_52_26
% 203.92/34.75    (37)  op(e1, e3) = all_52_5
% 203.92/34.75    (38)   ~ (all_6_2 = all_4_0)
% 203.92/34.75    (39)  all_32_2 = all_4_2
% 203.92/34.75    (40)  op(e2, e2) = all_4_2
% 203.92/34.75    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.92/34.75    (42)   ~ (all_52_3 = all_52_5)
% 203.92/34.75    (43)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 203.92/34.75    (44)  all_58_11 = all_52_29
% 203.92/34.75    (45)  all_56_5 = all_4_2
% 203.92/34.75    (46)   ~ (all_52_25 = all_14_2)
% 203.92/34.75    (47)   ~ (all_52_9 = all_52_15)
% 203.92/34.75    (48)   ~ (all_52_3 = all_52_27)
% 203.92/34.75    (49)  op(all_10_2, e1) = all_10_1
% 203.92/34.75    (50)  op(all_6_2, all_6_2) = all_52_0
% 203.92/34.75    (51)   ~ (all_52_7 = all_6_2)
% 203.92/34.75    (52)  all_58_2 = all_4_0
% 203.92/34.75    (53)  op(e0, e0) = all_14_2
% 203.92/34.75    (54)  all_56_15 = all_14_2
% 203.92/34.75    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.92/34.75    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.92/34.75    (57)  op(all_4_2, e2) = e3
% 203.92/34.75    (58)  all_56_11 = all_52_29
% 203.92/34.75    (59)   ~ (all_4_1 = e1)
% 203.92/34.75    (60)   ~ (all_4_0 = e3)
% 203.92/34.75    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.92/34.75    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.92/34.75    (63)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.92/34.75    (64)  all_56_9 = all_52_13
% 203.92/34.75    (65)   ~ (e2 = e1)
% 203.92/34.75    (66)   ~ (all_52_13 = all_10_2)
% 203.92/34.75    (67)   ~ (all_6_0 = e1)
% 203.92/34.75    (68)  all_58_10 = all_52_27
% 203.92/34.75    (69)  all_56_8 = all_52_5
% 203.92/34.75    (70)  op(all_52_9, all_52_9) = all_52_8
% 203.92/34.75    (71)  op(all_52_15, all_52_15) = all_52_14
% 203.92/34.75    (72)   ~ (all_52_19 = all_52_23)
% 203.92/34.75    (73)   ~ (all_52_25 = all_52_29)
% 203.92/34.75    (74)   ~ (all_52_29 = all_10_2)
% 203.92/34.75    (75)  all_58_7 = all_52_13
% 203.92/34.75    (76)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.92/34.75    (77)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.92/34.75    (78)   ~ (all_52_5 = all_52_7)
% 203.92/34.75    (79)  all_58_12 = all_52_7
% 203.92/34.75    (80)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.92/34.75    (81)   ~ (all_52_7 = all_14_2)
% 203.92/34.75    (82)   ~ (all_14_2 = e0)
% 203.92/34.75    (83)  all_58_2 = all_52_3
% 203.92/34.75    (84)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.92/34.75    (85)  all_56_2 = all_52_17
% 203.92/34.75    (86)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.92/34.75    (87)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.92/34.75    (88)  op(all_4_0, all_4_0) = all_52_2
% 203.92/34.75    (89)  op(e3, all_6_1) = all_6_0
% 203.92/34.75    (90)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.92/34.75    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.92/34.75    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.92/34.75    (93)   ~ (e2 = e0)
% 203.92/34.75    (94)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.92/34.75    (95)  op(all_4_2, e2) = all_4_1
% 203.92/34.75    (96)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.92/34.75    (97)   ~ (all_52_5 = all_52_29)
% 203.92/34.75    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.92/34.75    (99)  all_56_6 = all_52_19
% 203.92/34.75    (100)   ~ (all_52_15 = all_14_2)
% 203.92/34.75    (101)   ~ (all_52_19 = all_52_27)
% 203.92/34.75    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.92/34.75    (103)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.92/34.75    (104)  all_56_4 = all_4_0
% 203.92/34.75    (105)   ~ (all_6_0 = e2)
% 203.92/34.75    (106)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.92/34.75    (107)   ~ (all_52_13 = all_4_2)
% 203.92/34.75    (108)  op(e3, e1) = all_52_17
% 203.92/34.75    (109)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.92/34.75    (110)  op(e0, e3) = all_52_7
% 203.92/34.75    (111)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.92/34.75    (112)   ~ (all_52_9 = all_52_25)
% 203.92/34.75    (113)  all_58_15 = all_14_2
% 203.92/34.75    (114)   ~ (all_52_19 = all_10_2)
% 203.92/34.75    (115)  op(all_52_23, all_52_23) = all_52_22
% 203.92/34.75    (116)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.92/34.75    (117)  all_58_8 = all_10_2
% 203.92/34.75    (118)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.92/34.75    (119)   ~ (all_52_5 = all_10_2)
% 203.92/34.75    (120)  op(all_52_29, all_52_29) = all_52_28
% 203.92/34.75    (121)   ~ (all_52_7 = all_4_0)
% 203.92/34.75    (122)   ~ (all_52_23 = all_14_2)
% 203.92/34.75    (123)  all_56_12 = all_52_7
% 203.92/34.75    (124)  op(all_52_17, all_52_17) = all_52_16
% 203.92/34.75    (125)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.92/34.75    (126)   ~ (all_52_25 = all_6_2)
% 203.92/34.75    (127)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.92/34.75    (128)   ~ (all_52_9 = all_4_2)
% 203.92/34.75    (129)   ~ (all_52_5 = all_6_2)
% 203.92/34.75    (130)   ~ (all_52_9 = all_6_2)
% 203.92/34.75    (131)   ~ (all_52_13 = all_52_15)
% 203.92/34.75    (132)  all_56_0 = all_6_2
% 203.92/34.75    (133)  op(e3, e3) = all_6_2
% 203.92/34.75    (134)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.92/34.75    (135)   ~ (all_52_27 = all_14_2)
% 203.92/34.75    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.92/34.75    (137)  all_56_14 = all_52_23
% 203.92/34.75    (138)  op(all_4_2, all_4_2) = all_52_10
% 203.92/34.75    (139)  all_32_0 = all_4_0
% 203.92/34.75    (140)  all_56_3 = all_52_25
% 203.92/34.75    (141)   ~ (all_52_3 = all_52_7)
% 203.92/34.75    (142)  op(all_14_2, all_14_2) = all_52_30
% 203.92/34.75    (143)  all_58_5 = all_52_19
% 203.92/34.75    (144)  all_56_1 = all_52_9
% 203.92/34.75    (145)   ~ (all_52_15 = all_4_2)
% 203.92/34.75    (146)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.92/34.75           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.92/34.75           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.92/34.75           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.92/34.75    (147)   ~ (all_52_27 = all_4_2)
% 203.92/34.75    (148)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.92/34.75    (149)  all_58_6 = all_52_5
% 203.92/34.75    (150)   ~ (all_4_0 = all_4_2)
% 203.92/34.75    (151)  op(e3, e2) = all_52_9
% 203.92/34.75    (152)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.92/34.75    (153)   ~ (all_52_17 = all_6_2)
% 203.92/34.75    (154)   ~ (e1 = e0)
% 203.92/34.75    (155)   ~ (e3 = e2)
% 203.92/34.75    (156)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.92/34.75    (157)   ~ (all_52_9 = all_52_17)
% 203.92/34.75    (158)  all_56_10 = all_10_2
% 203.92/34.75    (159)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.92/34.75    (160)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.92/34.75    (161)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.92/34.75    (162)  op(all_52_13, all_52_13) = all_52_12
% 203.92/34.75    (163)   ~ (all_6_1 = e2)
% 203.92/34.75    (164)  op(e1, e1) = all_10_2
% 203.92/34.75    (165)   ~ (all_52_23 = all_10_2)
% 203.92/34.75    (166)   ~ (all_52_7 = all_52_23)
% 203.92/34.75    (167)   ~ (all_52_17 = all_52_19)
% 203.92/34.75    (168)  all_58_3 = all_4_2
% 203.92/34.75    (169)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.92/34.75    (170)  all_56_13 = all_52_15
% 203.92/34.75    (171)   ~ (all_52_3 = all_4_2)
% 203.92/34.75    (172)   ~ (all_52_19 = all_4_2)
% 203.92/34.75    (173)   ~ (all_52_17 = all_52_23)
% 203.92/34.75    (174)  op(all_6_2, e3) = all_6_1
% 203.92/34.75    (175)  all_58_4 = all_52_17
% 203.92/34.75    (176)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.92/34.75    (177)  op(all_52_25, all_52_25) = all_52_24
% 203.92/34.75  
% 203.92/34.75  Begin of proof
% 203.92/34.75  | 
% 203.92/34.75  | BETA: splitting (92) gives:
% 203.92/34.75  | 
% 203.92/34.75  | Case 1:
% 203.92/34.75  | | 
% 203.92/34.75  | |   (178)  all_56_4 = e3
% 203.92/34.75  | | 
% 203.92/34.75  | | REF_CLOSE: (60), (104), (178) are inconsistent by sub-proof #980.
% 203.92/34.75  | | 
% 203.92/34.75  | Case 2:
% 203.92/34.75  | | 
% 203.92/34.75  | |   (179)   ~ (all_56_4 = e3)
% 203.92/34.75  | |   (180)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.92/34.75  | | 
% 203.92/34.75  | | BETA: splitting (146) gives:
% 203.92/34.75  | | 
% 203.92/34.75  | | Case 1:
% 203.92/34.75  | | | 
% 203.92/34.75  | | |   (181)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.92/34.75  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.92/34.75  | | |            e0)
% 203.92/34.75  | | | 
% 203.92/34.75  | | | BETA: splitting (181) gives:
% 203.92/34.75  | | | 
% 203.92/34.75  | | | Case 1:
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | |   (182)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | | ALPHA: (182) implies:
% 203.92/34.75  | | | |   (183)  all_52_6 = e0
% 203.92/34.75  | | | |   (184)  all_52_4 = e1
% 203.92/34.75  | | | |   (185)  all_52_0 = e3
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | | REDUCE: (26), (184) imply:
% 203.92/34.75  | | | |   (186)  op(all_52_5, all_52_5) = e1
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | | REDUCE: (18), (183) imply:
% 203.92/34.75  | | | |   (187)  op(all_52_7, all_52_7) = e0
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | | REDUCE: (50), (185) imply:
% 203.92/34.75  | | | |   (188)  op(all_6_2, all_6_2) = e3
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | | BETA: splitting (118) gives:
% 203.92/34.75  | | | | 
% 203.92/34.75  | | | | Case 1:
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | |   (189)  all_56_15 = e3
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | COMBINE_EQS: (54), (189) imply:
% 203.92/34.75  | | | | |   (190)  all_14_2 = e3
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | SIMP: (190) implies:
% 203.92/34.75  | | | | |   (191)  all_14_2 = e3
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | REDUCE: (81), (191) imply:
% 203.92/34.75  | | | | |   (192)   ~ (all_52_7 = e3)
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | REDUCE: (142), (191) imply:
% 203.92/34.75  | | | | |   (193)  op(e3, e3) = all_52_30
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_30, e3, e3,
% 203.92/34.75  | | | | |              simplifying with (133), (193) gives:
% 203.92/34.75  | | | | |   (194)  all_52_30 = all_6_2
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | BETA: splitting (87) gives:
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | Case 1:
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | |   (195)  all_58_0 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | COMBINE_EQS: (22), (195) imply:
% 203.92/34.75  | | | | | |   (196)  all_6_2 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (129), (196) imply:
% 203.92/34.75  | | | | | |   (197)   ~ (all_52_5 = e3)
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (174), (196) imply:
% 203.92/34.75  | | | | | |   (198)  op(e3, e3) = all_6_1
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (133), (196) imply:
% 203.92/34.75  | | | | | |   (199)  op(e3, e3) = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | GROUND_INST: instantiating (8) with e3, all_6_1, e3, e3, simplifying
% 203.92/34.75  | | | | | |              with (198), (199) gives:
% 203.92/34.75  | | | | | |   (200)  all_6_1 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (89), (200) imply:
% 203.92/34.75  | | | | | |   (201)  op(e3, e3) = all_6_0
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | GROUND_INST: instantiating (8) with e3, all_6_0, e3, e3, simplifying
% 203.92/34.75  | | | | | |              with (199), (201) gives:
% 203.92/34.75  | | | | | |   (202)  all_6_0 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REF_CLOSE: (5), (8), (12), (14), (20), (33), (39), (40), (41), (45),
% 203.92/34.75  | | | | | |            (52), (57), (69), (78), (79), (91), (94), (98), (104),
% 203.92/34.75  | | | | | |            (116), (119), (121), (128), (138), (139), (148), (149),
% 203.92/34.75  | | | | | |            (150), (151), (164), (180), (186), (187), (195), (197)
% 203.92/34.75  | | | | | |            are inconsistent by sub-proof #671.
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | Case 2:
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | |   (203)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REF_CLOSE: (8), (52), (60), (79), (119), (133), (149), (164), (186),
% 203.92/34.75  | | | | | |            (188), (192), (203) are inconsistent by sub-proof #849.
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | End of split
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | Case 2:
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | |   (204)   ~ (all_56_15 = e3)
% 203.92/34.75  | | | | |   (205)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | REDUCE: (54), (204) imply:
% 203.92/34.75  | | | | |   (206)   ~ (all_14_2 = e3)
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | BETA: splitting (61) gives:
% 203.92/34.75  | | | | | 
% 203.92/34.75  | | | | | Case 1:
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | |   (207)  all_56_13 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | COMBINE_EQS: (170), (207) imply:
% 203.92/34.75  | | | | | |   (208)  all_52_15 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | SIMP: (208) implies:
% 203.92/34.75  | | | | | |   (209)  all_52_15 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | COMBINE_EQS: (29), (209) imply:
% 203.92/34.75  | | | | | |   (210)  all_58_13 = e3
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (16), (209) imply:
% 203.92/34.75  | | | | | |   (211)   ~ (all_52_7 = e3)
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (71), (209) imply:
% 203.92/34.75  | | | | | |   (212)  op(e3, e3) = all_52_14
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REF_CLOSE: (4), (8), (12), (14), (22), (52), (60), (67), (79), (87),
% 203.92/34.75  | | | | | |            (89), (91), (98), (106), (119), (133), (149), (154),
% 203.92/34.75  | | | | | |            (164), (165), (174), (186), (187), (188), (210), (211),
% 203.92/34.75  | | | | | |            (212) are inconsistent by sub-proof #848.
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | Case 2:
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | |   (213)   ~ (all_56_13 = e3)
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | REDUCE: (170), (213) imply:
% 203.92/34.75  | | | | | |   (214)   ~ (all_52_15 = e3)
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | BETA: splitting (152) gives:
% 203.92/34.75  | | | | | | 
% 203.92/34.75  | | | | | | Case 1:
% 203.92/34.75  | | | | | | | 
% 203.92/34.75  | | | | | | |   (215)  all_58_12 = e3
% 203.92/34.75  | | | | | | | 
% 203.92/34.75  | | | | | | | REF_CLOSE: (5), (8), (14), (22), (52), (79), (91), (119), (133),
% 203.92/34.75  | | | | | | |            (149), (154), (164), (186), (187), (215) are
% 203.92/34.75  | | | | | | |            inconsistent by sub-proof #844.
% 203.92/34.75  | | | | | | | 
% 203.92/34.75  | | | | | | Case 2:
% 203.92/34.75  | | | | | | | 
% 203.92/34.75  | | | | | | |   (216)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.92/34.75  | | | | | | | 
% 203.92/34.75  | | | | | | | BETA: splitting (216) gives:
% 203.92/34.75  | | | | | | | 
% 203.92/34.75  | | | | | | | Case 1:
% 203.92/34.75  | | | | | | | | 
% 203.92/34.75  | | | | | | | |   (217)  all_58_13 = e3
% 203.92/34.75  | | | | | | | | 
% 203.92/34.75  | | | | | | | | REF_CLOSE: (29), (214), (217) are inconsistent by sub-proof
% 203.92/34.75  | | | | | | | |            #1360.
% 203.92/34.75  | | | | | | | | 
% 203.92/34.75  | | | | | | | Case 2:
% 203.92/34.75  | | | | | | | | 
% 203.92/34.75  | | | | | | | |   (218)  all_58_14 = e3 | all_58_15 = e3
% 203.92/34.75  | | | | | | | | 
% 203.92/34.75  | | | | | | | | BETA: splitting (218) gives:
% 203.92/34.75  | | | | | | | | 
% 203.92/34.75  | | | | | | | | Case 1:
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | |   (219)  all_58_14 = e3
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | COMBINE_EQS: (4), (219) imply:
% 203.92/34.75  | | | | | | | | |   (220)  all_52_23 = e3
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | SIMP: (220) implies:
% 203.92/34.75  | | | | | | | | |   (221)  all_52_23 = e3
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | REDUCE: (166), (221) imply:
% 203.92/34.75  | | | | | | | | |   (222)   ~ (all_52_7 = e3)
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | REDUCE: (115), (221) imply:
% 203.92/34.75  | | | | | | | | |   (223)  op(e3, e3) = all_52_22
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_22, e3, e3,
% 203.92/34.75  | | | | | | | | |              simplifying with (133), (223) gives:
% 203.92/34.75  | | | | | | | | |   (224)  all_52_22 = all_6_2
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | BETA: splitting (87) gives:
% 203.92/34.75  | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | Case 1:
% 203.92/34.75  | | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | |   (225)  all_58_0 = e3
% 203.92/34.75  | | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | | COMBINE_EQS: (22), (225) imply:
% 203.92/34.75  | | | | | | | | | |   (226)  all_6_2 = e3
% 203.92/34.75  | | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | | REDUCE: (129), (226) imply:
% 203.92/34.75  | | | | | | | | | |   (227)   ~ (all_52_5 = e3)
% 203.92/34.75  | | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | | REDUCE: (174), (226) imply:
% 203.92/34.75  | | | | | | | | | |   (228)  op(e3, e3) = all_6_1
% 203.92/34.75  | | | | | | | | | | 
% 203.92/34.75  | | | | | | | | | | REDUCE: (133), (226) imply:
% 203.92/34.75  | | | | | | | | | |   (229)  op(e3, e3) = e3
% 203.92/34.75  | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | GROUND_INST: instantiating (8) with e3, all_6_1, e3, e3,
% 203.92/34.76  | | | | | | | | | |              simplifying with (228), (229) gives:
% 203.92/34.76  | | | | | | | | | |   (230)  all_6_1 = e3
% 203.92/34.76  | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | REDUCE: (89), (230) imply:
% 203.92/34.76  | | | | | | | | | |   (231)  op(e3, e3) = all_6_0
% 203.92/34.76  | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | GROUND_INST: instantiating (8) with e3, all_6_0, e3, e3,
% 203.92/34.76  | | | | | | | | | |              simplifying with (229), (231) gives:
% 203.92/34.76  | | | | | | | | | |   (232)  all_6_0 = e3
% 203.92/34.76  | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | BETA: splitting (91) gives:
% 203.92/34.76  | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | |   (233)  all_58_0 = e1
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | COMBINE_EQS: (225), (233) imply:
% 203.92/34.76  | | | | | | | | | | |   (234)  e3 = e1
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | REDUCE: (5), (234) imply:
% 203.92/34.76  | | | | | | | | | | |   (235)  $false
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | |   (236)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | BETA: splitting (116) gives:
% 203.92/34.76  | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | |   (237)  all_56_8 = e3
% 203.92/34.76  | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | REF_CLOSE: (69), (227), (237) are inconsistent by sub-proof
% 203.92/34.76  | | | | | | | | | | | |            #1325.
% 203.92/34.76  | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | |   (238)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.92/34.76  | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | BETA: splitting (98) gives:
% 203.92/34.76  | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | |   (239)  all_58_12 = e1
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | COMBINE_EQS: (79), (239) imply:
% 203.92/34.76  | | | | | | | | | | | | |   (240)  all_52_7 = e1
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | SIMP: (240) implies:
% 203.92/34.76  | | | | | | | | | | | | |   (241)  all_52_7 = e1
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | REDUCE: (78), (241) imply:
% 203.92/34.76  | | | | | | | | | | | | |   (242)   ~ (all_52_5 = e1)
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | REDUCE: (81), (241) imply:
% 203.92/34.76  | | | | | | | | | | | | |   (243)   ~ (all_14_2 = e1)
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | SIMP: (243) implies:
% 203.92/34.76  | | | | | | | | | | | | |   (244)   ~ (all_14_2 = e1)
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | REDUCE: (121), (241) imply:
% 203.92/34.76  | | | | | | | | | | | | |   (245)   ~ (all_4_0 = e1)
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | REDUCE: (187), (241) imply:
% 203.92/34.76  | | | | | | | | | | | | |   (246)  op(e1, e1) = e0
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | BETA: splitting (106) gives:
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | |   (247)  all_58_12 = e0
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | REF_CLOSE: (154), (239), (247) are inconsistent by sub-proof
% 203.92/34.76  | | | | | | | | | | | | | |            #1173.
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | |   (248)  all_58_13 = e0 | all_58_14 = e0
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | |   (249)  all_58_13 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | COMBINE_EQS: (29), (249) imply:
% 203.92/34.76  | | | | | | | | | | | | | | |   (250)  all_52_15 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | SIMP: (250) implies:
% 203.92/34.76  | | | | | | | | | | | | | | |   (251)  all_52_15 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | REDUCE: (100), (251) imply:
% 203.92/34.76  | | | | | | | | | | | | | | |   (252)   ~ (all_14_2 = e0)
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | REDUCE: (145), (251) imply:
% 203.92/34.76  | | | | | | | | | | | | | | |   (253)   ~ (all_4_2 = e0)
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | SIMP: (253) implies:
% 203.92/34.76  | | | | | | | | | | | | | | |   (254)   ~ (all_4_2 = e0)
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | |   (255)  all_56_15 = e2
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (255) imply:
% 203.92/34.76  | | | | | | | | | | | | | | | |   (256)  all_14_2 = e2
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 203.92/34.76  | | | | | | | | | | | | | | | |   (257)  all_14_2 = e2
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | REDUCE: (142), (257) imply:
% 203.92/34.76  | | | | | | | | | | | | | | | |   (258)  op(e2, e2) = all_52_30
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, e0, e1, e1,
% 203.92/34.76  | | | | | | | | | | | | | | | |              simplifying with (164), (246) gives:
% 203.92/34.76  | | | | | | | | | | | | | | | |   (259)  all_10_2 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, all_52_30, e2, e2,
% 203.92/34.76  | | | | | | | | | | | | | | | |              simplifying with (40), (258) gives:
% 203.92/34.76  | | | | | | | | | | | | | | | |   (260)  all_52_30 = all_4_2
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | REDUCE: (119), (259) imply:
% 203.92/34.76  | | | | | | | | | | | | | | | |   (261)   ~ (all_52_5 = e0)
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | Case 1:
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | |   (262)  all_58_2 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (262) imply:
% 203.92/34.76  | | | | | | | | | | | | | | | | |   (263)  all_4_0 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | | SIMP: (263) implies:
% 203.92/34.76  | | | | | | | | | | | | | | | | |   (264)  all_4_0 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (264) imply:
% 203.92/34.76  | | | | | | | | | | | | | | | | |   (265)  all_32_0 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (40), (45), (57), (94), (128), (138),
% 203.92/34.76  | | | | | | | | | | | | | | | | |            (148), (151), (254), (265) are inconsistent by
% 203.92/34.76  | | | | | | | | | | | | | | | | |            sub-proof #972.
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | |   (266)   ~ (all_58_2 = e0)
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | | REDUCE: (52), (266) imply:
% 203.92/34.76  | | | | | | | | | | | | | | | | |   (267)   ~ (all_4_0 = e0)
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (33), (69), (104), (149), (180),
% 203.92/34.76  | | | | | | | | | | | | | | | | |            (238), (242), (261), (267) are inconsistent by
% 203.92/34.76  | | | | | | | | | | | | | | | | |            sub-proof #672.
% 203.92/34.76  | | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | End of split
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | |   (268)  all_56_15 = e1 | all_56_15 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | | REF_CLOSE: (54), (82), (244), (268) are inconsistent by
% 203.92/34.76  | | | | | | | | | | | | | | | |            sub-proof #1161.
% 203.92/34.76  | | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | End of split
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | |   (269)  all_58_14 = e0
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | | REF_CLOSE: (12), (219), (269) are inconsistent by sub-proof
% 203.92/34.76  | | | | | | | | | | | | | | |            #1151.
% 203.92/34.76  | | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | | End of split
% 203.92/34.76  | | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | End of split
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | Case 2:
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | |   (270)   ~ (all_58_12 = e1)
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | | REF_CLOSE: (8), (14), (52), (79), (119), (149), (164), (186),
% 203.92/34.76  | | | | | | | | | | | | |            (236), (270) are inconsistent by sub-proof #850.
% 203.92/34.76  | | | | | | | | | | | | | 
% 203.92/34.76  | | | | | | | | | | | | End of split
% 203.92/34.76  | | | | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | | | End of split
% 203.95/34.76  | | | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | | End of split
% 203.95/34.76  | | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | Case 2:
% 203.95/34.76  | | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | |   (271)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.76  | | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | | REF_CLOSE: (8), (52), (60), (79), (119), (133), (149), (164),
% 203.95/34.76  | | | | | | | | | |            (186), (188), (222), (271) are inconsistent by
% 203.95/34.76  | | | | | | | | | |            sub-proof #849.
% 203.95/34.76  | | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | End of split
% 203.95/34.76  | | | | | | | | | 
% 203.95/34.76  | | | | | | | | Case 2:
% 203.95/34.76  | | | | | | | | | 
% 203.95/34.76  | | | | | | | | |   (272)  all_58_15 = e3
% 203.95/34.76  | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | COMBINE_EQS: (113), (272) imply:
% 203.95/34.76  | | | | | | | | |   (273)  all_14_2 = e3
% 203.95/34.76  | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | REDUCE: (206), (273) imply:
% 203.95/34.76  | | | | | | | | |   (274)  $false
% 203.95/34.76  | | | | | | | | | 
% 203.95/34.76  | | | | | | | | | CLOSE: (274) is inconsistent.
% 203.95/34.76  | | | | | | | | | 
% 203.95/34.76  | | | | | | | | End of split
% 203.95/34.76  | | | | | | | | 
% 203.95/34.76  | | | | | | | End of split
% 203.95/34.76  | | | | | | | 
% 203.95/34.76  | | | | | | End of split
% 203.95/34.76  | | | | | | 
% 203.95/34.76  | | | | | End of split
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | End of split
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | Case 2:
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | |   (275)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 203.95/34.76  | | | |          e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | ALPHA: (275) implies:
% 203.95/34.76  | | | |   (276)  all_52_14 = e0
% 203.95/34.76  | | | |   (277)  all_52_12 = e1
% 203.95/34.76  | | | |   (278)  all_52_10 = e2
% 203.95/34.76  | | | |   (279)  all_52_8 = e3
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (70), (279) imply:
% 203.95/34.76  | | | |   (280)  op(all_52_9, all_52_9) = e3
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (162), (277) imply:
% 203.95/34.76  | | | |   (281)  op(all_52_13, all_52_13) = e1
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (71), (276) imply:
% 203.95/34.76  | | | |   (282)  op(all_52_15, all_52_15) = e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (138), (278) imply:
% 203.95/34.76  | | | |   (283)  op(all_4_2, all_4_2) = e2
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (15),
% 203.95/34.76  | | | |            (16), (18), (19), (22), (24), (25), (26), (29), (31), (32),
% 203.95/34.76  | | | |            (34), (37), (38), (40), (41), (42), (44), (45), (46), (50),
% 203.95/34.76  | | | |            (51), (52), (53), (54), (55), (57), (59), (60), (61), (62),
% 203.95/34.76  | | | |            (64), (65), (67), (68), (69), (72), (75), (78), (79), (80),
% 203.95/34.76  | | | |            (81), (83), (84), (85), (87), (88), (89), (91), (93), (94),
% 203.95/34.76  | | | |            (95), (97), (99), (100), (103), (105), (106), (110), (111),
% 203.95/34.76  | | | |            (112), (113), (114), (115), (116), (117), (118), (120),
% 203.95/34.76  | | | |            (122), (123), (126), (127), (128), (129), (130), (133),
% 203.95/34.76  | | | |            (134), (135), (136), (140), (141), (142), (143), (144),
% 203.95/34.76  | | | |            (147), (149), (150), (151), (152), (153), (154), (155),
% 203.95/34.76  | | | |            (156), (157), (160), (163), (164), (166), (168), (170),
% 203.95/34.76  | | | |            (171), (173), (174), (175), (177), (280), (281), (282), (283)
% 203.95/34.76  | | | |            are inconsistent by sub-proof #931.
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | End of split
% 203.95/34.76  | | | 
% 203.95/34.76  | | Case 2:
% 203.95/34.76  | | | 
% 203.95/34.76  | | |   (284)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.95/34.76  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 203.95/34.76  | | |            all_52_30 = e0)
% 203.95/34.76  | | | 
% 203.95/34.76  | | | BETA: splitting (284) gives:
% 203.95/34.76  | | | 
% 203.95/34.76  | | | Case 1:
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | |   (285)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 203.95/34.76  | | | |          e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | ALPHA: (285) implies:
% 203.95/34.76  | | | |   (286)  all_52_22 = e0
% 203.95/34.76  | | | |   (287)  all_52_20 = e1
% 203.95/34.76  | | | |   (288)  all_52_18 = e2
% 203.95/34.76  | | | |   (289)  all_52_16 = e3
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (124), (289) imply:
% 203.95/34.76  | | | |   (290)  op(all_52_17, all_52_17) = e3
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (27), (288) imply:
% 203.95/34.76  | | | |   (291)  op(all_52_19, all_52_19) = e2
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (115), (286) imply:
% 203.95/34.76  | | | |   (292)  op(all_52_23, all_52_23) = e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (30), (287) imply:
% 203.95/34.76  | | | |   (293)  op(all_10_2, all_10_2) = e1
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (12), (14), (15), (16),
% 203.95/34.76  | | | |            (17), (18), (19), (22), (26), (29), (31), (32), (35), (36),
% 203.95/34.76  | | | |            (37), (38), (39), (40), (42), (44), (45), (46), (47), (49),
% 203.95/34.76  | | | |            (50), (51), (52), (53), (54), (55), (57), (58), (60), (61),
% 203.95/34.76  | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (72),
% 203.95/34.76  | | | |            (73), (74), (75), (78), (79), (80), (81), (83), (84), (85),
% 203.95/34.76  | | | |            (86), (87), (89), (90), (93), (94), (96), (97), (99), (100),
% 203.95/34.76  | | | |            (101), (102), (103), (104), (105), (106), (107), (108),
% 203.95/34.76  | | | |            (110), (111), (112), (113), (114), (116), (117), (118),
% 203.95/34.76  | | | |            (119), (120), (122), (123), (127), (128), (129), (130),
% 203.95/34.76  | | | |            (131), (132), (133), (135), (136), (138), (139), (140),
% 203.95/34.76  | | | |            (141), (143), (144), (147), (148), (149), (150), (151),
% 203.95/34.76  | | | |            (152), (153), (154), (155), (156), (157), (158), (159),
% 203.95/34.76  | | | |            (160), (161), (162), (163), (164), (166), (168), (169),
% 203.95/34.76  | | | |            (170), (171), (172), (174), (175), (176), (177), (180),
% 203.95/34.76  | | | |            (290), (291), (292), (293) are inconsistent by sub-proof
% 203.95/34.76  | | | |            #929.
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | Case 2:
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | |   (294)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.95/34.76  | | | |          e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (13), (15), (16),
% 203.95/34.76  | | | |            (18), (19), (21), (22), (23), (24), (25), (26), (27), (28),
% 203.95/34.76  | | | |            (29), (31), (32), (34), (36), (37), (40), (42), (44), (45),
% 203.95/34.76  | | | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 203.95/34.76  | | | |            (58), (61), (62), (63), (67), (68), (69), (70), (71), (72),
% 203.95/34.76  | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 203.95/34.76  | | | |            (83), (85), (87), (89), (90), (91), (92), (94), (97), (100),
% 203.95/34.76  | | | |            (101), (102), (103), (105), (106), (107), (108), (109),
% 203.95/34.76  | | | |            (110), (111), (112), (113), (114), (115), (116), (117),
% 203.95/34.76  | | | |            (118), (119), (120), (122), (123), (124), (125), (126),
% 203.95/34.76  | | | |            (127), (128), (129), (130), (131), (132), (133), (134),
% 203.95/34.76  | | | |            (135), (136), (137), (140), (141), (142), (143), (144),
% 203.95/34.76  | | | |            (145), (147), (149), (152), (153), (155), (156), (161),
% 203.95/34.76  | | | |            (162), (163), (164), (166), (167), (168), (169), (170),
% 203.95/34.76  | | | |            (171), (172), (173), (174), (175), (177), (294) are
% 203.95/34.76  | | | |            inconsistent by sub-proof #1008.
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | End of split
% 203.95/34.76  | | | 
% 203.95/34.76  | | End of split
% 203.95/34.76  | | 
% 203.95/34.76  | End of split
% 203.95/34.76  | 
% 203.95/34.76  End of proof
% 203.95/34.76  
% 203.95/34.76  Sub-proof #671 shows that the following formulas are inconsistent:
% 203.95/34.76  ----------------------------------------------------------------
% 203.95/34.76    (1)   ~ (e3 = e1)
% 203.95/34.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.76    (3)  op(all_52_7, all_52_7) = e0
% 203.95/34.76    (4)  op(all_52_5, all_52_5) = e1
% 203.95/34.76    (5)   ~ (e3 = e0)
% 203.95/34.76    (6)   ~ (all_4_0 = e1)
% 203.95/34.76    (7)   ~ (all_52_5 = all_4_0)
% 203.95/34.76    (8)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.76    (9)  all_32_2 = all_4_2
% 203.95/34.76    (10)  op(e2, e2) = all_4_2
% 203.95/34.76    (11)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.95/34.76    (12)  all_56_5 = all_4_2
% 203.95/34.76    (13)  all_58_2 = all_4_0
% 203.95/34.76    (14)  op(all_4_2, e2) = e3
% 203.95/34.76    (15)  all_56_8 = all_52_5
% 203.95/34.76    (16)   ~ (all_52_5 = all_52_7)
% 203.95/34.76    (17)  all_58_12 = all_52_7
% 203.95/34.76    (18)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.76    (19)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.95/34.76    (20)   ~ (all_52_5 = e3)
% 203.95/34.76    (21)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.76    (22)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.76    (23)  all_56_4 = all_4_0
% 203.95/34.76    (24)  all_58_0 = e3
% 203.95/34.76    (25)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.76    (26)   ~ (all_52_5 = all_10_2)
% 203.95/34.76    (27)   ~ (all_52_7 = all_4_0)
% 203.95/34.76    (28)   ~ (all_52_9 = all_4_2)
% 203.95/34.76    (29)  op(all_4_2, all_4_2) = all_52_10
% 203.95/34.76    (30)  all_32_0 = all_4_0
% 203.95/34.76    (31)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.95/34.76    (32)  all_58_6 = all_52_5
% 203.95/34.76    (33)   ~ (all_4_0 = all_4_2)
% 203.95/34.76    (34)  op(e3, e2) = all_52_9
% 203.95/34.76    (35)  op(e1, e1) = all_10_2
% 203.95/34.76  
% 203.95/34.76  Begin of proof
% 203.95/34.76  | 
% 203.95/34.76  | BETA: splitting (18) gives:
% 203.95/34.76  | 
% 203.95/34.76  | Case 1:
% 203.95/34.76  | | 
% 203.95/34.76  | |   (36)  all_58_0 = e1
% 203.95/34.76  | | 
% 203.95/34.76  | | COMBINE_EQS: (24), (36) imply:
% 203.95/34.76  | |   (37)  e3 = e1
% 203.95/34.76  | | 
% 203.95/34.76  | | REDUCE: (1), (37) imply:
% 203.95/34.76  | |   (38)  $false
% 203.95/34.76  | | 
% 203.95/34.76  | | CLOSE: (38) is inconsistent.
% 203.95/34.76  | | 
% 203.95/34.76  | Case 2:
% 203.95/34.76  | | 
% 203.95/34.76  | |   (39)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.76  | | 
% 203.95/34.76  | | BETA: splitting (25) gives:
% 203.95/34.76  | | 
% 203.95/34.76  | | Case 1:
% 203.95/34.76  | | | 
% 203.95/34.76  | | |   (40)  all_56_8 = e3
% 203.95/34.76  | | | 
% 203.95/34.76  | | | REF_CLOSE: (15), (20), (40) are inconsistent by sub-proof #1325.
% 203.95/34.76  | | | 
% 203.95/34.76  | | Case 2:
% 203.95/34.76  | | | 
% 203.95/34.76  | | |   (41)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.76  | | | 
% 203.95/34.76  | | | BETA: splitting (21) gives:
% 203.95/34.76  | | | 
% 203.95/34.76  | | | Case 1:
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | |   (42)  all_58_12 = e1
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | COMBINE_EQS: (17), (42) imply:
% 203.95/34.76  | | | |   (43)  all_52_7 = e1
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | SIMP: (43) implies:
% 203.95/34.76  | | | |   (44)  all_52_7 = e1
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (16), (44) imply:
% 203.95/34.76  | | | |   (45)   ~ (all_52_5 = e1)
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (27), (44) imply:
% 203.95/34.76  | | | |   (46)   ~ (all_4_0 = e1)
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (3), (44) imply:
% 203.95/34.76  | | | |   (47)  op(e1, e1) = e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | GROUND_INST: instantiating (2) with all_10_2, e0, e1, e1, simplifying
% 203.95/34.76  | | | |              with (35), (47) gives:
% 203.95/34.76  | | | |   (48)  all_10_2 = e0
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | REDUCE: (26), (48) imply:
% 203.95/34.76  | | | |   (49)   ~ (all_52_5 = e0)
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | BETA: splitting (11) gives:
% 203.95/34.76  | | | | 
% 203.95/34.76  | | | | Case 1:
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | |   (50)  all_58_0 = e0
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | | COMBINE_EQS: (24), (50) imply:
% 203.95/34.76  | | | | |   (51)  e3 = e0
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | | REDUCE: (5), (51) imply:
% 203.95/34.76  | | | | |   (52)  $false
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | | CLOSE: (52) is inconsistent.
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | Case 2:
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | |   (53)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | | BETA: splitting (53) gives:
% 203.95/34.76  | | | | | 
% 203.95/34.76  | | | | | Case 1:
% 203.95/34.76  | | | | | | 
% 203.95/34.76  | | | | | |   (54)  all_58_2 = e0
% 203.95/34.76  | | | | | | 
% 203.95/34.76  | | | | | | REF_CLOSE: (2), (9), (10), (12), (13), (14), (19), (28), (29), (30),
% 203.95/34.76  | | | | | |            (31), (33), (34), (54) are inconsistent by sub-proof
% 203.95/34.76  | | | | | |            #675.
% 203.95/34.76  | | | | | | 
% 203.95/34.76  | | | | | Case 2:
% 203.95/34.76  | | | | | | 
% 203.95/34.76  | | | | | |   (55)   ~ (all_58_2 = e0)
% 203.95/34.76  | | | | | | 
% 203.95/34.76  | | | | | | REDUCE: (13), (55) imply:
% 203.95/34.76  | | | | | |   (56)   ~ (all_4_0 = e0)
% 203.95/34.76  | | | | | | 
% 203.95/34.77  | | | | | | REF_CLOSE: (6), (7), (8), (15), (22), (23), (32), (41), (45), (49),
% 203.95/34.77  | | | | | |            (56) are inconsistent by sub-proof #672.
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | End of split
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | End of split
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | Case 2:
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | |   (57)   ~ (all_58_12 = e1)
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | REF_CLOSE: (2), (4), (6), (13), (17), (26), (32), (35), (39), (57) are
% 203.95/34.77  | | | |            inconsistent by sub-proof #850.
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | End of split
% 203.95/34.77  | | | 
% 203.95/34.77  | | End of split
% 203.95/34.77  | | 
% 203.95/34.77  | End of split
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #672 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ~ (all_4_0 = e1)
% 203.95/34.77    (2)   ~ (all_52_5 = all_4_0)
% 203.95/34.77    (3)   ~ (all_52_5 = e1)
% 203.95/34.77    (4)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.77    (5)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.77    (6)  all_56_8 = all_52_5
% 203.95/34.77    (7)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.77    (8)  all_56_4 = all_4_0
% 203.95/34.77    (9)   ~ (all_52_5 = e0)
% 203.95/34.77    (10)   ~ (all_4_0 = e0)
% 203.95/34.77    (11)  all_58_6 = all_52_5
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | BETA: splitting (4) gives:
% 203.95/34.77  | 
% 203.95/34.77  | Case 1:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (12)  all_58_6 = e2
% 203.95/34.77  | | 
% 203.95/34.77  | | COMBINE_EQS: (11), (12) imply:
% 203.95/34.77  | |   (13)  all_52_5 = e2
% 203.95/34.77  | | 
% 203.95/34.77  | | SIMP: (13) implies:
% 203.95/34.77  | |   (14)  all_52_5 = e2
% 203.95/34.77  | | 
% 203.95/34.77  | | REDUCE: (2), (14) imply:
% 203.95/34.77  | |   (15)   ~ (all_4_0 = e2)
% 203.95/34.77  | | 
% 203.95/34.77  | | SIMP: (15) implies:
% 203.95/34.77  | |   (16)   ~ (all_4_0 = e2)
% 203.95/34.77  | | 
% 203.95/34.77  | | REF_CLOSE: (1), (7), (8), (10), (16) are inconsistent by sub-proof #673.
% 203.95/34.77  | | 
% 203.95/34.77  | Case 2:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (17)   ~ (all_58_6 = e2)
% 203.95/34.77  | | 
% 203.95/34.77  | | REDUCE: (11), (17) imply:
% 203.95/34.77  | |   (18)   ~ (all_52_5 = e2)
% 203.95/34.77  | | 
% 203.95/34.77  | | REF_CLOSE: (3), (5), (6), (9), (18) are inconsistent by sub-proof #1004.
% 203.95/34.77  | | 
% 203.95/34.77  | End of split
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #673 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ~ (all_4_0 = e1)
% 203.95/34.77    (2)   ~ (all_4_0 = e2)
% 203.95/34.77    (3)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.77    (4)  all_56_4 = all_4_0
% 203.95/34.77    (5)   ~ (all_4_0 = e0)
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | BETA: splitting (3) gives:
% 203.95/34.77  | 
% 203.95/34.77  | Case 1:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (6)  all_56_4 = e2
% 203.95/34.77  | | 
% 203.95/34.77  | | COMBINE_EQS: (4), (6) imply:
% 203.95/34.77  | |   (7)  all_4_0 = e2
% 203.95/34.77  | | 
% 203.95/34.77  | | REDUCE: (2), (7) imply:
% 203.95/34.77  | |   (8)  $false
% 203.95/34.77  | | 
% 203.95/34.77  | | CLOSE: (8) is inconsistent.
% 203.95/34.77  | | 
% 203.95/34.77  | Case 2:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (9)  all_56_4 = e1 | all_56_4 = e0
% 203.95/34.77  | | 
% 203.95/34.77  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #674.
% 203.95/34.77  | | 
% 203.95/34.77  | End of split
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #674 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)  all_56_4 = e1 | all_56_4 = e0
% 203.95/34.77    (2)  all_56_4 = all_4_0
% 203.95/34.77    (3)   ~ (all_4_0 = e1)
% 203.95/34.77    (4)   ~ (all_4_0 = e0)
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | BETA: splitting (1) gives:
% 203.95/34.77  | 
% 203.95/34.77  | Case 1:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (5)  all_56_4 = e1
% 203.95/34.77  | | 
% 203.95/34.77  | | COMBINE_EQS: (2), (5) imply:
% 203.95/34.77  | |   (6)  all_4_0 = e1
% 203.95/34.77  | | 
% 203.95/34.77  | | REDUCE: (3), (6) imply:
% 203.95/34.77  | |   (7)  $false
% 203.95/34.77  | | 
% 203.95/34.77  | | CLOSE: (7) is inconsistent.
% 203.95/34.77  | | 
% 203.95/34.77  | Case 2:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (8)  all_56_4 = e0
% 203.95/34.77  | | 
% 203.95/34.77  | | COMBINE_EQS: (2), (8) imply:
% 203.95/34.77  | |   (9)  all_4_0 = e0
% 203.95/34.77  | | 
% 203.95/34.77  | | REDUCE: (4), (9) imply:
% 203.95/34.77  | |   (10)  $false
% 203.95/34.77  | | 
% 203.95/34.77  | | CLOSE: (10) is inconsistent.
% 203.95/34.77  | | 
% 203.95/34.77  | End of split
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #675 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.77    (2)  all_32_2 = all_4_2
% 203.95/34.77    (3)  op(e2, e2) = all_4_2
% 203.95/34.77    (4)  all_56_5 = all_4_2
% 203.95/34.77    (5)  all_58_2 = all_4_0
% 203.95/34.77    (6)  op(all_4_2, e2) = e3
% 203.95/34.77    (7)  all_58_2 = e0
% 203.95/34.77    (8)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.95/34.77    (9)   ~ (all_52_9 = all_4_2)
% 203.95/34.77    (10)  op(all_4_2, all_4_2) = all_52_10
% 203.95/34.77    (11)  all_32_0 = all_4_0
% 203.95/34.77    (12)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 203.95/34.77    (13)   ~ (all_4_0 = all_4_2)
% 203.95/34.77    (14)  op(e3, e2) = all_52_9
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | COMBINE_EQS: (5), (7) imply:
% 203.95/34.77  |   (15)  all_4_0 = e0
% 203.95/34.77  | 
% 203.95/34.77  | SIMP: (15) implies:
% 203.95/34.77  |   (16)  all_4_0 = e0
% 203.95/34.77  | 
% 203.95/34.77  | COMBINE_EQS: (11), (16) imply:
% 203.95/34.77  |   (17)  all_32_0 = e0
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (13), (16) imply:
% 203.95/34.77  |   (18)   ~ (all_4_2 = e0)
% 203.95/34.77  | 
% 203.95/34.77  | SIMP: (18) implies:
% 203.95/34.77  |   (19)   ~ (all_4_2 = e0)
% 203.95/34.77  | 
% 203.95/34.77  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (14), (17), (19) are
% 203.95/34.77  |            inconsistent by sub-proof #972.
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #676 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.77    (2)  op(all_52_5, all_52_5) = e1
% 203.95/34.77    (3)   ~ (all_52_17 = all_52_25)
% 203.95/34.77    (4)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.95/34.77    (5)  all_58_0 = all_6_2
% 203.95/34.77    (6)  op(all_14_2, e0) = all_14_1
% 203.95/34.77    (7)   ~ (all_10_0 = e3)
% 203.95/34.77    (8)  all_40_2 = all_10_2
% 203.95/34.77    (9)  op(e3, e0) = all_52_25
% 203.95/34.77    (10)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.77    (11)   ~ (all_52_29 = all_14_2)
% 203.95/34.77    (12)  op(e2, e2) = all_4_2
% 203.95/34.77    (13)  all_58_7 = all_10_0
% 203.95/34.77    (14)  all_58_11 = all_52_29
% 203.95/34.77    (15)   ~ (all_52_25 = all_14_2)
% 203.95/34.77    (16)  op(e0, e1) = all_52_23
% 203.95/34.77    (17)  all_56_15 = all_14_2
% 203.95/34.77    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.77    (19)   ~ (all_10_0 = e2)
% 203.95/34.77    (20)  all_56_9 = all_10_0
% 203.95/34.77    (21)  op(all_6_2, all_6_2) = e3
% 203.95/34.77    (22)   ~ (all_52_5 = all_52_7)
% 203.95/34.77    (23)  all_58_12 = all_52_7
% 203.95/34.77    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.77    (25)   ~ (all_52_7 = all_14_2)
% 203.95/34.77    (26)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.95/34.77    (27)  all_58_2 = all_52_3
% 203.95/34.77    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.77    (29)  op(all_52_3, all_52_3) = e2
% 203.95/34.77    (30)  op(e3, e1) = all_52_17
% 203.95/34.77    (31)   ~ (all_52_9 = all_52_25)
% 203.95/34.77    (32)  all_58_8 = all_10_2
% 203.95/34.77    (33)   ~ (all_52_5 = all_10_2)
% 203.95/34.77    (34)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.77    (35)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.95/34.77    (36)   ~ (all_52_5 = all_6_2)
% 203.95/34.77    (37)   ~ (all_52_9 = all_6_2)
% 203.95/34.77    (38)  op(e3, e3) = all_6_2
% 203.95/34.77    (39)  all_56_15 = e3
% 203.95/34.77    (40)  all_40_0 = all_10_0
% 203.95/34.77    (41)  all_56_3 = all_52_25
% 203.95/34.77    (42)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.77    (43)  all_56_1 = all_52_9
% 203.95/34.77    (44)  op(e0, all_14_1) = e3
% 203.95/34.77    (45)  all_58_6 = all_52_5
% 203.95/34.77    (46)  op(all_10_2, e1) = e2
% 203.95/34.77    (47)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.77    (48)   ~ (all_52_9 = all_52_17)
% 203.95/34.77    (49)  op(e1, e1) = all_10_2
% 203.95/34.77    (50)   ~ (all_52_23 = all_10_2)
% 203.95/34.77    (51)   ~ (all_52_3 = all_4_2)
% 203.95/34.77    (52)   ~ (all_52_9 = all_10_0)
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | COMBINE_EQS: (17), (39) imply:
% 203.95/34.77  |   (53)  all_14_2 = e3
% 203.95/34.77  | 
% 203.95/34.77  | SIMP: (53) implies:
% 203.95/34.77  |   (54)  all_14_2 = e3
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (25), (54) imply:
% 203.95/34.77  |   (55)   ~ (all_52_7 = e3)
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (15), (54) imply:
% 203.95/34.77  |   (56)   ~ (all_52_25 = e3)
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (11), (54) imply:
% 203.95/34.77  |   (57)   ~ (all_52_29 = e3)
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (42), (54) imply:
% 203.95/34.77  |   (58)  op(e3, e3) = all_52_30
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (6), (54) imply:
% 203.95/34.77  |   (59)  op(e3, e0) = all_14_1
% 203.95/34.77  | 
% 203.95/34.77  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 203.95/34.77  |            (16), (18), (19), (20), (21), (22), (23), (24), (26), (27), (28),
% 203.95/34.77  |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (40),
% 203.95/34.77  |            (41), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 203.95/34.77  |            (55), (56), (57), (58), (59) are inconsistent by sub-proof #677.
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #677 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.77    (2)  op(all_52_5, all_52_5) = e1
% 203.95/34.77    (3)   ~ (all_52_17 = all_52_25)
% 203.95/34.77    (4)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.95/34.77    (5)  all_58_0 = all_6_2
% 203.95/34.77    (6)   ~ (all_10_0 = e3)
% 203.95/34.77    (7)  all_40_2 = all_10_2
% 203.95/34.77    (8)  op(e3, e0) = all_52_25
% 203.95/34.77    (9)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.77    (10)  op(e2, e2) = all_4_2
% 203.95/34.77    (11)  all_58_7 = all_10_0
% 203.95/34.77    (12)  all_58_11 = all_52_29
% 203.95/34.77    (13)  op(e0, e1) = all_52_23
% 203.95/34.77    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.77    (15)   ~ (all_10_0 = e2)
% 203.95/34.77    (16)  all_56_9 = all_10_0
% 203.95/34.77    (17)  op(all_6_2, all_6_2) = e3
% 203.95/34.77    (18)   ~ (all_52_5 = all_52_7)
% 203.95/34.77    (19)  all_58_12 = all_52_7
% 203.95/34.77    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.77    (21)   ~ (all_52_7 = e3)
% 203.95/34.77    (22)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.95/34.77    (23)  all_58_2 = all_52_3
% 203.95/34.77    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.77    (25)   ~ (all_52_29 = e3)
% 203.95/34.77    (26)   ~ (all_52_25 = e3)
% 203.95/34.77    (27)  op(all_52_3, all_52_3) = e2
% 203.95/34.77    (28)  op(e3, e3) = all_52_30
% 203.95/34.77    (29)  op(e3, e1) = all_52_17
% 203.95/34.77    (30)   ~ (all_52_9 = all_52_25)
% 203.95/34.77    (31)  all_58_8 = all_10_2
% 203.95/34.77    (32)   ~ (all_52_5 = all_10_2)
% 203.95/34.77    (33)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.77    (34)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.95/34.77    (35)   ~ (all_52_5 = all_6_2)
% 203.95/34.77    (36)   ~ (all_52_9 = all_6_2)
% 203.95/34.77    (37)  op(e3, e3) = all_6_2
% 203.95/34.77    (38)  op(e3, e0) = all_14_1
% 203.95/34.77    (39)  all_40_0 = all_10_0
% 203.95/34.77    (40)  all_56_3 = all_52_25
% 203.95/34.77    (41)  all_56_1 = all_52_9
% 203.95/34.77    (42)  op(e0, all_14_1) = e3
% 203.95/34.77    (43)  all_58_6 = all_52_5
% 203.95/34.77    (44)  op(all_10_2, e1) = e2
% 203.95/34.77    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.77    (46)   ~ (all_52_9 = all_52_17)
% 203.95/34.77    (47)  op(e1, e1) = all_10_2
% 203.95/34.77    (48)   ~ (all_52_23 = all_10_2)
% 203.95/34.77    (49)   ~ (all_52_3 = all_4_2)
% 203.95/34.77    (50)   ~ (all_52_9 = all_10_0)
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | GROUND_INST: instantiating (1) with all_52_25, all_14_1, e0, e3, simplifying
% 203.95/34.77  |              with (8), (38) gives:
% 203.95/34.77  |   (51)  all_52_25 = all_14_1
% 203.95/34.77  | 
% 203.95/34.77  | GROUND_INST: instantiating (1) with all_6_2, all_52_30, e3, e3, simplifying
% 203.95/34.77  |              with (28), (37) gives:
% 203.95/34.77  |   (52)  all_52_30 = all_6_2
% 203.95/34.77  | 
% 203.95/34.77  | COMBINE_EQS: (40), (51) imply:
% 203.95/34.77  |   (53)  all_56_3 = all_14_1
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (30), (51) imply:
% 203.95/34.77  |   (54)   ~ (all_52_9 = all_14_1)
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (3), (51) imply:
% 203.95/34.77  |   (55)   ~ (all_52_17 = all_14_1)
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (26), (51) imply:
% 203.95/34.77  |   (56)   ~ (all_14_1 = e3)
% 203.95/34.77  | 
% 203.95/34.77  | BETA: splitting (20) gives:
% 203.95/34.77  | 
% 203.95/34.77  | Case 1:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (57)  all_58_6 = e3
% 203.95/34.77  | | 
% 203.95/34.77  | | COMBINE_EQS: (43), (57) imply:
% 203.95/34.77  | |   (58)  all_52_5 = e3
% 203.95/34.77  | | 
% 203.95/34.77  | | SIMP: (58) implies:
% 203.95/34.77  | |   (59)  all_52_5 = e3
% 203.95/34.77  | | 
% 203.95/34.77  | | REF_CLOSE: (1), (2), (5), (10), (14), (17), (18), (19), (23), (24), (27),
% 203.95/34.77  | |            (32), (35), (37), (43), (47), (49), (59) are inconsistent by
% 203.95/34.77  | |            sub-proof #704.
% 203.95/34.77  | | 
% 203.95/34.77  | Case 2:
% 203.95/34.77  | | 
% 203.95/34.77  | |   (60)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.77  | | 
% 203.95/34.77  | | BETA: splitting (60) gives:
% 203.95/34.77  | | 
% 203.95/34.77  | | Case 1:
% 203.95/34.77  | | | 
% 203.95/34.77  | | |   (61)  all_58_7 = e3
% 203.95/34.77  | | | 
% 203.95/34.77  | | | COMBINE_EQS: (11), (61) imply:
% 203.95/34.77  | | |   (62)  all_10_0 = e3
% 203.95/34.77  | | | 
% 203.95/34.77  | | | REDUCE: (6), (62) imply:
% 203.95/34.77  | | |   (63)  $false
% 203.95/34.77  | | | 
% 203.95/34.77  | | | CLOSE: (63) is inconsistent.
% 203.95/34.77  | | | 
% 203.95/34.77  | | Case 2:
% 203.95/34.77  | | | 
% 203.95/34.77  | | |   (64)  all_58_8 = e3 | all_58_11 = e3
% 203.95/34.77  | | | 
% 203.95/34.77  | | | BETA: splitting (64) gives:
% 203.95/34.77  | | | 
% 203.95/34.77  | | | Case 1:
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | |   (65)  all_58_8 = e3
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | COMBINE_EQS: (31), (65) imply:
% 203.95/34.77  | | | |   (66)  all_10_2 = e3
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | COMBINE_EQS: (7), (66) imply:
% 203.95/34.77  | | | |   (67)  all_40_2 = e3
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | REDUCE: (48), (66) imply:
% 203.95/34.77  | | | |   (68)   ~ (all_52_23 = e3)
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | REDUCE: (9), (66) imply:
% 203.95/34.77  | | | |   (69)  op(e3, e3) = all_52_20
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | REDUCE: (44), (66) imply:
% 203.95/34.77  | | | |   (70)  op(e3, e1) = e2
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | BETA: splitting (22) gives:
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | Case 1:
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | |   (71)   ~ (all_40_2 = e3)
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | | REDUCE: (67), (71) imply:
% 203.95/34.77  | | | | |   (72)  $false
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | | CLOSE: (72) is inconsistent.
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | Case 2:
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | |   (73)   ~ (all_40_0 = e0)
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | | REDUCE: (39), (73) imply:
% 203.95/34.77  | | | | |   (74)   ~ (all_10_0 = e0)
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | | BETA: splitting (4) gives:
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | | Case 1:
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | |   (75)  all_56_9 = e2
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | | REF_CLOSE: (15), (16), (75) are inconsistent by sub-proof #991.
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | Case 2:
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | |   (76)  all_56_9 = e1 | all_56_9 = e0
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | | BETA: splitting (76) gives:
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | | Case 1:
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | |   (77)  all_56_9 = e1
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | COMBINE_EQS: (16), (77) imply:
% 203.95/34.77  | | | | | | |   (78)  all_10_0 = e1
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | SIMP: (78) implies:
% 203.95/34.77  | | | | | | |   (79)  all_10_0 = e1
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | REDUCE: (50), (79) imply:
% 203.95/34.77  | | | | | | |   (80)   ~ (all_52_9 = e1)
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | GROUND_INST: instantiating (1) with all_52_17, e2, e1, e3,
% 203.95/34.77  | | | | | | |              simplifying with (29), (70) gives:
% 203.95/34.77  | | | | | | |   (81)  all_52_17 = e2
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | GROUND_INST: instantiating (1) with all_6_2, all_52_20, e3, e3,
% 203.95/34.77  | | | | | | |              simplifying with (37), (69) gives:
% 203.95/34.77  | | | | | | |   (82)  all_52_20 = all_6_2
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | REDUCE: (46), (81) imply:
% 203.95/34.77  | | | | | | |   (83)   ~ (all_52_9 = e2)
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | REDUCE: (55), (81) imply:
% 203.95/34.77  | | | | | | |   (84)   ~ (all_14_1 = e2)
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | SIMP: (84) implies:
% 203.95/34.77  | | | | | | |   (85)   ~ (all_14_1 = e2)
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | REDUCE: (33), (81) imply:
% 203.95/34.77  | | | | | | |   (86)  op(e2, e2) = all_52_16
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_16, e2, e2,
% 203.95/34.77  | | | | | | |              simplifying with (10), (86) gives:
% 203.95/34.77  | | | | | | |   (87)  all_52_16 = all_4_2
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | BETA: splitting (45) gives:
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | Case 1:
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | |   (88)  all_56_1 = e3
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | | COMBINE_EQS: (41), (88) imply:
% 203.95/34.77  | | | | | | | |   (89)  all_52_9 = e3
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | | SIMP: (89) implies:
% 203.95/34.77  | | | | | | | |   (90)  all_52_9 = e3
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | | REF_CLOSE: (1), (2), (5), (10), (14), (17), (19), (21), (23),
% 203.95/34.77  | | | | | | | |            (24), (27), (32), (36), (37), (43), (47), (49), (90)
% 203.95/34.77  | | | | | | | |            are inconsistent by sub-proof #1195.
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | Case 2:
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | |   (91)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | | BETA: splitting (91) gives:
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | | Case 1:
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | |   (92)  all_56_1 = e2
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | REF_CLOSE: (41), (83), (92) are inconsistent by sub-proof
% 203.95/34.77  | | | | | | | | |            #1194.
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | Case 2:
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | |   (93)  all_56_1 = e1 | all_56_1 = e0
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | BETA: splitting (93) gives:
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | Case 1:
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | |   (94)  all_56_1 = e1
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | REF_CLOSE: (41), (80), (94) are inconsistent by sub-proof
% 203.95/34.77  | | | | | | | | | |            #1061.
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | Case 2:
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | |   (95)  all_56_1 = e0
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | COMBINE_EQS: (41), (95) imply:
% 203.95/34.77  | | | | | | | | | |   (96)  all_52_9 = e0
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | SIMP: (96) implies:
% 203.95/34.77  | | | | | | | | | |   (97)  all_52_9 = e0
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | REDUCE: (54), (97) imply:
% 203.95/34.77  | | | | | | | | | |   (98)   ~ (all_14_1 = e0)
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | SIMP: (98) implies:
% 203.95/34.77  | | | | | | | | | |   (99)   ~ (all_14_1 = e0)
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | BETA: splitting (34) gives:
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | Case 1:
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | |   (100)  all_56_3 = e3
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | REF_CLOSE: (53), (56), (100) are inconsistent by sub-proof
% 203.95/34.77  | | | | | | | | | | |            #1200.
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | Case 2:
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | |   (101)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | BETA: splitting (101) gives:
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | Case 1:
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | |   (102)  all_56_3 = e2
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | REF_CLOSE: (53), (85), (102) are inconsistent by sub-proof
% 203.95/34.77  | | | | | | | | | | | |            #1183.
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | Case 2:
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | |   (103)  all_56_3 = e1 | all_56_3 = e0
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | BETA: splitting (103) gives:
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | Case 1:
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | |   (104)  all_56_3 = e1
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | COMBINE_EQS: (53), (104) imply:
% 203.95/34.77  | | | | | | | | | | | | |   (105)  all_14_1 = e1
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | SIMP: (105) implies:
% 203.95/34.77  | | | | | | | | | | | | |   (106)  all_14_1 = e1
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | REDUCE: (42), (106) imply:
% 203.95/34.77  | | | | | | | | | | | | |   (107)  op(e0, e1) = e3
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_52_23, e3, e1, e0,
% 203.95/34.77  | | | | | | | | | | | | |              simplifying with (13), (107) gives:
% 203.95/34.77  | | | | | | | | | | | | |   (108)  all_52_23 = e3
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | REDUCE: (68), (108) imply:
% 203.95/34.77  | | | | | | | | | | | | |   (109)  $false
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | Case 2:
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | |   (110)  all_56_3 = e0
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | COMBINE_EQS: (53), (110) imply:
% 203.95/34.77  | | | | | | | | | | | | |   (111)  all_14_1 = e0
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | SIMP: (111) implies:
% 203.95/34.77  | | | | | | | | | | | | |   (112)  all_14_1 = e0
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | REDUCE: (99), (112) imply:
% 203.95/34.77  | | | | | | | | | | | | |   (113)  $false
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | | CLOSE: (113) is inconsistent.
% 203.95/34.77  | | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | | End of split
% 203.95/34.77  | | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | | End of split
% 203.95/34.77  | | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | | End of split
% 203.95/34.77  | | | | | | | | | | 
% 203.95/34.77  | | | | | | | | | End of split
% 203.95/34.77  | | | | | | | | | 
% 203.95/34.77  | | | | | | | | End of split
% 203.95/34.77  | | | | | | | | 
% 203.95/34.77  | | | | | | | End of split
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | Case 2:
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | |   (114)  all_56_9 = e0
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | | REF_CLOSE: (16), (74), (114) are inconsistent by sub-proof #989.
% 203.95/34.77  | | | | | | | 
% 203.95/34.77  | | | | | | End of split
% 203.95/34.77  | | | | | | 
% 203.95/34.77  | | | | | End of split
% 203.95/34.77  | | | | | 
% 203.95/34.77  | | | | End of split
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | Case 2:
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | |   (115)  all_58_11 = e3
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | | REF_CLOSE: (12), (25), (115) are inconsistent by sub-proof #1323.
% 203.95/34.77  | | | | 
% 203.95/34.77  | | | End of split
% 203.95/34.77  | | | 
% 203.95/34.77  | | End of split
% 203.95/34.77  | | 
% 203.95/34.77  | End of split
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #678 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.77    (2)   ~ (e3 = e0)
% 203.95/34.77    (3)  op(all_14_2, e0) = all_14_1
% 203.95/34.77    (4)  op(e0, e0) = all_14_2
% 203.95/34.77    (5)  all_58_15 = e0
% 203.95/34.77    (6)  all_58_15 = all_14_2
% 203.95/34.77    (7)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.77    (8)  op(e0, all_14_1) = e3
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | COMBINE_EQS: (5), (6) imply:
% 203.95/34.77  |   (9)  all_14_2 = e0
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (7), (9) imply:
% 203.95/34.77  |   (10)  op(e0, e0) = all_52_30
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (3), (9) imply:
% 203.95/34.77  |   (11)  op(e0, e0) = all_14_1
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (4), (9) imply:
% 203.95/34.77  |   (12)  op(e0, e0) = e0
% 203.95/34.77  | 
% 203.95/34.77  | GROUND_INST: instantiating (1) with all_14_1, all_52_30, e0, e0, simplifying
% 203.95/34.77  |              with (10), (11) gives:
% 203.95/34.77  |   (13)  all_52_30 = all_14_1
% 203.95/34.77  | 
% 203.95/34.77  | GROUND_INST: instantiating (1) with e0, all_52_30, e0, e0, simplifying with
% 203.95/34.77  |              (10), (12) gives:
% 203.95/34.77  |   (14)  all_52_30 = e0
% 203.95/34.77  | 
% 203.95/34.77  | REF_CLOSE: (1), (2), (8), (11), (13), (14) are inconsistent by sub-proof #679.
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #679 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.77    (2)   ~ (e3 = e0)
% 203.95/34.77    (3)  all_52_30 = e0
% 203.95/34.77    (4)  all_52_30 = all_14_1
% 203.95/34.77    (5)  op(e0, e0) = all_14_1
% 203.95/34.77    (6)  op(e0, all_14_1) = e3
% 203.95/34.77  
% 203.95/34.77  Begin of proof
% 203.95/34.77  | 
% 203.95/34.77  | COMBINE_EQS: (3), (4) imply:
% 203.95/34.77  |   (7)  all_14_1 = e0
% 203.95/34.77  | 
% 203.95/34.77  | SIMP: (7) implies:
% 203.95/34.77  |   (8)  all_14_1 = e0
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (6), (8) imply:
% 203.95/34.77  |   (9)  op(e0, e0) = e3
% 203.95/34.77  | 
% 203.95/34.77  | REDUCE: (5), (8) imply:
% 203.95/34.77  |   (10)  op(e0, e0) = e0
% 203.95/34.77  | 
% 203.95/34.77  | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #1336.
% 203.95/34.77  | 
% 203.95/34.77  End of proof
% 203.95/34.77  
% 203.95/34.77  Sub-proof #680 shows that the following formulas are inconsistent:
% 203.95/34.77  ----------------------------------------------------------------
% 203.95/34.77    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.95/34.77    (2)   ~ (all_52_15 = all_52_23)
% 203.95/34.77    (3)   ~ (all_52_25 = all_52_27)
% 203.95/34.77    (4)  all_58_14 = all_52_23
% 203.95/34.77    (5)   ~ (e3 = e1)
% 203.95/34.77    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.95/34.77    (7)  op(all_52_3, all_52_3) = all_52_2
% 203.95/34.77    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.77    (9)   ~ (all_52_5 = all_52_13)
% 203.95/34.77    (10)  all_58_1 = all_52_9
% 203.95/34.77    (11)   ~ (all_52_9 = all_52_13)
% 203.95/34.78    (12)   ~ (e3 = e0)
% 203.95/34.78    (13)  op(e2, e3) = all_52_3
% 203.95/34.78    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.78    (15)  op(e0, e2) = all_52_15
% 203.95/34.78    (16)   ~ (all_52_7 = all_52_15)
% 203.95/34.78    (17)   ~ (all_52_3 = all_52_19)
% 203.95/34.78    (18)  op(all_52_7, all_52_7) = all_52_6
% 203.95/34.78    (19)   ~ (all_52_17 = all_52_25)
% 203.95/34.78    (20)   ~ (all_52_3 = all_6_2)
% 203.95/34.78    (21)  all_58_0 = all_6_2
% 203.95/34.78    (22)  op(all_14_2, e0) = all_14_1
% 203.95/34.78    (23)  all_56_4 = all_52_3
% 203.95/34.78    (24)   ~ (all_52_17 = all_10_2)
% 203.95/34.78    (25)   ~ (all_10_0 = e3)
% 203.95/34.78    (26)  op(e3, e0) = all_52_25
% 203.95/34.78    (27)  op(all_52_5, all_52_5) = all_52_4
% 203.95/34.78    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 203.95/34.78    (29)  op(all_52_19, all_52_19) = all_52_18
% 203.95/34.78    (30)   ~ (all_52_27 = all_52_29)
% 203.95/34.78    (31)  all_58_13 = all_52_15
% 203.95/34.78    (32)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.78    (33)  all_58_9 = all_52_25
% 203.95/34.78    (34)   ~ (all_6_1 = e1)
% 203.95/34.78    (35)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.78    (36)   ~ (all_52_29 = all_14_2)
% 203.95/34.78    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.95/34.78    (38)  op(all_52_27, all_52_27) = all_52_26
% 203.95/34.78    (39)  op(e1, e3) = all_52_5
% 203.95/34.78    (40)  op(e2, e2) = all_4_2
% 203.95/34.78    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.95/34.78    (42)   ~ (all_52_3 = all_52_5)
% 203.95/34.78    (43)   ~ (all_4_1 = e3)
% 203.95/34.78    (44)  all_58_11 = all_52_29
% 203.95/34.78    (45)  all_56_5 = all_4_2
% 203.95/34.78    (46)   ~ (all_52_25 = all_14_2)
% 203.95/34.78    (47)   ~ (all_52_9 = all_52_15)
% 203.95/34.78    (48)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.78    (49)   ~ (all_52_3 = all_52_27)
% 203.95/34.78    (50)  op(all_10_2, e1) = all_10_1
% 203.95/34.78    (51)  op(all_6_2, all_6_2) = all_52_0
% 203.95/34.78    (52)   ~ (all_52_7 = all_6_2)
% 203.95/34.78    (53)  op(e0, e0) = all_14_2
% 203.95/34.78    (54)  op(e0, e1) = all_52_23
% 203.95/34.78    (55)  all_56_15 = all_14_2
% 203.95/34.78    (56)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.78    (57)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.95/34.78    (58)  op(e2, all_4_1) = all_4_0
% 203.95/34.78    (59)  op(e1, e0) = all_52_29
% 203.95/34.78    (60)  all_56_11 = all_52_29
% 203.95/34.78    (61)   ~ (all_10_0 = e2)
% 203.95/34.78    (62)   ~ (all_4_1 = e1)
% 203.95/34.78    (63)   ~ (all_4_0 = e3)
% 203.95/34.78    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.95/34.78    (65)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.95/34.78    (66)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 203.95/34.78    (67)  all_56_9 = all_52_13
% 203.95/34.78    (68)   ~ (e2 = e1)
% 203.95/34.78    (69)   ~ (all_52_13 = all_10_2)
% 203.95/34.78    (70)   ~ (all_6_0 = e1)
% 203.95/34.78    (71)  op(e1, all_10_1) = all_10_0
% 203.95/34.78    (72)  all_58_10 = all_52_27
% 203.95/34.78    (73)  all_56_8 = all_52_5
% 203.95/34.78    (74)  op(all_52_9, all_52_9) = all_52_8
% 203.95/34.78    (75)  op(all_52_15, all_52_15) = all_52_14
% 203.95/34.78    (76)   ~ (all_52_19 = all_52_23)
% 203.95/34.78    (77)   ~ (all_52_25 = all_52_29)
% 203.95/34.78    (78)   ~ (all_52_29 = all_10_2)
% 203.95/34.78    (79)  all_58_7 = all_52_13
% 203.95/34.78    (80)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.95/34.78    (81)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.95/34.78    (82)   ~ (all_52_5 = all_52_7)
% 203.95/34.78    (83)  all_58_12 = all_52_7
% 203.95/34.78    (84)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.78    (85)   ~ (all_52_7 = all_14_2)
% 203.95/34.78    (86)   ~ (all_14_2 = e0)
% 203.95/34.78    (87)  all_58_2 = all_52_3
% 203.95/34.78    (88)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.95/34.78    (89)  all_56_2 = all_52_17
% 203.95/34.78    (90)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.95/34.78    (91)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.78    (92)  op(e3, all_6_1) = all_6_0
% 203.95/34.78    (93)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.95/34.78    (94)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.78    (95)  all_56_7 = all_52_27
% 203.95/34.78    (96)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.78    (97)   ~ (e2 = e0)
% 203.95/34.78    (98)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.95/34.78    (99)  op(all_4_2, e2) = all_4_1
% 203.95/34.78    (100)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.95/34.78    (101)   ~ (all_52_5 = all_52_29)
% 203.95/34.78    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.78    (103)  all_56_6 = all_52_19
% 203.95/34.78    (104)   ~ (all_52_15 = all_14_2)
% 203.95/34.78    (105)   ~ (all_52_19 = all_52_27)
% 203.95/34.78    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.95/34.78    (107)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.78    (108)   ~ (all_6_0 = e2)
% 203.95/34.78    (109)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.95/34.78    (110)   ~ (all_52_13 = all_4_2)
% 203.95/34.78    (111)  op(e3, e1) = all_52_17
% 203.95/34.78    (112)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.95/34.78    (113)  op(e0, e3) = all_52_7
% 203.95/34.78    (114)  op(e1, e2) = all_52_13
% 203.95/34.78    (115)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.95/34.78    (116)   ~ (all_52_9 = all_52_25)
% 203.95/34.78    (117)  all_58_15 = all_14_2
% 203.95/34.78    (118)   ~ (all_52_19 = all_10_2)
% 203.95/34.78    (119)  op(all_52_23, all_52_23) = all_52_22
% 203.95/34.78    (120)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.78    (121)   ~ (all_10_1 = e2)
% 203.95/34.78    (122)  all_58_8 = all_10_2
% 203.95/34.78    (123)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.95/34.78    (124)   ~ (all_52_5 = all_10_2)
% 203.95/34.78    (125)  op(all_52_29, all_52_29) = all_52_28
% 203.95/34.78    (126)   ~ (all_52_23 = all_14_2)
% 203.95/34.78    (127)  all_56_12 = all_52_7
% 203.95/34.78    (128)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.78    (129)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.95/34.78    (130)   ~ (all_52_25 = all_6_2)
% 203.95/34.78    (131)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.95/34.78    (132)   ~ (all_52_9 = all_4_2)
% 203.95/34.78    (133)   ~ (all_52_5 = all_6_2)
% 203.95/34.78    (134)   ~ (all_52_9 = all_6_2)
% 203.95/34.78    (135)   ~ (all_52_13 = all_52_15)
% 203.95/34.78    (136)  all_56_0 = all_6_2
% 203.95/34.78    (137)  op(e3, e3) = all_6_2
% 203.95/34.78    (138)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.95/34.78    (139)   ~ (all_52_27 = all_14_2)
% 203.95/34.78    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.95/34.78    (141)  all_56_14 = all_52_23
% 203.95/34.78    (142)  op(all_4_2, all_4_2) = all_52_10
% 203.95/34.78    (143)  all_56_3 = all_52_25
% 203.95/34.78    (144)   ~ (all_52_3 = all_52_7)
% 203.95/34.78    (145)   ~ (all_10_1 = e3)
% 203.95/34.78    (146)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.78    (147)  all_58_5 = all_52_19
% 203.95/34.78    (148)  all_56_1 = all_52_9
% 203.95/34.78    (149)   ~ (all_52_15 = all_4_2)
% 203.95/34.78    (150)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.95/34.78           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 203.95/34.78           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.95/34.78           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.95/34.78    (151)   ~ (all_52_27 = all_4_2)
% 203.95/34.78    (152)  all_58_6 = all_52_5
% 203.95/34.78    (153)  op(e3, e2) = all_52_9
% 203.95/34.78    (154)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.95/34.78    (155)   ~ (all_52_17 = all_6_2)
% 203.95/34.78    (156)   ~ (e1 = e0)
% 203.95/34.78    (157)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.78    (158)   ~ (e3 = e2)
% 203.95/34.78    (159)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.78    (160)   ~ (all_52_9 = all_52_17)
% 203.95/34.78    (161)  all_56_10 = all_10_2
% 203.95/34.78    (162)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.78    (163)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.95/34.78    (164)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 203.95/34.78    (165)  op(all_52_13, all_52_13) = all_52_12
% 203.95/34.78    (166)   ~ (all_6_1 = e2)
% 203.95/34.78    (167)  op(e1, e1) = all_10_2
% 203.95/34.78    (168)   ~ (all_52_23 = all_10_2)
% 203.95/34.78    (169)   ~ (all_52_7 = all_52_23)
% 203.95/34.78    (170)   ~ (all_52_17 = all_52_19)
% 203.95/34.78    (171)  all_58_3 = all_4_2
% 203.95/34.78    (172)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.95/34.78    (173)  all_56_13 = all_52_15
% 203.95/34.78    (174)   ~ (all_52_3 = all_4_2)
% 203.95/34.78    (175)   ~ (all_52_19 = all_4_2)
% 203.95/34.78    (176)   ~ (all_52_17 = all_52_23)
% 203.95/34.78    (177)  op(all_6_2, e3) = all_6_1
% 203.95/34.78    (178)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.95/34.78    (179)   ~ (all_52_13 = all_52_29)
% 203.95/34.78    (180)  all_58_4 = all_52_17
% 203.95/34.78    (181)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.95/34.78    (182)  op(all_52_25, all_52_25) = all_52_24
% 203.95/34.78  
% 203.95/34.78  Begin of proof
% 203.95/34.78  | 
% 203.95/34.78  | BETA: splitting (150) gives:
% 203.95/34.78  | 
% 203.95/34.78  | Case 1:
% 203.95/34.78  | | 
% 203.95/34.78  | |   (183)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 203.95/34.78  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 203.95/34.78  | | 
% 203.95/34.78  | | BETA: splitting (183) gives:
% 203.95/34.78  | | 
% 203.95/34.78  | | Case 1:
% 203.95/34.78  | | | 
% 203.95/34.78  | | |   (184)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 203.95/34.78  | | | 
% 203.95/34.78  | | | ALPHA: (184) implies:
% 203.95/34.78  | | |   (185)  all_52_6 = e0
% 203.95/34.78  | | |   (186)  all_52_4 = e1
% 203.95/34.78  | | |   (187)  all_52_2 = e2
% 203.95/34.78  | | |   (188)  all_52_0 = e3
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REDUCE: (7), (187) imply:
% 203.95/34.78  | | |   (189)  op(all_52_3, all_52_3) = e2
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REDUCE: (27), (186) imply:
% 203.95/34.78  | | |   (190)  op(all_52_5, all_52_5) = e1
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REDUCE: (18), (185) imply:
% 203.95/34.78  | | |   (191)  op(all_52_7, all_52_7) = e0
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REDUCE: (51), (188) imply:
% 203.95/34.78  | | |   (192)  op(all_6_2, all_6_2) = e3
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (14), (15), (16),
% 203.95/34.78  | | |            (17), (20), (21), (22), (23), (25), (26), (29), (31), (32),
% 203.95/34.78  | | |            (33), (35), (36), (37), (40), (42), (43), (44), (45), (47),
% 203.95/34.78  | | |            (48), (50), (52), (53), (54), (55), (56), (58), (59), (61),
% 203.95/34.78  | | |            (62), (63), (64), (68), (70), (71), (72), (73), (74), (76),
% 203.95/34.78  | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 203.95/34.78  | | |            (88), (90), (91), (92), (93), (94), (96), (97), (98), (99),
% 203.95/34.78  | | |            (100), (102), (103), (104), (105), (107), (108), (109), (110),
% 203.95/34.78  | | |            (111), (114), (115), (116), (117), (118), (119), (120), (121),
% 203.95/34.78  | | |            (122), (123), (124), (125), (127), (128), (132), (133), (134),
% 203.95/34.78  | | |            (137), (139), (140), (141), (142), (144), (145), (146), (147),
% 203.95/34.78  | | |            (148), (149), (152), (153), (154), (155), (156), (157), (158),
% 203.95/34.78  | | |            (159), (160), (162), (165), (167), (168), (169), (171), (172),
% 203.95/34.78  | | |            (173), (174), (177), (178), (180), (189), (190), (191), (192)
% 203.95/34.78  | | |            are inconsistent by sub-proof #681.
% 203.95/34.78  | | | 
% 203.95/34.78  | | Case 2:
% 203.95/34.78  | | | 
% 203.95/34.78  | | |   (193)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 203.95/34.78  | | |            (14), (16), (18), (19), (20), (21), (22), (23), (24), (26),
% 203.95/34.78  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (36), (38),
% 203.95/34.78  | | |            (39), (40), (41), (42), (44), (45), (46), (49), (51), (52),
% 203.95/34.78  | | |            (53), (55), (56), (60), (62), (64), (65), (66), (67), (68),
% 203.95/34.78  | | |            (69), (70), (72), (73), (74), (75), (76), (77), (79), (81),
% 203.95/34.78  | | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 203.95/34.78  | | |            (92), (94), (95), (96), (97), (98), (99), (101), (102), (103),
% 203.95/34.78  | | |            (104), (105), (106), (107), (108), (109), (110), (113), (114),
% 203.95/34.78  | | |            (115), (116), (117), (118), (119), (120), (122), (123), (124),
% 203.95/34.78  | | |            (125), (126), (127), (128), (130), (131), (132), (133), (134),
% 203.95/34.78  | | |            (136), (137), (138), (139), (140), (142), (143), (144), (146),
% 203.95/34.78  | | |            (147), (148), (149), (151), (152), (153), (154), (155), (156),
% 203.95/34.78  | | |            (158), (159), (160), (161), (162), (163), (164), (165), (166),
% 203.95/34.78  | | |            (167), (168), (169), (170), (171), (173), (174), (175), (176),
% 203.95/34.78  | | |            (177), (179), (180), (181), (182), (193) are inconsistent by
% 203.95/34.78  | | |            sub-proof #731.
% 203.95/34.78  | | | 
% 203.95/34.78  | | End of split
% 203.95/34.78  | | 
% 203.95/34.78  | Case 2:
% 203.95/34.78  | | 
% 203.95/34.78  | |   (194)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 203.95/34.78  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 203.95/34.78  | |            e0)
% 203.95/34.78  | | 
% 203.95/34.78  | | BETA: splitting (194) gives:
% 203.95/34.78  | | 
% 203.95/34.78  | | Case 1:
% 203.95/34.78  | | | 
% 203.95/34.78  | | |   (195)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 203.95/34.78  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (26), (27),
% 203.95/34.78  | | |            (29), (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 203.95/34.78  | | |            (42), (44), (46), (47), (49), (50), (51), (52), (53), (55),
% 203.95/34.78  | | |            (56), (60), (64), (65), (66), (67), (68), (69), (70), (72),
% 203.95/34.78  | | |            (73), (74), (76), (77), (78), (79), (82), (83), (84), (85),
% 203.95/34.78  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (96), (97),
% 203.95/34.78  | | |            (100), (101), (102), (103), (104), (105), (106), (107), (108),
% 203.95/34.78  | | |            (109), (110), (111), (113), (115), (116), (117), (118), (119),
% 203.95/34.78  | | |            (120), (122), (123), (124), (125), (126), (127), (128), (130),
% 203.95/34.78  | | |            (131), (132), (133), (134), (135), (136), (137), (139), (140),
% 203.95/34.78  | | |            (142), (143), (144), (146), (147), (148), (151), (152), (154),
% 203.95/34.78  | | |            (155), (156), (158), (159), (160), (161), (162), (163), (164),
% 203.95/34.78  | | |            (165), (166), (167), (169), (170), (171), (172), (173), (174),
% 203.95/34.78  | | |            (177), (179), (180), (181), (182), (195) are inconsistent by
% 203.95/34.78  | | |            sub-proof #1042.
% 203.95/34.78  | | | 
% 203.95/34.78  | | Case 2:
% 203.95/34.78  | | | 
% 203.95/34.78  | | |   (196)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 203.95/34.78  | | | 
% 203.95/34.78  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (13), (14), (16),
% 203.95/34.78  | | |            (18), (19), (20), (21), (23), (24), (26), (27), (29), (30),
% 203.95/34.78  | | |            (31), (33), (34), (36), (38), (39), (40), (42), (44), (45),
% 203.95/34.78  | | |            (46), (47), (49), (50), (51), (52), (53), (55), (56), (57),
% 203.95/34.78  | | |            (60), (64), (65), (66), (70), (72), (73), (74), (75), (76),
% 203.95/34.78  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 203.95/34.78  | | |            (87), (89), (91), (92), (93), (94), (96), (98), (101), (104),
% 203.95/34.78  | | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 203.95/34.78  | | |            (115), (116), (117), (118), (119), (120), (122), (123), (124),
% 203.95/34.78  | | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 203.95/34.78  | | |            (134), (135), (136), (137), (138), (139), (140), (141), (143),
% 203.95/34.78  | | |            (144), (146), (147), (148), (149), (151), (152), (154), (155),
% 203.95/34.78  | | |            (158), (159), (164), (165), (166), (167), (169), (170), (171),
% 203.95/34.78  | | |            (172), (173), (174), (175), (176), (177), (180), (182), (196)
% 203.95/34.78  | | |            are inconsistent by sub-proof #1008.
% 203.95/34.78  | | | 
% 203.95/34.78  | | End of split
% 203.95/34.78  | | 
% 203.95/34.78  | End of split
% 203.95/34.78  | 
% 203.95/34.78  End of proof
% 203.95/34.78  
% 203.95/34.78  Sub-proof #681 shows that the following formulas are inconsistent:
% 203.95/34.78  ----------------------------------------------------------------
% 203.95/34.78    (1)   ~ (all_52_15 = all_52_23)
% 203.95/34.78    (2)  all_58_14 = all_52_23
% 203.95/34.78    (3)   ~ (e3 = e1)
% 203.95/34.78    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.95/34.78    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.78    (6)  op(all_52_7, all_52_7) = e0
% 203.95/34.78    (7)  all_58_1 = all_52_9
% 203.95/34.78    (8)   ~ (all_52_9 = all_52_13)
% 203.95/34.78    (9)  op(all_52_5, all_52_5) = e1
% 203.95/34.78    (10)   ~ (e3 = e0)
% 203.95/34.78    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.78    (12)  op(e0, e2) = all_52_15
% 203.95/34.78    (13)   ~ (all_52_7 = all_52_15)
% 203.95/34.78    (14)   ~ (all_52_3 = all_52_19)
% 203.95/34.78    (15)   ~ (all_52_3 = all_6_2)
% 203.95/34.78    (16)  all_58_0 = all_6_2
% 203.95/34.78    (17)  op(all_14_2, e0) = all_14_1
% 203.95/34.78    (18)  all_56_4 = all_52_3
% 203.95/34.78    (19)   ~ (all_10_0 = e3)
% 203.95/34.78    (20)  op(e3, e0) = all_52_25
% 203.95/34.78    (21)  op(all_52_19, all_52_19) = all_52_18
% 203.95/34.78    (22)  all_58_13 = all_52_15
% 203.95/34.78    (23)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.78    (24)  all_58_9 = all_52_25
% 203.95/34.78    (25)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.78    (26)   ~ (all_52_29 = all_14_2)
% 203.95/34.78    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.95/34.78    (28)  op(e2, e2) = all_4_2
% 203.95/34.78    (29)   ~ (all_52_3 = all_52_5)
% 203.95/34.78    (30)   ~ (all_4_1 = e3)
% 203.95/34.78    (31)  all_58_11 = all_52_29
% 203.95/34.78    (32)  all_56_5 = all_4_2
% 203.95/34.78    (33)   ~ (all_52_9 = all_52_15)
% 203.95/34.78    (34)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.78    (35)  op(all_10_2, e1) = all_10_1
% 203.95/34.78    (36)   ~ (all_52_7 = all_6_2)
% 203.95/34.78    (37)  op(e0, e0) = all_14_2
% 203.95/34.78    (38)  op(e0, e1) = all_52_23
% 203.95/34.78    (39)  all_56_15 = all_14_2
% 203.95/34.78    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.78    (41)  op(e2, all_4_1) = all_4_0
% 203.95/34.78    (42)  op(e1, e0) = all_52_29
% 203.95/34.78    (43)   ~ (all_10_0 = e2)
% 203.95/34.78    (44)   ~ (all_4_1 = e1)
% 203.95/34.78    (45)   ~ (all_4_0 = e3)
% 203.95/34.78    (46)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.95/34.78    (47)   ~ (e2 = e1)
% 203.95/34.78    (48)   ~ (all_6_0 = e1)
% 203.95/34.78    (49)  op(e1, all_10_1) = all_10_0
% 203.95/34.78    (50)  all_58_10 = all_52_27
% 203.95/34.78    (51)  all_56_8 = all_52_5
% 203.95/34.78    (52)  op(all_52_9, all_52_9) = all_52_8
% 203.95/34.78    (53)   ~ (all_52_19 = all_52_23)
% 203.95/34.78    (54)   ~ (all_52_29 = all_10_2)
% 203.95/34.78    (55)  all_58_7 = all_52_13
% 203.95/34.78    (56)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.95/34.78    (57)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.95/34.78    (58)  op(all_6_2, all_6_2) = e3
% 203.95/34.78    (59)   ~ (all_52_5 = all_52_7)
% 203.95/34.78    (60)  all_58_12 = all_52_7
% 203.95/34.78    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.78    (62)   ~ (all_52_7 = all_14_2)
% 203.95/34.78    (63)   ~ (all_14_2 = e0)
% 203.95/34.78    (64)  all_58_2 = all_52_3
% 203.95/34.78    (65)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.95/34.78    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.95/34.78    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.78    (68)  op(e3, all_6_1) = all_6_0
% 203.95/34.78    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.95/34.78    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.78    (71)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.78    (72)   ~ (e2 = e0)
% 203.95/34.78    (73)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.95/34.78    (74)  op(all_4_2, e2) = all_4_1
% 203.95/34.78    (75)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.95/34.78    (76)  op(all_52_3, all_52_3) = e2
% 203.95/34.78    (77)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.78    (78)  all_56_6 = all_52_19
% 203.95/34.78    (79)   ~ (all_52_15 = all_14_2)
% 203.95/34.78    (80)   ~ (all_52_19 = all_52_27)
% 203.95/34.78    (81)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.78    (82)   ~ (all_6_0 = e2)
% 203.95/34.78    (83)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.95/34.78    (84)   ~ (all_52_13 = all_4_2)
% 203.95/34.78    (85)  op(e3, e1) = all_52_17
% 203.95/34.78    (86)  op(e1, e2) = all_52_13
% 203.95/34.78    (87)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.95/34.78    (88)   ~ (all_52_9 = all_52_25)
% 203.95/34.78    (89)  all_58_15 = all_14_2
% 203.95/34.78    (90)   ~ (all_52_19 = all_10_2)
% 203.95/34.78    (91)  op(all_52_23, all_52_23) = all_52_22
% 203.95/34.78    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.78    (93)   ~ (all_10_1 = e2)
% 203.95/34.78    (94)  all_58_8 = all_10_2
% 203.95/34.78    (95)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.95/34.78    (96)   ~ (all_52_5 = all_10_2)
% 203.95/34.78    (97)  op(all_52_29, all_52_29) = all_52_28
% 203.95/34.78    (98)  all_56_12 = all_52_7
% 203.95/34.78    (99)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.78    (100)   ~ (all_52_9 = all_4_2)
% 203.95/34.78    (101)   ~ (all_52_5 = all_6_2)
% 203.95/34.78    (102)   ~ (all_52_9 = all_6_2)
% 203.95/34.78    (103)  op(e3, e3) = all_6_2
% 203.95/34.78    (104)   ~ (all_52_27 = all_14_2)
% 203.95/34.78    (105)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.95/34.78    (106)  all_56_14 = all_52_23
% 203.95/34.78    (107)  op(all_4_2, all_4_2) = all_52_10
% 203.95/34.78    (108)   ~ (all_52_3 = all_52_7)
% 203.95/34.78    (109)   ~ (all_10_1 = e3)
% 203.95/34.78    (110)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.78    (111)  all_58_5 = all_52_19
% 203.95/34.78    (112)  all_56_1 = all_52_9
% 203.95/34.78    (113)   ~ (all_52_15 = all_4_2)
% 203.95/34.78    (114)  all_58_6 = all_52_5
% 203.95/34.78    (115)  op(e3, e2) = all_52_9
% 203.95/34.78    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.95/34.78    (117)   ~ (all_52_17 = all_6_2)
% 203.95/34.78    (118)   ~ (e1 = e0)
% 203.95/34.78    (119)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.78    (120)   ~ (e3 = e2)
% 203.95/34.78    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.78    (122)   ~ (all_52_9 = all_52_17)
% 203.95/34.78    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.78    (124)  op(all_52_13, all_52_13) = all_52_12
% 203.95/34.78    (125)  op(e1, e1) = all_10_2
% 203.95/34.78    (126)   ~ (all_52_23 = all_10_2)
% 203.95/34.78    (127)   ~ (all_52_7 = all_52_23)
% 203.95/34.78    (128)  all_58_3 = all_4_2
% 203.95/34.78    (129)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.95/34.78    (130)  all_56_13 = all_52_15
% 203.95/34.78    (131)   ~ (all_52_3 = all_4_2)
% 203.95/34.78    (132)  op(all_6_2, e3) = all_6_1
% 203.95/34.79    (133)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.95/34.79    (134)  all_58_4 = all_52_17
% 203.95/34.79  
% 203.95/34.79  Begin of proof
% 203.95/34.79  | 
% 203.95/34.79  | BETA: splitting (95) gives:
% 203.95/34.79  | 
% 203.95/34.79  | Case 1:
% 203.95/34.79  | | 
% 203.95/34.79  | |   (135)  all_56_15 = e3
% 203.95/34.79  | | 
% 203.95/34.79  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 203.95/34.79  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 203.95/34.79  | |            (26), (27), (28), (29), (31), (33), (34), (35), (36), (37), (38),
% 203.95/34.79  | |            (39), (40), (42), (43), (44), (46), (47), (48), (49), (50), (51),
% 203.95/34.79  | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 203.95/34.79  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (74), (75),
% 203.95/34.79  | |            (76), (77), (78), (79), (80), (81), (82), (84), (85), (88), (90),
% 203.95/34.79  | |            (92), (93), (94), (96), (97), (98), (99), (100), (101), (102),
% 203.95/34.79  | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 203.95/34.79  | |            (112), (113), (114), (115), (117), (118), (119), (121), (122),
% 203.95/34.79  | |            (123), (125), (126), (127), (128), (130), (131), (132), (133),
% 203.95/34.79  | |            (134), (135) are inconsistent by sub-proof #682.
% 203.95/34.79  | | 
% 203.95/34.79  | Case 2:
% 203.95/34.79  | | 
% 203.95/34.79  | |   (136)   ~ (all_56_15 = e3)
% 203.95/34.79  | |   (137)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.95/34.79  | | 
% 203.95/34.79  | | REDUCE: (39), (136) imply:
% 203.95/34.79  | |   (138)   ~ (all_14_2 = e3)
% 203.95/34.79  | | 
% 203.95/34.79  | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (15), (16),
% 203.95/34.79  | |            (18), (22), (28), (29), (30), (32), (33), (34), (36), (37), (39),
% 203.95/34.79  | |            (40), (41), (44), (45), (46), (47), (52), (55), (57), (58), (60),
% 203.95/34.79  | |            (62), (63), (64), (67), (71), (72), (73), (74), (76), (77), (79),
% 203.95/34.79  | |            (81), (83), (86), (87), (89), (91), (96), (98), (100), (102),
% 203.95/34.79  | |            (103), (108), (110), (112), (113), (114), (115), (116), (118),
% 203.95/34.79  | |            (120), (121), (124), (125), (126), (127), (128), (129), (130),
% 203.95/34.79  | |            (131), (133), (137), (138) are inconsistent by sub-proof #1145.
% 203.95/34.79  | | 
% 203.95/34.79  | End of split
% 203.95/34.79  | 
% 203.95/34.79  End of proof
% 203.95/34.79  
% 203.95/34.79  Sub-proof #682 shows that the following formulas are inconsistent:
% 203.95/34.79  ----------------------------------------------------------------
% 203.95/34.79    (1)   ~ (all_52_15 = all_52_23)
% 203.95/34.79    (2)  all_58_14 = all_52_23
% 203.95/34.79    (3)   ~ (e3 = e1)
% 203.95/34.79    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.95/34.79    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.79    (6)  op(all_52_7, all_52_7) = e0
% 203.95/34.79    (7)  all_58_1 = all_52_9
% 203.95/34.79    (8)   ~ (all_52_9 = all_52_13)
% 203.95/34.79    (9)  op(all_52_5, all_52_5) = e1
% 203.95/34.79    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.79    (11)   ~ (all_52_7 = all_52_15)
% 203.95/34.79    (12)   ~ (all_52_3 = all_52_19)
% 203.95/34.79    (13)   ~ (all_52_3 = all_6_2)
% 203.95/34.79    (14)  all_58_0 = all_6_2
% 203.95/34.79    (15)  op(all_14_2, e0) = all_14_1
% 203.95/34.79    (16)  all_56_4 = all_52_3
% 203.95/34.79    (17)   ~ (all_10_0 = e3)
% 203.95/34.79    (18)  op(e3, e0) = all_52_25
% 203.95/34.79    (19)  op(all_52_19, all_52_19) = all_52_18
% 203.95/34.79    (20)  all_58_13 = all_52_15
% 203.95/34.79    (21)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.79    (22)  all_58_9 = all_52_25
% 203.95/34.79    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.79    (24)   ~ (all_52_29 = all_14_2)
% 203.95/34.79    (25)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.95/34.79    (26)  op(e2, e2) = all_4_2
% 203.95/34.79    (27)   ~ (all_52_3 = all_52_5)
% 203.95/34.79    (28)  all_58_11 = all_52_29
% 203.95/34.79    (29)   ~ (all_52_9 = all_52_15)
% 203.95/34.79    (30)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.79    (31)  op(all_10_2, e1) = all_10_1
% 203.95/34.79    (32)   ~ (all_52_7 = all_6_2)
% 203.95/34.79    (33)  op(e0, e0) = all_14_2
% 203.95/34.79    (34)  op(e0, e1) = all_52_23
% 203.95/34.79    (35)  all_56_15 = all_14_2
% 203.95/34.79    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.79    (37)  op(e1, e0) = all_52_29
% 203.95/34.79    (38)   ~ (all_10_0 = e2)
% 203.95/34.79    (39)   ~ (all_4_1 = e1)
% 203.95/34.79    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.95/34.79    (41)   ~ (e2 = e1)
% 203.95/34.79    (42)   ~ (all_6_0 = e1)
% 203.95/34.79    (43)  op(e1, all_10_1) = all_10_0
% 203.95/34.79    (44)  all_58_10 = all_52_27
% 203.95/34.79    (45)  all_56_8 = all_52_5
% 203.95/34.79    (46)   ~ (all_52_19 = all_52_23)
% 203.95/34.79    (47)   ~ (all_52_29 = all_10_2)
% 203.95/34.79    (48)  all_58_7 = all_52_13
% 203.95/34.79    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.95/34.79    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.95/34.79    (51)  op(all_6_2, all_6_2) = e3
% 203.95/34.79    (52)   ~ (all_52_5 = all_52_7)
% 203.95/34.79    (53)  all_58_12 = all_52_7
% 203.95/34.79    (54)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.79    (55)   ~ (all_52_7 = all_14_2)
% 203.95/34.79    (56)   ~ (all_14_2 = e0)
% 203.95/34.79    (57)  all_58_2 = all_52_3
% 203.95/34.79    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.95/34.79    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.95/34.79    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.79    (61)  op(e3, all_6_1) = all_6_0
% 203.95/34.79    (62)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.95/34.79    (63)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.79    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.79    (65)   ~ (e2 = e0)
% 203.95/34.79    (66)  op(all_4_2, e2) = all_4_1
% 203.95/34.79    (67)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.95/34.79    (68)  op(all_52_3, all_52_3) = e2
% 203.95/34.79    (69)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.79    (70)  all_56_6 = all_52_19
% 203.95/34.79    (71)   ~ (all_52_15 = all_14_2)
% 203.95/34.79    (72)   ~ (all_52_19 = all_52_27)
% 203.95/34.79    (73)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.79    (74)   ~ (all_6_0 = e2)
% 203.95/34.79    (75)   ~ (all_52_13 = all_4_2)
% 203.95/34.79    (76)  op(e3, e1) = all_52_17
% 203.95/34.79    (77)   ~ (all_52_9 = all_52_25)
% 203.95/34.79    (78)   ~ (all_52_19 = all_10_2)
% 203.95/34.79    (79)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.79    (80)   ~ (all_10_1 = e2)
% 203.95/34.79    (81)  all_58_8 = all_10_2
% 203.95/34.79    (82)   ~ (all_52_5 = all_10_2)
% 203.95/34.79    (83)  op(all_52_29, all_52_29) = all_52_28
% 203.95/34.79    (84)  all_56_12 = all_52_7
% 203.95/34.79    (85)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.79    (86)   ~ (all_52_9 = all_4_2)
% 203.95/34.79    (87)   ~ (all_52_5 = all_6_2)
% 203.95/34.79    (88)   ~ (all_52_9 = all_6_2)
% 203.95/34.79    (89)  op(e3, e3) = all_6_2
% 203.95/34.79    (90)  all_56_15 = e3
% 203.95/34.79    (91)   ~ (all_52_27 = all_14_2)
% 203.95/34.79    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.95/34.79    (93)  all_56_14 = all_52_23
% 203.95/34.79    (94)  op(all_4_2, all_4_2) = all_52_10
% 203.95/34.79    (95)   ~ (all_52_3 = all_52_7)
% 203.95/34.79    (96)   ~ (all_10_1 = e3)
% 203.95/34.79    (97)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.79    (98)  all_58_5 = all_52_19
% 203.95/34.79    (99)  all_56_1 = all_52_9
% 203.95/34.79    (100)   ~ (all_52_15 = all_4_2)
% 203.95/34.79    (101)  all_58_6 = all_52_5
% 203.95/34.79    (102)  op(e3, e2) = all_52_9
% 203.95/34.79    (103)   ~ (all_52_17 = all_6_2)
% 203.95/34.79    (104)   ~ (e1 = e0)
% 203.95/34.79    (105)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.79    (106)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.79    (107)   ~ (all_52_9 = all_52_17)
% 203.95/34.79    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.79    (109)  op(e1, e1) = all_10_2
% 203.95/34.79    (110)   ~ (all_52_23 = all_10_2)
% 203.95/34.79    (111)   ~ (all_52_7 = all_52_23)
% 203.95/34.79    (112)  all_58_3 = all_4_2
% 203.95/34.79    (113)  all_56_13 = all_52_15
% 203.95/34.79    (114)   ~ (all_52_3 = all_4_2)
% 203.95/34.79    (115)  op(all_6_2, e3) = all_6_1
% 203.95/34.79    (116)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.95/34.79    (117)  all_58_4 = all_52_17
% 203.95/34.79  
% 203.95/34.79  Begin of proof
% 203.95/34.79  | 
% 203.95/34.79  | COMBINE_EQS: (35), (90) imply:
% 203.95/34.79  |   (118)  all_14_2 = e3
% 203.95/34.79  | 
% 203.95/34.79  | SIMP: (118) implies:
% 203.95/34.79  |   (119)  all_14_2 = e3
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (55), (119) imply:
% 203.95/34.79  |   (120)   ~ (all_52_7 = e3)
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (71), (119) imply:
% 203.95/34.79  |   (121)   ~ (all_52_15 = e3)
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (91), (119) imply:
% 203.95/34.79  |   (122)   ~ (all_52_27 = e3)
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (24), (119) imply:
% 203.95/34.79  |   (123)   ~ (all_52_29 = e3)
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (56), (119) imply:
% 203.95/34.79  |   (124)   ~ (e3 = e0)
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (97), (119) imply:
% 203.95/34.79  |   (125)  op(e3, e3) = all_52_30
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (15), (119) imply:
% 203.95/34.79  |   (126)  op(e3, e0) = all_14_1
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (33), (119) imply:
% 203.95/34.79  |   (127)  op(e0, e0) = e3
% 203.95/34.79  | 
% 203.95/34.79  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 203.95/34.79  |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 203.95/34.79  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 203.95/34.79  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 203.95/34.79  |            (49), (50), (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 203.95/34.79  |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (72),
% 203.95/34.79  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 203.95/34.79  |            (84), (85), (86), (87), (88), (89), (92), (93), (94), (95), (96),
% 203.95/34.79  |            (98), (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 203.95/34.79  |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 203.95/34.79  |            (117), (120), (121), (122), (123), (124), (125), (126), (127) are
% 203.95/34.79  |            inconsistent by sub-proof #683.
% 203.95/34.79  | 
% 203.95/34.79  End of proof
% 203.95/34.79  
% 203.95/34.79  Sub-proof #683 shows that the following formulas are inconsistent:
% 203.95/34.79  ----------------------------------------------------------------
% 203.95/34.79    (1)   ~ (all_52_15 = all_52_23)
% 203.95/34.79    (2)  all_58_14 = all_52_23
% 203.95/34.79    (3)   ~ (e3 = e1)
% 203.95/34.79    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.95/34.79    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.79    (6)  op(all_52_7, all_52_7) = e0
% 203.95/34.79    (7)  all_58_1 = all_52_9
% 203.95/34.79    (8)   ~ (all_52_9 = all_52_13)
% 203.95/34.79    (9)  op(all_52_5, all_52_5) = e1
% 203.95/34.79    (10)   ~ (e3 = e0)
% 203.95/34.79    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.79    (12)   ~ (all_52_7 = all_52_15)
% 203.95/34.79    (13)   ~ (all_52_3 = all_52_19)
% 203.95/34.79    (14)   ~ (all_52_3 = all_6_2)
% 203.95/34.79    (15)  all_58_0 = all_6_2
% 203.95/34.79    (16)  all_56_4 = all_52_3
% 203.95/34.79    (17)   ~ (all_10_0 = e3)
% 203.95/34.79    (18)  op(e3, e0) = all_52_25
% 203.95/34.79    (19)  op(all_52_19, all_52_19) = all_52_18
% 203.95/34.79    (20)  all_58_13 = all_52_15
% 203.95/34.79    (21)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.79    (22)  all_58_9 = all_52_25
% 203.95/34.79    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.79    (24)   ~ (all_52_15 = e3)
% 203.95/34.79    (25)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.95/34.79    (26)  op(e2, e2) = all_4_2
% 203.95/34.79    (27)   ~ (all_52_3 = all_52_5)
% 203.95/34.79    (28)  all_58_11 = all_52_29
% 203.95/34.79    (29)   ~ (all_52_9 = all_52_15)
% 203.95/34.79    (30)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.79    (31)  op(all_10_2, e1) = all_10_1
% 203.95/34.79    (32)   ~ (all_52_7 = all_6_2)
% 203.95/34.79    (33)  op(e0, e0) = all_14_2
% 203.95/34.79    (34)  op(e0, e1) = all_52_23
% 203.95/34.79    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.79    (36)  op(e1, e0) = all_52_29
% 203.95/34.79    (37)   ~ (all_10_0 = e2)
% 203.95/34.79    (38)   ~ (all_4_1 = e1)
% 203.95/34.79    (39)  op(e0, e0) = e3
% 203.95/34.79    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.95/34.79    (41)   ~ (e2 = e1)
% 203.95/34.79    (42)   ~ (all_6_0 = e1)
% 203.95/34.79    (43)  op(e1, all_10_1) = all_10_0
% 203.95/34.79    (44)  all_58_10 = all_52_27
% 203.95/34.79    (45)  all_56_8 = all_52_5
% 203.95/34.79    (46)   ~ (all_52_19 = all_52_23)
% 203.95/34.79    (47)   ~ (all_52_29 = all_10_2)
% 203.95/34.79    (48)  all_58_7 = all_52_13
% 203.95/34.79    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.95/34.79    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.95/34.79    (51)  op(all_6_2, all_6_2) = e3
% 203.95/34.79    (52)   ~ (all_52_5 = all_52_7)
% 203.95/34.79    (53)  all_58_12 = all_52_7
% 203.95/34.79    (54)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.79    (55)   ~ (all_52_7 = e3)
% 203.95/34.79    (56)   ~ (all_52_7 = all_14_2)
% 203.95/34.79    (57)  all_58_2 = all_52_3
% 203.95/34.79    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.95/34.79    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.95/34.79    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.79    (61)   ~ (all_52_29 = e3)
% 203.95/34.79    (62)  op(e3, all_6_1) = all_6_0
% 203.95/34.79    (63)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.95/34.79    (64)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.79    (65)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.79    (66)   ~ (e2 = e0)
% 203.95/34.79    (67)  op(all_4_2, e2) = all_4_1
% 203.95/34.79    (68)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.95/34.79    (69)  op(all_52_3, all_52_3) = e2
% 203.95/34.79    (70)  op(e3, e3) = all_52_30
% 203.95/34.79    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.79    (72)  all_56_6 = all_52_19
% 203.95/34.79    (73)   ~ (all_52_19 = all_52_27)
% 203.95/34.79    (74)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.79    (75)   ~ (all_52_27 = e3)
% 203.95/34.79    (76)   ~ (all_6_0 = e2)
% 203.95/34.79    (77)   ~ (all_52_13 = all_4_2)
% 203.95/34.79    (78)  op(e3, e1) = all_52_17
% 203.95/34.79    (79)   ~ (all_52_9 = all_52_25)
% 203.95/34.79    (80)   ~ (all_52_19 = all_10_2)
% 203.95/34.79    (81)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.79    (82)   ~ (all_10_1 = e2)
% 203.95/34.79    (83)  all_58_8 = all_10_2
% 203.95/34.79    (84)   ~ (all_52_5 = all_10_2)
% 203.95/34.79    (85)  op(all_52_29, all_52_29) = all_52_28
% 203.95/34.79    (86)  all_56_12 = all_52_7
% 203.95/34.79    (87)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.79    (88)   ~ (all_52_9 = all_4_2)
% 203.95/34.79    (89)   ~ (all_52_5 = all_6_2)
% 203.95/34.79    (90)   ~ (all_52_9 = all_6_2)
% 203.95/34.79    (91)  op(e3, e3) = all_6_2
% 203.95/34.79    (92)  op(e3, e0) = all_14_1
% 203.95/34.79    (93)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.95/34.79    (94)  all_56_14 = all_52_23
% 203.95/34.79    (95)  op(all_4_2, all_4_2) = all_52_10
% 203.95/34.79    (96)   ~ (all_52_3 = all_52_7)
% 203.95/34.79    (97)   ~ (all_10_1 = e3)
% 203.95/34.79    (98)  all_58_5 = all_52_19
% 203.95/34.79    (99)  all_56_1 = all_52_9
% 203.95/34.79    (100)   ~ (all_52_15 = all_4_2)
% 203.95/34.79    (101)  all_58_6 = all_52_5
% 203.95/34.79    (102)  op(e3, e2) = all_52_9
% 203.95/34.79    (103)   ~ (all_52_17 = all_6_2)
% 203.95/34.79    (104)   ~ (e1 = e0)
% 203.95/34.79    (105)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.79    (106)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.79    (107)   ~ (all_52_9 = all_52_17)
% 203.95/34.79    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.79    (109)  op(e1, e1) = all_10_2
% 203.95/34.79    (110)   ~ (all_52_23 = all_10_2)
% 203.95/34.79    (111)   ~ (all_52_7 = all_52_23)
% 203.95/34.79    (112)  all_58_3 = all_4_2
% 203.95/34.79    (113)  all_56_13 = all_52_15
% 203.95/34.79    (114)   ~ (all_52_3 = all_4_2)
% 203.95/34.79    (115)  op(all_6_2, e3) = all_6_1
% 203.95/34.79    (116)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.95/34.79    (117)  all_58_4 = all_52_17
% 203.95/34.79  
% 203.95/34.79  Begin of proof
% 203.95/34.79  | 
% 203.95/34.79  | GROUND_INST: instantiating (5) with all_52_25, all_14_1, e0, e3, simplifying
% 203.95/34.79  |              with (18), (92) gives:
% 203.95/34.79  |   (118)  all_52_25 = all_14_1
% 203.95/34.79  | 
% 203.95/34.79  | GROUND_INST: instantiating (5) with all_6_2, all_52_30, e3, e3, simplifying
% 203.95/34.79  |              with (70), (91) gives:
% 203.95/34.79  |   (119)  all_52_30 = all_6_2
% 203.95/34.79  | 
% 203.95/34.79  | COMBINE_EQS: (22), (118) imply:
% 203.95/34.79  |   (120)  all_58_9 = all_14_1
% 203.95/34.79  | 
% 203.95/34.79  | REDUCE: (79), (118) imply:
% 203.95/34.79  |   (121)   ~ (all_52_9 = all_14_1)
% 203.95/34.79  | 
% 203.95/34.79  | BETA: splitting (40) gives:
% 203.95/34.79  | 
% 203.95/34.79  | Case 1:
% 203.95/34.79  | | 
% 203.95/34.79  | |   (122)  all_56_13 = e3
% 203.95/34.79  | | 
% 203.95/34.79  | | REF_CLOSE: (24), (113), (122) are inconsistent by sub-proof #1201.
% 203.95/34.79  | | 
% 203.95/34.79  | Case 2:
% 203.95/34.79  | | 
% 203.95/34.79  | |   (123)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.95/34.79  | | 
% 203.95/34.79  | | BETA: splitting (11) gives:
% 203.95/34.79  | | 
% 203.95/34.79  | | Case 1:
% 203.95/34.79  | | | 
% 203.95/34.79  | | |   (124)  all_56_12 = e3
% 203.95/34.79  | | | 
% 203.95/34.79  | | | REF_CLOSE: (55), (86), (124) are inconsistent by sub-proof #1383.
% 203.95/34.79  | | | 
% 203.95/34.79  | | Case 2:
% 203.95/34.79  | | | 
% 203.95/34.79  | | |   (125)   ~ (all_56_12 = e3)
% 203.95/34.79  | | |   (126)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.79  | | | 
% 203.95/34.79  | | | BETA: splitting (58) gives:
% 203.95/34.79  | | | 
% 203.95/34.79  | | | Case 1:
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | |   (127)  all_56_6 = e3
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | COMBINE_EQS: (72), (127) imply:
% 203.95/34.79  | | | |   (128)  all_52_19 = e3
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | SIMP: (128) implies:
% 203.95/34.79  | | | |   (129)  all_52_19 = e3
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | REDUCE: (13), (129) imply:
% 203.95/34.79  | | | |   (130)   ~ (all_52_3 = e3)
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | REDUCE: (73), (129) imply:
% 203.95/34.79  | | | |   (131)   ~ (all_52_27 = e3)
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | REDUCE: (19), (129) imply:
% 203.95/34.79  | | | |   (132)  op(e3, e3) = all_52_18
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_18, e3, e3,
% 203.95/34.79  | | | |              simplifying with (91), (132) gives:
% 203.95/34.79  | | | |   (133)  all_52_18 = all_6_2
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | BETA: splitting (60) gives:
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | Case 1:
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | |   (134)  all_58_0 = e3
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | COMBINE_EQS: (15), (134) imply:
% 203.95/34.79  | | | | |   (135)  all_6_2 = e3
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | BETA: splitting (50) gives:
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | Case 1:
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | |   (136)  all_58_2 = e1
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | COMBINE_EQS: (57), (136) imply:
% 203.95/34.79  | | | | | |   (137)  all_52_3 = e1
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (96), (137) imply:
% 203.95/34.79  | | | | | |   (138)   ~ (all_52_7 = e1)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | SIMP: (138) implies:
% 203.95/34.79  | | | | | |   (139)   ~ (all_52_7 = e1)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REF_CLOSE: (2), (5), (6), (9), (10), (13), (14), (15), (26), (27),
% 203.95/34.79  | | | | | |            (30), (33), (35), (39), (41), (42), (44), (45), (46),
% 203.95/34.79  | | | | | |            (50), (51), (53), (55), (56), (57), (58), (60), (62),
% 203.95/34.79  | | | | | |            (64), (69), (72), (74), (75), (80), (81), (83), (84),
% 203.95/34.79  | | | | | |            (86), (89), (91), (93), (98), (101), (103), (105), (108),
% 203.95/34.79  | | | | | |            (109), (112), (114), (115), (117), (126), (139) are
% 203.95/34.79  | | | | | |            inconsistent by sub-proof #691.
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | Case 2:
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | |   (140)   ~ (all_58_2 = e1)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (57), (140) imply:
% 203.95/34.79  | | | | | |   (141)   ~ (all_52_3 = e1)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REF_CLOSE: (3), (5), (6), (9), (31), (34), (49), (53), (57), (64),
% 203.95/34.79  | | | | | |            (71), (82), (84), (94), (97), (101), (109), (110), (111),
% 203.95/34.79  | | | | | |            (134), (141) are inconsistent by sub-proof #690.
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | End of split
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | Case 2:
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | |   (142)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | REF_CLOSE: (5), (9), (51), (53), (55), (57), (84), (91), (101), (109),
% 203.95/34.79  | | | | |            (130), (142) are inconsistent by sub-proof #1365.
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | End of split
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | Case 2:
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | |   (143)   ~ (all_56_6 = e3)
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | REDUCE: (72), (143) imply:
% 203.95/34.79  | | | |   (144)   ~ (all_52_19 = e3)
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | BETA: splitting (35) gives:
% 203.95/34.79  | | | | 
% 203.95/34.79  | | | | Case 1:
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | |   (145)  all_58_2 = e3
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | REF_CLOSE: (5), (26), (51), (57), (69), (91), (114), (145) are
% 203.95/34.79  | | | | |            inconsistent by sub-proof #1159.
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | Case 2:
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | |   (146)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | BETA: splitting (146) gives:
% 203.95/34.79  | | | | | 
% 203.95/34.79  | | | | | Case 1:
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | |   (147)  all_58_3 = e3
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | COMBINE_EQS: (112), (147) imply:
% 203.95/34.79  | | | | | |   (148)  all_4_2 = e3
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (114), (148) imply:
% 203.95/34.79  | | | | | |   (149)   ~ (all_52_3 = e3)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (88), (148) imply:
% 203.95/34.79  | | | | | |   (150)   ~ (all_52_9 = e3)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (77), (148) imply:
% 203.95/34.79  | | | | | |   (151)   ~ (all_52_13 = e3)
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (95), (148) imply:
% 203.95/34.79  | | | | | |   (152)  op(e3, e3) = all_52_10
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (67), (148) imply:
% 203.95/34.79  | | | | | |   (153)  op(e3, e2) = all_4_1
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | REDUCE: (26), (148) imply:
% 203.95/34.79  | | | | | |   (154)  op(e2, e2) = e3
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | GROUND_INST: instantiating (5) with all_52_9, all_4_1, e2, e3,
% 203.95/34.79  | | | | | |              simplifying with (102), (153) gives:
% 203.95/34.79  | | | | | |   (155)  all_52_9 = all_4_1
% 203.95/34.79  | | | | | | 
% 203.95/34.79  | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_10, e3, e3,
% 203.95/34.79  | | | | | |              simplifying with (91), (152) gives:
% 203.95/34.79  | | | | | |   (156)  all_52_10 = all_6_2
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | COMBINE_EQS: (99), (155) imply:
% 203.95/34.80  | | | | | |   (157)  all_56_1 = all_4_1
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | COMBINE_EQS: (7), (155) imply:
% 203.95/34.80  | | | | | |   (158)  all_58_1 = all_4_1
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REDUCE: (8), (155) imply:
% 203.95/34.80  | | | | | |   (159)   ~ (all_52_13 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | SIMP: (159) implies:
% 203.95/34.80  | | | | | |   (160)   ~ (all_52_13 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REDUCE: (29), (155) imply:
% 203.95/34.80  | | | | | |   (161)   ~ (all_52_15 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | SIMP: (161) implies:
% 203.95/34.80  | | | | | |   (162)   ~ (all_52_15 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REDUCE: (107), (155) imply:
% 203.95/34.80  | | | | | |   (163)   ~ (all_52_17 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | SIMP: (163) implies:
% 203.95/34.80  | | | | | |   (164)   ~ (all_52_17 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REDUCE: (121), (155) imply:
% 203.95/34.80  | | | | | |   (165)   ~ (all_14_1 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | SIMP: (165) implies:
% 203.95/34.80  | | | | | |   (166)   ~ (all_14_1 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REDUCE: (90), (155) imply:
% 203.95/34.80  | | | | | |   (167)   ~ (all_6_2 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | SIMP: (167) implies:
% 203.95/34.80  | | | | | |   (168)   ~ (all_6_2 = all_4_1)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REDUCE: (150), (155) imply:
% 203.95/34.80  | | | | | |   (169)   ~ (all_4_1 = e3)
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | BETA: splitting (106) gives:
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | Case 1:
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | |   (170)  all_56_1 = e3
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | REF_CLOSE: (157), (169), (170) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | |            #1167.
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | Case 2:
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | |   (171)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | BETA: splitting (54) gives:
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | |   (172)  all_58_6 = e3
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | COMBINE_EQS: (101), (172) imply:
% 203.95/34.80  | | | | | | | |   (173)  all_52_5 = e3
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | REF_CLOSE: (5), (9), (15), (26), (35), (51), (52), (53), (57),
% 203.95/34.80  | | | | | | | |            (60), (69), (84), (89), (91), (101), (109), (114),
% 203.95/34.80  | | | | | | | |            (173) are inconsistent by sub-proof #704.
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | |   (174)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | BETA: splitting (60) gives:
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | |   (175)  all_58_0 = e3
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | COMBINE_EQS: (15), (175) imply:
% 203.95/34.80  | | | | | | | | |   (176)  all_6_2 = e3
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REDUCE: (168), (176) imply:
% 203.95/34.80  | | | | | | | | |   (177)   ~ (all_4_1 = e3)
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REDUCE: (115), (176) imply:
% 203.95/34.80  | | | | | | | | |   (178)  op(e3, e3) = all_6_1
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REDUCE: (91), (176) imply:
% 203.95/34.80  | | | | | | | | |   (179)  op(e3, e3) = e3
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | BETA: splitting (174) gives:
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | |   (180)  all_58_7 = e3
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | COMBINE_EQS: (48), (180) imply:
% 203.95/34.80  | | | | | | | | | |   (181)  all_52_13 = e3
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | REDUCE: (151), (181) imply:
% 203.95/34.80  | | | | | | | | | |   (182)  $false
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | CLOSE: (182) is inconsistent.
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | |   (183)  all_58_8 = e3 | all_58_11 = e3
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | BETA: splitting (183) gives:
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | |   (184)  all_58_8 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | COMBINE_EQS: (83), (184) imply:
% 203.95/34.80  | | | | | | | | | | |   (185)  all_10_2 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | SIMP: (185) implies:
% 203.95/34.80  | | | | | | | | | | |   (186)  all_10_2 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (84), (186) imply:
% 203.95/34.80  | | | | | | | | | | |   (187)   ~ (all_52_5 = e3)
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (21), (186) imply:
% 203.95/34.80  | | | | | | | | | | |   (188)  op(e3, e3) = all_52_20
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (31), (186) imply:
% 203.95/34.80  | | | | | | | | | | |   (189)  op(e3, e1) = all_10_1
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (109), (186) imply:
% 203.95/34.80  | | | | | | | | | | |   (190)  op(e1, e1) = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_17, all_10_1, e1,
% 203.95/34.80  | | | | | | | | | | |              e3, simplifying with (78), (189) gives:
% 203.95/34.80  | | | | | | | | | | |   (191)  all_52_17 = all_10_1
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | GROUND_INST: instantiating (5) with all_6_1, all_52_20, e3, e3,
% 203.95/34.80  | | | | | | | | | | |              simplifying with (178), (188) gives:
% 203.95/34.80  | | | | | | | | | | |   (192)  all_52_20 = all_6_1
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | GROUND_INST: instantiating (5) with e3, all_52_20, e3, e3,
% 203.95/34.80  | | | | | | | | | | |              simplifying with (179), (188) gives:
% 203.95/34.80  | | | | | | | | | | |   (193)  all_52_20 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | COMBINE_EQS: (192), (193) imply:
% 203.95/34.80  | | | | | | | | | | |   (194)  all_6_1 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | SIMP: (194) implies:
% 203.95/34.80  | | | | | | | | | | |   (195)  all_6_1 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | COMBINE_EQS: (117), (191) imply:
% 203.95/34.80  | | | | | | | | | | |   (196)  all_58_4 = all_10_1
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (164), (191) imply:
% 203.95/34.80  | | | | | | | | | | |   (197)   ~ (all_10_1 = all_4_1)
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (87), (191) imply:
% 203.95/34.80  | | | | | | | | | | |   (198)  op(all_10_1, all_10_1) = all_52_16
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (62), (195) imply:
% 203.95/34.80  | | | | | | | | | | |   (199)  op(e3, e3) = all_6_0
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | GROUND_INST: instantiating (5) with e3, all_6_0, e3, e3,
% 203.95/34.80  | | | | | | | | | | |              simplifying with (179), (199) gives:
% 203.95/34.80  | | | | | | | | | | |   (200)  all_6_0 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (76), (200) imply:
% 203.95/34.80  | | | | | | | | | | |   (201)   ~ (e3 = e2)
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | BETA: splitting (68) gives:
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | |   (202)  all_58_0 = e1
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | REF_CLOSE: (3), (5), (26), (53), (55), (57), (60), (101),
% 203.95/34.80  | | | | | | | | | | | |            (114), (154), (187), (202) are inconsistent by
% 203.95/34.80  | | | | | | | | | | | |            sub-proof #1241.
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | |   (203)   ~ (all_58_0 = e1)
% 203.95/34.80  | | | | | | | | | | | |   (204)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | BETA: splitting (59) gives:
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | |   (205)  all_58_0 = e2
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | REF_CLOSE: (28), (61), (175), (183), (184), (201), (205) are
% 203.95/34.80  | | | | | | | | | | | | |            inconsistent by sub-proof #728.
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | |   (206)   ~ (all_58_0 = e2)
% 203.95/34.80  | | | | | | | | | | | | |   (207)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | BETA: splitting (65) gives:
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | |   (208)  all_56_4 = e3
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | REF_CLOSE: (16), (149), (208) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | |            #1340.
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | |   (209)   ~ (all_56_4 = e3)
% 203.95/34.80  | | | | | | | | | | | | | |   (210)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | |   (211)  all_58_6 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | COMBINE_EQS: (101), (211) imply:
% 203.95/34.80  | | | | | | | | | | | | | | |   (212)  all_52_5 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | REDUCE: (9), (212) imply:
% 203.95/34.80  | | | | | | | | | | | | | | |   (213)  op(e2, e2) = e1
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e3, e1, e2, e2, simplifying
% 203.95/34.80  | | | | | | | | | | | | | | |              with (154), (213) gives:
% 203.95/34.80  | | | | | | | | | | | | | | |   (214)  e3 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | COMBINE_EQS: (175), (214) imply:
% 203.95/34.80  | | | | | | | | | | | | | | |   (215)  all_58_0 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (26), (53), (55), (57), (60), (101),
% 203.95/34.80  | | | | | | | | | | | | | | |            (114), (154), (187), (215) are inconsistent by
% 203.95/34.80  | | | | | | | | | | | | | | |            sub-proof #1241.
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | |   (216)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | |   (217)  all_58_4 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (217) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | |   (218)  all_10_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | REDUCE: (198), (218) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | |   (219)  op(e1, e1) = all_52_16
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | REDUCE: (43), (218) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | |   (220)  op(e1, e1) = all_10_0
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17), (190), (219), (220) are inconsistent by
% 203.95/34.80  | | | | | | | | | | | | | | | |            sub-proof #689.
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | |   (221)   ~ (all_58_4 = e1)
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | REDUCE: (196), (221) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | |   (222)   ~ (all_10_1 = e1)
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | |   (223)  all_58_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (223) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | |   (224)  all_4_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | REDUCE: (38), (224) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | |   (225)  $false
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | |   (226)  all_58_4 = e1 | all_58_9 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | |   (227)  all_58_4 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (227) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | |   (228)  all_10_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | REDUCE: (222), (228) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | |   (229)  $false
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | |   (230)  all_58_9 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (230) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | |   (231)  all_14_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | REDUCE: (166), (231) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | |   (232)   ~ (all_4_1 = e1)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | |   (233)  all_58_1 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (233) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | |   (234)  all_4_1 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | REDUCE: (160), (234) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | |   (235)   ~ (all_52_13 = e2)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | REDUCE: (169), (234) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | |   (236)   ~ (e3 = e2)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |   (237)  all_58_7 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (237) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |   (238)  all_52_13 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | REDUCE: (235), (238) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |   (239)  $false
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |   (240)  all_58_8 = e2 | all_58_11 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (241)  all_58_8 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (61), (183), (201), (241) are inconsistent
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1271.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (242)  all_58_11 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (242) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (243)  all_52_29 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (243) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (244)  op(e1, e0) = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | |   (245)  all_58_0 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (245) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | |   (246)  e3 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (246) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | |   (247)  $false
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | |   (248)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_58_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (249) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | |   (250)  e2 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (250) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | |   (251)  $false
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_4 = e0 | all_58_9 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (253)  all_58_4 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (253) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_10_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_10_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (255) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (256)  op(e1, e0) = all_10_0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e2, all_10_0, e0, e1,
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (244), (256) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_10_0 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (257) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (258)  $false
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_58_9 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (230), (259) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | |            #865.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | |   (260)   ~ (all_58_1 = e2)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | REDUCE: (158), (260) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | |   (261)   ~ (all_4_1 = e2)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |   (262)  all_56_1 = e2
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (261), (262) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |            #1165.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | |   (263)  all_56_1 = e1 | all_56_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (264)  all_56_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (157), (264) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            #688.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (265)  all_56_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (265) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (266)  all_4_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (267)  all_4_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (267) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (268)   ~ (all_10_1 = e0)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (267) imply:
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |   (269)   ~ (e3 = e0)
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (10), (12), (13), (16),
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            (20), (24), (28), (30), (33), (38), (39), (41),
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (56), (57), (61), (69), (71),
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            (74), (85), (86), (96), (98), (101), (105), (113),
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            (116), (123), (126), (149), (154), (157), (160),
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            (162), (169), (171), (175), (183), (184), (196),
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            (201), (210), (268) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | |            #684.
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | |   (270)  all_58_11 = e3
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REF_CLOSE: (28), (61), (270) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | |            #1323.
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | |   (271)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REF_CLOSE: (5), (9), (51), (53), (55), (57), (84), (91),
% 203.95/34.80  | | | | | | | | |            (101), (109), (149), (271) are inconsistent by
% 203.95/34.80  | | | | | | | | |            sub-proof #1365.
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | End of split
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | End of split
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | End of split
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | Case 2:
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | |   (272)  all_58_5 = e3 | all_58_10 = e3
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REF_CLOSE: (44), (75), (98), (144), (272) are inconsistent by
% 203.95/34.80  | | | | | |            sub-proof #1132.
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | End of split
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | End of split
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | End of split
% 203.95/34.80  | | | 
% 203.95/34.80  | | End of split
% 203.95/34.80  | | 
% 203.95/34.80  | End of split
% 203.95/34.80  | 
% 203.95/34.80  End of proof
% 203.95/34.80  
% 203.95/34.80  Sub-proof #684 shows that the following formulas are inconsistent:
% 203.95/34.80  ----------------------------------------------------------------
% 203.95/34.80    (1)   ~ (all_52_15 = all_52_23)
% 203.95/34.80    (2)  all_58_14 = all_52_23
% 203.95/34.80    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.95/34.80    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.80    (5)  op(all_52_7, all_52_7) = e0
% 203.95/34.80    (6)   ~ (e3 = e0)
% 203.95/34.80    (7)   ~ (all_52_7 = all_52_15)
% 203.95/34.80    (8)   ~ (all_52_3 = all_52_19)
% 203.95/34.80    (9)  all_56_4 = all_52_3
% 203.95/34.80    (10)  all_58_13 = all_52_15
% 203.95/34.80    (11)   ~ (all_52_15 = e3)
% 203.95/34.80    (12)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.80    (13)  all_58_8 = e3
% 203.95/34.80    (14)   ~ (all_4_1 = e3)
% 203.95/34.80    (15)  all_58_11 = all_52_29
% 203.95/34.80    (16)   ~ (all_52_3 = e3)
% 203.95/34.80    (17)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.80    (18)  all_58_4 = all_10_1
% 203.95/34.80    (19)  all_56_1 = all_4_1
% 203.95/34.80    (20)  op(e0, e0) = all_14_2
% 203.95/34.80    (21)   ~ (all_4_1 = e1)
% 203.95/34.80    (22)  op(e0, e0) = e3
% 203.95/34.80    (23)   ~ (e2 = e1)
% 203.95/34.80    (24)   ~ (all_10_1 = e0)
% 203.95/34.80    (25)  all_58_7 = all_52_13
% 203.95/34.80    (26)   ~ (all_52_5 = all_52_7)
% 203.95/34.80    (27)  all_58_12 = all_52_7
% 203.95/34.80    (28)   ~ (all_52_7 = all_14_2)
% 203.95/34.80    (29)  all_58_8 = e3 | all_58_11 = e3
% 203.95/34.80    (30)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 203.95/34.80    (31)  all_58_2 = all_52_3
% 203.95/34.80    (32)   ~ (all_52_29 = e3)
% 203.95/34.80    (33)  op(all_52_3, all_52_3) = e2
% 203.95/34.80    (34)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.80    (35)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.80    (36)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.80    (37)  all_58_0 = e3
% 203.95/34.80    (38)   ~ (all_52_13 = all_4_1)
% 203.95/34.80    (39)  op(all_52_29, all_52_29) = all_52_28
% 203.95/34.80    (40)  all_56_12 = all_52_7
% 203.95/34.80    (41)  op(e2, e2) = e3
% 203.95/34.80    (42)   ~ (all_52_3 = all_52_7)
% 203.95/34.80    (43)  all_58_5 = all_52_19
% 203.95/34.80    (44)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 203.95/34.80    (45)  all_58_6 = all_52_5
% 203.95/34.80    (46)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.80    (47)   ~ (e3 = e2)
% 203.95/34.80    (48)   ~ (all_52_15 = all_4_1)
% 203.95/34.80    (49)  all_56_13 = all_52_15
% 203.95/34.80    (50)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 203.95/34.80  
% 203.95/34.80  Begin of proof
% 203.95/34.80  | 
% 203.95/34.80  | BETA: splitting (3) gives:
% 203.95/34.80  | 
% 203.95/34.80  | Case 1:
% 203.95/34.80  | | 
% 203.95/34.80  | |   (51)  all_58_4 = e0
% 203.95/34.80  | | 
% 203.95/34.80  | | COMBINE_EQS: (18), (51) imply:
% 203.95/34.80  | |   (52)  all_10_1 = e0
% 203.95/34.80  | | 
% 203.95/34.80  | | REDUCE: (24), (52) imply:
% 203.95/34.80  | |   (53)  $false
% 203.95/34.80  | | 
% 203.95/34.80  | | CLOSE: (53) is inconsistent.
% 203.95/34.80  | | 
% 203.95/34.80  | Case 2:
% 203.95/34.80  | | 
% 203.95/34.80  | |   (54)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 203.95/34.80  | | 
% 203.95/34.80  | | BETA: splitting (36) gives:
% 203.95/34.80  | | 
% 203.95/34.80  | | Case 1:
% 203.95/34.80  | | | 
% 203.95/34.80  | | |   (55)  all_58_0 = e2
% 203.95/34.80  | | | 
% 203.95/34.80  | | | REF_CLOSE: (13), (15), (29), (32), (37), (47), (55) are inconsistent by
% 203.95/34.80  | | |            sub-proof #728.
% 203.95/34.80  | | | 
% 203.95/34.80  | | Case 2:
% 203.95/34.80  | | | 
% 203.95/34.80  | | |   (56)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.80  | | | 
% 203.95/34.80  | | | BETA: splitting (50) gives:
% 203.95/34.80  | | | 
% 203.95/34.80  | | | Case 1:
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | |   (57)  all_58_2 = e2
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | | COMBINE_EQS: (31), (57) imply:
% 203.95/34.80  | | | |   (58)  all_52_3 = e2
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | | REF_CLOSE: (4), (16), (33), (41), (58) are inconsistent by sub-proof
% 203.95/34.80  | | | |            #687.
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | Case 2:
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | |   (59)   ~ (all_58_2 = e2)
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | | REDUCE: (31), (59) imply:
% 203.95/34.80  | | | |   (60)   ~ (all_52_3 = e2)
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | | BETA: splitting (34) gives:
% 203.95/34.80  | | | | 
% 203.95/34.80  | | | | Case 1:
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | |   (61)  all_58_12 = e1
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | COMBINE_EQS: (27), (61) imply:
% 203.95/34.80  | | | | |   (62)  all_52_7 = e1
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | REDUCE: (42), (62) imply:
% 203.95/34.80  | | | | |   (63)   ~ (all_52_3 = e1)
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | REDUCE: (26), (62) imply:
% 203.95/34.80  | | | | |   (64)   ~ (all_52_5 = e1)
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | REDUCE: (7), (62) imply:
% 203.95/34.80  | | | | |   (65)   ~ (all_52_15 = e1)
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | SIMP: (65) implies:
% 203.95/34.80  | | | | |   (66)   ~ (all_52_15 = e1)
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | BETA: splitting (35) gives:
% 203.95/34.80  | | | | | 
% 203.95/34.80  | | | | | Case 1:
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | |   (67)  all_56_4 = e2
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | REF_CLOSE: (9), (60), (67) are inconsistent by sub-proof #1155.
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | Case 2:
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | |   (68)   ~ (all_56_4 = e2)
% 203.95/34.80  | | | | | |   (69)  all_56_4 = e1 | all_56_4 = e0
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | BETA: splitting (56) gives:
% 203.95/34.80  | | | | | | 
% 203.95/34.80  | | | | | | Case 1:
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | |   (70)  all_58_2 = e2
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | COMBINE_EQS: (31), (70) imply:
% 203.95/34.80  | | | | | | |   (71)  all_52_3 = e2
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | REDUCE: (60), (71) imply:
% 203.95/34.80  | | | | | | |   (72)  $false
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | CLOSE: (72) is inconsistent.
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | Case 2:
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | |   (73)  all_58_6 = e2 | all_58_12 = e2
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | BETA: splitting (73) gives:
% 203.95/34.80  | | | | | | | 
% 203.95/34.80  | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | |   (74)  all_58_6 = e2
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | COMBINE_EQS: (45), (74) imply:
% 203.95/34.80  | | | | | | | |   (75)  all_52_5 = e2
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | BETA: splitting (69) gives:
% 203.95/34.80  | | | | | | | | 
% 203.95/34.80  | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | |   (76)  all_56_4 = e1
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REF_CLOSE: (9), (63), (76) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | |            #1310.
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | |   (77)  all_56_4 = e0
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | COMBINE_EQS: (9), (77) imply:
% 203.95/34.80  | | | | | | | | |   (78)  all_52_3 = e0
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | SIMP: (78) implies:
% 203.95/34.80  | | | | | | | | |   (79)  all_52_3 = e0
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REDUCE: (8), (79) imply:
% 203.95/34.80  | | | | | | | | |   (80)   ~ (all_52_19 = e0)
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | SIMP: (80) implies:
% 203.95/34.80  | | | | | | | | |   (81)   ~ (all_52_19 = e0)
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REDUCE: (16), (79) imply:
% 203.95/34.80  | | | | | | | | |   (82)   ~ (e3 = e0)
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | REDUCE: (33), (79) imply:
% 203.95/34.80  | | | | | | | | |   (83)  op(e0, e0) = e2
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | BETA: splitting (54) gives:
% 203.95/34.80  | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | |   (84)  all_58_5 = e0
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | REF_CLOSE: (43), (81), (84) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | |            #754.
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | |   (85)  all_58_8 = e0 | all_58_14 = e0
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | BETA: splitting (85) gives:
% 203.95/34.80  | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | |   (86)  all_58_8 = e0
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REF_CLOSE: (6), (13), (86) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | |            #686.
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | |   (87)  all_58_14 = e0
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | COMBINE_EQS: (2), (87) imply:
% 203.95/34.80  | | | | | | | | | | |   (88)  all_52_23 = e0
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | SIMP: (88) implies:
% 203.95/34.80  | | | | | | | | | | |   (89)  all_52_23 = e0
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | REDUCE: (1), (89) imply:
% 203.95/34.80  | | | | | | | | | | |   (90)   ~ (all_52_15 = e0)
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | BETA: splitting (17) gives:
% 203.95/34.80  | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | |   (91)  all_58_12 = e2
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | COMBINE_EQS: (61), (91) imply:
% 203.95/34.80  | | | | | | | | | | | |   (92)  e2 = e1
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | REDUCE: (23), (92) imply:
% 203.95/34.80  | | | | | | | | | | | |   (93)  $false
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | CLOSE: (93) is inconsistent.
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | |   (94)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | BETA: splitting (94) gives:
% 203.95/34.80  | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | |   (95)  all_58_13 = e2
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | COMBINE_EQS: (10), (95) imply:
% 203.95/34.80  | | | | | | | | | | | | |   (96)  all_52_15 = e2
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | SIMP: (96) implies:
% 203.95/34.80  | | | | | | | | | | | | |   (97)  all_52_15 = e2
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | REDUCE: (48), (97) imply:
% 203.95/34.80  | | | | | | | | | | | | |   (98)   ~ (all_4_1 = e2)
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | SIMP: (98) implies:
% 203.95/34.80  | | | | | | | | | | | | |   (99)   ~ (all_4_1 = e2)
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | REDUCE: (11), (97) imply:
% 203.95/34.80  | | | | | | | | | | | | |   (100)   ~ (e3 = e2)
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | BETA: splitting (44) gives:
% 203.95/34.80  | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | |   (101)  all_56_1 = e2
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | REF_CLOSE: (19), (99), (101) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | |            #1165.
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | |   (102)   ~ (all_56_1 = e2)
% 203.95/34.80  | | | | | | | | | | | | | |   (103)  all_56_1 = e1 | all_56_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 203.95/34.80  | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | Case 1:
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | |   (104)  all_56_1 = e1
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (104) are inconsistent by sub-proof
% 203.95/34.80  | | | | | | | | | | | | | | |            #688.
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | Case 2:
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | |   (105)  all_56_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | COMBINE_EQS: (19), (105) imply:
% 203.95/34.80  | | | | | | | | | | | | | | |   (106)  all_4_1 = e0
% 203.95/34.80  | | | | | | | | | | | | | | | 
% 203.95/34.80  | | | | | | | | | | | | | | | SIMP: (106) implies:
% 203.95/34.81  | | | | | | | | | | | | | | |   (107)  all_4_1 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | REDUCE: (38), (107) imply:
% 203.95/34.81  | | | | | | | | | | | | | | |   (108)   ~ (all_52_13 = e0)
% 203.95/34.81  | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | REDUCE: (99), (107) imply:
% 203.95/34.81  | | | | | | | | | | | | | | |   (109)   ~ (e2 = e0)
% 203.95/34.81  | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | SIMP: (109) implies:
% 203.95/34.81  | | | | | | | | | | | | | | |   (110)   ~ (e2 = e0)
% 203.95/34.81  | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 203.95/34.81  | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | |   (111)  all_58_6 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | REF_CLOSE: (74), (110), (111) are inconsistent by sub-proof
% 203.95/34.81  | | | | | | | | | | | | | | | |            #801.
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | |   (112)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | |   (113)  all_58_7 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (113) imply:
% 203.95/34.81  | | | | | | | | | | | | | | | | |   (114)  all_52_13 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | REDUCE: (108), (114) imply:
% 203.95/34.81  | | | | | | | | | | | | | | | | |   (115)  $false
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | |   (116)  all_58_8 = e0 | all_58_11 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (117)  all_58_8 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (117) imply:
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (118)  e3 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | REDUCE: (6), (118) imply:
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (119)  $false
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | CLOSE: (119) is inconsistent.
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (120)  all_58_11 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (120) imply:
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (121)  all_52_29 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | SIMP: (121) implies:
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (122)  all_52_29 = e0
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | REDUCE: (39), (122) imply:
% 203.95/34.81  | | | | | | | | | | | | | | | | | |   (123)  op(e0, e0) = all_52_28
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22), (47), (83), (123) are inconsistent by
% 203.95/34.81  | | | | | | | | | | | | | | | | | |            sub-proof #685.
% 203.95/34.81  | | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | |   (124)   ~ (all_58_13 = e2)
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | REDUCE: (10), (124) imply:
% 203.95/34.81  | | | | | | | | | | | | |   (125)   ~ (all_52_15 = e2)
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | REF_CLOSE: (30), (49), (66), (90), (125) are inconsistent by
% 203.95/34.81  | | | | | | | | | | | | |            sub-proof #1353.
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | |   (126)  all_58_12 = e2
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REF_CLOSE: (23), (61), (126) are inconsistent by sub-proof
% 203.95/34.81  | | | | | | | |            #1198.
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | End of split
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | End of split
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | End of split
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | Case 2:
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | |   (127)   ~ (all_58_12 = e1)
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | REDUCE: (27), (127) imply:
% 203.95/34.81  | | | | |   (128)   ~ (all_52_7 = e1)
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | REF_CLOSE: (4), (5), (6), (12), (17), (20), (27), (28), (40), (41),
% 203.95/34.81  | | | | |            (128) are inconsistent by sub-proof #1160.
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | End of split
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | End of split
% 203.95/34.81  | | | 
% 203.95/34.81  | | End of split
% 203.95/34.81  | | 
% 203.95/34.81  | End of split
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #685 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.81    (2)  op(e0, e0) = all_52_28
% 203.95/34.81    (3)  op(e0, e0) = e3
% 203.95/34.81    (4)  op(e0, e0) = e2
% 203.95/34.81    (5)   ~ (e3 = e2)
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | GROUND_INST: instantiating (1) with e3, all_52_28, e0, e0, simplifying with
% 203.95/34.81  |              (2), (3) gives:
% 203.95/34.81  |   (6)  all_52_28 = e3
% 203.95/34.81  | 
% 203.95/34.81  | GROUND_INST: instantiating (1) with e2, all_52_28, e0, e0, simplifying with
% 203.95/34.81  |              (2), (4) gives:
% 203.95/34.81  |   (7)  all_52_28 = e2
% 203.95/34.81  | 
% 203.95/34.81  | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #1095.
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #686 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)  all_58_8 = e3
% 203.95/34.81    (2)  all_58_8 = e0
% 203.95/34.81    (3)   ~ (e3 = e0)
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | COMBINE_EQS: (1), (2) imply:
% 203.95/34.81  |   (4)  e3 = e0
% 203.95/34.81  | 
% 203.95/34.81  | SIMP: (4) implies:
% 203.95/34.81  |   (5)  e3 = e0
% 203.95/34.81  | 
% 203.95/34.81  | REDUCE: (3), (5) imply:
% 203.95/34.81  |   (6)  $false
% 203.95/34.81  | 
% 203.95/34.81  | CLOSE: (6) is inconsistent.
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #687 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.81    (2)   ~ (all_52_3 = e3)
% 203.95/34.81    (3)  op(all_52_3, all_52_3) = e2
% 203.95/34.81    (4)  op(e2, e2) = e3
% 203.95/34.81    (5)  all_52_3 = e2
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | REDUCE: (2), (5) imply:
% 203.95/34.81  |   (6)   ~ (e3 = e2)
% 203.95/34.81  | 
% 203.95/34.81  | SIMP: (6) implies:
% 203.95/34.81  |   (7)   ~ (e3 = e2)
% 203.95/34.81  | 
% 203.95/34.81  | REDUCE: (3), (5) imply:
% 203.95/34.81  |   (8)  op(e2, e2) = e2
% 203.95/34.81  | 
% 203.95/34.81  | GROUND_INST: instantiating (1) with e3, e2, e2, e2, simplifying with (4), (8)
% 203.95/34.81  |              gives:
% 203.95/34.81  |   (9)  e3 = e2
% 203.95/34.81  | 
% 203.95/34.81  | REDUCE: (7), (9) imply:
% 203.95/34.81  |   (10)  $false
% 203.95/34.81  | 
% 203.95/34.81  | CLOSE: (10) is inconsistent.
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #688 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)  all_56_1 = all_4_1
% 203.95/34.81    (2)  all_56_1 = e1
% 203.95/34.81    (3)   ~ (all_4_1 = e1)
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | COMBINE_EQS: (1), (2) imply:
% 203.95/34.81  |   (4)  all_4_1 = e1
% 203.95/34.81  | 
% 203.95/34.81  | SIMP: (4) implies:
% 203.95/34.81  |   (5)  all_4_1 = e1
% 203.95/34.81  | 
% 203.95/34.81  | REDUCE: (3), (5) imply:
% 203.95/34.81  |   (6)  $false
% 203.95/34.81  | 
% 203.95/34.81  | CLOSE: (6) is inconsistent.
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #689 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.81    (2)   ~ (all_10_0 = e3)
% 203.95/34.81    (3)  op(e1, e1) = all_52_16
% 203.95/34.81    (4)  op(e1, e1) = all_10_0
% 203.95/34.81    (5)  op(e1, e1) = e3
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | GROUND_INST: instantiating (1) with e3, all_52_16, e1, e1, simplifying with
% 203.95/34.81  |              (3), (5) gives:
% 203.95/34.81  |   (6)  all_52_16 = e3
% 203.95/34.81  | 
% 203.95/34.81  | GROUND_INST: instantiating (1) with all_10_0, all_52_16, e1, e1, simplifying
% 203.95/34.81  |              with (3), (4) gives:
% 203.95/34.81  |   (7)  all_52_16 = all_10_0
% 203.95/34.81  | 
% 203.95/34.81  | COMBINE_EQS: (6), (7) imply:
% 203.95/34.81  |   (8)  all_10_0 = e3
% 203.95/34.81  | 
% 203.95/34.81  | REDUCE: (2), (8) imply:
% 203.95/34.81  |   (9)  $false
% 203.95/34.81  | 
% 203.95/34.81  | CLOSE: (9) is inconsistent.
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #690 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)   ~ (e3 = e1)
% 203.95/34.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.81    (3)  op(all_52_7, all_52_7) = e0
% 203.95/34.81    (4)  op(all_52_5, all_52_5) = e1
% 203.95/34.81    (5)  op(all_10_2, e1) = all_10_1
% 203.95/34.81    (6)  op(e0, e1) = all_52_23
% 203.95/34.81    (7)   ~ (all_52_3 = e1)
% 203.95/34.81    (8)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.95/34.81    (9)  all_58_12 = all_52_7
% 203.95/34.81    (10)  all_58_2 = all_52_3
% 203.95/34.81    (11)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.81    (12)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.81    (13)  all_58_0 = e3
% 203.95/34.81    (14)   ~ (all_10_1 = e2)
% 203.95/34.81    (15)   ~ (all_52_5 = all_10_2)
% 203.95/34.81    (16)  all_56_14 = all_52_23
% 203.95/34.81    (17)   ~ (all_10_1 = e3)
% 203.95/34.81    (18)  all_58_6 = all_52_5
% 203.95/34.81    (19)  op(e1, e1) = all_10_2
% 203.95/34.81    (20)   ~ (all_52_23 = all_10_2)
% 203.95/34.81    (21)   ~ (all_52_7 = all_52_23)
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | BETA: splitting (11) gives:
% 203.95/34.81  | 
% 203.95/34.81  | Case 1:
% 203.95/34.81  | | 
% 203.95/34.81  | |   (22)  all_58_0 = e1
% 203.95/34.81  | | 
% 203.95/34.81  | | COMBINE_EQS: (13), (22) imply:
% 203.95/34.81  | |   (23)  e3 = e1
% 203.95/34.81  | | 
% 203.95/34.81  | | REDUCE: (1), (23) imply:
% 203.95/34.81  | |   (24)  $false
% 203.95/34.81  | | 
% 203.95/34.81  | | CLOSE: (24) is inconsistent.
% 203.95/34.81  | | 
% 203.95/34.81  | Case 2:
% 203.95/34.81  | | 
% 203.95/34.81  | |   (25)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.81  | | 
% 203.95/34.81  | | BETA: splitting (12) gives:
% 203.95/34.81  | | 
% 203.95/34.81  | | Case 1:
% 203.95/34.81  | | | 
% 203.95/34.81  | | |   (26)  all_58_12 = e1
% 203.95/34.81  | | | 
% 203.95/34.81  | | | COMBINE_EQS: (9), (26) imply:
% 203.95/34.81  | | |   (27)  all_52_7 = e1
% 203.95/34.81  | | | 
% 203.95/34.81  | | | SIMP: (27) implies:
% 203.95/34.81  | | |   (28)  all_52_7 = e1
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REF_CLOSE: (2), (3), (5), (6), (8), (14), (16), (17), (19), (20), (21),
% 203.95/34.81  | | |            (28) are inconsistent by sub-proof #1379.
% 203.95/34.81  | | | 
% 203.95/34.81  | | Case 2:
% 203.95/34.81  | | | 
% 203.95/34.81  | | |   (29)   ~ (all_58_12 = e1)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (9), (29) imply:
% 203.95/34.81  | | |   (30)   ~ (all_52_7 = e1)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REF_CLOSE: (2), (4), (7), (9), (10), (15), (18), (19), (25), (30) are
% 203.95/34.81  | | |            inconsistent by sub-proof #705.
% 203.95/34.81  | | | 
% 203.95/34.81  | | End of split
% 203.95/34.81  | | 
% 203.95/34.81  | End of split
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #691 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)  all_58_14 = all_52_23
% 203.95/34.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.81    (3)  op(all_52_7, all_52_7) = e0
% 203.95/34.81    (4)  op(all_52_5, all_52_5) = e1
% 203.95/34.81    (5)   ~ (e3 = e0)
% 203.95/34.81    (6)   ~ (all_52_3 = all_52_19)
% 203.95/34.81    (7)   ~ (all_52_3 = all_6_2)
% 203.95/34.81    (8)  all_58_0 = all_6_2
% 203.95/34.81    (9)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.81    (10)  op(e2, e2) = all_4_2
% 203.95/34.81    (11)   ~ (all_52_3 = all_52_5)
% 203.95/34.81    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.81    (13)  op(e0, e0) = all_14_2
% 203.95/34.81    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.81    (15)  op(e0, e0) = e3
% 203.95/34.81    (16)   ~ (e2 = e1)
% 203.95/34.81    (17)   ~ (all_6_0 = e1)
% 203.95/34.81    (18)  all_58_10 = all_52_27
% 203.95/34.81    (19)  all_56_8 = all_52_5
% 203.95/34.81    (20)   ~ (all_52_19 = all_52_23)
% 203.95/34.81    (21)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.95/34.81    (22)  op(all_6_2, all_6_2) = e3
% 203.95/34.81    (23)  all_58_12 = all_52_7
% 203.95/34.81    (24)   ~ (all_52_7 = e3)
% 203.95/34.81    (25)   ~ (all_52_7 = all_14_2)
% 203.95/34.81    (26)  all_58_2 = all_52_3
% 203.95/34.81    (27)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 203.95/34.81    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.81    (29)  op(e3, all_6_1) = all_6_0
% 203.95/34.81    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.81    (31)  op(all_52_3, all_52_3) = e2
% 203.95/34.81    (32)  all_56_6 = all_52_19
% 203.95/34.81    (33)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.81    (34)   ~ (all_52_27 = e3)
% 203.95/34.81    (35)   ~ (all_52_19 = all_10_2)
% 203.95/34.81    (36)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.81    (37)  all_58_8 = all_10_2
% 203.95/34.81    (38)   ~ (all_52_5 = all_10_2)
% 203.95/34.81    (39)  all_56_12 = all_52_7
% 203.95/34.81    (40)   ~ (all_52_5 = all_6_2)
% 203.95/34.81    (41)  op(e3, e3) = all_6_2
% 203.95/34.81    (42)   ~ (all_52_7 = e1)
% 203.95/34.81    (43)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.95/34.81    (44)  all_58_5 = all_52_19
% 203.95/34.81    (45)  all_58_6 = all_52_5
% 203.95/34.81    (46)   ~ (all_52_17 = all_6_2)
% 203.95/34.81    (47)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 203.95/34.81    (48)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.81    (49)  op(e1, e1) = all_10_2
% 203.95/34.81    (50)  all_58_3 = all_4_2
% 203.95/34.81    (51)   ~ (all_52_3 = all_4_2)
% 203.95/34.81    (52)  op(all_6_2, e3) = all_6_1
% 203.95/34.81    (53)  all_58_4 = all_52_17
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | BETA: splitting (48) gives:
% 203.95/34.81  | 
% 203.95/34.81  | Case 1:
% 203.95/34.81  | | 
% 203.95/34.81  | |   (54)  all_58_4 = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | COMBINE_EQS: (53), (54) imply:
% 203.95/34.81  | |   (55)  all_52_17 = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | REF_CLOSE: (2), (4), (8), (10), (14), (22), (23), (24), (26), (28), (31),
% 203.95/34.81  | |            (38), (41), (45), (46), (49), (51), (55) are inconsistent by
% 203.95/34.81  | |            sub-proof #1199.
% 203.95/34.81  | | 
% 203.95/34.81  | Case 2:
% 203.95/34.81  | | 
% 203.95/34.81  | |   (56)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | BETA: splitting (43) gives:
% 203.95/34.81  | | 
% 203.95/34.81  | | Case 1:
% 203.95/34.81  | | | 
% 203.95/34.81  | | |   (57)  all_58_0 = e3
% 203.95/34.81  | | | 
% 203.95/34.81  | | | COMBINE_EQS: (8), (57) imply:
% 203.95/34.81  | | |   (58)  all_6_2 = e3
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (7), (58) imply:
% 203.95/34.81  | | |   (59)   ~ (all_52_3 = e3)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (40), (58) imply:
% 203.95/34.81  | | |   (60)   ~ (all_52_5 = e3)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (52), (58) imply:
% 203.95/34.81  | | |   (61)  op(e3, e3) = all_6_1
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (41), (58) imply:
% 203.95/34.81  | | |   (62)  op(e3, e3) = e3
% 203.95/34.81  | | | 
% 203.95/34.81  | | | GROUND_INST: instantiating (2) with e3, all_6_1, e3, e3, simplifying with
% 203.95/34.81  | | |              (61), (62) gives:
% 203.95/34.81  | | |   (63)  all_6_1 = e3
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (29), (63) imply:
% 203.95/34.81  | | |   (64)  op(e3, e3) = all_6_0
% 203.95/34.81  | | | 
% 203.95/34.81  | | | GROUND_INST: instantiating (2) with e3, all_6_0, e3, e3, simplifying with
% 203.95/34.81  | | |              (62), (64) gives:
% 203.95/34.81  | | |   (65)  all_6_0 = e3
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (17), (65) imply:
% 203.95/34.81  | | |   (66)   ~ (e3 = e1)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | BETA: splitting (14) gives:
% 203.95/34.81  | | | 
% 203.95/34.81  | | | Case 1:
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | |   (67)  all_58_2 = e3
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | | REF_CLOSE: (26), (59), (67) are inconsistent by sub-proof #1369.
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | Case 2:
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | |   (68)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | | BETA: splitting (30) gives:
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | | Case 1:
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | |   (69)  all_58_0 = e1
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | COMBINE_EQS: (57), (69) imply:
% 203.95/34.81  | | | | |   (70)  e3 = e1
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | REDUCE: (66), (70) imply:
% 203.95/34.81  | | | | |   (71)  $false
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | CLOSE: (71) is inconsistent.
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | Case 2:
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | |   (72)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | BETA: splitting (36) gives:
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | | Case 1:
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | |   (73)  all_56_8 = e3
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | | REF_CLOSE: (19), (60), (73) are inconsistent by sub-proof #1325.
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | Case 2:
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | |   (74)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | | BETA: splitting (27) gives:
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | | Case 1:
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | |   (75)  all_56_6 = e3
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | COMBINE_EQS: (32), (75) imply:
% 203.95/34.81  | | | | | | |   (76)  all_52_19 = e3
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | SIMP: (76) implies:
% 203.95/34.81  | | | | | | |   (77)  all_52_19 = e3
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | COMBINE_EQS: (44), (77) imply:
% 203.95/34.81  | | | | | | |   (78)  all_58_5 = e3
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | REDUCE: (20), (77) imply:
% 203.95/34.81  | | | | | | |   (79)   ~ (all_52_23 = e3)
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | SIMP: (79) implies:
% 203.95/34.81  | | | | | | |   (80)   ~ (all_52_23 = e3)
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | REDUCE: (35), (77) imply:
% 203.95/34.81  | | | | | | |   (81)   ~ (all_10_2 = e3)
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | SIMP: (81) implies:
% 203.95/34.81  | | | | | | |   (82)   ~ (all_10_2 = e3)
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | BETA: splitting (21) gives:
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | |   (83)  all_58_2 = e1
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | COMBINE_EQS: (26), (83) imply:
% 203.95/34.81  | | | | | | | |   (84)  all_52_3 = e1
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | SIMP: (84) implies:
% 203.95/34.81  | | | | | | | |   (85)  all_52_3 = e1
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REDUCE: (11), (85) imply:
% 203.95/34.81  | | | | | | | |   (86)   ~ (all_52_5 = e1)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | SIMP: (86) implies:
% 203.95/34.81  | | | | | | | |   (87)   ~ (all_52_5 = e1)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REDUCE: (59), (85) imply:
% 203.95/34.81  | | | | | | | |   (88)   ~ (e3 = e1)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REDUCE: (31), (85) imply:
% 203.95/34.81  | | | | | | | |   (89)  op(e1, e1) = e2
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | GROUND_INST: instantiating (2) with all_10_2, e2, e1, e1,
% 203.95/34.81  | | | | | | | |              simplifying with (49), (89) gives:
% 203.95/34.81  | | | | | | | |   (90)  all_10_2 = e2
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REDUCE: (38), (90) imply:
% 203.95/34.81  | | | | | | | |   (91)   ~ (all_52_5 = e2)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REDUCE: (82), (90) imply:
% 203.95/34.81  | | | | | | | |   (92)   ~ (e3 = e2)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | SIMP: (92) implies:
% 203.95/34.81  | | | | | | | |   (93)   ~ (e3 = e2)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | BETA: splitting (33) gives:
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | |   (94)  all_58_0 = e2
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | COMBINE_EQS: (57), (94) imply:
% 203.95/34.81  | | | | | | | | |   (95)  e3 = e2
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | REDUCE: (93), (95) imply:
% 203.95/34.81  | | | | | | | | |   (96)  $false
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | CLOSE: (96) is inconsistent.
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | |   (97)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | BETA: splitting (74) gives:
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | |   (98)  all_56_8 = e2
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | REF_CLOSE: (19), (91), (98) are inconsistent by sub-proof
% 203.95/34.81  | | | | | | | | | |            #1022.
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | |   (99)   ~ (all_56_8 = e2)
% 203.95/34.81  | | | | | | | | | |   (100)  all_56_8 = e1 | all_56_8 = e0
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | BETA: splitting (47) gives:
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | |   (101)  all_58_6 = e0
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | COMBINE_EQS: (45), (101) imply:
% 203.95/34.81  | | | | | | | | | | |   (102)  all_52_5 = e0
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | SIMP: (102) implies:
% 203.95/34.81  | | | | | | | | | | |   (103)  all_52_5 = e0
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | REDUCE: (91), (103) imply:
% 203.95/34.81  | | | | | | | | | | |   (104)   ~ (e2 = e0)
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | SIMP: (104) implies:
% 203.95/34.81  | | | | | | | | | | |   (105)   ~ (e2 = e0)
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | REDUCE: (4), (103) imply:
% 203.95/34.81  | | | | | | | | | | |   (106)  op(e0, e0) = e1
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | BETA: splitting (97) gives:
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | |   (107)  all_58_2 = e2
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | COMBINE_EQS: (83), (107) imply:
% 203.95/34.81  | | | | | | | | | | | |   (108)  e2 = e1
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | REDUCE: (16), (108) imply:
% 203.95/34.81  | | | | | | | | | | | |   (109)  $false
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | |   (110)  all_58_6 = e2 | all_58_12 = e2
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | BETA: splitting (110) gives:
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | Case 1:
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | |   (111)  all_58_6 = e2
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | COMBINE_EQS: (101), (111) imply:
% 203.95/34.81  | | | | | | | | | | | | |   (112)  e2 = e0
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | REDUCE: (105), (112) imply:
% 203.95/34.81  | | | | | | | | | | | | |   (113)  $false
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | CLOSE: (113) is inconsistent.
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e3, e1, e0, e0, simplifying
% 203.95/34.81  | | | | | | | | | | | | |              with (15), (106) gives:
% 203.95/34.81  | | | | | | | | | | | | |   (114)  e3 = e1
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | COMBINE_EQS: (78), (114) imply:
% 203.95/34.81  | | | | | | | | | | | | |   (115)  all_58_5 = e1
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | | REF_CLOSE: (1), (37), (56), (66), (80), (82), (115) are
% 203.95/34.81  | | | | | | | | | | | | |            inconsistent by sub-proof #1051.
% 203.95/34.81  | | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | |   (116)   ~ (all_58_6 = e0)
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | REDUCE: (45), (116) imply:
% 203.95/34.81  | | | | | | | | | | |   (117)   ~ (all_52_5 = e0)
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | | REF_CLOSE: (19), (87), (100), (117) are inconsistent by
% 203.95/34.81  | | | | | | | | | | |            sub-proof #1020.
% 203.95/34.81  | | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | | 
% 203.95/34.81  | | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | | 
% 203.95/34.81  | | | | | | | | End of split
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | Case 2:
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | |   (118)   ~ (all_58_2 = e1)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REDUCE: (26), (118) imply:
% 203.95/34.81  | | | | | | | |   (119)   ~ (all_52_3 = e1)
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | | REF_CLOSE: (2), (4), (23), (26), (38), (42), (45), (49), (72),
% 203.95/34.81  | | | | | | | |            (119) are inconsistent by sub-proof #705.
% 203.95/34.81  | | | | | | | | 
% 203.95/34.81  | | | | | | | End of split
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | Case 2:
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | |   (120)   ~ (all_56_6 = e3)
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | REDUCE: (32), (120) imply:
% 203.95/34.81  | | | | | | |   (121)   ~ (all_52_19 = e3)
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | | REF_CLOSE: (2), (3), (5), (9), (10), (12), (13), (18), (23), (25),
% 203.95/34.81  | | | | | | |            (34), (39), (42), (44), (50), (68), (121) are
% 203.95/34.81  | | | | | | |            inconsistent by sub-proof #692.
% 203.95/34.81  | | | | | | | 
% 203.95/34.81  | | | | | | End of split
% 203.95/34.81  | | | | | | 
% 203.95/34.81  | | | | | End of split
% 203.95/34.81  | | | | | 
% 203.95/34.81  | | | | End of split
% 203.95/34.81  | | | | 
% 203.95/34.81  | | | End of split
% 203.95/34.81  | | | 
% 203.95/34.81  | | Case 2:
% 203.95/34.81  | | | 
% 203.95/34.81  | | |   (122)   ~ (all_58_0 = e3)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REDUCE: (8), (122) imply:
% 203.95/34.81  | | |   (123)   ~ (all_6_2 = e3)
% 203.95/34.81  | | | 
% 203.95/34.81  | | | REF_CLOSE: (2), (4), (8), (10), (14), (22), (23), (24), (26), (28), (31),
% 203.95/34.81  | | |            (38), (41), (45), (49), (51), (123) are inconsistent by
% 203.95/34.81  | | |            sub-proof #1363.
% 203.95/34.81  | | | 
% 203.95/34.81  | | End of split
% 203.95/34.81  | | 
% 203.95/34.81  | End of split
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #692 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.81    (2)  op(all_52_7, all_52_7) = e0
% 203.95/34.81    (3)   ~ (e3 = e0)
% 203.95/34.81    (4)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.81    (5)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.81    (6)  op(e2, e2) = all_4_2
% 203.95/34.81    (7)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 203.95/34.81    (8)  op(e0, e0) = all_14_2
% 203.95/34.81    (9)  all_58_10 = all_52_27
% 203.95/34.81    (10)  all_58_12 = all_52_7
% 203.95/34.81    (11)   ~ (all_52_7 = all_14_2)
% 203.95/34.81    (12)   ~ (all_52_19 = e3)
% 203.95/34.81    (13)   ~ (all_52_27 = e3)
% 203.95/34.81    (14)  all_56_12 = all_52_7
% 203.95/34.81    (15)   ~ (all_52_7 = e1)
% 203.95/34.81    (16)  all_58_5 = all_52_19
% 203.95/34.81    (17)  all_58_3 = all_4_2
% 203.95/34.81  
% 203.95/34.81  Begin of proof
% 203.95/34.81  | 
% 203.95/34.81  | BETA: splitting (4) gives:
% 203.95/34.81  | 
% 203.95/34.81  | Case 1:
% 203.95/34.81  | | 
% 203.95/34.81  | |   (18)  all_58_3 = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | COMBINE_EQS: (17), (18) imply:
% 203.95/34.81  | |   (19)  all_4_2 = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | REDUCE: (6), (19) imply:
% 203.95/34.81  | |   (20)  op(e2, e2) = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (14), (15), (20) are
% 203.95/34.81  | |            inconsistent by sub-proof #1160.
% 203.95/34.81  | | 
% 203.95/34.81  | Case 2:
% 203.95/34.81  | | 
% 203.95/34.81  | |   (21)  all_58_5 = e3 | all_58_10 = e3
% 203.95/34.81  | | 
% 203.95/34.81  | | REF_CLOSE: (9), (12), (13), (16), (21) are inconsistent by sub-proof #1132.
% 203.95/34.81  | | 
% 203.95/34.81  | End of split
% 203.95/34.81  | 
% 203.95/34.81  End of proof
% 203.95/34.81  
% 203.95/34.81  Sub-proof #693 shows that the following formulas are inconsistent:
% 203.95/34.81  ----------------------------------------------------------------
% 203.95/34.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.82    (2)   ~ (e3 = e0)
% 203.95/34.82    (3)  op(all_14_2, e0) = all_14_1
% 203.95/34.82    (4)  op(e0, e0) = all_14_2
% 203.95/34.82    (5)  all_58_15 = e0
% 203.95/34.82    (6)  all_58_15 = all_14_2
% 203.95/34.82    (7)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.82    (8)  op(e0, all_14_1) = e3
% 203.95/34.82  
% 203.95/34.82  Begin of proof
% 203.95/34.82  | 
% 203.95/34.82  | COMBINE_EQS: (5), (6) imply:
% 203.95/34.82  |   (9)  all_14_2 = e0
% 203.95/34.82  | 
% 203.95/34.82  | REDUCE: (7), (9) imply:
% 203.95/34.82  |   (10)  op(e0, e0) = all_52_30
% 203.95/34.82  | 
% 203.95/34.82  | REDUCE: (3), (9) imply:
% 203.95/34.82  |   (11)  op(e0, e0) = all_14_1
% 203.95/34.82  | 
% 203.95/34.82  | REDUCE: (4), (9) imply:
% 203.95/34.82  |   (12)  op(e0, e0) = e0
% 203.95/34.82  | 
% 203.95/34.82  | GROUND_INST: instantiating (1) with all_14_1, all_52_30, e0, e0, simplifying
% 203.95/34.82  |              with (10), (11) gives:
% 203.95/34.82  |   (13)  all_52_30 = all_14_1
% 203.95/34.82  | 
% 203.95/34.82  | GROUND_INST: instantiating (1) with e0, all_52_30, e0, e0, simplifying with
% 203.95/34.82  |              (10), (12) gives:
% 203.95/34.82  |   (14)  all_52_30 = e0
% 203.95/34.82  | 
% 203.95/34.82  | COMBINE_EQS: (13), (14) imply:
% 203.95/34.82  |   (15)  all_14_1 = e0
% 203.95/34.82  | 
% 203.95/34.82  | REDUCE: (8), (15) imply:
% 203.95/34.82  |   (16)  op(e0, e0) = e3
% 203.95/34.82  | 
% 203.95/34.82  | REF_CLOSE: (1), (2), (12), (16) are inconsistent by sub-proof #1336.
% 203.95/34.82  | 
% 203.95/34.82  End of proof
% 203.95/34.82  
% 203.95/34.82  Sub-proof #694 shows that the following formulas are inconsistent:
% 203.95/34.82  ----------------------------------------------------------------
% 203.95/34.82    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 203.95/34.82    (2)   ~ (all_52_15 = all_52_23)
% 203.95/34.82    (3)   ~ (all_52_25 = all_52_27)
% 203.95/34.82    (4)  all_58_14 = all_52_23
% 203.95/34.82    (5)   ~ (e3 = e1)
% 203.95/34.82    (6)  op(all_52_3, all_52_3) = all_52_2
% 203.95/34.82    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 203.95/34.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 203.95/34.82    (8)  all_58_1 = all_52_9
% 203.95/34.82    (9)   ~ (all_52_9 = all_52_13)
% 203.95/34.82    (10)   ~ (e3 = e0)
% 203.95/34.82    (11)  op(e2, e3) = all_52_3
% 203.95/34.82    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 203.95/34.82    (13)   ~ (all_52_7 = all_52_15)
% 203.95/34.82    (14)   ~ (all_52_3 = all_52_19)
% 203.95/34.82    (15)  op(all_52_7, all_52_7) = all_52_6
% 203.95/34.82    (16)   ~ (all_52_17 = all_52_25)
% 203.95/34.82    (17)   ~ (all_4_2 = e3)
% 203.95/34.82    (18)   ~ (all_52_3 = all_6_2)
% 203.95/34.82    (19)  all_58_0 = all_6_2
% 203.95/34.82    (20)  op(all_14_2, e0) = all_14_1
% 203.95/34.82    (21)  all_56_4 = all_52_3
% 203.95/34.82    (22)   ~ (all_52_17 = all_10_2)
% 203.95/34.82    (23)   ~ (all_10_0 = e3)
% 203.95/34.82    (24)  all_40_2 = all_10_2
% 203.95/34.82    (25)  op(e3, e0) = all_52_25
% 203.95/34.82    (26)  op(all_52_5, all_52_5) = all_52_4
% 203.95/34.82    (27)  op(all_52_19, all_52_19) = all_52_18
% 203.95/34.82    (28)   ~ (all_52_27 = all_52_29)
% 203.95/34.82    (29)  all_58_13 = all_52_15
% 203.95/34.82    (30)  op(all_10_2, all_10_2) = all_52_20
% 203.95/34.82    (31)  all_58_9 = all_52_25
% 203.95/34.82    (32)   ~ (all_52_29 = all_14_2)
% 203.95/34.82    (33)   ~ (all_52_15 = e3)
% 203.95/34.82    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 203.95/34.82    (35)  op(all_52_27, all_52_27) = all_52_26
% 203.95/34.82    (36)  op(e1, e3) = all_52_5
% 203.95/34.82    (37)  op(e2, e2) = all_4_2
% 203.95/34.82    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 203.95/34.82    (39)  all_58_7 = all_10_0
% 203.95/34.82    (40)   ~ (all_52_3 = all_52_5)
% 203.95/34.82    (41)  all_58_11 = all_52_29
% 203.95/34.82    (42)  all_56_5 = all_4_2
% 203.95/34.82    (43)   ~ (all_52_25 = all_14_2)
% 203.95/34.82    (44)   ~ (all_52_3 = all_52_27)
% 203.95/34.82    (45)  op(all_10_2, e1) = all_10_1
% 203.95/34.82    (46)  all_58_1 = e3
% 203.95/34.82    (47)  op(all_6_2, all_6_2) = all_52_0
% 203.95/34.82    (48)   ~ (all_52_7 = all_6_2)
% 203.95/34.82    (49)  op(e0, e0) = all_14_2
% 203.95/34.82    (50)  all_56_15 = all_14_2
% 203.95/34.82    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 203.95/34.82    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 203.95/34.82    (53)  all_56_11 = all_52_29
% 203.95/34.82    (54)   ~ (all_10_0 = e2)
% 203.95/34.82    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 203.95/34.82    (56)   ~ (all_6_2 = e3)
% 203.95/34.82    (57)   ~ (e2 = e1)
% 203.95/34.82    (58)  all_58_10 = all_52_27
% 203.95/34.82    (59)  all_56_8 = all_52_5
% 203.95/34.82    (60)  op(all_52_9, all_52_9) = all_52_8
% 203.95/34.82    (61)   ~ (all_52_19 = all_52_23)
% 203.95/34.82    (62)  all_56_9 = all_10_0
% 203.95/34.82    (63)   ~ (all_52_25 = all_52_29)
% 203.95/34.82    (64)  op(all_6_2, e3) = e2
% 203.95/34.82    (65)   ~ (all_52_29 = all_10_2)
% 203.95/34.82    (66)  all_58_7 = all_52_13
% 203.95/34.82    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 203.95/34.82    (68)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 203.95/34.82    (69)   ~ (all_52_5 = all_52_7)
% 203.95/34.82    (70)  all_58_12 = all_52_7
% 203.95/34.82    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 203.95/34.82    (72)   ~ (all_52_7 = all_14_2)
% 203.95/34.82    (73)   ~ (all_14_2 = e0)
% 203.95/34.82    (74)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 203.95/34.82    (75)  all_58_2 = all_52_3
% 203.95/34.82    (76)  all_56_2 = all_52_17
% 203.95/34.82    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 203.95/34.82    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 203.95/34.82    (79)   ~ (all_52_25 = e3)
% 203.95/34.82    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 203.95/34.82    (81)   ~ (e2 = e0)
% 203.95/34.82    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 203.95/34.82    (83)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 203.95/34.82    (84)   ~ (all_52_5 = all_52_29)
% 203.95/34.82    (85)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 203.95/34.82    (86)   ~ (all_52_19 = all_52_27)
% 203.95/34.82    (87)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 203.95/34.82    (88)  op(e3, e3) = all_52_8
% 203.95/34.82    (89)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 203.95/34.82    (90)  op(e3, e1) = all_52_17
% 203.95/34.82    (91)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 203.95/34.82    (92)  op(e0, e3) = all_52_7
% 203.95/34.82    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 203.95/34.82    (94)   ~ (all_52_9 = all_52_25)
% 203.95/34.82    (95)  all_58_15 = all_14_2
% 203.95/34.82    (96)   ~ (all_52_19 = all_10_2)
% 203.95/34.82    (97)  op(all_52_23, all_52_23) = all_52_22
% 203.95/34.82    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 203.95/34.82    (99)  all_58_8 = all_10_2
% 203.95/34.82    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 203.95/34.82    (101)   ~ (all_52_5 = all_10_2)
% 203.95/34.82    (102)  op(all_52_29, all_52_29) = all_52_28
% 203.95/34.82    (103)   ~ (all_52_23 = all_14_2)
% 203.95/34.82    (104)  all_56_12 = all_52_7
% 203.95/34.82    (105)  op(all_52_17, all_52_17) = all_52_16
% 203.95/34.82    (106)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 203.95/34.82    (107)   ~ (all_52_25 = all_6_2)
% 203.95/34.82    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 203.95/34.82    (109)   ~ (all_52_9 = all_4_2)
% 203.95/34.82    (110)   ~ (all_52_5 = all_6_2)
% 203.95/34.82    (111)  op(e3, e3) = all_6_2
% 203.95/34.82    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 203.95/34.82    (113)   ~ (all_52_27 = all_14_2)
% 203.95/34.82    (114)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 203.95/34.82    (115)  all_56_14 = all_52_23
% 203.95/34.82    (116)   ~ (all_52_17 = e3)
% 203.95/34.82    (117)  all_40_0 = all_10_0
% 203.95/34.82    (118)  all_56_3 = all_52_25
% 203.95/34.82    (119)   ~ (all_52_3 = all_52_7)
% 203.95/34.82    (120)  op(all_14_2, all_14_2) = all_52_30
% 203.95/34.82    (121)  all_58_5 = all_52_19
% 203.95/34.82    (122)   ~ (all_52_15 = all_4_2)
% 203.95/34.82    (123)   ~ (all_52_27 = all_4_2)
% 203.95/34.82    (124)  all_58_6 = all_52_5
% 203.95/34.82    (125)  op(all_10_2, e1) = e2
% 203.95/34.82    (126)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 203.95/34.82    (127)   ~ (all_52_17 = all_6_2)
% 203.95/34.82    (128)   ~ (e1 = e0)
% 203.95/34.82    (129)   ~ (e3 = e2)
% 203.95/34.82    (130)  all_56_10 = all_10_2
% 203.95/34.82    (131)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 203.95/34.82    (132)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 203.95/34.82    (133)  op(all_52_13, all_52_13) = all_52_12
% 203.95/34.82    (134)  op(e1, e1) = all_10_2
% 203.95/34.82    (135)   ~ (all_52_23 = all_10_2)
% 203.95/34.82    (136)   ~ (all_52_7 = all_52_23)
% 203.95/34.82    (137)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 203.95/34.82           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 203.95/34.82    (138)   ~ (all_52_5 = all_10_0)
% 203.95/34.82    (139)  all_58_3 = all_4_2
% 203.95/34.82    (140)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 203.95/34.82    (141)   ~ (all_52_3 = all_4_2)
% 203.95/34.82    (142)   ~ (all_52_19 = all_4_2)
% 203.95/34.82    (143)   ~ (all_52_17 = all_52_23)
% 203.95/34.82    (144)  op(all_6_2, e3) = all_6_1
% 203.95/34.82    (145)  all_58_4 = all_52_17
% 203.95/34.82    (146)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 203.95/34.82    (147)  op(all_52_25, all_52_25) = all_52_24
% 203.95/34.82  
% 203.95/34.82  Begin of proof
% 203.95/34.82  | 
% 203.95/34.82  | BETA: splitting (137) gives:
% 203.95/34.82  | 
% 203.95/34.82  | Case 1:
% 203.95/34.82  | | 
% 203.95/34.82  | |   (148)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 203.95/34.82  | | 
% 203.95/34.82  | | REF_CLOSE: (4), (5), (7), (10), (11), (16), (17), (18), (19), (23), (24),
% 203.95/34.82  | |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (37), (39),
% 203.95/34.82  | |            (40), (41), (43), (45), (46), (48), (49), (50), (51), (53), (54),
% 203.95/34.82  | |            (55), (56), (57), (58), (61), (62), (64), (65), (70), (71), (72),
% 203.95/34.82  | |            (73), (74), (75), (76), (77), (78), (79), (81), (83), (85), (87),
% 203.95/34.82  | |            (88), (89), (90), (92), (95), (96), (97), (99), (100), (103),
% 203.95/34.82  | |            (105), (107), (108), (111), (113), (116), (117), (118), (119),
% 203.95/34.82  | |            (120), (121), (123), (124), (125), (126), (127), (128), (130),
% 203.95/34.82  | |            (131), (132), (134), (135), (136), (139), (141), (143), (145),
% 203.95/34.82  | |            (146), (148) are inconsistent by sub-proof #696.
% 203.95/34.82  | | 
% 203.95/34.82  | Case 2:
% 203.95/34.82  | | 
% 203.95/34.82  | |   (149)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 203.95/34.82  | | 
% 203.95/34.82  | | ALPHA: (149) implies:
% 204.02/34.82  | |   (150)  all_52_30 = e0
% 204.02/34.82  | |   (151)  all_52_28 = e1
% 204.02/34.82  | |   (152)  all_52_26 = e2
% 204.02/34.82  | |   (153)  all_52_24 = e3
% 204.02/34.82  | | 
% 204.02/34.82  | | REDUCE: (147), (153) imply:
% 204.02/34.82  | |   (154)  op(all_52_25, all_52_25) = e3
% 204.02/34.82  | | 
% 204.02/34.82  | | REDUCE: (35), (152) imply:
% 204.02/34.82  | |   (155)  op(all_52_27, all_52_27) = e2
% 204.02/34.82  | | 
% 204.02/34.82  | | REDUCE: (102), (151) imply:
% 204.02/34.82  | |   (156)  op(all_52_29, all_52_29) = e1
% 204.02/34.82  | | 
% 204.02/34.82  | | REDUCE: (120), (150) imply:
% 204.02/34.82  | |   (157)  op(all_14_2, all_14_2) = e0
% 204.02/34.82  | | 
% 204.02/34.82  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.02/34.82  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 204.02/34.82  | |            (25), (26), (27), (28), (29), (31), (32), (33), (36), (37), (38),
% 204.02/34.82  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 204.02/34.82  | |            (50), (51), (52), (53), (54), (55), (56), (58), (59), (60), (62),
% 204.02/34.82  | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 204.02/34.82  | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (84), (86),
% 204.02/34.82  | |            (87), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 204.02/34.82  | |            (99), (100), (101), (103), (104), (106), (107), (108), (109),
% 204.02/34.82  | |            (110), (111), (112), (113), (114), (115), (117), (118), (119),
% 204.02/34.82  | |            (121), (122), (123), (124), (126), (127), (128), (129), (132),
% 204.02/34.82  | |            (133), (134), (135), (136), (138), (139), (140), (141), (142),
% 204.02/34.82  | |            (143), (144), (145), (154), (155), (156), (157) are inconsistent
% 204.02/34.82  | |            by sub-proof #695.
% 204.02/34.82  | | 
% 204.02/34.82  | End of split
% 204.02/34.82  | 
% 204.02/34.82  End of proof
% 204.02/34.82  
% 204.02/34.82  Sub-proof #695 shows that the following formulas are inconsistent:
% 204.02/34.82  ----------------------------------------------------------------
% 204.02/34.82    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.02/34.82    (2)   ~ (all_52_15 = all_52_23)
% 204.02/34.82    (3)   ~ (all_52_25 = all_52_27)
% 204.02/34.82    (4)  all_58_14 = all_52_23
% 204.02/34.82    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.02/34.82    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.82    (7)  all_58_1 = all_52_9
% 204.02/34.82    (8)   ~ (all_52_9 = all_52_13)
% 204.02/34.82    (9)   ~ (e3 = e0)
% 204.02/34.82    (10)  op(e2, e3) = all_52_3
% 204.02/34.82    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.02/34.82    (12)   ~ (all_52_7 = all_52_15)
% 204.02/34.82    (13)   ~ (all_52_3 = all_52_19)
% 204.02/34.82    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.02/34.82    (15)   ~ (all_52_17 = all_52_25)
% 204.02/34.82    (16)   ~ (all_4_2 = e3)
% 204.02/34.82    (17)   ~ (all_52_3 = all_6_2)
% 204.02/34.82    (18)  all_58_0 = all_6_2
% 204.02/34.82    (19)  op(all_14_2, e0) = all_14_1
% 204.02/34.82    (20)  all_56_4 = all_52_3
% 204.02/34.82    (21)   ~ (all_52_17 = all_10_2)
% 204.02/34.82    (22)   ~ (all_10_0 = e3)
% 204.02/34.82    (23)  all_40_2 = all_10_2
% 204.02/34.82    (24)  op(e3, e0) = all_52_25
% 204.02/34.82    (25)  op(all_52_5, all_52_5) = all_52_4
% 204.02/34.82    (26)  op(all_52_19, all_52_19) = all_52_18
% 204.02/34.82    (27)   ~ (all_52_27 = all_52_29)
% 204.02/34.82    (28)  all_58_13 = all_52_15
% 204.02/34.82    (29)  all_58_9 = all_52_25
% 204.02/34.82    (30)   ~ (all_52_29 = all_14_2)
% 204.02/34.82    (31)   ~ (all_52_15 = e3)
% 204.02/34.82    (32)  op(e1, e3) = all_52_5
% 204.02/34.82    (33)  op(e2, e2) = all_4_2
% 204.02/34.82    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.02/34.82    (35)  all_58_7 = all_10_0
% 204.02/34.82    (36)   ~ (all_52_3 = all_52_5)
% 204.02/34.82    (37)  all_58_11 = all_52_29
% 204.02/34.82    (38)  all_56_5 = all_4_2
% 204.02/34.82    (39)   ~ (all_52_25 = all_14_2)
% 204.02/34.82    (40)   ~ (all_52_3 = all_52_27)
% 204.02/34.82    (41)  op(all_10_2, e1) = all_10_1
% 204.02/34.82    (42)  all_58_1 = e3
% 204.02/34.82    (43)  op(all_6_2, all_6_2) = all_52_0
% 204.02/34.82    (44)   ~ (all_52_7 = all_6_2)
% 204.02/34.82    (45)  op(e0, e0) = all_14_2
% 204.02/34.82    (46)  op(all_52_29, all_52_29) = e1
% 204.02/34.82    (47)  all_56_15 = all_14_2
% 204.02/34.82    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.02/34.82    (49)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.02/34.82    (50)  all_56_11 = all_52_29
% 204.02/34.82    (51)   ~ (all_10_0 = e2)
% 204.02/34.82    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.02/34.82    (53)   ~ (all_6_2 = e3)
% 204.02/34.82    (54)  all_58_10 = all_52_27
% 204.02/34.82    (55)  all_56_8 = all_52_5
% 204.02/34.82    (56)  op(all_52_9, all_52_9) = all_52_8
% 204.02/34.82    (57)  all_56_9 = all_10_0
% 204.02/34.82    (58)   ~ (all_52_25 = all_52_29)
% 204.02/34.82    (59)  op(all_6_2, e3) = e2
% 204.02/34.82    (60)   ~ (all_52_29 = all_10_2)
% 204.02/34.82    (61)  all_58_7 = all_52_13
% 204.02/34.82    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.02/34.82    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.02/34.82    (64)   ~ (all_52_5 = all_52_7)
% 204.02/34.82    (65)  all_58_12 = all_52_7
% 204.02/34.82    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.02/34.82    (67)   ~ (all_52_7 = all_14_2)
% 204.02/34.82    (68)   ~ (all_14_2 = e0)
% 204.02/34.82    (69)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.02/34.82    (70)  all_58_2 = all_52_3
% 204.02/34.82    (71)  all_56_2 = all_52_17
% 204.02/34.82    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.82    (73)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.02/34.82    (74)   ~ (all_52_25 = e3)
% 204.02/34.82    (75)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.02/34.82    (76)   ~ (e2 = e0)
% 204.02/34.82    (77)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.02/34.82    (78)  op(all_52_25, all_52_25) = e3
% 204.02/34.82    (79)   ~ (all_52_5 = all_52_29)
% 204.02/34.82    (80)   ~ (all_52_19 = all_52_27)
% 204.02/34.82    (81)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.02/34.82    (82)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.82    (83)  op(e3, e1) = all_52_17
% 204.02/34.82    (84)  op(all_52_27, all_52_27) = e2
% 204.02/34.82    (85)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.02/34.82    (86)  op(e0, e3) = all_52_7
% 204.02/34.82    (87)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.02/34.82    (88)   ~ (all_52_9 = all_52_25)
% 204.02/34.82    (89)  all_58_15 = all_14_2
% 204.02/34.82    (90)   ~ (all_52_19 = all_10_2)
% 204.02/34.82    (91)  op(all_52_23, all_52_23) = all_52_22
% 204.02/34.82    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.02/34.82    (93)  all_58_8 = all_10_2
% 204.02/34.82    (94)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.82    (95)   ~ (all_52_5 = all_10_2)
% 204.02/34.82    (96)   ~ (all_52_23 = all_14_2)
% 204.02/34.82    (97)  all_56_12 = all_52_7
% 204.02/34.82    (98)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.02/34.82    (99)   ~ (all_52_25 = all_6_2)
% 204.02/34.82    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.02/34.82    (101)   ~ (all_52_9 = all_4_2)
% 204.02/34.82    (102)   ~ (all_52_5 = all_6_2)
% 204.02/34.82    (103)  op(e3, e3) = all_6_2
% 204.02/34.82    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.02/34.82    (105)   ~ (all_52_27 = all_14_2)
% 204.02/34.82    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.02/34.82    (107)  all_56_14 = all_52_23
% 204.02/34.82    (108)  all_40_0 = all_10_0
% 204.02/34.82    (109)  all_56_3 = all_52_25
% 204.02/34.82    (110)   ~ (all_52_3 = all_52_7)
% 204.02/34.82    (111)  all_58_5 = all_52_19
% 204.02/34.82    (112)   ~ (all_52_15 = all_4_2)
% 204.02/34.82    (113)   ~ (all_52_27 = all_4_2)
% 204.02/34.82    (114)  all_58_6 = all_52_5
% 204.02/34.82    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.02/34.82    (116)   ~ (all_52_17 = all_6_2)
% 204.02/34.82    (117)   ~ (e1 = e0)
% 204.02/34.82    (118)  op(all_14_2, all_14_2) = e0
% 204.02/34.82    (119)   ~ (e3 = e2)
% 204.02/34.82    (120)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.82    (121)  op(all_52_13, all_52_13) = all_52_12
% 204.02/34.82    (122)  op(e1, e1) = all_10_2
% 204.02/34.82    (123)   ~ (all_52_23 = all_10_2)
% 204.02/34.82    (124)   ~ (all_52_7 = all_52_23)
% 204.02/34.82    (125)   ~ (all_52_5 = all_10_0)
% 204.02/34.82    (126)  all_58_3 = all_4_2
% 204.02/34.82    (127)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.02/34.82    (128)   ~ (all_52_3 = all_4_2)
% 204.02/34.82    (129)   ~ (all_52_19 = all_4_2)
% 204.02/34.82    (130)   ~ (all_52_17 = all_52_23)
% 204.02/34.82    (131)  op(all_6_2, e3) = all_6_1
% 204.02/34.82    (132)  all_58_4 = all_52_17
% 204.02/34.82  
% 204.02/34.82  Begin of proof
% 204.02/34.82  | 
% 204.02/34.82  | BETA: splitting (120) gives:
% 204.02/34.82  | 
% 204.02/34.82  | Case 1:
% 204.02/34.82  | | 
% 204.02/34.82  | |   (133)  all_56_9 = e3
% 204.02/34.82  | | 
% 204.02/34.82  | | REF_CLOSE: (22), (57), (133) are inconsistent by sub-proof #1006.
% 204.02/34.82  | | 
% 204.02/34.82  | Case 2:
% 204.02/34.82  | | 
% 204.02/34.82  | |   (134)   ~ (all_56_9 = e3)
% 204.02/34.82  | |   (135)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.82  | | 
% 204.02/34.82  | | BETA: splitting (127) gives:
% 204.02/34.82  | | 
% 204.02/34.82  | | Case 1:
% 204.02/34.82  | | | 
% 204.02/34.82  | | |   (136)  all_58_1 = e2
% 204.02/34.82  | | | 
% 204.02/34.82  | | | COMBINE_EQS: (42), (136) imply:
% 204.02/34.82  | | |   (137)  e3 = e2
% 204.02/34.82  | | | 
% 204.02/34.82  | | | REDUCE: (119), (137) imply:
% 204.02/34.82  | | |   (138)  $false
% 204.02/34.82  | | | 
% 204.02/34.82  | | | CLOSE: (138) is inconsistent.
% 204.02/34.82  | | | 
% 204.02/34.82  | | Case 2:
% 204.02/34.82  | | | 
% 204.02/34.82  | | |   (139)   ~ (all_58_1 = e2)
% 204.02/34.82  | | |   (140)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.02/34.82  | | | 
% 204.02/34.82  | | | BETA: splitting (94) gives:
% 204.02/34.82  | | | 
% 204.02/34.82  | | | Case 1:
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | |   (141)  all_56_15 = e3
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | COMBINE_EQS: (47), (141) imply:
% 204.02/34.82  | | | |   (142)  all_14_2 = e3
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | SIMP: (142) implies:
% 204.02/34.82  | | | |   (143)  all_14_2 = e3
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (67), (143) imply:
% 204.02/34.82  | | | |   (144)   ~ (all_52_7 = e3)
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (105), (143) imply:
% 204.02/34.82  | | | |   (145)   ~ (all_52_27 = e3)
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (30), (143) imply:
% 204.02/34.82  | | | |   (146)   ~ (all_52_29 = e3)
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (118), (143) imply:
% 204.02/34.82  | | | |   (147)  op(e3, e3) = e0
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (19), (143) imply:
% 204.02/34.82  | | | |   (148)  op(e3, e0) = all_14_1
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3,
% 204.02/34.82  | | | |              simplifying with (24), (148) gives:
% 204.02/34.82  | | | |   (149)  all_52_25 = all_14_1
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | GROUND_INST: instantiating (6) with all_6_2, e0, e3, e3, simplifying
% 204.02/34.82  | | | |              with (103), (147) gives:
% 204.02/34.82  | | | |   (150)  all_6_2 = e0
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | COMBINE_EQS: (109), (149) imply:
% 204.02/34.82  | | | |   (151)  all_56_3 = all_14_1
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | COMBINE_EQS: (29), (149) imply:
% 204.02/34.82  | | | |   (152)  all_58_9 = all_14_1
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (102), (150) imply:
% 204.02/34.82  | | | |   (153)   ~ (all_52_5 = e0)
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (99), (149), (150) imply:
% 204.02/34.82  | | | |   (154)   ~ (all_14_1 = e0)
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (74), (149) imply:
% 204.02/34.82  | | | |   (155)   ~ (all_14_1 = e3)
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (78), (149) imply:
% 204.02/34.82  | | | |   (156)  op(all_14_1, all_14_1) = e3
% 204.02/34.82  | | | | 
% 204.02/34.82  | | | | REDUCE: (59), (150) imply:
% 204.02/34.82  | | | |   (157)  op(e0, e3) = e2
% 204.02/34.82  | | | | 
% 204.02/34.83  | | | | GROUND_INST: instantiating (6) with all_52_7, e2, e3, e0, simplifying
% 204.02/34.83  | | | |              with (86), (157) gives:
% 204.02/34.83  | | | |   (158)  all_52_7 = e2
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | REDUCE: (64), (158) imply:
% 204.02/34.83  | | | |   (159)   ~ (all_52_5 = e2)
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | REDUCE: (12), (158) imply:
% 204.02/34.83  | | | |   (160)   ~ (all_52_15 = e2)
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | SIMP: (160) implies:
% 204.02/34.83  | | | |   (161)   ~ (all_52_15 = e2)
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | REDUCE: (144), (158) imply:
% 204.02/34.83  | | | |   (162)   ~ (e3 = e2)
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | BETA: splitting (140) gives:
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | Case 1:
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | |   (163)  all_58_3 = e2
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | | REF_CLOSE: (6), (16), (20), (22), (23), (33), (35), (36), (37), (48),
% 204.02/34.83  | | | | |            (49), (51), (54), (55), (57), (66), (69), (70), (75), (90),
% 204.02/34.83  | | | | |            (92), (93), (100), (108), (111), (114), (119), (122),
% 204.02/34.83  | | | | |            (125), (135), (145), (146), (151), (152), (153), (154),
% 204.02/34.83  | | | | |            (155), (156), (159), (163) are inconsistent by sub-proof
% 204.02/34.83  | | | | |            #785.
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | Case 2:
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | |   (164)  all_58_7 = e2 | all_58_13 = e2
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | | REF_CLOSE: (28), (35), (51), (161), (164) are inconsistent by
% 204.02/34.83  | | | | |            sub-proof #783.
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | End of split
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | Case 2:
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | |   (165)   ~ (all_56_15 = e3)
% 204.02/34.83  | | | |   (166)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | REDUCE: (47), (165) imply:
% 204.02/34.83  | | | |   (167)   ~ (all_14_2 = e3)
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 204.02/34.83  | | | |            (13), (14), (15), (16), (17), (18), (21), (22), (25), (26),
% 204.02/34.83  | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.02/34.83  | | | |            (37), (38), (39), (40), (41), (43), (44), (45), (46), (47),
% 204.02/34.83  | | | |            (48), (49), (50), (52), (53), (54), (55), (56), (58), (59),
% 204.02/34.83  | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 204.02/34.83  | | | |            (71), (72), (73), (74), (76), (77), (78), (79), (80), (81),
% 204.02/34.83  | | | |            (82), (83), (84), (85), (87), (88), (89), (90), (91), (92),
% 204.02/34.83  | | | |            (93), (95), (96), (97), (98), (99), (100), (101), (102),
% 204.02/34.83  | | | |            (103), (104), (105), (106), (107), (109), (110), (111),
% 204.02/34.83  | | | |            (112), (113), (114), (115), (116), (117), (118), (119),
% 204.02/34.83  | | | |            (121), (122), (123), (124), (126), (127), (128), (129),
% 204.02/34.83  | | | |            (130), (131), (132), (166), (167) are inconsistent by
% 204.02/34.83  | | | |            sub-proof #782.
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | End of split
% 204.02/34.83  | | | 
% 204.02/34.83  | | End of split
% 204.02/34.83  | | 
% 204.02/34.83  | End of split
% 204.02/34.83  | 
% 204.02/34.83  End of proof
% 204.02/34.83  
% 204.02/34.83  Sub-proof #696 shows that the following formulas are inconsistent:
% 204.02/34.83  ----------------------------------------------------------------
% 204.02/34.83    (1)  all_58_14 = all_52_23
% 204.02/34.83    (2)   ~ (e3 = e1)
% 204.02/34.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.83    (4)   ~ (e3 = e0)
% 204.02/34.83    (5)  op(e2, e3) = all_52_3
% 204.02/34.83    (6)   ~ (all_52_17 = all_52_25)
% 204.02/34.83    (7)   ~ (all_4_2 = e3)
% 204.02/34.83    (8)   ~ (all_52_3 = all_6_2)
% 204.02/34.83    (9)  all_58_0 = all_6_2
% 204.02/34.83    (10)   ~ (all_10_0 = e3)
% 204.02/34.83    (11)  all_40_2 = all_10_2
% 204.02/34.83    (12)  op(all_52_5, all_52_5) = all_52_4
% 204.02/34.83    (13)  op(all_52_19, all_52_19) = all_52_18
% 204.02/34.83    (14)  all_58_13 = all_52_15
% 204.02/34.83    (15)  op(all_10_2, all_10_2) = all_52_20
% 204.02/34.83    (16)  all_58_9 = all_52_25
% 204.02/34.83    (17)   ~ (all_52_29 = all_14_2)
% 204.02/34.83    (18)   ~ (all_52_15 = e3)
% 204.02/34.83    (19)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.02/34.83    (20)  op(all_52_27, all_52_27) = all_52_26
% 204.02/34.83    (21)  op(e2, e2) = all_4_2
% 204.02/34.83    (22)  all_58_7 = all_10_0
% 204.02/34.83    (23)   ~ (all_52_3 = all_52_5)
% 204.02/34.83    (24)  all_58_11 = all_52_29
% 204.02/34.83    (25)   ~ (all_52_25 = all_14_2)
% 204.02/34.83    (26)  op(all_10_2, e1) = all_10_1
% 204.02/34.83    (27)  all_58_1 = e3
% 204.02/34.83    (28)   ~ (all_52_7 = all_6_2)
% 204.02/34.83    (29)  op(e0, e0) = all_14_2
% 204.02/34.83    (30)  all_56_15 = all_14_2
% 204.02/34.83    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.02/34.83    (32)  all_56_11 = all_52_29
% 204.02/34.83    (33)   ~ (all_10_0 = e2)
% 204.02/34.83    (34)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.02/34.83    (35)   ~ (all_6_2 = e3)
% 204.02/34.83    (36)   ~ (e2 = e1)
% 204.02/34.83    (37)  all_58_10 = all_52_27
% 204.02/34.83    (38)   ~ (all_52_19 = all_52_23)
% 204.02/34.83    (39)  all_56_9 = all_10_0
% 204.02/34.83    (40)  op(all_6_2, e3) = e2
% 204.02/34.83    (41)   ~ (all_52_29 = all_10_2)
% 204.02/34.83    (42)  all_58_12 = all_52_7
% 204.02/34.83    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.02/34.83    (44)   ~ (all_52_7 = all_14_2)
% 204.02/34.83    (45)   ~ (all_14_2 = e0)
% 204.02/34.83    (46)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.02/34.83    (47)  all_58_2 = all_52_3
% 204.02/34.83    (48)  all_56_2 = all_52_17
% 204.02/34.83    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.83    (50)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.02/34.83    (51)   ~ (all_52_25 = e3)
% 204.02/34.83    (52)   ~ (e2 = e0)
% 204.02/34.83    (53)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.02/34.83    (54)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.02/34.83    (55)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.02/34.83    (56)  op(e3, e3) = all_52_8
% 204.02/34.83    (57)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.83    (58)  op(e3, e1) = all_52_17
% 204.02/34.83    (59)  op(e0, e3) = all_52_7
% 204.02/34.83    (60)  all_58_15 = all_14_2
% 204.02/34.83    (61)   ~ (all_52_19 = all_10_2)
% 204.02/34.83    (62)  op(all_52_23, all_52_23) = all_52_22
% 204.02/34.83    (63)  all_58_8 = all_10_2
% 204.02/34.83    (64)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.83    (65)   ~ (all_52_23 = all_14_2)
% 204.02/34.83    (66)  op(all_52_17, all_52_17) = all_52_16
% 204.02/34.83    (67)   ~ (all_52_25 = all_6_2)
% 204.02/34.83    (68)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.02/34.83    (69)  op(e3, e3) = all_6_2
% 204.02/34.83    (70)   ~ (all_52_27 = all_14_2)
% 204.02/34.83    (71)   ~ (all_52_17 = e3)
% 204.02/34.83    (72)  all_40_0 = all_10_0
% 204.02/34.83    (73)  all_56_3 = all_52_25
% 204.02/34.83    (74)   ~ (all_52_3 = all_52_7)
% 204.02/34.83    (75)  op(all_14_2, all_14_2) = all_52_30
% 204.02/34.83    (76)  all_58_5 = all_52_19
% 204.02/34.83    (77)   ~ (all_52_27 = all_4_2)
% 204.02/34.83    (78)  all_58_6 = all_52_5
% 204.02/34.83    (79)  op(all_10_2, e1) = e2
% 204.02/34.83    (80)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.02/34.83    (81)   ~ (all_52_17 = all_6_2)
% 204.02/34.83    (82)   ~ (e1 = e0)
% 204.02/34.83    (83)  all_56_10 = all_10_2
% 204.02/34.83    (84)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.02/34.83    (85)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.83    (86)  op(e1, e1) = all_10_2
% 204.02/34.83    (87)   ~ (all_52_23 = all_10_2)
% 204.02/34.83    (88)   ~ (all_52_7 = all_52_23)
% 204.02/34.83    (89)  all_58_3 = all_4_2
% 204.02/34.83    (90)   ~ (all_52_3 = all_4_2)
% 204.02/34.83    (91)   ~ (all_52_17 = all_52_23)
% 204.02/34.83    (92)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.02/34.83    (93)  all_58_4 = all_52_17
% 204.02/34.83    (94)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.02/34.83  
% 204.02/34.83  Begin of proof
% 204.02/34.83  | 
% 204.02/34.83  | ALPHA: (92) implies:
% 204.02/34.83  |   (95)  all_52_22 = e0
% 204.02/34.83  |   (96)  all_52_20 = e1
% 204.02/34.83  |   (97)  all_52_18 = e2
% 204.02/34.83  |   (98)  all_52_16 = e3
% 204.02/34.83  | 
% 204.02/34.83  | REDUCE: (66), (98) imply:
% 204.02/34.83  |   (99)  op(all_52_17, all_52_17) = e3
% 204.02/34.83  | 
% 204.02/34.83  | REDUCE: (13), (97) imply:
% 204.02/34.83  |   (100)  op(all_52_19, all_52_19) = e2
% 204.02/34.83  | 
% 204.02/34.83  | REDUCE: (62), (95) imply:
% 204.02/34.83  |   (101)  op(all_52_23, all_52_23) = e0
% 204.02/34.83  | 
% 204.02/34.83  | REDUCE: (15), (96) imply:
% 204.02/34.83  |   (102)  op(all_10_2, all_10_2) = e1
% 204.02/34.83  | 
% 204.02/34.83  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.02/34.83  |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.02/34.83  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.02/34.83  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 204.02/34.83  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 204.02/34.83  |            (59), (60), (61), (63), (64), (65), (67), (68), (69), (70), (71),
% 204.02/34.83  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 204.02/34.83  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (93), (94),
% 204.02/34.83  |            (99), (100), (101), (102) are inconsistent by sub-proof #787.
% 204.02/34.83  | 
% 204.02/34.83  End of proof
% 204.02/34.83  
% 204.02/34.83  Sub-proof #697 shows that the following formulas are inconsistent:
% 204.02/34.83  ----------------------------------------------------------------
% 204.02/34.83    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.02/34.83    (2)   ~ (all_52_15 = all_52_23)
% 204.02/34.83    (3)   ~ (all_52_25 = all_52_27)
% 204.02/34.83    (4)  all_58_14 = all_52_23
% 204.02/34.83    (5)   ~ (e3 = e1)
% 204.02/34.83    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.02/34.83    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.83    (8)   ~ (all_52_5 = all_52_13)
% 204.02/34.83    (9)  op(all_52_7, all_52_7) = e0
% 204.02/34.83    (10)  all_58_1 = all_52_9
% 204.02/34.83    (11)   ~ (all_52_9 = all_52_13)
% 204.02/34.83    (12)  op(all_52_5, all_52_5) = e1
% 204.02/34.83    (13)   ~ (e3 = e0)
% 204.02/34.83    (14)  all_24_1 = all_14_1
% 204.02/34.83    (15)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.02/34.83    (16)   ~ (all_52_7 = all_52_15)
% 204.02/34.83    (17)   ~ (all_52_3 = all_52_19)
% 204.02/34.83    (18)   ~ (all_52_17 = all_52_25)
% 204.02/34.83    (19)   ~ (all_52_3 = all_6_2)
% 204.02/34.83    (20)  all_58_0 = all_6_2
% 204.02/34.83    (21)  op(all_14_2, e0) = all_14_1
% 204.02/34.83    (22)  all_34_1 = all_14_1
% 204.02/34.83    (23)  all_56_4 = all_52_3
% 204.02/34.83    (24)  op(e3, e0) = all_52_25
% 204.02/34.83    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.02/34.83    (26)   ~ (all_52_27 = all_52_29)
% 204.02/34.83    (27)  all_58_13 = all_52_15
% 204.02/34.83    (28)  op(e0, all_14_1) = e1
% 204.02/34.83    (29)  op(all_10_2, all_10_2) = all_52_20
% 204.02/34.83    (30)  all_58_9 = all_52_25
% 204.02/34.83    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.02/34.83    (32)   ~ (all_52_29 = all_14_2)
% 204.02/34.83    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.02/34.83    (34)  op(e2, all_4_1) = e3
% 204.02/34.83    (35)  op(all_52_27, all_52_27) = all_52_26
% 204.02/34.83    (36)  op(e2, e2) = all_4_2
% 204.02/34.83    (37)   ~ (all_52_3 = all_52_5)
% 204.02/34.83    (38)  all_58_11 = all_52_29
% 204.02/34.83    (39)  all_56_5 = all_4_2
% 204.02/34.83    (40)   ~ (all_52_25 = all_14_2)
% 204.02/34.83    (41)   ~ (all_52_9 = all_52_15)
% 204.02/34.83    (42)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.02/34.83    (43)   ~ (all_52_3 = all_52_27)
% 204.02/34.83    (44)  op(all_10_2, e1) = all_10_1
% 204.02/34.83    (45)   ~ (all_52_7 = all_6_2)
% 204.02/34.83    (46)  op(e0, e0) = all_14_2
% 204.02/34.83    (47)  op(e0, e1) = all_52_23
% 204.02/34.83    (48)  all_56_15 = all_14_2
% 204.02/34.83    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.02/34.83    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.02/34.83    (51)  op(e1, e0) = all_52_29
% 204.02/34.83    (52)  all_56_11 = all_52_29
% 204.02/34.83    (53)   ~ (all_4_1 = e1)
% 204.02/34.83    (54)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.02/34.83    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.02/34.83    (56)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.02/34.83    (57)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.02/34.83    (58)  all_56_9 = all_52_13
% 204.02/34.83    (59)   ~ (e2 = e1)
% 204.02/34.83    (60)   ~ (all_52_13 = all_10_2)
% 204.02/34.83    (61)   ~ (all_6_0 = e1)
% 204.02/34.83    (62)  all_58_10 = all_52_27
% 204.02/34.83    (63)  all_56_8 = all_52_5
% 204.02/34.83    (64)  op(all_52_9, all_52_9) = all_52_8
% 204.02/34.83    (65)  op(all_52_15, all_52_15) = all_52_14
% 204.02/34.83    (66)   ~ (all_52_19 = all_52_23)
% 204.02/34.83    (67)   ~ (all_52_25 = all_52_29)
% 204.02/34.83    (68)   ~ (all_52_29 = all_10_2)
% 204.02/34.83    (69)  all_58_7 = all_52_13
% 204.02/34.83    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.02/34.83    (71)  op(all_6_2, all_6_2) = e3
% 204.02/34.83    (72)   ~ (all_52_5 = all_52_7)
% 204.02/34.83    (73)  all_58_12 = all_52_7
% 204.02/34.83    (74)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.02/34.83    (75)   ~ (all_52_7 = all_14_2)
% 204.02/34.83    (76)   ~ (all_14_2 = e0)
% 204.02/34.83    (77)  all_58_2 = all_52_3
% 204.02/34.83    (78)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.02/34.83    (79)  all_56_2 = all_52_17
% 204.02/34.83    (80)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.02/34.83    (81)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.83    (82)  op(e3, all_6_1) = all_6_0
% 204.02/34.83    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.02/34.83    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.02/34.83    (85)   ~ (e2 = e0)
% 204.02/34.83    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.02/34.83    (87)  op(all_4_2, e2) = all_4_1
% 204.02/34.83    (88)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.02/34.83    (89)  op(all_52_3, all_52_3) = e2
% 204.02/34.83    (90)   ~ (all_52_5 = all_52_29)
% 204.02/34.83    (91)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.02/34.83    (92)  all_56_6 = all_52_19
% 204.02/34.83    (93)   ~ (all_52_15 = all_14_2)
% 204.02/34.83    (94)   ~ (all_52_19 = all_52_27)
% 204.02/34.83    (95)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.02/34.83    (96)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.02/34.83    (97)   ~ (all_6_0 = e2)
% 204.02/34.83    (98)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.83    (99)   ~ (all_52_13 = all_4_2)
% 204.02/34.83    (100)  op(e3, e1) = all_52_17
% 204.02/34.83    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.02/34.83    (102)  op(e0, e3) = all_52_7
% 204.02/34.83    (103)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.02/34.83    (104)   ~ (all_52_9 = all_52_25)
% 204.02/34.83    (105)  all_58_15 = all_14_2
% 204.02/34.83    (106)   ~ (all_52_19 = all_10_2)
% 204.02/34.83    (107)  op(all_52_23, all_52_23) = all_52_22
% 204.02/34.83    (108)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.02/34.83    (109)  all_58_8 = all_10_2
% 204.02/34.83    (110)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.83    (111)  all_34_2 = all_14_2
% 204.02/34.83    (112)   ~ (all_52_5 = all_10_2)
% 204.02/34.83    (113)   ~ (all_52_23 = all_14_2)
% 204.02/34.83    (114)  all_56_12 = all_52_7
% 204.02/34.83    (115)  op(all_52_17, all_52_17) = all_52_16
% 204.02/34.83    (116)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.02/34.83    (117)   ~ (all_52_25 = all_6_2)
% 204.02/34.83    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.02/34.83    (119)   ~ (all_52_9 = all_4_2)
% 204.02/34.83    (120)   ~ (all_52_5 = all_6_2)
% 204.02/34.83    (121)   ~ (all_52_9 = all_6_2)
% 204.02/34.83    (122)  all_24_2 = all_14_2
% 204.02/34.83    (123)   ~ (all_52_13 = all_52_15)
% 204.02/34.83    (124)  op(e3, e3) = all_6_2
% 204.02/34.83    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.02/34.83    (126)   ~ (all_52_27 = all_14_2)
% 204.02/34.83    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.02/34.83    (128)  all_56_3 = all_52_25
% 204.02/34.83    (129)   ~ (all_52_3 = all_52_7)
% 204.02/34.83    (130)  op(all_14_2, all_14_2) = all_52_30
% 204.02/34.83    (131)  all_58_5 = all_52_19
% 204.02/34.83    (132)  all_56_1 = all_52_9
% 204.02/34.83    (133)   ~ (all_52_15 = all_4_2)
% 204.02/34.83    (134)   ~ (all_52_27 = all_4_2)
% 204.02/34.83    (135)  all_58_6 = all_52_5
% 204.02/34.83    (136)  op(e3, e2) = all_52_9
% 204.02/34.83    (137)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.02/34.83    (138)   ~ (all_52_17 = all_6_2)
% 204.02/34.83    (139)   ~ (e1 = e0)
% 204.02/34.83    (140)  op(e2, e0) = all_52_27
% 204.02/34.83    (141)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.02/34.83    (142)   ~ (e3 = e2)
% 204.02/34.83    (143)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.02/34.83    (144)   ~ (all_52_9 = all_52_17)
% 204.02/34.83    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.02/34.83    (146)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.83    (147)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.02/34.83    (148)  op(all_52_13, all_52_13) = all_52_12
% 204.02/34.83    (149)  op(e1, e1) = all_10_2
% 204.02/34.83    (150)   ~ (all_52_23 = all_10_2)
% 204.02/34.83    (151)   ~ (all_52_7 = all_52_23)
% 204.02/34.83    (152)   ~ (all_52_17 = all_52_19)
% 204.02/34.83    (153)  all_58_3 = all_4_2
% 204.02/34.83    (154)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.02/34.83    (155)  all_56_13 = all_52_15
% 204.02/34.83    (156)   ~ (all_52_3 = all_4_2)
% 204.02/34.83    (157)   ~ (all_52_19 = all_4_2)
% 204.02/34.83    (158)   ~ (all_52_17 = all_52_23)
% 204.02/34.83    (159)  op(all_6_2, e3) = all_6_1
% 204.02/34.83    (160)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.02/34.83    (161)   ~ (all_52_13 = all_52_29)
% 204.02/34.83    (162)  all_58_4 = all_52_17
% 204.02/34.83    (163)  op(all_52_25, all_52_25) = all_52_24
% 204.02/34.83  
% 204.02/34.83  Begin of proof
% 204.02/34.83  | 
% 204.02/34.83  | BETA: splitting (110) gives:
% 204.02/34.83  | 
% 204.02/34.83  | Case 1:
% 204.02/34.83  | | 
% 204.02/34.83  | |   (164)  all_56_15 = e3
% 204.02/34.83  | | 
% 204.02/34.83  | | COMBINE_EQS: (48), (164) imply:
% 204.02/34.83  | |   (165)  all_14_2 = e3
% 204.02/34.83  | | 
% 204.02/34.83  | | SIMP: (165) implies:
% 204.02/34.83  | |   (166)  all_14_2 = e3
% 204.02/34.83  | | 
% 204.02/34.83  | | REF_CLOSE: (3), (5), (7), (9), (12), (20), (21), (22), (24), (28), (30),
% 204.02/34.83  | |            (32), (36), (37), (38), (40), (46), (47), (49), (50), (54), (62),
% 204.02/34.83  | |            (66), (67), (69), (70), (71), (73), (74), (75), (77), (81), (89),
% 204.02/34.83  | |            (99), (107), (109), (111), (112), (113), (116), (118), (120),
% 204.02/34.83  | |            (124), (128), (130), (131), (135), (137), (142), (148), (149),
% 204.02/34.83  | |            (150), (153), (156), (163), (166) are inconsistent by sub-proof
% 204.02/34.83  | |            #713.
% 204.02/34.83  | | 
% 204.02/34.83  | Case 2:
% 204.02/34.83  | | 
% 204.02/34.83  | |   (167)   ~ (all_56_15 = e3)
% 204.02/34.83  | |   (168)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.83  | | 
% 204.02/34.83  | | REDUCE: (48), (167) imply:
% 204.02/34.83  | |   (169)   ~ (all_14_2 = e3)
% 204.02/34.83  | | 
% 204.02/34.83  | | BETA: splitting (55) gives:
% 204.02/34.83  | | 
% 204.02/34.83  | | Case 1:
% 204.02/34.83  | | | 
% 204.02/34.83  | | |   (170)  all_56_13 = e3
% 204.02/34.83  | | | 
% 204.02/34.83  | | | COMBINE_EQS: (155), (170) imply:
% 204.02/34.83  | | |   (171)  all_52_15 = e3
% 204.02/34.83  | | | 
% 204.02/34.83  | | | SIMP: (171) implies:
% 204.02/34.83  | | |   (172)  all_52_15 = e3
% 204.02/34.83  | | | 
% 204.02/34.83  | | | COMBINE_EQS: (27), (172) imply:
% 204.02/34.83  | | |   (173)  all_58_13 = e3
% 204.02/34.83  | | | 
% 204.02/34.83  | | | REDUCE: (16), (172) imply:
% 204.02/34.83  | | |   (174)   ~ (all_52_7 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | REDUCE: (123), (172) imply:
% 204.02/34.83  | | |   (175)   ~ (all_52_13 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | REDUCE: (2), (172) imply:
% 204.02/34.83  | | |   (176)   ~ (all_52_23 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | SIMP: (176) implies:
% 204.02/34.83  | | |   (177)   ~ (all_52_23 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | REDUCE: (93), (172) imply:
% 204.02/34.83  | | |   (178)   ~ (all_14_2 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | REDUCE: (133), (172) imply:
% 204.02/34.83  | | |   (179)   ~ (all_4_2 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | SIMP: (179) implies:
% 204.02/34.83  | | |   (180)   ~ (all_4_2 = e3)
% 204.02/34.83  | | | 
% 204.02/34.83  | | | REDUCE: (65), (172) imply:
% 204.02/34.83  | | |   (181)  op(e3, e3) = all_52_14
% 204.02/34.83  | | | 
% 204.02/34.83  | | | GROUND_INST: instantiating (7) with all_6_2, all_52_14, e3, e3,
% 204.02/34.83  | | |              simplifying with (124), (181) gives:
% 204.02/34.83  | | |   (182)  all_52_14 = all_6_2
% 204.02/34.83  | | | 
% 204.02/34.83  | | | BETA: splitting (15) gives:
% 204.02/34.83  | | | 
% 204.02/34.83  | | | Case 1:
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | |   (183)  all_56_12 = e3
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | REF_CLOSE: (114), (174), (183) are inconsistent by sub-proof #1383.
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | Case 2:
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | |   (184)   ~ (all_56_12 = e3)
% 204.02/34.83  | | | |   (185)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | BETA: splitting (57) gives:
% 204.02/34.83  | | | | 
% 204.02/34.83  | | | | Case 1:
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | |   (186)  all_58_1 = e1
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (12), (13), (17), (20), (25),
% 204.02/34.83  | | | | |            (29), (30), (33), (36), (38), (43), (44), (49), (50), (52),
% 204.02/34.83  | | | | |            (56), (59), (61), (62), (66), (68), (69), (70), (71), (73),
% 204.02/34.83  | | | | |            (74), (77), (79), (81), (82), (83), (85), (89), (90), (91),
% 204.02/34.83  | | | | |            (94), (95), (96), (97), (98), (100), (104), (105), (106),
% 204.02/34.83  | | | | |            (109), (112), (116), (117), (119), (120), (124), (125),
% 204.02/34.83  | | | | |            (126), (127), (130), (131), (135), (138), (139), (144),
% 204.02/34.83  | | | | |            (145), (149), (150), (153), (156), (159), (162), (169),
% 204.02/34.83  | | | | |            (173), (174), (175), (177), (186) are inconsistent by
% 204.02/34.83  | | | | |            sub-proof #708.
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | Case 2:
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | |   (187)   ~ (all_58_1 = e1)
% 204.02/34.83  | | | | |   (188)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | | REDUCE: (10), (187) imply:
% 204.02/34.83  | | | | |   (189)   ~ (all_52_9 = e1)
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | | BETA: splitting (81) gives:
% 204.02/34.83  | | | | | 
% 204.02/34.83  | | | | | Case 1:
% 204.02/34.83  | | | | | | 
% 204.02/34.83  | | | | | |   (190)  all_58_0 = e3
% 204.02/34.83  | | | | | | 
% 204.02/34.83  | | | | | | COMBINE_EQS: (20), (190) imply:
% 204.02/34.83  | | | | | |   (191)  all_6_2 = e3
% 204.02/34.83  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (19), (191) imply:
% 204.02/34.84  | | | | | |   (192)   ~ (all_52_3 = e3)
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (120), (191) imply:
% 204.02/34.84  | | | | | |   (193)   ~ (all_52_5 = e3)
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (138), (191) imply:
% 204.02/34.84  | | | | | |   (194)   ~ (all_52_17 = e3)
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (117), (191) imply:
% 204.02/34.84  | | | | | |   (195)   ~ (all_52_25 = e3)
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (159), (191) imply:
% 204.02/34.84  | | | | | |   (196)  op(e3, e3) = all_6_1
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (124), (191) imply:
% 204.02/34.84  | | | | | |   (197)  op(e3, e3) = e3
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | GROUND_INST: instantiating (7) with e3, all_6_1, e3, e3, simplifying
% 204.02/34.84  | | | | | |              with (196), (197) gives:
% 204.02/34.84  | | | | | |   (198)  all_6_1 = e3
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REDUCE: (82), (198) imply:
% 204.02/34.84  | | | | | |   (199)  op(e3, e3) = all_6_0
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | GROUND_INST: instantiating (7) with e3, all_6_0, e3, e3, simplifying
% 204.02/34.84  | | | | | |              with (197), (199) gives:
% 204.02/34.84  | | | | | |   (200)  all_6_0 = e3
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | BETA: splitting (49) gives:
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | Case 1:
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | |   (201)  all_58_2 = e3
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | REF_CLOSE: (77), (192), (201) are inconsistent by sub-proof #1369.
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | Case 2:
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | |   (202)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | BETA: splitting (88) gives:
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | |   (203)  all_58_0 = e1
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | COMBINE_EQS: (190), (203) imply:
% 204.02/34.84  | | | | | | | |   (204)  e3 = e1
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (5), (204) imply:
% 204.02/34.84  | | | | | | | |   (205)  $false
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | CLOSE: (205) is inconsistent.
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | |   (206)   ~ (all_58_0 = e1)
% 204.02/34.84  | | | | | | | |   (207)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | BETA: splitting (125) gives:
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | |   (208)  all_58_9 = e3
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | REF_CLOSE: (30), (195), (208) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | |            #1300.
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | |   (209)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | BETA: splitting (145) gives:
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | |   (210)  all_58_4 = e3
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | REF_CLOSE: (162), (194), (210) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | |            #1302.
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | |   (211)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | BETA: splitting (108) gives:
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | |   (212)  all_56_8 = e3
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | REF_CLOSE: (63), (193), (212) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | |            #1325.
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | |   (213)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | BETA: splitting (91) gives:
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | |   (214)  all_58_12 = e1
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (13), (73), (98), (139), (149),
% 204.02/34.84  | | | | | | | | | | | |            (150), (173), (214) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | | |            #1170.
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | |   (215)   ~ (all_58_12 = e1)
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | REDUCE: (73), (215) imply:
% 204.02/34.84  | | | | | | | | | | | |   (216)   ~ (all_52_7 = e1)
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | BETA: splitting (83) gives:
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | |   (217)  all_58_0 = e1
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | COMBINE_EQS: (190), (217) imply:
% 204.02/34.84  | | | | | | | | | | | | |   (218)  e3 = e1
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | REDUCE: (5), (218) imply:
% 204.02/34.84  | | | | | | | | | | | | |   (219)  $false
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | |   (220)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | BETA: splitting (78) gives:
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | |   (221)  all_56_6 = e3
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | COMBINE_EQS: (92), (221) imply:
% 204.02/34.84  | | | | | | | | | | | | | |   (222)  all_52_19 = e3
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | SIMP: (222) implies:
% 204.02/34.84  | | | | | | | | | | | | | |   (223)  all_52_19 = e3
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | REDUCE: (106), (223) imply:
% 204.02/34.84  | | | | | | | | | | | | | |   (224)   ~ (all_10_2 = e3)
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | SIMP: (224) implies:
% 204.02/34.84  | | | | | | | | | | | | | |   (225)   ~ (all_10_2 = e3)
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (10), (12), (13), (17), (18), (21),
% 204.02/34.84  | | | | | | | | | | | | | |            (28), (29), (30), (31), (33), (35), (36), (38),
% 204.02/34.84  | | | | | | | | | | | | | |            (40), (43), (44), (46), (48), (50), (51), (59),
% 204.02/34.84  | | | | | | | | | | | | | |            (62), (63), (66), (68), (69), (72), (73), (75),
% 204.02/34.84  | | | | | | | | | | | | | |            (76), (77), (89), (90), (94), (98), (99), (102),
% 204.02/34.84  | | | | | | | | | | | | | |            (105), (107), (109), (112), (114), (115), (116),
% 204.02/34.84  | | | | | | | | | | | | | |            (130), (131), (134), (135), (139), (140), (141),
% 204.02/34.84  | | | | | | | | | | | | | |            (149), (153), (157), (162), (168), (169), (173),
% 204.02/34.84  | | | | | | | | | | | | | |            (177), (185), (188), (189), (207), (209), (211),
% 204.02/34.84  | | | | | | | | | | | | | |            (213), (220), (225) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | | | | |            #706.
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | |   (226)   ~ (all_56_6 = e3)
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | REDUCE: (92), (226) imply:
% 204.02/34.84  | | | | | | | | | | | | | |   (227)   ~ (all_52_19 = e3)
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | |   (228)  all_58_3 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | COMBINE_EQS: (153), (228) imply:
% 204.02/34.84  | | | | | | | | | | | | | | |   (229)  all_4_2 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | REDUCE: (180), (229) imply:
% 204.02/34.84  | | | | | | | | | | | | | | |   (230)  $false
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | |   (231)  all_58_5 = e3 | all_58_10 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | |   (232)  all_58_5 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | REF_CLOSE: (131), (227), (232) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | | | | | | |            #1279.
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | |   (233)  all_58_10 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (233) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | |   (234)  all_52_27 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | SIMP: (234) implies:
% 204.02/34.84  | | | | | | | | | | | | | | | |   (235)  all_52_27 = e3
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | REDUCE: (26), (235) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | |   (236)   ~ (all_52_29 = e3)
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | SIMP: (236) implies:
% 204.02/34.84  | | | | | | | | | | | | | | | |   (237)   ~ (all_52_29 = e3)
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (238)  all_58_2 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (238) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (239)  all_52_3 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | SIMP: (239) implies:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (240)  all_52_3 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | REDUCE: (156), (240) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (241)   ~ (all_4_2 = e1)
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (242)   ~ (all_4_2 = e1)
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | REDUCE: (192), (240) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (243)   ~ (e3 = e1)
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | REDUCE: (89), (240) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (244)  op(e1, e1) = e2
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | |   (245)  all_58_3 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (245) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | | |   (246)  all_4_2 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | REDUCE: (242), (246) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | | |   (247)  $false
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | |   (248)  all_58_7 = e1 | all_58_13 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |   (249)  all_58_7 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (249) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |   (250)  all_52_13 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (12), (20), (36), (38), (46), (49),
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |            (69), (71), (73), (74), (75), (77), (81), (89),
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |            (109), (112), (120), (124), (135), (137), (142),
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |            (148), (149), (156), (175), (237), (244), (250)
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #725.
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |   (251)  all_58_13 = e1
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (173), (251) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | | | | | | | | | |            #770.
% 204.02/34.84  | | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (252)   ~ (all_58_2 = e1)
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | REDUCE: (77), (252) imply:
% 204.02/34.84  | | | | | | | | | | | | | | | | |   (253)   ~ (all_52_3 = e1)
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (73), (77), (112), (135), (149), (216),
% 204.02/34.84  | | | | | | | | | | | | | | | | |            (220), (253) are inconsistent by sub-proof #705.
% 204.02/34.84  | | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | End of split
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | End of split
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | End of split
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | Case 2:
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | |   (254)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REF_CLOSE: (7), (12), (36), (49), (71), (73), (77), (89), (112),
% 204.02/34.84  | | | | | |            (124), (135), (149), (156), (174), (254) are inconsistent
% 204.02/34.84  | | | | | |            by sub-proof #1364.
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | End of split
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | End of split
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | End of split
% 204.02/34.84  | | | 
% 204.02/34.84  | | Case 2:
% 204.02/34.84  | | | 
% 204.02/34.84  | | |   (255)   ~ (all_56_13 = e3)
% 204.02/34.84  | | | 
% 204.02/34.84  | | | REDUCE: (155), (255) imply:
% 204.02/34.84  | | |   (256)   ~ (all_52_15 = e3)
% 204.02/34.84  | | | 
% 204.02/34.84  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.02/34.84  | | |            (14), (15), (17), (18), (19), (20), (21), (23), (27), (29),
% 204.02/34.84  | | |            (30), (31), (32), (34), (36), (38), (39), (40), (41), (42),
% 204.02/34.84  | | |            (43), (44), (45), (46), (48), (49), (53), (56), (58), (60),
% 204.02/34.84  | | |            (62), (63), (64), (67), (69), (70), (71), (72), (73), (74),
% 204.02/34.84  | | |            (75), (77), (79), (80), (81), (82), (83), (84), (85), (86),
% 204.02/34.84  | | |            (87), (89), (97), (98), (99), (101), (103), (104), (105),
% 204.02/34.84  | | |            (107), (108), (109), (112), (113), (114), (115), (116), (117),
% 204.02/34.84  | | |            (120), (121), (122), (124), (125), (126), (129), (130), (131),
% 204.02/34.84  | | |            (132), (133), (134), (135), (136), (137), (138), (140), (143),
% 204.02/34.84  | | |            (144), (146), (147), (149), (150), (151), (152), (153), (154),
% 204.02/34.84  | | |            (156), (158), (159), (160), (161), (162), (168), (169), (256)
% 204.02/34.84  | | |            are inconsistent by sub-proof #698.
% 204.02/34.84  | | | 
% 204.02/34.84  | | End of split
% 204.02/34.84  | | 
% 204.02/34.84  | End of split
% 204.02/34.84  | 
% 204.02/34.84  End of proof
% 204.02/34.84  
% 204.02/34.84  Sub-proof #698 shows that the following formulas are inconsistent:
% 204.02/34.84  ----------------------------------------------------------------
% 204.02/34.84    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.02/34.84    (2)   ~ (all_52_15 = all_52_23)
% 204.02/34.84    (3)  all_58_14 = all_52_23
% 204.02/34.84    (4)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.02/34.84    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.84    (6)   ~ (all_52_5 = all_52_13)
% 204.02/34.84    (7)  op(all_52_7, all_52_7) = e0
% 204.02/34.84    (8)  all_58_1 = all_52_9
% 204.02/34.84    (9)   ~ (all_52_9 = all_52_13)
% 204.02/34.84    (10)  op(all_52_5, all_52_5) = e1
% 204.02/34.84    (11)   ~ (e3 = e0)
% 204.02/34.84    (12)  all_24_1 = all_14_1
% 204.02/34.84    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.02/34.84    (14)   ~ (all_52_3 = all_52_19)
% 204.02/34.84    (15)   ~ (all_52_17 = all_52_25)
% 204.02/34.84    (16)   ~ (all_52_3 = all_6_2)
% 204.02/34.84    (17)  all_58_0 = all_6_2
% 204.02/34.84    (18)  op(all_14_2, e0) = all_14_1
% 204.02/34.84    (19)  all_56_4 = all_52_3
% 204.02/34.84    (20)  all_58_13 = all_52_15
% 204.02/34.84    (21)  op(all_10_2, all_10_2) = all_52_20
% 204.02/34.84    (22)  all_58_9 = all_52_25
% 204.02/34.84    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.02/34.84    (24)   ~ (all_52_29 = all_14_2)
% 204.02/34.84    (25)   ~ (all_52_15 = e3)
% 204.02/34.84    (26)  op(e2, all_4_1) = e3
% 204.02/34.84    (27)  op(e2, e2) = all_4_2
% 204.02/34.84    (28)  all_58_11 = all_52_29
% 204.02/34.84    (29)  all_56_5 = all_4_2
% 204.02/34.84    (30)   ~ (all_52_25 = all_14_2)
% 204.02/34.84    (31)   ~ (all_52_9 = all_52_15)
% 204.02/34.84    (32)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.02/34.84    (33)   ~ (all_52_3 = all_52_27)
% 204.02/34.84    (34)  op(all_10_2, e1) = all_10_1
% 204.02/34.84    (35)   ~ (all_52_7 = all_6_2)
% 204.02/34.84    (36)  op(e0, e0) = all_14_2
% 204.02/34.84    (37)  all_56_15 = all_14_2
% 204.02/34.84    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.02/34.84    (39)   ~ (all_4_1 = e1)
% 204.02/34.84    (40)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.02/34.84    (41)  all_56_9 = all_52_13
% 204.02/34.84    (42)   ~ (all_52_13 = all_10_2)
% 204.02/34.84    (43)  all_58_10 = all_52_27
% 204.02/34.84    (44)  all_56_8 = all_52_5
% 204.02/34.84    (45)  op(all_52_9, all_52_9) = all_52_8
% 204.02/34.84    (46)   ~ (all_52_25 = all_52_29)
% 204.02/34.84    (47)  all_58_7 = all_52_13
% 204.02/34.84    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.02/34.84    (49)  op(all_6_2, all_6_2) = e3
% 204.02/34.84    (50)   ~ (all_52_5 = all_52_7)
% 204.02/34.84    (51)  all_58_12 = all_52_7
% 204.02/34.84    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.02/34.84    (53)   ~ (all_52_7 = all_14_2)
% 204.02/34.84    (54)  all_58_2 = all_52_3
% 204.02/34.84    (55)  all_56_2 = all_52_17
% 204.02/34.84    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.02/34.84    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.84    (58)  op(e3, all_6_1) = all_6_0
% 204.02/34.84    (59)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.02/34.84    (60)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.02/34.84    (61)   ~ (e2 = e0)
% 204.02/34.84    (62)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.02/34.84    (63)  op(all_4_2, e2) = all_4_1
% 204.02/34.84    (64)  op(all_52_3, all_52_3) = e2
% 204.02/34.84    (65)   ~ (all_6_0 = e2)
% 204.02/34.84    (66)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.84    (67)   ~ (all_52_13 = all_4_2)
% 204.02/34.84    (68)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.02/34.84    (69)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.02/34.84    (70)   ~ (all_52_9 = all_52_25)
% 204.02/34.84    (71)  all_58_15 = all_14_2
% 204.02/34.84    (72)  op(all_52_23, all_52_23) = all_52_22
% 204.02/34.84    (73)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.02/34.84    (74)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.84    (75)  all_58_8 = all_10_2
% 204.02/34.84    (76)   ~ (all_52_5 = all_10_2)
% 204.02/34.84    (77)   ~ (all_52_23 = all_14_2)
% 204.02/34.84    (78)  all_56_12 = all_52_7
% 204.02/34.84    (79)  op(all_52_17, all_52_17) = all_52_16
% 204.02/34.84    (80)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.02/34.84    (81)   ~ (all_52_25 = all_6_2)
% 204.02/34.84    (82)   ~ (all_52_5 = all_6_2)
% 204.02/34.84    (83)   ~ (all_52_9 = all_6_2)
% 204.02/34.84    (84)  all_24_2 = all_14_2
% 204.02/34.84    (85)  op(e3, e3) = all_6_2
% 204.02/34.84    (86)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.02/34.84    (87)   ~ (all_52_27 = all_14_2)
% 204.02/34.84    (88)   ~ (all_52_3 = all_52_7)
% 204.02/34.84    (89)  op(all_14_2, all_14_2) = all_52_30
% 204.02/34.84    (90)  all_58_5 = all_52_19
% 204.02/34.84    (91)  all_56_1 = all_52_9
% 204.02/34.84    (92)   ~ (all_52_15 = all_4_2)
% 204.02/34.84    (93)   ~ (all_52_27 = all_4_2)
% 204.02/34.84    (94)  all_58_6 = all_52_5
% 204.02/34.84    (95)  op(e3, e2) = all_52_9
% 204.02/34.84    (96)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.02/34.84    (97)   ~ (all_52_17 = all_6_2)
% 204.02/34.84    (98)  op(e2, e0) = all_52_27
% 204.02/34.84    (99)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.02/34.84    (100)   ~ (all_52_9 = all_52_17)
% 204.02/34.84    (101)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.84    (102)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.02/34.84    (103)  op(e1, e1) = all_10_2
% 204.02/34.84    (104)   ~ (all_52_23 = all_10_2)
% 204.02/34.84    (105)   ~ (all_52_7 = all_52_23)
% 204.02/34.84    (106)   ~ (all_52_17 = all_52_19)
% 204.02/34.84    (107)  all_58_3 = all_4_2
% 204.02/34.84    (108)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.02/34.84    (109)   ~ (all_52_3 = all_4_2)
% 204.02/34.84    (110)   ~ (all_52_17 = all_52_23)
% 204.02/34.84    (111)  op(all_6_2, e3) = all_6_1
% 204.02/34.84    (112)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.02/34.84    (113)   ~ (all_52_13 = all_52_29)
% 204.02/34.84    (114)  all_58_4 = all_52_17
% 204.02/34.84    (115)   ~ (all_14_2 = e3)
% 204.02/34.84  
% 204.02/34.84  Begin of proof
% 204.02/34.84  | 
% 204.02/34.84  | BETA: splitting (96) gives:
% 204.02/34.84  | 
% 204.02/34.84  | Case 1:
% 204.02/34.84  | | 
% 204.02/34.84  | |   (116)  all_58_12 = e3
% 204.02/34.84  | | 
% 204.02/34.84  | | COMBINE_EQS: (51), (116) imply:
% 204.02/34.84  | |   (117)  all_52_7 = e3
% 204.02/34.84  | | 
% 204.02/34.84  | | REF_CLOSE: (5), (7), (10), (17), (27), (35), (36), (38), (49), (51), (53),
% 204.02/34.84  | |            (54), (57), (64), (76), (85), (94), (96), (103), (109), (117) are
% 204.02/34.84  | |            inconsistent by sub-proof #1361.
% 204.02/34.84  | | 
% 204.02/34.84  | Case 2:
% 204.02/34.84  | | 
% 204.02/34.84  | |   (118)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.02/34.84  | | 
% 204.02/34.84  | | BETA: splitting (118) gives:
% 204.02/34.84  | | 
% 204.02/34.84  | | Case 1:
% 204.02/34.84  | | | 
% 204.02/34.84  | | |   (119)  all_58_13 = e3
% 204.02/34.84  | | | 
% 204.02/34.84  | | | REF_CLOSE: (20), (25), (119) are inconsistent by sub-proof #1360.
% 204.02/34.84  | | | 
% 204.02/34.84  | | Case 2:
% 204.02/34.84  | | | 
% 204.02/34.84  | | |   (120)  all_58_14 = e3 | all_58_15 = e3
% 204.02/34.84  | | | 
% 204.02/34.84  | | | BETA: splitting (120) gives:
% 204.02/34.84  | | | 
% 204.02/34.84  | | | Case 1:
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | |   (121)  all_58_14 = e3
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | COMBINE_EQS: (3), (121) imply:
% 204.02/34.84  | | | |   (122)  all_52_23 = e3
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | SIMP: (122) implies:
% 204.02/34.84  | | | |   (123)  all_52_23 = e3
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | REDUCE: (105), (123) imply:
% 204.02/34.84  | | | |   (124)   ~ (all_52_7 = e3)
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | REDUCE: (110), (123) imply:
% 204.02/34.84  | | | |   (125)   ~ (all_52_17 = e3)
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | REDUCE: (77), (123) imply:
% 204.02/34.84  | | | |   (126)   ~ (all_14_2 = e3)
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | REDUCE: (104), (123) imply:
% 204.02/34.84  | | | |   (127)   ~ (all_10_2 = e3)
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | SIMP: (127) implies:
% 204.02/34.84  | | | |   (128)   ~ (all_10_2 = e3)
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | REDUCE: (72), (123) imply:
% 204.02/34.84  | | | |   (129)  op(e3, e3) = all_52_22
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3,
% 204.02/34.84  | | | |              simplifying with (85), (129) gives:
% 204.02/34.84  | | | |   (130)  all_52_22 = all_6_2
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | BETA: splitting (13) gives:
% 204.02/34.84  | | | | 
% 204.02/34.84  | | | | Case 1:
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | |   (131)  all_56_12 = e3
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | | COMBINE_EQS: (78), (131) imply:
% 204.02/34.84  | | | | |   (132)  all_52_7 = e3
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | | REDUCE: (124), (132) imply:
% 204.02/34.84  | | | | |   (133)  $false
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | | CLOSE: (133) is inconsistent.
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | Case 2:
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | |   (134)   ~ (all_56_12 = e3)
% 204.02/34.84  | | | | |   (135)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | | BETA: splitting (40) gives:
% 204.02/34.84  | | | | | 
% 204.02/34.84  | | | | | Case 1:
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | |   (136)  all_56_2 = e3
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | REF_CLOSE: (55), (125), (136) are inconsistent by sub-proof #1327.
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | Case 2:
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | |   (137)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | BETA: splitting (73) gives:
% 204.02/34.84  | | | | | | 
% 204.02/34.84  | | | | | | Case 1:
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | |   (138)  all_56_8 = e3
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | COMBINE_EQS: (44), (138) imply:
% 204.02/34.84  | | | | | | |   (139)  all_52_5 = e3
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | SIMP: (139) implies:
% 204.02/34.84  | | | | | | |   (140)  all_52_5 = e3
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | REF_CLOSE: (5), (10), (17), (27), (38), (49), (50), (51), (54),
% 204.02/34.84  | | | | | | |            (57), (64), (76), (82), (85), (94), (103), (109), (140)
% 204.02/34.84  | | | | | | |            are inconsistent by sub-proof #704.
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | Case 2:
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | |   (141)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | BETA: splitting (57) gives:
% 204.02/34.84  | | | | | | | 
% 204.02/34.84  | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | |   (142)  all_58_0 = e3
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | COMBINE_EQS: (17), (142) imply:
% 204.02/34.84  | | | | | | | |   (143)  all_6_2 = e3
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (16), (143) imply:
% 204.02/34.84  | | | | | | | |   (144)   ~ (all_52_3 = e3)
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (82), (143) imply:
% 204.02/34.84  | | | | | | | |   (145)   ~ (all_52_5 = e3)
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (83), (143) imply:
% 204.02/34.84  | | | | | | | |   (146)   ~ (all_52_9 = e3)
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (81), (143) imply:
% 204.02/34.84  | | | | | | | |   (147)   ~ (all_52_25 = e3)
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (111), (143) imply:
% 204.02/34.84  | | | | | | | |   (148)  op(e3, e3) = all_6_1
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (85), (143) imply:
% 204.02/34.84  | | | | | | | |   (149)  op(e3, e3) = e3
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | GROUND_INST: instantiating (5) with e3, all_6_1, e3, e3,
% 204.02/34.84  | | | | | | | |              simplifying with (148), (149) gives:
% 204.02/34.84  | | | | | | | |   (150)  all_6_1 = e3
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (58), (150) imply:
% 204.02/34.84  | | | | | | | |   (151)  op(e3, e3) = all_6_0
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | GROUND_INST: instantiating (5) with e3, all_6_0, e3, e3,
% 204.02/34.84  | | | | | | | |              simplifying with (149), (151) gives:
% 204.02/34.84  | | | | | | | |   (152)  all_6_0 = e3
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | REDUCE: (65), (152) imply:
% 204.02/34.84  | | | | | | | |   (153)   ~ (e3 = e2)
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | BETA: splitting (52) gives:
% 204.02/34.84  | | | | | | | | 
% 204.02/34.84  | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | |   (154)  all_58_6 = e3
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | REF_CLOSE: (94), (145), (154) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | |            #1328.
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | |   (155)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | BETA: splitting (69) gives:
% 204.02/34.84  | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | |   (156)  all_58_1 = e3
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | COMBINE_EQS: (8), (156) imply:
% 204.02/34.84  | | | | | | | | | |   (157)  all_52_9 = e3
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | REDUCE: (146), (157) imply:
% 204.02/34.84  | | | | | | | | | |   (158)  $false
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | CLOSE: (158) is inconsistent.
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | |   (159)   ~ (all_58_1 = e3)
% 204.02/34.84  | | | | | | | | | |   (160)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | BETA: splitting (86) gives:
% 204.02/34.84  | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | |   (161)  all_58_9 = e3
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | REF_CLOSE: (22), (147), (161) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | |            #1300.
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | |   (162)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | BETA: splitting (60) gives:
% 204.02/34.84  | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | |   (163)  all_56_4 = e3
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | REF_CLOSE: (19), (144), (163) are inconsistent by sub-proof
% 204.02/34.84  | | | | | | | | | | | |            #1340.
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | |   (164)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | BETA: splitting (99) gives:
% 204.02/34.84  | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | |   (165)  all_56_1 = e3
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | COMBINE_EQS: (91), (165) imply:
% 204.02/34.84  | | | | | | | | | | | | |   (166)  all_52_9 = e3
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | REDUCE: (146), (166) imply:
% 204.02/34.84  | | | | | | | | | | | | |   (167)  $false
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | Case 2:
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | |   (168)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | BETA: splitting (62) gives:
% 204.02/34.84  | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | Case 1:
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.84  | | | | | | | | | | | | | |   (169)  all_56_5 = e3
% 204.02/34.84  | | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (14),
% 204.02/34.85  | | | | | | | | | | | | | |            (15), (19), (22), (23), (26), (27), (28), (29),
% 204.02/34.85  | | | | | | | | | | | | | |            (32), (33), (36), (39), (41), (42), (43), (44),
% 204.02/34.85  | | | | | | | | | | | | | |            (45), (46), (47), (48), (51), (53), (54), (55),
% 204.02/34.85  | | | | | | | | | | | | | |            (63), (64), (67), (70), (75), (76), (78), (88),
% 204.02/34.85  | | | | | | | | | | | | | |            (90), (91), (94), (95), (100), (101), (109),
% 204.02/34.85  | | | | | | | | | | | | | |            (112), (113), (114), (121), (125), (128), (135),
% 204.02/34.85  | | | | | | | | | | | | | |            (137), (141), (155), (164), (168), (169) are
% 204.02/34.85  | | | | | | | | | | | | | |            inconsistent by sub-proof #703.
% 204.02/34.85  | | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | | Case 2:
% 204.02/34.85  | | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | | |   (170)   ~ (all_56_5 = e3)
% 204.02/34.85  | | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | | | REDUCE: (29), (170) imply:
% 204.02/34.85  | | | | | | | | | | | | | |   (171)   ~ (all_4_2 = e3)
% 204.02/34.85  | | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (11), (12), (18),
% 204.02/34.85  | | | | | | | | | | | | | |            (20), (21), (22), (24), (25), (27), (28), (30),
% 204.02/34.85  | | | | | | | | | | | | | |            (31), (32), (34), (37), (43), (47), (51), (53),
% 204.02/34.85  | | | | | | | | | | | | | |            (54), (56), (59), (61), (64), (66), (68), (71),
% 204.02/34.85  | | | | | | | | | | | | | |            (74), (75), (76), (79), (80), (84), (87), (89),
% 204.02/34.85  | | | | | | | | | | | | | |            (90), (92), (93), (94), (98), (102), (103), (106),
% 204.02/34.85  | | | | | | | | | | | | | |            (107), (108), (109), (112), (113), (114), (115),
% 204.02/34.85  | | | | | | | | | | | | | |            (121), (125), (142), (153), (160), (162), (171)
% 204.02/34.85  | | | | | | | | | | | | | |            are inconsistent by sub-proof #699.
% 204.02/34.85  | | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | | End of split
% 204.02/34.85  | | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | | End of split
% 204.02/34.85  | | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | | End of split
% 204.02/34.85  | | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | | End of split
% 204.02/34.85  | | | | | | | | | | 
% 204.02/34.85  | | | | | | | | | End of split
% 204.02/34.85  | | | | | | | | | 
% 204.02/34.85  | | | | | | | | End of split
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | Case 2:
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | |   (172)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | | REF_CLOSE: (5), (10), (27), (38), (49), (51), (54), (64), (76),
% 204.02/34.85  | | | | | | | |            (85), (94), (103), (109), (124), (172) are
% 204.02/34.85  | | | | | | | |            inconsistent by sub-proof #1364.
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | End of split
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | End of split
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | End of split
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | End of split
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | Case 2:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (173)  all_58_15 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | COMBINE_EQS: (71), (173) imply:
% 204.02/34.85  | | | |   (174)  all_14_2 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REDUCE: (115), (174) imply:
% 204.02/34.85  | | | |   (175)  $false
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | CLOSE: (175) is inconsistent.
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | End of split
% 204.02/34.85  | | | 
% 204.02/34.85  | | End of split
% 204.02/34.85  | | 
% 204.02/34.85  | End of split
% 204.02/34.85  | 
% 204.02/34.85  End of proof
% 204.02/34.85  
% 204.02/34.85  Sub-proof #699 shows that the following formulas are inconsistent:
% 204.02/34.85  ----------------------------------------------------------------
% 204.02/34.85    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.02/34.85    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.85    (3)  op(all_52_7, all_52_7) = e0
% 204.02/34.85    (4)  all_58_1 = all_52_9
% 204.02/34.85    (5)   ~ (all_52_9 = all_52_13)
% 204.02/34.85    (6)  op(all_52_5, all_52_5) = e1
% 204.02/34.85    (7)   ~ (e3 = e0)
% 204.02/34.85    (8)  all_24_1 = all_14_1
% 204.02/34.85    (9)   ~ (all_4_2 = e3)
% 204.02/34.85    (10)  op(all_14_2, e0) = all_14_1
% 204.02/34.85    (11)  all_58_13 = all_52_15
% 204.02/34.85    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.02/34.85    (13)  all_58_9 = all_52_25
% 204.02/34.85    (14)   ~ (all_52_29 = all_14_2)
% 204.02/34.85    (15)   ~ (all_52_15 = e3)
% 204.02/34.85    (16)  op(e2, e2) = all_4_2
% 204.02/34.85    (17)  all_58_11 = all_52_29
% 204.02/34.85    (18)   ~ (all_52_25 = all_14_2)
% 204.02/34.85    (19)   ~ (all_52_9 = all_52_15)
% 204.02/34.85    (20)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.02/34.85    (21)  op(all_10_2, e1) = all_10_1
% 204.02/34.85    (22)  all_56_15 = all_14_2
% 204.02/34.85    (23)  all_58_10 = all_52_27
% 204.02/34.85    (24)  all_58_7 = all_52_13
% 204.02/34.85    (25)  all_58_12 = all_52_7
% 204.02/34.85    (26)   ~ (all_52_7 = all_14_2)
% 204.02/34.85    (27)  all_58_2 = all_52_3
% 204.02/34.85    (28)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.02/34.85    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.02/34.85    (30)   ~ (e2 = e0)
% 204.02/34.85    (31)  op(all_52_3, all_52_3) = e2
% 204.02/34.85    (32)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.85    (33)  all_58_0 = e3
% 204.02/34.85    (34)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.02/34.85    (35)  all_58_15 = all_14_2
% 204.02/34.85    (36)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.02/34.85    (37)  all_58_8 = all_10_2
% 204.02/34.85    (38)   ~ (all_52_5 = all_10_2)
% 204.02/34.85    (39)  op(all_52_17, all_52_17) = all_52_16
% 204.02/34.85    (40)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.02/34.85    (41)  all_24_2 = all_14_2
% 204.02/34.85    (42)   ~ (all_52_27 = all_14_2)
% 204.02/34.85    (43)   ~ (all_52_17 = e3)
% 204.02/34.85    (44)  op(all_14_2, all_14_2) = all_52_30
% 204.02/34.85    (45)  all_58_5 = all_52_19
% 204.02/34.85    (46)   ~ (all_52_15 = all_4_2)
% 204.02/34.85    (47)   ~ (all_52_27 = all_4_2)
% 204.02/34.85    (48)  all_58_6 = all_52_5
% 204.02/34.85    (49)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.02/34.85    (50)  op(e2, e0) = all_52_27
% 204.02/34.85    (51)   ~ (e3 = e2)
% 204.02/34.85    (52)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.02/34.85    (53)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.02/34.85    (54)  op(e1, e1) = all_10_2
% 204.02/34.85    (55)  all_58_14 = e3
% 204.02/34.85    (56)   ~ (all_52_17 = all_52_19)
% 204.02/34.85    (57)  all_58_3 = all_4_2
% 204.02/34.85    (58)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.02/34.85    (59)   ~ (all_52_3 = all_4_2)
% 204.02/34.85    (60)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.02/34.85    (61)   ~ (all_52_13 = all_52_29)
% 204.02/34.85    (62)  all_58_4 = all_52_17
% 204.02/34.85    (63)   ~ (all_14_2 = e3)
% 204.02/34.85  
% 204.02/34.85  Begin of proof
% 204.02/34.85  | 
% 204.02/34.85  | BETA: splitting (52) gives:
% 204.02/34.85  | 
% 204.02/34.85  | Case 1:
% 204.02/34.85  | | 
% 204.02/34.85  | |   (64)  all_58_3 = e3
% 204.02/34.85  | | 
% 204.02/34.85  | | COMBINE_EQS: (57), (64) imply:
% 204.02/34.85  | |   (65)  all_4_2 = e3
% 204.02/34.85  | | 
% 204.02/34.85  | | REDUCE: (9), (65) imply:
% 204.02/34.85  | |   (66)  $false
% 204.02/34.85  | | 
% 204.02/34.85  | | CLOSE: (66) is inconsistent.
% 204.02/34.85  | | 
% 204.02/34.85  | Case 2:
% 204.02/34.85  | | 
% 204.02/34.85  | |   (67)  all_58_7 = e3 | all_58_13 = e3
% 204.02/34.85  | | 
% 204.02/34.85  | | BETA: splitting (67) gives:
% 204.02/34.85  | | 
% 204.02/34.85  | | Case 1:
% 204.02/34.85  | | | 
% 204.02/34.85  | | |   (68)  all_58_7 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | COMBINE_EQS: (24), (68) imply:
% 204.02/34.85  | | |   (69)  all_52_13 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (5), (69) imply:
% 204.02/34.85  | | |   (70)   ~ (all_52_9 = e3)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (61), (69) imply:
% 204.02/34.85  | | |   (71)   ~ (all_52_29 = e3)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | SIMP: (71) implies:
% 204.02/34.85  | | |   (72)   ~ (all_52_29 = e3)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | BETA: splitting (49) gives:
% 204.02/34.85  | | | 
% 204.02/34.85  | | | Case 1:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (73)  all_58_10 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | COMBINE_EQS: (23), (73) imply:
% 204.02/34.85  | | | |   (74)  all_52_27 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | SIMP: (74) implies:
% 204.02/34.85  | | | |   (75)  all_52_27 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REDUCE: (42), (75) imply:
% 204.02/34.85  | | | |   (76)   ~ (all_14_2 = e3)
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REDUCE: (47), (75) imply:
% 204.02/34.85  | | | |   (77)   ~ (all_4_2 = e3)
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REDUCE: (50), (75) imply:
% 204.02/34.85  | | | |   (78)  op(e2, e0) = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | BETA: splitting (28) gives:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | Case 1:
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | |   (79)  all_58_0 = e2
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | | COMBINE_EQS: (33), (79) imply:
% 204.02/34.85  | | | | |   (80)  e3 = e2
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | | REDUCE: (51), (80) imply:
% 204.02/34.85  | | | | |   (81)  $false
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | | CLOSE: (81) is inconsistent.
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | Case 2:
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | |   (82)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | | BETA: splitting (34) gives:
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | | Case 1:
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | |   (83)  all_58_4 = e2
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | COMBINE_EQS: (62), (83) imply:
% 204.02/34.85  | | | | | |   (84)  all_52_17 = e2
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | SIMP: (84) implies:
% 204.02/34.85  | | | | | |   (85)  all_52_17 = e2
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | REDUCE: (56), (85) imply:
% 204.02/34.85  | | | | | |   (86)   ~ (all_52_19 = e2)
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | SIMP: (86) implies:
% 204.02/34.85  | | | | | |   (87)   ~ (all_52_19 = e2)
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | REDUCE: (43), (85) imply:
% 204.02/34.85  | | | | | |   (88)   ~ (e3 = e2)
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | REDUCE: (39), (85) imply:
% 204.02/34.85  | | | | | |   (89)  op(e2, e2) = all_52_16
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_16, e2, e2,
% 204.02/34.85  | | | | | |              simplifying with (16), (89) gives:
% 204.02/34.85  | | | | | |   (90)  all_52_16 = all_4_2
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | BETA: splitting (60) gives:
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | Case 1:
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | |   (91)  all_58_2 = e2
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | COMBINE_EQS: (27), (91) imply:
% 204.02/34.85  | | | | | | |   (92)  all_52_3 = e2
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | SIMP: (92) implies:
% 204.02/34.85  | | | | | | |   (93)  all_52_3 = e2
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | REF_CLOSE: (2), (16), (31), (59), (93) are inconsistent by
% 204.02/34.85  | | | | | | |            sub-proof #1157.
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | Case 2:
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | |   (94)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | BETA: splitting (94) gives:
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | Case 1:
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | |   (95)  all_58_3 = e2
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | | COMBINE_EQS: (57), (95) imply:
% 204.02/34.85  | | | | | | | |   (96)  all_4_2 = e2
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | | REDUCE: (46), (96) imply:
% 204.02/34.85  | | | | | | | |   (97)   ~ (all_52_15 = e2)
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (11), (16), (20), (25),
% 204.02/34.85  | | | | | | | |            (30), (32), (35), (41), (46), (53), (55), (78), (88),
% 204.02/34.85  | | | | | | | |            (97) are inconsistent by sub-proof #700.
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | Case 2:
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | |   (98)  all_58_5 = e2 | all_58_10 = e2
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | | REF_CLOSE: (45), (51), (73), (87), (98) are inconsistent by
% 204.02/34.85  | | | | | | | |            sub-proof #760.
% 204.02/34.85  | | | | | | | | 
% 204.02/34.85  | | | | | | | End of split
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | End of split
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | Case 2:
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | |   (99)   ~ (all_58_4 = e2)
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | REDUCE: (62), (99) imply:
% 204.02/34.85  | | | | | |   (100)   ~ (all_52_17 = e2)
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | BETA: splitting (58) gives:
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | | Case 1:
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | |   (101)  all_58_1 = e2
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | COMBINE_EQS: (4), (101) imply:
% 204.02/34.85  | | | | | | |   (102)  all_52_9 = e2
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | REDUCE: (19), (102) imply:
% 204.02/34.85  | | | | | | |   (103)   ~ (all_52_15 = e2)
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | SIMP: (103) implies:
% 204.02/34.85  | | | | | | |   (104)   ~ (all_52_15 = e2)
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | REDUCE: (70), (102) imply:
% 204.02/34.85  | | | | | | |   (105)   ~ (e3 = e2)
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (11), (16), (20), (25), (30),
% 204.02/34.85  | | | | | | |            (32), (35), (41), (46), (53), (55), (78), (104), (105)
% 204.02/34.85  | | | | | | |            are inconsistent by sub-proof #700.
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | Case 2:
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | |   (106)   ~ (all_58_1 = e2)
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | REDUCE: (4), (106) imply:
% 204.02/34.85  | | | | | | |   (107)   ~ (all_52_9 = e2)
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (12), (13), (14), (17), (18),
% 204.02/34.85  | | | | | | |            (21), (22), (25), (26), (27), (29), (30), (31), (33),
% 204.02/34.85  | | | | | | |            (36), (37), (38), (40), (44), (48), (54), (62), (63),
% 204.02/34.85  | | | | | | |            (68), (73), (82), (100), (107) are inconsistent by
% 204.02/34.85  | | | | | | |            sub-proof #746.
% 204.02/34.85  | | | | | | | 
% 204.02/34.85  | | | | | | End of split
% 204.02/34.85  | | | | | | 
% 204.02/34.85  | | | | | End of split
% 204.02/34.85  | | | | | 
% 204.02/34.85  | | | | End of split
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | Case 2:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (108)  all_58_11 = e3 | all_58_15 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REF_CLOSE: (17), (35), (63), (72), (108) are inconsistent by sub-proof
% 204.02/34.85  | | | |            #1103.
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | End of split
% 204.02/34.85  | | | 
% 204.02/34.85  | | Case 2:
% 204.02/34.85  | | | 
% 204.02/34.85  | | |   (109)  all_58_13 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REF_CLOSE: (11), (15), (109) are inconsistent by sub-proof #1360.
% 204.02/34.85  | | | 
% 204.02/34.85  | | End of split
% 204.02/34.85  | | 
% 204.02/34.85  | End of split
% 204.02/34.85  | 
% 204.02/34.85  End of proof
% 204.02/34.85  
% 204.02/34.85  Sub-proof #700 shows that the following formulas are inconsistent:
% 204.02/34.85  ----------------------------------------------------------------
% 204.02/34.85    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.85    (2)  op(all_52_7, all_52_7) = e0
% 204.02/34.85    (3)   ~ (e3 = e0)
% 204.02/34.85    (4)  all_24_1 = all_14_1
% 204.02/34.85    (5)  op(all_14_2, e0) = all_14_1
% 204.02/34.85    (6)   ~ (all_52_15 = e2)
% 204.02/34.85    (7)  all_58_13 = all_52_15
% 204.02/34.85    (8)   ~ (e3 = e2)
% 204.02/34.85    (9)  op(e2, e2) = all_4_2
% 204.02/34.85    (10)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.02/34.85    (11)  all_58_12 = all_52_7
% 204.02/34.85    (12)   ~ (e2 = e0)
% 204.02/34.85    (13)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.85    (14)  all_58_15 = all_14_2
% 204.02/34.85    (15)  all_24_2 = all_14_2
% 204.02/34.85    (16)  op(e2, e0) = e3
% 204.02/34.85    (17)   ~ (all_52_15 = all_4_2)
% 204.02/34.85    (18)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.02/34.85    (19)  all_58_14 = e3
% 204.02/34.85  
% 204.02/34.85  Begin of proof
% 204.02/34.85  | 
% 204.02/34.85  | SIMP: (8) implies:
% 204.02/34.85  |   (20)   ~ (e3 = e2)
% 204.02/34.85  | 
% 204.02/34.85  | BETA: splitting (10) gives:
% 204.02/34.85  | 
% 204.02/34.85  | Case 1:
% 204.02/34.85  | | 
% 204.02/34.85  | |   (21)  all_58_12 = e2
% 204.02/34.85  | | 
% 204.02/34.85  | | REF_CLOSE: (1), (2), (3), (7), (9), (11), (12), (13), (17), (19), (21) are
% 204.02/34.85  | |            inconsistent by sub-proof #702.
% 204.02/34.85  | | 
% 204.02/34.85  | Case 2:
% 204.02/34.85  | | 
% 204.02/34.85  | |   (22)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.02/34.85  | | 
% 204.02/34.85  | | BETA: splitting (22) gives:
% 204.02/34.85  | | 
% 204.02/34.85  | | Case 1:
% 204.02/34.85  | | | 
% 204.02/34.85  | | |   (23)  all_58_13 = e2
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REF_CLOSE: (6), (7), (23) are inconsistent by sub-proof #784.
% 204.02/34.85  | | | 
% 204.02/34.85  | | Case 2:
% 204.02/34.85  | | | 
% 204.02/34.85  | | |   (24)  all_58_14 = e2 | all_58_15 = e2
% 204.02/34.85  | | | 
% 204.02/34.85  | | | BETA: splitting (24) gives:
% 204.02/34.85  | | | 
% 204.02/34.85  | | | Case 1:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (25)  all_58_14 = e2
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REF_CLOSE: (19), (20), (25) are inconsistent by sub-proof #701.
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | Case 2:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (26)  all_58_15 = e2
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | COMBINE_EQS: (14), (26) imply:
% 204.02/34.85  | | | |   (27)  all_14_2 = e2
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REF_CLOSE: (1), (4), (5), (15), (16), (18), (27) are inconsistent by
% 204.02/34.85  | | | |            sub-proof #842.
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | End of split
% 204.02/34.85  | | | 
% 204.02/34.85  | | End of split
% 204.02/34.85  | | 
% 204.02/34.85  | End of split
% 204.02/34.85  | 
% 204.02/34.85  End of proof
% 204.02/34.85  
% 204.02/34.85  Sub-proof #701 shows that the following formulas are inconsistent:
% 204.02/34.85  ----------------------------------------------------------------
% 204.02/34.85    (1)  all_58_14 = e3
% 204.02/34.85    (2)  all_58_14 = e2
% 204.02/34.85    (3)   ~ (e3 = e2)
% 204.02/34.85  
% 204.02/34.85  Begin of proof
% 204.02/34.85  | 
% 204.02/34.85  | COMBINE_EQS: (1), (2) imply:
% 204.02/34.85  |   (4)  e3 = e2
% 204.02/34.85  | 
% 204.02/34.85  | SIMP: (4) implies:
% 204.02/34.85  |   (5)  e3 = e2
% 204.02/34.85  | 
% 204.02/34.85  | REDUCE: (3), (5) imply:
% 204.02/34.85  |   (6)  $false
% 204.02/34.85  | 
% 204.02/34.85  | CLOSE: (6) is inconsistent.
% 204.02/34.85  | 
% 204.02/34.85  End of proof
% 204.02/34.85  
% 204.02/34.85  Sub-proof #702 shows that the following formulas are inconsistent:
% 204.02/34.85  ----------------------------------------------------------------
% 204.02/34.85    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.85    (2)  op(all_52_7, all_52_7) = e0
% 204.02/34.85    (3)   ~ (e3 = e0)
% 204.02/34.85    (4)  all_58_13 = all_52_15
% 204.02/34.85    (5)  op(e2, e2) = all_4_2
% 204.02/34.85    (6)  all_58_12 = all_52_7
% 204.02/34.85    (7)   ~ (e2 = e0)
% 204.02/34.85    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.02/34.85    (9)  all_58_12 = e2
% 204.02/34.85    (10)   ~ (all_52_15 = all_4_2)
% 204.02/34.85    (11)  all_58_14 = e3
% 204.02/34.85  
% 204.02/34.85  Begin of proof
% 204.02/34.85  | 
% 204.02/34.85  | COMBINE_EQS: (6), (9) imply:
% 204.02/34.85  |   (12)  all_52_7 = e2
% 204.02/34.85  | 
% 204.02/34.85  | SIMP: (12) implies:
% 204.02/34.85  |   (13)  all_52_7 = e2
% 204.02/34.85  | 
% 204.02/34.85  | REDUCE: (2), (13) imply:
% 204.02/34.85  |   (14)  op(e2, e2) = e0
% 204.02/34.85  | 
% 204.02/34.85  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (14) are
% 204.02/34.85  |            inconsistent by sub-proof #1150.
% 204.02/34.85  | 
% 204.02/34.85  End of proof
% 204.02/34.85  
% 204.02/34.85  Sub-proof #703 shows that the following formulas are inconsistent:
% 204.02/34.85  ----------------------------------------------------------------
% 204.02/34.85    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.02/34.85    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.02/34.85    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.85    (4)   ~ (all_52_5 = all_52_13)
% 204.02/34.85    (5)  op(all_52_7, all_52_7) = e0
% 204.02/34.85    (6)   ~ (all_52_9 = all_52_13)
% 204.02/34.85    (7)  op(all_52_5, all_52_5) = e1
% 204.02/34.85    (8)   ~ (e3 = e0)
% 204.02/34.85    (9)   ~ (all_52_3 = all_52_19)
% 204.02/34.85    (10)   ~ (all_52_17 = all_52_25)
% 204.02/34.85    (11)  all_56_4 = all_52_3
% 204.02/34.85    (12)  all_58_9 = all_52_25
% 204.02/34.85    (13)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.02/34.85    (14)  op(e2, all_4_1) = e3
% 204.02/34.85    (15)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.02/34.85    (16)  op(e2, e2) = all_4_2
% 204.02/34.85    (17)  all_58_11 = all_52_29
% 204.02/34.85    (18)  all_56_5 = all_4_2
% 204.02/34.85    (19)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.02/34.85    (20)   ~ (all_52_3 = all_52_27)
% 204.02/34.85    (21)  op(e0, e0) = all_14_2
% 204.02/34.85    (22)   ~ (all_4_1 = e1)
% 204.02/34.85    (23)  all_56_9 = all_52_13
% 204.02/34.85    (24)   ~ (all_52_13 = all_10_2)
% 204.02/34.85    (25)  all_58_10 = all_52_27
% 204.02/34.85    (26)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.02/34.85    (27)  all_56_8 = all_52_5
% 204.02/34.85    (28)  op(all_52_9, all_52_9) = all_52_8
% 204.02/34.85    (29)   ~ (all_52_25 = all_52_29)
% 204.02/34.85    (30)  all_58_7 = all_52_13
% 204.02/34.85    (31)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.02/34.85    (32)  all_58_12 = all_52_7
% 204.02/34.85    (33)   ~ (all_52_7 = all_14_2)
% 204.02/34.85    (34)  all_58_2 = all_52_3
% 204.02/34.85    (35)  all_56_2 = all_52_17
% 204.02/34.85    (36)  op(all_4_2, e2) = all_4_1
% 204.02/34.85    (37)  op(all_52_3, all_52_3) = e2
% 204.02/34.85    (38)   ~ (all_10_2 = e3)
% 204.02/34.85    (39)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.02/34.85    (40)   ~ (all_52_13 = all_4_2)
% 204.02/34.85    (41)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.02/34.85    (42)   ~ (all_52_9 = all_52_25)
% 204.02/34.85    (43)  all_58_8 = all_10_2
% 204.02/34.85    (44)   ~ (all_52_5 = all_10_2)
% 204.02/34.85    (45)  all_56_12 = all_52_7
% 204.02/34.85    (46)   ~ (all_52_17 = e3)
% 204.02/34.85    (47)   ~ (all_52_3 = all_52_7)
% 204.02/34.85    (48)  all_58_5 = all_52_19
% 204.02/34.85    (49)  all_56_1 = all_52_9
% 204.02/34.85    (50)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.02/34.85    (51)  all_58_6 = all_52_5
% 204.02/34.85    (52)  op(e3, e2) = all_52_9
% 204.02/34.85    (53)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.02/34.85    (54)   ~ (all_52_9 = all_52_17)
% 204.02/34.85    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.85    (56)  all_58_14 = e3
% 204.02/34.85    (57)   ~ (all_52_3 = all_4_2)
% 204.02/34.85    (58)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.02/34.85    (59)   ~ (all_52_13 = all_52_29)
% 204.02/34.85    (60)  all_58_4 = all_52_17
% 204.02/34.85    (61)  all_56_5 = e3
% 204.02/34.85  
% 204.02/34.85  Begin of proof
% 204.02/34.85  | 
% 204.02/34.85  | COMBINE_EQS: (18), (61) imply:
% 204.02/34.85  |   (62)  all_4_2 = e3
% 204.02/34.85  | 
% 204.02/34.85  | SIMP: (62) implies:
% 204.02/34.85  |   (63)  all_4_2 = e3
% 204.02/34.85  | 
% 204.02/34.85  | REDUCE: (57), (63) imply:
% 204.02/34.85  |   (64)   ~ (all_52_3 = e3)
% 204.02/34.85  | 
% 204.02/34.85  | REDUCE: (40), (63) imply:
% 204.02/34.85  |   (65)   ~ (all_52_13 = e3)
% 204.02/34.85  | 
% 204.02/34.85  | REDUCE: (36), (63) imply:
% 204.02/34.85  |   (66)  op(e3, e2) = all_4_1
% 204.02/34.85  | 
% 204.02/34.85  | REDUCE: (16), (63) imply:
% 204.02/34.85  |   (67)  op(e2, e2) = e3
% 204.02/34.85  | 
% 204.02/34.85  | BETA: splitting (41) gives:
% 204.02/34.85  | 
% 204.02/34.85  | Case 1:
% 204.02/34.85  | | 
% 204.02/34.85  | |   (68)  all_58_7 = e3
% 204.02/34.85  | | 
% 204.02/34.85  | | COMBINE_EQS: (30), (68) imply:
% 204.02/34.85  | |   (69)  all_52_13 = e3
% 204.02/34.85  | | 
% 204.02/34.85  | | REDUCE: (65), (69) imply:
% 204.02/34.85  | |   (70)  $false
% 204.02/34.85  | | 
% 204.02/34.85  | | CLOSE: (70) is inconsistent.
% 204.02/34.85  | | 
% 204.02/34.85  | Case 2:
% 204.02/34.85  | | 
% 204.02/34.85  | |   (71)  all_58_8 = e3 | all_58_11 = e3
% 204.02/34.85  | | 
% 204.02/34.85  | | BETA: splitting (71) gives:
% 204.02/34.85  | | 
% 204.02/34.85  | | Case 1:
% 204.02/34.85  | | | 
% 204.02/34.85  | | |   (72)  all_58_8 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | COMBINE_EQS: (43), (72) imply:
% 204.02/34.85  | | |   (73)  all_10_2 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (38), (73) imply:
% 204.02/34.85  | | |   (74)  $false
% 204.02/34.85  | | | 
% 204.02/34.85  | | | CLOSE: (74) is inconsistent.
% 204.02/34.85  | | | 
% 204.02/34.85  | | Case 2:
% 204.02/34.85  | | | 
% 204.02/34.85  | | |   (75)  all_58_11 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | COMBINE_EQS: (17), (75) imply:
% 204.02/34.85  | | |   (76)  all_52_29 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | SIMP: (76) implies:
% 204.02/34.85  | | |   (77)  all_52_29 = e3
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (29), (77) imply:
% 204.02/34.85  | | |   (78)   ~ (all_52_25 = e3)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | GROUND_INST: instantiating (3) with all_52_9, all_4_1, e2, e3, simplifying
% 204.02/34.85  | | |              with (52), (66) gives:
% 204.02/34.85  | | |   (79)  all_52_9 = all_4_1
% 204.02/34.85  | | | 
% 204.02/34.85  | | | COMBINE_EQS: (49), (79) imply:
% 204.02/34.85  | | |   (80)  all_56_1 = all_4_1
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (6), (79) imply:
% 204.02/34.85  | | |   (81)   ~ (all_52_13 = all_4_1)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | SIMP: (81) implies:
% 204.02/34.85  | | |   (82)   ~ (all_52_13 = all_4_1)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (54), (79) imply:
% 204.02/34.85  | | |   (83)   ~ (all_52_17 = all_4_1)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | SIMP: (83) implies:
% 204.02/34.85  | | |   (84)   ~ (all_52_17 = all_4_1)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (42), (79) imply:
% 204.02/34.85  | | |   (85)   ~ (all_52_25 = all_4_1)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | SIMP: (85) implies:
% 204.02/34.85  | | |   (86)   ~ (all_52_25 = all_4_1)
% 204.02/34.85  | | | 
% 204.02/34.85  | | | REDUCE: (28), (79) imply:
% 204.02/34.85  | | |   (87)  op(all_4_1, all_4_1) = all_52_8
% 204.02/34.85  | | | 
% 204.02/34.85  | | | BETA: splitting (55) gives:
% 204.02/34.85  | | | 
% 204.02/34.85  | | | Case 1:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (88)  all_56_9 = e3
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REF_CLOSE: (23), (65), (88) are inconsistent by sub-proof #958.
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | Case 2:
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | |   (89)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 204.02/34.85  | | | |            (13), (14), (15), (19), (20), (21), (22), (23), (24), (25),
% 204.02/34.85  | | | |            (26), (27), (31), (32), (33), (34), (35), (37), (39), (43),
% 204.02/34.85  | | | |            (44), (45), (46), (47), (48), (50), (51), (53), (56), (58),
% 204.02/34.85  | | | |            (60), (64), (67), (75), (78), (80), (82), (84), (86), (87),
% 204.02/34.85  | | | |            (89) are inconsistent by sub-proof #752.
% 204.02/34.85  | | | | 
% 204.02/34.85  | | | End of split
% 204.02/34.85  | | | 
% 204.02/34.85  | | End of split
% 204.02/34.85  | | 
% 204.02/34.85  | End of split
% 204.02/34.85  | 
% 204.02/34.85  End of proof
% 204.02/34.85  
% 204.02/34.85  Sub-proof #704 shows that the following formulas are inconsistent:
% 204.02/34.85  ----------------------------------------------------------------
% 204.02/34.85    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.85    (2)  op(all_52_5, all_52_5) = e1
% 204.02/34.85    (3)  all_58_0 = all_6_2
% 204.02/34.85    (4)  op(e2, e2) = all_4_2
% 204.02/34.85    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.02/34.86    (6)  op(all_6_2, all_6_2) = e3
% 204.02/34.86    (7)   ~ (all_52_5 = all_52_7)
% 204.02/34.86    (8)  all_58_12 = all_52_7
% 204.02/34.86    (9)  all_58_2 = all_52_3
% 204.02/34.86    (10)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.02/34.86    (11)  op(all_52_3, all_52_3) = e2
% 204.02/34.86    (12)  all_52_5 = e3
% 204.02/34.86    (13)   ~ (all_52_5 = all_10_2)
% 204.02/34.86    (14)   ~ (all_52_5 = all_6_2)
% 204.02/34.86    (15)  op(e3, e3) = all_6_2
% 204.02/34.86    (16)  all_58_6 = all_52_5
% 204.02/34.86    (17)  op(e1, e1) = all_10_2
% 204.02/34.86    (18)   ~ (all_52_3 = all_4_2)
% 204.02/34.86  
% 204.02/34.86  Begin of proof
% 204.02/34.86  | 
% 204.02/34.86  | REDUCE: (7), (12) imply:
% 204.02/34.86  |   (19)   ~ (all_52_7 = e3)
% 204.02/34.86  | 
% 204.02/34.86  | SIMP: (19) implies:
% 204.02/34.86  |   (20)   ~ (all_52_7 = e3)
% 204.02/34.86  | 
% 204.02/34.86  | REDUCE: (12), (14) imply:
% 204.02/34.86  |   (21)   ~ (all_6_2 = e3)
% 204.02/34.86  | 
% 204.02/34.86  | SIMP: (21) implies:
% 204.02/34.86  |   (22)   ~ (all_6_2 = e3)
% 204.02/34.86  | 
% 204.02/34.86  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (15),
% 204.02/34.86  |            (16), (17), (18), (20), (22) are inconsistent by sub-proof #1363.
% 204.02/34.86  | 
% 204.02/34.86  End of proof
% 204.02/34.86  
% 204.02/34.86  Sub-proof #705 shows that the following formulas are inconsistent:
% 204.02/34.86  ----------------------------------------------------------------
% 204.02/34.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.02/34.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.02/34.86    (2)  op(all_52_5, all_52_5) = e1
% 204.02/34.86    (3)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.02/34.86    (4)   ~ (all_52_3 = e1)
% 204.02/34.86    (5)  all_58_12 = all_52_7
% 204.02/34.86    (6)  all_58_2 = all_52_3
% 204.02/34.86    (7)   ~ (all_52_5 = all_10_2)
% 204.02/34.86    (8)   ~ (all_52_7 = e1)
% 204.02/34.86    (9)  all_58_6 = all_52_5
% 204.02/34.86    (10)  op(e1, e1) = all_10_2
% 204.02/34.86  
% 204.02/34.86  Begin of proof
% 204.02/34.86  | 
% 204.02/34.86  | BETA: splitting (3) gives:
% 204.02/34.86  | 
% 204.02/34.86  | Case 1:
% 204.02/34.86  | | 
% 204.02/34.86  | |   (11)  all_58_2 = e1
% 204.02/34.86  | | 
% 204.02/34.86  | | COMBINE_EQS: (6), (11) imply:
% 204.02/34.86  | |   (12)  all_52_3 = e1
% 204.02/34.86  | | 
% 204.05/34.86  | | REDUCE: (4), (12) imply:
% 204.05/34.86  | |   (13)  $false
% 204.05/34.86  | | 
% 204.05/34.86  | | CLOSE: (13) is inconsistent.
% 204.05/34.86  | | 
% 204.05/34.86  | Case 2:
% 204.05/34.86  | | 
% 204.05/34.86  | |   (14)  all_58_6 = e1 | all_58_12 = e1
% 204.05/34.86  | | 
% 204.05/34.86  | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (14) are inconsistent by
% 204.05/34.86  | |            sub-proof #851.
% 204.05/34.86  | | 
% 204.05/34.86  | End of split
% 204.05/34.86  | 
% 204.05/34.86  End of proof
% 204.05/34.86  
% 204.05/34.86  Sub-proof #706 shows that the following formulas are inconsistent:
% 204.05/34.86  ----------------------------------------------------------------
% 204.05/34.86    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.05/34.86    (2)  all_58_14 = all_52_23
% 204.05/34.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.86    (4)  all_58_1 = all_52_9
% 204.05/34.86    (5)  op(all_52_5, all_52_5) = e1
% 204.05/34.86    (6)   ~ (e3 = e0)
% 204.05/34.86    (7)   ~ (all_52_3 = all_52_19)
% 204.05/34.86    (8)   ~ (all_52_17 = all_52_25)
% 204.05/34.86    (9)  op(all_14_2, e0) = all_14_1
% 204.05/34.86    (10)  all_58_13 = e3
% 204.05/34.86    (11)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.05/34.86    (12)  op(e0, all_14_1) = e1
% 204.05/34.86    (13)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.86    (14)  all_58_9 = all_52_25
% 204.05/34.86    (15)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.05/34.86    (16)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.05/34.86    (17)  op(all_52_27, all_52_27) = all_52_26
% 204.05/34.86    (18)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.86    (19)  op(e2, e2) = all_4_2
% 204.05/34.86    (20)  all_58_11 = all_52_29
% 204.05/34.86    (21)   ~ (all_52_25 = all_14_2)
% 204.05/34.86    (22)   ~ (all_52_3 = all_52_27)
% 204.05/34.86    (23)  op(all_10_2, e1) = all_10_1
% 204.05/34.86    (24)  op(e0, e0) = all_14_2
% 204.05/34.86    (25)  all_56_15 = all_14_2
% 204.05/34.86    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.86    (27)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.86    (28)  op(e1, e0) = all_52_29
% 204.05/34.86    (29)   ~ (e2 = e1)
% 204.05/34.86    (30)  all_58_10 = all_52_27
% 204.05/34.86    (31)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.86    (32)  all_56_8 = all_52_5
% 204.05/34.86    (33)   ~ (all_52_19 = all_52_23)
% 204.05/34.86    (34)   ~ (all_52_29 = all_10_2)
% 204.05/34.86    (35)  all_58_7 = all_52_13
% 204.05/34.86    (36)   ~ (all_52_5 = all_52_7)
% 204.05/34.86    (37)  all_58_12 = all_52_7
% 204.05/34.86    (38)   ~ (all_52_7 = all_14_2)
% 204.05/34.86    (39)   ~ (all_14_2 = e0)
% 204.05/34.86    (40)  all_58_2 = all_52_3
% 204.05/34.86    (41)   ~ (all_52_23 = e3)
% 204.05/34.86    (42)  op(all_52_3, all_52_3) = e2
% 204.05/34.86    (43)   ~ (all_52_5 = all_52_29)
% 204.05/34.86    (44)   ~ (all_10_2 = e3)
% 204.05/34.86    (45)   ~ (all_52_19 = all_52_27)
% 204.05/34.86    (46)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.86    (47)   ~ (all_52_13 = all_4_2)
% 204.05/34.86    (48)  op(e0, e3) = all_52_7
% 204.05/34.86    (49)  all_58_15 = all_14_2
% 204.05/34.86    (50)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.05/34.86    (51)  op(all_52_23, all_52_23) = all_52_22
% 204.05/34.86    (52)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.05/34.86    (53)  all_58_8 = all_10_2
% 204.05/34.86    (54)   ~ (all_52_5 = all_10_2)
% 204.05/34.86    (55)  all_56_12 = all_52_7
% 204.05/34.86    (56)  op(all_52_17, all_52_17) = all_52_16
% 204.05/34.86    (57)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.86    (58)   ~ (all_52_9 = e1)
% 204.05/34.86    (59)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.86    (60)  all_58_5 = all_52_19
% 204.05/34.86    (61)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.86    (62)   ~ (all_52_27 = all_4_2)
% 204.05/34.86    (63)  all_58_6 = all_52_5
% 204.05/34.86    (64)   ~ (e1 = e0)
% 204.05/34.86    (65)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.86    (66)  op(e2, e0) = all_52_27
% 204.05/34.86    (67)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.05/34.86    (68)  op(e1, e1) = all_10_2
% 204.05/34.86    (69)  all_58_3 = all_4_2
% 204.05/34.86    (70)   ~ (all_52_19 = all_4_2)
% 204.05/34.86    (71)  all_58_4 = all_52_17
% 204.05/34.86    (72)   ~ (all_14_2 = e3)
% 204.05/34.86  
% 204.05/34.86  Begin of proof
% 204.05/34.86  | 
% 204.05/34.86  | BETA: splitting (61) gives:
% 204.05/34.86  | 
% 204.05/34.86  | Case 1:
% 204.05/34.86  | | 
% 204.05/34.86  | |   (73)  all_58_5 = e3
% 204.05/34.86  | | 
% 204.05/34.86  | | COMBINE_EQS: (60), (73) imply:
% 204.05/34.86  | |   (74)  all_52_19 = e3
% 204.05/34.86  | | 
% 204.05/34.86  | | SIMP: (74) implies:
% 204.05/34.86  | |   (75)  all_52_19 = e3
% 204.05/34.86  | | 
% 204.05/34.86  | | REDUCE: (7), (75) imply:
% 204.05/34.86  | |   (76)   ~ (all_52_3 = e3)
% 204.05/34.86  | | 
% 204.05/34.86  | | REDUCE: (33), (75) imply:
% 204.05/34.86  | |   (77)   ~ (all_52_23 = e3)
% 204.05/34.86  | | 
% 204.05/34.86  | | REDUCE: (45), (75) imply:
% 204.05/34.86  | |   (78)   ~ (all_52_27 = e3)
% 204.05/34.86  | | 
% 204.05/34.86  | | SIMP: (78) implies:
% 204.05/34.86  | |   (79)   ~ (all_52_27 = e3)
% 204.05/34.86  | | 
% 204.05/34.86  | | REDUCE: (70), (75) imply:
% 204.05/34.86  | |   (80)   ~ (all_4_2 = e3)
% 204.05/34.86  | | 
% 204.05/34.86  | | SIMP: (80) implies:
% 204.05/34.86  | |   (81)   ~ (all_4_2 = e3)
% 204.05/34.86  | | 
% 204.05/34.86  | | BETA: splitting (65) gives:
% 204.05/34.86  | | 
% 204.05/34.86  | | Case 1:
% 204.05/34.86  | | | 
% 204.05/34.86  | | |   (82)  all_58_10 = e3
% 204.05/34.86  | | | 
% 204.05/34.86  | | | REF_CLOSE: (30), (79), (82) are inconsistent by sub-proof #1301.
% 204.05/34.86  | | | 
% 204.05/34.86  | | Case 2:
% 204.05/34.86  | | | 
% 204.05/34.86  | | |   (83)  all_58_11 = e3 | all_58_15 = e3
% 204.05/34.86  | | | 
% 204.05/34.86  | | | BETA: splitting (83) gives:
% 204.05/34.86  | | | 
% 204.05/34.86  | | | Case 1:
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | |   (84)  all_58_11 = e3
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | COMBINE_EQS: (20), (84) imply:
% 204.05/34.86  | | | |   (85)  all_52_29 = e3
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | SIMP: (85) implies:
% 204.05/34.86  | | | |   (86)  all_52_29 = e3
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | REDUCE: (43), (86) imply:
% 204.05/34.86  | | | |   (87)   ~ (all_52_5 = e3)
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | REDUCE: (34), (86) imply:
% 204.05/34.86  | | | |   (88)   ~ (all_10_2 = e3)
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | REDUCE: (28), (86) imply:
% 204.05/34.86  | | | |   (89)  op(e1, e0) = e3
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | BETA: splitting (16) gives:
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | Case 1:
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | |   (90)  all_58_4 = e1
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | COMBINE_EQS: (71), (90) imply:
% 204.05/34.86  | | | | |   (91)  all_52_17 = e1
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | SIMP: (91) implies:
% 204.05/34.86  | | | | |   (92)  all_52_17 = e1
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | REDUCE: (8), (92) imply:
% 204.05/34.86  | | | | |   (93)   ~ (all_52_25 = e1)
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | SIMP: (93) implies:
% 204.05/34.86  | | | | |   (94)   ~ (all_52_25 = e1)
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | REDUCE: (56), (92) imply:
% 204.05/34.86  | | | | |   (95)  op(e1, e1) = all_52_16
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_16, e1, e1,
% 204.05/34.86  | | | | |              simplifying with (68), (95) gives:
% 204.05/34.86  | | | | |   (96)  all_52_16 = all_10_2
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | BETA: splitting (57) gives:
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | Case 1:
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | |   (97)  all_58_6 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | COMBINE_EQS: (63), (97) imply:
% 204.05/34.86  | | | | | |   (98)  all_52_5 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | SIMP: (98) implies:
% 204.05/34.86  | | | | | |   (99)  all_52_5 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | REF_CLOSE: (3), (5), (54), (68), (99) are inconsistent by sub-proof
% 204.05/34.86  | | | | | |            #871.
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | Case 2:
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | |   (100)   ~ (all_58_6 = e1)
% 204.05/34.86  | | | | | |   (101)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | REDUCE: (63), (100) imply:
% 204.05/34.86  | | | | | |   (102)   ~ (all_52_5 = e1)
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | BETA: splitting (50) gives:
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | Case 1:
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | |   (103)  all_58_3 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | COMBINE_EQS: (69), (103) imply:
% 204.05/34.86  | | | | | | |   (104)  all_4_2 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REDUCE: (47), (104) imply:
% 204.05/34.86  | | | | | | |   (105)   ~ (all_52_13 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REDUCE: (62), (104) imply:
% 204.05/34.86  | | | | | | |   (106)   ~ (all_52_27 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REDUCE: (81), (104) imply:
% 204.05/34.86  | | | | | | |   (107)   ~ (e3 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | SIMP: (107) implies:
% 204.05/34.86  | | | | | | |   (108)   ~ (e3 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | BETA: splitting (26) gives:
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | |   (109)  all_58_9 = e1
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | REF_CLOSE: (14), (94), (109) are inconsistent by sub-proof #856.
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | |   (110)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | BETA: splitting (110) gives:
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | |   (111)  all_58_10 = e1
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | REF_CLOSE: (30), (106), (111) are inconsistent by sub-proof
% 204.05/34.86  | | | | | | | | |            #861.
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | |   (112)  all_58_11 = e1 | all_58_15 = e1
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | BETA: splitting (112) gives:
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | |   (113)  all_58_11 = e1
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | COMBINE_EQS: (84), (113) imply:
% 204.05/34.86  | | | | | | | | | |   (114)  e3 = e1
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REF_CLOSE: (2), (41), (44), (53), (61), (73), (108), (114)
% 204.05/34.86  | | | | | | | | | |            are inconsistent by sub-proof #712.
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | |   (115)  all_58_15 = e1
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | COMBINE_EQS: (49), (115) imply:
% 204.05/34.86  | | | | | | | | | |   (116)  all_14_2 = e1
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REDUCE: (38), (116) imply:
% 204.05/34.86  | | | | | | | | | |   (117)   ~ (all_52_7 = e1)
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REF_CLOSE: (2), (3), (13), (14), (22), (23), (26), (27),
% 204.05/34.86  | | | | | | | | | |            (29), (30), (35), (37), (40), (41), (42), (44),
% 204.05/34.86  | | | | | | | | | |            (49), (53), (59), (61), (63), (68), (73), (76),
% 204.05/34.86  | | | | | | | | | |            (84), (94), (101), (102), (105), (117) are
% 204.05/34.86  | | | | | | | | | |            inconsistent by sub-proof #711.
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | End of split
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | End of split
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | End of split
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | Case 2:
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | |   (118)   ~ (all_58_3 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REDUCE: (69), (118) imply:
% 204.05/34.86  | | | | | | |   (119)   ~ (all_4_2 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | BETA: splitting (15) gives:
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | |   (120)  all_58_6 = e2
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | COMBINE_EQS: (63), (120) imply:
% 204.05/34.86  | | | | | | | |   (121)  all_52_5 = e2
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | REDUCE: (5), (121) imply:
% 204.05/34.86  | | | | | | | |   (122)  op(e2, e2) = e1
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | REF_CLOSE: (3), (19), (119), (122) are inconsistent by sub-proof
% 204.05/34.86  | | | | | | | |            #1193.
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | |   (123)   ~ (all_58_6 = e2)
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | REDUCE: (63), (123) imply:
% 204.05/34.86  | | | | | | | |   (124)   ~ (all_52_5 = e2)
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | BETA: splitting (31) gives:
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | |   (125)  all_56_8 = e2
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | REF_CLOSE: (32), (124), (125) are inconsistent by sub-proof
% 204.05/34.86  | | | | | | | | |            #1022.
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | |   (126)   ~ (all_56_8 = e2)
% 204.05/34.86  | | | | | | | | |   (127)  all_56_8 = e1 | all_56_8 = e0
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | BETA: splitting (127) gives:
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | |   (128)  all_56_8 = e1
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REF_CLOSE: (32), (102), (128) are inconsistent by sub-proof
% 204.05/34.86  | | | | | | | | | |            #707.
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | |   (129)  all_56_8 = e0
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | COMBINE_EQS: (32), (129) imply:
% 204.05/34.86  | | | | | | | | | |   (130)  all_52_5 = e0
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | SIMP: (130) implies:
% 204.05/34.86  | | | | | | | | | |   (131)  all_52_5 = e0
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REDUCE: (36), (131) imply:
% 204.05/34.86  | | | | | | | | | |   (132)   ~ (all_52_7 = e0)
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | SIMP: (132) implies:
% 204.05/34.86  | | | | | | | | | |   (133)   ~ (all_52_7 = e0)
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REDUCE: (87), (131) imply:
% 204.05/34.86  | | | | | | | | | |   (134)   ~ (e3 = e0)
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | REDUCE: (5), (131) imply:
% 204.05/34.86  | | | | | | | | | |   (135)  op(e0, e0) = e1
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | BETA: splitting (46) gives:
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | |   (136)  all_58_12 = e0
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | REF_CLOSE: (37), (133), (136) are inconsistent by sub-proof
% 204.05/34.86  | | | | | | | | | | |            #1067.
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | |   (137)  all_58_13 = e0 | all_58_14 = e0
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | BETA: splitting (137) gives:
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | Case 1:
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | |   (138)  all_58_13 = e0
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | REF_CLOSE: (6), (10), (138) are inconsistent by sub-proof
% 204.05/34.86  | | | | | | | | | | | |            #1172.
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | Case 2:
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | |   (139)  all_58_14 = e0
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | COMBINE_EQS: (2), (139) imply:
% 204.05/34.86  | | | | | | | | | | | |   (140)  all_52_23 = e0
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | SIMP: (140) implies:
% 204.05/34.86  | | | | | | | | | | | |   (141)  all_52_23 = e0
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | REDUCE: (51), (141) imply:
% 204.05/34.86  | | | | | | | | | | | |   (142)  op(e0, e0) = all_52_22
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_22, e0,
% 204.05/34.86  | | | | | | | | | | | |              e0, simplifying with (24), (142) gives:
% 204.05/34.86  | | | | | | | | | | | |   (143)  all_52_22 = all_14_2
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_22, e0, e0,
% 204.05/34.86  | | | | | | | | | | | |              simplifying with (135), (142) gives:
% 204.05/34.86  | | | | | | | | | | | |   (144)  all_52_22 = e1
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | COMBINE_EQS: (143), (144) imply:
% 204.05/34.86  | | | | | | | | | | | |   (145)  all_14_2 = e1
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | SIMP: (145) implies:
% 204.05/34.86  | | | | | | | | | | | |   (146)  all_14_2 = e1
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | REDUCE: (38), (146) imply:
% 204.05/34.86  | | | | | | | | | | | |   (147)   ~ (all_52_7 = e1)
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | REDUCE: (9), (146) imply:
% 204.05/34.86  | | | | | | | | | | | |   (148)  op(e1, e0) = all_14_1
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | | REF_CLOSE: (3), (12), (18), (31), (32), (36), (48), (55),
% 204.05/34.86  | | | | | | | | | | | |            (63), (67), (89), (102), (124), (147), (148) are
% 204.05/34.86  | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 204.05/34.86  | | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | | End of split
% 204.05/34.86  | | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | | End of split
% 204.05/34.86  | | | | | | | | | | 
% 204.05/34.86  | | | | | | | | | End of split
% 204.05/34.86  | | | | | | | | | 
% 204.05/34.86  | | | | | | | | End of split
% 204.05/34.86  | | | | | | | | 
% 204.05/34.86  | | | | | | | End of split
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | End of split
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | End of split
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | Case 2:
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | |   (149)   ~ (all_58_4 = e1)
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | REDUCE: (71), (149) imply:
% 204.05/34.86  | | | | |   (150)   ~ (all_52_17 = e1)
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | BETA: splitting (11) gives:
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | | Case 1:
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | |   (151)  all_58_1 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | COMBINE_EQS: (4), (151) imply:
% 204.05/34.86  | | | | | |   (152)  all_52_9 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | REDUCE: (58), (152) imply:
% 204.05/34.86  | | | | | |   (153)  $false
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | CLOSE: (153) is inconsistent.
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | Case 2:
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | |   (154)  all_58_4 = e1 | all_58_9 = e1
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | BETA: splitting (154) gives:
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | | Case 1:
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | |   (155)  all_58_4 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | COMBINE_EQS: (71), (155) imply:
% 204.05/34.86  | | | | | | |   (156)  all_52_17 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | SIMP: (156) implies:
% 204.05/34.86  | | | | | | |   (157)  all_52_17 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REDUCE: (150), (157) imply:
% 204.05/34.86  | | | | | | |   (158)  $false
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | CLOSE: (158) is inconsistent.
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | Case 2:
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | |   (159)  all_58_9 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | COMBINE_EQS: (14), (159) imply:
% 204.05/34.86  | | | | | | |   (160)  all_52_25 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | SIMP: (160) implies:
% 204.05/34.86  | | | | | | |   (161)  all_52_25 = e1
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REDUCE: (21), (161) imply:
% 204.05/34.86  | | | | | | |   (162)   ~ (all_14_2 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | SIMP: (162) implies:
% 204.05/34.86  | | | | | | |   (163)   ~ (all_14_2 = e1)
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | | REF_CLOSE: (1), (3), (6), (9), (12), (17), (24), (25), (30), (39),
% 204.05/34.86  | | | | | | |            (52), (64), (66), (84), (159), (163) are inconsistent
% 204.05/34.86  | | | | | | |            by sub-proof #862.
% 204.05/34.86  | | | | | | | 
% 204.05/34.86  | | | | | | End of split
% 204.05/34.86  | | | | | | 
% 204.05/34.86  | | | | | End of split
% 204.05/34.86  | | | | | 
% 204.05/34.86  | | | | End of split
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | Case 2:
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | |   (164)  all_58_15 = e3
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | COMBINE_EQS: (49), (164) imply:
% 204.05/34.86  | | | |   (165)  all_14_2 = e3
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | REDUCE: (72), (165) imply:
% 204.05/34.86  | | | |   (166)  $false
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | | CLOSE: (166) is inconsistent.
% 204.05/34.86  | | | | 
% 204.05/34.86  | | | End of split
% 204.05/34.86  | | | 
% 204.05/34.86  | | End of split
% 204.05/34.86  | | 
% 204.05/34.86  | Case 2:
% 204.05/34.86  | | 
% 204.05/34.86  | |   (167)  all_58_8 = e3 | all_58_14 = e3
% 204.05/34.86  | | 
% 204.05/34.86  | | REF_CLOSE: (2), (41), (44), (53), (167) are inconsistent by sub-proof #1304.
% 204.05/34.86  | | 
% 204.05/34.86  | End of split
% 204.05/34.86  | 
% 204.05/34.86  End of proof
% 204.05/34.86  
% 204.05/34.86  Sub-proof #707 shows that the following formulas are inconsistent:
% 204.05/34.86  ----------------------------------------------------------------
% 204.05/34.86    (1)  all_56_8 = all_52_5
% 204.05/34.86    (2)  all_56_8 = e1
% 204.05/34.86    (3)   ~ (all_52_5 = e1)
% 204.05/34.86  
% 204.05/34.86  Begin of proof
% 204.05/34.86  | 
% 204.05/34.86  | COMBINE_EQS: (1), (2) imply:
% 204.05/34.86  |   (4)  all_52_5 = e1
% 204.05/34.86  | 
% 204.05/34.86  | SIMP: (4) implies:
% 204.05/34.86  |   (5)  all_52_5 = e1
% 204.05/34.86  | 
% 204.05/34.86  | REDUCE: (3), (5) imply:
% 204.05/34.86  |   (6)  $false
% 204.05/34.86  | 
% 204.05/34.86  | CLOSE: (6) is inconsistent.
% 204.05/34.86  | 
% 204.05/34.86  End of proof
% 204.05/34.86  
% 204.05/34.86  Sub-proof #708 shows that the following formulas are inconsistent:
% 204.05/34.86  ----------------------------------------------------------------
% 204.05/34.86    (1)  all_58_14 = all_52_23
% 204.05/34.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.86    (3)  op(all_52_7, all_52_7) = e0
% 204.05/34.86    (4)  all_58_1 = all_52_9
% 204.05/34.86    (5)   ~ (all_52_9 = all_52_13)
% 204.05/34.86    (6)  op(all_52_5, all_52_5) = e1
% 204.05/34.86    (7)   ~ (e3 = e0)
% 204.05/34.86    (8)   ~ (all_52_3 = all_52_19)
% 204.05/34.86    (9)  all_58_0 = all_6_2
% 204.05/34.86    (10)  all_58_13 = e3
% 204.05/34.86    (11)  op(all_52_19, all_52_19) = all_52_18
% 204.05/34.86    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.86    (13)  all_58_9 = all_52_25
% 204.05/34.86    (14)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.05/34.86    (15)  op(e2, e2) = all_4_2
% 204.05/34.86    (16)  all_58_11 = all_52_29
% 204.05/34.86    (17)   ~ (all_52_3 = all_52_27)
% 204.05/34.86    (18)  op(all_10_2, e1) = all_10_1
% 204.05/34.86    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.86    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.86    (21)  all_56_11 = all_52_29
% 204.05/34.86    (22)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.05/34.86    (23)   ~ (e2 = e1)
% 204.05/34.86    (24)   ~ (all_6_0 = e1)
% 204.05/34.86    (25)  all_58_10 = all_52_27
% 204.05/34.86    (26)   ~ (all_52_19 = all_52_23)
% 204.05/34.86    (27)   ~ (all_52_29 = all_10_2)
% 204.05/34.86    (28)  all_58_7 = all_52_13
% 204.05/34.86    (29)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.86    (30)  op(all_6_2, all_6_2) = e3
% 204.05/34.86    (31)  all_58_12 = all_52_7
% 204.05/34.86    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.86    (33)   ~ (all_52_7 = e3)
% 204.05/34.86    (34)  all_58_2 = all_52_3
% 204.05/34.86    (35)  all_56_2 = all_52_17
% 204.05/34.86    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.86    (37)  op(e3, all_6_1) = all_6_0
% 204.05/34.86    (38)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.86    (39)   ~ (e2 = e0)
% 204.05/34.86    (40)   ~ (all_52_23 = e3)
% 204.05/34.86    (41)  op(all_52_3, all_52_3) = e2
% 204.05/34.86    (42)   ~ (all_52_5 = all_52_29)
% 204.05/34.86    (43)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.86    (44)   ~ (all_52_19 = all_52_27)
% 204.05/34.86    (45)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.05/34.86    (46)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.86    (47)   ~ (all_6_0 = e2)
% 204.05/34.86    (48)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.86    (49)  op(e3, e1) = all_52_17
% 204.05/34.86    (50)   ~ (all_52_9 = all_52_25)
% 204.05/34.86    (51)  all_58_15 = all_14_2
% 204.05/34.86    (52)   ~ (all_52_19 = all_10_2)
% 204.05/34.86    (53)  all_58_8 = all_10_2
% 204.05/34.86    (54)   ~ (all_52_5 = all_10_2)
% 204.05/34.86    (55)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.86    (56)   ~ (all_52_25 = all_6_2)
% 204.05/34.86    (57)   ~ (all_52_9 = all_4_2)
% 204.05/34.86    (58)   ~ (all_52_5 = all_6_2)
% 204.05/34.86    (59)  op(e3, e3) = all_6_2
% 204.05/34.86    (60)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.86    (61)   ~ (all_52_13 = e3)
% 204.05/34.86    (62)   ~ (all_52_27 = all_14_2)
% 204.05/34.86    (63)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.05/34.86    (64)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.86    (65)  all_58_5 = all_52_19
% 204.05/34.86    (66)  all_58_6 = all_52_5
% 204.05/34.86    (67)   ~ (all_52_17 = all_6_2)
% 204.05/34.86    (68)   ~ (e1 = e0)
% 204.05/34.86    (69)   ~ (all_52_9 = all_52_17)
% 204.05/34.86    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.86    (71)  all_58_1 = e1
% 204.05/34.86    (72)  op(e1, e1) = all_10_2
% 204.05/34.86    (73)   ~ (all_52_23 = all_10_2)
% 204.05/34.86    (74)  all_58_3 = all_4_2
% 204.05/34.86    (75)   ~ (all_52_3 = all_4_2)
% 204.05/34.86    (76)  op(all_6_2, e3) = all_6_1
% 204.05/34.86    (77)  all_58_4 = all_52_17
% 204.05/34.86    (78)   ~ (all_14_2 = e3)
% 204.05/34.86  
% 204.05/34.86  Begin of proof
% 204.05/34.86  | 
% 204.05/34.86  | COMBINE_EQS: (4), (71) imply:
% 204.05/34.86  |   (79)  all_52_9 = e1
% 204.05/34.86  | 
% 204.05/34.86  | REDUCE: (5), (79) imply:
% 204.05/34.86  |   (80)   ~ (all_52_13 = e1)
% 204.05/34.86  | 
% 204.05/34.86  | SIMP: (80) implies:
% 204.05/34.86  |   (81)   ~ (all_52_13 = e1)
% 204.05/34.86  | 
% 204.05/34.86  | REDUCE: (69), (79) imply:
% 204.05/34.86  |   (82)   ~ (all_52_17 = e1)
% 204.05/34.86  | 
% 204.05/34.86  | SIMP: (82) implies:
% 204.05/34.86  |   (83)   ~ (all_52_17 = e1)
% 204.05/34.86  | 
% 204.05/34.87  | REDUCE: (50), (79) imply:
% 204.05/34.87  |   (84)   ~ (all_52_25 = e1)
% 204.05/34.87  | 
% 204.05/34.87  | SIMP: (84) implies:
% 204.05/34.87  |   (85)   ~ (all_52_25 = e1)
% 204.05/34.87  | 
% 204.05/34.87  | REDUCE: (57), (79) imply:
% 204.05/34.87  |   (86)   ~ (all_4_2 = e1)
% 204.05/34.87  | 
% 204.05/34.87  | SIMP: (86) implies:
% 204.05/34.87  |   (87)   ~ (all_4_2 = e1)
% 204.05/34.87  | 
% 204.05/34.87  | BETA: splitting (22) gives:
% 204.05/34.87  | 
% 204.05/34.87  | Case 1:
% 204.05/34.87  | | 
% 204.05/34.87  | |   (88)  all_56_2 = e3
% 204.05/34.87  | | 
% 204.05/34.87  | | COMBINE_EQS: (35), (88) imply:
% 204.05/34.87  | |   (89)  all_52_17 = e3
% 204.05/34.87  | | 
% 204.05/34.87  | | REF_CLOSE: (2), (6), (9), (15), (19), (30), (31), (33), (34), (36), (41),
% 204.05/34.87  | |            (54), (59), (66), (67), (72), (75), (89) are inconsistent by
% 204.05/34.87  | |            sub-proof #1199.
% 204.05/34.87  | | 
% 204.05/34.87  | Case 2:
% 204.05/34.87  | | 
% 204.05/34.87  | |   (90)   ~ (all_56_2 = e3)
% 204.05/34.87  | | 
% 204.05/34.87  | | REDUCE: (35), (90) imply:
% 204.05/34.87  | |   (91)   ~ (all_52_17 = e3)
% 204.05/34.87  | | 
% 204.05/34.87  | | BETA: splitting (70) gives:
% 204.05/34.87  | | 
% 204.05/34.87  | | Case 1:
% 204.05/34.87  | | | 
% 204.05/34.87  | | |   (92)  all_58_4 = e3
% 204.05/34.87  | | | 
% 204.05/34.87  | | | REF_CLOSE: (77), (91), (92) are inconsistent by sub-proof #1302.
% 204.05/34.87  | | | 
% 204.05/34.87  | | Case 2:
% 204.05/34.87  | | | 
% 204.05/34.87  | | |   (93)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.87  | | | 
% 204.05/34.87  | | | BETA: splitting (63) gives:
% 204.05/34.87  | | | 
% 204.05/34.87  | | | Case 1:
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | |   (94)  all_58_0 = e3
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | COMBINE_EQS: (9), (94) imply:
% 204.05/34.87  | | | |   (95)  all_6_2 = e3
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (58), (95) imply:
% 204.05/34.87  | | | |   (96)   ~ (all_52_5 = e3)
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (56), (95) imply:
% 204.05/34.87  | | | |   (97)   ~ (all_52_25 = e3)
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (76), (95) imply:
% 204.05/34.87  | | | |   (98)  op(e3, e3) = all_6_1
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (59), (95) imply:
% 204.05/34.87  | | | |   (99)  op(e3, e3) = e3
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | GROUND_INST: instantiating (2) with e3, all_6_1, e3, e3, simplifying
% 204.05/34.87  | | | |              with (98), (99) gives:
% 204.05/34.87  | | | |   (100)  all_6_1 = e3
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (37), (100) imply:
% 204.05/34.87  | | | |   (101)  op(e3, e3) = all_6_0
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | GROUND_INST: instantiating (2) with e3, all_6_0, e3, e3, simplifying
% 204.05/34.87  | | | |              with (99), (101) gives:
% 204.05/34.87  | | | |   (102)  all_6_0 = e3
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (47), (102) imply:
% 204.05/34.87  | | | |   (103)   ~ (e3 = e2)
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (24), (102) imply:
% 204.05/34.87  | | | |   (104)   ~ (e3 = e1)
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | BETA: splitting (32) gives:
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | Case 1:
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | |   (105)  all_58_6 = e3
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | REF_CLOSE: (66), (96), (105) are inconsistent by sub-proof #1328.
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | Case 2:
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | |   (106)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (14),
% 204.05/34.87  | | | | |            (15), (16), (17), (18), (20), (21), (23), (25), (26), (27),
% 204.05/34.87  | | | | |            (28), (29), (31), (34), (38), (39), (40), (41), (42), (43),
% 204.05/34.87  | | | | |            (44), (45), (46), (48), (49), (51), (52), (53), (54), (55),
% 204.05/34.87  | | | | |            (60), (61), (62), (64), (65), (66), (68), (72), (73), (74),
% 204.05/34.87  | | | | |            (75), (77), (78), (81), (83), (85), (87), (93), (94), (97),
% 204.05/34.87  | | | | |            (103), (104), (106) are inconsistent by sub-proof #709.
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | End of split
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | Case 2:
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | |   (107)   ~ (all_58_0 = e3)
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (9), (107) imply:
% 204.05/34.87  | | | |   (108)   ~ (all_6_2 = e3)
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REF_CLOSE: (2), (6), (9), (15), (19), (30), (31), (33), (34), (36),
% 204.05/34.87  | | | |            (41), (54), (59), (66), (72), (75), (108) are inconsistent by
% 204.05/34.87  | | | |            sub-proof #1363.
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | End of split
% 204.05/34.87  | | | 
% 204.05/34.87  | | End of split
% 204.05/34.87  | | 
% 204.05/34.87  | End of split
% 204.05/34.87  | 
% 204.05/34.87  End of proof
% 204.05/34.87  
% 204.05/34.87  Sub-proof #709 shows that the following formulas are inconsistent:
% 204.05/34.87  ----------------------------------------------------------------
% 204.05/34.87    (1)  all_58_14 = all_52_23
% 204.05/34.87    (2)   ~ (e3 = e1)
% 204.05/34.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.87    (4)  op(all_52_7, all_52_7) = e0
% 204.05/34.87    (5)  op(all_52_5, all_52_5) = e1
% 204.05/34.87    (6)   ~ (e3 = e0)
% 204.05/34.87    (7)   ~ (all_52_3 = all_52_19)
% 204.05/34.87    (8)  all_58_13 = e3
% 204.05/34.87    (9)  op(all_52_19, all_52_19) = all_52_18
% 204.05/34.87    (10)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.87    (11)  all_58_9 = all_52_25
% 204.05/34.87    (12)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.05/34.87    (13)  op(e2, e2) = all_4_2
% 204.05/34.87    (14)  all_58_11 = all_52_29
% 204.05/34.87    (15)   ~ (all_52_3 = all_52_27)
% 204.05/34.87    (16)  op(all_10_2, e1) = all_10_1
% 204.05/34.87    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.87    (18)  all_56_11 = all_52_29
% 204.05/34.87    (19)   ~ (e2 = e1)
% 204.05/34.87    (20)  all_58_10 = all_52_27
% 204.05/34.87    (21)   ~ (all_52_19 = all_52_23)
% 204.05/34.87    (22)   ~ (all_52_29 = all_10_2)
% 204.05/34.87    (23)  all_58_7 = all_52_13
% 204.05/34.87    (24)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.87    (25)  all_58_12 = all_52_7
% 204.05/34.87    (26)  all_58_2 = all_52_3
% 204.05/34.87    (27)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.87    (28)   ~ (all_52_25 = e3)
% 204.05/34.87    (29)   ~ (e2 = e0)
% 204.05/34.87    (30)   ~ (all_52_23 = e3)
% 204.05/34.87    (31)  op(all_52_3, all_52_3) = e2
% 204.05/34.87    (32)   ~ (all_52_5 = all_52_29)
% 204.05/34.87    (33)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.87    (34)   ~ (all_52_19 = all_52_27)
% 204.05/34.87    (35)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.05/34.87    (36)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.87    (37)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.87    (38)   ~ (all_52_13 = e1)
% 204.05/34.87    (39)  all_58_0 = e3
% 204.05/34.87    (40)  op(e3, e1) = all_52_17
% 204.05/34.87    (41)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.87    (42)   ~ (all_52_25 = e1)
% 204.05/34.87    (43)  all_58_15 = all_14_2
% 204.05/34.87    (44)   ~ (all_52_19 = all_10_2)
% 204.05/34.87    (45)  all_58_8 = all_10_2
% 204.05/34.87    (46)   ~ (all_52_5 = all_10_2)
% 204.05/34.87    (47)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.87    (48)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.87    (49)   ~ (all_52_13 = e3)
% 204.05/34.87    (50)   ~ (all_52_27 = all_14_2)
% 204.05/34.87    (51)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.87    (52)  all_58_5 = all_52_19
% 204.05/34.87    (53)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.87    (54)  all_58_6 = all_52_5
% 204.05/34.87    (55)   ~ (e1 = e0)
% 204.05/34.87    (56)   ~ (e3 = e2)
% 204.05/34.87    (57)   ~ (all_52_17 = e1)
% 204.05/34.87    (58)  op(e1, e1) = all_10_2
% 204.05/34.87    (59)   ~ (all_52_23 = all_10_2)
% 204.05/34.87    (60)  all_58_3 = all_4_2
% 204.05/34.87    (61)   ~ (all_52_3 = all_4_2)
% 204.05/34.87    (62)   ~ (all_4_2 = e1)
% 204.05/34.87    (63)  all_58_4 = all_52_17
% 204.05/34.87    (64)   ~ (all_14_2 = e3)
% 204.05/34.87  
% 204.05/34.87  Begin of proof
% 204.05/34.87  | 
% 204.05/34.87  | BETA: splitting (48) gives:
% 204.05/34.87  | 
% 204.05/34.87  | Case 1:
% 204.05/34.87  | | 
% 204.05/34.87  | |   (65)  all_58_9 = e3
% 204.05/34.87  | | 
% 204.05/34.87  | | REF_CLOSE: (11), (28), (65) are inconsistent by sub-proof #1300.
% 204.05/34.87  | | 
% 204.05/34.87  | Case 2:
% 204.05/34.87  | | 
% 204.05/34.87  | |   (66)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.87  | | 
% 204.05/34.87  | | BETA: splitting (33) gives:
% 204.05/34.87  | | 
% 204.05/34.87  | | Case 1:
% 204.05/34.87  | | | 
% 204.05/34.87  | | |   (67)  all_58_12 = e1
% 204.05/34.87  | | | 
% 204.05/34.87  | | | COMBINE_EQS: (25), (67) imply:
% 204.05/34.87  | | |   (68)  all_52_7 = e1
% 204.05/34.87  | | | 
% 204.05/34.87  | | | SIMP: (68) implies:
% 204.05/34.87  | | |   (69)  all_52_7 = e1
% 204.05/34.87  | | | 
% 204.05/34.87  | | | REDUCE: (4), (69) imply:
% 204.05/34.87  | | |   (70)  op(e1, e1) = e0
% 204.05/34.87  | | | 
% 204.05/34.87  | | | REF_CLOSE: (1), (3), (6), (8), (37), (55), (58), (59), (67), (70) are
% 204.05/34.87  | | |            inconsistent by sub-proof #1171.
% 204.05/34.87  | | | 
% 204.05/34.87  | | Case 2:
% 204.05/34.87  | | | 
% 204.05/34.87  | | |   (71)   ~ (all_58_12 = e1)
% 204.05/34.87  | | | 
% 204.05/34.87  | | | REDUCE: (25), (71) imply:
% 204.05/34.87  | | |   (72)   ~ (all_52_7 = e1)
% 204.05/34.87  | | | 
% 204.05/34.87  | | | BETA: splitting (27) gives:
% 204.05/34.87  | | | 
% 204.05/34.87  | | | Case 1:
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | |   (73)  all_58_0 = e1
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | COMBINE_EQS: (39), (73) imply:
% 204.05/34.87  | | | |   (74)  e3 = e1
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | REDUCE: (2), (74) imply:
% 204.05/34.87  | | | |   (75)  $false
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | CLOSE: (75) is inconsistent.
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | Case 2:
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | |   (76)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | BETA: splitting (35) gives:
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | | Case 1:
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | |   (77)  all_56_11 = e3
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | COMBINE_EQS: (18), (77) imply:
% 204.05/34.87  | | | | |   (78)  all_52_29 = e3
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | SIMP: (78) implies:
% 204.05/34.87  | | | | |   (79)  all_52_29 = e3
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | COMBINE_EQS: (14), (79) imply:
% 204.05/34.87  | | | | |   (80)  all_58_11 = e3
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | REDUCE: (22), (79) imply:
% 204.05/34.87  | | | | |   (81)   ~ (all_10_2 = e3)
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | SIMP: (81) implies:
% 204.05/34.87  | | | | |   (82)   ~ (all_10_2 = e3)
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | BETA: splitting (53) gives:
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | Case 1:
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | |   (83)  all_58_5 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | COMBINE_EQS: (52), (83) imply:
% 204.05/34.87  | | | | | |   (84)  all_52_19 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | SIMP: (84) implies:
% 204.05/34.87  | | | | | |   (85)  all_52_19 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | REDUCE: (7), (85) imply:
% 204.05/34.87  | | | | | |   (86)   ~ (all_52_3 = e3)
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | REDUCE: (21), (85) imply:
% 204.05/34.87  | | | | | |   (87)   ~ (all_52_23 = e3)
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | BETA: splitting (47) gives:
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | Case 1:
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | |   (88)  all_58_6 = e1
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | COMBINE_EQS: (54), (88) imply:
% 204.05/34.87  | | | | | | |   (89)  all_52_5 = e1
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | SIMP: (89) implies:
% 204.05/34.87  | | | | | | |   (90)  all_52_5 = e1
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REF_CLOSE: (3), (5), (46), (58), (90) are inconsistent by
% 204.05/34.87  | | | | | | |            sub-proof #871.
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | Case 2:
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | |   (91)   ~ (all_58_6 = e1)
% 204.05/34.87  | | | | | | |   (92)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REDUCE: (54), (91) imply:
% 204.05/34.87  | | | | | | |   (93)   ~ (all_52_5 = e1)
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REF_CLOSE: (1), (3), (10), (11), (15), (16), (17), (19), (20),
% 204.05/34.87  | | | | | | |            (23), (25), (26), (30), (31), (38), (42), (43), (45),
% 204.05/34.87  | | | | | | |            (51), (53), (54), (58), (72), (76), (80), (82), (83),
% 204.05/34.87  | | | | | | |            (86), (92), (93) are inconsistent by sub-proof #711.
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | End of split
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | Case 2:
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | |   (94)  all_58_8 = e3 | all_58_14 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | REF_CLOSE: (1), (30), (45), (82), (94) are inconsistent by sub-proof
% 204.05/34.87  | | | | | |            #1304.
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | End of split
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | Case 2:
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | |   (95)   ~ (all_56_11 = e3)
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | REDUCE: (18), (95) imply:
% 204.05/34.87  | | | | |   (96)   ~ (all_52_29 = e3)
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | BETA: splitting (41) gives:
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | | Case 1:
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | |   (97)  all_58_7 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | COMBINE_EQS: (23), (97) imply:
% 204.05/34.87  | | | | | |   (98)  all_52_13 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | REDUCE: (49), (98) imply:
% 204.05/34.87  | | | | | |   (99)  $false
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | CLOSE: (99) is inconsistent.
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | Case 2:
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | |   (100)  all_58_8 = e3 | all_58_11 = e3
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | BETA: splitting (100) gives:
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | | Case 1:
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | |   (101)  all_58_8 = e3
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | COMBINE_EQS: (45), (101) imply:
% 204.05/34.87  | | | | | | |   (102)  all_10_2 = e3
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | SIMP: (102) implies:
% 204.05/34.87  | | | | | | |   (103)  all_10_2 = e3
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REDUCE: (46), (103) imply:
% 204.05/34.87  | | | | | | |   (104)   ~ (all_52_5 = e3)
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REDUCE: (16), (103) imply:
% 204.05/34.87  | | | | | | |   (105)  op(e3, e1) = all_10_1
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REDUCE: (58), (103) imply:
% 204.05/34.87  | | | | | | |   (106)  op(e1, e1) = e3
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | BETA: splitting (66) gives:
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | |   (107)  all_58_10 = e3
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | COMBINE_EQS: (20), (107) imply:
% 204.05/34.87  | | | | | | | |   (108)  all_52_27 = e3
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | SIMP: (108) implies:
% 204.05/34.87  | | | | | | | |   (109)  all_52_27 = e3
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | REDUCE: (15), (109) imply:
% 204.05/34.87  | | | | | | | |   (110)   ~ (all_52_3 = e3)
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | REDUCE: (34), (109) imply:
% 204.05/34.87  | | | | | | | |   (111)   ~ (all_52_19 = e3)
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | REDUCE: (50), (109) imply:
% 204.05/34.87  | | | | | | | |   (112)   ~ (all_14_2 = e3)
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 204.05/34.87  | | | | | | | |              simplifying with (40), (105) gives:
% 204.05/34.87  | | | | | | | |   (113)  all_52_17 = all_10_1
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | COMBINE_EQS: (63), (113) imply:
% 204.05/34.87  | | | | | | | |   (114)  all_58_4 = all_10_1
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | REDUCE: (57), (113) imply:
% 204.05/34.87  | | | | | | | |   (115)   ~ (all_10_1 = e1)
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | BETA: splitting (12) gives:
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | |   (116)  all_58_4 = e1
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | COMBINE_EQS: (114), (116) imply:
% 204.05/34.87  | | | | | | | | |   (117)  all_10_1 = e1
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | REDUCE: (115), (117) imply:
% 204.05/34.87  | | | | | | | | |   (118)  $false
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | CLOSE: (118) is inconsistent.
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | |   (119)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | BETA: splitting (17) gives:
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | |   (120)  all_58_9 = e1
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | COMBINE_EQS: (11), (120) imply:
% 204.05/34.87  | | | | | | | | | |   (121)  all_52_25 = e1
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | REDUCE: (42), (121) imply:
% 204.05/34.87  | | | | | | | | | |   (122)  $false
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | CLOSE: (122) is inconsistent.
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | |   (123)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | BETA: splitting (24) gives:
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | |   (124)  all_58_2 = e1
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | COMBINE_EQS: (26), (124) imply:
% 204.05/34.87  | | | | | | | | | | |   (125)  all_52_3 = e1
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | REDUCE: (7), (125) imply:
% 204.05/34.87  | | | | | | | | | | |   (126)   ~ (all_52_19 = e1)
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | SIMP: (126) implies:
% 204.05/34.87  | | | | | | | | | | |   (127)   ~ (all_52_19 = e1)
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | REDUCE: (61), (125) imply:
% 204.05/34.87  | | | | | | | | | | |   (128)   ~ (all_4_2 = e1)
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | REDUCE: (110), (125) imply:
% 204.05/34.87  | | | | | | | | | | |   (129)   ~ (e3 = e1)
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | BETA: splitting (119) gives:
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | |   (130)  all_58_5 = e1
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | COMBINE_EQS: (52), (130) imply:
% 204.05/34.87  | | | | | | | | | | | |   (131)  all_52_19 = e1
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | REDUCE: (127), (131) imply:
% 204.05/34.87  | | | | | | | | | | | |   (132)  $false
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | |   (133)  all_58_8 = e1 | all_58_14 = e1
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | BETA: splitting (133) gives:
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | |   (134)  all_58_8 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | COMBINE_EQS: (101), (134) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (135)  e3 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | REDUCE: (2), (135) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (136)  $false
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | |   (137)  all_58_14 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | |   (138)  all_58_12 = e0
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | |   (139)  all_58_0 = e2
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | COMBINE_EQS: (39), (139) imply:
% 204.05/34.87  | | | | | | | | | | | | | | |   (140)  e3 = e2
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | REDUCE: (56), (140) imply:
% 204.05/34.87  | | | | | | | | | | | | | | |   (141)  $false
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | |   (142)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | |   (143)  all_58_2 = e2
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (143) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (144)  e2 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | REDUCE: (19), (144) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (145)  $false
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | |   (146)  all_58_6 = e2 | all_58_12 = e2
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (13), (29), (54), (62), (138), (146) are
% 204.05/34.87  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1149.
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | |   (147)  all_58_13 = e0 | all_58_14 = e0
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (55), (137), (147) are inconsistent by
% 204.05/34.87  | | | | | | | | | | | | | |            sub-proof #710.
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | |   (148)   ~ (all_58_2 = e1)
% 204.05/34.87  | | | | | | | | | | |   (149)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | REDUCE: (26), (148) imply:
% 204.05/34.87  | | | | | | | | | | |   (150)   ~ (all_52_3 = e1)
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | BETA: splitting (76) gives:
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | |   (151)  all_58_2 = e1
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | COMBINE_EQS: (26), (151) imply:
% 204.05/34.87  | | | | | | | | | | | |   (152)  all_52_3 = e1
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | REDUCE: (150), (152) imply:
% 204.05/34.87  | | | | | | | | | | | |   (153)  $false
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | |   (154)  all_58_6 = e1 | all_58_12 = e1
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | BETA: splitting (154) gives:
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | |   (155)  all_58_6 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | COMBINE_EQS: (54), (155) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (156)  all_52_5 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | REDUCE: (32), (156) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (157)   ~ (all_52_29 = e1)
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | SIMP: (157) implies:
% 204.05/34.87  | | | | | | | | | | | | |   (158)   ~ (all_52_29 = e1)
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | REDUCE: (104), (156) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (159)   ~ (e3 = e1)
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | REDUCE: (5), (156) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (160)  op(e1, e1) = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | BETA: splitting (123) gives:
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | |   (161)  all_58_10 = e1
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | COMBINE_EQS: (107), (161) imply:
% 204.05/34.87  | | | | | | | | | | | | | |   (162)  e3 = e1
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | REDUCE: (2), (162) imply:
% 204.05/34.87  | | | | | | | | | | | | | |   (163)  $false
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | CLOSE: (163) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | |   (164)  all_58_11 = e1 | all_58_15 = e1
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | |   (165)  all_58_11 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | COMBINE_EQS: (14), (165) imply:
% 204.05/34.87  | | | | | | | | | | | | | | |   (166)  all_52_29 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | REDUCE: (158), (166) imply:
% 204.05/34.87  | | | | | | | | | | | | | | |   (167)  $false
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | |   (168)  all_58_15 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | COMBINE_EQS: (43), (168) imply:
% 204.05/34.87  | | | | | | | | | | | | | | |   (169)  all_14_2 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | SIMP: (169) implies:
% 204.05/34.87  | | | | | | | | | | | | | | |   (170)  all_14_2 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | REDUCE: (51), (170) imply:
% 204.05/34.87  | | | | | | | | | | | | | | |   (171)  op(e1, e1) = all_52_30
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | |   (172)  all_58_5 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (172) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (173)  all_52_19 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (174)  all_52_19 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | REDUCE: (9), (174) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (175)  op(e1, e1) = all_52_18
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_52_30, e1, e1,
% 204.05/34.87  | | | | | | | | | | | | | | | |              simplifying with (106), (171) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (176)  all_52_30 = e3
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_30, all_52_18, e1,
% 204.05/34.87  | | | | | | | | | | | | | | | |              e1, simplifying with (171), (175) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (177)  all_52_18 = all_52_30
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_18, e1, e1,
% 204.05/34.87  | | | | | | | | | | | | | | | |              simplifying with (160), (175) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (178)  all_52_18 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (178) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (179)  all_52_30 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (180)  all_52_30 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (176), (180) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (181)  e3 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | SIMP: (181) implies:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (182)  e3 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | REDUCE: (2), (182) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (183)  $false
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | |   (184)   ~ (all_58_5 = e1)
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | REDUCE: (52), (184) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | |   (185)   ~ (all_52_19 = e1)
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | |   (186)  all_58_3 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (186) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | | |   (187)  all_4_2 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | REDUCE: (62), (187) imply:
% 204.05/34.87  | | | | | | | | | | | | | | | | |   (188)  $false
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | |   (189)  all_58_5 = e1 | all_58_10 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.87  | | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | |   (190)  all_58_5 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (185), (190) are inconsistent by sub-proof
% 204.05/34.87  | | | | | | | | | | | | | | | | | |            #857.
% 204.05/34.87  | | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | |   (191)  all_58_10 = e1
% 204.05/34.87  | | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (107), (191) are inconsistent by sub-proof
% 204.05/34.87  | | | | | | | | | | | | | | | | | |            #968.
% 204.05/34.87  | | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | |   (192)  all_58_12 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | COMBINE_EQS: (25), (192) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (193)  all_52_7 = e1
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | REDUCE: (72), (193) imply:
% 204.05/34.87  | | | | | | | | | | | | |   (194)  $false
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 204.05/34.87  | | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | | 
% 204.05/34.87  | | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | | 
% 204.05/34.87  | | | | | | | | End of split
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | Case 2:
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | |   (195)  all_58_11 = e3 | all_58_15 = e3
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | | REF_CLOSE: (14), (43), (64), (96), (195) are inconsistent by
% 204.05/34.87  | | | | | | | |            sub-proof #1103.
% 204.05/34.87  | | | | | | | | 
% 204.05/34.87  | | | | | | | End of split
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | Case 2:
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | |   (196)  all_58_11 = e3
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | | REF_CLOSE: (14), (96), (196) are inconsistent by sub-proof #1323.
% 204.05/34.87  | | | | | | | 
% 204.05/34.87  | | | | | | End of split
% 204.05/34.87  | | | | | | 
% 204.05/34.87  | | | | | End of split
% 204.05/34.87  | | | | | 
% 204.05/34.87  | | | | End of split
% 204.05/34.87  | | | | 
% 204.05/34.87  | | | End of split
% 204.05/34.87  | | | 
% 204.05/34.87  | | End of split
% 204.05/34.87  | | 
% 204.05/34.87  | End of split
% 204.05/34.87  | 
% 204.05/34.87  End of proof
% 204.05/34.87  
% 204.05/34.87  Sub-proof #710 shows that the following formulas are inconsistent:
% 204.05/34.87  ----------------------------------------------------------------
% 204.05/34.87    (1)  all_58_13 = e0 | all_58_14 = e0
% 204.05/34.87    (2)   ~ (e3 = e0)
% 204.05/34.87    (3)  all_58_13 = e3
% 204.05/34.87    (4)  all_58_14 = e1
% 204.05/34.87    (5)   ~ (e1 = e0)
% 204.05/34.87  
% 204.05/34.87  Begin of proof
% 204.05/34.87  | 
% 204.05/34.87  | BETA: splitting (1) gives:
% 204.05/34.87  | 
% 204.05/34.87  | Case 1:
% 204.05/34.87  | | 
% 204.05/34.87  | |   (6)  all_58_13 = e0
% 204.05/34.87  | | 
% 204.05/34.87  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1172.
% 204.05/34.87  | | 
% 204.05/34.87  | Case 2:
% 204.05/34.87  | | 
% 204.05/34.87  | |   (7)  all_58_14 = e0
% 204.05/34.87  | | 
% 204.05/34.87  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #761.
% 204.05/34.87  | | 
% 204.05/34.87  | End of split
% 204.05/34.87  | 
% 204.05/34.87  End of proof
% 204.05/34.87  
% 204.05/34.87  Sub-proof #711 shows that the following formulas are inconsistent:
% 204.05/34.87  ----------------------------------------------------------------
% 204.05/34.87    (1)  all_58_14 = all_52_23
% 204.05/34.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.87    (3)   ~ (all_52_5 = e1)
% 204.05/34.88    (4)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.88    (5)  all_58_9 = all_52_25
% 204.05/34.88    (6)   ~ (all_52_3 = e3)
% 204.05/34.88    (7)   ~ (all_52_3 = all_52_27)
% 204.05/34.88    (8)  op(all_10_2, e1) = all_10_1
% 204.05/34.88    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.88    (10)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.88    (11)  all_58_11 = e3
% 204.05/34.88    (12)   ~ (e2 = e1)
% 204.05/34.88    (13)  all_58_10 = all_52_27
% 204.05/34.88    (14)  all_58_7 = all_52_13
% 204.05/34.88    (15)  all_58_12 = all_52_7
% 204.05/34.88    (16)  all_58_2 = all_52_3
% 204.05/34.88    (17)   ~ (all_52_23 = e3)
% 204.05/34.88    (18)  op(all_52_3, all_52_3) = e2
% 204.05/34.88    (19)   ~ (all_10_2 = e3)
% 204.05/34.88    (20)   ~ (all_52_13 = e1)
% 204.05/34.88    (21)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.88    (22)   ~ (all_52_25 = e1)
% 204.05/34.88    (23)  all_58_15 = all_14_2
% 204.05/34.88    (24)  all_58_8 = all_10_2
% 204.05/34.88    (25)   ~ (all_52_7 = e1)
% 204.05/34.88    (26)  all_58_5 = e3
% 204.05/34.88    (27)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.88    (28)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.88    (29)  all_58_6 = all_52_5
% 204.05/34.88    (30)  op(e1, e1) = all_10_2
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | BETA: splitting (10) gives:
% 204.05/34.88  | 
% 204.05/34.88  | Case 1:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (31)  all_58_2 = e1
% 204.05/34.88  | | 
% 204.05/34.88  | | COMBINE_EQS: (16), (31) imply:
% 204.05/34.88  | |   (32)  all_52_3 = e1
% 204.05/34.88  | | 
% 204.05/34.88  | | SIMP: (32) implies:
% 204.05/34.88  | |   (33)  all_52_3 = e1
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (7), (33) imply:
% 204.05/34.88  | |   (34)   ~ (all_52_27 = e1)
% 204.05/34.88  | | 
% 204.05/34.88  | | SIMP: (34) implies:
% 204.05/34.88  | |   (35)   ~ (all_52_27 = e1)
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (6), (33) imply:
% 204.05/34.88  | |   (36)   ~ (e3 = e1)
% 204.05/34.88  | | 
% 204.05/34.88  | | SIMP: (36) implies:
% 204.05/34.88  | |   (37)   ~ (e3 = e1)
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (18), (33) imply:
% 204.05/34.88  | |   (38)  op(e1, e1) = e2
% 204.05/34.88  | | 
% 204.05/34.88  | | BETA: splitting (9) gives:
% 204.05/34.88  | | 
% 204.05/34.88  | | Case 1:
% 204.05/34.88  | | | 
% 204.05/34.88  | | |   (39)  all_58_9 = e1
% 204.05/34.88  | | | 
% 204.05/34.88  | | | REF_CLOSE: (5), (22), (39) are inconsistent by sub-proof #856.
% 204.05/34.88  | | | 
% 204.05/34.88  | | Case 2:
% 204.05/34.88  | | | 
% 204.05/34.88  | | |   (40)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.88  | | | 
% 204.05/34.88  | | | BETA: splitting (40) gives:
% 204.05/34.88  | | | 
% 204.05/34.88  | | | Case 1:
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | |   (41)  all_58_10 = e1
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | REF_CLOSE: (13), (35), (41) are inconsistent by sub-proof #861.
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | Case 2:
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | |   (42)  all_58_11 = e1 | all_58_15 = e1
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | BETA: splitting (21) gives:
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | Case 1:
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | |   (43)  all_58_7 = e1
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | COMBINE_EQS: (14), (43) imply:
% 204.05/34.88  | | | | |   (44)  all_52_13 = e1
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | REDUCE: (20), (44) imply:
% 204.05/34.88  | | | | |   (45)  $false
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | CLOSE: (45) is inconsistent.
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | Case 2:
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | |   (46)  all_58_8 = e1 | all_58_11 = e1
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | BETA: splitting (46) gives:
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | Case 1:
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | |   (47)  all_58_8 = e1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | COMBINE_EQS: (24), (47) imply:
% 204.05/34.88  | | | | | |   (48)  all_10_2 = e1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | SIMP: (48) implies:
% 204.05/34.88  | | | | | |   (49)  all_10_2 = e1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | REDUCE: (4), (49) imply:
% 204.05/34.88  | | | | | |   (50)  op(e1, e1) = all_52_20
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | REDUCE: (8), (49) imply:
% 204.05/34.88  | | | | | |   (51)  op(e1, e1) = all_10_1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | REDUCE: (30), (49) imply:
% 204.05/34.88  | | | | | |   (52)  op(e1, e1) = e1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | BETA: splitting (42) gives:
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | Case 1:
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | |   (53)  all_58_11 = e1
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | | COMBINE_EQS: (11), (53) imply:
% 204.05/34.88  | | | | | | |   (54)  e3 = e1
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | | REF_CLOSE: (1), (17), (19), (24), (26), (28), (37), (54) are
% 204.05/34.88  | | | | | | |            inconsistent by sub-proof #712.
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | Case 2:
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | |   (55)  all_58_15 = e1
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | | COMBINE_EQS: (23), (55) imply:
% 204.05/34.88  | | | | | | |   (56)  all_14_2 = e1
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | | REDUCE: (27), (56) imply:
% 204.05/34.88  | | | | | | |   (57)  op(e1, e1) = all_52_30
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | | REF_CLOSE: (2), (12), (38), (50), (51), (52), (57) are
% 204.05/34.88  | | | | | | |            inconsistent by sub-proof #749.
% 204.05/34.88  | | | | | | | 
% 204.05/34.88  | | | | | | End of split
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | Case 2:
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | |   (58)  all_58_11 = e1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | COMBINE_EQS: (11), (58) imply:
% 204.05/34.88  | | | | | |   (59)  e3 = e1
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | REF_CLOSE: (1), (17), (19), (24), (26), (28), (37), (59) are
% 204.05/34.88  | | | | | |            inconsistent by sub-proof #712.
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | End of split
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | End of split
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | End of split
% 204.05/34.88  | | | 
% 204.05/34.88  | | End of split
% 204.05/34.88  | | 
% 204.05/34.88  | Case 2:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (60)  all_58_6 = e1 | all_58_12 = e1
% 204.05/34.88  | | 
% 204.05/34.88  | | REF_CLOSE: (3), (15), (25), (29), (60) are inconsistent by sub-proof #748.
% 204.05/34.88  | | 
% 204.05/34.88  | End of split
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #712 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)  all_58_14 = all_52_23
% 204.05/34.88    (2)   ~ (e3 = e1)
% 204.05/34.88    (3)  e3 = e1
% 204.05/34.88    (4)   ~ (all_52_23 = e3)
% 204.05/34.88    (5)   ~ (all_10_2 = e3)
% 204.05/34.88    (6)  all_58_8 = all_10_2
% 204.05/34.88    (7)  all_58_5 = e3
% 204.05/34.88    (8)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | SIMP: (3) implies:
% 204.05/34.88  |   (9)  e3 = e1
% 204.05/34.88  | 
% 204.05/34.88  | COMBINE_EQS: (7), (9) imply:
% 204.05/34.88  |   (10)  all_58_5 = e1
% 204.05/34.88  | 
% 204.05/34.88  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10) are inconsistent by sub-proof
% 204.05/34.88  |            #1051.
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #713 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)   ~ (all_52_25 = all_52_27)
% 204.05/34.88    (2)   ~ (e3 = e1)
% 204.05/34.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.88    (4)  op(all_52_7, all_52_7) = e0
% 204.05/34.88    (5)  op(all_52_5, all_52_5) = e1
% 204.05/34.88    (6)  all_58_0 = all_6_2
% 204.05/34.88    (7)  op(all_14_2, e0) = all_14_1
% 204.05/34.88    (8)  all_34_1 = all_14_1
% 204.05/34.88    (9)  op(e3, e0) = all_52_25
% 204.05/34.88    (10)  op(e0, all_14_1) = e1
% 204.05/34.88    (11)  all_58_9 = all_52_25
% 204.05/34.88    (12)   ~ (all_52_29 = all_14_2)
% 204.05/34.88    (13)  op(e2, e2) = all_4_2
% 204.05/34.88    (14)   ~ (all_52_3 = all_52_5)
% 204.05/34.88    (15)  all_58_11 = all_52_29
% 204.05/34.88    (16)   ~ (all_52_25 = all_14_2)
% 204.05/34.88    (17)  op(e0, e0) = all_14_2
% 204.05/34.88    (18)  op(e0, e1) = all_52_23
% 204.05/34.88    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.88    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.88    (21)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.05/34.88    (22)  all_58_10 = all_52_27
% 204.05/34.88    (23)   ~ (all_52_19 = all_52_23)
% 204.05/34.88    (24)   ~ (all_52_25 = all_52_29)
% 204.05/34.88    (25)  all_58_7 = all_52_13
% 204.05/34.88    (26)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.88    (27)  op(all_6_2, all_6_2) = e3
% 204.05/34.88    (28)  all_58_12 = all_52_7
% 204.05/34.88    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.88    (30)   ~ (all_52_7 = all_14_2)
% 204.05/34.88    (31)  all_58_2 = all_52_3
% 204.05/34.88    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.88    (33)  op(all_52_3, all_52_3) = e2
% 204.05/34.88    (34)   ~ (all_52_13 = all_4_2)
% 204.05/34.88    (35)  op(all_52_23, all_52_23) = all_52_22
% 204.05/34.88    (36)  all_58_8 = all_10_2
% 204.05/34.88    (37)  all_34_2 = all_14_2
% 204.05/34.88    (38)   ~ (all_52_5 = all_10_2)
% 204.05/34.88    (39)   ~ (all_52_23 = all_14_2)
% 204.05/34.88    (40)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.88    (41)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.88    (42)   ~ (all_52_5 = all_6_2)
% 204.05/34.88    (43)  op(e3, e3) = all_6_2
% 204.05/34.88    (44)  all_56_3 = all_52_25
% 204.05/34.88    (45)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.88    (46)  all_58_5 = all_52_19
% 204.05/34.88    (47)  all_58_6 = all_52_5
% 204.05/34.88    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.88    (49)   ~ (e3 = e2)
% 204.05/34.88    (50)  op(all_52_13, all_52_13) = all_52_12
% 204.05/34.88    (51)  op(e1, e1) = all_10_2
% 204.05/34.88    (52)   ~ (all_52_23 = all_10_2)
% 204.05/34.88    (53)  all_58_3 = all_4_2
% 204.05/34.88    (54)   ~ (all_52_3 = all_4_2)
% 204.05/34.88    (55)  op(all_52_25, all_52_25) = all_52_24
% 204.05/34.88    (56)  all_14_2 = e3
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | COMBINE_EQS: (37), (56) imply:
% 204.05/34.88  |   (57)  all_34_2 = e3
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (39), (56) imply:
% 204.05/34.88  |   (58)   ~ (all_52_23 = e3)
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (16), (56) imply:
% 204.05/34.88  |   (59)   ~ (all_52_25 = e3)
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (12), (56) imply:
% 204.05/34.88  |   (60)   ~ (all_52_29 = e3)
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (45), (56) imply:
% 204.05/34.88  |   (61)  op(e3, e3) = all_52_30
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (7), (56) imply:
% 204.05/34.88  |   (62)  op(e3, e0) = all_14_1
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (17), (56) imply:
% 204.05/34.88  |   (63)  op(e0, e0) = e3
% 204.05/34.88  | 
% 204.05/34.88  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 204.05/34.88  |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 204.05/34.88  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (38),
% 204.05/34.88  |            (40), (41), (42), (43), (44), (46), (47), (48), (49), (50), (51),
% 204.05/34.88  |            (52), (53), (54), (55), (57), (58), (59), (60), (61), (62), (63)
% 204.05/34.88  |            are inconsistent by sub-proof #866.
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #714 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)   ~ (all_52_15 = all_52_23)
% 204.05/34.88    (2)  all_58_14 = all_52_23
% 204.05/34.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.88    (4)  all_58_1 = all_52_9
% 204.05/34.88    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.88    (6)   ~ (all_52_7 = all_52_15)
% 204.05/34.88    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.88    (8)  all_58_0 = all_6_2
% 204.05/34.88    (9)   ~ (all_10_0 = e3)
% 204.05/34.88    (10)  all_58_13 = all_52_15
% 204.05/34.88    (11)   ~ (all_6_1 = e1)
% 204.05/34.88    (12)  all_58_7 = all_10_0
% 204.05/34.88    (13)   ~ (all_52_7 = all_6_2)
% 204.05/34.88    (14)  all_56_15 = all_14_2
% 204.05/34.88    (15)   ~ (all_10_0 = e2)
% 204.05/34.88    (16)   ~ (all_4_1 = e1)
% 204.05/34.88    (17)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.05/34.88    (18)  op(all_52_9, all_52_9) = all_52_8
% 204.05/34.88    (19)  op(all_52_15, all_52_15) = all_52_14
% 204.05/34.88    (20)  all_56_9 = all_10_0
% 204.05/34.88    (21)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.05/34.88    (22)  all_58_12 = all_52_7
% 204.05/34.88    (23)   ~ (all_52_15 = all_10_0)
% 204.05/34.88    (24)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.05/34.88    (25)   ~ (e2 = e0)
% 204.05/34.88    (26)  op(all_4_2, e2) = all_4_1
% 204.05/34.88    (27)   ~ (all_52_15 = all_14_2)
% 204.05/34.88    (28)  op(e0, e3) = all_52_7
% 204.05/34.88    (29)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.88    (30)  all_58_15 = all_14_2
% 204.05/34.88    (31)   ~ (all_10_0 = all_10_2)
% 204.05/34.88    (32)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.05/34.88    (33)  all_56_12 = all_52_7
% 204.05/34.88    (34)   ~ (all_52_9 = all_4_2)
% 204.05/34.88    (35)   ~ (all_52_9 = all_6_2)
% 204.05/34.88    (36)  op(e3, e3) = all_6_2
% 204.05/34.88    (37)  all_56_14 = all_52_23
% 204.05/34.88    (38)  op(all_4_2, all_4_2) = all_52_10
% 204.05/34.88    (39)  all_56_1 = all_52_9
% 204.05/34.88    (40)   ~ (all_52_15 = all_4_2)
% 204.05/34.88    (41)  op(e3, e2) = all_52_9
% 204.05/34.88    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.88    (43)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.88    (44)  op(all_10_0, all_10_0) = all_52_12
% 204.05/34.88    (45)   ~ (all_6_1 = e2)
% 204.05/34.88    (46)  op(e1, e1) = all_10_2
% 204.05/34.88    (47)  all_58_3 = all_4_2
% 204.05/34.88    (48)   ~ (all_52_9 = all_10_0)
% 204.05/34.88    (49)  op(all_6_2, e3) = all_6_1
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | ALPHA: (17) implies:
% 204.05/34.88  |   (50)  all_52_14 = e0
% 204.05/34.88  |   (51)  all_52_12 = e1
% 204.05/34.88  |   (52)  all_52_10 = e2
% 204.05/34.88  |   (53)  all_52_8 = e3
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (18), (53) imply:
% 204.05/34.88  |   (54)  op(all_52_9, all_52_9) = e3
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (19), (50) imply:
% 204.05/34.88  |   (55)  op(all_52_15, all_52_15) = e0
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (44), (51) imply:
% 204.05/34.88  |   (56)  op(all_10_0, all_10_0) = e1
% 204.05/34.88  | 
% 204.05/34.88  | REDUCE: (38), (52) imply:
% 204.05/34.88  |   (57)  op(all_4_2, all_4_2) = e2
% 204.05/34.88  | 
% 204.05/34.88  | BETA: splitting (32) gives:
% 204.05/34.88  | 
% 204.05/34.88  | Case 1:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (58)  all_56_15 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | COMBINE_EQS: (14), (58) imply:
% 204.05/34.88  | |   (59)  all_14_2 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (27), (59) imply:
% 204.05/34.88  | |   (60)   ~ (all_52_15 = e3)
% 204.05/34.88  | | 
% 204.05/34.88  | | BETA: splitting (29) gives:
% 204.05/34.88  | | 
% 204.05/34.88  | | Case 1:
% 204.05/34.88  | | | 
% 204.05/34.88  | | |   (61)  all_58_1 = e3
% 204.05/34.88  | | | 
% 204.05/34.88  | | | REF_CLOSE: (3), (4), (5), (6), (10), (11), (12), (13), (28), (29), (33),
% 204.05/34.88  | | |            (34), (35), (36), (45), (47), (48), (49), (54), (55), (61) are
% 204.05/34.88  | | |            inconsistent by sub-proof #719.
% 204.05/34.88  | | | 
% 204.05/34.88  | | Case 2:
% 204.05/34.88  | | | 
% 204.05/34.88  | | |   (62)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.88  | | | 
% 204.05/34.88  | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (15), (16), (20), (24),
% 204.05/34.88  | | |            (25), (26), (31), (34), (35), (36), (39), (41), (43), (46),
% 204.05/34.88  | | |            (47), (48), (56), (57), (60), (62) are inconsistent by
% 204.05/34.88  | | |            sub-proof #716.
% 204.05/34.88  | | | 
% 204.05/34.88  | | End of split
% 204.05/34.88  | | 
% 204.05/34.88  | Case 2:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (63)   ~ (all_56_15 = e3)
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (14), (63) imply:
% 204.05/34.88  | |   (64)   ~ (all_14_2 = e3)
% 204.05/34.88  | | 
% 204.05/34.88  | | BETA: splitting (29) gives:
% 204.05/34.88  | | 
% 204.05/34.88  | | Case 1:
% 204.05/34.88  | | | 
% 204.05/34.88  | | |   (65)  all_58_1 = e3
% 204.05/34.88  | | | 
% 204.05/34.88  | | | REF_CLOSE: (3), (4), (5), (6), (10), (11), (12), (13), (28), (29), (33),
% 204.05/34.88  | | |            (34), (35), (36), (45), (47), (48), (49), (54), (55), (65) are
% 204.05/34.88  | | |            inconsistent by sub-proof #719.
% 204.05/34.88  | | | 
% 204.05/34.88  | | Case 2:
% 204.05/34.88  | | | 
% 204.05/34.88  | | |   (66)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.88  | | | 
% 204.05/34.88  | | | BETA: splitting (21) gives:
% 204.05/34.88  | | | 
% 204.05/34.88  | | | Case 1:
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | |   (67)  all_56_14 = e3
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | COMBINE_EQS: (37), (67) imply:
% 204.05/34.88  | | | |   (68)  all_52_23 = e3
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | SIMP: (68) implies:
% 204.05/34.88  | | | |   (69)  all_52_23 = e3
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | REDUCE: (1), (69) imply:
% 204.05/34.88  | | | |   (70)   ~ (all_52_15 = e3)
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (15), (16), (20), (24),
% 204.05/34.88  | | | |            (25), (26), (31), (34), (35), (36), (39), (41), (43), (46),
% 204.05/34.88  | | | |            (47), (48), (56), (57), (66), (70) are inconsistent by
% 204.05/34.88  | | | |            sub-proof #716.
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | Case 2:
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | |   (71)   ~ (all_56_14 = e3)
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | REDUCE: (37), (71) imply:
% 204.05/34.88  | | | |   (72)   ~ (all_52_23 = e3)
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | BETA: splitting (42) gives:
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | | Case 1:
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | |   (73)  all_58_12 = e3
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | COMBINE_EQS: (22), (73) imply:
% 204.05/34.88  | | | | |   (74)  all_52_7 = e3
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | SIMP: (74) implies:
% 204.05/34.88  | | | | |   (75)  all_52_7 = e3
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | REDUCE: (6), (75) imply:
% 204.05/34.88  | | | | |   (76)   ~ (all_52_15 = e3)
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | SIMP: (76) implies:
% 204.05/34.88  | | | | |   (77)   ~ (all_52_15 = e3)
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (15), (16), (20),
% 204.05/34.88  | | | | |            (24), (25), (26), (31), (34), (35), (36), (39), (41), (43),
% 204.05/34.88  | | | | |            (46), (47), (48), (56), (57), (66), (77) are inconsistent
% 204.05/34.88  | | | | |            by sub-proof #716.
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | Case 2:
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | |   (78)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | BETA: splitting (78) gives:
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | | Case 1:
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | |   (79)  all_58_13 = e3
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | REF_CLOSE: (3), (4), (5), (6), (10), (11), (12), (13), (23), (28),
% 204.05/34.88  | | | | | |            (29), (33), (35), (36), (40), (45), (47), (49), (54),
% 204.05/34.88  | | | | | |            (55), (79) are inconsistent by sub-proof #984.
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | Case 2:
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | |   (80)  all_58_14 = e3 | all_58_15 = e3
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | | REF_CLOSE: (2), (30), (64), (72), (80) are inconsistent by sub-proof
% 204.05/34.88  | | | | | |            #715.
% 204.05/34.88  | | | | | | 
% 204.05/34.88  | | | | | End of split
% 204.05/34.88  | | | | | 
% 204.05/34.88  | | | | End of split
% 204.05/34.88  | | | | 
% 204.05/34.88  | | | End of split
% 204.05/34.88  | | | 
% 204.05/34.88  | | End of split
% 204.05/34.88  | | 
% 204.05/34.88  | End of split
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #715 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)  all_58_14 = all_52_23
% 204.05/34.88    (2)   ~ (all_52_23 = e3)
% 204.05/34.88    (3)  all_58_14 = e3 | all_58_15 = e3
% 204.05/34.88    (4)  all_58_15 = all_14_2
% 204.05/34.88    (5)   ~ (all_14_2 = e3)
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | BETA: splitting (3) gives:
% 204.05/34.88  | 
% 204.05/34.88  | Case 1:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (6)  all_58_14 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #1305.
% 204.05/34.88  | | 
% 204.05/34.88  | Case 2:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (7)  all_58_15 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | COMBINE_EQS: (4), (7) imply:
% 204.05/34.88  | |   (8)  all_14_2 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (5), (8) imply:
% 204.05/34.88  | |   (9)  $false
% 204.05/34.88  | | 
% 204.05/34.88  | | CLOSE: (9) is inconsistent.
% 204.05/34.88  | | 
% 204.05/34.88  | End of split
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #716 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.88    (2)  all_58_1 = all_52_9
% 204.05/34.88    (3)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.88    (4)  all_58_0 = all_6_2
% 204.05/34.88    (5)   ~ (all_10_0 = e3)
% 204.05/34.88    (6)  all_58_13 = all_52_15
% 204.05/34.88    (7)  op(all_10_0, all_10_0) = e1
% 204.05/34.88    (8)   ~ (all_52_15 = e3)
% 204.05/34.88    (9)  all_58_7 = all_10_0
% 204.05/34.88    (10)   ~ (all_10_0 = e2)
% 204.05/34.88    (11)   ~ (all_4_1 = e1)
% 204.05/34.88    (12)  all_56_9 = all_10_0
% 204.05/34.88    (13)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.05/34.88    (14)   ~ (e2 = e0)
% 204.05/34.88    (15)  op(all_4_2, e2) = all_4_1
% 204.05/34.88    (16)   ~ (all_10_0 = all_10_2)
% 204.05/34.88    (17)   ~ (all_52_9 = all_4_2)
% 204.05/34.88    (18)  op(all_4_2, all_4_2) = e2
% 204.05/34.88    (19)   ~ (all_52_9 = all_6_2)
% 204.05/34.88    (20)  op(e3, e3) = all_6_2
% 204.05/34.88    (21)  all_56_1 = all_52_9
% 204.05/34.88    (22)  op(e3, e2) = all_52_9
% 204.05/34.88    (23)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.88    (24)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.88    (25)  op(e1, e1) = all_10_2
% 204.05/34.88    (26)  all_58_3 = all_4_2
% 204.05/34.88    (27)   ~ (all_52_9 = all_10_0)
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | BETA: splitting (23) gives:
% 204.05/34.88  | 
% 204.05/34.88  | Case 1:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (28)  all_58_3 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | COMBINE_EQS: (26), (28) imply:
% 204.05/34.88  | |   (29)  all_4_2 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (17), (29) imply:
% 204.05/34.88  | |   (30)   ~ (all_52_9 = e3)
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (18), (29) imply:
% 204.05/34.88  | |   (31)  op(e3, e3) = e2
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (15), (29) imply:
% 204.05/34.88  | |   (32)  op(e3, e2) = all_4_1
% 204.05/34.88  | | 
% 204.05/34.88  | | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3, simplifying
% 204.05/34.88  | |              with (22), (32) gives:
% 204.05/34.88  | |   (33)  all_52_9 = all_4_1
% 204.05/34.88  | | 
% 204.05/34.88  | | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with
% 204.05/34.88  | |              (20), (31) gives:
% 204.05/34.88  | |   (34)  all_6_2 = e2
% 204.05/34.88  | | 
% 204.05/34.88  | | REF_CLOSE: (1), (2), (3), (4), (7), (10), (11), (12), (13), (14), (16),
% 204.05/34.88  | |            (19), (21), (24), (25), (27), (30), (33), (34) are inconsistent
% 204.05/34.88  | |            by sub-proof #718.
% 204.05/34.88  | | 
% 204.05/34.88  | Case 2:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (35)  all_58_7 = e3 | all_58_13 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REF_CLOSE: (5), (6), (8), (9), (35) are inconsistent by sub-proof #717.
% 204.05/34.88  | | 
% 204.05/34.88  | End of split
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #717 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)   ~ (all_10_0 = e3)
% 204.05/34.88    (2)  all_58_13 = all_52_15
% 204.05/34.88    (3)   ~ (all_52_15 = e3)
% 204.05/34.88    (4)  all_58_7 = all_10_0
% 204.05/34.88    (5)  all_58_7 = e3 | all_58_13 = e3
% 204.05/34.88  
% 204.05/34.88  Begin of proof
% 204.05/34.88  | 
% 204.05/34.88  | BETA: splitting (5) gives:
% 204.05/34.88  | 
% 204.05/34.88  | Case 1:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (6)  all_58_7 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | COMBINE_EQS: (4), (6) imply:
% 204.05/34.88  | |   (7)  all_10_0 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REDUCE: (1), (7) imply:
% 204.05/34.88  | |   (8)  $false
% 204.05/34.88  | | 
% 204.05/34.88  | | CLOSE: (8) is inconsistent.
% 204.05/34.88  | | 
% 204.05/34.88  | Case 2:
% 204.05/34.88  | | 
% 204.05/34.88  | |   (9)  all_58_13 = e3
% 204.05/34.88  | | 
% 204.05/34.88  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1360.
% 204.05/34.88  | | 
% 204.05/34.88  | End of split
% 204.05/34.88  | 
% 204.05/34.88  End of proof
% 204.05/34.88  
% 204.05/34.88  Sub-proof #718 shows that the following formulas are inconsistent:
% 204.05/34.88  ----------------------------------------------------------------
% 204.05/34.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.88    (2)  all_58_1 = all_52_9
% 204.05/34.88    (3)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.88    (4)  all_58_0 = all_6_2
% 204.05/34.88    (5)  all_6_2 = e2
% 204.05/34.88    (6)  op(all_10_0, all_10_0) = e1
% 204.05/34.88    (7)   ~ (all_10_0 = e2)
% 204.05/34.88    (8)   ~ (all_4_1 = e1)
% 204.05/34.88    (9)  all_56_9 = all_10_0
% 204.05/34.88    (10)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.05/34.88    (11)   ~ (e2 = e0)
% 204.05/34.88    (12)   ~ (all_52_9 = e3)
% 204.05/34.88    (13)  all_52_9 = all_4_1
% 204.05/34.89    (14)   ~ (all_10_0 = all_10_2)
% 204.05/34.89    (15)   ~ (all_52_9 = all_6_2)
% 204.05/34.89    (16)  all_56_1 = all_52_9
% 204.05/34.89    (17)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.89    (18)  op(e1, e1) = all_10_2
% 204.05/34.89    (19)   ~ (all_52_9 = all_10_0)
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | COMBINE_EQS: (13), (16) imply:
% 204.05/34.89  |   (20)  all_56_1 = all_4_1
% 204.05/34.89  | 
% 204.05/34.89  | COMBINE_EQS: (2), (13) imply:
% 204.05/34.89  |   (21)  all_58_1 = all_4_1
% 204.05/34.89  | 
% 204.05/34.89  | COMBINE_EQS: (4), (5) imply:
% 204.05/34.89  |   (22)  all_58_0 = e2
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (13), (19) imply:
% 204.05/34.89  |   (23)   ~ (all_10_0 = all_4_1)
% 204.05/34.89  | 
% 204.05/34.89  | SIMP: (23) implies:
% 204.05/34.89  |   (24)   ~ (all_10_0 = all_4_1)
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (5), (13), (15) imply:
% 204.05/34.89  |   (25)   ~ (all_4_1 = e2)
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (12), (13) imply:
% 204.05/34.89  |   (26)   ~ (all_4_1 = e3)
% 204.05/34.89  | 
% 204.05/34.89  | BETA: splitting (17) gives:
% 204.05/34.89  | 
% 204.05/34.89  | Case 1:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (27)  all_56_1 = e3
% 204.05/34.89  | | 
% 204.05/34.89  | | COMBINE_EQS: (20), (27) imply:
% 204.05/34.89  | |   (28)  all_4_1 = e3
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (26), (28) imply:
% 204.05/34.89  | |   (29)  $false
% 204.05/34.89  | | 
% 204.05/34.89  | | CLOSE: (29) is inconsistent.
% 204.05/34.89  | | 
% 204.05/34.89  | Case 2:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (30)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.89  | | 
% 204.05/34.89  | | BETA: splitting (10) gives:
% 204.05/34.89  | | 
% 204.05/34.89  | | Case 1:
% 204.05/34.89  | | | 
% 204.05/34.89  | | |   (31)  all_58_0 = e0
% 204.05/34.89  | | | 
% 204.05/34.89  | | | COMBINE_EQS: (22), (31) imply:
% 204.05/34.89  | | |   (32)  e2 = e0
% 204.05/34.89  | | | 
% 204.05/34.89  | | | REDUCE: (11), (32) imply:
% 204.05/34.89  | | |   (33)  $false
% 204.05/34.89  | | | 
% 204.05/34.89  | | | CLOSE: (33) is inconsistent.
% 204.05/34.89  | | | 
% 204.05/34.89  | | Case 2:
% 204.05/34.89  | | | 
% 204.05/34.89  | | |   (34)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.05/34.89  | | | 
% 204.05/34.89  | | | BETA: splitting (30) gives:
% 204.05/34.89  | | | 
% 204.05/34.89  | | | Case 1:
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | |   (35)  all_56_1 = e2
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | COMBINE_EQS: (20), (35) imply:
% 204.05/34.89  | | | |   (36)  all_4_1 = e2
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | REDUCE: (25), (36) imply:
% 204.05/34.89  | | | |   (37)  $false
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | CLOSE: (37) is inconsistent.
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | Case 2:
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | |   (38)  all_56_1 = e1 | all_56_1 = e0
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | BETA: splitting (34) gives:
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | Case 1:
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | |   (39)  all_58_1 = e0
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | COMBINE_EQS: (21), (39) imply:
% 204.05/34.89  | | | | |   (40)  all_4_1 = e0
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REDUCE: (24), (40) imply:
% 204.05/34.89  | | | | |   (41)   ~ (all_10_0 = e0)
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REF_CLOSE: (1), (3), (6), (7), (9), (14), (18), (41) are inconsistent
% 204.05/34.89  | | | | |            by sub-proof #988.
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | Case 2:
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | |   (42)   ~ (all_58_1 = e0)
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REDUCE: (21), (42) imply:
% 204.05/34.89  | | | | |   (43)   ~ (all_4_1 = e0)
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REF_CLOSE: (8), (20), (38), (43) are inconsistent by sub-proof #1164.
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | End of split
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | End of split
% 204.05/34.89  | | | 
% 204.05/34.89  | | End of split
% 204.05/34.89  | | 
% 204.05/34.89  | End of split
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #719 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.89    (2)  all_58_1 = all_52_9
% 204.05/34.89    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.89    (4)   ~ (all_52_7 = all_52_15)
% 204.05/34.89    (5)  op(all_52_15, all_52_15) = e0
% 204.05/34.89    (6)  all_58_13 = all_52_15
% 204.05/34.89    (7)   ~ (all_6_1 = e1)
% 204.05/34.89    (8)  all_58_7 = all_10_0
% 204.05/34.89    (9)  all_58_1 = e3
% 204.05/34.89    (10)   ~ (all_52_7 = all_6_2)
% 204.05/34.89    (11)  op(e0, e3) = all_52_7
% 204.05/34.89    (12)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.89    (13)  all_56_12 = all_52_7
% 204.05/34.89    (14)   ~ (all_52_9 = all_4_2)
% 204.05/34.89    (15)   ~ (all_52_9 = all_6_2)
% 204.05/34.89    (16)  op(e3, e3) = all_6_2
% 204.05/34.89    (17)   ~ (all_6_1 = e2)
% 204.05/34.89    (18)  op(all_52_9, all_52_9) = e3
% 204.05/34.89    (19)  all_58_3 = all_4_2
% 204.05/34.89    (20)   ~ (all_52_9 = all_10_0)
% 204.05/34.89    (21)  op(all_6_2, e3) = all_6_1
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | COMBINE_EQS: (2), (9) imply:
% 204.05/34.89  |   (22)  all_52_9 = e3
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (20), (22) imply:
% 204.05/34.89  |   (23)   ~ (all_10_0 = e3)
% 204.05/34.89  | 
% 204.05/34.89  | SIMP: (23) implies:
% 204.05/34.89  |   (24)   ~ (all_10_0 = e3)
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (14), (22) imply:
% 204.05/34.89  |   (25)   ~ (all_4_2 = e3)
% 204.05/34.89  | 
% 204.05/34.89  | SIMP: (25) implies:
% 204.05/34.89  |   (26)   ~ (all_4_2 = e3)
% 204.05/34.89  | 
% 204.05/34.89  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 204.05/34.89  |            (15), (16), (17), (18), (19), (21), (24), (26) are inconsistent by
% 204.05/34.89  |            sub-proof #992.
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #720 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.89    (2)   ~ (all_4_2 = e3)
% 204.05/34.89    (3)  all_58_13 = e3
% 204.05/34.89    (4)  op(e2, all_4_1) = e3
% 204.05/34.89    (5)  op(e2, e2) = all_4_2
% 204.05/34.89    (6)  all_58_7 = all_10_0
% 204.05/34.89    (7)   ~ (all_10_0 = e2)
% 204.05/34.89    (8)  op(all_4_2, e2) = all_4_1
% 204.05/34.89    (9)  op(all_4_2, all_4_2) = all_52_10
% 204.05/34.89    (10)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.05/34.89    (11)   ~ (e3 = e2)
% 204.05/34.89    (12)  all_58_3 = all_4_2
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | BETA: splitting (10) gives:
% 204.05/34.89  | 
% 204.05/34.89  | Case 1:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (13)  all_58_3 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | COMBINE_EQS: (12), (13) imply:
% 204.05/34.89  | |   (14)  all_4_2 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (2), (14) imply:
% 204.05/34.89  | |   (15)   ~ (e3 = e2)
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (9), (14) imply:
% 204.05/34.89  | |   (16)  op(e2, e2) = all_52_10
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (8), (14) imply:
% 204.05/34.89  | |   (17)  op(e2, e2) = all_4_1
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (5), (14) imply:
% 204.05/34.89  | |   (18)  op(e2, e2) = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | GROUND_INST: instantiating (1) with all_4_1, all_52_10, e2, e2, simplifying
% 204.05/34.89  | |              with (16), (17) gives:
% 204.05/34.89  | |   (19)  all_52_10 = all_4_1
% 204.05/34.89  | | 
% 204.05/34.89  | | GROUND_INST: instantiating (1) with e2, all_52_10, e2, e2, simplifying with
% 204.05/34.89  | |              (16), (18) gives:
% 204.05/34.89  | |   (20)  all_52_10 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | COMBINE_EQS: (19), (20) imply:
% 204.05/34.89  | |   (21)  all_4_1 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | REF_CLOSE: (1), (4), (11), (16), (17), (21) are inconsistent by sub-proof
% 204.05/34.89  | |            #722.
% 204.05/34.89  | | 
% 204.05/34.89  | Case 2:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (22)  all_58_7 = e2 | all_58_13 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | REF_CLOSE: (3), (6), (7), (11), (22) are inconsistent by sub-proof #721.
% 204.05/34.89  | | 
% 204.05/34.89  | End of split
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #721 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)  all_58_13 = e3
% 204.05/34.89    (2)  all_58_7 = all_10_0
% 204.05/34.89    (3)   ~ (all_10_0 = e2)
% 204.05/34.89    (4)  all_58_7 = e2 | all_58_13 = e2
% 204.05/34.89    (5)   ~ (e3 = e2)
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | BETA: splitting (4) gives:
% 204.05/34.89  | 
% 204.05/34.89  | Case 1:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (6)  all_58_7 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | COMBINE_EQS: (2), (6) imply:
% 204.05/34.89  | |   (7)  all_10_0 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (3), (7) imply:
% 204.05/34.89  | |   (8)  $false
% 204.05/34.89  | | 
% 204.05/34.89  | | CLOSE: (8) is inconsistent.
% 204.05/34.89  | | 
% 204.05/34.89  | Case 2:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (9)  all_58_13 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1248.
% 204.05/34.89  | | 
% 204.05/34.89  | End of split
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #722 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.89    (2)  op(e2, e2) = all_52_10
% 204.05/34.89    (3)  op(e2, all_4_1) = e3
% 204.05/34.89    (4)  op(e2, e2) = all_4_1
% 204.05/34.89    (5)  all_4_1 = e2
% 204.05/34.89    (6)   ~ (e3 = e2)
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (3), (5) imply:
% 204.05/34.89  |   (7)  op(e2, e2) = e3
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (4), (5) imply:
% 204.05/34.89  |   (8)  op(e2, e2) = e2
% 204.05/34.89  | 
% 204.05/34.89  | REF_CLOSE: (1), (2), (6), (7), (8) are inconsistent by sub-proof #975.
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #723 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)  all_58_14 = all_52_23
% 204.05/34.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.89    (3)  op(all_52_7, all_52_7) = e0
% 204.05/34.89    (4)  op(all_52_5, all_52_5) = e1
% 204.05/34.89    (5)   ~ (e3 = e0)
% 204.05/34.89    (6)   ~ (all_52_3 = all_52_19)
% 204.05/34.89    (7)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.89    (8)  all_58_0 = all_6_2
% 204.05/34.89    (9)  all_56_4 = all_52_3
% 204.05/34.89    (10)  all_58_13 = e3
% 204.05/34.89    (11)  op(all_52_19, all_52_19) = all_52_18
% 204.05/34.89    (12)  all_58_9 = all_52_25
% 204.05/34.89    (13)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.05/34.89    (14)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.89    (15)  op(e2, e2) = all_4_2
% 204.05/34.89    (16)  all_58_11 = all_52_29
% 204.05/34.89    (17)  op(e0, e0) = all_14_2
% 204.05/34.89    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.89    (19)  all_56_9 = all_52_13
% 204.05/34.89    (20)   ~ (all_52_13 = all_10_2)
% 204.05/34.89    (21)   ~ (all_52_29 = all_10_2)
% 204.05/34.89    (22)  all_58_7 = all_52_13
% 204.05/34.89    (23)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.89    (24)  op(all_6_2, all_6_2) = e3
% 204.05/34.89    (25)   ~ (all_52_5 = all_52_7)
% 204.05/34.89    (26)  all_58_12 = all_52_7
% 204.05/34.89    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.89    (28)   ~ (all_52_7 = e3)
% 204.05/34.89    (29)   ~ (all_52_7 = all_14_2)
% 204.05/34.89    (30)  all_58_8 = e3 | all_58_11 = e3
% 204.05/34.89    (31)  all_58_2 = all_52_3
% 204.05/34.89    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.89    (33)   ~ (all_52_29 = e3)
% 204.05/34.89    (34)  op(all_52_3, all_52_3) = e2
% 204.05/34.89    (35)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.89    (36)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.05/34.89    (37)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.89    (38)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.89    (39)   ~ (all_52_13 = all_4_2)
% 204.05/34.89    (40)  all_58_0 = e3
% 204.05/34.89    (41)  all_58_15 = all_14_2
% 204.05/34.89    (42)   ~ (all_52_19 = all_10_2)
% 204.05/34.89    (43)  all_58_8 = all_10_2
% 204.05/34.89    (44)   ~ (all_52_5 = all_10_2)
% 204.05/34.89    (45)  op(all_52_29, all_52_29) = all_52_28
% 204.05/34.89    (46)  all_56_12 = all_52_7
% 204.05/34.89    (47)   ~ (all_52_25 = e2)
% 204.05/34.89    (48)   ~ (all_52_5 = all_6_2)
% 204.05/34.89    (49)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.05/34.89    (50)  all_58_10 = e3
% 204.05/34.89    (51)  op(e3, e3) = all_6_2
% 204.05/34.89    (52)   ~ (all_4_2 = e2)
% 204.05/34.89    (53)   ~ (all_52_3 = all_52_7)
% 204.05/34.89    (54)  all_58_5 = all_52_19
% 204.05/34.89    (55)  all_58_6 = all_52_5
% 204.05/34.89    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.89    (57)   ~ (e1 = e0)
% 204.05/34.89    (58)   ~ (e3 = e2)
% 204.05/34.89    (59)  op(all_52_13, all_52_13) = all_52_12
% 204.05/34.89    (60)  op(e1, e1) = all_10_2
% 204.05/34.89    (61)   ~ (all_52_23 = all_10_2)
% 204.05/34.89    (62)  all_58_3 = all_4_2
% 204.05/34.89    (63)   ~ (all_52_3 = all_4_2)
% 204.05/34.89    (64)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.05/34.89    (65)   ~ (all_52_13 = all_52_29)
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | BETA: splitting (30) gives:
% 204.05/34.89  | 
% 204.05/34.89  | Case 1:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (66)  all_58_8 = e3
% 204.05/34.89  | | 
% 204.05/34.89  | | COMBINE_EQS: (43), (66) imply:
% 204.05/34.89  | |   (67)  all_10_2 = e3
% 204.05/34.89  | | 
% 204.05/34.89  | | SIMP: (67) implies:
% 204.05/34.89  | |   (68)  all_10_2 = e3
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (20), (68) imply:
% 204.05/34.89  | |   (69)   ~ (all_52_13 = e3)
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (42), (68) imply:
% 204.05/34.89  | |   (70)   ~ (all_52_19 = e3)
% 204.05/34.89  | | 
% 204.05/34.89  | | BETA: splitting (64) gives:
% 204.05/34.89  | | 
% 204.05/34.89  | | Case 1:
% 204.05/34.89  | | | 
% 204.05/34.89  | | |   (71)  all_58_2 = e2
% 204.05/34.89  | | | 
% 204.05/34.89  | | | COMBINE_EQS: (31), (71) imply:
% 204.05/34.89  | | |   (72)  all_52_3 = e2
% 204.05/34.89  | | | 
% 204.05/34.89  | | | REF_CLOSE: (2), (15), (34), (63), (72) are inconsistent by sub-proof
% 204.05/34.89  | | |            #1157.
% 204.05/34.89  | | | 
% 204.05/34.89  | | Case 2:
% 204.05/34.89  | | | 
% 204.05/34.89  | | |   (73)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.05/34.89  | | | 
% 204.05/34.89  | | | BETA: splitting (73) gives:
% 204.05/34.89  | | | 
% 204.05/34.89  | | | Case 1:
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | |   (74)  all_58_3 = e2
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | COMBINE_EQS: (62), (74) imply:
% 204.05/34.89  | | | |   (75)  all_4_2 = e2
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | REDUCE: (52), (75) imply:
% 204.05/34.89  | | | |   (76)  $false
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | CLOSE: (76) is inconsistent.
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | Case 2:
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | |   (77)  all_58_5 = e2 | all_58_10 = e2
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | BETA: splitting (77) gives:
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | | Case 1:
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | |   (78)  all_58_5 = e2
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | COMBINE_EQS: (54), (78) imply:
% 204.05/34.89  | | | | |   (79)  all_52_19 = e2
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REDUCE: (6), (79) imply:
% 204.05/34.89  | | | | |   (80)   ~ (all_52_3 = e2)
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REDUCE: (70), (79) imply:
% 204.05/34.89  | | | | |   (81)   ~ (e3 = e2)
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REDUCE: (11), (79) imply:
% 204.05/34.89  | | | | |   (82)  op(e2, e2) = all_52_18
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_18, e2, e2,
% 204.05/34.89  | | | | |              simplifying with (15), (82) gives:
% 204.05/34.89  | | | | |   (83)  all_52_18 = all_4_2
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | BETA: splitting (49) gives:
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | Case 1:
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | |   (84)  all_58_9 = e2
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | | COMBINE_EQS: (12), (84) imply:
% 204.05/34.89  | | | | | |   (85)  all_52_25 = e2
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | | REDUCE: (47), (85) imply:
% 204.05/34.89  | | | | | |   (86)  $false
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | | CLOSE: (86) is inconsistent.
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | Case 2:
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | |   (87)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | | BETA: splitting (37) gives:
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | | Case 1:
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | |   (88)  all_58_0 = e2
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | | REF_CLOSE: (16), (30), (33), (40), (58), (66), (88) are
% 204.05/34.89  | | | | | | |            inconsistent by sub-proof #728.
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | Case 2:
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | |   (89)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | | BETA: splitting (13) gives:
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | |   (90)  all_58_6 = e2
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (10), (14), (17), (25), (26),
% 204.05/34.89  | | | | | | | |            (29), (35), (38), (46), (55), (57), (60), (61), (90)
% 204.05/34.89  | | | | | | | |            are inconsistent by sub-proof #727.
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | |   (91)   ~ (all_58_6 = e2)
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | | REDUCE: (55), (91) imply:
% 204.05/34.89  | | | | | | | |   (92)   ~ (all_52_5 = e2)
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | | BETA: splitting (89) gives:
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | |   (93)  all_58_2 = e2
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | COMBINE_EQS: (31), (93) imply:
% 204.05/34.89  | | | | | | | | |   (94)  all_52_3 = e2
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | REDUCE: (80), (94) imply:
% 204.05/34.89  | | | | | | | | |   (95)  $false
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | CLOSE: (95) is inconsistent.
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | |   (96)  all_58_6 = e2 | all_58_12 = e2
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | BETA: splitting (96) gives:
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | |   (97)  all_58_6 = e2
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | COMBINE_EQS: (55), (97) imply:
% 204.05/34.89  | | | | | | | | | |   (98)  all_52_5 = e2
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | REDUCE: (92), (98) imply:
% 204.05/34.89  | | | | | | | | | |   (99)  $false
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | CLOSE: (99) is inconsistent.
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | |   (100)  all_58_12 = e2
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | COMBINE_EQS: (26), (100) imply:
% 204.05/34.89  | | | | | | | | | |   (101)  all_52_7 = e2
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | REDUCE: (29), (101) imply:
% 204.05/34.89  | | | | | | | | | |   (102)   ~ (all_14_2 = e2)
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | SIMP: (102) implies:
% 204.05/34.89  | | | | | | | | | |   (103)   ~ (all_14_2 = e2)
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | REDUCE: (3), (101) imply:
% 204.05/34.89  | | | | | | | | | |   (104)  op(e2, e2) = e0
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | BETA: splitting (87) gives:
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | |   (105)  all_58_10 = e2
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | REF_CLOSE: (16), (30), (33), (50), (58), (66), (105) are
% 204.05/34.89  | | | | | | | | | | |            inconsistent by sub-proof #726.
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | |   (106)  all_58_11 = e2 | all_58_15 = e2
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | BETA: splitting (106) gives:
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | |   (107)  all_58_11 = e2
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | COMBINE_EQS: (16), (107) imply:
% 204.05/34.89  | | | | | | | | | | | |   (108)  all_52_29 = e2
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | REDUCE: (65), (108) imply:
% 204.05/34.89  | | | | | | | | | | | |   (109)   ~ (all_52_13 = e2)
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | REDUCE: (45), (108) imply:
% 204.05/34.89  | | | | | | | | | | | |   (110)  op(e2, e2) = all_52_28
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_28, e2, e2,
% 204.05/34.89  | | | | | | | | | | | |              simplifying with (15), (110) gives:
% 204.05/34.89  | | | | | | | | | | | |   (111)  all_52_28 = all_4_2
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_52_28, e2, e2,
% 204.05/34.89  | | | | | | | | | | | |              simplifying with (104), (110) gives:
% 204.05/34.89  | | | | | | | | | | | |   (112)  all_52_28 = e0
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | COMBINE_EQS: (111), (112) imply:
% 204.05/34.89  | | | | | | | | | | | |   (113)  all_4_2 = e0
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | SIMP: (113) implies:
% 204.05/34.89  | | | | | | | | | | | |   (114)  all_4_2 = e0
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | REDUCE: (63), (114) imply:
% 204.05/34.89  | | | | | | | | | | | |   (115)   ~ (all_52_3 = e0)
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | REDUCE: (39), (114) imply:
% 204.05/34.89  | | | | | | | | | | | |   (116)   ~ (all_52_13 = e0)
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | BETA: splitting (23) gives:
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | |   (117)  all_58_2 = e1
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | COMBINE_EQS: (31), (117) imply:
% 204.05/34.89  | | | | | | | | | | | | |   (118)  all_52_3 = e1
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | SIMP: (118) implies:
% 204.05/34.89  | | | | | | | | | | | | |   (119)  all_52_3 = e1
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | REDUCE: (34), (119) imply:
% 204.05/34.89  | | | | | | | | | | | | |   (120)  op(e1, e1) = e2
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | BETA: splitting (7) gives:
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | |   (121)  all_56_9 = e2
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | REF_CLOSE: (19), (109), (121) are inconsistent by sub-proof
% 204.05/34.89  | | | | | | | | | | | | | |            #955.
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | |   (122)  all_56_9 = e1 | all_56_9 = e0
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | Case 1:
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | |   (123)  all_56_9 = e1
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | | COMBINE_EQS: (19), (123) imply:
% 204.05/34.89  | | | | | | | | | | | | | | |   (124)  all_52_13 = e1
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | | SIMP: (124) implies:
% 204.05/34.89  | | | | | | | | | | | | | | |   (125)  all_52_13 = e1
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (15), (16), (17), (18), (22),
% 204.05/34.89  | | | | | | | | | | | | | | |            (24), (26), (27), (29), (31), (32), (33), (34),
% 204.05/34.89  | | | | | | | | | | | | | | |            (43), (44), (48), (51), (55), (56), (58), (59),
% 204.05/34.89  | | | | | | | | | | | | | | |            (60), (63), (69), (120), (125) are inconsistent by
% 204.05/34.89  | | | | | | | | | | | | | | |            sub-proof #725.
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | |   (126)  all_56_9 = e0
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | | REF_CLOSE: (19), (116), (126) are inconsistent by sub-proof
% 204.05/34.89  | | | | | | | | | | | | | | |            #953.
% 204.05/34.89  | | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | |   (127)   ~ (all_58_2 = e1)
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | REDUCE: (31), (127) imply:
% 204.05/34.89  | | | | | | | | | | | | |   (128)   ~ (all_52_3 = e1)
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (80), (115), (128) are inconsistent by
% 204.05/34.89  | | | | | | | | | | | | |            sub-proof #724.
% 204.05/34.89  | | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | Case 2:
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | |   (129)  all_58_15 = e2
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | COMBINE_EQS: (41), (129) imply:
% 204.05/34.89  | | | | | | | | | | | |   (130)  all_14_2 = e2
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | SIMP: (130) implies:
% 204.05/34.89  | | | | | | | | | | | |   (131)  all_14_2 = e2
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | REDUCE: (103), (131) imply:
% 204.05/34.89  | | | | | | | | | | | |   (132)  $false
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 204.05/34.89  | | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | | | 
% 204.05/34.89  | | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | | 
% 204.05/34.89  | | | | | | | | End of split
% 204.05/34.89  | | | | | | | | 
% 204.05/34.89  | | | | | | | End of split
% 204.05/34.89  | | | | | | | 
% 204.05/34.89  | | | | | | End of split
% 204.05/34.89  | | | | | | 
% 204.05/34.89  | | | | | End of split
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | Case 2:
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | |   (133)  all_58_10 = e2
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | | REF_CLOSE: (16), (30), (33), (50), (58), (66), (133) are inconsistent
% 204.05/34.89  | | | | |            by sub-proof #726.
% 204.05/34.89  | | | | | 
% 204.05/34.89  | | | | End of split
% 204.05/34.89  | | | | 
% 204.05/34.89  | | | End of split
% 204.05/34.89  | | | 
% 204.05/34.89  | | End of split
% 204.05/34.89  | | 
% 204.05/34.89  | Case 2:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (134)  all_58_11 = e3
% 204.05/34.89  | | 
% 204.05/34.89  | | REF_CLOSE: (16), (33), (134) are inconsistent by sub-proof #1323.
% 204.05/34.89  | | 
% 204.05/34.89  | End of split
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #724 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)  all_56_4 = all_52_3
% 204.05/34.89    (2)   ~ (all_52_3 = e1)
% 204.05/34.89    (3)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.05/34.89    (4)   ~ (all_52_3 = e0)
% 204.05/34.89    (5)   ~ (all_52_3 = e2)
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | BETA: splitting (3) gives:
% 204.05/34.89  | 
% 204.05/34.89  | Case 1:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (6)  all_56_4 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | COMBINE_EQS: (1), (6) imply:
% 204.05/34.89  | |   (7)  all_52_3 = e2
% 204.05/34.89  | | 
% 204.05/34.89  | | REDUCE: (5), (7) imply:
% 204.05/34.89  | |   (8)  $false
% 204.05/34.89  | | 
% 204.05/34.89  | | CLOSE: (8) is inconsistent.
% 204.05/34.89  | | 
% 204.05/34.89  | Case 2:
% 204.05/34.89  | | 
% 204.05/34.89  | |   (9)  all_56_4 = e1 | all_56_4 = e0
% 204.05/34.89  | | 
% 204.05/34.89  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #1308.
% 204.05/34.89  | | 
% 204.05/34.89  | End of split
% 204.05/34.89  | 
% 204.05/34.89  End of proof
% 204.05/34.89  
% 204.05/34.89  Sub-proof #725 shows that the following formulas are inconsistent:
% 204.05/34.89  ----------------------------------------------------------------
% 204.05/34.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.89    (2)  op(all_52_7, all_52_7) = e0
% 204.05/34.89    (3)  op(all_52_5, all_52_5) = e1
% 204.05/34.89    (4)  all_58_0 = all_6_2
% 204.05/34.89    (5)  op(e2, e2) = all_4_2
% 204.05/34.89    (6)  all_58_11 = all_52_29
% 204.05/34.89    (7)  op(e0, e0) = all_14_2
% 204.05/34.89    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.89    (9)  all_58_7 = all_52_13
% 204.05/34.89    (10)  op(all_6_2, all_6_2) = e3
% 204.05/34.89    (11)  all_58_12 = all_52_7
% 204.05/34.89    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.89    (13)   ~ (all_52_7 = all_14_2)
% 204.05/34.89    (14)  all_58_2 = all_52_3
% 204.05/34.89    (15)  op(e1, e1) = e2
% 204.05/34.89    (16)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.89    (17)   ~ (all_52_29 = e3)
% 204.05/34.89    (18)  op(all_52_3, all_52_3) = e2
% 204.05/34.89    (19)  all_52_13 = e1
% 204.05/34.89    (20)  all_58_8 = all_10_2
% 204.05/34.89    (21)   ~ (all_52_5 = all_10_2)
% 204.05/34.89    (22)   ~ (all_52_5 = all_6_2)
% 204.05/34.89    (23)  op(e3, e3) = all_6_2
% 204.05/34.89    (24)   ~ (all_52_13 = e3)
% 204.05/34.89    (25)  all_58_6 = all_52_5
% 204.05/34.89    (26)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.89    (27)   ~ (e3 = e2)
% 204.05/34.89    (28)  op(all_52_13, all_52_13) = all_52_12
% 204.05/34.89    (29)  op(e1, e1) = all_10_2
% 204.05/34.89    (30)   ~ (all_52_3 = all_4_2)
% 204.05/34.89  
% 204.05/34.89  Begin of proof
% 204.05/34.89  | 
% 204.05/34.89  | COMBINE_EQS: (9), (19) imply:
% 204.05/34.89  |   (31)  all_58_7 = e1
% 204.05/34.89  | 
% 204.05/34.89  | REDUCE: (19), (24) imply:
% 204.05/34.90  |   (32)   ~ (e3 = e1)
% 204.05/34.90  | 
% 204.05/34.90  | SIMP: (32) implies:
% 204.05/34.90  |   (33)   ~ (e3 = e1)
% 204.05/34.90  | 
% 204.05/34.90  | REDUCE: (19), (28) imply:
% 204.05/34.90  |   (34)  op(e1, e1) = all_52_12
% 204.05/34.90  | 
% 204.05/34.90  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 204.05/34.90  |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (25), (26),
% 204.05/34.90  |            (27), (29), (30), (31), (33), (34) are inconsistent by sub-proof
% 204.05/34.90  |            #875.
% 204.05/34.90  | 
% 204.05/34.90  End of proof
% 204.05/34.90  
% 204.05/34.90  Sub-proof #726 shows that the following formulas are inconsistent:
% 204.05/34.90  ----------------------------------------------------------------
% 204.05/34.90    (1)  all_58_10 = e2
% 204.05/34.90    (2)  all_58_8 = e3
% 204.05/34.90    (3)  all_58_11 = all_52_29
% 204.05/34.90    (4)  all_58_8 = e3 | all_58_11 = e3
% 204.05/34.90    (5)   ~ (all_52_29 = e3)
% 204.05/34.90    (6)  all_58_10 = e3
% 204.05/34.90    (7)   ~ (e3 = e2)
% 204.05/34.90  
% 204.05/34.90  Begin of proof
% 204.05/34.90  | 
% 204.05/34.90  | COMBINE_EQS: (1), (6) imply:
% 204.05/34.90  |   (8)  e3 = e2
% 204.05/34.90  | 
% 204.05/34.90  | COMBINE_EQS: (2), (8) imply:
% 204.05/34.90  |   (9)  all_58_8 = e2
% 204.05/34.90  | 
% 204.05/34.90  | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #1271.
% 204.05/34.90  | 
% 204.05/34.90  End of proof
% 204.05/34.90  
% 204.05/34.90  Sub-proof #727 shows that the following formulas are inconsistent:
% 204.05/34.90  ----------------------------------------------------------------
% 204.05/34.90    (1)  all_58_14 = all_52_23
% 204.05/34.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.90    (3)  all_58_6 = e2
% 204.05/34.90    (4)  op(all_52_7, all_52_7) = e0
% 204.05/34.90    (5)   ~ (e3 = e0)
% 204.05/34.90    (6)  all_58_13 = e3
% 204.05/34.90    (7)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.90    (8)  op(e0, e0) = all_14_2
% 204.05/34.90    (9)   ~ (all_52_5 = all_52_7)
% 204.05/34.90    (10)  all_58_12 = all_52_7
% 204.05/34.90    (11)   ~ (all_52_7 = all_14_2)
% 204.05/34.90    (12)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.90    (13)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.90    (14)  all_56_12 = all_52_7
% 204.05/34.90    (15)  all_58_6 = all_52_5
% 204.05/34.90    (16)   ~ (e1 = e0)
% 204.05/34.90    (17)  op(e1, e1) = all_10_2
% 204.05/34.90    (18)   ~ (all_52_23 = all_10_2)
% 204.05/34.90  
% 204.05/34.90  Begin of proof
% 204.05/34.90  | 
% 204.05/34.90  | COMBINE_EQS: (3), (15) imply:
% 204.05/34.90  |   (19)  all_52_5 = e2
% 204.05/34.90  | 
% 204.05/34.90  | REDUCE: (9), (19) imply:
% 204.05/34.90  |   (20)   ~ (all_52_7 = e2)
% 204.05/34.90  | 
% 204.05/34.90  | SIMP: (20) implies:
% 204.05/34.90  |   (21)   ~ (all_52_7 = e2)
% 204.05/34.90  | 
% 204.05/34.90  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 204.05/34.90  |            (16), (17), (18), (21) are inconsistent by sub-proof #1169.
% 204.05/34.90  | 
% 204.05/34.90  End of proof
% 204.05/34.90  
% 204.05/34.90  Sub-proof #728 shows that the following formulas are inconsistent:
% 204.05/34.90  ----------------------------------------------------------------
% 204.05/34.90    (1)  all_58_8 = e3
% 204.05/34.90    (2)  all_58_11 = all_52_29
% 204.05/34.90    (3)  all_58_8 = e3 | all_58_11 = e3
% 204.05/34.90    (4)   ~ (all_52_29 = e3)
% 204.05/34.90    (5)  all_58_0 = e3
% 204.05/34.90    (6)  all_58_0 = e2
% 204.05/34.90    (7)   ~ (e3 = e2)
% 204.05/34.90  
% 204.05/34.90  Begin of proof
% 204.05/34.90  | 
% 204.05/34.90  | COMBINE_EQS: (5), (6) imply:
% 204.05/34.90  |   (8)  e3 = e2
% 204.05/34.90  | 
% 204.05/34.90  | COMBINE_EQS: (1), (8) imply:
% 204.05/34.90  |   (9)  all_58_8 = e2
% 204.05/34.90  | 
% 204.05/34.90  | REF_CLOSE: (2), (3), (4), (7), (9) are inconsistent by sub-proof #1271.
% 204.05/34.90  | 
% 204.05/34.90  End of proof
% 204.05/34.90  
% 204.05/34.90  Sub-proof #729 shows that the following formulas are inconsistent:
% 204.05/34.90  ----------------------------------------------------------------
% 204.05/34.90    (1)   ~ (all_52_15 = all_52_23)
% 204.05/34.90    (2)   ~ (all_52_25 = all_52_27)
% 204.05/34.90    (3)  all_58_14 = all_52_23
% 204.05/34.90    (4)   ~ (e3 = e1)
% 204.05/34.90    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.05/34.90    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.90    (7)  all_58_1 = all_52_9
% 204.05/34.90    (8)   ~ (e3 = e0)
% 204.05/34.90    (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.05/34.90    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.90    (11)   ~ (all_52_7 = all_52_15)
% 204.05/34.90    (12)  op(all_52_7, all_52_7) = all_52_6
% 204.05/34.90    (13)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.90    (14)  all_58_0 = all_6_2
% 204.05/34.90    (15)   ~ (all_10_0 = e3)
% 204.05/34.90    (16)  all_40_2 = all_10_2
% 204.05/34.90    (17)  op(all_52_5, all_52_5) = all_52_4
% 204.05/34.90    (18)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.05/34.90    (19)   ~ (all_52_27 = all_52_29)
% 204.05/34.90    (20)  all_58_13 = all_52_15
% 204.05/34.90    (21)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.90    (22)  all_58_9 = all_52_25
% 204.05/34.90    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.05/34.90    (24)  op(all_52_27, all_52_27) = all_52_26
% 204.05/34.90    (25)  op(e2, e2) = all_4_2
% 204.05/34.90    (26)  all_58_7 = all_10_0
% 204.05/34.90    (27)  all_58_11 = all_52_29
% 204.05/34.90    (28)   ~ (all_52_3 = all_52_27)
% 204.05/34.90    (29)  op(all_6_2, all_6_2) = all_52_0
% 204.05/34.90    (30)   ~ (all_52_7 = all_6_2)
% 204.05/34.90    (31)  op(e0, e0) = all_14_2
% 204.05/34.90    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.90    (33)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.90    (34)  all_58_15 = e0
% 204.05/34.90    (35)  all_56_11 = all_52_29
% 204.05/34.90    (36)   ~ (all_10_0 = e2)
% 204.05/34.90    (37)   ~ (all_52_25 = e0)
% 204.05/34.90    (38)   ~ (e2 = e1)
% 204.05/34.90    (39)  op(e0, e0) = e0
% 204.05/34.90    (40)  all_58_10 = all_52_27
% 204.05/34.90    (41)  all_56_8 = all_52_5
% 204.05/34.90    (42)  op(all_52_15, all_52_15) = all_52_14
% 204.05/34.90    (43)  all_56_9 = all_10_0
% 204.05/34.90    (44)   ~ (all_52_25 = all_52_29)
% 204.05/34.90    (45)   ~ (all_10_0 = all_4_2)
% 204.05/34.90    (46)   ~ (all_52_5 = all_52_7)
% 204.05/34.90    (47)  all_58_12 = all_52_7
% 204.05/34.90    (48)  op(e2, e1) = all_52_19
% 204.05/34.90    (49)   ~ (all_52_7 = all_14_2)
% 204.05/34.90    (50)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.05/34.90    (51)  all_58_2 = all_52_3
% 204.05/34.90    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.90    (53)  all_56_7 = all_52_27
% 204.05/34.90    (54)   ~ (e2 = e0)
% 204.05/34.90    (55)   ~ (all_52_5 = all_52_29)
% 204.05/34.90    (56)   ~ (all_52_29 = e0)
% 204.05/34.90    (57)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.90    (58)   ~ (all_52_19 = all_52_27)
% 204.05/34.90    (59)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.05/34.90    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.90    (61)   ~ (all_52_19 = all_10_2)
% 204.05/34.90    (62)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.90    (63)  all_58_8 = all_10_2
% 204.05/34.90    (64)   ~ (all_52_5 = all_10_2)
% 204.05/34.90    (65)  op(all_52_29, all_52_29) = all_52_28
% 204.05/34.90    (66)  all_56_12 = all_52_7
% 204.05/34.90    (67)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.90    (68)   ~ (all_52_25 = all_6_2)
% 204.05/34.90    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.90    (70)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.05/34.90    (71)   ~ (all_52_9 = all_6_2)
% 204.05/34.90    (72)  op(e3, e3) = all_6_2
% 204.05/34.90    (73)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.90    (74)   ~ (all_52_29 = all_10_0)
% 204.05/34.90    (75)  op(all_4_2, all_4_2) = all_52_10
% 204.05/34.90    (76)  all_40_0 = all_10_0
% 204.05/34.90    (77)  all_56_3 = all_52_25
% 204.05/34.90    (78)  all_58_5 = all_52_19
% 204.05/34.90    (79)   ~ (all_52_27 = all_4_2)
% 204.05/34.90    (80)  all_58_6 = all_52_5
% 204.05/34.90    (81)  op(all_10_2, e1) = e2
% 204.05/34.90    (82)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.90    (83)   ~ (all_52_17 = all_6_2)
% 204.05/34.90    (84)   ~ (e1 = e0)
% 204.05/34.90    (85)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.05/34.90    (86)   ~ (e3 = e2)
% 204.05/34.90    (87)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.90    (88)  op(e1, e1) = all_10_2
% 204.05/34.90    (89)   ~ (all_52_5 = all_10_0)
% 204.05/34.90    (90)  all_58_3 = all_4_2
% 204.05/34.90    (91)   ~ (all_52_3 = all_4_2)
% 204.05/34.90    (92)  all_58_4 = all_52_17
% 204.05/34.90    (93)   ~ (all_52_7 = e0)
% 204.05/34.90    (94)  op(all_52_25, all_52_25) = all_52_24
% 204.05/34.90  
% 204.05/34.90  Begin of proof
% 204.05/34.90  | 
% 204.05/34.90  | ALPHA: (9) implies:
% 204.05/34.90  |   (95)  all_52_6 = e0
% 204.05/34.90  |   (96)  all_52_4 = e1
% 204.05/34.90  |   (97)  all_52_2 = e2
% 204.05/34.90  |   (98)  all_52_0 = e3
% 204.05/34.90  | 
% 204.05/34.90  | REDUCE: (5), (97) imply:
% 204.05/34.90  |   (99)  op(all_52_3, all_52_3) = e2
% 204.05/34.90  | 
% 204.05/34.90  | REDUCE: (17), (96) imply:
% 204.05/34.90  |   (100)  op(all_52_5, all_52_5) = e1
% 204.05/34.90  | 
% 204.05/34.90  | REDUCE: (12), (95) imply:
% 204.05/34.90  |   (101)  op(all_52_7, all_52_7) = e0
% 204.05/34.90  | 
% 204.05/34.90  | REDUCE: (29), (98) imply:
% 204.05/34.90  |   (102)  op(all_6_2, all_6_2) = e3
% 204.05/34.90  | 
% 204.05/34.90  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (13), (14), (15),
% 204.05/34.90  |            (16), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 204.05/34.90  |            (28), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 204.05/34.90  |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 204.05/34.90  |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 204.05/34.90  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 204.05/34.90  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 204.05/34.90  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 204.05/34.90  |            (99), (100), (101), (102) are inconsistent by sub-proof #994.
% 204.05/34.90  | 
% 204.05/34.90  End of proof
% 204.05/34.90  
% 204.05/34.90  Sub-proof #730 shows that the following formulas are inconsistent:
% 204.05/34.90  ----------------------------------------------------------------
% 204.05/34.90    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.05/34.90    (2)   ~ (all_52_15 = all_52_23)
% 204.05/34.90    (3)   ~ (all_52_25 = all_52_27)
% 204.05/34.90    (4)  all_58_14 = all_52_23
% 204.05/34.90    (5)   ~ (e3 = e1)
% 204.05/34.90    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.05/34.90    (7)  op(all_52_3, all_52_3) = all_52_2
% 204.05/34.90    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.90    (9)   ~ (all_52_5 = all_52_13)
% 204.05/34.90    (10)  all_58_1 = all_52_9
% 204.05/34.90    (11)   ~ (all_52_9 = all_52_13)
% 204.05/34.90    (12)   ~ (e3 = e0)
% 204.05/34.90    (13)  op(e2, e3) = all_52_3
% 204.05/34.90    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.90    (15)  op(e0, e2) = all_52_15
% 204.05/34.90    (16)   ~ (all_52_7 = all_52_15)
% 204.05/34.90    (17)   ~ (all_52_3 = all_52_19)
% 204.05/34.90    (18)  op(all_52_7, all_52_7) = all_52_6
% 204.05/34.90    (19)   ~ (all_52_17 = all_52_25)
% 204.05/34.90    (20)   ~ (all_52_3 = all_6_2)
% 204.05/34.90    (21)  all_58_0 = all_6_2
% 204.05/34.90    (22)  op(all_14_2, e0) = all_14_1
% 204.05/34.90    (23)  all_56_4 = all_52_3
% 204.05/34.90    (24)   ~ (all_52_17 = all_10_2)
% 204.05/34.90    (25)  op(e3, e0) = all_52_25
% 204.05/34.90    (26)  op(e0, all_14_1) = all_14_0
% 204.05/34.90    (27)  op(all_52_5, all_52_5) = all_52_4
% 204.05/34.90    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.05/34.90    (29)  op(all_52_19, all_52_19) = all_52_18
% 204.05/34.90    (30)   ~ (all_52_27 = all_52_29)
% 204.05/34.90    (31)  all_58_13 = all_52_15
% 204.05/34.90    (32)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.90    (33)  all_58_9 = all_52_25
% 204.05/34.90    (34)   ~ (all_6_1 = e1)
% 204.05/34.90    (35)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.05/34.90    (36)   ~ (all_52_29 = all_14_2)
% 204.05/34.90    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.05/34.90    (38)  op(e2, all_4_1) = e3
% 204.05/34.90    (39)  op(all_52_27, all_52_27) = all_52_26
% 204.05/34.90    (40)  op(e1, e3) = all_52_5
% 204.05/34.90    (41)  op(e2, e2) = all_4_2
% 204.05/34.90    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.05/34.90    (43)   ~ (all_52_3 = all_52_5)
% 204.05/34.90    (44)  all_58_11 = all_52_29
% 204.05/34.90    (45)  all_56_5 = all_4_2
% 204.05/34.90    (46)   ~ (all_52_25 = all_14_2)
% 204.05/34.90    (47)   ~ (all_52_9 = all_52_15)
% 204.05/34.90    (48)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.05/34.90    (49)   ~ (all_52_3 = all_52_27)
% 204.05/34.90    (50)  op(all_10_2, e1) = all_10_1
% 204.05/34.90    (51)  op(all_6_2, all_6_2) = all_52_0
% 204.05/34.90    (52)   ~ (all_52_7 = all_6_2)
% 204.05/34.90    (53)  op(e0, e0) = all_14_2
% 204.05/34.90    (54)  all_56_15 = all_14_2
% 204.05/34.90    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.90    (56)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.05/34.90    (57)  op(e2, all_4_1) = all_4_0
% 204.05/34.90    (58)  op(e1, e0) = all_52_29
% 204.05/34.90    (59)  all_56_11 = all_52_29
% 204.05/34.90    (60)   ~ (all_4_1 = e1)
% 204.05/34.90    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.05/34.90    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.05/34.90    (63)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.05/34.90    (64)  all_56_9 = all_52_13
% 204.05/34.90    (65)   ~ (e2 = e1)
% 204.05/34.90    (66)   ~ (all_52_13 = all_10_2)
% 204.05/34.90    (67)   ~ (all_6_0 = e1)
% 204.05/34.90    (68)  all_58_10 = all_52_27
% 204.05/34.90    (69)  all_56_8 = all_52_5
% 204.05/34.90    (70)  op(all_52_9, all_52_9) = all_52_8
% 204.05/34.90    (71)  op(all_52_15, all_52_15) = all_52_14
% 204.05/34.90    (72)   ~ (all_52_19 = all_52_23)
% 204.05/34.90    (73)   ~ (all_52_25 = all_52_29)
% 204.05/34.90    (74)   ~ (all_52_29 = all_10_2)
% 204.05/34.90    (75)  all_58_7 = all_52_13
% 204.05/34.90    (76)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.05/34.90    (77)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.90    (78)   ~ (all_52_5 = all_52_7)
% 204.05/34.90    (79)  all_58_12 = all_52_7
% 204.05/34.90    (80)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.90    (81)   ~ (all_52_7 = all_14_2)
% 204.05/34.90    (82)   ~ (all_14_2 = e0)
% 204.05/34.90    (83)  all_58_2 = all_52_3
% 204.05/34.90    (84)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.05/34.90    (85)  all_56_2 = all_52_17
% 204.05/34.90    (86)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.05/34.90    (87)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.90    (88)  op(e3, all_6_1) = all_6_0
% 204.05/34.90    (89)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.05/34.90    (90)   ~ (all_14_0 = e3)
% 204.05/34.90    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.90    (92)  all_56_7 = all_52_27
% 204.05/34.90    (93)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.05/34.90    (94)   ~ (e2 = e0)
% 204.05/34.90    (95)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.05/34.90    (96)  op(all_4_2, e2) = all_4_1
% 204.05/34.90    (97)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.05/34.90    (98)   ~ (all_52_5 = all_52_29)
% 204.05/34.90    (99)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.90    (100)  all_56_6 = all_52_19
% 204.05/34.90    (101)   ~ (all_52_15 = all_14_2)
% 204.05/34.90    (102)   ~ (all_52_19 = all_52_27)
% 204.05/34.90    (103)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.05/34.90    (104)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.90    (105)   ~ (all_6_0 = e2)
% 204.05/34.90    (106)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.90    (107)   ~ (all_52_13 = all_4_2)
% 204.05/34.90    (108)  op(e3, e1) = all_52_17
% 204.05/34.90    (109)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.05/34.90    (110)  op(e0, e3) = all_52_7
% 204.05/34.90    (111)  op(e1, e2) = all_52_13
% 204.05/34.90    (112)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.90    (113)   ~ (all_52_9 = all_52_25)
% 204.05/34.90    (114)  all_58_15 = all_14_2
% 204.05/34.90    (115)   ~ (all_52_19 = all_10_2)
% 204.05/34.90    (116)  op(all_52_23, all_52_23) = all_52_22
% 204.05/34.90    (117)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.90    (118)  all_58_8 = all_10_2
% 204.05/34.90    (119)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.05/34.90    (120)   ~ (all_52_5 = all_10_2)
% 204.05/34.90    (121)  op(all_52_29, all_52_29) = all_52_28
% 204.05/34.90    (122)   ~ (all_52_23 = all_14_2)
% 204.05/34.90    (123)  all_56_12 = all_52_7
% 204.05/34.90    (124)  op(all_52_17, all_52_17) = all_52_16
% 204.05/34.90    (125)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.05/34.90    (126)   ~ (all_52_25 = all_6_2)
% 204.05/34.90    (127)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.90    (128)   ~ (all_52_9 = all_4_2)
% 204.05/34.90    (129)   ~ (all_52_5 = all_6_2)
% 204.05/34.90    (130)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.05/34.90    (131)   ~ (all_52_9 = all_6_2)
% 204.05/34.90    (132)   ~ (all_52_13 = all_52_15)
% 204.05/34.90    (133)  all_56_0 = all_6_2
% 204.05/34.90    (134)  op(e3, e3) = all_6_2
% 204.05/34.90    (135)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.90    (136)   ~ (all_52_27 = all_14_2)
% 204.05/34.90    (137)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.05/34.90    (138)  all_56_14 = all_52_23
% 204.05/34.90    (139)  op(all_4_2, all_4_2) = all_52_10
% 204.05/34.90    (140)  all_56_3 = all_52_25
% 204.05/34.90    (141)   ~ (all_52_3 = all_52_7)
% 204.05/34.90    (142)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.90    (143)  all_58_5 = all_52_19
% 204.05/34.90    (144)  all_56_1 = all_52_9
% 204.05/34.90    (145)   ~ (all_52_15 = all_4_2)
% 204.05/34.90    (146)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.05/34.90           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.05/34.90           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.05/34.90           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.05/34.90    (147)   ~ (all_52_27 = all_4_2)
% 204.05/34.90    (148)  all_58_6 = all_52_5
% 204.05/34.90    (149)  op(e3, e2) = all_52_9
% 204.05/34.90    (150)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.90    (151)   ~ (all_52_17 = all_6_2)
% 204.05/34.90    (152)   ~ (e1 = e0)
% 204.05/34.90    (153)  op(e2, e0) = all_52_27
% 204.05/34.90    (154)   ~ (e3 = e2)
% 204.05/34.90    (155)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.90    (156)   ~ (all_52_9 = all_52_17)
% 204.05/34.90    (157)  all_56_10 = all_10_2
% 204.05/34.90    (158)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.90    (159)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.90    (160)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.05/34.90    (161)  op(all_52_13, all_52_13) = all_52_12
% 204.05/34.90    (162)   ~ (all_6_1 = e2)
% 204.05/34.90    (163)  op(e1, e1) = all_10_2
% 204.05/34.90    (164)   ~ (all_52_23 = all_10_2)
% 204.05/34.90    (165)   ~ (all_52_7 = all_52_23)
% 204.05/34.90    (166)   ~ (all_52_17 = all_52_19)
% 204.05/34.90    (167)  all_58_3 = all_4_2
% 204.05/34.90    (168)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.05/34.90    (169)  all_56_13 = all_52_15
% 204.05/34.90    (170)   ~ (all_52_3 = all_4_2)
% 204.05/34.90    (171)   ~ (all_52_19 = all_4_2)
% 204.05/34.90    (172)   ~ (all_52_17 = all_52_23)
% 204.05/34.90    (173)  op(all_6_2, e3) = all_6_1
% 204.05/34.90    (174)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.05/34.90    (175)   ~ (all_52_13 = all_52_29)
% 204.05/34.90    (176)  all_58_4 = all_52_17
% 204.05/34.90    (177)   ~ (all_14_0 = e1)
% 204.05/34.90    (178)   ~ (all_14_0 = e2)
% 204.05/34.90    (179)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.05/34.90    (180)  op(all_52_25, all_52_25) = all_52_24
% 204.05/34.90  
% 204.05/34.90  Begin of proof
% 204.05/34.90  | 
% 204.05/34.90  | BETA: splitting (146) gives:
% 204.05/34.90  | 
% 204.05/34.90  | Case 1:
% 204.05/34.90  | | 
% 204.05/34.90  | |   (181)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.05/34.90  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 204.05/34.90  | | 
% 204.05/34.90  | | BETA: splitting (181) gives:
% 204.05/34.90  | | 
% 204.05/34.90  | | Case 1:
% 204.05/34.90  | | | 
% 204.05/34.90  | | |   (182)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.05/34.90  | | | 
% 204.05/34.90  | | | ALPHA: (182) implies:
% 204.05/34.90  | | |   (183)  all_52_6 = e0
% 204.05/34.90  | | |   (184)  all_52_4 = e1
% 204.05/34.90  | | |   (185)  all_52_2 = e2
% 204.05/34.90  | | |   (186)  all_52_0 = e3
% 204.05/34.90  | | | 
% 204.05/34.90  | | | REDUCE: (7), (185) imply:
% 204.05/34.90  | | |   (187)  op(all_52_3, all_52_3) = e2
% 204.05/34.90  | | | 
% 204.05/34.90  | | | REDUCE: (27), (184) imply:
% 204.05/34.90  | | |   (188)  op(all_52_5, all_52_5) = e1
% 204.05/34.90  | | | 
% 204.05/34.90  | | | REDUCE: (18), (183) imply:
% 204.05/34.90  | | |   (189)  op(all_52_7, all_52_7) = e0
% 204.05/34.90  | | | 
% 204.05/34.90  | | | REDUCE: (51), (186) imply:
% 204.05/34.90  | | |   (190)  op(all_6_2, all_6_2) = e3
% 204.05/34.90  | | | 
% 204.05/34.90  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (14),
% 204.05/34.90  | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 204.05/34.90  | | |            (26), (28), (29), (31), (32), (33), (35), (36), (37), (38),
% 204.05/34.90  | | |            (39), (41), (44), (45), (46), (47), (48), (49), (50), (52),
% 204.05/34.90  | | |            (53), (54), (55), (57), (58), (59), (60), (61), (62), (63),
% 204.05/34.90  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (73), (75),
% 204.05/34.90  | | |            (76), (77), (79), (80), (81), (82), (83), (84), (85), (86),
% 204.05/34.90  | | |            (87), (88), (90), (91), (92), (93), (94), (95), (96), (98),
% 204.05/34.90  | | |            (99), (100), (101), (102), (103), (105), (106), (107), (110),
% 204.05/34.90  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 204.05/34.90  | | |            (121), (122), (123), (125), (126), (127), (128), (129), (130),
% 204.05/34.90  | | |            (131), (132), (133), (134), (135), (136), (137), (138), (139),
% 204.05/34.90  | | |            (140), (141), (142), (143), (144), (145), (147), (148), (149),
% 204.05/34.90  | | |            (150), (151), (152), (153), (155), (156), (158), (159), (160),
% 204.05/34.90  | | |            (161), (163), (164), (165), (167), (169), (170), (171), (172),
% 204.05/34.90  | | |            (173), (174), (175), (176), (177), (178), (180), (187), (188),
% 204.05/34.90  | | |            (189), (190) are inconsistent by sub-proof #741.
% 204.05/34.90  | | | 
% 204.05/34.90  | | Case 2:
% 204.05/34.90  | | | 
% 204.05/34.91  | | |   (191)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.05/34.91  | | | 
% 204.05/34.91  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 204.05/34.91  | | |            (14), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.05/34.91  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (36), (39),
% 204.05/34.91  | | |            (40), (41), (42), (43), (44), (45), (46), (49), (51), (52),
% 204.05/34.91  | | |            (53), (54), (55), (59), (60), (61), (62), (63), (64), (65),
% 204.05/34.91  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (75), (77),
% 204.05/34.91  | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 204.05/34.91  | | |            (88), (91), (92), (93), (94), (95), (96), (98), (99), (100),
% 204.05/34.91  | | |            (101), (102), (103), (104), (105), (106), (107), (110), (111),
% 204.05/34.91  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 204.05/34.91  | | |            (121), (122), (123), (124), (126), (127), (128), (129), (131),
% 204.05/34.91  | | |            (133), (134), (135), (136), (137), (139), (140), (141), (142),
% 204.05/34.91  | | |            (143), (144), (145), (147), (148), (149), (150), (151), (152),
% 204.05/34.91  | | |            (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 204.05/34.91  | | |            (163), (164), (165), (166), (167), (169), (170), (171), (172),
% 204.05/34.91  | | |            (173), (175), (176), (179), (180), (191) are inconsistent by
% 204.05/34.91  | | |            sub-proof #731.
% 204.05/34.91  | | | 
% 204.05/34.91  | | End of split
% 204.05/34.91  | | 
% 204.05/34.91  | Case 2:
% 204.05/34.91  | | 
% 204.05/34.91  | |   (192)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 204.05/34.91  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 204.05/34.91  | |            e0)
% 204.05/34.91  | | 
% 204.05/34.91  | | BETA: splitting (192) gives:
% 204.05/34.91  | | 
% 204.05/34.91  | | Case 1:
% 204.05/34.91  | | | 
% 204.05/34.91  | | |   (193)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.05/34.91  | | | 
% 204.05/34.91  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 204.05/34.91  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25), (27),
% 204.05/34.91  | | |            (29), (31), (32), (33), (34), (36), (37), (39), (40), (41),
% 204.05/34.91  | | |            (43), (44), (46), (47), (49), (50), (51), (52), (53), (54),
% 204.05/34.91  | | |            (55), (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 204.05/34.91  | | |            (69), (70), (72), (73), (74), (75), (78), (79), (80), (81),
% 204.05/34.91  | | |            (83), (84), (85), (86), (87), (88), (89), (91), (93), (94),
% 204.05/34.91  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 204.05/34.91  | | |            (106), (107), (108), (110), (112), (113), (114), (115), (116),
% 204.05/34.91  | | |            (117), (118), (119), (120), (121), (122), (123), (124), (126),
% 204.05/34.91  | | |            (127), (128), (129), (131), (132), (133), (134), (136), (137),
% 204.05/34.91  | | |            (139), (140), (141), (142), (143), (144), (147), (148), (150),
% 204.05/34.91  | | |            (151), (152), (154), (155), (156), (157), (158), (159), (160),
% 204.05/34.91  | | |            (161), (162), (163), (165), (166), (167), (168), (169), (170),
% 204.05/34.91  | | |            (173), (175), (176), (179), (180), (193) are inconsistent by
% 204.05/34.91  | | |            sub-proof #1042.
% 204.05/34.91  | | | 
% 204.05/34.91  | | Case 2:
% 204.05/34.91  | | | 
% 204.05/34.91  | | |   (194)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.05/34.91  | | | 
% 204.05/34.91  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (13), (14), (16),
% 204.05/34.91  | | |            (18), (19), (20), (21), (23), (24), (25), (27), (29), (30),
% 204.05/34.91  | | |            (31), (33), (34), (36), (39), (40), (41), (43), (44), (45),
% 204.05/34.91  | | |            (46), (47), (49), (50), (51), (52), (53), (54), (55), (56),
% 204.05/34.91  | | |            (59), (61), (62), (63), (67), (68), (69), (70), (71), (72),
% 204.05/34.91  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 204.05/34.91  | | |            (83), (85), (87), (88), (89), (91), (93), (95), (98), (101),
% 204.05/34.91  | | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 204.05/34.91  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 204.05/34.91  | | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 204.05/34.91  | | |            (131), (132), (133), (134), (135), (136), (137), (138), (140),
% 204.05/34.91  | | |            (141), (142), (143), (144), (145), (147), (148), (150), (151),
% 204.05/34.91  | | |            (154), (155), (160), (161), (162), (163), (165), (166), (167),
% 204.05/34.91  | | |            (168), (169), (170), (171), (172), (173), (176), (180), (194)
% 204.05/34.91  | | |            are inconsistent by sub-proof #1008.
% 204.05/34.91  | | | 
% 204.05/34.91  | | End of split
% 204.05/34.91  | | 
% 204.05/34.91  | End of split
% 204.05/34.91  | 
% 204.05/34.91  End of proof
% 204.05/34.91  
% 204.05/34.91  Sub-proof #731 shows that the following formulas are inconsistent:
% 204.05/34.91  ----------------------------------------------------------------
% 204.05/34.91    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.05/34.91    (2)   ~ (all_52_15 = all_52_23)
% 204.05/34.91    (3)   ~ (all_52_25 = all_52_27)
% 204.05/34.91    (4)  all_58_14 = all_52_23
% 204.05/34.91    (5)   ~ (e3 = e1)
% 204.05/34.91    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.05/34.91    (7)  op(all_52_3, all_52_3) = all_52_2
% 204.05/34.91    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.91    (9)   ~ (all_52_5 = all_52_13)
% 204.05/34.91    (10)  all_58_1 = all_52_9
% 204.05/34.91    (11)   ~ (all_52_9 = all_52_13)
% 204.05/34.91    (12)  op(e2, e3) = all_52_3
% 204.05/34.91    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.91    (14)   ~ (all_52_7 = all_52_15)
% 204.05/34.91    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.05/34.91    (16)   ~ (all_52_17 = all_52_25)
% 204.05/34.91    (17)   ~ (all_52_3 = all_6_2)
% 204.05/34.91    (18)  all_58_0 = all_6_2
% 204.05/34.91    (19)  op(all_14_2, e0) = all_14_1
% 204.05/34.91    (20)  all_56_4 = all_52_3
% 204.05/34.91    (21)   ~ (all_52_17 = all_10_2)
% 204.05/34.91    (22)  op(e3, e0) = all_52_25
% 204.05/34.91    (23)  op(all_52_5, all_52_5) = all_52_4
% 204.05/34.91    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.05/34.91    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.05/34.91    (26)   ~ (all_52_27 = all_52_29)
% 204.05/34.91    (27)  all_58_13 = all_52_15
% 204.05/34.91    (28)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.91    (29)  all_58_9 = all_52_25
% 204.05/34.91    (30)   ~ (all_6_1 = e1)
% 204.05/34.91    (31)   ~ (all_52_29 = all_14_2)
% 204.05/34.91    (32)  op(all_52_27, all_52_27) = all_52_26
% 204.05/34.91    (33)  op(e1, e3) = all_52_5
% 204.05/34.91    (34)  op(e2, e2) = all_4_2
% 204.05/34.91    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.05/34.91    (36)   ~ (all_52_3 = all_52_5)
% 204.05/34.91    (37)  all_58_11 = all_52_29
% 204.05/34.91    (38)  all_56_5 = all_4_2
% 204.05/34.91    (39)   ~ (all_52_25 = all_14_2)
% 204.05/34.91    (40)   ~ (all_52_3 = all_52_27)
% 204.05/34.91    (41)  op(all_6_2, all_6_2) = all_52_0
% 204.05/34.91    (42)   ~ (all_52_7 = all_6_2)
% 204.05/34.91    (43)  op(e0, e0) = all_14_2
% 204.05/34.91    (44)  all_56_15 = all_14_2
% 204.05/34.91    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.91    (46)  all_56_11 = all_52_29
% 204.05/34.91    (47)   ~ (all_4_1 = e1)
% 204.05/34.91    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.05/34.91    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.05/34.91    (50)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.05/34.91    (51)  all_56_9 = all_52_13
% 204.05/34.91    (52)   ~ (e2 = e1)
% 204.05/34.91    (53)   ~ (all_52_13 = all_10_2)
% 204.05/34.91    (54)   ~ (all_6_0 = e1)
% 204.05/34.91    (55)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.05/34.91    (56)  all_58_10 = all_52_27
% 204.05/34.91    (57)  all_56_8 = all_52_5
% 204.05/34.91    (58)  op(all_52_9, all_52_9) = all_52_8
% 204.05/34.91    (59)  op(all_52_15, all_52_15) = all_52_14
% 204.05/34.91    (60)   ~ (all_52_19 = all_52_23)
% 204.05/34.91    (61)   ~ (all_52_25 = all_52_29)
% 204.05/34.91    (62)  all_58_7 = all_52_13
% 204.05/34.91    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.91    (64)   ~ (all_52_5 = all_52_7)
% 204.05/34.91    (65)  all_58_12 = all_52_7
% 204.05/34.91    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.91    (67)   ~ (all_52_7 = all_14_2)
% 204.05/34.91    (68)   ~ (all_14_2 = e0)
% 204.05/34.91    (69)  all_58_2 = all_52_3
% 204.05/34.91    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.05/34.91    (71)  all_56_2 = all_52_17
% 204.05/34.91    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.05/34.91    (73)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.91    (74)  op(e3, all_6_1) = all_6_0
% 204.05/34.91    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.91    (76)  all_56_7 = all_52_27
% 204.05/34.91    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.05/34.91    (78)   ~ (e2 = e0)
% 204.05/34.91    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.05/34.91    (80)  op(all_4_2, e2) = all_4_1
% 204.05/34.91    (81)   ~ (all_52_5 = all_52_29)
% 204.05/34.91    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.91    (83)  all_56_6 = all_52_19
% 204.05/34.91    (84)   ~ (all_52_15 = all_14_2)
% 204.05/34.91    (85)   ~ (all_52_19 = all_52_27)
% 204.05/34.91    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.05/34.91    (87)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.91    (88)   ~ (all_6_0 = e2)
% 204.05/34.91    (89)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.91    (90)   ~ (all_52_13 = all_4_2)
% 204.05/34.91    (91)  op(e0, e3) = all_52_7
% 204.05/34.91    (92)  op(e1, e2) = all_52_13
% 204.05/34.91    (93)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.91    (94)   ~ (all_52_9 = all_52_25)
% 204.05/34.91    (95)  all_58_15 = all_14_2
% 204.05/34.91    (96)   ~ (all_52_19 = all_10_2)
% 204.05/34.91    (97)  op(all_52_23, all_52_23) = all_52_22
% 204.05/34.91    (98)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.91    (99)  all_58_8 = all_10_2
% 204.05/34.91    (100)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.05/34.91    (101)   ~ (all_52_5 = all_10_2)
% 204.05/34.91    (102)  op(all_52_29, all_52_29) = all_52_28
% 204.05/34.91    (103)   ~ (all_52_23 = all_14_2)
% 204.05/34.91    (104)  all_56_12 = all_52_7
% 204.05/34.91    (105)  op(all_52_17, all_52_17) = all_52_16
% 204.05/34.91    (106)   ~ (all_52_25 = all_6_2)
% 204.05/34.91    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.91    (108)   ~ (all_52_9 = all_4_2)
% 204.05/34.91    (109)   ~ (all_52_5 = all_6_2)
% 204.05/34.91    (110)   ~ (all_52_9 = all_6_2)
% 204.05/34.91    (111)  all_56_0 = all_6_2
% 204.05/34.91    (112)  op(e3, e3) = all_6_2
% 204.05/34.91    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.91    (114)   ~ (all_52_27 = all_14_2)
% 204.05/34.91    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.05/34.91    (116)  op(all_4_2, all_4_2) = all_52_10
% 204.05/34.91    (117)  all_56_3 = all_52_25
% 204.05/34.91    (118)   ~ (all_52_3 = all_52_7)
% 204.05/34.91    (119)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.91    (120)  all_58_5 = all_52_19
% 204.05/34.91    (121)  all_56_1 = all_52_9
% 204.05/34.91    (122)   ~ (all_52_15 = all_4_2)
% 204.05/34.91    (123)   ~ (all_52_27 = all_4_2)
% 204.05/34.91    (124)  all_58_6 = all_52_5
% 204.05/34.91    (125)  op(e3, e2) = all_52_9
% 204.05/34.91    (126)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.91    (127)   ~ (all_52_17 = all_6_2)
% 204.05/34.91    (128)   ~ (e1 = e0)
% 204.05/34.91    (129)   ~ (e3 = e2)
% 204.05/34.91    (130)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.91    (131)   ~ (all_52_9 = all_52_17)
% 204.05/34.91    (132)  all_56_10 = all_10_2
% 204.05/34.91    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.91    (134)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.91    (135)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.05/34.91    (136)  op(all_52_13, all_52_13) = all_52_12
% 204.05/34.91    (137)   ~ (all_6_1 = e2)
% 204.05/34.91    (138)  op(e1, e1) = all_10_2
% 204.05/34.91    (139)   ~ (all_52_23 = all_10_2)
% 204.05/34.91    (140)   ~ (all_52_7 = all_52_23)
% 204.05/34.91    (141)   ~ (all_52_17 = all_52_19)
% 204.05/34.91    (142)  all_58_3 = all_4_2
% 204.05/34.91    (143)  all_56_13 = all_52_15
% 204.05/34.91    (144)   ~ (all_52_3 = all_4_2)
% 204.05/34.91    (145)   ~ (all_52_19 = all_4_2)
% 204.05/34.91    (146)   ~ (all_52_17 = all_52_23)
% 204.05/34.91    (147)  op(all_6_2, e3) = all_6_1
% 204.05/34.91    (148)   ~ (all_52_13 = all_52_29)
% 204.05/34.91    (149)  all_58_4 = all_52_17
% 204.05/34.91    (150)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.05/34.91    (151)  op(all_52_25, all_52_25) = all_52_24
% 204.05/34.91  
% 204.05/34.91  Begin of proof
% 204.05/34.91  | 
% 204.05/34.91  | ALPHA: (55) implies:
% 204.05/34.91  |   (152)  all_52_14 = e0
% 204.05/34.91  |   (153)  all_52_12 = e1
% 204.05/34.91  |   (154)  all_52_10 = e2
% 204.05/34.91  |   (155)  all_52_8 = e3
% 204.05/34.91  | 
% 204.05/34.91  | REDUCE: (58), (155) imply:
% 204.05/34.91  |   (156)  op(all_52_9, all_52_9) = e3
% 204.05/34.91  | 
% 204.05/34.91  | REDUCE: (136), (153) imply:
% 204.05/34.91  |   (157)  op(all_52_13, all_52_13) = e1
% 204.05/34.91  | 
% 204.05/34.91  | REDUCE: (59), (152) imply:
% 204.05/34.91  |   (158)  op(all_52_15, all_52_15) = e0
% 204.05/34.91  | 
% 204.05/34.91  | REDUCE: (116), (154) imply:
% 204.05/34.91  |   (159)  op(all_4_2, all_4_2) = e2
% 204.05/34.91  | 
% 204.05/34.91  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.05/34.91  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.05/34.91  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.05/34.91  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.05/34.91  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 204.05/34.91  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.05/34.91  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 204.05/34.91  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 204.05/34.91  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 204.05/34.91  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 204.05/34.91  |            (112), (113), (114), (115), (117), (118), (119), (120), (121),
% 204.05/34.91  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 204.05/34.91  |            (131), (132), (133), (134), (135), (137), (138), (139), (140),
% 204.05/34.91  |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 204.05/34.91  |            (150), (151), (156), (157), (158), (159) are inconsistent by
% 204.05/34.91  |            sub-proof #732.
% 204.05/34.91  | 
% 204.05/34.91  End of proof
% 204.05/34.91  
% 204.05/34.91  Sub-proof #732 shows that the following formulas are inconsistent:
% 204.05/34.91  ----------------------------------------------------------------
% 204.05/34.91    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.05/34.91    (2)   ~ (all_52_15 = all_52_23)
% 204.05/34.91    (3)   ~ (all_52_25 = all_52_27)
% 204.05/34.91    (4)  all_58_14 = all_52_23
% 204.05/34.91    (5)   ~ (e3 = e1)
% 204.05/34.91    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.05/34.91    (7)  op(all_52_3, all_52_3) = all_52_2
% 204.05/34.91    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.91    (9)   ~ (all_52_5 = all_52_13)
% 204.05/34.91    (10)  all_58_1 = all_52_9
% 204.05/34.91    (11)   ~ (all_52_9 = all_52_13)
% 204.05/34.91    (12)  op(e2, e3) = all_52_3
% 204.05/34.91    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.05/34.91    (14)   ~ (all_52_7 = all_52_15)
% 204.05/34.91    (15)  op(all_52_15, all_52_15) = e0
% 204.05/34.91    (16)  op(all_52_7, all_52_7) = all_52_6
% 204.05/34.91    (17)   ~ (all_52_17 = all_52_25)
% 204.05/34.91    (18)   ~ (all_52_3 = all_6_2)
% 204.05/34.91    (19)  all_58_0 = all_6_2
% 204.05/34.91    (20)  op(all_14_2, e0) = all_14_1
% 204.05/34.91    (21)  all_56_4 = all_52_3
% 204.05/34.91    (22)   ~ (all_52_17 = all_10_2)
% 204.05/34.91    (23)  op(e3, e0) = all_52_25
% 204.05/34.91    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.05/34.91    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.05/34.91    (26)  op(all_52_19, all_52_19) = all_52_18
% 204.05/34.91    (27)   ~ (all_52_27 = all_52_29)
% 204.05/34.91    (28)  all_58_13 = all_52_15
% 204.05/34.91    (29)  op(all_52_13, all_52_13) = e1
% 204.05/34.91    (30)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.91    (31)  all_58_9 = all_52_25
% 204.05/34.91    (32)   ~ (all_6_1 = e1)
% 204.05/34.91    (33)   ~ (all_52_29 = all_14_2)
% 204.05/34.91    (34)  op(all_52_27, all_52_27) = all_52_26
% 204.05/34.91    (35)  op(e1, e3) = all_52_5
% 204.05/34.91    (36)  op(e2, e2) = all_4_2
% 204.05/34.91    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.05/34.91    (38)   ~ (all_52_3 = all_52_5)
% 204.05/34.91    (39)  all_58_11 = all_52_29
% 204.05/34.91    (40)  all_56_5 = all_4_2
% 204.05/34.91    (41)   ~ (all_52_25 = all_14_2)
% 204.05/34.91    (42)   ~ (all_52_3 = all_52_27)
% 204.05/34.91    (43)  op(all_6_2, all_6_2) = all_52_0
% 204.05/34.91    (44)   ~ (all_52_7 = all_6_2)
% 204.05/34.91    (45)  op(e0, e0) = all_14_2
% 204.05/34.91    (46)  all_56_15 = all_14_2
% 204.05/34.91    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.91    (48)  all_56_11 = all_52_29
% 204.05/34.91    (49)   ~ (all_4_1 = e1)
% 204.05/34.91    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.05/34.91    (51)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.05/34.91    (52)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.05/34.91    (53)  all_56_9 = all_52_13
% 204.05/34.91    (54)   ~ (e2 = e1)
% 204.05/34.91    (55)   ~ (all_52_13 = all_10_2)
% 204.05/34.91    (56)   ~ (all_6_0 = e1)
% 204.05/34.91    (57)  all_58_10 = all_52_27
% 204.05/34.91    (58)  all_56_8 = all_52_5
% 204.05/34.91    (59)   ~ (all_52_19 = all_52_23)
% 204.05/34.91    (60)   ~ (all_52_25 = all_52_29)
% 204.05/34.91    (61)  all_58_7 = all_52_13
% 204.05/34.91    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.05/34.91    (63)   ~ (all_52_5 = all_52_7)
% 204.05/34.91    (64)  all_58_12 = all_52_7
% 204.05/34.91    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.91    (66)   ~ (all_52_7 = all_14_2)
% 204.05/34.91    (67)   ~ (all_14_2 = e0)
% 204.05/34.91    (68)  all_58_2 = all_52_3
% 204.05/34.91    (69)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.05/34.91    (70)  all_56_2 = all_52_17
% 204.05/34.91    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.05/34.91    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.05/34.91    (73)  op(e3, all_6_1) = all_6_0
% 204.05/34.91    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.05/34.91    (75)  all_56_7 = all_52_27
% 204.05/34.91    (76)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.05/34.91    (77)   ~ (e2 = e0)
% 204.05/34.91    (78)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.05/34.91    (79)  op(all_4_2, e2) = all_4_1
% 204.05/34.91    (80)   ~ (all_52_5 = all_52_29)
% 204.05/34.91    (81)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.05/34.91    (82)  all_56_6 = all_52_19
% 204.05/34.91    (83)   ~ (all_52_15 = all_14_2)
% 204.05/34.91    (84)   ~ (all_52_19 = all_52_27)
% 204.05/34.91    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.05/34.91    (86)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.91    (87)   ~ (all_6_0 = e2)
% 204.05/34.91    (88)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.05/34.91    (89)   ~ (all_52_13 = all_4_2)
% 204.05/34.91    (90)  op(e0, e3) = all_52_7
% 204.05/34.91    (91)  op(e1, e2) = all_52_13
% 204.05/34.91    (92)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.05/34.91    (93)   ~ (all_52_9 = all_52_25)
% 204.05/34.91    (94)  all_58_15 = all_14_2
% 204.05/34.91    (95)   ~ (all_52_19 = all_10_2)
% 204.05/34.91    (96)  op(all_52_23, all_52_23) = all_52_22
% 204.05/34.91    (97)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.91    (98)  all_58_8 = all_10_2
% 204.05/34.91    (99)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.05/34.91    (100)   ~ (all_52_5 = all_10_2)
% 204.05/34.91    (101)  op(all_52_29, all_52_29) = all_52_28
% 204.05/34.91    (102)   ~ (all_52_23 = all_14_2)
% 204.05/34.91    (103)  all_56_12 = all_52_7
% 204.05/34.91    (104)  op(all_52_17, all_52_17) = all_52_16
% 204.05/34.91    (105)   ~ (all_52_25 = all_6_2)
% 204.05/34.91    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.91    (107)   ~ (all_52_9 = all_4_2)
% 204.05/34.91    (108)   ~ (all_52_5 = all_6_2)
% 204.05/34.91    (109)  op(all_4_2, all_4_2) = e2
% 204.05/34.91    (110)   ~ (all_52_9 = all_6_2)
% 204.05/34.91    (111)  all_56_0 = all_6_2
% 204.05/34.91    (112)  op(e3, e3) = all_6_2
% 204.05/34.91    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.05/34.91    (114)   ~ (all_52_27 = all_14_2)
% 204.05/34.91    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.05/34.91    (116)  all_56_3 = all_52_25
% 204.05/34.91    (117)   ~ (all_52_3 = all_52_7)
% 204.05/34.91    (118)  op(all_14_2, all_14_2) = all_52_30
% 204.05/34.91    (119)  all_58_5 = all_52_19
% 204.05/34.91    (120)  all_56_1 = all_52_9
% 204.05/34.91    (121)   ~ (all_52_15 = all_4_2)
% 204.05/34.91    (122)   ~ (all_52_27 = all_4_2)
% 204.05/34.91    (123)  all_58_6 = all_52_5
% 204.05/34.91    (124)  op(e3, e2) = all_52_9
% 204.05/34.91    (125)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.91    (126)   ~ (all_52_17 = all_6_2)
% 204.05/34.91    (127)   ~ (e1 = e0)
% 204.05/34.91    (128)   ~ (e3 = e2)
% 204.05/34.91    (129)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.91    (130)   ~ (all_52_9 = all_52_17)
% 204.05/34.91    (131)  all_56_10 = all_10_2
% 204.05/34.91    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.05/34.91    (133)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.05/34.91    (134)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.05/34.91    (135)   ~ (all_6_1 = e2)
% 204.05/34.91    (136)  op(e1, e1) = all_10_2
% 204.05/34.91    (137)  op(all_52_9, all_52_9) = e3
% 204.05/34.91    (138)   ~ (all_52_23 = all_10_2)
% 204.05/34.91    (139)   ~ (all_52_7 = all_52_23)
% 204.05/34.91    (140)   ~ (all_52_17 = all_52_19)
% 204.05/34.91    (141)  all_58_3 = all_4_2
% 204.05/34.91    (142)  all_56_13 = all_52_15
% 204.05/34.91    (143)   ~ (all_52_3 = all_4_2)
% 204.05/34.91    (144)   ~ (all_52_19 = all_4_2)
% 204.05/34.91    (145)   ~ (all_52_17 = all_52_23)
% 204.05/34.91    (146)  op(all_6_2, e3) = all_6_1
% 204.05/34.91    (147)   ~ (all_52_13 = all_52_29)
% 204.05/34.91    (148)  all_58_4 = all_52_17
% 204.05/34.91    (149)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.05/34.91    (150)  op(all_52_25, all_52_25) = all_52_24
% 204.05/34.91  
% 204.05/34.91  Begin of proof
% 204.05/34.91  | 
% 204.05/34.91  | BETA: splitting (99) gives:
% 204.05/34.91  | 
% 204.05/34.91  | Case 1:
% 204.05/34.91  | | 
% 204.05/34.91  | |   (151)  all_56_15 = e3
% 204.05/34.91  | | 
% 204.05/34.91  | | COMBINE_EQS: (46), (151) imply:
% 204.05/34.91  | |   (152)  all_14_2 = e3
% 204.05/34.91  | | 
% 204.05/34.91  | | SIMP: (152) implies:
% 204.05/34.91  | |   (153)  all_14_2 = e3
% 204.05/34.91  | | 
% 204.05/34.91  | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (12), (14), (16), (18), (19),
% 204.05/34.91  | |            (20), (21), (23), (24), (28), (29), (30), (31), (32), (33), (35),
% 204.05/34.91  | |            (36), (37), (38), (39), (41), (43), (44), (47), (49), (52), (54),
% 204.05/34.91  | |            (55), (56), (57), (61), (64), (65), (66), (67), (68), (71), (72),
% 204.05/34.91  | |            (73), (74), (76), (77), (79), (81), (83), (86), (87), (92), (93),
% 204.05/34.91  | |            (98), (104), (105), (106), (108), (109), (110), (112), (114),
% 204.05/34.91  | |            (115), (116), (117), (118), (119), (120), (123), (124), (126),
% 204.05/34.91  | |            (127), (128), (129), (130), (131), (132), (135), (136), (137),
% 204.05/34.91  | |            (140), (141), (143), (146), (148), (149), (153) are inconsistent
% 204.05/34.91  | |            by sub-proof #1117.
% 204.05/34.91  | | 
% 204.05/34.91  | Case 2:
% 204.05/34.91  | | 
% 204.05/34.91  | |   (154)   ~ (all_56_15 = e3)
% 204.05/34.91  | | 
% 204.05/34.91  | | REDUCE: (46), (154) imply:
% 204.05/34.91  | |   (155)   ~ (all_14_2 = e3)
% 204.05/34.91  | | 
% 204.05/34.91  | | BETA: splitting (50) gives:
% 204.05/34.91  | | 
% 204.05/34.91  | | Case 1:
% 204.05/34.91  | | | 
% 204.05/34.91  | | |   (156)  all_56_13 = e3
% 204.05/34.91  | | | 
% 204.05/34.91  | | | COMBINE_EQS: (142), (156) imply:
% 204.05/34.91  | | |   (157)  all_52_15 = e3
% 204.05/34.91  | | | 
% 204.05/34.91  | | | REF_CLOSE: (8), (13), (14), (15), (32), (44), (90), (103), (112), (135),
% 204.05/34.91  | | |            (146), (157) are inconsistent by sub-proof #1341.
% 204.05/34.91  | | | 
% 204.05/34.91  | | Case 2:
% 204.05/34.91  | | | 
% 204.05/34.92  | | |   (158)   ~ (all_56_13 = e3)
% 204.05/34.92  | | | 
% 204.05/34.92  | | | REDUCE: (142), (158) imply:
% 204.05/34.92  | | |   (159)   ~ (all_52_15 = e3)
% 204.05/34.92  | | | 
% 204.05/34.92  | | | BETA: splitting (125) gives:
% 204.05/34.92  | | | 
% 204.05/34.92  | | | Case 1:
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | |   (160)  all_58_12 = e3
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | COMBINE_EQS: (64), (160) imply:
% 204.05/34.92  | | | |   (161)  all_52_7 = e3
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | SIMP: (161) implies:
% 204.05/34.92  | | | |   (162)  all_52_7 = e3
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (117), (162) imply:
% 204.05/34.92  | | | |   (163)   ~ (all_52_3 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (63), (162) imply:
% 204.05/34.92  | | | |   (164)   ~ (all_52_5 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (14), (162) imply:
% 204.05/34.92  | | | |   (165)   ~ (all_52_15 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (139), (162) imply:
% 204.05/34.92  | | | |   (166)   ~ (all_52_23 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | SIMP: (166) implies:
% 204.05/34.92  | | | |   (167)   ~ (all_52_23 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (66), (162) imply:
% 204.05/34.92  | | | |   (168)   ~ (all_14_2 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (44), (162) imply:
% 204.05/34.92  | | | |   (169)   ~ (all_6_2 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | SIMP: (169) implies:
% 204.05/34.92  | | | |   (170)   ~ (all_6_2 = e3)
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (16), (162) imply:
% 204.05/34.92  | | | |   (171)  op(e3, e3) = all_52_6
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | REDUCE: (90), (162) imply:
% 204.05/34.92  | | | |   (172)  op(e0, e3) = e3
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | GROUND_INST: instantiating (8) with all_6_2, all_52_6, e3, e3,
% 204.05/34.92  | | | |              simplifying with (112), (171) gives:
% 204.05/34.92  | | | |   (173)  all_52_6 = all_6_2
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | BETA: splitting (76) gives:
% 204.05/34.92  | | | | 
% 204.05/34.92  | | | | Case 1:
% 204.05/34.92  | | | | | 
% 204.05/34.92  | | | | |   (174)  all_56_4 = e3
% 204.05/34.92  | | | | | 
% 204.05/34.92  | | | | | REF_CLOSE: (21), (163), (174) are inconsistent by sub-proof #1340.
% 204.05/34.92  | | | | | 
% 204.05/34.92  | | | | Case 2:
% 204.05/34.92  | | | | | 
% 204.05/34.92  | | | | |   (175)   ~ (all_56_4 = e3)
% 204.05/34.92  | | | | |   (176)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.05/34.92  | | | | | 
% 204.05/34.92  | | | | | BETA: splitting (134) gives:
% 204.05/34.92  | | | | | 
% 204.05/34.92  | | | | | Case 1:
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | |   (177)  all_56_0 = e3
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | | COMBINE_EQS: (111), (177) imply:
% 204.05/34.92  | | | | | |   (178)  all_6_2 = e3
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | | REDUCE: (170), (178) imply:
% 204.05/34.92  | | | | | |   (179)  $false
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | | CLOSE: (179) is inconsistent.
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | Case 2:
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | |   (180)   ~ (all_56_0 = e3)
% 204.05/34.92  | | | | | |   (181)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | | BETA: splitting (97) gives:
% 204.05/34.92  | | | | | | 
% 204.05/34.92  | | | | | | Case 1:
% 204.05/34.92  | | | | | | | 
% 204.05/34.92  | | | | | | |   (182)  all_56_8 = e3
% 204.05/34.92  | | | | | | | 
% 204.05/34.92  | | | | | | | REF_CLOSE: (58), (164), (182) are inconsistent by sub-proof #1325.
% 204.05/34.92  | | | | | | | 
% 204.05/34.92  | | | | | | Case 2:
% 204.05/34.92  | | | | | | | 
% 204.05/34.92  | | | | | | |   (183)   ~ (all_56_8 = e3)
% 204.05/34.92  | | | | | | |   (184)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.92  | | | | | | | 
% 204.05/34.92  | | | | | | | BETA: splitting (74) gives:
% 204.05/34.92  | | | | | | | 
% 204.05/34.92  | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | |   (185)  all_58_0 = e1
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | COMBINE_EQS: (19), (185) imply:
% 204.05/34.92  | | | | | | | |   (186)  all_6_2 = e1
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (18), (186) imply:
% 204.05/34.92  | | | | | | | |   (187)   ~ (all_52_3 = e1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (108), (186) imply:
% 204.05/34.92  | | | | | | | |   (188)   ~ (all_52_5 = e1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (126), (186) imply:
% 204.05/34.92  | | | | | | | |   (189)   ~ (all_52_17 = e1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (105), (186) imply:
% 204.05/34.92  | | | | | | | |   (190)   ~ (all_52_25 = e1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (43), (186) imply:
% 204.05/34.92  | | | | | | | |   (191)  op(e1, e1) = all_52_0
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (146), (186) imply:
% 204.05/34.92  | | | | | | | |   (192)  op(e1, e3) = all_6_1
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, all_52_0, e1, e1,
% 204.05/34.92  | | | | | | | |              simplifying with (136), (191) gives:
% 204.05/34.92  | | | | | | | |   (193)  all_52_0 = all_10_2
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | GROUND_INST: instantiating (8) with all_52_5, all_6_1, e3, e1,
% 204.05/34.92  | | | | | | | |              simplifying with (35), (192) gives:
% 204.05/34.92  | | | | | | | |   (194)  all_52_5 = all_6_1
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | COMBINE_EQS: (58), (194) imply:
% 204.05/34.92  | | | | | | | |   (195)  all_56_8 = all_6_1
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | COMBINE_EQS: (123), (194) imply:
% 204.05/34.92  | | | | | | | |   (196)  all_58_6 = all_6_1
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (80), (194) imply:
% 204.05/34.92  | | | | | | | |   (197)   ~ (all_52_29 = all_6_1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | SIMP: (197) implies:
% 204.05/34.92  | | | | | | | |   (198)   ~ (all_52_29 = all_6_1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (164), (194) imply:
% 204.05/34.92  | | | | | | | |   (199)   ~ (all_6_1 = e3)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (24), (194) imply:
% 204.05/34.92  | | | | | | | |   (200)  op(all_6_1, all_6_1) = all_52_4
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | BETA: splitting (86) gives:
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | |   (201)  all_58_0 = e2
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REF_CLOSE: (54), (185), (201) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | |            #1273.
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | |   (202)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | BETA: splitting (184) gives:
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | |   (203)  all_56_8 = e2
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | REF_CLOSE: (135), (195), (203) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | |            #1321.
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | |   (204)   ~ (all_56_8 = e2)
% 204.05/34.92  | | | | | | | | | |   (205)  all_56_8 = e1 | all_56_8 = e0
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | BETA: splitting (205) gives:
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | |   (206)  all_56_8 = e1
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REF_CLOSE: (32), (195), (206) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | |            #1320.
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | |   (207)  all_56_8 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | COMBINE_EQS: (195), (207) imply:
% 204.05/34.92  | | | | | | | | | | |   (208)  all_6_1 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (208) implies:
% 204.05/34.92  | | | | | | | | | | |   (209)  all_6_1 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | COMBINE_EQS: (196), (209) imply:
% 204.05/34.92  | | | | | | | | | | |   (210)  all_58_6 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (198), (209) imply:
% 204.05/34.92  | | | | | | | | | | |   (211)   ~ (all_52_29 = e0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (199), (209) imply:
% 204.05/34.92  | | | | | | | | | | |   (212)   ~ (e3 = e0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (212) implies:
% 204.05/34.92  | | | | | | | | | | |   (213)   ~ (e3 = e0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (200), (209) imply:
% 204.05/34.92  | | | | | | | | | | |   (214)  op(e0, e0) = all_52_4
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (73), (209) imply:
% 204.05/34.92  | | | | | | | | | | |   (215)  op(e3, e0) = all_6_0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | BETA: splitting (202) gives:
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | |   (216)  all_58_2 = e2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | COMBINE_EQS: (68), (216) imply:
% 204.05/34.92  | | | | | | | | | | | |   (217)  all_52_3 = e2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | SIMP: (217) implies:
% 204.05/34.92  | | | | | | | | | | | |   (218)  all_52_3 = e2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (143), (218) imply:
% 204.05/34.92  | | | | | | | | | | | |   (219)   ~ (all_4_2 = e2)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | SIMP: (219) implies:
% 204.05/34.92  | | | | | | | | | | | |   (220)   ~ (all_4_2 = e2)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (163), (218) imply:
% 204.05/34.92  | | | | | | | | | | | |   (221)   ~ (e3 = e2)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (7), (218) imply:
% 204.05/34.92  | | | | | | | | | | | |   (222)  op(e2, e2) = all_52_2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_4, e0, e0,
% 204.05/34.92  | | | | | | | | | | | |              simplifying with (45), (214) gives:
% 204.05/34.92  | | | | | | | | | | | |   (223)  all_52_4 = all_14_2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, all_52_2, e2, e2,
% 204.05/34.92  | | | | | | | | | | | |              simplifying with (36), (222) gives:
% 204.05/34.92  | | | | | | | | | | | |   (224)  all_52_2 = all_4_2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_25, all_6_0, e0, e3,
% 204.05/34.92  | | | | | | | | | | | |              simplifying with (23), (215) gives:
% 204.05/34.92  | | | | | | | | | | | |   (225)  all_52_25 = all_6_0
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | COMBINE_EQS: (116), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (226)  all_56_3 = all_6_0
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | COMBINE_EQS: (31), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (227)  all_58_9 = all_6_0
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (17), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (228)   ~ (all_52_17 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (3), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (229)   ~ (all_52_27 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | SIMP: (229) implies:
% 204.05/34.92  | | | | | | | | | | | |   (230)   ~ (all_52_27 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (60), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (231)   ~ (all_52_29 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | SIMP: (231) implies:
% 204.05/34.92  | | | | | | | | | | | |   (232)   ~ (all_52_29 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (41), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (233)   ~ (all_14_2 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | SIMP: (233) implies:
% 204.05/34.92  | | | | | | | | | | | |   (234)   ~ (all_14_2 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (150), (225) imply:
% 204.05/34.92  | | | | | | | | | | | |   (235)  op(all_6_0, all_6_0) = all_52_24
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | BETA: splitting (106) gives:
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | |   (236)  all_56_3 = e3
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | COMBINE_EQS: (226), (236) imply:
% 204.05/34.92  | | | | | | | | | | | | |   (237)  all_6_0 = e3
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | SIMP: (237) implies:
% 204.05/34.92  | | | | | | | | | | | | |   (238)  all_6_0 = e3
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | COMBINE_EQS: (227), (238) imply:
% 204.05/34.92  | | | | | | | | | | | | |   (239)  all_58_9 = e3
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | REDUCE: (228), (238) imply:
% 204.05/34.92  | | | | | | | | | | | | |   (240)   ~ (all_52_17 = e3)
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | REDUCE: (230), (238) imply:
% 204.05/34.92  | | | | | | | | | | | | |   (241)   ~ (all_52_27 = e3)
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | REDUCE: (232), (238) imply:
% 204.05/34.92  | | | | | | | | | | | | |   (242)   ~ (all_52_29 = e3)
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | BETA: splitting (1) gives:
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | |   (243)  all_58_9 = e0
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | REF_CLOSE: (213), (239), (243) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | |            #841.
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | |   (244)  all_58_10 = e0 | all_58_11 = e0
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | |   (245)  all_58_10 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | COMBINE_EQS: (57), (245) imply:
% 204.05/34.92  | | | | | | | | | | | | | | |   (246)  all_52_27 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | SIMP: (246) implies:
% 204.05/34.92  | | | | | | | | | | | | | | |   (247)  all_52_27 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | REDUCE: (84), (247) imply:
% 204.05/34.92  | | | | | | | | | | | | | | |   (248)   ~ (all_52_19 = e0)
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | REDUCE: (122), (247) imply:
% 204.05/34.92  | | | | | | | | | | | | | | |   (249)   ~ (all_4_2 = e0)
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | SIMP: (249) implies:
% 204.05/34.92  | | | | | | | | | | | | | | |   (250)   ~ (all_4_2 = e0)
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | REDUCE: (34), (247) imply:
% 204.05/34.92  | | | | | | | | | | | | | | |   (251)  op(e0, e0) = all_52_26
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_26, e0,
% 204.05/34.92  | | | | | | | | | | | | | | |              e0, simplifying with (45), (251) gives:
% 204.05/34.92  | | | | | | | | | | | | | | |   (252)  all_52_26 = all_14_2
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | |   (253)  all_56_2 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | REF_CLOSE: (70), (240), (253) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | | | |            #1327.
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | |   (254)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (255)  all_56_5 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (255) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (256)  all_4_2 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (257)  all_4_2 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | REDUCE: (144), (257) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (258)   ~ (all_52_19 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (17), (18),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (33), (34), (35), (36),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (45), (47), (48),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (49), (53), (54), (55), (57), (58), (60), (61),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (62), (65), (68), (73), (74), (75), (78), (79),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (80), (85), (86), (87), (89), (91), (92), (93),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (94), (95), (98), (100), (101), (104), (105),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (106), (107), (108), (109), (110), (112), (113),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (115), (116), (119), (120), (121), (122), (123),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (124), (126), (128), (129), (130), (132), (133),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (135), (137), (138), (141), (143), (144), (146),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (147), (148), (150), (155), (159), (160), (163),
% 204.05/34.92  | | | | | | | | | | | | | | | | |            (164), (167), (170), (171), (176), (184), (258)
% 204.05/34.92  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #738.
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (259)   ~ (all_56_5 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (260)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | REDUCE: (40), (259) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | |   (261)   ~ (all_4_2 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | |   (262)  all_58_2 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (216), (262) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | | | | | |            #1124.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | |   (263)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | |   (264)  all_56_5 = e2
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (220), (264) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | | | | | | |            #1315.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | |   (265)  all_56_5 = e1 | all_56_5 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |   (266)  all_56_5 = e1
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (266) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |   (267)  all_4_2 = e1
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | SIMP: (267) implies:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |   (268)  all_4_2 = e1
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (268) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_52_9 = e1)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (268) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |   (270)  op(e1, e1) = e2
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (271)  all_56_6 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (271) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (272)  all_52_19 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (273)  all_52_19 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (273) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (274)   ~ (all_10_2 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | SIMP: (274) implies:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (275)   ~ (all_10_2 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | |   (276)  all_58_6 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (210), (213), (276) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | |            #737.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | |   (277)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_7 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (278) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_52_13 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (279) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |   (280)   ~ (all_52_9 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_10_2, e2, e1, e1,
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (136), (270) gives:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_10_2 = e2
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (281) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |   (282)   ~ (all_52_17 = e2)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (70), (120), (129), (130), (137),
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |            (148), (189), (254), (261), (269), (280), (282)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #736.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_58_8 = e3 | all_58_11 = e3
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (98), (242), (275), (283) are inconsistent
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1140.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (284)   ~ (all_56_6 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (284) imply:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |   (285)   ~ (all_52_19 = e3)
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (119), (141), (241), (261), (263), (285) are
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1082.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |   (286)  all_56_5 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (250), (286) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | |            #1313.
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | |   (287)  all_58_11 = e0
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | | REF_CLOSE: (39), (211), (287) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | | | |            #1115.
% 204.05/34.92  | | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | |   (288)   ~ (all_56_3 = e3)
% 204.05/34.92  | | | | | | | | | | | | |   (289)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | REDUCE: (226), (288) imply:
% 204.05/34.92  | | | | | | | | | | | | |   (290)   ~ (all_6_0 = e3)
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (10), (19), (22), (23), (24), (25),
% 204.05/34.92  | | | | | | | | | | | | |            (27), (28), (29), (31), (33), (34), (35), (36),
% 204.05/34.92  | | | | | | | | | | | | |            (38), (39), (45), (48), (49), (54), (56), (57),
% 204.05/34.92  | | | | | | | | | | | | |            (58), (60), (61), (65), (68), (73), (74), (75),
% 204.05/34.92  | | | | | | | | | | | | |            (79), (85), (86), (87), (92), (93), (94), (98),
% 204.05/34.92  | | | | | | | | | | | | |            (101), (104), (105), (108), (109), (110), (112),
% 204.05/34.92  | | | | | | | | | | | | |            (113), (115), (116), (120), (122), (123), (124),
% 204.05/34.92  | | | | | | | | | | | | |            (128), (129), (130), (132), (135), (137), (141),
% 204.05/34.92  | | | | | | | | | | | | |            (146), (147), (148), (150), (155), (159), (160),
% 204.05/34.92  | | | | | | | | | | | | |            (164), (170), (171), (184), (226), (227), (235),
% 204.05/34.92  | | | | | | | | | | | | |            (289), (290) are inconsistent by sub-proof #735.
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | |   (291)  all_58_6 = e2 | all_58_12 = e2
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REF_CLOSE: (128), (135), (160), (196), (291) are inconsistent
% 204.05/34.92  | | | | | | | | | | | |            by sub-proof #1209.
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | End of split
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | |   (292)   ~ (all_58_0 = e1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | REDUCE: (19), (292) imply:
% 204.05/34.92  | | | | | | | |   (293)   ~ (all_6_2 = e1)
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | BETA: splitting (86) gives:
% 204.05/34.92  | | | | | | | | 
% 204.05/34.92  | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | |   (294)  all_58_0 = e2
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | COMBINE_EQS: (19), (294) imply:
% 204.05/34.92  | | | | | | | | |   (295)  all_6_2 = e2
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (18), (295) imply:
% 204.05/34.92  | | | | | | | | |   (296)   ~ (all_52_3 = e2)
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (105), (295) imply:
% 204.05/34.92  | | | | | | | | |   (297)   ~ (all_52_25 = e2)
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (170), (295) imply:
% 204.05/34.92  | | | | | | | | |   (298)   ~ (e3 = e2)
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (43), (295) imply:
% 204.05/34.92  | | | | | | | | |   (299)  op(e2, e2) = all_52_0
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (146), (295) imply:
% 204.05/34.92  | | | | | | | | |   (300)  op(e2, e3) = all_6_1
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, all_52_0, e2, e2,
% 204.05/34.92  | | | | | | | | |              simplifying with (36), (299) gives:
% 204.05/34.92  | | | | | | | | |   (301)  all_52_0 = all_4_2
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | GROUND_INST: instantiating (8) with all_52_3, all_6_1, e3, e2,
% 204.05/34.92  | | | | | | | | |              simplifying with (12), (300) gives:
% 204.05/34.92  | | | | | | | | |   (302)  all_52_3 = all_6_1
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | COMBINE_EQS: (21), (302) imply:
% 204.05/34.92  | | | | | | | | |   (303)  all_56_4 = all_6_1
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (42), (302) imply:
% 204.05/34.92  | | | | | | | | |   (304)   ~ (all_52_27 = all_6_1)
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | SIMP: (304) implies:
% 204.05/34.92  | | | | | | | | |   (305)   ~ (all_52_27 = all_6_1)
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (163), (302) imply:
% 204.05/34.92  | | | | | | | | |   (306)   ~ (all_6_1 = e3)
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | REDUCE: (7), (302) imply:
% 204.05/34.92  | | | | | | | | |   (307)  op(all_6_1, all_6_1) = all_52_2
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | BETA: splitting (176) gives:
% 204.05/34.92  | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | |   (308)  all_56_4 = e2
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | REF_CLOSE: (135), (303), (308) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | |            #1219.
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | |   (309)   ~ (all_56_4 = e2)
% 204.05/34.92  | | | | | | | | | |   (310)  all_56_4 = e1 | all_56_4 = e0
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | BETA: splitting (310) gives:
% 204.05/34.92  | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | |   (311)  all_56_4 = e1
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REF_CLOSE: (32), (303), (311) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | |            #1218.
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | |   (312)  all_56_4 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | COMBINE_EQS: (303), (312) imply:
% 204.05/34.92  | | | | | | | | | | |   (313)  all_6_1 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (313) implies:
% 204.05/34.92  | | | | | | | | | | |   (314)  all_6_1 = e0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (305), (314) imply:
% 204.05/34.92  | | | | | | | | | | |   (315)   ~ (all_52_27 = e0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (306), (314) imply:
% 204.05/34.92  | | | | | | | | | | |   (316)   ~ (e3 = e0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (316) implies:
% 204.05/34.92  | | | | | | | | | | |   (317)   ~ (e3 = e0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (307), (314) imply:
% 204.05/34.92  | | | | | | | | | | |   (318)  op(e0, e0) = all_52_2
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (73), (314) imply:
% 204.05/34.92  | | | | | | | | | | |   (319)  op(e3, e0) = all_6_0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_2, e0, e0,
% 204.05/34.92  | | | | | | | | | | |              simplifying with (45), (318) gives:
% 204.05/34.92  | | | | | | | | | | |   (320)  all_52_2 = all_14_2
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_25, all_6_0, e0, e3,
% 204.05/34.92  | | | | | | | | | | |              simplifying with (23), (319) gives:
% 204.05/34.92  | | | | | | | | | | |   (321)  all_52_25 = all_6_0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | COMBINE_EQS: (116), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (322)  all_56_3 = all_6_0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | COMBINE_EQS: (31), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (323)  all_58_9 = all_6_0
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (93), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (324)   ~ (all_52_9 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (3), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (325)   ~ (all_52_27 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (325) implies:
% 204.05/34.92  | | | | | | | | | | |   (326)   ~ (all_52_27 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (60), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (327)   ~ (all_52_29 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (327) implies:
% 204.05/34.92  | | | | | | | | | | |   (328)   ~ (all_52_29 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (41), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (329)   ~ (all_14_2 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | SIMP: (329) implies:
% 204.05/34.92  | | | | | | | | | | |   (330)   ~ (all_14_2 = all_6_0)
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | REDUCE: (150), (321) imply:
% 204.05/34.92  | | | | | | | | | | |   (331)  op(all_6_0, all_6_0) = all_52_24
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | BETA: splitting (106) gives:
% 204.05/34.92  | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | |   (332)  all_56_3 = e3
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | COMBINE_EQS: (322), (332) imply:
% 204.05/34.92  | | | | | | | | | | | |   (333)  all_6_0 = e3
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | SIMP: (333) implies:
% 204.05/34.92  | | | | | | | | | | | |   (334)  all_6_0 = e3
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | COMBINE_EQS: (323), (334) imply:
% 204.05/34.92  | | | | | | | | | | | |   (335)  all_58_9 = e3
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (324), (334) imply:
% 204.05/34.92  | | | | | | | | | | | |   (336)   ~ (all_52_9 = e3)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (326), (334) imply:
% 204.05/34.92  | | | | | | | | | | | |   (337)   ~ (all_52_27 = e3)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | REDUCE: (328), (334) imply:
% 204.05/34.92  | | | | | | | | | | | |   (338)   ~ (all_52_29 = e3)
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | BETA: splitting (1) gives:
% 204.05/34.92  | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | |   (339)  all_58_9 = e0
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | REF_CLOSE: (317), (335), (339) are inconsistent by sub-proof
% 204.05/34.92  | | | | | | | | | | | | |            #841.
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | Case 2:
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | |   (340)  all_58_10 = e0 | all_58_11 = e0
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | BETA: splitting (340) gives:
% 204.05/34.92  | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | Case 1:
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.92  | | | | | | | | | | | | | |   (341)  all_58_10 = e0
% 204.05/34.92  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | COMBINE_EQS: (57), (341) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (342)  all_52_27 = e0
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | SIMP: (342) implies:
% 204.05/34.93  | | | | | | | | | | | | | |   (343)  all_52_27 = e0
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | REDUCE: (315), (343) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (344)  $false
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | CLOSE: (344) is inconsistent.
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | |   (345)  all_58_11 = e0
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | COMBINE_EQS: (39), (345) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (346)  all_52_29 = e0
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | SIMP: (346) implies:
% 204.05/34.93  | | | | | | | | | | | | | |   (347)  all_52_29 = e0
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | REDUCE: (101), (347) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (348)  op(e0, e0) = all_52_28
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_28, e0,
% 204.05/34.93  | | | | | | | | | | | | | |              e0, simplifying with (45), (348) gives:
% 204.05/34.93  | | | | | | | | | | | | | |   (349)  all_52_28 = all_14_2
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | |   (350)  all_56_1 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | REF_CLOSE: (120), (336), (350) are inconsistent by sub-proof
% 204.05/34.93  | | | | | | | | | | | | | | |            #1326.
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | |   (351)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | REF_CLOSE: (8), (29), (30), (39), (45), (47), (49), (57),
% 204.05/34.93  | | | | | | | | | | | | | | |            (61), (65), (68), (79), (95), (98), (109), (110),
% 204.05/34.93  | | | | | | | | | | | | | | |            (112), (119), (120), (123), (124), (131), (137),
% 204.05/34.93  | | | | | | | | | | | | | | |            (141), (149), (155), (163), (164), (171), (293),
% 204.05/34.93  | | | | | | | | | | | | | | |            (337), (338), (351) are inconsistent by sub-proof
% 204.05/34.93  | | | | | | | | | | | | | | |            #733.
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | |   (352)   ~ (all_56_3 = e3)
% 204.05/34.93  | | | | | | | | | | | |   (353)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | REDUCE: (322), (352) imply:
% 204.05/34.93  | | | | | | | | | | | |   (354)   ~ (all_6_0 = e3)
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (10), (19), (22), (23), (24), (25),
% 204.05/34.93  | | | | | | | | | | | |            (27), (28), (29), (31), (33), (34), (35), (36),
% 204.05/34.93  | | | | | | | | | | | |            (38), (39), (45), (48), (49), (54), (56), (57),
% 204.05/34.93  | | | | | | | | | | | |            (58), (60), (61), (65), (68), (73), (74), (75),
% 204.05/34.93  | | | | | | | | | | | |            (79), (85), (86), (87), (92), (93), (94), (98),
% 204.05/34.93  | | | | | | | | | | | |            (101), (104), (105), (108), (109), (110), (112),
% 204.05/34.93  | | | | | | | | | | | |            (113), (115), (116), (120), (122), (123), (124),
% 204.05/34.93  | | | | | | | | | | | |            (128), (129), (130), (132), (135), (137), (141),
% 204.05/34.93  | | | | | | | | | | | |            (146), (147), (148), (150), (155), (159), (160),
% 204.05/34.93  | | | | | | | | | | | |            (164), (170), (171), (184), (322), (323), (331),
% 204.05/34.93  | | | | | | | | | | | |            (353), (354) are inconsistent by sub-proof #735.
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | 
% 204.05/34.93  | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | 
% 204.05/34.93  | | | | | | | | |   (355)   ~ (all_58_0 = e2)
% 204.05/34.93  | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | REDUCE: (19), (355) imply:
% 204.05/34.93  | | | | | | | | |   (356)   ~ (all_6_2 = e2)
% 204.05/34.93  | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | BETA: splitting (181) gives:
% 204.05/34.93  | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | |   (357)  all_56_0 = e2
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | COMBINE_EQS: (111), (357) imply:
% 204.05/34.93  | | | | | | | | | |   (358)  all_6_2 = e2
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | REDUCE: (356), (358) imply:
% 204.05/34.93  | | | | | | | | | |   (359)  $false
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | CLOSE: (359) is inconsistent.
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | |   (360)  all_56_0 = e1 | all_56_0 = e0
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | BETA: splitting (360) gives:
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | |   (361)  all_56_0 = e1
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | COMBINE_EQS: (111), (361) imply:
% 204.05/34.93  | | | | | | | | | | |   (362)  all_6_2 = e1
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | REDUCE: (293), (362) imply:
% 204.05/34.93  | | | | | | | | | | |   (363)  $false
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | CLOSE: (363) is inconsistent.
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | |   (364)  all_56_0 = e0
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | COMBINE_EQS: (111), (364) imply:
% 204.05/34.93  | | | | | | | | | | |   (365)  all_6_2 = e0
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | COMBINE_EQS: (19), (365) imply:
% 204.05/34.93  | | | | | | | | | | |   (366)  all_58_0 = e0
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | REDUCE: (170), (365) imply:
% 204.05/34.93  | | | | | | | | | | |   (367)   ~ (e3 = e0)
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | SIMP: (367) implies:
% 204.05/34.93  | | | | | | | | | | |   (368)   ~ (e3 = e0)
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | REDUCE: (43), (365) imply:
% 204.05/34.93  | | | | | | | | | | |   (369)  op(e0, e0) = all_52_0
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | REDUCE: (146), (365) imply:
% 204.05/34.93  | | | | | | | | | | |   (370)  op(e0, e3) = all_6_1
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_2, all_52_0, e0, e0,
% 204.05/34.93  | | | | | | | | | | |              simplifying with (45), (369) gives:
% 204.05/34.93  | | | | | | | | | | |   (371)  all_52_0 = all_14_2
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | GROUND_INST: instantiating (8) with e3, all_6_1, e3, e0,
% 204.05/34.93  | | | | | | | | | | |              simplifying with (172), (370) gives:
% 204.05/34.93  | | | | | | | | | | |   (372)  all_6_1 = e3
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | BETA: splitting (129) gives:
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | |   (373)  all_56_1 = e3
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | REF_CLOSE: (8), (112), (120), (137), (170), (373) are
% 204.05/34.93  | | | | | | | | | | | |            inconsistent by sub-proof #1110.
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | |   (374)   ~ (all_56_1 = e3)
% 204.05/34.93  | | | | | | | | | | | |   (375)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | REDUCE: (120), (374) imply:
% 204.05/34.93  | | | | | | | | | | | |   (376)   ~ (all_52_9 = e3)
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | BETA: splitting (115) gives:
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | |   (377)  all_58_0 = e3
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | REF_CLOSE: (366), (368), (377) are inconsistent by sub-proof
% 204.05/34.93  | | | | | | | | | | | | |            #1015.
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | |   (378)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | BETA: splitting (51) gives:
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | |   (379)  all_56_2 = e3
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | COMBINE_EQS: (70), (379) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (380)  all_52_17 = e3
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | SIMP: (380) implies:
% 204.05/34.93  | | | | | | | | | | | | | |   (381)  all_52_17 = e3
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | REDUCE: (17), (381) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (382)   ~ (all_52_25 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | SIMP: (382) implies:
% 204.05/34.93  | | | | | | | | | | | | | |   (383)   ~ (all_52_25 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (10), (19), (22), (23), (24), (25),
% 204.05/34.93  | | | | | | | | | | | | | |            (27), (28), (29), (31), (33), (34), (35), (36),
% 204.05/34.93  | | | | | | | | | | | | | |            (38), (39), (45), (48), (49), (54), (57), (58),
% 204.05/34.93  | | | | | | | | | | | | | |            (60), (61), (65), (68), (73), (74), (75), (79),
% 204.05/34.93  | | | | | | | | | | | | | |            (85), (86), (87), (92), (93), (94), (98), (101),
% 204.05/34.93  | | | | | | | | | | | | | |            (104), (105), (106), (108), (109), (110), (112),
% 204.05/34.93  | | | | | | | | | | | | | |            (113), (115), (116), (120), (122), (123), (124),
% 204.05/34.93  | | | | | | | | | | | | | |            (128), (129), (130), (132), (135), (137), (141),
% 204.05/34.93  | | | | | | | | | | | | | |            (146), (147), (148), (150), (155), (159), (160),
% 204.05/34.93  | | | | | | | | | | | | | |            (164), (170), (171), (184), (383) are inconsistent
% 204.05/34.93  | | | | | | | | | | | | | |            by sub-proof #739.
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | |   (384)   ~ (all_56_2 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | REDUCE: (70), (384) imply:
% 204.05/34.93  | | | | | | | | | | | | | |   (385)   ~ (all_52_17 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | BETA: splitting (378) gives:
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | |   (386)  all_58_1 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | COMBINE_EQS: (10), (386) imply:
% 204.05/34.93  | | | | | | | | | | | | | | |   (387)  all_52_9 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | REDUCE: (376), (387) imply:
% 204.05/34.93  | | | | | | | | | | | | | | |   (388)  $false
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | CLOSE: (388) is inconsistent.
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | |   (389)  all_58_4 = e3 | all_58_9 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | BETA: splitting (389) gives:
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | Case 1:
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | |   (390)  all_58_4 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | REF_CLOSE: (148), (385), (390) are inconsistent by sub-proof
% 204.05/34.93  | | | | | | | | | | | | | | | |            #1302.
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | Case 2:
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | |   (391)  all_58_9 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (391) imply:
% 204.05/34.93  | | | | | | | | | | | | | | | |   (392)  all_52_25 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | SIMP: (392) implies:
% 204.05/34.93  | | | | | | | | | | | | | | | |   (393)  all_52_25 = e3
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | REDUCE: (3), (393) imply:
% 204.05/34.93  | | | | | | | | | | | | | | | |   (394)   ~ (all_52_27 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | SIMP: (394) implies:
% 204.05/34.93  | | | | | | | | | | | | | | | |   (395)   ~ (all_52_27 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | REDUCE: (60), (393) imply:
% 204.05/34.93  | | | | | | | | | | | | | | | |   (396)   ~ (all_52_29 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | SIMP: (396) implies:
% 204.05/34.93  | | | | | | | | | | | | | | | |   (397)   ~ (all_52_29 = e3)
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (29), (30), (39), (45), (47), (49), (57),
% 204.05/34.93  | | | | | | | | | | | | | | | |            (61), (65), (68), (79), (95), (98), (109), (110),
% 204.05/34.93  | | | | | | | | | | | | | | | |            (112), (119), (120), (123), (124), (131), (137),
% 204.05/34.93  | | | | | | | | | | | | | | | |            (141), (149), (155), (163), (164), (171), (293),
% 204.05/34.93  | | | | | | | | | | | | | | | |            (375), (395), (397) are inconsistent by sub-proof
% 204.05/34.93  | | | | | | | | | | | | | | | |            #733.
% 204.05/34.93  | | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | | 
% 204.05/34.93  | | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | | 
% 204.05/34.93  | | | | | | | | End of split
% 204.05/34.93  | | | | | | | | 
% 204.05/34.93  | | | | | | | End of split
% 204.05/34.93  | | | | | | | 
% 204.05/34.93  | | | | | | End of split
% 204.05/34.93  | | | | | | 
% 204.05/34.93  | | | | | End of split
% 204.05/34.93  | | | | | 
% 204.05/34.93  | | | | End of split
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | Case 2:
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | |   (398)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (15), (19), (24), (28),
% 204.05/34.93  | | | |            (29), (31), (35), (36), (38), (39), (41), (43), (44), (45),
% 204.05/34.93  | | | |            (47), (49), (54), (56), (57), (58), (59), (61), (63), (64),
% 204.05/34.93  | | | |            (65), (68), (72), (73), (79), (83), (86), (87), (88), (92),
% 204.05/34.93  | | | |            (94), (96), (97), (101), (102), (105), (107), (108), (109),
% 204.05/34.93  | | | |            (110), (112), (113), (115), (117), (119), (120), (122),
% 204.05/34.93  | | | |            (123), (124), (128), (129), (135), (137), (139), (141),
% 204.05/34.93  | | | |            (143), (145), (146), (148), (150), (155), (159), (398) are
% 204.05/34.93  | | | |            inconsistent by sub-proof #1094.
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | End of split
% 204.05/34.93  | | | 
% 204.05/34.93  | | End of split
% 204.05/34.93  | | 
% 204.05/34.93  | End of split
% 204.05/34.93  | 
% 204.05/34.93  End of proof
% 204.05/34.93  
% 204.05/34.93  Sub-proof #733 shows that the following formulas are inconsistent:
% 204.05/34.93  ----------------------------------------------------------------
% 204.05/34.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.93    (2)  op(e3, e3) = all_52_6
% 204.05/34.93    (3)  op(all_52_13, all_52_13) = e1
% 204.05/34.93    (4)  op(all_10_2, all_10_2) = all_52_20
% 204.05/34.93    (5)  all_58_11 = all_52_29
% 204.05/34.93    (6)   ~ (all_52_3 = e3)
% 204.05/34.93    (7)  op(e0, e0) = all_14_2
% 204.05/34.93    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.93    (9)   ~ (all_4_1 = e1)
% 204.05/34.93    (10)  all_58_10 = all_52_27
% 204.05/34.93    (11)  all_58_7 = all_52_13
% 204.05/34.93    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.93    (13)  all_58_2 = all_52_3
% 204.05/34.93    (14)   ~ (all_52_29 = e3)
% 204.05/34.93    (15)  op(all_4_2, e2) = all_4_1
% 204.05/34.93    (16)   ~ (all_52_5 = e3)
% 204.05/34.93    (17)   ~ (all_52_27 = e3)
% 204.05/34.93    (18)   ~ (all_52_19 = all_10_2)
% 204.05/34.93    (19)  all_58_8 = all_10_2
% 204.05/34.93    (20)  op(all_4_2, all_4_2) = e2
% 204.05/34.93    (21)   ~ (all_52_9 = all_6_2)
% 204.05/34.93    (22)  op(e3, e3) = all_6_2
% 204.05/34.93    (23)  all_58_5 = all_52_19
% 204.05/34.93    (24)  all_56_1 = all_52_9
% 204.05/34.93    (25)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.93    (26)  all_58_6 = all_52_5
% 204.05/34.93    (27)  op(e3, e2) = all_52_9
% 204.05/34.93    (28)   ~ (all_6_2 = e1)
% 204.05/34.93    (29)  all_56_10 = all_10_2
% 204.05/34.93    (30)  op(all_52_9, all_52_9) = e3
% 204.05/34.93    (31)  all_58_3 = all_4_2
% 204.05/34.93    (32)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.05/34.93    (33)   ~ (all_14_2 = e3)
% 204.05/34.93  
% 204.05/34.93  Begin of proof
% 204.05/34.93  | 
% 204.05/34.93  | BETA: splitting (12) gives:
% 204.05/34.93  | 
% 204.05/34.93  | Case 1:
% 204.05/34.93  | | 
% 204.05/34.93  | |   (34)  all_58_6 = e3
% 204.05/34.93  | | 
% 204.05/34.93  | | REF_CLOSE: (16), (26), (34) are inconsistent by sub-proof #1328.
% 204.05/34.93  | | 
% 204.05/34.93  | Case 2:
% 204.05/34.93  | | 
% 204.05/34.93  | |   (35)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.93  | | 
% 204.05/34.93  | | BETA: splitting (8) gives:
% 204.05/34.93  | | 
% 204.05/34.93  | | Case 1:
% 204.05/34.93  | | | 
% 204.05/34.93  | | |   (36)  all_58_2 = e3
% 204.05/34.93  | | | 
% 204.05/34.93  | | | REF_CLOSE: (6), (13), (36) are inconsistent by sub-proof #1369.
% 204.05/34.93  | | | 
% 204.05/34.93  | | Case 2:
% 204.05/34.93  | | | 
% 204.05/34.93  | | |   (37)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.93  | | | 
% 204.05/34.93  | | | BETA: splitting (32) gives:
% 204.05/34.93  | | | 
% 204.05/34.93  | | | Case 1:
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | |   (38)  all_56_10 = e3
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | COMBINE_EQS: (29), (38) imply:
% 204.05/34.93  | | | |   (39)  all_10_2 = e3
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | SIMP: (39) implies:
% 204.05/34.93  | | | |   (40)  all_10_2 = e3
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | REDUCE: (18), (40) imply:
% 204.05/34.93  | | | |   (41)   ~ (all_52_19 = e3)
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | REDUCE: (4), (40) imply:
% 204.05/34.93  | | | |   (42)  op(e3, e3) = all_52_20
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | REF_CLOSE: (1), (7), (9), (10), (15), (17), (20), (21), (22), (23),
% 204.05/34.93  | | | |            (24), (25), (27), (30), (31), (33), (37), (41), (42) are
% 204.05/34.93  | | | |            inconsistent by sub-proof #734.
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | Case 2:
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | |   (43)   ~ (all_56_10 = e3)
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | REDUCE: (29), (43) imply:
% 204.05/34.93  | | | |   (44)   ~ (all_10_2 = e3)
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | | REF_CLOSE: (1), (2), (3), (5), (11), (14), (19), (22), (28), (35), (44)
% 204.05/34.93  | | | |            are inconsistent by sub-proof #1104.
% 204.05/34.93  | | | | 
% 204.05/34.93  | | | End of split
% 204.05/34.93  | | | 
% 204.05/34.93  | | End of split
% 204.05/34.93  | | 
% 204.05/34.93  | End of split
% 204.05/34.93  | 
% 204.05/34.93  End of proof
% 204.05/34.93  
% 204.05/34.93  Sub-proof #734 shows that the following formulas are inconsistent:
% 204.05/34.93  ----------------------------------------------------------------
% 204.05/34.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.93    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.05/34.93    (3)  op(e0, e0) = all_14_2
% 204.05/34.93    (4)   ~ (all_4_1 = e1)
% 204.05/34.93    (5)  all_58_10 = all_52_27
% 204.05/34.93    (6)  op(e3, e3) = all_52_20
% 204.05/34.93    (7)  op(all_4_2, e2) = all_4_1
% 204.05/34.93    (8)   ~ (all_52_19 = e3)
% 204.05/34.93    (9)   ~ (all_52_27 = e3)
% 204.05/34.93    (10)  op(all_4_2, all_4_2) = e2
% 204.05/34.93    (11)   ~ (all_52_9 = all_6_2)
% 204.05/34.93    (12)  op(e3, e3) = all_6_2
% 204.05/34.93    (13)  all_58_5 = all_52_19
% 204.05/34.93    (14)  all_56_1 = all_52_9
% 204.05/34.93    (15)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.05/34.93    (16)  op(e3, e2) = all_52_9
% 204.05/34.93    (17)  op(all_52_9, all_52_9) = e3
% 204.05/34.93    (18)  all_58_3 = all_4_2
% 204.05/34.93    (19)   ~ (all_14_2 = e3)
% 204.05/34.93  
% 204.05/34.93  Begin of proof
% 204.05/34.93  | 
% 204.05/34.93  | BETA: splitting (2) gives:
% 204.05/34.93  | 
% 204.05/34.93  | Case 1:
% 204.05/34.93  | | 
% 204.05/34.93  | |   (20)  all_58_3 = e3
% 204.05/34.93  | | 
% 204.05/34.93  | | COMBINE_EQS: (18), (20) imply:
% 204.05/34.93  | |   (21)  all_4_2 = e3
% 204.05/34.93  | | 
% 204.05/34.93  | | REDUCE: (10), (21) imply:
% 204.05/34.93  | |   (22)  op(e3, e3) = e2
% 204.05/34.93  | | 
% 204.05/34.93  | | REDUCE: (7), (21) imply:
% 204.05/34.93  | |   (23)  op(e3, e2) = all_4_1
% 204.05/34.93  | | 
% 204.05/34.93  | | REF_CLOSE: (1), (3), (4), (6), (11), (12), (14), (15), (16), (17), (19),
% 204.05/34.93  | |            (22), (23) are inconsistent by sub-proof #1113.
% 204.05/34.93  | | 
% 204.05/34.93  | Case 2:
% 204.05/34.93  | | 
% 204.05/34.93  | |   (24)  all_58_5 = e3 | all_58_10 = e3
% 204.05/34.93  | | 
% 204.05/34.93  | | REF_CLOSE: (5), (8), (9), (13), (24) are inconsistent by sub-proof #1132.
% 204.05/34.93  | | 
% 204.05/34.93  | End of split
% 204.05/34.93  | 
% 204.05/34.93  End of proof
% 204.05/34.93  
% 204.05/34.93  Sub-proof #735 shows that the following formulas are inconsistent:
% 204.05/34.93  ----------------------------------------------------------------
% 204.05/34.93    (1)   ~ (all_52_25 = all_52_27)
% 204.05/34.93    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.05/34.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.05/34.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.05/34.93    (4)  all_58_1 = all_52_9
% 204.05/34.93    (5)   ~ (all_6_0 = e3)
% 204.05/34.93    (6)  all_58_0 = all_6_2
% 204.05/34.93    (7)   ~ (all_52_17 = all_10_2)
% 204.05/34.93    (8)  op(e3, e3) = all_52_6
% 204.05/34.93    (9)  op(e3, e0) = all_52_25
% 204.05/34.93    (10)  op(all_52_5, all_52_5) = all_52_4
% 204.05/34.93    (11)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.05/34.93    (12)   ~ (all_52_27 = all_52_29)
% 204.05/34.93    (13)  all_58_13 = all_52_15
% 204.05/34.93    (14)  op(all_52_13, all_52_13) = e1
% 204.05/34.93    (15)  all_58_9 = all_52_25
% 204.05/34.93    (16)   ~ (all_52_29 = all_14_2)
% 204.05/34.93    (17)   ~ (all_52_15 = e3)
% 204.05/34.93    (18)  op(all_52_27, all_52_27) = all_52_26
% 204.05/34.93    (19)  op(e1, e3) = all_52_5
% 204.05/34.93    (20)  op(e2, e2) = all_4_2
% 204.05/34.93    (21)   ~ (all_52_3 = all_52_5)
% 204.05/34.93    (22)  all_58_11 = all_52_29
% 204.05/34.93    (23)  op(e0, e0) = all_14_2
% 204.05/34.93    (24)  all_56_11 = all_52_29
% 204.05/34.93    (25)   ~ (all_4_1 = e1)
% 204.05/34.93    (26)   ~ (all_6_2 = e3)
% 204.05/34.93    (27)   ~ (e2 = e1)
% 204.05/34.93    (28)   ~ (all_6_0 = e1)
% 204.05/34.93    (29)  all_58_10 = all_52_27
% 204.05/34.93    (30)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.05/34.93    (31)  all_56_8 = all_52_5
% 204.05/34.93    (32)   ~ (all_52_25 = all_52_29)
% 204.05/34.93    (33)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.05/34.93    (34)  all_56_3 = all_6_0
% 204.05/34.93    (35)  all_58_7 = all_52_13
% 204.05/34.93    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.05/34.93    (37)  all_58_2 = all_52_3
% 204.05/34.93    (38)  op(e3, all_6_1) = all_6_0
% 204.05/34.93    (39)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.93    (40)  all_56_7 = all_52_27
% 204.14/34.93    (41)  op(all_4_2, e2) = all_4_1
% 204.14/34.93    (42)   ~ (all_52_5 = e3)
% 204.14/34.93    (43)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.14/34.93    (44)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.14/34.93    (45)   ~ (all_6_0 = e2)
% 204.14/34.93    (46)  all_58_9 = all_6_0
% 204.14/34.93    (47)  op(all_6_0, all_6_0) = all_52_24
% 204.14/34.93    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.93    (49)   ~ (all_52_9 = all_52_25)
% 204.14/34.93    (50)  all_58_15 = all_14_2
% 204.14/34.93    (51)  all_58_8 = all_10_2
% 204.14/34.93    (52)  op(all_52_29, all_52_29) = all_52_28
% 204.14/34.93    (53)  op(all_52_17, all_52_17) = all_52_16
% 204.14/34.93    (54)   ~ (all_52_25 = all_6_2)
% 204.14/34.93    (55)   ~ (all_52_5 = all_6_2)
% 204.14/34.93    (56)  op(all_4_2, all_4_2) = e2
% 204.14/34.93    (57)   ~ (all_52_9 = all_6_2)
% 204.14/34.93    (58)  op(e3, e3) = all_6_2
% 204.14/34.93    (59)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.93    (60)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.93    (61)  all_56_3 = all_52_25
% 204.14/34.93    (62)  all_56_1 = all_52_9
% 204.14/34.93    (63)   ~ (all_52_27 = all_4_2)
% 204.14/34.93    (64)  all_58_6 = all_52_5
% 204.14/34.93    (65)  op(e3, e2) = all_52_9
% 204.14/34.93    (66)   ~ (e3 = e2)
% 204.14/34.93    (67)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.93    (68)   ~ (all_52_9 = all_52_17)
% 204.14/34.93    (69)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.14/34.93    (70)  all_58_12 = e3
% 204.14/34.93    (71)   ~ (all_6_1 = e2)
% 204.14/34.93    (72)  op(all_52_9, all_52_9) = e3
% 204.14/34.93    (73)  all_58_3 = all_4_2
% 204.14/34.93    (74)  op(all_6_2, e3) = all_6_1
% 204.14/34.93    (75)   ~ (all_52_13 = all_52_29)
% 204.14/34.93    (76)  all_58_4 = all_52_17
% 204.14/34.93    (77)  op(all_52_25, all_52_25) = all_52_24
% 204.14/34.93    (78)   ~ (all_14_2 = e3)
% 204.14/34.93  
% 204.14/34.93  Begin of proof
% 204.14/34.93  | 
% 204.14/34.93  | BETA: splitting (33) gives:
% 204.14/34.93  | 
% 204.14/34.93  | Case 1:
% 204.14/34.93  | | 
% 204.14/34.93  | |   (79)  all_56_3 = e2
% 204.14/34.93  | | 
% 204.14/34.93  | | REF_CLOSE: (34), (45), (79) are inconsistent by sub-proof #1075.
% 204.14/34.93  | | 
% 204.14/34.93  | Case 2:
% 204.14/34.93  | | 
% 204.14/34.93  | |   (80)   ~ (all_56_3 = e2)
% 204.14/34.93  | |   (81)  all_56_3 = e1 | all_56_3 = e0
% 204.14/34.93  | | 
% 204.14/34.93  | | BETA: splitting (81) gives:
% 204.14/34.93  | | 
% 204.14/34.93  | | Case 1:
% 204.14/34.93  | | | 
% 204.14/34.93  | | |   (82)  all_56_3 = e1
% 204.14/34.93  | | | 
% 204.14/34.93  | | | REF_CLOSE: (28), (34), (82) are inconsistent by sub-proof #1074.
% 204.14/34.93  | | | 
% 204.14/34.93  | | Case 2:
% 204.14/34.93  | | | 
% 204.14/34.93  | | |   (83)  all_56_3 = e0
% 204.14/34.93  | | | 
% 204.14/34.93  | | | COMBINE_EQS: (34), (83) imply:
% 204.14/34.93  | | |   (84)  all_6_0 = e0
% 204.14/34.93  | | | 
% 204.14/34.93  | | | SIMP: (84) implies:
% 204.14/34.93  | | |   (85)  all_6_0 = e0
% 204.14/34.93  | | | 
% 204.14/34.93  | | | COMBINE_EQS: (46), (85) imply:
% 204.14/34.93  | | |   (86)  all_58_9 = e0
% 204.14/34.93  | | | 
% 204.14/34.93  | | | REDUCE: (5), (85) imply:
% 204.14/34.93  | | |   (87)   ~ (e3 = e0)
% 204.14/34.93  | | | 
% 204.14/34.93  | | | SIMP: (87) implies:
% 204.14/34.93  | | |   (88)   ~ (e3 = e0)
% 204.14/34.93  | | | 
% 204.14/34.93  | | | REDUCE: (47), (85) imply:
% 204.14/34.93  | | |   (89)  op(e0, e0) = all_52_24
% 204.14/34.93  | | | 
% 204.14/34.93  | | | GROUND_INST: instantiating (3) with all_14_2, all_52_24, e0, e0,
% 204.14/34.93  | | |              simplifying with (23), (89) gives:
% 204.14/34.93  | | |   (90)  all_52_24 = all_14_2
% 204.14/34.93  | | | 
% 204.14/34.93  | | | BETA: splitting (59) gives:
% 204.14/34.93  | | | 
% 204.14/34.93  | | | Case 1:
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | |   (91)  all_58_9 = e3
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | | COMBINE_EQS: (86), (91) imply:
% 204.14/34.93  | | | |   (92)  e3 = e0
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | | REDUCE: (88), (92) imply:
% 204.14/34.93  | | | |   (93)  $false
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | | CLOSE: (93) is inconsistent.
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | Case 2:
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | |   (94)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 204.14/34.93  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 204.14/34.93  | | | |            (23), (24), (25), (26), (27), (29), (30), (31), (32), (33),
% 204.14/34.93  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 204.14/34.93  | | | |            (45), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 204.14/34.93  | | | |            (57), (58), (60), (61), (62), (63), (64), (65), (66), (67),
% 204.14/34.93  | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 204.14/34.93  | | | |            (78), (94) are inconsistent by sub-proof #1102.
% 204.14/34.93  | | | | 
% 204.14/34.93  | | | End of split
% 204.14/34.93  | | | 
% 204.14/34.93  | | End of split
% 204.14/34.93  | | 
% 204.14/34.93  | End of split
% 204.14/34.93  | 
% 204.14/34.93  End of proof
% 204.14/34.93  
% 204.14/34.93  Sub-proof #736 shows that the following formulas are inconsistent:
% 204.14/34.93  ----------------------------------------------------------------
% 204.14/34.93    (1)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.14/34.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.93    (3)   ~ (all_4_2 = e3)
% 204.14/34.93    (4)  op(e2, e2) = all_4_2
% 204.14/34.93    (5)  all_56_2 = all_52_17
% 204.14/34.93    (6)   ~ (all_52_9 = e3)
% 204.14/34.93    (7)   ~ (all_52_9 = e1)
% 204.14/34.93    (8)  all_56_1 = all_52_9
% 204.14/34.94    (9)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.14/34.94    (10)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.94    (11)   ~ (all_52_17 = e1)
% 204.14/34.94    (12)   ~ (all_52_9 = all_52_17)
% 204.14/34.94    (13)  op(all_52_9, all_52_9) = e3
% 204.14/34.94    (14)   ~ (all_52_17 = e2)
% 204.14/34.94    (15)  all_58_4 = all_52_17
% 204.14/34.94  
% 204.14/34.94  Begin of proof
% 204.14/34.94  | 
% 204.14/34.94  | BETA: splitting (10) gives:
% 204.14/34.94  | 
% 204.14/34.94  | Case 1:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (16)  all_56_1 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | COMBINE_EQS: (8), (16) imply:
% 204.14/34.94  | |   (17)  all_52_9 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | REDUCE: (6), (17) imply:
% 204.14/34.94  | |   (18)  $false
% 204.14/34.94  | | 
% 204.14/34.94  | | CLOSE: (18) is inconsistent.
% 204.14/34.94  | | 
% 204.14/34.94  | Case 2:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (19)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.94  | | 
% 204.14/34.94  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 204.14/34.94  | |            (15), (19) are inconsistent by sub-proof #937.
% 204.14/34.94  | | 
% 204.14/34.94  | End of split
% 204.14/34.94  | 
% 204.14/34.94  End of proof
% 204.14/34.94  
% 204.14/34.94  Sub-proof #737 shows that the following formulas are inconsistent:
% 204.14/34.94  ----------------------------------------------------------------
% 204.14/34.94    (1)  all_58_6 = e3
% 204.14/34.94    (2)  all_58_6 = e0
% 204.14/34.94    (3)   ~ (e3 = e0)
% 204.14/34.94  
% 204.14/34.94  Begin of proof
% 204.14/34.94  | 
% 204.14/34.94  | COMBINE_EQS: (1), (2) imply:
% 204.14/34.94  |   (4)  e3 = e0
% 204.14/34.94  | 
% 204.14/34.94  | SIMP: (4) implies:
% 204.14/34.94  |   (5)  e3 = e0
% 204.14/34.94  | 
% 204.14/34.94  | REDUCE: (3), (5) imply:
% 204.14/34.94  |   (6)  $false
% 204.14/34.94  | 
% 204.14/34.94  | CLOSE: (6) is inconsistent.
% 204.14/34.94  | 
% 204.14/34.94  End of proof
% 204.14/34.94  
% 204.14/34.94  Sub-proof #738 shows that the following formulas are inconsistent:
% 204.14/34.94  ----------------------------------------------------------------
% 204.14/34.94    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.94    (2)   ~ (all_52_25 = all_52_27)
% 204.14/34.94    (3)  all_58_14 = all_52_23
% 204.14/34.94    (4)  op(all_52_3, all_52_3) = all_52_2
% 204.14/34.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.94    (6)   ~ (all_52_5 = all_52_13)
% 204.14/34.94    (7)  all_58_1 = all_52_9
% 204.14/34.94    (8)   ~ (all_52_17 = all_52_25)
% 204.14/34.94    (9)   ~ (all_52_3 = all_6_2)
% 204.14/34.94    (10)  all_58_0 = all_6_2
% 204.14/34.94    (11)  all_56_4 = all_52_3
% 204.14/34.94    (12)   ~ (all_52_17 = all_10_2)
% 204.14/34.94    (13)  op(e3, e3) = all_52_6
% 204.14/34.94    (14)  op(e3, e0) = all_52_25
% 204.14/34.94    (15)  op(all_52_5, all_52_5) = all_52_4
% 204.14/34.94    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.14/34.94    (17)  op(all_52_19, all_52_19) = all_52_18
% 204.14/34.94    (18)   ~ (all_52_27 = all_52_29)
% 204.14/34.94    (19)  all_58_13 = all_52_15
% 204.14/34.94    (20)  op(all_52_13, all_52_13) = e1
% 204.14/34.94    (21)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.94    (22)  all_58_9 = all_52_25
% 204.14/34.94    (23)   ~ (all_52_29 = all_14_2)
% 204.14/34.94    (24)   ~ (all_52_15 = e3)
% 204.14/34.94    (25)  op(all_52_27, all_52_27) = all_52_26
% 204.14/34.94    (26)  op(e1, e3) = all_52_5
% 204.14/34.94    (27)  op(e2, e2) = all_4_2
% 204.14/34.94    (28)   ~ (all_52_3 = all_52_5)
% 204.14/34.94    (29)  all_58_11 = all_52_29
% 204.14/34.94    (30)   ~ (all_52_3 = e3)
% 204.14/34.94    (31)  all_56_5 = all_4_2
% 204.14/34.94    (32)   ~ (all_52_25 = all_14_2)
% 204.14/34.94    (33)   ~ (all_52_3 = all_52_27)
% 204.14/34.94    (34)  op(e0, e0) = all_14_2
% 204.14/34.94    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.14/34.94    (36)  all_56_11 = all_52_29
% 204.14/34.94    (37)   ~ (all_4_1 = e1)
% 204.14/34.94    (38)   ~ (all_6_2 = e3)
% 204.14/34.94    (39)  all_56_9 = all_52_13
% 204.14/34.94    (40)   ~ (e2 = e1)
% 204.14/34.94    (41)   ~ (all_52_13 = all_10_2)
% 204.14/34.94    (42)  all_58_10 = all_52_27
% 204.14/34.94    (43)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.94    (44)  all_56_8 = all_52_5
% 204.14/34.94    (45)   ~ (all_52_25 = all_52_29)
% 204.14/34.94    (46)  all_58_7 = all_52_13
% 204.14/34.94    (47)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.14/34.94    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.14/34.94    (49)  all_58_2 = all_52_3
% 204.14/34.94    (50)  op(e3, all_6_1) = all_6_0
% 204.14/34.94    (51)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.94    (52)  all_56_7 = all_52_27
% 204.14/34.94    (53)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.14/34.94    (54)  op(all_4_2, e2) = all_4_1
% 204.14/34.94    (55)   ~ (all_52_23 = e3)
% 204.14/34.94    (56)   ~ (all_52_19 = e3)
% 204.14/34.94    (57)   ~ (all_52_5 = e3)
% 204.14/34.94    (58)   ~ (all_52_5 = all_52_29)
% 204.14/34.94    (59)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.14/34.94    (60)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.94    (61)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.14/34.94    (62)   ~ (all_6_0 = e2)
% 204.14/34.94    (63)   ~ (all_52_13 = all_4_2)
% 204.14/34.94    (64)  op(e1, e2) = all_52_13
% 204.14/34.94    (65)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.94    (66)   ~ (all_52_9 = all_52_25)
% 204.14/34.94    (67)  all_58_15 = all_14_2
% 204.14/34.94    (68)   ~ (all_52_19 = all_10_2)
% 204.14/34.94    (69)  all_58_8 = all_10_2
% 204.14/34.94    (70)   ~ (all_52_5 = all_10_2)
% 204.14/34.94    (71)  op(all_52_29, all_52_29) = all_52_28
% 204.14/34.94    (72)  op(all_52_17, all_52_17) = all_52_16
% 204.14/34.94    (73)   ~ (all_52_25 = all_6_2)
% 204.14/34.94    (74)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.14/34.94    (75)   ~ (all_52_9 = all_4_2)
% 204.14/34.94    (76)   ~ (all_52_5 = all_6_2)
% 204.14/34.94    (77)  op(all_4_2, all_4_2) = e2
% 204.14/34.94    (78)   ~ (all_52_9 = all_6_2)
% 204.14/34.94    (79)  op(e3, e3) = all_6_2
% 204.14/34.94    (80)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.94    (81)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.94    (82)  all_56_3 = all_52_25
% 204.14/34.94    (83)  all_58_5 = all_52_19
% 204.14/34.94    (84)  all_56_1 = all_52_9
% 204.14/34.94    (85)   ~ (all_52_15 = all_4_2)
% 204.14/34.94    (86)   ~ (all_52_27 = all_4_2)
% 204.14/34.94    (87)  all_58_6 = all_52_5
% 204.14/34.94    (88)  op(e3, e2) = all_52_9
% 204.14/34.94    (89)   ~ (all_52_17 = all_6_2)
% 204.14/34.94    (90)   ~ (e3 = e2)
% 204.14/34.94    (91)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.94    (92)   ~ (all_52_9 = all_52_17)
% 204.14/34.94    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.14/34.94    (94)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.14/34.94    (95)  all_58_12 = e3
% 204.14/34.94    (96)   ~ (all_6_1 = e2)
% 204.14/34.94    (97)  op(all_52_9, all_52_9) = e3
% 204.14/34.94    (98)   ~ (all_52_23 = all_10_2)
% 204.14/34.94    (99)  all_58_3 = all_4_2
% 204.14/34.94    (100)   ~ (all_52_3 = all_4_2)
% 204.14/34.94    (101)   ~ (all_52_19 = all_4_2)
% 204.14/34.94    (102)  op(all_6_2, e3) = all_6_1
% 204.14/34.94    (103)   ~ (all_52_13 = all_52_29)
% 204.14/34.94    (104)  all_58_4 = all_52_17
% 204.14/34.94    (105)  op(all_52_25, all_52_25) = all_52_24
% 204.14/34.94    (106)   ~ (all_14_2 = e3)
% 204.14/34.94  
% 204.14/34.94  Begin of proof
% 204.14/34.94  | 
% 204.14/34.94  | BETA: splitting (93) gives:
% 204.14/34.94  | 
% 204.14/34.94  | Case 1:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (107)  all_58_4 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | COMBINE_EQS: (104), (107) imply:
% 204.14/34.94  | |   (108)  all_52_17 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | SIMP: (108) implies:
% 204.14/34.94  | |   (109)  all_52_17 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | REDUCE: (8), (109) imply:
% 204.14/34.94  | |   (110)   ~ (all_52_25 = e3)
% 204.14/34.94  | | 
% 204.14/34.94  | | SIMP: (110) implies:
% 204.14/34.94  | |   (111)   ~ (all_52_25 = e3)
% 204.14/34.94  | | 
% 204.14/34.94  | | REDUCE: (89), (109) imply:
% 204.14/34.94  | |   (112)   ~ (all_6_2 = e3)
% 204.14/34.94  | | 
% 204.14/34.94  | | REDUCE: (72), (109) imply:
% 204.14/34.94  | |   (113)  op(e3, e3) = all_52_16
% 204.14/34.94  | | 
% 204.14/34.94  | | GROUND_INST: instantiating (5) with all_6_2, all_52_16, e3, e3, simplifying
% 204.14/34.94  | |              with (79), (113) gives:
% 204.14/34.94  | |   (114)  all_52_16 = all_6_2
% 204.14/34.94  | | 
% 204.14/34.94  | | REF_CLOSE: (2), (4), (5), (7), (10), (12), (13), (14), (15), (16), (18),
% 204.14/34.94  | |            (19), (20), (22), (23), (24), (25), (26), (27), (28), (29), (34),
% 204.14/34.94  | |            (36), (37), (38), (40), (42), (43), (44), (45), (46), (48), (49),
% 204.14/34.94  | |            (50), (51), (52), (54), (57), (59), (61), (62), (65), (66), (67),
% 204.14/34.94  | |            (69), (71), (72), (73), (74), (76), (77), (78), (79), (80), (81),
% 204.14/34.94  | |            (82), (84), (86), (87), (88), (90), (91), (92), (93), (95), (96),
% 204.14/34.94  | |            (97), (99), (102), (103), (104), (105), (106), (111) are
% 204.14/34.94  | |            inconsistent by sub-proof #739.
% 204.14/34.94  | | 
% 204.14/34.94  | Case 2:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (115)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | BETA: splitting (115) gives:
% 204.14/34.94  | | 
% 204.14/34.94  | | Case 1:
% 204.14/34.94  | | | 
% 204.14/34.94  | | |   (116)  all_58_5 = e3
% 204.14/34.94  | | | 
% 204.14/34.94  | | | REF_CLOSE: (56), (83), (116) are inconsistent by sub-proof #1279.
% 204.14/34.94  | | | 
% 204.14/34.94  | | Case 2:
% 204.14/34.94  | | | 
% 204.14/34.94  | | |   (117)  all_58_8 = e3 | all_58_14 = e3
% 204.14/34.94  | | | 
% 204.14/34.94  | | | BETA: splitting (117) gives:
% 204.14/34.94  | | | 
% 204.14/34.94  | | | Case 1:
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | |   (118)  all_58_8 = e3
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | COMBINE_EQS: (69), (118) imply:
% 204.14/34.94  | | | |   (119)  all_10_2 = e3
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | REDUCE: (12), (119) imply:
% 204.14/34.94  | | | |   (120)   ~ (all_52_17 = e3)
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | REDUCE: (21), (119) imply:
% 204.14/34.94  | | | |   (121)  op(e3, e3) = all_52_20
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_20, e3, e3,
% 204.14/34.94  | | | |              simplifying with (79), (121) gives:
% 204.14/34.94  | | | |   (122)  all_52_20 = all_6_2
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | BETA: splitting (35) gives:
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | Case 1:
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | |   (123)  all_58_2 = e3
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | | REF_CLOSE: (30), (49), (123) are inconsistent by sub-proof #1369.
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | Case 2:
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | |   (124)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | | BETA: splitting (80) gives:
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | | Case 1:
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | |   (125)  all_58_9 = e3
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | COMBINE_EQS: (22), (125) imply:
% 204.14/34.94  | | | | | |   (126)  all_52_25 = e3
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | SIMP: (126) implies:
% 204.14/34.94  | | | | | |   (127)  all_52_25 = e3
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | REDUCE: (2), (127) imply:
% 204.14/34.94  | | | | | |   (128)   ~ (all_52_27 = e3)
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | SIMP: (128) implies:
% 204.14/34.94  | | | | | |   (129)   ~ (all_52_27 = e3)
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | REDUCE: (45), (127) imply:
% 204.14/34.94  | | | | | |   (130)   ~ (all_52_29 = e3)
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | SIMP: (130) implies:
% 204.14/34.94  | | | | | |   (131)   ~ (all_52_29 = e3)
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | REDUCE: (32), (127) imply:
% 204.14/34.94  | | | | | |   (132)   ~ (all_14_2 = e3)
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | BETA: splitting (124) gives:
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | Case 1:
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | |   (133)  all_58_3 = e3
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | COMBINE_EQS: (99), (133) imply:
% 204.14/34.94  | | | | | | |   (134)  all_4_2 = e3
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | REDUCE: (75), (134) imply:
% 204.14/34.94  | | | | | | |   (135)   ~ (all_52_9 = e3)
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | REDUCE: (54), (134) imply:
% 204.14/34.94  | | | | | | |   (136)  op(e3, e2) = all_4_1
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | GROUND_INST: instantiating (5) with all_52_9, all_4_1, e2, e3,
% 204.14/34.94  | | | | | | |              simplifying with (88), (136) gives:
% 204.14/34.94  | | | | | | |   (137)  all_52_9 = all_4_1
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | REDUCE: (135), (137) imply:
% 204.14/34.94  | | | | | | |   (138)   ~ (all_4_1 = e3)
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (11), (17), (19), (20),
% 204.14/34.94  | | | | | | |            (21), (24), (26), (27), (29), (31), (33), (34), (37),
% 204.14/34.94  | | | | | | |            (39), (41), (42), (43), (44), (46), (47), (48), (49),
% 204.14/34.94  | | | | | | |            (53), (54), (55), (57), (58), (60), (63), (64), (65),
% 204.14/34.94  | | | | | | |            (69), (76), (77), (78), (79), (83), (84), (86), (87),
% 204.14/34.94  | | | | | | |            (88), (91), (93), (94), (96), (97), (99), (100), (101),
% 204.14/34.94  | | | | | | |            (102), (104), (106), (120), (125), (131), (135), (138)
% 204.14/34.94  | | | | | | |            are inconsistent by sub-proof #1111.
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | Case 2:
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | |   (139)  all_58_5 = e3 | all_58_10 = e3
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | | REF_CLOSE: (42), (56), (83), (129), (139) are inconsistent by
% 204.14/34.94  | | | | | | |            sub-proof #1132.
% 204.14/34.94  | | | | | | | 
% 204.14/34.94  | | | | | | End of split
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | Case 2:
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | |   (140)   ~ (all_58_9 = e3)
% 204.14/34.94  | | | | | |   (141)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | REDUCE: (22), (140) imply:
% 204.14/34.94  | | | | | |   (142)   ~ (all_52_25 = e3)
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | | REF_CLOSE: (2), (4), (5), (7), (10), (12), (13), (14), (15), (16),
% 204.14/34.94  | | | | | |            (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 204.14/34.94  | | | | | |            (28), (29), (34), (36), (37), (38), (40), (42), (43),
% 204.14/34.94  | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52), (54),
% 204.14/34.94  | | | | | |            (57), (59), (61), (62), (65), (66), (67), (69), (71),
% 204.14/34.94  | | | | | |            (72), (73), (74), (76), (77), (78), (79), (81), (82),
% 204.14/34.94  | | | | | |            (84), (86), (87), (88), (90), (91), (92), (93), (95),
% 204.14/34.94  | | | | | |            (96), (97), (99), (102), (103), (104), (105), (106),
% 204.14/34.94  | | | | | |            (141), (142) are inconsistent by sub-proof #740.
% 204.14/34.94  | | | | | | 
% 204.14/34.94  | | | | | End of split
% 204.14/34.94  | | | | | 
% 204.14/34.94  | | | | End of split
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | Case 2:
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | |   (143)  all_58_14 = e3
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | | REF_CLOSE: (3), (55), (143) are inconsistent by sub-proof #1305.
% 204.14/34.94  | | | | 
% 204.14/34.94  | | | End of split
% 204.14/34.94  | | | 
% 204.14/34.94  | | End of split
% 204.14/34.94  | | 
% 204.14/34.94  | End of split
% 204.14/34.94  | 
% 204.14/34.94  End of proof
% 204.14/34.94  
% 204.14/34.94  Sub-proof #739 shows that the following formulas are inconsistent:
% 204.14/34.94  ----------------------------------------------------------------
% 204.14/34.94    (1)   ~ (all_52_25 = all_52_27)
% 204.14/34.94    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.14/34.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.94    (4)  all_58_1 = all_52_9
% 204.14/34.94    (5)  all_58_0 = all_6_2
% 204.14/34.94    (6)   ~ (all_52_17 = all_10_2)
% 204.14/34.94    (7)  op(e3, e3) = all_52_6
% 204.14/34.94    (8)  op(e3, e0) = all_52_25
% 204.14/34.94    (9)  op(all_52_5, all_52_5) = all_52_4
% 204.14/34.94    (10)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.14/34.94    (11)   ~ (all_52_27 = all_52_29)
% 204.14/34.94    (12)  all_58_13 = all_52_15
% 204.14/34.94    (13)  op(all_52_13, all_52_13) = e1
% 204.14/34.94    (14)  all_58_9 = all_52_25
% 204.14/34.94    (15)   ~ (all_52_29 = all_14_2)
% 204.14/34.94    (16)   ~ (all_52_15 = e3)
% 204.14/34.94    (17)  op(all_52_27, all_52_27) = all_52_26
% 204.14/34.94    (18)  op(e1, e3) = all_52_5
% 204.14/34.94    (19)  op(e2, e2) = all_4_2
% 204.14/34.94    (20)   ~ (all_52_3 = all_52_5)
% 204.14/34.94    (21)  all_58_11 = all_52_29
% 204.14/34.94    (22)  op(e0, e0) = all_14_2
% 204.14/34.94    (23)  all_56_11 = all_52_29
% 204.14/34.94    (24)   ~ (all_4_1 = e1)
% 204.14/34.94    (25)   ~ (all_6_2 = e3)
% 204.14/34.94    (26)   ~ (e2 = e1)
% 204.14/34.94    (27)  all_58_10 = all_52_27
% 204.14/34.94    (28)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.94    (29)  all_56_8 = all_52_5
% 204.14/34.94    (30)   ~ (all_52_25 = all_52_29)
% 204.14/34.94    (31)  all_58_7 = all_52_13
% 204.14/34.94    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.14/34.94    (33)  all_58_2 = all_52_3
% 204.14/34.94    (34)  op(e3, all_6_1) = all_6_0
% 204.14/34.94    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.94    (36)  all_56_7 = all_52_27
% 204.14/34.94    (37)   ~ (all_52_25 = e3)
% 204.14/34.94    (38)  op(all_4_2, e2) = all_4_1
% 204.14/34.94    (39)   ~ (all_52_5 = e3)
% 204.14/34.94    (40)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.14/34.94    (41)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.14/34.94    (42)   ~ (all_6_0 = e2)
% 204.14/34.94    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.94    (44)   ~ (all_52_9 = all_52_25)
% 204.14/34.94    (45)  all_58_15 = all_14_2
% 204.14/34.94    (46)  all_58_8 = all_10_2
% 204.14/34.94    (47)  op(all_52_29, all_52_29) = all_52_28
% 204.14/34.94    (48)  op(all_52_17, all_52_17) = all_52_16
% 204.14/34.94    (49)   ~ (all_52_25 = all_6_2)
% 204.14/34.94    (50)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.14/34.94    (51)   ~ (all_52_5 = all_6_2)
% 204.14/34.94    (52)  op(all_4_2, all_4_2) = e2
% 204.14/34.94    (53)   ~ (all_52_9 = all_6_2)
% 204.14/34.94    (54)  op(e3, e3) = all_6_2
% 204.14/34.94    (55)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.94    (56)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.94    (57)  all_56_3 = all_52_25
% 204.14/34.94    (58)  all_56_1 = all_52_9
% 204.14/34.94    (59)   ~ (all_52_27 = all_4_2)
% 204.14/34.94    (60)  all_58_6 = all_52_5
% 204.14/34.94    (61)  op(e3, e2) = all_52_9
% 204.14/34.94    (62)   ~ (e3 = e2)
% 204.14/34.94    (63)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.94    (64)   ~ (all_52_9 = all_52_17)
% 204.14/34.94    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.14/34.94    (66)  all_58_12 = e3
% 204.14/34.94    (67)   ~ (all_6_1 = e2)
% 204.14/34.94    (68)  op(all_52_9, all_52_9) = e3
% 204.14/34.94    (69)  all_58_3 = all_4_2
% 204.14/34.94    (70)  op(all_6_2, e3) = all_6_1
% 204.14/34.94    (71)   ~ (all_52_13 = all_52_29)
% 204.14/34.94    (72)  all_58_4 = all_52_17
% 204.14/34.94    (73)  op(all_52_25, all_52_25) = all_52_24
% 204.14/34.94    (74)   ~ (all_14_2 = e3)
% 204.14/34.94  
% 204.14/34.94  Begin of proof
% 204.14/34.94  | 
% 204.14/34.94  | BETA: splitting (55) gives:
% 204.14/34.94  | 
% 204.14/34.94  | Case 1:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (75)  all_58_9 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | REF_CLOSE: (14), (37), (75) are inconsistent by sub-proof #1300.
% 204.14/34.94  | | 
% 204.14/34.94  | Case 2:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (76)   ~ (all_58_9 = e3)
% 204.14/34.94  | |   (77)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.14/34.94  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.14/34.94  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.14/34.94  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.14/34.94  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 204.14/34.94  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 204.14/34.94  | |            (69), (70), (71), (72), (73), (74), (77) are inconsistent by
% 204.14/34.94  | |            sub-proof #740.
% 204.14/34.94  | | 
% 204.14/34.94  | End of split
% 204.14/34.94  | 
% 204.14/34.94  End of proof
% 204.14/34.94  
% 204.14/34.94  Sub-proof #740 shows that the following formulas are inconsistent:
% 204.14/34.94  ----------------------------------------------------------------
% 204.14/34.94    (1)   ~ (all_52_25 = all_52_27)
% 204.14/34.94    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.14/34.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.94    (4)  all_58_1 = all_52_9
% 204.14/34.94    (5)  all_58_0 = all_6_2
% 204.14/34.94    (6)   ~ (all_52_17 = all_10_2)
% 204.14/34.94    (7)  op(e3, e3) = all_52_6
% 204.14/34.94    (8)  op(e3, e0) = all_52_25
% 204.14/34.94    (9)  op(all_52_5, all_52_5) = all_52_4
% 204.14/34.94    (10)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.14/34.94    (11)   ~ (all_52_27 = all_52_29)
% 204.14/34.94    (12)  all_58_13 = all_52_15
% 204.14/34.94    (13)  op(all_52_13, all_52_13) = e1
% 204.14/34.94    (14)  all_58_9 = all_52_25
% 204.14/34.94    (15)   ~ (all_52_29 = all_14_2)
% 204.14/34.94    (16)   ~ (all_52_15 = e3)
% 204.14/34.94    (17)  op(all_52_27, all_52_27) = all_52_26
% 204.14/34.94    (18)  op(e1, e3) = all_52_5
% 204.14/34.94    (19)  op(e2, e2) = all_4_2
% 204.14/34.94    (20)   ~ (all_52_3 = all_52_5)
% 204.14/34.94    (21)  all_58_11 = all_52_29
% 204.14/34.94    (22)  op(e0, e0) = all_14_2
% 204.14/34.94    (23)  all_56_11 = all_52_29
% 204.14/34.94    (24)   ~ (all_4_1 = e1)
% 204.14/34.94    (25)   ~ (all_6_2 = e3)
% 204.14/34.94    (26)   ~ (e2 = e1)
% 204.14/34.94    (27)  all_58_10 = all_52_27
% 204.14/34.94    (28)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.94    (29)  all_56_8 = all_52_5
% 204.14/34.94    (30)   ~ (all_52_25 = all_52_29)
% 204.14/34.94    (31)  all_58_7 = all_52_13
% 204.14/34.94    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.14/34.94    (33)  all_58_2 = all_52_3
% 204.14/34.94    (34)  op(e3, all_6_1) = all_6_0
% 204.14/34.94    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.94    (36)  all_56_7 = all_52_27
% 204.14/34.94    (37)   ~ (all_52_25 = e3)
% 204.14/34.94    (38)  op(all_4_2, e2) = all_4_1
% 204.14/34.94    (39)   ~ (all_52_5 = e3)
% 204.14/34.94    (40)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.14/34.94    (41)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.14/34.94    (42)   ~ (all_6_0 = e2)
% 204.14/34.94    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.94    (44)   ~ (all_52_9 = all_52_25)
% 204.14/34.94    (45)  all_58_15 = all_14_2
% 204.14/34.94    (46)  all_58_8 = all_10_2
% 204.14/34.94    (47)  op(all_52_29, all_52_29) = all_52_28
% 204.14/34.94    (48)  op(all_52_17, all_52_17) = all_52_16
% 204.14/34.94    (49)   ~ (all_52_25 = all_6_2)
% 204.14/34.94    (50)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.14/34.94    (51)   ~ (all_52_5 = all_6_2)
% 204.14/34.94    (52)  op(all_4_2, all_4_2) = e2
% 204.14/34.94    (53)   ~ (all_52_9 = all_6_2)
% 204.14/34.94    (54)  op(e3, e3) = all_6_2
% 204.14/34.94    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.94    (56)  all_56_3 = all_52_25
% 204.14/34.94    (57)  all_56_1 = all_52_9
% 204.14/34.94    (58)   ~ (all_52_27 = all_4_2)
% 204.14/34.94    (59)  all_58_6 = all_52_5
% 204.14/34.94    (60)  op(e3, e2) = all_52_9
% 204.14/34.94    (61)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.94    (62)   ~ (e3 = e2)
% 204.14/34.94    (63)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.94    (64)   ~ (all_52_9 = all_52_17)
% 204.14/34.94    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.14/34.94    (66)  all_58_12 = e3
% 204.14/34.94    (67)   ~ (all_6_1 = e2)
% 204.14/34.94    (68)  op(all_52_9, all_52_9) = e3
% 204.14/34.94    (69)  all_58_3 = all_4_2
% 204.14/34.94    (70)  op(all_6_2, e3) = all_6_1
% 204.14/34.94    (71)   ~ (all_52_13 = all_52_29)
% 204.14/34.94    (72)  all_58_4 = all_52_17
% 204.14/34.94    (73)  op(all_52_25, all_52_25) = all_52_24
% 204.14/34.94    (74)   ~ (all_14_2 = e3)
% 204.14/34.94  
% 204.14/34.94  Begin of proof
% 204.14/34.94  | 
% 204.14/34.94  | BETA: splitting (50) gives:
% 204.14/34.94  | 
% 204.14/34.94  | Case 1:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (75)  all_56_3 = e3
% 204.14/34.94  | | 
% 204.14/34.94  | | REF_CLOSE: (37), (56), (75) are inconsistent by sub-proof #1339.
% 204.14/34.94  | | 
% 204.14/34.94  | Case 2:
% 204.14/34.94  | | 
% 204.14/34.94  | |   (76)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.14/34.94  | | 
% 204.14/34.94  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.14/34.94  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.14/34.94  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.14/34.94  | |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 204.14/34.94  | |            (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 204.14/34.94  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 204.14/34.94  | |            (70), (71), (72), (73), (74), (76) are inconsistent by sub-proof
% 204.14/34.94  | |            #1102.
% 204.14/34.94  | | 
% 204.14/34.94  | End of split
% 204.14/34.94  | 
% 204.14/34.94  End of proof
% 204.14/34.94  
% 204.14/34.94  Sub-proof #741 shows that the following formulas are inconsistent:
% 204.14/34.94  ----------------------------------------------------------------
% 204.14/34.94    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.94    (2)   ~ (all_52_15 = all_52_23)
% 204.14/34.94    (3)   ~ (all_52_25 = all_52_27)
% 204.14/34.94    (4)  all_58_14 = all_52_23
% 204.14/34.94    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.14/34.94    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.94    (7)   ~ (all_52_5 = all_52_13)
% 204.14/34.94    (8)  op(all_52_7, all_52_7) = e0
% 204.14/34.94    (9)  all_58_1 = all_52_9
% 204.14/34.94    (10)   ~ (all_52_9 = all_52_13)
% 204.14/34.94    (11)  op(all_52_5, all_52_5) = e1
% 204.14/34.94    (12)   ~ (e3 = e0)
% 204.14/34.94    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.94    (14)  op(e0, e2) = all_52_15
% 204.14/34.94    (15)   ~ (all_52_7 = all_52_15)
% 204.14/34.94    (16)   ~ (all_52_3 = all_52_19)
% 204.14/34.94    (17)   ~ (all_52_17 = all_52_25)
% 204.14/34.94    (18)   ~ (all_52_3 = all_6_2)
% 204.14/34.94    (19)  all_58_0 = all_6_2
% 204.14/34.94    (20)  op(all_14_2, e0) = all_14_1
% 204.14/34.94    (21)  all_56_4 = all_52_3
% 204.14/34.94    (22)   ~ (all_52_17 = all_10_2)
% 204.14/34.94    (23)  op(e3, e0) = all_52_25
% 204.14/34.94    (24)  op(e0, all_14_1) = all_14_0
% 204.14/34.94    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.14/34.94    (26)  op(all_52_19, all_52_19) = all_52_18
% 204.14/34.94    (27)  all_58_13 = all_52_15
% 204.14/34.94    (28)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.94    (29)  all_58_9 = all_52_25
% 204.14/34.94    (30)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.14/34.94    (31)   ~ (all_52_29 = all_14_2)
% 204.14/34.95    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.14/34.95    (33)  op(e2, all_4_1) = e3
% 204.14/34.95    (34)  op(all_52_27, all_52_27) = all_52_26
% 204.14/34.95    (35)  op(e2, e2) = all_4_2
% 204.14/34.95    (36)  all_58_11 = all_52_29
% 204.14/34.95    (37)  all_56_5 = all_4_2
% 204.14/34.95    (38)   ~ (all_52_25 = all_14_2)
% 204.14/34.95    (39)   ~ (all_52_9 = all_52_15)
% 204.14/34.95    (40)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.14/34.95    (41)   ~ (all_52_3 = all_52_27)
% 204.14/34.95    (42)  op(all_10_2, e1) = all_10_1
% 204.14/34.95    (43)   ~ (all_52_7 = all_6_2)
% 204.14/34.95    (44)  op(e0, e0) = all_14_2
% 204.14/34.95    (45)  all_56_15 = all_14_2
% 204.14/34.95    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.14/34.95    (47)  op(e2, all_4_1) = all_4_0
% 204.14/34.95    (48)  op(e1, e0) = all_52_29
% 204.14/34.95    (49)  all_56_11 = all_52_29
% 204.14/34.95    (50)   ~ (all_4_1 = e1)
% 204.14/34.95    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.14/34.95    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.14/34.95    (53)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.14/34.95    (54)  all_56_9 = all_52_13
% 204.14/34.95    (55)   ~ (e2 = e1)
% 204.14/34.95    (56)   ~ (all_52_13 = all_10_2)
% 204.14/34.95    (57)   ~ (all_6_0 = e1)
% 204.14/34.95    (58)  all_58_10 = all_52_27
% 204.14/34.95    (59)  all_56_8 = all_52_5
% 204.14/34.95    (60)  op(all_52_9, all_52_9) = all_52_8
% 204.14/34.95    (61)  op(all_52_15, all_52_15) = all_52_14
% 204.14/34.95    (62)   ~ (all_52_25 = all_52_29)
% 204.14/34.95    (63)  all_58_7 = all_52_13
% 204.14/34.95    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.14/34.95    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.14/34.95    (66)  op(all_6_2, all_6_2) = e3
% 204.14/34.95    (67)  all_58_12 = all_52_7
% 204.14/34.95    (68)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.14/34.95    (69)   ~ (all_52_7 = all_14_2)
% 204.14/34.95    (70)   ~ (all_14_2 = e0)
% 204.14/34.95    (71)  all_58_2 = all_52_3
% 204.14/34.95    (72)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.14/34.95    (73)  all_56_2 = all_52_17
% 204.14/34.95    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.14/34.95    (75)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.14/34.95    (76)  op(e3, all_6_1) = all_6_0
% 204.14/34.95    (77)   ~ (all_14_0 = e3)
% 204.14/34.95    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.95    (79)  all_56_7 = all_52_27
% 204.14/34.95    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.95    (81)   ~ (e2 = e0)
% 204.14/34.95    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.14/34.95    (83)  op(all_4_2, e2) = all_4_1
% 204.14/34.95    (84)  op(all_52_3, all_52_3) = e2
% 204.14/34.95    (85)   ~ (all_52_5 = all_52_29)
% 204.14/34.95    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.14/34.95    (87)  all_56_6 = all_52_19
% 204.14/34.95    (88)   ~ (all_52_15 = all_14_2)
% 204.14/34.95    (89)   ~ (all_52_19 = all_52_27)
% 204.14/34.95    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.14/34.95    (91)   ~ (all_6_0 = e2)
% 204.14/34.95    (92)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.14/34.95    (93)   ~ (all_52_13 = all_4_2)
% 204.14/34.95    (94)  op(e0, e3) = all_52_7
% 204.14/34.95    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.95    (96)   ~ (all_52_9 = all_52_25)
% 204.14/34.95    (97)  all_58_15 = all_14_2
% 204.14/34.95    (98)   ~ (all_52_19 = all_10_2)
% 204.14/34.95    (99)  op(all_52_23, all_52_23) = all_52_22
% 204.14/34.95    (100)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.95    (101)  all_58_8 = all_10_2
% 204.14/34.95    (102)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.95    (103)   ~ (all_52_5 = all_10_2)
% 204.14/34.95    (104)  op(all_52_29, all_52_29) = all_52_28
% 204.14/34.95    (105)   ~ (all_52_23 = all_14_2)
% 204.14/34.95    (106)  all_56_12 = all_52_7
% 204.14/34.95    (107)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.95    (108)   ~ (all_52_25 = all_6_2)
% 204.14/34.95    (109)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.14/34.95    (110)   ~ (all_52_9 = all_4_2)
% 204.14/34.95    (111)   ~ (all_52_5 = all_6_2)
% 204.14/34.95    (112)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.14/34.95    (113)   ~ (all_52_9 = all_6_2)
% 204.14/34.95    (114)   ~ (all_52_13 = all_52_15)
% 204.14/34.95    (115)  all_56_0 = all_6_2
% 204.14/34.95    (116)  op(e3, e3) = all_6_2
% 204.14/34.95    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.95    (118)   ~ (all_52_27 = all_14_2)
% 204.14/34.95    (119)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.95    (120)  all_56_14 = all_52_23
% 204.14/34.95    (121)  op(all_4_2, all_4_2) = all_52_10
% 204.14/34.95    (122)  all_56_3 = all_52_25
% 204.14/34.95    (123)   ~ (all_52_3 = all_52_7)
% 204.14/34.95    (124)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.95    (125)  all_58_5 = all_52_19
% 204.14/34.95    (126)  all_56_1 = all_52_9
% 204.14/34.95    (127)   ~ (all_52_15 = all_4_2)
% 204.14/34.95    (128)   ~ (all_52_27 = all_4_2)
% 204.14/34.95    (129)  all_58_6 = all_52_5
% 204.14/34.95    (130)  op(e3, e2) = all_52_9
% 204.14/34.95    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.14/34.95    (132)   ~ (all_52_17 = all_6_2)
% 204.14/34.95    (133)   ~ (e1 = e0)
% 204.14/34.95    (134)  op(e2, e0) = all_52_27
% 204.14/34.95    (135)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.95    (136)   ~ (all_52_9 = all_52_17)
% 204.14/34.95    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.14/34.95    (138)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.14/34.95    (139)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.14/34.95    (140)  op(all_52_13, all_52_13) = all_52_12
% 204.14/34.95    (141)  op(e1, e1) = all_10_2
% 204.14/34.95    (142)   ~ (all_52_23 = all_10_2)
% 204.14/34.95    (143)   ~ (all_52_7 = all_52_23)
% 204.14/34.95    (144)  all_58_3 = all_4_2
% 204.14/34.95    (145)  all_56_13 = all_52_15
% 204.14/34.95    (146)   ~ (all_52_3 = all_4_2)
% 204.14/34.95    (147)   ~ (all_52_19 = all_4_2)
% 204.14/34.95    (148)   ~ (all_52_17 = all_52_23)
% 204.14/34.95    (149)  op(all_6_2, e3) = all_6_1
% 204.14/34.95    (150)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.95    (151)   ~ (all_52_13 = all_52_29)
% 204.14/34.95    (152)  all_58_4 = all_52_17
% 204.14/34.95    (153)   ~ (all_14_0 = e1)
% 204.14/34.95    (154)   ~ (all_14_0 = e2)
% 204.14/34.95    (155)  op(all_52_25, all_52_25) = all_52_24
% 204.14/34.95  
% 204.14/34.95  Begin of proof
% 204.14/34.95  | 
% 204.14/34.95  | BETA: splitting (102) gives:
% 204.14/34.95  | 
% 204.14/34.95  | Case 1:
% 204.14/34.95  | | 
% 204.14/34.95  | |   (156)  all_56_15 = e3
% 204.14/34.95  | | 
% 204.14/34.95  | | REF_CLOSE: (4), (6), (8), (10), (11), (13), (14), (15), (17), (19), (20),
% 204.14/34.95  | |            (22), (23), (24), (26), (27), (28), (29), (30), (32), (35), (36),
% 204.14/34.95  | |            (37), (38), (39), (40), (44), (45), (46), (47), (50), (51), (52),
% 204.14/34.95  | |            (54), (55), (56), (60), (62), (63), (64), (66), (67), (69), (71),
% 204.14/34.95  | |            (73), (75), (76), (77), (82), (83), (84), (86), (88), (91), (93),
% 204.14/34.95  | |            (96), (101), (103), (105), (106), (109), (110), (112), (113),
% 204.14/34.95  | |            (114), (115), (116), (120), (121), (122), (124), (125), (126),
% 204.14/34.95  | |            (127), (129), (130), (132), (135), (136), (137), (138), (139),
% 204.14/34.95  | |            (140), (141), (142), (143), (145), (146), (148), (149), (152),
% 204.14/34.95  | |            (153), (154), (155), (156) are inconsistent by sub-proof #1174.
% 204.14/34.95  | | 
% 204.14/34.95  | Case 2:
% 204.14/34.95  | | 
% 204.14/34.95  | |   (157)   ~ (all_56_15 = e3)
% 204.14/34.95  | |   (158)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.95  | | 
% 204.14/34.95  | | REDUCE: (45), (157) imply:
% 204.14/34.95  | |   (159)   ~ (all_14_2 = e3)
% 204.14/34.95  | | 
% 204.14/34.95  | | BETA: splitting (51) gives:
% 204.14/34.95  | | 
% 204.14/34.95  | | Case 1:
% 204.14/34.95  | | | 
% 204.14/34.95  | | |   (160)  all_56_13 = e3
% 204.14/34.95  | | | 
% 204.14/34.95  | | | COMBINE_EQS: (145), (160) imply:
% 204.14/34.95  | | |   (161)  all_52_15 = e3
% 204.14/34.95  | | | 
% 204.14/34.95  | | | SIMP: (161) implies:
% 204.14/34.95  | | |   (162)  all_52_15 = e3
% 204.14/34.95  | | | 
% 204.14/34.95  | | | COMBINE_EQS: (27), (162) imply:
% 204.14/34.95  | | |   (163)  all_58_13 = e3
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REDUCE: (15), (162) imply:
% 204.14/34.95  | | |   (164)   ~ (all_52_7 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REDUCE: (39), (162) imply:
% 204.14/34.95  | | |   (165)   ~ (all_52_9 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REDUCE: (2), (162) imply:
% 204.14/34.95  | | |   (166)   ~ (all_52_23 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | SIMP: (166) implies:
% 204.14/34.95  | | |   (167)   ~ (all_52_23 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REDUCE: (88), (162) imply:
% 204.14/34.95  | | |   (168)   ~ (all_14_2 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REDUCE: (61), (162) imply:
% 204.14/34.95  | | |   (169)  op(e3, e3) = all_52_14
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (11), (12), (13), (16), (18),
% 204.14/34.95  | | |            (19), (20), (21), (24), (25), (29), (35), (36), (38), (40),
% 204.14/34.95  | | |            (41), (43), (44), (45), (46), (48), (53), (60), (64), (66),
% 204.14/34.95  | | |            (67), (69), (70), (71), (72), (75), (79), (80), (81), (84),
% 204.14/34.95  | | |            (86), (87), (89), (92), (94), (96), (97), (98), (103), (106),
% 204.14/34.95  | | |            (108), (109), (110), (116), (117), (119), (120), (122), (123),
% 204.14/34.95  | | |            (124), (125), (126), (128), (129), (131), (133), (135), (141),
% 204.14/34.95  | | |            (142), (143), (144), (146), (147), (150), (154), (158), (159),
% 204.14/34.95  | | |            (163), (164), (165), (167), (169) are inconsistent by sub-proof
% 204.14/34.95  | | |            #755.
% 204.14/34.95  | | | 
% 204.14/34.95  | | Case 2:
% 204.14/34.95  | | | 
% 204.14/34.95  | | |   (170)   ~ (all_56_13 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REDUCE: (145), (170) imply:
% 204.14/34.95  | | |   (171)   ~ (all_52_15 = e3)
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.14/34.95  | | |            (13), (16), (17), (19), (20), (21), (22), (24), (27), (28),
% 204.14/34.95  | | |            (29), (30), (31), (33), (34), (35), (36), (38), (40), (41),
% 204.14/34.95  | | |            (42), (43), (44), (45), (46), (49), (50), (52), (54), (55),
% 204.14/34.95  | | |            (56), (57), (58), (59), (60), (62), (63), (65), (66), (67),
% 204.14/34.95  | | |            (68), (69), (70), (71), (73), (74), (75), (76), (78), (80),
% 204.14/34.95  | | |            (81), (83), (84), (85), (86), (90), (93), (94), (95), (96),
% 204.14/34.95  | | |            (97), (98), (99), (100), (101), (103), (104), (105), (106),
% 204.14/34.95  | | |            (107), (108), (110), (111), (113), (116), (117), (118), (119),
% 204.14/34.95  | | |            (123), (124), (125), (126), (128), (129), (130), (131), (134),
% 204.14/34.95  | | |            (135), (136), (138), (140), (141), (142), (143), (144), (146),
% 204.14/34.95  | | |            (148), (149), (150), (151), (152), (153), (158), (159), (171)
% 204.14/34.95  | | |            are inconsistent by sub-proof #742.
% 204.14/34.95  | | | 
% 204.14/34.95  | | End of split
% 204.14/34.95  | | 
% 204.14/34.95  | End of split
% 204.14/34.95  | 
% 204.14/34.95  End of proof
% 204.14/34.95  
% 204.14/34.95  Sub-proof #742 shows that the following formulas are inconsistent:
% 204.14/34.95  ----------------------------------------------------------------
% 204.14/34.95    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.95    (2)   ~ (all_52_15 = all_52_23)
% 204.14/34.95    (3)   ~ (all_52_25 = all_52_27)
% 204.14/34.95    (4)  all_58_14 = all_52_23
% 204.14/34.95    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.14/34.95    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.95    (7)   ~ (all_52_5 = all_52_13)
% 204.14/34.95    (8)  op(all_52_7, all_52_7) = e0
% 204.14/34.95    (9)  all_58_1 = all_52_9
% 204.14/34.95    (10)   ~ (all_52_9 = all_52_13)
% 204.14/34.95    (11)  op(all_52_5, all_52_5) = e1
% 204.14/34.95    (12)   ~ (e3 = e0)
% 204.14/34.95    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.95    (14)   ~ (all_52_3 = all_52_19)
% 204.14/34.95    (15)   ~ (all_52_17 = all_52_25)
% 204.14/34.95    (16)  all_58_0 = all_6_2
% 204.14/34.95    (17)  op(all_14_2, e0) = all_14_1
% 204.14/34.95    (18)  all_56_4 = all_52_3
% 204.14/34.95    (19)   ~ (all_52_17 = all_10_2)
% 204.14/34.95    (20)  op(e0, all_14_1) = all_14_0
% 204.14/34.95    (21)  all_58_13 = all_52_15
% 204.14/34.95    (22)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.95    (23)  all_58_9 = all_52_25
% 204.14/34.95    (24)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.14/34.95    (25)   ~ (all_52_29 = all_14_2)
% 204.14/34.95    (26)   ~ (all_52_15 = e3)
% 204.14/34.95    (27)  op(e2, all_4_1) = e3
% 204.14/34.95    (28)  op(all_52_27, all_52_27) = all_52_26
% 204.14/34.95    (29)  op(e2, e2) = all_4_2
% 204.14/34.95    (30)  all_58_11 = all_52_29
% 204.14/34.95    (31)   ~ (all_52_25 = all_14_2)
% 204.14/34.95    (32)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.14/34.95    (33)   ~ (all_52_3 = all_52_27)
% 204.14/34.95    (34)  op(all_10_2, e1) = all_10_1
% 204.14/34.95    (35)   ~ (all_52_7 = all_6_2)
% 204.14/34.95    (36)  op(e0, e0) = all_14_2
% 204.14/34.95    (37)  all_56_15 = all_14_2
% 204.14/34.95    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.14/34.95    (39)  all_56_11 = all_52_29
% 204.14/34.95    (40)   ~ (all_4_1 = e1)
% 204.14/34.95    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.14/34.95    (42)  all_56_9 = all_52_13
% 204.14/34.95    (43)   ~ (e2 = e1)
% 204.14/34.95    (44)   ~ (all_52_13 = all_10_2)
% 204.14/34.95    (45)   ~ (all_6_0 = e1)
% 204.14/34.95    (46)  all_58_10 = all_52_27
% 204.14/34.95    (47)  all_56_8 = all_52_5
% 204.14/34.95    (48)  op(all_52_9, all_52_9) = all_52_8
% 204.14/34.95    (49)   ~ (all_52_25 = all_52_29)
% 204.14/34.95    (50)  all_58_7 = all_52_13
% 204.14/34.95    (51)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.14/34.95    (52)  op(all_6_2, all_6_2) = e3
% 204.14/34.95    (53)  all_58_12 = all_52_7
% 204.14/34.95    (54)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.14/34.95    (55)   ~ (all_52_7 = all_14_2)
% 204.14/34.95    (56)   ~ (all_14_2 = e0)
% 204.14/34.95    (57)  all_58_2 = all_52_3
% 204.14/34.95    (58)  all_56_2 = all_52_17
% 204.14/34.95    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.14/34.95    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.14/34.95    (61)  op(e3, all_6_1) = all_6_0
% 204.14/34.95    (62)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.95    (63)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.95    (64)   ~ (e2 = e0)
% 204.14/34.95    (65)  op(all_4_2, e2) = all_4_1
% 204.14/34.95    (66)  op(all_52_3, all_52_3) = e2
% 204.14/34.95    (67)   ~ (all_52_5 = all_52_29)
% 204.14/34.95    (68)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.14/34.95    (69)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.14/34.95    (70)   ~ (all_52_13 = all_4_2)
% 204.14/34.95    (71)  op(e0, e3) = all_52_7
% 204.14/34.95    (72)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.95    (73)   ~ (all_52_9 = all_52_25)
% 204.14/34.95    (74)  all_58_15 = all_14_2
% 204.14/34.95    (75)   ~ (all_52_19 = all_10_2)
% 204.14/34.95    (76)  op(all_52_23, all_52_23) = all_52_22
% 204.14/34.95    (77)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.95    (78)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.95    (79)  all_58_8 = all_10_2
% 204.14/34.95    (80)   ~ (all_52_5 = all_10_2)
% 204.14/34.95    (81)  op(all_52_29, all_52_29) = all_52_28
% 204.14/34.95    (82)   ~ (all_52_23 = all_14_2)
% 204.14/34.95    (83)  all_56_12 = all_52_7
% 204.14/34.95    (84)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.95    (85)   ~ (all_52_25 = all_6_2)
% 204.14/34.95    (86)   ~ (all_52_9 = all_4_2)
% 204.14/34.95    (87)   ~ (all_52_5 = all_6_2)
% 204.14/34.95    (88)   ~ (all_52_9 = all_6_2)
% 204.14/34.95    (89)  op(e3, e3) = all_6_2
% 204.14/34.95    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.95    (91)   ~ (all_52_27 = all_14_2)
% 204.14/34.95    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.95    (93)   ~ (all_52_3 = all_52_7)
% 204.14/34.95    (94)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.95    (95)  all_58_5 = all_52_19
% 204.14/34.95    (96)  all_56_1 = all_52_9
% 204.14/34.95    (97)   ~ (all_52_27 = all_4_2)
% 204.14/34.95    (98)  all_58_6 = all_52_5
% 204.14/34.95    (99)  op(e3, e2) = all_52_9
% 204.14/34.95    (100)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.14/34.95    (101)  op(e2, e0) = all_52_27
% 204.14/34.95    (102)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.95    (103)   ~ (all_52_9 = all_52_17)
% 204.14/34.95    (104)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.14/34.95    (105)  op(all_52_13, all_52_13) = all_52_12
% 204.14/34.95    (106)  op(e1, e1) = all_10_2
% 204.14/34.95    (107)   ~ (all_52_23 = all_10_2)
% 204.14/34.95    (108)   ~ (all_52_7 = all_52_23)
% 204.14/34.95    (109)  all_58_3 = all_4_2
% 204.14/34.95    (110)   ~ (all_52_3 = all_4_2)
% 204.14/34.95    (111)   ~ (all_52_17 = all_52_23)
% 204.14/34.95    (112)  op(all_6_2, e3) = all_6_1
% 204.14/34.95    (113)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.95    (114)   ~ (all_52_13 = all_52_29)
% 204.14/34.95    (115)  all_58_4 = all_52_17
% 204.14/34.95    (116)   ~ (all_14_0 = e1)
% 204.14/34.95    (117)   ~ (all_14_2 = e3)
% 204.14/34.95  
% 204.14/34.95  Begin of proof
% 204.14/34.95  | 
% 204.14/34.95  | BETA: splitting (100) gives:
% 204.14/34.95  | 
% 204.14/34.95  | Case 1:
% 204.14/34.95  | | 
% 204.14/34.95  | |   (118)  all_58_12 = e3
% 204.14/34.95  | | 
% 204.14/34.95  | | COMBINE_EQS: (53), (118) imply:
% 204.14/34.95  | |   (119)  all_52_7 = e3
% 204.14/34.95  | | 
% 204.14/34.95  | | REF_CLOSE: (6), (8), (11), (16), (29), (35), (36), (38), (52), (53), (55),
% 204.14/34.95  | |            (57), (60), (66), (80), (89), (98), (100), (106), (110), (119)
% 204.14/34.95  | |            are inconsistent by sub-proof #1361.
% 204.14/34.95  | | 
% 204.14/34.95  | Case 2:
% 204.14/34.95  | | 
% 204.14/34.95  | |   (120)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.14/34.95  | | 
% 204.14/34.95  | | BETA: splitting (120) gives:
% 204.14/34.95  | | 
% 204.14/34.95  | | Case 1:
% 204.14/34.95  | | | 
% 204.14/34.95  | | |   (121)  all_58_13 = e3
% 204.14/34.95  | | | 
% 204.14/34.95  | | | REF_CLOSE: (21), (26), (121) are inconsistent by sub-proof #1360.
% 204.14/34.95  | | | 
% 204.14/34.95  | | Case 2:
% 204.14/34.95  | | | 
% 204.14/34.95  | | |   (122)  all_58_14 = e3 | all_58_15 = e3
% 204.14/34.95  | | | 
% 204.14/34.95  | | | BETA: splitting (122) gives:
% 204.14/34.95  | | | 
% 204.14/34.95  | | | Case 1:
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | |   (123)  all_58_14 = e3
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | COMBINE_EQS: (4), (123) imply:
% 204.14/34.95  | | | |   (124)  all_52_23 = e3
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | SIMP: (124) implies:
% 204.14/34.95  | | | |   (125)  all_52_23 = e3
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | REDUCE: (108), (125) imply:
% 204.14/34.95  | | | |   (126)   ~ (all_52_7 = e3)
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | REDUCE: (111), (125) imply:
% 204.14/34.95  | | | |   (127)   ~ (all_52_17 = e3)
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | REDUCE: (82), (125) imply:
% 204.14/34.95  | | | |   (128)   ~ (all_14_2 = e3)
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | REDUCE: (107), (125) imply:
% 204.14/34.95  | | | |   (129)   ~ (all_10_2 = e3)
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | SIMP: (129) implies:
% 204.14/34.95  | | | |   (130)   ~ (all_10_2 = e3)
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | REDUCE: (76), (125) imply:
% 204.14/34.95  | | | |   (131)  op(e3, e3) = all_52_22
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 204.14/34.95  | | | |              simplifying with (89), (131) gives:
% 204.14/34.95  | | | |   (132)  all_52_22 = all_6_2
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | BETA: splitting (13) gives:
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | Case 1:
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | |   (133)  all_56_12 = e3
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | | REF_CLOSE: (83), (126), (133) are inconsistent by sub-proof #1383.
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | Case 2:
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | |   (134)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | | BETA: splitting (41) gives:
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | | Case 1:
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | |   (135)  all_56_2 = e3
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | | REF_CLOSE: (58), (127), (135) are inconsistent by sub-proof #1327.
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | Case 2:
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | |   (136)   ~ (all_56_2 = e3)
% 204.14/34.95  | | | | | |   (137)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | | BETA: splitting (69) gives:
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | | Case 1:
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | |   (138)  all_56_11 = e3
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | COMBINE_EQS: (39), (138) imply:
% 204.14/34.95  | | | | | | |   (139)  all_52_29 = e3
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | SIMP: (139) implies:
% 204.14/34.95  | | | | | | |   (140)  all_52_29 = e3
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | COMBINE_EQS: (30), (140) imply:
% 204.14/34.95  | | | | | | |   (141)  all_58_11 = e3
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | REDUCE: (67), (140) imply:
% 204.14/34.95  | | | | | | |   (142)   ~ (all_52_5 = e3)
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | REDUCE: (114), (140) imply:
% 204.14/34.95  | | | | | | |   (143)   ~ (all_52_13 = e3)
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | REDUCE: (49), (140) imply:
% 204.14/34.95  | | | | | | |   (144)   ~ (all_52_25 = e3)
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | REDUCE: (81), (140) imply:
% 204.14/34.95  | | | | | | |   (145)  op(e3, e3) = all_52_28
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_28, e3, e3,
% 204.14/34.95  | | | | | | |              simplifying with (89), (145) gives:
% 204.14/34.95  | | | | | | |   (146)  all_52_28 = all_6_2
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | BETA: splitting (72) gives:
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | Case 1:
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | |   (147)  all_58_1 = e3
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (16), (29), (36), (38), (52),
% 204.14/34.95  | | | | | | | |            (53), (55), (57), (60), (66), (80), (88), (89), (98),
% 204.14/34.95  | | | | | | | |            (100), (106), (110), (147) are inconsistent by
% 204.14/34.95  | | | | | | | |            sub-proof #1005.
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | Case 2:
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | |   (148)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (14),
% 204.14/34.95  | | | | | | | |            (15), (18), (21), (23), (24), (26), (27), (29), (32),
% 204.14/34.95  | | | | | | | |            (33), (36), (40), (42), (44), (46), (47), (48), (50),
% 204.14/34.95  | | | | | | | |            (51), (53), (55), (57), (58), (63), (65), (66), (70),
% 204.14/34.95  | | | | | | | |            (73), (77), (79), (80), (83), (86), (93), (95), (96),
% 204.14/34.95  | | | | | | | |            (98), (99), (102), (103), (104), (109), (110), (113),
% 204.14/34.95  | | | | | | | |            (115), (123), (127), (134), (137), (141), (142),
% 204.14/34.95  | | | | | | | |            (143), (144), (148) are inconsistent by sub-proof
% 204.14/34.95  | | | | | | | |            #751.
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | End of split
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | Case 2:
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | |   (149)   ~ (all_56_11 = e3)
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | REDUCE: (39), (149) imply:
% 204.14/34.95  | | | | | | |   (150)   ~ (all_52_29 = e3)
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | BETA: splitting (54) gives:
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | | Case 1:
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | |   (151)  all_58_6 = e3
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | | REF_CLOSE: (6), (8), (11), (16), (29), (36), (38), (52), (53),
% 204.14/34.95  | | | | | | | |            (55), (57), (60), (66), (80), (87), (89), (98),
% 204.14/34.95  | | | | | | | |            (100), (106), (110), (151) are inconsistent by
% 204.14/34.95  | | | | | | | |            sub-proof #876.
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | Case 2:
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | |   (152)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | | BETA: splitting (152) gives:
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | | Case 1:
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | |   (153)  all_58_7 = e3
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | | COMBINE_EQS: (50), (153) imply:
% 204.14/34.95  | | | | | | | | |   (154)  all_52_13 = e3
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | | REDUCE: (10), (154) imply:
% 204.14/34.95  | | | | | | | | |   (155)   ~ (all_52_9 = e3)
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | | REDUCE: (114), (154) imply:
% 204.14/34.95  | | | | | | | | |   (156)   ~ (all_52_29 = e3)
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | | REDUCE: (105), (154) imply:
% 204.14/34.95  | | | | | | | | |   (157)  op(e3, e3) = all_52_12
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (9), (11), (12), (16), (17),
% 204.14/34.95  | | | | | | | | |            (19), (20), (22), (23), (25), (28), (29), (30),
% 204.14/34.95  | | | | | | | | |            (31), (34), (36), (37), (38), (43), (45), (46),
% 204.14/34.95  | | | | | | | | |            (52), (53), (55), (56), (57), (59), (60), (61),
% 204.14/34.95  | | | | | | | | |            (62), (64), (66), (68), (71), (74), (75), (78),
% 204.14/34.95  | | | | | | | | |            (79), (80), (84), (85), (86), (89), (90), (91),
% 204.14/34.95  | | | | | | | | |            (92), (94), (95), (97), (98), (100), (101), (106),
% 204.14/34.95  | | | | | | | | |            (109), (110), (112), (113), (115), (116), (117),
% 204.14/34.95  | | | | | | | | |            (127), (130), (150), (153), (155), (157) are
% 204.14/34.95  | | | | | | | | |            inconsistent by sub-proof #743.
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | Case 2:
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | |   (158)  all_58_8 = e3 | all_58_11 = e3
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | | REF_CLOSE: (30), (79), (130), (150), (158) are inconsistent by
% 204.14/34.95  | | | | | | | | |            sub-proof #1140.
% 204.14/34.95  | | | | | | | | | 
% 204.14/34.95  | | | | | | | | End of split
% 204.14/34.95  | | | | | | | | 
% 204.14/34.95  | | | | | | | End of split
% 204.14/34.95  | | | | | | | 
% 204.14/34.95  | | | | | | End of split
% 204.14/34.95  | | | | | | 
% 204.14/34.95  | | | | | End of split
% 204.14/34.95  | | | | | 
% 204.14/34.95  | | | | End of split
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | Case 2:
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | |   (159)  all_58_15 = e3
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | COMBINE_EQS: (74), (159) imply:
% 204.14/34.95  | | | |   (160)  all_14_2 = e3
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | REDUCE: (117), (160) imply:
% 204.14/34.95  | | | |   (161)  $false
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | | CLOSE: (161) is inconsistent.
% 204.14/34.95  | | | | 
% 204.14/34.95  | | | End of split
% 204.14/34.95  | | | 
% 204.14/34.95  | | End of split
% 204.14/34.95  | | 
% 204.14/34.95  | End of split
% 204.14/34.95  | 
% 204.14/34.95  End of proof
% 204.14/34.95  
% 204.14/34.95  Sub-proof #743 shows that the following formulas are inconsistent:
% 204.14/34.95  ----------------------------------------------------------------
% 204.14/34.95    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.95    (2)   ~ (all_52_25 = all_52_27)
% 204.14/34.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.95    (4)  op(all_52_7, all_52_7) = e0
% 204.14/34.95    (5)  all_58_1 = all_52_9
% 204.14/34.95    (6)  op(all_52_5, all_52_5) = e1
% 204.14/34.95    (7)   ~ (e3 = e0)
% 204.14/34.95    (8)  all_58_0 = all_6_2
% 204.14/34.95    (9)  op(all_14_2, e0) = all_14_1
% 204.14/34.95    (10)   ~ (all_52_17 = all_10_2)
% 204.14/34.95    (11)  op(e0, all_14_1) = all_14_0
% 204.14/34.95    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.95    (13)  all_58_9 = all_52_25
% 204.14/34.95    (14)   ~ (all_52_29 = all_14_2)
% 204.14/34.95    (15)  op(all_52_27, all_52_27) = all_52_26
% 204.14/34.95    (16)  op(e2, e2) = all_4_2
% 204.14/34.95    (17)  all_58_11 = all_52_29
% 204.14/34.95    (18)  op(e3, e3) = all_52_12
% 204.14/34.95    (19)   ~ (all_52_25 = all_14_2)
% 204.14/34.95    (20)  op(all_10_2, e1) = all_10_1
% 204.14/34.95    (21)  op(e0, e0) = all_14_2
% 204.14/34.95    (22)  all_56_15 = all_14_2
% 204.14/34.95    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.14/34.95    (24)   ~ (e2 = e1)
% 204.14/34.95    (25)   ~ (all_6_0 = e1)
% 204.14/34.95    (26)  all_58_10 = all_52_27
% 204.14/34.95    (27)  op(all_6_2, all_6_2) = e3
% 204.14/34.95    (28)  all_58_12 = all_52_7
% 204.14/34.95    (29)   ~ (all_52_7 = all_14_2)
% 204.14/34.95    (30)   ~ (all_14_2 = e0)
% 204.14/34.95    (31)  all_58_2 = all_52_3
% 204.14/34.95    (32)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.14/34.95    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.14/34.95    (34)   ~ (all_52_29 = e3)
% 204.14/34.95    (35)  op(e3, all_6_1) = all_6_0
% 204.14/34.95    (36)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.95    (37)  all_58_7 = e3
% 204.14/34.95    (38)   ~ (e2 = e0)
% 204.14/34.95    (39)  op(all_52_3, all_52_3) = e2
% 204.14/34.95    (40)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.14/34.95    (41)   ~ (all_10_2 = e3)
% 204.14/34.95    (42)   ~ (all_52_9 = e3)
% 204.14/34.95    (43)  op(e0, e3) = all_52_7
% 204.14/34.95    (44)  all_58_15 = all_14_2
% 204.14/34.95    (45)   ~ (all_52_19 = all_10_2)
% 204.14/34.95    (46)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.95    (47)  all_58_8 = all_10_2
% 204.14/34.95    (48)   ~ (all_52_5 = all_10_2)
% 204.14/34.95    (49)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.95    (50)   ~ (all_52_25 = all_6_2)
% 204.14/34.95    (51)   ~ (all_52_9 = all_4_2)
% 204.14/34.95    (52)  op(e3, e3) = all_6_2
% 204.14/34.95    (53)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.95    (54)   ~ (all_52_27 = all_14_2)
% 204.14/34.95    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.95    (56)   ~ (all_52_17 = e3)
% 204.14/34.95    (57)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.95    (58)  all_58_5 = all_52_19
% 204.14/34.95    (59)   ~ (all_52_27 = all_4_2)
% 204.14/34.95    (60)  all_58_6 = all_52_5
% 204.14/34.95    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.14/34.95    (62)  op(e2, e0) = all_52_27
% 204.14/34.95    (63)  op(e1, e1) = all_10_2
% 204.14/34.96    (64)  all_58_3 = all_4_2
% 204.14/34.96    (65)   ~ (all_52_3 = all_4_2)
% 204.14/34.96    (66)  op(all_6_2, e3) = all_6_1
% 204.14/34.96    (67)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.96    (68)  all_58_4 = all_52_17
% 204.14/34.96    (69)   ~ (all_14_0 = e1)
% 204.14/34.96    (70)   ~ (all_14_2 = e3)
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | GROUND_INST: instantiating (3) with all_6_2, all_52_12, e3, e3, simplifying
% 204.14/34.96  |              with (18), (52) gives:
% 204.14/34.96  |   (71)  all_52_12 = all_6_2
% 204.14/34.96  | 
% 204.14/34.96  | BETA: splitting (53) gives:
% 204.14/34.96  | 
% 204.14/34.96  | Case 1:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (72)  all_58_9 = e3
% 204.14/34.96  | | 
% 204.14/34.96  | | COMBINE_EQS: (13), (72) imply:
% 204.14/34.96  | |   (73)  all_52_25 = e3
% 204.14/34.96  | | 
% 204.14/34.96  | | REF_CLOSE: (3), (4), (6), (8), (16), (21), (23), (27), (28), (29), (31),
% 204.14/34.96  | |            (33), (39), (48), (50), (52), (60), (61), (63), (65), (73) are
% 204.14/34.96  | |            inconsistent by sub-proof #1000.
% 204.14/34.96  | | 
% 204.14/34.96  | Case 2:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (74)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.96  | | 
% 204.14/34.96  | | BETA: splitting (74) gives:
% 204.14/34.96  | | 
% 204.14/34.96  | | Case 1:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (75)  all_58_10 = e3
% 204.14/34.96  | | | 
% 204.14/34.96  | | | COMBINE_EQS: (26), (75) imply:
% 204.14/34.96  | | |   (76)  all_52_27 = e3
% 204.14/34.96  | | | 
% 204.14/34.96  | | | SIMP: (76) implies:
% 204.14/34.96  | | |   (77)  all_52_27 = e3
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (2), (77) imply:
% 204.14/34.96  | | |   (78)   ~ (all_52_25 = e3)
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (54), (77) imply:
% 204.14/34.96  | | |   (79)   ~ (all_14_2 = e3)
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (59), (77) imply:
% 204.14/34.96  | | |   (80)   ~ (all_4_2 = e3)
% 204.14/34.96  | | | 
% 204.14/34.96  | | | SIMP: (80) implies:
% 204.14/34.96  | | |   (81)   ~ (all_4_2 = e3)
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (15), (77) imply:
% 204.14/34.96  | | |   (82)  op(e3, e3) = all_52_26
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (62), (77) imply:
% 204.14/34.96  | | |   (83)  op(e2, e0) = e3
% 204.14/34.96  | | | 
% 204.14/34.96  | | | BETA: splitting (55) gives:
% 204.14/34.96  | | | 
% 204.14/34.96  | | | Case 1:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (84)  all_58_0 = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | COMBINE_EQS: (8), (84) imply:
% 204.14/34.96  | | | |   (85)  all_6_2 = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (66), (85) imply:
% 204.14/34.96  | | | |   (86)  op(e3, e3) = all_6_1
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (52), (85) imply:
% 204.14/34.96  | | | |   (87)  op(e3, e3) = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | GROUND_INST: instantiating (3) with all_6_1, all_52_26, e3, e3,
% 204.14/34.96  | | | |              simplifying with (82), (86) gives:
% 204.14/34.96  | | | |   (88)  all_52_26 = all_6_1
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | GROUND_INST: instantiating (3) with e3, all_52_26, e3, e3, simplifying
% 204.14/34.96  | | | |              with (82), (87) gives:
% 204.14/34.96  | | | |   (89)  all_52_26 = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | COMBINE_EQS: (88), (89) imply:
% 204.14/34.96  | | | |   (90)  all_6_1 = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (35), (90) imply:
% 204.14/34.96  | | | |   (91)  op(e3, e3) = all_6_0
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3, simplifying
% 204.14/34.96  | | | |              with (87), (91) gives:
% 204.14/34.96  | | | |   (92)  all_6_0 = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (25), (92) imply:
% 204.14/34.96  | | | |   (93)   ~ (e3 = e1)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | BETA: splitting (36) gives:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | Case 1:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | |   (94)  all_58_0 = e1
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | COMBINE_EQS: (84), (94) imply:
% 204.14/34.96  | | | | |   (95)  e3 = e1
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | REDUCE: (93), (95) imply:
% 204.14/34.96  | | | | |   (96)  $false
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | CLOSE: (96) is inconsistent.
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | Case 2:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | |   (97)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | BETA: splitting (40) gives:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | Case 1:
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | |   (98)  all_58_12 = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | COMBINE_EQS: (28), (98) imply:
% 204.14/34.96  | | | | | |   (99)  all_52_7 = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | SIMP: (99) implies:
% 204.14/34.96  | | | | | |   (100)  all_52_7 = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | REDUCE: (29), (100) imply:
% 204.14/34.96  | | | | | |   (101)   ~ (all_14_2 = e1)
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | SIMP: (101) implies:
% 204.14/34.96  | | | | | |   (102)   ~ (all_14_2 = e1)
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | REDUCE: (43), (100) imply:
% 204.14/34.96  | | | | | |   (103)  op(e0, e3) = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | BETA: splitting (46) gives:
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | Case 1:
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | |   (104)  all_56_15 = e2
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | COMBINE_EQS: (22), (104) imply:
% 204.14/34.96  | | | | | | |   (105)  all_14_2 = e2
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | SIMP: (105) implies:
% 204.14/34.96  | | | | | | |   (106)  all_14_2 = e2
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | REDUCE: (9), (106) imply:
% 204.14/34.96  | | | | | | |   (107)  op(e2, e0) = all_14_1
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | GROUND_INST: instantiating (3) with e3, all_14_1, e0, e2,
% 204.14/34.96  | | | | | | |              simplifying with (83), (107) gives:
% 204.14/34.96  | | | | | | |   (108)  all_14_1 = e3
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | REDUCE: (11), (108) imply:
% 204.14/34.96  | | | | | | |   (109)  op(e0, e3) = all_14_0
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | GROUND_INST: instantiating (3) with e1, all_14_0, e3, e0,
% 204.14/34.96  | | | | | | |              simplifying with (103), (109) gives:
% 204.14/34.96  | | | | | | |   (110)  all_14_0 = e1
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | REDUCE: (69), (110) imply:
% 204.14/34.96  | | | | | | |   (111)  $false
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | CLOSE: (111) is inconsistent.
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | Case 2:
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | |   (112)  all_56_15 = e1 | all_56_15 = e0
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | REF_CLOSE: (22), (30), (102), (112) are inconsistent by sub-proof
% 204.14/34.96  | | | | | | |            #1161.
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | End of split
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | Case 2:
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | |   (113)   ~ (all_58_12 = e1)
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | REDUCE: (28), (113) imply:
% 204.14/34.96  | | | | | |   (114)   ~ (all_52_7 = e1)
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (10), (12), (13), (14), (17),
% 204.14/34.96  | | | | | |            (19), (20), (22), (24), (28), (29), (31), (32), (36),
% 204.14/34.96  | | | | | |            (37), (38), (39), (41), (45), (46), (47), (48), (49),
% 204.14/34.96  | | | | | |            (51), (57), (58), (60), (63), (64), (67), (68), (70),
% 204.14/34.96  | | | | | |            (75), (81), (84), (97), (114) are inconsistent by
% 204.14/34.96  | | | | | |            sub-proof #745.
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | End of split
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | End of split
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | Case 2:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (115)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REF_CLOSE: (5), (13), (42), (56), (68), (78), (115) are inconsistent by
% 204.14/34.96  | | | |            sub-proof #744.
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | End of split
% 204.14/34.96  | | | 
% 204.14/34.96  | | Case 2:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (116)  all_58_11 = e3 | all_58_15 = e3
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REF_CLOSE: (17), (34), (44), (70), (116) are inconsistent by sub-proof
% 204.14/34.96  | | |            #1103.
% 204.14/34.96  | | | 
% 204.14/34.96  | | End of split
% 204.14/34.96  | | 
% 204.14/34.96  | End of split
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #744 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)  all_58_1 = all_52_9
% 204.14/34.96    (2)  all_58_9 = all_52_25
% 204.14/34.96    (3)   ~ (all_52_25 = e3)
% 204.14/34.96    (4)   ~ (all_52_9 = e3)
% 204.14/34.96    (5)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.96    (6)   ~ (all_52_17 = e3)
% 204.14/34.96    (7)  all_58_4 = all_52_17
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | BETA: splitting (5) gives:
% 204.14/34.96  | 
% 204.14/34.96  | Case 1:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (8)  all_58_1 = e3
% 204.14/34.96  | | 
% 204.14/34.96  | | COMBINE_EQS: (1), (8) imply:
% 204.14/34.96  | |   (9)  all_52_9 = e3
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (4), (9) imply:
% 204.14/34.96  | |   (10)  $false
% 204.14/34.96  | | 
% 204.14/34.96  | | CLOSE: (10) is inconsistent.
% 204.14/34.96  | | 
% 204.14/34.96  | Case 2:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (11)  all_58_4 = e3 | all_58_9 = e3
% 204.14/34.96  | | 
% 204.14/34.96  | | REF_CLOSE: (2), (3), (6), (7), (11) are inconsistent by sub-proof #1276.
% 204.14/34.96  | | 
% 204.14/34.96  | End of split
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #745 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.96    (3)  all_58_1 = all_52_9
% 204.14/34.96    (4)  op(all_52_5, all_52_5) = e1
% 204.14/34.96    (5)   ~ (e3 = e0)
% 204.14/34.96    (6)   ~ (all_4_2 = e3)
% 204.14/34.96    (7)   ~ (all_52_17 = all_10_2)
% 204.14/34.96    (8)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.96    (9)  all_58_9 = all_52_25
% 204.14/34.96    (10)   ~ (all_52_29 = all_14_2)
% 204.14/34.96    (11)  all_58_11 = all_52_29
% 204.14/34.96    (12)   ~ (all_52_25 = all_14_2)
% 204.14/34.96    (13)  op(all_10_2, e1) = all_10_1
% 204.14/34.96    (14)  all_56_15 = all_14_2
% 204.14/34.96    (15)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96    (16)   ~ (e2 = e1)
% 204.14/34.96    (17)  all_58_12 = all_52_7
% 204.14/34.96    (18)   ~ (all_52_7 = all_14_2)
% 204.14/34.96    (19)  all_58_2 = all_52_3
% 204.14/34.96    (20)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.14/34.96    (21)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96    (22)  all_58_7 = e3
% 204.14/34.96    (23)   ~ (e2 = e0)
% 204.14/34.96    (24)  op(all_52_3, all_52_3) = e2
% 204.14/34.96    (25)   ~ (all_10_2 = e3)
% 204.14/34.96    (26)  all_58_0 = e3
% 204.14/34.96    (27)   ~ (all_52_19 = all_10_2)
% 204.14/34.96    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.96    (29)  all_58_8 = all_10_2
% 204.14/34.96    (30)   ~ (all_52_5 = all_10_2)
% 204.14/34.96    (31)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.96    (32)   ~ (all_52_9 = all_4_2)
% 204.14/34.96    (33)  all_58_10 = e3
% 204.14/34.96    (34)   ~ (all_52_7 = e1)
% 204.14/34.96    (35)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.96    (36)  all_58_5 = all_52_19
% 204.14/34.96    (37)  all_58_6 = all_52_5
% 204.14/34.96    (38)  op(e1, e1) = all_10_2
% 204.14/34.96    (39)  all_58_3 = all_4_2
% 204.14/34.96    (40)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.96    (41)  all_58_4 = all_52_17
% 204.14/34.96    (42)   ~ (all_14_2 = e3)
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | BETA: splitting (15) gives:
% 204.14/34.96  | 
% 204.14/34.96  | Case 1:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (43)  all_58_2 = e1
% 204.14/34.96  | | 
% 204.14/34.96  | | COMBINE_EQS: (19), (43) imply:
% 204.14/34.96  | |   (44)  all_52_3 = e1
% 204.14/34.96  | | 
% 204.14/34.96  | | SIMP: (44) implies:
% 204.14/34.96  | |   (45)  all_52_3 = e1
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (24), (45) imply:
% 204.14/34.96  | |   (46)  op(e1, e1) = e2
% 204.14/34.96  | | 
% 204.14/34.96  | | GROUND_INST: instantiating (2) with all_10_2, e2, e1, e1, simplifying with
% 204.14/34.96  | |              (38), (46) gives:
% 204.14/34.96  | |   (47)  all_10_2 = e2
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (7), (47) imply:
% 204.14/34.96  | |   (48)   ~ (all_52_17 = e2)
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (27), (47) imply:
% 204.14/34.96  | |   (49)   ~ (all_52_19 = e2)
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (25), (47) imply:
% 204.14/34.96  | |   (50)   ~ (e3 = e2)
% 204.14/34.96  | | 
% 204.14/34.96  | | SIMP: (50) implies:
% 204.14/34.96  | |   (51)   ~ (e3 = e2)
% 204.14/34.96  | | 
% 204.14/34.96  | | BETA: splitting (40) gives:
% 204.14/34.96  | | 
% 204.14/34.96  | | Case 1:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (52)  all_58_2 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | COMBINE_EQS: (43), (52) imply:
% 204.14/34.96  | | |   (53)  e2 = e1
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (16), (53) imply:
% 204.14/34.96  | | |   (54)  $false
% 204.14/34.96  | | | 
% 204.14/34.96  | | | CLOSE: (54) is inconsistent.
% 204.14/34.96  | | | 
% 204.14/34.96  | | Case 2:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (55)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | BETA: splitting (55) gives:
% 204.14/34.96  | | | 
% 204.14/34.96  | | | Case 1:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (56)  all_58_3 = e2
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | COMBINE_EQS: (39), (56) imply:
% 204.14/34.96  | | | |   (57)  all_4_2 = e2
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (32), (57) imply:
% 204.14/34.96  | | | |   (58)   ~ (all_52_9 = e2)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | BETA: splitting (20) gives:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | Case 1:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | |   (59)  all_58_0 = e2
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | COMBINE_EQS: (26), (59) imply:
% 204.14/34.96  | | | | |   (60)  e3 = e2
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | REDUCE: (51), (60) imply:
% 204.14/34.96  | | | | |   (61)  $false
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | CLOSE: (61) is inconsistent.
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | Case 2:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | |   (62)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13),
% 204.14/34.96  | | | | |            (14), (17), (18), (19), (21), (22), (23), (24), (26), (28),
% 204.14/34.96  | | | | |            (29), (30), (31), (33), (35), (37), (38), (41), (42), (48),
% 204.14/34.96  | | | | |            (58), (62) are inconsistent by sub-proof #746.
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | End of split
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | Case 2:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (63)  all_58_5 = e2 | all_58_10 = e2
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REF_CLOSE: (33), (36), (49), (51), (63) are inconsistent by sub-proof
% 204.14/34.96  | | | |            #760.
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | End of split
% 204.14/34.96  | | | 
% 204.14/34.96  | | End of split
% 204.14/34.96  | | 
% 204.14/34.96  | Case 2:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (64)  all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96  | | 
% 204.14/34.96  | | REF_CLOSE: (2), (4), (17), (30), (34), (37), (38), (64) are inconsistent by
% 204.14/34.96  | |            sub-proof #851.
% 204.14/34.96  | | 
% 204.14/34.96  | End of split
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #746 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.96    (3)  all_58_1 = all_52_9
% 204.14/34.96    (4)  op(all_52_5, all_52_5) = e1
% 204.14/34.96    (5)   ~ (e3 = e0)
% 204.14/34.96    (6)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.96    (7)  all_58_9 = all_52_25
% 204.14/34.96    (8)   ~ (all_52_29 = all_14_2)
% 204.14/34.96    (9)  all_58_11 = all_52_29
% 204.14/34.96    (10)   ~ (all_52_25 = all_14_2)
% 204.14/34.96    (11)  op(all_10_2, e1) = all_10_1
% 204.14/34.96    (12)  all_56_15 = all_14_2
% 204.14/34.96    (13)  all_58_12 = all_52_7
% 204.14/34.96    (14)   ~ (all_52_7 = all_14_2)
% 204.14/34.96    (15)  all_58_2 = all_52_3
% 204.14/34.96    (16)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96    (17)  all_58_7 = e3
% 204.14/34.96    (18)   ~ (e2 = e0)
% 204.14/34.96    (19)  op(all_52_3, all_52_3) = e2
% 204.14/34.96    (20)  all_58_0 = e3
% 204.14/34.96    (21)   ~ (all_52_9 = e2)
% 204.14/34.96    (22)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.14/34.96    (23)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.96    (24)  all_58_8 = all_10_2
% 204.14/34.96    (25)   ~ (all_52_5 = all_10_2)
% 204.14/34.96    (26)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.96    (27)  all_58_10 = e3
% 204.14/34.96    (28)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.96    (29)  all_58_6 = all_52_5
% 204.14/34.96    (30)  op(e1, e1) = all_10_2
% 204.14/34.96    (31)   ~ (all_52_17 = e2)
% 204.14/34.96    (32)  all_58_4 = all_52_17
% 204.14/34.96    (33)   ~ (all_14_2 = e3)
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | BETA: splitting (22) gives:
% 204.14/34.96  | 
% 204.14/34.96  | Case 1:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (34)  all_58_1 = e2
% 204.14/34.96  | | 
% 204.14/34.96  | | COMBINE_EQS: (3), (34) imply:
% 204.14/34.96  | |   (35)  all_52_9 = e2
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (21), (35) imply:
% 204.14/34.96  | |   (36)  $false
% 204.14/34.96  | | 
% 204.14/34.96  | | CLOSE: (36) is inconsistent.
% 204.14/34.96  | | 
% 204.14/34.96  | Case 2:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (37)  all_58_4 = e2 | all_58_9 = e2
% 204.14/34.96  | | 
% 204.14/34.96  | | BETA: splitting (37) gives:
% 204.14/34.96  | | 
% 204.14/34.96  | | Case 1:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (38)  all_58_4 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | COMBINE_EQS: (32), (38) imply:
% 204.14/34.96  | | |   (39)  all_52_17 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | SIMP: (39) implies:
% 204.14/34.96  | | |   (40)  all_52_17 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (31), (40) imply:
% 204.14/34.96  | | |   (41)  $false
% 204.14/34.96  | | | 
% 204.14/34.96  | | | CLOSE: (41) is inconsistent.
% 204.14/34.96  | | | 
% 204.14/34.96  | | Case 2:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (42)  all_58_9 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | COMBINE_EQS: (7), (42) imply:
% 204.14/34.96  | | |   (43)  all_52_25 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | SIMP: (43) implies:
% 204.14/34.96  | | |   (44)  all_52_25 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REDUCE: (10), (44) imply:
% 204.14/34.96  | | |   (45)   ~ (all_14_2 = e2)
% 204.14/34.96  | | | 
% 204.14/34.96  | | | SIMP: (45) implies:
% 204.14/34.96  | | |   (46)   ~ (all_14_2 = e2)
% 204.14/34.96  | | | 
% 204.14/34.96  | | | BETA: splitting (1) gives:
% 204.14/34.96  | | | 
% 204.14/34.96  | | | Case 1:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (47)  all_58_9 = e0
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REF_CLOSE: (18), (42), (47) are inconsistent by sub-proof #1084.
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | Case 2:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (48)  all_58_10 = e0 | all_58_11 = e0
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (13), (14), (15),
% 204.14/34.96  | | | |            (16), (17), (19), (20), (23), (24), (25), (26), (27), (28),
% 204.14/34.96  | | | |            (29), (30), (33), (46), (48) are inconsistent by sub-proof
% 204.14/34.96  | | | |            #747.
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | End of split
% 204.14/34.96  | | | 
% 204.14/34.96  | | End of split
% 204.14/34.96  | | 
% 204.14/34.96  | End of split
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #747 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.96    (2)  op(all_52_5, all_52_5) = e1
% 204.14/34.96    (3)   ~ (e3 = e0)
% 204.14/34.96    (4)   ~ (all_14_2 = e2)
% 204.14/34.96    (5)  op(all_10_2, all_10_2) = all_52_20
% 204.14/34.96    (6)   ~ (all_52_29 = all_14_2)
% 204.14/34.96    (7)  all_58_11 = all_52_29
% 204.14/34.96    (8)  op(all_10_2, e1) = all_10_1
% 204.14/34.96    (9)  all_56_15 = all_14_2
% 204.14/34.96    (10)  all_58_12 = all_52_7
% 204.14/34.96    (11)   ~ (all_52_7 = all_14_2)
% 204.14/34.96    (12)  all_58_2 = all_52_3
% 204.14/34.96    (13)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96    (14)  all_58_7 = e3
% 204.14/34.96    (15)  op(all_52_3, all_52_3) = e2
% 204.14/34.96    (16)  all_58_10 = e0 | all_58_11 = e0
% 204.14/34.96    (17)  all_58_0 = e3
% 204.14/34.96    (18)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.96    (19)  all_58_8 = all_10_2
% 204.14/34.96    (20)   ~ (all_52_5 = all_10_2)
% 204.14/34.96    (21)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.96    (22)  all_58_10 = e3
% 204.14/34.96    (23)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.96    (24)  all_58_6 = all_52_5
% 204.14/34.96    (25)  op(e1, e1) = all_10_2
% 204.14/34.96    (26)   ~ (all_14_2 = e3)
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | BETA: splitting (16) gives:
% 204.14/34.96  | 
% 204.14/34.96  | Case 1:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (27)  all_58_10 = e0
% 204.14/34.96  | | 
% 204.14/34.96  | | REF_CLOSE: (3), (22), (27) are inconsistent by sub-proof #750.
% 204.14/34.96  | | 
% 204.14/34.96  | Case 2:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (28)  all_58_11 = e0
% 204.14/34.96  | | 
% 204.14/34.96  | | COMBINE_EQS: (7), (28) imply:
% 204.14/34.96  | |   (29)  all_52_29 = e0
% 204.14/34.96  | | 
% 204.14/34.96  | | SIMP: (29) implies:
% 204.14/34.96  | |   (30)  all_52_29 = e0
% 204.14/34.96  | | 
% 204.14/34.96  | | REDUCE: (6), (30) imply:
% 204.14/34.96  | |   (31)   ~ (all_14_2 = e0)
% 204.14/34.96  | | 
% 204.14/34.96  | | SIMP: (31) implies:
% 204.14/34.96  | |   (32)   ~ (all_14_2 = e0)
% 204.14/34.96  | | 
% 204.14/34.96  | | BETA: splitting (18) gives:
% 204.14/34.96  | | 
% 204.14/34.96  | | Case 1:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (33)  all_56_15 = e2
% 204.14/34.96  | | | 
% 204.14/34.96  | | | REF_CLOSE: (4), (9), (33) are inconsistent by sub-proof #762.
% 204.14/34.96  | | | 
% 204.14/34.96  | | Case 2:
% 204.14/34.96  | | | 
% 204.14/34.96  | | |   (34)   ~ (all_56_15 = e2)
% 204.14/34.96  | | |   (35)  all_56_15 = e1 | all_56_15 = e0
% 204.14/34.96  | | | 
% 204.14/34.96  | | | BETA: splitting (35) gives:
% 204.14/34.96  | | | 
% 204.14/34.96  | | | Case 1:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (36)  all_56_15 = e1
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | COMBINE_EQS: (9), (36) imply:
% 204.14/34.96  | | | |   (37)  all_14_2 = e1
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | SIMP: (37) implies:
% 204.14/34.96  | | | |   (38)  all_14_2 = e1
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (11), (38) imply:
% 204.14/34.96  | | | |   (39)   ~ (all_52_7 = e1)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (26), (38) imply:
% 204.14/34.96  | | | |   (40)   ~ (e3 = e1)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | SIMP: (40) implies:
% 204.14/34.96  | | | |   (41)   ~ (e3 = e1)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (4), (38) imply:
% 204.14/34.96  | | | |   (42)   ~ (e2 = e1)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | SIMP: (42) implies:
% 204.14/34.96  | | | |   (43)   ~ (e2 = e1)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (32), (38) imply:
% 204.14/34.96  | | | |   (44)   ~ (e1 = e0)
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REDUCE: (23), (38) imply:
% 204.14/34.96  | | | |   (45)  op(e1, e1) = all_52_30
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | GROUND_INST: instantiating (1) with all_10_2, all_52_30, e1, e1,
% 204.14/34.96  | | | |              simplifying with (25), (45) gives:
% 204.14/34.96  | | | |   (46)  all_52_30 = all_10_2
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | BETA: splitting (21) gives:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | Case 1:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | |   (47)  all_58_6 = e1
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | COMBINE_EQS: (24), (47) imply:
% 204.14/34.96  | | | | |   (48)  all_52_5 = e1
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | REF_CLOSE: (1), (2), (20), (25), (48) are inconsistent by sub-proof
% 204.14/34.96  | | | | |            #871.
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | Case 2:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | |   (49)   ~ (all_58_6 = e1)
% 204.14/34.96  | | | | |   (50)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | REDUCE: (24), (49) imply:
% 204.14/34.96  | | | | |   (51)   ~ (all_52_5 = e1)
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | BETA: splitting (50) gives:
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | | Case 1:
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | |   (52)  all_58_7 = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | COMBINE_EQS: (14), (52) imply:
% 204.14/34.96  | | | | | |   (53)  e3 = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | REDUCE: (41), (53) imply:
% 204.14/34.96  | | | | | |   (54)  $false
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | CLOSE: (54) is inconsistent.
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | Case 2:
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | |   (55)   ~ (all_58_7 = e1)
% 204.14/34.96  | | | | | |   (56)  all_58_8 = e1 | all_58_11 = e1
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | BETA: splitting (13) gives:
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | | Case 1:
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | |   (57)  all_58_0 = e1
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | COMBINE_EQS: (17), (57) imply:
% 204.14/34.96  | | | | | | |   (58)  e3 = e1
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | REDUCE: (41), (58) imply:
% 204.14/34.96  | | | | | | |   (59)  $false
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | CLOSE: (59) is inconsistent.
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | Case 2:
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | |   (60)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | BETA: splitting (60) gives:
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | | Case 1:
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | |   (61)  all_58_2 = e1
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | | COMBINE_EQS: (12), (61) imply:
% 204.14/34.96  | | | | | | | |   (62)  all_52_3 = e1
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | | REDUCE: (15), (62) imply:
% 204.14/34.96  | | | | | | | |   (63)  op(e1, e1) = e2
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | | BETA: splitting (56) gives:
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | | Case 1:
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | |   (64)  all_58_8 = e1
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | COMBINE_EQS: (19), (64) imply:
% 204.14/34.96  | | | | | | | | |   (65)  all_10_2 = e1
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | REDUCE: (5), (65) imply:
% 204.14/34.96  | | | | | | | | |   (66)  op(e1, e1) = all_52_20
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | REDUCE: (8), (65) imply:
% 204.14/34.96  | | | | | | | | |   (67)  op(e1, e1) = all_10_1
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | REDUCE: (25), (65) imply:
% 204.14/34.96  | | | | | | | | |   (68)  op(e1, e1) = e1
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | REF_CLOSE: (1), (43), (45), (63), (66), (67), (68) are
% 204.14/34.96  | | | | | | | | |            inconsistent by sub-proof #749.
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | Case 2:
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | |   (69)  all_58_11 = e1
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | COMBINE_EQS: (28), (69) imply:
% 204.14/34.96  | | | | | | | | |   (70)  e1 = e0
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | SIMP: (70) implies:
% 204.14/34.96  | | | | | | | | |   (71)  e1 = e0
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | REDUCE: (44), (71) imply:
% 204.14/34.96  | | | | | | | | |   (72)  $false
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | | CLOSE: (72) is inconsistent.
% 204.14/34.96  | | | | | | | | | 
% 204.14/34.96  | | | | | | | | End of split
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | Case 2:
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | |   (73)  all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | | REF_CLOSE: (10), (24), (39), (51), (73) are inconsistent by
% 204.14/34.96  | | | | | | | |            sub-proof #748.
% 204.14/34.96  | | | | | | | | 
% 204.14/34.96  | | | | | | | End of split
% 204.14/34.96  | | | | | | | 
% 204.14/34.96  | | | | | | End of split
% 204.14/34.96  | | | | | | 
% 204.14/34.96  | | | | | End of split
% 204.14/34.96  | | | | | 
% 204.14/34.96  | | | | End of split
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | Case 2:
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | |   (74)  all_56_15 = e0
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | | REF_CLOSE: (9), (32), (74) are inconsistent by sub-proof #1162.
% 204.14/34.96  | | | | 
% 204.14/34.96  | | | End of split
% 204.14/34.96  | | | 
% 204.14/34.96  | | End of split
% 204.14/34.96  | | 
% 204.14/34.96  | End of split
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #748 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)   ~ (all_52_5 = e1)
% 204.14/34.96    (2)  all_58_6 = e1 | all_58_12 = e1
% 204.14/34.96    (3)  all_58_12 = all_52_7
% 204.14/34.96    (4)   ~ (all_52_7 = e1)
% 204.14/34.96    (5)  all_58_6 = all_52_5
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | BETA: splitting (2) gives:
% 204.14/34.96  | 
% 204.14/34.96  | Case 1:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (6)  all_58_6 = e1
% 204.14/34.96  | | 
% 204.14/34.96  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #963.
% 204.14/34.96  | | 
% 204.14/34.96  | Case 2:
% 204.14/34.96  | | 
% 204.14/34.96  | |   (7)  all_58_12 = e1
% 204.14/34.96  | | 
% 204.14/34.96  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1127.
% 204.14/34.96  | | 
% 204.14/34.96  | End of split
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #749 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.96    (2)   ~ (e2 = e1)
% 204.14/34.96    (3)  op(e1, e1) = all_10_1
% 204.14/34.96    (4)  op(e1, e1) = e2
% 204.14/34.96    (5)  op(e1, e1) = e1
% 204.14/34.96    (6)  op(e1, e1) = all_52_20
% 204.14/34.96    (7)  op(e1, e1) = all_52_30
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | GROUND_INST: instantiating (1) with all_10_1, all_52_30, e1, e1, simplifying
% 204.14/34.96  |              with (3), (7) gives:
% 204.14/34.96  |   (8)  all_52_30 = all_10_1
% 204.14/34.96  | 
% 204.14/34.96  | GROUND_INST: instantiating (1) with e2, all_52_30, e1, e1, simplifying with
% 204.14/34.96  |              (4), (7) gives:
% 204.14/34.96  |   (9)  all_52_30 = e2
% 204.14/34.96  | 
% 204.14/34.96  | GROUND_INST: instantiating (1) with all_10_1, all_52_20, e1, e1, simplifying
% 204.14/34.96  |              with (3), (6) gives:
% 204.14/34.96  |   (10)  all_52_20 = all_10_1
% 204.14/34.96  | 
% 204.14/34.96  | GROUND_INST: instantiating (1) with e1, all_52_20, e1, e1, simplifying with
% 204.14/34.96  |              (5), (6) gives:
% 204.14/34.96  |   (11)  all_52_20 = e1
% 204.14/34.96  | 
% 204.14/34.96  | COMBINE_EQS: (10), (11) imply:
% 204.14/34.96  |   (12)  all_10_1 = e1
% 204.14/34.96  | 
% 204.14/34.96  | SIMP: (12) implies:
% 204.14/34.96  |   (13)  all_10_1 = e1
% 204.14/34.96  | 
% 204.14/34.96  | COMBINE_EQS: (8), (9) imply:
% 204.14/34.96  |   (14)  all_10_1 = e2
% 204.14/34.96  | 
% 204.14/34.96  | SIMP: (14) implies:
% 204.14/34.96  |   (15)  all_10_1 = e2
% 204.14/34.96  | 
% 204.14/34.96  | COMBINE_EQS: (13), (15) imply:
% 204.14/34.96  |   (16)  e2 = e1
% 204.14/34.96  | 
% 204.14/34.96  | REDUCE: (2), (16) imply:
% 204.14/34.96  |   (17)  $false
% 204.14/34.96  | 
% 204.14/34.96  | CLOSE: (17) is inconsistent.
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #750 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)  all_58_10 = e3
% 204.14/34.96    (2)  all_58_10 = e0
% 204.14/34.96    (3)   ~ (e3 = e0)
% 204.14/34.96  
% 204.14/34.96  Begin of proof
% 204.14/34.96  | 
% 204.14/34.96  | COMBINE_EQS: (1), (2) imply:
% 204.14/34.96  |   (4)  e3 = e0
% 204.14/34.96  | 
% 204.14/34.96  | SIMP: (4) implies:
% 204.14/34.96  |   (5)  e3 = e0
% 204.14/34.96  | 
% 204.14/34.96  | REDUCE: (3), (5) imply:
% 204.14/34.96  |   (6)  $false
% 204.14/34.96  | 
% 204.14/34.96  | CLOSE: (6) is inconsistent.
% 204.14/34.96  | 
% 204.14/34.96  End of proof
% 204.14/34.96  
% 204.14/34.96  Sub-proof #751 shows that the following formulas are inconsistent:
% 204.14/34.96  ----------------------------------------------------------------
% 204.14/34.96    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.96    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.14/34.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.96    (4)   ~ (all_52_5 = all_52_13)
% 204.14/34.96    (5)  op(all_52_7, all_52_7) = e0
% 204.14/34.96    (6)   ~ (all_52_9 = all_52_13)
% 204.14/34.96    (7)  op(all_52_5, all_52_5) = e1
% 204.14/34.96    (8)   ~ (e3 = e0)
% 204.14/34.96    (9)   ~ (all_52_3 = all_52_19)
% 204.14/34.96    (10)   ~ (all_52_17 = all_52_25)
% 204.14/34.96    (11)  all_56_4 = all_52_3
% 204.14/34.96    (12)  all_58_13 = all_52_15
% 204.14/34.96    (13)  all_58_9 = all_52_25
% 204.14/34.96    (14)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.14/34.96    (15)   ~ (all_52_15 = e3)
% 204.14/34.96    (16)  op(e2, all_4_1) = e3
% 204.14/34.96    (17)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.96    (18)  op(e2, e2) = all_4_2
% 204.14/34.96    (19)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.14/34.96    (20)   ~ (all_52_3 = all_52_27)
% 204.14/34.96    (21)  op(e0, e0) = all_14_2
% 204.14/34.96    (22)   ~ (all_4_1 = e1)
% 204.14/34.96    (23)  all_58_11 = e3
% 204.14/34.96    (24)  all_56_9 = all_52_13
% 204.14/34.96    (25)   ~ (all_52_13 = all_10_2)
% 204.14/34.96    (26)  all_58_10 = all_52_27
% 204.14/34.96    (27)  all_56_8 = all_52_5
% 204.14/34.96    (28)  op(all_52_9, all_52_9) = all_52_8
% 204.14/34.96    (29)  all_58_7 = all_52_13
% 204.14/34.96    (30)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.14/34.96    (31)  all_58_12 = all_52_7
% 204.14/34.96    (32)   ~ (all_52_7 = all_14_2)
% 204.14/34.96    (33)  all_58_2 = all_52_3
% 204.14/34.96    (34)  all_56_2 = all_52_17
% 204.14/34.96    (35)   ~ (all_52_25 = e3)
% 204.14/34.96    (36)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.96    (37)  op(all_4_2, e2) = all_4_1
% 204.14/34.96    (38)  op(all_52_3, all_52_3) = e2
% 204.14/34.96    (39)   ~ (all_52_5 = e3)
% 204.14/34.96    (40)   ~ (all_52_13 = all_4_2)
% 204.14/34.96    (41)   ~ (all_52_9 = all_52_25)
% 204.14/34.96    (42)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.96    (43)  all_58_8 = all_10_2
% 204.14/34.96    (44)   ~ (all_52_5 = all_10_2)
% 204.14/34.96    (45)  all_56_12 = all_52_7
% 204.14/34.96    (46)   ~ (all_52_9 = all_4_2)
% 204.14/34.96    (47)   ~ (all_52_13 = e3)
% 204.14/34.96    (48)   ~ (all_52_17 = e3)
% 204.14/34.97    (49)   ~ (all_52_3 = all_52_7)
% 204.14/34.97    (50)  all_58_5 = all_52_19
% 204.14/34.97    (51)  all_56_1 = all_52_9
% 204.14/34.97    (52)  all_58_6 = all_52_5
% 204.14/34.97    (53)  op(e3, e2) = all_52_9
% 204.14/34.97    (54)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.14/34.97    (55)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.14/34.97    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.97    (57)   ~ (all_52_9 = all_52_17)
% 204.14/34.97    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.14/34.97    (59)  all_58_14 = e3
% 204.14/34.97    (60)  all_58_3 = all_4_2
% 204.14/34.97    (61)   ~ (all_52_3 = all_4_2)
% 204.14/34.97    (62)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.97    (63)  all_58_4 = all_52_17
% 204.14/34.97  
% 204.14/34.97  Begin of proof
% 204.14/34.97  | 
% 204.14/34.97  | BETA: splitting (55) gives:
% 204.14/34.97  | 
% 204.14/34.97  | Case 1:
% 204.14/34.97  | | 
% 204.14/34.97  | |   (64)  all_58_3 = e3
% 204.14/34.97  | | 
% 204.14/34.97  | | COMBINE_EQS: (60), (64) imply:
% 204.14/34.97  | |   (65)  all_4_2 = e3
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (61), (65) imply:
% 204.14/34.97  | |   (66)   ~ (all_52_3 = e3)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (46), (65) imply:
% 204.14/34.97  | |   (67)   ~ (all_52_9 = e3)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (37), (65) imply:
% 204.14/34.97  | |   (68)  op(e3, e2) = all_4_1
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (18), (65) imply:
% 204.14/34.97  | |   (69)  op(e2, e2) = e3
% 204.14/34.97  | | 
% 204.14/34.97  | | GROUND_INST: instantiating (3) with all_52_9, all_4_1, e2, e3, simplifying
% 204.14/34.97  | |              with (53), (68) gives:
% 204.14/34.97  | |   (70)  all_52_9 = all_4_1
% 204.14/34.97  | | 
% 204.14/34.97  | | COMBINE_EQS: (51), (70) imply:
% 204.14/34.97  | |   (71)  all_56_1 = all_4_1
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (6), (70) imply:
% 204.14/34.97  | |   (72)   ~ (all_52_13 = all_4_1)
% 204.14/34.97  | | 
% 204.14/34.97  | | SIMP: (72) implies:
% 204.14/34.97  | |   (73)   ~ (all_52_13 = all_4_1)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (57), (70) imply:
% 204.14/34.97  | |   (74)   ~ (all_52_17 = all_4_1)
% 204.14/34.97  | | 
% 204.14/34.97  | | SIMP: (74) implies:
% 204.14/34.97  | |   (75)   ~ (all_52_17 = all_4_1)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (41), (70) imply:
% 204.14/34.97  | |   (76)   ~ (all_52_25 = all_4_1)
% 204.14/34.97  | | 
% 204.14/34.97  | | SIMP: (76) implies:
% 204.14/34.97  | |   (77)   ~ (all_52_25 = all_4_1)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (67), (70) imply:
% 204.14/34.97  | |   (78)   ~ (all_4_1 = e3)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (28), (70) imply:
% 204.14/34.97  | |   (79)  op(all_4_1, all_4_1) = all_52_8
% 204.14/34.97  | | 
% 204.14/34.97  | | BETA: splitting (56) gives:
% 204.14/34.97  | | 
% 204.14/34.97  | | Case 1:
% 204.14/34.97  | | | 
% 204.14/34.97  | | |   (80)  all_56_1 = e3
% 204.14/34.97  | | | 
% 204.14/34.97  | | | REF_CLOSE: (71), (78), (80) are inconsistent by sub-proof #1167.
% 204.14/34.97  | | | 
% 204.14/34.97  | | Case 2:
% 204.14/34.97  | | | 
% 204.14/34.97  | | |   (81)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.97  | | | 
% 204.14/34.97  | | | BETA: splitting (58) gives:
% 204.14/34.97  | | | 
% 204.14/34.97  | | | Case 1:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | |   (82)  all_56_9 = e3
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | REF_CLOSE: (24), (47), (82) are inconsistent by sub-proof #958.
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | Case 2:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | |   (83)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | BETA: splitting (42) gives:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | Case 1:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | |   (84)  all_56_8 = e3
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | REF_CLOSE: (27), (39), (84) are inconsistent by sub-proof #1325.
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | Case 2:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | |   (85)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | BETA: splitting (36) gives:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | Case 1:
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | |   (86)  all_56_4 = e3
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | REF_CLOSE: (11), (66), (86) are inconsistent by sub-proof #1340.
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | Case 2:
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | |   (87)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13),
% 204.14/34.97  | | | | | |            (14), (16), (17), (19), (20), (21), (22), (23), (24),
% 204.14/34.97  | | | | | |            (25), (26), (27), (30), (31), (32), (33), (34), (35),
% 204.14/34.97  | | | | | |            (38), (43), (44), (45), (48), (49), (50), (52), (54),
% 204.14/34.97  | | | | | |            (59), (62), (63), (66), (69), (71), (73), (75), (77),
% 204.14/34.97  | | | | | |            (79), (81), (83), (85), (87) are inconsistent by
% 204.14/34.97  | | | | | |            sub-proof #752.
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | End of split
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | End of split
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | End of split
% 204.14/34.97  | | | 
% 204.14/34.97  | | End of split
% 204.14/34.97  | | 
% 204.14/34.97  | Case 2:
% 204.14/34.97  | | 
% 204.14/34.97  | |   (88)  all_58_7 = e3 | all_58_13 = e3
% 204.14/34.97  | | 
% 204.14/34.97  | | REF_CLOSE: (12), (15), (29), (47), (88) are inconsistent by sub-proof #1298.
% 204.14/34.97  | | 
% 204.14/34.97  | End of split
% 204.14/34.97  | 
% 204.14/34.97  End of proof
% 204.14/34.97  
% 204.14/34.97  Sub-proof #752 shows that the following formulas are inconsistent:
% 204.14/34.97  ----------------------------------------------------------------
% 204.14/34.97    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.97    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.14/34.97    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.97    (4)   ~ (all_52_5 = all_52_13)
% 204.14/34.97    (5)  op(all_52_7, all_52_7) = e0
% 204.14/34.97    (6)  op(all_52_5, all_52_5) = e1
% 204.14/34.97    (7)   ~ (e3 = e0)
% 204.14/34.97    (8)   ~ (all_52_3 = all_52_19)
% 204.14/34.97    (9)   ~ (all_52_17 = all_52_25)
% 204.14/34.97    (10)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.14/34.97    (11)   ~ (all_52_25 = all_4_1)
% 204.14/34.97    (12)  all_56_4 = all_52_3
% 204.14/34.97    (13)  all_58_9 = all_52_25
% 204.14/34.97    (14)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.14/34.97    (15)  op(e2, all_4_1) = e3
% 204.14/34.97    (16)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.97    (17)   ~ (all_52_3 = e3)
% 204.14/34.97    (18)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.14/34.97    (19)   ~ (all_52_3 = all_52_27)
% 204.14/34.97    (20)  all_56_1 = all_4_1
% 204.14/34.97    (21)  op(e0, e0) = all_14_2
% 204.14/34.97    (22)  op(all_4_1, all_4_1) = all_52_8
% 204.14/34.97    (23)   ~ (all_4_1 = e1)
% 204.14/34.97    (24)  all_58_11 = e3
% 204.14/34.97    (25)  all_56_9 = all_52_13
% 204.14/34.97    (26)   ~ (all_52_13 = all_10_2)
% 204.14/34.97    (27)  all_58_10 = all_52_27
% 204.14/34.97    (28)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.14/34.97    (29)  all_56_8 = all_52_5
% 204.14/34.97    (30)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.14/34.97    (31)  all_58_12 = all_52_7
% 204.14/34.97    (32)   ~ (all_52_7 = all_14_2)
% 204.14/34.97    (33)  all_58_2 = all_52_3
% 204.14/34.97    (34)   ~ (all_52_17 = all_4_1)
% 204.14/34.97    (35)  all_56_2 = all_52_17
% 204.14/34.97    (36)   ~ (all_52_25 = e3)
% 204.14/34.97    (37)  op(all_52_3, all_52_3) = e2
% 204.14/34.97    (38)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.97    (39)   ~ (all_52_13 = all_4_1)
% 204.14/34.97    (40)  all_58_8 = all_10_2
% 204.14/34.97    (41)   ~ (all_52_5 = all_10_2)
% 204.14/34.97    (42)  all_56_12 = all_52_7
% 204.14/34.97    (43)  op(e2, e2) = e3
% 204.14/34.97    (44)   ~ (all_52_17 = e3)
% 204.14/34.97    (45)   ~ (all_52_3 = all_52_7)
% 204.14/34.97    (46)  all_58_5 = all_52_19
% 204.14/34.97    (47)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.97    (48)  all_58_6 = all_52_5
% 204.14/34.97    (49)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.14/34.97    (50)  all_58_14 = e3
% 204.14/34.97    (51)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.97    (52)  all_58_4 = all_52_17
% 204.14/34.97  
% 204.14/34.97  Begin of proof
% 204.14/34.97  | 
% 204.14/34.97  | BETA: splitting (51) gives:
% 204.14/34.97  | 
% 204.14/34.97  | Case 1:
% 204.14/34.97  | | 
% 204.14/34.97  | |   (53)  all_58_2 = e2
% 204.14/34.97  | | 
% 204.14/34.97  | | COMBINE_EQS: (33), (53) imply:
% 204.14/34.97  | |   (54)  all_52_3 = e2
% 204.14/34.97  | | 
% 204.14/34.97  | | SIMP: (54) implies:
% 204.14/34.97  | |   (55)  all_52_3 = e2
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (17), (55) imply:
% 204.14/34.97  | |   (56)   ~ (e3 = e2)
% 204.14/34.97  | | 
% 204.14/34.97  | | SIMP: (56) implies:
% 204.14/34.97  | |   (57)   ~ (e3 = e2)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (37), (55) imply:
% 204.14/34.97  | |   (58)  op(e2, e2) = e2
% 204.14/34.97  | | 
% 204.14/34.97  | | GROUND_INST: instantiating (3) with e3, e2, e2, e2, simplifying with (43),
% 204.14/34.97  | |              (58) gives:
% 204.14/34.97  | |   (59)  e3 = e2
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (57), (59) imply:
% 204.14/34.97  | |   (60)  $false
% 204.14/34.97  | | 
% 204.14/34.97  | | CLOSE: (60) is inconsistent.
% 204.14/34.97  | | 
% 204.14/34.97  | Case 2:
% 204.14/34.97  | | 
% 204.14/34.97  | |   (61)   ~ (all_58_2 = e2)
% 204.14/34.97  | | 
% 204.14/34.97  | | REDUCE: (33), (61) imply:
% 204.14/34.97  | |   (62)   ~ (all_52_3 = e2)
% 204.14/34.97  | | 
% 204.14/34.97  | | BETA: splitting (30) gives:
% 204.14/34.97  | | 
% 204.14/34.97  | | Case 1:
% 204.14/34.97  | | | 
% 204.14/34.97  | | |   (63)  all_58_2 = e1
% 204.14/34.97  | | | 
% 204.14/34.97  | | | COMBINE_EQS: (33), (63) imply:
% 204.14/34.97  | | |   (64)  all_52_3 = e1
% 204.14/34.97  | | | 
% 204.14/34.97  | | | SIMP: (64) implies:
% 204.14/34.97  | | |   (65)  all_52_3 = e1
% 204.14/34.97  | | | 
% 204.14/34.97  | | | REDUCE: (45), (65) imply:
% 204.14/34.97  | | |   (66)   ~ (all_52_7 = e1)
% 204.14/34.97  | | | 
% 204.14/34.97  | | | SIMP: (66) implies:
% 204.14/34.97  | | |   (67)   ~ (all_52_7 = e1)
% 204.14/34.97  | | | 
% 204.14/34.97  | | | REF_CLOSE: (3), (5), (7), (16), (18), (21), (31), (32), (42), (43), (67)
% 204.14/34.97  | | |            are inconsistent by sub-proof #1160.
% 204.14/34.97  | | | 
% 204.14/34.97  | | Case 2:
% 204.14/34.97  | | | 
% 204.14/34.97  | | |   (68)   ~ (all_58_2 = e1)
% 204.14/34.97  | | | 
% 204.14/34.97  | | | REDUCE: (33), (68) imply:
% 204.14/34.97  | | |   (69)   ~ (all_52_3 = e1)
% 204.14/34.97  | | | 
% 204.14/34.97  | | | BETA: splitting (38) gives:
% 204.14/34.97  | | | 
% 204.14/34.97  | | | Case 1:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | |   (70)  all_56_4 = e2
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | REF_CLOSE: (12), (62), (70) are inconsistent by sub-proof #1155.
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | Case 2:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | |   (71)  all_56_4 = e1 | all_56_4 = e0
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | BETA: splitting (71) gives:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | Case 1:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | |   (72)  all_56_4 = e1
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | REF_CLOSE: (12), (69), (72) are inconsistent by sub-proof #1310.
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | Case 2:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | |   (73)  all_56_4 = e0
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | COMBINE_EQS: (12), (73) imply:
% 204.14/34.97  | | | | |   (74)  all_52_3 = e0
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | SIMP: (74) implies:
% 204.14/34.97  | | | | |   (75)  all_52_3 = e0
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | REDUCE: (8), (75) imply:
% 204.14/34.97  | | | | |   (76)   ~ (all_52_19 = e0)
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | SIMP: (76) implies:
% 204.14/34.97  | | | | |   (77)   ~ (all_52_19 = e0)
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | REDUCE: (19), (75) imply:
% 204.14/34.97  | | | | |   (78)   ~ (all_52_27 = e0)
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | SIMP: (78) implies:
% 204.14/34.97  | | | | |   (79)   ~ (all_52_27 = e0)
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | REDUCE: (17), (75) imply:
% 204.14/34.97  | | | | |   (80)   ~ (e3 = e0)
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | BETA: splitting (1) gives:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | Case 1:
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | |   (81)  all_58_9 = e0
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | COMBINE_EQS: (13), (81) imply:
% 204.14/34.97  | | | | | |   (82)  all_52_25 = e0
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | SIMP: (82) implies:
% 204.14/34.97  | | | | | |   (83)  all_52_25 = e0
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | REDUCE: (9), (83) imply:
% 204.14/34.97  | | | | | |   (84)   ~ (all_52_17 = e0)
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | REDUCE: (11), (83) imply:
% 204.14/34.97  | | | | | |   (85)   ~ (all_4_1 = e0)
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | SIMP: (85) implies:
% 204.14/34.97  | | | | | |   (86)   ~ (all_4_1 = e0)
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | BETA: splitting (47) gives:
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | Case 1:
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | |   (87)  all_56_1 = e2
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | COMBINE_EQS: (20), (87) imply:
% 204.14/34.97  | | | | | | |   (88)  all_4_1 = e2
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | SIMP: (88) implies:
% 204.14/34.97  | | | | | | |   (89)  all_4_1 = e2
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | REDUCE: (39), (89) imply:
% 204.14/34.97  | | | | | | |   (90)   ~ (all_52_13 = e2)
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | REDUCE: (34), (89) imply:
% 204.14/34.97  | | | | | | |   (91)   ~ (all_52_17 = e2)
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | REDUCE: (22), (89) imply:
% 204.14/34.97  | | | | | | |   (92)  op(e2, e2) = all_52_8
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | BETA: splitting (49) gives:
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | |   (93)  all_56_2 = e2
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | | REF_CLOSE: (35), (91), (93) are inconsistent by sub-proof #1264.
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | |   (94)  all_56_2 = e1 | all_56_2 = e0
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | | BETA: splitting (94) gives:
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | |   (95)  all_56_2 = e1
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | COMBINE_EQS: (35), (95) imply:
% 204.14/34.97  | | | | | | | | |   (96)  all_52_17 = e1
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | SIMP: (96) implies:
% 204.14/34.97  | | | | | | | | |   (97)  all_52_17 = e1
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | COMBINE_EQS: (52), (97) imply:
% 204.14/34.97  | | | | | | | | |   (98)  all_58_4 = e1
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | REDUCE: (44), (97) imply:
% 204.14/34.97  | | | | | | | | |   (99)   ~ (e3 = e1)
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | SIMP: (99) implies:
% 204.14/34.97  | | | | | | | | |   (100)   ~ (e3 = e1)
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | REDUCE: (84), (97) imply:
% 204.14/34.97  | | | | | | | | |   (101)   ~ (e1 = e0)
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | BETA: splitting (2) gives:
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | |   (102)  all_58_4 = e0
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | COMBINE_EQS: (98), (102) imply:
% 204.14/34.97  | | | | | | | | | |   (103)  e1 = e0
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | SIMP: (103) implies:
% 204.14/34.97  | | | | | | | | | |   (104)  e1 = e0
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | REDUCE: (101), (104) imply:
% 204.14/34.97  | | | | | | | | | |   (105)  $false
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | CLOSE: (105) is inconsistent.
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | |   (106)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | BETA: splitting (106) gives:
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | |   (107)  all_58_5 = e0
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | REF_CLOSE: (46), (77), (107) are inconsistent by sub-proof
% 204.14/34.97  | | | | | | | | | | |            #754.
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | |   (108)  all_58_8 = e0 | all_58_14 = e0
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | BETA: splitting (108) gives:
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | |   (109)  all_58_8 = e0
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | COMBINE_EQS: (40), (109) imply:
% 204.14/34.97  | | | | | | | | | | | |   (110)  all_10_2 = e0
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | REDUCE: (41), (110) imply:
% 204.14/34.97  | | | | | | | | | | | |   (111)   ~ (all_52_5 = e0)
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | REDUCE: (26), (110) imply:
% 204.14/34.97  | | | | | | | | | | | |   (112)   ~ (all_52_13 = e0)
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | BETA: splitting (14) gives:
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | |   (113)  all_58_6 = e2
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | COMBINE_EQS: (48), (113) imply:
% 204.14/34.97  | | | | | | | | | | | | |   (114)  all_52_5 = e2
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | SIMP: (114) implies:
% 204.14/34.97  | | | | | | | | | | | | |   (115)  all_52_5 = e2
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | REDUCE: (6), (115) imply:
% 204.14/34.97  | | | | | | | | | | | | |   (116)  op(e2, e2) = e1
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | REF_CLOSE: (3), (43), (92), (100), (116) are inconsistent by
% 204.14/34.97  | | | | | | | | | | | | |            sub-proof #753.
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | |   (117)   ~ (all_58_6 = e2)
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | REDUCE: (48), (117) imply:
% 204.14/34.97  | | | | | | | | | | | | |   (118)   ~ (all_52_5 = e2)
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | BETA: splitting (10) gives:
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | |   (119)  all_56_9 = e2
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | REF_CLOSE: (25), (90), (119) are inconsistent by sub-proof
% 204.14/34.97  | | | | | | | | | | | | | |            #955.
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | |   (120)  all_56_9 = e1 | all_56_9 = e0
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | Case 1:
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | |   (121)  all_56_9 = e1
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | | COMBINE_EQS: (25), (121) imply:
% 204.14/34.97  | | | | | | | | | | | | | | |   (122)  all_52_13 = e1
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | | SIMP: (122) implies:
% 204.14/34.97  | | | | | | | | | | | | | | |   (123)  all_52_13 = e1
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | | REDUCE: (4), (123) imply:
% 204.14/34.97  | | | | | | | | | | | | | | |   (124)   ~ (all_52_5 = e1)
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | | REF_CLOSE: (28), (29), (111), (118), (124) are inconsistent
% 204.14/34.97  | | | | | | | | | | | | | | |            by sub-proof #1004.
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | |   (125)  all_56_9 = e0
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | | REF_CLOSE: (25), (112), (125) are inconsistent by sub-proof
% 204.14/34.97  | | | | | | | | | | | | | | |            #953.
% 204.14/34.97  | | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | |   (126)  all_58_14 = e0
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | | REF_CLOSE: (7), (50), (126) are inconsistent by sub-proof
% 204.14/34.97  | | | | | | | | | | | |            #1151.
% 204.14/34.97  | | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | Case 2:
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | |   (127)  all_56_2 = e0
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | COMBINE_EQS: (35), (127) imply:
% 204.14/34.97  | | | | | | | | |   (128)  all_52_17 = e0
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | SIMP: (128) implies:
% 204.14/34.97  | | | | | | | | |   (129)  all_52_17 = e0
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | REDUCE: (84), (129) imply:
% 204.14/34.97  | | | | | | | | |   (130)  $false
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | | CLOSE: (130) is inconsistent.
% 204.14/34.97  | | | | | | | | | 
% 204.14/34.97  | | | | | | | | End of split
% 204.14/34.97  | | | | | | | | 
% 204.14/34.97  | | | | | | | End of split
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | Case 2:
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | |   (131)  all_56_1 = e1 | all_56_1 = e0
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | | REF_CLOSE: (20), (23), (86), (131) are inconsistent by sub-proof
% 204.14/34.97  | | | | | | |            #1164.
% 204.14/34.97  | | | | | | | 
% 204.14/34.97  | | | | | | End of split
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | Case 2:
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | |   (132)  all_58_10 = e0 | all_58_11 = e0
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | | REF_CLOSE: (7), (24), (27), (79), (132) are inconsistent by
% 204.14/34.97  | | | | | |            sub-proof #802.
% 204.14/34.97  | | | | | | 
% 204.14/34.97  | | | | | End of split
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | End of split
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | End of split
% 204.14/34.97  | | | 
% 204.14/34.97  | | End of split
% 204.14/34.97  | | 
% 204.14/34.97  | End of split
% 204.14/34.97  | 
% 204.14/34.97  End of proof
% 204.14/34.97  
% 204.14/34.97  Sub-proof #753 shows that the following formulas are inconsistent:
% 204.14/34.97  ----------------------------------------------------------------
% 204.14/34.97    (1)   ~ (e3 = e1)
% 204.14/34.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.97    (3)  op(e2, e2) = all_52_8
% 204.14/34.97    (4)  op(e2, e2) = e1
% 204.14/34.97    (5)  op(e2, e2) = e3
% 204.14/34.97  
% 204.14/34.97  Begin of proof
% 204.14/34.97  | 
% 204.14/34.97  | GROUND_INST: instantiating (2) with e3, all_52_8, e2, e2, simplifying with
% 204.14/34.97  |              (3), (5) gives:
% 204.14/34.97  |   (6)  all_52_8 = e3
% 204.14/34.97  | 
% 204.14/34.97  | GROUND_INST: instantiating (2) with e1, all_52_8, e2, e2, simplifying with
% 204.14/34.97  |              (3), (4) gives:
% 204.14/34.97  |   (7)  all_52_8 = e1
% 204.14/34.97  | 
% 204.14/34.97  | COMBINE_EQS: (6), (7) imply:
% 204.14/34.97  |   (8)  e3 = e1
% 204.14/34.97  | 
% 204.14/34.97  | SIMP: (8) implies:
% 204.14/34.97  |   (9)  e3 = e1
% 204.14/34.97  | 
% 204.14/34.97  | REDUCE: (1), (9) imply:
% 204.14/34.97  |   (10)  $false
% 204.14/34.97  | 
% 204.14/34.97  | CLOSE: (10) is inconsistent.
% 204.14/34.97  | 
% 204.14/34.97  End of proof
% 204.14/34.97  
% 204.14/34.97  Sub-proof #754 shows that the following formulas are inconsistent:
% 204.14/34.97  ----------------------------------------------------------------
% 204.14/34.97    (1)  all_58_5 = all_52_19
% 204.14/34.97    (2)  all_58_5 = e0
% 204.14/34.97    (3)   ~ (all_52_19 = e0)
% 204.14/34.97  
% 204.14/34.97  Begin of proof
% 204.14/34.97  | 
% 204.14/34.97  | COMBINE_EQS: (1), (2) imply:
% 204.14/34.97  |   (4)  all_52_19 = e0
% 204.14/34.97  | 
% 204.14/34.97  | SIMP: (4) implies:
% 204.14/34.97  |   (5)  all_52_19 = e0
% 204.14/34.97  | 
% 204.14/34.97  | REDUCE: (3), (5) imply:
% 204.14/34.97  |   (6)  $false
% 204.14/34.97  | 
% 204.14/34.97  | CLOSE: (6) is inconsistent.
% 204.14/34.97  | 
% 204.14/34.97  End of proof
% 204.14/34.97  
% 204.14/34.97  Sub-proof #755 shows that the following formulas are inconsistent:
% 204.14/34.97  ----------------------------------------------------------------
% 204.14/34.97    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.14/34.97    (2)   ~ (all_52_25 = all_52_27)
% 204.14/34.97    (3)  all_58_14 = all_52_23
% 204.14/34.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.14/34.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.14/34.97    (5)  op(all_52_7, all_52_7) = e0
% 204.14/34.97    (6)  all_58_1 = all_52_9
% 204.14/34.97    (7)  op(all_52_5, all_52_5) = e1
% 204.14/34.97    (8)   ~ (e3 = e0)
% 204.14/34.97    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.97    (10)   ~ (all_52_3 = all_52_19)
% 204.14/34.97    (11)   ~ (all_52_3 = all_6_2)
% 204.14/34.97    (12)  all_58_0 = all_6_2
% 204.14/34.97    (13)  op(all_14_2, e0) = all_14_1
% 204.14/34.97    (14)  all_56_4 = all_52_3
% 204.14/34.97    (15)  all_58_13 = e3
% 204.14/34.97    (16)  op(e0, all_14_1) = all_14_0
% 204.14/34.97    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.14/34.97    (18)  all_58_9 = all_52_25
% 204.14/34.97    (19)  op(e2, e2) = all_4_2
% 204.14/34.97    (20)  all_58_11 = all_52_29
% 204.14/34.97    (21)   ~ (all_52_25 = all_14_2)
% 204.14/34.97    (22)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.14/34.97    (23)   ~ (all_52_3 = all_52_27)
% 204.14/34.97    (24)   ~ (all_52_7 = all_6_2)
% 204.14/34.97    (25)  op(e0, e0) = all_14_2
% 204.14/34.97    (26)  all_56_15 = all_14_2
% 204.14/34.97    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.14/34.97    (28)  op(e1, e0) = all_52_29
% 204.14/34.97    (29)  op(e3, e3) = all_52_14
% 204.14/34.97    (30)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.14/34.97    (31)  op(all_52_9, all_52_9) = all_52_8
% 204.14/34.97    (32)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.14/34.97    (33)  op(all_6_2, all_6_2) = e3
% 204.14/34.97    (34)  all_58_12 = all_52_7
% 204.14/34.97    (35)   ~ (all_52_7 = e3)
% 204.14/34.97    (36)   ~ (all_52_7 = all_14_2)
% 204.14/34.97    (37)   ~ (all_14_2 = e0)
% 204.14/34.97    (38)  all_58_2 = all_52_3
% 204.14/34.97    (39)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.14/34.97    (40)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.14/34.97    (41)  all_56_7 = all_52_27
% 204.14/34.97    (42)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.14/34.97    (43)   ~ (e2 = e0)
% 204.14/34.97    (44)   ~ (all_52_23 = e3)
% 204.14/34.97    (45)  op(all_52_3, all_52_3) = e2
% 204.14/34.97    (46)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.14/34.97    (47)  all_56_6 = all_52_19
% 204.14/34.97    (48)   ~ (all_52_19 = all_52_27)
% 204.14/34.97    (49)   ~ (all_52_9 = e3)
% 204.14/34.97    (50)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.14/34.97    (51)  op(e0, e3) = all_52_7
% 204.14/34.97    (52)   ~ (all_52_9 = all_52_25)
% 204.14/34.97    (53)  all_58_15 = all_14_2
% 204.14/34.97    (54)   ~ (all_52_19 = all_10_2)
% 204.14/34.97    (55)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.14/34.97    (56)   ~ (all_52_5 = all_10_2)
% 204.14/34.97    (57)  all_56_12 = all_52_7
% 204.14/34.97    (58)   ~ (all_52_25 = all_6_2)
% 204.14/34.97    (59)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.14/34.97    (60)   ~ (all_52_9 = all_4_2)
% 204.14/34.97    (61)  op(e3, e3) = all_6_2
% 204.14/34.97    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.14/34.97    (63)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.14/34.97    (64)  all_56_14 = all_52_23
% 204.14/34.97    (65)  all_56_3 = all_52_25
% 204.14/34.97    (66)   ~ (all_52_3 = all_52_7)
% 204.14/34.97    (67)  op(all_14_2, all_14_2) = all_52_30
% 204.14/34.97    (68)  all_58_5 = all_52_19
% 204.14/34.97    (69)  all_56_1 = all_52_9
% 204.14/34.97    (70)   ~ (all_52_27 = all_4_2)
% 204.14/34.97    (71)  all_58_6 = all_52_5
% 204.14/34.97    (72)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.14/34.97    (73)   ~ (e1 = e0)
% 204.14/34.97    (74)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.97    (75)  op(e1, e1) = all_10_2
% 204.14/34.97    (76)   ~ (all_52_23 = all_10_2)
% 204.14/34.97    (77)   ~ (all_52_7 = all_52_23)
% 204.14/34.97    (78)  all_58_3 = all_4_2
% 204.14/34.97    (79)   ~ (all_52_3 = all_4_2)
% 204.14/34.97    (80)   ~ (all_52_19 = all_4_2)
% 204.14/34.97    (81)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.14/34.97    (82)   ~ (all_14_0 = e2)
% 204.14/34.97    (83)   ~ (all_14_2 = e3)
% 204.14/34.97  
% 204.14/34.97  Begin of proof
% 204.14/34.97  | 
% 204.14/34.97  | GROUND_INST: instantiating (4) with all_6_2, all_52_14, e3, e3, simplifying
% 204.14/34.97  |              with (29), (61) gives:
% 204.14/34.97  |   (84)  all_52_14 = all_6_2
% 204.14/34.97  | 
% 204.14/34.97  | BETA: splitting (32) gives:
% 204.14/34.97  | 
% 204.14/34.97  | Case 1:
% 204.14/34.97  | | 
% 204.14/34.97  | |   (85)  all_56_14 = e3
% 204.14/34.97  | | 
% 204.14/34.97  | | REF_CLOSE: (44), (64), (85) are inconsistent by sub-proof #1286.
% 204.14/34.97  | | 
% 204.14/34.97  | Case 2:
% 204.14/34.97  | | 
% 204.14/34.97  | |   (86)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.14/34.97  | | 
% 204.14/34.97  | | BETA: splitting (74) gives:
% 204.14/34.97  | | 
% 204.14/34.97  | | Case 1:
% 204.14/34.97  | | | 
% 204.14/34.97  | | |   (87)  all_56_1 = e3
% 204.14/34.97  | | | 
% 204.14/34.97  | | | REF_CLOSE: (49), (69), (87) are inconsistent by sub-proof #1326.
% 204.14/34.97  | | | 
% 204.14/34.97  | | Case 2:
% 204.14/34.97  | | | 
% 204.14/34.97  | | |   (88)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.14/34.97  | | | 
% 204.14/34.97  | | | BETA: splitting (9) gives:
% 204.14/34.97  | | | 
% 204.14/34.97  | | | Case 1:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | |   (89)  all_56_12 = e3
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | REF_CLOSE: (35), (57), (89) are inconsistent by sub-proof #1383.
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | Case 2:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | |   (90)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | BETA: splitting (59) gives:
% 204.14/34.97  | | | | 
% 204.14/34.97  | | | | Case 1:
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | |   (91)  all_56_3 = e3
% 204.14/34.97  | | | | | 
% 204.14/34.97  | | | | | COMBINE_EQS: (65), (91) imply:
% 204.14/34.97  | | | | |   (92)  all_52_25 = e3
% 204.14/34.97  | | | | | 
% 204.18/34.97  | | | | | REF_CLOSE: (4), (5), (7), (12), (19), (25), (27), (33), (34), (36),
% 204.18/34.97  | | | | |            (38), (40), (45), (56), (58), (61), (71), (72), (75), (79),
% 204.18/34.97  | | | | |            (92) are inconsistent by sub-proof #1000.
% 204.18/34.97  | | | | | 
% 204.18/34.97  | | | | Case 2:
% 204.18/34.97  | | | | | 
% 204.18/34.97  | | | | |   (93)   ~ (all_56_3 = e3)
% 204.18/34.97  | | | | |   (94)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/34.97  | | | | | 
% 204.18/34.97  | | | | | REDUCE: (65), (93) imply:
% 204.18/34.97  | | | | |   (95)   ~ (all_52_25 = e3)
% 204.18/34.97  | | | | | 
% 204.18/34.97  | | | | | BETA: splitting (62) gives:
% 204.18/34.97  | | | | | 
% 204.18/34.97  | | | | | Case 1:
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | |   (96)  all_58_9 = e3
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | | REF_CLOSE: (18), (95), (96) are inconsistent by sub-proof #1300.
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | Case 2:
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | |   (97)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | | BETA: splitting (63) gives:
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | | Case 1:
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | |   (98)  all_58_0 = e3
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | | COMBINE_EQS: (12), (98) imply:
% 204.18/34.97  | | | | | | |   (99)  all_6_2 = e3
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | | REDUCE: (11), (99) imply:
% 204.18/34.97  | | | | | | |   (100)   ~ (all_52_3 = e3)
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (13), (14),
% 204.18/34.97  | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.18/34.97  | | | | | | |            (25), (26), (28), (30), (31), (34), (35), (36), (37),
% 204.18/34.97  | | | | | | |            (38), (39), (41), (42), (43), (45), (46), (47), (48),
% 204.18/34.97  | | | | | | |            (50), (51), (52), (53), (54), (55), (57), (60), (64),
% 204.18/34.97  | | | | | | |            (65), (66), (67), (68), (69), (70), (73), (75), (76),
% 204.18/34.97  | | | | | | |            (77), (78), (79), (80), (81), (82), (83), (86), (88),
% 204.18/34.97  | | | | | | |            (90), (94), (95), (97), (100) are inconsistent by
% 204.18/34.97  | | | | | | |            sub-proof #756.
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | Case 2:
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | |   (101)   ~ (all_58_0 = e3)
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | | REDUCE: (12), (101) imply:
% 204.18/34.97  | | | | | | |   (102)   ~ (all_6_2 = e3)
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | | REF_CLOSE: (4), (5), (7), (12), (19), (25), (27), (33), (34),
% 204.18/34.97  | | | | | | |            (36), (38), (40), (45), (56), (61), (71), (72), (75),
% 204.18/34.97  | | | | | | |            (79), (102) are inconsistent by sub-proof #1362.
% 204.18/34.97  | | | | | | | 
% 204.18/34.97  | | | | | | End of split
% 204.18/34.97  | | | | | | 
% 204.18/34.97  | | | | | End of split
% 204.18/34.97  | | | | | 
% 204.18/34.97  | | | | End of split
% 204.18/34.97  | | | | 
% 204.18/34.97  | | | End of split
% 204.18/34.97  | | | 
% 204.18/34.97  | | End of split
% 204.18/34.97  | | 
% 204.18/34.97  | End of split
% 204.18/34.97  | 
% 204.18/34.97  End of proof
% 204.18/34.97  
% 204.18/34.97  Sub-proof #756 shows that the following formulas are inconsistent:
% 204.18/34.97  ----------------------------------------------------------------
% 204.18/34.97    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/34.97    (2)   ~ (all_52_25 = all_52_27)
% 204.18/34.97    (3)  all_58_14 = all_52_23
% 204.18/34.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.97    (5)  op(all_52_7, all_52_7) = e0
% 204.18/34.97    (6)  all_58_1 = all_52_9
% 204.18/34.97    (7)   ~ (e3 = e0)
% 204.18/34.97    (8)   ~ (all_52_3 = all_52_19)
% 204.18/34.97    (9)  op(all_14_2, e0) = all_14_1
% 204.18/34.97    (10)  all_56_4 = all_52_3
% 204.18/34.97    (11)  all_58_13 = e3
% 204.18/34.97    (12)  op(e0, all_14_1) = all_14_0
% 204.18/34.97    (13)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.18/34.97    (14)  all_58_9 = all_52_25
% 204.18/34.97    (15)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.97    (16)  op(e2, e2) = all_4_2
% 204.18/34.97    (17)  all_58_11 = all_52_29
% 204.18/34.97    (18)   ~ (all_52_3 = e3)
% 204.18/34.97    (19)   ~ (all_52_25 = all_14_2)
% 204.18/34.97    (20)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.97    (21)   ~ (all_52_3 = all_52_27)
% 204.18/34.97    (22)  op(e0, e0) = all_14_2
% 204.18/34.97    (23)  all_56_15 = all_14_2
% 204.18/34.97    (24)  op(e1, e0) = all_52_29
% 204.18/34.97    (25)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.18/34.97    (26)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.97    (27)  op(all_52_9, all_52_9) = all_52_8
% 204.18/34.97    (28)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/34.97    (29)  all_58_12 = all_52_7
% 204.18/34.97    (30)   ~ (all_52_7 = e3)
% 204.18/34.97    (31)   ~ (all_52_7 = all_14_2)
% 204.18/34.97    (32)   ~ (all_14_2 = e0)
% 204.18/34.97    (33)  all_58_2 = all_52_3
% 204.18/34.97    (34)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.97    (35)  all_56_7 = all_52_27
% 204.18/34.97    (36)   ~ (all_52_25 = e3)
% 204.18/34.97    (37)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/34.97    (38)   ~ (e2 = e0)
% 204.18/34.97    (39)  op(all_52_3, all_52_3) = e2
% 204.18/34.97    (40)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.97    (41)  all_56_6 = all_52_19
% 204.18/34.97    (42)   ~ (all_52_19 = all_52_27)
% 204.18/34.97    (43)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/34.98    (44)  op(e0, e3) = all_52_7
% 204.18/34.98    (45)   ~ (all_52_9 = all_52_25)
% 204.18/34.98    (46)  all_58_15 = all_14_2
% 204.18/34.98    (47)   ~ (all_52_19 = all_10_2)
% 204.18/34.98    (48)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/34.98    (49)  all_56_12 = all_52_7
% 204.18/34.98    (50)   ~ (all_52_9 = all_4_2)
% 204.18/34.98    (51)  all_56_14 = all_52_23
% 204.18/34.98    (52)  all_56_3 = all_52_25
% 204.18/34.98    (53)   ~ (all_52_3 = all_52_7)
% 204.18/34.98    (54)  op(all_14_2, all_14_2) = all_52_30
% 204.18/34.98    (55)  all_58_5 = all_52_19
% 204.18/34.98    (56)  all_56_1 = all_52_9
% 204.18/34.98    (57)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/34.98    (58)   ~ (all_52_27 = all_4_2)
% 204.18/34.98    (59)   ~ (e1 = e0)
% 204.18/34.98    (60)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/34.98    (61)  op(e1, e1) = all_10_2
% 204.18/34.98    (62)   ~ (all_52_23 = all_10_2)
% 204.18/34.98    (63)   ~ (all_52_7 = all_52_23)
% 204.18/34.98    (64)  all_58_3 = all_4_2
% 204.18/34.98    (65)   ~ (all_52_3 = all_4_2)
% 204.18/34.98    (66)   ~ (all_52_19 = all_4_2)
% 204.18/34.98    (67)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.18/34.98    (68)   ~ (all_14_0 = e2)
% 204.18/34.98    (69)   ~ (all_14_2 = e3)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | BETA: splitting (37) gives:
% 204.18/34.98  | 
% 204.18/34.98  | Case 1:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (70)  all_56_4 = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | REF_CLOSE: (10), (18), (70) are inconsistent by sub-proof #1340.
% 204.18/34.98  | | 
% 204.18/34.98  | Case 2:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (71)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/34.98  | | 
% 204.18/34.98  | | BETA: splitting (20) gives:
% 204.18/34.98  | | 
% 204.18/34.98  | | Case 1:
% 204.18/34.98  | | | 
% 204.18/34.98  | | |   (72)  all_58_12 = e2
% 204.18/34.98  | | | 
% 204.18/34.98  | | | COMBINE_EQS: (29), (72) imply:
% 204.18/34.98  | | |   (73)  all_52_7 = e2
% 204.18/34.98  | | | 
% 204.18/34.98  | | | SIMP: (73) implies:
% 204.18/34.98  | | |   (74)  all_52_7 = e2
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (53), (74) imply:
% 204.18/34.98  | | |   (75)   ~ (all_52_3 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (63), (74) imply:
% 204.18/34.98  | | |   (76)   ~ (all_52_23 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | SIMP: (76) implies:
% 204.18/34.98  | | |   (77)   ~ (all_52_23 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (31), (74) imply:
% 204.18/34.98  | | |   (78)   ~ (all_14_2 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | SIMP: (78) implies:
% 204.18/34.98  | | |   (79)   ~ (all_14_2 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (30), (74) imply:
% 204.18/34.98  | | |   (80)   ~ (e3 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | SIMP: (80) implies:
% 204.18/34.98  | | |   (81)   ~ (e3 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (5), (74) imply:
% 204.18/34.98  | | |   (82)  op(e2, e2) = e0
% 204.18/34.98  | | | 
% 204.18/34.98  | | | BETA: splitting (48) gives:
% 204.18/34.98  | | | 
% 204.18/34.98  | | | Case 1:
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | |   (83)  all_56_15 = e2
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | REF_CLOSE: (23), (79), (83) are inconsistent by sub-proof #762.
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | Case 2:
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | |   (84)  all_56_15 = e1 | all_56_15 = e0
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | BETA: splitting (84) gives:
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | Case 1:
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | |   (85)  all_56_15 = e1
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | COMBINE_EQS: (23), (85) imply:
% 204.18/34.98  | | | | |   (86)  all_14_2 = e1
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | SIMP: (86) implies:
% 204.18/34.98  | | | | |   (87)  all_14_2 = e1
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | REDUCE: (19), (87) imply:
% 204.18/34.98  | | | | |   (88)   ~ (all_52_25 = e1)
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | REDUCE: (54), (87) imply:
% 204.18/34.98  | | | | |   (89)  op(e1, e1) = all_52_30
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | BETA: splitting (43) gives:
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | Case 1:
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | |   (90)  all_58_12 = e0
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | | REF_CLOSE: (38), (72), (90) are inconsistent by sub-proof #1153.
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | Case 2:
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | |   (91)  all_58_13 = e0 | all_58_14 = e0
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | | BETA: splitting (26) gives:
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | | Case 1:
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | |   (92)  all_56_14 = e2
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | | REF_CLOSE: (51), (77), (92) are inconsistent by sub-proof #1285.
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | Case 2:
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | |   (93)  all_56_14 = e1 | all_56_14 = e0
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | | BETA: splitting (93) gives:
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | |   (94)  all_56_14 = e1
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | COMBINE_EQS: (51), (94) imply:
% 204.18/34.98  | | | | | | | |   (95)  all_52_23 = e1
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | SIMP: (95) implies:
% 204.18/34.98  | | | | | | | |   (96)  all_52_23 = e1
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | COMBINE_EQS: (3), (96) imply:
% 204.18/34.98  | | | | | | | |   (97)  all_58_14 = e1
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | BETA: splitting (91) gives:
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | |   (98)  all_58_13 = e0
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | REF_CLOSE: (7), (11), (98) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | |            #1172.
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | |   (99)  all_58_14 = e0
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | REF_CLOSE: (59), (97), (99) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | |            #761.
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | |   (100)  all_56_14 = e0
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | COMBINE_EQS: (51), (100) imply:
% 204.18/34.98  | | | | | | | |   (101)  all_52_23 = e0
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | SIMP: (101) implies:
% 204.18/34.98  | | | | | | | |   (102)  all_52_23 = e0
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | REDUCE: (62), (102) imply:
% 204.18/34.98  | | | | | | | |   (103)   ~ (all_10_2 = e0)
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | SIMP: (103) implies:
% 204.18/34.98  | | | | | | | |   (104)   ~ (all_10_2 = e0)
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | GROUND_INST: instantiating (4) with all_10_2, all_52_30, e1, e1,
% 204.18/34.98  | | | | | | | |              simplifying with (61), (89) gives:
% 204.18/34.98  | | | | | | | |   (105)  all_52_30 = all_10_2
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, e0, e2, e2,
% 204.18/34.98  | | | | | | | |              simplifying with (16), (82) gives:
% 204.18/34.98  | | | | | | | |   (106)  all_4_2 = e0
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | COMBINE_EQS: (64), (106) imply:
% 204.18/34.98  | | | | | | | |   (107)  all_58_3 = e0
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | REDUCE: (65), (106) imply:
% 204.18/34.98  | | | | | | | |   (108)   ~ (all_52_3 = e0)
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | REDUCE: (50), (106) imply:
% 204.18/34.98  | | | | | | | |   (109)   ~ (all_52_9 = e0)
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | REDUCE: (66), (106) imply:
% 204.18/34.98  | | | | | | | |   (110)   ~ (all_52_19 = e0)
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | REDUCE: (58), (106) imply:
% 204.18/34.98  | | | | | | | |   (111)   ~ (all_52_27 = e0)
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | BETA: splitting (71) gives:
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | |   (112)  all_56_4 = e2
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | REF_CLOSE: (10), (75), (112) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | |            #1155.
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | |   (113)   ~ (all_56_4 = e2)
% 204.18/34.98  | | | | | | | | |   (114)  all_56_4 = e1 | all_56_4 = e0
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | BETA: splitting (114) gives:
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | |   (115)  all_56_4 = e1
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | COMBINE_EQS: (10), (115) imply:
% 204.18/34.98  | | | | | | | | | |   (116)  all_52_3 = e1
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | SIMP: (116) implies:
% 204.18/34.98  | | | | | | | | | |   (117)  all_52_3 = e1
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | COMBINE_EQS: (33), (117) imply:
% 204.18/34.98  | | | | | | | | | |   (118)  all_58_2 = e1
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | REDUCE: (8), (117) imply:
% 204.18/34.98  | | | | | | | | | |   (119)   ~ (all_52_19 = e1)
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | SIMP: (119) implies:
% 204.18/34.98  | | | | | | | | | |   (120)   ~ (all_52_19 = e1)
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | REDUCE: (21), (117) imply:
% 204.18/34.98  | | | | | | | | | |   (121)   ~ (all_52_27 = e1)
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | SIMP: (121) implies:
% 204.18/34.98  | | | | | | | | | |   (122)   ~ (all_52_27 = e1)
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | REDUCE: (75), (117) imply:
% 204.18/34.98  | | | | | | | | | |   (123)   ~ (e2 = e1)
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | SIMP: (123) implies:
% 204.18/34.98  | | | | | | | | | |   (124)   ~ (e2 = e1)
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | REDUCE: (39), (117) imply:
% 204.18/34.98  | | | | | | | | | |   (125)  op(e1, e1) = e2
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | BETA: splitting (1) gives:
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | |   (126)  all_58_9 = e0
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | COMBINE_EQS: (14), (126) imply:
% 204.18/34.98  | | | | | | | | | | |   (127)  all_52_25 = e0
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | REDUCE: (36), (127) imply:
% 204.18/34.98  | | | | | | | | | | |   (128)   ~ (e3 = e0)
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | REDUCE: (88), (127) imply:
% 204.18/34.98  | | | | | | | | | | |   (129)   ~ (e1 = e0)
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | GROUND_INST: instantiating (4) with all_10_2, e2, e1, e1,
% 204.18/34.98  | | | | | | | | | | |              simplifying with (61), (125) gives:
% 204.18/34.98  | | | | | | | | | | |   (130)  all_10_2 = e2
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | REDUCE: (47), (130) imply:
% 204.18/34.98  | | | | | | | | | | |   (131)   ~ (all_52_19 = e2)
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | BETA: splitting (67) gives:
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | |   (132)  all_58_2 = e2
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | REF_CLOSE: (118), (124), (132) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | | | | |            #1116.
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | |   (133)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | BETA: splitting (133) gives:
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | |   (134)  all_58_3 = e2
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | COMBINE_EQS: (107), (134) imply:
% 204.18/34.98  | | | | | | | | | | | | |   (135)  e2 = e0
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | SIMP: (135) implies:
% 204.18/34.98  | | | | | | | | | | | | |   (136)  e2 = e0
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | REDUCE: (38), (136) imply:
% 204.18/34.98  | | | | | | | | | | | | |   (137)  $false
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | |   (138)  all_58_5 = e2 | all_58_10 = e2
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | BETA: splitting (60) gives:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | |   (139)  all_58_10 = e3
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | REF_CLOSE: (55), (81), (131), (138), (139) are inconsistent
% 204.18/34.98  | | | | | | | | | | | | | |            by sub-proof #760.
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | |   (140)  all_58_11 = e3 | all_58_15 = e3
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (9), (11), (12), (15), (17),
% 204.18/34.98  | | | | | | | | | | | | | |            (20), (22), (23), (24), (29), (31), (32), (40),
% 204.18/34.98  | | | | | | | | | | | | | |            (43), (44), (46), (48), (49), (59), (61), (62),
% 204.18/34.98  | | | | | | | | | | | | | |            (68), (69), (140) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | | | | | | |            #758.
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | |   (141)   ~ (all_58_9 = e0)
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | REDUCE: (14), (141) imply:
% 204.18/34.98  | | | | | | | | | | |   (142)   ~ (all_52_25 = e0)
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | BETA: splitting (28) gives:
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | |   (143)  all_56_3 = e2
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | COMBINE_EQS: (52), (143) imply:
% 204.18/34.98  | | | | | | | | | | | |   (144)  all_52_25 = e2
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | REDUCE: (45), (144) imply:
% 204.18/34.98  | | | | | | | | | | | |   (145)   ~ (all_52_9 = e2)
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | REDUCE: (2), (144) imply:
% 204.18/34.98  | | | | | | | | | | | |   (146)   ~ (all_52_27 = e2)
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | SIMP: (146) implies:
% 204.18/34.98  | | | | | | | | | | | |   (147)   ~ (all_52_27 = e2)
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | BETA: splitting (13) gives:
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | |   (148)  all_56_7 = e3
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | COMBINE_EQS: (35), (148) imply:
% 204.18/34.98  | | | | | | | | | | | | |   (149)  all_52_27 = e3
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | SIMP: (149) implies:
% 204.18/34.98  | | | | | | | | | | | | |   (150)  all_52_27 = e3
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | REDUCE: (42), (150) imply:
% 204.18/34.98  | | | | | | | | | | | | |   (151)   ~ (all_52_19 = e3)
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | BETA: splitting (34) gives:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | |   (152)  all_56_6 = e3
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | REF_CLOSE: (41), (151), (152) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | | | | | | |            #957.
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | |   (153)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | |   (154)  all_56_6 = e2
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | COMBINE_EQS: (41), (154) imply:
% 204.18/34.98  | | | | | | | | | | | | | | |   (155)  all_52_19 = e2
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | SIMP: (155) implies:
% 204.18/34.98  | | | | | | | | | | | | | | |   (156)  all_52_19 = e2
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | REDUCE: (47), (156) imply:
% 204.18/34.98  | | | | | | | | | | | | | | |   (157)   ~ (all_10_2 = e2)
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | SIMP: (157) implies:
% 204.18/34.98  | | | | | | | | | | | | | | |   (158)   ~ (all_10_2 = e2)
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | |   (159)  all_58_1 = e1
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (159) imply:
% 204.18/34.98  | | | | | | | | | | | | | | | |   (160)  all_52_9 = e1
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | | REDUCE: (27), (160) imply:
% 204.18/34.98  | | | | | | | | | | | | | | | |   (161)  op(e1, e1) = all_52_8
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (61), (125), (158), (161) are inconsistent by
% 204.18/34.98  | | | | | | | | | | | | | | | |            sub-proof #962.
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | |   (162)   ~ (all_58_1 = e1)
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | | REDUCE: (6), (162) imply:
% 204.18/34.98  | | | | | | | | | | | | | | | |   (163)   ~ (all_52_9 = e1)
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | | REF_CLOSE: (56), (57), (109), (145), (163) are inconsistent
% 204.18/34.98  | | | | | | | | | | | | | | | |            by sub-proof #1314.
% 204.18/34.98  | | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | |   (164)  all_56_6 = e1 | all_56_6 = e0
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | | REF_CLOSE: (41), (110), (120), (164) are inconsistent by
% 204.18/34.98  | | | | | | | | | | | | | | |            sub-proof #757.
% 204.18/34.98  | | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | |   (165)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | BETA: splitting (165) gives:
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | Case 1:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | |   (166)  all_56_7 = e2
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | REF_CLOSE: (35), (147), (166) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | | | | | | |            #918.
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | |   (167)  all_56_7 = e1 | all_56_7 = e0
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (122), (167) are inconsistent by
% 204.18/34.98  | | | | | | | | | | | | | |            sub-proof #902.
% 204.18/34.98  | | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | |   (168)  all_56_3 = e1 | all_56_3 = e0
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | | REF_CLOSE: (52), (88), (142), (168) are inconsistent by
% 204.18/34.98  | | | | | | | | | | | |            sub-proof #1330.
% 204.18/34.98  | | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | Case 2:
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | |   (169)  all_56_4 = e0
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | | REF_CLOSE: (10), (108), (169) are inconsistent by sub-proof
% 204.18/34.98  | | | | | | | | | |            #1309.
% 204.18/34.98  | | | | | | | | | | 
% 204.18/34.98  | | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | | 
% 204.18/34.98  | | | | | | | | End of split
% 204.18/34.98  | | | | | | | | 
% 204.18/34.98  | | | | | | | End of split
% 204.18/34.98  | | | | | | | 
% 204.18/34.98  | | | | | | End of split
% 204.18/34.98  | | | | | | 
% 204.18/34.98  | | | | | End of split
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | Case 2:
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | |   (170)  all_56_15 = e0
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | | REF_CLOSE: (23), (32), (170) are inconsistent by sub-proof #1162.
% 204.18/34.98  | | | | | 
% 204.18/34.98  | | | | End of split
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | End of split
% 204.18/34.98  | | | 
% 204.18/34.98  | | Case 2:
% 204.18/34.98  | | | 
% 204.18/34.98  | | |   (171)   ~ (all_58_12 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (29), (171) imply:
% 204.18/34.98  | | |   (172)   ~ (all_52_7 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REF_CLOSE: (3), (4), (5), (7), (11), (15), (22), (29), (31), (40), (43),
% 204.18/34.98  | | |            (49), (59), (61), (62), (172) are inconsistent by sub-proof
% 204.18/34.98  | | |            #1169.
% 204.18/34.98  | | | 
% 204.18/34.98  | | End of split
% 204.18/34.98  | | 
% 204.18/34.98  | End of split
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #757 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)  all_56_6 = e1 | all_56_6 = e0
% 204.18/34.98    (2)  all_56_6 = all_52_19
% 204.18/34.98    (3)   ~ (all_52_19 = e1)
% 204.18/34.98    (4)   ~ (all_52_19 = e0)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | BETA: splitting (1) gives:
% 204.18/34.98  | 
% 204.18/34.98  | Case 1:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (5)  all_56_6 = e1
% 204.18/34.98  | | 
% 204.18/34.98  | | COMBINE_EQS: (2), (5) imply:
% 204.18/34.98  | |   (6)  all_52_19 = e1
% 204.18/34.98  | | 
% 204.18/34.98  | | SIMP: (6) implies:
% 204.18/34.98  | |   (7)  all_52_19 = e1
% 204.18/34.98  | | 
% 204.18/34.98  | | REDUCE: (3), (7) imply:
% 204.18/34.98  | |   (8)  $false
% 204.18/34.98  | | 
% 204.18/34.98  | | CLOSE: (8) is inconsistent.
% 204.18/34.98  | | 
% 204.18/34.98  | Case 2:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (9)  all_56_6 = e0
% 204.18/34.98  | | 
% 204.18/34.98  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #952.
% 204.18/34.98  | | 
% 204.18/34.98  | End of split
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #758 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)  all_58_14 = all_52_23
% 204.18/34.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.98    (3)  op(all_52_7, all_52_7) = e0
% 204.18/34.98    (4)   ~ (e3 = e0)
% 204.18/34.98    (5)  op(all_14_2, e0) = all_14_1
% 204.18/34.98    (6)  all_58_13 = e3
% 204.18/34.98    (7)  op(e0, all_14_1) = all_14_0
% 204.18/34.98    (8)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.98    (9)  all_58_11 = all_52_29
% 204.18/34.98    (10)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.98    (11)  op(e0, e0) = all_14_2
% 204.18/34.98    (12)  all_56_15 = all_14_2
% 204.18/34.98    (13)  op(e1, e0) = all_52_29
% 204.18/34.98    (14)  all_58_11 = e3 | all_58_15 = e3
% 204.18/34.98    (15)  all_58_12 = all_52_7
% 204.18/34.98    (16)   ~ (all_52_7 = all_14_2)
% 204.18/34.98    (17)   ~ (all_14_2 = e0)
% 204.18/34.98    (18)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.98    (19)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/34.98    (20)  op(e0, e3) = all_52_7
% 204.18/34.98    (21)  all_58_15 = all_14_2
% 204.18/34.98    (22)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/34.98    (23)  all_56_12 = all_52_7
% 204.18/34.98    (24)   ~ (e1 = e0)
% 204.18/34.98    (25)  op(e1, e1) = all_10_2
% 204.18/34.98    (26)   ~ (all_52_23 = all_10_2)
% 204.18/34.98    (27)   ~ (all_14_0 = e2)
% 204.18/34.98    (28)   ~ (all_14_2 = e3)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | BETA: splitting (14) gives:
% 204.18/34.98  | 
% 204.18/34.98  | Case 1:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (29)  all_58_11 = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | COMBINE_EQS: (9), (29) imply:
% 204.18/34.98  | |   (30)  all_52_29 = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | SIMP: (30) implies:
% 204.18/34.98  | |   (31)  all_52_29 = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | REDUCE: (13), (31) imply:
% 204.18/34.98  | |   (32)  op(e1, e0) = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | BETA: splitting (10) gives:
% 204.18/34.98  | | 
% 204.18/34.98  | | Case 1:
% 204.18/34.98  | | | 
% 204.18/34.98  | | |   (33)  all_58_12 = e2
% 204.18/34.98  | | | 
% 204.18/34.98  | | | COMBINE_EQS: (15), (33) imply:
% 204.18/34.98  | | |   (34)  all_52_7 = e2
% 204.18/34.98  | | | 
% 204.18/34.98  | | | SIMP: (34) implies:
% 204.18/34.98  | | |   (35)  all_52_7 = e2
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (16), (35) imply:
% 204.18/34.98  | | |   (36)   ~ (all_14_2 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REF_CLOSE: (2), (3), (5), (7), (8), (11), (12), (16), (17), (20), (22),
% 204.18/34.98  | | |            (23), (27), (32), (36) are inconsistent by sub-proof #759.
% 204.18/34.98  | | | 
% 204.18/34.98  | | Case 2:
% 204.18/34.98  | | | 
% 204.18/34.98  | | |   (37)   ~ (all_58_12 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (15), (37) imply:
% 204.18/34.98  | | |   (38)   ~ (all_52_7 = e2)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (11), (15), (16), (18), (19),
% 204.18/34.98  | | |            (23), (24), (25), (26), (38) are inconsistent by sub-proof
% 204.18/34.98  | | |            #1169.
% 204.18/34.98  | | | 
% 204.18/34.98  | | End of split
% 204.18/34.98  | | 
% 204.18/34.98  | Case 2:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (39)  all_58_15 = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | COMBINE_EQS: (21), (39) imply:
% 204.18/34.98  | |   (40)  all_14_2 = e3
% 204.18/34.98  | | 
% 204.18/34.98  | | REDUCE: (28), (40) imply:
% 204.18/34.98  | |   (41)  $false
% 204.18/34.98  | | 
% 204.18/34.98  | | CLOSE: (41) is inconsistent.
% 204.18/34.98  | | 
% 204.18/34.98  | End of split
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #759 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.98    (2)  op(all_52_7, all_52_7) = e0
% 204.18/34.98    (3)  op(all_14_2, e0) = all_14_1
% 204.18/34.98    (4)  op(e0, all_14_1) = all_14_0
% 204.18/34.98    (5)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.98    (6)  op(e0, e0) = all_14_2
% 204.18/34.98    (7)  all_56_15 = all_14_2
% 204.18/34.98    (8)   ~ (all_52_7 = all_14_2)
% 204.18/34.98    (9)   ~ (all_14_2 = e0)
% 204.18/34.98    (10)   ~ (all_14_2 = e2)
% 204.18/34.98    (11)  op(e0, e3) = all_52_7
% 204.18/34.98    (12)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/34.98    (13)  all_56_12 = all_52_7
% 204.18/34.98    (14)  op(e1, e0) = e3
% 204.18/34.98    (15)   ~ (all_14_0 = e2)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | SIMP: (10) implies:
% 204.18/34.98  |   (16)   ~ (all_14_2 = e2)
% 204.18/34.98  | 
% 204.18/34.98  | BETA: splitting (12) gives:
% 204.18/34.98  | 
% 204.18/34.98  | Case 1:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (17)  all_56_15 = e2
% 204.18/34.98  | | 
% 204.18/34.98  | | REF_CLOSE: (7), (16), (17) are inconsistent by sub-proof #762.
% 204.18/34.98  | | 
% 204.18/34.98  | Case 2:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (18)  all_56_15 = e1 | all_56_15 = e0
% 204.18/34.98  | | 
% 204.18/34.98  | | BETA: splitting (18) gives:
% 204.18/34.98  | | 
% 204.18/34.98  | | Case 1:
% 204.18/34.98  | | | 
% 204.18/34.98  | | |   (19)  all_56_15 = e1
% 204.18/34.98  | | | 
% 204.18/34.98  | | | COMBINE_EQS: (7), (19) imply:
% 204.18/34.98  | | |   (20)  all_14_2 = e1
% 204.18/34.98  | | | 
% 204.18/34.98  | | | SIMP: (20) implies:
% 204.18/34.98  | | |   (21)  all_14_2 = e1
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (8), (21) imply:
% 204.18/34.98  | | |   (22)   ~ (all_52_7 = e1)
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (3), (21) imply:
% 204.18/34.98  | | |   (23)  op(e1, e0) = all_14_1
% 204.18/34.98  | | | 
% 204.18/34.98  | | | GROUND_INST: instantiating (1) with e3, all_14_1, e0, e1, simplifying with
% 204.18/34.98  | | |              (14), (23) gives:
% 204.18/34.98  | | |   (24)  all_14_1 = e3
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REDUCE: (4), (24) imply:
% 204.18/34.98  | | |   (25)  op(e0, e3) = all_14_0
% 204.18/34.98  | | | 
% 204.18/34.98  | | | GROUND_INST: instantiating (1) with all_52_7, all_14_0, e3, e0,
% 204.18/34.98  | | |              simplifying with (11), (25) gives:
% 204.18/34.98  | | |   (26)  all_52_7 = all_14_0
% 204.18/34.98  | | | 
% 204.18/34.98  | | | COMBINE_EQS: (13), (26) imply:
% 204.18/34.98  | | |   (27)  all_56_12 = all_14_0
% 204.18/34.98  | | | 
% 204.18/34.98  | | | BETA: splitting (5) gives:
% 204.18/34.98  | | | 
% 204.18/34.98  | | | Case 1:
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | |   (28)  all_56_12 = e2
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | COMBINE_EQS: (27), (28) imply:
% 204.18/34.98  | | | |   (29)  all_14_0 = e2
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | SIMP: (29) implies:
% 204.18/34.98  | | | |   (30)  all_14_0 = e2
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | REDUCE: (15), (30) imply:
% 204.18/34.98  | | | |   (31)  $false
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | CLOSE: (31) is inconsistent.
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | Case 2:
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | |   (32)  all_56_12 = e1 | all_56_12 = e0
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | | REF_CLOSE: (1), (2), (6), (8), (13), (22), (32) are inconsistent by
% 204.18/34.98  | | | |            sub-proof #1177.
% 204.18/34.98  | | | | 
% 204.18/34.98  | | | End of split
% 204.18/34.98  | | | 
% 204.18/34.98  | | Case 2:
% 204.18/34.98  | | | 
% 204.18/34.98  | | |   (33)  all_56_15 = e0
% 204.18/34.98  | | | 
% 204.18/34.98  | | | REF_CLOSE: (7), (9), (33) are inconsistent by sub-proof #1162.
% 204.18/34.98  | | | 
% 204.18/34.98  | | End of split
% 204.18/34.98  | | 
% 204.18/34.98  | End of split
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #760 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)  all_58_5 = e2 | all_58_10 = e2
% 204.18/34.98    (2)  all_58_10 = e3
% 204.18/34.98    (3)  all_58_5 = all_52_19
% 204.18/34.98    (4)   ~ (all_52_19 = e2)
% 204.18/34.98    (5)   ~ (e3 = e2)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | BETA: splitting (1) gives:
% 204.18/34.98  | 
% 204.18/34.98  | Case 1:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (6)  all_58_5 = e2
% 204.18/34.98  | | 
% 204.18/34.98  | | COMBINE_EQS: (3), (6) imply:
% 204.18/34.98  | |   (7)  all_52_19 = e2
% 204.18/34.98  | | 
% 204.18/34.98  | | SIMP: (7) implies:
% 204.18/34.98  | |   (8)  all_52_19 = e2
% 204.18/34.98  | | 
% 204.18/34.98  | | REDUCE: (4), (8) imply:
% 204.18/34.98  | |   (9)  $false
% 204.18/34.98  | | 
% 204.18/34.98  | | CLOSE: (9) is inconsistent.
% 204.18/34.98  | | 
% 204.18/34.98  | Case 2:
% 204.18/34.98  | | 
% 204.18/34.98  | |   (10)  all_58_10 = e2
% 204.18/34.98  | | 
% 204.18/34.98  | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #1220.
% 204.18/34.98  | | 
% 204.18/34.98  | End of split
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #761 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)  all_58_14 = e1
% 204.18/34.98    (2)  all_58_14 = e0
% 204.18/34.98    (3)   ~ (e1 = e0)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | COMBINE_EQS: (1), (2) imply:
% 204.18/34.98  |   (4)  e1 = e0
% 204.18/34.98  | 
% 204.18/34.98  | SIMP: (4) implies:
% 204.18/34.98  |   (5)  e1 = e0
% 204.18/34.98  | 
% 204.18/34.98  | REDUCE: (3), (5) imply:
% 204.18/34.98  |   (6)  $false
% 204.18/34.98  | 
% 204.18/34.98  | CLOSE: (6) is inconsistent.
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #762 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)  all_56_15 = all_14_2
% 204.18/34.98    (2)  all_56_15 = e2
% 204.18/34.98    (3)   ~ (all_14_2 = e2)
% 204.18/34.98  
% 204.18/34.98  Begin of proof
% 204.18/34.98  | 
% 204.18/34.98  | COMBINE_EQS: (1), (2) imply:
% 204.18/34.98  |   (4)  all_14_2 = e2
% 204.18/34.98  | 
% 204.18/34.98  | SIMP: (4) implies:
% 204.18/34.98  |   (5)  all_14_2 = e2
% 204.18/34.98  | 
% 204.18/34.98  | REDUCE: (3), (5) imply:
% 204.18/34.98  |   (6)  $false
% 204.18/34.98  | 
% 204.18/34.98  | CLOSE: (6) is inconsistent.
% 204.18/34.98  | 
% 204.18/34.98  End of proof
% 204.18/34.98  
% 204.18/34.98  Sub-proof #763 shows that the following formulas are inconsistent:
% 204.18/34.98  ----------------------------------------------------------------
% 204.18/34.98    (1)   ~ (all_52_15 = all_52_23)
% 204.18/34.98    (2)   ~ (all_52_25 = all_52_27)
% 204.18/34.98    (3)  all_58_14 = all_52_23
% 204.18/34.98    (4)   ~ (e3 = e1)
% 204.18/34.98    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.98    (6)   ~ (all_52_5 = all_52_13)
% 204.18/34.98    (7)  all_58_1 = all_52_9
% 204.18/34.98    (8)   ~ (e3 = e0)
% 204.18/34.98    (9)  op(e2, e3) = all_52_3
% 204.18/34.98    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.98    (11)  op(e0, e2) = all_52_15
% 204.18/34.98    (12)   ~ (all_52_7 = all_52_15)
% 204.18/34.98    (13)   ~ (all_52_3 = all_52_19)
% 204.18/34.98    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.18/34.98    (15)   ~ (all_52_17 = all_52_25)
% 204.18/34.98    (16)   ~ (all_52_3 = all_6_2)
% 204.18/34.98    (17)  all_58_0 = all_6_2
% 204.18/34.98    (18)  all_56_4 = all_52_3
% 204.18/34.98    (19)   ~ (all_52_17 = all_10_2)
% 204.18/34.98    (20)  op(e3, e0) = all_52_25
% 204.18/34.98    (21)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.18/34.98    (22)  op(all_52_19, all_52_19) = all_52_18
% 204.18/34.98    (23)  all_58_13 = all_52_15
% 204.18/34.98    (24)  op(all_10_2, all_10_2) = all_52_20
% 204.18/34.98    (25)  all_58_9 = all_52_25
% 204.18/34.98    (26)   ~ (all_6_1 = e1)
% 204.18/34.98    (27)  op(e2, all_4_1) = e3
% 204.18/34.98    (28)  op(all_52_27, all_52_27) = all_52_26
% 204.18/34.98    (29)  op(e1, e3) = all_52_5
% 204.18/34.98    (30)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.18/34.98    (31)  op(e2, e2) = all_4_2
% 204.18/34.98    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/34.98    (33)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 204.18/34.98    (34)  all_58_11 = all_52_29
% 204.18/34.98    (35)  all_56_5 = all_4_2
% 204.18/34.98    (36)   ~ (all_52_9 = all_52_15)
% 204.18/34.98    (37)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.98    (38)  op(all_10_2, e1) = all_10_1
% 204.18/34.98    (39)  op(all_6_2, all_6_2) = all_52_0
% 204.18/34.98    (40)   ~ (all_52_7 = all_6_2)
% 204.18/34.98    (41)  op(e0, e0) = all_14_2
% 204.18/34.98    (42)   ~ (all_52_15 = e0)
% 204.18/34.98    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/34.98    (44)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/34.98    (45)  all_58_15 = e0
% 204.18/34.98    (46)  all_56_11 = all_52_29
% 204.18/34.98    (47)   ~ (all_52_25 = e0)
% 204.18/34.98    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.18/34.98    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/34.98    (50)   ~ (e2 = e1)
% 204.18/34.98    (51)   ~ (all_52_13 = all_10_2)
% 204.18/34.98    (52)  op(e0, e0) = e0
% 204.18/34.98    (53)   ~ (all_6_0 = e1)
% 204.18/34.98    (54)  all_58_10 = all_52_27
% 204.18/34.98    (55)  all_56_8 = all_52_5
% 204.18/34.98    (56)  op(all_52_9, all_52_9) = all_52_8
% 204.18/34.98    (57)  op(all_52_15, all_52_15) = all_52_14
% 204.18/34.98    (58)   ~ (all_52_19 = all_52_23)
% 204.18/34.98    (59)   ~ (all_52_25 = all_52_29)
% 204.18/34.98    (60)   ~ (all_52_29 = all_10_2)
% 204.18/34.98    (61)  all_58_7 = all_52_13
% 204.18/34.98    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.98    (63)   ~ (all_52_5 = all_52_7)
% 204.18/34.98    (64)  all_58_12 = all_52_7
% 204.18/34.98    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/34.98    (66)  all_58_2 = all_52_3
% 204.18/34.98    (67)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.98    (68)  all_56_2 = all_52_17
% 204.18/34.98    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/34.98    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/34.98    (71)  op(e3, all_6_1) = all_6_0
% 204.18/34.98    (72)  all_56_7 = all_52_27
% 204.18/34.98    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/34.98    (74)   ~ (e2 = e0)
% 204.18/34.98    (75)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/34.98    (76)  op(all_4_2, e2) = all_4_1
% 204.18/34.98    (77)   ~ (all_52_5 = all_52_29)
% 204.18/34.98    (78)   ~ (all_52_29 = e0)
% 204.18/34.98    (79)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.98    (80)  all_56_6 = all_52_19
% 204.18/34.98    (81)   ~ (all_52_19 = all_52_27)
% 204.18/34.98    (82)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/34.98    (83)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.18/34.98    (84)   ~ (all_6_0 = e2)
% 204.18/34.98    (85)   ~ (all_52_13 = all_4_2)
% 204.18/34.98    (86)  op(e3, e1) = all_52_17
% 204.18/34.98    (87)  op(e0, e3) = all_52_7
% 204.18/34.98    (88)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/34.98    (89)   ~ (all_52_9 = all_52_25)
% 204.18/34.98    (90)   ~ (all_52_19 = all_10_2)
% 204.18/34.98    (91)  op(all_52_23, all_52_23) = all_52_22
% 204.18/34.98    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/34.98    (93)  all_58_8 = all_10_2
% 204.18/34.98    (94)   ~ (all_52_23 = e0)
% 204.18/34.98    (95)   ~ (all_52_5 = all_10_2)
% 204.18/34.98    (96)  op(all_52_29, all_52_29) = all_52_28
% 204.18/34.98    (97)  all_56_12 = all_52_7
% 204.18/34.98    (98)  op(all_52_17, all_52_17) = all_52_16
% 204.18/34.98    (99)   ~ (all_52_25 = all_6_2)
% 204.18/34.99    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/34.99    (101)   ~ (all_52_5 = all_6_2)
% 204.18/34.99    (102)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.18/34.99    (103)   ~ (all_52_9 = all_6_2)
% 204.18/34.99    (104)   ~ (all_52_13 = all_52_15)
% 204.18/34.99    (105)   ~ (all_52_27 = e0)
% 204.18/34.99    (106)  op(e3, e3) = all_6_2
% 204.18/34.99    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/34.99    (108)   ~ (all_52_27 = all_14_2)
% 204.18/34.99    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/34.99    (110)  all_56_14 = all_52_23
% 204.18/34.99    (111)  op(all_4_2, all_4_2) = all_52_10
% 204.18/34.99    (112)  all_56_3 = all_52_25
% 204.18/34.99    (113)   ~ (all_52_3 = all_52_7)
% 204.18/34.99    (114)  all_58_5 = all_52_19
% 204.18/34.99    (115)  all_56_1 = all_52_9
% 204.18/34.99    (116)   ~ (all_52_15 = all_4_2)
% 204.18/34.99    (117)  all_58_6 = all_52_5
% 204.18/34.99    (118)  op(e3, e2) = all_52_9
% 204.18/34.99    (119)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/34.99    (120)   ~ (all_52_17 = all_6_2)
% 204.18/34.99    (121)   ~ (e1 = e0)
% 204.18/34.99    (122)   ~ (e3 = e2)
% 204.18/34.99    (123)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/34.99    (124)   ~ (all_52_9 = all_52_17)
% 204.18/34.99    (125)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/34.99    (126)  op(all_52_13, all_52_13) = all_52_12
% 204.18/34.99    (127)   ~ (all_6_1 = e2)
% 204.18/34.99    (128)  op(e1, e1) = all_10_2
% 204.18/34.99    (129)   ~ (all_52_23 = all_10_2)
% 204.18/34.99    (130)   ~ (all_52_7 = all_52_23)
% 204.18/34.99    (131)   ~ (all_52_17 = all_52_19)
% 204.18/34.99    (132)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/34.99           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/34.99    (133)  all_58_3 = all_4_2
% 204.18/34.99    (134)  all_56_13 = all_52_15
% 204.18/34.99    (135)   ~ (all_52_3 = all_4_2)
% 204.18/34.99    (136)   ~ (all_52_19 = all_4_2)
% 204.18/34.99    (137)   ~ (all_52_17 = all_52_23)
% 204.18/34.99    (138)  op(all_6_2, e3) = all_6_1
% 204.18/34.99    (139)   ~ (all_52_13 = all_52_29)
% 204.18/34.99    (140)  all_58_4 = all_52_17
% 204.18/34.99    (141)   ~ (all_52_7 = e0)
% 204.18/34.99    (142)  op(all_52_25, all_52_25) = all_52_24
% 204.18/34.99  
% 204.18/34.99  Begin of proof
% 204.18/34.99  | 
% 204.18/34.99  | BETA: splitting (132) gives:
% 204.18/34.99  | 
% 204.18/34.99  | Case 1:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (143)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.18/34.99  | | 
% 204.18/34.99  | | ALPHA: (143) implies:
% 204.18/34.99  | |   (144)  all_52_22 = e0
% 204.18/34.99  | |   (145)  all_52_20 = e1
% 204.18/34.99  | |   (146)  all_52_18 = e2
% 204.18/34.99  | |   (147)  all_52_16 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (98), (147) imply:
% 204.18/34.99  | |   (148)  op(all_52_17, all_52_17) = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (22), (146) imply:
% 204.18/34.99  | |   (149)  op(all_52_19, all_52_19) = e2
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (91), (144) imply:
% 204.18/34.99  | |   (150)  op(all_52_23, all_52_23) = e0
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (24), (145) imply:
% 204.18/34.99  | |   (151)  op(all_10_2, all_10_2) = e1
% 204.18/34.99  | | 
% 204.18/34.99  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.18/34.99  | |            (14), (15), (16), (17), (19), (21), (23), (25), (26), (27), (28),
% 204.18/34.99  | |            (29), (30), (31), (34), (35), (37), (38), (40), (42), (45), (47),
% 204.18/34.99  | |            (48), (49), (50), (51), (52), (54), (55), (56), (57), (58), (59),
% 204.18/34.99  | |            (60), (61), (62), (63), (64), (65), (67), (68), (69), (72), (74),
% 204.18/34.99  | |            (75), (76), (79), (80), (81), (85), (86), (87), (88), (89), (90),
% 204.18/34.99  | |            (92), (93), (94), (95), (96), (97), (99), (100), (101), (103),
% 204.18/34.99  | |            (106), (107), (109), (110), (111), (112), (114), (115), (117),
% 204.18/34.99  | |            (118), (119), (120), (122), (123), (124), (125), (126), (127),
% 204.18/34.99  | |            (128), (129), (130), (131), (133), (134), (136), (137), (138),
% 204.18/34.99  | |            (139), (140), (141), (142), (148), (149), (150), (151) are
% 204.18/34.99  | |            inconsistent by sub-proof #764.
% 204.18/34.99  | | 
% 204.18/34.99  | Case 2:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (152)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.18/34.99  | | 
% 204.18/34.99  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (14), (15), (16),
% 204.18/34.99  | |            (17), (18), (19), (20), (21), (23), (25), (28), (29), (31), (32),
% 204.18/34.99  | |            (33), (34), (36), (37), (39), (40), (41), (42), (43), (44), (45),
% 204.18/34.99  | |            (46), (47), (48), (50), (51), (53), (54), (57), (59), (60), (61),
% 204.18/34.99  | |            (63), (64), (65), (66), (70), (71), (72), (73), (74), (77), (78),
% 204.18/34.99  | |            (79), (82), (83), (84), (90), (91), (93), (94), (95), (96), (97),
% 204.18/34.99  | |            (99), (100), (101), (102), (104), (105), (106), (107), (108),
% 204.18/34.99  | |            (109), (112), (113), (114), (116), (117), (119), (121), (122),
% 204.18/34.99  | |            (127), (128), (129), (130), (133), (134), (135), (138), (140),
% 204.18/34.99  | |            (141), (142), (152) are inconsistent by sub-proof #1203.
% 204.18/34.99  | | 
% 204.18/34.99  | End of split
% 204.18/34.99  | 
% 204.18/34.99  End of proof
% 204.18/34.99  
% 204.18/34.99  Sub-proof #764 shows that the following formulas are inconsistent:
% 204.18/34.99  ----------------------------------------------------------------
% 204.18/34.99    (1)   ~ (all_52_15 = all_52_23)
% 204.18/34.99    (2)   ~ (all_52_25 = all_52_27)
% 204.18/34.99    (3)  all_58_14 = all_52_23
% 204.18/34.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.99    (5)   ~ (all_52_5 = all_52_13)
% 204.18/34.99    (6)  all_58_1 = all_52_9
% 204.18/34.99    (7)   ~ (e3 = e0)
% 204.18/34.99    (8)  op(all_52_23, all_52_23) = e0
% 204.18/34.99    (9)  op(e2, e3) = all_52_3
% 204.18/34.99    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.99    (11)  op(e0, e2) = all_52_15
% 204.18/34.99    (12)   ~ (all_52_7 = all_52_15)
% 204.18/34.99    (13)   ~ (all_52_3 = all_52_19)
% 204.18/34.99    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.18/34.99    (15)   ~ (all_52_17 = all_52_25)
% 204.18/34.99    (16)   ~ (all_52_3 = all_6_2)
% 204.18/34.99    (17)  all_58_0 = all_6_2
% 204.18/34.99    (18)   ~ (all_52_17 = all_10_2)
% 204.18/34.99    (19)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.18/34.99    (20)  all_58_13 = all_52_15
% 204.18/34.99    (21)  all_58_9 = all_52_25
% 204.18/34.99    (22)   ~ (all_6_1 = e1)
% 204.18/34.99    (23)  op(e2, all_4_1) = e3
% 204.18/34.99    (24)  op(all_52_27, all_52_27) = all_52_26
% 204.18/34.99    (25)  op(e1, e3) = all_52_5
% 204.18/34.99    (26)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.18/34.99    (27)  op(e2, e2) = all_4_2
% 204.18/34.99    (28)  all_58_11 = all_52_29
% 204.18/34.99    (29)  all_56_5 = all_4_2
% 204.18/34.99    (30)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.99    (31)  op(all_10_2, e1) = all_10_1
% 204.18/34.99    (32)   ~ (all_52_7 = all_6_2)
% 204.18/34.99    (33)   ~ (all_52_15 = e0)
% 204.18/34.99    (34)  all_58_15 = e0
% 204.18/34.99    (35)   ~ (all_52_25 = e0)
% 204.18/34.99    (36)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.18/34.99    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/34.99    (38)   ~ (e2 = e1)
% 204.18/34.99    (39)   ~ (all_52_13 = all_10_2)
% 204.18/34.99    (40)  op(e0, e0) = e0
% 204.18/34.99    (41)  op(all_10_2, all_10_2) = e1
% 204.18/34.99    (42)  all_58_10 = all_52_27
% 204.18/34.99    (43)  all_56_8 = all_52_5
% 204.18/34.99    (44)  op(all_52_9, all_52_9) = all_52_8
% 204.18/34.99    (45)  op(all_52_15, all_52_15) = all_52_14
% 204.18/34.99    (46)   ~ (all_52_19 = all_52_23)
% 204.18/34.99    (47)   ~ (all_52_25 = all_52_29)
% 204.18/34.99    (48)   ~ (all_52_29 = all_10_2)
% 204.18/34.99    (49)  all_58_7 = all_52_13
% 204.18/34.99    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.99    (51)  op(all_52_19, all_52_19) = e2
% 204.18/34.99    (52)   ~ (all_52_5 = all_52_7)
% 204.18/34.99    (53)  all_58_12 = all_52_7
% 204.18/34.99    (54)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/34.99    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.99    (56)  all_56_2 = all_52_17
% 204.18/34.99    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/34.99    (58)  all_56_7 = all_52_27
% 204.18/34.99    (59)   ~ (e2 = e0)
% 204.18/34.99    (60)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/34.99    (61)  op(all_4_2, e2) = all_4_1
% 204.18/34.99    (62)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.99    (63)  all_56_6 = all_52_19
% 204.18/34.99    (64)   ~ (all_52_19 = all_52_27)
% 204.18/34.99    (65)   ~ (all_52_13 = all_4_2)
% 204.18/34.99    (66)  op(e3, e1) = all_52_17
% 204.18/34.99    (67)  op(e0, e3) = all_52_7
% 204.18/34.99    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/34.99    (69)   ~ (all_52_9 = all_52_25)
% 204.18/34.99    (70)   ~ (all_52_19 = all_10_2)
% 204.18/34.99    (71)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/34.99    (72)  all_58_8 = all_10_2
% 204.18/34.99    (73)   ~ (all_52_23 = e0)
% 204.18/34.99    (74)   ~ (all_52_5 = all_10_2)
% 204.18/34.99    (75)  op(all_52_29, all_52_29) = all_52_28
% 204.18/34.99    (76)  all_56_12 = all_52_7
% 204.18/34.99    (77)   ~ (all_52_25 = all_6_2)
% 204.18/34.99    (78)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/34.99    (79)   ~ (all_52_5 = all_6_2)
% 204.18/34.99    (80)   ~ (all_52_9 = all_6_2)
% 204.18/34.99    (81)  op(e3, e3) = all_6_2
% 204.18/34.99    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/34.99    (83)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/34.99    (84)  all_56_14 = all_52_23
% 204.18/34.99    (85)  op(all_4_2, all_4_2) = all_52_10
% 204.18/34.99    (86)  all_56_3 = all_52_25
% 204.18/34.99    (87)  all_58_5 = all_52_19
% 204.18/34.99    (88)  all_56_1 = all_52_9
% 204.18/34.99    (89)  op(all_52_17, all_52_17) = e3
% 204.18/34.99    (90)  all_58_6 = all_52_5
% 204.18/34.99    (91)  op(e3, e2) = all_52_9
% 204.18/34.99    (92)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/34.99    (93)   ~ (all_52_17 = all_6_2)
% 204.18/34.99    (94)   ~ (e3 = e2)
% 204.18/34.99    (95)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/34.99    (96)   ~ (all_52_9 = all_52_17)
% 204.18/34.99    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/34.99    (98)  op(all_52_13, all_52_13) = all_52_12
% 204.18/34.99    (99)   ~ (all_6_1 = e2)
% 204.18/34.99    (100)  op(e1, e1) = all_10_2
% 204.18/34.99    (101)   ~ (all_52_23 = all_10_2)
% 204.18/34.99    (102)   ~ (all_52_7 = all_52_23)
% 204.18/34.99    (103)   ~ (all_52_17 = all_52_19)
% 204.18/34.99    (104)  all_58_3 = all_4_2
% 204.18/34.99    (105)  all_56_13 = all_52_15
% 204.18/34.99    (106)   ~ (all_52_19 = all_4_2)
% 204.18/34.99    (107)   ~ (all_52_17 = all_52_23)
% 204.18/34.99    (108)  op(all_6_2, e3) = all_6_1
% 204.18/34.99    (109)   ~ (all_52_13 = all_52_29)
% 204.18/34.99    (110)  all_58_4 = all_52_17
% 204.18/34.99    (111)   ~ (all_52_7 = e0)
% 204.18/34.99    (112)  op(all_52_25, all_52_25) = all_52_24
% 204.18/34.99  
% 204.18/34.99  Begin of proof
% 204.18/34.99  | 
% 204.18/34.99  | BETA: splitting (36) gives:
% 204.18/34.99  | 
% 204.18/34.99  | Case 1:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (113)  all_56_13 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | REF_CLOSE: (1), (3), (4), (8), (9), (10), (11), (12), (13), (16), (20),
% 204.18/34.99  | |            (23), (27), (30), (34), (37), (38), (40), (41), (45), (46), (50),
% 204.18/34.99  | |            (53), (55), (56), (59), (61), (62), (63), (73), (76), (81), (84),
% 204.18/34.99  | |            (85), (89), (94), (100), (101), (102), (103), (105), (106),
% 204.18/34.99  | |            (107), (111), (113) are inconsistent by sub-proof #765.
% 204.18/34.99  | | 
% 204.18/34.99  | Case 2:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (114)   ~ (all_56_13 = e3)
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (105), (114) imply:
% 204.18/34.99  | |   (115)   ~ (all_52_15 = e3)
% 204.18/34.99  | | 
% 204.18/34.99  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), (15), (17),
% 204.18/34.99  | |            (18), (19), (20), (21), (22), (24), (25), (26), (28), (29), (31),
% 204.18/34.99  | |            (32), (33), (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 204.18/34.99  | |            (44), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 204.18/34.99  | |            (58), (60), (61), (64), (65), (66), (67), (68), (69), (70), (71),
% 204.18/34.99  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 204.18/34.99  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 204.18/34.99  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (104),
% 204.18/34.99  | |            (106), (107), (108), (109), (110), (111), (112), (115) are
% 204.18/34.99  | |            inconsistent by sub-proof #1250.
% 204.18/34.99  | | 
% 204.18/34.99  | End of split
% 204.18/34.99  | 
% 204.18/34.99  End of proof
% 204.18/34.99  
% 204.18/34.99  Sub-proof #765 shows that the following formulas are inconsistent:
% 204.18/34.99  ----------------------------------------------------------------
% 204.18/34.99    (1)   ~ (all_52_15 = all_52_23)
% 204.18/34.99    (2)  all_58_14 = all_52_23
% 204.18/34.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.99    (4)  op(all_52_23, all_52_23) = e0
% 204.18/34.99    (5)  op(e2, e3) = all_52_3
% 204.18/34.99    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.99    (7)  op(e0, e2) = all_52_15
% 204.18/34.99    (8)   ~ (all_52_7 = all_52_15)
% 204.18/34.99    (9)   ~ (all_52_3 = all_52_19)
% 204.18/34.99    (10)   ~ (all_52_3 = all_6_2)
% 204.18/34.99    (11)  all_58_13 = all_52_15
% 204.18/34.99    (12)  op(e2, all_4_1) = e3
% 204.18/34.99    (13)  op(e2, e2) = all_4_2
% 204.18/34.99    (14)  all_56_13 = e3
% 204.18/34.99    (15)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.99    (16)  all_58_15 = e0
% 204.18/34.99    (17)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/34.99    (18)   ~ (e2 = e1)
% 204.18/34.99    (19)  op(e0, e0) = e0
% 204.18/34.99    (20)  op(all_10_2, all_10_2) = e1
% 204.18/34.99    (21)  op(all_52_15, all_52_15) = all_52_14
% 204.18/34.99    (22)   ~ (all_52_19 = all_52_23)
% 204.18/34.99    (23)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.99    (24)  all_58_12 = all_52_7
% 204.18/34.99    (25)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.99    (26)  all_56_2 = all_52_17
% 204.18/34.99    (27)   ~ (e2 = e0)
% 204.18/34.99    (28)  op(all_4_2, e2) = all_4_1
% 204.18/34.99    (29)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.99    (30)  all_56_6 = all_52_19
% 204.18/34.99    (31)   ~ (all_52_23 = e0)
% 204.18/34.99    (32)  all_56_12 = all_52_7
% 204.18/34.99    (33)  op(e3, e3) = all_6_2
% 204.18/34.99    (34)  all_56_14 = all_52_23
% 204.18/34.99    (35)  op(all_4_2, all_4_2) = all_52_10
% 204.18/34.99    (36)  op(all_52_17, all_52_17) = e3
% 204.18/34.99    (37)   ~ (e3 = e2)
% 204.18/34.99    (38)  op(e1, e1) = all_10_2
% 204.18/34.99    (39)   ~ (all_52_23 = all_10_2)
% 204.18/34.99    (40)   ~ (all_52_7 = all_52_23)
% 204.18/34.99    (41)   ~ (all_52_17 = all_52_19)
% 204.18/34.99    (42)  all_56_13 = all_52_15
% 204.18/34.99    (43)   ~ (all_52_19 = all_4_2)
% 204.18/34.99    (44)   ~ (all_52_17 = all_52_23)
% 204.18/34.99    (45)   ~ (all_52_7 = e0)
% 204.18/34.99  
% 204.18/34.99  Begin of proof
% 204.18/34.99  | 
% 204.18/34.99  | COMBINE_EQS: (14), (42) imply:
% 204.18/34.99  |   (46)  all_52_15 = e3
% 204.18/34.99  | 
% 204.18/34.99  | SIMP: (46) implies:
% 204.18/34.99  |   (47)  all_52_15 = e3
% 204.18/34.99  | 
% 204.18/34.99  | COMBINE_EQS: (11), (47) imply:
% 204.18/34.99  |   (48)  all_58_13 = e3
% 204.18/34.99  | 
% 204.18/34.99  | REDUCE: (8), (47) imply:
% 204.18/34.99  |   (49)   ~ (all_52_7 = e3)
% 204.18/34.99  | 
% 204.18/34.99  | REDUCE: (1), (47) imply:
% 204.18/34.99  |   (50)   ~ (all_52_23 = e3)
% 204.18/34.99  | 
% 204.18/34.99  | SIMP: (50) implies:
% 204.18/34.99  |   (51)   ~ (all_52_23 = e3)
% 204.18/34.99  | 
% 204.18/34.99  | REDUCE: (21), (47) imply:
% 204.18/34.99  |   (52)  op(e3, e3) = all_52_14
% 204.18/34.99  | 
% 204.18/34.99  | REDUCE: (7), (47) imply:
% 204.18/34.99  |   (53)  op(e0, e2) = e3
% 204.18/34.99  | 
% 204.18/34.99  | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (13), (15), (16), (17),
% 204.18/34.99  |            (18), (19), (20), (22), (23), (24), (25), (26), (27), (28), (29),
% 204.18/34.99  |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 204.18/34.99  |            (41), (43), (44), (45), (48), (49), (51), (52), (53) are
% 204.18/34.99  |            inconsistent by sub-proof #766.
% 204.18/34.99  | 
% 204.18/34.99  End of proof
% 204.18/34.99  
% 204.18/34.99  Sub-proof #766 shows that the following formulas are inconsistent:
% 204.18/34.99  ----------------------------------------------------------------
% 204.18/34.99    (1)  all_58_14 = all_52_23
% 204.18/34.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.99    (3)  op(all_52_23, all_52_23) = e0
% 204.18/34.99    (4)  op(e2, e3) = all_52_3
% 204.18/34.99    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.99    (6)   ~ (all_52_3 = all_52_19)
% 204.18/34.99    (7)   ~ (all_52_3 = all_6_2)
% 204.18/34.99    (8)  all_58_13 = e3
% 204.18/34.99    (9)  op(e0, e2) = e3
% 204.18/34.99    (10)  op(e2, all_4_1) = e3
% 204.18/34.99    (11)  op(e2, e2) = all_4_2
% 204.18/34.99    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.99    (13)  all_58_15 = e0
% 204.18/34.99    (14)  op(e3, e3) = all_52_14
% 204.18/34.99    (15)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/34.99    (16)   ~ (e2 = e1)
% 204.18/34.99    (17)  op(e0, e0) = e0
% 204.18/34.99    (18)  op(all_10_2, all_10_2) = e1
% 204.18/34.99    (19)   ~ (all_52_19 = all_52_23)
% 204.18/34.99    (20)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.99    (21)  all_58_12 = all_52_7
% 204.18/34.99    (22)   ~ (all_52_7 = e3)
% 204.18/34.99    (23)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.99    (24)  all_56_2 = all_52_17
% 204.18/34.99    (25)   ~ (e2 = e0)
% 204.18/34.99    (26)  op(all_4_2, e2) = all_4_1
% 204.18/34.99    (27)   ~ (all_52_23 = e3)
% 204.18/34.99    (28)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.99    (29)  all_56_6 = all_52_19
% 204.18/34.99    (30)   ~ (all_52_23 = e0)
% 204.18/34.99    (31)  all_56_12 = all_52_7
% 204.18/34.99    (32)  op(e3, e3) = all_6_2
% 204.18/34.99    (33)  all_56_14 = all_52_23
% 204.18/34.99    (34)  op(all_4_2, all_4_2) = all_52_10
% 204.18/34.99    (35)  op(all_52_17, all_52_17) = e3
% 204.18/34.99    (36)   ~ (e3 = e2)
% 204.18/34.99    (37)  op(e1, e1) = all_10_2
% 204.18/34.99    (38)   ~ (all_52_23 = all_10_2)
% 204.18/34.99    (39)   ~ (all_52_7 = all_52_23)
% 204.18/34.99    (40)   ~ (all_52_17 = all_52_19)
% 204.18/34.99    (41)   ~ (all_52_19 = all_4_2)
% 204.18/34.99    (42)   ~ (all_52_17 = all_52_23)
% 204.18/34.99    (43)   ~ (all_52_7 = e0)
% 204.18/34.99  
% 204.18/34.99  Begin of proof
% 204.18/34.99  | 
% 204.18/34.99  | GROUND_INST: instantiating (2) with all_6_2, all_52_14, e3, e3, simplifying
% 204.18/34.99  |              with (14), (32) gives:
% 204.18/34.99  |   (44)  all_52_14 = all_6_2
% 204.18/34.99  | 
% 204.18/34.99  | BETA: splitting (5) gives:
% 204.18/34.99  | 
% 204.18/34.99  | Case 1:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (45)  all_56_12 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | REF_CLOSE: (22), (31), (45) are inconsistent by sub-proof #1383.
% 204.18/34.99  | | 
% 204.18/34.99  | Case 2:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (46)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.99  | | 
% 204.18/34.99  | | BETA: splitting (20) gives:
% 204.18/34.99  | | 
% 204.18/34.99  | | Case 1:
% 204.18/34.99  | | | 
% 204.18/34.99  | | |   (47)  all_56_14 = e3
% 204.18/34.99  | | | 
% 204.18/34.99  | | | REF_CLOSE: (27), (33), (47) are inconsistent by sub-proof #1286.
% 204.18/34.99  | | | 
% 204.18/34.99  | | Case 2:
% 204.18/34.99  | | | 
% 204.18/34.99  | | |   (48)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.99  | | | 
% 204.18/34.99  | | | BETA: splitting (28) gives:
% 204.18/34.99  | | | 
% 204.18/34.99  | | | Case 1:
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | |   (49)  all_58_12 = e1
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | | BETA: splitting (12) gives:
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | | Case 1:
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | |   (50)  all_58_12 = e2
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | | COMBINE_EQS: (49), (50) imply:
% 204.18/34.99  | | | | |   (51)  e2 = e1
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | | REDUCE: (16), (51) imply:
% 204.18/34.99  | | | | |   (52)  $false
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | | CLOSE: (52) is inconsistent.
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | Case 2:
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | |   (53)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | | BETA: splitting (53) gives:
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | | Case 1:
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | |   (54)  all_58_13 = e2
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | | REF_CLOSE: (8), (36), (54) are inconsistent by sub-proof #1248.
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | Case 2:
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | |   (55)  all_58_14 = e2 | all_58_15 = e2
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | | BETA: splitting (55) gives:
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | | Case 1:
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | |   (56)  all_58_14 = e2
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | COMBINE_EQS: (1), (56) imply:
% 204.18/34.99  | | | | | | |   (57)  all_52_23 = e2
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | SIMP: (57) implies:
% 204.18/34.99  | | | | | | |   (58)  all_52_23 = e2
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (42), (58) imply:
% 204.18/34.99  | | | | | | |   (59)   ~ (all_52_17 = e2)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (19), (58) imply:
% 204.18/34.99  | | | | | | |   (60)   ~ (all_52_19 = e2)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (3), (58) imply:
% 204.18/34.99  | | | | | | |   (61)  op(e2, e2) = e0
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | GROUND_INST: instantiating (2) with all_4_2, e0, e2, e2,
% 204.18/34.99  | | | | | | |              simplifying with (11), (61) gives:
% 204.18/34.99  | | | | | | |   (62)  all_4_2 = e0
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (41), (62) imply:
% 204.18/34.99  | | | | | | |   (63)   ~ (all_52_19 = e0)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (34), (62) imply:
% 204.18/34.99  | | | | | | |   (64)  op(e0, e0) = all_52_10
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (26), (62) imply:
% 204.18/34.99  | | | | | | |   (65)  op(e0, e2) = all_4_1
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | GROUND_INST: instantiating (2) with e0, all_52_10, e0, e0,
% 204.18/34.99  | | | | | | |              simplifying with (17), (64) gives:
% 204.18/34.99  | | | | | | |   (66)  all_52_10 = e0
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | GROUND_INST: instantiating (2) with e3, all_4_1, e2, e0,
% 204.18/34.99  | | | | | | |              simplifying with (9), (65) gives:
% 204.18/34.99  | | | | | | |   (67)  all_4_1 = e3
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (10), (67) imply:
% 204.18/34.99  | | | | | | |   (68)  op(e2, e3) = e3
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | GROUND_INST: instantiating (2) with all_52_3, e3, e3, e2,
% 204.18/34.99  | | | | | | |              simplifying with (4), (68) gives:
% 204.18/34.99  | | | | | | |   (69)  all_52_3 = e3
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (6), (69) imply:
% 204.18/34.99  | | | | | | |   (70)   ~ (all_52_19 = e3)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | SIMP: (70) implies:
% 204.18/34.99  | | | | | | |   (71)   ~ (all_52_19 = e3)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REDUCE: (7), (69) imply:
% 204.18/34.99  | | | | | | |   (72)   ~ (all_6_2 = e3)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | SIMP: (72) implies:
% 204.18/34.99  | | | | | | |   (73)   ~ (all_6_2 = e3)
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | BETA: splitting (23) gives:
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | Case 1:
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | |   (74)  all_56_6 = e3
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | | REF_CLOSE: (29), (71), (74) are inconsistent by sub-proof #957.
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | Case 2:
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | |   (75)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | | BETA: splitting (75) gives:
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | | Case 1:
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | |   (76)  all_56_6 = e2
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | REF_CLOSE: (29), (60), (76) are inconsistent by sub-proof
% 204.18/34.99  | | | | | | | | |            #956.
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | Case 2:
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | |   (77)  all_56_6 = e1 | all_56_6 = e0
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | BETA: splitting (77) gives:
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | Case 1:
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | |   (78)  all_56_6 = e1
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | | COMBINE_EQS: (29), (78) imply:
% 204.18/34.99  | | | | | | | | | |   (79)  all_52_19 = e1
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | | SIMP: (79) implies:
% 204.18/34.99  | | | | | | | | | |   (80)  all_52_19 = e1
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | | REDUCE: (40), (80) imply:
% 204.18/34.99  | | | | | | | | | |   (81)   ~ (all_52_17 = e1)
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | | REF_CLOSE: (2), (15), (17), (24), (32), (35), (59), (73),
% 204.18/34.99  | | | | | | | | | |            (81) are inconsistent by sub-proof #1261.
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | Case 2:
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | |   (82)  all_56_6 = e0
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | | REF_CLOSE: (29), (63), (82) are inconsistent by sub-proof
% 204.18/34.99  | | | | | | | | | |            #952.
% 204.18/34.99  | | | | | | | | | | 
% 204.18/34.99  | | | | | | | | | End of split
% 204.18/34.99  | | | | | | | | | 
% 204.18/34.99  | | | | | | | | End of split
% 204.18/34.99  | | | | | | | | 
% 204.18/34.99  | | | | | | | End of split
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | Case 2:
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | |   (83)  all_58_15 = e2
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | | REF_CLOSE: (13), (25), (83) are inconsistent by sub-proof #1223.
% 204.18/34.99  | | | | | | | 
% 204.18/34.99  | | | | | | End of split
% 204.18/34.99  | | | | | | 
% 204.18/34.99  | | | | | End of split
% 204.18/34.99  | | | | | 
% 204.18/34.99  | | | | End of split
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | Case 2:
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | |   (84)   ~ (all_58_12 = e1)
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | | REDUCE: (21), (84) imply:
% 204.18/34.99  | | | |   (85)   ~ (all_52_7 = e1)
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | | REF_CLOSE: (2), (3), (17), (18), (30), (31), (33), (37), (38), (39),
% 204.18/34.99  | | | |            (43), (46), (48), (85) are inconsistent by sub-proof #1283.
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | End of split
% 204.18/34.99  | | | 
% 204.18/34.99  | | End of split
% 204.18/34.99  | | 
% 204.18/34.99  | End of split
% 204.18/34.99  | 
% 204.18/34.99  End of proof
% 204.18/34.99  
% 204.18/34.99  Sub-proof #767 shows that the following formulas are inconsistent:
% 204.18/34.99  ----------------------------------------------------------------
% 204.18/34.99    (1)  all_58_14 = all_52_23
% 204.18/34.99    (2)   ~ (e3 = e1)
% 204.18/34.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/34.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/34.99    (4)  op(all_52_7, all_52_7) = e0
% 204.18/34.99    (5)  op(all_52_5, all_52_5) = e1
% 204.18/34.99    (6)   ~ (e3 = e0)
% 204.18/34.99    (7)  op(e2, e3) = all_52_3
% 204.18/34.99    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.99    (9)  op(e0, e2) = all_52_15
% 204.18/34.99    (10)   ~ (all_52_7 = all_52_15)
% 204.18/34.99    (11)  all_58_0 = all_6_2
% 204.18/34.99    (12)  all_58_13 = all_52_15
% 204.18/34.99    (13)  op(e2, all_4_1) = e3
% 204.18/34.99    (14)  op(e2, e2) = all_4_2
% 204.18/34.99    (15)  op(all_10_2, e1) = all_10_1
% 204.18/34.99    (16)   ~ (all_52_7 = all_6_2)
% 204.18/34.99    (17)  op(e0, e0) = all_14_2
% 204.18/34.99    (18)  op(e0, e1) = all_52_23
% 204.18/34.99    (19)   ~ (all_52_15 = e0)
% 204.18/34.99    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/34.99    (21)  all_58_15 = e0
% 204.18/34.99    (22)   ~ (all_4_1 = e1)
% 204.18/34.99    (23)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.18/34.99    (24)  op(all_52_15, all_52_15) = all_52_14
% 204.18/34.99    (25)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/34.99    (26)  op(all_6_2, all_6_2) = e3
% 204.18/34.99    (27)  all_58_12 = all_52_7
% 204.18/34.99    (28)   ~ (all_52_7 = all_14_2)
% 204.18/34.99    (29)  all_58_2 = all_52_3
% 204.18/34.99    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/34.99    (31)  op(all_4_2, e2) = all_4_1
% 204.18/34.99    (32)  op(all_52_3, all_52_3) = e2
% 204.18/34.99    (33)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/34.99    (34)   ~ (all_10_1 = e2)
% 204.18/34.99    (35)   ~ (all_52_5 = all_10_2)
% 204.18/34.99    (36)  all_56_12 = all_52_7
% 204.18/34.99    (37)  op(e3, e3) = all_6_2
% 204.18/34.99    (38)  all_56_14 = all_52_23
% 204.18/34.99    (39)   ~ (all_10_1 = e3)
% 204.18/34.99    (40)  all_58_6 = all_52_5
% 204.18/34.99    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/34.99    (42)   ~ (e1 = e0)
% 204.18/34.99    (43)  op(e1, e1) = all_10_2
% 204.18/34.99    (44)   ~ (all_52_23 = all_10_2)
% 204.18/34.99    (45)   ~ (all_52_7 = all_52_23)
% 204.18/34.99    (46)  all_56_13 = all_52_15
% 204.18/34.99    (47)   ~ (all_52_3 = all_4_2)
% 204.18/34.99    (48)   ~ (all_52_7 = e0)
% 204.18/34.99  
% 204.18/34.99  Begin of proof
% 204.18/34.99  | 
% 204.18/34.99  | BETA: splitting (23) gives:
% 204.18/34.99  | 
% 204.18/34.99  | Case 1:
% 204.18/34.99  | | 
% 204.18/34.99  | |   (49)  all_56_13 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | COMBINE_EQS: (46), (49) imply:
% 204.18/34.99  | |   (50)  all_52_15 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | SIMP: (50) implies:
% 204.18/34.99  | |   (51)  all_52_15 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | COMBINE_EQS: (12), (51) imply:
% 204.18/34.99  | |   (52)  all_58_13 = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (10), (51) imply:
% 204.18/34.99  | |   (53)   ~ (all_52_7 = e3)
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (24), (51) imply:
% 204.18/34.99  | |   (54)  op(e3, e3) = all_52_14
% 204.18/34.99  | | 
% 204.18/34.99  | | REDUCE: (9), (51) imply:
% 204.18/34.99  | |   (55)  op(e0, e2) = e3
% 204.18/34.99  | | 
% 204.18/34.99  | | GROUND_INST: instantiating (3) with all_6_2, all_52_14, e3, e3, simplifying
% 204.18/34.99  | |              with (37), (54) gives:
% 204.18/34.99  | |   (56)  all_52_14 = all_6_2
% 204.18/34.99  | | 
% 204.18/34.99  | | BETA: splitting (8) gives:
% 204.18/34.99  | | 
% 204.18/34.99  | | Case 1:
% 204.18/34.99  | | | 
% 204.18/34.99  | | |   (57)  all_56_12 = e3
% 204.18/34.99  | | | 
% 204.18/34.99  | | | REF_CLOSE: (36), (53), (57) are inconsistent by sub-proof #1383.
% 204.18/34.99  | | | 
% 204.18/34.99  | | Case 2:
% 204.18/34.99  | | | 
% 204.18/34.99  | | |   (58)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/34.99  | | | 
% 204.18/34.99  | | | BETA: splitting (33) gives:
% 204.18/34.99  | | | 
% 204.18/34.99  | | | Case 1:
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | |   (59)  all_58_12 = e1
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | | COMBINE_EQS: (27), (59) imply:
% 204.18/34.99  | | | |   (60)  all_52_7 = e1
% 204.18/34.99  | | | | 
% 204.18/34.99  | | | | SIMP: (60) implies:
% 204.18/35.00  | | | |   (61)  all_52_7 = e1
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REF_CLOSE: (3), (4), (15), (18), (25), (34), (38), (39), (43), (44),
% 204.18/35.00  | | | |            (45), (61) are inconsistent by sub-proof #1379.
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | Case 2:
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | |   (62)   ~ (all_58_12 = e1)
% 204.18/35.00  | | | |   (63)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REDUCE: (27), (62) imply:
% 204.18/35.00  | | | |   (64)   ~ (all_52_7 = e1)
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REF_CLOSE: (2), (3), (4), (7), (13), (14), (16), (21), (31), (32), (36),
% 204.18/35.00  | | | |            (37), (42), (48), (52), (55), (58), (63), (64) are
% 204.18/35.00  | | | |            inconsistent by sub-proof #768.
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | End of split
% 204.18/35.00  | | | 
% 204.18/35.00  | | End of split
% 204.18/35.00  | | 
% 204.18/35.00  | Case 2:
% 204.18/35.00  | | 
% 204.18/35.00  | |   (65)   ~ (all_56_13 = e3)
% 204.18/35.00  | |   (66)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.18/35.00  | | 
% 204.18/35.00  | | REDUCE: (46), (65) imply:
% 204.18/35.00  | |   (67)   ~ (all_52_15 = e3)
% 204.18/35.00  | | 
% 204.18/35.00  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 204.18/35.00  | |            (16), (17), (18), (19), (20), (21), (22), (26), (27), (28), (29),
% 204.18/35.00  | |            (30), (31), (32), (33), (35), (36), (37), (39), (40), (41), (43),
% 204.18/35.00  | |            (45), (46), (47), (48), (66), (67) are inconsistent by sub-proof
% 204.18/35.00  | |            #1349.
% 204.18/35.00  | | 
% 204.18/35.00  | End of split
% 204.18/35.00  | 
% 204.18/35.00  End of proof
% 204.18/35.00  
% 204.18/35.00  Sub-proof #768 shows that the following formulas are inconsistent:
% 204.18/35.00  ----------------------------------------------------------------
% 204.18/35.00    (1)   ~ (e3 = e1)
% 204.18/35.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.00    (3)  op(all_52_7, all_52_7) = e0
% 204.18/35.00    (4)  op(e2, e3) = all_52_3
% 204.18/35.00    (5)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.00    (6)  all_58_13 = e3
% 204.18/35.00    (7)  op(e0, e2) = e3
% 204.18/35.00    (8)  op(e2, all_4_1) = e3
% 204.18/35.00    (9)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.00    (10)  op(e2, e2) = all_4_2
% 204.18/35.00    (11)   ~ (all_52_7 = all_6_2)
% 204.18/35.00    (12)  all_58_15 = e0
% 204.18/35.00    (13)  op(all_4_2, e2) = all_4_1
% 204.18/35.00    (14)  op(all_52_3, all_52_3) = e2
% 204.18/35.00    (15)  all_56_12 = all_52_7
% 204.18/35.00    (16)  op(e3, e3) = all_6_2
% 204.18/35.00    (17)   ~ (all_52_7 = e1)
% 204.18/35.00    (18)   ~ (e1 = e0)
% 204.18/35.00    (19)   ~ (all_52_7 = e0)
% 204.18/35.00  
% 204.18/35.00  Begin of proof
% 204.18/35.00  | 
% 204.18/35.00  | BETA: splitting (5) gives:
% 204.18/35.00  | 
% 204.18/35.00  | Case 1:
% 204.18/35.00  | | 
% 204.18/35.00  | |   (20)  all_58_13 = e1
% 204.18/35.00  | | 
% 204.18/35.00  | | REF_CLOSE: (1), (6), (20) are inconsistent by sub-proof #770.
% 204.18/35.00  | | 
% 204.18/35.00  | Case 2:
% 204.18/35.00  | | 
% 204.18/35.00  | |   (21)  all_58_14 = e1 | all_58_15 = e1
% 204.18/35.00  | | 
% 204.18/35.00  | | BETA: splitting (9) gives:
% 204.18/35.00  | | 
% 204.18/35.00  | | Case 1:
% 204.18/35.00  | | | 
% 204.18/35.00  | | |   (22)  all_56_12 = e2
% 204.18/35.00  | | | 
% 204.18/35.00  | | | COMBINE_EQS: (15), (22) imply:
% 204.18/35.00  | | |   (23)  all_52_7 = e2
% 204.18/35.00  | | | 
% 204.18/35.00  | | | SIMP: (23) implies:
% 204.18/35.00  | | |   (24)  all_52_7 = e2
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (11), (24) imply:
% 204.18/35.00  | | |   (25)   ~ (all_6_2 = e2)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | SIMP: (25) implies:
% 204.18/35.00  | | |   (26)   ~ (all_6_2 = e2)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (3), (24) imply:
% 204.18/35.00  | | |   (27)  op(e2, e2) = e0
% 204.18/35.00  | | | 
% 204.18/35.00  | | | BETA: splitting (21) gives:
% 204.18/35.00  | | | 
% 204.18/35.00  | | | Case 1:
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | GROUND_INST: instantiating (2) with all_4_2, e0, e2, e2, simplifying
% 204.18/35.00  | | | |              with (10), (27) gives:
% 204.18/35.00  | | | |   (28)  all_4_2 = e0
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REDUCE: (13), (28) imply:
% 204.18/35.00  | | | |   (29)  op(e0, e2) = all_4_1
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | GROUND_INST: instantiating (2) with e3, all_4_1, e2, e0, simplifying
% 204.18/35.00  | | | |              with (7), (29) gives:
% 204.18/35.00  | | | |   (30)  all_4_1 = e3
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REDUCE: (8), (30) imply:
% 204.18/35.00  | | | |   (31)  op(e2, e3) = e3
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | GROUND_INST: instantiating (2) with all_52_3, e3, e3, e2, simplifying
% 204.18/35.00  | | | |              with (4), (31) gives:
% 204.18/35.00  | | | |   (32)  all_52_3 = e3
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REDUCE: (14), (32) imply:
% 204.18/35.00  | | | |   (33)  op(e3, e3) = e2
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REF_CLOSE: (2), (16), (26), (33) are inconsistent by sub-proof #769.
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | Case 2:
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | |   (34)  all_58_15 = e1
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REF_CLOSE: (12), (18), (34) are inconsistent by sub-proof #1207.
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | End of split
% 204.18/35.00  | | | 
% 204.18/35.00  | | Case 2:
% 204.18/35.00  | | | 
% 204.18/35.00  | | |   (35)  all_56_12 = e1 | all_56_12 = e0
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REF_CLOSE: (15), (17), (19), (35) are inconsistent by sub-proof #1374.
% 204.18/35.00  | | | 
% 204.18/35.00  | | End of split
% 204.18/35.00  | | 
% 204.18/35.00  | End of split
% 204.18/35.00  | 
% 204.18/35.00  End of proof
% 204.18/35.00  
% 204.18/35.00  Sub-proof #769 shows that the following formulas are inconsistent:
% 204.18/35.00  ----------------------------------------------------------------
% 204.18/35.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.00    (2)  op(e3, e3) = all_6_2
% 204.18/35.00    (3)  op(e3, e3) = e2
% 204.18/35.00    (4)   ~ (all_6_2 = e2)
% 204.18/35.00  
% 204.18/35.00  Begin of proof
% 204.18/35.00  | 
% 204.18/35.00  | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with (2),
% 204.18/35.00  |              (3) gives:
% 204.18/35.00  |   (5)  all_6_2 = e2
% 204.18/35.00  | 
% 204.18/35.00  | REDUCE: (4), (5) imply:
% 204.18/35.00  |   (6)  $false
% 204.18/35.00  | 
% 204.18/35.00  | CLOSE: (6) is inconsistent.
% 204.18/35.00  | 
% 204.18/35.00  End of proof
% 204.18/35.00  
% 204.18/35.00  Sub-proof #770 shows that the following formulas are inconsistent:
% 204.18/35.00  ----------------------------------------------------------------
% 204.18/35.00    (1)  all_58_13 = e3
% 204.18/35.00    (2)  all_58_13 = e1
% 204.18/35.00    (3)   ~ (e3 = e1)
% 204.18/35.00  
% 204.18/35.00  Begin of proof
% 204.18/35.00  | 
% 204.18/35.00  | COMBINE_EQS: (1), (2) imply:
% 204.18/35.00  |   (4)  e3 = e1
% 204.18/35.00  | 
% 204.18/35.00  | SIMP: (4) implies:
% 204.18/35.00  |   (5)  e3 = e1
% 204.18/35.00  | 
% 204.18/35.00  | REDUCE: (3), (5) imply:
% 204.18/35.00  |   (6)  $false
% 204.18/35.00  | 
% 204.18/35.00  | CLOSE: (6) is inconsistent.
% 204.18/35.00  | 
% 204.18/35.00  End of proof
% 204.18/35.00  
% 204.18/35.00  Sub-proof #771 shows that the following formulas are inconsistent:
% 204.18/35.00  ----------------------------------------------------------------
% 204.18/35.00    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.00    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.00    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.00    (4)  all_58_14 = all_52_23
% 204.18/35.00    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.00    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.00    (7)   ~ (all_52_5 = all_52_13)
% 204.18/35.00    (8)  all_58_1 = all_52_9
% 204.18/35.00    (9)   ~ (all_52_9 = all_52_13)
% 204.18/35.00    (10)   ~ (e3 = e0)
% 204.18/35.00    (11)  op(e2, e3) = all_52_3
% 204.18/35.00    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.00    (13)  op(e0, e2) = all_52_15
% 204.18/35.00    (14)   ~ (all_52_7 = all_52_15)
% 204.18/35.00    (15)   ~ (all_52_3 = all_52_19)
% 204.18/35.00    (16)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.00    (17)   ~ (all_52_17 = all_52_25)
% 204.18/35.00    (18)   ~ (all_52_3 = all_6_2)
% 204.18/35.00    (19)  all_58_0 = all_6_2
% 204.18/35.00    (20)  op(all_14_2, e0) = all_14_1
% 204.18/35.00    (21)  all_56_4 = all_52_3
% 204.18/35.00    (22)   ~ (all_52_17 = all_10_2)
% 204.18/35.00    (23)   ~ (all_10_0 = e3)
% 204.18/35.00    (24)  all_40_2 = all_10_2
% 204.18/35.00    (25)  op(e3, e0) = all_52_25
% 204.18/35.00    (26)  op(e0, all_14_1) = all_14_0
% 204.18/35.00    (27)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.00    (28)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.00    (29)   ~ (all_52_27 = all_52_29)
% 204.18/35.00    (30)  all_58_13 = all_52_15
% 204.18/35.00    (31)  op(e0, all_14_1) = e1
% 204.18/35.00    (32)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.00    (33)  all_58_9 = all_52_25
% 204.18/35.00    (34)   ~ (all_52_29 = all_14_2)
% 204.18/35.00    (35)  all_22_0 = all_6_0
% 204.18/35.00    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.00    (37)   ~ (all_52_17 = all_6_0)
% 204.18/35.00    (38)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.00    (39)  op(e1, e3) = all_52_5
% 204.18/35.00    (40)  all_40_1 = all_10_1
% 204.18/35.00    (41)  op(e2, e2) = all_4_2
% 204.18/35.00    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.00    (43)   ~ (all_52_3 = all_52_5)
% 204.18/35.00    (44)  all_58_11 = all_52_29
% 204.18/35.00    (45)  all_56_5 = all_4_2
% 204.18/35.00    (46)   ~ (all_52_25 = all_14_2)
% 204.18/35.00    (47)   ~ (all_52_3 = all_52_27)
% 204.18/35.00    (48)  op(all_10_2, e1) = all_10_1
% 204.18/35.00    (49)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.00    (50)   ~ (all_52_7 = all_6_2)
% 204.18/35.00    (51)  op(e0, e0) = all_14_2
% 204.18/35.00    (52)  all_56_15 = all_14_2
% 204.18/35.00    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.00    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.00    (55)  op(e2, all_4_1) = all_4_0
% 204.18/35.00    (56)  all_56_11 = all_52_29
% 204.18/35.00    (57)   ~ (all_10_0 = e2)
% 204.18/35.00    (58)   ~ (all_4_0 = e3)
% 204.18/35.00    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.00    (60)  all_56_9 = all_52_13
% 204.18/35.00    (61)   ~ (e2 = e1)
% 204.18/35.00    (62)   ~ (all_52_13 = all_10_2)
% 204.18/35.00    (63)   ~ (all_6_0 = e1)
% 204.18/35.00    (64)  op(e1, all_10_1) = all_10_0
% 204.18/35.00    (65)  all_58_10 = all_52_27
% 204.18/35.00    (66)  all_56_8 = all_52_5
% 204.18/35.00    (67)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.00    (68)   ~ (all_52_19 = all_52_23)
% 204.18/35.00    (69)   ~ (all_52_25 = all_52_29)
% 204.18/35.00    (70)  op(all_6_2, e3) = e2
% 204.18/35.00    (71)   ~ (all_52_29 = all_10_2)
% 204.18/35.00    (72)  all_58_7 = all_52_13
% 204.18/35.00    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.00    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.00    (75)  all_58_1 = all_6_0
% 204.18/35.00    (76)   ~ (all_52_5 = all_52_7)
% 204.18/35.00    (77)  all_58_12 = all_52_7
% 204.18/35.00    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.00    (79)   ~ (all_52_7 = all_14_2)
% 204.18/35.00    (80)  all_58_2 = all_52_3
% 204.18/35.00    (81)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/35.00    (82)  all_56_2 = all_52_17
% 204.18/35.00    (83)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/35.00    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.00    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.00    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.18/35.00    (87)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.00    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/35.00    (89)   ~ (e2 = e0)
% 204.18/35.00    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.00    (91)  op(all_4_2, e2) = all_4_1
% 204.18/35.00    (92)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.00    (93)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.00    (94)   ~ (all_52_5 = all_52_29)
% 204.18/35.00    (95)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.00    (96)  all_56_6 = all_52_19
% 204.18/35.00    (97)   ~ (all_52_15 = all_14_2)
% 204.18/35.00    (98)   ~ (all_52_13 = all_6_0)
% 204.18/35.00    (99)   ~ (all_52_19 = all_52_27)
% 204.18/35.00    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.00    (101)   ~ (all_6_0 = e2)
% 204.18/35.00    (102)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.18/35.00             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.18/35.00    (103)   ~ (all_52_13 = all_4_2)
% 204.18/35.00    (104)  op(e3, e1) = all_52_17
% 204.18/35.00    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.00    (106)  op(e0, e3) = all_52_7
% 204.18/35.00    (107)  op(e1, e2) = all_52_13
% 204.18/35.00    (108)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.00    (109)   ~ (all_52_9 = all_52_25)
% 204.18/35.00    (110)  all_58_15 = all_14_2
% 204.18/35.00    (111)   ~ (all_52_19 = all_10_2)
% 204.18/35.00    (112)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.00    (113)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3)
% 204.18/35.00    (114)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.00    (115)  all_58_8 = all_10_2
% 204.18/35.00    (116)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.00    (117)   ~ (all_52_5 = all_10_2)
% 204.18/35.00    (118)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.00    (119)   ~ (all_52_23 = all_14_2)
% 204.18/35.00    (120)  all_56_12 = all_52_7
% 204.18/35.00    (121)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.00    (122)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.00    (123)   ~ (all_52_25 = all_6_2)
% 204.18/35.00    (124)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.00    (125)   ~ (all_52_9 = all_4_2)
% 204.18/35.00    (126)   ~ (all_52_5 = all_6_2)
% 204.18/35.00    (127)  all_56_0 = all_6_2
% 204.18/35.00    (128)  op(e3, e3) = all_6_2
% 204.18/35.00    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.00    (130)   ~ (all_52_15 = all_6_0)
% 204.18/35.00    (131)   ~ (all_52_27 = all_14_2)
% 204.18/35.00    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.00    (133)  all_56_14 = all_52_23
% 204.18/35.00    (134)  op(all_4_2, all_4_2) = all_52_10
% 204.18/35.00    (135)  all_40_0 = all_10_0
% 204.18/35.00    (136)  all_56_3 = all_52_25
% 204.18/35.00    (137)   ~ (all_52_3 = all_52_7)
% 204.18/35.00    (138)   ~ (all_6_0 = all_6_2)
% 204.18/35.00    (139)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.00    (140)  all_58_5 = all_52_19
% 204.18/35.00    (141)   ~ (all_52_15 = all_4_2)
% 204.18/35.00    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.00           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.00           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.00           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.00    (143)   ~ (all_52_27 = all_4_2)
% 204.18/35.00    (144)  all_58_6 = all_52_5
% 204.18/35.00    (145)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.00    (146)   ~ (all_52_17 = all_6_2)
% 204.18/35.00    (147)  all_30_1 = all_10_1
% 204.18/35.00    (148)   ~ (e1 = e0)
% 204.18/35.00    (149)   ~ (e3 = e2)
% 204.18/35.00    (150)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.00    (151)   ~ (all_52_9 = all_52_17)
% 204.18/35.00    (152)  all_56_10 = all_10_2
% 204.18/35.00    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.00    (154)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2)
% 204.18/35.00    (155)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.18/35.00    (156)  all_56_1 = all_6_0
% 204.18/35.00    (157)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.00    (158)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.00    (159)   ~ (all_6_0 = all_4_2)
% 204.18/35.00    (160)  op(e1, e1) = all_10_2
% 204.18/35.00    (161)   ~ (all_52_23 = all_10_2)
% 204.18/35.00    (162)   ~ (all_52_7 = all_52_23)
% 204.18/35.00    (163)   ~ (all_52_17 = all_52_19)
% 204.18/35.00    (164)  all_58_3 = all_4_2
% 204.18/35.00    (165)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.00    (166)   ~ (all_52_3 = all_4_2)
% 204.18/35.00    (167)   ~ (all_52_19 = all_4_2)
% 204.18/35.00    (168)   ~ (all_52_17 = all_52_23)
% 204.18/35.00    (169)  op(all_6_2, e3) = all_6_1
% 204.18/35.00    (170)  all_22_2 = all_6_2
% 204.18/35.00    (171)  all_58_4 = all_52_17
% 204.18/35.00    (172)   ~ (all_14_0 = e2)
% 204.18/35.00    (173)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.00    (174)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.00  
% 204.18/35.00  Begin of proof
% 204.18/35.00  | 
% 204.18/35.00  | BETA: splitting (154) gives:
% 204.18/35.00  | 
% 204.18/35.00  | Case 1:
% 204.18/35.00  | | 
% 204.18/35.00  | |   (175)   ~ (all_30_1 = e3)
% 204.18/35.00  | | 
% 204.18/35.00  | | REDUCE: (147), (175) imply:
% 204.18/35.00  | |   (176)   ~ (all_10_1 = e3)
% 204.18/35.00  | | 
% 204.18/35.00  | | BETA: splitting (113) gives:
% 204.18/35.00  | | 
% 204.18/35.00  | | Case 1:
% 204.18/35.00  | | | 
% 204.18/35.00  | | |   (177)   ~ (all_40_1 = e2)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.00  | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (25),
% 204.18/35.00  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 204.18/35.00  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.18/35.00  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56),
% 204.18/35.00  | | |            (59), (61), (62), (63), (65), (66), (67), (68), (69), (70),
% 204.18/35.00  | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.18/35.00  | | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 204.18/35.00  | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 204.18/35.00  | | |            (102), (104), (105), (106), (108), (109), (110), (111), (112),
% 204.18/35.00  | | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 204.18/35.00  | | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 204.18/35.00  | | |            (132), (133), (136), (137), (138), (139), (140), (141), (142),
% 204.18/35.00  | | |            (143), (144), (145), (146), (148), (149), (150), (152), (153),
% 204.18/35.00  | | |            (156), (157), (158), (159), (160), (161), (162), (163), (164),
% 204.18/35.00  | | |            (165), (166), (167), (168), (169), (170), (171), (172), (173),
% 204.18/35.00  | | |            (174), (177) are inconsistent by sub-proof #774.
% 204.18/35.00  | | | 
% 204.18/35.00  | | Case 2:
% 204.18/35.00  | | | 
% 204.18/35.00  | | |   (178)  all_40_1 = e2
% 204.18/35.00  | | |   (179)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | COMBINE_EQS: (40), (178) imply:
% 204.18/35.00  | | |   (180)  all_10_1 = e2
% 204.18/35.00  | | | 
% 204.18/35.00  | | | SIMP: (180) implies:
% 204.18/35.00  | | |   (181)  all_10_1 = e2
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (176), (181) imply:
% 204.18/35.00  | | |   (182)   ~ (e3 = e2)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (48), (181) imply:
% 204.18/35.00  | | |   (183)  op(all_10_2, e1) = e2
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (64), (181) imply:
% 204.18/35.00  | | |   (184)  op(e1, e2) = all_10_0
% 204.18/35.00  | | | 
% 204.18/35.00  | | | GROUND_INST: instantiating (6) with all_52_13, all_10_0, e2, e1,
% 204.18/35.00  | | |              simplifying with (107), (184) gives:
% 204.18/35.00  | | |   (185)  all_52_13 = all_10_0
% 204.18/35.00  | | | 
% 204.18/35.00  | | | COMBINE_EQS: (60), (185) imply:
% 204.18/35.00  | | |   (186)  all_56_9 = all_10_0
% 204.18/35.00  | | | 
% 204.18/35.00  | | | COMBINE_EQS: (72), (185) imply:
% 204.18/35.00  | | |   (187)  all_58_7 = all_10_0
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (7), (185) imply:
% 204.18/35.00  | | |   (188)   ~ (all_52_5 = all_10_0)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (98), (185) imply:
% 204.18/35.00  | | |   (189)   ~ (all_10_0 = all_6_0)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | REDUCE: (103), (185) imply:
% 204.18/35.00  | | |   (190)   ~ (all_10_0 = all_4_2)
% 204.18/35.00  | | | 
% 204.18/35.00  | | | BETA: splitting (102) gives:
% 204.18/35.00  | | | 
% 204.18/35.00  | | | Case 1:
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | |   (191)  all_58_15 = e0
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REF_CLOSE: (6), (20), (31), (51), (110), (139), (148), (191) are
% 204.18/35.00  | | | |            inconsistent by sub-proof #877.
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | Case 2:
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | |   (192)   ~ (all_58_15 = e0)
% 204.18/35.00  | | | |   (193)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 204.18/35.00  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | ALPHA: (193) implies:
% 204.18/35.00  | | | |   (194)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/35.00  | | | |   (195)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REDUCE: (110), (192) imply:
% 204.18/35.00  | | | |   (196)   ~ (all_14_2 = e0)
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 204.18/35.00  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 204.18/35.00  | | | |            (25), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 204.18/35.00  | | | |            (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 204.18/35.00  | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 204.18/35.00  | | | |            (58), (59), (61), (63), (65), (66), (67), (68), (69), (70),
% 204.18/35.00  | | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.18/35.00  | | | |            (82), (84), (85), (87), (88), (89), (90), (91), (92), (93),
% 204.18/35.00  | | | |            (94), (95), (99), (100), (101), (104), (105), (106), (108),
% 204.18/35.00  | | | |            (109), (110), (111), (112), (114), (115), (116), (117),
% 204.18/35.00  | | | |            (118), (119), (120), (121), (122), (123), (124), (125),
% 204.18/35.00  | | | |            (126), (127), (128), (129), (130), (131), (132), (133),
% 204.18/35.00  | | | |            (134), (135), (136), (137), (138), (139), (140), (141),
% 204.18/35.00  | | | |            (142), (143), (144), (145), (146), (148), (149), (150),
% 204.18/35.00  | | | |            (152), (153), (155), (156), (157), (158), (159), (160),
% 204.18/35.00  | | | |            (161), (162), (164), (165), (166), (167), (168), (169),
% 204.18/35.00  | | | |            (170), (171), (173), (174), (179), (183), (186), (187),
% 204.18/35.00  | | | |            (188), (189), (190), (194), (195), (196) are inconsistent by
% 204.18/35.00  | | | |            sub-proof #781.
% 204.18/35.00  | | | | 
% 204.18/35.00  | | | End of split
% 204.18/35.00  | | | 
% 204.18/35.00  | | End of split
% 204.18/35.00  | | 
% 204.18/35.00  | Case 2:
% 204.18/35.00  | | 
% 204.18/35.00  | |   (197)  all_30_1 = e3
% 204.18/35.00  | | 
% 204.18/35.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (15),
% 204.18/35.00  | |            (16), (17), (18), (19), (20), (22), (23), (27), (28), (29), (30),
% 204.18/35.00  | |            (31), (32), (33), (34), (35), (36), (37), (38), (39), (41), (42),
% 204.18/35.00  | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 204.18/35.00  | |            (54), (56), (59), (61), (63), (64), (65), (66), (67), (68), (69),
% 204.18/35.00  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.18/35.00  | |            (82), (84), (85), (87), (89), (90), (92), (93), (94), (95), (98),
% 204.18/35.00  | |            (99), (100), (101), (102), (104), (105), (106), (108), (109),
% 204.18/35.00  | |            (110), (111), (112), (114), (115), (116), (117), (118), (119),
% 204.18/35.00  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 204.18/35.00  | |            (129), (130), (131), (132), (133), (136), (137), (138), (139),
% 204.18/35.00  | |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 204.18/35.00  | |            (149), (150), (151), (152), (153), (156), (157), (158), (159),
% 204.18/35.00  | |            (160), (161), (162), (164), (165), (166), (167), (168), (169),
% 204.18/35.00  | |            (170), (171), (173), (174), (197) are inconsistent by sub-proof
% 204.18/35.00  | |            #772.
% 204.18/35.00  | | 
% 204.18/35.00  | End of split
% 204.18/35.00  | 
% 204.18/35.00  End of proof
% 204.18/35.00  
% 204.18/35.00  Sub-proof #772 shows that the following formulas are inconsistent:
% 204.18/35.00  ----------------------------------------------------------------
% 204.18/35.00    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.00    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.00    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.00    (4)  all_58_14 = all_52_23
% 204.18/35.00    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.00    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.00    (7)  all_58_1 = all_52_9
% 204.18/35.00    (8)   ~ (all_52_9 = all_52_13)
% 204.18/35.00    (9)   ~ (e3 = e0)
% 204.18/35.00    (10)  op(e2, e3) = all_52_3
% 204.18/35.00    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.00    (12)   ~ (all_52_3 = all_52_19)
% 204.18/35.00    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.00    (14)   ~ (all_52_17 = all_52_25)
% 204.18/35.00    (15)   ~ (all_52_3 = all_6_2)
% 204.18/35.00    (16)  all_58_0 = all_6_2
% 204.18/35.00    (17)  op(all_14_2, e0) = all_14_1
% 204.18/35.00    (18)   ~ (all_52_17 = all_10_2)
% 204.18/35.00    (19)   ~ (all_10_0 = e3)
% 204.18/35.00    (20)  all_30_1 = e3
% 204.18/35.00    (21)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.00    (22)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.00    (23)   ~ (all_52_27 = all_52_29)
% 204.18/35.00    (24)  all_58_13 = all_52_15
% 204.18/35.00    (25)  op(e0, all_14_1) = e1
% 204.18/35.00    (26)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.00    (27)  all_58_9 = all_52_25
% 204.18/35.00    (28)   ~ (all_52_29 = all_14_2)
% 204.18/35.00    (29)  all_22_0 = all_6_0
% 204.18/35.00    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.00    (31)   ~ (all_52_17 = all_6_0)
% 204.18/35.00    (32)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.00    (33)  op(e1, e3) = all_52_5
% 204.18/35.00    (34)  op(e2, e2) = all_4_2
% 204.18/35.00    (35)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.00    (36)   ~ (all_52_3 = all_52_5)
% 204.18/35.00    (37)  all_58_11 = all_52_29
% 204.18/35.00    (38)  all_56_5 = all_4_2
% 204.18/35.00    (39)   ~ (all_52_25 = all_14_2)
% 204.18/35.00    (40)   ~ (all_52_3 = all_52_27)
% 204.18/35.00    (41)  op(all_10_2, e1) = all_10_1
% 204.18/35.00    (42)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.00    (43)   ~ (all_52_7 = all_6_2)
% 204.18/35.00    (44)  op(e0, e0) = all_14_2
% 204.18/35.00    (45)  all_56_15 = all_14_2
% 204.18/35.00    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.00    (47)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.00    (48)  all_56_11 = all_52_29
% 204.18/35.00    (49)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.00    (50)   ~ (e2 = e1)
% 204.18/35.00    (51)   ~ (all_6_0 = e1)
% 204.18/35.00    (52)  op(e1, all_10_1) = all_10_0
% 204.18/35.00    (53)  all_58_10 = all_52_27
% 204.18/35.00    (54)  all_56_8 = all_52_5
% 204.18/35.00    (55)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.00    (56)   ~ (all_52_19 = all_52_23)
% 204.18/35.00    (57)   ~ (all_52_25 = all_52_29)
% 204.18/35.00    (58)  op(all_6_2, e3) = e2
% 204.18/35.00    (59)   ~ (all_52_29 = all_10_2)
% 204.18/35.00    (60)  all_58_7 = all_52_13
% 204.18/35.00    (61)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.00    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.00    (63)  all_58_1 = all_6_0
% 204.18/35.00    (64)   ~ (all_52_5 = all_52_7)
% 204.18/35.00    (65)  all_58_12 = all_52_7
% 204.18/35.00    (66)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.00    (67)   ~ (all_52_7 = all_14_2)
% 204.18/35.00    (68)  all_58_2 = all_52_3
% 204.18/35.00    (69)  all_56_2 = all_52_17
% 204.18/35.00    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.00    (71)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.00    (72)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.00    (73)   ~ (e2 = e0)
% 204.18/35.00    (74)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.00    (75)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.00    (76)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.00    (77)   ~ (all_52_5 = all_52_29)
% 204.18/35.00    (78)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.00    (79)   ~ (all_52_13 = all_6_0)
% 204.18/35.00    (80)   ~ (all_52_19 = all_52_27)
% 204.18/35.00    (81)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.00    (82)   ~ (all_6_0 = e2)
% 204.18/35.00    (83)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.18/35.00            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.18/35.00    (84)  op(e3, e1) = all_52_17
% 204.18/35.00    (85)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.00    (86)  op(e0, e3) = all_52_7
% 204.18/35.00    (87)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.00    (88)   ~ (all_52_9 = all_52_25)
% 204.18/35.00    (89)  all_58_15 = all_14_2
% 204.18/35.00    (90)   ~ (all_52_19 = all_10_2)
% 204.18/35.00    (91)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.00    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.00    (93)  all_58_8 = all_10_2
% 204.18/35.00    (94)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.00    (95)   ~ (all_52_5 = all_10_2)
% 204.18/35.00    (96)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.00    (97)   ~ (all_52_23 = all_14_2)
% 204.18/35.00    (98)  all_56_12 = all_52_7
% 204.18/35.00    (99)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.01    (100)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.01    (101)   ~ (all_52_25 = all_6_2)
% 204.18/35.01    (102)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.01    (103)   ~ (all_52_9 = all_4_2)
% 204.18/35.01    (104)   ~ (all_52_5 = all_6_2)
% 204.18/35.01    (105)  all_56_0 = all_6_2
% 204.18/35.01    (106)  op(e3, e3) = all_6_2
% 204.18/35.01    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.01    (108)   ~ (all_52_15 = all_6_0)
% 204.18/35.01    (109)   ~ (all_52_27 = all_14_2)
% 204.18/35.01    (110)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.01    (111)  all_56_14 = all_52_23
% 204.18/35.01    (112)  all_56_3 = all_52_25
% 204.18/35.01    (113)   ~ (all_52_3 = all_52_7)
% 204.18/35.01    (114)   ~ (all_6_0 = all_6_2)
% 204.18/35.01    (115)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.01    (116)  all_58_5 = all_52_19
% 204.18/35.01    (117)   ~ (all_52_15 = all_4_2)
% 204.18/35.01    (118)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.01           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.01           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.01           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.01    (119)   ~ (all_52_27 = all_4_2)
% 204.18/35.01    (120)  all_58_6 = all_52_5
% 204.18/35.01    (121)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.01    (122)   ~ (all_52_17 = all_6_2)
% 204.18/35.01    (123)  all_30_1 = all_10_1
% 204.18/35.01    (124)   ~ (e1 = e0)
% 204.18/35.01    (125)   ~ (e3 = e2)
% 204.18/35.01    (126)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.01    (127)   ~ (all_52_9 = all_52_17)
% 204.18/35.01    (128)  all_56_10 = all_10_2
% 204.18/35.01    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.01    (130)  all_56_1 = all_6_0
% 204.18/35.01    (131)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.01    (132)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.01    (133)   ~ (all_6_0 = all_4_2)
% 204.18/35.01    (134)  op(e1, e1) = all_10_2
% 204.18/35.01    (135)   ~ (all_52_23 = all_10_2)
% 204.18/35.01    (136)   ~ (all_52_7 = all_52_23)
% 204.18/35.01    (137)  all_58_3 = all_4_2
% 204.18/35.01    (138)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.01    (139)   ~ (all_52_3 = all_4_2)
% 204.18/35.01    (140)   ~ (all_52_19 = all_4_2)
% 204.18/35.01    (141)   ~ (all_52_17 = all_52_23)
% 204.18/35.01    (142)  op(all_6_2, e3) = all_6_1
% 204.18/35.01    (143)  all_22_2 = all_6_2
% 204.18/35.01    (144)  all_58_4 = all_52_17
% 204.18/35.01    (145)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.01    (146)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.01  
% 204.18/35.01  Begin of proof
% 204.18/35.01  | 
% 204.18/35.01  | COMBINE_EQS: (20), (123) imply:
% 204.18/35.01  |   (147)  all_10_1 = e3
% 204.18/35.01  | 
% 204.18/35.01  | SIMP: (147) implies:
% 204.18/35.01  |   (148)  all_10_1 = e3
% 204.18/35.01  | 
% 204.18/35.01  | REDUCE: (41), (148) imply:
% 204.18/35.01  |   (149)  op(all_10_2, e1) = e3
% 204.18/35.01  | 
% 204.18/35.01  | REDUCE: (52), (148) imply:
% 204.18/35.01  |   (150)  op(e1, e3) = all_10_0
% 204.18/35.01  | 
% 204.18/35.01  | GROUND_INST: instantiating (6) with all_52_5, all_10_0, e3, e1, simplifying
% 204.18/35.01  |              with (33), (150) gives:
% 204.18/35.01  |   (151)  all_52_5 = all_10_0
% 204.18/35.01  | 
% 204.18/35.01  | COMBINE_EQS: (120), (151) imply:
% 204.18/35.01  |   (152)  all_58_6 = all_10_0
% 204.18/35.01  | 
% 204.18/35.01  | BETA: splitting (83) gives:
% 204.18/35.01  | 
% 204.18/35.01  | Case 1:
% 204.18/35.01  | | 
% 204.18/35.01  | |   (153)  all_58_15 = e0
% 204.18/35.01  | | 
% 204.18/35.01  | | REF_CLOSE: (6), (17), (25), (44), (89), (115), (124), (153) are inconsistent
% 204.18/35.01  | |            by sub-proof #877.
% 204.18/35.01  | | 
% 204.18/35.01  | Case 2:
% 204.18/35.01  | | 
% 204.18/35.01  | |   (154)   ~ (all_58_15 = e0)
% 204.18/35.01  | |   (155)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 204.18/35.01  | |            | all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.01  | | 
% 204.18/35.01  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.01  | |            (13), (14), (15), (16), (18), (19), (21), (22), (23), (24), (26),
% 204.18/35.01  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 204.18/35.01  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.18/35.01  | |            (49), (50), (51), (53), (54), (55), (56), (57), (58), (59), (60),
% 204.18/35.01  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 204.18/35.01  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 204.18/35.01  | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 204.18/35.01  | |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 204.18/35.01  | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 204.18/35.01  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 204.18/35.01  | |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 204.18/35.01  | |            (133), (134), (135), (136), (137), (138), (139), (140), (141),
% 204.18/35.01  | |            (142), (143), (144), (145), (146), (149), (152), (154), (155) are
% 204.18/35.01  | |            inconsistent by sub-proof #773.
% 204.18/35.01  | | 
% 204.18/35.01  | End of split
% 204.18/35.01  | 
% 204.18/35.01  End of proof
% 204.18/35.01  
% 204.18/35.01  Sub-proof #773 shows that the following formulas are inconsistent:
% 204.18/35.01  ----------------------------------------------------------------
% 204.18/35.01    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.01    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.01    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.01    (4)  all_58_14 = all_52_23
% 204.18/35.01    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.01    (7)  all_58_1 = all_52_9
% 204.18/35.01    (8)   ~ (all_52_9 = all_52_13)
% 204.18/35.01    (9)   ~ (e3 = e0)
% 204.18/35.01    (10)  op(e2, e3) = all_52_3
% 204.18/35.01    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.01    (12)   ~ (all_52_3 = all_52_19)
% 204.18/35.01    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.01    (14)   ~ (all_52_17 = all_52_25)
% 204.18/35.01    (15)   ~ (all_52_3 = all_6_2)
% 204.18/35.01    (16)  all_58_0 = all_6_2
% 204.18/35.01    (17)   ~ (all_52_17 = all_10_2)
% 204.18/35.01    (18)   ~ (all_10_0 = e3)
% 204.18/35.01    (19)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.01    (20)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.01    (21)   ~ (all_52_27 = all_52_29)
% 204.18/35.01    (22)  all_58_13 = all_52_15
% 204.18/35.01    (23)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.01    (24)  all_58_9 = all_52_25
% 204.18/35.01    (25)   ~ (all_52_29 = all_14_2)
% 204.18/35.01    (26)  all_22_0 = all_6_0
% 204.18/35.01    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.01    (28)   ~ (all_52_17 = all_6_0)
% 204.18/35.01    (29)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.01    (30)  op(e1, e3) = all_52_5
% 204.18/35.01    (31)  op(e2, e2) = all_4_2
% 204.18/35.01    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.01    (33)   ~ (all_52_3 = all_52_5)
% 204.18/35.01    (34)  all_58_11 = all_52_29
% 204.18/35.01    (35)  all_56_5 = all_4_2
% 204.18/35.01    (36)   ~ (all_52_25 = all_14_2)
% 204.18/35.01    (37)   ~ (all_52_3 = all_52_27)
% 204.18/35.01    (38)  op(all_10_2, e1) = all_10_1
% 204.18/35.01    (39)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.01    (40)   ~ (all_52_7 = all_6_2)
% 204.18/35.01    (41)  op(e0, e0) = all_14_2
% 204.18/35.01    (42)  all_56_15 = all_14_2
% 204.18/35.01    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.01    (44)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.01    (45)   ~ (all_58_15 = e0)
% 204.18/35.01    (46)  all_56_11 = all_52_29
% 204.18/35.01    (47)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.01    (48)   ~ (e2 = e1)
% 204.18/35.01    (49)   ~ (all_6_0 = e1)
% 204.18/35.01    (50)  all_58_10 = all_52_27
% 204.18/35.01    (51)  all_56_8 = all_52_5
% 204.18/35.01    (52)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.01    (53)   ~ (all_52_19 = all_52_23)
% 204.18/35.01    (54)   ~ (all_52_25 = all_52_29)
% 204.18/35.01    (55)  op(all_6_2, e3) = e2
% 204.18/35.01    (56)   ~ (all_52_29 = all_10_2)
% 204.18/35.01    (57)  op(all_10_2, e1) = e3
% 204.18/35.01    (58)  all_58_7 = all_52_13
% 204.18/35.01    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.01    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.01    (61)  all_58_1 = all_6_0
% 204.18/35.01    (62)   ~ (all_52_5 = all_52_7)
% 204.18/35.01    (63)  all_58_12 = all_52_7
% 204.18/35.01    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.01    (65)   ~ (all_52_7 = all_14_2)
% 204.18/35.01    (66)  all_58_2 = all_52_3
% 204.18/35.01    (67)  all_56_2 = all_52_17
% 204.18/35.01    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.01    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.01    (70)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.01    (71)   ~ (e2 = e0)
% 204.18/35.01    (72)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.01    (73)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.01    (74)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.01    (75)   ~ (all_52_5 = all_52_29)
% 204.18/35.01    (76)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.01    (77)   ~ (all_52_13 = all_6_0)
% 204.18/35.01    (78)   ~ (all_52_19 = all_52_27)
% 204.18/35.01    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.01    (80)   ~ (all_6_0 = e2)
% 204.18/35.01    (81)  op(e3, e1) = all_52_17
% 204.18/35.01    (82)  all_58_6 = all_10_0
% 204.18/35.01    (83)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.01    (84)  op(e0, e3) = all_52_7
% 204.18/35.01    (85)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.01    (86)   ~ (all_52_9 = all_52_25)
% 204.18/35.01    (87)  all_58_15 = all_14_2
% 204.18/35.01    (88)   ~ (all_52_19 = all_10_2)
% 204.18/35.01    (89)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.01    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.01    (91)  all_58_8 = all_10_2
% 204.18/35.01    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.01    (93)   ~ (all_52_5 = all_10_2)
% 204.18/35.01    (94)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.01    (95)   ~ (all_52_23 = all_14_2)
% 204.18/35.01    (96)  all_56_12 = all_52_7
% 204.18/35.01    (97)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.01    (98)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.01    (99)   ~ (all_52_25 = all_6_2)
% 204.18/35.01    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.01    (101)   ~ (all_52_9 = all_4_2)
% 204.18/35.01    (102)   ~ (all_52_5 = all_6_2)
% 204.18/35.01    (103)  all_56_0 = all_6_2
% 204.18/35.01    (104)  op(e3, e3) = all_6_2
% 204.18/35.01    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.01    (106)   ~ (all_52_15 = all_6_0)
% 204.18/35.01    (107)   ~ (all_52_27 = all_14_2)
% 204.18/35.01    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.01    (109)  all_56_14 = all_52_23
% 204.18/35.01    (110)  all_56_3 = all_52_25
% 204.18/35.01    (111)   ~ (all_52_3 = all_52_7)
% 204.18/35.01    (112)   ~ (all_6_0 = all_6_2)
% 204.18/35.01    (113)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.01    (114)  all_58_5 = all_52_19
% 204.18/35.01    (115)   ~ (all_52_15 = all_4_2)
% 204.18/35.01    (116)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.01           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.01           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.01           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.01    (117)   ~ (all_52_27 = all_4_2)
% 204.18/35.01    (118)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 204.18/35.01             all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.01    (119)  all_58_6 = all_52_5
% 204.18/35.01    (120)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.01    (121)   ~ (all_52_17 = all_6_2)
% 204.18/35.01    (122)   ~ (e1 = e0)
% 204.18/35.01    (123)   ~ (e3 = e2)
% 204.18/35.01    (124)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.01    (125)   ~ (all_52_9 = all_52_17)
% 204.18/35.01    (126)  all_56_10 = all_10_2
% 204.18/35.01    (127)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.01    (128)  all_56_1 = all_6_0
% 204.18/35.01    (129)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.01    (130)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.01    (131)   ~ (all_6_0 = all_4_2)
% 204.18/35.01    (132)  op(e1, e1) = all_10_2
% 204.18/35.01    (133)   ~ (all_52_23 = all_10_2)
% 204.18/35.01    (134)   ~ (all_52_7 = all_52_23)
% 204.18/35.01    (135)  all_58_3 = all_4_2
% 204.18/35.01    (136)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.01    (137)   ~ (all_52_3 = all_4_2)
% 204.18/35.01    (138)   ~ (all_52_19 = all_4_2)
% 204.18/35.01    (139)   ~ (all_52_17 = all_52_23)
% 204.18/35.01    (140)  op(all_6_2, e3) = all_6_1
% 204.18/35.01    (141)  all_22_2 = all_6_2
% 204.18/35.01    (142)  all_58_4 = all_52_17
% 204.18/35.01    (143)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.01    (144)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.01  
% 204.18/35.01  Begin of proof
% 204.18/35.01  | 
% 204.18/35.01  | ALPHA: (118) implies:
% 204.18/35.01  |   (145)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/35.01  |   (146)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.01  | 
% 204.18/35.01  | REDUCE: (45), (87) imply:
% 204.18/35.01  |   (147)   ~ (all_14_2 = e0)
% 204.18/35.01  | 
% 204.18/35.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.01  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.18/35.01  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.18/35.01  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (46),
% 204.18/35.01  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 204.18/35.01  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 204.18/35.01  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 204.18/35.01  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 204.18/35.01  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 204.18/35.01  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 204.18/35.01  |            (111), (112), (113), (114), (115), (116), (117), (119), (120),
% 204.18/35.01  |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 204.18/35.01  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 204.18/35.01  |            (139), (140), (141), (142), (143), (144), (145), (146), (147) are
% 204.18/35.01  |            inconsistent by sub-proof #778.
% 204.18/35.01  | 
% 204.18/35.01  End of proof
% 204.18/35.01  
% 204.18/35.01  Sub-proof #774 shows that the following formulas are inconsistent:
% 204.18/35.01  ----------------------------------------------------------------
% 204.18/35.01    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.01    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.01    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.01    (4)  all_58_14 = all_52_23
% 204.18/35.01    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.01    (7)   ~ (all_52_5 = all_52_13)
% 204.18/35.01    (8)  all_58_1 = all_52_9
% 204.18/35.01    (9)   ~ (all_52_9 = all_52_13)
% 204.18/35.01    (10)   ~ (e3 = e0)
% 204.18/35.01    (11)  op(e2, e3) = all_52_3
% 204.18/35.01    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.01    (13)  op(e0, e2) = all_52_15
% 204.18/35.01    (14)   ~ (all_52_3 = all_52_19)
% 204.18/35.01    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.01    (16)   ~ (all_52_17 = all_52_25)
% 204.18/35.01    (17)   ~ (all_52_3 = all_6_2)
% 204.18/35.01    (18)  all_58_0 = all_6_2
% 204.18/35.01    (19)  op(all_14_2, e0) = all_14_1
% 204.18/35.01    (20)  all_56_4 = all_52_3
% 204.18/35.01    (21)   ~ (all_52_17 = all_10_2)
% 204.18/35.01    (22)  op(e3, e0) = all_52_25
% 204.18/35.01    (23)  op(e0, all_14_1) = all_14_0
% 204.18/35.01    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.01    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.01    (26)   ~ (all_52_27 = all_52_29)
% 204.18/35.01    (27)  all_58_13 = all_52_15
% 204.18/35.01    (28)  op(e0, all_14_1) = e1
% 204.18/35.01    (29)   ~ (all_40_1 = e2)
% 204.18/35.01    (30)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.01    (31)  all_58_9 = all_52_25
% 204.18/35.01    (32)   ~ (all_52_29 = all_14_2)
% 204.18/35.01    (33)  all_22_0 = all_6_0
% 204.18/35.01    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.01    (35)   ~ (all_52_17 = all_6_0)
% 204.18/35.01    (36)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.01    (37)  op(e1, e3) = all_52_5
% 204.18/35.01    (38)  all_40_1 = all_10_1
% 204.18/35.01    (39)  op(e2, e2) = all_4_2
% 204.18/35.01    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.01    (41)   ~ (all_52_3 = all_52_5)
% 204.18/35.01    (42)  all_58_11 = all_52_29
% 204.18/35.01    (43)  all_56_5 = all_4_2
% 204.18/35.01    (44)   ~ (all_52_25 = all_14_2)
% 204.18/35.01    (45)   ~ (all_52_3 = all_52_27)
% 204.18/35.01    (46)  op(all_10_2, e1) = all_10_1
% 204.18/35.01    (47)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.01    (48)   ~ (all_52_7 = all_6_2)
% 204.18/35.01    (49)  op(e0, e0) = all_14_2
% 204.18/35.01    (50)  all_56_15 = all_14_2
% 204.18/35.01    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.01    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.01    (53)  all_56_11 = all_52_29
% 204.18/35.01    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.01    (55)   ~ (e2 = e1)
% 204.18/35.01    (56)   ~ (all_52_13 = all_10_2)
% 204.18/35.01    (57)   ~ (all_6_0 = e1)
% 204.18/35.01    (58)  all_58_10 = all_52_27
% 204.18/35.01    (59)  all_56_8 = all_52_5
% 204.18/35.01    (60)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.01    (61)   ~ (all_52_19 = all_52_23)
% 204.18/35.01    (62)   ~ (all_52_25 = all_52_29)
% 204.18/35.01    (63)  op(all_6_2, e3) = e2
% 204.18/35.01    (64)   ~ (all_52_29 = all_10_2)
% 204.18/35.01    (65)  all_58_7 = all_52_13
% 204.18/35.01    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.01    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.01    (68)  all_58_1 = all_6_0
% 204.18/35.01    (69)   ~ (all_52_5 = all_52_7)
% 204.18/35.01    (70)  all_58_12 = all_52_7
% 204.18/35.01    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.01    (72)   ~ (all_52_7 = all_14_2)
% 204.18/35.01    (73)  all_58_2 = all_52_3
% 204.18/35.01    (74)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/35.01    (75)  all_56_2 = all_52_17
% 204.18/35.01    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/35.01    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.01    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.01    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.18/35.01    (80)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.01    (81)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/35.01    (82)   ~ (e2 = e0)
% 204.18/35.01    (83)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.01    (84)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.01    (85)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.01    (86)   ~ (all_52_5 = all_52_29)
% 204.18/35.01    (87)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.01    (88)  all_56_6 = all_52_19
% 204.18/35.01    (89)   ~ (all_52_15 = all_14_2)
% 204.18/35.01    (90)   ~ (all_52_13 = all_6_0)
% 204.18/35.01    (91)   ~ (all_52_19 = all_52_27)
% 204.18/35.01    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.01    (93)   ~ (all_6_0 = e2)
% 204.18/35.01    (94)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.18/35.01            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.18/35.01    (95)  op(e3, e1) = all_52_17
% 204.18/35.01    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.01    (97)  op(e0, e3) = all_52_7
% 204.18/35.01    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.01    (99)   ~ (all_52_9 = all_52_25)
% 204.18/35.01    (100)  all_58_15 = all_14_2
% 204.18/35.01    (101)   ~ (all_52_19 = all_10_2)
% 204.18/35.01    (102)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.01    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.01    (104)  all_58_8 = all_10_2
% 204.18/35.01    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.01    (106)   ~ (all_52_5 = all_10_2)
% 204.18/35.01    (107)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.01    (108)   ~ (all_52_23 = all_14_2)
% 204.18/35.01    (109)  all_56_12 = all_52_7
% 204.18/35.01    (110)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.01    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.01    (112)   ~ (all_52_25 = all_6_2)
% 204.18/35.01    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.01    (114)   ~ (all_52_9 = all_4_2)
% 204.18/35.01    (115)   ~ (all_52_5 = all_6_2)
% 204.18/35.01    (116)  all_56_0 = all_6_2
% 204.18/35.01    (117)  op(e3, e3) = all_6_2
% 204.18/35.01    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.01    (119)   ~ (all_52_15 = all_6_0)
% 204.18/35.01    (120)   ~ (all_52_27 = all_14_2)
% 204.18/35.01    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.01    (122)  all_56_14 = all_52_23
% 204.18/35.01    (123)  all_56_3 = all_52_25
% 204.18/35.01    (124)   ~ (all_52_3 = all_52_7)
% 204.18/35.01    (125)   ~ (all_6_0 = all_6_2)
% 204.18/35.01    (126)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.01    (127)  all_58_5 = all_52_19
% 204.18/35.01    (128)   ~ (all_52_15 = all_4_2)
% 204.18/35.01    (129)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.01           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.01           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.01           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.01    (130)   ~ (all_52_27 = all_4_2)
% 204.18/35.01    (131)  all_58_6 = all_52_5
% 204.18/35.01    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.01    (133)   ~ (all_52_17 = all_6_2)
% 204.18/35.01    (134)   ~ (e1 = e0)
% 204.18/35.01    (135)   ~ (e3 = e2)
% 204.18/35.01    (136)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.01    (137)  all_56_10 = all_10_2
% 204.18/35.01    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.01    (139)  all_56_1 = all_6_0
% 204.18/35.01    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.01    (141)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.01    (142)   ~ (all_6_0 = all_4_2)
% 204.18/35.01    (143)  op(e1, e1) = all_10_2
% 204.18/35.01    (144)   ~ (all_52_23 = all_10_2)
% 204.18/35.01    (145)   ~ (all_52_7 = all_52_23)
% 204.18/35.01    (146)   ~ (all_52_17 = all_52_19)
% 204.18/35.01    (147)  all_58_3 = all_4_2
% 204.18/35.01    (148)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.01    (149)   ~ (all_52_3 = all_4_2)
% 204.18/35.01    (150)   ~ (all_52_19 = all_4_2)
% 204.18/35.01    (151)   ~ (all_52_17 = all_52_23)
% 204.18/35.01    (152)  op(all_6_2, e3) = all_6_1
% 204.18/35.01    (153)  all_22_2 = all_6_2
% 204.18/35.01    (154)  all_58_4 = all_52_17
% 204.18/35.01    (155)   ~ (all_14_0 = e2)
% 204.18/35.01    (156)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.01    (157)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.01  
% 204.18/35.01  Begin of proof
% 204.18/35.01  | 
% 204.18/35.01  | REDUCE: (29), (38) imply:
% 204.18/35.01  |   (158)   ~ (all_10_1 = e2)
% 204.18/35.01  | 
% 204.18/35.01  | BETA: splitting (94) gives:
% 204.18/35.01  | 
% 204.18/35.01  | Case 1:
% 204.18/35.01  | | 
% 204.18/35.01  | |   (159)  all_58_15 = e0
% 204.18/35.01  | | 
% 204.18/35.01  | | REF_CLOSE: (6), (19), (28), (49), (100), (126), (134), (159) are
% 204.18/35.01  | |            inconsistent by sub-proof #877.
% 204.18/35.01  | | 
% 204.18/35.01  | Case 2:
% 204.18/35.01  | | 
% 204.18/35.01  | |   (160)   ~ (all_58_15 = e0)
% 204.18/35.01  | |   (161)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 204.18/35.01  | |            | all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.01  | | 
% 204.18/35.01  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.01  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.18/35.01  | |            (24), (25), (26), (27), (30), (31), (32), (33), (34), (35), (36),
% 204.18/35.01  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.18/35.01  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 204.18/35.01  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.18/35.01  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 204.18/35.01  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 204.18/35.01  | |            (93), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 204.18/35.01  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 204.18/35.01  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 204.18/35.01  | |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 204.18/35.01  | |            (131), (132), (133), (134), (135), (136), (137), (138), (139),
% 204.18/35.01  | |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 204.18/35.01  | |            (149), (150), (151), (152), (153), (154), (155), (156), (157),
% 204.18/35.01  | |            (158), (160), (161) are inconsistent by sub-proof #775.
% 204.18/35.01  | | 
% 204.18/35.01  | End of split
% 204.18/35.01  | 
% 204.18/35.01  End of proof
% 204.18/35.01  
% 204.18/35.01  Sub-proof #775 shows that the following formulas are inconsistent:
% 204.18/35.01  ----------------------------------------------------------------
% 204.18/35.01    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.01    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.01    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.01    (4)  all_58_14 = all_52_23
% 204.18/35.01    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.01    (7)   ~ (all_52_5 = all_52_13)
% 204.18/35.01    (8)  all_58_1 = all_52_9
% 204.18/35.01    (9)   ~ (all_52_9 = all_52_13)
% 204.18/35.01    (10)   ~ (e3 = e0)
% 204.18/35.01    (11)  op(e2, e3) = all_52_3
% 204.18/35.01    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.01    (13)  op(e0, e2) = all_52_15
% 204.18/35.01    (14)   ~ (all_52_3 = all_52_19)
% 204.18/35.01    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.01    (16)   ~ (all_52_17 = all_52_25)
% 204.18/35.01    (17)   ~ (all_52_3 = all_6_2)
% 204.18/35.01    (18)  all_58_0 = all_6_2
% 204.18/35.01    (19)  op(all_14_2, e0) = all_14_1
% 204.18/35.01    (20)  all_56_4 = all_52_3
% 204.18/35.01    (21)   ~ (all_52_17 = all_10_2)
% 204.18/35.01    (22)  op(e3, e0) = all_52_25
% 204.18/35.01    (23)  op(e0, all_14_1) = all_14_0
% 204.18/35.01    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.01    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.01    (26)   ~ (all_52_27 = all_52_29)
% 204.18/35.01    (27)  all_58_13 = all_52_15
% 204.18/35.01    (28)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.01    (29)  all_58_9 = all_52_25
% 204.18/35.01    (30)   ~ (all_52_29 = all_14_2)
% 204.18/35.01    (31)  all_22_0 = all_6_0
% 204.18/35.01    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.01    (33)   ~ (all_52_17 = all_6_0)
% 204.18/35.01    (34)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.01    (35)  op(e1, e3) = all_52_5
% 204.18/35.01    (36)  op(e2, e2) = all_4_2
% 204.18/35.01    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.01    (38)   ~ (all_52_3 = all_52_5)
% 204.18/35.01    (39)  all_58_11 = all_52_29
% 204.18/35.01    (40)  all_56_5 = all_4_2
% 204.18/35.01    (41)   ~ (all_52_25 = all_14_2)
% 204.18/35.01    (42)   ~ (all_52_3 = all_52_27)
% 204.18/35.01    (43)  op(all_10_2, e1) = all_10_1
% 204.18/35.01    (44)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.01    (45)   ~ (all_52_7 = all_6_2)
% 204.18/35.01    (46)  op(e0, e0) = all_14_2
% 204.18/35.01    (47)  all_56_15 = all_14_2
% 204.18/35.01    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.02    (49)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.02    (50)   ~ (all_58_15 = e0)
% 204.18/35.02    (51)  all_56_11 = all_52_29
% 204.18/35.02    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.02    (53)   ~ (e2 = e1)
% 204.18/35.02    (54)   ~ (all_52_13 = all_10_2)
% 204.18/35.02    (55)   ~ (all_6_0 = e1)
% 204.18/35.02    (56)  all_58_10 = all_52_27
% 204.18/35.02    (57)  all_56_8 = all_52_5
% 204.18/35.02    (58)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.02    (59)   ~ (all_52_19 = all_52_23)
% 204.18/35.02    (60)   ~ (all_52_25 = all_52_29)
% 204.18/35.02    (61)  op(all_6_2, e3) = e2
% 204.18/35.02    (62)   ~ (all_52_29 = all_10_2)
% 204.18/35.02    (63)  all_58_7 = all_52_13
% 204.18/35.02    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.02    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.02    (66)  all_58_1 = all_6_0
% 204.18/35.02    (67)   ~ (all_52_5 = all_52_7)
% 204.18/35.02    (68)  all_58_12 = all_52_7
% 204.18/35.02    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.02    (70)   ~ (all_52_7 = all_14_2)
% 204.18/35.02    (71)  all_58_2 = all_52_3
% 204.18/35.02    (72)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/35.02    (73)  all_56_2 = all_52_17
% 204.18/35.02    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/35.02    (75)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.02    (76)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.02    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.18/35.02    (78)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.02    (79)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/35.02    (80)   ~ (e2 = e0)
% 204.18/35.02    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.02    (82)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.02    (83)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.02    (84)   ~ (all_52_5 = all_52_29)
% 204.18/35.02    (85)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.02    (86)  all_56_6 = all_52_19
% 204.18/35.02    (87)   ~ (all_52_15 = all_14_2)
% 204.18/35.02    (88)   ~ (all_52_13 = all_6_0)
% 204.18/35.02    (89)   ~ (all_52_19 = all_52_27)
% 204.18/35.02    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.02    (91)   ~ (all_6_0 = e2)
% 204.18/35.02    (92)  op(e3, e1) = all_52_17
% 204.18/35.02    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.02    (94)  op(e0, e3) = all_52_7
% 204.18/35.02    (95)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.02    (96)   ~ (all_52_9 = all_52_25)
% 204.18/35.02    (97)  all_58_15 = all_14_2
% 204.18/35.02    (98)   ~ (all_52_19 = all_10_2)
% 204.18/35.02    (99)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.02    (100)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.02    (101)   ~ (all_10_1 = e2)
% 204.18/35.02    (102)  all_58_8 = all_10_2
% 204.18/35.02    (103)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.02    (104)   ~ (all_52_5 = all_10_2)
% 204.18/35.02    (105)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.02    (106)   ~ (all_52_23 = all_14_2)
% 204.18/35.02    (107)  all_56_12 = all_52_7
% 204.18/35.02    (108)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.02    (109)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.02    (110)   ~ (all_52_25 = all_6_2)
% 204.18/35.02    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.02    (112)   ~ (all_52_9 = all_4_2)
% 204.18/35.02    (113)   ~ (all_52_5 = all_6_2)
% 204.18/35.02    (114)  all_56_0 = all_6_2
% 204.18/35.02    (115)  op(e3, e3) = all_6_2
% 204.18/35.02    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.02    (117)   ~ (all_52_15 = all_6_0)
% 204.18/35.02    (118)   ~ (all_52_27 = all_14_2)
% 204.18/35.02    (119)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.02    (120)  all_56_14 = all_52_23
% 204.18/35.02    (121)  all_56_3 = all_52_25
% 204.18/35.02    (122)   ~ (all_52_3 = all_52_7)
% 204.18/35.02    (123)   ~ (all_6_0 = all_6_2)
% 204.18/35.02    (124)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.02    (125)  all_58_5 = all_52_19
% 204.18/35.02    (126)   ~ (all_52_15 = all_4_2)
% 204.18/35.02    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.02           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.02           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.02           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.02    (128)   ~ (all_52_27 = all_4_2)
% 204.18/35.02    (129)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 204.18/35.02             all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.02    (130)  all_58_6 = all_52_5
% 204.18/35.02    (131)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.02    (132)   ~ (all_52_17 = all_6_2)
% 204.18/35.02    (133)   ~ (e1 = e0)
% 204.18/35.02    (134)   ~ (e3 = e2)
% 204.18/35.02    (135)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.02    (136)  all_56_10 = all_10_2
% 204.18/35.02    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.02    (138)  all_56_1 = all_6_0
% 204.18/35.02    (139)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.02    (140)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.02    (141)   ~ (all_6_0 = all_4_2)
% 204.18/35.02    (142)  op(e1, e1) = all_10_2
% 204.18/35.02    (143)   ~ (all_52_23 = all_10_2)
% 204.18/35.02    (144)   ~ (all_52_7 = all_52_23)
% 204.18/35.02    (145)   ~ (all_52_17 = all_52_19)
% 204.18/35.02    (146)  all_58_3 = all_4_2
% 204.18/35.02    (147)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.02    (148)   ~ (all_52_3 = all_4_2)
% 204.18/35.02    (149)   ~ (all_52_19 = all_4_2)
% 204.18/35.02    (150)   ~ (all_52_17 = all_52_23)
% 204.18/35.02    (151)  op(all_6_2, e3) = all_6_1
% 204.18/35.02    (152)  all_22_2 = all_6_2
% 204.18/35.02    (153)  all_58_4 = all_52_17
% 204.18/35.02    (154)   ~ (all_14_0 = e2)
% 204.18/35.02    (155)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.02    (156)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.02  
% 204.18/35.02  Begin of proof
% 204.18/35.02  | 
% 204.18/35.02  | ALPHA: (129) implies:
% 204.18/35.02  |   (157)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/35.02  |   (158)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.02  | 
% 204.18/35.02  | REDUCE: (50), (97) imply:
% 204.18/35.02  |   (159)   ~ (all_14_2 = e0)
% 204.18/35.02  | 
% 204.18/35.02  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.02  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.18/35.02  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.18/35.02  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.18/35.02  |            (46), (47), (48), (49), (51), (52), (53), (54), (55), (56), (57),
% 204.18/35.02  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 204.18/35.02  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 204.18/35.02  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 204.18/35.02  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 204.18/35.02  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 204.18/35.02  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 204.18/35.02  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 204.18/35.02  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 204.18/35.02  |            (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 204.18/35.02  |            (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 204.18/35.02  |            (157), (158), (159) are inconsistent by sub-proof #793.
% 204.18/35.02  | 
% 204.18/35.02  End of proof
% 204.18/35.02  
% 204.18/35.02  Sub-proof #776 shows that the following formulas are inconsistent:
% 204.18/35.02  ----------------------------------------------------------------
% 204.18/35.02    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.02    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.02    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.02    (4)  all_58_14 = all_52_23
% 204.18/35.02    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.02    (7)   ~ (all_52_5 = all_52_13)
% 204.18/35.02    (8)  all_58_1 = all_52_9
% 204.18/35.02    (9)   ~ (all_52_9 = all_52_13)
% 204.18/35.02    (10)   ~ (e3 = e0)
% 204.18/35.02    (11)  op(e2, e3) = all_52_3
% 204.18/35.02    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.02    (13)  op(e0, e2) = all_52_15
% 204.18/35.02    (14)   ~ (all_52_7 = all_52_15)
% 204.18/35.02    (15)   ~ (all_52_3 = all_52_19)
% 204.18/35.02    (16)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.02    (17)   ~ (all_52_17 = all_52_25)
% 204.18/35.02    (18)   ~ (all_52_3 = all_6_2)
% 204.18/35.02    (19)  all_58_0 = all_6_2
% 204.18/35.02    (20)  op(all_14_2, e0) = all_14_1
% 204.18/35.02    (21)  all_56_4 = all_52_3
% 204.18/35.02    (22)   ~ (all_52_17 = all_10_2)
% 204.18/35.02    (23)   ~ (all_10_0 = e3)
% 204.18/35.02    (24)  all_40_2 = all_10_2
% 204.18/35.02    (25)  op(e3, e0) = all_52_25
% 204.18/35.02    (26)  op(e0, all_14_1) = all_14_0
% 204.18/35.02    (27)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.02    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.18/35.02    (29)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.02    (30)   ~ (all_52_27 = all_52_29)
% 204.18/35.02    (31)  all_58_13 = all_52_15
% 204.18/35.02    (32)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.02    (33)  all_58_9 = all_52_25
% 204.18/35.02    (34)   ~ (all_52_29 = all_14_2)
% 204.18/35.02    (35)  all_22_0 = all_6_0
% 204.18/35.02    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.02    (37)   ~ (all_52_17 = all_6_0)
% 204.18/35.02    (38)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.02    (39)  op(e1, e3) = all_52_5
% 204.18/35.02    (40)  all_40_1 = all_10_1
% 204.18/35.02    (41)  op(e2, e2) = all_4_2
% 204.18/35.02    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.02    (43)   ~ (all_52_3 = all_52_5)
% 204.18/35.02    (44)  all_58_11 = all_52_29
% 204.18/35.02    (45)  all_56_5 = all_4_2
% 204.18/35.02    (46)   ~ (all_52_25 = all_14_2)
% 204.18/35.02    (47)   ~ (all_52_3 = all_52_27)
% 204.18/35.02    (48)  op(all_10_2, e1) = all_10_1
% 204.18/35.02    (49)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.02    (50)   ~ (all_52_7 = all_6_2)
% 204.18/35.02    (51)  op(e0, e0) = all_14_2
% 204.18/35.02    (52)  all_56_15 = all_14_2
% 204.18/35.02    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.02    (54)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.02    (55)  op(e2, all_4_1) = all_4_0
% 204.18/35.02    (56)  all_56_11 = all_52_29
% 204.18/35.02    (57)   ~ (all_10_0 = e2)
% 204.18/35.02    (58)   ~ (all_4_0 = e3)
% 204.18/35.02    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.02    (60)  all_56_9 = all_52_13
% 204.18/35.02    (61)   ~ (e2 = e1)
% 204.18/35.02    (62)   ~ (all_52_13 = all_10_2)
% 204.18/35.02    (63)   ~ (all_6_0 = e1)
% 204.18/35.02    (64)  op(e1, all_10_1) = all_10_0
% 204.18/35.02    (65)  all_58_10 = all_52_27
% 204.18/35.02    (66)  all_56_8 = all_52_5
% 204.18/35.02    (67)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.02    (68)   ~ (all_52_19 = all_52_23)
% 204.18/35.02    (69)   ~ (all_52_25 = all_52_29)
% 204.18/35.02    (70)  op(all_6_2, e3) = e2
% 204.18/35.02    (71)   ~ (all_52_29 = all_10_2)
% 204.18/35.02    (72)  all_58_7 = all_52_13
% 204.18/35.02    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.02    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.02    (75)  all_58_1 = all_6_0
% 204.18/35.02    (76)   ~ (all_52_5 = all_52_7)
% 204.18/35.02    (77)  all_58_12 = all_52_7
% 204.18/35.02    (78)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.02    (79)   ~ (all_52_7 = all_14_2)
% 204.18/35.02    (80)  all_58_2 = all_52_3
% 204.18/35.02    (81)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.18/35.02    (82)  all_56_2 = all_52_17
% 204.18/35.02    (83)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/35.02    (84)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.02    (85)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.02    (86)   ~ (all_14_0 = e3)
% 204.18/35.02    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.18/35.02    (88)  all_56_7 = all_52_27
% 204.18/35.02    (89)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.02    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.18/35.02    (91)   ~ (e2 = e0)
% 204.18/35.02    (92)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.02    (93)  op(all_4_2, e2) = all_4_1
% 204.18/35.02    (94)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.02    (95)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.02    (96)   ~ (all_52_5 = all_52_29)
% 204.18/35.02    (97)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.02    (98)  all_56_6 = all_52_19
% 204.18/35.02    (99)   ~ (all_52_15 = all_14_2)
% 204.18/35.02    (100)   ~ (all_52_13 = all_6_0)
% 204.18/35.02    (101)   ~ (all_52_19 = all_52_27)
% 204.18/35.02    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.02    (103)   ~ (all_6_0 = e2)
% 204.18/35.02    (104)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.18/35.02             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.18/35.02    (105)   ~ (all_52_13 = all_4_2)
% 204.18/35.02    (106)  op(e3, e1) = all_52_17
% 204.18/35.02    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.02    (108)  op(e0, e3) = all_52_7
% 204.18/35.02    (109)  op(e1, e2) = all_52_13
% 204.18/35.02    (110)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.02    (111)   ~ (all_52_9 = all_52_25)
% 204.18/35.02    (112)  all_58_15 = all_14_2
% 204.18/35.02    (113)   ~ (all_52_19 = all_10_2)
% 204.18/35.02    (114)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.02    (115)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e2) |  ~ (all_40_2 = e3)
% 204.18/35.02    (116)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.02    (117)  all_58_8 = all_10_2
% 204.18/35.02    (118)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.02    (119)   ~ (all_52_5 = all_10_2)
% 204.18/35.02    (120)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.02    (121)   ~ (all_52_23 = all_14_2)
% 204.18/35.02    (122)  all_56_12 = all_52_7
% 204.18/35.02    (123)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.02    (124)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.02    (125)   ~ (all_52_25 = all_6_2)
% 204.18/35.02    (126)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.02    (127)   ~ (all_52_9 = all_4_2)
% 204.18/35.02    (128)   ~ (all_52_5 = all_6_2)
% 204.18/35.02    (129)   ~ (all_52_9 = all_6_2)
% 204.18/35.02    (130)  all_56_0 = all_6_2
% 204.18/35.02    (131)  op(e3, e3) = all_6_2
% 204.18/35.02    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.02    (133)   ~ (all_52_15 = all_6_0)
% 204.18/35.02    (134)   ~ (all_52_27 = all_14_2)
% 204.18/35.02    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.02    (136)  all_56_14 = all_52_23
% 204.18/35.02    (137)  op(all_4_2, all_4_2) = all_52_10
% 204.18/35.02    (138)  all_40_0 = all_10_0
% 204.18/35.02    (139)  all_56_3 = all_52_25
% 204.18/35.02    (140)   ~ (all_52_3 = all_52_7)
% 204.18/35.02    (141)   ~ (all_6_0 = all_6_2)
% 204.18/35.02    (142)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.02    (143)  all_58_5 = all_52_19
% 204.18/35.02    (144)   ~ (all_52_15 = all_4_2)
% 204.18/35.02    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.02           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.02           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.02           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.02    (146)   ~ (all_52_27 = all_4_2)
% 204.18/35.02    (147)  all_58_6 = all_52_5
% 204.18/35.02    (148)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.02    (149)   ~ (all_52_17 = all_6_2)
% 204.18/35.02    (150)  all_30_1 = all_10_1
% 204.18/35.02    (151)   ~ (e1 = e0)
% 204.18/35.02    (152)   ~ (e3 = e2)
% 204.18/35.02    (153)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.02    (154)   ~ (all_52_9 = all_52_17)
% 204.18/35.02    (155)  all_56_10 = all_10_2
% 204.18/35.02    (156)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.02    (157)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e3) |  ~ (all_30_2 = e2)
% 204.18/35.02    (158)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.18/35.02    (159)  all_56_1 = all_6_0
% 204.18/35.02    (160)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.02    (161)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.02    (162)   ~ (all_6_0 = all_4_2)
% 204.18/35.02    (163)  op(e1, e1) = all_10_2
% 204.18/35.02    (164)   ~ (all_52_23 = all_10_2)
% 204.18/35.02    (165)   ~ (all_52_7 = all_52_23)
% 204.18/35.02    (166)   ~ (all_52_17 = all_52_19)
% 204.18/35.02    (167)  all_58_3 = all_4_2
% 204.18/35.02    (168)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.02    (169)   ~ (all_52_3 = all_4_2)
% 204.18/35.02    (170)   ~ (all_52_19 = all_4_2)
% 204.18/35.02    (171)   ~ (all_52_17 = all_52_23)
% 204.18/35.02    (172)  op(all_6_2, e3) = all_6_1
% 204.18/35.02    (173)  all_22_2 = all_6_2
% 204.18/35.02    (174)  all_58_4 = all_52_17
% 204.18/35.02    (175)   ~ (all_14_0 = e1)
% 204.18/35.02    (176)   ~ (all_14_0 = e2)
% 204.18/35.02    (177)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.02    (178)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.02  
% 204.18/35.02  Begin of proof
% 204.18/35.02  | 
% 204.18/35.02  | BETA: splitting (157) gives:
% 204.18/35.02  | 
% 204.18/35.02  | Case 1:
% 204.18/35.02  | | 
% 204.18/35.02  | |   (179)   ~ (all_30_1 = e3)
% 204.18/35.02  | | 
% 204.18/35.02  | | REDUCE: (150), (179) imply:
% 204.18/35.02  | |   (180)   ~ (all_10_1 = e3)
% 204.18/35.02  | | 
% 204.18/35.02  | | BETA: splitting (115) gives:
% 204.18/35.02  | | 
% 204.18/35.02  | | Case 1:
% 204.18/35.02  | | | 
% 204.18/35.02  | | |   (181)   ~ (all_40_1 = e2)
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.02  | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (25),
% 204.18/35.02  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 204.18/35.02  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.18/35.02  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56),
% 204.18/35.02  | | |            (59), (61), (62), (63), (65), (66), (67), (68), (69), (70),
% 204.18/35.02  | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.18/35.02  | | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 204.18/35.02  | | |            (91), (92), (94), (95), (96), (97), (98), (99), (100), (101),
% 204.18/35.02  | | |            (102), (103), (104), (106), (107), (108), (110), (111), (112),
% 204.18/35.02  | | |            (113), (114), (116), (117), (118), (119), (120), (121), (122),
% 204.18/35.02  | | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 204.18/35.02  | | |            (132), (133), (134), (135), (136), (139), (140), (141), (142),
% 204.18/35.02  | | |            (143), (144), (145), (146), (147), (148), (149), (151), (152),
% 204.18/35.02  | | |            (153), (155), (156), (159), (160), (161), (162), (163), (164),
% 204.18/35.02  | | |            (165), (166), (167), (168), (169), (170), (171), (172), (173),
% 204.18/35.02  | | |            (174), (175), (176), (177), (178), (181) are inconsistent by
% 204.18/35.02  | | |            sub-proof #792.
% 204.18/35.02  | | | 
% 204.18/35.02  | | Case 2:
% 204.18/35.02  | | | 
% 204.18/35.02  | | |   (182)  all_40_1 = e2
% 204.18/35.02  | | |   (183)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.18/35.02  | | | 
% 204.18/35.02  | | | COMBINE_EQS: (40), (182) imply:
% 204.18/35.02  | | |   (184)  all_10_1 = e2
% 204.18/35.02  | | | 
% 204.18/35.02  | | | SIMP: (184) implies:
% 204.18/35.02  | | |   (185)  all_10_1 = e2
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REDUCE: (180), (185) imply:
% 204.18/35.02  | | |   (186)   ~ (e3 = e2)
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REDUCE: (48), (185) imply:
% 204.18/35.02  | | |   (187)  op(all_10_2, e1) = e2
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REDUCE: (64), (185) imply:
% 204.18/35.02  | | |   (188)  op(e1, e2) = all_10_0
% 204.18/35.02  | | | 
% 204.18/35.02  | | | GROUND_INST: instantiating (6) with all_52_13, all_10_0, e2, e1,
% 204.18/35.02  | | |              simplifying with (109), (188) gives:
% 204.18/35.02  | | |   (189)  all_52_13 = all_10_0
% 204.18/35.02  | | | 
% 204.18/35.02  | | | COMBINE_EQS: (60), (189) imply:
% 204.18/35.02  | | |   (190)  all_56_9 = all_10_0
% 204.18/35.02  | | | 
% 204.18/35.02  | | | COMBINE_EQS: (72), (189) imply:
% 204.18/35.02  | | |   (191)  all_58_7 = all_10_0
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REDUCE: (7), (189) imply:
% 204.18/35.02  | | |   (192)   ~ (all_52_5 = all_10_0)
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REDUCE: (100), (189) imply:
% 204.18/35.02  | | |   (193)   ~ (all_10_0 = all_6_0)
% 204.18/35.02  | | | 
% 204.18/35.02  | | | REDUCE: (105), (189) imply:
% 204.18/35.02  | | |   (194)   ~ (all_10_0 = all_4_2)
% 204.18/35.02  | | | 
% 204.18/35.02  | | | BETA: splitting (104) gives:
% 204.18/35.02  | | | 
% 204.18/35.02  | | | Case 1:
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | |   (195)  all_58_15 = e0
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (16), (17), (18),
% 204.18/35.02  | | | |            (19), (20), (22), (26), (27), (28), (29), (31), (32), (33),
% 204.18/35.02  | | | |            (34), (35), (36), (37), (38), (41), (44), (46), (48), (49),
% 204.18/35.02  | | | |            (51), (53), (54), (56), (59), (61), (63), (65), (67), (68),
% 204.18/35.02  | | | |            (69), (70), (71), (72), (75), (77), (78), (79), (80), (82),
% 204.18/35.02  | | | |            (83), (84), (85), (86), (88), (89), (94), (95), (96), (100),
% 204.18/35.02  | | | |            (101), (102), (103), (106), (108), (110), (112), (113),
% 204.18/35.02  | | | |            (114), (117), (119), (120), (121), (123), (125), (126),
% 204.18/35.02  | | | |            (129), (130), (131), (132), (133), (139), (140), (141),
% 204.18/35.02  | | | |            (142), (143), (145), (147), (148), (149), (152), (153),
% 204.18/35.02  | | | |            (156), (159), (160), (162), (163), (164), (165), (166),
% 204.18/35.02  | | | |            (167), (169), (170), (171), (173), (174), (175), (176),
% 204.18/35.02  | | | |            (178), (195) are inconsistent by sub-proof #818.
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | Case 2:
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | |   (196)   ~ (all_58_15 = e0)
% 204.18/35.02  | | | |   (197)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 204.18/35.02  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | | ALPHA: (197) implies:
% 204.18/35.02  | | | |   (198)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/35.02  | | | |   (199)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | | REDUCE: (112), (196) imply:
% 204.18/35.02  | | | |   (200)   ~ (all_14_2 = e0)
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 204.18/35.02  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 204.18/35.02  | | | |            (25), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.18/35.02  | | | |            (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 204.18/35.02  | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 204.18/35.02  | | | |            (58), (59), (61), (63), (65), (66), (67), (68), (69), (70),
% 204.18/35.02  | | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.18/35.02  | | | |            (82), (84), (85), (89), (90), (91), (92), (93), (94), (95),
% 204.18/35.02  | | | |            (96), (97), (101), (102), (103), (106), (107), (108), (110),
% 204.18/35.02  | | | |            (111), (112), (113), (114), (116), (117), (118), (119),
% 204.18/35.02  | | | |            (120), (121), (122), (123), (124), (125), (126), (127),
% 204.18/35.02  | | | |            (128), (130), (131), (132), (133), (134), (135), (136),
% 204.18/35.02  | | | |            (137), (138), (139), (140), (141), (142), (143), (144),
% 204.18/35.02  | | | |            (145), (146), (147), (148), (149), (151), (152), (153),
% 204.18/35.02  | | | |            (155), (156), (158), (159), (160), (161), (162), (163),
% 204.18/35.02  | | | |            (164), (165), (167), (168), (169), (170), (171), (172),
% 204.18/35.02  | | | |            (173), (174), (177), (178), (183), (187), (190), (191),
% 204.18/35.02  | | | |            (192), (193), (194), (198), (199), (200) are inconsistent by
% 204.18/35.02  | | | |            sub-proof #781.
% 204.18/35.02  | | | | 
% 204.18/35.02  | | | End of split
% 204.18/35.02  | | | 
% 204.18/35.02  | | End of split
% 204.18/35.02  | | 
% 204.18/35.02  | Case 2:
% 204.18/35.02  | | 
% 204.18/35.02  | |   (201)  all_30_1 = e3
% 204.18/35.02  | | 
% 204.18/35.02  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (15),
% 204.18/35.02  | |            (16), (17), (18), (19), (20), (22), (23), (26), (27), (28), (29),
% 204.18/35.02  | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), (41),
% 204.18/35.02  | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 204.18/35.02  | |            (53), (54), (56), (59), (61), (63), (64), (65), (66), (67), (68),
% 204.18/35.02  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 204.18/35.02  | |            (80), (82), (83), (84), (85), (86), (88), (89), (91), (92), (94),
% 204.18/35.02  | |            (95), (96), (97), (100), (101), (102), (103), (104), (106),
% 204.18/35.02  | |            (107), (108), (110), (111), (112), (113), (114), (116), (117),
% 204.18/35.02  | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 204.18/35.02  | |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 204.18/35.02  | |            (136), (139), (140), (141), (142), (143), (144), (145), (146),
% 204.18/35.02  | |            (147), (148), (149), (150), (151), (152), (153), (154), (155),
% 204.18/35.02  | |            (156), (159), (160), (161), (162), (163), (164), (165), (166),
% 204.18/35.02  | |            (167), (168), (169), (170), (171), (172), (173), (174), (175),
% 204.18/35.02  | |            (176), (177), (178), (201) are inconsistent by sub-proof #777.
% 204.18/35.02  | | 
% 204.18/35.02  | End of split
% 204.18/35.02  | 
% 204.18/35.02  End of proof
% 204.18/35.02  
% 204.18/35.02  Sub-proof #777 shows that the following formulas are inconsistent:
% 204.18/35.02  ----------------------------------------------------------------
% 204.18/35.02    (1)   ~ (all_52_15 = all_52_23)
% 204.18/35.02    (2)   ~ (all_52_25 = all_6_0)
% 204.18/35.02    (3)   ~ (all_52_25 = all_52_27)
% 204.18/35.02    (4)  all_58_14 = all_52_23
% 204.18/35.02    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.02    (7)  all_58_1 = all_52_9
% 204.18/35.02    (8)   ~ (all_52_9 = all_52_13)
% 204.18/35.02    (9)   ~ (e3 = e0)
% 204.18/35.02    (10)  op(e2, e3) = all_52_3
% 204.18/35.02    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.02    (12)   ~ (all_52_3 = all_52_19)
% 204.18/35.02    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.02    (14)   ~ (all_52_17 = all_52_25)
% 204.18/35.02    (15)   ~ (all_52_3 = all_6_2)
% 204.18/35.02    (16)  all_58_0 = all_6_2
% 204.18/35.02    (17)  op(all_14_2, e0) = all_14_1
% 204.18/35.02    (18)   ~ (all_52_17 = all_10_2)
% 204.18/35.02    (19)   ~ (all_10_0 = e3)
% 204.18/35.02    (20)  all_30_1 = e3
% 204.18/35.02    (21)  op(e0, all_14_1) = all_14_0
% 204.18/35.02    (22)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.02    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.18/35.02    (24)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.02    (25)   ~ (all_52_27 = all_52_29)
% 204.18/35.02    (26)  all_58_13 = all_52_15
% 204.18/35.02    (27)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.02    (28)  all_58_9 = all_52_25
% 204.18/35.02    (29)   ~ (all_52_29 = all_14_2)
% 204.18/35.02    (30)  all_22_0 = all_6_0
% 204.18/35.02    (31)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.02    (32)   ~ (all_52_17 = all_6_0)
% 204.18/35.02    (33)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.02    (34)  op(e1, e3) = all_52_5
% 204.18/35.02    (35)  op(e2, e2) = all_4_2
% 204.18/35.02    (36)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.02    (37)   ~ (all_52_3 = all_52_5)
% 204.18/35.02    (38)  all_58_11 = all_52_29
% 204.18/35.02    (39)  all_56_5 = all_4_2
% 204.18/35.02    (40)   ~ (all_52_25 = all_14_2)
% 204.18/35.02    (41)   ~ (all_52_3 = all_52_27)
% 204.18/35.02    (42)  op(all_10_2, e1) = all_10_1
% 204.18/35.02    (43)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.02    (44)   ~ (all_52_7 = all_6_2)
% 204.18/35.02    (45)  op(e0, e0) = all_14_2
% 204.18/35.02    (46)  all_56_15 = all_14_2
% 204.18/35.02    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.02    (48)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.02    (49)  all_56_11 = all_52_29
% 204.18/35.02    (50)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.02    (51)   ~ (e2 = e1)
% 204.18/35.02    (52)   ~ (all_6_0 = e1)
% 204.18/35.02    (53)  op(e1, all_10_1) = all_10_0
% 204.18/35.02    (54)  all_58_10 = all_52_27
% 204.18/35.02    (55)  all_56_8 = all_52_5
% 204.18/35.02    (56)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.02    (57)   ~ (all_52_19 = all_52_23)
% 204.18/35.02    (58)   ~ (all_52_25 = all_52_29)
% 204.18/35.02    (59)  op(all_6_2, e3) = e2
% 204.18/35.02    (60)   ~ (all_52_29 = all_10_2)
% 204.18/35.02    (61)  all_58_7 = all_52_13
% 204.18/35.02    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.02    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.02    (64)  all_58_1 = all_6_0
% 204.18/35.02    (65)   ~ (all_52_5 = all_52_7)
% 204.18/35.02    (66)  all_58_12 = all_52_7
% 204.18/35.02    (67)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.02    (68)   ~ (all_52_7 = all_14_2)
% 204.18/35.02    (69)  all_58_2 = all_52_3
% 204.18/35.02    (70)  all_56_2 = all_52_17
% 204.18/35.03    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.18/35.03    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.03    (73)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.03    (74)   ~ (all_14_0 = e3)
% 204.18/35.03    (75)  all_56_7 = all_52_27
% 204.18/35.03    (76)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.03    (77)   ~ (e2 = e0)
% 204.18/35.03    (78)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.03    (79)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.03    (80)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.03    (81)   ~ (all_52_5 = all_52_29)
% 204.18/35.03    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.03    (83)   ~ (all_52_13 = all_6_0)
% 204.18/35.03    (84)   ~ (all_52_19 = all_52_27)
% 204.18/35.03    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.03    (86)   ~ (all_6_0 = e2)
% 204.18/35.03    (87)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.18/35.03            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.18/35.03    (88)  op(e3, e1) = all_52_17
% 204.18/35.03    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.03    (90)  op(e0, e3) = all_52_7
% 204.18/35.03    (91)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.03    (92)   ~ (all_52_9 = all_52_25)
% 204.18/35.03    (93)  all_58_15 = all_14_2
% 204.18/35.03    (94)   ~ (all_52_19 = all_10_2)
% 204.18/35.03    (95)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.03    (96)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.03    (97)  all_58_8 = all_10_2
% 204.18/35.03    (98)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.03    (99)   ~ (all_52_5 = all_10_2)
% 204.18/35.03    (100)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.03    (101)   ~ (all_52_23 = all_14_2)
% 204.18/35.03    (102)  all_56_12 = all_52_7
% 204.18/35.03    (103)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.03    (104)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.03    (105)   ~ (all_52_25 = all_6_2)
% 204.18/35.03    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.03    (107)   ~ (all_52_9 = all_4_2)
% 204.18/35.03    (108)   ~ (all_52_5 = all_6_2)
% 204.18/35.03    (109)   ~ (all_52_9 = all_6_2)
% 204.18/35.03    (110)  all_56_0 = all_6_2
% 204.18/35.03    (111)  op(e3, e3) = all_6_2
% 204.18/35.03    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.03    (113)   ~ (all_52_15 = all_6_0)
% 204.18/35.03    (114)   ~ (all_52_27 = all_14_2)
% 204.18/35.03    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.03    (116)  all_56_14 = all_52_23
% 204.18/35.03    (117)  all_56_3 = all_52_25
% 204.18/35.03    (118)   ~ (all_52_3 = all_52_7)
% 204.18/35.03    (119)   ~ (all_6_0 = all_6_2)
% 204.18/35.03    (120)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.03    (121)  all_58_5 = all_52_19
% 204.18/35.03    (122)   ~ (all_52_15 = all_4_2)
% 204.18/35.03    (123)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.03           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.03           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.03           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.03    (124)   ~ (all_52_27 = all_4_2)
% 204.18/35.03    (125)  all_58_6 = all_52_5
% 204.18/35.03    (126)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.03    (127)   ~ (all_52_17 = all_6_2)
% 204.18/35.03    (128)  all_30_1 = all_10_1
% 204.18/35.03    (129)   ~ (e1 = e0)
% 204.18/35.03    (130)   ~ (e3 = e2)
% 204.18/35.03    (131)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.03    (132)   ~ (all_52_9 = all_52_17)
% 204.18/35.03    (133)  all_56_10 = all_10_2
% 204.18/35.03    (134)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.03    (135)  all_56_1 = all_6_0
% 204.18/35.03    (136)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.03    (137)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.03    (138)   ~ (all_6_0 = all_4_2)
% 204.18/35.03    (139)  op(e1, e1) = all_10_2
% 204.18/35.03    (140)   ~ (all_52_23 = all_10_2)
% 204.18/35.03    (141)   ~ (all_52_7 = all_52_23)
% 204.18/35.03    (142)   ~ (all_52_17 = all_52_19)
% 204.18/35.03    (143)  all_58_3 = all_4_2
% 204.18/35.03    (144)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.03    (145)   ~ (all_52_3 = all_4_2)
% 204.18/35.03    (146)   ~ (all_52_19 = all_4_2)
% 204.18/35.03    (147)   ~ (all_52_17 = all_52_23)
% 204.18/35.03    (148)  op(all_6_2, e3) = all_6_1
% 204.18/35.03    (149)  all_22_2 = all_6_2
% 204.18/35.03    (150)  all_58_4 = all_52_17
% 204.18/35.03    (151)   ~ (all_14_0 = e1)
% 204.18/35.03    (152)   ~ (all_14_0 = e2)
% 204.18/35.03    (153)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.03    (154)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.03  
% 204.18/35.03  Begin of proof
% 204.18/35.03  | 
% 204.18/35.03  | COMBINE_EQS: (20), (128) imply:
% 204.18/35.03  |   (155)  all_10_1 = e3
% 204.18/35.03  | 
% 204.18/35.03  | REDUCE: (42), (155) imply:
% 204.18/35.03  |   (156)  op(all_10_2, e1) = e3
% 204.18/35.03  | 
% 204.18/35.03  | REDUCE: (53), (155) imply:
% 204.18/35.03  |   (157)  op(e1, e3) = all_10_0
% 204.18/35.03  | 
% 204.18/35.03  | GROUND_INST: instantiating (6) with all_52_5, all_10_0, e3, e1, simplifying
% 204.18/35.03  |              with (34), (157) gives:
% 204.18/35.03  |   (158)  all_52_5 = all_10_0
% 204.18/35.03  | 
% 204.18/35.03  | COMBINE_EQS: (125), (158) imply:
% 204.18/35.03  |   (159)  all_58_6 = all_10_0
% 204.18/35.03  | 
% 204.18/35.03  | BETA: splitting (87) gives:
% 204.18/35.03  | 
% 204.18/35.03  | Case 1:
% 204.18/35.03  | | 
% 204.18/35.03  | |   (160)  all_58_15 = e0
% 204.18/35.03  | | 
% 204.18/35.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (13), (14), (15), (16),
% 204.18/35.03  | |            (17), (18), (21), (22), (23), (24), (26), (27), (28), (29), (30),
% 204.18/35.03  | |            (31), (32), (33), (35), (38), (40), (42), (43), (45), (47), (48),
% 204.18/35.03  | |            (49), (50), (51), (52), (54), (56), (57), (58), (59), (60), (61),
% 204.18/35.03  | |            (64), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 204.18/35.03  | |            (76), (79), (80), (81), (83), (84), (85), (86), (88), (90), (91),
% 204.18/35.03  | |            (93), (94), (95), (97), (99), (100), (101), (103), (105), (106),
% 204.18/35.03  | |            (109), (110), (111), (112), (113), (117), (118), (119), (120),
% 204.18/35.03  | |            (121), (123), (125), (126), (127), (130), (131), (134), (135),
% 204.18/35.03  | |            (136), (138), (139), (140), (141), (142), (143), (145), (146),
% 204.18/35.03  | |            (147), (149), (150), (151), (152), (154), (160) are inconsistent
% 204.18/35.03  | |            by sub-proof #818.
% 204.18/35.03  | | 
% 204.18/35.03  | Case 2:
% 204.18/35.03  | | 
% 204.18/35.03  | |   (161)   ~ (all_58_15 = e0)
% 204.18/35.03  | |   (162)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 204.18/35.03  | |            | all_58_13 = e0 | all_58_14 = e0)
% 204.18/35.03  | | 
% 204.18/35.03  | | ALPHA: (162) implies:
% 204.18/35.03  | |   (163)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/35.03  | |   (164)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (93), (161) imply:
% 204.18/35.03  | |   (165)   ~ (all_14_2 = e0)
% 204.18/35.03  | | 
% 204.18/35.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.03  | |            (13), (14), (15), (16), (18), (19), (22), (24), (25), (26), (27),
% 204.18/35.03  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 204.18/35.03  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 204.18/35.03  | |            (50), (51), (52), (54), (55), (56), (57), (58), (59), (60), (61),
% 204.18/35.03  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (72), (73),
% 204.18/35.03  | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 204.18/35.03  | |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 204.18/35.03  | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 204.18/35.03  | |            (108), (110), (111), (112), (113), (114), (115), (116), (117),
% 204.18/35.03  | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 204.18/35.03  | |            (127), (129), (130), (131), (132), (133), (134), (135), (136),
% 204.18/35.03  | |            (137), (138), (139), (140), (141), (143), (144), (145), (146),
% 204.18/35.03  | |            (147), (148), (149), (150), (153), (154), (156), (159), (163),
% 204.18/35.03  | |            (164), (165) are inconsistent by sub-proof #778.
% 204.18/35.03  | | 
% 204.18/35.03  | End of split
% 204.18/35.03  | 
% 204.18/35.03  End of proof
% 204.18/35.03  
% 204.18/35.03  Sub-proof #778 shows that the following formulas are inconsistent:
% 204.18/35.03  ----------------------------------------------------------------
% 204.18/35.03    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.03    (2)   ~ (all_52_15 = all_52_23)
% 204.18/35.03    (3)   ~ (all_52_25 = all_6_0)
% 204.18/35.03    (4)   ~ (all_52_25 = all_52_27)
% 204.18/35.03    (5)  all_58_14 = all_52_23
% 204.18/35.03    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.03    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.03    (8)  all_58_1 = all_52_9
% 204.18/35.03    (9)   ~ (all_52_9 = all_52_13)
% 204.18/35.03    (10)   ~ (e3 = e0)
% 204.18/35.03    (11)  op(e2, e3) = all_52_3
% 204.18/35.03    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.03    (13)   ~ (all_52_3 = all_52_19)
% 204.18/35.03    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.03    (15)   ~ (all_52_17 = all_52_25)
% 204.18/35.03    (16)   ~ (all_52_3 = all_6_2)
% 204.18/35.03    (17)  all_58_0 = all_6_2
% 204.18/35.03    (18)   ~ (all_52_17 = all_10_2)
% 204.18/35.03    (19)   ~ (all_10_0 = e3)
% 204.18/35.03    (20)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.03    (21)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.03    (22)   ~ (all_52_27 = all_52_29)
% 204.18/35.03    (23)  all_58_13 = all_52_15
% 204.18/35.03    (24)  op(all_10_2, all_10_2) = all_52_20
% 204.18/35.03    (25)  all_58_9 = all_52_25
% 204.18/35.03    (26)   ~ (all_52_29 = all_14_2)
% 204.18/35.03    (27)  all_22_0 = all_6_0
% 204.18/35.03    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.18/35.03    (29)   ~ (all_52_17 = all_6_0)
% 204.18/35.03    (30)  op(all_52_27, all_52_27) = all_52_26
% 204.18/35.03    (31)  op(e1, e3) = all_52_5
% 204.18/35.03    (32)  op(e2, e2) = all_4_2
% 204.18/35.03    (33)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.18/35.03    (34)   ~ (all_52_3 = all_52_5)
% 204.18/35.03    (35)  all_58_11 = all_52_29
% 204.18/35.03    (36)  all_56_5 = all_4_2
% 204.18/35.03    (37)   ~ (all_52_25 = all_14_2)
% 204.18/35.03    (38)   ~ (all_52_3 = all_52_27)
% 204.18/35.03    (39)  op(all_10_2, e1) = all_10_1
% 204.18/35.03    (40)  op(all_6_2, all_6_2) = all_52_0
% 204.18/35.03    (41)   ~ (all_52_7 = all_6_2)
% 204.18/35.03    (42)  op(e0, e0) = all_14_2
% 204.18/35.03    (43)  all_56_15 = all_14_2
% 204.18/35.03    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.18/35.03    (45)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.18/35.03    (46)  all_56_11 = all_52_29
% 204.18/35.03    (47)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.18/35.03    (48)   ~ (e2 = e1)
% 204.18/35.03    (49)   ~ (all_6_0 = e1)
% 204.18/35.03    (50)  all_58_10 = all_52_27
% 204.18/35.03    (51)  all_56_8 = all_52_5
% 204.18/35.03    (52)  op(all_52_9, all_52_9) = all_52_8
% 204.18/35.03    (53)   ~ (all_52_19 = all_52_23)
% 204.18/35.03    (54)   ~ (all_52_25 = all_52_29)
% 204.18/35.03    (55)  op(all_6_2, e3) = e2
% 204.18/35.03    (56)   ~ (all_52_29 = all_10_2)
% 204.18/35.03    (57)  op(all_10_2, e1) = e3
% 204.18/35.03    (58)  all_58_7 = all_52_13
% 204.18/35.03    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.18/35.03    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.18/35.03    (61)  all_58_1 = all_6_0
% 204.18/35.03    (62)   ~ (all_52_5 = all_52_7)
% 204.18/35.03    (63)  all_58_12 = all_52_7
% 204.18/35.03    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.18/35.03    (65)   ~ (all_52_7 = all_14_2)
% 204.18/35.03    (66)   ~ (all_14_2 = e0)
% 204.18/35.03    (67)  all_58_2 = all_52_3
% 204.18/35.03    (68)  all_56_2 = all_52_17
% 204.18/35.03    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.03    (70)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.18/35.03    (71)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.18/35.03    (72)   ~ (e2 = e0)
% 204.18/35.03    (73)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.18/35.03    (74)  op(all_6_0, all_6_0) = all_52_8
% 204.18/35.03    (75)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.18/35.03    (76)   ~ (all_52_5 = all_52_29)
% 204.18/35.03    (77)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.18/35.03    (78)   ~ (all_52_13 = all_6_0)
% 204.18/35.03    (79)   ~ (all_52_19 = all_52_27)
% 204.18/35.03    (80)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.18/35.03    (81)   ~ (all_6_0 = e2)
% 204.18/35.03    (82)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.18/35.03    (83)  op(e3, e1) = all_52_17
% 204.18/35.03    (84)  all_58_6 = all_10_0
% 204.18/35.03    (85)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.18/35.03    (86)  op(e0, e3) = all_52_7
% 204.18/35.03    (87)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.03    (88)   ~ (all_52_9 = all_52_25)
% 204.18/35.03    (89)  all_58_15 = all_14_2
% 204.18/35.03    (90)   ~ (all_52_19 = all_10_2)
% 204.18/35.03    (91)  op(all_52_23, all_52_23) = all_52_22
% 204.18/35.03    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.18/35.03    (93)  all_58_8 = all_10_2
% 204.18/35.03    (94)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.03    (95)   ~ (all_52_5 = all_10_2)
% 204.18/35.03    (96)  op(all_52_29, all_52_29) = all_52_28
% 204.18/35.03    (97)   ~ (all_52_23 = all_14_2)
% 204.18/35.03    (98)  all_56_12 = all_52_7
% 204.18/35.03    (99)  op(all_52_17, all_52_17) = all_52_16
% 204.18/35.03    (100)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.18/35.03    (101)   ~ (all_52_25 = all_6_2)
% 204.18/35.03    (102)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.18/35.03    (103)   ~ (all_52_9 = all_4_2)
% 204.18/35.03    (104)   ~ (all_52_5 = all_6_2)
% 204.18/35.03    (105)  all_56_0 = all_6_2
% 204.18/35.03    (106)  op(e3, e3) = all_6_2
% 204.18/35.03    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.18/35.03    (108)   ~ (all_52_15 = all_6_0)
% 204.18/35.03    (109)   ~ (all_52_27 = all_14_2)
% 204.18/35.03    (110)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.03    (111)  all_56_14 = all_52_23
% 204.18/35.03    (112)  all_56_3 = all_52_25
% 204.18/35.03    (113)   ~ (all_52_3 = all_52_7)
% 204.18/35.03    (114)   ~ (all_6_0 = all_6_2)
% 204.18/35.03    (115)  op(all_14_2, all_14_2) = all_52_30
% 204.18/35.03    (116)  all_58_5 = all_52_19
% 204.18/35.03    (117)   ~ (all_52_15 = all_4_2)
% 204.18/35.03    (118)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.03           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.18/35.03           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.18/35.03           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.18/35.03    (119)   ~ (all_52_27 = all_4_2)
% 204.18/35.03    (120)  all_58_6 = all_52_5
% 204.18/35.03    (121)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.18/35.03    (122)   ~ (all_52_17 = all_6_2)
% 204.18/35.03    (123)   ~ (e1 = e0)
% 204.18/35.03    (124)   ~ (e3 = e2)
% 204.18/35.03    (125)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.03    (126)   ~ (all_52_9 = all_52_17)
% 204.18/35.03    (127)  all_56_10 = all_10_2
% 204.18/35.03    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.03    (129)  all_56_1 = all_6_0
% 204.18/35.03    (130)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.18/35.03    (131)  op(all_52_13, all_52_13) = all_52_12
% 204.18/35.03    (132)   ~ (all_6_0 = all_4_2)
% 204.18/35.03    (133)  op(e1, e1) = all_10_2
% 204.18/35.03    (134)   ~ (all_52_23 = all_10_2)
% 204.18/35.03    (135)   ~ (all_52_7 = all_52_23)
% 204.18/35.03    (136)  all_58_3 = all_4_2
% 204.18/35.03    (137)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.18/35.03    (138)   ~ (all_52_3 = all_4_2)
% 204.18/35.03    (139)   ~ (all_52_19 = all_4_2)
% 204.18/35.03    (140)   ~ (all_52_17 = all_52_23)
% 204.18/35.03    (141)  op(all_6_2, e3) = all_6_1
% 204.18/35.03    (142)  all_22_2 = all_6_2
% 204.18/35.03    (143)  all_58_4 = all_52_17
% 204.18/35.03    (144)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.18/35.03    (145)  op(all_52_25, all_52_25) = all_52_24
% 204.18/35.03  
% 204.18/35.03  Begin of proof
% 204.18/35.03  | 
% 204.18/35.03  | BETA: splitting (125) gives:
% 204.18/35.03  | 
% 204.18/35.03  | Case 1:
% 204.18/35.03  | | 
% 204.18/35.03  | |   (146)  all_56_1 = e3
% 204.18/35.03  | | 
% 204.18/35.03  | | COMBINE_EQS: (129), (146) imply:
% 204.18/35.03  | |   (147)  all_6_0 = e3
% 204.18/35.03  | | 
% 204.18/35.03  | | SIMP: (147) implies:
% 204.18/35.03  | |   (148)  all_6_0 = e3
% 204.18/35.03  | | 
% 204.18/35.03  | | COMBINE_EQS: (61), (148) imply:
% 204.18/35.03  | |   (149)  all_58_1 = e3
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (78), (148) imply:
% 204.18/35.03  | |   (150)   ~ (all_52_13 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (108), (148) imply:
% 204.18/35.03  | |   (151)   ~ (all_52_15 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (29), (148) imply:
% 204.18/35.03  | |   (152)   ~ (all_52_17 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (3), (148) imply:
% 204.18/35.03  | |   (153)   ~ (all_52_25 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (114), (148) imply:
% 204.18/35.03  | |   (154)   ~ (all_6_2 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | SIMP: (154) implies:
% 204.18/35.03  | |   (155)   ~ (all_6_2 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (132), (148) imply:
% 204.18/35.03  | |   (156)   ~ (all_4_2 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | SIMP: (156) implies:
% 204.18/35.03  | |   (157)   ~ (all_4_2 = e3)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (49), (148) imply:
% 204.18/35.03  | |   (158)   ~ (e3 = e1)
% 204.18/35.03  | | 
% 204.18/35.03  | | REDUCE: (74), (148) imply:
% 204.18/35.03  | |   (159)  op(e3, e3) = all_52_8
% 204.18/35.03  | | 
% 204.18/35.03  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 204.18/35.03  | |              with (106), (159) gives:
% 204.18/35.03  | |   (160)  all_52_8 = all_6_2
% 204.18/35.03  | | 
% 204.18/35.03  | | BETA: splitting (118) gives:
% 204.18/35.03  | | 
% 204.18/35.03  | | Case 1:
% 204.18/35.03  | | | 
% 204.18/35.03  | | |   (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.18/35.03  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.18/35.03  | | |            e0)
% 204.18/35.03  | | | 
% 204.18/35.03  | | | BETA: splitting (161) gives:
% 204.18/35.03  | | | 
% 204.18/35.03  | | | Case 1:
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | |   (162)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | ALPHA: (162) implies:
% 204.18/35.03  | | | |   (163)  all_52_6 = e0
% 204.18/35.03  | | | |   (164)  all_52_2 = e2
% 204.18/35.03  | | | |   (165)  all_52_0 = e3
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (6), (164) imply:
% 204.18/35.03  | | | |   (166)  op(all_52_3, all_52_3) = e2
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (14), (163) imply:
% 204.18/35.03  | | | |   (167)  op(all_52_7, all_52_7) = e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (40), (165) imply:
% 204.18/35.03  | | | |   (168)  op(all_6_2, all_6_2) = e3
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REF_CLOSE: (7), (17), (19), (32), (42), (63), (65), (67), (69), (84),
% 204.18/35.03  | | | |            (106), (121), (138), (155), (166), (167), (168) are
% 204.18/35.03  | | | |            inconsistent by sub-proof #919.
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | Case 2:
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | |   (169)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.18/35.03  | | | |          e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REF_CLOSE: (155), (160), (169) are inconsistent by sub-proof #791.
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | End of split
% 204.18/35.03  | | | 
% 204.18/35.03  | | Case 2:
% 204.18/35.03  | | | 
% 204.18/35.03  | | |   (170)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.18/35.03  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.18/35.03  | | |            all_52_30 = e0)
% 204.18/35.03  | | | 
% 204.18/35.03  | | | BETA: splitting (170) gives:
% 204.18/35.03  | | | 
% 204.18/35.03  | | | Case 1:
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | |   (171)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.18/35.03  | | | |          e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | ALPHA: (171) implies:
% 204.18/35.03  | | | |   (172)  all_52_22 = e0
% 204.18/35.03  | | | |   (173)  all_52_20 = e1
% 204.18/35.03  | | | |   (174)  all_52_18 = e2
% 204.18/35.03  | | | |   (175)  all_52_16 = e3
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (99), (175) imply:
% 204.18/35.03  | | | |   (176)  op(all_52_17, all_52_17) = e3
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (21), (174) imply:
% 204.18/35.03  | | | |   (177)  op(all_52_19, all_52_19) = e2
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (91), (172) imply:
% 204.18/35.03  | | | |   (178)  op(all_52_23, all_52_23) = e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (24), (173) imply:
% 204.18/35.03  | | | |   (179)  op(all_10_2, all_10_2) = e1
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | BETA: splitting (69) gives:
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | Case 1:
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | |   (180)  all_58_0 = e3
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | COMBINE_EQS: (17), (180) imply:
% 204.18/35.03  | | | | |   (181)  all_6_2 = e3
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | REDUCE: (155), (181) imply:
% 204.18/35.03  | | | | |   (182)  $false
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | CLOSE: (182) is inconsistent.
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | Case 2:
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | |   (183)   ~ (all_58_0 = e3)
% 204.18/35.03  | | | | |   (184)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | BETA: splitting (94) gives:
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | Case 1:
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | |   (185)  all_56_15 = e3
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | COMBINE_EQS: (43), (185) imply:
% 204.18/35.03  | | | | | |   (186)  all_14_2 = e3
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | SIMP: (186) implies:
% 204.18/35.03  | | | | | |   (187)  all_14_2 = e3
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REDUCE: (65), (187) imply:
% 204.18/35.03  | | | | | |   (188)   ~ (all_52_7 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REDUCE: (97), (187) imply:
% 204.18/35.03  | | | | | |   (189)   ~ (all_52_23 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REF_CLOSE: (5), (6), (7), (8), (13), (16), (17), (18), (19), (25),
% 204.18/35.03  | | | | | |            (57), (63), (67), (83), (84), (87), (93), (106), (110),
% 204.18/35.03  | | | | | |            (116), (122), (126), (128), (143), (153), (176), (184),
% 204.18/35.03  | | | | | |            (188), (189) are inconsistent by sub-proof #780.
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | Case 2:
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | |   (190)   ~ (all_56_15 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REDUCE: (43), (190) imply:
% 204.18/35.03  | | | | | |   (191)   ~ (all_14_2 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REF_CLOSE: (5), (7), (10), (15), (17), (23), (25), (28), (30), (32),
% 204.18/35.03  | | | | | |            (37), (39), (41), (42), (44), (47), (48), (50), (53),
% 204.18/35.03  | | | | | |            (55), (63), (65), (67), (68), (70), (72), (75), (77),
% 204.18/35.03  | | | | | |            (82), (83), (86), (89), (90), (93), (101), (102), (106),
% 204.18/35.03  | | | | | |            (109), (112), (113), (116), (119), (121), (122), (123),
% 204.18/35.03  | | | | | |            (127), (128), (133), (134), (135), (136), (140), (143),
% 204.18/35.03  | | | | | |            (144), (149), (151), (152), (153), (155), (157), (158),
% 204.18/35.03  | | | | | |            (159), (176), (177), (178), (179), (191) are inconsistent
% 204.18/35.03  | | | | | |            by sub-proof #813.
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | End of split
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | End of split
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | Case 2:
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | |   (192)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 204.18/35.03  | | | |          e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | ALPHA: (192) implies:
% 204.18/35.03  | | | |   (193)  all_52_30 = e0
% 204.18/35.03  | | | |   (194)  all_52_28 = e1
% 204.18/35.03  | | | |   (195)  all_52_26 = e2
% 204.18/35.03  | | | |   (196)  all_52_24 = e3
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (145), (196) imply:
% 204.18/35.03  | | | |   (197)  op(all_52_25, all_52_25) = e3
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (30), (195) imply:
% 204.18/35.03  | | | |   (198)  op(all_52_27, all_52_27) = e2
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (96), (194) imply:
% 204.18/35.03  | | | |   (199)  op(all_52_29, all_52_29) = e1
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | REDUCE: (115), (193) imply:
% 204.18/35.03  | | | |   (200)  op(all_14_2, all_14_2) = e0
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | BETA: splitting (69) gives:
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | | Case 1:
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | |   (201)  all_58_0 = e3
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | COMBINE_EQS: (17), (201) imply:
% 204.18/35.03  | | | | |   (202)  all_6_2 = e3
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | REDUCE: (155), (202) imply:
% 204.18/35.03  | | | | |   (203)  $false
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | CLOSE: (203) is inconsistent.
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | Case 2:
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | |   (204)   ~ (all_58_0 = e3)
% 204.18/35.03  | | | | |   (205)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | BETA: splitting (94) gives:
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | | Case 1:
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | |   (206)  all_56_15 = e3
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | COMBINE_EQS: (43), (206) imply:
% 204.18/35.03  | | | | | |   (207)  all_14_2 = e3
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | SIMP: (207) implies:
% 204.18/35.03  | | | | | |   (208)  all_14_2 = e3
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REDUCE: (65), (208) imply:
% 204.18/35.03  | | | | | |   (209)   ~ (all_52_7 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REDUCE: (97), (208) imply:
% 204.18/35.03  | | | | | |   (210)   ~ (all_52_23 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REF_CLOSE: (5), (7), (13), (18), (19), (57), (63), (67), (83), (84),
% 204.18/35.03  | | | | | |            (93), (116), (128), (143), (152), (205), (209), (210) are
% 204.18/35.03  | | | | | |            inconsistent by sub-proof #779.
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | Case 2:
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | |   (211)   ~ (all_56_15 = e3)
% 204.18/35.03  | | | | | |   (212)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REDUCE: (43), (211) imply:
% 204.18/35.03  | | | | | |   (213)   ~ (all_14_2 = e3)
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.18/35.03  | | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 204.18/35.03  | | | | | |            (23), (25), (26), (31), (32), (33), (34), (35), (36),
% 204.18/35.03  | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.18/35.03  | | | | | |            (46), (47), (50), (51), (52), (54), (55), (56), (58),
% 204.18/35.03  | | | | | |            (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 204.18/35.03  | | | | | |            (69), (70), (72), (73), (76), (79), (80), (82), (83),
% 204.18/35.03  | | | | | |            (85), (87), (88), (89), (90), (91), (92), (93), (95),
% 204.18/35.03  | | | | | |            (97), (98), (100), (101), (102), (103), (104), (106),
% 204.18/35.03  | | | | | |            (107), (109), (110), (111), (112), (113), (116), (117),
% 204.18/35.03  | | | | | |            (119), (120), (121), (122), (123), (124), (131), (133),
% 204.18/35.03  | | | | | |            (134), (135), (136), (137), (138), (139), (140), (141),
% 204.18/35.03  | | | | | |            (143), (150), (151), (153), (155), (157), (197), (198),
% 204.18/35.03  | | | | | |            (199), (200), (212), (213) are inconsistent by sub-proof
% 204.18/35.03  | | | | | |            #795.
% 204.18/35.03  | | | | | | 
% 204.18/35.03  | | | | | End of split
% 204.18/35.03  | | | | | 
% 204.18/35.03  | | | | End of split
% 204.18/35.03  | | | | 
% 204.18/35.03  | | | End of split
% 204.18/35.03  | | | 
% 204.18/35.03  | | End of split
% 204.18/35.03  | | 
% 204.18/35.03  | Case 2:
% 204.18/35.03  | | 
% 204.18/35.03  | |   (214)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.18/35.03  | | 
% 204.18/35.03  | | REF_CLOSE: (7), (11), (16), (27), (40), (49), (55), (71), (81), (105),
% 204.18/35.03  | |            (106), (114), (124), (129), (130), (142), (214) are inconsistent
% 204.18/35.03  | |            by sub-proof #820.
% 204.18/35.03  | | 
% 204.18/35.03  | End of split
% 204.18/35.03  | 
% 204.18/35.03  End of proof
% 204.18/35.03  
% 204.18/35.03  Sub-proof #779 shows that the following formulas are inconsistent:
% 204.18/35.03  ----------------------------------------------------------------
% 204.18/35.03    (1)  all_58_14 = all_52_23
% 204.18/35.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.03    (3)   ~ (all_52_3 = all_52_19)
% 204.18/35.03    (4)   ~ (all_52_17 = all_10_2)
% 204.18/35.03    (5)   ~ (all_10_0 = e3)
% 204.18/35.03    (6)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.03    (7)  op(all_10_2, e1) = e3
% 204.18/35.03    (8)  all_58_12 = all_52_7
% 204.18/35.03    (9)   ~ (all_52_7 = e3)
% 204.18/35.03    (10)  all_58_2 = all_52_3
% 204.18/35.03    (11)   ~ (all_52_23 = e3)
% 204.18/35.03    (12)  op(e3, e1) = all_52_17
% 204.18/35.03    (13)  all_58_6 = all_10_0
% 204.18/35.03    (14)  all_58_8 = all_10_2
% 204.18/35.03    (15)   ~ (all_52_17 = e3)
% 204.18/35.03    (16)  all_58_5 = all_52_19
% 204.18/35.03    (17)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.03    (18)  all_58_4 = all_52_17
% 204.18/35.03  
% 204.18/35.03  Begin of proof
% 204.18/35.03  | 
% 204.18/35.03  | BETA: splitting (6) gives:
% 204.18/35.03  | 
% 204.18/35.03  | Case 1:
% 204.18/35.03  | | 
% 204.18/35.03  | |   (19)  all_58_2 = e3
% 204.18/35.03  | | 
% 204.18/35.03  | | COMBINE_EQS: (10), (19) imply:
% 204.18/35.03  | |   (20)  all_52_3 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | SIMP: (20) implies:
% 204.18/35.04  | |   (21)  all_52_3 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | REDUCE: (3), (21) imply:
% 204.18/35.04  | |   (22)   ~ (all_52_19 = e3)
% 204.18/35.04  | | 
% 204.18/35.04  | | SIMP: (22) implies:
% 204.18/35.04  | |   (23)   ~ (all_52_19 = e3)
% 204.18/35.04  | | 
% 204.18/35.04  | | REF_CLOSE: (1), (2), (4), (7), (11), (12), (14), (15), (16), (17), (18),
% 204.18/35.04  | |            (23) are inconsistent by sub-proof #897.
% 204.18/35.04  | | 
% 204.18/35.04  | Case 2:
% 204.18/35.04  | | 
% 204.18/35.04  | |   (24)  all_58_6 = e3 | all_58_12 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | REF_CLOSE: (5), (8), (9), (13), (24) are inconsistent by sub-proof #921.
% 204.18/35.04  | | 
% 204.18/35.04  | End of split
% 204.18/35.04  | 
% 204.18/35.04  End of proof
% 204.18/35.04  
% 204.18/35.04  Sub-proof #780 shows that the following formulas are inconsistent:
% 204.18/35.04  ----------------------------------------------------------------
% 204.18/35.04    (1)  all_58_14 = all_52_23
% 204.18/35.04    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.04    (4)  all_58_1 = all_52_9
% 204.18/35.04    (5)   ~ (all_52_3 = all_52_19)
% 204.18/35.04    (6)   ~ (all_52_3 = all_6_2)
% 204.18/35.04    (7)  all_58_0 = all_6_2
% 204.18/35.04    (8)   ~ (all_52_17 = all_10_2)
% 204.18/35.04    (9)   ~ (all_10_0 = e3)
% 204.18/35.04    (10)  all_58_9 = all_52_25
% 204.18/35.04    (11)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.18/35.04    (12)  op(all_10_2, e1) = e3
% 204.18/35.04    (13)  all_58_12 = all_52_7
% 204.18/35.04    (14)   ~ (all_52_7 = e3)
% 204.18/35.04    (15)  all_58_2 = all_52_3
% 204.18/35.04    (16)   ~ (all_52_25 = e3)
% 204.18/35.04    (17)   ~ (all_52_23 = e3)
% 204.18/35.04    (18)  op(e3, e1) = all_52_17
% 204.18/35.04    (19)  all_58_6 = all_10_0
% 204.18/35.04    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.18/35.04    (21)  all_58_8 = all_10_2
% 204.18/35.04    (22)  op(e3, e3) = all_6_2
% 204.18/35.04    (23)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.04    (24)  all_58_5 = all_52_19
% 204.18/35.04    (25)  op(all_52_17, all_52_17) = e3
% 204.18/35.04    (26)   ~ (all_52_17 = all_6_2)
% 204.18/35.04    (27)   ~ (all_52_9 = all_52_17)
% 204.18/35.04    (28)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.04    (29)  all_58_4 = all_52_17
% 204.18/35.04  
% 204.18/35.04  Begin of proof
% 204.18/35.04  | 
% 204.18/35.04  | BETA: splitting (11) gives:
% 204.18/35.04  | 
% 204.18/35.04  | Case 1:
% 204.18/35.04  | | 
% 204.18/35.04  | |   (30)  all_58_2 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | COMBINE_EQS: (15), (30) imply:
% 204.18/35.04  | |   (31)  all_52_3 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | SIMP: (31) implies:
% 204.18/35.04  | |   (32)  all_52_3 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | REDUCE: (5), (32) imply:
% 204.18/35.04  | |   (33)   ~ (all_52_19 = e3)
% 204.18/35.04  | | 
% 204.18/35.04  | | SIMP: (33) implies:
% 204.18/35.04  | |   (34)   ~ (all_52_19 = e3)
% 204.18/35.04  | | 
% 204.18/35.04  | | REDUCE: (6), (32) imply:
% 204.18/35.04  | |   (35)   ~ (all_6_2 = e3)
% 204.18/35.04  | | 
% 204.18/35.04  | | SIMP: (35) implies:
% 204.18/35.04  | |   (36)   ~ (all_6_2 = e3)
% 204.18/35.04  | | 
% 204.18/35.04  | | REDUCE: (2), (32) imply:
% 204.18/35.04  | |   (37)  op(e3, e3) = all_52_2
% 204.18/35.04  | | 
% 204.18/35.04  | | GROUND_INST: instantiating (3) with all_6_2, all_52_2, e3, e3, simplifying
% 204.18/35.04  | |              with (22), (37) gives:
% 204.18/35.04  | |   (38)  all_52_2 = all_6_2
% 204.18/35.04  | | 
% 204.18/35.04  | | BETA: splitting (23) gives:
% 204.18/35.04  | | 
% 204.18/35.04  | | Case 1:
% 204.18/35.04  | | | 
% 204.18/35.04  | | |   (39)  all_58_0 = e3
% 204.18/35.04  | | | 
% 204.18/35.04  | | | COMBINE_EQS: (7), (39) imply:
% 204.18/35.04  | | |   (40)  all_6_2 = e3
% 204.18/35.04  | | | 
% 204.18/35.04  | | | REDUCE: (36), (40) imply:
% 204.18/35.04  | | |   (41)  $false
% 204.18/35.04  | | | 
% 204.18/35.04  | | | CLOSE: (41) is inconsistent.
% 204.18/35.04  | | | 
% 204.18/35.04  | | Case 2:
% 204.18/35.04  | | | 
% 204.18/35.04  | | |   (42)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.18/35.04  | | | 
% 204.18/35.04  | | | BETA: splitting (20) gives:
% 204.18/35.04  | | | 
% 204.18/35.04  | | | Case 1:
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | |   (43)  all_58_1 = e3
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | COMBINE_EQS: (4), (43) imply:
% 204.18/35.04  | | | |   (44)  all_52_9 = e3
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | REDUCE: (27), (44) imply:
% 204.18/35.04  | | | |   (45)   ~ (all_52_17 = e3)
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | SIMP: (45) implies:
% 204.18/35.04  | | | |   (46)   ~ (all_52_17 = e3)
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | BETA: splitting (28) gives:
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | Case 1:
% 204.18/35.04  | | | | | 
% 204.18/35.04  | | | | |   (47)  all_58_4 = e3
% 204.18/35.04  | | | | | 
% 204.18/35.04  | | | | | REF_CLOSE: (29), (46), (47) are inconsistent by sub-proof #1302.
% 204.18/35.04  | | | | | 
% 204.18/35.04  | | | | Case 2:
% 204.18/35.04  | | | | | 
% 204.18/35.04  | | | | |   (48)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.18/35.04  | | | | | 
% 204.18/35.04  | | | | | REF_CLOSE: (1), (3), (8), (12), (17), (18), (21), (24), (34), (48) are
% 204.18/35.04  | | | | |            inconsistent by sub-proof #898.
% 204.18/35.04  | | | | | 
% 204.18/35.04  | | | | End of split
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | Case 2:
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | |   (49)   ~ (all_58_1 = e3)
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | REDUCE: (4), (49) imply:
% 204.18/35.04  | | | |   (50)   ~ (all_52_9 = e3)
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | | REF_CLOSE: (3), (4), (10), (16), (22), (25), (26), (29), (42), (50) are
% 204.18/35.04  | | | |            inconsistent by sub-proof #1072.
% 204.18/35.04  | | | | 
% 204.18/35.04  | | | End of split
% 204.18/35.04  | | | 
% 204.18/35.04  | | End of split
% 204.18/35.04  | | 
% 204.18/35.04  | Case 2:
% 204.18/35.04  | | 
% 204.18/35.04  | |   (51)  all_58_6 = e3 | all_58_12 = e3
% 204.18/35.04  | | 
% 204.18/35.04  | | REF_CLOSE: (9), (13), (14), (19), (51) are inconsistent by sub-proof #921.
% 204.18/35.04  | | 
% 204.18/35.04  | End of split
% 204.18/35.04  | 
% 204.18/35.04  End of proof
% 204.18/35.04  
% 204.18/35.04  Sub-proof #781 shows that the following formulas are inconsistent:
% 204.18/35.04  ----------------------------------------------------------------
% 204.18/35.04    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.18/35.04    (2)   ~ (all_52_15 = all_52_23)
% 204.18/35.04    (3)   ~ (all_52_25 = all_6_0)
% 204.18/35.04    (4)   ~ (all_52_25 = all_52_27)
% 204.18/35.04    (5)  all_58_14 = all_52_23
% 204.18/35.04    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.18/35.04    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.18/35.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.18/35.04    (8)  all_58_1 = all_52_9
% 204.18/35.04    (9)   ~ (all_52_9 = all_52_13)
% 204.18/35.04    (10)   ~ (e3 = e0)
% 204.18/35.04    (11)  op(e2, e3) = all_52_3
% 204.18/35.04    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.18/35.04    (13)   ~ (all_52_7 = all_52_15)
% 204.18/35.04    (14)   ~ (all_52_3 = all_52_19)
% 204.18/35.04    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.18/35.04    (16)   ~ (all_52_17 = all_52_25)
% 204.18/35.04    (17)   ~ (all_52_3 = all_6_2)
% 204.18/35.04    (18)  all_58_0 = all_6_2
% 204.18/35.04    (19)  op(all_14_2, e0) = all_14_1
% 204.18/35.04    (20)  all_56_4 = all_52_3
% 204.18/35.04    (21)   ~ (all_52_17 = all_10_2)
% 204.18/35.04    (22)  all_40_2 = all_10_2
% 204.18/35.04    (23)  op(e3, e0) = all_52_25
% 204.18/35.04    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.18/35.04    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.18/35.04    (26)   ~ (all_52_27 = all_52_29)
% 204.24/35.04    (27)  all_58_13 = all_52_15
% 204.24/35.04    (28)  op(all_10_2, all_10_2) = all_52_20
% 204.24/35.04    (29)  all_58_9 = all_52_25
% 204.24/35.04    (30)   ~ (all_52_29 = all_14_2)
% 204.24/35.04    (31)  all_22_0 = all_6_0
% 204.24/35.04    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.24/35.04    (33)   ~ (all_52_17 = all_6_0)
% 204.24/35.04    (34)  op(all_52_27, all_52_27) = all_52_26
% 204.24/35.04    (35)  op(e1, e3) = all_52_5
% 204.24/35.04    (36)  op(e2, e2) = all_4_2
% 204.24/35.04    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.24/35.04    (38)  all_58_7 = all_10_0
% 204.24/35.04    (39)   ~ (all_52_3 = all_52_5)
% 204.24/35.04    (40)  all_58_11 = all_52_29
% 204.24/35.04    (41)  all_56_5 = all_4_2
% 204.24/35.04    (42)   ~ (all_52_25 = all_14_2)
% 204.24/35.04    (43)   ~ (all_52_3 = all_52_27)
% 204.24/35.04    (44)  op(all_10_2, e1) = all_10_1
% 204.24/35.04    (45)  op(all_6_2, all_6_2) = all_52_0
% 204.24/35.04    (46)   ~ (all_52_7 = all_6_2)
% 204.24/35.04    (47)  op(e0, e0) = all_14_2
% 204.24/35.04    (48)  all_56_15 = all_14_2
% 204.24/35.04    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.24/35.04    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.24/35.04    (51)  op(e2, all_4_1) = all_4_0
% 204.24/35.04    (52)  all_56_11 = all_52_29
% 204.24/35.04    (53)   ~ (all_10_0 = e2)
% 204.24/35.04    (54)   ~ (all_4_0 = e3)
% 204.24/35.04    (55)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.24/35.04    (56)   ~ (e2 = e1)
% 204.24/35.04    (57)   ~ (all_6_0 = e1)
% 204.24/35.04    (58)  all_58_10 = all_52_27
% 204.24/35.04    (59)  all_56_8 = all_52_5
% 204.24/35.04    (60)  op(all_52_9, all_52_9) = all_52_8
% 204.24/35.04    (61)   ~ (all_52_19 = all_52_23)
% 204.24/35.04    (62)  all_56_9 = all_10_0
% 204.24/35.04    (63)   ~ (all_52_25 = all_52_29)
% 204.24/35.04    (64)  op(all_6_2, e3) = e2
% 204.24/35.04    (65)   ~ (all_52_29 = all_10_2)
% 204.24/35.04    (66)  all_58_7 = all_52_13
% 204.24/35.04    (67)   ~ (all_10_0 = all_4_2)
% 204.24/35.04    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.24/35.04    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.24/35.04    (70)  all_58_1 = all_6_0
% 204.24/35.04    (71)   ~ (all_52_5 = all_52_7)
% 204.24/35.04    (72)  all_58_12 = all_52_7
% 204.24/35.04    (73)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.04    (74)   ~ (all_52_7 = all_14_2)
% 204.24/35.04    (75)   ~ (all_14_2 = e0)
% 204.24/35.04    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.24/35.04    (77)  all_58_2 = all_52_3
% 204.24/35.04    (78)  all_56_2 = all_52_17
% 204.24/35.04    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.24/35.04    (80)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.24/35.04    (81)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.24/35.04    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.24/35.04    (83)   ~ (e2 = e0)
% 204.24/35.04    (84)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.24/35.04    (85)  op(all_4_2, e2) = all_4_1
% 204.24/35.04    (86)  op(all_6_0, all_6_0) = all_52_8
% 204.24/35.04    (87)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.24/35.04    (88)   ~ (all_52_5 = all_52_29)
% 204.24/35.04    (89)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.24/35.04    (90)   ~ (all_52_19 = all_52_27)
% 204.24/35.04    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.24/35.04    (92)   ~ (all_6_0 = e2)
% 204.24/35.04    (93)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.24/35.04    (94)  op(e3, e1) = all_52_17
% 204.24/35.04    (95)   ~ (all_10_0 = all_6_0)
% 204.24/35.04    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.24/35.04    (97)  op(e0, e3) = all_52_7
% 204.24/35.04    (98)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.24/35.04    (99)   ~ (all_52_9 = all_52_25)
% 204.24/35.04    (100)  all_58_15 = all_14_2
% 204.24/35.04    (101)   ~ (all_52_19 = all_10_2)
% 204.24/35.04    (102)  op(all_52_23, all_52_23) = all_52_22
% 204.24/35.04    (103)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.24/35.04    (104)  all_58_8 = all_10_2
% 204.24/35.04    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.24/35.04    (106)   ~ (all_52_5 = all_10_2)
% 204.24/35.04    (107)  op(all_52_29, all_52_29) = all_52_28
% 204.24/35.04    (108)   ~ (all_52_23 = all_14_2)
% 204.24/35.04    (109)  all_56_12 = all_52_7
% 204.24/35.04    (110)  op(all_52_17, all_52_17) = all_52_16
% 204.24/35.04    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.24/35.04    (112)   ~ (all_52_25 = all_6_2)
% 204.24/35.04    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.24/35.04    (114)   ~ (all_52_9 = all_4_2)
% 204.24/35.04    (115)   ~ (all_52_5 = all_6_2)
% 204.24/35.04    (116)  all_56_0 = all_6_2
% 204.24/35.04    (117)  op(e3, e3) = all_6_2
% 204.24/35.04    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.24/35.04    (119)   ~ (all_52_15 = all_6_0)
% 204.24/35.04    (120)   ~ (all_52_27 = all_14_2)
% 204.24/35.04    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.24/35.04    (122)  all_56_14 = all_52_23
% 204.24/35.04    (123)  op(all_4_2, all_4_2) = all_52_10
% 204.24/35.04    (124)  all_40_0 = all_10_0
% 204.24/35.04    (125)  all_56_3 = all_52_25
% 204.24/35.04    (126)   ~ (all_52_3 = all_52_7)
% 204.24/35.04    (127)   ~ (all_6_0 = all_6_2)
% 204.24/35.04    (128)  op(all_14_2, all_14_2) = all_52_30
% 204.24/35.04    (129)  all_58_5 = all_52_19
% 204.24/35.04    (130)   ~ (all_52_15 = all_4_2)
% 204.24/35.04    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.24/35.04           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.24/35.04           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.24/35.04           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.24/35.04    (132)   ~ (all_52_27 = all_4_2)
% 204.24/35.04    (133)  all_58_6 = all_52_5
% 204.24/35.04    (134)  op(all_10_2, e1) = e2
% 204.24/35.04    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.24/35.04    (136)   ~ (all_52_17 = all_6_2)
% 204.24/35.04    (137)   ~ (e1 = e0)
% 204.24/35.04    (138)   ~ (e3 = e2)
% 204.24/35.04    (139)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.24/35.04    (140)  all_56_10 = all_10_2
% 204.24/35.04    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.24/35.04    (142)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.04    (143)  all_56_1 = all_6_0
% 204.24/35.04    (144)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.24/35.04    (145)  op(all_52_13, all_52_13) = all_52_12
% 204.24/35.04    (146)   ~ (all_6_0 = all_4_2)
% 204.24/35.04    (147)  op(e1, e1) = all_10_2
% 204.24/35.04    (148)   ~ (all_52_23 = all_10_2)
% 204.24/35.04    (149)   ~ (all_52_7 = all_52_23)
% 204.24/35.04    (150)   ~ (all_52_5 = all_10_0)
% 204.24/35.04    (151)  all_58_3 = all_4_2
% 204.24/35.04    (152)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.24/35.04    (153)   ~ (all_52_3 = all_4_2)
% 204.24/35.04    (154)   ~ (all_52_19 = all_4_2)
% 204.24/35.04    (155)   ~ (all_52_17 = all_52_23)
% 204.24/35.04    (156)  op(all_6_2, e3) = all_6_1
% 204.24/35.04    (157)  all_22_2 = all_6_2
% 204.24/35.04    (158)  all_58_4 = all_52_17
% 204.24/35.04    (159)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.24/35.04    (160)  op(all_52_25, all_52_25) = all_52_24
% 204.24/35.04  
% 204.24/35.04  Begin of proof
% 204.24/35.04  | 
% 204.24/35.04  | BETA: splitting (139) gives:
% 204.24/35.04  | 
% 204.24/35.04  | Case 1:
% 204.24/35.04  | | 
% 204.24/35.04  | |   (161)  all_56_1 = e3
% 204.24/35.04  | | 
% 204.24/35.04  | | COMBINE_EQS: (143), (161) imply:
% 204.24/35.04  | |   (162)  all_6_0 = e3
% 204.24/35.04  | | 
% 204.24/35.04  | | SIMP: (162) implies:
% 204.24/35.04  | |   (163)  all_6_0 = e3
% 204.24/35.04  | | 
% 204.24/35.04  | | COMBINE_EQS: (70), (163) imply:
% 204.24/35.04  | |   (164)  all_58_1 = e3
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (119), (163) imply:
% 204.24/35.04  | |   (165)   ~ (all_52_15 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (33), (163) imply:
% 204.24/35.04  | |   (166)   ~ (all_52_17 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (3), (163) imply:
% 204.24/35.04  | |   (167)   ~ (all_52_25 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (95), (163) imply:
% 204.24/35.04  | |   (168)   ~ (all_10_0 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (127), (163) imply:
% 204.24/35.04  | |   (169)   ~ (all_6_2 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | SIMP: (169) implies:
% 204.24/35.04  | |   (170)   ~ (all_6_2 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (146), (163) imply:
% 204.24/35.04  | |   (171)   ~ (all_4_2 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | SIMP: (171) implies:
% 204.24/35.04  | |   (172)   ~ (all_4_2 = e3)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (57), (163) imply:
% 204.24/35.04  | |   (173)   ~ (e3 = e1)
% 204.24/35.04  | | 
% 204.24/35.04  | | REDUCE: (86), (163) imply:
% 204.24/35.04  | |   (174)  op(e3, e3) = all_52_8
% 204.24/35.04  | | 
% 204.24/35.04  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 204.24/35.04  | |              with (117), (174) gives:
% 204.24/35.04  | |   (175)  all_52_8 = all_6_2
% 204.24/35.04  | | 
% 204.24/35.04  | | BETA: splitting (131) gives:
% 204.24/35.04  | | 
% 204.24/35.04  | | Case 1:
% 204.24/35.04  | | | 
% 204.24/35.04  | | |   (176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.24/35.04  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.24/35.04  | | |            e0)
% 204.24/35.04  | | | 
% 204.24/35.04  | | | BETA: splitting (176) gives:
% 204.24/35.04  | | | 
% 204.24/35.04  | | | Case 1:
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | |   (177)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REF_CLOSE: (6), (7), (15), (18), (24), (36), (45), (47), (49), (72),
% 204.24/35.04  | | | |            (74), (77), (79), (106), (117), (133), (135), (147), (153),
% 204.24/35.04  | | | |            (170), (177) are inconsistent by sub-proof #835.
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | Case 2:
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | |   (178)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.24/35.04  | | | |          e0
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REF_CLOSE: (170), (175), (178) are inconsistent by sub-proof #791.
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | End of split
% 204.24/35.04  | | | 
% 204.24/35.04  | | Case 2:
% 204.24/35.04  | | | 
% 204.24/35.04  | | |   (179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.24/35.04  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.24/35.04  | | |            all_52_30 = e0)
% 204.24/35.04  | | | 
% 204.24/35.04  | | | BETA: splitting (179) gives:
% 204.24/35.04  | | | 
% 204.24/35.04  | | | Case 1:
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | |   (180)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.24/35.04  | | | |          e0
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | ALPHA: (180) implies:
% 204.24/35.04  | | | |   (181)  all_52_22 = e0
% 204.24/35.04  | | | |   (182)  all_52_20 = e1
% 204.24/35.04  | | | |   (183)  all_52_18 = e2
% 204.24/35.04  | | | |   (184)  all_52_16 = e3
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (110), (184) imply:
% 204.24/35.04  | | | |   (185)  op(all_52_17, all_52_17) = e3
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (25), (183) imply:
% 204.24/35.04  | | | |   (186)  op(all_52_19, all_52_19) = e2
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (102), (181) imply:
% 204.24/35.04  | | | |   (187)  op(all_52_23, all_52_23) = e0
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (28), (182) imply:
% 204.24/35.04  | | | |   (188)  op(all_10_2, all_10_2) = e1
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REF_CLOSE: (5), (7), (10), (11), (16), (17), (18), (22), (24), (27),
% 204.24/35.04  | | | |            (29), (30), (32), (34), (36), (38), (39), (40), (42), (44),
% 204.24/35.04  | | | |            (46), (47), (48), (49), (52), (53), (55), (56), (58), (61),
% 204.24/35.04  | | | |            (62), (64), (65), (72), (73), (74), (75), (76), (77), (78),
% 204.24/35.04  | | | |            (79), (80), (83), (87), (89), (91), (93), (94), (97), (100),
% 204.24/35.04  | | | |            (101), (104), (105), (108), (112), (113), (117), (120),
% 204.24/35.04  | | | |            (124), (125), (126), (128), (129), (132), (133), (134),
% 204.24/35.04  | | | |            (135), (136), (137), (140), (141), (142), (147), (148),
% 204.24/35.04  | | | |            (149), (151), (153), (155), (158), (159), (164), (165),
% 204.24/35.04  | | | |            (166), (167), (168), (170), (172), (173), (174), (185),
% 204.24/35.04  | | | |            (186), (187), (188) are inconsistent by sub-proof #787.
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | Case 2:
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | |   (189)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 204.24/35.04  | | | |          e0
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | ALPHA: (189) implies:
% 204.24/35.04  | | | |   (190)  all_52_30 = e0
% 204.24/35.04  | | | |   (191)  all_52_28 = e1
% 204.24/35.04  | | | |   (192)  all_52_26 = e2
% 204.24/35.04  | | | |   (193)  all_52_24 = e3
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (160), (193) imply:
% 204.24/35.04  | | | |   (194)  op(all_52_25, all_52_25) = e3
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (34), (192) imply:
% 204.24/35.04  | | | |   (195)  op(all_52_27, all_52_27) = e2
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (107), (191) imply:
% 204.24/35.04  | | | |   (196)  op(all_52_29, all_52_29) = e1
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | REDUCE: (128), (190) imply:
% 204.24/35.04  | | | |   (197)  op(all_14_2, all_14_2) = e0
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | BETA: splitting (142) gives:
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | | Case 1:
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | |   (198)  all_56_9 = e3
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | | COMBINE_EQS: (62), (198) imply:
% 204.24/35.04  | | | | |   (199)  all_10_0 = e3
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | | REDUCE: (168), (199) imply:
% 204.24/35.04  | | | | |   (200)  $false
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | | CLOSE: (200) is inconsistent.
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | Case 2:
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | |   (201)   ~ (all_56_9 = e3)
% 204.24/35.04  | | | | |   (202)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | | BETA: splitting (152) gives:
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | | Case 1:
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | |   (203)  all_58_1 = e2
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | | COMBINE_EQS: (164), (203) imply:
% 204.24/35.04  | | | | | |   (204)  e3 = e2
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | | REDUCE: (138), (204) imply:
% 204.24/35.04  | | | | | |   (205)  $false
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | | CLOSE: (205) is inconsistent.
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | Case 2:
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | |   (206)   ~ (all_58_1 = e2)
% 204.24/35.04  | | | | | |   (207)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | | BETA: splitting (105) gives:
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | | Case 1:
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | |   (208)  all_56_15 = e3
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | COMBINE_EQS: (48), (208) imply:
% 204.24/35.04  | | | | | | |   (209)  all_14_2 = e3
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | SIMP: (209) implies:
% 204.24/35.04  | | | | | | |   (210)  all_14_2 = e3
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (120), (210) imply:
% 204.24/35.04  | | | | | | |   (211)   ~ (all_52_27 = e3)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (30), (210) imply:
% 204.24/35.04  | | | | | | |   (212)   ~ (all_52_29 = e3)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (197), (210) imply:
% 204.24/35.04  | | | | | | |   (213)  op(e3, e3) = e0
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (19), (210) imply:
% 204.24/35.04  | | | | | | |   (214)  op(e3, e0) = all_14_1
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3,
% 204.24/35.04  | | | | | | |              simplifying with (23), (214) gives:
% 204.24/35.04  | | | | | | |   (215)  all_52_25 = all_14_1
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | GROUND_INST: instantiating (7) with all_6_2, e0, e3, e3,
% 204.24/35.04  | | | | | | |              simplifying with (117), (213) gives:
% 204.24/35.04  | | | | | | |   (216)  all_6_2 = e0
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | COMBINE_EQS: (125), (215) imply:
% 204.24/35.04  | | | | | | |   (217)  all_56_3 = all_14_1
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | COMBINE_EQS: (29), (215) imply:
% 204.24/35.04  | | | | | | |   (218)  all_58_9 = all_14_1
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (115), (216) imply:
% 204.24/35.04  | | | | | | |   (219)   ~ (all_52_5 = e0)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (112), (215), (216) imply:
% 204.24/35.04  | | | | | | |   (220)   ~ (all_14_1 = e0)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (167), (215) imply:
% 204.24/35.04  | | | | | | |   (221)   ~ (all_14_1 = e3)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (194), (215) imply:
% 204.24/35.04  | | | | | | |   (222)  op(all_14_1, all_14_1) = e3
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (64), (216) imply:
% 204.24/35.04  | | | | | | |   (223)  op(e0, e3) = e2
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | GROUND_INST: instantiating (7) with all_52_7, e2, e3, e0,
% 204.24/35.04  | | | | | | |              simplifying with (97), (223) gives:
% 204.24/35.04  | | | | | | |   (224)  all_52_7 = e2
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (71), (224) imply:
% 204.24/35.04  | | | | | | |   (225)   ~ (all_52_5 = e2)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (13), (224) imply:
% 204.24/35.04  | | | | | | |   (226)   ~ (all_52_15 = e2)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | SIMP: (226) implies:
% 204.24/35.04  | | | | | | |   (227)   ~ (all_52_15 = e2)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (15), (224) imply:
% 204.24/35.04  | | | | | | |   (228)  op(e2, e2) = all_52_6
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | BETA: splitting (207) gives:
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | Case 1:
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | |   (229)  all_58_3 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | COMBINE_EQS: (151), (229) imply:
% 204.24/35.04  | | | | | | | |   (230)  all_4_2 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REDUCE: (123), (230) imply:
% 204.24/35.04  | | | | | | | |   (231)  op(e2, e2) = all_52_10
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REDUCE: (85), (230) imply:
% 204.24/35.04  | | | | | | | |   (232)  op(e2, e2) = all_4_1
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REDUCE: (36), (230) imply:
% 204.24/35.04  | | | | | | | |   (233)  op(e2, e2) = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | GROUND_INST: instantiating (7) with all_52_10, all_52_6, e2, e2,
% 204.24/35.04  | | | | | | | |              simplifying with (228), (231) gives:
% 204.24/35.04  | | | | | | | |   (234)  all_52_6 = all_52_10
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | GROUND_INST: instantiating (7) with all_4_1, all_52_6, e2, e2,
% 204.24/35.04  | | | | | | | |              simplifying with (228), (232) gives:
% 204.24/35.04  | | | | | | | |   (235)  all_52_6 = all_4_1
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | GROUND_INST: instantiating (7) with e2, all_52_6, e2, e2,
% 204.24/35.04  | | | | | | | |              simplifying with (228), (233) gives:
% 204.24/35.04  | | | | | | | |   (236)  all_52_6 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | COMBINE_EQS: (234), (236) imply:
% 204.24/35.04  | | | | | | | |   (237)  all_52_10 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | COMBINE_EQS: (234), (235) imply:
% 204.24/35.04  | | | | | | | |   (238)  all_52_10 = all_4_1
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | COMBINE_EQS: (237), (238) imply:
% 204.24/35.04  | | | | | | | |   (239)  all_4_1 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | SIMP: (239) implies:
% 204.24/35.04  | | | | | | | |   (240)  all_4_1 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REDUCE: (51), (240) imply:
% 204.24/35.04  | | | | | | | |   (241)  op(e2, e2) = all_4_0
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | GROUND_INST: instantiating (7) with e2, all_4_0, e2, e2,
% 204.24/35.04  | | | | | | | |              simplifying with (233), (241) gives:
% 204.24/35.04  | | | | | | | |   (242)  all_4_0 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REDUCE: (54), (242) imply:
% 204.24/35.04  | | | | | | | |   (243)   ~ (e3 = e2)
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REF_CLOSE: (7), (20), (22), (36), (38), (39), (40), (49), (50),
% 204.24/35.04  | | | | | | | |            (53), (58), (59), (62), (73), (76), (77), (82),
% 204.24/35.04  | | | | | | | |            (101), (103), (104), (113), (124), (129), (133),
% 204.24/35.04  | | | | | | | |            (138), (147), (150), (168), (172), (202), (211),
% 204.24/35.04  | | | | | | | |            (212), (217), (218), (219), (220), (221), (222),
% 204.24/35.04  | | | | | | | |            (225), (229) are inconsistent by sub-proof #785.
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | Case 2:
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | |   (244)  all_58_7 = e2 | all_58_13 = e2
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | | REF_CLOSE: (27), (38), (53), (227), (244) are inconsistent by
% 204.24/35.04  | | | | | | | |            sub-proof #783.
% 204.24/35.04  | | | | | | | | 
% 204.24/35.04  | | | | | | | End of split
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | Case 2:
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | |   (245)   ~ (all_56_15 = e3)
% 204.24/35.04  | | | | | | |   (246)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REDUCE: (48), (245) imply:
% 204.24/35.04  | | | | | | |   (247)   ~ (all_14_2 = e3)
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 204.24/35.04  | | | | | | |            (12), (14), (15), (16), (17), (18), (21), (24), (25),
% 204.24/35.04  | | | | | | |            (26), (27), (29), (30), (35), (36), (37), (38), (39),
% 204.24/35.04  | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.24/35.04  | | | | | | |            (49), (50), (52), (55), (58), (59), (60), (63), (64),
% 204.24/35.04  | | | | | | |            (65), (66), (68), (69), (71), (72), (73), (74), (75),
% 204.24/35.04  | | | | | | |            (77), (78), (79), (80), (83), (84), (88), (90), (91),
% 204.24/35.04  | | | | | | |            (93), (94), (96), (98), (99), (100), (101), (102),
% 204.24/35.04  | | | | | | |            (103), (104), (106), (108), (109), (111), (112), (113),
% 204.24/35.04  | | | | | | |            (114), (115), (117), (118), (120), (121), (122), (125),
% 204.24/35.04  | | | | | | |            (126), (129), (130), (132), (133), (135), (136), (137),
% 204.24/35.04  | | | | | | |            (138), (145), (147), (148), (149), (151), (152), (153),
% 204.24/35.04  | | | | | | |            (154), (155), (156), (158), (165), (167), (168), (170),
% 204.24/35.04  | | | | | | |            (172), (194), (195), (196), (197), (246), (247) are
% 204.24/35.04  | | | | | | |            inconsistent by sub-proof #782.
% 204.24/35.04  | | | | | | | 
% 204.24/35.04  | | | | | | End of split
% 204.24/35.04  | | | | | | 
% 204.24/35.04  | | | | | End of split
% 204.24/35.04  | | | | | 
% 204.24/35.04  | | | | End of split
% 204.24/35.04  | | | | 
% 204.24/35.04  | | | End of split
% 204.24/35.04  | | | 
% 204.24/35.05  | | End of split
% 204.24/35.05  | | 
% 204.24/35.05  | Case 2:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (248)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.24/35.05  | | 
% 204.24/35.05  | | REF_CLOSE: (7), (11), (17), (31), (45), (57), (64), (81), (92), (116),
% 204.24/35.05  | |            (117), (127), (138), (143), (144), (157), (248) are inconsistent
% 204.24/35.05  | |            by sub-proof #820.
% 204.24/35.05  | | 
% 204.24/35.05  | End of split
% 204.24/35.05  | 
% 204.24/35.05  End of proof
% 204.24/35.05  
% 204.24/35.05  Sub-proof #782 shows that the following formulas are inconsistent:
% 204.24/35.05  ----------------------------------------------------------------
% 204.24/35.05    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.24/35.05    (2)   ~ (all_52_15 = all_52_23)
% 204.24/35.05    (3)   ~ (all_52_25 = all_52_27)
% 204.24/35.05    (4)  all_58_14 = all_52_23
% 204.24/35.05    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.24/35.05    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.24/35.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.24/35.05    (7)  all_58_1 = all_52_9
% 204.24/35.05    (8)   ~ (all_52_9 = all_52_13)
% 204.24/35.05    (9)   ~ (e3 = e0)
% 204.24/35.05    (10)  op(e2, e3) = all_52_3
% 204.24/35.05    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.24/35.05    (12)   ~ (all_52_3 = all_52_19)
% 204.24/35.05    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.24/35.05    (14)   ~ (all_52_17 = all_52_25)
% 204.24/35.05    (15)   ~ (all_4_2 = e3)
% 204.24/35.05    (16)   ~ (all_52_3 = all_6_2)
% 204.24/35.05    (17)  all_58_0 = all_6_2
% 204.24/35.05    (18)   ~ (all_52_17 = all_10_2)
% 204.24/35.05    (19)   ~ (all_10_0 = e3)
% 204.24/35.05    (20)  op(all_52_5, all_52_5) = all_52_4
% 204.24/35.05    (21)  op(all_52_19, all_52_19) = all_52_18
% 204.24/35.05    (22)   ~ (all_52_27 = all_52_29)
% 204.24/35.05    (23)  all_58_13 = all_52_15
% 204.24/35.05    (24)  all_58_9 = all_52_25
% 204.24/35.05    (25)   ~ (all_52_29 = all_14_2)
% 204.24/35.05    (26)   ~ (all_52_15 = e3)
% 204.24/35.05    (27)  op(e1, e3) = all_52_5
% 204.24/35.05    (28)  op(e2, e2) = all_4_2
% 204.24/35.05    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.24/35.05    (30)  all_58_7 = all_10_0
% 204.24/35.05    (31)   ~ (all_52_3 = all_52_5)
% 204.24/35.05    (32)  all_58_11 = all_52_29
% 204.24/35.05    (33)  all_56_5 = all_4_2
% 204.24/35.05    (34)   ~ (all_52_25 = all_14_2)
% 204.24/35.05    (35)   ~ (all_52_3 = all_52_27)
% 204.24/35.05    (36)  op(all_10_2, e1) = all_10_1
% 204.24/35.05    (37)  op(all_6_2, all_6_2) = all_52_0
% 204.24/35.05    (38)   ~ (all_52_7 = all_6_2)
% 204.24/35.05    (39)  op(e0, e0) = all_14_2
% 204.24/35.05    (40)  op(all_52_29, all_52_29) = e1
% 204.24/35.05    (41)  all_56_15 = all_14_2
% 204.24/35.05    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.24/35.05    (43)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.24/35.05    (44)  all_56_11 = all_52_29
% 204.24/35.05    (45)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.24/35.05    (46)   ~ (all_6_2 = e3)
% 204.24/35.05    (47)  all_58_10 = all_52_27
% 204.24/35.05    (48)  all_56_8 = all_52_5
% 204.24/35.05    (49)  op(all_52_9, all_52_9) = all_52_8
% 204.24/35.05    (50)   ~ (all_52_25 = all_52_29)
% 204.24/35.05    (51)  op(all_6_2, e3) = e2
% 204.24/35.05    (52)   ~ (all_52_29 = all_10_2)
% 204.24/35.05    (53)  all_58_7 = all_52_13
% 204.24/35.05    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.24/35.05    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.24/35.05    (56)   ~ (all_52_5 = all_52_7)
% 204.24/35.05    (57)  all_58_12 = all_52_7
% 204.24/35.05    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05    (59)   ~ (all_52_7 = all_14_2)
% 204.24/35.05    (60)   ~ (all_14_2 = e0)
% 204.24/35.05    (61)  all_58_2 = all_52_3
% 204.24/35.05    (62)  all_56_2 = all_52_17
% 204.24/35.05    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.24/35.05    (64)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.24/35.05    (65)   ~ (all_52_25 = e3)
% 204.24/35.05    (66)   ~ (e2 = e0)
% 204.24/35.05    (67)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.24/35.05    (68)  op(all_52_25, all_52_25) = e3
% 204.24/35.05    (69)   ~ (all_52_5 = all_52_29)
% 204.24/35.05    (70)   ~ (all_52_19 = all_52_27)
% 204.24/35.05    (71)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.24/35.05    (72)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.24/35.05    (73)  op(e3, e1) = all_52_17
% 204.24/35.05    (74)  op(all_52_27, all_52_27) = e2
% 204.24/35.05    (75)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.24/35.05    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.24/35.05    (77)   ~ (all_52_9 = all_52_25)
% 204.24/35.05    (78)  all_58_15 = all_14_2
% 204.24/35.05    (79)   ~ (all_52_19 = all_10_2)
% 204.24/35.05    (80)  op(all_52_23, all_52_23) = all_52_22
% 204.24/35.05    (81)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.24/35.05    (82)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.24/35.05    (83)  all_58_8 = all_10_2
% 204.24/35.05    (84)   ~ (all_52_5 = all_10_2)
% 204.24/35.05    (85)   ~ (all_52_23 = all_14_2)
% 204.24/35.05    (86)  all_56_12 = all_52_7
% 204.24/35.05    (87)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.24/35.05    (88)   ~ (all_52_25 = all_6_2)
% 204.24/35.05    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.24/35.05    (90)   ~ (all_52_9 = all_4_2)
% 204.24/35.05    (91)   ~ (all_52_5 = all_6_2)
% 204.24/35.05    (92)  op(e3, e3) = all_6_2
% 204.24/35.05    (93)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.24/35.05    (94)   ~ (all_52_27 = all_14_2)
% 204.24/35.05    (95)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.24/35.05    (96)  all_56_14 = all_52_23
% 204.24/35.05    (97)  all_56_3 = all_52_25
% 204.24/35.05    (98)   ~ (all_52_3 = all_52_7)
% 204.24/35.05    (99)  all_58_5 = all_52_19
% 204.24/35.05    (100)   ~ (all_52_15 = all_4_2)
% 204.24/35.05    (101)   ~ (all_52_27 = all_4_2)
% 204.24/35.05    (102)  all_58_6 = all_52_5
% 204.24/35.05    (103)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.24/35.05    (104)   ~ (all_52_17 = all_6_2)
% 204.24/35.05    (105)   ~ (e1 = e0)
% 204.24/35.05    (106)  op(all_14_2, all_14_2) = e0
% 204.24/35.05    (107)   ~ (e3 = e2)
% 204.24/35.05    (108)  op(all_52_13, all_52_13) = all_52_12
% 204.24/35.05    (109)  op(e1, e1) = all_10_2
% 204.24/35.05    (110)   ~ (all_52_23 = all_10_2)
% 204.24/35.05    (111)   ~ (all_52_7 = all_52_23)
% 204.24/35.05    (112)  all_58_3 = all_4_2
% 204.24/35.05    (113)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.24/35.05    (114)   ~ (all_52_3 = all_4_2)
% 204.24/35.05    (115)   ~ (all_52_19 = all_4_2)
% 204.24/35.05    (116)   ~ (all_52_17 = all_52_23)
% 204.24/35.05    (117)  op(all_6_2, e3) = all_6_1
% 204.24/35.05    (118)  all_58_4 = all_52_17
% 204.24/35.05    (119)   ~ (all_14_2 = e3)
% 204.24/35.05  
% 204.24/35.05  Begin of proof
% 204.24/35.05  | 
% 204.24/35.05  | BETA: splitting (103) gives:
% 204.24/35.05  | 
% 204.24/35.05  | Case 1:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (120)  all_58_12 = e3
% 204.24/35.05  | | 
% 204.24/35.05  | | COMBINE_EQS: (57), (120) imply:
% 204.24/35.05  | |   (121)  all_52_7 = e3
% 204.24/35.05  | | 
% 204.24/35.05  | | SIMP: (121) implies:
% 204.24/35.05  | |   (122)  all_52_7 = e3
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (98), (122) imply:
% 204.24/35.05  | |   (123)   ~ (all_52_3 = e3)
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (56), (122) imply:
% 204.24/35.05  | |   (124)   ~ (all_52_5 = e3)
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (111), (122) imply:
% 204.24/35.05  | |   (125)   ~ (all_52_23 = e3)
% 204.24/35.05  | | 
% 204.24/35.05  | | SIMP: (125) implies:
% 204.24/35.05  | |   (126)   ~ (all_52_23 = e3)
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (59), (122) imply:
% 204.24/35.05  | |   (127)   ~ (all_14_2 = e3)
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (38), (122) imply:
% 204.24/35.05  | |   (128)   ~ (all_6_2 = e3)
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (13), (122) imply:
% 204.24/35.05  | |   (129)  op(e3, e3) = all_52_6
% 204.24/35.05  | | 
% 204.24/35.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 204.24/35.05  | |            (15), (17), (18), (21), (22), (23), (24), (25), (27), (28), (29),
% 204.24/35.05  | |            (31), (32), (33), (34), (35), (36), (37), (39), (40), (41), (42),
% 204.24/35.05  | |            (43), (44), (45), (46), (47), (48), (50), (51), (52), (53), (54),
% 204.24/35.05  | |            (55), (58), (60), (61), (62), (64), (65), (66), (67), (68), (69),
% 204.24/35.05  | |            (71), (72), (73), (74), (75), (76), (78), (79), (81), (82), (83),
% 204.24/35.05  | |            (85), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 204.24/35.05  | |            (97), (99), (100), (102), (104), (105), (106), (108), (109),
% 204.24/35.05  | |            (112), (113), (115), (116), (117), (118), (119), (120), (123),
% 204.24/35.05  | |            (124), (126), (129) are inconsistent by sub-proof #798.
% 204.24/35.05  | | 
% 204.24/35.05  | Case 2:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (130)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.24/35.05  | | 
% 204.24/35.05  | | BETA: splitting (130) gives:
% 204.24/35.05  | | 
% 204.24/35.05  | | Case 1:
% 204.24/35.05  | | | 
% 204.24/35.05  | | |   (131)  all_58_13 = e3
% 204.24/35.05  | | | 
% 204.24/35.05  | | | REF_CLOSE: (23), (26), (131) are inconsistent by sub-proof #1360.
% 204.24/35.05  | | | 
% 204.24/35.05  | | Case 2:
% 204.24/35.05  | | | 
% 204.24/35.05  | | |   (132)  all_58_14 = e3 | all_58_15 = e3
% 204.24/35.05  | | | 
% 204.24/35.05  | | | BETA: splitting (132) gives:
% 204.24/35.05  | | | 
% 204.24/35.05  | | | Case 1:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | |   (133)  all_58_14 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | COMBINE_EQS: (4), (133) imply:
% 204.24/35.05  | | | |   (134)  all_52_23 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | SIMP: (134) implies:
% 204.24/35.05  | | | |   (135)  all_52_23 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (111), (135) imply:
% 204.24/35.05  | | | |   (136)   ~ (all_52_7 = e3)
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (116), (135) imply:
% 204.24/35.05  | | | |   (137)   ~ (all_52_17 = e3)
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (85), (135) imply:
% 204.24/35.05  | | | |   (138)   ~ (all_14_2 = e3)
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (110), (135) imply:
% 204.24/35.05  | | | |   (139)   ~ (all_10_2 = e3)
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | SIMP: (139) implies:
% 204.24/35.05  | | | |   (140)   ~ (all_10_2 = e3)
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (80), (135) imply:
% 204.24/35.05  | | | |   (141)  op(e3, e3) = all_52_22
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 204.24/35.05  | | | |              simplifying with (92), (141) gives:
% 204.24/35.05  | | | |   (142)  all_52_22 = all_6_2
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | BETA: splitting (58) gives:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | Case 1:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | |   (143)  all_58_6 = e3
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | COMBINE_EQS: (102), (143) imply:
% 204.24/35.05  | | | | |   (144)  all_52_5 = e3
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | REF_CLOSE: (3), (6), (7), (14), (17), (18), (20), (24), (31), (32),
% 204.24/35.05  | | | | |            (39), (42), (43), (47), (49), (61), (68), (69), (70), (74),
% 204.24/35.05  | | | | |            (76), (77), (78), (84), (88), (89), (92), (93), (94), (95),
% 204.24/35.05  | | | | |            (97), (99), (101), (107), (109), (112), (118), (119), (144)
% 204.24/35.05  | | | | |            are inconsistent by sub-proof #797.
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | Case 2:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | |   (145)   ~ (all_58_6 = e3)
% 204.24/35.05  | | | | |   (146)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | REDUCE: (102), (145) imply:
% 204.24/35.05  | | | | |   (147)   ~ (all_52_5 = e3)
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | BETA: splitting (63) gives:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | Case 1:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | |   (148)  all_58_0 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | COMBINE_EQS: (17), (148) imply:
% 204.24/35.05  | | | | | |   (149)  all_6_2 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | REDUCE: (46), (149) imply:
% 204.24/35.05  | | | | | |   (150)  $false
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | CLOSE: (150) is inconsistent.
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | Case 2:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | |   (151)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | BETA: splitting (151) gives:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | Case 1:
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | |   (152)  all_58_2 = e3
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | COMBINE_EQS: (61), (152) imply:
% 204.24/35.05  | | | | | | |   (153)  all_52_3 = e3
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | REDUCE: (98), (153) imply:
% 204.24/35.05  | | | | | | |   (154)   ~ (all_52_7 = e3)
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | REDUCE: (16), (153) imply:
% 204.24/35.05  | | | | | | |   (155)   ~ (all_6_2 = e3)
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | REDUCE: (5), (153) imply:
% 204.24/35.05  | | | | | | |   (156)  op(e3, e3) = all_52_2
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | BETA: splitting (146) gives:
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | Case 1:
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | |   (157)  all_58_7 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | COMBINE_EQS: (30), (157) imply:
% 204.24/35.05  | | | | | | | |   (158)  all_10_0 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | REDUCE: (19), (158) imply:
% 204.24/35.05  | | | | | | | |   (159)  $false
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | CLOSE: (159) is inconsistent.
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | Case 2:
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | |   (160)  all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | REF_CLOSE: (6), (11), (13), (14), (17), (20), (22), (24), (25),
% 204.24/35.05  | | | | | | | |            (27), (28), (32), (37), (38), (39), (40), (43), (45),
% 204.24/35.05  | | | | | | | |            (46), (47), (50), (51), (52), (56), (57), (61), (62),
% 204.24/35.05  | | | | | | | |            (63), (68), (69), (75), (78), (83), (86), (88), (89),
% 204.24/35.05  | | | | | | | |            (92), (93), (97), (102), (104), (109), (114), (118),
% 204.24/35.05  | | | | | | | |            (136), (137), (140), (156), (160) are inconsistent by
% 204.24/35.05  | | | | | | | |            sub-proof #796.
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | End of split
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | Case 2:
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | |   (161)  all_58_6 = e3 | all_58_12 = e3
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | REF_CLOSE: (57), (102), (136), (147), (161) are inconsistent by
% 204.24/35.05  | | | | | | |            sub-proof #1243.
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | End of split
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | End of split
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | End of split
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | Case 2:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | |   (162)  all_58_15 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | COMBINE_EQS: (78), (162) imply:
% 204.24/35.05  | | | |   (163)  all_14_2 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (119), (163) imply:
% 204.24/35.05  | | | |   (164)  $false
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | CLOSE: (164) is inconsistent.
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | End of split
% 204.24/35.05  | | | 
% 204.24/35.05  | | End of split
% 204.24/35.05  | | 
% 204.24/35.05  | End of split
% 204.24/35.05  | 
% 204.24/35.05  End of proof
% 204.24/35.05  
% 204.24/35.05  Sub-proof #783 shows that the following formulas are inconsistent:
% 204.24/35.05  ----------------------------------------------------------------
% 204.24/35.05    (1)   ~ (all_52_15 = e2)
% 204.24/35.05    (2)  all_58_13 = all_52_15
% 204.24/35.05    (3)  all_58_7 = all_10_0
% 204.24/35.05    (4)   ~ (all_10_0 = e2)
% 204.24/35.05    (5)  all_58_7 = e2 | all_58_13 = e2
% 204.24/35.05  
% 204.24/35.05  Begin of proof
% 204.24/35.05  | 
% 204.24/35.05  | BETA: splitting (5) gives:
% 204.24/35.05  | 
% 204.24/35.05  | Case 1:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (6)  all_58_7 = e2
% 204.24/35.05  | | 
% 204.24/35.05  | | COMBINE_EQS: (3), (6) imply:
% 204.24/35.05  | |   (7)  all_10_0 = e2
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (4), (7) imply:
% 204.24/35.05  | |   (8)  $false
% 204.24/35.05  | | 
% 204.24/35.05  | | CLOSE: (8) is inconsistent.
% 204.24/35.05  | | 
% 204.24/35.05  | Case 2:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (9)  all_58_13 = e2
% 204.24/35.05  | | 
% 204.24/35.05  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #784.
% 204.24/35.05  | | 
% 204.24/35.05  | End of split
% 204.24/35.05  | 
% 204.24/35.05  End of proof
% 204.24/35.05  
% 204.24/35.05  Sub-proof #784 shows that the following formulas are inconsistent:
% 204.24/35.05  ----------------------------------------------------------------
% 204.24/35.05    (1)  all_58_13 = all_52_15
% 204.24/35.05    (2)  all_58_13 = e2
% 204.24/35.05    (3)   ~ (all_52_15 = e2)
% 204.24/35.05  
% 204.24/35.05  Begin of proof
% 204.24/35.05  | 
% 204.24/35.05  | COMBINE_EQS: (1), (2) imply:
% 204.24/35.05  |   (4)  all_52_15 = e2
% 204.24/35.05  | 
% 204.24/35.05  | SIMP: (4) implies:
% 204.24/35.05  |   (5)  all_52_15 = e2
% 204.24/35.05  | 
% 204.24/35.05  | REDUCE: (3), (5) imply:
% 204.24/35.05  |   (6)  $false
% 204.24/35.05  | 
% 204.24/35.05  | CLOSE: (6) is inconsistent.
% 204.24/35.05  | 
% 204.24/35.05  End of proof
% 204.24/35.05  
% 204.24/35.05  Sub-proof #785 shows that the following formulas are inconsistent:
% 204.24/35.05  ----------------------------------------------------------------
% 204.24/35.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.24/35.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.24/35.05    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.05    (3)   ~ (all_4_2 = e3)
% 204.24/35.05    (4)   ~ (all_14_1 = e3)
% 204.24/35.05    (5)  all_56_4 = all_52_3
% 204.24/35.05    (6)   ~ (all_10_0 = e3)
% 204.24/35.05    (7)  all_40_2 = all_10_2
% 204.24/35.05    (8)  op(e2, e2) = all_4_2
% 204.24/35.05    (9)  all_58_7 = all_10_0
% 204.24/35.05    (10)   ~ (all_52_3 = all_52_5)
% 204.24/35.05    (11)  all_58_11 = all_52_29
% 204.24/35.05    (12)  all_56_3 = all_14_1
% 204.24/35.05    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.24/35.05    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.24/35.05    (15)   ~ (all_10_0 = e2)
% 204.24/35.05    (16)  all_58_10 = all_52_27
% 204.24/35.05    (17)  all_56_8 = all_52_5
% 204.24/35.05    (18)  all_56_9 = all_10_0
% 204.24/35.05    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05    (20)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.24/35.05    (21)  all_58_2 = all_52_3
% 204.24/35.05    (22)   ~ (all_52_29 = e3)
% 204.24/35.05    (23)  all_58_9 = all_14_1
% 204.24/35.05    (24)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.24/35.05    (25)   ~ (all_52_27 = e3)
% 204.24/35.05    (26)   ~ (all_52_5 = e2)
% 204.24/35.05    (27)   ~ (all_52_19 = all_10_2)
% 204.24/35.05    (28)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.24/35.05    (29)  all_58_3 = e2
% 204.24/35.05    (30)  all_58_8 = all_10_2
% 204.24/35.05    (31)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.24/35.05    (32)   ~ (all_52_5 = e0)
% 204.24/35.05    (33)  all_40_0 = all_10_0
% 204.24/35.05    (34)  all_58_5 = all_52_19
% 204.24/35.05    (35)  all_58_6 = all_52_5
% 204.24/35.05    (36)  op(all_14_1, all_14_1) = e3
% 204.24/35.05    (37)   ~ (e3 = e2)
% 204.24/35.05    (38)   ~ (all_14_1 = e0)
% 204.24/35.05    (39)  op(e1, e1) = all_10_2
% 204.24/35.05    (40)   ~ (all_52_5 = all_10_0)
% 204.24/35.05  
% 204.24/35.05  Begin of proof
% 204.24/35.05  | 
% 204.24/35.05  | BETA: splitting (31) gives:
% 204.24/35.05  | 
% 204.24/35.05  | Case 1:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (41)  all_56_3 = e3
% 204.24/35.05  | | 
% 204.24/35.05  | | REF_CLOSE: (4), (12), (41) are inconsistent by sub-proof #1200.
% 204.24/35.05  | | 
% 204.24/35.05  | Case 2:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (42)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.24/35.05  | | 
% 204.24/35.05  | | BETA: splitting (24) gives:
% 204.24/35.05  | | 
% 204.24/35.05  | | Case 1:
% 204.24/35.05  | | | 
% 204.24/35.05  | | |   (43)  all_56_4 = e3
% 204.24/35.05  | | | 
% 204.24/35.05  | | | COMBINE_EQS: (5), (43) imply:
% 204.24/35.05  | | |   (44)  all_52_3 = e3
% 204.24/35.05  | | | 
% 204.24/35.05  | | | SIMP: (44) implies:
% 204.24/35.05  | | |   (45)  all_52_3 = e3
% 204.24/35.05  | | | 
% 204.24/35.05  | | | REDUCE: (10), (45) imply:
% 204.24/35.05  | | |   (46)   ~ (all_52_5 = e3)
% 204.24/35.05  | | | 
% 204.24/35.05  | | | SIMP: (46) implies:
% 204.24/35.05  | | |   (47)   ~ (all_52_5 = e3)
% 204.24/35.05  | | | 
% 204.24/35.05  | | | BETA: splitting (28) gives:
% 204.24/35.05  | | | 
% 204.24/35.05  | | | Case 1:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | |   (48)  all_56_8 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REF_CLOSE: (17), (47), (48) are inconsistent by sub-proof #1325.
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | Case 2:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | |   (49)   ~ (all_56_8 = e3)
% 204.24/35.05  | | | |   (50)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | BETA: splitting (50) gives:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | Case 1:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | |   (51)  all_56_8 = e2
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | REF_CLOSE: (17), (26), (51) are inconsistent by sub-proof #1022.
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | Case 2:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | |   (52)  all_56_8 = e1 | all_56_8 = e0
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | BETA: splitting (19) gives:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | Case 1:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | |   (53)  all_58_6 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | COMBINE_EQS: (35), (53) imply:
% 204.24/35.05  | | | | | |   (54)  all_52_5 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | REDUCE: (47), (54) imply:
% 204.24/35.05  | | | | | |   (55)  $false
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | CLOSE: (55) is inconsistent.
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | Case 2:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | |   (56)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | BETA: splitting (56) gives:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | Case 1:
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | |   (57)  all_58_7 = e3
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | COMBINE_EQS: (9), (57) imply:
% 204.24/35.05  | | | | | | |   (58)  all_10_0 = e3
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | REDUCE: (6), (58) imply:
% 204.24/35.05  | | | | | | |   (59)  $false
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | CLOSE: (59) is inconsistent.
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | Case 2:
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | |   (60)  all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | BETA: splitting (60) gives:
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | | Case 1:
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | |   (61)  all_58_8 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | COMBINE_EQS: (30), (61) imply:
% 204.24/35.05  | | | | | | | |   (62)  all_10_2 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | COMBINE_EQS: (7), (62) imply:
% 204.24/35.05  | | | | | | | |   (63)  all_40_2 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | BETA: splitting (20) gives:
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | Case 1:
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | |   (64)   ~ (all_40_2 = e3)
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | REDUCE: (63), (64) imply:
% 204.24/35.05  | | | | | | | | |   (65)  $false
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | CLOSE: (65) is inconsistent.
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | Case 2:
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | |   (66)   ~ (all_40_0 = e0)
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | REDUCE: (33), (66) imply:
% 204.24/35.05  | | | | | | | | |   (67)   ~ (all_10_0 = e0)
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | BETA: splitting (2) gives:
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | Case 1:
% 204.24/35.05  | | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | |   (68)  all_56_9 = e2
% 204.24/35.05  | | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | | REF_CLOSE: (15), (18), (68) are inconsistent by sub-proof
% 204.24/35.05  | | | | | | | | | |            #991.
% 204.24/35.05  | | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | Case 2:
% 204.24/35.05  | | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | |   (69)  all_56_9 = e1 | all_56_9 = e0
% 204.24/35.05  | | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | | REF_CLOSE: (17), (18), (32), (40), (52), (67), (69) are
% 204.24/35.05  | | | | | | | | | |            inconsistent by sub-proof #786.
% 204.24/35.05  | | | | | | | | | | 
% 204.24/35.05  | | | | | | | | | End of split
% 204.24/35.05  | | | | | | | | | 
% 204.24/35.05  | | | | | | | | End of split
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | Case 2:
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | |   (70)  all_58_11 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | COMBINE_EQS: (11), (70) imply:
% 204.24/35.05  | | | | | | | |   (71)  all_52_29 = e3
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | REDUCE: (22), (71) imply:
% 204.24/35.05  | | | | | | | |   (72)  $false
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | | CLOSE: (72) is inconsistent.
% 204.24/35.05  | | | | | | | | 
% 204.24/35.05  | | | | | | | End of split
% 204.24/35.05  | | | | | | | 
% 204.24/35.05  | | | | | | End of split
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | End of split
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | End of split
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | End of split
% 204.24/35.05  | | | 
% 204.24/35.05  | | Case 2:
% 204.24/35.05  | | | 
% 204.24/35.05  | | |   (73)   ~ (all_56_4 = e3)
% 204.24/35.05  | | | 
% 204.24/35.05  | | | REDUCE: (5), (73) imply:
% 204.24/35.05  | | |   (74)   ~ (all_52_3 = e3)
% 204.24/35.05  | | | 
% 204.24/35.05  | | | BETA: splitting (13) gives:
% 204.24/35.05  | | | 
% 204.24/35.05  | | | Case 1:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | |   (75)  all_58_2 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | COMBINE_EQS: (21), (75) imply:
% 204.24/35.05  | | | |   (76)  all_52_3 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | REDUCE: (74), (76) imply:
% 204.24/35.05  | | | |   (77)  $false
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | CLOSE: (77) is inconsistent.
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | Case 2:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | |   (78)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | BETA: splitting (78) gives:
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | | Case 1:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | |   (79)  all_58_3 = e3
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | COMBINE_EQS: (29), (79) imply:
% 204.24/35.05  | | | | |   (80)  e3 = e2
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | SIMP: (80) implies:
% 204.24/35.05  | | | | |   (81)  e3 = e2
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | REDUCE: (37), (81) imply:
% 204.24/35.05  | | | | |   (82)  $false
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | CLOSE: (82) is inconsistent.
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | Case 2:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | |   (83)  all_58_5 = e3 | all_58_10 = e3
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | BETA: splitting (83) gives:
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | | Case 1:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | |   (84)  all_58_5 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | COMBINE_EQS: (34), (84) imply:
% 204.24/35.05  | | | | | |   (85)  all_52_19 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | REDUCE: (27), (85) imply:
% 204.24/35.05  | | | | | |   (86)   ~ (all_10_2 = e3)
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | SIMP: (86) implies:
% 204.24/35.05  | | | | | |   (87)   ~ (all_10_2 = e3)
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | REF_CLOSE: (1), (3), (8), (12), (14), (23), (36), (38), (39), (42),
% 204.24/35.05  | | | | | |            (87) are inconsistent by sub-proof #804.
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | Case 2:
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | |   (88)  all_58_10 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | COMBINE_EQS: (16), (88) imply:
% 204.24/35.05  | | | | | |   (89)  all_52_27 = e3
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | REDUCE: (25), (89) imply:
% 204.24/35.05  | | | | | |   (90)  $false
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | | CLOSE: (90) is inconsistent.
% 204.24/35.05  | | | | | | 
% 204.24/35.05  | | | | | End of split
% 204.24/35.05  | | | | | 
% 204.24/35.05  | | | | End of split
% 204.24/35.05  | | | | 
% 204.24/35.05  | | | End of split
% 204.24/35.05  | | | 
% 204.24/35.05  | | End of split
% 204.24/35.05  | | 
% 204.24/35.05  | End of split
% 204.24/35.05  | 
% 204.24/35.05  End of proof
% 204.24/35.05  
% 204.24/35.05  Sub-proof #786 shows that the following formulas are inconsistent:
% 204.24/35.05  ----------------------------------------------------------------
% 204.24/35.05    (1)   ~ (all_10_0 = e0)
% 204.24/35.05    (2)  all_56_8 = all_52_5
% 204.24/35.05    (3)  all_56_9 = all_10_0
% 204.24/35.05    (4)  all_56_8 = e1 | all_56_8 = e0
% 204.24/35.05    (5)  all_56_9 = e1 | all_56_9 = e0
% 204.24/35.05    (6)   ~ (all_52_5 = e0)
% 204.24/35.05    (7)   ~ (all_52_5 = all_10_0)
% 204.24/35.05  
% 204.24/35.05  Begin of proof
% 204.24/35.05  | 
% 204.24/35.05  | BETA: splitting (5) gives:
% 204.24/35.05  | 
% 204.24/35.05  | Case 1:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (8)  all_56_9 = e1
% 204.24/35.05  | | 
% 204.24/35.05  | | COMBINE_EQS: (3), (8) imply:
% 204.24/35.05  | |   (9)  all_10_0 = e1
% 204.24/35.05  | | 
% 204.24/35.05  | | SIMP: (9) implies:
% 204.24/35.05  | |   (10)  all_10_0 = e1
% 204.24/35.05  | | 
% 204.24/35.05  | | REDUCE: (7), (10) imply:
% 204.24/35.05  | |   (11)   ~ (all_52_5 = e1)
% 204.24/35.05  | | 
% 204.24/35.05  | | REF_CLOSE: (2), (4), (6), (11) are inconsistent by sub-proof #1020.
% 204.24/35.05  | | 
% 204.24/35.05  | Case 2:
% 204.24/35.05  | | 
% 204.24/35.05  | |   (12)  all_56_9 = e0
% 204.24/35.05  | | 
% 204.24/35.05  | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #989.
% 204.24/35.05  | | 
% 204.24/35.05  | End of split
% 204.24/35.05  | 
% 204.24/35.05  End of proof
% 204.24/35.05  
% 204.24/35.05  Sub-proof #787 shows that the following formulas are inconsistent:
% 204.24/35.05  ----------------------------------------------------------------
% 204.24/35.05    (1)  all_58_14 = all_52_23
% 204.24/35.05    (2)   ~ (e3 = e1)
% 204.24/35.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.24/35.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.24/35.05    (4)   ~ (e3 = e0)
% 204.24/35.05    (5)  op(all_52_23, all_52_23) = e0
% 204.24/35.05    (6)  op(e2, e3) = all_52_3
% 204.24/35.05    (7)   ~ (all_52_17 = all_52_25)
% 204.24/35.05    (8)   ~ (all_4_2 = e3)
% 204.24/35.05    (9)   ~ (all_52_3 = all_6_2)
% 204.24/35.05    (10)  all_58_0 = all_6_2
% 204.24/35.05    (11)   ~ (all_10_0 = e3)
% 204.24/35.05    (12)  all_40_2 = all_10_2
% 204.24/35.05    (13)  op(all_52_5, all_52_5) = all_52_4
% 204.24/35.05    (14)  all_58_13 = all_52_15
% 204.24/35.05    (15)  all_58_9 = all_52_25
% 204.24/35.05    (16)   ~ (all_52_29 = all_14_2)
% 204.24/35.05    (17)   ~ (all_52_15 = e3)
% 204.24/35.05    (18)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.24/35.05    (19)  op(all_52_27, all_52_27) = all_52_26
% 204.24/35.05    (20)  op(e2, e2) = all_4_2
% 204.24/35.05    (21)  all_58_7 = all_10_0
% 204.24/35.05    (22)   ~ (all_52_3 = all_52_5)
% 204.24/35.05    (23)  all_58_11 = all_52_29
% 204.24/35.05    (24)   ~ (all_52_25 = all_14_2)
% 204.24/35.05    (25)  op(all_10_2, e1) = all_10_1
% 204.24/35.05    (26)  all_58_1 = e3
% 204.24/35.05    (27)   ~ (all_52_7 = all_6_2)
% 204.24/35.05    (28)  op(e0, e0) = all_14_2
% 204.24/35.05    (29)  all_56_15 = all_14_2
% 204.24/35.05    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.24/35.05    (31)  all_56_11 = all_52_29
% 204.24/35.05    (32)   ~ (all_10_0 = e2)
% 204.24/35.05    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.24/35.05    (34)   ~ (all_6_2 = e3)
% 204.24/35.05    (35)   ~ (e2 = e1)
% 204.24/35.05    (36)  op(all_10_2, all_10_2) = e1
% 204.24/35.05    (37)  all_58_10 = all_52_27
% 204.24/35.05    (38)   ~ (all_52_19 = all_52_23)
% 204.24/35.05    (39)  all_56_9 = all_10_0
% 204.24/35.05    (40)  op(all_6_2, e3) = e2
% 204.24/35.05    (41)   ~ (all_52_29 = all_10_2)
% 204.24/35.05    (42)  op(all_52_19, all_52_19) = e2
% 204.24/35.05    (43)  all_58_12 = all_52_7
% 204.24/35.05    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.05    (45)   ~ (all_52_7 = all_14_2)
% 204.24/35.05    (46)   ~ (all_14_2 = e0)
% 204.24/35.05    (47)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.24/35.05    (48)  all_58_2 = all_52_3
% 204.24/35.05    (49)  all_56_2 = all_52_17
% 204.24/35.05    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.24/35.05    (51)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.24/35.05    (52)   ~ (all_52_25 = e3)
% 204.24/35.05    (53)   ~ (e2 = e0)
% 204.24/35.05    (54)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.24/35.05    (55)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.24/35.05    (56)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.24/35.05    (57)  op(e3, e3) = all_52_8
% 204.24/35.05    (58)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.24/35.05    (59)  op(e3, e1) = all_52_17
% 204.24/35.05    (60)  op(e0, e3) = all_52_7
% 204.24/35.05    (61)  all_58_15 = all_14_2
% 204.24/35.05    (62)   ~ (all_52_19 = all_10_2)
% 204.24/35.05    (63)  all_58_8 = all_10_2
% 204.24/35.05    (64)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.24/35.05    (65)   ~ (all_52_23 = all_14_2)
% 204.24/35.05    (66)   ~ (all_52_25 = all_6_2)
% 204.24/35.05    (67)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.24/35.05    (68)  op(e3, e3) = all_6_2
% 204.24/35.05    (69)   ~ (all_52_27 = all_14_2)
% 204.24/35.05    (70)   ~ (all_52_17 = e3)
% 204.24/35.05    (71)  all_40_0 = all_10_0
% 204.24/35.05    (72)  all_56_3 = all_52_25
% 204.24/35.05    (73)   ~ (all_52_3 = all_52_7)
% 204.24/35.05    (74)  op(all_14_2, all_14_2) = all_52_30
% 204.24/35.06    (75)  all_58_5 = all_52_19
% 204.24/35.06    (76)   ~ (all_52_27 = all_4_2)
% 204.24/35.06    (77)  op(all_52_17, all_52_17) = e3
% 204.24/35.06    (78)  all_58_6 = all_52_5
% 204.24/35.06    (79)  op(all_10_2, e1) = e2
% 204.24/35.06    (80)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.24/35.06    (81)   ~ (all_52_17 = all_6_2)
% 204.24/35.06    (82)   ~ (e1 = e0)
% 204.24/35.06    (83)  all_56_10 = all_10_2
% 204.24/35.06    (84)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.24/35.06    (85)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.06    (86)  op(e1, e1) = all_10_2
% 204.24/35.06    (87)   ~ (all_52_23 = all_10_2)
% 204.24/35.06    (88)   ~ (all_52_7 = all_52_23)
% 204.24/35.06    (89)  all_58_3 = all_4_2
% 204.24/35.06    (90)   ~ (all_52_3 = all_4_2)
% 204.24/35.06    (91)   ~ (all_52_17 = all_52_23)
% 204.24/35.06    (92)  all_58_4 = all_52_17
% 204.24/35.06    (93)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.24/35.06  
% 204.24/35.06  Begin of proof
% 204.24/35.06  | 
% 204.24/35.06  | BETA: splitting (85) gives:
% 204.24/35.06  | 
% 204.24/35.06  | Case 1:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (94)  all_56_9 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | COMBINE_EQS: (39), (94) imply:
% 204.24/35.06  | |   (95)  all_10_0 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | REDUCE: (11), (95) imply:
% 204.24/35.06  | |   (96)  $false
% 204.24/35.06  | | 
% 204.24/35.06  | | CLOSE: (96) is inconsistent.
% 204.24/35.06  | | 
% 204.24/35.06  | Case 2:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (97)   ~ (all_56_9 = e3)
% 204.24/35.06  | |   (98)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.06  | | 
% 204.24/35.06  | | BETA: splitting (64) gives:
% 204.24/35.06  | | 
% 204.24/35.06  | | Case 1:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (99)  all_56_15 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | COMBINE_EQS: (29), (99) imply:
% 204.24/35.06  | | |   (100)  all_14_2 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | SIMP: (100) implies:
% 204.24/35.06  | | |   (101)  all_14_2 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REDUCE: (45), (101) imply:
% 204.24/35.06  | | |   (102)   ~ (all_52_7 = e3)
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REDUCE: (65), (101) imply:
% 204.24/35.06  | | |   (103)   ~ (all_52_23 = e3)
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REDUCE: (69), (101) imply:
% 204.24/35.06  | | |   (104)   ~ (all_52_27 = e3)
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REDUCE: (74), (101) imply:
% 204.24/35.06  | | |   (105)  op(e3, e3) = all_52_30
% 204.24/35.06  | | | 
% 204.24/35.06  | | | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3,
% 204.24/35.06  | | |              simplifying with (68), (105) gives:
% 204.24/35.06  | | |   (106)  all_52_30 = all_6_2
% 204.24/35.06  | | | 
% 204.24/35.06  | | | BETA: splitting (50) gives:
% 204.24/35.06  | | | 
% 204.24/35.06  | | | Case 1:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | |   (107)  all_58_0 = e3
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | COMBINE_EQS: (10), (107) imply:
% 204.24/35.06  | | | |   (108)  all_6_2 = e3
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REDUCE: (34), (108) imply:
% 204.24/35.06  | | | |   (109)  $false
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | CLOSE: (109) is inconsistent.
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | Case 2:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | |   (110)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | BETA: splitting (30) gives:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | Case 1:
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | |   (111)  all_58_2 = e3
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | COMBINE_EQS: (48), (111) imply:
% 204.24/35.06  | | | | |   (112)  all_52_3 = e3
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | SIMP: (112) implies:
% 204.24/35.06  | | | | |   (113)  all_52_3 = e3
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | REDUCE: (22), (113) imply:
% 204.24/35.06  | | | | |   (114)   ~ (all_52_5 = e3)
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | SIMP: (114) implies:
% 204.24/35.06  | | | | |   (115)   ~ (all_52_5 = e3)
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | REDUCE: (90), (113) imply:
% 204.24/35.06  | | | | |   (116)   ~ (all_4_2 = e3)
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (11), (12), (15), (16),
% 204.24/35.06  | | | | |            (18), (20), (21), (23), (26), (28), (31), (32), (35), (38),
% 204.24/35.06  | | | | |            (39), (41), (42), (44), (47), (51), (53), (54), (56), (57),
% 204.24/35.06  | | | | |            (59), (62), (63), (68), (70), (71), (75), (77), (78), (79),
% 204.24/35.06  | | | | |            (82), (84), (86), (92), (98), (103), (115) are inconsistent
% 204.24/35.06  | | | | |            by sub-proof #788.
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | Case 2:
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | |   (117)   ~ (all_58_2 = e3)
% 204.24/35.06  | | | | |   (118)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | REDUCE: (48), (117) imply:
% 204.24/35.06  | | | | |   (119)   ~ (all_52_3 = e3)
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | BETA: splitting (110) gives:
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | | Case 1:
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | |   (120)  all_58_2 = e3
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | | REF_CLOSE: (48), (119), (120) are inconsistent by sub-proof #1369.
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | Case 2:
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | |   (121)  all_58_6 = e3 | all_58_12 = e3
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | | BETA: splitting (121) gives:
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | | Case 1:
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | |   (122)  all_58_6 = e3
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | | COMBINE_EQS: (78), (122) imply:
% 204.24/35.06  | | | | | | |   (123)  all_52_5 = e3
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | | SIMP: (123) implies:
% 204.24/35.06  | | | | | | |   (124)  all_52_5 = e3
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | | REDUCE: (13), (124) imply:
% 204.24/35.06  | | | | | | |   (125)  op(e3, e3) = all_52_4
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | | REF_CLOSE: (3), (6), (8), (9), (37), (40), (42), (68), (75), (89),
% 204.24/35.06  | | | | | | |            (104), (118), (125) are inconsistent by sub-proof #817.
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | Case 2:
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | |   (126)  all_58_12 = e3
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | | REF_CLOSE: (43), (102), (126) are inconsistent by sub-proof #1367.
% 204.24/35.06  | | | | | | | 
% 204.24/35.06  | | | | | | End of split
% 204.24/35.06  | | | | | | 
% 204.24/35.06  | | | | | End of split
% 204.24/35.06  | | | | | 
% 204.24/35.06  | | | | End of split
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | End of split
% 204.24/35.06  | | | 
% 204.24/35.06  | | Case 2:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (127)   ~ (all_56_15 = e3)
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REDUCE: (29), (127) imply:
% 204.24/35.06  | | |   (128)   ~ (all_14_2 = e3)
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (14), (15), (17),
% 204.24/35.06  | | |            (18), (19), (20), (24), (25), (26), (27), (28), (30), (33),
% 204.24/35.06  | | |            (34), (35), (36), (37), (38), (40), (42), (43), (45), (48),
% 204.24/35.06  | | |            (49), (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 204.24/35.06  | | |            (61), (62), (63), (66), (67), (68), (69), (70), (72), (73),
% 204.24/35.06  | | |            (75), (76), (77), (80), (81), (82), (83), (84), (86), (87),
% 204.24/35.06  | | |            (88), (89), (91), (92), (93), (128) are inconsistent by
% 204.24/35.06  | | |            sub-proof #813.
% 204.24/35.06  | | | 
% 204.24/35.06  | | End of split
% 204.24/35.06  | | 
% 204.24/35.06  | End of split
% 204.24/35.06  | 
% 204.24/35.06  End of proof
% 204.24/35.06  
% 204.24/35.06  Sub-proof #788 shows that the following formulas are inconsistent:
% 204.24/35.06  ----------------------------------------------------------------
% 204.24/35.06    (1)  all_58_14 = all_52_23
% 204.24/35.06    (2)   ~ (e3 = e1)
% 204.24/35.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.24/35.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.24/35.06    (4)   ~ (e3 = e0)
% 204.24/35.06    (5)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.06    (6)   ~ (all_4_2 = e3)
% 204.24/35.06    (7)  all_58_0 = all_6_2
% 204.24/35.06    (8)   ~ (all_10_0 = e3)
% 204.24/35.06    (9)  all_40_2 = all_10_2
% 204.24/35.06    (10)  all_58_9 = all_52_25
% 204.24/35.06    (11)   ~ (all_52_29 = all_14_2)
% 204.24/35.06    (12)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.24/35.06    (13)  op(e2, e2) = all_4_2
% 204.24/35.06    (14)  all_58_7 = all_10_0
% 204.24/35.06    (15)  all_58_11 = all_52_29
% 204.24/35.06    (16)  all_58_1 = e3
% 204.24/35.06    (17)  op(e0, e0) = all_14_2
% 204.24/35.06    (18)  all_56_11 = all_52_29
% 204.24/35.06    (19)   ~ (all_10_0 = e2)
% 204.24/35.06    (20)   ~ (e2 = e1)
% 204.24/35.06    (21)   ~ (all_52_19 = all_52_23)
% 204.24/35.06    (22)  all_56_9 = all_10_0
% 204.24/35.06    (23)   ~ (all_52_29 = all_10_2)
% 204.24/35.06    (24)  op(all_52_19, all_52_19) = e2
% 204.24/35.06    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.06    (26)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.24/35.06    (27)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.24/35.06    (28)   ~ (e2 = e0)
% 204.24/35.06    (29)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.24/35.06    (30)   ~ (all_52_23 = e3)
% 204.24/35.06    (31)   ~ (all_52_5 = e3)
% 204.24/35.06    (32)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.24/35.06    (33)  op(e3, e3) = all_52_8
% 204.24/35.06    (34)  op(e3, e1) = all_52_17
% 204.24/35.06    (35)   ~ (all_52_19 = all_10_2)
% 204.24/35.06    (36)  all_58_8 = all_10_2
% 204.24/35.06    (37)  op(e3, e3) = all_6_2
% 204.24/35.06    (38)   ~ (all_52_17 = e3)
% 204.24/35.06    (39)  all_40_0 = all_10_0
% 204.24/35.06    (40)  all_58_5 = all_52_19
% 204.24/35.06    (41)  op(all_52_17, all_52_17) = e3
% 204.24/35.06    (42)  all_58_6 = all_52_5
% 204.24/35.06    (43)  op(all_10_2, e1) = e2
% 204.24/35.06    (44)   ~ (e1 = e0)
% 204.24/35.06    (45)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.24/35.06    (46)  op(e1, e1) = all_10_2
% 204.24/35.06    (47)  all_58_4 = all_52_17
% 204.24/35.06  
% 204.24/35.06  Begin of proof
% 204.24/35.06  | 
% 204.24/35.06  | BETA: splitting (45) gives:
% 204.24/35.06  | 
% 204.24/35.06  | Case 1:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (48)  all_58_4 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | REF_CLOSE: (38), (47), (48) are inconsistent by sub-proof #1302.
% 204.24/35.06  | | 
% 204.24/35.06  | Case 2:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (49)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | BETA: splitting (25) gives:
% 204.24/35.06  | | 
% 204.24/35.06  | | Case 1:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (50)  all_58_6 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REF_CLOSE: (31), (42), (50) are inconsistent by sub-proof #1328.
% 204.24/35.06  | | | 
% 204.24/35.06  | | Case 2:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (51)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | BETA: splitting (32) gives:
% 204.24/35.06  | | | 
% 204.24/35.06  | | | Case 1:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | |   (52)  all_56_11 = e3
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REF_CLOSE: (1), (2), (3), (4), (7), (10), (11), (12), (16), (17), (18),
% 204.24/35.06  | | | |            (20), (21), (23), (24), (27), (28), (29), (30), (33), (35),
% 204.24/35.06  | | | |            (36), (37), (40), (41), (44), (46), (47), (49), (52) are
% 204.24/35.06  | | | |            inconsistent by sub-proof #831.
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | Case 2:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | |   (53)   ~ (all_56_11 = e3)
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REDUCE: (18), (53) imply:
% 204.24/35.06  | | | |   (54)   ~ (all_52_29 = e3)
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REF_CLOSE: (3), (5), (6), (8), (9), (13), (14), (15), (19), (22), (26),
% 204.24/35.06  | | | |            (34), (36), (39), (41), (43), (51), (54) are inconsistent by
% 204.24/35.06  | | | |            sub-proof #789.
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | End of split
% 204.24/35.06  | | | 
% 204.24/35.06  | | End of split
% 204.24/35.06  | | 
% 204.24/35.06  | End of split
% 204.24/35.06  | 
% 204.24/35.06  End of proof
% 204.24/35.06  
% 204.24/35.06  Sub-proof #789 shows that the following formulas are inconsistent:
% 204.24/35.06  ----------------------------------------------------------------
% 204.24/35.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.24/35.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.24/35.06    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.06    (3)   ~ (all_4_2 = e3)
% 204.24/35.06    (4)   ~ (all_10_0 = e3)
% 204.24/35.06    (5)  all_40_2 = all_10_2
% 204.24/35.06    (6)  op(e2, e2) = all_4_2
% 204.24/35.06    (7)  all_58_7 = all_10_0
% 204.24/35.06    (8)  all_58_11 = all_52_29
% 204.24/35.06    (9)   ~ (all_10_0 = e2)
% 204.24/35.06    (10)  all_56_9 = all_10_0
% 204.24/35.06    (11)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.24/35.06    (12)   ~ (all_52_29 = e3)
% 204.24/35.06    (13)  op(e3, e1) = all_52_17
% 204.24/35.06    (14)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.24/35.06    (15)  all_58_8 = all_10_2
% 204.24/35.06    (16)  all_40_0 = all_10_0
% 204.24/35.06    (17)  op(all_52_17, all_52_17) = e3
% 204.24/35.06    (18)  op(all_10_2, e1) = e2
% 204.24/35.06  
% 204.24/35.06  Begin of proof
% 204.24/35.06  | 
% 204.24/35.06  | BETA: splitting (14) gives:
% 204.24/35.06  | 
% 204.24/35.06  | Case 1:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (19)  all_58_7 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | COMBINE_EQS: (7), (19) imply:
% 204.24/35.06  | |   (20)  all_10_0 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | REDUCE: (4), (20) imply:
% 204.24/35.06  | |   (21)  $false
% 204.24/35.06  | | 
% 204.24/35.06  | | CLOSE: (21) is inconsistent.
% 204.24/35.06  | | 
% 204.24/35.06  | Case 2:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (22)  all_58_8 = e3 | all_58_11 = e3
% 204.24/35.06  | | 
% 204.24/35.06  | | BETA: splitting (22) gives:
% 204.24/35.06  | | 
% 204.24/35.06  | | Case 1:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (23)  all_58_8 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | COMBINE_EQS: (15), (23) imply:
% 204.24/35.06  | | |   (24)  all_10_2 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | COMBINE_EQS: (5), (24) imply:
% 204.24/35.06  | | |   (25)  all_40_2 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REDUCE: (18), (24) imply:
% 204.24/35.06  | | |   (26)  op(e3, e1) = e2
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REF_CLOSE: (1), (2), (3), (6), (9), (10), (11), (13), (16), (17), (25),
% 204.24/35.06  | | |            (26) are inconsistent by sub-proof #790.
% 204.24/35.06  | | | 
% 204.24/35.06  | | Case 2:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (27)  all_58_11 = e3
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REF_CLOSE: (8), (12), (27) are inconsistent by sub-proof #1323.
% 204.24/35.06  | | | 
% 204.24/35.06  | | End of split
% 204.24/35.06  | | 
% 204.24/35.06  | End of split
% 204.24/35.06  | 
% 204.24/35.06  End of proof
% 204.24/35.06  
% 204.24/35.06  Sub-proof #790 shows that the following formulas are inconsistent:
% 204.24/35.06  ----------------------------------------------------------------
% 204.24/35.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.24/35.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.24/35.06    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.24/35.06    (3)   ~ (all_4_2 = e3)
% 204.24/35.06    (4)  op(e3, e1) = e2
% 204.24/35.06    (5)  op(e2, e2) = all_4_2
% 204.24/35.06    (6)   ~ (all_10_0 = e2)
% 204.24/35.06    (7)  all_56_9 = all_10_0
% 204.24/35.06    (8)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.24/35.06    (9)  op(e3, e1) = all_52_17
% 204.24/35.06    (10)  all_40_2 = e3
% 204.24/35.06    (11)  all_40_0 = all_10_0
% 204.24/35.06    (12)  op(all_52_17, all_52_17) = e3
% 204.24/35.06  
% 204.24/35.06  Begin of proof
% 204.24/35.06  | 
% 204.24/35.06  | BETA: splitting (8) gives:
% 204.24/35.06  | 
% 204.24/35.06  | Case 1:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (13)   ~ (all_40_2 = e3)
% 204.24/35.06  | | 
% 204.24/35.06  | | REDUCE: (10), (13) imply:
% 204.24/35.06  | |   (14)  $false
% 204.24/35.06  | | 
% 204.24/35.06  | | CLOSE: (14) is inconsistent.
% 204.24/35.06  | | 
% 204.24/35.06  | Case 2:
% 204.24/35.06  | | 
% 204.24/35.06  | |   (15)   ~ (all_40_0 = e0)
% 204.24/35.06  | | 
% 204.24/35.06  | | REDUCE: (11), (15) imply:
% 204.24/35.06  | |   (16)   ~ (all_10_0 = e0)
% 204.24/35.06  | | 
% 204.24/35.06  | | BETA: splitting (2) gives:
% 204.24/35.06  | | 
% 204.24/35.06  | | Case 1:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (17)  all_56_9 = e2
% 204.24/35.06  | | | 
% 204.24/35.06  | | | REF_CLOSE: (6), (7), (17) are inconsistent by sub-proof #991.
% 204.24/35.06  | | | 
% 204.24/35.06  | | Case 2:
% 204.24/35.06  | | | 
% 204.24/35.06  | | |   (18)  all_56_9 = e1 | all_56_9 = e0
% 204.24/35.06  | | | 
% 204.24/35.06  | | | BETA: splitting (18) gives:
% 204.24/35.06  | | | 
% 204.24/35.06  | | | Case 1:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | GROUND_INST: instantiating (1) with all_52_17, e2, e1, e3, simplifying
% 204.24/35.06  | | | |              with (4), (9) gives:
% 204.24/35.06  | | | |   (19)  all_52_17 = e2
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REDUCE: (12), (19) imply:
% 204.24/35.06  | | | |   (20)  op(e2, e2) = e3
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REF_CLOSE: (1), (3), (5), (20) are inconsistent by sub-proof #1318.
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | Case 2:
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | |   (21)  all_56_9 = e0
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | | REF_CLOSE: (7), (16), (21) are inconsistent by sub-proof #989.
% 204.24/35.06  | | | | 
% 204.24/35.06  | | | End of split
% 204.24/35.06  | | | 
% 204.24/35.06  | | End of split
% 204.24/35.06  | | 
% 204.24/35.06  | End of split
% 204.24/35.06  | 
% 204.24/35.06  End of proof
% 204.24/35.06  
% 204.24/35.06  Sub-proof #791 shows that the following formulas are inconsistent:
% 204.24/35.06  ----------------------------------------------------------------
% 204.24/35.06    (1)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.24/35.06    (2)  all_52_8 = all_6_2
% 204.24/35.06    (3)   ~ (all_6_2 = e3)
% 204.24/35.06  
% 204.24/35.06  Begin of proof
% 204.24/35.06  | 
% 204.24/35.06  | ALPHA: (1) implies:
% 204.24/35.06  |   (4)  all_52_8 = e3
% 204.24/35.06  | 
% 204.24/35.06  | COMBINE_EQS: (2), (4) imply:
% 204.24/35.06  |   (5)  all_6_2 = e3
% 204.24/35.06  | 
% 204.24/35.06  | SIMP: (5) implies:
% 204.24/35.06  |   (6)  all_6_2 = e3
% 204.24/35.06  | 
% 204.24/35.06  | REDUCE: (3), (6) imply:
% 204.24/35.06  |   (7)  $false
% 204.24/35.06  | 
% 204.24/35.06  | CLOSE: (7) is inconsistent.
% 204.24/35.06  | 
% 204.24/35.06  End of proof
% 204.24/35.06  
% 204.24/35.06  Sub-proof #792 shows that the following formulas are inconsistent:
% 204.24/35.06  ----------------------------------------------------------------
% 204.24/35.06    (1)   ~ (all_52_15 = all_52_23)
% 204.24/35.06    (2)   ~ (all_52_25 = all_6_0)
% 204.24/35.06    (3)   ~ (all_52_25 = all_52_27)
% 204.24/35.06    (4)  all_58_14 = all_52_23
% 204.24/35.06    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.06    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.06    (7)   ~ (all_52_5 = all_52_13)
% 204.26/35.06    (8)  all_58_1 = all_52_9
% 204.26/35.06    (9)   ~ (all_52_9 = all_52_13)
% 204.26/35.06    (10)   ~ (e3 = e0)
% 204.26/35.06    (11)  op(e2, e3) = all_52_3
% 204.26/35.06    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.06    (13)  op(e0, e2) = all_52_15
% 204.26/35.06    (14)   ~ (all_52_3 = all_52_19)
% 204.26/35.06    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.06    (16)   ~ (all_52_17 = all_52_25)
% 204.26/35.06    (17)   ~ (all_52_3 = all_6_2)
% 204.26/35.06    (18)  all_58_0 = all_6_2
% 204.26/35.06    (19)  op(all_14_2, e0) = all_14_1
% 204.26/35.06    (20)  all_56_4 = all_52_3
% 204.26/35.06    (21)   ~ (all_52_17 = all_10_2)
% 204.26/35.06    (22)  op(e3, e0) = all_52_25
% 204.26/35.06    (23)  op(e0, all_14_1) = all_14_0
% 204.26/35.06    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.06    (25)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.06    (26)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.06    (27)   ~ (all_52_27 = all_52_29)
% 204.26/35.06    (28)  all_58_13 = all_52_15
% 204.26/35.06    (29)   ~ (all_40_1 = e2)
% 204.26/35.06    (30)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.06    (31)  all_58_9 = all_52_25
% 204.26/35.06    (32)   ~ (all_52_29 = all_14_2)
% 204.26/35.06    (33)  all_22_0 = all_6_0
% 204.26/35.06    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.06    (35)   ~ (all_52_17 = all_6_0)
% 204.26/35.06    (36)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.06    (37)  op(e1, e3) = all_52_5
% 204.26/35.06    (38)  all_40_1 = all_10_1
% 204.26/35.06    (39)  op(e2, e2) = all_4_2
% 204.26/35.06    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.06    (41)   ~ (all_52_3 = all_52_5)
% 204.26/35.06    (42)  all_58_11 = all_52_29
% 204.26/35.06    (43)  all_56_5 = all_4_2
% 204.26/35.06    (44)   ~ (all_52_25 = all_14_2)
% 204.26/35.06    (45)   ~ (all_52_3 = all_52_27)
% 204.26/35.06    (46)  op(all_10_2, e1) = all_10_1
% 204.26/35.06    (47)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.06    (48)   ~ (all_52_7 = all_6_2)
% 204.26/35.06    (49)  op(e0, e0) = all_14_2
% 204.26/35.06    (50)  all_56_15 = all_14_2
% 204.26/35.06    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.06    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.06    (53)  all_56_11 = all_52_29
% 204.26/35.06    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.06    (55)   ~ (e2 = e1)
% 204.26/35.06    (56)   ~ (all_52_13 = all_10_2)
% 204.26/35.06    (57)   ~ (all_6_0 = e1)
% 204.26/35.06    (58)  all_58_10 = all_52_27
% 204.26/35.06    (59)  all_56_8 = all_52_5
% 204.26/35.06    (60)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.06    (61)   ~ (all_52_19 = all_52_23)
% 204.26/35.06    (62)   ~ (all_52_25 = all_52_29)
% 204.26/35.06    (63)  op(all_6_2, e3) = e2
% 204.26/35.06    (64)   ~ (all_52_29 = all_10_2)
% 204.26/35.06    (65)  all_58_7 = all_52_13
% 204.26/35.06    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.06    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.06    (68)  all_58_1 = all_6_0
% 204.26/35.06    (69)   ~ (all_52_5 = all_52_7)
% 204.26/35.06    (70)  all_58_12 = all_52_7
% 204.26/35.06    (71)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.06    (72)   ~ (all_52_7 = all_14_2)
% 204.26/35.06    (73)  all_58_2 = all_52_3
% 204.26/35.06    (74)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.06    (75)  all_56_2 = all_52_17
% 204.26/35.06    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.06    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.06    (78)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.06    (79)   ~ (all_14_0 = e3)
% 204.26/35.06    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.06    (81)  all_56_7 = all_52_27
% 204.26/35.06    (82)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.26/35.06    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.06    (84)   ~ (e2 = e0)
% 204.26/35.06    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.06    (86)  op(all_6_0, all_6_0) = all_52_8
% 204.26/35.06    (87)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.06    (88)   ~ (all_52_5 = all_52_29)
% 204.26/35.06    (89)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.06    (90)  all_56_6 = all_52_19
% 204.26/35.06    (91)   ~ (all_52_15 = all_14_2)
% 204.26/35.06    (92)   ~ (all_52_13 = all_6_0)
% 204.26/35.06    (93)   ~ (all_52_19 = all_52_27)
% 204.26/35.06    (94)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.06    (95)   ~ (all_6_0 = e2)
% 204.26/35.06    (96)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.26/35.06            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.26/35.06    (97)  op(e3, e1) = all_52_17
% 204.26/35.06    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.06    (99)  op(e0, e3) = all_52_7
% 204.26/35.06    (100)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.06    (101)   ~ (all_52_9 = all_52_25)
% 204.26/35.06    (102)  all_58_15 = all_14_2
% 204.26/35.06    (103)   ~ (all_52_19 = all_10_2)
% 204.26/35.06    (104)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.06    (105)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.06    (106)  all_58_8 = all_10_2
% 204.26/35.06    (107)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.06    (108)   ~ (all_52_5 = all_10_2)
% 204.26/35.06    (109)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.06    (110)   ~ (all_52_23 = all_14_2)
% 204.26/35.06    (111)  all_56_12 = all_52_7
% 204.26/35.06    (112)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.06    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.06    (114)   ~ (all_52_25 = all_6_2)
% 204.26/35.06    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.06    (116)   ~ (all_52_9 = all_4_2)
% 204.26/35.06    (117)   ~ (all_52_5 = all_6_2)
% 204.26/35.06    (118)   ~ (all_52_9 = all_6_2)
% 204.26/35.06    (119)  all_56_0 = all_6_2
% 204.26/35.06    (120)  op(e3, e3) = all_6_2
% 204.26/35.06    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.06    (122)   ~ (all_52_15 = all_6_0)
% 204.26/35.06    (123)   ~ (all_52_27 = all_14_2)
% 204.26/35.06    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.06    (125)  all_56_14 = all_52_23
% 204.26/35.06    (126)  all_56_3 = all_52_25
% 204.26/35.06    (127)   ~ (all_52_3 = all_52_7)
% 204.26/35.06    (128)   ~ (all_6_0 = all_6_2)
% 204.26/35.06    (129)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.06    (130)  all_58_5 = all_52_19
% 204.26/35.06    (131)   ~ (all_52_15 = all_4_2)
% 204.26/35.06    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.06           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.06           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.06           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.06    (133)   ~ (all_52_27 = all_4_2)
% 204.26/35.06    (134)  all_58_6 = all_52_5
% 204.26/35.06    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.06    (136)   ~ (all_52_17 = all_6_2)
% 204.26/35.06    (137)   ~ (e1 = e0)
% 204.26/35.06    (138)   ~ (e3 = e2)
% 204.26/35.06    (139)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.06    (140)  all_56_10 = all_10_2
% 204.26/35.06    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.06    (142)  all_56_1 = all_6_0
% 204.26/35.06    (143)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.06    (144)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.06    (145)   ~ (all_6_0 = all_4_2)
% 204.26/35.06    (146)  op(e1, e1) = all_10_2
% 204.26/35.06    (147)   ~ (all_52_23 = all_10_2)
% 204.26/35.06    (148)   ~ (all_52_7 = all_52_23)
% 204.26/35.06    (149)   ~ (all_52_17 = all_52_19)
% 204.26/35.06    (150)  all_58_3 = all_4_2
% 204.26/35.06    (151)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.06    (152)   ~ (all_52_3 = all_4_2)
% 204.26/35.06    (153)   ~ (all_52_19 = all_4_2)
% 204.26/35.06    (154)   ~ (all_52_17 = all_52_23)
% 204.26/35.06    (155)  op(all_6_2, e3) = all_6_1
% 204.26/35.06    (156)  all_22_2 = all_6_2
% 204.26/35.06    (157)  all_58_4 = all_52_17
% 204.26/35.06    (158)   ~ (all_14_0 = e1)
% 204.26/35.06    (159)   ~ (all_14_0 = e2)
% 204.26/35.06    (160)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.06    (161)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.06  
% 204.26/35.06  Begin of proof
% 204.26/35.06  | 
% 204.26/35.06  | REDUCE: (29), (38) imply:
% 204.26/35.06  |   (162)   ~ (all_10_1 = e2)
% 204.26/35.06  | 
% 204.26/35.06  | BETA: splitting (96) gives:
% 204.26/35.06  | 
% 204.26/35.06  | Case 1:
% 204.26/35.06  | | 
% 204.26/35.06  | |   (163)  all_58_15 = e0
% 204.26/35.06  | | 
% 204.26/35.06  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (15), (16), (17), (18),
% 204.26/35.06  | |            (19), (21), (23), (24), (25), (26), (28), (30), (31), (32), (33),
% 204.26/35.06  | |            (34), (35), (36), (39), (42), (44), (46), (47), (49), (51), (52),
% 204.26/35.06  | |            (53), (54), (55), (57), (58), (60), (61), (62), (63), (64), (65),
% 204.26/35.06  | |            (68), (70), (71), (72), (73), (75), (76), (77), (78), (79), (81),
% 204.26/35.06  | |            (82), (86), (87), (88), (92), (93), (94), (95), (97), (99),
% 204.26/35.06  | |            (100), (102), (103), (104), (106), (108), (109), (110), (112),
% 204.26/35.06  | |            (114), (115), (118), (119), (120), (121), (122), (126), (127),
% 204.26/35.06  | |            (128), (129), (130), (132), (134), (135), (136), (138), (139),
% 204.26/35.06  | |            (141), (142), (143), (145), (146), (147), (148), (149), (150),
% 204.26/35.06  | |            (152), (153), (154), (156), (157), (158), (159), (161), (163) are
% 204.26/35.06  | |            inconsistent by sub-proof #818.
% 204.26/35.06  | | 
% 204.26/35.06  | Case 2:
% 204.26/35.06  | | 
% 204.26/35.06  | |   (164)   ~ (all_58_15 = e0)
% 204.26/35.06  | |   (165)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 204.26/35.06  | |            | all_58_13 = e0 | all_58_14 = e0)
% 204.26/35.06  | | 
% 204.26/35.06  | | ALPHA: (165) implies:
% 204.26/35.06  | |   (166)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.06  | |   (167)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.06  | | 
% 204.26/35.06  | | REDUCE: (102), (164) imply:
% 204.26/35.06  | |   (168)   ~ (all_14_2 = e0)
% 204.26/35.06  | | 
% 204.26/35.06  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.26/35.06  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.26/35.06  | |            (24), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 204.26/35.06  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.26/35.06  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 204.26/35.06  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.26/35.06  | |            (71), (72), (73), (74), (75), (76), (77), (78), (80), (82), (83),
% 204.26/35.06  | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 204.26/35.06  | |            (95), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 204.26/35.06  | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 204.26/35.06  | |            (115), (116), (117), (119), (120), (121), (122), (123), (124),
% 204.26/35.06  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 204.26/35.06  | |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 204.26/35.06  | |            (143), (144), (145), (146), (147), (148), (149), (150), (151),
% 204.26/35.06  | |            (152), (153), (154), (155), (156), (157), (159), (160), (161),
% 204.26/35.06  | |            (162), (166), (167), (168) are inconsistent by sub-proof #793.
% 204.26/35.06  | | 
% 204.26/35.06  | End of split
% 204.26/35.06  | 
% 204.26/35.06  End of proof
% 204.26/35.06  
% 204.26/35.06  Sub-proof #793 shows that the following formulas are inconsistent:
% 204.26/35.06  ----------------------------------------------------------------
% 204.26/35.06    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.06    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.06    (3)   ~ (all_52_25 = all_6_0)
% 204.26/35.06    (4)   ~ (all_52_25 = all_52_27)
% 204.26/35.06    (5)  all_58_14 = all_52_23
% 204.26/35.06    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.06    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.06    (8)   ~ (all_52_5 = all_52_13)
% 204.26/35.06    (9)  all_58_1 = all_52_9
% 204.26/35.06    (10)   ~ (all_52_9 = all_52_13)
% 204.26/35.06    (11)   ~ (e3 = e0)
% 204.26/35.07    (12)  op(e2, e3) = all_52_3
% 204.26/35.07    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.07    (14)  op(e0, e2) = all_52_15
% 204.26/35.07    (15)   ~ (all_52_3 = all_52_19)
% 204.26/35.07    (16)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.07    (17)   ~ (all_52_17 = all_52_25)
% 204.26/35.07    (18)   ~ (all_52_3 = all_6_2)
% 204.26/35.07    (19)  all_58_0 = all_6_2
% 204.26/35.07    (20)  op(all_14_2, e0) = all_14_1
% 204.26/35.07    (21)  all_56_4 = all_52_3
% 204.26/35.07    (22)   ~ (all_52_17 = all_10_2)
% 204.26/35.07    (23)  op(e3, e0) = all_52_25
% 204.26/35.07    (24)  op(e0, all_14_1) = all_14_0
% 204.26/35.07    (25)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.07    (26)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.07    (27)   ~ (all_52_27 = all_52_29)
% 204.26/35.07    (28)  all_58_13 = all_52_15
% 204.26/35.07    (29)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.07    (30)  all_58_9 = all_52_25
% 204.26/35.07    (31)   ~ (all_52_29 = all_14_2)
% 204.26/35.07    (32)  all_22_0 = all_6_0
% 204.26/35.07    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.07    (34)   ~ (all_52_17 = all_6_0)
% 204.26/35.07    (35)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.07    (36)  op(e1, e3) = all_52_5
% 204.26/35.07    (37)  op(e2, e2) = all_4_2
% 204.26/35.07    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.07    (39)   ~ (all_52_3 = all_52_5)
% 204.26/35.07    (40)  all_58_11 = all_52_29
% 204.26/35.07    (41)  all_56_5 = all_4_2
% 204.26/35.07    (42)   ~ (all_52_25 = all_14_2)
% 204.26/35.07    (43)   ~ (all_52_3 = all_52_27)
% 204.26/35.07    (44)  op(all_10_2, e1) = all_10_1
% 204.26/35.07    (45)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.07    (46)   ~ (all_52_7 = all_6_2)
% 204.26/35.07    (47)  op(e0, e0) = all_14_2
% 204.26/35.07    (48)  all_56_15 = all_14_2
% 204.26/35.07    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.07    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.07    (51)  all_56_11 = all_52_29
% 204.26/35.07    (52)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.07    (53)   ~ (e2 = e1)
% 204.26/35.07    (54)   ~ (all_52_13 = all_10_2)
% 204.26/35.07    (55)   ~ (all_6_0 = e1)
% 204.26/35.07    (56)  all_58_10 = all_52_27
% 204.26/35.07    (57)  all_56_8 = all_52_5
% 204.26/35.07    (58)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.07    (59)   ~ (all_52_19 = all_52_23)
% 204.26/35.07    (60)   ~ (all_52_25 = all_52_29)
% 204.26/35.07    (61)  op(all_6_2, e3) = e2
% 204.26/35.07    (62)   ~ (all_52_29 = all_10_2)
% 204.26/35.07    (63)  all_58_7 = all_52_13
% 204.26/35.07    (64)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.07    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.07    (66)  all_58_1 = all_6_0
% 204.26/35.07    (67)   ~ (all_52_5 = all_52_7)
% 204.26/35.07    (68)  all_58_12 = all_52_7
% 204.26/35.07    (69)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.07    (70)   ~ (all_52_7 = all_14_2)
% 204.26/35.07    (71)   ~ (all_14_2 = e0)
% 204.26/35.07    (72)  all_58_2 = all_52_3
% 204.26/35.07    (73)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.07    (74)  all_56_2 = all_52_17
% 204.26/35.07    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.07    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.07    (77)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.07    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.07    (79)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.26/35.07    (80)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.07    (81)   ~ (e2 = e0)
% 204.26/35.07    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.07    (83)  op(all_6_0, all_6_0) = all_52_8
% 204.26/35.07    (84)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.07    (85)   ~ (all_52_5 = all_52_29)
% 204.26/35.07    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.07    (87)  all_56_6 = all_52_19
% 204.26/35.07    (88)   ~ (all_52_15 = all_14_2)
% 204.26/35.07    (89)   ~ (all_52_13 = all_6_0)
% 204.26/35.07    (90)   ~ (all_52_19 = all_52_27)
% 204.26/35.07    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.07    (92)   ~ (all_6_0 = e2)
% 204.26/35.07    (93)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.07    (94)  op(e3, e1) = all_52_17
% 204.26/35.07    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.07    (96)  op(e0, e3) = all_52_7
% 204.26/35.07    (97)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.07    (98)   ~ (all_52_9 = all_52_25)
% 204.26/35.07    (99)  all_58_15 = all_14_2
% 204.26/35.07    (100)   ~ (all_52_19 = all_10_2)
% 204.26/35.07    (101)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.07    (102)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.07    (103)   ~ (all_10_1 = e2)
% 204.26/35.07    (104)  all_58_8 = all_10_2
% 204.26/35.07    (105)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.07    (106)   ~ (all_52_5 = all_10_2)
% 204.26/35.07    (107)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.07    (108)   ~ (all_52_23 = all_14_2)
% 204.26/35.07    (109)  all_56_12 = all_52_7
% 204.26/35.07    (110)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.07    (111)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.07    (112)   ~ (all_52_25 = all_6_2)
% 204.26/35.07    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.07    (114)   ~ (all_52_9 = all_4_2)
% 204.26/35.07    (115)   ~ (all_52_5 = all_6_2)
% 204.26/35.07    (116)  all_56_0 = all_6_2
% 204.26/35.07    (117)  op(e3, e3) = all_6_2
% 204.26/35.07    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.07    (119)   ~ (all_52_15 = all_6_0)
% 204.26/35.07    (120)   ~ (all_52_27 = all_14_2)
% 204.26/35.07    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.07    (122)  all_56_14 = all_52_23
% 204.26/35.07    (123)  all_56_3 = all_52_25
% 204.26/35.07    (124)   ~ (all_52_3 = all_52_7)
% 204.26/35.07    (125)   ~ (all_6_0 = all_6_2)
% 204.26/35.07    (126)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.07    (127)  all_58_5 = all_52_19
% 204.26/35.07    (128)   ~ (all_52_15 = all_4_2)
% 204.26/35.07    (129)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.07           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.07           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.07           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.07    (130)   ~ (all_52_27 = all_4_2)
% 204.26/35.07    (131)  all_58_6 = all_52_5
% 204.26/35.07    (132)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.07    (133)   ~ (all_52_17 = all_6_2)
% 204.26/35.07    (134)   ~ (e1 = e0)
% 204.26/35.07    (135)   ~ (e3 = e2)
% 204.26/35.07    (136)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.07    (137)  all_56_10 = all_10_2
% 204.26/35.07    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.07    (139)  all_56_1 = all_6_0
% 204.26/35.07    (140)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.07    (141)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.07    (142)   ~ (all_6_0 = all_4_2)
% 204.26/35.07    (143)  op(e1, e1) = all_10_2
% 204.26/35.07    (144)   ~ (all_52_23 = all_10_2)
% 204.26/35.07    (145)   ~ (all_52_7 = all_52_23)
% 204.26/35.07    (146)   ~ (all_52_17 = all_52_19)
% 204.26/35.07    (147)  all_58_3 = all_4_2
% 204.26/35.07    (148)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.07    (149)   ~ (all_52_3 = all_4_2)
% 204.26/35.07    (150)   ~ (all_52_19 = all_4_2)
% 204.26/35.07    (151)   ~ (all_52_17 = all_52_23)
% 204.26/35.07    (152)  op(all_6_2, e3) = all_6_1
% 204.26/35.07    (153)  all_22_2 = all_6_2
% 204.26/35.07    (154)  all_58_4 = all_52_17
% 204.26/35.07    (155)   ~ (all_14_0 = e2)
% 204.26/35.07    (156)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.07    (157)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.07  
% 204.26/35.07  Begin of proof
% 204.26/35.07  | 
% 204.26/35.07  | BETA: splitting (136) gives:
% 204.26/35.07  | 
% 204.26/35.07  | Case 1:
% 204.26/35.07  | | 
% 204.26/35.07  | |   (158)  all_56_1 = e3
% 204.26/35.07  | | 
% 204.26/35.07  | | COMBINE_EQS: (139), (158) imply:
% 204.26/35.07  | |   (159)  all_6_0 = e3
% 204.26/35.07  | | 
% 204.26/35.07  | | SIMP: (159) implies:
% 204.26/35.07  | |   (160)  all_6_0 = e3
% 204.26/35.07  | | 
% 204.26/35.07  | | COMBINE_EQS: (66), (160) imply:
% 204.26/35.07  | |   (161)  all_58_1 = e3
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (89), (160) imply:
% 204.26/35.07  | |   (162)   ~ (all_52_13 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (119), (160) imply:
% 204.26/35.07  | |   (163)   ~ (all_52_15 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (34), (160) imply:
% 204.26/35.07  | |   (164)   ~ (all_52_17 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (3), (160) imply:
% 204.26/35.07  | |   (165)   ~ (all_52_25 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (125), (160) imply:
% 204.26/35.07  | |   (166)   ~ (all_6_2 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | SIMP: (166) implies:
% 204.26/35.07  | |   (167)   ~ (all_6_2 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (142), (160) imply:
% 204.26/35.07  | |   (168)   ~ (all_4_2 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | SIMP: (168) implies:
% 204.26/35.07  | |   (169)   ~ (all_4_2 = e3)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (55), (160) imply:
% 204.26/35.07  | |   (170)   ~ (e3 = e1)
% 204.26/35.07  | | 
% 204.26/35.07  | | REDUCE: (83), (160) imply:
% 204.26/35.07  | |   (171)  op(e3, e3) = all_52_8
% 204.26/35.07  | | 
% 204.26/35.07  | | GROUND_INST: instantiating (7) with all_6_2, all_52_8, e3, e3, simplifying
% 204.26/35.07  | |              with (117), (171) gives:
% 204.26/35.07  | |   (172)  all_52_8 = all_6_2
% 204.26/35.07  | | 
% 204.26/35.07  | | BETA: splitting (129) gives:
% 204.26/35.07  | | 
% 204.26/35.07  | | Case 1:
% 204.26/35.07  | | | 
% 204.26/35.07  | | |   (173)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.07  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.26/35.07  | | |            e0)
% 204.26/35.07  | | | 
% 204.26/35.07  | | | BETA: splitting (173) gives:
% 204.26/35.07  | | | 
% 204.26/35.07  | | | Case 1:
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | |   (174)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REF_CLOSE: (6), (7), (16), (19), (25), (37), (45), (47), (49), (68),
% 204.26/35.07  | | | |            (70), (72), (76), (106), (117), (131), (132), (143), (149),
% 204.26/35.07  | | | |            (167), (174) are inconsistent by sub-proof #835.
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | Case 2:
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | |   (175)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.26/35.07  | | | |          e0
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REF_CLOSE: (167), (172), (175) are inconsistent by sub-proof #834.
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | End of split
% 204.26/35.07  | | | 
% 204.26/35.07  | | Case 2:
% 204.26/35.07  | | | 
% 204.26/35.07  | | |   (176)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.26/35.07  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.26/35.07  | | |            all_52_30 = e0)
% 204.26/35.07  | | | 
% 204.26/35.07  | | | BETA: splitting (176) gives:
% 204.26/35.07  | | | 
% 204.26/35.07  | | | Case 1:
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | |   (177)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.26/35.07  | | | |          e0
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | ALPHA: (177) implies:
% 204.26/35.07  | | | |   (178)  all_52_22 = e0
% 204.26/35.07  | | | |   (179)  all_52_20 = e1
% 204.26/35.07  | | | |   (180)  all_52_18 = e2
% 204.26/35.07  | | | |   (181)  all_52_16 = e3
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (110), (181) imply:
% 204.26/35.07  | | | |   (182)  op(all_52_17, all_52_17) = e3
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (26), (180) imply:
% 204.26/35.07  | | | |   (183)  op(all_52_19, all_52_19) = e2
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (101), (178) imply:
% 204.26/35.07  | | | |   (184)  op(all_52_23, all_52_23) = e0
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (29), (179) imply:
% 204.26/35.07  | | | |   (185)  op(all_10_2, all_10_2) = e1
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | BETA: splitting (105) gives:
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | Case 1:
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | |   (186)  all_56_15 = e3
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | COMBINE_EQS: (48), (186) imply:
% 204.26/35.07  | | | | |   (187)  all_14_2 = e3
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | SIMP: (187) implies:
% 204.26/35.07  | | | | |   (188)  all_14_2 = e3
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | REDUCE: (120), (188) imply:
% 204.26/35.07  | | | | |   (189)   ~ (all_52_27 = e3)
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | REDUCE: (31), (188) imply:
% 204.26/35.07  | | | | |   (190)   ~ (all_52_29 = e3)
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | REDUCE: (126), (188) imply:
% 204.26/35.07  | | | | |   (191)  op(e3, e3) = all_52_30
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | REDUCE: (20), (188) imply:
% 204.26/35.07  | | | | |   (192)  op(e3, e0) = all_14_1
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3,
% 204.26/35.07  | | | | |              simplifying with (23), (192) gives:
% 204.26/35.07  | | | | |   (193)  all_52_25 = all_14_1
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_30, e3, e3,
% 204.26/35.07  | | | | |              simplifying with (117), (191) gives:
% 204.26/35.07  | | | | |   (194)  all_52_30 = all_6_2
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | COMBINE_EQS: (30), (193) imply:
% 204.26/35.07  | | | | |   (195)  all_58_9 = all_14_1
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | BETA: splitting (69) gives:
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | Case 1:
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | |   (196)  all_58_6 = e3
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | | COMBINE_EQS: (131), (196) imply:
% 204.26/35.07  | | | | | |   (197)  all_52_5 = e3
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | | REDUCE: (39), (197) imply:
% 204.26/35.07  | | | | | |   (198)   ~ (all_52_3 = e3)
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | | REDUCE: (25), (197) imply:
% 204.26/35.07  | | | | | |   (199)  op(e3, e3) = all_52_4
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | | REF_CLOSE: (7), (12), (18), (49), (56), (61), (72), (117), (127),
% 204.26/35.07  | | | | | |            (147), (169), (183), (189), (198), (199) are inconsistent
% 204.26/35.07  | | | | | |            by sub-proof #816.
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | Case 2:
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | |   (200)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | | BETA: splitting (200) gives:
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | | Case 1:
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | |   (201)  all_58_7 = e3
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | | COMBINE_EQS: (63), (201) imply:
% 204.26/35.07  | | | | | | |   (202)  all_52_13 = e3
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | | REDUCE: (162), (202) imply:
% 204.26/35.07  | | | | | | |   (203)  $false
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | | CLOSE: (203) is inconsistent.
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | Case 2:
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | |   (204)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | | BETA: splitting (204) gives:
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | |   (205)  all_58_8 = e3
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | COMBINE_EQS: (104), (205) imply:
% 204.26/35.07  | | | | | | | |   (206)  all_10_2 = e3
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | REDUCE: (185), (206) imply:
% 204.26/35.07  | | | | | | | |   (207)  op(e3, e3) = e1
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | REDUCE: (44), (206) imply:
% 204.26/35.07  | | | | | | | |   (208)  op(e3, e1) = all_10_1
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | REDUCE: (143), (206) imply:
% 204.26/35.07  | | | | | | | |   (209)  op(e1, e1) = e3
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | BETA: splitting (49) gives:
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | |   (210)  all_58_2 = e3
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | COMBINE_EQS: (72), (210) imply:
% 204.26/35.07  | | | | | | | | |   (211)  all_52_3 = e3
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | SIMP: (211) implies:
% 204.26/35.07  | | | | | | | | |   (212)  all_52_3 = e3
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (39), (212) imply:
% 204.26/35.07  | | | | | | | | |   (213)   ~ (all_52_5 = e3)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | SIMP: (213) implies:
% 204.26/35.07  | | | | | | | | |   (214)   ~ (all_52_5 = e3)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (15), (212) imply:
% 204.26/35.07  | | | | | | | | |   (215)   ~ (all_52_19 = e3)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | SIMP: (215) implies:
% 204.26/35.07  | | | | | | | | |   (216)   ~ (all_52_19 = e3)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (6), (212) imply:
% 204.26/35.07  | | | | | | | | |   (217)  op(e3, e3) = all_52_2
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | GROUND_INST: instantiating (7) with all_52_17, all_10_1, e1,
% 204.26/35.07  | | | | | | | | |              e3, simplifying with (94), (208) gives:
% 204.26/35.07  | | | | | | | | |   (218)  all_52_17 = all_10_1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_2, e3, e3,
% 204.26/35.07  | | | | | | | | |              simplifying with (117), (217) gives:
% 204.26/35.07  | | | | | | | | |   (219)  all_52_2 = all_6_2
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_52_2, e3, e3,
% 204.26/35.07  | | | | | | | | |              simplifying with (207), (217) gives:
% 204.26/35.07  | | | | | | | | |   (220)  all_52_2 = e1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | COMBINE_EQS: (219), (220) imply:
% 204.26/35.07  | | | | | | | | |   (221)  all_6_2 = e1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | SIMP: (221) implies:
% 204.26/35.07  | | | | | | | | |   (222)  all_6_2 = e1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | COMBINE_EQS: (74), (218) imply:
% 204.26/35.07  | | | | | | | | |   (223)  all_56_2 = all_10_1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | COMBINE_EQS: (154), (218) imply:
% 204.26/35.07  | | | | | | | | |   (224)  all_58_4 = all_10_1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | COMBINE_EQS: (19), (222) imply:
% 204.26/35.07  | | | | | | | | |   (225)  all_58_0 = e1
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (146), (218) imply:
% 204.26/35.07  | | | | | | | | |   (226)   ~ (all_52_19 = all_10_1)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | SIMP: (226) implies:
% 204.26/35.07  | | | | | | | | |   (227)   ~ (all_52_19 = all_10_1)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (133), (218), (222) imply:
% 204.26/35.07  | | | | | | | | |   (228)   ~ (all_10_1 = e1)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (164), (218) imply:
% 204.26/35.07  | | | | | | | | |   (229)   ~ (all_10_1 = e3)
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (45), (222) imply:
% 204.26/35.07  | | | | | | | | |   (230)  op(e1, e1) = all_52_0
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REDUCE: (61), (222) imply:
% 204.26/35.07  | | | | | | | | |   (231)  op(e1, e3) = e2
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | BETA: splitting (52) gives:
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | |   (232)  all_56_2 = e3
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | REF_CLOSE: (223), (229), (232) are inconsistent by sub-proof
% 204.26/35.07  | | | | | | | | | |            #1029.
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | |   (233)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | BETA: splitting (233) gives:
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | |   (234)  all_56_2 = e2
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | REF_CLOSE: (103), (223), (234) are inconsistent by sub-proof
% 204.26/35.07  | | | | | | | | | | |            #815.
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | |   (235)   ~ (all_56_2 = e2)
% 204.26/35.07  | | | | | | | | | | |   (236)  all_56_2 = e1 | all_56_2 = e0
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | BETA: splitting (75) gives:
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | |   (237)  all_58_0 = e2
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | REF_CLOSE: (53), (225), (237) are inconsistent by sub-proof
% 204.26/35.07  | | | | | | | | | | | |            #1273.
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | |   (238)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | BETA: splitting (238) gives:
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | |   (239)  all_58_1 = e2
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | REF_CLOSE: (28), (63), (97), (135), (147), (162), (163),
% 204.26/35.07  | | | | | | | | | | | | |            (169), (239) are inconsistent by sub-proof #1088.
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | |   (240)  all_58_4 = e2 | all_58_9 = e2
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | BETA: splitting (236) gives:
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | |   (241)  all_56_2 = e1
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | REF_CLOSE: (223), (228), (241) are inconsistent by sub-proof
% 204.26/35.07  | | | | | | | | | | | | | |            #1025.
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | |   (242)  all_56_2 = e0
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | COMBINE_EQS: (223), (242) imply:
% 204.26/35.07  | | | | | | | | | | | | | |   (243)  all_10_1 = e0
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | SIMP: (243) implies:
% 204.26/35.07  | | | | | | | | | | | | | |   (244)  all_10_1 = e0
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | COMBINE_EQS: (224), (244) imply:
% 204.26/35.07  | | | | | | | | | | | | | |   (245)  all_58_4 = e0
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | REDUCE: (227), (244) imply:
% 204.26/35.07  | | | | | | | | | | | | | |   (246)   ~ (all_52_19 = e0)
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | REDUCE: (103), (244) imply:
% 204.26/35.07  | | | | | | | | | | | | | |   (247)   ~ (e2 = e0)
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | |   (248)  all_58_4 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | COMBINE_EQS: (245), (248) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (249)  e2 = e0
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | REDUCE: (81), (249) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (250)  $false
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | |   (251)  all_58_9 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | COMBINE_EQS: (195), (251) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (252)  all_14_1 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | SIMP: (252) implies:
% 204.26/35.07  | | | | | | | | | | | | | | |   (253)  all_14_1 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | REDUCE: (24), (253) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (254)  op(e0, e2) = all_14_0
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_15, all_14_0, e2,
% 204.26/35.07  | | | | | | | | | | | | | | |              e0, simplifying with (14), (254) gives:
% 204.26/35.07  | | | | | | | | | | | | | | |   (255)  all_52_15 = all_14_0
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, all_52_0, e1, e1,
% 204.26/35.07  | | | | | | | | | | | | | | |              simplifying with (209), (230) gives:
% 204.26/35.07  | | | | | | | | | | | | | | |   (256)  all_52_0 = e3
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_5, e2, e3, e1,
% 204.26/35.07  | | | | | | | | | | | | | | |              simplifying with (36), (231) gives:
% 204.26/35.07  | | | | | | | | | | | | | | |   (257)  all_52_5 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | COMBINE_EQS: (28), (255) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (258)  all_58_13 = all_14_0
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | REDUCE: (8), (257) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (259)   ~ (all_52_13 = e2)
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | SIMP: (259) implies:
% 204.26/35.07  | | | | | | | | | | | | | | |   (260)   ~ (all_52_13 = e2)
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | REDUCE: (214), (257) imply:
% 204.26/35.07  | | | | | | | | | | | | | | |   (261)   ~ (e3 = e2)
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | |   (262)  all_58_1 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | REF_CLOSE: (28), (63), (97), (135), (147), (162), (163),
% 204.26/35.07  | | | | | | | | | | | | | | | |            (169), (262) are inconsistent by sub-proof #1088.
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | |   (263)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | |   (264)  all_58_3 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (264) imply:
% 204.26/35.07  | | | | | | | | | | | | | | | | |   (265)  all_4_2 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | REDUCE: (150), (265) imply:
% 204.26/35.07  | | | | | | | | | | | | | | | | |   (266)   ~ (all_52_19 = e2)
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (40), (73), (87), (135), (183), (190), (204),
% 204.26/35.07  | | | | | | | | | | | | | | | | |            (205), (209), (216), (246), (266) are inconsistent
% 204.26/35.07  | | | | | | | | | | | | | | | | |            by sub-proof #1054.
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | |   (267)  all_58_7 = e2 | all_58_13 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (268)  all_58_7 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (268) imply:
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (269)  all_52_13 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | REDUCE: (260), (269) imply:
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (270)  $false
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (271)  all_58_13 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (271) imply:
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (272)  all_14_0 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (273)  all_14_0 = e2
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | REDUCE: (155), (273) imply:
% 204.26/35.07  | | | | | | | | | | | | | | | | | |   (274)  $false
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent.
% 204.26/35.07  | | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | |   (275)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | | REF_CLOSE: (5), (7), (11), (12), (18), (19), (25), (30), (31),
% 204.26/35.07  | | | | | | | | |            (33), (40), (47), (51), (53), (56), (59), (61),
% 204.26/35.07  | | | | | | | | |            (62), (63), (69), (77), (81), (84), (91), (100),
% 204.26/35.07  | | | | | | | | |            (104), (117), (127), (131), (134), (138), (143),
% 204.26/35.07  | | | | | | | | |            (146), (147), (154), (161), (162), (169), (170),
% 204.26/35.07  | | | | | | | | |            (171), (182), (183), (185), (189), (275) are
% 204.26/35.07  | | | | | | | | |            inconsistent by sub-proof #828.
% 204.26/35.07  | | | | | | | | | 
% 204.26/35.07  | | | | | | | | End of split
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | Case 2:
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | |   (276)  all_58_11 = e3
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | COMBINE_EQS: (40), (276) imply:
% 204.26/35.07  | | | | | | | |   (277)  all_52_29 = e3
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | REDUCE: (190), (277) imply:
% 204.26/35.07  | | | | | | | |   (278)  $false
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | | CLOSE: (278) is inconsistent.
% 204.26/35.07  | | | | | | | | 
% 204.26/35.07  | | | | | | | End of split
% 204.26/35.07  | | | | | | | 
% 204.26/35.07  | | | | | | End of split
% 204.26/35.07  | | | | | | 
% 204.26/35.07  | | | | | End of split
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | Case 2:
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | |   (279)   ~ (all_56_15 = e3)
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | REDUCE: (48), (279) imply:
% 204.26/35.07  | | | | |   (280)   ~ (all_14_2 = e3)
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | | REF_CLOSE: (5), (7), (11), (17), (19), (28), (30), (33), (35), (37),
% 204.26/35.07  | | | | |            (42), (44), (46), (47), (49), (52), (53), (56), (59), (61),
% 204.26/35.07  | | | | |            (68), (70), (72), (74), (77), (81), (84), (86), (93), (94),
% 204.26/35.07  | | | | |            (96), (99), (100), (104), (112), (113), (117), (120),
% 204.26/35.07  | | | | |            (123), (124), (127), (130), (132), (133), (134), (137),
% 204.26/35.07  | | | | |            (138), (143), (144), (145), (147), (151), (154), (156),
% 204.26/35.07  | | | | |            (161), (163), (164), (165), (167), (169), (170), (171),
% 204.26/35.07  | | | | |            (182), (183), (184), (185), (280) are inconsistent by
% 204.26/35.07  | | | | |            sub-proof #813.
% 204.26/35.07  | | | | | 
% 204.26/35.07  | | | | End of split
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | Case 2:
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | |   (281)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 204.26/35.07  | | | |          e0
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | ALPHA: (281) implies:
% 204.26/35.07  | | | |   (282)  all_52_30 = e0
% 204.26/35.07  | | | |   (283)  all_52_28 = e1
% 204.26/35.07  | | | |   (284)  all_52_26 = e2
% 204.26/35.07  | | | |   (285)  all_52_24 = e3
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (157), (285) imply:
% 204.26/35.07  | | | |   (286)  op(all_52_25, all_52_25) = e3
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (35), (284) imply:
% 204.26/35.07  | | | |   (287)  op(all_52_27, all_52_27) = e2
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (107), (283) imply:
% 204.26/35.07  | | | |   (288)  op(all_52_29, all_52_29) = e1
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REDUCE: (126), (282) imply:
% 204.26/35.07  | | | |   (289)  op(all_14_2, all_14_2) = e0
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 204.26/35.07  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 204.26/35.07  | | | |            (26), (27), (28), (30), (31), (36), (37), (38), (39), (40),
% 204.26/35.07  | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 204.26/35.07  | | | |            (51), (52), (53), (54), (56), (57), (58), (60), (61), (62),
% 204.26/35.07  | | | |            (63), (64), (65), (67), (68), (69), (70), (71), (72), (74),
% 204.26/35.07  | | | |            (75), (76), (77), (78), (80), (81), (82), (85), (88), (90),
% 204.26/35.07  | | | |            (91), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 204.26/35.07  | | | |            (102), (103), (104), (105), (106), (108), (109), (111),
% 204.26/35.07  | | | |            (112), (113), (114), (115), (117), (118), (120), (121),
% 204.26/35.07  | | | |            (122), (123), (124), (127), (128), (130), (131), (132),
% 204.26/35.07  | | | |            (133), (134), (135), (141), (143), (144), (145), (147),
% 204.26/35.07  | | | |            (148), (149), (150), (151), (152), (154), (161), (162),
% 204.26/35.07  | | | |            (163), (164), (165), (167), (169), (170), (286), (287),
% 204.26/35.07  | | | |            (288), (289) are inconsistent by sub-proof #794.
% 204.26/35.07  | | | | 
% 204.26/35.07  | | | End of split
% 204.26/35.07  | | | 
% 204.26/35.07  | | End of split
% 204.26/35.07  | | 
% 204.26/35.07  | Case 2:
% 204.26/35.07  | | 
% 204.26/35.07  | |   (290)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.07  | | 
% 204.26/35.07  | | REF_CLOSE: (7), (12), (18), (32), (45), (55), (61), (79), (92), (116),
% 204.26/35.07  | |            (117), (125), (135), (139), (140), (153), (290) are inconsistent
% 204.26/35.07  | |            by sub-proof #820.
% 204.26/35.07  | | 
% 204.26/35.07  | End of split
% 204.26/35.07  | 
% 204.26/35.07  End of proof
% 204.26/35.07  
% 204.26/35.07  Sub-proof #794 shows that the following formulas are inconsistent:
% 204.26/35.07  ----------------------------------------------------------------
% 204.26/35.07    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.07    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.08    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.08    (4)  all_58_14 = all_52_23
% 204.26/35.08    (5)   ~ (e3 = e1)
% 204.26/35.08    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.08    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.08    (8)  all_58_1 = all_52_9
% 204.26/35.08    (9)   ~ (all_52_9 = all_52_13)
% 204.26/35.08    (10)   ~ (e3 = e0)
% 204.26/35.08    (11)  op(e2, e3) = all_52_3
% 204.26/35.08    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.08    (13)   ~ (all_52_3 = all_52_19)
% 204.26/35.08    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.08    (15)   ~ (all_52_17 = all_52_25)
% 204.26/35.08    (16)   ~ (all_4_2 = e3)
% 204.26/35.08    (17)   ~ (all_52_3 = all_6_2)
% 204.26/35.08    (18)  all_58_0 = all_6_2
% 204.26/35.08    (19)  op(all_14_2, e0) = all_14_1
% 204.26/35.08    (20)  all_56_4 = all_52_3
% 204.26/35.08    (21)   ~ (all_52_17 = all_10_2)
% 204.26/35.08    (22)  op(e3, e0) = all_52_25
% 204.26/35.08    (23)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.08    (24)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.08    (25)   ~ (all_52_27 = all_52_29)
% 204.26/35.08    (26)  all_58_13 = all_52_15
% 204.26/35.08    (27)  all_58_9 = all_52_25
% 204.26/35.08    (28)   ~ (all_52_29 = all_14_2)
% 204.26/35.08    (29)   ~ (all_52_15 = e3)
% 204.26/35.08    (30)  op(e1, e3) = all_52_5
% 204.26/35.08    (31)  op(e2, e2) = all_4_2
% 204.26/35.08    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.08    (33)   ~ (all_52_3 = all_52_5)
% 204.26/35.08    (34)  all_58_11 = all_52_29
% 204.26/35.08    (35)  all_56_5 = all_4_2
% 204.26/35.08    (36)   ~ (all_52_25 = all_14_2)
% 204.26/35.08    (37)   ~ (all_52_3 = all_52_27)
% 204.26/35.08    (38)  op(all_10_2, e1) = all_10_1
% 204.26/35.08    (39)  all_58_1 = e3
% 204.26/35.08    (40)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.08    (41)   ~ (all_52_7 = all_6_2)
% 204.26/35.08    (42)  op(e0, e0) = all_14_2
% 204.26/35.08    (43)  op(all_52_29, all_52_29) = e1
% 204.26/35.08    (44)  all_56_15 = all_14_2
% 204.26/35.08    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.08    (46)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.08    (47)  all_56_11 = all_52_29
% 204.26/35.08    (48)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.08    (49)   ~ (all_6_2 = e3)
% 204.26/35.08    (50)   ~ (e2 = e1)
% 204.26/35.08    (51)   ~ (all_52_13 = all_10_2)
% 204.26/35.08    (52)  all_58_10 = all_52_27
% 204.26/35.08    (53)  all_56_8 = all_52_5
% 204.26/35.08    (54)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.08    (55)   ~ (all_52_25 = all_52_29)
% 204.26/35.08    (56)  op(all_6_2, e3) = e2
% 204.26/35.08    (57)   ~ (all_52_29 = all_10_2)
% 204.26/35.08    (58)  all_58_7 = all_52_13
% 204.26/35.08    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.08    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.08    (61)   ~ (all_52_5 = all_52_7)
% 204.26/35.08    (62)  all_58_12 = all_52_7
% 204.26/35.08    (63)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.08    (64)   ~ (all_52_7 = all_14_2)
% 204.26/35.08    (65)   ~ (all_14_2 = e0)
% 204.26/35.08    (66)  all_58_2 = all_52_3
% 204.26/35.08    (67)  all_56_2 = all_52_17
% 204.26/35.08    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.08    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.08    (70)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.08    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.08    (72)   ~ (all_52_25 = e3)
% 204.26/35.08    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.08    (74)   ~ (e2 = e0)
% 204.26/35.08    (75)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.08    (76)  op(all_52_25, all_52_25) = e3
% 204.26/35.08    (77)   ~ (all_52_5 = all_52_29)
% 204.26/35.08    (78)   ~ (all_52_15 = all_14_2)
% 204.26/35.08    (79)   ~ (all_52_19 = all_52_27)
% 204.26/35.08    (80)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.08    (81)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.08    (82)  op(e3, e1) = all_52_17
% 204.26/35.08    (83)  op(all_52_27, all_52_27) = e2
% 204.26/35.08    (84)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.08    (85)  op(e0, e3) = all_52_7
% 204.26/35.08    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.08    (87)   ~ (all_52_9 = all_52_25)
% 204.26/35.08    (88)  all_58_15 = all_14_2
% 204.26/35.08    (89)   ~ (all_52_19 = all_10_2)
% 204.26/35.08    (90)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.08    (91)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.08    (92)   ~ (all_10_1 = e2)
% 204.26/35.08    (93)  all_58_8 = all_10_2
% 204.26/35.08    (94)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.08    (95)   ~ (all_52_5 = all_10_2)
% 204.26/35.08    (96)   ~ (all_52_23 = all_14_2)
% 204.26/35.08    (97)  all_56_12 = all_52_7
% 204.26/35.08    (98)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.08    (99)   ~ (all_52_25 = all_6_2)
% 204.26/35.08    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.08    (101)   ~ (all_52_9 = all_4_2)
% 204.26/35.08    (102)   ~ (all_52_5 = all_6_2)
% 204.26/35.08    (103)  op(e3, e3) = all_6_2
% 204.26/35.08    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.08    (105)   ~ (all_52_13 = e3)
% 204.26/35.08    (106)   ~ (all_52_27 = all_14_2)
% 204.26/35.08    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.08    (108)  all_56_14 = all_52_23
% 204.26/35.08    (109)   ~ (all_52_17 = e3)
% 204.26/35.08    (110)  all_56_3 = all_52_25
% 204.26/35.08    (111)   ~ (all_52_3 = all_52_7)
% 204.26/35.08    (112)  all_58_5 = all_52_19
% 204.26/35.08    (113)   ~ (all_52_15 = all_4_2)
% 204.26/35.08    (114)   ~ (all_52_27 = all_4_2)
% 204.26/35.08    (115)  all_58_6 = all_52_5
% 204.26/35.08    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.08    (117)   ~ (all_52_17 = all_6_2)
% 204.26/35.08    (118)   ~ (e1 = e0)
% 204.26/35.08    (119)  op(all_14_2, all_14_2) = e0
% 204.26/35.08    (120)   ~ (e3 = e2)
% 204.26/35.08    (121)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.08    (122)  op(e1, e1) = all_10_2
% 204.26/35.08    (123)   ~ (all_52_23 = all_10_2)
% 204.26/35.08    (124)   ~ (all_52_7 = all_52_23)
% 204.26/35.08    (125)  all_58_3 = all_4_2
% 204.26/35.08    (126)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.08    (127)   ~ (all_52_3 = all_4_2)
% 204.26/35.08    (128)   ~ (all_52_19 = all_4_2)
% 204.26/35.08    (129)   ~ (all_52_17 = all_52_23)
% 204.26/35.08    (130)  op(all_6_2, e3) = all_6_1
% 204.26/35.08    (131)  all_58_4 = all_52_17
% 204.26/35.08  
% 204.26/35.08  Begin of proof
% 204.26/35.08  | 
% 204.26/35.08  | BETA: splitting (94) gives:
% 204.26/35.08  | 
% 204.26/35.08  | Case 1:
% 204.26/35.08  | | 
% 204.26/35.08  | |   (132)  all_56_15 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | COMBINE_EQS: (44), (132) imply:
% 204.26/35.08  | |   (133)  all_14_2 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | SIMP: (133) implies:
% 204.26/35.08  | |   (134)  all_14_2 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (64), (134) imply:
% 204.26/35.08  | |   (135)   ~ (all_52_7 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (28), (134) imply:
% 204.26/35.08  | |   (136)   ~ (all_52_29 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (119), (134) imply:
% 204.26/35.08  | |   (137)  op(e3, e3) = e0
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (19), (134) imply:
% 204.26/35.08  | |   (138)  op(e3, e0) = all_14_1
% 204.26/35.08  | | 
% 204.26/35.08  | | GROUND_INST: instantiating (7) with all_52_25, all_14_1, e0, e3, simplifying
% 204.26/35.08  | |              with (22), (138) gives:
% 204.26/35.08  | |   (139)  all_52_25 = all_14_1
% 204.26/35.08  | | 
% 204.26/35.08  | | GROUND_INST: instantiating (7) with all_6_2, e0, e3, e3, simplifying with
% 204.26/35.08  | |              (103), (137) gives:
% 204.26/35.08  | |   (140)  all_6_2 = e0
% 204.26/35.08  | | 
% 204.26/35.08  | | COMBINE_EQS: (110), (139) imply:
% 204.26/35.08  | |   (141)  all_56_3 = all_14_1
% 204.26/35.08  | | 
% 204.26/35.08  | | COMBINE_EQS: (27), (139) imply:
% 204.26/35.08  | |   (142)  all_58_9 = all_14_1
% 204.26/35.08  | | 
% 204.26/35.08  | | COMBINE_EQS: (18), (140) imply:
% 204.26/35.08  | |   (143)  all_58_0 = e0
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (41), (140) imply:
% 204.26/35.08  | |   (144)   ~ (all_52_7 = e0)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (117), (140) imply:
% 204.26/35.08  | |   (145)   ~ (all_52_17 = e0)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (99), (139), (140) imply:
% 204.26/35.08  | |   (146)   ~ (all_14_1 = e0)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (72), (139) imply:
% 204.26/35.08  | |   (147)   ~ (all_14_1 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (49), (140) imply:
% 204.26/35.08  | |   (148)   ~ (e3 = e0)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (76), (139) imply:
% 204.26/35.08  | |   (149)  op(all_14_1, all_14_1) = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (56), (140) imply:
% 204.26/35.08  | |   (150)  op(e0, e3) = e2
% 204.26/35.08  | | 
% 204.26/35.08  | | GROUND_INST: instantiating (7) with all_52_7, e2, e3, e0, simplifying with
% 204.26/35.08  | |              (85), (150) gives:
% 204.26/35.08  | |   (151)  all_52_7 = e2
% 204.26/35.08  | | 
% 204.26/35.08  | | COMBINE_EQS: (62), (151) imply:
% 204.26/35.08  | |   (152)  all_58_12 = e2
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (111), (151) imply:
% 204.26/35.08  | |   (153)   ~ (all_52_3 = e2)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (135), (151) imply:
% 204.26/35.08  | |   (154)   ~ (e3 = e2)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (14), (151) imply:
% 204.26/35.08  | |   (155)  op(e2, e2) = all_52_6
% 204.26/35.08  | | 
% 204.26/35.08  | | GROUND_INST: instantiating (7) with all_4_2, all_52_6, e2, e2, simplifying
% 204.26/35.08  | |              with (31), (155) gives:
% 204.26/35.08  | |   (156)  all_52_6 = all_4_2
% 204.26/35.08  | | 
% 204.26/35.08  | | BETA: splitting (48) gives:
% 204.26/35.08  | | 
% 204.26/35.08  | | Case 1:
% 204.26/35.08  | | | 
% 204.26/35.08  | | |   (157)  all_56_2 = e3
% 204.26/35.08  | | | 
% 204.26/35.08  | | | REF_CLOSE: (67), (109), (157) are inconsistent by sub-proof #1327.
% 204.26/35.08  | | | 
% 204.26/35.08  | | Case 2:
% 204.26/35.08  | | | 
% 204.26/35.08  | | |   (158)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.08  | | | 
% 204.26/35.08  | | | BETA: splitting (100) gives:
% 204.26/35.08  | | | 
% 204.26/35.08  | | | Case 1:
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | |   (159)  all_56_3 = e3
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | REF_CLOSE: (141), (147), (159) are inconsistent by sub-proof #1200.
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | Case 2:
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | |   (160)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | BETA: splitting (73) gives:
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | Case 1:
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | |   (161)  all_56_4 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | COMBINE_EQS: (20), (161) imply:
% 204.26/35.08  | | | | |   (162)  all_52_3 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | SIMP: (162) implies:
% 204.26/35.08  | | | | |   (163)  all_52_3 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | COMBINE_EQS: (66), (163) imply:
% 204.26/35.08  | | | | |   (164)  all_58_2 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | REDUCE: (33), (163) imply:
% 204.26/35.08  | | | | |   (165)   ~ (all_52_5 = e3)
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | SIMP: (165) implies:
% 204.26/35.08  | | | | |   (166)   ~ (all_52_5 = e3)
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | REDUCE: (127), (163) imply:
% 204.26/35.08  | | | | |   (167)   ~ (all_4_2 = e3)
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | BETA: splitting (71) gives:
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | Case 1:
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | |   (168)  all_58_0 = e1
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | REF_CLOSE: (118), (143), (168) are inconsistent by sub-proof #847.
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | Case 2:
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | |   (169)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | BETA: splitting (63) gives:
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | Case 1:
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | |   (170)  all_58_6 = e3
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | | COMBINE_EQS: (115), (170) imply:
% 204.26/35.08  | | | | | | |   (171)  all_52_5 = e3
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | | REDUCE: (166), (171) imply:
% 204.26/35.08  | | | | | | |   (172)  $false
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | | CLOSE: (172) is inconsistent.
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | Case 2:
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | |   (173)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | | BETA: splitting (173) gives:
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | | Case 1:
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | |   (174)  all_58_7 = e3
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | | COMBINE_EQS: (58), (174) imply:
% 204.26/35.08  | | | | | | | |   (175)  all_52_13 = e3
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | | REDUCE: (105), (175) imply:
% 204.26/35.08  | | | | | | | |   (176)  $false
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | | CLOSE: (176) is inconsistent.
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | Case 2:
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | |   (177)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | | BETA: splitting (177) gives:
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | | Case 1:
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | |   (178)  all_58_8 = e3
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | COMBINE_EQS: (93), (178) imply:
% 204.26/35.08  | | | | | | | | |   (179)  all_10_2 = e3
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | REDUCE: (38), (179) imply:
% 204.26/35.08  | | | | | | | | |   (180)  op(e3, e1) = all_10_1
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | BETA: splitting (169) gives:
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | Case 1:
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | |   (181)  all_58_2 = e1
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | COMBINE_EQS: (164), (181) imply:
% 204.26/35.08  | | | | | | | | | |   (182)  e3 = e1
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | REDUCE: (5), (182) imply:
% 204.26/35.08  | | | | | | | | | |   (183)  $false
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | CLOSE: (183) is inconsistent.
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | Case 2:
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | |   (184)  all_58_6 = e1 | all_58_12 = e1
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | BETA: splitting (184) gives:
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | Case 1:
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_17, all_10_1, e1,
% 204.26/35.08  | | | | | | | | | | |              e3, simplifying with (82), (180) gives:
% 204.26/35.08  | | | | | | | | | | |   (185)  all_52_17 = all_10_1
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | COMBINE_EQS: (67), (185) imply:
% 204.26/35.08  | | | | | | | | | | |   (186)  all_56_2 = all_10_1
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | COMBINE_EQS: (131), (185) imply:
% 204.26/35.08  | | | | | | | | | | |   (187)  all_58_4 = all_10_1
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | REDUCE: (145), (185) imply:
% 204.26/35.08  | | | | | | | | | | |   (188)   ~ (all_10_1 = e0)
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | REF_CLOSE: (7), (16), (26), (29), (31), (58), (68), (74),
% 204.26/35.08  | | | | | | | | | | |            (86), (92), (105), (120), (125), (142), (143),
% 204.26/35.08  | | | | | | | | | | |            (149), (158), (186), (187), (188) are inconsistent
% 204.26/35.08  | | | | | | | | | | |            by sub-proof #807.
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | Case 2:
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | |   (189)  all_58_12 = e1
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | COMBINE_EQS: (152), (189) imply:
% 204.26/35.08  | | | | | | | | | | |   (190)  e2 = e1
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | REDUCE: (50), (190) imply:
% 204.26/35.08  | | | | | | | | | | |   (191)  $false
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 204.26/35.08  | | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | | End of split
% 204.26/35.08  | | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | End of split
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | Case 2:
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | |   (192)  all_58_11 = e3
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | COMBINE_EQS: (34), (192) imply:
% 204.26/35.08  | | | | | | | | |   (193)  all_52_29 = e3
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | REDUCE: (136), (193) imply:
% 204.26/35.08  | | | | | | | | |   (194)  $false
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | | CLOSE: (194) is inconsistent.
% 204.26/35.08  | | | | | | | | | 
% 204.26/35.08  | | | | | | | | End of split
% 204.26/35.08  | | | | | | | | 
% 204.26/35.08  | | | | | | | End of split
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | End of split
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | End of split
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | Case 2:
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | |   (195)   ~ (all_56_4 = e3)
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | REDUCE: (20), (195) imply:
% 204.26/35.08  | | | | |   (196)   ~ (all_52_3 = e3)
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | REF_CLOSE: (7), (10), (16), (26), (29), (31), (39), (46), (58), (66),
% 204.26/35.08  | | | | |            (69), (86), (95), (105), (115), (120), (122), (125), (141),
% 204.26/35.08  | | | | |            (142), (143), (146), (149), (152), (160), (196) are
% 204.26/35.08  | | | | |            inconsistent by sub-proof #803.
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | End of split
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | End of split
% 204.26/35.08  | | | 
% 204.26/35.08  | | End of split
% 204.26/35.08  | | 
% 204.26/35.08  | Case 2:
% 204.26/35.08  | | 
% 204.26/35.08  | |   (197)   ~ (all_56_15 = e3)
% 204.26/35.08  | |   (198)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (44), (197) imply:
% 204.26/35.08  | |   (199)   ~ (all_14_2 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.26/35.08  | |            (14), (15), (16), (17), (18), (21), (23), (24), (25), (26), (27),
% 204.26/35.08  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 204.26/35.08  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (52),
% 204.26/35.08  | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 204.26/35.08  | |            (64), (65), (66), (67), (69), (70), (72), (74), (75), (76), (77),
% 204.26/35.08  | |            (79), (80), (81), (82), (83), (84), (86), (87), (88), (89), (90),
% 204.26/35.08  | |            (91), (93), (95), (96), (97), (98), (99), (100), (101), (102),
% 204.26/35.08  | |            (103), (104), (105), (106), (107), (108), (110), (111), (112),
% 204.26/35.08  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 204.26/35.08  | |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 204.26/35.08  | |            (131), (198), (199) are inconsistent by sub-proof #795.
% 204.26/35.08  | | 
% 204.26/35.08  | End of split
% 204.26/35.08  | 
% 204.26/35.08  End of proof
% 204.26/35.08  
% 204.26/35.08  Sub-proof #795 shows that the following formulas are inconsistent:
% 204.26/35.08  ----------------------------------------------------------------
% 204.26/35.08    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.08    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.08    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.08    (4)  all_58_14 = all_52_23
% 204.26/35.08    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.08    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.08    (7)  all_58_1 = all_52_9
% 204.26/35.08    (8)   ~ (all_52_9 = all_52_13)
% 204.26/35.08    (9)   ~ (e3 = e0)
% 204.26/35.08    (10)  op(e2, e3) = all_52_3
% 204.26/35.08    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.08    (12)   ~ (all_52_3 = all_52_19)
% 204.26/35.08    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.08    (14)   ~ (all_52_17 = all_52_25)
% 204.26/35.08    (15)   ~ (all_4_2 = e3)
% 204.26/35.08    (16)   ~ (all_52_3 = all_6_2)
% 204.26/35.08    (17)  all_58_0 = all_6_2
% 204.26/35.08    (18)   ~ (all_52_17 = all_10_2)
% 204.26/35.08    (19)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.08    (20)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.08    (21)   ~ (all_52_27 = all_52_29)
% 204.26/35.08    (22)  all_58_13 = all_52_15
% 204.26/35.08    (23)  all_58_9 = all_52_25
% 204.26/35.08    (24)   ~ (all_52_29 = all_14_2)
% 204.26/35.08    (25)   ~ (all_52_15 = e3)
% 204.26/35.08    (26)  op(e1, e3) = all_52_5
% 204.26/35.08    (27)  op(e2, e2) = all_4_2
% 204.26/35.08    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.08    (29)   ~ (all_52_3 = all_52_5)
% 204.26/35.08    (30)  all_58_11 = all_52_29
% 204.26/35.08    (31)  all_56_5 = all_4_2
% 204.26/35.08    (32)   ~ (all_52_25 = all_14_2)
% 204.26/35.08    (33)   ~ (all_52_3 = all_52_27)
% 204.26/35.08    (34)  op(all_10_2, e1) = all_10_1
% 204.26/35.08    (35)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.08    (36)   ~ (all_52_7 = all_6_2)
% 204.26/35.08    (37)  op(e0, e0) = all_14_2
% 204.26/35.08    (38)  op(all_52_29, all_52_29) = e1
% 204.26/35.08    (39)  all_56_15 = all_14_2
% 204.26/35.08    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.08    (41)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.08    (42)  all_56_11 = all_52_29
% 204.26/35.08    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.08    (44)   ~ (all_6_2 = e3)
% 204.26/35.08    (45)  all_58_10 = all_52_27
% 204.26/35.08    (46)  all_56_8 = all_52_5
% 204.26/35.08    (47)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.08    (48)   ~ (all_52_25 = all_52_29)
% 204.26/35.08    (49)  op(all_6_2, e3) = e2
% 204.26/35.08    (50)   ~ (all_52_29 = all_10_2)
% 204.26/35.08    (51)  all_58_7 = all_52_13
% 204.26/35.08    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.08    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.08    (54)   ~ (all_52_5 = all_52_7)
% 204.26/35.08    (55)  all_58_12 = all_52_7
% 204.26/35.08    (56)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.08    (57)   ~ (all_52_7 = all_14_2)
% 204.26/35.08    (58)   ~ (all_14_2 = e0)
% 204.26/35.08    (59)  all_58_2 = all_52_3
% 204.26/35.08    (60)  all_56_2 = all_52_17
% 204.26/35.08    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.08    (62)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.08    (63)   ~ (all_52_25 = e3)
% 204.26/35.08    (64)   ~ (e2 = e0)
% 204.26/35.08    (65)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.08    (66)  op(all_52_25, all_52_25) = e3
% 204.26/35.08    (67)   ~ (all_52_5 = all_52_29)
% 204.26/35.08    (68)   ~ (all_52_19 = all_52_27)
% 204.26/35.08    (69)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.08    (70)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.08    (71)  op(e3, e1) = all_52_17
% 204.26/35.08    (72)  op(all_52_27, all_52_27) = e2
% 204.26/35.08    (73)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.08    (74)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.08    (75)   ~ (all_52_9 = all_52_25)
% 204.26/35.08    (76)  all_58_15 = all_14_2
% 204.26/35.08    (77)   ~ (all_52_19 = all_10_2)
% 204.26/35.08    (78)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.08    (79)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.08    (80)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.08    (81)  all_58_8 = all_10_2
% 204.26/35.08    (82)   ~ (all_52_5 = all_10_2)
% 204.26/35.08    (83)   ~ (all_52_23 = all_14_2)
% 204.26/35.08    (84)  all_56_12 = all_52_7
% 204.26/35.08    (85)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.08    (86)   ~ (all_52_25 = all_6_2)
% 204.26/35.08    (87)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.08    (88)   ~ (all_52_9 = all_4_2)
% 204.26/35.08    (89)   ~ (all_52_5 = all_6_2)
% 204.26/35.08    (90)  op(e3, e3) = all_6_2
% 204.26/35.08    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.08    (92)   ~ (all_52_13 = e3)
% 204.26/35.08    (93)   ~ (all_52_27 = all_14_2)
% 204.26/35.08    (94)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.08    (95)  all_56_14 = all_52_23
% 204.26/35.08    (96)  all_56_3 = all_52_25
% 204.26/35.08    (97)   ~ (all_52_3 = all_52_7)
% 204.26/35.08    (98)  all_58_5 = all_52_19
% 204.26/35.08    (99)   ~ (all_52_15 = all_4_2)
% 204.26/35.08    (100)   ~ (all_52_27 = all_4_2)
% 204.26/35.08    (101)  all_58_6 = all_52_5
% 204.26/35.08    (102)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.08    (103)   ~ (all_52_17 = all_6_2)
% 204.26/35.08    (104)   ~ (e1 = e0)
% 204.26/35.08    (105)  op(all_14_2, all_14_2) = e0
% 204.26/35.08    (106)   ~ (e3 = e2)
% 204.26/35.08    (107)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.08    (108)  op(e1, e1) = all_10_2
% 204.26/35.08    (109)   ~ (all_52_23 = all_10_2)
% 204.26/35.08    (110)   ~ (all_52_7 = all_52_23)
% 204.26/35.08    (111)  all_58_3 = all_4_2
% 204.26/35.08    (112)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.08    (113)   ~ (all_52_3 = all_4_2)
% 204.26/35.08    (114)   ~ (all_52_19 = all_4_2)
% 204.26/35.08    (115)   ~ (all_52_17 = all_52_23)
% 204.26/35.08    (116)  op(all_6_2, e3) = all_6_1
% 204.26/35.08    (117)  all_58_4 = all_52_17
% 204.26/35.08    (118)   ~ (all_14_2 = e3)
% 204.26/35.08  
% 204.26/35.08  Begin of proof
% 204.26/35.08  | 
% 204.26/35.08  | BETA: splitting (102) gives:
% 204.26/35.08  | 
% 204.26/35.08  | Case 1:
% 204.26/35.08  | | 
% 204.26/35.08  | |   (119)  all_58_12 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | COMBINE_EQS: (55), (119) imply:
% 204.26/35.08  | |   (120)  all_52_7 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | SIMP: (120) implies:
% 204.26/35.08  | |   (121)  all_52_7 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (97), (121) imply:
% 204.26/35.08  | |   (122)   ~ (all_52_3 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (54), (121) imply:
% 204.26/35.08  | |   (123)   ~ (all_52_5 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (110), (121) imply:
% 204.26/35.08  | |   (124)   ~ (all_52_23 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | SIMP: (124) implies:
% 204.26/35.08  | |   (125)   ~ (all_52_23 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (57), (121) imply:
% 204.26/35.08  | |   (126)   ~ (all_14_2 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (36), (121) imply:
% 204.26/35.08  | |   (127)   ~ (all_6_2 = e3)
% 204.26/35.08  | | 
% 204.26/35.08  | | REDUCE: (13), (121) imply:
% 204.26/35.08  | |   (128)  op(e3, e3) = all_52_6
% 204.26/35.08  | | 
% 204.26/35.08  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 204.26/35.08  | |            (15), (17), (18), (20), (21), (22), (23), (24), (26), (27), (28),
% 204.26/35.08  | |            (29), (30), (31), (32), (33), (34), (35), (37), (38), (39), (40),
% 204.26/35.08  | |            (41), (42), (43), (44), (45), (46), (48), (49), (50), (51), (52),
% 204.26/35.08  | |            (53), (56), (58), (59), (60), (62), (63), (64), (65), (66), (67),
% 204.26/35.08  | |            (69), (70), (71), (72), (73), (74), (76), (77), (79), (80), (81),
% 204.26/35.08  | |            (83), (85), (86), (87), (88), (89), (90), (91), (93), (94), (95),
% 204.26/35.08  | |            (96), (98), (99), (101), (103), (104), (105), (107), (108),
% 204.26/35.08  | |            (111), (112), (114), (115), (116), (117), (118), (119), (122),
% 204.26/35.08  | |            (123), (125), (128) are inconsistent by sub-proof #798.
% 204.26/35.08  | | 
% 204.26/35.08  | Case 2:
% 204.26/35.08  | | 
% 204.26/35.08  | |   (129)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.08  | | 
% 204.26/35.08  | | BETA: splitting (129) gives:
% 204.26/35.08  | | 
% 204.26/35.08  | | Case 1:
% 204.26/35.08  | | | 
% 204.26/35.08  | | |   (130)  all_58_13 = e3
% 204.26/35.08  | | | 
% 204.26/35.08  | | | REF_CLOSE: (22), (25), (130) are inconsistent by sub-proof #1360.
% 204.26/35.08  | | | 
% 204.26/35.08  | | Case 2:
% 204.26/35.08  | | | 
% 204.26/35.08  | | |   (131)  all_58_14 = e3 | all_58_15 = e3
% 204.26/35.08  | | | 
% 204.26/35.08  | | | BETA: splitting (131) gives:
% 204.26/35.08  | | | 
% 204.26/35.08  | | | Case 1:
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | |   (132)  all_58_14 = e3
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | COMBINE_EQS: (4), (132) imply:
% 204.26/35.08  | | | |   (133)  all_52_23 = e3
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | SIMP: (133) implies:
% 204.26/35.08  | | | |   (134)  all_52_23 = e3
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | REDUCE: (110), (134) imply:
% 204.26/35.08  | | | |   (135)   ~ (all_52_7 = e3)
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | REDUCE: (115), (134) imply:
% 204.26/35.08  | | | |   (136)   ~ (all_52_17 = e3)
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | REDUCE: (83), (134) imply:
% 204.26/35.08  | | | |   (137)   ~ (all_14_2 = e3)
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | REDUCE: (109), (134) imply:
% 204.26/35.08  | | | |   (138)   ~ (all_10_2 = e3)
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | SIMP: (138) implies:
% 204.26/35.08  | | | |   (139)   ~ (all_10_2 = e3)
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | REDUCE: (78), (134) imply:
% 204.26/35.08  | | | |   (140)  op(e3, e3) = all_52_22
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 204.26/35.08  | | | |              simplifying with (90), (140) gives:
% 204.26/35.08  | | | |   (141)  all_52_22 = all_6_2
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | BETA: splitting (61) gives:
% 204.26/35.08  | | | | 
% 204.26/35.08  | | | | Case 1:
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | |   (142)  all_58_0 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | COMBINE_EQS: (17), (142) imply:
% 204.26/35.08  | | | | |   (143)  all_6_2 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | REDUCE: (44), (143) imply:
% 204.26/35.08  | | | | |   (144)  $false
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | CLOSE: (144) is inconsistent.
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | Case 2:
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | |   (145)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | BETA: splitting (56) gives:
% 204.26/35.08  | | | | | 
% 204.26/35.08  | | | | | Case 1:
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | |   (146)  all_58_6 = e3
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | COMBINE_EQS: (101), (146) imply:
% 204.26/35.08  | | | | | |   (147)  all_52_5 = e3
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | SIMP: (147) implies:
% 204.26/35.08  | | | | | |   (148)  all_52_5 = e3
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | REF_CLOSE: (3), (6), (7), (14), (17), (18), (19), (23), (29), (30),
% 204.26/35.08  | | | | | |            (37), (40), (41), (45), (47), (59), (66), (67), (68),
% 204.26/35.08  | | | | | |            (72), (74), (75), (76), (82), (86), (87), (90), (91),
% 204.26/35.08  | | | | | |            (93), (94), (96), (98), (100), (106), (108), (111),
% 204.26/35.08  | | | | | |            (117), (118), (148) are inconsistent by sub-proof #797.
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | Case 2:
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | |   (149)   ~ (all_58_6 = e3)
% 204.26/35.08  | | | | | |   (150)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | REDUCE: (101), (149) imply:
% 204.26/35.08  | | | | | |   (151)   ~ (all_52_5 = e3)
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | BETA: splitting (150) gives:
% 204.26/35.08  | | | | | | 
% 204.26/35.08  | | | | | | Case 1:
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | |   (152)  all_58_7 = e3
% 204.26/35.08  | | | | | | | 
% 204.26/35.08  | | | | | | | COMBINE_EQS: (51), (152) imply:
% 204.26/35.08  | | | | | | |   (153)  all_52_13 = e3
% 204.26/35.08  | | | | | | | 
% 204.26/35.09  | | | | | | | REDUCE: (92), (153) imply:
% 204.26/35.09  | | | | | | |   (154)  $false
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | CLOSE: (154) is inconsistent.
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | Case 2:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | |   (155)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | BETA: splitting (145) gives:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | Case 1:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | |   (156)  all_58_2 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | COMBINE_EQS: (59), (156) imply:
% 204.26/35.09  | | | | | | | |   (157)  all_52_3 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | SIMP: (157) implies:
% 204.26/35.09  | | | | | | | |   (158)  all_52_3 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REDUCE: (97), (158) imply:
% 204.26/35.09  | | | | | | | |   (159)   ~ (all_52_7 = e3)
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REDUCE: (16), (158) imply:
% 204.26/35.09  | | | | | | | |   (160)   ~ (all_6_2 = e3)
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REDUCE: (5), (158) imply:
% 204.26/35.09  | | | | | | | |   (161)  op(e3, e3) = all_52_2
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REF_CLOSE: (6), (11), (13), (14), (17), (19), (21), (23), (24),
% 204.26/35.09  | | | | | | | |            (26), (27), (30), (35), (36), (37), (38), (41), (43),
% 204.26/35.09  | | | | | | | |            (44), (45), (48), (49), (50), (54), (55), (59), (60),
% 204.26/35.09  | | | | | | | |            (61), (66), (67), (73), (76), (81), (84), (86), (87),
% 204.26/35.09  | | | | | | | |            (90), (91), (96), (101), (103), (108), (113), (117),
% 204.26/35.09  | | | | | | | |            (135), (136), (139), (155), (161) are inconsistent by
% 204.26/35.09  | | | | | | | |            sub-proof #796.
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | Case 2:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | |   (162)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REF_CLOSE: (55), (101), (135), (151), (162) are inconsistent by
% 204.26/35.09  | | | | | | | |            sub-proof #1243.
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | End of split
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | End of split
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | End of split
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | End of split
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | Case 2:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | |   (163)  all_58_15 = e3
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | COMBINE_EQS: (76), (163) imply:
% 204.26/35.09  | | | |   (164)  all_14_2 = e3
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | REDUCE: (118), (164) imply:
% 204.26/35.09  | | | |   (165)  $false
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | CLOSE: (165) is inconsistent.
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | End of split
% 204.26/35.09  | | | 
% 204.26/35.09  | | End of split
% 204.26/35.09  | | 
% 204.26/35.09  | End of split
% 204.26/35.09  | 
% 204.26/35.09  End of proof
% 204.26/35.09  
% 204.26/35.09  Sub-proof #796 shows that the following formulas are inconsistent:
% 204.26/35.09  ----------------------------------------------------------------
% 204.26/35.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.09    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.09    (3)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.09    (4)   ~ (all_52_17 = all_52_25)
% 204.26/35.09    (5)  all_58_0 = all_6_2
% 204.26/35.09    (6)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.09    (7)   ~ (all_52_27 = all_52_29)
% 204.26/35.09    (8)  all_58_9 = all_52_25
% 204.26/35.09    (9)   ~ (all_52_29 = all_14_2)
% 204.26/35.09    (10)  op(e1, e3) = all_52_5
% 204.26/35.09    (11)  op(e2, e2) = all_4_2
% 204.26/35.09    (12)  all_58_11 = all_52_29
% 204.26/35.09    (13)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.09    (14)   ~ (all_52_7 = all_6_2)
% 204.26/35.09    (15)  op(e0, e0) = all_14_2
% 204.26/35.09    (16)  op(all_52_29, all_52_29) = e1
% 204.26/35.09    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.09    (18)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.09    (19)   ~ (all_6_2 = e3)
% 204.26/35.09    (20)  all_58_10 = all_52_27
% 204.26/35.09    (21)   ~ (all_52_25 = all_52_29)
% 204.26/35.09    (22)  op(all_6_2, e3) = e2
% 204.26/35.09    (23)   ~ (all_52_29 = all_10_2)
% 204.26/35.09    (24)   ~ (all_52_5 = all_52_7)
% 204.26/35.09    (25)  all_58_12 = all_52_7
% 204.26/35.09    (26)   ~ (all_52_7 = e3)
% 204.26/35.09    (27)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.09    (28)  all_58_2 = all_52_3
% 204.26/35.09    (29)  all_56_2 = all_52_17
% 204.26/35.09    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.09    (31)  op(all_52_25, all_52_25) = e3
% 204.26/35.09    (32)   ~ (all_52_5 = all_52_29)
% 204.26/35.09    (33)   ~ (all_10_2 = e3)
% 204.26/35.09    (34)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.09    (35)  all_58_15 = all_14_2
% 204.26/35.09    (36)  all_58_8 = all_10_2
% 204.26/35.09    (37)  all_56_12 = all_52_7
% 204.26/35.09    (38)   ~ (all_52_25 = all_6_2)
% 204.26/35.09    (39)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.09    (40)  op(e3, e3) = all_52_2
% 204.26/35.09    (41)  op(e3, e3) = all_6_2
% 204.26/35.09    (42)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.09    (43)   ~ (all_52_17 = e3)
% 204.26/35.09    (44)  all_56_3 = all_52_25
% 204.26/35.09    (45)  all_58_6 = all_52_5
% 204.26/35.09    (46)   ~ (all_52_17 = all_6_2)
% 204.26/35.09    (47)  op(e1, e1) = all_10_2
% 204.26/35.09    (48)   ~ (all_52_3 = all_4_2)
% 204.26/35.09    (49)  all_58_4 = all_52_17
% 204.26/35.09  
% 204.26/35.09  Begin of proof
% 204.26/35.09  | 
% 204.26/35.09  | BETA: splitting (27) gives:
% 204.26/35.09  | 
% 204.26/35.09  | Case 1:
% 204.26/35.09  | | 
% 204.26/35.09  | |   (50)  all_58_8 = e3
% 204.26/35.09  | | 
% 204.26/35.09  | | REF_CLOSE: (33), (36), (50) are inconsistent by sub-proof #950.
% 204.26/35.09  | | 
% 204.26/35.09  | Case 2:
% 204.26/35.09  | | 
% 204.26/35.09  | |   (51)  all_58_11 = e3
% 204.26/35.09  | | 
% 204.26/35.09  | | COMBINE_EQS: (12), (51) imply:
% 204.26/35.09  | |   (52)  all_52_29 = e3
% 204.26/35.09  | | 
% 204.26/35.09  | | SIMP: (52) implies:
% 204.26/35.09  | |   (53)  all_52_29 = e3
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (21), (53) imply:
% 204.26/35.09  | |   (54)   ~ (all_52_25 = e3)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (7), (53) imply:
% 204.26/35.09  | |   (55)   ~ (all_52_27 = e3)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (9), (53) imply:
% 204.26/35.09  | |   (56)   ~ (all_14_2 = e3)
% 204.26/35.09  | | 
% 204.26/35.09  | | SIMP: (56) implies:
% 204.26/35.09  | |   (57)   ~ (all_14_2 = e3)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (23), (53) imply:
% 204.26/35.09  | |   (58)   ~ (all_10_2 = e3)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (16), (53) imply:
% 204.26/35.09  | |   (59)  op(e3, e3) = e1
% 204.26/35.09  | | 
% 204.26/35.09  | | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3, simplifying
% 204.26/35.09  | |              with (40), (41) gives:
% 204.26/35.09  | |   (60)  all_52_2 = all_6_2
% 204.26/35.09  | | 
% 204.26/35.09  | | GROUND_INST: instantiating (1) with e1, all_52_2, e3, e3, simplifying with
% 204.26/35.09  | |              (40), (59) gives:
% 204.26/35.09  | |   (61)  all_52_2 = e1
% 204.26/35.09  | | 
% 204.26/35.09  | | COMBINE_EQS: (60), (61) imply:
% 204.26/35.09  | |   (62)  all_6_2 = e1
% 204.26/35.09  | | 
% 204.26/35.09  | | SIMP: (62) implies:
% 204.26/35.09  | |   (63)  all_6_2 = e1
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (14), (63) imply:
% 204.26/35.09  | |   (64)   ~ (all_52_7 = e1)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (46), (63) imply:
% 204.26/35.09  | |   (65)   ~ (all_52_17 = e1)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (19), (63) imply:
% 204.26/35.09  | |   (66)   ~ (e3 = e1)
% 204.26/35.09  | | 
% 204.26/35.09  | | SIMP: (66) implies:
% 204.26/35.09  | |   (67)   ~ (e3 = e1)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (13), (63) imply:
% 204.26/35.09  | |   (68)  op(e1, e1) = all_52_0
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (22), (63) imply:
% 204.26/35.09  | |   (69)  op(e1, e3) = e2
% 204.26/35.09  | | 
% 204.26/35.09  | | GROUND_INST: instantiating (1) with all_10_2, all_52_0, e1, e1, simplifying
% 204.26/35.09  | |              with (47), (68) gives:
% 204.26/35.09  | |   (70)  all_52_0 = all_10_2
% 204.26/35.09  | | 
% 204.26/35.09  | | GROUND_INST: instantiating (1) with all_52_5, e2, e3, e1, simplifying with
% 204.26/35.09  | |              (10), (69) gives:
% 204.26/35.09  | |   (71)  all_52_5 = e2
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (24), (71) imply:
% 204.26/35.09  | |   (72)   ~ (all_52_7 = e2)
% 204.26/35.09  | | 
% 204.26/35.09  | | SIMP: (72) implies:
% 204.26/35.09  | |   (73)   ~ (all_52_7 = e2)
% 204.26/35.09  | | 
% 204.26/35.09  | | REDUCE: (6), (71) imply:
% 204.26/35.09  | |   (74)  op(e2, e2) = all_52_4
% 204.26/35.09  | | 
% 204.26/35.09  | | BETA: splitting (2) gives:
% 204.26/35.09  | | 
% 204.26/35.09  | | Case 1:
% 204.26/35.09  | | | 
% 204.26/35.09  | | |   (75)  all_56_12 = e3
% 204.26/35.09  | | | 
% 204.26/35.09  | | | REF_CLOSE: (26), (37), (75) are inconsistent by sub-proof #1383.
% 204.26/35.09  | | | 
% 204.26/35.09  | | Case 2:
% 204.26/35.09  | | | 
% 204.26/35.09  | | |   (76)   ~ (all_56_12 = e3)
% 204.26/35.09  | | |   (77)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.09  | | | 
% 204.26/35.09  | | | BETA: splitting (77) gives:
% 204.26/35.09  | | | 
% 204.26/35.09  | | | Case 1:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | |   (78)  all_56_12 = e2
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | REF_CLOSE: (37), (73), (78) are inconsistent by sub-proof #1178.
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | Case 2:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | |   (79)  all_56_12 = e1 | all_56_12 = e0
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | BETA: splitting (79) gives:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | Case 1:
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | |   (80)  all_56_12 = e1
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | REF_CLOSE: (37), (64), (80) are inconsistent by sub-proof #1376.
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | Case 2:
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | |   (81)  all_56_12 = e0
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | COMBINE_EQS: (37), (81) imply:
% 204.26/35.09  | | | | |   (82)  all_52_7 = e0
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | SIMP: (82) implies:
% 204.26/35.09  | | | | |   (83)  all_52_7 = e0
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | REDUCE: (3), (83) imply:
% 204.26/35.09  | | | | |   (84)  op(e0, e0) = all_52_6
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | GROUND_INST: instantiating (1) with all_14_2, all_52_6, e0, e0,
% 204.26/35.09  | | | | |              simplifying with (15), (84) gives:
% 204.26/35.09  | | | | |   (85)  all_52_6 = all_14_2
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | GROUND_INST: instantiating (1) with all_4_2, all_52_4, e2, e2,
% 204.26/35.09  | | | | |              simplifying with (11), (74) gives:
% 204.26/35.09  | | | | |   (86)  all_52_4 = all_4_2
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | BETA: splitting (18) gives:
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | Case 1:
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | |   (87)  all_56_2 = e3
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | | REF_CLOSE: (29), (43), (87) are inconsistent by sub-proof #1327.
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | Case 2:
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | |   (88)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | | BETA: splitting (39) gives:
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | | Case 1:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | |   (89)  all_56_3 = e3
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | REF_CLOSE: (44), (54), (89) are inconsistent by sub-proof #1339.
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | Case 2:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | |   (90)   ~ (all_56_3 = e3)
% 204.26/35.09  | | | | | | |   (91)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | BETA: splitting (34) gives:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | Case 1:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | |   (92)  all_58_4 = e2
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | COMBINE_EQS: (49), (92) imply:
% 204.26/35.09  | | | | | | | |   (93)  all_52_17 = e2
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REDUCE: (4), (93) imply:
% 204.26/35.09  | | | | | | | |   (94)   ~ (all_52_25 = e2)
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | SIMP: (94) implies:
% 204.26/35.09  | | | | | | | |   (95)   ~ (all_52_25 = e2)
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REF_CLOSE: (1), (8), (15), (17), (31), (33), (44), (47), (57),
% 204.26/35.09  | | | | | | | |            (91), (95) are inconsistent by sub-proof #1232.
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | Case 2:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | |   (96)   ~ (all_58_4 = e2)
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REDUCE: (49), (96) imply:
% 204.26/35.09  | | | | | | | |   (97)   ~ (all_52_17 = e2)
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | BETA: splitting (88) gives:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | Case 1:
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | |   (98)  all_56_2 = e2
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | REF_CLOSE: (29), (97), (98) are inconsistent by sub-proof
% 204.26/35.09  | | | | | | | | |            #1264.
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | Case 2:
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | |   (99)  all_56_2 = e1 | all_56_2 = e0
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | BETA: splitting (99) gives:
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | Case 1:
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | |   (100)  all_56_2 = e1
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | | REF_CLOSE: (29), (65), (100) are inconsistent by sub-proof
% 204.26/35.09  | | | | | | | | | |            #1263.
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | Case 2:
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | |   (101)  all_56_2 = e0
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | | COMBINE_EQS: (29), (101) imply:
% 204.26/35.09  | | | | | | | | | |   (102)  all_52_17 = e0
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | | SIMP: (102) implies:
% 204.26/35.09  | | | | | | | | | |   (103)  all_52_17 = e0
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | | REDUCE: (4), (103) imply:
% 204.26/35.09  | | | | | | | | | |   (104)   ~ (all_52_25 = e0)
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | | SIMP: (104) implies:
% 204.26/35.09  | | | | | | | | | |   (105)   ~ (all_52_25 = e0)
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | | REF_CLOSE: (1), (5), (8), (11), (12), (16), (20), (21), (25),
% 204.26/35.09  | | | | | | | | | |            (26), (28), (30), (31), (32), (35), (38), (39),
% 204.26/35.09  | | | | | | | | | |            (41), (42), (44), (45), (48), (54), (55), (57),
% 204.26/35.09  | | | | | | | | | |            (67), (105) are inconsistent by sub-proof #1036.
% 204.26/35.09  | | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | End of split
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | End of split
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | End of split
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | End of split
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | End of split
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | End of split
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | End of split
% 204.26/35.09  | | | 
% 204.26/35.09  | | End of split
% 204.26/35.09  | | 
% 204.26/35.09  | End of split
% 204.26/35.09  | 
% 204.26/35.09  End of proof
% 204.26/35.09  
% 204.26/35.09  Sub-proof #797 shows that the following formulas are inconsistent:
% 204.26/35.09  ----------------------------------------------------------------
% 204.26/35.09    (1)   ~ (all_52_25 = all_52_27)
% 204.26/35.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.09    (3)  all_58_1 = all_52_9
% 204.26/35.09    (4)   ~ (all_52_17 = all_52_25)
% 204.26/35.09    (5)  all_58_0 = all_6_2
% 204.26/35.09    (6)   ~ (all_52_17 = all_10_2)
% 204.26/35.09    (7)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.09    (8)  all_58_9 = all_52_25
% 204.26/35.09    (9)   ~ (all_52_3 = all_52_5)
% 204.26/35.09    (10)  all_58_11 = all_52_29
% 204.26/35.09    (11)  op(e0, e0) = all_14_2
% 204.26/35.09    (12)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.09    (13)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.09    (14)  all_58_10 = all_52_27
% 204.26/35.09    (15)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.09    (16)  all_58_2 = all_52_3
% 204.26/35.09    (17)  all_52_5 = e3
% 204.26/35.09    (18)  op(all_52_25, all_52_25) = e3
% 204.26/35.09    (19)   ~ (all_52_5 = all_52_29)
% 204.26/35.09    (20)   ~ (all_52_19 = all_52_27)
% 204.26/35.09    (21)  op(all_52_27, all_52_27) = e2
% 204.26/35.09    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.09    (23)   ~ (all_52_9 = all_52_25)
% 204.26/35.09    (24)  all_58_15 = all_14_2
% 204.26/35.09    (25)   ~ (all_52_5 = all_10_2)
% 204.26/35.09    (26)   ~ (all_52_25 = all_6_2)
% 204.26/35.09    (27)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.09    (28)  op(e3, e3) = all_6_2
% 204.26/35.09    (29)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.09    (30)   ~ (all_52_27 = all_14_2)
% 204.26/35.09    (31)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.09    (32)  all_56_3 = all_52_25
% 204.26/35.09    (33)  all_58_5 = all_52_19
% 204.26/35.09    (34)   ~ (all_52_27 = all_4_2)
% 204.26/35.09    (35)   ~ (e3 = e2)
% 204.26/35.09    (36)  op(e1, e1) = all_10_2
% 204.26/35.09    (37)  all_58_3 = all_4_2
% 204.26/35.09    (38)  all_58_4 = all_52_17
% 204.26/35.09    (39)   ~ (all_14_2 = e3)
% 204.26/35.09  
% 204.26/35.09  Begin of proof
% 204.26/35.09  | 
% 204.26/35.09  | REDUCE: (9), (17) imply:
% 204.26/35.09  |   (40)   ~ (all_52_3 = e3)
% 204.26/35.09  | 
% 204.26/35.09  | REDUCE: (17), (19) imply:
% 204.26/35.09  |   (41)   ~ (all_52_29 = e3)
% 204.26/35.09  | 
% 204.26/35.09  | SIMP: (41) implies:
% 204.26/35.09  |   (42)   ~ (all_52_29 = e3)
% 204.26/35.09  | 
% 204.26/35.09  | REDUCE: (17), (25) imply:
% 204.26/35.09  |   (43)   ~ (all_10_2 = e3)
% 204.26/35.09  | 
% 204.26/35.09  | SIMP: (43) implies:
% 204.26/35.09  |   (44)   ~ (all_10_2 = e3)
% 204.26/35.09  | 
% 204.26/35.09  | REDUCE: (7), (17) imply:
% 204.26/35.09  |   (45)  op(e3, e3) = all_52_4
% 204.26/35.09  | 
% 204.26/35.09  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 204.26/35.09  |            (15), (16), (18), (20), (21), (22), (23), (24), (26), (27), (28),
% 204.26/35.09  |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 204.26/35.09  |            (40), (42), (44), (45) are inconsistent by sub-proof #1039.
% 204.26/35.09  | 
% 204.26/35.09  End of proof
% 204.26/35.09  
% 204.26/35.09  Sub-proof #798 shows that the following formulas are inconsistent:
% 204.26/35.09  ----------------------------------------------------------------
% 204.26/35.09    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.09    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.09    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.09    (4)  all_58_14 = all_52_23
% 204.26/35.09    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.09    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.09    (7)  all_58_1 = all_52_9
% 204.26/35.09    (8)   ~ (all_52_9 = all_52_13)
% 204.26/35.09    (9)   ~ (e3 = e0)
% 204.26/35.09    (10)  op(e2, e3) = all_52_3
% 204.26/35.09    (11)   ~ (all_52_3 = all_52_19)
% 204.26/35.09    (12)   ~ (all_52_17 = all_52_25)
% 204.26/35.09    (13)   ~ (all_4_2 = e3)
% 204.26/35.09    (14)  all_58_0 = all_6_2
% 204.26/35.09    (15)   ~ (all_52_17 = all_10_2)
% 204.26/35.09    (16)  op(e3, e3) = all_52_6
% 204.26/35.09    (17)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.09    (18)   ~ (all_52_27 = all_52_29)
% 204.26/35.09    (19)  all_58_13 = all_52_15
% 204.26/35.09    (20)  all_58_9 = all_52_25
% 204.26/35.09    (21)   ~ (all_52_29 = all_14_2)
% 204.26/35.09    (22)  op(e1, e3) = all_52_5
% 204.26/35.09    (23)  op(e2, e2) = all_4_2
% 204.26/35.09    (24)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.09    (25)   ~ (all_52_3 = all_52_5)
% 204.26/35.09    (26)  all_58_11 = all_52_29
% 204.26/35.09    (27)   ~ (all_52_3 = e3)
% 204.26/35.09    (28)  all_56_5 = all_4_2
% 204.26/35.09    (29)   ~ (all_52_25 = all_14_2)
% 204.26/35.09    (30)   ~ (all_52_3 = all_52_27)
% 204.26/35.09    (31)  op(all_10_2, e1) = all_10_1
% 204.26/35.09    (32)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.09    (33)  op(e0, e0) = all_14_2
% 204.26/35.09    (34)  op(all_52_29, all_52_29) = e1
% 204.26/35.09    (35)  all_56_15 = all_14_2
% 204.26/35.09    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.09    (37)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.09    (38)  all_56_11 = all_52_29
% 204.26/35.09    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.09    (40)   ~ (all_6_2 = e3)
% 204.26/35.09    (41)  all_58_10 = all_52_27
% 204.26/35.09    (42)  all_56_8 = all_52_5
% 204.26/35.09    (43)   ~ (all_52_25 = all_52_29)
% 204.26/35.09    (44)  op(all_6_2, e3) = e2
% 204.26/35.09    (45)   ~ (all_52_29 = all_10_2)
% 204.26/35.09    (46)  all_58_7 = all_52_13
% 204.26/35.09    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.09    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.09    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.09    (50)   ~ (all_14_2 = e0)
% 204.26/35.09    (51)  all_58_2 = all_52_3
% 204.26/35.09    (52)  all_56_2 = all_52_17
% 204.26/35.09    (53)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.09    (54)   ~ (all_52_25 = e3)
% 204.26/35.09    (55)   ~ (e2 = e0)
% 204.26/35.09    (56)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.09    (57)   ~ (all_52_23 = e3)
% 204.26/35.09    (58)   ~ (all_52_5 = e3)
% 204.26/35.09    (59)  op(all_52_25, all_52_25) = e3
% 204.26/35.09    (60)   ~ (all_52_5 = all_52_29)
% 204.26/35.09    (61)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.09    (62)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.09    (63)  op(e3, e1) = all_52_17
% 204.26/35.09    (64)  op(all_52_27, all_52_27) = e2
% 204.26/35.09    (65)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.09    (66)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.09    (67)  all_58_15 = all_14_2
% 204.26/35.09    (68)   ~ (all_52_19 = all_10_2)
% 204.26/35.09    (69)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.09    (70)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.09    (71)  all_58_8 = all_10_2
% 204.26/35.09    (72)   ~ (all_52_23 = all_14_2)
% 204.26/35.09    (73)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.09    (74)   ~ (all_52_25 = all_6_2)
% 204.26/35.09    (75)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.09    (76)   ~ (all_52_9 = all_4_2)
% 204.26/35.09    (77)   ~ (all_52_5 = all_6_2)
% 204.26/35.09    (78)  op(e3, e3) = all_6_2
% 204.26/35.09    (79)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.09    (80)   ~ (all_52_27 = all_14_2)
% 204.26/35.09    (81)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.09    (82)  all_56_14 = all_52_23
% 204.26/35.09    (83)  all_56_3 = all_52_25
% 204.26/35.09    (84)  all_58_5 = all_52_19
% 204.26/35.09    (85)   ~ (all_52_15 = all_4_2)
% 204.26/35.09    (86)  all_58_6 = all_52_5
% 204.26/35.09    (87)   ~ (all_52_17 = all_6_2)
% 204.26/35.09    (88)   ~ (e1 = e0)
% 204.26/35.09    (89)  op(all_14_2, all_14_2) = e0
% 204.26/35.09    (90)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.09    (91)  all_58_12 = e3
% 204.26/35.09    (92)  op(e1, e1) = all_10_2
% 204.26/35.09    (93)  all_58_3 = all_4_2
% 204.26/35.09    (94)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.09    (95)   ~ (all_52_19 = all_4_2)
% 204.26/35.09    (96)   ~ (all_52_17 = all_52_23)
% 204.26/35.09    (97)  op(all_6_2, e3) = all_6_1
% 204.26/35.09    (98)  all_58_4 = all_52_17
% 204.26/35.09    (99)   ~ (all_14_2 = e3)
% 204.26/35.09  
% 204.26/35.09  Begin of proof
% 204.26/35.09  | 
% 204.26/35.09  | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 204.26/35.09  |              with (16), (78) gives:
% 204.26/35.09  |   (100)  all_52_6 = all_6_2
% 204.26/35.09  | 
% 204.26/35.09  | BETA: splitting (79) gives:
% 204.26/35.09  | 
% 204.26/35.09  | Case 1:
% 204.26/35.09  | | 
% 204.26/35.09  | |   (101)  all_58_9 = e3
% 204.26/35.09  | | 
% 204.26/35.09  | | REF_CLOSE: (20), (54), (101) are inconsistent by sub-proof #1300.
% 204.26/35.09  | | 
% 204.26/35.09  | Case 2:
% 204.26/35.09  | | 
% 204.26/35.09  | |   (102)   ~ (all_58_9 = e3)
% 204.26/35.09  | |   (103)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.09  | | 
% 204.26/35.09  | | BETA: splitting (36) gives:
% 204.26/35.09  | | 
% 204.26/35.09  | | Case 1:
% 204.26/35.09  | | | 
% 204.26/35.09  | | |   (104)  all_58_2 = e3
% 204.26/35.09  | | | 
% 204.26/35.09  | | | REF_CLOSE: (27), (51), (104) are inconsistent by sub-proof #1369.
% 204.26/35.09  | | | 
% 204.26/35.09  | | Case 2:
% 204.26/35.09  | | | 
% 204.26/35.09  | | |   (105)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.09  | | | 
% 204.26/35.09  | | | BETA: splitting (75) gives:
% 204.26/35.09  | | | 
% 204.26/35.09  | | | Case 1:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | |   (106)  all_56_3 = e3
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | REF_CLOSE: (54), (83), (106) are inconsistent by sub-proof #1339.
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | Case 2:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | |   (107)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | BETA: splitting (47) gives:
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | | Case 1:
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | |   (108)  all_56_14 = e3
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | REF_CLOSE: (57), (82), (108) are inconsistent by sub-proof #1286.
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | Case 2:
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | |   (109)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | BETA: splitting (69) gives:
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | | Case 1:
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | |   (110)  all_56_8 = e3
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | | REF_CLOSE: (42), (58), (110) are inconsistent by sub-proof #1325.
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | Case 2:
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | |   (111)   ~ (all_56_8 = e3)
% 204.26/35.09  | | | | | |   (112)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | | BETA: splitting (61) gives:
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | | Case 1:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | |   (113)  all_56_11 = e3
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | COMBINE_EQS: (38), (113) imply:
% 204.26/35.09  | | | | | | |   (114)  all_52_29 = e3
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | COMBINE_EQS: (26), (114) imply:
% 204.26/35.09  | | | | | | |   (115)  all_58_11 = e3
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | REDUCE: (18), (114) imply:
% 204.26/35.09  | | | | | | |   (116)   ~ (all_52_27 = e3)
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | REDUCE: (21), (114) imply:
% 204.26/35.09  | | | | | | |   (117)   ~ (all_14_2 = e3)
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | REDUCE: (34), (114) imply:
% 204.26/35.09  | | | | | | |   (118)  op(e3, e3) = e1
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | BETA: splitting (105) gives:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | Case 1:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | |   (119)  all_58_3 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | COMBINE_EQS: (93), (119) imply:
% 204.26/35.09  | | | | | | | |   (120)  all_4_2 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | REDUCE: (13), (120) imply:
% 204.26/35.09  | | | | | | | |   (121)  $false
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | CLOSE: (121) is inconsistent.
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | Case 2:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | |   (122)  all_58_5 = e3 | all_58_10 = e3
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | BETA: splitting (122) gives:
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | | Case 1:
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | |   (123)  all_58_5 = e3
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | COMBINE_EQS: (84), (123) imply:
% 204.26/35.09  | | | | | | | | |   (124)  all_52_19 = e3
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | SIMP: (124) implies:
% 204.26/35.09  | | | | | | | | |   (125)  all_52_19 = e3
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | REDUCE: (17), (125) imply:
% 204.26/35.09  | | | | | | | | |   (126)  op(e3, e3) = all_52_18
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_18, e3, e3,
% 204.26/35.09  | | | | | | | | |              simplifying with (78), (126) gives:
% 204.26/35.09  | | | | | | | | |   (127)  all_52_18 = all_6_2
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | GROUND_INST: instantiating (6) with e1, all_52_18, e3, e3,
% 204.26/35.09  | | | | | | | | |              simplifying with (118), (126) gives:
% 204.26/35.09  | | | | | | | | |   (128)  all_52_18 = e1
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | COMBINE_EQS: (127), (128) imply:
% 204.26/35.09  | | | | | | | | |   (129)  all_6_2 = e1
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | SIMP: (129) implies:
% 204.26/35.09  | | | | | | | | |   (130)  all_6_2 = e1
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (14), (20), (22), (24), (27),
% 204.26/35.09  | | | | | | | | |            (30), (33), (41), (44), (51), (55), (59), (86),
% 204.26/35.09  | | | | | | | | |            (88), (91), (99), (115), (130) are inconsistent by
% 204.26/35.09  | | | | | | | | |            sub-proof #799.
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | Case 2:
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | |   (131)  all_58_10 = e3
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | | REF_CLOSE: (41), (116), (131) are inconsistent by sub-proof
% 204.26/35.09  | | | | | | | | |            #1301.
% 204.26/35.09  | | | | | | | | | 
% 204.26/35.09  | | | | | | | | End of split
% 204.26/35.09  | | | | | | | | 
% 204.26/35.09  | | | | | | | End of split
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | Case 2:
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | |   (132)   ~ (all_56_11 = e3)
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | REDUCE: (38), (132) imply:
% 204.26/35.09  | | | | | | |   (133)   ~ (all_52_29 = e3)
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12), (14),
% 204.26/35.09  | | | | | | |            (15), (17), (18), (19), (20), (21), (23), (25), (26),
% 204.26/35.09  | | | | | | |            (28), (29), (31), (32), (33), (35), (37), (38), (39),
% 204.26/35.09  | | | | | | |            (40), (41), (42), (43), (45), (46), (48), (49), (50),
% 204.26/35.09  | | | | | | |            (51), (52), (53), (55), (56), (58), (59), (60), (61),
% 204.26/35.09  | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (70), (71),
% 204.26/35.09  | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (80), (81),
% 204.26/35.09  | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 204.26/35.09  | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 204.26/35.09  | | | | | | |            (103), (107), (109), (112), (133) are inconsistent by
% 204.26/35.09  | | | | | | |            sub-proof #1017.
% 204.26/35.09  | | | | | | | 
% 204.26/35.09  | | | | | | End of split
% 204.26/35.09  | | | | | | 
% 204.26/35.09  | | | | | End of split
% 204.26/35.09  | | | | | 
% 204.26/35.09  | | | | End of split
% 204.26/35.09  | | | | 
% 204.26/35.09  | | | End of split
% 204.26/35.09  | | | 
% 204.26/35.09  | | End of split
% 204.26/35.09  | | 
% 204.26/35.09  | End of split
% 204.26/35.09  | 
% 204.26/35.09  End of proof
% 204.26/35.09  
% 204.26/35.09  Sub-proof #799 shows that the following formulas are inconsistent:
% 204.26/35.09  ----------------------------------------------------------------
% 204.26/35.09    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.09    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.09    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.09    (4)   ~ (e3 = e0)
% 204.26/35.09    (5)  all_58_0 = all_6_2
% 204.26/35.09    (6)  all_58_9 = all_52_25
% 204.26/35.09    (7)  op(e1, e3) = all_52_5
% 204.26/35.09    (8)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.09    (9)   ~ (all_52_3 = e3)
% 204.26/35.09    (10)   ~ (all_52_3 = all_52_27)
% 204.26/35.09    (11)  op(e0, e0) = all_14_2
% 204.26/35.09    (12)  all_58_11 = e3
% 204.26/35.09    (13)  all_58_10 = all_52_27
% 204.26/35.09    (14)  op(all_6_2, e3) = e2
% 204.26/35.09    (15)  all_58_2 = all_52_3
% 204.26/35.09    (16)   ~ (e2 = e0)
% 204.26/35.09    (17)  op(all_52_25, all_52_25) = e3
% 204.26/35.09    (18)  all_58_6 = all_52_5
% 204.26/35.09    (19)   ~ (e1 = e0)
% 204.26/35.09    (20)  all_6_2 = e1
% 204.26/35.09    (21)  all_58_12 = e3
% 204.26/35.09    (22)   ~ (all_14_2 = e3)
% 204.26/35.09  
% 204.26/35.09  Begin of proof
% 204.26/35.09  | 
% 204.26/35.09  | COMBINE_EQS: (5), (20) imply:
% 204.26/35.09  |   (23)  all_58_0 = e1
% 204.26/35.09  | 
% 204.26/35.09  | REDUCE: (14), (20) imply:
% 204.26/35.09  |   (24)  op(e1, e3) = e2
% 204.26/35.09  | 
% 204.26/35.09  | GROUND_INST: instantiating (3) with all_52_5, e2, e3, e1, simplifying with
% 204.26/35.09  |              (7), (24) gives:
% 204.26/35.09  |   (25)  all_52_5 = e2
% 204.26/35.09  | 
% 204.26/35.09  | COMBINE_EQS: (18), (25) imply:
% 204.26/35.09  |   (26)  all_58_6 = e2
% 204.26/35.09  | 
% 204.26/35.10  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (15),
% 204.26/35.10  |            (16), (17), (19), (21), (22), (23), (26) are inconsistent by
% 204.26/35.10  |            sub-proof #800.
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #800 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.10    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (4)  all_58_6 = e2
% 204.26/35.10    (5)   ~ (e3 = e0)
% 204.26/35.10    (6)  all_58_9 = all_52_25
% 204.26/35.10    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.10    (8)   ~ (all_52_3 = e3)
% 204.26/35.10    (9)   ~ (all_52_3 = all_52_27)
% 204.26/35.10    (10)  op(e0, e0) = all_14_2
% 204.26/35.10    (11)  all_58_11 = e3
% 204.26/35.10    (12)  all_58_10 = all_52_27
% 204.26/35.10    (13)  all_58_2 = all_52_3
% 204.26/35.10    (14)   ~ (e2 = e0)
% 204.26/35.10    (15)  op(all_52_25, all_52_25) = e3
% 204.26/35.10    (16)   ~ (e1 = e0)
% 204.26/35.10    (17)  all_58_12 = e3
% 204.26/35.10    (18)  all_58_0 = e1
% 204.26/35.10    (19)   ~ (all_14_2 = e3)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (7) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (20)  all_58_0 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (18), (20) imply:
% 204.26/35.10  | |   (21)  e1 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (16), (21) imply:
% 204.26/35.10  | |   (22)  $false
% 204.26/35.10  | | 
% 204.26/35.10  | | CLOSE: (22) is inconsistent.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (23)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | BETA: splitting (23) gives:
% 204.26/35.10  | | 
% 204.26/35.10  | | Case 1:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (24)  all_58_2 = e0
% 204.26/35.10  | | | 
% 204.26/35.10  | | | COMBINE_EQS: (13), (24) imply:
% 204.26/35.10  | | |   (25)  all_52_3 = e0
% 204.26/35.10  | | | 
% 204.26/35.10  | | | SIMP: (25) implies:
% 204.26/35.10  | | |   (26)  all_52_3 = e0
% 204.26/35.10  | | | 
% 204.26/35.10  | | | REDUCE: (9), (26) imply:
% 204.26/35.10  | | |   (27)   ~ (all_52_27 = e0)
% 204.26/35.10  | | | 
% 204.26/35.10  | | | SIMP: (27) implies:
% 204.26/35.10  | | |   (28)   ~ (all_52_27 = e0)
% 204.26/35.10  | | | 
% 204.26/35.10  | | | REDUCE: (8), (26) imply:
% 204.26/35.10  | | |   (29)   ~ (e3 = e0)
% 204.26/35.10  | | | 
% 204.26/35.10  | | | REDUCE: (2), (26) imply:
% 204.26/35.10  | | |   (30)  op(e0, e0) = all_52_2
% 204.26/35.10  | | | 
% 204.26/35.10  | | | BETA: splitting (1) gives:
% 204.26/35.10  | | | 
% 204.26/35.10  | | | Case 1:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (31)  all_58_9 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | COMBINE_EQS: (6), (31) imply:
% 204.26/35.10  | | | |   (32)  all_52_25 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (15), (32) imply:
% 204.26/35.10  | | | |   (33)  op(e0, e0) = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (3), (10), (19), (30), (33) are inconsistent by sub-proof
% 204.26/35.10  | | | |            #1030.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | Case 2:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (34)  all_58_10 = e0 | all_58_11 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (5), (11), (12), (28), (34) are inconsistent by sub-proof
% 204.26/35.10  | | | |            #802.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | End of split
% 204.26/35.10  | | | 
% 204.26/35.10  | | Case 2:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (35)  all_58_6 = e0 | all_58_12 = e0
% 204.26/35.10  | | | 
% 204.26/35.10  | | | BETA: splitting (35) gives:
% 204.26/35.10  | | | 
% 204.26/35.10  | | | Case 1:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (36)  all_58_6 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (4), (14), (36) are inconsistent by sub-proof #801.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | Case 2:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (37)  all_58_12 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (5), (17), (37) are inconsistent by sub-proof #1212.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | End of split
% 204.26/35.10  | | | 
% 204.26/35.10  | | End of split
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #801 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_58_6 = e2
% 204.26/35.10    (2)  all_58_6 = e0
% 204.26/35.10    (3)   ~ (e2 = e0)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.10  |   (4)  e2 = e0
% 204.26/35.10  | 
% 204.26/35.10  | SIMP: (4) implies:
% 204.26/35.10  |   (5)  e2 = e0
% 204.26/35.10  | 
% 204.26/35.10  | REDUCE: (3), (5) imply:
% 204.26/35.10  |   (6)  $false
% 204.26/35.10  | 
% 204.26/35.10  | CLOSE: (6) is inconsistent.
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #802 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ~ (e3 = e0)
% 204.26/35.10    (2)  all_58_11 = e3
% 204.26/35.10    (3)  all_58_10 = all_52_27
% 204.26/35.10    (4)  all_58_10 = e0 | all_58_11 = e0
% 204.26/35.10    (5)   ~ (all_52_27 = e0)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (4) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (6)  all_58_10 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (3), (6) imply:
% 204.26/35.10  | |   (7)  all_52_27 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (5), (7) imply:
% 204.26/35.10  | |   (8)  $false
% 204.26/35.10  | | 
% 204.26/35.10  | | CLOSE: (8) is inconsistent.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (9)  all_58_11 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (2), (9) imply:
% 204.26/35.10  | |   (10)  e3 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (1), (10) imply:
% 204.26/35.10  | |   (11)  $false
% 204.26/35.10  | | 
% 204.26/35.10  | | CLOSE: (11) is inconsistent.
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #803 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (2)   ~ (e3 = e0)
% 204.26/35.10    (3)   ~ (all_4_2 = e3)
% 204.26/35.10    (4)  all_58_13 = all_52_15
% 204.26/35.10    (5)   ~ (all_52_15 = e3)
% 204.26/35.10    (6)  op(e2, e2) = all_4_2
% 204.26/35.10    (7)   ~ (all_52_3 = e3)
% 204.26/35.10    (8)  all_58_1 = e3
% 204.26/35.10    (9)  all_56_3 = all_14_1
% 204.26/35.10    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.10    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10    (12)  all_58_7 = all_52_13
% 204.26/35.10    (13)  all_58_2 = all_52_3
% 204.26/35.10    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.10    (15)  all_58_9 = all_14_1
% 204.26/35.10    (16)  all_58_0 = e0
% 204.26/35.10    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.10    (18)   ~ (all_52_5 = all_10_2)
% 204.26/35.10    (19)   ~ (all_52_13 = e3)
% 204.26/35.10    (20)  all_58_12 = e2
% 204.26/35.10    (21)  all_58_6 = all_52_5
% 204.26/35.10    (22)  op(all_14_1, all_14_1) = e3
% 204.26/35.10    (23)   ~ (e3 = e2)
% 204.26/35.10    (24)   ~ (all_14_1 = e0)
% 204.26/35.10    (25)  op(e1, e1) = all_10_2
% 204.26/35.10    (26)  all_58_3 = all_4_2
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (14) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (27)  all_58_0 = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (2), (16), (27) are inconsistent by sub-proof #1015.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (28)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | BETA: splitting (28) gives:
% 204.26/35.10  | | 
% 204.26/35.10  | | Case 1:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (29)  all_58_2 = e3
% 204.26/35.10  | | | 
% 204.26/35.10  | | | COMBINE_EQS: (13), (29) imply:
% 204.26/35.10  | | |   (30)  all_52_3 = e3
% 204.26/35.10  | | | 
% 204.26/35.10  | | | REDUCE: (7), (30) imply:
% 204.26/35.10  | | |   (31)  $false
% 204.26/35.10  | | | 
% 204.26/35.10  | | | CLOSE: (31) is inconsistent.
% 204.26/35.10  | | | 
% 204.26/35.10  | | Case 2:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (32)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.10  | | | 
% 204.26/35.10  | | | BETA: splitting (32) gives:
% 204.26/35.10  | | | 
% 204.26/35.10  | | | Case 1:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (33)  all_58_6 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | COMBINE_EQS: (21), (33) imply:
% 204.26/35.10  | | | |   (34)  all_52_5 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (18), (34) imply:
% 204.26/35.10  | | | |   (35)   ~ (all_10_2 = e3)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | SIMP: (35) implies:
% 204.26/35.10  | | | |   (36)   ~ (all_10_2 = e3)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (1), (3), (6), (9), (10), (11), (15), (22), (24), (25), (36)
% 204.26/35.10  | | | |            are inconsistent by sub-proof #804.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | Case 2:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (37)  all_58_12 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | COMBINE_EQS: (20), (37) imply:
% 204.26/35.10  | | | |   (38)  e3 = e2
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | SIMP: (38) implies:
% 204.26/35.10  | | | |   (39)  e3 = e2
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (3), (4), (5), (8), (12), (17), (19), (23), (26), (39) are
% 204.26/35.10  | | | |            inconsistent by sub-proof #1089.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | End of split
% 204.26/35.10  | | | 
% 204.26/35.10  | | End of split
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #804 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (2)   ~ (all_4_2 = e3)
% 204.26/35.10    (3)  op(e2, e2) = all_4_2
% 204.26/35.10    (4)  all_56_3 = all_14_1
% 204.26/35.10    (5)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.10    (6)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10    (7)  all_58_9 = all_14_1
% 204.26/35.10    (8)   ~ (all_10_2 = e3)
% 204.26/35.10    (9)  op(all_14_1, all_14_1) = e3
% 204.26/35.10    (10)   ~ (all_14_1 = e0)
% 204.26/35.10    (11)  op(e1, e1) = all_10_2
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (6) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (12)  all_56_3 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (4), (12) imply:
% 204.26/35.10  | |   (13)  all_14_1 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | SIMP: (13) implies:
% 204.26/35.10  | |   (14)  all_14_1 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (9), (14) imply:
% 204.26/35.10  | |   (15)  op(e2, e2) = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (1), (2), (3), (15) are inconsistent by sub-proof #1318.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (16)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16) are inconsistent
% 204.26/35.10  | |            by sub-proof #805.
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #805 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (2)  all_56_3 = all_14_1
% 204.26/35.10    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.10    (4)  all_58_9 = all_14_1
% 204.26/35.10    (5)   ~ (all_10_2 = e3)
% 204.26/35.10    (6)  op(all_14_1, all_14_1) = e3
% 204.26/35.10    (7)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10    (8)   ~ (all_14_1 = e0)
% 204.26/35.10    (9)  op(e1, e1) = all_10_2
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (3) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (10)  all_58_9 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (4), (10) imply:
% 204.26/35.10  | |   (11)  all_14_1 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (6), (11) imply:
% 204.26/35.10  | |   (12)  op(e1, e1) = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (1), (5), (9), (12) are inconsistent by sub-proof #1368.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (13)   ~ (all_58_9 = e1)
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (4), (13) imply:
% 204.26/35.10  | |   (14)   ~ (all_14_1 = e1)
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (2), (7), (8), (14) are inconsistent by sub-proof #806.
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #806 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10    (2)  all_56_3 = all_14_1
% 204.26/35.10    (3)   ~ (all_14_1 = e1)
% 204.26/35.10    (4)   ~ (all_14_1 = e0)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (1) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (5)  all_56_3 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (2), (5) imply:
% 204.26/35.10  | |   (6)  all_14_1 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (3), (6) imply:
% 204.26/35.10  | |   (7)  $false
% 204.26/35.10  | | 
% 204.26/35.10  | | CLOSE: (7) is inconsistent.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (8)  all_56_3 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (2), (8) imply:
% 204.26/35.10  | |   (9)  all_14_1 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (4), (9) imply:
% 204.26/35.10  | |   (10)  $false
% 204.26/35.10  | | 
% 204.26/35.10  | | CLOSE: (10) is inconsistent.
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #807 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (2)   ~ (all_4_2 = e3)
% 204.26/35.10    (3)  all_58_13 = all_52_15
% 204.26/35.10    (4)   ~ (all_52_15 = e3)
% 204.26/35.10    (5)  op(e2, e2) = all_4_2
% 204.26/35.10    (6)  all_58_4 = all_10_1
% 204.26/35.10    (7)   ~ (all_10_1 = e0)
% 204.26/35.10    (8)  all_58_7 = all_52_13
% 204.26/35.10    (9)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.10    (10)  all_58_9 = all_14_1
% 204.26/35.10    (11)   ~ (e2 = e0)
% 204.26/35.10    (12)  all_58_0 = e0
% 204.26/35.10    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.10    (14)   ~ (all_10_1 = e2)
% 204.26/35.10    (15)  all_56_2 = all_10_1
% 204.26/35.10    (16)   ~ (all_52_13 = e3)
% 204.26/35.10    (17)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.10    (18)  op(all_14_1, all_14_1) = e3
% 204.26/35.10    (19)   ~ (e3 = e2)
% 204.26/35.10    (20)  all_58_3 = all_4_2
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (9) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (21)  all_58_0 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (11), (12), (21) are inconsistent by sub-proof #812.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (22)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | BETA: splitting (22) gives:
% 204.26/35.10  | | 
% 204.26/35.10  | | Case 1:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (23)  all_58_1 = e2
% 204.26/35.10  | | | 
% 204.26/35.10  | | | REF_CLOSE: (2), (3), (4), (8), (13), (16), (19), (20), (23) are
% 204.26/35.10  | | |            inconsistent by sub-proof #1088.
% 204.26/35.10  | | | 
% 204.26/35.10  | | Case 2:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (24)  all_58_4 = e2 | all_58_9 = e2
% 204.26/35.10  | | | 
% 204.26/35.10  | | | BETA: splitting (17) gives:
% 204.26/35.10  | | | 
% 204.26/35.10  | | | Case 1:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (25)  all_56_2 = e2
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (14), (15), (25) are inconsistent by sub-proof #815.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | Case 2:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (26)   ~ (all_56_2 = e2)
% 204.26/35.10  | | | |   (27)  all_56_2 = e1 | all_56_2 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (14), (15), (18), (24), (27)
% 204.26/35.10  | | | |            are inconsistent by sub-proof #808.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | End of split
% 204.26/35.10  | | | 
% 204.26/35.10  | | End of split
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #808 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (2)   ~ (all_4_2 = e3)
% 204.26/35.10    (3)  op(e2, e2) = all_4_2
% 204.26/35.10    (4)  all_58_4 = all_10_1
% 204.26/35.10    (5)   ~ (all_10_1 = e0)
% 204.26/35.10    (6)  all_58_9 = all_14_1
% 204.26/35.10    (7)   ~ (all_10_1 = e2)
% 204.26/35.10    (8)  all_58_4 = e2 | all_58_9 = e2
% 204.26/35.10    (9)  all_56_2 = all_10_1
% 204.26/35.10    (10)  all_56_2 = e1 | all_56_2 = e0
% 204.26/35.10    (11)  op(all_14_1, all_14_1) = e3
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (10) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (12)  all_56_2 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (9), (12) imply:
% 204.26/35.10  | |   (13)  all_10_1 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | SIMP: (13) implies:
% 204.26/35.10  | |   (14)  all_10_1 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (4), (14) imply:
% 204.26/35.10  | |   (15)  all_58_4 = e1
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (7), (14) imply:
% 204.26/35.10  | |   (16)   ~ (e2 = e1)
% 204.26/35.10  | | 
% 204.26/35.10  | | SIMP: (16) implies:
% 204.26/35.10  | |   (17)   ~ (e2 = e1)
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (1), (2), (3), (6), (8), (11), (15), (17) are inconsistent by
% 204.26/35.10  | |            sub-proof #810.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (18)  all_56_2 = e0
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (5), (9), (18) are inconsistent by sub-proof #809.
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #809 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_56_2 = all_10_1
% 204.26/35.10    (2)  all_56_2 = e0
% 204.26/35.10    (3)   ~ (all_10_1 = e0)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.10  |   (4)  all_10_1 = e0
% 204.26/35.10  | 
% 204.26/35.10  | SIMP: (4) implies:
% 204.26/35.10  |   (5)  all_10_1 = e0
% 204.26/35.10  | 
% 204.26/35.10  | REDUCE: (3), (5) imply:
% 204.26/35.10  |   (6)  $false
% 204.26/35.10  | 
% 204.26/35.10  | CLOSE: (6) is inconsistent.
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #810 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (2)  all_58_4 = e1
% 204.26/35.10    (3)   ~ (all_4_2 = e3)
% 204.26/35.10    (4)  op(e2, e2) = all_4_2
% 204.26/35.10    (5)   ~ (e2 = e1)
% 204.26/35.10    (6)  all_58_9 = all_14_1
% 204.26/35.10    (7)  all_58_4 = e2 | all_58_9 = e2
% 204.26/35.10    (8)  op(all_14_1, all_14_1) = e3
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (7) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (9)  all_58_4 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #811.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (10)  all_58_9 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (6), (10) imply:
% 204.26/35.10  | |   (11)  all_14_1 = e2
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (8), (11) imply:
% 204.26/35.10  | |   (12)  op(e2, e2) = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #1318.
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #811 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_58_4 = e2
% 204.26/35.10    (2)  all_58_4 = e1
% 204.26/35.10    (3)   ~ (e2 = e1)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.10  |   (4)  e2 = e1
% 204.26/35.10  | 
% 204.26/35.10  | SIMP: (4) implies:
% 204.26/35.10  |   (5)  e2 = e1
% 204.26/35.10  | 
% 204.26/35.10  | REDUCE: (3), (5) imply:
% 204.26/35.10  |   (6)  $false
% 204.26/35.10  | 
% 204.26/35.10  | CLOSE: (6) is inconsistent.
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #812 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_58_0 = e2
% 204.26/35.10    (2)  all_58_0 = e0
% 204.26/35.10    (3)   ~ (e2 = e0)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.10  |   (4)  e2 = e0
% 204.26/35.10  | 
% 204.26/35.10  | SIMP: (4) implies:
% 204.26/35.10  |   (5)  e2 = e0
% 204.26/35.10  | 
% 204.26/35.10  | REDUCE: (3), (5) imply:
% 204.26/35.10  |   (6)  $false
% 204.26/35.10  | 
% 204.26/35.10  | CLOSE: (6) is inconsistent.
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #813 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_58_14 = all_52_23
% 204.26/35.10    (2)   ~ (e3 = e1)
% 204.26/35.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.10    (4)   ~ (e3 = e0)
% 204.26/35.10    (5)  op(all_52_23, all_52_23) = e0
% 204.26/35.10    (6)   ~ (all_52_17 = all_52_25)
% 204.26/35.10    (7)   ~ (all_4_2 = e3)
% 204.26/35.10    (8)  all_58_0 = all_6_2
% 204.26/35.10    (9)  all_58_13 = all_52_15
% 204.26/35.10    (10)  all_58_9 = all_52_25
% 204.26/35.10    (11)   ~ (all_52_15 = e3)
% 204.26/35.10    (12)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.10    (13)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.10    (14)  op(e2, e2) = all_4_2
% 204.26/35.10    (15)   ~ (all_52_25 = all_14_2)
% 204.26/35.10    (16)  op(all_10_2, e1) = all_10_1
% 204.26/35.10    (17)  all_58_1 = e3
% 204.26/35.10    (18)   ~ (all_52_7 = all_6_2)
% 204.26/35.10    (19)  op(e0, e0) = all_14_2
% 204.26/35.10    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.10    (21)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.10    (22)   ~ (all_6_2 = e3)
% 204.26/35.10    (23)   ~ (e2 = e1)
% 204.26/35.10    (24)  op(all_10_2, all_10_2) = e1
% 204.26/35.10    (25)  all_58_10 = all_52_27
% 204.26/35.10    (26)   ~ (all_52_19 = all_52_23)
% 204.26/35.10    (27)  op(all_6_2, e3) = e2
% 204.26/35.10    (28)  op(all_52_19, all_52_19) = e2
% 204.26/35.10    (29)  all_58_12 = all_52_7
% 204.26/35.10    (30)   ~ (all_52_7 = all_14_2)
% 204.26/35.10    (31)  all_58_2 = all_52_3
% 204.26/35.10    (32)  all_56_2 = all_52_17
% 204.26/35.10    (33)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.10    (34)   ~ (all_52_25 = e3)
% 204.26/35.10    (35)   ~ (e2 = e0)
% 204.26/35.10    (36)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.10    (37)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.10    (38)  op(e3, e3) = all_52_8
% 204.26/35.10    (39)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.10    (40)  op(e3, e1) = all_52_17
% 204.26/35.10    (41)  op(e0, e3) = all_52_7
% 204.26/35.10    (42)  all_58_15 = all_14_2
% 204.26/35.10    (43)   ~ (all_52_19 = all_10_2)
% 204.26/35.10    (44)  all_58_8 = all_10_2
% 204.26/35.10    (45)   ~ (all_52_25 = all_6_2)
% 204.26/35.10    (46)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10    (47)  op(e3, e3) = all_6_2
% 204.26/35.10    (48)   ~ (all_52_27 = all_14_2)
% 204.26/35.10    (49)   ~ (all_52_17 = e3)
% 204.26/35.10    (50)  all_56_3 = all_52_25
% 204.26/35.10    (51)   ~ (all_52_3 = all_52_7)
% 204.26/35.10    (52)  all_58_5 = all_52_19
% 204.26/35.10    (53)   ~ (all_52_27 = all_4_2)
% 204.26/35.10    (54)  op(all_52_17, all_52_17) = e3
% 204.26/35.10    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.10    (56)   ~ (all_52_17 = all_6_2)
% 204.26/35.10    (57)   ~ (e1 = e0)
% 204.26/35.10    (58)  all_56_10 = all_10_2
% 204.26/35.10    (59)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.10    (60)  op(e1, e1) = all_10_2
% 204.26/35.10    (61)   ~ (all_52_23 = all_10_2)
% 204.26/35.10    (62)   ~ (all_52_7 = all_52_23)
% 204.26/35.10    (63)  all_58_3 = all_4_2
% 204.26/35.10    (64)   ~ (all_52_17 = all_52_23)
% 204.26/35.10    (65)  all_58_4 = all_52_17
% 204.26/35.10    (66)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.10    (67)   ~ (all_14_2 = e3)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | BETA: splitting (55) gives:
% 204.26/35.10  | 
% 204.26/35.10  | Case 1:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (68)  all_58_12 = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | COMBINE_EQS: (29), (68) imply:
% 204.26/35.10  | |   (69)  all_52_7 = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | SIMP: (69) implies:
% 204.26/35.10  | |   (70)  all_52_7 = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (51), (70) imply:
% 204.26/35.10  | |   (71)   ~ (all_52_3 = e3)
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (62), (70) imply:
% 204.26/35.10  | |   (72)   ~ (all_52_23 = e3)
% 204.26/35.10  | | 
% 204.26/35.10  | | SIMP: (72) implies:
% 204.26/35.10  | |   (73)   ~ (all_52_23 = e3)
% 204.26/35.10  | | 
% 204.26/35.10  | | REDUCE: (30), (70) imply:
% 204.26/35.10  | |   (74)   ~ (all_14_2 = e3)
% 204.26/35.10  | | 
% 204.26/35.10  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (12), (13), (14), (16), (17),
% 204.26/35.10  | |            (19), (20), (21), (23), (24), (25), (26), (28), (31), (32), (33),
% 204.26/35.10  | |            (35), (36), (38), (40), (43), (44), (47), (48), (49), (52), (53),
% 204.26/35.10  | |            (54), (56), (57), (58), (59), (60), (63), (65), (66), (67), (71),
% 204.26/35.10  | |            (73) are inconsistent by sub-proof #1047.
% 204.26/35.10  | | 
% 204.26/35.10  | Case 2:
% 204.26/35.10  | | 
% 204.26/35.10  | |   (75)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.10  | | 
% 204.26/35.10  | | BETA: splitting (75) gives:
% 204.26/35.10  | | 
% 204.26/35.10  | | Case 1:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (76)  all_58_13 = e3
% 204.26/35.10  | | | 
% 204.26/35.10  | | | REF_CLOSE: (9), (11), (76) are inconsistent by sub-proof #1360.
% 204.26/35.10  | | | 
% 204.26/35.10  | | Case 2:
% 204.26/35.10  | | | 
% 204.26/35.10  | | |   (77)  all_58_14 = e3 | all_58_15 = e3
% 204.26/35.10  | | | 
% 204.26/35.10  | | | BETA: splitting (77) gives:
% 204.26/35.10  | | | 
% 204.26/35.10  | | | Case 1:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (78)  all_58_14 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | COMBINE_EQS: (1), (78) imply:
% 204.26/35.10  | | | |   (79)  all_52_23 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | SIMP: (79) implies:
% 204.26/35.10  | | | |   (80)  all_52_23 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (61), (80) imply:
% 204.26/35.10  | | | |   (81)   ~ (all_10_2 = e3)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | SIMP: (81) implies:
% 204.26/35.10  | | | |   (82)   ~ (all_10_2 = e3)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (5), (80) imply:
% 204.26/35.10  | | | |   (83)  op(e3, e3) = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | GROUND_INST: instantiating (3) with all_6_2, e0, e3, e3, simplifying
% 204.26/35.10  | | | |              with (47), (83) gives:
% 204.26/35.10  | | | |   (84)  all_6_2 = e0
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (18), (84) imply:
% 204.26/35.10  | | | |   (85)   ~ (all_52_7 = e0)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (56), (84) imply:
% 204.26/35.10  | | | |   (86)   ~ (all_52_17 = e0)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (45), (84) imply:
% 204.26/35.10  | | | |   (87)   ~ (all_52_25 = e0)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (22), (84) imply:
% 204.26/35.10  | | | |   (88)   ~ (e3 = e0)
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (27), (84) imply:
% 204.26/35.10  | | | |   (89)  op(e0, e3) = e2
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | BETA: splitting (39) gives:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | Case 1:
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | |   (90)  all_58_12 = e0
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | | REF_CLOSE: (29), (85), (90) are inconsistent by sub-proof #1067.
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | Case 2:
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | |   (91)  all_58_13 = e0 | all_58_14 = e0
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | | BETA: splitting (91) gives:
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | | Case 1:
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | |   (92)  all_58_13 = e0
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | | GROUND_INST: instantiating (3) with all_52_7, e2, e3, e0,
% 204.26/35.10  | | | | | |              simplifying with (41), (89) gives:
% 204.26/35.10  | | | | | |   (93)  all_52_7 = e2
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | | COMBINE_EQS: (29), (93) imply:
% 204.26/35.10  | | | | | |   (94)  all_58_12 = e2
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | | BETA: splitting (37) gives:
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | | Case 1:
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | |   (95)  all_58_12 = e1
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | | REF_CLOSE: (23), (94), (95) are inconsistent by sub-proof #1198.
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | Case 2:
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | |   (96)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | | BETA: splitting (96) gives:
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | | Case 1:
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | |   (97)  all_58_13 = e1
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | | COMBINE_EQS: (92), (97) imply:
% 204.26/35.10  | | | | | | | |   (98)  e1 = e0
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | | REDUCE: (57), (98) imply:
% 204.26/35.10  | | | | | | | |   (99)  $false
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | | CLOSE: (99) is inconsistent.
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | Case 2:
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | |   (100)  all_58_14 = e1 | all_58_15 = e1
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | | BETA: splitting (100) gives:
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | | Case 1:
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | |   (101)  all_58_14 = e1
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | REF_CLOSE: (2), (78), (101) are inconsistent by sub-proof
% 204.26/35.10  | | | | | | | | |            #814.
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | Case 2:
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | |   (102)  all_58_15 = e1
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | COMBINE_EQS: (42), (102) imply:
% 204.26/35.10  | | | | | | | | |   (103)  all_14_2 = e1
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | REDUCE: (15), (103) imply:
% 204.26/35.10  | | | | | | | | |   (104)   ~ (all_52_25 = e1)
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | BETA: splitting (46) gives:
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | Case 1:
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | |   (105)  all_56_3 = e3
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | | COMBINE_EQS: (50), (105) imply:
% 204.26/35.10  | | | | | | | | | |   (106)  all_52_25 = e3
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | | REDUCE: (34), (106) imply:
% 204.26/35.10  | | | | | | | | | |   (107)  $false
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | | CLOSE: (107) is inconsistent.
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | Case 2:
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | |   (108)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | | REF_CLOSE: (3), (6), (21), (32), (49), (50), (54), (60),
% 204.26/35.10  | | | | | | | | | |            (82), (86), (87), (104), (108) are inconsistent by
% 204.26/35.10  | | | | | | | | | |            sub-proof #827.
% 204.26/35.10  | | | | | | | | | | 
% 204.26/35.10  | | | | | | | | | End of split
% 204.26/35.10  | | | | | | | | | 
% 204.26/35.10  | | | | | | | | End of split
% 204.26/35.10  | | | | | | | | 
% 204.26/35.10  | | | | | | | End of split
% 204.26/35.10  | | | | | | | 
% 204.26/35.10  | | | | | | End of split
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | Case 2:
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | |   (109)  all_58_14 = e0
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | | REF_CLOSE: (4), (78), (109) are inconsistent by sub-proof #1151.
% 204.26/35.10  | | | | | | 
% 204.26/35.10  | | | | | End of split
% 204.26/35.10  | | | | | 
% 204.26/35.10  | | | | End of split
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | Case 2:
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | |   (110)  all_58_15 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | COMBINE_EQS: (42), (110) imply:
% 204.26/35.10  | | | |   (111)  all_14_2 = e3
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | REDUCE: (67), (111) imply:
% 204.26/35.10  | | | |   (112)  $false
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | | CLOSE: (112) is inconsistent.
% 204.26/35.10  | | | | 
% 204.26/35.10  | | | End of split
% 204.26/35.10  | | | 
% 204.26/35.10  | | End of split
% 204.26/35.10  | | 
% 204.26/35.10  | End of split
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #814 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_58_14 = e3
% 204.26/35.10    (2)  all_58_14 = e1
% 204.26/35.10    (3)   ~ (e3 = e1)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.10  |   (4)  e3 = e1
% 204.26/35.10  | 
% 204.26/35.10  | SIMP: (4) implies:
% 204.26/35.10  |   (5)  e3 = e1
% 204.26/35.10  | 
% 204.26/35.10  | REDUCE: (3), (5) imply:
% 204.26/35.10  |   (6)  $false
% 204.26/35.10  | 
% 204.26/35.10  | CLOSE: (6) is inconsistent.
% 204.26/35.10  | 
% 204.26/35.10  End of proof
% 204.26/35.10  
% 204.26/35.10  Sub-proof #815 shows that the following formulas are inconsistent:
% 204.26/35.10  ----------------------------------------------------------------
% 204.26/35.10    (1)  all_56_2 = all_10_1
% 204.26/35.10    (2)  all_56_2 = e2
% 204.26/35.10    (3)   ~ (all_10_1 = e2)
% 204.26/35.10  
% 204.26/35.10  Begin of proof
% 204.26/35.10  | 
% 204.26/35.10  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.10  |   (4)  all_10_1 = e2
% 204.26/35.10  | 
% 204.26/35.11  | SIMP: (4) implies:
% 204.26/35.11  |   (5)  all_10_1 = e2
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (3), (5) imply:
% 204.26/35.11  |   (6)  $false
% 204.26/35.11  | 
% 204.26/35.11  | CLOSE: (6) is inconsistent.
% 204.26/35.11  | 
% 204.26/35.11  End of proof
% 204.26/35.11  
% 204.26/35.11  Sub-proof #816 shows that the following formulas are inconsistent:
% 204.26/35.11  ----------------------------------------------------------------
% 204.26/35.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.11    (2)  op(e2, e3) = all_52_3
% 204.26/35.11    (3)   ~ (all_4_2 = e3)
% 204.26/35.11    (4)   ~ (all_52_3 = all_6_2)
% 204.26/35.11    (5)   ~ (all_52_3 = e3)
% 204.26/35.11    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.11    (7)  all_58_10 = all_52_27
% 204.26/35.11    (8)  op(all_6_2, e3) = e2
% 204.26/35.11    (9)  op(all_52_19, all_52_19) = e2
% 204.26/35.11    (10)  all_58_2 = all_52_3
% 204.26/35.11    (11)   ~ (all_52_27 = e3)
% 204.26/35.11    (12)  op(e3, e3) = all_52_4
% 204.26/35.11    (13)  op(e3, e3) = all_6_2
% 204.26/35.11    (14)  all_58_5 = all_52_19
% 204.26/35.11    (15)  all_58_3 = all_4_2
% 204.26/35.11  
% 204.26/35.11  Begin of proof
% 204.26/35.11  | 
% 204.26/35.11  | BETA: splitting (6) gives:
% 204.26/35.11  | 
% 204.26/35.11  | Case 1:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (16)  all_58_2 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | REF_CLOSE: (5), (10), (16) are inconsistent by sub-proof #1369.
% 204.26/35.11  | | 
% 204.26/35.11  | Case 2:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (17)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (13), (14), (15),
% 204.26/35.11  | |            (17) are inconsistent by sub-proof #817.
% 204.26/35.11  | | 
% 204.26/35.11  | End of split
% 204.26/35.11  | 
% 204.26/35.11  End of proof
% 204.26/35.11  
% 204.26/35.11  Sub-proof #817 shows that the following formulas are inconsistent:
% 204.26/35.11  ----------------------------------------------------------------
% 204.26/35.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.11    (2)  op(e2, e3) = all_52_3
% 204.26/35.11    (3)   ~ (all_4_2 = e3)
% 204.26/35.11    (4)   ~ (all_52_3 = all_6_2)
% 204.26/35.11    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.11    (6)  all_58_10 = all_52_27
% 204.26/35.11    (7)  op(all_6_2, e3) = e2
% 204.26/35.11    (8)  op(all_52_19, all_52_19) = e2
% 204.26/35.11    (9)   ~ (all_52_27 = e3)
% 204.26/35.11    (10)  op(e3, e3) = all_52_4
% 204.26/35.11    (11)  op(e3, e3) = all_6_2
% 204.26/35.11    (12)  all_58_5 = all_52_19
% 204.26/35.11    (13)  all_58_3 = all_4_2
% 204.26/35.11  
% 204.26/35.11  Begin of proof
% 204.26/35.11  | 
% 204.26/35.11  | BETA: splitting (5) gives:
% 204.26/35.11  | 
% 204.26/35.11  | Case 1:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (14)  all_58_3 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | COMBINE_EQS: (13), (14) imply:
% 204.26/35.11  | |   (15)  all_4_2 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (3), (15) imply:
% 204.26/35.11  | |   (16)  $false
% 204.26/35.11  | | 
% 204.26/35.11  | | CLOSE: (16) is inconsistent.
% 204.26/35.11  | | 
% 204.26/35.11  | Case 2:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (17)  all_58_5 = e3 | all_58_10 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | BETA: splitting (17) gives:
% 204.26/35.11  | | 
% 204.26/35.11  | | Case 1:
% 204.26/35.11  | | | 
% 204.26/35.11  | | |   (18)  all_58_5 = e3
% 204.26/35.11  | | | 
% 204.26/35.11  | | | COMBINE_EQS: (12), (18) imply:
% 204.26/35.11  | | |   (19)  all_52_19 = e3
% 204.26/35.11  | | | 
% 204.26/35.11  | | | SIMP: (19) implies:
% 204.26/35.11  | | |   (20)  all_52_19 = e3
% 204.26/35.11  | | | 
% 204.26/35.11  | | | REDUCE: (8), (20) imply:
% 204.26/35.11  | | |   (21)  op(e3, e3) = e2
% 204.26/35.11  | | | 
% 204.26/35.11  | | | REF_CLOSE: (1), (2), (4), (7), (10), (11), (21) are inconsistent by
% 204.26/35.11  | | |            sub-proof #832.
% 204.26/35.11  | | | 
% 204.26/35.11  | | Case 2:
% 204.26/35.11  | | | 
% 204.26/35.11  | | |   (22)  all_58_10 = e3
% 204.26/35.11  | | | 
% 204.26/35.11  | | | REF_CLOSE: (6), (9), (22) are inconsistent by sub-proof #1301.
% 204.26/35.11  | | | 
% 204.26/35.11  | | End of split
% 204.26/35.11  | | 
% 204.26/35.11  | End of split
% 204.26/35.11  | 
% 204.26/35.11  End of proof
% 204.26/35.11  
% 204.26/35.11  Sub-proof #818 shows that the following formulas are inconsistent:
% 204.26/35.11  ----------------------------------------------------------------
% 204.26/35.11    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.11    (2)   ~ (all_52_25 = all_6_0)
% 204.26/35.11    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.11    (4)  all_58_14 = all_52_23
% 204.26/35.11    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.11    (7)  all_58_1 = all_52_9
% 204.26/35.11    (8)  op(e2, e3) = all_52_3
% 204.26/35.11    (9)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.11    (10)   ~ (all_52_17 = all_52_25)
% 204.26/35.11    (11)   ~ (all_52_3 = all_6_2)
% 204.26/35.11    (12)  all_58_0 = all_6_2
% 204.26/35.11    (13)  op(all_14_2, e0) = all_14_1
% 204.26/35.11    (14)   ~ (all_52_17 = all_10_2)
% 204.26/35.11    (15)  op(e0, all_14_1) = all_14_0
% 204.26/35.11    (16)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.11    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.11    (18)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.11    (19)  all_58_13 = all_52_15
% 204.26/35.11    (20)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.11    (21)  all_58_9 = all_52_25
% 204.26/35.11    (22)   ~ (all_52_29 = all_14_2)
% 204.26/35.11    (23)  all_22_0 = all_6_0
% 204.26/35.11    (24)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.11    (25)   ~ (all_52_17 = all_6_0)
% 204.26/35.11    (26)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.11    (27)  op(e2, e2) = all_4_2
% 204.26/35.11    (28)  all_58_11 = all_52_29
% 204.26/35.11    (29)   ~ (all_52_25 = all_14_2)
% 204.26/35.11    (30)  op(all_10_2, e1) = all_10_1
% 204.26/35.11    (31)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.11    (32)  op(e0, e0) = all_14_2
% 204.26/35.11    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.11    (34)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.11    (35)  all_58_15 = e0
% 204.26/35.11    (36)  all_56_11 = all_52_29
% 204.26/35.11    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.11    (38)   ~ (e2 = e1)
% 204.26/35.11    (39)   ~ (all_6_0 = e1)
% 204.26/35.11    (40)  all_58_10 = all_52_27
% 204.26/35.11    (41)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.11    (42)   ~ (all_52_19 = all_52_23)
% 204.26/35.11    (43)   ~ (all_52_25 = all_52_29)
% 204.26/35.11    (44)  op(all_6_2, e3) = e2
% 204.26/35.11    (45)   ~ (all_52_29 = all_10_2)
% 204.26/35.11    (46)  all_58_7 = all_52_13
% 204.26/35.11    (47)  all_58_1 = all_6_0
% 204.26/35.11    (48)  all_58_12 = all_52_7
% 204.26/35.11    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.11    (50)   ~ (all_52_7 = all_14_2)
% 204.26/35.11    (51)  all_58_2 = all_52_3
% 204.26/35.11    (52)  all_56_2 = all_52_17
% 204.26/35.11    (53)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.11    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.11    (55)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.11    (56)   ~ (all_14_0 = e3)
% 204.26/35.11    (57)  all_56_7 = all_52_27
% 204.26/35.11    (58)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.26/35.11    (59)  op(all_6_0, all_6_0) = all_52_8
% 204.26/35.11    (60)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.11    (61)   ~ (all_52_5 = all_52_29)
% 204.26/35.11    (62)   ~ (all_52_13 = all_6_0)
% 204.26/35.11    (63)   ~ (all_52_19 = all_52_27)
% 204.26/35.11    (64)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.11    (65)   ~ (all_6_0 = e2)
% 204.26/35.11    (66)  op(e3, e1) = all_52_17
% 204.26/35.11    (67)  op(e0, e3) = all_52_7
% 204.26/35.11    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.11    (69)  all_58_15 = all_14_2
% 204.26/35.11    (70)   ~ (all_52_19 = all_10_2)
% 204.26/35.11    (71)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.11    (72)  all_58_8 = all_10_2
% 204.26/35.11    (73)   ~ (all_52_5 = all_10_2)
% 204.26/35.11    (74)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.11    (75)   ~ (all_52_23 = all_14_2)
% 204.26/35.11    (76)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.11    (77)   ~ (all_52_25 = all_6_2)
% 204.26/35.11    (78)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.11    (79)   ~ (all_52_9 = all_6_2)
% 204.26/35.11    (80)  all_56_0 = all_6_2
% 204.26/35.11    (81)  op(e3, e3) = all_6_2
% 204.26/35.11    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.11    (83)   ~ (all_52_15 = all_6_0)
% 204.26/35.11    (84)  all_56_3 = all_52_25
% 204.26/35.11    (85)   ~ (all_52_3 = all_52_7)
% 204.26/35.11    (86)   ~ (all_6_0 = all_6_2)
% 204.26/35.11    (87)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.11    (88)  all_58_5 = all_52_19
% 204.26/35.11    (89)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.11          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.11          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.11          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.11    (90)  all_58_6 = all_52_5
% 204.26/35.11    (91)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.11    (92)   ~ (all_52_17 = all_6_2)
% 204.26/35.11    (93)   ~ (e3 = e2)
% 204.26/35.11    (94)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.11    (95)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.11    (96)  all_56_1 = all_6_0
% 204.26/35.11    (97)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.11    (98)   ~ (all_6_0 = all_4_2)
% 204.26/35.11    (99)  op(e1, e1) = all_10_2
% 204.26/35.11    (100)   ~ (all_52_23 = all_10_2)
% 204.26/35.11    (101)   ~ (all_52_7 = all_52_23)
% 204.26/35.11    (102)   ~ (all_52_17 = all_52_19)
% 204.26/35.11    (103)  all_58_3 = all_4_2
% 204.26/35.11    (104)   ~ (all_52_3 = all_4_2)
% 204.26/35.11    (105)   ~ (all_52_19 = all_4_2)
% 204.26/35.11    (106)   ~ (all_52_17 = all_52_23)
% 204.26/35.11    (107)  all_22_2 = all_6_2
% 204.26/35.11    (108)  all_58_4 = all_52_17
% 204.26/35.11    (109)   ~ (all_14_0 = e1)
% 204.26/35.11    (110)   ~ (all_14_0 = e2)
% 204.26/35.11    (111)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.11  
% 204.26/35.11  Begin of proof
% 204.26/35.11  | 
% 204.26/35.11  | COMBINE_EQS: (35), (69) imply:
% 204.26/35.11  |   (112)  all_14_2 = e0
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (50), (112) imply:
% 204.26/35.11  |   (113)   ~ (all_52_7 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (75), (112) imply:
% 204.26/35.11  |   (114)   ~ (all_52_23 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (29), (112) imply:
% 204.26/35.11  |   (115)   ~ (all_52_25 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (87), (112) imply:
% 204.26/35.11  |   (116)  op(e0, e0) = all_52_30
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (13), (112) imply:
% 204.26/35.11  |   (117)  op(e0, e0) = all_14_1
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (32), (112) imply:
% 204.26/35.11  |   (118)  op(e0, e0) = e0
% 204.26/35.11  | 
% 204.26/35.11  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.26/35.11  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 204.26/35.11  |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 204.26/35.11  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 204.26/35.11  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 204.26/35.11  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 204.26/35.11  |            (71), (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 204.26/35.11  |            (83), (84), (85), (86), (88), (89), (90), (91), (92), (93), (94),
% 204.26/35.11  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 204.26/35.11  |            (105), (106), (107), (108), (109), (110), (111), (113), (114),
% 204.26/35.11  |            (115), (116), (117), (118) are inconsistent by sub-proof #819.
% 204.26/35.11  | 
% 204.26/35.11  End of proof
% 204.26/35.11  
% 204.26/35.11  Sub-proof #819 shows that the following formulas are inconsistent:
% 204.26/35.11  ----------------------------------------------------------------
% 204.26/35.11    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.11    (2)   ~ (all_52_25 = all_6_0)
% 204.26/35.11    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.11    (4)  all_58_14 = all_52_23
% 204.26/35.11    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.11    (7)  all_58_1 = all_52_9
% 204.26/35.11    (8)  op(e2, e3) = all_52_3
% 204.26/35.11    (9)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.11    (10)   ~ (all_52_17 = all_52_25)
% 204.26/35.11    (11)   ~ (all_52_3 = all_6_2)
% 204.26/35.11    (12)  all_58_0 = all_6_2
% 204.26/35.11    (13)   ~ (all_52_17 = all_10_2)
% 204.26/35.11    (14)  op(e0, all_14_1) = all_14_0
% 204.26/35.11    (15)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.11    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.11    (17)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.11    (18)  all_58_13 = all_52_15
% 204.26/35.11    (19)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.11    (20)  all_58_9 = all_52_25
% 204.26/35.11    (21)   ~ (all_52_29 = all_14_2)
% 204.26/35.11    (22)  all_22_0 = all_6_0
% 204.26/35.11    (23)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.11    (24)  op(e0, e0) = all_52_30
% 204.26/35.11    (25)   ~ (all_52_17 = all_6_0)
% 204.26/35.11    (26)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.11    (27)  op(e2, e2) = all_4_2
% 204.26/35.11    (28)  all_58_11 = all_52_29
% 204.26/35.11    (29)  op(all_10_2, e1) = all_10_1
% 204.26/35.11    (30)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.11    (31)  op(e0, e0) = all_14_2
% 204.26/35.11    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.11    (33)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.11    (34)  all_58_15 = e0
% 204.26/35.11    (35)  all_56_11 = all_52_29
% 204.26/35.11    (36)   ~ (all_52_25 = e0)
% 204.26/35.11    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.11    (38)   ~ (e2 = e1)
% 204.26/35.11    (39)  op(e0, e0) = e0
% 204.26/35.11    (40)   ~ (all_6_0 = e1)
% 204.26/35.11    (41)  all_58_10 = all_52_27
% 204.26/35.11    (42)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.11    (43)   ~ (all_52_19 = all_52_23)
% 204.26/35.11    (44)   ~ (all_52_25 = all_52_29)
% 204.26/35.11    (45)  op(all_6_2, e3) = e2
% 204.26/35.11    (46)   ~ (all_52_29 = all_10_2)
% 204.26/35.11    (47)  all_58_7 = all_52_13
% 204.26/35.11    (48)  all_58_1 = all_6_0
% 204.26/35.11    (49)  all_58_12 = all_52_7
% 204.26/35.11    (50)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.11    (51)   ~ (all_52_7 = all_14_2)
% 204.26/35.11    (52)  all_58_2 = all_52_3
% 204.26/35.11    (53)  all_56_2 = all_52_17
% 204.26/35.11    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.11    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.11    (56)  op(e0, e0) = all_14_1
% 204.26/35.11    (57)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.11    (58)   ~ (all_14_0 = e3)
% 204.26/35.11    (59)  all_56_7 = all_52_27
% 204.26/35.11    (60)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.26/35.11    (61)  op(all_6_0, all_6_0) = all_52_8
% 204.26/35.11    (62)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.11    (63)   ~ (all_52_5 = all_52_29)
% 204.26/35.11    (64)   ~ (all_52_13 = all_6_0)
% 204.26/35.11    (65)   ~ (all_52_19 = all_52_27)
% 204.26/35.11    (66)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.11    (67)   ~ (all_6_0 = e2)
% 204.26/35.11    (68)  op(e3, e1) = all_52_17
% 204.26/35.11    (69)  op(e0, e3) = all_52_7
% 204.26/35.11    (70)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.11    (71)   ~ (all_52_19 = all_10_2)
% 204.26/35.11    (72)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.11    (73)  all_58_8 = all_10_2
% 204.26/35.11    (74)   ~ (all_52_23 = e0)
% 204.26/35.11    (75)   ~ (all_52_5 = all_10_2)
% 204.26/35.11    (76)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.11    (77)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.11    (78)   ~ (all_52_25 = all_6_2)
% 204.26/35.11    (79)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.11    (80)   ~ (all_52_9 = all_6_2)
% 204.26/35.11    (81)  all_56_0 = all_6_2
% 204.26/35.11    (82)  op(e3, e3) = all_6_2
% 204.26/35.11    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.11    (84)   ~ (all_52_15 = all_6_0)
% 204.26/35.11    (85)  all_56_3 = all_52_25
% 204.26/35.11    (86)   ~ (all_52_3 = all_52_7)
% 204.26/35.11    (87)   ~ (all_6_0 = all_6_2)
% 204.26/35.11    (88)  all_58_5 = all_52_19
% 204.26/35.11    (89)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.11          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.11          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.11          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.11    (90)  all_58_6 = all_52_5
% 204.26/35.11    (91)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.11    (92)   ~ (all_52_17 = all_6_2)
% 204.26/35.11    (93)   ~ (e3 = e2)
% 204.26/35.11    (94)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.11    (95)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.11    (96)  all_56_1 = all_6_0
% 204.26/35.11    (97)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.11    (98)   ~ (all_6_0 = all_4_2)
% 204.26/35.11    (99)  op(e1, e1) = all_10_2
% 204.26/35.11    (100)   ~ (all_52_23 = all_10_2)
% 204.26/35.11    (101)   ~ (all_52_7 = all_52_23)
% 204.26/35.11    (102)   ~ (all_52_17 = all_52_19)
% 204.26/35.11    (103)  all_58_3 = all_4_2
% 204.26/35.11    (104)   ~ (all_52_3 = all_4_2)
% 204.26/35.11    (105)   ~ (all_52_19 = all_4_2)
% 204.26/35.11    (106)   ~ (all_52_17 = all_52_23)
% 204.26/35.11    (107)  all_22_2 = all_6_2
% 204.26/35.11    (108)  all_58_4 = all_52_17
% 204.26/35.11    (109)   ~ (all_14_0 = e1)
% 204.26/35.11    (110)   ~ (all_14_0 = e2)
% 204.26/35.11    (111)   ~ (all_52_7 = e0)
% 204.26/35.11    (112)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.11  
% 204.26/35.11  Begin of proof
% 204.26/35.11  | 
% 204.26/35.11  | GROUND_INST: instantiating (6) with all_14_1, all_52_30, e0, e0, simplifying
% 204.26/35.11  |              with (24), (56) gives:
% 204.26/35.11  |   (113)  all_52_30 = all_14_1
% 204.26/35.11  | 
% 204.26/35.11  | GROUND_INST: instantiating (6) with e0, all_52_30, e0, e0, simplifying with
% 204.26/35.11  |              (24), (39) gives:
% 204.26/35.11  |   (114)  all_52_30 = e0
% 204.26/35.11  | 
% 204.26/35.11  | COMBINE_EQS: (113), (114) imply:
% 204.26/35.11  |   (115)  all_14_1 = e0
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (14), (115) imply:
% 204.26/35.11  |   (116)  op(e0, e0) = all_14_0
% 204.26/35.11  | 
% 204.26/35.11  | GROUND_INST: instantiating (6) with e0, all_14_0, e0, e0, simplifying with
% 204.26/35.11  |              (39), (116) gives:
% 204.26/35.11  |   (117)  all_14_0 = e0
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (58), (117) imply:
% 204.26/35.11  |   (118)   ~ (e3 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | SIMP: (118) implies:
% 204.26/35.11  |   (119)   ~ (e3 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (110), (117) imply:
% 204.26/35.11  |   (120)   ~ (e2 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | SIMP: (120) implies:
% 204.26/35.11  |   (121)   ~ (e2 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | REDUCE: (109), (117) imply:
% 204.26/35.11  |   (122)   ~ (e1 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | SIMP: (122) implies:
% 204.26/35.11  |   (123)   ~ (e1 = e0)
% 204.26/35.11  | 
% 204.26/35.11  | BETA: splitting (94) gives:
% 204.26/35.11  | 
% 204.26/35.11  | Case 1:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (124)  all_56_1 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | COMBINE_EQS: (96), (124) imply:
% 204.26/35.11  | |   (125)  all_6_0 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | COMBINE_EQS: (48), (125) imply:
% 204.26/35.11  | |   (126)  all_58_1 = e3
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (64), (125) imply:
% 204.26/35.11  | |   (127)   ~ (all_52_13 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (84), (125) imply:
% 204.26/35.11  | |   (128)   ~ (all_52_15 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (25), (125) imply:
% 204.26/35.11  | |   (129)   ~ (all_52_17 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (2), (125) imply:
% 204.26/35.11  | |   (130)   ~ (all_52_25 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (87), (125) imply:
% 204.26/35.11  | |   (131)   ~ (all_6_2 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | SIMP: (131) implies:
% 204.26/35.11  | |   (132)   ~ (all_6_2 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (98), (125) imply:
% 204.26/35.11  | |   (133)   ~ (all_4_2 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | SIMP: (133) implies:
% 204.26/35.11  | |   (134)   ~ (all_4_2 = e3)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (40), (125) imply:
% 204.26/35.11  | |   (135)   ~ (e3 = e1)
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (61), (125) imply:
% 204.26/35.11  | |   (136)  op(e3, e3) = all_52_8
% 204.26/35.11  | | 
% 204.26/35.11  | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3, simplifying
% 204.26/35.11  | |              with (82), (136) gives:
% 204.26/35.11  | |   (137)  all_52_8 = all_6_2
% 204.26/35.11  | | 
% 204.26/35.11  | | BETA: splitting (89) gives:
% 204.26/35.11  | | 
% 204.26/35.11  | | Case 1:
% 204.26/35.11  | | | 
% 204.26/35.11  | | |   (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.11  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.26/35.11  | | |            e0)
% 204.26/35.11  | | | 
% 204.26/35.11  | | | BETA: splitting (138) gives:
% 204.26/35.11  | | | 
% 204.26/35.11  | | | Case 1:
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | |   (139)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | REF_CLOSE: (5), (6), (9), (12), (15), (27), (30), (31), (32), (49),
% 204.26/35.11  | | | |            (51), (52), (55), (75), (82), (90), (91), (99), (104), (132),
% 204.26/35.11  | | | |            (139) are inconsistent by sub-proof #835.
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | Case 2:
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | |   (140)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.26/35.11  | | | |          e0
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | REF_CLOSE: (132), (137), (140) are inconsistent by sub-proof #834.
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | End of split
% 204.26/35.11  | | | 
% 204.26/35.11  | | Case 2:
% 204.26/35.11  | | | 
% 204.26/35.11  | | |   (141)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.26/35.11  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.26/35.11  | | |            all_52_30 = e0)
% 204.26/35.11  | | | 
% 204.26/35.11  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.26/35.11  | | |            (15), (16), (17), (18), (19), (20), (21), (23), (26), (27),
% 204.26/35.11  | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 204.26/35.11  | | |            (38), (39), (41), (42), (43), (44), (45), (46), (47), (49),
% 204.26/35.11  | | |            (50), (52), (53), (54), (55), (57), (59), (62), (63), (65),
% 204.26/35.11  | | |            (66), (68), (69), (70), (71), (72), (73), (74), (76), (77),
% 204.26/35.11  | | |            (78), (79), (80), (82), (83), (85), (86), (88), (90), (91),
% 204.26/35.11  | | |            (92), (95), (99), (100), (101), (102), (103), (104), (105),
% 204.26/35.11  | | |            (106), (108), (111), (112), (119), (121), (123), (126), (127),
% 204.26/35.11  | | |            (128), (129), (130), (134), (135), (136), (141) are
% 204.26/35.11  | | |            inconsistent by sub-proof #822.
% 204.26/35.11  | | | 
% 204.26/35.11  | | End of split
% 204.26/35.11  | | 
% 204.26/35.11  | Case 2:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (142)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.11  | | 
% 204.26/35.11  | | REF_CLOSE: (6), (8), (11), (22), (30), (40), (45), (60), (67), (81), (82),
% 204.26/35.11  | |            (87), (93), (96), (97), (107), (142) are inconsistent by
% 204.26/35.11  | |            sub-proof #820.
% 204.26/35.11  | | 
% 204.26/35.11  | End of split
% 204.26/35.11  | 
% 204.26/35.11  End of proof
% 204.26/35.11  
% 204.26/35.11  Sub-proof #820 shows that the following formulas are inconsistent:
% 204.26/35.11  ----------------------------------------------------------------
% 204.26/35.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.11    (2)  op(e2, e3) = all_52_3
% 204.26/35.11    (3)   ~ (all_52_3 = all_6_2)
% 204.26/35.11    (4)  all_22_0 = all_6_0
% 204.26/35.11    (5)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.11    (6)   ~ (all_6_0 = e1)
% 204.26/35.11    (7)  op(all_6_2, e3) = e2
% 204.26/35.11    (8)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e1)
% 204.26/35.11    (9)   ~ (all_6_0 = e2)
% 204.26/35.11    (10)  all_56_0 = all_6_2
% 204.26/35.11    (11)  op(e3, e3) = all_6_2
% 204.26/35.11    (12)   ~ (all_6_0 = all_6_2)
% 204.26/35.11    (13)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.11    (14)   ~ (e3 = e2)
% 204.26/35.11    (15)  all_56_1 = all_6_0
% 204.26/35.11    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.11    (17)  all_22_2 = all_6_2
% 204.26/35.11  
% 204.26/35.11  Begin of proof
% 204.26/35.11  | 
% 204.26/35.11  | BETA: splitting (13) gives:
% 204.26/35.11  | 
% 204.26/35.11  | Case 1:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (18)  all_56_1 = e2
% 204.26/35.11  | | 
% 204.26/35.11  | | COMBINE_EQS: (15), (18) imply:
% 204.26/35.11  | |   (19)  all_6_0 = e2
% 204.26/35.11  | | 
% 204.26/35.11  | | SIMP: (19) implies:
% 204.26/35.11  | |   (20)  all_6_0 = e2
% 204.26/35.11  | | 
% 204.26/35.11  | | REDUCE: (9), (20) imply:
% 204.26/35.11  | |   (21)  $false
% 204.26/35.11  | | 
% 204.26/35.11  | | CLOSE: (21) is inconsistent.
% 204.26/35.11  | | 
% 204.26/35.11  | Case 2:
% 204.26/35.11  | | 
% 204.26/35.11  | |   (22)  all_56_1 = e1 | all_56_1 = e0
% 204.26/35.11  | | 
% 204.26/35.11  | | BETA: splitting (22) gives:
% 204.26/35.11  | | 
% 204.26/35.11  | | Case 1:
% 204.26/35.11  | | | 
% 204.26/35.11  | | |   (23)  all_56_1 = e1
% 204.26/35.11  | | | 
% 204.26/35.11  | | | COMBINE_EQS: (15), (23) imply:
% 204.26/35.11  | | |   (24)  all_6_0 = e1
% 204.26/35.11  | | | 
% 204.26/35.11  | | | SIMP: (24) implies:
% 204.26/35.11  | | |   (25)  all_6_0 = e1
% 204.26/35.11  | | | 
% 204.26/35.11  | | | REDUCE: (6), (25) imply:
% 204.26/35.11  | | |   (26)  $false
% 204.26/35.11  | | | 
% 204.26/35.11  | | | CLOSE: (26) is inconsistent.
% 204.26/35.11  | | | 
% 204.26/35.11  | | Case 2:
% 204.26/35.11  | | | 
% 204.26/35.11  | | |   (27)  all_56_1 = e0
% 204.26/35.11  | | | 
% 204.26/35.11  | | | COMBINE_EQS: (15), (27) imply:
% 204.26/35.11  | | |   (28)  all_6_0 = e0
% 204.26/35.11  | | | 
% 204.26/35.11  | | | SIMP: (28) implies:
% 204.26/35.11  | | |   (29)  all_6_0 = e0
% 204.26/35.11  | | | 
% 204.26/35.11  | | | COMBINE_EQS: (4), (29) imply:
% 204.26/35.11  | | |   (30)  all_22_0 = e0
% 204.26/35.11  | | | 
% 204.26/35.11  | | | REDUCE: (12), (29) imply:
% 204.26/35.11  | | |   (31)   ~ (all_6_2 = e0)
% 204.26/35.11  | | | 
% 204.26/35.11  | | | SIMP: (31) implies:
% 204.26/35.11  | | |   (32)   ~ (all_6_2 = e0)
% 204.26/35.11  | | | 
% 204.26/35.11  | | | BETA: splitting (8) gives:
% 204.26/35.11  | | | 
% 204.26/35.11  | | | Case 1:
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | |   (33)   ~ (all_22_2 = e1)
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | REDUCE: (17), (33) imply:
% 204.26/35.11  | | | |   (34)   ~ (all_6_2 = e1)
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | BETA: splitting (16) gives:
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | Case 1:
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | |   (35)  all_56_0 = e3
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | COMBINE_EQS: (10), (35) imply:
% 204.26/35.11  | | | | |   (36)  all_6_2 = e3
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | SIMP: (36) implies:
% 204.26/35.11  | | | | |   (37)  all_6_2 = e3
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | REDUCE: (5), (37) imply:
% 204.26/35.11  | | | | |   (38)  op(e3, e3) = all_52_0
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | REDUCE: (7), (37) imply:
% 204.26/35.11  | | | | |   (39)  op(e3, e3) = e2
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | REDUCE: (11), (37) imply:
% 204.26/35.11  | | | | |   (40)  op(e3, e3) = e3
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | REF_CLOSE: (1), (14), (38), (39), (40) are inconsistent by sub-proof
% 204.26/35.11  | | | | |            #821.
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | Case 2:
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | |   (41)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | BETA: splitting (41) gives:
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | | Case 1:
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | |   (42)  all_56_0 = e2
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | | COMBINE_EQS: (10), (42) imply:
% 204.26/35.11  | | | | | |   (43)  all_6_2 = e2
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | | REF_CLOSE: (1), (2), (3), (7), (43) are inconsistent by sub-proof
% 204.26/35.11  | | | | | |            #833.
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | Case 2:
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | |   (44)  all_56_0 = e1 | all_56_0 = e0
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | | REF_CLOSE: (10), (32), (34), (44) are inconsistent by sub-proof
% 204.26/35.11  | | | | | |            #1066.
% 204.26/35.11  | | | | | | 
% 204.26/35.11  | | | | | End of split
% 204.26/35.11  | | | | | 
% 204.26/35.11  | | | | End of split
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | Case 2:
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | |   (45)   ~ (all_22_0 = e0)
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | REDUCE: (30), (45) imply:
% 204.26/35.11  | | | |   (46)  $false
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | | CLOSE: (46) is inconsistent.
% 204.26/35.11  | | | | 
% 204.26/35.11  | | | End of split
% 204.26/35.11  | | | 
% 204.26/35.11  | | End of split
% 204.26/35.11  | | 
% 204.26/35.11  | End of split
% 204.26/35.11  | 
% 204.26/35.11  End of proof
% 204.26/35.11  
% 204.26/35.11  Sub-proof #821 shows that the following formulas are inconsistent:
% 204.26/35.11  ----------------------------------------------------------------
% 204.26/35.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.12    (2)  op(e3, e3) = all_52_0
% 204.26/35.12    (3)  op(e3, e3) = e2
% 204.26/35.12    (4)  op(e3, e3) = e3
% 204.26/35.12    (5)   ~ (e3 = e2)
% 204.26/35.12  
% 204.26/35.12  Begin of proof
% 204.26/35.12  | 
% 204.26/35.12  | GROUND_INST: instantiating (1) with e3, all_52_0, e3, e3, simplifying with
% 204.26/35.12  |              (2), (4) gives:
% 204.26/35.12  |   (6)  all_52_0 = e3
% 204.26/35.12  | 
% 204.26/35.12  | GROUND_INST: instantiating (1) with e2, all_52_0, e3, e3, simplifying with
% 204.26/35.12  |              (2), (3) gives:
% 204.26/35.12  |   (7)  all_52_0 = e2
% 204.26/35.12  | 
% 204.26/35.12  | COMBINE_EQS: (6), (7) imply:
% 204.26/35.12  |   (8)  e3 = e2
% 204.26/35.12  | 
% 204.26/35.12  | SIMP: (8) implies:
% 204.26/35.12  |   (9)  e3 = e2
% 204.26/35.12  | 
% 204.26/35.12  | REDUCE: (5), (9) imply:
% 204.26/35.12  |   (10)  $false
% 204.26/35.12  | 
% 204.26/35.12  | CLOSE: (10) is inconsistent.
% 204.26/35.12  | 
% 204.26/35.12  End of proof
% 204.26/35.12  
% 204.26/35.12  Sub-proof #822 shows that the following formulas are inconsistent:
% 204.26/35.12  ----------------------------------------------------------------
% 204.26/35.12    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.12    (2)   ~ (all_52_25 = all_52_27)
% 204.26/35.12    (3)  all_58_14 = all_52_23
% 204.26/35.12    (4)   ~ (e3 = e1)
% 204.26/35.12    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.12    (6)  all_58_1 = all_52_9
% 204.26/35.12    (7)   ~ (e3 = e0)
% 204.26/35.12    (8)  op(e2, e3) = all_52_3
% 204.26/35.12    (9)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.12    (10)   ~ (all_52_17 = all_52_25)
% 204.26/35.12    (11)   ~ (all_4_2 = e3)
% 204.26/35.12    (12)   ~ (all_52_3 = all_6_2)
% 204.26/35.12    (13)  all_58_0 = all_6_2
% 204.26/35.12    (14)   ~ (all_52_17 = all_10_2)
% 204.26/35.12    (15)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.12    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.12    (17)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.12    (18)  all_58_13 = all_52_15
% 204.26/35.12    (19)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.12    (20)  all_58_9 = all_52_25
% 204.26/35.12    (21)   ~ (all_52_29 = all_14_2)
% 204.26/35.12    (22)   ~ (all_52_15 = e3)
% 204.26/35.12    (23)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.12    (24)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.12    (25)  op(e2, e2) = all_4_2
% 204.26/35.12    (26)  all_58_11 = all_52_29
% 204.26/35.12    (27)  op(all_10_2, e1) = all_10_1
% 204.26/35.12    (28)  all_58_1 = e3
% 204.26/35.12    (29)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.12    (30)  op(e0, e0) = all_14_2
% 204.26/35.12    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.12    (32)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.12    (33)  all_58_15 = e0
% 204.26/35.12    (34)  all_56_11 = all_52_29
% 204.26/35.12    (35)   ~ (all_52_25 = e0)
% 204.26/35.12    (36)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.12    (37)   ~ (e2 = e1)
% 204.26/35.12    (38)  op(e0, e0) = e0
% 204.26/35.12    (39)  all_58_10 = all_52_27
% 204.26/35.12    (40)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.12    (41)   ~ (all_52_19 = all_52_23)
% 204.26/35.12    (42)   ~ (all_52_25 = all_52_29)
% 204.26/35.12    (43)  op(all_6_2, e3) = e2
% 204.26/35.12    (44)   ~ (all_52_29 = all_10_2)
% 204.26/35.12    (45)  all_58_7 = all_52_13
% 204.26/35.12    (46)  all_58_12 = all_52_7
% 204.26/35.12    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.12    (48)  all_58_2 = all_52_3
% 204.26/35.12    (49)  all_56_2 = all_52_17
% 204.26/35.12    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.12    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.12    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.12    (53)  all_56_7 = all_52_27
% 204.26/35.12    (54)   ~ (all_52_25 = e3)
% 204.26/35.12    (55)   ~ (e2 = e0)
% 204.26/35.12    (56)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.12    (57)   ~ (all_52_5 = all_52_29)
% 204.26/35.12    (58)   ~ (all_52_19 = all_52_27)
% 204.26/35.12    (59)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.12    (60)  op(e3, e3) = all_52_8
% 204.26/35.12    (61)  op(e3, e1) = all_52_17
% 204.26/35.12    (62)  op(e0, e3) = all_52_7
% 204.26/35.12    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.12    (64)   ~ (all_52_19 = all_10_2)
% 204.26/35.12    (65)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.12    (66)  all_58_8 = all_10_2
% 204.26/35.12    (67)   ~ (all_52_23 = e0)
% 204.26/35.12    (68)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.12    (69)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.12    (70)   ~ (all_52_25 = all_6_2)
% 204.26/35.12    (71)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12    (72)   ~ (all_52_9 = all_6_2)
% 204.26/35.12    (73)  op(e3, e3) = all_6_2
% 204.26/35.12    (74)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.12    (75)   ~ (all_52_13 = e3)
% 204.26/35.12    (76)   ~ (all_52_17 = e3)
% 204.26/35.12    (77)  all_56_3 = all_52_25
% 204.26/35.12    (78)   ~ (all_52_3 = all_52_7)
% 204.26/35.12    (79)  all_58_5 = all_52_19
% 204.26/35.12    (80)  all_58_6 = all_52_5
% 204.26/35.12    (81)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.12    (82)   ~ (all_52_17 = all_6_2)
% 204.26/35.12    (83)   ~ (e1 = e0)
% 204.26/35.12    (84)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.12    (85)  op(e1, e1) = all_10_2
% 204.26/35.12    (86)   ~ (all_52_23 = all_10_2)
% 204.26/35.12    (87)   ~ (all_52_7 = all_52_23)
% 204.26/35.12    (88)   ~ (all_52_17 = all_52_19)
% 204.26/35.12    (89)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.12          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.12    (90)  all_58_3 = all_4_2
% 204.26/35.12    (91)   ~ (all_52_3 = all_4_2)
% 204.26/35.12    (92)   ~ (all_52_19 = all_4_2)
% 204.26/35.12    (93)   ~ (all_52_17 = all_52_23)
% 204.26/35.12    (94)  all_58_4 = all_52_17
% 204.26/35.12    (95)   ~ (all_52_7 = e0)
% 204.26/35.12    (96)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.12  
% 204.26/35.12  Begin of proof
% 204.26/35.12  | 
% 204.26/35.12  | BETA: splitting (89) gives:
% 204.26/35.12  | 
% 204.26/35.12  | Case 1:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (97)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.26/35.12  | | 
% 204.26/35.12  | | ALPHA: (97) implies:
% 204.26/35.12  | |   (98)  all_52_22 = e0
% 204.26/35.12  | |   (99)  all_52_20 = e1
% 204.26/35.12  | |   (100)  all_52_18 = e2
% 204.26/35.12  | |   (101)  all_52_16 = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (69), (101) imply:
% 204.26/35.12  | |   (102)  op(all_52_17, all_52_17) = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (17), (100) imply:
% 204.26/35.12  | |   (103)  op(all_52_19, all_52_19) = e2
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (65), (98) imply:
% 204.26/35.12  | |   (104)  op(all_52_23, all_52_23) = e0
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (19), (99) imply:
% 204.26/35.12  | |   (105)  op(all_10_2, all_10_2) = e1
% 204.26/35.12  | | 
% 204.26/35.12  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.26/35.12  | |            (14), (15), (16), (18), (20), (21), (22), (23), (25), (26), (27),
% 204.26/35.12  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 204.26/35.12  | |            (39), (40), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 204.26/35.12  | |            (52), (53), (54), (55), (56), (58), (59), (60), (61), (62), (63),
% 204.26/35.12  | |            (64), (66), (70), (71), (72), (73), (75), (76), (77), (78), (79),
% 204.26/35.12  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (90), (93),
% 204.26/35.12  | |            (94), (95), (102), (103), (104), (105) are inconsistent by
% 204.26/35.12  | |            sub-proof #826.
% 204.26/35.12  | | 
% 204.26/35.12  | Case 2:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (106)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.26/35.12  | | 
% 204.26/35.12  | | ALPHA: (106) implies:
% 204.26/35.12  | |   (107)  all_52_28 = e1
% 204.26/35.12  | |   (108)  all_52_26 = e2
% 204.26/35.12  | |   (109)  all_52_24 = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (96), (109) imply:
% 204.26/35.12  | |   (110)  op(all_52_25, all_52_25) = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (24), (108) imply:
% 204.26/35.12  | |   (111)  op(all_52_27, all_52_27) = e2
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (68), (107) imply:
% 204.26/35.12  | |   (112)  op(all_52_29, all_52_29) = e1
% 204.26/35.12  | | 
% 204.26/35.12  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (16), (18),
% 204.26/35.12  | |            (19), (20), (22), (25), (26), (31), (32), (33), (35), (39), (42),
% 204.26/35.12  | |            (43), (46), (48), (51), (53), (54), (57), (58), (64), (65), (66),
% 204.26/35.12  | |            (67), (70), (71), (73), (74), (76), (77), (78), (79), (80), (81),
% 204.26/35.12  | |            (84), (85), (86), (87), (90), (91), (92), (94), (110), (111),
% 204.26/35.12  | |            (112) are inconsistent by sub-proof #823.
% 204.26/35.12  | | 
% 204.26/35.12  | End of split
% 204.26/35.12  | 
% 204.26/35.12  End of proof
% 204.26/35.12  
% 204.26/35.12  Sub-proof #823 shows that the following formulas are inconsistent:
% 204.26/35.12  ----------------------------------------------------------------
% 204.26/35.12    (1)   ~ (all_52_25 = all_52_27)
% 204.26/35.12    (2)  all_58_14 = all_52_23
% 204.26/35.12    (3)   ~ (e3 = e1)
% 204.26/35.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.12    (5)   ~ (e3 = e0)
% 204.26/35.12    (6)  op(e2, e3) = all_52_3
% 204.26/35.12    (7)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.12    (8)   ~ (all_4_2 = e3)
% 204.26/35.12    (9)   ~ (all_52_3 = all_6_2)
% 204.26/35.12    (10)  all_58_0 = all_6_2
% 204.26/35.12    (11)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.12    (12)  all_58_13 = all_52_15
% 204.26/35.12    (13)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.12    (14)  all_58_9 = all_52_25
% 204.26/35.12    (15)   ~ (all_52_15 = e3)
% 204.26/35.12    (16)  op(e2, e2) = all_4_2
% 204.26/35.12    (17)  all_58_11 = all_52_29
% 204.26/35.12    (18)  op(all_52_29, all_52_29) = e1
% 204.26/35.12    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.12    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.12    (21)  all_58_15 = e0
% 204.26/35.12    (22)   ~ (all_52_25 = e0)
% 204.26/35.12    (23)  all_58_10 = all_52_27
% 204.26/35.12    (24)   ~ (all_52_25 = all_52_29)
% 204.26/35.12    (25)  op(all_6_2, e3) = e2
% 204.26/35.12    (26)  all_58_12 = all_52_7
% 204.26/35.12    (27)  all_58_2 = all_52_3
% 204.26/35.12    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.12    (29)  all_56_7 = all_52_27
% 204.26/35.12    (30)   ~ (all_52_25 = e3)
% 204.26/35.12    (31)  op(all_52_25, all_52_25) = e3
% 204.26/35.12    (32)   ~ (all_52_5 = all_52_29)
% 204.26/35.12    (33)   ~ (all_52_19 = all_52_27)
% 204.26/35.12    (34)  op(all_52_27, all_52_27) = e2
% 204.26/35.12    (35)   ~ (all_52_19 = all_10_2)
% 204.26/35.12    (36)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.12    (37)  all_58_8 = all_10_2
% 204.26/35.12    (38)   ~ (all_52_23 = e0)
% 204.26/35.12    (39)   ~ (all_52_25 = all_6_2)
% 204.26/35.12    (40)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12    (41)  op(e3, e3) = all_6_2
% 204.26/35.12    (42)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.12    (43)   ~ (all_52_17 = e3)
% 204.26/35.12    (44)  all_56_3 = all_52_25
% 204.26/35.12    (45)   ~ (all_52_3 = all_52_7)
% 204.26/35.12    (46)  all_58_5 = all_52_19
% 204.26/35.12    (47)  all_58_6 = all_52_5
% 204.26/35.12    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.12    (49)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.12    (50)  op(e1, e1) = all_10_2
% 204.26/35.12    (51)   ~ (all_52_23 = all_10_2)
% 204.26/35.12    (52)   ~ (all_52_7 = all_52_23)
% 204.26/35.12    (53)  all_58_3 = all_4_2
% 204.26/35.12    (54)   ~ (all_52_3 = all_4_2)
% 204.26/35.12    (55)   ~ (all_52_19 = all_4_2)
% 204.26/35.12    (56)  all_58_4 = all_52_17
% 204.26/35.12  
% 204.26/35.12  Begin of proof
% 204.26/35.12  | 
% 204.26/35.12  | BETA: splitting (40) gives:
% 204.26/35.12  | 
% 204.26/35.12  | Case 1:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (57)  all_56_3 = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REF_CLOSE: (30), (44), (57) are inconsistent by sub-proof #1339.
% 204.26/35.12  | | 
% 204.26/35.12  | Case 2:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (58)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12  | | 
% 204.26/35.12  | | BETA: splitting (48) gives:
% 204.26/35.12  | | 
% 204.26/35.12  | | Case 1:
% 204.26/35.12  | | | 
% 204.26/35.12  | | |   (59)  all_58_12 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | COMBINE_EQS: (26), (59) imply:
% 204.26/35.12  | | |   (60)  all_52_7 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | SIMP: (60) implies:
% 204.26/35.12  | | |   (61)  all_52_7 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REDUCE: (45), (61) imply:
% 204.26/35.12  | | |   (62)   ~ (all_52_3 = e3)
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REDUCE: (52), (61) imply:
% 204.26/35.12  | | |   (63)   ~ (all_52_23 = e3)
% 204.26/35.12  | | | 
% 204.26/35.12  | | | SIMP: (63) implies:
% 204.26/35.12  | | |   (64)   ~ (all_52_23 = e3)
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REDUCE: (7), (61) imply:
% 204.26/35.12  | | |   (65)  op(e3, e3) = all_52_6
% 204.26/35.12  | | | 
% 204.26/35.12  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 204.26/35.12  | | |              with (41), (65) gives:
% 204.26/35.12  | | |   (66)  all_52_6 = all_6_2
% 204.26/35.12  | | | 
% 204.26/35.12  | | | BETA: splitting (19) gives:
% 204.26/35.12  | | | 
% 204.26/35.12  | | | Case 1:
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | |   (67)  all_58_2 = e3
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | | REF_CLOSE: (27), (62), (67) are inconsistent by sub-proof #1369.
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | Case 2:
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | |   (68)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | | BETA: splitting (49) gives:
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | | Case 1:
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | |   (69)  all_58_4 = e3
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | | REF_CLOSE: (43), (56), (69) are inconsistent by sub-proof #1302.
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | Case 2:
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | |   (70)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | | BETA: splitting (11) gives:
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | | Case 1:
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | |   (71)  all_56_7 = e3
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | COMBINE_EQS: (29), (71) imply:
% 204.26/35.12  | | | | | |   (72)  all_52_27 = e3
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | REDUCE: (33), (72) imply:
% 204.26/35.12  | | | | | |   (73)   ~ (all_52_19 = e3)
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | REDUCE: (34), (72) imply:
% 204.26/35.12  | | | | | |   (74)  op(e3, e3) = e2
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | BETA: splitting (70) gives:
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | Case 1:
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | |   (75)  all_58_5 = e3
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | REF_CLOSE: (46), (73), (75) are inconsistent by sub-proof #1279.
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | Case 2:
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | |   (76)  all_58_8 = e3 | all_58_14 = e3
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | BETA: splitting (76) gives:
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | Case 1:
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | |   (77)  all_58_8 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | COMBINE_EQS: (37), (77) imply:
% 204.26/35.12  | | | | | | | |   (78)  all_10_2 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | SIMP: (78) implies:
% 204.26/35.12  | | | | | | | |   (79)  all_10_2 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REDUCE: (13), (79) imply:
% 204.26/35.12  | | | | | | | |   (80)  op(e3, e3) = all_52_20
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_20, e3, e3,
% 204.26/35.12  | | | | | | | |              simplifying with (41), (80) gives:
% 204.26/35.12  | | | | | | | |   (81)  all_52_20 = all_6_2
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | GROUND_INST: instantiating (4) with e2, all_52_20, e3, e3,
% 204.26/35.12  | | | | | | | |              simplifying with (74), (80) gives:
% 204.26/35.12  | | | | | | | |   (82)  all_52_20 = e2
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | COMBINE_EQS: (81), (82) imply:
% 204.26/35.12  | | | | | | | |   (83)  all_6_2 = e2
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REF_CLOSE: (4), (6), (9), (25), (83) are inconsistent by
% 204.26/35.12  | | | | | | | |            sub-proof #825.
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | Case 2:
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | |   (84)  all_58_14 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REF_CLOSE: (2), (64), (84) are inconsistent by sub-proof #1305.
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | End of split
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | End of split
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | Case 2:
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | |   (85)   ~ (all_56_7 = e3)
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | REDUCE: (29), (85) imply:
% 204.26/35.12  | | | | | |   (86)   ~ (all_52_27 = e3)
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | BETA: splitting (68) gives:
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | Case 1:
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | |   (87)  all_58_3 = e3
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | COMBINE_EQS: (53), (87) imply:
% 204.26/35.12  | | | | | | |   (88)  all_4_2 = e3
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | REDUCE: (8), (88) imply:
% 204.26/35.12  | | | | | | |   (89)  $false
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | CLOSE: (89) is inconsistent.
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | Case 2:
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | |   (90)  all_58_5 = e3 | all_58_10 = e3
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | BETA: splitting (90) gives:
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | | Case 1:
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | |   (91)  all_58_5 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | COMBINE_EQS: (46), (91) imply:
% 204.26/35.12  | | | | | | | |   (92)  all_52_19 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | SIMP: (92) implies:
% 204.26/35.12  | | | | | | | |   (93)  all_52_19 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REDUCE: (35), (93) imply:
% 204.26/35.12  | | | | | | | |   (94)   ~ (all_10_2 = e3)
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | SIMP: (94) implies:
% 204.26/35.12  | | | | | | | |   (95)   ~ (all_10_2 = e3)
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REDUCE: (55), (93) imply:
% 204.26/35.12  | | | | | | | |   (96)   ~ (all_4_2 = e3)
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REF_CLOSE: (4), (8), (14), (16), (20), (22), (31), (44), (50),
% 204.26/35.12  | | | | | | | |            (58), (95) are inconsistent by sub-proof #824.
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | Case 2:
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | |   (97)  all_58_10 = e3
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | | REF_CLOSE: (23), (86), (97) are inconsistent by sub-proof #1301.
% 204.26/35.12  | | | | | | | | 
% 204.26/35.12  | | | | | | | End of split
% 204.26/35.12  | | | | | | | 
% 204.26/35.12  | | | | | | End of split
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | End of split
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | End of split
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | End of split
% 204.26/35.12  | | | 
% 204.26/35.12  | | Case 2:
% 204.26/35.12  | | | 
% 204.26/35.12  | | |   (98)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REF_CLOSE: (1), (2), (3), (4), (5), (10), (12), (14), (15), (16), (17),
% 204.26/35.12  | | |            (18), (20), (21), (22), (23), (24), (26), (27), (28), (31),
% 204.26/35.12  | | |            (32), (34), (36), (38), (39), (40), (41), (42), (44), (47),
% 204.26/35.12  | | |            (50), (51), (52), (54), (98) are inconsistent by sub-proof
% 204.26/35.12  | | |            #1205.
% 204.26/35.12  | | | 
% 204.26/35.12  | | End of split
% 204.26/35.12  | | 
% 204.26/35.12  | End of split
% 204.26/35.12  | 
% 204.26/35.12  End of proof
% 204.26/35.12  
% 204.26/35.12  Sub-proof #824 shows that the following formulas are inconsistent:
% 204.26/35.12  ----------------------------------------------------------------
% 204.26/35.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.12    (2)   ~ (all_4_2 = e3)
% 204.26/35.12    (3)  all_58_9 = all_52_25
% 204.26/35.12    (4)  op(e2, e2) = all_4_2
% 204.26/35.12    (5)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.12    (6)   ~ (all_52_25 = e0)
% 204.26/35.12    (7)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12    (8)  op(all_52_25, all_52_25) = e3
% 204.26/35.12    (9)   ~ (all_10_2 = e3)
% 204.26/35.12    (10)  all_56_3 = all_52_25
% 204.26/35.12    (11)  op(e1, e1) = all_10_2
% 204.26/35.12  
% 204.26/35.12  Begin of proof
% 204.26/35.12  | 
% 204.26/35.12  | BETA: splitting (7) gives:
% 204.26/35.12  | 
% 204.26/35.12  | Case 1:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (12)  all_56_3 = e2
% 204.26/35.12  | | 
% 204.26/35.12  | | COMBINE_EQS: (10), (12) imply:
% 204.26/35.12  | |   (13)  all_52_25 = e2
% 204.26/35.12  | | 
% 204.26/35.12  | | SIMP: (13) implies:
% 204.26/35.12  | |   (14)  all_52_25 = e2
% 204.26/35.12  | | 
% 204.26/35.12  | | REDUCE: (8), (14) imply:
% 204.26/35.12  | |   (15)  op(e2, e2) = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REF_CLOSE: (1), (2), (4), (15) are inconsistent by sub-proof #1318.
% 204.26/35.12  | | 
% 204.26/35.12  | Case 2:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (16)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12  | | 
% 204.26/35.12  | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (16) are inconsistent
% 204.26/35.12  | |            by sub-proof #1245.
% 204.26/35.12  | | 
% 204.26/35.12  | End of split
% 204.26/35.12  | 
% 204.26/35.12  End of proof
% 204.26/35.12  
% 204.26/35.12  Sub-proof #825 shows that the following formulas are inconsistent:
% 204.26/35.12  ----------------------------------------------------------------
% 204.26/35.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.12    (2)  op(e2, e3) = all_52_3
% 204.26/35.12    (3)   ~ (all_52_3 = all_6_2)
% 204.26/35.12    (4)  all_6_2 = e2
% 204.26/35.12    (5)  op(all_6_2, e3) = e2
% 204.26/35.12  
% 204.26/35.12  Begin of proof
% 204.26/35.12  | 
% 204.26/35.12  | REDUCE: (3), (4) imply:
% 204.26/35.12  |   (6)   ~ (all_52_3 = e2)
% 204.26/35.12  | 
% 204.26/35.12  | REDUCE: (4), (5) imply:
% 204.26/35.12  |   (7)  op(e2, e3) = e2
% 204.26/35.12  | 
% 204.26/35.12  | GROUND_INST: instantiating (1) with all_52_3, e2, e3, e2, simplifying with
% 204.26/35.12  |              (2), (7) gives:
% 204.26/35.12  |   (8)  all_52_3 = e2
% 204.26/35.12  | 
% 204.26/35.12  | REDUCE: (6), (8) imply:
% 204.26/35.12  |   (9)  $false
% 204.26/35.12  | 
% 204.26/35.12  | CLOSE: (9) is inconsistent.
% 204.26/35.12  | 
% 204.26/35.12  End of proof
% 204.26/35.12  
% 204.26/35.12  Sub-proof #826 shows that the following formulas are inconsistent:
% 204.26/35.12  ----------------------------------------------------------------
% 204.26/35.12    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.12    (2)  all_58_14 = all_52_23
% 204.26/35.12    (3)   ~ (e3 = e1)
% 204.26/35.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.12    (5)  all_58_1 = all_52_9
% 204.26/35.12    (6)   ~ (e3 = e0)
% 204.26/35.12    (7)  op(all_52_23, all_52_23) = e0
% 204.26/35.12    (8)  op(e2, e3) = all_52_3
% 204.26/35.12    (9)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.12    (10)   ~ (all_52_17 = all_52_25)
% 204.26/35.12    (11)   ~ (all_4_2 = e3)
% 204.26/35.12    (12)   ~ (all_52_3 = all_6_2)
% 204.26/35.12    (13)  all_58_0 = all_6_2
% 204.26/35.12    (14)   ~ (all_52_17 = all_10_2)
% 204.26/35.12    (15)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.12    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.12    (17)  all_58_13 = all_52_15
% 204.26/35.12    (18)  all_58_9 = all_52_25
% 204.26/35.12    (19)   ~ (all_52_29 = all_14_2)
% 204.26/35.12    (20)   ~ (all_52_15 = e3)
% 204.26/35.12    (21)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.12    (22)  op(e2, e2) = all_4_2
% 204.26/35.12    (23)  all_58_11 = all_52_29
% 204.26/35.12    (24)  op(all_10_2, e1) = all_10_1
% 204.26/35.12    (25)  all_58_1 = e3
% 204.26/35.12    (26)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.12    (27)  op(e0, e0) = all_14_2
% 204.26/35.12    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.12    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.12    (30)  all_58_15 = e0
% 204.26/35.12    (31)  all_56_11 = all_52_29
% 204.26/35.12    (32)   ~ (all_52_25 = e0)
% 204.26/35.12    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.12    (34)   ~ (e2 = e1)
% 204.26/35.12    (35)  op(e0, e0) = e0
% 204.26/35.12    (36)  op(all_10_2, all_10_2) = e1
% 204.26/35.12    (37)  all_58_10 = all_52_27
% 204.26/35.12    (38)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.12    (39)   ~ (all_52_19 = all_52_23)
% 204.26/35.12    (40)  op(all_6_2, e3) = e2
% 204.26/35.12    (41)   ~ (all_52_29 = all_10_2)
% 204.26/35.12    (42)  all_58_7 = all_52_13
% 204.26/35.12    (43)  op(all_52_19, all_52_19) = e2
% 204.26/35.12    (44)  all_58_12 = all_52_7
% 204.26/35.12    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.12    (46)  all_58_2 = all_52_3
% 204.26/35.12    (47)  all_56_2 = all_52_17
% 204.26/35.12    (48)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.12    (49)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.12    (50)  all_56_7 = all_52_27
% 204.26/35.12    (51)   ~ (all_52_25 = e3)
% 204.26/35.12    (52)   ~ (e2 = e0)
% 204.26/35.12    (53)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.12    (54)   ~ (all_52_19 = all_52_27)
% 204.26/35.12    (55)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.12    (56)  op(e3, e3) = all_52_8
% 204.26/35.12    (57)  op(e3, e1) = all_52_17
% 204.26/35.12    (58)  op(e0, e3) = all_52_7
% 204.26/35.12    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.12    (60)   ~ (all_52_19 = all_10_2)
% 204.26/35.12    (61)  all_58_8 = all_10_2
% 204.26/35.12    (62)   ~ (all_52_25 = all_6_2)
% 204.26/35.12    (63)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12    (64)   ~ (all_52_9 = all_6_2)
% 204.26/35.12    (65)  op(e3, e3) = all_6_2
% 204.26/35.12    (66)   ~ (all_52_13 = e3)
% 204.26/35.12    (67)   ~ (all_52_17 = e3)
% 204.26/35.12    (68)  all_56_3 = all_52_25
% 204.26/35.12    (69)   ~ (all_52_3 = all_52_7)
% 204.26/35.12    (70)  all_58_5 = all_52_19
% 204.26/35.12    (71)  op(all_52_17, all_52_17) = e3
% 204.26/35.12    (72)  all_58_6 = all_52_5
% 204.26/35.12    (73)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.12    (74)   ~ (all_52_17 = all_6_2)
% 204.26/35.12    (75)   ~ (e1 = e0)
% 204.26/35.12    (76)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.12    (77)  op(e1, e1) = all_10_2
% 204.26/35.12    (78)   ~ (all_52_23 = all_10_2)
% 204.26/35.12    (79)   ~ (all_52_7 = all_52_23)
% 204.26/35.12    (80)   ~ (all_52_17 = all_52_19)
% 204.26/35.12    (81)  all_58_3 = all_4_2
% 204.26/35.12    (82)   ~ (all_52_17 = all_52_23)
% 204.26/35.12    (83)  all_58_4 = all_52_17
% 204.26/35.12    (84)   ~ (all_52_7 = e0)
% 204.26/35.12  
% 204.26/35.12  Begin of proof
% 204.26/35.12  | 
% 204.26/35.12  | BETA: splitting (63) gives:
% 204.26/35.12  | 
% 204.26/35.12  | Case 1:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (85)  all_56_3 = e3
% 204.26/35.12  | | 
% 204.26/35.12  | | REF_CLOSE: (51), (68), (85) are inconsistent by sub-proof #1339.
% 204.26/35.12  | | 
% 204.26/35.12  | Case 2:
% 204.26/35.12  | | 
% 204.26/35.12  | |   (86)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.12  | | 
% 204.26/35.12  | | BETA: splitting (73) gives:
% 204.26/35.12  | | 
% 204.26/35.12  | | Case 1:
% 204.26/35.12  | | | 
% 204.26/35.12  | | |   (87)  all_58_12 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | COMBINE_EQS: (44), (87) imply:
% 204.26/35.12  | | |   (88)  all_52_7 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | SIMP: (88) implies:
% 204.26/35.12  | | |   (89)  all_52_7 = e3
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REDUCE: (69), (89) imply:
% 204.26/35.12  | | |   (90)   ~ (all_52_3 = e3)
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REDUCE: (79), (89) imply:
% 204.26/35.12  | | |   (91)   ~ (all_52_23 = e3)
% 204.26/35.12  | | | 
% 204.26/35.12  | | | SIMP: (91) implies:
% 204.26/35.12  | | |   (92)   ~ (all_52_23 = e3)
% 204.26/35.12  | | | 
% 204.26/35.12  | | | REDUCE: (9), (89) imply:
% 204.26/35.12  | | |   (93)  op(e3, e3) = all_52_6
% 204.26/35.12  | | | 
% 204.26/35.12  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 204.26/35.12  | | |              with (65), (93) gives:
% 204.26/35.12  | | |   (94)  all_52_6 = all_6_2
% 204.26/35.12  | | | 
% 204.26/35.12  | | | BETA: splitting (28) gives:
% 204.26/35.12  | | | 
% 204.26/35.12  | | | Case 1:
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | |   (95)  all_58_2 = e3
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | | REF_CLOSE: (46), (90), (95) are inconsistent by sub-proof #1369.
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | Case 2:
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | |   (96)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | | BETA: splitting (76) gives:
% 204.26/35.12  | | | | 
% 204.26/35.12  | | | | Case 1:
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | |   (97)  all_58_4 = e3
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | | REF_CLOSE: (67), (83), (97) are inconsistent by sub-proof #1302.
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | Case 2:
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | |   (98)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | | BETA: splitting (16) gives:
% 204.26/35.12  | | | | | 
% 204.26/35.12  | | | | | Case 1:
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | |   (99)  all_56_7 = e3
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | COMBINE_EQS: (50), (99) imply:
% 204.26/35.12  | | | | | |   (100)  all_52_27 = e3
% 204.26/35.12  | | | | | | 
% 204.26/35.12  | | | | | | REDUCE: (54), (100) imply:
% 204.26/35.12  | | | | | |   (101)   ~ (all_52_19 = e3)
% 204.26/35.12  | | | | | | 
% 204.26/35.13  | | | | | | REF_CLOSE: (2), (4), (10), (14), (24), (32), (33), (35), (36), (47),
% 204.26/35.13  | | | | | |            (56), (57), (61), (62), (65), (68), (70), (71), (74),
% 204.26/35.13  | | | | | |            (86), (92), (98), (101) are inconsistent by sub-proof
% 204.26/35.13  | | | | | |            #1277.
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | Case 2:
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | |   (102)   ~ (all_56_7 = e3)
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | | REDUCE: (50), (102) imply:
% 204.26/35.13  | | | | | |   (103)   ~ (all_52_27 = e3)
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (11), (12), (13), (15), (18),
% 204.26/35.13  | | | | | |            (19), (21), (23), (25), (27), (31), (34), (36), (37),
% 204.26/35.13  | | | | | |            (39), (40), (41), (42), (43), (45), (49), (52), (53),
% 204.26/35.13  | | | | | |            (55), (56), (60), (61), (65), (66), (70), (71), (72),
% 204.26/35.13  | | | | | |            (75), (76), (77), (80), (81), (83), (96), (103) are
% 204.26/35.13  | | | | | |            inconsistent by sub-proof #828.
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | End of split
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | End of split
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | End of split
% 204.26/35.13  | | | 
% 204.26/35.13  | | Case 2:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (104)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | BETA: splitting (104) gives:
% 204.26/35.13  | | | 
% 204.26/35.13  | | | Case 1:
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | |   (105)  all_58_13 = e3
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | REF_CLOSE: (17), (20), (105) are inconsistent by sub-proof #1360.
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | Case 2:
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | |   (106)  all_58_14 = e3 | all_58_15 = e3
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | BETA: splitting (106) gives:
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | Case 1:
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | |   (107)  all_58_14 = e3
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | COMBINE_EQS: (2), (107) imply:
% 204.26/35.13  | | | | |   (108)  all_52_23 = e3
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | SIMP: (108) implies:
% 204.26/35.13  | | | | |   (109)  all_52_23 = e3
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (79), (109) imply:
% 204.26/35.13  | | | | |   (110)   ~ (all_52_7 = e3)
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (78), (109) imply:
% 204.26/35.13  | | | | |   (111)   ~ (all_10_2 = e3)
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | SIMP: (111) implies:
% 204.26/35.13  | | | | |   (112)   ~ (all_10_2 = e3)
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (7), (109) imply:
% 204.26/35.13  | | | | |   (113)  op(e3, e3) = e0
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | GROUND_INST: instantiating (4) with all_6_2, e0, e3, e3, simplifying
% 204.26/35.13  | | | | |              with (65), (113) gives:
% 204.26/35.13  | | | | |   (114)  all_6_2 = e0
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (74), (114) imply:
% 204.26/35.13  | | | | |   (115)   ~ (all_52_17 = e0)
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (26), (114) imply:
% 204.26/35.13  | | | | |   (116)  op(e0, e0) = all_52_0
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (40), (114) imply:
% 204.26/35.13  | | | | |   (117)  op(e0, e3) = e2
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | GROUND_INST: instantiating (4) with e0, all_52_0, e0, e0, simplifying
% 204.26/35.13  | | | | |              with (35), (116) gives:
% 204.26/35.13  | | | | |   (118)  all_52_0 = e0
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | GROUND_INST: instantiating (4) with all_52_7, e2, e3, e0, simplifying
% 204.26/35.13  | | | | |              with (58), (117) gives:
% 204.26/35.13  | | | | |   (119)  all_52_7 = e2
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (110), (119) imply:
% 204.26/35.13  | | | | |   (120)   ~ (e3 = e2)
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | SIMP: (120) implies:
% 204.26/35.13  | | | | |   (121)   ~ (e3 = e2)
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | BETA: splitting (29) gives:
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | Case 1:
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | |   (122)  all_58_9 = e1
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | | REF_CLOSE: (4), (5), (10), (11), (13), (17), (20), (22), (32), (33),
% 204.26/35.13  | | | | | |            (34), (35), (38), (42), (47), (48), (59), (62), (64),
% 204.26/35.13  | | | | | |            (65), (66), (68), (71), (74), (81), (83), (86), (121),
% 204.26/35.13  | | | | | |            (122) are inconsistent by sub-proof #951.
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | Case 2:
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | |   (123)   ~ (all_58_9 = e1)
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | | REDUCE: (18), (123) imply:
% 204.26/35.13  | | | | | |   (124)   ~ (all_52_25 = e1)
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | | REF_CLOSE: (4), (10), (32), (33), (47), (67), (68), (71), (77),
% 204.26/35.13  | | | | | |            (86), (112), (115), (124) are inconsistent by sub-proof
% 204.26/35.13  | | | | | |            #827.
% 204.26/35.13  | | | | | | 
% 204.26/35.13  | | | | | End of split
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | Case 2:
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | |   (125)  all_58_15 = e3
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | COMBINE_EQS: (30), (125) imply:
% 204.26/35.13  | | | | |   (126)  e3 = e0
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | REDUCE: (6), (126) imply:
% 204.26/35.13  | | | | |   (127)  $false
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | | CLOSE: (127) is inconsistent.
% 204.26/35.13  | | | | | 
% 204.26/35.13  | | | | End of split
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | End of split
% 204.26/35.13  | | | 
% 204.26/35.13  | | End of split
% 204.26/35.13  | | 
% 204.26/35.13  | End of split
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #827 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (2)   ~ (all_52_17 = all_52_25)
% 204.26/35.13    (3)   ~ (all_52_25 = e0)
% 204.26/35.13    (4)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.13    (5)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.13    (6)  all_56_2 = all_52_17
% 204.26/35.13    (7)   ~ (all_10_2 = e3)
% 204.26/35.13    (8)   ~ (all_52_25 = e1)
% 204.26/35.13    (9)   ~ (all_52_17 = e3)
% 204.26/35.13    (10)  all_56_3 = all_52_25
% 204.26/35.13    (11)  op(all_52_17, all_52_17) = e3
% 204.26/35.13    (12)   ~ (all_52_17 = e0)
% 204.26/35.13    (13)  op(e1, e1) = all_10_2
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | BETA: splitting (5) gives:
% 204.26/35.13  | 
% 204.26/35.13  | Case 1:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (14)  all_56_3 = e2
% 204.26/35.13  | | 
% 204.26/35.13  | | COMBINE_EQS: (10), (14) imply:
% 204.26/35.13  | |   (15)  all_52_25 = e2
% 204.26/35.13  | | 
% 204.26/35.13  | | REDUCE: (2), (15) imply:
% 204.26/35.13  | |   (16)   ~ (all_52_17 = e2)
% 204.26/35.13  | | 
% 204.26/35.13  | | REF_CLOSE: (1), (4), (6), (7), (9), (11), (12), (13), (16) are inconsistent
% 204.26/35.13  | |            by sub-proof #1073.
% 204.26/35.13  | | 
% 204.26/35.13  | Case 2:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (17)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.13  | | 
% 204.26/35.13  | | REF_CLOSE: (3), (8), (10), (17) are inconsistent by sub-proof #1330.
% 204.26/35.13  | | 
% 204.26/35.13  | End of split
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #828 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  all_58_14 = all_52_23
% 204.26/35.13    (2)   ~ (e3 = e1)
% 204.26/35.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (4)   ~ (e3 = e0)
% 204.26/35.13    (5)  op(e2, e3) = all_52_3
% 204.26/35.13    (6)   ~ (all_4_2 = e3)
% 204.26/35.13    (7)   ~ (all_52_3 = all_6_2)
% 204.26/35.13    (8)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.13    (9)  all_58_0 = all_6_2
% 204.26/35.13    (10)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.13    (11)  all_58_9 = all_52_25
% 204.26/35.13    (12)   ~ (all_52_29 = all_14_2)
% 204.26/35.13    (13)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.13    (14)  all_58_11 = all_52_29
% 204.26/35.13    (15)  all_58_1 = e3
% 204.26/35.13    (16)  op(e0, e0) = all_14_2
% 204.26/35.13    (17)  all_56_11 = all_52_29
% 204.26/35.13    (18)   ~ (e2 = e1)
% 204.26/35.13    (19)  op(all_10_2, all_10_2) = e1
% 204.26/35.13    (20)  all_58_10 = all_52_27
% 204.26/35.13    (21)   ~ (all_52_19 = all_52_23)
% 204.26/35.13    (22)  op(all_6_2, e3) = e2
% 204.26/35.13    (23)   ~ (all_52_29 = all_10_2)
% 204.26/35.13    (24)  all_58_7 = all_52_13
% 204.26/35.13    (25)  op(all_52_19, all_52_19) = e2
% 204.26/35.13    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.13    (27)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.13    (28)   ~ (e2 = e0)
% 204.26/35.13    (29)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.13    (30)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.13    (31)   ~ (all_52_27 = e3)
% 204.26/35.13    (32)  op(e3, e3) = all_52_8
% 204.26/35.13    (33)   ~ (all_52_19 = all_10_2)
% 204.26/35.13    (34)  all_58_8 = all_10_2
% 204.26/35.13    (35)  op(e3, e3) = all_6_2
% 204.26/35.13    (36)   ~ (all_52_13 = e3)
% 204.26/35.13    (37)  all_58_5 = all_52_19
% 204.26/35.13    (38)  op(all_52_17, all_52_17) = e3
% 204.26/35.13    (39)  all_58_6 = all_52_5
% 204.26/35.13    (40)   ~ (e1 = e0)
% 204.26/35.13    (41)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.13    (42)  op(e1, e1) = all_10_2
% 204.26/35.13    (43)   ~ (all_52_17 = all_52_19)
% 204.26/35.13    (44)  all_58_3 = all_4_2
% 204.26/35.13    (45)  all_58_4 = all_52_17
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | BETA: splitting (8) gives:
% 204.26/35.13  | 
% 204.26/35.13  | Case 1:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (46)  all_58_3 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | COMBINE_EQS: (44), (46) imply:
% 204.26/35.13  | |   (47)  all_4_2 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | REDUCE: (6), (47) imply:
% 204.26/35.13  | |   (48)  $false
% 204.26/35.13  | | 
% 204.26/35.13  | | CLOSE: (48) is inconsistent.
% 204.26/35.13  | | 
% 204.26/35.13  | Case 2:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (49)  all_58_5 = e3 | all_58_10 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | BETA: splitting (49) gives:
% 204.26/35.13  | | 
% 204.26/35.13  | | Case 1:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (50)  all_58_5 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | COMBINE_EQS: (37), (50) imply:
% 204.26/35.13  | | |   (51)  all_52_19 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | SIMP: (51) implies:
% 204.26/35.13  | | |   (52)  all_52_19 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REDUCE: (43), (52) imply:
% 204.26/35.13  | | |   (53)   ~ (all_52_17 = e3)
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REDUCE: (21), (52) imply:
% 204.26/35.13  | | |   (54)   ~ (all_52_23 = e3)
% 204.26/35.13  | | | 
% 204.26/35.13  | | | SIMP: (54) implies:
% 204.26/35.13  | | |   (55)   ~ (all_52_23 = e3)
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REDUCE: (25), (52) imply:
% 204.26/35.13  | | |   (56)  op(e3, e3) = e2
% 204.26/35.13  | | | 
% 204.26/35.13  | | | BETA: splitting (26) gives:
% 204.26/35.13  | | | 
% 204.26/35.13  | | | Case 1:
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | |   (57)  all_58_6 = e3
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | COMBINE_EQS: (39), (57) imply:
% 204.26/35.13  | | | |   (58)  all_52_5 = e3
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | SIMP: (58) implies:
% 204.26/35.13  | | | |   (59)  all_52_5 = e3
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | REDUCE: (10), (59) imply:
% 204.26/35.13  | | | |   (60)  op(e3, e3) = all_52_4
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | REF_CLOSE: (3), (5), (7), (22), (35), (56), (60) are inconsistent by
% 204.26/35.13  | | | |            sub-proof #832.
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | Case 2:
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | |   (61)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | | REF_CLOSE: (1), (2), (3), (4), (9), (11), (12), (13), (14), (15), (16),
% 204.26/35.13  | | | |            (17), (18), (19), (21), (23), (24), (25), (27), (28), (29),
% 204.26/35.13  | | | |            (30), (32), (33), (34), (35), (36), (37), (38), (40), (41),
% 204.26/35.13  | | | |            (42), (45), (53), (55), (56), (61) are inconsistent by
% 204.26/35.13  | | | |            sub-proof #829.
% 204.26/35.13  | | | | 
% 204.26/35.13  | | | End of split
% 204.26/35.13  | | | 
% 204.26/35.13  | | Case 2:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (62)  all_58_10 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REF_CLOSE: (20), (31), (62) are inconsistent by sub-proof #1301.
% 204.26/35.13  | | | 
% 204.26/35.13  | | End of split
% 204.26/35.13  | | 
% 204.26/35.13  | End of split
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #829 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  all_58_14 = all_52_23
% 204.26/35.13    (2)   ~ (e3 = e1)
% 204.26/35.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (4)   ~ (e3 = e0)
% 204.26/35.13    (5)  all_58_0 = all_6_2
% 204.26/35.13    (6)  all_58_9 = all_52_25
% 204.26/35.13    (7)   ~ (all_52_29 = all_14_2)
% 204.26/35.13    (8)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.13    (9)  all_58_11 = all_52_29
% 204.26/35.13    (10)  all_58_1 = e3
% 204.26/35.13    (11)  op(e0, e0) = all_14_2
% 204.26/35.13    (12)  op(e3, e3) = e2
% 204.26/35.13    (13)  all_56_11 = all_52_29
% 204.26/35.13    (14)   ~ (e2 = e1)
% 204.26/35.13    (15)  op(all_10_2, all_10_2) = e1
% 204.26/35.13    (16)   ~ (all_52_19 = all_52_23)
% 204.26/35.13    (17)   ~ (all_52_29 = all_10_2)
% 204.26/35.13    (18)  all_58_7 = all_52_13
% 204.26/35.13    (19)  op(all_52_19, all_52_19) = e2
% 204.26/35.13    (20)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.13    (21)   ~ (e2 = e0)
% 204.26/35.13    (22)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.13    (23)   ~ (all_52_23 = e3)
% 204.26/35.13    (24)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.13    (25)  op(e3, e3) = all_52_8
% 204.26/35.13    (26)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.13    (27)   ~ (all_52_19 = all_10_2)
% 204.26/35.13    (28)  all_58_8 = all_10_2
% 204.26/35.13    (29)  op(e3, e3) = all_6_2
% 204.26/35.13    (30)   ~ (all_52_13 = e3)
% 204.26/35.13    (31)   ~ (all_52_17 = e3)
% 204.26/35.13    (32)  all_58_5 = all_52_19
% 204.26/35.13    (33)  op(all_52_17, all_52_17) = e3
% 204.26/35.13    (34)   ~ (e1 = e0)
% 204.26/35.13    (35)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.13    (36)  op(e1, e1) = all_10_2
% 204.26/35.13    (37)  all_58_4 = all_52_17
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | BETA: splitting (35) gives:
% 204.26/35.13  | 
% 204.26/35.13  | Case 1:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (38)  all_58_4 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | REF_CLOSE: (31), (37), (38) are inconsistent by sub-proof #1302.
% 204.26/35.13  | | 
% 204.26/35.13  | Case 2:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (39)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | BETA: splitting (24) gives:
% 204.26/35.13  | | 
% 204.26/35.13  | | Case 1:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (40)  all_56_11 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 204.26/35.13  | | |            (16), (17), (19), (20), (21), (22), (23), (25), (27), (28),
% 204.26/35.13  | | |            (29), (32), (33), (34), (36), (37), (39), (40) are inconsistent
% 204.26/35.13  | | |            by sub-proof #831.
% 204.26/35.13  | | | 
% 204.26/35.13  | | Case 2:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (41)   ~ (all_56_11 = e3)
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REDUCE: (13), (41) imply:
% 204.26/35.13  | | |   (42)   ~ (all_52_29 = e3)
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REF_CLOSE: (3), (9), (12), (14), (15), (18), (25), (26), (28), (30), (42)
% 204.26/35.13  | | |            are inconsistent by sub-proof #830.
% 204.26/35.13  | | | 
% 204.26/35.13  | | End of split
% 204.26/35.13  | | 
% 204.26/35.13  | End of split
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #830 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (2)  all_58_11 = all_52_29
% 204.26/35.13    (3)  op(e3, e3) = e2
% 204.26/35.13    (4)   ~ (e2 = e1)
% 204.26/35.13    (5)  op(all_10_2, all_10_2) = e1
% 204.26/35.13    (6)  all_58_7 = all_52_13
% 204.26/35.13    (7)   ~ (all_52_29 = e3)
% 204.26/35.13    (8)  op(e3, e3) = all_52_8
% 204.26/35.13    (9)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.13    (10)  all_58_8 = all_10_2
% 204.26/35.13    (11)   ~ (all_52_13 = e3)
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | BETA: splitting (9) gives:
% 204.26/35.13  | 
% 204.26/35.13  | Case 1:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (12)  all_58_7 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | COMBINE_EQS: (6), (12) imply:
% 204.26/35.13  | |   (13)  all_52_13 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | REDUCE: (11), (13) imply:
% 204.26/35.13  | |   (14)  $false
% 204.26/35.13  | | 
% 204.26/35.13  | | CLOSE: (14) is inconsistent.
% 204.26/35.13  | | 
% 204.26/35.13  | Case 2:
% 204.26/35.13  | | 
% 204.26/35.13  | |   (15)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.13  | | 
% 204.26/35.13  | | BETA: splitting (15) gives:
% 204.26/35.13  | | 
% 204.26/35.13  | | Case 1:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (16)  all_58_8 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | COMBINE_EQS: (10), (16) imply:
% 204.26/35.13  | | |   (17)  all_10_2 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | SIMP: (17) implies:
% 204.26/35.13  | | |   (18)  all_10_2 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REDUCE: (5), (18) imply:
% 204.26/35.13  | | |   (19)  op(e3, e3) = e1
% 204.26/35.13  | | | 
% 204.26/35.13  | | | GROUND_INST: instantiating (1) with e2, all_52_8, e3, e3, simplifying with
% 204.26/35.13  | | |              (3), (8) gives:
% 204.26/35.13  | | |   (20)  all_52_8 = e2
% 204.26/35.13  | | | 
% 204.26/35.13  | | | GROUND_INST: instantiating (1) with e1, all_52_8, e3, e3, simplifying with
% 204.26/35.13  | | |              (8), (19) gives:
% 204.26/35.13  | | |   (21)  all_52_8 = e1
% 204.26/35.13  | | | 
% 204.26/35.13  | | | COMBINE_EQS: (20), (21) imply:
% 204.26/35.13  | | |   (22)  e2 = e1
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REDUCE: (4), (22) imply:
% 204.26/35.13  | | |   (23)  $false
% 204.26/35.13  | | | 
% 204.26/35.13  | | | CLOSE: (23) is inconsistent.
% 204.26/35.13  | | | 
% 204.26/35.13  | | Case 2:
% 204.26/35.13  | | | 
% 204.26/35.13  | | |   (24)  all_58_11 = e3
% 204.26/35.13  | | | 
% 204.26/35.13  | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #1323.
% 204.26/35.13  | | | 
% 204.26/35.13  | | End of split
% 204.26/35.13  | | 
% 204.26/35.13  | End of split
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #831 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  all_58_14 = all_52_23
% 204.26/35.13    (2)   ~ (e3 = e1)
% 204.26/35.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (4)   ~ (e3 = e0)
% 204.26/35.13    (5)  all_58_0 = all_6_2
% 204.26/35.13    (6)  all_58_9 = all_52_25
% 204.26/35.13    (7)   ~ (all_52_29 = all_14_2)
% 204.26/35.13    (8)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.13    (9)  all_58_1 = e3
% 204.26/35.13    (10)  op(e0, e0) = all_14_2
% 204.26/35.13    (11)  all_56_11 = all_52_29
% 204.26/35.13    (12)   ~ (e2 = e1)
% 204.26/35.13    (13)   ~ (all_52_19 = all_52_23)
% 204.26/35.13    (14)   ~ (all_52_29 = all_10_2)
% 204.26/35.13    (15)  op(all_52_19, all_52_19) = e2
% 204.26/35.13    (16)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.13    (17)   ~ (e2 = e0)
% 204.26/35.13    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.13    (19)   ~ (all_52_23 = e3)
% 204.26/35.13    (20)  op(e3, e3) = all_52_8
% 204.26/35.13    (21)  all_56_11 = e3
% 204.26/35.13    (22)   ~ (all_52_19 = all_10_2)
% 204.26/35.13    (23)  all_58_8 = all_10_2
% 204.26/35.13    (24)  op(e3, e3) = all_6_2
% 204.26/35.13    (25)  all_58_5 = all_52_19
% 204.26/35.13    (26)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.13    (27)  op(all_52_17, all_52_17) = e3
% 204.26/35.13    (28)   ~ (e1 = e0)
% 204.26/35.13    (29)  op(e1, e1) = all_10_2
% 204.26/35.13    (30)  all_58_4 = all_52_17
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | COMBINE_EQS: (11), (21) imply:
% 204.26/35.13  |   (31)  all_52_29 = e3
% 204.26/35.13  | 
% 204.26/35.13  | SIMP: (31) implies:
% 204.26/35.13  |   (32)  all_52_29 = e3
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (7), (32) imply:
% 204.26/35.13  |   (33)   ~ (all_14_2 = e3)
% 204.26/35.13  | 
% 204.26/35.13  | SIMP: (33) implies:
% 204.26/35.13  |   (34)   ~ (all_14_2 = e3)
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (14), (32) imply:
% 204.26/35.13  |   (35)   ~ (all_10_2 = e3)
% 204.26/35.13  | 
% 204.26/35.13  | SIMP: (35) implies:
% 204.26/35.13  |   (36)   ~ (all_10_2 = e3)
% 204.26/35.13  | 
% 204.26/35.13  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (15),
% 204.26/35.13  |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 204.26/35.13  |            (28), (29), (30), (34), (36) are inconsistent by sub-proof #1049.
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #832 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (2)  op(e2, e3) = all_52_3
% 204.26/35.13    (3)   ~ (all_52_3 = all_6_2)
% 204.26/35.13    (4)  op(e3, e3) = e2
% 204.26/35.13    (5)  op(all_6_2, e3) = e2
% 204.26/35.13    (6)  op(e3, e3) = all_52_4
% 204.26/35.13    (7)  op(e3, e3) = all_6_2
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | GROUND_INST: instantiating (1) with all_6_2, all_52_4, e3, e3, simplifying
% 204.26/35.13  |              with (6), (7) gives:
% 204.26/35.13  |   (8)  all_52_4 = all_6_2
% 204.26/35.13  | 
% 204.26/35.13  | GROUND_INST: instantiating (1) with e2, all_52_4, e3, e3, simplifying with
% 204.26/35.13  |              (4), (6) gives:
% 204.26/35.13  |   (9)  all_52_4 = e2
% 204.26/35.13  | 
% 204.26/35.13  | COMBINE_EQS: (8), (9) imply:
% 204.26/35.13  |   (10)  all_6_2 = e2
% 204.26/35.13  | 
% 204.26/35.13  | REF_CLOSE: (1), (2), (3), (5), (10) are inconsistent by sub-proof #833.
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #833 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  all_6_2 = e2
% 204.26/35.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (3)  op(e2, e3) = all_52_3
% 204.26/35.13    (4)   ~ (all_52_3 = all_6_2)
% 204.26/35.13    (5)  op(all_6_2, e3) = e2
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | SIMP: (1) implies:
% 204.26/35.13  |   (6)  all_6_2 = e2
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (4), (6) imply:
% 204.26/35.13  |   (7)   ~ (all_52_3 = e2)
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (5), (6) imply:
% 204.26/35.13  |   (8)  op(e2, e3) = e2
% 204.26/35.13  | 
% 204.26/35.13  | GROUND_INST: instantiating (2) with all_52_3, e2, e3, e2, simplifying with
% 204.26/35.13  |              (3), (8) gives:
% 204.26/35.13  |   (9)  all_52_3 = e2
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (7), (9) imply:
% 204.26/35.13  |   (10)  $false
% 204.26/35.13  | 
% 204.26/35.13  | CLOSE: (10) is inconsistent.
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #834 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.26/35.13    (2)  all_52_8 = all_6_2
% 204.26/35.13    (3)   ~ (all_6_2 = e3)
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | ALPHA: (1) implies:
% 204.26/35.13  |   (4)  all_52_8 = e3
% 204.26/35.13  | 
% 204.26/35.13  | COMBINE_EQS: (2), (4) imply:
% 204.26/35.13  |   (5)  all_6_2 = e3
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (3), (5) imply:
% 204.26/35.13  |   (6)  $false
% 204.26/35.13  | 
% 204.26/35.13  | CLOSE: (6) is inconsistent.
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #835 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (3)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.26/35.13    (4)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.13    (5)  all_58_0 = all_6_2
% 204.26/35.13    (6)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.13    (7)  op(e2, e2) = all_4_2
% 204.26/35.13    (8)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.13    (9)  op(e0, e0) = all_14_2
% 204.26/35.13    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.13    (11)   ~ (all_6_2 = e3)
% 204.26/35.13    (12)  all_58_12 = all_52_7
% 204.26/35.13    (13)   ~ (all_52_7 = all_14_2)
% 204.26/35.13    (14)  all_58_2 = all_52_3
% 204.26/35.13    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.13    (16)   ~ (all_52_5 = all_10_2)
% 204.26/35.13    (17)  op(e3, e3) = all_6_2
% 204.26/35.13    (18)  all_58_6 = all_52_5
% 204.26/35.13    (19)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.13    (20)  op(e1, e1) = all_10_2
% 204.26/35.13    (21)   ~ (all_52_3 = all_4_2)
% 204.26/35.13  
% 204.26/35.13  Begin of proof
% 204.26/35.13  | 
% 204.26/35.13  | ALPHA: (3) implies:
% 204.26/35.13  |   (22)  all_52_6 = e0
% 204.26/35.13  |   (23)  all_52_4 = e1
% 204.26/35.13  |   (24)  all_52_2 = e2
% 204.26/35.13  |   (25)  all_52_0 = e3
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (1), (24) imply:
% 204.26/35.13  |   (26)  op(all_52_3, all_52_3) = e2
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (6), (23) imply:
% 204.26/35.13  |   (27)  op(all_52_5, all_52_5) = e1
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (4), (22) imply:
% 204.26/35.13  |   (28)  op(all_52_7, all_52_7) = e0
% 204.26/35.13  | 
% 204.26/35.13  | REDUCE: (8), (25) imply:
% 204.26/35.13  |   (29)  op(all_6_2, all_6_2) = e3
% 204.26/35.13  | 
% 204.26/35.13  | REF_CLOSE: (2), (5), (7), (9), (10), (11), (12), (13), (14), (15), (16), (17),
% 204.26/35.13  |            (18), (19), (20), (21), (26), (27), (28), (29) are inconsistent by
% 204.26/35.13  |            sub-proof #1362.
% 204.26/35.13  | 
% 204.26/35.13  End of proof
% 204.26/35.13  
% 204.26/35.13  Sub-proof #836 shows that the following formulas are inconsistent:
% 204.26/35.13  ----------------------------------------------------------------
% 204.26/35.13    (1)  all_24_0 = e1
% 204.26/35.13    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.13    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.13    (4)  all_58_14 = all_52_23
% 204.26/35.13    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.13    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.13    (7)   ~ (all_52_5 = all_52_13)
% 204.26/35.13    (8)  all_58_1 = all_52_9
% 204.26/35.13    (9)   ~ (all_52_9 = all_52_13)
% 204.26/35.13    (10)   ~ (e3 = e0)
% 204.26/35.13    (11)  op(e2, e3) = all_52_3
% 204.26/35.13    (12)  all_24_1 = all_14_1
% 204.26/35.13    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.13    (14)  op(e0, e2) = all_52_15
% 204.26/35.13    (15)   ~ (all_52_7 = all_52_15)
% 204.26/35.13    (16)  all_34_0 = all_14_0
% 204.26/35.13    (17)   ~ (all_52_3 = all_52_19)
% 204.26/35.13    (18)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.13    (19)   ~ (all_52_17 = all_52_25)
% 204.26/35.13    (20)   ~ (all_52_3 = all_6_2)
% 204.26/35.13    (21)  all_58_0 = all_6_2
% 204.26/35.13    (22)  op(all_14_2, e0) = all_14_1
% 204.26/35.13    (23)  all_34_1 = all_14_1
% 204.26/35.13    (24)  all_56_4 = all_52_3
% 204.26/35.13    (25)  all_38_2 = all_4_2
% 204.26/35.13    (26)   ~ (all_52_17 = all_10_2)
% 204.26/35.13    (27)  op(e3, e0) = all_52_25
% 204.26/35.13    (28)  op(e0, all_14_1) = all_14_0
% 204.26/35.13    (29)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.13    (30)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.13    (31)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.13    (32)   ~ (all_52_27 = all_52_29)
% 204.26/35.13    (33)  all_58_13 = all_52_15
% 204.26/35.13    (34)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.13    (35)  all_58_9 = all_52_25
% 204.26/35.13    (36)   ~ (all_6_1 = e1)
% 204.26/35.13    (37)   ~ (all_52_29 = all_14_2)
% 204.26/35.13    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.13    (39)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.13    (40)  op(e1, e3) = all_52_5
% 204.26/35.13    (41)  op(e2, e2) = all_4_2
% 204.26/35.13    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.13    (43)   ~ (all_52_3 = all_52_5)
% 204.26/35.13    (44)  all_58_11 = all_52_29
% 204.26/35.13    (45)  all_56_5 = all_4_2
% 204.26/35.13    (46)   ~ (all_52_25 = all_14_2)
% 204.26/35.13    (47)   ~ (all_52_9 = all_52_15)
% 204.26/35.13    (48)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.13    (49)   ~ (all_52_3 = all_52_27)
% 204.26/35.13    (50)  op(all_10_2, e1) = all_10_1
% 204.26/35.13    (51)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.13    (52)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.13    (53)   ~ (all_52_7 = all_6_2)
% 204.26/35.13    (54)  op(e0, e0) = all_14_2
% 204.26/35.13    (55)  op(e0, e1) = all_52_23
% 204.26/35.13    (56)  all_56_15 = all_14_2
% 204.26/35.13    (57)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.13    (58)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.13    (59)  op(e2, all_4_1) = all_4_0
% 204.26/35.13    (60)  op(e1, e0) = all_52_29
% 204.26/35.13    (61)  all_56_11 = all_52_29
% 204.26/35.13    (62)   ~ (all_4_1 = e1)
% 204.26/35.13    (63)   ~ (all_4_0 = e3)
% 204.26/35.13    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.13    (65)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.13    (66)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.13    (67)  all_56_9 = all_52_13
% 204.26/35.13    (68)   ~ (all_52_13 = all_10_2)
% 204.26/35.13    (69)   ~ (all_6_0 = e1)
% 204.26/35.13    (70)  all_58_10 = all_52_27
% 204.26/35.13    (71)  all_24_0 = all_14_0
% 204.26/35.13    (72)  all_56_8 = all_52_5
% 204.26/35.13    (73)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.14    (74)  op(all_52_15, all_52_15) = all_52_14
% 204.26/35.14    (75)   ~ (all_52_19 = all_52_23)
% 204.26/35.14    (76)   ~ (all_52_25 = all_52_29)
% 204.26/35.14    (77)   ~ (all_52_29 = all_10_2)
% 204.26/35.14    (78)  all_58_7 = all_52_13
% 204.26/35.14    (79)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.14    (80)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.14    (81)   ~ (all_52_5 = all_52_7)
% 204.26/35.14    (82)  all_58_12 = all_52_7
% 204.26/35.14    (83)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.14    (84)   ~ (all_52_7 = all_14_2)
% 204.26/35.14    (85)  all_38_0 = all_4_0
% 204.26/35.14    (86)  all_58_2 = all_52_3
% 204.26/35.14    (87)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.14    (88)  all_56_2 = all_52_17
% 204.26/35.14    (89)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.14    (90)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.14    (91)  op(e3, all_6_1) = all_6_0
% 204.26/35.14    (92)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.14    (93)   ~ (all_14_0 = e3)
% 204.26/35.14    (94)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.14    (95)  all_56_7 = all_52_27
% 204.26/35.14    (96)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.14    (97)   ~ (e2 = e0)
% 204.26/35.14    (98)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.14    (99)  op(all_4_2, e2) = all_4_1
% 204.26/35.14    (100)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.14    (101)   ~ (all_52_5 = all_52_29)
% 204.26/35.14    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.14    (103)  all_56_6 = all_52_19
% 204.26/35.14    (104)  all_38_1 = all_4_1
% 204.26/35.14    (105)   ~ (all_52_15 = all_14_2)
% 204.26/35.14    (106)   ~ (all_52_19 = all_52_27)
% 204.26/35.14    (107)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.14    (108)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.14    (109)   ~ (all_6_0 = e2)
% 204.26/35.14    (110)   ~ (all_32_0 = e0) |  ~ (all_32_1 = e3) |  ~ (all_32_2 = e1)
% 204.26/35.14    (111)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.26/35.14             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.26/35.14    (112)   ~ (all_52_13 = all_4_2)
% 204.26/35.14    (113)  op(e3, e1) = all_52_17
% 204.26/35.14    (114)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.14    (115)  op(e0, e3) = all_52_7
% 204.26/35.14    (116)  op(e1, e2) = all_52_13
% 204.26/35.14    (117)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.14    (118)   ~ (all_52_9 = all_52_25)
% 204.26/35.14    (119)  all_58_15 = all_14_2
% 204.26/35.14    (120)   ~ (all_52_19 = all_10_2)
% 204.26/35.14    (121)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.14    (122)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.14    (123)  all_58_8 = all_10_2
% 204.26/35.14    (124)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.14    (125)  all_34_2 = all_14_2
% 204.26/35.14    (126)   ~ (all_52_5 = all_10_2)
% 204.26/35.14    (127)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.14    (128)   ~ (all_52_23 = all_14_2)
% 204.26/35.14    (129)  all_56_12 = all_52_7
% 204.26/35.14    (130)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.14    (131)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.14    (132)   ~ (all_52_25 = all_6_2)
% 204.26/35.14    (133)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.14    (134)   ~ (all_52_9 = all_4_2)
% 204.26/35.14    (135)   ~ (all_52_5 = all_6_2)
% 204.26/35.14    (136)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.26/35.14    (137)  all_32_1 = all_4_1
% 204.26/35.14    (138)   ~ (all_52_9 = all_6_2)
% 204.26/35.14    (139)  all_24_2 = all_14_2
% 204.26/35.14    (140)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 204.26/35.14    (141)   ~ (all_52_13 = all_52_15)
% 204.26/35.14    (142)  all_56_0 = all_6_2
% 204.26/35.14    (143)  op(e3, e3) = all_6_2
% 204.26/35.14    (144)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.14    (145)   ~ (all_52_27 = all_14_2)
% 204.26/35.14    (146)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.14    (147)  all_56_14 = all_52_23
% 204.26/35.14    (148)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.14    (149)  all_56_3 = all_52_25
% 204.26/35.14    (150)   ~ (all_52_3 = all_52_7)
% 204.26/35.14    (151)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.14    (152)  all_58_5 = all_52_19
% 204.26/35.14    (153)  all_56_1 = all_52_9
% 204.26/35.14    (154)   ~ (all_52_15 = all_4_2)
% 204.26/35.14    (155)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.14           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.14           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.14           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.14    (156)   ~ (all_52_27 = all_4_2)
% 204.26/35.14    (157)  all_58_6 = all_52_5
% 204.26/35.14    (158)  op(e3, e2) = all_52_9
% 204.26/35.14    (159)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.14    (160)   ~ (all_52_17 = all_6_2)
% 204.26/35.14    (161)   ~ (e1 = e0)
% 204.26/35.14    (162)  op(e2, e0) = all_52_27
% 204.26/35.14    (163)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.26/35.14    (164)   ~ (e3 = e2)
% 204.26/35.14    (165)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.14    (166)   ~ (all_52_9 = all_52_17)
% 204.26/35.14    (167)  all_56_10 = all_10_2
% 204.26/35.14    (168)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.14    (169)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.14    (170)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.26/35.14    (171)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.14    (172)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.14    (173)   ~ (all_6_1 = e2)
% 204.26/35.14    (174)  op(e1, e1) = all_10_2
% 204.26/35.14    (175)   ~ (all_52_23 = all_10_2)
% 204.26/35.14    (176)   ~ (all_52_7 = all_52_23)
% 204.26/35.14    (177)   ~ (all_52_17 = all_52_19)
% 204.26/35.14    (178)  all_58_3 = all_4_2
% 204.26/35.14    (179)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.14    (180)  all_56_13 = all_52_15
% 204.26/35.14    (181)   ~ (all_52_3 = all_4_2)
% 204.26/35.14    (182)   ~ (all_52_19 = all_4_2)
% 204.26/35.14    (183)   ~ (all_52_17 = all_52_23)
% 204.26/35.14    (184)  op(all_6_2, e3) = all_6_1
% 204.26/35.14    (185)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.26/35.14    (186)   ~ (all_52_13 = all_52_29)
% 204.26/35.14    (187)  all_58_4 = all_52_17
% 204.26/35.14    (188)   ~ (all_14_0 = e2)
% 204.26/35.14    (189)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.14    (190)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.14  
% 204.26/35.14  Begin of proof
% 204.26/35.14  | 
% 204.26/35.14  | COMBINE_EQS: (1), (71) imply:
% 204.26/35.14  |   (191)  all_14_0 = e1
% 204.26/35.14  | 
% 204.26/35.14  | SIMP: (191) implies:
% 204.26/35.14  |   (192)  all_14_0 = e1
% 204.26/35.14  | 
% 204.26/35.14  | COMBINE_EQS: (16), (192) imply:
% 204.26/35.14  |   (193)  all_34_0 = e1
% 204.26/35.14  | 
% 204.26/35.14  | REDUCE: (93), (192) imply:
% 204.26/35.14  |   (194)   ~ (e3 = e1)
% 204.26/35.14  | 
% 204.26/35.14  | SIMP: (194) implies:
% 204.26/35.14  |   (195)   ~ (e3 = e1)
% 204.26/35.14  | 
% 204.26/35.14  | REDUCE: (188), (192) imply:
% 204.26/35.14  |   (196)   ~ (e2 = e1)
% 204.26/35.14  | 
% 204.26/35.14  | SIMP: (196) implies:
% 204.26/35.14  |   (197)   ~ (e2 = e1)
% 204.26/35.14  | 
% 204.26/35.14  | REDUCE: (28), (192) imply:
% 204.26/35.14  |   (198)  op(e0, all_14_1) = e1
% 204.26/35.14  | 
% 204.26/35.14  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.26/35.14  |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.26/35.14  |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 204.26/35.14  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.26/35.14  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 204.26/35.14  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.26/35.14  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 204.26/35.14  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (94),
% 204.26/35.14  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 204.26/35.14  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 204.26/35.14  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 204.26/35.14  |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 204.26/35.14  |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 204.26/35.14  |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 204.26/35.14  |            (150), (151), (152), (153), (154), (155), (156), (157), (158),
% 204.26/35.14  |            (159), (160), (161), (162), (163), (164), (165), (166), (167),
% 204.26/35.14  |            (168), (169), (170), (171), (172), (173), (174), (175), (176),
% 204.26/35.14  |            (177), (178), (179), (180), (181), (182), (183), (184), (185),
% 204.26/35.14  |            (186), (187), (189), (190), (193), (195), (197), (198) are
% 204.26/35.14  |            inconsistent by sub-proof #837.
% 204.26/35.14  | 
% 204.26/35.14  End of proof
% 204.26/35.14  
% 204.26/35.14  Sub-proof #837 shows that the following formulas are inconsistent:
% 204.26/35.14  ----------------------------------------------------------------
% 204.26/35.14    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.14    (2)   ~ (all_52_25 = all_52_27)
% 204.26/35.14    (3)  all_58_14 = all_52_23
% 204.26/35.14    (4)   ~ (e3 = e1)
% 204.26/35.14    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.14    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.14    (7)   ~ (all_52_5 = all_52_13)
% 204.26/35.14    (8)  all_58_1 = all_52_9
% 204.26/35.14    (9)   ~ (all_52_9 = all_52_13)
% 204.26/35.14    (10)   ~ (e3 = e0)
% 204.26/35.14    (11)  op(e2, e3) = all_52_3
% 204.26/35.14    (12)  all_24_1 = all_14_1
% 204.26/35.14    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.14    (14)  op(e0, e2) = all_52_15
% 204.26/35.14    (15)   ~ (all_52_7 = all_52_15)
% 204.26/35.14    (16)   ~ (all_52_3 = all_52_19)
% 204.26/35.14    (17)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.14    (18)   ~ (all_52_17 = all_52_25)
% 204.26/35.14    (19)   ~ (all_52_3 = all_6_2)
% 204.26/35.14    (20)  all_58_0 = all_6_2
% 204.26/35.14    (21)  op(all_14_2, e0) = all_14_1
% 204.26/35.14    (22)  all_34_1 = all_14_1
% 204.26/35.14    (23)  all_56_4 = all_52_3
% 204.26/35.14    (24)  all_38_2 = all_4_2
% 204.26/35.14    (25)   ~ (all_52_17 = all_10_2)
% 204.26/35.14    (26)  op(e3, e0) = all_52_25
% 204.26/35.14    (27)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.14    (28)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.14    (29)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.14    (30)   ~ (all_52_27 = all_52_29)
% 204.26/35.14    (31)  all_58_13 = all_52_15
% 204.26/35.14    (32)  op(e0, all_14_1) = e1
% 204.26/35.14    (33)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.14    (34)  all_58_9 = all_52_25
% 204.26/35.14    (35)   ~ (all_6_1 = e1)
% 204.26/35.14    (36)   ~ (all_52_29 = all_14_2)
% 204.26/35.14    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.14    (38)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.14    (39)  op(e1, e3) = all_52_5
% 204.26/35.14    (40)  op(e2, e2) = all_4_2
% 204.26/35.14    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.14    (42)   ~ (all_52_3 = all_52_5)
% 204.26/35.14    (43)  all_58_11 = all_52_29
% 204.26/35.14    (44)  all_56_5 = all_4_2
% 204.26/35.14    (45)   ~ (all_52_25 = all_14_2)
% 204.26/35.14    (46)   ~ (all_52_9 = all_52_15)
% 204.26/35.14    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.14    (48)   ~ (all_52_3 = all_52_27)
% 204.26/35.14    (49)  op(all_10_2, e1) = all_10_1
% 204.26/35.14    (50)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.14    (51)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.14    (52)   ~ (all_52_7 = all_6_2)
% 204.26/35.14    (53)  op(e0, e0) = all_14_2
% 204.26/35.14    (54)  op(e0, e1) = all_52_23
% 204.26/35.14    (55)  all_56_15 = all_14_2
% 204.26/35.14    (56)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.14    (57)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.14    (58)  op(e2, all_4_1) = all_4_0
% 204.26/35.14    (59)  op(e1, e0) = all_52_29
% 204.26/35.14    (60)  all_56_11 = all_52_29
% 204.26/35.14    (61)   ~ (all_4_1 = e1)
% 204.26/35.14    (62)   ~ (all_4_0 = e3)
% 204.26/35.14    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.14    (64)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.14    (65)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.14    (66)  all_56_9 = all_52_13
% 204.26/35.14    (67)   ~ (e2 = e1)
% 204.26/35.14    (68)   ~ (all_52_13 = all_10_2)
% 204.26/35.14    (69)   ~ (all_6_0 = e1)
% 204.26/35.14    (70)  all_58_10 = all_52_27
% 204.26/35.14    (71)  all_56_8 = all_52_5
% 204.26/35.14    (72)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.14    (73)  op(all_52_15, all_52_15) = all_52_14
% 204.26/35.14    (74)   ~ (all_52_19 = all_52_23)
% 204.26/35.14    (75)   ~ (all_52_25 = all_52_29)
% 204.26/35.14    (76)   ~ (all_52_29 = all_10_2)
% 204.26/35.14    (77)  all_58_7 = all_52_13
% 204.26/35.14    (78)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.14    (79)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.14    (80)   ~ (all_52_5 = all_52_7)
% 204.26/35.14    (81)  all_58_12 = all_52_7
% 204.26/35.14    (82)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.14    (83)   ~ (all_52_7 = all_14_2)
% 204.26/35.14    (84)  all_38_0 = all_4_0
% 204.26/35.14    (85)  all_58_2 = all_52_3
% 204.26/35.14    (86)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.14    (87)  all_56_2 = all_52_17
% 204.26/35.14    (88)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.14    (89)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.14    (90)  op(e3, all_6_1) = all_6_0
% 204.26/35.14    (91)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.14    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.14    (93)  all_56_7 = all_52_27
% 204.26/35.14    (94)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.14    (95)   ~ (e2 = e0)
% 204.26/35.14    (96)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.14    (97)  op(all_4_2, e2) = all_4_1
% 204.26/35.14    (98)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.14    (99)   ~ (all_52_5 = all_52_29)
% 204.26/35.14    (100)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.14    (101)  all_56_6 = all_52_19
% 204.26/35.14    (102)  all_38_1 = all_4_1
% 204.26/35.14    (103)   ~ (all_52_15 = all_14_2)
% 204.26/35.14    (104)   ~ (all_52_19 = all_52_27)
% 204.26/35.14    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.14    (106)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.14    (107)   ~ (all_6_0 = e2)
% 204.26/35.14    (108)   ~ (all_32_0 = e0) |  ~ (all_32_1 = e3) |  ~ (all_32_2 = e1)
% 204.26/35.14    (109)  all_34_0 = e1
% 204.26/35.14    (110)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.26/35.14             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 204.26/35.14    (111)   ~ (all_52_13 = all_4_2)
% 204.26/35.14    (112)  op(e3, e1) = all_52_17
% 204.26/35.14    (113)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.14    (114)  op(e0, e3) = all_52_7
% 204.26/35.14    (115)  op(e1, e2) = all_52_13
% 204.26/35.14    (116)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.14    (117)   ~ (all_52_9 = all_52_25)
% 204.26/35.14    (118)  all_58_15 = all_14_2
% 204.26/35.14    (119)   ~ (all_52_19 = all_10_2)
% 204.26/35.14    (120)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.14    (121)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.14    (122)  all_58_8 = all_10_2
% 204.26/35.14    (123)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.14    (124)  all_34_2 = all_14_2
% 204.26/35.14    (125)   ~ (all_52_5 = all_10_2)
% 204.26/35.14    (126)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.14    (127)   ~ (all_52_23 = all_14_2)
% 204.26/35.14    (128)  all_56_12 = all_52_7
% 204.26/35.14    (129)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.14    (130)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.14    (131)   ~ (all_52_25 = all_6_2)
% 204.26/35.14    (132)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.14    (133)   ~ (all_52_9 = all_4_2)
% 204.26/35.14    (134)   ~ (all_52_5 = all_6_2)
% 204.26/35.14    (135)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.26/35.14    (136)  all_32_1 = all_4_1
% 204.26/35.14    (137)   ~ (all_52_9 = all_6_2)
% 204.26/35.14    (138)  all_24_2 = all_14_2
% 204.26/35.14    (139)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 204.26/35.14    (140)   ~ (all_52_13 = all_52_15)
% 204.26/35.14    (141)  all_56_0 = all_6_2
% 204.26/35.14    (142)  op(e3, e3) = all_6_2
% 204.26/35.14    (143)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.14    (144)   ~ (all_52_27 = all_14_2)
% 204.26/35.14    (145)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.14    (146)  all_56_14 = all_52_23
% 204.26/35.14    (147)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.14    (148)  all_56_3 = all_52_25
% 204.26/35.14    (149)   ~ (all_52_3 = all_52_7)
% 204.26/35.14    (150)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.14    (151)  all_58_5 = all_52_19
% 204.26/35.14    (152)  all_56_1 = all_52_9
% 204.26/35.14    (153)   ~ (all_52_15 = all_4_2)
% 204.26/35.14    (154)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.14           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.14           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.14           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.14    (155)   ~ (all_52_27 = all_4_2)
% 204.26/35.14    (156)  all_58_6 = all_52_5
% 204.26/35.14    (157)  op(e3, e2) = all_52_9
% 204.26/35.14    (158)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.14    (159)   ~ (all_52_17 = all_6_2)
% 204.26/35.14    (160)   ~ (e1 = e0)
% 204.26/35.14    (161)  op(e2, e0) = all_52_27
% 204.26/35.14    (162)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.26/35.14    (163)   ~ (e3 = e2)
% 204.26/35.14    (164)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.14    (165)   ~ (all_52_9 = all_52_17)
% 204.26/35.14    (166)  all_56_10 = all_10_2
% 204.26/35.14    (167)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.14    (168)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.14    (169)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.26/35.14    (170)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.14    (171)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.14    (172)   ~ (all_6_1 = e2)
% 204.26/35.14    (173)  op(e1, e1) = all_10_2
% 204.26/35.14    (174)   ~ (all_52_23 = all_10_2)
% 204.26/35.14    (175)   ~ (all_52_7 = all_52_23)
% 204.26/35.14    (176)   ~ (all_52_17 = all_52_19)
% 204.26/35.14    (177)  all_58_3 = all_4_2
% 204.26/35.14    (178)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.14    (179)  all_56_13 = all_52_15
% 204.26/35.14    (180)   ~ (all_52_3 = all_4_2)
% 204.26/35.14    (181)   ~ (all_52_19 = all_4_2)
% 204.26/35.14    (182)   ~ (all_52_17 = all_52_23)
% 204.26/35.14    (183)  op(all_6_2, e3) = all_6_1
% 204.26/35.14    (184)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.26/35.14    (185)   ~ (all_52_13 = all_52_29)
% 204.26/35.14    (186)  all_58_4 = all_52_17
% 204.26/35.14    (187)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.14    (188)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.14  
% 204.26/35.14  Begin of proof
% 204.26/35.14  | 
% 204.26/35.14  | BETA: splitting (108) gives:
% 204.26/35.14  | 
% 204.26/35.14  | Case 1:
% 204.26/35.14  | | 
% 204.26/35.14  | |   (189)   ~ (all_32_1 = e3)
% 204.26/35.14  | | 
% 204.26/35.14  | | REDUCE: (136), (189) imply:
% 204.26/35.14  | |   (190)   ~ (all_4_1 = e3)
% 204.26/35.14  | | 
% 204.26/35.14  | | BETA: splitting (50) gives:
% 204.26/35.14  | | 
% 204.26/35.14  | | Case 1:
% 204.26/35.14  | | | 
% 204.26/35.14  | | |   (191)   ~ (all_34_0 = e1)
% 204.26/35.14  | | | 
% 204.26/35.14  | | | REDUCE: (109), (191) imply:
% 204.26/35.14  | | |   (192)  $false
% 204.26/35.14  | | | 
% 204.26/35.14  | | | CLOSE: (192) is inconsistent.
% 204.26/35.14  | | | 
% 204.26/35.14  | | Case 2:
% 204.26/35.14  | | | 
% 204.26/35.14  | | |   (193)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.14  | | | 
% 204.26/35.14  | | | BETA: splitting (110) gives:
% 204.26/35.14  | | | 
% 204.26/35.14  | | | Case 1:
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | |   (194)  all_58_15 = e0
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | | REF_CLOSE: (6), (21), (32), (53), (118), (150), (160), (194) are
% 204.26/35.14  | | | |            inconsistent by sub-proof #877.
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | Case 2:
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | |   (195)   ~ (all_58_15 = e0)
% 204.26/35.14  | | | |   (196)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 204.26/35.14  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | | ALPHA: (196) implies:
% 204.26/35.14  | | | |   (197)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.14  | | | |   (198)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | | REDUCE: (118), (195) imply:
% 204.26/35.14  | | | |   (199)   ~ (all_14_2 = e0)
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | | BETA: splitting (154) gives:
% 204.26/35.14  | | | | 
% 204.26/35.14  | | | | Case 1:
% 204.26/35.14  | | | | | 
% 204.26/35.14  | | | | |   (200)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 204.26/35.14  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 204.26/35.14  | | | | |            all_52_14 = e0)
% 204.26/35.14  | | | | | 
% 204.26/35.14  | | | | | BETA: splitting (200) gives:
% 204.26/35.14  | | | | | 
% 204.26/35.14  | | | | | Case 1:
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | |   (201)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 204.26/35.14  | | | | | |          e0
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | ALPHA: (201) implies:
% 204.26/35.14  | | | | | |   (202)  all_52_6 = e0
% 204.26/35.14  | | | | | |   (203)  all_52_4 = e1
% 204.26/35.14  | | | | | |   (204)  all_52_2 = e2
% 204.26/35.14  | | | | | |   (205)  all_52_0 = e3
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | REDUCE: (5), (204) imply:
% 204.26/35.14  | | | | | |   (206)  op(all_52_3, all_52_3) = e2
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | REDUCE: (27), (203) imply:
% 204.26/35.14  | | | | | |   (207)  op(all_52_5, all_52_5) = e1
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | REDUCE: (17), (202) imply:
% 204.26/35.14  | | | | | |   (208)  op(all_52_7, all_52_7) = e0
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | REDUCE: (51), (205) imply:
% 204.26/35.14  | | | | | |   (209)  op(all_6_2, all_6_2) = e3
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | BETA: splitting (123) gives:
% 204.26/35.14  | | | | | | 
% 204.26/35.14  | | | | | | Case 1:
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | |   (210)  all_56_15 = e3
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | COMBINE_EQS: (55), (210) imply:
% 204.26/35.14  | | | | | | |   (211)  all_14_2 = e3
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | SIMP: (211) implies:
% 204.26/35.14  | | | | | | |   (212)  all_14_2 = e3
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | COMBINE_EQS: (124), (212) imply:
% 204.26/35.14  | | | | | | |   (213)  all_34_2 = e3
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (127), (212) imply:
% 204.26/35.14  | | | | | | |   (214)   ~ (all_52_23 = e3)
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (45), (212) imply:
% 204.26/35.14  | | | | | | |   (215)   ~ (all_52_25 = e3)
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (36), (212) imply:
% 204.26/35.14  | | | | | | |   (216)   ~ (all_52_29 = e3)
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (150), (212) imply:
% 204.26/35.14  | | | | | | |   (217)  op(e3, e3) = all_52_30
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (21), (212) imply:
% 204.26/35.14  | | | | | | |   (218)  op(e3, e0) = all_14_1
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (53), (212) imply:
% 204.26/35.14  | | | | | | |   (219)  op(e0, e0) = e3
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REF_CLOSE: (2), (4), (6), (20), (22), (26), (32), (34), (40),
% 204.26/35.14  | | | | | | |            (42), (43), (53), (54), (56), (57), (70), (74), (75),
% 204.26/35.14  | | | | | | |            (77), (79), (81), (82), (83), (85), (89), (111), (120),
% 204.26/35.14  | | | | | | |            (122), (125), (130), (132), (134), (142), (148), (151),
% 204.26/35.14  | | | | | | |            (156), (158), (163), (171), (173), (174), (177), (180),
% 204.26/35.14  | | | | | | |            (188), (193), (206), (207), (208), (209), (213), (214),
% 204.26/35.14  | | | | | | |            (215), (216), (217), (218), (219) are inconsistent by
% 204.26/35.14  | | | | | | |            sub-proof #866.
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | Case 2:
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | |   (220)   ~ (all_56_15 = e3)
% 204.26/35.14  | | | | | | |   (221)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | REDUCE: (55), (220) imply:
% 204.26/35.14  | | | | | | |   (222)   ~ (all_14_2 = e3)
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | BETA: splitting (63) gives:
% 204.26/35.14  | | | | | | | 
% 204.26/35.14  | | | | | | | Case 1:
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | |   (223)  all_56_13 = e3
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | | COMBINE_EQS: (179), (223) imply:
% 204.26/35.14  | | | | | | | |   (224)  all_52_15 = e3
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | | SIMP: (224) implies:
% 204.26/35.14  | | | | | | | |   (225)  all_52_15 = e3
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | | REF_CLOSE: (3), (6), (10), (13), (14), (15), (31), (40), (47),
% 204.26/35.14  | | | | | | | |            (53), (81), (83), (97), (100), (128), (160), (173),
% 204.26/35.14  | | | | | | | |            (174), (190), (197), (208), (225) are inconsistent by
% 204.26/35.14  | | | | | | | |            sub-proof #1168.
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | Case 2:
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | |   (226)   ~ (all_56_13 = e3)
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | | REDUCE: (179), (226) imply:
% 204.26/35.14  | | | | | | | |   (227)   ~ (all_52_15 = e3)
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | | BETA: splitting (158) gives:
% 204.26/35.14  | | | | | | | | 
% 204.26/35.14  | | | | | | | | Case 1:
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | |   (228)  all_58_12 = e3
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | COMBINE_EQS: (81), (228) imply:
% 204.26/35.14  | | | | | | | | |   (229)  all_52_7 = e3
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | REF_CLOSE: (6), (20), (40), (52), (53), (56), (81), (83),
% 204.26/35.14  | | | | | | | | |            (85), (89), (125), (142), (156), (158), (173),
% 204.26/35.14  | | | | | | | | |            (180), (206), (207), (208), (209), (229) are
% 204.26/35.14  | | | | | | | | |            inconsistent by sub-proof #1361.
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | Case 2:
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | |   (230)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | BETA: splitting (230) gives:
% 204.26/35.14  | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | Case 1:
% 204.26/35.14  | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | |   (231)  all_58_13 = e3
% 204.26/35.14  | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | REF_CLOSE: (31), (227), (231) are inconsistent by sub-proof
% 204.26/35.14  | | | | | | | | | |            #1360.
% 204.26/35.14  | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | Case 2:
% 204.26/35.14  | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | |   (232)  all_58_14 = e3 | all_58_15 = e3
% 204.26/35.14  | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | BETA: splitting (232) gives:
% 204.26/35.14  | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | Case 1:
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | |   (233)  all_58_14 = e3
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | COMBINE_EQS: (3), (233) imply:
% 204.26/35.14  | | | | | | | | | | |   (234)  all_52_23 = e3
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | SIMP: (234) implies:
% 204.26/35.14  | | | | | | | | | | |   (235)  all_52_23 = e3
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | REDUCE: (175), (235) imply:
% 204.26/35.14  | | | | | | | | | | |   (236)   ~ (all_52_7 = e3)
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | REDUCE: (127), (235) imply:
% 204.26/35.14  | | | | | | | | | | |   (237)   ~ (all_14_2 = e3)
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | REDUCE: (120), (235) imply:
% 204.26/35.14  | | | | | | | | | | |   (238)  op(e3, e3) = all_52_22
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 204.26/35.14  | | | | | | | | | | |              simplifying with (142), (238) gives:
% 204.26/35.14  | | | | | | | | | | |   (239)  all_52_22 = all_6_2
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | BETA: splitting (13) gives:
% 204.26/35.14  | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | Case 1:
% 204.26/35.14  | | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | |   (240)  all_56_12 = e3
% 204.26/35.14  | | | | | | | | | | | | 
% 204.26/35.14  | | | | | | | | | | | | REF_CLOSE: (128), (236), (240) are inconsistent by sub-proof
% 204.26/35.14  | | | | | | | | | | | |            #1383.
% 204.26/35.15  | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | |   (241)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.15  | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | BETA: splitting (143) gives:
% 204.26/35.15  | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | |   (242)  all_58_9 = e3
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | COMBINE_EQS: (34), (242) imply:
% 204.26/35.15  | | | | | | | | | | | | |   (243)  all_52_25 = e3
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | REF_CLOSE: (6), (20), (40), (53), (56), (81), (83), (85),
% 204.26/35.15  | | | | | | | | | | | | |            (89), (125), (131), (142), (156), (158), (173),
% 204.26/35.15  | | | | | | | | | | | | |            (180), (206), (207), (208), (209), (243) are
% 204.26/35.15  | | | | | | | | | | | | |            inconsistent by sub-proof #1000.
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | |   (244)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | BETA: splitting (145) gives:
% 204.26/35.15  | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | |   (245)  all_58_0 = e3
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | COMBINE_EQS: (20), (245) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (246)  all_6_2 = e3
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (134), (246) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (247)   ~ (all_52_5 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (137), (246) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (248)   ~ (all_52_9 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (159), (246) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (249)   ~ (all_52_17 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (131), (246) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (250)   ~ (all_52_25 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (183), (246) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (251)  op(e3, e3) = all_6_1
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (142), (246) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (252)  op(e3, e3) = e3
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_1, e3, e3,
% 204.26/35.15  | | | | | | | | | | | | | |              simplifying with (251), (252) gives:
% 204.26/35.15  | | | | | | | | | | | | | |   (253)  all_6_1 = e3
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | REDUCE: (90), (253) imply:
% 204.26/35.15  | | | | | | | | | | | | | |   (254)  op(e3, e3) = all_6_0
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_0, e3, e3,
% 204.26/35.15  | | | | | | | | | | | | | |              simplifying with (252), (254) gives:
% 204.26/35.15  | | | | | | | | | | | | | |   (255)  all_6_0 = e3
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 204.26/35.15  | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | |   (256)  all_58_1 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | COMBINE_EQS: (8), (256) imply:
% 204.26/35.15  | | | | | | | | | | | | | | |   (257)  all_52_9 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | REDUCE: (248), (257) imply:
% 204.26/35.15  | | | | | | | | | | | | | | |   (258)  $false
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent.
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | |   (259)   ~ (all_58_1 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | |   (260)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | |   (261)  all_56_3 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | REF_CLOSE: (148), (250), (261) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | |            #1339.
% 204.26/35.15  | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | |   (262)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | |   (263)  all_56_8 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (247), (263) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | |            #1325.
% 204.26/35.15  | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | |   (264)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | |   (265)  all_56_1 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (152), (248), (265) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | |            #1326.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | |   (266)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (267)  all_58_3 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (267) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (268)  all_4_2 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | REDUCE: (180), (268) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_52_3 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | REDUCE: (155), (268) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (270)   ~ (all_52_27 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | REDUCE: (97), (268) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (271)  op(e3, e2) = all_4_1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | REDUCE: (40), (268) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (272)  op(e2, e2) = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | |   (273)  all_58_10 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (270), (273) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | |            #1301.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | |   (274)  all_58_11 = e3 | all_58_15 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_11 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (275) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (276)  all_52_29 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | SIMP: (276) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (277)  all_52_29 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (277) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (278)   ~ (all_52_13 = e3)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (277) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (279)  op(e1, e0) = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_9, all_4_1, e2, e3,
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |              simplifying with (157), (271) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (280)  all_52_9 = all_4_1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (280) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (281)  all_56_1 = all_4_1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (280) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (282)  all_58_1 = all_4_1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (280) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (283)   ~ (all_52_17 = all_4_1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (284)   ~ (all_52_17 = all_4_1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (280) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (285)   ~ (all_52_25 = all_4_1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | SIMP: (285) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (286)   ~ (all_52_25 = all_4_1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (280) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (287)  op(all_4_1, all_4_1) = all_52_8
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | |   (288)  all_58_0 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (40), (81), (85), (89), (156), (180),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | |            (236), (247), (272), (288) are inconsistent by
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1241.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | |   (289)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_58_9 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (290) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_52_25 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (291) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_52_25 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (292) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (293)   ~ (all_14_2 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (294)   ~ (all_14_2 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (21), (32), (38), (53), (55), (70),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (198), (199), (221), (275), (290),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |            (294) are inconsistent by sub-proof #862.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (295)   ~ (all_58_9 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (295) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | |   (297)   ~ (all_52_25 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_58_1 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (298) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_4_1 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (299) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | |   (300)  $false
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_58_4 = e1 | all_58_9 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_58_4 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (302) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_52_17 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (303) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_52_17 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (304) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (305)   ~ (all_52_19 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (306)   ~ (all_52_19 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (304) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (307)   ~ (all_10_2 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (307) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (308)   ~ (all_10_2 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (284), (304) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (309)   ~ (all_4_1 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (304) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (310)   ~ (e3 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (304) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  op(e1, e1) = all_52_16
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_16, e1,
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (173), (311) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_52_16 = all_10_2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_58_0 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (313) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  e3 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (314) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  $false
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_58_2 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (317) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_52_3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_52_3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (319) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)   ~ (all_52_5 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (320) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)   ~ (all_52_5 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (319) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)   ~ (all_52_27 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (322) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)   ~ (all_52_27 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (319) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  op(e1, e1) = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_58_6 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (321), (325) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #963.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_58_7 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (327) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_52_13 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (328) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  op(e1, e1) = all_52_12
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_10 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (323), (330) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #861.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_58_11 = e1 | all_58_15 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_58_11 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (332) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  e3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (40), (81), (85), (89), (156), (180),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (245), (247), (272), (333) are inconsistent
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #860.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  all_58_15 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (334) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_14_2 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (335) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)   ~ (all_52_7 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (335) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  op(e1, e1) = all_52_30
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (335) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  op(e1, e0) = all_14_1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_14_1, e0, e1,
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (279), (338) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_14_1 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_30, e1,
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (173), (337) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  all_52_30 = all_10_2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_30, all_52_12, e1,
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (329), (337) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_52_12 = all_52_30
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_52_12, e1, e1,
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (324), (329) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_52_12 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (342) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_52_30 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (343) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  all_52_30 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (340), (344) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  all_10_2 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (345) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)  all_10_2 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (346) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)   ~ (all_52_5 = e2)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (32), (71), (80), (114), (128), (156), (162),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (264), (279), (321), (336), (338), (347)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #858.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_58_8 = e1 | all_58_11 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  all_58_8 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (308), (349) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_58_11 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (350) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  e3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (40), (81), (85), (89), (156), (180),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (245), (247), (272), (351) are inconsistent
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #860.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  all_58_3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (353) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  e3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (354) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_58_0 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (40), (81), (85), (89), (156), (180),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (247), (272), (355) are inconsistent by
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1241.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_58_5 = e1 | all_58_10 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_58_5 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (151), (306), (357) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #857.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_58_10 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (358) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_52_27 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (359) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)  all_52_27 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (360) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)   ~ (all_14_2 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (361) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)   ~ (all_14_2 = e1)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  all_56_15 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (363) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_14_2 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (364) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)   ~ (all_52_25 = e2)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (364) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  op(e2, e2) = all_52_30
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  all_56_3 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (365), (367) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1259.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  all_56_3 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (369) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)  all_52_25 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (370) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  all_52_25 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (371) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_58_9 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (21), (32), (38), (53), (55), (70),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (198), (199), (221), (275), (362),
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (372) are inconsistent by sub-proof #862.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  all_56_3 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (373) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)  all_52_25 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (374) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)  all_52_25 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (286), (375) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)   ~ (all_4_1 = e0)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (376) implies:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)   ~ (all_4_1 = e0)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)  all_58_1 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (378) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  all_4_1 = e2
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (287), (379) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  op(e2, e2) = all_52_8
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (379) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  op(e2, e2) = all_4_0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (272), (366), (380), (381) are
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1166.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)   ~ (all_58_1 = e2)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (382) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)   ~ (all_4_1 = e2)
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (266), (281), (377), (383) are inconsistent
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1163.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  all_56_15 = e1 | all_56_15 = e0
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (199), (362), (384) are inconsistent by
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  all_58_9 = e1
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (297), (385) are inconsistent by sub-proof
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | |            #856.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (386)  all_58_15 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (386) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (387)  all_14_2 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (387) imply:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | |   (388)  $false
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | CLOSE: (388) is inconsistent.
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.15  | | | | | | | | | | | | | | | | | | |   (389)  all_58_7 = e3 | all_58_13 = e3
% 204.26/35.15  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (19), (20), (23), (31), (40), (42),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |            (47), (56), (67), (77), (79), (81), (85), (89),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |            (94), (95), (97), (100), (106), (115), (125),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |            (128), (142), (149), (153), (156), (163), (171),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |            (173), (177), (180), (184), (190), (197), (206),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (227), (233), (236), (241),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |            (389) are inconsistent by sub-proof #1147.
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | |   (390)   ~ (all_58_0 = e3)
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | REDUCE: (20), (390) imply:
% 204.26/35.16  | | | | | | | | | | | | | |   (391)   ~ (all_6_2 = e3)
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | REF_CLOSE: (6), (20), (40), (53), (56), (81), (83), (85),
% 204.26/35.16  | | | | | | | | | | | | | |            (89), (125), (142), (156), (158), (173), (180),
% 204.26/35.16  | | | | | | | | | | | | | |            (206), (207), (208), (209), (391) are inconsistent
% 204.26/35.16  | | | | | | | | | | | | | |            by sub-proof #1362.
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | |   (392)  all_58_15 = e3
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | COMBINE_EQS: (118), (392) imply:
% 204.26/35.16  | | | | | | | | | | |   (393)  all_14_2 = e3
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (222), (393) imply:
% 204.26/35.16  | | | | | | | | | | |   (394)  $false
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | CLOSE: (394) is inconsistent.
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | End of split
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | End of split
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | Case 2:
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | |   (395)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 204.26/35.16  | | | | | |          = e0
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | ALPHA: (395) implies:
% 204.26/35.16  | | | | | |   (396)  all_52_14 = e0
% 204.26/35.16  | | | | | |   (397)  all_52_12 = e1
% 204.26/35.16  | | | | | |   (398)  all_52_10 = e2
% 204.26/35.16  | | | | | |   (399)  all_52_8 = e3
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (72), (399) imply:
% 204.26/35.16  | | | | | |   (400)  op(all_52_9, all_52_9) = e3
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (171), (397) imply:
% 204.26/35.16  | | | | | |   (401)  op(all_52_13, all_52_13) = e1
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (73), (396) imply:
% 204.26/35.16  | | | | | |   (402)  op(all_52_15, all_52_15) = e0
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (147), (398) imply:
% 204.26/35.16  | | | | | |   (403)  op(all_4_2, all_4_2) = e2
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | BETA: splitting (123) gives:
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | Case 1:
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | |   (404)  all_56_15 = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | COMBINE_EQS: (55), (404) imply:
% 204.26/35.16  | | | | | | |   (405)  all_14_2 = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | SIMP: (405) implies:
% 204.26/35.16  | | | | | | |   (406)  all_14_2 = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | COMBINE_EQS: (124), (406) imply:
% 204.26/35.16  | | | | | | |   (407)  all_34_2 = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (127), (406) imply:
% 204.26/35.16  | | | | | | |   (408)   ~ (all_52_23 = e3)
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (45), (406) imply:
% 204.26/35.16  | | | | | | |   (409)   ~ (all_52_25 = e3)
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (36), (406) imply:
% 204.26/35.16  | | | | | | |   (410)   ~ (all_52_29 = e3)
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (21), (406) imply:
% 204.26/35.16  | | | | | | |   (411)  op(e3, e0) = all_14_1
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (53), (406) imply:
% 204.26/35.16  | | | | | | |   (412)  op(e0, e0) = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REF_CLOSE: (2), (4), (6), (22), (26), (27), (32), (34), (42),
% 204.26/35.16  | | | | | | |            (43), (54), (57), (68), (70), (74), (75), (77), (79),
% 204.26/35.16  | | | | | | |            (82), (85), (97), (111), (115), (120), (122), (130),
% 204.26/35.16  | | | | | | |            (132), (148), (151), (156), (163), (173), (174), (177),
% 204.26/35.16  | | | | | | |            (188), (190), (193), (401), (403), (407), (408), (409),
% 204.26/35.16  | | | | | | |            (410), (411), (412) are inconsistent by sub-proof #855.
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | Case 2:
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | |   (413)   ~ (all_56_15 = e3)
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (55), (413) imply:
% 204.26/35.16  | | | | | | |   (414)   ~ (all_14_2 = e3)
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13), (15),
% 204.26/35.16  | | | | | | |            (17), (18), (19), (20), (23), (25), (26), (27), (28),
% 204.26/35.16  | | | | | | |            (29), (30), (31), (33), (34), (35), (36), (38), (39),
% 204.26/35.16  | | | | | | |            (40), (42), (43), (44), (45), (48), (51), (52), (53),
% 204.26/35.16  | | | | | | |            (56), (60), (61), (63), (66), (67), (68), (69), (70),
% 204.26/35.16  | | | | | | |            (71), (74), (75), (77), (79), (80), (81), (82), (83),
% 204.26/35.16  | | | | | | |            (85), (89), (90), (92), (93), (94), (96), (97), (99),
% 204.26/35.16  | | | | | | |            (103), (105), (106), (107), (111), (114), (115), (116),
% 204.26/35.16  | | | | | | |            (117), (118), (120), (121), (122), (126), (127), (128),
% 204.26/35.16  | | | | | | |            (129), (131), (132), (133), (134), (137), (142), (143),
% 204.26/35.16  | | | | | | |            (145), (148), (149), (151), (152), (155), (156), (157),
% 204.26/35.16  | | | | | | |            (158), (163), (164), (165), (167), (168), (172), (175),
% 204.26/35.16  | | | | | | |            (177), (179), (180), (181), (182), (183), (185), (186),
% 204.26/35.16  | | | | | | |            (188), (190), (197), (198), (400), (401), (402), (403),
% 204.26/35.16  | | | | | | |            (414) are inconsistent by sub-proof #1093.
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | End of split
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | End of split
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | Case 2:
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | |   (415)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 204.26/35.16  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.26/35.16  | | | | |            all_52_30 = e0)
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | BETA: splitting (415) gives:
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | Case 1:
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | |   (416)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 204.26/35.16  | | | | | |          all_52_22 = e0
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | ALPHA: (416) implies:
% 204.26/35.16  | | | | | |   (417)  all_52_22 = e0
% 204.26/35.16  | | | | | |   (418)  all_52_20 = e1
% 204.26/35.16  | | | | | |   (419)  all_52_18 = e2
% 204.26/35.16  | | | | | |   (420)  all_52_16 = e3
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (129), (420) imply:
% 204.26/35.16  | | | | | |   (421)  op(all_52_17, all_52_17) = e3
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (29), (419) imply:
% 204.26/35.16  | | | | | |   (422)  op(all_52_19, all_52_19) = e2
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (120), (417) imply:
% 204.26/35.16  | | | | | |   (423)  op(all_52_23, all_52_23) = e0
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (33), (418) imply:
% 204.26/35.16  | | | | | |   (424)  op(all_10_2, all_10_2) = e1
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (13), (15), (16),
% 204.26/35.16  | | | | | |            (17), (18), (20), (21), (22), (26), (27), (31), (32),
% 204.26/35.16  | | | | | |            (34), (35), (36), (37), (38), (39), (40), (42), (43),
% 204.26/35.16  | | | | | |            (45), (46), (49), (51), (52), (53), (54), (55), (56),
% 204.26/35.16  | | | | | |            (57), (60), (63), (64), (65), (66), (67), (68), (69),
% 204.26/35.16  | | | | | |            (70), (71), (72), (74), (75), (76), (77), (80), (81),
% 204.26/35.16  | | | | | |            (82), (83), (85), (86), (87), (88), (89), (90), (91),
% 204.26/35.16  | | | | | |            (95), (98), (99), (101), (103), (104), (105), (106),
% 204.26/35.16  | | | | | |            (107), (111), (112), (114), (116), (117), (118), (119),
% 204.26/35.16  | | | | | |            (121), (122), (123), (124), (125), (126), (127), (128),
% 204.26/35.16  | | | | | |            (132), (133), (134), (137), (140), (141), (142), (144),
% 204.26/35.16  | | | | | |            (145), (147), (148), (149), (151), (152), (155), (156),
% 204.26/35.16  | | | | | |            (158), (159), (160), (163), (164), (165), (166), (167),
% 204.26/35.16  | | | | | |            (168), (170), (171), (172), (173), (174), (175), (177),
% 204.26/35.16  | | | | | |            (178), (179), (180), (183), (186), (187), (188), (193),
% 204.26/35.16  | | | | | |            (197), (198), (421), (422), (423), (424) are inconsistent
% 204.26/35.16  | | | | | |            by sub-proof #852.
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | Case 2:
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | |   (425)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.26/35.16  | | | | | |          all_52_30 = e0
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | ALPHA: (425) implies:
% 204.26/35.16  | | | | | |   (426)  all_52_30 = e0
% 204.26/35.16  | | | | | |   (427)  all_52_28 = e1
% 204.26/35.16  | | | | | |   (428)  all_52_26 = e2
% 204.26/35.16  | | | | | |   (429)  all_52_24 = e3
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (188), (429) imply:
% 204.26/35.16  | | | | | |   (430)  op(all_52_25, all_52_25) = e3
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (38), (428) imply:
% 204.26/35.16  | | | | | |   (431)  op(all_52_27, all_52_27) = e2
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (126), (427) imply:
% 204.26/35.16  | | | | | |   (432)  op(all_52_29, all_52_29) = e1
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REDUCE: (150), (426) imply:
% 204.26/35.16  | | | | | |   (433)  op(all_14_2, all_14_2) = e0
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (13), (15),
% 204.26/35.16  | | | | | |            (17), (18), (19), (20), (23), (25), (26), (27), (29),
% 204.26/35.16  | | | | | |            (30), (31), (34), (35), (36), (39), (40), (42), (43),
% 204.26/35.16  | | | | | |            (44), (45), (46), (48), (49), (51), (52), (53), (55),
% 204.26/35.16  | | | | | |            (56), (57), (60), (63), (64), (65), (69), (70), (71),
% 204.26/35.16  | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.26/35.16  | | | | | |            (81), (82), (83), (85), (87), (89), (90), (91), (92),
% 204.26/35.16  | | | | | |            (94), (96), (99), (103), (104), (105), (106), (107),
% 204.26/35.16  | | | | | |            (111), (112), (113), (114), (116), (117), (118), (119),
% 204.26/35.16  | | | | | |            (120), (121), (122), (123), (125), (127), (128), (129),
% 204.26/35.16  | | | | | |            (130), (131), (132), (133), (134), (137), (140), (141),
% 204.26/35.16  | | | | | |            (142), (143), (144), (145), (146), (148), (149), (151),
% 204.26/35.16  | | | | | |            (152), (153), (155), (156), (158), (159), (163), (164),
% 204.26/35.16  | | | | | |            (170), (171), (172), (173), (175), (176), (177), (178),
% 204.26/35.16  | | | | | |            (179), (180), (181), (182), (183), (186), (197), (199),
% 204.26/35.16  | | | | | |            (430), (431), (432), (433) are inconsistent by sub-proof
% 204.26/35.16  | | | | | |            #1009.
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | End of split
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | End of split
% 204.26/35.16  | | | | 
% 204.26/35.16  | | | End of split
% 204.26/35.16  | | | 
% 204.26/35.16  | | End of split
% 204.26/35.16  | | 
% 204.26/35.16  | Case 2:
% 204.26/35.16  | | 
% 204.26/35.16  | |   (434)  all_32_1 = e3
% 204.26/35.16  | | 
% 204.26/35.16  | | COMBINE_EQS: (136), (434) imply:
% 204.26/35.16  | |   (435)  all_4_1 = e3
% 204.26/35.16  | | 
% 204.26/35.16  | | COMBINE_EQS: (102), (435) imply:
% 204.26/35.16  | |   (436)  all_38_1 = e3
% 204.26/35.16  | | 
% 204.26/35.16  | | REDUCE: (97), (435) imply:
% 204.26/35.16  | |   (437)  op(all_4_2, e2) = e3
% 204.26/35.16  | | 
% 204.26/35.16  | | REDUCE: (58), (435) imply:
% 204.26/35.16  | |   (438)  op(e2, e3) = all_4_0
% 204.26/35.16  | | 
% 204.26/35.16  | | GROUND_INST: instantiating (6) with all_52_3, all_4_0, e3, e2, simplifying
% 204.26/35.16  | |              with (11), (438) gives:
% 204.26/35.16  | |   (439)  all_52_3 = all_4_0
% 204.26/35.16  | | 
% 204.26/35.16  | | COMBINE_EQS: (85), (439) imply:
% 204.26/35.16  | |   (440)  all_58_2 = all_4_0
% 204.26/35.16  | | 
% 204.26/35.16  | | REDUCE: (19), (439) imply:
% 204.26/35.16  | |   (441)   ~ (all_6_2 = all_4_0)
% 204.26/35.16  | | 
% 204.26/35.16  | | SIMP: (441) implies:
% 204.26/35.16  | |   (442)   ~ (all_6_2 = all_4_0)
% 204.26/35.16  | | 
% 204.26/35.16  | | REDUCE: (180), (439) imply:
% 204.26/35.16  | |   (443)   ~ (all_4_0 = all_4_2)
% 204.26/35.16  | | 
% 204.26/35.16  | | REDUCE: (5), (439) imply:
% 204.26/35.16  | |   (444)  op(all_4_0, all_4_0) = all_52_2
% 204.26/35.16  | | 
% 204.26/35.16  | | BETA: splitting (50) gives:
% 204.26/35.16  | | 
% 204.26/35.16  | | Case 1:
% 204.26/35.16  | | | 
% 204.26/35.16  | | |   (445)   ~ (all_34_0 = e1)
% 204.26/35.16  | | | 
% 204.26/35.16  | | | REDUCE: (109), (445) imply:
% 204.26/35.16  | | |   (446)  $false
% 204.26/35.16  | | | 
% 204.26/35.16  | | | CLOSE: (446) is inconsistent.
% 204.26/35.16  | | | 
% 204.26/35.16  | | Case 2:
% 204.26/35.16  | | | 
% 204.26/35.16  | | |   (447)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.16  | | | 
% 204.26/35.16  | | | BETA: splitting (139) gives:
% 204.26/35.16  | | | 
% 204.26/35.16  | | | Case 1:
% 204.26/35.16  | | | | 
% 204.26/35.16  | | | |   (448)   ~ (all_38_0 = e1)
% 204.26/35.16  | | | | 
% 204.26/35.16  | | | | REDUCE: (84), (448) imply:
% 204.26/35.16  | | | |   (449)   ~ (all_4_0 = e1)
% 204.26/35.16  | | | | 
% 204.26/35.16  | | | | BETA: splitting (110) gives:
% 204.26/35.16  | | | | 
% 204.26/35.16  | | | | Case 1:
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | |   (450)  all_58_15 = e0
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | REF_CLOSE: (6), (21), (32), (53), (118), (150), (160), (450) are
% 204.26/35.16  | | | | |            inconsistent by sub-proof #877.
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | Case 2:
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | |   (451)   ~ (all_58_15 = e0)
% 204.26/35.16  | | | | |   (452)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 204.26/35.16  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | ALPHA: (452) implies:
% 204.26/35.16  | | | | |   (453)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.16  | | | | |   (454)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | REDUCE: (118), (451) imply:
% 204.26/35.16  | | | | |   (455)   ~ (all_14_2 = e0)
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | BETA: splitting (154) gives:
% 204.26/35.16  | | | | | 
% 204.26/35.16  | | | | | Case 1:
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | |   (456)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 204.26/35.16  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 204.26/35.16  | | | | | |            all_52_14 = e0)
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | BETA: splitting (456) gives:
% 204.26/35.16  | | | | | | 
% 204.26/35.16  | | | | | | Case 1:
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | |   (457)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 204.26/35.16  | | | | | | |          = e0
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | ALPHA: (457) implies:
% 204.26/35.16  | | | | | | |   (458)  all_52_6 = e0
% 204.26/35.16  | | | | | | |   (459)  all_52_4 = e1
% 204.26/35.16  | | | | | | |   (460)  all_52_0 = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (27), (459) imply:
% 204.26/35.16  | | | | | | |   (461)  op(all_52_5, all_52_5) = e1
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (17), (458) imply:
% 204.26/35.16  | | | | | | |   (462)  op(all_52_7, all_52_7) = e0
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | REDUCE: (51), (460) imply:
% 204.26/35.16  | | | | | | |   (463)  op(all_6_2, all_6_2) = e3
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | BETA: splitting (123) gives:
% 204.26/35.16  | | | | | | | 
% 204.26/35.16  | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | |   (464)  all_56_15 = e3
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | COMBINE_EQS: (55), (464) imply:
% 204.26/35.16  | | | | | | | |   (465)  all_14_2 = e3
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | COMBINE_EQS: (124), (465) imply:
% 204.26/35.16  | | | | | | | |   (466)  all_34_2 = e3
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | REDUCE: (45), (465) imply:
% 204.26/35.16  | | | | | | | |   (467)   ~ (all_52_25 = e3)
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | REDUCE: (21), (465) imply:
% 204.26/35.16  | | | | | | | |   (468)  op(e3, e0) = all_14_1
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | REDUCE: (53), (465) imply:
% 204.26/35.16  | | | | | | | |   (469)  op(e0, e0) = e3
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | BETA: splitting (447) gives:
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | |   (470)   ~ (all_34_1 = e2)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (22), (470) imply:
% 204.26/35.16  | | | | | | | | |   (471)   ~ (all_14_1 = e2)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0,
% 204.26/35.16  | | | | | | | | |              e3, simplifying with (26), (468) gives:
% 204.26/35.16  | | | | | | | | |   (472)  all_52_25 = all_14_1
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | COMBINE_EQS: (148), (472) imply:
% 204.26/35.16  | | | | | | | | |   (473)  all_56_3 = all_14_1
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | COMBINE_EQS: (34), (472) imply:
% 204.26/35.16  | | | | | | | | |   (474)  all_58_9 = all_14_1
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (2), (472) imply:
% 204.26/35.16  | | | | | | | | |   (475)   ~ (all_52_27 = all_14_1)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | SIMP: (475) implies:
% 204.26/35.16  | | | | | | | | |   (476)   ~ (all_52_27 = all_14_1)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (75), (472) imply:
% 204.26/35.16  | | | | | | | | |   (477)   ~ (all_52_29 = all_14_1)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | SIMP: (477) implies:
% 204.26/35.16  | | | | | | | | |   (478)   ~ (all_52_29 = all_14_1)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (467), (472) imply:
% 204.26/35.16  | | | | | | | | |   (479)   ~ (all_14_1 = e3)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (188), (472) imply:
% 204.26/35.16  | | | | | | | | |   (480)  op(all_14_1, all_14_1) = all_52_24
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | BETA: splitting (132) gives:
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | |   (481)  all_56_3 = e3
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | REF_CLOSE: (473), (479), (481) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | |            #1200.
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | |   (482)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | BETA: splitting (57) gives:
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | |   (483)  all_58_9 = e1
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | COMBINE_EQS: (474), (483) imply:
% 204.26/35.16  | | | | | | | | | | |   (484)  all_14_1 = e1
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | SIMP: (484) implies:
% 204.26/35.16  | | | | | | | | | | |   (485)  all_14_1 = e1
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (476), (485) imply:
% 204.26/35.16  | | | | | | | | | | |   (486)   ~ (all_52_27 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (478), (485) imply:
% 204.26/35.16  | | | | | | | | | | |   (487)   ~ (all_52_29 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (480), (485) imply:
% 204.26/35.16  | | | | | | | | | | |   (488)  op(e1, e1) = all_52_24
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (32), (485) imply:
% 204.26/35.16  | | | | | | | | | | |   (489)  op(e0, e1) = e1
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_23, e1, e1, e0,
% 204.26/35.16  | | | | | | | | | | |              simplifying with (54), (489) gives:
% 204.26/35.16  | | | | | | | | | | |   (490)  all_52_23 = e1
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_24, e1,
% 204.26/35.16  | | | | | | | | | | |              e1, simplifying with (173), (488) gives:
% 204.26/35.16  | | | | | | | | | | |   (491)  all_52_24 = all_10_2
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (74), (490) imply:
% 204.26/35.16  | | | | | | | | | | |   (492)   ~ (all_52_19 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (174), (490) imply:
% 204.26/35.16  | | | | | | | | | | |   (493)   ~ (all_10_2 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | SIMP: (493) implies:
% 204.26/35.16  | | | | | | | | | | |   (494)   ~ (all_10_2 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | BETA: splitting (79) gives:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | |   (495)  all_58_2 = e1
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | REF_CLOSE: (440), (449), (495) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | | | |            #967.
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | |   (496)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | REF_CLOSE: (6), (43), (70), (77), (111), (122), (125), (130),
% 204.26/35.16  | | | | | | | | | | | |            (151), (156), (173), (177), (461), (486), (487),
% 204.26/35.16  | | | | | | | | | | | |            (492), (494), (496) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | | | |            #868.
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | |   (497)   ~ (all_58_9 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REDUCE: (474), (497) imply:
% 204.26/35.16  | | | | | | | | | | |   (498)   ~ (all_14_1 = e1)
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REF_CLOSE: (4), (6), (32), (469), (471), (473), (480), (482),
% 204.26/35.16  | | | | | | | | | | |            (498) are inconsistent by sub-proof #867.
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | |   (499)   ~ (all_34_2 = e3)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (466), (499) imply:
% 204.26/35.16  | | | | | | | | |   (500)  $false
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | CLOSE: (500) is inconsistent.
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | |   (501)   ~ (all_56_15 = e3)
% 204.26/35.16  | | | | | | | |   (502)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | REDUCE: (55), (501) imply:
% 204.26/35.16  | | | | | | | |   (503)   ~ (all_14_2 = e3)
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | BETA: splitting (63) gives:
% 204.26/35.16  | | | | | | | | 
% 204.26/35.16  | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | |   (504)  all_56_13 = e3
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | COMBINE_EQS: (179), (504) imply:
% 204.26/35.16  | | | | | | | | |   (505)  all_52_15 = e3
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | COMBINE_EQS: (31), (505) imply:
% 204.26/35.16  | | | | | | | | |   (506)  all_58_13 = e3
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (15), (505) imply:
% 204.26/35.16  | | | | | | | | |   (507)   ~ (all_52_7 = e3)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (73), (505) imply:
% 204.26/35.16  | | | | | | | | |   (508)  op(e3, e3) = all_52_14
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REF_CLOSE: (3), (6), (10), (20), (62), (69), (81), (89), (90),
% 204.26/35.16  | | | | | | | | |            (92), (100), (125), (142), (156), (160), (173),
% 204.26/35.16  | | | | | | | | |            (174), (183), (440), (449), (453), (461), (462),
% 204.26/35.16  | | | | | | | | |            (463), (506), (507), (508) are inconsistent by
% 204.26/35.16  | | | | | | | | |            sub-proof #848.
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | |   (509)   ~ (all_56_13 = e3)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | REDUCE: (179), (509) imply:
% 204.26/35.16  | | | | | | | | |   (510)   ~ (all_52_15 = e3)
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | BETA: splitting (158) gives:
% 204.26/35.16  | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | |   (511)  all_58_12 = e3
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | REF_CLOSE: (4), (6), (20), (81), (92), (125), (142), (156),
% 204.26/35.16  | | | | | | | | | |            (160), (173), (440), (449), (461), (462), (511)
% 204.26/35.16  | | | | | | | | | |            are inconsistent by sub-proof #844.
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | |   (512)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | BETA: splitting (512) gives:
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | |   (513)  all_58_13 = e3
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | REF_CLOSE: (31), (510), (513) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | | |            #1360.
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | |   (514)  all_58_14 = e3 | all_58_15 = e3
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | BETA: splitting (514) gives:
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | |   (515)  all_58_14 = e3
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | COMBINE_EQS: (3), (515) imply:
% 204.26/35.16  | | | | | | | | | | | |   (516)  all_52_23 = e3
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | SIMP: (516) implies:
% 204.26/35.16  | | | | | | | | | | | |   (517)  all_52_23 = e3
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | REDUCE: (175), (517) imply:
% 204.26/35.16  | | | | | | | | | | | |   (518)   ~ (all_52_7 = e3)
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | REDUCE: (127), (517) imply:
% 204.26/35.16  | | | | | | | | | | | |   (519)   ~ (all_14_2 = e3)
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | REDUCE: (120), (517) imply:
% 204.26/35.16  | | | | | | | | | | | |   (520)  op(e3, e3) = all_52_22
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 204.26/35.16  | | | | | | | | | | | |              simplifying with (142), (520) gives:
% 204.26/35.16  | | | | | | | | | | | |   (521)  all_52_22 = all_6_2
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | BETA: splitting (89) gives:
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | |   (522)  all_58_0 = e3
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | COMBINE_EQS: (20), (522) imply:
% 204.26/35.16  | | | | | | | | | | | | |   (523)  all_6_2 = e3
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | REDUCE: (137), (523) imply:
% 204.26/35.16  | | | | | | | | | | | | |   (524)   ~ (all_52_9 = e3)
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | REDUCE: (131), (523) imply:
% 204.26/35.16  | | | | | | | | | | | | |   (525)   ~ (all_52_25 = e3)
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | REDUCE: (183), (523) imply:
% 204.26/35.16  | | | | | | | | | | | | |   (526)  op(e3, e3) = all_6_1
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | REDUCE: (142), (523) imply:
% 204.26/35.16  | | | | | | | | | | | | |   (527)  op(e3, e3) = e3
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_1, e3, e3,
% 204.26/35.16  | | | | | | | | | | | | |              simplifying with (526), (527) gives:
% 204.26/35.16  | | | | | | | | | | | | |   (528)  all_6_1 = e3
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | REDUCE: (90), (528) imply:
% 204.26/35.16  | | | | | | | | | | | | |   (529)  op(e3, e3) = all_6_0
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_0, e3, e3,
% 204.26/35.16  | | | | | | | | | | | | |              simplifying with (527), (529) gives:
% 204.26/35.16  | | | | | | | | | | | | |   (530)  all_6_0 = e3
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | BETA: splitting (116) gives:
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | |   (531)  all_58_1 = e3
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | COMBINE_EQS: (8), (531) imply:
% 204.26/35.16  | | | | | | | | | | | | | |   (532)  all_52_9 = e3
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | REDUCE: (524), (532) imply:
% 204.26/35.16  | | | | | | | | | | | | | |   (533)  $false
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | CLOSE: (533) is inconsistent.
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | |   (534)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | |   (535)  all_58_0 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | COMBINE_EQS: (522), (535) imply:
% 204.26/35.16  | | | | | | | | | | | | | | |   (536)  e3 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | REDUCE: (4), (536) imply:
% 204.26/35.16  | | | | | | | | | | | | | | |   (537)  $false
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | CLOSE: (537) is inconsistent.
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | |   (538)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | |   (539)  all_58_9 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | REF_CLOSE: (34), (525), (539) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | | | | | | | |            #1300.
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | |   (540)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (541)  all_56_9 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (541) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (542)  all_52_13 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | SIMP: (542) implies:
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (543)  all_52_13 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | REDUCE: (185), (543) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (544)   ~ (all_52_29 = e3)
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | SIMP: (544) implies:
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (545)   ~ (all_52_29 = e3)
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | BETA: splitting (540) gives:
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | |   (546)  all_58_10 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (546) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | | |   (547)  all_52_27 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | SIMP: (547) implies:
% 204.26/35.16  | | | | | | | | | | | | | | | | | |   (548)  all_52_27 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | REDUCE: (161), (548) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | | |   (549)  op(e2, e0) = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (550)  all_58_12 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (550) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (551)  all_52_7 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | SIMP: (551) implies:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (552)  all_52_7 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | REDUCE: (83), (552) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (553)   ~ (all_14_2 = e1)
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | SIMP: (553) implies:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (554)   ~ (all_14_2 = e1)
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |   (555)  all_56_15 = e2
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (555) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |   (556)  all_14_2 = e2
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (21), (138), (169), (549), (556) are
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #842.
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |   (557)  all_56_15 = e1 | all_56_15 = e0
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (455), (554), (557) are inconsistent by
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (558)   ~ (all_58_12 = e1)
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | REDUCE: (81), (558) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | |   (559)   ~ (all_52_7 = e1)
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |   (560)  all_58_2 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (440), (449), (560) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |            #967.
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |   (561)  all_58_6 = e1 | all_58_12 = e1
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (81), (125), (156), (173), (461), (559),
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | |            (561) are inconsistent by sub-proof #851.
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | |   (562)  all_58_11 = e3 | all_58_15 = e3
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (118), (503), (545), (562) are inconsistent
% 204.26/35.16  | | | | | | | | | | | | | | | | | |            by sub-proof #1103.
% 204.26/35.16  | | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (563)   ~ (all_56_9 = e3)
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | REDUCE: (66), (563) imply:
% 204.26/35.16  | | | | | | | | | | | | | | | | |   (564)   ~ (all_52_13 = e3)
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (31), (77), (133), (157), (177), (437),
% 204.26/35.16  | | | | | | | | | | | | | | | | |            (510), (534), (564) are inconsistent by sub-proof
% 204.26/35.16  | | | | | | | | | | | | | | | | |            #939.
% 204.26/35.16  | | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | |   (565)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (81), (125), (142), (156), (173),
% 204.26/35.16  | | | | | | | | | | | | |            (440), (461), (463), (518), (565) are inconsistent
% 204.26/35.16  | | | | | | | | | | | | |            by sub-proof #849.
% 204.26/35.16  | | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | Case 2:
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | |   (566)  all_58_15 = e3
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | COMBINE_EQS: (118), (566) imply:
% 204.26/35.16  | | | | | | | | | | | |   (567)  all_14_2 = e3
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | REDUCE: (503), (567) imply:
% 204.26/35.16  | | | | | | | | | | | |   (568)  $false
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | | CLOSE: (568) is inconsistent.
% 204.26/35.16  | | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | | End of split
% 204.26/35.16  | | | | | | | | | | 
% 204.26/35.16  | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | End of split
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | Case 2:
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | |   (569)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 204.26/35.17  | | | | | | |          all_52_14 = e0
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | ALPHA: (569) implies:
% 204.26/35.17  | | | | | | |   (570)  all_52_14 = e0
% 204.26/35.17  | | | | | | |   (571)  all_52_12 = e1
% 204.26/35.17  | | | | | | |   (572)  all_52_10 = e2
% 204.26/35.17  | | | | | | |   (573)  all_52_8 = e3
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | REDUCE: (72), (573) imply:
% 204.26/35.17  | | | | | | |   (574)  op(all_52_9, all_52_9) = e3
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | REDUCE: (171), (571) imply:
% 204.26/35.17  | | | | | | |   (575)  op(all_52_13, all_52_13) = e1
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | REDUCE: (73), (570) imply:
% 204.26/35.17  | | | | | | |   (576)  op(all_52_15, all_52_15) = e0
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | REDUCE: (147), (572) imply:
% 204.26/35.17  | | | | | | |   (577)  op(all_4_2, all_4_2) = e2
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | BETA: splitting (123) gives:
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | |   (578)  all_56_15 = e3
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | COMBINE_EQS: (55), (578) imply:
% 204.26/35.17  | | | | | | | |   (579)  all_14_2 = e3
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | COMBINE_EQS: (124), (579) imply:
% 204.26/35.17  | | | | | | | |   (580)  all_34_2 = e3
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (83), (579) imply:
% 204.26/35.17  | | | | | | | |   (581)   ~ (all_52_7 = e3)
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (103), (579) imply:
% 204.26/35.17  | | | | | | | |   (582)   ~ (all_52_15 = e3)
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (127), (579) imply:
% 204.26/35.17  | | | | | | | |   (583)   ~ (all_52_23 = e3)
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (45), (579) imply:
% 204.26/35.17  | | | | | | | |   (584)   ~ (all_52_25 = e3)
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (150), (579) imply:
% 204.26/35.17  | | | | | | | |   (585)  op(e3, e3) = all_52_30
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (21), (579) imply:
% 204.26/35.17  | | | | | | | |   (586)  op(e3, e0) = all_14_1
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (53), (579) imply:
% 204.26/35.17  | | | | | | | |   (587)  op(e0, e0) = e3
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | BETA: splitting (447) gives:
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | |   (588)   ~ (all_34_1 = e2)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REDUCE: (22), (588) imply:
% 204.26/35.17  | | | | | | | | |   (589)   ~ (all_14_1 = e2)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0,
% 204.26/35.17  | | | | | | | | |              e3, simplifying with (26), (586) gives:
% 204.26/35.17  | | | | | | | | |   (590)  all_52_25 = all_14_1
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3,
% 204.26/35.17  | | | | | | | | |              simplifying with (142), (585) gives:
% 204.26/35.17  | | | | | | | | |   (591)  all_52_30 = all_6_2
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | COMBINE_EQS: (148), (590) imply:
% 204.26/35.17  | | | | | | | | |   (592)  all_56_3 = all_14_1
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | COMBINE_EQS: (34), (590) imply:
% 204.26/35.17  | | | | | | | | |   (593)  all_58_9 = all_14_1
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REDUCE: (2), (590) imply:
% 204.26/35.17  | | | | | | | | |   (594)   ~ (all_52_27 = all_14_1)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | SIMP: (594) implies:
% 204.26/35.17  | | | | | | | | |   (595)   ~ (all_52_27 = all_14_1)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REDUCE: (584), (590) imply:
% 204.26/35.17  | | | | | | | | |   (596)   ~ (all_14_1 = e3)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REDUCE: (188), (590) imply:
% 204.26/35.17  | | | | | | | | |   (597)  op(all_14_1, all_14_1) = all_52_24
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | BETA: splitting (132) gives:
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | |   (598)  all_56_3 = e3
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | REF_CLOSE: (592), (596), (598) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | |            #1200.
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | |   (599)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | BETA: splitting (89) gives:
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | |   (600)  all_58_0 = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | COMBINE_EQS: (20), (600) imply:
% 204.26/35.17  | | | | | | | | | | |   (601)  all_6_2 = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (137), (601) imply:
% 204.26/35.17  | | | | | | | | | | |   (602)   ~ (all_52_9 = e3)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (51), (601) imply:
% 204.26/35.17  | | | | | | | | | | |   (603)  op(e3, e3) = all_52_0
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (183), (601) imply:
% 204.26/35.17  | | | | | | | | | | |   (604)  op(e3, e3) = all_6_1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (142), (601) imply:
% 204.26/35.17  | | | | | | | | | | |   (605)  op(e3, e3) = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_1, all_52_0, e3, e3,
% 204.26/35.17  | | | | | | | | | | |              simplifying with (603), (604) gives:
% 204.26/35.17  | | | | | | | | | | |   (606)  all_52_0 = all_6_1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e3, e3,
% 204.26/35.17  | | | | | | | | | | |              simplifying with (603), (605) gives:
% 204.26/35.17  | | | | | | | | | | |   (607)  all_52_0 = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | COMBINE_EQS: (606), (607) imply:
% 204.26/35.17  | | | | | | | | | | |   (608)  all_6_1 = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (90), (608) imply:
% 204.26/35.17  | | | | | | | | | | |   (609)  op(e3, e3) = all_6_0
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_0, e3, e3,
% 204.26/35.17  | | | | | | | | | | |              simplifying with (605), (609) gives:
% 204.26/35.17  | | | | | | | | | | |   (610)  all_6_0 = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | BETA: splitting (116) gives:
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | |   (611)  all_58_1 = e3
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | COMBINE_EQS: (8), (611) imply:
% 204.26/35.17  | | | | | | | | | | | |   (612)  all_52_9 = e3
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | REDUCE: (602), (612) imply:
% 204.26/35.17  | | | | | | | | | | | |   (613)  $false
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | CLOSE: (613) is inconsistent.
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | |   (614)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | BETA: splitting (57) gives:
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | |   (615)  all_58_9 = e1
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | COMBINE_EQS: (593), (615) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (616)  all_14_1 = e1
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | SIMP: (616) implies:
% 204.26/35.17  | | | | | | | | | | | | |   (617)  all_14_1 = e1
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REDUCE: (595), (617) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (618)   ~ (all_52_27 = e1)
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REDUCE: (32), (617) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (619)  op(e0, e1) = e1
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_23, e1, e1, e0,
% 204.26/35.17  | | | | | | | | | | | | |              simplifying with (54), (619) gives:
% 204.26/35.17  | | | | | | | | | | | | |   (620)  all_52_23 = e1
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REDUCE: (74), (620) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (621)   ~ (all_52_19 = e1)
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REDUCE: (583), (620) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (622)   ~ (e3 = e1)
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | |   (623)  all_58_2 = e1
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | REF_CLOSE: (440), (449), (623) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | |            #967.
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | |   (624)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | BETA: splitting (624) gives:
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | |   (625)  all_58_3 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | COMBINE_EQS: (177), (625) imply:
% 204.26/35.17  | | | | | | | | | | | | | | |   (626)  all_4_2 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | REDUCE: (111), (626) imply:
% 204.26/35.17  | | | | | | | | | | | | | | |   (627)   ~ (all_52_13 = e1)
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | BETA: splitting (614) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | |   (628)  all_58_3 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (625), (628) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (629)  e3 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | SIMP: (629) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (630)  e3 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (4), (630) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (631)  $false
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | CLOSE: (631) is inconsistent.
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | |   (632)  all_58_7 = e3 | all_58_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | BETA: splitting (632) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (633)  all_58_7 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (633) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (634)  all_52_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | REDUCE: (575), (634) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (635)  op(e3, e3) = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (603), (605), (635) are inconsistent by
% 204.26/35.17  | | | | | | | | | | | | | | | | |            sub-proof #1237.
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (636)  all_58_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (582), (636) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | | | |            #1360.
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | |   (637)  all_58_5 = e1 | all_58_10 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | REF_CLOSE: (70), (151), (618), (621), (637) are inconsistent
% 204.26/35.17  | | | | | | | | | | | | | | |            by sub-proof #869.
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | |   (638)   ~ (all_58_9 = e1)
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REDUCE: (593), (638) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (639)   ~ (all_14_1 = e1)
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (32), (587), (589), (592), (597), (599),
% 204.26/35.17  | | | | | | | | | | | | |            (639) are inconsistent by sub-proof #867.
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | |   (640)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (27), (31), (62), (77), (81),
% 204.26/35.17  | | | | | | | | | | |            (116), (133), (137), (142), (156), (157), (177),
% 204.26/35.17  | | | | | | | | | | |            (437), (440), (574), (581), (582), (640) are
% 204.26/35.17  | | | | | | | | | | |            inconsistent by sub-proof #938.
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | |   (641)   ~ (all_34_2 = e3)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REDUCE: (580), (641) imply:
% 204.26/35.17  | | | | | | | | |   (642)  $false
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | CLOSE: (642) is inconsistent.
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | |   (643)   ~ (all_56_15 = e3)
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | REDUCE: (55), (643) imply:
% 204.26/35.17  | | | | | | | |   (644)   ~ (all_14_2 = e3)
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | BETA: splitting (63) gives:
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | |   (645)  all_56_13 = e3
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REF_CLOSE: (6), (13), (15), (35), (52), (114), (128), (142),
% 204.26/35.17  | | | | | | | | |            (172), (179), (183), (576), (645) are inconsistent
% 204.26/35.17  | | | | | | | | |            by sub-proof #893.
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | |   (646)   ~ (all_56_13 = e3)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | REDUCE: (179), (646) imply:
% 204.26/35.17  | | | | | | | | |   (647)   ~ (all_52_15 = e3)
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | BETA: splitting (158) gives:
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | |   (648)  all_58_12 = e3
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | COMBINE_EQS: (81), (648) imply:
% 204.26/35.17  | | | | | | | | | |   (649)  all_52_7 = e3
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | SIMP: (649) implies:
% 204.26/35.17  | | | | | | | | | |   (650)  all_52_7 = e3
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | REDUCE: (80), (650) imply:
% 204.26/35.17  | | | | | | | | | |   (651)   ~ (all_52_5 = e3)
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | REDUCE: (15), (650) imply:
% 204.26/35.17  | | | | | | | | | |   (652)   ~ (all_52_15 = e3)
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | REDUCE: (52), (650) imply:
% 204.26/35.17  | | | | | | | | | |   (653)   ~ (all_6_2 = e3)
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | SIMP: (653) implies:
% 204.26/35.17  | | | | | | | | | |   (654)   ~ (all_6_2 = e3)
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | REDUCE: (17), (650) imply:
% 204.26/35.17  | | | | | | | | | |   (655)  op(e3, e3) = all_52_6
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3,
% 204.26/35.17  | | | | | | | | | |              simplifying with (142), (655) gives:
% 204.26/35.17  | | | | | | | | | |   (656)  all_52_6 = all_6_2
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | BETA: splitting (92) gives:
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | |   (657)  all_58_0 = e1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | COMBINE_EQS: (20), (657) imply:
% 204.26/35.17  | | | | | | | | | | |   (658)  all_6_2 = e1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (137), (658) imply:
% 204.26/35.17  | | | | | | | | | | |   (659)   ~ (all_52_9 = e1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (159), (658) imply:
% 204.26/35.17  | | | | | | | | | | |   (660)   ~ (all_52_17 = e1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (131), (658) imply:
% 204.26/35.17  | | | | | | | | | | |   (661)   ~ (all_52_25 = e1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (442), (658) imply:
% 204.26/35.17  | | | | | | | | | | |   (662)   ~ (all_4_0 = e1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (51), (658) imply:
% 204.26/35.17  | | | | | | | | | | |   (663)  op(e1, e1) = all_52_0
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (183), (658) imply:
% 204.26/35.17  | | | | | | | | | | |   (664)  op(e1, e3) = all_6_1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_0, e1, e1,
% 204.26/35.17  | | | | | | | | | | |              simplifying with (173), (663) gives:
% 204.26/35.17  | | | | | | | | | | |   (665)  all_52_0 = all_10_2
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 204.26/35.17  | | | | | | | | | | |              simplifying with (39), (664) gives:
% 204.26/35.17  | | | | | | | | | | |   (666)  all_52_5 = all_6_1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | COMBINE_EQS: (156), (666) imply:
% 204.26/35.17  | | | | | | | | | | |   (667)  all_58_6 = all_6_1
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (99), (666) imply:
% 204.26/35.17  | | | | | | | | | | |   (668)   ~ (all_52_29 = all_6_1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | SIMP: (668) implies:
% 204.26/35.17  | | | | | | | | | | |   (669)   ~ (all_52_29 = all_6_1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (125), (666) imply:
% 204.26/35.17  | | | | | | | | | | |   (670)   ~ (all_10_2 = all_6_1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | SIMP: (670) implies:
% 204.26/35.17  | | | | | | | | | | |   (671)   ~ (all_10_2 = all_6_1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (651), (666) imply:
% 204.26/35.17  | | | | | | | | | | |   (672)   ~ (all_6_1 = e3)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (27), (666) imply:
% 204.26/35.17  | | | | | | | | | | |   (673)  op(all_6_1, all_6_1) = all_52_4
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | BETA: splitting (106) gives:
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | |   (674)  all_58_0 = e2
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | REF_CLOSE: (67), (657), (674) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | |            #1273.
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | |   (675)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | BETA: splitting (675) gives:
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | |   (676)  all_58_2 = e2
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | COMBINE_EQS: (440), (676) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (677)  all_4_0 = e2
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | SIMP: (677) implies:
% 204.26/35.17  | | | | | | | | | | | | |   (678)  all_4_0 = e2
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REDUCE: (444), (678) imply:
% 204.26/35.17  | | | | | | | | | | | | |   (679)  op(e2, e2) = all_52_2
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | BETA: splitting (41) gives:
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | |   (680)  all_58_0 = e0
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | COMBINE_EQS: (657), (680) imply:
% 204.26/35.17  | | | | | | | | | | | | | |   (681)  e1 = e0
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | REDUCE: (160), (681) imply:
% 204.26/35.17  | | | | | | | | | | | | | |   (682)  $false
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | CLOSE: (682) is inconsistent.
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | |   (683)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | BETA: splitting (683) gives:
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | |   (684)  all_58_2 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | REF_CLOSE: (95), (676), (684) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | |            #1213.
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | |   (685)  all_58_6 = e0 | all_58_12 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | BETA: splitting (685) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | |   (686)  all_58_6 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (667), (686) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (687)  all_6_1 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | SIMP: (687) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (688)  all_6_1 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (669), (688) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (689)   ~ (all_52_29 = e0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (671), (688) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (690)   ~ (all_10_2 = e0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (672), (688) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (691)   ~ (e3 = e0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (673), (688) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (692)  op(e0, e0) = all_52_4
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (90), (688) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (693)  op(e3, e0) = all_6_0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_14_2, all_52_4, e0, e0,
% 204.26/35.17  | | | | | | | | | | | | | | | |              simplifying with (53), (692) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (694)  all_52_4 = all_14_2
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_4_2, all_52_2, e2, e2,
% 204.26/35.17  | | | | | | | | | | | | | | | |              simplifying with (40), (679) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (695)  all_52_2 = all_4_2
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_25, all_6_0, e0, e3,
% 204.26/35.17  | | | | | | | | | | | | | | | |              simplifying with (26), (693) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (696)  all_52_25 = all_6_0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (696) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (697)  all_56_3 = all_6_0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (696) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (698)  all_58_9 = all_6_0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (117), (696) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (699)   ~ (all_52_9 = all_6_0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (18), (696) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (700)   ~ (all_52_17 = all_6_0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REDUCE: (75), (696) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (701)   ~ (all_52_29 = all_6_0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | SIMP: (701) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | |   (702)   ~ (all_52_29 = all_6_0)
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (703)  all_56_3 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (697), (703) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (704)  all_6_0 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | SIMP: (704) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (705)  all_6_0 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (698), (705) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (706)  all_58_9 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | REDUCE: (699), (705) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (707)   ~ (all_52_9 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | REDUCE: (702), (705) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (708)   ~ (all_52_29 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | BETA: splitting (454) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | |   (709)  all_58_9 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (706), (709) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | | | | |            #841.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | |   (710)  all_58_10 = e0 | all_58_11 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (711)  all_58_10 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (711) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (712)  all_52_27 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | SIMP: (712) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (713)  all_52_27 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | REDUCE: (30), (713) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (714)   ~ (all_52_29 = e0)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | REDUCE: (155), (713) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (715)   ~ (all_4_2 = e0)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | SIMP: (715) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (716)   ~ (all_4_2 = e0)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | REDUCE: (38), (713) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (717)  op(e0, e0) = all_52_26
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | REDUCE: (161), (713) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (718)  op(e2, e0) = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_14_2, all_52_26, e0,
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |              e0, simplifying with (53), (717) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (719)  all_52_26 = all_14_2
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | |   (720)  all_56_11 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (708), (720) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | |            #1028.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | |   (721)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | |   (722)  all_56_5 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (44), (133), (157), (437), (722) are
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | |   (723)   ~ (all_56_5 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | |   (724)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (723) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | |   (725)   ~ (all_4_2 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | |   (726)  all_58_1 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (726) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | |   (727)  all_52_9 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (707), (727) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | |   (728)  $false
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (728) is inconsistent.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | |   (729)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | |   (730)  all_58_3 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (730) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | |   (731)  all_4_2 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (725), (731) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | |   (732)  $false
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (732) is inconsistent.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | |   (733)  all_58_7 = e3 | all_58_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |   (734)  all_58_7 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (734) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |   (735)  all_52_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (735) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |   (736)   ~ (all_10_2 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (736) implies:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |   (737)   ~ (all_10_2 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (735) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |   (738)   ~ (all_4_2 = e3)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (739)  all_58_2 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (676), (739) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  e2 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (740) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  $false
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (741) is inconsistent.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (742) gives:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  all_58_3 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (743) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (744)  all_4_2 = e1
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (744) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (745)  op(e1, e1) = e2
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (32), (36), (43), (53), (60), (76),
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (135), (173), (689), (690), (706), (711),
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            (717), (718), (721), (737), (745) are inconsistent
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #839.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (746)   ~ (all_58_3 = e1)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (746) imply:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (747)   ~ (all_4_2 = e1)
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (44), (147), (437), (716), (724),
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            (725), (747) are inconsistent by sub-proof #974.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |   (748)  all_58_13 = e3
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (647), (748) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | |            #1360.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |   (749)  all_58_11 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (689), (749) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | | | | | |            #1115.
% 204.26/35.17  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | |   (750)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (64), (69), (87), (107), (142), (152),
% 204.26/35.17  | | | | | | | | | | | | | | | | |            (157), (164), (165), (437), (574), (654), (659),
% 204.26/35.17  | | | | | | | | | | | | | | | | |            (660), (697), (699), (700), (750) are inconsistent
% 204.26/35.17  | | | | | | | | | | | | | | | | |            by sub-proof #934.
% 204.26/35.17  | | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | |   (751)  all_58_12 = e0
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (648), (751) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | | | | | | |            #1212.
% 204.26/35.17  | | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | |   (752)  all_58_6 = e2 | all_58_12 = e2
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | | REF_CLOSE: (163), (172), (648), (667), (752) are inconsistent
% 204.26/35.17  | | | | | | | | | | | | |            by sub-proof #1209.
% 204.26/35.17  | | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | |   (753)   ~ (all_58_0 = e1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REDUCE: (20), (753) imply:
% 204.26/35.17  | | | | | | | | | | |   (754)   ~ (all_6_2 = e1)
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | | REF_CLOSE: (6), (8), (31), (66), (77), (116), (133), (137),
% 204.26/35.17  | | | | | | | | | | |            (142), (157), (168), (177), (437), (574), (575),
% 204.26/35.17  | | | | | | | | | | |            (647), (655), (754) are inconsistent by sub-proof
% 204.26/35.17  | | | | | | | | | | |            #932.
% 204.26/35.17  | | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | Case 2:
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | |   (755)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (20), (27),
% 204.26/35.17  | | | | | | | | | |            (31), (34), (39), (40), (42), (43), (45), (51),
% 204.26/35.17  | | | | | | | | | |            (52), (53), (56), (61), (67), (69), (70), (71),
% 204.26/35.17  | | | | | | | | | |            (74), (77), (80), (81), (82), (85), (89), (90),
% 204.26/35.17  | | | | | | | | | |            (97), (103), (106), (107), (116), (118), (120),
% 204.26/35.17  | | | | | | | | | |            (121), (126), (127), (131), (133), (134), (137),
% 204.26/35.17  | | | | | | | | | |            (142), (143), (145), (149), (151), (152), (155),
% 204.26/35.17  | | | | | | | | | |            (156), (157), (163), (164), (172), (175), (177),
% 204.26/35.17  | | | | | | | | | |            (180), (182), (183), (186), (188), (453), (574),
% 204.26/35.17  | | | | | | | | | |            (575), (576), (577), (644), (647), (755) are
% 204.26/35.17  | | | | | | | | | |            inconsistent by sub-proof #1094.
% 204.26/35.17  | | | | | | | | | | 
% 204.26/35.17  | | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | | 
% 204.26/35.17  | | | | | | | | End of split
% 204.26/35.17  | | | | | | | | 
% 204.26/35.17  | | | | | | | End of split
% 204.26/35.17  | | | | | | | 
% 204.26/35.17  | | | | | | End of split
% 204.26/35.17  | | | | | | 
% 204.26/35.17  | | | | | Case 2:
% 204.26/35.17  | | | | | | 
% 204.26/35.17  | | | | | |   (756)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 204.26/35.17  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 204.26/35.17  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.17  | | | | | | 
% 204.26/35.17  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13),
% 204.26/35.17  | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.26/35.17  | | | | | |            (25), (26), (27), (29), (30), (31), (32), (33), (34),
% 204.26/35.17  | | | | | |            (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 204.26/35.17  | | | | | |            (45), (46), (48), (49), (51), (52), (53), (54), (55),
% 204.26/35.17  | | | | | |            (56), (57), (60), (63), (64), (65), (66), (67), (68),
% 204.26/35.17  | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 204.26/35.17  | | | | | |            (78), (79), (80), (81), (82), (83), (85), (86), (87),
% 204.26/35.17  | | | | | |            (88), (89), (90), (91), (92), (94), (95), (96), (98),
% 204.26/35.17  | | | | | |            (99), (101), (103), (104), (105), (106), (107), (111),
% 204.26/35.17  | | | | | |            (112), (113), (114), (116), (117), (118), (119), (120),
% 204.26/35.17  | | | | | |            (121), (122), (123), (124), (125), (126), (127), (128),
% 204.26/35.17  | | | | | |            (129), (130), (131), (132), (133), (134), (137), (140),
% 204.26/35.17  | | | | | |            (141), (142), (143), (144), (145), (146), (147), (148),
% 204.26/35.17  | | | | | |            (149), (150), (151), (152), (153), (155), (156), (158),
% 204.26/35.17  | | | | | |            (159), (160), (163), (164), (165), (166), (167), (168),
% 204.26/35.17  | | | | | |            (170), (171), (172), (173), (174), (175), (176), (177),
% 204.26/35.17  | | | | | |            (178), (179), (180), (181), (182), (183), (186), (187),
% 204.26/35.17  | | | | | |            (188), (447), (453), (454), (455), (756) are inconsistent
% 204.26/35.17  | | | | | |            by sub-proof #838.
% 204.26/35.17  | | | | | | 
% 204.26/35.17  | | | | | End of split
% 204.26/35.17  | | | | | 
% 204.26/35.17  | | | | End of split
% 204.26/35.17  | | | | 
% 204.26/35.17  | | | Case 2:
% 204.26/35.17  | | | | 
% 204.26/35.17  | | | |   (757)  all_38_0 = e1
% 204.26/35.17  | | | |   (758)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 204.26/35.17  | | | | 
% 204.26/35.17  | | | | COMBINE_EQS: (84), (757) imply:
% 204.26/35.17  | | | |   (759)  all_4_0 = e1
% 204.26/35.17  | | | | 
% 204.26/35.17  | | | | SIMP: (759) implies:
% 204.26/35.17  | | | |   (760)  all_4_0 = e1
% 204.26/35.17  | | | | 
% 204.26/35.17  | | | | REF_CLOSE: (6), (24), (40), (44), (96), (133), (147), (157), (436),
% 204.26/35.17  | | | |            (437), (443), (758), (760) are inconsistent by sub-proof
% 204.26/35.17  | | | |            #927.
% 204.26/35.17  | | | | 
% 204.26/35.17  | | | End of split
% 204.26/35.17  | | | 
% 204.26/35.17  | | End of split
% 204.26/35.17  | | 
% 204.26/35.17  | End of split
% 204.26/35.17  | 
% 204.26/35.17  End of proof
% 204.26/35.17  
% 204.26/35.17  Sub-proof #838 shows that the following formulas are inconsistent:
% 204.26/35.17  ----------------------------------------------------------------
% 204.26/35.17    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.17    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.17    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.17    (4)  all_58_14 = all_52_23
% 204.26/35.17    (5)   ~ (e3 = e1)
% 204.26/35.17    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.17    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.17    (8)  all_58_1 = all_52_9
% 204.26/35.17    (9)   ~ (all_52_9 = all_52_13)
% 204.26/35.17    (10)   ~ (e3 = e0)
% 204.26/35.17    (11)  op(e2, e3) = all_52_3
% 204.26/35.18    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.18    (13)   ~ (all_52_7 = all_52_15)
% 204.26/35.18    (14)   ~ (all_52_3 = all_52_19)
% 204.26/35.18    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.18    (16)   ~ (all_52_17 = all_52_25)
% 204.26/35.18    (17)   ~ (all_52_3 = all_6_2)
% 204.26/35.18    (18)  all_58_0 = all_6_2
% 204.26/35.18    (19)  op(all_14_2, e0) = all_14_1
% 204.26/35.18    (20)  all_34_1 = all_14_1
% 204.26/35.18    (21)  all_56_4 = all_52_3
% 204.26/35.18    (22)   ~ (all_52_17 = all_10_2)
% 204.26/35.18    (23)  op(e3, e0) = all_52_25
% 204.26/35.18    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.18    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.18    (26)   ~ (all_52_27 = all_52_29)
% 204.26/35.18    (27)  all_58_13 = all_52_15
% 204.26/35.18    (28)  op(e0, all_14_1) = e1
% 204.26/35.18    (29)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.18    (30)  all_58_9 = all_52_25
% 204.26/35.18    (31)   ~ (all_6_1 = e1)
% 204.26/35.18    (32)   ~ (all_52_29 = all_14_2)
% 204.26/35.18    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.18    (34)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.18    (35)  op(e1, e3) = all_52_5
% 204.26/35.18    (36)  op(e2, e2) = all_4_2
% 204.26/35.18    (37)   ~ (all_52_3 = all_52_5)
% 204.26/35.18    (38)  all_58_11 = all_52_29
% 204.26/35.18    (39)  all_56_5 = all_4_2
% 204.26/35.18    (40)   ~ (all_52_25 = all_14_2)
% 204.26/35.18    (41)   ~ (all_52_9 = all_52_15)
% 204.26/35.18    (42)   ~ (all_52_3 = all_52_27)
% 204.26/35.18    (43)  op(all_10_2, e1) = all_10_1
% 204.26/35.18    (44)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.18    (45)   ~ (all_52_7 = all_6_2)
% 204.26/35.18    (46)  op(e0, e0) = all_14_2
% 204.26/35.18    (47)  op(e0, e1) = all_52_23
% 204.26/35.18    (48)  all_56_15 = all_14_2
% 204.26/35.18    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.18    (50)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.18    (51)  all_56_11 = all_52_29
% 204.26/35.18    (52)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.18    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.18    (54)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.18    (55)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.18    (56)  all_56_9 = all_52_13
% 204.26/35.18    (57)   ~ (e2 = e1)
% 204.26/35.18    (58)   ~ (all_52_13 = all_10_2)
% 204.26/35.18    (59)   ~ (all_6_0 = e1)
% 204.26/35.18    (60)  all_58_10 = all_52_27
% 204.26/35.18    (61)  all_56_8 = all_52_5
% 204.26/35.18    (62)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.18    (63)  op(all_52_15, all_52_15) = all_52_14
% 204.26/35.18    (64)   ~ (all_52_19 = all_52_23)
% 204.26/35.18    (65)   ~ (all_52_25 = all_52_29)
% 204.26/35.18    (66)   ~ (all_52_29 = all_10_2)
% 204.26/35.18    (67)  all_58_7 = all_52_13
% 204.26/35.18    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.18    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.18    (70)   ~ (all_52_5 = all_52_7)
% 204.26/35.18    (71)  all_58_12 = all_52_7
% 204.26/35.18    (72)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.18    (73)   ~ (all_52_7 = all_14_2)
% 204.26/35.18    (74)   ~ (all_14_2 = e0)
% 204.26/35.18    (75)  all_58_2 = all_52_3
% 204.26/35.18    (76)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.18    (77)  all_56_2 = all_52_17
% 204.26/35.18    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.18    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.18    (80)  op(e3, all_6_1) = all_6_0
% 204.26/35.18    (81)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.18    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.18    (84)   ~ (e2 = e0)
% 204.26/35.18    (85)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.18    (86)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.18    (87)   ~ (all_52_5 = all_52_29)
% 204.26/35.18    (88)  all_56_6 = all_52_19
% 204.26/35.18    (89)   ~ (all_52_15 = all_14_2)
% 204.26/35.18    (90)   ~ (all_52_19 = all_52_27)
% 204.26/35.18    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.18    (92)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.18    (93)   ~ (all_6_0 = e2)
% 204.26/35.18    (94)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.18    (95)   ~ (all_52_13 = all_4_2)
% 204.26/35.18    (96)  op(e3, e1) = all_52_17
% 204.26/35.18    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.18    (98)  op(e0, e3) = all_52_7
% 204.26/35.18    (99)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.18    (100)   ~ (all_52_9 = all_52_25)
% 204.26/35.18    (101)  all_58_15 = all_14_2
% 204.26/35.18    (102)   ~ (all_52_19 = all_10_2)
% 204.26/35.18    (103)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.18    (104)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.18    (105)  all_58_8 = all_10_2
% 204.26/35.18    (106)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.18    (107)  all_34_2 = all_14_2
% 204.26/35.18    (108)   ~ (all_52_5 = all_10_2)
% 204.26/35.18    (109)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.18    (110)   ~ (all_52_23 = all_14_2)
% 204.26/35.18    (111)  all_56_12 = all_52_7
% 204.26/35.18    (112)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.18    (113)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.18    (114)   ~ (all_52_25 = all_6_2)
% 204.26/35.18    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.18    (116)   ~ (all_52_9 = all_4_2)
% 204.26/35.18    (117)   ~ (all_52_5 = all_6_2)
% 204.26/35.18    (118)   ~ (all_52_9 = all_6_2)
% 204.26/35.18    (119)   ~ (all_52_13 = all_52_15)
% 204.26/35.18    (120)  all_56_0 = all_6_2
% 204.26/35.18    (121)  op(e3, e3) = all_6_2
% 204.26/35.18    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.18    (123)   ~ (all_52_27 = all_14_2)
% 204.26/35.18    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.18    (125)  all_56_14 = all_52_23
% 204.26/35.18    (126)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.18    (127)  all_56_3 = all_52_25
% 204.26/35.18    (128)   ~ (all_52_3 = all_52_7)
% 204.26/35.18    (129)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.18    (130)  all_58_5 = all_52_19
% 204.26/35.18    (131)  all_56_1 = all_52_9
% 204.26/35.18    (132)   ~ (all_52_15 = all_4_2)
% 204.26/35.18    (133)   ~ (all_52_27 = all_4_2)
% 204.26/35.18    (134)  all_58_6 = all_52_5
% 204.26/35.18    (135)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.18    (136)   ~ (all_52_17 = all_6_2)
% 204.26/35.18    (137)   ~ (e1 = e0)
% 204.26/35.18    (138)   ~ (e3 = e2)
% 204.26/35.18    (139)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.18    (140)   ~ (all_52_9 = all_52_17)
% 204.26/35.18    (141)  all_56_10 = all_10_2
% 204.26/35.18    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.18    (143)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.18    (144)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.18    (145)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.18    (146)   ~ (all_6_1 = e2)
% 204.26/35.18    (147)  op(e1, e1) = all_10_2
% 204.26/35.18    (148)   ~ (all_52_23 = all_10_2)
% 204.26/35.18    (149)   ~ (all_52_7 = all_52_23)
% 204.26/35.18    (150)   ~ (all_52_17 = all_52_19)
% 204.26/35.18    (151)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.18           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.18    (152)  all_58_3 = all_4_2
% 204.26/35.18    (153)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.18    (154)  all_56_13 = all_52_15
% 204.26/35.18    (155)   ~ (all_52_3 = all_4_2)
% 204.26/35.18    (156)   ~ (all_52_19 = all_4_2)
% 204.26/35.18    (157)   ~ (all_52_17 = all_52_23)
% 204.26/35.18    (158)  op(all_6_2, e3) = all_6_1
% 204.26/35.18    (159)  all_58_4 = all_52_17
% 204.26/35.18    (160)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.18    (161)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | BETA: splitting (151) gives:
% 204.26/35.18  | 
% 204.26/35.18  | Case 1:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (162)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.26/35.18  | | 
% 204.26/35.18  | | ALPHA: (162) implies:
% 204.26/35.18  | |   (163)  all_52_22 = e0
% 204.26/35.18  | |   (164)  all_52_20 = e1
% 204.26/35.18  | |   (165)  all_52_18 = e2
% 204.26/35.18  | |   (166)  all_52_16 = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (112), (166) imply:
% 204.26/35.18  | |   (167)  op(all_52_17, all_52_17) = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (25), (165) imply:
% 204.26/35.18  | |   (168)  op(all_52_19, all_52_19) = e2
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (103), (163) imply:
% 204.26/35.18  | |   (169)  op(all_52_23, all_52_23) = e0
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (29), (164) imply:
% 204.26/35.18  | |   (170)  op(all_10_2, all_10_2) = e1
% 204.26/35.18  | | 
% 204.26/35.18  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 204.26/35.18  | |            (16), (18), (19), (20), (23), (24), (27), (28), (30), (31), (32),
% 204.26/35.18  | |            (33), (34), (35), (36), (37), (38), (40), (41), (43), (44), (45),
% 204.26/35.18  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 204.26/35.18  | |            (57), (58), (59), (60), (61), (62), (64), (65), (66), (67), (70),
% 204.26/35.18  | |            (71), (72), (73), (75), (76), (77), (78), (79), (80), (81), (84),
% 204.26/35.18  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 204.26/35.18  | |            (98), (99), (100), (101), (102), (104), (105), (106), (107),
% 204.26/35.18  | |            (108), (109), (110), (111), (115), (116), (117), (118), (119),
% 204.26/35.18  | |            (120), (121), (123), (124), (126), (127), (128), (130), (131),
% 204.26/35.18  | |            (133), (134), (135), (136), (137), (138), (139), (140), (141),
% 204.26/35.18  | |            (142), (143), (144), (145), (146), (147), (148), (149), (152),
% 204.26/35.18  | |            (153), (154), (155), (158), (159), (160), (161), (167), (168),
% 204.26/35.18  | |            (169), (170) are inconsistent by sub-proof #852.
% 204.26/35.18  | | 
% 204.26/35.18  | Case 2:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (171)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.26/35.18  | | 
% 204.26/35.18  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 204.26/35.18  | |            (16), (17), (18), (21), (22), (23), (24), (25), (26), (27), (30),
% 204.26/35.18  | |            (31), (32), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 204.26/35.18  | |            (43), (44), (45), (46), (48), (49), (50), (51), (53), (54), (55),
% 204.26/35.18  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 204.26/35.18  | |            (70), (71), (72), (73), (74), (75), (77), (79), (80), (81), (82),
% 204.26/35.18  | |            (83), (85), (87), (89), (90), (91), (92), (93), (94), (95), (96),
% 204.26/35.18  | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 204.26/35.18  | |            (106), (108), (109), (110), (111), (112), (113), (114), (115),
% 204.26/35.18  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 204.26/35.18  | |            (125), (127), (128), (129), (130), (131), (132), (133), (134),
% 204.26/35.18  | |            (135), (136), (138), (139), (144), (145), (146), (147), (149),
% 204.26/35.18  | |            (150), (152), (153), (154), (155), (156), (157), (158), (159),
% 204.26/35.18  | |            (161), (171) are inconsistent by sub-proof #1008.
% 204.26/35.18  | | 
% 204.26/35.18  | End of split
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #839 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (2)  all_58_9 = e3
% 204.26/35.18    (3)  op(all_14_2, e0) = all_14_1
% 204.26/35.18    (4)   ~ (all_10_2 = e0)
% 204.26/35.18    (5)  op(e0, all_14_1) = e1
% 204.26/35.18    (6)   ~ (all_52_29 = all_14_2)
% 204.26/35.18    (7)  all_58_11 = all_52_29
% 204.26/35.18    (8)  op(e0, e0) = all_14_2
% 204.26/35.18    (9)  all_56_11 = all_52_29
% 204.26/35.18    (10)  op(e0, e0) = all_52_26
% 204.26/35.18    (11)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.18    (12)   ~ (all_52_29 = all_10_2)
% 204.26/35.18    (13)  op(e2, e0) = e0
% 204.26/35.18    (14)  op(e1, e1) = e2
% 204.26/35.18    (15)   ~ (all_52_29 = e0)
% 204.26/35.18    (16)   ~ (all_10_2 = e3)
% 204.26/35.18    (17)  all_58_15 = all_14_2
% 204.26/35.18    (18)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.26/35.18    (19)  all_58_10 = e0
% 204.26/35.18    (20)  op(e1, e1) = all_10_2
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | GROUND_INST: instantiating (1) with all_10_2, e2, e1, e1, simplifying with
% 204.26/35.18  |              (14), (20) gives:
% 204.26/35.18  |   (21)  all_10_2 = e2
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (12), (21) imply:
% 204.26/35.18  |   (22)   ~ (all_52_29 = e2)
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (16), (21) imply:
% 204.26/35.18  |   (23)   ~ (e3 = e2)
% 204.26/35.18  | 
% 204.26/35.18  | SIMP: (23) implies:
% 204.26/35.18  |   (24)   ~ (e3 = e2)
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (4), (21) imply:
% 204.26/35.18  |   (25)   ~ (e2 = e0)
% 204.26/35.18  | 
% 204.26/35.18  | BETA: splitting (18) gives:
% 204.26/35.18  | 
% 204.26/35.18  | Case 1:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (26)  all_58_9 = e2
% 204.26/35.18  | | 
% 204.26/35.18  | | REF_CLOSE: (2), (24), (26) are inconsistent by sub-proof #840.
% 204.26/35.18  | | 
% 204.26/35.18  | Case 2:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (27)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.26/35.18  | | 
% 204.26/35.18  | | BETA: splitting (11) gives:
% 204.26/35.18  | | 
% 204.26/35.18  | | Case 1:
% 204.26/35.18  | | | 
% 204.26/35.18  | | |   (28)  all_56_11 = e2
% 204.26/35.18  | | | 
% 204.26/35.18  | | | REF_CLOSE: (9), (22), (28) are inconsistent by sub-proof #1024.
% 204.26/35.18  | | | 
% 204.26/35.18  | | Case 2:
% 204.26/35.18  | | | 
% 204.26/35.18  | | |   (29)   ~ (all_56_11 = e2)
% 204.26/35.18  | | |   (30)  all_56_11 = e1 | all_56_11 = e0
% 204.26/35.18  | | | 
% 204.26/35.18  | | | BETA: splitting (30) gives:
% 204.26/35.18  | | | 
% 204.26/35.18  | | | Case 1:
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | |   (31)  all_56_11 = e1
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | COMBINE_EQS: (9), (31) imply:
% 204.26/35.18  | | | |   (32)  all_52_29 = e1
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | SIMP: (32) implies:
% 204.26/35.18  | | | |   (33)  all_52_29 = e1
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | COMBINE_EQS: (7), (33) imply:
% 204.26/35.18  | | | |   (34)  all_58_11 = e1
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | REDUCE: (6), (33) imply:
% 204.26/35.18  | | | |   (35)   ~ (all_14_2 = e1)
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | SIMP: (35) implies:
% 204.26/35.18  | | | |   (36)   ~ (all_14_2 = e1)
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | REDUCE: (22), (33) imply:
% 204.26/35.18  | | | |   (37)   ~ (e2 = e1)
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | SIMP: (37) implies:
% 204.26/35.18  | | | |   (38)   ~ (e2 = e1)
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | BETA: splitting (27) gives:
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | Case 1:
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | |   (39)  all_58_10 = e2
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | | COMBINE_EQS: (19), (39) imply:
% 204.26/35.18  | | | | |   (40)  e2 = e0
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | | REDUCE: (25), (40) imply:
% 204.26/35.18  | | | | |   (41)  $false
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | | CLOSE: (41) is inconsistent.
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | Case 2:
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | |   (42)  all_58_11 = e2 | all_58_15 = e2
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | | BETA: splitting (42) gives:
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | | Case 1:
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | |   (43)  all_58_11 = e2
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | COMBINE_EQS: (34), (43) imply:
% 204.26/35.18  | | | | | |   (44)  e2 = e1
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | REDUCE: (38), (44) imply:
% 204.26/35.18  | | | | | |   (45)  $false
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | CLOSE: (45) is inconsistent.
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | Case 2:
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | |   (46)  all_58_15 = e2
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | COMBINE_EQS: (17), (46) imply:
% 204.26/35.18  | | | | | |   (47)  all_14_2 = e2
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | REDUCE: (3), (47) imply:
% 204.26/35.18  | | | | | |   (48)  op(e2, e0) = all_14_1
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | REDUCE: (8), (47) imply:
% 204.26/35.18  | | | | | |   (49)  op(e0, e0) = e2
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | | REF_CLOSE: (1), (5), (10), (13), (38), (48), (49) are inconsistent
% 204.26/35.18  | | | | | |            by sub-proof #864.
% 204.26/35.18  | | | | | | 
% 204.26/35.18  | | | | | End of split
% 204.26/35.18  | | | | | 
% 204.26/35.18  | | | | End of split
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | Case 2:
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | |   (50)  all_56_11 = e0
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | | REF_CLOSE: (9), (15), (50) are inconsistent by sub-proof #1002.
% 204.26/35.18  | | | | 
% 204.26/35.18  | | | End of split
% 204.26/35.18  | | | 
% 204.26/35.18  | | End of split
% 204.26/35.18  | | 
% 204.26/35.18  | End of split
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #840 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)  all_58_9 = e3
% 204.26/35.18    (2)  all_58_9 = e2
% 204.26/35.18    (3)   ~ (e3 = e2)
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.18  |   (4)  e3 = e2
% 204.26/35.18  | 
% 204.26/35.18  | SIMP: (4) implies:
% 204.26/35.18  |   (5)  e3 = e2
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (3), (5) imply:
% 204.26/35.18  |   (6)  $false
% 204.26/35.18  | 
% 204.26/35.18  | CLOSE: (6) is inconsistent.
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #841 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)  all_58_9 = e3
% 204.26/35.18    (2)  all_58_9 = e0
% 204.26/35.18    (3)   ~ (e3 = e0)
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.18  |   (4)  e3 = e0
% 204.26/35.18  | 
% 204.26/35.18  | SIMP: (4) implies:
% 204.26/35.18  |   (5)  e3 = e0
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (3), (5) imply:
% 204.26/35.18  |   (6)  $false
% 204.26/35.18  | 
% 204.26/35.18  | CLOSE: (6) is inconsistent.
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #842 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (2)  all_24_1 = all_14_1
% 204.26/35.18    (3)  op(all_14_2, e0) = all_14_1
% 204.26/35.18    (4)  all_14_2 = e2
% 204.26/35.18    (5)  all_24_2 = all_14_2
% 204.26/35.18    (6)  op(e2, e0) = e3
% 204.26/35.18    (7)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | SIMP: (4) implies:
% 204.26/35.18  |   (8)  all_14_2 = e2
% 204.26/35.18  | 
% 204.26/35.18  | COMBINE_EQS: (5), (8) imply:
% 204.26/35.18  |   (9)  all_24_2 = e2
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (3), (8) imply:
% 204.26/35.18  |   (10)  op(e2, e0) = all_14_1
% 204.26/35.18  | 
% 204.26/35.18  | REF_CLOSE: (1), (2), (6), (7), (9), (10) are inconsistent by sub-proof #843.
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #843 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (2)  all_24_1 = all_14_1
% 204.26/35.18    (3)  all_24_2 = e2
% 204.26/35.18    (4)  op(e2, e0) = e3
% 204.26/35.18    (5)  op(e2, e0) = all_14_1
% 204.26/35.18    (6)   ~ (all_24_1 = e3) |  ~ (all_24_2 = e2)
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | BETA: splitting (6) gives:
% 204.26/35.18  | 
% 204.26/35.18  | Case 1:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (7)   ~ (all_24_1 = e3)
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (2), (7) imply:
% 204.26/35.18  | |   (8)   ~ (all_14_1 = e3)
% 204.26/35.18  | | 
% 204.26/35.18  | | GROUND_INST: instantiating (1) with e3, all_14_1, e0, e2, simplifying with
% 204.26/35.18  | |              (4), (5) gives:
% 204.26/35.18  | |   (9)  all_14_1 = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (8), (9) imply:
% 204.26/35.18  | |   (10)  $false
% 204.26/35.18  | | 
% 204.26/35.18  | | CLOSE: (10) is inconsistent.
% 204.26/35.18  | | 
% 204.26/35.18  | Case 2:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (11)   ~ (all_24_2 = e2)
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (3), (11) imply:
% 204.26/35.18  | |   (12)  $false
% 204.26/35.18  | | 
% 204.26/35.18  | | CLOSE: (12) is inconsistent.
% 204.26/35.18  | | 
% 204.26/35.18  | End of split
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #844 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)   ~ (e3 = e1)
% 204.26/35.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (3)  op(all_52_7, all_52_7) = e0
% 204.26/35.18    (4)  op(all_52_5, all_52_5) = e1
% 204.26/35.18    (5)   ~ (all_4_0 = e1)
% 204.26/35.18    (6)  all_58_0 = all_6_2
% 204.26/35.18    (7)  all_58_2 = all_4_0
% 204.26/35.18    (8)  all_58_12 = all_52_7
% 204.26/35.18    (9)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18    (10)   ~ (all_52_5 = all_10_2)
% 204.26/35.18    (11)  op(e3, e3) = all_6_2
% 204.26/35.18    (12)  all_58_6 = all_52_5
% 204.26/35.18    (13)   ~ (e1 = e0)
% 204.26/35.18    (14)  all_58_12 = e3
% 204.26/35.18    (15)  op(e1, e1) = all_10_2
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | COMBINE_EQS: (8), (14) imply:
% 204.26/35.18  |   (16)  all_52_7 = e3
% 204.26/35.18  | 
% 204.26/35.18  | SIMP: (16) implies:
% 204.26/35.18  |   (17)  all_52_7 = e3
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (3), (17) imply:
% 204.26/35.18  |   (18)  op(e3, e3) = e0
% 204.26/35.18  | 
% 204.26/35.18  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 204.26/35.18  |            (15), (18) are inconsistent by sub-proof #845.
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #845 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)   ~ (e3 = e1)
% 204.26/35.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (3)  op(all_52_5, all_52_5) = e1
% 204.26/35.18    (4)   ~ (all_4_0 = e1)
% 204.26/35.18    (5)  all_58_0 = all_6_2
% 204.26/35.18    (6)  all_58_2 = all_4_0
% 204.26/35.18    (7)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18    (8)   ~ (all_52_5 = all_10_2)
% 204.26/35.18    (9)  op(e3, e3) = e0
% 204.26/35.18    (10)  op(e3, e3) = all_6_2
% 204.26/35.18    (11)  all_58_6 = all_52_5
% 204.26/35.18    (12)   ~ (e1 = e0)
% 204.26/35.18    (13)  all_58_12 = e3
% 204.26/35.18    (14)  op(e1, e1) = all_10_2
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | GROUND_INST: instantiating (2) with all_6_2, e0, e3, e3, simplifying with (9),
% 204.26/35.18  |              (10) gives:
% 204.26/35.18  |   (15)  all_6_2 = e0
% 204.26/35.18  | 
% 204.26/35.18  | COMBINE_EQS: (5), (15) imply:
% 204.26/35.18  |   (16)  all_58_0 = e0
% 204.26/35.18  | 
% 204.26/35.18  | BETA: splitting (7) gives:
% 204.26/35.18  | 
% 204.26/35.18  | Case 1:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (17)  all_58_0 = e1
% 204.26/35.18  | | 
% 204.26/35.18  | | REF_CLOSE: (12), (16), (17) are inconsistent by sub-proof #847.
% 204.26/35.18  | | 
% 204.26/35.18  | Case 2:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (18)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18  | | 
% 204.26/35.18  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (11), (13), (14), (18) are
% 204.26/35.18  | |            inconsistent by sub-proof #846.
% 204.26/35.18  | | 
% 204.26/35.18  | End of split
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #846 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)   ~ (e3 = e1)
% 204.26/35.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (3)  op(all_52_5, all_52_5) = e1
% 204.26/35.18    (4)   ~ (all_4_0 = e1)
% 204.26/35.18    (5)  all_58_2 = all_4_0
% 204.26/35.18    (6)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18    (7)   ~ (all_52_5 = all_10_2)
% 204.26/35.18    (8)  all_58_6 = all_52_5
% 204.26/35.18    (9)  all_58_12 = e3
% 204.26/35.18    (10)  op(e1, e1) = all_10_2
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | BETA: splitting (6) gives:
% 204.26/35.18  | 
% 204.26/35.18  | Case 1:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (11)  all_58_2 = e1
% 204.26/35.18  | | 
% 204.26/35.18  | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #967.
% 204.26/35.18  | | 
% 204.26/35.18  | Case 2:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (12)  all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18  | | 
% 204.26/35.18  | | BETA: splitting (12) gives:
% 204.26/35.18  | | 
% 204.26/35.18  | | Case 1:
% 204.26/35.18  | | | 
% 204.26/35.18  | | |   (13)  all_58_6 = e1
% 204.26/35.18  | | | 
% 204.26/35.18  | | | COMBINE_EQS: (8), (13) imply:
% 204.26/35.18  | | |   (14)  all_52_5 = e1
% 204.26/35.18  | | | 
% 204.26/35.18  | | | SIMP: (14) implies:
% 204.26/35.18  | | |   (15)  all_52_5 = e1
% 204.26/35.18  | | | 
% 204.26/35.18  | | | REDUCE: (7), (15) imply:
% 204.26/35.18  | | |   (16)   ~ (all_10_2 = e1)
% 204.26/35.18  | | | 
% 204.26/35.18  | | | SIMP: (16) implies:
% 204.26/35.18  | | |   (17)   ~ (all_10_2 = e1)
% 204.26/35.18  | | | 
% 204.26/35.18  | | | REDUCE: (3), (15) imply:
% 204.26/35.18  | | |   (18)  op(e1, e1) = e1
% 204.26/35.18  | | | 
% 204.26/35.18  | | | GROUND_INST: instantiating (2) with all_10_2, e1, e1, e1, simplifying with
% 204.26/35.18  | | |              (10), (18) gives:
% 204.26/35.18  | | |   (19)  all_10_2 = e1
% 204.26/35.18  | | | 
% 204.26/35.18  | | | REDUCE: (17), (19) imply:
% 204.26/35.18  | | |   (20)  $false
% 204.26/35.18  | | | 
% 204.26/35.18  | | | CLOSE: (20) is inconsistent.
% 204.26/35.18  | | | 
% 204.26/35.18  | | Case 2:
% 204.26/35.18  | | | 
% 204.26/35.18  | | |   (21)  all_58_12 = e1
% 204.26/35.18  | | | 
% 204.26/35.18  | | | REF_CLOSE: (1), (9), (21) are inconsistent by sub-proof #894.
% 204.26/35.18  | | | 
% 204.26/35.18  | | End of split
% 204.26/35.18  | | 
% 204.26/35.18  | End of split
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #847 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)  all_58_0 = e1
% 204.26/35.18    (2)  all_58_0 = e0
% 204.26/35.18    (3)   ~ (e1 = e0)
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.18  |   (4)  e1 = e0
% 204.26/35.18  | 
% 204.26/35.18  | SIMP: (4) implies:
% 204.26/35.18  |   (5)  e1 = e0
% 204.26/35.18  | 
% 204.26/35.18  | REDUCE: (3), (5) imply:
% 204.26/35.18  |   (6)  $false
% 204.26/35.18  | 
% 204.26/35.18  | CLOSE: (6) is inconsistent.
% 204.26/35.18  | 
% 204.26/35.18  End of proof
% 204.26/35.18  
% 204.26/35.18  Sub-proof #848 shows that the following formulas are inconsistent:
% 204.26/35.18  ----------------------------------------------------------------
% 204.26/35.18    (1)  all_58_14 = all_52_23
% 204.26/35.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.18    (3)  op(all_52_7, all_52_7) = e0
% 204.26/35.18    (4)  op(all_52_5, all_52_5) = e1
% 204.26/35.18    (5)   ~ (e3 = e0)
% 204.26/35.18    (6)   ~ (all_4_0 = e1)
% 204.26/35.18    (7)  all_58_0 = all_6_2
% 204.26/35.18    (8)  all_58_13 = e3
% 204.26/35.18    (9)  all_58_2 = all_4_0
% 204.26/35.18    (10)  op(e3, e3) = all_52_14
% 204.26/35.18    (11)   ~ (all_4_0 = e3)
% 204.26/35.18    (12)   ~ (all_6_0 = e1)
% 204.26/35.18    (13)  op(all_6_2, all_6_2) = e3
% 204.26/35.18    (14)  all_58_12 = all_52_7
% 204.26/35.18    (15)   ~ (all_52_7 = e3)
% 204.26/35.18    (16)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.18    (17)  op(e3, all_6_1) = all_6_0
% 204.26/35.18    (18)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.18    (19)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.18    (20)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.18    (21)   ~ (all_52_5 = all_10_2)
% 204.26/35.18    (22)  op(e3, e3) = all_6_2
% 204.26/35.18    (23)  all_58_6 = all_52_5
% 204.26/35.18    (24)   ~ (e1 = e0)
% 204.26/35.18    (25)  op(e1, e1) = all_10_2
% 204.26/35.18    (26)   ~ (all_52_23 = all_10_2)
% 204.26/35.18    (27)  op(all_6_2, e3) = all_6_1
% 204.26/35.18  
% 204.26/35.18  Begin of proof
% 204.26/35.18  | 
% 204.26/35.18  | GROUND_INST: instantiating (2) with all_6_2, all_52_14, e3, e3, simplifying
% 204.26/35.18  |              with (10), (22) gives:
% 204.26/35.18  |   (28)  all_52_14 = all_6_2
% 204.26/35.18  | 
% 204.26/35.18  | BETA: splitting (16) gives:
% 204.26/35.18  | 
% 204.26/35.18  | Case 1:
% 204.26/35.18  | | 
% 204.26/35.18  | |   (29)  all_58_0 = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | COMBINE_EQS: (7), (29) imply:
% 204.26/35.18  | |   (30)  all_6_2 = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (27), (30) imply:
% 204.26/35.18  | |   (31)  op(e3, e3) = all_6_1
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (22), (30) imply:
% 204.26/35.18  | |   (32)  op(e3, e3) = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | GROUND_INST: instantiating (2) with e3, all_6_1, e3, e3, simplifying with
% 204.26/35.18  | |              (31), (32) gives:
% 204.26/35.18  | |   (33)  all_6_1 = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (17), (33) imply:
% 204.26/35.18  | |   (34)  op(e3, e3) = all_6_0
% 204.26/35.18  | | 
% 204.26/35.18  | | GROUND_INST: instantiating (2) with e3, all_6_0, e3, e3, simplifying with
% 204.26/35.18  | |              (32), (34) gives:
% 204.26/35.18  | |   (35)  all_6_0 = e3
% 204.26/35.18  | | 
% 204.26/35.18  | | REDUCE: (12), (35) imply:
% 204.26/35.18  | |   (36)   ~ (e3 = e1)
% 204.26/35.18  | | 
% 204.26/35.18  | | BETA: splitting (18) gives:
% 204.26/35.18  | | 
% 204.26/35.18  | | Case 1:
% 204.26/35.18  | | | 
% 204.26/35.18  | | |   (37)  all_58_0 = e1
% 204.26/35.19  | | | 
% 204.26/35.19  | | | COMBINE_EQS: (29), (37) imply:
% 204.26/35.19  | | |   (38)  e3 = e1
% 204.26/35.19  | | | 
% 204.26/35.19  | | | REDUCE: (36), (38) imply:
% 204.26/35.19  | | |   (39)  $false
% 204.26/35.19  | | | 
% 204.26/35.19  | | | CLOSE: (39) is inconsistent.
% 204.26/35.19  | | | 
% 204.26/35.19  | | Case 2:
% 204.26/35.19  | | | 
% 204.26/35.19  | | |   (40)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.19  | | | 
% 204.26/35.19  | | | BETA: splitting (19) gives:
% 204.26/35.19  | | | 
% 204.26/35.19  | | | Case 1:
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | |   (41)  all_58_12 = e1
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REF_CLOSE: (1), (2), (3), (5), (8), (14), (20), (24), (25), (26), (41)
% 204.26/35.19  | | | |            are inconsistent by sub-proof #1170.
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | Case 2:
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | |   (42)   ~ (all_58_12 = e1)
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REF_CLOSE: (2), (4), (6), (9), (14), (21), (23), (25), (40), (42) are
% 204.26/35.19  | | | |            inconsistent by sub-proof #850.
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | End of split
% 204.26/35.19  | | | 
% 204.26/35.19  | | End of split
% 204.26/35.19  | | 
% 204.26/35.19  | Case 2:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (43)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (2), (4), (9), (11), (13), (14), (15), (21), (22), (23), (25),
% 204.26/35.19  | |            (43) are inconsistent by sub-proof #849.
% 204.26/35.19  | | 
% 204.26/35.19  | End of split
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #849 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (2)  op(all_52_5, all_52_5) = e1
% 204.26/35.19    (3)  all_58_2 = all_4_0
% 204.26/35.19    (4)   ~ (all_4_0 = e3)
% 204.26/35.19    (5)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.19    (6)  op(all_6_2, all_6_2) = e3
% 204.26/35.19    (7)  all_58_12 = all_52_7
% 204.26/35.19    (8)   ~ (all_52_7 = e3)
% 204.26/35.19    (9)   ~ (all_52_5 = all_10_2)
% 204.26/35.19    (10)  op(e3, e3) = all_6_2
% 204.26/35.19    (11)  all_58_6 = all_52_5
% 204.26/35.19    (12)  op(e1, e1) = all_10_2
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | BETA: splitting (5) gives:
% 204.26/35.19  | 
% 204.26/35.19  | Case 1:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (13)  all_58_2 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #948.
% 204.26/35.19  | | 
% 204.26/35.19  | Case 2:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (14)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (14) are
% 204.26/35.19  | |            inconsistent by sub-proof #1366.
% 204.26/35.19  | | 
% 204.26/35.19  | End of split
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #850 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (2)  op(all_52_5, all_52_5) = e1
% 204.26/35.19    (3)   ~ (all_4_0 = e1)
% 204.26/35.19    (4)  all_58_2 = all_4_0
% 204.26/35.19    (5)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.19    (6)  all_58_12 = all_52_7
% 204.26/35.19    (7)   ~ (all_52_5 = all_10_2)
% 204.26/35.19    (8)  all_58_6 = all_52_5
% 204.26/35.19    (9)  op(e1, e1) = all_10_2
% 204.26/35.19    (10)   ~ (all_58_12 = e1)
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | REDUCE: (6), (10) imply:
% 204.26/35.19  |   (11)   ~ (all_52_7 = e1)
% 204.26/35.19  | 
% 204.26/35.19  | BETA: splitting (5) gives:
% 204.26/35.19  | 
% 204.26/35.19  | Case 1:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (12)  all_58_2 = e1
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #967.
% 204.26/35.19  | | 
% 204.26/35.19  | Case 2:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (13)  all_58_6 = e1 | all_58_12 = e1
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (11), (13) are inconsistent by
% 204.26/35.19  | |            sub-proof #851.
% 204.26/35.19  | | 
% 204.26/35.19  | End of split
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #851 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (2)  op(all_52_5, all_52_5) = e1
% 204.26/35.19    (3)  all_58_6 = e1 | all_58_12 = e1
% 204.26/35.19    (4)  all_58_12 = all_52_7
% 204.26/35.19    (5)   ~ (all_52_5 = all_10_2)
% 204.26/35.19    (6)   ~ (all_52_7 = e1)
% 204.26/35.19    (7)  all_58_6 = all_52_5
% 204.26/35.19    (8)  op(e1, e1) = all_10_2
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | BETA: splitting (3) gives:
% 204.26/35.19  | 
% 204.26/35.19  | Case 1:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (9)  all_58_6 = e1
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (7), (9) imply:
% 204.26/35.19  | |   (10)  all_52_5 = e1
% 204.26/35.19  | | 
% 204.26/35.19  | | SIMP: (10) implies:
% 204.26/35.19  | |   (11)  all_52_5 = e1
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (1), (2), (5), (8), (11) are inconsistent by sub-proof #871.
% 204.26/35.19  | | 
% 204.26/35.19  | Case 2:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (12)  all_58_12 = e1
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #1127.
% 204.26/35.19  | | 
% 204.26/35.19  | End of split
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #852 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.19    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.19    (3)  all_58_14 = all_52_23
% 204.26/35.19    (4)   ~ (e3 = e1)
% 204.26/35.19    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.19    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (7)  all_58_1 = all_52_9
% 204.26/35.19    (8)   ~ (e3 = e0)
% 204.26/35.19    (9)  op(all_52_23, all_52_23) = e0
% 204.26/35.19    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.19    (11)   ~ (all_52_7 = all_52_15)
% 204.26/35.19    (12)   ~ (all_52_3 = all_52_19)
% 204.26/35.19    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.19    (14)   ~ (all_52_17 = all_52_25)
% 204.26/35.19    (15)  all_58_0 = all_6_2
% 204.26/35.19    (16)  op(all_14_2, e0) = all_14_1
% 204.26/35.19    (17)  all_34_1 = all_14_1
% 204.26/35.19    (18)  op(e3, e0) = all_52_25
% 204.26/35.19    (19)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.19    (20)  all_58_13 = all_52_15
% 204.26/35.19    (21)  op(e0, all_14_1) = e1
% 204.26/35.19    (22)  all_58_9 = all_52_25
% 204.26/35.19    (23)   ~ (all_6_1 = e1)
% 204.26/35.19    (24)   ~ (all_52_29 = all_14_2)
% 204.26/35.19    (25)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.19    (26)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.19    (27)  op(e1, e3) = all_52_5
% 204.26/35.19    (28)  op(e2, e2) = all_4_2
% 204.26/35.19    (29)   ~ (all_52_3 = all_52_5)
% 204.26/35.19    (30)  all_58_11 = all_52_29
% 204.26/35.19    (31)   ~ (all_52_25 = all_14_2)
% 204.26/35.19    (32)   ~ (all_52_9 = all_52_15)
% 204.26/35.19    (33)  op(all_10_2, e1) = all_10_1
% 204.26/35.19    (34)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.19    (35)   ~ (all_52_7 = all_6_2)
% 204.26/35.19    (36)  op(e0, e0) = all_14_2
% 204.26/35.19    (37)  op(e0, e1) = all_52_23
% 204.26/35.19    (38)  all_56_15 = all_14_2
% 204.26/35.19    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.19    (40)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.19    (41)  all_56_11 = all_52_29
% 204.26/35.19    (42)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.19    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.19    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.19    (45)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.19    (46)  all_56_9 = all_52_13
% 204.26/35.19    (47)   ~ (e2 = e1)
% 204.26/35.19    (48)   ~ (all_52_13 = all_10_2)
% 204.26/35.19    (49)   ~ (all_6_0 = e1)
% 204.26/35.19    (50)  op(all_10_2, all_10_2) = e1
% 204.26/35.19    (51)  all_58_10 = all_52_27
% 204.26/35.19    (52)  all_56_8 = all_52_5
% 204.26/35.19    (53)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.19    (54)   ~ (all_52_19 = all_52_23)
% 204.26/35.19    (55)   ~ (all_52_25 = all_52_29)
% 204.26/35.19    (56)   ~ (all_52_29 = all_10_2)
% 204.26/35.19    (57)  all_58_7 = all_52_13
% 204.26/35.19    (58)  op(all_52_19, all_52_19) = e2
% 204.26/35.19    (59)   ~ (all_52_5 = all_52_7)
% 204.26/35.19    (60)  all_58_12 = all_52_7
% 204.26/35.19    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.19    (62)   ~ (all_52_7 = all_14_2)
% 204.26/35.19    (63)  all_58_2 = all_52_3
% 204.26/35.19    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.19    (65)  all_56_2 = all_52_17
% 204.26/35.19    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.19    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.19    (68)  op(e3, all_6_1) = all_6_0
% 204.26/35.19    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.19    (70)   ~ (e2 = e0)
% 204.26/35.19    (71)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.19    (72)   ~ (all_52_5 = all_52_29)
% 204.26/35.19    (73)  all_56_6 = all_52_19
% 204.26/35.19    (74)   ~ (all_52_15 = all_14_2)
% 204.26/35.19    (75)   ~ (all_52_19 = all_52_27)
% 204.26/35.19    (76)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.19    (77)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.19    (78)   ~ (all_6_0 = e2)
% 204.26/35.19    (79)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.19    (80)   ~ (all_52_13 = all_4_2)
% 204.26/35.19    (81)  op(e3, e1) = all_52_17
% 204.26/35.19    (82)  op(e0, e3) = all_52_7
% 204.26/35.19    (83)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.19    (84)   ~ (all_52_9 = all_52_25)
% 204.26/35.19    (85)  all_58_15 = all_14_2
% 204.26/35.19    (86)   ~ (all_52_19 = all_10_2)
% 204.26/35.19    (87)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.19    (88)  all_58_8 = all_10_2
% 204.26/35.19    (89)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.19    (90)  all_34_2 = all_14_2
% 204.26/35.19    (91)   ~ (all_52_5 = all_10_2)
% 204.26/35.19    (92)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.19    (93)   ~ (all_52_23 = all_14_2)
% 204.26/35.19    (94)  all_56_12 = all_52_7
% 204.26/35.19    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.19    (96)   ~ (all_52_9 = all_4_2)
% 204.26/35.19    (97)   ~ (all_52_5 = all_6_2)
% 204.26/35.19    (98)   ~ (all_52_9 = all_6_2)
% 204.26/35.19    (99)   ~ (all_52_13 = all_52_15)
% 204.26/35.19    (100)  all_56_0 = all_6_2
% 204.26/35.19    (101)  op(e3, e3) = all_6_2
% 204.26/35.19    (102)   ~ (all_52_27 = all_14_2)
% 204.26/35.19    (103)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.19    (104)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.19    (105)  all_56_3 = all_52_25
% 204.26/35.19    (106)   ~ (all_52_3 = all_52_7)
% 204.26/35.19    (107)  all_58_5 = all_52_19
% 204.26/35.19    (108)  all_56_1 = all_52_9
% 204.26/35.19    (109)   ~ (all_52_27 = all_4_2)
% 204.26/35.19    (110)  op(all_52_17, all_52_17) = e3
% 204.26/35.19    (111)  all_58_6 = all_52_5
% 204.26/35.19    (112)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.19    (113)   ~ (all_52_17 = all_6_2)
% 204.26/35.19    (114)   ~ (e1 = e0)
% 204.26/35.19    (115)   ~ (e3 = e2)
% 204.26/35.19    (116)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.19    (117)   ~ (all_52_9 = all_52_17)
% 204.26/35.19    (118)  all_56_10 = all_10_2
% 204.26/35.19    (119)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.19    (120)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.19    (121)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.19    (122)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.19    (123)   ~ (all_6_1 = e2)
% 204.26/35.19    (124)  op(e1, e1) = all_10_2
% 204.26/35.19    (125)   ~ (all_52_23 = all_10_2)
% 204.26/35.19    (126)   ~ (all_52_7 = all_52_23)
% 204.26/35.19    (127)  all_58_3 = all_4_2
% 204.26/35.19    (128)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.19    (129)  all_56_13 = all_52_15
% 204.26/35.19    (130)   ~ (all_52_3 = all_4_2)
% 204.26/35.19    (131)  op(all_6_2, e3) = all_6_1
% 204.26/35.19    (132)  all_58_4 = all_52_17
% 204.26/35.19    (133)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.19    (134)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | BETA: splitting (89) gives:
% 204.26/35.19  | 
% 204.26/35.19  | Case 1:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (135)  all_56_15 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (38), (135) imply:
% 204.26/35.19  | |   (136)  all_14_2 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | SIMP: (136) implies:
% 204.26/35.19  | |   (137)  all_14_2 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (90), (137) imply:
% 204.26/35.19  | |   (138)  all_34_2 = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (93), (137) imply:
% 204.26/35.19  | |   (139)   ~ (all_52_23 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (31), (137) imply:
% 204.26/35.19  | |   (140)   ~ (all_52_25 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (24), (137) imply:
% 204.26/35.19  | |   (141)   ~ (all_52_29 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (16), (137) imply:
% 204.26/35.19  | |   (142)  op(e3, e0) = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (36), (137) imply:
% 204.26/35.19  | |   (143)  op(e0, e0) = e3
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (1), (4), (6), (9), (17), (18), (21), (22), (26), (30), (37),
% 204.26/35.19  | |            (40), (41), (42), (50), (51), (55), (56), (76), (95), (105),
% 204.26/35.19  | |            (124), (125), (134), (138), (139), (140), (141), (142), (143) are
% 204.26/35.19  | |            inconsistent by sub-proof #853.
% 204.26/35.19  | | 
% 204.26/35.19  | Case 2:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (144)   ~ (all_56_15 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (38), (144) imply:
% 204.26/35.19  | |   (145)   ~ (all_14_2 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.26/35.19  | |            (13), (14), (15), (19), (20), (22), (23), (25), (26), (27), (28),
% 204.26/35.19  | |            (29), (30), (31), (32), (33), (34), (35), (36), (39), (41), (43),
% 204.26/35.19  | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 204.26/35.19  | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 204.26/35.19  | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 204.26/35.19  | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 204.26/35.19  | |            (88), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 204.26/35.19  | |            (100), (101), (102), (103), (104), (105), (106), (107), (108),
% 204.26/35.19  | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 204.26/35.19  | |            (118), (119), (120), (121), (122), (123), (124), (126), (127),
% 204.26/35.19  | |            (128), (129), (130), (131), (132), (133), (134), (145) are
% 204.26/35.19  | |            inconsistent by sub-proof #1044.
% 204.26/35.19  | | 
% 204.26/35.19  | End of split
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #853 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.19    (2)   ~ (e3 = e1)
% 204.26/35.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (4)  op(all_52_23, all_52_23) = e0
% 204.26/35.19    (5)  all_34_1 = all_14_1
% 204.26/35.19    (6)  op(e3, e0) = all_52_25
% 204.26/35.19    (7)  op(e0, all_14_1) = e1
% 204.26/35.19    (8)  all_58_9 = all_52_25
% 204.26/35.19    (9)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.19    (10)  all_58_11 = all_52_29
% 204.26/35.19    (11)  op(e0, e1) = all_52_23
% 204.26/35.19    (12)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.19    (13)  all_56_11 = all_52_29
% 204.26/35.19    (14)  op(e0, e0) = e3
% 204.26/35.19    (15)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.19    (16)  op(all_10_2, all_10_2) = e1
% 204.26/35.19    (17)  all_58_10 = all_52_27
% 204.26/35.19    (18)   ~ (all_52_25 = all_52_29)
% 204.26/35.19    (19)   ~ (all_52_29 = all_10_2)
% 204.26/35.19    (20)  all_34_2 = e3
% 204.26/35.19    (21)   ~ (all_52_29 = e3)
% 204.26/35.19    (22)   ~ (all_52_25 = e3)
% 204.26/35.19    (23)   ~ (all_52_23 = e3)
% 204.26/35.19    (24)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.19    (25)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.19    (26)  op(e3, e0) = all_14_1
% 204.26/35.19    (27)  all_56_3 = all_52_25
% 204.26/35.19    (28)  op(e1, e1) = all_10_2
% 204.26/35.19    (29)   ~ (all_52_23 = all_10_2)
% 204.26/35.19    (30)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | BETA: splitting (15) gives:
% 204.26/35.19  | 
% 204.26/35.19  | Case 1:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (31)   ~ (all_34_1 = e2)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (5), (31) imply:
% 204.26/35.19  | |   (32)   ~ (all_14_1 = e2)
% 204.26/35.19  | | 
% 204.26/35.19  | | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 204.26/35.19  | |              with (6), (26) gives:
% 204.26/35.19  | |   (33)  all_52_25 = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (27), (33) imply:
% 204.26/35.19  | |   (34)  all_56_3 = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (8), (33) imply:
% 204.26/35.19  | |   (35)  all_58_9 = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (18), (33) imply:
% 204.26/35.19  | |   (36)   ~ (all_52_29 = all_14_1)
% 204.26/35.19  | | 
% 204.26/35.19  | | SIMP: (36) implies:
% 204.26/35.19  | |   (37)   ~ (all_52_29 = all_14_1)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (22), (33) imply:
% 204.26/35.19  | |   (38)   ~ (all_14_1 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (30), (33) imply:
% 204.26/35.19  | |   (39)  op(all_14_1, all_14_1) = all_52_24
% 204.26/35.19  | | 
% 204.26/35.19  | | BETA: splitting (25) gives:
% 204.26/35.19  | | 
% 204.26/35.19  | | Case 1:
% 204.26/35.19  | | | 
% 204.26/35.19  | | |   (40)  all_56_3 = e3
% 204.26/35.19  | | | 
% 204.26/35.19  | | | REF_CLOSE: (34), (38), (40) are inconsistent by sub-proof #1200.
% 204.26/35.19  | | | 
% 204.26/35.19  | | Case 2:
% 204.26/35.19  | | | 
% 204.26/35.19  | | |   (41)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.19  | | | 
% 204.26/35.19  | | | BETA: splitting (24) gives:
% 204.26/35.19  | | | 
% 204.26/35.19  | | | Case 1:
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | |   (42)  all_56_11 = e3
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | COMBINE_EQS: (13), (42) imply:
% 204.26/35.19  | | | |   (43)  all_52_29 = e3
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REDUCE: (21), (43) imply:
% 204.26/35.19  | | | |   (44)  $false
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | CLOSE: (44) is inconsistent.
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | Case 2:
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | |   (45)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | BETA: splitting (12) gives:
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | Case 1:
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | |   (46)  all_58_9 = e1
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | COMBINE_EQS: (35), (46) imply:
% 204.26/35.19  | | | | |   (47)  all_14_1 = e1
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | SIMP: (47) implies:
% 204.26/35.19  | | | | |   (48)  all_14_1 = e1
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (37), (48) imply:
% 204.26/35.19  | | | | |   (49)   ~ (all_52_29 = e1)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (39), (48) imply:
% 204.26/35.19  | | | | |   (50)  op(e1, e1) = all_52_24
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (7), (48) imply:
% 204.26/35.19  | | | | |   (51)  op(e0, e1) = e1
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | GROUND_INST: instantiating (3) with all_52_23, e1, e1, e0, simplifying
% 204.26/35.19  | | | | |              with (11), (51) gives:
% 204.26/35.19  | | | | |   (52)  all_52_23 = e1
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_24, e1, e1,
% 204.26/35.19  | | | | |              simplifying with (28), (50) gives:
% 204.26/35.19  | | | | |   (53)  all_52_24 = all_10_2
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (29), (52) imply:
% 204.26/35.19  | | | | |   (54)   ~ (all_10_2 = e1)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | SIMP: (54) implies:
% 204.26/35.19  | | | | |   (55)   ~ (all_10_2 = e1)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (23), (52) imply:
% 204.26/35.19  | | | | |   (56)   ~ (e3 = e1)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (4), (52) imply:
% 204.26/35.19  | | | | |   (57)  op(e1, e1) = e0
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | GROUND_INST: instantiating (3) with all_10_2, e0, e1, e1, simplifying
% 204.26/35.19  | | | | |              with (28), (57) gives:
% 204.26/35.19  | | | | |   (58)  all_10_2 = e0
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (19), (58) imply:
% 204.26/35.19  | | | | |   (59)   ~ (all_52_29 = e0)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (55), (58) imply:
% 204.26/35.19  | | | | |   (60)   ~ (e1 = e0)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | SIMP: (60) implies:
% 204.26/35.19  | | | | |   (61)   ~ (e1 = e0)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (16), (58) imply:
% 204.26/35.19  | | | | |   (62)  op(e0, e0) = e1
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | BETA: splitting (45) gives:
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | Case 1:
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | |   (63)  all_56_11 = e2
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | COMBINE_EQS: (13), (63) imply:
% 204.26/35.19  | | | | | |   (64)  all_52_29 = e2
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | SIMP: (64) implies:
% 204.26/35.19  | | | | | |   (65)  all_52_29 = e2
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | COMBINE_EQS: (10), (65) imply:
% 204.26/35.19  | | | | | |   (66)  all_58_11 = e2
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | REDUCE: (59), (65) imply:
% 204.26/35.19  | | | | | |   (67)   ~ (e2 = e0)
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | BETA: splitting (1) gives:
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | Case 1:
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | |   (68)  all_58_9 = e0
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | | REF_CLOSE: (46), (61), (68) are inconsistent by sub-proof #865.
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | Case 2:
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | |   (69)  all_58_10 = e0 | all_58_11 = e0
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | | BETA: splitting (69) gives:
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | | Case 1:
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | |   (70)  all_58_10 = e0
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | | COMBINE_EQS: (17), (70) imply:
% 204.26/35.19  | | | | | | | |   (71)  all_52_27 = e0
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | | REF_CLOSE: (2), (3), (9), (14), (62), (71) are inconsistent by
% 204.26/35.19  | | | | | | | |            sub-proof #854.
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | Case 2:
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | |   (72)  all_58_11 = e0
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | | COMBINE_EQS: (66), (72) imply:
% 204.26/35.19  | | | | | | | |   (73)  e2 = e0
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | | SIMP: (73) implies:
% 204.26/35.19  | | | | | | | |   (74)  e2 = e0
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | | REDUCE: (67), (74) imply:
% 204.26/35.19  | | | | | | | |   (75)  $false
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | | CLOSE: (75) is inconsistent.
% 204.26/35.19  | | | | | | | | 
% 204.26/35.19  | | | | | | | End of split
% 204.26/35.19  | | | | | | | 
% 204.26/35.19  | | | | | | End of split
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | Case 2:
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | |   (76)  all_56_11 = e1 | all_56_11 = e0
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | | REF_CLOSE: (13), (49), (59), (76) are inconsistent by sub-proof
% 204.26/35.19  | | | | | |            #1001.
% 204.26/35.19  | | | | | | 
% 204.26/35.19  | | | | | End of split
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | Case 2:
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | |   (77)   ~ (all_58_9 = e1)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REDUCE: (35), (77) imply:
% 204.26/35.19  | | | | |   (78)   ~ (all_14_1 = e1)
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | | REF_CLOSE: (2), (3), (7), (14), (32), (34), (39), (41), (78) are
% 204.26/35.19  | | | | |            inconsistent by sub-proof #867.
% 204.26/35.19  | | | | | 
% 204.26/35.19  | | | | End of split
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | End of split
% 204.26/35.19  | | | 
% 204.26/35.19  | | End of split
% 204.26/35.19  | | 
% 204.26/35.19  | Case 2:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (79)   ~ (all_34_2 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (20), (79) imply:
% 204.26/35.19  | |   (80)  $false
% 204.26/35.19  | | 
% 204.26/35.19  | | CLOSE: (80) is inconsistent.
% 204.26/35.19  | | 
% 204.26/35.19  | End of split
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #854 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)   ~ (e3 = e1)
% 204.26/35.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (3)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.19    (4)  op(e0, e0) = e3
% 204.26/35.19    (5)  op(e0, e0) = e1
% 204.26/35.19    (6)  all_52_27 = e0
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | SIMP: (6) implies:
% 204.26/35.19  |   (7)  all_52_27 = e0
% 204.26/35.19  | 
% 204.26/35.19  | REDUCE: (3), (7) imply:
% 204.26/35.19  |   (8)  op(e0, e0) = all_52_26
% 204.26/35.19  | 
% 204.26/35.19  | GROUND_INST: instantiating (2) with e3, all_52_26, e0, e0, simplifying with
% 204.26/35.19  |              (4), (8) gives:
% 204.26/35.19  |   (9)  all_52_26 = e3
% 204.26/35.19  | 
% 204.26/35.19  | GROUND_INST: instantiating (2) with e1, all_52_26, e0, e0, simplifying with
% 204.26/35.19  |              (5), (8) gives:
% 204.26/35.19  |   (10)  all_52_26 = e1
% 204.26/35.19  | 
% 204.26/35.19  | COMBINE_EQS: (9), (10) imply:
% 204.26/35.19  |   (11)  e3 = e1
% 204.26/35.19  | 
% 204.26/35.19  | REDUCE: (1), (11) imply:
% 204.26/35.19  |   (12)  $false
% 204.26/35.19  | 
% 204.26/35.19  | CLOSE: (12) is inconsistent.
% 204.26/35.19  | 
% 204.26/35.19  End of proof
% 204.26/35.19  
% 204.26/35.19  Sub-proof #855 shows that the following formulas are inconsistent:
% 204.26/35.19  ----------------------------------------------------------------
% 204.26/35.19    (1)   ~ (all_52_25 = all_52_27)
% 204.26/35.19    (2)   ~ (e3 = e1)
% 204.26/35.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.19    (4)  all_34_1 = all_14_1
% 204.26/35.19    (5)  op(e3, e0) = all_52_25
% 204.26/35.19    (6)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.19    (7)  op(all_52_13, all_52_13) = e1
% 204.26/35.19    (8)  op(e0, all_14_1) = e1
% 204.26/35.19    (9)  all_58_9 = all_52_25
% 204.26/35.19    (10)   ~ (all_52_3 = all_52_5)
% 204.26/35.19    (11)   ~ (all_4_1 = e3)
% 204.26/35.19    (12)  all_58_11 = all_52_29
% 204.26/35.19    (13)  op(e0, e1) = all_52_23
% 204.26/35.19    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.19    (15)  op(e0, e0) = e3
% 204.26/35.19    (16)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.19    (17)   ~ (all_52_13 = all_10_2)
% 204.26/35.19    (18)  all_58_10 = all_52_27
% 204.26/35.19    (19)   ~ (all_52_19 = all_52_23)
% 204.26/35.19    (20)   ~ (all_52_25 = all_52_29)
% 204.26/35.19    (21)  all_58_7 = all_52_13
% 204.26/35.19    (22)  all_34_2 = e3
% 204.26/35.19    (23)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.19    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.19    (25)  all_58_2 = all_52_3
% 204.26/35.19    (26)   ~ (all_52_29 = e3)
% 204.26/35.19    (27)   ~ (all_52_25 = e3)
% 204.26/35.19    (28)  op(all_4_2, e2) = all_4_1
% 204.26/35.19    (29)   ~ (all_52_23 = e3)
% 204.26/35.19    (30)   ~ (all_52_13 = all_4_2)
% 204.26/35.19    (31)  op(e1, e2) = all_52_13
% 204.26/35.19    (32)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.19    (33)  all_58_8 = all_10_2
% 204.26/35.19    (34)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.19    (35)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.19    (36)  op(all_4_2, all_4_2) = e2
% 204.26/35.19    (37)  op(e3, e0) = all_14_1
% 204.26/35.19    (38)  all_56_3 = all_52_25
% 204.26/35.19    (39)  all_58_5 = all_52_19
% 204.26/35.19    (40)  all_58_6 = all_52_5
% 204.26/35.19    (41)   ~ (e3 = e2)
% 204.26/35.19    (42)  op(e1, e1) = all_10_2
% 204.26/35.19    (43)   ~ (all_52_23 = all_10_2)
% 204.26/35.19    (44)  all_58_3 = all_4_2
% 204.26/35.19    (45)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.19  
% 204.26/35.19  Begin of proof
% 204.26/35.19  | 
% 204.26/35.19  | BETA: splitting (16) gives:
% 204.26/35.19  | 
% 204.26/35.19  | Case 1:
% 204.26/35.19  | | 
% 204.26/35.19  | |   (46)   ~ (all_34_1 = e2)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (4), (46) imply:
% 204.26/35.19  | |   (47)   ~ (all_14_1 = e2)
% 204.26/35.19  | | 
% 204.26/35.19  | | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 204.26/35.19  | |              with (5), (37) gives:
% 204.26/35.19  | |   (48)  all_52_25 = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (38), (48) imply:
% 204.26/35.19  | |   (49)  all_56_3 = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | COMBINE_EQS: (9), (48) imply:
% 204.26/35.19  | |   (50)  all_58_9 = all_14_1
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (1), (48) imply:
% 204.26/35.19  | |   (51)   ~ (all_52_27 = all_14_1)
% 204.26/35.19  | | 
% 204.26/35.19  | | SIMP: (51) implies:
% 204.26/35.19  | |   (52)   ~ (all_52_27 = all_14_1)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (20), (48) imply:
% 204.26/35.19  | |   (53)   ~ (all_52_29 = all_14_1)
% 204.26/35.19  | | 
% 204.26/35.19  | | SIMP: (53) implies:
% 204.26/35.19  | |   (54)   ~ (all_52_29 = all_14_1)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (27), (48) imply:
% 204.26/35.19  | |   (55)   ~ (all_14_1 = e3)
% 204.26/35.19  | | 
% 204.26/35.19  | | REDUCE: (45), (48) imply:
% 204.26/35.19  | |   (56)  op(all_14_1, all_14_1) = all_52_24
% 204.26/35.19  | | 
% 204.26/35.19  | | BETA: splitting (35) gives:
% 204.26/35.19  | | 
% 204.26/35.19  | | Case 1:
% 204.26/35.19  | | | 
% 204.26/35.19  | | |   (57)  all_56_3 = e3
% 204.26/35.19  | | | 
% 204.26/35.19  | | | REF_CLOSE: (49), (55), (57) are inconsistent by sub-proof #1200.
% 204.26/35.19  | | | 
% 204.26/35.19  | | Case 2:
% 204.26/35.19  | | | 
% 204.26/35.19  | | |   (58)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.19  | | | 
% 204.26/35.19  | | | BETA: splitting (14) gives:
% 204.26/35.19  | | | 
% 204.26/35.19  | | | Case 1:
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | |   (59)  all_58_9 = e1
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | COMBINE_EQS: (50), (59) imply:
% 204.26/35.19  | | | |   (60)  all_14_1 = e1
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | SIMP: (60) implies:
% 204.26/35.19  | | | |   (61)  all_14_1 = e1
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REDUCE: (52), (61) imply:
% 204.26/35.19  | | | |   (62)   ~ (all_52_27 = e1)
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REDUCE: (54), (61) imply:
% 204.26/35.19  | | | |   (63)   ~ (all_52_29 = e1)
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REDUCE: (56), (61) imply:
% 204.26/35.19  | | | |   (64)  op(e1, e1) = all_52_24
% 204.26/35.19  | | | | 
% 204.26/35.19  | | | | REDUCE: (8), (61) imply:
% 204.26/35.19  | | | |   (65)  op(e0, e1) = e1
% 204.26/35.19  | | | | 
% 204.26/35.20  | | | | GROUND_INST: instantiating (3) with all_52_23, e1, e1, e0, simplifying
% 204.26/35.20  | | | |              with (13), (65) gives:
% 204.26/35.20  | | | |   (66)  all_52_23 = e1
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_24, e1, e1,
% 204.26/35.20  | | | |              simplifying with (42), (64) gives:
% 204.26/35.20  | | | |   (67)  all_52_24 = all_10_2
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (19), (66) imply:
% 204.26/35.20  | | | |   (68)   ~ (all_52_19 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (43), (66) imply:
% 204.26/35.20  | | | |   (69)   ~ (all_10_2 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | SIMP: (69) implies:
% 204.26/35.20  | | | |   (70)   ~ (all_10_2 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (29), (66) imply:
% 204.26/35.20  | | | |   (71)   ~ (e3 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (32), (66) imply:
% 204.26/35.20  | | | |   (72)  op(e1, e1) = all_52_22
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_22, e1, e1,
% 204.26/35.20  | | | |              simplifying with (42), (72) gives:
% 204.26/35.20  | | | |   (73)  all_52_22 = all_10_2
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | BETA: splitting (23) gives:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | Case 1:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | |   (74)  all_58_2 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | COMBINE_EQS: (25), (74) imply:
% 204.26/35.20  | | | | |   (75)  all_52_3 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | SIMP: (75) implies:
% 204.26/35.20  | | | | |   (76)  all_52_3 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | REDUCE: (10), (76) imply:
% 204.26/35.20  | | | | |   (77)   ~ (all_52_5 = e1)
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | SIMP: (77) implies:
% 204.26/35.20  | | | | |   (78)   ~ (all_52_5 = e1)
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | BETA: splitting (34) gives:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | Case 1:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | |   (79)  all_58_6 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | REF_CLOSE: (40), (78), (79) are inconsistent by sub-proof #963.
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | Case 2:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | |   (80)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | BETA: splitting (80) gives:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | Case 1:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | |   (81)  all_58_7 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | COMBINE_EQS: (21), (81) imply:
% 204.26/35.20  | | | | | | |   (82)  all_52_13 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REF_CLOSE: (3), (7), (17), (42), (82) are inconsistent by
% 204.26/35.20  | | | | | | |            sub-proof #1134.
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | Case 2:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | |   (83)  all_58_8 = e1 | all_58_11 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REF_CLOSE: (12), (33), (63), (70), (83) are inconsistent by
% 204.26/35.20  | | | | | | |            sub-proof #872.
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | End of split
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | End of split
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | Case 2:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | |   (84)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | BETA: splitting (84) gives:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | Case 1:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | |   (85)  all_58_3 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | COMBINE_EQS: (44), (85) imply:
% 204.26/35.20  | | | | | |   (86)  all_4_2 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | REDUCE: (30), (86) imply:
% 204.26/35.20  | | | | | |   (87)   ~ (all_52_13 = e1)
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | REDUCE: (36), (86) imply:
% 204.26/35.20  | | | | | |   (88)  op(e1, e1) = e2
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | REDUCE: (28), (86) imply:
% 204.26/35.20  | | | | | |   (89)  op(e1, e2) = all_4_1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | BETA: splitting (34) gives:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | Case 1:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | |   (90)  all_58_6 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | COMBINE_EQS: (40), (90) imply:
% 204.26/35.20  | | | | | | |   (91)  all_52_5 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | SIMP: (91) implies:
% 204.26/35.20  | | | | | | |   (92)  all_52_5 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REDUCE: (6), (92) imply:
% 204.26/35.20  | | | | | | |   (93)  op(e1, e1) = all_52_4
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_4, e1, e1,
% 204.26/35.20  | | | | | | |              simplifying with (42), (93) gives:
% 204.26/35.20  | | | | | | |   (94)  all_52_4 = all_10_2
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | GROUND_INST: instantiating (3) with e2, all_52_4, e1, e1,
% 204.26/35.20  | | | | | | |              simplifying with (88), (93) gives:
% 204.26/35.20  | | | | | | |   (95)  all_52_4 = e2
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | GROUND_INST: instantiating (3) with all_52_13, all_4_1, e2, e1,
% 204.26/35.20  | | | | | | |              simplifying with (31), (89) gives:
% 204.26/35.20  | | | | | | |   (96)  all_52_13 = all_4_1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | COMBINE_EQS: (94), (95) imply:
% 204.26/35.20  | | | | | | |   (97)  all_10_2 = e2
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | SIMP: (97) implies:
% 204.26/35.20  | | | | | | |   (98)  all_10_2 = e2
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | COMBINE_EQS: (33), (98) imply:
% 204.26/35.20  | | | | | | |   (99)  all_58_8 = e2
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | COMBINE_EQS: (21), (96) imply:
% 204.26/35.20  | | | | | | |   (100)  all_58_7 = all_4_1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | BETA: splitting (24) gives:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | Case 1:
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | |   (101)  all_58_6 = e3
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | | COMBINE_EQS: (90), (101) imply:
% 204.26/35.20  | | | | | | | |   (102)  e3 = e1
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | | REDUCE: (2), (102) imply:
% 204.26/35.20  | | | | | | | |   (103)  $false
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | | CLOSE: (103) is inconsistent.
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | Case 2:
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | |   (104)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | | BETA: splitting (104) gives:
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | | Case 1:
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | |   (105)  all_58_7 = e3
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | | COMBINE_EQS: (100), (105) imply:
% 204.26/35.20  | | | | | | | | |   (106)  all_4_1 = e3
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | | REDUCE: (11), (106) imply:
% 204.26/35.20  | | | | | | | | |   (107)  $false
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | | CLOSE: (107) is inconsistent.
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | Case 2:
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | |   (108)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | | REF_CLOSE: (12), (26), (41), (99), (108) are inconsistent by
% 204.26/35.20  | | | | | | | | |            sub-proof #1271.
% 204.26/35.20  | | | | | | | | | 
% 204.26/35.20  | | | | | | | | End of split
% 204.26/35.20  | | | | | | | | 
% 204.26/35.20  | | | | | | | End of split
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | Case 2:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | |   (109)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REF_CLOSE: (12), (21), (33), (63), (70), (87), (109) are
% 204.26/35.20  | | | | | | |            inconsistent by sub-proof #870.
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | End of split
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | Case 2:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | |   (110)  all_58_5 = e1 | all_58_10 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | REF_CLOSE: (18), (39), (62), (68), (110) are inconsistent by
% 204.26/35.20  | | | | | |            sub-proof #869.
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | End of split
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | End of split
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | Case 2:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | |   (111)   ~ (all_58_9 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (50), (111) imply:
% 204.26/35.20  | | | |   (112)   ~ (all_14_1 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REF_CLOSE: (2), (3), (8), (15), (47), (49), (56), (58), (112) are
% 204.26/35.20  | | | |            inconsistent by sub-proof #867.
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | End of split
% 204.26/35.20  | | | 
% 204.26/35.20  | | End of split
% 204.26/35.20  | | 
% 204.26/35.20  | Case 2:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (113)   ~ (all_34_2 = e3)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (22), (113) imply:
% 204.26/35.20  | |   (114)  $false
% 204.26/35.20  | | 
% 204.26/35.20  | | CLOSE: (114) is inconsistent.
% 204.26/35.20  | | 
% 204.26/35.20  | End of split
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #856 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)  all_58_9 = all_52_25
% 204.26/35.20    (2)  all_58_9 = e1
% 204.26/35.20    (3)   ~ (all_52_25 = e1)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.20  |   (4)  all_52_25 = e1
% 204.26/35.20  | 
% 204.26/35.20  | SIMP: (4) implies:
% 204.26/35.20  |   (5)  all_52_25 = e1
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (3), (5) imply:
% 204.26/35.20  |   (6)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (6) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #857 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)  all_58_5 = all_52_19
% 204.26/35.20    (2)  all_58_5 = e1
% 204.26/35.20    (3)   ~ (all_52_19 = e1)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.20  |   (4)  all_52_19 = e1
% 204.26/35.20  | 
% 204.26/35.20  | SIMP: (4) implies:
% 204.26/35.20  |   (5)  all_52_19 = e1
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (3), (5) imply:
% 204.26/35.20  |   (6)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (6) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #858 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (2)  op(e0, all_14_1) = e1
% 204.26/35.20    (3)   ~ (all_52_5 = e1)
% 204.26/35.20    (4)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.20    (5)  op(e1, e0) = all_14_1
% 204.26/35.20    (6)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.20    (7)  all_56_8 = all_52_5
% 204.26/35.20    (8)   ~ (all_52_5 = all_52_7)
% 204.26/35.20    (9)   ~ (all_52_5 = e2)
% 204.26/35.20    (10)  op(e0, e3) = all_52_7
% 204.26/35.20    (11)  all_56_12 = all_52_7
% 204.26/35.20    (12)  op(e1, e0) = e3
% 204.26/35.20    (13)   ~ (all_52_7 = e1)
% 204.26/35.20    (14)  all_58_6 = all_52_5
% 204.26/35.20    (15)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | BETA: splitting (15) gives:
% 204.26/35.20  | 
% 204.26/35.20  | Case 1:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (16)  all_58_6 = e0
% 204.26/35.20  | | 
% 204.26/35.20  | | COMBINE_EQS: (14), (16) imply:
% 204.26/35.20  | |   (17)  all_52_5 = e0
% 204.26/35.20  | | 
% 204.26/35.20  | | SIMP: (17) implies:
% 204.26/35.20  | |   (18)  all_52_5 = e0
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (8), (18) imply:
% 204.26/35.20  | |   (19)   ~ (all_52_7 = e0)
% 204.26/35.20  | | 
% 204.26/35.20  | | SIMP: (19) implies:
% 204.26/35.20  | |   (20)   ~ (all_52_7 = e0)
% 204.26/35.20  | | 
% 204.26/35.20  | | BETA: splitting (4) gives:
% 204.26/35.20  | | 
% 204.26/35.20  | | Case 1:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (21)  all_56_12 = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | COMBINE_EQS: (11), (21) imply:
% 204.26/35.20  | | |   (22)  all_52_7 = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | SIMP: (22) implies:
% 204.26/35.20  | | |   (23)  all_52_7 = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (13), (23) imply:
% 204.26/35.20  | | |   (24)   ~ (e2 = e1)
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (10), (23) imply:
% 204.26/35.20  | | |   (25)  op(e0, e3) = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REF_CLOSE: (1), (2), (5), (12), (24), (25) are inconsistent by sub-proof
% 204.26/35.20  | | |            #859.
% 204.26/35.20  | | | 
% 204.26/35.20  | | Case 2:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (26)  all_56_12 = e1 | all_56_12 = e0
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REF_CLOSE: (11), (13), (20), (26) are inconsistent by sub-proof #1374.
% 204.26/35.20  | | | 
% 204.26/35.20  | | End of split
% 204.26/35.20  | | 
% 204.26/35.20  | Case 2:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (27)   ~ (all_58_6 = e0)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (14), (27) imply:
% 204.26/35.20  | |   (28)   ~ (all_52_5 = e0)
% 204.26/35.20  | | 
% 204.26/35.20  | | REF_CLOSE: (3), (6), (7), (9), (28) are inconsistent by sub-proof #1004.
% 204.26/35.20  | | 
% 204.26/35.20  | End of split
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #859 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (2)  op(e0, all_14_1) = e1
% 204.26/35.20    (3)  op(e1, e0) = all_14_1
% 204.26/35.20    (4)   ~ (e2 = e1)
% 204.26/35.20    (5)  op(e0, e3) = e2
% 204.26/35.20    (6)  op(e1, e0) = e3
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | GROUND_INST: instantiating (1) with e3, all_14_1, e0, e1, simplifying with
% 204.26/35.20  |              (3), (6) gives:
% 204.26/35.20  |   (7)  all_14_1 = e3
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (2), (7) imply:
% 204.26/35.20  |   (8)  op(e0, e3) = e1
% 204.26/35.20  | 
% 204.26/35.20  | GROUND_INST: instantiating (1) with e2, e1, e3, e0, simplifying with (5), (8)
% 204.26/35.20  |              gives:
% 204.26/35.20  |   (9)  e2 = e1
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (4), (9) imply:
% 204.26/35.20  |   (10)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (10) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #860 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)   ~ (e3 = e1)
% 204.26/35.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (3)  e3 = e1
% 204.26/35.20    (4)  op(e2, e2) = all_4_2
% 204.26/35.20    (5)  all_58_12 = all_52_7
% 204.26/35.20    (6)   ~ (all_52_7 = e3)
% 204.26/35.20    (7)  all_58_2 = all_52_3
% 204.26/35.20    (8)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.20    (9)   ~ (all_52_5 = e3)
% 204.26/35.20    (10)  all_58_0 = e3
% 204.26/35.20    (11)  op(e2, e2) = e3
% 204.26/35.20    (12)  all_58_6 = all_52_5
% 204.26/35.20    (13)   ~ (all_52_3 = all_4_2)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | SIMP: (3) implies:
% 204.26/35.20  |   (14)  e3 = e1
% 204.26/35.20  | 
% 204.26/35.20  | COMBINE_EQS: (10), (14) imply:
% 204.26/35.20  |   (15)  all_58_0 = e1
% 204.26/35.20  | 
% 204.26/35.20  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15) are
% 204.26/35.20  |            inconsistent by sub-proof #1241.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #861 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)  all_58_10 = all_52_27
% 204.26/35.20    (2)  all_58_10 = e1
% 204.26/35.20    (3)   ~ (all_52_27 = e1)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.20  |   (4)  all_52_27 = e1
% 204.26/35.20  | 
% 204.26/35.20  | SIMP: (4) implies:
% 204.26/35.20  |   (5)  all_52_27 = e1
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (3), (5) imply:
% 204.26/35.20  |   (6)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (6) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #862 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (3)   ~ (e3 = e0)
% 204.26/35.20    (4)  op(all_14_2, e0) = all_14_1
% 204.26/35.20    (5)  all_58_9 = e1
% 204.26/35.20    (6)  op(e0, all_14_1) = e1
% 204.26/35.20    (7)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.20    (8)  op(e0, e0) = all_14_2
% 204.26/35.20    (9)  all_56_15 = all_14_2
% 204.26/35.20    (10)  all_58_11 = e3
% 204.26/35.20    (11)  all_58_10 = all_52_27
% 204.26/35.20    (12)   ~ (all_14_2 = e0)
% 204.26/35.20    (13)   ~ (all_14_2 = e1)
% 204.26/35.20    (14)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.20    (15)   ~ (e1 = e0)
% 204.26/35.20    (16)  op(e2, e0) = all_52_27
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | BETA: splitting (1) gives:
% 204.26/35.20  | 
% 204.26/35.20  | Case 1:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (17)  all_58_9 = e0
% 204.26/35.20  | | 
% 204.26/35.20  | | REF_CLOSE: (5), (15), (17) are inconsistent by sub-proof #865.
% 204.26/35.20  | | 
% 204.26/35.20  | Case 2:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (18)  all_58_10 = e0 | all_58_11 = e0
% 204.26/35.20  | | 
% 204.26/35.20  | | BETA: splitting (14) gives:
% 204.26/35.20  | | 
% 204.26/35.20  | | Case 1:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (19)  all_56_15 = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | COMBINE_EQS: (9), (19) imply:
% 204.26/35.20  | | |   (20)  all_14_2 = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (13), (20) imply:
% 204.26/35.20  | | |   (21)   ~ (e2 = e1)
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (4), (20) imply:
% 204.26/35.20  | | |   (22)  op(e2, e0) = all_14_1
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (8), (20) imply:
% 204.26/35.20  | | |   (23)  op(e0, e0) = e2
% 204.26/35.20  | | | 
% 204.26/35.20  | | | BETA: splitting (18) gives:
% 204.26/35.20  | | | 
% 204.26/35.20  | | | Case 1:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | |   (24)  all_58_10 = e0
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | COMBINE_EQS: (11), (24) imply:
% 204.26/35.20  | | | |   (25)  all_52_27 = e0
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | SIMP: (25) implies:
% 204.26/35.20  | | | |   (26)  all_52_27 = e0
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (7), (26) imply:
% 204.26/35.20  | | | |   (27)  op(e0, e0) = all_52_26
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (16), (26) imply:
% 204.26/35.20  | | | |   (28)  op(e2, e0) = e0
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REF_CLOSE: (2), (6), (21), (22), (23), (27), (28) are inconsistent by
% 204.26/35.20  | | | |            sub-proof #864.
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | Case 2:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | |   (29)  all_58_11 = e0
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REF_CLOSE: (3), (10), (29) are inconsistent by sub-proof #863.
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | End of split
% 204.26/35.20  | | | 
% 204.26/35.20  | | Case 2:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (30)  all_56_15 = e1 | all_56_15 = e0
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REF_CLOSE: (9), (12), (13), (30) are inconsistent by sub-proof #1161.
% 204.26/35.20  | | | 
% 204.26/35.20  | | End of split
% 204.26/35.20  | | 
% 204.26/35.20  | End of split
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #863 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)  all_58_11 = e3
% 204.26/35.20    (2)  all_58_11 = e0
% 204.26/35.20    (3)   ~ (e3 = e0)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.20  |   (4)  e3 = e0
% 204.26/35.20  | 
% 204.26/35.20  | SIMP: (4) implies:
% 204.26/35.20  |   (5)  e3 = e0
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (3), (5) imply:
% 204.26/35.20  |   (6)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (6) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #864 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (2)  op(e0, all_14_1) = e1
% 204.26/35.20    (3)  op(e0, e0) = all_52_26
% 204.26/35.20    (4)   ~ (e2 = e1)
% 204.26/35.20    (5)  op(e2, e0) = e0
% 204.26/35.20    (6)  op(e0, e0) = e2
% 204.26/35.20    (7)  op(e2, e0) = all_14_1
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | GROUND_INST: instantiating (1) with e2, all_52_26, e0, e0, simplifying with
% 204.26/35.20  |              (3), (6) gives:
% 204.26/35.20  |   (8)  all_52_26 = e2
% 204.26/35.20  | 
% 204.26/35.20  | GROUND_INST: instantiating (1) with e0, all_14_1, e0, e2, simplifying with
% 204.26/35.20  |              (5), (7) gives:
% 204.26/35.20  |   (9)  all_14_1 = e0
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (2), (9) imply:
% 204.26/35.20  |   (10)  op(e0, e0) = e1
% 204.26/35.20  | 
% 204.26/35.20  | GROUND_INST: instantiating (1) with e2, e1, e0, e0, simplifying with (6), (10)
% 204.26/35.20  |              gives:
% 204.26/35.20  |   (11)  e2 = e1
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (4), (11) imply:
% 204.26/35.20  |   (12)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (12) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #865 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)  all_58_9 = e1
% 204.26/35.20    (2)  all_58_9 = e0
% 204.26/35.20    (3)   ~ (e1 = e0)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.20  |   (4)  e1 = e0
% 204.26/35.20  | 
% 204.26/35.20  | SIMP: (4) implies:
% 204.26/35.20  |   (5)  e1 = e0
% 204.26/35.20  | 
% 204.26/35.20  | REDUCE: (3), (5) imply:
% 204.26/35.20  |   (6)  $false
% 204.26/35.20  | 
% 204.26/35.20  | CLOSE: (6) is inconsistent.
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #866 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)   ~ (all_52_25 = all_52_27)
% 204.26/35.20    (2)   ~ (e3 = e1)
% 204.26/35.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (4)  op(all_52_7, all_52_7) = e0
% 204.26/35.20    (5)  op(all_52_5, all_52_5) = e1
% 204.26/35.20    (6)  all_58_0 = all_6_2
% 204.26/35.20    (7)  all_34_1 = all_14_1
% 204.26/35.20    (8)  op(e3, e0) = all_52_25
% 204.26/35.20    (9)  op(e0, all_14_1) = e1
% 204.26/35.20    (10)  all_58_9 = all_52_25
% 204.26/35.20    (11)  op(e2, e2) = all_4_2
% 204.26/35.20    (12)   ~ (all_52_3 = all_52_5)
% 204.26/35.20    (13)  all_58_11 = all_52_29
% 204.26/35.20    (14)  op(e0, e0) = all_14_2
% 204.26/35.20    (15)  op(e0, e1) = all_52_23
% 204.26/35.20    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.20    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.20    (18)  op(e0, e0) = e3
% 204.26/35.20    (19)   ~ (all_34_1 = e2) |  ~ (all_34_2 = e3)
% 204.26/35.20    (20)  all_58_10 = all_52_27
% 204.26/35.20    (21)   ~ (all_52_19 = all_52_23)
% 204.26/35.20    (22)   ~ (all_52_25 = all_52_29)
% 204.26/35.20    (23)  all_58_7 = all_52_13
% 204.26/35.20    (24)  all_34_2 = e3
% 204.26/35.20    (25)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.20    (26)  op(all_6_2, all_6_2) = e3
% 204.26/35.20    (27)  all_58_12 = all_52_7
% 204.26/35.20    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.20    (29)   ~ (all_52_7 = all_14_2)
% 204.26/35.20    (30)  all_58_2 = all_52_3
% 204.26/35.20    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.20    (32)   ~ (all_52_29 = e3)
% 204.26/35.20    (33)   ~ (all_52_25 = e3)
% 204.26/35.20    (34)   ~ (all_52_23 = e3)
% 204.26/35.20    (35)  op(all_52_3, all_52_3) = e2
% 204.26/35.20    (36)  op(e3, e3) = all_52_30
% 204.26/35.20    (37)   ~ (all_52_13 = all_4_2)
% 204.26/35.20    (38)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.20    (39)  all_58_8 = all_10_2
% 204.26/35.20    (40)   ~ (all_52_5 = all_10_2)
% 204.26/35.20    (41)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.20    (42)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.20    (43)   ~ (all_52_5 = all_6_2)
% 204.26/35.20    (44)  op(e3, e3) = all_6_2
% 204.26/35.20    (45)  op(e3, e0) = all_14_1
% 204.26/35.20    (46)  all_56_3 = all_52_25
% 204.26/35.20    (47)  all_58_5 = all_52_19
% 204.26/35.20    (48)  all_58_6 = all_52_5
% 204.26/35.20    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.20    (50)   ~ (e3 = e2)
% 204.26/35.20    (51)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.20    (52)  op(e1, e1) = all_10_2
% 204.26/35.20    (53)   ~ (all_52_23 = all_10_2)
% 204.26/35.20    (54)  all_58_3 = all_4_2
% 204.26/35.20    (55)   ~ (all_52_3 = all_4_2)
% 204.26/35.20    (56)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | BETA: splitting (19) gives:
% 204.26/35.20  | 
% 204.26/35.20  | Case 1:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (57)   ~ (all_34_1 = e2)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (7), (57) imply:
% 204.26/35.20  | |   (58)   ~ (all_14_1 = e2)
% 204.26/35.20  | | 
% 204.26/35.20  | | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 204.26/35.20  | |              with (8), (45) gives:
% 204.26/35.20  | |   (59)  all_52_25 = all_14_1
% 204.26/35.20  | | 
% 204.26/35.20  | | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3, simplifying
% 204.26/35.20  | |              with (36), (44) gives:
% 204.26/35.20  | |   (60)  all_52_30 = all_6_2
% 204.26/35.20  | | 
% 204.26/35.20  | | COMBINE_EQS: (46), (59) imply:
% 204.26/35.20  | |   (61)  all_56_3 = all_14_1
% 204.26/35.20  | | 
% 204.26/35.20  | | COMBINE_EQS: (10), (59) imply:
% 204.26/35.20  | |   (62)  all_58_9 = all_14_1
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (1), (59) imply:
% 204.26/35.20  | |   (63)   ~ (all_52_27 = all_14_1)
% 204.26/35.20  | | 
% 204.26/35.20  | | SIMP: (63) implies:
% 204.26/35.20  | |   (64)   ~ (all_52_27 = all_14_1)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (22), (59) imply:
% 204.26/35.20  | |   (65)   ~ (all_52_29 = all_14_1)
% 204.26/35.20  | | 
% 204.26/35.20  | | SIMP: (65) implies:
% 204.26/35.20  | |   (66)   ~ (all_52_29 = all_14_1)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (33), (59) imply:
% 204.26/35.20  | |   (67)   ~ (all_14_1 = e3)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (56), (59) imply:
% 204.26/35.20  | |   (68)  op(all_14_1, all_14_1) = all_52_24
% 204.26/35.20  | | 
% 204.26/35.20  | | BETA: splitting (42) gives:
% 204.26/35.20  | | 
% 204.26/35.20  | | Case 1:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (69)  all_56_3 = e3
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REF_CLOSE: (61), (67), (69) are inconsistent by sub-proof #1200.
% 204.26/35.20  | | | 
% 204.26/35.20  | | Case 2:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (70)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.20  | | | 
% 204.26/35.20  | | | BETA: splitting (17) gives:
% 204.26/35.20  | | | 
% 204.26/35.20  | | | Case 1:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | |   (71)  all_58_9 = e1
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | COMBINE_EQS: (62), (71) imply:
% 204.26/35.20  | | | |   (72)  all_14_1 = e1
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | SIMP: (72) implies:
% 204.26/35.20  | | | |   (73)  all_14_1 = e1
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (64), (73) imply:
% 204.26/35.20  | | | |   (74)   ~ (all_52_27 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (66), (73) imply:
% 204.26/35.20  | | | |   (75)   ~ (all_52_29 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (68), (73) imply:
% 204.26/35.20  | | | |   (76)  op(e1, e1) = all_52_24
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (9), (73) imply:
% 204.26/35.20  | | | |   (77)  op(e0, e1) = e1
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | GROUND_INST: instantiating (3) with all_52_23, e1, e1, e0, simplifying
% 204.26/35.20  | | | |              with (15), (77) gives:
% 204.26/35.20  | | | |   (78)  all_52_23 = e1
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_24, e1, e1,
% 204.26/35.20  | | | |              simplifying with (52), (76) gives:
% 204.26/35.20  | | | |   (79)  all_52_24 = all_10_2
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (21), (78) imply:
% 204.26/35.20  | | | |   (80)   ~ (all_52_19 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (53), (78) imply:
% 204.26/35.20  | | | |   (81)   ~ (all_10_2 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | SIMP: (81) implies:
% 204.26/35.20  | | | |   (82)   ~ (all_10_2 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (34), (78) imply:
% 204.26/35.20  | | | |   (83)   ~ (e3 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (38), (78) imply:
% 204.26/35.20  | | | |   (84)  op(e1, e1) = all_52_22
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_22, e1, e1,
% 204.26/35.20  | | | |              simplifying with (52), (84) gives:
% 204.26/35.20  | | | |   (85)  all_52_22 = all_10_2
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | BETA: splitting (25) gives:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | Case 1:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | |   (86)  all_58_2 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | COMBINE_EQS: (30), (86) imply:
% 204.26/35.20  | | | | |   (87)  all_52_3 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | SIMP: (87) implies:
% 204.26/35.20  | | | | |   (88)  all_52_3 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | REDUCE: (12), (88) imply:
% 204.26/35.20  | | | | |   (89)   ~ (all_52_5 = e1)
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | SIMP: (89) implies:
% 204.26/35.20  | | | | |   (90)   ~ (all_52_5 = e1)
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | REDUCE: (35), (88) imply:
% 204.26/35.20  | | | | |   (91)  op(e1, e1) = e2
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | BETA: splitting (41) gives:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | Case 1:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | |   (92)  all_58_6 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | REF_CLOSE: (48), (90), (92) are inconsistent by sub-proof #963.
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | Case 2:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | |   (93)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | BETA: splitting (93) gives:
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | | Case 1:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | |   (94)  all_58_7 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | COMBINE_EQS: (23), (94) imply:
% 204.26/35.20  | | | | | | |   (95)  all_52_13 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REDUCE: (51), (95) imply:
% 204.26/35.20  | | | | | | |   (96)  op(e1, e1) = all_52_12
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (11), (13), (14), (16), (26),
% 204.26/35.20  | | | | | | |            (27), (28), (29), (30), (31), (32), (35), (39), (40),
% 204.26/35.20  | | | | | | |            (43), (44), (48), (49), (50), (52), (55), (91), (94),
% 204.26/35.20  | | | | | | |            (96) are inconsistent by sub-proof #875.
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | Case 2:
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | |   (97)  all_58_8 = e1 | all_58_11 = e1
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | | REF_CLOSE: (13), (39), (75), (82), (97) are inconsistent by
% 204.26/35.20  | | | | | | |            sub-proof #872.
% 204.26/35.20  | | | | | | | 
% 204.26/35.20  | | | | | | End of split
% 204.26/35.20  | | | | | | 
% 204.26/35.20  | | | | | End of split
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | Case 2:
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | |   (98)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | | REF_CLOSE: (3), (5), (13), (20), (23), (37), (39), (40), (41), (47),
% 204.26/35.20  | | | | |            (48), (52), (54), (74), (75), (80), (82), (98) are
% 204.26/35.20  | | | | |            inconsistent by sub-proof #868.
% 204.26/35.20  | | | | | 
% 204.26/35.20  | | | | End of split
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | Case 2:
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | |   (99)   ~ (all_58_9 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REDUCE: (62), (99) imply:
% 204.26/35.20  | | | |   (100)   ~ (all_14_1 = e1)
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | | REF_CLOSE: (2), (3), (9), (18), (58), (61), (68), (70), (100) are
% 204.26/35.20  | | | |            inconsistent by sub-proof #867.
% 204.26/35.20  | | | | 
% 204.26/35.20  | | | End of split
% 204.26/35.20  | | | 
% 204.26/35.20  | | End of split
% 204.26/35.20  | | 
% 204.26/35.20  | Case 2:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (101)   ~ (all_34_2 = e3)
% 204.26/35.20  | | 
% 204.26/35.20  | | REDUCE: (24), (101) imply:
% 204.26/35.20  | |   (102)  $false
% 204.26/35.20  | | 
% 204.26/35.20  | | CLOSE: (102) is inconsistent.
% 204.26/35.20  | | 
% 204.26/35.20  | End of split
% 204.26/35.20  | 
% 204.26/35.20  End of proof
% 204.26/35.20  
% 204.26/35.20  Sub-proof #867 shows that the following formulas are inconsistent:
% 204.26/35.20  ----------------------------------------------------------------
% 204.26/35.20    (1)   ~ (e3 = e1)
% 204.26/35.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.20    (3)   ~ (all_14_1 = e2)
% 204.26/35.20    (4)  op(e0, all_14_1) = e1
% 204.26/35.20    (5)  all_56_3 = all_14_1
% 204.26/35.20    (6)  op(e0, e0) = e3
% 204.26/35.20    (7)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.20    (8)  op(all_14_1, all_14_1) = all_52_24
% 204.26/35.20    (9)   ~ (all_14_1 = e1)
% 204.26/35.20  
% 204.26/35.20  Begin of proof
% 204.26/35.20  | 
% 204.26/35.20  | BETA: splitting (7) gives:
% 204.26/35.20  | 
% 204.26/35.20  | Case 1:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (10)  all_56_3 = e2
% 204.26/35.20  | | 
% 204.26/35.20  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #1183.
% 204.26/35.20  | | 
% 204.26/35.20  | Case 2:
% 204.26/35.20  | | 
% 204.26/35.20  | |   (11)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.20  | | 
% 204.26/35.20  | | BETA: splitting (11) gives:
% 204.26/35.20  | | 
% 204.26/35.20  | | Case 1:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (12)  all_56_3 = e1
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #1182.
% 204.26/35.20  | | | 
% 204.26/35.20  | | Case 2:
% 204.26/35.20  | | | 
% 204.26/35.20  | | |   (13)  all_56_3 = e0
% 204.26/35.20  | | | 
% 204.26/35.20  | | | COMBINE_EQS: (5), (13) imply:
% 204.26/35.20  | | |   (14)  all_14_1 = e0
% 204.26/35.20  | | | 
% 204.26/35.20  | | | SIMP: (14) implies:
% 204.26/35.20  | | |   (15)  all_14_1 = e0
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (8), (15) imply:
% 204.26/35.20  | | |   (16)  op(e0, e0) = all_52_24
% 204.26/35.20  | | | 
% 204.26/35.20  | | | REDUCE: (4), (15) imply:
% 204.26/35.20  | | |   (17)  op(e0, e0) = e1
% 204.26/35.20  | | | 
% 204.26/35.20  | | | GROUND_INST: instantiating (2) with e3, all_52_24, e0, e0, simplifying
% 204.26/35.20  | | |              with (6), (16) gives:
% 204.26/35.20  | | |   (18)  all_52_24 = e3
% 204.26/35.20  | | | 
% 204.26/35.20  | | | GROUND_INST: instantiating (2) with e1, all_52_24, e0, e0, simplifying
% 204.26/35.20  | | |              with (16), (17) gives:
% 204.26/35.21  | | |   (19)  all_52_24 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | COMBINE_EQS: (18), (19) imply:
% 204.26/35.21  | | |   (20)  e3 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | SIMP: (20) implies:
% 204.26/35.21  | | |   (21)  e3 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | REDUCE: (1), (21) imply:
% 204.26/35.21  | | |   (22)  $false
% 204.26/35.21  | | | 
% 204.26/35.21  | | | CLOSE: (22) is inconsistent.
% 204.26/35.21  | | | 
% 204.26/35.21  | | End of split
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #868 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (2)  op(all_52_5, all_52_5) = e1
% 204.26/35.21    (3)  all_58_11 = all_52_29
% 204.26/35.21    (4)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.21    (5)   ~ (all_52_27 = e1)
% 204.26/35.21    (6)  all_58_10 = all_52_27
% 204.26/35.21    (7)  all_58_7 = all_52_13
% 204.26/35.21    (8)   ~ (all_10_2 = e1)
% 204.26/35.21    (9)   ~ (all_52_13 = all_4_2)
% 204.26/35.21    (10)  all_58_8 = all_10_2
% 204.26/35.21    (11)   ~ (all_52_5 = all_10_2)
% 204.26/35.21    (12)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.21    (13)  all_58_5 = all_52_19
% 204.26/35.21    (14)   ~ (all_52_19 = e1)
% 204.26/35.21    (15)   ~ (all_52_29 = e1)
% 204.26/35.21    (16)  all_58_6 = all_52_5
% 204.26/35.21    (17)  op(e1, e1) = all_10_2
% 204.26/35.21    (18)  all_58_3 = all_4_2
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | BETA: splitting (4) gives:
% 204.26/35.21  | 
% 204.26/35.21  | Case 1:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (19)  all_58_3 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | COMBINE_EQS: (18), (19) imply:
% 204.26/35.21  | |   (20)  all_4_2 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REDUCE: (9), (20) imply:
% 204.26/35.21  | |   (21)   ~ (all_52_13 = e1)
% 204.26/35.21  | | 
% 204.26/35.21  | | BETA: splitting (12) gives:
% 204.26/35.21  | | 
% 204.26/35.21  | | Case 1:
% 204.26/35.21  | | | 
% 204.26/35.21  | | |   (22)  all_58_6 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | COMBINE_EQS: (16), (22) imply:
% 204.26/35.21  | | |   (23)  all_52_5 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | SIMP: (23) implies:
% 204.26/35.21  | | |   (24)  all_52_5 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | REF_CLOSE: (1), (2), (11), (17), (24) are inconsistent by sub-proof #871.
% 204.26/35.21  | | | 
% 204.26/35.21  | | Case 2:
% 204.26/35.21  | | | 
% 204.26/35.21  | | |   (25)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | REF_CLOSE: (3), (7), (8), (10), (15), (21), (25) are inconsistent by
% 204.26/35.21  | | |            sub-proof #870.
% 204.26/35.21  | | | 
% 204.26/35.21  | | End of split
% 204.26/35.21  | | 
% 204.26/35.21  | Case 2:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (26)  all_58_5 = e1 | all_58_10 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (5), (6), (13), (14), (26) are inconsistent by sub-proof #869.
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #869 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ~ (all_52_27 = e1)
% 204.26/35.21    (2)  all_58_10 = all_52_27
% 204.26/35.21    (3)  all_58_5 = all_52_19
% 204.26/35.21    (4)   ~ (all_52_19 = e1)
% 204.26/35.21    (5)  all_58_5 = e1 | all_58_10 = e1
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | BETA: splitting (5) gives:
% 204.26/35.21  | 
% 204.26/35.21  | Case 1:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (6)  all_58_5 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | COMBINE_EQS: (3), (6) imply:
% 204.26/35.21  | |   (7)  all_52_19 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REDUCE: (4), (7) imply:
% 204.26/35.21  | |   (8)  $false
% 204.26/35.21  | | 
% 204.26/35.21  | | CLOSE: (8) is inconsistent.
% 204.26/35.21  | | 
% 204.26/35.21  | Case 2:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (9)  all_58_10 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | COMBINE_EQS: (2), (9) imply:
% 204.26/35.21  | |   (10)  all_52_27 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REDUCE: (1), (10) imply:
% 204.26/35.21  | |   (11)  $false
% 204.26/35.21  | | 
% 204.26/35.21  | | CLOSE: (11) is inconsistent.
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #870 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)  all_58_11 = all_52_29
% 204.26/35.21    (2)  all_58_7 = all_52_13
% 204.26/35.21    (3)   ~ (all_10_2 = e1)
% 204.26/35.21    (4)   ~ (all_52_13 = e1)
% 204.26/35.21    (5)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.21    (6)  all_58_8 = all_10_2
% 204.26/35.21    (7)   ~ (all_52_29 = e1)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | BETA: splitting (5) gives:
% 204.26/35.21  | 
% 204.26/35.21  | Case 1:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (8)  all_58_7 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | COMBINE_EQS: (2), (8) imply:
% 204.26/35.21  | |   (9)  all_52_13 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REDUCE: (4), (9) imply:
% 204.26/35.21  | |   (10)  $false
% 204.26/35.21  | | 
% 204.26/35.21  | | CLOSE: (10) is inconsistent.
% 204.26/35.21  | | 
% 204.26/35.21  | Case 2:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (11)  all_58_8 = e1 | all_58_11 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (1), (3), (6), (7), (11) are inconsistent by sub-proof #872.
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #871 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (2)  op(all_52_5, all_52_5) = e1
% 204.26/35.21    (3)  all_52_5 = e1
% 204.26/35.21    (4)   ~ (all_52_5 = all_10_2)
% 204.26/35.21    (5)  op(e1, e1) = all_10_2
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (3), (4) imply:
% 204.26/35.21  |   (6)   ~ (all_10_2 = e1)
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (6) implies:
% 204.26/35.21  |   (7)   ~ (all_10_2 = e1)
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (2), (3) imply:
% 204.26/35.21  |   (8)  op(e1, e1) = e1
% 204.26/35.21  | 
% 204.26/35.21  | REF_CLOSE: (1), (5), (7), (8) are inconsistent by sub-proof #1135.
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #872 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)  all_58_8 = e1 | all_58_11 = e1
% 204.26/35.21    (2)  all_58_11 = all_52_29
% 204.26/35.21    (3)   ~ (all_10_2 = e1)
% 204.26/35.21    (4)  all_58_8 = all_10_2
% 204.26/35.21    (5)   ~ (all_52_29 = e1)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | BETA: splitting (1) gives:
% 204.26/35.21  | 
% 204.26/35.21  | Case 1:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (6)  all_58_8 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #874.
% 204.26/35.21  | | 
% 204.26/35.21  | Case 2:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (7)  all_58_11 = e1
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #873.
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #873 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)  all_58_11 = all_52_29
% 204.26/35.21    (2)  all_58_11 = e1
% 204.26/35.21    (3)   ~ (all_52_29 = e1)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.21  |   (4)  all_52_29 = e1
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (4) implies:
% 204.26/35.21  |   (5)  all_52_29 = e1
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (3), (5) imply:
% 204.26/35.21  |   (6)  $false
% 204.26/35.21  | 
% 204.26/35.21  | CLOSE: (6) is inconsistent.
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #874 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)  all_58_8 = all_10_2
% 204.26/35.21    (2)  all_58_8 = e1
% 204.26/35.21    (3)   ~ (all_10_2 = e1)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.21  |   (4)  all_10_2 = e1
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (4) implies:
% 204.26/35.21  |   (5)  all_10_2 = e1
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (3), (5) imply:
% 204.26/35.21  |   (6)  $false
% 204.26/35.21  | 
% 204.26/35.21  | CLOSE: (6) is inconsistent.
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #875 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ~ (e3 = e1)
% 204.26/35.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (3)  op(all_52_7, all_52_7) = e0
% 204.26/35.21    (4)  op(all_52_5, all_52_5) = e1
% 204.26/35.21    (5)  all_58_0 = all_6_2
% 204.26/35.21    (6)  all_58_7 = e1
% 204.26/35.21    (7)  op(e2, e2) = all_4_2
% 204.26/35.21    (8)  all_58_11 = all_52_29
% 204.26/35.21    (9)  op(e0, e0) = all_14_2
% 204.26/35.21    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.21    (11)  op(all_6_2, all_6_2) = e3
% 204.26/35.21    (12)  all_58_12 = all_52_7
% 204.26/35.21    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.21    (14)   ~ (all_52_7 = all_14_2)
% 204.26/35.21    (15)  op(e1, e1) = all_52_12
% 204.26/35.21    (16)  all_58_2 = all_52_3
% 204.26/35.21    (17)  op(e1, e1) = e2
% 204.26/35.21    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.21    (19)   ~ (all_52_29 = e3)
% 204.26/35.21    (20)  op(all_52_3, all_52_3) = e2
% 204.26/35.21    (21)  all_58_8 = all_10_2
% 204.26/35.21    (22)   ~ (all_52_5 = all_10_2)
% 204.26/35.21    (23)   ~ (all_52_5 = all_6_2)
% 204.26/35.21    (24)  op(e3, e3) = all_6_2
% 204.26/35.21    (25)  all_58_6 = all_52_5
% 204.26/35.21    (26)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.21    (27)   ~ (e3 = e2)
% 204.26/35.21    (28)  op(e1, e1) = all_10_2
% 204.26/35.21    (29)   ~ (all_52_3 = all_4_2)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | GROUND_INST: instantiating (2) with all_10_2, all_52_12, e1, e1, simplifying
% 204.26/35.21  |              with (15), (28) gives:
% 204.26/35.21  |   (30)  all_52_12 = all_10_2
% 204.26/35.21  | 
% 204.26/35.21  | GROUND_INST: instantiating (2) with e2, all_52_12, e1, e1, simplifying with
% 204.26/35.21  |              (15), (17) gives:
% 204.26/35.21  |   (31)  all_52_12 = e2
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (30), (31) imply:
% 204.26/35.21  |   (32)  all_10_2 = e2
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (32) implies:
% 204.26/35.21  |   (33)  all_10_2 = e2
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (21), (33) imply:
% 204.26/35.21  |   (34)  all_58_8 = e2
% 204.26/35.21  | 
% 204.26/35.21  | BETA: splitting (13) gives:
% 204.26/35.21  | 
% 204.26/35.21  | Case 1:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (35)  all_58_6 = e3
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (14), (16), (18),
% 204.26/35.21  | |            (20), (22), (23), (24), (25), (26), (28), (29), (35) are
% 204.26/35.21  | |            inconsistent by sub-proof #876.
% 204.26/35.21  | | 
% 204.26/35.21  | Case 2:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (36)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.21  | | 
% 204.26/35.21  | | BETA: splitting (36) gives:
% 204.26/35.21  | | 
% 204.26/35.21  | | Case 1:
% 204.26/35.21  | | | 
% 204.26/35.21  | | |   (37)  all_58_7 = e3
% 204.26/35.21  | | | 
% 204.26/35.21  | | | COMBINE_EQS: (6), (37) imply:
% 204.26/35.21  | | |   (38)  e3 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | SIMP: (38) implies:
% 204.26/35.21  | | |   (39)  e3 = e1
% 204.26/35.21  | | | 
% 204.26/35.21  | | | REDUCE: (1), (39) imply:
% 204.26/35.21  | | |   (40)  $false
% 204.26/35.21  | | | 
% 204.26/35.21  | | | CLOSE: (40) is inconsistent.
% 204.26/35.21  | | | 
% 204.26/35.21  | | Case 2:
% 204.26/35.21  | | | 
% 204.26/35.21  | | |   (41)  all_58_8 = e3 | all_58_11 = e3
% 204.26/35.21  | | | 
% 204.26/35.21  | | | REF_CLOSE: (8), (19), (27), (34), (41) are inconsistent by sub-proof
% 204.26/35.21  | | |            #1271.
% 204.26/35.21  | | | 
% 204.26/35.21  | | End of split
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #876 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (2)  op(all_52_7, all_52_7) = e0
% 204.26/35.21    (3)  op(all_52_5, all_52_5) = e1
% 204.26/35.21    (4)  all_58_0 = all_6_2
% 204.26/35.21    (5)  op(e2, e2) = all_4_2
% 204.26/35.21    (6)  op(e0, e0) = all_14_2
% 204.26/35.21    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.21    (8)  all_58_6 = e3
% 204.26/35.21    (9)  op(all_6_2, all_6_2) = e3
% 204.26/35.21    (10)  all_58_12 = all_52_7
% 204.26/35.21    (11)   ~ (all_52_7 = all_14_2)
% 204.26/35.21    (12)  all_58_2 = all_52_3
% 204.26/35.21    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.21    (14)  op(all_52_3, all_52_3) = e2
% 204.26/35.21    (15)   ~ (all_52_5 = all_10_2)
% 204.26/35.21    (16)   ~ (all_52_5 = all_6_2)
% 204.26/35.21    (17)  op(e3, e3) = all_6_2
% 204.26/35.21    (18)  all_58_6 = all_52_5
% 204.26/35.21    (19)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.21    (20)  op(e1, e1) = all_10_2
% 204.26/35.21    (21)   ~ (all_52_3 = all_4_2)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (8), (18) imply:
% 204.26/35.21  |   (22)  all_52_5 = e3
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (22) implies:
% 204.26/35.21  |   (23)  all_52_5 = e3
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (16), (23) imply:
% 204.26/35.21  |   (24)   ~ (all_6_2 = e3)
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (24) implies:
% 204.26/35.21  |   (25)   ~ (all_6_2 = e3)
% 204.26/35.21  | 
% 204.26/35.21  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 204.26/35.21  |            (14), (15), (17), (18), (19), (20), (21), (25) are inconsistent by
% 204.26/35.21  |            sub-proof #1362.
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #877 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (2)  op(all_14_2, e0) = all_14_1
% 204.26/35.21    (3)  op(e0, all_14_1) = e1
% 204.26/35.21    (4)  op(e0, e0) = all_14_2
% 204.26/35.21    (5)  all_58_15 = e0
% 204.26/35.21    (6)  all_58_15 = all_14_2
% 204.26/35.21    (7)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.21    (8)   ~ (e1 = e0)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (5), (6) imply:
% 204.26/35.21  |   (9)  all_14_2 = e0
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (7), (9) imply:
% 204.26/35.21  |   (10)  op(e0, e0) = all_52_30
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (2), (9) imply:
% 204.26/35.21  |   (11)  op(e0, e0) = all_14_1
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (4), (9) imply:
% 204.26/35.21  |   (12)  op(e0, e0) = e0
% 204.26/35.21  | 
% 204.26/35.21  | GROUND_INST: instantiating (1) with all_14_1, all_52_30, e0, e0, simplifying
% 204.26/35.21  |              with (10), (11) gives:
% 204.26/35.21  |   (13)  all_52_30 = all_14_1
% 204.26/35.21  | 
% 204.26/35.21  | GROUND_INST: instantiating (1) with e0, all_52_30, e0, e0, simplifying with
% 204.26/35.21  |              (10), (12) gives:
% 204.26/35.21  |   (14)  all_52_30 = e0
% 204.26/35.21  | 
% 204.26/35.21  | COMBINE_EQS: (13), (14) imply:
% 204.26/35.21  |   (15)  all_14_1 = e0
% 204.26/35.21  | 
% 204.26/35.21  | SIMP: (15) implies:
% 204.26/35.21  |   (16)  all_14_1 = e0
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (3), (16) imply:
% 204.26/35.21  |   (17)  op(e0, e0) = e1
% 204.26/35.21  | 
% 204.26/35.21  | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (12),
% 204.26/35.21  |              (17) gives:
% 204.26/35.21  |   (18)  e1 = e0
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (8), (18) imply:
% 204.26/35.21  |   (19)  $false
% 204.26/35.21  | 
% 204.26/35.21  | CLOSE: (19) is inconsistent.
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #878 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ~ (e3 = e1)
% 204.26/35.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (3)   ~ (e3 = e0)
% 204.26/35.21    (4)   ~ (all_4_0 = e1)
% 204.26/35.21    (5)  all_58_0 = all_6_2
% 204.26/35.21    (6)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.21    (7)   ~ (all_52_27 = all_52_29)
% 204.26/35.21    (8)  all_58_9 = all_52_25
% 204.26/35.21    (9)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.21    (10)   ~ (all_6_2 = all_4_0)
% 204.26/35.21    (11)  all_32_2 = all_4_2
% 204.26/35.21    (12)  op(e2, e2) = all_4_2
% 204.26/35.21    (13)  all_58_11 = all_52_29
% 204.26/35.21    (14)  all_56_5 = all_4_2
% 204.26/35.21    (15)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.21    (16)  all_58_2 = all_4_0
% 204.26/35.21    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.21    (18)  op(all_4_2, e2) = e3
% 204.26/35.21    (19)  all_58_15 = e0
% 204.26/35.21    (20)   ~ (all_4_0 = e3)
% 204.26/35.21    (21)   ~ (all_52_25 = e0)
% 204.26/35.21    (22)  all_58_10 = all_52_27
% 204.26/35.21    (23)   ~ (all_52_25 = all_52_29)
% 204.26/35.21    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.21    (25)  all_56_7 = all_52_27
% 204.26/35.21    (26)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.21    (27)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.21    (28)  all_56_4 = all_4_0
% 204.26/35.21    (29)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.21    (30)   ~ (all_52_25 = all_6_2)
% 204.26/35.21    (31)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.21    (32)   ~ (all_52_9 = all_4_2)
% 204.26/35.21    (33)  op(e3, e3) = all_6_2
% 204.26/35.21    (34)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.21    (35)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.21    (36)  all_32_0 = all_4_0
% 204.26/35.21    (37)  all_56_3 = all_52_25
% 204.26/35.21    (38)  all_58_5 = all_52_19
% 204.26/35.21    (39)   ~ (all_52_27 = all_4_2)
% 204.26/35.21    (40)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.26/35.21    (41)   ~ (all_4_0 = all_4_2)
% 204.26/35.21    (42)  op(e3, e2) = all_52_9
% 204.26/35.21    (43)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.26/35.21    (44)  all_58_3 = all_4_2
% 204.26/35.21    (45)   ~ (all_52_19 = all_4_2)
% 204.26/35.21    (46)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | ALPHA: (43) implies:
% 204.26/35.21  |   (47)  all_52_28 = e1
% 204.26/35.21  |   (48)  all_52_26 = e2
% 204.26/35.21  |   (49)  all_52_24 = e3
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (46), (49) imply:
% 204.26/35.21  |   (50)  op(all_52_25, all_52_25) = e3
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (9), (48) imply:
% 204.26/35.21  |   (51)  op(all_52_27, all_52_27) = e2
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (29), (47) imply:
% 204.26/35.21  |   (52)  op(all_52_29, all_52_29) = e1
% 204.26/35.21  | 
% 204.26/35.21  | BETA: splitting (26) gives:
% 204.26/35.21  | 
% 204.26/35.21  | Case 1:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (53)  all_56_4 = e3
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (20), (28), (53) are inconsistent by sub-proof #980.
% 204.26/35.21  | | 
% 204.26/35.21  | Case 2:
% 204.26/35.21  | | 
% 204.26/35.21  | |   (54)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.21  | | 
% 204.26/35.21  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 204.26/35.21  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 204.26/35.21  | |            (25), (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 204.26/35.21  | |            (38), (39), (40), (41), (42), (44), (45), (50), (51), (52), (54)
% 204.26/35.21  | |            are inconsistent by sub-proof #941.
% 204.26/35.21  | | 
% 204.26/35.21  | End of split
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #879 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ~ (all_52_25 = all_52_27)
% 204.26/35.21    (2)  all_58_14 = all_52_23
% 204.26/35.21    (3)   ~ (e3 = e1)
% 204.26/35.21    (4)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.21    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (6)   ~ (all_52_7 = all_10_0)
% 204.26/35.21    (7)  all_58_1 = all_52_9
% 204.26/35.21    (8)   ~ (e3 = e0)
% 204.26/35.21    (9)  op(e2, e3) = all_52_3
% 204.26/35.21    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.21    (11)   ~ (all_52_7 = all_52_15)
% 204.26/35.21    (12)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.21    (13)   ~ (all_52_17 = all_52_25)
% 204.26/35.21    (14)   ~ (all_52_3 = all_6_2)
% 204.26/35.21    (15)  all_58_0 = all_6_2
% 204.26/35.21    (16)  all_56_4 = all_52_3
% 204.26/35.21    (17)   ~ (all_52_17 = all_10_2)
% 204.26/35.21    (18)  op(e3, e0) = all_52_25
% 204.26/35.21    (19)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.21    (20)  all_58_13 = all_52_15
% 204.26/35.21    (21)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.21    (22)  all_58_9 = all_52_25
% 204.26/35.21    (23)   ~ (all_6_1 = e1)
% 204.26/35.21    (24)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.21    (25)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.26/35.21    (26)  op(e2, e2) = all_4_2
% 204.26/35.21    (27)  all_58_11 = all_52_29
% 204.26/35.21    (28)  all_56_5 = all_4_2
% 204.26/35.21    (29)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.21    (30)   ~ (all_52_3 = all_52_27)
% 204.26/35.21    (31)   ~ (all_52_7 = all_6_2)
% 204.26/35.21    (32)   ~ (all_10_0 = all_6_2)
% 204.26/35.21    (33)   ~ (all_52_15 = e0)
% 204.26/35.21    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.21    (35)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.21    (36)  all_58_15 = e0
% 204.26/35.21    (37)  all_56_11 = all_52_29
% 204.26/35.21    (38)   ~ (all_10_0 = e2)
% 204.26/35.21    (39)   ~ (all_52_25 = e0)
% 204.26/35.21    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.21    (41)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.21    (42)  all_56_9 = all_52_13
% 204.26/35.21    (43)   ~ (e2 = e1)
% 204.26/35.21    (44)   ~ (all_52_13 = all_10_2)
% 204.26/35.21    (45)  op(e0, e0) = e0
% 204.26/35.21    (46)   ~ (all_6_0 = e1)
% 204.26/35.21    (47)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.26/35.21    (48)  all_58_10 = all_52_27
% 204.26/35.21    (49)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.21    (50)   ~ (all_52_3 = all_10_0)
% 204.26/35.21    (51)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.21    (52)  op(all_52_15, all_52_15) = all_52_14
% 204.26/35.21    (53)   ~ (all_52_29 = all_10_2)
% 204.26/35.21    (54)  op(all_10_2, e1) = e3
% 204.26/35.21    (55)  all_58_7 = all_52_13
% 204.26/35.21    (56)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 204.26/35.21    (57)  all_58_12 = all_52_7
% 204.26/35.21    (58)  all_30_2 = all_10_2
% 204.26/35.21    (59)  all_58_2 = all_52_3
% 204.26/35.21    (60)  op(e3, all_6_1) = all_6_0
% 204.26/35.21    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.21    (62)  all_56_7 = all_52_27
% 204.26/35.21    (63)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.21    (64)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.21    (65)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.21    (66)  all_56_8 = all_10_0
% 204.26/35.21    (67)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.21    (68)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.21    (69)  op(e3, e1) = all_52_17
% 204.26/35.21    (70)  all_30_0 = all_10_0
% 204.26/35.21    (71)  all_58_6 = all_10_0
% 204.26/35.21    (72)  op(e0, e3) = all_52_7
% 204.26/35.21    (73)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.21    (74)   ~ (all_52_9 = all_52_25)
% 204.26/35.21    (75)   ~ (all_52_19 = all_10_2)
% 204.26/35.21    (76)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.21    (77)   ~ (all_10_0 = all_10_2)
% 204.26/35.21    (78)  all_58_8 = all_10_2
% 204.26/35.21    (79)  all_56_12 = all_52_7
% 204.26/35.21    (80)   ~ (all_52_25 = all_6_2)
% 204.26/35.21    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.21    (82)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.26/35.21    (83)   ~ (all_52_9 = all_6_2)
% 204.26/35.21    (84)   ~ (all_52_13 = all_52_15)
% 204.26/35.21    (85)   ~ (all_52_27 = e0)
% 204.26/35.21    (86)  op(e3, e3) = all_6_2
% 204.26/35.21    (87)   ~ (all_52_29 = all_10_0)
% 204.26/35.21    (88)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.21    (89)  all_56_3 = all_52_25
% 204.26/35.21    (90)   ~ (all_52_3 = all_52_7)
% 204.26/35.21    (91)  all_58_5 = all_52_19
% 204.26/35.21    (92)  op(all_10_0, all_10_0) = all_52_4
% 204.26/35.21    (93)  all_56_1 = all_52_9
% 204.26/35.21    (94)   ~ (all_52_15 = all_4_2)
% 204.26/35.21    (95)   ~ (all_52_27 = all_4_2)
% 204.26/35.21    (96)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.21    (97)   ~ (e1 = e0)
% 204.26/35.21    (98)   ~ (e3 = e2)
% 204.26/35.21    (99)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.21    (100)  all_56_10 = all_10_2
% 204.26/35.21    (101)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.21    (102)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.21    (103)   ~ (all_52_13 = all_10_0)
% 204.26/35.21    (104)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.21    (105)   ~ (all_6_1 = e2)
% 204.26/35.21    (106)  op(e1, e1) = all_10_2
% 204.26/35.21    (107)   ~ (all_52_7 = all_52_23)
% 204.26/35.21    (108)  all_58_3 = all_4_2
% 204.26/35.21    (109)  all_56_13 = all_52_15
% 204.26/35.21    (110)   ~ (all_52_3 = all_4_2)
% 204.26/35.21    (111)   ~ (all_52_19 = all_4_2)
% 204.26/35.21    (112)  op(all_6_2, e3) = all_6_1
% 204.26/35.21    (113)   ~ (all_52_13 = all_52_29)
% 204.26/35.21    (114)  all_58_4 = all_52_17
% 204.26/35.21    (115)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.21    (116)   ~ (all_52_7 = e0)
% 204.26/35.21  
% 204.26/35.21  Begin of proof
% 204.26/35.21  | 
% 204.26/35.21  | ALPHA: (47) implies:
% 204.26/35.21  |   (117)  all_52_14 = e0
% 204.26/35.21  |   (118)  all_52_12 = e1
% 204.26/35.21  |   (119)  all_52_10 = e2
% 204.26/35.21  |   (120)  all_52_8 = e3
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (51), (120) imply:
% 204.26/35.21  |   (121)  op(all_52_9, all_52_9) = e3
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (104), (118) imply:
% 204.26/35.21  |   (122)  op(all_52_13, all_52_13) = e1
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (52), (117) imply:
% 204.26/35.21  |   (123)  op(all_52_15, all_52_15) = e0
% 204.26/35.21  | 
% 204.26/35.21  | REDUCE: (88), (119) imply:
% 204.26/35.21  |   (124)  op(all_4_2, all_4_2) = e2
% 204.26/35.21  | 
% 204.26/35.21  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.26/35.21  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.26/35.21  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.26/35.21  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.26/35.21  |            (46), (48), (49), (50), (53), (54), (55), (56), (57), (58), (59),
% 204.26/35.21  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.26/35.21  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 204.26/35.21  |            (82), (83), (84), (85), (86), (87), (89), (90), (91), (92), (93),
% 204.26/35.21  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 204.26/35.21  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 204.26/35.21  |            (114), (115), (116), (121), (122), (123), (124) are inconsistent by
% 204.26/35.21  |            sub-proof #880.
% 204.26/35.21  | 
% 204.26/35.21  End of proof
% 204.26/35.21  
% 204.26/35.21  Sub-proof #880 shows that the following formulas are inconsistent:
% 204.26/35.21  ----------------------------------------------------------------
% 204.26/35.21    (1)   ~ (all_52_25 = all_52_27)
% 204.26/35.21    (2)  all_58_14 = all_52_23
% 204.26/35.21    (3)   ~ (e3 = e1)
% 204.26/35.21    (4)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.21    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.21    (6)   ~ (all_52_7 = all_10_0)
% 204.26/35.21    (7)  all_58_1 = all_52_9
% 204.26/35.21    (8)   ~ (e3 = e0)
% 204.26/35.21    (9)  op(e2, e3) = all_52_3
% 204.26/35.21    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.21    (11)   ~ (all_52_7 = all_52_15)
% 204.26/35.21    (12)  op(all_52_15, all_52_15) = e0
% 204.26/35.21    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.21    (14)   ~ (all_52_17 = all_52_25)
% 204.26/35.21    (15)   ~ (all_52_3 = all_6_2)
% 204.26/35.21    (16)  all_58_0 = all_6_2
% 204.26/35.21    (17)  all_56_4 = all_52_3
% 204.26/35.21    (18)   ~ (all_52_17 = all_10_2)
% 204.26/35.21    (19)  op(e3, e0) = all_52_25
% 204.26/35.21    (20)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.21    (21)  all_58_13 = all_52_15
% 204.26/35.21    (22)  op(all_52_13, all_52_13) = e1
% 204.26/35.21    (23)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.21    (24)  all_58_9 = all_52_25
% 204.26/35.21    (25)   ~ (all_6_1 = e1)
% 204.26/35.21    (26)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.22    (27)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.26/35.22    (28)  op(e2, e2) = all_4_2
% 204.26/35.22    (29)  all_58_11 = all_52_29
% 204.26/35.22    (30)  all_56_5 = all_4_2
% 204.26/35.22    (31)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.22    (32)   ~ (all_52_3 = all_52_27)
% 204.26/35.22    (33)   ~ (all_52_7 = all_6_2)
% 204.26/35.22    (34)   ~ (all_10_0 = all_6_2)
% 204.26/35.22    (35)   ~ (all_52_15 = e0)
% 204.26/35.22    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.22    (37)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.22    (38)  all_58_15 = e0
% 204.26/35.22    (39)  all_56_11 = all_52_29
% 204.26/35.22    (40)   ~ (all_10_0 = e2)
% 204.26/35.22    (41)   ~ (all_52_25 = e0)
% 204.26/35.22    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.22    (43)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.22    (44)  all_56_9 = all_52_13
% 204.26/35.22    (45)   ~ (e2 = e1)
% 204.26/35.22    (46)   ~ (all_52_13 = all_10_2)
% 204.26/35.22    (47)  op(e0, e0) = e0
% 204.26/35.22    (48)   ~ (all_6_0 = e1)
% 204.26/35.22    (49)  all_58_10 = all_52_27
% 204.26/35.22    (50)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.22    (51)   ~ (all_52_3 = all_10_0)
% 204.26/35.22    (52)   ~ (all_52_29 = all_10_2)
% 204.26/35.22    (53)  op(all_10_2, e1) = e3
% 204.26/35.22    (54)  all_58_7 = all_52_13
% 204.26/35.22    (55)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 204.26/35.22    (56)  all_58_12 = all_52_7
% 204.26/35.22    (57)  all_30_2 = all_10_2
% 204.26/35.22    (58)  all_58_2 = all_52_3
% 204.26/35.22    (59)  op(e3, all_6_1) = all_6_0
% 204.26/35.22    (60)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.22    (61)  all_56_7 = all_52_27
% 204.26/35.22    (62)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.22    (63)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.22    (64)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.22    (65)  all_56_8 = all_10_0
% 204.26/35.22    (66)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.22    (67)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.22    (68)  op(e3, e1) = all_52_17
% 204.26/35.22    (69)  all_30_0 = all_10_0
% 204.26/35.22    (70)  all_58_6 = all_10_0
% 204.26/35.22    (71)  op(e0, e3) = all_52_7
% 204.26/35.22    (72)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.22    (73)   ~ (all_52_9 = all_52_25)
% 204.26/35.22    (74)   ~ (all_52_19 = all_10_2)
% 204.26/35.22    (75)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.22    (76)   ~ (all_10_0 = all_10_2)
% 204.26/35.22    (77)  all_58_8 = all_10_2
% 204.26/35.22    (78)  all_56_12 = all_52_7
% 204.26/35.22    (79)   ~ (all_52_25 = all_6_2)
% 204.26/35.22    (80)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.22    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.26/35.22    (82)  op(all_4_2, all_4_2) = e2
% 204.26/35.22    (83)   ~ (all_52_9 = all_6_2)
% 204.26/35.22    (84)   ~ (all_52_13 = all_52_15)
% 204.26/35.22    (85)   ~ (all_52_27 = e0)
% 204.26/35.22    (86)  op(e3, e3) = all_6_2
% 204.26/35.22    (87)   ~ (all_52_29 = all_10_0)
% 204.26/35.22    (88)  all_56_3 = all_52_25
% 204.26/35.22    (89)   ~ (all_52_3 = all_52_7)
% 204.26/35.22    (90)  all_58_5 = all_52_19
% 204.26/35.22    (91)  op(all_10_0, all_10_0) = all_52_4
% 204.26/35.22    (92)  all_56_1 = all_52_9
% 204.26/35.22    (93)   ~ (all_52_15 = all_4_2)
% 204.26/35.22    (94)   ~ (all_52_27 = all_4_2)
% 204.26/35.22    (95)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.22    (96)   ~ (e1 = e0)
% 204.26/35.22    (97)   ~ (e3 = e2)
% 204.26/35.22    (98)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.22    (99)  all_56_10 = all_10_2
% 204.26/35.22    (100)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.22    (101)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.22    (102)   ~ (all_52_13 = all_10_0)
% 204.26/35.22    (103)   ~ (all_6_1 = e2)
% 204.26/35.22    (104)  op(e1, e1) = all_10_2
% 204.26/35.22    (105)  op(all_52_9, all_52_9) = e3
% 204.26/35.22    (106)   ~ (all_52_7 = all_52_23)
% 204.26/35.22    (107)  all_58_3 = all_4_2
% 204.26/35.22    (108)  all_56_13 = all_52_15
% 204.26/35.22    (109)   ~ (all_52_3 = all_4_2)
% 204.26/35.22    (110)   ~ (all_52_19 = all_4_2)
% 204.26/35.22    (111)  op(all_6_2, e3) = all_6_1
% 204.26/35.22    (112)   ~ (all_52_13 = all_52_29)
% 204.26/35.22    (113)  all_58_4 = all_52_17
% 204.26/35.22    (114)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.22    (115)   ~ (all_52_7 = e0)
% 204.26/35.22  
% 204.26/35.22  Begin of proof
% 204.26/35.22  | 
% 204.26/35.22  | BETA: splitting (42) gives:
% 204.26/35.22  | 
% 204.26/35.22  | Case 1:
% 204.26/35.22  | | 
% 204.26/35.22  | |   (116)  all_56_13 = e3
% 204.26/35.22  | | 
% 204.26/35.22  | | COMBINE_EQS: (108), (116) imply:
% 204.26/35.22  | |   (117)  all_52_15 = e3
% 204.26/35.22  | | 
% 204.26/35.22  | | REF_CLOSE: (5), (10), (11), (12), (25), (33), (71), (78), (86), (103),
% 204.26/35.22  | |            (111), (117) are inconsistent by sub-proof #1341.
% 204.26/35.22  | | 
% 204.26/35.22  | Case 2:
% 204.26/35.22  | | 
% 204.26/35.22  | |   (118)   ~ (all_56_13 = e3)
% 204.26/35.22  | |   (119)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.22  | | 
% 204.26/35.22  | | REDUCE: (108), (118) imply:
% 204.26/35.22  | |   (120)   ~ (all_52_15 = e3)
% 204.26/35.22  | | 
% 204.26/35.22  | | BETA: splitting (95) gives:
% 204.26/35.22  | | 
% 204.26/35.22  | | Case 1:
% 204.26/35.22  | | | 
% 204.26/35.22  | | |   (121)  all_58_12 = e3
% 204.26/35.22  | | | 
% 204.26/35.22  | | | COMBINE_EQS: (56), (121) imply:
% 204.26/35.22  | | |   (122)  all_52_7 = e3
% 204.26/35.22  | | | 
% 204.26/35.22  | | | SIMP: (122) implies:
% 204.26/35.22  | | |   (123)  all_52_7 = e3
% 204.26/35.22  | | | 
% 204.26/35.22  | | | REDUCE: (89), (123) imply:
% 204.26/35.22  | | |   (124)   ~ (all_52_3 = e3)
% 204.26/35.22  | | | 
% 204.26/35.22  | | | REDUCE: (106), (123) imply:
% 204.26/35.22  | | |   (125)   ~ (all_52_23 = e3)
% 204.26/35.22  | | | 
% 204.26/35.22  | | | SIMP: (125) implies:
% 204.26/35.22  | | |   (126)   ~ (all_52_23 = e3)
% 204.26/35.22  | | | 
% 204.26/35.22  | | | REDUCE: (13), (123) imply:
% 204.26/35.22  | | |   (127)  op(e3, e3) = all_52_6
% 204.26/35.22  | | | 
% 204.26/35.22  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 204.26/35.22  | | |              with (86), (127) gives:
% 204.26/35.22  | | |   (128)  all_52_6 = all_6_2
% 204.26/35.22  | | | 
% 204.26/35.22  | | | BETA: splitting (67) gives:
% 204.26/35.22  | | | 
% 204.26/35.22  | | | Case 1:
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | |   (129)  all_58_0 = e2
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | COMBINE_EQS: (16), (129) imply:
% 204.26/35.22  | | | |   (130)  all_6_2 = e2
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (15), (130) imply:
% 204.26/35.22  | | | |   (131)   ~ (all_52_3 = e2)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (83), (130) imply:
% 204.26/35.22  | | | |   (132)   ~ (all_52_9 = e2)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (79), (130) imply:
% 204.26/35.22  | | | |   (133)   ~ (all_52_25 = e2)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (111), (130) imply:
% 204.26/35.22  | | | |   (134)  op(e2, e3) = all_6_1
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | GROUND_INST: instantiating (5) with all_52_3, all_6_1, e3, e2,
% 204.26/35.22  | | | |              simplifying with (9), (134) gives:
% 204.26/35.22  | | | |   (135)  all_52_3 = all_6_1
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | COMBINE_EQS: (17), (135) imply:
% 204.26/35.22  | | | |   (136)  all_56_4 = all_6_1
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | COMBINE_EQS: (58), (135) imply:
% 204.26/35.22  | | | |   (137)  all_58_2 = all_6_1
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (32), (135) imply:
% 204.26/35.22  | | | |   (138)   ~ (all_52_27 = all_6_1)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | SIMP: (138) implies:
% 204.26/35.22  | | | |   (139)   ~ (all_52_27 = all_6_1)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (51), (135) imply:
% 204.26/35.22  | | | |   (140)   ~ (all_10_0 = all_6_1)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | SIMP: (140) implies:
% 204.26/35.22  | | | |   (141)   ~ (all_10_0 = all_6_1)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (124), (135) imply:
% 204.26/35.22  | | | |   (142)   ~ (all_6_1 = e3)
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | REDUCE: (4), (135) imply:
% 204.26/35.22  | | | |   (143)  op(all_6_1, all_6_1) = all_52_2
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | BETA: splitting (62) gives:
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | Case 1:
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | |   (144)  all_56_4 = e3
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REF_CLOSE: (136), (142), (144) are inconsistent by sub-proof #900.
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | Case 2:
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | |   (145)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | BETA: splitting (145) gives:
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | Case 1:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | |   (146)  all_56_4 = e2
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | REF_CLOSE: (103), (136), (146) are inconsistent by sub-proof #1219.
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | Case 2:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | |   (147)  all_56_4 = e1 | all_56_4 = e0
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | BETA: splitting (60) gives:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | Case 1:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | |   (148)  all_58_0 = e1
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | COMBINE_EQS: (129), (148) imply:
% 204.26/35.22  | | | | | | |   (149)  e2 = e1
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | REDUCE: (45), (149) imply:
% 204.26/35.22  | | | | | | |   (150)  $false
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | CLOSE: (150) is inconsistent.
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | Case 2:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | |   (151)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | BETA: splitting (151) gives:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | |   (152)  all_58_2 = e1
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | COMBINE_EQS: (137), (152) imply:
% 204.26/35.22  | | | | | | | |   (153)  all_6_1 = e1
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | SIMP: (153) implies:
% 204.26/35.22  | | | | | | | |   (154)  all_6_1 = e1
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | REDUCE: (25), (154) imply:
% 204.26/35.22  | | | | | | | |   (155)  $false
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | CLOSE: (155) is inconsistent.
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | |   (156)  all_58_6 = e1 | all_58_12 = e1
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | BETA: splitting (156) gives:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | |   (157)  all_58_6 = e1
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | COMBINE_EQS: (70), (157) imply:
% 204.26/35.22  | | | | | | | | |   (158)  all_10_0 = e1
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | SIMP: (158) implies:
% 204.26/35.22  | | | | | | | | |   (159)  all_10_0 = e1
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | REDUCE: (141), (159) imply:
% 204.26/35.22  | | | | | | | | |   (160)   ~ (all_6_1 = e1)
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | REDUCE: (91), (159) imply:
% 204.26/35.22  | | | | | | | | |   (161)  op(e1, e1) = all_52_4
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | BETA: splitting (147) gives:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | |   (162)  all_56_4 = e1
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REF_CLOSE: (25), (136), (162) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | |            #1218.
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | |   (163)  all_56_4 = e0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | COMBINE_EQS: (136), (163) imply:
% 204.26/35.22  | | | | | | | | | |   (164)  all_6_1 = e0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | SIMP: (164) implies:
% 204.26/35.22  | | | | | | | | | |   (165)  all_6_1 = e0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | COMBINE_EQS: (137), (165) imply:
% 204.26/35.22  | | | | | | | | | |   (166)  all_58_2 = e0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (25), (165) imply:
% 204.26/35.22  | | | | | | | | | |   (167)   ~ (e1 = e0)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (143), (165) imply:
% 204.26/35.22  | | | | | | | | | |   (168)  op(e0, e0) = all_52_2
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (59), (165) imply:
% 204.26/35.22  | | | | | | | | | |   (169)  op(e3, e0) = all_6_0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_52_2, e0, e0,
% 204.26/35.22  | | | | | | | | | |              simplifying with (47), (168) gives:
% 204.26/35.22  | | | | | | | | | |   (170)  all_52_2 = e0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_4, e1, e1,
% 204.26/35.22  | | | | | | | | | |              simplifying with (104), (161) gives:
% 204.26/35.22  | | | | | | | | | |   (171)  all_52_4 = all_10_2
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_25, all_6_0, e0, e3,
% 204.26/35.22  | | | | | | | | | |              simplifying with (19), (169) gives:
% 204.26/35.22  | | | | | | | | | |   (172)  all_52_25 = all_6_0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | COMBINE_EQS: (88), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (173)  all_56_3 = all_6_0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | COMBINE_EQS: (24), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (174)  all_58_9 = all_6_0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (73), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (175)   ~ (all_52_9 = all_6_0)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (14), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (176)   ~ (all_52_17 = all_6_0)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (1), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (177)   ~ (all_52_27 = all_6_0)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | SIMP: (177) implies:
% 204.26/35.22  | | | | | | | | | |   (178)   ~ (all_52_27 = all_6_0)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (133), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (179)   ~ (all_6_0 = e2)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REDUCE: (41), (172) imply:
% 204.26/35.22  | | | | | | | | | |   (180)   ~ (all_6_0 = e0)
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | BETA: splitting (80) gives:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | |   (181)  all_56_3 = e3
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | COMBINE_EQS: (173), (181) imply:
% 204.26/35.22  | | | | | | | | | | |   (182)  all_6_0 = e3
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | SIMP: (182) implies:
% 204.26/35.22  | | | | | | | | | | |   (183)  all_6_0 = e3
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | COMBINE_EQS: (174), (183) imply:
% 204.26/35.22  | | | | | | | | | | |   (184)  all_58_9 = e3
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | REDUCE: (175), (183) imply:
% 204.26/35.22  | | | | | | | | | | |   (185)   ~ (all_52_9 = e3)
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | REDUCE: (176), (183) imply:
% 204.26/35.22  | | | | | | | | | | |   (186)   ~ (all_52_17 = e3)
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | REDUCE: (178), (183) imply:
% 204.26/35.22  | | | | | | | | | | |   (187)   ~ (all_52_27 = e3)
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | BETA: splitting (37) gives:
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | |   (188)  all_58_9 = e1
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | COMBINE_EQS: (184), (188) imply:
% 204.26/35.22  | | | | | | | | | | | |   (189)  e3 = e1
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | REDUCE: (3), (189) imply:
% 204.26/35.22  | | | | | | | | | | | |   (190)  $false
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | |   (191)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | BETA: splitting (191) gives:
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | |   (192)  all_58_10 = e1
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | COMBINE_EQS: (49), (192) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (193)  all_52_27 = e1
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | SIMP: (193) implies:
% 204.26/35.22  | | | | | | | | | | | | |   (194)  all_52_27 = e1
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | REDUCE: (187), (194) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (195)   ~ (e3 = e1)
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | REDUCE: (26), (194) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (196)  op(e1, e1) = all_52_26
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_26, e1,
% 204.26/35.22  | | | | | | | | | | | | |              e1, simplifying with (104), (196) gives:
% 204.26/35.22  | | | | | | | | | | | | |   (197)  all_52_26 = all_10_2
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | BETA: splitting (98) gives:
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | |   (198)  all_56_1 = e3
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | REF_CLOSE: (92), (185), (198) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | | | | |            #1326.
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | |   (199)   ~ (all_56_1 = e3)
% 204.26/35.22  | | | | | | | | | | | | | |   (200)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | |   (201)  all_56_5 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | COMBINE_EQS: (30), (201) imply:
% 204.26/35.22  | | | | | | | | | | | | | | |   (202)  all_4_2 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | SIMP: (202) implies:
% 204.26/35.22  | | | | | | | | | | | | | | |   (203)  all_4_2 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | REDUCE: (110), (203) imply:
% 204.26/35.22  | | | | | | | | | | | | | | |   (204)   ~ (all_52_19 = e3)
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (18), (53), (68), (77), (90), (100),
% 204.26/35.22  | | | | | | | | | | | | | | |            (113), (126), (186), (204) are inconsistent by
% 204.26/35.22  | | | | | | | | | | | | | | |            sub-proof #897.
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | |   (205)   ~ (all_56_5 = e3)
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | REDUCE: (30), (205) imply:
% 204.26/35.22  | | | | | | | | | | | | | | |   (206)   ~ (all_4_2 = e3)
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | |   (207)  all_58_2 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (207) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | | | | | | |            #1123.
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | |   (208)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | |   (209)  all_58_3 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (209) imply:
% 204.26/35.22  | | | | | | | | | | | | | | | | |   (210)  all_4_2 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | REDUCE: (206), (210) imply:
% 204.26/35.22  | | | | | | | | | | | | | | | | |   (211)  $false
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | |   (212)  all_58_5 = e3 | all_58_10 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | |   (213)  all_58_5 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (213) imply:
% 204.26/35.22  | | | | | | | | | | | | | | | | | |   (214)  all_52_19 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | REDUCE: (74), (214) imply:
% 204.26/35.22  | | | | | | | | | | | | | | | | | |   (215)   ~ (all_10_2 = e3)
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 204.26/35.22  | | | | | | | | | | | | | | | | | |   (216)   ~ (all_10_2 = e3)
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |   (217)  all_58_1 = e0
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (105), (185), (217) are
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |   (218)   ~ (all_58_1 = e0)
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | REDUCE: (7), (218) imply:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |   (219)   ~ (all_52_9 = e0)
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (43), (92), (104), (105), (132), (200),
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |            (216), (219) are inconsistent by sub-proof #896.
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | |   (220)  all_58_10 = e3
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (192), (220) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |            #968.
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |   (221)  all_58_11 = e1 | all_58_15 = e1
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18), (29), (38), (40), (50), (53), (55),
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |            (57), (65), (68), (69), (76), (87), (96), (99),
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |            (104), (114), (221) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | | | | | | | | | |            #895.
% 204.26/35.22  | | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | |   (222)  all_58_11 = e1 | all_58_15 = e1
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | REF_CLOSE: (5), (18), (29), (38), (40), (50), (53), (55),
% 204.26/35.22  | | | | | | | | | | | | |            (57), (65), (68), (69), (76), (87), (96), (99),
% 204.26/35.22  | | | | | | | | | | | | |            (104), (114), (222) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | | | |            #895.
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | |   (223)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | BETA: splitting (223) gives:
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | |   (224)  all_56_3 = e2
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | REF_CLOSE: (173), (179), (224) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | | |            #1075.
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | |   (225)  all_56_3 = e1 | all_56_3 = e0
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | BETA: splitting (225) gives:
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | |   (226)  all_56_3 = e1
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | COMBINE_EQS: (173), (226) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (227)  all_6_0 = e1
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | REDUCE: (48), (227) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (228)  $false
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | |   (229)  all_56_3 = e0
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | COMBINE_EQS: (173), (229) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (230)  all_6_0 = e0
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | REDUCE: (180), (230) imply:
% 204.26/35.22  | | | | | | | | | | | | |   (231)  $false
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 204.26/35.22  | | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | |   (232)  all_58_12 = e1
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | REF_CLOSE: (3), (121), (232) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | |            #894.
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | End of split
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | End of split
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | End of split
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | End of split
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | Case 2:
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | |   (233)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | BETA: splitting (233) gives:
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | | Case 1:
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | |   (234)  all_58_2 = e2
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | COMBINE_EQS: (58), (234) imply:
% 204.26/35.22  | | | | |   (235)  all_52_3 = e2
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | SIMP: (235) implies:
% 204.26/35.22  | | | | |   (236)  all_52_3 = e2
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REDUCE: (32), (236) imply:
% 204.26/35.22  | | | | |   (237)   ~ (all_52_27 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | SIMP: (237) implies:
% 204.26/35.22  | | | | |   (238)   ~ (all_52_27 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REDUCE: (51), (236) imply:
% 204.26/35.22  | | | | |   (239)   ~ (all_10_0 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REDUCE: (15), (236) imply:
% 204.26/35.22  | | | | |   (240)   ~ (all_6_2 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | SIMP: (240) implies:
% 204.26/35.22  | | | | |   (241)   ~ (all_6_2 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REDUCE: (109), (236) imply:
% 204.26/35.22  | | | | |   (242)   ~ (all_4_2 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | SIMP: (242) implies:
% 204.26/35.22  | | | | |   (243)   ~ (all_4_2 = e2)
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REDUCE: (4), (236) imply:
% 204.26/35.22  | | | | |   (244)  op(e2, e2) = all_52_2
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_2, e2, e2,
% 204.26/35.22  | | | | |              simplifying with (28), (244) gives:
% 204.26/35.22  | | | | |   (245)  all_52_2 = all_4_2
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | BETA: splitting (20) gives:
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | Case 1:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | |   (246)  all_56_7 = e3
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | COMBINE_EQS: (61), (246) imply:
% 204.26/35.22  | | | | | |   (247)  all_52_27 = e3
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | COMBINE_EQS: (49), (247) imply:
% 204.26/35.22  | | | | | |   (248)  all_58_10 = e3
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | REDUCE: (1), (247) imply:
% 204.26/35.22  | | | | | |   (249)   ~ (all_52_25 = e3)
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | REDUCE: (94), (247) imply:
% 204.26/35.22  | | | | | |   (250)   ~ (all_4_2 = e3)
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | SIMP: (250) implies:
% 204.26/35.22  | | | | | |   (251)   ~ (all_4_2 = e3)
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | REDUCE: (26), (247) imply:
% 204.26/35.22  | | | | | |   (252)  op(e3, e3) = all_52_26
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_26, e3, e3,
% 204.26/35.22  | | | | | |              simplifying with (86), (252) gives:
% 204.26/35.22  | | | | | |   (253)  all_52_26 = all_6_2
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | BETA: splitting (80) gives:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | Case 1:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | |   (254)  all_56_3 = e3
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | REF_CLOSE: (88), (249), (254) are inconsistent by sub-proof #1339.
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | Case 2:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | |   (255)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | BETA: splitting (81) gives:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | |   (256)  all_58_9 = e2
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | BETA: splitting (37) gives:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | |   (257)  all_58_9 = e1
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | REF_CLOSE: (45), (256), (257) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | |            #1214.
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | |   (258)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | BETA: splitting (258) gives:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | |   (259)  all_58_10 = e1
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REF_CLOSE: (3), (248), (259) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | |            #968.
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | |   (260)  all_58_11 = e1 | all_58_15 = e1
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REF_CLOSE: (5), (18), (29), (38), (40), (50), (53), (55),
% 204.26/35.22  | | | | | | | | | |            (57), (65), (68), (69), (76), (87), (96), (99),
% 204.26/35.22  | | | | | | | | | |            (104), (114), (260) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | |            #895.
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | |   (261)   ~ (all_58_9 = e2)
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | REF_CLOSE: (5), (7), (10), (11), (12), (21), (22), (24), (25),
% 204.26/35.22  | | | | | | | |            (33), (37), (41), (42), (54), (71), (72), (78), (79),
% 204.26/35.22  | | | | | | | |            (83), (86), (88), (103), (105), (107), (108), (111),
% 204.26/35.22  | | | | | | | |            (251), (255), (261) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | |            #891.
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | End of split
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | End of split
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | Case 2:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | |   (262)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | BETA: splitting (262) gives:
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | | Case 1:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | |   (263)  all_56_7 = e2
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | COMBINE_EQS: (61), (263) imply:
% 204.26/35.22  | | | | | | |   (264)  all_52_27 = e2
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | REDUCE: (238), (264) imply:
% 204.26/35.22  | | | | | | |   (265)  $false
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | CLOSE: (265) is inconsistent.
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | Case 2:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | |   (266)  all_56_7 = e1 | all_56_7 = e0
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | BETA: splitting (266) gives:
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | |   (267)  all_56_7 = e1
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | COMBINE_EQS: (61), (267) imply:
% 204.26/35.22  | | | | | | | |   (268)  all_52_27 = e1
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | REDUCE: (94), (268) imply:
% 204.26/35.22  | | | | | | | |   (269)   ~ (all_4_2 = e1)
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | SIMP: (269) implies:
% 204.26/35.22  | | | | | | | |   (270)   ~ (all_4_2 = e1)
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | BETA: splitting (63) gives:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | |   (271)  all_56_5 = e3
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | COMBINE_EQS: (30), (271) imply:
% 204.26/35.22  | | | | | | | | |   (272)  all_4_2 = e3
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | SIMP: (272) implies:
% 204.26/35.22  | | | | | | | | |   (273)  all_4_2 = e3
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | REDUCE: (82), (273) imply:
% 204.26/35.22  | | | | | | | | |   (274)  op(e3, e3) = e2
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | REF_CLOSE: (5), (86), (127), (241), (274) are inconsistent by
% 204.26/35.22  | | | | | | | | |            sub-proof #890.
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | |   (275)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | BETA: splitting (275) gives:
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | |   (276)  all_56_5 = e2
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | REF_CLOSE: (30), (243), (276) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | |            #1315.
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | |   (277)   ~ (all_56_5 = e2)
% 204.26/35.22  | | | | | | | | | |   (278)  all_56_5 = e1 | all_56_5 = e0
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | BETA: splitting (278) gives:
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | Case 1:
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | |   (279)  all_56_5 = e1
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | REF_CLOSE: (30), (270), (279) are inconsistent by sub-proof
% 204.26/35.22  | | | | | | | | | | |            #1188.
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | |   (280)  all_56_5 = e0
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | COMBINE_EQS: (30), (280) imply:
% 204.26/35.22  | | | | | | | | | | |   (281)  all_4_2 = e0
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | SIMP: (281) implies:
% 204.26/35.22  | | | | | | | | | | |   (282)  all_4_2 = e0
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | REDUCE: (28), (282) imply:
% 204.26/35.22  | | | | | | | | | | |   (283)  op(e2, e2) = e0
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | | REF_CLOSE: (5), (28), (47), (82), (243), (283) are
% 204.26/35.22  | | | | | | | | | | |            inconsistent by sub-proof #1317.
% 204.26/35.22  | | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | | 
% 204.26/35.22  | | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | | 
% 204.26/35.22  | | | | | | | | End of split
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | Case 2:
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | |   (284)  all_56_7 = e0
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | COMBINE_EQS: (61), (284) imply:
% 204.26/35.22  | | | | | | | |   (285)  all_52_27 = e0
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | REDUCE: (85), (285) imply:
% 204.26/35.22  | | | | | | | |   (286)  $false
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | | CLOSE: (286) is inconsistent.
% 204.26/35.22  | | | | | | | | 
% 204.26/35.22  | | | | | | | End of split
% 204.26/35.22  | | | | | | | 
% 204.26/35.22  | | | | | | End of split
% 204.26/35.22  | | | | | | 
% 204.26/35.22  | | | | | End of split
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | Case 2:
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | |   (287)  all_58_6 = e2 | all_58_12 = e2
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | | REF_CLOSE: (40), (70), (97), (121), (287) are inconsistent by
% 204.26/35.22  | | | | |            sub-proof #889.
% 204.26/35.22  | | | | | 
% 204.26/35.22  | | | | End of split
% 204.26/35.22  | | | | 
% 204.26/35.22  | | | End of split
% 204.26/35.22  | | | 
% 204.26/35.22  | | Case 2:
% 204.26/35.22  | | | 
% 204.26/35.22  | | |   (288)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.22  | | | 
% 204.26/35.22  | | | REF_CLOSE: (2), (5), (6), (8), (10), (11), (12), (13), (21), (22), (23),
% 204.26/35.22  | | |            (28), (31), (34), (35), (38), (39), (44), (46), (47), (50),
% 204.26/35.22  | | |            (52), (56), (64), (65), (66), (75), (76), (78), (82), (84),
% 204.26/35.22  | | |            (86), (87), (93), (101), (102), (104), (106), (108), (112),
% 204.26/35.22  | | |            (115), (119), (120), (288) are inconsistent by sub-proof #881.
% 204.26/35.22  | | | 
% 204.26/35.22  | | End of split
% 204.26/35.22  | | 
% 204.26/35.22  | End of split
% 204.26/35.22  | 
% 204.26/35.22  End of proof
% 204.26/35.22  
% 204.26/35.22  Sub-proof #881 shows that the following formulas are inconsistent:
% 204.26/35.22  ----------------------------------------------------------------
% 204.26/35.22    (1)  all_58_14 = all_52_23
% 204.26/35.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.22    (3)   ~ (all_52_7 = all_10_0)
% 204.26/35.22    (4)   ~ (e3 = e0)
% 204.26/35.22    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.22    (6)   ~ (all_52_7 = all_52_15)
% 204.26/35.22    (7)  op(all_52_15, all_52_15) = e0
% 204.26/35.22    (8)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.22    (9)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.22    (10)  all_58_13 = all_52_15
% 204.26/35.22    (11)  op(all_52_13, all_52_13) = e1
% 204.26/35.22    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.22    (13)   ~ (all_52_15 = e3)
% 204.26/35.22    (14)  op(e2, e2) = all_4_2
% 204.26/35.22    (15)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.22    (16)   ~ (all_10_0 = all_6_2)
% 204.26/35.22    (17)   ~ (all_52_15 = e0)
% 204.26/35.22    (18)  all_58_15 = e0
% 204.26/35.22    (19)  all_56_11 = all_52_29
% 204.26/35.22    (20)  all_56_9 = all_52_13
% 204.26/35.22    (21)   ~ (all_52_13 = all_10_2)
% 204.26/35.22    (22)  op(e0, e0) = e0
% 204.26/35.22    (23)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.22    (24)   ~ (all_52_29 = all_10_2)
% 204.26/35.23    (25)  all_58_12 = all_52_7
% 204.26/35.23    (26)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23    (27)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.23    (28)  all_56_8 = all_10_0
% 204.26/35.23    (29)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.23    (30)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.23    (31)   ~ (all_10_0 = all_10_2)
% 204.26/35.23    (32)  all_56_12 = all_52_7
% 204.26/35.23    (33)  op(all_4_2, all_4_2) = e2
% 204.26/35.23    (34)   ~ (all_52_13 = all_52_15)
% 204.26/35.23    (35)  op(e3, e3) = all_6_2
% 204.26/35.23    (36)   ~ (all_52_29 = all_10_0)
% 204.26/35.23    (37)   ~ (all_52_15 = all_4_2)
% 204.26/35.23    (38)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23    (39)   ~ (all_52_13 = all_10_0)
% 204.26/35.23    (40)  op(e1, e1) = all_10_2
% 204.26/35.23    (41)   ~ (all_52_7 = all_52_23)
% 204.26/35.23    (42)  all_56_13 = all_52_15
% 204.26/35.23    (43)   ~ (all_52_13 = all_52_29)
% 204.26/35.23    (44)   ~ (all_52_7 = e0)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (9) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (45)  all_58_13 = e3
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (10), (13), (45) are inconsistent by sub-proof #1360.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (46)  all_58_14 = e3 | all_58_15 = e3
% 204.26/35.23  | | 
% 204.26/35.23  | | BETA: splitting (46) gives:
% 204.26/35.23  | | 
% 204.26/35.23  | | Case 1:
% 204.26/35.23  | | | 
% 204.26/35.23  | | |   (47)  all_58_14 = e3
% 204.26/35.23  | | | 
% 204.26/35.23  | | | COMBINE_EQS: (1), (47) imply:
% 204.26/35.23  | | |   (48)  all_52_23 = e3
% 204.26/35.23  | | | 
% 204.26/35.23  | | | SIMP: (48) implies:
% 204.26/35.23  | | |   (49)  all_52_23 = e3
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REDUCE: (41), (49) imply:
% 204.26/35.23  | | |   (50)   ~ (all_52_7 = e3)
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REDUCE: (30), (49) imply:
% 204.26/35.23  | | |   (51)  op(e3, e3) = all_52_22
% 204.26/35.23  | | | 
% 204.26/35.23  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_22, e3, e3,
% 204.26/35.23  | | |              simplifying with (35), (51) gives:
% 204.26/35.23  | | |   (52)  all_52_22 = all_6_2
% 204.26/35.23  | | | 
% 204.26/35.23  | | | BETA: splitting (5) gives:
% 204.26/35.23  | | | 
% 204.26/35.23  | | | Case 1:
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | |   (53)  all_56_12 = e3
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | | REF_CLOSE: (32), (50), (53) are inconsistent by sub-proof #1383.
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | Case 2:
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | |   (54)   ~ (all_56_12 = e3)
% 204.26/35.23  | | | |   (55)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | | BETA: splitting (15) gives:
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | | Case 1:
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | |   (56)  all_58_12 = e2
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | COMBINE_EQS: (25), (56) imply:
% 204.26/35.23  | | | | |   (57)  all_52_7 = e2
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | SIMP: (57) implies:
% 204.26/35.23  | | | | |   (58)  all_52_7 = e2
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | REDUCE: (6), (58) imply:
% 204.26/35.23  | | | | |   (59)   ~ (all_52_15 = e2)
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | SIMP: (59) implies:
% 204.26/35.23  | | | | |   (60)   ~ (all_52_15 = e2)
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | REDUCE: (3), (58) imply:
% 204.26/35.23  | | | | |   (61)   ~ (all_10_0 = e2)
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | SIMP: (61) implies:
% 204.26/35.23  | | | | |   (62)   ~ (all_10_0 = e2)
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | REDUCE: (8), (58) imply:
% 204.26/35.23  | | | | |   (63)  op(e2, e2) = all_52_6
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | BETA: splitting (26) gives:
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | Case 1:
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | |   (64)  all_56_13 = e2
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | | REF_CLOSE: (42), (60), (64) are inconsistent by sub-proof #1356.
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | Case 2:
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | |   (65)  all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | | BETA: splitting (65) gives:
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | | Case 1:
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | |   (66)  all_56_13 = e1
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | COMBINE_EQS: (42), (66) imply:
% 204.26/35.23  | | | | | | |   (67)  all_52_15 = e1
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | SIMP: (67) implies:
% 204.26/35.23  | | | | | | |   (68)  all_52_15 = e1
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | REDUCE: (7), (68) imply:
% 204.26/35.23  | | | | | | |   (69)  op(e1, e1) = e0
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | GROUND_INST: instantiating (2) with all_10_2, e0, e1, e1,
% 204.26/35.23  | | | | | | |              simplifying with (40), (69) gives:
% 204.26/35.23  | | | | | | |   (70)  all_10_2 = e0
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_6, e2, e2,
% 204.26/35.23  | | | | | | |              simplifying with (14), (63) gives:
% 204.26/35.23  | | | | | | |   (71)  all_52_6 = all_4_2
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | REDUCE: (21), (70) imply:
% 204.26/35.23  | | | | | | |   (72)   ~ (all_52_13 = e0)
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | REDUCE: (24), (70) imply:
% 204.26/35.23  | | | | | | |   (73)   ~ (all_52_29 = e0)
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | REDUCE: (31), (70) imply:
% 204.26/35.23  | | | | | | |   (74)   ~ (all_10_0 = e0)
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | REDUCE: (12), (70) imply:
% 204.26/35.23  | | | | | | |   (75)  op(e0, e0) = all_52_20
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | BETA: splitting (23) gives:
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | |   (76)  all_56_8 = e2
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | | REF_CLOSE: (28), (62), (76) are inconsistent by sub-proof #915.
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | |   (77)   ~ (all_56_8 = e2)
% 204.26/35.23  | | | | | | | |   (78)  all_56_8 = e1 | all_56_8 = e0
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | | BETA: splitting (78) gives:
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | |   (79)  all_56_8 = e1
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | COMBINE_EQS: (28), (79) imply:
% 204.26/35.23  | | | | | | | | |   (80)  all_10_0 = e1
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | SIMP: (80) implies:
% 204.26/35.23  | | | | | | | | |   (81)  all_10_0 = e1
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | REDUCE: (39), (81) imply:
% 204.26/35.23  | | | | | | | | |   (82)   ~ (all_52_13 = e1)
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | REDUCE: (36), (81) imply:
% 204.26/35.23  | | | | | | | | |   (83)   ~ (all_52_29 = e1)
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | REDUCE: (16), (81) imply:
% 204.26/35.23  | | | | | | | | |   (84)   ~ (all_6_2 = e1)
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | SIMP: (84) implies:
% 204.26/35.23  | | | | | | | | |   (85)   ~ (all_6_2 = e1)
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | REDUCE: (62), (81) imply:
% 204.26/35.23  | | | | | | | | |   (86)   ~ (e2 = e1)
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | SIMP: (86) implies:
% 204.26/35.23  | | | | | | | | |   (87)   ~ (e2 = e1)
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_52_20, e0, e0,
% 204.26/35.23  | | | | | | | | |              simplifying with (22), (75) gives:
% 204.26/35.23  | | | | | | | | |   (88)  all_52_20 = e0
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | BETA: splitting (29) gives:
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | |   (89)  all_56_11 = e3
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | COMBINE_EQS: (19), (89) imply:
% 204.26/35.23  | | | | | | | | | |   (90)  all_52_29 = e3
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | SIMP: (90) implies:
% 204.26/35.23  | | | | | | | | | |   (91)  all_52_29 = e3
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | REDUCE: (43), (91) imply:
% 204.26/35.23  | | | | | | | | | |   (92)   ~ (all_52_13 = e3)
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | BETA: splitting (5) gives:
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | |   (93)  all_56_12 = e3
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | REF_CLOSE: (32), (50), (93) are inconsistent by sub-proof
% 204.26/35.23  | | | | | | | | | | |            #1383.
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | BETA: splitting (27) gives:
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | |   (94)  all_58_12 = e1
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (14), (15), (17), (22), (25),
% 204.26/35.23  | | | | | | | | | | | |            (26), (33), (37), (42), (87), (94) are
% 204.26/35.23  | | | | | | | | | | | |            inconsistent by sub-proof #888.
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | |   (95)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | BETA: splitting (95) gives:
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | |   (96)  all_58_13 = e1
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | REDUCE: (6), (68) imply:
% 204.26/35.23  | | | | | | | | | | | | |   (97)   ~ (all_52_7 = e1)
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | REDUCE: (37), (68) imply:
% 204.26/35.23  | | | | | | | | | | | | |   (98)   ~ (all_4_2 = e1)
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | SIMP: (98) implies:
% 204.26/35.23  | | | | | | | | | | | | |   (99)   ~ (all_4_2 = e1)
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | BETA: splitting (55) gives:
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | |   (100)  all_56_12 = e2
% 204.26/35.23  | | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | | REF_CLOSE: (2), (11), (14), (20), (38), (72), (82), (92),
% 204.26/35.23  | | | | | | | | | | | | | |            (99) are inconsistent by sub-proof #887.
% 204.26/35.23  | | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | |   (101)  all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23  | | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | | REF_CLOSE: (32), (44), (97), (101) are inconsistent by
% 204.26/35.23  | | | | | | | | | | | | | |            sub-proof #1374.
% 204.26/35.23  | | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | |   (102)   ~ (all_58_13 = e1)
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | REDUCE: (10), (102) imply:
% 204.26/35.23  | | | | | | | | | | | | |   (103)   ~ (all_52_15 = e1)
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | | REF_CLOSE: (2), (7), (14), (17), (22), (26), (33), (37),
% 204.26/35.23  | | | | | | | | | | | | |            (42), (103) are inconsistent by sub-proof #886.
% 204.26/35.23  | | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | |   (104)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | BETA: splitting (104) gives:
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | |   (105)  all_56_11 = e2
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | COMBINE_EQS: (19), (105) imply:
% 204.26/35.23  | | | | | | | | | | |   (106)  all_52_29 = e2
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | SIMP: (106) implies:
% 204.26/35.23  | | | | | | | | | | |   (107)  all_52_29 = e2
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | REDUCE: (43), (107) imply:
% 204.26/35.23  | | | | | | | | | | |   (108)   ~ (all_52_13 = e2)
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | BETA: splitting (38) gives:
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | Case 1:
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | |   (109)  all_56_9 = e3
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | COMBINE_EQS: (20), (109) imply:
% 204.26/35.23  | | | | | | | | | | | |   (110)  all_52_13 = e3
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | REDUCE: (11), (110) imply:
% 204.26/35.23  | | | | | | | | | | | |   (111)  op(e3, e3) = e1
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | REF_CLOSE: (2), (35), (85), (111) are inconsistent by
% 204.26/35.23  | | | | | | | | | | | |            sub-proof #885.
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | |   (112)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | | REF_CLOSE: (20), (72), (82), (108), (112) are inconsistent by
% 204.26/35.23  | | | | | | | | | | | |            sub-proof #884.
% 204.26/35.23  | | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | |   (113)  all_56_11 = e1 | all_56_11 = e0
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | | REF_CLOSE: (19), (73), (83), (113) are inconsistent by
% 204.26/35.23  | | | | | | | | | | |            sub-proof #1001.
% 204.26/35.23  | | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | Case 2:
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | |   (114)  all_56_8 = e0
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | | REF_CLOSE: (28), (74), (114) are inconsistent by sub-proof
% 204.26/35.23  | | | | | | | | |            #883.
% 204.26/35.23  | | | | | | | | | 
% 204.26/35.23  | | | | | | | | End of split
% 204.26/35.23  | | | | | | | | 
% 204.26/35.23  | | | | | | | End of split
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | Case 2:
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | |   (115)  all_56_13 = e0
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | | REF_CLOSE: (17), (42), (115) are inconsistent by sub-proof #1354.
% 204.26/35.23  | | | | | | | 
% 204.26/35.23  | | | | | | End of split
% 204.26/35.23  | | | | | | 
% 204.26/35.23  | | | | | End of split
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | Case 2:
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | |   (116)   ~ (all_58_12 = e2)
% 204.26/35.23  | | | | |   (117)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | REDUCE: (25), (116) imply:
% 204.26/35.23  | | | | |   (118)   ~ (all_52_7 = e2)
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | | REF_CLOSE: (2), (6), (7), (10), (14), (17), (22), (26), (32), (33),
% 204.26/35.23  | | | | |            (37), (42), (44), (55), (117), (118) are inconsistent by
% 204.26/35.23  | | | | |            sub-proof #882.
% 204.26/35.23  | | | | | 
% 204.26/35.23  | | | | End of split
% 204.26/35.23  | | | | 
% 204.26/35.23  | | | End of split
% 204.26/35.23  | | | 
% 204.26/35.23  | | Case 2:
% 204.26/35.23  | | | 
% 204.26/35.23  | | |   (119)  all_58_15 = e3
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REF_CLOSE: (4), (18), (119) are inconsistent by sub-proof #1350.
% 204.26/35.23  | | | 
% 204.26/35.23  | | End of split
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #882 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)   ~ (all_52_7 = all_52_15)
% 204.26/35.23    (3)  op(all_52_15, all_52_15) = e0
% 204.26/35.23    (4)  all_58_13 = all_52_15
% 204.26/35.23    (5)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23    (6)  op(e2, e2) = all_4_2
% 204.26/35.23    (7)   ~ (all_52_15 = e0)
% 204.26/35.23    (8)  op(e0, e0) = e0
% 204.26/35.23    (9)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.23    (10)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23    (11)   ~ (all_52_7 = e2)
% 204.26/35.23    (12)  all_56_12 = all_52_7
% 204.26/35.23    (13)  op(all_4_2, all_4_2) = e2
% 204.26/35.23    (14)   ~ (all_52_15 = all_4_2)
% 204.26/35.23    (15)  all_56_13 = all_52_15
% 204.26/35.23    (16)   ~ (all_52_7 = e0)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (5) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (17)  all_56_12 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (11), (12), (17) are inconsistent by sub-proof #1178.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (18)  all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23  | | 
% 204.26/35.23  | | BETA: splitting (18) gives:
% 204.26/35.23  | | 
% 204.26/35.23  | | Case 1:
% 204.26/35.23  | | | 
% 204.26/35.23  | | |   (19)  all_56_12 = e1
% 204.26/35.23  | | | 
% 204.26/35.23  | | | COMBINE_EQS: (12), (19) imply:
% 204.26/35.23  | | |   (20)  all_52_7 = e1
% 204.26/35.23  | | | 
% 204.26/35.23  | | | SIMP: (20) implies:
% 204.26/35.23  | | |   (21)  all_52_7 = e1
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REDUCE: (2), (21) imply:
% 204.26/35.23  | | |   (22)   ~ (all_52_15 = e1)
% 204.26/35.23  | | | 
% 204.26/35.23  | | | SIMP: (22) implies:
% 204.26/35.23  | | |   (23)   ~ (all_52_15 = e1)
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (13), (14), (15), (23)
% 204.26/35.23  | | |            are inconsistent by sub-proof #1291.
% 204.26/35.23  | | | 
% 204.26/35.23  | | Case 2:
% 204.26/35.23  | | | 
% 204.26/35.23  | | |   (24)  all_56_12 = e0
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REF_CLOSE: (12), (16), (24) are inconsistent by sub-proof #1375.
% 204.26/35.23  | | | 
% 204.26/35.23  | | End of split
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #883 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)  all_56_8 = all_10_0
% 204.26/35.23    (2)  all_56_8 = e0
% 204.26/35.23    (3)   ~ (all_10_0 = e0)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.23  |   (4)  all_10_0 = e0
% 204.26/35.23  | 
% 204.26/35.23  | SIMP: (4) implies:
% 204.26/35.23  |   (5)  all_10_0 = e0
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (3), (5) imply:
% 204.26/35.23  |   (6)  $false
% 204.26/35.23  | 
% 204.26/35.23  | CLOSE: (6) is inconsistent.
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #884 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23    (2)  all_56_9 = all_52_13
% 204.26/35.23    (3)   ~ (all_52_13 = e1)
% 204.26/35.23    (4)   ~ (all_52_13 = e2)
% 204.26/35.23    (5)   ~ (all_52_13 = e0)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (1) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (6)  all_56_9 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | COMBINE_EQS: (2), (6) imply:
% 204.26/35.23  | |   (7)  all_52_13 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | REDUCE: (4), (7) imply:
% 204.26/35.23  | |   (8)  $false
% 204.26/35.23  | | 
% 204.26/35.23  | | CLOSE: (8) is inconsistent.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (9)  all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1185.
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #885 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)  op(e3, e3) = all_6_2
% 204.26/35.23    (3)  op(e3, e3) = e1
% 204.26/35.23    (4)   ~ (all_6_2 = e1)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | GROUND_INST: instantiating (1) with all_6_2, e1, e3, e3, simplifying with (2),
% 204.26/35.23  |              (3) gives:
% 204.26/35.23  |   (5)  all_6_2 = e1
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (4), (5) imply:
% 204.26/35.23  |   (6)  $false
% 204.26/35.23  | 
% 204.26/35.23  | CLOSE: (6) is inconsistent.
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #886 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ~ (all_52_15 = e1)
% 204.26/35.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (3)  op(all_52_15, all_52_15) = e0
% 204.26/35.23    (4)  op(e2, e2) = all_4_2
% 204.26/35.23    (5)   ~ (all_52_15 = e0)
% 204.26/35.23    (6)  op(e0, e0) = e0
% 204.26/35.23    (7)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23    (8)  op(all_4_2, all_4_2) = e2
% 204.26/35.23    (9)   ~ (all_52_15 = all_4_2)
% 204.26/35.23    (10)  all_56_13 = all_52_15
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (7) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (11)  all_56_13 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | COMBINE_EQS: (10), (11) imply:
% 204.26/35.23  | |   (12)  all_52_15 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | REDUCE: (9), (12) imply:
% 204.26/35.23  | |   (13)   ~ (all_4_2 = e2)
% 204.26/35.23  | | 
% 204.26/35.23  | | SIMP: (13) implies:
% 204.26/35.23  | |   (14)   ~ (all_4_2 = e2)
% 204.26/35.23  | | 
% 204.26/35.23  | | REDUCE: (3), (12) imply:
% 204.26/35.23  | |   (15)  op(e2, e2) = e0
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (2), (4), (6), (8), (14), (15) are inconsistent by sub-proof
% 204.26/35.23  | |            #1317.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (16)  all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (1), (5), (10), (16) are inconsistent by sub-proof #959.
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #887 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)  op(all_52_13, all_52_13) = e1
% 204.26/35.23    (3)  op(e2, e2) = all_4_2
% 204.26/35.23    (4)  all_56_9 = all_52_13
% 204.26/35.23    (5)   ~ (all_52_13 = e1)
% 204.26/35.23    (6)   ~ (all_52_13 = e3)
% 204.26/35.23    (7)   ~ (all_52_13 = e0)
% 204.26/35.23    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23    (9)   ~ (all_4_2 = e1)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (8) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (10)  all_56_9 = e3
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #958.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (11)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23  | | 
% 204.26/35.23  | | BETA: splitting (11) gives:
% 204.26/35.23  | | 
% 204.26/35.23  | | Case 1:
% 204.26/35.23  | | | 
% 204.26/35.23  | | |   (12)  all_56_9 = e2
% 204.26/35.23  | | | 
% 204.26/35.23  | | | COMBINE_EQS: (4), (12) imply:
% 204.26/35.23  | | |   (13)  all_52_13 = e2
% 204.26/35.23  | | | 
% 204.26/35.23  | | | SIMP: (13) implies:
% 204.26/35.23  | | |   (14)  all_52_13 = e2
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REDUCE: (2), (14) imply:
% 204.26/35.23  | | |   (15)  op(e2, e2) = e1
% 204.26/35.23  | | | 
% 204.26/35.23  | | | GROUND_INST: instantiating (1) with all_4_2, e1, e2, e2, simplifying with
% 204.26/35.23  | | |              (3), (15) gives:
% 204.26/35.23  | | |   (16)  all_4_2 = e1
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REDUCE: (9), (16) imply:
% 204.26/35.23  | | |   (17)  $false
% 204.26/35.23  | | | 
% 204.26/35.23  | | | CLOSE: (17) is inconsistent.
% 204.26/35.23  | | | 
% 204.26/35.23  | | Case 2:
% 204.26/35.23  | | | 
% 204.26/35.23  | | |   (18)  all_56_9 = e1 | all_56_9 = e0
% 204.26/35.23  | | | 
% 204.26/35.23  | | | REF_CLOSE: (4), (5), (7), (18) are inconsistent by sub-proof #1185.
% 204.26/35.23  | | | 
% 204.26/35.23  | | End of split
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #888 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)   ~ (all_52_7 = all_52_15)
% 204.26/35.23    (3)  op(all_52_15, all_52_15) = e0
% 204.26/35.23    (4)  all_58_13 = all_52_15
% 204.26/35.23    (5)  op(e2, e2) = all_4_2
% 204.26/35.23    (6)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.23    (7)   ~ (all_52_15 = e0)
% 204.26/35.23    (8)   ~ (e2 = e1)
% 204.26/35.23    (9)  op(e0, e0) = e0
% 204.26/35.23    (10)  all_58_12 = all_52_7
% 204.26/35.23    (11)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23    (12)  op(all_4_2, all_4_2) = e2
% 204.26/35.23    (13)   ~ (all_52_15 = all_4_2)
% 204.26/35.23    (14)  all_58_12 = e1
% 204.26/35.23    (15)  all_56_13 = all_52_15
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | COMBINE_EQS: (10), (14) imply:
% 204.26/35.23  |   (16)  all_52_7 = e1
% 204.26/35.23  | 
% 204.26/35.23  | SIMP: (16) implies:
% 204.26/35.23  |   (17)  all_52_7 = e1
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (2), (17) imply:
% 204.26/35.23  |   (18)   ~ (all_52_15 = e1)
% 204.26/35.23  | 
% 204.26/35.23  | SIMP: (18) implies:
% 204.26/35.23  |   (19)   ~ (all_52_15 = e1)
% 204.26/35.23  | 
% 204.26/35.23  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 204.26/35.23  |            (15), (19) are inconsistent by sub-proof #1290.
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #889 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)  all_58_6 = e2 | all_58_12 = e2
% 204.26/35.23    (2)   ~ (all_10_0 = e2)
% 204.26/35.23    (3)  all_58_6 = all_10_0
% 204.26/35.23    (4)   ~ (e3 = e2)
% 204.26/35.23    (5)  all_58_12 = e3
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (1) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (6)  all_58_6 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #917.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (7)  all_58_12 = e2
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1210.
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #890 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)  op(e3, e3) = all_52_6
% 204.26/35.23    (3)   ~ (all_6_2 = e2)
% 204.26/35.23    (4)  op(e3, e3) = e2
% 204.26/35.23    (5)  op(e3, e3) = all_6_2
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | GROUND_INST: instantiating (1) with all_6_2, all_52_6, e3, e3, simplifying
% 204.26/35.23  |              with (2), (5) gives:
% 204.26/35.23  |   (6)  all_52_6 = all_6_2
% 204.26/35.23  | 
% 204.26/35.23  | GROUND_INST: instantiating (1) with e2, all_52_6, e3, e3, simplifying with
% 204.26/35.23  |              (2), (4) gives:
% 204.26/35.23  |   (7)  all_52_6 = e2
% 204.26/35.23  | 
% 204.26/35.23  | COMBINE_EQS: (6), (7) imply:
% 204.26/35.23  |   (8)  all_6_2 = e2
% 204.26/35.23  | 
% 204.26/35.23  | SIMP: (8) implies:
% 204.26/35.23  |   (9)  all_6_2 = e2
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (3), (9) imply:
% 204.26/35.23  |   (10)  $false
% 204.26/35.23  | 
% 204.26/35.23  | CLOSE: (10) is inconsistent.
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #891 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)  all_58_1 = all_52_9
% 204.26/35.23    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23    (4)   ~ (all_52_7 = all_52_15)
% 204.26/35.23    (5)  op(all_52_15, all_52_15) = e0
% 204.26/35.23    (6)   ~ (all_4_2 = e3)
% 204.26/35.23    (7)  all_58_13 = all_52_15
% 204.26/35.23    (8)  op(all_52_13, all_52_13) = e1
% 204.26/35.23    (9)  all_58_9 = all_52_25
% 204.26/35.23    (10)   ~ (all_6_1 = e1)
% 204.26/35.23    (11)   ~ (all_52_7 = all_6_2)
% 204.26/35.23    (12)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.23    (13)   ~ (all_52_25 = e0)
% 204.26/35.23    (14)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23    (15)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.23    (16)  all_58_7 = all_52_13
% 204.26/35.23    (17)   ~ (all_58_9 = e2)
% 204.26/35.23    (18)  op(e0, e3) = all_52_7
% 204.26/35.23    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.23    (20)  all_56_12 = all_52_7
% 204.26/35.23    (21)   ~ (all_52_25 = all_6_2)
% 204.26/35.23    (22)   ~ (all_52_9 = all_6_2)
% 204.26/35.23    (23)  op(e3, e3) = all_6_2
% 204.26/35.23    (24)  all_56_3 = all_52_25
% 204.26/35.23    (25)   ~ (all_6_1 = e2)
% 204.26/35.23    (26)  op(all_52_9, all_52_9) = e3
% 204.26/35.23    (27)  all_58_3 = all_4_2
% 204.26/35.23    (28)  all_56_13 = all_52_15
% 204.26/35.23    (29)  op(all_6_2, e3) = all_6_1
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (9), (17) imply:
% 204.26/35.23  |   (30)   ~ (all_52_25 = e2)
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (12) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (31)  all_58_9 = e1
% 204.26/35.23  | | 
% 204.26/35.23  | | COMBINE_EQS: (9), (31) imply:
% 204.26/35.23  | |   (32)  all_52_25 = e1
% 204.26/35.23  | | 
% 204.26/35.23  | | SIMP: (32) implies:
% 204.26/35.23  | |   (33)  all_52_25 = e1
% 204.26/35.23  | | 
% 204.26/35.23  | | REDUCE: (21), (33) imply:
% 204.26/35.23  | |   (34)   ~ (all_6_2 = e1)
% 204.26/35.23  | | 
% 204.26/35.23  | | SIMP: (34) implies:
% 204.26/35.23  | |   (35)   ~ (all_6_2 = e1)
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14), (16),
% 204.26/35.23  | |            (18), (19), (20), (22), (23), (25), (26), (27), (28), (29), (35)
% 204.26/35.23  | |            are inconsistent by sub-proof #892.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (36)   ~ (all_58_9 = e1)
% 204.26/35.23  | | 
% 204.26/35.23  | | REDUCE: (9), (36) imply:
% 204.26/35.23  | |   (37)   ~ (all_52_25 = e1)
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (13), (15), (24), (30), (37) are inconsistent by sub-proof #1215.
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #892 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)  all_58_1 = all_52_9
% 204.26/35.23    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23    (4)   ~ (all_52_7 = all_52_15)
% 204.26/35.23    (5)  op(all_52_15, all_52_15) = e0
% 204.26/35.23    (6)   ~ (all_4_2 = e3)
% 204.26/35.23    (7)  all_58_13 = all_52_15
% 204.26/35.23    (8)  op(all_52_13, all_52_13) = e1
% 204.26/35.23    (9)   ~ (all_6_1 = e1)
% 204.26/35.23    (10)   ~ (all_52_7 = all_6_2)
% 204.26/35.23    (11)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.23    (12)  all_58_7 = all_52_13
% 204.26/35.23    (13)  op(e0, e3) = all_52_7
% 204.26/35.23    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.23    (15)  all_56_12 = all_52_7
% 204.26/35.23    (16)   ~ (all_52_9 = all_6_2)
% 204.26/35.23    (17)  op(e3, e3) = all_6_2
% 204.26/35.23    (18)   ~ (all_6_2 = e1)
% 204.26/35.23    (19)   ~ (all_6_1 = e2)
% 204.26/35.23    (20)  op(all_52_9, all_52_9) = e3
% 204.26/35.23    (21)  all_58_3 = all_4_2
% 204.26/35.23    (22)  all_56_13 = all_52_15
% 204.26/35.23    (23)  op(all_6_2, e3) = all_6_1
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | BETA: splitting (11) gives:
% 204.26/35.23  | 
% 204.26/35.23  | Case 1:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (24)  all_56_13 = e3
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (13), (15), (17), (19), (22),
% 204.26/35.23  | |            (23), (24) are inconsistent by sub-proof #893.
% 204.26/35.23  | | 
% 204.26/35.23  | Case 2:
% 204.26/35.23  | | 
% 204.26/35.23  | |   (25)   ~ (all_56_13 = e3)
% 204.26/35.23  | | 
% 204.26/35.23  | | REDUCE: (22), (25) imply:
% 204.26/35.23  | |   (26)   ~ (all_52_15 = e3)
% 204.26/35.23  | | 
% 204.26/35.23  | | REF_CLOSE: (1), (2), (6), (7), (8), (12), (14), (16), (17), (18), (20),
% 204.26/35.23  | |            (21), (26) are inconsistent by sub-proof #1142.
% 204.26/35.23  | | 
% 204.26/35.23  | End of split
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #893 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.23    (3)   ~ (all_52_7 = all_52_15)
% 204.26/35.23    (4)  op(all_52_15, all_52_15) = e0
% 204.26/35.23    (5)   ~ (all_6_1 = e1)
% 204.26/35.23    (6)  all_56_13 = e3
% 204.26/35.23    (7)   ~ (all_52_7 = all_6_2)
% 204.26/35.23    (8)  op(e0, e3) = all_52_7
% 204.26/35.23    (9)  all_56_12 = all_52_7
% 204.26/35.23    (10)  op(e3, e3) = all_6_2
% 204.26/35.23    (11)   ~ (all_6_1 = e2)
% 204.26/35.23    (12)  all_56_13 = all_52_15
% 204.26/35.23    (13)  op(all_6_2, e3) = all_6_1
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | COMBINE_EQS: (6), (12) imply:
% 204.26/35.23  |   (14)  all_52_15 = e3
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (3), (14) imply:
% 204.26/35.23  |   (15)   ~ (all_52_7 = e3)
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (4), (14) imply:
% 204.26/35.23  |   (16)  op(e3, e3) = e0
% 204.26/35.23  | 
% 204.26/35.23  | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (13), (15), (16) are
% 204.26/35.23  |            inconsistent by sub-proof #1342.
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #894 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)  all_58_12 = e3
% 204.26/35.23    (2)  all_58_12 = e1
% 204.26/35.23    (3)   ~ (e3 = e1)
% 204.26/35.23  
% 204.26/35.23  Begin of proof
% 204.26/35.23  | 
% 204.26/35.23  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.23  |   (4)  e3 = e1
% 204.26/35.23  | 
% 204.26/35.23  | SIMP: (4) implies:
% 204.26/35.23  |   (5)  e3 = e1
% 204.26/35.23  | 
% 204.26/35.23  | REDUCE: (3), (5) imply:
% 204.26/35.23  |   (6)  $false
% 204.26/35.23  | 
% 204.26/35.23  | CLOSE: (6) is inconsistent.
% 204.26/35.23  | 
% 204.26/35.23  End of proof
% 204.26/35.23  
% 204.26/35.23  Sub-proof #895 shows that the following formulas are inconsistent:
% 204.26/35.23  ----------------------------------------------------------------
% 204.26/35.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.23    (2)   ~ (all_52_17 = all_10_2)
% 204.26/35.23    (3)  all_58_11 = e1 | all_58_15 = e1
% 204.26/35.23    (4)  all_58_11 = all_52_29
% 204.26/35.23    (5)  all_58_15 = e0
% 204.26/35.23    (6)   ~ (all_10_0 = e2)
% 204.26/35.23    (7)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.23    (8)  op(all_10_2, e1) = e3
% 204.26/35.23    (9)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 204.26/35.23    (10)  all_30_2 = all_10_2
% 204.26/35.24    (11)  all_56_8 = all_10_0
% 204.26/35.24    (12)  op(e3, e1) = all_52_17
% 204.26/35.24    (13)  all_30_0 = all_10_0
% 204.26/35.24    (14)   ~ (all_10_0 = all_10_2)
% 204.26/35.24    (15)   ~ (all_52_29 = all_10_0)
% 204.26/35.24    (16)   ~ (e1 = e0)
% 204.26/35.24    (17)  all_56_10 = all_10_2
% 204.26/35.24    (18)  op(e1, e1) = all_10_2
% 204.26/35.24    (19)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (3) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (20)  all_58_11 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (4), (20) imply:
% 204.26/35.24  | |   (21)  all_52_29 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | SIMP: (21) implies:
% 204.26/35.24  | |   (22)  all_52_29 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (15), (22) imply:
% 204.26/35.24  | |   (23)   ~ (all_10_0 = e1)
% 204.26/35.24  | | 
% 204.26/35.24  | | SIMP: (23) implies:
% 204.26/35.24  | |   (24)   ~ (all_10_0 = e1)
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (14), (17),
% 204.26/35.24  | |            (18), (19), (24) are inconsistent by sub-proof #909.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (25)  all_58_15 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (5), (25) imply:
% 204.26/35.24  | |   (26)  e1 = e0
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (16), (26) imply:
% 204.26/35.24  | |   (27)  $false
% 204.26/35.24  | | 
% 204.26/35.24  | | CLOSE: (27) is inconsistent.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #896 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)  all_58_1 = all_52_9
% 204.26/35.24    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.24    (4)   ~ (all_10_2 = e3)
% 204.26/35.24    (5)   ~ (all_52_9 = e2)
% 204.26/35.24    (6)  all_56_1 = all_52_9
% 204.26/35.24    (7)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.24    (8)  op(e1, e1) = all_10_2
% 204.26/35.24    (9)   ~ (all_52_9 = e0)
% 204.26/35.24    (10)  op(all_52_9, all_52_9) = e3
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (3) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (11)  all_58_1 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (2), (11) imply:
% 204.26/35.24  | |   (12)  all_52_9 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (10), (12) imply:
% 204.26/35.24  | |   (13)  op(e1, e1) = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (4), (8), (13) are inconsistent by sub-proof #1368.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (14)   ~ (all_58_1 = e1)
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (2), (14) imply:
% 204.26/35.24  | |   (15)   ~ (all_52_9 = e1)
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (5), (6), (7), (9), (15) are inconsistent by sub-proof #1314.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #897 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_58_14 = all_52_23
% 204.26/35.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (3)   ~ (all_52_17 = all_10_2)
% 204.26/35.24    (4)  op(all_10_2, e1) = e3
% 204.26/35.24    (5)   ~ (all_52_23 = e3)
% 204.26/35.24    (6)   ~ (all_52_19 = e3)
% 204.26/35.24    (7)  op(e3, e1) = all_52_17
% 204.26/35.24    (8)  all_58_8 = all_10_2
% 204.26/35.24    (9)   ~ (all_52_17 = e3)
% 204.26/35.24    (10)  all_58_5 = all_52_19
% 204.26/35.24    (11)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.24    (12)  all_58_4 = all_52_17
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (11) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (13)  all_58_4 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (9), (12), (13) are inconsistent by sub-proof #1302.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (14)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (14) are
% 204.26/35.24  | |            inconsistent by sub-proof #898.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #898 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_58_14 = all_52_23
% 204.26/35.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (3)   ~ (all_52_17 = all_10_2)
% 204.26/35.24    (4)  op(all_10_2, e1) = e3
% 204.26/35.24    (5)   ~ (all_52_23 = e3)
% 204.26/35.24    (6)   ~ (all_52_19 = e3)
% 204.26/35.24    (7)  op(e3, e1) = all_52_17
% 204.26/35.24    (8)  all_58_8 = all_10_2
% 204.26/35.24    (9)  all_58_5 = all_52_19
% 204.26/35.24    (10)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (10) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (11)  all_58_5 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (6), (9), (11) are inconsistent by sub-proof #1279.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (12)  all_58_8 = e3 | all_58_14 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (12) are inconsistent by
% 204.26/35.24  | |            sub-proof #899.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #899 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_58_14 = all_52_23
% 204.26/35.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (3)   ~ (all_52_17 = all_10_2)
% 204.26/35.24    (4)  all_58_8 = e3 | all_58_14 = e3
% 204.26/35.24    (5)  op(all_10_2, e1) = e3
% 204.26/35.24    (6)   ~ (all_52_23 = e3)
% 204.26/35.24    (7)  op(e3, e1) = all_52_17
% 204.26/35.24    (8)  all_58_8 = all_10_2
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (4) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (9)  all_58_8 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (8), (9) imply:
% 204.26/35.24  | |   (10)  all_10_2 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (2), (3), (5), (7), (10) are inconsistent by sub-proof #925.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (11)  all_58_14 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (6), (11) are inconsistent by sub-proof #1305.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #900 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_4 = all_6_1
% 204.26/35.24    (2)  all_56_4 = e3
% 204.26/35.24    (3)   ~ (all_6_1 = e3)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_6_1 = e3
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_6_1 = e3
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #901 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ~ (all_52_27 = e1)
% 204.26/35.24    (2)  all_56_7 = all_52_27
% 204.26/35.24    (3)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.26/35.24    (4)   ~ (all_52_27 = e0)
% 204.26/35.24    (5)   ~ (all_52_27 = e2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (3) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (6)  all_56_7 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #918.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (7)  all_56_7 = e1 | all_56_7 = e0
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #902.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #902 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_7 = e1 | all_56_7 = e0
% 204.26/35.24    (2)  all_56_7 = all_52_27
% 204.26/35.24    (3)   ~ (all_52_27 = e1)
% 204.26/35.24    (4)   ~ (all_52_27 = e0)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (1) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (5)  all_56_7 = e1
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #903.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (6)  all_56_7 = e0
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #906.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #903 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_7 = all_52_27
% 204.26/35.24    (2)  all_56_7 = e1
% 204.26/35.24    (3)   ~ (all_52_27 = e1)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_52_27 = e1
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_52_27 = e1
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #904 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)  op(all_52_7, all_52_7) = e0
% 204.26/35.24    (3)  op(e2, e3) = all_52_3
% 204.26/35.24    (4)   ~ (all_10_0 = e3)
% 204.26/35.24    (5)  op(e2, e2) = all_4_2
% 204.26/35.24    (6)  op(e3, e3) = e2
% 204.26/35.24    (7)  all_58_12 = all_52_7
% 204.26/35.24    (8)  all_58_2 = all_52_3
% 204.26/35.24    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24    (10)   ~ (e2 = e0)
% 204.26/35.24    (11)  op(e2, e3) = all_6_1
% 204.26/35.24    (12)  all_58_6 = all_10_0
% 204.26/35.24    (13)  all_58_0 = e2
% 204.26/35.24    (14)  op(e2, e2) = e3
% 204.26/35.24    (15)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.24    (16)   ~ (e3 = e2)
% 204.26/35.24    (17)   ~ (all_52_3 = all_4_2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying with (5),
% 204.26/35.24  |              (14) gives:
% 204.26/35.24  |   (18)  all_4_2 = e3
% 204.26/35.24  | 
% 204.26/35.24  | GROUND_INST: instantiating (1) with all_52_3, all_6_1, e3, e2, simplifying
% 204.26/35.24  |              with (3), (11) gives:
% 204.26/35.24  |   (19)  all_52_3 = all_6_1
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (8), (19) imply:
% 204.26/35.24  |   (20)  all_58_2 = all_6_1
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (17), (18), (19) imply:
% 204.26/35.24  |   (21)   ~ (all_6_1 = e3)
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (15), (18) imply:
% 204.26/35.24  |   (22)  op(e3, e3) = all_52_10
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (9) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (23)  all_58_0 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (13), (16), (23) are inconsistent by sub-proof #1235.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (24)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | BETA: splitting (24) gives:
% 204.26/35.24  | | 
% 204.26/35.24  | | Case 1:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (25)  all_58_2 = e3
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REF_CLOSE: (20), (21), (25) are inconsistent by sub-proof #905.
% 204.26/35.24  | | | 
% 204.26/35.24  | | Case 2:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (26)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24  | | | 
% 204.26/35.24  | | | BETA: splitting (26) gives:
% 204.26/35.24  | | | 
% 204.26/35.24  | | | Case 1:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (27)  all_58_6 = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REF_CLOSE: (4), (12), (27) are inconsistent by sub-proof #922.
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | Case 2:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (28)  all_58_12 = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | COMBINE_EQS: (7), (28) imply:
% 204.26/35.24  | | | |   (29)  all_52_7 = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | SIMP: (29) implies:
% 204.26/35.24  | | | |   (30)  all_52_7 = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REDUCE: (2), (30) imply:
% 204.26/35.24  | | | |   (31)  op(e3, e3) = e0
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | GROUND_INST: instantiating (1) with e2, all_52_10, e3, e3, simplifying
% 204.26/35.24  | | | |              with (6), (22) gives:
% 204.26/35.24  | | | |   (32)  all_52_10 = e2
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | GROUND_INST: instantiating (1) with e0, all_52_10, e3, e3, simplifying
% 204.26/35.24  | | | |              with (22), (31) gives:
% 204.26/35.24  | | | |   (33)  all_52_10 = e0
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | COMBINE_EQS: (32), (33) imply:
% 204.26/35.24  | | | |   (34)  e2 = e0
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | SIMP: (34) implies:
% 204.26/35.24  | | | |   (35)  e2 = e0
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REDUCE: (10), (35) imply:
% 204.26/35.24  | | | |   (36)  $false
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | CLOSE: (36) is inconsistent.
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | End of split
% 204.26/35.24  | | | 
% 204.26/35.24  | | End of split
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #905 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_58_2 = all_6_1
% 204.26/35.24    (2)  all_58_2 = e3
% 204.26/35.24    (3)   ~ (all_6_1 = e3)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_6_1 = e3
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_6_1 = e3
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #906 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_7 = all_52_27
% 204.26/35.24    (2)  all_56_7 = e0
% 204.26/35.24    (3)   ~ (all_52_27 = e0)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_52_27 = e0
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_52_27 = e0
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #907 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)  all_58_0 = all_6_2
% 204.26/35.24    (3)   ~ (all_10_0 = e3)
% 204.26/35.24    (4)  op(e2, e2) = all_4_2
% 204.26/35.24    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.24    (6)   ~ (all_10_0 = e2)
% 204.26/35.24    (7)   ~ (all_6_2 = e3)
% 204.26/35.24    (8)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.24    (9)  op(all_6_2, all_6_2) = e3
% 204.26/35.24    (10)  all_58_2 = all_52_3
% 204.26/35.24    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24    (12)  op(all_52_3, all_52_3) = e2
% 204.26/35.24    (13)  all_58_6 = all_10_0
% 204.26/35.24    (14)  op(e3, e3) = all_6_2
% 204.26/35.24    (15)   ~ (e3 = e2)
% 204.26/35.24    (16)   ~ (all_52_3 = all_4_2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (11) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (17)  all_58_0 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (2), (17) imply:
% 204.26/35.24  | |   (18)  all_6_2 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (7), (18) imply:
% 204.26/35.24  | |   (19)  $false
% 204.26/35.24  | | 
% 204.26/35.24  | | CLOSE: (19) is inconsistent.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (20)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | BETA: splitting (5) gives:
% 204.26/35.24  | | 
% 204.26/35.24  | | Case 1:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (21)  all_58_2 = e3
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REF_CLOSE: (1), (4), (9), (10), (12), (14), (16), (21) are inconsistent by
% 204.26/35.24  | | |            sub-proof #1159.
% 204.26/35.24  | | | 
% 204.26/35.24  | | Case 2:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (22)   ~ (all_58_2 = e3)
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REDUCE: (10), (22) imply:
% 204.26/35.24  | | |   (23)   ~ (all_52_3 = e3)
% 204.26/35.24  | | | 
% 204.26/35.24  | | | BETA: splitting (20) gives:
% 204.26/35.24  | | | 
% 204.26/35.24  | | | Case 1:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (24)  all_58_2 = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REF_CLOSE: (10), (23), (24) are inconsistent by sub-proof #1369.
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | Case 2:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (25)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | BETA: splitting (25) gives:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | Case 1:
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | |   (26)  all_58_6 = e3
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | REF_CLOSE: (3), (13), (26) are inconsistent by sub-proof #922.
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | Case 2:
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | |   (27)  all_58_12 = e3
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | REF_CLOSE: (1), (4), (6), (8), (10), (12), (13), (15), (16), (27) are
% 204.26/35.24  | | | | |            inconsistent by sub-proof #916.
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | End of split
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | End of split
% 204.26/35.24  | | | 
% 204.26/35.24  | | End of split
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #908 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)   ~ (all_52_7 = all_10_0)
% 204.26/35.24    (3)   ~ (all_52_17 = all_10_2)
% 204.26/35.24    (4)   ~ (all_10_0 = e2)
% 204.26/35.24    (5)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.24    (6)  op(all_10_2, e1) = e3
% 204.26/35.24    (7)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 204.26/35.24    (8)  all_30_2 = all_10_2
% 204.26/35.24    (9)  all_56_8 = all_10_0
% 204.26/35.24    (10)  op(e3, e1) = all_52_17
% 204.26/35.24    (11)  all_30_0 = all_10_0
% 204.26/35.24    (12)   ~ (all_10_0 = all_10_2)
% 204.26/35.24    (13)  all_52_7 = e1
% 204.26/35.24    (14)  all_56_10 = all_10_2
% 204.26/35.24    (15)  op(e1, e1) = all_10_2
% 204.26/35.24    (16)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (2), (13) imply:
% 204.26/35.24  |   (17)   ~ (all_10_0 = e1)
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (17) implies:
% 204.26/35.24  |   (18)   ~ (all_10_0 = e1)
% 204.26/35.24  | 
% 204.26/35.24  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 204.26/35.24  |            (15), (16), (18) are inconsistent by sub-proof #909.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #909 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)   ~ (all_52_17 = all_10_2)
% 204.26/35.24    (3)   ~ (all_10_0 = e1)
% 204.26/35.24    (4)   ~ (all_10_0 = e2)
% 204.26/35.24    (5)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.24    (6)  op(all_10_2, e1) = e3
% 204.26/35.24    (7)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e2)
% 204.26/35.24    (8)  all_30_2 = all_10_2
% 204.26/35.24    (9)  all_56_8 = all_10_0
% 204.26/35.24    (10)  op(e3, e1) = all_52_17
% 204.26/35.24    (11)  all_30_0 = all_10_0
% 204.26/35.24    (12)   ~ (all_10_0 = all_10_2)
% 204.26/35.24    (13)  all_56_10 = all_10_2
% 204.26/35.24    (14)  op(e1, e1) = all_10_2
% 204.26/35.24    (15)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (5) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (16)  all_56_8 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (4), (9), (16) are inconsistent by sub-proof #915.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (17)  all_56_8 = e1 | all_56_8 = e0
% 204.26/35.24  | | 
% 204.26/35.24  | | BETA: splitting (17) gives:
% 204.26/35.24  | | 
% 204.26/35.24  | | Case 1:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (18)  all_56_8 = e1
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REF_CLOSE: (3), (9), (18) are inconsistent by sub-proof #914.
% 204.26/35.24  | | | 
% 204.26/35.24  | | Case 2:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (19)  all_56_8 = e0
% 204.26/35.24  | | | 
% 204.26/35.24  | | | COMBINE_EQS: (9), (19) imply:
% 204.26/35.24  | | |   (20)  all_10_0 = e0
% 204.26/35.24  | | | 
% 204.26/35.24  | | | SIMP: (20) implies:
% 204.26/35.24  | | |   (21)  all_10_0 = e0
% 204.26/35.24  | | | 
% 204.26/35.24  | | | COMBINE_EQS: (11), (21) imply:
% 204.26/35.24  | | |   (22)  all_30_0 = e0
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REDUCE: (12), (21) imply:
% 204.26/35.24  | | |   (23)   ~ (all_10_2 = e0)
% 204.26/35.24  | | | 
% 204.26/35.24  | | | SIMP: (23) implies:
% 204.26/35.24  | | |   (24)   ~ (all_10_2 = e0)
% 204.26/35.24  | | | 
% 204.26/35.24  | | | BETA: splitting (7) gives:
% 204.26/35.24  | | | 
% 204.26/35.24  | | | Case 1:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (25)   ~ (all_30_2 = e2)
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REDUCE: (8), (25) imply:
% 204.26/35.24  | | | |   (26)   ~ (all_10_2 = e2)
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | BETA: splitting (15) gives:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | Case 1:
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | |   (27)  all_56_10 = e3
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | COMBINE_EQS: (13), (27) imply:
% 204.26/35.24  | | | | |   (28)  all_10_2 = e3
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | SIMP: (28) implies:
% 204.26/35.24  | | | | |   (29)  all_10_2 = e3
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | REF_CLOSE: (1), (2), (6), (10), (29) are inconsistent by sub-proof
% 204.26/35.24  | | | | |            #925.
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | Case 2:
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | |   (30)   ~ (all_56_10 = e3)
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | REDUCE: (13), (30) imply:
% 204.26/35.24  | | | | |   (31)   ~ (all_10_2 = e3)
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | | REF_CLOSE: (1), (6), (13), (14), (15), (24), (26), (31) are
% 204.26/35.24  | | | | |            inconsistent by sub-proof #910.
% 204.26/35.24  | | | | | 
% 204.26/35.24  | | | | End of split
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | Case 2:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (32)   ~ (all_30_0 = e0)
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REDUCE: (22), (32) imply:
% 204.26/35.24  | | | |   (33)  $false
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | CLOSE: (33) is inconsistent.
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | End of split
% 204.26/35.24  | | | 
% 204.26/35.24  | | End of split
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #910 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)   ~ (all_10_2 = e0)
% 204.26/35.24    (3)  op(all_10_2, e1) = e3
% 204.26/35.24    (4)   ~ (all_10_2 = e3)
% 204.26/35.24    (5)   ~ (all_10_2 = e2)
% 204.26/35.24    (6)  all_56_10 = all_10_2
% 204.26/35.24    (7)  op(e1, e1) = all_10_2
% 204.26/35.24    (8)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (8) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (9)  all_56_10 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #913.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (10)   ~ (all_56_10 = e3)
% 204.26/35.24  | |   (11)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.24  | | 
% 204.26/35.24  | | BETA: splitting (11) gives:
% 204.26/35.24  | | 
% 204.26/35.24  | | Case 1:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (12)  all_56_10 = e2
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #912.
% 204.26/35.24  | | | 
% 204.26/35.24  | | Case 2:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (13)  all_56_10 = e1 | all_56_10 = e0
% 204.26/35.24  | | | 
% 204.26/35.24  | | | BETA: splitting (13) gives:
% 204.26/35.24  | | | 
% 204.26/35.24  | | | Case 1:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (14)  all_56_10 = e1
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | COMBINE_EQS: (6), (14) imply:
% 204.26/35.24  | | | |   (15)  all_10_2 = e1
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | SIMP: (15) implies:
% 204.26/35.24  | | | |   (16)  all_10_2 = e1
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REDUCE: (3), (16) imply:
% 204.26/35.24  | | | |   (17)  op(e1, e1) = e3
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REF_CLOSE: (1), (4), (7), (17) are inconsistent by sub-proof #1368.
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | Case 2:
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | |   (18)  all_56_10 = e0
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | | REF_CLOSE: (2), (6), (18) are inconsistent by sub-proof #911.
% 204.26/35.24  | | | | 
% 204.26/35.24  | | | End of split
% 204.26/35.24  | | | 
% 204.26/35.24  | | End of split
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #911 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_10 = all_10_2
% 204.26/35.24    (2)  all_56_10 = e0
% 204.26/35.24    (3)   ~ (all_10_2 = e0)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_10_2 = e0
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_10_2 = e0
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #912 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_10 = all_10_2
% 204.26/35.24    (2)  all_56_10 = e2
% 204.26/35.24    (3)   ~ (all_10_2 = e2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_10_2 = e2
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_10_2 = e2
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #913 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_10 = all_10_2
% 204.26/35.24    (2)  all_56_10 = e3
% 204.26/35.24    (3)   ~ (all_10_2 = e3)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_10_2 = e3
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_10_2 = e3
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #914 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_8 = all_10_0
% 204.26/35.24    (2)  all_56_8 = e1
% 204.26/35.24    (3)   ~ (all_10_0 = e1)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_10_0 = e1
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_10_0 = e1
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #915 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_8 = all_10_0
% 204.26/35.24    (2)  all_56_8 = e2
% 204.26/35.24    (3)   ~ (all_10_0 = e2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_10_0 = e2
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_10_0 = e2
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #916 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)  op(e2, e2) = all_4_2
% 204.26/35.24    (3)   ~ (all_10_0 = e2)
% 204.26/35.24    (4)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.24    (5)  all_58_2 = all_52_3
% 204.26/35.24    (6)  op(all_52_3, all_52_3) = e2
% 204.26/35.24    (7)  all_58_6 = all_10_0
% 204.26/35.24    (8)   ~ (e3 = e2)
% 204.26/35.24    (9)  all_58_12 = e3
% 204.26/35.24    (10)   ~ (all_52_3 = all_4_2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (4) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (11)  all_58_2 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (5), (11) imply:
% 204.26/35.24  | |   (12)  all_52_3 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | SIMP: (12) implies:
% 204.26/35.24  | |   (13)  all_52_3 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (10), (13) imply:
% 204.26/35.24  | |   (14)   ~ (all_4_2 = e2)
% 204.26/35.24  | | 
% 204.26/35.24  | | SIMP: (14) implies:
% 204.26/35.24  | |   (15)   ~ (all_4_2 = e2)
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (6), (13) imply:
% 204.26/35.24  | |   (16)  op(e2, e2) = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e2, simplifying with
% 204.26/35.24  | |              (2), (16) gives:
% 204.26/35.24  | |   (17)  all_4_2 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (15), (17) imply:
% 204.26/35.24  | |   (18)  $false
% 204.26/35.24  | | 
% 204.26/35.24  | | CLOSE: (18) is inconsistent.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (19)  all_58_6 = e2 | all_58_12 = e2
% 204.26/35.24  | | 
% 204.26/35.24  | | BETA: splitting (19) gives:
% 204.26/35.24  | | 
% 204.26/35.24  | | Case 1:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (20)  all_58_6 = e2
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REF_CLOSE: (3), (7), (20) are inconsistent by sub-proof #917.
% 204.26/35.24  | | | 
% 204.26/35.24  | | Case 2:
% 204.26/35.24  | | | 
% 204.26/35.24  | | |   (21)  all_58_12 = e2
% 204.26/35.24  | | | 
% 204.26/35.24  | | | REF_CLOSE: (8), (9), (21) are inconsistent by sub-proof #1210.
% 204.26/35.24  | | | 
% 204.26/35.24  | | End of split
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #917 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_58_6 = all_10_0
% 204.26/35.24    (2)  all_58_6 = e2
% 204.26/35.24    (3)   ~ (all_10_0 = e2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_10_0 = e2
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_10_0 = e2
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #918 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)  all_56_7 = all_52_27
% 204.26/35.24    (2)  all_56_7 = e2
% 204.26/35.24    (3)   ~ (all_52_27 = e2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.24  |   (4)  all_52_27 = e2
% 204.26/35.24  | 
% 204.26/35.24  | SIMP: (4) implies:
% 204.26/35.24  |   (5)  all_52_27 = e2
% 204.26/35.24  | 
% 204.26/35.24  | REDUCE: (3), (5) imply:
% 204.26/35.24  |   (6)  $false
% 204.26/35.24  | 
% 204.26/35.24  | CLOSE: (6) is inconsistent.
% 204.26/35.24  | 
% 204.26/35.24  End of proof
% 204.26/35.24  
% 204.26/35.24  Sub-proof #919 shows that the following formulas are inconsistent:
% 204.26/35.24  ----------------------------------------------------------------
% 204.26/35.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.24    (2)  op(all_52_7, all_52_7) = e0
% 204.26/35.24    (3)  all_58_0 = all_6_2
% 204.26/35.24    (4)   ~ (all_10_0 = e3)
% 204.26/35.24    (5)  op(e2, e2) = all_4_2
% 204.26/35.24    (6)  op(e0, e0) = all_14_2
% 204.26/35.24    (7)   ~ (all_6_2 = e3)
% 204.26/35.24    (8)  op(all_6_2, all_6_2) = e3
% 204.26/35.24    (9)  all_58_12 = all_52_7
% 204.26/35.24    (10)   ~ (all_52_7 = all_14_2)
% 204.26/35.24    (11)  all_58_2 = all_52_3
% 204.26/35.24    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24    (13)  op(all_52_3, all_52_3) = e2
% 204.26/35.24    (14)  all_58_6 = all_10_0
% 204.26/35.24    (15)  op(e3, e3) = all_6_2
% 204.26/35.24    (16)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.24    (17)   ~ (all_52_3 = all_4_2)
% 204.26/35.24  
% 204.26/35.24  Begin of proof
% 204.26/35.24  | 
% 204.26/35.24  | BETA: splitting (12) gives:
% 204.26/35.24  | 
% 204.26/35.24  | Case 1:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (18)  all_58_0 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | COMBINE_EQS: (3), (18) imply:
% 204.26/35.24  | |   (19)  all_6_2 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REDUCE: (7), (19) imply:
% 204.26/35.24  | |   (20)  $false
% 204.26/35.24  | | 
% 204.26/35.24  | | CLOSE: (20) is inconsistent.
% 204.26/35.24  | | 
% 204.26/35.24  | Case 2:
% 204.26/35.24  | | 
% 204.26/35.24  | |   (21)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.24  | | 
% 204.26/35.24  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 204.26/35.24  | |            (16), (17), (21) are inconsistent by sub-proof #920.
% 204.26/35.24  | | 
% 204.26/35.24  | End of split
% 204.26/35.24  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #920 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.25    (2)  op(all_52_7, all_52_7) = e0
% 204.26/35.25    (3)   ~ (all_10_0 = e3)
% 204.26/35.25    (4)  op(e2, e2) = all_4_2
% 204.26/35.25    (5)  op(e0, e0) = all_14_2
% 204.26/35.25    (6)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.25    (7)  op(all_6_2, all_6_2) = e3
% 204.26/35.25    (8)  all_58_12 = all_52_7
% 204.26/35.25    (9)   ~ (all_52_7 = all_14_2)
% 204.26/35.25    (10)  all_58_2 = all_52_3
% 204.26/35.25    (11)  op(all_52_3, all_52_3) = e2
% 204.26/35.25    (12)  all_58_6 = all_10_0
% 204.26/35.25    (13)  op(e3, e3) = all_6_2
% 204.26/35.25    (14)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.25    (15)   ~ (all_52_3 = all_4_2)
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | BETA: splitting (14) gives:
% 204.26/35.25  | 
% 204.26/35.25  | Case 1:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (16)  all_58_12 = e3
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (13), (16) are inconsistent by
% 204.26/35.25  | |            sub-proof #1371.
% 204.26/35.25  | | 
% 204.26/35.25  | Case 2:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (17)   ~ (all_58_12 = e3)
% 204.26/35.25  | | 
% 204.26/35.25  | | REDUCE: (8), (17) imply:
% 204.26/35.25  | |   (18)   ~ (all_52_7 = e3)
% 204.26/35.25  | | 
% 204.26/35.25  | | BETA: splitting (6) gives:
% 204.26/35.25  | | 
% 204.26/35.25  | | Case 1:
% 204.26/35.25  | | | 
% 204.26/35.25  | | |   (19)  all_58_2 = e3
% 204.26/35.25  | | | 
% 204.26/35.25  | | | REF_CLOSE: (1), (4), (7), (10), (11), (13), (15), (19) are inconsistent by
% 204.26/35.25  | | |            sub-proof #1159.
% 204.26/35.25  | | | 
% 204.26/35.25  | | Case 2:
% 204.26/35.25  | | | 
% 204.26/35.25  | | |   (20)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.25  | | | 
% 204.26/35.25  | | | REF_CLOSE: (3), (8), (12), (18), (20) are inconsistent by sub-proof #921.
% 204.26/35.25  | | | 
% 204.26/35.25  | | End of split
% 204.26/35.25  | | 
% 204.26/35.25  | End of split
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #921 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ~ (all_10_0 = e3)
% 204.26/35.25    (2)  all_58_12 = all_52_7
% 204.26/35.25    (3)   ~ (all_52_7 = e3)
% 204.26/35.25    (4)  all_58_6 = all_10_0
% 204.26/35.25    (5)  all_58_6 = e3 | all_58_12 = e3
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | BETA: splitting (5) gives:
% 204.26/35.25  | 
% 204.26/35.25  | Case 1:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (6)  all_58_6 = e3
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #922.
% 204.26/35.25  | | 
% 204.26/35.25  | Case 2:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (7)  all_58_12 = e3
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #1367.
% 204.26/35.25  | | 
% 204.26/35.25  | End of split
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #922 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)  all_58_6 = all_10_0
% 204.26/35.25    (2)  all_58_6 = e3
% 204.26/35.25    (3)   ~ (all_10_0 = e3)
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.25  |   (4)  all_10_0 = e3
% 204.26/35.25  | 
% 204.26/35.25  | SIMP: (4) implies:
% 204.26/35.25  |   (5)  all_10_0 = e3
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (3), (5) imply:
% 204.26/35.25  |   (6)  $false
% 204.26/35.25  | 
% 204.26/35.25  | CLOSE: (6) is inconsistent.
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #923 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.25    (3)  op(all_52_7, all_52_7) = e0
% 204.26/35.25    (4)  op(e0, e2) = all_52_15
% 204.26/35.25    (5)   ~ (all_52_7 = all_52_15)
% 204.26/35.25    (6)  all_58_13 = all_52_15
% 204.26/35.25    (7)  op(e2, e2) = all_4_2
% 204.26/35.25    (8)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.25    (9)   ~ (all_10_0 = e2)
% 204.26/35.25    (10)   ~ (all_4_1 = e1)
% 204.26/35.25    (11)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.25    (12)   ~ (e2 = e1)
% 204.26/35.25    (13)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.25    (14)  all_58_12 = all_52_7
% 204.26/35.25    (15)  all_58_2 = all_52_3
% 204.26/35.25    (16)  op(all_4_2, e2) = all_4_1
% 204.26/35.25    (17)  op(all_52_3, all_52_3) = e2
% 204.26/35.25    (18)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.25    (19)  all_58_6 = all_10_0
% 204.26/35.25    (20)   ~ (all_52_15 = all_4_2)
% 204.26/35.25    (21)  all_52_23 = e3
% 204.26/35.25    (22)  all_56_13 = all_52_15
% 204.26/35.25    (23)   ~ (all_52_3 = all_4_2)
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | SIMP: (21) implies:
% 204.26/35.25  |   (24)  all_52_23 = e3
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (1), (24) imply:
% 204.26/35.25  |   (25)   ~ (all_52_15 = e3)
% 204.26/35.25  | 
% 204.26/35.25  | BETA: splitting (11) gives:
% 204.26/35.25  | 
% 204.26/35.25  | Case 1:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (26)  all_56_13 = e3
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (22), (25), (26) are inconsistent by sub-proof #1201.
% 204.26/35.25  | | 
% 204.26/35.25  | Case 2:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (27)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 204.26/35.25  | |            (15), (16), (17), (18), (19), (20), (22), (23), (27) are
% 204.26/35.25  | |            inconsistent by sub-proof #924.
% 204.26/35.25  | | 
% 204.26/35.25  | End of split
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #924 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.25    (2)  op(all_52_7, all_52_7) = e0
% 204.26/35.25    (3)  op(e0, e2) = all_52_15
% 204.26/35.25    (4)   ~ (all_52_7 = all_52_15)
% 204.26/35.25    (5)  all_58_13 = all_52_15
% 204.26/35.25    (6)  op(e2, e2) = all_4_2
% 204.26/35.25    (7)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.26/35.25    (8)   ~ (all_10_0 = e2)
% 204.26/35.25    (9)   ~ (all_4_1 = e1)
% 204.26/35.25    (10)   ~ (e2 = e1)
% 204.26/35.25    (11)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.25    (12)  all_58_12 = all_52_7
% 204.26/35.25    (13)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.25    (14)  all_58_2 = all_52_3
% 204.26/35.25    (15)  op(all_4_2, e2) = all_4_1
% 204.26/35.25    (16)  op(all_52_3, all_52_3) = e2
% 204.26/35.25    (17)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.26/35.25    (18)  all_58_6 = all_10_0
% 204.26/35.25    (19)   ~ (all_52_15 = all_4_2)
% 204.26/35.25    (20)  all_56_13 = all_52_15
% 204.26/35.25    (21)   ~ (all_52_3 = all_4_2)
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | BETA: splitting (7) gives:
% 204.26/35.25  | 
% 204.26/35.25  | Case 1:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (22)  all_58_12 = e2
% 204.26/35.25  | | 
% 204.26/35.25  | | COMBINE_EQS: (12), (22) imply:
% 204.26/35.25  | |   (23)  all_52_7 = e2
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (13), (15), (17), (19),
% 204.26/35.25  | |            (20), (22), (23) are inconsistent by sub-proof #1196.
% 204.26/35.25  | | 
% 204.26/35.25  | Case 2:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (24)   ~ (all_58_12 = e2)
% 204.26/35.25  | | 
% 204.26/35.25  | | REDUCE: (12), (24) imply:
% 204.26/35.25  | |   (25)   ~ (all_52_7 = e2)
% 204.26/35.25  | | 
% 204.26/35.25  | | BETA: splitting (11) gives:
% 204.26/35.25  | | 
% 204.26/35.25  | | Case 1:
% 204.26/35.25  | | | 
% 204.26/35.25  | | |   (26)  all_58_2 = e2
% 204.26/35.25  | | | 
% 204.26/35.25  | | | COMBINE_EQS: (14), (26) imply:
% 204.26/35.25  | | |   (27)  all_52_3 = e2
% 204.26/35.25  | | | 
% 204.26/35.25  | | | REF_CLOSE: (1), (6), (16), (21), (27) are inconsistent by sub-proof #1157.
% 204.26/35.25  | | | 
% 204.26/35.25  | | Case 2:
% 204.26/35.25  | | | 
% 204.26/35.25  | | |   (28)  all_58_6 = e2 | all_58_12 = e2
% 204.26/35.25  | | | 
% 204.26/35.25  | | | BETA: splitting (28) gives:
% 204.26/35.25  | | | 
% 204.26/35.25  | | | Case 1:
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | |   (29)  all_58_6 = e2
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | COMBINE_EQS: (18), (29) imply:
% 204.26/35.25  | | | |   (30)  all_10_0 = e2
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (8), (30) imply:
% 204.26/35.25  | | | |   (31)  $false
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | CLOSE: (31) is inconsistent.
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | Case 2:
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | |   (32)  all_58_12 = e2
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | COMBINE_EQS: (12), (32) imply:
% 204.26/35.25  | | | |   (33)  all_52_7 = e2
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (25), (33) imply:
% 204.26/35.25  | | | |   (34)  $false
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | CLOSE: (34) is inconsistent.
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | End of split
% 204.26/35.25  | | | 
% 204.26/35.25  | | End of split
% 204.26/35.25  | | 
% 204.26/35.25  | End of split
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #925 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.25    (2)   ~ (all_52_17 = all_10_2)
% 204.26/35.25    (3)  op(all_10_2, e1) = e3
% 204.26/35.25    (4)  all_10_2 = e3
% 204.26/35.25    (5)  op(e3, e1) = all_52_17
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (2), (4) imply:
% 204.26/35.25  |   (6)   ~ (all_52_17 = e3)
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (3), (4) imply:
% 204.26/35.25  |   (7)  op(e3, e1) = e3
% 204.26/35.25  | 
% 204.26/35.25  | GROUND_INST: instantiating (1) with all_52_17, e3, e1, e3, simplifying with
% 204.26/35.25  |              (5), (7) gives:
% 204.26/35.25  |   (8)  all_52_17 = e3
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (6), (8) imply:
% 204.26/35.25  |   (9)  $false
% 204.26/35.25  | 
% 204.26/35.25  | CLOSE: (9) is inconsistent.
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #926 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)  all_56_8 = all_10_0
% 204.26/35.25    (2)  all_56_8 = e3
% 204.26/35.25    (3)   ~ (all_10_0 = e3)
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | COMBINE_EQS: (1), (2) imply:
% 204.26/35.25  |   (4)  all_10_0 = e3
% 204.26/35.25  | 
% 204.26/35.25  | SIMP: (4) implies:
% 204.26/35.25  |   (5)  all_10_0 = e3
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (3), (5) imply:
% 204.26/35.25  |   (6)  $false
% 204.26/35.25  | 
% 204.26/35.25  | CLOSE: (6) is inconsistent.
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #927 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.25    (2)  all_4_0 = e1
% 204.26/35.25    (3)  all_38_2 = all_4_2
% 204.26/35.25    (4)  op(e2, e2) = all_4_2
% 204.26/35.25    (5)  all_56_5 = all_4_2
% 204.26/35.25    (6)  op(all_4_2, e2) = e3
% 204.26/35.25    (7)   ~ (all_38_1 = e3) |  ~ (all_38_2 = e0)
% 204.26/35.25    (8)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.25    (9)   ~ (all_52_9 = all_4_2)
% 204.26/35.25    (10)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.25    (11)   ~ (all_4_0 = all_4_2)
% 204.26/35.25    (12)  op(e3, e2) = all_52_9
% 204.26/35.25    (13)  all_38_1 = e3
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (2), (11) imply:
% 204.26/35.25  |   (14)   ~ (all_4_2 = e1)
% 204.26/35.25  | 
% 204.26/35.25  | SIMP: (14) implies:
% 204.26/35.25  |   (15)   ~ (all_4_2 = e1)
% 204.26/35.25  | 
% 204.26/35.25  | BETA: splitting (7) gives:
% 204.26/35.25  | 
% 204.26/35.25  | Case 1:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (16)   ~ (all_38_1 = e3)
% 204.26/35.25  | | 
% 204.26/35.25  | | REDUCE: (13), (16) imply:
% 204.26/35.25  | |   (17)  $false
% 204.26/35.25  | | 
% 204.26/35.25  | | CLOSE: (17) is inconsistent.
% 204.26/35.25  | | 
% 204.26/35.25  | Case 2:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (18)   ~ (all_38_2 = e0)
% 204.26/35.25  | | 
% 204.26/35.25  | | REDUCE: (3), (18) imply:
% 204.26/35.25  | |   (19)   ~ (all_4_2 = e0)
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (12), (15), (19) are
% 204.26/35.25  | |            inconsistent by sub-proof #973.
% 204.26/35.25  | | 
% 204.26/35.25  | End of split
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #928 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)   ~ (all_52_15 = all_52_23)
% 204.26/35.25    (2)   ~ (all_52_25 = all_52_27)
% 204.26/35.25    (3)  all_58_14 = all_52_23
% 204.26/35.25    (4)   ~ (e3 = e1)
% 204.26/35.25    (5)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.26/35.25    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.25    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.25    (8)   ~ (all_52_5 = all_52_13)
% 204.26/35.25    (9)  all_58_1 = all_52_9
% 204.26/35.25    (10)   ~ (all_52_9 = all_52_13)
% 204.26/35.25    (11)   ~ (e3 = e0)
% 204.26/35.25    (12)  op(e2, e3) = all_52_3
% 204.26/35.25    (13)   ~ (all_4_0 = e1)
% 204.26/35.25    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.25    (15)   ~ (all_52_7 = all_52_15)
% 204.26/35.25    (16)   ~ (all_52_3 = all_52_19)
% 204.26/35.25    (17)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.25    (18)   ~ (all_52_17 = all_52_25)
% 204.26/35.25    (19)   ~ (all_52_3 = all_6_2)
% 204.26/35.25    (20)  all_58_0 = all_6_2
% 204.26/35.25    (21)  all_56_4 = all_52_3
% 204.26/35.25    (22)   ~ (all_52_17 = all_10_2)
% 204.26/35.25    (23)  op(e3, e0) = all_52_25
% 204.26/35.25    (24)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.25    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.26/35.25    (26)   ~ (all_52_27 = all_52_29)
% 204.26/35.25    (27)  all_58_13 = all_52_15
% 204.26/35.25    (28)  op(all_10_2, all_10_2) = all_52_20
% 204.26/35.25    (29)  all_58_9 = all_52_25
% 204.26/35.25    (30)   ~ (all_6_1 = e1)
% 204.26/35.25    (31)   ~ (all_52_29 = all_14_2)
% 204.26/35.25    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.25    (33)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.25    (34)  op(e1, e3) = all_52_5
% 204.26/35.25    (35)   ~ (all_6_2 = all_4_0)
% 204.26/35.25    (36)  all_32_2 = all_4_2
% 204.26/35.25    (37)  op(e2, e2) = all_4_2
% 204.26/35.25    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.25    (39)   ~ (all_52_3 = all_52_5)
% 204.26/35.25    (40)  all_58_11 = all_52_29
% 204.26/35.25    (41)  all_56_5 = all_4_2
% 204.26/35.25    (42)   ~ (all_52_25 = all_14_2)
% 204.26/35.25    (43)   ~ (all_52_9 = all_52_15)
% 204.26/35.25    (44)   ~ (all_52_3 = all_52_27)
% 204.26/35.25    (45)  op(all_10_2, e1) = all_10_1
% 204.26/35.25    (46)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.25    (47)   ~ (all_52_7 = all_6_2)
% 204.26/35.25    (48)  all_58_2 = all_4_0
% 204.26/35.25    (49)  op(e0, e0) = all_14_2
% 204.26/35.25    (50)  all_56_15 = all_14_2
% 204.26/35.25    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.25    (52)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.26/35.25    (53)  op(all_4_2, e2) = e3
% 204.26/35.25    (54)   ~ (all_58_15 = e0)
% 204.26/35.25    (55)  all_56_11 = all_52_29
% 204.26/35.25    (56)   ~ (all_4_1 = e1)
% 204.26/35.25    (57)   ~ (all_4_0 = e3)
% 204.26/35.25    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.25    (59)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.25    (60)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.25    (61)  all_56_9 = all_52_13
% 204.26/35.25    (62)   ~ (e2 = e1)
% 204.26/35.25    (63)   ~ (all_52_13 = all_10_2)
% 204.26/35.25    (64)   ~ (all_6_0 = e1)
% 204.26/35.25    (65)  all_58_10 = all_52_27
% 204.26/35.25    (66)  all_56_8 = all_52_5
% 204.26/35.25    (67)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.25    (68)  op(all_52_15, all_52_15) = all_52_14
% 204.26/35.25    (69)   ~ (all_52_19 = all_52_23)
% 204.26/35.25    (70)   ~ (all_52_25 = all_52_29)
% 204.26/35.25    (71)   ~ (all_52_29 = all_10_2)
% 204.26/35.25    (72)  all_58_7 = all_52_13
% 204.26/35.25    (73)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.26/35.25    (74)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.26/35.25    (75)   ~ (all_52_5 = all_52_7)
% 204.26/35.25    (76)  all_58_12 = all_52_7
% 204.26/35.25    (77)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.25    (78)   ~ (all_52_7 = all_14_2)
% 204.26/35.25    (79)  all_58_2 = all_52_3
% 204.26/35.25    (80)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.25    (81)  all_56_2 = all_52_17
% 204.26/35.25    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.25    (83)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.25    (84)  op(all_4_0, all_4_0) = all_52_2
% 204.26/35.25    (85)  op(e3, all_6_1) = all_6_0
% 204.26/35.25    (86)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.25    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.26/35.25    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.25    (89)   ~ (e2 = e0)
% 204.26/35.25    (90)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.25    (91)  op(all_4_2, e2) = all_4_1
% 204.26/35.25    (92)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.25    (93)   ~ (all_52_5 = all_52_29)
% 204.26/35.25    (94)  all_56_6 = all_52_19
% 204.26/35.25    (95)   ~ (all_52_15 = all_14_2)
% 204.26/35.25    (96)   ~ (all_52_19 = all_52_27)
% 204.26/35.25    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.25    (98)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.25    (99)  all_56_4 = all_4_0
% 204.26/35.25    (100)   ~ (all_6_0 = e2)
% 204.26/35.25    (101)   ~ (all_52_13 = all_4_2)
% 204.26/35.25    (102)  op(e3, e1) = all_52_17
% 204.26/35.25    (103)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.26/35.25    (104)  op(e0, e3) = all_52_7
% 204.26/35.25    (105)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.25    (106)   ~ (all_52_9 = all_52_25)
% 204.26/35.25    (107)  all_58_15 = all_14_2
% 204.26/35.25    (108)   ~ (all_52_19 = all_10_2)
% 204.26/35.25    (109)  op(all_52_23, all_52_23) = all_52_22
% 204.26/35.25    (110)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.25    (111)  all_58_8 = all_10_2
% 204.26/35.25    (112)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.25    (113)   ~ (all_52_5 = all_10_2)
% 204.26/35.25    (114)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.25    (115)   ~ (all_52_23 = all_14_2)
% 204.26/35.25    (116)  all_56_12 = all_52_7
% 204.26/35.25    (117)  op(all_52_17, all_52_17) = all_52_16
% 204.26/35.25    (118)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.26/35.25    (119)   ~ (all_52_25 = all_6_2)
% 204.26/35.25    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.25    (121)   ~ (all_52_9 = all_4_2)
% 204.26/35.25    (122)   ~ (all_52_5 = all_6_2)
% 204.26/35.25    (123)   ~ (all_52_9 = all_6_2)
% 204.26/35.25    (124)   ~ (all_52_13 = all_52_15)
% 204.26/35.25    (125)  all_56_0 = all_6_2
% 204.26/35.25    (126)  op(e3, e3) = all_6_2
% 204.26/35.25    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.26/35.25    (128)   ~ (all_52_27 = all_14_2)
% 204.26/35.25    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.25    (130)  all_56_14 = all_52_23
% 204.26/35.25    (131)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.25    (132)  all_32_0 = all_4_0
% 204.26/35.25    (133)  all_56_3 = all_52_25
% 204.26/35.25    (134)   ~ (all_52_3 = all_52_7)
% 204.26/35.25    (135)  op(all_14_2, all_14_2) = all_52_30
% 204.26/35.25    (136)  all_58_5 = all_52_19
% 204.26/35.25    (137)  all_56_1 = all_52_9
% 204.26/35.25    (138)   ~ (all_52_15 = all_4_2)
% 204.26/35.25    (139)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.25           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.26/35.25           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.26/35.25           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.26/35.25    (140)   ~ (all_52_27 = all_4_2)
% 204.26/35.25    (141)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 204.26/35.25             all_58_13 = e0 | all_58_14 = e0)
% 204.26/35.25    (142)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.26/35.25    (143)  all_58_6 = all_52_5
% 204.26/35.25    (144)   ~ (all_4_0 = all_4_2)
% 204.26/35.25    (145)  op(e3, e2) = all_52_9
% 204.26/35.25    (146)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.25    (147)   ~ (all_52_17 = all_6_2)
% 204.26/35.25    (148)   ~ (e1 = e0)
% 204.26/35.25    (149)   ~ (e3 = e2)
% 204.26/35.25    (150)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.25    (151)   ~ (all_52_9 = all_52_17)
% 204.26/35.25    (152)  all_56_10 = all_10_2
% 204.26/35.25    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.25    (154)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.25    (155)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.25    (156)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.25    (157)   ~ (all_6_1 = e2)
% 204.26/35.25    (158)  op(e1, e1) = all_10_2
% 204.26/35.25    (159)   ~ (all_52_7 = all_52_23)
% 204.26/35.25    (160)   ~ (all_52_17 = all_52_19)
% 204.26/35.25    (161)  all_58_3 = all_4_2
% 204.26/35.25    (162)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.25    (163)  all_56_13 = all_52_15
% 204.26/35.25    (164)   ~ (all_52_3 = all_4_2)
% 204.26/35.25    (165)   ~ (all_52_19 = all_4_2)
% 204.26/35.25    (166)   ~ (all_52_17 = all_52_23)
% 204.26/35.25    (167)  op(all_6_2, e3) = all_6_1
% 204.26/35.25    (168)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.26/35.25    (169)  all_58_4 = all_52_17
% 204.26/35.25    (170)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.25    (171)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.25  
% 204.26/35.25  Begin of proof
% 204.26/35.25  | 
% 204.26/35.25  | ALPHA: (141) implies:
% 204.26/35.25  |   (172)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.25  |   (173)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.25  | 
% 204.26/35.25  | REDUCE: (54), (107) imply:
% 204.26/35.25  |   (174)   ~ (all_14_2 = e0)
% 204.26/35.25  | 
% 204.26/35.25  | BETA: splitting (88) gives:
% 204.26/35.25  | 
% 204.26/35.25  | Case 1:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (175)  all_56_4 = e3
% 204.26/35.25  | | 
% 204.26/35.25  | | REF_CLOSE: (57), (99), (175) are inconsistent by sub-proof #980.
% 204.26/35.25  | | 
% 204.26/35.25  | Case 2:
% 204.26/35.25  | | 
% 204.26/35.25  | |   (176)   ~ (all_56_4 = e3)
% 204.26/35.25  | |   (177)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.25  | | 
% 204.26/35.25  | | BETA: splitting (139) gives:
% 204.26/35.25  | | 
% 204.26/35.25  | | Case 1:
% 204.26/35.25  | | | 
% 204.26/35.25  | | |   (178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.26/35.25  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.26/35.25  | | |            e0)
% 204.26/35.25  | | | 
% 204.26/35.25  | | | BETA: splitting (178) gives:
% 204.26/35.25  | | | 
% 204.26/35.25  | | | Case 1:
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | |   (179)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REF_CLOSE: (7), (13), (36), (37), (41), (48), (53), (84), (90), (99),
% 204.26/35.25  | | | |            (121), (131), (132), (142), (144), (145), (168), (177), (179)
% 204.26/35.25  | | | |            are inconsistent by sub-proof #970.
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | Case 2:
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | |   (180)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 204.26/35.25  | | | |          e0
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | ALPHA: (180) implies:
% 204.26/35.25  | | | |   (181)  all_52_14 = e0
% 204.26/35.25  | | | |   (182)  all_52_12 = e1
% 204.26/35.25  | | | |   (183)  all_52_10 = e2
% 204.26/35.25  | | | |   (184)  all_52_8 = e3
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (67), (184) imply:
% 204.26/35.25  | | | |   (185)  op(all_52_9, all_52_9) = e3
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (156), (182) imply:
% 204.26/35.25  | | | |   (186)  op(all_52_13, all_52_13) = e1
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (68), (181) imply:
% 204.26/35.25  | | | |   (187)  op(all_52_15, all_52_15) = e0
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (131), (183) imply:
% 204.26/35.25  | | | |   (188)  op(all_4_2, all_4_2) = e2
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (14), (15),
% 204.26/35.25  | | | |            (17), (18), (20), (22), (23), (24), (27), (29), (30), (31),
% 204.26/35.25  | | | |            (34), (35), (37), (38), (39), (40), (41), (42), (46), (47),
% 204.26/35.25  | | | |            (48), (49), (50), (51), (53), (56), (57), (58), (59), (61),
% 204.26/35.25  | | | |            (62), (64), (65), (66), (69), (72), (75), (76), (77), (78),
% 204.26/35.25  | | | |            (79), (80), (81), (83), (84), (85), (87), (89), (90), (91),
% 204.26/35.25  | | | |            (93), (94), (95), (98), (100), (104), (105), (106), (107),
% 204.26/35.25  | | | |            (108), (109), (110), (111), (112), (114), (115), (116),
% 204.26/35.25  | | | |            (119), (120), (121), (122), (123), (126), (127), (128),
% 204.26/35.25  | | | |            (129), (133), (134), (135), (136), (137), (140), (143),
% 204.26/35.25  | | | |            (144), (145), (146), (147), (148), (149), (150), (151),
% 204.26/35.25  | | | |            (154), (157), (158), (159), (161), (163), (164), (166),
% 204.26/35.25  | | | |            (167), (169), (171), (172), (173), (185), (186), (187), (188)
% 204.26/35.25  | | | |            are inconsistent by sub-proof #931.
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | End of split
% 204.26/35.25  | | | 
% 204.26/35.25  | | Case 2:
% 204.26/35.25  | | | 
% 204.26/35.25  | | |   (189)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.26/35.25  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 204.26/35.25  | | |            all_52_30 = e0)
% 204.26/35.25  | | | 
% 204.26/35.25  | | | BETA: splitting (189) gives:
% 204.26/35.25  | | | 
% 204.26/35.25  | | | Case 1:
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | |   (190)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 204.26/35.25  | | | |          e0
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | ALPHA: (190) implies:
% 204.26/35.25  | | | |   (191)  all_52_22 = e0
% 204.26/35.25  | | | |   (192)  all_52_20 = e1
% 204.26/35.25  | | | |   (193)  all_52_18 = e2
% 204.26/35.25  | | | |   (194)  all_52_16 = e3
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (117), (194) imply:
% 204.26/35.25  | | | |   (195)  op(all_52_17, all_52_17) = e3
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (25), (193) imply:
% 204.26/35.25  | | | |   (196)  op(all_52_19, all_52_19) = e2
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (109), (191) imply:
% 204.26/35.25  | | | |   (197)  op(all_52_23, all_52_23) = e0
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REDUCE: (28), (192) imply:
% 204.26/35.25  | | | |   (198)  op(all_10_2, all_10_2) = e1
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (13), (14), (15), (16),
% 204.26/35.25  | | | |            (17), (18), (20), (24), (27), (29), (30), (32), (33), (34),
% 204.26/35.25  | | | |            (35), (36), (37), (39), (40), (41), (42), (43), (45), (46),
% 204.26/35.25  | | | |            (47), (48), (49), (50), (51), (53), (55), (57), (58), (59),
% 204.26/35.25  | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (69), (70),
% 204.26/35.25  | | | |            (71), (72), (75), (76), (77), (78), (79), (80), (81), (82),
% 204.26/35.25  | | | |            (83), (85), (86), (89), (90), (92), (93), (94), (95), (96),
% 204.26/35.25  | | | |            (97), (98), (99), (100), (101), (102), (104), (105), (106),
% 204.26/35.25  | | | |            (107), (108), (110), (111), (112), (113), (114), (115),
% 204.26/35.25  | | | |            (116), (120), (121), (122), (123), (124), (125), (126),
% 204.26/35.25  | | | |            (128), (129), (131), (132), (133), (134), (136), (137),
% 204.26/35.25  | | | |            (140), (142), (143), (144), (145), (146), (147), (148),
% 204.26/35.25  | | | |            (149), (150), (151), (152), (153), (154), (155), (156),
% 204.26/35.25  | | | |            (157), (158), (159), (161), (162), (163), (164), (165),
% 204.26/35.25  | | | |            (167), (169), (170), (171), (172), (173), (177), (195),
% 204.26/35.25  | | | |            (196), (197), (198) are inconsistent by sub-proof #929.
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | Case 2:
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | |   (199)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 204.26/35.25  | | | |          e0
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (14), (15),
% 204.26/35.25  | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 204.26/35.25  | | | |            (27), (29), (30), (31), (33), (34), (37), (39), (40), (41),
% 204.26/35.25  | | | |            (42), (43), (44), (45), (46), (47), (49), (50), (51), (52),
% 204.26/35.25  | | | |            (55), (58), (59), (60), (64), (65), (66), (67), (68), (69),
% 204.26/35.25  | | | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 204.26/35.25  | | | |            (81), (83), (85), (86), (87), (88), (90), (93), (95), (96),
% 204.26/35.25  | | | |            (97), (98), (100), (101), (102), (103), (104), (105), (106),
% 204.26/35.25  | | | |            (107), (108), (109), (110), (111), (112), (113), (114),
% 204.26/35.25  | | | |            (115), (116), (117), (118), (119), (120), (121), (122),
% 204.26/35.25  | | | |            (123), (124), (125), (126), (127), (128), (129), (130),
% 204.26/35.25  | | | |            (133), (134), (135), (136), (137), (138), (140), (143),
% 204.26/35.25  | | | |            (146), (147), (149), (150), (155), (156), (157), (158),
% 204.26/35.25  | | | |            (159), (160), (161), (162), (163), (164), (165), (166),
% 204.26/35.25  | | | |            (167), (169), (171), (172), (174), (199) are inconsistent by
% 204.26/35.25  | | | |            sub-proof #1008.
% 204.26/35.25  | | | | 
% 204.26/35.25  | | | End of split
% 204.26/35.25  | | | 
% 204.26/35.25  | | End of split
% 204.26/35.25  | | 
% 204.26/35.25  | End of split
% 204.26/35.25  | 
% 204.26/35.25  End of proof
% 204.26/35.25  
% 204.26/35.25  Sub-proof #929 shows that the following formulas are inconsistent:
% 204.26/35.25  ----------------------------------------------------------------
% 204.26/35.25    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.25    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.25    (3)  all_58_14 = all_52_23
% 204.26/35.26    (4)   ~ (e3 = e1)
% 204.26/35.26    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.26/35.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.26    (7)  all_58_1 = all_52_9
% 204.26/35.26    (8)   ~ (e3 = e0)
% 204.26/35.26    (9)  op(all_52_23, all_52_23) = e0
% 204.26/35.26    (10)   ~ (all_4_0 = e1)
% 204.26/35.26    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.26    (12)   ~ (all_52_7 = all_52_15)
% 204.26/35.26    (13)   ~ (all_52_3 = all_52_19)
% 204.26/35.26    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.26    (15)   ~ (all_52_17 = all_52_25)
% 204.26/35.26    (16)  all_58_0 = all_6_2
% 204.26/35.26    (17)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.26    (18)  all_58_13 = all_52_15
% 204.26/35.26    (19)  all_58_9 = all_52_25
% 204.26/35.26    (20)   ~ (all_6_1 = e1)
% 204.26/35.26    (21)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.26/35.26    (22)  op(all_52_27, all_52_27) = all_52_26
% 204.26/35.26    (23)  op(e1, e3) = all_52_5
% 204.26/35.26    (24)   ~ (all_6_2 = all_4_0)
% 204.26/35.26    (25)  all_32_2 = all_4_2
% 204.26/35.26    (26)  op(e2, e2) = all_4_2
% 204.26/35.26    (27)   ~ (all_52_3 = all_52_5)
% 204.26/35.26    (28)  all_58_11 = all_52_29
% 204.26/35.26    (29)  all_56_5 = all_4_2
% 204.26/35.26    (30)   ~ (all_52_25 = all_14_2)
% 204.26/35.26    (31)   ~ (all_52_9 = all_52_15)
% 204.26/35.26    (32)  op(all_10_2, e1) = all_10_1
% 204.26/35.26    (33)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.26    (34)   ~ (all_52_7 = all_6_2)
% 204.26/35.26    (35)  all_58_2 = all_4_0
% 204.26/35.26    (36)  op(e0, e0) = all_14_2
% 204.26/35.26    (37)  all_56_15 = all_14_2
% 204.26/35.26    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.26    (39)  op(all_4_2, e2) = e3
% 204.26/35.26    (40)  all_56_11 = all_52_29
% 204.26/35.26    (41)   ~ (all_4_0 = e3)
% 204.26/35.26    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.26    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.26    (44)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.26/35.26    (45)  all_56_9 = all_52_13
% 204.26/35.26    (46)   ~ (e2 = e1)
% 204.26/35.26    (47)   ~ (all_52_13 = all_10_2)
% 204.26/35.26    (48)   ~ (all_6_0 = e1)
% 204.26/35.26    (49)  op(all_10_2, all_10_2) = e1
% 204.26/35.26    (50)  all_58_10 = all_52_27
% 204.26/35.26    (51)  all_56_8 = all_52_5
% 204.26/35.26    (52)  op(all_52_9, all_52_9) = all_52_8
% 204.26/35.26    (53)   ~ (all_52_19 = all_52_23)
% 204.26/35.26    (54)   ~ (all_52_25 = all_52_29)
% 204.26/35.26    (55)   ~ (all_52_29 = all_10_2)
% 204.26/35.26    (56)  all_58_7 = all_52_13
% 204.26/35.26    (57)  op(all_52_19, all_52_19) = e2
% 204.26/35.26    (58)   ~ (all_52_5 = all_52_7)
% 204.26/35.26    (59)  all_58_12 = all_52_7
% 204.26/35.26    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.26/35.26    (61)   ~ (all_52_7 = all_14_2)
% 204.26/35.26    (62)  all_58_2 = all_52_3
% 204.26/35.26    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.26    (64)  all_56_2 = all_52_17
% 204.26/35.26    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.26/35.26    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.26/35.26    (67)  op(e3, all_6_1) = all_6_0
% 204.26/35.26    (68)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.26/35.26    (69)   ~ (e2 = e0)
% 204.26/35.26    (70)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.26    (71)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.26/35.26    (72)   ~ (all_52_5 = all_52_29)
% 204.26/35.26    (73)  all_56_6 = all_52_19
% 204.26/35.26    (74)   ~ (all_52_15 = all_14_2)
% 204.26/35.26    (75)   ~ (all_52_19 = all_52_27)
% 204.26/35.26    (76)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.26/35.26    (77)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.26    (78)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.26/35.26    (79)  all_56_4 = all_4_0
% 204.26/35.26    (80)   ~ (all_6_0 = e2)
% 204.26/35.26    (81)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.26/35.26    (82)   ~ (all_52_13 = all_4_2)
% 204.26/35.26    (83)  op(e3, e1) = all_52_17
% 204.26/35.26    (84)  op(e0, e3) = all_52_7
% 204.26/35.26    (85)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.26/35.26    (86)   ~ (all_52_9 = all_52_25)
% 204.26/35.26    (87)  all_58_15 = all_14_2
% 204.26/35.26    (88)   ~ (all_52_19 = all_10_2)
% 204.26/35.26    (89)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.26/35.26    (90)  all_58_8 = all_10_2
% 204.26/35.26    (91)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.26/35.26    (92)   ~ (all_52_5 = all_10_2)
% 204.26/35.26    (93)  op(all_52_29, all_52_29) = all_52_28
% 204.26/35.26    (94)   ~ (all_52_23 = all_14_2)
% 204.26/35.26    (95)  all_56_12 = all_52_7
% 204.26/35.26    (96)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.26/35.26    (97)   ~ (all_52_9 = all_4_2)
% 204.26/35.26    (98)   ~ (all_52_5 = all_6_2)
% 204.26/35.26    (99)   ~ (all_52_9 = all_6_2)
% 204.26/35.26    (100)   ~ (all_52_13 = all_52_15)
% 204.26/35.26    (101)  all_56_0 = all_6_2
% 204.26/35.26    (102)  op(e3, e3) = all_6_2
% 204.26/35.26    (103)   ~ (all_52_27 = all_14_2)
% 204.26/35.26    (104)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.26/35.26    (105)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.26    (106)  all_32_0 = all_4_0
% 204.26/35.26    (107)  all_56_3 = all_52_25
% 204.26/35.26    (108)   ~ (all_52_3 = all_52_7)
% 204.26/35.26    (109)  all_58_5 = all_52_19
% 204.26/35.26    (110)  all_56_1 = all_52_9
% 204.26/35.26    (111)   ~ (all_52_27 = all_4_2)
% 204.26/35.26    (112)  op(all_52_17, all_52_17) = e3
% 204.26/35.26    (113)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.26/35.26    (114)  all_58_6 = all_52_5
% 204.26/35.26    (115)   ~ (all_4_0 = all_4_2)
% 204.26/35.26    (116)  op(e3, e2) = all_52_9
% 204.26/35.26    (117)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.26/35.26    (118)   ~ (all_52_17 = all_6_2)
% 204.26/35.26    (119)   ~ (e1 = e0)
% 204.26/35.26    (120)   ~ (e3 = e2)
% 204.26/35.26    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.26/35.26    (122)   ~ (all_52_9 = all_52_17)
% 204.26/35.26    (123)  all_56_10 = all_10_2
% 204.26/35.26    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.26/35.26    (125)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.26/35.26    (126)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.26/35.26    (127)  op(all_52_13, all_52_13) = all_52_12
% 204.26/35.26    (128)   ~ (all_6_1 = e2)
% 204.26/35.26    (129)  op(e1, e1) = all_10_2
% 204.26/35.26    (130)   ~ (all_52_7 = all_52_23)
% 204.26/35.26    (131)  all_58_3 = all_4_2
% 204.26/35.26    (132)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.26/35.26    (133)  all_56_13 = all_52_15
% 204.26/35.26    (134)   ~ (all_52_3 = all_4_2)
% 204.26/35.26    (135)   ~ (all_52_19 = all_4_2)
% 204.26/35.26    (136)  op(all_6_2, e3) = all_6_1
% 204.26/35.26    (137)  all_58_4 = all_52_17
% 204.26/35.26    (138)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.26/35.26    (139)  op(all_52_25, all_52_25) = all_52_24
% 204.26/35.26  
% 204.26/35.26  Begin of proof
% 204.26/35.26  | 
% 204.26/35.26  | BETA: splitting (91) gives:
% 204.26/35.26  | 
% 204.26/35.26  | Case 1:
% 204.26/35.26  | | 
% 204.26/35.26  | |   (140)  all_56_15 = e3
% 204.26/35.26  | | 
% 204.26/35.26  | | REF_CLOSE: (6), (10), (24), (25), (26), (29), (33), (35), (37), (38), (39),
% 204.26/35.26  | |            (41), (50), (57), (63), (70), (73), (77), (79), (97), (102),
% 204.26/35.26  | |            (103), (105), (106), (109), (113), (115), (116), (131), (135),
% 204.26/35.26  | |            (140) are inconsistent by sub-proof #930.
% 204.26/35.26  | | 
% 204.26/35.26  | Case 2:
% 204.26/35.26  | | 
% 204.26/35.26  | |   (141)   ~ (all_56_15 = e3)
% 204.26/35.26  | | 
% 204.26/35.26  | | REDUCE: (37), (141) imply:
% 204.26/35.26  | |   (142)   ~ (all_14_2 = e3)
% 204.26/35.26  | | 
% 204.26/35.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 204.26/35.26  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 204.26/35.26  | |            (27), (28), (30), (31), (32), (33), (34), (36), (38), (40), (42),
% 204.26/35.26  | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 204.26/35.26  | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 204.26/35.26  | |            (65), (66), (67), (68), (69), (71), (72), (73), (74), (75), (76),
% 204.26/35.26  | |            (78), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 204.26/35.26  | |            (90), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 204.26/35.26  | |            (101), (102), (103), (104), (105), (107), (108), (109), (110),
% 204.26/35.26  | |            (111), (112), (114), (117), (118), (119), (120), (121), (122),
% 204.26/35.26  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 204.26/35.26  | |            (132), (133), (134), (136), (137), (138), (139), (142) are
% 204.26/35.26  | |            inconsistent by sub-proof #1044.
% 204.26/35.26  | | 
% 204.26/35.26  | End of split
% 204.26/35.26  | 
% 204.26/35.26  End of proof
% 204.26/35.26  
% 204.26/35.26  Sub-proof #930 shows that the following formulas are inconsistent:
% 204.26/35.26  ----------------------------------------------------------------
% 204.26/35.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.26    (2)   ~ (all_4_0 = e1)
% 204.26/35.26    (3)   ~ (all_6_2 = all_4_0)
% 204.26/35.26    (4)  all_32_2 = all_4_2
% 204.26/35.26    (5)  op(e2, e2) = all_4_2
% 204.26/35.26    (6)  all_56_5 = all_4_2
% 204.26/35.26    (7)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.26    (8)  all_58_2 = all_4_0
% 204.26/35.26    (9)  all_56_15 = all_14_2
% 204.26/35.26    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.26    (11)  op(all_4_2, e2) = e3
% 204.26/35.26    (12)   ~ (all_4_0 = e3)
% 204.26/35.26    (13)  all_58_10 = all_52_27
% 204.26/35.26    (14)  op(all_52_19, all_52_19) = e2
% 204.26/35.26    (15)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.26/35.26    (16)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.26/35.26    (17)  all_56_6 = all_52_19
% 204.26/35.26    (18)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.26/35.26    (19)  all_56_4 = all_4_0
% 204.26/35.26    (20)   ~ (all_52_9 = all_4_2)
% 204.26/35.26    (21)  op(e3, e3) = all_6_2
% 204.26/35.26    (22)  all_56_15 = e3
% 204.26/35.26    (23)   ~ (all_52_27 = all_14_2)
% 204.26/35.26    (24)  op(all_4_2, all_4_2) = all_52_10
% 204.26/35.26    (25)  all_32_0 = all_4_0
% 204.26/35.26    (26)  all_58_5 = all_52_19
% 204.26/35.26    (27)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.26/35.26    (28)   ~ (all_4_0 = all_4_2)
% 204.26/35.26    (29)  op(e3, e2) = all_52_9
% 204.26/35.26    (30)  all_58_3 = all_4_2
% 204.26/35.26    (31)   ~ (all_52_19 = all_4_2)
% 204.26/35.26  
% 204.26/35.26  Begin of proof
% 204.26/35.26  | 
% 204.26/35.26  | COMBINE_EQS: (9), (22) imply:
% 204.26/35.26  |   (32)  all_14_2 = e3
% 204.26/35.26  | 
% 204.26/35.26  | SIMP: (32) implies:
% 204.26/35.26  |   (33)  all_14_2 = e3
% 204.26/35.26  | 
% 204.26/35.26  | REDUCE: (23), (33) imply:
% 204.26/35.26  |   (34)   ~ (all_52_27 = e3)
% 204.26/35.26  | 
% 204.26/35.26  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 204.26/35.26  |            (14), (15), (16), (17), (18), (19), (20), (21), (24), (25), (26),
% 204.26/35.26  |            (27), (28), (29), (30), (31), (34) are inconsistent by sub-proof
% 204.26/35.26  |            #944.
% 204.26/35.26  | 
% 204.26/35.26  End of proof
% 204.26/35.26  
% 204.26/35.26  Sub-proof #931 shows that the following formulas are inconsistent:
% 204.26/35.26  ----------------------------------------------------------------
% 204.26/35.26    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.26/35.26    (2)   ~ (all_52_15 = all_52_23)
% 204.26/35.26    (3)   ~ (all_52_25 = all_52_27)
% 204.26/35.26    (4)  all_58_14 = all_52_23
% 204.26/35.26    (5)   ~ (e3 = e1)
% 204.26/35.26    (6)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.26/35.26    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.26/35.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.26/35.26    (8)   ~ (all_52_5 = all_52_13)
% 204.26/35.26    (9)  all_58_1 = all_52_9
% 204.26/35.26    (10)   ~ (e3 = e0)
% 204.26/35.26    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.26/35.26    (12)   ~ (all_52_7 = all_52_15)
% 204.26/35.26    (13)  op(all_52_15, all_52_15) = e0
% 204.26/35.26    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.26/35.26    (15)   ~ (all_52_17 = all_52_25)
% 204.26/35.26    (16)  all_58_0 = all_6_2
% 204.26/35.26    (17)   ~ (all_52_17 = all_10_2)
% 204.26/35.26    (18)  op(e3, e0) = all_52_25
% 204.26/35.26    (19)  op(all_52_5, all_52_5) = all_52_4
% 204.26/35.26    (20)  all_58_13 = all_52_15
% 204.26/35.26    (21)  op(all_52_13, all_52_13) = e1
% 204.26/35.26    (22)  all_58_9 = all_52_25
% 204.26/35.26    (23)   ~ (all_6_1 = e1)
% 204.26/35.26    (24)   ~ (all_52_29 = all_14_2)
% 204.26/35.26    (25)  op(e1, e3) = all_52_5
% 204.26/35.26    (26)   ~ (all_6_2 = all_4_0)
% 204.26/35.26    (27)  op(e2, e2) = all_4_2
% 204.26/35.26    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.26/35.26    (29)   ~ (all_52_3 = all_52_5)
% 204.26/35.26    (30)  all_58_11 = all_52_29
% 204.26/35.26    (31)  all_56_5 = all_4_2
% 204.26/35.26    (32)   ~ (all_52_25 = all_14_2)
% 204.26/35.26    (33)  op(all_6_2, all_6_2) = all_52_0
% 204.26/35.26    (34)   ~ (all_52_7 = all_6_2)
% 204.26/35.26    (35)  all_58_2 = all_4_0
% 204.26/35.26    (36)  op(e0, e0) = all_14_2
% 204.26/35.26    (37)  all_56_15 = all_14_2
% 204.26/35.26    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.26/35.26    (39)  op(all_4_2, e2) = e3
% 204.26/35.26    (40)   ~ (all_4_1 = e1)
% 204.26/35.26    (41)   ~ (all_4_0 = e3)
% 204.26/35.26    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.26/35.26    (43)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.26/35.26    (44)  all_56_9 = all_52_13
% 204.26/35.26    (45)   ~ (e2 = e1)
% 204.26/35.26    (46)   ~ (all_6_0 = e1)
% 204.26/35.26    (47)  all_58_10 = all_52_27
% 204.26/35.26    (48)  all_56_8 = all_52_5
% 204.26/35.26    (49)   ~ (all_52_19 = all_52_23)
% 204.47/35.26    (50)  all_58_7 = all_52_13
% 204.47/35.26    (51)   ~ (all_52_5 = all_52_7)
% 204.47/35.26    (52)  all_58_12 = all_52_7
% 204.47/35.26    (53)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.47/35.26    (54)   ~ (all_52_7 = all_14_2)
% 204.47/35.26    (55)  all_58_2 = all_52_3
% 204.47/35.26    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.47/35.26    (57)  all_56_2 = all_52_17
% 204.47/35.26    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.26    (59)  op(all_4_0, all_4_0) = all_52_2
% 204.47/35.26    (60)  op(e3, all_6_1) = all_6_0
% 204.47/35.26    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.47/35.26    (62)   ~ (e2 = e0)
% 204.47/35.26    (63)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.26    (64)  op(all_4_2, e2) = all_4_1
% 204.47/35.26    (65)   ~ (all_52_5 = all_52_29)
% 204.47/35.26    (66)  all_56_6 = all_52_19
% 204.47/35.26    (67)   ~ (all_52_15 = all_14_2)
% 204.47/35.26    (68)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.47/35.26    (69)   ~ (all_6_0 = e2)
% 204.47/35.26    (70)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.47/35.26    (71)  op(e0, e3) = all_52_7
% 204.47/35.26    (72)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.26    (73)   ~ (all_52_9 = all_52_25)
% 204.47/35.26    (74)  all_58_15 = all_14_2
% 204.47/35.26    (75)   ~ (all_52_19 = all_10_2)
% 204.47/35.26    (76)  op(all_52_23, all_52_23) = all_52_22
% 204.47/35.26    (77)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.47/35.26    (78)  all_58_8 = all_10_2
% 204.47/35.26    (79)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.47/35.26    (80)  op(all_52_29, all_52_29) = all_52_28
% 204.47/35.26    (81)   ~ (all_52_23 = all_14_2)
% 204.47/35.26    (82)  all_56_12 = all_52_7
% 204.47/35.26    (83)   ~ (all_52_25 = all_6_2)
% 204.47/35.26    (84)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.26    (85)   ~ (all_52_9 = all_4_2)
% 204.47/35.26    (86)   ~ (all_52_5 = all_6_2)
% 204.47/35.26    (87)  op(all_4_2, all_4_2) = e2
% 204.47/35.26    (88)   ~ (all_52_9 = all_6_2)
% 204.47/35.26    (89)  op(e3, e3) = all_6_2
% 204.47/35.26    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.47/35.26    (91)   ~ (all_52_27 = all_14_2)
% 204.47/35.26    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.47/35.26    (93)  all_56_3 = all_52_25
% 204.47/35.26    (94)   ~ (all_52_3 = all_52_7)
% 204.47/35.26    (95)  op(all_14_2, all_14_2) = all_52_30
% 204.47/35.26    (96)  all_58_5 = all_52_19
% 204.47/35.26    (97)  all_56_1 = all_52_9
% 204.47/35.26    (98)   ~ (all_52_27 = all_4_2)
% 204.47/35.26    (99)  all_58_6 = all_52_5
% 204.47/35.26    (100)   ~ (all_4_0 = all_4_2)
% 204.47/35.26    (101)  op(e3, e2) = all_52_9
% 204.47/35.26    (102)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.47/35.26    (103)   ~ (all_52_17 = all_6_2)
% 204.47/35.26    (104)   ~ (e1 = e0)
% 204.47/35.26    (105)   ~ (e3 = e2)
% 204.47/35.26    (106)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.26    (107)   ~ (all_52_9 = all_52_17)
% 204.47/35.26    (108)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.47/35.26    (109)   ~ (all_6_1 = e2)
% 204.47/35.26    (110)  op(e1, e1) = all_10_2
% 204.47/35.26    (111)  op(all_52_9, all_52_9) = e3
% 204.47/35.26    (112)   ~ (all_52_7 = all_52_23)
% 204.47/35.26    (113)  all_58_3 = all_4_2
% 204.47/35.26    (114)  all_56_13 = all_52_15
% 204.47/35.26    (115)   ~ (all_52_3 = all_4_2)
% 204.47/35.26    (116)   ~ (all_52_17 = all_52_23)
% 204.47/35.26    (117)  op(all_6_2, e3) = all_6_1
% 204.47/35.26    (118)  all_58_4 = all_52_17
% 204.47/35.26    (119)  op(all_52_25, all_52_25) = all_52_24
% 204.47/35.26  
% 204.47/35.26  Begin of proof
% 204.47/35.26  | 
% 204.47/35.26  | BETA: splitting (79) gives:
% 204.47/35.26  | 
% 204.47/35.26  | Case 1:
% 204.47/35.26  | | 
% 204.47/35.26  | |   (120)  all_56_15 = e3
% 204.47/35.26  | | 
% 204.47/35.26  | | COMBINE_EQS: (37), (120) imply:
% 204.47/35.26  | |   (121)  all_14_2 = e3
% 204.47/35.26  | | 
% 204.47/35.26  | | SIMP: (121) implies:
% 204.47/35.26  | |   (122)  all_14_2 = e3
% 204.47/35.26  | | 
% 204.47/35.26  | | REDUCE: (54), (122) imply:
% 204.47/35.26  | |   (123)   ~ (all_52_7 = e3)
% 204.47/35.26  | | 
% 204.47/35.26  | | REDUCE: (67), (122) imply:
% 204.47/35.26  | |   (124)   ~ (all_52_15 = e3)
% 204.47/35.26  | | 
% 204.47/35.26  | | REDUCE: (91), (122) imply:
% 204.47/35.26  | |   (125)   ~ (all_52_27 = e3)
% 204.47/35.26  | | 
% 204.47/35.26  | | REDUCE: (24), (122) imply:
% 204.47/35.26  | |   (126)   ~ (all_52_29 = e3)
% 204.47/35.26  | | 
% 204.47/35.26  | | REDUCE: (95), (122) imply:
% 204.47/35.26  | |   (127)  op(e3, e3) = all_52_30
% 204.47/35.26  | | 
% 204.47/35.26  | | GROUND_INST: instantiating (7) with all_6_2, all_52_30, e3, e3, simplifying
% 204.47/35.26  | |              with (89), (127) gives:
% 204.47/35.26  | |   (128)  all_52_30 = all_6_2
% 204.47/35.26  | | 
% 204.47/35.26  | | BETA: splitting (58) gives:
% 204.47/35.26  | | 
% 204.47/35.26  | | Case 1:
% 204.47/35.26  | | | 
% 204.47/35.26  | | |   (129)  all_58_0 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | COMBINE_EQS: (16), (129) imply:
% 204.47/35.26  | | |   (130)  all_6_2 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (86), (130) imply:
% 204.47/35.26  | | |   (131)   ~ (all_52_5 = e3)
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (26), (130) imply:
% 204.47/35.26  | | |   (132)   ~ (all_4_0 = e3)
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (33), (130) imply:
% 204.47/35.26  | | |   (133)  op(e3, e3) = all_52_0
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (117), (130) imply:
% 204.47/35.26  | | |   (134)  op(e3, e3) = all_6_1
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (89), (130) imply:
% 204.47/35.26  | | |   (135)  op(e3, e3) = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | GROUND_INST: instantiating (7) with all_6_1, all_52_0, e3, e3, simplifying
% 204.47/35.26  | | |              with (133), (134) gives:
% 204.47/35.26  | | |   (136)  all_52_0 = all_6_1
% 204.47/35.26  | | | 
% 204.47/35.26  | | | GROUND_INST: instantiating (7) with e3, all_52_0, e3, e3, simplifying with
% 204.47/35.26  | | |              (133), (135) gives:
% 204.47/35.26  | | |   (137)  all_52_0 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | COMBINE_EQS: (136), (137) imply:
% 204.47/35.26  | | |   (138)  all_6_1 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (60), (138) imply:
% 204.47/35.26  | | |   (139)  op(e3, e3) = all_6_0
% 204.47/35.26  | | | 
% 204.47/35.26  | | | GROUND_INST: instantiating (7) with e3, all_6_0, e3, e3, simplifying with
% 204.47/35.26  | | |              (135), (139) gives:
% 204.47/35.26  | | |   (140)  all_6_0 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | BETA: splitting (38) gives:
% 204.47/35.26  | | | 
% 204.47/35.26  | | | Case 1:
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | |   (141)  all_58_2 = e3
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | REF_CLOSE: (35), (41), (141) are inconsistent by sub-proof #948.
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | Case 2:
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | |   (142)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | BETA: splitting (53) gives:
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | Case 1:
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | |   (143)  all_58_6 = e3
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REF_CLOSE: (99), (131), (143) are inconsistent by sub-proof #1328.
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | Case 2:
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | |   (144)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | BETA: splitting (56) gives:
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | Case 1:
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | |   (145)  all_56_6 = e3
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | COMBINE_EQS: (66), (145) imply:
% 204.47/35.26  | | | | | |   (146)  all_52_19 = e3
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | SIMP: (146) implies:
% 204.47/35.26  | | | | | |   (147)  all_52_19 = e3
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | REDUCE: (75), (147) imply:
% 204.47/35.26  | | | | | |   (148)   ~ (all_10_2 = e3)
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | SIMP: (148) implies:
% 204.47/35.26  | | | | | |   (149)   ~ (all_10_2 = e3)
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | REF_CLOSE: (5), (7), (21), (30), (50), (78), (126), (133), (135),
% 204.47/35.26  | | | | | |            (144), (149) are inconsistent by sub-proof #1139.
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | Case 2:
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | |   (150)   ~ (all_56_6 = e3)
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | REDUCE: (66), (150) imply:
% 204.47/35.26  | | | | | |   (151)   ~ (all_52_19 = e3)
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | REF_CLOSE: (7), (39), (47), (85), (96), (101), (113), (125), (142),
% 204.47/35.26  | | | | | |            (151) are inconsistent by sub-proof #945.
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | End of split
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | End of split
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | End of split
% 204.47/35.26  | | | 
% 204.47/35.26  | | Case 2:
% 204.47/35.26  | | | 
% 204.47/35.26  | | |   (152)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REF_CLOSE: (7), (8), (9), (19), (20), (35), (39), (41), (50), (52), (72),
% 204.47/35.26  | | |            (85), (88), (89), (99), (101), (111), (113), (123), (124),
% 204.47/35.26  | | |            (152) are inconsistent by sub-proof #938.
% 204.47/35.26  | | | 
% 204.47/35.26  | | End of split
% 204.47/35.26  | | 
% 204.47/35.26  | Case 2:
% 204.47/35.26  | | 
% 204.47/35.26  | |   (153)   ~ (all_56_15 = e3)
% 204.47/35.26  | | 
% 204.47/35.26  | | REDUCE: (37), (153) imply:
% 204.47/35.26  | |   (154)   ~ (all_14_2 = e3)
% 204.47/35.26  | | 
% 204.47/35.26  | | BETA: splitting (42) gives:
% 204.47/35.26  | | 
% 204.47/35.26  | | Case 1:
% 204.47/35.26  | | | 
% 204.47/35.26  | | |   (155)  all_56_13 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | COMBINE_EQS: (114), (155) imply:
% 204.47/35.26  | | |   (156)  all_52_15 = e3
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REF_CLOSE: (7), (11), (12), (13), (23), (34), (71), (82), (89), (109),
% 204.47/35.26  | | |            (117), (156) are inconsistent by sub-proof #1341.
% 204.47/35.26  | | | 
% 204.47/35.26  | | Case 2:
% 204.47/35.26  | | | 
% 204.47/35.26  | | |   (157)   ~ (all_56_13 = e3)
% 204.47/35.26  | | | 
% 204.47/35.26  | | | REDUCE: (114), (157) imply:
% 204.47/35.26  | | |   (158)   ~ (all_52_15 = e3)
% 204.47/35.26  | | | 
% 204.47/35.26  | | | BETA: splitting (102) gives:
% 204.47/35.26  | | | 
% 204.47/35.26  | | | Case 1:
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | |   (159)  all_58_12 = e3
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | COMBINE_EQS: (52), (159) imply:
% 204.47/35.26  | | | |   (160)  all_52_7 = e3
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | SIMP: (160) implies:
% 204.47/35.26  | | | |   (161)  all_52_7 = e3
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | REDUCE: (51), (161) imply:
% 204.47/35.26  | | | |   (162)   ~ (all_52_5 = e3)
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | REDUCE: (12), (161) imply:
% 204.47/35.26  | | | |   (163)   ~ (all_52_15 = e3)
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | REDUCE: (34), (161) imply:
% 204.47/35.26  | | | |   (164)   ~ (all_6_2 = e3)
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | SIMP: (164) implies:
% 204.47/35.26  | | | |   (165)   ~ (all_6_2 = e3)
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | REDUCE: (14), (161) imply:
% 204.47/35.26  | | | |   (166)  op(e3, e3) = all_52_6
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3,
% 204.47/35.26  | | | |              simplifying with (89), (166) gives:
% 204.47/35.26  | | | |   (167)  all_52_6 = all_6_2
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | BETA: splitting (61) gives:
% 204.47/35.26  | | | | 
% 204.47/35.26  | | | | Case 1:
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | |   (168)  all_58_0 = e1
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | COMBINE_EQS: (16), (168) imply:
% 204.47/35.26  | | | | |   (169)  all_6_2 = e1
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (88), (169) imply:
% 204.47/35.26  | | | | |   (170)   ~ (all_52_9 = e1)
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (103), (169) imply:
% 204.47/35.26  | | | | |   (171)   ~ (all_52_17 = e1)
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (83), (169) imply:
% 204.47/35.26  | | | | |   (172)   ~ (all_52_25 = e1)
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (33), (169) imply:
% 204.47/35.26  | | | | |   (173)  op(e1, e1) = all_52_0
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (117), (169) imply:
% 204.47/35.26  | | | | |   (174)  op(e1, e3) = all_6_1
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | GROUND_INST: instantiating (7) with all_10_2, all_52_0, e1, e1,
% 204.47/35.26  | | | | |              simplifying with (110), (173) gives:
% 204.47/35.26  | | | | |   (175)  all_52_0 = all_10_2
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | GROUND_INST: instantiating (7) with all_52_5, all_6_1, e3, e1,
% 204.47/35.26  | | | | |              simplifying with (25), (174) gives:
% 204.47/35.26  | | | | |   (176)  all_52_5 = all_6_1
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | COMBINE_EQS: (99), (176) imply:
% 204.47/35.26  | | | | |   (177)  all_58_6 = all_6_1
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (65), (176) imply:
% 204.47/35.26  | | | | |   (178)   ~ (all_52_29 = all_6_1)
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | SIMP: (178) implies:
% 204.47/35.26  | | | | |   (179)   ~ (all_52_29 = all_6_1)
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | REDUCE: (162), (176) imply:
% 204.47/35.26  | | | | |   (180)   ~ (all_6_1 = e3)
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | BETA: splitting (68) gives:
% 204.47/35.26  | | | | | 
% 204.47/35.26  | | | | | Case 1:
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | |   (181)  all_58_0 = e2
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | REF_CLOSE: (45), (168), (181) are inconsistent by sub-proof #1273.
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | Case 2:
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | |   (182)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | BETA: splitting (182) gives:
% 204.47/35.26  | | | | | | 
% 204.47/35.26  | | | | | | Case 1:
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | |   (183)  all_58_2 = e2
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | COMBINE_EQS: (35), (183) imply:
% 204.47/35.26  | | | | | | |   (184)  all_4_0 = e2
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | SIMP: (184) implies:
% 204.47/35.26  | | | | | | |   (185)  all_4_0 = e2
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | REDUCE: (100), (185) imply:
% 204.47/35.26  | | | | | | |   (186)   ~ (all_4_2 = e2)
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | SIMP: (186) implies:
% 204.47/35.26  | | | | | | |   (187)   ~ (all_4_2 = e2)
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | REDUCE: (59), (185) imply:
% 204.47/35.26  | | | | | | |   (188)  op(e2, e2) = all_52_2
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | BETA: splitting (28) gives:
% 204.47/35.26  | | | | | | | 
% 204.47/35.26  | | | | | | | Case 1:
% 204.47/35.26  | | | | | | | | 
% 204.47/35.26  | | | | | | | |   (189)  all_58_0 = e0
% 204.47/35.26  | | | | | | | | 
% 204.47/35.26  | | | | | | | | COMBINE_EQS: (168), (189) imply:
% 204.47/35.26  | | | | | | | |   (190)  e1 = e0
% 204.47/35.26  | | | | | | | | 
% 204.47/35.26  | | | | | | | | REDUCE: (104), (190) imply:
% 204.47/35.26  | | | | | | | |   (191)  $false
% 204.47/35.26  | | | | | | | | 
% 204.47/35.26  | | | | | | | | CLOSE: (191) is inconsistent.
% 204.47/35.26  | | | | | | | | 
% 204.47/35.26  | | | | | | | Case 2:
% 204.47/35.26  | | | | | | | | 
% 204.47/35.27  | | | | | | | |   (192)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.47/35.27  | | | | | | | | 
% 204.47/35.27  | | | | | | | | BETA: splitting (192) gives:
% 204.47/35.27  | | | | | | | | 
% 204.47/35.27  | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | |   (193)  all_58_2 = e0
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | REF_CLOSE: (62), (183), (193) are inconsistent by sub-proof
% 204.47/35.27  | | | | | | | | |            #1213.
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | |   (194)  all_58_6 = e0 | all_58_12 = e0
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | BETA: splitting (194) gives:
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | |   (195)  all_58_6 = e0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | COMBINE_EQS: (177), (195) imply:
% 204.47/35.27  | | | | | | | | | |   (196)  all_6_1 = e0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | SIMP: (196) implies:
% 204.47/35.27  | | | | | | | | | |   (197)  all_6_1 = e0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | REDUCE: (179), (197) imply:
% 204.47/35.27  | | | | | | | | | |   (198)   ~ (all_52_29 = e0)
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | REDUCE: (180), (197) imply:
% 204.47/35.27  | | | | | | | | | |   (199)   ~ (e3 = e0)
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | REDUCE: (60), (197) imply:
% 204.47/35.27  | | | | | | | | | |   (200)  op(e3, e0) = all_6_0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | GROUND_INST: instantiating (7) with all_4_2, all_52_2, e2, e2,
% 204.47/35.27  | | | | | | | | | |              simplifying with (27), (188) gives:
% 204.47/35.27  | | | | | | | | | |   (201)  all_52_2 = all_4_2
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_25, all_6_0, e0, e3,
% 204.47/35.27  | | | | | | | | | |              simplifying with (18), (200) gives:
% 204.47/35.27  | | | | | | | | | |   (202)  all_52_25 = all_6_0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | COMBINE_EQS: (93), (202) imply:
% 204.47/35.27  | | | | | | | | | |   (203)  all_56_3 = all_6_0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | COMBINE_EQS: (22), (202) imply:
% 204.47/35.27  | | | | | | | | | |   (204)  all_58_9 = all_6_0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | REDUCE: (73), (202) imply:
% 204.47/35.27  | | | | | | | | | |   (205)   ~ (all_52_9 = all_6_0)
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | REDUCE: (15), (202) imply:
% 204.47/35.27  | | | | | | | | | |   (206)   ~ (all_52_17 = all_6_0)
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | BETA: splitting (84) gives:
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | |   (207)  all_56_3 = e3
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | COMBINE_EQS: (203), (207) imply:
% 204.47/35.27  | | | | | | | | | | |   (208)  all_6_0 = e3
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | SIMP: (208) implies:
% 204.47/35.27  | | | | | | | | | | |   (209)  all_6_0 = e3
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | COMBINE_EQS: (204), (209) imply:
% 204.47/35.27  | | | | | | | | | | |   (210)  all_58_9 = e3
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | REDUCE: (205), (209) imply:
% 204.47/35.27  | | | | | | | | | | |   (211)   ~ (all_52_9 = e3)
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | REDUCE: (206), (209) imply:
% 204.47/35.27  | | | | | | | | | | |   (212)   ~ (all_52_17 = e3)
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | BETA: splitting (1) gives:
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | |   (213)  all_58_9 = e0
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | COMBINE_EQS: (210), (213) imply:
% 204.47/35.27  | | | | | | | | | | | |   (214)  e3 = e0
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | REDUCE: (10), (214) imply:
% 204.47/35.27  | | | | | | | | | | | |   (215)  $false
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | CLOSE: (215) is inconsistent.
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | |   (216)  all_58_10 = e0 | all_58_11 = e0
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | BETA: splitting (216) gives:
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | |   (217)  all_58_10 = e0
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | COMBINE_EQS: (47), (217) imply:
% 204.47/35.27  | | | | | | | | | | | | |   (218)  all_52_27 = e0
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | REDUCE: (98), (218) imply:
% 204.47/35.27  | | | | | | | | | | | | |   (219)   ~ (all_4_2 = e0)
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | SIMP: (219) implies:
% 204.47/35.27  | | | | | | | | | | | | |   (220)   ~ (all_4_2 = e0)
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | BETA: splitting (106) gives:
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | |   (221)  all_56_1 = e3
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | REF_CLOSE: (97), (211), (221) are inconsistent by sub-proof
% 204.47/35.27  | | | | | | | | | | | | | |            #1326.
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | |   (222)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | |   (223)  all_56_2 = e3
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | REF_CLOSE: (57), (212), (223) are inconsistent by sub-proof
% 204.47/35.27  | | | | | | | | | | | | | | |            #1327.
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | |   (224)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | Case 1:
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | |   (225)  all_56_5 = e3
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (31), (39), (85), (101), (225) are
% 204.47/35.27  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | |   (226)   ~ (all_56_5 = e3)
% 204.47/35.27  | | | | | | | | | | | | | | | |   (227)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | | REDUCE: (31), (226) imply:
% 204.47/35.27  | | | | | | | | | | | | | | | |   (228)   ~ (all_4_2 = e3)
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (17), (27), (31), (57), (85), (87),
% 204.47/35.27  | | | | | | | | | | | | | | | |            (97), (107), (110), (111), (118), (171), (187),
% 204.47/35.27  | | | | | | | | | | | | | | | |            (220), (222), (224), (227), (228) are inconsistent
% 204.47/35.27  | | | | | | | | | | | | | | | |            by sub-proof #936.
% 204.47/35.27  | | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | |   (229)  all_58_11 = e0
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | COMBINE_EQS: (30), (229) imply:
% 204.47/35.27  | | | | | | | | | | | | |   (230)  all_52_29 = e0
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | REDUCE: (198), (230) imply:
% 204.47/35.27  | | | | | | | | | | | | |   (231)  $false
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 204.47/35.27  | | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | |   (232)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | | REF_CLOSE: (7), (27), (39), (43), (46), (57), (69), (89),
% 204.47/35.27  | | | | | | | | | | |            (97), (101), (106), (107), (111), (165), (170),
% 204.47/35.27  | | | | | | | | | | |            (171), (203), (205), (206), (232) are inconsistent
% 204.47/35.27  | | | | | | | | | | |            by sub-proof #934.
% 204.47/35.27  | | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | Case 2:
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | |   (233)  all_58_12 = e0
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | | REF_CLOSE: (10), (159), (233) are inconsistent by sub-proof
% 204.47/35.27  | | | | | | | | | |            #1212.
% 204.47/35.27  | | | | | | | | | | 
% 204.47/35.27  | | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | | 
% 204.47/35.27  | | | | | | | | End of split
% 204.47/35.27  | | | | | | | | 
% 204.47/35.27  | | | | | | | End of split
% 204.47/35.27  | | | | | | | 
% 204.47/35.27  | | | | | | Case 2:
% 204.47/35.27  | | | | | | | 
% 204.47/35.27  | | | | | | |   (234)  all_58_6 = e2 | all_58_12 = e2
% 204.47/35.27  | | | | | | | 
% 204.47/35.27  | | | | | | | REF_CLOSE: (105), (109), (159), (177), (234) are inconsistent by
% 204.47/35.27  | | | | | | |            sub-proof #1209.
% 204.47/35.27  | | | | | | | 
% 204.47/35.27  | | | | | | End of split
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | End of split
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | Case 2:
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | |   (235)   ~ (all_58_0 = e1)
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | REDUCE: (16), (235) imply:
% 204.47/35.27  | | | | |   (236)   ~ (all_6_2 = e1)
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | REF_CLOSE: (7), (9), (20), (21), (39), (44), (50), (72), (85), (88),
% 204.47/35.27  | | | | |            (89), (101), (108), (111), (113), (158), (166), (236) are
% 204.47/35.27  | | | | |            inconsistent by sub-proof #932.
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | End of split
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | Case 2:
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | |   (237)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (13), (16), (19), (20),
% 204.47/35.27  | | | |            (21), (22), (25), (27), (29), (30), (32), (33), (34), (36),
% 204.47/35.27  | | | |            (38), (40), (45), (46), (47), (48), (49), (50), (51), (52),
% 204.47/35.27  | | | |            (53), (55), (58), (60), (64), (67), (68), (69), (70), (72),
% 204.47/35.27  | | | |            (74), (76), (77), (80), (81), (83), (85), (86), (87), (88),
% 204.47/35.27  | | | |            (89), (90), (92), (94), (96), (97), (98), (99), (101), (105),
% 204.47/35.27  | | | |            (106), (109), (111), (112), (113), (115), (116), (117),
% 204.47/35.27  | | | |            (118), (119), (154), (158), (237) are inconsistent by
% 204.47/35.27  | | | |            sub-proof #1094.
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | End of split
% 204.47/35.27  | | | 
% 204.47/35.27  | | End of split
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #932 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (2)  all_58_1 = all_52_9
% 204.47/35.27    (3)  op(e3, e3) = all_52_6
% 204.47/35.27    (4)  all_58_13 = all_52_15
% 204.47/35.27    (5)  op(all_52_13, all_52_13) = e1
% 204.47/35.27    (6)   ~ (all_52_15 = e3)
% 204.47/35.27    (7)  op(all_4_2, e2) = e3
% 204.47/35.27    (8)  all_56_9 = all_52_13
% 204.47/35.27    (9)  all_58_7 = all_52_13
% 204.47/35.27    (10)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27    (11)   ~ (all_52_9 = all_4_2)
% 204.47/35.27    (12)   ~ (all_52_9 = all_6_2)
% 204.47/35.27    (13)  op(e3, e3) = all_6_2
% 204.47/35.27    (14)  op(e3, e2) = all_52_9
% 204.47/35.27    (15)   ~ (all_6_2 = e1)
% 204.47/35.27    (16)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.47/35.27    (17)  op(all_52_9, all_52_9) = e3
% 204.47/35.27    (18)  all_58_3 = all_4_2
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (16) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (19)  all_56_9 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | COMBINE_EQS: (8), (19) imply:
% 204.47/35.27  | |   (20)  all_52_13 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | SIMP: (20) implies:
% 204.47/35.27  | |   (21)  all_52_13 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REDUCE: (5), (21) imply:
% 204.47/35.27  | |   (22)  op(e3, e3) = e1
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (1), (3), (13), (15), (22) are inconsistent by sub-proof #1105.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (23)   ~ (all_56_9 = e3)
% 204.47/35.27  | | 
% 204.47/35.27  | | REDUCE: (8), (23) imply:
% 204.47/35.27  | |   (24)   ~ (all_52_13 = e3)
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 204.47/35.27  | |            (17), (18), (24) are inconsistent by sub-proof #933.
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #933 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (2)  all_58_1 = all_52_9
% 204.47/35.27    (3)  op(e3, e3) = all_52_6
% 204.47/35.27    (4)  all_58_13 = all_52_15
% 204.47/35.27    (5)   ~ (all_52_15 = e3)
% 204.47/35.27    (6)  op(all_4_2, e2) = e3
% 204.47/35.27    (7)  all_58_7 = all_52_13
% 204.47/35.27    (8)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27    (9)   ~ (all_52_9 = all_4_2)
% 204.47/35.27    (10)   ~ (all_52_9 = all_6_2)
% 204.47/35.27    (11)  op(e3, e3) = all_6_2
% 204.47/35.27    (12)   ~ (all_52_13 = e3)
% 204.47/35.27    (13)  op(e3, e2) = all_52_9
% 204.47/35.27    (14)  op(all_52_9, all_52_9) = e3
% 204.47/35.27    (15)  all_58_3 = all_4_2
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | GROUND_INST: instantiating (1) with all_6_2, all_52_6, e3, e3, simplifying
% 204.47/35.27  |              with (3), (11) gives:
% 204.47/35.27  |   (16)  all_52_6 = all_6_2
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (8) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (17)  all_58_1 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | COMBINE_EQS: (2), (17) imply:
% 204.47/35.27  | |   (18)  all_52_9 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (1), (10), (11), (14), (18) are inconsistent by sub-proof #1337.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (19)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (12), (13), (15), (19) are
% 204.47/35.27  | |            inconsistent by sub-proof #939.
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #934 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (2)   ~ (all_52_17 = all_6_0)
% 204.47/35.27    (3)  op(e2, e2) = all_4_2
% 204.47/35.27    (4)  op(all_4_2, e2) = e3
% 204.47/35.27    (5)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.27    (6)   ~ (all_6_2 = e3)
% 204.47/35.27    (7)   ~ (all_6_0 = e1)
% 204.47/35.27    (8)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.27    (9)  all_56_3 = all_6_0
% 204.47/35.27    (10)  all_56_2 = all_52_17
% 204.47/35.27    (11)   ~ (all_6_0 = e2)
% 204.47/35.27    (12)   ~ (all_52_9 = all_6_0)
% 204.47/35.27    (13)   ~ (all_52_9 = e1)
% 204.47/35.27    (14)  op(e3, e3) = all_6_2
% 204.47/35.27    (15)  all_56_1 = all_52_9
% 204.47/35.27    (16)  op(e3, e2) = all_52_9
% 204.47/35.27    (17)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27    (18)   ~ (all_52_17 = e1)
% 204.47/35.27    (19)   ~ (all_52_9 = all_52_17)
% 204.47/35.27    (20)  op(all_52_9, all_52_9) = e3
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (8) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (21)  all_56_3 = e2
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (9), (11), (21) are inconsistent by sub-proof #1075.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (22)  all_56_3 = e1 | all_56_3 = e0
% 204.47/35.27  | | 
% 204.47/35.27  | | BETA: splitting (22) gives:
% 204.47/35.27  | | 
% 204.47/35.27  | | Case 1:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (23)  all_56_3 = e1
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REF_CLOSE: (7), (9), (23) are inconsistent by sub-proof #1074.
% 204.47/35.27  | | | 
% 204.47/35.27  | | Case 2:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (24)  all_56_3 = e0
% 204.47/35.27  | | | 
% 204.47/35.27  | | | COMBINE_EQS: (9), (24) imply:
% 204.47/35.27  | | |   (25)  all_6_0 = e0
% 204.47/35.27  | | | 
% 204.47/35.27  | | | SIMP: (25) implies:
% 204.47/35.27  | | |   (26)  all_6_0 = e0
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (12), (26) imply:
% 204.47/35.27  | | |   (27)   ~ (all_52_9 = e0)
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (2), (26) imply:
% 204.47/35.27  | | |   (28)   ~ (all_52_17 = e0)
% 204.47/35.27  | | | 
% 204.47/35.27  | | | BETA: splitting (5) gives:
% 204.47/35.27  | | | 
% 204.47/35.27  | | | Case 1:
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | |   (29)  all_56_2 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | COMBINE_EQS: (10), (29) imply:
% 204.47/35.27  | | | |   (30)  all_52_17 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | SIMP: (30) implies:
% 204.47/35.27  | | | |   (31)  all_52_17 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | REDUCE: (19), (31) imply:
% 204.47/35.27  | | | |   (32)   ~ (all_52_9 = e3)
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | REF_CLOSE: (1), (3), (4), (13), (15), (16), (17), (20), (27), (32) are
% 204.47/35.27  | | | |            inconsistent by sub-proof #935.
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | Case 2:
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | |   (33)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | BETA: splitting (33) gives:
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | Case 1:
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | |   (34)  all_56_2 = e2
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | COMBINE_EQS: (10), (34) imply:
% 204.47/35.27  | | | | |   (35)  all_52_17 = e2
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | SIMP: (35) implies:
% 204.47/35.27  | | | | |   (36)  all_52_17 = e2
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | REDUCE: (19), (36) imply:
% 204.47/35.27  | | | | |   (37)   ~ (all_52_9 = e2)
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | BETA: splitting (17) gives:
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | Case 1:
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | |   (38)  all_56_1 = e3
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | | REF_CLOSE: (1), (6), (14), (15), (20), (38) are inconsistent by
% 204.47/35.27  | | | | | |            sub-proof #1110.
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | Case 2:
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | |   (39)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | | REF_CLOSE: (13), (15), (27), (37), (39) are inconsistent by
% 204.47/35.27  | | | | | |            sub-proof #1314.
% 204.47/35.27  | | | | | | 
% 204.47/35.27  | | | | | End of split
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | Case 2:
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | |   (40)  all_56_2 = e1 | all_56_2 = e0
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | | REF_CLOSE: (10), (18), (28), (40) are inconsistent by sub-proof #1307.
% 204.47/35.27  | | | | | 
% 204.47/35.27  | | | | End of split
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | End of split
% 204.47/35.27  | | | 
% 204.47/35.27  | | End of split
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #935 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (2)  op(e2, e2) = all_4_2
% 204.47/35.27    (3)  op(all_4_2, e2) = e3
% 204.47/35.27    (4)   ~ (all_52_9 = e3)
% 204.47/35.27    (5)   ~ (all_52_9 = e1)
% 204.47/35.27    (6)  all_56_1 = all_52_9
% 204.47/35.27    (7)  op(e3, e2) = all_52_9
% 204.47/35.27    (8)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27    (9)   ~ (all_52_9 = e0)
% 204.47/35.27    (10)  op(all_52_9, all_52_9) = e3
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (8) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (11)  all_56_1 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #1326.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (12)   ~ (all_56_1 = e3)
% 204.47/35.27  | |   (13)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27  | | 
% 204.47/35.27  | | BETA: splitting (13) gives:
% 204.47/35.27  | | 
% 204.47/35.27  | | Case 1:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (14)  all_56_1 = e2
% 204.47/35.27  | | | 
% 204.47/35.27  | | | COMBINE_EQS: (6), (14) imply:
% 204.47/35.27  | | |   (15)  all_52_9 = e2
% 204.47/35.27  | | | 
% 204.47/35.27  | | | SIMP: (15) implies:
% 204.47/35.27  | | |   (16)  all_52_9 = e2
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (10), (16) imply:
% 204.47/35.27  | | |   (17)  op(e2, e2) = e3
% 204.47/35.27  | | | 
% 204.47/35.27  | | | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying with
% 204.47/35.27  | | |              (2), (17) gives:
% 204.47/35.27  | | |   (18)  all_4_2 = e3
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REF_CLOSE: (1), (3), (4), (7), (18) are inconsistent by sub-proof #977.
% 204.47/35.27  | | | 
% 204.47/35.27  | | Case 2:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (19)  all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REF_CLOSE: (5), (6), (9), (19) are inconsistent by sub-proof #1334.
% 204.47/35.27  | | | 
% 204.47/35.27  | | End of split
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #936 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.47/35.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (3)   ~ (all_4_2 = e3)
% 204.47/35.27    (4)   ~ (all_52_17 = all_10_2)
% 204.47/35.27    (5)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.27    (6)   ~ (all_4_2 = e0)
% 204.47/35.27    (7)  op(e2, e2) = all_4_2
% 204.47/35.27    (8)  all_56_5 = all_4_2
% 204.47/35.27    (9)  all_56_2 = all_52_17
% 204.47/35.27    (10)   ~ (all_52_9 = all_4_2)
% 204.47/35.27    (11)  op(all_4_2, all_4_2) = e2
% 204.47/35.27    (12)   ~ (all_4_2 = e2)
% 204.47/35.27    (13)  all_56_1 = all_52_9
% 204.47/35.27    (14)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27    (15)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.27    (16)   ~ (all_52_17 = e1)
% 204.47/35.27    (17)   ~ (all_52_9 = all_52_17)
% 204.47/35.27    (18)  op(e1, e1) = all_10_2
% 204.47/35.27    (19)  op(all_52_9, all_52_9) = e3
% 204.47/35.27    (20)  all_58_4 = all_52_17
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (5) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (21)  all_56_5 = e2
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (8), (12), (21) are inconsistent by sub-proof #1315.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (22)  all_56_5 = e1 | all_56_5 = e0
% 204.47/35.27  | | 
% 204.47/35.27  | | BETA: splitting (22) gives:
% 204.47/35.27  | | 
% 204.47/35.27  | | Case 1:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (23)  all_56_5 = e1
% 204.47/35.27  | | | 
% 204.47/35.27  | | | COMBINE_EQS: (8), (23) imply:
% 204.47/35.27  | | |   (24)  all_4_2 = e1
% 204.47/35.27  | | | 
% 204.47/35.27  | | | SIMP: (24) implies:
% 204.47/35.27  | | |   (25)  all_4_2 = e1
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (10), (25) imply:
% 204.47/35.27  | | |   (26)   ~ (all_52_9 = e1)
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (11), (25) imply:
% 204.47/35.27  | | |   (27)  op(e1, e1) = e2
% 204.47/35.27  | | | 
% 204.47/35.27  | | | GROUND_INST: instantiating (2) with all_10_2, e2, e1, e1, simplifying with
% 204.47/35.27  | | |              (18), (27) gives:
% 204.47/35.27  | | |   (28)  all_10_2 = e2
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (4), (28) imply:
% 204.47/35.27  | | |   (29)   ~ (all_52_17 = e2)
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REF_CLOSE: (1), (2), (3), (7), (9), (13), (14), (15), (16), (17), (19),
% 204.47/35.27  | | |            (20), (26), (29) are inconsistent by sub-proof #937.
% 204.47/35.27  | | | 
% 204.47/35.27  | | Case 2:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (30)  all_56_5 = e0
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REF_CLOSE: (6), (8), (30) are inconsistent by sub-proof #1313.
% 204.47/35.27  | | | 
% 204.47/35.27  | | End of split
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #937 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.47/35.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (3)   ~ (all_4_2 = e3)
% 204.47/35.27    (4)  op(e2, e2) = all_4_2
% 204.47/35.27    (5)  all_56_2 = all_52_17
% 204.47/35.27    (6)   ~ (all_52_9 = e1)
% 204.47/35.27    (7)  all_56_1 = all_52_9
% 204.47/35.27    (8)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.27    (9)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.27    (10)   ~ (all_52_17 = e1)
% 204.47/35.27    (11)   ~ (all_52_9 = all_52_17)
% 204.47/35.27    (12)  op(all_52_9, all_52_9) = e3
% 204.47/35.27    (13)   ~ (all_52_17 = e2)
% 204.47/35.27    (14)  all_58_4 = all_52_17
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (1) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (15)  all_58_4 = e0
% 204.47/35.27  | | 
% 204.47/35.27  | | COMBINE_EQS: (14), (15) imply:
% 204.47/35.27  | |   (16)  all_52_17 = e0
% 204.47/35.27  | | 
% 204.47/35.27  | | SIMP: (16) implies:
% 204.47/35.27  | |   (17)  all_52_17 = e0
% 204.47/35.27  | | 
% 204.47/35.27  | | REDUCE: (11), (17) imply:
% 204.47/35.27  | |   (18)   ~ (all_52_9 = e0)
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (12), (18) are inconsistent by
% 204.47/35.27  | |            sub-proof #1109.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (19)   ~ (all_58_4 = e0)
% 204.47/35.27  | | 
% 204.47/35.27  | | REDUCE: (14), (19) imply:
% 204.47/35.27  | |   (20)   ~ (all_52_17 = e0)
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (5), (9), (10), (13), (20) are inconsistent by sub-proof #1180.
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #938 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (2)   ~ (all_52_5 = all_52_13)
% 204.47/35.27    (3)  all_58_1 = all_52_9
% 204.47/35.27    (4)  op(all_52_5, all_52_5) = all_52_4
% 204.47/35.27    (5)  all_58_13 = all_52_15
% 204.47/35.27    (6)   ~ (all_52_15 = e3)
% 204.47/35.27    (7)  all_58_2 = all_4_0
% 204.47/35.27    (8)  op(all_4_2, e2) = e3
% 204.47/35.27    (9)   ~ (all_4_0 = e3)
% 204.47/35.27    (10)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.27    (11)  all_58_7 = all_52_13
% 204.47/35.27    (12)  all_58_12 = all_52_7
% 204.47/35.27    (13)   ~ (all_52_7 = e3)
% 204.47/35.27    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27    (15)   ~ (all_52_9 = all_4_2)
% 204.47/35.27    (16)   ~ (all_52_9 = all_6_2)
% 204.47/35.27    (17)  op(e3, e3) = all_6_2
% 204.47/35.27    (18)  all_58_6 = all_52_5
% 204.47/35.27    (19)  op(e3, e2) = all_52_9
% 204.47/35.27    (20)  op(all_52_9, all_52_9) = e3
% 204.47/35.27    (21)  all_58_3 = all_4_2
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (10) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (22)  all_58_2 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (7), (9), (22) are inconsistent by sub-proof #948.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (23)  all_58_6 = e3 | all_58_12 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | BETA: splitting (23) gives:
% 204.47/35.27  | | 
% 204.47/35.27  | | Case 1:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (24)  all_58_6 = e3
% 204.47/35.27  | | | 
% 204.47/35.27  | | | COMBINE_EQS: (18), (24) imply:
% 204.47/35.27  | | |   (25)  all_52_5 = e3
% 204.47/35.27  | | | 
% 204.47/35.27  | | | SIMP: (25) implies:
% 204.47/35.27  | | |   (26)  all_52_5 = e3
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (2), (26) imply:
% 204.47/35.27  | | |   (27)   ~ (all_52_13 = e3)
% 204.47/35.27  | | | 
% 204.47/35.27  | | | SIMP: (27) implies:
% 204.47/35.27  | | |   (28)   ~ (all_52_13 = e3)
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REDUCE: (4), (26) imply:
% 204.47/35.27  | | |   (29)  op(e3, e3) = all_52_4
% 204.47/35.27  | | | 
% 204.47/35.27  | | | GROUND_INST: instantiating (1) with all_6_2, all_52_4, e3, e3, simplifying
% 204.47/35.27  | | |              with (17), (29) gives:
% 204.47/35.27  | | |   (30)  all_52_4 = all_6_2
% 204.47/35.27  | | | 
% 204.47/35.27  | | | BETA: splitting (14) gives:
% 204.47/35.27  | | | 
% 204.47/35.27  | | | Case 1:
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | |   (31)  all_58_1 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | COMBINE_EQS: (3), (31) imply:
% 204.47/35.27  | | | |   (32)  all_52_9 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | REF_CLOSE: (1), (16), (17), (20), (32) are inconsistent by sub-proof
% 204.47/35.27  | | | |            #1337.
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | Case 2:
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | |   (33)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | | REF_CLOSE: (1), (5), (6), (8), (11), (15), (19), (21), (28), (33) are
% 204.47/35.27  | | | |            inconsistent by sub-proof #939.
% 204.47/35.27  | | | | 
% 204.47/35.27  | | | End of split
% 204.47/35.27  | | | 
% 204.47/35.27  | | Case 2:
% 204.47/35.27  | | | 
% 204.47/35.27  | | |   (34)  all_58_12 = e3
% 204.47/35.27  | | | 
% 204.47/35.27  | | | REF_CLOSE: (12), (13), (34) are inconsistent by sub-proof #1367.
% 204.47/35.27  | | | 
% 204.47/35.27  | | End of split
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #939 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (2)  all_58_13 = all_52_15
% 204.47/35.27    (3)   ~ (all_52_15 = e3)
% 204.47/35.27    (4)  op(all_4_2, e2) = e3
% 204.47/35.27    (5)  all_58_7 = all_52_13
% 204.47/35.27    (6)   ~ (all_52_9 = all_4_2)
% 204.47/35.27    (7)   ~ (all_52_13 = e3)
% 204.47/35.27    (8)  op(e3, e2) = all_52_9
% 204.47/35.27    (9)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27    (10)  all_58_3 = all_4_2
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | BETA: splitting (9) gives:
% 204.47/35.27  | 
% 204.47/35.27  | Case 1:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (11)  all_58_3 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | COMBINE_EQS: (10), (11) imply:
% 204.47/35.27  | |   (12)  all_4_2 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REDUCE: (6), (12) imply:
% 204.47/35.27  | |   (13)   ~ (all_52_9 = e3)
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (1), (4), (8), (12), (13) are inconsistent by sub-proof #977.
% 204.47/35.27  | | 
% 204.47/35.27  | Case 2:
% 204.47/35.27  | | 
% 204.47/35.27  | |   (14)  all_58_7 = e3 | all_58_13 = e3
% 204.47/35.27  | | 
% 204.47/35.27  | | REF_CLOSE: (2), (3), (5), (7), (14) are inconsistent by sub-proof #1298.
% 204.47/35.27  | | 
% 204.47/35.27  | End of split
% 204.47/35.27  | 
% 204.47/35.27  End of proof
% 204.47/35.27  
% 204.47/35.27  Sub-proof #940 shows that the following formulas are inconsistent:
% 204.47/35.27  ----------------------------------------------------------------
% 204.47/35.27    (1)   ~ (e3 = e1)
% 204.47/35.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.27    (3)   ~ (e3 = e0)
% 204.47/35.27    (4)   ~ (all_4_0 = e1)
% 204.47/35.27    (5)  all_58_0 = all_6_2
% 204.47/35.27    (6)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.47/35.27    (7)   ~ (all_52_27 = all_52_29)
% 204.47/35.27    (8)  all_58_9 = all_52_25
% 204.47/35.27    (9)  op(all_52_27, all_52_27) = all_52_26
% 204.47/35.27    (10)   ~ (all_6_2 = all_4_0)
% 204.47/35.27    (11)  all_32_2 = all_4_2
% 204.47/35.27    (12)  op(e2, e2) = all_4_2
% 204.47/35.27    (13)  all_58_11 = all_52_29
% 204.47/35.27    (14)  all_56_5 = all_4_2
% 204.47/35.27    (15)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.27    (16)  all_58_2 = all_4_0
% 204.47/35.27    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.27    (18)  op(all_4_2, e2) = e3
% 204.47/35.27    (19)  all_58_15 = e0
% 204.47/35.27    (20)   ~ (all_4_0 = e3)
% 204.47/35.27    (21)   ~ (all_52_25 = e0)
% 204.47/35.27    (22)  all_58_10 = all_52_27
% 204.47/35.27    (23)   ~ (all_52_25 = all_52_29)
% 204.47/35.27    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.27    (25)  all_56_7 = all_52_27
% 204.47/35.27    (26)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.27    (27)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.27    (28)  all_56_4 = all_4_0
% 204.47/35.27    (29)  op(all_52_29, all_52_29) = all_52_28
% 204.47/35.27    (30)   ~ (all_52_25 = all_6_2)
% 204.47/35.27    (31)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.27    (32)   ~ (all_52_9 = all_4_2)
% 204.47/35.27    (33)  op(e3, e3) = all_6_2
% 204.47/35.27    (34)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.47/35.27    (35)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.27    (36)  all_32_0 = all_4_0
% 204.47/35.27    (37)  all_56_3 = all_52_25
% 204.47/35.27    (38)  all_58_5 = all_52_19
% 204.47/35.27    (39)   ~ (all_52_27 = all_4_2)
% 204.47/35.27    (40)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.27    (41)   ~ (all_4_0 = all_4_2)
% 204.47/35.27    (42)  op(e3, e2) = all_52_9
% 204.47/35.27    (43)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.47/35.27    (44)  all_58_3 = all_4_2
% 204.47/35.27    (45)   ~ (all_52_19 = all_4_2)
% 204.47/35.27    (46)  op(all_52_25, all_52_25) = all_52_24
% 204.47/35.27  
% 204.47/35.27  Begin of proof
% 204.47/35.27  | 
% 204.47/35.27  | ALPHA: (43) implies:
% 204.47/35.28  |   (47)  all_52_28 = e1
% 204.47/35.28  |   (48)  all_52_26 = e2
% 204.47/35.28  |   (49)  all_52_24 = e3
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (46), (49) imply:
% 204.47/35.28  |   (50)  op(all_52_25, all_52_25) = e3
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (9), (48) imply:
% 204.47/35.28  |   (51)  op(all_52_27, all_52_27) = e2
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (29), (47) imply:
% 204.47/35.28  |   (52)  op(all_52_29, all_52_29) = e1
% 204.47/35.28  | 
% 204.47/35.28  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 204.47/35.28  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 204.47/35.28  |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 204.47/35.28  |            (37), (38), (39), (40), (41), (42), (44), (45), (50), (51), (52)
% 204.47/35.28  |            are inconsistent by sub-proof #941.
% 204.47/35.28  | 
% 204.47/35.28  End of proof
% 204.47/35.28  
% 204.47/35.28  Sub-proof #941 shows that the following formulas are inconsistent:
% 204.47/35.28  ----------------------------------------------------------------
% 204.47/35.28    (1)   ~ (e3 = e1)
% 204.47/35.28    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.28    (3)   ~ (e3 = e0)
% 204.47/35.28    (4)   ~ (all_4_0 = e1)
% 204.47/35.28    (5)  all_58_0 = all_6_2
% 204.47/35.28    (6)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.47/35.28    (7)   ~ (all_52_27 = all_52_29)
% 204.47/35.28    (8)  all_58_9 = all_52_25
% 204.47/35.28    (9)   ~ (all_6_2 = all_4_0)
% 204.47/35.28    (10)  all_32_2 = all_4_2
% 204.47/35.28    (11)  op(e2, e2) = all_4_2
% 204.47/35.28    (12)  all_58_11 = all_52_29
% 204.47/35.28    (13)  all_56_5 = all_4_2
% 204.47/35.28    (14)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.28    (15)  all_58_2 = all_4_0
% 204.47/35.28    (16)  op(all_52_29, all_52_29) = e1
% 204.47/35.28    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.28    (18)  op(all_4_2, e2) = e3
% 204.47/35.28    (19)  all_58_15 = e0
% 204.47/35.28    (20)   ~ (all_4_0 = e3)
% 204.47/35.28    (21)   ~ (all_52_25 = e0)
% 204.47/35.28    (22)  all_58_10 = all_52_27
% 204.47/35.28    (23)   ~ (all_52_25 = all_52_29)
% 204.47/35.28    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.28    (25)  all_56_7 = all_52_27
% 204.47/35.28    (26)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.28    (27)  op(all_52_25, all_52_25) = e3
% 204.47/35.28    (28)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.28    (29)  all_56_4 = all_4_0
% 204.47/35.28    (30)  op(all_52_27, all_52_27) = e2
% 204.47/35.28    (31)   ~ (all_52_25 = all_6_2)
% 204.47/35.28    (32)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.28    (33)   ~ (all_52_9 = all_4_2)
% 204.47/35.28    (34)  op(e3, e3) = all_6_2
% 204.47/35.28    (35)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.47/35.28    (36)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.28    (37)  all_32_0 = all_4_0
% 204.47/35.28    (38)  all_56_3 = all_52_25
% 204.47/35.28    (39)  all_58_5 = all_52_19
% 204.47/35.28    (40)   ~ (all_52_27 = all_4_2)
% 204.47/35.28    (41)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.28    (42)   ~ (all_4_0 = all_4_2)
% 204.47/35.28    (43)  op(e3, e2) = all_52_9
% 204.47/35.28    (44)  all_58_3 = all_4_2
% 204.47/35.28    (45)   ~ (all_52_19 = all_4_2)
% 204.47/35.28  
% 204.47/35.28  Begin of proof
% 204.47/35.28  | 
% 204.47/35.28  | BETA: splitting (6) gives:
% 204.47/35.28  | 
% 204.47/35.28  | Case 1:
% 204.47/35.28  | | 
% 204.47/35.28  | |   (46)  all_56_7 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | COMBINE_EQS: (25), (46) imply:
% 204.47/35.28  | |   (47)  all_52_27 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | SIMP: (47) implies:
% 204.47/35.28  | |   (48)  all_52_27 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (40), (48) imply:
% 204.47/35.28  | |   (49)   ~ (all_4_2 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | SIMP: (49) implies:
% 204.47/35.28  | |   (50)   ~ (all_4_2 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (30), (48) imply:
% 204.47/35.28  | |   (51)  op(e3, e3) = e2
% 204.47/35.28  | | 
% 204.47/35.28  | | REF_CLOSE: (2), (4), (9), (10), (11), (13), (14), (18), (26), (28), (29),
% 204.47/35.28  | |            (34), (36), (37), (41), (42), (50), (51) are inconsistent by
% 204.47/35.28  | |            sub-proof #947.
% 204.47/35.28  | | 
% 204.47/35.28  | Case 2:
% 204.47/35.28  | | 
% 204.47/35.28  | |   (52)   ~ (all_56_7 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (25), (52) imply:
% 204.47/35.28  | |   (53)   ~ (all_52_27 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | BETA: splitting (17) gives:
% 204.47/35.28  | | 
% 204.47/35.28  | | Case 1:
% 204.47/35.28  | | | 
% 204.47/35.28  | | |   (54)  all_58_2 = e3
% 204.47/35.28  | | | 
% 204.47/35.28  | | | REF_CLOSE: (15), (20), (54) are inconsistent by sub-proof #948.
% 204.47/35.28  | | | 
% 204.47/35.28  | | Case 2:
% 204.47/35.28  | | | 
% 204.47/35.28  | | |   (55)   ~ (all_58_2 = e3)
% 204.47/35.28  | | |   (56)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.28  | | | 
% 204.47/35.28  | | | BETA: splitting (35) gives:
% 204.47/35.28  | | | 
% 204.47/35.28  | | | Case 1:
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | |   (57)  all_58_9 = e3
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | COMBINE_EQS: (8), (57) imply:
% 204.47/35.28  | | | |   (58)  all_52_25 = e3
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | REF_CLOSE: (2), (27), (31), (34), (58) are inconsistent by sub-proof
% 204.47/35.28  | | | |            #1246.
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | Case 2:
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | |   (59)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | BETA: splitting (59) gives:
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | Case 1:
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | |   (60)  all_58_10 = e3
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | | REF_CLOSE: (22), (53), (60) are inconsistent by sub-proof #1301.
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | Case 2:
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | |   (61)  all_58_11 = e3 | all_58_15 = e3
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | | BETA: splitting (61) gives:
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | | Case 1:
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | |   (62)  all_58_11 = e3
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | COMBINE_EQS: (12), (62) imply:
% 204.47/35.28  | | | | | |   (63)  all_52_29 = e3
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | SIMP: (63) implies:
% 204.47/35.28  | | | | | |   (64)  all_52_29 = e3
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | REDUCE: (23), (64) imply:
% 204.47/35.28  | | | | | |   (65)   ~ (all_52_25 = e3)
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | REDUCE: (16), (64) imply:
% 204.47/35.28  | | | | | |   (66)  op(e3, e3) = e1
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | GROUND_INST: instantiating (2) with all_6_2, e1, e3, e3, simplifying
% 204.47/35.28  | | | | | |              with (34), (66) gives:
% 204.47/35.28  | | | | | |   (67)  all_6_2 = e1
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | COMBINE_EQS: (5), (67) imply:
% 204.47/35.28  | | | | | |   (68)  all_58_0 = e1
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | REDUCE: (31), (67) imply:
% 204.47/35.28  | | | | | |   (69)   ~ (all_52_25 = e1)
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | BETA: splitting (32) gives:
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | Case 1:
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | |   (70)  all_56_3 = e3
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | REF_CLOSE: (38), (65), (70) are inconsistent by sub-proof #1339.
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | Case 2:
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | |   (71)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | BETA: splitting (24) gives:
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | Case 1:
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | |   (72)  all_58_0 = e3
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | | REF_CLOSE: (1), (68), (72) are inconsistent by sub-proof #1244.
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | Case 2:
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | |   (73)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | | BETA: splitting (71) gives:
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | | Case 1:
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | |   (74)  all_56_3 = e2
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | COMBINE_EQS: (38), (74) imply:
% 204.47/35.28  | | | | | | | | |   (75)  all_52_25 = e2
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | SIMP: (75) implies:
% 204.47/35.28  | | | | | | | | |   (76)  all_52_25 = e2
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | REDUCE: (27), (76) imply:
% 204.47/35.28  | | | | | | | | |   (77)  op(e2, e2) = e3
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | BETA: splitting (73) gives:
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | Case 1:
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | |   (78)  all_58_2 = e3
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | | REF_CLOSE: (15), (20), (78) are inconsistent by sub-proof
% 204.47/35.28  | | | | | | | | | |            #948.
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | Case 2:
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, e3, e2, e2,
% 204.47/35.28  | | | | | | | | | |              simplifying with (11), (77) gives:
% 204.47/35.28  | | | | | | | | | |   (79)  all_4_2 = e3
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | | REDUCE: (45), (79) imply:
% 204.47/35.28  | | | | | | | | | |   (80)   ~ (all_52_19 = e3)
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | | REF_CLOSE: (2), (18), (22), (33), (39), (43), (44), (53),
% 204.47/35.28  | | | | | | | | | |            (56), (80) are inconsistent by sub-proof #945.
% 204.47/35.28  | | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | End of split
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | Case 2:
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | |   (81)  all_56_3 = e1 | all_56_3 = e0
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | | REF_CLOSE: (21), (38), (69), (81) are inconsistent by
% 204.47/35.28  | | | | | | | | |            sub-proof #1330.
% 204.47/35.28  | | | | | | | | | 
% 204.47/35.28  | | | | | | | | End of split
% 204.47/35.28  | | | | | | | | 
% 204.47/35.28  | | | | | | | End of split
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | End of split
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | Case 2:
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | |   (82)  all_58_15 = e3
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | REF_CLOSE: (3), (19), (82) are inconsistent by sub-proof #1350.
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | End of split
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | End of split
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | End of split
% 204.47/35.28  | | | 
% 204.47/35.28  | | End of split
% 204.47/35.28  | | 
% 204.47/35.28  | End of split
% 204.47/35.28  | 
% 204.47/35.28  End of proof
% 204.47/35.28  
% 204.47/35.28  Sub-proof #942 shows that the following formulas are inconsistent:
% 204.47/35.28  ----------------------------------------------------------------
% 204.47/35.28    (1)   ~ (all_52_15 = all_52_23)
% 204.47/35.28    (2)   ~ (all_52_25 = all_52_27)
% 204.47/35.28    (3)  all_58_14 = all_52_23
% 204.47/35.28    (4)   ~ (e3 = e1)
% 204.47/35.28    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.28    (6)  all_58_1 = all_52_9
% 204.47/35.28    (7)   ~ (all_52_9 = all_52_13)
% 204.47/35.28    (8)   ~ (all_4_0 = e1)
% 204.47/35.28    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.47/35.28    (10)   ~ (all_52_7 = all_52_15)
% 204.47/35.28    (11)  op(all_52_7, all_52_7) = all_52_6
% 204.47/35.28    (12)   ~ (all_52_17 = all_52_25)
% 204.47/35.28    (13)  all_58_0 = all_6_2
% 204.47/35.28    (14)  op(e3, e0) = all_52_25
% 204.47/35.28    (15)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.47/35.28    (16)  op(all_52_19, all_52_19) = all_52_18
% 204.47/35.28    (17)   ~ (all_52_27 = all_52_29)
% 204.47/35.28    (18)  all_58_13 = all_52_15
% 204.47/35.28    (19)  op(all_10_2, all_10_2) = all_52_20
% 204.47/35.28    (20)  all_58_9 = all_52_25
% 204.47/35.28    (21)   ~ (all_6_1 = e1)
% 204.47/35.28    (22)  op(all_52_27, all_52_27) = all_52_26
% 204.47/35.28    (23)  op(e1, e3) = all_52_5
% 204.47/35.28    (24)   ~ (all_6_2 = all_4_0)
% 204.47/35.28    (25)  all_32_2 = all_4_2
% 204.47/35.28    (26)  op(e2, e2) = all_4_2
% 204.47/35.28    (27)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.47/35.28    (28)  all_58_11 = all_52_29
% 204.47/35.28    (29)  all_56_5 = all_4_2
% 204.47/35.28    (30)   ~ (all_52_9 = all_52_15)
% 204.47/35.28    (31)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.28    (32)   ~ (all_52_7 = all_6_2)
% 204.47/35.28    (33)  all_58_2 = all_4_0
% 204.47/35.28    (34)   ~ (all_52_15 = e0)
% 204.47/35.28    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.28    (36)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.47/35.28    (37)  op(all_4_2, e2) = e3
% 204.47/35.28    (38)  all_58_15 = e0
% 204.47/35.28    (39)   ~ (all_4_0 = e3)
% 204.47/35.28    (40)   ~ (all_52_25 = e0)
% 204.47/35.28    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.47/35.28    (42)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.28    (43)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.47/35.28    (44)  all_56_9 = all_52_13
% 204.47/35.28    (45)   ~ (e2 = e1)
% 204.47/35.28    (46)   ~ (all_52_13 = all_10_2)
% 204.47/35.28    (47)  op(e0, e0) = e0
% 204.47/35.28    (48)  all_58_10 = all_52_27
% 204.47/35.28    (49)  op(all_52_9, all_52_9) = all_52_8
% 204.47/35.28    (50)   ~ (all_52_19 = all_52_23)
% 204.47/35.28    (51)   ~ (all_52_25 = all_52_29)
% 204.47/35.28    (52)  all_58_7 = all_52_13
% 204.47/35.28    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.47/35.28    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.47/35.28    (55)  all_58_12 = all_52_7
% 204.47/35.28    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.47/35.28    (57)  all_56_2 = all_52_17
% 204.47/35.28    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.47/35.28    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.28    (60)  op(e3, all_6_1) = all_6_0
% 204.47/35.28    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.47/35.28    (62)  all_56_7 = all_52_27
% 204.47/35.28    (63)   ~ (e2 = e0)
% 204.47/35.28    (64)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.28    (65)   ~ (all_52_5 = all_52_29)
% 204.47/35.28    (66)   ~ (all_52_29 = e0)
% 204.47/35.28    (67)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.47/35.28    (68)  all_56_6 = all_52_19
% 204.47/35.28    (69)   ~ (all_52_19 = all_52_27)
% 204.47/35.28    (70)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.28    (71)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.47/35.28    (72)  all_56_4 = all_4_0
% 204.47/35.28    (73)   ~ (all_6_0 = e2)
% 204.47/35.28    (74)   ~ (all_52_13 = all_4_2)
% 204.47/35.28    (75)  op(e0, e3) = all_52_7
% 204.47/35.28    (76)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.28    (77)   ~ (all_52_9 = all_52_25)
% 204.47/35.28    (78)  op(all_52_23, all_52_23) = all_52_22
% 204.47/35.28    (79)  all_58_8 = all_10_2
% 204.47/35.28    (80)   ~ (all_52_23 = e0)
% 204.47/35.28    (81)  op(all_52_29, all_52_29) = all_52_28
% 204.47/35.28    (82)   ~ (all_52_7 = all_4_0)
% 204.47/35.28    (83)  all_56_12 = all_52_7
% 204.47/35.28    (84)  op(all_52_17, all_52_17) = all_52_16
% 204.47/35.28    (85)   ~ (all_52_25 = all_6_2)
% 204.47/35.28    (86)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.28    (87)   ~ (all_52_9 = all_4_2)
% 204.47/35.28    (88)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.47/35.28    (89)   ~ (all_52_9 = all_6_2)
% 204.47/35.28    (90)   ~ (all_52_13 = all_52_15)
% 204.47/35.28    (91)  op(e3, e3) = all_6_2
% 204.47/35.28    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.47/35.28    (93)  all_56_14 = all_52_23
% 204.47/35.28    (94)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.28    (95)  all_32_0 = all_4_0
% 204.47/35.28    (96)  all_56_3 = all_52_25
% 204.47/35.28    (97)  all_58_5 = all_52_19
% 204.47/35.28    (98)  all_56_1 = all_52_9
% 204.47/35.28    (99)   ~ (all_52_27 = all_4_2)
% 204.47/35.28    (100)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.28    (101)  all_58_6 = all_52_5
% 204.47/35.28    (102)   ~ (all_4_0 = all_4_2)
% 204.47/35.28    (103)  op(e3, e2) = all_52_9
% 204.47/35.28    (104)   ~ (all_52_17 = all_6_2)
% 204.47/35.28    (105)   ~ (e1 = e0)
% 204.47/35.28    (106)   ~ (e3 = e2)
% 204.47/35.28    (107)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.28    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.47/35.28    (109)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.47/35.28    (110)  op(all_52_13, all_52_13) = all_52_12
% 204.47/35.28    (111)   ~ (all_6_1 = e2)
% 204.47/35.28    (112)  op(e1, e1) = all_10_2
% 204.47/35.28    (113)   ~ (all_52_23 = all_10_2)
% 204.47/35.28    (114)   ~ (all_52_7 = all_52_23)
% 204.47/35.28    (115)  all_58_3 = all_4_2
% 204.47/35.28    (116)  all_56_13 = all_52_15
% 204.47/35.28    (117)   ~ (all_52_19 = all_4_2)
% 204.47/35.28    (118)  op(all_6_2, e3) = all_6_1
% 204.47/35.28    (119)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.47/35.28    (120)   ~ (all_52_13 = all_52_29)
% 204.47/35.28    (121)  all_58_4 = all_52_17
% 204.47/35.28    (122)   ~ (all_52_7 = e0)
% 204.47/35.28    (123)  op(all_52_25, all_52_25) = all_52_24
% 204.47/35.28  
% 204.47/35.28  Begin of proof
% 204.47/35.28  | 
% 204.47/35.28  | ALPHA: (119) implies:
% 204.47/35.28  |   (124)  all_52_22 = e0
% 204.47/35.28  |   (125)  all_52_20 = e1
% 204.47/35.28  |   (126)  all_52_18 = e2
% 204.47/35.28  |   (127)  all_52_16 = e3
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (84), (127) imply:
% 204.47/35.28  |   (128)  op(all_52_17, all_52_17) = e3
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (16), (126) imply:
% 204.47/35.28  |   (129)  op(all_52_19, all_52_19) = e2
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (78), (124) imply:
% 204.47/35.28  |   (130)  op(all_52_23, all_52_23) = e0
% 204.47/35.28  | 
% 204.47/35.28  | REDUCE: (19), (125) imply:
% 204.47/35.28  |   (131)  op(all_10_2, all_10_2) = e1
% 204.47/35.28  | 
% 204.47/35.28  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.47/35.28  |            (13), (14), (15), (17), (18), (20), (21), (22), (23), (24), (25),
% 204.47/35.28  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.47/35.28  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 204.47/35.28  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 204.47/35.28  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 204.47/35.28  |            (70), (71), (72), (73), (74), (75), (76), (77), (79), (80), (81),
% 204.47/35.28  |            (82), (83), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 204.47/35.28  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 204.47/35.28  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 204.47/35.28  |            (113), (114), (115), (116), (117), (118), (120), (121), (122),
% 204.47/35.28  |            (123), (128), (129), (130), (131) are inconsistent by sub-proof
% 204.47/35.28  |            #943.
% 204.47/35.28  | 
% 204.47/35.28  End of proof
% 204.47/35.28  
% 204.47/35.28  Sub-proof #943 shows that the following formulas are inconsistent:
% 204.47/35.28  ----------------------------------------------------------------
% 204.47/35.28    (1)   ~ (all_52_15 = all_52_23)
% 204.47/35.28    (2)   ~ (all_52_25 = all_52_27)
% 204.47/35.28    (3)  all_58_14 = all_52_23
% 204.47/35.28    (4)   ~ (e3 = e1)
% 204.47/35.28    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.28    (6)  all_58_1 = all_52_9
% 204.47/35.28    (7)   ~ (all_52_9 = all_52_13)
% 204.47/35.28    (8)  op(all_52_23, all_52_23) = e0
% 204.47/35.28    (9)   ~ (all_4_0 = e1)
% 204.47/35.28    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.47/35.28    (11)   ~ (all_52_7 = all_52_15)
% 204.47/35.28    (12)  op(all_52_7, all_52_7) = all_52_6
% 204.47/35.28    (13)   ~ (all_52_17 = all_52_25)
% 204.47/35.28    (14)  all_58_0 = all_6_2
% 204.47/35.28    (15)  op(e3, e0) = all_52_25
% 204.47/35.28    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.47/35.28    (17)   ~ (all_52_27 = all_52_29)
% 204.47/35.28    (18)  all_58_13 = all_52_15
% 204.47/35.28    (19)  all_58_9 = all_52_25
% 204.47/35.28    (20)   ~ (all_6_1 = e1)
% 204.47/35.28    (21)  op(all_52_27, all_52_27) = all_52_26
% 204.47/35.28    (22)  op(e1, e3) = all_52_5
% 204.47/35.28    (23)   ~ (all_6_2 = all_4_0)
% 204.47/35.28    (24)  all_32_2 = all_4_2
% 204.47/35.28    (25)  op(e2, e2) = all_4_2
% 204.47/35.28    (26)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.47/35.28    (27)  all_58_11 = all_52_29
% 204.47/35.28    (28)  all_56_5 = all_4_2
% 204.47/35.28    (29)   ~ (all_52_9 = all_52_15)
% 204.47/35.28    (30)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.28    (31)   ~ (all_52_7 = all_6_2)
% 204.47/35.28    (32)  all_58_2 = all_4_0
% 204.47/35.28    (33)   ~ (all_52_15 = e0)
% 204.47/35.28    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.28    (35)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.47/35.28    (36)  op(all_4_2, e2) = e3
% 204.47/35.28    (37)  all_58_15 = e0
% 204.47/35.28    (38)   ~ (all_4_0 = e3)
% 204.47/35.28    (39)   ~ (all_52_25 = e0)
% 204.47/35.28    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.47/35.28    (41)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.47/35.28    (42)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.47/35.28    (43)  all_56_9 = all_52_13
% 204.47/35.28    (44)   ~ (e2 = e1)
% 204.47/35.28    (45)   ~ (all_52_13 = all_10_2)
% 204.47/35.28    (46)  op(e0, e0) = e0
% 204.47/35.28    (47)  op(all_10_2, all_10_2) = e1
% 204.47/35.28    (48)  all_58_10 = all_52_27
% 204.47/35.28    (49)  op(all_52_9, all_52_9) = all_52_8
% 204.47/35.28    (50)   ~ (all_52_19 = all_52_23)
% 204.47/35.28    (51)   ~ (all_52_25 = all_52_29)
% 204.47/35.28    (52)  all_58_7 = all_52_13
% 204.47/35.28    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.47/35.28    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.47/35.28    (55)  op(all_52_19, all_52_19) = e2
% 204.47/35.28    (56)  all_58_12 = all_52_7
% 204.47/35.28    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.47/35.28    (58)  all_56_2 = all_52_17
% 204.47/35.28    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.47/35.28    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.47/35.28    (61)  op(e3, all_6_1) = all_6_0
% 204.47/35.28    (62)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.47/35.28    (63)  all_56_7 = all_52_27
% 204.47/35.28    (64)   ~ (e2 = e0)
% 204.47/35.28    (65)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.28    (66)   ~ (all_52_5 = all_52_29)
% 204.47/35.28    (67)   ~ (all_52_29 = e0)
% 204.47/35.28    (68)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.47/35.28    (69)  all_56_6 = all_52_19
% 204.47/35.28    (70)   ~ (all_52_19 = all_52_27)
% 204.47/35.28    (71)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.28    (72)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.47/35.28    (73)  all_56_4 = all_4_0
% 204.47/35.28    (74)   ~ (all_6_0 = e2)
% 204.47/35.28    (75)   ~ (all_52_13 = all_4_2)
% 204.47/35.28    (76)  op(e0, e3) = all_52_7
% 204.47/35.28    (77)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.28    (78)   ~ (all_52_9 = all_52_25)
% 204.47/35.28    (79)  all_58_8 = all_10_2
% 204.47/35.28    (80)   ~ (all_52_23 = e0)
% 204.47/35.28    (81)  op(all_52_29, all_52_29) = all_52_28
% 204.47/35.28    (82)   ~ (all_52_7 = all_4_0)
% 204.47/35.28    (83)  all_56_12 = all_52_7
% 204.47/35.28    (84)   ~ (all_52_25 = all_6_2)
% 204.47/35.28    (85)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.28    (86)   ~ (all_52_9 = all_4_2)
% 204.47/35.28    (87)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.47/35.28    (88)   ~ (all_52_9 = all_6_2)
% 204.47/35.28    (89)   ~ (all_52_13 = all_52_15)
% 204.47/35.28    (90)  op(e3, e3) = all_6_2
% 204.47/35.28    (91)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.47/35.28    (92)  all_56_14 = all_52_23
% 204.47/35.28    (93)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.28    (94)  all_32_0 = all_4_0
% 204.47/35.28    (95)  all_56_3 = all_52_25
% 204.47/35.28    (96)  all_58_5 = all_52_19
% 204.47/35.28    (97)  all_56_1 = all_52_9
% 204.47/35.28    (98)   ~ (all_52_27 = all_4_2)
% 204.47/35.28    (99)  op(all_52_17, all_52_17) = e3
% 204.47/35.28    (100)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.28    (101)  all_58_6 = all_52_5
% 204.47/35.28    (102)   ~ (all_4_0 = all_4_2)
% 204.47/35.28    (103)  op(e3, e2) = all_52_9
% 204.47/35.28    (104)   ~ (all_52_17 = all_6_2)
% 204.47/35.28    (105)   ~ (e1 = e0)
% 204.47/35.28    (106)   ~ (e3 = e2)
% 204.47/35.28    (107)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.28    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.47/35.28    (109)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.47/35.28    (110)  op(all_52_13, all_52_13) = all_52_12
% 204.47/35.28    (111)   ~ (all_6_1 = e2)
% 204.47/35.28    (112)  op(e1, e1) = all_10_2
% 204.47/35.28    (113)   ~ (all_52_23 = all_10_2)
% 204.47/35.28    (114)   ~ (all_52_7 = all_52_23)
% 204.47/35.28    (115)  all_58_3 = all_4_2
% 204.47/35.28    (116)  all_56_13 = all_52_15
% 204.47/35.28    (117)   ~ (all_52_19 = all_4_2)
% 204.47/35.28    (118)  op(all_6_2, e3) = all_6_1
% 204.47/35.28    (119)   ~ (all_52_13 = all_52_29)
% 204.47/35.28    (120)  all_58_4 = all_52_17
% 204.47/35.28    (121)   ~ (all_52_7 = e0)
% 204.47/35.28    (122)  op(all_52_25, all_52_25) = all_52_24
% 204.47/35.28  
% 204.47/35.28  Begin of proof
% 204.47/35.28  | 
% 204.47/35.28  | BETA: splitting (16) gives:
% 204.47/35.28  | 
% 204.47/35.28  | Case 1:
% 204.47/35.28  | | 
% 204.47/35.28  | |   (123)  all_56_7 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | COMBINE_EQS: (63), (123) imply:
% 204.47/35.28  | |   (124)  all_52_27 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | SIMP: (124) implies:
% 204.47/35.28  | |   (125)  all_52_27 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | COMBINE_EQS: (48), (125) imply:
% 204.47/35.28  | |   (126)  all_58_10 = e3
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (70), (125) imply:
% 204.47/35.28  | |   (127)   ~ (all_52_19 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (2), (125) imply:
% 204.47/35.28  | |   (128)   ~ (all_52_25 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (17), (125) imply:
% 204.47/35.28  | |   (129)   ~ (all_52_29 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | SIMP: (129) implies:
% 204.47/35.28  | |   (130)   ~ (all_52_29 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (98), (125) imply:
% 204.47/35.28  | |   (131)   ~ (all_4_2 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | SIMP: (131) implies:
% 204.47/35.28  | |   (132)   ~ (all_4_2 = e3)
% 204.47/35.28  | | 
% 204.47/35.28  | | REDUCE: (21), (125) imply:
% 204.47/35.28  | |   (133)  op(e3, e3) = all_52_26
% 204.47/35.28  | | 
% 204.47/35.28  | | GROUND_INST: instantiating (5) with all_6_2, all_52_26, e3, e3, simplifying
% 204.47/35.28  | |              with (90), (133) gives:
% 204.47/35.28  | |   (134)  all_52_26 = all_6_2
% 204.47/35.28  | | 
% 204.47/35.28  | | BETA: splitting (85) gives:
% 204.47/35.28  | | 
% 204.47/35.28  | | Case 1:
% 204.47/35.28  | | | 
% 204.47/35.28  | | |   (135)  all_56_3 = e3
% 204.47/35.28  | | | 
% 204.47/35.28  | | | REF_CLOSE: (95), (128), (135) are inconsistent by sub-proof #1339.
% 204.47/35.28  | | | 
% 204.47/35.28  | | Case 2:
% 204.47/35.28  | | | 
% 204.47/35.28  | | |   (136)   ~ (all_56_3 = e3)
% 204.47/35.28  | | |   (137)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.47/35.28  | | | 
% 204.47/35.28  | | | BETA: splitting (87) gives:
% 204.47/35.28  | | | 
% 204.47/35.28  | | | Case 1:
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | |   (138)  all_58_9 = e2
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | COMBINE_EQS: (19), (138) imply:
% 204.47/35.28  | | | |   (139)  all_52_25 = e2
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | SIMP: (139) implies:
% 204.47/35.28  | | | |   (140)  all_52_25 = e2
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | REDUCE: (78), (140) imply:
% 204.47/35.28  | | | |   (141)   ~ (all_52_9 = e2)
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | REDUCE: (84), (140) imply:
% 204.47/35.28  | | | |   (142)   ~ (all_6_2 = e2)
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | SIMP: (142) implies:
% 204.47/35.28  | | | |   (143)   ~ (all_6_2 = e2)
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | REDUCE: (128), (140) imply:
% 204.47/35.28  | | | |   (144)   ~ (e3 = e2)
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | REDUCE: (122), (140) imply:
% 204.47/35.28  | | | |   (145)  op(e2, e2) = all_52_24
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | REDUCE: (15), (140) imply:
% 204.47/35.28  | | | |   (146)  op(e3, e0) = e2
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | BETA: splitting (35) gives:
% 204.47/35.28  | | | | 
% 204.47/35.28  | | | | Case 1:
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | |   (147)  all_58_9 = e1
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | | REF_CLOSE: (44), (138), (147) are inconsistent by sub-proof #1214.
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | Case 2:
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | |   (148)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | | BETA: splitting (148) gives:
% 204.47/35.28  | | | | | 
% 204.47/35.28  | | | | | Case 1:
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | |   (149)  all_58_10 = e1
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | REF_CLOSE: (4), (126), (149) are inconsistent by sub-proof #968.
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | Case 2:
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | |   (150)  all_58_11 = e1 | all_58_15 = e1
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | BETA: splitting (150) gives:
% 204.47/35.28  | | | | | | 
% 204.47/35.28  | | | | | | Case 1:
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | |   (151)  all_58_11 = e1
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | COMBINE_EQS: (27), (151) imply:
% 204.47/35.28  | | | | | | |   (152)  all_52_29 = e1
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | SIMP: (152) implies:
% 204.47/35.28  | | | | | | |   (153)  all_52_29 = e1
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | REDUCE: (66), (153) imply:
% 204.47/35.28  | | | | | | |   (154)   ~ (all_52_5 = e1)
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | REDUCE: (81), (153) imply:
% 204.47/35.28  | | | | | | |   (155)  op(e1, e1) = all_52_28
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_28, e1, e1,
% 204.47/35.28  | | | | | | |              simplifying with (112), (155) gives:
% 204.47/35.28  | | | | | | |   (156)  all_52_28 = all_10_2
% 204.47/35.28  | | | | | | | 
% 204.47/35.28  | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_24, e2, e2,
% 204.47/35.28  | | | | | | |              simplifying with (25), (145) gives:
% 204.47/35.28  | | | | | | |   (157)  all_52_24 = all_4_2
% 204.47/35.28  | | | | | | | 
% 204.47/35.29  | | | | | | | BETA: splitting (54) gives:
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | |   (158)  all_58_2 = e1
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | REF_CLOSE: (9), (32), (158) are inconsistent by sub-proof #967.
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | |   (159)   ~ (all_58_2 = e1)
% 204.47/35.29  | | | | | | | |   (160)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | BETA: splitting (62) gives:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | |   (161)  all_58_0 = e1
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | REF_CLOSE: (5), (10), (14), (22), (23), (24), (25), (26),
% 204.47/35.29  | | | | | | | | |            (28), (31), (36), (56), (61), (64), (65), (71),
% 204.47/35.29  | | | | | | | | |            (72), (73), (74), (82), (83), (86), (93), (94),
% 204.47/35.29  | | | | | | | | |            (100), (101), (102), (103), (105), (106), (111),
% 204.47/35.29  | | | | | | | | |            (118), (121), (143), (146), (161) are inconsistent
% 204.47/35.29  | | | | | | | | |            by sub-proof #964.
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | |   (162)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | BETA: splitting (162) gives:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | |   (163)  all_58_2 = e1
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | REF_CLOSE: (9), (32), (163) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | |            #967.
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | |   (164)  all_58_6 = e1 | all_58_12 = e1
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | BETA: splitting (164) gives:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | |   (165)  all_58_6 = e1
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REF_CLOSE: (101), (154), (165) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | |            #963.
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | |   (166)  all_58_12 = e1
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | COMBINE_EQS: (56), (166) imply:
% 204.47/35.29  | | | | | | | | | | |   (167)  all_52_7 = e1
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | SIMP: (167) implies:
% 204.47/35.29  | | | | | | | | | | |   (168)  all_52_7 = e1
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (11), (168) imply:
% 204.47/35.29  | | | | | | | | | | |   (169)   ~ (all_52_15 = e1)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | SIMP: (169) implies:
% 204.47/35.29  | | | | | | | | | | |   (170)   ~ (all_52_15 = e1)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (114), (168) imply:
% 204.47/35.29  | | | | | | | | | | |   (171)   ~ (all_52_23 = e1)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | SIMP: (171) implies:
% 204.47/35.29  | | | | | | | | | | |   (172)   ~ (all_52_23 = e1)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (12), (168) imply:
% 204.47/35.29  | | | | | | | | | | |   (173)  op(e1, e1) = all_52_6
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (76), (168) imply:
% 204.47/35.29  | | | | | | | | | | |   (174)  op(e0, e3) = e1
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_6, e1, e1,
% 204.47/35.29  | | | | | | | | | | |              simplifying with (112), (173) gives:
% 204.47/35.29  | | | | | | | | | | |   (175)  all_52_6 = all_10_2
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | BETA: splitting (40) gives:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | |   (176)  all_56_13 = e3
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | COMBINE_EQS: (116), (176) imply:
% 204.47/35.29  | | | | | | | | | | | |   (177)  all_52_15 = e3
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | SIMP: (177) implies:
% 204.47/35.29  | | | | | | | | | | | |   (178)  all_52_15 = e3
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (29), (178) imply:
% 204.47/35.29  | | | | | | | | | | | |   (179)   ~ (all_52_9 = e3)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (1), (178) imply:
% 204.47/35.29  | | | | | | | | | | | |   (180)   ~ (all_52_23 = e3)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | SIMP: (180) implies:
% 204.47/35.29  | | | | | | | | | | | |   (181)   ~ (all_52_23 = e3)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | BETA: splitting (53) gives:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (182)  all_56_14 = e3
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | COMBINE_EQS: (92), (182) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (183)  all_52_23 = e3
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (181), (183) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (184)  $false
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (185)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (186)  all_56_14 = e2
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | COMBINE_EQS: (92), (186) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (187)  all_52_23 = e2
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REDUCE: (113), (187) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (188)   ~ (all_10_2 = e2)
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | SIMP: (188) implies:
% 204.47/35.29  | | | | | | | | | | | | | |   (189)   ~ (all_10_2 = e2)
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REDUCE: (8), (187) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (190)  op(e2, e2) = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, e0, e2, e2,
% 204.47/35.29  | | | | | | | | | | | | | |              simplifying with (25), (190) gives:
% 204.47/35.29  | | | | | | | | | | | | | |   (191)  all_4_2 = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | COMBINE_EQS: (115), (191) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (192)  all_58_3 = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REDUCE: (86), (191) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (193)   ~ (all_52_9 = e0)
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | |   (194)  all_56_1 = e3
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | REF_CLOSE: (97), (179), (194) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | |            #1326.
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | |   (195)   ~ (all_56_1 = e3)
% 204.47/35.29  | | | | | | | | | | | | | | |   (196)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | |   (197)  all_58_1 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (197) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | |   (198)  all_52_9 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | REDUCE: (179), (198) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | |   (199)   ~ (e3 = e1)
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | REDUCE: (49), (198) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | |   (200)  op(e1, e1) = all_52_8
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (201)  all_58_3 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (201) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (202)  e1 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | SIMP: (202) implies:
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (203)  e1 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | REDUCE: (105), (203) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (204)  $false
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (205)  all_58_5 = e1 | all_58_10 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (206)  all_58_5 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (206) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (207)  all_52_19 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (208)  all_52_19 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | REDUCE: (55), (208) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (209)  op(e1, e1) = e2
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (112), (189), (200), (209) are inconsistent
% 204.47/35.29  | | | | | | | | | | | | | | | | | |            by sub-proof #962.
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (210)  all_58_10 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (126), (210) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | | | | |            #968.
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | |   (211)   ~ (all_58_1 = e1)
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | REDUCE: (6), (211) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | |   (212)   ~ (all_52_9 = e1)
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | REF_CLOSE: (97), (141), (193), (196), (212) are inconsistent
% 204.47/35.29  | | | | | | | | | | | | | | | |            by sub-proof #1314.
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (213)  all_56_14 = e1 | all_56_14 = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REF_CLOSE: (80), (92), (172), (213) are inconsistent by
% 204.47/35.29  | | | | | | | | | | | | | |            sub-proof #1381.
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | |   (214)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | BETA: splitting (214) gives:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (215)  all_56_13 = e2
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | COMBINE_EQS: (116), (215) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (216)  all_52_15 = e2
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | SIMP: (216) implies:
% 204.47/35.29  | | | | | | | | | | | | |   (217)  all_52_15 = e2
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (1), (217) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (218)   ~ (all_52_23 = e2)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | SIMP: (218) implies:
% 204.47/35.29  | | | | | | | | | | | | |   (219)   ~ (all_52_23 = e2)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | BETA: splitting (53) gives:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (220)  all_56_14 = e3
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | COMBINE_EQS: (92), (220) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (221)  all_52_23 = e3
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REDUCE: (8), (221) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (222)  op(e3, e3) = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, e0, e3, e3,
% 204.47/35.29  | | | | | | | | | | | | | |              simplifying with (90), (222) gives:
% 204.47/35.29  | | | | | | | | | | | | | |   (223)  all_6_2 = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REDUCE: (118), (223) imply:
% 204.47/35.29  | | | | | | | | | | | | | |   (224)  op(e0, e3) = all_6_1
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REF_CLOSE: (5), (20), (174), (224) are inconsistent by
% 204.47/35.29  | | | | | | | | | | | | | |            sub-proof #961.
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (225)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REF_CLOSE: (80), (92), (172), (219), (225) are inconsistent
% 204.47/35.29  | | | | | | | | | | | | | |            by sub-proof #960.
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (226)  all_56_13 = e1 | all_56_13 = e0
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REF_CLOSE: (33), (116), (170), (226) are inconsistent by
% 204.47/35.29  | | | | | | | | | | | | |            sub-proof #959.
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | End of split
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | Case 2:
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | |   (227)  all_58_15 = e1
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | REF_CLOSE: (37), (105), (227) are inconsistent by sub-proof #1207.
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | End of split
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | End of split
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | End of split
% 204.47/35.29  | | | | 
% 204.47/35.29  | | | Case 2:
% 204.47/35.29  | | | | 
% 204.47/35.29  | | | |   (228)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.47/35.29  | | | | 
% 204.47/35.29  | | | | BETA: splitting (228) gives:
% 204.47/35.29  | | | | 
% 204.47/35.29  | | | | Case 1:
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | |   (229)  all_58_10 = e2
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | | REF_CLOSE: (106), (126), (229) are inconsistent by sub-proof #1220.
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | Case 2:
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | |   (230)  all_58_11 = e2 | all_58_15 = e2
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | | BETA: splitting (230) gives:
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | | Case 1:
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | |   (231)  all_58_11 = e2
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | COMBINE_EQS: (27), (231) imply:
% 204.47/35.29  | | | | | |   (232)  all_52_29 = e2
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | SIMP: (232) implies:
% 204.47/35.29  | | | | | |   (233)  all_52_29 = e2
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | REDUCE: (119), (233) imply:
% 204.47/35.29  | | | | | |   (234)   ~ (all_52_13 = e2)
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | REDUCE: (51), (233) imply:
% 204.47/35.29  | | | | | |   (235)   ~ (all_52_25 = e2)
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | REDUCE: (130), (233) imply:
% 204.47/35.29  | | | | | |   (236)   ~ (e3 = e2)
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | REDUCE: (81), (233) imply:
% 204.47/35.29  | | | | | |   (237)  op(e2, e2) = all_52_28
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | BETA: splitting (35) gives:
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | Case 1:
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | |   (238)  all_58_9 = e1
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | COMBINE_EQS: (19), (238) imply:
% 204.47/35.29  | | | | | | |   (239)  all_52_25 = e1
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | SIMP: (239) implies:
% 204.47/35.29  | | | | | | |   (240)  all_52_25 = e1
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | REDUCE: (235), (240) imply:
% 204.47/35.29  | | | | | | |   (241)   ~ (e2 = e1)
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | REDUCE: (122), (240) imply:
% 204.47/35.29  | | | | | | |   (242)  op(e1, e1) = all_52_24
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_24, e1, e1,
% 204.47/35.29  | | | | | | |              simplifying with (112), (242) gives:
% 204.47/35.29  | | | | | | |   (243)  all_52_24 = all_10_2
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_28, e2, e2,
% 204.47/35.29  | | | | | | |              simplifying with (25), (237) gives:
% 204.47/35.29  | | | | | | |   (244)  all_52_28 = all_4_2
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | BETA: splitting (40) gives:
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | |   (245)  all_56_13 = e3
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | COMBINE_EQS: (116), (245) imply:
% 204.47/35.29  | | | | | | | |   (246)  all_52_15 = e3
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | REDUCE: (11), (246) imply:
% 204.47/35.29  | | | | | | | |   (247)   ~ (all_52_7 = e3)
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | REDUCE: (89), (246) imply:
% 204.47/35.29  | | | | | | | |   (248)   ~ (all_52_13 = e3)
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | REDUCE: (1), (246) imply:
% 204.47/35.29  | | | | | | | |   (249)   ~ (all_52_23 = e3)
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | SIMP: (249) implies:
% 204.47/35.29  | | | | | | | |   (250)   ~ (all_52_23 = e3)
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | BETA: splitting (109) gives:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | |   (251)  all_56_9 = e3
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | REF_CLOSE: (43), (248), (251) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | |            #958.
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | |   (252)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | BETA: splitting (53) gives:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | |   (253)  all_56_14 = e3
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | COMBINE_EQS: (92), (253) imply:
% 204.47/35.29  | | | | | | | | | |   (254)  all_52_23 = e3
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | REDUCE: (250), (254) imply:
% 204.47/35.29  | | | | | | | | | |   (255)  $false
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | CLOSE: (255) is inconsistent.
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | |   (256)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | BETA: splitting (10) gives:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | |   (257)  all_56_12 = e3
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REF_CLOSE: (83), (247), (257) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | |            #1383.
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | |   (258)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | BETA: splitting (68) gives:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | |   (259)  all_58_12 = e1
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | COMBINE_EQS: (56), (259) imply:
% 204.47/35.29  | | | | | | | | | | | |   (260)  all_52_7 = e1
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | SIMP: (260) implies:
% 204.47/35.29  | | | | | | | | | | | |   (261)  all_52_7 = e1
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (114), (261) imply:
% 204.47/35.29  | | | | | | | | | | | |   (262)   ~ (all_52_23 = e1)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | SIMP: (262) implies:
% 204.47/35.29  | | | | | | | | | | | |   (263)   ~ (all_52_23 = e1)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (12), (261) imply:
% 204.47/35.29  | | | | | | | | | | | |   (264)  op(e1, e1) = all_52_6
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | BETA: splitting (256) gives:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (265)  all_56_14 = e2
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | COMBINE_EQS: (92), (265) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (266)  all_52_23 = e2
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (50), (266) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (267)   ~ (all_52_19 = e2)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (113), (266) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (268)   ~ (all_10_2 = e2)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | SIMP: (268) implies:
% 204.47/35.29  | | | | | | | | | | | | |   (269)   ~ (all_10_2 = e2)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (8), (266) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (270)  op(e2, e2) = e0
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_6, e1, e1,
% 204.47/35.29  | | | | | | | | | | | | |              simplifying with (112), (264) gives:
% 204.47/35.29  | | | | | | | | | | | | |   (271)  all_52_6 = all_10_2
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, e0, e2, e2,
% 204.47/35.29  | | | | | | | | | | | | |              simplifying with (25), (270) gives:
% 204.47/35.29  | | | | | | | | | | | | |   (272)  all_4_2 = e0
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (75), (272) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (273)   ~ (all_52_13 = e0)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REDUCE: (117), (272) imply:
% 204.47/35.29  | | | | | | | | | | | | |   (274)   ~ (all_52_19 = e0)
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | BETA: splitting (57) gives:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (275)  all_56_6 = e3
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REF_CLOSE: (69), (127), (275) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | |            #957.
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (276)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | |   (277)  all_56_6 = e2
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | REF_CLOSE: (69), (267), (277) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | |            #956.
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | |   (278)  all_56_6 = e1 | all_56_6 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | |   (279)  all_56_9 = e2
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | REF_CLOSE: (43), (234), (279) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | | |            #955.
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | |   (280)  all_56_9 = e1 | all_56_9 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (281)  all_56_6 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (281) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (282)  all_52_19 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | SIMP: (282) implies:
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (283)  all_52_19 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | REDUCE: (55), (283) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (284)  op(e1, e1) = e2
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (285)  all_56_9 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (285) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (286)  all_52_13 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | SIMP: (286) implies:
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (287)  all_52_13 = e1
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | REDUCE: (110), (287) imply:
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (288)  op(e1, e1) = all_52_12
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (112), (269), (284), (288) are inconsistent
% 204.47/35.29  | | | | | | | | | | | | | | | | | |            by sub-proof #954.
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | |   (289)  all_56_9 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (273), (289) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | | | | |            #953.
% 204.47/35.29  | | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | |   (290)  all_56_6 = e0
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (274), (290) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | | | |            #952.
% 204.47/35.29  | | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (291)  all_56_14 = e1 | all_56_14 = e0
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REF_CLOSE: (80), (92), (263), (291) are inconsistent by
% 204.47/35.29  | | | | | | | | | | | | |            sub-proof #1381.
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | |   (292)   ~ (all_58_12 = e1)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (56), (292) imply:
% 204.47/35.29  | | | | | | | | | | | |   (293)   ~ (all_52_7 = e1)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REF_CLOSE: (5), (8), (46), (47), (80), (83), (92), (112),
% 204.47/35.29  | | | | | | | | | | | |            (113), (114), (121), (256), (258), (293) are
% 204.47/35.29  | | | | | | | | | | | |            inconsistent by sub-proof #1283.
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | |   (294)   ~ (all_56_13 = e3)
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | REDUCE: (116), (294) imply:
% 204.47/35.29  | | | | | | | |   (295)   ~ (all_52_15 = e3)
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | BETA: splitting (77) gives:
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | |   (296)  all_58_1 = e3
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | COMBINE_EQS: (6), (296) imply:
% 204.47/35.29  | | | | | | | | |   (297)  all_52_9 = e3
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | REDUCE: (7), (297) imply:
% 204.47/35.29  | | | | | | | | |   (298)   ~ (all_52_13 = e3)
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | SIMP: (298) implies:
% 204.47/35.29  | | | | | | | | |   (299)   ~ (all_52_13 = e3)
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | REDUCE: (29), (297) imply:
% 204.47/35.29  | | | | | | | | |   (300)   ~ (all_52_15 = e3)
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | REDUCE: (49), (297) imply:
% 204.47/35.29  | | | | | | | | |   (301)  op(e3, e3) = all_52_8
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_8, e3, e3,
% 204.47/35.29  | | | | | | | | |              simplifying with (90), (301) gives:
% 204.47/35.29  | | | | | | | | |   (302)  all_52_8 = all_6_2
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | REF_CLOSE: (5), (6), (13), (14), (18), (25), (39), (41), (44),
% 204.47/35.29  | | | | | | | | |            (46), (49), (52), (58), (59), (77), (84), (88),
% 204.47/35.29  | | | | | | | | |            (90), (95), (99), (104), (106), (115), (120),
% 204.47/35.29  | | | | | | | | |            (132), (137), (238), (295), (299) are inconsistent
% 204.47/35.29  | | | | | | | | |            by sub-proof #951.
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | |   (303)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | BETA: splitting (303) gives:
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | |   (304)  all_58_3 = e3
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | COMBINE_EQS: (115), (304) imply:
% 204.47/35.29  | | | | | | | | | |   (305)  all_4_2 = e3
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | REDUCE: (132), (305) imply:
% 204.47/35.29  | | | | | | | | | |   (306)  $false
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | CLOSE: (306) is inconsistent.
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | |   (307)  all_58_7 = e3 | all_58_13 = e3
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | BETA: splitting (307) gives:
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | |   (308)  all_58_7 = e3
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | COMBINE_EQS: (52), (308) imply:
% 204.47/35.29  | | | | | | | | | | |   (309)  all_52_13 = e3
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (7), (309) imply:
% 204.47/35.29  | | | | | | | | | | |   (310)   ~ (all_52_9 = e3)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (45), (309) imply:
% 204.47/35.29  | | | | | | | | | | |   (311)   ~ (all_10_2 = e3)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | SIMP: (311) implies:
% 204.47/35.29  | | | | | | | | | | |   (312)   ~ (all_10_2 = e3)
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REDUCE: (110), (309) imply:
% 204.47/35.29  | | | | | | | | | | |   (313)  op(e3, e3) = all_52_12
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_12, e3, e3,
% 204.47/35.29  | | | | | | | | | | |              simplifying with (90), (313) gives:
% 204.47/35.29  | | | | | | | | | | |   (314)  all_52_12 = all_6_2
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | BETA: splitting (60) gives:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | |   (315)  all_58_0 = e3
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | COMBINE_EQS: (14), (315) imply:
% 204.47/35.29  | | | | | | | | | | | |   (316)  all_6_2 = e3
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (104), (316) imply:
% 204.47/35.29  | | | | | | | | | | | |   (317)   ~ (all_52_17 = e3)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (30), (316) imply:
% 204.47/35.29  | | | | | | | | | | | |   (318)  op(e3, e3) = all_52_0
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (118), (316) imply:
% 204.47/35.29  | | | | | | | | | | | |   (319)  op(e3, e3) = all_6_1
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (90), (316) imply:
% 204.47/35.29  | | | | | | | | | | | |   (320)  op(e3, e3) = e3
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | BETA: splitting (108) gives:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (321)  all_58_4 = e3
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | REF_CLOSE: (120), (317), (321) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | |            #1302.
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | |   (322)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | BETA: splitting (322) gives:
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (323)  all_58_5 = e3
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | REF_CLOSE: (96), (127), (323) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | |            #1279.
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | |   (324)  all_58_8 = e3 | all_58_14 = e3
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | Case 1:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | |   (325)  all_58_8 = e3
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | REF_CLOSE: (79), (312), (325) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | | | | | |            #950.
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | |   (326)  all_58_14 = e3
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | COMBINE_EQS: (3), (326) imply:
% 204.47/35.29  | | | | | | | | | | | | | | |   (327)  all_52_23 = e3
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | SIMP: (327) implies:
% 204.47/35.29  | | | | | | | | | | | | | | |   (328)  all_52_23 = e3
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | REDUCE: (80), (328) imply:
% 204.47/35.29  | | | | | | | | | | | | | | |   (329)   ~ (e3 = e0)
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | REDUCE: (8), (328) imply:
% 204.47/35.29  | | | | | | | | | | | | | | |   (330)  op(e3, e3) = e0
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | | REF_CLOSE: (5), (318), (319), (320), (329), (330) are
% 204.47/35.29  | | | | | | | | | | | | | | |            inconsistent by sub-proof #949.
% 204.47/35.29  | | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | |   (331)   ~ (all_58_0 = e3)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REDUCE: (14), (331) imply:
% 204.47/35.29  | | | | | | | | | | | |   (332)   ~ (all_6_2 = e3)
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (19), (90), (91), (99), (104),
% 204.47/35.29  | | | | | | | | | | | |            (120), (128), (310), (332) are inconsistent by
% 204.47/35.29  | | | | | | | | | | | |            sub-proof #1071.
% 204.47/35.29  | | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | Case 2:
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | |   (333)  all_58_13 = e3
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | | REF_CLOSE: (18), (295), (333) are inconsistent by sub-proof
% 204.47/35.29  | | | | | | | | | | |            #1360.
% 204.47/35.29  | | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | | 
% 204.47/35.29  | | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | | 
% 204.47/35.29  | | | | | | | | End of split
% 204.47/35.29  | | | | | | | | 
% 204.47/35.29  | | | | | | | End of split
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | Case 2:
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | |   (334)   ~ (all_58_9 = e1)
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | REDUCE: (19), (334) imply:
% 204.47/35.29  | | | | | | |   (335)   ~ (all_52_25 = e1)
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | | REF_CLOSE: (39), (95), (137), (235), (335) are inconsistent by
% 204.47/35.29  | | | | | | |            sub-proof #1215.
% 204.47/35.29  | | | | | | | 
% 204.47/35.29  | | | | | | End of split
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | Case 2:
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | |   (336)  all_58_15 = e2
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | | REF_CLOSE: (37), (64), (336) are inconsistent by sub-proof #1223.
% 204.47/35.29  | | | | | | 
% 204.47/35.29  | | | | | End of split
% 204.47/35.29  | | | | | 
% 204.47/35.29  | | | | End of split
% 204.47/35.29  | | | | 
% 204.47/35.29  | | | End of split
% 204.47/35.29  | | | 
% 204.47/35.29  | | End of split
% 204.47/35.29  | | 
% 204.47/35.29  | Case 2:
% 204.47/35.29  | | 
% 204.47/35.29  | |   (337)   ~ (all_56_7 = e3)
% 204.47/35.29  | | 
% 204.47/35.29  | | REDUCE: (63), (337) imply:
% 204.47/35.29  | |   (338)   ~ (all_52_27 = e3)
% 204.47/35.29  | | 
% 204.47/35.29  | | REF_CLOSE: (5), (9), (23), (24), (25), (28), (30), (32), (34), (36), (38),
% 204.47/35.29  | |            (48), (55), (57), (65), (69), (71), (73), (86), (90), (93), (94),
% 204.47/35.29  | |            (96), (100), (102), (103), (115), (117), (338) are inconsistent
% 204.47/35.29  | |            by sub-proof #944.
% 204.47/35.29  | | 
% 204.47/35.29  | End of split
% 204.47/35.29  | 
% 204.47/35.29  End of proof
% 204.47/35.29  
% 204.47/35.29  Sub-proof #944 shows that the following formulas are inconsistent:
% 204.47/35.29  ----------------------------------------------------------------
% 204.47/35.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.29    (2)   ~ (all_4_0 = e1)
% 204.47/35.29    (3)   ~ (all_6_2 = all_4_0)
% 204.47/35.29    (4)  all_32_2 = all_4_2
% 204.47/35.29    (5)  op(e2, e2) = all_4_2
% 204.47/35.29    (6)  all_56_5 = all_4_2
% 204.47/35.29    (7)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.29    (8)  all_58_2 = all_4_0
% 204.47/35.29    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.29    (10)  op(all_4_2, e2) = e3
% 204.47/35.29    (11)   ~ (all_4_0 = e3)
% 204.47/35.29    (12)  all_58_10 = all_52_27
% 204.47/35.29    (13)  op(all_52_19, all_52_19) = e2
% 204.47/35.29    (14)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.47/35.29    (15)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.29    (16)  all_56_6 = all_52_19
% 204.47/35.29    (17)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.29    (18)  all_56_4 = all_4_0
% 204.47/35.29    (19)   ~ (all_52_27 = e3)
% 204.47/35.29    (20)   ~ (all_52_9 = all_4_2)
% 204.47/35.29    (21)  op(e3, e3) = all_6_2
% 204.47/35.29    (22)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.29    (23)  all_32_0 = all_4_0
% 204.47/35.29    (24)  all_58_5 = all_52_19
% 204.47/35.29    (25)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.29    (26)   ~ (all_4_0 = all_4_2)
% 204.47/35.29    (27)  op(e3, e2) = all_52_9
% 204.47/35.29    (28)  all_58_3 = all_4_2
% 204.47/35.29    (29)   ~ (all_52_19 = all_4_2)
% 204.47/35.29  
% 204.47/35.29  Begin of proof
% 204.47/35.29  | 
% 204.47/35.29  | BETA: splitting (9) gives:
% 204.47/35.29  | 
% 204.47/35.29  | Case 1:
% 204.47/35.29  | | 
% 204.47/35.29  | |   (30)  all_58_2 = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | REF_CLOSE: (8), (11), (30) are inconsistent by sub-proof #948.
% 204.47/35.29  | | 
% 204.47/35.29  | Case 2:
% 204.47/35.29  | | 
% 204.47/35.29  | |   (31)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | BETA: splitting (14) gives:
% 204.47/35.29  | | 
% 204.47/35.29  | | Case 1:
% 204.47/35.29  | | | 
% 204.47/35.29  | | |   (32)  all_56_6 = e3
% 204.47/35.29  | | | 
% 204.47/35.29  | | | COMBINE_EQS: (16), (32) imply:
% 204.47/35.29  | | |   (33)  all_52_19 = e3
% 204.47/35.29  | | | 
% 204.47/35.29  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (13), (15), (17),
% 204.47/35.29  | | |            (18), (21), (22), (23), (25), (26), (29), (33) are inconsistent
% 204.47/35.29  | | |            by sub-proof #946.
% 204.47/35.29  | | | 
% 204.47/35.29  | | Case 2:
% 204.47/35.29  | | | 
% 204.47/35.29  | | |   (34)   ~ (all_56_6 = e3)
% 204.47/35.29  | | | 
% 204.47/35.29  | | | REDUCE: (16), (34) imply:
% 204.47/35.29  | | |   (35)   ~ (all_52_19 = e3)
% 204.47/35.29  | | | 
% 204.47/35.29  | | | REF_CLOSE: (1), (10), (12), (19), (20), (24), (27), (28), (31), (35) are
% 204.47/35.29  | | |            inconsistent by sub-proof #945.
% 204.47/35.29  | | | 
% 204.47/35.29  | | End of split
% 204.47/35.29  | | 
% 204.47/35.29  | End of split
% 204.47/35.29  | 
% 204.47/35.29  End of proof
% 204.47/35.29  
% 204.47/35.29  Sub-proof #945 shows that the following formulas are inconsistent:
% 204.47/35.29  ----------------------------------------------------------------
% 204.47/35.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.29    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.47/35.29    (3)  op(all_4_2, e2) = e3
% 204.47/35.29    (4)  all_58_10 = all_52_27
% 204.47/35.29    (5)   ~ (all_52_19 = e3)
% 204.47/35.29    (6)   ~ (all_52_27 = e3)
% 204.47/35.29    (7)   ~ (all_52_9 = all_4_2)
% 204.47/35.29    (8)  all_58_5 = all_52_19
% 204.47/35.29    (9)  op(e3, e2) = all_52_9
% 204.47/35.29    (10)  all_58_3 = all_4_2
% 204.47/35.29  
% 204.47/35.29  Begin of proof
% 204.47/35.29  | 
% 204.47/35.29  | BETA: splitting (2) gives:
% 204.47/35.29  | 
% 204.47/35.29  | Case 1:
% 204.47/35.29  | | 
% 204.47/35.29  | |   (11)  all_58_3 = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | COMBINE_EQS: (10), (11) imply:
% 204.47/35.29  | |   (12)  all_4_2 = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | REDUCE: (7), (12) imply:
% 204.47/35.29  | |   (13)   ~ (all_52_9 = e3)
% 204.47/35.29  | | 
% 204.47/35.29  | | REDUCE: (3), (12) imply:
% 204.47/35.29  | |   (14)  op(e3, e2) = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | GROUND_INST: instantiating (1) with all_52_9, e3, e2, e3, simplifying with
% 204.47/35.29  | |              (9), (14) gives:
% 204.47/35.29  | |   (15)  all_52_9 = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | REDUCE: (13), (15) imply:
% 204.47/35.29  | |   (16)  $false
% 204.47/35.29  | | 
% 204.47/35.29  | | CLOSE: (16) is inconsistent.
% 204.47/35.29  | | 
% 204.47/35.29  | Case 2:
% 204.47/35.29  | | 
% 204.47/35.29  | |   (17)  all_58_5 = e3 | all_58_10 = e3
% 204.47/35.29  | | 
% 204.47/35.29  | | BETA: splitting (17) gives:
% 204.47/35.29  | | 
% 204.47/35.29  | | Case 1:
% 204.47/35.29  | | | 
% 204.47/35.29  | | |   (18)  all_58_5 = e3
% 204.47/35.29  | | | 
% 204.47/35.29  | | | REF_CLOSE: (5), (8), (18) are inconsistent by sub-proof #1279.
% 204.47/35.29  | | | 
% 204.47/35.29  | | Case 2:
% 204.47/35.29  | | | 
% 204.47/35.29  | | |   (19)  all_58_10 = e3
% 204.47/35.29  | | | 
% 204.47/35.29  | | | REF_CLOSE: (4), (6), (19) are inconsistent by sub-proof #1301.
% 204.47/35.29  | | | 
% 204.47/35.29  | | End of split
% 204.47/35.29  | | 
% 204.47/35.29  | End of split
% 204.47/35.29  | 
% 204.47/35.29  End of proof
% 204.47/35.29  
% 204.47/35.29  Sub-proof #946 shows that the following formulas are inconsistent:
% 204.47/35.29  ----------------------------------------------------------------
% 204.47/35.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.29    (2)   ~ (all_4_0 = e1)
% 204.47/35.29    (3)  all_52_19 = e3
% 204.47/35.29    (4)   ~ (all_6_2 = all_4_0)
% 204.47/35.29    (5)  all_32_2 = all_4_2
% 204.47/35.29    (6)  op(e2, e2) = all_4_2
% 204.47/35.29    (7)  all_56_5 = all_4_2
% 204.47/35.29    (8)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.29    (9)  op(all_4_2, e2) = e3
% 204.47/35.29    (10)  op(all_52_19, all_52_19) = e2
% 204.47/35.29    (11)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.29    (12)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.29    (13)  all_56_4 = all_4_0
% 204.47/35.29    (14)  op(e3, e3) = all_6_2
% 204.47/35.29    (15)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.29    (16)  all_32_0 = all_4_0
% 204.47/35.29    (17)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.29    (18)   ~ (all_4_0 = all_4_2)
% 204.47/35.30    (19)   ~ (all_52_19 = all_4_2)
% 204.47/35.30  
% 204.47/35.30  Begin of proof
% 204.47/35.30  | 
% 204.47/35.30  | SIMP: (3) implies:
% 204.47/35.30  |   (20)  all_52_19 = e3
% 204.47/35.30  | 
% 204.47/35.30  | REDUCE: (19), (20) imply:
% 204.47/35.30  |   (21)   ~ (all_4_2 = e3)
% 204.47/35.30  | 
% 204.47/35.30  | SIMP: (21) implies:
% 204.47/35.30  |   (22)   ~ (all_4_2 = e3)
% 204.47/35.30  | 
% 204.47/35.30  | REDUCE: (10), (20) imply:
% 204.47/35.30  |   (23)  op(e3, e3) = e2
% 204.47/35.30  | 
% 204.47/35.30  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 204.47/35.30  |            (15), (16), (17), (18), (22), (23) are inconsistent by sub-proof
% 204.47/35.30  |            #947.
% 204.47/35.30  | 
% 204.47/35.30  End of proof
% 204.47/35.30  
% 204.47/35.30  Sub-proof #947 shows that the following formulas are inconsistent:
% 204.47/35.30  ----------------------------------------------------------------
% 204.47/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.47/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.47/35.30    (2)   ~ (all_4_0 = e1)
% 204.47/35.30    (3)   ~ (all_4_2 = e3)
% 204.47/35.30    (4)   ~ (all_6_2 = all_4_0)
% 204.47/35.30    (5)  all_32_2 = all_4_2
% 204.47/35.30    (6)  op(e2, e2) = all_4_2
% 204.47/35.30    (7)  all_56_5 = all_4_2
% 204.47/35.30    (8)  op(all_6_2, all_6_2) = all_52_0
% 204.47/35.30    (9)  op(e3, e3) = e2
% 204.47/35.30    (10)  op(all_4_2, e2) = e3
% 204.47/35.30    (11)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.47/35.30    (12)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.47/35.30    (13)  all_56_4 = all_4_0
% 204.47/35.30    (14)  op(e3, e3) = all_6_2
% 204.47/35.30    (15)  op(all_4_2, all_4_2) = all_52_10
% 204.47/35.30    (16)  all_32_0 = all_4_0
% 204.47/35.30    (17)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.47/35.30    (18)   ~ (all_4_0 = all_4_2)
% 204.47/35.30  
% 204.47/35.30  Begin of proof
% 204.47/35.30  | 
% 204.47/35.30  | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with (9),
% 204.47/35.30  |              (14) gives:
% 204.47/35.30  |   (19)  all_6_2 = e2
% 204.47/35.30  | 
% 204.47/35.30  | REDUCE: (4), (19) imply:
% 204.47/35.30  |   (20)   ~ (all_4_0 = e2)
% 204.47/35.30  | 
% 204.47/35.30  | SIMP: (20) implies:
% 204.47/35.30  |   (21)   ~ (all_4_0 = e2)
% 204.47/35.30  | 
% 204.47/35.30  | REDUCE: (8), (19) imply:
% 204.47/35.30  |   (22)  op(e2, e2) = all_52_0
% 204.47/35.30  | 
% 204.47/35.30  | BETA: splitting (12) gives:
% 204.47/35.30  | 
% 204.47/35.30  | Case 1:
% 204.47/35.30  | | 
% 204.47/35.30  | |   (23)  all_56_4 = e2
% 204.47/35.30  | | 
% 204.47/35.30  | | REF_CLOSE: (13), (21), (23) are inconsistent by sub-proof #979.
% 204.47/35.30  | | 
% 204.47/35.30  | Case 2:
% 204.47/35.30  | | 
% 204.47/35.30  | |   (24)  all_56_4 = e1 | all_56_4 = e0
% 204.47/35.30  | | 
% 204.47/35.30  | | BETA: splitting (24) gives:
% 204.47/35.30  | | 
% 204.47/35.30  | | Case 1:
% 204.47/35.30  | | | 
% 204.47/35.30  | | |   (25)  all_56_4 = e1
% 204.47/35.30  | | | 
% 204.47/35.30  | | | REF_CLOSE: (2), (13), (25) are inconsistent by sub-proof #978.
% 204.47/35.30  | | | 
% 204.47/35.30  | | Case 2:
% 204.47/35.30  | | | 
% 204.47/35.30  | | |   (26)  all_56_4 = e0
% 204.47/35.30  | | | 
% 204.47/35.30  | | | COMBINE_EQS: (13), (26) imply:
% 204.47/35.30  | | |   (27)  all_4_0 = e0
% 204.47/35.30  | | | 
% 204.47/35.30  | | | SIMP: (27) implies:
% 204.47/35.30  | | |   (28)  all_4_0 = e0
% 204.47/35.30  | | | 
% 204.47/35.30  | | | COMBINE_EQS: (16), (28) imply:
% 204.47/35.30  | | |   (29)  all_32_0 = e0
% 204.47/35.30  | | | 
% 204.47/35.30  | | | REDUCE: (18), (28) imply:
% 204.47/35.30  | | |   (30)   ~ (all_4_2 = e0)
% 204.47/35.30  | | | 
% 204.47/35.30  | | | SIMP: (30) implies:
% 204.47/35.30  | | |   (31)   ~ (all_4_2 = e0)
% 204.47/35.30  | | | 
% 204.47/35.30  | | | BETA: splitting (17) gives:
% 204.47/35.30  | | | 
% 204.47/35.30  | | | Case 1:
% 204.47/35.30  | | | | 
% 204.47/35.30  | | | |   (32)   ~ (all_32_2 = e1)
% 204.47/35.30  | | | | 
% 204.47/35.30  | | | | REDUCE: (5), (32) imply:
% 204.47/35.30  | | | |   (33)   ~ (all_4_2 = e1)
% 204.47/35.30  | | | | 
% 204.47/35.30  | | | | BETA: splitting (11) gives:
% 204.47/35.30  | | | | 
% 204.47/35.30  | | | | Case 1:
% 204.47/35.30  | | | | | 
% 204.47/35.30  | | | | |   (34)  all_56_5 = e3
% 204.47/35.30  | | | | | 
% 204.47/35.30  | | | | | REF_CLOSE: (3), (7), (34) are inconsistent by sub-proof #1319.
% 204.47/35.30  | | | | | 
% 204.47/35.30  | | | | Case 2:
% 204.47/35.30  | | | | | 
% 204.56/35.30  | | | | |   (35)   ~ (all_56_5 = e3)
% 204.56/35.30  | | | | |   (36)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.30  | | | | | 
% 204.56/35.30  | | | | | BETA: splitting (36) gives:
% 204.56/35.30  | | | | | 
% 204.56/35.30  | | | | | Case 1:
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | |   (37)  all_56_5 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | COMBINE_EQS: (7), (37) imply:
% 204.56/35.30  | | | | | |   (38)  all_4_2 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | SIMP: (38) implies:
% 204.56/35.30  | | | | | |   (39)  all_4_2 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | REDUCE: (3), (39) imply:
% 204.56/35.30  | | | | | |   (40)   ~ (e3 = e2)
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | SIMP: (40) implies:
% 204.56/35.30  | | | | | |   (41)   ~ (e3 = e2)
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | REDUCE: (15), (39) imply:
% 204.56/35.30  | | | | | |   (42)  op(e2, e2) = all_52_10
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | REDUCE: (10), (39) imply:
% 204.56/35.30  | | | | | |   (43)  op(e2, e2) = e3
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | REDUCE: (6), (39) imply:
% 204.56/35.30  | | | | | |   (44)  op(e2, e2) = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | GROUND_INST: instantiating (1) with e3, all_52_10, e2, e2,
% 204.56/35.30  | | | | | |              simplifying with (42), (43) gives:
% 204.56/35.30  | | | | | |   (45)  all_52_10 = e3
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | GROUND_INST: instantiating (1) with all_52_10, all_52_0, e2, e2,
% 204.56/35.30  | | | | | |              simplifying with (22), (42) gives:
% 204.56/35.30  | | | | | |   (46)  all_52_0 = all_52_10
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | GROUND_INST: instantiating (1) with e2, all_52_0, e2, e2,
% 204.56/35.30  | | | | | |              simplifying with (22), (44) gives:
% 204.56/35.30  | | | | | |   (47)  all_52_0 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | COMBINE_EQS: (46), (47) imply:
% 204.56/35.30  | | | | | |   (48)  all_52_10 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | SIMP: (48) implies:
% 204.56/35.30  | | | | | |   (49)  all_52_10 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | COMBINE_EQS: (45), (49) imply:
% 204.56/35.30  | | | | | |   (50)  e3 = e2
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | REDUCE: (41), (50) imply:
% 204.56/35.30  | | | | | |   (51)  $false
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | CLOSE: (51) is inconsistent.
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | Case 2:
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | |   (52)  all_56_5 = e1 | all_56_5 = e0
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | | REF_CLOSE: (7), (31), (33), (52) are inconsistent by sub-proof
% 204.56/35.30  | | | | | |            #1187.
% 204.56/35.30  | | | | | | 
% 204.56/35.30  | | | | | End of split
% 204.56/35.30  | | | | | 
% 204.56/35.30  | | | | End of split
% 204.56/35.30  | | | | 
% 204.56/35.30  | | | Case 2:
% 204.56/35.30  | | | | 
% 204.56/35.30  | | | |   (53)   ~ (all_32_0 = e0)
% 204.56/35.30  | | | | 
% 204.56/35.30  | | | | REDUCE: (29), (53) imply:
% 204.56/35.30  | | | |   (54)  $false
% 204.56/35.30  | | | | 
% 204.56/35.30  | | | | CLOSE: (54) is inconsistent.
% 204.56/35.30  | | | | 
% 204.56/35.30  | | | End of split
% 204.56/35.30  | | | 
% 204.56/35.30  | | End of split
% 204.56/35.30  | | 
% 204.56/35.30  | End of split
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #948 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_58_2 = all_4_0
% 204.56/35.30    (2)  all_58_2 = e3
% 204.56/35.30    (3)   ~ (all_4_0 = e3)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_4_0 = e3
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_4_0 = e3
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #949 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)  op(e3, e3) = all_52_0
% 204.56/35.30    (3)   ~ (e3 = e0)
% 204.56/35.30    (4)  op(e3, e3) = all_6_1
% 204.56/35.30    (5)  op(e3, e3) = e3
% 204.56/35.30    (6)  op(e3, e3) = e0
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with e0, all_6_1, e3, e3, simplifying with (4),
% 204.56/35.30  |              (6) gives:
% 204.56/35.30  |   (7)  all_6_1 = e0
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with all_6_1, all_52_0, e3, e3, simplifying
% 204.56/35.30  |              with (2), (4) gives:
% 204.56/35.30  |   (8)  all_52_0 = all_6_1
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with e3, all_52_0, e3, e3, simplifying with
% 204.56/35.30  |              (2), (5) gives:
% 204.56/35.30  |   (9)  all_52_0 = e3
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (8), (9) imply:
% 204.56/35.30  |   (10)  all_6_1 = e3
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (10) implies:
% 204.56/35.30  |   (11)  all_6_1 = e3
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (7), (11) imply:
% 204.56/35.30  |   (12)  e3 = e0
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (12) implies:
% 204.56/35.30  |   (13)  e3 = e0
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (13) imply:
% 204.56/35.30  |   (14)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (14) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #950 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_58_8 = all_10_2
% 204.56/35.30    (2)  all_58_8 = e3
% 204.56/35.30    (3)   ~ (all_10_2 = e3)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_10_2 = e3
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_10_2 = e3
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #951 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)  all_58_1 = all_52_9
% 204.56/35.30    (3)   ~ (all_52_17 = all_52_25)
% 204.56/35.30    (4)   ~ (all_4_2 = e3)
% 204.56/35.30    (5)  all_58_0 = all_6_2
% 204.56/35.30    (6)  all_58_9 = e1
% 204.56/35.30    (7)  all_58_13 = all_52_15
% 204.56/35.30    (8)   ~ (all_52_15 = e3)
% 204.56/35.30    (9)  op(e2, e2) = all_4_2
% 204.56/35.30    (10)   ~ (all_52_25 = e0)
% 204.56/35.30    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.30    (12)   ~ (e2 = e1)
% 204.56/35.30    (13)  op(e0, e0) = e0
% 204.56/35.30    (14)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.30    (15)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.30    (16)  all_58_7 = all_52_13
% 204.56/35.30    (17)  all_56_2 = all_52_17
% 204.56/35.30    (18)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.56/35.30    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.30    (20)   ~ (all_52_25 = all_6_2)
% 204.56/35.30    (21)   ~ (all_52_9 = all_6_2)
% 204.56/35.30    (22)  op(e3, e3) = all_6_2
% 204.56/35.30    (23)   ~ (all_52_13 = e3)
% 204.56/35.30    (24)  all_56_3 = all_52_25
% 204.56/35.30    (25)  op(all_52_17, all_52_17) = e3
% 204.56/35.30    (26)   ~ (all_52_17 = all_6_2)
% 204.56/35.30    (27)   ~ (e3 = e2)
% 204.56/35.30    (28)  all_58_3 = all_4_2
% 204.56/35.30    (29)  all_58_4 = all_52_17
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | BETA: splitting (18) gives:
% 204.56/35.30  | 
% 204.56/35.30  | Case 1:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (30)  all_58_0 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | COMBINE_EQS: (5), (30) imply:
% 204.56/35.30  | |   (31)  all_6_2 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | REDUCE: (22), (31) imply:
% 204.56/35.30  | |   (32)  op(e3, e3) = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (13), (14), (15), (16),
% 204.56/35.30  | |            (17), (19), (20), (21), (22), (23), (24), (25), (26), (28), (32)
% 204.56/35.30  | |            are inconsistent by sub-proof #1255.
% 204.56/35.30  | | 
% 204.56/35.30  | Case 2:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (33)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (12), (16), (19), (23), (25), (27),
% 204.56/35.30  | |            (28), (29), (33) are inconsistent by sub-proof #1086.
% 204.56/35.30  | | 
% 204.56/35.30  | End of split
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #952 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_6 = all_52_19
% 204.56/35.30    (2)  all_56_6 = e0
% 204.56/35.30    (3)   ~ (all_52_19 = e0)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_19 = e0
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_19 = e0
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #953 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_9 = all_52_13
% 204.56/35.30    (2)  all_56_9 = e0
% 204.56/35.30    (3)   ~ (all_52_13 = e0)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_13 = e0
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_13 = e0
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #954 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)  op(e1, e1) = all_52_12
% 204.56/35.30    (3)  op(e1, e1) = e2
% 204.56/35.30    (4)   ~ (all_10_2 = e2)
% 204.56/35.30    (5)  op(e1, e1) = all_10_2
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with all_10_2, all_52_12, e1, e1, simplifying
% 204.56/35.30  |              with (2), (5) gives:
% 204.56/35.30  |   (6)  all_52_12 = all_10_2
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with e2, all_52_12, e1, e1, simplifying with
% 204.56/35.30  |              (2), (3) gives:
% 204.56/35.30  |   (7)  all_52_12 = e2
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (6), (7) imply:
% 204.56/35.30  |   (8)  all_10_2 = e2
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (4), (8) imply:
% 204.56/35.30  |   (9)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (9) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #955 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_9 = all_52_13
% 204.56/35.30    (2)  all_56_9 = e2
% 204.56/35.30    (3)   ~ (all_52_13 = e2)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_13 = e2
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_13 = e2
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #956 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_6 = all_52_19
% 204.56/35.30    (2)  all_56_6 = e2
% 204.56/35.30    (3)   ~ (all_52_19 = e2)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_19 = e2
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_19 = e2
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #957 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_6 = all_52_19
% 204.56/35.30    (2)  all_56_6 = e3
% 204.56/35.30    (3)   ~ (all_52_19 = e3)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_19 = e3
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_19 = e3
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #958 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_9 = all_52_13
% 204.56/35.30    (2)  all_56_9 = e3
% 204.56/35.30    (3)   ~ (all_52_13 = e3)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_13 = e3
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_13 = e3
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #959 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_13 = e1 | all_56_13 = e0
% 204.56/35.30    (2)  all_56_13 = all_52_15
% 204.56/35.30    (3)   ~ (all_52_15 = e1)
% 204.56/35.30    (4)   ~ (all_52_15 = e0)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | BETA: splitting (1) gives:
% 204.56/35.30  | 
% 204.56/35.30  | Case 1:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (5)  all_56_13 = e1
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1355.
% 204.56/35.30  | | 
% 204.56/35.30  | Case 2:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (6)  all_56_13 = e0
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1354.
% 204.56/35.30  | | 
% 204.56/35.30  | End of split
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #960 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.30    (2)   ~ (all_52_23 = e2)
% 204.56/35.30    (3)   ~ (all_52_23 = e1)
% 204.56/35.30    (4)   ~ (all_52_23 = e0)
% 204.56/35.30    (5)  all_56_14 = all_52_23
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | BETA: splitting (1) gives:
% 204.56/35.30  | 
% 204.56/35.30  | Case 1:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (6)  all_56_14 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #1285.
% 204.56/35.30  | | 
% 204.56/35.30  | Case 2:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (7)  all_56_14 = e1 | all_56_14 = e0
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1381.
% 204.56/35.30  | | 
% 204.56/35.30  | End of split
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #961 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)  op(e0, e3) = all_6_1
% 204.56/35.30    (3)  op(e0, e3) = e1
% 204.56/35.30    (4)   ~ (all_6_1 = e1)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with e1, all_6_1, e3, e0, simplifying with (2),
% 204.56/35.30  |              (3) gives:
% 204.56/35.30  |   (5)  all_6_1 = e1
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (4), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #962 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)  op(e1, e1) = e2
% 204.56/35.30    (3)  op(e1, e1) = all_52_8
% 204.56/35.30    (4)   ~ (all_10_2 = e2)
% 204.56/35.30    (5)  op(e1, e1) = all_10_2
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with all_10_2, all_52_8, e1, e1, simplifying
% 204.56/35.30  |              with (3), (5) gives:
% 204.56/35.30  |   (6)  all_52_8 = all_10_2
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with e2, all_52_8, e1, e1, simplifying with
% 204.56/35.30  |              (2), (3) gives:
% 204.56/35.30  |   (7)  all_52_8 = e2
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (6), (7) imply:
% 204.56/35.30  |   (8)  all_10_2 = e2
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (4), (8) imply:
% 204.56/35.30  |   (9)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (9) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #963 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_58_6 = all_52_5
% 204.56/35.30    (2)  all_58_6 = e1
% 204.56/35.30    (3)   ~ (all_52_5 = e1)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_52_5 = e1
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_52_5 = e1
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #964 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.30    (3)  all_58_0 = all_6_2
% 204.56/35.30    (4)   ~ (all_6_2 = e2)
% 204.56/35.30    (5)  op(e1, e3) = all_52_5
% 204.56/35.30    (6)   ~ (all_6_2 = all_4_0)
% 204.56/35.30    (7)  all_32_2 = all_4_2
% 204.56/35.30    (8)  op(e2, e2) = all_4_2
% 204.56/35.30    (9)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.56/35.30    (10)  all_56_5 = all_4_2
% 204.56/35.30    (11)   ~ (all_52_7 = all_6_2)
% 204.56/35.30    (12)  op(all_4_2, e2) = e3
% 204.56/35.30    (13)  all_58_12 = all_52_7
% 204.56/35.30    (14)  op(e3, all_6_1) = all_6_0
% 204.56/35.30    (15)   ~ (e2 = e0)
% 204.56/35.30    (16)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.30    (17)  op(e3, e0) = e2
% 204.56/35.30    (18)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.30    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.56/35.30    (20)  all_56_4 = all_4_0
% 204.56/35.30    (21)   ~ (all_6_0 = e2)
% 204.56/35.30    (22)   ~ (all_52_7 = all_4_0)
% 204.56/35.30    (23)  all_56_12 = all_52_7
% 204.56/35.30    (24)   ~ (all_52_9 = all_4_2)
% 204.56/35.30    (25)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.30    (26)  all_32_0 = all_4_0
% 204.56/35.30    (27)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.56/35.30    (28)  all_58_6 = all_52_5
% 204.56/35.30    (29)   ~ (all_4_0 = all_4_2)
% 204.56/35.30    (30)  op(e3, e2) = all_52_9
% 204.56/35.30    (31)   ~ (e1 = e0)
% 204.56/35.30    (32)   ~ (e3 = e2)
% 204.56/35.30    (33)   ~ (all_6_1 = e2)
% 204.56/35.30    (34)  op(all_6_2, e3) = all_6_1
% 204.56/35.30    (35)  all_58_0 = e1
% 204.56/35.30    (36)   ~ (all_52_7 = e0)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (3), (35) imply:
% 204.56/35.30  |   (37)  all_6_2 = e1
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (11), (37) imply:
% 204.56/35.30  |   (38)   ~ (all_52_7 = e1)
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (6), (37) imply:
% 204.56/35.30  |   (39)   ~ (all_4_0 = e1)
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (39) implies:
% 204.56/35.30  |   (40)   ~ (all_4_0 = e1)
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (4), (37) imply:
% 204.56/35.30  |   (41)   ~ (e2 = e1)
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (41) implies:
% 204.56/35.30  |   (42)   ~ (e2 = e1)
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (34), (37) imply:
% 204.56/35.30  |   (43)  op(e1, e3) = all_6_1
% 204.56/35.30  | 
% 204.56/35.30  | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), (16),
% 204.56/35.30  |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 204.56/35.30  |            (28), (29), (30), (31), (32), (33), (35), (36), (38), (40), (42),
% 204.56/35.30  |            (43) are inconsistent by sub-proof #965.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #965 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)   ~ (all_4_0 = e1)
% 204.56/35.30    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.30    (4)  op(e1, e3) = all_52_5
% 204.56/35.30    (5)  all_32_2 = all_4_2
% 204.56/35.30    (6)  op(e2, e2) = all_4_2
% 204.56/35.30    (7)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.56/35.30    (8)  all_56_5 = all_4_2
% 204.56/35.30    (9)  op(all_4_2, e2) = e3
% 204.56/35.30    (10)  op(e1, e3) = all_6_1
% 204.56/35.30    (11)   ~ (e2 = e1)
% 204.56/35.30    (12)  all_58_12 = all_52_7
% 204.56/35.30    (13)  op(e3, all_6_1) = all_6_0
% 204.56/35.30    (14)   ~ (e2 = e0)
% 204.56/35.30    (15)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.30    (16)  op(e3, e0) = e2
% 204.56/35.30    (17)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.30    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.56/35.30    (19)  all_56_4 = all_4_0
% 204.56/35.30    (20)   ~ (all_6_0 = e2)
% 204.56/35.30    (21)   ~ (all_52_7 = all_4_0)
% 204.56/35.30    (22)  all_56_12 = all_52_7
% 204.56/35.30    (23)   ~ (all_52_9 = all_4_2)
% 204.56/35.30    (24)   ~ (all_52_7 = e1)
% 204.56/35.30    (25)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.30    (26)  all_32_0 = all_4_0
% 204.56/35.30    (27)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.56/35.30    (28)  all_58_6 = all_52_5
% 204.56/35.30    (29)   ~ (all_4_0 = all_4_2)
% 204.56/35.30    (30)  op(e3, e2) = all_52_9
% 204.56/35.30    (31)   ~ (e1 = e0)
% 204.56/35.30    (32)   ~ (e3 = e2)
% 204.56/35.30    (33)   ~ (all_6_1 = e2)
% 204.56/35.30    (34)  all_58_0 = e1
% 204.56/35.30    (35)   ~ (all_52_7 = e0)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1, simplifying
% 204.56/35.30  |              with (4), (10) gives:
% 204.56/35.30  |   (36)  all_52_5 = all_6_1
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (28), (36) imply:
% 204.56/35.30  |   (37)  all_58_6 = all_6_1
% 204.56/35.30  | 
% 204.56/35.30  | BETA: splitting (3) gives:
% 204.56/35.30  | 
% 204.56/35.30  | Case 1:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (38)  all_56_12 = e3
% 204.56/35.30  | | 
% 204.56/35.30  | | COMBINE_EQS: (22), (38) imply:
% 204.56/35.30  | |   (39)  all_52_7 = e3
% 204.56/35.30  | | 
% 204.56/35.30  | | SIMP: (39) implies:
% 204.56/35.30  | |   (40)  all_52_7 = e3
% 204.56/35.30  | | 
% 204.56/35.30  | | COMBINE_EQS: (12), (40) imply:
% 204.56/35.30  | |   (41)  all_58_12 = e3
% 204.56/35.30  | | 
% 204.56/35.30  | | REDUCE: (35), (40) imply:
% 204.56/35.30  | |   (42)   ~ (e3 = e0)
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (1), (7), (11), (13), (14), (16), (18), (20), (31), (32), (33),
% 204.56/35.30  | |            (34), (37), (41), (42) are inconsistent by sub-proof #1208.
% 204.56/35.30  | | 
% 204.56/35.30  | Case 2:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (43)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (15), (17), (19), (21), (22), (23),
% 204.56/35.30  | |            (24), (25), (26), (27), (29), (30), (35), (43) are inconsistent
% 204.56/35.30  | |            by sub-proof #966.
% 204.56/35.30  | | 
% 204.56/35.30  | End of split
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #966 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.30    (2)   ~ (all_4_0 = e1)
% 204.56/35.30    (3)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.30    (4)  all_32_2 = all_4_2
% 204.56/35.30    (5)  op(e2, e2) = all_4_2
% 204.56/35.30    (6)  all_56_5 = all_4_2
% 204.56/35.30    (7)  op(all_4_2, e2) = e3
% 204.56/35.30    (8)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.30    (9)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.30    (10)  all_56_4 = all_4_0
% 204.56/35.30    (11)   ~ (all_52_7 = all_4_0)
% 204.56/35.30    (12)  all_56_12 = all_52_7
% 204.56/35.30    (13)   ~ (all_52_9 = all_4_2)
% 204.56/35.30    (14)   ~ (all_52_7 = e1)
% 204.56/35.30    (15)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.30    (16)  all_32_0 = all_4_0
% 204.56/35.30    (17)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.56/35.30    (18)   ~ (all_4_0 = all_4_2)
% 204.56/35.30    (19)  op(e3, e2) = all_52_9
% 204.56/35.30    (20)   ~ (all_52_7 = e0)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | BETA: splitting (3) gives:
% 204.56/35.30  | 
% 204.56/35.30  | Case 1:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (21)  all_56_12 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | COMBINE_EQS: (12), (21) imply:
% 204.56/35.30  | |   (22)  all_52_7 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | SIMP: (22) implies:
% 204.56/35.30  | |   (23)  all_52_7 = e2
% 204.56/35.30  | | 
% 204.56/35.30  | | REDUCE: (11), (23) imply:
% 204.56/35.30  | |   (24)   ~ (all_4_0 = e2)
% 204.56/35.30  | | 
% 204.56/35.30  | | SIMP: (24) implies:
% 204.56/35.30  | |   (25)   ~ (all_4_0 = e2)
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (13), (15), (16),
% 204.56/35.30  | |            (17), (18), (19), (25) are inconsistent by sub-proof #971.
% 204.56/35.30  | | 
% 204.56/35.30  | Case 2:
% 204.56/35.30  | | 
% 204.56/35.30  | |   (26)  all_56_12 = e1 | all_56_12 = e0
% 204.56/35.30  | | 
% 204.56/35.30  | | REF_CLOSE: (12), (14), (20), (26) are inconsistent by sub-proof #1374.
% 204.56/35.30  | | 
% 204.56/35.30  | End of split
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #967 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_58_2 = all_4_0
% 204.56/35.30    (2)  all_58_2 = e1
% 204.56/35.30    (3)   ~ (all_4_0 = e1)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  all_4_0 = e1
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  all_4_0 = e1
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #968 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)  all_58_10 = e3
% 204.56/35.30    (2)  all_58_10 = e1
% 204.56/35.30    (3)   ~ (e3 = e1)
% 204.56/35.30  
% 204.56/35.30  Begin of proof
% 204.56/35.30  | 
% 204.56/35.30  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.30  |   (4)  e3 = e1
% 204.56/35.30  | 
% 204.56/35.30  | SIMP: (4) implies:
% 204.56/35.30  |   (5)  e3 = e1
% 204.56/35.30  | 
% 204.56/35.30  | REDUCE: (3), (5) imply:
% 204.56/35.30  |   (6)  $false
% 204.56/35.30  | 
% 204.56/35.30  | CLOSE: (6) is inconsistent.
% 204.56/35.30  | 
% 204.56/35.30  End of proof
% 204.56/35.30  
% 204.56/35.30  Sub-proof #969 shows that the following formulas are inconsistent:
% 204.56/35.30  ----------------------------------------------------------------
% 204.56/35.30    (1)   ~ (all_52_25 = all_52_27)
% 204.56/35.30    (2)  all_58_14 = all_52_23
% 204.56/35.30    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.56/35.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (5)   ~ (all_52_5 = all_52_13)
% 204.56/35.31    (6)  all_58_1 = all_52_9
% 204.56/35.31    (7)   ~ (all_52_9 = all_52_13)
% 204.56/35.31    (8)   ~ (e3 = e0)
% 204.56/35.31    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.31    (10)   ~ (all_52_7 = all_52_15)
% 204.56/35.31    (11)   ~ (all_52_17 = all_52_25)
% 204.56/35.31    (12)   ~ (all_52_3 = all_6_2)
% 204.56/35.31    (13)  all_58_0 = all_6_2
% 204.56/35.31    (14)  all_56_4 = all_52_3
% 204.56/35.31    (15)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.56/35.31    (16)  op(all_52_19, all_52_19) = all_52_18
% 204.56/35.31    (17)  all_58_13 = all_52_15
% 204.56/35.31    (18)  op(all_10_2, all_10_2) = all_52_20
% 204.56/35.31    (19)  all_58_9 = all_52_25
% 204.56/35.31    (20)   ~ (all_6_1 = e1)
% 204.56/35.31    (21)  op(all_52_27, all_52_27) = all_52_26
% 204.56/35.31    (22)  op(e1, e3) = all_52_5
% 204.56/35.31    (23)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.56/35.31    (24)  op(e2, e2) = all_4_2
% 204.56/35.31    (25)   ~ (all_52_3 = all_52_5)
% 204.56/35.31    (26)  all_58_11 = all_52_29
% 204.56/35.31    (27)  all_56_5 = all_4_2
% 204.56/35.31    (28)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.56/35.31    (29)  op(all_10_2, e1) = all_10_1
% 204.56/35.31    (30)   ~ (all_52_7 = all_6_2)
% 204.56/35.31    (31)  op(e0, e1) = all_52_23
% 204.56/35.31    (32)   ~ (all_52_15 = e0)
% 204.56/35.31    (33)  all_58_15 = e0
% 204.56/35.31    (34)   ~ (all_4_1 = e1)
% 204.56/35.31    (35)   ~ (all_52_25 = e0)
% 204.56/35.31    (36)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.31    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.31    (38)   ~ (e2 = e1)
% 204.56/35.31    (39)   ~ (all_52_13 = all_10_2)
% 204.56/35.31    (40)  op(e0, e0) = e0
% 204.56/35.31    (41)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.56/35.31    (42)  all_58_10 = all_52_27
% 204.56/35.31    (43)  all_56_8 = all_52_5
% 204.56/35.31    (44)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.31    (45)  op(all_52_15, all_52_15) = all_52_14
% 204.56/35.31    (46)   ~ (all_52_25 = all_52_29)
% 204.56/35.31    (47)  all_58_7 = all_52_13
% 204.56/35.31    (48)   ~ (all_52_5 = all_52_7)
% 204.56/35.31    (49)  all_58_12 = all_52_7
% 204.56/35.31    (50)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.31    (51)  all_56_2 = all_52_17
% 204.56/35.31    (52)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.56/35.31    (53)  all_56_7 = all_52_27
% 204.56/35.31    (54)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.31    (55)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31    (56)  op(all_4_2, e2) = all_4_1
% 204.56/35.31    (57)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.56/35.31    (58)   ~ (all_52_13 = all_4_2)
% 204.56/35.31    (59)  op(e0, e3) = all_52_7
% 204.56/35.31    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.31    (61)   ~ (all_52_9 = all_52_25)
% 204.56/35.31    (62)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.31    (63)  all_58_8 = all_10_2
% 204.56/35.31    (64)  all_56_12 = all_52_7
% 204.56/35.31    (65)  op(all_52_17, all_52_17) = all_52_16
% 204.56/35.31    (66)   ~ (all_52_25 = all_6_2)
% 204.56/35.31    (67)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.31    (68)   ~ (all_52_9 = all_4_2)
% 204.56/35.31    (69)   ~ (all_52_5 = all_6_2)
% 204.56/35.31    (70)   ~ (all_52_9 = all_6_2)
% 204.56/35.31    (71)   ~ (all_52_13 = all_52_15)
% 204.56/35.31    (72)  op(e3, e3) = all_6_2
% 204.56/35.31    (73)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.31    (74)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.31    (75)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.31    (76)  all_56_3 = all_52_25
% 204.56/35.31    (77)   ~ (all_52_3 = all_52_7)
% 204.56/35.31    (78)   ~ (all_10_1 = e3)
% 204.56/35.31    (79)  all_58_5 = all_52_19
% 204.56/35.31    (80)  all_56_1 = all_52_9
% 204.56/35.31    (81)   ~ (all_52_15 = all_4_2)
% 204.56/35.31    (82)   ~ (all_52_27 = all_4_2)
% 204.56/35.31    (83)  all_58_6 = all_52_5
% 204.56/35.31    (84)  op(e3, e2) = all_52_9
% 204.56/35.31    (85)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.31    (86)   ~ (all_52_17 = all_6_2)
% 204.56/35.31    (87)   ~ (e1 = e0)
% 204.56/35.31    (88)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.31    (89)   ~ (all_52_9 = all_52_17)
% 204.56/35.31    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.56/35.31    (91)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.31    (92)   ~ (all_6_1 = e2)
% 204.56/35.31    (93)  op(e1, e1) = all_10_2
% 204.56/35.31    (94)   ~ (all_52_7 = all_52_23)
% 204.56/35.31    (95)  all_58_3 = all_4_2
% 204.56/35.31    (96)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.56/35.31    (97)  all_56_13 = all_52_15
% 204.56/35.31    (98)   ~ (all_52_3 = all_4_2)
% 204.56/35.31    (99)   ~ (all_52_19 = all_4_2)
% 204.56/35.31    (100)  op(all_6_2, e3) = all_6_1
% 204.56/35.31    (101)   ~ (all_52_13 = all_52_29)
% 204.56/35.31    (102)  all_58_4 = all_52_17
% 204.56/35.31    (103)   ~ (all_52_7 = e0)
% 204.56/35.31    (104)  op(all_52_25, all_52_25) = all_52_24
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | ALPHA: (41) implies:
% 204.56/35.31  |   (105)  all_52_14 = e0
% 204.56/35.31  |   (106)  all_52_12 = e1
% 204.56/35.31  |   (107)  all_52_10 = e2
% 204.56/35.31  |   (108)  all_52_8 = e3
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (44), (108) imply:
% 204.56/35.31  |   (109)  op(all_52_9, all_52_9) = e3
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (91), (106) imply:
% 204.56/35.31  |   (110)  op(all_52_13, all_52_13) = e1
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (45), (105) imply:
% 204.56/35.31  |   (111)  op(all_52_15, all_52_15) = e0
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (75), (107) imply:
% 204.56/35.31  |   (112)  op(all_4_2, all_4_2) = e2
% 204.56/35.31  | 
% 204.56/35.31  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.56/35.31  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.56/35.31  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.56/35.31  |            (35), (36), (37), (38), (39), (40), (42), (43), (46), (47), (48),
% 204.56/35.31  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 204.56/35.31  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.56/35.31  |            (71), (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 204.56/35.31  |            (83), (84), (85), (86), (87), (88), (89), (90), (92), (93), (94),
% 204.56/35.31  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 204.56/35.31  |            (109), (110), (111), (112) are inconsistent by sub-proof #1287.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #970 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)   ~ (all_4_0 = e1)
% 204.56/35.31    (3)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.56/35.31    (4)  all_32_2 = all_4_2
% 204.56/35.31    (5)  op(e2, e2) = all_4_2
% 204.56/35.31    (6)  all_56_5 = all_4_2
% 204.56/35.31    (7)  all_58_2 = all_4_0
% 204.56/35.31    (8)  op(all_4_2, e2) = e3
% 204.56/35.31    (9)  op(all_4_0, all_4_0) = all_52_2
% 204.56/35.31    (10)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31    (11)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.31    (12)  all_56_4 = all_4_0
% 204.56/35.31    (13)   ~ (all_52_9 = all_4_2)
% 204.56/35.31    (14)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.31    (15)  all_32_0 = all_4_0
% 204.56/35.31    (16)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.56/35.31    (17)   ~ (all_4_0 = all_4_2)
% 204.56/35.31    (18)  op(e3, e2) = all_52_9
% 204.56/35.31    (19)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | ALPHA: (3) implies:
% 204.56/35.31  |   (20)  all_52_2 = e2
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (9), (20) imply:
% 204.56/35.31  |   (21)  op(all_4_0, all_4_0) = e2
% 204.56/35.31  | 
% 204.56/35.31  | BETA: splitting (19) gives:
% 204.56/35.31  | 
% 204.56/35.31  | Case 1:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (22)  all_58_2 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | COMBINE_EQS: (7), (22) imply:
% 204.56/35.31  | |   (23)  all_4_0 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | SIMP: (23) implies:
% 204.56/35.31  | |   (24)  all_4_0 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (17), (24) imply:
% 204.56/35.31  | |   (25)   ~ (all_4_2 = e2)
% 204.56/35.31  | | 
% 204.56/35.31  | | SIMP: (25) implies:
% 204.56/35.31  | |   (26)   ~ (all_4_2 = e2)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (21), (24) imply:
% 204.56/35.31  | |   (27)  op(e2, e2) = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (1), (5), (26), (27) are inconsistent by sub-proof #1158.
% 204.56/35.31  | | 
% 204.56/35.31  | Case 2:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (28)   ~ (all_58_2 = e2)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (7), (28) imply:
% 204.56/35.31  | |   (29)   ~ (all_4_0 = e2)
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 204.56/35.31  | |            (16), (17), (18), (29) are inconsistent by sub-proof #971.
% 204.56/35.31  | | 
% 204.56/35.31  | End of split
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #971 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)   ~ (all_4_0 = e1)
% 204.56/35.31    (3)   ~ (all_4_0 = e2)
% 204.56/35.31    (4)  all_32_2 = all_4_2
% 204.56/35.31    (5)  op(e2, e2) = all_4_2
% 204.56/35.31    (6)  all_56_5 = all_4_2
% 204.56/35.31    (7)  op(all_4_2, e2) = e3
% 204.56/35.31    (8)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31    (9)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.31    (10)  all_56_4 = all_4_0
% 204.56/35.31    (11)   ~ (all_52_9 = all_4_2)
% 204.56/35.31    (12)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.31    (13)  all_32_0 = all_4_0
% 204.56/35.31    (14)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.56/35.31    (15)   ~ (all_4_0 = all_4_2)
% 204.56/35.31    (16)  op(e3, e2) = all_52_9
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | BETA: splitting (9) gives:
% 204.56/35.31  | 
% 204.56/35.31  | Case 1:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (17)  all_56_4 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (3), (10), (17) are inconsistent by sub-proof #979.
% 204.56/35.31  | | 
% 204.56/35.31  | Case 2:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (18)  all_56_4 = e1 | all_56_4 = e0
% 204.56/35.31  | | 
% 204.56/35.31  | | BETA: splitting (18) gives:
% 204.56/35.31  | | 
% 204.56/35.31  | | Case 1:
% 204.56/35.31  | | | 
% 204.56/35.31  | | |   (19)  all_56_4 = e1
% 204.56/35.31  | | | 
% 204.56/35.31  | | | REF_CLOSE: (2), (10), (19) are inconsistent by sub-proof #978.
% 204.56/35.31  | | | 
% 204.56/35.31  | | Case 2:
% 204.56/35.31  | | | 
% 204.56/35.31  | | |   (20)  all_56_4 = e0
% 204.56/35.31  | | | 
% 204.56/35.31  | | | COMBINE_EQS: (10), (20) imply:
% 204.56/35.31  | | |   (21)  all_4_0 = e0
% 204.56/35.31  | | | 
% 204.56/35.31  | | | SIMP: (21) implies:
% 204.56/35.31  | | |   (22)  all_4_0 = e0
% 204.56/35.31  | | | 
% 204.56/35.31  | | | COMBINE_EQS: (13), (22) imply:
% 204.56/35.31  | | |   (23)  all_32_0 = e0
% 204.56/35.31  | | | 
% 204.56/35.31  | | | REDUCE: (15), (22) imply:
% 204.56/35.31  | | |   (24)   ~ (all_4_2 = e0)
% 204.56/35.31  | | | 
% 204.56/35.31  | | | SIMP: (24) implies:
% 204.56/35.31  | | |   (25)   ~ (all_4_2 = e0)
% 204.56/35.31  | | | 
% 204.56/35.31  | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (11), (12), (14), (16), (23),
% 204.56/35.31  | | |            (25) are inconsistent by sub-proof #972.
% 204.56/35.31  | | | 
% 204.56/35.31  | | End of split
% 204.56/35.31  | | 
% 204.56/35.31  | End of split
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #972 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)   ~ (all_4_2 = e0)
% 204.56/35.31    (3)  all_32_2 = all_4_2
% 204.56/35.31    (4)  op(e2, e2) = all_4_2
% 204.56/35.31    (5)  all_56_5 = all_4_2
% 204.56/35.31    (6)  op(all_4_2, e2) = e3
% 204.56/35.31    (7)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31    (8)  all_32_0 = e0
% 204.56/35.31    (9)   ~ (all_52_9 = all_4_2)
% 204.56/35.31    (10)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.31    (11)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e1)
% 204.56/35.31    (12)  op(e3, e2) = all_52_9
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | BETA: splitting (11) gives:
% 204.56/35.31  | 
% 204.56/35.31  | Case 1:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (13)   ~ (all_32_2 = e1)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (3), (13) imply:
% 204.56/35.31  | |   (14)   ~ (all_4_2 = e1)
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (12), (14) are
% 204.56/35.31  | |            inconsistent by sub-proof #973.
% 204.56/35.31  | | 
% 204.56/35.31  | Case 2:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (15)   ~ (all_32_0 = e0)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (8), (15) imply:
% 204.56/35.31  | |   (16)  $false
% 204.56/35.31  | | 
% 204.56/35.31  | | CLOSE: (16) is inconsistent.
% 204.56/35.31  | | 
% 204.56/35.31  | End of split
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #973 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)   ~ (all_4_2 = e0)
% 204.56/35.31    (3)  op(e2, e2) = all_4_2
% 204.56/35.31    (4)  all_56_5 = all_4_2
% 204.56/35.31    (5)  op(all_4_2, e2) = e3
% 204.56/35.31    (6)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31    (7)   ~ (all_52_9 = all_4_2)
% 204.56/35.31    (8)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.31    (9)  op(e3, e2) = all_52_9
% 204.56/35.31    (10)   ~ (all_4_2 = e1)
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | BETA: splitting (6) gives:
% 204.56/35.31  | 
% 204.56/35.31  | Case 1:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (11)  all_56_5 = e3
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (1), (4), (5), (7), (9), (11) are inconsistent by sub-proof #976.
% 204.56/35.31  | | 
% 204.56/35.31  | Case 2:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (12)   ~ (all_56_5 = e3)
% 204.56/35.31  | |   (13)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (4), (12) imply:
% 204.56/35.31  | |   (14)   ~ (all_4_2 = e3)
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (13), (14) are inconsistent
% 204.56/35.31  | |            by sub-proof #974.
% 204.56/35.31  | | 
% 204.56/35.31  | End of split
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #974 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)   ~ (all_4_2 = e3)
% 204.56/35.31    (3)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31    (4)   ~ (all_4_2 = e0)
% 204.56/35.31    (5)  op(e2, e2) = all_4_2
% 204.56/35.31    (6)  all_56_5 = all_4_2
% 204.56/35.31    (7)  op(all_4_2, e2) = e3
% 204.56/35.31    (8)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.31    (9)   ~ (all_4_2 = e1)
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | BETA: splitting (3) gives:
% 204.56/35.31  | 
% 204.56/35.31  | Case 1:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (10)  all_56_5 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | COMBINE_EQS: (6), (10) imply:
% 204.56/35.31  | |   (11)  all_4_2 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | SIMP: (11) implies:
% 204.56/35.31  | |   (12)  all_4_2 = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (2), (12) imply:
% 204.56/35.31  | |   (13)   ~ (e3 = e2)
% 204.56/35.31  | | 
% 204.56/35.31  | | SIMP: (13) implies:
% 204.56/35.31  | |   (14)   ~ (e3 = e2)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (8), (12) imply:
% 204.56/35.31  | |   (15)  op(e2, e2) = all_52_10
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (7), (12) imply:
% 204.56/35.31  | |   (16)  op(e2, e2) = e3
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (5), (12) imply:
% 204.56/35.31  | |   (17)  op(e2, e2) = e2
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (1), (14), (15), (16), (17) are inconsistent by sub-proof #975.
% 204.56/35.31  | | 
% 204.56/35.31  | Case 2:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (18)  all_56_5 = e1 | all_56_5 = e0
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (4), (6), (9), (18) are inconsistent by sub-proof #1187.
% 204.56/35.31  | | 
% 204.56/35.31  | End of split
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #975 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)  op(e2, e2) = all_52_10
% 204.56/35.31    (3)  op(e2, e2) = e3
% 204.56/35.31    (4)   ~ (e3 = e2)
% 204.56/35.31    (5)  op(e2, e2) = e2
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | GROUND_INST: instantiating (1) with e3, all_52_10, e2, e2, simplifying with
% 204.56/35.31  |              (2), (3) gives:
% 204.56/35.31  |   (6)  all_52_10 = e3
% 204.56/35.31  | 
% 204.56/35.31  | GROUND_INST: instantiating (1) with e2, all_52_10, e2, e2, simplifying with
% 204.56/35.31  |              (2), (5) gives:
% 204.56/35.31  |   (7)  all_52_10 = e2
% 204.56/35.31  | 
% 204.56/35.31  | COMBINE_EQS: (6), (7) imply:
% 204.56/35.31  |   (8)  e3 = e2
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (4), (8) imply:
% 204.56/35.31  |   (9)  $false
% 204.56/35.31  | 
% 204.56/35.31  | CLOSE: (9) is inconsistent.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #976 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)  all_56_5 = all_4_2
% 204.56/35.31    (3)  op(all_4_2, e2) = e3
% 204.56/35.31    (4)   ~ (all_52_9 = all_4_2)
% 204.56/35.31    (5)  op(e3, e2) = all_52_9
% 204.56/35.31    (6)  all_56_5 = e3
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | COMBINE_EQS: (2), (6) imply:
% 204.56/35.31  |   (7)  all_4_2 = e3
% 204.56/35.31  | 
% 204.56/35.31  | SIMP: (7) implies:
% 204.56/35.31  |   (8)  all_4_2 = e3
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (4), (8) imply:
% 204.56/35.31  |   (9)   ~ (all_52_9 = e3)
% 204.56/35.31  | 
% 204.56/35.31  | REF_CLOSE: (1), (3), (5), (8), (9) are inconsistent by sub-proof #977.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #977 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (2)  all_4_2 = e3
% 204.56/35.31    (3)  op(all_4_2, e2) = e3
% 204.56/35.31    (4)   ~ (all_52_9 = e3)
% 204.56/35.31    (5)  op(e3, e2) = all_52_9
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (2), (3) imply:
% 204.56/35.31  |   (6)  op(e3, e2) = e3
% 204.56/35.31  | 
% 204.56/35.31  | GROUND_INST: instantiating (1) with all_52_9, e3, e2, e3, simplifying with
% 204.56/35.31  |              (5), (6) gives:
% 204.56/35.31  |   (7)  all_52_9 = e3
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (4), (7) imply:
% 204.56/35.31  |   (8)  $false
% 204.56/35.31  | 
% 204.56/35.31  | CLOSE: (8) is inconsistent.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #978 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)  all_56_4 = all_4_0
% 204.56/35.31    (2)  all_56_4 = e1
% 204.56/35.31    (3)   ~ (all_4_0 = e1)
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.31  |   (4)  all_4_0 = e1
% 204.56/35.31  | 
% 204.56/35.31  | SIMP: (4) implies:
% 204.56/35.31  |   (5)  all_4_0 = e1
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (3), (5) imply:
% 204.56/35.31  |   (6)  $false
% 204.56/35.31  | 
% 204.56/35.31  | CLOSE: (6) is inconsistent.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #979 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)  all_56_4 = all_4_0
% 204.56/35.31    (2)  all_56_4 = e2
% 204.56/35.31    (3)   ~ (all_4_0 = e2)
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.31  |   (4)  all_4_0 = e2
% 204.56/35.31  | 
% 204.56/35.31  | SIMP: (4) implies:
% 204.56/35.31  |   (5)  all_4_0 = e2
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (3), (5) imply:
% 204.56/35.31  |   (6)  $false
% 204.56/35.31  | 
% 204.56/35.31  | CLOSE: (6) is inconsistent.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #980 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)  all_56_4 = all_4_0
% 204.56/35.31    (2)  all_56_4 = e3
% 204.56/35.31    (3)   ~ (all_4_0 = e3)
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.31  |   (4)  all_4_0 = e3
% 204.56/35.31  | 
% 204.56/35.31  | SIMP: (4) implies:
% 204.56/35.31  |   (5)  all_4_0 = e3
% 204.56/35.31  | 
% 204.56/35.31  | REDUCE: (3), (5) imply:
% 204.56/35.31  |   (6)  $false
% 204.56/35.31  | 
% 204.56/35.31  | CLOSE: (6) is inconsistent.
% 204.56/35.31  | 
% 204.56/35.31  End of proof
% 204.56/35.31  
% 204.56/35.31  Sub-proof #981 shows that the following formulas are inconsistent:
% 204.56/35.31  ----------------------------------------------------------------
% 204.56/35.31    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.31    (2)   ~ (all_52_25 = all_52_27)
% 204.56/35.31    (3)  all_58_14 = all_52_23
% 204.56/35.31    (4)   ~ (e3 = e1)
% 204.56/35.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.31    (6)  all_58_1 = all_52_9
% 204.56/35.31    (7)   ~ (e3 = e0)
% 204.56/35.31    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.31    (9)   ~ (all_52_7 = all_52_15)
% 204.56/35.31    (10)  op(all_52_15, all_52_15) = e0
% 204.56/35.31    (11)  op(all_52_7, all_52_7) = all_52_6
% 204.56/35.31    (12)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.56/35.31    (13)  all_58_0 = all_6_2
% 204.56/35.31    (14)   ~ (all_10_0 = e3)
% 204.56/35.31    (15)  all_40_2 = all_10_2
% 204.56/35.31    (16)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.31    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.56/35.31    (18)   ~ (all_52_27 = all_52_29)
% 204.56/35.31    (19)  all_58_13 = all_52_15
% 204.56/35.31    (20)  op(all_10_0, all_10_0) = e1
% 204.56/35.31    (21)  all_58_9 = all_52_25
% 204.56/35.31    (22)   ~ (all_6_1 = e1)
% 204.56/35.31    (23)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.31    (24)  op(all_52_27, all_52_27) = all_52_26
% 204.56/35.31    (25)  op(e2, e2) = all_4_2
% 204.56/35.31    (26)  all_58_7 = all_10_0
% 204.56/35.31    (27)  all_58_11 = all_52_29
% 204.56/35.31    (28)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.56/35.31    (29)  op(all_10_2, e1) = all_10_1
% 204.56/35.31    (30)   ~ (all_52_7 = all_6_2)
% 204.56/35.31    (31)  op(e0, e1) = all_52_23
% 204.56/35.31    (32)   ~ (all_52_15 = e0)
% 204.56/35.31    (33)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.31    (34)  all_58_15 = e0
% 204.56/35.31    (35)   ~ (all_10_0 = e2)
% 204.56/35.31    (36)   ~ (all_4_1 = e1)
% 204.56/35.31    (37)   ~ (all_52_25 = e0)
% 204.56/35.31    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.31    (39)   ~ (e2 = e1)
% 204.56/35.31    (40)  op(e0, e0) = e0
% 204.56/35.31    (41)  all_58_10 = all_52_27
% 204.56/35.31    (42)  all_56_9 = all_10_0
% 204.56/35.31    (43)   ~ (all_52_25 = all_52_29)
% 204.56/35.31    (44)  all_58_7 = all_52_13
% 204.56/35.31    (45)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.31    (46)   ~ (all_52_5 = all_52_7)
% 204.56/35.31    (47)  all_58_12 = all_52_7
% 204.56/35.31    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.31    (49)  op(e2, e1) = all_52_19
% 204.56/35.31    (50)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.56/35.31    (51)   ~ (all_52_15 = all_10_0)
% 204.56/35.31    (52)  all_56_7 = all_52_27
% 204.56/35.31    (53)   ~ (e2 = e0)
% 204.56/35.31    (54)  op(all_4_2, e2) = all_4_1
% 204.56/35.31    (55)   ~ (all_52_29 = e0)
% 204.56/35.31    (56)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.56/35.31    (57)  op(e0, e3) = all_52_7
% 204.56/35.31    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.31    (59)   ~ (all_52_9 = all_52_25)
% 204.56/35.31    (60)   ~ (all_52_19 = all_10_2)
% 204.56/35.31    (61)   ~ (all_10_0 = all_10_2)
% 204.56/35.31    (62)  all_58_8 = all_10_2
% 204.56/35.31    (63)  op(all_52_29, all_52_29) = all_52_28
% 204.56/35.31    (64)  all_56_12 = all_52_7
% 204.56/35.31    (65)  op(all_52_17, all_52_17) = all_52_16
% 204.56/35.31    (66)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.31    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.56/35.31    (68)  op(all_4_2, all_4_2) = e2
% 204.56/35.31    (69)   ~ (all_52_9 = all_6_2)
% 204.56/35.31    (70)  op(e3, e3) = all_6_2
% 204.56/35.31    (71)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.31    (72)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.31    (73)  all_56_14 = all_52_23
% 204.56/35.31    (74)  all_40_0 = all_10_0
% 204.56/35.31    (75)  all_56_3 = all_52_25
% 204.56/35.31    (76)   ~ (all_10_1 = e3)
% 204.56/35.31    (77)  all_56_1 = all_52_9
% 204.56/35.31    (78)   ~ (all_52_15 = all_4_2)
% 204.56/35.31    (79)   ~ (all_52_27 = all_4_2)
% 204.56/35.31    (80)  all_58_6 = all_52_5
% 204.56/35.31    (81)  op(all_10_2, e1) = e2
% 204.56/35.31    (82)  op(e3, e2) = all_52_9
% 204.56/35.31    (83)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.31    (84)   ~ (e1 = e0)
% 204.56/35.31    (85)   ~ (e3 = e2)
% 204.56/35.31    (86)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.31    (87)   ~ (all_52_9 = all_52_17)
% 204.56/35.31    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.56/35.31    (89)   ~ (all_6_1 = e2)
% 204.56/35.31    (90)  op(e1, e1) = all_10_2
% 204.56/35.31    (91)  op(all_52_9, all_52_9) = e3
% 204.56/35.31    (92)   ~ (all_52_7 = all_52_23)
% 204.56/35.31    (93)  all_58_3 = all_4_2
% 204.56/35.31    (94)  all_56_13 = all_52_15
% 204.56/35.31    (95)  op(all_6_2, e3) = all_6_1
% 204.56/35.31    (96)   ~ (all_52_13 = all_52_29)
% 204.56/35.31    (97)  all_58_4 = all_52_17
% 204.56/35.31    (98)   ~ (all_52_7 = e0)
% 204.56/35.31    (99)  op(all_52_25, all_52_25) = all_52_24
% 204.56/35.31  
% 204.56/35.31  Begin of proof
% 204.56/35.31  | 
% 204.56/35.31  | BETA: splitting (17) gives:
% 204.56/35.31  | 
% 204.56/35.31  | Case 1:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (100)  all_56_7 = e3
% 204.56/35.31  | | 
% 204.56/35.31  | | COMBINE_EQS: (52), (100) imply:
% 204.56/35.31  | |   (101)  all_52_27 = e3
% 204.56/35.31  | | 
% 204.56/35.31  | | SIMP: (101) implies:
% 204.56/35.31  | |   (102)  all_52_27 = e3
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (79), (102) imply:
% 204.56/35.31  | |   (103)   ~ (all_4_2 = e3)
% 204.56/35.31  | | 
% 204.56/35.31  | | SIMP: (103) implies:
% 204.56/35.31  | |   (104)   ~ (all_4_2 = e3)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (24), (102) imply:
% 204.56/35.31  | |   (105)  op(e3, e3) = all_52_26
% 204.56/35.31  | | 
% 204.56/35.31  | | GROUND_INST: instantiating (5) with all_6_2, all_52_26, e3, e3, simplifying
% 204.56/35.31  | |              with (70), (105) gives:
% 204.56/35.31  | |   (106)  all_52_26 = all_6_2
% 204.56/35.31  | | 
% 204.56/35.31  | | REF_CLOSE: (5), (6), (8), (9), (10), (14), (19), (22), (26), (30), (57),
% 204.56/35.31  | |            (58), (64), (69), (70), (89), (91), (93), (95), (104) are
% 204.56/35.31  | |            inconsistent by sub-proof #992.
% 204.56/35.31  | | 
% 204.56/35.31  | Case 2:
% 204.56/35.31  | | 
% 204.56/35.31  | |   (107)   ~ (all_56_7 = e3)
% 204.56/35.31  | | 
% 204.56/35.31  | | REDUCE: (52), (107) imply:
% 204.56/35.31  | |   (108)   ~ (all_52_27 = e3)
% 204.56/35.31  | | 
% 204.56/35.31  | | BETA: splitting (71) gives:
% 204.56/35.31  | | 
% 204.56/35.31  | | Case 1:
% 204.56/35.31  | | | 
% 204.56/35.31  | | |   (109)  all_58_9 = e3
% 204.56/35.31  | | | 
% 204.56/35.31  | | | COMBINE_EQS: (21), (109) imply:
% 204.56/35.31  | | |   (110)  all_52_25 = e3
% 204.56/35.31  | | | 
% 204.56/35.31  | | | SIMP: (110) implies:
% 204.56/35.31  | | |   (111)  all_52_25 = e3
% 204.56/35.31  | | | 
% 204.56/35.31  | | | REDUCE: (59), (111) imply:
% 204.56/35.31  | | |   (112)   ~ (all_52_9 = e3)
% 204.56/35.31  | | | 
% 204.56/35.31  | | | REDUCE: (43), (111) imply:
% 204.56/35.31  | | |   (113)   ~ (all_52_29 = e3)
% 204.56/35.31  | | | 
% 204.56/35.31  | | | SIMP: (113) implies:
% 204.56/35.31  | | |   (114)   ~ (all_52_29 = e3)
% 204.56/35.31  | | | 
% 204.56/35.31  | | | REDUCE: (99), (111) imply:
% 204.56/35.31  | | |   (115)  op(e3, e3) = all_52_24
% 204.56/35.31  | | | 
% 204.56/35.31  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 204.56/35.31  | | |              simplifying with (70), (115) gives:
% 204.56/35.31  | | |   (116)  all_52_24 = all_6_2
% 204.56/35.31  | | | 
% 204.56/35.31  | | | BETA: splitting (58) gives:
% 204.56/35.31  | | | 
% 204.56/35.31  | | | Case 1:
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | |   (117)  all_58_1 = e3
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | | COMBINE_EQS: (6), (117) imply:
% 204.56/35.31  | | | |   (118)  all_52_9 = e3
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | | REDUCE: (112), (118) imply:
% 204.56/35.31  | | | |   (119)  $false
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | | CLOSE: (119) is inconsistent.
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | Case 2:
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | |   (120)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | | BETA: splitting (48) gives:
% 204.56/35.31  | | | | 
% 204.56/35.31  | | | | Case 1:
% 204.56/35.31  | | | | | 
% 204.56/35.31  | | | | |   (121)  all_58_6 = e3
% 204.56/35.31  | | | | | 
% 204.56/35.31  | | | | | COMBINE_EQS: (80), (121) imply:
% 204.56/35.32  | | | | |   (122)  all_52_5 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | SIMP: (122) implies:
% 204.56/35.32  | | | | |   (123)  all_52_5 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (46), (123) imply:
% 204.56/35.32  | | | | |   (124)   ~ (all_52_7 = e3)
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | SIMP: (124) implies:
% 204.56/35.32  | | | | |   (125)   ~ (all_52_7 = e3)
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (16), (123) imply:
% 204.56/35.32  | | | | |   (126)  op(e3, e3) = all_52_4
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 204.56/35.32  | | | | |              simplifying with (70), (126) gives:
% 204.56/35.32  | | | | |   (127)  all_52_4 = all_6_2
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | BETA: splitting (83) gives:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | Case 1:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | |   (128)  all_58_12 = e3
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | COMBINE_EQS: (47), (128) imply:
% 204.56/35.32  | | | | | |   (129)  all_52_7 = e3
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | REDUCE: (125), (129) imply:
% 204.56/35.32  | | | | | |   (130)  $false
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | CLOSE: (130) is inconsistent.
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | Case 2:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | |   (131)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | BETA: splitting (38) gives:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | Case 1:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | |   (132)  all_56_13 = e3
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | COMBINE_EQS: (94), (132) imply:
% 204.56/35.32  | | | | | | |   (133)  all_52_15 = e3
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | SIMP: (133) implies:
% 204.56/35.32  | | | | | | |   (134)  all_52_15 = e3
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REDUCE: (51), (134) imply:
% 204.56/35.32  | | | | | | |   (135)   ~ (all_10_0 = e3)
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REDUCE: (78), (134) imply:
% 204.56/35.32  | | | | | | |   (136)   ~ (all_4_2 = e3)
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | SIMP: (136) implies:
% 204.56/35.32  | | | | | | |   (137)   ~ (all_4_2 = e3)
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REF_CLOSE: (5), (8), (9), (10), (14), (19), (22), (26), (30),
% 204.56/35.32  | | | | | | |            (57), (64), (70), (89), (93), (95), (120), (137) are
% 204.56/35.32  | | | | | | |            inconsistent by sub-proof #993.
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | Case 2:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | |   (138)   ~ (all_56_13 = e3)
% 204.56/35.32  | | | | | | |   (139)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REDUCE: (94), (138) imply:
% 204.56/35.32  | | | | | | |   (140)   ~ (all_52_15 = e3)
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (19), (25), (28), (29),
% 204.56/35.32  | | | | | | |            (31), (32), (34), (39), (40), (47), (56), (64), (68),
% 204.56/35.32  | | | | | | |            (76), (78), (90), (92), (94), (98), (131), (139), (140)
% 204.56/35.32  | | | | | | |            are inconsistent by sub-proof #1288.
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | End of split
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | End of split
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | Case 2:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | |   (141)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REF_CLOSE: (5), (12), (14), (15), (20), (26), (27), (35), (42), (50),
% 204.56/35.32  | | | | |            (61), (62), (74), (90), (114), (141) are inconsistent by
% 204.56/35.32  | | | | |            sub-proof #986.
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | End of split
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | End of split
% 204.56/35.32  | | | 
% 204.56/35.32  | | Case 2:
% 204.56/35.32  | | | 
% 204.56/35.32  | | |   (142)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.32  | | | 
% 204.56/35.32  | | | BETA: splitting (142) gives:
% 204.56/35.32  | | | 
% 204.56/35.32  | | | Case 1:
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | |   (143)  all_58_10 = e3
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | REF_CLOSE: (41), (108), (143) are inconsistent by sub-proof #1301.
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | Case 2:
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | |   (144)  all_58_11 = e3 | all_58_15 = e3
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | BETA: splitting (144) gives:
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | Case 1:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | |   (145)  all_58_11 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | COMBINE_EQS: (27), (145) imply:
% 204.56/35.32  | | | | |   (146)  all_52_29 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | SIMP: (146) implies:
% 204.56/35.32  | | | | |   (147)  all_52_29 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (43), (147) imply:
% 204.56/35.32  | | | | |   (148)   ~ (all_52_25 = e3)
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (63), (147) imply:
% 204.56/35.32  | | | | |   (149)  op(e3, e3) = all_52_28
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_28, e3, e3,
% 204.56/35.32  | | | | |              simplifying with (70), (149) gives:
% 204.56/35.32  | | | | |   (150)  all_52_28 = all_6_2
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | BETA: splitting (66) gives:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | Case 1:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | |   (151)  all_56_3 = e3
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | REF_CLOSE: (75), (148), (151) are inconsistent by sub-proof #1339.
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | Case 2:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | |   (152)   ~ (all_56_3 = e3)
% 204.56/35.32  | | | | | |   (153)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | BETA: splitting (67) gives:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | Case 1:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | |   (154)  all_58_9 = e2
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | COMBINE_EQS: (21), (154) imply:
% 204.56/35.32  | | | | | | |   (155)  all_52_25 = e2
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REDUCE: (148), (155) imply:
% 204.56/35.32  | | | | | | |   (156)   ~ (e3 = e2)
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REDUCE: (99), (155) imply:
% 204.56/35.32  | | | | | | |   (157)  op(e2, e2) = all_52_24
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | BETA: splitting (33) gives:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | Case 1:
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | |   (158)  all_58_9 = e1
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | REF_CLOSE: (39), (154), (158) are inconsistent by sub-proof
% 204.56/35.32  | | | | | | | |            #1214.
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | Case 2:
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | |   (159)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | BETA: splitting (159) gives:
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | Case 1:
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | |   (160)  all_58_10 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | COMBINE_EQS: (41), (160) imply:
% 204.56/35.32  | | | | | | | | |   (161)  all_52_27 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | SIMP: (161) implies:
% 204.56/35.32  | | | | | | | | |   (162)  all_52_27 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | REDUCE: (24), (162) imply:
% 204.56/35.32  | | | | | | | | |   (163)  op(e1, e1) = all_52_26
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_26, e1,
% 204.56/35.32  | | | | | | | | |              e1, simplifying with (90), (163) gives:
% 204.56/35.32  | | | | | | | | |   (164)  all_52_26 = all_10_2
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_24, e2, e2,
% 204.56/35.32  | | | | | | | | |              simplifying with (25), (157) gives:
% 204.56/35.32  | | | | | | | | |   (165)  all_52_24 = all_4_2
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | BETA: splitting (23) gives:
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | Case 1:
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | |   (166)  all_58_6 = e2
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | COMBINE_EQS: (80), (166) imply:
% 204.56/35.32  | | | | | | | | | |   (167)  all_52_5 = e2
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REDUCE: (46), (167) imply:
% 204.56/35.32  | | | | | | | | | |   (168)   ~ (all_52_7 = e2)
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | SIMP: (168) implies:
% 204.56/35.32  | | | | | | | | | |   (169)   ~ (all_52_7 = e2)
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REDUCE: (16), (167) imply:
% 204.56/35.32  | | | | | | | | | |   (170)  op(e2, e2) = all_52_4
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11),
% 204.56/35.32  | | | | | | | | | |            (13), (19), (21), (22), (25), (26), (27), (28),
% 204.56/35.32  | | | | | | | | | |            (29), (30), (31), (32), (34), (36), (38), (40),
% 204.56/35.32  | | | | | | | | | |            (43), (44), (45), (47), (51), (54), (56), (57),
% 204.56/35.32  | | | | | | | | | |            (58), (64), (65), (68), (69), (70), (72), (73),
% 204.56/35.32  | | | | | | | | | |            (76), (77), (78), (82), (83), (86), (87), (88),
% 204.56/35.32  | | | | | | | | | |            (89), (90), (91), (93), (94), (95), (96), (97),
% 204.56/35.32  | | | | | | | | | |            (98), (144), (169), (170) are inconsistent by
% 204.56/35.32  | | | | | | | | | |            sub-proof #982.
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | Case 2:
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | |   (171)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REF_CLOSE: (5), (26), (35), (49), (60), (62), (81), (85),
% 204.56/35.32  | | | | | | | | | |            (145), (171) are inconsistent by sub-proof #997.
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | End of split
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | Case 2:
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | |   (172)  all_58_11 = e1 | all_58_15 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | REF_CLOSE: (4), (34), (84), (145), (172) are inconsistent by
% 204.56/35.32  | | | | | | | | |            sub-proof #1206.
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | End of split
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | End of split
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | Case 2:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | |   (173)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | BETA: splitting (173) gives:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | Case 1:
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | |   (174)  all_58_10 = e2
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | COMBINE_EQS: (41), (174) imply:
% 204.56/35.32  | | | | | | | |   (175)  all_52_27 = e2
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | REDUCE: (2), (175) imply:
% 204.56/35.32  | | | | | | | |   (176)   ~ (all_52_25 = e2)
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | REDUCE: (108), (175) imply:
% 204.56/35.32  | | | | | | | |   (177)   ~ (e3 = e2)
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | REDUCE: (24), (175) imply:
% 204.56/35.32  | | | | | | | |   (178)  op(e2, e2) = all_52_26
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | BETA: splitting (33) gives:
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | Case 1:
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | |   (179)  all_58_9 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | COMBINE_EQS: (21), (179) imply:
% 204.56/35.32  | | | | | | | | |   (180)  all_52_25 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | SIMP: (180) implies:
% 204.56/35.32  | | | | | | | | |   (181)  all_52_25 = e1
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | REDUCE: (99), (181) imply:
% 204.56/35.32  | | | | | | | | |   (182)  op(e1, e1) = all_52_24
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_24, e1,
% 204.56/35.32  | | | | | | | | |              e1, simplifying with (90), (182) gives:
% 204.56/35.32  | | | | | | | | |   (183)  all_52_24 = all_10_2
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_26, e2, e2,
% 204.56/35.32  | | | | | | | | |              simplifying with (25), (178) gives:
% 204.56/35.32  | | | | | | | | |   (184)  all_52_26 = all_4_2
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | BETA: splitting (23) gives:
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | Case 1:
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | |   (185)  all_58_6 = e2
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | COMBINE_EQS: (80), (185) imply:
% 204.56/35.32  | | | | | | | | | |   (186)  all_52_5 = e2
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REDUCE: (46), (186) imply:
% 204.56/35.32  | | | | | | | | | |   (187)   ~ (all_52_7 = e2)
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | SIMP: (187) implies:
% 204.56/35.32  | | | | | | | | | |   (188)   ~ (all_52_7 = e2)
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REDUCE: (16), (186) imply:
% 204.56/35.32  | | | | | | | | | |   (189)  op(e2, e2) = all_52_4
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11),
% 204.56/35.32  | | | | | | | | | |            (13), (19), (21), (22), (25), (26), (27), (28),
% 204.56/35.32  | | | | | | | | | |            (29), (30), (31), (32), (34), (36), (38), (40),
% 204.56/35.32  | | | | | | | | | |            (43), (44), (45), (47), (51), (54), (56), (57),
% 204.56/35.32  | | | | | | | | | |            (58), (64), (65), (68), (69), (70), (72), (73),
% 204.56/35.32  | | | | | | | | | |            (76), (77), (78), (82), (83), (86), (87), (88),
% 204.56/35.32  | | | | | | | | | |            (89), (90), (91), (93), (94), (95), (96), (97),
% 204.56/35.32  | | | | | | | | | |            (98), (144), (188), (189) are inconsistent by
% 204.56/35.32  | | | | | | | | | |            sub-proof #982.
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | Case 2:
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | |   (190)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | | REF_CLOSE: (5), (26), (35), (49), (60), (62), (81), (85),
% 204.56/35.32  | | | | | | | | | |            (145), (190) are inconsistent by sub-proof #997.
% 204.56/35.32  | | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | End of split
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | Case 2:
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | |   (191)   ~ (all_58_9 = e1)
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | REDUCE: (21), (191) imply:
% 204.56/35.32  | | | | | | | | |   (192)   ~ (all_52_25 = e1)
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | | REF_CLOSE: (37), (75), (153), (176), (192) are inconsistent by
% 204.56/35.32  | | | | | | | | |            sub-proof #1215.
% 204.56/35.32  | | | | | | | | | 
% 204.56/35.32  | | | | | | | | End of split
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | Case 2:
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | |   (193)  all_58_11 = e2 | all_58_15 = e2
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | | REF_CLOSE: (34), (53), (85), (145), (193) are inconsistent by
% 204.56/35.32  | | | | | | | |            sub-proof #995.
% 204.56/35.32  | | | | | | | | 
% 204.56/35.32  | | | | | | | End of split
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | End of split
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | End of split
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | Case 2:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | |   (194)  all_58_15 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REF_CLOSE: (7), (34), (194) are inconsistent by sub-proof #1350.
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | End of split
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | End of split
% 204.56/35.32  | | | 
% 204.56/35.32  | | End of split
% 204.56/35.32  | | 
% 204.56/35.32  | End of split
% 204.56/35.32  | 
% 204.56/35.32  End of proof
% 204.56/35.32  
% 204.56/35.32  Sub-proof #982 shows that the following formulas are inconsistent:
% 204.56/35.32  ----------------------------------------------------------------
% 204.56/35.32    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.32    (2)  all_58_14 = all_52_23
% 204.56/35.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.32    (4)  all_58_1 = all_52_9
% 204.56/35.32    (5)   ~ (e3 = e0)
% 204.56/35.32    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.32    (7)   ~ (all_52_7 = all_52_15)
% 204.56/35.32    (8)  op(all_52_15, all_52_15) = e0
% 204.56/35.32    (9)  op(all_52_7, all_52_7) = all_52_6
% 204.56/35.32    (10)  all_58_0 = all_6_2
% 204.56/35.32    (11)  all_58_13 = all_52_15
% 204.56/35.32    (12)  all_58_9 = all_52_25
% 204.56/35.32    (13)   ~ (all_6_1 = e1)
% 204.56/35.32    (14)  op(e2, e2) = all_4_2
% 204.56/35.32    (15)  all_58_7 = all_10_0
% 204.56/35.32    (16)  all_58_11 = all_52_29
% 204.56/35.32    (17)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.56/35.32    (18)  op(all_10_2, e1) = all_10_1
% 204.56/35.32    (19)   ~ (all_52_7 = all_6_2)
% 204.56/35.32    (20)  op(e0, e1) = all_52_23
% 204.56/35.32    (21)   ~ (all_52_15 = e0)
% 204.56/35.32    (22)  all_58_15 = e0
% 204.56/35.32    (23)   ~ (all_4_1 = e1)
% 204.56/35.32    (24)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.32    (25)  op(e2, e2) = all_52_4
% 204.56/35.32    (26)  op(e0, e0) = e0
% 204.56/35.32    (27)   ~ (all_52_25 = all_52_29)
% 204.56/35.32    (28)  all_58_11 = e3 | all_58_15 = e3
% 204.56/35.32    (29)  all_58_7 = all_52_13
% 204.56/35.32    (30)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.32    (31)  all_58_12 = all_52_7
% 204.56/35.32    (32)   ~ (all_52_15 = all_10_0)
% 204.56/35.32    (33)  op(all_4_2, e2) = all_4_1
% 204.56/35.32    (34)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.56/35.32    (35)   ~ (all_52_7 = e2)
% 204.56/35.32    (36)  op(e0, e3) = all_52_7
% 204.56/35.32    (37)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.32    (38)  all_56_12 = all_52_7
% 204.56/35.32    (39)  op(all_52_17, all_52_17) = all_52_16
% 204.56/35.32    (40)  op(all_4_2, all_4_2) = e2
% 204.56/35.32    (41)   ~ (all_52_9 = all_6_2)
% 204.56/35.32    (42)  op(e3, e3) = all_6_2
% 204.56/35.32    (43)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.32    (44)  all_56_14 = all_52_23
% 204.56/35.32    (45)   ~ (all_10_1 = e3)
% 204.56/35.32    (46)  all_56_1 = all_52_9
% 204.56/35.32    (47)   ~ (all_52_15 = all_4_2)
% 204.56/35.32    (48)  op(e3, e2) = all_52_9
% 204.56/35.32    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.32    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.32    (51)   ~ (all_52_9 = all_52_17)
% 204.56/35.32    (52)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.56/35.32    (53)   ~ (all_6_1 = e2)
% 204.56/35.32    (54)  op(e1, e1) = all_10_2
% 204.56/35.32    (55)  op(all_52_9, all_52_9) = e3
% 204.56/35.32    (56)  all_58_3 = all_4_2
% 204.56/35.32    (57)  all_56_13 = all_52_15
% 204.56/35.32    (58)  op(all_6_2, e3) = all_6_1
% 204.56/35.32    (59)   ~ (all_52_13 = all_52_29)
% 204.56/35.32    (60)  all_58_4 = all_52_17
% 204.56/35.32    (61)   ~ (all_52_7 = e0)
% 204.56/35.32  
% 204.56/35.32  Begin of proof
% 204.56/35.32  | 
% 204.56/35.32  | GROUND_INST: instantiating (3) with all_4_2, all_52_4, e2, e2, simplifying
% 204.56/35.32  |              with (14), (25) gives:
% 204.56/35.32  |   (62)  all_52_4 = all_4_2
% 204.56/35.32  | 
% 204.56/35.32  | BETA: splitting (6) gives:
% 204.56/35.32  | 
% 204.56/35.32  | Case 1:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (63)  all_56_12 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | COMBINE_EQS: (38), (63) imply:
% 204.56/35.32  | |   (64)  all_52_7 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | REDUCE: (7), (64) imply:
% 204.56/35.32  | |   (65)   ~ (all_52_15 = e3)
% 204.56/35.32  | | 
% 204.56/35.32  | | SIMP: (65) implies:
% 204.56/35.32  | |   (66)   ~ (all_52_15 = e3)
% 204.56/35.32  | | 
% 204.56/35.32  | | REDUCE: (19), (64) imply:
% 204.56/35.32  | |   (67)   ~ (all_6_2 = e3)
% 204.56/35.32  | | 
% 204.56/35.32  | | SIMP: (67) implies:
% 204.56/35.32  | |   (68)   ~ (all_6_2 = e3)
% 204.56/35.32  | | 
% 204.56/35.32  | | REF_CLOSE: (3), (4), (5), (10), (11), (12), (16), (22), (23), (26), (27),
% 204.56/35.32  | |            (28), (29), (33), (37), (39), (40), (41), (42), (43), (46), (48),
% 204.56/35.32  | |            (50), (51), (52), (55), (56), (59), (60), (66), (68) are
% 204.56/35.32  | |            inconsistent by sub-proof #1295.
% 204.56/35.32  | | 
% 204.56/35.32  | Case 2:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (69)   ~ (all_56_12 = e3)
% 204.56/35.32  | |   (70)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.32  | | 
% 204.56/35.32  | | REDUCE: (38), (69) imply:
% 204.56/35.32  | |   (71)   ~ (all_52_7 = e3)
% 204.56/35.32  | | 
% 204.56/35.32  | | BETA: splitting (70) gives:
% 204.56/35.32  | | 
% 204.56/35.32  | | Case 1:
% 204.56/35.32  | | | 
% 204.56/35.32  | | |   (72)  all_56_12 = e2
% 204.56/35.32  | | | 
% 204.56/35.32  | | | COMBINE_EQS: (38), (72) imply:
% 204.56/35.32  | | |   (73)  all_52_7 = e2
% 204.56/35.32  | | | 
% 204.56/35.32  | | | REDUCE: (35), (73) imply:
% 204.56/35.32  | | |   (74)  $false
% 204.56/35.32  | | | 
% 204.56/35.32  | | | CLOSE: (74) is inconsistent.
% 204.56/35.32  | | | 
% 204.56/35.32  | | Case 2:
% 204.56/35.32  | | | 
% 204.56/35.32  | | |   (75)   ~ (all_56_12 = e2)
% 204.56/35.32  | | |   (76)  all_56_12 = e1 | all_56_12 = e0
% 204.56/35.32  | | | 
% 204.56/35.32  | | | BETA: splitting (76) gives:
% 204.56/35.32  | | | 
% 204.56/35.32  | | | Case 1:
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | |   (77)  all_56_12 = e1
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | COMBINE_EQS: (38), (77) imply:
% 204.56/35.32  | | | |   (78)  all_52_7 = e1
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | COMBINE_EQS: (31), (78) imply:
% 204.56/35.32  | | | |   (79)  all_58_12 = e1
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | REDUCE: (71), (78) imply:
% 204.56/35.32  | | | |   (80)   ~ (e3 = e1)
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | SIMP: (80) implies:
% 204.56/35.32  | | | |   (81)   ~ (e3 = e1)
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | REDUCE: (35), (78) imply:
% 204.56/35.32  | | | |   (82)   ~ (e2 = e1)
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | SIMP: (82) implies:
% 204.56/35.32  | | | |   (83)   ~ (e2 = e1)
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | REDUCE: (9), (78) imply:
% 204.56/35.32  | | | |   (84)  op(e1, e1) = all_52_6
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_6, e1, e1,
% 204.56/35.32  | | | |              simplifying with (54), (84) gives:
% 204.56/35.32  | | | |   (85)  all_52_6 = all_10_2
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | BETA: splitting (30) gives:
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | Case 1:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | |   (86)  all_56_14 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | COMBINE_EQS: (44), (86) imply:
% 204.56/35.32  | | | | |   (87)  all_52_23 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | SIMP: (87) implies:
% 204.56/35.32  | | | | |   (88)  all_52_23 = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (1), (88) imply:
% 204.56/35.32  | | | | |   (89)   ~ (all_52_15 = e3)
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (20), (88) imply:
% 204.56/35.32  | | | | |   (90)  op(e0, e1) = e3
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REF_CLOSE: (3), (6), (7), (8), (11), (14), (17), (18), (21), (24),
% 204.56/35.32  | | | | |            (26), (31), (34), (38), (40), (45), (47), (54), (57), (61),
% 204.56/35.32  | | | | |            (71), (83), (89), (90) are inconsistent by sub-proof #985.
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | Case 2:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | |   (91)   ~ (all_56_14 = e3)
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | REDUCE: (44), (91) imply:
% 204.56/35.32  | | | | |   (92)   ~ (all_52_23 = e3)
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | BETA: splitting (49) gives:
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | | Case 1:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | |   (93)  all_58_12 = e3
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | COMBINE_EQS: (79), (93) imply:
% 204.56/35.32  | | | | | |   (94)  e3 = e1
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | REDUCE: (81), (94) imply:
% 204.56/35.32  | | | | | |   (95)  $false
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | CLOSE: (95) is inconsistent.
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | Case 2:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | |   (96)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | BETA: splitting (96) gives:
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | | Case 1:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | |   (97)  all_58_13 = e3
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (11), (13), (15), (19), (32),
% 204.56/35.32  | | | | | | |            (36), (37), (38), (41), (42), (47), (53), (55), (56),
% 204.56/35.32  | | | | | | |            (58), (97) are inconsistent by sub-proof #984.
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | Case 2:
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | |   (98)  all_58_14 = e3 | all_58_15 = e3
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | | REF_CLOSE: (2), (5), (22), (92), (98) are inconsistent by
% 204.56/35.32  | | | | | | |            sub-proof #983.
% 204.56/35.32  | | | | | | | 
% 204.56/35.32  | | | | | | End of split
% 204.56/35.32  | | | | | | 
% 204.56/35.32  | | | | | End of split
% 204.56/35.32  | | | | | 
% 204.56/35.32  | | | | End of split
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | Case 2:
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | |   (99)  all_56_12 = e0
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | COMBINE_EQS: (38), (99) imply:
% 204.56/35.32  | | | |   (100)  all_52_7 = e0
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | REDUCE: (61), (100) imply:
% 204.56/35.32  | | | |   (101)  $false
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | | CLOSE: (101) is inconsistent.
% 204.56/35.32  | | | | 
% 204.56/35.32  | | | End of split
% 204.56/35.32  | | | 
% 204.56/35.32  | | End of split
% 204.56/35.32  | | 
% 204.56/35.32  | End of split
% 204.56/35.32  | 
% 204.56/35.32  End of proof
% 204.56/35.32  
% 204.56/35.32  Sub-proof #983 shows that the following formulas are inconsistent:
% 204.56/35.32  ----------------------------------------------------------------
% 204.56/35.32    (1)  all_58_14 = all_52_23
% 204.56/35.32    (2)   ~ (e3 = e0)
% 204.56/35.32    (3)  all_58_15 = e0
% 204.56/35.32    (4)   ~ (all_52_23 = e3)
% 204.56/35.32    (5)  all_58_14 = e3 | all_58_15 = e3
% 204.56/35.32  
% 204.56/35.32  Begin of proof
% 204.56/35.32  | 
% 204.56/35.32  | BETA: splitting (5) gives:
% 204.56/35.32  | 
% 204.56/35.32  | Case 1:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (6)  all_58_14 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #1305.
% 204.56/35.32  | | 
% 204.56/35.32  | Case 2:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (7)  all_58_15 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | COMBINE_EQS: (3), (7) imply:
% 204.56/35.32  | |   (8)  e3 = e0
% 204.56/35.32  | | 
% 204.56/35.32  | | REDUCE: (2), (8) imply:
% 204.56/35.32  | |   (9)  $false
% 204.56/35.32  | | 
% 204.56/35.32  | | CLOSE: (9) is inconsistent.
% 204.56/35.32  | | 
% 204.56/35.32  | End of split
% 204.56/35.32  | 
% 204.56/35.32  End of proof
% 204.56/35.32  
% 204.56/35.32  Sub-proof #984 shows that the following formulas are inconsistent:
% 204.56/35.32  ----------------------------------------------------------------
% 204.56/35.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.32    (2)  all_58_1 = all_52_9
% 204.56/35.32    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.32    (4)   ~ (all_52_7 = all_52_15)
% 204.56/35.32    (5)  op(all_52_15, all_52_15) = e0
% 204.56/35.32    (6)  all_58_13 = e3
% 204.56/35.32    (7)  all_58_13 = all_52_15
% 204.56/35.32    (8)   ~ (all_6_1 = e1)
% 204.56/35.32    (9)  all_58_7 = all_10_0
% 204.56/35.32    (10)   ~ (all_52_7 = all_6_2)
% 204.56/35.32    (11)   ~ (all_52_15 = all_10_0)
% 204.56/35.32    (12)  op(e0, e3) = all_52_7
% 204.56/35.32    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.32    (14)  all_56_12 = all_52_7
% 204.56/35.32    (15)   ~ (all_52_9 = all_6_2)
% 204.56/35.32    (16)  op(e3, e3) = all_6_2
% 204.56/35.32    (17)   ~ (all_52_15 = all_4_2)
% 204.56/35.32    (18)   ~ (all_6_1 = e2)
% 204.56/35.32    (19)  op(all_52_9, all_52_9) = e3
% 204.56/35.32    (20)  all_58_3 = all_4_2
% 204.56/35.32    (21)  op(all_6_2, e3) = all_6_1
% 204.56/35.32  
% 204.56/35.32  Begin of proof
% 204.56/35.32  | 
% 204.56/35.32  | COMBINE_EQS: (6), (7) imply:
% 204.56/35.32  |   (22)  all_52_15 = e3
% 204.56/35.32  | 
% 204.56/35.32  | SIMP: (22) implies:
% 204.56/35.32  |   (23)  all_52_15 = e3
% 204.56/35.32  | 
% 204.56/35.32  | REDUCE: (11), (23) imply:
% 204.56/35.32  |   (24)   ~ (all_10_0 = e3)
% 204.56/35.32  | 
% 204.56/35.32  | SIMP: (24) implies:
% 204.56/35.32  |   (25)   ~ (all_10_0 = e3)
% 204.56/35.32  | 
% 204.56/35.32  | REDUCE: (17), (23) imply:
% 204.56/35.32  |   (26)   ~ (all_4_2 = e3)
% 204.56/35.32  | 
% 204.56/35.32  | SIMP: (26) implies:
% 204.56/35.32  |   (27)   ~ (all_4_2 = e3)
% 204.56/35.32  | 
% 204.56/35.32  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 204.56/35.32  |            (15), (16), (18), (19), (20), (21), (25), (27) are inconsistent by
% 204.56/35.32  |            sub-proof #992.
% 204.56/35.32  | 
% 204.56/35.32  End of proof
% 204.56/35.32  
% 204.56/35.32  Sub-proof #985 shows that the following formulas are inconsistent:
% 204.56/35.32  ----------------------------------------------------------------
% 204.56/35.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.32    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.32    (3)   ~ (all_52_7 = all_52_15)
% 204.56/35.32    (4)  op(all_52_15, all_52_15) = e0
% 204.56/35.32    (5)  all_58_13 = all_52_15
% 204.56/35.32    (6)   ~ (all_52_15 = e3)
% 204.56/35.32    (7)  op(e2, e2) = all_4_2
% 204.56/35.32    (8)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.56/35.32    (9)  op(all_10_2, e1) = all_10_1
% 204.56/35.32    (10)   ~ (all_52_15 = e0)
% 204.56/35.32    (11)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.32    (12)   ~ (e2 = e1)
% 204.56/35.32    (13)  op(e0, e0) = e0
% 204.56/35.32    (14)  all_58_12 = all_52_7
% 204.56/35.32    (15)   ~ (all_52_7 = e3)
% 204.56/35.32    (16)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.56/35.32    (17)  all_56_12 = all_52_7
% 204.56/35.32    (18)  op(all_4_2, all_4_2) = e2
% 204.56/35.32    (19)   ~ (all_10_1 = e3)
% 204.56/35.32    (20)   ~ (all_52_15 = all_4_2)
% 204.56/35.32    (21)  op(e1, e1) = all_10_2
% 204.56/35.32    (22)  all_56_13 = all_52_15
% 204.56/35.32    (23)  op(e0, e1) = e3
% 204.56/35.32    (24)   ~ (all_52_7 = e0)
% 204.56/35.32  
% 204.56/35.32  Begin of proof
% 204.56/35.32  | 
% 204.56/35.32  | BETA: splitting (11) gives:
% 204.56/35.32  | 
% 204.56/35.32  | Case 1:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (25)  all_56_13 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | COMBINE_EQS: (22), (25) imply:
% 204.56/35.32  | |   (26)  all_52_15 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | REDUCE: (6), (26) imply:
% 204.56/35.32  | |   (27)  $false
% 204.56/35.32  | | 
% 204.56/35.32  | | CLOSE: (27) is inconsistent.
% 204.56/35.32  | | 
% 204.56/35.32  | Case 2:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (28)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.32  | | 
% 204.56/35.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 204.56/35.32  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (28)
% 204.56/35.32  | |            are inconsistent by sub-proof #1289.
% 204.56/35.32  | | 
% 204.56/35.32  | End of split
% 204.56/35.32  | 
% 204.56/35.32  End of proof
% 204.56/35.32  
% 204.56/35.32  Sub-proof #986 shows that the following formulas are inconsistent:
% 204.56/35.32  ----------------------------------------------------------------
% 204.56/35.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.32    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.56/35.32    (3)   ~ (all_10_0 = e3)
% 204.56/35.32    (4)  all_40_2 = all_10_2
% 204.56/35.32    (5)  op(all_10_0, all_10_0) = e1
% 204.56/35.32    (6)  all_58_7 = all_10_0
% 204.56/35.32    (7)  all_58_11 = all_52_29
% 204.56/35.32    (8)   ~ (all_10_0 = e2)
% 204.56/35.32    (9)  all_56_9 = all_10_0
% 204.56/35.32    (10)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.56/35.32    (11)   ~ (all_52_29 = e3)
% 204.56/35.32    (12)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.32    (13)   ~ (all_10_0 = all_10_2)
% 204.56/35.32    (14)  all_58_8 = all_10_2
% 204.56/35.32    (15)  all_40_0 = all_10_0
% 204.56/35.32    (16)  op(e1, e1) = all_10_2
% 204.56/35.32  
% 204.56/35.32  Begin of proof
% 204.56/35.32  | 
% 204.56/35.32  | BETA: splitting (12) gives:
% 204.56/35.32  | 
% 204.56/35.32  | Case 1:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (17)  all_58_7 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | COMBINE_EQS: (6), (17) imply:
% 204.56/35.32  | |   (18)  all_10_0 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | REDUCE: (3), (18) imply:
% 204.56/35.32  | |   (19)  $false
% 204.56/35.32  | | 
% 204.56/35.32  | | CLOSE: (19) is inconsistent.
% 204.56/35.32  | | 
% 204.56/35.32  | Case 2:
% 204.56/35.32  | | 
% 204.56/35.32  | |   (20)  all_58_8 = e3 | all_58_11 = e3
% 204.56/35.32  | | 
% 204.56/35.32  | | BETA: splitting (20) gives:
% 204.56/35.32  | | 
% 204.56/35.32  | | Case 1:
% 204.56/35.32  | | | 
% 204.56/35.32  | | |   (21)  all_58_8 = e3
% 204.56/35.32  | | | 
% 204.56/35.32  | | | COMBINE_EQS: (14), (21) imply:
% 204.56/35.32  | | |   (22)  all_10_2 = e3
% 204.56/35.32  | | | 
% 204.56/35.32  | | | SIMP: (22) implies:
% 204.56/35.32  | | |   (23)  all_10_2 = e3
% 204.56/35.32  | | | 
% 204.56/35.32  | | | COMBINE_EQS: (4), (23) imply:
% 204.56/35.32  | | |   (24)  all_40_2 = e3
% 204.56/35.32  | | | 
% 204.56/35.32  | | | REF_CLOSE: (1), (2), (5), (8), (9), (10), (13), (15), (16), (24) are
% 204.56/35.32  | | |            inconsistent by sub-proof #987.
% 204.56/35.32  | | | 
% 204.56/35.32  | | Case 2:
% 204.56/35.32  | | | 
% 204.56/35.32  | | |   (25)  all_58_11 = e3
% 204.56/35.32  | | | 
% 204.56/35.32  | | | REF_CLOSE: (7), (11), (25) are inconsistent by sub-proof #1323.
% 204.56/35.32  | | | 
% 204.56/35.32  | | End of split
% 204.56/35.32  | | 
% 204.56/35.32  | End of split
% 204.56/35.32  | 
% 204.56/35.32  End of proof
% 204.56/35.32  
% 204.56/35.32  Sub-proof #987 shows that the following formulas are inconsistent:
% 204.56/35.32  ----------------------------------------------------------------
% 204.56/35.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.32    (2)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.56/35.32    (3)  op(all_10_0, all_10_0) = e1
% 204.56/35.32    (4)   ~ (all_10_0 = e2)
% 204.56/35.32    (5)  all_56_9 = all_10_0
% 204.56/35.32    (6)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.56/35.32    (7)   ~ (all_10_0 = all_10_2)
% 204.56/35.32    (8)  all_40_2 = e3
% 204.56/35.32    (9)  all_40_0 = all_10_0
% 204.56/35.33    (10)  op(e1, e1) = all_10_2
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | BETA: splitting (6) gives:
% 204.56/35.33  | 
% 204.56/35.33  | Case 1:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (11)   ~ (all_40_2 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (8), (11) imply:
% 204.56/35.33  | |   (12)  $false
% 204.56/35.33  | | 
% 204.56/35.33  | | CLOSE: (12) is inconsistent.
% 204.56/35.33  | | 
% 204.56/35.33  | Case 2:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (13)   ~ (all_40_0 = e0)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (9), (13) imply:
% 204.56/35.33  | |   (14)   ~ (all_10_0 = e0)
% 204.56/35.33  | | 
% 204.56/35.33  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (14) are inconsistent by
% 204.56/35.33  | |            sub-proof #988.
% 204.56/35.33  | | 
% 204.56/35.33  | End of split
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #988 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.33    (2)   ~ (all_10_0 = e0)
% 204.56/35.33    (3)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.56/35.33    (4)  op(all_10_0, all_10_0) = e1
% 204.56/35.33    (5)   ~ (all_10_0 = e2)
% 204.56/35.33    (6)  all_56_9 = all_10_0
% 204.56/35.33    (7)   ~ (all_10_0 = all_10_2)
% 204.56/35.33    (8)  op(e1, e1) = all_10_2
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | BETA: splitting (3) gives:
% 204.56/35.33  | 
% 204.56/35.33  | Case 1:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (9)  all_56_9 = e2
% 204.56/35.33  | | 
% 204.56/35.33  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #991.
% 204.56/35.33  | | 
% 204.56/35.33  | Case 2:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (10)  all_56_9 = e1 | all_56_9 = e0
% 204.56/35.33  | | 
% 204.56/35.33  | | BETA: splitting (10) gives:
% 204.56/35.33  | | 
% 204.56/35.33  | | Case 1:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (11)  all_56_9 = e1
% 204.56/35.33  | | | 
% 204.56/35.33  | | | COMBINE_EQS: (6), (11) imply:
% 204.56/35.33  | | |   (12)  all_10_0 = e1
% 204.56/35.33  | | | 
% 204.56/35.33  | | | REF_CLOSE: (1), (4), (7), (8), (12) are inconsistent by sub-proof #990.
% 204.56/35.33  | | | 
% 204.56/35.33  | | Case 2:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (13)  all_56_9 = e0
% 204.56/35.33  | | | 
% 204.56/35.33  | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #989.
% 204.56/35.33  | | | 
% 204.56/35.33  | | End of split
% 204.56/35.33  | | 
% 204.56/35.33  | End of split
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #989 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)  all_56_9 = all_10_0
% 204.56/35.33    (2)  all_56_9 = e0
% 204.56/35.33    (3)   ~ (all_10_0 = e0)
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.33  |   (4)  all_10_0 = e0
% 204.56/35.33  | 
% 204.56/35.33  | SIMP: (4) implies:
% 204.56/35.33  |   (5)  all_10_0 = e0
% 204.56/35.33  | 
% 204.56/35.33  | REDUCE: (3), (5) imply:
% 204.56/35.33  |   (6)  $false
% 204.56/35.33  | 
% 204.56/35.33  | CLOSE: (6) is inconsistent.
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #990 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.33    (2)  op(all_10_0, all_10_0) = e1
% 204.56/35.33    (3)  all_10_0 = e1
% 204.56/35.33    (4)   ~ (all_10_0 = all_10_2)
% 204.56/35.33    (5)  op(e1, e1) = all_10_2
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | SIMP: (3) implies:
% 204.56/35.33  |   (6)  all_10_0 = e1
% 204.56/35.33  | 
% 204.56/35.33  | REDUCE: (4), (6) imply:
% 204.56/35.33  |   (7)   ~ (all_10_2 = e1)
% 204.56/35.33  | 
% 204.56/35.33  | SIMP: (7) implies:
% 204.56/35.33  |   (8)   ~ (all_10_2 = e1)
% 204.56/35.33  | 
% 204.56/35.33  | REDUCE: (2), (6) imply:
% 204.56/35.33  |   (9)  op(e1, e1) = e1
% 204.56/35.33  | 
% 204.56/35.33  | REF_CLOSE: (1), (5), (8), (9) are inconsistent by sub-proof #1135.
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #991 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)  all_56_9 = all_10_0
% 204.56/35.33    (2)  all_56_9 = e2
% 204.56/35.33    (3)   ~ (all_10_0 = e2)
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.33  |   (4)  all_10_0 = e2
% 204.56/35.33  | 
% 204.56/35.33  | SIMP: (4) implies:
% 204.56/35.33  |   (5)  all_10_0 = e2
% 204.56/35.33  | 
% 204.56/35.33  | REDUCE: (3), (5) imply:
% 204.56/35.33  |   (6)  $false
% 204.56/35.33  | 
% 204.56/35.33  | CLOSE: (6) is inconsistent.
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #992 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.33    (2)  all_58_1 = all_52_9
% 204.56/35.33    (3)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.33    (4)   ~ (all_52_7 = all_52_15)
% 204.56/35.33    (5)  op(all_52_15, all_52_15) = e0
% 204.56/35.33    (6)   ~ (all_4_2 = e3)
% 204.56/35.33    (7)   ~ (all_10_0 = e3)
% 204.56/35.33    (8)  all_58_13 = all_52_15
% 204.56/35.33    (9)   ~ (all_6_1 = e1)
% 204.56/35.33    (10)  all_58_7 = all_10_0
% 204.56/35.33    (11)   ~ (all_52_7 = all_6_2)
% 204.56/35.33    (12)  op(e0, e3) = all_52_7
% 204.56/35.33    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33    (14)  all_56_12 = all_52_7
% 204.56/35.33    (15)   ~ (all_52_9 = all_6_2)
% 204.56/35.33    (16)  op(e3, e3) = all_6_2
% 204.56/35.33    (17)   ~ (all_6_1 = e2)
% 204.56/35.33    (18)  op(all_52_9, all_52_9) = e3
% 204.56/35.33    (19)  all_58_3 = all_4_2
% 204.56/35.33    (20)  op(all_6_2, e3) = all_6_1
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | BETA: splitting (13) gives:
% 204.56/35.33  | 
% 204.56/35.33  | Case 1:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (21)  all_58_1 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | COMBINE_EQS: (2), (21) imply:
% 204.56/35.33  | |   (22)  all_52_9 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | REF_CLOSE: (1), (15), (16), (18), (22) are inconsistent by sub-proof #1337.
% 204.56/35.33  | | 
% 204.56/35.33  | Case 2:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (23)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 204.56/35.33  | |            (16), (17), (19), (20), (23) are inconsistent by sub-proof #993.
% 204.56/35.33  | | 
% 204.56/35.33  | End of split
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #993 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.33    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.33    (3)   ~ (all_52_7 = all_52_15)
% 204.56/35.33    (4)  op(all_52_15, all_52_15) = e0
% 204.56/35.33    (5)   ~ (all_4_2 = e3)
% 204.56/35.33    (6)   ~ (all_10_0 = e3)
% 204.56/35.33    (7)  all_58_13 = all_52_15
% 204.56/35.33    (8)   ~ (all_6_1 = e1)
% 204.56/35.33    (9)  all_58_7 = all_10_0
% 204.56/35.33    (10)   ~ (all_52_7 = all_6_2)
% 204.56/35.33    (11)  op(e0, e3) = all_52_7
% 204.56/35.33    (12)  all_56_12 = all_52_7
% 204.56/35.33    (13)  op(e3, e3) = all_6_2
% 204.56/35.33    (14)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33    (15)   ~ (all_6_1 = e2)
% 204.56/35.33    (16)  all_58_3 = all_4_2
% 204.56/35.33    (17)  op(all_6_2, e3) = all_6_1
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | BETA: splitting (14) gives:
% 204.56/35.33  | 
% 204.56/35.33  | Case 1:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (18)  all_58_3 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | COMBINE_EQS: (16), (18) imply:
% 204.56/35.33  | |   (19)  all_4_2 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (5), (19) imply:
% 204.56/35.33  | |   (20)  $false
% 204.56/35.33  | | 
% 204.56/35.33  | | CLOSE: (20) is inconsistent.
% 204.56/35.33  | | 
% 204.56/35.33  | Case 2:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (21)  all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | BETA: splitting (21) gives:
% 204.56/35.33  | | 
% 204.56/35.33  | | Case 1:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (22)  all_58_7 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | COMBINE_EQS: (9), (22) imply:
% 204.56/35.33  | | |   (23)  all_10_0 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | REDUCE: (6), (23) imply:
% 204.56/35.33  | | |   (24)  $false
% 204.56/35.33  | | | 
% 204.56/35.33  | | | CLOSE: (24) is inconsistent.
% 204.56/35.33  | | | 
% 204.56/35.33  | | Case 2:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (25)  all_58_13 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | COMBINE_EQS: (7), (25) imply:
% 204.56/35.33  | | |   (26)  all_52_15 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (11), (12), (13), (15), (17),
% 204.56/35.33  | | |            (26) are inconsistent by sub-proof #1341.
% 204.56/35.33  | | | 
% 204.56/35.33  | | End of split
% 204.56/35.33  | | 
% 204.56/35.33  | End of split
% 204.56/35.33  | 
% 204.56/35.33  End of proof
% 204.56/35.33  
% 204.56/35.33  Sub-proof #994 shows that the following formulas are inconsistent:
% 204.56/35.33  ----------------------------------------------------------------
% 204.56/35.33    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.33    (2)   ~ (all_52_25 = all_52_27)
% 204.56/35.33    (3)  all_58_14 = all_52_23
% 204.56/35.33    (4)   ~ (e3 = e1)
% 204.56/35.33    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.33    (6)  op(all_52_7, all_52_7) = e0
% 204.56/35.33    (7)  all_58_1 = all_52_9
% 204.56/35.33    (8)  op(all_52_5, all_52_5) = e1
% 204.56/35.33    (9)   ~ (e3 = e0)
% 204.56/35.33    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.33    (11)   ~ (all_52_7 = all_52_15)
% 204.56/35.33    (12)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.56/35.33    (13)  all_58_0 = all_6_2
% 204.56/35.33    (14)   ~ (all_10_0 = e3)
% 204.56/35.33    (15)  all_40_2 = all_10_2
% 204.56/35.33    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.56/35.33    (17)   ~ (all_52_27 = all_52_29)
% 204.56/35.33    (18)  all_58_13 = all_52_15
% 204.56/35.33    (19)  op(all_10_2, all_10_2) = all_52_20
% 204.56/35.33    (20)  all_58_9 = all_52_25
% 204.56/35.33    (21)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.33    (22)  op(all_52_27, all_52_27) = all_52_26
% 204.56/35.33    (23)  op(e2, e2) = all_4_2
% 204.56/35.33    (24)  all_58_7 = all_10_0
% 204.56/35.33    (25)  all_58_11 = all_52_29
% 204.56/35.33    (26)   ~ (all_52_3 = all_52_27)
% 204.56/35.33    (27)   ~ (all_52_7 = all_6_2)
% 204.56/35.33    (28)  op(e0, e0) = all_14_2
% 204.56/35.33    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.33    (30)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.33    (31)  all_58_15 = e0
% 204.56/35.33    (32)  all_56_11 = all_52_29
% 204.56/35.33    (33)   ~ (all_10_0 = e2)
% 204.56/35.33    (34)   ~ (all_52_25 = e0)
% 204.56/35.33    (35)   ~ (e2 = e1)
% 204.56/35.33    (36)  op(e0, e0) = e0
% 204.56/35.33    (37)  all_58_10 = all_52_27
% 204.56/35.33    (38)  all_56_8 = all_52_5
% 204.56/35.33    (39)  op(all_52_15, all_52_15) = all_52_14
% 204.56/35.33    (40)  all_56_9 = all_10_0
% 204.56/35.33    (41)   ~ (all_52_25 = all_52_29)
% 204.56/35.33    (42)   ~ (all_10_0 = all_4_2)
% 204.56/35.33    (43)  op(all_6_2, all_6_2) = e3
% 204.56/35.33    (44)   ~ (all_52_5 = all_52_7)
% 204.56/35.33    (45)  all_58_12 = all_52_7
% 204.56/35.33    (46)  op(e2, e1) = all_52_19
% 204.56/35.33    (47)   ~ (all_52_7 = all_14_2)
% 204.56/35.33    (48)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e3)
% 204.56/35.33    (49)  all_58_2 = all_52_3
% 204.56/35.33    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.33    (51)  all_56_7 = all_52_27
% 204.56/35.33    (52)   ~ (e2 = e0)
% 204.56/35.33    (53)  op(all_52_3, all_52_3) = e2
% 204.56/35.33    (54)   ~ (all_52_5 = all_52_29)
% 204.56/35.33    (55)   ~ (all_52_29 = e0)
% 204.56/35.33    (56)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.56/35.33    (57)   ~ (all_52_19 = all_52_27)
% 204.56/35.33    (58)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.33    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33    (60)   ~ (all_52_19 = all_10_2)
% 204.56/35.33    (61)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.33    (62)  all_58_8 = all_10_2
% 204.56/35.33    (63)   ~ (all_52_5 = all_10_2)
% 204.56/35.33    (64)  op(all_52_29, all_52_29) = all_52_28
% 204.56/35.33    (65)  all_56_12 = all_52_7
% 204.56/35.33    (66)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.33    (67)   ~ (all_52_25 = all_6_2)
% 204.56/35.33    (68)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.33    (69)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.56/35.33    (70)   ~ (all_52_9 = all_6_2)
% 204.56/35.33    (71)  op(e3, e3) = all_6_2
% 204.56/35.33    (72)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.33    (73)   ~ (all_52_29 = all_10_0)
% 204.56/35.33    (74)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.33    (75)  all_40_0 = all_10_0
% 204.56/35.33    (76)  all_56_3 = all_52_25
% 204.56/35.33    (77)  all_58_5 = all_52_19
% 204.56/35.33    (78)   ~ (all_52_27 = all_4_2)
% 204.56/35.33    (79)  all_58_6 = all_52_5
% 204.56/35.33    (80)  op(all_10_2, e1) = e2
% 204.56/35.33    (81)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.33    (82)   ~ (all_52_17 = all_6_2)
% 204.56/35.33    (83)   ~ (e1 = e0)
% 204.56/35.33    (84)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.56/35.33    (85)   ~ (e3 = e2)
% 204.56/35.33    (86)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.56/35.33    (87)  op(e1, e1) = all_10_2
% 204.56/35.33    (88)   ~ (all_52_5 = all_10_0)
% 204.56/35.33    (89)  all_58_3 = all_4_2
% 204.56/35.33    (90)   ~ (all_52_3 = all_4_2)
% 204.56/35.33    (91)  all_58_4 = all_52_17
% 204.56/35.33    (92)   ~ (all_52_7 = e0)
% 204.56/35.33    (93)  op(all_52_25, all_52_25) = all_52_24
% 204.56/35.33  
% 204.56/35.33  Begin of proof
% 204.56/35.33  | 
% 204.56/35.33  | BETA: splitting (16) gives:
% 204.56/35.33  | 
% 204.56/35.33  | Case 1:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (94)  all_56_7 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | COMBINE_EQS: (51), (94) imply:
% 204.56/35.33  | |   (95)  all_52_27 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | SIMP: (95) implies:
% 204.56/35.33  | |   (96)  all_52_27 = e3
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (26), (96) imply:
% 204.56/35.33  | |   (97)   ~ (all_52_3 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (57), (96) imply:
% 204.56/35.33  | |   (98)   ~ (all_52_19 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (17), (96) imply:
% 204.56/35.33  | |   (99)   ~ (all_52_29 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | SIMP: (99) implies:
% 204.56/35.33  | |   (100)   ~ (all_52_29 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (78), (96) imply:
% 204.56/35.33  | |   (101)   ~ (all_4_2 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | SIMP: (101) implies:
% 204.56/35.33  | |   (102)   ~ (all_4_2 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (22), (96) imply:
% 204.56/35.33  | |   (103)  op(e3, e3) = all_52_26
% 204.56/35.33  | | 
% 204.56/35.33  | | GROUND_INST: instantiating (5) with all_6_2, all_52_26, e3, e3, simplifying
% 204.56/35.33  | |              with (71), (103) gives:
% 204.56/35.33  | |   (104)  all_52_26 = all_6_2
% 204.56/35.33  | | 
% 204.56/35.33  | | BETA: splitting (58) gives:
% 204.56/35.33  | | 
% 204.56/35.33  | | Case 1:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (105)  all_56_11 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | COMBINE_EQS: (32), (105) imply:
% 204.56/35.33  | | |   (106)  all_52_29 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | REDUCE: (100), (106) imply:
% 204.56/35.33  | | |   (107)  $false
% 204.56/35.33  | | | 
% 204.56/35.33  | | | CLOSE: (107) is inconsistent.
% 204.56/35.33  | | | 
% 204.56/35.33  | | Case 2:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (108)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.33  | | | 
% 204.56/35.33  | | | BETA: splitting (59) gives:
% 204.56/35.33  | | | 
% 204.56/35.33  | | | Case 1:
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | |   (109)  all_58_1 = e3
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | | REF_CLOSE: (5), (6), (7), (8), (13), (23), (28), (29), (43), (45), (47),
% 204.56/35.33  | | | |            (49), (50), (53), (63), (70), (71), (79), (81), (87), (90),
% 204.56/35.33  | | | |            (109) are inconsistent by sub-proof #1005.
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | Case 2:
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | |   (110)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | | BETA: splitting (110) gives:
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | | Case 1:
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | |   (111)  all_58_3 = e3
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | COMBINE_EQS: (89), (111) imply:
% 204.56/35.33  | | | | |   (112)  all_4_2 = e3
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | REDUCE: (102), (112) imply:
% 204.56/35.33  | | | | |   (113)  $false
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | CLOSE: (113) is inconsistent.
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | Case 2:
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | |   (114)  all_58_7 = e3 | all_58_13 = e3
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | BETA: splitting (114) gives:
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | Case 1:
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | |   (115)  all_58_7 = e3
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | COMBINE_EQS: (24), (115) imply:
% 204.56/35.33  | | | | | |   (116)  all_10_0 = e3
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | REDUCE: (14), (116) imply:
% 204.56/35.33  | | | | | |   (117)  $false
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | CLOSE: (117) is inconsistent.
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | Case 2:
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | |   (118)  all_58_13 = e3
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | COMBINE_EQS: (18), (118) imply:
% 204.56/35.33  | | | | | |   (119)  all_52_15 = e3
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | SIMP: (119) implies:
% 204.56/35.33  | | | | | |   (120)  all_52_15 = e3
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | REDUCE: (11), (120) imply:
% 204.56/35.33  | | | | | |   (121)   ~ (all_52_7 = e3)
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | REDUCE: (1), (120) imply:
% 204.56/35.33  | | | | | |   (122)   ~ (all_52_23 = e3)
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | SIMP: (122) implies:
% 204.56/35.33  | | | | | |   (123)   ~ (all_52_23 = e3)
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | REDUCE: (39), (120) imply:
% 204.56/35.33  | | | | | |   (124)  op(e3, e3) = all_52_14
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_14, e3, e3,
% 204.56/35.33  | | | | | |              simplifying with (71), (124) gives:
% 204.56/35.33  | | | | | |   (125)  all_52_14 = all_6_2
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | BETA: splitting (50) gives:
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | Case 1:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | |   (126)  all_58_0 = e3
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | COMBINE_EQS: (13), (126) imply:
% 204.56/35.33  | | | | | | |   (127)  all_6_2 = e3
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | REDUCE: (82), (127) imply:
% 204.56/35.33  | | | | | | |   (128)   ~ (all_52_17 = e3)
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | BETA: splitting (86) gives:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | |   (129)  all_58_4 = e3
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | REF_CLOSE: (91), (128), (129) are inconsistent by sub-proof
% 204.56/35.33  | | | | | | | |            #1302.
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | |   (130)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | BETA: splitting (130) gives:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | |   (131)  all_58_5 = e3
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | REF_CLOSE: (77), (98), (131) are inconsistent by sub-proof
% 204.56/35.33  | | | | | | | | |            #1279.
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | |   (132)  all_58_8 = e3 | all_58_14 = e3
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | BETA: splitting (132) gives:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | |   (133)  all_58_8 = e3
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | COMBINE_EQS: (62), (133) imply:
% 204.56/35.33  | | | | | | | | | |   (134)  all_10_2 = e3
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | SIMP: (134) implies:
% 204.56/35.33  | | | | | | | | | |   (135)  all_10_2 = e3
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | COMBINE_EQS: (15), (135) imply:
% 204.56/35.33  | | | | | | | | | |   (136)  all_40_2 = e3
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (63), (135) imply:
% 204.56/35.33  | | | | | | | | | |   (137)   ~ (all_52_5 = e3)
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | BETA: splitting (48) gives:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | |   (138)   ~ (all_40_2 = e3)
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | REDUCE: (136), (138) imply:
% 204.56/35.33  | | | | | | | | | | |   (139)  $false
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | |   (140)   ~ (all_40_0 = e0)
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | REDUCE: (75), (140) imply:
% 204.56/35.33  | | | | | | | | | | |   (141)   ~ (all_10_0 = e0)
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | BETA: splitting (12) gives:
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | |   (142)  all_56_9 = e2
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | COMBINE_EQS: (40), (142) imply:
% 204.56/35.33  | | | | | | | | | | | |   (143)  all_10_0 = e2
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | REDUCE: (33), (143) imply:
% 204.56/35.33  | | | | | | | | | | | |   (144)  $false
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | |   (145)  all_56_9 = e1 | all_56_9 = e0
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | BETA: splitting (145) gives:
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | |   (146)  all_56_9 = e1
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | COMBINE_EQS: (40), (146) imply:
% 204.56/35.33  | | | | | | | | | | | | |   (147)  all_10_0 = e1
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | REDUCE: (88), (147) imply:
% 204.56/35.33  | | | | | | | | | | | | |   (148)   ~ (all_52_5 = e1)
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | REDUCE: (73), (147) imply:
% 204.56/35.33  | | | | | | | | | | | | |   (149)   ~ (all_52_29 = e1)
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | BETA: splitting (108) gives:
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | |   (150)  all_56_11 = e2
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | COMBINE_EQS: (32), (150) imply:
% 204.56/35.33  | | | | | | | | | | | | | |   (151)  all_52_29 = e2
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | SIMP: (151) implies:
% 204.56/35.33  | | | | | | | | | | | | | |   (152)  all_52_29 = e2
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | REDUCE: (54), (152) imply:
% 204.56/35.33  | | | | | | | | | | | | | |   (153)   ~ (all_52_5 = e2)
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | |   (154)  all_56_8 = e3
% 204.56/35.33  | | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | | REF_CLOSE: (38), (137), (154) are inconsistent by sub-proof
% 204.56/35.33  | | | | | | | | | | | | | | |            #1325.
% 204.56/35.33  | | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | |   (155)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.33  | | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (36), (38), (79), (84), (148), (153),
% 204.56/35.33  | | | | | | | | | | | | | | |            (155) are inconsistent by sub-proof #1003.
% 204.56/35.33  | | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | |   (156)  all_56_11 = e1 | all_56_11 = e0
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | | REF_CLOSE: (32), (55), (149), (156) are inconsistent by
% 204.56/35.33  | | | | | | | | | | | | | |            sub-proof #1001.
% 204.56/35.33  | | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | |   (157)  all_56_9 = e0
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | COMBINE_EQS: (40), (157) imply:
% 204.56/35.33  | | | | | | | | | | | | |   (158)  all_10_0 = e0
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | REDUCE: (141), (158) imply:
% 204.56/35.33  | | | | | | | | | | | | |   (159)  $false
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 204.56/35.33  | | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | |   (160)  all_58_14 = e3
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REF_CLOSE: (3), (123), (160) are inconsistent by sub-proof
% 204.56/35.33  | | | | | | | | | |            #1305.
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | End of split
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | Case 2:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | |   (161)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | REF_CLOSE: (5), (8), (43), (45), (49), (63), (71), (79), (87),
% 204.56/35.33  | | | | | | |            (97), (121), (161) are inconsistent by sub-proof #1365.
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | End of split
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | End of split
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | End of split
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | End of split
% 204.56/35.33  | | | 
% 204.56/35.33  | | End of split
% 204.56/35.33  | | 
% 204.56/35.33  | Case 2:
% 204.56/35.33  | | 
% 204.56/35.33  | |   (162)   ~ (all_56_7 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | REDUCE: (51), (162) imply:
% 204.56/35.33  | |   (163)   ~ (all_52_27 = e3)
% 204.56/35.33  | | 
% 204.56/35.33  | | BETA: splitting (72) gives:
% 204.56/35.33  | | 
% 204.56/35.33  | | Case 1:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (164)  all_58_9 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | COMBINE_EQS: (20), (164) imply:
% 204.56/35.33  | | |   (165)  all_52_25 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | REF_CLOSE: (5), (6), (8), (13), (23), (28), (29), (43), (45), (47), (49),
% 204.56/35.33  | | |            (50), (53), (63), (67), (71), (79), (81), (87), (90), (165) are
% 204.56/35.33  | | |            inconsistent by sub-proof #1000.
% 204.56/35.33  | | | 
% 204.56/35.33  | | Case 2:
% 204.56/35.33  | | | 
% 204.56/35.33  | | |   (166)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.33  | | | 
% 204.56/35.33  | | | BETA: splitting (166) gives:
% 204.56/35.33  | | | 
% 204.56/35.33  | | | Case 1:
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | |   (167)  all_58_10 = e3
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | | REF_CLOSE: (37), (163), (167) are inconsistent by sub-proof #1301.
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | Case 2:
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | |   (168)  all_58_11 = e3 | all_58_15 = e3
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | | BETA: splitting (168) gives:
% 204.56/35.33  | | | | 
% 204.56/35.33  | | | | Case 1:
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | |   (169)  all_58_11 = e3
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | COMBINE_EQS: (25), (169) imply:
% 204.56/35.33  | | | | |   (170)  all_52_29 = e3
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | SIMP: (170) implies:
% 204.56/35.33  | | | | |   (171)  all_52_29 = e3
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | REDUCE: (41), (171) imply:
% 204.56/35.33  | | | | |   (172)   ~ (all_52_25 = e3)
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | REDUCE: (64), (171) imply:
% 204.56/35.33  | | | | |   (173)  op(e3, e3) = all_52_28
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_28, e3, e3,
% 204.56/35.33  | | | | |              simplifying with (71), (173) gives:
% 204.56/35.33  | | | | |   (174)  all_52_28 = all_6_2
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | BETA: splitting (68) gives:
% 204.56/35.33  | | | | | 
% 204.56/35.33  | | | | | Case 1:
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | |   (175)  all_56_3 = e3
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | REF_CLOSE: (76), (172), (175) are inconsistent by sub-proof #1339.
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | Case 2:
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | |   (176)   ~ (all_56_3 = e3)
% 204.56/35.33  | | | | | |   (177)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | BETA: splitting (69) gives:
% 204.56/35.33  | | | | | | 
% 204.56/35.33  | | | | | | Case 1:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | |   (178)  all_58_9 = e2
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | COMBINE_EQS: (20), (178) imply:
% 204.56/35.33  | | | | | | |   (179)  all_52_25 = e2
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | REDUCE: (172), (179) imply:
% 204.56/35.33  | | | | | | |   (180)   ~ (e3 = e2)
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | REDUCE: (93), (179) imply:
% 204.56/35.33  | | | | | | |   (181)  op(e2, e2) = all_52_24
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | BETA: splitting (30) gives:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | |   (182)  all_58_9 = e1
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | REF_CLOSE: (35), (178), (182) are inconsistent by sub-proof
% 204.56/35.33  | | | | | | | |            #1214.
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | |   (183)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | BETA: splitting (183) gives:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | |   (184)  all_58_10 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | COMBINE_EQS: (37), (184) imply:
% 204.56/35.33  | | | | | | | | |   (185)  all_52_27 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | SIMP: (185) implies:
% 204.56/35.33  | | | | | | | | |   (186)  all_52_27 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | REDUCE: (78), (186) imply:
% 204.56/35.33  | | | | | | | | |   (187)   ~ (all_4_2 = e1)
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | SIMP: (187) implies:
% 204.56/35.33  | | | | | | | | |   (188)   ~ (all_4_2 = e1)
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_24, e2, e2,
% 204.56/35.33  | | | | | | | | |              simplifying with (23), (181) gives:
% 204.56/35.33  | | | | | | | | |   (189)  all_52_24 = all_4_2
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | BETA: splitting (21) gives:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | |   (190)  all_58_6 = e2
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | COMBINE_EQS: (79), (190) imply:
% 204.56/35.33  | | | | | | | | | |   (191)  all_52_5 = e2
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (8), (191) imply:
% 204.56/35.33  | | | | | | | | | |   (192)  op(e2, e2) = e1
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REF_CLOSE: (5), (23), (188), (192) are inconsistent by
% 204.56/35.33  | | | | | | | | | |            sub-proof #1193.
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | |   (193)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REF_CLOSE: (5), (24), (33), (46), (60), (62), (80), (85),
% 204.56/35.33  | | | | | | | | | |            (169), (193) are inconsistent by sub-proof #997.
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | Case 2:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | |   (194)  all_58_11 = e1 | all_58_15 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | REF_CLOSE: (4), (31), (83), (169), (194) are inconsistent by
% 204.56/35.33  | | | | | | | | |            sub-proof #1206.
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | End of split
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | End of split
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | Case 2:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | |   (195)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | BETA: splitting (195) gives:
% 204.56/35.33  | | | | | | | 
% 204.56/35.33  | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | |   (196)  all_58_10 = e2
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | COMBINE_EQS: (37), (196) imply:
% 204.56/35.33  | | | | | | | |   (197)  all_52_27 = e2
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | REDUCE: (2), (197) imply:
% 204.56/35.33  | | | | | | | |   (198)   ~ (all_52_25 = e2)
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | REDUCE: (78), (197) imply:
% 204.56/35.33  | | | | | | | |   (199)   ~ (all_4_2 = e2)
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | SIMP: (199) implies:
% 204.56/35.33  | | | | | | | |   (200)   ~ (all_4_2 = e2)
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | REDUCE: (163), (197) imply:
% 204.56/35.33  | | | | | | | |   (201)   ~ (e3 = e2)
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | REDUCE: (22), (197) imply:
% 204.56/35.33  | | | | | | | |   (202)  op(e2, e2) = all_52_26
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | BETA: splitting (30) gives:
% 204.56/35.33  | | | | | | | | 
% 204.56/35.33  | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | |   (203)  all_58_9 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | COMBINE_EQS: (20), (203) imply:
% 204.56/35.33  | | | | | | | | |   (204)  all_52_25 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | SIMP: (204) implies:
% 204.56/35.33  | | | | | | | | |   (205)  all_52_25 = e1
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | REDUCE: (172), (205) imply:
% 204.56/35.33  | | | | | | | | |   (206)   ~ (e3 = e1)
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | REDUCE: (93), (205) imply:
% 204.56/35.33  | | | | | | | | |   (207)  op(e1, e1) = all_52_24
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | GROUND_INST: instantiating (5) with all_10_2, all_52_24, e1,
% 204.56/35.33  | | | | | | | | |              e1, simplifying with (87), (207) gives:
% 204.56/35.33  | | | | | | | | |   (208)  all_52_24 = all_10_2
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_52_26, e2, e2,
% 204.56/35.33  | | | | | | | | |              simplifying with (23), (202) gives:
% 204.56/35.33  | | | | | | | | |   (209)  all_52_26 = all_4_2
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | BETA: splitting (21) gives:
% 204.56/35.33  | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | |   (210)  all_58_6 = e2
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | COMBINE_EQS: (79), (210) imply:
% 204.56/35.33  | | | | | | | | | |   (211)  all_52_5 = e2
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (44), (211) imply:
% 204.56/35.33  | | | | | | | | | |   (212)   ~ (all_52_7 = e2)
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | SIMP: (212) implies:
% 204.56/35.33  | | | | | | | | | |   (213)   ~ (all_52_7 = e2)
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (8), (211) imply:
% 204.56/35.33  | | | | | | | | | |   (214)  op(e2, e2) = e1
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | GROUND_INST: instantiating (5) with all_4_2, e1, e2, e2,
% 204.56/35.33  | | | | | | | | | |              simplifying with (23), (214) gives:
% 204.56/35.33  | | | | | | | | | |   (215)  all_4_2 = e1
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (42), (215) imply:
% 204.56/35.33  | | | | | | | | | |   (216)   ~ (all_10_0 = e1)
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (200), (215) imply:
% 204.56/35.33  | | | | | | | | | |   (217)   ~ (e2 = e1)
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | REDUCE: (74), (215) imply:
% 204.56/35.33  | | | | | | | | | |   (218)  op(e1, e1) = all_52_10
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | BETA: splitting (66) gives:
% 204.56/35.33  | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | Case 1:
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.33  | | | | | | | | | | |   (219)  all_58_6 = e1
% 204.56/35.33  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | COMBINE_EQS: (210), (219) imply:
% 204.56/35.34  | | | | | | | | | | |   (220)  e2 = e1
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | REDUCE: (35), (220) imply:
% 204.56/35.34  | | | | | | | | | | |   (221)  $false
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | |   (222)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | BETA: splitting (222) gives:
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | Case 1:
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | |   (223)  all_58_7 = e1
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | COMBINE_EQS: (24), (223) imply:
% 204.56/35.34  | | | | | | | | | | | |   (224)  all_10_0 = e1
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | REDUCE: (216), (224) imply:
% 204.56/35.34  | | | | | | | | | | | |   (225)  $false
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | |   (226)  all_58_8 = e1 | all_58_11 = e1
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | BETA: splitting (226) gives:
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | Case 1:
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | |   (227)  all_58_8 = e1
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | COMBINE_EQS: (62), (227) imply:
% 204.56/35.34  | | | | | | | | | | | | |   (228)  all_10_2 = e1
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | REDUCE: (19), (228) imply:
% 204.56/35.34  | | | | | | | | | | | | |   (229)  op(e1, e1) = all_52_20
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | REDUCE: (80), (228) imply:
% 204.56/35.34  | | | | | | | | | | | | |   (230)  op(e1, e1) = e2
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | REDUCE: (87), (228) imply:
% 204.56/35.34  | | | | | | | | | | | | |   (231)  op(e1, e1) = e1
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | BETA: splitting (56) gives:
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | Case 1:
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | |   (232)  all_58_12 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | COMBINE_EQS: (45), (232) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (233)  all_52_7 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | SIMP: (233) implies:
% 204.56/35.34  | | | | | | | | | | | | | |   (234)  all_52_7 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | REDUCE: (6), (234) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (235)  op(e1, e1) = e0
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, e2, e1, e1, simplifying
% 204.56/35.34  | | | | | | | | | | | | | |              with (230), (235) gives:
% 204.56/35.34  | | | | | | | | | | | | | |   (236)  e2 = e0
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_20, e1, e1,
% 204.56/35.34  | | | | | | | | | | | | | |              simplifying with (229), (230) gives:
% 204.56/35.34  | | | | | | | | | | | | | |   (237)  all_52_20 = e2
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_20, all_52_10, e1,
% 204.56/35.34  | | | | | | | | | | | | | |              e1, simplifying with (218), (229) gives:
% 204.56/35.34  | | | | | | | | | | | | | |   (238)  all_52_10 = all_52_20
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e1, all_52_10, e1, e1,
% 204.56/35.34  | | | | | | | | | | | | | |              simplifying with (218), (231) gives:
% 204.56/35.34  | | | | | | | | | | | | | |   (239)  all_52_10 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | COMBINE_EQS: (238), (239) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (240)  all_52_20 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | SIMP: (240) implies:
% 204.56/35.34  | | | | | | | | | | | | | |   (241)  all_52_20 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | COMBINE_EQS: (237), (241) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (242)  e2 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | SIMP: (242) implies:
% 204.56/35.34  | | | | | | | | | | | | | |   (243)  e2 = e1
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | COMBINE_EQS: (236), (243) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (244)  e1 = e0
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | REDUCE: (83), (244) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (245)  $false
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | |   (246)   ~ (all_58_12 = e1)
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | REDUCE: (45), (246) imply:
% 204.56/35.34  | | | | | | | | | | | | | |   (247)   ~ (all_52_7 = e1)
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (10), (13), (23), (27), (28), (29),
% 204.56/35.34  | | | | | | | | | | | | | |            (43), (45), (47), (49), (50), (53), (63), (65),
% 204.56/35.34  | | | | | | | | | | | | | |            (71), (79), (81), (87), (90), (213), (247) are
% 204.56/35.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 204.56/35.34  | | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | End of split
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | |   (248)  all_58_11 = e1
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | COMBINE_EQS: (169), (248) imply:
% 204.56/35.34  | | | | | | | | | | | | |   (249)  e3 = e1
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | REDUCE: (4), (249) imply:
% 204.56/35.34  | | | | | | | | | | | | |   (250)  $false
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 204.56/35.34  | | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | | End of split
% 204.56/35.34  | | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | | End of split
% 204.56/35.34  | | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | End of split
% 204.56/35.34  | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | |   (251)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.34  | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | | REF_CLOSE: (5), (24), (33), (46), (60), (62), (80), (85),
% 204.56/35.34  | | | | | | | | | |            (169), (251) are inconsistent by sub-proof #997.
% 204.56/35.34  | | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | End of split
% 204.56/35.34  | | | | | | | | | 
% 204.56/35.34  | | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | | 
% 204.56/35.34  | | | | | | | | |   (252)   ~ (all_58_9 = e1)
% 204.56/35.34  | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | REDUCE: (20), (252) imply:
% 204.56/35.34  | | | | | | | | |   (253)   ~ (all_52_25 = e1)
% 204.56/35.34  | | | | | | | | | 
% 204.56/35.34  | | | | | | | | | REF_CLOSE: (34), (76), (177), (198), (253) are inconsistent by
% 204.56/35.34  | | | | | | | | |            sub-proof #1215.
% 204.56/35.34  | | | | | | | | | 
% 204.56/35.34  | | | | | | | | End of split
% 204.56/35.34  | | | | | | | | 
% 204.56/35.34  | | | | | | | Case 2:
% 204.56/35.34  | | | | | | | | 
% 204.56/35.34  | | | | | | | |   (254)  all_58_11 = e2 | all_58_15 = e2
% 204.56/35.34  | | | | | | | | 
% 204.56/35.34  | | | | | | | | REF_CLOSE: (31), (52), (85), (169), (254) are inconsistent by
% 204.56/35.34  | | | | | | | |            sub-proof #995.
% 204.56/35.34  | | | | | | | | 
% 204.56/35.34  | | | | | | | End of split
% 204.56/35.34  | | | | | | | 
% 204.56/35.34  | | | | | | End of split
% 204.56/35.34  | | | | | | 
% 204.56/35.34  | | | | | End of split
% 204.56/35.34  | | | | | 
% 204.56/35.34  | | | | Case 2:
% 204.56/35.34  | | | | | 
% 204.56/35.34  | | | | |   (255)  all_58_15 = e3
% 204.56/35.34  | | | | | 
% 204.56/35.34  | | | | | REF_CLOSE: (9), (31), (255) are inconsistent by sub-proof #1350.
% 204.56/35.34  | | | | | 
% 204.56/35.34  | | | | End of split
% 204.56/35.34  | | | | 
% 204.56/35.34  | | | End of split
% 204.56/35.34  | | | 
% 204.56/35.34  | | End of split
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #995 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)  all_58_15 = e0
% 204.56/35.34    (2)  all_58_11 = e3
% 204.56/35.34    (3)  all_58_11 = e2 | all_58_15 = e2
% 204.56/35.34    (4)   ~ (e2 = e0)
% 204.56/35.34    (5)   ~ (e3 = e2)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | BETA: splitting (3) gives:
% 204.56/35.34  | 
% 204.56/35.34  | Case 1:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (6)  all_58_11 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | COMBINE_EQS: (2), (6) imply:
% 204.56/35.34  | |   (7)  e3 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (5), (7) imply:
% 204.56/35.34  | |   (8)  $false
% 204.56/35.34  | | 
% 204.56/35.34  | | CLOSE: (8) is inconsistent.
% 204.56/35.34  | | 
% 204.56/35.34  | Case 2:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (9)  all_58_15 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | COMBINE_EQS: (1), (9) imply:
% 204.56/35.34  | |   (10)  e2 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (4), (10) imply:
% 204.56/35.34  | |   (11)  $false
% 204.56/35.34  | | 
% 204.56/35.34  | | CLOSE: (11) is inconsistent.
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #996 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (2)  op(all_52_7, all_52_7) = e0
% 204.56/35.34    (3)  op(all_52_5, all_52_5) = e1
% 204.56/35.34    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.34    (5)  all_58_0 = all_6_2
% 204.56/35.34    (6)  op(e2, e2) = all_4_2
% 204.56/35.34    (7)   ~ (all_52_7 = all_6_2)
% 204.56/35.34    (8)  op(e0, e0) = all_14_2
% 204.56/35.34    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.34    (10)  op(all_6_2, all_6_2) = e3
% 204.56/35.34    (11)  all_58_12 = all_52_7
% 204.56/35.34    (12)   ~ (all_52_7 = all_14_2)
% 204.56/35.34    (13)  all_58_2 = all_52_3
% 204.56/35.34    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.34    (15)  op(all_52_3, all_52_3) = e2
% 204.56/35.34    (16)   ~ (all_52_7 = e2)
% 204.56/35.34    (17)   ~ (all_52_5 = all_10_2)
% 204.56/35.34    (18)  all_56_12 = all_52_7
% 204.56/35.34    (19)  op(e3, e3) = all_6_2
% 204.56/35.34    (20)   ~ (all_52_7 = e1)
% 204.56/35.34    (21)  all_58_6 = all_52_5
% 204.56/35.34    (22)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.34    (23)  op(e1, e1) = all_10_2
% 204.56/35.34    (24)   ~ (all_52_3 = all_4_2)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | BETA: splitting (4) gives:
% 204.56/35.34  | 
% 204.56/35.34  | Case 1:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (25)  all_56_12 = e3
% 204.56/35.34  | | 
% 204.56/35.34  | | COMBINE_EQS: (18), (25) imply:
% 204.56/35.34  | |   (26)  all_52_7 = e3
% 204.56/35.34  | | 
% 204.56/35.34  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.56/35.34  | |            (14), (15), (17), (19), (21), (22), (23), (24), (26) are
% 204.56/35.34  | |            inconsistent by sub-proof #1361.
% 204.56/35.34  | | 
% 204.56/35.34  | Case 2:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (27)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | BETA: splitting (27) gives:
% 204.56/35.34  | | 
% 204.56/35.34  | | Case 1:
% 204.56/35.34  | | | 
% 204.56/35.34  | | |   (28)  all_56_12 = e2
% 204.56/35.34  | | | 
% 204.56/35.34  | | | REF_CLOSE: (16), (18), (28) are inconsistent by sub-proof #1178.
% 204.56/35.34  | | | 
% 204.56/35.34  | | Case 2:
% 204.56/35.34  | | | 
% 204.56/35.34  | | |   (29)  all_56_12 = e1 | all_56_12 = e0
% 204.56/35.34  | | | 
% 204.56/35.34  | | | REF_CLOSE: (1), (2), (8), (12), (18), (20), (29) are inconsistent by
% 204.56/35.34  | | |            sub-proof #1177.
% 204.56/35.34  | | | 
% 204.56/35.34  | | End of split
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #997 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (2)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.34    (3)  all_58_7 = all_10_0
% 204.56/35.34    (4)   ~ (all_10_0 = e2)
% 204.56/35.34    (5)  all_58_11 = e3
% 204.56/35.34    (6)  op(e2, e1) = all_52_19
% 204.56/35.34    (7)   ~ (all_52_19 = all_10_2)
% 204.56/35.34    (8)  all_58_8 = all_10_2
% 204.56/35.34    (9)  op(all_10_2, e1) = e2
% 204.56/35.34    (10)   ~ (e3 = e2)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | BETA: splitting (2) gives:
% 204.56/35.34  | 
% 204.56/35.34  | Case 1:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (11)  all_58_7 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | COMBINE_EQS: (3), (11) imply:
% 204.56/35.34  | |   (12)  all_10_0 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (4), (12) imply:
% 204.56/35.34  | |   (13)  $false
% 204.56/35.34  | | 
% 204.56/35.34  | | CLOSE: (13) is inconsistent.
% 204.56/35.34  | | 
% 204.56/35.34  | Case 2:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (14)  all_58_8 = e2 | all_58_11 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | BETA: splitting (14) gives:
% 204.56/35.34  | | 
% 204.56/35.34  | | Case 1:
% 204.56/35.34  | | | 
% 204.56/35.34  | | |   (15)  all_58_8 = e2
% 204.56/35.34  | | | 
% 204.56/35.34  | | | REF_CLOSE: (1), (6), (7), (8), (9), (15) are inconsistent by sub-proof
% 204.56/35.34  | | |            #999.
% 204.56/35.34  | | | 
% 204.56/35.34  | | Case 2:
% 204.56/35.34  | | | 
% 204.56/35.34  | | |   (16)  all_58_11 = e2
% 204.56/35.34  | | | 
% 204.56/35.34  | | | REF_CLOSE: (5), (10), (16) are inconsistent by sub-proof #998.
% 204.56/35.34  | | | 
% 204.56/35.34  | | End of split
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #998 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)  all_58_11 = e3
% 204.56/35.34    (2)  all_58_11 = e2
% 204.56/35.34    (3)   ~ (e3 = e2)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.34  |   (4)  e3 = e2
% 204.56/35.34  | 
% 204.56/35.34  | SIMP: (4) implies:
% 204.56/35.34  |   (5)  e3 = e2
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (3), (5) imply:
% 204.56/35.34  |   (6)  $false
% 204.56/35.34  | 
% 204.56/35.34  | CLOSE: (6) is inconsistent.
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #999 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (2)  all_58_8 = e2
% 204.56/35.34    (3)  op(e2, e1) = all_52_19
% 204.56/35.34    (4)   ~ (all_52_19 = all_10_2)
% 204.56/35.34    (5)  all_58_8 = all_10_2
% 204.56/35.34    (6)  op(all_10_2, e1) = e2
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | COMBINE_EQS: (2), (5) imply:
% 204.56/35.34  |   (7)  all_10_2 = e2
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (4), (7) imply:
% 204.56/35.34  |   (8)   ~ (all_52_19 = e2)
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (6), (7) imply:
% 204.56/35.34  |   (9)  op(e2, e1) = e2
% 204.56/35.34  | 
% 204.56/35.34  | GROUND_INST: instantiating (1) with all_52_19, e2, e1, e2, simplifying with
% 204.56/35.34  |              (3), (9) gives:
% 204.56/35.34  |   (10)  all_52_19 = e2
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (8), (10) imply:
% 204.56/35.34  |   (11)  $false
% 204.56/35.34  | 
% 204.56/35.34  | CLOSE: (11) is inconsistent.
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1000 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (2)  op(all_52_7, all_52_7) = e0
% 204.56/35.34    (3)  op(all_52_5, all_52_5) = e1
% 204.56/35.34    (4)  all_58_0 = all_6_2
% 204.56/35.34    (5)  op(e2, e2) = all_4_2
% 204.56/35.34    (6)  op(e0, e0) = all_14_2
% 204.56/35.34    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.34    (8)  op(all_6_2, all_6_2) = e3
% 204.56/35.34    (9)  all_58_12 = all_52_7
% 204.56/35.34    (10)   ~ (all_52_7 = all_14_2)
% 204.56/35.34    (11)  all_58_2 = all_52_3
% 204.56/35.34    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.34    (13)  op(all_52_3, all_52_3) = e2
% 204.56/35.34    (14)   ~ (all_52_5 = all_10_2)
% 204.56/35.34    (15)   ~ (all_52_25 = all_6_2)
% 204.56/35.34    (16)  op(e3, e3) = all_6_2
% 204.56/35.34    (17)  all_58_6 = all_52_5
% 204.56/35.34    (18)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.34    (19)  all_52_25 = e3
% 204.56/35.34    (20)  op(e1, e1) = all_10_2
% 204.56/35.34    (21)   ~ (all_52_3 = all_4_2)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | SIMP: (19) implies:
% 204.56/35.34  |   (22)  all_52_25 = e3
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (15), (22) imply:
% 204.56/35.34  |   (23)   ~ (all_6_2 = e3)
% 204.56/35.34  | 
% 204.56/35.34  | SIMP: (23) implies:
% 204.56/35.34  |   (24)   ~ (all_6_2 = e3)
% 204.56/35.34  | 
% 204.56/35.34  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.56/35.34  |            (13), (14), (16), (17), (18), (20), (21), (24) are inconsistent by
% 204.56/35.34  |            sub-proof #1362.
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1001 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)  all_56_11 = e1 | all_56_11 = e0
% 204.56/35.34    (2)  all_56_11 = all_52_29
% 204.56/35.34    (3)   ~ (all_52_29 = e1)
% 204.56/35.34    (4)   ~ (all_52_29 = e0)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | BETA: splitting (1) gives:
% 204.56/35.34  | 
% 204.56/35.34  | Case 1:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (5)  all_56_11 = e1
% 204.56/35.34  | | 
% 204.56/35.34  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1023.
% 204.56/35.34  | | 
% 204.56/35.34  | Case 2:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (6)  all_56_11 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1002.
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1002 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)  all_56_11 = all_52_29
% 204.56/35.34    (2)  all_56_11 = e0
% 204.56/35.34    (3)   ~ (all_52_29 = e0)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.34  |   (4)  all_52_29 = e0
% 204.56/35.34  | 
% 204.56/35.34  | SIMP: (4) implies:
% 204.56/35.34  |   (5)  all_52_29 = e0
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (3), (5) imply:
% 204.56/35.34  |   (6)  $false
% 204.56/35.34  | 
% 204.56/35.34  | CLOSE: (6) is inconsistent.
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1003 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (2)  op(all_52_5, all_52_5) = e1
% 204.56/35.34    (3)   ~ (all_52_5 = e1)
% 204.56/35.34    (4)  op(e0, e0) = e0
% 204.56/35.34    (5)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.34    (6)  all_56_8 = all_52_5
% 204.56/35.34    (7)   ~ (all_52_5 = e2)
% 204.56/35.34    (8)  all_58_6 = all_52_5
% 204.56/35.34    (9)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | BETA: splitting (9) gives:
% 204.56/35.34  | 
% 204.56/35.34  | Case 1:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (10)  all_58_6 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | COMBINE_EQS: (8), (10) imply:
% 204.56/35.34  | |   (11)  all_52_5 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | SIMP: (11) implies:
% 204.56/35.34  | |   (12)  all_52_5 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (3), (12) imply:
% 204.56/35.34  | |   (13)   ~ (e1 = e0)
% 204.56/35.34  | | 
% 204.56/35.34  | | SIMP: (13) implies:
% 204.56/35.34  | |   (14)   ~ (e1 = e0)
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (2), (12) imply:
% 204.56/35.34  | |   (15)  op(e0, e0) = e1
% 204.56/35.34  | | 
% 204.56/35.34  | | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (4),
% 204.56/35.34  | |              (15) gives:
% 204.56/35.34  | |   (16)  e1 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (14), (16) imply:
% 204.56/35.34  | |   (17)  $false
% 204.56/35.34  | | 
% 204.56/35.34  | | CLOSE: (17) is inconsistent.
% 204.56/35.34  | | 
% 204.56/35.34  | Case 2:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (18)   ~ (all_58_6 = e0)
% 204.56/35.34  | | 
% 204.56/35.34  | | REDUCE: (8), (18) imply:
% 204.56/35.34  | |   (19)   ~ (all_52_5 = e0)
% 204.56/35.34  | | 
% 204.56/35.34  | | REF_CLOSE: (3), (5), (6), (7), (19) are inconsistent by sub-proof #1004.
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1004 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ~ (all_52_5 = e1)
% 204.56/35.34    (2)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.34    (3)  all_56_8 = all_52_5
% 204.56/35.34    (4)   ~ (all_52_5 = e2)
% 204.56/35.34    (5)   ~ (all_52_5 = e0)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | BETA: splitting (2) gives:
% 204.56/35.34  | 
% 204.56/35.34  | Case 1:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (6)  all_56_8 = e2
% 204.56/35.34  | | 
% 204.56/35.34  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #1022.
% 204.56/35.34  | | 
% 204.56/35.34  | Case 2:
% 204.56/35.34  | | 
% 204.56/35.34  | |   (7)  all_56_8 = e1 | all_56_8 = e0
% 204.56/35.34  | | 
% 204.56/35.34  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #1020.
% 204.56/35.34  | | 
% 204.56/35.34  | End of split
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1005 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (2)  op(all_52_7, all_52_7) = e0
% 204.56/35.34    (3)  all_58_1 = all_52_9
% 204.56/35.34    (4)  op(all_52_5, all_52_5) = e1
% 204.56/35.34    (5)  all_58_0 = all_6_2
% 204.56/35.34    (6)  op(e2, e2) = all_4_2
% 204.56/35.34    (7)  all_58_1 = e3
% 204.56/35.34    (8)  op(e0, e0) = all_14_2
% 204.56/35.34    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.34    (10)  op(all_6_2, all_6_2) = e3
% 204.56/35.34    (11)  all_58_12 = all_52_7
% 204.56/35.34    (12)   ~ (all_52_7 = all_14_2)
% 204.56/35.34    (13)  all_58_2 = all_52_3
% 204.56/35.34    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.34    (15)  op(all_52_3, all_52_3) = e2
% 204.56/35.34    (16)   ~ (all_52_5 = all_10_2)
% 204.56/35.34    (17)   ~ (all_52_9 = all_6_2)
% 204.56/35.34    (18)  op(e3, e3) = all_6_2
% 204.56/35.34    (19)  all_58_6 = all_52_5
% 204.56/35.34    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.34    (21)  op(e1, e1) = all_10_2
% 204.56/35.34    (22)   ~ (all_52_3 = all_4_2)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | COMBINE_EQS: (3), (7) imply:
% 204.56/35.34  |   (23)  all_52_9 = e3
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (17), (23) imply:
% 204.56/35.34  |   (24)   ~ (all_6_2 = e3)
% 204.56/35.34  | 
% 204.56/35.34  | SIMP: (24) implies:
% 204.56/35.34  |   (25)   ~ (all_6_2 = e3)
% 204.56/35.34  | 
% 204.56/35.34  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 204.56/35.34  |            (15), (16), (18), (19), (20), (21), (22), (25) are inconsistent by
% 204.56/35.34  |            sub-proof #1362.
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1006 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)  all_56_9 = all_10_0
% 204.56/35.34    (2)  all_56_9 = e3
% 204.56/35.34    (3)   ~ (all_10_0 = e3)
% 204.56/35.34  
% 204.56/35.34  Begin of proof
% 204.56/35.34  | 
% 204.56/35.34  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.34  |   (4)  all_10_0 = e3
% 204.56/35.34  | 
% 204.56/35.34  | SIMP: (4) implies:
% 204.56/35.34  |   (5)  all_10_0 = e3
% 204.56/35.34  | 
% 204.56/35.34  | REDUCE: (3), (5) imply:
% 204.56/35.34  |   (6)  $false
% 204.56/35.34  | 
% 204.56/35.34  | CLOSE: (6) is inconsistent.
% 204.56/35.34  | 
% 204.56/35.34  End of proof
% 204.56/35.34  
% 204.56/35.34  Sub-proof #1007 shows that the following formulas are inconsistent:
% 204.56/35.34  ----------------------------------------------------------------
% 204.56/35.34    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.56/35.34    (2)   ~ (all_52_15 = all_52_23)
% 204.56/35.34    (3)   ~ (all_52_25 = all_52_27)
% 204.56/35.34    (4)  all_58_14 = all_52_23
% 204.56/35.34    (5)   ~ (e3 = e1)
% 204.56/35.34    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.56/35.34    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.34    (8)   ~ (all_52_5 = all_52_13)
% 204.56/35.34    (9)  all_58_1 = all_52_9
% 204.56/35.34    (10)   ~ (all_52_9 = all_52_13)
% 204.56/35.34    (11)   ~ (e3 = e0)
% 204.56/35.34    (12)  op(e2, e3) = all_52_3
% 204.56/35.34    (13)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.34    (14)  op(e0, e2) = all_52_15
% 204.56/35.34    (15)   ~ (all_52_7 = all_52_15)
% 204.56/35.34    (16)   ~ (all_52_3 = all_52_19)
% 204.56/35.34    (17)  op(all_52_7, all_52_7) = all_52_6
% 204.56/35.34    (18)   ~ (all_52_17 = all_52_25)
% 204.56/35.34    (19)   ~ (all_52_3 = all_6_2)
% 204.56/35.34    (20)  all_58_0 = all_6_2
% 204.56/35.34    (21)  op(all_14_2, e0) = all_14_1
% 204.56/35.34    (22)  all_56_4 = all_52_3
% 204.56/35.34    (23)   ~ (all_52_17 = all_10_2)
% 204.56/35.34    (24)  op(e3, e0) = all_52_25
% 204.56/35.34    (25)  op(e0, all_14_1) = all_14_0
% 204.56/35.34    (26)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.34    (27)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.56/35.34    (28)  op(all_52_19, all_52_19) = all_52_18
% 204.56/35.34    (29)   ~ (all_52_27 = all_52_29)
% 204.56/35.34    (30)  all_58_13 = all_52_15
% 204.56/35.34    (31)  op(all_10_2, all_10_2) = all_52_20
% 204.56/35.34    (32)  all_58_9 = all_52_25
% 204.56/35.34    (33)   ~ (all_6_1 = e1)
% 204.56/35.34    (34)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.56/35.34    (35)   ~ (all_52_29 = all_14_2)
% 204.56/35.34    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.56/35.34    (37)  op(all_52_27, all_52_27) = all_52_26
% 204.56/35.34    (38)  op(e1, e3) = all_52_5
% 204.56/35.34    (39)  op(e2, e2) = all_4_2
% 204.56/35.34    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.56/35.34    (41)   ~ (all_52_3 = all_52_5)
% 204.56/35.34    (42)   ~ (all_4_1 = e3)
% 204.56/35.34    (43)  all_58_11 = all_52_29
% 204.56/35.34    (44)  all_56_5 = all_4_2
% 204.56/35.34    (45)   ~ (all_52_25 = all_14_2)
% 204.56/35.34    (46)   ~ (all_52_9 = all_52_15)
% 204.56/35.34    (47)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.56/35.34    (48)   ~ (all_52_3 = all_52_27)
% 204.56/35.34    (49)  op(all_10_2, e1) = all_10_1
% 204.56/35.34    (50)  op(all_6_2, all_6_2) = all_52_0
% 204.56/35.34    (51)   ~ (all_52_7 = all_6_2)
% 204.56/35.34    (52)  op(e0, e0) = all_14_2
% 204.56/35.34    (53)  all_56_15 = all_14_2
% 204.56/35.34    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.34    (55)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.34    (56)  op(e2, all_4_1) = all_4_0
% 204.56/35.34    (57)  all_56_11 = all_52_29
% 204.56/35.34    (58)   ~ (all_4_1 = e1)
% 204.56/35.34    (59)   ~ (all_4_0 = e3)
% 204.56/35.34    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.34    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.34    (62)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.56/35.34    (63)  all_56_9 = all_52_13
% 204.56/35.34    (64)   ~ (e2 = e1)
% 204.56/35.34    (65)   ~ (all_52_13 = all_10_2)
% 204.56/35.34    (66)   ~ (all_6_0 = e1)
% 204.56/35.34    (67)  all_58_10 = all_52_27
% 204.56/35.34    (68)  all_56_8 = all_52_5
% 204.56/35.34    (69)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.34    (70)  op(all_52_15, all_52_15) = all_52_14
% 204.56/35.34    (71)   ~ (all_52_19 = all_52_23)
% 204.56/35.34    (72)   ~ (all_52_25 = all_52_29)
% 204.56/35.34    (73)   ~ (all_52_29 = all_10_2)
% 204.56/35.34    (74)  all_58_7 = all_52_13
% 204.56/35.34    (75)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.34    (76)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.56/35.34    (77)   ~ (all_52_5 = all_52_7)
% 204.56/35.34    (78)  all_58_12 = all_52_7
% 204.56/35.34    (79)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.34    (80)   ~ (all_52_7 = all_14_2)
% 204.56/35.34    (81)   ~ (all_14_2 = e0)
% 204.56/35.34    (82)  all_58_2 = all_52_3
% 204.56/35.34    (83)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.56/35.34    (84)  all_56_2 = all_52_17
% 204.56/35.34    (85)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.56/35.34    (86)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.34    (87)  op(e3, all_6_1) = all_6_0
% 204.56/35.34    (88)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.56/35.34    (89)   ~ (all_14_0 = e3)
% 204.56/35.34    (90)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.56/35.34    (91)  all_56_7 = all_52_27
% 204.56/35.34    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.34    (93)   ~ (e2 = e0)
% 204.56/35.34    (94)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.34    (95)  op(all_4_2, e2) = all_4_1
% 204.56/35.34    (96)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.56/35.34    (97)   ~ (all_52_5 = all_52_29)
% 204.56/35.34    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.56/35.34    (99)  all_56_6 = all_52_19
% 204.56/35.34    (100)   ~ (all_52_15 = all_14_2)
% 204.56/35.34    (101)   ~ (all_52_19 = all_52_27)
% 204.56/35.34    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.34    (103)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.56/35.34    (104)   ~ (all_6_0 = e2)
% 204.56/35.34    (105)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.56/35.34    (106)   ~ (all_52_13 = all_4_2)
% 204.56/35.34    (107)  op(e3, e1) = all_52_17
% 204.56/35.34    (108)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.56/35.34    (109)  op(e0, e3) = all_52_7
% 204.56/35.34    (110)  op(e1, e2) = all_52_13
% 204.56/35.34    (111)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.34    (112)   ~ (all_52_9 = all_52_25)
% 204.56/35.34    (113)  all_58_15 = all_14_2
% 204.56/35.34    (114)   ~ (all_52_19 = all_10_2)
% 204.56/35.34    (115)  op(all_52_23, all_52_23) = all_52_22
% 204.56/35.34    (116)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.34    (117)  all_58_8 = all_10_2
% 204.56/35.34    (118)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.34    (119)   ~ (all_52_5 = all_10_2)
% 204.56/35.34    (120)  op(all_52_29, all_52_29) = all_52_28
% 204.56/35.34    (121)   ~ (all_52_23 = all_14_2)
% 204.56/35.34    (122)  all_56_12 = all_52_7
% 204.56/35.34    (123)  op(all_52_17, all_52_17) = all_52_16
% 204.56/35.34    (124)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.34    (125)   ~ (all_52_25 = all_6_2)
% 204.56/35.34    (126)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.34    (127)   ~ (all_52_9 = all_4_2)
% 204.56/35.34    (128)   ~ (all_52_5 = all_6_2)
% 204.56/35.34    (129)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.56/35.34    (130)   ~ (all_52_9 = all_6_2)
% 204.56/35.34    (131)   ~ (all_52_13 = all_52_15)
% 204.56/35.34    (132)  all_56_0 = all_6_2
% 204.56/35.34    (133)  op(e3, e3) = all_6_2
% 204.56/35.34    (134)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.34    (135)   ~ (all_52_27 = all_14_2)
% 204.56/35.34    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.34    (137)  all_56_14 = all_52_23
% 204.56/35.34    (138)  op(all_4_2, all_4_2) = all_52_10
% 204.56/35.34    (139)  all_56_3 = all_52_25
% 204.56/35.34    (140)   ~ (all_52_3 = all_52_7)
% 204.56/35.34    (141)  op(all_14_2, all_14_2) = all_52_30
% 204.56/35.34    (142)  all_58_5 = all_52_19
% 204.56/35.34    (143)  all_56_1 = all_52_9
% 204.56/35.34    (144)   ~ (all_52_15 = all_4_2)
% 204.56/35.35    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.56/35.35           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 204.56/35.35           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.56/35.35           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.56/35.35    (146)   ~ (all_52_27 = all_4_2)
% 204.56/35.35    (147)  all_58_6 = all_52_5
% 204.56/35.35    (148)  op(e3, e2) = all_52_9
% 204.56/35.35    (149)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.35    (150)   ~ (all_52_17 = all_6_2)
% 204.56/35.35    (151)   ~ (e1 = e0)
% 204.56/35.35    (152)   ~ (e3 = e2)
% 204.56/35.35    (153)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.35    (154)   ~ (all_52_9 = all_52_17)
% 204.56/35.35    (155)  all_56_10 = all_10_2
% 204.56/35.35    (156)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.56/35.35    (157)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.56/35.35    (158)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.56/35.35    (159)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.35    (160)   ~ (all_6_1 = e2)
% 204.56/35.35    (161)  op(e1, e1) = all_10_2
% 204.56/35.35    (162)   ~ (all_52_23 = all_10_2)
% 204.56/35.35    (163)   ~ (all_52_7 = all_52_23)
% 204.56/35.35    (164)   ~ (all_52_17 = all_52_19)
% 204.56/35.35    (165)  all_58_3 = all_4_2
% 204.56/35.35    (166)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.56/35.35    (167)  all_56_13 = all_52_15
% 204.56/35.35    (168)   ~ (all_52_3 = all_4_2)
% 204.56/35.35    (169)   ~ (all_52_19 = all_4_2)
% 204.56/35.35    (170)   ~ (all_52_17 = all_52_23)
% 204.56/35.35    (171)  op(all_6_2, e3) = all_6_1
% 204.56/35.35    (172)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.56/35.35    (173)   ~ (all_52_13 = all_52_29)
% 204.56/35.35    (174)  all_58_4 = all_52_17
% 204.56/35.35    (175)   ~ (all_14_0 = e1)
% 204.56/35.35    (176)   ~ (all_14_0 = e2)
% 204.56/35.35    (177)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.56/35.35    (178)  op(all_52_25, all_52_25) = all_52_24
% 204.56/35.35  
% 204.56/35.35  Begin of proof
% 204.56/35.35  | 
% 204.56/35.35  | BETA: splitting (145) gives:
% 204.56/35.35  | 
% 204.56/35.35  | Case 1:
% 204.56/35.35  | | 
% 204.56/35.35  | |   (179)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 204.56/35.35  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 204.56/35.35  | | 
% 204.56/35.35  | | BETA: splitting (179) gives:
% 204.56/35.35  | | 
% 204.56/35.35  | | Case 1:
% 204.56/35.35  | | | 
% 204.56/35.35  | | |   (180)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 204.56/35.35  | | | 
% 204.56/35.35  | | | ALPHA: (180) implies:
% 204.56/35.35  | | |   (181)  all_52_6 = e0
% 204.56/35.35  | | |   (182)  all_52_4 = e1
% 204.56/35.35  | | |   (183)  all_52_2 = e2
% 204.56/35.35  | | |   (184)  all_52_0 = e3
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REDUCE: (6), (183) imply:
% 204.56/35.35  | | |   (185)  op(all_52_3, all_52_3) = e2
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REDUCE: (26), (182) imply:
% 204.56/35.35  | | |   (186)  op(all_52_5, all_52_5) = e1
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REDUCE: (17), (181) imply:
% 204.56/35.35  | | |   (187)  op(all_52_7, all_52_7) = e0
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REDUCE: (50), (184) imply:
% 204.56/35.35  | | |   (188)  op(all_6_2, all_6_2) = e3
% 204.56/35.35  | | | 
% 204.56/35.35  | | | BETA: splitting (118) gives:
% 204.56/35.35  | | | 
% 204.56/35.35  | | | Case 1:
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | |   (189)  all_56_15 = e3
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REF_CLOSE: (4), (7), (10), (13), (14), (15), (18), (20), (21), (23),
% 204.56/35.35  | | | |            (24), (25), (28), (30), (31), (32), (34), (36), (39), (43),
% 204.56/35.35  | | | |            (44), (45), (46), (47), (52), (53), (54), (56), (58), (60),
% 204.56/35.35  | | | |            (61), (63), (64), (65), (69), (72), (74), (75), (78), (80),
% 204.56/35.35  | | | |            (82), (84), (86), (87), (89), (94), (95), (98), (100), (104),
% 204.56/35.35  | | | |            (106), (112), (117), (119), (121), (122), (126), (127),
% 204.56/35.35  | | | |            (129), (130), (131), (132), (133), (137), (138), (139),
% 204.56/35.35  | | | |            (141), (142), (143), (144), (147), (148), (150), (153),
% 204.56/35.35  | | | |            (154), (156), (157), (158), (159), (161), (162), (163),
% 204.56/35.35  | | | |            (167), (168), (170), (171), (174), (175), (176), (178),
% 204.56/35.35  | | | |            (185), (186), (187), (188), (189) are inconsistent by
% 204.56/35.35  | | | |            sub-proof #1174.
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | Case 2:
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | |   (190)   ~ (all_56_15 = e3)
% 204.56/35.35  | | | |   (191)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (53), (190) imply:
% 204.56/35.35  | | | |   (192)   ~ (all_14_2 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REF_CLOSE: (2), (4), (7), (9), (11), (13), (14), (15), (19), (20), (22),
% 204.56/35.35  | | | |            (30), (39), (41), (42), (44), (46), (47), (51), (52), (53),
% 204.56/35.35  | | | |            (54), (56), (58), (59), (60), (64), (69), (74), (76), (78),
% 204.56/35.35  | | | |            (80), (81), (82), (86), (92), (93), (94), (95), (98), (100),
% 204.56/35.35  | | | |            (103), (105), (110), (111), (113), (115), (119), (122),
% 204.56/35.35  | | | |            (127), (130), (133), (140), (141), (143), (144), (147),
% 204.56/35.35  | | | |            (148), (149), (151), (152), (153), (159), (161), (162),
% 204.56/35.35  | | | |            (163), (165), (166), (167), (168), (172), (185), (186),
% 204.56/35.35  | | | |            (187), (188), (191), (192) are inconsistent by sub-proof
% 204.56/35.35  | | | |            #1145.
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | End of split
% 204.56/35.35  | | | 
% 204.56/35.35  | | Case 2:
% 204.56/35.35  | | | 
% 204.56/35.35  | | |   (193)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 204.56/35.35  | | |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 204.56/35.35  | | |            (27), (28), (29), (30), (31), (32), (33), (35), (37), (38),
% 204.56/35.35  | | |            (39), (40), (41), (42), (43), (44), (45), (48), (50), (51),
% 204.56/35.35  | | |            (52), (53), (54), (57), (58), (60), (62), (63), (64), (65),
% 204.56/35.35  | | |            (66), (67), (68), (69), (70), (71), (72), (74), (76), (77),
% 204.56/35.35  | | |            (78), (79), (80), (81), (82), (85), (86), (87), (90), (91),
% 204.56/35.35  | | |            (92), (93), (94), (95), (97), (98), (100), (102), (103), (104),
% 204.56/35.35  | | |            (105), (106), (109), (110), (111), (112), (113), (115), (116),
% 204.56/35.35  | | |            (117), (118), (120), (121), (122), (123), (125), (126), (127),
% 204.56/35.35  | | |            (128), (130), (133), (134), (135), (136), (138), (139), (140),
% 204.56/35.35  | | |            (141), (142), (143), (146), (147), (148), (149), (150), (151),
% 204.56/35.35  | | |            (152), (153), (154), (155), (156), (157), (159), (160), (161),
% 204.56/35.35  | | |            (163), (164), (165), (167), (168), (169), (170), (171), (173),
% 204.56/35.35  | | |            (174), (177), (178), (193) are inconsistent by sub-proof #1091.
% 204.56/35.35  | | | 
% 204.56/35.35  | | End of split
% 204.56/35.35  | | 
% 204.56/35.35  | Case 2:
% 204.56/35.35  | | 
% 204.56/35.35  | |   (194)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 204.56/35.35  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 204.56/35.35  | |            e0)
% 204.56/35.35  | | 
% 204.56/35.35  | | BETA: splitting (194) gives:
% 204.56/35.35  | | 
% 204.56/35.35  | | Case 1:
% 204.56/35.35  | | | 
% 204.56/35.35  | | |   (195)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 204.56/35.35  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (26),
% 204.56/35.35  | | |            (28), (30), (31), (32), (33), (35), (36), (37), (38), (39),
% 204.56/35.35  | | |            (41), (43), (45), (46), (48), (49), (50), (51), (52), (53),
% 204.56/35.35  | | |            (54), (57), (60), (61), (62), (63), (64), (65), (66), (67),
% 204.56/35.35  | | |            (68), (69), (71), (72), (73), (74), (77), (78), (79), (80),
% 204.56/35.35  | | |            (82), (83), (84), (85), (86), (87), (88), (90), (92), (93),
% 204.56/35.35  | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 204.56/35.35  | | |            (105), (106), (107), (109), (111), (112), (113), (114), (115),
% 204.56/35.35  | | |            (116), (117), (118), (119), (120), (121), (122), (123), (125),
% 204.56/35.35  | | |            (126), (127), (128), (130), (131), (132), (133), (135), (136),
% 204.56/35.35  | | |            (138), (139), (140), (141), (142), (143), (146), (147), (149),
% 204.56/35.35  | | |            (150), (151), (152), (153), (154), (155), (156), (157), (158),
% 204.56/35.35  | | |            (159), (160), (161), (163), (164), (165), (166), (167), (168),
% 204.56/35.35  | | |            (171), (173), (174), (177), (178), (195) are inconsistent by
% 204.56/35.35  | | |            sub-proof #1042.
% 204.56/35.35  | | | 
% 204.56/35.35  | | Case 2:
% 204.56/35.35  | | | 
% 204.56/35.35  | | |   (196)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (15),
% 204.56/35.35  | | |            (17), (18), (19), (20), (22), (23), (24), (26), (28), (29),
% 204.56/35.35  | | |            (30), (32), (33), (35), (37), (38), (39), (41), (43), (44),
% 204.56/35.35  | | |            (45), (46), (48), (49), (50), (51), (52), (53), (54), (55),
% 204.56/35.35  | | |            (57), (60), (61), (62), (66), (67), (68), (69), (70), (71),
% 204.56/35.35  | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 204.56/35.35  | | |            (82), (84), (86), (87), (88), (90), (92), (94), (97), (100),
% 204.56/35.35  | | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 204.56/35.35  | | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 204.56/35.35  | | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 204.56/35.35  | | |            (130), (131), (132), (133), (134), (135), (136), (137), (139),
% 204.56/35.35  | | |            (140), (141), (142), (143), (144), (146), (147), (149), (150),
% 204.56/35.35  | | |            (152), (153), (158), (159), (160), (161), (163), (164), (165),
% 204.56/35.35  | | |            (166), (167), (168), (169), (170), (171), (174), (178), (196)
% 204.56/35.35  | | |            are inconsistent by sub-proof #1008.
% 204.56/35.35  | | | 
% 204.56/35.35  | | End of split
% 204.56/35.35  | | 
% 204.56/35.35  | End of split
% 204.56/35.35  | 
% 204.56/35.35  End of proof
% 204.56/35.35  
% 204.56/35.35  Sub-proof #1008 shows that the following formulas are inconsistent:
% 204.56/35.35  ----------------------------------------------------------------
% 204.56/35.35    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.35    (2)   ~ (all_52_25 = all_52_27)
% 204.56/35.35    (3)  all_58_14 = all_52_23
% 204.56/35.35    (4)   ~ (e3 = e1)
% 204.56/35.35    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.56/35.35    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.35    (7)  all_58_1 = all_52_9
% 204.56/35.35    (8)   ~ (all_52_9 = all_52_13)
% 204.56/35.35    (9)  op(e2, e3) = all_52_3
% 204.56/35.35    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.35    (11)   ~ (all_52_7 = all_52_15)
% 204.56/35.35    (12)  op(all_52_7, all_52_7) = all_52_6
% 204.56/35.35    (13)   ~ (all_52_17 = all_52_25)
% 204.56/35.35    (14)   ~ (all_52_3 = all_6_2)
% 204.56/35.35    (15)  all_58_0 = all_6_2
% 204.56/35.35    (16)  all_56_4 = all_52_3
% 204.56/35.35    (17)   ~ (all_52_17 = all_10_2)
% 204.56/35.35    (18)  op(e3, e0) = all_52_25
% 204.56/35.35    (19)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.35    (20)  op(all_52_19, all_52_19) = all_52_18
% 204.56/35.35    (21)   ~ (all_52_27 = all_52_29)
% 204.56/35.35    (22)  all_58_13 = all_52_15
% 204.56/35.35    (23)  all_58_9 = all_52_25
% 204.56/35.35    (24)   ~ (all_6_1 = e1)
% 204.56/35.35    (25)   ~ (all_52_29 = all_14_2)
% 204.56/35.35    (26)  op(all_52_27, all_52_27) = all_52_26
% 204.56/35.35    (27)  op(e1, e3) = all_52_5
% 204.56/35.35    (28)  op(e2, e2) = all_4_2
% 204.56/35.35    (29)   ~ (all_52_3 = all_52_5)
% 204.56/35.35    (30)  all_58_11 = all_52_29
% 204.56/35.35    (31)  all_56_5 = all_4_2
% 204.56/35.35    (32)   ~ (all_52_25 = all_14_2)
% 204.56/35.35    (33)   ~ (all_52_9 = all_52_15)
% 204.56/35.35    (34)   ~ (all_52_3 = all_52_27)
% 204.56/35.35    (35)  op(all_10_2, e1) = all_10_1
% 204.56/35.35    (36)  op(all_6_2, all_6_2) = all_52_0
% 204.56/35.35    (37)   ~ (all_52_7 = all_6_2)
% 204.56/35.35    (38)  op(e0, e0) = all_14_2
% 204.56/35.35    (39)  all_56_15 = all_14_2
% 204.56/35.35    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.35    (41)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.35    (42)  all_56_11 = all_52_29
% 204.56/35.35    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.35    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.35    (45)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.56/35.35    (46)   ~ (all_6_0 = e1)
% 204.56/35.35    (47)  all_58_10 = all_52_27
% 204.56/35.35    (48)  all_56_8 = all_52_5
% 204.56/35.35    (49)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.35    (50)  op(all_52_15, all_52_15) = all_52_14
% 204.56/35.35    (51)   ~ (all_52_19 = all_52_23)
% 204.56/35.35    (52)   ~ (all_52_25 = all_52_29)
% 204.56/35.35    (53)   ~ (all_52_29 = all_10_2)
% 204.56/35.35    (54)  all_58_7 = all_52_13
% 204.56/35.35    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.35    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.56/35.35    (57)   ~ (all_52_5 = all_52_7)
% 204.56/35.35    (58)  all_58_12 = all_52_7
% 204.56/35.35    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.35    (60)   ~ (all_52_7 = all_14_2)
% 204.56/35.35    (61)   ~ (all_14_2 = e0)
% 204.56/35.35    (62)  all_58_2 = all_52_3
% 204.56/35.35    (63)  all_56_2 = all_52_17
% 204.56/35.35    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.35    (65)  op(e3, all_6_1) = all_6_0
% 204.56/35.35    (66)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.56/35.35    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.56/35.35    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.35    (69)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.35    (70)   ~ (all_52_5 = all_52_29)
% 204.56/35.35    (71)   ~ (all_52_15 = all_14_2)
% 204.56/35.35    (72)   ~ (all_52_19 = all_52_27)
% 204.56/35.35    (73)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.35    (74)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.56/35.35    (75)   ~ (all_6_0 = e2)
% 204.56/35.35    (76)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.56/35.35    (77)   ~ (all_52_13 = all_4_2)
% 204.56/35.35    (78)  op(e3, e1) = all_52_17
% 204.56/35.35    (79)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.56/35.35    (80)  op(e0, e3) = all_52_7
% 204.56/35.35    (81)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.35    (82)   ~ (all_52_9 = all_52_25)
% 204.56/35.35    (83)  all_58_15 = all_14_2
% 204.56/35.35    (84)   ~ (all_52_19 = all_10_2)
% 204.56/35.35    (85)  op(all_52_23, all_52_23) = all_52_22
% 204.56/35.35    (86)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.35    (87)  all_58_8 = all_10_2
% 204.56/35.35    (88)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.35    (89)   ~ (all_52_5 = all_10_2)
% 204.56/35.35    (90)  op(all_52_29, all_52_29) = all_52_28
% 204.56/35.35    (91)   ~ (all_52_23 = all_14_2)
% 204.56/35.35    (92)  all_56_12 = all_52_7
% 204.56/35.35    (93)  op(all_52_17, all_52_17) = all_52_16
% 204.56/35.35    (94)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.35    (95)   ~ (all_52_25 = all_6_2)
% 204.56/35.35    (96)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.35    (97)   ~ (all_52_9 = all_4_2)
% 204.56/35.35    (98)   ~ (all_52_5 = all_6_2)
% 204.56/35.35    (99)   ~ (all_52_9 = all_6_2)
% 204.56/35.35    (100)   ~ (all_52_13 = all_52_15)
% 204.56/35.35    (101)  all_56_0 = all_6_2
% 204.56/35.35    (102)  op(e3, e3) = all_6_2
% 204.56/35.35    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.35    (104)   ~ (all_52_27 = all_14_2)
% 204.56/35.35    (105)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.35    (106)  all_56_14 = all_52_23
% 204.56/35.35    (107)  all_56_3 = all_52_25
% 204.56/35.35    (108)   ~ (all_52_3 = all_52_7)
% 204.56/35.35    (109)  op(all_14_2, all_14_2) = all_52_30
% 204.56/35.35    (110)  all_58_5 = all_52_19
% 204.56/35.35    (111)  all_56_1 = all_52_9
% 204.56/35.35    (112)   ~ (all_52_15 = all_4_2)
% 204.56/35.35    (113)   ~ (all_52_27 = all_4_2)
% 204.56/35.35    (114)  all_58_6 = all_52_5
% 204.56/35.35    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.35    (116)   ~ (all_52_17 = all_6_2)
% 204.56/35.35    (117)   ~ (e3 = e2)
% 204.56/35.35    (118)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.35    (119)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.56/35.35    (120)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.56/35.35    (121)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.35    (122)   ~ (all_6_1 = e2)
% 204.56/35.35    (123)  op(e1, e1) = all_10_2
% 204.56/35.35    (124)   ~ (all_52_7 = all_52_23)
% 204.56/35.35    (125)   ~ (all_52_17 = all_52_19)
% 204.56/35.35    (126)  all_58_3 = all_4_2
% 204.56/35.35    (127)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.56/35.35    (128)  all_56_13 = all_52_15
% 204.56/35.35    (129)   ~ (all_52_3 = all_4_2)
% 204.56/35.35    (130)   ~ (all_52_19 = all_4_2)
% 204.56/35.35    (131)   ~ (all_52_17 = all_52_23)
% 204.56/35.35    (132)  op(all_6_2, e3) = all_6_1
% 204.56/35.35    (133)  all_58_4 = all_52_17
% 204.56/35.35    (134)  op(all_52_25, all_52_25) = all_52_24
% 204.56/35.35  
% 204.56/35.35  Begin of proof
% 204.56/35.35  | 
% 204.56/35.35  | ALPHA: (119) implies:
% 204.56/35.35  |   (135)  all_52_30 = e0
% 204.56/35.35  |   (136)  all_52_28 = e1
% 204.56/35.35  |   (137)  all_52_26 = e2
% 204.56/35.35  |   (138)  all_52_24 = e3
% 204.56/35.35  | 
% 204.56/35.35  | REDUCE: (134), (138) imply:
% 204.56/35.35  |   (139)  op(all_52_25, all_52_25) = e3
% 204.56/35.35  | 
% 204.56/35.35  | REDUCE: (26), (137) imply:
% 204.56/35.35  |   (140)  op(all_52_27, all_52_27) = e2
% 204.56/35.35  | 
% 204.56/35.35  | REDUCE: (90), (136) imply:
% 204.56/35.35  |   (141)  op(all_52_29, all_52_29) = e1
% 204.56/35.35  | 
% 204.56/35.35  | REDUCE: (109), (135) imply:
% 204.56/35.35  |   (142)  op(all_14_2, all_14_2) = e0
% 204.56/35.35  | 
% 204.56/35.35  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.56/35.35  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.56/35.35  |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 204.56/35.35  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 204.56/35.35  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 204.56/35.35  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 204.56/35.35  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 204.56/35.35  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (91),
% 204.56/35.35  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 204.56/35.35  |            (102), (103), (104), (105), (106), (107), (108), (110), (111),
% 204.56/35.35  |            (112), (113), (114), (115), (116), (117), (118), (120), (121),
% 204.56/35.35  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 204.56/35.35  |            (131), (132), (133), (139), (140), (141), (142) are inconsistent by
% 204.56/35.35  |            sub-proof #1009.
% 204.56/35.35  | 
% 204.56/35.35  End of proof
% 204.56/35.35  
% 204.56/35.35  Sub-proof #1009 shows that the following formulas are inconsistent:
% 204.56/35.35  ----------------------------------------------------------------
% 204.56/35.35    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.35    (2)   ~ (all_52_25 = all_52_27)
% 204.56/35.35    (3)  all_58_14 = all_52_23
% 204.56/35.35    (4)   ~ (e3 = e1)
% 204.56/35.35    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.56/35.35    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.35    (7)  all_58_1 = all_52_9
% 204.56/35.35    (8)   ~ (all_52_9 = all_52_13)
% 204.56/35.35    (9)  op(e2, e3) = all_52_3
% 204.56/35.35    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.56/35.35    (11)   ~ (all_52_7 = all_52_15)
% 204.56/35.35    (12)  op(all_52_7, all_52_7) = all_52_6
% 204.56/35.35    (13)   ~ (all_52_17 = all_52_25)
% 204.56/35.35    (14)   ~ (all_52_3 = all_6_2)
% 204.56/35.35    (15)  all_58_0 = all_6_2
% 204.56/35.35    (16)  all_56_4 = all_52_3
% 204.56/35.35    (17)   ~ (all_52_17 = all_10_2)
% 204.56/35.35    (18)  op(e3, e0) = all_52_25
% 204.56/35.35    (19)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.35    (20)  op(all_52_19, all_52_19) = all_52_18
% 204.56/35.35    (21)   ~ (all_52_27 = all_52_29)
% 204.56/35.35    (22)  all_58_13 = all_52_15
% 204.56/35.35    (23)  all_58_9 = all_52_25
% 204.56/35.35    (24)   ~ (all_6_1 = e1)
% 204.56/35.35    (25)   ~ (all_52_29 = all_14_2)
% 204.56/35.35    (26)  op(e1, e3) = all_52_5
% 204.56/35.35    (27)  op(e2, e2) = all_4_2
% 204.56/35.35    (28)   ~ (all_52_3 = all_52_5)
% 204.56/35.35    (29)  all_58_11 = all_52_29
% 204.56/35.35    (30)  all_56_5 = all_4_2
% 204.56/35.35    (31)   ~ (all_52_25 = all_14_2)
% 204.56/35.35    (32)   ~ (all_52_9 = all_52_15)
% 204.56/35.35    (33)   ~ (all_52_3 = all_52_27)
% 204.56/35.35    (34)  op(all_10_2, e1) = all_10_1
% 204.56/35.35    (35)  op(all_6_2, all_6_2) = all_52_0
% 204.56/35.35    (36)   ~ (all_52_7 = all_6_2)
% 204.56/35.35    (37)  op(e0, e0) = all_14_2
% 204.56/35.35    (38)  op(all_52_29, all_52_29) = e1
% 204.56/35.35    (39)  all_56_15 = all_14_2
% 204.56/35.35    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.35    (41)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.35    (42)  all_56_11 = all_52_29
% 204.56/35.35    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.56/35.35    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.35    (45)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.56/35.35    (46)   ~ (all_6_0 = e1)
% 204.56/35.35    (47)  all_58_10 = all_52_27
% 204.56/35.35    (48)  all_56_8 = all_52_5
% 204.56/35.35    (49)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.35    (50)  op(all_52_15, all_52_15) = all_52_14
% 204.56/35.35    (51)   ~ (all_52_19 = all_52_23)
% 204.56/35.35    (52)   ~ (all_52_25 = all_52_29)
% 204.56/35.35    (53)   ~ (all_52_29 = all_10_2)
% 204.56/35.35    (54)  all_58_7 = all_52_13
% 204.56/35.35    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.35    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.56/35.35    (57)   ~ (all_52_5 = all_52_7)
% 204.56/35.35    (58)  all_58_12 = all_52_7
% 204.56/35.35    (59)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.35    (60)   ~ (all_52_7 = all_14_2)
% 204.56/35.35    (61)   ~ (all_14_2 = e0)
% 204.56/35.35    (62)  all_58_2 = all_52_3
% 204.56/35.35    (63)  all_56_2 = all_52_17
% 204.56/35.35    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.35    (65)  op(e3, all_6_1) = all_6_0
% 204.56/35.35    (66)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.56/35.35    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.56/35.35    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.35    (69)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.35    (70)  op(all_52_25, all_52_25) = e3
% 204.56/35.35    (71)   ~ (all_52_5 = all_52_29)
% 204.56/35.35    (72)   ~ (all_52_15 = all_14_2)
% 204.56/35.35    (73)   ~ (all_52_19 = all_52_27)
% 204.56/35.35    (74)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.35    (75)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.56/35.35    (76)   ~ (all_6_0 = e2)
% 204.56/35.35    (77)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.56/35.35    (78)   ~ (all_52_13 = all_4_2)
% 204.56/35.35    (79)  op(e3, e1) = all_52_17
% 204.56/35.35    (80)  op(all_52_27, all_52_27) = e2
% 204.56/35.35    (81)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.56/35.35    (82)  op(e0, e3) = all_52_7
% 204.56/35.35    (83)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.35    (84)   ~ (all_52_9 = all_52_25)
% 204.56/35.35    (85)  all_58_15 = all_14_2
% 204.56/35.35    (86)   ~ (all_52_19 = all_10_2)
% 204.56/35.35    (87)  op(all_52_23, all_52_23) = all_52_22
% 204.56/35.35    (88)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.35    (89)  all_58_8 = all_10_2
% 204.56/35.35    (90)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.35    (91)   ~ (all_52_5 = all_10_2)
% 204.56/35.35    (92)   ~ (all_52_23 = all_14_2)
% 204.56/35.35    (93)  all_56_12 = all_52_7
% 204.56/35.35    (94)  op(all_52_17, all_52_17) = all_52_16
% 204.56/35.35    (95)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.35    (96)   ~ (all_52_25 = all_6_2)
% 204.56/35.35    (97)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.35    (98)   ~ (all_52_9 = all_4_2)
% 204.56/35.35    (99)   ~ (all_52_5 = all_6_2)
% 204.56/35.35    (100)   ~ (all_52_9 = all_6_2)
% 204.56/35.35    (101)   ~ (all_52_13 = all_52_15)
% 204.56/35.35    (102)  all_56_0 = all_6_2
% 204.56/35.35    (103)  op(e3, e3) = all_6_2
% 204.56/35.35    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.35    (105)   ~ (all_52_27 = all_14_2)
% 204.56/35.35    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.35    (107)  all_56_14 = all_52_23
% 204.56/35.35    (108)  all_56_3 = all_52_25
% 204.56/35.35    (109)   ~ (all_52_3 = all_52_7)
% 204.56/35.35    (110)  all_58_5 = all_52_19
% 204.56/35.35    (111)  all_56_1 = all_52_9
% 204.56/35.35    (112)   ~ (all_52_15 = all_4_2)
% 204.56/35.35    (113)   ~ (all_52_27 = all_4_2)
% 204.56/35.35    (114)  all_58_6 = all_52_5
% 204.56/35.35    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.35    (116)   ~ (all_52_17 = all_6_2)
% 204.56/35.35    (117)  op(all_14_2, all_14_2) = e0
% 204.56/35.35    (118)   ~ (e3 = e2)
% 204.56/35.35    (119)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.35    (120)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.56/35.35    (121)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.35    (122)   ~ (all_6_1 = e2)
% 204.56/35.35    (123)  op(e1, e1) = all_10_2
% 204.56/35.35    (124)   ~ (all_52_7 = all_52_23)
% 204.56/35.35    (125)   ~ (all_52_17 = all_52_19)
% 204.56/35.35    (126)  all_58_3 = all_4_2
% 204.56/35.35    (127)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.56/35.35    (128)  all_56_13 = all_52_15
% 204.56/35.35    (129)   ~ (all_52_3 = all_4_2)
% 204.56/35.35    (130)   ~ (all_52_19 = all_4_2)
% 204.56/35.35    (131)   ~ (all_52_17 = all_52_23)
% 204.56/35.35    (132)  op(all_6_2, e3) = all_6_1
% 204.56/35.35    (133)  all_58_4 = all_52_17
% 204.56/35.35  
% 204.56/35.35  Begin of proof
% 204.56/35.35  | 
% 204.56/35.35  | BETA: splitting (90) gives:
% 204.56/35.35  | 
% 204.56/35.35  | Case 1:
% 204.56/35.35  | | 
% 204.56/35.35  | |   (134)  all_56_15 = e3
% 204.56/35.35  | | 
% 204.56/35.35  | | COMBINE_EQS: (39), (134) imply:
% 204.56/35.35  | |   (135)  all_14_2 = e3
% 204.56/35.35  | | 
% 204.56/35.35  | | SIMP: (135) implies:
% 204.56/35.35  | |   (136)  all_14_2 = e3
% 204.56/35.35  | | 
% 204.56/35.35  | | REDUCE: (60), (136) imply:
% 204.56/35.35  | |   (137)   ~ (all_52_7 = e3)
% 204.56/35.35  | | 
% 204.56/35.35  | | REDUCE: (117), (136) imply:
% 204.56/35.35  | |   (138)  op(e3, e3) = e0
% 204.56/35.35  | | 
% 204.56/35.35  | | REF_CLOSE: (6), (10), (24), (36), (82), (93), (103), (122), (132), (137),
% 204.56/35.35  | |            (138) are inconsistent by sub-proof #1342.
% 204.56/35.35  | | 
% 204.56/35.35  | Case 2:
% 204.56/35.35  | | 
% 204.56/35.35  | |   (139)   ~ (all_56_15 = e3)
% 204.56/35.35  | |   (140)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.35  | | 
% 204.56/35.35  | | REDUCE: (39), (139) imply:
% 204.56/35.35  | |   (141)   ~ (all_14_2 = e3)
% 204.56/35.35  | | 
% 204.56/35.35  | | BETA: splitting (43) gives:
% 204.56/35.35  | | 
% 204.56/35.35  | | Case 1:
% 204.56/35.35  | | | 
% 204.56/35.35  | | |   (142)  all_56_13 = e3
% 204.56/35.35  | | | 
% 204.56/35.35  | | | COMBINE_EQS: (128), (142) imply:
% 204.56/35.35  | | |   (143)  all_52_15 = e3
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REF_CLOSE: (2), (4), (6), (7), (11), (13), (14), (15), (17), (19), (23),
% 204.56/35.35  | | |            (27), (28), (29), (32), (33), (35), (37), (38), (40), (41),
% 204.56/35.35  | | |            (42), (44), (45), (46), (47), (49), (50), (52), (54), (58),
% 204.56/35.35  | | |            (59), (62), (63), (64), (65), (70), (71), (72), (73), (74),
% 204.56/35.35  | | |            (76), (80), (83), (84), (85), (86), (89), (91), (94), (96),
% 204.56/35.35  | | |            (97), (99), (100), (101), (103), (104), (105), (106), (108),
% 204.56/35.35  | | |            (109), (110), (111), (112), (113), (114), (116), (118), (119),
% 204.56/35.35  | | |            (123), (125), (126), (127), (129), (132), (133), (143) are
% 204.56/35.35  | | |            inconsistent by sub-proof #1033.
% 204.56/35.35  | | | 
% 204.56/35.35  | | Case 2:
% 204.56/35.35  | | | 
% 204.56/35.35  | | |   (144)   ~ (all_56_13 = e3)
% 204.56/35.35  | | | 
% 204.56/35.35  | | | REDUCE: (128), (144) imply:
% 204.56/35.35  | | |   (145)   ~ (all_52_15 = e3)
% 204.56/35.35  | | | 
% 204.56/35.35  | | | BETA: splitting (115) gives:
% 204.56/35.35  | | | 
% 204.56/35.35  | | | Case 1:
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | |   (146)  all_58_12 = e3
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | COMBINE_EQS: (58), (146) imply:
% 204.56/35.35  | | | |   (147)  all_52_7 = e3
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | SIMP: (147) implies:
% 204.56/35.35  | | | |   (148)  all_52_7 = e3
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (109), (148) imply:
% 204.56/35.35  | | | |   (149)   ~ (all_52_3 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (57), (148) imply:
% 204.56/35.35  | | | |   (150)   ~ (all_52_5 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (124), (148) imply:
% 204.56/35.35  | | | |   (151)   ~ (all_52_23 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | SIMP: (151) implies:
% 204.56/35.35  | | | |   (152)   ~ (all_52_23 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (60), (148) imply:
% 204.56/35.35  | | | |   (153)   ~ (all_14_2 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (36), (148) imply:
% 204.56/35.35  | | | |   (154)   ~ (all_6_2 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | SIMP: (154) implies:
% 204.56/35.35  | | | |   (155)   ~ (all_6_2 = e3)
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (12), (148) imply:
% 204.56/35.35  | | | |   (156)  op(e3, e3) = all_52_6
% 204.56/35.35  | | | | 
% 204.56/35.35  | | | | REDUCE: (82), (148) imply:
% 204.56/35.35  | | | |   (157)  op(e0, e3) = e3
% 204.56/35.35  | | | | 
% 204.56/35.36  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (13), (14), (15),
% 204.56/35.36  | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.56/35.36  | | | |            (26), (27), (28), (29), (30), (31), (34), (35), (37), (38),
% 204.56/35.36  | | | |            (39), (41), (42), (44), (46), (47), (48), (52), (53), (54),
% 204.56/35.36  | | | |            (55), (56), (59), (61), (62), (63), (65), (66), (67), (68),
% 204.56/35.36  | | | |            (69), (70), (71), (74), (75), (76), (77), (79), (80), (81),
% 204.56/35.36  | | | |            (83), (84), (85), (86), (88), (89), (92), (95), (96), (97),
% 204.56/35.36  | | | |            (98), (99), (100), (102), (103), (104), (105), (106), (107),
% 204.56/35.36  | | | |            (108), (110), (111), (112), (114), (116), (117), (119),
% 204.56/35.36  | | | |            (120), (121), (122), (123), (126), (127), (130), (131),
% 204.56/35.36  | | | |            (132), (133), (140), (141), (146), (149), (150), (152),
% 204.56/35.36  | | | |            (155), (156), (157) are inconsistent by sub-proof #1014.
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | Case 2:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | |   (158)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | BETA: splitting (158) gives:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | Case 1:
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | |   (159)  all_58_13 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REF_CLOSE: (22), (145), (159) are inconsistent by sub-proof #1360.
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | Case 2:
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | |   (160)  all_58_14 = e3 | all_58_15 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | BETA: splitting (160) gives:
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | Case 1:
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | |   (161)  all_58_14 = e3
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | COMBINE_EQS: (3), (161) imply:
% 204.56/35.36  | | | | | |   (162)  all_52_23 = e3
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | SIMP: (162) implies:
% 204.56/35.36  | | | | | |   (163)  all_52_23 = e3
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REDUCE: (124), (163) imply:
% 204.56/35.36  | | | | | |   (164)   ~ (all_52_7 = e3)
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REDUCE: (131), (163) imply:
% 204.56/35.36  | | | | | |   (165)   ~ (all_52_17 = e3)
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REDUCE: (51), (163) imply:
% 204.56/35.36  | | | | | |   (166)   ~ (all_52_19 = e3)
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REDUCE: (92), (163) imply:
% 204.56/35.36  | | | | | |   (167)   ~ (all_14_2 = e3)
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REDUCE: (87), (163) imply:
% 204.56/35.36  | | | | | |   (168)  op(e3, e3) = all_52_22
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_22, e3, e3,
% 204.56/35.36  | | | | | |              simplifying with (103), (168) gives:
% 204.56/35.36  | | | | | |   (169)  all_52_22 = all_6_2
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | BETA: splitting (104) gives:
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | Case 1:
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | |   (170)  all_58_9 = e3
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | | COMBINE_EQS: (23), (170) imply:
% 204.56/35.36  | | | | | | |   (171)  all_52_25 = e3
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | | REF_CLOSE: (6), (70), (96), (103), (171) are inconsistent by
% 204.56/35.36  | | | | | | |            sub-proof #1246.
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | Case 2:
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | |   (172)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | | BETA: splitting (106) gives:
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | | Case 1:
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | |   (173)  all_58_0 = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | COMBINE_EQS: (15), (173) imply:
% 204.56/35.36  | | | | | | | |   (174)  all_6_2 = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | REDUCE: (100), (174) imply:
% 204.56/35.36  | | | | | | | |   (175)   ~ (all_52_9 = e3)
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | REDUCE: (35), (174) imply:
% 204.56/35.36  | | | | | | | |   (176)  op(e3, e3) = all_52_0
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | REDUCE: (132), (174) imply:
% 204.56/35.36  | | | | | | | |   (177)  op(e3, e3) = all_6_1
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | REDUCE: (103), (174) imply:
% 204.56/35.36  | | | | | | | |   (178)  op(e3, e3) = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | GROUND_INST: instantiating (6) with all_6_1, all_52_0, e3, e3,
% 204.56/35.36  | | | | | | | |              simplifying with (176), (177) gives:
% 204.56/35.36  | | | | | | | |   (179)  all_52_0 = all_6_1
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e3, e3,
% 204.56/35.36  | | | | | | | |              simplifying with (176), (178) gives:
% 204.56/35.36  | | | | | | | |   (180)  all_52_0 = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | COMBINE_EQS: (179), (180) imply:
% 204.56/35.36  | | | | | | | |   (181)  all_6_1 = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | REDUCE: (65), (181) imply:
% 204.56/35.36  | | | | | | | |   (182)  op(e3, e3) = all_6_0
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_0, e3, e3,
% 204.56/35.36  | | | | | | | |              simplifying with (178), (182) gives:
% 204.56/35.36  | | | | | | | |   (183)  all_6_0 = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | BETA: splitting (83) gives:
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | Case 1:
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | |   (184)  all_58_1 = e3
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | COMBINE_EQS: (7), (184) imply:
% 204.56/35.36  | | | | | | | | |   (185)  all_52_9 = e3
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | REDUCE: (175), (185) imply:
% 204.56/35.36  | | | | | | | | |   (186)  $false
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | CLOSE: (186) is inconsistent.
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | Case 2:
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | |   (187)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | BETA: splitting (187) gives:
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | Case 1:
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | |   (188)  all_58_3 = e3
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | COMBINE_EQS: (126), (188) imply:
% 204.56/35.36  | | | | | | | | | |   (189)  all_4_2 = e3
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | REDUCE: (113), (189) imply:
% 204.56/35.36  | | | | | | | | | |   (190)   ~ (all_52_27 = e3)
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | BETA: splitting (172) gives:
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | Case 1:
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | |   (191)  all_58_10 = e3
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | REF_CLOSE: (47), (190), (191) are inconsistent by sub-proof
% 204.56/35.36  | | | | | | | | | | |            #1301.
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | Case 2:
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | |   (192)  all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | BETA: splitting (192) gives:
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | Case 1:
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | |   (193)  all_58_11 = e3
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | | COMBINE_EQS: (29), (193) imply:
% 204.56/35.36  | | | | | | | | | | | |   (194)  all_52_29 = e3
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | | REF_CLOSE: (4), (6), (38), (176), (178), (194) are
% 204.56/35.36  | | | | | | | | | | | |            inconsistent by sub-proof #1236.
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | Case 2:
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | |   (195)  all_58_15 = e3
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | | COMBINE_EQS: (85), (195) imply:
% 204.56/35.36  | | | | | | | | | | | |   (196)  all_14_2 = e3
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | | REDUCE: (141), (196) imply:
% 204.56/35.36  | | | | | | | | | | | |   (197)  $false
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 204.56/35.36  | | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | | End of split
% 204.56/35.36  | | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | End of split
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | Case 2:
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | |   (198)  all_58_7 = e3 | all_58_13 = e3
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (13), (14), (15), (17), (22),
% 204.56/35.36  | | | | | | | | | |            (23), (37), (40), (41), (47), (54), (62), (70),
% 204.56/35.36  | | | | | | | | | |            (78), (80), (96), (97), (103), (104), (105),
% 204.56/35.36  | | | | | | | | | |            (106), (108), (110), (118), (121), (123), (126),
% 204.56/35.36  | | | | | | | | | |            (133), (145), (165), (166), (198) are inconsistent
% 204.56/35.36  | | | | | | | | | |            by sub-proof #1012.
% 204.56/35.36  | | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | End of split
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | End of split
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | Case 2:
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | |   (199)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | BETA: splitting (199) gives:
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | | Case 1:
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | |   (200)  all_58_1 = e3
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | COMBINE_EQS: (7), (200) imply:
% 204.56/35.36  | | | | | | | | |   (201)  all_52_9 = e3
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | REDUCE: (84), (201) imply:
% 204.56/35.36  | | | | | | | | |   (202)   ~ (all_52_25 = e3)
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | SIMP: (202) implies:
% 204.56/35.36  | | | | | | | | |   (203)   ~ (all_52_25 = e3)
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | REDUCE: (100), (201) imply:
% 204.56/35.36  | | | | | | | | |   (204)   ~ (all_6_2 = e3)
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | SIMP: (204) implies:
% 204.56/35.36  | | | | | | | | |   (205)   ~ (all_6_2 = e3)
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | REDUCE: (49), (201) imply:
% 204.56/35.36  | | | | | | | | |   (206)  op(e3, e3) = all_52_8
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | REF_CLOSE: (2), (5), (6), (7), (13), (14), (15), (17), (18),
% 204.56/35.36  | | | | | | | | |            (19), (23), (25), (26), (29), (33), (37), (38),
% 204.56/35.36  | | | | | | | | |            (40), (41), (47), (48), (49), (58), (62), (64),
% 204.56/35.36  | | | | | | | | |            (65), (70), (71), (73), (76), (80), (83), (84),
% 204.56/35.36  | | | | | | | | |            (85), (88), (91), (96), (97), (99), (103), (104),
% 204.56/35.36  | | | | | | | | |            (105), (106), (108), (110), (113), (114), (118),
% 204.56/35.36  | | | | | | | | |            (122), (123), (126), (132), (133), (141), (164),
% 204.56/35.36  | | | | | | | | |            (203), (205), (206) are inconsistent by sub-proof
% 204.56/35.36  | | | | | | | | |            #1010.
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | Case 2:
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | |   (207)  all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | | REF_CLOSE: (6), (23), (70), (96), (103), (104), (133), (165),
% 204.56/35.36  | | | | | | | | |            (207) are inconsistent by sub-proof #1226.
% 204.56/35.36  | | | | | | | | | 
% 204.56/35.36  | | | | | | | | End of split
% 204.56/35.36  | | | | | | | | 
% 204.56/35.36  | | | | | | | End of split
% 204.56/35.36  | | | | | | | 
% 204.56/35.36  | | | | | | End of split
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | Case 2:
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | |   (208)  all_58_15 = e3
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | COMBINE_EQS: (85), (208) imply:
% 204.56/35.36  | | | | | |   (209)  all_14_2 = e3
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REDUCE: (141), (209) imply:
% 204.56/35.36  | | | | | |   (210)  $false
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | CLOSE: (210) is inconsistent.
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | End of split
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | End of split
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | End of split
% 204.56/35.36  | | | 
% 204.56/35.36  | | End of split
% 204.56/35.36  | | 
% 204.56/35.36  | End of split
% 204.56/35.36  | 
% 204.56/35.36  End of proof
% 204.56/35.36  
% 204.56/35.36  Sub-proof #1010 shows that the following formulas are inconsistent:
% 204.56/35.36  ----------------------------------------------------------------
% 204.56/35.36    (1)   ~ (all_52_25 = all_52_27)
% 204.56/35.36    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.56/35.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.36    (4)  all_58_1 = all_52_9
% 204.56/35.36    (5)   ~ (all_52_17 = all_52_25)
% 204.56/35.36    (6)   ~ (all_52_3 = all_6_2)
% 204.56/35.36    (7)  all_58_0 = all_6_2
% 204.56/35.36    (8)   ~ (all_52_17 = all_10_2)
% 204.56/35.36    (9)  op(e3, e0) = all_52_25
% 204.56/35.36    (10)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.36    (11)  all_58_9 = all_52_25
% 204.56/35.36    (12)   ~ (all_52_29 = all_14_2)
% 204.56/35.36    (13)  op(e1, e3) = all_52_5
% 204.56/35.36    (14)  all_58_11 = all_52_29
% 204.56/35.36    (15)   ~ (all_52_3 = all_52_27)
% 204.56/35.36    (16)  op(e0, e0) = all_14_2
% 204.56/35.36    (17)  op(all_52_29, all_52_29) = e1
% 204.56/35.36    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.36    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.36    (20)   ~ (all_6_2 = e3)
% 204.56/35.36    (21)  all_58_10 = all_52_27
% 204.56/35.36    (22)  all_56_8 = all_52_5
% 204.56/35.36    (23)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.36    (24)  all_58_12 = all_52_7
% 204.56/35.36    (25)   ~ (all_52_7 = e3)
% 204.56/35.36    (26)  all_58_2 = all_52_3
% 204.56/35.36    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.36    (28)  op(e3, all_6_1) = all_6_0
% 204.56/35.36    (29)   ~ (all_52_25 = e3)
% 204.56/35.36    (30)  op(all_52_25, all_52_25) = e3
% 204.56/35.36    (31)   ~ (all_52_5 = all_52_29)
% 204.56/35.36    (32)   ~ (all_52_19 = all_52_27)
% 204.56/35.36    (33)   ~ (all_6_0 = e2)
% 204.56/35.36    (34)  op(e3, e3) = all_52_8
% 204.56/35.36    (35)  op(all_52_27, all_52_27) = e2
% 204.56/35.36    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.36    (37)   ~ (all_52_9 = all_52_25)
% 204.56/35.36    (38)  all_58_15 = all_14_2
% 204.56/35.36    (39)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.36    (40)   ~ (all_52_5 = all_10_2)
% 204.56/35.36    (41)   ~ (all_52_25 = all_6_2)
% 204.56/35.36    (42)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.36    (43)   ~ (all_52_5 = all_6_2)
% 204.56/35.36    (44)  op(e3, e3) = all_6_2
% 204.56/35.36    (45)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36    (46)   ~ (all_52_27 = all_14_2)
% 204.56/35.36    (47)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36    (48)  all_56_3 = all_52_25
% 204.56/35.36    (49)  all_58_5 = all_52_19
% 204.56/35.36    (50)   ~ (all_52_27 = all_4_2)
% 204.56/35.36    (51)  all_58_6 = all_52_5
% 204.56/35.36    (52)   ~ (e3 = e2)
% 204.56/35.36    (53)   ~ (all_6_1 = e2)
% 204.56/35.36    (54)  op(e1, e1) = all_10_2
% 204.56/35.36    (55)  all_58_3 = all_4_2
% 204.56/35.36    (56)  op(all_6_2, e3) = all_6_1
% 204.56/35.36    (57)  all_58_4 = all_52_17
% 204.56/35.36    (58)   ~ (all_14_2 = e3)
% 204.56/35.36  
% 204.56/35.36  Begin of proof
% 204.56/35.36  | 
% 204.56/35.36  | GROUND_INST: instantiating (3) with all_6_2, all_52_8, e3, e3, simplifying
% 204.56/35.36  |              with (34), (44) gives:
% 204.56/35.36  |   (59)  all_52_8 = all_6_2
% 204.56/35.36  | 
% 204.56/35.36  | BETA: splitting (18) gives:
% 204.56/35.36  | 
% 204.56/35.36  | Case 1:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (60)  all_58_2 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | COMBINE_EQS: (26), (60) imply:
% 204.56/35.36  | |   (61)  all_52_3 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | SIMP: (61) implies:
% 204.56/35.36  | |   (62)  all_52_3 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (15), (62) imply:
% 204.56/35.36  | |   (63)   ~ (all_52_27 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | SIMP: (63) implies:
% 204.56/35.36  | |   (64)   ~ (all_52_27 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (6), (62) imply:
% 204.56/35.36  | |   (65)   ~ (all_6_2 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (2), (62) imply:
% 204.56/35.36  | |   (66)  op(e3, e3) = all_52_2
% 204.56/35.36  | | 
% 204.56/35.36  | | BETA: splitting (45) gives:
% 204.56/35.36  | | 
% 204.56/35.36  | | Case 1:
% 204.56/35.36  | | | 
% 204.56/35.36  | | |   (67)  all_58_9 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | REF_CLOSE: (11), (29), (67) are inconsistent by sub-proof #1300.
% 204.56/35.36  | | | 
% 204.56/35.36  | | Case 2:
% 204.56/35.36  | | | 
% 204.56/35.36  | | |   (68)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | BETA: splitting (68) gives:
% 204.56/35.36  | | | 
% 204.56/35.36  | | | Case 1:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | |   (69)  all_58_10 = e3
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | REF_CLOSE: (21), (64), (69) are inconsistent by sub-proof #1301.
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | Case 2:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | |   (70)  all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | BETA: splitting (70) gives:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | Case 1:
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | |   (71)  all_58_11 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | COMBINE_EQS: (14), (71) imply:
% 204.56/35.36  | | | | |   (72)  all_52_29 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | SIMP: (72) implies:
% 204.56/35.36  | | | | |   (73)  all_52_29 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (31), (73) imply:
% 204.56/35.36  | | | | |   (74)   ~ (all_52_5 = e3)
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (12), (73) imply:
% 204.56/35.36  | | | | |   (75)   ~ (all_14_2 = e3)
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (17), (73) imply:
% 204.56/35.36  | | | | |   (76)  op(e3, e3) = e1
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_2, e3, e3,
% 204.56/35.36  | | | | |              simplifying with (44), (66) gives:
% 204.56/35.36  | | | | |   (77)  all_52_2 = all_6_2
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | GROUND_INST: instantiating (3) with e1, all_52_2, e3, e3, simplifying
% 204.56/35.36  | | | | |              with (66), (76) gives:
% 204.56/35.36  | | | | |   (78)  all_52_2 = e1
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | COMBINE_EQS: (77), (78) imply:
% 204.56/35.36  | | | | |   (79)  all_6_2 = e1
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (43), (79) imply:
% 204.56/35.36  | | | | |   (80)   ~ (all_52_5 = e1)
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (41), (79) imply:
% 204.56/35.36  | | | | |   (81)   ~ (all_52_25 = e1)
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (56), (79) imply:
% 204.56/35.36  | | | | |   (82)  op(e1, e3) = all_6_1
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | GROUND_INST: instantiating (3) with all_52_5, all_6_1, e3, e1,
% 204.56/35.36  | | | | |              simplifying with (13), (82) gives:
% 204.56/35.36  | | | | |   (83)  all_52_5 = all_6_1
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | COMBINE_EQS: (22), (83) imply:
% 204.56/35.36  | | | | |   (84)  all_56_8 = all_6_1
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (74), (83) imply:
% 204.56/35.36  | | | | |   (85)   ~ (all_6_1 = e3)
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (80), (83) imply:
% 204.56/35.36  | | | | |   (86)   ~ (all_6_1 = e1)
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (10), (83) imply:
% 204.56/35.36  | | | | |   (87)  op(all_6_1, all_6_1) = all_52_4
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | BETA: splitting (39) gives:
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | Case 1:
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | |   (88)  all_56_8 = e3
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REF_CLOSE: (84), (85), (88) are inconsistent by sub-proof #1101.
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | Case 2:
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | |   (89)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | | REF_CLOSE: (3), (9), (16), (20), (28), (30), (33), (42), (44), (48),
% 204.56/35.36  | | | | | |            (53), (58), (81), (84), (86), (87), (89) are inconsistent
% 204.56/35.36  | | | | | |            by sub-proof #1031.
% 204.56/35.36  | | | | | | 
% 204.56/35.36  | | | | | End of split
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | Case 2:
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | |   (90)  all_58_15 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | COMBINE_EQS: (38), (90) imply:
% 204.56/35.36  | | | | |   (91)  all_14_2 = e3
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | REDUCE: (58), (91) imply:
% 204.56/35.36  | | | | |   (92)  $false
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | | CLOSE: (92) is inconsistent.
% 204.56/35.36  | | | | | 
% 204.56/35.36  | | | | End of split
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | End of split
% 204.56/35.36  | | | 
% 204.56/35.36  | | End of split
% 204.56/35.36  | | 
% 204.56/35.36  | Case 2:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (93)   ~ (all_58_2 = e3)
% 204.56/35.36  | |   (94)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (26), (93) imply:
% 204.56/35.36  | |   (95)   ~ (all_52_3 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | BETA: splitting (27) gives:
% 204.56/35.36  | | 
% 204.56/35.36  | | Case 1:
% 204.56/35.36  | | | 
% 204.56/35.36  | | |   (96)  all_58_0 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | COMBINE_EQS: (7), (96) imply:
% 204.56/35.36  | | |   (97)  all_6_2 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | REDUCE: (20), (97) imply:
% 204.56/35.36  | | |   (98)  $false
% 204.56/35.36  | | | 
% 204.56/35.36  | | | CLOSE: (98) is inconsistent.
% 204.56/35.36  | | | 
% 204.56/35.36  | | Case 2:
% 204.56/35.36  | | | 
% 204.56/35.36  | | |   (99)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | BETA: splitting (99) gives:
% 204.56/35.36  | | | 
% 204.56/35.36  | | | Case 1:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | |   (100)  all_58_2 = e3
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | REF_CLOSE: (26), (95), (100) are inconsistent by sub-proof #1369.
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | Case 2:
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | |   (101)  all_58_6 = e3 | all_58_12 = e3
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (14), (16), (19),
% 204.56/35.36  | | | |            (21), (23), (24), (25), (30), (31), (32), (35), (36), (37),
% 204.56/35.36  | | | |            (38), (40), (41), (42), (44), (45), (46), (47), (48), (49),
% 204.56/35.36  | | | |            (50), (51), (52), (54), (55), (57), (58), (94), (101) are
% 204.56/35.36  | | | |            inconsistent by sub-proof #1011.
% 204.56/35.36  | | | | 
% 204.56/35.36  | | | End of split
% 204.56/35.36  | | | 
% 204.56/35.36  | | End of split
% 204.56/35.36  | | 
% 204.56/35.36  | End of split
% 204.56/35.36  | 
% 204.56/35.36  End of proof
% 204.56/35.36  
% 204.56/35.36  Sub-proof #1011 shows that the following formulas are inconsistent:
% 204.56/35.36  ----------------------------------------------------------------
% 204.56/35.36    (1)   ~ (all_52_25 = all_52_27)
% 204.56/35.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.36    (3)  all_58_1 = all_52_9
% 204.56/35.36    (4)   ~ (all_52_17 = all_52_25)
% 204.56/35.36    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.36    (6)  all_58_0 = all_6_2
% 204.56/35.36    (7)   ~ (all_52_17 = all_10_2)
% 204.56/35.36    (8)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.36    (9)  all_58_9 = all_52_25
% 204.56/35.36    (10)  all_58_11 = all_52_29
% 204.56/35.36    (11)  op(e0, e0) = all_14_2
% 204.56/35.36    (12)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.36    (13)  all_58_10 = all_52_27
% 204.56/35.36    (14)  op(all_52_9, all_52_9) = all_52_8
% 204.56/35.36    (15)  all_58_12 = all_52_7
% 204.56/35.36    (16)   ~ (all_52_7 = e3)
% 204.56/35.36    (17)  op(all_52_25, all_52_25) = e3
% 204.56/35.36    (18)   ~ (all_52_5 = all_52_29)
% 204.56/35.36    (19)   ~ (all_52_19 = all_52_27)
% 204.56/35.36    (20)  op(all_52_27, all_52_27) = e2
% 204.56/35.36    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.36    (22)   ~ (all_52_9 = all_52_25)
% 204.56/35.36    (23)  all_58_15 = all_14_2
% 204.56/35.36    (24)   ~ (all_52_5 = all_10_2)
% 204.56/35.36    (25)   ~ (all_52_25 = all_6_2)
% 204.56/35.36    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.36    (27)  op(e3, e3) = all_6_2
% 204.56/35.36    (28)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36    (29)   ~ (all_52_27 = all_14_2)
% 204.56/35.36    (30)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36    (31)  all_56_3 = all_52_25
% 204.56/35.36    (32)  all_58_5 = all_52_19
% 204.56/35.36    (33)   ~ (all_52_27 = all_4_2)
% 204.56/35.36    (34)  all_58_6 = all_52_5
% 204.56/35.36    (35)   ~ (e3 = e2)
% 204.56/35.36    (36)  op(e1, e1) = all_10_2
% 204.56/35.36    (37)  all_58_3 = all_4_2
% 204.56/35.36    (38)  all_58_6 = e3 | all_58_12 = e3
% 204.56/35.36    (39)  all_58_4 = all_52_17
% 204.56/35.36    (40)   ~ (all_14_2 = e3)
% 204.56/35.36  
% 204.56/35.36  Begin of proof
% 204.56/35.36  | 
% 204.56/35.36  | BETA: splitting (38) gives:
% 204.56/35.36  | 
% 204.56/35.36  | Case 1:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (41)  all_58_6 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | COMBINE_EQS: (34), (41) imply:
% 204.56/35.36  | |   (42)  all_52_5 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | SIMP: (42) implies:
% 204.56/35.36  | |   (43)  all_52_5 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (18), (43) imply:
% 204.56/35.36  | |   (44)   ~ (all_52_29 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | SIMP: (44) implies:
% 204.56/35.36  | |   (45)   ~ (all_52_29 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (24), (43) imply:
% 204.56/35.36  | |   (46)   ~ (all_10_2 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | SIMP: (46) implies:
% 204.56/35.36  | |   (47)   ~ (all_10_2 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (8), (43) imply:
% 204.56/35.36  | |   (48)  op(e3, e3) = all_52_4
% 204.56/35.36  | | 
% 204.56/35.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 204.56/35.36  | |            (14), (17), (19), (20), (21), (22), (23), (25), (26), (27), (28),
% 204.56/35.36  | |            (29), (30), (31), (32), (33), (35), (36), (37), (39), (40), (45),
% 204.56/35.36  | |            (47), (48) are inconsistent by sub-proof #1040.
% 204.56/35.36  | | 
% 204.56/35.36  | Case 2:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (49)  all_58_12 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REF_CLOSE: (15), (16), (49) are inconsistent by sub-proof #1367.
% 204.56/35.36  | | 
% 204.56/35.36  | End of split
% 204.56/35.36  | 
% 204.56/35.36  End of proof
% 204.56/35.36  
% 204.56/35.36  Sub-proof #1012 shows that the following formulas are inconsistent:
% 204.56/35.36  ----------------------------------------------------------------
% 204.56/35.36    (1)   ~ (all_52_25 = all_52_27)
% 204.56/35.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.36    (3)  all_58_1 = all_52_9
% 204.56/35.36    (4)   ~ (all_52_9 = all_52_13)
% 204.56/35.36    (5)   ~ (all_52_17 = all_52_25)
% 204.56/35.36    (6)   ~ (all_52_3 = all_6_2)
% 204.56/35.36    (7)  all_58_0 = all_6_2
% 204.56/35.36    (8)   ~ (all_52_17 = all_10_2)
% 204.56/35.36    (9)  all_58_13 = all_52_15
% 204.56/35.36    (10)  all_58_9 = all_52_25
% 204.56/35.36    (11)   ~ (all_52_15 = e3)
% 204.56/35.36    (12)  op(e0, e0) = all_14_2
% 204.56/35.36    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.36    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.36    (15)  all_58_10 = all_52_27
% 204.56/35.36    (16)  all_58_7 = all_52_13
% 204.56/35.36    (17)  all_58_2 = all_52_3
% 204.56/35.36    (18)   ~ (all_52_19 = e3)
% 204.56/35.36    (19)  op(all_52_25, all_52_25) = e3
% 204.56/35.36    (20)   ~ (all_52_13 = all_4_2)
% 204.56/35.36    (21)  op(all_52_27, all_52_27) = e2
% 204.56/35.36    (22)   ~ (all_52_25 = all_6_2)
% 204.56/35.36    (23)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.36    (24)  all_58_7 = e3 | all_58_13 = e3
% 204.56/35.36    (25)  op(e3, e3) = all_6_2
% 204.56/35.36    (26)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36    (27)   ~ (all_52_27 = all_14_2)
% 204.56/35.36    (28)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36    (29)   ~ (all_52_17 = e3)
% 204.56/35.36    (30)  all_56_3 = all_52_25
% 204.56/35.36    (31)  all_58_5 = all_52_19
% 204.56/35.36    (32)   ~ (e3 = e2)
% 204.56/35.36    (33)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.36    (34)  op(e1, e1) = all_10_2
% 204.56/35.36    (35)  all_58_3 = all_4_2
% 204.56/35.36    (36)  all_58_4 = all_52_17
% 204.56/35.36  
% 204.56/35.36  Begin of proof
% 204.56/35.36  | 
% 204.56/35.36  | BETA: splitting (24) gives:
% 204.56/35.36  | 
% 204.56/35.36  | Case 1:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (37)  all_58_7 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | COMBINE_EQS: (16), (37) imply:
% 204.56/35.36  | |   (38)  all_52_13 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (4), (38) imply:
% 204.56/35.36  | |   (39)   ~ (all_52_9 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (20), (38) imply:
% 204.56/35.36  | |   (40)   ~ (all_4_2 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | SIMP: (40) implies:
% 204.56/35.36  | |   (41)   ~ (all_4_2 = e3)
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (33), (38) imply:
% 204.56/35.36  | |   (42)  op(e3, e3) = all_52_12
% 204.56/35.36  | | 
% 204.56/35.36  | | GROUND_INST: instantiating (2) with all_6_2, all_52_12, e3, e3, simplifying
% 204.56/35.36  | |              with (25), (42) gives:
% 204.56/35.36  | |   (43)  all_52_12 = all_6_2
% 204.56/35.36  | | 
% 204.56/35.36  | | BETA: splitting (13) gives:
% 204.56/35.36  | | 
% 204.56/35.36  | | Case 1:
% 204.56/35.36  | | | 
% 204.56/35.36  | | |   (44)  all_58_2 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | COMBINE_EQS: (17), (44) imply:
% 204.56/35.36  | | |   (45)  all_52_3 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | SIMP: (45) implies:
% 204.56/35.36  | | |   (46)  all_52_3 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | REDUCE: (6), (46) imply:
% 204.56/35.36  | | |   (47)   ~ (all_6_2 = e3)
% 204.56/35.36  | | | 
% 204.56/35.36  | | | SIMP: (47) implies:
% 204.56/35.36  | | |   (48)   ~ (all_6_2 = e3)
% 204.56/35.36  | | | 
% 204.56/35.36  | | | REF_CLOSE: (2), (3), (7), (10), (19), (22), (25), (26), (28), (29), (36),
% 204.56/35.36  | | |            (39), (48) are inconsistent by sub-proof #1013.
% 204.56/35.36  | | | 
% 204.56/35.36  | | Case 2:
% 204.56/35.36  | | | 
% 204.56/35.36  | | |   (49)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.56/35.36  | | | 
% 204.56/35.36  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (12), (14), (15), (18),
% 204.56/35.36  | | |            (19), (21), (22), (23), (25), (27), (28), (30), (31), (32),
% 204.56/35.36  | | |            (34), (35), (36), (39), (41), (49) are inconsistent by
% 204.56/35.36  | | |            sub-proof #1228.
% 204.56/35.36  | | | 
% 204.56/35.36  | | End of split
% 204.56/35.36  | | 
% 204.56/35.36  | Case 2:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (50)  all_58_13 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REF_CLOSE: (9), (11), (50) are inconsistent by sub-proof #1360.
% 204.56/35.36  | | 
% 204.56/35.36  | End of split
% 204.56/35.36  | 
% 204.56/35.36  End of proof
% 204.56/35.36  
% 204.56/35.36  Sub-proof #1013 shows that the following formulas are inconsistent:
% 204.56/35.36  ----------------------------------------------------------------
% 204.56/35.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.36    (2)  all_58_1 = all_52_9
% 204.56/35.36    (3)  all_58_0 = all_6_2
% 204.56/35.36    (4)  all_58_9 = all_52_25
% 204.56/35.36    (5)   ~ (all_6_2 = e3)
% 204.56/35.36    (6)  op(all_52_25, all_52_25) = e3
% 204.56/35.36    (7)   ~ (all_52_9 = e3)
% 204.56/35.36    (8)   ~ (all_52_25 = all_6_2)
% 204.56/35.36    (9)  op(e3, e3) = all_6_2
% 204.56/35.36    (10)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.36    (11)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36    (12)   ~ (all_52_17 = e3)
% 204.56/35.36    (13)  all_58_4 = all_52_17
% 204.56/35.36  
% 204.56/35.36  Begin of proof
% 204.56/35.36  | 
% 204.56/35.36  | BETA: splitting (11) gives:
% 204.56/35.36  | 
% 204.56/35.36  | Case 1:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (14)  all_58_0 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | COMBINE_EQS: (3), (14) imply:
% 204.56/35.36  | |   (15)  all_6_2 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REDUCE: (5), (15) imply:
% 204.56/35.36  | |   (16)  $false
% 204.56/35.36  | | 
% 204.56/35.36  | | CLOSE: (16) is inconsistent.
% 204.56/35.36  | | 
% 204.56/35.36  | Case 2:
% 204.56/35.36  | | 
% 204.56/35.36  | |   (17)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.36  | | 
% 204.56/35.36  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (12), (13), (17) are
% 204.56/35.36  | |            inconsistent by sub-proof #1225.
% 204.56/35.36  | | 
% 204.56/35.36  | End of split
% 204.56/35.36  | 
% 204.56/35.36  End of proof
% 204.56/35.36  
% 204.56/35.36  Sub-proof #1014 shows that the following formulas are inconsistent:
% 204.56/35.36  ----------------------------------------------------------------
% 204.56/35.36    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.36    (2)   ~ (all_52_25 = all_52_27)
% 204.56/35.36    (3)  all_58_14 = all_52_23
% 204.56/35.36    (4)  op(all_52_3, all_52_3) = all_52_2
% 204.56/35.36    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.36    (6)  all_58_1 = all_52_9
% 204.56/35.36    (7)   ~ (all_52_9 = all_52_13)
% 204.56/35.36    (8)  op(e2, e3) = all_52_3
% 204.56/35.36    (9)   ~ (all_52_17 = all_52_25)
% 204.56/35.36    (10)   ~ (all_52_3 = all_6_2)
% 204.56/35.36    (11)  all_58_0 = all_6_2
% 204.56/35.36    (12)  all_56_4 = all_52_3
% 204.56/35.36    (13)   ~ (all_52_17 = all_10_2)
% 204.56/35.36    (14)  op(e3, e3) = all_52_6
% 204.56/35.36    (15)  op(e3, e0) = all_52_25
% 204.56/35.36    (16)  op(all_52_5, all_52_5) = all_52_4
% 204.56/35.36    (17)  op(all_52_19, all_52_19) = all_52_18
% 204.56/35.36    (18)   ~ (all_52_27 = all_52_29)
% 204.56/35.36    (19)  all_58_13 = all_52_15
% 204.56/35.36    (20)  all_58_9 = all_52_25
% 204.56/35.36    (21)   ~ (all_6_1 = e1)
% 204.56/35.36    (22)   ~ (all_52_29 = all_14_2)
% 204.56/35.36    (23)  op(e1, e3) = all_52_5
% 204.56/35.36    (24)  op(e2, e2) = all_4_2
% 204.56/35.36    (25)   ~ (all_52_3 = all_52_5)
% 204.56/35.36    (26)  all_58_11 = all_52_29
% 204.56/35.36    (27)   ~ (all_52_3 = e3)
% 204.56/35.36    (28)  all_56_5 = all_4_2
% 204.56/35.36    (29)   ~ (all_52_25 = all_14_2)
% 204.56/35.36    (30)  op(all_10_2, e1) = all_10_1
% 204.56/35.36    (31)  op(all_6_2, all_6_2) = all_52_0
% 204.56/35.36    (32)  op(e0, e0) = all_14_2
% 204.56/35.36    (33)  op(all_52_29, all_52_29) = e1
% 204.56/35.36    (34)  all_56_15 = all_14_2
% 204.56/35.36    (35)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.36    (36)  all_56_11 = all_52_29
% 204.56/35.36    (37)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.36    (38)   ~ (all_6_2 = e3)
% 204.56/35.36    (39)   ~ (all_6_0 = e1)
% 204.56/35.36    (40)  all_58_10 = all_52_27
% 204.56/35.36    (41)  all_56_8 = all_52_5
% 204.56/35.36    (42)   ~ (all_52_25 = all_52_29)
% 204.56/35.36    (43)   ~ (all_52_29 = all_10_2)
% 204.56/35.36    (44)  all_58_7 = all_52_13
% 204.56/35.36    (45)  op(e0, e3) = e3
% 204.56/35.37    (46)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.37    (47)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.56/35.37    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.37    (49)   ~ (all_14_2 = e0)
% 204.56/35.37    (50)  all_58_2 = all_52_3
% 204.56/35.37    (51)  all_56_2 = all_52_17
% 204.56/35.37    (52)  op(e3, all_6_1) = all_6_0
% 204.56/35.37    (53)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.56/35.37    (54)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.56/35.37    (55)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.37    (56)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.37    (57)   ~ (all_52_23 = e3)
% 204.56/35.37    (58)   ~ (all_52_5 = e3)
% 204.56/35.37    (59)  op(all_52_25, all_52_25) = e3
% 204.56/35.37    (60)   ~ (all_52_5 = all_52_29)
% 204.56/35.37    (61)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.37    (62)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.56/35.37    (63)   ~ (all_6_0 = e2)
% 204.56/35.37    (64)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.56/35.37    (65)  op(e3, e1) = all_52_17
% 204.56/35.37    (66)  op(all_52_27, all_52_27) = e2
% 204.56/35.37    (67)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.56/35.37    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.37    (69)   ~ (all_52_9 = all_52_25)
% 204.56/35.37    (70)  all_58_15 = all_14_2
% 204.56/35.37    (71)   ~ (all_52_19 = all_10_2)
% 204.56/35.37    (72)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.37    (73)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.37    (74)  all_58_8 = all_10_2
% 204.56/35.37    (75)   ~ (all_52_23 = all_14_2)
% 204.56/35.37    (76)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.37    (77)   ~ (all_52_25 = all_6_2)
% 204.56/35.37    (78)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.37    (79)   ~ (all_52_9 = all_4_2)
% 204.56/35.37    (80)   ~ (all_52_5 = all_6_2)
% 204.56/35.37    (81)   ~ (all_52_9 = all_6_2)
% 204.56/35.37    (82)  all_56_0 = all_6_2
% 204.56/35.37    (83)  op(e3, e3) = all_6_2
% 204.56/35.37    (84)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.37    (85)   ~ (all_52_27 = all_14_2)
% 204.56/35.37    (86)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.37    (87)  all_56_14 = all_52_23
% 204.56/35.37    (88)  all_56_3 = all_52_25
% 204.56/35.37    (89)  all_58_5 = all_52_19
% 204.56/35.37    (90)  all_56_1 = all_52_9
% 204.56/35.37    (91)   ~ (all_52_15 = all_4_2)
% 204.56/35.37    (92)  all_58_6 = all_52_5
% 204.56/35.37    (93)   ~ (all_52_17 = all_6_2)
% 204.56/35.37    (94)  op(all_14_2, all_14_2) = e0
% 204.56/35.37    (95)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.56/35.37    (96)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.56/35.37    (97)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.37    (98)  all_58_12 = e3
% 204.56/35.37    (99)   ~ (all_6_1 = e2)
% 204.56/35.37    (100)  op(e1, e1) = all_10_2
% 204.56/35.37    (101)  all_58_3 = all_4_2
% 204.56/35.37    (102)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.56/35.37    (103)   ~ (all_52_19 = all_4_2)
% 204.56/35.37    (104)   ~ (all_52_17 = all_52_23)
% 204.56/35.37    (105)  op(all_6_2, e3) = all_6_1
% 204.56/35.37    (106)  all_58_4 = all_52_17
% 204.56/35.37    (107)   ~ (all_14_2 = e3)
% 204.56/35.37  
% 204.56/35.37  Begin of proof
% 204.56/35.37  | 
% 204.56/35.37  | GROUND_INST: instantiating (5) with all_6_2, all_52_6, e3, e3, simplifying
% 204.56/35.37  |              with (14), (83) gives:
% 204.56/35.37  |   (108)  all_52_6 = all_6_2
% 204.56/35.37  | 
% 204.56/35.37  | BETA: splitting (46) gives:
% 204.56/35.37  | 
% 204.56/35.37  | Case 1:
% 204.56/35.37  | | 
% 204.56/35.37  | |   (109)  all_56_14 = e3
% 204.56/35.37  | | 
% 204.56/35.37  | | REF_CLOSE: (57), (87), (109) are inconsistent by sub-proof #1286.
% 204.56/35.37  | | 
% 204.56/35.37  | Case 2:
% 204.56/35.37  | | 
% 204.56/35.37  | |   (110)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.37  | | 
% 204.56/35.37  | | BETA: splitting (55) gives:
% 204.56/35.37  | | 
% 204.56/35.37  | | Case 1:
% 204.56/35.37  | | | 
% 204.56/35.37  | | |   (111)  all_56_4 = e3
% 204.56/35.37  | | | 
% 204.56/35.37  | | | REF_CLOSE: (12), (27), (111) are inconsistent by sub-proof #1340.
% 204.56/35.37  | | | 
% 204.56/35.37  | | Case 2:
% 204.56/35.37  | | | 
% 204.56/35.37  | | |   (112)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.56/35.37  | | | 
% 204.56/35.37  | | | BETA: splitting (96) gives:
% 204.56/35.37  | | | 
% 204.56/35.37  | | | Case 1:
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | |   (113)  all_56_0 = e3
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | | COMBINE_EQS: (82), (113) imply:
% 204.56/35.37  | | | |   (114)  all_6_2 = e3
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | | REDUCE: (38), (114) imply:
% 204.56/35.37  | | | |   (115)  $false
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | | CLOSE: (115) is inconsistent.
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | Case 2:
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | |   (116)   ~ (all_56_0 = e3)
% 204.56/35.37  | | | |   (117)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | | BETA: splitting (72) gives:
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | | Case 1:
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | |   (118)  all_56_8 = e3
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | | REF_CLOSE: (41), (58), (118) are inconsistent by sub-proof #1325.
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | Case 2:
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | |   (119)   ~ (all_56_8 = e3)
% 204.56/35.37  | | | | |   (120)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | | BETA: splitting (54) gives:
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | | Case 1:
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | |   (121)  all_58_0 = e1
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | COMBINE_EQS: (11), (121) imply:
% 204.56/35.37  | | | | | |   (122)  all_6_2 = e1
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | REDUCE: (80), (122) imply:
% 204.56/35.37  | | | | | |   (123)   ~ (all_52_5 = e1)
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | REDUCE: (77), (122) imply:
% 204.56/35.37  | | | | | |   (124)   ~ (all_52_25 = e1)
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | REDUCE: (105), (122) imply:
% 204.56/35.37  | | | | | |   (125)  op(e1, e3) = all_6_1
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | GROUND_INST: instantiating (5) with all_52_5, all_6_1, e3, e1,
% 204.56/35.37  | | | | | |              simplifying with (23), (125) gives:
% 204.56/35.37  | | | | | |   (126)  all_52_5 = all_6_1
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | COMBINE_EQS: (41), (126) imply:
% 204.56/35.37  | | | | | |   (127)  all_56_8 = all_6_1
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | REDUCE: (16), (126) imply:
% 204.56/35.37  | | | | | |   (128)  op(all_6_1, all_6_1) = all_52_4
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | REF_CLOSE: (5), (15), (21), (32), (38), (52), (59), (63), (78),
% 204.56/35.37  | | | | | |            (83), (88), (99), (107), (120), (124), (127), (128) are
% 204.56/35.37  | | | | | |            inconsistent by sub-proof #1031.
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | Case 2:
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | |   (129)   ~ (all_58_0 = e1)
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | REDUCE: (11), (129) imply:
% 204.56/35.37  | | | | | |   (130)   ~ (all_6_2 = e1)
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | BETA: splitting (62) gives:
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | | Case 1:
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | |   (131)  all_58_0 = e2
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | COMBINE_EQS: (11), (131) imply:
% 204.56/35.37  | | | | | | |   (132)  all_6_2 = e2
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | REDUCE: (10), (132) imply:
% 204.56/35.37  | | | | | | |   (133)   ~ (all_52_3 = e2)
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | REDUCE: (77), (132) imply:
% 204.56/35.37  | | | | | | |   (134)   ~ (all_52_25 = e2)
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | REDUCE: (105), (132) imply:
% 204.56/35.37  | | | | | | |   (135)  op(e2, e3) = all_6_1
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | GROUND_INST: instantiating (5) with all_52_3, all_6_1, e3, e2,
% 204.56/35.37  | | | | | | |              simplifying with (8), (135) gives:
% 204.56/35.37  | | | | | | |   (136)  all_52_3 = all_6_1
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | COMBINE_EQS: (12), (136) imply:
% 204.56/35.37  | | | | | | |   (137)  all_56_4 = all_6_1
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | REDUCE: (4), (136) imply:
% 204.56/35.37  | | | | | | |   (138)  op(all_6_1, all_6_1) = all_52_2
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | BETA: splitting (112) gives:
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | |   (139)  all_56_4 = e2
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | REF_CLOSE: (99), (137), (139) are inconsistent by sub-proof
% 204.56/35.37  | | | | | | | |            #1219.
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | |   (140)  all_56_4 = e1 | all_56_4 = e0
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | BETA: splitting (140) gives:
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | |   (141)  all_56_4 = e1
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REF_CLOSE: (21), (137), (141) are inconsistent by sub-proof
% 204.56/35.37  | | | | | | | | |            #1218.
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | |   (142)  all_56_4 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | COMBINE_EQS: (137), (142) imply:
% 204.56/35.37  | | | | | | | | |   (143)  all_6_1 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | SIMP: (143) implies:
% 204.56/35.37  | | | | | | | | |   (144)  all_6_1 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (138), (144) imply:
% 204.56/35.37  | | | | | | | | |   (145)  op(e0, e0) = all_52_2
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (52), (144) imply:
% 204.56/35.37  | | | | | | | | |   (146)  op(e3, e0) = all_6_0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | GROUND_INST: instantiating (5) with all_14_2, all_52_2, e0, e0,
% 204.56/35.37  | | | | | | | | |              simplifying with (32), (145) gives:
% 204.56/35.37  | | | | | | | | |   (147)  all_52_2 = all_14_2
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | GROUND_INST: instantiating (5) with all_52_25, all_6_0, e0, e3,
% 204.56/35.37  | | | | | | | | |              simplifying with (15), (146) gives:
% 204.56/35.37  | | | | | | | | |   (148)  all_52_25 = all_6_0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | COMBINE_EQS: (88), (148) imply:
% 204.56/35.37  | | | | | | | | |   (149)  all_56_3 = all_6_0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (59), (148) imply:
% 204.56/35.37  | | | | | | | | |   (150)  op(all_6_0, all_6_0) = e3
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | BETA: splitting (78) gives:
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | |   (151)  all_56_3 = e3
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | REF_CLOSE: (5), (38), (83), (149), (150), (151) are
% 204.56/35.37  | | | | | | | | | |            inconsistent by sub-proof #1032.
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | |   (152)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | BETA: splitting (152) gives:
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | |   (153)  all_56_3 = e2
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | REF_CLOSE: (63), (149), (153) are inconsistent by sub-proof
% 204.56/35.37  | | | | | | | | | | |            #1075.
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | |   (154)  all_56_3 = e1 | all_56_3 = e0
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | BETA: splitting (154) gives:
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | |   (155)  all_56_3 = e1
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REF_CLOSE: (39), (149), (155) are inconsistent by sub-proof
% 204.56/35.37  | | | | | | | | | | | |            #1074.
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | |   (156)  all_56_3 = e0
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | COMBINE_EQS: (149), (156) imply:
% 204.56/35.37  | | | | | | | | | | | |   (157)  all_6_0 = e0
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | SIMP: (157) implies:
% 204.56/35.37  | | | | | | | | | | | |   (158)  all_6_0 = e0
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REDUCE: (150), (158) imply:
% 204.56/35.37  | | | | | | | | | | | |   (159)  op(e0, e0) = e3
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REF_CLOSE: (5), (32), (107), (145), (159) are inconsistent by
% 204.56/35.37  | | | | | | | | | | | |            sub-proof #1030.
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | End of split
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | Case 2:
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | |   (160)   ~ (all_58_0 = e2)
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | REDUCE: (11), (160) imply:
% 204.56/35.37  | | | | | | |   (161)   ~ (all_6_2 = e2)
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | BETA: splitting (117) gives:
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | |   (162)  all_56_0 = e2
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | COMBINE_EQS: (82), (162) imply:
% 204.56/35.37  | | | | | | | |   (163)  all_6_2 = e2
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | REDUCE: (161), (163) imply:
% 204.56/35.37  | | | | | | | |   (164)  $false
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | CLOSE: (164) is inconsistent.
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | |   (165)  all_56_0 = e1 | all_56_0 = e0
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | BETA: splitting (165) gives:
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | |   (166)  all_56_0 = e1
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | COMBINE_EQS: (82), (166) imply:
% 204.56/35.37  | | | | | | | | |   (167)  all_6_2 = e1
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (130), (167) imply:
% 204.56/35.37  | | | | | | | | |   (168)  $false
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | CLOSE: (168) is inconsistent.
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | |   (169)  all_56_0 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | COMBINE_EQS: (82), (169) imply:
% 204.56/35.37  | | | | | | | | |   (170)  all_6_2 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | COMBINE_EQS: (11), (170) imply:
% 204.56/35.37  | | | | | | | | |   (171)  all_58_0 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (81), (170) imply:
% 204.56/35.37  | | | | | | | | |   (172)   ~ (all_52_9 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (93), (170) imply:
% 204.56/35.37  | | | | | | | | |   (173)   ~ (all_52_17 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (38), (170) imply:
% 204.56/35.37  | | | | | | | | |   (174)   ~ (e3 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | SIMP: (174) implies:
% 204.56/35.37  | | | | | | | | |   (175)   ~ (e3 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (31), (170) imply:
% 204.56/35.37  | | | | | | | | |   (176)  op(e0, e0) = all_52_0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (105), (170) imply:
% 204.56/35.37  | | | | | | | | |   (177)  op(e0, e3) = all_6_1
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (83), (170) imply:
% 204.56/35.37  | | | | | | | | |   (178)  op(e3, e3) = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | GROUND_INST: instantiating (5) with all_14_2, all_52_0, e0, e0,
% 204.56/35.37  | | | | | | | | |              simplifying with (32), (176) gives:
% 204.56/35.37  | | | | | | | | |   (179)  all_52_0 = all_14_2
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | GROUND_INST: instantiating (5) with e3, all_6_1, e3, e0,
% 204.56/35.37  | | | | | | | | |              simplifying with (45), (177) gives:
% 204.56/35.37  | | | | | | | | |   (180)  all_6_1 = e3
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (52), (180) imply:
% 204.56/35.37  | | | | | | | | |   (181)  op(e3, e3) = all_6_0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_6_0, e3, e3,
% 204.56/35.37  | | | | | | | | |              simplifying with (178), (181) gives:
% 204.56/35.37  | | | | | | | | |   (182)  all_6_0 = e0
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (63), (182) imply:
% 204.56/35.37  | | | | | | | | |   (183)   ~ (e2 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | SIMP: (183) implies:
% 204.56/35.37  | | | | | | | | |   (184)   ~ (e2 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | REDUCE: (39), (182) imply:
% 204.56/35.37  | | | | | | | | |   (185)   ~ (e1 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | SIMP: (185) implies:
% 204.56/35.37  | | | | | | | | |   (186)   ~ (e1 = e0)
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | BETA: splitting (95) gives:
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | |   (187)  all_56_1 = e3
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | COMBINE_EQS: (90), (187) imply:
% 204.56/35.37  | | | | | | | | | |   (188)  all_52_9 = e3
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | REDUCE: (69), (188) imply:
% 204.56/35.37  | | | | | | | | | |   (189)   ~ (all_52_25 = e3)
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | SIMP: (189) implies:
% 204.56/35.37  | | | | | | | | | |   (190)   ~ (all_52_25 = e3)
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11),
% 204.56/35.37  | | | | | | | | | |            (13), (14), (17), (18), (19), (20), (22), (24),
% 204.56/35.37  | | | | | | | | | |            (25), (26), (28), (29), (30), (31), (32), (33),
% 204.56/35.37  | | | | | | | | | |            (34), (35), (36), (37), (38), (40), (41), (42),
% 204.56/35.37  | | | | | | | | | |            (43), (44), (47), (48), (49), (50), (51), (53),
% 204.56/35.37  | | | | | | | | | |            (56), (58), (59), (60), (61), (64), (65), (66),
% 204.56/35.37  | | | | | | | | | |            (67), (68), (70), (71), (73), (74), (75), (76),
% 204.56/35.37  | | | | | | | | | |            (77), (78), (79), (80), (83), (84), (85), (86),
% 204.56/35.37  | | | | | | | | | |            (87), (88), (89), (91), (92), (93), (94), (97),
% 204.56/35.37  | | | | | | | | | |            (98), (100), (101), (102), (103), (104), (105),
% 204.56/35.37  | | | | | | | | | |            (106), (107), (110), (120), (130), (175), (184),
% 204.56/35.37  | | | | | | | | | |            (186), (190) are inconsistent by sub-proof #1016.
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | |   (191)   ~ (all_56_1 = e3)
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | REDUCE: (90), (191) imply:
% 204.56/35.37  | | | | | | | | | |   (192)   ~ (all_52_9 = e3)
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | BETA: splitting (86) gives:
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | |   (193)  all_58_0 = e3
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | REF_CLOSE: (171), (175), (193) are inconsistent by sub-proof
% 204.56/35.37  | | | | | | | | | | |            #1015.
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | |   (194)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | BETA: splitting (37) gives:
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | Case 1:
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | |   (195)  all_56_2 = e3
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | COMBINE_EQS: (51), (195) imply:
% 204.56/35.37  | | | | | | | | | | | |   (196)  all_52_17 = e3
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | SIMP: (196) implies:
% 204.56/35.37  | | | | | | | | | | | |   (197)  all_52_17 = e3
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REDUCE: (9), (197) imply:
% 204.56/35.37  | | | | | | | | | | | |   (198)   ~ (all_52_25 = e3)
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | SIMP: (198) implies:
% 204.56/35.37  | | | | | | | | | | | |   (199)   ~ (all_52_25 = e3)
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11),
% 204.56/35.37  | | | | | | | | | | | |            (13), (14), (17), (18), (19), (20), (22), (24),
% 204.56/35.37  | | | | | | | | | | | |            (25), (26), (28), (29), (30), (31), (32), (33),
% 204.56/35.37  | | | | | | | | | | | |            (34), (35), (36), (37), (38), (40), (41), (42),
% 204.56/35.37  | | | | | | | | | | | |            (43), (44), (47), (48), (49), (50), (51), (53),
% 204.56/35.37  | | | | | | | | | | | |            (56), (58), (59), (60), (61), (64), (65), (66),
% 204.56/35.37  | | | | | | | | | | | |            (67), (68), (70), (71), (73), (74), (75), (76),
% 204.56/35.37  | | | | | | | | | | | |            (77), (78), (79), (80), (83), (84), (85), (86),
% 204.56/35.37  | | | | | | | | | | | |            (87), (88), (89), (91), (92), (93), (94), (97),
% 204.56/35.37  | | | | | | | | | | | |            (98), (100), (101), (102), (103), (104), (105),
% 204.56/35.37  | | | | | | | | | | | |            (106), (107), (110), (120), (130), (175), (184),
% 204.56/35.37  | | | | | | | | | | | |            (186), (199) are inconsistent by sub-proof #1016.
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | Case 2:
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | |   (200)   ~ (all_56_2 = e3)
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REDUCE: (51), (200) imply:
% 204.56/35.37  | | | | | | | | | | | |   (201)   ~ (all_52_17 = e3)
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | | REF_CLOSE: (5), (6), (20), (59), (77), (83), (84), (106),
% 204.56/35.37  | | | | | | | | | | | |            (192), (194), (201) are inconsistent by sub-proof
% 204.56/35.37  | | | | | | | | | | | |            #1225.
% 204.56/35.37  | | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | | | 
% 204.56/35.37  | | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | | 
% 204.56/35.37  | | | | | | | | End of split
% 204.56/35.37  | | | | | | | | 
% 204.56/35.37  | | | | | | | End of split
% 204.56/35.37  | | | | | | | 
% 204.56/35.37  | | | | | | End of split
% 204.56/35.37  | | | | | | 
% 204.56/35.37  | | | | | End of split
% 204.56/35.37  | | | | | 
% 204.56/35.37  | | | | End of split
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | End of split
% 204.56/35.37  | | | 
% 204.56/35.37  | | End of split
% 204.56/35.37  | | 
% 204.56/35.37  | End of split
% 204.56/35.37  | 
% 204.56/35.37  End of proof
% 204.56/35.37  
% 204.56/35.37  Sub-proof #1015 shows that the following formulas are inconsistent:
% 204.56/35.37  ----------------------------------------------------------------
% 204.56/35.37    (1)  all_58_0 = e3
% 204.56/35.37    (2)  all_58_0 = e0
% 204.56/35.37    (3)   ~ (e3 = e0)
% 204.56/35.37  
% 204.56/35.37  Begin of proof
% 204.56/35.37  | 
% 204.56/35.37  | COMBINE_EQS: (1), (2) imply:
% 204.56/35.37  |   (4)  e3 = e0
% 204.56/35.37  | 
% 204.56/35.37  | SIMP: (4) implies:
% 204.56/35.37  |   (5)  e3 = e0
% 204.56/35.37  | 
% 204.56/35.37  | REDUCE: (3), (5) imply:
% 204.56/35.37  |   (6)  $false
% 204.56/35.37  | 
% 204.56/35.37  | CLOSE: (6) is inconsistent.
% 204.56/35.37  | 
% 204.56/35.37  End of proof
% 204.56/35.37  
% 204.56/35.37  Sub-proof #1016 shows that the following formulas are inconsistent:
% 204.56/35.37  ----------------------------------------------------------------
% 204.56/35.37    (1)   ~ (all_52_15 = all_52_23)
% 204.56/35.37    (2)   ~ (all_52_25 = all_52_27)
% 204.56/35.37    (3)  all_58_14 = all_52_23
% 204.56/35.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.56/35.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.56/35.37    (5)  all_58_1 = all_52_9
% 204.56/35.37    (6)   ~ (all_52_9 = all_52_13)
% 204.56/35.37    (7)   ~ (e3 = e0)
% 204.56/35.37    (8)  op(e2, e3) = all_52_3
% 204.56/35.37    (9)   ~ (all_52_17 = all_52_25)
% 204.56/35.37    (10)  all_58_0 = all_6_2
% 204.56/35.37    (11)   ~ (all_52_17 = all_10_2)
% 204.56/35.37    (12)  op(e3, e3) = all_52_6
% 204.56/35.37    (13)  op(all_52_19, all_52_19) = all_52_18
% 204.56/35.37    (14)   ~ (all_52_27 = all_52_29)
% 204.56/35.37    (15)  all_58_13 = all_52_15
% 204.56/35.37    (16)  all_58_9 = all_52_25
% 204.56/35.37    (17)   ~ (all_52_29 = all_14_2)
% 204.56/35.37    (18)  op(e2, e2) = all_4_2
% 204.56/35.37    (19)   ~ (all_52_3 = all_52_5)
% 204.56/35.37    (20)  all_58_11 = all_52_29
% 204.56/35.37    (21)  all_56_5 = all_4_2
% 204.56/35.37    (22)   ~ (all_52_25 = all_14_2)
% 204.56/35.37    (23)  op(all_10_2, e1) = all_10_1
% 204.56/35.37    (24)  op(all_6_2, all_6_2) = all_52_0
% 204.56/35.37    (25)  op(e0, e0) = all_14_2
% 204.56/35.37    (26)  op(all_52_29, all_52_29) = e1
% 204.56/35.37    (27)  all_56_15 = all_14_2
% 204.56/35.37    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.56/35.37    (29)  all_56_11 = all_52_29
% 204.56/35.37    (30)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.56/35.37    (31)   ~ (all_6_2 = e3)
% 204.56/35.37    (32)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.56/35.37    (33)  all_58_10 = all_52_27
% 204.56/35.37    (34)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.56/35.37    (35)  all_56_8 = all_52_5
% 204.56/35.37    (36)   ~ (all_52_25 = all_52_29)
% 204.56/35.37    (37)   ~ (all_52_29 = all_10_2)
% 204.56/35.37    (38)  all_58_7 = all_52_13
% 204.56/35.37    (39)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.56/35.37    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.56/35.37    (41)   ~ (all_14_2 = e0)
% 204.56/35.37    (42)  all_58_2 = all_52_3
% 204.56/35.37    (43)  all_56_2 = all_52_17
% 204.56/35.37    (44)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.56/35.37    (45)   ~ (all_52_25 = e3)
% 204.56/35.37    (46)   ~ (e2 = e0)
% 204.56/35.37    (47)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.56/35.37    (48)   ~ (all_52_5 = e3)
% 204.56/35.37    (49)  op(all_52_25, all_52_25) = e3
% 204.56/35.37    (50)   ~ (all_52_5 = all_52_29)
% 204.56/35.37    (51)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.56/35.37    (52)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.56/35.37    (53)  op(e3, e1) = all_52_17
% 204.56/35.37    (54)  op(all_52_27, all_52_27) = e2
% 204.56/35.37    (55)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.56/35.37    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.56/35.37    (57)  all_58_15 = all_14_2
% 204.56/35.37    (58)   ~ (all_52_19 = all_10_2)
% 204.56/35.37    (59)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.56/35.37    (60)  all_58_8 = all_10_2
% 204.56/35.37    (61)   ~ (all_52_23 = all_14_2)
% 204.56/35.37    (62)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.56/35.37    (63)   ~ (all_52_25 = all_6_2)
% 204.56/35.37    (64)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.37    (65)   ~ (all_52_9 = all_4_2)
% 204.56/35.37    (66)   ~ (all_52_5 = all_6_2)
% 204.56/35.37    (67)  op(e3, e3) = all_6_2
% 204.56/35.37    (68)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.37    (69)   ~ (all_52_27 = all_14_2)
% 204.56/35.37    (70)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.56/35.37    (71)  all_56_14 = all_52_23
% 204.56/35.37    (72)  all_56_3 = all_52_25
% 204.56/35.37    (73)  all_58_5 = all_52_19
% 204.56/35.37    (74)   ~ (all_52_15 = all_4_2)
% 204.56/35.37    (75)  all_58_6 = all_52_5
% 204.56/35.37    (76)   ~ (all_52_17 = all_6_2)
% 204.56/35.37    (77)   ~ (e1 = e0)
% 204.56/35.37    (78)  op(all_14_2, all_14_2) = e0
% 204.56/35.37    (79)   ~ (all_6_2 = e1)
% 204.56/35.37    (80)  op(all_52_13, all_52_13) = all_52_12
% 204.56/35.37    (81)  all_58_12 = e3
% 204.56/35.37    (82)  op(e1, e1) = all_10_2
% 204.56/35.37    (83)  all_58_3 = all_4_2
% 204.56/35.37    (84)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.56/35.37    (85)   ~ (all_52_19 = all_4_2)
% 204.56/35.37    (86)   ~ (all_52_17 = all_52_23)
% 204.56/35.37    (87)  op(all_6_2, e3) = all_6_1
% 204.56/35.37    (88)  all_58_4 = all_52_17
% 204.56/35.37    (89)   ~ (all_14_2 = e3)
% 204.56/35.37  
% 204.56/35.37  Begin of proof
% 204.56/35.37  | 
% 204.56/35.37  | BETA: splitting (64) gives:
% 204.56/35.37  | 
% 204.56/35.37  | Case 1:
% 204.56/35.37  | | 
% 204.56/35.37  | |   (90)  all_56_3 = e3
% 204.56/35.37  | | 
% 204.56/35.37  | | REF_CLOSE: (45), (72), (90) are inconsistent by sub-proof #1339.
% 204.56/35.37  | | 
% 204.56/35.37  | Case 2:
% 204.56/35.37  | | 
% 204.56/35.37  | |   (91)   ~ (all_56_3 = e3)
% 204.56/35.37  | |   (92)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.56/35.37  | | 
% 204.56/35.37  | | BETA: splitting (68) gives:
% 204.56/35.37  | | 
% 204.56/35.37  | | Case 1:
% 204.56/35.37  | | | 
% 204.56/35.37  | | |   (93)  all_58_9 = e3
% 204.56/35.37  | | | 
% 204.56/35.37  | | | REF_CLOSE: (16), (45), (93) are inconsistent by sub-proof #1300.
% 204.56/35.37  | | | 
% 204.56/35.37  | | Case 2:
% 204.56/35.37  | | | 
% 204.56/35.37  | | |   (94)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.56/35.37  | | | 
% 204.56/35.37  | | | BETA: splitting (51) gives:
% 204.56/35.37  | | | 
% 204.56/35.37  | | | Case 1:
% 204.56/35.37  | | | | 
% 204.56/35.37  | | | |   (95)  all_56_11 = e3
% 204.56/35.37  | | | | 
% 204.64/35.37  | | | | COMBINE_EQS: (29), (95) imply:
% 204.64/35.37  | | | |   (96)  all_52_29 = e3
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | | SIMP: (96) implies:
% 204.64/35.37  | | | |   (97)  all_52_29 = e3
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | | REDUCE: (26), (97) imply:
% 204.64/35.37  | | | |   (98)  op(e3, e3) = e1
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | | REF_CLOSE: (4), (12), (67), (79), (98) are inconsistent by sub-proof
% 204.64/35.37  | | | |            #1105.
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | Case 2:
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | |   (99)   ~ (all_56_11 = e3)
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | | REDUCE: (29), (99) imply:
% 204.64/35.37  | | | |   (100)   ~ (all_52_29 = e3)
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 204.64/35.37  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 204.64/35.37  | | | |            (23), (24), (25), (27), (28), (29), (30), (31), (32), (33),
% 204.64/35.37  | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 204.64/35.37  | | | |            (44), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 204.64/35.37  | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 204.64/35.37  | | | |            (65), (66), (67), (69), (70), (71), (72), (73), (74), (75),
% 204.64/35.37  | | | |            (76), (77), (78), (80), (81), (82), (83), (84), (85), (86),
% 204.64/35.37  | | | |            (87), (88), (89), (92), (94), (100) are inconsistent by
% 204.64/35.37  | | | |            sub-proof #1017.
% 204.64/35.37  | | | | 
% 204.64/35.37  | | | End of split
% 204.64/35.37  | | | 
% 204.64/35.37  | | End of split
% 204.64/35.37  | | 
% 204.64/35.37  | End of split
% 204.64/35.37  | 
% 204.64/35.37  End of proof
% 204.64/35.37  
% 204.64/35.37  Sub-proof #1017 shows that the following formulas are inconsistent:
% 204.64/35.37  ----------------------------------------------------------------
% 204.64/35.37    (1)   ~ (all_52_15 = all_52_23)
% 204.64/35.37    (2)   ~ (all_52_25 = all_52_27)
% 204.64/35.37    (3)  all_58_14 = all_52_23
% 204.64/35.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.37    (5)  all_58_1 = all_52_9
% 204.64/35.37    (6)   ~ (all_52_9 = all_52_13)
% 204.64/35.37    (7)   ~ (e3 = e0)
% 204.64/35.37    (8)  op(e2, e3) = all_52_3
% 204.64/35.37    (9)   ~ (all_52_17 = all_52_25)
% 204.64/35.37    (10)  all_58_0 = all_6_2
% 204.64/35.37    (11)   ~ (all_52_17 = all_10_2)
% 204.64/35.37    (12)  op(all_52_19, all_52_19) = all_52_18
% 204.64/35.37    (13)   ~ (all_52_27 = all_52_29)
% 204.64/35.37    (14)  all_58_13 = all_52_15
% 204.64/35.37    (15)  all_58_9 = all_52_25
% 204.64/35.37    (16)   ~ (all_52_29 = all_14_2)
% 204.64/35.37    (17)  op(e2, e2) = all_4_2
% 204.64/35.37    (18)   ~ (all_52_3 = all_52_5)
% 204.64/35.37    (19)  all_58_11 = all_52_29
% 204.64/35.37    (20)  all_56_5 = all_4_2
% 204.64/35.37    (21)   ~ (all_52_25 = all_14_2)
% 204.64/35.37    (22)  op(all_10_2, e1) = all_10_1
% 204.64/35.37    (23)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.37    (24)  op(e0, e0) = all_14_2
% 204.64/35.37    (25)  all_56_15 = all_14_2
% 204.64/35.37    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.37    (27)  all_56_11 = all_52_29
% 204.64/35.37    (28)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.37    (29)   ~ (all_6_2 = e3)
% 204.64/35.37    (30)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.64/35.37    (31)  all_58_10 = all_52_27
% 204.64/35.37    (32)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.37    (33)  all_56_8 = all_52_5
% 204.64/35.37    (34)   ~ (all_52_25 = all_52_29)
% 204.64/35.37    (35)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.37    (36)   ~ (all_52_29 = all_10_2)
% 204.64/35.37    (37)  all_58_7 = all_52_13
% 204.64/35.37    (38)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.64/35.37    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.37    (40)   ~ (all_14_2 = e0)
% 204.64/35.37    (41)  all_58_2 = all_52_3
% 204.64/35.37    (42)  all_56_2 = all_52_17
% 204.64/35.37    (43)   ~ (all_52_29 = e3)
% 204.64/35.37    (44)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.37    (45)   ~ (e2 = e0)
% 204.64/35.37    (46)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.64/35.37    (47)   ~ (all_52_5 = e3)
% 204.64/35.37    (48)  op(all_52_25, all_52_25) = e3
% 204.64/35.37    (49)   ~ (all_52_5 = all_52_29)
% 204.64/35.37    (50)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.37    (51)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.37    (52)  op(e3, e1) = all_52_17
% 204.64/35.37    (53)  op(all_52_27, all_52_27) = e2
% 204.64/35.37    (54)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.64/35.37    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.37    (56)  all_58_15 = all_14_2
% 204.64/35.37    (57)   ~ (all_52_19 = all_10_2)
% 204.64/35.37    (58)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.64/35.37    (59)  all_58_8 = all_10_2
% 204.64/35.37    (60)   ~ (all_52_23 = all_14_2)
% 204.64/35.37    (61)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.64/35.37    (62)   ~ (all_52_25 = all_6_2)
% 204.64/35.37    (63)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.37    (64)   ~ (all_52_9 = all_4_2)
% 204.64/35.37    (65)   ~ (all_52_5 = all_6_2)
% 204.64/35.37    (66)  op(e3, e3) = all_6_2
% 204.64/35.37    (67)   ~ (all_52_27 = all_14_2)
% 204.64/35.37    (68)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.37    (69)  all_56_14 = all_52_23
% 204.64/35.37    (70)  all_56_3 = all_52_25
% 204.64/35.37    (71)  all_58_5 = all_52_19
% 204.64/35.38    (72)   ~ (all_52_15 = all_4_2)
% 204.64/35.38    (73)  all_58_6 = all_52_5
% 204.64/35.38    (74)   ~ (all_52_17 = all_6_2)
% 204.64/35.38    (75)   ~ (e1 = e0)
% 204.64/35.38    (76)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.38    (77)  op(all_14_2, all_14_2) = e0
% 204.64/35.38    (78)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.38    (79)  all_58_12 = e3
% 204.64/35.38    (80)  op(e1, e1) = all_10_2
% 204.64/35.38    (81)  all_58_3 = all_4_2
% 204.64/35.38    (82)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.38    (83)   ~ (all_52_19 = all_4_2)
% 204.64/35.38    (84)   ~ (all_52_17 = all_52_23)
% 204.64/35.38    (85)  op(all_6_2, e3) = all_6_1
% 204.64/35.38    (86)  all_58_4 = all_52_17
% 204.64/35.38    (87)   ~ (all_14_2 = e3)
% 204.64/35.38  
% 204.64/35.38  Begin of proof
% 204.64/35.38  | 
% 204.64/35.38  | BETA: splitting (76) gives:
% 204.64/35.38  | 
% 204.64/35.38  | Case 1:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (88)  all_58_10 = e3
% 204.64/35.38  | | 
% 204.64/35.38  | | COMBINE_EQS: (31), (88) imply:
% 204.64/35.38  | |   (89)  all_52_27 = e3
% 204.64/35.38  | | 
% 204.64/35.38  | | SIMP: (89) implies:
% 204.64/35.38  | |   (90)  all_52_27 = e3
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (2), (90) imply:
% 204.64/35.38  | |   (91)   ~ (all_52_25 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (13), (90) imply:
% 204.64/35.38  | |   (92)   ~ (all_52_29 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (67), (90) imply:
% 204.64/35.38  | |   (93)   ~ (all_14_2 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (53), (90) imply:
% 204.64/35.38  | |   (94)  op(e3, e3) = e2
% 204.64/35.38  | | 
% 204.64/35.38  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 204.64/35.38  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.64/35.38  | |            (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37),
% 204.64/35.38  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.64/35.38  | |            (49), (50), (51), (52), (54), (55), (57), (58), (59), (60), (61),
% 204.64/35.38  | |            (62), (63), (64), (65), (66), (68), (69), (70), (71), (72), (73),
% 204.64/35.38  | |            (74), (75), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 204.64/35.38  | |            (86), (87), (91), (94) are inconsistent by sub-proof #1018.
% 204.64/35.38  | | 
% 204.64/35.38  | Case 2:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (95)  all_58_11 = e3 | all_58_15 = e3
% 204.64/35.38  | | 
% 204.64/35.38  | | REF_CLOSE: (19), (43), (56), (87), (95) are inconsistent by sub-proof #1103.
% 204.64/35.38  | | 
% 204.64/35.38  | End of split
% 204.64/35.38  | 
% 204.64/35.38  End of proof
% 204.64/35.38  
% 204.64/35.38  Sub-proof #1018 shows that the following formulas are inconsistent:
% 204.64/35.38  ----------------------------------------------------------------
% 204.64/35.38    (1)   ~ (all_52_15 = all_52_23)
% 204.64/35.38    (2)  all_58_14 = all_52_23
% 204.64/35.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.38    (4)  all_58_1 = all_52_9
% 204.64/35.38    (5)   ~ (all_52_9 = all_52_13)
% 204.64/35.38    (6)   ~ (e3 = e0)
% 204.64/35.38    (7)  op(e2, e3) = all_52_3
% 204.64/35.38    (8)   ~ (all_52_17 = all_52_25)
% 204.64/35.38    (9)  all_58_0 = all_6_2
% 204.64/35.38    (10)   ~ (all_52_17 = all_10_2)
% 204.64/35.38    (11)  op(all_52_19, all_52_19) = all_52_18
% 204.64/35.38    (12)  all_58_13 = all_52_15
% 204.64/35.38    (13)  all_58_9 = all_52_25
% 204.64/35.38    (14)   ~ (all_52_29 = all_14_2)
% 204.64/35.38    (15)  op(e2, e2) = all_4_2
% 204.64/35.38    (16)   ~ (all_52_3 = all_52_5)
% 204.64/35.38    (17)  all_58_11 = all_52_29
% 204.64/35.38    (18)  all_56_5 = all_4_2
% 204.64/35.38    (19)   ~ (all_52_25 = all_14_2)
% 204.64/35.38    (20)  op(all_10_2, e1) = all_10_1
% 204.64/35.38    (21)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.38    (22)  op(e0, e0) = all_14_2
% 204.64/35.38    (23)  all_56_15 = all_14_2
% 204.64/35.38    (24)  op(e3, e3) = e2
% 204.64/35.38    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.38    (26)  all_56_11 = all_52_29
% 204.64/35.38    (27)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.38    (28)   ~ (all_6_2 = e3)
% 204.64/35.38    (29)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.64/35.38    (30)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.38    (31)  all_56_8 = all_52_5
% 204.64/35.38    (32)   ~ (all_52_25 = all_52_29)
% 204.64/35.38    (33)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.38    (34)   ~ (all_52_29 = all_10_2)
% 204.64/35.38    (35)  all_58_7 = all_52_13
% 204.64/35.38    (36)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.64/35.38    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.38    (38)   ~ (all_14_2 = e0)
% 204.64/35.38    (39)  all_58_2 = all_52_3
% 204.64/35.38    (40)  all_56_2 = all_52_17
% 204.64/35.38    (41)   ~ (all_52_29 = e3)
% 204.64/35.38    (42)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.38    (43)   ~ (all_52_25 = e3)
% 204.64/35.38    (44)   ~ (e2 = e0)
% 204.64/35.38    (45)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.64/35.38    (46)   ~ (all_52_5 = e3)
% 204.64/35.38    (47)  op(all_52_25, all_52_25) = e3
% 204.64/35.38    (48)   ~ (all_52_5 = all_52_29)
% 204.64/35.38    (49)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.38    (50)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.38    (51)  op(e3, e1) = all_52_17
% 204.64/35.38    (52)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.64/35.38    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.38    (54)   ~ (all_52_19 = all_10_2)
% 204.64/35.38    (55)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.64/35.38    (56)  all_58_8 = all_10_2
% 204.64/35.38    (57)   ~ (all_52_23 = all_14_2)
% 204.64/35.38    (58)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 204.64/35.38    (59)   ~ (all_52_25 = all_6_2)
% 204.64/35.38    (60)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.38    (61)   ~ (all_52_9 = all_4_2)
% 204.64/35.38    (62)   ~ (all_52_5 = all_6_2)
% 204.64/35.38    (63)  op(e3, e3) = all_6_2
% 204.64/35.38    (64)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.38    (65)  all_56_14 = all_52_23
% 204.64/35.38    (66)  all_56_3 = all_52_25
% 204.64/35.38    (67)  all_58_5 = all_52_19
% 204.64/35.38    (68)   ~ (all_52_15 = all_4_2)
% 204.64/35.38    (69)  all_58_6 = all_52_5
% 204.64/35.38    (70)   ~ (all_52_17 = all_6_2)
% 204.64/35.38    (71)   ~ (e1 = e0)
% 204.64/35.38    (72)  op(all_14_2, all_14_2) = e0
% 204.64/35.38    (73)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.38    (74)  all_58_12 = e3
% 204.64/35.38    (75)  op(e1, e1) = all_10_2
% 204.64/35.38    (76)  all_58_3 = all_4_2
% 204.64/35.38    (77)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.38    (78)   ~ (all_52_19 = all_4_2)
% 204.64/35.38    (79)   ~ (all_52_17 = all_52_23)
% 204.64/35.38    (80)  op(all_6_2, e3) = all_6_1
% 204.64/35.38    (81)  all_58_4 = all_52_17
% 204.64/35.38    (82)   ~ (all_14_2 = e3)
% 204.64/35.38  
% 204.64/35.38  Begin of proof
% 204.64/35.38  | 
% 204.64/35.38  | GROUND_INST: instantiating (3) with all_6_2, e2, e3, e3, simplifying with
% 204.64/35.38  |              (24), (63) gives:
% 204.64/35.38  |   (83)  all_6_2 = e2
% 204.64/35.38  | 
% 204.64/35.38  | COMBINE_EQS: (9), (83) imply:
% 204.64/35.38  |   (84)  all_58_0 = e2
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (62), (83) imply:
% 204.64/35.38  |   (85)   ~ (all_52_5 = e2)
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (70), (83) imply:
% 204.64/35.38  |   (86)   ~ (all_52_17 = e2)
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (59), (83) imply:
% 204.64/35.38  |   (87)   ~ (all_52_25 = e2)
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (28), (83) imply:
% 204.64/35.38  |   (88)   ~ (e3 = e2)
% 204.64/35.38  | 
% 204.64/35.38  | SIMP: (88) implies:
% 204.64/35.38  |   (89)   ~ (e3 = e2)
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (21), (83) imply:
% 204.64/35.38  |   (90)  op(e2, e2) = all_52_0
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (80), (83) imply:
% 204.64/35.38  |   (91)  op(e2, e3) = all_6_1
% 204.64/35.38  | 
% 204.64/35.38  | GROUND_INST: instantiating (3) with all_4_2, all_52_0, e2, e2, simplifying
% 204.64/35.38  |              with (15), (90) gives:
% 204.64/35.38  |   (92)  all_52_0 = all_4_2
% 204.64/35.38  | 
% 204.64/35.38  | GROUND_INST: instantiating (3) with all_52_3, all_6_1, e3, e2, simplifying
% 204.64/35.38  |              with (7), (91) gives:
% 204.64/35.38  |   (93)  all_52_3 = all_6_1
% 204.64/35.38  | 
% 204.64/35.38  | COMBINE_EQS: (39), (93) imply:
% 204.64/35.38  |   (94)  all_58_2 = all_6_1
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (16), (93) imply:
% 204.64/35.38  |   (95)   ~ (all_52_5 = all_6_1)
% 204.64/35.38  | 
% 204.64/35.38  | SIMP: (95) implies:
% 204.64/35.38  |   (96)   ~ (all_52_5 = all_6_1)
% 204.64/35.38  | 
% 204.64/35.38  | BETA: splitting (53) gives:
% 204.64/35.38  | 
% 204.64/35.38  | Case 1:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (97)  all_58_1 = e3
% 204.64/35.38  | | 
% 204.64/35.38  | | COMBINE_EQS: (4), (97) imply:
% 204.64/35.38  | |   (98)  all_52_9 = e3
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (5), (98) imply:
% 204.64/35.38  | |   (99)   ~ (all_52_13 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | SIMP: (99) implies:
% 204.64/35.38  | |   (100)   ~ (all_52_13 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (61), (98) imply:
% 204.64/35.38  | |   (101)   ~ (all_4_2 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | SIMP: (101) implies:
% 204.64/35.38  | |   (102)   ~ (all_4_2 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | BETA: splitting (37) gives:
% 204.64/35.38  | | 
% 204.64/35.38  | | Case 1:
% 204.64/35.38  | | | 
% 204.64/35.38  | | |   (103)  all_58_6 = e3
% 204.64/35.38  | | | 
% 204.64/35.38  | | | REF_CLOSE: (46), (69), (103) are inconsistent by sub-proof #1328.
% 204.64/35.38  | | | 
% 204.64/35.38  | | Case 2:
% 204.64/35.38  | | | 
% 204.64/35.38  | | |   (104)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.38  | | | 
% 204.64/35.38  | | | BETA: splitting (104) gives:
% 204.64/35.38  | | | 
% 204.64/35.38  | | | Case 1:
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | |   (105)  all_58_7 = e3
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | | COMBINE_EQS: (35), (105) imply:
% 204.64/35.38  | | | |   (106)  all_52_13 = e3
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | | REDUCE: (100), (106) imply:
% 204.64/35.38  | | | |   (107)  $false
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | | CLOSE: (107) is inconsistent.
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | Case 2:
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | |   (108)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | | BETA: splitting (108) gives:
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | | Case 1:
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | |   (109)  all_58_8 = e3
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | COMBINE_EQS: (56), (109) imply:
% 204.64/35.38  | | | | |   (110)  all_10_2 = e3
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | SIMP: (110) implies:
% 204.64/35.38  | | | | |   (111)  all_10_2 = e3
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (10), (111) imply:
% 204.64/35.38  | | | | |   (112)   ~ (all_52_17 = e3)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (54), (111) imply:
% 204.64/35.38  | | | | |   (113)   ~ (all_52_19 = e3)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (20), (111) imply:
% 204.64/35.38  | | | | |   (114)  op(e3, e1) = all_10_1
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 204.64/35.38  | | | | |              simplifying with (51), (114) gives:
% 204.64/35.38  | | | | |   (115)  all_52_17 = all_10_1
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | COMBINE_EQS: (40), (115) imply:
% 204.64/35.38  | | | | |   (116)  all_56_2 = all_10_1
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | COMBINE_EQS: (81), (115) imply:
% 204.64/35.38  | | | | |   (117)  all_58_4 = all_10_1
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (79), (115) imply:
% 204.64/35.38  | | | | |   (118)   ~ (all_52_23 = all_10_1)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | SIMP: (118) implies:
% 204.64/35.38  | | | | |   (119)   ~ (all_52_23 = all_10_1)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (8), (115) imply:
% 204.64/35.38  | | | | |   (120)   ~ (all_52_25 = all_10_1)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | SIMP: (120) implies:
% 204.64/35.38  | | | | |   (121)   ~ (all_52_25 = all_10_1)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (112), (115) imply:
% 204.64/35.38  | | | | |   (122)   ~ (all_10_1 = e3)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REDUCE: (86), (115) imply:
% 204.64/35.38  | | | | |   (123)   ~ (all_10_1 = e2)
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | BETA: splitting (27) gives:
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | Case 1:
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | |   (124)  all_56_2 = e3
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | | REF_CLOSE: (116), (122), (124) are inconsistent by sub-proof #1029.
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | Case 2:
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | |   (125)   ~ (all_56_2 = e3)
% 204.64/35.38  | | | | | |   (126)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | | BETA: splitting (52) gives:
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | | Case 1:
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | |   (127)  all_58_4 = e2
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | | COMBINE_EQS: (117), (127) imply:
% 204.64/35.38  | | | | | | |   (128)  all_10_1 = e2
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | | REDUCE: (123), (128) imply:
% 204.64/35.38  | | | | | | |   (129)  $false
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | | CLOSE: (129) is inconsistent.
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | Case 2:
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | |   (130)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | | BETA: splitting (49) gives:
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | |   (131)  all_56_11 = e3
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | | REF_CLOSE: (26), (41), (131) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | |            #1028.
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | |   (132)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | | BETA: splitting (45) gives:
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | |   (133)  all_56_5 = e3
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | REF_CLOSE: (18), (102), (133) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | |            #1319.
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | |   (134)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | BETA: splitting (42) gives:
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | |   (135)  all_58_0 = e0
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | COMBINE_EQS: (84), (135) imply:
% 204.64/35.38  | | | | | | | | | |   (136)  e2 = e0
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | REDUCE: (44), (136) imply:
% 204.64/35.38  | | | | | | | | | |   (137)  $false
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | CLOSE: (137) is inconsistent.
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | |   (138)   ~ (all_58_0 = e0)
% 204.64/35.38  | | | | | | | | | |   (139)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | BETA: splitting (25) gives:
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | |   (140)  all_58_9 = e1
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | COMBINE_EQS: (13), (140) imply:
% 204.64/35.38  | | | | | | | | | | |   (141)  all_52_25 = e1
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | REDUCE: (32), (141) imply:
% 204.64/35.38  | | | | | | | | | | |   (142)   ~ (all_52_29 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | SIMP: (142) implies:
% 204.64/35.38  | | | | | | | | | | |   (143)   ~ (all_52_29 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | REDUCE: (19), (141) imply:
% 204.64/35.38  | | | | | | | | | | |   (144)   ~ (all_14_2 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | SIMP: (144) implies:
% 204.64/35.38  | | | | | | | | | | |   (145)   ~ (all_14_2 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | REDUCE: (121), (141) imply:
% 204.64/35.38  | | | | | | | | | | |   (146)   ~ (all_10_1 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | SIMP: (146) implies:
% 204.64/35.38  | | | | | | | | | | |   (147)   ~ (all_10_1 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | BETA: splitting (126) gives:
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | |   (148)  all_56_2 = e2
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | COMBINE_EQS: (116), (148) imply:
% 204.64/35.38  | | | | | | | | | | | |   (149)  all_10_1 = e2
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | SIMP: (149) implies:
% 204.64/35.38  | | | | | | | | | | | |   (150)  all_10_1 = e2
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | COMBINE_EQS: (117), (150) imply:
% 204.64/35.38  | | | | | | | | | | | |   (151)  all_58_4 = e2
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | REF_CLOSE: (6), (44), (71), (97), (139), (140), (151) are
% 204.64/35.38  | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | |   (152)  all_56_2 = e1 | all_56_2 = e0
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | BETA: splitting (152) gives:
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | |   (153)  all_56_2 = e1
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | REF_CLOSE: (116), (147), (153) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | |            #1025.
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | |   (154)  all_56_2 = e0
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | COMBINE_EQS: (116), (154) imply:
% 204.64/35.38  | | | | | | | | | | | | |   (155)  all_10_1 = e0
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | SIMP: (155) implies:
% 204.64/35.38  | | | | | | | | | | | | |   (156)  all_10_1 = e0
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | REDUCE: (119), (156) imply:
% 204.64/35.38  | | | | | | | | | | | | |   (157)   ~ (all_52_23 = e0)
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | REDUCE: (122), (156) imply:
% 204.64/35.38  | | | | | | | | | | | | |   (158)   ~ (e3 = e0)
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | BETA: splitting (50) gives:
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | |   (159)  all_58_12 = e0
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | COMBINE_EQS: (74), (159) imply:
% 204.64/35.38  | | | | | | | | | | | | | |   (160)  e3 = e0
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | REDUCE: (6), (160) imply:
% 204.64/35.38  | | | | | | | | | | | | | |   (161)  $false
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | |   (162)  all_58_13 = e0 | all_58_14 = e0
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | |   (163)  all_56_15 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | COMBINE_EQS: (23), (163) imply:
% 204.64/35.38  | | | | | | | | | | | | | | |   (164)  all_14_2 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | SIMP: (164) implies:
% 204.64/35.38  | | | | | | | | | | | | | | |   (165)  all_14_2 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | REDUCE: (57), (165) imply:
% 204.64/35.38  | | | | | | | | | | | | | | |   (166)   ~ (all_52_23 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | REDUCE: (14), (165) imply:
% 204.64/35.38  | | | | | | | | | | | | | | |   (167)   ~ (all_52_29 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | REDUCE: (72), (165) imply:
% 204.64/35.38  | | | | | | | | | | | | | | |   (168)  op(e2, e2) = e0
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | |   (169)  all_58_13 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (169) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | |   (170)  all_52_15 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | SIMP: (170) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | |   (171)  all_52_15 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | REDUCE: (1), (171) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | |   (172)   ~ (all_52_23 = e0)
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | REDUCE: (68), (171) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | |   (173)   ~ (all_4_2 = e0)
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | |   (174)   ~ (all_4_2 = e0)
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (175)  all_58_5 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (175) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (176)  all_52_19 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (177)  all_52_19 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | REDUCE: (78), (177) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (178)   ~ (all_4_2 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (179)   ~ (all_4_2 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | REDUCE: (11), (177) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (180)  op(e2, e2) = all_52_18
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | |   (181)  all_56_11 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (167), (181) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | | | |            #1024.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | |   (182)   ~ (all_56_11 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | | | |   (183)  all_56_11 = e1 | all_56_11 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (184)  all_56_11 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (143), (184) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |            #1023.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (185)  all_56_11 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (185) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (186)  all_52_29 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | SIMP: (186) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (187)  all_52_29 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | REDUCE: (48), (187) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (188)   ~ (all_52_5 = e0)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | REDUCE: (167), (187) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (189)   ~ (e2 = e0)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (190)  all_58_1 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (190) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (191)  e3 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (191) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (192)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (193)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | |   (194)  all_58_3 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (194) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | |   (195)  all_4_2 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | SIMP: (195) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | |   (196)  all_4_2 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (196) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | |   (197)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | |   (198)   ~ (all_58_3 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | |   (199)  all_58_7 = e2 | all_58_13 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_5 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (179), (200) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | |            #1315.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | |   (201)  all_56_5 = e1 | all_56_5 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_56_8 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (85), (202) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | |            #1022.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_56_8 = e1 | all_56_8 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_58_6 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (204) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_52_5 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_52_5 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (206) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (207)   ~ (all_6_1 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (208)   ~ (all_6_1 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_58_2 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (209) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_6_1 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (210) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_58_3 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (213) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_4_2 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_4_2 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (215) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  op(e2, e2) = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_58_7 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (217) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_52_13 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (218) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_52_13 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (219) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  op(e2, e2) = all_52_12
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_18, e2, e2,
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (180), (216) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_52_18 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_18, all_52_12, e2,
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (180), (220) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_52_12 = all_52_18
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_52_12, e2, e2,
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (168), (220) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_52_12 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (222), (223) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  all_52_18 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (224) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_52_18 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (225) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  e1 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (226) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_58_13 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (228) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  e2 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (229) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)   ~ (all_58_3 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (231) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)   ~ (all_4_2 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (174), (201), (232) are inconsistent by
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1021.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (233)   ~ (all_58_6 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (233) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |   (234)   ~ (all_52_5 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (188), (203), (234) are inconsistent by
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1020.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | |   (235)  all_58_8 = e2 | all_58_14 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | |   (236)  all_56_14 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (166), (236) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | | | |            #1285.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | |   (237)   ~ (all_56_14 = e2)
% 204.64/35.38  | | | | | | | | | | | | | | | | | |   (238)  all_56_14 = e1 | all_56_14 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (239)  all_56_14 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (239) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (240)  all_52_23 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | SIMP: (240) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (241)  all_52_23 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (241) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (242)  all_58_14 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | REDUCE: (166), (241) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (243)   ~ (e2 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | SIMP: (243) implies:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (244)   ~ (e2 = e1)
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (245)  all_58_8 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (245) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (246)  e3 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (246) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (247)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (248)  all_58_14 = e2
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (248) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (249)  e2 = e1
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (244), (249) imply:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | |   (250)  $false
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |   (251)  all_56_14 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (157), (251) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | | | | |            #1382.
% 204.64/35.38  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | |   (252)  all_58_14 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (157), (252) are inconsistent by sub-proof
% 204.64/35.38  | | | | | | | | | | | | | | | |            #1019.
% 204.64/35.38  | | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | |   (253)  all_56_15 = e1 | all_56_15 = e0
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | | REF_CLOSE: (23), (38), (145), (253) are inconsistent by
% 204.64/35.38  | | | | | | | | | | | | | | |            sub-proof #1161.
% 204.64/35.38  | | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | Case 2:
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | |   (254)   ~ (all_58_9 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | REDUCE: (13), (254) imply:
% 204.64/35.38  | | | | | | | | | | |   (255)   ~ (all_52_25 = e1)
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | | REF_CLOSE: (3), (22), (33), (47), (66), (82), (87), (255) are
% 204.64/35.38  | | | | | | | | | | |            inconsistent by sub-proof #1233.
% 204.64/35.38  | | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | | 
% 204.64/35.38  | | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | | 
% 204.64/35.38  | | | | | | | | End of split
% 204.64/35.38  | | | | | | | | 
% 204.64/35.38  | | | | | | | End of split
% 204.64/35.38  | | | | | | | 
% 204.64/35.38  | | | | | | End of split
% 204.64/35.38  | | | | | | 
% 204.64/35.38  | | | | | End of split
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | Case 2:
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | |   (256)  all_58_11 = e3
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | | REF_CLOSE: (17), (41), (256) are inconsistent by sub-proof #1323.
% 204.64/35.38  | | | | | 
% 204.64/35.38  | | | | End of split
% 204.64/35.38  | | | | 
% 204.64/35.38  | | | End of split
% 204.64/35.38  | | | 
% 204.64/35.38  | | End of split
% 204.64/35.38  | | 
% 204.64/35.38  | Case 2:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (257)   ~ (all_58_1 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (4), (257) imply:
% 204.64/35.38  | |   (258)   ~ (all_52_9 = e3)
% 204.64/35.38  | | 
% 204.64/35.38  | | REF_CLOSE: (3), (4), (8), (10), (13), (22), (25), (43), (47), (60), (64),
% 204.64/35.38  | |            (66), (75), (81), (82), (84), (87), (89), (258) are inconsistent
% 204.64/35.38  | |            by sub-proof #1229.
% 204.64/35.38  | | 
% 204.64/35.38  | End of split
% 204.64/35.38  | 
% 204.64/35.38  End of proof
% 204.64/35.38  
% 204.64/35.38  Sub-proof #1019 shows that the following formulas are inconsistent:
% 204.64/35.38  ----------------------------------------------------------------
% 204.64/35.38    (1)  all_58_14 = all_52_23
% 204.64/35.38    (2)  all_58_14 = e0
% 204.64/35.38    (3)   ~ (all_52_23 = e0)
% 204.64/35.38  
% 204.64/35.38  Begin of proof
% 204.64/35.38  | 
% 204.64/35.38  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.38  |   (4)  all_52_23 = e0
% 204.64/35.38  | 
% 204.64/35.38  | SIMP: (4) implies:
% 204.64/35.38  |   (5)  all_52_23 = e0
% 204.64/35.38  | 
% 204.64/35.38  | REDUCE: (3), (5) imply:
% 204.64/35.38  |   (6)  $false
% 204.64/35.38  | 
% 204.64/35.38  | CLOSE: (6) is inconsistent.
% 204.64/35.38  | 
% 204.64/35.38  End of proof
% 204.64/35.38  
% 204.64/35.38  Sub-proof #1020 shows that the following formulas are inconsistent:
% 204.64/35.38  ----------------------------------------------------------------
% 204.64/35.38    (1)  all_56_8 = e1 | all_56_8 = e0
% 204.64/35.38    (2)  all_56_8 = all_52_5
% 204.64/35.38    (3)   ~ (all_52_5 = e1)
% 204.64/35.38    (4)   ~ (all_52_5 = e0)
% 204.64/35.38  
% 204.64/35.38  Begin of proof
% 204.64/35.38  | 
% 204.64/35.38  | BETA: splitting (1) gives:
% 204.64/35.38  | 
% 204.64/35.38  | Case 1:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (5)  all_56_8 = e1
% 204.64/35.38  | | 
% 204.64/35.38  | | COMBINE_EQS: (2), (5) imply:
% 204.64/35.38  | |   (6)  all_52_5 = e1
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (3), (6) imply:
% 204.64/35.38  | |   (7)  $false
% 204.64/35.38  | | 
% 204.64/35.38  | | CLOSE: (7) is inconsistent.
% 204.64/35.38  | | 
% 204.64/35.38  | Case 2:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (8)  all_56_8 = e0
% 204.64/35.38  | | 
% 204.64/35.38  | | COMBINE_EQS: (2), (8) imply:
% 204.64/35.38  | |   (9)  all_52_5 = e0
% 204.64/35.38  | | 
% 204.64/35.38  | | REDUCE: (4), (9) imply:
% 204.64/35.38  | |   (10)  $false
% 204.64/35.38  | | 
% 204.64/35.38  | | CLOSE: (10) is inconsistent.
% 204.64/35.38  | | 
% 204.64/35.38  | End of split
% 204.64/35.38  | 
% 204.64/35.38  End of proof
% 204.64/35.38  
% 204.64/35.38  Sub-proof #1021 shows that the following formulas are inconsistent:
% 204.64/35.38  ----------------------------------------------------------------
% 204.64/35.38    (1)  all_56_5 = e1 | all_56_5 = e0
% 204.64/35.38    (2)  all_56_5 = all_4_2
% 204.64/35.38    (3)   ~ (all_4_2 = e1)
% 204.64/35.38    (4)   ~ (all_4_2 = e0)
% 204.64/35.38  
% 204.64/35.38  Begin of proof
% 204.64/35.38  | 
% 204.64/35.38  | BETA: splitting (1) gives:
% 204.64/35.38  | 
% 204.64/35.38  | Case 1:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (5)  all_56_5 = e1
% 204.64/35.38  | | 
% 204.64/35.38  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1188.
% 204.64/35.38  | | 
% 204.64/35.38  | Case 2:
% 204.64/35.38  | | 
% 204.64/35.38  | |   (6)  all_56_5 = e0
% 204.64/35.38  | | 
% 204.64/35.39  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1313.
% 204.64/35.39  | | 
% 204.64/35.39  | End of split
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1022 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_56_8 = all_52_5
% 204.64/35.39    (2)  all_56_8 = e2
% 204.64/35.39    (3)   ~ (all_52_5 = e2)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.39  |   (4)  all_52_5 = e2
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (4) implies:
% 204.64/35.39  |   (5)  all_52_5 = e2
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (3), (5) imply:
% 204.64/35.39  |   (6)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (6) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1023 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_56_11 = all_52_29
% 204.64/35.39    (2)  all_56_11 = e1
% 204.64/35.39    (3)   ~ (all_52_29 = e1)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.39  |   (4)  all_52_29 = e1
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (4) implies:
% 204.64/35.39  |   (5)  all_52_29 = e1
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (3), (5) imply:
% 204.64/35.39  |   (6)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (6) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1024 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_56_11 = all_52_29
% 204.64/35.39    (2)  all_56_11 = e2
% 204.64/35.39    (3)   ~ (all_52_29 = e2)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.39  |   (4)  all_52_29 = e2
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (4) implies:
% 204.64/35.39  |   (5)  all_52_29 = e2
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (3), (5) imply:
% 204.64/35.39  |   (6)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (6) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1025 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_56_2 = all_10_1
% 204.64/35.39    (2)  all_56_2 = e1
% 204.64/35.39    (3)   ~ (all_10_1 = e1)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.39  |   (4)  all_10_1 = e1
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (4) implies:
% 204.64/35.39  |   (5)  all_10_1 = e1
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (3), (5) imply:
% 204.64/35.39  |   (6)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (6) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1026 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ~ (e3 = e0)
% 204.64/35.39    (2)  all_58_4 = e2
% 204.64/35.39    (3)  all_58_9 = e1
% 204.64/35.39    (4)  all_58_1 = e3
% 204.64/35.39    (5)   ~ (e2 = e0)
% 204.64/35.39    (6)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.39    (7)   ~ (e1 = e0)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | BETA: splitting (6) gives:
% 204.64/35.39  | 
% 204.64/35.39  | Case 1:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (8)  all_58_1 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | COMBINE_EQS: (4), (8) imply:
% 204.64/35.39  | |   (9)  e3 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | REDUCE: (1), (9) imply:
% 204.64/35.39  | |   (10)  $false
% 204.64/35.39  | | 
% 204.64/35.39  | | CLOSE: (10) is inconsistent.
% 204.64/35.39  | | 
% 204.64/35.39  | Case 2:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (11)  all_58_4 = e0 | all_58_9 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | REF_CLOSE: (2), (3), (5), (7), (11) are inconsistent by sub-proof #1027.
% 204.64/35.39  | | 
% 204.64/35.39  | End of split
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1027 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_58_4 = e2
% 204.64/35.39    (2)  all_58_9 = e1
% 204.64/35.39    (3)  all_58_4 = e0 | all_58_9 = e0
% 204.64/35.39    (4)   ~ (e2 = e0)
% 204.64/35.39    (5)   ~ (e1 = e0)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | BETA: splitting (3) gives:
% 204.64/35.39  | 
% 204.64/35.39  | Case 1:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (6)  all_58_4 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | COMBINE_EQS: (1), (6) imply:
% 204.64/35.39  | |   (7)  e2 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | REDUCE: (4), (7) imply:
% 204.64/35.39  | |   (8)  $false
% 204.64/35.39  | | 
% 204.64/35.39  | | CLOSE: (8) is inconsistent.
% 204.64/35.39  | | 
% 204.64/35.39  | Case 2:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (9)  all_58_9 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | COMBINE_EQS: (2), (9) imply:
% 204.64/35.39  | |   (10)  e1 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | REDUCE: (5), (10) imply:
% 204.64/35.39  | |   (11)  $false
% 204.64/35.39  | | 
% 204.64/35.39  | | CLOSE: (11) is inconsistent.
% 204.64/35.39  | | 
% 204.64/35.39  | End of split
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1028 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_56_11 = all_52_29
% 204.64/35.39    (2)  all_56_11 = e3
% 204.64/35.39    (3)   ~ (all_52_29 = e3)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.39  |   (4)  all_52_29 = e3
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (4) implies:
% 204.64/35.39  |   (5)  all_52_29 = e3
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (3), (5) imply:
% 204.64/35.39  |   (6)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (6) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1029 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)  all_56_2 = all_10_1
% 204.64/35.39    (2)  all_56_2 = e3
% 204.64/35.39    (3)   ~ (all_10_1 = e3)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.39  |   (4)  all_10_1 = e3
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (4) implies:
% 204.64/35.39  |   (5)  all_10_1 = e3
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (3), (5) imply:
% 204.64/35.39  |   (6)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (6) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1030 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.39    (2)  op(e0, e0) = all_14_2
% 204.64/35.39    (3)  op(e0, e0) = e3
% 204.64/35.39    (4)  op(e0, e0) = all_52_2
% 204.64/35.39    (5)   ~ (all_14_2 = e3)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | GROUND_INST: instantiating (1) with all_14_2, all_52_2, e0, e0, simplifying
% 204.64/35.39  |              with (2), (4) gives:
% 204.64/35.39  |   (6)  all_52_2 = all_14_2
% 204.64/35.39  | 
% 204.64/35.39  | GROUND_INST: instantiating (1) with e3, all_52_2, e0, e0, simplifying with
% 204.64/35.39  |              (3), (4) gives:
% 204.64/35.39  |   (7)  all_52_2 = e3
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (6), (7) imply:
% 204.64/35.39  |   (8)  all_14_2 = e3
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (8) implies:
% 204.64/35.39  |   (9)  all_14_2 = e3
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (5), (9) imply:
% 204.64/35.39  |   (10)  $false
% 204.64/35.39  | 
% 204.64/35.39  | CLOSE: (10) is inconsistent.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1031 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.39    (2)  all_56_8 = all_6_1
% 204.64/35.39    (3)  op(e3, e0) = all_52_25
% 204.64/35.39    (4)   ~ (all_6_1 = e1)
% 204.64/35.39    (5)  op(e0, e0) = all_14_2
% 204.64/35.39    (6)   ~ (all_6_2 = e3)
% 204.64/35.39    (7)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.39    (8)  op(e3, all_6_1) = all_6_0
% 204.64/35.39    (9)  op(all_52_25, all_52_25) = e3
% 204.64/35.39    (10)   ~ (all_6_0 = e2)
% 204.64/35.39    (11)   ~ (all_52_25 = e1)
% 204.64/35.39    (12)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.39    (13)  op(e3, e3) = all_6_2
% 204.64/35.39    (14)  all_56_3 = all_52_25
% 204.64/35.39    (15)   ~ (all_6_1 = e2)
% 204.64/35.39    (16)  op(all_6_1, all_6_1) = all_52_4
% 204.64/35.39    (17)   ~ (all_14_2 = e3)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | BETA: splitting (7) gives:
% 204.64/35.39  | 
% 204.64/35.39  | Case 1:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (18)  all_56_8 = e2
% 204.64/35.39  | | 
% 204.64/35.39  | | REF_CLOSE: (2), (15), (18) are inconsistent by sub-proof #1321.
% 204.64/35.39  | | 
% 204.64/35.39  | Case 2:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (19)  all_56_8 = e1 | all_56_8 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | BETA: splitting (19) gives:
% 204.64/35.39  | | 
% 204.64/35.39  | | Case 1:
% 204.64/35.39  | | | 
% 204.64/35.39  | | |   (20)  all_56_8 = e1
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REF_CLOSE: (2), (4), (20) are inconsistent by sub-proof #1320.
% 204.64/35.39  | | | 
% 204.64/35.39  | | Case 2:
% 204.64/35.39  | | | 
% 204.64/35.39  | | |   (21)  all_56_8 = e0
% 204.64/35.39  | | | 
% 204.64/35.39  | | | COMBINE_EQS: (2), (21) imply:
% 204.64/35.39  | | |   (22)  all_6_1 = e0
% 204.64/35.39  | | | 
% 204.64/35.39  | | | SIMP: (22) implies:
% 204.64/35.39  | | |   (23)  all_6_1 = e0
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REDUCE: (16), (23) imply:
% 204.64/35.39  | | |   (24)  op(e0, e0) = all_52_4
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REDUCE: (8), (23) imply:
% 204.64/35.39  | | |   (25)  op(e3, e0) = all_6_0
% 204.64/35.39  | | | 
% 204.64/35.39  | | | GROUND_INST: instantiating (1) with all_14_2, all_52_4, e0, e0,
% 204.64/35.39  | | |              simplifying with (5), (24) gives:
% 204.64/35.39  | | |   (26)  all_52_4 = all_14_2
% 204.64/35.39  | | | 
% 204.64/35.39  | | | GROUND_INST: instantiating (1) with all_52_25, all_6_0, e0, e3,
% 204.64/35.39  | | |              simplifying with (3), (25) gives:
% 204.64/35.39  | | |   (27)  all_52_25 = all_6_0
% 204.64/35.39  | | | 
% 204.64/35.39  | | | COMBINE_EQS: (14), (27) imply:
% 204.64/35.39  | | |   (28)  all_56_3 = all_6_0
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REDUCE: (9), (27) imply:
% 204.64/35.39  | | |   (29)  op(all_6_0, all_6_0) = e3
% 204.64/35.39  | | | 
% 204.64/35.39  | | | BETA: splitting (12) gives:
% 204.64/35.39  | | | 
% 204.64/35.39  | | | Case 1:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | |   (30)  all_56_3 = e3
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REF_CLOSE: (1), (6), (13), (28), (29), (30) are inconsistent by
% 204.64/35.39  | | | |            sub-proof #1032.
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | Case 2:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | |   (31)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | BETA: splitting (31) gives:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | Case 1:
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | |   (32)  all_56_3 = e2
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | REF_CLOSE: (10), (28), (32) are inconsistent by sub-proof #1075.
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | Case 2:
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | |   (33)  all_56_3 = e1 | all_56_3 = e0
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | REF_CLOSE: (1), (5), (9), (11), (14), (17), (33) are inconsistent by
% 204.64/35.39  | | | | |            sub-proof #1234.
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | End of split
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | End of split
% 204.64/35.39  | | | 
% 204.64/35.39  | | End of split
% 204.64/35.39  | | 
% 204.64/35.39  | End of split
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1032 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.39    (2)  all_56_3 = e3
% 204.64/35.39    (3)   ~ (all_6_2 = e3)
% 204.64/35.39    (4)  all_56_3 = all_6_0
% 204.64/35.39    (5)  op(e3, e3) = all_6_2
% 204.64/35.39    (6)  op(all_6_0, all_6_0) = e3
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | COMBINE_EQS: (2), (4) imply:
% 204.64/35.39  |   (7)  all_6_0 = e3
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (7) implies:
% 204.64/35.39  |   (8)  all_6_0 = e3
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (6), (8) imply:
% 204.64/35.39  |   (9)  op(e3, e3) = e3
% 204.64/35.39  | 
% 204.64/35.39  | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1338.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1033 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.39    (2)   ~ (e3 = e1)
% 204.64/35.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.39    (4)  all_58_1 = all_52_9
% 204.64/35.39    (5)   ~ (all_52_7 = all_52_15)
% 204.64/35.39    (6)   ~ (all_52_17 = all_52_25)
% 204.64/35.39    (7)   ~ (all_52_3 = all_6_2)
% 204.64/35.39    (8)  all_58_0 = all_6_2
% 204.64/35.39    (9)   ~ (all_52_17 = all_10_2)
% 204.64/35.39    (10)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.39    (11)  all_58_9 = all_52_25
% 204.64/35.39    (12)  op(e2, e2) = all_4_2
% 204.64/35.39    (13)   ~ (all_52_3 = all_52_5)
% 204.64/35.39    (14)  all_58_11 = all_52_29
% 204.64/35.39    (15)   ~ (all_52_9 = all_52_15)
% 204.64/35.39    (16)   ~ (all_52_3 = all_52_27)
% 204.64/35.39    (17)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.39    (18)  op(e0, e0) = all_14_2
% 204.64/35.39    (19)  all_52_15 = e3
% 204.64/35.39    (20)  op(all_52_29, all_52_29) = e1
% 204.64/35.39    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.39    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.39    (23)  all_56_11 = all_52_29
% 204.64/35.39    (24)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.39    (25)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.64/35.39    (26)   ~ (all_6_0 = e1)
% 204.64/35.39    (27)  all_58_10 = all_52_27
% 204.64/35.39    (28)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.39    (29)  op(all_52_15, all_52_15) = all_52_14
% 204.64/35.39    (30)   ~ (all_52_25 = all_52_29)
% 204.64/35.39    (31)  all_58_7 = all_52_13
% 204.64/35.39    (32)  all_58_12 = all_52_7
% 204.64/35.39    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.39    (34)  all_58_2 = all_52_3
% 204.64/35.39    (35)  all_56_2 = all_52_17
% 204.64/35.39    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.39    (37)  op(e3, all_6_1) = all_6_0
% 204.64/35.39    (38)  op(all_52_25, all_52_25) = e3
% 204.64/35.39    (39)   ~ (all_52_5 = all_52_29)
% 204.64/35.39    (40)   ~ (all_52_15 = all_14_2)
% 204.64/35.39    (41)   ~ (all_52_19 = all_52_27)
% 204.64/35.39    (42)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.39    (43)   ~ (all_6_0 = e2)
% 204.64/35.39    (44)  op(all_52_27, all_52_27) = e2
% 204.64/35.39    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.39    (46)   ~ (all_52_9 = all_52_25)
% 204.64/35.39    (47)  all_58_15 = all_14_2
% 204.64/35.39    (48)   ~ (all_52_19 = all_10_2)
% 204.64/35.39    (49)  all_58_8 = all_10_2
% 204.64/35.39    (50)   ~ (all_52_5 = all_10_2)
% 204.64/35.39    (51)  op(all_52_17, all_52_17) = all_52_16
% 204.64/35.39    (52)   ~ (all_52_25 = all_6_2)
% 204.64/35.39    (53)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.39    (54)   ~ (all_52_5 = all_6_2)
% 204.64/35.39    (55)   ~ (all_52_9 = all_6_2)
% 204.64/35.39    (56)   ~ (all_52_13 = all_52_15)
% 204.64/35.39    (57)  op(e3, e3) = all_6_2
% 204.64/35.39    (58)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.39    (59)   ~ (all_52_27 = all_14_2)
% 204.64/35.39    (60)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.39    (61)  all_56_3 = all_52_25
% 204.64/35.39    (62)   ~ (all_52_3 = all_52_7)
% 204.64/35.39    (63)  all_58_5 = all_52_19
% 204.64/35.39    (64)  all_56_1 = all_52_9
% 204.64/35.39    (65)   ~ (all_52_15 = all_4_2)
% 204.64/35.39    (66)   ~ (all_52_27 = all_4_2)
% 204.64/35.39    (67)  all_58_6 = all_52_5
% 204.64/35.39    (68)   ~ (all_52_17 = all_6_2)
% 204.64/35.39    (69)   ~ (e3 = e2)
% 204.64/35.39    (70)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.39    (71)  op(e1, e1) = all_10_2
% 204.64/35.39    (72)   ~ (all_52_17 = all_52_19)
% 204.64/35.39    (73)  all_58_3 = all_4_2
% 204.64/35.39    (74)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.39    (75)   ~ (all_52_3 = all_4_2)
% 204.64/35.39    (76)  op(all_6_2, e3) = all_6_1
% 204.64/35.39    (77)  all_58_4 = all_52_17
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (19) implies:
% 204.64/35.39  |   (78)  all_52_15 = e3
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (5), (78) imply:
% 204.64/35.39  |   (79)   ~ (all_52_7 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (15), (78) imply:
% 204.64/35.39  |   (80)   ~ (all_52_9 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (56), (78) imply:
% 204.64/35.39  |   (81)   ~ (all_52_13 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (40), (78) imply:
% 204.64/35.39  |   (82)   ~ (all_14_2 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (82) implies:
% 204.64/35.39  |   (83)   ~ (all_14_2 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (65), (78) imply:
% 204.64/35.39  |   (84)   ~ (all_4_2 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | SIMP: (84) implies:
% 204.64/35.39  |   (85)   ~ (all_4_2 = e3)
% 204.64/35.39  | 
% 204.64/35.39  | REDUCE: (29), (78) imply:
% 204.64/35.39  |   (86)  op(e3, e3) = all_52_14
% 204.64/35.39  | 
% 204.64/35.39  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.64/35.39  |            (14), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 204.64/35.39  |            (27), (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 204.64/35.39  |            (39), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 204.64/35.39  |            (51), (52), (53), (54), (55), (57), (58), (59), (60), (61), (62),
% 204.64/35.39  |            (63), (64), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 204.64/35.39  |            (75), (76), (77), (79), (80), (81), (83), (85), (86) are
% 204.64/35.39  |            inconsistent by sub-proof #1034.
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1034 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.39    (2)   ~ (e3 = e1)
% 204.64/35.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.39    (4)  all_58_1 = all_52_9
% 204.64/35.39    (5)   ~ (all_52_17 = all_52_25)
% 204.64/35.39    (6)   ~ (all_4_2 = e3)
% 204.64/35.39    (7)   ~ (all_52_3 = all_6_2)
% 204.64/35.39    (8)  all_58_0 = all_6_2
% 204.64/35.39    (9)   ~ (all_52_17 = all_10_2)
% 204.64/35.39    (10)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.39    (11)  all_58_9 = all_52_25
% 204.64/35.39    (12)  op(e2, e2) = all_4_2
% 204.64/35.39    (13)   ~ (all_52_3 = all_52_5)
% 204.64/35.39    (14)  all_58_11 = all_52_29
% 204.64/35.39    (15)   ~ (all_52_3 = all_52_27)
% 204.64/35.39    (16)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.39    (17)  op(e0, e0) = all_14_2
% 204.64/35.39    (18)  op(all_52_29, all_52_29) = e1
% 204.64/35.39    (19)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.39    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.39    (21)  all_56_11 = all_52_29
% 204.64/35.39    (22)  op(e3, e3) = all_52_14
% 204.64/35.39    (23)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.39    (24)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.64/35.39    (25)   ~ (all_6_0 = e1)
% 204.64/35.39    (26)  all_58_10 = all_52_27
% 204.64/35.39    (27)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.39    (28)   ~ (all_52_25 = all_52_29)
% 204.64/35.39    (29)  all_58_7 = all_52_13
% 204.64/35.39    (30)  all_58_12 = all_52_7
% 204.64/35.39    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.39    (32)   ~ (all_52_7 = e3)
% 204.64/35.39    (33)  all_58_2 = all_52_3
% 204.64/35.39    (34)  all_56_2 = all_52_17
% 204.64/35.39    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.39    (36)  op(e3, all_6_1) = all_6_0
% 204.64/35.39    (37)  op(all_52_25, all_52_25) = e3
% 204.64/35.39    (38)   ~ (all_52_5 = all_52_29)
% 204.64/35.39    (39)   ~ (all_52_19 = all_52_27)
% 204.64/35.39    (40)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.39    (41)   ~ (all_6_0 = e2)
% 204.64/35.39    (42)   ~ (all_52_9 = e3)
% 204.64/35.39    (43)  op(all_52_27, all_52_27) = e2
% 204.64/35.39    (44)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.39    (45)   ~ (all_52_9 = all_52_25)
% 204.64/35.39    (46)  all_58_15 = all_14_2
% 204.64/35.39    (47)   ~ (all_52_19 = all_10_2)
% 204.64/35.39    (48)  all_58_8 = all_10_2
% 204.64/35.39    (49)   ~ (all_52_5 = all_10_2)
% 204.64/35.39    (50)  op(all_52_17, all_52_17) = all_52_16
% 204.64/35.39    (51)   ~ (all_52_25 = all_6_2)
% 204.64/35.39    (52)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.39    (53)   ~ (all_52_5 = all_6_2)
% 204.64/35.39    (54)   ~ (all_52_9 = all_6_2)
% 204.64/35.39    (55)  op(e3, e3) = all_6_2
% 204.64/35.39    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.39    (57)   ~ (all_52_13 = e3)
% 204.64/35.39    (58)   ~ (all_52_27 = all_14_2)
% 204.64/35.39    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.39    (60)  all_56_3 = all_52_25
% 204.64/35.39    (61)   ~ (all_52_3 = all_52_7)
% 204.64/35.39    (62)  all_58_5 = all_52_19
% 204.64/35.39    (63)  all_56_1 = all_52_9
% 204.64/35.39    (64)   ~ (all_52_27 = all_4_2)
% 204.64/35.39    (65)  all_58_6 = all_52_5
% 204.64/35.39    (66)   ~ (all_52_17 = all_6_2)
% 204.64/35.39    (67)   ~ (e3 = e2)
% 204.64/35.39    (68)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.39    (69)  op(e1, e1) = all_10_2
% 204.64/35.39    (70)   ~ (all_52_17 = all_52_19)
% 204.64/35.39    (71)  all_58_3 = all_4_2
% 204.64/35.39    (72)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.39    (73)   ~ (all_52_3 = all_4_2)
% 204.64/35.39    (74)  op(all_6_2, e3) = all_6_1
% 204.64/35.39    (75)  all_58_4 = all_52_17
% 204.64/35.39    (76)   ~ (all_14_2 = e3)
% 204.64/35.39  
% 204.64/35.39  Begin of proof
% 204.64/35.39  | 
% 204.64/35.39  | BETA: splitting (68) gives:
% 204.64/35.39  | 
% 204.64/35.39  | Case 1:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (77)  all_56_1 = e3
% 204.64/35.39  | | 
% 204.64/35.39  | | REF_CLOSE: (42), (63), (77) are inconsistent by sub-proof #1326.
% 204.64/35.39  | | 
% 204.64/35.39  | Case 2:
% 204.64/35.39  | | 
% 204.64/35.39  | |   (78)   ~ (all_56_1 = e3)
% 204.64/35.39  | |   (79)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.39  | | 
% 204.64/35.39  | | BETA: splitting (24) gives:
% 204.64/35.39  | | 
% 204.64/35.39  | | Case 1:
% 204.64/35.39  | | | 
% 204.64/35.39  | | |   (80)  all_58_1 = e1
% 204.64/35.39  | | | 
% 204.64/35.39  | | | COMBINE_EQS: (4), (80) imply:
% 204.64/35.39  | | |   (81)  all_52_9 = e1
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REDUCE: (54), (81) imply:
% 204.64/35.39  | | |   (82)   ~ (all_6_2 = e1)
% 204.64/35.39  | | | 
% 204.64/35.39  | | | SIMP: (82) implies:
% 204.64/35.39  | | |   (83)   ~ (all_6_2 = e1)
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REDUCE: (27), (81) imply:
% 204.64/35.39  | | |   (84)  op(e1, e1) = all_52_8
% 204.64/35.39  | | | 
% 204.64/35.39  | | | GROUND_INST: instantiating (3) with all_10_2, all_52_8, e1, e1,
% 204.64/35.39  | | |              simplifying with (69), (84) gives:
% 204.64/35.39  | | |   (85)  all_52_8 = all_10_2
% 204.64/35.39  | | | 
% 204.64/35.39  | | | BETA: splitting (23) gives:
% 204.64/35.39  | | | 
% 204.64/35.39  | | | Case 1:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | |   (86)  all_56_2 = e3
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | COMBINE_EQS: (34), (86) imply:
% 204.64/35.39  | | | |   (87)  all_52_17 = e3
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | SIMP: (87) implies:
% 204.64/35.39  | | | |   (88)  all_52_17 = e3
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REDUCE: (5), (88) imply:
% 204.64/35.39  | | | |   (89)   ~ (all_52_25 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | SIMP: (89) implies:
% 204.64/35.39  | | | |   (90)   ~ (all_52_25 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REDUCE: (66), (88) imply:
% 204.64/35.39  | | | |   (91)   ~ (all_6_2 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | SIMP: (91) implies:
% 204.64/35.39  | | | |   (92)   ~ (all_6_2 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REDUCE: (50), (88) imply:
% 204.64/35.39  | | | |   (93)  op(e3, e3) = all_52_16
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_16, e3, e3,
% 204.64/35.39  | | | |              simplifying with (55), (93) gives:
% 204.64/35.39  | | | |   (94)  all_52_16 = all_6_2
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | BETA: splitting (56) gives:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | Case 1:
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | |   (95)  all_58_9 = e3
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | REF_CLOSE: (11), (90), (95) are inconsistent by sub-proof #1300.
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | Case 2:
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | |   (96)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (13), (14), (15),
% 204.64/35.39  | | | | |            (17), (18), (19), (20), (22), (26), (27), (30), (31), (32),
% 204.64/35.39  | | | | |            (33), (35), (37), (38), (39), (43), (44), (45), (46), (49),
% 204.64/35.39  | | | | |            (51), (52), (55), (56), (58), (59), (60), (62), (64), (65),
% 204.64/35.39  | | | | |            (67), (69), (71), (75), (76), (83), (92), (96) are
% 204.64/35.39  | | | | |            inconsistent by sub-proof #1038.
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | End of split
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | Case 2:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | |   (97)   ~ (all_56_2 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REDUCE: (34), (97) imply:
% 204.64/35.39  | | | |   (98)   ~ (all_52_17 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (14), (16),
% 204.64/35.39  | | | |            (17), (18), (19), (20), (21), (25), (26), (29), (31), (33),
% 204.64/35.39  | | | |            (36), (37), (40), (41), (42), (43), (47), (48), (51), (52),
% 204.64/35.39  | | | |            (53), (55), (56), (57), (58), (59), (60), (62), (65), (69),
% 204.64/35.39  | | | |            (71), (74), (75), (98) are inconsistent by sub-proof #1224.
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | End of split
% 204.64/35.39  | | | 
% 204.64/35.39  | | Case 2:
% 204.64/35.39  | | | 
% 204.64/35.39  | | |   (99)   ~ (all_58_1 = e1)
% 204.64/35.39  | | | 
% 204.64/35.39  | | | REDUCE: (4), (99) imply:
% 204.64/35.39  | | |   (100)   ~ (all_52_9 = e1)
% 204.64/35.39  | | | 
% 204.64/35.39  | | | BETA: splitting (35) gives:
% 204.64/35.39  | | | 
% 204.64/35.39  | | | Case 1:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | |   (101)  all_58_0 = e3
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | COMBINE_EQS: (8), (101) imply:
% 204.64/35.39  | | | |   (102)  all_6_2 = e3
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REDUCE: (66), (102) imply:
% 204.64/35.39  | | | |   (103)   ~ (all_52_17 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (14), (16),
% 204.64/35.39  | | | |            (17), (18), (19), (20), (21), (25), (26), (29), (31), (33),
% 204.64/35.39  | | | |            (36), (37), (40), (41), (42), (43), (47), (48), (51), (52),
% 204.64/35.39  | | | |            (53), (55), (56), (57), (58), (59), (60), (62), (65), (69),
% 204.64/35.39  | | | |            (71), (74), (75), (103) are inconsistent by sub-proof #1224.
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | Case 2:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | |   (104)   ~ (all_58_0 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | REDUCE: (8), (104) imply:
% 204.64/35.39  | | | |   (105)   ~ (all_6_2 = e3)
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | BETA: splitting (59) gives:
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | | Case 1:
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | |   (106)  all_58_0 = e3
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | COMBINE_EQS: (8), (106) imply:
% 204.64/35.39  | | | | |   (107)  all_6_2 = e3
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | REDUCE: (105), (107) imply:
% 204.64/35.39  | | | | |   (108)  $false
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | CLOSE: (108) is inconsistent.
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | Case 2:
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | |   (109)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (14),
% 204.64/35.39  | | | | |            (15), (17), (18), (19), (20), (23), (26), (27), (28), (30),
% 204.64/35.39  | | | | |            (33), (34), (35), (37), (38), (42), (43), (45), (46), (50),
% 204.64/35.39  | | | | |            (51), (52), (55), (56), (58), (59), (60), (61), (62), (63),
% 204.64/35.39  | | | | |            (65), (67), (69), (70), (71), (72), (73), (75), (76), (79),
% 204.64/35.39  | | | | |            (100), (109) are inconsistent by sub-proof #1035.
% 204.64/35.39  | | | | | 
% 204.64/35.39  | | | | End of split
% 204.64/35.39  | | | | 
% 204.64/35.39  | | | End of split
% 204.64/35.39  | | | 
% 204.64/35.39  | | End of split
% 204.64/35.39  | | 
% 204.64/35.39  | End of split
% 204.64/35.39  | 
% 204.64/35.39  End of proof
% 204.64/35.39  
% 204.64/35.39  Sub-proof #1035 shows that the following formulas are inconsistent:
% 204.64/35.39  ----------------------------------------------------------------
% 204.64/35.39    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.39    (2)   ~ (e3 = e1)
% 204.64/35.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.39    (4)  all_58_1 = all_52_9
% 204.64/35.39    (5)   ~ (all_52_17 = all_52_25)
% 204.64/35.39    (6)   ~ (all_4_2 = e3)
% 204.64/35.39    (7)  all_58_0 = all_6_2
% 204.64/35.39    (8)   ~ (all_52_17 = all_10_2)
% 204.64/35.39    (9)  all_58_9 = all_52_25
% 204.64/35.39    (10)  op(e2, e2) = all_4_2
% 204.64/35.39    (11)  all_58_11 = all_52_29
% 204.64/35.39    (12)   ~ (all_52_3 = all_52_27)
% 204.64/35.39    (13)  op(e0, e0) = all_14_2
% 204.64/35.39    (14)  op(all_52_29, all_52_29) = e1
% 204.64/35.39    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.39    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.39    (17)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.39    (18)  all_58_10 = all_52_27
% 204.64/35.39    (19)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.39    (20)   ~ (all_52_25 = all_52_29)
% 204.64/35.39    (21)  all_58_12 = all_52_7
% 204.64/35.39    (22)  all_58_2 = all_52_3
% 204.64/35.39    (23)  all_56_2 = all_52_17
% 204.64/35.39    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.39    (25)  op(all_52_25, all_52_25) = e3
% 204.64/35.39    (26)   ~ (all_52_5 = all_52_29)
% 204.64/35.39    (27)   ~ (all_52_9 = e3)
% 204.64/35.39    (28)  op(all_52_27, all_52_27) = e2
% 204.64/35.39    (29)   ~ (all_52_9 = all_52_25)
% 204.64/35.39    (30)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.39    (31)  all_58_15 = all_14_2
% 204.64/35.39    (32)  op(all_52_17, all_52_17) = all_52_16
% 204.64/35.39    (33)   ~ (all_52_25 = all_6_2)
% 204.64/35.39    (34)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.39    (35)   ~ (all_52_9 = e1)
% 204.64/35.39    (36)  op(e3, e3) = all_6_2
% 204.64/35.39    (37)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.39    (38)   ~ (all_52_27 = all_14_2)
% 204.64/35.39    (39)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.39    (40)  all_56_3 = all_52_25
% 204.64/35.39    (41)   ~ (all_52_3 = all_52_7)
% 204.64/35.39    (42)  all_58_5 = all_52_19
% 204.64/35.39    (43)  all_56_1 = all_52_9
% 204.64/35.39    (44)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.40    (45)  all_58_6 = all_52_5
% 204.64/35.40    (46)   ~ (e3 = e2)
% 204.64/35.40    (47)  op(e1, e1) = all_10_2
% 204.64/35.40    (48)   ~ (all_52_17 = all_52_19)
% 204.64/35.40    (49)  all_58_3 = all_4_2
% 204.64/35.40    (50)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.40    (51)   ~ (all_52_3 = all_4_2)
% 204.64/35.40    (52)  all_58_4 = all_52_17
% 204.64/35.40    (53)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (50) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (54)  all_58_1 = e2
% 204.64/35.40  | | 
% 204.64/35.40  | | COMBINE_EQS: (4), (54) imply:
% 204.64/35.40  | |   (55)  all_52_9 = e2
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (29), (55) imply:
% 204.64/35.40  | |   (56)   ~ (all_52_25 = e2)
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (56) implies:
% 204.64/35.40  | |   (57)   ~ (all_52_25 = e2)
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (3), (4), (5), (8), (9), (13), (16), (17), (23), (25), (27),
% 204.64/35.40  | |            (30), (33), (34), (36), (37), (40), (47), (52), (53), (57) are
% 204.64/35.40  | |            inconsistent by sub-proof #1037.
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (58)   ~ (all_58_1 = e2)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (4), (58) imply:
% 204.64/35.40  | |   (59)   ~ (all_52_9 = e2)
% 204.64/35.40  | | 
% 204.64/35.40  | | BETA: splitting (44) gives:
% 204.64/35.40  | | 
% 204.64/35.40  | | Case 1:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (60)  all_56_1 = e2
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REF_CLOSE: (43), (59), (60) are inconsistent by sub-proof #1194.
% 204.64/35.40  | | | 
% 204.64/35.40  | | Case 2:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (61)  all_56_1 = e1 | all_56_1 = e0
% 204.64/35.40  | | | 
% 204.64/35.40  | | | BETA: splitting (61) gives:
% 204.64/35.40  | | | 
% 204.64/35.40  | | | Case 1:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | |   (62)  all_56_1 = e1
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REF_CLOSE: (35), (43), (62) are inconsistent by sub-proof #1061.
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | Case 2:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | |   (63)  all_56_1 = e0
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | COMBINE_EQS: (43), (63) imply:
% 204.64/35.40  | | | |   (64)  all_52_9 = e0
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | SIMP: (64) implies:
% 204.64/35.40  | | | |   (65)  all_52_9 = e0
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REDUCE: (29), (65) imply:
% 204.64/35.40  | | | |   (66)   ~ (all_52_25 = e0)
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | SIMP: (66) implies:
% 204.64/35.40  | | | |   (67)   ~ (all_52_25 = e0)
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REDUCE: (19), (65) imply:
% 204.64/35.40  | | | |   (68)  op(e0, e0) = all_52_8
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_8, e0, e0,
% 204.64/35.40  | | | |              simplifying with (13), (68) gives:
% 204.64/35.40  | | | |   (69)  all_52_8 = all_14_2
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | BETA: splitting (17) gives:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | Case 1:
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | |   (70)  all_56_2 = e3
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | COMBINE_EQS: (23), (70) imply:
% 204.64/35.40  | | | | |   (71)  all_52_17 = e3
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | SIMP: (71) implies:
% 204.64/35.40  | | | | |   (72)  all_52_17 = e3
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | REDUCE: (48), (72) imply:
% 204.64/35.40  | | | | |   (73)   ~ (all_52_19 = e3)
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | SIMP: (73) implies:
% 204.64/35.40  | | | | |   (74)   ~ (all_52_19 = e3)
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | REDUCE: (5), (72) imply:
% 204.64/35.40  | | | | |   (75)   ~ (all_52_25 = e3)
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | SIMP: (75) implies:
% 204.64/35.40  | | | | |   (76)   ~ (all_52_25 = e3)
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | REDUCE: (32), (72) imply:
% 204.64/35.40  | | | | |   (77)  op(e3, e3) = all_52_16
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_16, e3, e3,
% 204.64/35.40  | | | | |              simplifying with (36), (77) gives:
% 204.64/35.40  | | | | |   (78)  all_52_16 = all_6_2
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | BETA: splitting (15) gives:
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | Case 1:
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | |   (79)  all_58_2 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | COMBINE_EQS: (22), (79) imply:
% 204.64/35.40  | | | | | |   (80)  all_52_3 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | SIMP: (80) implies:
% 204.64/35.40  | | | | | |   (81)  all_52_3 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REDUCE: (41), (81) imply:
% 204.64/35.40  | | | | | |   (82)   ~ (all_52_7 = e3)
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | SIMP: (82) implies:
% 204.64/35.40  | | | | | |   (83)   ~ (all_52_7 = e3)
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REDUCE: (12), (81) imply:
% 204.64/35.40  | | | | | |   (84)   ~ (all_52_27 = e3)
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | SIMP: (84) implies:
% 204.64/35.40  | | | | | |   (85)   ~ (all_52_27 = e3)
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REF_CLOSE: (2), (3), (7), (9), (10), (11), (14), (18), (20), (21),
% 204.64/35.40  | | | | | |            (22), (24), (25), (26), (31), (33), (34), (36), (37),
% 204.64/35.40  | | | | | |            (40), (45), (51), (53), (67), (76), (83), (85) are
% 204.64/35.40  | | | | | |            inconsistent by sub-proof #1036.
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | Case 2:
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | |   (86)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (13), (16), (18),
% 204.64/35.40  | | | | | |            (25), (27), (28), (33), (34), (36), (38), (39), (40),
% 204.64/35.40  | | | | | |            (42), (46), (47), (49), (52), (74), (86) are inconsistent
% 204.64/35.40  | | | | | |            by sub-proof #1228.
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | End of split
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | Case 2:
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | |   (87)   ~ (all_56_2 = e3)
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | REDUCE: (23), (87) imply:
% 204.64/35.40  | | | | |   (88)   ~ (all_52_17 = e3)
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | REF_CLOSE: (3), (4), (9), (25), (27), (30), (33), (36), (37), (52),
% 204.64/35.40  | | | | |            (88) are inconsistent by sub-proof #1225.
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | End of split
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | End of split
% 204.64/35.40  | | | 
% 204.64/35.40  | | End of split
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1036 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)   ~ (e3 = e1)
% 204.64/35.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (3)  all_58_0 = all_6_2
% 204.64/35.40    (4)  all_58_9 = all_52_25
% 204.64/35.40    (5)  op(e2, e2) = all_4_2
% 204.64/35.40    (6)  all_58_11 = all_52_29
% 204.64/35.40    (7)  op(all_52_29, all_52_29) = e1
% 204.64/35.40    (8)   ~ (all_52_25 = e0)
% 204.64/35.40    (9)  all_58_10 = all_52_27
% 204.64/35.40    (10)   ~ (all_52_25 = all_52_29)
% 204.64/35.40    (11)  all_58_12 = all_52_7
% 204.64/35.40    (12)   ~ (all_52_7 = e3)
% 204.64/35.40    (13)  all_58_2 = all_52_3
% 204.64/35.40    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.40    (15)   ~ (all_52_25 = e3)
% 204.64/35.40    (16)  op(all_52_25, all_52_25) = e3
% 204.64/35.40    (17)   ~ (all_52_5 = all_52_29)
% 204.64/35.40    (18)   ~ (all_52_27 = e3)
% 204.64/35.40    (19)  all_58_15 = all_14_2
% 204.64/35.40    (20)   ~ (all_52_25 = all_6_2)
% 204.64/35.40    (21)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.40    (22)  op(e3, e3) = all_6_2
% 204.64/35.40    (23)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (24)  all_56_3 = all_52_25
% 204.64/35.40    (25)  all_58_6 = all_52_5
% 204.64/35.40    (26)   ~ (all_52_3 = all_4_2)
% 204.64/35.40    (27)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (23) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (28)  all_58_9 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (4), (15), (28) are inconsistent by sub-proof #1300.
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (29)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | BETA: splitting (29) gives:
% 204.64/35.40  | | 
% 204.64/35.40  | | Case 1:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (30)  all_58_10 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REF_CLOSE: (9), (18), (30) are inconsistent by sub-proof #1301.
% 204.64/35.40  | | | 
% 204.64/35.40  | | Case 2:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (31)  all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | BETA: splitting (31) gives:
% 204.64/35.40  | | | 
% 204.64/35.40  | | | Case 1:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | |   (32)  all_58_11 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | COMBINE_EQS: (6), (32) imply:
% 204.64/35.40  | | | |   (33)  all_52_29 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | SIMP: (33) implies:
% 204.64/35.40  | | | |   (34)  all_52_29 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REDUCE: (17), (34) imply:
% 204.64/35.40  | | | |   (35)   ~ (all_52_5 = e3)
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REDUCE: (7), (34) imply:
% 204.64/35.40  | | | |   (36)  op(e3, e3) = e1
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REF_CLOSE: (1), (2), (3), (5), (8), (11), (12), (13), (14), (15), (16),
% 204.64/35.40  | | | |            (20), (21), (22), (24), (25), (26), (35), (36) are
% 204.64/35.40  | | | |            inconsistent by sub-proof #1240.
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | Case 2:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | |   (37)  all_58_15 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | COMBINE_EQS: (19), (37) imply:
% 204.64/35.40  | | | |   (38)  all_14_2 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REDUCE: (27), (38) imply:
% 204.64/35.40  | | | |   (39)  $false
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | CLOSE: (39) is inconsistent.
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | End of split
% 204.64/35.40  | | | 
% 204.64/35.40  | | End of split
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1037 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (2)  all_58_1 = all_52_9
% 204.64/35.40    (3)   ~ (all_52_17 = all_52_25)
% 204.64/35.40    (4)   ~ (all_52_17 = all_10_2)
% 204.64/35.40    (5)  all_58_9 = all_52_25
% 204.64/35.40    (6)  op(e0, e0) = all_14_2
% 204.64/35.40    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.40    (8)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.40    (9)  all_56_2 = all_52_17
% 204.64/35.40    (10)  op(all_52_25, all_52_25) = e3
% 204.64/35.40    (11)   ~ (all_52_9 = e3)
% 204.64/35.40    (12)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.40    (13)   ~ (all_52_25 = e2)
% 204.64/35.40    (14)   ~ (all_52_25 = all_6_2)
% 204.64/35.40    (15)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.40    (16)  op(e3, e3) = all_6_2
% 204.64/35.40    (17)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (18)  all_56_3 = all_52_25
% 204.64/35.40    (19)  op(e1, e1) = all_10_2
% 204.64/35.40    (20)  all_58_4 = all_52_17
% 204.64/35.40    (21)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (8) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (22)  all_56_2 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | COMBINE_EQS: (9), (22) imply:
% 204.64/35.40  | |   (23)  all_52_17 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (23) implies:
% 204.64/35.40  | |   (24)  all_52_17 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (3), (24) imply:
% 204.64/35.40  | |   (25)   ~ (all_52_25 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (25) implies:
% 204.64/35.40  | |   (26)   ~ (all_52_25 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (15),
% 204.64/35.40  | |            (18), (19), (20), (21), (26) are inconsistent by sub-proof #1230.
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (27)   ~ (all_56_2 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (9), (27) imply:
% 204.64/35.40  | |   (28)   ~ (all_52_17 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (1), (2), (5), (10), (11), (12), (14), (16), (17), (20), (28) are
% 204.64/35.40  | |            inconsistent by sub-proof #1225.
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1038 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (3)  all_58_1 = all_52_9
% 204.64/35.40    (4)   ~ (all_52_17 = all_52_25)
% 204.64/35.40    (5)  all_58_0 = all_6_2
% 204.64/35.40    (6)   ~ (all_52_17 = all_10_2)
% 204.64/35.40    (7)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.40    (8)  all_58_9 = all_52_25
% 204.64/35.40    (9)   ~ (all_52_3 = all_52_5)
% 204.64/35.40    (10)  all_58_11 = all_52_29
% 204.64/35.40    (11)   ~ (all_52_3 = all_52_27)
% 204.64/35.40    (12)  op(e0, e0) = all_14_2
% 204.64/35.40    (13)  op(all_52_29, all_52_29) = e1
% 204.64/35.40    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.40    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.40    (16)  op(e3, e3) = all_52_14
% 204.64/35.40    (17)   ~ (all_6_2 = e3)
% 204.64/35.40    (18)  all_58_10 = all_52_27
% 204.64/35.40    (19)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.40    (20)  all_58_12 = all_52_7
% 204.64/35.40    (21)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.40    (22)   ~ (all_52_7 = e3)
% 204.64/35.40    (23)  all_58_2 = all_52_3
% 204.64/35.40    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.40    (25)  op(all_52_25, all_52_25) = e3
% 204.64/35.40    (26)   ~ (all_52_5 = all_52_29)
% 204.64/35.40    (27)   ~ (all_52_19 = all_52_27)
% 204.64/35.40    (28)  op(all_52_27, all_52_27) = e2
% 204.64/35.40    (29)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.40    (30)   ~ (all_52_9 = all_52_25)
% 204.64/35.40    (31)  all_58_15 = all_14_2
% 204.64/35.40    (32)   ~ (all_52_5 = all_10_2)
% 204.64/35.40    (33)   ~ (all_52_25 = all_6_2)
% 204.64/35.40    (34)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.40    (35)  op(e3, e3) = all_6_2
% 204.64/35.40    (36)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (37)   ~ (all_52_27 = all_14_2)
% 204.64/35.40    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.40    (39)  all_56_3 = all_52_25
% 204.64/35.40    (40)  all_58_5 = all_52_19
% 204.64/35.40    (41)   ~ (all_52_27 = all_4_2)
% 204.64/35.40    (42)  all_58_6 = all_52_5
% 204.64/35.40    (43)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (44)   ~ (e3 = e2)
% 204.64/35.40    (45)   ~ (all_6_2 = e1)
% 204.64/35.40    (46)  op(e1, e1) = all_10_2
% 204.64/35.40    (47)  all_58_3 = all_4_2
% 204.64/35.40    (48)  all_58_4 = all_52_17
% 204.64/35.40    (49)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (21) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (50)  all_58_6 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | COMBINE_EQS: (42), (50) imply:
% 204.64/35.40  | |   (51)  all_52_5 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (51) implies:
% 204.64/35.40  | |   (52)  all_52_5 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (9), (52) imply:
% 204.64/35.40  | |   (53)   ~ (all_52_3 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (26), (52) imply:
% 204.64/35.40  | |   (54)   ~ (all_52_29 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (54) implies:
% 204.64/35.40  | |   (55)   ~ (all_52_29 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (32), (52) imply:
% 204.64/35.40  | |   (56)   ~ (all_10_2 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (56) implies:
% 204.64/35.40  | |   (57)   ~ (all_10_2 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (7), (52) imply:
% 204.64/35.40  | |   (58)  op(e3, e3) = all_52_4
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (12), (14), (15), (18),
% 204.64/35.40  | |            (19), (23), (25), (27), (28), (29), (30), (31), (33), (34), (35),
% 204.64/35.40  | |            (36), (37), (38), (39), (40), (41), (44), (46), (47), (48), (49),
% 204.64/35.40  | |            (53), (55), (57), (58) are inconsistent by sub-proof #1039.
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (59)   ~ (all_58_6 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (42), (59) imply:
% 204.64/35.40  | |   (60)   ~ (all_52_5 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | BETA: splitting (24) gives:
% 204.64/35.40  | | 
% 204.64/35.40  | | Case 1:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (61)  all_58_0 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | COMBINE_EQS: (5), (61) imply:
% 204.64/35.40  | | |   (62)  all_6_2 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REDUCE: (17), (62) imply:
% 204.64/35.40  | | |   (63)  $false
% 204.64/35.40  | | | 
% 204.64/35.40  | | | CLOSE: (63) is inconsistent.
% 204.64/35.40  | | | 
% 204.64/35.40  | | Case 2:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (64)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | BETA: splitting (64) gives:
% 204.64/35.40  | | | 
% 204.64/35.40  | | | Case 1:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | |   (65)  all_58_2 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | COMBINE_EQS: (23), (65) imply:
% 204.64/35.40  | | | |   (66)  all_52_3 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | SIMP: (66) implies:
% 204.64/35.40  | | | |   (67)  all_52_3 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REDUCE: (11), (67) imply:
% 204.64/35.40  | | | |   (68)   ~ (all_52_27 = e3)
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | SIMP: (68) implies:
% 204.64/35.40  | | | |   (69)   ~ (all_52_27 = e3)
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | BETA: splitting (43) gives:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | Case 1:
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | |   (70)  all_58_10 = e3
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | REF_CLOSE: (18), (69), (70) are inconsistent by sub-proof #1301.
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | Case 2:
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | |   (71)  all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | BETA: splitting (71) gives:
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | | Case 1:
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | |   (72)  all_58_11 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | COMBINE_EQS: (10), (72) imply:
% 204.64/35.40  | | | | | |   (73)  all_52_29 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | SIMP: (73) implies:
% 204.64/35.40  | | | | | |   (74)  all_52_29 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REDUCE: (13), (74) imply:
% 204.64/35.40  | | | | | |   (75)  op(e3, e3) = e1
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REF_CLOSE: (2), (16), (35), (45), (75) are inconsistent by sub-proof
% 204.64/35.40  | | | | | |            #1247.
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | Case 2:
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | |   (76)  all_58_15 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | COMBINE_EQS: (31), (76) imply:
% 204.64/35.40  | | | | | |   (77)  all_14_2 = e3
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | REDUCE: (49), (77) imply:
% 204.64/35.40  | | | | | |   (78)  $false
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | | CLOSE: (78) is inconsistent.
% 204.64/35.40  | | | | | | 
% 204.64/35.40  | | | | | End of split
% 204.64/35.40  | | | | | 
% 204.64/35.40  | | | | End of split
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | Case 2:
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | |   (79)  all_58_6 = e3 | all_58_12 = e3
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | | REF_CLOSE: (20), (22), (42), (60), (79) are inconsistent by sub-proof
% 204.64/35.40  | | | |            #1243.
% 204.64/35.40  | | | | 
% 204.64/35.40  | | | End of split
% 204.64/35.40  | | | 
% 204.64/35.40  | | End of split
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1039 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (3)  all_58_1 = all_52_9
% 204.64/35.40    (4)   ~ (all_52_17 = all_52_25)
% 204.64/35.40    (5)  all_58_0 = all_6_2
% 204.64/35.40    (6)   ~ (all_52_17 = all_10_2)
% 204.64/35.40    (7)  all_58_9 = all_52_25
% 204.64/35.40    (8)  all_58_11 = all_52_29
% 204.64/35.40    (9)   ~ (all_52_3 = e3)
% 204.64/35.40    (10)  op(e0, e0) = all_14_2
% 204.64/35.40    (11)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.40    (12)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.40    (13)  all_58_10 = all_52_27
% 204.64/35.40    (14)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.40    (15)  all_58_2 = all_52_3
% 204.64/35.40    (16)   ~ (all_52_29 = e3)
% 204.64/35.40    (17)  op(all_52_25, all_52_25) = e3
% 204.64/35.40    (18)   ~ (all_10_2 = e3)
% 204.64/35.40    (19)   ~ (all_52_19 = all_52_27)
% 204.64/35.40    (20)  op(all_52_27, all_52_27) = e2
% 204.64/35.40    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.40    (22)   ~ (all_52_9 = all_52_25)
% 204.64/35.40    (23)  all_58_15 = all_14_2
% 204.64/35.40    (24)  op(e3, e3) = all_52_4
% 204.64/35.40    (25)   ~ (all_52_25 = all_6_2)
% 204.64/35.40    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.40    (27)  op(e3, e3) = all_6_2
% 204.64/35.40    (28)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (29)   ~ (all_52_27 = all_14_2)
% 204.64/35.40    (30)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.40    (31)  all_56_3 = all_52_25
% 204.64/35.40    (32)  all_58_5 = all_52_19
% 204.64/35.40    (33)   ~ (all_52_27 = all_4_2)
% 204.64/35.40    (34)   ~ (e3 = e2)
% 204.64/35.40    (35)  op(e1, e1) = all_10_2
% 204.64/35.40    (36)  all_58_3 = all_4_2
% 204.64/35.40    (37)  all_58_4 = all_52_17
% 204.64/35.40    (38)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (11) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (39)  all_58_2 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (9), (15), (39) are inconsistent by sub-proof #1369.
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (40)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 204.64/35.40  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 204.64/35.40  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 204.64/35.40  | |            (38), (40) are inconsistent by sub-proof #1040.
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1040 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (3)  all_58_1 = all_52_9
% 204.64/35.40    (4)   ~ (all_52_17 = all_52_25)
% 204.64/35.40    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.40    (6)  all_58_0 = all_6_2
% 204.64/35.40    (7)   ~ (all_52_17 = all_10_2)
% 204.64/35.40    (8)  all_58_9 = all_52_25
% 204.64/35.40    (9)  all_58_11 = all_52_29
% 204.64/35.40    (10)  op(e0, e0) = all_14_2
% 204.64/35.40    (11)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.40    (12)  all_58_10 = all_52_27
% 204.64/35.40    (13)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.40    (14)   ~ (all_52_29 = e3)
% 204.64/35.40    (15)  op(all_52_25, all_52_25) = e3
% 204.64/35.40    (16)   ~ (all_10_2 = e3)
% 204.64/35.40    (17)   ~ (all_52_19 = all_52_27)
% 204.64/35.40    (18)  op(all_52_27, all_52_27) = e2
% 204.64/35.40    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.40    (20)   ~ (all_52_9 = all_52_25)
% 204.64/35.40    (21)  all_58_15 = all_14_2
% 204.64/35.40    (22)  op(e3, e3) = all_52_4
% 204.64/35.40    (23)   ~ (all_52_25 = all_6_2)
% 204.64/35.40    (24)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.40    (25)  op(e3, e3) = all_6_2
% 204.64/35.40    (26)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (27)   ~ (all_52_27 = all_14_2)
% 204.64/35.40    (28)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.40    (29)  all_56_3 = all_52_25
% 204.64/35.40    (30)  all_58_5 = all_52_19
% 204.64/35.40    (31)   ~ (all_52_27 = all_4_2)
% 204.64/35.40    (32)   ~ (e3 = e2)
% 204.64/35.40    (33)  op(e1, e1) = all_10_2
% 204.64/35.40    (34)  all_58_3 = all_4_2
% 204.64/35.40    (35)  all_58_4 = all_52_17
% 204.64/35.40    (36)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | GROUND_INST: instantiating (2) with all_6_2, all_52_4, e3, e3, simplifying
% 204.64/35.40  |              with (22), (25) gives:
% 204.64/35.40  |   (37)  all_52_4 = all_6_2
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (26) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (38)  all_58_9 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | COMBINE_EQS: (8), (38) imply:
% 204.64/35.40  | |   (39)  all_52_25 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (2), (15), (23), (25), (39) are inconsistent by sub-proof #1246.
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (40)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.64/35.40  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 204.64/35.40  | |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.64/35.40  | |            (40) are inconsistent by sub-proof #1041.
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1041 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)   ~ (all_52_25 = all_52_27)
% 204.64/35.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (3)  all_58_1 = all_52_9
% 204.64/35.40    (4)   ~ (all_52_17 = all_52_25)
% 204.64/35.40    (5)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.40    (6)  all_58_0 = all_6_2
% 204.64/35.40    (7)   ~ (all_52_17 = all_10_2)
% 204.64/35.40    (8)  all_58_9 = all_52_25
% 204.64/35.40    (9)  all_58_11 = all_52_29
% 204.64/35.40    (10)  op(e0, e0) = all_14_2
% 204.64/35.40    (11)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.64/35.40    (12)  all_58_10 = all_52_27
% 204.64/35.40    (13)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.40    (14)   ~ (all_52_29 = e3)
% 204.64/35.40    (15)  op(all_52_25, all_52_25) = e3
% 204.64/35.40    (16)   ~ (all_10_2 = e3)
% 204.64/35.40    (17)   ~ (all_52_19 = all_52_27)
% 204.64/35.40    (18)  op(all_52_27, all_52_27) = e2
% 204.64/35.40    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.40    (20)   ~ (all_52_9 = all_52_25)
% 204.64/35.40    (21)  all_58_15 = all_14_2
% 204.64/35.40    (22)   ~ (all_52_25 = all_6_2)
% 204.64/35.40    (23)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.40    (24)  op(e3, e3) = all_6_2
% 204.64/35.40    (25)   ~ (all_52_27 = all_14_2)
% 204.64/35.40    (26)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.40    (27)  all_56_3 = all_52_25
% 204.64/35.40    (28)  all_58_5 = all_52_19
% 204.64/35.40    (29)   ~ (all_52_27 = all_4_2)
% 204.64/35.40    (30)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40    (31)   ~ (e3 = e2)
% 204.64/35.40    (32)  op(e1, e1) = all_10_2
% 204.64/35.40    (33)  all_58_3 = all_4_2
% 204.64/35.40    (34)  all_58_4 = all_52_17
% 204.64/35.40    (35)   ~ (all_14_2 = e3)
% 204.64/35.40  
% 204.64/35.40  Begin of proof
% 204.64/35.40  | 
% 204.64/35.40  | BETA: splitting (30) gives:
% 204.64/35.40  | 
% 204.64/35.40  | Case 1:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (36)  all_58_10 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | COMBINE_EQS: (12), (36) imply:
% 204.64/35.40  | |   (37)  all_52_27 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (37) implies:
% 204.64/35.40  | |   (38)  all_52_27 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (17), (38) imply:
% 204.64/35.40  | |   (39)   ~ (all_52_19 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (25), (38) imply:
% 204.64/35.40  | |   (40)   ~ (all_14_2 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (29), (38) imply:
% 204.64/35.40  | |   (41)   ~ (all_4_2 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | SIMP: (41) implies:
% 204.64/35.40  | |   (42)   ~ (all_4_2 = e3)
% 204.64/35.40  | | 
% 204.64/35.40  | | REDUCE: (18), (38) imply:
% 204.64/35.40  | |   (43)  op(e3, e3) = e2
% 204.64/35.40  | | 
% 204.64/35.40  | | BETA: splitting (19) gives:
% 204.64/35.40  | | 
% 204.64/35.40  | | Case 1:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (44)  all_58_1 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | COMBINE_EQS: (3), (44) imply:
% 204.64/35.40  | | |   (45)  all_52_9 = e3
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REDUCE: (20), (45) imply:
% 204.64/35.40  | | |   (46)   ~ (all_52_25 = e3)
% 204.64/35.40  | | | 
% 204.64/35.40  | | | SIMP: (46) implies:
% 204.64/35.40  | | |   (47)   ~ (all_52_25 = e3)
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REDUCE: (13), (45) imply:
% 204.64/35.40  | | |   (48)  op(e3, e3) = all_52_8
% 204.64/35.40  | | | 
% 204.64/35.40  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_8, e3, e3, simplifying
% 204.64/35.40  | | |              with (24), (48) gives:
% 204.64/35.40  | | |   (49)  all_52_8 = all_6_2
% 204.64/35.40  | | | 
% 204.64/35.40  | | | GROUND_INST: instantiating (2) with e2, all_52_8, e3, e3, simplifying with
% 204.64/35.40  | | |              (43), (48) gives:
% 204.64/35.40  | | |   (50)  all_52_8 = e2
% 204.64/35.40  | | | 
% 204.64/35.40  | | | COMBINE_EQS: (49), (50) imply:
% 204.64/35.40  | | |   (51)  all_6_2 = e2
% 204.64/35.40  | | | 
% 204.64/35.40  | | | SIMP: (51) implies:
% 204.64/35.40  | | |   (52)  all_6_2 = e2
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REDUCE: (22), (52) imply:
% 204.64/35.40  | | |   (53)   ~ (all_52_25 = e2)
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REF_CLOSE: (2), (8), (10), (11), (15), (16), (23), (27), (32), (35), (47),
% 204.64/35.40  | | |            (53) are inconsistent by sub-proof #1231.
% 204.64/35.40  | | | 
% 204.64/35.40  | | Case 2:
% 204.64/35.40  | | | 
% 204.64/35.40  | | |   (54)   ~ (all_58_1 = e3)
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REDUCE: (3), (54) imply:
% 204.64/35.40  | | |   (55)   ~ (all_52_9 = e3)
% 204.64/35.40  | | | 
% 204.64/35.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 204.64/35.40  | | |            (18), (22), (23), (24), (25), (26), (27), (28), (31), (32),
% 204.64/35.40  | | |            (33), (34), (39), (42), (55) are inconsistent by sub-proof
% 204.64/35.40  | | |            #1228.
% 204.64/35.40  | | | 
% 204.64/35.40  | | End of split
% 204.64/35.40  | | 
% 204.64/35.40  | Case 2:
% 204.64/35.40  | | 
% 204.64/35.40  | |   (56)  all_58_11 = e3 | all_58_15 = e3
% 204.64/35.40  | | 
% 204.64/35.40  | | REF_CLOSE: (9), (14), (21), (35), (56) are inconsistent by sub-proof #1103.
% 204.64/35.40  | | 
% 204.64/35.40  | End of split
% 204.64/35.40  | 
% 204.64/35.40  End of proof
% 204.64/35.40  
% 204.64/35.40  Sub-proof #1042 shows that the following formulas are inconsistent:
% 204.64/35.40  ----------------------------------------------------------------
% 204.64/35.40    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.64/35.40    (2)   ~ (all_52_15 = all_52_23)
% 204.64/35.40    (3)  all_58_14 = all_52_23
% 204.64/35.40    (4)   ~ (e3 = e1)
% 204.64/35.40    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.40    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.40    (7)  all_58_1 = all_52_9
% 204.64/35.40    (8)   ~ (all_52_9 = all_52_13)
% 204.64/35.40    (9)   ~ (e3 = e0)
% 204.64/35.40    (10)  op(e2, e3) = all_52_3
% 204.64/35.40    (11)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.64/35.40    (12)   ~ (all_52_7 = all_52_15)
% 204.64/35.40    (13)   ~ (all_52_3 = all_52_19)
% 204.64/35.40    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.40    (15)   ~ (all_52_17 = all_52_25)
% 204.64/35.40    (16)   ~ (all_52_3 = all_6_2)
% 204.64/35.40    (17)  all_58_0 = all_6_2
% 204.64/35.40    (18)  op(all_14_2, e0) = all_14_1
% 204.64/35.40    (19)  all_56_4 = all_52_3
% 204.64/35.40    (20)  op(e3, e0) = all_52_25
% 204.64/35.41    (21)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.41    (22)  op(all_52_19, all_52_19) = all_52_18
% 204.64/35.41    (23)  all_58_13 = all_52_15
% 204.64/35.41    (24)  op(all_10_2, all_10_2) = all_52_20
% 204.64/35.41    (25)  all_58_9 = all_52_25
% 204.64/35.41    (26)   ~ (all_6_1 = e1)
% 204.64/35.41    (27)   ~ (all_52_29 = all_14_2)
% 204.64/35.41    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.41    (29)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.41    (30)  op(e1, e3) = all_52_5
% 204.64/35.41    (31)  op(e2, e2) = all_4_2
% 204.64/35.41    (32)   ~ (all_52_3 = all_52_5)
% 204.64/35.41    (33)  all_58_11 = all_52_29
% 204.64/35.41    (34)   ~ (all_52_25 = all_14_2)
% 204.64/35.41    (35)   ~ (all_52_9 = all_52_15)
% 204.64/35.41    (36)   ~ (all_52_3 = all_52_27)
% 204.64/35.41    (37)  op(all_10_2, e1) = all_10_1
% 204.64/35.41    (38)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.41    (39)   ~ (all_52_7 = all_6_2)
% 204.64/35.41    (40)  op(e0, e0) = all_14_2
% 204.64/35.41    (41)  all_56_15 = all_14_2
% 204.64/35.41    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.41    (43)  all_56_11 = all_52_29
% 204.64/35.41    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.64/35.41    (45)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.41    (46)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.64/35.41    (47)  all_56_9 = all_52_13
% 204.64/35.41    (48)   ~ (e2 = e1)
% 204.64/35.41    (49)   ~ (all_52_13 = all_10_2)
% 204.64/35.41    (50)   ~ (all_6_0 = e1)
% 204.64/35.41    (51)  all_58_10 = all_52_27
% 204.64/35.41    (52)  all_56_8 = all_52_5
% 204.64/35.41    (53)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.41    (54)   ~ (all_52_19 = all_52_23)
% 204.64/35.41    (55)   ~ (all_52_25 = all_52_29)
% 204.64/35.41    (56)   ~ (all_52_29 = all_10_2)
% 204.64/35.41    (57)  all_58_7 = all_52_13
% 204.64/35.41    (58)   ~ (all_52_5 = all_52_7)
% 204.64/35.41    (59)  all_58_12 = all_52_7
% 204.64/35.41    (60)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.41    (61)   ~ (all_52_7 = all_14_2)
% 204.64/35.41    (62)  all_58_2 = all_52_3
% 204.64/35.41    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.64/35.41    (64)  all_56_2 = all_52_17
% 204.64/35.41    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.41    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.41    (67)  op(e3, all_6_1) = all_6_0
% 204.64/35.41    (68)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.41    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.64/35.41    (70)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.64/35.41    (71)   ~ (e2 = e0)
% 204.64/35.41    (72)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.41    (73)   ~ (all_52_5 = all_52_29)
% 204.64/35.41    (74)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.64/35.41    (75)  all_56_6 = all_52_19
% 204.64/35.41    (76)   ~ (all_52_15 = all_14_2)
% 204.64/35.41    (77)   ~ (all_52_19 = all_52_27)
% 204.64/35.41    (78)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.41    (79)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.41    (80)   ~ (all_6_0 = e2)
% 204.64/35.41    (81)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.41    (82)   ~ (all_52_13 = all_4_2)
% 204.64/35.41    (83)  op(e3, e1) = all_52_17
% 204.64/35.41    (84)  op(e0, e3) = all_52_7
% 204.64/35.41    (85)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.41    (86)   ~ (all_52_9 = all_52_25)
% 204.64/35.41    (87)  all_58_15 = all_14_2
% 204.64/35.41    (88)   ~ (all_52_19 = all_10_2)
% 204.64/35.41    (89)  op(all_52_23, all_52_23) = all_52_22
% 204.64/35.41    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.41    (91)  all_58_8 = all_10_2
% 204.64/35.41    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.64/35.41    (93)   ~ (all_52_5 = all_10_2)
% 204.64/35.41    (94)  op(all_52_29, all_52_29) = all_52_28
% 204.64/35.41    (95)   ~ (all_52_23 = all_14_2)
% 204.64/35.41    (96)  all_56_12 = all_52_7
% 204.64/35.41    (97)  op(all_52_17, all_52_17) = all_52_16
% 204.64/35.41    (98)   ~ (all_52_25 = all_6_2)
% 204.64/35.41    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.41    (100)   ~ (all_52_9 = all_4_2)
% 204.64/35.41    (101)   ~ (all_52_5 = all_6_2)
% 204.64/35.41    (102)   ~ (all_52_9 = all_6_2)
% 204.64/35.41    (103)   ~ (all_52_13 = all_52_15)
% 204.64/35.41    (104)  all_56_0 = all_6_2
% 204.64/35.41    (105)  op(e3, e3) = all_6_2
% 204.64/35.41    (106)   ~ (all_52_27 = all_14_2)
% 204.64/35.41    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.41    (108)  op(all_4_2, all_4_2) = all_52_10
% 204.64/35.41    (109)  all_56_3 = all_52_25
% 204.64/35.41    (110)   ~ (all_52_3 = all_52_7)
% 204.64/35.41    (111)  op(all_14_2, all_14_2) = all_52_30
% 204.64/35.41    (112)  all_58_5 = all_52_19
% 204.64/35.41    (113)  all_56_1 = all_52_9
% 204.64/35.41    (114)   ~ (all_52_27 = all_4_2)
% 204.64/35.41    (115)  all_58_6 = all_52_5
% 204.64/35.41    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.64/35.41    (117)   ~ (all_52_17 = all_6_2)
% 204.64/35.41    (118)   ~ (e1 = e0)
% 204.64/35.41    (119)   ~ (e3 = e2)
% 204.64/35.41    (120)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.41    (121)   ~ (all_52_9 = all_52_17)
% 204.64/35.41    (122)  all_56_10 = all_10_2
% 204.64/35.41    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.41    (124)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.64/35.41    (125)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.41    (126)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.41    (127)   ~ (all_6_1 = e2)
% 204.64/35.41    (128)  op(e1, e1) = all_10_2
% 204.64/35.41    (129)   ~ (all_52_7 = all_52_23)
% 204.64/35.41    (130)   ~ (all_52_17 = all_52_19)
% 204.64/35.41    (131)  all_58_3 = all_4_2
% 204.64/35.41    (132)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.41    (133)  all_56_13 = all_52_15
% 204.64/35.41    (134)   ~ (all_52_3 = all_4_2)
% 204.64/35.41    (135)  op(all_6_2, e3) = all_6_1
% 204.64/35.41    (136)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.64/35.41    (137)   ~ (all_52_13 = all_52_29)
% 204.64/35.41    (138)  all_58_4 = all_52_17
% 204.64/35.41    (139)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.64/35.41    (140)  op(all_52_25, all_52_25) = all_52_24
% 204.64/35.41  
% 204.64/35.41  Begin of proof
% 204.64/35.41  | 
% 204.64/35.41  | ALPHA: (136) implies:
% 204.64/35.41  |   (141)  all_52_22 = e0
% 204.64/35.41  |   (142)  all_52_20 = e1
% 204.64/35.41  |   (143)  all_52_18 = e2
% 204.64/35.41  |   (144)  all_52_16 = e3
% 204.64/35.41  | 
% 204.64/35.41  | REDUCE: (97), (144) imply:
% 204.64/35.41  |   (145)  op(all_52_17, all_52_17) = e3
% 204.64/35.41  | 
% 204.64/35.41  | REDUCE: (22), (143) imply:
% 204.64/35.41  |   (146)  op(all_52_19, all_52_19) = e2
% 204.64/35.41  | 
% 204.64/35.41  | REDUCE: (89), (141) imply:
% 204.64/35.41  |   (147)  op(all_52_23, all_52_23) = e0
% 204.64/35.41  | 
% 204.64/35.41  | REDUCE: (24), (142) imply:
% 204.64/35.41  |   (148)  op(all_10_2, all_10_2) = e1
% 204.64/35.41  | 
% 204.64/35.41  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.64/35.41  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (25),
% 204.64/35.41  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.64/35.41  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 204.64/35.41  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 204.64/35.41  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 204.64/35.41  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.64/35.41  |            (81), (82), (83), (84), (85), (86), (87), (88), (90), (91), (92),
% 204.64/35.41  |            (93), (94), (95), (96), (98), (99), (100), (101), (102), (103),
% 204.64/35.41  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 204.64/35.41  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 204.64/35.41  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 204.64/35.41  |            (131), (132), (133), (134), (135), (137), (138), (139), (140),
% 204.64/35.41  |            (145), (146), (147), (148) are inconsistent by sub-proof #1043.
% 204.64/35.41  | 
% 204.64/35.41  End of proof
% 204.64/35.41  
% 204.64/35.41  Sub-proof #1043 shows that the following formulas are inconsistent:
% 204.64/35.41  ----------------------------------------------------------------
% 204.64/35.41    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.64/35.41    (2)   ~ (all_52_15 = all_52_23)
% 204.64/35.41    (3)  all_58_14 = all_52_23
% 204.64/35.41    (4)   ~ (e3 = e1)
% 204.64/35.41    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.41    (7)  all_58_1 = all_52_9
% 204.64/35.41    (8)   ~ (all_52_9 = all_52_13)
% 204.64/35.41    (9)   ~ (e3 = e0)
% 204.64/35.41    (10)  op(all_52_23, all_52_23) = e0
% 204.64/35.41    (11)  op(e2, e3) = all_52_3
% 204.64/35.41    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.64/35.41    (13)   ~ (all_52_7 = all_52_15)
% 204.64/35.41    (14)   ~ (all_52_3 = all_52_19)
% 204.64/35.41    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.41    (16)   ~ (all_52_17 = all_52_25)
% 204.64/35.41    (17)   ~ (all_52_3 = all_6_2)
% 204.64/35.41    (18)  all_58_0 = all_6_2
% 204.64/35.41    (19)  op(all_14_2, e0) = all_14_1
% 204.64/35.41    (20)  all_56_4 = all_52_3
% 204.64/35.41    (21)  op(e3, e0) = all_52_25
% 204.64/35.41    (22)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.41    (23)  all_58_13 = all_52_15
% 204.64/35.41    (24)  all_58_9 = all_52_25
% 204.64/35.41    (25)   ~ (all_6_1 = e1)
% 204.64/35.41    (26)   ~ (all_52_29 = all_14_2)
% 204.64/35.41    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.41    (28)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.41    (29)  op(e1, e3) = all_52_5
% 204.64/35.41    (30)  op(e2, e2) = all_4_2
% 204.64/35.41    (31)   ~ (all_52_3 = all_52_5)
% 204.64/35.41    (32)  all_58_11 = all_52_29
% 204.64/35.41    (33)   ~ (all_52_25 = all_14_2)
% 204.64/35.41    (34)   ~ (all_52_9 = all_52_15)
% 204.64/35.41    (35)   ~ (all_52_3 = all_52_27)
% 204.64/35.41    (36)  op(all_10_2, e1) = all_10_1
% 204.64/35.41    (37)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.41    (38)   ~ (all_52_7 = all_6_2)
% 204.64/35.41    (39)  op(e0, e0) = all_14_2
% 204.64/35.41    (40)  all_56_15 = all_14_2
% 204.64/35.41    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.41    (42)  all_56_11 = all_52_29
% 204.64/35.41    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.64/35.41    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.41    (45)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.64/35.41    (46)  all_56_9 = all_52_13
% 204.64/35.41    (47)   ~ (e2 = e1)
% 204.64/35.41    (48)   ~ (all_52_13 = all_10_2)
% 204.64/35.41    (49)   ~ (all_6_0 = e1)
% 204.64/35.41    (50)  op(all_10_2, all_10_2) = e1
% 204.64/35.41    (51)  all_58_10 = all_52_27
% 204.64/35.41    (52)  all_56_8 = all_52_5
% 204.64/35.41    (53)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.41    (54)   ~ (all_52_19 = all_52_23)
% 204.64/35.41    (55)   ~ (all_52_25 = all_52_29)
% 204.64/35.41    (56)   ~ (all_52_29 = all_10_2)
% 204.64/35.41    (57)  all_58_7 = all_52_13
% 204.64/35.41    (58)  op(all_52_19, all_52_19) = e2
% 204.64/35.41    (59)   ~ (all_52_5 = all_52_7)
% 204.64/35.41    (60)  all_58_12 = all_52_7
% 204.64/35.41    (61)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.41    (62)   ~ (all_52_7 = all_14_2)
% 204.64/35.41    (63)  all_58_2 = all_52_3
% 204.64/35.41    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.64/35.41    (65)  all_56_2 = all_52_17
% 204.64/35.41    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.41    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.41    (68)  op(e3, all_6_1) = all_6_0
% 204.64/35.41    (69)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.41    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.64/35.41    (71)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.64/35.41    (72)   ~ (e2 = e0)
% 204.64/35.41    (73)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.41    (74)   ~ (all_52_5 = all_52_29)
% 204.64/35.41    (75)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.64/35.41    (76)  all_56_6 = all_52_19
% 204.64/35.41    (77)   ~ (all_52_15 = all_14_2)
% 204.64/35.41    (78)   ~ (all_52_19 = all_52_27)
% 204.64/35.41    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.41    (80)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.41    (81)   ~ (all_6_0 = e2)
% 204.64/35.41    (82)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.41    (83)   ~ (all_52_13 = all_4_2)
% 204.64/35.41    (84)  op(e3, e1) = all_52_17
% 204.64/35.41    (85)  op(e0, e3) = all_52_7
% 204.64/35.41    (86)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.41    (87)   ~ (all_52_9 = all_52_25)
% 204.64/35.41    (88)  all_58_15 = all_14_2
% 204.64/35.41    (89)   ~ (all_52_19 = all_10_2)
% 204.64/35.41    (90)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.41    (91)  all_58_8 = all_10_2
% 204.64/35.41    (92)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.64/35.41    (93)   ~ (all_52_5 = all_10_2)
% 204.64/35.41    (94)  op(all_52_29, all_52_29) = all_52_28
% 204.64/35.41    (95)   ~ (all_52_23 = all_14_2)
% 204.64/35.41    (96)  all_56_12 = all_52_7
% 204.64/35.41    (97)   ~ (all_52_25 = all_6_2)
% 204.64/35.41    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.41    (99)   ~ (all_52_9 = all_4_2)
% 204.64/35.41    (100)   ~ (all_52_5 = all_6_2)
% 204.64/35.41    (101)   ~ (all_52_9 = all_6_2)
% 204.64/35.41    (102)   ~ (all_52_13 = all_52_15)
% 204.64/35.41    (103)  all_56_0 = all_6_2
% 204.64/35.41    (104)  op(e3, e3) = all_6_2
% 204.64/35.41    (105)   ~ (all_52_27 = all_14_2)
% 204.64/35.41    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.41    (107)  op(all_4_2, all_4_2) = all_52_10
% 204.64/35.41    (108)  all_56_3 = all_52_25
% 204.64/35.41    (109)   ~ (all_52_3 = all_52_7)
% 204.64/35.41    (110)  op(all_14_2, all_14_2) = all_52_30
% 204.64/35.41    (111)  all_58_5 = all_52_19
% 204.64/35.41    (112)  all_56_1 = all_52_9
% 204.64/35.41    (113)   ~ (all_52_27 = all_4_2)
% 204.64/35.41    (114)  op(all_52_17, all_52_17) = e3
% 204.64/35.41    (115)  all_58_6 = all_52_5
% 204.64/35.41    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.64/35.41    (117)   ~ (all_52_17 = all_6_2)
% 204.64/35.41    (118)   ~ (e1 = e0)
% 204.64/35.41    (119)   ~ (e3 = e2)
% 204.64/35.41    (120)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.41    (121)   ~ (all_52_9 = all_52_17)
% 204.64/35.41    (122)  all_56_10 = all_10_2
% 204.64/35.41    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.41    (124)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.64/35.41    (125)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.41    (126)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.41    (127)   ~ (all_6_1 = e2)
% 204.64/35.41    (128)  op(e1, e1) = all_10_2
% 204.64/35.41    (129)   ~ (all_52_7 = all_52_23)
% 204.64/35.41    (130)   ~ (all_52_17 = all_52_19)
% 204.64/35.41    (131)  all_58_3 = all_4_2
% 204.64/35.41    (132)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.41    (133)  all_56_13 = all_52_15
% 204.64/35.41    (134)   ~ (all_52_3 = all_4_2)
% 204.64/35.41    (135)  op(all_6_2, e3) = all_6_1
% 204.64/35.41    (136)   ~ (all_52_13 = all_52_29)
% 204.64/35.41    (137)  all_58_4 = all_52_17
% 204.64/35.41    (138)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.64/35.41    (139)  op(all_52_25, all_52_25) = all_52_24
% 204.64/35.41  
% 204.64/35.41  Begin of proof
% 204.64/35.41  | 
% 204.64/35.41  | BETA: splitting (92) gives:
% 204.64/35.41  | 
% 204.64/35.41  | Case 1:
% 204.64/35.41  | | 
% 204.64/35.41  | |   (140)  all_56_15 = e3
% 204.64/35.41  | | 
% 204.64/35.41  | | COMBINE_EQS: (40), (140) imply:
% 204.64/35.41  | |   (141)  all_14_2 = e3
% 204.64/35.41  | | 
% 204.64/35.41  | | SIMP: (141) implies:
% 204.64/35.41  | |   (142)  all_14_2 = e3
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (62), (142) imply:
% 204.64/35.41  | |   (143)   ~ (all_52_7 = e3)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (95), (142) imply:
% 204.64/35.41  | |   (144)   ~ (all_52_23 = e3)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (33), (142) imply:
% 204.64/35.41  | |   (145)   ~ (all_52_25 = e3)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (105), (142) imply:
% 204.64/35.41  | |   (146)   ~ (all_52_27 = e3)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (26), (142) imply:
% 204.64/35.41  | |   (147)   ~ (all_52_29 = e3)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (110), (142) imply:
% 204.64/35.41  | |   (148)  op(e3, e3) = all_52_30
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (19), (142) imply:
% 204.64/35.41  | |   (149)  op(e3, e0) = all_14_1
% 204.64/35.41  | | 
% 204.64/35.41  | | GROUND_INST: instantiating (6) with all_52_25, all_14_1, e0, e3, simplifying
% 204.64/35.41  | |              with (21), (149) gives:
% 204.64/35.41  | |   (150)  all_52_25 = all_14_1
% 204.64/35.41  | | 
% 204.64/35.41  | | GROUND_INST: instantiating (6) with all_6_2, all_52_30, e3, e3, simplifying
% 204.64/35.41  | |              with (104), (148) gives:
% 204.64/35.41  | |   (151)  all_52_30 = all_6_2
% 204.64/35.41  | | 
% 204.64/35.41  | | COMBINE_EQS: (108), (150) imply:
% 204.64/35.41  | |   (152)  all_56_3 = all_14_1
% 204.64/35.41  | | 
% 204.64/35.41  | | COMBINE_EQS: (24), (150) imply:
% 204.64/35.41  | |   (153)  all_58_9 = all_14_1
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (16), (150) imply:
% 204.64/35.41  | |   (154)   ~ (all_52_17 = all_14_1)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (97), (150) imply:
% 204.64/35.41  | |   (155)   ~ (all_14_1 = all_6_2)
% 204.64/35.41  | | 
% 204.64/35.41  | | REDUCE: (145), (150) imply:
% 204.64/35.41  | |   (156)   ~ (all_14_1 = e3)
% 204.64/35.41  | | 
% 204.64/35.41  | | BETA: splitting (98) gives:
% 204.64/35.41  | | 
% 204.64/35.41  | | Case 1:
% 204.64/35.41  | | | 
% 204.64/35.41  | | |   (157)  all_56_3 = e3
% 204.64/35.41  | | | 
% 204.64/35.41  | | | REF_CLOSE: (152), (156), (157) are inconsistent by sub-proof #1200.
% 204.64/35.41  | | | 
% 204.64/35.41  | | Case 2:
% 204.64/35.41  | | | 
% 204.64/35.41  | | |   (158)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.41  | | | 
% 204.64/35.41  | | | BETA: splitting (75) gives:
% 204.64/35.41  | | | 
% 204.64/35.41  | | | Case 1:
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | |   (159)  all_58_12 = e1
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | COMBINE_EQS: (60), (159) imply:
% 204.64/35.41  | | | |   (160)  all_52_7 = e1
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | SIMP: (160) implies:
% 204.64/35.41  | | | |   (161)  all_52_7 = e1
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | REDUCE: (109), (161) imply:
% 204.64/35.41  | | | |   (162)   ~ (all_52_3 = e1)
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | REDUCE: (143), (161) imply:
% 204.64/35.41  | | | |   (163)   ~ (e3 = e1)
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | REDUCE: (15), (161) imply:
% 204.64/35.41  | | | |   (164)  op(e1, e1) = all_52_6
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | GROUND_INST: instantiating (6) with all_10_2, all_52_6, e1, e1,
% 204.64/35.41  | | | |              simplifying with (128), (164) gives:
% 204.64/35.41  | | | |   (165)  all_52_6 = all_10_2
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | BETA: splitting (71) gives:
% 204.64/35.41  | | | | 
% 204.64/35.41  | | | | Case 1:
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | |   (166)  all_56_4 = e3
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | COMBINE_EQS: (20), (166) imply:
% 204.64/35.41  | | | | |   (167)  all_52_3 = e3
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | SIMP: (167) implies:
% 204.64/35.41  | | | | |   (168)  all_52_3 = e3
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | REDUCE: (14), (168) imply:
% 204.64/35.41  | | | | |   (169)   ~ (all_52_19 = e3)
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | SIMP: (169) implies:
% 204.64/35.41  | | | | |   (170)   ~ (all_52_19 = e3)
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | REDUCE: (35), (168) imply:
% 204.64/35.41  | | | | |   (171)   ~ (all_52_27 = e3)
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | REDUCE: (17), (168) imply:
% 204.64/35.41  | | | | |   (172)   ~ (all_6_2 = e3)
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | SIMP: (172) implies:
% 204.64/35.41  | | | | |   (173)   ~ (all_6_2 = e3)
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | REDUCE: (5), (168) imply:
% 204.64/35.41  | | | | |   (174)  op(e3, e3) = all_52_2
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_2, e3, e3,
% 204.64/35.41  | | | | |              simplifying with (104), (174) gives:
% 204.64/35.41  | | | | |   (175)  all_52_2 = all_6_2
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | BETA: splitting (123) gives:
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | Case 1:
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | |   (176)  all_58_4 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | COMBINE_EQS: (137), (176) imply:
% 204.64/35.41  | | | | | |   (177)  all_52_17 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | SIMP: (177) implies:
% 204.64/35.41  | | | | | |   (178)  all_52_17 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | REF_CLOSE: (6), (104), (114), (117), (178) are inconsistent by
% 204.64/35.41  | | | | | |            sub-proof #1280.
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | Case 2:
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | |   (179)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | BETA: splitting (179) gives:
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | Case 1:
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | |   (180)  all_58_5 = e3
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | | REF_CLOSE: (111), (170), (180) are inconsistent by sub-proof
% 204.64/35.41  | | | | | | |            #1279.
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | Case 2:
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | |   (181)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | | REF_CLOSE: (3), (5), (6), (7), (15), (17), (18), (23), (24), (29),
% 204.64/35.41  | | | | | | |            (30), (31), (34), (36), (38), (41), (47), (48), (50),
% 204.64/35.41  | | | | | | |            (51), (52), (57), (59), (60), (63), (66), (67), (68),
% 204.64/35.41  | | | | | | |            (80), (81), (84), (86), (89), (90), (91), (99), (100),
% 204.64/35.41  | | | | | | |            (104), (106), (109), (111), (114), (115), (117), (119),
% 204.64/35.41  | | | | | | |            (127), (131), (134), (135), (137), (144), (145), (146),
% 204.64/35.41  | | | | | | |            (149), (152), (153), (158), (173), (181) are
% 204.64/35.41  | | | | | | |            inconsistent by sub-proof #1079.
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | End of split
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | End of split
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | Case 2:
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | |   (182)   ~ (all_56_4 = e3)
% 204.64/35.41  | | | | |   (183)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | REDUCE: (20), (182) imply:
% 204.64/35.41  | | | | |   (184)   ~ (all_52_3 = e3)
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | BETA: splitting (67) gives:
% 204.64/35.41  | | | | | 
% 204.64/35.41  | | | | | Case 1:
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | |   (185)  all_58_0 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | COMBINE_EQS: (18), (185) imply:
% 204.64/35.41  | | | | | |   (186)  all_6_2 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | REDUCE: (100), (186) imply:
% 204.64/35.41  | | | | | |   (187)   ~ (all_52_5 = e3)
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | REDUCE: (37), (186) imply:
% 204.64/35.41  | | | | | |   (188)  op(e3, e3) = all_52_0
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | REDUCE: (135), (186) imply:
% 204.64/35.41  | | | | | |   (189)  op(e3, e3) = all_6_1
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | REDUCE: (104), (186) imply:
% 204.64/35.41  | | | | | |   (190)  op(e3, e3) = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | REF_CLOSE: (6), (32), (41), (49), (50), (51), (57), (58), (61),
% 204.64/35.41  | | | | | |            (63), (68), (81), (83), (89), (91), (111), (115), (126),
% 204.64/35.41  | | | | | |            (131), (136), (146), (147), (184), (187), (188), (189),
% 204.64/35.41  | | | | | |            (190) are inconsistent by sub-proof #1076.
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | Case 2:
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | |   (191)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | BETA: splitting (191) gives:
% 204.64/35.41  | | | | | | 
% 204.64/35.41  | | | | | | Case 1:
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | |   (192)  all_58_2 = e3
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | | REF_CLOSE: (63), (184), (192) are inconsistent by sub-proof #1369.
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | Case 2:
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | |   (193)  all_58_6 = e3 | all_58_12 = e3
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | | BETA: splitting (193) gives:
% 204.64/35.41  | | | | | | | 
% 204.64/35.41  | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | |   (194)  all_58_6 = e3
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | COMBINE_EQS: (115), (194) imply:
% 204.64/35.41  | | | | | | | |   (195)  all_52_5 = e3
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | SIMP: (195) implies:
% 204.64/35.41  | | | | | | | |   (196)  all_52_5 = e3
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | REDUCE: (93), (196) imply:
% 204.64/35.41  | | | | | | | |   (197)   ~ (all_10_2 = e3)
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | SIMP: (197) implies:
% 204.64/35.41  | | | | | | | |   (198)   ~ (all_10_2 = e3)
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | REDUCE: (100), (196) imply:
% 204.64/35.41  | | | | | | | |   (199)   ~ (all_6_2 = e3)
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | SIMP: (199) implies:
% 204.64/35.41  | | | | | | | |   (200)   ~ (all_6_2 = e3)
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | REDUCE: (22), (196) imply:
% 204.64/35.41  | | | | | | | |   (201)  op(e3, e3) = all_52_4
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_4, e3, e3,
% 204.64/35.41  | | | | | | | |              simplifying with (104), (201) gives:
% 204.64/35.41  | | | | | | | |   (202)  all_52_4 = all_6_2
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | BETA: splitting (86) gives:
% 204.64/35.41  | | | | | | | | 
% 204.64/35.41  | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | |   (203)  all_58_1 = e3
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | COMBINE_EQS: (7), (203) imply:
% 204.64/35.41  | | | | | | | | |   (204)  all_52_9 = e3
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | REDUCE: (121), (204) imply:
% 204.64/35.41  | | | | | | | | |   (205)   ~ (all_52_17 = e3)
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | SIMP: (205) implies:
% 204.64/35.41  | | | | | | | | |   (206)   ~ (all_52_17 = e3)
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | REDUCE: (53), (204) imply:
% 204.64/35.41  | | | | | | | | |   (207)  op(e3, e3) = all_52_8
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | BETA: splitting (123) gives:
% 204.64/35.41  | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | |   (208)  all_58_4 = e3
% 204.64/35.41  | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | REF_CLOSE: (137), (206), (208) are inconsistent by sub-proof
% 204.64/35.41  | | | | | | | | | |            #1302.
% 204.64/35.41  | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | Case 2:
% 204.64/35.41  | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | |   (209)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.41  | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | BETA: splitting (209) gives:
% 204.64/35.41  | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | |   (210)  all_58_5 = e3
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | COMBINE_EQS: (111), (210) imply:
% 204.64/35.41  | | | | | | | | | | |   (211)  all_52_19 = e3
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | SIMP: (211) implies:
% 204.64/35.41  | | | | | | | | | | |   (212)  all_52_19 = e3
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | REDUCE: (58), (212) imply:
% 204.64/35.41  | | | | | | | | | | |   (213)  op(e3, e3) = e2
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 204.64/35.41  | | | | | | | | | | |              simplifying with (104), (207) gives:
% 204.64/35.41  | | | | | | | | | | |   (214)  all_52_8 = all_6_2
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_52_8, e3, e3,
% 204.64/35.41  | | | | | | | | | | |              simplifying with (207), (213) gives:
% 204.64/35.41  | | | | | | | | | | |   (215)  all_52_8 = e2
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | COMBINE_EQS: (214), (215) imply:
% 204.64/35.41  | | | | | | | | | | |   (216)  all_6_2 = e2
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | SIMP: (216) implies:
% 204.64/35.41  | | | | | | | | | | |   (217)  all_6_2 = e2
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | REDUCE: (17), (217) imply:
% 204.64/35.41  | | | | | | | | | | |   (218)   ~ (all_52_3 = e2)
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | REDUCE: (117), (217) imply:
% 204.64/35.41  | | | | | | | | | | |   (219)   ~ (all_52_17 = e2)
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | REDUCE: (155), (217) imply:
% 204.64/35.41  | | | | | | | | | | |   (220)   ~ (all_14_1 = e2)
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | REDUCE: (135), (217) imply:
% 204.64/35.41  | | | | | | | | | | |   (221)  op(e2, e3) = all_6_1
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | BETA: splitting (183) gives:
% 204.64/35.41  | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | |   (222)  all_56_4 = e2
% 204.64/35.41  | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | REF_CLOSE: (20), (218), (222) are inconsistent by sub-proof
% 204.64/35.41  | | | | | | | | | | | |            #1155.
% 204.64/35.41  | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | Case 2:
% 204.64/35.41  | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | |   (223)  all_56_4 = e1 | all_56_4 = e0
% 204.64/35.41  | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | BETA: splitting (223) gives:
% 204.64/35.41  | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | |   (224)  all_56_4 = e1
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | REF_CLOSE: (20), (162), (224) are inconsistent by sub-proof
% 204.64/35.41  | | | | | | | | | | | | |            #1310.
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | Case 2:
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | |   (225)  all_56_4 = e0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | COMBINE_EQS: (20), (225) imply:
% 204.64/35.41  | | | | | | | | | | | | |   (226)  all_52_3 = e0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | SIMP: (226) implies:
% 204.64/35.41  | | | | | | | | | | | | |   (227)  all_52_3 = e0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | REDUCE: (11), (227) imply:
% 204.64/35.41  | | | | | | | | | | | | |   (228)  op(e2, e3) = e0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e0, all_6_1, e3, e2,
% 204.64/35.41  | | | | | | | | | | | | |              simplifying with (221), (228) gives:
% 204.64/35.41  | | | | | | | | | | | | |   (229)  all_6_1 = e0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | REDUCE: (68), (229) imply:
% 204.64/35.41  | | | | | | | | | | | | |   (230)  op(e3, e0) = all_6_0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_14_1, all_6_0, e0, e3,
% 204.64/35.41  | | | | | | | | | | | | |              simplifying with (149), (230) gives:
% 204.64/35.41  | | | | | | | | | | | | |   (231)  all_14_1 = all_6_0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | COMBINE_EQS: (152), (231) imply:
% 204.64/35.41  | | | | | | | | | | | | |   (232)  all_56_3 = all_6_0
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | REDUCE: (154), (231) imply:
% 204.64/35.41  | | | | | | | | | | | | |   (233)   ~ (all_52_17 = all_6_0)
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | BETA: splitting (158) gives:
% 204.64/35.41  | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | |   (234)  all_56_3 = e2
% 204.64/35.41  | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | | REF_CLOSE: (81), (232), (234) are inconsistent by sub-proof
% 204.64/35.41  | | | | | | | | | | | | | |            #1075.
% 204.64/35.41  | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | Case 2:
% 204.64/35.41  | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | |   (235)  all_56_3 = e1 | all_56_3 = e0
% 204.64/35.41  | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 204.64/35.41  | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | | Case 1:
% 204.64/35.41  | | | | | | | | | | | | | | | 
% 204.64/35.41  | | | | | | | | | | | | | | |   (236)  all_56_3 = e1
% 204.64/35.41  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | | REF_CLOSE: (49), (232), (236) are inconsistent by sub-proof
% 204.64/35.42  | | | | | | | | | | | | | | |            #1074.
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | |   (237)  all_56_3 = e0
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | | COMBINE_EQS: (232), (237) imply:
% 204.64/35.42  | | | | | | | | | | | | | | |   (238)  all_6_0 = e0
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | | SIMP: (238) implies:
% 204.64/35.42  | | | | | | | | | | | | | | |   (239)  all_6_0 = e0
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | | REDUCE: (233), (239) imply:
% 204.64/35.42  | | | | | | | | | | | | | | |   (240)   ~ (all_52_17 = e0)
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | | REF_CLOSE: (6), (44), (65), (114), (128), (198), (206),
% 204.64/35.42  | | | | | | | | | | | | | | |            (219), (240) are inconsistent by sub-proof #1073.
% 204.64/35.42  | | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | |   (241)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.42  | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | | REF_CLOSE: (3), (91), (144), (198), (241) are inconsistent by
% 204.64/35.42  | | | | | | | | | | |            sub-proof #1304.
% 204.64/35.42  | | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | |   (242)   ~ (all_58_1 = e3)
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | REDUCE: (7), (242) imply:
% 204.64/35.42  | | | | | | | | |   (243)   ~ (all_52_9 = e3)
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | REF_CLOSE: (6), (7), (18), (24), (104), (106), (114), (117),
% 204.64/35.42  | | | | | | | | |            (137), (145), (200), (243) are inconsistent by
% 204.64/35.42  | | | | | | | | |            sub-proof #1071.
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | |   (244)  all_58_12 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | COMBINE_EQS: (159), (244) imply:
% 204.64/35.42  | | | | | | | |   (245)  e3 = e1
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | REDUCE: (4), (245) imply:
% 204.64/35.42  | | | | | | | |   (246)  $false
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | CLOSE: (246) is inconsistent.
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | End of split
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | End of split
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | End of split
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | End of split
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | Case 2:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | |   (247)   ~ (all_58_12 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | REDUCE: (60), (247) imply:
% 204.64/35.42  | | | |   (248)   ~ (all_52_7 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | BETA: splitting (123) gives:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | Case 1:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (249)  all_58_4 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | COMBINE_EQS: (137), (249) imply:
% 204.64/35.42  | | | | |   (250)  all_52_17 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | SIMP: (250) implies:
% 204.64/35.42  | | | | |   (251)  all_52_17 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REF_CLOSE: (6), (104), (114), (117), (251) are inconsistent by
% 204.64/35.42  | | | | |            sub-proof #1280.
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | Case 2:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (252)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | BETA: splitting (106) gives:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | Case 1:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | |   (253)  all_58_0 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | COMBINE_EQS: (18), (253) imply:
% 204.64/35.42  | | | | | |   (254)  all_6_2 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REDUCE: (17), (254) imply:
% 204.64/35.42  | | | | | |   (255)   ~ (all_52_3 = e3)
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REDUCE: (100), (254) imply:
% 204.64/35.42  | | | | | |   (256)   ~ (all_52_5 = e3)
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REDUCE: (37), (254) imply:
% 204.64/35.42  | | | | | |   (257)  op(e3, e3) = all_52_0
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REDUCE: (135), (254) imply:
% 204.64/35.42  | | | | | |   (258)  op(e3, e3) = all_6_1
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REDUCE: (104), (254) imply:
% 204.64/35.42  | | | | | |   (259)  op(e3, e3) = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REF_CLOSE: (6), (32), (41), (49), (50), (51), (57), (58), (61),
% 204.64/35.42  | | | | | |            (63), (68), (81), (83), (89), (91), (111), (115), (126),
% 204.64/35.42  | | | | | |            (131), (136), (146), (147), (255), (256), (257), (258),
% 204.64/35.42  | | | | | |            (259) are inconsistent by sub-proof #1076.
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | Case 2:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | |   (260)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | BETA: splitting (260) gives:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | Case 1:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | |   (261)  all_58_1 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | COMBINE_EQS: (7), (261) imply:
% 204.64/35.42  | | | | | | |   (262)  all_52_9 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (8), (262) imply:
% 204.64/35.42  | | | | | | |   (263)   ~ (all_52_13 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | SIMP: (263) implies:
% 204.64/35.42  | | | | | | |   (264)   ~ (all_52_13 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (34), (262) imply:
% 204.64/35.42  | | | | | | |   (265)   ~ (all_52_15 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | SIMP: (265) implies:
% 204.64/35.42  | | | | | | |   (266)   ~ (all_52_15 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (99), (262) imply:
% 204.64/35.42  | | | | | | |   (267)   ~ (all_4_2 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | SIMP: (267) implies:
% 204.64/35.42  | | | | | | |   (268)   ~ (all_4_2 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (53), (262) imply:
% 204.64/35.42  | | | | | | |   (269)  op(e3, e3) = all_52_8
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_8, e3, e3,
% 204.64/35.42  | | | | | | |              simplifying with (104), (269) gives:
% 204.64/35.42  | | | | | | |   (270)  all_52_8 = all_6_2
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | BETA: splitting (61) gives:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | Case 1:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | |   (271)  all_58_6 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | COMBINE_EQS: (115), (271) imply:
% 204.64/35.42  | | | | | | | |   (272)  all_52_5 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | SIMP: (272) implies:
% 204.64/35.42  | | | | | | | |   (273)  all_52_5 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | REDUCE: (93), (273) imply:
% 204.64/35.42  | | | | | | | |   (274)   ~ (all_10_2 = e3)
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | SIMP: (274) implies:
% 204.64/35.42  | | | | | | | |   (275)   ~ (all_10_2 = e3)
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | REDUCE: (22), (273) imply:
% 204.64/35.42  | | | | | | | |   (276)  op(e3, e3) = all_52_4
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | REF_CLOSE: (3), (4), (6), (11), (14), (17), (18), (20), (25),
% 204.64/35.42  | | | | | | | |            (47), (58), (60), (63), (70), (71), (91), (104),
% 204.64/35.42  | | | | | | | |            (111), (118), (135), (144), (248), (252), (271),
% 204.64/35.42  | | | | | | | |            (275), (276) are inconsistent by sub-proof #1070.
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | |   (277)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | BETA: splitting (277) gives:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | Case 1:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | |   (278)  all_58_7 = e3
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | COMBINE_EQS: (57), (278) imply:
% 204.64/35.42  | | | | | | | | |   (279)  all_52_13 = e3
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | REDUCE: (264), (279) imply:
% 204.64/35.42  | | | | | | | | |   (280)  $false
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | CLOSE: (280) is inconsistent.
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | |   (281)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | BETA: splitting (281) gives:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | Case 1:
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | |   (282)  all_58_8 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | COMBINE_EQS: (91), (282) imply:
% 204.64/35.42  | | | | | | | | | |   (283)  all_10_2 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | SIMP: (283) implies:
% 204.64/35.42  | | | | | | | | | |   (284)  all_10_2 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | REDUCE: (89), (284) imply:
% 204.64/35.42  | | | | | | | | | |   (285)   ~ (all_52_19 = e3)
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | REDUCE: (50), (284) imply:
% 204.64/35.42  | | | | | | | | | |   (286)  op(e3, e3) = e1
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | REDUCE: (36), (284) imply:
% 204.64/35.42  | | | | | | | | | |   (287)  op(e3, e1) = all_10_1
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | REF_CLOSE: (5), (6), (15), (17), (18), (23), (29), (30),
% 204.64/35.42  | | | | | | | | | |            (31), (38), (41), (47), (51), (52), (57), (59),
% 204.64/35.42  | | | | | | | | | |            (60), (63), (66), (67), (68), (80), (81), (84),
% 204.64/35.42  | | | | | | | | | |            (86), (90), (100), (104), (109), (111), (114),
% 204.64/35.42  | | | | | | | | | |            (115), (119), (127), (131), (134), (135), (137),
% 204.64/35.42  | | | | | | | | | |            (146), (149), (152), (153), (158), (261), (264),
% 204.64/35.42  | | | | | | | | | |            (266), (268), (285), (286), (287) are inconsistent
% 204.64/35.42  | | | | | | | | | |            by sub-proof #1081.
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | |   (288)  all_58_11 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | REF_CLOSE: (32), (147), (288) are inconsistent by sub-proof
% 204.64/35.42  | | | | | | | | | |            #1323.
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | End of split
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | End of split
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | Case 2:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | |   (289)  all_58_4 = e3 | all_58_9 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REF_CLOSE: (6), (24), (104), (114), (117), (137), (145), (289) are
% 204.64/35.42  | | | | | | |            inconsistent by sub-proof #1080.
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | End of split
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | End of split
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | End of split
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | End of split
% 204.64/35.42  | | | 
% 204.64/35.42  | | End of split
% 204.64/35.42  | | 
% 204.64/35.42  | Case 2:
% 204.64/35.42  | | 
% 204.64/35.42  | |   (290)   ~ (all_56_15 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (40), (290) imply:
% 204.64/35.42  | |   (291)   ~ (all_14_2 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14),
% 204.64/35.42  | |            (15), (16), (18), (22), (23), (24), (25), (27), (28), (29), (30),
% 204.64/35.42  | |            (31), (32), (33), (34), (36), (37), (38), (39), (41), (42), (43),
% 204.64/35.42  | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 204.64/35.42  | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 204.64/35.42  | |            (66), (67), (68), (69), (72), (73), (74), (76), (77), (78), (79),
% 204.64/35.42  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 204.64/35.42  | |            (91), (93), (94), (95), (96), (98), (99), (100), (101), (102),
% 204.64/35.42  | |            (103), (104), (105), (106), (107), (108), (109), (111), (112),
% 204.64/35.42  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 204.64/35.42  | |            (122), (123), (124), (125), (126), (127), (128), (129), (131),
% 204.64/35.42  | |            (132), (133), (134), (135), (137), (138), (139), (291) are
% 204.64/35.42  | |            inconsistent by sub-proof #1044.
% 204.64/35.42  | | 
% 204.64/35.42  | End of split
% 204.64/35.42  | 
% 204.64/35.42  End of proof
% 204.64/35.42  
% 204.64/35.42  Sub-proof #1044 shows that the following formulas are inconsistent:
% 204.64/35.42  ----------------------------------------------------------------
% 204.64/35.42    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.64/35.42    (2)   ~ (all_52_15 = all_52_23)
% 204.64/35.42    (3)  all_58_14 = all_52_23
% 204.64/35.42    (4)   ~ (e3 = e1)
% 204.64/35.42    (5)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.42    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.42    (7)  all_58_1 = all_52_9
% 204.64/35.42    (8)   ~ (e3 = e0)
% 204.64/35.42    (9)  op(all_52_23, all_52_23) = e0
% 204.64/35.42    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.64/35.42    (11)   ~ (all_52_7 = all_52_15)
% 204.64/35.42    (12)   ~ (all_52_3 = all_52_19)
% 204.64/35.42    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.42    (14)   ~ (all_52_17 = all_52_25)
% 204.64/35.42    (15)  all_58_0 = all_6_2
% 204.64/35.42    (16)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.42    (17)  all_58_13 = all_52_15
% 204.64/35.42    (18)  all_58_9 = all_52_25
% 204.64/35.42    (19)   ~ (all_6_1 = e1)
% 204.64/35.42    (20)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.42    (21)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.42    (22)  op(e1, e3) = all_52_5
% 204.64/35.42    (23)  op(e2, e2) = all_4_2
% 204.64/35.42    (24)   ~ (all_52_3 = all_52_5)
% 204.64/35.42    (25)  all_58_11 = all_52_29
% 204.64/35.42    (26)   ~ (all_52_25 = all_14_2)
% 204.64/35.42    (27)   ~ (all_52_9 = all_52_15)
% 204.64/35.42    (28)  op(all_10_2, e1) = all_10_1
% 204.64/35.42    (29)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.42    (30)   ~ (all_52_7 = all_6_2)
% 204.64/35.42    (31)  op(e0, e0) = all_14_2
% 204.64/35.42    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.42    (33)  all_56_11 = all_52_29
% 204.64/35.42    (34)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.64/35.42    (35)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.42    (36)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.64/35.42    (37)  all_56_9 = all_52_13
% 204.64/35.42    (38)   ~ (e2 = e1)
% 204.64/35.42    (39)   ~ (all_52_13 = all_10_2)
% 204.64/35.42    (40)   ~ (all_6_0 = e1)
% 204.64/35.42    (41)  op(all_10_2, all_10_2) = e1
% 204.64/35.42    (42)  all_58_10 = all_52_27
% 204.64/35.42    (43)  all_56_8 = all_52_5
% 204.64/35.42    (44)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.42    (45)   ~ (all_52_19 = all_52_23)
% 204.64/35.42    (46)   ~ (all_52_25 = all_52_29)
% 204.64/35.42    (47)   ~ (all_52_29 = all_10_2)
% 204.64/35.42    (48)  all_58_7 = all_52_13
% 204.64/35.42    (49)  op(all_52_19, all_52_19) = e2
% 204.64/35.42    (50)   ~ (all_52_5 = all_52_7)
% 204.64/35.42    (51)  all_58_12 = all_52_7
% 204.64/35.42    (52)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.42    (53)   ~ (all_52_7 = all_14_2)
% 204.64/35.42    (54)  all_58_2 = all_52_3
% 204.64/35.42    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.64/35.42    (56)  all_56_2 = all_52_17
% 204.64/35.42    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.42    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.42    (59)  op(e3, all_6_1) = all_6_0
% 204.64/35.42    (60)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.42    (61)   ~ (e2 = e0)
% 204.64/35.42    (62)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.42    (63)   ~ (all_52_5 = all_52_29)
% 204.64/35.42    (64)  all_56_6 = all_52_19
% 204.64/35.42    (65)   ~ (all_52_15 = all_14_2)
% 204.64/35.42    (66)   ~ (all_52_19 = all_52_27)
% 204.64/35.42    (67)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.42    (68)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.42    (69)   ~ (all_6_0 = e2)
% 204.64/35.42    (70)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.42    (71)   ~ (all_52_13 = all_4_2)
% 204.64/35.42    (72)  op(e3, e1) = all_52_17
% 204.64/35.42    (73)  op(e0, e3) = all_52_7
% 204.64/35.42    (74)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.42    (75)   ~ (all_52_9 = all_52_25)
% 204.64/35.42    (76)  all_58_15 = all_14_2
% 204.64/35.42    (77)   ~ (all_52_19 = all_10_2)
% 204.64/35.42    (78)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.42    (79)  all_58_8 = all_10_2
% 204.64/35.42    (80)   ~ (all_52_5 = all_10_2)
% 204.64/35.42    (81)  op(all_52_29, all_52_29) = all_52_28
% 204.64/35.42    (82)   ~ (all_52_23 = all_14_2)
% 204.64/35.42    (83)  all_56_12 = all_52_7
% 204.64/35.42    (84)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.42    (85)   ~ (all_52_9 = all_4_2)
% 204.64/35.42    (86)   ~ (all_52_5 = all_6_2)
% 204.64/35.42    (87)   ~ (all_52_9 = all_6_2)
% 204.64/35.42    (88)   ~ (all_52_13 = all_52_15)
% 204.64/35.42    (89)  all_56_0 = all_6_2
% 204.64/35.42    (90)  op(e3, e3) = all_6_2
% 204.64/35.42    (91)   ~ (all_52_27 = all_14_2)
% 204.64/35.42    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.42    (93)  op(all_4_2, all_4_2) = all_52_10
% 204.64/35.42    (94)  all_56_3 = all_52_25
% 204.64/35.42    (95)   ~ (all_52_3 = all_52_7)
% 204.64/35.42    (96)  all_58_5 = all_52_19
% 204.64/35.42    (97)  all_56_1 = all_52_9
% 204.64/35.42    (98)   ~ (all_52_27 = all_4_2)
% 204.64/35.42    (99)  op(all_52_17, all_52_17) = e3
% 204.64/35.42    (100)  all_58_6 = all_52_5
% 204.64/35.42    (101)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.64/35.42    (102)   ~ (all_52_17 = all_6_2)
% 204.64/35.42    (103)   ~ (e1 = e0)
% 204.64/35.42    (104)   ~ (e3 = e2)
% 204.64/35.42    (105)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.42    (106)   ~ (all_52_9 = all_52_17)
% 204.64/35.42    (107)  all_56_10 = all_10_2
% 204.64/35.42    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.42    (109)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.64/35.42    (110)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.42    (111)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.42    (112)   ~ (all_6_1 = e2)
% 204.64/35.42    (113)  op(e1, e1) = all_10_2
% 204.64/35.42    (114)   ~ (all_52_7 = all_52_23)
% 204.64/35.42    (115)  all_58_3 = all_4_2
% 204.64/35.42    (116)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.42    (117)  all_56_13 = all_52_15
% 204.64/35.42    (118)   ~ (all_52_3 = all_4_2)
% 204.64/35.42    (119)  op(all_6_2, e3) = all_6_1
% 204.64/35.42    (120)  all_58_4 = all_52_17
% 204.64/35.42    (121)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.64/35.42    (122)  op(all_52_25, all_52_25) = all_52_24
% 204.64/35.42    (123)   ~ (all_14_2 = e3)
% 204.64/35.42  
% 204.64/35.42  Begin of proof
% 204.64/35.42  | 
% 204.64/35.42  | BETA: splitting (34) gives:
% 204.64/35.42  | 
% 204.64/35.42  | Case 1:
% 204.64/35.42  | | 
% 204.64/35.42  | |   (124)  all_56_13 = e3
% 204.64/35.42  | | 
% 204.64/35.42  | | COMBINE_EQS: (117), (124) imply:
% 204.64/35.42  | |   (125)  all_52_15 = e3
% 204.64/35.42  | | 
% 204.64/35.42  | | SIMP: (125) implies:
% 204.64/35.42  | |   (126)  all_52_15 = e3
% 204.64/35.42  | | 
% 204.64/35.42  | | COMBINE_EQS: (17), (126) imply:
% 204.64/35.42  | |   (127)  all_58_13 = e3
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (11), (126) imply:
% 204.64/35.42  | |   (128)   ~ (all_52_7 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (27), (126) imply:
% 204.64/35.42  | |   (129)   ~ (all_52_9 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (88), (126) imply:
% 204.64/35.42  | |   (130)   ~ (all_52_13 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (2), (126) imply:
% 204.64/35.42  | |   (131)   ~ (all_52_23 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | SIMP: (131) implies:
% 204.64/35.42  | |   (132)   ~ (all_52_23 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (65), (126) imply:
% 204.64/35.42  | |   (133)   ~ (all_14_2 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | BETA: splitting (105) gives:
% 204.64/35.42  | | 
% 204.64/35.42  | | Case 1:
% 204.64/35.42  | | | 
% 204.64/35.42  | | |   (134)  all_56_1 = e3
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REF_CLOSE: (97), (129), (134) are inconsistent by sub-proof #1326.
% 204.64/35.42  | | | 
% 204.64/35.42  | | Case 2:
% 204.64/35.42  | | | 
% 204.64/35.42  | | |   (135)   ~ (all_56_1 = e3)
% 204.64/35.42  | | |   (136)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.42  | | | 
% 204.64/35.42  | | | BETA: splitting (36) gives:
% 204.64/35.42  | | | 
% 204.64/35.42  | | | Case 1:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | |   (137)  all_58_1 = e1
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | COMBINE_EQS: (7), (137) imply:
% 204.64/35.42  | | | |   (138)  all_52_9 = e1
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | REDUCE: (106), (138) imply:
% 204.64/35.42  | | | |   (139)   ~ (all_52_17 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | SIMP: (139) implies:
% 204.64/35.42  | | | |   (140)   ~ (all_52_17 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | REDUCE: (87), (138) imply:
% 204.64/35.42  | | | |   (141)   ~ (all_6_2 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | SIMP: (141) implies:
% 204.64/35.42  | | | |   (142)   ~ (all_6_2 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | BETA: splitting (35) gives:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | Case 1:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (143)  all_56_2 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | COMBINE_EQS: (56), (143) imply:
% 204.64/35.42  | | | | |   (144)  all_52_17 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | SIMP: (144) implies:
% 204.64/35.42  | | | | |   (145)  all_52_17 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REF_CLOSE: (6), (90), (99), (102), (145) are inconsistent by sub-proof
% 204.64/35.42  | | | | |            #1280.
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | Case 2:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (146)   ~ (all_56_2 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (56), (146) imply:
% 204.64/35.42  | | | | |   (147)   ~ (all_52_17 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | BETA: splitting (108) gives:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | Case 1:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | |   (148)  all_58_4 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REF_CLOSE: (120), (147), (148) are inconsistent by sub-proof #1302.
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | Case 2:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | |   (149)   ~ (all_58_4 = e3)
% 204.64/35.42  | | | | | |   (150)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | BETA: splitting (92) gives:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | Case 1:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | |   (151)  all_58_0 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | COMBINE_EQS: (15), (151) imply:
% 204.64/35.42  | | | | | | |   (152)  all_6_2 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (86), (152) imply:
% 204.64/35.42  | | | | | | |   (153)   ~ (all_52_5 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (29), (152) imply:
% 204.64/35.42  | | | | | | |   (154)  op(e3, e3) = all_52_0
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (119), (152) imply:
% 204.64/35.42  | | | | | | |   (155)  op(e3, e3) = all_6_1
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (90), (152) imply:
% 204.64/35.42  | | | | | | |   (156)  op(e3, e3) = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | GROUND_INST: instantiating (6) with all_6_1, all_52_0, e3, e3,
% 204.64/35.42  | | | | | | |              simplifying with (154), (155) gives:
% 204.64/35.42  | | | | | | |   (157)  all_52_0 = all_6_1
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e3, e3,
% 204.64/35.42  | | | | | | |              simplifying with (154), (156) gives:
% 204.64/35.42  | | | | | | |   (158)  all_52_0 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | COMBINE_EQS: (157), (158) imply:
% 204.64/35.42  | | | | | | |   (159)  all_6_1 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | SIMP: (159) implies:
% 204.64/35.42  | | | | | | |   (160)  all_6_1 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (59), (160) imply:
% 204.64/35.42  | | | | | | |   (161)  op(e3, e3) = all_6_0
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | GROUND_INST: instantiating (6) with e3, all_6_0, e3, e3,
% 204.64/35.42  | | | | | | |              simplifying with (156), (161) gives:
% 204.64/35.42  | | | | | | |   (162)  all_6_0 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REF_CLOSE: (3), (4), (6), (25), (33), (41), (47), (48), (49),
% 204.64/35.42  | | | | | | |            (52), (67), (79), (81), (96), (100), (104), (130),
% 204.64/35.42  | | | | | | |            (132), (150), (153), (154), (156) are inconsistent by
% 204.64/35.42  | | | | | | |            sub-proof #1069.
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | Case 2:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | |   (163)   ~ (all_58_0 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REDUCE: (15), (163) imply:
% 204.64/35.42  | | | | | | |   (164)   ~ (all_6_2 = e3)
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REF_CLOSE: (3), (6), (9), (15), (29), (30), (31), (35), (51),
% 204.64/35.42  | | | | | | |            (56), (57), (60), (70), (82), (89), (99), (102), (110),
% 204.64/35.42  | | | | | | |            (123), (127), (140), (142), (147), (164) are
% 204.64/35.42  | | | | | | |            inconsistent by sub-proof #1064.
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | End of split
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | End of split
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | End of split
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | Case 2:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | |   (165)   ~ (all_58_1 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | REDUCE: (7), (165) imply:
% 204.64/35.42  | | | |   (166)   ~ (all_52_9 = e1)
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | BETA: splitting (58) gives:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | Case 1:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (167)  all_58_0 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | COMBINE_EQS: (15), (167) imply:
% 204.64/35.42  | | | | |   (168)  all_6_2 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (86), (168) imply:
% 204.64/35.42  | | | | |   (169)   ~ (all_52_5 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (102), (168) imply:
% 204.64/35.42  | | | | |   (170)   ~ (all_52_17 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (29), (168) imply:
% 204.64/35.42  | | | | |   (171)  op(e3, e3) = all_52_0
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (119), (168) imply:
% 204.64/35.42  | | | | |   (172)  op(e3, e3) = all_6_1
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (90), (168) imply:
% 204.64/35.42  | | | | |   (173)  op(e3, e3) = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | GROUND_INST: instantiating (6) with all_6_1, all_52_0, e3, e3,
% 204.64/35.42  | | | | |              simplifying with (171), (172) gives:
% 204.64/35.42  | | | | |   (174)  all_52_0 = all_6_1
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e3, e3, simplifying
% 204.64/35.42  | | | | |              with (171), (173) gives:
% 204.64/35.42  | | | | |   (175)  all_52_0 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | COMBINE_EQS: (174), (175) imply:
% 204.64/35.42  | | | | |   (176)  all_6_1 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (59), (176) imply:
% 204.64/35.42  | | | | |   (177)  op(e3, e3) = all_6_0
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | GROUND_INST: instantiating (6) with e3, all_6_0, e3, e3, simplifying
% 204.64/35.42  | | | | |              with (173), (177) gives:
% 204.64/35.42  | | | | |   (178)  all_6_0 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REF_CLOSE: (3), (4), (6), (25), (33), (41), (47), (48), (49), (52),
% 204.64/35.42  | | | | |            (67), (79), (81), (96), (100), (104), (108), (120), (130),
% 204.64/35.42  | | | | |            (132), (169), (170), (171), (173) are inconsistent by
% 204.64/35.42  | | | | |            sub-proof #1063.
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | Case 2:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (179)   ~ (all_58_0 = e3)
% 204.64/35.42  | | | | |   (180)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (15), (179) imply:
% 204.64/35.42  | | | | |   (181)   ~ (all_6_2 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (14), (15), (16), (18), (20),
% 204.64/35.42  | | | | |            (23), (24), (25), (26), (28), (29), (30), (31), (35), (38),
% 204.64/35.42  | | | | |            (41), (44), (46), (48), (49), (51), (52), (54), (56), (57),
% 204.64/35.42  | | | | |            (58), (60), (62), (70), (72), (77), (79), (80), (82), (87),
% 204.64/35.42  | | | | |            (89), (90), (92), (95), (96), (97), (99), (100), (102),
% 204.64/35.42  | | | | |            (104), (106), (108), (110), (113), (116), (118), (120),
% 204.64/35.42  | | | | |            (122), (123), (127), (128), (129), (130), (132), (136),
% 204.64/35.42  | | | | |            (166), (180), (181) are inconsistent by sub-proof #1055.
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | End of split
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | End of split
% 204.64/35.42  | | | 
% 204.64/35.42  | | End of split
% 204.64/35.42  | | 
% 204.64/35.42  | Case 2:
% 204.64/35.42  | | 
% 204.64/35.42  | |   (182)   ~ (all_56_13 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | REDUCE: (117), (182) imply:
% 204.64/35.42  | |   (183)   ~ (all_52_15 = e3)
% 204.64/35.42  | | 
% 204.64/35.42  | | BETA: splitting (101) gives:
% 204.64/35.42  | | 
% 204.64/35.42  | | Case 1:
% 204.64/35.42  | | | 
% 204.64/35.42  | | |   (184)  all_58_12 = e3
% 204.64/35.42  | | | 
% 204.64/35.42  | | | COMBINE_EQS: (51), (184) imply:
% 204.64/35.42  | | |   (185)  all_52_7 = e3
% 204.64/35.42  | | | 
% 204.64/35.42  | | | SIMP: (185) implies:
% 204.64/35.42  | | |   (186)  all_52_7 = e3
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (95), (186) imply:
% 204.64/35.42  | | |   (187)   ~ (all_52_3 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (50), (186) imply:
% 204.64/35.42  | | |   (188)   ~ (all_52_5 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (11), (186) imply:
% 204.64/35.42  | | |   (189)   ~ (all_52_15 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (114), (186) imply:
% 204.64/35.42  | | |   (190)   ~ (all_52_23 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | SIMP: (190) implies:
% 204.64/35.42  | | |   (191)   ~ (all_52_23 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (53), (186) imply:
% 204.64/35.42  | | |   (192)   ~ (all_14_2 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (30), (186) imply:
% 204.64/35.42  | | |   (193)   ~ (all_6_2 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | SIMP: (193) implies:
% 204.64/35.42  | | |   (194)   ~ (all_6_2 = e3)
% 204.64/35.42  | | | 
% 204.64/35.42  | | | REDUCE: (13), (186) imply:
% 204.64/35.42  | | |   (195)  op(e3, e3) = all_52_6
% 204.64/35.42  | | | 
% 204.64/35.42  | | | GROUND_INST: instantiating (6) with all_6_2, all_52_6, e3, e3, simplifying
% 204.64/35.42  | | |              with (90), (195) gives:
% 204.64/35.42  | | |   (196)  all_52_6 = all_6_2
% 204.64/35.42  | | | 
% 204.64/35.42  | | | BETA: splitting (78) gives:
% 204.64/35.42  | | | 
% 204.64/35.42  | | | Case 1:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | |   (197)  all_56_8 = e3
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | REF_CLOSE: (43), (188), (197) are inconsistent by sub-proof #1325.
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | Case 2:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | |   (198)   ~ (all_56_8 = e3)
% 204.64/35.42  | | | |   (199)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | BETA: splitting (84) gives:
% 204.64/35.42  | | | | 
% 204.64/35.42  | | | | Case 1:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | |   (200)  all_56_3 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | COMBINE_EQS: (94), (200) imply:
% 204.64/35.42  | | | | |   (201)  all_52_25 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | SIMP: (201) implies:
% 204.64/35.42  | | | | |   (202)  all_52_25 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | COMBINE_EQS: (18), (202) imply:
% 204.64/35.42  | | | | |   (203)  all_58_9 = e3
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (75), (202) imply:
% 204.64/35.42  | | | | |   (204)   ~ (all_52_9 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (14), (202) imply:
% 204.64/35.42  | | | | |   (205)   ~ (all_52_17 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (46), (202) imply:
% 204.64/35.42  | | | | |   (206)   ~ (all_52_29 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | SIMP: (206) implies:
% 204.64/35.42  | | | | |   (207)   ~ (all_52_29 = e3)
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | REDUCE: (122), (202) imply:
% 204.64/35.42  | | | | |   (208)  op(e3, e3) = all_52_24
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_24, e3, e3,
% 204.64/35.42  | | | | |              simplifying with (90), (208) gives:
% 204.64/35.42  | | | | |   (209)  all_52_24 = all_6_2
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | BETA: splitting (74) gives:
% 204.64/35.42  | | | | | 
% 204.64/35.42  | | | | | Case 1:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | |   (210)  all_58_1 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | COMBINE_EQS: (7), (210) imply:
% 204.64/35.42  | | | | | |   (211)  all_52_9 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | REDUCE: (204), (211) imply:
% 204.64/35.42  | | | | | |   (212)  $false
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | CLOSE: (212) is inconsistent.
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | Case 2:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | |   (213)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | BETA: splitting (108) gives:
% 204.64/35.42  | | | | | | 
% 204.64/35.42  | | | | | | Case 1:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | |   (214)  all_58_4 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | REF_CLOSE: (120), (205), (214) are inconsistent by sub-proof
% 204.64/35.42  | | | | | | |            #1302.
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | Case 2:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | |   (215)   ~ (all_58_4 = e3)
% 204.64/35.42  | | | | | | |   (216)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | BETA: splitting (52) gives:
% 204.64/35.42  | | | | | | | 
% 204.64/35.42  | | | | | | | Case 1:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | |   (217)  all_58_6 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | REF_CLOSE: (100), (188), (217) are inconsistent by sub-proof
% 204.64/35.42  | | | | | | | |            #1328.
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | |   (218)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | BETA: splitting (35) gives:
% 204.64/35.42  | | | | | | | | 
% 204.64/35.42  | | | | | | | | Case 1:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | |   (219)  all_56_2 = e3
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | REF_CLOSE: (56), (205), (219) are inconsistent by sub-proof
% 204.64/35.42  | | | | | | | | |            #1327.
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | Case 2:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | |   (220)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | BETA: splitting (109) gives:
% 204.64/35.42  | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | Case 1:
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | |   (221)  all_56_9 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | COMBINE_EQS: (37), (221) imply:
% 204.64/35.42  | | | | | | | | | |   (222)  all_52_13 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | SIMP: (222) implies:
% 204.64/35.42  | | | | | | | | | |   (223)  all_52_13 = e3
% 204.64/35.42  | | | | | | | | | | 
% 204.64/35.42  | | | | | | | | | | REDUCE: (39), (223) imply:
% 204.64/35.42  | | | | | | | | | |   (224)   ~ (all_10_2 = e3)
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | SIMP: (224) implies:
% 204.64/35.43  | | | | | | | | | |   (225)   ~ (all_10_2 = e3)
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | REDUCE: (111), (223) imply:
% 204.64/35.43  | | | | | | | | | |   (226)  op(e3, e3) = all_52_12
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | BETA: splitting (216) gives:
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | |   (227)  all_58_5 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | COMBINE_EQS: (96), (227) imply:
% 204.64/35.43  | | | | | | | | | | |   (228)  all_52_19 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | SIMP: (228) implies:
% 204.64/35.43  | | | | | | | | | | |   (229)  all_52_19 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | REDUCE: (49), (229) imply:
% 204.64/35.43  | | | | | | | | | | |   (230)  op(e3, e3) = e2
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_12, e3, e3,
% 204.64/35.43  | | | | | | | | | | |              simplifying with (90), (226) gives:
% 204.64/35.43  | | | | | | | | | | |   (231)  all_52_12 = all_6_2
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_52_12, e3, e3,
% 204.64/35.43  | | | | | | | | | | |              simplifying with (226), (230) gives:
% 204.64/35.43  | | | | | | | | | | |   (232)  all_52_12 = e2
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | COMBINE_EQS: (231), (232) imply:
% 204.64/35.43  | | | | | | | | | | |   (233)  all_6_2 = e2
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | REDUCE: (102), (233) imply:
% 204.64/35.43  | | | | | | | | | | |   (234)   ~ (all_52_17 = e2)
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | REF_CLOSE: (6), (20), (31), (56), (99), (113), (120), (123),
% 204.64/35.43  | | | | | | | | | | |            (220), (225), (234) are inconsistent by sub-proof
% 204.64/35.43  | | | | | | | | | | |            #1058.
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | |   (235)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | REF_CLOSE: (3), (79), (191), (225), (235) are inconsistent by
% 204.64/35.43  | | | | | | | | | | |            sub-proof #1304.
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | |   (236)   ~ (all_56_9 = e3)
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | REDUCE: (37), (236) imply:
% 204.64/35.43  | | | | | | | | | |   (237)   ~ (all_52_13 = e3)
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | BETA: splitting (213) gives:
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | |   (238)  all_58_3 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | COMBINE_EQS: (115), (238) imply:
% 204.64/35.43  | | | | | | | | | | |   (239)  all_4_2 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | REDUCE: (93), (239) imply:
% 204.64/35.43  | | | | | | | | | | |   (240)  op(e3, e3) = all_52_10
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | BETA: splitting (218) gives:
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | |   (241)  all_58_7 = e3
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | COMBINE_EQS: (48), (241) imply:
% 204.64/35.43  | | | | | | | | | | | |   (242)  all_52_13 = e3
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | REDUCE: (237), (242) imply:
% 204.64/35.43  | | | | | | | | | | | |   (243)  $false
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | |   (244)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | BETA: splitting (244) gives:
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | |   (245)  all_58_8 = e3
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | COMBINE_EQS: (79), (245) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (246)  all_10_2 = e3
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (77), (246) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (247)   ~ (all_52_19 = e3)
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (41), (246) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (248)  op(e3, e3) = e1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (113), (246) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (249)  op(e1, e1) = e3
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_6_2, all_52_10, e3, e3,
% 204.64/35.43  | | | | | | | | | | | | |              simplifying with (90), (240) gives:
% 204.64/35.43  | | | | | | | | | | | | |   (250)  all_52_10 = all_6_2
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e1, all_52_10, e3, e3,
% 204.64/35.43  | | | | | | | | | | | | |              simplifying with (240), (248) gives:
% 204.64/35.43  | | | | | | | | | | | | |   (251)  all_52_10 = e1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | COMBINE_EQS: (250), (251) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (252)  all_6_2 = e1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | COMBINE_EQS: (15), (252) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (253)  all_58_0 = e1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (86), (252) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (254)   ~ (all_52_5 = e1)
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (29), (252) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (255)  op(e1, e1) = all_52_0
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (119), (252) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (256)  op(e1, e3) = all_6_1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_0, e1, e1,
% 204.64/35.43  | | | | | | | | | | | | |              simplifying with (249), (255) gives:
% 204.64/35.43  | | | | | | | | | | | | |   (257)  all_52_0 = e3
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_5, all_6_1, e3, e1,
% 204.64/35.43  | | | | | | | | | | | | |              simplifying with (22), (256) gives:
% 204.64/35.43  | | | | | | | | | | | | |   (258)  all_52_5 = all_6_1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | COMBINE_EQS: (43), (258) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (259)  all_56_8 = all_6_1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | COMBINE_EQS: (100), (258) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (260)  all_58_6 = all_6_1
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (63), (258) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (261)   ~ (all_52_29 = all_6_1)
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | SIMP: (261) implies:
% 204.64/35.43  | | | | | | | | | | | | |   (262)   ~ (all_52_29 = all_6_1)
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REDUCE: (188), (258) imply:
% 204.64/35.43  | | | | | | | | | | | | |   (263)   ~ (all_6_1 = e3)
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | |   (264)  all_56_8 = e2
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | REF_CLOSE: (112), (259), (264) are inconsistent by sub-proof
% 204.64/35.43  | | | | | | | | | | | | | |            #1321.
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | |   (265)   ~ (all_56_8 = e2)
% 204.64/35.43  | | | | | | | | | | | | | |   (266)  all_56_8 = e1 | all_56_8 = e0
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | |   (267)  all_58_0 = e2
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | REF_CLOSE: (38), (253), (267) are inconsistent by sub-proof
% 204.64/35.43  | | | | | | | | | | | | | | |            #1273.
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | |   (268)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | |   (269)  all_58_2 = e2
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (269) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | |   (270)  all_52_3 = e2
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | SIMP: (270) implies:
% 204.64/35.43  | | | | | | | | | | | | | | | |   (271)  all_52_3 = e2
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | REDUCE: (12), (271) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | |   (272)   ~ (all_52_19 = e2)
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 204.64/35.43  | | | | | | | | | | | | | | | |   (273)   ~ (all_52_19 = e2)
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | REDUCE: (187), (271) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | |   (274)   ~ (e3 = e2)
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | |   (275)  all_56_8 = e1
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (259), (275) are inconsistent by sub-proof
% 204.64/35.43  | | | | | | | | | | | | | | | | |            #1320.
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | |   (276)  all_56_8 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (276) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | |   (277)  all_6_1 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 204.64/35.43  | | | | | | | | | | | | | | | | |   (278)  all_6_1 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | REDUCE: (262), (278) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | |   (279)   ~ (all_52_29 = e0)
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | REDUCE: (263), (278) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | |   (280)   ~ (e3 = e0)
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | |   (281)  all_58_9 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (281) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | | |   (282)  e3 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | REDUCE: (8), (282) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | | |   (283)  $false
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent.
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | |   (284)  all_58_10 = e0 | all_58_11 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |   (285)  all_58_10 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (285) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |   (286)  all_52_27 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | REDUCE: (66), (286) imply:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |   (287)   ~ (all_52_19 = e0)
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (25), (49), (55), (64), (104), (207), (244),
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |            (245), (247), (249), (273), (287) are inconsistent
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |            by sub-proof #1054.
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |   (288)  all_58_11 = e0
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (279), (288) are inconsistent by sub-proof
% 204.64/35.43  | | | | | | | | | | | | | | | | | | |            #1115.
% 204.64/35.43  | | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | |   (289)  all_58_6 = e2 | all_58_12 = e2
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | | REF_CLOSE: (104), (112), (184), (260), (289) are inconsistent
% 204.64/35.43  | | | | | | | | | | | | | | | |            by sub-proof #1209.
% 204.64/35.43  | | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | |   (290)  all_58_11 = e3
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | | REF_CLOSE: (25), (207), (290) are inconsistent by sub-proof
% 204.64/35.43  | | | | | | | | | | | | |            #1323.
% 204.64/35.43  | | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | Case 2:
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | |   (291)  all_58_7 = e3 | all_58_13 = e3
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | | REF_CLOSE: (17), (48), (183), (237), (291) are inconsistent
% 204.64/35.43  | | | | | | | | | | |            by sub-proof #1298.
% 204.64/35.43  | | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | | 
% 204.64/35.43  | | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | | 
% 204.64/35.43  | | | | | | | | End of split
% 204.64/35.43  | | | | | | | | 
% 204.64/35.43  | | | | | | | End of split
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | End of split
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | End of split
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | Case 2:
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | |   (292)   ~ (all_56_3 = e3)
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (15), (18), (20), (21), (23),
% 204.64/35.43  | | | | |            (28), (31), (32), (35), (38), (41), (42), (44), (45), (49),
% 204.64/35.43  | | | | |            (54), (56), (60), (61), (62), (72), (77), (79), (85), (90),
% 204.64/35.43  | | | | |            (91), (92), (94), (96), (98), (99), (102), (103), (106),
% 204.64/35.43  | | | | |            (107), (108), (113), (115), (120), (121), (123), (187),
% 204.64/35.43  | | | | |            (191), (194), (292) are inconsistent by sub-proof #1046.
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | End of split
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | End of split
% 204.64/35.43  | | | 
% 204.64/35.43  | | Case 2:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (293)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REF_CLOSE: (3), (6), (9), (10), (17), (19), (30), (73), (76), (83), (90),
% 204.64/35.43  | | |            (112), (114), (119), (123), (183), (293) are inconsistent by
% 204.64/35.43  | | |            sub-proof #1045.
% 204.64/35.43  | | | 
% 204.64/35.43  | | End of split
% 204.64/35.43  | | 
% 204.64/35.43  | End of split
% 204.64/35.43  | 
% 204.64/35.43  End of proof
% 204.64/35.43  
% 204.64/35.43  Sub-proof #1045 shows that the following formulas are inconsistent:
% 204.64/35.43  ----------------------------------------------------------------
% 204.64/35.43    (1)  all_58_14 = all_52_23
% 204.64/35.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.43    (3)  op(all_52_23, all_52_23) = e0
% 204.64/35.43    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.64/35.43    (5)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.64/35.43    (6)  all_58_13 = all_52_15
% 204.64/35.43    (7)   ~ (all_6_1 = e1)
% 204.64/35.43    (8)   ~ (all_52_15 = e3)
% 204.64/35.43    (9)   ~ (all_52_7 = all_6_2)
% 204.64/35.43    (10)  op(e0, e3) = all_52_7
% 204.64/35.43    (11)  all_58_15 = all_14_2
% 204.64/35.43    (12)  all_56_12 = all_52_7
% 204.64/35.43    (13)  op(e3, e3) = all_6_2
% 204.64/35.43    (14)   ~ (all_6_1 = e2)
% 204.64/35.43    (15)   ~ (all_52_7 = all_52_23)
% 204.64/35.43    (16)  op(all_6_2, e3) = all_6_1
% 204.64/35.43    (17)   ~ (all_14_2 = e3)
% 204.64/35.43  
% 204.64/35.43  Begin of proof
% 204.64/35.43  | 
% 204.64/35.43  | BETA: splitting (5) gives:
% 204.64/35.43  | 
% 204.64/35.43  | Case 1:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (18)  all_58_13 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | REF_CLOSE: (6), (8), (18) are inconsistent by sub-proof #1360.
% 204.64/35.43  | | 
% 204.64/35.43  | Case 2:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (19)  all_58_14 = e3 | all_58_15 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | BETA: splitting (19) gives:
% 204.64/35.43  | | 
% 204.64/35.43  | | Case 1:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (20)  all_58_14 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (12), (13), (14), (15),
% 204.64/35.43  | | |            (16), (20) are inconsistent by sub-proof #1251.
% 204.64/35.43  | | | 
% 204.64/35.43  | | Case 2:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (21)  all_58_15 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | COMBINE_EQS: (11), (21) imply:
% 204.64/35.43  | | |   (22)  all_14_2 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REDUCE: (17), (22) imply:
% 204.64/35.43  | | |   (23)  $false
% 204.64/35.43  | | | 
% 204.64/35.43  | | | CLOSE: (23) is inconsistent.
% 204.64/35.43  | | | 
% 204.64/35.43  | | End of split
% 204.64/35.43  | | 
% 204.64/35.43  | End of split
% 204.64/35.43  | 
% 204.64/35.43  End of proof
% 204.64/35.43  
% 204.64/35.43  Sub-proof #1046 shows that the following formulas are inconsistent:
% 204.64/35.43  ----------------------------------------------------------------
% 204.64/35.43    (1)  all_58_14 = all_52_23
% 204.64/35.43    (2)   ~ (e3 = e1)
% 204.64/35.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.43    (4)  all_58_1 = all_52_9
% 204.64/35.43    (5)   ~ (e3 = e0)
% 204.64/35.43    (6)  all_58_0 = all_6_2
% 204.64/35.43    (7)  all_58_9 = all_52_25
% 204.64/35.43    (8)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.43    (9)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.43    (10)  op(e2, e2) = all_4_2
% 204.64/35.43    (11)   ~ (all_52_3 = e3)
% 204.64/35.43    (12)  op(all_10_2, e1) = all_10_1
% 204.64/35.43    (13)  op(e0, e0) = all_14_2
% 204.64/35.43    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.43    (15)   ~ (all_56_3 = e3)
% 204.64/35.43    (16)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.43    (17)   ~ (all_6_2 = e3)
% 204.64/35.43    (18)   ~ (e2 = e1)
% 204.64/35.43    (19)  op(all_10_2, all_10_2) = e1
% 204.64/35.43    (20)  all_58_10 = all_52_27
% 204.64/35.43    (21)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.43    (22)   ~ (all_52_19 = all_52_23)
% 204.64/35.43    (23)  op(all_52_19, all_52_19) = e2
% 204.64/35.43    (24)  all_58_2 = all_52_3
% 204.64/35.43    (25)  all_56_2 = all_52_17
% 204.64/35.43    (26)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.43    (27)   ~ (e2 = e0)
% 204.64/35.43    (28)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.43    (29)   ~ (all_52_23 = e3)
% 204.64/35.43    (30)  op(e3, e1) = all_52_17
% 204.64/35.43    (31)   ~ (all_52_19 = all_10_2)
% 204.64/35.43    (32)  all_58_8 = all_10_2
% 204.64/35.43    (33)   ~ (all_52_9 = all_4_2)
% 204.64/35.43    (34)  op(e3, e3) = all_6_2
% 204.64/35.43    (35)   ~ (all_52_27 = all_14_2)
% 204.64/35.43    (36)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.43    (37)  all_56_3 = all_52_25
% 204.64/35.43    (38)  all_58_5 = all_52_19
% 204.64/35.43    (39)   ~ (all_52_27 = all_4_2)
% 204.64/35.43    (40)  op(all_52_17, all_52_17) = e3
% 204.64/35.43    (41)   ~ (all_52_17 = all_6_2)
% 204.64/35.43    (42)   ~ (e1 = e0)
% 204.64/35.43    (43)   ~ (all_52_9 = all_52_17)
% 204.64/35.43    (44)  all_56_10 = all_10_2
% 204.64/35.43    (45)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.43    (46)  op(e1, e1) = all_10_2
% 204.64/35.43    (47)  all_58_3 = all_4_2
% 204.64/35.43    (48)  all_58_4 = all_52_17
% 204.64/35.43    (49)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.64/35.43    (50)   ~ (all_14_2 = e3)
% 204.64/35.43  
% 204.64/35.43  Begin of proof
% 204.64/35.43  | 
% 204.64/35.43  | REDUCE: (15), (37) imply:
% 204.64/35.43  |   (51)   ~ (all_52_25 = e3)
% 204.64/35.43  | 
% 204.64/35.43  | BETA: splitting (36) gives:
% 204.64/35.43  | 
% 204.64/35.43  | Case 1:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (52)  all_58_0 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | COMBINE_EQS: (6), (52) imply:
% 204.64/35.43  | |   (53)  all_6_2 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | REDUCE: (17), (53) imply:
% 204.64/35.43  | |   (54)  $false
% 204.64/35.43  | | 
% 204.64/35.43  | | CLOSE: (54) is inconsistent.
% 204.64/35.43  | | 
% 204.64/35.43  | Case 2:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (55)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | BETA: splitting (55) gives:
% 204.64/35.43  | | 
% 204.64/35.43  | | Case 1:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (56)  all_58_1 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | COMBINE_EQS: (4), (56) imply:
% 204.64/35.43  | | |   (57)  all_52_9 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REDUCE: (43), (57) imply:
% 204.64/35.43  | | |   (58)   ~ (all_52_17 = e3)
% 204.64/35.43  | | | 
% 204.64/35.43  | | | SIMP: (58) implies:
% 204.64/35.43  | | |   (59)   ~ (all_52_17 = e3)
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REDUCE: (33), (57) imply:
% 204.64/35.43  | | |   (60)   ~ (all_4_2 = e3)
% 204.64/35.43  | | | 
% 204.64/35.43  | | | SIMP: (60) implies:
% 204.64/35.43  | | |   (61)   ~ (all_4_2 = e3)
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REDUCE: (21), (57) imply:
% 204.64/35.43  | | |   (62)  op(e3, e3) = all_52_8
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 204.64/35.43  | | |            (14), (16), (18), (19), (20), (22), (23), (24), (25), (26),
% 204.64/35.43  | | |            (27), (28), (29), (30), (31), (32), (34), (35), (38), (39),
% 204.64/35.43  | | |            (40), (41), (42), (44), (45), (46), (47), (48), (49), (50),
% 204.64/35.43  | | |            (56), (59), (61), (62) are inconsistent by sub-proof #1047.
% 204.64/35.43  | | | 
% 204.64/35.43  | | Case 2:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (63)  all_58_4 = e3 | all_58_9 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REF_CLOSE: (3), (7), (34), (40), (41), (48), (51), (63) are inconsistent
% 204.64/35.43  | | |            by sub-proof #1080.
% 204.64/35.43  | | | 
% 204.64/35.43  | | End of split
% 204.64/35.43  | | 
% 204.64/35.43  | End of split
% 204.64/35.43  | 
% 204.64/35.43  End of proof
% 204.64/35.43  
% 204.64/35.43  Sub-proof #1047 shows that the following formulas are inconsistent:
% 204.64/35.43  ----------------------------------------------------------------
% 204.64/35.43    (1)  all_58_14 = all_52_23
% 204.64/35.43    (2)   ~ (e3 = e1)
% 204.64/35.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.43    (4)   ~ (e3 = e0)
% 204.64/35.43    (5)   ~ (all_4_2 = e3)
% 204.64/35.43    (6)  all_58_0 = all_6_2
% 204.64/35.43    (7)  all_58_9 = all_52_25
% 204.64/35.43    (8)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.43    (9)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.43    (10)  op(e2, e2) = all_4_2
% 204.64/35.43    (11)   ~ (all_52_3 = e3)
% 204.64/35.43    (12)  op(all_10_2, e1) = all_10_1
% 204.64/35.43    (13)  all_58_1 = e3
% 204.64/35.43    (14)  op(e0, e0) = all_14_2
% 204.64/35.43    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.43    (16)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.43    (17)   ~ (e2 = e1)
% 204.64/35.43    (18)  op(all_10_2, all_10_2) = e1
% 204.64/35.43    (19)  all_58_10 = all_52_27
% 204.64/35.43    (20)   ~ (all_52_19 = all_52_23)
% 204.64/35.43    (21)  op(all_52_19, all_52_19) = e2
% 204.64/35.43    (22)  all_58_2 = all_52_3
% 204.64/35.43    (23)  all_56_2 = all_52_17
% 204.64/35.43    (24)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.43    (25)   ~ (e2 = e0)
% 204.64/35.43    (26)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.43    (27)   ~ (all_52_23 = e3)
% 204.64/35.43    (28)  op(e3, e3) = all_52_8
% 204.64/35.43    (29)  op(e3, e1) = all_52_17
% 204.64/35.43    (30)   ~ (all_52_19 = all_10_2)
% 204.64/35.43    (31)  all_58_8 = all_10_2
% 204.64/35.43    (32)  op(e3, e3) = all_6_2
% 204.64/35.43    (33)   ~ (all_52_27 = all_14_2)
% 204.64/35.43    (34)   ~ (all_52_17 = e3)
% 204.64/35.43    (35)  all_58_5 = all_52_19
% 204.64/35.43    (36)   ~ (all_52_27 = all_4_2)
% 204.64/35.43    (37)  op(all_52_17, all_52_17) = e3
% 204.64/35.43    (38)   ~ (all_52_17 = all_6_2)
% 204.64/35.43    (39)   ~ (e1 = e0)
% 204.64/35.43    (40)  all_56_10 = all_10_2
% 204.64/35.43    (41)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.43    (42)  op(e1, e1) = all_10_2
% 204.64/35.43    (43)  all_58_3 = all_4_2
% 204.64/35.43    (44)  all_58_4 = all_52_17
% 204.64/35.43    (45)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.64/35.43    (46)   ~ (all_14_2 = e3)
% 204.64/35.43  
% 204.64/35.43  Begin of proof
% 204.64/35.43  | 
% 204.64/35.43  | BETA: splitting (15) gives:
% 204.64/35.43  | 
% 204.64/35.43  | Case 1:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (47)  all_58_2 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | REF_CLOSE: (11), (22), (47) are inconsistent by sub-proof #1369.
% 204.64/35.43  | | 
% 204.64/35.43  | Case 2:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (48)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | BETA: splitting (16) gives:
% 204.64/35.43  | | 
% 204.64/35.43  | | Case 1:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (49)  all_56_2 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | COMBINE_EQS: (23), (49) imply:
% 204.64/35.43  | | |   (50)  all_52_17 = e3
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REDUCE: (34), (50) imply:
% 204.64/35.43  | | |   (51)  $false
% 204.64/35.43  | | | 
% 204.64/35.43  | | | CLOSE: (51) is inconsistent.
% 204.64/35.43  | | | 
% 204.64/35.43  | | Case 2:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (52)   ~ (all_56_2 = e3)
% 204.64/35.43  | | |   (53)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.43  | | | 
% 204.64/35.43  | | | BETA: splitting (45) gives:
% 204.64/35.43  | | | 
% 204.64/35.43  | | | Case 1:
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | |   (54)  all_56_10 = e3
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | COMBINE_EQS: (40), (54) imply:
% 204.64/35.43  | | | |   (55)  all_10_2 = e3
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | SIMP: (55) implies:
% 204.64/35.43  | | | |   (56)  all_10_2 = e3
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | REDUCE: (30), (56) imply:
% 204.64/35.43  | | | |   (57)   ~ (all_52_19 = e3)
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | REDUCE: (18), (56) imply:
% 204.64/35.43  | | | |   (58)  op(e3, e3) = e1
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | REDUCE: (12), (56) imply:
% 204.64/35.43  | | | |   (59)  op(e3, e1) = all_10_1
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | BETA: splitting (48) gives:
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | Case 1:
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | |   (60)  all_58_3 = e3
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | COMBINE_EQS: (43), (60) imply:
% 204.64/35.43  | | | | |   (61)  all_4_2 = e3
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | REDUCE: (5), (61) imply:
% 204.64/35.43  | | | | |   (62)  $false
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | CLOSE: (62) is inconsistent.
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | Case 2:
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | |   (63)  all_58_5 = e3 | all_58_10 = e3
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | REF_CLOSE: (3), (9), (10), (14), (19), (23), (29), (32), (33), (35),
% 204.64/35.43  | | | | |            (36), (37), (38), (53), (57), (58), (59), (63) are
% 204.64/35.43  | | | | |            inconsistent by sub-proof #1052.
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | End of split
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | Case 2:
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | |   (64)   ~ (all_56_10 = e3)
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | REDUCE: (40), (64) imply:
% 204.64/35.43  | | | |   (65)   ~ (all_10_2 = e3)
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (13), (14), (17), (20),
% 204.64/35.43  | | | |            (21), (24), (25), (26), (27), (28), (30), (31), (32), (34),
% 204.64/35.43  | | | |            (35), (37), (39), (41), (42), (44), (46), (65) are
% 204.64/35.43  | | | |            inconsistent by sub-proof #1048.
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | End of split
% 204.64/35.43  | | | 
% 204.64/35.43  | | End of split
% 204.64/35.43  | | 
% 204.64/35.43  | End of split
% 204.64/35.43  | 
% 204.64/35.43  End of proof
% 204.64/35.43  
% 204.64/35.43  Sub-proof #1048 shows that the following formulas are inconsistent:
% 204.64/35.43  ----------------------------------------------------------------
% 204.64/35.43    (1)  all_58_14 = all_52_23
% 204.64/35.43    (2)   ~ (e3 = e1)
% 204.64/35.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.43    (4)   ~ (e3 = e0)
% 204.64/35.43    (5)  all_58_0 = all_6_2
% 204.64/35.43    (6)  all_58_9 = all_52_25
% 204.64/35.43    (7)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.43    (8)  all_58_1 = e3
% 204.64/35.43    (9)  op(e0, e0) = all_14_2
% 204.64/35.43    (10)   ~ (e2 = e1)
% 204.64/35.43    (11)   ~ (all_52_19 = all_52_23)
% 204.64/35.43    (12)  op(all_52_19, all_52_19) = e2
% 204.64/35.43    (13)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.43    (14)   ~ (e2 = e0)
% 204.64/35.43    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.43    (16)   ~ (all_52_23 = e3)
% 204.64/35.43    (17)   ~ (all_10_2 = e3)
% 204.64/35.43    (18)  op(e3, e3) = all_52_8
% 204.64/35.43    (19)   ~ (all_52_19 = all_10_2)
% 204.64/35.43    (20)  all_58_8 = all_10_2
% 204.64/35.43    (21)  op(e3, e3) = all_6_2
% 204.64/35.43    (22)   ~ (all_52_17 = e3)
% 204.64/35.43    (23)  all_58_5 = all_52_19
% 204.64/35.43    (24)  op(all_52_17, all_52_17) = e3
% 204.64/35.43    (25)   ~ (e1 = e0)
% 204.64/35.43    (26)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.43    (27)  op(e1, e1) = all_10_2
% 204.64/35.43    (28)  all_58_4 = all_52_17
% 204.64/35.43    (29)   ~ (all_14_2 = e3)
% 204.64/35.43  
% 204.64/35.43  Begin of proof
% 204.64/35.43  | 
% 204.64/35.43  | BETA: splitting (26) gives:
% 204.64/35.43  | 
% 204.64/35.43  | Case 1:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (30)  all_58_4 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | REF_CLOSE: (22), (28), (30) are inconsistent by sub-proof #1302.
% 204.64/35.43  | | 
% 204.64/35.43  | Case 2:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (31)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.64/35.43  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 204.64/35.43  | |            (25), (27), (28), (29), (31) are inconsistent by sub-proof #1049.
% 204.64/35.43  | | 
% 204.64/35.43  | End of split
% 204.64/35.43  | 
% 204.64/35.43  End of proof
% 204.64/35.43  
% 204.64/35.43  Sub-proof #1049 shows that the following formulas are inconsistent:
% 204.64/35.43  ----------------------------------------------------------------
% 204.64/35.43    (1)  all_58_14 = all_52_23
% 204.64/35.43    (2)   ~ (e3 = e1)
% 204.64/35.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.43    (4)   ~ (e3 = e0)
% 204.64/35.43    (5)  all_58_0 = all_6_2
% 204.64/35.43    (6)  all_58_9 = all_52_25
% 204.64/35.43    (7)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.43    (8)  all_58_1 = e3
% 204.64/35.43    (9)  op(e0, e0) = all_14_2
% 204.64/35.43    (10)   ~ (e2 = e1)
% 204.64/35.43    (11)   ~ (all_52_19 = all_52_23)
% 204.64/35.43    (12)  op(all_52_19, all_52_19) = e2
% 204.64/35.43    (13)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.43    (14)   ~ (e2 = e0)
% 204.64/35.43    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.43    (16)   ~ (all_52_23 = e3)
% 204.64/35.43    (17)   ~ (all_10_2 = e3)
% 204.64/35.43    (18)  op(e3, e3) = all_52_8
% 204.64/35.43    (19)   ~ (all_52_19 = all_10_2)
% 204.64/35.43    (20)  all_58_8 = all_10_2
% 204.64/35.43    (21)  op(e3, e3) = all_6_2
% 204.64/35.43    (22)  all_58_5 = all_52_19
% 204.64/35.43    (23)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.43    (24)  op(all_52_17, all_52_17) = e3
% 204.64/35.43    (25)   ~ (e1 = e0)
% 204.64/35.43    (26)  op(e1, e1) = all_10_2
% 204.64/35.43    (27)  all_58_4 = all_52_17
% 204.64/35.43    (28)   ~ (all_14_2 = e3)
% 204.64/35.43  
% 204.64/35.43  Begin of proof
% 204.64/35.43  | 
% 204.64/35.43  | BETA: splitting (23) gives:
% 204.64/35.43  | 
% 204.64/35.43  | Case 1:
% 204.64/35.43  | | 
% 204.64/35.43  | |   (29)  all_58_5 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | COMBINE_EQS: (22), (29) imply:
% 204.64/35.43  | |   (30)  all_52_19 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | SIMP: (30) implies:
% 204.64/35.43  | |   (31)  all_52_19 = e3
% 204.64/35.43  | | 
% 204.64/35.43  | | REDUCE: (11), (31) imply:
% 204.64/35.43  | |   (32)   ~ (all_52_23 = e3)
% 204.64/35.43  | | 
% 204.64/35.43  | | REDUCE: (19), (31) imply:
% 204.64/35.43  | |   (33)   ~ (all_10_2 = e3)
% 204.64/35.43  | | 
% 204.64/35.43  | | REDUCE: (12), (31) imply:
% 204.64/35.43  | |   (34)  op(e3, e3) = e2
% 204.64/35.43  | | 
% 204.64/35.43  | | GROUND_INST: instantiating (3) with all_6_2, all_52_8, e3, e3, simplifying
% 204.64/35.43  | |              with (18), (21) gives:
% 204.64/35.43  | |   (35)  all_52_8 = all_6_2
% 204.64/35.43  | | 
% 204.64/35.43  | | GROUND_INST: instantiating (3) with e2, all_52_8, e3, e3, simplifying with
% 204.64/35.43  | |              (18), (34) gives:
% 204.64/35.43  | |   (36)  all_52_8 = e2
% 204.64/35.43  | | 
% 204.64/35.43  | | COMBINE_EQS: (35), (36) imply:
% 204.64/35.43  | |   (37)  all_6_2 = e2
% 204.64/35.43  | | 
% 204.64/35.43  | | SIMP: (37) implies:
% 204.64/35.43  | |   (38)  all_6_2 = e2
% 204.64/35.43  | | 
% 204.64/35.43  | | COMBINE_EQS: (5), (38) imply:
% 204.64/35.43  | |   (39)  all_58_0 = e2
% 204.64/35.43  | | 
% 204.64/35.43  | | BETA: splitting (15) gives:
% 204.64/35.43  | | 
% 204.64/35.43  | | Case 1:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (40)  all_58_0 = e1
% 204.64/35.43  | | | 
% 204.64/35.43  | | | COMBINE_EQS: (39), (40) imply:
% 204.64/35.43  | | |   (41)  e2 = e1
% 204.64/35.43  | | | 
% 204.64/35.43  | | | REDUCE: (10), (41) imply:
% 204.64/35.43  | | |   (42)  $false
% 204.64/35.43  | | | 
% 204.64/35.43  | | | CLOSE: (42) is inconsistent.
% 204.64/35.43  | | | 
% 204.64/35.43  | | Case 2:
% 204.64/35.43  | | | 
% 204.64/35.43  | | |   (43)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.43  | | | 
% 204.64/35.43  | | | BETA: splitting (13) gives:
% 204.64/35.43  | | | 
% 204.64/35.43  | | | Case 1:
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | |   (44)  all_58_0 = e0
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | COMBINE_EQS: (39), (44) imply:
% 204.64/35.43  | | | |   (45)  e2 = e0
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | REDUCE: (14), (45) imply:
% 204.64/35.43  | | | |   (46)  $false
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | CLOSE: (46) is inconsistent.
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | Case 2:
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | |   (47)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | BETA: splitting (7) gives:
% 204.64/35.43  | | | | 
% 204.64/35.43  | | | | Case 1:
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | |   (48)  all_58_4 = e1
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | COMBINE_EQS: (27), (48) imply:
% 204.64/35.43  | | | | |   (49)  all_52_17 = e1
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | REDUCE: (24), (49) imply:
% 204.64/35.43  | | | | |   (50)  op(e1, e1) = e3
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | REF_CLOSE: (3), (17), (26), (50) are inconsistent by sub-proof #1368.
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | Case 2:
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | |   (51)   ~ (all_58_4 = e1)
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | REDUCE: (27), (51) imply:
% 204.64/35.43  | | | | |   (52)   ~ (all_52_17 = e1)
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | BETA: splitting (43) gives:
% 204.64/35.43  | | | | | 
% 204.64/35.43  | | | | | Case 1:
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | |   (53)  all_58_1 = e1
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | | REF_CLOSE: (1), (2), (8), (16), (17), (20), (23), (29), (53) are
% 204.64/35.43  | | | | | |            inconsistent by sub-proof #1050.
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | Case 2:
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | |   (54)  all_58_4 = e1 | all_58_9 = e1
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | | BETA: splitting (54) gives:
% 204.64/35.43  | | | | | | 
% 204.64/35.43  | | | | | | Case 1:
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | |   (55)  all_58_4 = e1
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | | COMBINE_EQS: (27), (55) imply:
% 204.64/35.43  | | | | | | |   (56)  all_52_17 = e1
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | | REDUCE: (52), (56) imply:
% 204.64/35.43  | | | | | | |   (57)  $false
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | | CLOSE: (57) is inconsistent.
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | Case 2:
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | |   (58)  all_58_9 = e1
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | | COMBINE_EQS: (6), (58) imply:
% 204.64/35.43  | | | | | | |   (59)  all_52_25 = e1
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | | BETA: splitting (47) gives:
% 204.64/35.43  | | | | | | | 
% 204.64/35.43  | | | | | | | Case 1:
% 204.64/35.43  | | | | | | | | 
% 204.64/35.43  | | | | | | | |   (60)  all_58_1 = e0
% 204.64/35.43  | | | | | | | | 
% 204.64/35.43  | | | | | | | | COMBINE_EQS: (8), (60) imply:
% 204.64/35.43  | | | | | | | |   (61)  e3 = e0
% 204.64/35.43  | | | | | | | | 
% 204.64/35.43  | | | | | | | | REDUCE: (4), (61) imply:
% 204.64/35.44  | | | | | | | |   (62)  $false
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | | CLOSE: (62) is inconsistent.
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | |   (63)  all_58_4 = e0 | all_58_9 = e0
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | | BETA: splitting (63) gives:
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | | Case 1:
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | |   (64)  all_58_4 = e0
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | COMBINE_EQS: (27), (64) imply:
% 204.64/35.44  | | | | | | | | |   (65)  all_52_17 = e0
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REDUCE: (24), (65) imply:
% 204.64/35.44  | | | | | | | | |   (66)  op(e0, e0) = e3
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REF_CLOSE: (3), (9), (28), (66) are inconsistent by sub-proof
% 204.64/35.44  | | | | | | | | |            #1372.
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | |   (67)  all_58_9 = e0
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | COMBINE_EQS: (58), (67) imply:
% 204.64/35.44  | | | | | | | | |   (68)  e1 = e0
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REDUCE: (25), (68) imply:
% 204.64/35.44  | | | | | | | | |   (69)  $false
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | CLOSE: (69) is inconsistent.
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | End of split
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | End of split
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | End of split
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | End of split
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | End of split
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | End of split
% 204.64/35.44  | | | 
% 204.64/35.44  | | End of split
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (70)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REF_CLOSE: (1), (16), (17), (20), (70) are inconsistent by sub-proof #1304.
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1050 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)  all_58_14 = all_52_23
% 204.64/35.44    (2)   ~ (e3 = e1)
% 204.64/35.44    (3)  all_58_1 = e3
% 204.64/35.44    (4)   ~ (all_52_23 = e3)
% 204.64/35.44    (5)   ~ (all_10_2 = e3)
% 204.64/35.44    (6)  all_58_8 = all_10_2
% 204.64/35.44    (7)  all_58_5 = e3
% 204.64/35.44    (8)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44    (9)  all_58_1 = e1
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | COMBINE_EQS: (3), (9) imply:
% 204.64/35.44  |   (10)  e3 = e1
% 204.64/35.44  | 
% 204.64/35.44  | COMBINE_EQS: (7), (10) imply:
% 204.64/35.44  |   (11)  all_58_5 = e1
% 204.64/35.44  | 
% 204.64/35.44  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (11) are inconsistent by sub-proof
% 204.64/35.44  |            #1051.
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1051 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)  all_58_14 = all_52_23
% 204.64/35.44    (2)   ~ (e3 = e1)
% 204.64/35.44    (3)  all_58_5 = e1
% 204.64/35.44    (4)   ~ (all_52_23 = e3)
% 204.64/35.44    (5)   ~ (all_10_2 = e3)
% 204.64/35.44    (6)  all_58_8 = all_10_2
% 204.64/35.44    (7)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | BETA: splitting (7) gives:
% 204.64/35.44  | 
% 204.64/35.44  | Case 1:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (8)  all_58_5 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (3), (8) imply:
% 204.64/35.44  | |   (9)  e3 = e1
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (2), (9) imply:
% 204.64/35.44  | |   (10)  $false
% 204.64/35.44  | | 
% 204.64/35.44  | | CLOSE: (10) is inconsistent.
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (11)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REF_CLOSE: (1), (4), (5), (6), (11) are inconsistent by sub-proof #1304.
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1052 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.44    (2)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.44    (3)  op(e2, e2) = all_4_2
% 204.64/35.44    (4)  op(e0, e0) = all_14_2
% 204.64/35.44    (5)  all_58_10 = all_52_27
% 204.64/35.44    (6)  all_58_5 = e3 | all_58_10 = e3
% 204.64/35.44    (7)  all_56_2 = all_52_17
% 204.64/35.44    (8)  op(e3, e1) = all_10_1
% 204.64/35.44    (9)   ~ (all_52_19 = e3)
% 204.64/35.44    (10)  op(e3, e1) = all_52_17
% 204.64/35.44    (11)  op(e3, e3) = all_6_2
% 204.64/35.44    (12)   ~ (all_52_27 = all_14_2)
% 204.64/35.44    (13)  op(e3, e3) = e1
% 204.64/35.44    (14)  all_58_5 = all_52_19
% 204.64/35.44    (15)   ~ (all_52_27 = all_4_2)
% 204.64/35.44    (16)  op(all_52_17, all_52_17) = e3
% 204.64/35.44    (17)   ~ (all_52_17 = all_6_2)
% 204.64/35.44    (18)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | BETA: splitting (6) gives:
% 204.64/35.44  | 
% 204.64/35.44  | Case 1:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (19)  all_58_5 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REF_CLOSE: (9), (14), (19) are inconsistent by sub-proof #1279.
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (20)  all_58_10 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (5), (20) imply:
% 204.64/35.44  | |   (21)  all_52_27 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | SIMP: (21) implies:
% 204.64/35.44  | |   (22)  all_52_27 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (12), (22) imply:
% 204.64/35.44  | |   (23)   ~ (all_14_2 = e3)
% 204.64/35.44  | | 
% 204.64/35.44  | | SIMP: (23) implies:
% 204.64/35.44  | |   (24)   ~ (all_14_2 = e3)
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (15), (22) imply:
% 204.64/35.44  | |   (25)   ~ (all_4_2 = e3)
% 204.64/35.44  | | 
% 204.64/35.44  | | SIMP: (25) implies:
% 204.64/35.44  | |   (26)   ~ (all_4_2 = e3)
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (2), (22) imply:
% 204.64/35.44  | |   (27)  op(e3, e3) = all_52_26
% 204.64/35.44  | | 
% 204.64/35.44  | | GROUND_INST: instantiating (1) with all_52_17, all_10_1, e1, e3, simplifying
% 204.64/35.44  | |              with (8), (10) gives:
% 204.64/35.44  | |   (28)  all_52_17 = all_10_1
% 204.64/35.44  | | 
% 204.64/35.44  | | GROUND_INST: instantiating (1) with all_6_2, all_52_26, e3, e3, simplifying
% 204.64/35.44  | |              with (11), (27) gives:
% 204.64/35.44  | |   (29)  all_52_26 = all_6_2
% 204.64/35.44  | | 
% 204.64/35.44  | | GROUND_INST: instantiating (1) with e1, all_52_26, e3, e3, simplifying with
% 204.64/35.44  | |              (13), (27) gives:
% 204.64/35.44  | |   (30)  all_52_26 = e1
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (29), (30) imply:
% 204.64/35.44  | |   (31)  all_6_2 = e1
% 204.64/35.44  | | 
% 204.64/35.44  | | SIMP: (31) implies:
% 204.64/35.44  | |   (32)  all_6_2 = e1
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (7), (28) imply:
% 204.64/35.44  | |   (33)  all_56_2 = all_10_1
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (17), (28), (32) imply:
% 204.64/35.44  | |   (34)   ~ (all_10_1 = e1)
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (16), (28) imply:
% 204.64/35.44  | |   (35)  op(all_10_1, all_10_1) = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | BETA: splitting (18) gives:
% 204.64/35.44  | | 
% 204.64/35.44  | | Case 1:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (36)  all_56_2 = e2
% 204.64/35.44  | | | 
% 204.64/35.44  | | | COMBINE_EQS: (33), (36) imply:
% 204.64/35.44  | | |   (37)  all_10_1 = e2
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REDUCE: (35), (37) imply:
% 204.64/35.44  | | |   (38)  op(e2, e2) = e3
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REF_CLOSE: (1), (3), (26), (38) are inconsistent by sub-proof #1318.
% 204.64/35.44  | | | 
% 204.64/35.44  | | Case 2:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (39)  all_56_2 = e1 | all_56_2 = e0
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REF_CLOSE: (1), (4), (24), (33), (34), (35), (39) are inconsistent by
% 204.64/35.44  | | |            sub-proof #1053.
% 204.64/35.44  | | | 
% 204.64/35.44  | | End of split
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1053 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.44    (2)   ~ (all_10_1 = e1)
% 204.64/35.44    (3)  op(e0, e0) = all_14_2
% 204.64/35.44    (4)  op(all_10_1, all_10_1) = e3
% 204.64/35.44    (5)  all_56_2 = all_10_1
% 204.64/35.44    (6)  all_56_2 = e1 | all_56_2 = e0
% 204.64/35.44    (7)   ~ (all_14_2 = e3)
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | BETA: splitting (6) gives:
% 204.64/35.44  | 
% 204.64/35.44  | Case 1:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (8)  all_56_2 = e1
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (5), (8) imply:
% 204.64/35.44  | |   (9)  all_10_1 = e1
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (2), (9) imply:
% 204.64/35.44  | |   (10)  $false
% 204.64/35.44  | | 
% 204.64/35.44  | | CLOSE: (10) is inconsistent.
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (11)  all_56_2 = e0
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (5), (11) imply:
% 204.64/35.44  | |   (12)  all_10_1 = e0
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (4), (12) imply:
% 204.64/35.44  | |   (13)  op(e0, e0) = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REF_CLOSE: (1), (3), (7), (13) are inconsistent by sub-proof #1372.
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1054 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.44    (2)  all_58_8 = e3
% 204.64/35.44    (3)  all_58_11 = all_52_29
% 204.64/35.44    (4)   ~ (all_52_19 = e0)
% 204.64/35.44    (5)  op(all_52_19, all_52_19) = e2
% 204.64/35.44    (6)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.44    (7)  op(e1, e1) = e3
% 204.64/35.44    (8)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.64/35.44    (9)   ~ (all_52_29 = e3)
% 204.64/35.44    (10)   ~ (all_52_19 = e3)
% 204.64/35.44    (11)  all_56_6 = all_52_19
% 204.64/35.44    (12)   ~ (all_52_19 = e2)
% 204.64/35.44    (13)   ~ (e3 = e2)
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | BETA: splitting (8) gives:
% 204.64/35.44  | 
% 204.64/35.44  | Case 1:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (14)  all_56_6 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (11), (14) imply:
% 204.64/35.44  | |   (15)  all_52_19 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (10), (15) imply:
% 204.64/35.44  | |   (16)  $false
% 204.64/35.44  | | 
% 204.64/35.44  | | CLOSE: (16) is inconsistent.
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (17)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 204.64/35.44  | | 
% 204.64/35.44  | | BETA: splitting (17) gives:
% 204.64/35.44  | | 
% 204.64/35.44  | | Case 1:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (18)  all_56_6 = e2
% 204.64/35.44  | | | 
% 204.64/35.44  | | | COMBINE_EQS: (11), (18) imply:
% 204.64/35.44  | | |   (19)  all_52_19 = e2
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REDUCE: (12), (19) imply:
% 204.64/35.44  | | |   (20)  $false
% 204.64/35.44  | | | 
% 204.64/35.44  | | | CLOSE: (20) is inconsistent.
% 204.64/35.44  | | | 
% 204.64/35.44  | | Case 2:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (21)  all_56_6 = e1 | all_56_6 = e0
% 204.64/35.44  | | | 
% 204.64/35.44  | | | BETA: splitting (21) gives:
% 204.64/35.44  | | | 
% 204.64/35.44  | | | Case 1:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | |   (22)  all_56_6 = e1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (11), (22) imply:
% 204.64/35.44  | | | |   (23)  all_52_19 = e1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (5), (23) imply:
% 204.64/35.44  | | | |   (24)  op(e1, e1) = e2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | GROUND_INST: instantiating (1) with e3, e2, e1, e1, simplifying with
% 204.64/35.44  | | | |              (7), (24) gives:
% 204.64/35.44  | | | |   (25)  e3 = e2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (2), (25) imply:
% 204.64/35.44  | | | |   (26)  all_58_8 = e2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REF_CLOSE: (3), (6), (9), (13), (26) are inconsistent by sub-proof
% 204.64/35.44  | | | |            #1271.
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | Case 2:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | |   (27)  all_56_6 = e0
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (11), (27) imply:
% 204.64/35.44  | | | |   (28)  all_52_19 = e0
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (4), (28) imply:
% 204.64/35.44  | | | |   (29)  $false
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | CLOSE: (29) is inconsistent.
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | End of split
% 204.64/35.44  | | | 
% 204.64/35.44  | | End of split
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1055 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)  all_58_14 = all_52_23
% 204.64/35.44    (2)   ~ (e3 = e1)
% 204.64/35.44    (3)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.44    (5)  all_58_1 = all_52_9
% 204.64/35.44    (6)  op(all_52_23, all_52_23) = e0
% 204.64/35.44    (7)   ~ (all_52_17 = all_52_25)
% 204.64/35.44    (8)  all_58_0 = all_6_2
% 204.64/35.44    (9)  all_58_13 = e3
% 204.64/35.44    (10)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.44    (11)  all_58_9 = all_52_25
% 204.64/35.44    (12)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.44    (13)  op(e2, e2) = all_4_2
% 204.64/35.44    (14)   ~ (all_52_3 = all_52_5)
% 204.64/35.44    (15)  all_58_11 = all_52_29
% 204.64/35.44    (16)   ~ (all_52_25 = all_14_2)
% 204.64/35.44    (17)  op(all_10_2, e1) = all_10_1
% 204.64/35.44    (18)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.44    (19)   ~ (all_52_7 = all_6_2)
% 204.64/35.44    (20)  op(e0, e0) = all_14_2
% 204.64/35.44    (21)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.44    (22)   ~ (all_6_2 = e3)
% 204.64/35.44    (23)   ~ (e2 = e1)
% 204.64/35.44    (24)  op(all_10_2, all_10_2) = e1
% 204.64/35.44    (25)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.44    (26)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.44    (27)   ~ (all_52_25 = all_52_29)
% 204.64/35.44    (28)  all_58_7 = all_52_13
% 204.64/35.44    (29)  op(all_52_19, all_52_19) = e2
% 204.64/35.44    (30)  all_58_12 = all_52_7
% 204.64/35.44    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.44    (32)   ~ (all_52_7 = e3)
% 204.64/35.44    (33)  all_58_2 = all_52_3
% 204.64/35.44    (34)  all_56_2 = all_52_17
% 204.64/35.44    (35)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.44    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.44    (37)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.44    (38)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.44    (39)   ~ (all_52_23 = e3)
% 204.64/35.44    (40)   ~ (all_52_9 = e3)
% 204.64/35.44    (41)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.44    (42)  op(e3, e1) = all_52_17
% 204.64/35.44    (43)   ~ (all_52_19 = all_10_2)
% 204.64/35.44    (44)  all_58_8 = all_10_2
% 204.64/35.44    (45)   ~ (all_52_5 = all_10_2)
% 204.64/35.44    (46)   ~ (all_52_23 = all_14_2)
% 204.64/35.44    (47)   ~ (all_52_9 = all_6_2)
% 204.64/35.44    (48)   ~ (all_52_9 = e1)
% 204.64/35.44    (49)  all_56_0 = all_6_2
% 204.64/35.44    (50)  op(e3, e3) = all_6_2
% 204.64/35.44    (51)   ~ (all_52_13 = e3)
% 204.64/35.44    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.44    (53)   ~ (all_52_3 = all_52_7)
% 204.64/35.44    (54)  all_58_5 = all_52_19
% 204.64/35.44    (55)  all_56_1 = all_52_9
% 204.64/35.44    (56)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.44    (57)  op(all_52_17, all_52_17) = e3
% 204.64/35.44    (58)  all_58_6 = all_52_5
% 204.64/35.44    (59)   ~ (all_52_17 = all_6_2)
% 204.64/35.44    (60)   ~ (e3 = e2)
% 204.64/35.44    (61)   ~ (all_52_9 = all_52_17)
% 204.64/35.44    (62)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44    (63)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.44    (64)  op(e1, e1) = all_10_2
% 204.64/35.44    (65)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.64/35.44    (66)   ~ (all_52_3 = all_4_2)
% 204.64/35.44    (67)  all_58_4 = all_52_17
% 204.64/35.44    (68)  op(all_52_25, all_52_25) = all_52_24
% 204.64/35.44    (69)   ~ (all_14_2 = e3)
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | BETA: splitting (52) gives:
% 204.64/35.44  | 
% 204.64/35.44  | Case 1:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (70)  all_58_0 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (8), (70) imply:
% 204.64/35.44  | |   (71)  all_6_2 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (22), (71) imply:
% 204.64/35.44  | |   (72)  $false
% 204.64/35.44  | | 
% 204.64/35.44  | | CLOSE: (72) is inconsistent.
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (73)   ~ (all_58_0 = e3)
% 204.64/35.44  | |   (74)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | BETA: splitting (63) gives:
% 204.64/35.44  | | 
% 204.64/35.44  | | Case 1:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (75)  all_56_0 = e3
% 204.64/35.44  | | | 
% 204.64/35.44  | | | COMBINE_EQS: (49), (75) imply:
% 204.64/35.44  | | |   (76)  all_6_2 = e3
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REDUCE: (22), (76) imply:
% 204.64/35.44  | | |   (77)  $false
% 204.64/35.44  | | | 
% 204.64/35.44  | | | CLOSE: (77) is inconsistent.
% 204.64/35.44  | | | 
% 204.64/35.44  | | Case 2:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (78)   ~ (all_56_0 = e3)
% 204.64/35.44  | | |   (79)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.44  | | | 
% 204.64/35.44  | | | BETA: splitting (65) gives:
% 204.64/35.44  | | | 
% 204.64/35.44  | | | Case 1:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | |   (80)  all_58_1 = e2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (5), (80) imply:
% 204.64/35.44  | | | |   (81)  all_52_9 = e2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (61), (81) imply:
% 204.64/35.44  | | | |   (82)   ~ (all_52_17 = e2)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | SIMP: (82) implies:
% 204.64/35.44  | | | |   (83)   ~ (all_52_17 = e2)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (47), (81) imply:
% 204.64/35.44  | | | |   (84)   ~ (all_6_2 = e2)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | SIMP: (84) implies:
% 204.64/35.44  | | | |   (85)   ~ (all_6_2 = e2)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | BETA: splitting (21) gives:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | Case 1:
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | |   (86)  all_56_2 = e3
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | COMBINE_EQS: (34), (86) imply:
% 204.64/35.44  | | | | |   (87)  all_52_17 = e3
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | SIMP: (87) implies:
% 204.64/35.44  | | | | |   (88)  all_52_17 = e3
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | REF_CLOSE: (4), (50), (57), (59), (88) are inconsistent by sub-proof
% 204.64/35.44  | | | | |            #1280.
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | Case 2:
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | |   (89)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (18), (19), (20), (22), (30),
% 204.64/35.44  | | | | |            (34), (37), (38), (41), (46), (49), (57), (59), (69), (79),
% 204.64/35.44  | | | | |            (83), (85), (89) are inconsistent by sub-proof #1062.
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | End of split
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | Case 2:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | |   (90)   ~ (all_58_1 = e2)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (5), (90) imply:
% 204.64/35.44  | | | |   (91)   ~ (all_52_9 = e2)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | BETA: splitting (56) gives:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | Case 1:
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | |   (92)  all_56_1 = e2
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | REF_CLOSE: (55), (91), (92) are inconsistent by sub-proof #1194.
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | Case 2:
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | |   (93)   ~ (all_56_1 = e2)
% 204.64/35.44  | | | | |   (94)  all_56_1 = e1 | all_56_1 = e0
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | BETA: splitting (94) gives:
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | | Case 1:
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | |   (95)  all_56_1 = e1
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | REF_CLOSE: (48), (55), (95) are inconsistent by sub-proof #1061.
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | Case 2:
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | |   (96)  all_56_1 = e0
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | COMBINE_EQS: (55), (96) imply:
% 204.64/35.44  | | | | | |   (97)  all_52_9 = e0
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | SIMP: (97) implies:
% 204.64/35.44  | | | | | |   (98)  all_52_9 = e0
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | COMBINE_EQS: (5), (98) imply:
% 204.64/35.44  | | | | | |   (99)  all_58_1 = e0
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | REDUCE: (40), (98) imply:
% 204.64/35.44  | | | | | |   (100)   ~ (e3 = e0)
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | SIMP: (100) implies:
% 204.64/35.44  | | | | | |   (101)   ~ (e3 = e0)
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | REDUCE: (91), (98) imply:
% 204.64/35.44  | | | | | |   (102)   ~ (e2 = e0)
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | SIMP: (102) implies:
% 204.64/35.44  | | | | | |   (103)   ~ (e2 = e0)
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | REDUCE: (26), (98) imply:
% 204.64/35.44  | | | | | |   (104)  op(e0, e0) = all_52_8
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | GROUND_INST: instantiating (4) with all_14_2, all_52_8, e0, e0,
% 204.64/35.44  | | | | | |              simplifying with (20), (104) gives:
% 204.64/35.44  | | | | | |   (105)  all_52_8 = all_14_2
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | BETA: splitting (21) gives:
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | | Case 1:
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | |   (106)  all_56_2 = e3
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | | COMBINE_EQS: (34), (106) imply:
% 204.64/35.44  | | | | | | |   (107)  all_52_17 = e3
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | | SIMP: (107) implies:
% 204.64/35.44  | | | | | | |   (108)  all_52_17 = e3
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | | REF_CLOSE: (4), (50), (57), (59), (108) are inconsistent by
% 204.64/35.44  | | | | | | |            sub-proof #1280.
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | Case 2:
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | |   (109)   ~ (all_56_2 = e3)
% 204.64/35.44  | | | | | | |   (110)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | | REDUCE: (34), (109) imply:
% 204.64/35.44  | | | | | | |   (111)   ~ (all_52_17 = e3)
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | | BETA: splitting (74) gives:
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | | Case 1:
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | |   (112)  all_58_1 = e3
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | | REF_CLOSE: (99), (101), (112) are inconsistent by sub-proof
% 204.64/35.44  | | | | | | | |            #1060.
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | |   (113)  all_58_4 = e3 | all_58_9 = e3
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | | BETA: splitting (113) gives:
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | | Case 1:
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | |   (114)  all_58_4 = e3
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REF_CLOSE: (67), (111), (114) are inconsistent by sub-proof
% 204.64/35.44  | | | | | | | | |            #1302.
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | |   (115)  all_58_9 = e3
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | COMBINE_EQS: (11), (115) imply:
% 204.64/35.44  | | | | | | | | |   (116)  all_52_25 = e3
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | SIMP: (116) implies:
% 204.64/35.44  | | | | | | | | |   (117)  all_52_25 = e3
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REDUCE: (27), (117) imply:
% 204.64/35.44  | | | | | | | | |   (118)   ~ (all_52_29 = e3)
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | SIMP: (118) implies:
% 204.64/35.44  | | | | | | | | |   (119)   ~ (all_52_29 = e3)
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REDUCE: (16), (117) imply:
% 204.64/35.44  | | | | | | | | |   (120)   ~ (all_14_2 = e3)
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | REDUCE: (68), (117) imply:
% 204.64/35.44  | | | | | | | | |   (121)  op(e3, e3) = all_52_24
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_24, e3, e3,
% 204.64/35.44  | | | | | | | | |              simplifying with (50), (121) gives:
% 204.64/35.44  | | | | | | | | |   (122)  all_52_24 = all_6_2
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | BETA: splitting (62) gives:
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | Case 1:
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | |   (123)  all_58_4 = e3
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | REF_CLOSE: (67), (111), (123) are inconsistent by sub-proof
% 204.64/35.44  | | | | | | | | | |            #1302.
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | |   (124)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | BETA: splitting (31) gives:
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | Case 1:
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | |   (125)  all_58_6 = e3
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | COMBINE_EQS: (58), (125) imply:
% 204.64/35.44  | | | | | | | | | | |   (126)  all_52_5 = e3
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | SIMP: (126) implies:
% 204.64/35.44  | | | | | | | | | | |   (127)  all_52_5 = e3
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | REDUCE: (45), (127) imply:
% 204.64/35.44  | | | | | | | | | | |   (128)   ~ (all_10_2 = e3)
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | SIMP: (128) implies:
% 204.64/35.44  | | | | | | | | | | |   (129)   ~ (all_10_2 = e3)
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | REDUCE: (10), (127) imply:
% 204.64/35.44  | | | | | | | | | | |   (130)  op(e3, e3) = all_52_4
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | BETA: splitting (124) gives:
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | Case 1:
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | |   (131)  all_58_5 = e3
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | COMBINE_EQS: (54), (131) imply:
% 204.64/35.44  | | | | | | | | | | | |   (132)  all_52_19 = e3
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | SIMP: (132) implies:
% 204.64/35.44  | | | | | | | | | | | |   (133)  all_52_19 = e3
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | REDUCE: (29), (133) imply:
% 204.64/35.44  | | | | | | | | | | | |   (134)  op(e3, e3) = e2
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_4, e3, e3,
% 204.64/35.44  | | | | | | | | | | | |              simplifying with (50), (130) gives:
% 204.64/35.44  | | | | | | | | | | | |   (135)  all_52_4 = all_6_2
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | GROUND_INST: instantiating (4) with e2, all_52_4, e3, e3,
% 204.64/35.44  | | | | | | | | | | | |              simplifying with (130), (134) gives:
% 204.64/35.44  | | | | | | | | | | | |   (136)  all_52_4 = e2
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | COMBINE_EQS: (135), (136) imply:
% 204.64/35.44  | | | | | | | | | | | |   (137)  all_6_2 = e2
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | SIMP: (137) implies:
% 204.64/35.44  | | | | | | | | | | | |   (138)  all_6_2 = e2
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | REDUCE: (59), (138) imply:
% 204.64/35.44  | | | | | | | | | | | |   (139)   ~ (all_52_17 = e2)
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | REF_CLOSE: (4), (12), (20), (34), (57), (64), (67), (69),
% 204.64/35.44  | | | | | | | | | | | |            (110), (129), (139) are inconsistent by sub-proof
% 204.64/35.44  | | | | | | | | | | | |            #1058.
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | |   (140)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | | REF_CLOSE: (1), (39), (44), (129), (140) are inconsistent by
% 204.64/35.44  | | | | | | | | | | | |            sub-proof #1304.
% 204.64/35.44  | | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | End of split
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | Case 2:
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | |   (141)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (13), (14), (15), (17), (23),
% 204.64/35.44  | | | | | | | | | | |            (24), (25), (28), (30), (32), (33), (35), (36),
% 204.64/35.44  | | | | | | | | | | |            (42), (44), (45), (50), (51), (53), (57), (58),
% 204.64/35.44  | | | | | | | | | | |            (60), (66), (67), (99), (103), (115), (119), (141)
% 204.64/35.44  | | | | | | | | | | |            are inconsistent by sub-proof #1056.
% 204.64/35.44  | | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | | End of split
% 204.64/35.44  | | | | | | | | | | 
% 204.64/35.44  | | | | | | | | | End of split
% 204.64/35.44  | | | | | | | | | 
% 204.64/35.44  | | | | | | | | End of split
% 204.64/35.44  | | | | | | | | 
% 204.64/35.44  | | | | | | | End of split
% 204.64/35.44  | | | | | | | 
% 204.64/35.44  | | | | | | End of split
% 204.64/35.44  | | | | | | 
% 204.64/35.44  | | | | | End of split
% 204.64/35.44  | | | | | 
% 204.64/35.44  | | | | End of split
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | End of split
% 204.64/35.44  | | | 
% 204.64/35.44  | | End of split
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1056 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)   ~ (e3 = e1)
% 204.64/35.44    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.44    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.44    (4)  all_58_1 = e0
% 204.64/35.44    (5)  all_58_9 = e3
% 204.64/35.44    (6)  all_58_0 = all_6_2
% 204.64/35.44    (7)  op(e2, e2) = all_4_2
% 204.64/35.44    (8)   ~ (all_52_3 = all_52_5)
% 204.64/35.44    (9)  all_58_11 = all_52_29
% 204.64/35.44    (10)  op(all_10_2, e1) = all_10_1
% 204.64/35.44    (11)   ~ (e2 = e1)
% 204.64/35.44    (12)  op(all_10_2, all_10_2) = e1
% 204.64/35.44    (13)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.44    (14)  all_58_7 = all_52_13
% 204.64/35.44    (15)  all_58_12 = all_52_7
% 204.64/35.44    (16)   ~ (all_52_7 = e3)
% 204.64/35.44    (17)  all_58_2 = all_52_3
% 204.64/35.44    (18)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.44    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.44    (20)   ~ (all_52_29 = e3)
% 204.64/35.44    (21)   ~ (e2 = e0)
% 204.64/35.44    (22)  op(e3, e1) = all_52_17
% 204.64/35.44    (23)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.44    (24)  all_58_8 = all_10_2
% 204.64/35.44    (25)   ~ (all_52_5 = all_10_2)
% 204.64/35.44    (26)  op(e3, e3) = all_6_2
% 204.64/35.44    (27)   ~ (all_52_13 = e3)
% 204.64/35.44    (28)   ~ (all_52_3 = all_52_7)
% 204.64/35.44    (29)  op(all_52_17, all_52_17) = e3
% 204.64/35.44    (30)  all_58_6 = all_52_5
% 204.64/35.44    (31)   ~ (e3 = e2)
% 204.64/35.44    (32)   ~ (all_52_3 = all_4_2)
% 204.64/35.44    (33)  all_58_4 = all_52_17
% 204.64/35.44  
% 204.64/35.44  Begin of proof
% 204.64/35.44  | 
% 204.64/35.44  | BETA: splitting (23) gives:
% 204.64/35.44  | 
% 204.64/35.44  | Case 1:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (34)  all_58_7 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | COMBINE_EQS: (14), (34) imply:
% 204.64/35.44  | |   (35)  all_52_13 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | REDUCE: (27), (35) imply:
% 204.64/35.44  | |   (36)  $false
% 204.64/35.44  | | 
% 204.64/35.44  | | CLOSE: (36) is inconsistent.
% 204.64/35.44  | | 
% 204.64/35.44  | Case 2:
% 204.64/35.44  | | 
% 204.64/35.44  | |   (37)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.44  | | 
% 204.64/35.44  | | BETA: splitting (37) gives:
% 204.64/35.44  | | 
% 204.64/35.44  | | Case 1:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (38)  all_58_8 = e3
% 204.64/35.44  | | | 
% 204.64/35.44  | | | COMBINE_EQS: (24), (38) imply:
% 204.64/35.44  | | |   (39)  all_10_2 = e3
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REDUCE: (25), (39) imply:
% 204.64/35.44  | | |   (40)   ~ (all_52_5 = e3)
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REDUCE: (12), (39) imply:
% 204.64/35.44  | | |   (41)  op(e3, e3) = e1
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REDUCE: (10), (39) imply:
% 204.64/35.44  | | |   (42)  op(e3, e1) = all_10_1
% 204.64/35.44  | | | 
% 204.64/35.44  | | | BETA: splitting (13) gives:
% 204.64/35.44  | | | 
% 204.64/35.44  | | | Case 1:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | |   (43)  all_58_2 = e3
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (17), (43) imply:
% 204.64/35.44  | | | |   (44)  all_52_3 = e3
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | SIMP: (44) implies:
% 204.64/35.44  | | | |   (45)  all_52_3 = e3
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (8), (45) imply:
% 204.64/35.44  | | | |   (46)   ~ (all_52_5 = e3)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (28), (45) imply:
% 204.64/35.44  | | | |   (47)   ~ (all_52_7 = e3)
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REDUCE: (2), (45) imply:
% 204.64/35.44  | | | |   (48)  op(e3, e3) = all_52_2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1, e3,
% 204.64/35.44  | | | |              simplifying with (22), (42) gives:
% 204.64/35.44  | | | |   (49)  all_52_17 = all_10_1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_2, e3, e3,
% 204.64/35.44  | | | |              simplifying with (26), (48) gives:
% 204.64/35.44  | | | |   (50)  all_52_2 = all_6_2
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | GROUND_INST: instantiating (3) with e1, all_52_2, e3, e3, simplifying
% 204.64/35.44  | | | |              with (41), (48) gives:
% 204.64/35.44  | | | |   (51)  all_52_2 = e1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (50), (51) imply:
% 204.64/35.44  | | | |   (52)  all_6_2 = e1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | SIMP: (52) implies:
% 204.64/35.44  | | | |   (53)  all_6_2 = e1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (33), (49) imply:
% 204.64/35.44  | | | |   (54)  all_58_4 = all_10_1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | COMBINE_EQS: (6), (53) imply:
% 204.64/35.44  | | | |   (55)  all_58_0 = e1
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (15), (16), (17), (18),
% 204.64/35.44  | | | |            (19), (21), (22), (26), (29), (30), (31), (32), (40), (41),
% 204.64/35.44  | | | |            (42), (54), (55) are inconsistent by sub-proof #1057.
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | Case 2:
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | |   (56)  all_58_6 = e3 | all_58_12 = e3
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | | REF_CLOSE: (15), (16), (30), (40), (56) are inconsistent by sub-proof
% 204.64/35.44  | | | |            #1243.
% 204.64/35.44  | | | | 
% 204.64/35.44  | | | End of split
% 204.64/35.44  | | | 
% 204.64/35.44  | | Case 2:
% 204.64/35.44  | | | 
% 204.64/35.44  | | |   (57)  all_58_11 = e3
% 204.64/35.44  | | | 
% 204.64/35.44  | | | REF_CLOSE: (9), (20), (57) are inconsistent by sub-proof #1323.
% 204.64/35.44  | | | 
% 204.64/35.44  | | End of split
% 204.64/35.44  | | 
% 204.64/35.44  | End of split
% 204.64/35.44  | 
% 204.64/35.44  End of proof
% 204.64/35.44  
% 204.64/35.44  Sub-proof #1057 shows that the following formulas are inconsistent:
% 204.64/35.44  ----------------------------------------------------------------
% 204.64/35.44    (1)   ~ (e3 = e1)
% 204.64/35.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.44    (3)  all_58_1 = e0
% 204.64/35.44    (4)  all_58_9 = e3
% 204.64/35.44    (5)  all_58_0 = all_6_2
% 204.64/35.44    (6)  op(e2, e2) = all_4_2
% 204.64/35.44    (7)  all_58_4 = all_10_1
% 204.64/35.44    (8)   ~ (e2 = e1)
% 204.64/35.44    (9)  all_58_12 = all_52_7
% 204.64/35.44    (10)   ~ (all_52_7 = e3)
% 204.64/35.45    (11)  all_58_2 = all_52_3
% 204.64/35.45    (12)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.45    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.45    (14)  op(e3, e1) = all_10_1
% 204.64/35.45    (15)   ~ (e2 = e0)
% 204.64/35.45    (16)   ~ (all_52_5 = e3)
% 204.64/35.45    (17)  op(e3, e1) = all_52_17
% 204.64/35.45    (18)  op(e3, e3) = all_6_2
% 204.64/35.45    (19)  op(e3, e3) = e1
% 204.64/35.45    (20)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (21)  all_58_6 = all_52_5
% 204.64/35.45    (22)   ~ (e3 = e2)
% 204.64/35.45    (23)   ~ (all_52_3 = all_4_2)
% 204.64/35.45    (24)  all_58_0 = e1
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (12) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (25)  all_58_0 = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (8), (24), (25) are inconsistent by sub-proof #1273.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (26)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | BETA: splitting (26) gives:
% 204.64/35.45  | | 
% 204.64/35.45  | | Case 1:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (27)  all_58_1 = e2
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REF_CLOSE: (3), (15), (27) are inconsistent by sub-proof #1272.
% 204.64/35.45  | | | 
% 204.64/35.45  | | Case 2:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (28)  all_58_4 = e2 | all_58_9 = e2
% 204.64/35.45  | | | 
% 204.64/35.45  | | | BETA: splitting (28) gives:
% 204.64/35.45  | | | 
% 204.64/35.45  | | | Case 1:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (29)  all_58_4 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | COMBINE_EQS: (7), (29) imply:
% 204.64/35.45  | | | |   (30)  all_10_1 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REDUCE: (14), (30) imply:
% 204.64/35.45  | | | |   (31)  op(e3, e1) = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (1), (2), (5), (6), (9), (10), (11), (13), (16), (17), (18),
% 204.64/35.45  | | | |            (19), (20), (21), (23), (31) are inconsistent by sub-proof
% 204.64/35.45  | | | |            #1085.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | Case 2:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (32)  all_58_9 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | COMBINE_EQS: (4), (32) imply:
% 204.64/35.45  | | | |   (33)  e3 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REDUCE: (22), (33) imply:
% 204.64/35.45  | | | |   (34)  $false
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | CLOSE: (34) is inconsistent.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | End of split
% 204.64/35.45  | | | 
% 204.64/35.45  | | End of split
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1058 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (2)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.64/35.45    (3)  op(e0, e0) = all_14_2
% 204.64/35.45    (4)  all_56_2 = all_52_17
% 204.64/35.45    (5)   ~ (all_10_2 = e3)
% 204.64/35.45    (6)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (7)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45    (8)  op(e1, e1) = all_10_2
% 204.64/35.45    (9)   ~ (all_52_17 = e2)
% 204.64/35.45    (10)  all_58_4 = all_52_17
% 204.64/35.45    (11)   ~ (all_14_2 = e3)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (2) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (12)  all_58_4 = e1
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (5), (6), (8), (10), (12) are inconsistent by sub-proof
% 204.64/35.45  | |            #1059.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (13)   ~ (all_58_4 = e1)
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (10), (13) imply:
% 204.64/35.45  | |   (14)   ~ (all_52_17 = e1)
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (14) are inconsistent by
% 204.64/35.45  | |            sub-proof #1068.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1059 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (2)  all_58_4 = e1
% 204.64/35.45    (3)   ~ (all_10_2 = e3)
% 204.64/35.45    (4)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (5)  op(e1, e1) = all_10_2
% 204.64/35.45    (6)  all_58_4 = all_52_17
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | COMBINE_EQS: (2), (6) imply:
% 204.64/35.45  |   (7)  all_52_17 = e1
% 204.64/35.45  | 
% 204.64/35.45  | SIMP: (7) implies:
% 204.64/35.45  |   (8)  all_52_17 = e1
% 204.64/35.45  | 
% 204.64/35.45  | REDUCE: (4), (8) imply:
% 204.64/35.45  |   (9)  op(e1, e1) = e3
% 204.64/35.45  | 
% 204.64/35.45  | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1368.
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1060 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_1 = e3
% 204.64/35.45    (2)  all_58_1 = e0
% 204.64/35.45    (3)   ~ (e3 = e0)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.45  |   (4)  e3 = e0
% 204.64/35.45  | 
% 204.64/35.45  | SIMP: (4) implies:
% 204.64/35.45  |   (5)  e3 = e0
% 204.64/35.45  | 
% 204.64/35.45  | REDUCE: (3), (5) imply:
% 204.64/35.45  |   (6)  $false
% 204.64/35.45  | 
% 204.64/35.45  | CLOSE: (6) is inconsistent.
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1061 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_56_1 = all_52_9
% 204.64/35.45    (2)  all_56_1 = e1
% 204.64/35.45    (3)   ~ (all_52_9 = e1)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.45  |   (4)  all_52_9 = e1
% 204.64/35.45  | 
% 204.64/35.45  | SIMP: (4) implies:
% 204.64/35.45  |   (5)  all_52_9 = e1
% 204.64/35.45  | 
% 204.64/35.45  | REDUCE: (3), (5) imply:
% 204.64/35.45  |   (6)  $false
% 204.64/35.45  | 
% 204.64/35.45  | CLOSE: (6) is inconsistent.
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1062 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_14 = all_52_23
% 204.64/35.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (3)  op(all_52_23, all_52_23) = e0
% 204.64/35.45    (4)  all_58_0 = all_6_2
% 204.64/35.45    (5)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.45    (6)  all_58_13 = e3
% 204.64/35.45    (7)   ~ (all_6_2 = e2)
% 204.64/35.45    (8)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.45    (9)   ~ (all_52_7 = all_6_2)
% 204.64/35.45    (10)  op(e0, e0) = all_14_2
% 204.64/35.45    (11)   ~ (all_6_2 = e3)
% 204.64/35.45    (12)  all_58_12 = all_52_7
% 204.64/35.45    (13)  all_56_2 = all_52_17
% 204.64/35.45    (14)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.45    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 204.64/35.45    (16)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.45    (17)   ~ (all_52_23 = all_14_2)
% 204.64/35.45    (18)  all_56_0 = all_6_2
% 204.64/35.45    (19)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (20)   ~ (all_52_17 = all_6_2)
% 204.64/35.45    (21)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45    (22)   ~ (all_52_17 = e2)
% 204.64/35.45    (23)   ~ (all_14_2 = e3)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (15) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (24)  all_58_0 = e1
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (4), (24) imply:
% 204.64/35.45  | |   (25)  all_6_2 = e1
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (20), (25) imply:
% 204.64/35.45  | |   (26)   ~ (all_52_17 = e1)
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (2), (10), (13), (19), (21), (22), (23), (26) are inconsistent by
% 204.64/35.45  | |            sub-proof #1068.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (27)   ~ (all_58_0 = e1)
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (4), (27) imply:
% 204.64/35.45  | |   (28)   ~ (all_6_2 = e1)
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.64/35.45  | |            (14), (16), (17), (18), (28) are inconsistent by sub-proof #1065.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1063 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_14 = all_52_23
% 204.64/35.45    (2)   ~ (e3 = e1)
% 204.64/35.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (4)  op(e3, e3) = all_52_0
% 204.64/35.45    (5)  all_58_11 = all_52_29
% 204.64/35.45    (6)  all_56_11 = all_52_29
% 204.64/35.45    (7)  op(all_10_2, all_10_2) = e1
% 204.64/35.45    (8)   ~ (all_52_29 = all_10_2)
% 204.64/35.45    (9)  all_58_7 = all_52_13
% 204.64/35.45    (10)  op(all_52_19, all_52_19) = e2
% 204.64/35.45    (11)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.45    (12)  op(e3, e3) = e3
% 204.64/35.45    (13)   ~ (all_52_23 = e3)
% 204.64/35.45    (14)   ~ (all_52_5 = e3)
% 204.64/35.45    (15)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.45    (16)  all_58_8 = all_10_2
% 204.64/35.45    (17)  op(all_52_29, all_52_29) = all_52_28
% 204.64/35.45    (18)   ~ (all_52_13 = e3)
% 204.64/35.45    (19)   ~ (all_52_17 = e3)
% 204.64/35.45    (20)  all_58_5 = all_52_19
% 204.64/35.45    (21)  all_58_6 = all_52_5
% 204.64/35.45    (22)   ~ (e3 = e2)
% 204.64/35.45    (23)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.45    (24)  all_58_4 = all_52_17
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (23) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (25)  all_58_4 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (19), (24), (25) are inconsistent by sub-proof #1302.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (26)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.64/35.45  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (26) are
% 204.64/35.45  | |            inconsistent by sub-proof #1069.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1064 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_14 = all_52_23
% 204.64/35.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (3)  op(all_52_23, all_52_23) = e0
% 204.64/35.45    (4)  all_58_0 = all_6_2
% 204.64/35.45    (5)  all_58_13 = e3
% 204.64/35.45    (6)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.45    (7)   ~ (all_52_7 = all_6_2)
% 204.64/35.45    (8)  op(e0, e0) = all_14_2
% 204.64/35.45    (9)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45    (10)   ~ (all_6_2 = e3)
% 204.64/35.45    (11)  all_58_12 = all_52_7
% 204.64/35.45    (12)  all_56_2 = all_52_17
% 204.64/35.45    (13)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.45    (14)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.45    (15)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.45    (16)   ~ (all_52_23 = all_14_2)
% 204.64/35.45    (17)  all_56_0 = all_6_2
% 204.64/35.45    (18)   ~ (all_52_17 = e3)
% 204.64/35.45    (19)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (20)   ~ (all_52_17 = all_6_2)
% 204.64/35.45    (21)   ~ (all_6_2 = e1)
% 204.64/35.45    (22)   ~ (all_52_17 = e1)
% 204.64/35.45    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.45    (24)   ~ (all_14_2 = e3)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (9) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (25)  all_56_2 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (12), (18), (25) are inconsistent by sub-proof #1327.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (26)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45  | | 
% 204.64/35.45  | | BETA: splitting (23) gives:
% 204.64/35.45  | | 
% 204.64/35.45  | | Case 1:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (27)  all_56_0 = e3
% 204.64/35.45  | | | 
% 204.64/35.45  | | | COMBINE_EQS: (17), (27) imply:
% 204.64/35.45  | | |   (28)  all_6_2 = e3
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (10), (28) imply:
% 204.64/35.45  | | |   (29)  $false
% 204.64/35.45  | | | 
% 204.64/35.45  | | | CLOSE: (29) is inconsistent.
% 204.64/35.45  | | | 
% 204.64/35.45  | | Case 2:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (30)   ~ (all_56_0 = e3)
% 204.64/35.45  | | |   (31)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.45  | | | 
% 204.64/35.45  | | | BETA: splitting (13) gives:
% 204.64/35.45  | | | 
% 204.64/35.45  | | | Case 1:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (32)  all_58_0 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | COMBINE_EQS: (4), (32) imply:
% 204.64/35.45  | | | |   (33)  all_6_2 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REDUCE: (20), (33) imply:
% 204.64/35.45  | | | |   (34)   ~ (all_52_17 = e2)
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (2), (8), (12), (19), (22), (24), (26), (34) are inconsistent
% 204.64/35.45  | | | |            by sub-proof #1068.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | Case 2:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (35)   ~ (all_58_0 = e2)
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REDUCE: (4), (35) imply:
% 204.64/35.45  | | | |   (36)   ~ (all_6_2 = e2)
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14),
% 204.64/35.45  | | | |            (15), (16), (17), (21), (31), (36) are inconsistent by
% 204.64/35.45  | | | |            sub-proof #1065.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | End of split
% 204.64/35.45  | | | 
% 204.64/35.45  | | End of split
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1065 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_14 = all_52_23
% 204.64/35.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (3)  op(all_52_23, all_52_23) = e0
% 204.64/35.45    (4)  all_58_0 = all_6_2
% 204.64/35.45    (5)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.64/35.45    (6)  all_58_13 = e3
% 204.64/35.45    (7)   ~ (all_6_2 = e2)
% 204.64/35.45    (8)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.45    (9)   ~ (all_52_7 = all_6_2)
% 204.64/35.45    (10)  op(e0, e0) = all_14_2
% 204.64/35.45    (11)   ~ (all_6_2 = e3)
% 204.64/35.45    (12)  all_58_12 = all_52_7
% 204.64/35.45    (13)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.64/35.45    (14)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.45    (15)   ~ (all_52_23 = all_14_2)
% 204.64/35.45    (16)  all_56_0 = all_6_2
% 204.64/35.45    (17)   ~ (all_6_2 = e1)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (5) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (18)  all_56_0 = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (16), (18) imply:
% 204.64/35.45  | |   (19)  all_6_2 = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (7), (19) imply:
% 204.64/35.45  | |   (20)  $false
% 204.64/35.45  | | 
% 204.64/35.45  | | CLOSE: (20) is inconsistent.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (21)  all_56_0 = e1 | all_56_0 = e0
% 204.64/35.45  | | 
% 204.64/35.45  | | BETA: splitting (13) gives:
% 204.64/35.45  | | 
% 204.64/35.45  | | Case 1:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (22)  all_58_0 = e0
% 204.64/35.45  | | | 
% 204.64/35.45  | | | COMBINE_EQS: (4), (22) imply:
% 204.64/35.45  | | |   (23)  all_6_2 = e0
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (9), (23) imply:
% 204.64/35.45  | | |   (24)   ~ (all_52_7 = e0)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (11), (23) imply:
% 204.64/35.45  | | |   (25)   ~ (e3 = e0)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | SIMP: (25) implies:
% 204.64/35.45  | | |   (26)   ~ (e3 = e0)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (8), (23) imply:
% 204.64/35.45  | | |   (27)  op(e0, e0) = all_52_0
% 204.64/35.45  | | | 
% 204.64/35.45  | | | BETA: splitting (14) gives:
% 204.64/35.45  | | | 
% 204.64/35.45  | | | Case 1:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (28)  all_58_12 = e0
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (12), (24), (28) are inconsistent by sub-proof #1067.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | Case 2:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (29)  all_58_13 = e0 | all_58_14 = e0
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | BETA: splitting (29) gives:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | Case 1:
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | |   (30)  all_58_13 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | REF_CLOSE: (6), (26), (30) are inconsistent by sub-proof #1172.
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | Case 2:
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | |   (31)  all_58_14 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | COMBINE_EQS: (1), (31) imply:
% 204.64/35.45  | | | | |   (32)  all_52_23 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | SIMP: (32) implies:
% 204.64/35.45  | | | | |   (33)  all_52_23 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | REDUCE: (15), (33) imply:
% 204.64/35.45  | | | | |   (34)   ~ (all_14_2 = e0)
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | SIMP: (34) implies:
% 204.64/35.45  | | | | |   (35)   ~ (all_14_2 = e0)
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | REDUCE: (3), (33) imply:
% 204.64/35.45  | | | | |   (36)  op(e0, e0) = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | GROUND_INST: instantiating (2) with all_14_2, all_52_0, e0, e0,
% 204.64/35.45  | | | | |              simplifying with (10), (27) gives:
% 204.64/35.45  | | | | |   (37)  all_52_0 = all_14_2
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | GROUND_INST: instantiating (2) with e0, all_52_0, e0, e0, simplifying
% 204.64/35.45  | | | | |              with (27), (36) gives:
% 204.64/35.45  | | | | |   (38)  all_52_0 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | COMBINE_EQS: (37), (38) imply:
% 204.64/35.45  | | | | |   (39)  all_14_2 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | SIMP: (39) implies:
% 204.64/35.45  | | | | |   (40)  all_14_2 = e0
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | REDUCE: (35), (40) imply:
% 204.64/35.45  | | | | |   (41)  $false
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | | CLOSE: (41) is inconsistent.
% 204.64/35.45  | | | | | 
% 204.64/35.45  | | | | End of split
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | End of split
% 204.64/35.45  | | | 
% 204.64/35.45  | | Case 2:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (42)   ~ (all_58_0 = e0)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (4), (42) imply:
% 204.64/35.45  | | |   (43)   ~ (all_6_2 = e0)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REF_CLOSE: (16), (17), (21), (43) are inconsistent by sub-proof #1066.
% 204.64/35.45  | | | 
% 204.64/35.45  | | End of split
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1066 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_56_0 = e1 | all_56_0 = e0
% 204.64/35.45    (2)  all_56_0 = all_6_2
% 204.64/35.45    (3)   ~ (all_6_2 = e1)
% 204.64/35.45    (4)   ~ (all_6_2 = e0)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (1) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (5)  all_56_0 = e1
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (2), (5) imply:
% 204.64/35.45  | |   (6)  all_6_2 = e1
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (3), (6) imply:
% 204.64/35.45  | |   (7)  $false
% 204.64/35.45  | | 
% 204.64/35.45  | | CLOSE: (7) is inconsistent.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (8)  all_56_0 = e0
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (2), (8) imply:
% 204.64/35.45  | |   (9)  all_6_2 = e0
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (4), (9) imply:
% 204.64/35.45  | |   (10)  $false
% 204.64/35.45  | | 
% 204.64/35.45  | | CLOSE: (10) is inconsistent.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1067 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_12 = all_52_7
% 204.64/35.45    (2)  all_58_12 = e0
% 204.64/35.45    (3)   ~ (all_52_7 = e0)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.45  |   (4)  all_52_7 = e0
% 204.64/35.45  | 
% 204.64/35.45  | SIMP: (4) implies:
% 204.64/35.45  |   (5)  all_52_7 = e0
% 204.64/35.45  | 
% 204.64/35.45  | REDUCE: (3), (5) imply:
% 204.64/35.45  |   (6)  $false
% 204.64/35.45  | 
% 204.64/35.45  | CLOSE: (6) is inconsistent.
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1068 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (2)  op(e0, e0) = all_14_2
% 204.64/35.45    (3)  all_56_2 = all_52_17
% 204.64/35.45    (4)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (5)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45    (6)   ~ (all_52_17 = e1)
% 204.64/35.45    (7)   ~ (all_52_17 = e2)
% 204.64/35.45    (8)   ~ (all_14_2 = e3)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (5) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (9)  all_56_2 = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (3), (9) imply:
% 204.64/35.45  | |   (10)  all_52_17 = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (7), (10) imply:
% 204.64/35.45  | |   (11)  $false
% 204.64/35.45  | | 
% 204.64/35.45  | | CLOSE: (11) is inconsistent.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (12)  all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45  | | 
% 204.64/35.45  | | BETA: splitting (12) gives:
% 204.64/35.45  | | 
% 204.64/35.45  | | Case 1:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (13)  all_56_2 = e1
% 204.64/35.45  | | | 
% 204.64/35.45  | | | COMBINE_EQS: (3), (13) imply:
% 204.64/35.45  | | |   (14)  all_52_17 = e1
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (6), (14) imply:
% 204.64/35.45  | | |   (15)  $false
% 204.64/35.45  | | | 
% 204.64/35.45  | | | CLOSE: (15) is inconsistent.
% 204.64/35.45  | | | 
% 204.64/35.45  | | Case 2:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (16)  all_56_2 = e0
% 204.64/35.45  | | | 
% 204.64/35.45  | | | COMBINE_EQS: (3), (16) imply:
% 204.64/35.45  | | |   (17)  all_52_17 = e0
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (4), (17) imply:
% 204.64/35.45  | | |   (18)  op(e0, e0) = e3
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REF_CLOSE: (1), (2), (8), (18) are inconsistent by sub-proof #1372.
% 204.64/35.45  | | | 
% 204.64/35.45  | | End of split
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1069 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_14 = all_52_23
% 204.64/35.45    (2)   ~ (e3 = e1)
% 204.64/35.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (4)  op(e3, e3) = all_52_0
% 204.64/35.45    (5)  all_58_11 = all_52_29
% 204.64/35.45    (6)  all_56_11 = all_52_29
% 204.64/35.45    (7)  op(all_10_2, all_10_2) = e1
% 204.64/35.45    (8)   ~ (all_52_29 = all_10_2)
% 204.64/35.45    (9)  all_58_7 = all_52_13
% 204.64/35.45    (10)  op(all_52_19, all_52_19) = e2
% 204.64/35.45    (11)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.45    (12)  op(e3, e3) = e3
% 204.64/35.45    (13)   ~ (all_52_23 = e3)
% 204.64/35.45    (14)   ~ (all_52_5 = e3)
% 204.64/35.45    (15)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.45    (16)  all_58_8 = all_10_2
% 204.64/35.45    (17)  op(all_52_29, all_52_29) = all_52_28
% 204.64/35.45    (18)   ~ (all_52_13 = e3)
% 204.64/35.45    (19)  all_58_5 = all_52_19
% 204.64/35.45    (20)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.45    (21)  all_58_6 = all_52_5
% 204.64/35.45    (22)   ~ (e3 = e2)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (11) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (23)  all_58_6 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (14), (21), (23) are inconsistent by sub-proof #1328.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (24)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | BETA: splitting (15) gives:
% 204.64/35.45  | | 
% 204.64/35.45  | | Case 1:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (25)  all_56_11 = e3
% 204.64/35.45  | | | 
% 204.64/35.45  | | | COMBINE_EQS: (6), (25) imply:
% 204.64/35.45  | | |   (26)  all_52_29 = e3
% 204.64/35.45  | | | 
% 204.64/35.45  | | | SIMP: (26) implies:
% 204.64/35.45  | | |   (27)  all_52_29 = e3
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (8), (27) imply:
% 204.64/35.45  | | |   (28)   ~ (all_10_2 = e3)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | SIMP: (28) implies:
% 204.64/35.45  | | |   (29)   ~ (all_10_2 = e3)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (17), (27) imply:
% 204.64/35.45  | | |   (30)  op(e3, e3) = all_52_28
% 204.64/35.45  | | | 
% 204.64/35.45  | | | BETA: splitting (20) gives:
% 204.64/35.45  | | | 
% 204.64/35.45  | | | Case 1:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (31)  all_58_5 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | COMBINE_EQS: (19), (31) imply:
% 204.64/35.45  | | | |   (32)  all_52_19 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | SIMP: (32) implies:
% 204.64/35.45  | | | |   (33)  all_52_19 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REDUCE: (10), (33) imply:
% 204.64/35.45  | | | |   (34)  op(e3, e3) = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | GROUND_INST: instantiating (3) with e3, all_52_28, e3, e3, simplifying
% 204.64/35.45  | | | |              with (12), (30) gives:
% 204.64/35.45  | | | |   (35)  all_52_28 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | GROUND_INST: instantiating (3) with e2, all_52_28, e3, e3, simplifying
% 204.64/35.45  | | | |              with (30), (34) gives:
% 204.64/35.45  | | | |   (36)  all_52_28 = e2
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (22), (35), (36) are inconsistent by sub-proof #1095.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | Case 2:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (37)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (1), (13), (16), (29), (37) are inconsistent by sub-proof
% 204.64/35.45  | | | |            #1304.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | End of split
% 204.64/35.45  | | | 
% 204.64/35.45  | | Case 2:
% 204.64/35.45  | | | 
% 204.64/35.45  | | |   (38)   ~ (all_56_11 = e3)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | REDUCE: (6), (38) imply:
% 204.64/35.45  | | |   (39)   ~ (all_52_29 = e3)
% 204.64/35.45  | | | 
% 204.64/35.45  | | | BETA: splitting (24) gives:
% 204.64/35.45  | | | 
% 204.64/35.45  | | | Case 1:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (40)  all_58_7 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | COMBINE_EQS: (9), (40) imply:
% 204.64/35.45  | | | |   (41)  all_52_13 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REDUCE: (18), (41) imply:
% 204.64/35.45  | | | |   (42)  $false
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | CLOSE: (42) is inconsistent.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | Case 2:
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | |   (43)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | | REF_CLOSE: (2), (3), (4), (5), (7), (12), (16), (39), (43) are
% 204.64/35.45  | | | |            inconsistent by sub-proof #1078.
% 204.64/35.45  | | | | 
% 204.64/35.45  | | | End of split
% 204.64/35.45  | | | 
% 204.64/35.45  | | End of split
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1070 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)  all_58_14 = all_52_23
% 204.64/35.45    (2)   ~ (e3 = e1)
% 204.64/35.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (4)  op(e2, e3) = all_52_3
% 204.64/35.45    (5)   ~ (all_52_3 = all_52_19)
% 204.64/35.45    (6)   ~ (all_52_3 = all_6_2)
% 204.64/35.45    (7)  all_58_0 = all_6_2
% 204.64/35.45    (8)  all_56_4 = all_52_3
% 204.64/35.45    (9)   ~ (all_6_1 = e1)
% 204.64/35.45    (10)  all_58_6 = e3
% 204.64/35.45    (11)   ~ (e2 = e1)
% 204.64/35.45    (12)  op(all_52_19, all_52_19) = e2
% 204.64/35.45    (13)  all_58_12 = all_52_7
% 204.64/35.45    (14)  all_58_2 = all_52_3
% 204.64/35.45    (15)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.64/35.45    (16)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.64/35.45    (17)   ~ (all_52_23 = e3)
% 204.64/35.45    (18)   ~ (all_10_2 = e3)
% 204.64/35.45    (19)  all_58_8 = all_10_2
% 204.64/35.45    (20)  op(e3, e3) = all_52_4
% 204.64/35.45    (21)  op(e3, e3) = all_6_2
% 204.64/35.45    (22)   ~ (all_52_7 = e1)
% 204.64/35.45    (23)  all_58_5 = all_52_19
% 204.64/35.45    (24)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.45    (25)   ~ (e1 = e0)
% 204.64/35.45    (26)  op(all_6_2, e3) = all_6_1
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (24) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (27)  all_58_5 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (23), (27) imply:
% 204.64/35.45  | |   (28)  all_52_19 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | SIMP: (28) implies:
% 204.64/35.45  | |   (29)  all_52_19 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (5), (29) imply:
% 204.64/35.45  | |   (30)   ~ (all_52_3 = e3)
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (12), (29) imply:
% 204.64/35.45  | |   (31)  op(e3, e3) = e2
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 204.64/35.45  | |            (16), (20), (21), (22), (25), (26), (30), (31) are inconsistent
% 204.64/35.45  | |            by sub-proof #1125.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (32)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (17), (18), (19), (32) are inconsistent by sub-proof #1304.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1071 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (2)  all_58_1 = all_52_9
% 204.64/35.45    (3)  all_58_0 = all_6_2
% 204.64/35.45    (4)  all_58_9 = all_52_25
% 204.64/35.45    (5)   ~ (all_6_2 = e3)
% 204.64/35.45    (6)   ~ (all_52_25 = e3)
% 204.64/35.45    (7)   ~ (all_52_9 = e3)
% 204.64/35.45    (8)  op(e3, e3) = all_6_2
% 204.64/35.45    (9)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.45    (10)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (11)   ~ (all_52_17 = all_6_2)
% 204.64/35.45    (12)  all_58_4 = all_52_17
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (9) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (13)  all_58_0 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (3), (13) imply:
% 204.64/35.45  | |   (14)  all_6_2 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (5), (14) imply:
% 204.64/35.45  | |   (15)  $false
% 204.64/35.45  | | 
% 204.64/35.45  | | CLOSE: (15) is inconsistent.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (16)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (16) are
% 204.64/35.45  | |            inconsistent by sub-proof #1072.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1072 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (2)  all_58_1 = all_52_9
% 204.64/35.45    (3)  all_58_9 = all_52_25
% 204.64/35.45    (4)   ~ (all_52_25 = e3)
% 204.64/35.45    (5)   ~ (all_52_9 = e3)
% 204.64/35.45    (6)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.45    (7)  op(e3, e3) = all_6_2
% 204.64/35.45    (8)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (9)   ~ (all_52_17 = all_6_2)
% 204.64/35.45    (10)  all_58_4 = all_52_17
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (6) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (11)  all_58_1 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (2), (11) imply:
% 204.64/35.45  | |   (12)  all_52_9 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REDUCE: (5), (12) imply:
% 204.64/35.45  | |   (13)  $false
% 204.64/35.45  | | 
% 204.64/35.45  | | CLOSE: (13) is inconsistent.
% 204.64/35.45  | | 
% 204.64/35.45  | Case 2:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (14)  all_58_4 = e3 | all_58_9 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (14) are inconsistent by
% 204.64/35.45  | |            sub-proof #1080.
% 204.64/35.45  | | 
% 204.64/35.45  | End of split
% 204.64/35.45  | 
% 204.64/35.45  End of proof
% 204.64/35.45  
% 204.64/35.45  Sub-proof #1073 shows that the following formulas are inconsistent:
% 204.64/35.45  ----------------------------------------------------------------
% 204.64/35.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.45    (2)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.45    (3)  all_56_2 = all_52_17
% 204.64/35.45    (4)   ~ (all_10_2 = e3)
% 204.64/35.45    (5)   ~ (all_52_17 = e3)
% 204.64/35.45    (6)  op(all_52_17, all_52_17) = e3
% 204.64/35.45    (7)   ~ (all_52_17 = e0)
% 204.64/35.45    (8)  op(e1, e1) = all_10_2
% 204.64/35.45    (9)   ~ (all_52_17 = e2)
% 204.64/35.45  
% 204.64/35.45  Begin of proof
% 204.64/35.45  | 
% 204.64/35.45  | BETA: splitting (2) gives:
% 204.64/35.45  | 
% 204.64/35.45  | Case 1:
% 204.64/35.45  | | 
% 204.64/35.45  | |   (10)  all_56_2 = e3
% 204.64/35.45  | | 
% 204.64/35.45  | | COMBINE_EQS: (3), (10) imply:
% 204.64/35.46  | |   (11)  all_52_17 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (5), (11) imply:
% 204.64/35.46  | |   (12)  $false
% 204.64/35.46  | | 
% 204.64/35.46  | | CLOSE: (12) is inconsistent.
% 204.64/35.46  | | 
% 204.64/35.46  | Case 2:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (13)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (13) are inconsistent by
% 204.64/35.46  | |            sub-proof #1266.
% 204.64/35.46  | | 
% 204.64/35.46  | End of split
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1074 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)  all_56_3 = all_6_0
% 204.64/35.46    (2)  all_56_3 = e1
% 204.64/35.46    (3)   ~ (all_6_0 = e1)
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.46  |   (4)  all_6_0 = e1
% 204.64/35.46  | 
% 204.64/35.46  | SIMP: (4) implies:
% 204.64/35.46  |   (5)  all_6_0 = e1
% 204.64/35.46  | 
% 204.64/35.46  | REDUCE: (3), (5) imply:
% 204.64/35.46  |   (6)  $false
% 204.64/35.46  | 
% 204.64/35.46  | CLOSE: (6) is inconsistent.
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1075 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)  all_56_3 = all_6_0
% 204.64/35.46    (2)  all_56_3 = e2
% 204.64/35.46    (3)   ~ (all_6_0 = e2)
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.46  |   (4)  all_6_0 = e2
% 204.64/35.46  | 
% 204.64/35.46  | SIMP: (4) implies:
% 204.64/35.46  |   (5)  all_6_0 = e2
% 204.64/35.46  | 
% 204.64/35.46  | REDUCE: (3), (5) imply:
% 204.64/35.46  |   (6)  $false
% 204.64/35.46  | 
% 204.64/35.46  | CLOSE: (6) is inconsistent.
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1076 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.46    (2)  op(e3, e3) = all_52_0
% 204.64/35.46    (3)  all_58_11 = all_52_29
% 204.64/35.46    (4)   ~ (all_52_3 = e3)
% 204.64/35.46    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.46    (6)   ~ (all_6_0 = e1)
% 204.64/35.46    (7)  op(all_10_2, all_10_2) = e1
% 204.64/35.46    (8)  op(e3, e3) = all_6_1
% 204.64/35.46    (9)  all_58_10 = all_52_27
% 204.64/35.46    (10)  all_58_7 = all_52_13
% 204.64/35.46    (11)  op(all_52_19, all_52_19) = e2
% 204.64/35.46    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.46    (13)  all_58_2 = all_52_3
% 204.64/35.46    (14)  op(e3, e3) = e3
% 204.64/35.46    (15)   ~ (all_52_29 = e3)
% 204.64/35.46    (16)  op(e3, all_6_1) = all_6_0
% 204.64/35.46    (17)   ~ (all_52_5 = e3)
% 204.64/35.46    (18)   ~ (all_52_27 = e3)
% 204.64/35.46    (19)   ~ (all_6_0 = e2)
% 204.64/35.46    (20)   ~ (all_52_13 = all_4_2)
% 204.64/35.46    (21)   ~ (all_52_19 = all_10_2)
% 204.64/35.46    (22)  all_58_8 = all_10_2
% 204.64/35.46    (23)  all_58_5 = all_52_19
% 204.64/35.46    (24)  all_58_6 = all_52_5
% 204.64/35.46    (25)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.46    (26)  all_58_3 = all_4_2
% 204.64/35.46    (27)   ~ (all_52_13 = all_52_29)
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | GROUND_INST: instantiating (1) with all_6_1, all_52_0, e3, e3, simplifying
% 204.64/35.46  |              with (2), (8) gives:
% 204.64/35.46  |   (28)  all_52_0 = all_6_1
% 204.64/35.46  | 
% 204.64/35.46  | GROUND_INST: instantiating (1) with e3, all_52_0, e3, e3, simplifying with
% 204.64/35.46  |              (2), (14) gives:
% 204.64/35.46  |   (29)  all_52_0 = e3
% 204.64/35.46  | 
% 204.64/35.46  | COMBINE_EQS: (28), (29) imply:
% 204.64/35.46  |   (30)  all_6_1 = e3
% 204.64/35.46  | 
% 204.64/35.46  | SIMP: (30) implies:
% 204.64/35.46  |   (31)  all_6_1 = e3
% 204.64/35.46  | 
% 204.64/35.46  | REDUCE: (16), (31) imply:
% 204.64/35.46  |   (32)  op(e3, e3) = all_6_0
% 204.64/35.46  | 
% 204.64/35.46  | GROUND_INST: instantiating (1) with e3, all_6_0, e3, e3, simplifying with
% 204.64/35.46  |              (14), (32) gives:
% 204.64/35.46  |   (33)  all_6_0 = e3
% 204.64/35.46  | 
% 204.64/35.46  | REDUCE: (19), (33) imply:
% 204.64/35.46  |   (34)   ~ (e3 = e2)
% 204.64/35.46  | 
% 204.64/35.46  | REDUCE: (6), (33) imply:
% 204.64/35.46  |   (35)   ~ (e3 = e1)
% 204.64/35.46  | 
% 204.64/35.46  | BETA: splitting (12) gives:
% 204.64/35.46  | 
% 204.64/35.46  | Case 1:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (36)  all_58_6 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (17), (24), (36) are inconsistent by sub-proof #1328.
% 204.64/35.46  | | 
% 204.64/35.46  | Case 2:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (37)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (13), (14), (15),
% 204.64/35.46  | |            (18), (20), (21), (22), (23), (25), (26), (27), (34), (35), (37)
% 204.64/35.46  | |            are inconsistent by sub-proof #1077.
% 204.64/35.46  | | 
% 204.64/35.46  | End of split
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1077 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)   ~ (e3 = e1)
% 204.64/35.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.46    (3)  op(e3, e3) = all_52_0
% 204.64/35.46    (4)  all_58_11 = all_52_29
% 204.64/35.46    (5)   ~ (all_52_3 = e3)
% 204.64/35.46    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.46    (7)  op(all_10_2, all_10_2) = e1
% 204.64/35.46    (8)  all_58_10 = all_52_27
% 204.64/35.46    (9)  all_58_7 = all_52_13
% 204.64/35.46    (10)  op(all_52_19, all_52_19) = e2
% 204.64/35.46    (11)  all_58_2 = all_52_3
% 204.64/35.46    (12)  op(e3, e3) = e3
% 204.64/35.46    (13)   ~ (all_52_29 = e3)
% 204.64/35.46    (14)   ~ (all_52_27 = e3)
% 204.64/35.46    (15)   ~ (all_52_13 = all_4_2)
% 204.64/35.46    (16)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.46    (17)   ~ (all_52_19 = all_10_2)
% 204.64/35.46    (18)  all_58_8 = all_10_2
% 204.64/35.46    (19)  all_58_5 = all_52_19
% 204.64/35.46    (20)   ~ (e3 = e2)
% 204.64/35.46    (21)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.46    (22)  all_58_3 = all_4_2
% 204.64/35.46    (23)   ~ (all_52_13 = all_52_29)
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | BETA: splitting (6) gives:
% 204.64/35.46  | 
% 204.64/35.46  | Case 1:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (24)  all_58_2 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (5), (11), (24) are inconsistent by sub-proof #1369.
% 204.64/35.46  | | 
% 204.64/35.46  | Case 2:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (25)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | BETA: splitting (16) gives:
% 204.64/35.46  | | 
% 204.64/35.46  | | Case 1:
% 204.64/35.46  | | | 
% 204.64/35.46  | | |   (26)  all_58_7 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | COMBINE_EQS: (9), (26) imply:
% 204.64/35.46  | | |   (27)  all_52_13 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REDUCE: (23), (27) imply:
% 204.64/35.46  | | |   (28)   ~ (all_52_29 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REDUCE: (15), (27) imply:
% 204.64/35.46  | | |   (29)   ~ (all_4_2 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | SIMP: (29) implies:
% 204.64/35.46  | | |   (30)   ~ (all_4_2 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | BETA: splitting (25) gives:
% 204.64/35.46  | | | 
% 204.64/35.46  | | | Case 1:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | |   (31)  all_58_3 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | COMBINE_EQS: (22), (31) imply:
% 204.64/35.46  | | | |   (32)  all_4_2 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REDUCE: (30), (32) imply:
% 204.64/35.46  | | | |   (33)  $false
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | CLOSE: (33) is inconsistent.
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | Case 2:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | |   (34)  all_58_5 = e3 | all_58_10 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | BETA: splitting (34) gives:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | Case 1:
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | |   (35)  all_58_5 = e3
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | COMBINE_EQS: (19), (35) imply:
% 204.64/35.46  | | | | |   (36)  all_52_19 = e3
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | SIMP: (36) implies:
% 204.64/35.46  | | | | |   (37)  all_52_19 = e3
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | REDUCE: (17), (37) imply:
% 204.64/35.46  | | | | |   (38)   ~ (all_10_2 = e3)
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | SIMP: (38) implies:
% 204.64/35.46  | | | | |   (39)   ~ (all_10_2 = e3)
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | REDUCE: (10), (37) imply:
% 204.64/35.46  | | | | |   (40)  op(e3, e3) = e2
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | BETA: splitting (16) gives:
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | Case 1:
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | REDUCE: (21), (27) imply:
% 204.64/35.46  | | | | | |   (41)  op(e3, e3) = all_52_12
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | GROUND_INST: instantiating (2) with e3, all_52_12, e3, e3,
% 204.64/35.46  | | | | | |              simplifying with (12), (41) gives:
% 204.64/35.46  | | | | | |   (42)  all_52_12 = e3
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | GROUND_INST: instantiating (2) with e2, all_52_12, e3, e3,
% 204.64/35.46  | | | | | |              simplifying with (40), (41) gives:
% 204.64/35.46  | | | | | |   (43)  all_52_12 = e2
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | COMBINE_EQS: (42), (43) imply:
% 204.64/35.46  | | | | | |   (44)  e3 = e2
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | REDUCE: (20), (44) imply:
% 204.64/35.46  | | | | | |   (45)  $false
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | CLOSE: (45) is inconsistent.
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | Case 2:
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | |   (46)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | REF_CLOSE: (4), (13), (18), (39), (46) are inconsistent by sub-proof
% 204.64/35.46  | | | | | |            #1140.
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | End of split
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | Case 2:
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | |   (47)  all_58_10 = e3
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | REF_CLOSE: (8), (14), (47) are inconsistent by sub-proof #1301.
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | End of split
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | End of split
% 204.64/35.46  | | | 
% 204.64/35.46  | | Case 2:
% 204.64/35.46  | | | 
% 204.64/35.46  | | |   (48)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REF_CLOSE: (1), (2), (3), (4), (7), (12), (13), (18), (48) are
% 204.64/35.46  | | |            inconsistent by sub-proof #1078.
% 204.64/35.46  | | | 
% 204.64/35.46  | | End of split
% 204.64/35.46  | | 
% 204.64/35.46  | End of split
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1078 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)   ~ (e3 = e1)
% 204.64/35.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.46    (3)  op(e3, e3) = all_52_0
% 204.64/35.46    (4)  all_58_11 = all_52_29
% 204.64/35.46    (5)  op(all_10_2, all_10_2) = e1
% 204.64/35.46    (6)  all_58_8 = e3 | all_58_11 = e3
% 204.64/35.46    (7)  op(e3, e3) = e3
% 204.64/35.46    (8)   ~ (all_52_29 = e3)
% 204.64/35.46    (9)  all_58_8 = all_10_2
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | BETA: splitting (6) gives:
% 204.64/35.46  | 
% 204.64/35.46  | Case 1:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (10)  all_58_8 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (9), (10) imply:
% 204.64/35.46  | |   (11)  all_10_2 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (11) implies:
% 204.64/35.46  | |   (12)  all_10_2 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (5), (12) imply:
% 204.64/35.46  | |   (13)  op(e3, e3) = e1
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (1), (2), (3), (7), (13) are inconsistent by sub-proof #1237.
% 204.64/35.46  | | 
% 204.64/35.46  | Case 2:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (14)  all_58_11 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (4), (8), (14) are inconsistent by sub-proof #1323.
% 204.64/35.46  | | 
% 204.64/35.46  | End of split
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1079 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)  all_58_14 = all_52_23
% 204.64/35.46    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.46    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.46    (4)  all_58_1 = all_52_9
% 204.64/35.46    (5)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.46    (6)   ~ (all_52_3 = all_6_2)
% 204.64/35.46    (7)  all_58_0 = all_6_2
% 204.64/35.46    (8)  all_58_13 = all_52_15
% 204.64/35.46    (9)  all_58_9 = all_52_25
% 204.64/35.46    (10)  op(e1, e3) = all_52_5
% 204.64/35.46    (11)  op(e2, e2) = all_4_2
% 204.64/35.46    (12)   ~ (all_52_3 = all_52_5)
% 204.64/35.46    (13)   ~ (all_52_9 = all_52_15)
% 204.64/35.46    (14)  op(all_10_2, e1) = all_10_1
% 204.64/35.46    (15)  all_56_3 = all_14_1
% 204.64/35.46    (16)   ~ (all_52_7 = all_6_2)
% 204.64/35.46    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.46    (18)  all_58_8 = e3 | all_58_14 = e3
% 204.64/35.46    (19)   ~ (all_6_2 = e3)
% 204.64/35.46    (20)   ~ (e2 = e1)
% 204.64/35.46    (21)   ~ (all_52_13 = all_10_2)
% 204.64/35.46    (22)  op(all_10_2, all_10_2) = e1
% 204.64/35.46    (23)  all_58_10 = all_52_27
% 204.64/35.46    (24)  all_56_8 = all_52_5
% 204.64/35.46    (25)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.46    (26)  all_58_7 = all_52_13
% 204.64/35.46    (27)   ~ (all_52_5 = all_52_7)
% 204.64/35.46    (28)  all_58_12 = all_52_7
% 204.64/35.46    (29)  all_58_2 = all_52_3
% 204.64/35.46    (30)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.46    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.46    (32)  op(e3, all_6_1) = all_6_0
% 204.64/35.46    (33)  all_58_9 = all_14_1
% 204.64/35.46    (34)   ~ (all_52_25 = e3)
% 204.64/35.46    (35)   ~ (all_52_23 = e3)
% 204.64/35.46    (36)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.46    (37)   ~ (all_52_27 = e3)
% 204.64/35.46    (38)   ~ (all_6_0 = e2)
% 204.64/35.46    (39)  op(e3, e1) = all_52_17
% 204.64/35.46    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.46    (41)   ~ (all_52_19 = all_10_2)
% 204.64/35.46    (42)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.46    (43)  all_58_8 = all_10_2
% 204.64/35.46    (44)   ~ (all_52_9 = all_4_2)
% 204.64/35.46    (45)   ~ (all_52_5 = all_6_2)
% 204.64/35.46    (46)  op(e3, e3) = all_6_2
% 204.64/35.46    (47)  op(e3, e0) = all_14_1
% 204.64/35.46    (48)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.46    (49)   ~ (all_52_3 = all_52_7)
% 204.64/35.46    (50)  all_58_5 = all_52_19
% 204.64/35.46    (51)  op(all_52_17, all_52_17) = e3
% 204.64/35.46    (52)  all_58_6 = all_52_5
% 204.64/35.46    (53)   ~ (all_52_17 = all_6_2)
% 204.64/35.46    (54)   ~ (e3 = e2)
% 204.64/35.46    (55)   ~ (all_6_1 = e2)
% 204.64/35.46    (56)  all_58_3 = all_4_2
% 204.64/35.46    (57)   ~ (all_52_3 = all_4_2)
% 204.64/35.46    (58)  op(all_6_2, e3) = all_6_1
% 204.64/35.46    (59)  all_58_4 = all_52_17
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | BETA: splitting (48) gives:
% 204.64/35.46  | 
% 204.64/35.46  | Case 1:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (60)  all_58_0 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (7), (60) imply:
% 204.64/35.46  | |   (61)  all_6_2 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (19), (61) imply:
% 204.64/35.46  | |   (62)  $false
% 204.64/35.46  | | 
% 204.64/35.46  | | CLOSE: (62) is inconsistent.
% 204.64/35.46  | | 
% 204.64/35.46  | Case 2:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (63)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | BETA: splitting (63) gives:
% 204.64/35.46  | | 
% 204.64/35.46  | | Case 1:
% 204.64/35.46  | | | 
% 204.64/35.46  | | |   (64)  all_58_1 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | COMBINE_EQS: (4), (64) imply:
% 204.64/35.46  | | |   (65)  all_52_9 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REDUCE: (13), (65) imply:
% 204.64/35.46  | | |   (66)   ~ (all_52_15 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | SIMP: (66) implies:
% 204.64/35.46  | | |   (67)   ~ (all_52_15 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REDUCE: (44), (65) imply:
% 204.64/35.46  | | |   (68)   ~ (all_4_2 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | SIMP: (68) implies:
% 204.64/35.46  | | |   (69)   ~ (all_4_2 = e3)
% 204.64/35.46  | | | 
% 204.64/35.46  | | | BETA: splitting (18) gives:
% 204.64/35.46  | | | 
% 204.64/35.46  | | | Case 1:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | |   (70)  all_58_8 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | COMBINE_EQS: (43), (70) imply:
% 204.64/35.46  | | | |   (71)  all_10_2 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | SIMP: (71) implies:
% 204.64/35.46  | | | |   (72)  all_10_2 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REDUCE: (21), (72) imply:
% 204.64/35.46  | | | |   (73)   ~ (all_52_13 = e3)
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REDUCE: (41), (72) imply:
% 204.64/35.46  | | | |   (74)   ~ (all_52_19 = e3)
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REDUCE: (22), (72) imply:
% 204.64/35.46  | | | |   (75)  op(e3, e3) = e1
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REDUCE: (14), (72) imply:
% 204.64/35.46  | | | |   (76)  op(e3, e1) = all_10_1
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12), (15), (16),
% 204.64/35.46  | | | |            (17), (20), (23), (24), (25), (26), (27), (28), (29), (30),
% 204.64/35.46  | | | |            (31), (32), (33), (36), (37), (38), (39), (40), (42), (45),
% 204.64/35.46  | | | |            (46), (47), (49), (50), (51), (52), (54), (55), (56), (57),
% 204.64/35.46  | | | |            (58), (59), (64), (67), (69), (73), (74), (75), (76) are
% 204.64/35.46  | | | |            inconsistent by sub-proof #1081.
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | Case 2:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | |   (77)  all_58_14 = e3
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REF_CLOSE: (1), (35), (77) are inconsistent by sub-proof #1305.
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | End of split
% 204.64/35.46  | | | 
% 204.64/35.46  | | Case 2:
% 204.64/35.46  | | | 
% 204.64/35.46  | | |   (78)  all_58_4 = e3 | all_58_9 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REF_CLOSE: (3), (9), (34), (46), (51), (53), (59), (78) are inconsistent
% 204.64/35.46  | | |            by sub-proof #1080.
% 204.64/35.46  | | | 
% 204.64/35.46  | | End of split
% 204.64/35.46  | | 
% 204.64/35.46  | End of split
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1080 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.46    (2)  all_58_9 = all_52_25
% 204.64/35.46    (3)  all_58_4 = e3 | all_58_9 = e3
% 204.64/35.46    (4)   ~ (all_52_25 = e3)
% 204.64/35.46    (5)  op(e3, e3) = all_6_2
% 204.64/35.46    (6)  op(all_52_17, all_52_17) = e3
% 204.64/35.46    (7)   ~ (all_52_17 = all_6_2)
% 204.64/35.46    (8)  all_58_4 = all_52_17
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | BETA: splitting (3) gives:
% 204.64/35.46  | 
% 204.64/35.46  | Case 1:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (9)  all_58_4 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (8), (9) imply:
% 204.64/35.46  | |   (10)  all_52_17 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (10) implies:
% 204.64/35.46  | |   (11)  all_52_17 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (1), (5), (6), (7), (11) are inconsistent by sub-proof #1280.
% 204.64/35.46  | | 
% 204.64/35.46  | Case 2:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (12)  all_58_9 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REF_CLOSE: (2), (4), (12) are inconsistent by sub-proof #1300.
% 204.64/35.46  | | 
% 204.64/35.46  | End of split
% 204.64/35.46  | 
% 204.64/35.46  End of proof
% 204.64/35.46  
% 204.64/35.46  Sub-proof #1081 shows that the following formulas are inconsistent:
% 204.64/35.46  ----------------------------------------------------------------
% 204.64/35.46    (1)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.46    (3)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.46    (4)   ~ (all_4_2 = e3)
% 204.64/35.46    (5)   ~ (all_52_3 = all_6_2)
% 204.64/35.46    (6)  all_58_0 = all_6_2
% 204.64/35.46    (7)  all_58_13 = all_52_15
% 204.64/35.46    (8)   ~ (all_52_15 = e3)
% 204.64/35.46    (9)  op(e1, e3) = all_52_5
% 204.64/35.46    (10)  op(e2, e2) = all_4_2
% 204.64/35.46    (11)   ~ (all_52_3 = all_52_5)
% 204.64/35.46    (12)  all_58_1 = e3
% 204.64/35.46    (13)  all_56_3 = all_14_1
% 204.64/35.46    (14)   ~ (all_52_7 = all_6_2)
% 204.64/35.46    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.46    (16)   ~ (e2 = e1)
% 204.64/35.46    (17)  all_58_10 = all_52_27
% 204.64/35.46    (18)  all_56_8 = all_52_5
% 204.64/35.46    (19)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.46    (20)  all_58_7 = all_52_13
% 204.64/35.46    (21)   ~ (all_52_5 = all_52_7)
% 204.64/35.46    (22)  all_58_12 = all_52_7
% 204.64/35.46    (23)  all_58_2 = all_52_3
% 204.64/35.46    (24)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.46    (25)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.46    (26)  op(e3, all_6_1) = all_6_0
% 204.64/35.46    (27)  op(e3, e1) = all_10_1
% 204.64/35.46    (28)  all_58_9 = all_14_1
% 204.64/35.46    (29)   ~ (all_52_19 = e3)
% 204.64/35.46    (30)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.46    (31)   ~ (all_52_27 = e3)
% 204.64/35.46    (32)   ~ (all_6_0 = e2)
% 204.64/35.46    (33)  op(e3, e1) = all_52_17
% 204.64/35.46    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.46    (35)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.46    (36)   ~ (all_52_5 = all_6_2)
% 204.64/35.46    (37)  op(e3, e3) = all_6_2
% 204.64/35.46    (38)  op(e3, e0) = all_14_1
% 204.64/35.46    (39)   ~ (all_52_13 = e3)
% 204.64/35.46    (40)  op(e3, e3) = e1
% 204.64/35.46    (41)   ~ (all_52_3 = all_52_7)
% 204.64/35.46    (42)  all_58_5 = all_52_19
% 204.64/35.46    (43)  op(all_52_17, all_52_17) = e3
% 204.64/35.46    (44)  all_58_6 = all_52_5
% 204.64/35.46    (45)   ~ (e3 = e2)
% 204.64/35.46    (46)   ~ (all_6_1 = e2)
% 204.64/35.46    (47)  all_58_3 = all_4_2
% 204.64/35.46    (48)   ~ (all_52_3 = all_4_2)
% 204.64/35.46    (49)  op(all_6_2, e3) = all_6_1
% 204.64/35.46    (50)  all_58_4 = all_52_17
% 204.64/35.46  
% 204.64/35.46  Begin of proof
% 204.64/35.46  | 
% 204.64/35.46  | BETA: splitting (15) gives:
% 204.64/35.46  | 
% 204.64/35.46  | Case 1:
% 204.64/35.46  | | 
% 204.64/35.46  | |   (51)  all_58_2 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (23), (51) imply:
% 204.64/35.46  | |   (52)  all_52_3 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (52) implies:
% 204.64/35.46  | |   (53)  all_52_3 = e3
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (11), (53) imply:
% 204.64/35.46  | |   (54)   ~ (all_52_5 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (54) implies:
% 204.64/35.46  | |   (55)   ~ (all_52_5 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (41), (53) imply:
% 204.64/35.46  | |   (56)   ~ (all_52_7 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (56) implies:
% 204.64/35.46  | |   (57)   ~ (all_52_7 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (5), (53) imply:
% 204.64/35.46  | |   (58)   ~ (all_6_2 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (58) implies:
% 204.64/35.46  | |   (59)   ~ (all_6_2 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (48), (53) imply:
% 204.64/35.46  | |   (60)   ~ (all_4_2 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (1), (53) imply:
% 204.64/35.46  | |   (61)  op(e3, e3) = all_52_2
% 204.64/35.46  | | 
% 204.64/35.46  | | GROUND_INST: instantiating (2) with all_52_17, all_10_1, e1, e3, simplifying
% 204.64/35.46  | |              with (27), (33) gives:
% 204.64/35.46  | |   (62)  all_52_17 = all_10_1
% 204.64/35.46  | | 
% 204.64/35.46  | | GROUND_INST: instantiating (2) with all_6_2, all_52_2, e3, e3, simplifying
% 204.64/35.46  | |              with (37), (61) gives:
% 204.64/35.46  | |   (63)  all_52_2 = all_6_2
% 204.64/35.46  | | 
% 204.64/35.46  | | GROUND_INST: instantiating (2) with e1, all_52_2, e3, e3, simplifying with
% 204.64/35.46  | |              (40), (61) gives:
% 204.64/35.46  | |   (64)  all_52_2 = e1
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (63), (64) imply:
% 204.64/35.46  | |   (65)  all_6_2 = e1
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (65) implies:
% 204.64/35.46  | |   (66)  all_6_2 = e1
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (50), (62) imply:
% 204.64/35.46  | |   (67)  all_58_4 = all_10_1
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (6), (66) imply:
% 204.64/35.46  | |   (68)  all_58_0 = e1
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (36), (66) imply:
% 204.64/35.46  | |   (69)   ~ (all_52_5 = e1)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (14), (66) imply:
% 204.64/35.46  | |   (70)   ~ (all_52_7 = e1)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (59), (66) imply:
% 204.64/35.46  | |   (71)   ~ (e3 = e1)
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (71) implies:
% 204.64/35.46  | |   (72)   ~ (e3 = e1)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (49), (66) imply:
% 204.64/35.46  | |   (73)  op(e1, e3) = all_6_1
% 204.64/35.46  | | 
% 204.64/35.46  | | GROUND_INST: instantiating (2) with all_52_5, all_6_1, e3, e1, simplifying
% 204.64/35.46  | |              with (9), (73) gives:
% 204.64/35.46  | |   (74)  all_52_5 = all_6_1
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (18), (74) imply:
% 204.64/35.46  | |   (75)  all_56_8 = all_6_1
% 204.64/35.46  | | 
% 204.64/35.46  | | COMBINE_EQS: (44), (74) imply:
% 204.64/35.46  | |   (76)  all_58_6 = all_6_1
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (21), (74) imply:
% 204.64/35.46  | |   (77)   ~ (all_52_7 = all_6_1)
% 204.64/35.46  | | 
% 204.64/35.46  | | SIMP: (77) implies:
% 204.64/35.46  | |   (78)   ~ (all_52_7 = all_6_1)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (55), (74) imply:
% 204.64/35.46  | |   (79)   ~ (all_6_1 = e3)
% 204.64/35.46  | | 
% 204.64/35.46  | | REDUCE: (69), (74) imply:
% 204.64/35.46  | |   (80)   ~ (all_6_1 = e1)
% 204.64/35.46  | | 
% 204.64/35.46  | | BETA: splitting (35) gives:
% 204.64/35.46  | | 
% 204.64/35.46  | | Case 1:
% 204.64/35.46  | | | 
% 204.64/35.46  | | |   (81)  all_56_8 = e3
% 204.64/35.46  | | | 
% 204.64/35.46  | | | REF_CLOSE: (75), (79), (81) are inconsistent by sub-proof #1101.
% 204.64/35.46  | | | 
% 204.64/35.46  | | Case 2:
% 204.64/35.46  | | | 
% 204.64/35.46  | | |   (82)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.46  | | | 
% 204.64/35.46  | | | BETA: splitting (30) gives:
% 204.64/35.46  | | | 
% 204.64/35.46  | | | Case 1:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | |   (83)  all_58_0 = e2
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | REF_CLOSE: (16), (68), (83) are inconsistent by sub-proof #1273.
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | Case 2:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | |   (84)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | BETA: splitting (84) gives:
% 204.64/35.46  | | | | 
% 204.64/35.46  | | | | Case 1:
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | |   (85)  all_58_2 = e2
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | COMBINE_EQS: (51), (85) imply:
% 204.64/35.46  | | | | |   (86)  e3 = e2
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | SIMP: (86) implies:
% 204.64/35.46  | | | | |   (87)  e3 = e2
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | REF_CLOSE: (4), (7), (8), (12), (20), (34), (39), (45), (47), (87) are
% 204.64/35.46  | | | | |            inconsistent by sub-proof #1089.
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | Case 2:
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | |   (88)  all_58_6 = e2 | all_58_12 = e2
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | BETA: splitting (82) gives:
% 204.64/35.46  | | | | | 
% 204.64/35.46  | | | | | Case 1:
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | |   (89)  all_56_8 = e2
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | REF_CLOSE: (46), (75), (89) are inconsistent by sub-proof #1321.
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | Case 2:
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | |   (90)   ~ (all_56_8 = e2)
% 204.64/35.46  | | | | | |   (91)  all_56_8 = e1 | all_56_8 = e0
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | BETA: splitting (88) gives:
% 204.64/35.46  | | | | | | 
% 204.64/35.46  | | | | | | Case 1:
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | |   (92)  all_58_6 = e2
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | REF_CLOSE: (46), (76), (92) are inconsistent by sub-proof #1211.
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | Case 2:
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | |   (93)  all_58_12 = e2
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | COMBINE_EQS: (22), (93) imply:
% 204.64/35.46  | | | | | | |   (94)  all_52_7 = e2
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | SIMP: (94) implies:
% 204.64/35.46  | | | | | | |   (95)  all_52_7 = e2
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | REDUCE: (78), (95) imply:
% 204.64/35.46  | | | | | | |   (96)   ~ (all_6_1 = e2)
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | REDUCE: (57), (95) imply:
% 204.64/35.46  | | | | | | |   (97)   ~ (e3 = e2)
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | REDUCE: (3), (95) imply:
% 204.64/35.46  | | | | | | |   (98)  op(e2, e2) = all_52_6
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | BETA: splitting (91) gives:
% 204.64/35.46  | | | | | | | 
% 204.64/35.46  | | | | | | | Case 1:
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | |   (99)  all_56_8 = e1
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | REF_CLOSE: (75), (80), (99) are inconsistent by sub-proof #1320.
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | Case 2:
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | |   (100)  all_56_8 = e0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | COMBINE_EQS: (75), (100) imply:
% 204.64/35.46  | | | | | | | |   (101)  all_6_1 = e0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | SIMP: (101) implies:
% 204.64/35.46  | | | | | | | |   (102)  all_6_1 = e0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | REDUCE: (46), (102) imply:
% 204.64/35.46  | | | | | | | |   (103)   ~ (e2 = e0)
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | SIMP: (103) implies:
% 204.64/35.46  | | | | | | | |   (104)   ~ (e2 = e0)
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | REDUCE: (26), (102) imply:
% 204.64/35.46  | | | | | | | |   (105)  op(e3, e0) = all_6_0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | GROUND_INST: instantiating (2) with all_4_2, all_52_6, e2, e2,
% 204.64/35.46  | | | | | | | |              simplifying with (10), (98) gives:
% 204.64/35.46  | | | | | | | |   (106)  all_52_6 = all_4_2
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | GROUND_INST: instantiating (2) with all_14_1, all_6_0, e0, e3,
% 204.64/35.46  | | | | | | | |              simplifying with (38), (105) gives:
% 204.64/35.46  | | | | | | | |   (107)  all_14_1 = all_6_0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | COMBINE_EQS: (13), (107) imply:
% 204.64/35.46  | | | | | | | |   (108)  all_56_3 = all_6_0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | COMBINE_EQS: (28), (107) imply:
% 204.64/35.46  | | | | | | | |   (109)  all_58_9 = all_6_0
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | BETA: splitting (24) gives:
% 204.64/35.46  | | | | | | | | 
% 204.64/35.46  | | | | | | | | Case 1:
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | |   (110)  all_58_0 = e2
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | REF_CLOSE: (16), (68), (110) are inconsistent by sub-proof
% 204.64/35.46  | | | | | | | | |            #1273.
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | Case 2:
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | |   (111)   ~ (all_58_0 = e2)
% 204.64/35.46  | | | | | | | | |   (112)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | REDUCE: (68), (111) imply:
% 204.64/35.46  | | | | | | | | |   (113)   ~ (e2 = e1)
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | BETA: splitting (19) gives:
% 204.64/35.46  | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | Case 1:
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | |   (114)  all_56_3 = e2
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | COMBINE_EQS: (108), (114) imply:
% 204.64/35.46  | | | | | | | | | |   (115)  all_6_0 = e2
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | REDUCE: (32), (115) imply:
% 204.64/35.46  | | | | | | | | | |   (116)  $false
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | CLOSE: (116) is inconsistent.
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | Case 2:
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | |   (117)  all_56_3 = e1 | all_56_3 = e0
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | BETA: splitting (117) gives:
% 204.64/35.46  | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | Case 1:
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | |   (118)  all_56_3 = e1
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | | COMBINE_EQS: (108), (118) imply:
% 204.64/35.46  | | | | | | | | | | |   (119)  all_6_0 = e1
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | | COMBINE_EQS: (109), (119) imply:
% 204.64/35.46  | | | | | | | | | | |   (120)  all_58_9 = e1
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (10), (16), (20), (34), (39),
% 204.64/35.46  | | | | | | | | | | |            (43), (45), (47), (50), (112), (120) are
% 204.64/35.46  | | | | | | | | | | |            inconsistent by sub-proof #1086.
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | Case 2:
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | |   (121)  all_56_3 = e0
% 204.64/35.46  | | | | | | | | | | | 
% 204.64/35.46  | | | | | | | | | | | COMBINE_EQS: (108), (121) imply:
% 204.64/35.46  | | | | | | | | | | |   (122)  all_6_0 = e0
% 204.64/35.47  | | | | | | | | | | | 
% 204.64/35.47  | | | | | | | | | | | COMBINE_EQS: (109), (122) imply:
% 204.64/35.47  | | | | | | | | | | |   (123)  all_58_9 = e0
% 204.64/35.47  | | | | | | | | | | | 
% 204.64/35.47  | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (20), (22), (23),
% 204.64/35.47  | | | | | | | | | | |            (25), (27), (33), (34), (37), (39), (40), (43),
% 204.64/35.47  | | | | | | | | | | |            (44), (45), (47), (48), (55), (57), (67), (72),
% 204.64/35.47  | | | | | | | | | | |            (104), (112), (123) are inconsistent by sub-proof
% 204.64/35.47  | | | | | | | | | | |            #1083.
% 204.64/35.47  | | | | | | | | | | | 
% 204.64/35.47  | | | | | | | | | | End of split
% 204.64/35.47  | | | | | | | | | | 
% 204.64/35.47  | | | | | | | | | End of split
% 204.64/35.47  | | | | | | | | | 
% 204.64/35.47  | | | | | | | | End of split
% 204.64/35.47  | | | | | | | | 
% 204.64/35.47  | | | | | | | End of split
% 204.64/35.47  | | | | | | | 
% 204.64/35.47  | | | | | | End of split
% 204.64/35.47  | | | | | | 
% 204.64/35.47  | | | | | End of split
% 204.64/35.47  | | | | | 
% 204.64/35.47  | | | | End of split
% 204.64/35.47  | | | | 
% 204.64/35.47  | | | End of split
% 204.64/35.47  | | | 
% 204.64/35.47  | | End of split
% 204.64/35.47  | | 
% 204.64/35.47  | Case 2:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (124)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (4), (17), (29), (31), (42), (47), (124) are inconsistent by
% 204.64/35.47  | |            sub-proof #1082.
% 204.64/35.47  | | 
% 204.64/35.47  | End of split
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1082 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ~ (all_4_2 = e3)
% 204.64/35.47    (2)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.47    (3)  all_58_10 = all_52_27
% 204.64/35.47    (4)   ~ (all_52_19 = e3)
% 204.64/35.47    (5)   ~ (all_52_27 = e3)
% 204.64/35.47    (6)  all_58_5 = all_52_19
% 204.64/35.47    (7)  all_58_3 = all_4_2
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | BETA: splitting (2) gives:
% 204.64/35.47  | 
% 204.64/35.47  | Case 1:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (8)  all_58_3 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | COMBINE_EQS: (7), (8) imply:
% 204.64/35.47  | |   (9)  all_4_2 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | REDUCE: (1), (9) imply:
% 204.64/35.47  | |   (10)  $false
% 204.64/35.47  | | 
% 204.64/35.47  | | CLOSE: (10) is inconsistent.
% 204.64/35.47  | | 
% 204.64/35.47  | Case 2:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (11)  all_58_5 = e3 | all_58_10 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (3), (4), (5), (6), (11) are inconsistent by sub-proof #1132.
% 204.64/35.47  | | 
% 204.64/35.47  | End of split
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1083 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ~ (e3 = e1)
% 204.64/35.47    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.47    (3)  all_58_9 = e0
% 204.64/35.47    (4)   ~ (all_4_2 = e3)
% 204.64/35.47    (5)  all_58_0 = all_6_2
% 204.64/35.47    (6)  all_58_13 = all_52_15
% 204.64/35.47    (7)   ~ (all_52_15 = e3)
% 204.64/35.47    (8)  op(e2, e2) = all_4_2
% 204.64/35.47    (9)  all_58_4 = all_10_1
% 204.64/35.47    (10)  all_58_7 = all_52_13
% 204.64/35.47    (11)  all_58_12 = all_52_7
% 204.64/35.47    (12)   ~ (all_52_7 = e3)
% 204.64/35.47    (13)  all_58_2 = all_52_3
% 204.64/35.47    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.47    (15)  op(e3, e1) = all_10_1
% 204.64/35.47    (16)   ~ (e2 = e0)
% 204.64/35.47    (17)   ~ (all_52_5 = e3)
% 204.64/35.47    (18)  op(e3, e1) = all_52_17
% 204.64/35.47    (19)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.47    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47    (21)  op(e3, e3) = all_6_2
% 204.64/35.47    (22)   ~ (all_52_13 = e3)
% 204.64/35.47    (23)  op(e3, e3) = e1
% 204.64/35.47    (24)  op(all_52_17, all_52_17) = e3
% 204.64/35.47    (25)  all_58_6 = all_52_5
% 204.64/35.47    (26)   ~ (e3 = e2)
% 204.64/35.47    (27)  all_58_3 = all_4_2
% 204.64/35.47    (28)   ~ (all_52_3 = all_4_2)
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | BETA: splitting (19) gives:
% 204.64/35.47  | 
% 204.64/35.47  | Case 1:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (29)  all_58_1 = e2
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (4), (6), (7), (10), (20), (22), (26), (27), (29) are
% 204.64/35.47  | |            inconsistent by sub-proof #1088.
% 204.64/35.47  | | 
% 204.64/35.47  | Case 2:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (30)  all_58_4 = e2 | all_58_9 = e2
% 204.64/35.47  | | 
% 204.64/35.47  | | BETA: splitting (30) gives:
% 204.64/35.47  | | 
% 204.64/35.47  | | Case 1:
% 204.64/35.47  | | | 
% 204.64/35.47  | | |   (31)  all_58_4 = e2
% 204.64/35.47  | | | 
% 204.64/35.47  | | | COMBINE_EQS: (9), (31) imply:
% 204.64/35.47  | | |   (32)  all_10_1 = e2
% 204.64/35.47  | | | 
% 204.64/35.47  | | | REDUCE: (15), (32) imply:
% 204.64/35.47  | | |   (33)  op(e3, e1) = e2
% 204.64/35.47  | | | 
% 204.64/35.47  | | | REF_CLOSE: (1), (2), (5), (8), (11), (12), (13), (14), (17), (18), (21),
% 204.64/35.47  | | |            (23), (24), (25), (28), (33) are inconsistent by sub-proof
% 204.64/35.47  | | |            #1085.
% 204.64/35.47  | | | 
% 204.64/35.47  | | Case 2:
% 204.64/35.47  | | | 
% 204.64/35.47  | | |   (34)  all_58_9 = e2
% 204.64/35.47  | | | 
% 204.64/35.47  | | | REF_CLOSE: (3), (16), (34) are inconsistent by sub-proof #1084.
% 204.64/35.47  | | | 
% 204.64/35.47  | | End of split
% 204.64/35.47  | | 
% 204.64/35.47  | End of split
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1084 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)  all_58_9 = e2
% 204.64/35.47    (2)  all_58_9 = e0
% 204.64/35.47    (3)   ~ (e2 = e0)
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.47  |   (4)  e2 = e0
% 204.64/35.47  | 
% 204.64/35.47  | SIMP: (4) implies:
% 204.64/35.47  |   (5)  e2 = e0
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (3), (5) imply:
% 204.64/35.47  |   (6)  $false
% 204.64/35.47  | 
% 204.64/35.47  | CLOSE: (6) is inconsistent.
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1085 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ~ (e3 = e1)
% 204.64/35.47    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.47    (3)  op(e3, e1) = e2
% 204.64/35.47    (4)  all_58_0 = all_6_2
% 204.64/35.47    (5)  op(e2, e2) = all_4_2
% 204.64/35.47    (6)  all_58_12 = all_52_7
% 204.64/35.47    (7)   ~ (all_52_7 = e3)
% 204.64/35.47    (8)  all_58_2 = all_52_3
% 204.64/35.47    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.47    (10)   ~ (all_52_5 = e3)
% 204.64/35.47    (11)  op(e3, e1) = all_52_17
% 204.64/35.47    (12)  op(e3, e3) = all_6_2
% 204.64/35.47    (13)  op(e3, e3) = e1
% 204.64/35.47    (14)  op(all_52_17, all_52_17) = e3
% 204.64/35.47    (15)  all_58_6 = all_52_5
% 204.64/35.47    (16)   ~ (all_52_3 = all_4_2)
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | GROUND_INST: instantiating (2) with all_52_17, e2, e1, e3, simplifying with
% 204.64/35.47  |              (3), (11) gives:
% 204.64/35.47  |   (17)  all_52_17 = e2
% 204.64/35.47  | 
% 204.64/35.47  | GROUND_INST: instantiating (2) with all_6_2, e1, e3, e3, simplifying with
% 204.64/35.47  |              (12), (13) gives:
% 204.64/35.47  |   (18)  all_6_2 = e1
% 204.64/35.47  | 
% 204.64/35.47  | COMBINE_EQS: (4), (18) imply:
% 204.64/35.47  |   (19)  all_58_0 = e1
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (14), (17) imply:
% 204.64/35.47  |   (20)  op(e2, e2) = e3
% 204.64/35.47  | 
% 204.64/35.47  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (15), (16), (19), (20) are
% 204.64/35.47  |            inconsistent by sub-proof #1241.
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1086 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.47    (2)   ~ (all_4_2 = e3)
% 204.64/35.47    (3)  all_58_9 = e1
% 204.64/35.47    (4)  all_58_13 = all_52_15
% 204.64/35.47    (5)   ~ (all_52_15 = e3)
% 204.64/35.47    (6)  op(e2, e2) = all_4_2
% 204.64/35.47    (7)   ~ (e2 = e1)
% 204.64/35.47    (8)  all_58_7 = all_52_13
% 204.64/35.47    (9)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.47    (10)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47    (11)   ~ (all_52_13 = e3)
% 204.64/35.47    (12)  op(all_52_17, all_52_17) = e3
% 204.64/35.47    (13)   ~ (e3 = e2)
% 204.64/35.47    (14)  all_58_3 = all_4_2
% 204.64/35.47    (15)  all_58_4 = all_52_17
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | BETA: splitting (9) gives:
% 204.64/35.47  | 
% 204.64/35.47  | Case 1:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (16)  all_58_1 = e2
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (13), (14), (16) are inconsistent
% 204.64/35.47  | |            by sub-proof #1088.
% 204.64/35.47  | | 
% 204.64/35.47  | Case 2:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (17)  all_58_4 = e2 | all_58_9 = e2
% 204.64/35.47  | | 
% 204.64/35.47  | | BETA: splitting (17) gives:
% 204.64/35.47  | | 
% 204.64/35.47  | | Case 1:
% 204.64/35.47  | | | 
% 204.64/35.47  | | |   (18)  all_58_4 = e2
% 204.64/35.47  | | | 
% 204.64/35.47  | | | REF_CLOSE: (1), (2), (6), (12), (15), (18) are inconsistent by sub-proof
% 204.64/35.47  | | |            #1087.
% 204.64/35.47  | | | 
% 204.64/35.47  | | Case 2:
% 204.64/35.47  | | | 
% 204.64/35.47  | | |   (19)  all_58_9 = e2
% 204.64/35.47  | | | 
% 204.64/35.47  | | | COMBINE_EQS: (3), (19) imply:
% 204.64/35.47  | | |   (20)  e2 = e1
% 204.64/35.47  | | | 
% 204.64/35.47  | | | REDUCE: (7), (20) imply:
% 204.64/35.47  | | |   (21)  $false
% 204.64/35.47  | | | 
% 204.64/35.47  | | | CLOSE: (21) is inconsistent.
% 204.64/35.47  | | | 
% 204.64/35.47  | | End of split
% 204.64/35.47  | | 
% 204.64/35.47  | End of split
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1087 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.47    (2)   ~ (all_4_2 = e3)
% 204.64/35.47    (3)  all_58_4 = e2
% 204.64/35.47    (4)  op(e2, e2) = all_4_2
% 204.64/35.47    (5)  op(all_52_17, all_52_17) = e3
% 204.64/35.47    (6)  all_58_4 = all_52_17
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | COMBINE_EQS: (3), (6) imply:
% 204.64/35.47  |   (7)  all_52_17 = e2
% 204.64/35.47  | 
% 204.64/35.47  | SIMP: (7) implies:
% 204.64/35.47  |   (8)  all_52_17 = e2
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (5), (8) imply:
% 204.64/35.47  |   (9)  op(e2, e2) = e3
% 204.64/35.47  | 
% 204.64/35.47  | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #1318.
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1088 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ~ (all_4_2 = e3)
% 204.64/35.47    (2)  all_58_13 = all_52_15
% 204.64/35.47    (3)   ~ (all_52_15 = e3)
% 204.64/35.47    (4)  all_58_7 = all_52_13
% 204.64/35.47    (5)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47    (6)   ~ (all_52_13 = e3)
% 204.64/35.47    (7)   ~ (e3 = e2)
% 204.64/35.47    (8)  all_58_3 = all_4_2
% 204.64/35.47    (9)  all_58_1 = e2
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | BETA: splitting (5) gives:
% 204.64/35.47  | 
% 204.64/35.47  | Case 1:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (10)  all_58_1 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (7), (9), (10) are inconsistent by sub-proof #1090.
% 204.64/35.47  | | 
% 204.64/35.47  | Case 2:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (11)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (11) are inconsistent by sub-proof
% 204.64/35.47  | |            #1256.
% 204.64/35.47  | | 
% 204.64/35.47  | End of split
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1089 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)   ~ (all_4_2 = e3)
% 204.64/35.47    (2)  all_58_13 = all_52_15
% 204.64/35.47    (3)   ~ (all_52_15 = e3)
% 204.64/35.47    (4)  all_58_1 = e3
% 204.64/35.47    (5)  all_58_7 = all_52_13
% 204.64/35.47    (6)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47    (7)   ~ (all_52_13 = e3)
% 204.64/35.47    (8)   ~ (e3 = e2)
% 204.64/35.47    (9)  e3 = e2
% 204.64/35.47    (10)  all_58_3 = all_4_2
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | COMBINE_EQS: (4), (9) imply:
% 204.64/35.47  |   (11)  all_58_1 = e2
% 204.64/35.47  | 
% 204.64/35.47  | BETA: splitting (6) gives:
% 204.64/35.47  | 
% 204.64/35.47  | Case 1:
% 204.64/35.47  | | 
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #1090.
% 204.64/35.47  | | 
% 204.64/35.47  | Case 2:
% 204.64/35.47  | | 
% 204.64/35.47  | |   (12)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47  | | 
% 204.64/35.47  | | REF_CLOSE: (1), (2), (3), (5), (7), (10), (12) are inconsistent by sub-proof
% 204.64/35.47  | |            #1256.
% 204.64/35.47  | | 
% 204.64/35.47  | End of split
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1090 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)  all_58_1 = e3
% 204.64/35.47    (2)  all_58_1 = e2
% 204.64/35.47    (3)   ~ (e3 = e2)
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | COMBINE_EQS: (1), (2) imply:
% 204.64/35.47  |   (4)  e3 = e2
% 204.64/35.47  | 
% 204.64/35.47  | SIMP: (4) implies:
% 204.64/35.47  |   (5)  e3 = e2
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (3), (5) imply:
% 204.64/35.47  |   (6)  $false
% 204.64/35.47  | 
% 204.64/35.47  | CLOSE: (6) is inconsistent.
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1091 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.64/35.47    (2)   ~ (all_52_15 = all_52_23)
% 204.64/35.47    (3)   ~ (all_52_25 = all_52_27)
% 204.64/35.47    (4)  all_58_14 = all_52_23
% 204.64/35.47    (5)   ~ (e3 = e1)
% 204.64/35.47    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.47    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.47    (8)   ~ (all_52_5 = all_52_13)
% 204.64/35.47    (9)  all_58_1 = all_52_9
% 204.64/35.47    (10)   ~ (all_52_9 = all_52_13)
% 204.64/35.47    (11)  op(e2, e3) = all_52_3
% 204.64/35.47    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.64/35.47    (13)   ~ (all_52_7 = all_52_15)
% 204.64/35.47    (14)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.47    (15)   ~ (all_52_17 = all_52_25)
% 204.64/35.47    (16)   ~ (all_52_3 = all_6_2)
% 204.64/35.47    (17)  all_58_0 = all_6_2
% 204.64/35.47    (18)  op(all_14_2, e0) = all_14_1
% 204.64/35.47    (19)  all_56_4 = all_52_3
% 204.64/35.47    (20)   ~ (all_52_17 = all_10_2)
% 204.64/35.47    (21)  op(e3, e0) = all_52_25
% 204.64/35.47    (22)  op(all_52_5, all_52_5) = all_52_4
% 204.64/35.47    (23)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.64/35.47    (24)  op(all_52_19, all_52_19) = all_52_18
% 204.64/35.47    (25)   ~ (all_52_27 = all_52_29)
% 204.64/35.47    (26)  all_58_13 = all_52_15
% 204.64/35.47    (27)  op(all_10_2, all_10_2) = all_52_20
% 204.64/35.47    (28)  all_58_9 = all_52_25
% 204.64/35.47    (29)   ~ (all_6_1 = e1)
% 204.64/35.47    (30)   ~ (all_52_29 = all_14_2)
% 204.64/35.47    (31)  op(all_52_27, all_52_27) = all_52_26
% 204.64/35.47    (32)  op(e1, e3) = all_52_5
% 204.64/35.47    (33)  op(e2, e2) = all_4_2
% 204.64/35.47    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.64/35.47    (35)   ~ (all_52_3 = all_52_5)
% 204.64/35.47    (36)   ~ (all_4_1 = e3)
% 204.64/35.47    (37)  all_58_11 = all_52_29
% 204.64/35.47    (38)  all_56_5 = all_4_2
% 204.64/35.47    (39)   ~ (all_52_25 = all_14_2)
% 204.64/35.47    (40)   ~ (all_52_3 = all_52_27)
% 204.64/35.47    (41)  op(all_6_2, all_6_2) = all_52_0
% 204.64/35.47    (42)   ~ (all_52_7 = all_6_2)
% 204.64/35.47    (43)  op(e0, e0) = all_14_2
% 204.64/35.47    (44)  all_56_15 = all_14_2
% 204.64/35.47    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.64/35.47    (46)  all_56_11 = all_52_29
% 204.64/35.47    (47)   ~ (all_4_1 = e1)
% 204.64/35.47    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.64/35.47    (49)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.64/35.47    (50)  all_56_9 = all_52_13
% 204.64/35.47    (51)   ~ (e2 = e1)
% 204.64/35.47    (52)   ~ (all_52_13 = all_10_2)
% 204.64/35.47    (53)   ~ (all_6_0 = e1)
% 204.64/35.47    (54)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 204.64/35.47    (55)  all_58_10 = all_52_27
% 204.64/35.47    (56)  all_56_8 = all_52_5
% 204.64/35.47    (57)  op(all_52_9, all_52_9) = all_52_8
% 204.64/35.47    (58)  op(all_52_15, all_52_15) = all_52_14
% 204.64/35.47    (59)   ~ (all_52_19 = all_52_23)
% 204.64/35.47    (60)   ~ (all_52_25 = all_52_29)
% 204.64/35.47    (61)  all_58_7 = all_52_13
% 204.64/35.47    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.64/35.47    (63)   ~ (all_52_5 = all_52_7)
% 204.64/35.47    (64)  all_58_12 = all_52_7
% 204.64/35.47    (65)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.64/35.47    (66)   ~ (all_52_7 = all_14_2)
% 204.64/35.47    (67)   ~ (all_14_2 = e0)
% 204.64/35.47    (68)  all_58_2 = all_52_3
% 204.64/35.47    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.64/35.47    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.64/35.47    (71)  op(e3, all_6_1) = all_6_0
% 204.64/35.47    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.64/35.47    (73)  all_56_7 = all_52_27
% 204.64/35.47    (74)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.64/35.47    (75)   ~ (e2 = e0)
% 204.64/35.47    (76)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.64/35.47    (77)  op(all_4_2, e2) = all_4_1
% 204.64/35.47    (78)   ~ (all_52_5 = all_52_29)
% 204.64/35.47    (79)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.64/35.47    (80)   ~ (all_52_15 = all_14_2)
% 204.64/35.47    (81)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.64/35.47    (82)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.64/35.47    (83)   ~ (all_6_0 = e2)
% 204.64/35.47    (84)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.64/35.47    (85)   ~ (all_52_13 = all_4_2)
% 204.64/35.47    (86)  op(e0, e3) = all_52_7
% 204.64/35.47    (87)  op(e1, e2) = all_52_13
% 204.64/35.47    (88)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.64/35.47    (89)   ~ (all_52_9 = all_52_25)
% 204.64/35.47    (90)  all_58_15 = all_14_2
% 204.64/35.47    (91)  op(all_52_23, all_52_23) = all_52_22
% 204.64/35.47    (92)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.64/35.47    (93)  all_58_8 = all_10_2
% 204.64/35.47    (94)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.64/35.47    (95)  op(all_52_29, all_52_29) = all_52_28
% 204.64/35.47    (96)   ~ (all_52_23 = all_14_2)
% 204.64/35.47    (97)  all_56_12 = all_52_7
% 204.64/35.47    (98)  op(all_52_17, all_52_17) = all_52_16
% 204.64/35.47    (99)   ~ (all_52_25 = all_6_2)
% 204.64/35.47    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.64/35.47    (101)   ~ (all_52_9 = all_4_2)
% 204.64/35.47    (102)   ~ (all_52_5 = all_6_2)
% 204.64/35.47    (103)   ~ (all_52_9 = all_6_2)
% 204.64/35.47    (104)  op(e3, e3) = all_6_2
% 204.64/35.47    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.64/35.47    (106)   ~ (all_52_27 = all_14_2)
% 204.64/35.47    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.64/35.47    (108)  op(all_4_2, all_4_2) = all_52_10
% 204.64/35.47    (109)  all_56_3 = all_52_25
% 204.64/35.47    (110)   ~ (all_52_3 = all_52_7)
% 204.64/35.47    (111)  op(all_14_2, all_14_2) = all_52_30
% 204.64/35.47    (112)  all_58_5 = all_52_19
% 204.64/35.47    (113)  all_56_1 = all_52_9
% 204.64/35.47    (114)   ~ (all_52_27 = all_4_2)
% 204.64/35.47    (115)  all_58_6 = all_52_5
% 204.64/35.47    (116)  op(e3, e2) = all_52_9
% 204.64/35.47    (117)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.64/35.47    (118)   ~ (all_52_17 = all_6_2)
% 204.64/35.47    (119)   ~ (e1 = e0)
% 204.64/35.47    (120)   ~ (e3 = e2)
% 204.64/35.47    (121)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.64/35.47    (122)   ~ (all_52_9 = all_52_17)
% 204.64/35.47    (123)  all_56_10 = all_10_2
% 204.64/35.47    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.64/35.47    (125)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.64/35.47    (126)  op(all_52_13, all_52_13) = all_52_12
% 204.64/35.47    (127)   ~ (all_6_1 = e2)
% 204.64/35.47    (128)  op(e1, e1) = all_10_2
% 204.64/35.47    (129)   ~ (all_52_7 = all_52_23)
% 204.64/35.47    (130)   ~ (all_52_17 = all_52_19)
% 204.64/35.47    (131)  all_58_3 = all_4_2
% 204.64/35.47    (132)  all_56_13 = all_52_15
% 204.64/35.47    (133)   ~ (all_52_3 = all_4_2)
% 204.64/35.47    (134)   ~ (all_52_19 = all_4_2)
% 204.64/35.47    (135)   ~ (all_52_17 = all_52_23)
% 204.64/35.47    (136)  op(all_6_2, e3) = all_6_1
% 204.64/35.47    (137)   ~ (all_52_13 = all_52_29)
% 204.64/35.47    (138)  all_58_4 = all_52_17
% 204.64/35.47    (139)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.64/35.47    (140)  op(all_52_25, all_52_25) = all_52_24
% 204.64/35.47  
% 204.64/35.47  Begin of proof
% 204.64/35.47  | 
% 204.64/35.47  | ALPHA: (54) implies:
% 204.64/35.47  |   (141)  all_52_14 = e0
% 204.64/35.47  |   (142)  all_52_12 = e1
% 204.64/35.47  |   (143)  all_52_10 = e2
% 204.64/35.47  |   (144)  all_52_8 = e3
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (57), (144) imply:
% 204.64/35.47  |   (145)  op(all_52_9, all_52_9) = e3
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (126), (142) imply:
% 204.64/35.47  |   (146)  op(all_52_13, all_52_13) = e1
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (58), (141) imply:
% 204.64/35.47  |   (147)  op(all_52_15, all_52_15) = e0
% 204.64/35.47  | 
% 204.64/35.47  | REDUCE: (108), (143) imply:
% 204.64/35.47  |   (148)  op(all_4_2, all_4_2) = e2
% 204.64/35.47  | 
% 204.64/35.47  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.64/35.47  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.64/35.47  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 204.64/35.47  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.64/35.47  |            (46), (47), (48), (49), (50), (51), (52), (53), (55), (56), (59),
% 204.64/35.47  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 204.64/35.47  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 204.64/35.47  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 204.64/35.47  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 204.64/35.47  |            (103), (104), (105), (106), (107), (109), (110), (111), (112),
% 204.64/35.47  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 204.64/35.47  |            (122), (123), (124), (125), (127), (128), (129), (130), (131),
% 204.64/35.47  |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 204.64/35.47  |            (145), (146), (147), (148) are inconsistent by sub-proof #1092.
% 204.64/35.47  | 
% 204.64/35.47  End of proof
% 204.64/35.47  
% 204.64/35.47  Sub-proof #1092 shows that the following formulas are inconsistent:
% 204.64/35.47  ----------------------------------------------------------------
% 204.64/35.47    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.64/35.47    (2)   ~ (all_52_15 = all_52_23)
% 204.64/35.47    (3)   ~ (all_52_25 = all_52_27)
% 204.64/35.47    (4)  all_58_14 = all_52_23
% 204.64/35.47    (5)   ~ (e3 = e1)
% 204.64/35.47    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.64/35.47    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.64/35.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.64/35.47    (8)   ~ (all_52_5 = all_52_13)
% 204.64/35.47    (9)  all_58_1 = all_52_9
% 204.64/35.47    (10)   ~ (all_52_9 = all_52_13)
% 204.64/35.47    (11)  op(e2, e3) = all_52_3
% 204.64/35.47    (12)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.64/35.47    (13)   ~ (all_52_7 = all_52_15)
% 204.64/35.47    (14)  op(all_52_15, all_52_15) = e0
% 204.64/35.47    (15)  op(all_52_7, all_52_7) = all_52_6
% 204.64/35.47    (16)   ~ (all_52_17 = all_52_25)
% 204.64/35.47    (17)   ~ (all_52_3 = all_6_2)
% 204.64/35.47    (18)  all_58_0 = all_6_2
% 204.64/35.47    (19)  op(all_14_2, e0) = all_14_1
% 204.64/35.47    (20)  all_56_4 = all_52_3
% 204.64/35.47    (21)   ~ (all_52_17 = all_10_2)
% 204.64/35.47    (22)  op(e3, e0) = all_52_25
% 204.74/35.47    (23)  op(all_52_5, all_52_5) = all_52_4
% 204.74/35.47    (24)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.74/35.47    (25)  op(all_52_19, all_52_19) = all_52_18
% 204.74/35.47    (26)   ~ (all_52_27 = all_52_29)
% 204.74/35.47    (27)  all_58_13 = all_52_15
% 204.74/35.47    (28)  op(all_52_13, all_52_13) = e1
% 204.74/35.47    (29)  op(all_10_2, all_10_2) = all_52_20
% 204.74/35.47    (30)  all_58_9 = all_52_25
% 204.74/35.47    (31)   ~ (all_6_1 = e1)
% 204.74/35.47    (32)   ~ (all_52_29 = all_14_2)
% 204.74/35.47    (33)  op(all_52_27, all_52_27) = all_52_26
% 204.74/35.47    (34)  op(e1, e3) = all_52_5
% 204.74/35.47    (35)  op(e2, e2) = all_4_2
% 204.74/35.47    (36)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.74/35.47    (37)   ~ (all_52_3 = all_52_5)
% 204.74/35.47    (38)   ~ (all_4_1 = e3)
% 204.74/35.47    (39)  all_58_11 = all_52_29
% 204.74/35.47    (40)  all_56_5 = all_4_2
% 204.74/35.47    (41)   ~ (all_52_25 = all_14_2)
% 204.74/35.47    (42)   ~ (all_52_3 = all_52_27)
% 204.74/35.47    (43)  op(all_6_2, all_6_2) = all_52_0
% 204.74/35.47    (44)   ~ (all_52_7 = all_6_2)
% 204.74/35.47    (45)  op(e0, e0) = all_14_2
% 204.74/35.47    (46)  all_56_15 = all_14_2
% 204.74/35.47    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.74/35.47    (48)  all_56_11 = all_52_29
% 204.74/35.47    (49)   ~ (all_4_1 = e1)
% 204.74/35.47    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.74/35.47    (51)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.74/35.47    (52)  all_56_9 = all_52_13
% 204.74/35.47    (53)   ~ (e2 = e1)
% 204.74/35.47    (54)   ~ (all_52_13 = all_10_2)
% 204.74/35.47    (55)   ~ (all_6_0 = e1)
% 204.74/35.47    (56)  all_58_10 = all_52_27
% 204.74/35.47    (57)  all_56_8 = all_52_5
% 204.74/35.47    (58)   ~ (all_52_19 = all_52_23)
% 204.74/35.47    (59)   ~ (all_52_25 = all_52_29)
% 204.74/35.47    (60)  all_58_7 = all_52_13
% 204.74/35.47    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.74/35.47    (62)   ~ (all_52_5 = all_52_7)
% 204.74/35.47    (63)  all_58_12 = all_52_7
% 204.74/35.47    (64)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.74/35.47    (65)   ~ (all_52_7 = all_14_2)
% 204.74/35.47    (66)   ~ (all_14_2 = e0)
% 204.74/35.47    (67)  all_58_2 = all_52_3
% 204.74/35.47    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.74/35.47    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.47    (70)  op(e3, all_6_1) = all_6_0
% 204.74/35.47    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.74/35.47    (72)  all_56_7 = all_52_27
% 204.74/35.47    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.74/35.47    (74)   ~ (e2 = e0)
% 204.74/35.47    (75)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.74/35.47    (76)  op(all_4_2, e2) = all_4_1
% 204.74/35.47    (77)   ~ (all_52_5 = all_52_29)
% 204.74/35.47    (78)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.74/35.47    (79)   ~ (all_52_15 = all_14_2)
% 204.74/35.47    (80)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.74/35.47    (81)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.47    (82)   ~ (all_6_0 = e2)
% 204.74/35.47    (83)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.74/35.47    (84)   ~ (all_52_13 = all_4_2)
% 204.74/35.47    (85)  op(e0, e3) = all_52_7
% 204.74/35.47    (86)  op(e1, e2) = all_52_13
% 204.74/35.47    (87)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.47    (88)   ~ (all_52_9 = all_52_25)
% 204.74/35.47    (89)  all_58_15 = all_14_2
% 204.74/35.47    (90)  op(all_52_23, all_52_23) = all_52_22
% 204.74/35.47    (91)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.47    (92)  all_58_8 = all_10_2
% 204.74/35.47    (93)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.74/35.47    (94)  op(all_52_29, all_52_29) = all_52_28
% 204.74/35.47    (95)   ~ (all_52_23 = all_14_2)
% 204.74/35.47    (96)  all_56_12 = all_52_7
% 204.74/35.47    (97)  op(all_52_17, all_52_17) = all_52_16
% 204.74/35.47    (98)   ~ (all_52_25 = all_6_2)
% 204.74/35.47    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.74/35.47    (100)   ~ (all_52_9 = all_4_2)
% 204.74/35.47    (101)   ~ (all_52_5 = all_6_2)
% 204.74/35.47    (102)  op(all_4_2, all_4_2) = e2
% 204.74/35.47    (103)   ~ (all_52_9 = all_6_2)
% 204.74/35.47    (104)  op(e3, e3) = all_6_2
% 204.74/35.47    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.74/35.47    (106)   ~ (all_52_27 = all_14_2)
% 204.74/35.47    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.74/35.47    (108)  all_56_3 = all_52_25
% 204.74/35.47    (109)   ~ (all_52_3 = all_52_7)
% 204.74/35.47    (110)  op(all_14_2, all_14_2) = all_52_30
% 204.74/35.47    (111)  all_58_5 = all_52_19
% 204.74/35.48    (112)  all_56_1 = all_52_9
% 204.74/35.48    (113)   ~ (all_52_27 = all_4_2)
% 204.74/35.48    (114)  all_58_6 = all_52_5
% 204.74/35.48    (115)  op(e3, e2) = all_52_9
% 204.74/35.48    (116)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.74/35.48    (117)   ~ (all_52_17 = all_6_2)
% 204.74/35.48    (118)   ~ (e1 = e0)
% 204.74/35.48    (119)   ~ (e3 = e2)
% 204.74/35.48    (120)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.74/35.48    (121)   ~ (all_52_9 = all_52_17)
% 204.74/35.48    (122)  all_56_10 = all_10_2
% 204.74/35.48    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.74/35.48    (124)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.74/35.48    (125)   ~ (all_6_1 = e2)
% 204.74/35.48    (126)  op(e1, e1) = all_10_2
% 204.74/35.48    (127)  op(all_52_9, all_52_9) = e3
% 204.74/35.48    (128)   ~ (all_52_7 = all_52_23)
% 204.74/35.48    (129)   ~ (all_52_17 = all_52_19)
% 204.74/35.48    (130)  all_58_3 = all_4_2
% 204.74/35.48    (131)  all_56_13 = all_52_15
% 204.74/35.48    (132)   ~ (all_52_3 = all_4_2)
% 204.74/35.48    (133)   ~ (all_52_19 = all_4_2)
% 204.74/35.48    (134)   ~ (all_52_17 = all_52_23)
% 204.74/35.48    (135)  op(all_6_2, e3) = all_6_1
% 204.74/35.48    (136)   ~ (all_52_13 = all_52_29)
% 204.74/35.48    (137)  all_58_4 = all_52_17
% 204.74/35.48    (138)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.74/35.48    (139)  op(all_52_25, all_52_25) = all_52_24
% 204.74/35.48  
% 204.74/35.48  Begin of proof
% 204.74/35.48  | 
% 204.74/35.48  | BETA: splitting (93) gives:
% 204.74/35.48  | 
% 204.74/35.48  | Case 1:
% 204.74/35.48  | | 
% 204.74/35.48  | |   (140)  all_56_15 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | COMBINE_EQS: (46), (140) imply:
% 204.74/35.48  | |   (141)  all_14_2 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | SIMP: (141) implies:
% 204.74/35.48  | |   (142)  all_14_2 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (13), (15), (17), (18),
% 204.74/35.48  | |            (19), (20), (22), (23), (27), (28), (29), (30), (31), (32), (34),
% 204.74/35.48  | |            (35), (36), (37), (39), (41), (43), (44), (47), (49), (51), (53),
% 204.74/35.48  | |            (54), (55), (56), (60), (63), (64), (65), (66), (67), (68), (69),
% 204.74/35.48  | |            (70), (71), (73), (74), (76), (78), (79), (81), (82), (87), (88),
% 204.74/35.48  | |            (92), (97), (98), (99), (101), (102), (103), (104), (106), (107),
% 204.74/35.48  | |            (108), (109), (110), (111), (112), (114), (115), (117), (118),
% 204.74/35.48  | |            (119), (120), (121), (122), (123), (125), (126), (127), (129),
% 204.74/35.48  | |            (130), (132), (135), (137), (138), (142) are inconsistent by
% 204.74/35.48  | |            sub-proof #1117.
% 204.74/35.48  | | 
% 204.74/35.48  | Case 2:
% 204.74/35.48  | | 
% 204.74/35.48  | |   (143)   ~ (all_56_15 = e3)
% 204.74/35.48  | | 
% 204.74/35.48  | | REDUCE: (46), (143) imply:
% 204.74/35.48  | |   (144)   ~ (all_14_2 = e3)
% 204.74/35.48  | | 
% 204.74/35.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 204.74/35.48  | |            (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 204.74/35.48  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (37), (38),
% 204.74/35.48  | |            (39), (40), (41), (42), (43), (44), (45), (47), (48), (49), (50),
% 204.74/35.48  | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 204.74/35.48  | |            (63), (64), (65), (67), (69), (70), (71), (72), (73), (75), (76),
% 204.74/35.48  | |            (77), (79), (80), (81), (82), (83), (84), (85), (86), (87), (88),
% 204.74/35.48  | |            (89), (90), (91), (92), (94), (95), (96), (97), (98), (99),
% 204.74/35.48  | |            (100), (101), (102), (103), (104), (105), (107), (108), (109),
% 204.74/35.48  | |            (111), (112), (113), (114), (115), (116), (119), (120), (121),
% 204.74/35.48  | |            (123), (124), (125), (127), (128), (130), (131), (132), (133),
% 204.74/35.48  | |            (134), (135), (136), (137), (139), (144) are inconsistent by
% 204.74/35.48  | |            sub-proof #1093.
% 204.74/35.48  | | 
% 204.74/35.48  | End of split
% 204.74/35.48  | 
% 204.74/35.48  End of proof
% 204.74/35.48  
% 204.74/35.48  Sub-proof #1093 shows that the following formulas are inconsistent:
% 204.74/35.48  ----------------------------------------------------------------
% 204.74/35.48    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.74/35.48    (2)   ~ (all_52_15 = all_52_23)
% 204.74/35.48    (3)   ~ (all_52_25 = all_52_27)
% 204.74/35.48    (4)  all_58_14 = all_52_23
% 204.74/35.48    (5)   ~ (e3 = e1)
% 204.74/35.48    (6)  op(all_52_3, all_52_3) = all_52_2
% 204.74/35.48    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.48    (8)   ~ (all_52_5 = all_52_13)
% 204.74/35.48    (9)  all_58_1 = all_52_9
% 204.74/35.48    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.74/35.48    (11)   ~ (all_52_7 = all_52_15)
% 204.74/35.48    (12)  op(all_52_15, all_52_15) = e0
% 204.74/35.48    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.74/35.48    (14)   ~ (all_52_17 = all_52_25)
% 204.74/35.48    (15)   ~ (all_52_3 = all_6_2)
% 204.74/35.48    (16)  all_58_0 = all_6_2
% 204.74/35.48    (17)  all_56_4 = all_52_3
% 204.74/35.48    (18)   ~ (all_52_17 = all_10_2)
% 204.74/35.48    (19)  op(e3, e0) = all_52_25
% 204.74/35.48    (20)  op(all_52_5, all_52_5) = all_52_4
% 204.74/35.48    (21)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.74/35.48    (22)  op(all_52_19, all_52_19) = all_52_18
% 204.74/35.48    (23)   ~ (all_52_27 = all_52_29)
% 204.74/35.48    (24)  all_58_13 = all_52_15
% 204.74/35.48    (25)  op(all_52_13, all_52_13) = e1
% 204.74/35.48    (26)  op(all_10_2, all_10_2) = all_52_20
% 204.74/35.48    (27)  all_58_9 = all_52_25
% 204.74/35.48    (28)   ~ (all_6_1 = e1)
% 204.74/35.48    (29)   ~ (all_52_29 = all_14_2)
% 204.74/35.48    (30)  op(all_52_27, all_52_27) = all_52_26
% 204.74/35.48    (31)  op(e1, e3) = all_52_5
% 204.74/35.48    (32)  op(e2, e2) = all_4_2
% 204.74/35.48    (33)   ~ (all_52_3 = all_52_5)
% 204.74/35.48    (34)   ~ (all_4_1 = e3)
% 204.74/35.48    (35)  all_58_11 = all_52_29
% 204.74/35.48    (36)  all_56_5 = all_4_2
% 204.74/35.48    (37)   ~ (all_52_25 = all_14_2)
% 204.74/35.48    (38)   ~ (all_52_3 = all_52_27)
% 204.74/35.48    (39)  op(all_6_2, all_6_2) = all_52_0
% 204.74/35.48    (40)   ~ (all_52_7 = all_6_2)
% 204.74/35.48    (41)  op(e0, e0) = all_14_2
% 204.74/35.48    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.74/35.48    (43)  all_56_11 = all_52_29
% 204.74/35.48    (44)   ~ (all_4_1 = e1)
% 204.74/35.48    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.74/35.48    (46)  all_56_9 = all_52_13
% 204.74/35.48    (47)   ~ (e2 = e1)
% 204.74/35.48    (48)   ~ (all_52_13 = all_10_2)
% 204.74/35.48    (49)   ~ (all_6_0 = e1)
% 204.74/35.48    (50)  all_58_10 = all_52_27
% 204.74/35.48    (51)  all_56_8 = all_52_5
% 204.74/35.48    (52)   ~ (all_52_19 = all_52_23)
% 204.74/35.48    (53)   ~ (all_52_25 = all_52_29)
% 204.74/35.48    (54)  all_58_7 = all_52_13
% 204.74/35.48    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.74/35.48    (56)   ~ (all_52_5 = all_52_7)
% 204.74/35.48    (57)  all_58_12 = all_52_7
% 204.74/35.48    (58)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.74/35.48    (59)   ~ (all_52_7 = all_14_2)
% 204.74/35.48    (60)  all_58_2 = all_52_3
% 204.74/35.48    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.48    (62)  op(e3, all_6_1) = all_6_0
% 204.74/35.48    (63)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.74/35.48    (64)  all_56_7 = all_52_27
% 204.74/35.48    (65)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.74/35.48    (66)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.74/35.48    (67)  op(all_4_2, e2) = all_4_1
% 204.74/35.48    (68)   ~ (all_52_5 = all_52_29)
% 204.74/35.48    (69)   ~ (all_52_15 = all_14_2)
% 204.74/35.48    (70)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.74/35.48    (71)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.48    (72)   ~ (all_6_0 = e2)
% 204.74/35.48    (73)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.74/35.48    (74)   ~ (all_52_13 = all_4_2)
% 204.74/35.48    (75)  op(e0, e3) = all_52_7
% 204.74/35.48    (76)  op(e1, e2) = all_52_13
% 204.74/35.48    (77)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.48    (78)   ~ (all_52_9 = all_52_25)
% 204.74/35.48    (79)  all_58_15 = all_14_2
% 204.74/35.48    (80)  op(all_52_23, all_52_23) = all_52_22
% 204.74/35.48    (81)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.48    (82)  all_58_8 = all_10_2
% 204.74/35.48    (83)  op(all_52_29, all_52_29) = all_52_28
% 204.74/35.48    (84)   ~ (all_52_23 = all_14_2)
% 204.74/35.48    (85)  all_56_12 = all_52_7
% 204.74/35.48    (86)  op(all_52_17, all_52_17) = all_52_16
% 204.74/35.48    (87)   ~ (all_52_25 = all_6_2)
% 204.74/35.48    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.74/35.48    (89)   ~ (all_52_9 = all_4_2)
% 204.74/35.48    (90)   ~ (all_52_5 = all_6_2)
% 204.74/35.48    (91)  op(all_4_2, all_4_2) = e2
% 204.74/35.48    (92)   ~ (all_52_9 = all_6_2)
% 204.74/35.48    (93)  op(e3, e3) = all_6_2
% 204.74/35.48    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.74/35.48    (95)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.74/35.48    (96)  all_56_3 = all_52_25
% 204.74/35.48    (97)   ~ (all_52_3 = all_52_7)
% 204.74/35.48    (98)  all_58_5 = all_52_19
% 204.74/35.48    (99)  all_56_1 = all_52_9
% 204.74/35.48    (100)   ~ (all_52_27 = all_4_2)
% 204.74/35.48    (101)  all_58_6 = all_52_5
% 204.74/35.48    (102)  op(e3, e2) = all_52_9
% 204.74/35.48    (103)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.74/35.48    (104)   ~ (e3 = e2)
% 204.74/35.48    (105)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.74/35.48    (106)   ~ (all_52_9 = all_52_17)
% 204.74/35.48    (107)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.74/35.48    (108)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.74/35.48    (109)   ~ (all_6_1 = e2)
% 204.74/35.48    (110)  op(all_52_9, all_52_9) = e3
% 204.74/35.48    (111)   ~ (all_52_7 = all_52_23)
% 204.74/35.48    (112)  all_58_3 = all_4_2
% 204.74/35.48    (113)  all_56_13 = all_52_15
% 204.74/35.48    (114)   ~ (all_52_3 = all_4_2)
% 204.74/35.48    (115)   ~ (all_52_19 = all_4_2)
% 204.74/35.48    (116)   ~ (all_52_17 = all_52_23)
% 204.74/35.48    (117)  op(all_6_2, e3) = all_6_1
% 204.74/35.48    (118)   ~ (all_52_13 = all_52_29)
% 204.74/35.48    (119)  all_58_4 = all_52_17
% 204.74/35.48    (120)  op(all_52_25, all_52_25) = all_52_24
% 204.74/35.48    (121)   ~ (all_14_2 = e3)
% 204.74/35.48  
% 204.74/35.48  Begin of proof
% 204.74/35.48  | 
% 204.74/35.48  | BETA: splitting (45) gives:
% 204.74/35.48  | 
% 204.74/35.48  | Case 1:
% 204.74/35.48  | | 
% 204.74/35.48  | |   (122)  all_56_13 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | COMBINE_EQS: (113), (122) imply:
% 204.74/35.48  | |   (123)  all_52_15 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | REF_CLOSE: (7), (10), (11), (12), (28), (40), (75), (85), (93), (109),
% 204.74/35.48  | |            (117), (123) are inconsistent by sub-proof #1341.
% 204.74/35.48  | | 
% 204.74/35.48  | Case 2:
% 204.74/35.48  | | 
% 204.74/35.48  | |   (124)   ~ (all_56_13 = e3)
% 204.74/35.48  | | 
% 204.74/35.48  | | REDUCE: (113), (124) imply:
% 204.74/35.48  | |   (125)   ~ (all_52_15 = e3)
% 204.74/35.48  | | 
% 204.74/35.48  | | BETA: splitting (103) gives:
% 204.74/35.48  | | 
% 204.74/35.48  | | Case 1:
% 204.74/35.48  | | | 
% 204.74/35.48  | | |   (126)  all_58_12 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | COMBINE_EQS: (57), (126) imply:
% 204.74/35.48  | | |   (127)  all_52_7 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | SIMP: (127) implies:
% 204.74/35.48  | | |   (128)  all_52_7 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (97), (128) imply:
% 204.74/35.48  | | |   (129)   ~ (all_52_3 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (56), (128) imply:
% 204.74/35.48  | | |   (130)   ~ (all_52_5 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (11), (128) imply:
% 204.74/35.48  | | |   (131)   ~ (all_52_15 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (111), (128) imply:
% 204.74/35.48  | | |   (132)   ~ (all_52_23 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | SIMP: (132) implies:
% 204.74/35.48  | | |   (133)   ~ (all_52_23 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (59), (128) imply:
% 204.74/35.48  | | |   (134)   ~ (all_14_2 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (40), (128) imply:
% 204.74/35.48  | | |   (135)   ~ (all_6_2 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | SIMP: (135) implies:
% 204.74/35.48  | | |   (136)   ~ (all_6_2 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (13), (128) imply:
% 204.74/35.48  | | |   (137)  op(e3, e3) = all_52_6
% 204.74/35.48  | | | 
% 204.74/35.48  | | | GROUND_INST: instantiating (7) with all_6_2, all_52_6, e3, e3, simplifying
% 204.74/35.48  | | |              with (93), (137) gives:
% 204.74/35.48  | | |   (138)  all_52_6 = all_6_2
% 204.74/35.48  | | | 
% 204.74/35.48  | | | BETA: splitting (81) gives:
% 204.74/35.48  | | | 
% 204.74/35.48  | | | Case 1:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | |   (139)  all_56_8 = e3
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | REF_CLOSE: (51), (130), (139) are inconsistent by sub-proof #1325.
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | Case 2:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | |   (140)   ~ (all_56_8 = e3)
% 204.74/35.48  | | | |   (141)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | BETA: splitting (65) gives:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | Case 1:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | |   (142)  all_56_4 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REF_CLOSE: (17), (129), (142) are inconsistent by sub-proof #1340.
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | Case 2:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | |   (143)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | BETA: splitting (88) gives:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | Case 1:
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | |   (144)  all_56_3 = e3
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | COMBINE_EQS: (96), (144) imply:
% 204.74/35.48  | | | | | |   (145)  all_52_25 = e3
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | SIMP: (145) implies:
% 204.74/35.48  | | | | | |   (146)  all_52_25 = e3
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | COMBINE_EQS: (27), (146) imply:
% 204.74/35.48  | | | | | |   (147)  all_58_9 = e3
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REDUCE: (78), (146) imply:
% 204.74/35.48  | | | | | |   (148)   ~ (all_52_9 = e3)
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REDUCE: (14), (146) imply:
% 204.74/35.48  | | | | | |   (149)   ~ (all_52_17 = e3)
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REDUCE: (53), (146) imply:
% 204.74/35.48  | | | | | |   (150)   ~ (all_52_29 = e3)
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | SIMP: (150) implies:
% 204.74/35.48  | | | | | |   (151)   ~ (all_52_29 = e3)
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REDUCE: (120), (146) imply:
% 204.74/35.48  | | | | | |   (152)  op(e3, e3) = all_52_24
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | GROUND_INST: instantiating (7) with all_6_2, all_52_24, e3, e3,
% 204.74/35.48  | | | | | |              simplifying with (93), (152) gives:
% 204.74/35.48  | | | | | |   (153)  all_52_24 = all_6_2
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (15), (17), (22), (24), (25),
% 204.74/35.48  | | | | | |            (26), (31), (32), (34), (35), (36), (38), (41), (44),
% 204.74/35.48  | | | | | |            (46), (48), (50), (51), (54), (55), (58), (60), (66),
% 204.74/35.48  | | | | | |            (67), (68), (74), (76), (77), (82), (90), (91), (92),
% 204.74/35.48  | | | | | |            (93), (98), (99), (100), (101), (102), (105), (107),
% 204.74/35.48  | | | | | |            (108), (109), (110), (112), (114), (115), (117), (119),
% 204.74/35.48  | | | | | |            (121), (125), (130), (133), (141), (143), (147), (148),
% 204.74/35.48  | | | | | |            (149), (151) are inconsistent by sub-proof #1111.
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | Case 2:
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | |   (154)   ~ (all_56_3 = e3)
% 204.74/35.48  | | | | | |   (155)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REDUCE: (96), (154) imply:
% 204.74/35.48  | | | | | |   (156)   ~ (all_52_25 = e3)
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | BETA: splitting (94) gives:
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | Case 1:
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | |   (157)  all_58_9 = e3
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REF_CLOSE: (27), (156), (157) are inconsistent by sub-proof #1300.
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | Case 2:
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | |   (158)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REF_CLOSE: (3), (6), (7), (9), (16), (18), (19), (20), (21), (23),
% 204.74/35.48  | | | | | | |            (24), (25), (27), (29), (30), (31), (32), (33), (35),
% 204.74/35.48  | | | | | | |            (41), (43), (44), (47), (50), (51), (53), (54), (58),
% 204.74/35.48  | | | | | | |            (60), (62), (63), (64), (67), (70), (71), (72), (77),
% 204.74/35.48  | | | | | | |            (78), (79), (82), (83), (86), (87), (90), (91), (92),
% 204.74/35.48  | | | | | | |            (93), (95), (96), (99), (100), (101), (102), (104),
% 204.74/35.48  | | | | | | |            (105), (106), (107), (109), (110), (112), (117), (118),
% 204.74/35.48  | | | | | | |            (119), (120), (121), (125), (126), (130), (136), (137),
% 204.74/35.48  | | | | | | |            (141), (155), (158) are inconsistent by sub-proof
% 204.74/35.48  | | | | | | |            #1102.
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | End of split
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | End of split
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | End of split
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | End of split
% 204.74/35.48  | | | 
% 204.74/35.48  | | Case 2:
% 204.74/35.48  | | | 
% 204.74/35.48  | | |   (159)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (12), (16), (20), (24),
% 204.74/35.48  | | |            (25), (27), (31), (32), (33), (35), (37), (39), (40), (41),
% 204.74/35.48  | | |            (42), (44), (47), (49), (50), (51), (52), (54), (56), (57),
% 204.74/35.48  | | |            (58), (60), (61), (62), (67), (69), (71), (72), (73), (77),
% 204.74/35.48  | | |            (79), (80), (81), (83), (84), (87), (89), (90), (91), (92),
% 204.74/35.48  | | |            (93), (94), (95), (97), (98), (99), (100), (101), (102), (104),
% 204.74/35.48  | | |            (105), (109), (110), (111), (112), (114), (116), (117), (119),
% 204.74/35.48  | | |            (120), (121), (125), (159) are inconsistent by sub-proof #1094.
% 204.74/35.48  | | | 
% 204.74/35.48  | | End of split
% 204.74/35.48  | | 
% 204.74/35.48  | End of split
% 204.74/35.48  | 
% 204.74/35.48  End of proof
% 204.74/35.48  
% 204.74/35.48  Sub-proof #1094 shows that the following formulas are inconsistent:
% 204.74/35.48  ----------------------------------------------------------------
% 204.74/35.48    (1)   ~ (all_52_15 = all_52_23)
% 204.74/35.48    (2)   ~ (all_52_25 = all_52_27)
% 204.74/35.48    (3)  all_58_14 = all_52_23
% 204.74/35.48    (4)   ~ (e3 = e1)
% 204.74/35.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.48    (6)   ~ (all_52_5 = all_52_13)
% 204.74/35.48    (7)  all_58_1 = all_52_9
% 204.74/35.48    (8)  op(all_52_15, all_52_15) = e0
% 204.74/35.48    (9)  all_58_0 = all_6_2
% 204.74/35.48    (10)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.74/35.48    (11)  op(all_52_5, all_52_5) = all_52_4
% 204.74/35.48    (12)  all_58_13 = all_52_15
% 204.74/35.48    (13)  op(all_52_13, all_52_13) = e1
% 204.74/35.48    (14)  all_58_9 = all_52_25
% 204.74/35.48    (15)   ~ (all_52_15 = e3)
% 204.74/35.48    (16)  op(e1, e3) = all_52_5
% 204.74/35.48    (17)  op(e2, e2) = all_4_2
% 204.74/35.48    (18)   ~ (all_52_3 = all_52_5)
% 204.74/35.48    (19)  all_58_11 = all_52_29
% 204.74/35.48    (20)   ~ (all_52_25 = all_14_2)
% 204.74/35.48    (21)  op(all_6_2, all_6_2) = all_52_0
% 204.74/35.48    (22)   ~ (all_52_7 = all_6_2)
% 204.74/35.48    (23)  op(e0, e0) = all_14_2
% 204.74/35.48    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.74/35.48    (25)   ~ (all_4_1 = e1)
% 204.74/35.48    (26)   ~ (e2 = e1)
% 204.74/35.48    (27)   ~ (all_6_0 = e1)
% 204.74/35.48    (28)  all_58_10 = all_52_27
% 204.74/35.48    (29)  all_56_8 = all_52_5
% 204.74/35.48    (30)   ~ (all_52_19 = all_52_23)
% 204.74/35.48    (31)  all_58_7 = all_52_13
% 204.74/35.48    (32)   ~ (all_52_5 = all_52_7)
% 204.74/35.48    (33)  all_58_12 = all_52_7
% 204.74/35.48    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.74/35.48    (35)  all_58_2 = all_52_3
% 204.74/35.48    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.48    (37)  op(e3, all_6_1) = all_6_0
% 204.74/35.48    (38)  op(all_4_2, e2) = all_4_1
% 204.74/35.48    (39)   ~ (all_52_15 = all_14_2)
% 204.74/35.48    (40)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.48    (41)   ~ (all_6_0 = e2)
% 204.74/35.48    (42)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.74/35.48    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.48    (44)  all_58_15 = all_14_2
% 204.74/35.48    (45)  op(all_52_23, all_52_23) = all_52_22
% 204.74/35.48    (46)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.48    (47)  op(all_52_29, all_52_29) = all_52_28
% 204.74/35.48    (48)   ~ (all_52_23 = all_14_2)
% 204.74/35.48    (49)   ~ (all_52_25 = all_6_2)
% 204.74/35.48    (50)   ~ (all_52_9 = all_4_2)
% 204.74/35.48    (51)   ~ (all_52_5 = all_6_2)
% 204.74/35.48    (52)  op(all_4_2, all_4_2) = e2
% 204.74/35.48    (53)   ~ (all_52_9 = all_6_2)
% 204.74/35.48    (54)  op(e3, e3) = all_6_2
% 204.74/35.48    (55)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.74/35.48    (56)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.74/35.48    (57)   ~ (all_52_3 = all_52_7)
% 204.74/35.48    (58)  all_58_5 = all_52_19
% 204.74/35.48    (59)  all_56_1 = all_52_9
% 204.74/35.48    (60)   ~ (all_52_27 = all_4_2)
% 204.74/35.48    (61)  all_58_6 = all_52_5
% 204.74/35.48    (62)  op(e3, e2) = all_52_9
% 204.74/35.48    (63)   ~ (e3 = e2)
% 204.74/35.48    (64)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.74/35.48    (65)   ~ (all_6_1 = e2)
% 204.74/35.48    (66)  op(all_52_9, all_52_9) = e3
% 204.74/35.48    (67)   ~ (all_52_7 = all_52_23)
% 204.74/35.48    (68)  all_58_3 = all_4_2
% 204.74/35.48    (69)   ~ (all_52_3 = all_4_2)
% 204.74/35.48    (70)   ~ (all_52_17 = all_52_23)
% 204.74/35.48    (71)  op(all_6_2, e3) = all_6_1
% 204.74/35.48    (72)  all_58_4 = all_52_17
% 204.74/35.48    (73)  op(all_52_25, all_52_25) = all_52_24
% 204.74/35.48    (74)   ~ (all_14_2 = e3)
% 204.74/35.48  
% 204.74/35.48  Begin of proof
% 204.74/35.48  | 
% 204.74/35.48  | BETA: splitting (10) gives:
% 204.74/35.48  | 
% 204.74/35.48  | Case 1:
% 204.74/35.48  | | 
% 204.74/35.48  | |   (75)  all_58_13 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | REF_CLOSE: (12), (15), (75) are inconsistent by sub-proof #1360.
% 204.74/35.48  | | 
% 204.74/35.48  | Case 2:
% 204.74/35.48  | | 
% 204.74/35.48  | |   (76)  all_58_14 = e3 | all_58_15 = e3
% 204.74/35.48  | | 
% 204.74/35.48  | | BETA: splitting (76) gives:
% 204.74/35.48  | | 
% 204.74/35.48  | | Case 1:
% 204.74/35.48  | | | 
% 204.74/35.48  | | |   (77)  all_58_14 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | COMBINE_EQS: (3), (77) imply:
% 204.74/35.48  | | |   (78)  all_52_23 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | SIMP: (78) implies:
% 204.74/35.48  | | |   (79)  all_52_23 = e3
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (67), (79) imply:
% 204.74/35.48  | | |   (80)   ~ (all_52_7 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (70), (79) imply:
% 204.74/35.48  | | |   (81)   ~ (all_52_17 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (30), (79) imply:
% 204.74/35.48  | | |   (82)   ~ (all_52_19 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (48), (79) imply:
% 204.74/35.48  | | |   (83)   ~ (all_14_2 = e3)
% 204.74/35.48  | | | 
% 204.74/35.48  | | | REDUCE: (45), (79) imply:
% 204.74/35.48  | | |   (84)  op(e3, e3) = all_52_22
% 204.74/35.48  | | | 
% 204.74/35.48  | | | GROUND_INST: instantiating (5) with all_6_2, all_52_22, e3, e3,
% 204.74/35.48  | | |              simplifying with (54), (84) gives:
% 204.74/35.48  | | |   (85)  all_52_22 = all_6_2
% 204.74/35.48  | | | 
% 204.74/35.48  | | | BETA: splitting (55) gives:
% 204.74/35.48  | | | 
% 204.74/35.48  | | | Case 1:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | |   (86)  all_58_9 = e3
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | COMBINE_EQS: (14), (86) imply:
% 204.74/35.48  | | | |   (87)  all_52_25 = e3
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | SIMP: (87) implies:
% 204.74/35.48  | | | |   (88)  all_52_25 = e3
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | REDUCE: (2), (88) imply:
% 204.74/35.48  | | | |   (89)   ~ (all_52_27 = e3)
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | SIMP: (89) implies:
% 204.74/35.48  | | | |   (90)   ~ (all_52_27 = e3)
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | REDUCE: (49), (88) imply:
% 204.74/35.48  | | | |   (91)   ~ (all_6_2 = e3)
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | SIMP: (91) implies:
% 204.74/35.48  | | | |   (92)   ~ (all_6_2 = e3)
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | REDUCE: (73), (88) imply:
% 204.74/35.48  | | | |   (93)  op(e3, e3) = all_52_24
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_24, e3, e3,
% 204.74/35.48  | | | |              simplifying with (54), (93) gives:
% 204.74/35.48  | | | |   (94)  all_52_24 = all_6_2
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | BETA: splitting (36) gives:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | Case 1:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | |   (95)  all_58_0 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | COMBINE_EQS: (9), (95) imply:
% 204.74/35.48  | | | | |   (96)  all_6_2 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REDUCE: (92), (96) imply:
% 204.74/35.48  | | | | |   (97)  $false
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | CLOSE: (97) is inconsistent.
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | Case 2:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | |   (98)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | BETA: splitting (24) gives:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | Case 1:
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | |   (99)  all_58_2 = e3
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (12), (13), (15), (16),
% 204.74/35.48  | | | | | |            (18), (23), (26), (29), (31), (32), (33), (35), (36),
% 204.74/35.48  | | | | | |            (39), (40), (42), (43), (46), (51), (53), (54), (57),
% 204.74/35.48  | | | | | |            (61), (63), (65), (66), (68), (69), (71), (77), (99) are
% 204.74/35.48  | | | | | |            inconsistent by sub-proof #1097.
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | Case 2:
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | |   (100)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | BETA: splitting (100) gives:
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | | Case 1:
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | |   (101)  all_58_3 = e3
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | COMBINE_EQS: (68), (101) imply:
% 204.74/35.48  | | | | | | |   (102)  all_4_2 = e3
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REDUCE: (50), (102) imply:
% 204.74/35.48  | | | | | | |   (103)   ~ (all_52_9 = e3)
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REDUCE: (52), (102) imply:
% 204.74/35.48  | | | | | | |   (104)  op(e3, e3) = e2
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REDUCE: (38), (102) imply:
% 204.74/35.48  | | | | | | |   (105)  op(e3, e2) = all_4_1
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REDUCE: (17), (102) imply:
% 204.74/35.48  | | | | | | |   (106)  op(e2, e2) = e3
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | BETA: splitting (34) gives:
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | Case 1:
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | |   (107)  all_58_6 = e3
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | COMBINE_EQS: (61), (107) imply:
% 204.74/35.48  | | | | | | | |   (108)  all_52_5 = e3
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | SIMP: (108) implies:
% 204.74/35.48  | | | | | | | |   (109)  all_52_5 = e3
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | REDUCE: (11), (109) imply:
% 204.74/35.48  | | | | | | | |   (110)  op(e3, e3) = all_52_4
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | GROUND_INST: instantiating (5) with all_52_9, all_4_1, e2, e3,
% 204.74/35.48  | | | | | | | |              simplifying with (62), (105) gives:
% 204.74/35.48  | | | | | | | |   (111)  all_52_9 = all_4_1
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | GROUND_INST: instantiating (5) with all_6_2, all_52_4, e3, e3,
% 204.74/35.48  | | | | | | | |              simplifying with (54), (110) gives:
% 204.74/35.48  | | | | | | | |   (112)  all_52_4 = all_6_2
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_4, e3, e3,
% 204.74/35.48  | | | | | | | |              simplifying with (104), (110) gives:
% 204.74/35.48  | | | | | | | |   (113)  all_52_4 = e2
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | COMBINE_EQS: (112), (113) imply:
% 204.74/35.48  | | | | | | | |   (114)  all_6_2 = e2
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | SIMP: (114) implies:
% 204.74/35.48  | | | | | | | |   (115)  all_6_2 = e2
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | REF_CLOSE: (5), (23), (25), (53), (59), (64), (66), (74), (103),
% 204.74/35.48  | | | | | | | |            (111), (115) are inconsistent by sub-proof #1096.
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | Case 2:
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | |   (116)   ~ (all_58_6 = e3)
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | REDUCE: (61), (116) imply:
% 204.74/35.48  | | | | | | | |   (117)   ~ (all_52_5 = e3)
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | | REF_CLOSE: (5), (17), (33), (35), (61), (69), (80), (98), (106),
% 204.74/35.48  | | | | | | | |            (117) are inconsistent by sub-proof #1242.
% 204.74/35.48  | | | | | | | | 
% 204.74/35.48  | | | | | | | End of split
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | Case 2:
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | |   (118)  all_58_5 = e3 | all_58_10 = e3
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | | REF_CLOSE: (28), (58), (82), (90), (118) are inconsistent by
% 204.74/35.48  | | | | | | |            sub-proof #1132.
% 204.74/35.48  | | | | | | | 
% 204.74/35.48  | | | | | | End of split
% 204.74/35.48  | | | | | | 
% 204.74/35.48  | | | | | End of split
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | End of split
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | Case 2:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | |   (119)   ~ (all_58_9 = e3)
% 204.74/35.48  | | | |   (120)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | REDUCE: (14), (119) imply:
% 204.74/35.48  | | | |   (121)   ~ (all_52_25 = e3)
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | BETA: splitting (56) gives:
% 204.74/35.48  | | | | 
% 204.74/35.48  | | | | Case 1:
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | |   (122)  all_58_0 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | COMBINE_EQS: (9), (122) imply:
% 204.74/35.48  | | | | |   (123)  all_6_2 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REDUCE: (53), (123) imply:
% 204.74/35.48  | | | | |   (124)   ~ (all_52_9 = e3)
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REDUCE: (21), (123) imply:
% 204.74/35.48  | | | | |   (125)  op(e3, e3) = all_52_0
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REDUCE: (71), (123) imply:
% 204.74/35.48  | | | | |   (126)  op(e3, e3) = all_6_1
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REDUCE: (54), (123) imply:
% 204.74/35.48  | | | | |   (127)  op(e3, e3) = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | GROUND_INST: instantiating (5) with all_6_1, all_52_0, e3, e3,
% 204.74/35.48  | | | | |              simplifying with (125), (126) gives:
% 204.74/35.48  | | | | |   (128)  all_52_0 = all_6_1
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | GROUND_INST: instantiating (5) with e3, all_52_0, e3, e3, simplifying
% 204.74/35.48  | | | | |              with (125), (127) gives:
% 204.74/35.48  | | | | |   (129)  all_52_0 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | COMBINE_EQS: (128), (129) imply:
% 204.74/35.48  | | | | |   (130)  all_6_1 = e3
% 204.74/35.48  | | | | | 
% 204.74/35.48  | | | | | REDUCE: (37), (130) imply:
% 204.74/35.48  | | | | |   (131)  op(e3, e3) = all_6_0
% 204.74/35.48  | | | | | 
% 204.74/35.49  | | | | | GROUND_INST: instantiating (5) with e3, all_6_0, e3, e3, simplifying
% 204.74/35.49  | | | | |              with (127), (131) gives:
% 204.74/35.49  | | | | |   (132)  all_6_0 = e3
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | BETA: splitting (43) gives:
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | Case 1:
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | |   (133)  all_58_1 = e3
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | COMBINE_EQS: (7), (133) imply:
% 204.74/35.49  | | | | | |   (134)  all_52_9 = e3
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | REDUCE: (124), (134) imply:
% 204.74/35.49  | | | | | |   (135)  $false
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | CLOSE: (135) is inconsistent.
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | Case 2:
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | |   (136)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | BETA: splitting (136) gives:
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | Case 1:
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | |   (137)  all_58_3 = e3
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | COMBINE_EQS: (68), (137) imply:
% 204.74/35.49  | | | | | | |   (138)  all_4_2 = e3
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | REDUCE: (60), (138) imply:
% 204.74/35.49  | | | | | | |   (139)   ~ (all_52_27 = e3)
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | REDUCE: (52), (138) imply:
% 204.74/35.49  | | | | | | |   (140)  op(e3, e3) = e2
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | BETA: splitting (120) gives:
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | |   (141)  all_58_10 = e3
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | | REF_CLOSE: (28), (139), (141) are inconsistent by sub-proof
% 204.74/35.49  | | | | | | | |            #1301.
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | |   (142)  all_58_11 = e3 | all_58_15 = e3
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | | BETA: splitting (142) gives:
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | |   (143)  all_58_11 = e3
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | COMBINE_EQS: (19), (143) imply:
% 204.74/35.49  | | | | | | | | |   (144)  all_52_29 = e3
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | SIMP: (144) implies:
% 204.74/35.49  | | | | | | | | |   (145)  all_52_29 = e3
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REDUCE: (47), (145) imply:
% 204.74/35.49  | | | | | | | | |   (146)  op(e3, e3) = all_52_28
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | GROUND_INST: instantiating (5) with e3, all_52_28, e3, e3,
% 204.74/35.49  | | | | | | | | |              simplifying with (127), (146) gives:
% 204.74/35.49  | | | | | | | | |   (147)  all_52_28 = e3
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_28, e3, e3,
% 204.74/35.49  | | | | | | | | |              simplifying with (140), (146) gives:
% 204.74/35.49  | | | | | | | | |   (148)  all_52_28 = e2
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REF_CLOSE: (63), (147), (148) are inconsistent by sub-proof
% 204.74/35.49  | | | | | | | | |            #1095.
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | |   (149)  all_58_15 = e3
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | COMBINE_EQS: (44), (149) imply:
% 204.74/35.49  | | | | | | | | |   (150)  all_14_2 = e3
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REDUCE: (74), (150) imply:
% 204.74/35.49  | | | | | | | | |   (151)  $false
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | CLOSE: (151) is inconsistent.
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | End of split
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | End of split
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | Case 2:
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | |   (152)  all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (13), (15), (16), (18),
% 204.74/35.49  | | | | | | |            (23), (26), (29), (31), (32), (33), (35), (36), (39),
% 204.74/35.49  | | | | | | |            (40), (42), (46), (51), (54), (61), (63), (65), (71),
% 204.74/35.49  | | | | | | |            (77), (80), (152) are inconsistent by sub-proof #1099.
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | End of split
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | End of split
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | Case 2:
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | |   (153)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | REF_CLOSE: (5), (7), (14), (53), (54), (66), (72), (81), (121), (153)
% 204.74/35.49  | | | | |            are inconsistent by sub-proof #1138.
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | End of split
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | End of split
% 204.74/35.49  | | | 
% 204.74/35.49  | | Case 2:
% 204.74/35.49  | | | 
% 204.74/35.49  | | |   (154)  all_58_15 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | COMBINE_EQS: (44), (154) imply:
% 204.74/35.49  | | |   (155)  all_14_2 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (74), (155) imply:
% 204.74/35.49  | | |   (156)  $false
% 204.74/35.49  | | | 
% 204.74/35.49  | | | CLOSE: (156) is inconsistent.
% 204.74/35.49  | | | 
% 204.74/35.49  | | End of split
% 204.74/35.49  | | 
% 204.74/35.49  | End of split
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1095 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)  all_52_28 = e3
% 204.74/35.49    (2)  all_52_28 = e2
% 204.74/35.49    (3)   ~ (e3 = e2)
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | COMBINE_EQS: (1), (2) imply:
% 204.74/35.49  |   (4)  e3 = e2
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (4) implies:
% 204.74/35.49  |   (5)  e3 = e2
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (3), (5) imply:
% 204.74/35.49  |   (6)  $false
% 204.74/35.49  | 
% 204.74/35.49  | CLOSE: (6) is inconsistent.
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1096 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.49    (2)  all_6_2 = e2
% 204.74/35.49    (3)  op(e0, e0) = all_14_2
% 204.74/35.49    (4)   ~ (all_4_1 = e1)
% 204.74/35.49    (5)   ~ (all_52_9 = e3)
% 204.74/35.49    (6)  all_52_9 = all_4_1
% 204.74/35.49    (7)   ~ (all_52_9 = all_6_2)
% 204.74/35.49    (8)  all_56_1 = all_52_9
% 204.74/35.49    (9)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.74/35.49    (10)  op(all_52_9, all_52_9) = e3
% 204.74/35.49    (11)   ~ (all_14_2 = e3)
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | COMBINE_EQS: (6), (8) imply:
% 204.74/35.49  |   (12)  all_56_1 = all_4_1
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (2), (6), (7) imply:
% 204.74/35.49  |   (13)   ~ (all_4_1 = e2)
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (5), (6) imply:
% 204.74/35.49  |   (14)   ~ (all_4_1 = e3)
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (6), (10) imply:
% 204.74/35.49  |   (15)  op(all_4_1, all_4_1) = e3
% 204.74/35.49  | 
% 204.74/35.49  | BETA: splitting (9) gives:
% 204.74/35.49  | 
% 204.74/35.49  | Case 1:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (16)  all_56_1 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | COMBINE_EQS: (12), (16) imply:
% 204.74/35.49  | |   (17)  all_4_1 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | REDUCE: (14), (17) imply:
% 204.74/35.49  | |   (18)  $false
% 204.74/35.49  | | 
% 204.74/35.49  | | CLOSE: (18) is inconsistent.
% 204.74/35.49  | | 
% 204.74/35.49  | Case 2:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (19)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.74/35.49  | | 
% 204.74/35.49  | | REF_CLOSE: (1), (3), (4), (11), (12), (13), (15), (19) are inconsistent by
% 204.74/35.49  | |            sub-proof #1114.
% 204.74/35.49  | | 
% 204.74/35.49  | End of split
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1097 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)   ~ (e3 = e1)
% 204.74/35.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.49    (3)   ~ (all_52_5 = all_52_13)
% 204.74/35.49    (4)  all_58_1 = all_52_9
% 204.74/35.49    (5)  op(all_52_15, all_52_15) = e0
% 204.74/35.49    (6)  all_58_0 = all_6_2
% 204.74/35.49    (7)  all_58_13 = all_52_15
% 204.74/35.49    (8)  op(all_52_13, all_52_13) = e1
% 204.74/35.49    (9)   ~ (all_52_15 = e3)
% 204.74/35.49    (10)  op(e1, e3) = all_52_5
% 204.74/35.49    (11)   ~ (all_52_3 = all_52_5)
% 204.74/35.49    (12)  op(e0, e0) = all_14_2
% 204.74/35.49    (13)   ~ (e2 = e1)
% 204.74/35.49    (14)  all_56_8 = all_52_5
% 204.74/35.49    (15)  all_58_7 = all_52_13
% 204.74/35.49    (16)   ~ (all_52_5 = all_52_7)
% 204.74/35.49    (17)  all_58_12 = all_52_7
% 204.74/35.49    (18)  all_58_2 = all_52_3
% 204.74/35.49    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.49    (20)   ~ (all_52_15 = all_14_2)
% 204.74/35.49    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49    (22)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.74/35.49    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49    (24)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.49    (25)   ~ (all_52_5 = all_6_2)
% 204.74/35.49    (26)   ~ (all_52_9 = all_6_2)
% 204.74/35.49    (27)  op(e3, e3) = all_6_2
% 204.74/35.49    (28)   ~ (all_52_3 = all_52_7)
% 204.74/35.49    (29)  all_58_6 = all_52_5
% 204.74/35.49    (30)   ~ (e3 = e2)
% 204.74/35.49    (31)   ~ (all_6_1 = e2)
% 204.74/35.49    (32)  op(all_52_9, all_52_9) = e3
% 204.74/35.49    (33)  all_58_14 = e3
% 204.74/35.49    (34)  all_58_3 = all_4_2
% 204.74/35.49    (35)   ~ (all_52_3 = all_4_2)
% 204.74/35.49    (36)  op(all_6_2, e3) = all_6_1
% 204.74/35.49    (37)  all_58_2 = e3
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | COMBINE_EQS: (18), (37) imply:
% 204.74/35.49  |   (38)  all_52_3 = e3
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (38) implies:
% 204.74/35.49  |   (39)  all_52_3 = e3
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (28), (39) imply:
% 204.74/35.49  |   (40)   ~ (all_52_7 = e3)
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (40) implies:
% 204.74/35.49  |   (41)   ~ (all_52_7 = e3)
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (35), (39) imply:
% 204.74/35.49  |   (42)   ~ (all_4_2 = e3)
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (42) implies:
% 204.74/35.49  |   (43)   ~ (all_4_2 = e3)
% 204.74/35.49  | 
% 204.74/35.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.74/35.49  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.74/35.49  |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34), (36),
% 204.74/35.49  |            (41), (43) are inconsistent by sub-proof #1098.
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1098 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)   ~ (e3 = e1)
% 204.74/35.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.49    (3)   ~ (all_52_5 = all_52_13)
% 204.74/35.49    (4)  all_58_1 = all_52_9
% 204.74/35.49    (5)  op(all_52_15, all_52_15) = e0
% 204.74/35.49    (6)   ~ (all_4_2 = e3)
% 204.74/35.49    (7)  all_58_0 = all_6_2
% 204.74/35.49    (8)  all_58_13 = all_52_15
% 204.74/35.49    (9)  op(all_52_13, all_52_13) = e1
% 204.74/35.49    (10)   ~ (all_52_15 = e3)
% 204.74/35.49    (11)  op(e1, e3) = all_52_5
% 204.74/35.49    (12)   ~ (all_52_3 = all_52_5)
% 204.74/35.49    (13)  op(e0, e0) = all_14_2
% 204.74/35.49    (14)   ~ (e2 = e1)
% 204.74/35.49    (15)  all_56_8 = all_52_5
% 204.74/35.49    (16)  all_58_7 = all_52_13
% 204.74/35.49    (17)   ~ (all_52_5 = all_52_7)
% 204.74/35.49    (18)  all_58_12 = all_52_7
% 204.74/35.49    (19)   ~ (all_52_7 = e3)
% 204.74/35.49    (20)  all_58_2 = all_52_3
% 204.74/35.49    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.49    (22)   ~ (all_52_15 = all_14_2)
% 204.74/35.49    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49    (24)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.74/35.49    (25)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49    (26)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.49    (27)   ~ (all_52_5 = all_6_2)
% 204.74/35.49    (28)   ~ (all_52_9 = all_6_2)
% 204.74/35.49    (29)  op(e3, e3) = all_6_2
% 204.74/35.49    (30)  all_58_6 = all_52_5
% 204.74/35.49    (31)   ~ (e3 = e2)
% 204.74/35.49    (32)   ~ (all_6_1 = e2)
% 204.74/35.49    (33)  op(all_52_9, all_52_9) = e3
% 204.74/35.49    (34)  all_58_14 = e3
% 204.74/35.49    (35)  all_58_3 = all_4_2
% 204.74/35.49    (36)  op(all_6_2, e3) = all_6_1
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | BETA: splitting (25) gives:
% 204.74/35.49  | 
% 204.74/35.49  | Case 1:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (37)  all_58_1 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | COMBINE_EQS: (4), (37) imply:
% 204.74/35.49  | |   (38)  all_52_9 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | REF_CLOSE: (2), (28), (29), (33), (38) are inconsistent by sub-proof #1337.
% 204.74/35.49  | | 
% 204.74/35.49  | Case 2:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (39)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | BETA: splitting (39) gives:
% 204.74/35.49  | | 
% 204.74/35.49  | | Case 1:
% 204.74/35.49  | | | 
% 204.74/35.49  | | |   (40)  all_58_3 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | COMBINE_EQS: (35), (40) imply:
% 204.74/35.49  | | |   (41)  all_4_2 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (6), (41) imply:
% 204.74/35.49  | | |   (42)  $false
% 204.74/35.49  | | | 
% 204.74/35.49  | | | CLOSE: (42) is inconsistent.
% 204.74/35.49  | | | 
% 204.74/35.49  | | Case 2:
% 204.74/35.49  | | | 
% 204.74/35.49  | | |   (43)  all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 204.74/35.49  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.74/35.49  | | |            (24), (26), (27), (29), (30), (31), (32), (34), (36), (43) are
% 204.74/35.49  | | |            inconsistent by sub-proof #1099.
% 204.74/35.49  | | | 
% 204.74/35.49  | | End of split
% 204.74/35.49  | | 
% 204.74/35.49  | End of split
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1099 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)   ~ (e3 = e1)
% 204.74/35.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.49    (3)   ~ (all_52_5 = all_52_13)
% 204.74/35.49    (4)  op(all_52_15, all_52_15) = e0
% 204.74/35.49    (5)  all_58_0 = all_6_2
% 204.74/35.49    (6)  all_58_13 = all_52_15
% 204.74/35.49    (7)  op(all_52_13, all_52_13) = e1
% 204.74/35.49    (8)   ~ (all_52_15 = e3)
% 204.74/35.49    (9)  op(e1, e3) = all_52_5
% 204.74/35.49    (10)   ~ (all_52_3 = all_52_5)
% 204.74/35.49    (11)  op(e0, e0) = all_14_2
% 204.74/35.49    (12)   ~ (e2 = e1)
% 204.74/35.49    (13)  all_56_8 = all_52_5
% 204.74/35.49    (14)  all_58_7 = all_52_13
% 204.74/35.49    (15)   ~ (all_52_5 = all_52_7)
% 204.74/35.49    (16)  all_58_12 = all_52_7
% 204.74/35.49    (17)   ~ (all_52_7 = e3)
% 204.74/35.49    (18)  all_58_2 = all_52_3
% 204.74/35.49    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.49    (20)   ~ (all_52_15 = all_14_2)
% 204.74/35.49    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49    (22)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.74/35.49    (23)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.49    (24)   ~ (all_52_5 = all_6_2)
% 204.74/35.49    (25)  all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49    (26)  op(e3, e3) = all_6_2
% 204.74/35.49    (27)  all_58_6 = all_52_5
% 204.74/35.49    (28)   ~ (e3 = e2)
% 204.74/35.49    (29)   ~ (all_6_1 = e2)
% 204.74/35.49    (30)  all_58_14 = e3
% 204.74/35.49    (31)  op(all_6_2, e3) = all_6_1
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | BETA: splitting (25) gives:
% 204.74/35.49  | 
% 204.74/35.49  | Case 1:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (32)  all_58_7 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | COMBINE_EQS: (14), (32) imply:
% 204.74/35.49  | |   (33)  all_52_13 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | REDUCE: (3), (33) imply:
% 204.74/35.49  | |   (34)   ~ (all_52_5 = e3)
% 204.74/35.49  | | 
% 204.74/35.49  | | REDUCE: (7), (33) imply:
% 204.74/35.49  | |   (35)  op(e3, e3) = e1
% 204.74/35.49  | | 
% 204.74/35.49  | | GROUND_INST: instantiating (2) with all_6_2, e1, e3, e3, simplifying with
% 204.74/35.49  | |              (26), (35) gives:
% 204.74/35.49  | |   (36)  all_6_2 = e1
% 204.74/35.49  | | 
% 204.74/35.49  | | COMBINE_EQS: (5), (36) imply:
% 204.74/35.49  | |   (37)  all_58_0 = e1
% 204.74/35.49  | | 
% 204.74/35.49  | | REDUCE: (24), (36) imply:
% 204.74/35.49  | |   (38)   ~ (all_52_5 = e1)
% 204.74/35.49  | | 
% 204.74/35.49  | | REDUCE: (31), (36) imply:
% 204.74/35.49  | |   (39)  op(e1, e3) = all_6_1
% 204.74/35.49  | | 
% 204.74/35.49  | | BETA: splitting (19) gives:
% 204.74/35.49  | | 
% 204.74/35.49  | | Case 1:
% 204.74/35.49  | | | 
% 204.74/35.49  | | |   (40)  all_58_0 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REF_CLOSE: (1), (37), (40) are inconsistent by sub-proof #1244.
% 204.74/35.49  | | | 
% 204.74/35.49  | | Case 2:
% 204.74/35.49  | | | 
% 204.74/35.49  | | |   (41)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.74/35.49  | | | 
% 204.74/35.49  | | | BETA: splitting (41) gives:
% 204.74/35.49  | | | 
% 204.74/35.49  | | | Case 1:
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | |   (42)  all_58_2 = e3
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | COMBINE_EQS: (18), (42) imply:
% 204.74/35.49  | | | |   (43)  all_52_3 = e3
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | SIMP: (43) implies:
% 204.74/35.49  | | | |   (44)  all_52_3 = e3
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | REDUCE: (10), (44) imply:
% 204.74/35.49  | | | |   (45)   ~ (all_52_5 = e3)
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | GROUND_INST: instantiating (2) with all_52_5, all_6_1, e3, e1,
% 204.74/35.49  | | | |              simplifying with (9), (39) gives:
% 204.74/35.49  | | | |   (46)  all_52_5 = all_6_1
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | COMBINE_EQS: (13), (46) imply:
% 204.74/35.49  | | | |   (47)  all_56_8 = all_6_1
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | COMBINE_EQS: (27), (46) imply:
% 204.74/35.49  | | | |   (48)  all_58_6 = all_6_1
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | REDUCE: (15), (46) imply:
% 204.74/35.49  | | | |   (49)   ~ (all_52_7 = all_6_1)
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | SIMP: (49) implies:
% 204.74/35.49  | | | |   (50)   ~ (all_52_7 = all_6_1)
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | REDUCE: (34), (46) imply:
% 204.74/35.49  | | | |   (51)   ~ (all_6_1 = e3)
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | REDUCE: (38), (46) imply:
% 204.74/35.49  | | | |   (52)   ~ (all_6_1 = e1)
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | BETA: splitting (23) gives:
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | Case 1:
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | |   (53)  all_56_8 = e3
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | REF_CLOSE: (47), (51), (53) are inconsistent by sub-proof #1101.
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | Case 2:
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | |   (54)   ~ (all_56_8 = e3)
% 204.74/35.49  | | | | |   (55)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | BETA: splitting (55) gives:
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | Case 1:
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | |   (56)  all_56_8 = e2
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | REF_CLOSE: (29), (47), (56) are inconsistent by sub-proof #1321.
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | Case 2:
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | |   (57)   ~ (all_56_8 = e2)
% 204.74/35.49  | | | | | |   (58)  all_56_8 = e1 | all_56_8 = e0
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | BETA: splitting (21) gives:
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | | Case 1:
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | |   (59)  all_58_0 = e2
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | REF_CLOSE: (12), (37), (59) are inconsistent by sub-proof #1273.
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | Case 2:
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | |   (60)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | BETA: splitting (60) gives:
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | |   (61)  all_58_2 = e2
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | | REF_CLOSE: (28), (42), (61) are inconsistent by sub-proof #1124.
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | |   (62)  all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | | BETA: splitting (58) gives:
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | |   (63)  all_56_8 = e1
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REF_CLOSE: (47), (52), (63) are inconsistent by sub-proof
% 204.74/35.49  | | | | | | | | |            #1320.
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | |   (64)  all_56_8 = e0
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | COMBINE_EQS: (47), (64) imply:
% 204.74/35.49  | | | | | | | | |   (65)  all_6_1 = e0
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | SIMP: (65) implies:
% 204.74/35.49  | | | | | | | | |   (66)  all_6_1 = e0
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | COMBINE_EQS: (48), (66) imply:
% 204.74/35.49  | | | | | | | | |   (67)  all_58_6 = e0
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REDUCE: (50), (66) imply:
% 204.74/35.49  | | | | | | | | |   (68)   ~ (all_52_7 = e0)
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REDUCE: (51), (66) imply:
% 204.74/35.49  | | | | | | | | |   (69)   ~ (e3 = e0)
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | SIMP: (69) implies:
% 204.74/35.49  | | | | | | | | |   (70)   ~ (e3 = e0)
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | REDUCE: (29), (66) imply:
% 204.74/35.49  | | | | | | | | |   (71)   ~ (e2 = e0)
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | SIMP: (71) implies:
% 204.74/35.49  | | | | | | | | |   (72)   ~ (e2 = e0)
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | BETA: splitting (62) gives:
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | |   (73)  all_58_6 = e2
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | COMBINE_EQS: (67), (73) imply:
% 204.74/35.49  | | | | | | | | | |   (74)  e2 = e0
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | REDUCE: (72), (74) imply:
% 204.74/35.49  | | | | | | | | | |   (75)  $false
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | CLOSE: (75) is inconsistent.
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | |   (76)  all_58_12 = e2
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | COMBINE_EQS: (16), (76) imply:
% 204.74/35.49  | | | | | | | | | |   (77)  all_52_7 = e2
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | SIMP: (77) implies:
% 204.74/35.49  | | | | | | | | | |   (78)  all_52_7 = e2
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | BETA: splitting (22) gives:
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | |   (79)  all_58_12 = e0
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | REF_CLOSE: (72), (76), (79) are inconsistent by sub-proof
% 204.74/35.49  | | | | | | | | | | |            #1153.
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | |   (80)  all_58_13 = e0 | all_58_14 = e0
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | BETA: splitting (80) gives:
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | Case 1:
% 204.74/35.49  | | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | |   (81)  all_58_13 = e0
% 204.74/35.49  | | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (11), (20), (81) are inconsistent
% 204.74/35.49  | | | | | | | | | | | |            by sub-proof #1100.
% 204.74/35.49  | | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | Case 2:
% 204.74/35.49  | | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | |   (82)  all_58_14 = e0
% 204.74/35.49  | | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | | REF_CLOSE: (30), (70), (82) are inconsistent by sub-proof
% 204.74/35.49  | | | | | | | | | | | |            #1151.
% 204.74/35.49  | | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | | End of split
% 204.74/35.49  | | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | | End of split
% 204.74/35.49  | | | | | | | | | | 
% 204.74/35.49  | | | | | | | | | End of split
% 204.74/35.49  | | | | | | | | | 
% 204.74/35.49  | | | | | | | | End of split
% 204.74/35.49  | | | | | | | | 
% 204.74/35.49  | | | | | | | End of split
% 204.74/35.49  | | | | | | | 
% 204.74/35.49  | | | | | | End of split
% 204.74/35.49  | | | | | | 
% 204.74/35.49  | | | | | End of split
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | End of split
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | Case 2:
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | |   (83)  all_58_6 = e3 | all_58_12 = e3
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | REF_CLOSE: (16), (17), (27), (34), (83) are inconsistent by sub-proof
% 204.74/35.49  | | | |            #1243.
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | End of split
% 204.74/35.49  | | | 
% 204.74/35.49  | | End of split
% 204.74/35.49  | | 
% 204.74/35.49  | Case 2:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (84)  all_58_13 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | REF_CLOSE: (6), (8), (84) are inconsistent by sub-proof #1360.
% 204.74/35.49  | | 
% 204.74/35.49  | End of split
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1100 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.49    (2)  op(all_52_15, all_52_15) = e0
% 204.74/35.49    (3)  all_58_13 = all_52_15
% 204.74/35.49    (4)  op(e0, e0) = all_14_2
% 204.74/35.49    (5)   ~ (all_52_15 = all_14_2)
% 204.74/35.49    (6)  all_58_13 = e0
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | COMBINE_EQS: (3), (6) imply:
% 204.74/35.49  |   (7)  all_52_15 = e0
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (7) implies:
% 204.74/35.49  |   (8)  all_52_15 = e0
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (5), (8) imply:
% 204.74/35.49  |   (9)   ~ (all_14_2 = e0)
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (9) implies:
% 204.74/35.49  |   (10)   ~ (all_14_2 = e0)
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (2), (8) imply:
% 204.74/35.49  |   (11)  op(e0, e0) = e0
% 204.74/35.49  | 
% 204.74/35.49  | GROUND_INST: instantiating (1) with all_14_2, e0, e0, e0, simplifying with
% 204.74/35.49  |              (4), (11) gives:
% 204.74/35.49  |   (12)  all_14_2 = e0
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (10), (12) imply:
% 204.74/35.49  |   (13)  $false
% 204.74/35.49  | 
% 204.74/35.49  | CLOSE: (13) is inconsistent.
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1101 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)  all_56_8 = all_6_1
% 204.74/35.49    (2)  all_56_8 = e3
% 204.74/35.49    (3)   ~ (all_6_1 = e3)
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | COMBINE_EQS: (1), (2) imply:
% 204.74/35.49  |   (4)  all_6_1 = e3
% 204.74/35.49  | 
% 204.74/35.49  | SIMP: (4) implies:
% 204.74/35.49  |   (5)  all_6_1 = e3
% 204.74/35.49  | 
% 204.74/35.49  | REDUCE: (3), (5) imply:
% 204.74/35.49  |   (6)  $false
% 204.74/35.49  | 
% 204.74/35.49  | CLOSE: (6) is inconsistent.
% 204.74/35.49  | 
% 204.74/35.49  End of proof
% 204.74/35.49  
% 204.74/35.49  Sub-proof #1102 shows that the following formulas are inconsistent:
% 204.74/35.49  ----------------------------------------------------------------
% 204.74/35.49    (1)   ~ (all_52_25 = all_52_27)
% 204.74/35.49    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.74/35.49    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.49    (4)  all_58_1 = all_52_9
% 204.74/35.49    (5)  all_58_0 = all_6_2
% 204.74/35.49    (6)   ~ (all_52_17 = all_10_2)
% 204.74/35.49    (7)  op(e3, e3) = all_52_6
% 204.74/35.49    (8)  op(e3, e0) = all_52_25
% 204.74/35.49    (9)  op(all_52_5, all_52_5) = all_52_4
% 204.74/35.49    (10)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.74/35.49    (11)   ~ (all_52_27 = all_52_29)
% 204.74/35.49    (12)  all_58_13 = all_52_15
% 204.74/35.49    (13)  op(all_52_13, all_52_13) = e1
% 204.74/35.49    (14)  all_58_9 = all_52_25
% 204.74/35.49    (15)   ~ (all_52_29 = all_14_2)
% 204.74/35.49    (16)   ~ (all_52_15 = e3)
% 204.74/35.49    (17)  op(all_52_27, all_52_27) = all_52_26
% 204.74/35.49    (18)  op(e1, e3) = all_52_5
% 204.74/35.49    (19)  op(e2, e2) = all_4_2
% 204.74/35.49    (20)   ~ (all_52_3 = all_52_5)
% 204.74/35.49    (21)  all_58_11 = all_52_29
% 204.74/35.49    (22)  op(e0, e0) = all_14_2
% 204.74/35.49    (23)  all_56_11 = all_52_29
% 204.74/35.49    (24)   ~ (all_4_1 = e1)
% 204.74/35.49    (25)   ~ (all_6_2 = e3)
% 204.74/35.49    (26)   ~ (e2 = e1)
% 204.74/35.49    (27)  all_58_10 = all_52_27
% 204.74/35.49    (28)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.74/35.49    (29)  all_56_8 = all_52_5
% 204.74/35.49    (30)   ~ (all_52_25 = all_52_29)
% 204.74/35.49    (31)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.74/35.49    (32)  all_58_7 = all_52_13
% 204.74/35.49    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.74/35.49    (34)  all_58_2 = all_52_3
% 204.74/35.49    (35)  op(e3, all_6_1) = all_6_0
% 204.74/35.49    (36)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.74/35.49    (37)  all_56_7 = all_52_27
% 204.74/35.49    (38)  op(all_4_2, e2) = all_4_1
% 204.74/35.49    (39)   ~ (all_52_5 = e3)
% 204.74/35.49    (40)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.74/35.49    (41)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49    (42)   ~ (all_6_0 = e2)
% 204.74/35.49    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.74/35.49    (44)   ~ (all_52_9 = all_52_25)
% 204.74/35.49    (45)  all_58_15 = all_14_2
% 204.74/35.49    (46)  all_58_8 = all_10_2
% 204.74/35.49    (47)  op(all_52_29, all_52_29) = all_52_28
% 204.74/35.49    (48)  op(all_52_17, all_52_17) = all_52_16
% 204.74/35.49    (49)   ~ (all_52_25 = all_6_2)
% 204.74/35.49    (50)   ~ (all_52_5 = all_6_2)
% 204.74/35.49    (51)  op(all_4_2, all_4_2) = e2
% 204.74/35.49    (52)   ~ (all_52_9 = all_6_2)
% 204.74/35.49    (53)  op(e3, e3) = all_6_2
% 204.74/35.49    (54)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.74/35.49    (55)  all_56_3 = all_52_25
% 204.74/35.49    (56)  all_56_1 = all_52_9
% 204.74/35.49    (57)   ~ (all_52_27 = all_4_2)
% 204.74/35.49    (58)  all_58_6 = all_52_5
% 204.74/35.49    (59)  op(e3, e2) = all_52_9
% 204.74/35.49    (60)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.74/35.49    (61)   ~ (e3 = e2)
% 204.74/35.49    (62)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.74/35.49    (63)   ~ (all_52_9 = all_52_17)
% 204.74/35.49    (64)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.74/35.49    (65)  all_58_12 = e3
% 204.74/35.49    (66)   ~ (all_6_1 = e2)
% 204.74/35.49    (67)  op(all_52_9, all_52_9) = e3
% 204.74/35.49    (68)  all_58_3 = all_4_2
% 204.74/35.49    (69)  op(all_6_2, e3) = all_6_1
% 204.74/35.49    (70)   ~ (all_52_13 = all_52_29)
% 204.74/35.49    (71)  all_58_4 = all_52_17
% 204.74/35.49    (72)  op(all_52_25, all_52_25) = all_52_24
% 204.74/35.49    (73)   ~ (all_14_2 = e3)
% 204.74/35.49  
% 204.74/35.49  Begin of proof
% 204.74/35.49  | 
% 204.74/35.49  | BETA: splitting (54) gives:
% 204.74/35.49  | 
% 204.74/35.49  | Case 1:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (74)  all_58_0 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | COMBINE_EQS: (5), (74) imply:
% 204.74/35.49  | |   (75)  all_6_2 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | REDUCE: (25), (75) imply:
% 204.74/35.49  | |   (76)  $false
% 204.74/35.49  | | 
% 204.74/35.49  | | CLOSE: (76) is inconsistent.
% 204.74/35.49  | | 
% 204.74/35.49  | Case 2:
% 204.74/35.49  | | 
% 204.74/35.49  | |   (77)   ~ (all_58_0 = e3)
% 204.74/35.49  | |   (78)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.74/35.49  | | 
% 204.74/35.49  | | BETA: splitting (36) gives:
% 204.74/35.49  | | 
% 204.74/35.49  | | Case 1:
% 204.74/35.49  | | | 
% 204.74/35.49  | | |   (79)  all_58_0 = e1
% 204.74/35.49  | | | 
% 204.74/35.49  | | | COMBINE_EQS: (5), (79) imply:
% 204.74/35.49  | | |   (80)  all_6_2 = e1
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (50), (80) imply:
% 204.74/35.49  | | |   (81)   ~ (all_52_5 = e1)
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (52), (80) imply:
% 204.74/35.49  | | |   (82)   ~ (all_52_9 = e1)
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (49), (80) imply:
% 204.74/35.49  | | |   (83)   ~ (all_52_25 = e1)
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (69), (80) imply:
% 204.74/35.49  | | |   (84)  op(e1, e3) = all_6_1
% 204.74/35.49  | | | 
% 204.74/35.49  | | | GROUND_INST: instantiating (3) with all_52_5, all_6_1, e3, e1, simplifying
% 204.74/35.49  | | |              with (18), (84) gives:
% 204.74/35.49  | | |   (85)  all_52_5 = all_6_1
% 204.74/35.49  | | | 
% 204.74/35.49  | | | COMBINE_EQS: (29), (85) imply:
% 204.74/35.49  | | |   (86)  all_56_8 = all_6_1
% 204.74/35.49  | | | 
% 204.74/35.49  | | | COMBINE_EQS: (58), (85) imply:
% 204.74/35.49  | | |   (87)  all_58_6 = all_6_1
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (20), (85) imply:
% 204.74/35.49  | | |   (88)   ~ (all_52_3 = all_6_1)
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (81), (85) imply:
% 204.74/35.49  | | |   (89)   ~ (all_6_1 = e1)
% 204.74/35.49  | | | 
% 204.74/35.49  | | | REDUCE: (9), (85) imply:
% 204.74/35.49  | | |   (90)  op(all_6_1, all_6_1) = all_52_4
% 204.74/35.49  | | | 
% 204.74/35.49  | | | BETA: splitting (41) gives:
% 204.74/35.49  | | | 
% 204.74/35.49  | | | Case 1:
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | |   (91)  all_58_0 = e2
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | REF_CLOSE: (26), (79), (91) are inconsistent by sub-proof #1273.
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | Case 2:
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | |   (92)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | BETA: splitting (92) gives:
% 204.74/35.49  | | | | 
% 204.74/35.49  | | | | Case 1:
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | |   (93)  all_58_2 = e2
% 204.74/35.49  | | | | | 
% 204.74/35.49  | | | | | COMBINE_EQS: (34), (93) imply:
% 204.74/35.50  | | | | |   (94)  all_52_3 = e2
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | SIMP: (94) implies:
% 204.74/35.50  | | | | |   (95)  all_52_3 = e2
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | REDUCE: (88), (95) imply:
% 204.74/35.50  | | | | |   (96)   ~ (all_6_1 = e2)
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | REDUCE: (2), (95) imply:
% 204.74/35.50  | | | | |   (97)  op(e2, e2) = all_52_2
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | BETA: splitting (28) gives:
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | Case 1:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | |   (98)  all_56_8 = e2
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | REF_CLOSE: (66), (86), (98) are inconsistent by sub-proof #1321.
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | Case 2:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | |   (99)  all_56_8 = e1 | all_56_8 = e0
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | BETA: splitting (99) gives:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | Case 1:
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | |   (100)  all_56_8 = e1
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REF_CLOSE: (86), (89), (100) are inconsistent by sub-proof #1320.
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | Case 2:
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | |   (101)  all_56_8 = e0
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | COMBINE_EQS: (86), (101) imply:
% 204.74/35.50  | | | | | | |   (102)  all_6_1 = e0
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | SIMP: (102) implies:
% 204.74/35.50  | | | | | | |   (103)  all_6_1 = e0
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (90), (103) imply:
% 204.74/35.50  | | | | | | |   (104)  op(e0, e0) = all_52_4
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (35), (103) imply:
% 204.74/35.50  | | | | | | |   (105)  op(e3, e0) = all_6_0
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | GROUND_INST: instantiating (3) with all_14_2, all_52_4, e0, e0,
% 204.74/35.50  | | | | | | |              simplifying with (22), (104) gives:
% 204.74/35.50  | | | | | | |   (106)  all_52_4 = all_14_2
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_52_2, e2, e2,
% 204.74/35.50  | | | | | | |              simplifying with (19), (97) gives:
% 204.74/35.50  | | | | | | |   (107)  all_52_2 = all_4_2
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | GROUND_INST: instantiating (3) with all_52_25, all_6_0, e0, e3,
% 204.74/35.50  | | | | | | |              simplifying with (8), (105) gives:
% 204.74/35.50  | | | | | | |   (108)  all_52_25 = all_6_0
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | COMBINE_EQS: (55), (108) imply:
% 204.74/35.50  | | | | | | |   (109)  all_56_3 = all_6_0
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (44), (108) imply:
% 204.74/35.50  | | | | | | |   (110)   ~ (all_52_9 = all_6_0)
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (83), (108) imply:
% 204.74/35.50  | | | | | | |   (111)   ~ (all_6_0 = e1)
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (72), (108) imply:
% 204.74/35.50  | | | | | | |   (112)  op(all_6_0, all_6_0) = all_52_24
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | BETA: splitting (31) gives:
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | Case 1:
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | |   (113)  all_56_3 = e2
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | | COMBINE_EQS: (109), (113) imply:
% 204.74/35.50  | | | | | | | |   (114)  all_6_0 = e2
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | | REDUCE: (42), (114) imply:
% 204.74/35.50  | | | | | | | |   (115)  $false
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | | CLOSE: (115) is inconsistent.
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | Case 2:
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | |   (116)  all_56_3 = e1 | all_56_3 = e0
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | | BETA: splitting (116) gives:
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | | Case 1:
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | |   (117)  all_56_3 = e1
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | COMBINE_EQS: (109), (117) imply:
% 204.74/35.50  | | | | | | | | |   (118)  all_6_0 = e1
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | REDUCE: (111), (118) imply:
% 204.74/35.50  | | | | | | | | |   (119)  $false
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | CLOSE: (119) is inconsistent.
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | Case 2:
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | |   (120)  all_56_3 = e0
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | COMBINE_EQS: (109), (120) imply:
% 204.74/35.50  | | | | | | | | |   (121)  all_6_0 = e0
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | REDUCE: (110), (121) imply:
% 204.74/35.50  | | | | | | | | |   (122)   ~ (all_52_9 = e0)
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | REDUCE: (112), (121) imply:
% 204.74/35.50  | | | | | | | | |   (123)  op(e0, e0) = all_52_24
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | | REF_CLOSE: (3), (4), (10), (12), (14), (15), (16), (19), (21),
% 204.74/35.50  | | | | | | | | |            (22), (24), (25), (27), (30), (32), (37), (38),
% 204.74/35.50  | | | | | | | | |            (43), (45), (47), (48), (51), (52), (53), (56),
% 204.74/35.50  | | | | | | | | |            (57), (59), (60), (62), (63), (64), (67), (68),
% 204.74/35.50  | | | | | | | | |            (70), (71), (73), (78), (82), (122), (123) are
% 204.74/35.50  | | | | | | | | |            inconsistent by sub-proof #1106.
% 204.74/35.50  | | | | | | | | | 
% 204.74/35.50  | | | | | | | | End of split
% 204.74/35.50  | | | | | | | | 
% 204.74/35.50  | | | | | | | End of split
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | End of split
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | End of split
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | Case 2:
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | |   (124)  all_58_6 = e2 | all_58_12 = e2
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | BETA: splitting (124) gives:
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | Case 1:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | |   (125)  all_58_6 = e2
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | REF_CLOSE: (66), (87), (125) are inconsistent by sub-proof #1211.
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | Case 2:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | |   (126)  all_58_12 = e2
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | REF_CLOSE: (61), (65), (126) are inconsistent by sub-proof #1210.
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | End of split
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | End of split
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | End of split
% 204.74/35.50  | | | 
% 204.74/35.50  | | Case 2:
% 204.74/35.50  | | | 
% 204.74/35.50  | | |   (127)   ~ (all_58_0 = e1)
% 204.74/35.50  | | | 
% 204.74/35.50  | | | REDUCE: (5), (127) imply:
% 204.74/35.50  | | |   (128)   ~ (all_6_2 = e1)
% 204.74/35.50  | | | 
% 204.74/35.50  | | | BETA: splitting (40) gives:
% 204.74/35.50  | | | 
% 204.74/35.50  | | | Case 1:
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | |   (129)  all_56_11 = e3
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | COMBINE_EQS: (23), (129) imply:
% 204.74/35.50  | | | |   (130)  all_52_29 = e3
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | SIMP: (130) implies:
% 204.74/35.50  | | | |   (131)  all_52_29 = e3
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | REDUCE: (11), (131) imply:
% 204.74/35.50  | | | |   (132)   ~ (all_52_27 = e3)
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | REDUCE: (15), (131) imply:
% 204.74/35.50  | | | |   (133)   ~ (all_14_2 = e3)
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | REF_CLOSE: (3), (4), (12), (14), (15), (16), (21), (22), (24), (27),
% 204.74/35.50  | | | |            (30), (32), (38), (43), (45), (47), (48), (51), (52), (53),
% 204.74/35.50  | | | |            (56), (59), (60), (62), (63), (64), (67), (68), (70), (71),
% 204.74/35.50  | | | |            (73), (78), (132) are inconsistent by sub-proof #1107.
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | Case 2:
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | |   (134)   ~ (all_56_11 = e3)
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | REDUCE: (23), (134) imply:
% 204.74/35.50  | | | |   (135)   ~ (all_52_29 = e3)
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | BETA: splitting (60) gives:
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | | Case 1:
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | |   (136)  all_58_10 = e3
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | COMBINE_EQS: (27), (136) imply:
% 204.74/35.50  | | | | |   (137)  all_52_27 = e3
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | SIMP: (137) implies:
% 204.74/35.50  | | | | |   (138)  all_52_27 = e3
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | REDUCE: (1), (138) imply:
% 204.74/35.50  | | | | |   (139)   ~ (all_52_25 = e3)
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | REDUCE: (11), (138) imply:
% 204.74/35.50  | | | | |   (140)   ~ (all_52_29 = e3)
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | REDUCE: (17), (138) imply:
% 204.74/35.50  | | | | |   (141)  op(e3, e3) = all_52_26
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_26, e3, e3,
% 204.74/35.50  | | | | |              simplifying with (53), (141) gives:
% 204.74/35.50  | | | | |   (142)  all_52_26 = all_6_2
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | BETA: splitting (33) gives:
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | Case 1:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | |   (143)  all_58_6 = e3
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | REF_CLOSE: (39), (58), (143) are inconsistent by sub-proof #1328.
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | Case 2:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | |   (144)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | BETA: splitting (64) gives:
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | | Case 1:
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | |   (145)  all_58_4 = e3
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | COMBINE_EQS: (71), (145) imply:
% 204.74/35.50  | | | | | | |   (146)  all_52_17 = e3
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | SIMP: (146) implies:
% 204.74/35.50  | | | | | | |   (147)  all_52_17 = e3
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (6), (147) imply:
% 204.74/35.50  | | | | | | |   (148)   ~ (all_10_2 = e3)
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | SIMP: (148) implies:
% 204.74/35.50  | | | | | | |   (149)   ~ (all_10_2 = e3)
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REF_CLOSE: (3), (7), (13), (21), (32), (46), (53), (128), (135),
% 204.74/35.50  | | | | | | |            (144), (149) are inconsistent by sub-proof #1104.
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | Case 2:
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | |   (150)   ~ (all_58_4 = e3)
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REDUCE: (71), (150) imply:
% 204.74/35.50  | | | | | | |   (151)   ~ (all_52_17 = e3)
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | | REF_CLOSE: (3), (4), (14), (52), (53), (67), (71), (78), (139),
% 204.74/35.50  | | | | | | |            (151) are inconsistent by sub-proof #1138.
% 204.74/35.50  | | | | | | | 
% 204.74/35.50  | | | | | | End of split
% 204.74/35.50  | | | | | | 
% 204.74/35.50  | | | | | End of split
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | Case 2:
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | |   (152)  all_58_11 = e3 | all_58_15 = e3
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | | REF_CLOSE: (21), (45), (73), (135), (152) are inconsistent by
% 204.74/35.50  | | | | |            sub-proof #1103.
% 204.74/35.50  | | | | | 
% 204.74/35.50  | | | | End of split
% 204.74/35.50  | | | | 
% 204.74/35.50  | | | End of split
% 204.74/35.50  | | | 
% 204.74/35.50  | | End of split
% 204.74/35.50  | | 
% 204.74/35.50  | End of split
% 204.74/35.50  | 
% 204.74/35.50  End of proof
% 204.74/35.50  
% 204.74/35.50  Sub-proof #1103 shows that the following formulas are inconsistent:
% 204.74/35.50  ----------------------------------------------------------------
% 204.74/35.50    (1)  all_58_11 = all_52_29
% 204.74/35.50    (2)  all_58_11 = e3 | all_58_15 = e3
% 204.74/35.50    (3)   ~ (all_52_29 = e3)
% 204.74/35.50    (4)  all_58_15 = all_14_2
% 204.74/35.50    (5)   ~ (all_14_2 = e3)
% 204.74/35.50  
% 204.74/35.50  Begin of proof
% 204.74/35.50  | 
% 204.74/35.50  | BETA: splitting (2) gives:
% 204.74/35.50  | 
% 204.74/35.50  | Case 1:
% 204.74/35.50  | | 
% 204.74/35.50  | |   (6)  all_58_11 = e3
% 204.74/35.50  | | 
% 204.74/35.50  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #1323.
% 204.74/35.50  | | 
% 204.74/35.50  | Case 2:
% 204.74/35.50  | | 
% 204.74/35.50  | |   (7)  all_58_15 = e3
% 204.74/35.50  | | 
% 204.74/35.50  | | COMBINE_EQS: (4), (7) imply:
% 204.74/35.50  | |   (8)  all_14_2 = e3
% 204.74/35.50  | | 
% 204.74/35.50  | | REDUCE: (5), (8) imply:
% 204.74/35.50  | |   (9)  $false
% 204.74/35.50  | | 
% 204.74/35.50  | | CLOSE: (9) is inconsistent.
% 204.74/35.50  | | 
% 204.74/35.50  | End of split
% 204.74/35.50  | 
% 204.74/35.50  End of proof
% 204.74/35.50  
% 204.74/35.50  Sub-proof #1104 shows that the following formulas are inconsistent:
% 204.74/35.50  ----------------------------------------------------------------
% 204.74/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.74/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.74/35.50    (2)  op(e3, e3) = all_52_6
% 204.74/35.50    (3)  op(all_52_13, all_52_13) = e1
% 204.74/35.50    (4)  all_58_11 = all_52_29
% 204.74/35.50    (5)  all_58_7 = all_52_13
% 204.74/35.50    (6)   ~ (all_52_29 = e3)
% 204.74/35.50    (7)   ~ (all_10_2 = e3)
% 204.74/35.50    (8)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.74/35.50    (9)  all_58_8 = all_10_2
% 204.74/35.50    (10)  op(e3, e3) = all_6_2
% 204.74/35.50    (11)   ~ (all_6_2 = e1)
% 204.74/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | BETA: splitting (8) gives:
% 204.76/35.50  | 
% 204.76/35.50  | Case 1:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (12)  all_58_7 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | COMBINE_EQS: (5), (12) imply:
% 204.76/35.50  | |   (13)  all_52_13 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | REDUCE: (3), (13) imply:
% 204.76/35.50  | |   (14)  op(e3, e3) = e1
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (1), (2), (10), (11), (14) are inconsistent by sub-proof #1105.
% 204.76/35.50  | | 
% 204.76/35.50  | Case 2:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (15)  all_58_8 = e3 | all_58_11 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (4), (6), (7), (9), (15) are inconsistent by sub-proof #1140.
% 204.76/35.50  | | 
% 204.76/35.50  | End of split
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1105 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (2)  op(e3, e3) = all_52_6
% 204.76/35.50    (3)  op(e3, e3) = all_6_2
% 204.76/35.50    (4)  op(e3, e3) = e1
% 204.76/35.50    (5)   ~ (all_6_2 = e1)
% 204.76/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | GROUND_INST: instantiating (1) with all_6_2, all_52_6, e3, e3, simplifying
% 204.76/35.50  |              with (2), (3) gives:
% 204.76/35.50  |   (6)  all_52_6 = all_6_2
% 204.76/35.50  | 
% 204.76/35.50  | GROUND_INST: instantiating (1) with e1, all_52_6, e3, e3, simplifying with
% 204.76/35.50  |              (2), (4) gives:
% 204.76/35.50  |   (7)  all_52_6 = e1
% 204.76/35.50  | 
% 204.76/35.50  | COMBINE_EQS: (6), (7) imply:
% 204.76/35.50  |   (8)  all_6_2 = e1
% 204.76/35.50  | 
% 204.76/35.50  | SIMP: (8) implies:
% 204.76/35.50  |   (9)  all_6_2 = e1
% 204.76/35.50  | 
% 204.76/35.50  | REDUCE: (5), (9) imply:
% 204.76/35.50  |   (10)  $false
% 204.76/35.50  | 
% 204.76/35.50  | CLOSE: (10) is inconsistent.
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1106 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (2)  all_58_1 = all_52_9
% 204.76/35.50    (3)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.76/35.50    (4)  all_58_13 = all_52_15
% 204.76/35.50    (5)  all_58_9 = all_52_25
% 204.76/35.50    (6)   ~ (all_52_29 = all_14_2)
% 204.76/35.50    (7)   ~ (all_52_15 = e3)
% 204.76/35.50    (8)  op(e2, e2) = all_4_2
% 204.76/35.50    (9)  all_58_11 = all_52_29
% 204.76/35.50    (10)  op(e0, e0) = all_14_2
% 204.76/35.50    (11)   ~ (all_4_1 = e1)
% 204.76/35.50    (12)   ~ (all_6_2 = e3)
% 204.76/35.50    (13)  all_58_10 = all_52_27
% 204.76/35.50    (14)   ~ (all_52_25 = all_52_29)
% 204.76/35.50    (15)  all_58_7 = all_52_13
% 204.76/35.50    (16)  all_56_7 = all_52_27
% 204.76/35.50    (17)  op(all_4_2, e2) = all_4_1
% 204.76/35.50    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.50    (19)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.76/35.50    (20)  all_58_15 = all_14_2
% 204.76/35.50    (21)  op(e0, e0) = all_52_24
% 204.76/35.50    (22)  op(all_52_29, all_52_29) = all_52_28
% 204.76/35.50    (23)  op(all_52_17, all_52_17) = all_52_16
% 204.76/35.50    (24)  op(all_4_2, all_4_2) = e2
% 204.76/35.50    (25)   ~ (all_52_9 = all_6_2)
% 204.76/35.50    (26)   ~ (all_52_9 = e1)
% 204.76/35.50    (27)  op(e3, e3) = all_6_2
% 204.76/35.50    (28)  all_56_1 = all_52_9
% 204.76/35.50    (29)   ~ (all_52_27 = all_4_2)
% 204.76/35.50    (30)  op(e3, e2) = all_52_9
% 204.76/35.50    (31)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.76/35.50    (32)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50    (33)   ~ (all_52_9 = all_52_17)
% 204.76/35.50    (34)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.76/35.50    (35)   ~ (all_52_9 = e0)
% 204.76/35.50    (36)  op(all_52_9, all_52_9) = e3
% 204.76/35.50    (37)  all_58_3 = all_4_2
% 204.76/35.50    (38)   ~ (all_52_13 = all_52_29)
% 204.76/35.50    (39)  all_58_4 = all_52_17
% 204.76/35.50    (40)   ~ (all_14_2 = e3)
% 204.76/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | GROUND_INST: instantiating (1) with all_14_2, all_52_24, e0, e0, simplifying
% 204.76/35.50  |              with (10), (21) gives:
% 204.76/35.50  |   (41)  all_52_24 = all_14_2
% 204.76/35.50  | 
% 204.76/35.50  | BETA: splitting (3) gives:
% 204.76/35.50  | 
% 204.76/35.50  | Case 1:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (42)  all_56_7 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | COMBINE_EQS: (16), (42) imply:
% 204.76/35.50  | |   (43)  all_52_27 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | SIMP: (43) implies:
% 204.76/35.50  | |   (44)  all_52_27 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | REDUCE: (29), (44) imply:
% 204.76/35.50  | |   (45)   ~ (all_4_2 = e3)
% 204.76/35.50  | | 
% 204.76/35.50  | | SIMP: (45) implies:
% 204.76/35.50  | |   (46)   ~ (all_4_2 = e3)
% 204.76/35.50  | | 
% 204.76/35.50  | | BETA: splitting (32) gives:
% 204.76/35.50  | | 
% 204.76/35.50  | | Case 1:
% 204.76/35.50  | | | 
% 204.76/35.50  | | |   (47)  all_56_1 = e3
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REF_CLOSE: (1), (12), (27), (28), (36), (47) are inconsistent by sub-proof
% 204.76/35.50  | | |            #1110.
% 204.76/35.50  | | | 
% 204.76/35.50  | | Case 2:
% 204.76/35.50  | | | 
% 204.76/35.50  | | |   (48)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REF_CLOSE: (1), (8), (26), (28), (35), (36), (46), (48) are inconsistent
% 204.76/35.50  | | |            by sub-proof #1109.
% 204.76/35.50  | | | 
% 204.76/35.50  | | End of split
% 204.76/35.50  | | 
% 204.76/35.50  | Case 2:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (49)   ~ (all_56_7 = e3)
% 204.76/35.50  | | 
% 204.76/35.50  | | REDUCE: (16), (49) imply:
% 204.76/35.50  | |   (50)   ~ (all_52_27 = e3)
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13), (14), (15),
% 204.76/35.50  | |            (17), (18), (19), (20), (22), (23), (24), (25), (27), (28), (30),
% 204.76/35.50  | |            (31), (32), (33), (34), (36), (37), (38), (39), (40), (50) are
% 204.76/35.50  | |            inconsistent by sub-proof #1107.
% 204.76/35.50  | | 
% 204.76/35.50  | End of split
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1107 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (2)  all_58_1 = all_52_9
% 204.76/35.50    (3)  all_58_13 = all_52_15
% 204.76/35.50    (4)  all_58_9 = all_52_25
% 204.76/35.50    (5)   ~ (all_52_29 = all_14_2)
% 204.76/35.50    (6)   ~ (all_52_15 = e3)
% 204.76/35.50    (7)  all_58_11 = all_52_29
% 204.76/35.50    (8)  op(e0, e0) = all_14_2
% 204.76/35.50    (9)   ~ (all_4_1 = e1)
% 204.76/35.50    (10)  all_58_10 = all_52_27
% 204.76/35.50    (11)   ~ (all_52_25 = all_52_29)
% 204.76/35.50    (12)  all_58_7 = all_52_13
% 204.76/35.50    (13)  op(all_4_2, e2) = all_4_1
% 204.76/35.50    (14)   ~ (all_52_27 = e3)
% 204.76/35.50    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.50    (16)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.76/35.50    (17)  all_58_15 = all_14_2
% 204.76/35.50    (18)  op(all_52_29, all_52_29) = all_52_28
% 204.76/35.50    (19)  op(all_52_17, all_52_17) = all_52_16
% 204.76/35.50    (20)  op(all_4_2, all_4_2) = e2
% 204.76/35.50    (21)   ~ (all_52_9 = all_6_2)
% 204.76/35.50    (22)  op(e3, e3) = all_6_2
% 204.76/35.50    (23)  all_56_1 = all_52_9
% 204.76/35.50    (24)  op(e3, e2) = all_52_9
% 204.76/35.50    (25)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.76/35.50    (26)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50    (27)   ~ (all_52_9 = all_52_17)
% 204.76/35.50    (28)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.76/35.50    (29)  op(all_52_9, all_52_9) = e3
% 204.76/35.50    (30)  all_58_3 = all_4_2
% 204.76/35.50    (31)   ~ (all_52_13 = all_52_29)
% 204.76/35.50    (32)  all_58_4 = all_52_17
% 204.76/35.50    (33)   ~ (all_14_2 = e3)
% 204.76/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | BETA: splitting (25) gives:
% 204.76/35.50  | 
% 204.76/35.50  | Case 1:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (34)  all_58_10 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (10), (14), (34) are inconsistent by sub-proof #1301.
% 204.76/35.50  | | 
% 204.76/35.50  | Case 2:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (35)  all_58_11 = e3 | all_58_15 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | BETA: splitting (35) gives:
% 204.76/35.50  | | 
% 204.76/35.50  | | Case 1:
% 204.76/35.50  | | | 
% 204.76/35.50  | | |   (36)  all_58_11 = e3
% 204.76/35.50  | | | 
% 204.76/35.50  | | | COMBINE_EQS: (7), (36) imply:
% 204.76/35.50  | | |   (37)  all_52_29 = e3
% 204.76/35.50  | | | 
% 204.76/35.50  | | | SIMP: (37) implies:
% 204.76/35.50  | | |   (38)  all_52_29 = e3
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REDUCE: (31), (38) imply:
% 204.76/35.50  | | |   (39)   ~ (all_52_13 = e3)
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REDUCE: (11), (38) imply:
% 204.76/35.50  | | |   (40)   ~ (all_52_25 = e3)
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REDUCE: (5), (38) imply:
% 204.76/35.50  | | |   (41)   ~ (all_14_2 = e3)
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REDUCE: (18), (38) imply:
% 204.76/35.50  | | |   (42)  op(e3, e3) = all_52_28
% 204.76/35.50  | | | 
% 204.76/35.50  | | | GROUND_INST: instantiating (1) with all_6_2, all_52_28, e3, e3,
% 204.76/35.50  | | |              simplifying with (22), (42) gives:
% 204.76/35.50  | | |   (43)  all_52_28 = all_6_2
% 204.76/35.50  | | | 
% 204.76/35.50  | | | BETA: splitting (15) gives:
% 204.76/35.50  | | | 
% 204.76/35.50  | | | Case 1:
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | |   (44)  all_58_1 = e3
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | | COMBINE_EQS: (2), (44) imply:
% 204.76/35.50  | | | |   (45)  all_52_9 = e3
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | | REF_CLOSE: (1), (21), (22), (29), (45) are inconsistent by sub-proof
% 204.76/35.50  | | | |            #1337.
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | Case 2:
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | |   (46)   ~ (all_58_1 = e3)
% 204.76/35.50  | | | |   (47)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | | REDUCE: (2), (46) imply:
% 204.76/35.50  | | | |   (48)   ~ (all_52_9 = e3)
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | | BETA: splitting (16) gives:
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | | Case 1:
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | |   (49)  all_58_1 = e3
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | | COMBINE_EQS: (2), (49) imply:
% 204.76/35.50  | | | | |   (50)  all_52_9 = e3
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | | REDUCE: (48), (50) imply:
% 204.76/35.50  | | | | |   (51)  $false
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | | CLOSE: (51) is inconsistent.
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | Case 2:
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | |   (52)  all_58_4 = e3 | all_58_9 = e3
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | | BETA: splitting (47) gives:
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | | Case 1:
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | |   (53)  all_58_3 = e3
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | | COMBINE_EQS: (30), (53) imply:
% 204.76/35.50  | | | | | |   (54)  all_4_2 = e3
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | | REDUCE: (20), (54) imply:
% 204.76/35.50  | | | | | |   (55)  op(e3, e3) = e2
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | | REDUCE: (13), (54) imply:
% 204.76/35.50  | | | | | |   (56)  op(e3, e2) = all_4_1
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | | BETA: splitting (28) gives:
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | | Case 1:
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | |   (57)  all_58_4 = e3
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | | COMBINE_EQS: (32), (57) imply:
% 204.76/35.50  | | | | | | |   (58)  all_52_17 = e3
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | | SIMP: (58) implies:
% 204.76/35.50  | | | | | | |   (59)  all_52_17 = e3
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | | REDUCE: (19), (59) imply:
% 204.76/35.50  | | | | | | |   (60)  op(e3, e3) = all_52_16
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | | REF_CLOSE: (1), (8), (9), (21), (22), (23), (24), (26), (29),
% 204.76/35.50  | | | | | | |            (33), (48), (55), (56), (60) are inconsistent by
% 204.76/35.50  | | | | | | |            sub-proof #1108.
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | Case 2:
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | |   (61)   ~ (all_58_4 = e3)
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | | REDUCE: (32), (61) imply:
% 204.76/35.50  | | | | | | |   (62)   ~ (all_52_17 = e3)
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | | REF_CLOSE: (4), (32), (40), (52), (62) are inconsistent by
% 204.76/35.50  | | | | | | |            sub-proof #1299.
% 204.76/35.50  | | | | | | | 
% 204.76/35.50  | | | | | | End of split
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | Case 2:
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | |   (63)  all_58_7 = e3 | all_58_13 = e3
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | | REF_CLOSE: (3), (6), (12), (39), (63) are inconsistent by sub-proof
% 204.76/35.50  | | | | | |            #1298.
% 204.76/35.50  | | | | | | 
% 204.76/35.50  | | | | | End of split
% 204.76/35.50  | | | | | 
% 204.76/35.50  | | | | End of split
% 204.76/35.50  | | | | 
% 204.76/35.50  | | | End of split
% 204.76/35.50  | | | 
% 204.76/35.50  | | Case 2:
% 204.76/35.50  | | | 
% 204.76/35.50  | | |   (64)  all_58_15 = e3
% 204.76/35.50  | | | 
% 204.76/35.50  | | | COMBINE_EQS: (17), (64) imply:
% 204.76/35.50  | | |   (65)  all_14_2 = e3
% 204.76/35.50  | | | 
% 204.76/35.50  | | | REDUCE: (33), (65) imply:
% 204.76/35.50  | | |   (66)  $false
% 204.76/35.50  | | | 
% 204.76/35.50  | | | CLOSE: (66) is inconsistent.
% 204.76/35.50  | | | 
% 204.76/35.50  | | End of split
% 204.76/35.50  | | 
% 204.76/35.50  | End of split
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1108 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (2)  op(e0, e0) = all_14_2
% 204.76/35.50    (3)  op(e3, e3) = e2
% 204.76/35.50    (4)   ~ (all_4_1 = e1)
% 204.76/35.50    (5)  op(e3, e2) = all_4_1
% 204.76/35.50    (6)  op(e3, e3) = all_52_16
% 204.76/35.50    (7)   ~ (all_52_9 = e3)
% 204.76/35.50    (8)   ~ (all_52_9 = all_6_2)
% 204.76/35.50    (9)  op(e3, e3) = all_6_2
% 204.76/35.50    (10)  all_56_1 = all_52_9
% 204.76/35.50    (11)  op(e3, e2) = all_52_9
% 204.76/35.50    (12)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50    (13)  op(all_52_9, all_52_9) = e3
% 204.76/35.50    (14)   ~ (all_14_2 = e3)
% 204.76/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3, simplifying
% 204.76/35.50  |              with (5), (11) gives:
% 204.76/35.50  |   (15)  all_52_9 = all_4_1
% 204.76/35.50  | 
% 204.76/35.50  | GROUND_INST: instantiating (1) with all_6_2, all_52_16, e3, e3, simplifying
% 204.76/35.50  |              with (6), (9) gives:
% 204.76/35.50  |   (16)  all_52_16 = all_6_2
% 204.76/35.50  | 
% 204.76/35.50  | GROUND_INST: instantiating (1) with e2, all_52_16, e3, e3, simplifying with
% 204.76/35.50  |              (3), (6) gives:
% 204.76/35.50  |   (17)  all_52_16 = e2
% 204.76/35.50  | 
% 204.76/35.50  | COMBINE_EQS: (16), (17) imply:
% 204.76/35.50  |   (18)  all_6_2 = e2
% 204.76/35.50  | 
% 204.76/35.50  | SIMP: (18) implies:
% 204.76/35.50  |   (19)  all_6_2 = e2
% 204.76/35.50  | 
% 204.76/35.50  | COMBINE_EQS: (10), (15) imply:
% 204.76/35.50  |   (20)  all_56_1 = all_4_1
% 204.76/35.50  | 
% 204.76/35.50  | REDUCE: (8), (15), (19) imply:
% 204.76/35.50  |   (21)   ~ (all_4_1 = e2)
% 204.76/35.50  | 
% 204.76/35.50  | REDUCE: (7), (15) imply:
% 204.76/35.50  |   (22)   ~ (all_4_1 = e3)
% 204.76/35.50  | 
% 204.76/35.50  | REDUCE: (13), (15) imply:
% 204.76/35.50  |   (23)  op(all_4_1, all_4_1) = e3
% 204.76/35.50  | 
% 204.76/35.50  | BETA: splitting (12) gives:
% 204.76/35.50  | 
% 204.76/35.50  | Case 1:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (24)  all_56_1 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | COMBINE_EQS: (20), (24) imply:
% 204.76/35.50  | |   (25)  all_4_1 = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | REDUCE: (22), (25) imply:
% 204.76/35.50  | |   (26)  $false
% 204.76/35.50  | | 
% 204.76/35.50  | | CLOSE: (26) is inconsistent.
% 204.76/35.50  | | 
% 204.76/35.50  | Case 2:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (27)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (1), (2), (4), (14), (20), (21), (23), (27) are inconsistent by
% 204.76/35.50  | |            sub-proof #1114.
% 204.76/35.50  | | 
% 204.76/35.50  | End of split
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1109 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (2)   ~ (all_4_2 = e3)
% 204.76/35.50    (3)  op(e2, e2) = all_4_2
% 204.76/35.50    (4)   ~ (all_52_9 = e1)
% 204.76/35.50    (5)  all_56_1 = all_52_9
% 204.76/35.50    (6)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50    (7)   ~ (all_52_9 = e0)
% 204.76/35.50    (8)  op(all_52_9, all_52_9) = e3
% 204.76/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | BETA: splitting (6) gives:
% 204.76/35.50  | 
% 204.76/35.50  | Case 1:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (9)  all_56_1 = e2
% 204.76/35.50  | | 
% 204.76/35.50  | | COMBINE_EQS: (5), (9) imply:
% 204.76/35.50  | |   (10)  all_52_9 = e2
% 204.76/35.50  | | 
% 204.76/35.50  | | SIMP: (10) implies:
% 204.76/35.50  | |   (11)  all_52_9 = e2
% 204.76/35.50  | | 
% 204.76/35.50  | | REDUCE: (8), (11) imply:
% 204.76/35.50  | |   (12)  op(e2, e2) = e3
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (1), (2), (3), (12) are inconsistent by sub-proof #1318.
% 204.76/35.50  | | 
% 204.76/35.50  | Case 2:
% 204.76/35.50  | | 
% 204.76/35.50  | |   (13)  all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50  | | 
% 204.76/35.50  | | REF_CLOSE: (4), (5), (7), (13) are inconsistent by sub-proof #1334.
% 204.76/35.50  | | 
% 204.76/35.50  | End of split
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1110 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (2)   ~ (all_6_2 = e3)
% 204.76/35.50    (3)  op(e3, e3) = all_6_2
% 204.76/35.50    (4)  all_56_1 = all_52_9
% 204.76/35.50    (5)  all_56_1 = e3
% 204.76/35.50    (6)  op(all_52_9, all_52_9) = e3
% 204.76/35.50  
% 204.76/35.50  Begin of proof
% 204.76/35.50  | 
% 204.76/35.50  | COMBINE_EQS: (4), (5) imply:
% 204.76/35.50  |   (7)  all_52_9 = e3
% 204.76/35.50  | 
% 204.76/35.50  | SIMP: (7) implies:
% 204.76/35.50  |   (8)  all_52_9 = e3
% 204.76/35.50  | 
% 204.76/35.50  | REDUCE: (6), (8) imply:
% 204.76/35.50  |   (9)  op(e3, e3) = e3
% 204.76/35.50  | 
% 204.76/35.50  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1338.
% 204.76/35.50  | 
% 204.76/35.50  End of proof
% 204.76/35.50  
% 204.76/35.50  Sub-proof #1111 shows that the following formulas are inconsistent:
% 204.76/35.50  ----------------------------------------------------------------
% 204.76/35.50    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 204.76/35.50    (2)  all_58_14 = all_52_23
% 204.76/35.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.50    (4)   ~ (all_52_5 = all_52_13)
% 204.76/35.50    (5)  all_58_1 = all_52_9
% 204.76/35.50    (6)  all_58_9 = e3
% 204.76/35.50    (7)   ~ (all_52_3 = all_6_2)
% 204.76/35.50    (8)  all_56_4 = all_52_3
% 204.76/35.50    (9)  op(all_52_19, all_52_19) = all_52_18
% 204.76/35.50    (10)  all_58_13 = all_52_15
% 204.76/35.50    (11)  op(all_52_13, all_52_13) = e1
% 204.76/35.50    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.76/35.50    (13)   ~ (all_52_15 = e3)
% 204.76/35.50    (14)  op(e1, e3) = all_52_5
% 204.76/35.50    (15)  op(e2, e2) = all_4_2
% 204.76/35.50    (16)   ~ (all_4_1 = e3)
% 204.76/35.50    (17)  all_58_11 = all_52_29
% 204.76/35.50    (18)  all_56_5 = all_4_2
% 204.76/35.50    (19)   ~ (all_52_3 = all_52_27)
% 204.76/35.50    (20)  op(e0, e0) = all_14_2
% 204.76/35.50    (21)   ~ (all_4_1 = e1)
% 204.76/35.50    (22)  all_56_9 = all_52_13
% 204.76/35.50    (23)   ~ (all_52_13 = all_10_2)
% 204.76/35.50    (24)  all_58_10 = all_52_27
% 204.76/35.50    (25)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.76/35.50    (26)  all_56_8 = all_52_5
% 204.76/35.50    (27)  all_58_7 = all_52_13
% 204.76/35.50    (28)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.76/35.50    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.76/35.50    (30)  all_58_2 = all_52_3
% 204.76/35.50    (31)   ~ (all_52_29 = e3)
% 204.76/35.50    (32)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.76/35.50    (33)  op(all_4_2, e2) = all_4_1
% 204.76/35.50    (34)   ~ (all_52_23 = e3)
% 204.76/35.50    (35)   ~ (all_52_5 = e3)
% 204.76/35.50    (36)   ~ (all_52_5 = all_52_29)
% 204.76/35.50    (37)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.76/35.50    (38)   ~ (all_52_9 = e3)
% 204.76/35.50    (39)   ~ (all_52_13 = all_4_2)
% 204.76/35.50    (40)  op(e1, e2) = all_52_13
% 204.76/35.50    (41)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.50    (42)  all_58_8 = all_10_2
% 204.76/35.50    (43)   ~ (all_52_5 = all_6_2)
% 204.76/35.50    (44)  op(all_4_2, all_4_2) = e2
% 204.76/35.50    (45)   ~ (all_52_9 = all_6_2)
% 204.76/35.50    (46)  op(e3, e3) = all_6_2
% 204.76/35.50    (47)   ~ (all_52_17 = e3)
% 204.76/35.50    (48)  all_58_5 = all_52_19
% 204.76/35.50    (49)  all_56_1 = all_52_9
% 204.76/35.50    (50)   ~ (all_52_27 = all_4_2)
% 204.76/35.50    (51)  all_58_6 = all_52_5
% 204.76/35.50    (52)  op(e3, e2) = all_52_9
% 204.76/35.50    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.50    (54)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.76/35.51    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.76/35.51    (56)   ~ (all_6_1 = e2)
% 204.76/35.51    (57)  op(all_52_9, all_52_9) = e3
% 204.76/35.51    (58)  all_58_3 = all_4_2
% 204.76/35.51    (59)   ~ (all_52_3 = all_4_2)
% 204.76/35.51    (60)   ~ (all_52_19 = all_4_2)
% 204.76/35.51    (61)  op(all_6_2, e3) = all_6_1
% 204.76/35.51    (62)  all_58_4 = all_52_17
% 204.76/35.51    (63)   ~ (all_14_2 = e3)
% 204.76/35.51  
% 204.76/35.51  Begin of proof
% 204.76/35.51  | 
% 204.76/35.51  | BETA: splitting (41) gives:
% 204.76/35.51  | 
% 204.76/35.51  | Case 1:
% 204.76/35.51  | | 
% 204.76/35.51  | |   (64)  all_58_1 = e3
% 204.76/35.51  | | 
% 204.76/35.51  | | COMBINE_EQS: (5), (64) imply:
% 204.76/35.51  | |   (65)  all_52_9 = e3
% 204.76/35.51  | | 
% 204.76/35.51  | | REDUCE: (38), (65) imply:
% 204.76/35.51  | |   (66)  $false
% 204.76/35.51  | | 
% 204.76/35.51  | | CLOSE: (66) is inconsistent.
% 204.76/35.51  | | 
% 204.76/35.51  | Case 2:
% 204.76/35.51  | | 
% 204.76/35.51  | |   (67)   ~ (all_58_1 = e3)
% 204.76/35.51  | |   (68)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.51  | | 
% 204.76/35.51  | | BETA: splitting (54) gives:
% 204.76/35.51  | | 
% 204.76/35.51  | | Case 1:
% 204.76/35.51  | | | 
% 204.76/35.51  | | |   (69)  all_58_4 = e3
% 204.76/35.51  | | | 
% 204.76/35.51  | | | REF_CLOSE: (47), (62), (69) are inconsistent by sub-proof #1302.
% 204.76/35.51  | | | 
% 204.76/35.51  | | Case 2:
% 204.76/35.51  | | | 
% 204.76/35.51  | | |   (70)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.76/35.51  | | | 
% 204.76/35.51  | | | BETA: splitting (29) gives:
% 204.76/35.51  | | | 
% 204.76/35.51  | | | Case 1:
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | |   (71)  all_58_6 = e3
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | REF_CLOSE: (35), (51), (71) are inconsistent by sub-proof #1328.
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | Case 2:
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | |   (72)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | BETA: splitting (53) gives:
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | Case 1:
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | |   (73)  all_56_1 = e3
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | | REF_CLOSE: (38), (49), (73) are inconsistent by sub-proof #1326.
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | Case 2:
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | |   (74)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | | BETA: splitting (55) gives:
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | | Case 1:
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | |   (75)  all_56_9 = e3
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | COMBINE_EQS: (22), (75) imply:
% 204.76/35.51  | | | | | |   (76)  all_52_13 = e3
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | SIMP: (76) implies:
% 204.76/35.51  | | | | | |   (77)  all_52_13 = e3
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | REDUCE: (23), (77) imply:
% 204.76/35.51  | | | | | |   (78)   ~ (all_10_2 = e3)
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | SIMP: (78) implies:
% 204.76/35.51  | | | | | |   (79)   ~ (all_10_2 = e3)
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | REDUCE: (11), (77) imply:
% 204.76/35.51  | | | | | |   (80)  op(e3, e3) = e1
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | REDUCE: (40), (77) imply:
% 204.76/35.51  | | | | | |   (81)  op(e1, e2) = e3
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | BETA: splitting (70) gives:
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | Case 1:
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | |   (82)  all_58_5 = e3
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | COMBINE_EQS: (48), (82) imply:
% 204.76/35.51  | | | | | | |   (83)  all_52_19 = e3
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | SIMP: (83) implies:
% 204.76/35.51  | | | | | | |   (84)  all_52_19 = e3
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (60), (84) imply:
% 204.76/35.51  | | | | | | |   (85)   ~ (all_4_2 = e3)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | SIMP: (85) implies:
% 204.76/35.51  | | | | | | |   (86)   ~ (all_4_2 = e3)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (9), (84) imply:
% 204.76/35.51  | | | | | | |   (87)  op(e3, e3) = all_52_18
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_18, e3, e3,
% 204.76/35.51  | | | | | | |              simplifying with (46), (87) gives:
% 204.76/35.51  | | | | | | |   (88)  all_52_18 = all_6_2
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_18, e3, e3,
% 204.76/35.51  | | | | | | |              simplifying with (80), (87) gives:
% 204.76/35.51  | | | | | | |   (89)  all_52_18 = e1
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | COMBINE_EQS: (88), (89) imply:
% 204.76/35.51  | | | | | | |   (90)  all_6_2 = e1
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (7), (90) imply:
% 204.76/35.51  | | | | | | |   (91)   ~ (all_52_3 = e1)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (43), (90) imply:
% 204.76/35.51  | | | | | | |   (92)   ~ (all_52_5 = e1)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (61), (90) imply:
% 204.76/35.51  | | | | | | |   (93)  op(e1, e3) = all_6_1
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | GROUND_INST: instantiating (3) with all_52_5, all_6_1, e3, e1,
% 204.76/35.51  | | | | | | |              simplifying with (14), (93) gives:
% 204.76/35.51  | | | | | | |   (94)  all_52_5 = all_6_1
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | COMBINE_EQS: (26), (94) imply:
% 204.76/35.51  | | | | | | |   (95)  all_56_8 = all_6_1
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (36), (94) imply:
% 204.76/35.51  | | | | | | |   (96)   ~ (all_52_29 = all_6_1)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | SIMP: (96) implies:
% 204.76/35.51  | | | | | | |   (97)   ~ (all_52_29 = all_6_1)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (35), (94) imply:
% 204.76/35.51  | | | | | | |   (98)   ~ (all_6_1 = e3)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REDUCE: (92), (94) imply:
% 204.76/35.51  | | | | | | |   (99)   ~ (all_6_1 = e1)
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | BETA: splitting (25) gives:
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | |   (100)  all_56_8 = e2
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | | REF_CLOSE: (56), (95), (100) are inconsistent by sub-proof
% 204.76/35.51  | | | | | | | |            #1321.
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | |   (101)  all_56_8 = e1 | all_56_8 = e0
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | | BETA: splitting (101) gives:
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | |   (102)  all_56_8 = e1
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | REF_CLOSE: (95), (99), (102) are inconsistent by sub-proof
% 204.76/35.51  | | | | | | | | |            #1320.
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | |   (103)  all_56_8 = e0
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | COMBINE_EQS: (95), (103) imply:
% 204.76/35.51  | | | | | | | | |   (104)  all_6_1 = e0
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | SIMP: (104) implies:
% 204.76/35.51  | | | | | | | | |   (105)  all_6_1 = e0
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | REDUCE: (97), (105) imply:
% 204.76/35.51  | | | | | | | | |   (106)   ~ (all_52_29 = e0)
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | REDUCE: (98), (105) imply:
% 204.76/35.51  | | | | | | | | |   (107)   ~ (e3 = e0)
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | SIMP: (107) implies:
% 204.76/35.51  | | | | | | | | |   (108)   ~ (e3 = e0)
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | BETA: splitting (1) gives:
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | |   (109)  all_58_9 = e0
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | COMBINE_EQS: (6), (109) imply:
% 204.76/35.51  | | | | | | | | | |   (110)  e3 = e0
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | REDUCE: (108), (110) imply:
% 204.76/35.51  | | | | | | | | | |   (111)  $false
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | CLOSE: (111) is inconsistent.
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | |   (112)  all_58_10 = e0 | all_58_11 = e0
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | BETA: splitting (112) gives:
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | |   (113)  all_58_10 = e0
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | COMBINE_EQS: (24), (113) imply:
% 204.76/35.51  | | | | | | | | | | |   (114)  all_52_27 = e0
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | SIMP: (114) implies:
% 204.76/35.51  | | | | | | | | | | |   (115)  all_52_27 = e0
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | REDUCE: (19), (115) imply:
% 204.76/35.51  | | | | | | | | | | |   (116)   ~ (all_52_3 = e0)
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | REDUCE: (50), (115) imply:
% 204.76/35.51  | | | | | | | | | | |   (117)   ~ (all_4_2 = e0)
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | SIMP: (117) implies:
% 204.76/35.51  | | | | | | | | | | |   (118)   ~ (all_4_2 = e0)
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | BETA: splitting (37) gives:
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | |   (119)  all_56_4 = e2
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | COMBINE_EQS: (8), (119) imply:
% 204.76/35.51  | | | | | | | | | | | |   (120)  all_52_3 = e2
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | COMBINE_EQS: (30), (120) imply:
% 204.76/35.51  | | | | | | | | | | | |   (121)  all_58_2 = e2
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | REDUCE: (59), (120) imply:
% 204.76/35.51  | | | | | | | | | | | |   (122)   ~ (all_4_2 = e2)
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | SIMP: (122) implies:
% 204.76/35.51  | | | | | | | | | | | |   (123)   ~ (all_4_2 = e2)
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | REDUCE: (91), (120) imply:
% 204.76/35.51  | | | | | | | | | | | |   (124)   ~ (e2 = e1)
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | BETA: splitting (32) gives:
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | |   (125)  all_56_5 = e3
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | COMBINE_EQS: (18), (125) imply:
% 204.76/35.51  | | | | | | | | | | | | |   (126)  all_4_2 = e3
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | REDUCE: (86), (126) imply:
% 204.76/35.51  | | | | | | | | | | | | |   (127)  $false
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | |   (128)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | BETA: splitting (28) gives:
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | |   (129)  all_58_2 = e1
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | REF_CLOSE: (121), (124), (129) are inconsistent by sub-proof
% 204.76/35.51  | | | | | | | | | | | | | |            #1116.
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | |   (130)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | |   (131)  all_56_5 = e2
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | COMBINE_EQS: (18), (131) imply:
% 204.76/35.51  | | | | | | | | | | | | | | |   (132)  all_4_2 = e2
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | REDUCE: (123), (132) imply:
% 204.76/35.51  | | | | | | | | | | | | | | |   (133)  $false
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | |   (134)  all_56_5 = e1 | all_56_5 = e0
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | Case 1:
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | |   (135)  all_56_5 = e1
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (135) imply:
% 204.76/35.51  | | | | | | | | | | | | | | | |   (136)  all_4_2 = e1
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | | REDUCE: (15), (136) imply:
% 204.76/35.51  | | | | | | | | | | | | | | | |   (137)  op(e2, e2) = e1
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (15), (16), (33), (58), (81), (130), (137)
% 204.76/35.51  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1154.
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | |   (138)  all_56_5 = e0
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (138) imply:
% 204.76/35.51  | | | | | | | | | | | | | | | |   (139)  all_4_2 = e0
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | | REDUCE: (118), (139) imply:
% 204.76/35.51  | | | | | | | | | | | | | | | |   (140)  $false
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 204.76/35.51  | | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | |   (141)  all_56_4 = e1 | all_56_4 = e0
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | | REF_CLOSE: (8), (91), (116), (141) are inconsistent by
% 204.76/35.51  | | | | | | | | | | | |            sub-proof #1308.
% 204.76/35.51  | | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | Case 2:
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | |   (142)  all_58_11 = e0
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | | REF_CLOSE: (17), (106), (142) are inconsistent by sub-proof
% 204.76/35.51  | | | | | | | | | | |            #1115.
% 204.76/35.51  | | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | | 
% 204.76/35.51  | | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | | 
% 204.76/35.51  | | | | | | | | End of split
% 204.76/35.51  | | | | | | | | 
% 204.76/35.51  | | | | | | | End of split
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | Case 2:
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | |   (143)  all_58_8 = e3 | all_58_14 = e3
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | | REF_CLOSE: (2), (34), (42), (79), (143) are inconsistent by
% 204.76/35.51  | | | | | | |            sub-proof #1304.
% 204.76/35.51  | | | | | | | 
% 204.76/35.51  | | | | | | End of split
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | Case 2:
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | |   (144)   ~ (all_56_9 = e3)
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | REDUCE: (22), (144) imply:
% 204.76/35.51  | | | | | |   (145)   ~ (all_52_13 = e3)
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | | REF_CLOSE: (3), (10), (12), (13), (17), (20), (21), (27), (31),
% 204.76/35.51  | | | | | |            (33), (39), (42), (44), (45), (46), (49), (52), (57),
% 204.76/35.51  | | | | | |            (58), (63), (68), (72), (74), (145) are inconsistent by
% 204.76/35.51  | | | | | |            sub-proof #1112.
% 204.76/35.51  | | | | | | 
% 204.76/35.51  | | | | | End of split
% 204.76/35.51  | | | | | 
% 204.76/35.51  | | | | End of split
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | End of split
% 204.76/35.51  | | | 
% 204.76/35.51  | | End of split
% 204.76/35.51  | | 
% 204.76/35.51  | End of split
% 204.76/35.51  | 
% 204.76/35.51  End of proof
% 204.76/35.51  
% 204.76/35.51  Sub-proof #1112 shows that the following formulas are inconsistent:
% 204.76/35.51  ----------------------------------------------------------------
% 204.76/35.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.51    (2)  all_58_13 = all_52_15
% 204.76/35.51    (3)  op(all_10_2, all_10_2) = all_52_20
% 204.76/35.51    (4)   ~ (all_52_15 = e3)
% 204.76/35.51    (5)  all_58_11 = all_52_29
% 204.76/35.51    (6)  op(e0, e0) = all_14_2
% 204.76/35.51    (7)   ~ (all_4_1 = e1)
% 204.76/35.51    (8)  all_58_7 = all_52_13
% 204.76/35.51    (9)   ~ (all_52_29 = e3)
% 204.76/35.51    (10)  op(all_4_2, e2) = all_4_1
% 204.76/35.51    (11)   ~ (all_52_13 = all_4_2)
% 204.76/35.51    (12)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.76/35.51    (13)  all_58_8 = all_10_2
% 204.76/35.51    (14)  op(all_4_2, all_4_2) = e2
% 204.76/35.51    (15)   ~ (all_52_9 = all_6_2)
% 204.76/35.51    (16)  op(e3, e3) = all_6_2
% 204.76/35.51    (17)   ~ (all_52_13 = e3)
% 204.76/35.51    (18)  all_56_1 = all_52_9
% 204.76/35.51    (19)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.51    (20)  op(e3, e2) = all_52_9
% 204.76/35.51    (21)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.51    (22)  op(all_52_9, all_52_9) = e3
% 204.76/35.51    (23)  all_58_3 = all_4_2
% 204.76/35.51    (24)   ~ (all_14_2 = e3)
% 204.76/35.51  
% 204.76/35.51  Begin of proof
% 204.76/35.51  | 
% 204.76/35.51  | BETA: splitting (21) gives:
% 204.76/35.51  | 
% 204.76/35.51  | Case 1:
% 204.76/35.51  | | 
% 204.76/35.51  | |   (25)  all_58_3 = e3
% 204.76/35.51  | | 
% 204.76/35.51  | | COMBINE_EQS: (23), (25) imply:
% 204.76/35.51  | |   (26)  all_4_2 = e3
% 204.76/35.51  | | 
% 204.76/35.51  | | REDUCE: (14), (26) imply:
% 204.76/35.51  | |   (27)  op(e3, e3) = e2
% 204.76/35.51  | | 
% 204.76/35.51  | | REDUCE: (10), (26) imply:
% 204.76/35.51  | |   (28)  op(e3, e2) = all_4_1
% 204.76/35.51  | | 
% 204.76/35.51  | | BETA: splitting (12) gives:
% 204.76/35.51  | | 
% 204.76/35.51  | | Case 1:
% 204.76/35.51  | | | 
% 204.76/35.51  | | |   (29)  all_58_7 = e3
% 204.76/35.51  | | | 
% 204.76/35.51  | | | COMBINE_EQS: (8), (29) imply:
% 204.76/35.51  | | |   (30)  all_52_13 = e3
% 204.76/35.51  | | | 
% 204.76/35.51  | | | REDUCE: (17), (30) imply:
% 204.76/35.51  | | |   (31)  $false
% 204.76/35.51  | | | 
% 204.76/35.51  | | | CLOSE: (31) is inconsistent.
% 204.76/35.51  | | | 
% 204.76/35.51  | | Case 2:
% 204.76/35.51  | | | 
% 204.76/35.51  | | |   (32)  all_58_8 = e3 | all_58_11 = e3
% 204.76/35.51  | | | 
% 204.76/35.51  | | | BETA: splitting (32) gives:
% 204.76/35.51  | | | 
% 204.76/35.51  | | | Case 1:
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | |   (33)  all_58_8 = e3
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | COMBINE_EQS: (13), (33) imply:
% 204.76/35.51  | | | |   (34)  all_10_2 = e3
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | REDUCE: (3), (34) imply:
% 204.76/35.51  | | | |   (35)  op(e3, e3) = all_52_20
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | REF_CLOSE: (1), (6), (7), (15), (16), (18), (19), (20), (22), (24),
% 204.76/35.51  | | | |            (27), (28), (35) are inconsistent by sub-proof #1113.
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | Case 2:
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | |   (36)  all_58_11 = e3
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | | REF_CLOSE: (5), (9), (36) are inconsistent by sub-proof #1323.
% 204.76/35.51  | | | | 
% 204.76/35.51  | | | End of split
% 204.76/35.51  | | | 
% 204.76/35.51  | | End of split
% 204.76/35.51  | | 
% 204.76/35.51  | Case 2:
% 204.76/35.51  | | 
% 204.76/35.51  | |   (37)  all_58_7 = e3 | all_58_13 = e3
% 204.76/35.51  | | 
% 204.76/35.51  | | REF_CLOSE: (2), (4), (8), (17), (37) are inconsistent by sub-proof #1298.
% 204.76/35.51  | | 
% 204.76/35.51  | End of split
% 204.76/35.51  | 
% 204.76/35.51  End of proof
% 204.76/35.51  
% 204.76/35.51  Sub-proof #1113 shows that the following formulas are inconsistent:
% 204.76/35.51  ----------------------------------------------------------------
% 204.76/35.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.51    (2)  op(e0, e0) = all_14_2
% 204.76/35.51    (3)  op(e3, e3) = e2
% 204.76/35.51    (4)   ~ (all_4_1 = e1)
% 204.76/35.51    (5)  op(e3, e2) = all_4_1
% 204.76/35.51    (6)  op(e3, e3) = all_52_20
% 204.76/35.51    (7)   ~ (all_52_9 = all_6_2)
% 204.76/35.51    (8)  op(e3, e3) = all_6_2
% 204.76/35.51    (9)  all_56_1 = all_52_9
% 204.76/35.51    (10)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.51    (11)  op(e3, e2) = all_52_9
% 204.76/35.51    (12)  op(all_52_9, all_52_9) = e3
% 204.76/35.51    (13)   ~ (all_14_2 = e3)
% 204.76/35.51  
% 204.76/35.51  Begin of proof
% 204.76/35.51  | 
% 204.76/35.51  | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3, simplifying
% 204.76/35.51  |              with (5), (11) gives:
% 204.76/35.51  |   (14)  all_52_9 = all_4_1
% 204.76/35.51  | 
% 204.76/35.51  | GROUND_INST: instantiating (1) with all_6_2, all_52_20, e3, e3, simplifying
% 204.76/35.51  |              with (6), (8) gives:
% 204.76/35.51  |   (15)  all_52_20 = all_6_2
% 204.76/35.51  | 
% 204.76/35.51  | GROUND_INST: instantiating (1) with e2, all_52_20, e3, e3, simplifying with
% 204.76/35.51  |              (3), (6) gives:
% 204.76/35.51  |   (16)  all_52_20 = e2
% 204.76/35.51  | 
% 204.76/35.51  | COMBINE_EQS: (15), (16) imply:
% 204.76/35.51  |   (17)  all_6_2 = e2
% 204.76/35.51  | 
% 204.76/35.51  | SIMP: (17) implies:
% 204.76/35.51  |   (18)  all_6_2 = e2
% 204.76/35.51  | 
% 204.76/35.51  | COMBINE_EQS: (9), (14) imply:
% 204.76/35.51  |   (19)  all_56_1 = all_4_1
% 204.76/35.51  | 
% 204.76/35.51  | REDUCE: (7), (14), (18) imply:
% 204.76/35.51  |   (20)   ~ (all_4_1 = e2)
% 204.76/35.51  | 
% 204.76/35.51  | REDUCE: (12), (14) imply:
% 204.76/35.51  |   (21)  op(all_4_1, all_4_1) = e3
% 204.76/35.51  | 
% 204.76/35.51  | REF_CLOSE: (1), (2), (4), (10), (13), (19), (20), (21) are inconsistent by
% 204.76/35.51  |            sub-proof #1114.
% 204.76/35.51  | 
% 204.76/35.51  End of proof
% 204.76/35.51  
% 204.76/35.51  Sub-proof #1114 shows that the following formulas are inconsistent:
% 204.76/35.51  ----------------------------------------------------------------
% 204.76/35.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.51    (2)  all_56_1 = all_4_1
% 204.76/35.51    (3)  op(e0, e0) = all_14_2
% 204.76/35.51    (4)   ~ (all_4_1 = e1)
% 204.76/35.51    (5)   ~ (all_4_1 = e2)
% 204.76/35.51    (6)  op(all_4_1, all_4_1) = e3
% 204.76/35.51    (7)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.51    (8)   ~ (all_14_2 = e3)
% 204.76/35.51  
% 204.76/35.51  Begin of proof
% 204.76/35.51  | 
% 204.76/35.51  | BETA: splitting (7) gives:
% 204.76/35.51  | 
% 204.76/35.51  | Case 1:
% 204.76/35.51  | | 
% 204.76/35.51  | |   (9)  all_56_1 = e2
% 204.76/35.51  | | 
% 204.76/35.51  | | COMBINE_EQS: (2), (9) imply:
% 204.76/35.51  | |   (10)  all_4_1 = e2
% 204.76/35.51  | | 
% 204.76/35.51  | | REDUCE: (5), (10) imply:
% 204.76/35.51  | |   (11)  $false
% 204.76/35.51  | | 
% 204.76/35.51  | | CLOSE: (11) is inconsistent.
% 204.76/35.51  | | 
% 204.76/35.51  | Case 2:
% 204.76/35.51  | | 
% 204.76/35.51  | |   (12)  all_56_1 = e1 | all_56_1 = e0
% 204.76/35.51  | | 
% 204.76/35.51  | | BETA: splitting (12) gives:
% 204.76/35.51  | | 
% 204.76/35.51  | | Case 1:
% 204.76/35.51  | | | 
% 204.76/35.51  | | |   (13)  all_56_1 = e1
% 204.76/35.51  | | | 
% 204.76/35.51  | | | COMBINE_EQS: (2), (13) imply:
% 204.76/35.51  | | |   (14)  all_4_1 = e1
% 204.76/35.51  | | | 
% 204.76/35.51  | | | REDUCE: (4), (14) imply:
% 204.76/35.51  | | |   (15)  $false
% 204.76/35.51  | | | 
% 204.76/35.51  | | | CLOSE: (15) is inconsistent.
% 204.76/35.51  | | | 
% 204.76/35.51  | | Case 2:
% 204.76/35.51  | | | 
% 204.76/35.51  | | |   (16)  all_56_1 = e0
% 204.76/35.51  | | | 
% 204.76/35.51  | | | COMBINE_EQS: (2), (16) imply:
% 204.76/35.51  | | |   (17)  all_4_1 = e0
% 204.76/35.51  | | | 
% 204.76/35.51  | | | REDUCE: (6), (17) imply:
% 204.76/35.51  | | |   (18)  op(e0, e0) = e3
% 204.76/35.51  | | | 
% 204.76/35.51  | | | REF_CLOSE: (1), (3), (8), (18) are inconsistent by sub-proof #1372.
% 204.76/35.51  | | | 
% 204.76/35.51  | | End of split
% 204.76/35.51  | | 
% 204.76/35.51  | End of split
% 204.76/35.51  | 
% 204.76/35.51  End of proof
% 204.76/35.51  
% 204.76/35.51  Sub-proof #1115 shows that the following formulas are inconsistent:
% 204.76/35.51  ----------------------------------------------------------------
% 204.76/35.51    (1)  all_58_11 = all_52_29
% 204.76/35.51    (2)  all_58_11 = e0
% 204.76/35.51    (3)   ~ (all_52_29 = e0)
% 204.76/35.51  
% 204.76/35.51  Begin of proof
% 204.76/35.51  | 
% 204.76/35.51  | COMBINE_EQS: (1), (2) imply:
% 204.76/35.51  |   (4)  all_52_29 = e0
% 204.76/35.51  | 
% 204.76/35.51  | SIMP: (4) implies:
% 204.76/35.51  |   (5)  all_52_29 = e0
% 204.76/35.51  | 
% 204.76/35.51  | REDUCE: (3), (5) imply:
% 204.76/35.51  |   (6)  $false
% 204.76/35.51  | 
% 204.76/35.51  | CLOSE: (6) is inconsistent.
% 204.76/35.51  | 
% 204.76/35.51  End of proof
% 204.76/35.51  
% 204.76/35.51  Sub-proof #1116 shows that the following formulas are inconsistent:
% 204.76/35.51  ----------------------------------------------------------------
% 204.76/35.51    (1)  all_58_2 = e2
% 204.76/35.51    (2)  all_58_2 = e1
% 204.76/35.51    (3)   ~ (e2 = e1)
% 204.76/35.51  
% 204.76/35.51  Begin of proof
% 204.76/35.51  | 
% 204.76/35.51  | COMBINE_EQS: (1), (2) imply:
% 204.76/35.51  |   (4)  e2 = e1
% 204.76/35.51  | 
% 204.76/35.51  | SIMP: (4) implies:
% 204.76/35.51  |   (5)  e2 = e1
% 204.76/35.51  | 
% 204.76/35.51  | REDUCE: (3), (5) imply:
% 204.76/35.51  |   (6)  $false
% 204.76/35.51  | 
% 204.76/35.51  | CLOSE: (6) is inconsistent.
% 204.76/35.51  | 
% 204.76/35.51  End of proof
% 204.76/35.51  
% 204.76/35.51  Sub-proof #1117 shows that the following formulas are inconsistent:
% 204.76/35.51  ----------------------------------------------------------------
% 204.76/35.51    (1)   ~ (e3 = e1)
% 204.76/35.51    (2)  op(all_52_3, all_52_3) = all_52_2
% 204.76/35.51    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.51    (4)   ~ (all_52_5 = all_52_13)
% 204.76/35.51    (5)  all_58_1 = all_52_9
% 204.76/35.51    (6)   ~ (all_52_9 = all_52_13)
% 204.76/35.51    (7)  op(e2, e3) = all_52_3
% 204.76/35.51    (8)   ~ (all_52_7 = all_52_15)
% 204.76/35.51    (9)  op(all_52_7, all_52_7) = all_52_6
% 204.76/35.51    (10)   ~ (all_52_3 = all_6_2)
% 204.76/35.51    (11)  all_58_0 = all_6_2
% 204.76/35.51    (12)  op(all_14_2, e0) = all_14_1
% 204.76/35.51    (13)  all_56_4 = all_52_3
% 204.76/35.51    (14)  op(e3, e0) = all_52_25
% 204.76/35.51    (15)  op(all_52_5, all_52_5) = all_52_4
% 204.76/35.51    (16)  all_58_13 = all_52_15
% 204.76/35.51    (17)  op(all_52_13, all_52_13) = e1
% 204.76/35.51    (18)  op(all_10_2, all_10_2) = all_52_20
% 204.76/35.51    (19)  all_58_9 = all_52_25
% 204.76/35.51    (20)   ~ (all_6_1 = e1)
% 204.76/35.51    (21)   ~ (all_52_29 = all_14_2)
% 204.76/35.51    (22)  op(e1, e3) = all_52_5
% 204.76/35.51    (23)  op(e2, e2) = all_4_2
% 204.76/35.51    (24)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.76/35.51    (25)   ~ (all_52_3 = all_52_5)
% 204.76/35.51    (26)  all_58_11 = all_52_29
% 204.76/35.51    (27)   ~ (all_52_25 = all_14_2)
% 204.76/35.51    (28)  op(all_6_2, all_6_2) = all_52_0
% 204.76/35.51    (29)   ~ (all_52_7 = all_6_2)
% 204.76/35.51    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.76/35.51    (31)   ~ (all_4_1 = e1)
% 204.76/35.51    (32)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.76/35.51    (33)   ~ (e2 = e1)
% 204.76/35.51    (34)   ~ (all_52_13 = all_10_2)
% 204.76/35.51    (35)   ~ (all_6_0 = e1)
% 204.76/35.51    (36)  all_58_10 = all_52_27
% 204.76/35.51    (37)  all_58_7 = all_52_13
% 204.76/35.51    (38)  all_58_12 = all_52_7
% 204.76/35.51    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.76/35.51    (40)   ~ (all_52_7 = all_14_2)
% 204.76/35.51    (41)   ~ (all_14_2 = e0)
% 204.76/35.51    (42)  all_58_2 = all_52_3
% 204.76/35.51    (43)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.76/35.51    (44)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.76/35.51    (45)  op(e3, all_6_1) = all_6_0
% 204.76/35.51    (46)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.76/35.51    (47)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.76/35.51    (48)   ~ (e2 = e0)
% 204.76/35.51    (49)  op(all_4_2, e2) = all_4_1
% 204.76/35.51    (50)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.76/35.51    (51)   ~ (all_52_15 = all_14_2)
% 204.76/35.51    (52)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.76/35.51    (53)   ~ (all_6_0 = e2)
% 204.76/35.51    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.51    (55)   ~ (all_52_9 = all_52_25)
% 204.76/35.51    (56)  all_58_8 = all_10_2
% 204.76/35.51    (57)  op(all_52_17, all_52_17) = all_52_16
% 204.76/35.51    (58)   ~ (all_52_25 = all_6_2)
% 204.76/35.51    (59)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.76/35.51    (60)   ~ (all_52_5 = all_6_2)
% 204.76/35.51    (61)  op(all_4_2, all_4_2) = e2
% 204.76/35.51    (62)   ~ (all_52_9 = all_6_2)
% 204.76/35.51    (63)  op(e3, e3) = all_6_2
% 204.76/35.51    (64)   ~ (all_52_27 = all_14_2)
% 204.76/35.51    (65)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.76/35.51    (66)  all_56_3 = all_52_25
% 204.76/35.51    (67)   ~ (all_52_3 = all_52_7)
% 204.76/35.51    (68)  op(all_14_2, all_14_2) = all_52_30
% 204.76/35.51    (69)  all_58_5 = all_52_19
% 204.76/35.51    (70)  all_56_1 = all_52_9
% 204.76/35.51    (71)  all_58_6 = all_52_5
% 204.76/35.52    (72)  op(e3, e2) = all_52_9
% 204.76/35.52    (73)   ~ (all_52_17 = all_6_2)
% 204.76/35.52    (74)   ~ (e1 = e0)
% 204.76/35.52    (75)   ~ (e3 = e2)
% 204.76/35.52    (76)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.52    (77)   ~ (all_52_9 = all_52_17)
% 204.76/35.52    (78)  all_56_10 = all_10_2
% 204.76/35.52    (79)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.76/35.52    (80)   ~ (all_6_1 = e2)
% 204.76/35.52    (81)  op(e1, e1) = all_10_2
% 204.76/35.52    (82)  op(all_52_9, all_52_9) = e3
% 204.76/35.52    (83)   ~ (all_52_17 = all_52_19)
% 204.76/35.52    (84)  all_58_3 = all_4_2
% 204.76/35.52    (85)   ~ (all_52_3 = all_4_2)
% 204.76/35.52    (86)  op(all_6_2, e3) = all_6_1
% 204.76/35.52    (87)  all_58_4 = all_52_17
% 204.76/35.52    (88)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.76/35.52    (89)  all_14_2 = e3
% 204.76/35.52  
% 204.76/35.52  Begin of proof
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (40), (89) imply:
% 204.76/35.52  |   (90)   ~ (all_52_7 = e3)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (51), (89) imply:
% 204.76/35.52  |   (91)   ~ (all_52_15 = e3)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (27), (89) imply:
% 204.76/35.52  |   (92)   ~ (all_52_25 = e3)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (64), (89) imply:
% 204.76/35.52  |   (93)   ~ (all_52_27 = e3)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (21), (89) imply:
% 204.76/35.52  |   (94)   ~ (all_52_29 = e3)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (41), (89) imply:
% 204.76/35.52  |   (95)   ~ (e3 = e0)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (68), (89) imply:
% 204.76/35.52  |   (96)  op(e3, e3) = all_52_30
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (12), (89) imply:
% 204.76/35.52  |   (97)  op(e3, e0) = all_14_1
% 204.76/35.52  | 
% 204.76/35.52  | GROUND_INST: instantiating (3) with all_52_25, all_14_1, e0, e3, simplifying
% 204.76/35.52  |              with (14), (97) gives:
% 204.76/35.52  |   (98)  all_52_25 = all_14_1
% 204.76/35.52  | 
% 204.76/35.52  | GROUND_INST: instantiating (3) with all_6_2, all_52_30, e3, e3, simplifying
% 204.76/35.52  |              with (63), (96) gives:
% 204.76/35.52  |   (99)  all_52_30 = all_6_2
% 204.76/35.52  | 
% 204.76/35.52  | COMBINE_EQS: (66), (98) imply:
% 204.76/35.52  |   (100)  all_56_3 = all_14_1
% 204.76/35.52  | 
% 204.76/35.52  | COMBINE_EQS: (19), (98) imply:
% 204.76/35.52  |   (101)  all_58_9 = all_14_1
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (55), (98) imply:
% 204.76/35.52  |   (102)   ~ (all_52_9 = all_14_1)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (58), (98) imply:
% 204.76/35.52  |   (103)   ~ (all_14_1 = all_6_2)
% 204.76/35.52  | 
% 204.76/35.52  | REDUCE: (92), (98) imply:
% 204.76/35.52  |   (104)   ~ (all_14_1 = e3)
% 204.76/35.52  | 
% 204.76/35.52  | BETA: splitting (59) gives:
% 204.76/35.52  | 
% 204.76/35.52  | Case 1:
% 204.76/35.52  | | 
% 204.76/35.52  | |   (105)  all_56_3 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | REF_CLOSE: (100), (104), (105) are inconsistent by sub-proof #1200.
% 204.76/35.52  | | 
% 204.76/35.52  | Case 2:
% 204.76/35.52  | | 
% 204.76/35.52  | |   (106)   ~ (all_56_3 = e3)
% 204.76/35.52  | |   (107)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.76/35.52  | | 
% 204.76/35.52  | | BETA: splitting (50) gives:
% 204.76/35.52  | | 
% 204.76/35.52  | | Case 1:
% 204.76/35.52  | | | 
% 204.76/35.52  | | |   (108)  all_58_12 = e1
% 204.76/35.52  | | | 
% 204.76/35.52  | | | COMBINE_EQS: (38), (108) imply:
% 204.76/35.52  | | |   (109)  all_52_7 = e1
% 204.76/35.52  | | | 
% 204.76/35.52  | | | SIMP: (109) implies:
% 204.76/35.52  | | |   (110)  all_52_7 = e1
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (8), (110) imply:
% 204.76/35.52  | | |   (111)   ~ (all_52_15 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | SIMP: (111) implies:
% 204.76/35.52  | | |   (112)   ~ (all_52_15 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (29), (110) imply:
% 204.76/35.52  | | |   (113)   ~ (all_6_2 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | SIMP: (113) implies:
% 204.76/35.52  | | |   (114)   ~ (all_6_2 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (90), (110) imply:
% 204.76/35.52  | | |   (115)   ~ (e3 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (9), (110) imply:
% 204.76/35.52  | | |   (116)  op(e1, e1) = all_52_6
% 204.76/35.52  | | | 
% 204.76/35.52  | | | GROUND_INST: instantiating (3) with all_10_2, all_52_6, e1, e1,
% 204.76/35.52  | | |              simplifying with (81), (116) gives:
% 204.76/35.52  | | |   (117)  all_52_6 = all_10_2
% 204.76/35.52  | | | 
% 204.76/35.52  | | | BETA: splitting (47) gives:
% 204.76/35.52  | | | 
% 204.76/35.52  | | | Case 1:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | |   (118)  all_56_4 = e3
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REF_CLOSE: (3), (5), (13), (16), (17), (37), (54), (62), (63), (82),
% 204.76/35.52  | | | |            (84), (85), (91), (114), (118) are inconsistent by sub-proof
% 204.76/35.52  | | | |            #1141.
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | Case 2:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | |   (119)   ~ (all_56_4 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (13), (119) imply:
% 204.76/35.52  | | | |   (120)   ~ (all_52_3 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | BETA: splitting (44) gives:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | Case 1:
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | |   (121)  all_58_0 = e3
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REF_CLOSE: (3), (5), (11), (16), (17), (18), (19), (26), (28), (34),
% 204.76/35.52  | | | | |            (35), (37), (39), (45), (53), (54), (56), (60), (61), (62),
% 204.76/35.52  | | | | |            (63), (65), (71), (73), (78), (82), (84), (86), (87), (88),
% 204.76/35.52  | | | | |            (91), (92), (94), (121) are inconsistent by sub-proof
% 204.76/35.52  | | | | |            #1136.
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | Case 2:
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | |   (122)   ~ (all_58_0 = e3)
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REF_CLOSE: (1), (3), (5), (11), (16), (17), (30), (31), (32), (34),
% 204.76/35.52  | | | | |            (36), (37), (42), (49), (54), (62), (63), (65), (69), (72),
% 204.76/35.52  | | | | |            (81), (82), (83), (84), (87), (93), (101), (104), (112),
% 204.76/35.52  | | | | |            (120), (122) are inconsistent by sub-proof #1130.
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | End of split
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | End of split
% 204.76/35.52  | | | 
% 204.76/35.52  | | Case 2:
% 204.76/35.52  | | | 
% 204.76/35.52  | | |   (123)   ~ (all_58_12 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (38), (123) imply:
% 204.76/35.52  | | |   (124)   ~ (all_52_7 = e1)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | BETA: splitting (79) gives:
% 204.76/35.52  | | | 
% 204.76/35.52  | | | Case 1:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | |   (125)  all_58_4 = e3
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | COMBINE_EQS: (87), (125) imply:
% 204.76/35.52  | | | |   (126)  all_52_17 = e3
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | SIMP: (126) implies:
% 204.76/35.52  | | | |   (127)  all_52_17 = e3
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (77), (127) imply:
% 204.76/35.52  | | | |   (128)   ~ (all_52_9 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (83), (127) imply:
% 204.76/35.52  | | | |   (129)   ~ (all_52_19 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | SIMP: (129) implies:
% 204.76/35.52  | | | |   (130)   ~ (all_52_19 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (73), (127) imply:
% 204.76/35.52  | | | |   (131)   ~ (all_6_2 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | SIMP: (131) implies:
% 204.76/35.52  | | | |   (132)   ~ (all_6_2 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (57), (127) imply:
% 204.76/35.52  | | | |   (133)  op(e3, e3) = all_52_16
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_16, e3, e3,
% 204.76/35.52  | | | |              simplifying with (63), (133) gives:
% 204.76/35.52  | | | |   (134)  all_52_16 = all_6_2
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | BETA: splitting (39) gives:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | Case 1:
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | |   (135)  all_58_6 = e3
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | COMBINE_EQS: (71), (135) imply:
% 204.76/35.52  | | | | |   (136)  all_52_5 = e3
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | SIMP: (136) implies:
% 204.76/35.52  | | | | |   (137)  all_52_5 = e3
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REDUCE: (25), (137) imply:
% 204.76/35.52  | | | | |   (138)   ~ (all_52_3 = e3)
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REDUCE: (15), (137) imply:
% 204.76/35.52  | | | | |   (139)  op(e3, e3) = all_52_4
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | BETA: splitting (30) gives:
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | Case 1:
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | |   (140)  all_58_2 = e3
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | | REF_CLOSE: (42), (138), (140) are inconsistent by sub-proof #1369.
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | Case 2:
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | |   (141)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | | BETA: splitting (141) gives:
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | | Case 1:
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | |   (142)  all_58_3 = e3
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | | COMBINE_EQS: (84), (142) imply:
% 204.76/35.52  | | | | | | |   (143)  all_4_2 = e3
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | | REDUCE: (61), (143) imply:
% 204.76/35.52  | | | | | | |   (144)  op(e3, e3) = e2
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | | REF_CLOSE: (1), (3), (7), (10), (11), (13), (20), (33), (38),
% 204.76/35.52  | | | | | | |            (42), (46), (47), (63), (74), (86), (124), (135),
% 204.76/35.52  | | | | | | |            (138), (139), (144) are inconsistent by sub-proof
% 204.76/35.52  | | | | | | |            #1125.
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | Case 2:
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | |   (145)  all_58_5 = e3 | all_58_10 = e3
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | | REF_CLOSE: (36), (69), (93), (130), (145) are inconsistent by
% 204.76/35.52  | | | | | | |            sub-proof #1132.
% 204.76/35.52  | | | | | | | 
% 204.76/35.52  | | | | | | End of split
% 204.76/35.52  | | | | | | 
% 204.76/35.52  | | | | | End of split
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | Case 2:
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | |   (146)   ~ (all_58_6 = e3)
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REDUCE: (71), (146) imply:
% 204.76/35.52  | | | | |   (147)   ~ (all_52_5 = e3)
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (16), (17), (22),
% 204.76/35.52  | | | | |            (23), (24), (29), (33), (37), (38), (42), (43), (44), (45),
% 204.76/35.52  | | | | |            (48), (52), (53), (54), (62), (63), (67), (70), (71), (74),
% 204.76/35.52  | | | | |            (75), (76), (80), (82), (84), (85), (86), (90), (91), (95),
% 204.76/35.52  | | | | |            (97), (100), (102), (103), (107), (128), (132), (147) are
% 204.76/35.52  | | | | |            inconsistent by sub-proof #1118.
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | End of split
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | Case 2:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | |   (148)   ~ (all_58_4 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (87), (148) imply:
% 204.76/35.52  | | | |   (149)   ~ (all_52_17 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REF_CLOSE: (3), (5), (11), (16), (17), (18), (19), (26), (28), (34),
% 204.76/35.52  | | | |            (35), (37), (39), (45), (53), (54), (56), (60), (61), (62),
% 204.76/35.52  | | | |            (63), (65), (71), (78), (82), (84), (86), (87), (88), (91),
% 204.76/35.52  | | | |            (92), (94), (149) are inconsistent by sub-proof #1137.
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | End of split
% 204.76/35.52  | | | 
% 204.76/35.52  | | End of split
% 204.76/35.52  | | 
% 204.76/35.52  | End of split
% 204.76/35.52  | 
% 204.76/35.52  End of proof
% 204.76/35.52  
% 204.76/35.52  Sub-proof #1118 shows that the following formulas are inconsistent:
% 204.76/35.52  ----------------------------------------------------------------
% 204.76/35.52    (1)  op(all_52_3, all_52_3) = all_52_2
% 204.76/35.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.52    (3)   ~ (all_52_5 = all_52_13)
% 204.76/35.52    (4)  all_58_1 = all_52_9
% 204.76/35.52    (5)   ~ (all_52_9 = all_52_13)
% 204.76/35.52    (6)   ~ (e3 = e0)
% 204.76/35.52    (7)  op(all_52_7, all_52_7) = all_52_6
% 204.76/35.52    (8)   ~ (all_52_3 = all_6_2)
% 204.76/35.52    (9)  all_58_0 = all_6_2
% 204.76/35.52    (10)  all_58_13 = all_52_15
% 204.76/35.52    (11)  op(all_52_13, all_52_13) = e1
% 204.76/35.52    (12)   ~ (all_52_15 = e3)
% 204.76/35.52    (13)  op(e1, e3) = all_52_5
% 204.76/35.52    (14)  op(e2, e2) = all_4_2
% 204.76/35.52    (15)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.76/35.52    (16)  all_56_3 = all_14_1
% 204.76/35.52    (17)   ~ (all_52_7 = all_6_2)
% 204.76/35.52    (18)   ~ (all_52_9 = all_14_1)
% 204.76/35.52    (19)   ~ (all_6_2 = e3)
% 204.76/35.52    (20)   ~ (e2 = e1)
% 204.76/35.52    (21)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.76/35.52    (22)  all_58_7 = all_52_13
% 204.76/35.52    (23)  all_58_12 = all_52_7
% 204.76/35.52    (24)   ~ (all_52_7 = e3)
% 204.76/35.52    (25)  all_58_2 = all_52_3
% 204.76/35.52    (26)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.76/35.52    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.76/35.52    (28)  op(e3, all_6_1) = all_6_0
% 204.76/35.52    (29)   ~ (e2 = e0)
% 204.76/35.52    (30)   ~ (all_14_1 = all_6_2)
% 204.76/35.52    (31)   ~ (all_52_5 = e3)
% 204.76/35.52    (32)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.76/35.52    (33)   ~ (all_6_0 = e2)
% 204.76/35.52    (34)   ~ (all_52_9 = e3)
% 204.76/35.52    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.52    (36)   ~ (all_52_9 = all_6_2)
% 204.76/35.52    (37)  op(e3, e3) = all_6_2
% 204.76/35.52    (38)  op(e3, e0) = all_14_1
% 204.76/35.52    (39)   ~ (all_52_3 = all_52_7)
% 204.76/35.52    (40)  all_56_1 = all_52_9
% 204.76/35.52    (41)  all_58_6 = all_52_5
% 204.76/35.52    (42)   ~ (e1 = e0)
% 204.76/35.52    (43)   ~ (e3 = e2)
% 204.76/35.52    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.52    (45)   ~ (all_6_1 = e2)
% 204.76/35.52    (46)  op(all_52_9, all_52_9) = e3
% 204.76/35.52    (47)  all_58_3 = all_4_2
% 204.76/35.52    (48)   ~ (all_52_3 = all_4_2)
% 204.76/35.52    (49)  op(all_6_2, e3) = all_6_1
% 204.76/35.52  
% 204.76/35.52  Begin of proof
% 204.76/35.52  | 
% 204.76/35.52  | BETA: splitting (27) gives:
% 204.76/35.52  | 
% 204.76/35.52  | Case 1:
% 204.76/35.52  | | 
% 204.76/35.52  | |   (50)  all_58_0 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | COMBINE_EQS: (9), (50) imply:
% 204.76/35.52  | |   (51)  all_6_2 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | REDUCE: (19), (51) imply:
% 204.76/35.52  | |   (52)  $false
% 204.76/35.52  | | 
% 204.76/35.52  | | CLOSE: (52) is inconsistent.
% 204.76/35.52  | | 
% 204.76/35.52  | Case 2:
% 204.76/35.52  | | 
% 204.76/35.52  | |   (53)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | BETA: splitting (53) gives:
% 204.76/35.52  | | 
% 204.76/35.52  | | Case 1:
% 204.76/35.52  | | | 
% 204.76/35.52  | | |   (54)  all_58_2 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | COMBINE_EQS: (25), (54) imply:
% 204.76/35.52  | | |   (55)  all_52_3 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | SIMP: (55) implies:
% 204.76/35.52  | | |   (56)  all_52_3 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (39), (56) imply:
% 204.76/35.52  | | |   (57)   ~ (all_52_7 = e3)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (8), (56) imply:
% 204.76/35.52  | | |   (58)   ~ (all_6_2 = e3)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (48), (56) imply:
% 204.76/35.52  | | |   (59)   ~ (all_4_2 = e3)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | SIMP: (59) implies:
% 204.76/35.52  | | |   (60)   ~ (all_4_2 = e3)
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (1), (56) imply:
% 204.76/35.52  | | |   (61)  op(e3, e3) = all_52_2
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 204.76/35.52  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.76/35.52  | | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 204.76/35.52  | | |            (35), (36), (37), (38), (40), (41), (42), (43), (44), (45),
% 204.76/35.52  | | |            (46), (47), (48), (49), (54), (60), (61) are inconsistent by
% 204.76/35.52  | | |            sub-proof #1119.
% 204.76/35.52  | | | 
% 204.76/35.52  | | Case 2:
% 204.76/35.52  | | | 
% 204.76/35.52  | | |   (62)  all_58_6 = e3 | all_58_12 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REF_CLOSE: (23), (24), (31), (41), (62) are inconsistent by sub-proof
% 204.76/35.52  | | |            #1243.
% 204.76/35.52  | | | 
% 204.76/35.52  | | End of split
% 204.76/35.52  | | 
% 204.76/35.52  | End of split
% 204.76/35.52  | 
% 204.76/35.52  End of proof
% 204.76/35.52  
% 204.76/35.52  Sub-proof #1119 shows that the following formulas are inconsistent:
% 204.76/35.52  ----------------------------------------------------------------
% 204.76/35.52    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.76/35.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.76/35.52    (2)   ~ (all_52_5 = all_52_13)
% 204.76/35.52    (3)  all_58_1 = all_52_9
% 204.76/35.52    (4)   ~ (all_52_9 = all_52_13)
% 204.76/35.52    (5)   ~ (e3 = e0)
% 204.76/35.52    (6)  op(all_52_7, all_52_7) = all_52_6
% 204.76/35.52    (7)   ~ (all_4_2 = e3)
% 204.76/35.52    (8)  all_58_0 = all_6_2
% 204.76/35.52    (9)  all_58_13 = all_52_15
% 204.76/35.52    (10)  op(all_52_13, all_52_13) = e1
% 204.76/35.52    (11)   ~ (all_52_15 = e3)
% 204.76/35.52    (12)  op(e1, e3) = all_52_5
% 204.76/35.52    (13)  op(e2, e2) = all_4_2
% 204.76/35.52    (14)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.76/35.52    (15)  all_56_3 = all_14_1
% 204.76/35.52    (16)   ~ (all_52_7 = all_6_2)
% 204.76/35.52    (17)   ~ (all_52_9 = all_14_1)
% 204.76/35.52    (18)   ~ (all_6_2 = e3)
% 204.76/35.52    (19)   ~ (e2 = e1)
% 204.76/35.52    (20)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.76/35.52    (21)  all_58_7 = all_52_13
% 204.76/35.52    (22)  all_58_12 = all_52_7
% 204.76/35.52    (23)   ~ (all_52_7 = e3)
% 204.76/35.52    (24)  all_58_2 = all_52_3
% 204.76/35.52    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.76/35.52    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.76/35.52    (27)  op(e3, all_6_1) = all_6_0
% 204.76/35.52    (28)   ~ (e2 = e0)
% 204.76/35.52    (29)   ~ (all_14_1 = all_6_2)
% 204.76/35.52    (30)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.76/35.52    (31)   ~ (all_6_0 = e2)
% 204.76/35.52    (32)   ~ (all_52_9 = e3)
% 204.76/35.52    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.52    (34)  op(e3, e3) = all_52_2
% 204.76/35.52    (35)   ~ (all_52_9 = all_6_2)
% 204.76/35.52    (36)  op(e3, e3) = all_6_2
% 204.76/35.52    (37)  op(e3, e0) = all_14_1
% 204.76/35.52    (38)  all_56_1 = all_52_9
% 204.76/35.52    (39)  all_58_6 = all_52_5
% 204.76/35.52    (40)   ~ (e1 = e0)
% 204.76/35.52    (41)   ~ (e3 = e2)
% 204.76/35.52    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.76/35.52    (43)   ~ (all_6_1 = e2)
% 204.76/35.52    (44)  op(all_52_9, all_52_9) = e3
% 204.76/35.52    (45)  all_58_3 = all_4_2
% 204.76/35.52    (46)   ~ (all_52_3 = all_4_2)
% 204.76/35.52    (47)  op(all_6_2, e3) = all_6_1
% 204.76/35.52    (48)  all_58_2 = e3
% 204.76/35.52  
% 204.76/35.52  Begin of proof
% 204.76/35.52  | 
% 204.76/35.52  | BETA: splitting (33) gives:
% 204.76/35.52  | 
% 204.76/35.52  | Case 1:
% 204.76/35.52  | | 
% 204.76/35.52  | |   (49)  all_58_1 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | COMBINE_EQS: (3), (49) imply:
% 204.76/35.52  | |   (50)  all_52_9 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | REDUCE: (32), (50) imply:
% 204.76/35.52  | |   (51)  $false
% 204.76/35.52  | | 
% 204.76/35.52  | | CLOSE: (51) is inconsistent.
% 204.76/35.52  | | 
% 204.76/35.52  | Case 2:
% 204.76/35.52  | | 
% 204.76/35.52  | |   (52)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.76/35.52  | | 
% 204.76/35.52  | | BETA: splitting (52) gives:
% 204.76/35.52  | | 
% 204.76/35.52  | | Case 1:
% 204.76/35.52  | | | 
% 204.76/35.52  | | |   (53)  all_58_3 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | COMBINE_EQS: (45), (53) imply:
% 204.76/35.52  | | |   (54)  all_4_2 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | REDUCE: (7), (54) imply:
% 204.76/35.52  | | |   (55)  $false
% 204.76/35.52  | | | 
% 204.76/35.52  | | | CLOSE: (55) is inconsistent.
% 204.76/35.52  | | | 
% 204.76/35.52  | | Case 2:
% 204.76/35.52  | | | 
% 204.76/35.52  | | |   (56)  all_58_7 = e3 | all_58_13 = e3
% 204.76/35.52  | | | 
% 204.76/35.52  | | | BETA: splitting (56) gives:
% 204.76/35.52  | | | 
% 204.76/35.52  | | | Case 1:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | |   (57)  all_58_7 = e3
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | COMBINE_EQS: (21), (57) imply:
% 204.76/35.52  | | | |   (58)  all_52_13 = e3
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (2), (58) imply:
% 204.76/35.52  | | | |   (59)   ~ (all_52_5 = e3)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (10), (58) imply:
% 204.76/35.52  | | | |   (60)  op(e3, e3) = e1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | GROUND_INST: instantiating (1) with all_6_2, all_52_2, e3, e3,
% 204.76/35.52  | | | |              simplifying with (34), (36) gives:
% 204.76/35.52  | | | |   (61)  all_52_2 = all_6_2
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | GROUND_INST: instantiating (1) with e1, all_52_2, e3, e3, simplifying
% 204.76/35.52  | | | |              with (34), (60) gives:
% 204.76/35.52  | | | |   (62)  all_52_2 = e1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | COMBINE_EQS: (61), (62) imply:
% 204.76/35.52  | | | |   (63)  all_6_2 = e1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | SIMP: (63) implies:
% 204.76/35.52  | | | |   (64)  all_6_2 = e1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | COMBINE_EQS: (8), (64) imply:
% 204.76/35.52  | | | |   (65)  all_58_0 = e1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (16), (64) imply:
% 204.76/35.52  | | | |   (66)   ~ (all_52_7 = e1)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (35), (64) imply:
% 204.76/35.52  | | | |   (67)   ~ (all_52_9 = e1)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (29), (64) imply:
% 204.76/35.52  | | | |   (68)   ~ (all_14_1 = e1)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (18), (64) imply:
% 204.76/35.52  | | | |   (69)   ~ (e3 = e1)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | SIMP: (69) implies:
% 204.76/35.52  | | | |   (70)   ~ (e3 = e1)
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | REDUCE: (47), (64) imply:
% 204.76/35.52  | | | |   (71)  op(e1, e3) = all_6_1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | GROUND_INST: instantiating (1) with all_52_5, all_6_1, e3, e1,
% 204.76/35.52  | | | |              simplifying with (12), (71) gives:
% 204.76/35.52  | | | |   (72)  all_52_5 = all_6_1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | COMBINE_EQS: (39), (72) imply:
% 204.76/35.52  | | | |   (73)  all_58_6 = all_6_1
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | BETA: splitting (30) gives:
% 204.76/35.52  | | | | 
% 204.76/35.52  | | | | Case 1:
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | |   (74)  all_58_0 = e2
% 204.76/35.52  | | | | | 
% 204.76/35.52  | | | | | REF_CLOSE: (19), (65), (74) are inconsistent by sub-proof #1273.
% 204.76/35.52  | | | | | 
% 204.79/35.52  | | | | Case 2:
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | |   (75)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | | BETA: splitting (75) gives:
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | | Case 1:
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | |   (76)  all_58_2 = e2
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | | REF_CLOSE: (41), (48), (76) are inconsistent by sub-proof #1124.
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | Case 2:
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | |   (77)  all_58_6 = e2 | all_58_12 = e2
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | | BETA: splitting (77) gives:
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | | Case 1:
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | |   (78)  all_58_6 = e2
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | | REF_CLOSE: (43), (73), (78) are inconsistent by sub-proof #1211.
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | Case 2:
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | |   (79)  all_58_12 = e2
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | | COMBINE_EQS: (22), (79) imply:
% 204.79/35.52  | | | | | | |   (80)  all_52_7 = e2
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | | SIMP: (80) implies:
% 204.79/35.52  | | | | | | |   (81)  all_52_7 = e2
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | | REDUCE: (6), (81) imply:
% 204.79/35.52  | | | | | | |   (82)  op(e2, e2) = all_52_6
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | | BETA: splitting (14) gives:
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | | Case 1:
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | |   (83)  all_58_0 = e0
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | | COMBINE_EQS: (65), (83) imply:
% 204.79/35.52  | | | | | | | |   (84)  e1 = e0
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | | REDUCE: (40), (84) imply:
% 204.79/35.52  | | | | | | | |   (85)  $false
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | | CLOSE: (85) is inconsistent.
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | Case 2:
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | |   (86)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | | BETA: splitting (86) gives:
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | | Case 1:
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | |   (87)  all_58_2 = e0
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | REF_CLOSE: (5), (48), (87) are inconsistent by sub-proof
% 204.79/35.52  | | | | | | | | |            #1123.
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | Case 2:
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | |   (88)  all_58_6 = e0 | all_58_12 = e0
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | BETA: splitting (88) gives:
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | Case 1:
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | |   (89)  all_58_6 = e0
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | | COMBINE_EQS: (73), (89) imply:
% 204.79/35.52  | | | | | | | | | |   (90)  all_6_1 = e0
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | | SIMP: (90) implies:
% 204.79/35.52  | | | | | | | | | |   (91)  all_6_1 = e0
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | | REDUCE: (27), (91) imply:
% 204.79/35.52  | | | | | | | | | |   (92)  op(e3, e0) = all_6_0
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | | REF_CLOSE: (1), (3), (13), (15), (17), (19), (20), (22),
% 204.79/35.52  | | | | | | | | | |            (23), (24), (25), (26), (31), (32), (37), (38),
% 204.79/35.52  | | | | | | | | | |            (39), (42), (44), (46), (59), (65), (67), (68),
% 204.79/35.52  | | | | | | | | | |            (70), (82), (92) are inconsistent by sub-proof
% 204.79/35.52  | | | | | | | | | |            #1120.
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | Case 2:
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | |   (93)  all_58_12 = e0
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | | REF_CLOSE: (28), (79), (93) are inconsistent by sub-proof
% 204.79/35.52  | | | | | | | | | |            #1153.
% 204.79/35.52  | | | | | | | | | | 
% 204.79/35.52  | | | | | | | | | End of split
% 204.79/35.52  | | | | | | | | | 
% 204.79/35.52  | | | | | | | | End of split
% 204.79/35.52  | | | | | | | | 
% 204.79/35.52  | | | | | | | End of split
% 204.79/35.52  | | | | | | | 
% 204.79/35.52  | | | | | | End of split
% 204.79/35.52  | | | | | | 
% 204.79/35.52  | | | | | End of split
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | End of split
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | Case 2:
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | |   (94)  all_58_13 = e3
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | | REF_CLOSE: (9), (11), (94) are inconsistent by sub-proof #1360.
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | End of split
% 204.79/35.52  | | | 
% 204.79/35.52  | | End of split
% 204.79/35.52  | | 
% 204.79/35.52  | End of split
% 204.79/35.52  | 
% 204.79/35.52  End of proof
% 204.79/35.52  
% 204.79/35.52  Sub-proof #1120 shows that the following formulas are inconsistent:
% 204.79/35.52  ----------------------------------------------------------------
% 204.79/35.52    (1)   ~ (e3 = e1)
% 204.79/35.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.52    (3)  all_58_1 = all_52_9
% 204.79/35.52    (4)  op(e2, e2) = all_52_6
% 204.79/35.52    (5)  op(e2, e2) = all_4_2
% 204.79/35.52    (6)  op(e3, e0) = all_6_0
% 204.79/35.52    (7)  all_56_3 = all_14_1
% 204.79/35.52    (8)   ~ (all_52_9 = all_14_1)
% 204.79/35.52    (9)   ~ (e2 = e1)
% 204.79/35.52    (10)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.52    (11)  all_58_12 = all_52_7
% 204.79/35.52    (12)   ~ (all_52_7 = e3)
% 204.79/35.52    (13)  all_58_2 = all_52_3
% 204.79/35.52    (14)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.79/35.52    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.52    (16)   ~ (all_52_5 = e3)
% 204.79/35.52    (17)   ~ (all_6_0 = e2)
% 204.79/35.52    (18)   ~ (all_52_9 = e3)
% 204.79/35.52    (19)   ~ (all_52_9 = e1)
% 204.79/35.52    (20)   ~ (all_14_1 = e1)
% 204.79/35.52    (21)  op(e3, e0) = all_14_1
% 204.79/35.52    (22)  all_56_1 = all_52_9
% 204.79/35.52    (23)  all_58_6 = all_52_5
% 204.79/35.52    (24)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.52    (25)  op(all_52_9, all_52_9) = e3
% 204.79/35.52    (26)   ~ (all_52_3 = all_4_2)
% 204.79/35.52    (27)  all_58_0 = e1
% 204.79/35.52  
% 204.79/35.52  Begin of proof
% 204.79/35.52  | 
% 204.79/35.52  | GROUND_INST: instantiating (2) with all_4_2, all_52_6, e2, e2, simplifying
% 204.79/35.52  |              with (4), (5) gives:
% 204.79/35.52  |   (28)  all_52_6 = all_4_2
% 204.79/35.52  | 
% 204.79/35.52  | GROUND_INST: instantiating (2) with all_14_1, all_6_0, e0, e3, simplifying
% 204.79/35.52  |              with (6), (21) gives:
% 204.79/35.52  |   (29)  all_14_1 = all_6_0
% 204.79/35.52  | 
% 204.79/35.52  | COMBINE_EQS: (7), (29) imply:
% 204.79/35.52  |   (30)  all_56_3 = all_6_0
% 204.79/35.52  | 
% 204.79/35.52  | BETA: splitting (14) gives:
% 204.79/35.52  | 
% 204.79/35.52  | Case 1:
% 204.79/35.52  | | 
% 204.79/35.52  | |   (31)  all_58_0 = e2
% 204.79/35.52  | | 
% 204.79/35.52  | | REF_CLOSE: (9), (27), (31) are inconsistent by sub-proof #1273.
% 204.79/35.52  | | 
% 204.79/35.52  | Case 2:
% 204.79/35.52  | | 
% 204.79/35.52  | |   (32)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.79/35.52  | | 
% 204.79/35.52  | | BETA: splitting (32) gives:
% 204.79/35.52  | | 
% 204.79/35.52  | | Case 1:
% 204.79/35.52  | | | 
% 204.79/35.52  | | |   (33)  all_58_1 = e2
% 204.79/35.52  | | | 
% 204.79/35.52  | | | REF_CLOSE: (1), (2), (3), (5), (11), (12), (13), (15), (16), (23), (25),
% 204.79/35.52  | | |            (26), (27), (33) are inconsistent by sub-proof #1122.
% 204.79/35.52  | | | 
% 204.79/35.52  | | Case 2:
% 204.79/35.52  | | | 
% 204.79/35.52  | | |   (34)   ~ (all_58_1 = e2)
% 204.79/35.52  | | | 
% 204.79/35.52  | | | REDUCE: (3), (34) imply:
% 204.79/35.52  | | |   (35)   ~ (all_52_9 = e2)
% 204.79/35.52  | | | 
% 204.79/35.52  | | | BETA: splitting (24) gives:
% 204.79/35.52  | | | 
% 204.79/35.52  | | | Case 1:
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | |   (36)  all_56_1 = e3
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | | COMBINE_EQS: (22), (36) imply:
% 204.79/35.52  | | | |   (37)  all_52_9 = e3
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | | REDUCE: (18), (37) imply:
% 204.79/35.52  | | | |   (38)  $false
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | | CLOSE: (38) is inconsistent.
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | Case 2:
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | |   (39)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | | BETA: splitting (10) gives:
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | | Case 1:
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | |   (40)  all_56_3 = e2
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | | COMBINE_EQS: (30), (40) imply:
% 204.79/35.52  | | | | |   (41)  all_6_0 = e2
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | | REDUCE: (17), (41) imply:
% 204.79/35.52  | | | | |   (42)  $false
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | | CLOSE: (42) is inconsistent.
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | Case 2:
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | |   (43)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | | REF_CLOSE: (7), (8), (19), (20), (22), (35), (39), (43) are
% 204.79/35.52  | | | | |            inconsistent by sub-proof #1121.
% 204.79/35.52  | | | | | 
% 204.79/35.52  | | | | End of split
% 204.79/35.52  | | | | 
% 204.79/35.52  | | | End of split
% 204.79/35.52  | | | 
% 204.79/35.52  | | End of split
% 204.79/35.52  | | 
% 204.79/35.52  | End of split
% 204.79/35.52  | 
% 204.79/35.52  End of proof
% 204.79/35.52  
% 204.79/35.52  Sub-proof #1121 shows that the following formulas are inconsistent:
% 204.79/35.52  ----------------------------------------------------------------
% 204.79/35.52    (1)  all_56_3 = all_14_1
% 204.79/35.52    (2)   ~ (all_52_9 = all_14_1)
% 204.79/35.52    (3)   ~ (all_52_9 = e2)
% 204.79/35.52    (4)   ~ (all_52_9 = e1)
% 204.79/35.52    (5)   ~ (all_14_1 = e1)
% 204.79/35.52    (6)  all_56_1 = all_52_9
% 204.79/35.52    (7)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.52    (8)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.52  
% 204.79/35.52  Begin of proof
% 204.79/35.52  | 
% 204.79/35.52  | BETA: splitting (8) gives:
% 204.79/35.52  | 
% 204.79/35.52  | Case 1:
% 204.79/35.52  | | 
% 204.79/35.52  | |   (9)  all_56_3 = e1
% 204.79/35.52  | | 
% 204.79/35.52  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1182.
% 204.79/35.52  | | 
% 204.79/35.52  | Case 2:
% 204.79/35.52  | | 
% 204.79/35.52  | |   (10)  all_56_3 = e0
% 204.79/35.52  | | 
% 204.79/35.52  | | COMBINE_EQS: (1), (10) imply:
% 204.79/35.52  | |   (11)  all_14_1 = e0
% 204.79/35.52  | | 
% 204.79/35.52  | | SIMP: (11) implies:
% 204.79/35.52  | |   (12)  all_14_1 = e0
% 204.79/35.52  | | 
% 204.79/35.52  | | REDUCE: (2), (12) imply:
% 204.79/35.52  | |   (13)   ~ (all_52_9 = e0)
% 204.79/35.52  | | 
% 204.79/35.52  | | REF_CLOSE: (3), (4), (6), (7), (13) are inconsistent by sub-proof #1314.
% 204.79/35.52  | | 
% 204.79/35.52  | End of split
% 204.79/35.52  | 
% 204.79/35.52  End of proof
% 204.79/35.52  
% 204.79/35.52  Sub-proof #1122 shows that the following formulas are inconsistent:
% 204.79/35.52  ----------------------------------------------------------------
% 204.79/35.52    (1)   ~ (e3 = e1)
% 204.79/35.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.52    (3)  all_58_1 = all_52_9
% 204.79/35.52    (4)  op(e2, e2) = all_4_2
% 204.79/35.52    (5)  all_58_12 = all_52_7
% 204.79/35.52    (6)   ~ (all_52_7 = e3)
% 204.79/35.52    (7)  all_58_2 = all_52_3
% 204.79/35.53    (8)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.53    (9)   ~ (all_52_5 = e3)
% 204.79/35.53    (10)  all_58_6 = all_52_5
% 204.79/35.53    (11)  op(all_52_9, all_52_9) = e3
% 204.79/35.53    (12)   ~ (all_52_3 = all_4_2)
% 204.79/35.53    (13)  all_58_1 = e2
% 204.79/35.53    (14)  all_58_0 = e1
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (3), (13) imply:
% 204.79/35.53  |   (15)  all_52_9 = e2
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (11), (15) imply:
% 204.79/35.53  |   (16)  op(e2, e2) = e3
% 204.79/35.53  | 
% 204.79/35.53  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (14), (16) are
% 204.79/35.53  |            inconsistent by sub-proof #1241.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1123 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_2 = e3
% 204.79/35.53    (2)  all_58_2 = e0
% 204.79/35.53    (3)   ~ (e3 = e0)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  e3 = e0
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  e3 = e0
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1124 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_2 = e3
% 204.79/35.53    (2)  all_58_2 = e2
% 204.79/35.53    (3)   ~ (e3 = e2)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  e3 = e2
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  e3 = e2
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1125 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ~ (e3 = e1)
% 204.79/35.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (3)  op(e2, e3) = all_52_3
% 204.79/35.53    (4)   ~ (all_52_3 = all_6_2)
% 204.79/35.53    (5)  all_58_0 = all_6_2
% 204.79/35.53    (6)  all_56_4 = all_52_3
% 204.79/35.53    (7)   ~ (all_6_1 = e1)
% 204.79/35.53    (8)   ~ (all_52_3 = e3)
% 204.79/35.53    (9)  op(e3, e3) = e2
% 204.79/35.53    (10)  all_58_6 = e3
% 204.79/35.53    (11)   ~ (e2 = e1)
% 204.79/35.53    (12)  all_58_12 = all_52_7
% 204.79/35.53    (13)  all_58_2 = all_52_3
% 204.79/35.53    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.79/35.53    (15)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.53    (16)  op(e3, e3) = all_52_4
% 204.79/35.53    (17)  op(e3, e3) = all_6_2
% 204.79/35.53    (18)   ~ (all_52_7 = e1)
% 204.79/35.53    (19)   ~ (e1 = e0)
% 204.79/35.53    (20)  op(all_6_2, e3) = all_6_1
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | GROUND_INST: instantiating (2) with all_6_2, all_52_4, e3, e3, simplifying
% 204.79/35.53  |              with (16), (17) gives:
% 204.79/35.53  |   (21)  all_52_4 = all_6_2
% 204.79/35.53  | 
% 204.79/35.53  | GROUND_INST: instantiating (2) with e2, all_52_4, e3, e3, simplifying with
% 204.79/35.53  |              (9), (16) gives:
% 204.79/35.53  |   (22)  all_52_4 = e2
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (21), (22) imply:
% 204.79/35.53  |   (23)  all_6_2 = e2
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (23) implies:
% 204.79/35.53  |   (24)  all_6_2 = e2
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (5), (24) imply:
% 204.79/35.53  |   (25)  all_58_0 = e2
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (4), (24) imply:
% 204.79/35.53  |   (26)   ~ (all_52_3 = e2)
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (20), (24) imply:
% 204.79/35.53  |   (27)  op(e2, e3) = all_6_1
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (14) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (28)  all_58_0 = e1
% 204.79/35.53  | | 
% 204.79/35.53  | | COMBINE_EQS: (25), (28) imply:
% 204.79/35.53  | |   (29)  e2 = e1
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (11), (29) imply:
% 204.79/35.53  | |   (30)  $false
% 204.79/35.53  | | 
% 204.79/35.53  | | CLOSE: (30) is inconsistent.
% 204.79/35.53  | | 
% 204.79/35.53  | Case 2:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (31)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.79/35.53  | | 
% 204.79/35.53  | | BETA: splitting (15) gives:
% 204.79/35.53  | | 
% 204.79/35.53  | | Case 1:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (32)  all_56_4 = e3
% 204.79/35.53  | | | 
% 204.79/35.53  | | | REF_CLOSE: (6), (8), (32) are inconsistent by sub-proof #1340.
% 204.79/35.53  | | | 
% 204.79/35.53  | | Case 2:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (33)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.53  | | | 
% 204.79/35.53  | | | BETA: splitting (33) gives:
% 204.79/35.53  | | | 
% 204.79/35.53  | | | Case 1:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | |   (34)  all_56_4 = e2
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | REF_CLOSE: (6), (26), (34) are inconsistent by sub-proof #1155.
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | Case 2:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | |   (35)  all_56_4 = e1 | all_56_4 = e0
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | BETA: splitting (35) gives:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | Case 1:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | |   (36)  all_56_4 = e1
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | COMBINE_EQS: (6), (36) imply:
% 204.79/35.53  | | | | |   (37)  all_52_3 = e1
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | SIMP: (37) implies:
% 204.79/35.53  | | | | |   (38)  all_52_3 = e1
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REDUCE: (3), (38) imply:
% 204.79/35.53  | | | | |   (39)  op(e2, e3) = e1
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | GROUND_INST: instantiating (2) with e1, all_6_1, e3, e2, simplifying
% 204.79/35.53  | | | | |              with (27), (39) gives:
% 204.79/35.53  | | | | |   (40)  all_6_1 = e1
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REDUCE: (7), (40) imply:
% 204.79/35.53  | | | | |   (41)  $false
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | CLOSE: (41) is inconsistent.
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | Case 2:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | |   (42)  all_56_4 = e0
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | COMBINE_EQS: (6), (42) imply:
% 204.79/35.53  | | | | |   (43)  all_52_3 = e0
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | SIMP: (43) implies:
% 204.79/35.53  | | | | |   (44)  all_52_3 = e0
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | COMBINE_EQS: (13), (44) imply:
% 204.79/35.53  | | | | |   (45)  all_58_2 = e0
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REF_CLOSE: (1), (10), (12), (18), (19), (31), (45) are inconsistent by
% 204.79/35.53  | | | | |            sub-proof #1126.
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | End of split
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | End of split
% 204.79/35.53  | | | 
% 204.79/35.53  | | End of split
% 204.79/35.53  | | 
% 204.79/35.53  | End of split
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1126 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ~ (e3 = e1)
% 204.79/35.53    (2)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 204.79/35.53    (3)  all_58_6 = e3
% 204.79/35.53    (4)  all_58_12 = all_52_7
% 204.79/35.53    (5)  all_58_2 = e0
% 204.79/35.53    (6)   ~ (all_52_7 = e1)
% 204.79/35.53    (7)   ~ (e1 = e0)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (2) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (8)  all_58_2 = e1
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (5), (7), (8) are inconsistent by sub-proof #1129.
% 204.79/35.53  | | 
% 204.79/35.53  | Case 2:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (9)  all_58_6 = e1 | all_58_12 = e1
% 204.79/35.53  | | 
% 204.79/35.53  | | BETA: splitting (9) gives:
% 204.79/35.53  | | 
% 204.79/35.53  | | Case 1:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (10)  all_58_6 = e1
% 204.79/35.53  | | | 
% 204.79/35.53  | | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #1128.
% 204.79/35.53  | | | 
% 204.79/35.53  | | Case 2:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (11)  all_58_12 = e1
% 204.79/35.53  | | | 
% 204.79/35.53  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #1127.
% 204.79/35.53  | | | 
% 204.79/35.53  | | End of split
% 204.79/35.53  | | 
% 204.79/35.53  | End of split
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1127 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_12 = all_52_7
% 204.79/35.53    (2)  all_58_12 = e1
% 204.79/35.53    (3)   ~ (all_52_7 = e1)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  all_52_7 = e1
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  all_52_7 = e1
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1128 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_6 = e3
% 204.79/35.53    (2)  all_58_6 = e1
% 204.79/35.53    (3)   ~ (e3 = e1)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  e3 = e1
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  e3 = e1
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1129 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_2 = e1
% 204.79/35.53    (2)  all_58_2 = e0
% 204.79/35.53    (3)   ~ (e1 = e0)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  e1 = e0
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  e1 = e0
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1130 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ~ (all_52_15 = e1)
% 204.79/35.53    (2)   ~ (e3 = e1)
% 204.79/35.53    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (4)  all_58_1 = all_52_9
% 204.79/35.53    (5)   ~ (all_14_1 = e3)
% 204.79/35.53    (6)  all_58_0 = all_6_2
% 204.79/35.53    (7)  all_58_13 = all_52_15
% 204.79/35.53    (8)  op(all_52_13, all_52_13) = e1
% 204.79/35.53    (9)   ~ (all_52_3 = e3)
% 204.79/35.53    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.53    (11)   ~ (all_4_1 = e1)
% 204.79/35.53    (12)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.79/35.53    (13)   ~ (all_52_13 = all_10_2)
% 204.79/35.53    (14)  all_58_10 = all_52_27
% 204.79/35.53    (15)  all_58_7 = all_52_13
% 204.79/35.53    (16)  all_58_2 = all_52_3
% 204.79/35.53    (17)  all_58_9 = all_14_1
% 204.79/35.53    (18)  op(all_4_2, e2) = all_4_1
% 204.79/35.53    (19)   ~ (all_52_27 = e3)
% 204.79/35.53    (20)   ~ (all_58_0 = e3)
% 204.79/35.53    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.53    (22)   ~ (all_52_9 = all_6_2)
% 204.79/35.53    (23)  op(e3, e3) = all_6_2
% 204.79/35.53    (24)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53    (25)  all_58_5 = all_52_19
% 204.79/35.53    (26)  op(e3, e2) = all_52_9
% 204.79/35.53    (27)  op(e1, e1) = all_10_2
% 204.79/35.53    (28)  op(all_52_9, all_52_9) = e3
% 204.79/35.53    (29)   ~ (all_52_17 = all_52_19)
% 204.79/35.53    (30)  all_58_3 = all_4_2
% 204.79/35.53    (31)  all_58_4 = all_52_17
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (6), (20) imply:
% 204.79/35.53  |   (32)   ~ (all_6_2 = e3)
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (10) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (33)  all_58_2 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (9), (16), (33) are inconsistent by sub-proof #1369.
% 204.79/35.53  | | 
% 204.79/35.53  | Case 2:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (34)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | BETA: splitting (21) gives:
% 204.79/35.53  | | 
% 204.79/35.53  | | Case 1:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (35)  all_58_1 = e3
% 204.79/35.53  | | | 
% 204.79/35.53  | | | COMBINE_EQS: (4), (35) imply:
% 204.79/35.53  | | |   (36)  all_52_9 = e3
% 204.79/35.53  | | | 
% 204.79/35.53  | | | REF_CLOSE: (3), (22), (23), (28), (36) are inconsistent by sub-proof
% 204.79/35.53  | | |            #1337.
% 204.79/35.53  | | | 
% 204.79/35.53  | | Case 2:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (37)   ~ (all_58_1 = e3)
% 204.79/35.53  | | | 
% 204.79/35.53  | | | REDUCE: (4), (37) imply:
% 204.79/35.53  | | |   (38)   ~ (all_52_9 = e3)
% 204.79/35.53  | | | 
% 204.79/35.53  | | | BETA: splitting (24) gives:
% 204.79/35.53  | | | 
% 204.79/35.53  | | | Case 1:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | |   (39)  all_58_0 = e3
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | COMBINE_EQS: (6), (39) imply:
% 204.79/35.53  | | | |   (40)  all_6_2 = e3
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | REDUCE: (32), (40) imply:
% 204.79/35.53  | | | |   (41)  $false
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | CLOSE: (41) is inconsistent.
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | Case 2:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | |   (42)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | BETA: splitting (42) gives:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | Case 1:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | |   (43)  all_58_1 = e3
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | COMBINE_EQS: (4), (43) imply:
% 204.79/35.53  | | | | |   (44)  all_52_9 = e3
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REDUCE: (38), (44) imply:
% 204.79/35.53  | | | | |   (45)  $false
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | CLOSE: (45) is inconsistent.
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | Case 2:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | |   (46)  all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | BETA: splitting (46) gives:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | Case 1:
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | |   (47)  all_58_4 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | COMBINE_EQS: (31), (47) imply:
% 204.79/35.53  | | | | | |   (48)  all_52_17 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | SIMP: (48) implies:
% 204.79/35.53  | | | | | |   (49)  all_52_17 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | REDUCE: (29), (49) imply:
% 204.79/35.53  | | | | | |   (50)   ~ (all_52_19 = e3)
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | SIMP: (50) implies:
% 204.79/35.53  | | | | | |   (51)   ~ (all_52_19 = e3)
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | BETA: splitting (34) gives:
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | Case 1:
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | |   (52)  all_58_3 = e3
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | COMBINE_EQS: (30), (52) imply:
% 204.79/35.53  | | | | | | |   (53)  all_4_2 = e3
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | REDUCE: (18), (53) imply:
% 204.79/35.53  | | | | | | |   (54)  op(e3, e2) = all_4_1
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | GROUND_INST: instantiating (3) with all_52_9, all_4_1, e2, e3,
% 204.79/35.53  | | | | | | |              simplifying with (26), (54) gives:
% 204.79/35.53  | | | | | | |   (55)  all_52_9 = all_4_1
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | COMBINE_EQS: (4), (55) imply:
% 204.79/35.53  | | | | | | |   (56)  all_58_1 = all_4_1
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | BETA: splitting (12) gives:
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | Case 1:
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | |   (57)  all_58_1 = e1
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | | COMBINE_EQS: (56), (57) imply:
% 204.79/35.53  | | | | | | | |   (58)  all_4_1 = e1
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | | REDUCE: (11), (58) imply:
% 204.79/35.53  | | | | | | | |   (59)  $false
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | | CLOSE: (59) is inconsistent.
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | Case 2:
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | |   (60)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | | BETA: splitting (60) gives:
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | | Case 1:
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | |   (61)  all_58_3 = e1
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | COMBINE_EQS: (52), (61) imply:
% 204.79/35.53  | | | | | | | | |   (62)  e3 = e1
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | REDUCE: (2), (62) imply:
% 204.79/35.53  | | | | | | | | |   (63)  $false
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | CLOSE: (63) is inconsistent.
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | Case 2:
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | |   (64)  all_58_7 = e1 | all_58_13 = e1
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | BETA: splitting (64) gives:
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | Case 1:
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | |   (65)  all_58_7 = e1
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | | COMBINE_EQS: (15), (65) imply:
% 204.79/35.53  | | | | | | | | | |   (66)  all_52_13 = e1
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | | REF_CLOSE: (3), (8), (13), (27), (66) are inconsistent by
% 204.79/35.53  | | | | | | | | | |            sub-proof #1134.
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | Case 2:
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | |   (67)  all_58_13 = e1
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | | REF_CLOSE: (1), (7), (67) are inconsistent by sub-proof
% 204.79/35.53  | | | | | | | | | |            #1133.
% 204.79/35.53  | | | | | | | | | | 
% 204.79/35.53  | | | | | | | | | End of split
% 204.79/35.53  | | | | | | | | | 
% 204.79/35.53  | | | | | | | | End of split
% 204.79/35.53  | | | | | | | | 
% 204.79/35.53  | | | | | | | End of split
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | Case 2:
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | |   (68)  all_58_5 = e3 | all_58_10 = e3
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | | REF_CLOSE: (14), (19), (25), (51), (68) are inconsistent by
% 204.79/35.53  | | | | | | |            sub-proof #1132.
% 204.79/35.53  | | | | | | | 
% 204.79/35.53  | | | | | | End of split
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | Case 2:
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | |   (69)  all_58_9 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | REF_CLOSE: (5), (17), (69) are inconsistent by sub-proof #1131.
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | End of split
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | End of split
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | End of split
% 204.79/35.53  | | | 
% 204.79/35.53  | | End of split
% 204.79/35.53  | | 
% 204.79/35.53  | End of split
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1131 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_9 = all_14_1
% 204.79/35.53    (2)  all_58_9 = e3
% 204.79/35.53    (3)   ~ (all_14_1 = e3)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  all_14_1 = e3
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  all_14_1 = e3
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1132 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_10 = all_52_27
% 204.79/35.53    (2)  all_58_5 = e3 | all_58_10 = e3
% 204.79/35.53    (3)   ~ (all_52_19 = e3)
% 204.79/35.53    (4)   ~ (all_52_27 = e3)
% 204.79/35.53    (5)  all_58_5 = all_52_19
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (2) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (6)  all_58_5 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #1279.
% 204.79/35.53  | | 
% 204.79/35.53  | Case 2:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (7)  all_58_10 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1301.
% 204.79/35.53  | | 
% 204.79/35.53  | End of split
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1133 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)  all_58_13 = all_52_15
% 204.79/35.53    (2)  all_58_13 = e1
% 204.79/35.53    (3)   ~ (all_52_15 = e1)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.53  |   (4)  all_52_15 = e1
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (4) implies:
% 204.79/35.53  |   (5)  all_52_15 = e1
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1134 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (2)  op(all_52_13, all_52_13) = e1
% 204.79/35.53    (3)   ~ (all_52_13 = all_10_2)
% 204.79/35.53    (4)  all_52_13 = e1
% 204.79/35.53    (5)  op(e1, e1) = all_10_2
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (3), (4) imply:
% 204.79/35.53  |   (6)   ~ (all_10_2 = e1)
% 204.79/35.53  | 
% 204.79/35.53  | SIMP: (6) implies:
% 204.79/35.53  |   (7)   ~ (all_10_2 = e1)
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (2), (4) imply:
% 204.79/35.53  |   (8)  op(e1, e1) = e1
% 204.79/35.53  | 
% 204.79/35.53  | REF_CLOSE: (1), (5), (7), (8) are inconsistent by sub-proof #1135.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1135 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (2)  op(e1, e1) = all_10_2
% 204.79/35.53    (3)  op(e1, e1) = e1
% 204.79/35.53    (4)   ~ (all_10_2 = e1)
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | GROUND_INST: instantiating (1) with all_10_2, e1, e1, e1, simplifying with
% 204.79/35.53  |              (2), (3) gives:
% 204.79/35.53  |   (5)  all_10_2 = e1
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (4), (5) imply:
% 204.79/35.53  |   (6)  $false
% 204.79/35.53  | 
% 204.79/35.53  | CLOSE: (6) is inconsistent.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1136 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (2)  all_58_1 = all_52_9
% 204.79/35.53    (3)  all_58_0 = all_6_2
% 204.79/35.53    (4)  all_58_13 = all_52_15
% 204.79/35.53    (5)  op(all_52_13, all_52_13) = e1
% 204.79/35.53    (6)  op(all_10_2, all_10_2) = all_52_20
% 204.79/35.53    (7)  all_58_9 = all_52_25
% 204.79/35.53    (8)   ~ (all_52_15 = e3)
% 204.79/35.53    (9)  all_58_11 = all_52_29
% 204.79/35.53    (10)  op(all_6_2, all_6_2) = all_52_0
% 204.79/35.53    (11)   ~ (all_52_13 = all_10_2)
% 204.79/35.53    (12)   ~ (all_6_0 = e1)
% 204.79/35.53    (13)  all_58_7 = all_52_13
% 204.79/35.53    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.53    (15)   ~ (all_52_29 = e3)
% 204.79/35.53    (16)  op(e3, all_6_1) = all_6_0
% 204.79/35.53    (17)   ~ (all_52_25 = e3)
% 204.79/35.53    (18)   ~ (all_6_0 = e2)
% 204.79/35.53    (19)  all_58_0 = e3
% 204.79/35.53    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.53    (21)  all_58_8 = all_10_2
% 204.79/35.53    (22)   ~ (all_52_5 = all_6_2)
% 204.79/35.53    (23)  op(all_4_2, all_4_2) = e2
% 204.79/35.53    (24)   ~ (all_52_9 = all_6_2)
% 204.79/35.53    (25)  op(e3, e3) = all_6_2
% 204.79/35.53    (26)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53    (27)  all_58_6 = all_52_5
% 204.79/35.53    (28)   ~ (all_52_17 = all_6_2)
% 204.79/35.53    (29)  all_56_10 = all_10_2
% 204.79/35.53    (30)  op(all_52_9, all_52_9) = e3
% 204.79/35.53    (31)  all_58_3 = all_4_2
% 204.79/35.53    (32)  op(all_6_2, e3) = all_6_1
% 204.79/35.53    (33)  all_58_4 = all_52_17
% 204.79/35.53    (34)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | COMBINE_EQS: (3), (19) imply:
% 204.79/35.53  |   (35)  all_6_2 = e3
% 204.79/35.53  | 
% 204.79/35.53  | REDUCE: (28), (35) imply:
% 204.79/35.53  |   (36)   ~ (all_52_17 = e3)
% 204.79/35.53  | 
% 204.79/35.53  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.79/35.53  |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 204.79/35.53  |            (25), (26), (27), (29), (30), (31), (32), (33), (34), (36) are
% 204.79/35.53  |            inconsistent by sub-proof #1137.
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1137 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (2)  all_58_1 = all_52_9
% 204.79/35.53    (3)  all_58_0 = all_6_2
% 204.79/35.53    (4)  all_58_13 = all_52_15
% 204.79/35.53    (5)  op(all_52_13, all_52_13) = e1
% 204.79/35.53    (6)  op(all_10_2, all_10_2) = all_52_20
% 204.79/35.53    (7)  all_58_9 = all_52_25
% 204.79/35.53    (8)   ~ (all_52_15 = e3)
% 204.79/35.53    (9)  all_58_11 = all_52_29
% 204.79/35.53    (10)  op(all_6_2, all_6_2) = all_52_0
% 204.79/35.53    (11)   ~ (all_52_13 = all_10_2)
% 204.79/35.53    (12)   ~ (all_6_0 = e1)
% 204.79/35.53    (13)  all_58_7 = all_52_13
% 204.79/35.53    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.53    (15)   ~ (all_52_29 = e3)
% 204.79/35.53    (16)  op(e3, all_6_1) = all_6_0
% 204.79/35.53    (17)   ~ (all_52_25 = e3)
% 204.79/35.53    (18)   ~ (all_6_0 = e2)
% 204.79/35.53    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.53    (20)  all_58_8 = all_10_2
% 204.79/35.53    (21)   ~ (all_52_5 = all_6_2)
% 204.79/35.53    (22)  op(all_4_2, all_4_2) = e2
% 204.79/35.53    (23)   ~ (all_52_9 = all_6_2)
% 204.79/35.53    (24)  op(e3, e3) = all_6_2
% 204.79/35.53    (25)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53    (26)   ~ (all_52_17 = e3)
% 204.79/35.53    (27)  all_58_6 = all_52_5
% 204.79/35.53    (28)  all_56_10 = all_10_2
% 204.79/35.53    (29)  op(all_52_9, all_52_9) = e3
% 204.79/35.53    (30)  all_58_3 = all_4_2
% 204.79/35.53    (31)  op(all_6_2, e3) = all_6_1
% 204.79/35.53    (32)  all_58_4 = all_52_17
% 204.79/35.53    (33)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (25) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (34)  all_58_0 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | COMBINE_EQS: (3), (34) imply:
% 204.79/35.53  | |   (35)  all_6_2 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (21), (35) imply:
% 204.79/35.53  | |   (36)   ~ (all_52_5 = e3)
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (23), (35) imply:
% 204.79/35.53  | |   (37)   ~ (all_52_9 = e3)
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (10), (35) imply:
% 204.79/35.53  | |   (38)  op(e3, e3) = all_52_0
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (31), (35) imply:
% 204.79/35.53  | |   (39)  op(e3, e3) = all_6_1
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (24), (35) imply:
% 204.79/35.53  | |   (40)  op(e3, e3) = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | GROUND_INST: instantiating (1) with all_6_1, all_52_0, e3, e3, simplifying
% 204.79/35.53  | |              with (38), (39) gives:
% 204.79/35.53  | |   (41)  all_52_0 = all_6_1
% 204.79/35.53  | | 
% 204.79/35.53  | | GROUND_INST: instantiating (1) with e3, all_52_0, e3, e3, simplifying with
% 204.79/35.53  | |              (38), (40) gives:
% 204.79/35.53  | |   (42)  all_52_0 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | COMBINE_EQS: (41), (42) imply:
% 204.79/35.53  | |   (43)  all_6_1 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | SIMP: (43) implies:
% 204.79/35.53  | |   (44)  all_6_1 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (16), (44) imply:
% 204.79/35.53  | |   (45)  op(e3, e3) = all_6_0
% 204.79/35.53  | | 
% 204.79/35.53  | | GROUND_INST: instantiating (1) with e3, all_6_0, e3, e3, simplifying with
% 204.79/35.53  | |              (40), (45) gives:
% 204.79/35.53  | |   (46)  all_6_0 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (18), (46) imply:
% 204.79/35.53  | |   (47)   ~ (e3 = e2)
% 204.79/35.53  | | 
% 204.79/35.53  | | REDUCE: (12), (46) imply:
% 204.79/35.53  | |   (48)   ~ (e3 = e1)
% 204.79/35.53  | | 
% 204.79/35.53  | | BETA: splitting (14) gives:
% 204.79/35.53  | | 
% 204.79/35.53  | | Case 1:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (49)  all_58_6 = e3
% 204.79/35.53  | | | 
% 204.79/35.53  | | | REF_CLOSE: (27), (36), (49) are inconsistent by sub-proof #1328.
% 204.79/35.53  | | | 
% 204.79/35.53  | | Case 2:
% 204.79/35.53  | | | 
% 204.79/35.53  | | |   (50)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.53  | | | 
% 204.79/35.53  | | | BETA: splitting (19) gives:
% 204.79/35.53  | | | 
% 204.79/35.53  | | | Case 1:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | |   (51)  all_58_1 = e3
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | COMBINE_EQS: (2), (51) imply:
% 204.79/35.53  | | | |   (52)  all_52_9 = e3
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | REDUCE: (37), (52) imply:
% 204.79/35.53  | | | |   (53)  $false
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | CLOSE: (53) is inconsistent.
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | Case 2:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | |   (54)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | BETA: splitting (33) gives:
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | | Case 1:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | |   (55)  all_56_10 = e3
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | COMBINE_EQS: (28), (55) imply:
% 204.79/35.53  | | | | |   (56)  all_10_2 = e3
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REDUCE: (11), (56) imply:
% 204.79/35.53  | | | | |   (57)   ~ (all_52_13 = e3)
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REDUCE: (6), (56) imply:
% 204.79/35.53  | | | | |   (58)  op(e3, e3) = all_52_20
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | BETA: splitting (54) gives:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | Case 1:
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | |   (59)  all_58_3 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | COMBINE_EQS: (30), (59) imply:
% 204.79/35.53  | | | | | |   (60)  all_4_2 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | REDUCE: (22), (60) imply:
% 204.79/35.53  | | | | | |   (61)  op(e3, e3) = e2
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | GROUND_INST: instantiating (1) with e3, all_52_20, e3, e3,
% 204.79/35.53  | | | | | |              simplifying with (40), (58) gives:
% 204.79/35.53  | | | | | |   (62)  all_52_20 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | GROUND_INST: instantiating (1) with e2, all_52_20, e3, e3,
% 204.79/35.53  | | | | | |              simplifying with (58), (61) gives:
% 204.79/35.53  | | | | | |   (63)  all_52_20 = e2
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | COMBINE_EQS: (62), (63) imply:
% 204.79/35.53  | | | | | |   (64)  e3 = e2
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | REDUCE: (47), (64) imply:
% 204.79/35.53  | | | | | |   (65)  $false
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | CLOSE: (65) is inconsistent.
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | Case 2:
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | |   (66)  all_58_7 = e3 | all_58_13 = e3
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | | REF_CLOSE: (4), (8), (13), (57), (66) are inconsistent by sub-proof
% 204.79/35.53  | | | | | |            #1298.
% 204.79/35.53  | | | | | | 
% 204.79/35.53  | | | | | End of split
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | Case 2:
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | |   (67)   ~ (all_56_10 = e3)
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REDUCE: (28), (67) imply:
% 204.79/35.53  | | | | |   (68)   ~ (all_10_2 = e3)
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | | REF_CLOSE: (1), (5), (9), (13), (15), (20), (38), (40), (48), (50),
% 204.79/35.53  | | | | |            (68) are inconsistent by sub-proof #1139.
% 204.79/35.53  | | | | | 
% 204.79/35.53  | | | | End of split
% 204.79/35.53  | | | | 
% 204.79/35.53  | | | End of split
% 204.79/35.53  | | | 
% 204.79/35.53  | | End of split
% 204.79/35.53  | | 
% 204.79/35.53  | Case 2:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (69)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (1), (2), (7), (17), (23), (24), (26), (29), (32), (69) are
% 204.79/35.53  | |            inconsistent by sub-proof #1138.
% 204.79/35.53  | | 
% 204.79/35.53  | End of split
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1138 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (2)  all_58_1 = all_52_9
% 204.79/35.53    (3)  all_58_9 = all_52_25
% 204.79/35.53    (4)   ~ (all_52_25 = e3)
% 204.79/35.53    (5)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53    (6)   ~ (all_52_9 = all_6_2)
% 204.79/35.53    (7)  op(e3, e3) = all_6_2
% 204.79/35.53    (8)   ~ (all_52_17 = e3)
% 204.79/35.53    (9)  op(all_52_9, all_52_9) = e3
% 204.79/35.53    (10)  all_58_4 = all_52_17
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (5) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (11)  all_58_1 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | COMBINE_EQS: (2), (11) imply:
% 204.79/35.53  | |   (12)  all_52_9 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (1), (6), (7), (9), (12) are inconsistent by sub-proof #1337.
% 204.79/35.53  | | 
% 204.79/35.53  | Case 2:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (13)  all_58_4 = e3 | all_58_9 = e3
% 204.79/35.53  | | 
% 204.79/35.53  | | REF_CLOSE: (3), (4), (8), (10), (13) are inconsistent by sub-proof #1276.
% 204.79/35.53  | | 
% 204.79/35.53  | End of split
% 204.79/35.53  | 
% 204.79/35.53  End of proof
% 204.79/35.53  
% 204.79/35.53  Sub-proof #1139 shows that the following formulas are inconsistent:
% 204.79/35.53  ----------------------------------------------------------------
% 204.79/35.53    (1)   ~ (e3 = e1)
% 204.79/35.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.53    (3)  op(e3, e3) = all_52_0
% 204.79/35.53    (4)  op(all_52_13, all_52_13) = e1
% 204.79/35.53    (5)  all_58_11 = all_52_29
% 204.79/35.53    (6)  all_58_7 = all_52_13
% 204.79/35.53    (7)  op(e3, e3) = e3
% 204.79/35.53    (8)   ~ (all_52_29 = e3)
% 204.79/35.53    (9)   ~ (all_10_2 = e3)
% 204.79/35.53    (10)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.53    (11)  all_58_8 = all_10_2
% 204.79/35.53  
% 204.79/35.53  Begin of proof
% 204.79/35.53  | 
% 204.79/35.53  | BETA: splitting (10) gives:
% 204.79/35.53  | 
% 204.79/35.53  | Case 1:
% 204.79/35.53  | | 
% 204.79/35.53  | |   (12)  all_58_7 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (6), (12) imply:
% 204.79/35.54  | |   (13)  all_52_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (4), (13) imply:
% 204.79/35.54  | |   (14)  op(e3, e3) = e1
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (1), (2), (3), (7), (14) are inconsistent by sub-proof #1237.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (15)  all_58_8 = e3 | all_58_11 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (5), (8), (9), (11), (15) are inconsistent by sub-proof #1140.
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1140 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)  all_58_11 = all_52_29
% 204.79/35.54    (2)  all_58_8 = e3 | all_58_11 = e3
% 204.79/35.54    (3)   ~ (all_52_29 = e3)
% 204.79/35.54    (4)   ~ (all_10_2 = e3)
% 204.79/35.54    (5)  all_58_8 = all_10_2
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (2) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (6)  all_58_8 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (5), (6) imply:
% 204.79/35.54  | |   (7)  all_10_2 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (4), (7) imply:
% 204.79/35.54  | |   (8)  $false
% 204.79/35.54  | | 
% 204.79/35.54  | | CLOSE: (8) is inconsistent.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (9)  all_58_11 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1323.
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1141 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (2)  all_58_1 = all_52_9
% 204.79/35.54    (3)  all_56_4 = all_52_3
% 204.79/35.54    (4)  all_58_13 = all_52_15
% 204.79/35.54    (5)  op(all_52_13, all_52_13) = e1
% 204.79/35.54    (6)   ~ (all_52_15 = e3)
% 204.79/35.54    (7)  all_58_7 = all_52_13
% 204.79/35.54    (8)  all_56_4 = e3
% 204.79/35.54    (9)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (10)   ~ (all_52_9 = all_6_2)
% 204.79/35.54    (11)  op(e3, e3) = all_6_2
% 204.79/35.54    (12)   ~ (all_6_2 = e1)
% 204.79/35.54    (13)  op(all_52_9, all_52_9) = e3
% 204.79/35.54    (14)  all_58_3 = all_4_2
% 204.79/35.54    (15)   ~ (all_52_3 = all_4_2)
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | COMBINE_EQS: (3), (8) imply:
% 204.79/35.54  |   (16)  all_52_3 = e3
% 204.79/35.54  | 
% 204.79/35.54  | SIMP: (16) implies:
% 204.79/35.54  |   (17)  all_52_3 = e3
% 204.79/35.54  | 
% 204.79/35.54  | REDUCE: (15), (17) imply:
% 204.79/35.54  |   (18)   ~ (all_4_2 = e3)
% 204.79/35.54  | 
% 204.79/35.54  | SIMP: (18) implies:
% 204.79/35.54  |   (19)   ~ (all_4_2 = e3)
% 204.79/35.54  | 
% 204.79/35.54  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 204.79/35.54  |            (19) are inconsistent by sub-proof #1142.
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1142 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (2)  all_58_1 = all_52_9
% 204.79/35.54    (3)   ~ (all_4_2 = e3)
% 204.79/35.54    (4)  all_58_13 = all_52_15
% 204.79/35.54    (5)  op(all_52_13, all_52_13) = e1
% 204.79/35.54    (6)   ~ (all_52_15 = e3)
% 204.79/35.54    (7)  all_58_7 = all_52_13
% 204.79/35.54    (8)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (9)   ~ (all_52_9 = all_6_2)
% 204.79/35.54    (10)  op(e3, e3) = all_6_2
% 204.79/35.54    (11)   ~ (all_6_2 = e1)
% 204.79/35.54    (12)  op(all_52_9, all_52_9) = e3
% 204.79/35.54    (13)  all_58_3 = all_4_2
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (8) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (14)  all_58_1 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (2), (14) imply:
% 204.79/35.54  | |   (15)  all_52_9 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (1), (9), (10), (12), (15) are inconsistent by sub-proof #1337.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (16)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (13), (16) are
% 204.79/35.54  | |            inconsistent by sub-proof #1143.
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1143 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (2)   ~ (all_4_2 = e3)
% 204.79/35.54    (3)  all_58_13 = all_52_15
% 204.79/35.54    (4)  op(all_52_13, all_52_13) = e1
% 204.79/35.54    (5)   ~ (all_52_15 = e3)
% 204.79/35.54    (6)  all_58_7 = all_52_13
% 204.79/35.54    (7)  op(e3, e3) = all_6_2
% 204.79/35.54    (8)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (9)   ~ (all_6_2 = e1)
% 204.79/35.54    (10)  all_58_3 = all_4_2
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (8) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (11)  all_58_3 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (10), (11) imply:
% 204.79/35.54  | |   (12)  all_4_2 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (2), (12) imply:
% 204.79/35.54  | |   (13)  $false
% 204.79/35.54  | | 
% 204.79/35.54  | | CLOSE: (13) is inconsistent.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (14)  all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (14) are inconsistent by
% 204.79/35.54  | |            sub-proof #1144.
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1144 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (2)  all_58_13 = all_52_15
% 204.79/35.54    (3)  op(all_52_13, all_52_13) = e1
% 204.79/35.54    (4)   ~ (all_52_15 = e3)
% 204.79/35.54    (5)  all_58_7 = all_52_13
% 204.79/35.54    (6)  all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (7)  op(e3, e3) = all_6_2
% 204.79/35.54    (8)   ~ (all_6_2 = e1)
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (6) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (9)  all_58_7 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (5), (9) imply:
% 204.79/35.54  | |   (10)  all_52_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (3), (10) imply:
% 204.79/35.54  | |   (11)  op(e3, e3) = e1
% 204.79/35.54  | | 
% 204.79/35.54  | | GROUND_INST: instantiating (1) with all_6_2, e1, e3, e3, simplifying with
% 204.79/35.54  | |              (7), (11) gives:
% 204.79/35.54  | |   (12)  all_6_2 = e1
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (8), (12) imply:
% 204.79/35.54  | |   (13)  $false
% 204.79/35.54  | | 
% 204.79/35.54  | | CLOSE: (13) is inconsistent.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (14)  all_58_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #1360.
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1145 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ~ (all_52_15 = all_52_23)
% 204.79/35.54    (2)  all_58_14 = all_52_23
% 204.79/35.54    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (4)  op(all_52_7, all_52_7) = e0
% 204.79/35.54    (5)  all_58_1 = all_52_9
% 204.79/35.54    (6)  op(all_52_5, all_52_5) = e1
% 204.79/35.54    (7)   ~ (e3 = e0)
% 204.79/35.54    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.54    (9)  op(e0, e2) = all_52_15
% 204.79/35.54    (10)   ~ (all_52_7 = all_52_15)
% 204.79/35.54    (11)   ~ (all_52_3 = all_6_2)
% 204.79/35.54    (12)  all_58_0 = all_6_2
% 204.79/35.54    (13)  all_56_4 = all_52_3
% 204.79/35.54    (14)  all_58_13 = all_52_15
% 204.79/35.54    (15)  op(e2, e2) = all_4_2
% 204.79/35.54    (16)   ~ (all_52_3 = all_52_5)
% 204.79/35.54    (17)   ~ (all_4_1 = e3)
% 204.79/35.54    (18)  all_56_5 = all_4_2
% 204.79/35.54    (19)   ~ (all_52_9 = all_52_15)
% 204.79/35.54    (20)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.54    (21)   ~ (all_52_7 = all_6_2)
% 204.79/35.54    (22)  op(e0, e0) = all_14_2
% 204.79/35.54    (23)  all_56_15 = all_14_2
% 204.79/35.54    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.54    (25)  op(e2, all_4_1) = all_4_0
% 204.79/35.54    (26)   ~ (all_4_1 = e1)
% 204.79/35.54    (27)   ~ (all_4_0 = e3)
% 204.79/35.54    (28)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.54    (29)   ~ (e2 = e1)
% 204.79/35.54    (30)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.54    (31)  all_58_7 = all_52_13
% 204.79/35.54    (32)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.79/35.54    (33)  op(all_6_2, all_6_2) = e3
% 204.79/35.54    (34)  all_58_12 = all_52_7
% 204.79/35.54    (35)   ~ (all_52_7 = all_14_2)
% 204.79/35.54    (36)   ~ (all_14_2 = e0)
% 204.79/35.54    (37)  all_58_2 = all_52_3
% 204.79/35.54    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.54    (39)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.54    (40)   ~ (e2 = e0)
% 204.79/35.54    (41)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.54    (42)  op(all_4_2, e2) = all_4_1
% 204.79/35.54    (43)  op(all_52_3, all_52_3) = e2
% 204.79/35.54    (44)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.54    (45)   ~ (all_52_15 = all_14_2)
% 204.79/35.54    (46)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.54    (47)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.54    (48)  op(e1, e2) = all_52_13
% 204.79/35.54    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (50)  all_58_15 = all_14_2
% 204.79/35.54    (51)  op(all_52_23, all_52_23) = all_52_22
% 204.79/35.54    (52)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 204.79/35.54    (53)   ~ (all_52_5 = all_10_2)
% 204.79/35.54    (54)  all_56_12 = all_52_7
% 204.79/35.54    (55)   ~ (all_52_9 = all_4_2)
% 204.79/35.54    (56)   ~ (all_52_9 = all_6_2)
% 204.79/35.54    (57)  op(e3, e3) = all_6_2
% 204.79/35.54    (58)   ~ (all_52_3 = all_52_7)
% 204.79/35.54    (59)  op(all_14_2, all_14_2) = all_52_30
% 204.79/35.54    (60)  all_56_1 = all_52_9
% 204.79/35.54    (61)   ~ (all_52_15 = all_4_2)
% 204.79/35.54    (62)  all_58_6 = all_52_5
% 204.79/35.54    (63)  op(e3, e2) = all_52_9
% 204.79/35.54    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.54    (65)   ~ (e1 = e0)
% 204.79/35.54    (66)   ~ (e3 = e2)
% 204.79/35.54    (67)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.54    (68)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.54    (69)  op(e1, e1) = all_10_2
% 204.79/35.54    (70)   ~ (all_52_23 = all_10_2)
% 204.79/35.54    (71)   ~ (all_52_7 = all_52_23)
% 204.79/35.54    (72)  all_58_3 = all_4_2
% 204.79/35.54    (73)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.79/35.54    (74)  all_56_13 = all_52_15
% 204.79/35.54    (75)   ~ (all_52_3 = all_4_2)
% 204.79/35.54    (76)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.79/35.54    (77)   ~ (all_14_2 = e3)
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (28) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (78)  all_56_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (74), (78) imply:
% 204.79/35.54  | |   (79)  all_52_15 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | SIMP: (79) implies:
% 204.79/35.54  | |   (80)  all_52_15 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (14), (15), (17), (20), (22),
% 204.79/35.54  | |            (34), (35), (42), (44), (47), (54), (65), (69), (70), (80) are
% 204.79/35.54  | |            inconsistent by sub-proof #1168.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (81)   ~ (all_56_13 = e3)
% 204.79/35.54  | |   (82)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (74), (81) imply:
% 204.79/35.54  | |   (83)   ~ (all_52_15 = e3)
% 204.79/35.54  | | 
% 204.79/35.54  | | BETA: splitting (64) gives:
% 204.79/35.54  | | 
% 204.79/35.54  | | Case 1:
% 204.79/35.54  | | | 
% 204.79/35.54  | | |   (84)  all_58_12 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | COMBINE_EQS: (34), (84) imply:
% 204.79/35.54  | | |   (85)  all_52_7 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | REF_CLOSE: (3), (4), (6), (12), (15), (21), (22), (24), (33), (34), (35),
% 204.79/35.54  | | |            (37), (38), (43), (53), (57), (62), (64), (69), (75), (85) are
% 204.79/35.54  | | |            inconsistent by sub-proof #1361.
% 204.79/35.54  | | | 
% 204.79/35.54  | | Case 2:
% 204.79/35.54  | | | 
% 204.79/35.54  | | |   (86)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | BETA: splitting (86) gives:
% 204.79/35.54  | | | 
% 204.79/35.54  | | | Case 1:
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | |   (87)  all_58_13 = e3
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | | REF_CLOSE: (14), (83), (87) are inconsistent by sub-proof #1360.
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | Case 2:
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | |   (88)  all_58_14 = e3 | all_58_15 = e3
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | | BETA: splitting (88) gives:
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | | Case 1:
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | |   (89)  all_58_14 = e3
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | COMBINE_EQS: (2), (89) imply:
% 204.79/35.54  | | | | |   (90)  all_52_23 = e3
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | SIMP: (90) implies:
% 204.79/35.54  | | | | |   (91)  all_52_23 = e3
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | REDUCE: (71), (91) imply:
% 204.79/35.54  | | | | |   (92)   ~ (all_52_7 = e3)
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | REDUCE: (51), (91) imply:
% 204.79/35.54  | | | | |   (93)  op(e3, e3) = all_52_22
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_22, e3, e3,
% 204.79/35.54  | | | | |              simplifying with (57), (93) gives:
% 204.79/35.54  | | | | |   (94)  all_52_22 = all_6_2
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | BETA: splitting (8) gives:
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | Case 1:
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | |   (95)  all_56_12 = e3
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | | REF_CLOSE: (54), (92), (95) are inconsistent by sub-proof #1383.
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | Case 2:
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | |   (96)   ~ (all_56_12 = e3)
% 204.79/35.54  | | | | | |   (97)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | | BETA: splitting (41) gives:
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | | Case 1:
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | |   (98)  all_56_5 = e3
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | COMBINE_EQS: (18), (98) imply:
% 204.79/35.54  | | | | | | |   (99)  all_4_2 = e3
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | SIMP: (99) implies:
% 204.79/35.54  | | | | | | |   (100)  all_4_2 = e3
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REDUCE: (55), (100) imply:
% 204.79/35.54  | | | | | | |   (101)   ~ (all_52_9 = e3)
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REDUCE: (42), (100) imply:
% 204.79/35.54  | | | | | | |   (102)  op(e3, e2) = all_4_1
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REDUCE: (15), (100) imply:
% 204.79/35.54  | | | | | | |   (103)  op(e2, e2) = e3
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | GROUND_INST: instantiating (3) with all_52_9, all_4_1, e2, e3,
% 204.79/35.54  | | | | | | |              simplifying with (63), (102) gives:
% 204.79/35.54  | | | | | | |   (104)  all_52_9 = all_4_1
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | COMBINE_EQS: (60), (104) imply:
% 204.79/35.54  | | | | | | |   (105)  all_56_1 = all_4_1
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | COMBINE_EQS: (5), (104) imply:
% 204.79/35.54  | | | | | | |   (106)  all_58_1 = all_4_1
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REDUCE: (19), (104) imply:
% 204.79/35.54  | | | | | | |   (107)   ~ (all_52_15 = all_4_1)
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | SIMP: (107) implies:
% 204.79/35.54  | | | | | | |   (108)   ~ (all_52_15 = all_4_1)
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REDUCE: (30), (104) imply:
% 204.79/35.54  | | | | | | |   (109)  op(all_4_1, all_4_1) = all_52_8
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | BETA: splitting (67) gives:
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | Case 1:
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | |   (110)  all_56_1 = e3
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | | REF_CLOSE: (17), (105), (110) are inconsistent by sub-proof
% 204.79/35.54  | | | | | | | |            #1167.
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | Case 2:
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | |   (111)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | | BETA: splitting (44) gives:
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | | Case 1:
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | |   (112)  all_58_12 = e1
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | COMBINE_EQS: (34), (112) imply:
% 204.79/35.54  | | | | | | | | |   (113)  all_52_7 = e1
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | REDUCE: (10), (113) imply:
% 204.79/35.54  | | | | | | | | |   (114)   ~ (all_52_15 = e1)
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | SIMP: (114) implies:
% 204.79/35.54  | | | | | | | | |   (115)   ~ (all_52_15 = e1)
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | REDUCE: (35), (113) imply:
% 204.79/35.54  | | | | | | | | |   (116)   ~ (all_14_2 = e1)
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | SIMP: (116) implies:
% 204.79/35.54  | | | | | | | | |   (117)   ~ (all_14_2 = e1)
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | BETA: splitting (52) gives:
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | Case 1:
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | |   (118)  all_56_15 = e2
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | COMBINE_EQS: (23), (118) imply:
% 204.79/35.54  | | | | | | | | | |   (119)  all_14_2 = e2
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | SIMP: (119) implies:
% 204.79/35.54  | | | | | | | | | |   (120)  all_14_2 = e2
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | REDUCE: (45), (120) imply:
% 204.79/35.54  | | | | | | | | | |   (121)   ~ (all_52_15 = e2)
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | REDUCE: (59), (120) imply:
% 204.79/35.54  | | | | | | | | | |   (122)  op(e2, e2) = all_52_30
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | BETA: splitting (82) gives:
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | Case 1:
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | |   (123)  all_56_13 = e2
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | COMBINE_EQS: (74), (123) imply:
% 204.79/35.54  | | | | | | | | | | |   (124)  all_52_15 = e2
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | REDUCE: (121), (124) imply:
% 204.79/35.54  | | | | | | | | | | |   (125)  $false
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | CLOSE: (125) is inconsistent.
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | Case 2:
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | |   (126)  all_56_13 = e1 | all_56_13 = e0
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | BETA: splitting (126) gives:
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | Case 1:
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | |   (127)  all_56_13 = e1
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | COMBINE_EQS: (74), (127) imply:
% 204.79/35.54  | | | | | | | | | | | |   (128)  all_52_15 = e1
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | REDUCE: (115), (128) imply:
% 204.79/35.54  | | | | | | | | | | | |   (129)  $false
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | Case 2:
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | |   (130)  all_56_13 = e0
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | COMBINE_EQS: (74), (130) imply:
% 204.79/35.54  | | | | | | | | | | | |   (131)  all_52_15 = e0
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | REDUCE: (108), (131) imply:
% 204.79/35.54  | | | | | | | | | | | |   (132)   ~ (all_4_1 = e0)
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | SIMP: (132) implies:
% 204.79/35.54  | | | | | | | | | | | |   (133)   ~ (all_4_1 = e0)
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | BETA: splitting (73) gives:
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | Case 1:
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | |   (134)  all_58_1 = e2
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | | COMBINE_EQS: (106), (134) imply:
% 204.79/35.54  | | | | | | | | | | | | |   (135)  all_4_1 = e2
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | | REDUCE: (109), (135) imply:
% 204.79/35.54  | | | | | | | | | | | | |   (136)  op(e2, e2) = all_52_8
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | | REDUCE: (25), (135) imply:
% 204.79/35.54  | | | | | | | | | | | | |   (137)  op(e2, e2) = all_4_0
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | | REF_CLOSE: (3), (27), (103), (122), (136), (137) are
% 204.79/35.54  | | | | | | | | | | | | |            inconsistent by sub-proof #1166.
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | Case 2:
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | |   (138)   ~ (all_58_1 = e2)
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | | REDUCE: (106), (138) imply:
% 204.79/35.54  | | | | | | | | | | | | |   (139)   ~ (all_4_1 = e2)
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | | REF_CLOSE: (26), (105), (111), (133), (139) are inconsistent
% 204.79/35.54  | | | | | | | | | | | | |            by sub-proof #1163.
% 204.79/35.54  | | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | | End of split
% 204.79/35.54  | | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | | End of split
% 204.79/35.54  | | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | End of split
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | Case 2:
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | |   (140)  all_56_15 = e1 | all_56_15 = e0
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | | REF_CLOSE: (23), (36), (117), (140) are inconsistent by
% 204.79/35.54  | | | | | | | | | |            sub-proof #1161.
% 204.79/35.54  | | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | End of split
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | Case 2:
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | |   (141)   ~ (all_58_12 = e1)
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | REDUCE: (34), (141) imply:
% 204.79/35.54  | | | | | | | | |   (142)   ~ (all_52_7 = e1)
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | | REF_CLOSE: (3), (4), (7), (20), (22), (34), (35), (54), (97),
% 204.79/35.54  | | | | | | | | |            (103), (142) are inconsistent by sub-proof #1160.
% 204.79/35.54  | | | | | | | | | 
% 204.79/35.54  | | | | | | | | End of split
% 204.79/35.54  | | | | | | | | 
% 204.79/35.54  | | | | | | | End of split
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | Case 2:
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | |   (143)   ~ (all_56_5 = e3)
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REDUCE: (18), (143) imply:
% 204.79/35.54  | | | | | | |   (144)   ~ (all_4_2 = e3)
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (12), (13), (14), (15),
% 204.79/35.54  | | | | | | |            (16), (17), (20), (24), (29), (31), (32), (33), (34),
% 204.79/35.54  | | | | | | |            (37), (38), (39), (40), (42), (43), (44), (46), (47),
% 204.79/35.54  | | | | | | |            (48), (49), (53), (54), (56), (57), (58), (61), (62),
% 204.79/35.54  | | | | | | |            (66), (68), (69), (72), (75), (76), (83), (89), (92),
% 204.79/35.54  | | | | | | |            (97), (144) are inconsistent by sub-proof #1146.
% 204.79/35.54  | | | | | | | 
% 204.79/35.54  | | | | | | End of split
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | End of split
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | Case 2:
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | |   (145)  all_58_15 = e3
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | COMBINE_EQS: (50), (145) imply:
% 204.79/35.54  | | | | |   (146)  all_14_2 = e3
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | REDUCE: (77), (146) imply:
% 204.79/35.54  | | | | |   (147)  $false
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | CLOSE: (147) is inconsistent.
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | End of split
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | End of split
% 204.79/35.54  | | | 
% 204.79/35.54  | | End of split
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1146 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (2)  op(all_52_7, all_52_7) = e0
% 204.79/35.54    (3)  all_58_1 = all_52_9
% 204.79/35.54    (4)  op(all_52_5, all_52_5) = e1
% 204.79/35.54    (5)   ~ (e3 = e0)
% 204.79/35.54    (6)   ~ (all_4_2 = e3)
% 204.79/35.54    (7)   ~ (all_52_3 = all_6_2)
% 204.79/35.54    (8)  all_58_0 = all_6_2
% 204.79/35.54    (9)  all_56_4 = all_52_3
% 204.79/35.54    (10)  all_58_13 = all_52_15
% 204.79/35.54    (11)   ~ (all_52_15 = e3)
% 204.79/35.54    (12)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.54    (13)  op(e2, e2) = all_4_2
% 204.79/35.54    (14)   ~ (all_52_3 = all_52_5)
% 204.79/35.54    (15)   ~ (all_4_1 = e3)
% 204.79/35.54    (16)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.54    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.54    (18)   ~ (e2 = e1)
% 204.79/35.54    (19)  all_58_7 = all_52_13
% 204.79/35.54    (20)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.79/35.54    (21)  op(all_6_2, all_6_2) = e3
% 204.79/35.54    (22)  all_58_12 = all_52_7
% 204.79/35.54    (23)   ~ (all_52_7 = e3)
% 204.79/35.54    (24)  all_58_2 = all_52_3
% 204.79/35.54    (25)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.54    (26)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.54    (27)   ~ (e2 = e0)
% 204.79/35.54    (28)  op(all_4_2, e2) = all_4_1
% 204.79/35.54    (29)  op(all_52_3, all_52_3) = e2
% 204.79/35.54    (30)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.54    (31)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.54    (32)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.54    (33)  op(e1, e2) = all_52_13
% 204.79/35.54    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (35)   ~ (all_52_5 = all_10_2)
% 204.79/35.54    (36)  all_56_12 = all_52_7
% 204.79/35.54    (37)   ~ (all_52_9 = all_6_2)
% 204.79/35.54    (38)  op(e3, e3) = all_6_2
% 204.79/35.54    (39)   ~ (all_52_3 = all_52_7)
% 204.79/35.54    (40)   ~ (all_52_15 = all_4_2)
% 204.79/35.54    (41)  all_58_6 = all_52_5
% 204.79/35.54    (42)   ~ (e3 = e2)
% 204.79/35.54    (43)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.54    (44)  op(e1, e1) = all_10_2
% 204.79/35.54    (45)  all_58_14 = e3
% 204.79/35.54    (46)  all_58_3 = all_4_2
% 204.79/35.54    (47)   ~ (all_52_3 = all_4_2)
% 204.79/35.54    (48)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (34) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (49)  all_58_1 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (3), (49) imply:
% 204.79/35.54  | |   (50)  all_52_9 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REF_CLOSE: (1), (4), (8), (13), (17), (21), (22), (23), (24), (25), (29),
% 204.79/35.54  | |            (35), (37), (38), (41), (44), (47), (50) are inconsistent by
% 204.79/35.54  | |            sub-proof #1195.
% 204.79/35.54  | | 
% 204.79/35.54  | Case 2:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (51)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | BETA: splitting (51) gives:
% 204.79/35.54  | | 
% 204.79/35.54  | | Case 1:
% 204.79/35.54  | | | 
% 204.79/35.54  | | |   (52)  all_58_3 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | COMBINE_EQS: (46), (52) imply:
% 204.79/35.54  | | |   (53)  all_4_2 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | REDUCE: (6), (53) imply:
% 204.79/35.54  | | |   (54)  $false
% 204.79/35.54  | | | 
% 204.79/35.54  | | | CLOSE: (54) is inconsistent.
% 204.79/35.54  | | | 
% 204.79/35.54  | | Case 2:
% 204.79/35.54  | | | 
% 204.79/35.54  | | |   (55)  all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 204.79/35.54  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 204.79/35.54  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 204.79/35.54  | | |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 204.79/35.54  | | |            (46), (47), (48), (55) are inconsistent by sub-proof #1147.
% 204.79/35.54  | | | 
% 204.79/35.54  | | End of split
% 204.79/35.54  | | 
% 204.79/35.54  | End of split
% 204.79/35.54  | 
% 204.79/35.54  End of proof
% 204.79/35.54  
% 204.79/35.54  Sub-proof #1147 shows that the following formulas are inconsistent:
% 204.79/35.54  ----------------------------------------------------------------
% 204.79/35.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.54    (2)  op(all_52_7, all_52_7) = e0
% 204.79/35.54    (3)  op(all_52_5, all_52_5) = e1
% 204.79/35.54    (4)   ~ (e3 = e0)
% 204.79/35.54    (5)   ~ (all_52_3 = all_6_2)
% 204.79/35.54    (6)  all_58_0 = all_6_2
% 204.79/35.54    (7)  all_56_4 = all_52_3
% 204.79/35.54    (8)  all_58_13 = all_52_15
% 204.79/35.54    (9)   ~ (all_52_15 = e3)
% 204.79/35.54    (10)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.54    (11)  op(e2, e2) = all_4_2
% 204.79/35.54    (12)   ~ (all_52_3 = all_52_5)
% 204.79/35.54    (13)   ~ (all_4_1 = e3)
% 204.79/35.54    (14)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.54    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.54    (16)   ~ (e2 = e1)
% 204.79/35.54    (17)  all_58_7 = all_52_13
% 204.79/35.54    (18)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.79/35.54    (19)  op(all_6_2, all_6_2) = e3
% 204.79/35.54    (20)  all_58_12 = all_52_7
% 204.79/35.54    (21)   ~ (all_52_7 = e3)
% 204.79/35.54    (22)  all_58_2 = all_52_3
% 204.79/35.54    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.54    (24)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.54    (25)   ~ (e2 = e0)
% 204.79/35.54    (26)  op(all_4_2, e2) = all_4_1
% 204.79/35.54    (27)  op(all_52_3, all_52_3) = e2
% 204.79/35.54    (28)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.54    (29)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.54    (30)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.54    (31)  op(e1, e2) = all_52_13
% 204.79/35.54    (32)   ~ (all_52_5 = all_10_2)
% 204.79/35.54    (33)  all_56_12 = all_52_7
% 204.79/35.54    (34)  all_58_7 = e3 | all_58_13 = e3
% 204.79/35.54    (35)  op(e3, e3) = all_6_2
% 204.79/35.54    (36)   ~ (all_52_3 = all_52_7)
% 204.79/35.54    (37)   ~ (all_52_15 = all_4_2)
% 204.79/35.54    (38)  all_58_6 = all_52_5
% 204.79/35.54    (39)   ~ (e3 = e2)
% 204.79/35.54    (40)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.54    (41)  op(e1, e1) = all_10_2
% 204.79/35.54    (42)  all_58_14 = e3
% 204.79/35.54    (43)  all_58_3 = all_4_2
% 204.79/35.54    (44)   ~ (all_52_3 = all_4_2)
% 204.79/35.54    (45)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 204.79/35.54  
% 204.79/35.54  Begin of proof
% 204.79/35.54  | 
% 204.79/35.54  | BETA: splitting (34) gives:
% 204.79/35.54  | 
% 204.79/35.54  | Case 1:
% 204.79/35.54  | | 
% 204.79/35.54  | |   (46)  all_58_7 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | COMBINE_EQS: (17), (46) imply:
% 204.79/35.54  | |   (47)  all_52_13 = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (40), (47) imply:
% 204.79/35.54  | |   (48)  op(e3, e3) = all_52_12
% 204.79/35.54  | | 
% 204.79/35.54  | | REDUCE: (31), (47) imply:
% 204.79/35.54  | |   (49)  op(e1, e2) = e3
% 204.79/35.54  | | 
% 204.79/35.54  | | GROUND_INST: instantiating (1) with all_6_2, all_52_12, e3, e3, simplifying
% 204.79/35.54  | |              with (35), (48) gives:
% 204.79/35.54  | |   (50)  all_52_12 = all_6_2
% 204.79/35.54  | | 
% 204.79/35.54  | | BETA: splitting (15) gives:
% 204.79/35.54  | | 
% 204.79/35.54  | | Case 1:
% 204.79/35.54  | | | 
% 204.79/35.54  | | |   (51)  all_58_2 = e3
% 204.79/35.54  | | | 
% 204.79/35.54  | | | REF_CLOSE: (1), (11), (19), (22), (27), (35), (44), (51) are inconsistent
% 204.79/35.54  | | |            by sub-proof #1159.
% 204.79/35.54  | | | 
% 204.79/35.54  | | Case 2:
% 204.79/35.54  | | | 
% 204.79/35.54  | | |   (52)   ~ (all_58_2 = e3)
% 204.79/35.54  | | | 
% 204.79/35.54  | | | REDUCE: (22), (52) imply:
% 204.79/35.54  | | |   (53)   ~ (all_52_3 = e3)
% 204.79/35.54  | | | 
% 204.79/35.54  | | | BETA: splitting (23) gives:
% 204.79/35.54  | | | 
% 204.79/35.54  | | | Case 1:
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | |   (54)  all_58_0 = e3
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | | COMBINE_EQS: (6), (54) imply:
% 204.79/35.54  | | | |   (55)  all_6_2 = e3
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | | BETA: splitting (24) gives:
% 204.79/35.54  | | | | 
% 204.79/35.54  | | | | Case 1:
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | |   (56)  all_56_4 = e3
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | REF_CLOSE: (7), (53), (56) are inconsistent by sub-proof #1340.
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | Case 2:
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | |   (57)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | BETA: splitting (45) gives:
% 204.79/35.54  | | | | | 
% 204.79/35.54  | | | | | Case 1:
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | |   (58)  all_58_2 = e2
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | | COMBINE_EQS: (22), (58) imply:
% 204.79/35.54  | | | | | |   (59)  all_52_3 = e2
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | | SIMP: (59) implies:
% 204.79/35.54  | | | | | |   (60)  all_52_3 = e2
% 204.79/35.54  | | | | | | 
% 204.79/35.54  | | | | | | REF_CLOSE: (1), (11), (27), (44), (60) are inconsistent by sub-proof
% 204.79/35.54  | | | | | |            #1157.
% 204.79/35.54  | | | | | | 
% 204.79/35.55  | | | | | Case 2:
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | |   (61)   ~ (all_58_2 = e2)
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | REDUCE: (22), (61) imply:
% 204.79/35.55  | | | | | |   (62)   ~ (all_52_3 = e2)
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | BETA: splitting (29) gives:
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | Case 1:
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | |   (63)  all_58_0 = e2
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | | COMBINE_EQS: (54), (63) imply:
% 204.79/35.55  | | | | | | |   (64)  e3 = e2
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | | REDUCE: (39), (64) imply:
% 204.79/35.55  | | | | | | |   (65)  $false
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | | CLOSE: (65) is inconsistent.
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | Case 2:
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | |   (66)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | | BETA: splitting (28) gives:
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | |   (67)  all_58_12 = e1
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | COMBINE_EQS: (20), (67) imply:
% 204.79/35.55  | | | | | | | |   (68)  all_52_7 = e1
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | SIMP: (68) implies:
% 204.79/35.55  | | | | | | | |   (69)  all_52_7 = e1
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | REDUCE: (36), (69) imply:
% 204.79/35.55  | | | | | | | |   (70)   ~ (all_52_3 = e1)
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | BETA: splitting (66) gives:
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | |   (71)  all_58_2 = e2
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | REF_CLOSE: (22), (62), (71) are inconsistent by sub-proof
% 204.79/35.55  | | | | | | | | |            #1156.
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | |   (72)  all_58_6 = e2 | all_58_12 = e2
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | BETA: splitting (72) gives:
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | |   (73)  all_58_6 = e2
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | COMBINE_EQS: (38), (73) imply:
% 204.79/35.55  | | | | | | | | | |   (74)  all_52_5 = e2
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | SIMP: (74) implies:
% 204.79/35.55  | | | | | | | | | |   (75)  all_52_5 = e2
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | REDUCE: (3), (75) imply:
% 204.79/35.55  | | | | | | | | | |   (76)  op(e2, e2) = e1
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | BETA: splitting (57) gives:
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | |   (77)  all_56_4 = e2
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | REF_CLOSE: (7), (62), (77) are inconsistent by sub-proof
% 204.79/35.55  | | | | | | | | | | |            #1155.
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | |   (78)  all_56_4 = e1 | all_56_4 = e0
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | BETA: splitting (78) gives:
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | |   (79)  all_56_4 = e1
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | REF_CLOSE: (7), (70), (79) are inconsistent by sub-proof
% 204.79/35.55  | | | | | | | | | | | |            #1310.
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | |   (80)  all_56_4 = e0
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | COMBINE_EQS: (7), (80) imply:
% 204.79/35.55  | | | | | | | | | | | |   (81)  all_52_3 = e0
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | SIMP: (81) implies:
% 204.79/35.55  | | | | | | | | | | | |   (82)  all_52_3 = e0
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | COMBINE_EQS: (22), (82) imply:
% 204.79/35.55  | | | | | | | | | | | |   (83)  all_58_2 = e0
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | REDUCE: (70), (82) imply:
% 204.79/35.55  | | | | | | | | | | | |   (84)   ~ (e1 = e0)
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | SIMP: (84) implies:
% 204.79/35.55  | | | | | | | | | | | |   (85)   ~ (e1 = e0)
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | BETA: splitting (18) gives:
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | |   (86)  all_58_2 = e1
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | | COMBINE_EQS: (83), (86) imply:
% 204.79/35.55  | | | | | | | | | | | | |   (87)  e1 = e0
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | | REDUCE: (85), (87) imply:
% 204.79/35.55  | | | | | | | | | | | | |   (88)  $false
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | | CLOSE: (88) is inconsistent.
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | |   (89)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | | REF_CLOSE: (1), (11), (13), (26), (43), (49), (76), (89) are
% 204.79/35.55  | | | | | | | | | | | | |            inconsistent by sub-proof #1154.
% 204.79/35.55  | | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | | End of split
% 204.79/35.55  | | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | | End of split
% 204.79/35.55  | | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | End of split
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | |   (90)  all_58_12 = e2
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | COMBINE_EQS: (67), (90) imply:
% 204.79/35.55  | | | | | | | | | |   (91)  e2 = e1
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | REDUCE: (16), (91) imply:
% 204.79/35.55  | | | | | | | | | |   (92)  $false
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | | CLOSE: (92) is inconsistent.
% 204.79/35.55  | | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | End of split
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | End of split
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | |   (93)   ~ (all_58_12 = e1)
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | REDUCE: (20), (93) imply:
% 204.79/35.55  | | | | | | | |   (94)   ~ (all_52_7 = e1)
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | BETA: splitting (14) gives:
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | | Case 1:
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | |   (95)  all_58_12 = e2
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | COMBINE_EQS: (20), (95) imply:
% 204.79/35.55  | | | | | | | | |   (96)  all_52_7 = e2
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | SIMP: (96) implies:
% 204.79/35.55  | | | | | | | | |   (97)  all_52_7 = e2
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | REDUCE: (2), (97) imply:
% 204.79/35.55  | | | | | | | | |   (98)  op(e2, e2) = e0
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | REF_CLOSE: (1), (4), (8), (11), (25), (30), (37), (42), (95),
% 204.79/35.55  | | | | | | | | |            (98) are inconsistent by sub-proof #1150.
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | Case 2:
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | |   (99)   ~ (all_58_12 = e2)
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | REDUCE: (20), (99) imply:
% 204.79/35.55  | | | | | | | | |   (100)   ~ (all_52_7 = e2)
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | | REF_CLOSE: (1), (3), (7), (10), (11), (20), (22), (33), (36),
% 204.79/35.55  | | | | | | | | |            (38), (44), (57), (62), (66), (94), (100) are
% 204.79/35.55  | | | | | | | | |            inconsistent by sub-proof #1148.
% 204.79/35.55  | | | | | | | | | 
% 204.79/35.55  | | | | | | | | End of split
% 204.79/35.55  | | | | | | | | 
% 204.79/35.55  | | | | | | | End of split
% 204.79/35.55  | | | | | | | 
% 204.79/35.55  | | | | | | End of split
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | End of split
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | End of split
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | Case 2:
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | |   (101)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | | REF_CLOSE: (1), (3), (19), (20), (21), (22), (32), (35), (38), (41),
% 204.79/35.55  | | | |            (53), (101) are inconsistent by sub-proof #1365.
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | End of split
% 204.79/35.55  | | | 
% 204.79/35.55  | | End of split
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (102)  all_58_13 = e3
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (8), (9), (102) are inconsistent by sub-proof #1360.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1148 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(all_52_5, all_52_5) = e1
% 204.79/35.55    (3)  all_56_4 = all_52_3
% 204.79/35.55    (4)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.55    (5)  op(e2, e2) = all_4_2
% 204.79/35.55    (6)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.55    (7)  all_58_12 = all_52_7
% 204.79/35.55    (8)  all_58_2 = all_52_3
% 204.79/35.55    (9)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.55    (10)   ~ (all_52_7 = e2)
% 204.79/35.55    (11)  all_56_12 = all_52_7
% 204.79/35.55    (12)   ~ (all_52_7 = e1)
% 204.79/35.55    (13)   ~ (all_52_3 = all_52_7)
% 204.79/35.55    (14)  all_58_6 = all_52_5
% 204.79/35.55    (15)   ~ (all_52_3 = e2)
% 204.79/35.55    (16)   ~ (all_52_3 = all_4_2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (4) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (17)  all_56_12 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (11), (17) imply:
% 204.79/35.55  | |   (18)  all_52_7 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (10), (18) imply:
% 204.79/35.55  | |   (19)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (19) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (20)   ~ (all_56_12 = e2)
% 204.79/35.55  | |   (21)  all_56_12 = e1 | all_56_12 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | BETA: splitting (21) gives:
% 204.79/35.55  | | 
% 204.79/35.55  | | Case 1:
% 204.79/35.55  | | | 
% 204.79/35.55  | | |   (22)  all_56_12 = e1
% 204.79/35.55  | | | 
% 204.79/35.55  | | | COMBINE_EQS: (11), (22) imply:
% 204.79/35.55  | | |   (23)  all_52_7 = e1
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REDUCE: (12), (23) imply:
% 204.79/35.55  | | |   (24)  $false
% 204.79/35.55  | | | 
% 204.79/35.55  | | | CLOSE: (24) is inconsistent.
% 204.79/35.55  | | | 
% 204.79/35.55  | | Case 2:
% 204.79/35.55  | | | 
% 204.79/35.55  | | |   (25)  all_56_12 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | COMBINE_EQS: (11), (25) imply:
% 204.79/35.55  | | |   (26)  all_52_7 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | COMBINE_EQS: (7), (26) imply:
% 204.79/35.55  | | |   (27)  all_58_12 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REDUCE: (13), (26) imply:
% 204.79/35.55  | | |   (28)   ~ (all_52_3 = e0)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REDUCE: (10), (26) imply:
% 204.79/35.55  | | |   (29)   ~ (e2 = e0)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | SIMP: (29) implies:
% 204.79/35.55  | | |   (30)   ~ (e2 = e0)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | BETA: splitting (6) gives:
% 204.79/35.55  | | | 
% 204.79/35.55  | | | Case 1:
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | |   (31)  all_58_2 = e2
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | | REF_CLOSE: (8), (15), (31) are inconsistent by sub-proof #1156.
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | Case 2:
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | |   (32)   ~ (all_58_2 = e2)
% 204.79/35.55  | | | |   (33)  all_58_6 = e2 | all_58_12 = e2
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | | BETA: splitting (9) gives:
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | | Case 1:
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | |   (34)  all_56_4 = e2
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | | REF_CLOSE: (3), (15), (34) are inconsistent by sub-proof #1155.
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | Case 2:
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | |   (35)  all_56_4 = e1 | all_56_4 = e0
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | | BETA: splitting (35) gives:
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | | Case 1:
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | |   (36)  all_56_4 = e1
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | COMBINE_EQS: (3), (36) imply:
% 204.79/35.55  | | | | | |   (37)  all_52_3 = e1
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | SIMP: (37) implies:
% 204.79/35.55  | | | | | |   (38)  all_52_3 = e1
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | REDUCE: (16), (38) imply:
% 204.79/35.55  | | | | | |   (39)   ~ (all_4_2 = e1)
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | SIMP: (39) implies:
% 204.79/35.55  | | | | | |   (40)   ~ (all_4_2 = e1)
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | REF_CLOSE: (1), (2), (5), (14), (27), (30), (33), (40) are
% 204.79/35.55  | | | | | |            inconsistent by sub-proof #1149.
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | Case 2:
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | |   (41)  all_56_4 = e0
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | | REF_CLOSE: (3), (28), (41) are inconsistent by sub-proof #1309.
% 204.79/35.55  | | | | | | 
% 204.79/35.55  | | | | | End of split
% 204.79/35.55  | | | | | 
% 204.79/35.55  | | | | End of split
% 204.79/35.55  | | | | 
% 204.79/35.55  | | | End of split
% 204.79/35.55  | | | 
% 204.79/35.55  | | End of split
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1149 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(all_52_5, all_52_5) = e1
% 204.79/35.55    (3)  all_58_6 = e2 | all_58_12 = e2
% 204.79/35.55    (4)  all_58_12 = e0
% 204.79/35.55    (5)  op(e2, e2) = all_4_2
% 204.79/35.55    (6)   ~ (e2 = e0)
% 204.79/35.55    (7)  all_58_6 = all_52_5
% 204.79/35.55    (8)   ~ (all_4_2 = e1)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (3) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (9)  all_58_6 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (1), (2), (5), (7), (8), (9) are inconsistent by sub-proof #1192.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (10)  all_58_12 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (4), (10) imply:
% 204.79/35.55  | |   (11)  e2 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (6), (11) imply:
% 204.79/35.55  | |   (12)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (12) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1150 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)   ~ (e3 = e0)
% 204.79/35.55    (3)  all_58_13 = all_52_15
% 204.79/35.55    (4)  op(e2, e2) = all_4_2
% 204.79/35.55    (5)   ~ (e2 = e0)
% 204.79/35.55    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.55    (7)  op(e2, e2) = e0
% 204.79/35.55    (8)  all_58_12 = e2
% 204.79/35.55    (9)   ~ (all_52_15 = all_4_2)
% 204.79/35.55    (10)  all_58_14 = e3
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (6) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (11)  all_58_12 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (5), (8), (11) are inconsistent by sub-proof #1153.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (12)  all_58_13 = e0 | all_58_14 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | BETA: splitting (12) gives:
% 204.79/35.55  | | 
% 204.79/35.55  | | Case 1:
% 204.79/35.55  | | | 
% 204.79/35.55  | | |   (13)  all_58_13 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | COMBINE_EQS: (3), (13) imply:
% 204.79/35.55  | | |   (14)  all_52_15 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | SIMP: (14) implies:
% 204.79/35.55  | | |   (15)  all_52_15 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REDUCE: (9), (15) imply:
% 204.79/35.55  | | |   (16)   ~ (all_4_2 = e0)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | SIMP: (16) implies:
% 204.79/35.55  | | |   (17)   ~ (all_4_2 = e0)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REF_CLOSE: (1), (4), (7), (17) are inconsistent by sub-proof #1152.
% 204.79/35.55  | | | 
% 204.79/35.55  | | Case 2:
% 204.79/35.55  | | | 
% 204.79/35.55  | | |   (18)  all_58_14 = e0
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REF_CLOSE: (2), (10), (18) are inconsistent by sub-proof #1151.
% 204.79/35.55  | | | 
% 204.79/35.55  | | End of split
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1151 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_58_14 = e3
% 204.79/35.55    (2)  all_58_14 = e0
% 204.79/35.55    (3)   ~ (e3 = e0)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  e3 = e0
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  e3 = e0
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1152 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(e2, e2) = all_4_2
% 204.79/35.55    (3)  op(e2, e2) = e0
% 204.79/35.55    (4)   ~ (all_4_2 = e0)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e2, simplifying with (2),
% 204.79/35.55  |              (3) gives:
% 204.79/35.55  |   (5)  all_4_2 = e0
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (4), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1153 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_58_12 = e2
% 204.79/35.55    (2)  all_58_12 = e0
% 204.79/35.55    (3)   ~ (e2 = e0)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  e2 = e0
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  e2 = e0
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1154 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(e2, e2) = e1
% 204.79/35.55    (3)  op(e2, e2) = all_4_2
% 204.79/35.55    (4)   ~ (all_4_1 = e3)
% 204.79/35.55    (5)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 204.79/35.55    (6)  op(e1, e2) = e3
% 204.79/35.55    (7)  op(all_4_2, e2) = all_4_1
% 204.79/35.55    (8)  all_58_3 = all_4_2
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (5) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (9)  all_58_3 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (8), (9) imply:
% 204.79/35.55  | |   (10)  all_4_2 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (7), (10) imply:
% 204.79/35.55  | |   (11)  op(e1, e2) = all_4_1
% 204.79/35.55  | | 
% 204.79/35.55  | | GROUND_INST: instantiating (1) with e3, all_4_1, e2, e1, simplifying with
% 204.79/35.55  | |              (6), (11) gives:
% 204.79/35.55  | |   (12)  all_4_1 = e3
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (4), (12) imply:
% 204.79/35.55  | |   (13)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (13) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (14)   ~ (all_58_3 = e1)
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (8), (14) imply:
% 204.79/35.55  | |   (15)   ~ (all_4_2 = e1)
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (1), (2), (3), (15) are inconsistent by sub-proof #1193.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1155 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_4 = all_52_3
% 204.79/35.55    (2)  all_56_4 = e2
% 204.79/35.55    (3)   ~ (all_52_3 = e2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  all_52_3 = e2
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  all_52_3 = e2
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1156 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_58_2 = all_52_3
% 204.79/35.55    (2)  all_58_2 = e2
% 204.79/35.55    (3)   ~ (all_52_3 = e2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  all_52_3 = e2
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  all_52_3 = e2
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1157 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(e2, e2) = all_4_2
% 204.79/35.55    (3)  op(all_52_3, all_52_3) = e2
% 204.79/35.55    (4)  all_52_3 = e2
% 204.79/35.55    (5)   ~ (all_52_3 = all_4_2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (4), (5) imply:
% 204.79/35.55  |   (6)   ~ (all_4_2 = e2)
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (6) implies:
% 204.79/35.55  |   (7)   ~ (all_4_2 = e2)
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (4) imply:
% 204.79/35.55  |   (8)  op(e2, e2) = e2
% 204.79/35.55  | 
% 204.79/35.55  | REF_CLOSE: (1), (2), (7), (8) are inconsistent by sub-proof #1158.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1158 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(e2, e2) = all_4_2
% 204.79/35.55    (3)  op(e2, e2) = e2
% 204.79/35.55    (4)   ~ (all_4_2 = e2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e2, simplifying with (2),
% 204.79/35.55  |              (3) gives:
% 204.79/35.55  |   (5)  all_4_2 = e2
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (4), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1159 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(e2, e2) = all_4_2
% 204.79/35.55    (3)  op(all_6_2, all_6_2) = e3
% 204.79/35.55    (4)  all_58_2 = all_52_3
% 204.79/35.55    (5)  op(all_52_3, all_52_3) = e2
% 204.79/35.55    (6)  op(e3, e3) = all_6_2
% 204.79/35.55    (7)   ~ (all_52_3 = all_4_2)
% 204.79/35.55    (8)  all_58_2 = e3
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (4), (8) imply:
% 204.79/35.55  |   (9)  all_52_3 = e3
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (9) implies:
% 204.79/35.55  |   (10)  all_52_3 = e3
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (7), (10) imply:
% 204.79/35.55  |   (11)   ~ (all_4_2 = e3)
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (11) implies:
% 204.79/35.55  |   (12)   ~ (all_4_2 = e3)
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (5), (10) imply:
% 204.79/35.55  |   (13)  op(e3, e3) = e2
% 204.79/35.55  | 
% 204.79/35.55  | REF_CLOSE: (1), (2), (3), (6), (12), (13) are inconsistent by sub-proof #1370.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1160 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(all_52_7, all_52_7) = e0
% 204.79/35.55    (3)   ~ (e3 = e0)
% 204.79/35.55    (4)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.55    (5)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.55    (6)  op(e0, e0) = all_14_2
% 204.79/35.55    (7)  all_58_12 = all_52_7
% 204.79/35.55    (8)   ~ (all_52_7 = all_14_2)
% 204.79/35.55    (9)  all_56_12 = all_52_7
% 204.79/35.55    (10)   ~ (all_52_7 = e1)
% 204.79/35.55    (11)  op(e2, e2) = e3
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (5) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (12)  all_58_12 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (7), (12) imply:
% 204.79/35.55  | |   (13)  all_52_7 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (2), (13) imply:
% 204.79/35.55  | |   (14)  op(e2, e2) = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | GROUND_INST: instantiating (1) with e3, e0, e2, e2, simplifying with (11),
% 204.79/35.55  | |              (14) gives:
% 204.79/35.55  | |   (15)  e3 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (3), (15) imply:
% 204.79/35.55  | |   (16)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (16) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (17)   ~ (all_58_12 = e2)
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (7), (17) imply:
% 204.79/35.55  | |   (18)   ~ (all_52_7 = e2)
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (18) are inconsistent by
% 204.79/35.55  | |            sub-proof #1176.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1161 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_15 = e1 | all_56_15 = e0
% 204.79/35.55    (2)  all_56_15 = all_14_2
% 204.79/35.55    (3)   ~ (all_14_2 = e1)
% 204.79/35.55    (4)   ~ (all_14_2 = e0)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (1) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (5)  all_56_15 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (2), (5) imply:
% 204.79/35.55  | |   (6)  all_14_2 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | SIMP: (6) implies:
% 204.79/35.55  | |   (7)  all_14_2 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (3), (7) imply:
% 204.79/35.55  | |   (8)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (8) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (9)  all_56_15 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1162.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1162 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_15 = all_14_2
% 204.79/35.55    (2)  all_56_15 = e0
% 204.79/35.55    (3)   ~ (all_14_2 = e0)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  all_14_2 = e0
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  all_14_2 = e0
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1163 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_1 = all_4_1
% 204.79/35.55    (2)   ~ (all_4_1 = e1)
% 204.79/35.55    (3)   ~ (all_4_1 = e2)
% 204.79/35.55    (4)   ~ (all_4_1 = e0)
% 204.79/35.55    (5)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (5) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (6)  all_56_1 = e2
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #1165.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (7)  all_56_1 = e1 | all_56_1 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #1164.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1164 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_1 = e1 | all_56_1 = e0
% 204.79/35.55    (2)  all_56_1 = all_4_1
% 204.79/35.55    (3)   ~ (all_4_1 = e1)
% 204.79/35.55    (4)   ~ (all_4_1 = e0)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (1) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (5)  all_56_1 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (2), (5) imply:
% 204.79/35.55  | |   (6)  all_4_1 = e1
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (3), (6) imply:
% 204.79/35.55  | |   (7)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (7) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (8)  all_56_1 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | COMBINE_EQS: (2), (8) imply:
% 204.79/35.55  | |   (9)  all_4_1 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | REDUCE: (4), (9) imply:
% 204.79/35.55  | |   (10)  $false
% 204.79/35.55  | | 
% 204.79/35.55  | | CLOSE: (10) is inconsistent.
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1165 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_1 = all_4_1
% 204.79/35.55    (2)  all_56_1 = e2
% 204.79/35.55    (3)   ~ (all_4_1 = e2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  all_4_1 = e2
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  all_4_1 = e2
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1166 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (2)  op(e2, e2) = all_52_8
% 204.79/35.55    (3)  op(e2, e2) = all_4_0
% 204.79/35.55    (4)  op(e2, e2) = all_52_30
% 204.79/35.55    (5)   ~ (all_4_0 = e3)
% 204.79/35.55    (6)  op(e2, e2) = e3
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | GROUND_INST: instantiating (1) with e3, all_52_30, e2, e2, simplifying with
% 204.79/35.55  |              (4), (6) gives:
% 204.79/35.55  |   (7)  all_52_30 = e3
% 204.79/35.55  | 
% 204.79/35.55  | GROUND_INST: instantiating (1) with all_52_30, all_52_8, e2, e2, simplifying
% 204.79/35.55  |              with (2), (4) gives:
% 204.79/35.55  |   (8)  all_52_8 = all_52_30
% 204.79/35.55  | 
% 204.79/35.55  | GROUND_INST: instantiating (1) with all_4_0, all_52_8, e2, e2, simplifying
% 204.79/35.55  |              with (2), (3) gives:
% 204.79/35.55  |   (9)  all_52_8 = all_4_0
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (8), (9) imply:
% 204.79/35.55  |   (10)  all_52_30 = all_4_0
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (10) implies:
% 204.79/35.55  |   (11)  all_52_30 = all_4_0
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (7), (11) imply:
% 204.79/35.55  |   (12)  all_4_0 = e3
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (5), (12) imply:
% 204.79/35.55  |   (13)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (13) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1167 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_56_1 = all_4_1
% 204.79/35.55    (2)  all_56_1 = e3
% 204.79/35.55    (3)   ~ (all_4_1 = e3)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.55  |   (4)  all_4_1 = e3
% 204.79/35.55  | 
% 204.79/35.55  | SIMP: (4) implies:
% 204.79/35.55  |   (5)  all_4_1 = e3
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (3), (5) imply:
% 204.79/35.55  |   (6)  $false
% 204.79/35.55  | 
% 204.79/35.55  | CLOSE: (6) is inconsistent.
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1168 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_58_14 = all_52_23
% 204.79/35.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (3)  op(all_52_7, all_52_7) = e0
% 204.79/35.55    (4)   ~ (e3 = e0)
% 204.79/35.55    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.55    (6)  op(e0, e2) = all_52_15
% 204.79/35.55    (7)   ~ (all_52_7 = all_52_15)
% 204.79/35.55    (8)  all_58_13 = all_52_15
% 204.79/35.55    (9)  all_52_15 = e3
% 204.79/35.55    (10)  op(e2, e2) = all_4_2
% 204.79/35.55    (11)   ~ (all_4_1 = e3)
% 204.79/35.55    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.55    (13)  op(e0, e0) = all_14_2
% 204.79/35.55    (14)  all_58_12 = all_52_7
% 204.79/35.55    (15)   ~ (all_52_7 = all_14_2)
% 204.79/35.55    (16)  op(all_4_2, e2) = all_4_1
% 204.79/35.55    (17)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.55    (18)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.55    (19)  all_56_12 = all_52_7
% 204.79/35.55    (20)   ~ (e1 = e0)
% 204.79/35.55    (21)  op(e1, e1) = all_10_2
% 204.79/35.55    (22)   ~ (all_52_23 = all_10_2)
% 204.79/35.55  
% 204.79/35.55  Begin of proof
% 204.79/35.55  | 
% 204.79/35.55  | COMBINE_EQS: (8), (9) imply:
% 204.79/35.55  |   (23)  all_58_13 = e3
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (7), (9) imply:
% 204.79/35.55  |   (24)   ~ (all_52_7 = e3)
% 204.79/35.55  | 
% 204.79/35.55  | REDUCE: (6), (9) imply:
% 204.79/35.55  |   (25)  op(e0, e2) = e3
% 204.79/35.55  | 
% 204.79/35.55  | BETA: splitting (5) gives:
% 204.79/35.55  | 
% 204.79/35.55  | Case 1:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (26)  all_56_12 = e3
% 204.79/35.55  | | 
% 204.79/35.55  | | REF_CLOSE: (19), (24), (26) are inconsistent by sub-proof #1383.
% 204.79/35.55  | | 
% 204.79/35.55  | Case 2:
% 204.79/35.55  | | 
% 204.79/35.55  | |   (27)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.55  | | 
% 204.79/35.55  | | BETA: splitting (12) gives:
% 204.79/35.55  | | 
% 204.79/35.55  | | Case 1:
% 204.79/35.55  | | | 
% 204.79/35.55  | | |   (28)  all_58_12 = e2
% 204.79/35.55  | | | 
% 204.79/35.55  | | | COMBINE_EQS: (14), (28) imply:
% 204.79/35.55  | | |   (29)  all_52_7 = e2
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REF_CLOSE: (2), (3), (10), (11), (16), (25), (29) are inconsistent by
% 204.79/35.55  | | |            sub-proof #1377.
% 204.79/35.55  | | | 
% 204.79/35.55  | | Case 2:
% 204.79/35.55  | | | 
% 204.79/35.55  | | |   (30)   ~ (all_58_12 = e2)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REDUCE: (14), (30) imply:
% 204.79/35.55  | | |   (31)   ~ (all_52_7 = e2)
% 204.79/35.55  | | | 
% 204.79/35.55  | | | REF_CLOSE: (1), (2), (3), (4), (13), (14), (15), (17), (18), (19), (20),
% 204.79/35.55  | | |            (21), (22), (23), (27), (31) are inconsistent by sub-proof
% 204.79/35.55  | | |            #1169.
% 204.79/35.55  | | | 
% 204.79/35.55  | | End of split
% 204.79/35.55  | | 
% 204.79/35.55  | End of split
% 204.79/35.55  | 
% 204.79/35.55  End of proof
% 204.79/35.55  
% 204.79/35.55  Sub-proof #1169 shows that the following formulas are inconsistent:
% 204.79/35.55  ----------------------------------------------------------------
% 204.79/35.55    (1)  all_58_14 = all_52_23
% 204.79/35.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.55    (3)  op(all_52_7, all_52_7) = e0
% 204.79/35.56    (4)   ~ (e3 = e0)
% 204.79/35.56    (5)  all_58_13 = e3
% 204.79/35.56    (6)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56    (7)  op(e0, e0) = all_14_2
% 204.79/35.56    (8)  all_58_12 = all_52_7
% 204.79/35.56    (9)   ~ (all_52_7 = all_14_2)
% 204.79/35.56    (10)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.56    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.56    (12)   ~ (all_52_7 = e2)
% 204.79/35.56    (13)  all_56_12 = all_52_7
% 204.79/35.56    (14)   ~ (e1 = e0)
% 204.79/35.56    (15)  op(e1, e1) = all_10_2
% 204.79/35.56    (16)   ~ (all_52_23 = all_10_2)
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | BETA: splitting (10) gives:
% 204.79/35.56  | 
% 204.79/35.56  | Case 1:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (17)  all_58_12 = e1
% 204.79/35.56  | | 
% 204.79/35.56  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (11), (14), (15), (16), (17) are
% 204.79/35.56  | |            inconsistent by sub-proof #1170.
% 204.79/35.56  | | 
% 204.79/35.56  | Case 2:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (18)   ~ (all_58_12 = e1)
% 204.79/35.56  | | 
% 204.79/35.56  | | REDUCE: (8), (18) imply:
% 204.79/35.56  | |   (19)   ~ (all_52_7 = e1)
% 204.79/35.56  | | 
% 204.79/35.56  | | BETA: splitting (6) gives:
% 204.79/35.56  | | 
% 204.79/35.56  | | Case 1:
% 204.79/35.56  | | | 
% 204.79/35.56  | | |   (20)  all_56_12 = e2
% 204.79/35.56  | | | 
% 204.79/35.56  | | | REF_CLOSE: (12), (13), (20) are inconsistent by sub-proof #1178.
% 204.79/35.56  | | | 
% 204.79/35.56  | | Case 2:
% 204.79/35.56  | | | 
% 204.79/35.56  | | |   (21)  all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56  | | | 
% 204.79/35.56  | | | REF_CLOSE: (2), (3), (7), (9), (13), (19), (21) are inconsistent by
% 204.79/35.56  | | |            sub-proof #1177.
% 204.79/35.56  | | | 
% 204.79/35.56  | | End of split
% 204.79/35.56  | | 
% 204.79/35.56  | End of split
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1170 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_58_14 = all_52_23
% 204.79/35.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.56    (3)  op(all_52_7, all_52_7) = e0
% 204.79/35.56    (4)   ~ (e3 = e0)
% 204.79/35.56    (5)  all_58_13 = e3
% 204.79/35.56    (6)  all_58_12 = all_52_7
% 204.79/35.56    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.56    (8)   ~ (e1 = e0)
% 204.79/35.56    (9)  op(e1, e1) = all_10_2
% 204.79/35.56    (10)   ~ (all_52_23 = all_10_2)
% 204.79/35.56    (11)  all_58_12 = e1
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (6), (11) imply:
% 204.79/35.56  |   (12)  all_52_7 = e1
% 204.79/35.56  | 
% 204.79/35.56  | SIMP: (12) implies:
% 204.79/35.56  |   (13)  all_52_7 = e1
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (3), (13) imply:
% 204.79/35.56  |   (14)  op(e1, e1) = e0
% 204.79/35.56  | 
% 204.79/35.56  | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (14) are
% 204.79/35.56  |            inconsistent by sub-proof #1171.
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1171 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_58_14 = all_52_23
% 204.79/35.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.56    (3)   ~ (e3 = e0)
% 204.79/35.56    (4)  all_58_13 = e3
% 204.79/35.56    (5)  op(e1, e1) = e0
% 204.79/35.56    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 204.79/35.56    (7)   ~ (e1 = e0)
% 204.79/35.56    (8)  op(e1, e1) = all_10_2
% 204.79/35.56    (9)   ~ (all_52_23 = all_10_2)
% 204.79/35.56    (10)  all_58_12 = e1
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | BETA: splitting (6) gives:
% 204.79/35.56  | 
% 204.79/35.56  | Case 1:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (11)  all_58_12 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | REF_CLOSE: (7), (10), (11) are inconsistent by sub-proof #1173.
% 204.79/35.56  | | 
% 204.79/35.56  | Case 2:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (12)  all_58_13 = e0 | all_58_14 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | BETA: splitting (12) gives:
% 204.79/35.56  | | 
% 204.79/35.56  | | Case 1:
% 204.79/35.56  | | | 
% 204.79/35.56  | | |   (13)  all_58_13 = e0
% 204.79/35.56  | | | 
% 204.79/35.56  | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #1172.
% 204.79/35.56  | | | 
% 204.79/35.56  | | Case 2:
% 204.79/35.56  | | | 
% 204.79/35.56  | | |   (14)  all_58_14 = e0
% 204.79/35.56  | | | 
% 204.79/35.56  | | | COMBINE_EQS: (1), (14) imply:
% 204.79/35.56  | | |   (15)  all_52_23 = e0
% 204.79/35.56  | | | 
% 204.79/35.56  | | | SIMP: (15) implies:
% 204.79/35.56  | | |   (16)  all_52_23 = e0
% 204.79/35.56  | | | 
% 204.79/35.56  | | | REDUCE: (9), (16) imply:
% 204.79/35.56  | | |   (17)   ~ (all_10_2 = e0)
% 204.79/35.56  | | | 
% 204.79/35.56  | | | SIMP: (17) implies:
% 204.79/35.56  | | |   (18)   ~ (all_10_2 = e0)
% 204.79/35.56  | | | 
% 204.79/35.56  | | | REF_CLOSE: (2), (5), (8), (18) are inconsistent by sub-proof #1190.
% 204.79/35.56  | | | 
% 204.79/35.56  | | End of split
% 204.79/35.56  | | 
% 204.79/35.56  | End of split
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1172 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_58_13 = e3
% 204.79/35.56    (2)  all_58_13 = e0
% 204.79/35.56    (3)   ~ (e3 = e0)
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.56  |   (4)  e3 = e0
% 204.79/35.56  | 
% 204.79/35.56  | SIMP: (4) implies:
% 204.79/35.56  |   (5)  e3 = e0
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (3), (5) imply:
% 204.79/35.56  |   (6)  $false
% 204.79/35.56  | 
% 204.79/35.56  | CLOSE: (6) is inconsistent.
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1173 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_58_12 = e1
% 204.79/35.56    (2)  all_58_12 = e0
% 204.79/35.56    (3)   ~ (e1 = e0)
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.56  |   (4)  e1 = e0
% 204.79/35.56  | 
% 204.79/35.56  | SIMP: (4) implies:
% 204.79/35.56  |   (5)  e1 = e0
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (3), (5) imply:
% 204.79/35.56  |   (6)  $false
% 204.79/35.56  | 
% 204.79/35.56  | CLOSE: (6) is inconsistent.
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1174 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_58_14 = all_52_23
% 204.79/35.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.56    (3)  op(all_52_7, all_52_7) = e0
% 204.79/35.56    (4)   ~ (all_52_9 = all_52_13)
% 204.79/35.56    (5)  op(all_52_5, all_52_5) = e1
% 204.79/35.56    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56    (7)  op(e0, e2) = all_52_15
% 204.79/35.56    (8)   ~ (all_52_7 = all_52_15)
% 204.79/35.56    (9)   ~ (all_52_17 = all_52_25)
% 204.79/35.56    (10)  all_58_0 = all_6_2
% 204.79/35.56    (11)  op(all_14_2, e0) = all_14_1
% 204.79/35.56    (12)   ~ (all_52_17 = all_10_2)
% 204.79/35.56    (13)  op(e3, e0) = all_52_25
% 204.79/35.56    (14)  op(e0, all_14_1) = all_14_0
% 204.79/35.56    (15)  op(all_52_19, all_52_19) = all_52_18
% 204.79/35.56    (16)  all_58_13 = all_52_15
% 204.79/35.56    (17)  op(all_10_2, all_10_2) = all_52_20
% 204.79/35.56    (18)  all_58_9 = all_52_25
% 204.79/35.56    (19)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.79/35.56    (20)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.79/35.56    (21)  op(e2, e2) = all_4_2
% 204.79/35.56    (22)  all_58_11 = all_52_29
% 204.79/35.56    (23)  all_56_5 = all_4_2
% 204.79/35.56    (24)   ~ (all_52_25 = all_14_2)
% 204.79/35.56    (25)   ~ (all_52_9 = all_52_15)
% 204.79/35.56    (26)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.56    (27)  op(e0, e0) = all_14_2
% 204.79/35.56    (28)  all_56_15 = all_14_2
% 204.79/35.56    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.56    (30)  op(e2, all_4_1) = all_4_0
% 204.79/35.56    (31)   ~ (all_4_1 = e1)
% 204.79/35.56    (32)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.56    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.56    (34)  all_56_9 = all_52_13
% 204.79/35.56    (35)   ~ (e2 = e1)
% 204.79/35.56    (36)   ~ (all_52_13 = all_10_2)
% 204.79/35.56    (37)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.56    (38)   ~ (all_52_25 = all_52_29)
% 204.79/35.56    (39)  all_58_7 = all_52_13
% 204.79/35.56    (40)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.56    (41)  op(all_6_2, all_6_2) = e3
% 204.79/35.56    (42)  all_58_12 = all_52_7
% 204.79/35.56    (43)   ~ (all_52_7 = all_14_2)
% 204.79/35.56    (44)  all_58_2 = all_52_3
% 204.79/35.56    (45)  all_56_2 = all_52_17
% 204.79/35.56    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.56    (47)  op(e3, all_6_1) = all_6_0
% 204.79/35.56    (48)   ~ (all_14_0 = e3)
% 204.79/35.56    (49)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.56    (50)  op(all_4_2, e2) = all_4_1
% 204.79/35.56    (51)  op(all_52_3, all_52_3) = e2
% 204.79/35.56    (52)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.56    (53)   ~ (all_52_15 = all_14_2)
% 204.79/35.56    (54)   ~ (all_6_0 = e2)
% 204.79/35.56    (55)   ~ (all_52_13 = all_4_2)
% 204.79/35.56    (56)   ~ (all_52_9 = all_52_25)
% 204.79/35.56    (57)  all_58_8 = all_10_2
% 204.79/35.56    (58)   ~ (all_52_5 = all_10_2)
% 204.79/35.56    (59)   ~ (all_52_23 = all_14_2)
% 204.79/35.56    (60)  all_56_12 = all_52_7
% 204.79/35.56    (61)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.56    (62)   ~ (all_52_9 = all_4_2)
% 204.79/35.56    (63)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.79/35.56    (64)   ~ (all_52_9 = all_6_2)
% 204.79/35.56    (65)   ~ (all_52_13 = all_52_15)
% 204.79/35.56    (66)  all_56_0 = all_6_2
% 204.79/35.56    (67)  op(e3, e3) = all_6_2
% 204.79/35.56    (68)  all_56_15 = e3
% 204.79/35.56    (69)  all_56_14 = all_52_23
% 204.79/35.56    (70)  op(all_4_2, all_4_2) = all_52_10
% 204.79/35.56    (71)  all_56_3 = all_52_25
% 204.79/35.56    (72)  op(all_14_2, all_14_2) = all_52_30
% 204.79/35.56    (73)  all_58_5 = all_52_19
% 204.79/35.56    (74)  all_56_1 = all_52_9
% 204.79/35.56    (75)   ~ (all_52_15 = all_4_2)
% 204.79/35.56    (76)  all_58_6 = all_52_5
% 204.79/35.56    (77)  op(e3, e2) = all_52_9
% 204.79/35.56    (78)   ~ (all_52_17 = all_6_2)
% 204.79/35.56    (79)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.56    (80)   ~ (all_52_9 = all_52_17)
% 204.79/35.56    (81)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.56    (82)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.79/35.56    (83)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.79/35.56    (84)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.56    (85)  op(e1, e1) = all_10_2
% 204.79/35.56    (86)   ~ (all_52_23 = all_10_2)
% 204.79/35.56    (87)   ~ (all_52_7 = all_52_23)
% 204.79/35.56    (88)  all_56_13 = all_52_15
% 204.79/35.56    (89)   ~ (all_52_3 = all_4_2)
% 204.79/35.56    (90)   ~ (all_52_17 = all_52_23)
% 204.79/35.56    (91)  op(all_6_2, e3) = all_6_1
% 204.79/35.56    (92)  all_58_4 = all_52_17
% 204.79/35.56    (93)   ~ (all_14_0 = e1)
% 204.79/35.56    (94)   ~ (all_14_0 = e2)
% 204.79/35.56    (95)  op(all_52_25, all_52_25) = all_52_24
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (28), (68) imply:
% 204.79/35.56  |   (96)  all_14_2 = e3
% 204.79/35.56  | 
% 204.79/35.56  | SIMP: (96) implies:
% 204.79/35.56  |   (97)  all_14_2 = e3
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (43), (97) imply:
% 204.79/35.56  |   (98)   ~ (all_52_7 = e3)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (53), (97) imply:
% 204.79/35.56  |   (99)   ~ (all_52_15 = e3)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (59), (97) imply:
% 204.79/35.56  |   (100)   ~ (all_52_23 = e3)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (24), (97) imply:
% 204.79/35.56  |   (101)   ~ (all_52_25 = e3)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (72), (97) imply:
% 204.79/35.56  |   (102)  op(e3, e3) = all_52_30
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (11), (97) imply:
% 204.79/35.56  |   (103)  op(e3, e0) = all_14_1
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (27), (97) imply:
% 204.79/35.56  |   (104)  op(e0, e0) = e3
% 204.79/35.56  | 
% 204.79/35.56  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 204.79/35.56  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 204.79/35.56  |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 204.79/35.56  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 204.79/35.56  |            (49), (50), (51), (52), (54), (55), (56), (57), (58), (60), (61),
% 204.79/35.56  |            (62), (63), (64), (65), (66), (67), (69), (70), (71), (73), (74),
% 204.79/35.56  |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 204.79/35.56  |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (98),
% 204.79/35.56  |            (99), (100), (101), (102), (103), (104) are inconsistent by
% 204.79/35.56  |            sub-proof #1175.
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1175 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_58_14 = all_52_23
% 204.79/35.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.56    (3)  op(all_52_7, all_52_7) = e0
% 204.79/35.56    (4)   ~ (all_52_9 = all_52_13)
% 204.79/35.56    (5)  op(all_52_5, all_52_5) = e1
% 204.79/35.56    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56    (7)  op(e0, e2) = all_52_15
% 204.79/35.56    (8)   ~ (all_52_7 = all_52_15)
% 204.79/35.56    (9)   ~ (all_52_17 = all_52_25)
% 204.79/35.56    (10)  all_58_0 = all_6_2
% 204.79/35.56    (11)   ~ (all_52_17 = all_10_2)
% 204.79/35.56    (12)  op(e3, e0) = all_52_25
% 204.79/35.56    (13)  op(e0, all_14_1) = all_14_0
% 204.79/35.56    (14)  op(all_52_19, all_52_19) = all_52_18
% 204.79/35.56    (15)  all_58_13 = all_52_15
% 204.79/35.56    (16)  op(all_10_2, all_10_2) = all_52_20
% 204.79/35.56    (17)  all_58_9 = all_52_25
% 204.79/35.56    (18)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.79/35.56    (19)   ~ (all_52_15 = e3)
% 204.79/35.56    (20)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.79/35.56    (21)  op(e2, e2) = all_4_2
% 204.79/35.56    (22)  all_58_11 = all_52_29
% 204.79/35.56    (23)  all_56_5 = all_4_2
% 204.79/35.56    (24)   ~ (all_52_9 = all_52_15)
% 204.79/35.56    (25)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.56    (26)  op(e0, e0) = all_14_2
% 204.79/35.56    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.56    (28)  op(e2, all_4_1) = all_4_0
% 204.79/35.56    (29)   ~ (all_4_1 = e1)
% 204.79/35.56    (30)  op(e0, e0) = e3
% 204.79/35.56    (31)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.56    (32)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.56    (33)  all_56_9 = all_52_13
% 204.79/35.56    (34)   ~ (e2 = e1)
% 204.79/35.56    (35)   ~ (all_52_13 = all_10_2)
% 204.79/35.56    (36)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.56    (37)   ~ (all_52_25 = all_52_29)
% 204.79/35.56    (38)  all_58_7 = all_52_13
% 204.79/35.56    (39)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.56    (40)  op(all_6_2, all_6_2) = e3
% 204.79/35.56    (41)  all_58_12 = all_52_7
% 204.79/35.56    (42)   ~ (all_52_7 = e3)
% 204.79/35.56    (43)   ~ (all_52_7 = all_14_2)
% 204.79/35.56    (44)  all_58_2 = all_52_3
% 204.79/35.56    (45)  all_56_2 = all_52_17
% 204.79/35.56    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.56    (47)  op(e3, all_6_1) = all_6_0
% 204.79/35.56    (48)   ~ (all_14_0 = e3)
% 204.79/35.56    (49)   ~ (all_52_25 = e3)
% 204.79/35.56    (50)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.56    (51)  op(all_4_2, e2) = all_4_1
% 204.79/35.56    (52)   ~ (all_52_23 = e3)
% 204.79/35.56    (53)  op(all_52_3, all_52_3) = e2
% 204.79/35.56    (54)  op(e3, e3) = all_52_30
% 204.79/35.56    (55)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.56    (56)   ~ (all_6_0 = e2)
% 204.79/35.56    (57)   ~ (all_52_13 = all_4_2)
% 204.79/35.56    (58)   ~ (all_52_9 = all_52_25)
% 204.79/35.56    (59)  all_58_8 = all_10_2
% 204.79/35.56    (60)   ~ (all_52_5 = all_10_2)
% 204.79/35.56    (61)  all_56_12 = all_52_7
% 204.79/35.56    (62)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.56    (63)   ~ (all_52_9 = all_4_2)
% 204.79/35.56    (64)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.79/35.56    (65)   ~ (all_52_9 = all_6_2)
% 204.79/35.56    (66)   ~ (all_52_13 = all_52_15)
% 204.79/35.56    (67)  all_56_0 = all_6_2
% 204.79/35.56    (68)  op(e3, e3) = all_6_2
% 204.79/35.56    (69)  op(e3, e0) = all_14_1
% 204.79/35.56    (70)  all_56_14 = all_52_23
% 204.79/35.56    (71)  op(all_4_2, all_4_2) = all_52_10
% 204.79/35.56    (72)  all_56_3 = all_52_25
% 204.79/35.56    (73)  all_58_5 = all_52_19
% 204.79/35.56    (74)  all_56_1 = all_52_9
% 204.79/35.56    (75)   ~ (all_52_15 = all_4_2)
% 204.79/35.56    (76)  all_58_6 = all_52_5
% 204.79/35.56    (77)  op(e3, e2) = all_52_9
% 204.79/35.56    (78)   ~ (all_52_17 = all_6_2)
% 204.79/35.56    (79)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.56    (80)   ~ (all_52_9 = all_52_17)
% 204.79/35.56    (81)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.56    (82)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.79/35.56    (83)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.79/35.56    (84)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.56    (85)  op(e1, e1) = all_10_2
% 204.79/35.56    (86)   ~ (all_52_23 = all_10_2)
% 204.79/35.56    (87)   ~ (all_52_7 = all_52_23)
% 204.79/35.56    (88)  all_56_13 = all_52_15
% 204.79/35.56    (89)   ~ (all_52_3 = all_4_2)
% 204.79/35.56    (90)   ~ (all_52_17 = all_52_23)
% 204.79/35.56    (91)  op(all_6_2, e3) = all_6_1
% 204.79/35.56    (92)  all_58_4 = all_52_17
% 204.79/35.56    (93)   ~ (all_14_0 = e1)
% 204.79/35.56    (94)   ~ (all_14_0 = e2)
% 204.79/35.56    (95)  op(all_52_25, all_52_25) = all_52_24
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | GROUND_INST: instantiating (2) with all_52_25, all_14_1, e0, e3, simplifying
% 204.79/35.56  |              with (12), (69) gives:
% 204.79/35.56  |   (96)  all_52_25 = all_14_1
% 204.79/35.56  | 
% 204.79/35.56  | GROUND_INST: instantiating (2) with all_6_2, all_52_30, e3, e3, simplifying
% 204.79/35.56  |              with (54), (68) gives:
% 204.79/35.56  |   (97)  all_52_30 = all_6_2
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (72), (96) imply:
% 204.79/35.56  |   (98)  all_56_3 = all_14_1
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (17), (96) imply:
% 204.79/35.56  |   (99)  all_58_9 = all_14_1
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (58), (96) imply:
% 204.79/35.56  |   (100)   ~ (all_52_9 = all_14_1)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (9), (96) imply:
% 204.79/35.56  |   (101)   ~ (all_52_17 = all_14_1)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (37), (96) imply:
% 204.79/35.56  |   (102)   ~ (all_52_29 = all_14_1)
% 204.79/35.56  | 
% 204.79/35.56  | SIMP: (102) implies:
% 204.79/35.56  |   (103)   ~ (all_52_29 = all_14_1)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (49), (96) imply:
% 204.79/35.56  |   (104)   ~ (all_14_1 = e3)
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (95), (96) imply:
% 204.79/35.56  |   (105)  op(all_14_1, all_14_1) = all_52_24
% 204.79/35.56  | 
% 204.79/35.56  | BETA: splitting (31) gives:
% 204.79/35.56  | 
% 204.79/35.56  | Case 1:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (106)  all_56_13 = e3
% 204.79/35.56  | | 
% 204.79/35.56  | | REF_CLOSE: (19), (88), (106) are inconsistent by sub-proof #1201.
% 204.79/35.56  | | 
% 204.79/35.56  | Case 2:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (107)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | BETA: splitting (39) gives:
% 204.79/35.56  | | 
% 204.79/35.56  | | Case 1:
% 204.79/35.56  | | | 
% 204.79/35.56  | | |   (108)  all_56_14 = e3
% 204.79/35.56  | | | 
% 204.79/35.56  | | | REF_CLOSE: (52), (70), (108) are inconsistent by sub-proof #1286.
% 204.79/35.56  | | | 
% 204.79/35.56  | | Case 2:
% 204.79/35.56  | | | 
% 204.79/35.56  | | |   (109)   ~ (all_56_14 = e3)
% 204.79/35.56  | | |   (110)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.56  | | | 
% 204.79/35.56  | | | BETA: splitting (62) gives:
% 204.79/35.56  | | | 
% 204.79/35.56  | | | Case 1:
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | |   (111)  all_56_3 = e3
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | | REF_CLOSE: (98), (104), (111) are inconsistent by sub-proof #1200.
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | Case 2:
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | |   (112)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | | BETA: splitting (6) gives:
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | | Case 1:
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | |   (113)  all_56_12 = e3
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | | COMBINE_EQS: (61), (113) imply:
% 204.79/35.56  | | | | |   (114)  all_52_7 = e3
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | | REDUCE: (42), (114) imply:
% 204.79/35.56  | | | | |   (115)  $false
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | | CLOSE: (115) is inconsistent.
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | Case 2:
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | |   (116)   ~ (all_56_12 = e3)
% 204.79/35.56  | | | | |   (117)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | | BETA: splitting (81) gives:
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | | Case 1:
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | |   (118)  all_58_4 = e3
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | | COMBINE_EQS: (92), (118) imply:
% 204.79/35.56  | | | | | |   (119)  all_52_17 = e3
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | | REF_CLOSE: (2), (5), (10), (21), (27), (40), (41), (42), (44), (46),
% 204.79/35.56  | | | | | |            (53), (60), (68), (76), (78), (85), (89), (119) are
% 204.79/35.56  | | | | | |            inconsistent by sub-proof #1199.
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | Case 2:
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | |   (120)   ~ (all_58_4 = e3)
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | | REDUCE: (92), (120) imply:
% 204.79/35.56  | | | | | |   (121)   ~ (all_52_17 = e3)
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | | BETA: splitting (32) gives:
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | | Case 1:
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | |   (122)  all_56_2 = e3
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | | REF_CLOSE: (45), (121), (122) are inconsistent by sub-proof #1327.
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | Case 2:
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | |   (123)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | | BETA: splitting (25) gives:
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | | Case 1:
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | |   (124)  all_58_12 = e2
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | | COMBINE_EQS: (41), (124) imply:
% 204.79/35.56  | | | | | | | |   (125)  all_52_7 = e2
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | | SIMP: (125) implies:
% 204.79/35.56  | | | | | | | |   (126)  all_52_7 = e2
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | | REF_CLOSE: (2), (3), (7), (8), (15), (21), (29), (34), (51),
% 204.79/35.56  | | | | | | | |            (55), (75), (88), (107), (124), (126) are
% 204.79/35.56  | | | | | | | |            inconsistent by sub-proof #1196.
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | Case 2:
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | |   (127)   ~ (all_58_12 = e2)
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | | REDUCE: (41), (127) imply:
% 204.79/35.56  | | | | | | | |   (128)   ~ (all_52_7 = e2)
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | | BETA: splitting (64) gives:
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | | Case 1:
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | |   (129)  all_58_9 = e2
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | COMBINE_EQS: (99), (129) imply:
% 204.79/35.56  | | | | | | | | |   (130)  all_14_1 = e2
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | SIMP: (130) implies:
% 204.79/35.56  | | | | | | | | |   (131)  all_14_1 = e2
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REDUCE: (100), (131) imply:
% 204.79/35.56  | | | | | | | | |   (132)   ~ (all_52_9 = e2)
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REDUCE: (101), (131) imply:
% 204.79/35.56  | | | | | | | | |   (133)   ~ (all_52_17 = e2)
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REDUCE: (103), (131) imply:
% 204.79/35.56  | | | | | | | | |   (134)   ~ (all_52_29 = e2)
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REDUCE: (105), (131) imply:
% 204.79/35.56  | | | | | | | | |   (135)  op(e2, e2) = all_52_24
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REDUCE: (13), (131) imply:
% 204.79/35.56  | | | | | | | | |   (136)  op(e0, e2) = all_14_0
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11),
% 204.79/35.56  | | | | | | | | |            (14), (16), (18), (21), (22), (23), (24), (25),
% 204.79/35.56  | | | | | | | | |            (27), (28), (29), (32), (33), (35), (36), (38),
% 204.79/35.56  | | | | | | | | |            (40), (41), (42), (44), (45), (46), (47), (50),
% 204.79/35.56  | | | | | | | | |            (51), (52), (53), (56), (57), (59), (60), (61),
% 204.79/35.56  | | | | | | | | |            (63), (65), (66), (67), (68), (71), (73), (74),
% 204.79/35.56  | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82),
% 204.79/35.56  | | | | | | | | |            (83), (84), (85), (88), (89), (91), (92), (93),
% 204.79/35.56  | | | | | | | | |            (94), (107), (117), (132), (133), (134), (135),
% 204.79/35.56  | | | | | | | | |            (136) are inconsistent by sub-proof #1184.
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | Case 2:
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | |   (137)   ~ (all_58_9 = e2)
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | REDUCE: (99), (137) imply:
% 204.79/35.56  | | | | | | | | |   (138)   ~ (all_14_1 = e2)
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | BETA: splitting (55) gives:
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | Case 1:
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | |   (139)  all_58_12 = e1
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | COMBINE_EQS: (41), (139) imply:
% 204.79/35.56  | | | | | | | | | |   (140)  all_52_7 = e1
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | SIMP: (140) implies:
% 204.79/35.56  | | | | | | | | | |   (141)  all_52_7 = e1
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | REDUCE: (87), (141) imply:
% 204.79/35.56  | | | | | | | | | |   (142)   ~ (all_52_23 = e1)
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | SIMP: (142) implies:
% 204.79/35.56  | | | | | | | | | |   (143)   ~ (all_52_23 = e1)
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | REDUCE: (3), (141) imply:
% 204.79/35.56  | | | | | | | | | |   (144)  op(e1, e1) = e0
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | REF_CLOSE: (2), (11), (13), (20), (30), (45), (48), (70),
% 204.79/35.56  | | | | | | | | | |            (85), (86), (90), (92), (98), (101), (105), (110),
% 204.79/35.56  | | | | | | | | | |            (112), (123), (138), (143), (144) are inconsistent
% 204.79/35.56  | | | | | | | | | |            by sub-proof #1179.
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | Case 2:
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | |   (145)   ~ (all_58_12 = e1)
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | REDUCE: (41), (145) imply:
% 204.79/35.56  | | | | | | | | | |   (146)   ~ (all_52_7 = e1)
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | | REF_CLOSE: (2), (3), (26), (43), (61), (117), (128), (146)
% 204.79/35.56  | | | | | | | | | |            are inconsistent by sub-proof #1176.
% 204.79/35.56  | | | | | | | | | | 
% 204.79/35.56  | | | | | | | | | End of split
% 204.79/35.56  | | | | | | | | | 
% 204.79/35.56  | | | | | | | | End of split
% 204.79/35.56  | | | | | | | | 
% 204.79/35.56  | | | | | | | End of split
% 204.79/35.56  | | | | | | | 
% 204.79/35.56  | | | | | | End of split
% 204.79/35.56  | | | | | | 
% 204.79/35.56  | | | | | End of split
% 204.79/35.56  | | | | | 
% 204.79/35.56  | | | | End of split
% 204.79/35.56  | | | | 
% 204.79/35.56  | | | End of split
% 204.79/35.56  | | | 
% 204.79/35.56  | | End of split
% 204.79/35.56  | | 
% 204.79/35.56  | End of split
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1176 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.56    (2)  op(all_52_7, all_52_7) = e0
% 204.79/35.56    (3)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56    (4)  op(e0, e0) = all_14_2
% 204.79/35.56    (5)   ~ (all_52_7 = all_14_2)
% 204.79/35.56    (6)   ~ (all_52_7 = e2)
% 204.79/35.56    (7)  all_56_12 = all_52_7
% 204.79/35.56    (8)   ~ (all_52_7 = e1)
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | BETA: splitting (3) gives:
% 204.79/35.56  | 
% 204.79/35.56  | Case 1:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (9)  all_56_12 = e2
% 204.79/35.56  | | 
% 204.79/35.56  | | REF_CLOSE: (6), (7), (9) are inconsistent by sub-proof #1178.
% 204.79/35.56  | | 
% 204.79/35.56  | Case 2:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (10)  all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10) are inconsistent by sub-proof
% 204.79/35.56  | |            #1177.
% 204.79/35.56  | | 
% 204.79/35.56  | End of split
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1177 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.56    (2)  op(all_52_7, all_52_7) = e0
% 204.79/35.56    (3)  all_56_12 = e1 | all_56_12 = e0
% 204.79/35.56    (4)  op(e0, e0) = all_14_2
% 204.79/35.56    (5)   ~ (all_52_7 = all_14_2)
% 204.79/35.56    (6)  all_56_12 = all_52_7
% 204.79/35.56    (7)   ~ (all_52_7 = e1)
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | BETA: splitting (3) gives:
% 204.79/35.56  | 
% 204.79/35.56  | Case 1:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (8)  all_56_12 = e1
% 204.79/35.56  | | 
% 204.79/35.56  | | REF_CLOSE: (6), (7), (8) are inconsistent by sub-proof #1376.
% 204.79/35.56  | | 
% 204.79/35.56  | Case 2:
% 204.79/35.56  | | 
% 204.79/35.56  | |   (9)  all_56_12 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | COMBINE_EQS: (6), (9) imply:
% 204.79/35.56  | |   (10)  all_52_7 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | SIMP: (10) implies:
% 204.79/35.56  | |   (11)  all_52_7 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | REDUCE: (5), (11) imply:
% 204.79/35.56  | |   (12)   ~ (all_14_2 = e0)
% 204.79/35.56  | | 
% 204.79/35.56  | | SIMP: (12) implies:
% 204.79/35.56  | |   (13)   ~ (all_14_2 = e0)
% 204.79/35.56  | | 
% 204.79/35.56  | | REDUCE: (2), (11) imply:
% 204.79/35.56  | |   (14)  op(e0, e0) = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | GROUND_INST: instantiating (1) with all_14_2, e0, e0, e0, simplifying with
% 204.79/35.56  | |              (4), (14) gives:
% 204.79/35.56  | |   (15)  all_14_2 = e0
% 204.79/35.56  | | 
% 204.79/35.56  | | REDUCE: (13), (15) imply:
% 204.79/35.56  | |   (16)  $false
% 204.79/35.56  | | 
% 204.79/35.56  | | CLOSE: (16) is inconsistent.
% 204.79/35.56  | | 
% 204.79/35.56  | End of split
% 204.79/35.56  | 
% 204.79/35.56  End of proof
% 204.79/35.56  
% 204.79/35.56  Sub-proof #1178 shows that the following formulas are inconsistent:
% 204.79/35.56  ----------------------------------------------------------------
% 204.79/35.56    (1)  all_56_12 = all_52_7
% 204.79/35.56    (2)  all_56_12 = e2
% 204.79/35.56    (3)   ~ (all_52_7 = e2)
% 204.79/35.56  
% 204.79/35.56  Begin of proof
% 204.79/35.56  | 
% 204.79/35.56  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.56  |   (4)  all_52_7 = e2
% 204.79/35.56  | 
% 204.79/35.56  | SIMP: (4) implies:
% 204.79/35.56  |   (5)  all_52_7 = e2
% 204.79/35.56  | 
% 204.79/35.56  | REDUCE: (3), (5) imply:
% 204.79/35.57  |   (6)  $false
% 204.79/35.57  | 
% 204.79/35.57  | CLOSE: (6) is inconsistent.
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1179 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.57    (2)   ~ (all_14_1 = e2)
% 204.79/35.57    (3)   ~ (all_52_17 = all_10_2)
% 204.79/35.57    (4)  op(e0, all_14_1) = all_14_0
% 204.79/35.57    (5)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 204.79/35.57    (6)   ~ (all_52_17 = all_14_1)
% 204.79/35.57    (7)  all_56_3 = all_14_1
% 204.79/35.57    (8)  op(e1, e1) = e0
% 204.79/35.57    (9)  op(e0, e0) = e3
% 204.79/35.57    (10)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.57    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.57    (12)  all_56_2 = all_52_17
% 204.79/35.57    (13)   ~ (all_14_0 = e3)
% 204.79/35.57    (14)  op(all_14_1, all_14_1) = all_52_24
% 204.79/35.57    (15)   ~ (all_52_23 = e1)
% 204.79/35.57    (16)  all_56_14 = all_52_23
% 204.79/35.57    (17)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.57    (18)  op(e1, e1) = all_10_2
% 204.79/35.57    (19)   ~ (all_52_23 = all_10_2)
% 204.79/35.57    (20)   ~ (all_52_17 = all_52_23)
% 204.79/35.57    (21)  all_58_4 = all_52_17
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 204.79/35.57  |              (8), (18) gives:
% 204.79/35.57  |   (22)  all_10_2 = e0
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (3), (22) imply:
% 204.79/35.57  |   (23)   ~ (all_52_17 = e0)
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (19), (22) imply:
% 204.79/35.57  |   (24)   ~ (all_52_23 = e0)
% 204.79/35.57  | 
% 204.79/35.57  | BETA: splitting (5) gives:
% 204.79/35.57  | 
% 204.79/35.57  | Case 1:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (25)  all_58_4 = e1
% 204.79/35.57  | | 
% 204.79/35.57  | | COMBINE_EQS: (21), (25) imply:
% 204.79/35.57  | |   (26)  all_52_17 = e1
% 204.79/35.57  | | 
% 204.79/35.57  | | SIMP: (26) implies:
% 204.79/35.57  | |   (27)  all_52_17 = e1
% 204.79/35.57  | | 
% 204.79/35.57  | | REDUCE: (6), (27) imply:
% 204.79/35.57  | |   (28)   ~ (all_14_1 = e1)
% 204.79/35.57  | | 
% 204.79/35.57  | | SIMP: (28) implies:
% 204.79/35.57  | |   (29)   ~ (all_14_1 = e1)
% 204.79/35.57  | | 
% 204.79/35.57  | | REF_CLOSE: (1), (2), (4), (7), (9), (11), (13), (14), (29) are inconsistent
% 204.79/35.57  | |            by sub-proof #1181.
% 204.79/35.57  | | 
% 204.79/35.57  | Case 2:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (30)   ~ (all_58_4 = e1)
% 204.79/35.57  | | 
% 204.79/35.57  | | REDUCE: (21), (30) imply:
% 204.79/35.57  | |   (31)   ~ (all_52_17 = e1)
% 204.79/35.57  | | 
% 204.79/35.57  | | BETA: splitting (10) gives:
% 204.79/35.57  | | 
% 204.79/35.57  | | Case 1:
% 204.79/35.57  | | | 
% 204.79/35.57  | | |   (32)  all_56_14 = e2
% 204.79/35.57  | | | 
% 204.79/35.57  | | | COMBINE_EQS: (16), (32) imply:
% 204.79/35.57  | | |   (33)  all_52_23 = e2
% 204.79/35.57  | | | 
% 204.79/35.57  | | | SIMP: (33) implies:
% 204.79/35.57  | | |   (34)  all_52_23 = e2
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (20), (34) imply:
% 204.79/35.57  | | |   (35)   ~ (all_52_17 = e2)
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REF_CLOSE: (12), (17), (23), (31), (35) are inconsistent by sub-proof
% 204.79/35.57  | | |            #1180.
% 204.79/35.57  | | | 
% 204.79/35.57  | | Case 2:
% 204.79/35.57  | | | 
% 204.79/35.57  | | |   (36)  all_56_14 = e1 | all_56_14 = e0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REF_CLOSE: (15), (16), (24), (36) are inconsistent by sub-proof #1381.
% 204.79/35.57  | | | 
% 204.79/35.57  | | End of split
% 204.79/35.57  | | 
% 204.79/35.57  | End of split
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1180 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)  all_56_2 = all_52_17
% 204.79/35.57    (2)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.57    (3)   ~ (all_52_17 = e1)
% 204.79/35.57    (4)   ~ (all_52_17 = e0)
% 204.79/35.57    (5)   ~ (all_52_17 = e2)
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | BETA: splitting (2) gives:
% 204.79/35.57  | 
% 204.79/35.57  | Case 1:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (6)  all_56_2 = e2
% 204.79/35.57  | | 
% 204.79/35.57  | | COMBINE_EQS: (1), (6) imply:
% 204.79/35.57  | |   (7)  all_52_17 = e2
% 204.79/35.57  | | 
% 204.79/35.57  | | REDUCE: (5), (7) imply:
% 204.79/35.57  | |   (8)  $false
% 204.79/35.57  | | 
% 204.79/35.57  | | CLOSE: (8) is inconsistent.
% 204.79/35.57  | | 
% 204.79/35.57  | Case 2:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (9)  all_56_2 = e1 | all_56_2 = e0
% 204.79/35.57  | | 
% 204.79/35.57  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1307.
% 204.79/35.57  | | 
% 204.79/35.57  | End of split
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1181 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.57    (2)   ~ (all_14_1 = e2)
% 204.79/35.57    (3)  op(e0, all_14_1) = all_14_0
% 204.79/35.57    (4)  all_56_3 = all_14_1
% 204.79/35.57    (5)  op(e0, e0) = e3
% 204.79/35.57    (6)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.57    (7)   ~ (all_14_0 = e3)
% 204.79/35.57    (8)  op(all_14_1, all_14_1) = all_52_24
% 204.79/35.57    (9)   ~ (all_14_1 = e1)
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | BETA: splitting (6) gives:
% 204.79/35.57  | 
% 204.79/35.57  | Case 1:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (10)  all_56_3 = e2
% 204.79/35.57  | | 
% 204.79/35.57  | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #1183.
% 204.79/35.57  | | 
% 204.79/35.57  | Case 2:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (11)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.57  | | 
% 204.79/35.57  | | BETA: splitting (11) gives:
% 204.79/35.57  | | 
% 204.79/35.57  | | Case 1:
% 204.79/35.57  | | | 
% 204.79/35.57  | | |   (12)  all_56_3 = e1
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REF_CLOSE: (4), (9), (12) are inconsistent by sub-proof #1182.
% 204.79/35.57  | | | 
% 204.79/35.57  | | Case 2:
% 204.79/35.57  | | | 
% 204.79/35.57  | | |   (13)  all_56_3 = e0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | COMBINE_EQS: (4), (13) imply:
% 204.79/35.57  | | |   (14)  all_14_1 = e0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | SIMP: (14) implies:
% 204.79/35.57  | | |   (15)  all_14_1 = e0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (8), (15) imply:
% 204.79/35.57  | | |   (16)  op(e0, e0) = all_52_24
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (3), (15) imply:
% 204.79/35.57  | | |   (17)  op(e0, e0) = all_14_0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | GROUND_INST: instantiating (1) with e3, all_52_24, e0, e0, simplifying
% 204.79/35.57  | | |              with (5), (16) gives:
% 204.79/35.57  | | |   (18)  all_52_24 = e3
% 204.79/35.57  | | | 
% 204.79/35.57  | | | GROUND_INST: instantiating (1) with all_14_0, all_52_24, e0, e0,
% 204.79/35.57  | | |              simplifying with (16), (17) gives:
% 204.79/35.57  | | |   (19)  all_52_24 = all_14_0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | COMBINE_EQS: (18), (19) imply:
% 204.79/35.57  | | |   (20)  all_14_0 = e3
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (7), (20) imply:
% 204.79/35.57  | | |   (21)  $false
% 204.79/35.57  | | | 
% 204.79/35.57  | | | CLOSE: (21) is inconsistent.
% 204.79/35.57  | | | 
% 204.79/35.57  | | End of split
% 204.79/35.57  | | 
% 204.79/35.57  | End of split
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1182 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)  all_56_3 = all_14_1
% 204.79/35.57    (2)  all_56_3 = e1
% 204.79/35.57    (3)   ~ (all_14_1 = e1)
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.57  |   (4)  all_14_1 = e1
% 204.79/35.57  | 
% 204.79/35.57  | SIMP: (4) implies:
% 204.79/35.57  |   (5)  all_14_1 = e1
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (3), (5) imply:
% 204.79/35.57  |   (6)  $false
% 204.79/35.57  | 
% 204.79/35.57  | CLOSE: (6) is inconsistent.
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1183 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)  all_56_3 = all_14_1
% 204.79/35.57    (2)  all_56_3 = e2
% 204.79/35.57    (3)   ~ (all_14_1 = e2)
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.57  |   (4)  all_14_1 = e2
% 204.79/35.57  | 
% 204.79/35.57  | SIMP: (4) implies:
% 204.79/35.57  |   (5)  all_14_1 = e2
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (3), (5) imply:
% 204.79/35.57  |   (6)  $false
% 204.79/35.57  | 
% 204.79/35.57  | CLOSE: (6) is inconsistent.
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1184 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)  op(e0, e2) = all_14_0
% 204.79/35.57    (2)  all_58_14 = all_52_23
% 204.79/35.57    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.57    (4)  op(all_52_7, all_52_7) = e0
% 204.79/35.57    (5)   ~ (all_52_9 = all_52_13)
% 204.79/35.57    (6)  op(all_52_5, all_52_5) = e1
% 204.79/35.57    (7)  op(e0, e2) = all_52_15
% 204.79/35.57    (8)   ~ (all_52_7 = all_52_15)
% 204.79/35.57    (9)  all_58_0 = all_6_2
% 204.79/35.57    (10)   ~ (all_52_17 = all_10_2)
% 204.79/35.57    (11)  op(all_52_19, all_52_19) = all_52_18
% 204.79/35.57    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.79/35.57    (13)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.79/35.57    (14)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.57    (15)  op(e2, e2) = all_4_2
% 204.79/35.57    (16)  all_58_11 = all_52_29
% 204.79/35.57    (17)  all_56_5 = all_4_2
% 204.79/35.57    (18)   ~ (all_52_29 = e2)
% 204.79/35.57    (19)   ~ (all_52_9 = all_52_15)
% 204.79/35.57    (20)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.57    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.57    (22)  op(e2, e2) = all_52_24
% 204.79/35.57    (23)  op(e2, all_4_1) = all_4_0
% 204.79/35.57    (24)   ~ (all_4_1 = e1)
% 204.79/35.57    (25)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.57    (26)  all_56_9 = all_52_13
% 204.79/35.57    (27)   ~ (all_52_13 = all_10_2)
% 204.79/35.57    (28)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.57    (29)  all_58_7 = all_52_13
% 204.79/35.57    (30)  op(all_6_2, all_6_2) = e3
% 204.79/35.57    (31)  all_58_12 = all_52_7
% 204.79/35.57    (32)   ~ (all_52_7 = e3)
% 204.79/35.57    (33)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.57    (34)  all_58_2 = all_52_3
% 204.79/35.57    (35)  all_56_2 = all_52_17
% 204.79/35.57    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.57    (37)  op(e3, all_6_1) = all_6_0
% 204.79/35.57    (38)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.57    (39)  op(all_4_2, e2) = all_4_1
% 204.79/35.57    (40)   ~ (all_52_23 = e3)
% 204.79/35.57    (41)  op(all_52_3, all_52_3) = e2
% 204.79/35.57    (42)   ~ (all_6_0 = e2)
% 204.79/35.57    (43)   ~ (all_52_13 = all_4_2)
% 204.79/35.57    (44)   ~ (all_52_9 = e2)
% 204.79/35.57    (45)  all_58_8 = all_10_2
% 204.79/35.57    (46)   ~ (all_52_5 = all_10_2)
% 204.79/35.57    (47)  all_56_12 = all_52_7
% 204.79/35.57    (48)   ~ (all_52_9 = all_4_2)
% 204.79/35.57    (49)   ~ (all_52_9 = all_6_2)
% 204.79/35.57    (50)   ~ (all_52_13 = all_52_15)
% 204.79/35.57    (51)  all_56_0 = all_6_2
% 204.79/35.57    (52)  op(e3, e3) = all_6_2
% 204.79/35.57    (53)  op(all_4_2, all_4_2) = all_52_10
% 204.79/35.57    (54)  all_58_5 = all_52_19
% 204.79/35.57    (55)  all_56_1 = all_52_9
% 204.79/35.57    (56)   ~ (all_52_15 = all_4_2)
% 204.79/35.57    (57)  all_58_6 = all_52_5
% 204.79/35.57    (58)  op(e3, e2) = all_52_9
% 204.79/35.57    (59)   ~ (all_52_17 = all_6_2)
% 204.79/35.57    (60)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.57    (61)   ~ (all_52_9 = all_52_17)
% 204.79/35.57    (62)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.57    (63)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.79/35.57    (64)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 204.79/35.57    (65)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.57    (66)  op(e1, e1) = all_10_2
% 204.79/35.57    (67)   ~ (all_52_17 = e2)
% 204.79/35.57    (68)  all_56_13 = all_52_15
% 204.79/35.57    (69)   ~ (all_52_3 = all_4_2)
% 204.79/35.57    (70)  op(all_6_2, e3) = all_6_1
% 204.79/35.57    (71)  all_58_4 = all_52_17
% 204.79/35.57    (72)   ~ (all_14_0 = e1)
% 204.79/35.57    (73)   ~ (all_14_0 = e2)
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | GROUND_INST: instantiating (3) with all_52_15, all_14_0, e2, e0, simplifying
% 204.79/35.57  |              with (1), (7) gives:
% 204.79/35.57  |   (74)  all_52_15 = all_14_0
% 204.79/35.57  | 
% 204.79/35.57  | GROUND_INST: instantiating (3) with all_4_2, all_52_24, e2, e2, simplifying
% 204.79/35.57  |              with (15), (22) gives:
% 204.79/35.57  |   (75)  all_52_24 = all_4_2
% 204.79/35.57  | 
% 204.79/35.57  | COMBINE_EQS: (68), (74) imply:
% 204.79/35.57  |   (76)  all_56_13 = all_14_0
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (8), (74) imply:
% 204.79/35.57  |   (77)   ~ (all_52_7 = all_14_0)
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (19), (74) imply:
% 204.79/35.57  |   (78)   ~ (all_52_9 = all_14_0)
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (50), (74) imply:
% 204.79/35.57  |   (79)   ~ (all_52_13 = all_14_0)
% 204.79/35.57  | 
% 204.79/35.57  | REDUCE: (56), (74) imply:
% 204.79/35.57  |   (80)   ~ (all_14_0 = all_4_2)
% 204.79/35.57  | 
% 204.79/35.57  | BETA: splitting (33) gives:
% 204.79/35.57  | 
% 204.79/35.57  | Case 1:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (81)  all_56_13 = e2
% 204.79/35.57  | | 
% 204.79/35.57  | | COMBINE_EQS: (76), (81) imply:
% 204.79/35.57  | |   (82)  all_14_0 = e2
% 204.79/35.57  | | 
% 204.79/35.57  | | REDUCE: (73), (82) imply:
% 204.79/35.57  | |   (83)  $false
% 204.79/35.57  | | 
% 204.79/35.57  | | CLOSE: (83) is inconsistent.
% 204.79/35.57  | | 
% 204.79/35.57  | Case 2:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (84)  all_56_13 = e1 | all_56_13 = e0
% 204.79/35.57  | | 
% 204.79/35.57  | | BETA: splitting (84) gives:
% 204.79/35.57  | | 
% 204.79/35.57  | | Case 1:
% 204.79/35.57  | | | 
% 204.79/35.57  | | |   (85)  all_56_13 = e1
% 204.79/35.57  | | | 
% 204.79/35.57  | | | COMBINE_EQS: (76), (85) imply:
% 204.79/35.57  | | |   (86)  all_14_0 = e1
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (72), (86) imply:
% 204.79/35.57  | | |   (87)  $false
% 204.79/35.57  | | | 
% 204.79/35.57  | | | CLOSE: (87) is inconsistent.
% 204.79/35.57  | | | 
% 204.79/35.57  | | Case 2:
% 204.79/35.57  | | | 
% 204.79/35.57  | | |   (88)  all_56_13 = e0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | COMBINE_EQS: (76), (88) imply:
% 204.79/35.57  | | |   (89)  all_14_0 = e0
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (77), (89) imply:
% 204.79/35.57  | | |   (90)   ~ (all_52_7 = e0)
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (78), (89) imply:
% 204.79/35.57  | | |   (91)   ~ (all_52_9 = e0)
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (79), (89) imply:
% 204.79/35.57  | | |   (92)   ~ (all_52_13 = e0)
% 204.79/35.57  | | | 
% 204.79/35.57  | | | REDUCE: (80), (89) imply:
% 204.79/35.57  | | |   (93)   ~ (all_4_2 = e0)
% 204.79/35.57  | | | 
% 204.79/35.57  | | | SIMP: (93) implies:
% 204.79/35.57  | | |   (94)   ~ (all_4_2 = e0)
% 204.79/35.57  | | | 
% 204.79/35.57  | | | BETA: splitting (60) gives:
% 204.79/35.57  | | | 
% 204.79/35.57  | | | Case 1:
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | |   (95)  all_56_1 = e3
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | | COMBINE_EQS: (55), (95) imply:
% 204.79/35.57  | | | |   (96)  all_52_9 = e3
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | | SIMP: (96) implies:
% 204.79/35.57  | | | |   (97)  all_52_9 = e3
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | | REF_CLOSE: (3), (6), (9), (15), (21), (30), (31), (32), (34), (36),
% 204.79/35.57  | | | |            (41), (46), (49), (52), (57), (66), (69), (97) are
% 204.79/35.57  | | | |            inconsistent by sub-proof #1195.
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | Case 2:
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | |   (98)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | | BETA: splitting (98) gives:
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | | Case 1:
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | |   (99)  all_56_1 = e2
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | | REF_CLOSE: (44), (55), (99) are inconsistent by sub-proof #1194.
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | Case 2:
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | |   (100)   ~ (all_56_1 = e2)
% 204.79/35.57  | | | | |   (101)  all_56_1 = e1 | all_56_1 = e0
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | | BETA: splitting (101) gives:
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | | Case 1:
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | |   (102)  all_56_1 = e1
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | COMBINE_EQS: (55), (102) imply:
% 204.79/35.57  | | | | | |   (103)  all_52_9 = e1
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | SIMP: (103) implies:
% 204.79/35.57  | | | | | |   (104)  all_52_9 = e1
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | REDUCE: (5), (104) imply:
% 204.79/35.57  | | | | | |   (105)   ~ (all_52_13 = e1)
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | SIMP: (105) implies:
% 204.79/35.57  | | | | | |   (106)   ~ (all_52_13 = e1)
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | REDUCE: (61), (104) imply:
% 204.79/35.57  | | | | | |   (107)   ~ (all_52_17 = e1)
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | SIMP: (107) implies:
% 204.79/35.57  | | | | | |   (108)   ~ (all_52_17 = e1)
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | REDUCE: (48), (104) imply:
% 204.79/35.57  | | | | | |   (109)   ~ (all_4_2 = e1)
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | SIMP: (109) implies:
% 204.79/35.57  | | | | | |   (110)   ~ (all_4_2 = e1)
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | REDUCE: (28), (104) imply:
% 204.79/35.57  | | | | | |   (111)  op(e1, e1) = all_52_8
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | REDUCE: (58), (104) imply:
% 204.79/35.57  | | | | | |   (112)  op(e3, e2) = e1
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | GROUND_INST: instantiating (3) with all_10_2, all_52_8, e1, e1,
% 204.79/35.57  | | | | | |              simplifying with (66), (111) gives:
% 204.79/35.57  | | | | | |   (113)  all_52_8 = all_10_2
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | BETA: splitting (63) gives:
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | Case 1:
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | |   (114)  all_56_9 = e3
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | COMBINE_EQS: (26), (114) imply:
% 204.79/35.57  | | | | | | |   (115)  all_52_13 = e3
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | SIMP: (115) implies:
% 204.79/35.57  | | | | | | |   (116)  all_52_13 = e3
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | COMBINE_EQS: (29), (116) imply:
% 204.79/35.57  | | | | | | |   (117)  all_58_7 = e3
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | REDUCE: (27), (116) imply:
% 204.79/35.57  | | | | | | |   (118)   ~ (all_10_2 = e3)
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | SIMP: (118) implies:
% 204.79/35.57  | | | | | | |   (119)   ~ (all_10_2 = e3)
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | REDUCE: (43), (116) imply:
% 204.79/35.57  | | | | | | |   (120)   ~ (all_4_2 = e3)
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | SIMP: (120) implies:
% 204.79/35.57  | | | | | | |   (121)   ~ (all_4_2 = e3)
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | REDUCE: (65), (116) imply:
% 204.79/35.57  | | | | | | |   (122)  op(e3, e3) = all_52_12
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | BETA: splitting (38) gives:
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | |   (123)  all_56_5 = e3
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | REF_CLOSE: (17), (121), (123) are inconsistent by sub-proof
% 204.79/35.57  | | | | | | | |            #1319.
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | |   (124)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | BETA: splitting (124) gives:
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | |   (125)  all_56_5 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | COMBINE_EQS: (17), (125) imply:
% 204.79/35.57  | | | | | | | | |   (126)  all_4_2 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | SIMP: (126) implies:
% 204.79/35.57  | | | | | | | | |   (127)  all_4_2 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REDUCE: (53), (127) imply:
% 204.79/35.57  | | | | | | | | |   (128)  op(e2, e2) = all_52_10
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REDUCE: (39), (127) imply:
% 204.79/35.57  | | | | | | | | |   (129)  op(e2, e2) = all_4_1
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REDUCE: (15), (127) imply:
% 204.79/35.57  | | | | | | | | |   (130)  op(e2, e2) = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | GROUND_INST: instantiating (3) with all_4_1, all_52_10, e2, e2,
% 204.79/35.57  | | | | | | | | |              simplifying with (128), (129) gives:
% 204.79/35.57  | | | | | | | | |   (131)  all_52_10 = all_4_1
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_52_10, e2, e2,
% 204.79/35.57  | | | | | | | | |              simplifying with (128), (130) gives:
% 204.79/35.57  | | | | | | | | |   (132)  all_52_10 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_12, e3, e3,
% 204.79/35.57  | | | | | | | | |              simplifying with (52), (122) gives:
% 204.79/35.57  | | | | | | | | |   (133)  all_52_12 = all_6_2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | COMBINE_EQS: (131), (132) imply:
% 204.79/35.57  | | | | | | | | |   (134)  all_4_1 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | SIMP: (134) implies:
% 204.79/35.57  | | | | | | | | |   (135)  all_4_1 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REDUCE: (23), (135) imply:
% 204.79/35.57  | | | | | | | | |   (136)  op(e2, e2) = all_4_0
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_4_0, e2, e2,
% 204.79/35.57  | | | | | | | | |              simplifying with (130), (136) gives:
% 204.79/35.57  | | | | | | | | |   (137)  all_4_0 = e2
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | BETA: splitting (64) gives:
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | |   (138)  all_56_0 = e3
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | COMBINE_EQS: (51), (138) imply:
% 204.79/35.57  | | | | | | | | | |   (139)  all_6_2 = e3
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | SIMP: (139) implies:
% 204.79/35.57  | | | | | | | | | |   (140)  all_6_2 = e3
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | REDUCE: (59), (140) imply:
% 204.79/35.57  | | | | | | | | | |   (141)   ~ (all_52_17 = e3)
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | REDUCE: (70), (140) imply:
% 204.79/35.57  | | | | | | | | | |   (142)  op(e3, e3) = all_6_1
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | REDUCE: (52), (140) imply:
% 204.79/35.57  | | | | | | | | | |   (143)  op(e3, e3) = e3
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | BETA: splitting (25) gives:
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | |   (144)  all_56_2 = e3
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | REF_CLOSE: (35), (141), (144) are inconsistent by sub-proof
% 204.79/35.57  | | | | | | | | | | |            #1327.
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | |   (145)   ~ (all_56_2 = e3)
% 204.79/35.57  | | | | | | | | | | |   (146)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | BETA: splitting (62) gives:
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | |   (147)  all_58_4 = e3
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | COMBINE_EQS: (71), (147) imply:
% 204.79/35.57  | | | | | | | | | | | |   (148)  all_52_17 = e3
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | REDUCE: (141), (148) imply:
% 204.79/35.57  | | | | | | | | | | | |   (149)  $false
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | |   (150)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | BETA: splitting (150) gives:
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | |   (151)  all_58_5 = e3
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | COMBINE_EQS: (54), (151) imply:
% 204.79/35.57  | | | | | | | | | | | | |   (152)  all_52_19 = e3
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | REDUCE: (11), (152) imply:
% 204.79/35.57  | | | | | | | | | | | | |   (153)  op(e3, e3) = all_52_18
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | BETA: splitting (146) gives:
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | |   (154)  all_56_2 = e2
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | REF_CLOSE: (35), (67), (154) are inconsistent by sub-proof
% 204.79/35.57  | | | | | | | | | | | | | |            #1264.
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | |   (155)  all_56_2 = e1 | all_56_2 = e0
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | |   (156)  all_56_2 = e1
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | REF_CLOSE: (35), (108), (156) are inconsistent by sub-proof
% 204.79/35.57  | | | | | | | | | | | | | | |            #1263.
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | |   (157)  all_56_2 = e0
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | COMBINE_EQS: (35), (157) imply:
% 204.79/35.57  | | | | | | | | | | | | | | |   (158)  all_52_17 = e0
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | SIMP: (158) implies:
% 204.79/35.57  | | | | | | | | | | | | | | |   (159)  all_52_17 = e0
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | REDUCE: (10), (159) imply:
% 204.79/35.57  | | | | | | | | | | | | | | |   (160)   ~ (all_10_2 = e0)
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | SIMP: (160) implies:
% 204.79/35.57  | | | | | | | | | | | | | | |   (161)   ~ (all_10_2 = e0)
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_6_1, all_52_18, e3, e3,
% 204.79/35.57  | | | | | | | | | | | | | | |              simplifying with (142), (153) gives:
% 204.79/35.57  | | | | | | | | | | | | | | |   (162)  all_52_18 = all_6_1
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_52_18, e3, e3,
% 204.79/35.57  | | | | | | | | | | | | | | |              simplifying with (143), (153) gives:
% 204.79/35.57  | | | | | | | | | | | | | | |   (163)  all_52_18 = e3
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply:
% 204.79/35.57  | | | | | | | | | | | | | | |   (164)  all_6_1 = e3
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | REDUCE: (37), (164) imply:
% 204.79/35.57  | | | | | | | | | | | | | | |   (165)  op(e3, e3) = all_6_0
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_6_0, e3, e3,
% 204.79/35.57  | | | | | | | | | | | | | | |              simplifying with (143), (165) gives:
% 204.79/35.57  | | | | | | | | | | | | | | |   (166)  all_6_0 = e3
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | REDUCE: (42), (166) imply:
% 204.79/35.57  | | | | | | | | | | | | | | |   (167)   ~ (e3 = e2)
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | |   (168)  all_58_6 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (15), (57), (110), (168) are
% 204.79/35.57  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1192.
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | |   (169)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | |   (170)  all_58_7 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (170) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | |   (171)  e3 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | SIMP: (171) implies:
% 204.79/35.57  | | | | | | | | | | | | | | | | |   (172)  e3 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | REDUCE: (167), (172) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | |   (173)  $false
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | |   (174)  all_58_8 = e2 | all_58_11 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | |   (175)  all_58_8 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (175) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | |   (176)  all_10_2 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | REDUCE: (12), (176) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | |   (177)  op(e2, e2) = all_52_20
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (178)  all_58_12 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (178) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (179)  all_52_7 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (180)  all_52_7 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | REDUCE: (90), (180) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (181)   ~ (e2 = e0)
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | REDUCE: (4), (180) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (182)  op(e2, e2) = e0
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (128), (129), (130), (177), (181), (182) are
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1191.
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_58_12 = e2)
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | REDUCE: (31), (183) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | |   (184)   ~ (all_52_7 = e2)
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | |   (185)  all_56_12 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (185) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | |   (186)  all_52_7 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (186) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | |   (187)  $false
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent.
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | |   (188)  all_56_12 = e1 | all_56_12 = e0
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |   (189)  all_56_12 = e1
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (189) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |   (190)  all_52_7 = e1
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (190) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |   (191)  op(e1, e1) = e0
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (66), (161), (191) are inconsistent by
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1190.
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |   (192)  all_56_12 = e0
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (192) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |   (193)  all_52_7 = e0
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (193) imply:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | |   (194)  $false
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | |   (195)  all_58_11 = e2
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (195) are inconsistent by sub-proof
% 204.79/35.57  | | | | | | | | | | | | | | | | | |            #1189.
% 204.79/35.57  | | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | |   (196)  all_58_8 = e3 | all_58_14 = e3
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | | REF_CLOSE: (2), (40), (45), (119), (196) are inconsistent by
% 204.79/35.57  | | | | | | | | | | | | |            sub-proof #1304.
% 204.79/35.57  | | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | |   (197)   ~ (all_56_0 = e3)
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | REDUCE: (51), (197) imply:
% 204.79/35.57  | | | | | | | | | |   (198)   ~ (all_6_2 = e3)
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | | REF_CLOSE: (3), (6), (9), (15), (21), (30), (31), (32), (34),
% 204.79/35.57  | | | | | | | | | |            (36), (41), (46), (52), (57), (66), (69), (198)
% 204.79/35.57  | | | | | | | | | |            are inconsistent by sub-proof #1363.
% 204.79/35.57  | | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | |   (199)  all_56_5 = e1 | all_56_5 = e0
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REF_CLOSE: (17), (44), (48), (55), (91), (94), (98), (199) are
% 204.79/35.57  | | | | | | | | |            inconsistent by sub-proof #1312.
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | End of split
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | Case 2:
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | |   (200)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | BETA: splitting (200) gives:
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | |   (201)  all_56_9 = e2
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | COMBINE_EQS: (26), (201) imply:
% 204.79/35.57  | | | | | | | |   (202)  all_52_13 = e2
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | SIMP: (202) implies:
% 204.79/35.57  | | | | | | | |   (203)  all_52_13 = e2
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | REDUCE: (43), (203) imply:
% 204.79/35.57  | | | | | | | |   (204)   ~ (all_4_2 = e2)
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | SIMP: (204) implies:
% 204.79/35.57  | | | | | | | |   (205)   ~ (all_4_2 = e2)
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | BETA: splitting (38) gives:
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | Case 1:
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | |   (206)  all_56_5 = e3
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | COMBINE_EQS: (17), (206) imply:
% 204.79/35.57  | | | | | | | | |   (207)  all_4_2 = e3
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | SIMP: (207) implies:
% 204.79/35.57  | | | | | | | | |   (208)  all_4_2 = e3
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REDUCE: (39), (208) imply:
% 204.79/35.57  | | | | | | | | |   (209)  op(e3, e2) = all_4_1
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_4_1, e2, e3,
% 204.79/35.57  | | | | | | | | |              simplifying with (112), (209) gives:
% 204.79/35.57  | | | | | | | | |   (210)  all_4_1 = e1
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REDUCE: (24), (210) imply:
% 204.79/35.57  | | | | | | | | |   (211)  $false
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | CLOSE: (211) is inconsistent.
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | |   (212)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | | REF_CLOSE: (17), (94), (110), (205), (212) are inconsistent by
% 204.79/35.57  | | | | | | | | |            sub-proof #1186.
% 204.79/35.57  | | | | | | | | | 
% 204.79/35.57  | | | | | | | | End of split
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | Case 2:
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | |   (213)  all_56_9 = e1 | all_56_9 = e0
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | | REF_CLOSE: (26), (92), (106), (213) are inconsistent by
% 204.79/35.57  | | | | | | | |            sub-proof #1185.
% 204.79/35.57  | | | | | | | | 
% 204.79/35.57  | | | | | | | End of split
% 204.79/35.57  | | | | | | | 
% 204.79/35.57  | | | | | | End of split
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | Case 2:
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | |   (214)  all_56_1 = e0
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | COMBINE_EQS: (55), (214) imply:
% 204.79/35.57  | | | | | |   (215)  all_52_9 = e0
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | SIMP: (215) implies:
% 204.79/35.57  | | | | | |   (216)  all_52_9 = e0
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | REDUCE: (91), (216) imply:
% 204.79/35.57  | | | | | |   (217)  $false
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | | CLOSE: (217) is inconsistent.
% 204.79/35.57  | | | | | | 
% 204.79/35.57  | | | | | End of split
% 204.79/35.57  | | | | | 
% 204.79/35.57  | | | | End of split
% 204.79/35.57  | | | | 
% 204.79/35.57  | | | End of split
% 204.79/35.57  | | | 
% 204.79/35.57  | | End of split
% 204.79/35.57  | | 
% 204.79/35.57  | End of split
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1185 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)  all_56_9 = e1 | all_56_9 = e0
% 204.79/35.57    (2)  all_56_9 = all_52_13
% 204.79/35.57    (3)   ~ (all_52_13 = e1)
% 204.79/35.57    (4)   ~ (all_52_13 = e0)
% 204.79/35.57  
% 204.79/35.57  Begin of proof
% 204.79/35.57  | 
% 204.79/35.57  | BETA: splitting (1) gives:
% 204.79/35.57  | 
% 204.79/35.57  | Case 1:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (5)  all_56_9 = e1
% 204.79/35.57  | | 
% 204.79/35.57  | | COMBINE_EQS: (2), (5) imply:
% 204.79/35.57  | |   (6)  all_52_13 = e1
% 204.79/35.57  | | 
% 204.79/35.57  | | REDUCE: (3), (6) imply:
% 204.79/35.57  | |   (7)  $false
% 204.79/35.57  | | 
% 204.79/35.57  | | CLOSE: (7) is inconsistent.
% 204.79/35.57  | | 
% 204.79/35.57  | Case 2:
% 204.79/35.57  | | 
% 204.79/35.57  | |   (8)  all_56_9 = e0
% 204.79/35.57  | | 
% 204.79/35.57  | | COMBINE_EQS: (2), (8) imply:
% 204.79/35.57  | |   (9)  all_52_13 = e0
% 204.79/35.57  | | 
% 204.79/35.57  | | REDUCE: (4), (9) imply:
% 204.79/35.57  | |   (10)  $false
% 204.79/35.57  | | 
% 204.79/35.57  | | CLOSE: (10) is inconsistent.
% 204.79/35.57  | | 
% 204.79/35.57  | End of split
% 204.79/35.57  | 
% 204.79/35.57  End of proof
% 204.79/35.57  
% 204.79/35.57  Sub-proof #1186 shows that the following formulas are inconsistent:
% 204.79/35.57  ----------------------------------------------------------------
% 204.79/35.57    (1)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.57    (2)   ~ (all_4_2 = e0)
% 204.79/35.58    (3)  all_56_5 = all_4_2
% 204.79/35.58    (4)   ~ (all_4_2 = e2)
% 204.79/35.58    (5)   ~ (all_4_2 = e1)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | BETA: splitting (1) gives:
% 204.79/35.58  | 
% 204.79/35.58  | Case 1:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (6)  all_56_5 = e2
% 204.79/35.58  | | 
% 204.79/35.58  | | COMBINE_EQS: (3), (6) imply:
% 204.79/35.58  | |   (7)  all_4_2 = e2
% 204.79/35.58  | | 
% 204.79/35.58  | | REDUCE: (4), (7) imply:
% 204.79/35.58  | |   (8)  $false
% 204.79/35.58  | | 
% 204.79/35.58  | | CLOSE: (8) is inconsistent.
% 204.79/35.58  | | 
% 204.79/35.58  | Case 2:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (9)  all_56_5 = e1 | all_56_5 = e0
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1187.
% 204.79/35.58  | | 
% 204.79/35.58  | End of split
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1187 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_56_5 = e1 | all_56_5 = e0
% 204.79/35.58    (2)  all_56_5 = all_4_2
% 204.79/35.58    (3)   ~ (all_4_2 = e1)
% 204.79/35.58    (4)   ~ (all_4_2 = e0)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | BETA: splitting (1) gives:
% 204.79/35.58  | 
% 204.79/35.58  | Case 1:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (5)  all_56_5 = e1
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1188.
% 204.79/35.58  | | 
% 204.79/35.58  | Case 2:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (6)  all_56_5 = e0
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1313.
% 204.79/35.58  | | 
% 204.79/35.58  | End of split
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1188 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_56_5 = all_4_2
% 204.79/35.58    (2)  all_56_5 = e1
% 204.79/35.58    (3)   ~ (all_4_2 = e1)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.58  |   (4)  all_4_2 = e1
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (4) implies:
% 204.79/35.58  |   (5)  all_4_2 = e1
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1189 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_58_11 = all_52_29
% 204.79/35.58    (2)  all_58_11 = e2
% 204.79/35.58    (3)   ~ (all_52_29 = e2)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.58  |   (4)  all_52_29 = e2
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (4) implies:
% 204.79/35.58  |   (5)  all_52_29 = e2
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1190 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(e1, e1) = all_10_2
% 204.79/35.58    (3)  op(e1, e1) = e0
% 204.79/35.58    (4)   ~ (all_10_2 = e0)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 204.79/35.58  |              (2), (3) gives:
% 204.79/35.58  |   (5)  all_10_2 = e0
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (4), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1191 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(e2, e2) = all_52_10
% 204.79/35.58    (3)  op(e2, e2) = all_4_1
% 204.79/35.58    (4)  op(e2, e2) = all_52_20
% 204.79/35.58    (5)   ~ (e2 = e0)
% 204.79/35.58    (6)  op(e2, e2) = e0
% 204.79/35.58    (7)  op(e2, e2) = e2
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with e0, all_52_20, e2, e2, simplifying with
% 204.79/35.58  |              (4), (6) gives:
% 204.79/35.58  |   (8)  all_52_20 = e0
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with all_52_20, all_52_10, e2, e2, simplifying
% 204.79/35.58  |              with (2), (4) gives:
% 204.79/35.58  |   (9)  all_52_10 = all_52_20
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with all_4_1, all_52_10, e2, e2, simplifying
% 204.79/35.58  |              with (2), (3) gives:
% 204.79/35.58  |   (10)  all_52_10 = all_4_1
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with e2, all_52_10, e2, e2, simplifying with
% 204.79/35.58  |              (2), (7) gives:
% 204.79/35.58  |   (11)  all_52_10 = e2
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (10), (11) imply:
% 204.79/35.58  |   (12)  all_4_1 = e2
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (9), (10) imply:
% 204.79/35.58  |   (13)  all_52_20 = all_4_1
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (13) implies:
% 204.79/35.58  |   (14)  all_52_20 = all_4_1
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (8), (14) imply:
% 204.79/35.58  |   (15)  all_4_1 = e0
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (15) implies:
% 204.79/35.58  |   (16)  all_4_1 = e0
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (12), (16) imply:
% 204.79/35.58  |   (17)  e2 = e0
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (5), (17) imply:
% 204.79/35.58  |   (18)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (18) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1192 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  all_58_6 = e2
% 204.79/35.58    (3)  op(all_52_5, all_52_5) = e1
% 204.79/35.58    (4)  op(e2, e2) = all_4_2
% 204.79/35.58    (5)  all_58_6 = all_52_5
% 204.79/35.58    (6)   ~ (all_4_2 = e1)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (2), (5) imply:
% 204.79/35.58  |   (7)  all_52_5 = e2
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (7) implies:
% 204.79/35.58  |   (8)  all_52_5 = e2
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (8) imply:
% 204.79/35.58  |   (9)  op(e2, e2) = e1
% 204.79/35.58  | 
% 204.79/35.58  | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #1193.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1193 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(e2, e2) = all_4_2
% 204.79/35.58    (3)  op(e2, e2) = e1
% 204.79/35.58    (4)   ~ (all_4_2 = e1)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with all_4_2, e1, e2, e2, simplifying with (2),
% 204.79/35.58  |              (3) gives:
% 204.79/35.58  |   (5)  all_4_2 = e1
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (4), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1194 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_56_1 = all_52_9
% 204.79/35.58    (2)  all_56_1 = e2
% 204.79/35.58    (3)   ~ (all_52_9 = e2)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.58  |   (4)  all_52_9 = e2
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (4) implies:
% 204.79/35.58  |   (5)  all_52_9 = e2
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1195 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(all_52_5, all_52_5) = e1
% 204.79/35.58    (3)  all_58_0 = all_6_2
% 204.79/35.58    (4)  op(e2, e2) = all_4_2
% 204.79/35.58    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.58    (6)  op(all_6_2, all_6_2) = e3
% 204.79/35.58    (7)  all_58_12 = all_52_7
% 204.79/35.58    (8)   ~ (all_52_7 = e3)
% 204.79/35.58    (9)  all_58_2 = all_52_3
% 204.79/35.58    (10)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.58    (11)  op(all_52_3, all_52_3) = e2
% 204.79/35.58    (12)  all_52_9 = e3
% 204.79/35.58    (13)   ~ (all_52_5 = all_10_2)
% 204.79/35.58    (14)   ~ (all_52_9 = all_6_2)
% 204.79/35.58    (15)  op(e3, e3) = all_6_2
% 204.79/35.58    (16)  all_58_6 = all_52_5
% 204.79/35.58    (17)  op(e1, e1) = all_10_2
% 204.79/35.58    (18)   ~ (all_52_3 = all_4_2)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (12), (14) imply:
% 204.79/35.58  |   (19)   ~ (all_6_2 = e3)
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (19) implies:
% 204.79/35.58  |   (20)   ~ (all_6_2 = e3)
% 204.79/35.58  | 
% 204.79/35.58  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 204.79/35.58  |            (15), (16), (17), (18), (20) are inconsistent by sub-proof #1363.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1196 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(all_52_7, all_52_7) = e0
% 204.79/35.58    (3)  op(e0, e2) = all_52_15
% 204.79/35.58    (4)   ~ (all_52_7 = all_52_15)
% 204.79/35.58    (5)  all_58_13 = all_52_15
% 204.79/35.58    (6)  op(e2, e2) = all_4_2
% 204.79/35.58    (7)   ~ (all_4_1 = e1)
% 204.79/35.58    (8)   ~ (e2 = e1)
% 204.79/35.58    (9)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.58    (10)  op(all_4_2, e2) = all_4_1
% 204.79/35.58    (11)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.58    (12)  all_52_7 = e2
% 204.79/35.58    (13)  all_58_12 = e2
% 204.79/35.58    (14)   ~ (all_52_15 = all_4_2)
% 204.79/35.58    (15)  all_56_13 = all_52_15
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (4), (12) imply:
% 204.79/35.58  |   (16)   ~ (all_52_15 = e2)
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (16) implies:
% 204.79/35.58  |   (17)   ~ (all_52_15 = e2)
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (2), (12) imply:
% 204.79/35.58  |   (18)  op(e2, e2) = e0
% 204.79/35.58  | 
% 204.79/35.58  | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e2, simplifying with (6),
% 204.79/35.58  |              (18) gives:
% 204.79/35.58  |   (19)  all_4_2 = e0
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (14), (19) imply:
% 204.79/35.58  |   (20)   ~ (all_52_15 = e0)
% 204.79/35.58  | 
% 204.79/35.58  | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (13), (15), (17),
% 204.79/35.58  |            (18), (20) are inconsistent by sub-proof #1197.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1197 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(e0, e2) = all_52_15
% 204.79/35.58    (3)   ~ (all_52_15 = e2)
% 204.79/35.58    (4)  all_58_13 = all_52_15
% 204.79/35.58    (5)  op(e2, e2) = all_4_2
% 204.79/35.58    (6)   ~ (all_52_15 = e0)
% 204.79/35.58    (7)   ~ (all_4_1 = e1)
% 204.79/35.58    (8)   ~ (e2 = e1)
% 204.79/35.58    (9)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.58    (10)  op(all_4_2, e2) = all_4_1
% 204.79/35.58    (11)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.58    (12)  op(e2, e2) = e0
% 204.79/35.58    (13)  all_58_12 = e2
% 204.79/35.58    (14)  all_56_13 = all_52_15
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | BETA: splitting (11) gives:
% 204.79/35.58  | 
% 204.79/35.58  | Case 1:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (15)  all_58_12 = e1
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (8), (13), (15) are inconsistent by sub-proof #1198.
% 204.79/35.58  | | 
% 204.79/35.58  | Case 2:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (16)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (14), (16)
% 204.79/35.58  | |            are inconsistent by sub-proof #1352.
% 204.79/35.58  | | 
% 204.79/35.58  | End of split
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1198 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_58_12 = e2
% 204.79/35.58    (2)  all_58_12 = e1
% 204.79/35.58    (3)   ~ (e2 = e1)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.58  |   (4)  e2 = e1
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (4) implies:
% 204.79/35.58  |   (5)  e2 = e1
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1199 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (2)  op(all_52_5, all_52_5) = e1
% 204.79/35.58    (3)  all_58_0 = all_6_2
% 204.79/35.58    (4)  op(e2, e2) = all_4_2
% 204.79/35.58    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.58    (6)  op(all_6_2, all_6_2) = e3
% 204.79/35.58    (7)  all_58_12 = all_52_7
% 204.79/35.58    (8)   ~ (all_52_7 = e3)
% 204.79/35.58    (9)  all_58_2 = all_52_3
% 204.79/35.58    (10)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.58    (11)  op(all_52_3, all_52_3) = e2
% 204.79/35.58    (12)   ~ (all_52_5 = all_10_2)
% 204.79/35.58    (13)  op(e3, e3) = all_6_2
% 204.79/35.58    (14)  all_58_6 = all_52_5
% 204.79/35.58    (15)   ~ (all_52_17 = all_6_2)
% 204.79/35.58    (16)  all_52_17 = e3
% 204.79/35.58    (17)  op(e1, e1) = all_10_2
% 204.79/35.58    (18)   ~ (all_52_3 = all_4_2)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (16) implies:
% 204.79/35.58  |   (19)  all_52_17 = e3
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (15), (19) imply:
% 204.79/35.58  |   (20)   ~ (all_6_2 = e3)
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (20) implies:
% 204.79/35.58  |   (21)   ~ (all_6_2 = e3)
% 204.79/35.58  | 
% 204.79/35.58  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.79/35.58  |            (13), (14), (17), (18), (21) are inconsistent by sub-proof #1363.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1200 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_56_3 = all_14_1
% 204.79/35.58    (2)  all_56_3 = e3
% 204.79/35.58    (3)   ~ (all_14_1 = e3)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.58  |   (4)  all_14_1 = e3
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (4) implies:
% 204.79/35.58  |   (5)  all_14_1 = e3
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1201 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)  all_56_13 = all_52_15
% 204.79/35.58    (2)  all_56_13 = e3
% 204.79/35.58    (3)   ~ (all_52_15 = e3)
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.58  |   (4)  all_52_15 = e3
% 204.79/35.58  | 
% 204.79/35.58  | SIMP: (4) implies:
% 204.79/35.58  |   (5)  all_52_15 = e3
% 204.79/35.58  | 
% 204.79/35.58  | REDUCE: (3), (5) imply:
% 204.79/35.58  |   (6)  $false
% 204.79/35.58  | 
% 204.79/35.58  | CLOSE: (6) is inconsistent.
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1202 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ~ (all_52_15 = all_52_23)
% 204.79/35.58    (2)   ~ (all_52_25 = all_52_27)
% 204.79/35.58    (3)  all_58_14 = all_52_23
% 204.79/35.58    (4)   ~ (e3 = e1)
% 204.79/35.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (6)   ~ (all_52_5 = all_52_13)
% 204.79/35.58    (7)  all_58_1 = all_52_9
% 204.79/35.58    (8)   ~ (e3 = e0)
% 204.79/35.58    (9)  op(e2, e3) = all_52_3
% 204.79/35.58    (10)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.58    (11)  op(e0, e2) = all_52_15
% 204.79/35.58    (12)   ~ (all_52_7 = all_52_15)
% 204.79/35.58    (13)  op(all_52_7, all_52_7) = all_52_6
% 204.79/35.58    (14)   ~ (all_52_17 = all_52_25)
% 204.79/35.58    (15)   ~ (all_52_3 = all_6_2)
% 204.79/35.58    (16)  all_58_0 = all_6_2
% 204.79/35.58    (17)  all_56_4 = all_52_3
% 204.79/35.58    (18)   ~ (all_52_17 = all_10_2)
% 204.79/35.58    (19)  op(e3, e0) = all_52_25
% 204.79/35.58    (20)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.79/35.58    (21)  op(all_52_19, all_52_19) = all_52_18
% 204.79/35.58    (22)  all_58_13 = all_52_15
% 204.79/35.58    (23)  op(all_10_2, all_10_2) = all_52_20
% 204.79/35.58    (24)  all_58_9 = all_52_25
% 204.79/35.58    (25)   ~ (all_6_1 = e1)
% 204.79/35.58    (26)  op(all_52_27, all_52_27) = all_52_26
% 204.79/35.58    (27)  op(e1, e3) = all_52_5
% 204.79/35.58    (28)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.79/35.58    (29)  op(e2, e2) = all_4_2
% 204.79/35.58    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.79/35.58    (31)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 204.79/35.58    (32)   ~ (all_4_1 = e3)
% 204.79/35.58    (33)  all_58_11 = all_52_29
% 204.79/35.58    (34)  all_56_5 = all_4_2
% 204.79/35.58    (35)   ~ (all_52_9 = all_52_15)
% 204.79/35.58    (36)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.58    (37)  op(all_10_2, e1) = all_10_1
% 204.79/35.58    (38)  op(all_6_2, all_6_2) = all_52_0
% 204.79/35.58    (39)   ~ (all_52_7 = all_6_2)
% 204.79/35.58    (40)  op(e0, e0) = all_14_2
% 204.79/35.58    (41)   ~ (all_52_15 = e0)
% 204.79/35.58    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.58    (43)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.58    (44)  all_58_15 = e0
% 204.79/35.58    (45)  all_56_11 = all_52_29
% 204.79/35.58    (46)   ~ (all_52_25 = e0)
% 204.79/35.58    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.58    (48)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.58    (49)   ~ (e2 = e1)
% 204.79/35.58    (50)   ~ (all_52_13 = all_10_2)
% 204.79/35.58    (51)  op(e0, e0) = e0
% 204.79/35.58    (52)   ~ (all_6_0 = e1)
% 204.79/35.58    (53)  all_58_10 = all_52_27
% 204.79/35.58    (54)  all_56_8 = all_52_5
% 204.79/35.58    (55)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.58    (56)  op(all_52_15, all_52_15) = all_52_14
% 204.79/35.58    (57)   ~ (all_52_25 = all_52_29)
% 204.79/35.58    (58)   ~ (all_52_29 = all_10_2)
% 204.79/35.58    (59)  all_58_7 = all_52_13
% 204.79/35.58    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.58    (61)   ~ (all_52_5 = all_52_7)
% 204.79/35.58    (62)  all_58_12 = all_52_7
% 204.79/35.58    (63)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.58    (64)  all_58_2 = all_52_3
% 204.79/35.58    (65)  all_56_2 = all_52_17
% 204.79/35.58    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.79/35.58    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.58    (68)  op(e3, all_6_1) = all_6_0
% 204.79/35.58    (69)  all_56_7 = all_52_27
% 204.79/35.58    (70)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.58    (71)   ~ (e2 = e0)
% 204.79/35.58    (72)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.58    (73)  op(all_4_2, e2) = all_4_1
% 204.79/35.58    (74)   ~ (all_52_5 = all_52_29)
% 204.79/35.58    (75)   ~ (all_52_29 = e0)
% 204.79/35.58    (76)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.58    (77)   ~ (all_52_19 = all_52_27)
% 204.79/35.58    (78)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.79/35.58    (79)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.58    (80)   ~ (all_6_0 = e2)
% 204.79/35.58    (81)   ~ (all_52_13 = all_4_2)
% 204.79/35.58    (82)  op(e3, e1) = all_52_17
% 204.79/35.58    (83)  op(e0, e3) = all_52_7
% 204.79/35.58    (84)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.58    (85)   ~ (all_52_9 = all_52_25)
% 204.79/35.58    (86)   ~ (all_52_19 = all_10_2)
% 204.79/35.58    (87)  op(all_52_23, all_52_23) = all_52_22
% 204.79/35.58    (88)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.79/35.58    (89)  all_58_8 = all_10_2
% 204.79/35.58    (90)   ~ (all_52_23 = e0)
% 204.79/35.58    (91)   ~ (all_52_5 = all_10_2)
% 204.79/35.58    (92)  op(all_52_29, all_52_29) = all_52_28
% 204.79/35.58    (93)  all_56_12 = all_52_7
% 204.79/35.58    (94)  op(all_52_17, all_52_17) = all_52_16
% 204.79/35.58    (95)   ~ (all_52_25 = all_6_2)
% 204.79/35.58    (96)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.58    (97)   ~ (all_52_5 = all_6_2)
% 204.79/35.58    (98)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.79/35.58    (99)   ~ (all_52_9 = all_6_2)
% 204.79/35.58    (100)   ~ (all_52_13 = all_52_15)
% 204.79/35.58    (101)   ~ (all_52_27 = e0)
% 204.79/35.58    (102)  op(e3, e3) = all_6_2
% 204.79/35.58    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.58    (104)   ~ (all_52_27 = all_14_2)
% 204.79/35.58    (105)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.58    (106)  all_56_14 = all_52_23
% 204.79/35.58    (107)  op(all_4_2, all_4_2) = all_52_10
% 204.79/35.58    (108)  all_56_3 = all_52_25
% 204.79/35.58    (109)   ~ (all_52_3 = all_52_7)
% 204.79/35.58    (110)  all_58_5 = all_52_19
% 204.79/35.58    (111)  all_56_1 = all_52_9
% 204.79/35.58    (112)   ~ (all_52_15 = all_4_2)
% 204.79/35.58    (113)  all_58_6 = all_52_5
% 204.79/35.58    (114)  op(e3, e2) = all_52_9
% 204.79/35.58    (115)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.58    (116)   ~ (all_52_17 = all_6_2)
% 204.79/35.58    (117)   ~ (e1 = e0)
% 204.79/35.58    (118)   ~ (e3 = e2)
% 204.79/35.58    (119)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.58    (120)   ~ (all_52_9 = all_52_17)
% 204.79/35.58    (121)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.58    (122)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.58    (123)   ~ (all_6_1 = e2)
% 204.79/35.58    (124)  op(e1, e1) = all_10_2
% 204.79/35.58    (125)   ~ (all_52_23 = all_10_2)
% 204.79/35.58    (126)   ~ (all_52_7 = all_52_23)
% 204.79/35.58    (127)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 204.79/35.58           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 204.79/35.58    (128)  all_58_3 = all_4_2
% 204.79/35.58    (129)  all_56_13 = all_52_15
% 204.79/35.58    (130)   ~ (all_52_3 = all_4_2)
% 204.79/35.58    (131)   ~ (all_52_19 = all_4_2)
% 204.79/35.58    (132)   ~ (all_52_17 = all_52_23)
% 204.79/35.58    (133)  op(all_6_2, e3) = all_6_1
% 204.79/35.58    (134)   ~ (all_52_13 = all_52_29)
% 204.79/35.58    (135)  all_58_4 = all_52_17
% 204.79/35.58    (136)   ~ (all_52_7 = e0)
% 204.79/35.58    (137)  op(all_52_25, all_52_25) = all_52_24
% 204.79/35.58  
% 204.79/35.58  Begin of proof
% 204.79/35.58  | 
% 204.79/35.58  | BETA: splitting (127) gives:
% 204.79/35.58  | 
% 204.79/35.58  | Case 1:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (138)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 204.79/35.58  | | 
% 204.79/35.58  | | ALPHA: (138) implies:
% 204.79/35.58  | |   (139)  all_52_22 = e0
% 204.79/35.58  | |   (140)  all_52_20 = e1
% 204.79/35.58  | |   (141)  all_52_18 = e2
% 204.79/35.58  | |   (142)  all_52_16 = e3
% 204.79/35.58  | | 
% 204.79/35.58  | | REDUCE: (94), (142) imply:
% 204.79/35.58  | |   (143)  op(all_52_17, all_52_17) = e3
% 204.79/35.58  | | 
% 204.79/35.58  | | REDUCE: (21), (141) imply:
% 204.79/35.58  | |   (144)  op(all_52_19, all_52_19) = e2
% 204.79/35.58  | | 
% 204.79/35.58  | | REDUCE: (87), (139) imply:
% 204.79/35.58  | |   (145)  op(all_52_23, all_52_23) = e0
% 204.79/35.58  | | 
% 204.79/35.58  | | REDUCE: (23), (140) imply:
% 204.79/35.58  | |   (146)  op(all_10_2, all_10_2) = e1
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 204.79/35.58  | |            (16), (18), (20), (22), (24), (25), (26), (27), (28), (29), (32),
% 204.79/35.58  | |            (33), (34), (37), (39), (41), (44), (46), (47), (48), (49), (50),
% 204.79/35.58  | |            (51), (53), (54), (55), (57), (58), (59), (60), (61), (62), (63),
% 204.79/35.58  | |            (65), (66), (69), (72), (73), (76), (77), (81), (82), (83), (84),
% 204.79/35.58  | |            (85), (86), (88), (89), (90), (91), (92), (93), (95), (96), (97),
% 204.79/35.58  | |            (99), (102), (103), (105), (106), (107), (108), (110), (111),
% 204.79/35.58  | |            (113), (114), (115), (116), (118), (119), (120), (121), (122),
% 204.79/35.58  | |            (123), (124), (125), (126), (128), (129), (131), (132), (133),
% 204.79/35.58  | |            (134), (135), (136), (137), (143), (144), (145), (146) are
% 204.79/35.58  | |            inconsistent by sub-proof #1249.
% 204.79/35.58  | | 
% 204.79/35.58  | Case 2:
% 204.79/35.58  | | 
% 204.79/35.58  | |   (147)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.79/35.58  | | 
% 204.79/35.58  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15),
% 204.79/35.58  | |            (16), (17), (18), (19), (20), (22), (24), (26), (27), (29), (30),
% 204.79/35.58  | |            (31), (33), (35), (36), (38), (39), (40), (41), (42), (43), (44),
% 204.79/35.58  | |            (45), (46), (47), (49), (50), (52), (53), (56), (57), (58), (59),
% 204.79/35.58  | |            (61), (62), (63), (64), (67), (68), (69), (70), (71), (74), (75),
% 204.79/35.58  | |            (76), (78), (79), (80), (86), (87), (89), (90), (91), (92), (93),
% 204.79/35.58  | |            (95), (96), (97), (98), (100), (101), (102), (103), (104), (105),
% 204.79/35.58  | |            (108), (109), (110), (112), (113), (115), (117), (118), (123),
% 204.79/35.58  | |            (124), (125), (126), (128), (129), (130), (133), (135), (136),
% 204.79/35.58  | |            (137), (147) are inconsistent by sub-proof #1203.
% 204.79/35.58  | | 
% 204.79/35.58  | End of split
% 204.79/35.58  | 
% 204.79/35.58  End of proof
% 204.79/35.58  
% 204.79/35.58  Sub-proof #1203 shows that the following formulas are inconsistent:
% 204.79/35.58  ----------------------------------------------------------------
% 204.79/35.58    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.58    (2)  all_58_14 = all_52_23
% 204.79/35.58    (3)   ~ (e3 = e1)
% 204.79/35.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.58    (5)  all_58_1 = all_52_9
% 204.79/35.58    (6)   ~ (e3 = e0)
% 204.79/35.58    (7)  op(e2, e3) = all_52_3
% 204.79/35.58    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.58    (9)   ~ (all_52_7 = all_52_15)
% 204.79/35.58    (10)  op(all_52_7, all_52_7) = all_52_6
% 204.79/35.58    (11)   ~ (all_52_17 = all_52_25)
% 204.79/35.58    (12)   ~ (all_52_3 = all_6_2)
% 204.79/35.58    (13)  all_58_0 = all_6_2
% 204.79/35.58    (14)  all_56_4 = all_52_3
% 204.79/35.58    (15)   ~ (all_52_17 = all_10_2)
% 204.79/35.58    (16)  op(e3, e0) = all_52_25
% 204.79/35.58    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.79/35.58    (18)  all_58_13 = all_52_15
% 204.79/35.58    (19)  all_58_9 = all_52_25
% 204.79/35.58    (20)  op(all_52_27, all_52_27) = all_52_26
% 204.79/35.58    (21)  op(e1, e3) = all_52_5
% 204.79/35.58    (22)  op(e2, e2) = all_4_2
% 204.79/35.58    (23)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.79/35.58    (24)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 204.79/35.58    (25)  all_58_11 = all_52_29
% 204.79/35.58    (26)   ~ (all_52_9 = all_52_15)
% 204.79/35.58    (27)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.58    (28)  op(all_6_2, all_6_2) = all_52_0
% 204.79/35.58    (29)   ~ (all_52_7 = all_6_2)
% 204.79/35.58    (30)  op(e0, e0) = all_14_2
% 204.79/35.58    (31)   ~ (all_52_15 = e0)
% 204.79/35.58    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.58    (33)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.58    (34)  all_58_15 = e0
% 204.79/35.58    (35)  all_56_11 = all_52_29
% 204.79/35.58    (36)   ~ (all_52_25 = e0)
% 204.79/35.58    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.58    (38)   ~ (e2 = e1)
% 204.79/35.58    (39)   ~ (all_52_13 = all_10_2)
% 204.79/35.58    (40)   ~ (all_6_0 = e1)
% 204.79/35.58    (41)  all_58_10 = all_52_27
% 204.79/35.58    (42)  op(all_52_15, all_52_15) = all_52_14
% 204.79/35.58    (43)   ~ (all_52_25 = all_52_29)
% 204.79/35.58    (44)   ~ (all_52_29 = all_10_2)
% 204.79/35.58    (45)  all_58_7 = all_52_13
% 204.79/35.58    (46)   ~ (all_52_5 = all_52_7)
% 204.79/35.58    (47)  all_58_12 = all_52_7
% 204.79/35.58    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.58    (49)  all_58_2 = all_52_3
% 204.79/35.58    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.58    (51)  op(e3, all_6_1) = all_6_0
% 204.79/35.58    (52)  all_56_7 = all_52_27
% 204.79/35.58    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.58    (54)   ~ (e2 = e0)
% 204.79/35.58    (55)   ~ (all_52_5 = all_52_29)
% 204.79/35.58    (56)   ~ (all_52_29 = e0)
% 204.79/35.58    (57)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.58    (58)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.79/35.58    (59)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.58    (60)   ~ (all_6_0 = e2)
% 204.79/35.58    (61)   ~ (all_52_19 = all_10_2)
% 204.79/35.58    (62)  op(all_52_23, all_52_23) = all_52_22
% 204.79/35.58    (63)  all_58_8 = all_10_2
% 204.79/35.58    (64)   ~ (all_52_23 = e0)
% 204.79/35.58    (65)   ~ (all_52_5 = all_10_2)
% 204.79/35.58    (66)  op(all_52_29, all_52_29) = all_52_28
% 204.79/35.58    (67)  all_56_12 = all_52_7
% 204.79/35.59    (68)   ~ (all_52_25 = all_6_2)
% 204.79/35.59    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.59    (70)   ~ (all_52_5 = all_6_2)
% 204.79/35.59    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.79/35.59    (72)   ~ (all_52_13 = all_52_15)
% 204.79/35.59    (73)   ~ (all_52_27 = e0)
% 204.79/35.59    (74)  op(e3, e3) = all_6_2
% 204.79/35.59    (75)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.59    (76)   ~ (all_52_27 = all_14_2)
% 204.79/35.59    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.59    (78)  all_56_3 = all_52_25
% 204.79/35.59    (79)   ~ (all_52_3 = all_52_7)
% 204.79/35.59    (80)  all_58_5 = all_52_19
% 204.79/35.59    (81)   ~ (all_52_15 = all_4_2)
% 204.79/35.59    (82)  all_58_6 = all_52_5
% 204.79/35.59    (83)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.59    (84)   ~ (e1 = e0)
% 204.79/35.59    (85)   ~ (e3 = e2)
% 204.79/35.59    (86)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 204.79/35.59    (87)   ~ (all_6_1 = e2)
% 204.79/35.59    (88)  op(e1, e1) = all_10_2
% 204.79/35.59    (89)   ~ (all_52_23 = all_10_2)
% 204.79/35.59    (90)   ~ (all_52_7 = all_52_23)
% 204.79/35.59    (91)  all_58_3 = all_4_2
% 204.79/35.59    (92)  all_56_13 = all_52_15
% 204.79/35.59    (93)   ~ (all_52_3 = all_4_2)
% 204.79/35.59    (94)  op(all_6_2, e3) = all_6_1
% 204.79/35.59    (95)  all_58_4 = all_52_17
% 204.79/35.59    (96)   ~ (all_52_7 = e0)
% 204.79/35.59    (97)  op(all_52_25, all_52_25) = all_52_24
% 204.79/35.59  
% 204.79/35.59  Begin of proof
% 204.79/35.59  | 
% 204.79/35.59  | ALPHA: (86) implies:
% 204.79/35.59  |   (98)  all_52_28 = e1
% 204.79/35.59  |   (99)  all_52_26 = e2
% 204.79/35.59  |   (100)  all_52_24 = e3
% 204.79/35.59  | 
% 204.79/35.59  | REDUCE: (97), (100) imply:
% 204.79/35.59  |   (101)  op(all_52_25, all_52_25) = e3
% 204.79/35.59  | 
% 204.79/35.59  | REDUCE: (20), (99) imply:
% 204.79/35.59  |   (102)  op(all_52_27, all_52_27) = e2
% 204.79/35.59  | 
% 204.79/35.59  | REDUCE: (66), (98) imply:
% 204.79/35.59  |   (103)  op(all_52_29, all_52_29) = e1
% 204.79/35.59  | 
% 204.79/35.59  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.79/35.59  |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 204.79/35.59  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 204.79/35.59  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 204.79/35.59  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 204.79/35.59  |            (58), (59), (60), (61), (62), (63), (64), (65), (67), (68), (69),
% 204.79/35.59  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 204.79/35.59  |            (81), (82), (83), (84), (85), (87), (88), (89), (90), (91), (92),
% 204.79/35.59  |            (93), (94), (95), (96), (101), (102), (103) are inconsistent by
% 204.79/35.59  |            sub-proof #1204.
% 204.79/35.59  | 
% 204.79/35.59  End of proof
% 204.79/35.59  
% 204.79/35.59  Sub-proof #1204 shows that the following formulas are inconsistent:
% 204.79/35.59  ----------------------------------------------------------------
% 204.79/35.59    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.59    (2)  all_58_14 = all_52_23
% 204.79/35.59    (3)   ~ (e3 = e1)
% 204.79/35.59    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.59    (5)  all_58_1 = all_52_9
% 204.79/35.59    (6)   ~ (e3 = e0)
% 204.79/35.59    (7)  op(e2, e3) = all_52_3
% 204.79/35.59    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.59    (9)   ~ (all_52_7 = all_52_15)
% 204.79/35.59    (10)  op(all_52_7, all_52_7) = all_52_6
% 204.79/35.59    (11)   ~ (all_52_17 = all_52_25)
% 204.79/35.59    (12)   ~ (all_52_3 = all_6_2)
% 204.79/35.59    (13)  all_58_0 = all_6_2
% 204.79/35.59    (14)  all_56_4 = all_52_3
% 204.79/35.59    (15)   ~ (all_52_17 = all_10_2)
% 204.79/35.59    (16)  op(e3, e0) = all_52_25
% 204.79/35.59    (17)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.79/35.59    (18)  all_58_13 = all_52_15
% 204.79/35.59    (19)  all_58_9 = all_52_25
% 204.79/35.59    (20)  op(e1, e3) = all_52_5
% 204.79/35.59    (21)  op(e2, e2) = all_4_2
% 204.79/35.59    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.79/35.59    (23)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 204.79/35.59    (24)  all_58_11 = all_52_29
% 204.79/35.59    (25)   ~ (all_52_9 = all_52_15)
% 204.79/35.59    (26)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.59    (27)  op(all_6_2, all_6_2) = all_52_0
% 204.79/35.59    (28)   ~ (all_52_7 = all_6_2)
% 204.79/35.59    (29)  op(e0, e0) = all_14_2
% 204.79/35.59    (30)  op(all_52_29, all_52_29) = e1
% 204.79/35.59    (31)   ~ (all_52_15 = e0)
% 204.79/35.59    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.59    (33)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.59    (34)  all_58_15 = e0
% 204.79/35.59    (35)  all_56_11 = all_52_29
% 204.79/35.59    (36)   ~ (all_52_25 = e0)
% 204.79/35.59    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.59    (38)   ~ (e2 = e1)
% 204.79/35.59    (39)   ~ (all_52_13 = all_10_2)
% 204.79/35.59    (40)   ~ (all_6_0 = e1)
% 204.79/35.59    (41)  all_58_10 = all_52_27
% 204.79/35.59    (42)  op(all_52_15, all_52_15) = all_52_14
% 204.79/35.59    (43)   ~ (all_52_25 = all_52_29)
% 204.79/35.59    (44)   ~ (all_52_29 = all_10_2)
% 204.79/35.59    (45)  all_58_7 = all_52_13
% 204.79/35.59    (46)   ~ (all_52_5 = all_52_7)
% 204.79/35.59    (47)  all_58_12 = all_52_7
% 204.79/35.59    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.59    (49)  all_58_2 = all_52_3
% 204.79/35.59    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.59    (51)  op(e3, all_6_1) = all_6_0
% 204.79/35.59    (52)  all_56_7 = all_52_27
% 204.79/35.59    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.59    (54)   ~ (e2 = e0)
% 204.79/35.59    (55)  op(all_52_25, all_52_25) = e3
% 204.79/35.59    (56)   ~ (all_52_5 = all_52_29)
% 204.79/35.59    (57)   ~ (all_52_29 = e0)
% 204.79/35.59    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.59    (59)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.79/35.59    (60)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.59    (61)   ~ (all_6_0 = e2)
% 204.79/35.59    (62)  op(all_52_27, all_52_27) = e2
% 204.79/35.59    (63)   ~ (all_52_19 = all_10_2)
% 204.79/35.59    (64)  op(all_52_23, all_52_23) = all_52_22
% 204.79/35.59    (65)  all_58_8 = all_10_2
% 204.79/35.59    (66)   ~ (all_52_23 = e0)
% 204.79/35.59    (67)   ~ (all_52_5 = all_10_2)
% 204.79/35.59    (68)  all_56_12 = all_52_7
% 204.79/35.59    (69)   ~ (all_52_25 = all_6_2)
% 204.79/35.59    (70)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.59    (71)   ~ (all_52_5 = all_6_2)
% 204.79/35.59    (72)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.79/35.59    (73)   ~ (all_52_13 = all_52_15)
% 204.79/35.59    (74)   ~ (all_52_27 = e0)
% 204.79/35.59    (75)  op(e3, e3) = all_6_2
% 204.79/35.59    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.59    (77)   ~ (all_52_27 = all_14_2)
% 204.79/35.59    (78)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.59    (79)  all_56_3 = all_52_25
% 204.79/35.59    (80)   ~ (all_52_3 = all_52_7)
% 204.79/35.59    (81)  all_58_5 = all_52_19
% 204.79/35.59    (82)   ~ (all_52_15 = all_4_2)
% 204.79/35.59    (83)  all_58_6 = all_52_5
% 204.79/35.59    (84)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.59    (85)   ~ (e1 = e0)
% 204.79/35.59    (86)   ~ (e3 = e2)
% 204.79/35.59    (87)   ~ (all_6_1 = e2)
% 204.79/35.59    (88)  op(e1, e1) = all_10_2
% 204.79/35.59    (89)   ~ (all_52_23 = all_10_2)
% 204.79/35.59    (90)   ~ (all_52_7 = all_52_23)
% 204.79/35.59    (91)  all_58_3 = all_4_2
% 204.79/35.59    (92)  all_56_13 = all_52_15
% 204.79/35.59    (93)   ~ (all_52_3 = all_4_2)
% 204.79/35.59    (94)  op(all_6_2, e3) = all_6_1
% 204.79/35.59    (95)  all_58_4 = all_52_17
% 204.79/35.59    (96)   ~ (all_52_7 = e0)
% 204.79/35.59  
% 204.79/35.59  Begin of proof
% 204.79/35.59  | 
% 204.79/35.59  | BETA: splitting (37) gives:
% 204.79/35.59  | 
% 204.79/35.59  | Case 1:
% 204.79/35.59  | | 
% 204.79/35.59  | |   (97)  all_56_13 = e3
% 204.79/35.59  | | 
% 204.79/35.59  | | COMBINE_EQS: (92), (97) imply:
% 204.79/35.59  | |   (98)  all_52_15 = e3
% 204.79/35.59  | | 
% 204.79/35.59  | | SIMP: (98) implies:
% 204.79/35.59  | |   (99)  all_52_15 = e3
% 204.79/35.59  | | 
% 204.79/35.59  | | COMBINE_EQS: (18), (99) imply:
% 204.79/35.59  | |   (100)  all_58_13 = e3
% 204.79/35.59  | | 
% 204.79/35.59  | | REDUCE: (9), (99) imply:
% 204.79/35.59  | |   (101)   ~ (all_52_7 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | REDUCE: (25), (99) imply:
% 204.79/35.59  | |   (102)   ~ (all_52_9 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | REDUCE: (73), (99) imply:
% 204.79/35.59  | |   (103)   ~ (all_52_13 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | REDUCE: (82), (99) imply:
% 204.79/35.59  | |   (104)   ~ (all_4_2 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | SIMP: (104) implies:
% 204.79/35.59  | |   (105)   ~ (all_4_2 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | REDUCE: (42), (99) imply:
% 204.79/35.59  | |   (106)  op(e3, e3) = all_52_14
% 204.79/35.59  | | 
% 204.79/35.59  | | GROUND_INST: instantiating (4) with all_6_2, all_52_14, e3, e3, simplifying
% 204.79/35.59  | |              with (75), (106) gives:
% 204.79/35.59  | |   (107)  all_52_14 = all_6_2
% 204.79/35.59  | | 
% 204.79/35.59  | | BETA: splitting (8) gives:
% 204.79/35.59  | | 
% 204.79/35.59  | | Case 1:
% 204.79/35.59  | | | 
% 204.79/35.59  | | |   (108)  all_56_12 = e3
% 204.79/35.59  | | | 
% 204.79/35.59  | | | REF_CLOSE: (68), (101), (108) are inconsistent by sub-proof #1383.
% 204.79/35.59  | | | 
% 204.79/35.59  | | Case 2:
% 204.79/35.59  | | | 
% 204.79/35.59  | | |   (109)   ~ (all_56_12 = e3)
% 204.79/35.59  | | |   (110)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.59  | | | 
% 204.79/35.59  | | | BETA: splitting (58) gives:
% 204.79/35.59  | | | 
% 204.79/35.59  | | | Case 1:
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | |   (111)  all_58_12 = e1
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | COMBINE_EQS: (47), (111) imply:
% 204.79/35.59  | | | |   (112)  all_52_7 = e1
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | SIMP: (112) implies:
% 204.79/35.59  | | | |   (113)  all_52_7 = e1
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | REDUCE: (46), (113) imply:
% 204.79/35.59  | | | |   (114)   ~ (all_52_5 = e1)
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | REDUCE: (28), (113) imply:
% 204.79/35.59  | | | |   (115)   ~ (all_6_2 = e1)
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | SIMP: (115) implies:
% 204.79/35.59  | | | |   (116)   ~ (all_6_2 = e1)
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | REDUCE: (10), (113) imply:
% 204.79/35.59  | | | |   (117)  op(e1, e1) = all_52_6
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | BETA: splitting (26) gives:
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | Case 1:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | |   (118)  all_58_12 = e2
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | COMBINE_EQS: (111), (118) imply:
% 204.79/35.59  | | | | |   (119)  e2 = e1
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (38), (119) imply:
% 204.79/35.59  | | | | |   (120)  $false
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | CLOSE: (120) is inconsistent.
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | Case 2:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | |   (121)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | BETA: splitting (121) gives:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | Case 1:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | |   (122)  all_58_13 = e2
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | REF_CLOSE: (86), (100), (122) are inconsistent by sub-proof #1248.
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | Case 2:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | |   (123)  all_58_14 = e2 | all_58_15 = e2
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | BETA: splitting (123) gives:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | Case 1:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | |   (124)  all_58_14 = e2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | COMBINE_EQS: (2), (124) imply:
% 204.79/35.59  | | | | | | |   (125)  all_52_23 = e2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | SIMP: (125) implies:
% 204.79/35.59  | | | | | | |   (126)  all_52_23 = e2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | REDUCE: (64), (126) imply:
% 204.79/35.59  | | | | | | |   (127)  op(e2, e2) = all_52_22
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | GROUND_INST: instantiating (4) with all_10_2, all_52_6, e1, e1,
% 204.79/35.59  | | | | | | |              simplifying with (88), (117) gives:
% 204.79/35.59  | | | | | | |   (128)  all_52_6 = all_10_2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_22, e2, e2,
% 204.79/35.59  | | | | | | |              simplifying with (21), (127) gives:
% 204.79/35.59  | | | | | | |   (129)  all_52_22 = all_4_2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | BETA: splitting (59) gives:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | |   (130)  all_56_11 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | COMBINE_EQS: (35), (130) imply:
% 204.79/35.59  | | | | | | | |   (131)  all_52_29 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | SIMP: (131) implies:
% 204.79/35.59  | | | | | | | |   (132)  all_52_29 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (30), (132) imply:
% 204.79/35.59  | | | | | | | |   (133)  op(e3, e3) = e1
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REF_CLOSE: (4), (75), (106), (116), (133) are inconsistent by
% 204.79/35.59  | | | | | | | |            sub-proof #1247.
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | |   (134)   ~ (all_56_11 = e3)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (35), (134) imply:
% 204.79/35.59  | | | | | | | |   (135)   ~ (all_52_29 = e3)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | BETA: splitting (48) gives:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | |   (136)  all_58_6 = e3
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | COMBINE_EQS: (83), (136) imply:
% 204.79/35.59  | | | | | | | | |   (137)  all_52_5 = e3
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | REDUCE: (67), (137) imply:
% 204.79/35.59  | | | | | | | | |   (138)   ~ (all_10_2 = e3)
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | SIMP: (138) implies:
% 204.79/35.59  | | | | | | | | |   (139)   ~ (all_10_2 = e3)
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (13), (19), (21), (24), (30),
% 204.79/35.59  | | | | | | | | |            (33), (34), (36), (41), (43), (47), (49), (50),
% 204.79/35.59  | | | | | | | | |            (55), (56), (62), (69), (70), (75), (76), (79),
% 204.79/35.59  | | | | | | | | |            (83), (88), (93), (101), (139) are inconsistent by
% 204.79/35.59  | | | | | | | | |            sub-proof #1238.
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | |   (140)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | BETA: splitting (140) gives:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | |   (141)  all_58_7 = e3
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (45), (141) imply:
% 204.79/35.59  | | | | | | | | | |   (142)  all_52_13 = e3
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (103), (142) imply:
% 204.79/35.59  | | | | | | | | | |   (143)  $false
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | CLOSE: (143) is inconsistent.
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | |   (144)  all_58_8 = e3 | all_58_11 = e3
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | BETA: splitting (144) gives:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | |   (145)  all_58_8 = e3
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | COMBINE_EQS: (65), (145) imply:
% 204.79/35.59  | | | | | | | | | | |   (146)  all_10_2 = e3
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REDUCE: (15), (146) imply:
% 204.79/35.59  | | | | | | | | | | |   (147)   ~ (all_52_17 = e3)
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (11), (12), (13), (15), (19), (24),
% 204.79/35.59  | | | | | | | | | | |            (27), (29), (30), (32), (33), (35), (40), (41),
% 204.79/35.59  | | | | | | | | | | |            (45), (48), (49), (51), (55), (59), (61), (62),
% 204.79/35.59  | | | | | | | | | | |            (63), (65), (69), (70), (71), (75), (76), (77),
% 204.79/35.59  | | | | | | | | | | |            (78), (79), (81), (83), (88), (91), (94), (95),
% 204.79/35.59  | | | | | | | | | | |            (102), (103), (105), (147) are inconsistent by
% 204.79/35.59  | | | | | | | | | | |            sub-proof #1224.
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | |   (148)  all_58_11 = e3
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | COMBINE_EQS: (24), (148) imply:
% 204.79/35.59  | | | | | | | | | | |   (149)  all_52_29 = e3
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REDUCE: (135), (149) imply:
% 204.79/35.59  | | | | | | | | | | |   (150)  $false
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | End of split
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | Case 2:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | |   (151)  all_58_15 = e2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | REF_CLOSE: (34), (54), (151) are inconsistent by sub-proof #1223.
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | End of split
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | End of split
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | End of split
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | Case 2:
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | |   (152)   ~ (all_58_12 = e1)
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | REF_CLOSE: (3), (4), (6), (13), (17), (19), (21), (24), (28), (30),
% 204.79/35.59  | | | |            (34), (36), (41), (43), (47), (49), (50), (52), (55), (56),
% 204.79/35.59  | | | |            (62), (68), (69), (70), (75), (76), (79), (83), (93), (96),
% 204.79/35.59  | | | |            (101), (110), (152) are inconsistent by sub-proof #1222.
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | End of split
% 204.79/35.59  | | | 
% 204.79/35.59  | | End of split
% 204.79/35.59  | | 
% 204.79/35.59  | Case 2:
% 204.79/35.59  | | 
% 204.79/35.59  | |   (153)   ~ (all_56_13 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | REDUCE: (92), (153) imply:
% 204.79/35.59  | |   (154)   ~ (all_52_15 = e3)
% 204.79/35.59  | | 
% 204.79/35.59  | | BETA: splitting (84) gives:
% 204.79/35.59  | | 
% 204.79/35.59  | | Case 1:
% 204.79/35.59  | | | 
% 204.79/35.59  | | |   (155)  all_58_12 = e3
% 204.79/35.59  | | | 
% 204.79/35.59  | | | COMBINE_EQS: (47), (155) imply:
% 204.79/35.59  | | |   (156)  all_52_7 = e3
% 204.79/35.59  | | | 
% 204.79/35.59  | | | SIMP: (156) implies:
% 204.79/35.59  | | |   (157)  all_52_7 = e3
% 204.79/35.59  | | | 
% 204.79/35.59  | | | REDUCE: (80), (157) imply:
% 204.79/35.59  | | |   (158)   ~ (all_52_3 = e3)
% 204.79/35.59  | | | 
% 204.79/35.59  | | | REDUCE: (28), (157) imply:
% 204.79/35.59  | | |   (159)   ~ (all_6_2 = e3)
% 204.79/35.59  | | | 
% 204.79/35.59  | | | SIMP: (159) implies:
% 204.79/35.59  | | |   (160)   ~ (all_6_2 = e3)
% 204.79/35.59  | | | 
% 204.79/35.59  | | | REDUCE: (10), (157) imply:
% 204.79/35.59  | | |   (161)  op(e3, e3) = all_52_6
% 204.79/35.59  | | | 
% 204.79/35.59  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_6, e3, e3, simplifying
% 204.79/35.59  | | |              with (75), (161) gives:
% 204.79/35.59  | | |   (162)  all_52_6 = all_6_2
% 204.79/35.59  | | | 
% 204.79/35.59  | | | BETA: splitting (53) gives:
% 204.79/35.59  | | | 
% 204.79/35.59  | | | Case 1:
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | |   (163)  all_56_4 = e3
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | REF_CLOSE: (14), (158), (163) are inconsistent by sub-proof #1340.
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | Case 2:
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | |   (164)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | BETA: splitting (17) gives:
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | | Case 1:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | |   (165)  all_56_7 = e3
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | COMBINE_EQS: (52), (165) imply:
% 204.79/35.59  | | | | |   (166)  all_52_27 = e3
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | SIMP: (166) implies:
% 204.79/35.59  | | | | |   (167)  all_52_27 = e3
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | COMBINE_EQS: (41), (167) imply:
% 204.79/35.59  | | | | |   (168)  all_58_10 = e3
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (1), (167) imply:
% 204.79/35.59  | | | | |   (169)   ~ (all_52_25 = e3)
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (62), (167) imply:
% 204.79/35.59  | | | | |   (170)  op(e3, e3) = e2
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | GROUND_INST: instantiating (4) with all_6_2, e2, e3, e3, simplifying
% 204.79/35.59  | | | | |              with (75), (170) gives:
% 204.79/35.59  | | | | |   (171)  all_6_2 = e2
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (12), (171) imply:
% 204.79/35.59  | | | | |   (172)   ~ (all_52_3 = e2)
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (69), (171) imply:
% 204.79/35.59  | | | | |   (173)   ~ (all_52_25 = e2)
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (160), (171) imply:
% 204.79/35.59  | | | | |   (174)   ~ (e3 = e2)
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (27), (171) imply:
% 204.79/35.59  | | | | |   (175)  op(e2, e2) = all_52_0
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (94), (171) imply:
% 204.79/35.59  | | | | |   (176)  op(e2, e3) = all_6_1
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | BETA: splitting (70) gives:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | Case 1:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | |   (177)  all_56_3 = e3
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | REF_CLOSE: (79), (169), (177) are inconsistent by sub-proof #1339.
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | Case 2:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | |   (178)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | BETA: splitting (72) gives:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | Case 1:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | |   (179)  all_58_9 = e2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | REF_CLOSE: (19), (173), (179) are inconsistent by sub-proof #1221.
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | Case 2:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | |   (180)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | BETA: splitting (180) gives:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | |   (181)  all_58_10 = e2
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REF_CLOSE: (86), (168), (181) are inconsistent by sub-proof
% 204.79/35.59  | | | | | | | |            #1220.
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | |   (182)  all_58_11 = e2 | all_58_15 = e2
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | BETA: splitting (182) gives:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | |   (183)  all_58_11 = e2
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | COMBINE_EQS: (24), (183) imply:
% 204.79/35.59  | | | | | | | | |   (184)  all_52_29 = e2
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | SIMP: (184) implies:
% 204.79/35.59  | | | | | | | | |   (185)  all_52_29 = e2
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | REDUCE: (30), (185) imply:
% 204.79/35.59  | | | | | | | | |   (186)  op(e2, e2) = e1
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | BETA: splitting (33) gives:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | |   (187)  all_58_9 = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (19), (187) imply:
% 204.79/35.59  | | | | | | | | | |   (188)  all_52_25 = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | SIMP: (188) implies:
% 204.79/35.59  | | | | | | | | | |   (189)  all_52_25 = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (16), (189) imply:
% 204.79/35.59  | | | | | | | | | |   (190)  op(e3, e0) = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_52_0, e2, e2,
% 204.79/35.59  | | | | | | | | | |              simplifying with (21), (175) gives:
% 204.79/35.59  | | | | | | | | | |   (191)  all_52_0 = all_4_2
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_52_0, e2, e2,
% 204.79/35.59  | | | | | | | | | |              simplifying with (175), (186) gives:
% 204.79/35.59  | | | | | | | | | |   (192)  all_52_0 = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_3, all_6_1, e3, e2,
% 204.79/35.59  | | | | | | | | | |              simplifying with (7), (176) gives:
% 204.79/35.59  | | | | | | | | | |   (193)  all_52_3 = all_6_1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (191), (192) imply:
% 204.79/35.59  | | | | | | | | | |   (194)  all_4_2 = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | SIMP: (194) implies:
% 204.79/35.59  | | | | | | | | | |   (195)  all_4_2 = e1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (14), (193) imply:
% 204.79/35.59  | | | | | | | | | |   (196)  all_56_4 = all_6_1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (49), (193) imply:
% 204.79/35.59  | | | | | | | | | |   (197)  all_58_2 = all_6_1
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (93), (193), (195) imply:
% 204.79/35.59  | | | | | | | | | |   (198)   ~ (all_6_1 = e1)
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | BETA: splitting (23) gives:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | |   (199)  all_58_2 = e0
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | COMBINE_EQS: (197), (199) imply:
% 204.79/35.59  | | | | | | | | | | |   (200)  all_6_1 = e0
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | SIMP: (200) implies:
% 204.79/35.59  | | | | | | | | | | |   (201)  all_6_1 = e0
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REDUCE: (51), (201) imply:
% 204.79/35.59  | | | | | | | | | | |   (202)  op(e3, e0) = all_6_0
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_6_0, e0, e3,
% 204.79/35.59  | | | | | | | | | | |              simplifying with (190), (202) gives:
% 204.79/35.59  | | | | | | | | | | |   (203)  all_6_0 = e1
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REDUCE: (40), (203) imply:
% 204.79/35.59  | | | | | | | | | | |   (204)  $false
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | |   (205)   ~ (all_58_2 = e0)
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REDUCE: (197), (205) imply:
% 204.79/35.59  | | | | | | | | | | |   (206)   ~ (all_6_1 = e0)
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REF_CLOSE: (87), (164), (196), (198), (206) are inconsistent
% 204.79/35.59  | | | | | | | | | | |            by sub-proof #1216.
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | |   (207)   ~ (all_58_9 = e1)
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (19), (207) imply:
% 204.79/35.59  | | | | | | | | | |   (208)   ~ (all_52_25 = e1)
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REF_CLOSE: (36), (79), (173), (178), (208) are inconsistent
% 204.79/35.59  | | | | | | | | | |            by sub-proof #1215.
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | |   (209)  all_58_15 = e2
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | REF_CLOSE: (34), (54), (209) are inconsistent by sub-proof
% 204.79/35.59  | | | | | | | | |            #1223.
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | End of split
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | End of split
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | End of split
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | Case 2:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | |   (210)   ~ (all_56_7 = e3)
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | REDUCE: (52), (210) imply:
% 204.79/35.59  | | | | |   (211)   ~ (all_52_27 = e3)
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | BETA: splitting (76) gives:
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | | Case 1:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | |   (212)  all_58_9 = e3
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | COMBINE_EQS: (19), (212) imply:
% 204.79/35.59  | | | | | |   (213)  all_52_25 = e3
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | REF_CLOSE: (4), (55), (69), (75), (213) are inconsistent by
% 204.79/35.59  | | | | | |            sub-proof #1246.
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | Case 2:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | |   (214)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | BETA: splitting (214) gives:
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | | Case 1:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | |   (215)  all_58_10 = e3
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | REF_CLOSE: (41), (211), (215) are inconsistent by sub-proof #1301.
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | Case 2:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | |   (216)  all_58_11 = e3 | all_58_15 = e3
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | BETA: splitting (216) gives:
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | |   (217)  all_58_11 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | COMBINE_EQS: (24), (217) imply:
% 204.79/35.59  | | | | | | | |   (218)  all_52_29 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | SIMP: (218) implies:
% 204.79/35.59  | | | | | | | |   (219)  all_52_29 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (43), (219) imply:
% 204.79/35.59  | | | | | | | |   (220)   ~ (all_52_25 = e3)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (44), (219) imply:
% 204.79/35.59  | | | | | | | |   (221)   ~ (all_10_2 = e3)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | SIMP: (221) implies:
% 204.79/35.59  | | | | | | | |   (222)   ~ (all_10_2 = e3)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (30), (219) imply:
% 204.79/35.59  | | | | | | | |   (223)  op(e3, e3) = e1
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, e1, e3, e3,
% 204.79/35.59  | | | | | | | |              simplifying with (75), (223) gives:
% 204.79/35.59  | | | | | | | |   (224)  all_6_2 = e1
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | COMBINE_EQS: (13), (224) imply:
% 204.79/35.59  | | | | | | | |   (225)  all_58_0 = e1
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (69), (224) imply:
% 204.79/35.59  | | | | | | | |   (226)   ~ (all_52_25 = e1)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (160), (224) imply:
% 204.79/35.59  | | | | | | | |   (227)   ~ (e3 = e1)
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (94), (224) imply:
% 204.79/35.59  | | | | | | | |   (228)  op(e1, e3) = all_6_1
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | BETA: splitting (70) gives:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | |   (229)  all_56_3 = e3
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | REF_CLOSE: (79), (220), (229) are inconsistent by sub-proof
% 204.79/35.59  | | | | | | | | |            #1339.
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | |   (230)   ~ (all_56_3 = e3)
% 204.79/35.59  | | | | | | | | |   (231)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | BETA: splitting (231) gives:
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | |   (232)  all_56_3 = e2
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (79), (232) imply:
% 204.79/35.59  | | | | | | | | | |   (233)  all_52_25 = e2
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | SIMP: (233) implies:
% 204.79/35.59  | | | | | | | | | |   (234)  all_52_25 = e2
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | COMBINE_EQS: (19), (234) imply:
% 204.79/35.59  | | | | | | | | | |   (235)  all_58_9 = e2
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (1), (234) imply:
% 204.79/35.59  | | | | | | | | | |   (236)   ~ (all_52_27 = e2)
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | SIMP: (236) implies:
% 204.79/35.59  | | | | | | | | | |   (237)   ~ (all_52_27 = e2)
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (220), (234) imply:
% 204.79/35.59  | | | | | | | | | |   (238)   ~ (e3 = e2)
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REDUCE: (16), (234) imply:
% 204.79/35.59  | | | | | | | | | |   (239)  op(e3, e0) = e2
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | BETA: splitting (33) gives:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | |   (240)  all_58_9 = e1
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | REF_CLOSE: (38), (235), (240) are inconsistent by sub-proof
% 204.79/35.59  | | | | | | | | | | |            #1214.
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | |   (241)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | BETA: splitting (241) gives:
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | Case 1:
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | |   (242)  all_58_10 = e1
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | COMBINE_EQS: (41), (242) imply:
% 204.79/35.59  | | | | | | | | | | | |   (243)  all_52_27 = e1
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | SIMP: (243) implies:
% 204.79/35.59  | | | | | | | | | | | |   (244)  all_52_27 = e1
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | REDUCE: (237), (244) imply:
% 204.79/35.59  | | | | | | | | | | | |   (245)   ~ (e2 = e1)
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_5, all_6_1, e3, e1,
% 204.79/35.59  | | | | | | | | | | | |              simplifying with (20), (228) gives:
% 204.79/35.59  | | | | | | | | | | | |   (246)  all_52_5 = all_6_1
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | COMBINE_EQS: (83), (246) imply:
% 204.79/35.59  | | | | | | | | | | | |   (247)  all_58_6 = all_6_1
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | REF_CLOSE: (4), (6), (22), (38), (51), (54), (60), (61),
% 204.79/35.59  | | | | | | | | | | | |            (85), (86), (87), (155), (225), (239), (247) are
% 204.79/35.59  | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | |   (248)  all_58_11 = e1 | all_58_15 = e1
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | | REF_CLOSE: (3), (34), (85), (217), (248) are inconsistent by
% 204.79/35.59  | | | | | | | | | | | |            sub-proof #1206.
% 204.79/35.59  | | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | |   (249)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | | REF_CLOSE: (4), (19), (33), (36), (55), (79), (88), (222),
% 204.79/35.59  | | | | | | | | | |            (249) are inconsistent by sub-proof #1245.
% 204.79/35.59  | | | | | | | | | | 
% 204.79/35.59  | | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | | 
% 204.79/35.59  | | | | | | | | End of split
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | Case 2:
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | |   (250)  all_58_15 = e3
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | COMBINE_EQS: (34), (250) imply:
% 204.79/35.59  | | | | | | | |   (251)  e3 = e0
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | REDUCE: (6), (251) imply:
% 204.79/35.59  | | | | | | | |   (252)  $false
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | | CLOSE: (252) is inconsistent.
% 204.79/35.59  | | | | | | | | 
% 204.79/35.59  | | | | | | | End of split
% 204.79/35.59  | | | | | | | 
% 204.79/35.59  | | | | | | End of split
% 204.79/35.59  | | | | | | 
% 204.79/35.59  | | | | | End of split
% 204.79/35.59  | | | | | 
% 204.79/35.59  | | | | End of split
% 204.79/35.59  | | | | 
% 204.79/35.59  | | | End of split
% 204.79/35.59  | | | 
% 204.79/35.59  | | Case 2:
% 204.79/35.59  | | | 
% 204.79/35.59  | | |   (253)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.59  | | | 
% 204.79/35.59  | | | REF_CLOSE: (1), (2), (3), (4), (6), (13), (18), (19), (21), (24), (30),
% 204.79/35.59  | | |            (33), (34), (36), (41), (43), (47), (49), (50), (55), (56),
% 204.79/35.59  | | |            (62), (64), (66), (69), (70), (75), (76), (79), (83), (88),
% 204.79/35.59  | | |            (89), (90), (93), (154), (253) are inconsistent by sub-proof
% 204.79/35.59  | | |            #1205.
% 204.79/35.59  | | | 
% 204.79/35.59  | | End of split
% 204.79/35.59  | | 
% 204.79/35.59  | End of split
% 204.79/35.59  | 
% 204.79/35.59  End of proof
% 204.79/35.59  
% 204.79/35.59  Sub-proof #1205 shows that the following formulas are inconsistent:
% 204.79/35.59  ----------------------------------------------------------------
% 204.79/35.59    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.59    (2)  all_58_14 = all_52_23
% 204.79/35.59    (3)   ~ (e3 = e1)
% 204.79/35.59    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.59    (5)   ~ (e3 = e0)
% 204.79/35.59    (6)  all_58_0 = all_6_2
% 204.79/35.59    (7)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.59    (8)  all_58_13 = all_52_15
% 204.79/35.59    (9)  all_58_9 = all_52_25
% 204.79/35.59    (10)   ~ (all_52_15 = e3)
% 204.79/35.60    (11)  op(e2, e2) = all_4_2
% 204.79/35.60    (12)  all_58_11 = all_52_29
% 204.79/35.60    (13)  op(all_52_29, all_52_29) = e1
% 204.79/35.60    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.60    (15)  all_58_15 = e0
% 204.79/35.60    (16)   ~ (all_52_25 = e0)
% 204.79/35.60    (17)  all_58_10 = all_52_27
% 204.79/35.60    (18)   ~ (all_52_25 = all_52_29)
% 204.79/35.60    (19)  all_58_12 = all_52_7
% 204.79/35.60    (20)  all_58_2 = all_52_3
% 204.79/35.60    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.60    (22)  op(all_52_25, all_52_25) = e3
% 204.79/35.60    (23)   ~ (all_52_5 = all_52_29)
% 204.79/35.60    (24)  op(all_52_27, all_52_27) = e2
% 204.79/35.60    (25)  op(all_52_23, all_52_23) = all_52_22
% 204.79/35.60    (26)   ~ (all_52_23 = e0)
% 204.79/35.60    (27)   ~ (all_52_25 = all_6_2)
% 204.79/35.60    (28)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.60    (29)  op(e3, e3) = all_6_2
% 204.79/35.60    (30)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60    (31)  all_56_3 = all_52_25
% 204.79/35.60    (32)  all_58_6 = all_52_5
% 204.79/35.60    (33)  op(e1, e1) = all_10_2
% 204.79/35.60    (34)   ~ (all_52_23 = all_10_2)
% 204.79/35.60    (35)   ~ (all_52_7 = all_52_23)
% 204.79/35.60    (36)   ~ (all_52_3 = all_4_2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (7) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (37)  all_58_13 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (8), (10), (37) are inconsistent by sub-proof #1360.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (38)  all_58_14 = e3 | all_58_15 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | BETA: splitting (38) gives:
% 204.79/35.60  | | 
% 204.79/35.60  | | Case 1:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (39)  all_58_14 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | COMBINE_EQS: (2), (39) imply:
% 204.79/35.60  | | |   (40)  all_52_23 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | SIMP: (40) implies:
% 204.79/35.60  | | |   (41)  all_52_23 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REDUCE: (35), (41) imply:
% 204.79/35.60  | | |   (42)   ~ (all_52_7 = e3)
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REDUCE: (34), (41) imply:
% 204.79/35.60  | | |   (43)   ~ (all_10_2 = e3)
% 204.79/35.60  | | | 
% 204.79/35.60  | | | SIMP: (43) implies:
% 204.79/35.60  | | |   (44)   ~ (all_10_2 = e3)
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REDUCE: (25), (41) imply:
% 204.79/35.60  | | |   (45)  op(e3, e3) = all_52_22
% 204.79/35.60  | | | 
% 204.79/35.60  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_22, e3, e3,
% 204.79/35.60  | | |              simplifying with (29), (45) gives:
% 204.79/35.60  | | |   (46)  all_52_22 = all_6_2
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (11), (12), (13), (14), (15),
% 204.79/35.60  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (27),
% 204.79/35.60  | | |            (28), (29), (30), (31), (32), (33), (36), (42), (44) are
% 204.79/35.60  | | |            inconsistent by sub-proof #1238.
% 204.79/35.60  | | | 
% 204.79/35.60  | | Case 2:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (47)  all_58_15 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REF_CLOSE: (5), (15), (47) are inconsistent by sub-proof #1350.
% 204.79/35.60  | | | 
% 204.79/35.60  | | End of split
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1206 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ~ (e3 = e1)
% 204.79/35.60    (2)  all_58_11 = e1 | all_58_15 = e1
% 204.79/35.60    (3)  all_58_15 = e0
% 204.79/35.60    (4)  all_58_11 = e3
% 204.79/35.60    (5)   ~ (e1 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (2) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (6)  all_58_11 = e1
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (4), (6) imply:
% 204.79/35.60  | |   (7)  e3 = e1
% 204.79/35.60  | | 
% 204.79/35.60  | | SIMP: (7) implies:
% 204.79/35.60  | |   (8)  e3 = e1
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (1), (8) imply:
% 204.79/35.60  | |   (9)  $false
% 204.79/35.60  | | 
% 204.79/35.60  | | CLOSE: (9) is inconsistent.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (10)  all_58_15 = e1
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #1207.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1207 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_15 = e1
% 204.79/35.60    (2)  all_58_15 = e0
% 204.79/35.60    (3)   ~ (e1 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e1 = e0
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e1 = e0
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1208 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.60    (2)   ~ (e3 = e0)
% 204.79/35.60    (3)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.79/35.60    (4)   ~ (e2 = e1)
% 204.79/35.60    (5)  op(e3, all_6_1) = all_6_0
% 204.79/35.60    (6)   ~ (e2 = e0)
% 204.79/35.60    (7)  op(e3, e0) = e2
% 204.79/35.60    (8)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.60    (9)   ~ (all_6_0 = e2)
% 204.79/35.60    (10)  all_58_6 = all_6_1
% 204.79/35.60    (11)   ~ (e1 = e0)
% 204.79/35.60    (12)   ~ (e3 = e2)
% 204.79/35.60    (13)  all_58_12 = e3
% 204.79/35.60    (14)   ~ (all_6_1 = e2)
% 204.79/35.60    (15)  all_58_0 = e1
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (8) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (16)  all_58_0 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (4), (15), (16) are inconsistent by sub-proof #1273.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (17)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | BETA: splitting (17) gives:
% 204.79/35.60  | | 
% 204.79/35.60  | | Case 1:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (18)  all_58_2 = e2
% 204.79/35.60  | | | 
% 204.79/35.60  | | | BETA: splitting (3) gives:
% 204.79/35.60  | | | 
% 204.79/35.60  | | | Case 1:
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | |   (19)  all_58_0 = e0
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | COMBINE_EQS: (15), (19) imply:
% 204.79/35.60  | | | |   (20)  e1 = e0
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | REDUCE: (11), (20) imply:
% 204.79/35.60  | | | |   (21)  $false
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | CLOSE: (21) is inconsistent.
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | Case 2:
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | |   (22)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | BETA: splitting (22) gives:
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | Case 1:
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | |   (23)  all_58_2 = e0
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | | REF_CLOSE: (6), (18), (23) are inconsistent by sub-proof #1213.
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | Case 2:
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | |   (24)  all_58_6 = e0 | all_58_12 = e0
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | | BETA: splitting (24) gives:
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | | Case 1:
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | |   (25)  all_58_6 = e0
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | COMBINE_EQS: (10), (25) imply:
% 204.79/35.60  | | | | | |   (26)  all_6_1 = e0
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | SIMP: (26) implies:
% 204.79/35.60  | | | | | |   (27)  all_6_1 = e0
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | REDUCE: (5), (27) imply:
% 204.79/35.60  | | | | | |   (28)  op(e3, e0) = all_6_0
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | GROUND_INST: instantiating (1) with e2, all_6_0, e0, e3, simplifying
% 204.79/35.60  | | | | | |              with (7), (28) gives:
% 204.79/35.60  | | | | | |   (29)  all_6_0 = e2
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | REDUCE: (9), (29) imply:
% 204.79/35.60  | | | | | |   (30)  $false
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | CLOSE: (30) is inconsistent.
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | Case 2:
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | |   (31)  all_58_12 = e0
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | | REF_CLOSE: (2), (13), (31) are inconsistent by sub-proof #1212.
% 204.79/35.60  | | | | | | 
% 204.79/35.60  | | | | | End of split
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | End of split
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | End of split
% 204.79/35.60  | | | 
% 204.79/35.60  | | Case 2:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (32)  all_58_6 = e2 | all_58_12 = e2
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REF_CLOSE: (10), (12), (13), (14), (32) are inconsistent by sub-proof
% 204.79/35.60  | | |            #1209.
% 204.79/35.60  | | | 
% 204.79/35.60  | | End of split
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1209 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_6 = e2 | all_58_12 = e2
% 204.79/35.60    (2)  all_58_6 = all_6_1
% 204.79/35.60    (3)   ~ (e3 = e2)
% 204.79/35.60    (4)  all_58_12 = e3
% 204.79/35.60    (5)   ~ (all_6_1 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (1) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (6)  all_58_6 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #1211.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (7)  all_58_12 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1210.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1210 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_12 = e3
% 204.79/35.60    (2)  all_58_12 = e2
% 204.79/35.60    (3)   ~ (e3 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e3 = e2
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e3 = e2
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1211 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_6 = all_6_1
% 204.79/35.60    (2)  all_58_6 = e2
% 204.79/35.60    (3)   ~ (all_6_1 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  all_6_1 = e2
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  all_6_1 = e2
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1212 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_12 = e3
% 204.79/35.60    (2)  all_58_12 = e0
% 204.79/35.60    (3)   ~ (e3 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e3 = e0
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e3 = e0
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1213 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_2 = e2
% 204.79/35.60    (2)  all_58_2 = e0
% 204.79/35.60    (3)   ~ (e2 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e2 = e0
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e2 = e0
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1214 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_9 = e2
% 204.79/35.60    (2)  all_58_9 = e1
% 204.79/35.60    (3)   ~ (e2 = e1)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e2 = e1
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e2 = e1
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1215 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ~ (all_52_25 = e0)
% 204.79/35.60    (2)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.60    (3)   ~ (all_52_25 = e1)
% 204.79/35.60    (4)   ~ (all_52_25 = e2)
% 204.79/35.60    (5)  all_56_3 = all_52_25
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (2) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (6)  all_56_3 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (5), (6) imply:
% 204.79/35.60  | |   (7)  all_52_25 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (4), (7) imply:
% 204.79/35.60  | |   (8)  $false
% 204.79/35.60  | | 
% 204.79/35.60  | | CLOSE: (8) is inconsistent.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (9)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1330.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1216 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ~ (all_6_1 = e1)
% 204.79/35.60    (2)   ~ (all_6_1 = e0)
% 204.79/35.60    (3)  all_56_4 = all_6_1
% 204.79/35.60    (4)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.79/35.60    (5)   ~ (all_6_1 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (4) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (6)  all_56_4 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #1219.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (7)  all_56_4 = e1 | all_56_4 = e0
% 204.79/35.60  | | 
% 204.79/35.60  | | BETA: splitting (7) gives:
% 204.79/35.60  | | 
% 204.79/35.60  | | Case 1:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (8)  all_56_4 = e1
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1218.
% 204.79/35.60  | | | 
% 204.79/35.60  | | Case 2:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (9)  all_56_4 = e0
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1217.
% 204.79/35.60  | | | 
% 204.79/35.60  | | End of split
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1217 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_56_4 = all_6_1
% 204.79/35.60    (2)  all_56_4 = e0
% 204.79/35.60    (3)   ~ (all_6_1 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  all_6_1 = e0
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  all_6_1 = e0
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1218 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_56_4 = all_6_1
% 204.79/35.60    (2)  all_56_4 = e1
% 204.79/35.60    (3)   ~ (all_6_1 = e1)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  all_6_1 = e1
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  all_6_1 = e1
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1219 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_56_4 = all_6_1
% 204.79/35.60    (2)  all_56_4 = e2
% 204.79/35.60    (3)   ~ (all_6_1 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  all_6_1 = e2
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  all_6_1 = e2
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1220 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_10 = e3
% 204.79/35.60    (2)  all_58_10 = e2
% 204.79/35.60    (3)   ~ (e3 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e3 = e2
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e3 = e2
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1221 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_9 = all_52_25
% 204.79/35.60    (2)  all_58_9 = e2
% 204.79/35.60    (3)   ~ (all_52_25 = e2)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  all_52_25 = e2
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  all_52_25 = e2
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1222 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ~ (e3 = e1)
% 204.79/35.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.60    (3)   ~ (e3 = e0)
% 204.79/35.60    (4)  all_58_0 = all_6_2
% 204.79/35.60    (5)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.79/35.60    (6)  all_58_9 = all_52_25
% 204.79/35.60    (7)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.60    (8)  op(e2, e2) = all_4_2
% 204.79/35.60    (9)  all_58_11 = all_52_29
% 204.79/35.60    (10)   ~ (all_52_7 = all_6_2)
% 204.79/35.60    (11)  op(all_52_29, all_52_29) = e1
% 204.79/35.60    (12)  all_58_15 = e0
% 204.79/35.60    (13)   ~ (all_52_25 = e0)
% 204.79/35.60    (14)  all_58_10 = all_52_27
% 204.79/35.60    (15)   ~ (all_52_25 = all_52_29)
% 204.79/35.60    (16)  all_58_12 = all_52_7
% 204.79/35.60    (17)   ~ (all_52_7 = e3)
% 204.79/35.60    (18)  all_58_2 = all_52_3
% 204.79/35.60    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.60    (20)  all_56_7 = all_52_27
% 204.79/35.60    (21)  op(all_52_25, all_52_25) = e3
% 204.79/35.60    (22)   ~ (all_52_5 = all_52_29)
% 204.79/35.60    (23)  op(all_52_27, all_52_27) = e2
% 204.79/35.60    (24)  all_56_12 = all_52_7
% 204.79/35.60    (25)   ~ (all_52_25 = all_6_2)
% 204.79/35.60    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.60    (27)  op(e3, e3) = all_6_2
% 204.79/35.60    (28)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60    (29)  all_56_3 = all_52_25
% 204.79/35.60    (30)  all_58_6 = all_52_5
% 204.79/35.60    (31)   ~ (all_58_12 = e1)
% 204.79/35.60    (32)   ~ (all_52_3 = all_4_2)
% 204.79/35.60    (33)   ~ (all_52_7 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (16), (31) imply:
% 204.79/35.60  |   (34)   ~ (all_52_7 = e1)
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (7) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (35)  all_56_12 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (24), (35) imply:
% 204.79/35.60  | |   (36)  all_52_7 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | SIMP: (36) implies:
% 204.79/35.60  | |   (37)  all_52_7 = e2
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (10), (37) imply:
% 204.79/35.60  | |   (38)   ~ (all_6_2 = e2)
% 204.79/35.60  | | 
% 204.79/35.60  | | SIMP: (38) implies:
% 204.79/35.60  | |   (39)   ~ (all_6_2 = e2)
% 204.79/35.60  | | 
% 204.79/35.60  | | BETA: splitting (5) gives:
% 204.79/35.60  | | 
% 204.79/35.60  | | Case 1:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (40)  all_56_7 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | COMBINE_EQS: (20), (40) imply:
% 204.79/35.60  | | |   (41)  all_52_27 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | SIMP: (41) implies:
% 204.79/35.60  | | |   (42)  all_52_27 = e3
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REDUCE: (23), (42) imply:
% 204.79/35.60  | | |   (43)  op(e3, e3) = e2
% 204.79/35.60  | | | 
% 204.79/35.60  | | | GROUND_INST: instantiating (2) with all_6_2, e2, e3, e3, simplifying with
% 204.79/35.60  | | |              (27), (43) gives:
% 204.79/35.60  | | |   (44)  all_6_2 = e2
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REDUCE: (39), (44) imply:
% 204.79/35.60  | | |   (45)  $false
% 204.79/35.60  | | | 
% 204.79/35.60  | | | CLOSE: (45) is inconsistent.
% 204.79/35.60  | | | 
% 204.79/35.60  | | Case 2:
% 204.79/35.60  | | | 
% 204.79/35.60  | | |   (46)   ~ (all_56_7 = e3)
% 204.79/35.60  | | | 
% 204.79/35.60  | | | REDUCE: (20), (46) imply:
% 204.79/35.60  | | |   (47)   ~ (all_52_27 = e3)
% 204.79/35.60  | | | 
% 204.79/35.60  | | | BETA: splitting (28) gives:
% 204.79/35.60  | | | 
% 204.79/35.60  | | | Case 1:
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | |   (48)  all_58_9 = e3
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | COMBINE_EQS: (6), (48) imply:
% 204.79/35.60  | | | |   (49)  all_52_25 = e3
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | REF_CLOSE: (2), (21), (25), (27), (49) are inconsistent by sub-proof
% 204.79/35.60  | | | |            #1246.
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | Case 2:
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | |   (50)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | BETA: splitting (50) gives:
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | | Case 1:
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | |   (51)  all_58_10 = e3
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | | REF_CLOSE: (14), (47), (51) are inconsistent by sub-proof #1301.
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | Case 2:
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | |   (52)  all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (11), (12), (13), (15), (16),
% 204.79/35.60  | | | | |            (17), (18), (19), (21), (22), (25), (26), (27), (29), (30),
% 204.79/35.60  | | | | |            (32), (52) are inconsistent by sub-proof #1239.
% 204.79/35.60  | | | | | 
% 204.79/35.60  | | | | End of split
% 204.79/35.60  | | | | 
% 204.79/35.60  | | | End of split
% 204.79/35.60  | | | 
% 204.79/35.60  | | End of split
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (53)  all_56_12 = e1 | all_56_12 = e0
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (24), (33), (34), (53) are inconsistent by sub-proof #1374.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1223 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)  all_58_15 = e2
% 204.79/35.60    (2)  all_58_15 = e0
% 204.79/35.60    (3)   ~ (e2 = e0)
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.60  |   (4)  e2 = e0
% 204.79/35.60  | 
% 204.79/35.60  | SIMP: (4) implies:
% 204.79/35.60  |   (5)  e2 = e0
% 204.79/35.60  | 
% 204.79/35.60  | REDUCE: (3), (5) imply:
% 204.79/35.60  |   (6)  $false
% 204.79/35.60  | 
% 204.79/35.60  | CLOSE: (6) is inconsistent.
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1224 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.60    (3)  all_58_1 = all_52_9
% 204.79/35.60    (4)   ~ (all_52_17 = all_52_25)
% 204.79/35.60    (5)   ~ (all_4_2 = e3)
% 204.79/35.60    (6)   ~ (all_52_3 = all_6_2)
% 204.79/35.60    (7)  all_58_0 = all_6_2
% 204.79/35.60    (8)   ~ (all_52_17 = all_10_2)
% 204.79/35.60    (9)  all_58_9 = all_52_25
% 204.79/35.60    (10)  all_58_11 = all_52_29
% 204.79/35.60    (11)  op(all_6_2, all_6_2) = all_52_0
% 204.79/35.60    (12)  op(e0, e0) = all_14_2
% 204.79/35.60    (13)  op(all_52_29, all_52_29) = e1
% 204.79/35.60    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.60    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.60    (16)  all_56_11 = all_52_29
% 204.79/35.60    (17)   ~ (all_6_0 = e1)
% 204.79/35.60    (18)  all_58_10 = all_52_27
% 204.79/35.60    (19)  all_58_7 = all_52_13
% 204.79/35.60    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.60    (21)  all_58_2 = all_52_3
% 204.79/35.60    (22)  op(e3, all_6_1) = all_6_0
% 204.79/35.60    (23)  op(all_52_25, all_52_25) = e3
% 204.79/35.60    (24)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.79/35.60    (25)   ~ (all_6_0 = e2)
% 204.79/35.60    (26)   ~ (all_52_9 = e3)
% 204.79/35.60    (27)  op(all_52_27, all_52_27) = e2
% 204.79/35.60    (28)   ~ (all_52_19 = all_10_2)
% 204.79/35.60    (29)  all_58_8 = all_10_2
% 204.79/35.60    (30)   ~ (all_52_25 = all_6_2)
% 204.79/35.60    (31)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.60    (32)   ~ (all_52_5 = all_6_2)
% 204.79/35.60    (33)  op(e3, e3) = all_6_2
% 204.79/35.60    (34)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60    (35)   ~ (all_52_13 = e3)
% 204.79/35.60    (36)   ~ (all_52_27 = all_14_2)
% 204.79/35.60    (37)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.60    (38)   ~ (all_52_17 = e3)
% 204.79/35.60    (39)  all_56_3 = all_52_25
% 204.79/35.60    (40)  all_58_5 = all_52_19
% 204.79/35.60    (41)  all_58_6 = all_52_5
% 204.79/35.60    (42)  op(e1, e1) = all_10_2
% 204.79/35.60    (43)  all_58_3 = all_4_2
% 204.79/35.60    (44)  op(all_6_2, e3) = all_6_1
% 204.79/35.60    (45)  all_58_4 = all_52_17
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (37) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (46)  all_58_0 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (7), (46) imply:
% 204.79/35.60  | |   (47)  all_6_2 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (6), (47) imply:
% 204.79/35.60  | |   (48)   ~ (all_52_3 = e3)
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (32), (47) imply:
% 204.79/35.60  | |   (49)   ~ (all_52_5 = e3)
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (11), (47) imply:
% 204.79/35.60  | |   (50)  op(e3, e3) = all_52_0
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (44), (47) imply:
% 204.79/35.60  | |   (51)  op(e3, e3) = all_6_1
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (33), (47) imply:
% 204.79/35.60  | |   (52)  op(e3, e3) = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | GROUND_INST: instantiating (2) with all_6_1, all_52_0, e3, e3, simplifying
% 204.79/35.60  | |              with (50), (51) gives:
% 204.79/35.60  | |   (53)  all_52_0 = all_6_1
% 204.79/35.60  | | 
% 204.79/35.60  | | GROUND_INST: instantiating (2) with e3, all_52_0, e3, e3, simplifying with
% 204.79/35.60  | |              (50), (52) gives:
% 204.79/35.60  | |   (54)  all_52_0 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (53), (54) imply:
% 204.79/35.60  | |   (55)  all_6_1 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | SIMP: (55) implies:
% 204.79/35.60  | |   (56)  all_6_1 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (22), (56) imply:
% 204.79/35.60  | |   (57)  op(e3, e3) = all_6_0
% 204.79/35.60  | | 
% 204.79/35.60  | | GROUND_INST: instantiating (2) with e3, all_6_0, e3, e3, simplifying with
% 204.79/35.60  | |              (52), (57) gives:
% 204.79/35.60  | |   (58)  all_6_0 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (25), (58) imply:
% 204.79/35.60  | |   (59)   ~ (e3 = e2)
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (17), (58) imply:
% 204.79/35.60  | |   (60)   ~ (e3 = e1)
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 204.79/35.60  | |            (15), (16), (18), (19), (20), (21), (23), (24), (26), (27), (28),
% 204.79/35.60  | |            (29), (30), (31), (33), (35), (36), (37), (39), (40), (41), (42),
% 204.79/35.60  | |            (43), (45), (48), (49), (50), (52), (59), (60) are inconsistent
% 204.79/35.60  | |            by sub-proof #1227.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (61)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (2), (3), (9), (23), (26), (30), (33), (34), (38), (45), (61) are
% 204.79/35.60  | |            inconsistent by sub-proof #1225.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1225 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.60    (2)  all_58_1 = all_52_9
% 204.79/35.60    (3)  all_58_9 = all_52_25
% 204.79/35.60    (4)  op(all_52_25, all_52_25) = e3
% 204.79/35.60    (5)   ~ (all_52_9 = e3)
% 204.79/35.60    (6)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.60    (7)   ~ (all_52_25 = all_6_2)
% 204.79/35.60    (8)  op(e3, e3) = all_6_2
% 204.79/35.60    (9)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60    (10)   ~ (all_52_17 = e3)
% 204.79/35.60    (11)  all_58_4 = all_52_17
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (6) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (12)  all_58_1 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (2), (12) imply:
% 204.79/35.60  | |   (13)  all_52_9 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (5), (13) imply:
% 204.79/35.60  | |   (14)  $false
% 204.79/35.60  | | 
% 204.79/35.60  | | CLOSE: (14) is inconsistent.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (15)  all_58_4 = e3 | all_58_9 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (15) are inconsistent
% 204.79/35.60  | |            by sub-proof #1226.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1226 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.60    (2)  all_58_9 = all_52_25
% 204.79/35.60    (3)  all_58_4 = e3 | all_58_9 = e3
% 204.79/35.60    (4)  op(all_52_25, all_52_25) = e3
% 204.79/35.60    (5)   ~ (all_52_25 = all_6_2)
% 204.79/35.60    (6)  op(e3, e3) = all_6_2
% 204.79/35.60    (7)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.60    (8)   ~ (all_52_17 = e3)
% 204.79/35.60    (9)  all_58_4 = all_52_17
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (7) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (10)  all_58_9 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | COMBINE_EQS: (2), (10) imply:
% 204.79/35.60  | |   (11)  all_52_25 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (1), (4), (5), (6), (11) are inconsistent by sub-proof #1246.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (12)   ~ (all_58_9 = e3)
% 204.79/35.60  | | 
% 204.79/35.60  | | REDUCE: (2), (12) imply:
% 204.79/35.60  | |   (13)   ~ (all_52_25 = e3)
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (2), (3), (8), (9), (13) are inconsistent by sub-proof #1299.
% 204.79/35.60  | | 
% 204.79/35.60  | End of split
% 204.79/35.60  | 
% 204.79/35.60  End of proof
% 204.79/35.60  
% 204.79/35.60  Sub-proof #1227 shows that the following formulas are inconsistent:
% 204.79/35.60  ----------------------------------------------------------------
% 204.79/35.60    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.60    (2)   ~ (e3 = e1)
% 204.79/35.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.60    (4)  all_58_1 = all_52_9
% 204.79/35.60    (5)  op(e3, e3) = all_52_0
% 204.79/35.60    (6)   ~ (all_52_17 = all_52_25)
% 204.79/35.60    (7)   ~ (all_4_2 = e3)
% 204.79/35.60    (8)  all_58_0 = all_6_2
% 204.79/35.60    (9)   ~ (all_52_17 = all_10_2)
% 204.79/35.60    (10)  all_58_9 = all_52_25
% 204.79/35.60    (11)  all_58_11 = all_52_29
% 204.79/35.60    (12)   ~ (all_52_3 = e3)
% 204.79/35.60    (13)  op(e0, e0) = all_14_2
% 204.79/35.60    (14)  op(all_52_29, all_52_29) = e1
% 204.79/35.60    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.60    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.60    (17)  all_56_11 = all_52_29
% 204.79/35.60    (18)  all_58_10 = all_52_27
% 204.79/35.60    (19)  all_58_7 = all_52_13
% 204.79/35.60    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.60    (21)  all_58_2 = all_52_3
% 204.79/35.60    (22)  op(e3, e3) = e3
% 204.79/35.60    (23)   ~ (all_52_5 = e3)
% 204.79/35.60    (24)  op(all_52_25, all_52_25) = e3
% 204.79/35.60    (25)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 204.79/35.60    (26)   ~ (all_52_9 = e3)
% 204.79/35.60    (27)  op(all_52_27, all_52_27) = e2
% 204.79/35.60    (28)   ~ (all_52_19 = all_10_2)
% 204.79/35.60    (29)  all_58_8 = all_10_2
% 204.79/35.60    (30)   ~ (all_52_25 = all_6_2)
% 204.79/35.60    (31)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.60    (32)  op(e3, e3) = all_6_2
% 204.79/35.60    (33)   ~ (all_52_13 = e3)
% 204.79/35.60    (34)   ~ (all_52_27 = all_14_2)
% 204.79/35.60    (35)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.60    (36)  all_56_3 = all_52_25
% 204.79/35.60    (37)  all_58_5 = all_52_19
% 204.79/35.60    (38)  all_58_6 = all_52_5
% 204.79/35.60    (39)   ~ (e3 = e2)
% 204.79/35.60    (40)  op(e1, e1) = all_10_2
% 204.79/35.60    (41)  all_58_3 = all_4_2
% 204.79/35.60    (42)  all_58_4 = all_52_17
% 204.79/35.60  
% 204.79/35.60  Begin of proof
% 204.79/35.60  | 
% 204.79/35.60  | BETA: splitting (20) gives:
% 204.79/35.60  | 
% 204.79/35.60  | Case 1:
% 204.79/35.60  | | 
% 204.79/35.60  | |   (43)  all_58_6 = e3
% 204.79/35.60  | | 
% 204.79/35.60  | | REF_CLOSE: (23), (38), (43) are inconsistent by sub-proof #1328.
% 204.79/35.60  | | 
% 204.79/35.60  | Case 2:
% 204.79/35.60  | | 
% 204.79/35.61  | |   (44)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | BETA: splitting (15) gives:
% 204.79/35.61  | | 
% 204.79/35.61  | | Case 1:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (45)  all_58_2 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (12), (21), (45) are inconsistent by sub-proof #1369.
% 204.79/35.61  | | | 
% 204.79/35.61  | | Case 2:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (46)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | BETA: splitting (25) gives:
% 204.79/35.61  | | | 
% 204.79/35.61  | | | Case 1:
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | |   (47)  all_56_11 = e3
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | COMBINE_EQS: (17), (47) imply:
% 204.79/35.61  | | | |   (48)  all_52_29 = e3
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | REF_CLOSE: (2), (3), (5), (14), (22), (48) are inconsistent by sub-proof
% 204.79/35.61  | | | |            #1236.
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | Case 2:
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | |   (49)   ~ (all_56_11 = e3)
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | REDUCE: (17), (49) imply:
% 204.79/35.61  | | | |   (50)   ~ (all_52_29 = e3)
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | BETA: splitting (44) gives:
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | Case 1:
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | |   (51)  all_58_7 = e3
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | COMBINE_EQS: (19), (51) imply:
% 204.79/35.61  | | | | |   (52)  all_52_13 = e3
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | REDUCE: (33), (52) imply:
% 204.79/35.61  | | | | |   (53)  $false
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | CLOSE: (53) is inconsistent.
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | Case 2:
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | |   (54)  all_58_8 = e3 | all_58_11 = e3
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | BETA: splitting (54) gives:
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | Case 1:
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | |   (55)  all_58_8 = e3
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | | COMBINE_EQS: (29), (55) imply:
% 204.79/35.61  | | | | | |   (56)  all_10_2 = e3
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | | SIMP: (56) implies:
% 204.79/35.61  | | | | | |   (57)  all_10_2 = e3
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | | REDUCE: (28), (57) imply:
% 204.79/35.61  | | | | | |   (58)   ~ (all_52_19 = e3)
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (13), (16),
% 204.79/35.61  | | | | | |            (18), (24), (26), (27), (30), (31), (32), (34), (35),
% 204.79/35.61  | | | | | |            (36), (37), (39), (40), (41), (42), (46), (58) are
% 204.79/35.61  | | | | | |            inconsistent by sub-proof #1228.
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | Case 2:
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | |   (59)  all_58_11 = e3
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | | REF_CLOSE: (11), (50), (59) are inconsistent by sub-proof #1323.
% 204.79/35.61  | | | | | | 
% 204.79/35.61  | | | | | End of split
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | End of split
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | End of split
% 204.79/35.61  | | | 
% 204.79/35.61  | | End of split
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1228 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (3)  all_58_1 = all_52_9
% 204.79/35.61    (4)   ~ (all_52_17 = all_52_25)
% 204.79/35.61    (5)   ~ (all_4_2 = e3)
% 204.79/35.61    (6)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.79/35.61    (7)  all_58_0 = all_6_2
% 204.79/35.61    (8)   ~ (all_52_17 = all_10_2)
% 204.79/35.61    (9)  all_58_9 = all_52_25
% 204.79/35.61    (10)  op(e0, e0) = all_14_2
% 204.79/35.61    (11)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.61    (12)  all_58_10 = all_52_27
% 204.79/35.61    (13)   ~ (all_52_19 = e3)
% 204.79/35.61    (14)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (15)   ~ (all_52_9 = e3)
% 204.79/35.61    (16)  op(all_52_27, all_52_27) = e2
% 204.79/35.61    (17)   ~ (all_52_25 = all_6_2)
% 204.79/35.61    (18)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (19)  op(e3, e3) = all_6_2
% 204.79/35.61    (20)   ~ (all_52_27 = all_14_2)
% 204.79/35.61    (21)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.61    (22)  all_56_3 = all_52_25
% 204.79/35.61    (23)  all_58_5 = all_52_19
% 204.79/35.61    (24)   ~ (e3 = e2)
% 204.79/35.61    (25)  op(e1, e1) = all_10_2
% 204.79/35.61    (26)  all_58_3 = all_4_2
% 204.79/35.61    (27)  all_58_4 = all_52_17
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (6) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (28)  all_58_3 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (26), (28) imply:
% 204.79/35.61  | |   (29)  all_4_2 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (5), (29) imply:
% 204.79/35.61  | |   (30)  $false
% 204.79/35.61  | | 
% 204.79/35.61  | | CLOSE: (30) is inconsistent.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (31)  all_58_5 = e3 | all_58_10 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | BETA: splitting (31) gives:
% 204.79/35.61  | | 
% 204.79/35.61  | | Case 1:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (32)  all_58_5 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (13), (23), (32) are inconsistent by sub-proof #1279.
% 204.79/35.61  | | | 
% 204.79/35.61  | | Case 2:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (33)  all_58_10 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | COMBINE_EQS: (12), (33) imply:
% 204.79/35.61  | | |   (34)  all_52_27 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | SIMP: (34) implies:
% 204.79/35.61  | | |   (35)  all_52_27 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (1), (35) imply:
% 204.79/35.61  | | |   (36)   ~ (all_52_25 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (20), (35) imply:
% 204.79/35.61  | | |   (37)   ~ (all_14_2 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | SIMP: (37) implies:
% 204.79/35.61  | | |   (38)   ~ (all_14_2 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (16), (35) imply:
% 204.79/35.61  | | |   (39)  op(e3, e3) = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | GROUND_INST: instantiating (2) with all_6_2, e2, e3, e3, simplifying with
% 204.79/35.61  | | |              (19), (39) gives:
% 204.79/35.61  | | |   (40)  all_6_2 = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | COMBINE_EQS: (7), (40) imply:
% 204.79/35.61  | | |   (41)  all_58_0 = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (17), (40) imply:
% 204.79/35.61  | | |   (42)   ~ (all_52_25 = e2)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (11), (14), (15), (18), (21),
% 204.79/35.61  | | |            (22), (24), (25), (27), (36), (38), (41), (42) are inconsistent
% 204.79/35.61  | | |            by sub-proof #1229.
% 204.79/35.61  | | | 
% 204.79/35.61  | | End of split
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1229 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  all_58_1 = all_52_9
% 204.79/35.61    (3)   ~ (all_52_17 = all_52_25)
% 204.79/35.61    (4)   ~ (all_52_17 = all_10_2)
% 204.79/35.61    (5)  all_58_9 = all_52_25
% 204.79/35.61    (6)  op(e0, e0) = all_14_2
% 204.79/35.61    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.61    (8)   ~ (all_52_25 = e3)
% 204.79/35.61    (9)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (10)   ~ (all_52_9 = e3)
% 204.79/35.61    (11)  all_58_0 = e2
% 204.79/35.61    (12)   ~ (all_52_25 = e2)
% 204.79/35.61    (13)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (14)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.61    (15)  all_56_3 = all_52_25
% 204.79/35.61    (16)   ~ (e3 = e2)
% 204.79/35.61    (17)  op(e1, e1) = all_10_2
% 204.79/35.61    (18)  all_58_4 = all_52_17
% 204.79/35.61    (19)   ~ (all_14_2 = e3)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (14) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (20)  all_58_0 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (11), (16), (20) are inconsistent by sub-proof #1235.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (21)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 204.79/35.61  | |            (15), (17), (18), (19), (21) are inconsistent by sub-proof #1230.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1230 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  all_58_1 = all_52_9
% 204.79/35.61    (3)   ~ (all_52_17 = all_52_25)
% 204.79/35.61    (4)   ~ (all_52_17 = all_10_2)
% 204.79/35.61    (5)  all_58_9 = all_52_25
% 204.79/35.61    (6)  op(e0, e0) = all_14_2
% 204.79/35.61    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.61    (8)   ~ (all_52_25 = e3)
% 204.79/35.61    (9)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (10)   ~ (all_52_9 = e3)
% 204.79/35.61    (11)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.61    (12)   ~ (all_52_25 = e2)
% 204.79/35.61    (13)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (14)  all_56_3 = all_52_25
% 204.79/35.61    (15)  op(e1, e1) = all_10_2
% 204.79/35.61    (16)  all_58_4 = all_52_17
% 204.79/35.61    (17)   ~ (all_14_2 = e3)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (11) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (18)  all_58_1 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (2), (18) imply:
% 204.79/35.61  | |   (19)  all_52_9 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (10), (19) imply:
% 204.79/35.61  | |   (20)  $false
% 204.79/35.61  | | 
% 204.79/35.61  | | CLOSE: (20) is inconsistent.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (21)  all_58_4 = e3 | all_58_9 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | BETA: splitting (21) gives:
% 204.79/35.61  | | 
% 204.79/35.61  | | Case 1:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (22)  all_58_4 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | COMBINE_EQS: (16), (22) imply:
% 204.79/35.61  | | |   (23)  all_52_17 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (3), (23) imply:
% 204.79/35.61  | | |   (24)   ~ (all_52_25 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (4), (23) imply:
% 204.79/35.61  | | |   (25)   ~ (all_10_2 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | SIMP: (25) implies:
% 204.79/35.61  | | |   (26)   ~ (all_10_2 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (12), (13), (14), (15), (17),
% 204.79/35.61  | | |            (26) are inconsistent by sub-proof #1231.
% 204.79/35.61  | | | 
% 204.79/35.61  | | Case 2:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (27)  all_58_9 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | COMBINE_EQS: (5), (27) imply:
% 204.79/35.61  | | |   (28)  all_52_25 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (8), (28) imply:
% 204.79/35.61  | | |   (29)  $false
% 204.79/35.61  | | | 
% 204.79/35.61  | | | CLOSE: (29) is inconsistent.
% 204.79/35.61  | | | 
% 204.79/35.61  | | End of split
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1231 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  all_58_9 = all_52_25
% 204.79/35.61    (3)  op(e0, e0) = all_14_2
% 204.79/35.61    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.61    (5)   ~ (all_52_25 = e3)
% 204.79/35.61    (6)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (7)   ~ (all_10_2 = e3)
% 204.79/35.61    (8)   ~ (all_52_25 = e2)
% 204.79/35.61    (9)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (10)  all_56_3 = all_52_25
% 204.79/35.61    (11)  op(e1, e1) = all_10_2
% 204.79/35.61    (12)   ~ (all_14_2 = e3)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (9) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (13)  all_56_3 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (5), (10), (13) are inconsistent by sub-proof #1339.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (14)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (14) are
% 204.79/35.61  | |            inconsistent by sub-proof #1232.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1232 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  all_58_9 = all_52_25
% 204.79/35.61    (3)  op(e0, e0) = all_14_2
% 204.79/35.61    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.61    (5)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (6)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (7)   ~ (all_10_2 = e3)
% 204.79/35.61    (8)   ~ (all_52_25 = e2)
% 204.79/35.61    (9)  all_56_3 = all_52_25
% 204.79/35.61    (10)  op(e1, e1) = all_10_2
% 204.79/35.61    (11)   ~ (all_14_2 = e3)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (4) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (12)  all_58_9 = e1
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (2), (12) imply:
% 204.79/35.61  | |   (13)  all_52_25 = e1
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (6), (13) imply:
% 204.79/35.61  | |   (14)  op(e1, e1) = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (7), (10), (14) are inconsistent by sub-proof #1368.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (15)   ~ (all_58_9 = e1)
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (2), (15) imply:
% 204.79/35.61  | |   (16)   ~ (all_52_25 = e1)
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (16) are inconsistent by
% 204.79/35.61  | |            sub-proof #1233.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1233 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  op(e0, e0) = all_14_2
% 204.79/35.61    (3)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (4)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (5)   ~ (all_52_25 = e1)
% 204.79/35.61    (6)   ~ (all_52_25 = e2)
% 204.79/35.61    (7)  all_56_3 = all_52_25
% 204.79/35.61    (8)   ~ (all_14_2 = e3)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (3) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (9)  all_56_3 = e2
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (7), (9) imply:
% 204.79/35.61  | |   (10)  all_52_25 = e2
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (6), (10) imply:
% 204.79/35.61  | |   (11)  $false
% 204.79/35.61  | | 
% 204.79/35.61  | | CLOSE: (11) is inconsistent.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (12)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (12) are inconsistent by sub-proof
% 204.79/35.61  | |            #1234.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1234 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  op(e0, e0) = all_14_2
% 204.79/35.61    (3)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (4)   ~ (all_52_25 = e1)
% 204.79/35.61    (5)  all_56_3 = all_52_25
% 204.79/35.61    (6)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (7)   ~ (all_14_2 = e3)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (6) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (8)  all_56_3 = e1
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (5), (8) imply:
% 204.79/35.61  | |   (9)  all_52_25 = e1
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (4), (9) imply:
% 204.79/35.61  | |   (10)  $false
% 204.79/35.61  | | 
% 204.79/35.61  | | CLOSE: (10) is inconsistent.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (11)  all_56_3 = e0
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (5), (11) imply:
% 204.79/35.61  | |   (12)  all_52_25 = e0
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (3), (12) imply:
% 204.79/35.61  | |   (13)  op(e0, e0) = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | GROUND_INST: instantiating (1) with all_14_2, e3, e0, e0, simplifying with
% 204.79/35.61  | |              (2), (13) gives:
% 204.79/35.61  | |   (14)  all_14_2 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (7), (14) imply:
% 204.79/35.61  | |   (15)  $false
% 204.79/35.61  | | 
% 204.79/35.61  | | CLOSE: (15) is inconsistent.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1235 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)  all_58_0 = e3
% 204.79/35.61    (2)  all_58_0 = e2
% 204.79/35.61    (3)   ~ (e3 = e2)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.61  |   (4)  e3 = e2
% 204.79/35.61  | 
% 204.79/35.61  | SIMP: (4) implies:
% 204.79/35.61  |   (5)  e3 = e2
% 204.79/35.61  | 
% 204.79/35.61  | REDUCE: (3), (5) imply:
% 204.79/35.61  |   (6)  $false
% 204.79/35.61  | 
% 204.79/35.61  | CLOSE: (6) is inconsistent.
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1236 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)  all_52_29 = e3
% 204.79/35.61    (2)   ~ (e3 = e1)
% 204.79/35.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (4)  op(e3, e3) = all_52_0
% 204.79/35.61    (5)  op(all_52_29, all_52_29) = e1
% 204.79/35.61    (6)  op(e3, e3) = e3
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | SIMP: (1) implies:
% 204.79/35.61  |   (7)  all_52_29 = e3
% 204.79/35.61  | 
% 204.79/35.61  | REDUCE: (5), (7) imply:
% 204.79/35.61  |   (8)  op(e3, e3) = e1
% 204.79/35.61  | 
% 204.79/35.61  | REF_CLOSE: (2), (3), (4), (6), (8) are inconsistent by sub-proof #1237.
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1237 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ~ (e3 = e1)
% 204.79/35.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (3)  op(e3, e3) = all_52_0
% 204.79/35.61    (4)  op(e3, e3) = e3
% 204.79/35.61    (5)  op(e3, e3) = e1
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | GROUND_INST: instantiating (2) with e3, all_52_0, e3, e3, simplifying with
% 204.79/35.61  |              (3), (4) gives:
% 204.79/35.61  |   (6)  all_52_0 = e3
% 204.79/35.61  | 
% 204.79/35.61  | GROUND_INST: instantiating (2) with e1, all_52_0, e3, e3, simplifying with
% 204.79/35.61  |              (3), (5) gives:
% 204.79/35.61  |   (7)  all_52_0 = e1
% 204.79/35.61  | 
% 204.79/35.61  | COMBINE_EQS: (6), (7) imply:
% 204.79/35.61  |   (8)  e3 = e1
% 204.79/35.61  | 
% 204.79/35.61  | SIMP: (8) implies:
% 204.79/35.61  |   (9)  e3 = e1
% 204.79/35.61  | 
% 204.79/35.61  | REDUCE: (1), (9) imply:
% 204.79/35.61  |   (10)  $false
% 204.79/35.61  | 
% 204.79/35.61  | CLOSE: (10) is inconsistent.
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1238 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.61    (2)   ~ (e3 = e1)
% 204.79/35.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (4)   ~ (e3 = e0)
% 204.79/35.61    (5)  all_58_0 = all_6_2
% 204.79/35.61    (6)  all_58_9 = all_52_25
% 204.79/35.61    (7)  op(e2, e2) = all_4_2
% 204.79/35.61    (8)  all_58_11 = all_52_29
% 204.79/35.61    (9)  op(all_52_29, all_52_29) = e1
% 204.79/35.61    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.61    (11)  all_58_15 = e0
% 204.79/35.61    (12)   ~ (all_52_25 = e0)
% 204.79/35.61    (13)  all_58_10 = all_52_27
% 204.79/35.61    (14)   ~ (all_52_25 = all_52_29)
% 204.79/35.61    (15)  all_58_12 = all_52_7
% 204.79/35.61    (16)   ~ (all_52_7 = e3)
% 204.79/35.61    (17)  all_58_2 = all_52_3
% 204.79/35.61    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61    (19)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (20)   ~ (all_52_5 = all_52_29)
% 204.79/35.61    (21)   ~ (all_10_2 = e3)
% 204.79/35.61    (22)  op(all_52_27, all_52_27) = e2
% 204.79/35.61    (23)   ~ (all_52_25 = all_6_2)
% 204.79/35.61    (24)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (25)  op(e3, e3) = all_6_2
% 204.79/35.61    (26)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.61    (27)  all_56_3 = all_52_25
% 204.79/35.61    (28)  all_58_6 = all_52_5
% 204.79/35.61    (29)  op(e1, e1) = all_10_2
% 204.79/35.61    (30)   ~ (all_52_3 = all_4_2)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (26) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (31)  all_58_9 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (6), (31) imply:
% 204.79/35.61  | |   (32)  all_52_25 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (3), (19), (23), (25), (32) are inconsistent by sub-proof #1246.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (33)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | BETA: splitting (33) gives:
% 204.79/35.61  | | 
% 204.79/35.61  | | Case 1:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (34)  all_58_10 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | COMBINE_EQS: (13), (34) imply:
% 204.79/35.61  | | |   (35)  all_52_27 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | SIMP: (35) implies:
% 204.79/35.61  | | |   (36)  all_52_27 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (1), (36) imply:
% 204.79/35.61  | | |   (37)   ~ (all_52_25 = e3)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (22), (36) imply:
% 204.79/35.61  | | |   (38)  op(e3, e3) = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | GROUND_INST: instantiating (3) with all_6_2, e2, e3, e3, simplifying with
% 204.79/35.61  | | |              (25), (38) gives:
% 204.79/35.61  | | |   (39)  all_6_2 = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (23), (39) imply:
% 204.79/35.61  | | |   (40)   ~ (all_52_25 = e2)
% 204.79/35.61  | | | 
% 204.79/35.61  | | | BETA: splitting (24) gives:
% 204.79/35.61  | | | 
% 204.79/35.61  | | | Case 1:
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | |   (41)  all_56_3 = e3
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | REF_CLOSE: (27), (37), (41) are inconsistent by sub-proof #1339.
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | Case 2:
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | |   (42)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | BETA: splitting (42) gives:
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | | Case 1:
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | |   (43)  all_56_3 = e2
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | REF_CLOSE: (27), (40), (43) are inconsistent by sub-proof #1259.
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | Case 2:
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | |   (44)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | | REF_CLOSE: (3), (6), (10), (12), (19), (21), (27), (29), (44) are
% 204.79/35.61  | | | | |            inconsistent by sub-proof #1245.
% 204.79/35.61  | | | | | 
% 204.79/35.61  | | | | End of split
% 204.79/35.61  | | | | 
% 204.79/35.61  | | | End of split
% 204.79/35.61  | | | 
% 204.79/35.61  | | Case 2:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (45)  all_58_11 = e3 | all_58_15 = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11), (12), (14), (15),
% 204.79/35.61  | | |            (16), (17), (18), (19), (20), (23), (24), (25), (27), (28),
% 204.79/35.61  | | |            (30), (45) are inconsistent by sub-proof #1239.
% 204.79/35.61  | | | 
% 204.79/35.61  | | End of split
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1239 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ~ (e3 = e1)
% 204.79/35.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (3)   ~ (e3 = e0)
% 204.79/35.61    (4)  all_58_0 = all_6_2
% 204.79/35.61    (5)  op(e2, e2) = all_4_2
% 204.79/35.61    (6)  all_58_11 = all_52_29
% 204.79/35.61    (7)  op(all_52_29, all_52_29) = e1
% 204.79/35.61    (8)  all_58_15 = e0
% 204.79/35.61    (9)   ~ (all_52_25 = e0)
% 204.79/35.61    (10)   ~ (all_52_25 = all_52_29)
% 204.79/35.61    (11)  all_58_11 = e3 | all_58_15 = e3
% 204.79/35.61    (12)  all_58_12 = all_52_7
% 204.79/35.61    (13)   ~ (all_52_7 = e3)
% 204.79/35.61    (14)  all_58_2 = all_52_3
% 204.79/35.61    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61    (16)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (17)   ~ (all_52_5 = all_52_29)
% 204.79/35.61    (18)   ~ (all_52_25 = all_6_2)
% 204.79/35.61    (19)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (20)  op(e3, e3) = all_6_2
% 204.79/35.61    (21)  all_56_3 = all_52_25
% 204.79/35.61    (22)  all_58_6 = all_52_5
% 204.79/35.61    (23)   ~ (all_52_3 = all_4_2)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (11) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (24)  all_58_11 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (6), (24) imply:
% 204.79/35.61  | |   (25)  all_52_29 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | SIMP: (25) implies:
% 204.79/35.61  | |   (26)  all_52_29 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (17), (26) imply:
% 204.79/35.61  | |   (27)   ~ (all_52_5 = e3)
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (10), (26) imply:
% 204.79/35.61  | |   (28)   ~ (all_52_25 = e3)
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (7), (26) imply:
% 204.79/35.61  | |   (29)  op(e3, e3) = e1
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (2), (4), (5), (9), (12), (13), (14), (15), (16), (18),
% 204.79/35.61  | |            (19), (20), (21), (22), (23), (27), (28), (29) are inconsistent
% 204.79/35.61  | |            by sub-proof #1240.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (30)  all_58_15 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (3), (8), (30) are inconsistent by sub-proof #1350.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1240 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ~ (e3 = e1)
% 204.79/35.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (3)  all_58_0 = all_6_2
% 204.79/35.61    (4)  op(e2, e2) = all_4_2
% 204.79/35.61    (5)   ~ (all_52_25 = e0)
% 204.79/35.61    (6)  all_58_12 = all_52_7
% 204.79/35.61    (7)   ~ (all_52_7 = e3)
% 204.79/35.61    (8)  all_58_2 = all_52_3
% 204.79/35.61    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61    (10)   ~ (all_52_25 = e3)
% 204.79/35.61    (11)   ~ (all_52_5 = e3)
% 204.79/35.61    (12)  op(all_52_25, all_52_25) = e3
% 204.79/35.61    (13)   ~ (all_52_25 = all_6_2)
% 204.79/35.61    (14)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61    (15)  op(e3, e3) = all_6_2
% 204.79/35.61    (16)  all_56_3 = all_52_25
% 204.79/35.61    (17)  op(e3, e3) = e1
% 204.79/35.61    (18)  all_58_6 = all_52_5
% 204.79/35.61    (19)   ~ (all_52_3 = all_4_2)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | GROUND_INST: instantiating (2) with all_6_2, e1, e3, e3, simplifying with
% 204.79/35.61  |              (15), (17) gives:
% 204.79/35.61  |   (20)  all_6_2 = e1
% 204.79/35.61  | 
% 204.79/35.61  | COMBINE_EQS: (3), (20) imply:
% 204.79/35.61  |   (21)  all_58_0 = e1
% 204.79/35.61  | 
% 204.79/35.61  | REDUCE: (13), (20) imply:
% 204.79/35.61  |   (22)   ~ (all_52_25 = e1)
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (14) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (23)  all_56_3 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (10), (16), (23) are inconsistent by sub-proof #1339.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (24)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61  | | 
% 204.79/35.61  | | BETA: splitting (24) gives:
% 204.79/35.61  | | 
% 204.79/35.61  | | Case 1:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (25)  all_56_3 = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | COMBINE_EQS: (16), (25) imply:
% 204.79/35.61  | | |   (26)  all_52_25 = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | SIMP: (26) implies:
% 204.79/35.61  | | |   (27)  all_52_25 = e2
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REDUCE: (12), (27) imply:
% 204.79/35.61  | | |   (28)  op(e2, e2) = e3
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (18), (19), (21), (28)
% 204.79/35.61  | | |            are inconsistent by sub-proof #1241.
% 204.79/35.61  | | | 
% 204.79/35.61  | | Case 2:
% 204.79/35.61  | | | 
% 204.79/35.61  | | |   (29)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.61  | | | 
% 204.79/35.61  | | | REF_CLOSE: (5), (16), (22), (29) are inconsistent by sub-proof #1330.
% 204.79/35.61  | | | 
% 204.79/35.61  | | End of split
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1241 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ~ (e3 = e1)
% 204.79/35.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (3)  op(e2, e2) = all_4_2
% 204.79/35.61    (4)  all_58_12 = all_52_7
% 204.79/35.61    (5)   ~ (all_52_7 = e3)
% 204.79/35.61    (6)  all_58_2 = all_52_3
% 204.79/35.61    (7)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61    (8)   ~ (all_52_5 = e3)
% 204.79/35.61    (9)  op(e2, e2) = e3
% 204.79/35.61    (10)  all_58_6 = all_52_5
% 204.79/35.61    (11)   ~ (all_52_3 = all_4_2)
% 204.79/35.61    (12)  all_58_0 = e1
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (7) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (13)  all_58_0 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (12), (13) are inconsistent by sub-proof #1244.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (14)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (14) are
% 204.79/35.61  | |            inconsistent by sub-proof #1242.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1242 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.61    (2)  op(e2, e2) = all_4_2
% 204.79/35.61    (3)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61    (4)  all_58_12 = all_52_7
% 204.79/35.61    (5)   ~ (all_52_7 = e3)
% 204.79/35.61    (6)  all_58_2 = all_52_3
% 204.79/35.61    (7)   ~ (all_52_5 = e3)
% 204.79/35.61    (8)  op(e2, e2) = e3
% 204.79/35.61    (9)  all_58_6 = all_52_5
% 204.79/35.61    (10)   ~ (all_52_3 = all_4_2)
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (3) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (11)  all_58_2 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | COMBINE_EQS: (6), (11) imply:
% 204.79/35.61  | |   (12)  all_52_3 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | SIMP: (12) implies:
% 204.79/35.61  | |   (13)  all_52_3 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REDUCE: (10), (13) imply:
% 204.79/35.61  | |   (14)   ~ (all_4_2 = e3)
% 204.79/35.61  | | 
% 204.79/35.61  | | SIMP: (14) implies:
% 204.79/35.61  | |   (15)   ~ (all_4_2 = e3)
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (1), (2), (8), (15) are inconsistent by sub-proof #1318.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (16)  all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (4), (5), (7), (9), (16) are inconsistent by sub-proof #1243.
% 204.79/35.61  | | 
% 204.79/35.61  | End of split
% 204.79/35.61  | 
% 204.79/35.61  End of proof
% 204.79/35.61  
% 204.79/35.61  Sub-proof #1243 shows that the following formulas are inconsistent:
% 204.79/35.61  ----------------------------------------------------------------
% 204.79/35.61    (1)  all_58_12 = all_52_7
% 204.79/35.61    (2)   ~ (all_52_7 = e3)
% 204.79/35.61    (3)   ~ (all_52_5 = e3)
% 204.79/35.61    (4)  all_58_6 = all_52_5
% 204.79/35.61    (5)  all_58_6 = e3 | all_58_12 = e3
% 204.79/35.61  
% 204.79/35.61  Begin of proof
% 204.79/35.61  | 
% 204.79/35.61  | BETA: splitting (5) gives:
% 204.79/35.61  | 
% 204.79/35.61  | Case 1:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (6)  all_58_6 = e3
% 204.79/35.61  | | 
% 204.79/35.61  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #1328.
% 204.79/35.61  | | 
% 204.79/35.61  | Case 2:
% 204.79/35.61  | | 
% 204.79/35.61  | |   (7)  all_58_12 = e3
% 204.79/35.61  | | 
% 204.79/35.62  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1367.
% 204.79/35.62  | | 
% 204.79/35.62  | End of split
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1244 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)  all_58_0 = e3
% 204.79/35.62    (2)  all_58_0 = e1
% 204.79/35.62    (3)   ~ (e3 = e1)
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.62  |   (4)  e3 = e1
% 204.79/35.62  | 
% 204.79/35.62  | SIMP: (4) implies:
% 204.79/35.62  |   (5)  e3 = e1
% 204.79/35.62  | 
% 204.79/35.62  | REDUCE: (3), (5) imply:
% 204.79/35.62  |   (6)  $false
% 204.79/35.62  | 
% 204.79/35.62  | CLOSE: (6) is inconsistent.
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1245 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.62    (2)  all_58_9 = all_52_25
% 204.79/35.62    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 204.79/35.62    (4)   ~ (all_52_25 = e0)
% 204.79/35.62    (5)  op(all_52_25, all_52_25) = e3
% 204.79/35.62    (6)   ~ (all_10_2 = e3)
% 204.79/35.62    (7)  all_56_3 = all_52_25
% 204.79/35.62    (8)  all_56_3 = e1 | all_56_3 = e0
% 204.79/35.62    (9)  op(e1, e1) = all_10_2
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | BETA: splitting (3) gives:
% 204.79/35.62  | 
% 204.79/35.62  | Case 1:
% 204.79/35.62  | | 
% 204.79/35.62  | |   (10)  all_58_9 = e1
% 204.79/35.62  | | 
% 204.79/35.62  | | COMBINE_EQS: (2), (10) imply:
% 204.79/35.62  | |   (11)  all_52_25 = e1
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (5), (11) imply:
% 204.79/35.62  | |   (12)  op(e1, e1) = e3
% 204.79/35.62  | | 
% 204.79/35.62  | | REF_CLOSE: (1), (6), (9), (12) are inconsistent by sub-proof #1368.
% 204.79/35.62  | | 
% 204.79/35.62  | Case 2:
% 204.79/35.62  | | 
% 204.79/35.62  | |   (13)   ~ (all_58_9 = e1)
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (2), (13) imply:
% 204.79/35.62  | |   (14)   ~ (all_52_25 = e1)
% 204.79/35.62  | | 
% 204.79/35.62  | | REF_CLOSE: (4), (7), (8), (14) are inconsistent by sub-proof #1330.
% 204.79/35.62  | | 
% 204.79/35.62  | End of split
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1246 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.62    (2)  op(all_52_25, all_52_25) = e3
% 204.79/35.62    (3)   ~ (all_52_25 = all_6_2)
% 204.79/35.62    (4)  op(e3, e3) = all_6_2
% 204.79/35.62    (5)  all_52_25 = e3
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | SIMP: (5) implies:
% 204.79/35.62  |   (6)  all_52_25 = e3
% 204.79/35.62  | 
% 204.79/35.62  | REDUCE: (3), (6) imply:
% 204.79/35.62  |   (7)   ~ (all_6_2 = e3)
% 204.79/35.62  | 
% 204.79/35.62  | SIMP: (7) implies:
% 204.79/35.62  |   (8)   ~ (all_6_2 = e3)
% 204.79/35.62  | 
% 204.79/35.62  | REDUCE: (2), (6) imply:
% 204.79/35.62  |   (9)  op(e3, e3) = e3
% 204.79/35.62  | 
% 204.79/35.62  | REF_CLOSE: (1), (4), (8), (9) are inconsistent by sub-proof #1338.
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1247 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.62    (2)  op(e3, e3) = all_52_14
% 204.79/35.62    (3)  op(e3, e3) = all_6_2
% 204.79/35.62    (4)  op(e3, e3) = e1
% 204.79/35.62    (5)   ~ (all_6_2 = e1)
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | GROUND_INST: instantiating (1) with all_6_2, all_52_14, e3, e3, simplifying
% 204.79/35.62  |              with (2), (3) gives:
% 204.79/35.62  |   (6)  all_52_14 = all_6_2
% 204.79/35.62  | 
% 204.79/35.62  | GROUND_INST: instantiating (1) with e1, all_52_14, e3, e3, simplifying with
% 204.79/35.62  |              (2), (4) gives:
% 204.79/35.62  |   (7)  all_52_14 = e1
% 204.79/35.62  | 
% 204.79/35.62  | COMBINE_EQS: (6), (7) imply:
% 204.79/35.62  |   (8)  all_6_2 = e1
% 204.79/35.62  | 
% 204.79/35.62  | SIMP: (8) implies:
% 204.79/35.62  |   (9)  all_6_2 = e1
% 204.79/35.62  | 
% 204.79/35.62  | REDUCE: (5), (9) imply:
% 204.79/35.62  |   (10)  $false
% 204.79/35.62  | 
% 204.79/35.62  | CLOSE: (10) is inconsistent.
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1248 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)  all_58_13 = e3
% 204.79/35.62    (2)  all_58_13 = e2
% 204.79/35.62    (3)   ~ (e3 = e2)
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | COMBINE_EQS: (1), (2) imply:
% 204.79/35.62  |   (4)  e3 = e2
% 204.79/35.62  | 
% 204.79/35.62  | SIMP: (4) implies:
% 204.79/35.62  |   (5)  e3 = e2
% 204.79/35.62  | 
% 204.79/35.62  | REDUCE: (3), (5) imply:
% 204.79/35.62  |   (6)  $false
% 204.79/35.62  | 
% 204.79/35.62  | CLOSE: (6) is inconsistent.
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1249 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)   ~ (all_52_15 = all_52_23)
% 204.79/35.62    (2)   ~ (all_52_25 = all_52_27)
% 204.79/35.62    (3)  all_58_14 = all_52_23
% 204.79/35.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.62    (5)   ~ (all_52_5 = all_52_13)
% 204.79/35.62    (6)  all_58_1 = all_52_9
% 204.79/35.62    (7)   ~ (e3 = e0)
% 204.79/35.62    (8)  op(all_52_23, all_52_23) = e0
% 204.79/35.62    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.62    (10)  op(e0, e2) = all_52_15
% 204.79/35.62    (11)   ~ (all_52_7 = all_52_15)
% 204.79/35.62    (12)  op(all_52_7, all_52_7) = all_52_6
% 204.79/35.62    (13)   ~ (all_52_17 = all_52_25)
% 204.79/35.62    (14)  all_58_0 = all_6_2
% 204.79/35.62    (15)   ~ (all_52_17 = all_10_2)
% 204.79/35.62    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.79/35.62    (17)  all_58_13 = all_52_15
% 204.79/35.62    (18)  all_58_9 = all_52_25
% 204.79/35.62    (19)   ~ (all_6_1 = e1)
% 204.79/35.62    (20)  op(all_52_27, all_52_27) = all_52_26
% 204.79/35.62    (21)  op(e1, e3) = all_52_5
% 204.79/35.62    (22)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.79/35.62    (23)  op(e2, e2) = all_4_2
% 204.79/35.62    (24)   ~ (all_4_1 = e3)
% 204.79/35.62    (25)  all_58_11 = all_52_29
% 204.79/35.62    (26)  all_56_5 = all_4_2
% 204.79/35.62    (27)  op(all_10_2, e1) = all_10_1
% 204.79/35.62    (28)   ~ (all_52_7 = all_6_2)
% 204.79/35.62    (29)   ~ (all_52_15 = e0)
% 204.79/35.62    (30)  all_58_15 = e0
% 204.79/35.62    (31)   ~ (all_52_25 = e0)
% 204.79/35.62    (32)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.79/35.62    (33)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.62    (34)   ~ (e2 = e1)
% 204.79/35.62    (35)   ~ (all_52_13 = all_10_2)
% 204.79/35.62    (36)  op(e0, e0) = e0
% 204.79/35.62    (37)  op(all_10_2, all_10_2) = e1
% 204.79/35.62    (38)  all_58_10 = all_52_27
% 204.79/35.62    (39)  all_56_8 = all_52_5
% 204.79/35.62    (40)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.62    (41)   ~ (all_52_25 = all_52_29)
% 204.79/35.62    (42)   ~ (all_52_29 = all_10_2)
% 204.79/35.62    (43)  all_58_7 = all_52_13
% 204.79/35.62    (44)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.62    (45)  op(all_52_19, all_52_19) = e2
% 204.79/35.62    (46)   ~ (all_52_5 = all_52_7)
% 204.79/35.62    (47)  all_58_12 = all_52_7
% 204.79/35.62    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.62    (49)  all_56_2 = all_52_17
% 204.79/35.62    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.79/35.62    (51)  all_56_7 = all_52_27
% 204.79/35.62    (52)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.62    (53)  op(all_4_2, e2) = all_4_1
% 204.79/35.62    (54)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.79/35.62    (55)   ~ (all_52_19 = all_52_27)
% 204.79/35.62    (56)   ~ (all_52_13 = all_4_2)
% 204.79/35.62    (57)  op(e3, e1) = all_52_17
% 204.79/35.62    (58)  op(e0, e3) = all_52_7
% 204.79/35.62    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.62    (60)   ~ (all_52_9 = all_52_25)
% 204.79/35.62    (61)   ~ (all_52_19 = all_10_2)
% 204.79/35.62    (62)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.79/35.62    (63)  all_58_8 = all_10_2
% 204.79/35.62    (64)   ~ (all_52_23 = e0)
% 204.79/35.62    (65)   ~ (all_52_5 = all_10_2)
% 204.79/35.62    (66)  op(all_52_29, all_52_29) = all_52_28
% 204.79/35.62    (67)  all_56_12 = all_52_7
% 204.79/35.62    (68)   ~ (all_52_25 = all_6_2)
% 204.79/35.62    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.62    (70)   ~ (all_52_5 = all_6_2)
% 204.79/35.62    (71)   ~ (all_52_9 = all_6_2)
% 204.79/35.62    (72)  op(e3, e3) = all_6_2
% 204.79/35.62    (73)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.62    (74)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.62    (75)  all_56_14 = all_52_23
% 204.79/35.62    (76)  op(all_4_2, all_4_2) = all_52_10
% 204.79/35.62    (77)  all_56_3 = all_52_25
% 204.79/35.62    (78)  all_58_5 = all_52_19
% 204.79/35.62    (79)  all_56_1 = all_52_9
% 204.79/35.62    (80)  op(all_52_17, all_52_17) = e3
% 204.79/35.62    (81)  all_58_6 = all_52_5
% 204.79/35.62    (82)  op(e3, e2) = all_52_9
% 204.79/35.62    (83)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.62    (84)   ~ (all_52_17 = all_6_2)
% 204.79/35.62    (85)   ~ (e3 = e2)
% 204.79/35.62    (86)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.62    (87)   ~ (all_52_9 = all_52_17)
% 204.79/35.62    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.62    (89)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.62    (90)   ~ (all_6_1 = e2)
% 204.79/35.62    (91)  op(e1, e1) = all_10_2
% 204.79/35.62    (92)   ~ (all_52_23 = all_10_2)
% 204.79/35.62    (93)   ~ (all_52_7 = all_52_23)
% 204.79/35.62    (94)  all_58_3 = all_4_2
% 204.79/35.62    (95)  all_56_13 = all_52_15
% 204.79/35.62    (96)   ~ (all_52_19 = all_4_2)
% 204.79/35.62    (97)   ~ (all_52_17 = all_52_23)
% 204.79/35.62    (98)  op(all_6_2, e3) = all_6_1
% 204.79/35.62    (99)   ~ (all_52_13 = all_52_29)
% 204.79/35.62    (100)  all_58_4 = all_52_17
% 204.79/35.62    (101)   ~ (all_52_7 = e0)
% 204.79/35.62    (102)  op(all_52_25, all_52_25) = all_52_24
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | BETA: splitting (32) gives:
% 204.79/35.62  | 
% 204.79/35.62  | Case 1:
% 204.79/35.62  | | 
% 204.79/35.62  | |   (103)  all_56_13 = e3
% 204.79/35.62  | | 
% 204.79/35.62  | | REF_CLOSE: (1), (4), (8), (9), (10), (11), (23), (24), (36), (37), (44),
% 204.79/35.62  | |            (47), (53), (54), (64), (67), (75), (91), (92), (93), (95),
% 204.79/35.62  | |            (101), (103) are inconsistent by sub-proof #1281.
% 204.79/35.62  | | 
% 204.79/35.62  | Case 2:
% 204.79/35.62  | | 
% 204.79/35.62  | |   (104)   ~ (all_56_13 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (95), (104) imply:
% 204.79/35.62  | |   (105)   ~ (all_52_15 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 204.79/35.62  | |            (15), (16), (17), (18), (19), (20), (21), (22), (25), (26), (27),
% 204.79/35.62  | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (38), (39),
% 204.79/35.62  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 204.79/35.62  | |            (51), (52), (53), (55), (56), (57), (58), (59), (60), (61), (62),
% 204.79/35.62  | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 204.79/35.62  | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 204.79/35.62  | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (96),
% 204.79/35.62  | |            (97), (98), (99), (100), (101), (102), (105) are inconsistent by
% 204.79/35.62  | |            sub-proof #1250.
% 204.79/35.62  | | 
% 204.79/35.62  | End of split
% 204.79/35.62  | 
% 204.79/35.62  End of proof
% 204.79/35.62  
% 204.79/35.62  Sub-proof #1250 shows that the following formulas are inconsistent:
% 204.79/35.62  ----------------------------------------------------------------
% 204.79/35.62    (1)   ~ (all_52_25 = all_52_27)
% 204.79/35.62    (2)  all_58_14 = all_52_23
% 204.79/35.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.79/35.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.79/35.62    (4)   ~ (all_52_5 = all_52_13)
% 204.79/35.62    (5)  all_58_1 = all_52_9
% 204.79/35.62    (6)   ~ (e3 = e0)
% 204.79/35.62    (7)  op(all_52_23, all_52_23) = e0
% 204.79/35.62    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.79/35.62    (9)   ~ (all_52_7 = all_52_15)
% 204.79/35.62    (10)  op(all_52_7, all_52_7) = all_52_6
% 204.79/35.62    (11)   ~ (all_52_17 = all_52_25)
% 204.79/35.62    (12)  all_58_0 = all_6_2
% 204.79/35.62    (13)   ~ (all_52_17 = all_10_2)
% 204.79/35.62    (14)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.79/35.62    (15)  all_58_13 = all_52_15
% 204.79/35.62    (16)  all_58_9 = all_52_25
% 204.79/35.62    (17)   ~ (all_6_1 = e1)
% 204.79/35.62    (18)   ~ (all_52_15 = e3)
% 204.79/35.62    (19)  op(all_52_27, all_52_27) = all_52_26
% 204.79/35.62    (20)  op(e1, e3) = all_52_5
% 204.79/35.62    (21)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.79/35.62    (22)  all_58_11 = all_52_29
% 204.79/35.62    (23)  all_56_5 = all_4_2
% 204.79/35.62    (24)  op(all_10_2, e1) = all_10_1
% 204.79/35.62    (25)   ~ (all_52_7 = all_6_2)
% 204.79/35.62    (26)   ~ (all_52_15 = e0)
% 204.79/35.62    (27)  all_58_15 = e0
% 204.79/35.62    (28)   ~ (all_52_25 = e0)
% 204.79/35.62    (29)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.79/35.62    (30)   ~ (e2 = e1)
% 204.79/35.62    (31)   ~ (all_52_13 = all_10_2)
% 204.79/35.62    (32)  op(e0, e0) = e0
% 204.79/35.62    (33)  op(all_10_2, all_10_2) = e1
% 204.79/35.62    (34)  all_58_10 = all_52_27
% 204.79/35.62    (35)  all_56_8 = all_52_5
% 204.79/35.62    (36)  op(all_52_9, all_52_9) = all_52_8
% 204.79/35.62    (37)   ~ (all_52_25 = all_52_29)
% 204.79/35.62    (38)   ~ (all_52_29 = all_10_2)
% 204.79/35.62    (39)  all_58_7 = all_52_13
% 204.79/35.62    (40)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.62    (41)  op(all_52_19, all_52_19) = e2
% 204.79/35.62    (42)   ~ (all_52_5 = all_52_7)
% 204.79/35.62    (43)  all_58_12 = all_52_7
% 204.79/35.62    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.79/35.62    (45)  all_56_2 = all_52_17
% 204.79/35.62    (46)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.79/35.62    (47)  all_56_7 = all_52_27
% 204.79/35.62    (48)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.79/35.62    (49)  op(all_4_2, e2) = all_4_1
% 204.79/35.62    (50)   ~ (all_52_19 = all_52_27)
% 204.79/35.62    (51)   ~ (all_52_13 = all_4_2)
% 204.79/35.62    (52)  op(e3, e1) = all_52_17
% 204.79/35.62    (53)  op(e0, e3) = all_52_7
% 204.79/35.62    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.79/35.62    (55)   ~ (all_52_9 = all_52_25)
% 204.79/35.62    (56)   ~ (all_52_19 = all_10_2)
% 204.79/35.62    (57)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.79/35.62    (58)  all_58_8 = all_10_2
% 204.79/35.62    (59)   ~ (all_52_23 = e0)
% 204.79/35.62    (60)   ~ (all_52_5 = all_10_2)
% 204.79/35.62    (61)  op(all_52_29, all_52_29) = all_52_28
% 204.79/35.62    (62)  all_56_12 = all_52_7
% 204.79/35.62    (63)   ~ (all_52_25 = all_6_2)
% 204.79/35.62    (64)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.79/35.62    (65)   ~ (all_52_5 = all_6_2)
% 204.79/35.62    (66)   ~ (all_52_9 = all_6_2)
% 204.79/35.62    (67)  op(e3, e3) = all_6_2
% 204.79/35.62    (68)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.79/35.62    (69)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.79/35.62    (70)  all_56_14 = all_52_23
% 204.79/35.62    (71)  op(all_4_2, all_4_2) = all_52_10
% 204.79/35.62    (72)  all_56_3 = all_52_25
% 204.79/35.62    (73)  all_58_5 = all_52_19
% 204.79/35.62    (74)  all_56_1 = all_52_9
% 204.79/35.62    (75)  op(all_52_17, all_52_17) = e3
% 204.79/35.62    (76)  all_58_6 = all_52_5
% 204.79/35.62    (77)  op(e3, e2) = all_52_9
% 204.79/35.62    (78)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.79/35.62    (79)   ~ (all_52_17 = all_6_2)
% 204.79/35.62    (80)   ~ (e3 = e2)
% 204.79/35.62    (81)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.79/35.62    (82)   ~ (all_52_9 = all_52_17)
% 204.79/35.62    (83)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.79/35.62    (84)  op(all_52_13, all_52_13) = all_52_12
% 204.79/35.62    (85)   ~ (all_6_1 = e2)
% 204.79/35.62    (86)  op(e1, e1) = all_10_2
% 204.79/35.62    (87)   ~ (all_52_23 = all_10_2)
% 204.79/35.62    (88)   ~ (all_52_7 = all_52_23)
% 204.79/35.62    (89)  all_58_3 = all_4_2
% 204.79/35.62    (90)   ~ (all_52_19 = all_4_2)
% 204.79/35.62    (91)   ~ (all_52_17 = all_52_23)
% 204.79/35.62    (92)  op(all_6_2, e3) = all_6_1
% 204.79/35.62    (93)   ~ (all_52_13 = all_52_29)
% 204.79/35.62    (94)  all_58_4 = all_52_17
% 204.79/35.62    (95)   ~ (all_52_7 = e0)
% 204.79/35.62    (96)  op(all_52_25, all_52_25) = all_52_24
% 204.79/35.62  
% 204.79/35.62  Begin of proof
% 204.79/35.62  | 
% 204.79/35.62  | BETA: splitting (78) gives:
% 204.79/35.62  | 
% 204.79/35.62  | Case 1:
% 204.79/35.62  | | 
% 204.79/35.62  | |   (97)  all_58_12 = e3
% 204.79/35.62  | | 
% 204.79/35.62  | | COMBINE_EQS: (43), (97) imply:
% 204.79/35.62  | |   (98)  all_52_7 = e3
% 204.79/35.62  | | 
% 204.79/35.62  | | SIMP: (98) implies:
% 204.79/35.62  | |   (99)  all_52_7 = e3
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (42), (99) imply:
% 204.79/35.62  | |   (100)   ~ (all_52_5 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (9), (99) imply:
% 204.79/35.62  | |   (101)   ~ (all_52_15 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (88), (99) imply:
% 204.79/35.62  | |   (102)   ~ (all_52_23 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | SIMP: (102) implies:
% 204.79/35.62  | |   (103)   ~ (all_52_23 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (25), (99) imply:
% 204.79/35.62  | |   (104)   ~ (all_6_2 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | SIMP: (104) implies:
% 204.79/35.62  | |   (105)   ~ (all_6_2 = e3)
% 204.79/35.62  | | 
% 204.79/35.62  | | REDUCE: (10), (99) imply:
% 204.79/35.62  | |   (106)  op(e3, e3) = all_52_6
% 204.79/35.62  | | 
% 204.79/35.62  | | GROUND_INST: instantiating (3) with all_6_2, all_52_6, e3, e3, simplifying
% 204.79/35.62  | |              with (67), (106) gives:
% 204.79/35.62  | |   (107)  all_52_6 = all_6_2
% 204.79/35.62  | | 
% 204.79/35.62  | | BETA: splitting (40) gives:
% 204.79/35.62  | | 
% 204.79/35.62  | | Case 1:
% 204.79/35.62  | | | 
% 204.79/35.62  | | |   (108)  all_56_14 = e3
% 204.79/35.62  | | | 
% 204.79/35.62  | | | REF_CLOSE: (70), (103), (108) are inconsistent by sub-proof #1286.
% 204.79/35.62  | | | 
% 204.79/35.62  | | Case 2:
% 204.79/35.62  | | | 
% 204.79/35.62  | | |   (109)   ~ (all_56_14 = e3)
% 204.79/35.62  | | |   (110)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.79/35.62  | | | 
% 204.79/35.62  | | | BETA: splitting (14) gives:
% 204.79/35.62  | | | 
% 204.79/35.62  | | | Case 1:
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | |   (111)  all_56_7 = e3
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | | REF_CLOSE: (1), (2), (3), (5), (11), (12), (13), (16), (19), (24), (28),
% 204.79/35.62  | | | |            (29), (32), (33), (36), (45), (47), (50), (52), (58), (63),
% 204.79/35.62  | | | |            (64), (67), (69), (72), (73), (75), (79), (83), (94), (103),
% 204.79/35.62  | | | |            (105), (111) are inconsistent by sub-proof #1274.
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | Case 2:
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | |   (112)   ~ (all_56_7 = e3)
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | | REDUCE: (47), (112) imply:
% 204.79/35.62  | | | |   (113)   ~ (all_52_27 = e3)
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | | BETA: splitting (68) gives:
% 204.79/35.62  | | | | 
% 204.79/35.62  | | | | Case 1:
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | |   (114)  all_58_9 = e3
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | COMBINE_EQS: (16), (114) imply:
% 204.79/35.62  | | | | |   (115)  all_52_25 = e3
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | SIMP: (115) implies:
% 204.79/35.62  | | | | |   (116)  all_52_25 = e3
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | REDUCE: (55), (116) imply:
% 204.79/35.62  | | | | |   (117)   ~ (all_52_9 = e3)
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | REDUCE: (11), (116) imply:
% 204.79/35.62  | | | | |   (118)   ~ (all_52_17 = e3)
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | REDUCE: (37), (116) imply:
% 204.79/35.62  | | | | |   (119)   ~ (all_52_29 = e3)
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | SIMP: (119) implies:
% 204.79/35.62  | | | | |   (120)   ~ (all_52_29 = e3)
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | REDUCE: (96), (116) imply:
% 204.79/35.62  | | | | |   (121)  op(e3, e3) = all_52_24
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_24, e3, e3,
% 204.79/35.62  | | | | |              simplifying with (67), (121) gives:
% 204.79/35.62  | | | | |   (122)  all_52_24 = all_6_2
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | BETA: splitting (54) gives:
% 204.79/35.62  | | | | | 
% 204.79/35.62  | | | | | Case 1:
% 204.79/35.62  | | | | | | 
% 204.79/35.62  | | | | | |   (123)  all_58_1 = e3
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | | COMBINE_EQS: (5), (123) imply:
% 204.90/35.62  | | | | | |   (124)  all_52_9 = e3
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | | REDUCE: (117), (124) imply:
% 204.90/35.62  | | | | | |   (125)  $false
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | | CLOSE: (125) is inconsistent.
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | Case 2:
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | |   (126)   ~ (all_58_1 = e3)
% 204.90/35.62  | | | | | |   (127)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | | BETA: splitting (83) gives:
% 204.90/35.62  | | | | | | 
% 204.90/35.62  | | | | | | Case 1:
% 204.90/35.62  | | | | | | | 
% 204.90/35.62  | | | | | | |   (128)  all_58_4 = e3
% 204.90/35.62  | | | | | | | 
% 204.90/35.62  | | | | | | | REF_CLOSE: (94), (118), (128) are inconsistent by sub-proof #1302.
% 204.90/35.62  | | | | | | | 
% 204.90/35.62  | | | | | | Case 2:
% 204.90/35.62  | | | | | | | 
% 204.90/35.62  | | | | | | |   (129)   ~ (all_58_4 = e3)
% 204.90/35.62  | | | | | | |   (130)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.62  | | | | | | | 
% 204.90/35.62  | | | | | | | BETA: splitting (44) gives:
% 204.90/35.62  | | | | | | | 
% 204.90/35.62  | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | 
% 204.90/35.62  | | | | | | | |   (131)  all_58_6 = e3
% 204.90/35.62  | | | | | | | | 
% 204.90/35.62  | | | | | | | | REF_CLOSE: (76), (100), (131) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | |            #1328.
% 204.90/35.62  | | | | | | | | 
% 204.90/35.62  | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | 
% 204.90/35.62  | | | | | | | |   (132)   ~ (all_58_6 = e3)
% 204.90/35.62  | | | | | | | |   (133)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.62  | | | | | | | | 
% 204.90/35.62  | | | | | | | | BETA: splitting (29) gives:
% 204.90/35.62  | | | | | | | | 
% 204.90/35.62  | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | 
% 204.90/35.62  | | | | | | | | |   (134)  all_56_2 = e3
% 204.90/35.62  | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | REF_CLOSE: (45), (118), (134) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | | |            #1327.
% 204.90/35.62  | | | | | | | | | 
% 204.90/35.62  | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | 
% 204.90/35.62  | | | | | | | | |   (135)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.62  | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | BETA: splitting (81) gives:
% 204.90/35.62  | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | |   (136)  all_56_1 = e3
% 204.90/35.62  | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | REF_CLOSE: (74), (117), (136) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | | | |            #1326.
% 204.90/35.62  | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | |   (137)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.62  | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | BETA: splitting (57) gives:
% 204.90/35.62  | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | |   (138)  all_56_8 = e3
% 204.90/35.62  | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | REF_CLOSE: (35), (100), (138) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | | | | |            #1325.
% 204.90/35.62  | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | |   (139)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.90/35.62  | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | BETA: splitting (48) gives:
% 204.90/35.62  | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | |   (140)  all_56_5 = e3
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | COMBINE_EQS: (23), (140) imply:
% 204.90/35.62  | | | | | | | | | | | |   (141)  all_4_2 = e3
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | SIMP: (141) implies:
% 204.90/35.62  | | | | | | | | | | | |   (142)  all_4_2 = e3
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | COMBINE_EQS: (89), (142) imply:
% 204.90/35.62  | | | | | | | | | | | |   (143)  all_58_3 = e3
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | REDUCE: (51), (142) imply:
% 204.90/35.62  | | | | | | | | | | | |   (144)   ~ (all_52_13 = e3)
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | REDUCE: (71), (142) imply:
% 204.90/35.62  | | | | | | | | | | | |   (145)  op(e3, e3) = all_52_10
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | REDUCE: (49), (142) imply:
% 204.90/35.62  | | | | | | | | | | | |   (146)  op(e3, e2) = all_4_1
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | BETA: splitting (133) gives:
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | |   (147)  all_58_7 = e3
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | COMBINE_EQS: (39), (147) imply:
% 204.90/35.62  | | | | | | | | | | | | |   (148)  all_52_13 = e3
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | REDUCE: (144), (148) imply:
% 204.90/35.62  | | | | | | | | | | | | |   (149)  $false
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | |   (150)  all_58_8 = e3 | all_58_11 = e3
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | BETA: splitting (150) gives:
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | |   (151)  all_58_8 = e3
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | COMBINE_EQS: (58), (151) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (152)  all_10_2 = e3
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | SIMP: (152) implies:
% 204.90/35.62  | | | | | | | | | | | | | |   (153)  all_10_2 = e3
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (33), (153) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (154)  op(e3, e3) = e1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (24), (153) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (155)  op(e3, e1) = all_10_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_17, all_10_1, e1,
% 204.90/35.62  | | | | | | | | | | | | | |              e3, simplifying with (52), (155) gives:
% 204.90/35.62  | | | | | | | | | | | | | |   (156)  all_52_17 = all_10_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_9, all_4_1, e2, e3,
% 204.90/35.62  | | | | | | | | | | | | | |              simplifying with (77), (146) gives:
% 204.90/35.62  | | | | | | | | | | | | | |   (157)  all_52_9 = all_4_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_10, e3, e3,
% 204.90/35.62  | | | | | | | | | | | | | |              simplifying with (67), (145) gives:
% 204.90/35.62  | | | | | | | | | | | | | |   (158)  all_52_10 = all_6_2
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_10, e3, e3,
% 204.90/35.62  | | | | | | | | | | | | | |              simplifying with (145), (154) gives:
% 204.90/35.62  | | | | | | | | | | | | | |   (159)  all_52_10 = e1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | COMBINE_EQS: (158), (159) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (160)  all_6_2 = e1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | COMBINE_EQS: (94), (156) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (161)  all_58_4 = all_10_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | COMBINE_EQS: (5), (157) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (162)  all_58_1 = all_4_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | COMBINE_EQS: (12), (160) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (163)  all_58_0 = e1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (65), (160) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (164)   ~ (all_52_5 = e1)
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (91), (156) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (165)   ~ (all_52_23 = all_10_1)
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | SIMP: (165) implies:
% 204.90/35.62  | | | | | | | | | | | | | |   (166)   ~ (all_52_23 = all_10_1)
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (92), (160) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (167)  op(e1, e3) = all_6_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_5, all_6_1, e3, e1,
% 204.90/35.62  | | | | | | | | | | | | | |              simplifying with (20), (167) gives:
% 204.90/35.62  | | | | | | | | | | | | | |   (168)  all_52_5 = all_6_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | COMBINE_EQS: (35), (168) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (169)  all_56_8 = all_6_1
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (4), (168) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (170)   ~ (all_52_13 = all_6_1)
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | SIMP: (170) implies:
% 204.90/35.62  | | | | | | | | | | | | | |   (171)   ~ (all_52_13 = all_6_1)
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REDUCE: (100), (168) imply:
% 204.90/35.62  | | | | | | | | | | | | | |   (172)   ~ (all_6_1 = e3)
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | |   (173)  all_56_8 = e2
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | REF_CLOSE: (85), (169), (173) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | | | | | | | | |            #1321.
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | |   (174)   ~ (all_56_8 = e2)
% 204.90/35.62  | | | | | | | | | | | | | | |   (175)  all_56_8 = e1 | all_56_8 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | |   (176)  all_56_8 = e1
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (169), (176) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | | | | | | | | | |            #1320.
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | |   (177)  all_56_8 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (177) imply:
% 204.90/35.62  | | | | | | | | | | | | | | | |   (178)  all_6_1 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 204.90/35.62  | | | | | | | | | | | | | | | |   (179)  all_6_1 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | REDUCE: (171), (179) imply:
% 204.90/35.62  | | | | | | | | | | | | | | | |   (180)   ~ (all_52_13 = e0)
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | REDUCE: (172), (179) imply:
% 204.90/35.62  | | | | | | | | | | | | | | | |   (181)   ~ (e3 = e0)
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | REDUCE: (85), (179) imply:
% 204.90/35.62  | | | | | | | | | | | | | | | |   (182)   ~ (e2 = e0)
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 204.90/35.62  | | | | | | | | | | | | | | | |   (183)   ~ (e2 = e0)
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | Case 1:
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | |   (184)  all_58_1 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (184) imply:
% 204.90/35.62  | | | | | | | | | | | | | | | | |   (185)  all_4_1 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (22), (30), (32), (33), (46), (59),
% 204.90/35.62  | | | | | | | | | | | | | | | | |            (70), (80), (86), (87), (110), (114), (120),
% 204.90/35.62  | | | | | | | | | | | | | | | | |            (150), (151), (161), (163), (166), (183), (184)
% 204.90/35.62  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1270.
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | |   (186)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (26), (39), (143), (180), (186) are
% 204.90/35.62  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1267.
% 204.90/35.62  | | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | | End of split
% 204.90/35.62  | | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | | End of split
% 204.90/35.62  | | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | End of split
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | |   (187)  all_58_11 = e3
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | | REF_CLOSE: (22), (120), (187) are inconsistent by sub-proof
% 204.90/35.62  | | | | | | | | | | | | | |            #1323.
% 204.90/35.62  | | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | | End of split
% 204.90/35.62  | | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | End of split
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | Case 2:
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | |   (188)   ~ (all_56_5 = e3)
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | REDUCE: (23), (188) imply:
% 204.90/35.62  | | | | | | | | | | | |   (189)   ~ (all_4_2 = e3)
% 204.90/35.62  | | | | | | | | | | | | 
% 204.90/35.62  | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (15), (18), (21), (29), (31), (32),
% 204.90/35.62  | | | | | | | | | | | |            (39), (41), (45), (56), (58), (66), (67), (73),
% 204.90/35.63  | | | | | | | | | | | |            (74), (75), (79), (82), (84), (86), (89), (103),
% 204.90/35.63  | | | | | | | | | | | |            (105), (127), (130), (135), (137), (189) are
% 204.90/35.63  | | | | | | | | | | | |            inconsistent by sub-proof #1260.
% 204.90/35.63  | | | | | | | | | | | | 
% 204.90/35.63  | | | | | | | | | | | End of split
% 204.90/35.63  | | | | | | | | | | | 
% 204.90/35.63  | | | | | | | | | | End of split
% 204.90/35.63  | | | | | | | | | | 
% 204.90/35.63  | | | | | | | | | End of split
% 204.90/35.63  | | | | | | | | | 
% 204.90/35.63  | | | | | | | | End of split
% 204.90/35.63  | | | | | | | | 
% 204.90/35.63  | | | | | | | End of split
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | End of split
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | End of split
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | Case 2:
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | |   (190)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | REF_CLOSE: (2), (3), (5), (6), (11), (15), (18), (22), (27), (28),
% 204.90/35.63  | | | | |            (29), (32), (34), (36), (37), (38), (39), (41), (45), (54),
% 204.90/35.63  | | | | |            (58), (61), (63), (64), (66), (67), (72), (73), (75), (79),
% 204.90/35.63  | | | | |            (83), (89), (90), (93), (94), (103), (113), (190) are
% 204.90/35.63  | | | | |            inconsistent by sub-proof #1252.
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | End of split
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | End of split
% 204.90/35.63  | | | 
% 204.90/35.63  | | End of split
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (191)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | BETA: splitting (191) gives:
% 204.90/35.63  | | 
% 204.90/35.63  | | Case 1:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (192)  all_58_13 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REF_CLOSE: (15), (18), (192) are inconsistent by sub-proof #1360.
% 204.90/35.63  | | | 
% 204.90/35.63  | | Case 2:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (193)  all_58_14 = e3 | all_58_15 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | BETA: splitting (193) gives:
% 204.90/35.63  | | | 
% 204.90/35.63  | | | Case 1:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | |   (194)  all_58_14 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REF_CLOSE: (2), (3), (7), (8), (17), (25), (53), (62), (67), (85), (88),
% 204.90/35.63  | | | |            (92), (194) are inconsistent by sub-proof #1251.
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | Case 2:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | |   (195)  all_58_15 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REF_CLOSE: (6), (27), (195) are inconsistent by sub-proof #1350.
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | End of split
% 204.90/35.63  | | | 
% 204.90/35.63  | | End of split
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1251 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_58_14 = all_52_23
% 204.90/35.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (3)  op(all_52_23, all_52_23) = e0
% 204.90/35.63    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.63    (5)   ~ (all_6_1 = e1)
% 204.90/35.63    (6)   ~ (all_52_7 = all_6_2)
% 204.90/35.63    (7)  op(e0, e3) = all_52_7
% 204.90/35.63    (8)  all_56_12 = all_52_7
% 204.90/35.63    (9)  op(e3, e3) = all_6_2
% 204.90/35.63    (10)   ~ (all_6_1 = e2)
% 204.90/35.63    (11)  all_58_14 = e3
% 204.90/35.63    (12)   ~ (all_52_7 = all_52_23)
% 204.90/35.63    (13)  op(all_6_2, e3) = all_6_1
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | COMBINE_EQS: (1), (11) imply:
% 204.90/35.63  |   (14)  all_52_23 = e3
% 204.90/35.63  | 
% 204.90/35.63  | SIMP: (14) implies:
% 204.90/35.63  |   (15)  all_52_23 = e3
% 204.90/35.63  | 
% 204.90/35.63  | REDUCE: (12), (15) imply:
% 204.90/35.63  |   (16)   ~ (all_52_7 = e3)
% 204.90/35.63  | 
% 204.90/35.63  | REDUCE: (3), (15) imply:
% 204.90/35.63  |   (17)  op(e3, e3) = e0
% 204.90/35.63  | 
% 204.90/35.63  | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (13), (16), (17) are
% 204.90/35.63  |            inconsistent by sub-proof #1342.
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1252 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_58_14 = all_52_23
% 204.90/35.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (3)  all_58_1 = all_52_9
% 204.90/35.63    (4)   ~ (e3 = e0)
% 204.90/35.63    (5)   ~ (all_52_17 = all_52_25)
% 204.90/35.63    (6)  all_58_13 = all_52_15
% 204.90/35.63    (7)   ~ (all_52_15 = e3)
% 204.90/35.63    (8)  all_58_11 = all_52_29
% 204.90/35.63    (9)  all_58_15 = e0
% 204.90/35.63    (10)   ~ (all_52_25 = e0)
% 204.90/35.63    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (12)  op(e0, e0) = e0
% 204.90/35.63    (13)  all_58_10 = all_52_27
% 204.90/35.63    (14)  op(all_52_9, all_52_9) = all_52_8
% 204.90/35.63    (15)   ~ (all_52_25 = all_52_29)
% 204.90/35.63    (16)   ~ (all_52_29 = all_10_2)
% 204.90/35.63    (17)  all_58_7 = all_52_13
% 204.90/35.63    (18)  op(all_52_19, all_52_19) = e2
% 204.90/35.63    (19)  all_56_2 = all_52_17
% 204.90/35.63    (20)   ~ (all_52_23 = e3)
% 204.90/35.63    (21)   ~ (all_52_27 = e3)
% 204.90/35.63    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63    (23)  all_58_8 = all_10_2
% 204.90/35.63    (24)  op(all_52_29, all_52_29) = all_52_28
% 204.90/35.63    (25)   ~ (all_52_25 = all_6_2)
% 204.90/35.63    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63    (27)   ~ (all_52_9 = all_6_2)
% 204.90/35.63    (28)  op(e3, e3) = all_6_2
% 204.90/35.63    (29)  all_56_3 = all_52_25
% 204.90/35.63    (30)  all_58_5 = all_52_19
% 204.90/35.63    (31)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (32)   ~ (all_52_17 = all_6_2)
% 204.90/35.63    (33)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.63    (34)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63    (35)  all_58_3 = all_4_2
% 204.90/35.63    (36)   ~ (all_52_19 = all_4_2)
% 204.90/35.63    (37)   ~ (all_52_13 = all_52_29)
% 204.90/35.63    (38)  all_58_4 = all_52_17
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (33) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (39)  all_58_10 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (13), (21), (39) are inconsistent by sub-proof #1301.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (40)  all_58_11 = e3 | all_58_15 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.90/35.63  | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 204.90/35.63  | |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 204.90/35.63  | |            (38), (40) are inconsistent by sub-proof #1253.
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1253 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_58_14 = all_52_23
% 204.90/35.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (3)  all_58_1 = all_52_9
% 204.90/35.63    (4)   ~ (e3 = e0)
% 204.90/35.63    (5)   ~ (all_52_17 = all_52_25)
% 204.90/35.63    (6)  all_58_13 = all_52_15
% 204.90/35.63    (7)   ~ (all_52_15 = e3)
% 204.90/35.63    (8)  all_58_11 = all_52_29
% 204.90/35.63    (9)  all_58_15 = e0
% 204.90/35.63    (10)   ~ (all_52_25 = e0)
% 204.90/35.63    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (12)  op(e0, e0) = e0
% 204.90/35.63    (13)  op(all_52_9, all_52_9) = all_52_8
% 204.90/35.63    (14)   ~ (all_52_25 = all_52_29)
% 204.90/35.63    (15)  all_58_11 = e3 | all_58_15 = e3
% 204.90/35.63    (16)   ~ (all_52_29 = all_10_2)
% 204.90/35.63    (17)  all_58_7 = all_52_13
% 204.90/35.63    (18)  op(all_52_19, all_52_19) = e2
% 204.90/35.63    (19)  all_56_2 = all_52_17
% 204.90/35.63    (20)   ~ (all_52_23 = e3)
% 204.90/35.63    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63    (22)  all_58_8 = all_10_2
% 204.90/35.63    (23)  op(all_52_29, all_52_29) = all_52_28
% 204.90/35.63    (24)   ~ (all_52_25 = all_6_2)
% 204.90/35.63    (25)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63    (26)   ~ (all_52_9 = all_6_2)
% 204.90/35.63    (27)  op(e3, e3) = all_6_2
% 204.90/35.63    (28)  all_56_3 = all_52_25
% 204.90/35.63    (29)  all_58_5 = all_52_19
% 204.90/35.63    (30)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (31)   ~ (all_52_17 = all_6_2)
% 204.90/35.63    (32)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63    (33)  all_58_3 = all_4_2
% 204.90/35.63    (34)   ~ (all_52_19 = all_4_2)
% 204.90/35.63    (35)   ~ (all_52_13 = all_52_29)
% 204.90/35.63    (36)  all_58_4 = all_52_17
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (15) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (37)  all_58_11 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | COMBINE_EQS: (8), (37) imply:
% 204.90/35.63  | |   (38)  all_52_29 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | SIMP: (38) implies:
% 204.90/35.63  | |   (39)  all_52_29 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (35), (39) imply:
% 204.90/35.63  | |   (40)   ~ (all_52_13 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (14), (39) imply:
% 204.90/35.63  | |   (41)   ~ (all_52_25 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (16), (39) imply:
% 204.90/35.63  | |   (42)   ~ (all_10_2 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | SIMP: (42) implies:
% 204.90/35.63  | |   (43)   ~ (all_10_2 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (23), (39) imply:
% 204.90/35.63  | |   (44)  op(e3, e3) = all_52_28
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (11), (12), (13), (17), (18),
% 204.90/35.63  | |            (19), (20), (21), (22), (24), (25), (26), (27), (28), (29), (30),
% 204.90/35.63  | |            (31), (32), (33), (34), (36), (40), (41), (43), (44) are
% 204.90/35.63  | |            inconsistent by sub-proof #1254.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (45)  all_58_15 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (4), (9), (45) are inconsistent by sub-proof #1350.
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1254 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_58_14 = all_52_23
% 204.90/35.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (3)  all_58_1 = all_52_9
% 204.90/35.63    (4)   ~ (all_52_17 = all_52_25)
% 204.90/35.63    (5)  all_58_13 = all_52_15
% 204.90/35.63    (6)   ~ (all_52_15 = e3)
% 204.90/35.63    (7)  op(e3, e3) = all_52_28
% 204.90/35.63    (8)   ~ (all_52_25 = e0)
% 204.90/35.63    (9)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (10)  op(e0, e0) = e0
% 204.90/35.63    (11)  op(all_52_9, all_52_9) = all_52_8
% 204.90/35.63    (12)  all_58_7 = all_52_13
% 204.90/35.63    (13)  op(all_52_19, all_52_19) = e2
% 204.90/35.63    (14)  all_56_2 = all_52_17
% 204.90/35.63    (15)   ~ (all_52_25 = e3)
% 204.90/35.63    (16)   ~ (all_52_23 = e3)
% 204.90/35.63    (17)   ~ (all_10_2 = e3)
% 204.90/35.63    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63    (19)  all_58_8 = all_10_2
% 204.90/35.63    (20)   ~ (all_52_25 = all_6_2)
% 204.90/35.63    (21)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63    (22)   ~ (all_52_9 = all_6_2)
% 204.90/35.63    (23)  op(e3, e3) = all_6_2
% 204.90/35.63    (24)   ~ (all_52_13 = e3)
% 204.90/35.63    (25)  all_56_3 = all_52_25
% 204.90/35.63    (26)  all_58_5 = all_52_19
% 204.90/35.63    (27)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (28)   ~ (all_52_17 = all_6_2)
% 204.90/35.63    (29)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63    (30)  all_58_3 = all_4_2
% 204.90/35.63    (31)   ~ (all_52_19 = all_4_2)
% 204.90/35.63    (32)  all_58_4 = all_52_17
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | GROUND_INST: instantiating (2) with all_6_2, all_52_28, e3, e3, simplifying
% 204.90/35.63  |              with (7), (23) gives:
% 204.90/35.63  |   (33)  all_52_28 = all_6_2
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (21) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (34)  all_56_3 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (15), (25), (34) are inconsistent by sub-proof #1339.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (35)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63  | | 
% 204.90/35.63  | | BETA: splitting (29) gives:
% 204.90/35.63  | | 
% 204.90/35.63  | | Case 1:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (36)  all_58_4 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | COMBINE_EQS: (32), (36) imply:
% 204.90/35.63  | | |   (37)  all_52_17 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | SIMP: (37) implies:
% 204.90/35.63  | | |   (38)  all_52_17 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REF_CLOSE: (2), (23), (27), (28), (38) are inconsistent by sub-proof
% 204.90/35.63  | | |            #1280.
% 204.90/35.63  | | | 
% 204.90/35.63  | | Case 2:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (39)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | BETA: splitting (39) gives:
% 204.90/35.63  | | | 
% 204.90/35.63  | | | Case 1:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | |   (40)  all_58_5 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | COMBINE_EQS: (26), (40) imply:
% 204.90/35.63  | | | |   (41)  all_52_19 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | SIMP: (41) implies:
% 204.90/35.63  | | | |   (42)  all_52_19 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REDUCE: (31), (42) imply:
% 204.90/35.63  | | | |   (43)   ~ (all_4_2 = e3)
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | SIMP: (43) implies:
% 204.90/35.63  | | | |   (44)   ~ (all_4_2 = e3)
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REDUCE: (13), (42) imply:
% 204.90/35.63  | | | |   (45)  op(e3, e3) = e2
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 204.90/35.63  | | | |            (18), (20), (22), (23), (24), (25), (27), (28), (30), (35),
% 204.90/35.63  | | | |            (44), (45) are inconsistent by sub-proof #1255.
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | Case 2:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | |   (46)  all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REF_CLOSE: (1), (16), (17), (19), (46) are inconsistent by sub-proof
% 204.90/35.63  | | | |            #1304.
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | End of split
% 204.90/35.63  | | | 
% 204.90/35.63  | | End of split
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1255 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (2)  all_58_1 = all_52_9
% 204.90/35.63    (3)   ~ (all_52_17 = all_52_25)
% 204.90/35.63    (4)   ~ (all_4_2 = e3)
% 204.90/35.63    (5)  all_58_13 = all_52_15
% 204.90/35.63    (6)   ~ (all_52_15 = e3)
% 204.90/35.63    (7)  op(e3, e3) = e2
% 204.90/35.63    (8)   ~ (all_52_25 = e0)
% 204.90/35.63    (9)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (10)  op(e0, e0) = e0
% 204.90/35.63    (11)  op(all_52_9, all_52_9) = all_52_8
% 204.90/35.63    (12)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63    (13)  all_58_7 = all_52_13
% 204.90/35.63    (14)  all_56_2 = all_52_17
% 204.90/35.63    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63    (16)   ~ (all_52_25 = all_6_2)
% 204.90/35.63    (17)   ~ (all_52_9 = all_6_2)
% 204.90/35.63    (18)  op(e3, e3) = all_6_2
% 204.90/35.63    (19)   ~ (all_52_13 = e3)
% 204.90/35.63    (20)  all_56_3 = all_52_25
% 204.90/35.63    (21)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (22)   ~ (all_52_17 = all_6_2)
% 204.90/35.63    (23)  all_58_3 = all_4_2
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (15) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (24)  all_58_1 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | COMBINE_EQS: (2), (24) imply:
% 204.90/35.63  | |   (25)  all_52_9 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (17), (25) imply:
% 204.90/35.63  | |   (26)   ~ (all_6_2 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | SIMP: (26) implies:
% 204.90/35.63  | |   (27)   ~ (all_6_2 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (11), (25) imply:
% 204.90/35.63  | |   (28)  op(e3, e3) = all_52_8
% 204.90/35.63  | | 
% 204.90/35.63  | | GROUND_INST: instantiating (1) with all_6_2, all_52_8, e3, e3, simplifying
% 204.90/35.63  | |              with (18), (28) gives:
% 204.90/35.63  | |   (29)  all_52_8 = all_6_2
% 204.90/35.63  | | 
% 204.90/35.63  | | GROUND_INST: instantiating (1) with e2, all_52_8, e3, e3, simplifying with
% 204.90/35.63  | |              (7), (28) gives:
% 204.90/35.63  | |   (30)  all_52_8 = e2
% 204.90/35.63  | | 
% 204.90/35.63  | | COMBINE_EQS: (29), (30) imply:
% 204.90/35.63  | |   (31)  all_6_2 = e2
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (22), (31) imply:
% 204.90/35.63  | |   (32)   ~ (all_52_17 = e2)
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (16), (31) imply:
% 204.90/35.63  | |   (33)   ~ (all_52_25 = e2)
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (1), (3), (8), (9), (10), (12), (14), (18), (20), (21), (27),
% 204.90/35.63  | |            (32), (33) are inconsistent by sub-proof #1257.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (34)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (4), (5), (6), (13), (19), (23), (34) are inconsistent by
% 204.90/35.63  | |            sub-proof #1256.
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1256 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)   ~ (all_4_2 = e3)
% 204.90/35.63    (2)  all_58_13 = all_52_15
% 204.90/35.63    (3)   ~ (all_52_15 = e3)
% 204.90/35.63    (4)  all_58_7 = all_52_13
% 204.90/35.63    (5)   ~ (all_52_13 = e3)
% 204.90/35.63    (6)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63    (7)  all_58_3 = all_4_2
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (6) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (8)  all_58_3 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | COMBINE_EQS: (7), (8) imply:
% 204.90/35.63  | |   (9)  all_4_2 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (1), (9) imply:
% 204.90/35.63  | |   (10)  $false
% 204.90/35.63  | | 
% 204.90/35.63  | | CLOSE: (10) is inconsistent.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (11)  all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (2), (3), (4), (5), (11) are inconsistent by sub-proof #1298.
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1257 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (2)   ~ (all_52_17 = all_52_25)
% 204.90/35.63    (3)   ~ (all_52_25 = e0)
% 204.90/35.63    (4)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (5)   ~ (all_6_2 = e3)
% 204.90/35.63    (6)  op(e0, e0) = e0
% 204.90/35.63    (7)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63    (8)  all_56_2 = all_52_17
% 204.90/35.63    (9)   ~ (all_52_25 = e2)
% 204.90/35.63    (10)  op(e3, e3) = all_6_2
% 204.90/35.63    (11)  all_56_3 = all_52_25
% 204.90/35.63    (12)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (13)   ~ (all_52_17 = e2)
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (7) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (14)  all_56_3 = e2
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (9), (11), (14) are inconsistent by sub-proof #1259.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (15)  all_56_3 = e1 | all_56_3 = e0
% 204.90/35.63  | | 
% 204.90/35.63  | | BETA: splitting (15) gives:
% 204.90/35.63  | | 
% 204.90/35.63  | | Case 1:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (16)  all_56_3 = e1
% 204.90/35.63  | | | 
% 204.90/35.63  | | | COMBINE_EQS: (11), (16) imply:
% 204.90/35.63  | | |   (17)  all_52_25 = e1
% 204.90/35.63  | | | 
% 204.90/35.63  | | | SIMP: (17) implies:
% 204.90/35.63  | | |   (18)  all_52_25 = e1
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REDUCE: (2), (18) imply:
% 204.90/35.63  | | |   (19)   ~ (all_52_17 = e1)
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REF_CLOSE: (1), (4), (5), (6), (8), (10), (12), (13), (19) are
% 204.90/35.63  | | |            inconsistent by sub-proof #1261.
% 204.90/35.63  | | | 
% 204.90/35.63  | | Case 2:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (20)  all_56_3 = e0
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REF_CLOSE: (3), (11), (20) are inconsistent by sub-proof #1258.
% 204.90/35.63  | | | 
% 204.90/35.63  | | End of split
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1258 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_56_3 = all_52_25
% 204.90/35.63    (2)  all_56_3 = e0
% 204.90/35.63    (3)   ~ (all_52_25 = e0)
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.63  |   (4)  all_52_25 = e0
% 204.90/35.63  | 
% 204.90/35.63  | SIMP: (4) implies:
% 204.90/35.63  |   (5)  all_52_25 = e0
% 204.90/35.63  | 
% 204.90/35.63  | REDUCE: (3), (5) imply:
% 204.90/35.63  |   (6)  $false
% 204.90/35.63  | 
% 204.90/35.63  | CLOSE: (6) is inconsistent.
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1259 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_56_3 = all_52_25
% 204.90/35.63    (2)  all_56_3 = e2
% 204.90/35.63    (3)   ~ (all_52_25 = e2)
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.63  |   (4)  all_52_25 = e2
% 204.90/35.63  | 
% 204.90/35.63  | SIMP: (4) implies:
% 204.90/35.63  |   (5)  all_52_25 = e2
% 204.90/35.63  | 
% 204.90/35.63  | REDUCE: (3), (5) imply:
% 204.90/35.63  |   (6)  $false
% 204.90/35.63  | 
% 204.90/35.63  | CLOSE: (6) is inconsistent.
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1260 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)  all_58_14 = all_52_23
% 204.90/35.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (3)  all_58_1 = all_52_9
% 204.90/35.63    (4)   ~ (all_4_2 = e3)
% 204.90/35.63    (5)  all_58_13 = all_52_15
% 204.90/35.63    (6)   ~ (all_52_15 = e3)
% 204.90/35.63    (7)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.63    (8)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (9)   ~ (all_6_2 = e3)
% 204.90/35.63    (10)   ~ (all_52_13 = all_10_2)
% 204.90/35.63    (11)  op(e0, e0) = e0
% 204.90/35.63    (12)  all_58_7 = all_52_13
% 204.90/35.63    (13)  op(all_52_19, all_52_19) = e2
% 204.90/35.63    (14)  all_56_2 = all_52_17
% 204.90/35.63    (15)   ~ (all_52_23 = e3)
% 204.90/35.63    (16)   ~ (all_52_19 = all_10_2)
% 204.90/35.63    (17)  all_58_8 = all_10_2
% 204.90/35.63    (18)   ~ (all_52_9 = all_6_2)
% 204.90/35.63    (19)  op(e3, e3) = all_6_2
% 204.90/35.63    (20)  all_58_5 = all_52_19
% 204.90/35.63    (21)  all_56_1 = all_52_9
% 204.90/35.63    (22)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.63    (23)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63    (24)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (25)   ~ (all_52_17 = all_6_2)
% 204.90/35.63    (26)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (27)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63    (28)   ~ (all_52_9 = all_52_17)
% 204.90/35.63    (29)  op(all_52_13, all_52_13) = all_52_12
% 204.90/35.63    (30)  op(e1, e1) = all_10_2
% 204.90/35.63    (31)  all_58_3 = all_4_2
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (27) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (32)  all_58_3 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | COMBINE_EQS: (31), (32) imply:
% 204.90/35.63  | |   (33)  all_4_2 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (4), (33) imply:
% 204.90/35.63  | |   (34)  $false
% 204.90/35.63  | | 
% 204.90/35.63  | | CLOSE: (34) is inconsistent.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (35)  all_58_7 = e3 | all_58_13 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | BETA: splitting (35) gives:
% 204.90/35.63  | | 
% 204.90/35.63  | | Case 1:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (36)  all_58_7 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | COMBINE_EQS: (12), (36) imply:
% 204.90/35.63  | | |   (37)  all_52_13 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REDUCE: (10), (37) imply:
% 204.90/35.63  | | |   (38)   ~ (all_10_2 = e3)
% 204.90/35.63  | | | 
% 204.90/35.63  | | | SIMP: (38) implies:
% 204.90/35.63  | | |   (39)   ~ (all_10_2 = e3)
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REDUCE: (29), (37) imply:
% 204.90/35.63  | | |   (40)  op(e3, e3) = all_52_12
% 204.90/35.63  | | | 
% 204.90/35.63  | | | BETA: splitting (23) gives:
% 204.90/35.63  | | | 
% 204.90/35.63  | | | Case 1:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | |   (41)  all_58_5 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | COMBINE_EQS: (20), (41) imply:
% 204.90/35.63  | | | |   (42)  all_52_19 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | SIMP: (42) implies:
% 204.90/35.63  | | | |   (43)  all_52_19 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REDUCE: (13), (43) imply:
% 204.90/35.63  | | | |   (44)  op(e3, e3) = e2
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | GROUND_INST: instantiating (2) with all_6_2, all_52_12, e3, e3,
% 204.90/35.63  | | | |              simplifying with (19), (40) gives:
% 204.90/35.63  | | | |   (45)  all_52_12 = all_6_2
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | GROUND_INST: instantiating (2) with e2, all_52_12, e3, e3, simplifying
% 204.90/35.63  | | | |              with (40), (44) gives:
% 204.90/35.63  | | | |   (46)  all_52_12 = e2
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | COMBINE_EQS: (45), (46) imply:
% 204.90/35.63  | | | |   (47)  all_6_2 = e2
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | SIMP: (47) implies:
% 204.90/35.63  | | | |   (48)  all_6_2 = e2
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REDUCE: (18), (48) imply:
% 204.90/35.63  | | | |   (49)   ~ (all_52_9 = e2)
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REDUCE: (25), (48) imply:
% 204.90/35.63  | | | |   (50)   ~ (all_52_17 = e2)
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | BETA: splitting (7) gives:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | Case 1:
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | |   (51)  all_58_1 = e0
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | COMBINE_EQS: (3), (51) imply:
% 204.90/35.63  | | | | |   (52)  all_52_9 = e0
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | REDUCE: (28), (52) imply:
% 204.90/35.63  | | | | |   (53)   ~ (all_52_17 = e0)
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | SIMP: (53) implies:
% 204.90/35.63  | | | | |   (54)   ~ (all_52_17 = e0)
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | REF_CLOSE: (2), (14), (24), (26), (30), (39), (50), (54) are
% 204.90/35.63  | | | | |            inconsistent by sub-proof #1266.
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | Case 2:
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | |   (55)   ~ (all_58_1 = e0)
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | REDUCE: (3), (55) imply:
% 204.90/35.63  | | | | |   (56)   ~ (all_52_9 = e0)
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | BETA: splitting (22) gives:
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | | Case 1:
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | |   (57)  all_56_1 = e2
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | | COMBINE_EQS: (21), (57) imply:
% 204.90/35.63  | | | | | |   (58)  all_52_9 = e2
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | | REDUCE: (49), (58) imply:
% 204.90/35.63  | | | | | |   (59)  $false
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | | CLOSE: (59) is inconsistent.
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | Case 2:
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | |   (60)  all_56_1 = e1 | all_56_1 = e0
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | | BETA: splitting (60) gives:
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | | Case 1:
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | |   (61)  all_56_1 = e1
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | COMBINE_EQS: (21), (61) imply:
% 204.90/35.63  | | | | | | |   (62)  all_52_9 = e1
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | REDUCE: (28), (62) imply:
% 204.90/35.63  | | | | | | |   (63)   ~ (all_52_17 = e1)
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | SIMP: (63) implies:
% 204.90/35.63  | | | | | | |   (64)   ~ (all_52_17 = e1)
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | REF_CLOSE: (2), (8), (9), (11), (14), (19), (24), (50), (64) are
% 204.90/35.63  | | | | | | |            inconsistent by sub-proof #1261.
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | Case 2:
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | |   (65)  all_56_1 = e0
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | COMBINE_EQS: (21), (65) imply:
% 204.90/35.63  | | | | | | |   (66)  all_52_9 = e0
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | REDUCE: (56), (66) imply:
% 204.90/35.63  | | | | | | |   (67)  $false
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | | CLOSE: (67) is inconsistent.
% 204.90/35.63  | | | | | | | 
% 204.90/35.63  | | | | | | End of split
% 204.90/35.63  | | | | | | 
% 204.90/35.63  | | | | | End of split
% 204.90/35.63  | | | | | 
% 204.90/35.63  | | | | End of split
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | Case 2:
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | |   (68)  all_58_8 = e3 | all_58_14 = e3
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | | REF_CLOSE: (1), (15), (17), (39), (68) are inconsistent by sub-proof
% 204.90/35.63  | | | |            #1304.
% 204.90/35.63  | | | | 
% 204.90/35.63  | | | End of split
% 204.90/35.63  | | | 
% 204.90/35.63  | | Case 2:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (69)  all_58_13 = e3
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REF_CLOSE: (5), (6), (69) are inconsistent by sub-proof #1360.
% 204.90/35.63  | | | 
% 204.90/35.63  | | End of split
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1261 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (2)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (3)   ~ (all_6_2 = e3)
% 204.90/35.63    (4)  op(e0, e0) = e0
% 204.90/35.63    (5)  all_56_2 = all_52_17
% 204.90/35.63    (6)  op(e3, e3) = all_6_2
% 204.90/35.63    (7)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (8)   ~ (all_52_17 = e1)
% 204.90/35.63    (9)   ~ (all_52_17 = e2)
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (2) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (10)  all_56_2 = e3
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (1), (3), (5), (6), (7), (10) are inconsistent by sub-proof
% 204.90/35.63  | |            #1265.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (11)   ~ (all_56_2 = e3)
% 204.90/35.63  | |   (12)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63  | | 
% 204.90/35.63  | | REDUCE: (5), (11) imply:
% 204.90/35.63  | |   (13)   ~ (all_52_17 = e3)
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (12), (13) are inconsistent by
% 204.90/35.63  | |            sub-proof #1262.
% 204.90/35.63  | | 
% 204.90/35.63  | End of split
% 204.90/35.63  | 
% 204.90/35.63  End of proof
% 204.90/35.63  
% 204.90/35.63  Sub-proof #1262 shows that the following formulas are inconsistent:
% 204.90/35.63  ----------------------------------------------------------------
% 204.90/35.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.63    (2)  op(e0, e0) = e0
% 204.90/35.63    (3)  all_56_2 = all_52_17
% 204.90/35.63    (4)   ~ (all_52_17 = e3)
% 204.90/35.63    (5)  op(all_52_17, all_52_17) = e3
% 204.90/35.63    (6)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63    (7)   ~ (all_52_17 = e1)
% 204.90/35.63    (8)   ~ (all_52_17 = e2)
% 204.90/35.63  
% 204.90/35.63  Begin of proof
% 204.90/35.63  | 
% 204.90/35.63  | BETA: splitting (6) gives:
% 204.90/35.63  | 
% 204.90/35.63  | Case 1:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (9)  all_56_2 = e2
% 204.90/35.63  | | 
% 204.90/35.63  | | REF_CLOSE: (3), (8), (9) are inconsistent by sub-proof #1264.
% 204.90/35.63  | | 
% 204.90/35.63  | Case 2:
% 204.90/35.63  | | 
% 204.90/35.63  | |   (10)  all_56_2 = e1 | all_56_2 = e0
% 204.90/35.63  | | 
% 204.90/35.63  | | BETA: splitting (10) gives:
% 204.90/35.63  | | 
% 204.90/35.63  | | Case 1:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (11)  all_56_2 = e1
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #1263.
% 204.90/35.63  | | | 
% 204.90/35.63  | | Case 2:
% 204.90/35.63  | | | 
% 204.90/35.63  | | |   (12)  all_56_2 = e0
% 204.90/35.63  | | | 
% 204.90/35.63  | | | COMBINE_EQS: (3), (12) imply:
% 204.90/35.63  | | |   (13)  all_52_17 = e0
% 204.90/35.63  | | | 
% 204.90/35.63  | | | SIMP: (13) implies:
% 204.90/35.63  | | |   (14)  all_52_17 = e0
% 204.90/35.63  | | | 
% 204.90/35.63  | | | REDUCE: (4), (14) imply:
% 204.90/35.63  | | |   (15)   ~ (e3 = e0)
% 204.90/35.63  | | | 
% 204.90/35.63  | | | SIMP: (15) implies:
% 204.90/35.64  | | |   (16)   ~ (e3 = e0)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (5), (14) imply:
% 204.90/35.64  | | |   (17)  op(e0, e0) = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | GROUND_INST: instantiating (1) with e0, e3, e0, e0, simplifying with (2),
% 204.90/35.64  | | |              (17) gives:
% 204.90/35.64  | | |   (18)  e3 = e0
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (16), (18) imply:
% 204.90/35.64  | | |   (19)  $false
% 204.90/35.64  | | | 
% 204.90/35.64  | | | CLOSE: (19) is inconsistent.
% 204.90/35.64  | | | 
% 204.90/35.64  | | End of split
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1263 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_56_2 = all_52_17
% 204.90/35.64    (2)  all_56_2 = e1
% 204.90/35.64    (3)   ~ (all_52_17 = e1)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.64  |   (4)  all_52_17 = e1
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (4) implies:
% 204.90/35.64  |   (5)  all_52_17 = e1
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)  $false
% 204.90/35.64  | 
% 204.90/35.64  | CLOSE: (6) is inconsistent.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1264 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_56_2 = all_52_17
% 204.90/35.64    (2)  all_56_2 = e2
% 204.90/35.64    (3)   ~ (all_52_17 = e2)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.64  |   (4)  all_52_17 = e2
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (4) implies:
% 204.90/35.64  |   (5)  all_52_17 = e2
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)  $false
% 204.90/35.64  | 
% 204.90/35.64  | CLOSE: (6) is inconsistent.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1265 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (2)  all_56_2 = e3
% 204.90/35.64    (3)   ~ (all_6_2 = e3)
% 204.90/35.64    (4)  all_56_2 = all_52_17
% 204.90/35.64    (5)  op(e3, e3) = all_6_2
% 204.90/35.64    (6)  op(all_52_17, all_52_17) = e3
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (2), (4) imply:
% 204.90/35.64  |   (7)  all_52_17 = e3
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (7) implies:
% 204.90/35.64  |   (8)  all_52_17 = e3
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (6), (8) imply:
% 204.90/35.64  |   (9)  op(e3, e3) = e3
% 204.90/35.64  | 
% 204.90/35.64  | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1338.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1266 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (2)  all_56_2 = all_52_17
% 204.90/35.64    (3)   ~ (all_10_2 = e3)
% 204.90/35.64    (4)  op(all_52_17, all_52_17) = e3
% 204.90/35.64    (5)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64    (6)   ~ (all_52_17 = e0)
% 204.90/35.64    (7)  op(e1, e1) = all_10_2
% 204.90/35.64    (8)   ~ (all_52_17 = e2)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (5) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (9)  all_56_2 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | COMBINE_EQS: (2), (9) imply:
% 204.90/35.64  | |   (10)  all_52_17 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | REDUCE: (8), (10) imply:
% 204.90/35.64  | |   (11)  $false
% 204.90/35.64  | | 
% 204.90/35.64  | | CLOSE: (11) is inconsistent.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (12)  all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | BETA: splitting (12) gives:
% 204.90/35.64  | | 
% 204.90/35.64  | | Case 1:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (13)  all_56_2 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (2), (13) imply:
% 204.90/35.64  | | |   (14)  all_52_17 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (4), (14) imply:
% 204.90/35.64  | | |   (15)  op(e1, e1) = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REF_CLOSE: (1), (3), (7), (15) are inconsistent by sub-proof #1368.
% 204.90/35.64  | | | 
% 204.90/35.64  | | Case 2:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (16)  all_56_2 = e0
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (2), (16) imply:
% 204.90/35.64  | | |   (17)  all_52_17 = e0
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (6), (17) imply:
% 204.90/35.64  | | |   (18)  $false
% 204.90/35.64  | | | 
% 204.90/35.64  | | | CLOSE: (18) is inconsistent.
% 204.90/35.64  | | | 
% 204.90/35.64  | | End of split
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1267 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ~ (e3 = e0)
% 204.90/35.64    (2)  all_58_3 = e3
% 204.90/35.64    (3)  all_58_13 = all_52_15
% 204.90/35.64    (4)   ~ (all_52_15 = e0)
% 204.90/35.64    (5)  all_58_7 = all_52_13
% 204.90/35.64    (6)   ~ (all_52_13 = e0)
% 204.90/35.64    (7)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (7) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (8)  all_58_3 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | COMBINE_EQS: (2), (8) imply:
% 204.90/35.64  | |   (9)  e3 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | REDUCE: (1), (9) imply:
% 204.90/35.64  | |   (10)  $false
% 204.90/35.64  | | 
% 204.90/35.64  | | CLOSE: (10) is inconsistent.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (11)  all_58_7 = e0 | all_58_13 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (3), (4), (5), (6), (11) are inconsistent by sub-proof #1268.
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1268 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_13 = all_52_15
% 204.90/35.64    (2)   ~ (all_52_15 = e0)
% 204.90/35.64    (3)  all_58_7 = all_52_13
% 204.90/35.64    (4)  all_58_7 = e0 | all_58_13 = e0
% 204.90/35.64    (5)   ~ (all_52_13 = e0)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (4) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (6)  all_58_7 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | COMBINE_EQS: (3), (6) imply:
% 204.90/35.64  | |   (7)  all_52_13 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | REDUCE: (5), (7) imply:
% 204.90/35.64  | |   (8)  $false
% 204.90/35.64  | | 
% 204.90/35.64  | | CLOSE: (8) is inconsistent.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (9)  all_58_13 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1269.
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1269 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_13 = all_52_15
% 204.90/35.64    (2)  all_58_13 = e0
% 204.90/35.64    (3)   ~ (all_52_15 = e0)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.64  |   (4)  all_52_15 = e0
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (4) implies:
% 204.90/35.64  |   (5)  all_52_15 = e0
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)  $false
% 204.90/35.64  | 
% 204.90/35.64  | CLOSE: (6) is inconsistent.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1270 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (2)  all_58_1 = e0
% 204.90/35.64    (3)  op(all_52_23, all_52_23) = e0
% 204.90/35.64    (4)  all_58_9 = e3
% 204.90/35.64    (5)  all_58_8 = e3
% 204.90/35.64    (6)  all_58_11 = all_52_29
% 204.90/35.64    (7)  all_58_4 = all_10_1
% 204.90/35.64    (8)   ~ (e2 = e1)
% 204.90/35.64    (9)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.64    (10)  op(e0, e0) = e0
% 204.90/35.64    (11)  op(all_10_2, all_10_2) = e1
% 204.90/35.64    (12)  all_58_8 = e3 | all_58_11 = e3
% 204.90/35.64    (13)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.90/35.64    (14)   ~ (all_52_29 = e3)
% 204.90/35.64    (15)   ~ (e2 = e0)
% 204.90/35.64    (16)   ~ (all_52_23 = e0)
% 204.90/35.64    (17)   ~ (all_52_23 = all_10_1)
% 204.90/35.64    (18)  all_56_14 = all_52_23
% 204.90/35.64    (19)   ~ (e3 = e2)
% 204.90/35.64    (20)  op(e1, e1) = all_10_2
% 204.90/35.64    (21)   ~ (all_52_23 = all_10_2)
% 204.90/35.64    (22)  all_58_0 = e1
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (13) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (23)  all_58_0 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (8), (22), (23) are inconsistent by sub-proof #1273.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (24)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | BETA: splitting (24) gives:
% 204.90/35.64  | | 
% 204.90/35.64  | | Case 1:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (25)  all_58_1 = e2
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REF_CLOSE: (2), (15), (25) are inconsistent by sub-proof #1272.
% 204.90/35.64  | | | 
% 204.90/35.64  | | Case 2:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (26)  all_58_4 = e2 | all_58_9 = e2
% 204.90/35.64  | | | 
% 204.90/35.64  | | | BETA: splitting (26) gives:
% 204.90/35.64  | | | 
% 204.90/35.64  | | | Case 1:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | |   (27)  all_58_4 = e2
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | COMBINE_EQS: (7), (27) imply:
% 204.90/35.64  | | | |   (28)  all_10_1 = e2
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | REDUCE: (17), (28) imply:
% 204.90/35.64  | | | |   (29)   ~ (all_52_23 = e2)
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | REF_CLOSE: (1), (3), (9), (10), (11), (16), (18), (20), (21), (29) are
% 204.90/35.64  | | | |            inconsistent by sub-proof #1284.
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | Case 2:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | |   (30)  all_58_9 = e2
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | COMBINE_EQS: (4), (30) imply:
% 204.90/35.64  | | | |   (31)  e3 = e2
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | COMBINE_EQS: (5), (31) imply:
% 204.90/35.64  | | | |   (32)  all_58_8 = e2
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | REF_CLOSE: (6), (12), (14), (19), (32) are inconsistent by sub-proof
% 204.90/35.64  | | | |            #1271.
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | End of split
% 204.90/35.64  | | | 
% 204.90/35.64  | | End of split
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1271 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_11 = all_52_29
% 204.90/35.64    (2)  all_58_8 = e2
% 204.90/35.64    (3)  all_58_8 = e3 | all_58_11 = e3
% 204.90/35.64    (4)   ~ (all_52_29 = e3)
% 204.90/35.64    (5)   ~ (e3 = e2)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (3) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (6)  all_58_8 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | COMBINE_EQS: (2), (6) imply:
% 204.90/35.64  | |   (7)  e3 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | SIMP: (7) implies:
% 204.90/35.64  | |   (8)  e3 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | REDUCE: (5), (8) imply:
% 204.90/35.64  | |   (9)  $false
% 204.90/35.64  | | 
% 204.90/35.64  | | CLOSE: (9) is inconsistent.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (10)  all_58_11 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (1), (4), (10) are inconsistent by sub-proof #1323.
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1272 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_1 = e2
% 204.90/35.64    (2)  all_58_1 = e0
% 204.90/35.64    (3)   ~ (e2 = e0)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.64  |   (4)  e2 = e0
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (4) implies:
% 204.90/35.64  |   (5)  e2 = e0
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)  $false
% 204.90/35.64  | 
% 204.90/35.64  | CLOSE: (6) is inconsistent.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1273 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_0 = e2
% 204.90/35.64    (2)  all_58_0 = e1
% 204.90/35.64    (3)   ~ (e2 = e1)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.64  |   (4)  e2 = e1
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (4) implies:
% 204.90/35.64  |   (5)  e2 = e1
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)  $false
% 204.90/35.64  | 
% 204.90/35.64  | CLOSE: (6) is inconsistent.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1274 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ~ (all_52_25 = all_52_27)
% 204.90/35.64    (2)  all_58_14 = all_52_23
% 204.90/35.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (4)  all_58_1 = all_52_9
% 204.90/35.64    (5)   ~ (all_52_17 = all_52_25)
% 204.90/35.64    (6)  all_58_0 = all_6_2
% 204.90/35.64    (7)   ~ (all_52_17 = all_10_2)
% 204.90/35.64    (8)  all_58_9 = all_52_25
% 204.90/35.64    (9)  op(all_52_27, all_52_27) = all_52_26
% 204.90/35.64    (10)  op(all_10_2, e1) = all_10_1
% 204.90/35.64    (11)   ~ (all_52_25 = e0)
% 204.90/35.64    (12)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64    (13)   ~ (all_6_2 = e3)
% 204.90/35.64    (14)  op(e0, e0) = e0
% 204.90/35.64    (15)  op(all_10_2, all_10_2) = e1
% 204.90/35.64    (16)  op(all_52_9, all_52_9) = all_52_8
% 204.90/35.64    (17)  all_56_2 = all_52_17
% 204.90/35.64    (18)  all_56_7 = e3
% 204.90/35.64    (19)  all_56_7 = all_52_27
% 204.90/35.64    (20)   ~ (all_52_23 = e3)
% 204.90/35.64    (21)   ~ (all_52_19 = all_52_27)
% 204.90/35.64    (22)  op(e3, e1) = all_52_17
% 204.90/35.64    (23)  all_58_8 = all_10_2
% 204.90/35.64    (24)   ~ (all_52_25 = all_6_2)
% 204.90/35.64    (25)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.64    (26)  op(e3, e3) = all_6_2
% 204.90/35.64    (27)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.64    (28)  all_56_3 = all_52_25
% 204.90/35.64    (29)  all_58_5 = all_52_19
% 204.90/35.64    (30)  op(all_52_17, all_52_17) = e3
% 204.90/35.64    (31)   ~ (all_52_17 = all_6_2)
% 204.90/35.64    (32)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.64    (33)  all_58_4 = all_52_17
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (18), (19) imply:
% 204.90/35.64  |   (34)  all_52_27 = e3
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (34) implies:
% 204.90/35.64  |   (35)  all_52_27 = e3
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (21), (35) imply:
% 204.90/35.64  |   (36)   ~ (all_52_19 = e3)
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (1), (35) imply:
% 204.90/35.64  |   (37)   ~ (all_52_25 = e3)
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (9), (35) imply:
% 204.90/35.64  |   (38)  op(e3, e3) = all_52_26
% 204.90/35.64  | 
% 204.90/35.64  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 204.90/35.64  |            (15), (16), (17), (20), (22), (23), (24), (25), (26), (27), (28),
% 204.90/35.64  |            (29), (30), (31), (32), (33), (36), (37), (38) are inconsistent by
% 204.90/35.64  |            sub-proof #1275.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1275 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_14 = all_52_23
% 204.90/35.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (3)  all_58_1 = all_52_9
% 204.90/35.64    (4)   ~ (all_52_17 = all_52_25)
% 204.90/35.64    (5)  all_58_0 = all_6_2
% 204.90/35.64    (6)   ~ (all_52_17 = all_10_2)
% 204.90/35.64    (7)  all_58_9 = all_52_25
% 204.90/35.64    (8)  op(e3, e3) = all_52_26
% 204.90/35.64    (9)  op(all_10_2, e1) = all_10_1
% 204.90/35.64    (10)   ~ (all_52_25 = e0)
% 204.90/35.64    (11)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64    (12)   ~ (all_6_2 = e3)
% 204.90/35.64    (13)  op(e0, e0) = e0
% 204.90/35.64    (14)  op(all_10_2, all_10_2) = e1
% 204.90/35.64    (15)  op(all_52_9, all_52_9) = all_52_8
% 204.90/35.64    (16)  all_56_2 = all_52_17
% 204.90/35.64    (17)   ~ (all_52_25 = e3)
% 204.90/35.64    (18)   ~ (all_52_23 = e3)
% 204.90/35.64    (19)   ~ (all_52_19 = e3)
% 204.90/35.64    (20)  op(e3, e1) = all_52_17
% 204.90/35.64    (21)  all_58_8 = all_10_2
% 204.90/35.64    (22)   ~ (all_52_25 = all_6_2)
% 204.90/35.64    (23)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.64    (24)  op(e3, e3) = all_6_2
% 204.90/35.64    (25)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.64    (26)  all_56_3 = all_52_25
% 204.90/35.64    (27)  all_58_5 = all_52_19
% 204.90/35.64    (28)  op(all_52_17, all_52_17) = e3
% 204.90/35.64    (29)   ~ (all_52_17 = all_6_2)
% 204.90/35.64    (30)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.64    (31)  all_58_4 = all_52_17
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | GROUND_INST: instantiating (2) with all_6_2, all_52_26, e3, e3, simplifying
% 204.90/35.64  |              with (8), (24) gives:
% 204.90/35.64  |   (32)  all_52_26 = all_6_2
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (23) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (33)  all_56_3 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (17), (26), (33) are inconsistent by sub-proof #1339.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (34)   ~ (all_56_3 = e3)
% 204.90/35.64  | |   (35)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | BETA: splitting (30) gives:
% 204.90/35.64  | | 
% 204.90/35.64  | | Case 1:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (36)  all_58_4 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (31), (36) imply:
% 204.90/35.64  | | |   (37)  all_52_17 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | SIMP: (37) implies:
% 204.90/35.64  | | |   (38)  all_52_17 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REF_CLOSE: (2), (24), (28), (29), (38) are inconsistent by sub-proof
% 204.90/35.64  | | |            #1280.
% 204.90/35.64  | | | 
% 204.90/35.64  | | Case 2:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (39)   ~ (all_58_4 = e3)
% 204.90/35.64  | | |   (40)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (31), (39) imply:
% 204.90/35.64  | | |   (41)   ~ (all_52_17 = e3)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | BETA: splitting (25) gives:
% 204.90/35.64  | | | 
% 204.90/35.64  | | | Case 1:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | |   (42)  all_58_0 = e3
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | COMBINE_EQS: (5), (42) imply:
% 204.90/35.64  | | | |   (43)  all_6_2 = e3
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | REDUCE: (12), (43) imply:
% 204.90/35.64  | | | |   (44)  $false
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | CLOSE: (44) is inconsistent.
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | Case 2:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | |   (45)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | BETA: splitting (45) gives:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | Case 1:
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | |   (46)  all_58_1 = e3
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | COMBINE_EQS: (3), (46) imply:
% 204.90/35.64  | | | | |   (47)  all_52_9 = e3
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | REDUCE: (15), (47) imply:
% 204.90/35.64  | | | | |   (48)  op(e3, e3) = all_52_8
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | REF_CLOSE: (1), (2), (4), (6), (9), (10), (11), (13), (14), (16),
% 204.90/35.64  | | | | |            (18), (19), (20), (21), (22), (24), (26), (27), (28), (29),
% 204.90/35.64  | | | | |            (35), (40), (48) are inconsistent by sub-proof #1277.
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | Case 2:
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | |   (49)  all_58_4 = e3 | all_58_9 = e3
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | REF_CLOSE: (7), (17), (31), (41), (49) are inconsistent by sub-proof
% 204.90/35.64  | | | | |            #1276.
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | End of split
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | End of split
% 204.90/35.64  | | | 
% 204.90/35.64  | | End of split
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1276 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_9 = all_52_25
% 204.90/35.64    (2)  all_58_4 = e3 | all_58_9 = e3
% 204.90/35.64    (3)   ~ (all_52_25 = e3)
% 204.90/35.64    (4)   ~ (all_52_17 = e3)
% 204.90/35.64    (5)  all_58_4 = all_52_17
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (2) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (6)  all_58_4 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #1302.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (7)  all_58_9 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #1300.
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1277 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_14 = all_52_23
% 204.90/35.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (3)   ~ (all_52_17 = all_52_25)
% 204.90/35.64    (4)   ~ (all_52_17 = all_10_2)
% 204.90/35.64    (5)  op(all_10_2, e1) = all_10_1
% 204.90/35.64    (6)   ~ (all_52_25 = e0)
% 204.90/35.64    (7)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64    (8)  op(e0, e0) = e0
% 204.90/35.64    (9)  op(all_10_2, all_10_2) = e1
% 204.90/35.64    (10)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.64    (11)  all_56_2 = all_52_17
% 204.90/35.64    (12)   ~ (all_52_23 = e3)
% 204.90/35.64    (13)   ~ (all_52_19 = e3)
% 204.90/35.64    (14)  op(e3, e3) = all_52_8
% 204.90/35.64    (15)  op(e3, e1) = all_52_17
% 204.90/35.64    (16)  all_58_8 = all_10_2
% 204.90/35.64    (17)   ~ (all_52_25 = all_6_2)
% 204.90/35.64    (18)  op(e3, e3) = all_6_2
% 204.90/35.64    (19)  all_56_3 = all_52_25
% 204.90/35.64    (20)  all_58_5 = all_52_19
% 204.90/35.64    (21)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.64    (22)  op(all_52_17, all_52_17) = e3
% 204.90/35.64    (23)   ~ (all_52_17 = all_6_2)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (21) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (24)  all_58_5 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | REF_CLOSE: (13), (20), (24) are inconsistent by sub-proof #1279.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (25)  all_58_8 = e3 | all_58_14 = e3
% 204.90/35.64  | | 
% 204.90/35.64  | | BETA: splitting (25) gives:
% 204.90/35.64  | | 
% 204.90/35.64  | | Case 1:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (26)  all_58_8 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (16), (26) imply:
% 204.90/35.64  | | |   (27)  all_10_2 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (4), (27) imply:
% 204.90/35.64  | | |   (28)   ~ (all_52_17 = e3)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (9), (27) imply:
% 204.90/35.64  | | |   (29)  op(e3, e3) = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (5), (27) imply:
% 204.90/35.64  | | |   (30)  op(e3, e1) = all_10_1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | GROUND_INST: instantiating (2) with all_52_17, all_10_1, e1, e3,
% 204.90/35.64  | | |              simplifying with (15), (30) gives:
% 204.90/35.64  | | |   (31)  all_52_17 = all_10_1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | GROUND_INST: instantiating (2) with all_6_2, all_52_8, e3, e3, simplifying
% 204.90/35.64  | | |              with (14), (18) gives:
% 204.90/35.64  | | |   (32)  all_52_8 = all_6_2
% 204.90/35.64  | | | 
% 204.90/35.64  | | | GROUND_INST: instantiating (2) with e1, all_52_8, e3, e3, simplifying with
% 204.90/35.64  | | |              (14), (29) gives:
% 204.90/35.64  | | |   (33)  all_52_8 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (32), (33) imply:
% 204.90/35.64  | | |   (34)  all_6_2 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | SIMP: (34) implies:
% 204.90/35.64  | | |   (35)  all_6_2 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (11), (31) imply:
% 204.90/35.64  | | |   (36)  all_56_2 = all_10_1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (3), (31) imply:
% 204.90/35.64  | | |   (37)   ~ (all_52_25 = all_10_1)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | SIMP: (37) implies:
% 204.90/35.64  | | |   (38)   ~ (all_52_25 = all_10_1)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (23), (31), (35) imply:
% 204.90/35.64  | | |   (39)   ~ (all_10_1 = e1)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (28), (31) imply:
% 204.90/35.64  | | |   (40)   ~ (all_10_1 = e3)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (17), (35) imply:
% 204.90/35.64  | | |   (41)   ~ (all_52_25 = e1)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (22), (31) imply:
% 204.90/35.64  | | |   (42)  op(all_10_1, all_10_1) = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | BETA: splitting (7) gives:
% 204.90/35.64  | | | 
% 204.90/35.64  | | | Case 1:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | |   (43)  all_56_2 = e3
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | COMBINE_EQS: (36), (43) imply:
% 204.90/35.64  | | | |   (44)  all_10_1 = e3
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | REDUCE: (40), (44) imply:
% 204.90/35.64  | | | |   (45)  $false
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | CLOSE: (45) is inconsistent.
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | Case 2:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | |   (46)   ~ (all_56_2 = e3)
% 204.90/35.64  | | | |   (47)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | BETA: splitting (10) gives:
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | | Case 1:
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | |   (48)  all_56_3 = e2
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | COMBINE_EQS: (19), (48) imply:
% 204.90/35.64  | | | | |   (49)  all_52_25 = e2
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | REDUCE: (38), (49) imply:
% 204.90/35.64  | | | | |   (50)   ~ (all_10_1 = e2)
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | SIMP: (50) implies:
% 204.90/35.64  | | | | |   (51)   ~ (all_10_1 = e2)
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | REF_CLOSE: (2), (8), (36), (39), (40), (42), (47), (51) are
% 204.90/35.64  | | | | |            inconsistent by sub-proof #1278.
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | Case 2:
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | |   (52)  all_56_3 = e1 | all_56_3 = e0
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | | REF_CLOSE: (6), (19), (41), (52) are inconsistent by sub-proof #1330.
% 204.90/35.64  | | | | | 
% 204.90/35.64  | | | | End of split
% 204.90/35.64  | | | | 
% 204.90/35.64  | | | End of split
% 204.90/35.64  | | | 
% 204.90/35.64  | | Case 2:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (53)  all_58_14 = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REF_CLOSE: (1), (12), (53) are inconsistent by sub-proof #1305.
% 204.90/35.64  | | | 
% 204.90/35.64  | | End of split
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1278 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (2)   ~ (all_10_1 = e1)
% 204.90/35.64    (3)  op(e0, e0) = e0
% 204.90/35.64    (4)  op(all_10_1, all_10_1) = e3
% 204.90/35.64    (5)   ~ (all_10_1 = e2)
% 204.90/35.64    (6)  all_56_2 = all_10_1
% 204.90/35.64    (7)   ~ (all_10_1 = e3)
% 204.90/35.64    (8)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | BETA: splitting (8) gives:
% 204.90/35.64  | 
% 204.90/35.64  | Case 1:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (9)  all_56_2 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | COMBINE_EQS: (6), (9) imply:
% 204.90/35.64  | |   (10)  all_10_1 = e2
% 204.90/35.64  | | 
% 204.90/35.64  | | REDUCE: (5), (10) imply:
% 204.90/35.64  | |   (11)  $false
% 204.90/35.64  | | 
% 204.90/35.64  | | CLOSE: (11) is inconsistent.
% 204.90/35.64  | | 
% 204.90/35.64  | Case 2:
% 204.90/35.64  | | 
% 204.90/35.64  | |   (12)  all_56_2 = e1 | all_56_2 = e0
% 204.90/35.64  | | 
% 204.90/35.64  | | BETA: splitting (12) gives:
% 204.90/35.64  | | 
% 204.90/35.64  | | Case 1:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (13)  all_56_2 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (6), (13) imply:
% 204.90/35.64  | | |   (14)  all_10_1 = e1
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (2), (14) imply:
% 204.90/35.64  | | |   (15)  $false
% 204.90/35.64  | | | 
% 204.90/35.64  | | | CLOSE: (15) is inconsistent.
% 204.90/35.64  | | | 
% 204.90/35.64  | | Case 2:
% 204.90/35.64  | | | 
% 204.90/35.64  | | |   (16)  all_56_2 = e0
% 204.90/35.64  | | | 
% 204.90/35.64  | | | COMBINE_EQS: (6), (16) imply:
% 204.90/35.64  | | |   (17)  all_10_1 = e0
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (7), (17) imply:
% 204.90/35.64  | | |   (18)   ~ (e3 = e0)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | SIMP: (18) implies:
% 204.90/35.64  | | |   (19)   ~ (e3 = e0)
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REDUCE: (4), (17) imply:
% 204.90/35.64  | | |   (20)  op(e0, e0) = e3
% 204.90/35.64  | | | 
% 204.90/35.64  | | | REF_CLOSE: (1), (3), (19), (20) are inconsistent by sub-proof #1336.
% 204.90/35.64  | | | 
% 204.90/35.64  | | End of split
% 204.90/35.64  | | 
% 204.90/35.64  | End of split
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1279 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)  all_58_5 = all_52_19
% 204.90/35.64    (2)  all_58_5 = e3
% 204.90/35.64    (3)   ~ (all_52_19 = e3)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.64  |   (4)  all_52_19 = e3
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (4) implies:
% 204.90/35.64  |   (5)  all_52_19 = e3
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)  $false
% 204.90/35.64  | 
% 204.90/35.64  | CLOSE: (6) is inconsistent.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1280 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (2)  op(e3, e3) = all_6_2
% 204.90/35.64    (3)  all_52_17 = e3
% 204.90/35.64    (4)  op(all_52_17, all_52_17) = e3
% 204.90/35.64    (5)   ~ (all_52_17 = all_6_2)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (5) imply:
% 204.90/35.64  |   (6)   ~ (all_6_2 = e3)
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (6) implies:
% 204.90/35.64  |   (7)   ~ (all_6_2 = e3)
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (3), (4) imply:
% 204.90/35.64  |   (8)  op(e3, e3) = e3
% 204.90/35.64  | 
% 204.90/35.64  | REF_CLOSE: (1), (2), (7), (8) are inconsistent by sub-proof #1338.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1281 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ~ (all_52_15 = all_52_23)
% 204.90/35.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.64    (3)  op(all_52_23, all_52_23) = e0
% 204.90/35.64    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.64    (5)  op(e0, e2) = all_52_15
% 204.90/35.64    (6)   ~ (all_52_7 = all_52_15)
% 204.90/35.64    (7)  op(e2, e2) = all_4_2
% 204.90/35.64    (8)   ~ (all_4_1 = e3)
% 204.90/35.64    (9)  all_56_13 = e3
% 204.90/35.64    (10)  op(e0, e0) = e0
% 204.90/35.64    (11)  op(all_10_2, all_10_2) = e1
% 204.90/35.64    (12)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.64    (13)  all_58_12 = all_52_7
% 204.90/35.64    (14)  op(all_4_2, e2) = all_4_1
% 204.90/35.64    (15)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.64    (16)   ~ (all_52_23 = e0)
% 204.90/35.64    (17)  all_56_12 = all_52_7
% 204.90/35.64    (18)  all_56_14 = all_52_23
% 204.90/35.64    (19)  op(e1, e1) = all_10_2
% 204.90/35.64    (20)   ~ (all_52_23 = all_10_2)
% 204.90/35.64    (21)   ~ (all_52_7 = all_52_23)
% 204.90/35.64    (22)  all_56_13 = all_52_15
% 204.90/35.64    (23)   ~ (all_52_7 = e0)
% 204.90/35.64  
% 204.90/35.64  Begin of proof
% 204.90/35.64  | 
% 204.90/35.64  | COMBINE_EQS: (9), (22) imply:
% 204.90/35.64  |   (24)  all_52_15 = e3
% 204.90/35.64  | 
% 204.90/35.64  | SIMP: (24) implies:
% 204.90/35.64  |   (25)  all_52_15 = e3
% 204.90/35.64  | 
% 204.90/35.64  | REDUCE: (6), (25) imply:
% 204.90/35.64  |   (26)   ~ (all_52_7 = e3)
% 204.90/35.64  | 
% 204.90/35.64  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 204.90/35.64  |            (15), (16), (17), (18), (19), (20), (21), (23), (25), (26) are
% 204.90/35.64  |            inconsistent by sub-proof #1282.
% 204.90/35.64  | 
% 204.90/35.64  End of proof
% 204.90/35.64  
% 204.90/35.64  Sub-proof #1282 shows that the following formulas are inconsistent:
% 204.90/35.64  ----------------------------------------------------------------
% 204.90/35.64    (1)   ~ (all_52_15 = all_52_23)
% 204.90/35.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (3)  op(all_52_23, all_52_23) = e0
% 204.90/35.65    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65    (5)  op(e0, e2) = all_52_15
% 204.90/35.65    (6)  all_52_15 = e3
% 204.90/35.65    (7)  op(e2, e2) = all_4_2
% 204.90/35.65    (8)   ~ (all_4_1 = e3)
% 204.90/35.65    (9)  op(e0, e0) = e0
% 204.90/35.65    (10)  op(all_10_2, all_10_2) = e1
% 204.90/35.65    (11)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.65    (12)  all_58_12 = all_52_7
% 204.90/35.65    (13)   ~ (all_52_7 = e3)
% 204.90/35.65    (14)  op(all_4_2, e2) = all_4_1
% 204.90/35.65    (15)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.65    (16)   ~ (all_52_23 = e0)
% 204.90/35.65    (17)  all_56_12 = all_52_7
% 204.90/35.65    (18)  all_56_14 = all_52_23
% 204.90/35.65    (19)  op(e1, e1) = all_10_2
% 204.90/35.65    (20)   ~ (all_52_23 = all_10_2)
% 204.90/35.65    (21)   ~ (all_52_7 = all_52_23)
% 204.90/35.65    (22)   ~ (all_52_7 = e0)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | REDUCE: (1), (6) imply:
% 204.90/35.65  |   (23)   ~ (all_52_23 = e3)
% 204.90/35.65  | 
% 204.90/35.65  | SIMP: (23) implies:
% 204.90/35.65  |   (24)   ~ (all_52_23 = e3)
% 204.90/35.65  | 
% 204.90/35.65  | REDUCE: (5), (6) imply:
% 204.90/35.65  |   (25)  op(e0, e2) = e3
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (11) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (26)  all_56_14 = e3
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (18), (24), (26) are inconsistent by sub-proof #1286.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (27)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.65  | | 
% 204.90/35.65  | | BETA: splitting (4) gives:
% 204.90/35.65  | | 
% 204.90/35.65  | | Case 1:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (28)  all_56_12 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (13), (17), (28) are inconsistent by sub-proof #1383.
% 204.90/35.65  | | | 
% 204.90/35.65  | | Case 2:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (29)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65  | | | 
% 204.90/35.65  | | | BETA: splitting (15) gives:
% 204.90/35.65  | | | 
% 204.90/35.65  | | | Case 1:
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | |   (30)  all_58_12 = e1
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | COMBINE_EQS: (12), (30) imply:
% 204.90/35.65  | | | |   (31)  all_52_7 = e1
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | SIMP: (31) implies:
% 204.90/35.65  | | | |   (32)  all_52_7 = e1
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | REDUCE: (21), (32) imply:
% 204.90/35.65  | | | |   (33)   ~ (all_52_23 = e1)
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | SIMP: (33) implies:
% 204.90/35.65  | | | |   (34)   ~ (all_52_23 = e1)
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | BETA: splitting (27) gives:
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | Case 1:
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | |   (35)  all_56_14 = e2
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | COMBINE_EQS: (18), (35) imply:
% 204.90/35.65  | | | | |   (36)  all_52_23 = e2
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | SIMP: (36) implies:
% 204.90/35.65  | | | | |   (37)  all_52_23 = e2
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REDUCE: (3), (37) imply:
% 204.90/35.65  | | | | |   (38)  op(e2, e2) = e0
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REF_CLOSE: (2), (7), (8), (14), (25), (38) are inconsistent by
% 204.90/35.65  | | | | |            sub-proof #1378.
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | Case 2:
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | |   (39)  all_56_14 = e1 | all_56_14 = e0
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REF_CLOSE: (16), (18), (34), (39) are inconsistent by sub-proof #1381.
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | End of split
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | Case 2:
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | |   (40)   ~ (all_58_12 = e1)
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | REDUCE: (12), (40) imply:
% 204.90/35.65  | | | |   (41)   ~ (all_52_7 = e1)
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | REF_CLOSE: (2), (3), (9), (10), (16), (17), (18), (19), (20), (21),
% 204.90/35.65  | | | |            (22), (27), (29), (41) are inconsistent by sub-proof #1283.
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | End of split
% 204.90/35.65  | | | 
% 204.90/35.65  | | End of split
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1283 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (2)  op(all_52_23, all_52_23) = e0
% 204.90/35.65    (3)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65    (4)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.65    (5)  op(e0, e0) = e0
% 204.90/35.65    (6)  op(all_10_2, all_10_2) = e1
% 204.90/35.65    (7)   ~ (all_52_23 = e0)
% 204.90/35.65    (8)  all_56_12 = all_52_7
% 204.90/35.65    (9)   ~ (all_52_7 = e1)
% 204.90/35.65    (10)  all_56_14 = all_52_23
% 204.90/35.65    (11)  op(e1, e1) = all_10_2
% 204.90/35.65    (12)   ~ (all_52_23 = all_10_2)
% 204.90/35.65    (13)   ~ (all_52_7 = all_52_23)
% 204.90/35.65    (14)   ~ (all_52_7 = e0)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (3) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (15)  all_56_12 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | COMBINE_EQS: (8), (15) imply:
% 204.90/35.65  | |   (16)  all_52_7 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | SIMP: (16) implies:
% 204.90/35.65  | |   (17)  all_52_7 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | REDUCE: (13), (17) imply:
% 204.90/35.65  | |   (18)   ~ (all_52_23 = e2)
% 204.90/35.65  | | 
% 204.90/35.65  | | SIMP: (18) implies:
% 204.90/35.65  | |   (19)   ~ (all_52_23 = e2)
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (19) are
% 204.90/35.65  | |            inconsistent by sub-proof #1284.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (20)  all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (8), (9), (14), (20) are inconsistent by sub-proof #1374.
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1284 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (2)  op(all_52_23, all_52_23) = e0
% 204.90/35.65    (3)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.65    (4)  op(e0, e0) = e0
% 204.90/35.65    (5)  op(all_10_2, all_10_2) = e1
% 204.90/35.65    (6)   ~ (all_52_23 = e2)
% 204.90/35.65    (7)   ~ (all_52_23 = e0)
% 204.90/35.65    (8)  all_56_14 = all_52_23
% 204.90/35.65    (9)  op(e1, e1) = all_10_2
% 204.90/35.65    (10)   ~ (all_52_23 = all_10_2)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (3) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (11)  all_56_14 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (6), (8), (11) are inconsistent by sub-proof #1285.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (12)  all_56_14 = e1 | all_56_14 = e0
% 204.90/35.65  | | 
% 204.90/35.65  | | BETA: splitting (12) gives:
% 204.90/35.65  | | 
% 204.90/35.65  | | Case 1:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (13)  all_56_14 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | COMBINE_EQS: (8), (13) imply:
% 204.90/35.65  | | |   (14)  all_52_23 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | SIMP: (14) implies:
% 204.90/35.65  | | |   (15)  all_52_23 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (10), (15) imply:
% 204.90/35.65  | | |   (16)   ~ (all_10_2 = e1)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | SIMP: (16) implies:
% 204.90/35.65  | | |   (17)   ~ (all_10_2 = e1)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (2), (15) imply:
% 204.90/35.65  | | |   (18)  op(e1, e1) = e0
% 204.90/35.65  | | | 
% 204.90/35.65  | | | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 204.90/35.65  | | |              (9), (18) gives:
% 204.90/35.65  | | |   (19)  all_10_2 = e0
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (17), (19) imply:
% 204.90/35.65  | | |   (20)   ~ (e1 = e0)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | SIMP: (20) implies:
% 204.90/35.65  | | |   (21)   ~ (e1 = e0)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (5), (19) imply:
% 204.90/35.65  | | |   (22)  op(e0, e0) = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (4),
% 204.90/35.65  | | |              (22) gives:
% 204.90/35.65  | | |   (23)  e1 = e0
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (21), (23) imply:
% 204.90/35.65  | | |   (24)  $false
% 204.90/35.65  | | | 
% 204.90/35.65  | | | CLOSE: (24) is inconsistent.
% 204.90/35.65  | | | 
% 204.90/35.65  | | Case 2:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (25)  all_56_14 = e0
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (7), (8), (25) are inconsistent by sub-proof #1382.
% 204.90/35.65  | | | 
% 204.90/35.65  | | End of split
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1285 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)  all_56_14 = all_52_23
% 204.90/35.65    (2)  all_56_14 = e2
% 204.90/35.65    (3)   ~ (all_52_23 = e2)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.65  |   (4)  all_52_23 = e2
% 204.90/35.65  | 
% 204.90/35.65  | SIMP: (4) implies:
% 204.90/35.65  |   (5)  all_52_23 = e2
% 204.90/35.65  | 
% 204.90/35.65  | REDUCE: (3), (5) imply:
% 204.90/35.65  |   (6)  $false
% 204.90/35.65  | 
% 204.90/35.65  | CLOSE: (6) is inconsistent.
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1286 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)  all_56_14 = all_52_23
% 204.90/35.65    (2)  all_56_14 = e3
% 204.90/35.65    (3)   ~ (all_52_23 = e3)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.65  |   (4)  all_52_23 = e3
% 204.90/35.65  | 
% 204.90/35.65  | SIMP: (4) implies:
% 204.90/35.65  |   (5)  all_52_23 = e3
% 204.90/35.65  | 
% 204.90/35.65  | REDUCE: (3), (5) imply:
% 204.90/35.65  |   (6)  $false
% 204.90/35.65  | 
% 204.90/35.65  | CLOSE: (6) is inconsistent.
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1287 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ~ (all_52_25 = all_52_27)
% 204.90/35.65    (2)  all_58_14 = all_52_23
% 204.90/35.65    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.90/35.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (5)   ~ (all_52_5 = all_52_13)
% 204.90/35.65    (6)  all_58_1 = all_52_9
% 204.90/35.65    (7)   ~ (all_52_9 = all_52_13)
% 204.90/35.65    (8)   ~ (e3 = e0)
% 204.90/35.65    (9)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65    (10)   ~ (all_52_7 = all_52_15)
% 204.90/35.65    (11)  op(all_52_15, all_52_15) = e0
% 204.90/35.65    (12)   ~ (all_52_17 = all_52_25)
% 204.90/35.65    (13)   ~ (all_52_3 = all_6_2)
% 204.90/35.65    (14)  all_58_0 = all_6_2
% 204.90/35.65    (15)  all_56_4 = all_52_3
% 204.90/35.65    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.90/35.65    (17)  op(all_52_19, all_52_19) = all_52_18
% 204.90/35.65    (18)  all_58_13 = all_52_15
% 204.90/35.65    (19)  op(all_52_13, all_52_13) = e1
% 204.90/35.65    (20)  op(all_10_2, all_10_2) = all_52_20
% 204.90/35.65    (21)  all_58_9 = all_52_25
% 204.90/35.65    (22)   ~ (all_6_1 = e1)
% 204.90/35.65    (23)  op(all_52_27, all_52_27) = all_52_26
% 204.90/35.65    (24)  op(e1, e3) = all_52_5
% 204.90/35.65    (25)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.65    (26)  op(e2, e2) = all_4_2
% 204.90/35.65    (27)   ~ (all_52_3 = all_52_5)
% 204.90/35.65    (28)  all_58_11 = all_52_29
% 204.90/35.65    (29)  all_56_5 = all_4_2
% 204.90/35.65    (30)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.90/35.65    (31)  op(all_10_2, e1) = all_10_1
% 204.90/35.65    (32)   ~ (all_52_7 = all_6_2)
% 204.90/35.65    (33)  op(e0, e1) = all_52_23
% 204.90/35.65    (34)   ~ (all_52_15 = e0)
% 204.90/35.65    (35)  all_58_15 = e0
% 204.90/35.65    (36)   ~ (all_4_1 = e1)
% 204.90/35.65    (37)   ~ (all_52_25 = e0)
% 204.90/35.65    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.65    (39)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.65    (40)   ~ (e2 = e1)
% 204.90/35.65    (41)   ~ (all_52_13 = all_10_2)
% 204.90/35.65    (42)  op(e0, e0) = e0
% 204.90/35.65    (43)  all_58_10 = all_52_27
% 204.90/35.65    (44)  all_56_8 = all_52_5
% 204.90/35.65    (45)   ~ (all_52_25 = all_52_29)
% 204.90/35.65    (46)  all_58_7 = all_52_13
% 204.90/35.65    (47)   ~ (all_52_5 = all_52_7)
% 204.90/35.65    (48)  all_58_12 = all_52_7
% 204.90/35.65    (49)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.65    (50)  all_56_2 = all_52_17
% 204.90/35.65    (51)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.65    (52)  all_56_7 = all_52_27
% 204.90/35.65    (53)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.90/35.65    (54)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.90/35.65    (55)  op(all_4_2, e2) = all_4_1
% 204.90/35.65    (56)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.65    (57)   ~ (all_52_13 = all_4_2)
% 204.90/35.65    (58)  op(e0, e3) = all_52_7
% 204.90/35.65    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.65    (60)   ~ (all_52_9 = all_52_25)
% 204.90/35.65    (61)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.90/35.65    (62)  all_58_8 = all_10_2
% 204.90/35.65    (63)  all_56_12 = all_52_7
% 204.90/35.65    (64)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.65    (65)   ~ (all_52_25 = all_6_2)
% 204.90/35.65    (66)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.65    (67)   ~ (all_52_9 = all_4_2)
% 204.90/35.65    (68)   ~ (all_52_5 = all_6_2)
% 204.90/35.65    (69)  op(all_4_2, all_4_2) = e2
% 204.90/35.65    (70)   ~ (all_52_9 = all_6_2)
% 204.90/35.65    (71)   ~ (all_52_13 = all_52_15)
% 204.90/35.65    (72)  op(e3, e3) = all_6_2
% 204.90/35.65    (73)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.65    (74)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.65    (75)  all_56_3 = all_52_25
% 204.90/35.65    (76)   ~ (all_52_3 = all_52_7)
% 204.90/35.65    (77)   ~ (all_10_1 = e3)
% 204.90/35.65    (78)  all_58_5 = all_52_19
% 204.90/35.65    (79)  all_56_1 = all_52_9
% 204.90/35.65    (80)   ~ (all_52_15 = all_4_2)
% 204.90/35.65    (81)   ~ (all_52_27 = all_4_2)
% 204.90/35.65    (82)  all_58_6 = all_52_5
% 204.90/35.65    (83)  op(e3, e2) = all_52_9
% 204.90/35.65    (84)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.65    (85)   ~ (all_52_17 = all_6_2)
% 204.90/35.65    (86)   ~ (e1 = e0)
% 204.90/35.65    (87)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.65    (88)   ~ (all_52_9 = all_52_17)
% 204.90/35.65    (89)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.65    (90)   ~ (all_6_1 = e2)
% 204.90/35.65    (91)  op(e1, e1) = all_10_2
% 204.90/35.65    (92)  op(all_52_9, all_52_9) = e3
% 204.90/35.65    (93)   ~ (all_52_7 = all_52_23)
% 204.90/35.65    (94)  all_58_3 = all_4_2
% 204.90/35.65    (95)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.90/35.65    (96)  all_56_13 = all_52_15
% 204.90/35.65    (97)   ~ (all_52_3 = all_4_2)
% 204.90/35.65    (98)   ~ (all_52_19 = all_4_2)
% 204.90/35.65    (99)  op(all_6_2, e3) = all_6_1
% 204.90/35.65    (100)   ~ (all_52_13 = all_52_29)
% 204.90/35.65    (101)  all_58_4 = all_52_17
% 204.90/35.65    (102)   ~ (all_52_7 = e0)
% 204.90/35.65    (103)  op(all_52_25, all_52_25) = all_52_24
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (38) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (104)  all_56_13 = e3
% 204.90/35.65  | | 
% 204.90/35.65  | | COMBINE_EQS: (96), (104) imply:
% 204.90/35.65  | |   (105)  all_52_15 = e3
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (4), (9), (10), (11), (22), (32), (58), (63), (72), (90), (99),
% 204.90/35.65  | |            (105) are inconsistent by sub-proof #1341.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (106)   ~ (all_56_13 = e3)
% 204.90/35.65  | |   (107)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.65  | | 
% 204.90/35.65  | | REDUCE: (96), (106) imply:
% 204.90/35.65  | |   (108)   ~ (all_52_15 = e3)
% 204.90/35.65  | | 
% 204.90/35.65  | | BETA: splitting (84) gives:
% 204.90/35.65  | | 
% 204.90/35.65  | | Case 1:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (109)  all_58_12 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12), (13), (14),
% 204.90/35.65  | | |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 204.90/35.65  | | |            (26), (27), (28), (29), (32), (35), (36), (37), (39), (41),
% 204.90/35.65  | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 204.90/35.65  | | |            (52), (53), (54), (55), (57), (59), (60), (61), (62), (64),
% 204.90/35.65  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 204.90/35.65  | | |            (75), (76), (78), (79), (81), (82), (83), (85), (86), (87),
% 204.90/35.65  | | |            (88), (89), (90), (92), (93), (94), (95), (97), (98), (99),
% 204.90/35.65  | | |            (100), (101), (102), (103), (109) are inconsistent by sub-proof
% 204.90/35.65  | | |            #1292.
% 204.90/35.65  | | | 
% 204.90/35.65  | | Case 2:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (110)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (2), (4), (8), (9), (10), (11), (18), (26), (30), (31), (33),
% 204.90/35.65  | | |            (34), (35), (40), (42), (48), (56), (63), (69), (77), (80),
% 204.90/35.65  | | |            (91), (93), (96), (102), (107), (108), (110) are inconsistent
% 204.90/35.65  | | |            by sub-proof #1288.
% 204.90/35.65  | | | 
% 204.90/35.65  | | End of split
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1288 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)  all_58_14 = all_52_23
% 204.90/35.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (3)   ~ (e3 = e0)
% 204.90/35.65    (4)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65    (5)   ~ (all_52_7 = all_52_15)
% 204.90/35.65    (6)  op(all_52_15, all_52_15) = e0
% 204.90/35.65    (7)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.65    (8)  all_58_13 = all_52_15
% 204.90/35.65    (9)   ~ (all_52_15 = e3)
% 204.90/35.65    (10)  op(e2, e2) = all_4_2
% 204.90/35.65    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.90/35.65    (12)  op(all_10_2, e1) = all_10_1
% 204.90/35.65    (13)  op(e0, e1) = all_52_23
% 204.90/35.65    (14)   ~ (all_52_15 = e0)
% 204.90/35.65    (15)  all_58_15 = e0
% 204.90/35.65    (16)   ~ (e2 = e1)
% 204.90/35.65    (17)  op(e0, e0) = e0
% 204.90/35.65    (18)  all_58_12 = all_52_7
% 204.90/35.65    (19)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.65    (20)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.65    (21)  all_56_12 = all_52_7
% 204.90/35.65    (22)  op(all_4_2, all_4_2) = e2
% 204.90/35.65    (23)   ~ (all_10_1 = e3)
% 204.90/35.65    (24)   ~ (all_52_15 = all_4_2)
% 204.90/35.65    (25)  op(e1, e1) = all_10_2
% 204.90/35.65    (26)   ~ (all_52_7 = all_52_23)
% 204.90/35.65    (27)  all_56_13 = all_52_15
% 204.90/35.65    (28)   ~ (all_52_7 = e0)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (7) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (29)  all_58_13 = e3
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (8), (9), (29) are inconsistent by sub-proof #1360.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (30)  all_58_14 = e3 | all_58_15 = e3
% 204.90/35.65  | | 
% 204.90/35.65  | | BETA: splitting (30) gives:
% 204.90/35.65  | | 
% 204.90/35.65  | | Case 1:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (31)  all_58_14 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | COMBINE_EQS: (1), (31) imply:
% 204.90/35.65  | | |   (32)  all_52_23 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | SIMP: (32) implies:
% 204.90/35.65  | | |   (33)  all_52_23 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (26), (33) imply:
% 204.90/35.65  | | |   (34)   ~ (all_52_7 = e3)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (13), (33) imply:
% 204.90/35.65  | | |   (35)  op(e0, e1) = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (14), (16), (17),
% 204.90/35.65  | | |            (18), (19), (20), (21), (22), (23), (24), (25), (27), (28),
% 204.90/35.65  | | |            (34), (35) are inconsistent by sub-proof #1289.
% 204.90/35.65  | | | 
% 204.90/35.65  | | Case 2:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (36)  all_58_15 = e3
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (3), (15), (36) are inconsistent by sub-proof #1350.
% 204.90/35.65  | | | 
% 204.90/35.65  | | End of split
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1289 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65    (3)   ~ (all_52_7 = all_52_15)
% 204.90/35.65    (4)  op(all_52_15, all_52_15) = e0
% 204.90/35.65    (5)  all_58_13 = all_52_15
% 204.90/35.65    (6)  op(e2, e2) = all_4_2
% 204.90/35.65    (7)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.90/35.65    (8)  op(all_10_2, e1) = all_10_1
% 204.90/35.65    (9)   ~ (all_52_15 = e0)
% 204.90/35.65    (10)   ~ (e2 = e1)
% 204.90/35.65    (11)  op(e0, e0) = e0
% 204.90/35.65    (12)  all_58_12 = all_52_7
% 204.90/35.65    (13)   ~ (all_52_7 = e3)
% 204.90/35.65    (14)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.65    (15)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.65    (16)  all_56_12 = all_52_7
% 204.90/35.65    (17)  op(all_4_2, all_4_2) = e2
% 204.90/35.65    (18)   ~ (all_10_1 = e3)
% 204.90/35.65    (19)   ~ (all_52_15 = all_4_2)
% 204.90/35.65    (20)  op(e1, e1) = all_10_2
% 204.90/35.65    (21)  all_56_13 = all_52_15
% 204.90/35.65    (22)  op(e0, e1) = e3
% 204.90/35.65    (23)   ~ (all_52_7 = e0)
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (2) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (24)  all_56_12 = e3
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (13), (16), (24) are inconsistent by sub-proof #1383.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (25)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65  | | 
% 204.90/35.65  | | BETA: splitting (15) gives:
% 204.90/35.65  | | 
% 204.90/35.65  | | Case 1:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (26)  all_58_12 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | COMBINE_EQS: (12), (26) imply:
% 204.90/35.65  | | |   (27)  all_52_7 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | SIMP: (27) implies:
% 204.90/35.65  | | |   (28)  all_52_7 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (3), (28) imply:
% 204.90/35.65  | | |   (29)   ~ (all_52_15 = e1)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | SIMP: (29) implies:
% 204.90/35.65  | | |   (30)   ~ (all_52_15 = e1)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (14), (17), (19),
% 204.90/35.65  | | |            (21), (26), (30) are inconsistent by sub-proof #1290.
% 204.90/35.65  | | | 
% 204.90/35.65  | | Case 2:
% 204.90/35.65  | | | 
% 204.90/35.65  | | |   (31)   ~ (all_58_12 = e1)
% 204.90/35.65  | | |   (32)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.65  | | | 
% 204.90/35.65  | | | REDUCE: (12), (31) imply:
% 204.90/35.65  | | |   (33)   ~ (all_52_7 = e1)
% 204.90/35.65  | | | 
% 204.90/35.65  | | | BETA: splitting (25) gives:
% 204.90/35.65  | | | 
% 204.90/35.65  | | | Case 1:
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | |   (34)  all_56_12 = e2
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | COMBINE_EQS: (16), (34) imply:
% 204.90/35.65  | | | |   (35)  all_52_7 = e2
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | SIMP: (35) implies:
% 204.90/35.65  | | | |   (36)  all_52_7 = e2
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | REDUCE: (3), (36) imply:
% 204.90/35.65  | | | |   (37)   ~ (all_52_15 = e2)
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | SIMP: (37) implies:
% 204.90/35.65  | | | |   (38)   ~ (all_52_15 = e2)
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | BETA: splitting (32) gives:
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | Case 1:
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | |   (39)  all_58_13 = e1
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | COMBINE_EQS: (5), (39) imply:
% 204.90/35.65  | | | | |   (40)  all_52_15 = e1
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | SIMP: (40) implies:
% 204.90/35.65  | | | | |   (41)  all_52_15 = e1
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REDUCE: (4), (41) imply:
% 204.90/35.65  | | | | |   (42)  op(e1, e1) = e0
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REF_CLOSE: (1), (8), (18), (20), (22), (42) are inconsistent by
% 204.90/35.65  | | | | |            sub-proof #1359.
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | Case 2:
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | |   (43)   ~ (all_58_13 = e1)
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REDUCE: (5), (43) imply:
% 204.90/35.65  | | | | |   (44)   ~ (all_52_15 = e1)
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | | REF_CLOSE: (9), (14), (21), (38), (44) are inconsistent by sub-proof
% 204.90/35.65  | | | | |            #1353.
% 204.90/35.65  | | | | | 
% 204.90/35.65  | | | | End of split
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | Case 2:
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | |   (45)  all_56_12 = e1 | all_56_12 = e0
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | | REF_CLOSE: (16), (23), (33), (45) are inconsistent by sub-proof #1374.
% 204.90/35.65  | | | | 
% 204.90/35.65  | | | End of split
% 204.90/35.65  | | | 
% 204.90/35.65  | | End of split
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1290 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ~ (all_52_15 = e1)
% 204.90/35.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (3)  op(all_52_15, all_52_15) = e0
% 204.90/35.65    (4)  all_58_13 = all_52_15
% 204.90/35.65    (5)  op(e2, e2) = all_4_2
% 204.90/35.65    (6)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.90/35.65    (7)   ~ (all_52_15 = e0)
% 204.90/35.65    (8)   ~ (e2 = e1)
% 204.90/35.65    (9)  op(e0, e0) = e0
% 204.90/35.65    (10)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.65    (11)  op(all_4_2, all_4_2) = e2
% 204.90/35.65    (12)   ~ (all_52_15 = all_4_2)
% 204.90/35.65    (13)  all_58_12 = e1
% 204.90/35.65    (14)  all_56_13 = all_52_15
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (6) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (15)  all_58_12 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | COMBINE_EQS: (13), (15) imply:
% 204.90/35.65  | |   (16)  e2 = e1
% 204.90/35.65  | | 
% 204.90/35.65  | | REDUCE: (8), (16) imply:
% 204.90/35.65  | |   (17)  $false
% 204.90/35.65  | | 
% 204.90/35.65  | | CLOSE: (17) is inconsistent.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (18)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (14), (18)
% 204.90/35.65  | |            are inconsistent by sub-proof #1291.
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1291 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ~ (all_52_15 = e1)
% 204.90/35.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (3)  op(all_52_15, all_52_15) = e0
% 204.90/35.65    (4)  all_58_13 = all_52_15
% 204.90/35.65    (5)  op(e2, e2) = all_4_2
% 204.90/35.65    (6)   ~ (all_52_15 = e0)
% 204.90/35.65    (7)  op(e0, e0) = e0
% 204.90/35.65    (8)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 204.90/35.65    (9)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.65    (10)  op(all_4_2, all_4_2) = e2
% 204.90/35.65    (11)   ~ (all_52_15 = all_4_2)
% 204.90/35.65    (12)  all_56_13 = all_52_15
% 204.90/35.65  
% 204.90/35.65  Begin of proof
% 204.90/35.65  | 
% 204.90/35.65  | BETA: splitting (8) gives:
% 204.90/35.65  | 
% 204.90/35.65  | Case 1:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (13)  all_58_13 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | COMBINE_EQS: (4), (13) imply:
% 204.90/35.65  | |   (14)  all_52_15 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | SIMP: (14) implies:
% 204.90/35.65  | |   (15)  all_52_15 = e2
% 204.90/35.65  | | 
% 204.90/35.65  | | REDUCE: (11), (15) imply:
% 204.90/35.65  | |   (16)   ~ (all_4_2 = e2)
% 204.90/35.65  | | 
% 204.90/35.65  | | SIMP: (16) implies:
% 204.90/35.65  | |   (17)   ~ (all_4_2 = e2)
% 204.90/35.65  | | 
% 204.90/35.65  | | REDUCE: (3), (15) imply:
% 204.90/35.65  | |   (18)  op(e2, e2) = e0
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (2), (5), (7), (10), (17), (18) are inconsistent by sub-proof
% 204.90/35.65  | |            #1317.
% 204.90/35.65  | | 
% 204.90/35.65  | Case 2:
% 204.90/35.65  | | 
% 204.90/35.65  | |   (19)   ~ (all_58_13 = e2)
% 204.90/35.65  | | 
% 204.90/35.65  | | REDUCE: (4), (19) imply:
% 204.90/35.65  | |   (20)   ~ (all_52_15 = e2)
% 204.90/35.65  | | 
% 204.90/35.65  | | REF_CLOSE: (1), (6), (9), (12), (20) are inconsistent by sub-proof #1353.
% 204.90/35.65  | | 
% 204.90/35.65  | End of split
% 204.90/35.65  | 
% 204.90/35.65  End of proof
% 204.90/35.65  
% 204.90/35.65  Sub-proof #1292 shows that the following formulas are inconsistent:
% 204.90/35.65  ----------------------------------------------------------------
% 204.90/35.65    (1)   ~ (all_52_25 = all_52_27)
% 204.90/35.65    (2)  all_58_14 = all_52_23
% 204.90/35.65    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.90/35.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.65    (5)   ~ (all_52_5 = all_52_13)
% 204.90/35.65    (6)  all_58_1 = all_52_9
% 204.90/35.65    (7)   ~ (all_52_9 = all_52_13)
% 204.90/35.65    (8)   ~ (all_52_7 = all_52_15)
% 204.90/35.65    (9)   ~ (all_52_17 = all_52_25)
% 204.90/35.65    (10)   ~ (all_52_3 = all_6_2)
% 204.90/35.65    (11)  all_58_0 = all_6_2
% 204.90/35.65    (12)  all_56_4 = all_52_3
% 204.90/35.65    (13)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.90/35.65    (14)  op(all_52_19, all_52_19) = all_52_18
% 204.90/35.65    (15)  all_58_13 = all_52_15
% 204.90/35.65    (16)  op(all_52_13, all_52_13) = e1
% 204.90/35.65    (17)  op(all_10_2, all_10_2) = all_52_20
% 204.90/35.65    (18)  all_58_9 = all_52_25
% 204.90/35.65    (19)  op(all_52_27, all_52_27) = all_52_26
% 204.90/35.65    (20)  op(e1, e3) = all_52_5
% 204.90/35.65    (21)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.65    (22)  op(e2, e2) = all_4_2
% 204.90/35.65    (23)   ~ (all_52_3 = all_52_5)
% 204.90/35.65    (24)  all_58_11 = all_52_29
% 204.90/35.65    (25)  all_56_5 = all_4_2
% 204.90/35.65    (26)   ~ (all_52_7 = all_6_2)
% 204.90/35.65    (27)  all_58_15 = e0
% 204.90/35.65    (28)   ~ (all_4_1 = e1)
% 204.90/35.65    (29)   ~ (all_52_25 = e0)
% 204.90/35.65    (30)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.65    (31)   ~ (all_52_13 = all_10_2)
% 204.90/35.65    (32)  op(e0, e0) = e0
% 204.90/35.65    (33)  all_58_10 = all_52_27
% 204.90/35.65    (34)  all_56_8 = all_52_5
% 204.90/35.65    (35)   ~ (all_52_25 = all_52_29)
% 204.90/35.65    (36)  all_58_7 = all_52_13
% 204.90/35.65    (37)   ~ (all_52_5 = all_52_7)
% 204.90/35.65    (38)  all_58_12 = all_52_7
% 204.90/35.65    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.65    (40)  all_56_2 = all_52_17
% 204.90/35.65    (41)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.65    (42)  all_56_7 = all_52_27
% 204.90/35.65    (43)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.90/35.65    (44)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.90/35.66    (45)  op(all_4_2, e2) = all_4_1
% 204.90/35.66    (46)   ~ (all_52_13 = all_4_2)
% 204.90/35.66    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66    (48)   ~ (all_52_9 = all_52_25)
% 204.90/35.66    (49)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.90/35.66    (50)  all_58_8 = all_10_2
% 204.90/35.66    (51)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.66    (52)   ~ (all_52_25 = all_6_2)
% 204.90/35.66    (53)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.66    (54)   ~ (all_52_9 = all_4_2)
% 204.90/35.66    (55)   ~ (all_52_5 = all_6_2)
% 204.90/35.66    (56)  op(all_4_2, all_4_2) = e2
% 204.90/35.66    (57)   ~ (all_52_9 = all_6_2)
% 204.90/35.66    (58)   ~ (all_52_13 = all_52_15)
% 204.90/35.66    (59)  op(e3, e3) = all_6_2
% 204.90/35.66    (60)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.66    (61)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66    (62)  all_56_3 = all_52_25
% 204.90/35.66    (63)   ~ (all_52_3 = all_52_7)
% 204.90/35.66    (64)  all_58_5 = all_52_19
% 204.90/35.66    (65)  all_56_1 = all_52_9
% 204.90/35.66    (66)   ~ (all_52_27 = all_4_2)
% 204.90/35.66    (67)  all_58_6 = all_52_5
% 204.90/35.66    (68)  op(e3, e2) = all_52_9
% 204.90/35.66    (69)   ~ (all_52_17 = all_6_2)
% 204.90/35.66    (70)   ~ (e1 = e0)
% 204.90/35.66    (71)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.66    (72)   ~ (all_52_9 = all_52_17)
% 204.90/35.66    (73)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66    (74)  all_58_12 = e3
% 204.90/35.66    (75)   ~ (all_6_1 = e2)
% 204.90/35.66    (76)  op(all_52_9, all_52_9) = e3
% 204.90/35.66    (77)   ~ (all_52_7 = all_52_23)
% 204.90/35.66    (78)  all_58_3 = all_4_2
% 204.90/35.66    (79)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.90/35.66    (80)   ~ (all_52_3 = all_4_2)
% 204.90/35.66    (81)   ~ (all_52_19 = all_4_2)
% 204.90/35.66    (82)  op(all_6_2, e3) = all_6_1
% 204.90/35.66    (83)   ~ (all_52_13 = all_52_29)
% 204.90/35.66    (84)  all_58_4 = all_52_17
% 204.90/35.66    (85)   ~ (all_52_7 = e0)
% 204.90/35.66    (86)  op(all_52_25, all_52_25) = all_52_24
% 204.90/35.66  
% 204.90/35.66  Begin of proof
% 204.90/35.66  | 
% 204.90/35.66  | COMBINE_EQS: (38), (74) imply:
% 204.90/35.66  |   (87)  all_52_7 = e3
% 204.90/35.66  | 
% 204.90/35.66  | SIMP: (87) implies:
% 204.90/35.66  |   (88)  all_52_7 = e3
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (63), (88) imply:
% 204.90/35.66  |   (89)   ~ (all_52_3 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (37), (88) imply:
% 204.90/35.66  |   (90)   ~ (all_52_5 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (8), (88) imply:
% 204.90/35.66  |   (91)   ~ (all_52_15 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | SIMP: (91) implies:
% 204.90/35.66  |   (92)   ~ (all_52_15 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (77), (88) imply:
% 204.90/35.66  |   (93)   ~ (all_52_23 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | SIMP: (93) implies:
% 204.90/35.66  |   (94)   ~ (all_52_23 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (26), (88) imply:
% 204.90/35.66  |   (95)   ~ (all_6_2 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | SIMP: (95) implies:
% 204.90/35.66  |   (96)   ~ (all_6_2 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (85), (88) imply:
% 204.90/35.66  |   (97)   ~ (e3 = e0)
% 204.90/35.66  | 
% 204.90/35.66  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 204.90/35.66  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 204.90/35.66  |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 204.90/35.66  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 204.90/35.66  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 204.90/35.66  |            (61), (62), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 204.90/35.66  |            (73), (75), (76), (78), (79), (80), (81), (82), (83), (84), (86),
% 204.90/35.66  |            (89), (90), (92), (94), (96), (97) are inconsistent by sub-proof
% 204.90/35.66  |            #1293.
% 204.90/35.66  | 
% 204.90/35.66  End of proof
% 204.90/35.66  
% 204.90/35.66  Sub-proof #1293 shows that the following formulas are inconsistent:
% 204.90/35.66  ----------------------------------------------------------------
% 204.90/35.66    (1)   ~ (all_52_25 = all_52_27)
% 204.90/35.66    (2)  all_58_14 = all_52_23
% 204.90/35.66    (3)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.90/35.66    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.66    (5)   ~ (all_52_5 = all_52_13)
% 204.90/35.66    (6)  all_58_1 = all_52_9
% 204.90/35.66    (7)   ~ (all_52_9 = all_52_13)
% 204.90/35.66    (8)   ~ (e3 = e0)
% 204.90/35.66    (9)   ~ (all_52_17 = all_52_25)
% 204.90/35.66    (10)   ~ (all_52_3 = all_6_2)
% 204.90/35.66    (11)  all_58_0 = all_6_2
% 204.90/35.66    (12)  all_56_4 = all_52_3
% 204.90/35.66    (13)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 204.90/35.66    (14)  op(all_52_19, all_52_19) = all_52_18
% 204.90/35.66    (15)  all_58_13 = all_52_15
% 204.90/35.66    (16)  op(all_52_13, all_52_13) = e1
% 204.90/35.66    (17)  op(all_10_2, all_10_2) = all_52_20
% 204.90/35.66    (18)  all_58_9 = all_52_25
% 204.90/35.66    (19)   ~ (all_52_15 = e3)
% 204.90/35.66    (20)  op(all_52_27, all_52_27) = all_52_26
% 204.90/35.66    (21)  op(e1, e3) = all_52_5
% 204.90/35.66    (22)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.66    (23)  op(e2, e2) = all_4_2
% 204.90/35.66    (24)   ~ (all_52_3 = all_52_5)
% 204.90/35.66    (25)  all_58_11 = all_52_29
% 204.90/35.66    (26)   ~ (all_52_3 = e3)
% 204.90/35.66    (27)  all_56_5 = all_4_2
% 204.90/35.66    (28)  all_58_15 = e0
% 204.90/35.66    (29)   ~ (all_4_1 = e1)
% 204.90/35.66    (30)   ~ (all_52_25 = e0)
% 204.90/35.66    (31)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.66    (32)   ~ (all_6_2 = e3)
% 204.90/35.66    (33)   ~ (all_52_13 = all_10_2)
% 204.90/35.66    (34)  op(e0, e0) = e0
% 204.90/35.66    (35)  all_58_10 = all_52_27
% 204.90/35.66    (36)  all_56_8 = all_52_5
% 204.90/35.66    (37)   ~ (all_52_25 = all_52_29)
% 204.90/35.66    (38)  all_58_7 = all_52_13
% 204.90/35.66    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.66    (40)  all_56_2 = all_52_17
% 204.90/35.66    (41)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.66    (42)  all_56_7 = all_52_27
% 204.90/35.66    (43)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.90/35.66    (44)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.90/35.66    (45)  op(all_4_2, e2) = all_4_1
% 204.90/35.66    (46)   ~ (all_52_23 = e3)
% 204.90/35.66    (47)   ~ (all_52_5 = e3)
% 204.90/35.66    (48)   ~ (all_52_13 = all_4_2)
% 204.90/35.66    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66    (50)   ~ (all_52_9 = all_52_25)
% 204.90/35.66    (51)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.90/35.66    (52)  all_58_8 = all_10_2
% 204.90/35.66    (53)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.66    (54)   ~ (all_52_25 = all_6_2)
% 204.90/35.66    (55)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.66    (56)   ~ (all_52_9 = all_4_2)
% 204.90/35.66    (57)   ~ (all_52_5 = all_6_2)
% 204.90/35.66    (58)  op(all_4_2, all_4_2) = e2
% 204.90/35.66    (59)   ~ (all_52_9 = all_6_2)
% 204.90/35.66    (60)   ~ (all_52_13 = all_52_15)
% 204.90/35.66    (61)  op(e3, e3) = all_6_2
% 204.90/35.66    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.66    (63)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66    (64)  all_56_3 = all_52_25
% 204.90/35.66    (65)  all_58_5 = all_52_19
% 204.90/35.66    (66)  all_56_1 = all_52_9
% 204.90/35.66    (67)   ~ (all_52_27 = all_4_2)
% 204.90/35.66    (68)  all_58_6 = all_52_5
% 204.90/35.66    (69)  op(e3, e2) = all_52_9
% 204.90/35.66    (70)   ~ (all_52_17 = all_6_2)
% 204.90/35.66    (71)   ~ (e1 = e0)
% 204.90/35.66    (72)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.66    (73)   ~ (all_52_9 = all_52_17)
% 204.90/35.66    (74)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66    (75)   ~ (all_6_1 = e2)
% 204.90/35.66    (76)  op(all_52_9, all_52_9) = e3
% 204.90/35.66    (77)  all_58_3 = all_4_2
% 204.90/35.66    (78)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.90/35.66    (79)   ~ (all_52_3 = all_4_2)
% 204.90/35.66    (80)   ~ (all_52_19 = all_4_2)
% 204.90/35.66    (81)  op(all_6_2, e3) = all_6_1
% 204.90/35.66    (82)   ~ (all_52_13 = all_52_29)
% 204.90/35.66    (83)  all_58_4 = all_52_17
% 204.90/35.66    (84)  op(all_52_25, all_52_25) = all_52_24
% 204.90/35.66  
% 204.90/35.66  Begin of proof
% 204.90/35.66  | 
% 204.90/35.66  | BETA: splitting (43) gives:
% 204.90/35.66  | 
% 204.90/35.66  | Case 1:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (85)  all_56_4 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REF_CLOSE: (12), (26), (85) are inconsistent by sub-proof #1340.
% 204.90/35.66  | | 
% 204.90/35.66  | Case 2:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (86)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.90/35.66  | | 
% 204.90/35.66  | | BETA: splitting (13) gives:
% 204.90/35.66  | | 
% 204.90/35.66  | | Case 1:
% 204.90/35.66  | | | 
% 204.90/35.66  | | |   (87)  all_56_7 = e3
% 204.90/35.66  | | | 
% 204.90/35.66  | | | COMBINE_EQS: (42), (87) imply:
% 204.90/35.66  | | |   (88)  all_52_27 = e3
% 204.90/35.66  | | | 
% 204.90/35.66  | | | SIMP: (88) implies:
% 204.90/35.66  | | |   (89)  all_52_27 = e3
% 204.90/35.66  | | | 
% 204.90/35.66  | | | REDUCE: (1), (89) imply:
% 204.90/35.66  | | |   (90)   ~ (all_52_25 = e3)
% 204.90/35.66  | | | 
% 204.90/35.66  | | | REDUCE: (67), (89) imply:
% 204.90/35.66  | | |   (91)   ~ (all_4_2 = e3)
% 204.90/35.66  | | | 
% 204.90/35.66  | | | SIMP: (91) implies:
% 204.90/35.66  | | |   (92)   ~ (all_4_2 = e3)
% 204.90/35.66  | | | 
% 204.90/35.66  | | | REDUCE: (20), (89) imply:
% 204.90/35.66  | | |   (93)  op(e3, e3) = all_52_26
% 204.90/35.66  | | | 
% 204.90/35.66  | | | GROUND_INST: instantiating (4) with all_6_2, all_52_26, e3, e3,
% 204.90/35.66  | | |              simplifying with (61), (93) gives:
% 204.90/35.66  | | |   (94)  all_52_26 = all_6_2
% 204.90/35.66  | | | 
% 204.90/35.66  | | | BETA: splitting (55) gives:
% 204.90/35.66  | | | 
% 204.90/35.66  | | | Case 1:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | |   (95)  all_56_3 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REF_CLOSE: (64), (90), (95) are inconsistent by sub-proof #1339.
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | Case 2:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | |   (96)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | BETA: splitting (49) gives:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | Case 1:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | |   (97)  all_58_1 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | COMBINE_EQS: (6), (97) imply:
% 204.90/35.66  | | | | |   (98)  all_52_9 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | REF_CLOSE: (4), (59), (61), (76), (98) are inconsistent by sub-proof
% 204.90/35.66  | | | | |            #1337.
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | Case 2:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | |   (99)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | BETA: splitting (99) gives:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | Case 1:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | |   (100)  all_58_3 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | COMBINE_EQS: (77), (100) imply:
% 204.90/35.66  | | | | | |   (101)  all_4_2 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | REDUCE: (92), (101) imply:
% 204.90/35.66  | | | | | |   (102)  $false
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | CLOSE: (102) is inconsistent.
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | Case 2:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | |   (103)  all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | BETA: splitting (103) gives:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | Case 1:
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | |   (104)  all_58_7 = e3
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | COMBINE_EQS: (38), (104) imply:
% 204.90/35.66  | | | | | | |   (105)  all_52_13 = e3
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | REDUCE: (7), (105) imply:
% 204.90/35.66  | | | | | | |   (106)   ~ (all_52_9 = e3)
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | REDUCE: (60), (105) imply:
% 204.90/35.66  | | | | | | |   (107)   ~ (all_52_15 = e3)
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | REDUCE: (82), (105) imply:
% 204.90/35.66  | | | | | | |   (108)   ~ (all_52_29 = e3)
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | SIMP: (108) implies:
% 204.90/35.66  | | | | | | |   (109)   ~ (all_52_29 = e3)
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | REDUCE: (16), (105) imply:
% 204.90/35.66  | | | | | | |   (110)  op(e3, e3) = e1
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | BETA: splitting (74) gives:
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | Case 1:
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | |   (111)  all_58_4 = e3
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | | COMBINE_EQS: (83), (111) imply:
% 204.90/35.66  | | | | | | | |   (112)  all_52_17 = e3
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | | SIMP: (112) implies:
% 204.90/35.66  | | | | | | | |   (113)  all_52_17 = e3
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | | REDUCE: (53), (113) imply:
% 204.90/35.66  | | | | | | | |   (114)  op(e3, e3) = all_52_16
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | | REF_CLOSE: (4), (6), (11), (30), (34), (41), (50), (54), (59),
% 204.90/35.66  | | | | | | | |            (61), (64), (66), (71), (72), (76), (96), (106),
% 204.90/35.66  | | | | | | | |            (110), (114) are inconsistent by sub-proof #1329.
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | Case 2:
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | |   (115)   ~ (all_58_4 = e3)
% 204.90/35.66  | | | | | | | |   (116)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | | REDUCE: (83), (115) imply:
% 204.90/35.66  | | | | | | | |   (117)   ~ (all_52_17 = e3)
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (12), (14),
% 204.90/35.66  | | | | | | | |            (15), (16), (17), (19), (21), (22), (23), (24), (25),
% 204.90/35.66  | | | | | | | |            (27), (29), (31), (33), (34), (36), (38), (39), (40),
% 204.90/35.66  | | | | | | | |            (41), (44), (45), (46), (47), (48), (51), (52), (56),
% 204.90/35.66  | | | | | | | |            (57), (58), (59), (61), (65), (66), (68), (69), (70),
% 204.90/35.66  | | | | | | | |            (72), (73), (75), (76), (77), (78), (79), (80), (81),
% 204.90/35.66  | | | | | | | |            (83), (86), (99), (106), (109), (116), (117) are
% 204.90/35.66  | | | | | | | |            inconsistent by sub-proof #1303.
% 204.90/35.66  | | | | | | | | 
% 204.90/35.66  | | | | | | | End of split
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | Case 2:
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | |   (118)  all_58_13 = e3
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | | REF_CLOSE: (15), (19), (118) are inconsistent by sub-proof #1360.
% 204.90/35.66  | | | | | | | 
% 204.90/35.66  | | | | | | End of split
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | End of split
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | End of split
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | End of split
% 204.90/35.66  | | | 
% 204.90/35.66  | | Case 2:
% 204.90/35.66  | | | 
% 204.90/35.66  | | |   (119)   ~ (all_56_7 = e3)
% 204.90/35.66  | | | 
% 204.90/35.66  | | | REDUCE: (42), (119) imply:
% 204.90/35.66  | | |   (120)   ~ (all_52_27 = e3)
% 204.90/35.66  | | | 
% 204.90/35.66  | | | BETA: splitting (62) gives:
% 204.90/35.66  | | | 
% 204.90/35.66  | | | Case 1:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | |   (121)  all_58_9 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | COMBINE_EQS: (18), (121) imply:
% 204.90/35.66  | | | |   (122)  all_52_25 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | SIMP: (122) implies:
% 204.90/35.66  | | | |   (123)  all_52_25 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REDUCE: (50), (123) imply:
% 204.90/35.66  | | | |   (124)   ~ (all_52_9 = e3)
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REDUCE: (9), (123) imply:
% 204.90/35.66  | | | |   (125)   ~ (all_52_17 = e3)
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REDUCE: (37), (123) imply:
% 204.90/35.66  | | | |   (126)   ~ (all_52_29 = e3)
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | SIMP: (126) implies:
% 204.90/35.66  | | | |   (127)   ~ (all_52_29 = e3)
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REDUCE: (84), (123) imply:
% 204.90/35.66  | | | |   (128)  op(e3, e3) = all_52_24
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | GROUND_INST: instantiating (4) with all_6_2, all_52_24, e3, e3,
% 204.90/35.66  | | | |              simplifying with (61), (128) gives:
% 204.90/35.66  | | | |   (129)  all_52_24 = all_6_2
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | BETA: splitting (49) gives:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | Case 1:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | |   (130)  all_58_1 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | COMBINE_EQS: (6), (130) imply:
% 204.90/35.66  | | | | |   (131)  all_52_9 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | REDUCE: (124), (131) imply:
% 204.90/35.66  | | | | |   (132)  $false
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | CLOSE: (132) is inconsistent.
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | Case 2:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | |   (133)   ~ (all_58_1 = e3)
% 204.90/35.66  | | | | |   (134)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | BETA: splitting (74) gives:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | Case 1:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | |   (135)  all_58_4 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | REF_CLOSE: (83), (125), (135) are inconsistent by sub-proof #1302.
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | Case 2:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | |   (136)   ~ (all_58_4 = e3)
% 204.90/35.66  | | | | | |   (137)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (12), (14), (15),
% 204.90/35.66  | | | | | |            (16), (17), (19), (21), (22), (23), (24), (25), (27),
% 204.90/35.66  | | | | | |            (29), (31), (33), (34), (36), (38), (39), (40), (41),
% 204.90/35.66  | | | | | |            (44), (45), (46), (47), (48), (51), (52), (56), (57),
% 204.90/35.66  | | | | | |            (58), (59), (61), (65), (66), (68), (69), (70), (72),
% 204.90/35.66  | | | | | |            (73), (75), (76), (77), (78), (79), (80), (81), (83),
% 204.90/35.66  | | | | | |            (86), (124), (125), (127), (134), (137) are inconsistent
% 204.90/35.66  | | | | | |            by sub-proof #1303.
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | End of split
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | End of split
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | Case 2:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | |   (138)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REF_CLOSE: (4), (6), (8), (11), (15), (18), (19), (25), (28), (29),
% 204.90/35.66  | | | |            (32), (34), (35), (37), (38), (45), (49), (53), (58), (59),
% 204.90/35.66  | | | |            (61), (63), (66), (69), (72), (73), (74), (76), (77), (82),
% 204.90/35.66  | | | |            (83), (120), (138) are inconsistent by sub-proof #1294.
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | End of split
% 204.90/35.66  | | | 
% 204.90/35.66  | | End of split
% 204.90/35.66  | | 
% 204.90/35.66  | End of split
% 204.90/35.66  | 
% 204.90/35.66  End of proof
% 204.90/35.66  
% 204.90/35.66  Sub-proof #1294 shows that the following formulas are inconsistent:
% 204.90/35.66  ----------------------------------------------------------------
% 204.90/35.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.66    (2)  all_58_1 = all_52_9
% 204.90/35.66    (3)   ~ (e3 = e0)
% 204.90/35.66    (4)  all_58_0 = all_6_2
% 204.90/35.66    (5)  all_58_13 = all_52_15
% 204.90/35.66    (6)  all_58_9 = all_52_25
% 204.90/35.66    (7)   ~ (all_52_15 = e3)
% 204.90/35.66    (8)  all_58_11 = all_52_29
% 204.90/35.66    (9)  all_58_15 = e0
% 204.90/35.66    (10)   ~ (all_4_1 = e1)
% 204.90/35.66    (11)   ~ (all_6_2 = e3)
% 204.90/35.66    (12)  op(e0, e0) = e0
% 204.90/35.66    (13)  all_58_10 = all_52_27
% 204.90/35.66    (14)   ~ (all_52_25 = all_52_29)
% 204.90/35.66    (15)  all_58_7 = all_52_13
% 204.90/35.66    (16)  op(all_4_2, e2) = all_4_1
% 204.90/35.66    (17)   ~ (all_52_27 = e3)
% 204.90/35.66    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66    (19)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.66    (20)  op(all_4_2, all_4_2) = e2
% 204.90/35.66    (21)   ~ (all_52_9 = all_6_2)
% 204.90/35.66    (22)  op(e3, e3) = all_6_2
% 204.90/35.66    (23)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66    (24)  all_56_1 = all_52_9
% 204.90/35.66    (25)  op(e3, e2) = all_52_9
% 204.90/35.66    (26)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 204.90/35.66    (27)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.66    (28)   ~ (all_52_9 = all_52_17)
% 204.90/35.66    (29)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66    (30)  op(all_52_9, all_52_9) = e3
% 204.90/35.66    (31)  all_58_3 = all_4_2
% 204.90/35.66    (32)   ~ (all_52_13 = all_52_29)
% 204.90/35.66    (33)  all_58_4 = all_52_17
% 204.90/35.66  
% 204.90/35.66  Begin of proof
% 204.90/35.66  | 
% 204.90/35.66  | BETA: splitting (26) gives:
% 204.90/35.66  | 
% 204.90/35.66  | Case 1:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (34)  all_58_10 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REF_CLOSE: (13), (17), (34) are inconsistent by sub-proof #1301.
% 204.90/35.66  | | 
% 204.90/35.66  | Case 2:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (35)  all_58_11 = e3 | all_58_15 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 204.90/35.66  | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.90/35.66  | |            (27), (28), (29), (30), (31), (32), (33), (35) are inconsistent
% 204.90/35.66  | |            by sub-proof #1295.
% 204.90/35.66  | | 
% 204.90/35.66  | End of split
% 204.90/35.66  | 
% 204.90/35.66  End of proof
% 204.90/35.66  
% 204.90/35.66  Sub-proof #1295 shows that the following formulas are inconsistent:
% 204.90/35.66  ----------------------------------------------------------------
% 204.90/35.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.66    (2)  all_58_1 = all_52_9
% 204.90/35.66    (3)   ~ (e3 = e0)
% 204.90/35.66    (4)  all_58_0 = all_6_2
% 204.90/35.66    (5)  all_58_13 = all_52_15
% 204.90/35.66    (6)  all_58_9 = all_52_25
% 204.90/35.66    (7)   ~ (all_52_15 = e3)
% 204.90/35.66    (8)  all_58_11 = all_52_29
% 204.90/35.66    (9)  all_58_15 = e0
% 204.90/35.66    (10)   ~ (all_4_1 = e1)
% 204.90/35.66    (11)   ~ (all_6_2 = e3)
% 204.90/35.66    (12)  op(e0, e0) = e0
% 204.90/35.66    (13)   ~ (all_52_25 = all_52_29)
% 204.90/35.66    (14)  all_58_11 = e3 | all_58_15 = e3
% 204.90/35.66    (15)  all_58_7 = all_52_13
% 204.90/35.66    (16)  op(all_4_2, e2) = all_4_1
% 204.90/35.66    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66    (18)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.66    (19)  op(all_4_2, all_4_2) = e2
% 204.90/35.66    (20)   ~ (all_52_9 = all_6_2)
% 204.90/35.66    (21)  op(e3, e3) = all_6_2
% 204.90/35.66    (22)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66    (23)  all_56_1 = all_52_9
% 204.90/35.66    (24)  op(e3, e2) = all_52_9
% 204.90/35.66    (25)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.66    (26)   ~ (all_52_9 = all_52_17)
% 204.90/35.66    (27)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66    (28)  op(all_52_9, all_52_9) = e3
% 204.90/35.66    (29)  all_58_3 = all_4_2
% 204.90/35.66    (30)   ~ (all_52_13 = all_52_29)
% 204.90/35.66    (31)  all_58_4 = all_52_17
% 204.90/35.66  
% 204.90/35.66  Begin of proof
% 204.90/35.66  | 
% 204.90/35.66  | BETA: splitting (14) gives:
% 204.90/35.66  | 
% 204.90/35.66  | Case 1:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (32)  all_58_11 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | COMBINE_EQS: (8), (32) imply:
% 204.90/35.66  | |   (33)  all_52_29 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (13), (15), (16),
% 204.90/35.66  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 204.90/35.66  | |            (28), (29), (30), (31), (33) are inconsistent by sub-proof #1296.
% 204.90/35.66  | | 
% 204.90/35.66  | Case 2:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (34)  all_58_15 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REF_CLOSE: (3), (9), (34) are inconsistent by sub-proof #1350.
% 204.90/35.66  | | 
% 204.90/35.66  | End of split
% 204.90/35.66  | 
% 204.90/35.66  End of proof
% 204.90/35.66  
% 204.90/35.66  Sub-proof #1296 shows that the following formulas are inconsistent:
% 204.90/35.66  ----------------------------------------------------------------
% 204.90/35.66    (1)  all_52_29 = e3
% 204.90/35.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.66    (3)  all_58_1 = all_52_9
% 204.90/35.66    (4)  all_58_0 = all_6_2
% 204.90/35.66    (5)  all_58_13 = all_52_15
% 204.90/35.66    (6)  all_58_9 = all_52_25
% 204.90/35.66    (7)   ~ (all_52_15 = e3)
% 204.90/35.66    (8)   ~ (all_4_1 = e1)
% 204.90/35.66    (9)   ~ (all_6_2 = e3)
% 204.90/35.66    (10)  op(e0, e0) = e0
% 204.90/35.66    (11)   ~ (all_52_25 = all_52_29)
% 204.90/35.66    (12)  all_58_7 = all_52_13
% 204.90/35.66    (13)  op(all_4_2, e2) = all_4_1
% 204.90/35.66    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66    (15)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.66    (16)  op(all_4_2, all_4_2) = e2
% 204.90/35.66    (17)   ~ (all_52_9 = all_6_2)
% 204.90/35.66    (18)  op(e3, e3) = all_6_2
% 204.90/35.66    (19)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66    (20)  all_56_1 = all_52_9
% 204.90/35.66    (21)  op(e3, e2) = all_52_9
% 204.90/35.66    (22)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.66    (23)   ~ (all_52_9 = all_52_17)
% 204.90/35.66    (24)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66    (25)  op(all_52_9, all_52_9) = e3
% 204.90/35.66    (26)  all_58_3 = all_4_2
% 204.90/35.66    (27)   ~ (all_52_13 = all_52_29)
% 204.90/35.66    (28)  all_58_4 = all_52_17
% 204.90/35.66  
% 204.90/35.66  Begin of proof
% 204.90/35.66  | 
% 204.90/35.66  | SIMP: (1) implies:
% 204.90/35.66  |   (29)  all_52_29 = e3
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (27), (29) imply:
% 204.90/35.66  |   (30)   ~ (all_52_13 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REDUCE: (11), (29) imply:
% 204.90/35.66  |   (31)   ~ (all_52_25 = e3)
% 204.90/35.66  | 
% 204.90/35.66  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 204.90/35.66  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 204.90/35.66  |            (26), (28), (30), (31) are inconsistent by sub-proof #1297.
% 204.90/35.66  | 
% 204.90/35.66  End of proof
% 204.90/35.66  
% 204.90/35.66  Sub-proof #1297 shows that the following formulas are inconsistent:
% 204.90/35.66  ----------------------------------------------------------------
% 204.90/35.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.66    (2)  all_58_1 = all_52_9
% 204.90/35.66    (3)  all_58_0 = all_6_2
% 204.90/35.66    (4)  all_58_13 = all_52_15
% 204.90/35.66    (5)  all_58_9 = all_52_25
% 204.90/35.66    (6)   ~ (all_52_15 = e3)
% 204.90/35.66    (7)   ~ (all_4_1 = e1)
% 204.90/35.66    (8)   ~ (all_6_2 = e3)
% 204.90/35.66    (9)  op(e0, e0) = e0
% 204.90/35.66    (10)  all_58_7 = all_52_13
% 204.90/35.66    (11)   ~ (all_52_25 = e3)
% 204.90/35.66    (12)  op(all_4_2, e2) = all_4_1
% 204.90/35.66    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66    (14)  op(all_52_17, all_52_17) = all_52_16
% 204.90/35.66    (15)  op(all_4_2, all_4_2) = e2
% 204.90/35.66    (16)   ~ (all_52_9 = all_6_2)
% 204.90/35.66    (17)  op(e3, e3) = all_6_2
% 204.90/35.66    (18)   ~ (all_52_13 = e3)
% 204.90/35.66    (19)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66    (20)  all_56_1 = all_52_9
% 204.90/35.66    (21)  op(e3, e2) = all_52_9
% 204.90/35.66    (22)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.66    (23)   ~ (all_52_9 = all_52_17)
% 204.90/35.66    (24)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.66    (25)  op(all_52_9, all_52_9) = e3
% 204.90/35.66    (26)  all_58_3 = all_4_2
% 204.90/35.66    (27)  all_58_4 = all_52_17
% 204.90/35.66  
% 204.90/35.66  Begin of proof
% 204.90/35.66  | 
% 204.90/35.66  | BETA: splitting (13) gives:
% 204.90/35.66  | 
% 204.90/35.66  | Case 1:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (28)  all_58_1 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | COMBINE_EQS: (2), (28) imply:
% 204.90/35.66  | |   (29)  all_52_9 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REF_CLOSE: (1), (16), (17), (25), (29) are inconsistent by sub-proof #1337.
% 204.90/35.66  | | 
% 204.90/35.66  | Case 2:
% 204.90/35.66  | | 
% 204.90/35.66  | |   (30)   ~ (all_58_1 = e3)
% 204.90/35.66  | |   (31)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.66  | | 
% 204.90/35.66  | | REDUCE: (2), (30) imply:
% 204.90/35.66  | |   (32)   ~ (all_52_9 = e3)
% 204.90/35.66  | | 
% 204.90/35.66  | | BETA: splitting (19) gives:
% 204.90/35.66  | | 
% 204.90/35.66  | | Case 1:
% 204.90/35.66  | | | 
% 204.90/35.66  | | |   (33)  all_58_0 = e3
% 204.90/35.66  | | | 
% 204.90/35.66  | | | COMBINE_EQS: (3), (33) imply:
% 204.90/35.66  | | |   (34)  all_6_2 = e3
% 204.90/35.66  | | | 
% 204.90/35.66  | | | REDUCE: (8), (34) imply:
% 204.90/35.66  | | |   (35)  $false
% 204.90/35.66  | | | 
% 204.90/35.66  | | | CLOSE: (35) is inconsistent.
% 204.90/35.66  | | | 
% 204.90/35.66  | | Case 2:
% 204.90/35.66  | | | 
% 204.90/35.66  | | |   (36)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66  | | | 
% 204.90/35.66  | | | BETA: splitting (36) gives:
% 204.90/35.66  | | | 
% 204.90/35.66  | | | Case 1:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | |   (37)  all_58_1 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | COMBINE_EQS: (2), (37) imply:
% 204.90/35.66  | | | |   (38)  all_52_9 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | REDUCE: (32), (38) imply:
% 204.90/35.66  | | | |   (39)  $false
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | CLOSE: (39) is inconsistent.
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | Case 2:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | |   (40)  all_58_4 = e3 | all_58_9 = e3
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | BETA: splitting (31) gives:
% 204.90/35.66  | | | | 
% 204.90/35.66  | | | | Case 1:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | |   (41)  all_58_3 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | COMBINE_EQS: (26), (41) imply:
% 204.90/35.66  | | | | |   (42)  all_4_2 = e3
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | REDUCE: (15), (42) imply:
% 204.90/35.66  | | | | |   (43)  op(e3, e3) = e2
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | REDUCE: (12), (42) imply:
% 204.90/35.66  | | | | |   (44)  op(e3, e2) = all_4_1
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | BETA: splitting (24) gives:
% 204.90/35.66  | | | | | 
% 204.90/35.66  | | | | | Case 1:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | |   (45)  all_58_4 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | COMBINE_EQS: (27), (45) imply:
% 204.90/35.66  | | | | | |   (46)  all_52_17 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | SIMP: (46) implies:
% 204.90/35.66  | | | | | |   (47)  all_52_17 = e3
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | REDUCE: (14), (47) imply:
% 204.90/35.66  | | | | | |   (48)  op(e3, e3) = all_52_16
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3,
% 204.90/35.66  | | | | | |              simplifying with (21), (44) gives:
% 204.90/35.66  | | | | | |   (49)  all_52_9 = all_4_1
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | GROUND_INST: instantiating (1) with all_6_2, all_52_16, e3, e3,
% 204.90/35.66  | | | | | |              simplifying with (17), (48) gives:
% 204.90/35.66  | | | | | |   (50)  all_52_16 = all_6_2
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | GROUND_INST: instantiating (1) with e2, all_52_16, e3, e3,
% 204.90/35.66  | | | | | |              simplifying with (43), (48) gives:
% 204.90/35.66  | | | | | |   (51)  all_52_16 = e2
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | COMBINE_EQS: (50), (51) imply:
% 204.90/35.66  | | | | | |   (52)  all_6_2 = e2
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | SIMP: (52) implies:
% 204.90/35.66  | | | | | |   (53)  all_6_2 = e2
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | REF_CLOSE: (1), (7), (9), (16), (20), (22), (25), (32), (49), (53)
% 204.90/35.66  | | | | | |            are inconsistent by sub-proof #1324.
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | Case 2:
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | |   (54)   ~ (all_58_4 = e3)
% 204.90/35.66  | | | | | | 
% 204.90/35.66  | | | | | | REDUCE: (27), (54) imply:
% 204.90/35.67  | | | | | |   (55)   ~ (all_52_17 = e3)
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | REF_CLOSE: (5), (11), (27), (40), (55) are inconsistent by sub-proof
% 204.90/35.67  | | | | | |            #1299.
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | End of split
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | Case 2:
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | |   (56)  all_58_7 = e3 | all_58_13 = e3
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | | REF_CLOSE: (4), (6), (10), (18), (56) are inconsistent by sub-proof
% 204.90/35.67  | | | | |            #1298.
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | End of split
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | End of split
% 204.90/35.67  | | | 
% 204.90/35.67  | | End of split
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1298 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_13 = all_52_15
% 204.90/35.67    (2)   ~ (all_52_15 = e3)
% 204.90/35.67    (3)  all_58_7 = all_52_13
% 204.90/35.67    (4)  all_58_7 = e3 | all_58_13 = e3
% 204.90/35.67    (5)   ~ (all_52_13 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (4) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (6)  all_58_7 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (3), (6) imply:
% 204.90/35.67  | |   (7)  all_52_13 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (5), (7) imply:
% 204.90/35.67  | |   (8)  $false
% 204.90/35.67  | | 
% 204.90/35.67  | | CLOSE: (8) is inconsistent.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (9)  all_58_13 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1360.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1299 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_9 = all_52_25
% 204.90/35.67    (2)  all_58_4 = e3 | all_58_9 = e3
% 204.90/35.67    (3)   ~ (all_52_25 = e3)
% 204.90/35.67    (4)   ~ (all_52_17 = e3)
% 204.90/35.67    (5)  all_58_4 = all_52_17
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (2) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (6)  all_58_4 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #1302.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (7)  all_58_9 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #1300.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1300 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_9 = all_52_25
% 204.90/35.67    (2)  all_58_9 = e3
% 204.90/35.67    (3)   ~ (all_52_25 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_52_25 = e3
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_52_25 = e3
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1301 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_10 = all_52_27
% 204.90/35.67    (2)  all_58_10 = e3
% 204.90/35.67    (3)   ~ (all_52_27 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_52_27 = e3
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_52_27 = e3
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1302 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_4 = all_52_17
% 204.90/35.67    (2)  all_58_4 = e3
% 204.90/35.67    (3)   ~ (all_52_17 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_52_17 = e3
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_52_17 = e3
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1303 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_14 = all_52_23
% 204.90/35.67    (2)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 204.90/35.67    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.67    (4)  all_58_1 = all_52_9
% 204.90/35.67    (5)   ~ (all_52_9 = all_52_13)
% 204.90/35.67    (6)   ~ (all_52_3 = all_6_2)
% 204.90/35.67    (7)  all_58_0 = all_6_2
% 204.90/35.67    (8)  all_56_4 = all_52_3
% 204.90/35.67    (9)  op(all_52_19, all_52_19) = all_52_18
% 204.90/35.67    (10)  all_58_13 = all_52_15
% 204.90/35.67    (11)  op(all_52_13, all_52_13) = e1
% 204.90/35.67    (12)  op(all_10_2, all_10_2) = all_52_20
% 204.90/35.67    (13)   ~ (all_52_15 = e3)
% 204.90/35.67    (14)  op(e1, e3) = all_52_5
% 204.90/35.67    (15)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.67    (16)  op(e2, e2) = all_4_2
% 204.90/35.67    (17)   ~ (all_52_3 = all_52_5)
% 204.90/35.67    (18)  all_58_11 = all_52_29
% 204.90/35.67    (19)  all_56_5 = all_4_2
% 204.90/35.67    (20)   ~ (all_4_1 = e1)
% 204.90/35.67    (21)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.67    (22)   ~ (all_52_13 = all_10_2)
% 204.90/35.67    (23)  op(e0, e0) = e0
% 204.90/35.67    (24)  all_56_8 = all_52_5
% 204.90/35.67    (25)  all_58_7 = all_52_13
% 204.90/35.67    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.67    (27)  all_56_2 = all_52_17
% 204.90/35.67    (28)   ~ (all_52_29 = e3)
% 204.90/35.67    (29)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.67    (30)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.90/35.67    (31)  op(all_4_2, e2) = all_4_1
% 204.90/35.67    (32)   ~ (all_52_23 = e3)
% 204.90/35.67    (33)   ~ (all_52_5 = e3)
% 204.90/35.67    (34)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 204.90/35.67    (35)   ~ (all_52_9 = e3)
% 204.90/35.67    (36)   ~ (all_52_13 = all_4_2)
% 204.90/35.67    (37)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.90/35.67    (38)  all_58_8 = all_10_2
% 204.90/35.67    (39)   ~ (all_52_9 = all_4_2)
% 204.90/35.67    (40)   ~ (all_52_5 = all_6_2)
% 204.90/35.67    (41)  op(all_4_2, all_4_2) = e2
% 204.90/35.67    (42)   ~ (all_52_9 = all_6_2)
% 204.90/35.67    (43)  op(e3, e3) = all_6_2
% 204.90/35.67    (44)   ~ (all_52_17 = e3)
% 204.90/35.67    (45)  all_58_5 = all_52_19
% 204.90/35.67    (46)  all_56_1 = all_52_9
% 204.90/35.67    (47)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 204.90/35.67    (48)  all_58_6 = all_52_5
% 204.90/35.67    (49)  op(e3, e2) = all_52_9
% 204.90/35.67    (50)   ~ (all_52_17 = all_6_2)
% 204.90/35.67    (51)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 204.90/35.67    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67    (53)   ~ (all_52_9 = all_52_17)
% 204.90/35.67    (54)   ~ (all_6_1 = e2)
% 204.90/35.67    (55)  op(all_52_9, all_52_9) = e3
% 204.90/35.67    (56)  all_58_3 = all_4_2
% 204.90/35.67    (57)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 204.90/35.67    (58)   ~ (all_52_3 = all_4_2)
% 204.90/35.67    (59)   ~ (all_52_19 = all_4_2)
% 204.90/35.67    (60)  op(all_6_2, e3) = all_6_1
% 204.90/35.67    (61)  all_58_4 = all_52_17
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (26) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (62)  all_58_6 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (33), (48), (62) are inconsistent by sub-proof #1328.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (63)   ~ (all_58_6 = e3)
% 204.90/35.67  | |   (64)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | BETA: splitting (21) gives:
% 204.90/35.67  | | 
% 204.90/35.67  | | Case 1:
% 204.90/35.67  | | | 
% 204.90/35.67  | | |   (65)  all_56_2 = e3
% 204.90/35.67  | | | 
% 204.90/35.67  | | | REF_CLOSE: (27), (44), (65) are inconsistent by sub-proof #1327.
% 204.90/35.67  | | | 
% 204.90/35.67  | | Case 2:
% 204.90/35.67  | | | 
% 204.90/35.67  | | |   (66)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.67  | | | 
% 204.90/35.67  | | | BETA: splitting (52) gives:
% 204.90/35.67  | | | 
% 204.90/35.67  | | | Case 1:
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | |   (67)  all_56_1 = e3
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | | REF_CLOSE: (35), (46), (67) are inconsistent by sub-proof #1326.
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | Case 2:
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | |   (68)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | | BETA: splitting (37) gives:
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | | Case 1:
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | |   (69)  all_56_8 = e3
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | | REF_CLOSE: (24), (33), (69) are inconsistent by sub-proof #1325.
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | Case 2:
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | |   (70)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | | BETA: splitting (30) gives:
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | | Case 1:
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | |   (71)  all_56_5 = e3
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | COMBINE_EQS: (19), (71) imply:
% 204.90/35.67  | | | | | |   (72)  all_4_2 = e3
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | SIMP: (72) implies:
% 204.90/35.67  | | | | | |   (73)  all_4_2 = e3
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | REDUCE: (36), (73) imply:
% 204.90/35.67  | | | | | |   (74)   ~ (all_52_13 = e3)
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | REDUCE: (41), (73) imply:
% 204.90/35.67  | | | | | |   (75)  op(e3, e3) = e2
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | REDUCE: (31), (73) imply:
% 204.90/35.67  | | | | | |   (76)  op(e3, e2) = all_4_1
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | REF_CLOSE: (3), (12), (18), (20), (23), (25), (28), (35), (38),
% 204.90/35.67  | | | | | |            (42), (43), (46), (49), (52), (55), (64), (74), (75),
% 204.90/35.67  | | | | | |            (76) are inconsistent by sub-proof #1322.
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | Case 2:
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | |   (77)   ~ (all_56_5 = e3)
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | REDUCE: (19), (77) imply:
% 204.90/35.67  | | | | | |   (78)   ~ (all_4_2 = e3)
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | BETA: splitting (51) gives:
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | | Case 1:
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | |   (79)  all_58_3 = e3
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | | COMBINE_EQS: (56), (79) imply:
% 204.90/35.67  | | | | | | |   (80)  all_4_2 = e3
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | | REDUCE: (78), (80) imply:
% 204.90/35.67  | | | | | | |   (81)  $false
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | | CLOSE: (81) is inconsistent.
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | Case 2:
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | |   (82)  all_58_7 = e3 | all_58_13 = e3
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | | BETA: splitting (82) gives:
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | |   (83)  all_58_7 = e3
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | COMBINE_EQS: (25), (83) imply:
% 204.90/35.67  | | | | | | | |   (84)  all_52_13 = e3
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | REDUCE: (22), (84) imply:
% 204.90/35.67  | | | | | | | |   (85)   ~ (all_10_2 = e3)
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | SIMP: (85) implies:
% 204.90/35.67  | | | | | | | |   (86)   ~ (all_10_2 = e3)
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | REDUCE: (11), (84) imply:
% 204.90/35.67  | | | | | | | |   (87)  op(e3, e3) = e1
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | BETA: splitting (47) gives:
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | |   (88)  all_58_5 = e3
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | COMBINE_EQS: (45), (88) imply:
% 204.90/35.67  | | | | | | | | |   (89)  all_52_19 = e3
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | SIMP: (89) implies:
% 204.90/35.67  | | | | | | | | |   (90)  all_52_19 = e3
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (59), (90) imply:
% 204.90/35.67  | | | | | | | | |   (91)   ~ (all_4_2 = e3)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (9), (90) imply:
% 204.90/35.67  | | | | | | | | |   (92)  op(e3, e3) = all_52_18
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | GROUND_INST: instantiating (3) with all_6_2, all_52_18, e3, e3,
% 204.90/35.67  | | | | | | | | |              simplifying with (43), (92) gives:
% 204.90/35.67  | | | | | | | | |   (93)  all_52_18 = all_6_2
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_18, e3, e3,
% 204.90/35.67  | | | | | | | | |              simplifying with (87), (92) gives:
% 204.90/35.67  | | | | | | | | |   (94)  all_52_18 = e1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | COMBINE_EQS: (93), (94) imply:
% 204.90/35.67  | | | | | | | | |   (95)  all_6_2 = e1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | SIMP: (95) implies:
% 204.90/35.67  | | | | | | | | |   (96)  all_6_2 = e1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | COMBINE_EQS: (7), (96) imply:
% 204.90/35.67  | | | | | | | | |   (97)  all_58_0 = e1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (6), (96) imply:
% 204.90/35.67  | | | | | | | | |   (98)   ~ (all_52_3 = e1)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (40), (96) imply:
% 204.90/35.67  | | | | | | | | |   (99)   ~ (all_52_5 = e1)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (42), (96) imply:
% 204.90/35.67  | | | | | | | | |   (100)   ~ (all_52_9 = e1)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (50), (96) imply:
% 204.90/35.67  | | | | | | | | |   (101)   ~ (all_52_17 = e1)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (60), (96) imply:
% 204.90/35.67  | | | | | | | | |   (102)  op(e1, e3) = all_6_1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | GROUND_INST: instantiating (3) with all_52_5, all_6_1, e3, e1,
% 204.90/35.67  | | | | | | | | |              simplifying with (14), (102) gives:
% 204.90/35.67  | | | | | | | | |   (103)  all_52_5 = all_6_1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | COMBINE_EQS: (24), (103) imply:
% 204.90/35.67  | | | | | | | | |   (104)  all_56_8 = all_6_1
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (17), (103) imply:
% 204.90/35.67  | | | | | | | | |   (105)   ~ (all_52_3 = all_6_1)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REDUCE: (99), (103) imply:
% 204.90/35.67  | | | | | | | | |   (106)   ~ (all_6_1 = e1)
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | BETA: splitting (70) gives:
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | |   (107)  all_56_8 = e2
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | REF_CLOSE: (54), (104), (107) are inconsistent by sub-proof
% 204.90/35.67  | | | | | | | | | |            #1321.
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | |   (108)  all_56_8 = e1 | all_56_8 = e0
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | BETA: splitting (108) gives:
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | |   (109)  all_56_8 = e1
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | REF_CLOSE: (104), (106), (109) are inconsistent by sub-proof
% 204.90/35.67  | | | | | | | | | | |            #1320.
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | |   (110)  all_56_8 = e0
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | COMBINE_EQS: (104), (110) imply:
% 204.90/35.67  | | | | | | | | | | |   (111)  all_6_1 = e0
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | SIMP: (111) implies:
% 204.90/35.67  | | | | | | | | | | |   (112)  all_6_1 = e0
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | REDUCE: (105), (112) imply:
% 204.90/35.67  | | | | | | | | | | |   (113)   ~ (all_52_3 = e0)
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | REDUCE: (106), (112) imply:
% 204.90/35.67  | | | | | | | | | | |   (114)   ~ (e1 = e0)
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | SIMP: (114) implies:
% 204.90/35.67  | | | | | | | | | | |   (115)   ~ (e1 = e0)
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | BETA: splitting (2) gives:
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | |   (116)  all_58_4 = e0
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | COMBINE_EQS: (61), (116) imply:
% 204.90/35.67  | | | | | | | | | | | |   (117)  all_52_17 = e0
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | REDUCE: (53), (117) imply:
% 204.90/35.67  | | | | | | | | | | | |   (118)   ~ (all_52_9 = e0)
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | BETA: splitting (34) gives:
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | |   (119)  all_56_4 = e2
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | COMBINE_EQS: (8), (119) imply:
% 204.90/35.67  | | | | | | | | | | | | |   (120)  all_52_3 = e2
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | SIMP: (120) implies:
% 204.90/35.67  | | | | | | | | | | | | |   (121)  all_52_3 = e2
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | REDUCE: (58), (121) imply:
% 204.90/35.67  | | | | | | | | | | | | |   (122)   ~ (all_4_2 = e2)
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | SIMP: (122) implies:
% 204.90/35.67  | | | | | | | | | | | | |   (123)   ~ (all_4_2 = e2)
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | BETA: splitting (30) gives:
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | |   (124)  all_56_5 = e3
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | REF_CLOSE: (19), (78), (124) are inconsistent by sub-proof
% 204.90/35.67  | | | | | | | | | | | | | |            #1319.
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | |   (125)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | |   (126)  all_58_1 = e2
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | COMBINE_EQS: (4), (126) imply:
% 204.90/35.67  | | | | | | | | | | | | | | |   (127)  all_52_9 = e2
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | REDUCE: (55), (127) imply:
% 204.90/35.67  | | | | | | | | | | | | | | |   (128)  op(e2, e2) = e3
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (78), (128) are inconsistent by
% 204.90/35.67  | | | | | | | | | | | | | | |            sub-proof #1318.
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | |   (129)   ~ (all_58_1 = e2)
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | REDUCE: (4), (129) imply:
% 204.90/35.67  | | | | | | | | | | | | | | |   (130)   ~ (all_52_9 = e2)
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | |   (131)  all_58_1 = e0
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (131) imply:
% 204.90/35.67  | | | | | | | | | | | | | | | |   (132)  all_52_9 = e0
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | REDUCE: (118), (132) imply:
% 204.90/35.67  | | | | | | | | | | | | | | | |   (133)  $false
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | |   (134)   ~ (all_58_1 = e0)
% 204.90/35.67  | | | | | | | | | | | | | | | |   (135)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | Case 1:
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | |   (136)  all_58_3 = e0
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (23), (41), (56), (123), (136) are
% 204.90/35.67  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1316.
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | |   (137)   ~ (all_58_3 = e0)
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | | REDUCE: (56), (137) imply:
% 204.90/35.67  | | | | | | | | | | | | | | | | |   (138)   ~ (all_4_2 = e0)
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (39), (46), (68), (118), (123), (125),
% 204.90/35.67  | | | | | | | | | | | | | | | | |            (130), (138) are inconsistent by sub-proof #1311.
% 204.90/35.67  | | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | |   (139)  all_56_4 = e1 | all_56_4 = e0
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | | REF_CLOSE: (8), (98), (113), (139) are inconsistent by
% 204.90/35.67  | | | | | | | | | | | | |            sub-proof #1308.
% 204.90/35.67  | | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | |   (140)   ~ (all_58_4 = e0)
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | | REF_CLOSE: (3), (4), (23), (27), (29), (35), (46), (53),
% 204.90/35.67  | | | | | | | | | | | |            (55), (61), (66), (68), (97), (100), (101), (115),
% 204.90/35.67  | | | | | | | | | | | |            (140) are inconsistent by sub-proof #1306.
% 204.90/35.67  | | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | |   (141)  all_58_8 = e3 | all_58_14 = e3
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | | REF_CLOSE: (1), (32), (38), (86), (141) are inconsistent by
% 204.90/35.67  | | | | | | | | |            sub-proof #1304.
% 204.90/35.67  | | | | | | | | | 
% 204.90/35.67  | | | | | | | | End of split
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | Case 2:
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | |   (142)  all_58_13 = e3
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | | REF_CLOSE: (10), (13), (142) are inconsistent by sub-proof
% 204.90/35.67  | | | | | | | |            #1360.
% 204.90/35.67  | | | | | | | | 
% 204.90/35.67  | | | | | | | End of split
% 204.90/35.67  | | | | | | | 
% 204.90/35.67  | | | | | | End of split
% 204.90/35.67  | | | | | | 
% 204.90/35.67  | | | | | End of split
% 204.90/35.67  | | | | | 
% 204.90/35.67  | | | | End of split
% 204.90/35.67  | | | | 
% 204.90/35.67  | | | End of split
% 204.90/35.67  | | | 
% 204.90/35.67  | | End of split
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1304 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_14 = all_52_23
% 204.90/35.67    (2)  all_58_8 = e3 | all_58_14 = e3
% 204.90/35.67    (3)   ~ (all_52_23 = e3)
% 204.90/35.67    (4)   ~ (all_10_2 = e3)
% 204.90/35.67    (5)  all_58_8 = all_10_2
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (2) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (6)  all_58_8 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (5), (6) imply:
% 204.90/35.67  | |   (7)  all_10_2 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (4), (7) imply:
% 204.90/35.67  | |   (8)  $false
% 204.90/35.67  | | 
% 204.90/35.67  | | CLOSE: (8) is inconsistent.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (9)  all_58_14 = e3
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1305.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1305 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_58_14 = all_52_23
% 204.90/35.67    (2)  all_58_14 = e3
% 204.90/35.67    (3)   ~ (all_52_23 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_52_23 = e3
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_52_23 = e3
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1306 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.67    (2)  all_58_1 = all_52_9
% 204.90/35.67    (3)  op(e0, e0) = e0
% 204.90/35.67    (4)  all_56_2 = all_52_17
% 204.90/35.67    (5)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.67    (6)   ~ (all_52_9 = e3)
% 204.90/35.67    (7)   ~ (all_52_9 = e1)
% 204.90/35.67    (8)  all_56_1 = all_52_9
% 204.90/35.67    (9)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67    (10)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 204.90/35.67    (11)   ~ (e1 = e0)
% 204.90/35.67    (12)   ~ (all_58_4 = e0)
% 204.90/35.67    (13)   ~ (all_52_17 = e1)
% 204.90/35.67    (14)   ~ (all_52_9 = all_52_17)
% 204.90/35.67    (15)  op(all_52_9, all_52_9) = e3
% 204.90/35.67    (16)  all_58_0 = e1
% 204.90/35.67    (17)  all_58_4 = all_52_17
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (12), (17) imply:
% 204.90/35.67  |   (18)   ~ (all_52_17 = e0)
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (10) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (19)  all_56_2 = e2
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (4), (19) imply:
% 204.90/35.67  | |   (20)  all_52_17 = e2
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (14), (20) imply:
% 204.90/35.67  | |   (21)   ~ (all_52_9 = e2)
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (15), (16), (21)
% 204.90/35.67  | |            are inconsistent by sub-proof #1332.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (22)  all_56_2 = e1 | all_56_2 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (4), (13), (18), (22) are inconsistent by sub-proof #1307.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1307 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_2 = e1 | all_56_2 = e0
% 204.90/35.67    (2)  all_56_2 = all_52_17
% 204.90/35.67    (3)   ~ (all_52_17 = e1)
% 204.90/35.67    (4)   ~ (all_52_17 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (1) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (5)  all_56_2 = e1
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (2), (5) imply:
% 204.90/35.67  | |   (6)  all_52_17 = e1
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (3), (6) imply:
% 204.90/35.67  | |   (7)  $false
% 204.90/35.67  | | 
% 204.90/35.67  | | CLOSE: (7) is inconsistent.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (8)  all_56_2 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (2), (8) imply:
% 204.90/35.67  | |   (9)  all_52_17 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (4), (9) imply:
% 204.90/35.67  | |   (10)  $false
% 204.90/35.67  | | 
% 204.90/35.67  | | CLOSE: (10) is inconsistent.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1308 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_4 = e1 | all_56_4 = e0
% 204.90/35.67    (2)  all_56_4 = all_52_3
% 204.90/35.67    (3)   ~ (all_52_3 = e1)
% 204.90/35.67    (4)   ~ (all_52_3 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (1) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (5)  all_56_4 = e1
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1310.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (6)  all_56_4 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1309.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1309 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_4 = all_52_3
% 204.90/35.67    (2)  all_56_4 = e0
% 204.90/35.67    (3)   ~ (all_52_3 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_52_3 = e0
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_52_3 = e0
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1310 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_4 = all_52_3
% 204.90/35.67    (2)  all_56_4 = e1
% 204.90/35.67    (3)   ~ (all_52_3 = e1)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_52_3 = e1
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_52_3 = e1
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1311 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 204.90/35.67    (2)   ~ (all_4_2 = e0)
% 204.90/35.67    (3)  all_56_5 = all_4_2
% 204.90/35.67    (4)   ~ (all_52_9 = e2)
% 204.90/35.67    (5)   ~ (all_52_9 = all_4_2)
% 204.90/35.67    (6)   ~ (all_4_2 = e2)
% 204.90/35.67    (7)  all_56_1 = all_52_9
% 204.90/35.67    (8)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67    (9)   ~ (all_52_9 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (1) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (10)  all_56_5 = e2
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #1315.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (11)  all_56_5 = e1 | all_56_5 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11) are inconsistent by
% 204.90/35.67  | |            sub-proof #1312.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1312 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)   ~ (all_4_2 = e0)
% 204.90/35.67    (2)  all_56_5 = all_4_2
% 204.90/35.67    (3)   ~ (all_52_9 = e2)
% 204.90/35.67    (4)   ~ (all_52_9 = all_4_2)
% 204.90/35.67    (5)  all_56_1 = all_52_9
% 204.90/35.67    (6)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67    (7)  all_56_5 = e1 | all_56_5 = e0
% 204.90/35.67    (8)   ~ (all_52_9 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (7) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (9)  all_56_5 = e1
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (2), (9) imply:
% 204.90/35.67  | |   (10)  all_4_2 = e1
% 204.90/35.67  | | 
% 204.90/35.67  | | SIMP: (10) implies:
% 204.90/35.67  | |   (11)  all_4_2 = e1
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (4), (11) imply:
% 204.90/35.67  | |   (12)   ~ (all_52_9 = e1)
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (3), (5), (6), (8), (12) are inconsistent by sub-proof #1314.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (13)  all_56_5 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (1), (2), (13) are inconsistent by sub-proof #1313.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1313 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_5 = all_4_2
% 204.90/35.67    (2)  all_56_5 = e0
% 204.90/35.67    (3)   ~ (all_4_2 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_4_2 = e0
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_4_2 = e0
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1314 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)   ~ (all_52_9 = e2)
% 204.90/35.67    (2)   ~ (all_52_9 = e1)
% 204.90/35.67    (3)  all_56_1 = all_52_9
% 204.90/35.67    (4)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67    (5)   ~ (all_52_9 = e0)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | BETA: splitting (4) gives:
% 204.90/35.67  | 
% 204.90/35.67  | Case 1:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (6)  all_56_1 = e2
% 204.90/35.67  | | 
% 204.90/35.67  | | COMBINE_EQS: (3), (6) imply:
% 204.90/35.67  | |   (7)  all_52_9 = e2
% 204.90/35.67  | | 
% 204.90/35.67  | | REDUCE: (1), (7) imply:
% 204.90/35.67  | |   (8)  $false
% 204.90/35.67  | | 
% 204.90/35.67  | | CLOSE: (8) is inconsistent.
% 204.90/35.67  | | 
% 204.90/35.67  | Case 2:
% 204.90/35.67  | | 
% 204.90/35.67  | |   (9)  all_56_1 = e1 | all_56_1 = e0
% 204.90/35.67  | | 
% 204.90/35.67  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1334.
% 204.90/35.67  | | 
% 204.90/35.67  | End of split
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1315 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_5 = all_4_2
% 204.90/35.67    (2)  all_56_5 = e2
% 204.90/35.67    (3)   ~ (all_4_2 = e2)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_4_2 = e2
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_4_2 = e2
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1316 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.67    (2)  op(e2, e2) = all_4_2
% 204.90/35.67    (3)  op(e0, e0) = e0
% 204.90/35.67    (4)  all_58_3 = e0
% 204.90/35.67    (5)  op(all_4_2, all_4_2) = e2
% 204.90/35.67    (6)   ~ (all_4_2 = e2)
% 204.90/35.67    (7)  all_58_3 = all_4_2
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (4), (7) imply:
% 204.90/35.67  |   (8)  all_4_2 = e0
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (2), (8) imply:
% 204.90/35.67  |   (9)  op(e2, e2) = e0
% 204.90/35.67  | 
% 204.90/35.67  | REF_CLOSE: (1), (2), (3), (5), (6), (9) are inconsistent by sub-proof #1317.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1317 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.67    (2)  op(e2, e2) = all_4_2
% 204.90/35.67    (3)  op(e0, e0) = e0
% 204.90/35.67    (4)  op(e2, e2) = e0
% 204.90/35.67    (5)  op(all_4_2, all_4_2) = e2
% 204.90/35.67    (6)   ~ (all_4_2 = e2)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e2, simplifying with (2),
% 204.90/35.67  |              (4) gives:
% 204.90/35.67  |   (7)  all_4_2 = e0
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (6), (7) imply:
% 204.90/35.67  |   (8)   ~ (e2 = e0)
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (8) implies:
% 204.90/35.67  |   (9)   ~ (e2 = e0)
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (5), (7) imply:
% 204.90/35.67  |   (10)  op(e0, e0) = e2
% 204.90/35.67  | 
% 204.90/35.67  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (3), (10)
% 204.90/35.67  |              gives:
% 204.90/35.67  |   (11)  e2 = e0
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (9), (11) imply:
% 204.90/35.67  |   (12)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (12) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1318 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.67    (2)  op(e2, e2) = all_4_2
% 204.90/35.67    (3)  op(e2, e2) = e3
% 204.90/35.67    (4)   ~ (all_4_2 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying with (2),
% 204.90/35.67  |              (3) gives:
% 204.90/35.67  |   (5)  all_4_2 = e3
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (4), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1319 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_5 = all_4_2
% 204.90/35.67    (2)  all_56_5 = e3
% 204.90/35.67    (3)   ~ (all_4_2 = e3)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_4_2 = e3
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_4_2 = e3
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1320 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_8 = all_6_1
% 204.90/35.67    (2)  all_56_8 = e1
% 204.90/35.67    (3)   ~ (all_6_1 = e1)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_6_1 = e1
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_6_1 = e1
% 204.90/35.67  | 
% 204.90/35.67  | REDUCE: (3), (5) imply:
% 204.90/35.67  |   (6)  $false
% 204.90/35.67  | 
% 204.90/35.67  | CLOSE: (6) is inconsistent.
% 204.90/35.67  | 
% 204.90/35.67  End of proof
% 204.90/35.67  
% 204.90/35.67  Sub-proof #1321 shows that the following formulas are inconsistent:
% 204.90/35.67  ----------------------------------------------------------------
% 204.90/35.67    (1)  all_56_8 = all_6_1
% 204.90/35.67    (2)  all_56_8 = e2
% 204.90/35.67    (3)   ~ (all_6_1 = e2)
% 204.90/35.67  
% 204.90/35.67  Begin of proof
% 204.90/35.67  | 
% 204.90/35.67  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.67  |   (4)  all_6_1 = e2
% 204.90/35.67  | 
% 204.90/35.67  | SIMP: (4) implies:
% 204.90/35.67  |   (5)  all_6_1 = e2
% 204.90/35.67  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1322 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  op(all_10_2, all_10_2) = all_52_20
% 204.90/35.68    (3)  all_58_11 = all_52_29
% 204.90/35.68    (4)  op(e3, e3) = e2
% 204.90/35.68    (5)   ~ (all_4_1 = e1)
% 204.90/35.68    (6)  op(e3, e2) = all_4_1
% 204.90/35.68    (7)  op(e0, e0) = e0
% 204.90/35.68    (8)  all_58_7 = all_52_13
% 204.90/35.68    (9)   ~ (all_52_29 = e3)
% 204.90/35.68    (10)   ~ (all_52_9 = e3)
% 204.90/35.68    (11)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 204.90/35.68    (12)  all_58_8 = all_10_2
% 204.90/35.68    (13)   ~ (all_52_9 = all_6_2)
% 204.90/35.68    (14)  op(e3, e3) = all_6_2
% 204.90/35.68    (15)   ~ (all_52_13 = e3)
% 204.90/35.68    (16)  all_56_1 = all_52_9
% 204.90/35.68    (17)  op(e3, e2) = all_52_9
% 204.90/35.68    (18)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (19)  op(all_52_9, all_52_9) = e3
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (11) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (20)  all_58_7 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (8), (20) imply:
% 204.90/35.68  | |   (21)  all_52_13 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (15), (21) imply:
% 204.90/35.68  | |   (22)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (22) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (23)  all_58_8 = e3 | all_58_11 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | BETA: splitting (23) gives:
% 204.90/35.68  | | 
% 204.90/35.68  | | Case 1:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (24)  all_58_8 = e3
% 204.90/35.68  | | | 
% 204.90/35.68  | | | COMBINE_EQS: (12), (24) imply:
% 204.90/35.68  | | |   (25)  all_10_2 = e3
% 204.90/35.68  | | | 
% 204.90/35.68  | | | SIMP: (25) implies:
% 204.90/35.68  | | |   (26)  all_10_2 = e3
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REDUCE: (2), (26) imply:
% 204.90/35.68  | | |   (27)  op(e3, e3) = all_52_20
% 204.90/35.68  | | | 
% 204.90/35.68  | | | GROUND_INST: instantiating (1) with all_52_9, all_4_1, e2, e3, simplifying
% 204.90/35.68  | | |              with (6), (17) gives:
% 204.90/35.68  | | |   (28)  all_52_9 = all_4_1
% 204.90/35.68  | | | 
% 204.90/35.68  | | | GROUND_INST: instantiating (1) with all_6_2, all_52_20, e3, e3,
% 204.90/35.68  | | |              simplifying with (14), (27) gives:
% 204.90/35.68  | | |   (29)  all_52_20 = all_6_2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | GROUND_INST: instantiating (1) with e2, all_52_20, e3, e3, simplifying
% 204.90/35.68  | | |              with (4), (27) gives:
% 204.90/35.68  | | |   (30)  all_52_20 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | COMBINE_EQS: (29), (30) imply:
% 204.90/35.68  | | |   (31)  all_6_2 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REF_CLOSE: (1), (5), (7), (10), (13), (16), (18), (19), (28), (31) are
% 204.90/35.68  | | |            inconsistent by sub-proof #1324.
% 204.90/35.68  | | | 
% 204.90/35.68  | | Case 2:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (32)  all_58_11 = e3
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REF_CLOSE: (3), (9), (32) are inconsistent by sub-proof #1323.
% 204.90/35.68  | | | 
% 204.90/35.68  | | End of split
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1323 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_58_11 = all_52_29
% 204.90/35.68    (2)  all_58_11 = e3
% 204.90/35.68    (3)   ~ (all_52_29 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_29 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_29 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1324 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_6_2 = e2
% 204.90/35.68    (3)   ~ (all_4_1 = e1)
% 204.90/35.68    (4)  op(e0, e0) = e0
% 204.90/35.68    (5)   ~ (all_52_9 = e3)
% 204.90/35.68    (6)  all_52_9 = all_4_1
% 204.90/35.68    (7)   ~ (all_52_9 = all_6_2)
% 204.90/35.68    (8)  all_56_1 = all_52_9
% 204.90/35.68    (9)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (10)  op(all_52_9, all_52_9) = e3
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (6), (8) imply:
% 204.90/35.68  |   (11)  all_56_1 = all_4_1
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (2), (6), (7) imply:
% 204.90/35.68  |   (12)   ~ (all_4_1 = e2)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (5), (6) imply:
% 204.90/35.68  |   (13)   ~ (all_4_1 = e3)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (6), (10) imply:
% 204.90/35.68  |   (14)  op(all_4_1, all_4_1) = e3
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (9) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (15)  all_56_1 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (11), (15) imply:
% 204.90/35.68  | |   (16)  all_4_1 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (13), (16) imply:
% 204.90/35.68  | |   (17)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (17) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (18)   ~ (all_56_1 = e3)
% 204.90/35.68  | |   (19)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | BETA: splitting (19) gives:
% 204.90/35.68  | | 
% 204.90/35.68  | | Case 1:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (20)  all_56_1 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | COMBINE_EQS: (11), (20) imply:
% 204.90/35.68  | | |   (21)  all_4_1 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REDUCE: (12), (21) imply:
% 204.90/35.68  | | |   (22)  $false
% 204.90/35.68  | | | 
% 204.90/35.68  | | | CLOSE: (22) is inconsistent.
% 204.90/35.68  | | | 
% 204.90/35.68  | | Case 2:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (23)  all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68  | | | 
% 204.90/35.68  | | | BETA: splitting (23) gives:
% 204.90/35.68  | | | 
% 204.90/35.68  | | | Case 1:
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | |   (24)  all_56_1 = e1
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | COMBINE_EQS: (11), (24) imply:
% 204.90/35.68  | | | |   (25)  all_4_1 = e1
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | REDUCE: (3), (25) imply:
% 204.90/35.68  | | | |   (26)  $false
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | CLOSE: (26) is inconsistent.
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | Case 2:
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | |   (27)  all_56_1 = e0
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | COMBINE_EQS: (11), (27) imply:
% 204.90/35.68  | | | |   (28)  all_4_1 = e0
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | REDUCE: (13), (28) imply:
% 204.90/35.68  | | | |   (29)   ~ (e3 = e0)
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | SIMP: (29) implies:
% 204.90/35.68  | | | |   (30)   ~ (e3 = e0)
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | REDUCE: (14), (28) imply:
% 204.90/35.68  | | | |   (31)  op(e0, e0) = e3
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | | REF_CLOSE: (1), (4), (30), (31) are inconsistent by sub-proof #1336.
% 204.90/35.68  | | | | 
% 204.90/35.68  | | | End of split
% 204.90/35.68  | | | 
% 204.90/35.68  | | End of split
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1325 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_8 = all_52_5
% 204.90/35.68    (2)  all_56_8 = e3
% 204.90/35.68    (3)   ~ (all_52_5 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_5 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_5 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1326 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_1 = all_52_9
% 204.90/35.68    (2)  all_56_1 = e3
% 204.90/35.68    (3)   ~ (all_52_9 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_9 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_9 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1327 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_2 = all_52_17
% 204.90/35.68    (2)  all_56_2 = e3
% 204.90/35.68    (3)   ~ (all_52_17 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_17 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_17 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1328 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_58_6 = all_52_5
% 204.90/35.68    (2)  all_58_6 = e3
% 204.90/35.68    (3)   ~ (all_52_5 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_5 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_5 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1329 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_58_1 = all_52_9
% 204.90/35.68    (3)  all_58_0 = all_6_2
% 204.90/35.68    (4)   ~ (all_52_25 = e0)
% 204.90/35.68    (5)  op(e0, e0) = e0
% 204.90/35.68    (6)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 204.90/35.68    (7)  op(e3, e3) = all_52_16
% 204.90/35.68    (8)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.68    (9)   ~ (all_52_9 = e3)
% 204.90/35.68    (10)   ~ (all_52_9 = all_52_25)
% 204.90/35.68    (11)   ~ (all_52_25 = all_6_2)
% 204.90/35.68    (12)   ~ (all_52_9 = all_6_2)
% 204.90/35.68    (13)  op(e3, e3) = all_6_2
% 204.90/35.68    (14)  all_56_3 = all_52_25
% 204.90/35.68    (15)  op(e3, e3) = e1
% 204.90/35.68    (16)  all_56_1 = all_52_9
% 204.90/35.68    (17)   ~ (e1 = e0)
% 204.90/35.68    (18)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (19)  op(all_52_9, all_52_9) = e3
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | GROUND_INST: instantiating (1) with all_6_2, all_52_16, e3, e3, simplifying
% 204.90/35.68  |              with (7), (13) gives:
% 204.90/35.68  |   (20)  all_52_16 = all_6_2
% 204.90/35.68  | 
% 204.90/35.68  | GROUND_INST: instantiating (1) with e1, all_52_16, e3, e3, simplifying with
% 204.90/35.68  |              (7), (15) gives:
% 204.90/35.68  |   (21)  all_52_16 = e1
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (20), (21) imply:
% 204.90/35.68  |   (22)  all_6_2 = e1
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (22) implies:
% 204.90/35.68  |   (23)  all_6_2 = e1
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (3), (23) imply:
% 204.90/35.68  |   (24)  all_58_0 = e1
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (12), (23) imply:
% 204.90/35.68  |   (25)   ~ (all_52_9 = e1)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (11), (23) imply:
% 204.90/35.68  |   (26)   ~ (all_52_25 = e1)
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (6) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (27)  all_56_3 = e2
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (14), (27) imply:
% 204.90/35.68  | |   (28)  all_52_25 = e2
% 204.90/35.68  | | 
% 204.90/35.68  | | SIMP: (28) implies:
% 204.90/35.68  | |   (29)  all_52_25 = e2
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (10), (29) imply:
% 204.90/35.68  | |   (30)   ~ (all_52_9 = e2)
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (1), (2), (5), (8), (9), (16), (17), (18), (19), (24), (25), (30)
% 204.90/35.68  | |            are inconsistent by sub-proof #1331.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (31)  all_56_3 = e1 | all_56_3 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (4), (14), (26), (31) are inconsistent by sub-proof #1330.
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1330 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_3 = e1 | all_56_3 = e0
% 204.90/35.68    (2)  all_56_3 = all_52_25
% 204.90/35.68    (3)   ~ (all_52_25 = e1)
% 204.90/35.68    (4)   ~ (all_52_25 = e0)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (1) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (5)  all_56_3 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (2), (5) imply:
% 204.90/35.68  | |   (6)  all_52_25 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (3), (6) imply:
% 204.90/35.68  | |   (7)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (7) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (8)  all_56_3 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (2), (8) imply:
% 204.90/35.68  | |   (9)  all_52_25 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (4), (9) imply:
% 204.90/35.68  | |   (10)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (10) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1331 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_58_1 = all_52_9
% 204.90/35.68    (3)  op(e0, e0) = e0
% 204.90/35.68    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.68    (5)   ~ (all_52_9 = e3)
% 204.90/35.68    (6)   ~ (all_52_9 = e2)
% 204.90/35.68    (7)   ~ (all_52_9 = e1)
% 204.90/35.68    (8)  all_56_1 = all_52_9
% 204.90/35.68    (9)   ~ (e1 = e0)
% 204.90/35.68    (10)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (11)  op(all_52_9, all_52_9) = e3
% 204.90/35.68    (12)  all_58_0 = e1
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (10) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (13)  all_56_1 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (8), (13) imply:
% 204.90/35.68  | |   (14)  all_52_9 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (5), (14) imply:
% 204.90/35.68  | |   (15)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (15) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (16)   ~ (all_56_1 = e3)
% 204.90/35.68  | |   (17)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (17) are
% 204.90/35.68  | |            inconsistent by sub-proof #1332.
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1332 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_58_1 = all_52_9
% 204.90/35.68    (3)  op(e0, e0) = e0
% 204.90/35.68    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.68    (5)   ~ (all_52_9 = e3)
% 204.90/35.68    (6)   ~ (all_52_9 = e2)
% 204.90/35.68    (7)   ~ (all_52_9 = e1)
% 204.90/35.68    (8)  all_56_1 = all_52_9
% 204.90/35.68    (9)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (10)   ~ (e1 = e0)
% 204.90/35.68    (11)  op(all_52_9, all_52_9) = e3
% 204.90/35.68    (12)  all_58_0 = e1
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (4) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (13)  all_58_0 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (12), (13) imply:
% 204.90/35.68  | |   (14)  e1 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (10), (14) imply:
% 204.90/35.68  | |   (15)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (15) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (16)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | BETA: splitting (9) gives:
% 204.90/35.68  | | 
% 204.90/35.68  | | Case 1:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (17)  all_56_1 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | COMBINE_EQS: (8), (17) imply:
% 204.90/35.68  | | |   (18)  all_52_9 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REDUCE: (6), (18) imply:
% 204.90/35.68  | | |   (19)  $false
% 204.90/35.68  | | | 
% 204.90/35.68  | | | CLOSE: (19) is inconsistent.
% 204.90/35.68  | | | 
% 204.90/35.68  | | Case 2:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (20)  all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (11), (16), (20) are inconsistent
% 204.90/35.68  | | |            by sub-proof #1333.
% 204.90/35.68  | | | 
% 204.90/35.68  | | End of split
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1333 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_58_1 = all_52_9
% 204.90/35.68    (3)  op(e0, e0) = e0
% 204.90/35.68    (4)  all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (5)   ~ (all_52_9 = e3)
% 204.90/35.68    (6)   ~ (all_52_9 = e1)
% 204.90/35.68    (7)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 204.90/35.68    (8)  all_56_1 = all_52_9
% 204.90/35.68    (9)  op(all_52_9, all_52_9) = e3
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (7) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (10)  all_58_1 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (1), (2), (3), (5), (9), (10) are inconsistent by sub-proof
% 204.90/35.68  | |            #1335.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (11)   ~ (all_58_1 = e0)
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (2), (11) imply:
% 204.90/35.68  | |   (12)   ~ (all_52_9 = e0)
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (4), (6), (8), (12) are inconsistent by sub-proof #1334.
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1334 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_1 = e1 | all_56_1 = e0
% 204.90/35.68    (2)  all_56_1 = all_52_9
% 204.90/35.68    (3)   ~ (all_52_9 = e1)
% 204.90/35.68    (4)   ~ (all_52_9 = e0)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (1) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (5)  all_56_1 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (2), (5) imply:
% 204.90/35.68  | |   (6)  all_52_9 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (3), (6) imply:
% 204.90/35.68  | |   (7)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (7) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (8)  all_56_1 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (2), (8) imply:
% 204.90/35.68  | |   (9)  all_52_9 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (4), (9) imply:
% 204.90/35.68  | |   (10)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (10) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1335 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_58_1 = e0
% 204.90/35.68    (3)  all_58_1 = all_52_9
% 204.90/35.68    (4)  op(e0, e0) = e0
% 204.90/35.68    (5)   ~ (all_52_9 = e3)
% 204.90/35.68    (6)  op(all_52_9, all_52_9) = e3
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (2), (3) imply:
% 204.90/35.68  |   (7)  all_52_9 = e0
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (5), (7) imply:
% 204.90/35.68  |   (8)   ~ (e3 = e0)
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (8) implies:
% 204.90/35.68  |   (9)   ~ (e3 = e0)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (6), (7) imply:
% 204.90/35.68  |   (10)  op(e0, e0) = e3
% 204.90/35.68  | 
% 204.90/35.68  | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #1336.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1336 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  op(e0, e0) = e3
% 204.90/35.68    (3)  op(e0, e0) = e0
% 204.90/35.68    (4)   ~ (e3 = e0)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | GROUND_INST: instantiating (1) with e0, e3, e0, e0, simplifying with (2), (3)
% 204.90/35.68  |              gives:
% 204.90/35.68  |   (5)  e3 = e0
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (4), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1337 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_52_9 = e3
% 204.90/35.68    (3)   ~ (all_52_9 = all_6_2)
% 204.90/35.68    (4)  op(e3, e3) = all_6_2
% 204.90/35.68    (5)  op(all_52_9, all_52_9) = e3
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (2), (3) imply:
% 204.90/35.68  |   (6)   ~ (all_6_2 = e3)
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (6) implies:
% 204.90/35.68  |   (7)   ~ (all_6_2 = e3)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (2), (5) imply:
% 204.90/35.68  |   (8)  op(e3, e3) = e3
% 204.90/35.68  | 
% 204.90/35.68  | REF_CLOSE: (1), (4), (7), (8) are inconsistent by sub-proof #1338.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1338 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  op(e3, e3) = all_6_2
% 204.90/35.68    (3)  op(e3, e3) = e3
% 204.90/35.68    (4)   ~ (all_6_2 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | GROUND_INST: instantiating (1) with all_6_2, e3, e3, e3, simplifying with (2),
% 204.90/35.68  |              (3) gives:
% 204.90/35.68  |   (5)  all_6_2 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (4), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1339 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_3 = all_52_25
% 204.90/35.68    (2)  all_56_3 = e3
% 204.90/35.68    (3)   ~ (all_52_25 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_25 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_25 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1340 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_4 = all_52_3
% 204.90/35.68    (2)  all_56_4 = e3
% 204.90/35.68    (3)   ~ (all_52_3 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_52_3 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_52_3 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1341 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68    (3)   ~ (all_52_7 = all_52_15)
% 204.90/35.68    (4)  op(all_52_15, all_52_15) = e0
% 204.90/35.68    (5)   ~ (all_6_1 = e1)
% 204.90/35.68    (6)   ~ (all_52_7 = all_6_2)
% 204.90/35.68    (7)  all_52_15 = e3
% 204.90/35.68    (8)  op(e0, e3) = all_52_7
% 204.90/35.68    (9)  all_56_12 = all_52_7
% 204.90/35.68    (10)  op(e3, e3) = all_6_2
% 204.90/35.68    (11)   ~ (all_6_1 = e2)
% 204.90/35.68    (12)  op(all_6_2, e3) = all_6_1
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (7) implies:
% 204.90/35.68  |   (13)  all_52_15 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (13) imply:
% 204.90/35.68  |   (14)   ~ (all_52_7 = e3)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (4), (13) imply:
% 204.90/35.68  |   (15)  op(e3, e3) = e0
% 204.90/35.68  | 
% 204.90/35.68  | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (14), (15) are
% 204.90/35.68  |            inconsistent by sub-proof #1342.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1342 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68    (3)   ~ (all_6_1 = e1)
% 204.90/35.68    (4)   ~ (all_52_7 = all_6_2)
% 204.90/35.68    (5)   ~ (all_52_7 = e3)
% 204.90/35.68    (6)  op(e0, e3) = all_52_7
% 204.90/35.68    (7)  all_56_12 = all_52_7
% 204.90/35.68    (8)  op(e3, e3) = e0
% 204.90/35.68    (9)  op(e3, e3) = all_6_2
% 204.90/35.68    (10)   ~ (all_6_1 = e2)
% 204.90/35.68    (11)  op(all_6_2, e3) = all_6_1
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | GROUND_INST: instantiating (1) with all_6_2, e0, e3, e3, simplifying with (8),
% 204.90/35.68  |              (9) gives:
% 204.90/35.68  |   (12)  all_6_2 = e0
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (4), (12) imply:
% 204.90/35.68  |   (13)   ~ (all_52_7 = e0)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (11), (12) imply:
% 204.90/35.68  |   (14)  op(e0, e3) = all_6_1
% 204.90/35.68  | 
% 204.90/35.68  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (13), (14) are inconsistent by
% 204.90/35.68  |            sub-proof #1343.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1343 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (2)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68    (3)   ~ (all_6_1 = e1)
% 204.90/35.68    (4)   ~ (all_52_7 = e3)
% 204.90/35.68    (5)  op(e0, e3) = all_52_7
% 204.90/35.68    (6)  all_56_12 = all_52_7
% 204.90/35.68    (7)  op(e0, e3) = all_6_1
% 204.90/35.68    (8)   ~ (all_6_1 = e2)
% 204.90/35.68    (9)   ~ (all_52_7 = e0)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | GROUND_INST: instantiating (1) with all_52_7, all_6_1, e3, e0, simplifying
% 204.90/35.68  |              with (5), (7) gives:
% 204.90/35.68  |   (10)  all_52_7 = all_6_1
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (6), (10) imply:
% 204.90/35.68  |   (11)  all_56_12 = all_6_1
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (4), (10) imply:
% 204.90/35.68  |   (12)   ~ (all_6_1 = e3)
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (9), (10) imply:
% 204.90/35.68  |   (13)   ~ (all_6_1 = e0)
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (2) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (14)  all_56_12 = e3
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (11), (12), (14) are inconsistent by sub-proof #1347.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (15)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | BETA: splitting (15) gives:
% 204.90/35.68  | | 
% 204.90/35.68  | | Case 1:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (16)  all_56_12 = e2
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REF_CLOSE: (8), (11), (16) are inconsistent by sub-proof #1346.
% 204.90/35.68  | | | 
% 204.90/35.68  | | Case 2:
% 204.90/35.68  | | | 
% 204.90/35.68  | | |   (17)  all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68  | | | 
% 204.90/35.68  | | | REF_CLOSE: (3), (11), (13), (17) are inconsistent by sub-proof #1344.
% 204.90/35.68  | | | 
% 204.90/35.68  | | End of split
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1344 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68    (2)  all_56_12 = all_6_1
% 204.90/35.68    (3)   ~ (all_6_1 = e1)
% 204.90/35.68    (4)   ~ (all_6_1 = e0)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | BETA: splitting (1) gives:
% 204.90/35.68  | 
% 204.90/35.68  | Case 1:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (5)  all_56_12 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | COMBINE_EQS: (2), (5) imply:
% 204.90/35.68  | |   (6)  all_6_1 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | SIMP: (6) implies:
% 204.90/35.68  | |   (7)  all_6_1 = e1
% 204.90/35.68  | | 
% 204.90/35.68  | | REDUCE: (3), (7) imply:
% 204.90/35.68  | |   (8)  $false
% 204.90/35.68  | | 
% 204.90/35.68  | | CLOSE: (8) is inconsistent.
% 204.90/35.68  | | 
% 204.90/35.68  | Case 2:
% 204.90/35.68  | | 
% 204.90/35.68  | |   (9)  all_56_12 = e0
% 204.90/35.68  | | 
% 204.90/35.68  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1345.
% 204.90/35.68  | | 
% 204.90/35.68  | End of split
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1345 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_12 = all_6_1
% 204.90/35.68    (2)  all_56_12 = e0
% 204.90/35.68    (3)   ~ (all_6_1 = e0)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_6_1 = e0
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_6_1 = e0
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1346 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_12 = all_6_1
% 204.90/35.68    (2)  all_56_12 = e2
% 204.90/35.68    (3)   ~ (all_6_1 = e2)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_6_1 = e2
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_6_1 = e2
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1347 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_56_12 = all_6_1
% 204.90/35.68    (2)  all_56_12 = e3
% 204.90/35.68    (3)   ~ (all_6_1 = e3)
% 204.90/35.68  
% 204.90/35.68  Begin of proof
% 204.90/35.68  | 
% 204.90/35.68  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.68  |   (4)  all_6_1 = e3
% 204.90/35.68  | 
% 204.90/35.68  | SIMP: (4) implies:
% 204.90/35.68  |   (5)  all_6_1 = e3
% 204.90/35.68  | 
% 204.90/35.68  | REDUCE: (3), (5) imply:
% 204.90/35.68  |   (6)  $false
% 204.90/35.68  | 
% 204.90/35.68  | CLOSE: (6) is inconsistent.
% 204.90/35.68  | 
% 204.90/35.68  End of proof
% 204.90/35.68  
% 204.90/35.68  Sub-proof #1348 shows that the following formulas are inconsistent:
% 204.90/35.68  ----------------------------------------------------------------
% 204.90/35.68    (1)  all_58_14 = all_52_23
% 204.90/35.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.68    (3)  op(all_52_7, all_52_7) = e0
% 204.90/35.68    (4)  op(all_52_5, all_52_5) = e1
% 204.90/35.68    (5)   ~ (e3 = e0)
% 204.90/35.68    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.68    (7)  op(e0, e2) = all_52_15
% 204.90/35.68    (8)   ~ (all_52_7 = all_52_15)
% 204.90/35.68    (9)  all_58_0 = all_6_2
% 204.90/35.68    (10)  all_58_13 = all_52_15
% 204.90/35.68    (11)  op(e2, e2) = all_4_2
% 204.90/35.68    (12)   ~ (all_4_1 = e3)
% 204.90/35.68    (13)  op(all_10_2, e1) = all_10_1
% 204.90/35.68    (14)   ~ (all_52_7 = all_6_2)
% 204.90/35.68    (15)  op(e0, e0) = all_14_2
% 204.90/35.68    (16)  op(e0, e1) = all_52_23
% 204.90/35.68    (17)   ~ (all_52_15 = e0)
% 204.90/35.68    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.90/35.68    (19)  all_58_15 = e0
% 204.90/35.68    (20)   ~ (all_4_1 = e1)
% 204.90/35.68    (21)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.68    (22)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.90/35.68    (23)  op(all_6_2, all_6_2) = e3
% 204.90/35.68    (24)  all_58_12 = all_52_7
% 204.90/35.68    (25)   ~ (all_52_7 = all_14_2)
% 204.90/35.69    (26)  all_58_2 = all_52_3
% 204.90/35.69    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (28)  op(all_4_2, e2) = all_4_1
% 204.90/35.69    (29)  op(all_52_3, all_52_3) = e2
% 204.90/35.69    (30)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.69    (31)   ~ (all_10_1 = e2)
% 204.90/35.69    (32)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (33)  all_56_12 = all_52_7
% 204.90/35.69    (34)  op(e3, e3) = all_6_2
% 204.90/35.69    (35)  all_56_14 = all_52_23
% 204.90/35.69    (36)   ~ (all_10_1 = e3)
% 204.90/35.69    (37)  all_58_6 = all_52_5
% 204.90/35.69    (38)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.69    (39)  op(e1, e1) = all_10_2
% 204.90/35.69    (40)   ~ (all_52_23 = all_10_2)
% 204.90/35.69    (41)   ~ (all_52_7 = all_52_23)
% 204.90/35.69    (42)  all_56_13 = all_52_15
% 204.90/35.69    (43)   ~ (all_52_3 = all_4_2)
% 204.90/35.69    (44)   ~ (all_52_7 = e0)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (21) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (45)  all_56_13 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | COMBINE_EQS: (42), (45) imply:
% 204.90/35.69  | |   (46)  all_52_15 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | SIMP: (46) implies:
% 204.90/35.69  | |   (47)  all_52_15 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (8), (47) imply:
% 204.90/35.69  | |   (48)   ~ (all_52_7 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (7), (47) imply:
% 204.90/35.69  | |   (49)  op(e0, e2) = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | BETA: splitting (6) gives:
% 204.90/35.69  | | 
% 204.90/35.69  | | Case 1:
% 204.90/35.69  | | | 
% 204.90/35.69  | | |   (50)  all_56_12 = e3
% 204.90/35.69  | | | 
% 204.90/35.69  | | | REF_CLOSE: (33), (48), (50) are inconsistent by sub-proof #1383.
% 204.90/35.69  | | | 
% 204.90/35.69  | | Case 2:
% 204.90/35.69  | | | 
% 204.90/35.69  | | |   (51)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.69  | | | 
% 204.90/35.69  | | | BETA: splitting (30) gives:
% 204.90/35.69  | | | 
% 204.90/35.69  | | | Case 1:
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | |   (52)  all_58_12 = e1
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | COMBINE_EQS: (24), (52) imply:
% 204.90/35.69  | | | |   (53)  all_52_7 = e1
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | REF_CLOSE: (2), (3), (13), (16), (22), (31), (35), (36), (39), (40),
% 204.90/35.69  | | | |            (41), (53) are inconsistent by sub-proof #1379.
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | Case 2:
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | |   (54)   ~ (all_58_12 = e1)
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | REDUCE: (24), (54) imply:
% 204.90/35.69  | | | |   (55)   ~ (all_52_7 = e1)
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | REF_CLOSE: (2), (3), (11), (12), (28), (33), (44), (49), (51), (55) are
% 204.90/35.69  | | | |            inconsistent by sub-proof #1373.
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | End of split
% 204.90/35.69  | | | 
% 204.90/35.69  | | End of split
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (56)   ~ (all_56_13 = e3)
% 204.90/35.69  | |   (57)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (42), (56) imply:
% 204.90/35.69  | |   (58)   ~ (all_52_15 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 204.90/35.69  | |            (14), (15), (16), (17), (18), (19), (20), (23), (24), (25), (26),
% 204.90/35.69  | |            (27), (28), (29), (30), (32), (33), (34), (36), (37), (38), (39),
% 204.90/35.69  | |            (41), (42), (43), (44), (57), (58) are inconsistent by sub-proof
% 204.90/35.69  | |            #1349.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1349 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)  all_58_14 = all_52_23
% 204.90/35.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (3)  op(all_52_7, all_52_7) = e0
% 204.90/35.69    (4)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (5)   ~ (e3 = e0)
% 204.90/35.69    (6)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.69    (7)  op(e0, e2) = all_52_15
% 204.90/35.69    (8)   ~ (all_52_7 = all_52_15)
% 204.90/35.69    (9)  all_58_0 = all_6_2
% 204.90/35.69    (10)  all_58_13 = all_52_15
% 204.90/35.69    (11)   ~ (all_52_15 = e3)
% 204.90/35.69    (12)  op(e2, e2) = all_4_2
% 204.90/35.69    (13)  op(all_10_2, e1) = all_10_1
% 204.90/35.69    (14)   ~ (all_52_7 = all_6_2)
% 204.90/35.69    (15)  op(e0, e0) = all_14_2
% 204.90/35.69    (16)  op(e0, e1) = all_52_23
% 204.90/35.69    (17)   ~ (all_52_15 = e0)
% 204.90/35.69    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.90/35.69    (19)  all_58_15 = e0
% 204.90/35.69    (20)   ~ (all_4_1 = e1)
% 204.90/35.69    (21)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (22)  all_58_12 = all_52_7
% 204.90/35.69    (23)   ~ (all_52_7 = all_14_2)
% 204.90/35.69    (24)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.69    (25)  all_58_2 = all_52_3
% 204.90/35.69    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (27)  op(all_4_2, e2) = all_4_1
% 204.90/35.69    (28)  op(all_52_3, all_52_3) = e2
% 204.90/35.69    (29)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.69    (30)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (31)  all_56_12 = all_52_7
% 204.90/35.69    (32)  op(e3, e3) = all_6_2
% 204.90/35.69    (33)   ~ (all_10_1 = e3)
% 204.90/35.69    (34)  all_58_6 = all_52_5
% 204.90/35.69    (35)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.69    (36)  op(e1, e1) = all_10_2
% 204.90/35.69    (37)   ~ (all_52_7 = all_52_23)
% 204.90/35.69    (38)  all_56_13 = all_52_15
% 204.90/35.69    (39)   ~ (all_52_3 = all_4_2)
% 204.90/35.69    (40)   ~ (all_52_7 = e0)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (35) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (41)  all_58_12 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | COMBINE_EQS: (22), (41) imply:
% 204.90/35.69  | |   (42)  all_52_7 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (2), (3), (4), (9), (12), (14), (15), (18), (21), (22), (23),
% 204.90/35.69  | |            (25), (26), (28), (30), (32), (34), (35), (36), (39), (42) are
% 204.90/35.69  | |            inconsistent by sub-proof #1361.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (43)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | BETA: splitting (43) gives:
% 204.90/35.69  | | 
% 204.90/35.69  | | Case 1:
% 204.90/35.69  | | | 
% 204.90/35.69  | | |   (44)  all_58_13 = e3
% 204.90/35.69  | | | 
% 204.90/35.69  | | | REF_CLOSE: (10), (11), (44) are inconsistent by sub-proof #1360.
% 204.90/35.69  | | | 
% 204.90/35.69  | | Case 2:
% 204.90/35.69  | | | 
% 204.90/35.69  | | |   (45)  all_58_14 = e3 | all_58_15 = e3
% 204.90/35.69  | | | 
% 204.90/35.69  | | | BETA: splitting (45) gives:
% 204.90/35.69  | | | 
% 204.90/35.69  | | | Case 1:
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | |   (46)  all_58_14 = e3
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | COMBINE_EQS: (1), (46) imply:
% 204.90/35.69  | | | |   (47)  all_52_23 = e3
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | SIMP: (47) implies:
% 204.90/35.69  | | | |   (48)  all_52_23 = e3
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | REDUCE: (37), (48) imply:
% 204.90/35.69  | | | |   (49)   ~ (all_52_7 = e3)
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | REDUCE: (16), (48) imply:
% 204.90/35.69  | | | |   (50)  op(e0, e1) = e3
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | BETA: splitting (6) gives:
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | Case 1:
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | |   (51)  all_56_12 = e3
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | | REF_CLOSE: (31), (49), (51) are inconsistent by sub-proof #1383.
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | Case 2:
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | |   (52)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | | BETA: splitting (29) gives:
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | | Case 1:
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | |   (53)  all_58_12 = e1
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | | REF_CLOSE: (2), (3), (13), (22), (33), (36), (50), (53) are
% 204.90/35.69  | | | | | |            inconsistent by sub-proof #1358.
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | Case 2:
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | |   (54)   ~ (all_58_12 = e1)
% 204.90/35.69  | | | | | |   (55)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | | REDUCE: (22), (54) imply:
% 204.90/35.69  | | | | | |   (56)   ~ (all_52_7 = e1)
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (12), (17), (20), (24), (27),
% 204.90/35.69  | | | | | |            (31), (38), (40), (52), (55), (56) are inconsistent by
% 204.90/35.69  | | | | | |            sub-proof #1351.
% 204.90/35.69  | | | | | | 
% 204.90/35.69  | | | | | End of split
% 204.90/35.69  | | | | | 
% 204.90/35.69  | | | | End of split
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | Case 2:
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | |   (57)  all_58_15 = e3
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | | REF_CLOSE: (5), (19), (57) are inconsistent by sub-proof #1350.
% 204.90/35.69  | | | | 
% 204.90/35.69  | | | End of split
% 204.90/35.69  | | | 
% 204.90/35.69  | | End of split
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1350 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)  all_58_15 = e3
% 204.90/35.69    (2)  all_58_15 = e0
% 204.90/35.69    (3)   ~ (e3 = e0)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.69  |   (4)  e3 = e0
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (4) implies:
% 204.90/35.69  |   (5)  e3 = e0
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (3), (5) imply:
% 204.90/35.69  |   (6)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (6) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1351 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_7, all_52_7) = e0
% 204.90/35.69    (3)  op(e0, e2) = all_52_15
% 204.90/35.69    (4)   ~ (all_52_7 = all_52_15)
% 204.90/35.69    (5)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.69    (6)  all_58_13 = all_52_15
% 204.90/35.69    (7)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.90/35.69    (8)  op(e2, e2) = all_4_2
% 204.90/35.69    (9)   ~ (all_52_15 = e0)
% 204.90/35.69    (10)   ~ (all_4_1 = e1)
% 204.90/35.69    (11)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.69    (12)  op(all_4_2, e2) = all_4_1
% 204.90/35.69    (13)  all_56_12 = all_52_7
% 204.90/35.69    (14)   ~ (all_52_7 = e1)
% 204.90/35.69    (15)  all_56_13 = all_52_15
% 204.90/35.69    (16)   ~ (all_52_7 = e0)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (7) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (17)  all_56_12 = e2
% 204.90/35.69  | | 
% 204.90/35.69  | | COMBINE_EQS: (13), (17) imply:
% 204.90/35.69  | |   (18)  all_52_7 = e2
% 204.90/35.69  | | 
% 204.90/35.69  | | SIMP: (18) implies:
% 204.90/35.69  | |   (19)  all_52_7 = e2
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (4), (19) imply:
% 204.90/35.69  | |   (20)   ~ (all_52_15 = e2)
% 204.90/35.69  | | 
% 204.90/35.69  | | SIMP: (20) implies:
% 204.90/35.69  | |   (21)   ~ (all_52_15 = e2)
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (2), (19) imply:
% 204.90/35.69  | |   (22)  op(e2, e2) = e0
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (15), (21), (22)
% 204.90/35.69  | |            are inconsistent by sub-proof #1352.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (23)  all_56_12 = e1 | all_56_12 = e0
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (13), (14), (16), (23) are inconsistent by sub-proof #1374.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1352 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(e0, e2) = all_52_15
% 204.90/35.69    (3)   ~ (all_52_15 = e2)
% 204.90/35.69    (4)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 204.90/35.69    (5)  all_58_13 = all_52_15
% 204.90/35.69    (6)  op(e2, e2) = all_4_2
% 204.90/35.69    (7)   ~ (all_52_15 = e0)
% 204.90/35.69    (8)   ~ (all_4_1 = e1)
% 204.90/35.69    (9)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.69    (10)  op(all_4_2, e2) = all_4_1
% 204.90/35.69    (11)  op(e2, e2) = e0
% 204.90/35.69    (12)  all_56_13 = all_52_15
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (4) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (13)  all_58_13 = e1
% 204.90/35.69  | | 
% 204.90/35.69  | | COMBINE_EQS: (5), (13) imply:
% 204.90/35.69  | |   (14)  all_52_15 = e1
% 204.90/35.69  | | 
% 204.90/35.69  | | SIMP: (14) implies:
% 204.90/35.69  | |   (15)  all_52_15 = e1
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (2), (15) imply:
% 204.90/35.69  | |   (16)  op(e0, e2) = e1
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (6), (8), (10), (11), (16) are inconsistent by sub-proof
% 204.90/35.69  | |            #1357.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (17)   ~ (all_58_13 = e1)
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (5), (17) imply:
% 204.90/35.69  | |   (18)   ~ (all_52_15 = e1)
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (3), (7), (9), (12), (18) are inconsistent by sub-proof #1353.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1353 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ~ (all_52_15 = e1)
% 204.90/35.69    (2)   ~ (all_52_15 = e2)
% 204.90/35.69    (3)   ~ (all_52_15 = e0)
% 204.90/35.69    (4)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 204.90/35.69    (5)  all_56_13 = all_52_15
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (4) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (6)  all_56_13 = e2
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #1356.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (7)  all_56_13 = e1 | all_56_13 = e0
% 204.90/35.69  | | 
% 204.90/35.69  | | BETA: splitting (7) gives:
% 204.90/35.69  | | 
% 204.90/35.69  | | Case 1:
% 204.90/35.69  | | | 
% 204.90/35.69  | | |   (8)  all_56_13 = e1
% 204.90/35.69  | | | 
% 204.90/35.69  | | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1355.
% 204.90/35.69  | | | 
% 204.90/35.69  | | Case 2:
% 204.90/35.69  | | | 
% 204.90/35.69  | | |   (9)  all_56_13 = e0
% 204.90/35.69  | | | 
% 204.90/35.69  | | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1354.
% 204.90/35.69  | | | 
% 204.90/35.69  | | End of split
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1354 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)  all_56_13 = all_52_15
% 204.90/35.69    (2)  all_56_13 = e0
% 204.90/35.69    (3)   ~ (all_52_15 = e0)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.69  |   (4)  all_52_15 = e0
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (4) implies:
% 204.90/35.69  |   (5)  all_52_15 = e0
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (3), (5) imply:
% 204.90/35.69  |   (6)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (6) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1355 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)  all_56_13 = all_52_15
% 204.90/35.69    (2)  all_56_13 = e1
% 204.90/35.69    (3)   ~ (all_52_15 = e1)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.69  |   (4)  all_52_15 = e1
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (4) implies:
% 204.90/35.69  |   (5)  all_52_15 = e1
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (3), (5) imply:
% 204.90/35.69  |   (6)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (6) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1356 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)  all_56_13 = all_52_15
% 204.90/35.69    (2)  all_56_13 = e2
% 204.90/35.69    (3)   ~ (all_52_15 = e2)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.69  |   (4)  all_52_15 = e2
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (4) implies:
% 204.90/35.69  |   (5)  all_52_15 = e2
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (3), (5) imply:
% 204.90/35.69  |   (6)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (6) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1357 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(e2, e2) = all_4_2
% 204.90/35.69    (3)   ~ (all_4_1 = e1)
% 204.90/35.69    (4)  op(e0, e2) = e1
% 204.90/35.69    (5)  op(all_4_2, e2) = all_4_1
% 204.90/35.69    (6)  op(e2, e2) = e0
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e2, simplifying with (2),
% 204.90/35.69  |              (6) gives:
% 204.90/35.69  |   (7)  all_4_2 = e0
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (5), (7) imply:
% 204.90/35.69  |   (8)  op(e0, e2) = all_4_1
% 204.90/35.69  | 
% 204.90/35.69  | GROUND_INST: instantiating (1) with e1, all_4_1, e2, e0, simplifying with (4),
% 204.90/35.69  |              (8) gives:
% 204.90/35.69  |   (9)  all_4_1 = e1
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (3), (9) imply:
% 204.90/35.69  |   (10)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (10) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1358 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_7, all_52_7) = e0
% 204.90/35.69    (3)  op(all_10_2, e1) = all_10_1
% 204.90/35.69    (4)  all_58_12 = all_52_7
% 204.90/35.69    (5)   ~ (all_10_1 = e3)
% 204.90/35.69    (6)  op(e1, e1) = all_10_2
% 204.90/35.69    (7)  all_58_12 = e1
% 204.90/35.69    (8)  op(e0, e1) = e3
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | COMBINE_EQS: (4), (7) imply:
% 204.90/35.69  |   (9)  all_52_7 = e1
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (9) implies:
% 204.90/35.69  |   (10)  all_52_7 = e1
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (2), (10) imply:
% 204.90/35.69  |   (11)  op(e1, e1) = e0
% 204.90/35.69  | 
% 204.90/35.69  | REF_CLOSE: (1), (3), (5), (6), (8), (11) are inconsistent by sub-proof #1359.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1359 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_10_2, e1) = all_10_1
% 204.90/35.69    (3)  op(e1, e1) = e0
% 204.90/35.69    (4)   ~ (all_10_1 = e3)
% 204.90/35.69    (5)  op(e1, e1) = all_10_2
% 204.90/35.69    (6)  op(e0, e1) = e3
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 204.90/35.69  |              (3), (5) gives:
% 204.90/35.69  |   (7)  all_10_2 = e0
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (2), (7) imply:
% 204.90/35.69  |   (8)  op(e0, e1) = all_10_1
% 204.90/35.69  | 
% 204.90/35.69  | GROUND_INST: instantiating (1) with e3, all_10_1, e1, e0, simplifying with
% 204.90/35.69  |              (6), (8) gives:
% 204.90/35.69  |   (9)  all_10_1 = e3
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (4), (9) imply:
% 204.90/35.69  |   (10)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (10) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1360 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)  all_58_13 = all_52_15
% 204.90/35.69    (2)  all_58_13 = e3
% 204.90/35.69    (3)   ~ (all_52_15 = e3)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.69  |   (4)  all_52_15 = e3
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (4) implies:
% 204.90/35.69  |   (5)  all_52_15 = e3
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (3), (5) imply:
% 204.90/35.69  |   (6)  $false
% 204.90/35.69  | 
% 204.90/35.69  | CLOSE: (6) is inconsistent.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1361 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_7, all_52_7) = e0
% 204.90/35.69    (3)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (4)  all_58_0 = all_6_2
% 204.90/35.69    (5)  op(e2, e2) = all_4_2
% 204.90/35.69    (6)   ~ (all_52_7 = all_6_2)
% 204.90/35.69    (7)  op(e0, e0) = all_14_2
% 204.90/35.69    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.90/35.69    (9)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (10)  all_58_12 = all_52_7
% 204.90/35.69    (11)   ~ (all_52_7 = all_14_2)
% 204.90/35.69    (12)  all_58_2 = all_52_3
% 204.90/35.69    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (14)  op(all_52_3, all_52_3) = e2
% 204.90/35.69    (15)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (16)  op(e3, e3) = all_6_2
% 204.90/35.69    (17)  all_58_6 = all_52_5
% 204.90/35.69    (18)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.69    (19)  op(e1, e1) = all_10_2
% 204.90/35.69    (20)  all_52_7 = e3
% 204.90/35.69    (21)   ~ (all_52_3 = all_4_2)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (20) implies:
% 204.90/35.69  |   (22)  all_52_7 = e3
% 204.90/35.69  | 
% 204.90/35.69  | REDUCE: (6), (22) imply:
% 204.90/35.69  |   (23)   ~ (all_6_2 = e3)
% 204.90/35.69  | 
% 204.90/35.69  | SIMP: (23) implies:
% 204.90/35.69  |   (24)   ~ (all_6_2 = e3)
% 204.90/35.69  | 
% 204.90/35.69  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 204.90/35.69  |            (14), (15), (16), (17), (18), (19), (21), (24) are inconsistent by
% 204.90/35.69  |            sub-proof #1362.
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1362 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_7, all_52_7) = e0
% 204.90/35.69    (3)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (4)  all_58_0 = all_6_2
% 204.90/35.69    (5)  op(e2, e2) = all_4_2
% 204.90/35.69    (6)  op(e0, e0) = all_14_2
% 204.90/35.69    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.90/35.69    (8)   ~ (all_6_2 = e3)
% 204.90/35.69    (9)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (10)  all_58_12 = all_52_7
% 204.90/35.69    (11)   ~ (all_52_7 = all_14_2)
% 204.90/35.69    (12)  all_58_2 = all_52_3
% 204.90/35.69    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (14)  op(all_52_3, all_52_3) = e2
% 204.90/35.69    (15)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (16)  op(e3, e3) = all_6_2
% 204.90/35.69    (17)  all_58_6 = all_52_5
% 204.90/35.69    (18)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 204.90/35.69    (19)  op(e1, e1) = all_10_2
% 204.90/35.69    (20)   ~ (all_52_3 = all_4_2)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (18) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (21)  all_58_12 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (2), (6), (9), (10), (11), (16), (21) are inconsistent by
% 204.90/35.69  | |            sub-proof #1371.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (22)   ~ (all_58_12 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (10), (22) imply:
% 204.90/35.69  | |   (23)   ~ (all_52_7 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15),
% 204.90/35.69  | |            (16), (17), (19), (20), (23) are inconsistent by sub-proof #1363.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1363 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (3)  all_58_0 = all_6_2
% 204.90/35.69    (4)  op(e2, e2) = all_4_2
% 204.90/35.69    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.90/35.69    (6)   ~ (all_6_2 = e3)
% 204.90/35.69    (7)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (8)  all_58_12 = all_52_7
% 204.90/35.69    (9)   ~ (all_52_7 = e3)
% 204.90/35.69    (10)  all_58_2 = all_52_3
% 204.90/35.69    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (12)  op(all_52_3, all_52_3) = e2
% 204.90/35.69    (13)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (14)  op(e3, e3) = all_6_2
% 204.90/35.69    (15)  all_58_6 = all_52_5
% 204.90/35.69    (16)  op(e1, e1) = all_10_2
% 204.90/35.69    (17)   ~ (all_52_3 = all_4_2)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (11) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (18)  all_58_0 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | COMBINE_EQS: (3), (18) imply:
% 204.90/35.69  | |   (19)  all_6_2 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (6), (19) imply:
% 204.90/35.69  | |   (20)  $false
% 204.90/35.69  | | 
% 204.90/35.69  | | CLOSE: (20) is inconsistent.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (21)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15),
% 204.90/35.69  | |            (16), (17), (21) are inconsistent by sub-proof #1364.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1364 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (3)  op(e2, e2) = all_4_2
% 204.90/35.69    (4)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 204.90/35.69    (5)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (6)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (7)  all_58_12 = all_52_7
% 204.90/35.69    (8)   ~ (all_52_7 = e3)
% 204.90/35.69    (9)  all_58_2 = all_52_3
% 204.90/35.69    (10)  op(all_52_3, all_52_3) = e2
% 204.90/35.69    (11)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (12)  op(e3, e3) = all_6_2
% 204.90/35.69    (13)  all_58_6 = all_52_5
% 204.90/35.69    (14)  op(e1, e1) = all_10_2
% 204.90/35.69    (15)   ~ (all_52_3 = all_4_2)
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (4) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (16)  all_58_2 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | COMBINE_EQS: (9), (16) imply:
% 204.90/35.69  | |   (17)  all_52_3 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | SIMP: (17) implies:
% 204.90/35.69  | |   (18)  all_52_3 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (15), (18) imply:
% 204.90/35.69  | |   (19)   ~ (all_4_2 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | SIMP: (19) implies:
% 204.90/35.69  | |   (20)   ~ (all_4_2 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (10), (18) imply:
% 204.90/35.69  | |   (21)  op(e3, e3) = e2
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (3), (6), (12), (20), (21) are inconsistent by sub-proof
% 204.90/35.69  | |            #1370.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (22)   ~ (all_58_2 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REDUCE: (9), (22) imply:
% 204.90/35.69  | |   (23)   ~ (all_52_3 = e3)
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13), (14), (23)
% 204.90/35.69  | |            are inconsistent by sub-proof #1365.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1365 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (3)   ~ (all_52_3 = e3)
% 204.90/35.69    (4)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69    (5)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (6)  all_58_12 = all_52_7
% 204.90/35.69    (7)   ~ (all_52_7 = e3)
% 204.90/35.69    (8)  all_58_2 = all_52_3
% 204.90/35.69    (9)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (10)  op(e3, e3) = all_6_2
% 204.90/35.69    (11)  all_58_6 = all_52_5
% 204.90/35.69    (12)  op(e1, e1) = all_10_2
% 204.90/35.69  
% 204.90/35.69  Begin of proof
% 204.90/35.69  | 
% 204.90/35.69  | BETA: splitting (4) gives:
% 204.90/35.69  | 
% 204.90/35.69  | Case 1:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (13)  all_58_2 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #1369.
% 204.90/35.69  | | 
% 204.90/35.69  | Case 2:
% 204.90/35.69  | | 
% 204.90/35.69  | |   (14)  all_58_6 = e3 | all_58_12 = e3
% 204.90/35.69  | | 
% 204.90/35.69  | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (14) are
% 204.90/35.69  | |            inconsistent by sub-proof #1366.
% 204.90/35.69  | | 
% 204.90/35.69  | End of split
% 204.90/35.69  | 
% 204.90/35.69  End of proof
% 204.90/35.69  
% 204.90/35.69  Sub-proof #1366 shows that the following formulas are inconsistent:
% 204.90/35.69  ----------------------------------------------------------------
% 204.90/35.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.69    (2)  op(all_52_5, all_52_5) = e1
% 204.90/35.69    (3)  op(all_6_2, all_6_2) = e3
% 204.90/35.69    (4)  all_58_12 = all_52_7
% 204.90/35.69    (5)   ~ (all_52_7 = e3)
% 204.90/35.69    (6)   ~ (all_52_5 = all_10_2)
% 204.90/35.69    (7)  op(e3, e3) = all_6_2
% 204.90/35.69    (8)  all_58_6 = all_52_5
% 204.90/35.69    (9)  op(e1, e1) = all_10_2
% 204.90/35.70    (10)  all_58_6 = e3 | all_58_12 = e3
% 204.90/35.70  
% 204.90/35.70  Begin of proof
% 204.90/35.70  | 
% 204.90/35.70  | BETA: splitting (10) gives:
% 204.90/35.70  | 
% 204.90/35.70  | Case 1:
% 204.90/35.70  | | 
% 204.90/35.70  | |   (11)  all_58_6 = e3
% 204.90/35.70  | | 
% 204.90/35.70  | | COMBINE_EQS: (8), (11) imply:
% 204.90/35.70  | |   (12)  all_52_5 = e3
% 204.90/35.70  | | 
% 204.90/35.70  | | SIMP: (12) implies:
% 204.90/35.70  | |   (13)  all_52_5 = e3
% 204.90/35.70  | | 
% 204.90/35.70  | | REDUCE: (6), (13) imply:
% 204.90/35.70  | |   (14)   ~ (all_10_2 = e3)
% 204.90/35.70  | | 
% 204.90/35.70  | | SIMP: (14) implies:
% 204.90/35.70  | |   (15)   ~ (all_10_2 = e3)
% 204.90/35.70  | | 
% 204.90/35.70  | | REDUCE: (2), (13) imply:
% 204.90/35.70  | |   (16)  op(e3, e3) = e1
% 204.90/35.70  | | 
% 204.90/35.70  | | GROUND_INST: instantiating (1) with all_6_2, e1, e3, e3, simplifying with
% 204.90/35.70  | |              (7), (16) gives:
% 204.90/35.70  | |   (17)  all_6_2 = e1
% 204.90/35.70  | | 
% 204.90/35.70  | | REDUCE: (3), (17) imply:
% 204.90/35.70  | |   (18)  op(e1, e1) = e3
% 204.90/35.70  | | 
% 204.90/35.70  | | REF_CLOSE: (1), (9), (15), (18) are inconsistent by sub-proof #1368.
% 204.90/35.70  | | 
% 204.90/35.70  | Case 2:
% 204.90/35.70  | | 
% 204.90/35.70  | |   (19)  all_58_12 = e3
% 204.90/35.70  | | 
% 204.90/35.70  | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #1367.
% 204.90/35.70  | | 
% 204.90/35.70  | End of split
% 204.90/35.70  | 
% 204.90/35.70  End of proof
% 204.90/35.70  
% 204.90/35.70  Sub-proof #1367 shows that the following formulas are inconsistent:
% 204.90/35.70  ----------------------------------------------------------------
% 204.90/35.70    (1)  all_58_12 = all_52_7
% 204.90/35.70    (2)  all_58_12 = e3
% 204.90/35.70    (3)   ~ (all_52_7 = e3)
% 204.90/35.70  
% 204.90/35.70  Begin of proof
% 204.90/35.70  | 
% 204.90/35.70  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.70  |   (4)  all_52_7 = e3
% 204.90/35.70  | 
% 204.90/35.70  | SIMP: (4) implies:
% 204.90/35.70  |   (5)  all_52_7 = e3
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (3), (5) imply:
% 204.90/35.70  |   (6)  $false
% 204.90/35.70  | 
% 204.90/35.70  | CLOSE: (6) is inconsistent.
% 204.90/35.70  | 
% 204.90/35.70  End of proof
% 204.90/35.70  
% 204.90/35.70  Sub-proof #1368 shows that the following formulas are inconsistent:
% 204.90/35.70  ----------------------------------------------------------------
% 204.90/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.70    (2)  op(e1, e1) = all_10_2
% 204.90/35.70    (3)  op(e1, e1) = e3
% 204.90/35.70    (4)   ~ (all_10_2 = e3)
% 204.90/35.70  
% 204.90/35.70  Begin of proof
% 204.90/35.70  | 
% 204.90/35.70  | GROUND_INST: instantiating (1) with all_10_2, e3, e1, e1, simplifying with
% 204.90/35.70  |              (2), (3) gives:
% 204.90/35.70  |   (5)  all_10_2 = e3
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (4), (5) imply:
% 204.90/35.70  |   (6)  $false
% 204.90/35.70  | 
% 204.90/35.70  | CLOSE: (6) is inconsistent.
% 204.90/35.70  | 
% 204.90/35.70  End of proof
% 204.90/35.70  
% 204.90/35.70  Sub-proof #1369 shows that the following formulas are inconsistent:
% 204.90/35.70  ----------------------------------------------------------------
% 204.90/35.70    (1)  all_58_2 = all_52_3
% 204.90/35.70    (2)  all_58_2 = e3
% 204.90/35.70    (3)   ~ (all_52_3 = e3)
% 204.90/35.70  
% 204.90/35.70  Begin of proof
% 204.90/35.70  | 
% 204.90/35.70  | COMBINE_EQS: (1), (2) imply:
% 204.90/35.70  |   (4)  all_52_3 = e3
% 204.90/35.70  | 
% 204.90/35.70  | SIMP: (4) implies:
% 204.90/35.70  |   (5)  all_52_3 = e3
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (3), (5) imply:
% 204.90/35.70  |   (6)  $false
% 204.90/35.70  | 
% 204.90/35.70  | CLOSE: (6) is inconsistent.
% 204.90/35.70  | 
% 204.90/35.70  End of proof
% 204.90/35.70  
% 204.90/35.70  Sub-proof #1370 shows that the following formulas are inconsistent:
% 204.90/35.70  ----------------------------------------------------------------
% 204.90/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.70    (2)   ~ (all_4_2 = e3)
% 204.90/35.70    (3)  op(e2, e2) = all_4_2
% 204.90/35.70    (4)  op(e3, e3) = e2
% 204.90/35.70    (5)  op(all_6_2, all_6_2) = e3
% 204.90/35.70    (6)  op(e3, e3) = all_6_2
% 204.90/35.70  
% 204.90/35.70  Begin of proof
% 204.90/35.70  | 
% 204.90/35.70  | GROUND_INST: instantiating (1) with all_6_2, e2, e3, e3, simplifying with (4),
% 204.90/35.70  |              (6) gives:
% 204.90/35.70  |   (7)  all_6_2 = e2
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (5), (7) imply:
% 204.90/35.70  |   (8)  op(e2, e2) = e3
% 204.90/35.70  | 
% 204.90/35.70  | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying with (3),
% 204.90/35.70  |              (8) gives:
% 204.90/35.70  |   (9)  all_4_2 = e3
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (2), (9) imply:
% 204.90/35.70  |   (10)  $false
% 204.90/35.70  | 
% 204.90/35.70  | CLOSE: (10) is inconsistent.
% 204.90/35.70  | 
% 204.90/35.70  End of proof
% 204.90/35.70  
% 204.90/35.70  Sub-proof #1371 shows that the following formulas are inconsistent:
% 204.90/35.70  ----------------------------------------------------------------
% 204.90/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.90/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.90/35.70    (2)  op(all_52_7, all_52_7) = e0
% 204.90/35.70    (3)  op(e0, e0) = all_14_2
% 204.90/35.70    (4)  op(all_6_2, all_6_2) = e3
% 204.90/35.70    (5)  all_58_12 = all_52_7
% 204.90/35.70    (6)   ~ (all_52_7 = all_14_2)
% 204.90/35.70    (7)  op(e3, e3) = all_6_2
% 204.90/35.70    (8)  all_58_12 = e3
% 204.90/35.70  
% 204.90/35.70  Begin of proof
% 204.90/35.70  | 
% 204.90/35.70  | COMBINE_EQS: (5), (8) imply:
% 204.90/35.70  |   (9)  all_52_7 = e3
% 204.90/35.70  | 
% 204.90/35.70  | SIMP: (9) implies:
% 204.90/35.70  |   (10)  all_52_7 = e3
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (6), (10) imply:
% 204.90/35.70  |   (11)   ~ (all_14_2 = e3)
% 204.90/35.70  | 
% 204.90/35.70  | SIMP: (11) implies:
% 204.90/35.70  |   (12)   ~ (all_14_2 = e3)
% 204.90/35.70  | 
% 204.90/35.70  | REDUCE: (2), (10) imply:
% 204.90/35.70  |   (13)  op(e3, e3) = e0
% 204.97/35.70  | 
% 204.97/35.70  | GROUND_INST: instantiating (1) with all_6_2, e0, e3, e3, simplifying with (7),
% 204.97/35.70  |              (13) gives:
% 204.97/35.70  |   (14)  all_6_2 = e0
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (4), (14) imply:
% 204.97/35.70  |   (15)  op(e0, e0) = e3
% 204.97/35.70  | 
% 204.97/35.70  | REF_CLOSE: (1), (3), (12), (15) are inconsistent by sub-proof #1372.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1372 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.97/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.97/35.70    (2)  op(e0, e0) = all_14_2
% 204.97/35.70    (3)  op(e0, e0) = e3
% 204.97/35.70    (4)   ~ (all_14_2 = e3)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | GROUND_INST: instantiating (1) with all_14_2, e3, e0, e0, simplifying with
% 204.97/35.70  |              (2), (3) gives:
% 204.97/35.70  |   (5)  all_14_2 = e3
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (4), (5) imply:
% 204.97/35.70  |   (6)  $false
% 204.97/35.70  | 
% 204.97/35.70  | CLOSE: (6) is inconsistent.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1373 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.97/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.97/35.70    (2)  op(all_52_7, all_52_7) = e0
% 204.97/35.70    (3)  op(e0, e2) = e3
% 204.97/35.70    (4)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 204.97/35.70    (5)  op(e2, e2) = all_4_2
% 204.97/35.70    (6)   ~ (all_4_1 = e3)
% 204.97/35.70    (7)  op(all_4_2, e2) = all_4_1
% 204.97/35.70    (8)  all_56_12 = all_52_7
% 204.97/35.70    (9)   ~ (all_52_7 = e1)
% 204.97/35.70    (10)   ~ (all_52_7 = e0)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | BETA: splitting (4) gives:
% 204.97/35.70  | 
% 204.97/35.70  | Case 1:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (11)  all_56_12 = e2
% 204.97/35.70  | | 
% 204.97/35.70  | | COMBINE_EQS: (8), (11) imply:
% 204.97/35.70  | |   (12)  all_52_7 = e2
% 204.97/35.70  | | 
% 204.97/35.70  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (12) are inconsistent by sub-proof
% 204.97/35.70  | |            #1377.
% 204.97/35.70  | | 
% 204.97/35.70  | Case 2:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (13)  all_56_12 = e1 | all_56_12 = e0
% 204.97/35.70  | | 
% 204.97/35.70  | | REF_CLOSE: (8), (9), (10), (13) are inconsistent by sub-proof #1374.
% 204.97/35.70  | | 
% 204.97/35.70  | End of split
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1374 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)  all_56_12 = e1 | all_56_12 = e0
% 204.97/35.70    (2)  all_56_12 = all_52_7
% 204.97/35.70    (3)   ~ (all_52_7 = e1)
% 204.97/35.70    (4)   ~ (all_52_7 = e0)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | BETA: splitting (1) gives:
% 204.97/35.70  | 
% 204.97/35.70  | Case 1:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (5)  all_56_12 = e1
% 204.97/35.70  | | 
% 204.97/35.70  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1376.
% 204.97/35.70  | | 
% 204.97/35.70  | Case 2:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (6)  all_56_12 = e0
% 204.97/35.70  | | 
% 204.97/35.70  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1375.
% 204.97/35.70  | | 
% 204.97/35.70  | End of split
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1375 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)  all_56_12 = all_52_7
% 204.97/35.70    (2)  all_56_12 = e0
% 204.97/35.70    (3)   ~ (all_52_7 = e0)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | COMBINE_EQS: (1), (2) imply:
% 204.97/35.70  |   (4)  all_52_7 = e0
% 204.97/35.70  | 
% 204.97/35.70  | SIMP: (4) implies:
% 204.97/35.70  |   (5)  all_52_7 = e0
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (3), (5) imply:
% 204.97/35.70  |   (6)  $false
% 204.97/35.70  | 
% 204.97/35.70  | CLOSE: (6) is inconsistent.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1376 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)  all_56_12 = all_52_7
% 204.97/35.70    (2)  all_56_12 = e1
% 204.97/35.70    (3)   ~ (all_52_7 = e1)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | COMBINE_EQS: (1), (2) imply:
% 204.97/35.70  |   (4)  all_52_7 = e1
% 204.97/35.70  | 
% 204.97/35.70  | SIMP: (4) implies:
% 204.97/35.70  |   (5)  all_52_7 = e1
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (3), (5) imply:
% 204.97/35.70  |   (6)  $false
% 204.97/35.70  | 
% 204.97/35.70  | CLOSE: (6) is inconsistent.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1377 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.97/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.97/35.70    (2)  op(all_52_7, all_52_7) = e0
% 204.97/35.70    (3)  op(e0, e2) = e3
% 204.97/35.70    (4)  op(e2, e2) = all_4_2
% 204.97/35.70    (5)   ~ (all_4_1 = e3)
% 204.97/35.70    (6)  op(all_4_2, e2) = all_4_1
% 204.97/35.70    (7)  all_52_7 = e2
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | SIMP: (7) implies:
% 204.97/35.70  |   (8)  all_52_7 = e2
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (2), (8) imply:
% 204.97/35.70  |   (9)  op(e2, e2) = e0
% 204.97/35.70  | 
% 204.97/35.70  | REF_CLOSE: (1), (3), (4), (5), (6), (9) are inconsistent by sub-proof #1378.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1378 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.97/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.97/35.70    (2)  op(e0, e2) = e3
% 204.97/35.70    (3)  op(e2, e2) = all_4_2
% 204.97/35.70    (4)   ~ (all_4_1 = e3)
% 204.97/35.70    (5)  op(all_4_2, e2) = all_4_1
% 204.97/35.70    (6)  op(e2, e2) = e0
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e2, simplifying with (3),
% 204.97/35.70  |              (6) gives:
% 204.97/35.70  |   (7)  all_4_2 = e0
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (5), (7) imply:
% 204.97/35.70  |   (8)  op(e0, e2) = all_4_1
% 204.97/35.70  | 
% 204.97/35.70  | GROUND_INST: instantiating (1) with e3, all_4_1, e2, e0, simplifying with (2),
% 204.97/35.70  |              (8) gives:
% 204.97/35.70  |   (9)  all_4_1 = e3
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (4), (9) imply:
% 204.97/35.70  |   (10)  $false
% 204.97/35.70  | 
% 204.97/35.70  | CLOSE: (10) is inconsistent.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1379 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.97/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.97/35.70    (2)  op(all_52_7, all_52_7) = e0
% 204.97/35.70    (3)  op(all_10_2, e1) = all_10_1
% 204.97/35.70    (4)  op(e0, e1) = all_52_23
% 204.97/35.70    (5)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.97/35.70    (6)   ~ (all_10_1 = e2)
% 204.97/35.70    (7)  all_52_7 = e1
% 204.97/35.70    (8)  all_56_14 = all_52_23
% 204.97/35.70    (9)   ~ (all_10_1 = e3)
% 204.97/35.70    (10)  op(e1, e1) = all_10_2
% 204.97/35.70    (11)   ~ (all_52_23 = all_10_2)
% 204.97/35.70    (12)   ~ (all_52_7 = all_52_23)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (7), (12) imply:
% 204.97/35.70  |   (13)   ~ (all_52_23 = e1)
% 204.97/35.70  | 
% 204.97/35.70  | SIMP: (13) implies:
% 204.97/35.70  |   (14)   ~ (all_52_23 = e1)
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (2), (7) imply:
% 204.97/35.70  |   (15)  op(e1, e1) = e0
% 204.97/35.70  | 
% 204.97/35.70  | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (14), (15) are
% 204.97/35.70  |            inconsistent by sub-proof #1380.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1380 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 204.97/35.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 204.97/35.70    (2)  op(all_10_2, e1) = all_10_1
% 204.97/35.70    (3)  op(e0, e1) = all_52_23
% 204.97/35.70    (4)  op(e1, e1) = e0
% 204.97/35.70    (5)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.97/35.70    (6)   ~ (all_52_23 = e1)
% 204.97/35.70    (7)   ~ (all_10_1 = e2)
% 204.97/35.70    (8)  all_56_14 = all_52_23
% 204.97/35.70    (9)   ~ (all_10_1 = e3)
% 204.97/35.70    (10)  op(e1, e1) = all_10_2
% 204.97/35.70    (11)   ~ (all_52_23 = all_10_2)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | GROUND_INST: instantiating (1) with all_10_2, e0, e1, e1, simplifying with
% 204.97/35.70  |              (4), (10) gives:
% 204.97/35.70  |   (12)  all_10_2 = e0
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (11), (12) imply:
% 204.97/35.70  |   (13)   ~ (all_52_23 = e0)
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (2), (12) imply:
% 204.97/35.70  |   (14)  op(e0, e1) = all_10_1
% 204.97/35.70  | 
% 204.97/35.70  | GROUND_INST: instantiating (1) with all_52_23, all_10_1, e1, e0, simplifying
% 204.97/35.70  |              with (3), (14) gives:
% 204.97/35.70  |   (15)  all_52_23 = all_10_1
% 204.97/35.70  | 
% 204.97/35.70  | COMBINE_EQS: (8), (15) imply:
% 204.97/35.70  |   (16)  all_56_14 = all_10_1
% 204.97/35.70  | 
% 204.97/35.70  | BETA: splitting (5) gives:
% 204.97/35.70  | 
% 204.97/35.70  | Case 1:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (17)  all_56_14 = e3
% 204.97/35.70  | | 
% 204.97/35.70  | | COMBINE_EQS: (16), (17) imply:
% 204.97/35.70  | |   (18)  all_10_1 = e3
% 204.97/35.70  | | 
% 204.97/35.70  | | SIMP: (18) implies:
% 204.97/35.70  | |   (19)  all_10_1 = e3
% 204.97/35.70  | | 
% 204.97/35.70  | | REDUCE: (9), (19) imply:
% 204.97/35.70  | |   (20)  $false
% 204.97/35.70  | | 
% 204.97/35.70  | | CLOSE: (20) is inconsistent.
% 204.97/35.70  | | 
% 204.97/35.70  | Case 2:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (21)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 204.97/35.70  | | 
% 204.97/35.70  | | BETA: splitting (21) gives:
% 204.97/35.70  | | 
% 204.97/35.70  | | Case 1:
% 204.97/35.70  | | | 
% 204.97/35.70  | | |   (22)  all_56_14 = e2
% 204.97/35.70  | | | 
% 204.97/35.70  | | | COMBINE_EQS: (16), (22) imply:
% 204.97/35.70  | | |   (23)  all_10_1 = e2
% 204.97/35.70  | | | 
% 204.97/35.70  | | | SIMP: (23) implies:
% 204.97/35.70  | | |   (24)  all_10_1 = e2
% 204.97/35.70  | | | 
% 204.97/35.70  | | | REDUCE: (7), (24) imply:
% 204.97/35.70  | | |   (25)  $false
% 204.97/35.70  | | | 
% 204.97/35.70  | | | CLOSE: (25) is inconsistent.
% 204.97/35.70  | | | 
% 204.97/35.70  | | Case 2:
% 204.97/35.70  | | | 
% 204.97/35.70  | | |   (26)  all_56_14 = e1 | all_56_14 = e0
% 204.97/35.70  | | | 
% 204.97/35.70  | | | REF_CLOSE: (6), (8), (13), (26) are inconsistent by sub-proof #1381.
% 204.97/35.70  | | | 
% 204.97/35.70  | | End of split
% 204.97/35.70  | | 
% 204.97/35.70  | End of split
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1381 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)  all_56_14 = e1 | all_56_14 = e0
% 204.97/35.70    (2)  all_56_14 = all_52_23
% 204.97/35.70    (3)   ~ (all_52_23 = e1)
% 204.97/35.70    (4)   ~ (all_52_23 = e0)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | BETA: splitting (1) gives:
% 204.97/35.70  | 
% 204.97/35.70  | Case 1:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (5)  all_56_14 = e1
% 204.97/35.70  | | 
% 204.97/35.70  | | COMBINE_EQS: (2), (5) imply:
% 204.97/35.70  | |   (6)  all_52_23 = e1
% 204.97/35.70  | | 
% 204.97/35.70  | | SIMP: (6) implies:
% 204.97/35.70  | |   (7)  all_52_23 = e1
% 204.97/35.70  | | 
% 204.97/35.70  | | REDUCE: (3), (7) imply:
% 204.97/35.70  | |   (8)  $false
% 204.97/35.70  | | 
% 204.97/35.70  | | CLOSE: (8) is inconsistent.
% 204.97/35.70  | | 
% 204.97/35.70  | Case 2:
% 204.97/35.70  | | 
% 204.97/35.70  | |   (9)  all_56_14 = e0
% 204.97/35.70  | | 
% 204.97/35.70  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1382.
% 204.97/35.70  | | 
% 204.97/35.70  | End of split
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1382 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)  all_56_14 = all_52_23
% 204.97/35.70    (2)  all_56_14 = e0
% 204.97/35.70    (3)   ~ (all_52_23 = e0)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | COMBINE_EQS: (1), (2) imply:
% 204.97/35.70  |   (4)  all_52_23 = e0
% 204.97/35.70  | 
% 204.97/35.70  | SIMP: (4) implies:
% 204.97/35.70  |   (5)  all_52_23 = e0
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (3), (5) imply:
% 204.97/35.70  |   (6)  $false
% 204.97/35.70  | 
% 204.97/35.70  | CLOSE: (6) is inconsistent.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  
% 204.97/35.70  Sub-proof #1383 shows that the following formulas are inconsistent:
% 204.97/35.70  ----------------------------------------------------------------
% 204.97/35.70    (1)  all_56_12 = all_52_7
% 204.97/35.70    (2)  all_56_12 = e3
% 204.97/35.70    (3)   ~ (all_52_7 = e3)
% 204.97/35.70  
% 204.97/35.70  Begin of proof
% 204.97/35.70  | 
% 204.97/35.70  | COMBINE_EQS: (1), (2) imply:
% 204.97/35.70  |   (4)  all_52_7 = e3
% 204.97/35.70  | 
% 204.97/35.70  | SIMP: (4) implies:
% 204.97/35.70  |   (5)  all_52_7 = e3
% 204.97/35.70  | 
% 204.97/35.70  | REDUCE: (3), (5) imply:
% 204.97/35.70  |   (6)  $false
% 204.97/35.70  | 
% 204.97/35.70  | CLOSE: (6) is inconsistent.
% 204.97/35.70  | 
% 204.97/35.70  End of proof
% 204.97/35.70  % SZS output end Proof for theBenchmark
% 204.97/35.70  
% 204.97/35.70  35232ms
%------------------------------------------------------------------------------